LMFDB - Embedded newform 378.3.x.a.103.42

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,3,Mod(103,378)] 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("378.103"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 15])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.x (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$48$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			103.42
Character	$\chi$	$=$	378.103
Dual form			378.3.x.a.367.42

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.245576 + 1.39273i) q^{2} +(2.12584 + 2.11679i) q^{3} +(-1.87939 + 0.684040i) q^{4} +(-5.27455 - 0.930046i) q^{5} +(-2.42605 + 3.48055i) q^{6} +(-4.88560 - 5.01308i) q^{7} +(-1.41421 - 2.44949i) q^{8} +(0.0384216 + 8.99992i) q^{9} -7.57442i q^{10} +(-1.68636 - 9.56381i) q^{11} +(-5.44325 - 2.52410i) q^{12} +(-3.24463 + 3.86680i) q^{13} +(5.78207 - 8.03540i) q^{14} +(-9.24416 - 13.1422i) q^{15} +(3.06418 - 2.57115i) q^{16} +6.57243i q^{17} +(-12.5250 + 2.26367i) q^{18} -28.3279i q^{19} +(10.5491 - 1.86009i) q^{20} +(0.225611 - 20.9988i) q^{21} +(12.9057 - 4.69728i) q^{22} +(-10.8255 - 9.08369i) q^{23} +(2.17865 - 8.20082i) q^{24} +(3.46360 + 1.26065i) q^{25} +(-6.18221 - 3.56930i) q^{26} +(-18.9692 + 19.2137i) q^{27} +(12.6111 + 6.07956i) q^{28} +(4.80424 - 4.03124i) q^{29} +(16.0334 - 16.1020i) q^{30} +(-16.2841 - 44.7401i) q^{31} +(4.33340 + 3.63616i) q^{32} +(16.6596 - 23.9008i) q^{33} +(-9.15361 + 1.61403i) q^{34} +(21.1069 + 30.9856i) q^{35} +(-6.22852 - 16.8880i) q^{36} +(5.39894 + 9.35124i) q^{37} +(39.4530 - 6.95663i) q^{38} +(-15.0828 + 1.35202i) q^{39} +(5.18121 + 14.2352i) q^{40} +(-48.4582 + 57.7502i) q^{41} +(29.3010 - 4.84258i) q^{42} +(3.26038 + 1.18668i) q^{43} +(9.71135 + 16.8205i) q^{44} +(8.16768 - 47.5063i) q^{45} +(9.99263 - 17.3077i) q^{46} +(-4.05958 + 11.1536i) q^{47} +(11.9565 + 1.02035i) q^{48} +(-1.26191 + 48.9837i) q^{49} +(-0.905164 + 5.13344i) q^{50} +(-13.9124 + 13.9720i) q^{51} +(3.45286 - 9.48667i) q^{52} +(-1.24246 - 2.15200i) q^{53} +(-31.4179 - 21.7006i) q^{54} +52.0132i q^{55} +(-5.37021 + 19.0568i) q^{56} +(59.9640 - 60.2206i) q^{57} +(6.79423 + 5.70103i) q^{58} +(-49.2676 + 58.7149i) q^{59} +(26.3632 + 18.3759i) q^{60} +(12.7999 - 35.1674i) q^{61} +(58.3119 - 33.6664i) q^{62} +(44.9296 - 44.1626i) q^{63} +(-4.00000 + 6.92820i) q^{64} +(20.7103 - 17.3780i) q^{65} +(37.3785 + 17.3329i) q^{66} +(-2.30547 + 13.0750i) q^{67} +(-4.49581 - 12.3521i) q^{68} +(-3.78512 - 42.2258i) q^{69} +(-37.9711 + 37.0055i) q^{70} +(-2.32931 + 4.03448i) q^{71} +(21.9909 - 12.8219i) q^{72} +(-84.2726 - 48.6548i) q^{73} +(-11.6979 + 9.81570i) q^{74} +(4.69455 + 10.0116i) q^{75} +(19.3774 + 53.2389i) q^{76} +(-39.7053 + 55.1787i) q^{77} +(-5.58696 - 20.6742i) q^{78} +(-14.4804 - 82.1223i) q^{79} +(-18.5535 + 10.7118i) q^{80} +(-80.9970 + 0.691583i) q^{81} +(-92.3305 - 53.3070i) q^{82} +(31.7429 + 37.8297i) q^{83} +(13.9400 + 39.6191i) q^{84} +(6.11266 - 34.6666i) q^{85} +(-0.852054 + 4.83224i) q^{86} +(18.7463 + 1.59978i) q^{87} +(-21.0416 + 17.6560i) q^{88} -84.0015i q^{89} +(68.1691 - 0.291021i) q^{90} +(35.2365 - 2.62603i) q^{91} +(26.5589 + 9.66666i) q^{92} +(60.0879 - 129.580i) q^{93} +(-16.5309 - 2.91484i) q^{94} +(-26.3462 + 149.417i) q^{95} +(1.51517 + 16.9028i) q^{96} +(8.15244 - 22.3986i) q^{97} +(-68.5310 + 10.2717i) q^{98} +(86.0087 - 15.5445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 36 q^{6} - 12 q^{9} + 36 q^{11} + 36 q^{14} - 24 q^{15} + 186 q^{21} + 126 q^{23} + 36 q^{29} - 72 q^{30} + 162 q^{35} - 48 q^{36} + 246 q^{39} - 48 q^{42} + 324 q^{47} - 72 q^{49} + 288 q^{50}+ \cdots - 216 q^{99}+O(q^{100}) $ 288 * q - 36 * q^6 - 12 * q^9 + 36 * q^11 + 36 * q^14 - 24 * q^15 + 186 * q^21 + 126 * q^23 + 36 * q^29 - 72 * q^30 + 162 * q^35 - 48 * q^36 + 246 * q^39 - 48 * q^42 + 324 * q^47 - 72 * q^49 + 288 * q^50 - 198 * q^51 + 270 * q^53 + 432 * q^54 - 144 * q^56 + 354 * q^57 + 270 * q^59 + 72 * q^60 + 138 * q^63 - 1152 * q^64 - 360 * q^65 + 72 * q^69 + 180 * q^70 + 216 * q^71 - 96 * q^72 + 216 * q^74 - 1170 * q^75 + 234 * q^77 - 96 * q^78 - 36 * q^79 + 324 * q^81 - 24 * q^84 - 360 * q^85 + 144 * q^86 - 990 * q^87 - 198 * q^91 - 180 * q^92 + 168 * q^93 - 72 * q^95 + 216 * q^98 - 216 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.245576	+	1.39273i	0.122788	+	0.696364i
$2$	0.245576	+	1.39273i	0.122788	+	0.696364i
$3$	2.12584	+	2.11679i	0.708615	+	0.705596i
$3$	2.12584	+	2.11679i	0.708615	+	0.705596i
$4$	−1.87939	+	0.684040i	−0.469846	+	0.171010i
$5$	−5.27455	−	0.930046i	−1.05491	−	0.186009i	−0.380813	−	0.924652i	$-0.624356\pi$
$5$	−5.27455	−	0.930046i	−1.05491	−	0.186009i	−0.674097	+	0.738643i	$0.735467\pi$
$6$	−2.42605	+	3.48055i	−0.404342	+	0.580092i
$7$	−4.88560	−	5.01308i	−0.697942	−	0.716154i
$7$	−4.88560	−	5.01308i	−0.697942	−	0.716154i
$8$	−1.41421	−	2.44949i	−0.176777	−	0.306186i
$9$	0.0384216	+	8.99992i	0.00426907	+	0.999991i
$10$		−	7.57442i		−	0.757442i
$11$	−1.68636	−	9.56381i	−0.153305	−	0.869437i	−0.960319	−	0.278904i	$-0.910029\pi$
$11$	−1.68636	−	9.56381i	−0.153305	−	0.869437i	0.807014	−	0.590533i	$-0.201082\pi$
$12$	−5.44325	−	2.52410i	−0.453604	−	0.210341i
$13$	−3.24463	+	3.86680i	−0.249587	+	0.297446i	−0.876262	−	0.481834i	$-0.839971\pi$
$13$	−3.24463	+	3.86680i	−0.249587	+	0.297446i	0.626675	+	0.779280i	$0.284415\pi$
$14$	5.78207	−	8.03540i	0.413005	−	0.573957i
$15$	−9.24416	−	13.1422i	−0.616278	−	0.876149i
$16$	3.06418	−	2.57115i	0.191511	−	0.160697i
$17$			6.57243i			0.386614i	0.981138	+	0.193307i	$0.0619213\pi$
$17$			6.57243i			0.386614i	−0.981138	+	0.193307i	$0.938079\pi$
$18$	−12.5250	+	2.26367i	−0.695834	+	0.125760i
$19$		−	28.3279i		−	1.49094i	−0.666539	−	0.745470i	$-0.732225\pi$
$19$		−	28.3279i		−	1.49094i	0.666539	−	0.745470i	$-0.267775\pi$
$20$	10.5491	−	1.86009i	0.527455	−	0.0930046i
$21$	0.225611	−	20.9988i	0.0107434	−	0.999942i
$22$	12.9057	−	4.69728i	0.586621	−	0.213513i
$23$	−10.8255	−	9.08369i	−0.470675	−	0.394943i	0.376366	−	0.926471i	$-0.377174\pi$
$23$	−10.8255	−	9.08369i	−0.470675	−	0.394943i	−0.847041	+	0.531528i	$0.821618\pi$
$24$	2.17865	−	8.20082i	0.0907772	−	0.341701i
$25$	3.46360	+	1.26065i	0.138544	+	0.0504259i
$26$	−6.18221	−	3.56930i	−0.237777	−	0.137281i
$27$	−18.9692	+	19.2137i	−0.702564	+	0.711620i
$28$	12.6111	+	6.07956i	0.450395	+	0.217127i
$29$	4.80424	−	4.03124i	0.165664	−	0.139008i	−0.556187	−	0.831057i	$-0.687736\pi$
$29$	4.80424	−	4.03124i	0.165664	−	0.139008i	0.721851	+	0.692049i	$0.243292\pi$
$30$	16.0334	−	16.1020i	0.534448	−	0.536734i
$31$	−16.2841	−	44.7401i	−0.525293	−	1.44323i	−0.864555	−	0.502538i	$-0.832400\pi$
$31$	−16.2841	−	44.7401i	−0.525293	−	1.44323i	0.339263	−	0.940692i	$-0.389822\pi$
$32$	4.33340	+	3.63616i	0.135419	+	0.113630i
$33$	16.6596	−	23.9008i	0.504837	−	0.724267i
$34$	−9.15361	+	1.61403i	−0.269224	+	0.0474714i
$35$	21.1069	+	30.9856i	0.603055	+	0.885302i
$36$	−6.22852	−	16.8880i	−0.173014	−	0.469112i
$37$	5.39894	+	9.35124i	0.145917	+	0.252736i	0.929715	−	0.368280i	$-0.120053\pi$
$37$	5.39894	+	9.35124i	0.145917	+	0.252736i	−0.783797	+	0.621017i	$0.786720\pi$
$38$	39.4530	−	6.95663i	1.03824	−	0.183069i
$39$	−15.0828	+	1.35202i	−0.386738	+	0.0346672i
$40$	5.18121	+	14.2352i	0.129530	+	0.355881i
$41$	−48.4582	+	57.7502i	−1.18191	+	1.40854i	−0.289578	+	0.957154i	$0.593515\pi$
$41$	−48.4582	+	57.7502i	−1.18191	+	1.40854i	−0.892328	+	0.451387i	$0.850929\pi$
$42$	29.3010	−	4.84258i	0.697643	−	0.115299i
$43$	3.26038	+	1.18668i	0.0758227	+	0.0275972i	0.379653	−	0.925129i	$-0.376043\pi$
$43$	3.26038	+	1.18668i	0.0758227	+	0.0275972i	−0.303830	+	0.952726i	$0.598266\pi$
$44$	9.71135	+	16.8205i	0.220712	+	0.382285i
$45$	8.16768	−	47.5063i	0.181504	−	1.05569i
$46$	9.99263	−	17.3077i	0.217231	−	0.376255i
$47$	−4.05958	+	11.1536i	−0.0863740	+	0.237311i	−0.975358	−	0.220627i	$-0.929190\pi$
$47$	−4.05958	+	11.1536i	−0.0863740	+	0.237311i	0.888984	+	0.457938i	$0.151412\pi$
$48$	11.9565	+	1.02035i	0.249095	+	0.0212573i
$49$	−1.26191	+	48.9837i	−0.0257534	+	0.999668i
$50$	−0.905164	+	5.13344i	−0.0181033	+	0.102669i
$51$	−13.9124	+	13.9720i	−0.272793	+	0.273960i
$52$	3.45286	−	9.48667i	0.0664012	−	0.182436i
$53$	−1.24246	−	2.15200i	−0.0234426	−	0.0406037i	0.854066	−	0.520164i	$-0.174129\pi$
$53$	−1.24246	−	2.15200i	−0.0234426	−	0.0406037i	−0.877509	+	0.479561i	$0.840796\pi$
$54$	−31.4179	−	21.7006i	−0.581813	−	0.401862i
$55$			52.0132i			0.945694i
$56$	−5.37021	+	19.0568i	−0.0958966	+	0.340300i
$57$	59.9640	−	60.2206i	1.05200	−	1.05650i
$58$	6.79423	+	5.70103i	0.117142	+	0.0982937i
$59$	−49.2676	+	58.7149i	−0.835044	+	0.995167i	0.164916	+	0.986308i	$0.447265\pi$
$59$	−49.2676	+	58.7149i	−0.835044	+	0.995167i	−0.999961	+	0.00885969i	$0.997180\pi$
$60$	26.3632	+	18.3759i	0.439386	+	0.306266i
$61$	12.7999	−	35.1674i	0.209834	−	0.576515i	−0.789471	−	0.613788i	$-0.789645\pi$
$61$	12.7999	−	35.1674i	0.209834	−	0.576515i	0.999305	+	0.0372733i	$0.0118672\pi$
$62$	58.3119	−	33.6664i	0.940514	−	0.543006i
$63$	44.9296	−	44.1626i	0.713168	−	0.700993i
$64$	−4.00000	+	6.92820i	−0.0625000	+	0.108253i
$65$	20.7103	−	17.3780i	0.318620	−	0.267354i
$66$	37.3785	+	17.3329i	0.566342	+	0.262619i
$67$	−2.30547	+	13.0750i	−0.0344100	+	0.195149i	−0.997167	−	0.0752193i	$-0.976034\pi$
$67$	−2.30547	+	13.0750i	−0.0344100	+	0.195149i	0.962757	+	0.270368i	$0.0871454\pi$
$68$	−4.49581	−	12.3521i	−0.0661148	−	0.181649i
$69$	−3.78512	−	42.2258i	−0.0548568	−	0.611968i
$70$	−37.9711	+	37.0055i	−0.542445	+	0.528650i
$71$	−2.32931	+	4.03448i	−0.0328072	+	0.0568237i	−0.881963	−	0.471319i	$-0.843778\pi$
$71$	−2.32931	+	4.03448i	−0.0328072	+	0.0568237i	0.849156	+	0.528143i	$0.177111\pi$
$72$	21.9909	−	12.8219i	0.305429	−	0.178082i
$73$	−84.2726	−	48.6548i	−1.15442	−	0.666504i	−0.204459	−	0.978875i	$-0.565543\pi$
$73$	−84.2726	−	48.6548i	−1.15442	−	0.666504i	−0.949960	+	0.312371i	$0.898877\pi$
$74$	−11.6979	+	9.81570i	−0.158080	+	0.132645i
$75$	4.69455	+	10.0116i	0.0625940	+	0.133489i
$76$	19.3774	+	53.2389i	0.254966	+	0.700512i
$77$	−39.7053	+	55.1787i	−0.515653	+	0.716607i
$78$	−5.58696	−	20.6742i	−0.0716277	−	0.265054i
$79$	−14.4804	−	82.1223i	−0.183296	−	1.03952i	−0.928125	−	0.372268i	$-0.878580\pi$
$79$	−14.4804	−	82.1223i	−0.183296	−	1.03952i	0.744829	−	0.667255i	$-0.232531\pi$
$80$	−18.5535	+	10.7118i	−0.231918	+	0.133898i
$81$	−80.9970	+	0.691583i	−0.999964	+	0.00853806i
$82$	−92.3305	−	53.3070i	−1.12598	−	0.650086i
$83$	31.7429	+	37.8297i	0.382444	+	0.455779i	0.922584	−	0.385796i	$-0.126073\pi$
$83$	31.7429	+	37.8297i	0.382444	+	0.455779i	−0.540140	+	0.841575i	$0.681629\pi$
$84$	13.9400	+	39.6191i	0.165952	+	0.471656i
$85$	6.11266	−	34.6666i	0.0719137	−	0.407843i
$86$	−0.852054	+	4.83224i	−0.00990760	+	0.0561888i
$87$	18.7463	+	1.59978i	0.215475	+	0.0183883i
$88$	−21.0416	+	17.6560i	−0.239109	+	0.200636i
$89$		−	84.0015i		−	0.943837i	−0.881642	−	0.471918i	$-0.843562\pi$
$89$		−	84.0015i		−	0.943837i	0.881642	−	0.471918i	$-0.156438\pi$
$90$	68.1691	−	0.291021i	0.757435	−	0.00323357i
$91$	35.2365	−	2.62603i	0.387215	−	0.0288575i
$92$	26.5589	+	9.66666i	0.288684	+	0.105072i
$93$	60.0879	−	129.580i	0.646107	−	1.39334i
$94$	−16.5309	−	2.91484i	−0.175860	−	0.0310089i
$95$	−26.3462	+	149.417i	−0.277328	+	1.57281i
$96$	1.51517	+	16.9028i	0.0157830	+	0.176071i
$97$	8.15244	−	22.3986i	0.0840458	−	0.230914i	−0.890550	−	0.454886i	$-0.849680\pi$
$97$	8.15244	−	22.3986i	0.0840458	−	0.230914i	0.974596	+	0.223972i	$0.0719024\pi$
$98$	−68.5310	+	10.2717i	−0.699295	+	0.104813i
$99$	86.0087	−	15.5445i	0.868775	−	0.157016i
$100$	−7.37178			−0.0737178
$101$	23.0322	+	27.4487i	0.228042	+	0.271769i	0.867917	−	0.496709i	$-0.165459\pi$
$101$	23.0322	+	27.4487i	0.228042	+	0.271769i	−0.639875	+	0.768479i	$0.721014\pi$
$102$	−22.8757	−	15.9451i	−0.224272	−	0.156324i
$103$	22.5355	+	3.97361i	0.218791	+	0.0385787i	0.281969	−	0.959424i	$-0.409012\pi$
$103$	22.5355	+	3.97361i	0.218791	+	0.0385787i	−0.0631780	+	0.998002i	$0.520124\pi$
$104$	14.0603	+	2.47921i	0.135195	+	0.0238385i
$105$	−20.7198	+	110.549i	−0.197332	+	1.05285i
$106$	2.69203	−	2.25888i	0.0253965	−	0.0213102i
$107$	−36.2624	+	62.8084i	−0.338901	+	0.586994i	−0.984226	−	0.176914i	$-0.943389\pi$
$107$	−36.2624	+	62.8084i	−0.338901	+	0.586994i	0.645325	+	0.763908i	$0.276722\pi$
$108$	22.5075	−	49.0858i	0.208403	−	0.454498i
$109$	−19.6543	−	34.0423i	−0.180315	−	0.312314i	0.761673	−	0.647962i	$-0.224378\pi$
$109$	−19.6543	−	34.0423i	−0.180315	−	0.312314i	−0.941988	+	0.335647i	$0.891045\pi$
$110$	−72.4403	+	12.7732i	−0.658548	+	0.116120i
$111$	−8.31728	+	31.3077i	−0.0749305	+	0.282051i
$112$	−27.8597	−	2.79936i	−0.248747	−	0.0249943i
$113$	−174.286	+	63.4351i	−1.54236	+	0.561372i	−0.966609	−	0.256255i	$-0.917511\pi$
$113$	−174.286	+	63.4351i	−1.54236	+	0.561372i	−0.575748	+	0.817627i	$0.695289\pi$
$114$	98.5966	+	68.7249i	0.864883	+	0.602850i
$115$	48.6515	+	57.9806i	0.423057	+	0.504179i
$116$	−6.27150	+	10.8625i	−0.0540646	+	0.0936427i
$117$	−34.9256	−	29.0529i	−0.298509	−	0.248315i
$118$	−93.8728	−	54.1975i	−0.795532	−	0.459301i
$119$	32.9481	−	32.1102i	0.276875	−	0.269834i
$120$	−19.1186	+	41.2294i	−0.159321	+	0.343578i
$121$	25.0802	−	9.12844i	0.207274	−	0.0754417i
$122$	52.1220	+	9.19051i	0.427229	+	0.0753320i
$123$	−225.259	+	20.1922i	−1.83138	+	0.164165i
$124$	61.2081	+	72.9450i	0.493614	+	0.588266i
$125$	98.8626	+	57.0783i	0.790901	+	0.456627i
$126$	72.5401	+	51.7295i	0.575715	+	0.410551i
$127$	−35.1199	−	60.8294i	−0.276534	−	0.478972i	0.693987	−	0.719988i	$-0.255853\pi$
$127$	−35.1199	−	60.8294i	−0.276534	−	0.478972i	−0.970521	+	0.241016i	$0.922519\pi$
$128$	−10.6314	−	3.86952i	−0.0830579	−	0.0302306i
$129$	4.41910	+	9.42422i	0.0342566	+	0.0730559i
$130$	29.2888	+	24.5762i	0.225298	+	0.189048i
$131$	−71.9646	+	85.7641i	−0.549348	+	0.654688i	−0.967256	−	0.253801i	$-0.918319\pi$
$131$	−71.9646	+	85.7641i	−0.549348	+	0.654688i	0.417908	+	0.908489i	$0.362763\pi$
$132$	−14.9607	+	56.3147i	−0.113339	+	0.426626i
$133$	−142.010	+	138.398i	−1.06774	+	1.04059i
$134$	−18.7761			−0.140120
$135$	117.924	−	83.7017i	0.873510	−	0.620012i
$136$	16.0991	−	9.29482i	0.118376	−	0.0683443i
$137$	184.388	+	67.1116i	1.34590	+	0.489866i	0.911664	−	0.410936i	$-0.134798\pi$
$137$	184.388	+	67.1116i	1.34590	+	0.489866i	0.434231	+	0.900802i	$0.357020\pi$
$138$	57.8796	−	15.6413i	0.419417	−	0.113343i
$139$	−129.349	−	22.8077i	−0.930569	−	0.164084i	−0.312240	−	0.950003i	$-0.601079\pi$
$139$	−129.349	−	22.8077i	−0.930569	−	0.164084i	−0.618330	+	0.785919i	$0.712190\pi$
$140$	−60.8634	−	43.7958i	−0.434739	−	0.312827i
$141$	−32.2398	+	15.1175i	−0.228651	+	0.107217i
$142$	−6.19096	−	2.25333i	−0.0435983	−	0.0158685i
$143$	42.4530	+	24.5102i	0.296874	+	0.171400i
$144$	23.2579	+	27.4786i	0.161513	+	0.190823i
$145$	−29.0895	+	16.7948i	−0.200617	+	0.115826i
$146$	47.0676	−	129.317i	0.322381	−	0.885735i
$147$	−106.371	+	101.461i	−0.723611	+	0.690208i
$148$	−16.5433	−	13.8815i	−0.111779	−	0.0937939i
$149$	208.379	−	75.8437i	1.39852	−	0.509018i	0.470778	−	0.882252i	$-0.343973\pi$
$149$	208.379	−	75.8437i	1.39852	−	0.509018i	0.927737	+	0.373233i	$0.121751\pi$
$150$	−12.7906	+	8.99685i	−0.0852709	+	0.0599790i
$151$	−8.75081	−	49.6283i	−0.0579524	−	0.328664i	0.942024	−	0.335546i	$-0.108921\pi$
$151$	−8.75081	−	49.6283i	−0.0579524	−	0.328664i	−0.999976	+	0.00688140i	$0.997810\pi$
$152$	−69.3888	+	40.0616i	−0.456505	+	0.263563i
$153$	−59.1514	+	0.252524i	−0.386610	+	0.00165048i
$154$	−86.5996	−	41.7481i	−0.562335	−	0.271092i
$155$	44.2808	+	251.129i	0.285683	+	1.62019i
$156$	27.4215	−	12.8582i	0.175779	−	0.0824243i
$157$	−158.816	+	189.269i	−1.01157	+	1.20554i	−0.0330316	+	0.999454i	$0.510516\pi$
$157$	−158.816	+	189.269i	−1.01157	+	1.20554i	−0.978534	+	0.206083i	$0.933928\pi$
$158$	110.818	−	40.3345i	0.701380	−	0.255282i
$159$	1.91405	−	7.20483i	0.0120381	−	0.0453134i
$160$	−19.4750	−	23.2094i	−0.121719	−	0.145058i
$161$	7.35186	+	98.6484i	0.0456637	+	0.612723i
$162$	−20.8541	−	112.637i	−0.128729	−	0.695290i
$163$	54.5064	−	94.4078i	0.334395	−	0.579189i	−0.648973	−	0.760811i	$-0.724801\pi$
$163$	54.5064	−	94.4078i	0.334395	−	0.579189i	0.983368	+	0.181622i	$0.0581347\pi$
$164$	51.5681	−	141.682i	0.314440	−	0.863916i
$165$	−110.101	+	110.572i	−0.667278	+	0.670133i
$166$	−44.8912	+	53.4992i	−0.270429	+	0.322285i
$167$	76.3263	+	209.705i	0.457044	+	1.25572i	0.927675	+	0.373388i	$0.121804\pi$
$167$	76.3263	+	209.705i	0.457044	+	1.25572i	−0.470632	+	0.882330i	$0.655974\pi$
$168$	−51.7554	+	29.1441i	−0.308068	+	0.173477i
$169$	24.9220	+	141.340i	0.147468	+	0.836330i
$170$	49.7823			0.292837
$171$	254.948	−	1.08840i	1.49093	−	0.00636493i
$172$	−6.93924			−0.0403444
$173$	−171.456	−	204.333i	−0.991073	−	1.18111i	−0.983457	−	0.181144i	$-0.942020\pi$
$173$	−171.456	−	204.333i	−0.991073	−	1.18111i	−0.00761618	−	0.999971i	$-0.502424\pi$
$174$	2.37559	+	26.5014i	0.0136528	+	0.152307i
$175$	−10.6020	−	23.5223i	−0.0605830	−	0.134413i
$176$	−29.7573	−	24.9693i	−0.169075	−	0.141871i
$177$	−229.022	+	20.5295i	−1.29391	+	0.115986i
$178$	116.991	−	20.6287i	0.657254	−	0.115892i
$179$	290.718			1.62412			0.812062	−	0.583571i	$-0.198345\pi$
$179$	290.718			1.62412			0.812062	+	0.583571i	$0.198345\pi$
$180$	17.1460	+	94.8696i	0.0952555	+	0.527053i
$181$	−264.845	+	152.908i	−1.46323	+	0.844797i	−0.999159	−	0.0410010i	$-0.986945\pi$
$181$	−264.845	+	152.908i	−1.46323	+	0.844797i	−0.464072	+	0.885798i	$0.653612\pi$
$182$	12.3106	+	48.4300i	0.0676406	+	0.266099i
$183$	101.652	−	47.6657i	0.555478	−	0.260469i
$184$	−6.94081	+	39.3633i	−0.0377218	+	0.213931i
$185$	−19.7799	−	54.3449i	−0.106918	−	0.293756i
$186$	195.226	+	51.8644i	1.04960	+	0.278841i
$187$	62.8575	−	11.0835i	0.336136	−	0.0592699i
$188$		−	23.7388i		−	0.126270i
$189$	188.996	+	1.22367i	0.999979	+	0.00647444i
$190$	−214.567			−1.12930
$191$	−41.3898	−	234.733i	−0.216701	−	1.22897i	−0.877931	−	0.478788i	$-0.841076\pi$
$191$	−41.3898	−	234.733i	−0.216701	−	1.22897i	0.661230	−	0.750183i	$-0.270035\pi$
$192$	−23.1689	+	6.26113i	−0.120671	+	0.0326100i
$193$	321.272	−	116.934i	1.66462	−	0.605874i	0.673545	−	0.739147i	$-0.264771\pi$
$193$	321.272	−	116.934i	1.66462	−	0.605874i	0.991079	+	0.133273i	$0.0425487\pi$
$194$	33.1973	+	5.85357i	0.171120	+	0.0301731i
$195$	80.8123	+	6.89638i	0.414422	+	0.0353660i
$196$	−31.1352	−	92.9225i	−0.158853	−	0.474095i
$197$	−57.0819	−	98.8687i	−0.289756	−	0.501872i	0.683996	−	0.729486i	$-0.260241\pi$
$197$	−57.0819	−	98.8687i	−0.289756	−	0.501872i	−0.973751	+	0.227615i	$0.926907\pi$
$198$	42.7710	+	115.969i	0.216015	+	0.585704i
$199$		−	308.012i		−	1.54780i	−0.633309	−	0.773899i	$-0.718304\pi$
$199$		−	308.012i		−	1.54780i	0.633309	−	0.773899i	$-0.281696\pi$
$200$	−1.81033	−	10.2669i	−0.00905164	−	0.0513344i
$201$	−32.5780	+	22.9152i	−0.162080	+	0.114006i
$202$	−32.5724	+	38.8183i	−0.161250	+	0.192170i
$203$	−43.6805	−	4.38905i	−0.215175	−	0.0216209i
$204$	16.5895	−	35.7754i	0.0813209	−	0.175369i
$205$	309.306	−	259.538i	1.50881	−	1.26604i
$206$			32.3616i			0.157095i
$207$	81.3365	−	97.7778i	0.392930	−	0.472356i
$208$			20.1910i			0.0970721i
$209$	−270.922	+	47.7709i	−1.29628	+	0.228569i
$210$	−159.054	−	1.70887i	−0.757398	−	0.00813747i
$211$	−19.7508	+	7.18869i	−0.0936055	+	0.0340696i	−0.388398	−	0.921492i	$-0.626972\pi$
$211$	−19.7508	+	7.18869i	−0.0936055	+	0.0340696i	0.294793	+	0.955561i	$0.404749\pi$
$212$	3.80711	+	3.19454i	0.0179581	+	0.0150686i
$213$	−13.4919	+	3.64603i	−0.0633422	+	0.0171175i
$214$	−96.3802	−	35.0795i	−0.450375	−	0.163923i
$215$	−16.0934	−	9.29150i	−0.0748528	−	0.0432163i
$216$	73.8904	+	19.2926i	0.342085	+	0.0893176i
$217$	−144.728	+	300.215i	−0.666951	+	1.38348i
$218$	42.5850	−	35.7331i	0.195344	−	0.163913i
$219$	−76.1585	−	281.820i	−0.347756	−	1.28685i
$220$	−35.5791	−	97.7528i	−0.161723	−	0.444331i
$221$	−25.4143	−	21.3251i	−0.114997	−	0.0964938i
$222$	−45.6456	−	3.89531i	−0.205611	−	0.0175465i
$223$	320.912	−	56.5855i	1.43907	−	0.253747i	0.600973	−	0.799269i	$-0.294780\pi$
$223$	320.912	−	56.5855i	1.43907	−	0.253747i	0.838096	+	0.545523i	$0.183669\pi$
$224$	−2.94291	−	39.4885i	−0.0131380	−	0.176288i
$225$	−11.2126	+	31.2206i	−0.0498340	+	0.138758i
$226$	−131.148	−	227.156i	−0.580302	−	1.00511i
$227$	92.2155	−	16.2601i	0.406236	−	0.0716303i	0.0332032	−	0.999449i	$-0.489429\pi$
$227$	92.2155	−	16.2601i	0.406236	−	0.0716303i	0.373032	+	0.927818i	$0.378318\pi$
$228$	−71.5022	+	154.195i	−0.313606	+	0.676296i
$229$	−80.8135	−	222.033i	−0.352897	−	0.969578i	−0.981434	−	0.191798i	$-0.938568\pi$
$229$	−80.8135	−	222.033i	−0.352897	−	0.969578i	0.628537	−	0.777780i	$-0.283654\pi$
$230$	−68.8036	+	81.9970i	−0.299146	+	0.356509i
$231$	−201.209	+	33.2538i	−0.871034	+	0.143956i
$232$	−16.6687	−	6.06691i	−0.0718479	−	0.0261505i
$233$	63.7969	+	110.499i	0.273806	+	0.474246i	0.969833	−	0.243769i	$-0.0783840\pi$
$233$	63.7969	+	110.499i	0.273806	+	0.474246i	−0.696027	+	0.718016i	$0.745051\pi$
$234$	31.8859	−	55.7765i	0.136264	−	0.238361i
$235$	31.7858	−	55.0547i	0.135259	−	0.234275i
$236$	52.4295	−	144.049i	0.222159	−	0.610377i
$237$	143.053	−	205.231i	0.603597	−	0.865954i
$238$	52.8121	+	38.0023i	0.221900	+	0.159674i
$239$	68.1637	−	386.576i	0.285204	−	1.61747i	−0.419352	−	0.907824i	$-0.637743\pi$
$239$	68.1637	−	386.576i	0.285204	−	1.61747i	0.704556	−	0.709648i	$-0.251146\pi$
$240$	−62.1164	−	16.5020i	−0.258818	−	0.0687584i
$241$	−147.168	+	404.341i	−0.610657	+	1.67777i	0.118108	+	0.993001i	$0.462317\pi$
$241$	−147.168	+	404.341i	−0.610657	+	1.67777i	−0.728764	+	0.684765i	$0.759905\pi$
$242$	18.8725	+	32.6882i	0.0779856	+	0.135075i
$243$	−173.651	−	169.983i	−0.714613	−	0.699520i
$244$			74.8487i			0.306757i
$245$	52.2132	−	257.194i	0.213115	−	1.04977i
$246$	−83.4405	−	308.766i	−0.339189	−	1.25515i
$247$	109.538	+	91.9135i	0.443474	+	0.372119i
$248$	−86.5613	+	103.160i	−0.349038	+	0.415967i
$249$	−12.5970	+	147.613i	−0.0505904	+	0.592823i
$250$	−55.2164	+	151.706i	−0.220866	+	0.606823i
$251$	−57.1203	+	32.9784i	−0.227571	+	0.131388i	−0.609451	−	0.792824i	$-0.708610\pi$
$251$	−57.1203	+	32.9784i	−0.227571	+	0.131388i	0.381880	+	0.924212i	$0.375277\pi$
$252$	−54.2310	+	113.732i	−0.215202	+	0.451318i
$253$	−68.6190	+	118.852i	−0.271221	+	0.469769i
$254$	76.0942	−	63.8506i	0.299584	−	0.251380i
$255$	86.3765	−	60.7566i	0.338731	−	0.238261i
$256$	2.77837	−	15.7569i	0.0108530	−	0.0615505i
$257$	−119.191	−	327.474i	−0.463777	−	1.27422i	−0.922624	−	0.385701i	$-0.873960\pi$
$257$	−119.191	−	327.474i	−0.463777	−	1.27422i	0.458847	−	0.888515i	$-0.348263\pi$
$258$	−12.0402	+	8.46896i	−0.0466673	+	0.0328254i
$259$	20.5015	−	72.7517i	0.0791562	−	0.280895i
$260$	−27.0354	+	46.8266i	−0.103982	+	0.180102i
$261$	36.4654	+	43.0829i	0.139714	+	0.165069i
$262$	−137.119	−	79.1656i	−0.523355	−	0.302159i
$263$	−98.0674	+	82.2883i	−0.372880	+	0.312883i	−0.809900	−	0.586569i	$-0.800478\pi$
$263$	−98.0674	+	82.2883i	−0.372880	+	0.312883i	0.437020	+	0.899452i	$0.356034\pi$
$264$	−82.1051	−	7.00670i	−0.311004	−	0.0265405i
$265$	4.55194	+	12.5064i	0.0171771	+	0.0471938i
$266$	−227.626	−	163.794i	−0.855735	−	0.615766i
$267$	177.813	−	178.574i	0.665967	−	0.668817i
$268$	−4.61094	−	26.1500i	−0.0172050	−	0.0975745i
$269$	−177.602	+	102.538i	−0.660229	+	0.381183i	−0.792364	−	0.610048i	$-0.791150\pi$
$269$	−177.602	+	102.538i	−0.660229	+	0.381183i	0.132135	+	0.991232i	$0.457817\pi$
$270$	145.533	+	143.681i	0.539011	+	0.532151i
$271$	287.595	+	166.043i	1.06123	+	0.612704i	0.925774	−	0.378078i	$-0.123415\pi$
$271$	287.595	+	166.043i	1.06123	+	0.612704i	0.135461	+	0.990783i	$0.456748\pi$
$272$	16.8987	+	20.1391i	0.0621276	+	0.0740408i
$273$	80.4661	+	69.0057i	0.294748	+	0.252768i
$274$	−48.1872	+	273.283i	−0.175866	+	0.997383i
$275$	6.21572	−	35.2511i	0.0226026	−	0.128186i
$276$	35.9979	+	76.7694i	0.130427	+	0.278150i
$277$	378.334	−	317.460i	1.36583	−	1.14607i	0.391694	−	0.920096i	$-0.371889\pi$
$277$	378.334	−	317.460i	1.36583	−	1.14607i	0.974134	−	0.225970i	$-0.0725552\pi$
$278$		−	185.749i		−	0.668163i
$279$	402.032	−	148.274i	1.44097	−	0.531449i
$280$	46.0491	−	95.5214i	0.164461	−	0.341148i
$281$	508.580	+	185.108i	1.80989	+	0.658748i	0.997092	+	0.0762079i	$0.0242813\pi$
$281$	508.580	+	185.108i	1.80989	+	0.658748i	0.812802	+	0.582540i	$0.197941\pi$
$282$	−28.9719	−	41.1888i	−0.102737	−	0.146060i
$283$	433.442	+	76.4276i	1.53160	+	0.270062i	0.874979	−	0.484160i	$-0.160875\pi$
$283$	433.442	+	76.4276i	1.53160	+	0.270062i	0.656619	+	0.754222i	$0.271986\pi$
$284$	1.61792	−	9.17569i	0.00569691	−	0.0323088i
$285$	−372.291	+	261.867i	−1.30629	+	0.918833i
$286$	−23.7107	+	65.1446i	−0.0829045	+	0.227778i
$287$	526.253	−	39.2195i	1.83364	−	0.136653i
$288$	−32.5586	+	39.1400i	−0.113051	+	0.135903i
$289$	245.803			0.850530
$290$	−30.5343	−	36.3893i	−0.105291	−	0.125480i
$291$	64.7440	−	30.3590i	0.222488	−	0.104327i
$292$	191.663	+	33.7953i	0.656378	+	0.115737i
$293$	−290.093	−	51.1512i	−0.990078	−	0.174577i	−0.344925	−	0.938630i	$-0.612095\pi$
$293$	−290.093	−	51.1512i	−0.990078	−	0.174577i	−0.645154	+	0.764053i	$0.723207\pi$
$294$	−167.429	−	123.229i	−0.569487	−	0.419148i
$295$	314.472	−	263.873i	1.06601	−	0.894486i
$296$	15.2705	−	26.4493i	0.0515896	−	0.0893557i
$297$	215.746	+	149.017i	0.726416	+	0.501740i
$298$	156.802	+	271.590i	0.526183	+	0.911375i
$299$	70.2496	−	12.3869i	0.234949	−	0.0414278i
$300$	−15.6712	−	15.6045i	−0.0522375	−	0.0520149i
$301$	−9.97996	−	22.1422i	−0.0331560	−	0.0735620i
$302$	66.9698	−	24.3750i	0.221754	−	0.0807119i
$303$	−9.14022	+	107.106i	−0.0301658	+	0.353485i
$304$	−72.8352	−	86.8016i	−0.239589	−	0.285532i
$305$	−100.221	+	173.588i	−0.328593	+	0.569140i
$306$	−14.8778	−	82.3198i	−0.0486204	−	0.269019i
$307$	−398.747	−	230.217i	−1.29885	−	0.749891i	−0.318644	−	0.947874i	$-0.603228\pi$
$307$	−398.747	−	230.217i	−1.29885	−	0.749891i	−0.980205	+	0.197983i	$0.936561\pi$
$308$	36.8770	−	130.862i	0.119731	−	0.424877i
$309$	39.4956	+	56.1501i	0.127817	+	0.181715i
$310$	−338.880	+	123.342i	−1.09316	+	0.397878i
$311$	−520.480	−	91.7748i	−1.67357	−	0.295096i	−0.745225	−	0.666813i	$-0.767658\pi$
$311$	−520.480	−	91.7748i	−1.67357	−	0.295096i	−0.928346	+	0.371718i	$0.878769\pi$
$312$	24.6420	+	35.0331i	0.0789808	+	0.112285i
$313$	83.0535	+	98.9793i	0.265347	+	0.316228i	0.882223	−	0.470833i	$-0.156046\pi$
$313$	83.0535	+	98.9793i	0.265347	+	0.316228i	−0.616876	+	0.787060i	$0.711602\pi$
$314$	−302.602	−	174.707i	−0.963701	−	0.556393i
$315$	−278.057	+	191.151i	−0.882720	+	0.606829i
$316$	83.3892	+	144.434i	0.263890	+	0.457071i
$317$	−461.527	−	167.982i	−1.45592	−	0.529912i	−0.511683	−	0.859174i	$-0.670978\pi$
$317$	−461.527	−	167.982i	−1.45592	−	0.529912i	−0.944238	+	0.329262i	$0.893200\pi$
$318$	10.5044	+	0.896427i	0.0330327	+	0.00281895i
$319$	−46.6557	−	39.1488i	−0.146256	−	0.122723i
$320$	27.5418	−	32.8230i	0.0860680	−	0.102572i
$321$	−210.040	+	56.7609i	−0.654331	+	0.176825i
$322$	−135.585	+	34.4648i	−0.421071	+	0.107033i
$323$	186.183			0.576418
$324$	151.752	−	56.7050i	0.468369	−	0.175015i
$325$	−16.1128	+	9.30272i	−0.0495778	+	0.0286238i
$326$	144.870	+	52.7283i	0.444386	+	0.161743i
$327$	30.2783	−	113.973i	0.0925941	−	0.348540i
$328$	209.989	+	37.0267i	0.640210	+	0.112886i
$329$	75.7473	−	34.1410i	0.230235	−	0.103772i
$330$	−181.035	−	126.187i	−0.548590	−	0.382384i
$331$	−76.2889	−	27.7669i	−0.230480	−	0.0838879i	0.224198	−	0.974544i	$-0.428024\pi$
$331$	−76.2889	−	27.7669i	−0.230480	−	0.0838879i	−0.454679	+	0.890656i	$0.650246\pi$
$332$	−85.5341	−	49.3831i	−0.257633	−	0.148744i
$333$	−83.9530	+	48.9493i	−0.252111	+	0.146995i
$334$	−273.318	+	157.800i	−0.818317	+	0.472456i
$335$	24.3207	−	66.8205i	0.0725990	−	0.199464i
$336$	−53.2997	−	64.9241i	−0.158630	−	0.193226i
$337$	274.690	+	230.492i	0.815103	+	0.683952i	0.951820	−	0.306658i	$-0.0992107\pi$
$337$	274.690	+	230.492i	0.815103	+	0.683952i	−0.136717	+	0.990610i	$0.543655\pi$
$338$	−190.728	+	69.4192i	−0.564283	+	0.205382i
$339$	−504.784	−	234.074i	−1.48904	−	0.690484i
$340$	12.2253	+	69.3333i	0.0359569	+	0.203921i
$341$	−400.425	+	231.186i	−1.17427	+	0.677963i
$342$	64.1249	+	354.807i	0.187500	+	1.03745i
$343$	251.725	−	232.989i	0.733891	−	0.679267i
$344$	−1.70411	−	9.66447i	−0.00495380	−	0.0280944i
$345$	−19.3071	+	226.243i	−0.0559627	+	0.655776i
$346$	242.475	−	288.970i	0.700794	−	0.835174i
$347$	−225.134	+	81.9420i	−0.648800	+	0.236144i	−0.645394	−	0.763850i	$-0.723307\pi$
$347$	−225.134	+	81.9420i	−0.648800	+	0.236144i	−0.00340668	+	0.999994i	$0.501084\pi$
$348$	−36.3259	+	9.81666i	−0.104385	+	0.0282088i
$349$	−446.165	−	531.719i	−1.27841	−	1.52355i	−0.719966	−	0.694010i	$-0.755843\pi$
$349$	−446.165	−	531.719i	−1.27841	−	1.52355i	−0.558445	−	0.829541i	$-0.688602\pi$
$350$	30.1566	−	20.5423i	0.0861617	−	0.0586922i
$351$	−12.7476	−	135.692i	−0.0363179	−	0.386586i
$352$	27.4678	−	47.5757i	0.0780336	−	0.135158i
$353$	19.6500	−	53.9879i	0.0556657	−	0.152940i	−0.908743	−	0.417356i	$-0.862957\pi$
$353$	19.6500	−	53.9879i	0.0556657	−	0.152940i	0.964409	+	0.264416i	$0.0851791\pi$
$354$	−84.8343	−	313.924i	−0.239645	−	0.886791i
$355$	16.0383	−	19.1137i	0.0451784	−	0.0538415i
$356$	57.4604	+	157.871i	0.161406	+	0.443458i
$357$	138.013	+	1.48281i	0.386591	+	0.00415353i
$358$	71.3933	+	404.892i	0.199423	+	1.13098i
$359$	379.040			1.05582			0.527910	−	0.849300i	$-0.322976\pi$
$359$	379.040			1.05582			0.527910	+	0.849300i	$0.322976\pi$
$360$	−127.917	+	47.1774i	−0.355325	+	0.131048i
$361$	−441.467			−1.22290
$362$	−277.999	−	331.306i	−0.767953	−	0.915211i
$363$	72.6395	+	33.6838i	0.200109	+	0.0927928i
$364$	−64.4267	+	29.0385i	−0.176996	+	0.0797762i
$365$	399.249	+	335.010i	1.09383	+	0.917835i
$366$	91.3488	+	129.869i	0.249587	+	0.354833i
$367$	433.621	−	76.4591i	1.18153	−	0.208336i	0.451830	−	0.892104i	$-0.350771\pi$
$367$	433.621	−	76.4591i	1.18153	−	0.208336i	0.729699	+	0.683768i	$0.239660\pi$
$368$	−56.5268			−0.153606
$369$	−521.609	−	433.901i	−1.41357	−	1.17588i
$370$	70.8302	−	40.8938i	0.191433	−	0.110524i
$371$	−4.71799	+	16.7423i	−0.0127170	+	0.0451275i
$372$	−24.2902	+	284.634i	−0.0652961	+	0.765145i
$373$	−69.4192	+	393.696i	−0.186111	+	1.05549i	0.738410	+	0.674352i	$0.235577\pi$
$373$	−69.4192	+	393.696i	−0.186111	+	1.05549i	−0.924520	+	0.381133i	$0.875534\pi$
$374$	30.8725	+	84.8216i	0.0825469	+	0.226796i
$375$	89.3437	+	330.611i	0.238250	+	0.881629i
$376$	33.0617	−	5.82968i	0.0879302	−	0.0155045i
$377$			31.6569i			0.0839707i
$378$	44.7086	+	263.521i	0.118277	+	0.697145i
$379$	34.1015			0.0899775			0.0449888	−	0.998987i	$-0.485675\pi$
$379$	34.1015			0.0899775			0.0449888	+	0.998987i	$0.485675\pi$
$380$	−52.6924	−	298.833i	−0.138664	−	0.786404i
$381$	54.1035	−	203.655i	0.142004	−	0.534528i
$382$	316.756	−	115.290i	0.829203	−	0.301805i
$383$	−291.279	−	51.3604i	−0.760520	−	0.134100i	−0.220079	−	0.975482i	$-0.570632\pi$
$383$	−291.279	−	51.3604i	−0.760520	−	0.134100i	−0.540441	+	0.841382i	$0.681743\pi$
$384$	−14.4098	−	30.7304i	−0.0375254	−	0.0800271i
$385$	260.746	−	254.115i	0.677263	−	0.660040i
$386$	241.753	+	418.729i	0.626304	+	1.08479i
$387$	−10.5547	+	29.3887i	−0.0272733	+	0.0759398i
$388$			47.6723i			0.122867i
$389$	29.7249	+	168.578i	0.0764136	+	0.433363i	0.998881	+	0.0472887i	$0.0150581\pi$
$389$	29.7249	+	168.578i	0.0764136	+	0.433363i	−0.922468	+	0.386074i	$0.873831\pi$
$390$	10.2408	+	114.243i	0.0262584	+	0.292931i
$391$	59.7019	−	71.1500i	0.152690	−	0.181969i
$392$	121.770	−	66.1824i	0.310637	−	0.168833i
$393$	−334.530	+	29.9873i	−0.851221	+	0.0763034i
$394$	123.679	−	103.779i	0.313907	−	0.263399i
$395$			446.626i			1.13070i
$396$	−151.010	+	88.0476i	−0.381339	+	0.222342i
$397$		−	157.429i		−	0.396547i	−0.980147	−	0.198273i	$-0.936467\pi$
$397$		−	157.429i		−	0.396547i	0.980147	−	0.198273i	$-0.0635334\pi$
$398$	428.977	−	75.6402i	1.07783	−	0.190051i
$399$	−594.851	−	6.39106i	−1.49085	−	0.0160177i
$400$	13.8544	−	5.04259i	0.0346360	−	0.0126065i
$401$	−260.824	−	218.858i	−0.650435	−	0.545780i	0.256768	−	0.966473i	$-0.417342\pi$
$401$	−260.824	−	218.858i	−0.650435	−	0.545780i	−0.907203	+	0.420693i	$0.861787\pi$
$402$	−39.9150	−	39.7449i	−0.0992910	−	0.0988680i
$403$	225.837	+	82.1979i	0.560389	+	0.203965i
$404$	−62.0624	−	35.8317i	−0.153620	−	0.0886924i
$405$	427.866	+	71.6832i	1.05646	+	0.176996i
$406$	−4.61412	−	61.9129i	−0.0113648	−	0.152495i
$407$	80.3289	−	67.4040i	0.197368	−	0.165612i
$408$	53.8994	+	14.3190i	0.132106	+	0.0350957i
$409$	177.170	+	486.769i	0.433178	+	1.19015i	0.943851	+	0.330371i	$0.107174\pi$
$409$	177.170	+	486.769i	0.433178	+	1.19015i	−0.510674	+	0.859775i	$0.670604\pi$
$410$	437.424	+	367.042i	1.06689	+	0.895225i
$411$	249.918	+	532.978i	0.608074	+	1.29678i
$412$	−45.0709	+	7.94722i	−0.109395	+	0.0192894i
$413$	535.044	−	39.8746i	1.29551	−	0.0965487i
$414$	156.152	+	89.2678i	0.377179	+	0.215623i
$415$	−132.246	−	229.057i	−0.318665	−	0.551944i
$416$	−28.1206	+	4.95842i	−0.0675976	+	0.0119193i
$417$	−226.697	−	322.290i	−0.543638	−	0.772879i
$418$	−133.064	−	365.590i	−0.318334	−	0.874616i
$419$	−193.527	+	230.636i	−0.461877	+	0.550444i	−0.945835	−	0.324647i	$-0.894754\pi$
$419$	−193.527	+	230.636i	−0.461877	+	0.550444i	0.483958	+	0.875091i	$0.339199\pi$
$420$	−36.6797	−	221.938i	−0.0873326	−	0.528424i
$421$	−96.1065	−	34.9799i	−0.228282	−	0.0830877i	0.225347	−	0.974279i	$-0.427648\pi$
$421$	−96.1065	−	34.9799i	−0.228282	−	0.0830877i	−0.453628	+	0.891191i	$0.649871\pi$
$422$	−14.8622	−	25.7421i	−0.0352185	−	0.0610002i
$423$	−100.537	−	36.1073i	−0.237677	−	0.0853601i
$424$	−3.51420	+	6.08677i	−0.00828820	+	0.0143556i
$425$	−8.28552	+	22.7643i	−0.0194953	+	0.0535630i
$426$	−8.39120	−	17.8952i	−0.0196977	−	0.0420074i
$427$	−238.832	+	107.647i	−0.559325	+	0.252100i
$428$	25.1876	−	142.846i	0.0588496	−	0.333753i
$429$	38.3654	+	141.969i	0.0894298	+	0.330930i
$430$	8.98840	−	24.6954i	0.0209033	−	0.0574313i
$431$	−265.592	−	460.019i	−0.616222	−	1.06733i	−0.990169	−	0.139878i	$-0.955329\pi$
$431$	−265.592	−	460.019i	−0.616222	−	1.06733i	0.373946	−	0.927450i	$-0.378004\pi$
$432$	−8.72367	+	107.647i	−0.0201937	+	0.249183i
$433$			573.403i			1.32426i	0.749391	+	0.662128i	$0.230346\pi$
$433$			573.403i			1.32426i	−0.749391	+	0.662128i	$0.769654\pi$
$434$	−453.660	−	127.842i	−1.04530	−	0.294566i
$435$	−97.3907	−	25.8731i	−0.223887	−	0.0594784i
$436$	60.2243	+	50.5342i	0.138129	+	0.115904i
$437$	−257.321	+	306.664i	−0.588836	+	0.701748i
$438$	373.796	−	175.276i	0.853415	−	0.400174i
$439$	−74.0523	+	203.457i	−0.168684	+	0.463455i	−0.995015	−	0.0997300i	$-0.968202\pi$
$439$	−74.0523	+	203.457i	−0.168684	+	0.463455i	0.826331	+	0.563185i	$0.190424\pi$
$440$	127.406	−	73.5578i	0.289559	−	0.167177i
$441$	−440.898	−	9.47509i	−0.999769	−	0.0214855i
$442$	23.4590	−	40.6321i	0.0530746	−	0.0919279i
$443$	−96.5725	+	81.0340i	−0.217997	+	0.182921i	−0.745246	−	0.666790i	$-0.767668\pi$
$443$	−96.5725	+	81.0340i	−0.217997	+	0.182921i	0.527249	+	0.849711i	$0.323223\pi$
$444$	−5.78434	−	64.5286i	−0.0130278	−	0.145335i
$445$	−78.1252	+	443.070i	−0.175562	+	0.995663i
$446$	157.617	+	433.048i	0.353400	+	0.970959i
$447$	603.526	+	279.862i	1.35017	+	0.626089i
$448$	54.2740	−	13.7961i	0.121147	−	0.0307948i
$449$	228.731	−	396.174i	0.509424	−	0.882349i	−0.490516	−	0.871432i	$-0.663192\pi$
$449$	228.731	−	396.174i	0.509424	−	0.882349i	0.999940	−	0.0109165i	$-0.00347489\pi$
$450$	−46.2353	−	7.94917i	−0.102745	−	0.0176648i
$451$	634.030	+	366.057i	1.40583	+	0.811657i
$452$	284.159	−	238.438i	0.628671	−	0.527517i
$453$	86.4497	−	124.026i	0.190838	−	0.273787i
$454$	45.2917	+	124.438i	0.0997616	+	0.274093i
$455$	−188.299	−	18.9204i	−0.413845	−	0.0415834i
$456$	−232.312	−	61.7165i	−0.509455	−	0.135343i
$457$	−112.583	−	638.490i	−0.246352	−	1.39713i	−0.817331	−	0.576168i	$-0.804547\pi$
$457$	−112.583	−	638.490i	−0.246352	−	1.39713i	0.570979	−	0.820965i	$-0.306564\pi$
$458$	289.386	−	167.077i	0.631848	−	0.364797i
$459$	−126.281	−	124.674i	−0.275122	−	0.271621i
$460$	−131.096	−	75.6883i	−0.284991	−	0.164540i
$461$	−118.428	−	141.137i	−0.256895	−	0.306155i	0.622147	−	0.782901i	$-0.286261\pi$
$461$	−118.428	−	141.137i	−0.256895	−	0.306155i	−0.879041	+	0.476746i	$0.841816\pi$
$462$	−95.7254	−	272.063i	−0.207198	−	0.588881i
$463$	−104.961	+	595.264i	−0.226698	+	1.28567i	0.632715	+	0.774385i	$0.281940\pi$
$463$	−104.961	+	595.264i	−0.226698	+	1.28567i	−0.859413	+	0.511282i	$0.829171\pi$
$464$	4.35613	−	24.7049i	0.00938822	−	0.0532433i
$465$	−437.453	+	627.594i	−0.940758	+	1.34966i
$466$	−138.229	+	115.988i	−0.296628	+	0.248901i
$467$			263.638i			0.564535i	0.959336	+	0.282267i	$0.0910866\pi$
$467$			263.638i			0.564535i	−0.959336	+	0.282267i	$0.908913\pi$
$468$	85.5119	+	30.7110i	0.182718	+	0.0656218i
$469$	76.8095	−	52.3215i	0.163773	−	0.111560i
$470$	84.4820	+	30.7489i	0.179749	+	0.0654233i
$471$	−738.261	+	66.1777i	−1.56743	+	0.140505i
$472$	213.496	+	37.6452i	0.452323	+	0.0797567i
$473$	5.85102	−	33.1828i	0.0123700	−	0.0701538i
$474$	320.961	+	148.834i	0.677134	+	0.313995i
$475$	35.7114	−	98.1164i	0.0751820	−	0.206561i
$476$	−39.9575	+	82.8854i	−0.0839444	+	0.174129i
$477$	19.3201	−	11.2647i	0.0405033	−	0.0236157i
$478$	555.134			1.16137
$479$	203.140	+	242.093i	0.424093	+	0.505414i	0.935208	−	0.354098i	$-0.115212\pi$
$479$	203.140	+	242.093i	0.424093	+	0.505414i	−0.511116	+	0.859512i	$0.670768\pi$
$480$	7.72855	−	90.5638i	0.0161011	−	0.188675i
$481$	−53.6770	−	9.46470i	−0.111595	−	0.0196771i
$482$	−599.279	−	105.669i	−1.24332	−	0.219230i
$483$	−193.189	+	225.273i	−0.399977	+	0.466405i
$484$	−40.8911	+	34.3117i	−0.0844858	+	0.0708920i
$485$	−63.8322	+	110.561i	−0.131613	+	0.227960i
$486$	194.096	−	283.592i	0.399375	−	0.583524i
$487$	292.049	+	505.843i	0.599689	+	1.03869i	0.992867	+	0.119229i	$0.0380424\pi$
$487$	292.049	+	505.843i	0.599689	+	1.03869i	−0.393178	+	0.919462i	$0.628624\pi$
$488$	−104.244	+	18.3810i	−0.213615	+	0.0376660i
$489$	315.713	−	85.3178i	0.645630	−	0.174474i
$490$	371.023	+	9.55827i	0.757190	+	0.0195067i
$491$	22.0562	−	8.02780i	0.0449210	−	0.0163499i	−0.319462	−	0.947599i	$-0.603502\pi$
$491$	22.0562	−	8.02780i	0.0449210	−	0.0163499i	0.364383	+	0.931249i	$0.381280\pi$
$492$	409.537	−	192.035i	0.832392	−	0.390316i
$493$	26.4951	+	31.5756i	0.0537425	+	0.0640478i
$494$	−101.111	+	175.129i	−0.204677	+	0.354511i
$495$	−468.114	+	1.99843i	−0.945686	+	0.00403724i
$496$	−164.931	−	95.2229i	−0.332522	−	0.191982i
$497$	31.6052	−	8.03384i	0.0635921	−	0.0161647i
$498$	−208.678	+	18.7059i	−0.419033	+	0.0375621i
$499$	−643.887	+	234.356i	−1.29035	+	0.469650i	−0.893843	−	0.448380i	$-0.852001\pi$
$499$	−643.887	+	234.356i	−1.29035	+	0.469650i	−0.396511	+	0.918030i	$0.629779\pi$
$500$	−224.845	−	39.6462i	−0.449690	−	0.0792924i
$501$	−281.643	+	607.366i	−0.562161	+	1.21231i
$502$	−59.9574	−	71.4544i	−0.119437	−	0.142340i
$503$	323.521	+	186.785i	0.643183	+	0.371342i	0.785839	−	0.618431i	$-0.212231\pi$
$503$	323.521	+	186.785i	0.643183	+	0.371342i	−0.142657	+	0.989772i	$0.545565\pi$
$504$	−171.716	−	47.5993i	−0.340706	−	0.0944430i
$505$	−95.9560	−	166.201i	−0.190012	−	0.329110i
$506$	−182.379	−	66.3805i	−0.360433	−	0.131187i
$507$	−246.206	+	353.221i	−0.485613	+	0.696688i
$508$	107.613	+	90.2984i	0.211838	+	0.177753i
$509$	491.640	−	585.914i	0.965894	−	1.15111i	−0.0225841	−	0.999745i	$-0.507189\pi$
$509$	491.640	−	585.914i	0.965894	−	1.15111i	0.988478	−	0.151363i	$-0.0483662\pi$
$510$	105.829	+	105.379i	0.207509	+	0.206625i
$511$	167.811	+	660.173i	0.328398	+	1.29192i
$512$	22.6274			0.0441942
$513$	544.284	+	537.358i	1.06098	+	1.04748i
$514$	426.812	−	246.420i	0.830373	−	0.479416i
$515$	−115.169	−	41.9180i	−0.223629	−	0.0813942i
$516$	−14.7517	−	14.6889i	−0.0285886	−	0.0284668i
$517$	113.517	+	20.0161i	0.219568	+	0.0387158i
$518$	106.358	+	10.6869i	0.205324	+	0.0206311i
$519$	68.0414	−	797.315i	0.131101	−	1.53625i
$520$	−71.8560	−	26.1534i	−0.138185	−	0.0502951i
$521$	−572.436	−	330.496i	−1.09873	−	0.634349i	−0.162840	−	0.986653i	$-0.552065\pi$
$521$	−572.436	−	330.496i	−1.09873	−	0.634349i	−0.935886	+	0.352303i	$0.885399\pi$
$522$	−51.0478	+	61.3665i	−0.0977927	+	0.117560i
$523$	312.065	−	180.171i	0.596683	−	0.344495i	−0.171053	−	0.985262i	$-0.554717\pi$
$523$	312.065	−	180.171i	0.596683	−	0.344495i	0.767735	+	0.640767i	$0.221384\pi$
$524$	76.5832	−	210.411i	0.146151	−	0.401547i
$525$	27.2535	−	72.4470i	0.0519114	−	0.137994i
$526$	−138.688	−	116.373i	−0.263666	−	0.221242i
$527$	294.051	−	107.026i	0.557972	−	0.203085i
$528$	−10.4046	−	116.071i	−0.0197056	−	0.219831i
$529$	−57.1814	−	324.292i	−0.108093	−	0.613028i
$530$	−16.3001	+	9.41088i	−0.0307550	+	0.0177564i
$531$	−530.322	−	441.149i	−0.998723	−	0.830788i
$532$	172.221	−	357.244i	0.323724	−	0.671512i
$533$	−66.0796	−	374.756i	−0.123977	−	0.703107i
$534$	292.372	+	203.792i	0.547513	+	0.381633i
$535$	249.683	−	297.560i	0.466697	−	0.556188i
$536$	35.2875	−	12.8436i	0.0658348	−	0.0239619i
$537$	618.022	+	615.389i	1.15088	+	1.14598i
$538$	−186.423	−	222.170i	−0.346511	−	0.412955i
$539$	470.599	−	70.5354i	0.873097	−	0.130863i
$540$	−164.369	+	237.972i	−0.304387	+	0.440690i
$541$	−92.5757	+	160.346i	−0.171120	+	0.296388i	−0.938812	−	0.344431i	$-0.888072\pi$
$541$	−92.5757	+	160.346i	−0.171120	+	0.296388i	0.767692	+	0.640819i	$0.221405\pi$
$542$	−160.626	+	441.317i	−0.296359	+	0.814239i
$543$	−886.693	−	235.561i	−1.63295	−	0.433814i
$544$	−23.8984	+	28.4810i	−0.0439309	+	0.0523548i
$545$	72.0068	+	197.837i	0.132123	+	0.363004i
$546$	−76.3457	+	129.014i	−0.139827	+	0.236289i
$547$	−46.3576	−	262.907i	−0.0847489	−	0.480635i	−0.997410	−	0.0719187i	$-0.977088\pi$
$547$	−46.3576	−	262.907i	−0.0847489	−	0.480635i	0.912662	−	0.408716i	$-0.134023\pi$
$548$	−392.442			−0.716136
$549$	316.995	+	113.847i	0.577405	+	0.207371i
$550$	50.6217			0.0920394
$551$	−114.196	−	136.094i	−0.207253	−	0.246994i
$552$	−98.0788	+	68.9879i	−0.177679	+	0.124978i
$553$	−340.940	+	473.808i	−0.616529	+	0.856795i
$554$	535.046	+	448.957i	0.965786	+	0.810391i
$555$	72.9875	−	157.399i	0.131509	−	0.283601i
$556$	258.698	−	45.6155i	0.465285	−	0.0820422i
$557$	−322.264			−0.578570			−0.289285	−	0.957243i	$-0.593418\pi$
$557$	−322.264			−0.578570			−0.289285	+	0.957243i	$0.593418\pi$
$558$	305.235	+	523.508i	0.547016	+	0.938187i
$559$	−15.1674	+	8.75689i	−0.0271330	+	0.0156653i
$560$	144.344	+	40.6762i	0.257757	+	0.0726361i
$561$	157.087	+	109.494i	0.280012	+	0.195177i
$562$	−132.910	+	753.772i	−0.236495	+	1.34123i
$563$	−273.830	−	752.342i	−0.486377	−	1.33631i	−0.903939	−	0.427661i	$-0.859338\pi$
$563$	−273.830	−	752.342i	−0.486377	−	1.33631i	0.417563	−	0.908648i	$-0.362884\pi$
$564$	50.2500	−	50.4650i	0.0890958	−	0.0894770i
$565$	978.280	−	172.497i	1.73147	−	0.305305i
$566$			622.436i			1.09971i
$567$	399.186	+	402.666i	0.704031	+	0.710169i
$568$	13.1766			0.0231982
$569$	−20.3708	−	115.528i	−0.0358010	−	0.203038i	0.961661	−	0.274242i	$-0.0884269\pi$
$569$	−20.3708	−	115.528i	−0.0358010	−	0.203038i	−0.997462	+	0.0712042i	$0.977316\pi$
$570$	−456.136	−	454.193i	−0.800238	−	0.796829i
$571$	−568.132	+	206.783i	−0.994977	+	0.362142i	−0.787646	−	0.616129i	$-0.788700\pi$
$571$	−568.132	+	206.783i	−0.994977	+	0.362142i	−0.207332	+	0.978271i	$0.566478\pi$
$572$	−96.5514	−	17.0246i	−0.168796	−	0.0297633i
$573$	408.893	−	586.620i	0.713599	−	1.02377i
$574$	183.857	+	723.297i	0.320308	+	1.26010i
$575$	−26.0439	−	45.1094i	−0.0452938	−	0.0784512i
$576$	−62.5069	−	35.7335i	−0.108519	−	0.0620373i
$577$		−	465.575i		−	0.806890i	−0.915004	−	0.403445i	$-0.867813\pi$
$577$		−	465.575i		−	0.806890i	0.915004	−	0.403445i	$-0.132187\pi$
$578$	60.3633	+	342.337i	0.104435	+	0.592279i
$579$	930.499	+	431.483i	1.60708	+	0.745221i
$580$	43.1820	−	51.4623i	0.0744517	−	0.0887281i
$581$	34.5603	−	343.950i	0.0594842	−	0.591997i
$582$	58.1814	+	82.7153i	0.0999681	+	0.142123i
$583$	−18.4861	+	15.5117i	−0.0317085	+	0.0266066i
$584$			275.233i			0.471290i
$585$	157.196	+	185.723i	0.268711	+	0.317475i
$586$		−	416.582i		−	0.710891i
$587$	406.547	−	71.6852i	0.692584	−	0.122121i	0.183733	−	0.982976i	$-0.441182\pi$
$587$	406.547	−	71.6852i	0.692584	−	0.122121i	0.508851	+	0.860855i	$0.330071\pi$
$588$	130.509	−	263.445i	0.221953	−	0.448036i
$589$	−1267.39	+	461.293i	−2.15177	+	0.783180i
$590$	444.731	+	373.173i	0.753781	+	0.632497i
$591$	87.9369	−	331.010i	0.148793	−	0.560084i
$592$	40.5868	+	14.7724i	0.0685587	+	0.0249533i
$593$	63.5985	+	36.7186i	0.107249	+	0.0619201i	0.552665	−	0.833404i	$-0.313611\pi$
$593$	63.5985	+	36.7186i	0.107249	+	0.0619201i	−0.445416	+	0.895324i	$0.646944\pi$
$594$	−154.558	+	337.070i	−0.260199	+	0.567458i
$595$	−203.651	+	138.724i	−0.342270	+	0.233149i
$596$	−339.744	+	285.079i	−0.570040	+	0.478321i
$597$	651.996	−	654.785i	1.09212	−	1.09679i
$598$	34.5032	+	94.7968i	0.0576977	+	0.158523i
$599$	−602.936	−	505.923i	−1.00657	−	0.844613i	−0.0186899	−	0.999825i	$-0.505950\pi$
$599$	−602.936	−	505.923i	−1.00657	−	0.844613i	−0.987881	+	0.155212i	$0.950394\pi$
$600$	17.8843	−	25.6579i	0.0298072	−	0.0427631i
$601$	−330.237	+	58.2298i	−0.549480	+	0.0968881i	−0.441494	−	0.897264i	$-0.645551\pi$
$601$	−330.237	+	58.2298i	−0.549480	+	0.0968881i	−0.107986	+	0.994152i	$0.534440\pi$
$602$	28.3872	−	19.3369i	0.0471548	−	0.0321212i
$603$	−117.762	−	20.2467i	−0.195294	−	0.0335766i
$604$	50.3939	+	87.2848i	0.0834336	+	0.144511i
$605$	−140.777	+	24.8227i	−0.232689	+	0.0410293i
$606$	−151.414	+	13.5727i	−0.249858	+	0.0223973i
$607$	110.084	+	302.453i	0.181357	+	0.498275i	0.996743	−	0.0806431i	$-0.0256974\pi$
$607$	110.084	+	302.453i	0.181357	+	0.498275i	−0.815386	+	0.578918i	$0.803475\pi$
$608$	103.004	−	122.756i	0.169415	−	0.201901i
$609$	−83.5673	−	101.793i	−0.137220	−	0.167147i
$610$	−266.372	−	96.9517i	−0.436676	−	0.158937i
$611$	−29.9569	−	51.8869i	−0.0490293	−	0.0849213i
$612$	110.995	−	40.9365i	0.181365	−	0.0668897i
$613$	−190.832	+	330.530i	−0.311308	+	0.539201i	−0.978646	−	0.205554i	$-0.934100\pi$
$613$	−190.832	+	330.530i	−0.311308	+	0.539201i	0.667338	+	0.744755i	$0.267434\pi$
$614$	222.707	−	611.882i	0.362715	−	0.996550i
$615$	1206.92	+	102.997i	1.96248	+	0.167474i
$616$	191.311	+	19.2231i	0.310571	+	0.0312063i
$617$	57.0170	−	323.359i	0.0924100	−	0.524083i	−0.903100	−	0.429430i	$-0.858715\pi$
$617$	57.0170	−	323.359i	0.0924100	−	0.524083i	0.995510	−	0.0946534i	$-0.0301743\pi$
$618$	−68.5026	+	68.7957i	−0.110846	+	0.111320i
$619$	−67.4836	+	185.410i	−0.109020	+	0.299531i	−0.982191	−	0.187883i	$-0.939837\pi$
$619$	−67.4836	+	185.410i	−0.109020	+	0.299531i	0.873171	+	0.487414i	$0.162060\pi$
$620$	−255.003	−	441.678i	−0.411295	−	0.712384i
$621$	379.884	−	35.6882i	0.611729	−	0.0574689i
$622$		−	747.426i		−	1.20165i
$623$	−421.106	+	410.397i	−0.675933	+	0.658744i
$624$	−42.7401	+	42.9229i	−0.0684937	+	0.0687867i
$625$	−538.959	−	452.241i	−0.862335	−	0.723585i
$626$	−117.455	+	139.978i	−0.187628	+	0.223607i
$627$	−677.059	−	471.931i	−1.07984	−	0.752681i
$628$	169.008	−	464.347i	0.269122	−	0.739405i
$629$	−61.4604	+	35.4842i	−0.0977113	+	0.0564136i
$630$	−334.506	−	340.315i	−0.530961	−	0.540183i
$631$	−32.3897	+	56.1006i	−0.0513308	+	0.0889075i	−0.890549	−	0.454887i	$-0.849680\pi$
$631$	−32.3897	+	56.1006i	−0.0513308	+	0.0889075i	0.839218	+	0.543795i	$0.183013\pi$
$632$	−180.679	+	151.608i	−0.285885	+	0.239886i
$633$	−57.2040	−	26.5261i	−0.0903696	−	0.0419054i
$634$	120.614	−	684.034i	0.190242	−	1.07892i
$635$	128.667	+	353.511i	0.202626	+	0.556710i
$636$	1.33115	+	14.8499i	0.00209300	+	0.0233490i
$637$	−185.316	−	163.814i	−0.290920	−	0.257165i
$638$	43.0661	−	74.5927i	0.0675017	−	0.116916i
$639$	−36.3995	−	20.8086i	−0.0569632	−	0.0325643i
$640$	52.4771	+	30.2977i	0.0819955	+	0.0473401i
$641$	−333.783	+	280.077i	−0.520723	+	0.436938i	−0.864884	−	0.501973i	$-0.832608\pi$
$641$	−333.783	+	280.077i	−0.520723	+	0.436938i	0.344161	+	0.938911i	$0.388163\pi$
$642$	−130.633	−	278.590i	−0.203479	−	0.433941i
$643$	−338.999	−	931.393i	−0.527215	−	1.44851i	−0.862336	−	0.506337i	$-0.830999\pi$
$643$	−338.999	−	931.393i	−0.527215	−	1.44851i	0.335121	−	0.942175i	$-0.391223\pi$
$644$	−81.2965	−	180.369i	−0.126237	−	0.280077i
$645$	−14.5438	−	53.8185i	−0.0225486	−	0.0834395i
$646$	45.7220	+	259.302i	0.0707771	+	0.401397i
$647$	−239.977	+	138.551i	−0.370908	+	0.214144i	−0.673855	−	0.738864i	$-0.735363\pi$
$647$	−239.977	+	138.551i	−0.370908	+	0.214144i	0.302947	+	0.953007i	$0.402029\pi$
$648$	116.241	+	197.423i	0.179384	+	0.304666i
$649$	644.621	+	372.172i	0.993252	+	0.573454i
$650$	−16.9131	−	20.1562i	−0.0260201	−	0.0310096i
$651$	−943.162	+	331.852i	−1.44879	+	0.509757i
$652$	−37.8597	+	214.713i	−0.0580671	+	0.329315i
$653$	53.6472	−	304.248i	0.0821550	−	0.465924i	−0.915779	−	0.401682i	$-0.868426\pi$
$653$	53.6472	−	304.248i	0.0821550	−	0.465924i	0.997934	−	0.0642424i	$-0.0204631\pi$
$654$	166.168	+	14.1805i	0.254080	+	0.0216827i
$655$	459.346	−	385.437i	0.701291	−	0.588453i
$656$			301.550i			0.459680i
$657$	434.651	−	760.316i	0.661570	−	1.15725i
$658$	66.1508	+	97.1113i	0.100533	+	0.147586i
$659$	−134.045	−	48.7885i	−0.203407	−	0.0740341i	0.238307	−	0.971190i	$-0.423407\pi$
$659$	−134.045	−	48.7885i	−0.203407	−	0.0740341i	−0.441715	+	0.897156i	$0.645630\pi$
$660$	131.286	−	283.121i	0.198919	−	0.428971i
$661$	−1229.64	−	216.818i	−1.86027	−	0.328015i	−0.873078	−	0.487580i	$-0.837880\pi$
$661$	−1229.64	−	216.818i	−1.86027	−	0.328015i	−0.987187	+	0.159565i	$0.948991\pi$
$662$	19.9370	−	113.069i	0.0301164	−	0.170799i
$663$	−8.88606	−	99.1305i	−0.0134028	−	0.149518i
$664$	47.7722	−	131.253i	0.0719461	−	0.197670i
$665$	877.755	−	597.914i	1.31993	−	0.899119i
$666$	−88.7899	−	104.903i	−0.133318	−	0.157512i
$667$	−88.6270			−0.132874
$668$	−286.893	−	341.906i	−0.429481	−	0.511835i
$669$	801.989	+	559.011i	1.19879	+	0.835592i
$670$	99.0353	+	17.4626i	0.147814	+	0.0260636i
$671$	−357.919	−	63.1108i	−0.533412	−	0.0940549i
$672$	77.3325	−	90.1758i	0.115078	−	0.134190i
$673$	−169.302	+	142.061i	−0.251563	+	0.211087i	−0.759845	−	0.650104i	$-0.774725\pi$
$673$	−169.302	+	142.061i	−0.251563	+	0.211087i	0.508282	+	0.861191i	$0.330281\pi$
$674$	−253.556	+	439.171i	−0.376195	+	0.651589i
$675$	−89.9236	+	42.6352i	−0.133220	+	0.0631633i
$676$	−143.520	−	248.584i	−0.212308	−	0.367728i
$677$	−755.085	+	133.142i	−1.11534	+	0.196664i	−0.700794	−	0.713364i	$-0.747171\pi$
$677$	−755.085	+	133.142i	−1.11534	+	0.196664i	−0.414546	+	0.910028i	$0.636060\pi$
$678$	202.039	−	760.510i	0.297993	−	1.12170i
$679$	−152.116	+	68.5619i	−0.224029	+	0.100975i
$680$	−93.5602	+	34.0531i	−0.137589	+	0.0500781i
$681$	230.455	+	160.634i	0.338407	+	0.235880i
$682$	−420.313	−	500.910i	−0.616295	−	0.734472i
$683$	438.684	−	759.823i	0.642290	−	1.11248i	−0.342630	−	0.939470i	$-0.611318\pi$
$683$	438.684	−	759.823i	0.642290	−	1.11248i	0.984920	−	0.173009i	$-0.0553490\pi$
$684$	−478.402	+	176.440i	−0.699418	+	0.257954i
$685$	−910.145	−	525.473i	−1.32868	−	0.767113i
$686$	386.307	+	293.368i	0.563130	+	0.427650i
$687$	298.200	−	643.073i	0.434062	−	0.936060i
$688$	13.0415	−	4.74672i	0.0189557	−	0.00689930i
$689$	12.3527	+	2.17811i	0.0179284	+	0.00316126i
$690$	−319.836	+	28.6701i	−0.463530	+	0.0415508i
$691$	−286.485	−	341.420i	−0.414595	−	0.494095i	0.517817	−	0.855491i	$-0.326745\pi$
$691$	−286.485	−	341.420i	−0.414595	−	0.494095i	−0.932412	+	0.361396i	$0.882300\pi$
$692$	462.003	+	266.738i	0.667634	+	0.385459i
$693$	−498.130	−	355.224i	−0.718802	−	0.512589i
$694$	−169.410	−	293.427i	−0.244107	−	0.422806i
$695$	661.047	+	240.601i	0.951146	+	0.346189i
$696$	−22.5927	−	48.1814i	−0.0324608	−	0.0692262i
$697$	−379.559	−	318.488i	−0.544561	−	0.456941i
$698$	630.973	−	751.965i	0.903973	−	1.07731i
$699$	−98.2816	+	369.949i	−0.140603	+	0.529254i
$700$	36.0155	+	36.9553i	0.0514507	+	0.0527933i
$701$	390.691			0.557334			0.278667	−	0.960388i	$-0.410108\pi$
$701$	390.691			0.557334			0.278667	+	0.960388i	$0.410108\pi$
$702$	185.851	−	51.0765i	0.264746	−	0.0727585i
$703$	264.901	−	152.940i	0.376814	−	0.217554i
$704$	73.0054	+	26.5718i	0.103701	+	0.0377440i
$705$	184.111	−	49.7538i	0.261150	−	0.0705727i
$706$	80.0161	+	14.1090i	0.113337	+	0.0199844i
$707$	25.0765	−	249.565i	0.0354689	−	0.352992i
$708$	416.378	−	195.243i	0.588104	−	0.275767i
$709$	−532.503	−	193.815i	−0.751062	−	0.273364i	−0.0620094	−	0.998076i	$-0.519751\pi$
$709$	−532.503	−	193.815i	−0.751062	−	0.273364i	−0.689053	+	0.724711i	$0.741973\pi$
$710$	30.5589	+	17.6432i	0.0430406	+	0.0248495i
$711$	738.538	−	133.478i	1.03873	−	0.187732i
$712$	−205.761	+	118.796i	−0.288990	+	0.166848i
$713$	−230.122	+	632.254i	−0.322751	+	0.886752i
$714$	31.8275	+	192.579i	0.0445763	+	0.269718i
$715$	−201.125	−	168.764i	−0.281293	−	0.236033i
$716$	−546.372	+	198.863i	−0.763089	+	0.277742i
$717$	963.204	−	677.511i	1.34338	−	0.944925i
$718$	93.0829	+	527.899i	0.129642	+	0.735236i
$719$	−345.841	+	199.671i	−0.481002	+	0.277707i	−0.720834	−	0.693108i	$-0.756241\pi$
$719$	−345.841	+	199.671i	−0.481002	+	0.277707i	0.239832	+	0.970814i	$0.422908\pi$
$720$	−97.1186	−	166.568i	−0.134887	−	0.231344i
$721$	−90.1791	−	132.385i	−0.125075	−	0.183614i
$722$	−108.414	−	614.844i	−0.150157	−	0.851584i
$723$	−1168.76	+	548.043i	−1.61654	+	0.758012i
$724$	393.150	−	468.538i	0.543025	−	0.647152i
$725$	21.7220	−	7.90615i	0.0299613	−	0.0109050i
$726$	−29.0739	+	109.439i	−0.0400467	+	0.150742i
$727$	137.527	+	163.899i	0.189171	+	0.225445i	0.852291	−	0.523068i	$-0.175213\pi$
$727$	137.527	+	163.899i	0.189171	+	0.225445i	−0.663120	+	0.748513i	$0.730768\pi$
$728$	−56.2644	−	82.5978i	−0.0772863	−	0.113458i
$729$	−9.33623	−	728.940i	−0.0128069	−	0.999918i
$730$	−368.532	+	638.316i	−0.504838	+	0.874405i
$731$	−7.79937	+	21.4286i	−0.0106695	+	0.0293141i
$732$	−158.439	+	159.117i	−0.216446	+	0.217372i
$733$	278.292	−	331.656i	0.379662	−	0.452464i	−0.542045	−	0.840349i	$-0.682350\pi$
$733$	278.292	−	331.656i	0.379662	−	0.452464i	0.921708	+	0.387885i	$0.126794\pi$
$734$	212.974	+	585.140i	0.290155	+	0.797194i
$735$	655.421	−	436.229i	0.891730	−	0.593509i
$736$	−13.8816	−	78.7265i	−0.0188609	−	0.106965i
$737$	128.934			0.174945
$738$	476.211	−	833.015i	0.645273	−	1.12875i
$739$	−628.761			−0.850827			−0.425413	−	0.904999i	$-0.639871\pi$
$739$	−628.761			−0.850827			−0.425413	+	0.904999i	$0.639871\pi$
$740$	74.3482	+	88.6047i	0.100470	+	0.119736i
$741$	38.2998	+	427.263i	0.0516866	+	0.576603i
$742$	−24.4761	−	2.45938i	−0.0329867	−	0.00331453i
$743$	476.976	+	400.230i	0.641959	+	0.538668i	0.904619	−	0.426221i	$-0.140155\pi$
$743$	476.976	+	400.230i	0.641959	+	0.538668i	−0.262660	+	0.964888i	$0.584600\pi$
$744$	−402.383	+	36.0696i	−0.540837	+	0.0484806i
$745$	−1169.64	+	206.240i	−1.56999	+	0.276832i
$746$	−565.359			−0.757854
$747$	−339.244	+	287.137i	−0.454142	+	0.384386i
$748$	−110.552	+	63.8272i	−0.147797	+	0.0853304i
$749$	492.027	−	125.070i	0.656912	−	0.166982i
$750$	−438.510	+	205.621i	−0.584681	+	0.274162i
$751$	40.4403	−	229.348i	0.0538486	−	0.305390i	−0.945974	−	0.324243i	$-0.894890\pi$
$751$	40.4403	−	229.348i	0.0538486	−	0.305390i	0.999822	+	0.0188529i	$0.00600142\pi$
$752$	16.2383	+	44.6144i	0.0215935	+	0.0593277i
$753$	−191.237	−	50.8046i	−0.253967	−	0.0674696i
$754$	−44.0895	+	7.77417i	−0.0584742	+	0.0103106i
$755$			269.906i			0.357491i
$756$	−356.033	+	126.981i	−0.470944	+	0.167964i
$757$	−960.874			−1.26932			−0.634659	−	0.772792i	$-0.718859\pi$
$757$	−960.874			−1.26932			−0.634659	+	0.772792i	$0.718859\pi$
$758$	8.37449	+	47.4941i	0.0110481	+	0.0626571i
$759$	−397.457	+	107.408i	−0.523658	+	0.141513i
$760$	403.254	−	146.772i	0.530597	−	0.193122i
$761$	256.583	+	45.2425i	0.337166	+	0.0594514i	0.339668	−	0.940545i	$-0.389685\pi$
$761$	256.583	+	45.2425i	0.337166	+	0.0594514i	−0.00250220	+	0.999997i	$0.500796\pi$
$762$	296.923	+	25.3388i	0.389662	+	0.0332531i
$763$	−74.6336	+	264.845i	−0.0978159	+	0.347111i
$764$	238.355	+	412.842i	0.311982	+	0.540369i
$765$	312.232	+	53.6815i	0.408146	+	0.0701719i
$766$		−	418.286i		−	0.546065i
$767$	−67.1834	−	381.016i	−0.0875925	−	0.496762i
$768$	39.2604	−	27.6155i	0.0511204	−	0.0359577i
$769$	835.712	−	995.963i	1.08675	−	1.29514i	0.134137	−	0.990963i	$-0.457174\pi$
$769$	835.712	−	995.963i	1.08675	−	1.29514i	0.952615	−	0.304178i	$-0.0983818\pi$
$770$	417.947	+	300.744i	0.542788	+	0.390577i
$771$	439.812	−	948.459i	0.570443	−	1.23017i
$772$	−523.807	+	439.527i	−0.678507	+	0.569335i
$773$			755.238i			0.977022i	0.872558	+	0.488511i	$0.162460\pi$
$773$			755.238i			0.977022i	−0.872558	+	0.488511i	$0.837540\pi$
$774$	−43.5225	−	7.48275i	−0.0562306	−	0.00966764i
$775$		−	175.490i		−	0.226439i
$776$	−66.3945	+	11.7071i	−0.0855600	+	0.0150865i
$777$	197.583	−	111.261i	0.254289	−	0.143194i
$778$	−227.484	+	82.7974i	−0.292396	+	0.106423i
$779$	1635.94	+	1372.72i	2.10005	+	1.76215i
$780$	−156.595	+	42.3179i	−0.200763	+	0.0542538i
$781$	42.5131	+	15.4735i	0.0544342	+	0.0198124i
$782$	113.754	+	65.6759i	0.145465	+	0.0839845i
$783$	−13.6776	+	168.777i	−0.0174682	+	0.215552i
$784$	122.078	+	153.339i	0.155712	+	0.195586i
$785$	1013.71	−	850.605i	1.29135	−	1.08357i
$786$	−123.917	−	458.545i	−0.157655	−	0.583391i
$787$	−455.699	−	1252.02i	−0.579034	−	1.59088i	−0.789813	−	0.613348i	$-0.789822\pi$
$787$	−455.699	−	1252.02i	−0.579034	−	1.59088i	0.210779	−	0.977534i	$-0.432400\pi$
$788$	174.909	+	146.766i	0.221966	+	0.186251i
$789$	−382.663	−	32.6558i	−0.484997	−	0.0413888i
$790$	−622.029	+	109.680i	−0.787378	+	0.138836i
$791$	1169.50	+	563.793i	1.47851	+	0.712760i
$792$	−159.711	−	188.694i	−0.201655	−	0.238250i
$793$	94.4544	+	163.600i	0.119110	+	0.206305i
$794$	219.256	−	38.6607i	0.276141	−	0.0486911i
$795$	−16.7966	+	36.2221i	−0.0211278	+	0.0455624i
$796$	210.693	+	578.873i	0.264689	+	0.727227i
$797$	771.623	−	919.584i	0.968159	−	1.15381i	−0.0199110	−	0.999802i	$-0.506338\pi$
$797$	771.623	−	919.584i	0.968159	−	1.15381i	0.988070	−	0.154005i	$-0.0492173\pi$
$798$	−137.180	−	830.035i	−0.171904	−	1.04014i
$799$	−73.3063	−	26.6813i	−0.0917475	−	0.0333934i
$800$	10.4253	+	18.0571i	0.0130316	+	0.0225714i
$801$	756.006	−	3.22747i	0.943828	−	0.00402931i
$802$	240.757	−	417.004i	0.300196	−	0.519955i
$803$	−323.212	+	888.016i	−0.402505	+	1.10587i
$804$	45.5518	−	65.3511i	0.0566564	−	0.0812825i
$805$	52.9698	−	527.164i	0.0658010	−	0.654862i
$806$	−59.0194	+	334.715i	−0.0732250	+	0.415280i
$807$	−594.605	−	157.964i	−0.736809	−	0.195743i
$808$	34.6629	−	95.2354i	0.0428996	−	0.117866i
$809$	−240.585	−	416.706i	−0.297386	−	0.515088i	0.678151	−	0.734922i	$-0.262781\pi$
$809$	−240.585	−	416.706i	−0.297386	−	0.515088i	−0.975537	+	0.219835i	$0.929448\pi$
$810$	5.23834	+	613.505i	0.00646708	+	0.757414i
$811$			1403.79i			1.73094i	0.500965	+	0.865468i	$0.332979\pi$
$811$			1403.79i			1.73094i	−0.500965	+	0.865468i	$0.667021\pi$
$812$	85.0948	−	21.6305i	0.104797	−	0.0266386i
$813$	259.904	+	961.758i	0.319685	+	1.18297i
$814$	113.602	+	95.3236i	0.139561	+	0.117105i
$815$	−375.300	+	447.266i	−0.460491	+	0.548792i
$816$	−6.70618	+	78.5836i	−0.00821836	+	0.0963034i
$817$	33.6161	−	92.3594i	0.0411458	−	0.113047i
$818$	−634.429	+	366.288i	−0.775586	+	0.447785i
$819$	24.9879	+	317.025i	0.0305103	+	0.387088i
$820$	−403.770	+	699.350i	−0.492402	+	0.852865i
$821$	−1060.88	+	890.185i	−1.29218	+	1.08427i	−0.300741	+	0.953706i	$0.597234\pi$
$821$	−1060.88	+	890.185i	−1.29218	+	1.08427i	−0.991440	+	0.130563i	$0.958322\pi$
$822$	−680.920	+	478.955i	−0.828370	+	0.582670i
$823$	87.8706	−	498.339i	0.106769	−	0.605515i	−0.883730	−	0.467996i	$-0.844976\pi$
$823$	87.8706	−	498.339i	0.106769	−	0.605515i	0.990499	−	0.137519i	$-0.0439128\pi$
$824$	−22.1366	−	60.8199i	−0.0268649	−	0.0738106i
$825$	87.8328	−	61.7810i	0.106464	−	0.0748861i
$826$	186.928	+	735.379i	0.226305	+	0.890289i
$827$	−1.49295	+	2.58587i	−0.00180526	+	0.00312681i	−0.866927	−	0.498436i	$-0.833908\pi$
$827$	−1.49295	+	2.58587i	−0.00180526	+	0.00312681i	0.865121	+	0.501563i	$0.167241\pi$
$828$	−85.9787	+	239.400i	−0.103839	+	0.289130i
$829$	543.058	+	313.535i	0.655076	+	0.378208i	0.790398	−	0.612593i	$-0.209874\pi$
$829$	543.058	+	313.535i	0.655076	+	0.378208i	−0.135322	+	0.990802i	$0.543207\pi$
$830$	286.538	−	240.434i	0.345226	−	0.289679i
$831$	1476.28	+	125.983i	1.77650	+	0.151604i
$832$	−13.8115	−	37.9467i	−0.0166003	−	0.0456090i
$833$	−321.942	−	8.29385i	−0.386485	−	0.00995660i
$834$	393.192	−	394.874i	0.471453	−	0.473470i
$835$	−207.552	−	1177.09i	−0.248565	−	1.40968i
$836$	476.490	−	275.102i	0.569964	−	0.329069i
$837$	1168.52	+	535.808i	1.39608	+	0.640153i
$838$	−368.739	−	212.891i	−0.440022	−	0.254047i
$839$	381.544	+	454.707i	0.454761	+	0.541963i	0.943895	−	0.330246i	$-0.107132\pi$
$839$	381.544	+	454.707i	0.454761	+	0.541963i	−0.489134	+	0.872209i	$0.662687\pi$
$840$	300.092	−	105.587i	0.357252	−	0.125699i
$841$	−139.208	+	789.489i	−0.165527	+	0.938751i
$842$	25.1161	−	142.441i	0.0298291	−	0.169169i
$843$	689.328	+	1470.07i	0.817708	+	1.74385i
$844$	32.2019	−	27.0206i	0.0381540	−	0.0320150i
$845$		−	768.683i		−	0.909684i
$846$	25.5982	−	148.888i	0.0302579	−	0.175991i
$847$	−168.293	−	81.1311i	−0.198693	−	0.0957864i
$848$	−9.34022	−	3.39956i	−0.0110144	−	0.00400892i
$849$	759.650	+	1079.98i	0.894758	+	1.27206i
$850$	−33.7392	−	5.94913i	−0.0396932	−	0.00699898i
$851$	26.4974	−	150.274i	0.0311368	−	0.176586i
$852$	22.8624	−	16.0813i	0.0268338	−	0.0188747i
$853$	−336.225	+	923.771i	−0.394168	+	1.08297i	0.570912	+	0.821011i	$0.306590\pi$
$853$	−336.225	+	923.771i	−0.394168	+	1.08297i	−0.965080	+	0.261956i	$0.915632\pi$
$854$	−208.574	−	306.193i	−0.244232	−	0.358539i
$855$	−1345.75	−	231.373i	−1.57398	−	0.270611i
$856$	205.131			0.239639
$857$	209.194	+	249.307i	0.244100	+	0.290907i	0.874159	−	0.485641i	$-0.161414\pi$
$857$	209.194	+	249.307i	0.244100	+	0.290907i	−0.630059	+	0.776548i	$0.716969\pi$
$858$	−188.302	+	88.2967i	−0.219467	+	0.102910i
$859$	1428.17	+	251.825i	1.66260	+	0.293161i	0.924400	−	0.381425i	$-0.124567\pi$
$859$	1428.17	+	251.825i	1.66260	+	0.293161i	0.738197	+	0.674586i	$0.235678\pi$
$860$	36.6014	+	6.45381i	0.0425597	+	0.00750443i
$861$	1201.75	+	1030.59i	1.39576	+	1.19697i
$862$	575.458	−	482.867i	0.667585	−	0.560170i
$863$	−308.913	+	535.053i	−0.357952	+	0.619991i	−0.987619	−	0.156874i	$-0.949858\pi$
$863$	−308.913	+	535.053i	−0.357952	+	0.619991i	0.629666	+	0.776866i	$0.283192\pi$
$864$	−152.065	+	14.2858i	−0.176002	+	0.0165345i
$865$	714.313	+	1237.23i	0.825795	+	1.43032i
$866$	−798.594	+	140.814i	−0.922164	+	0.162602i
$867$	522.539	+	520.313i	0.602698	+	0.600130i
$868$	66.6409	−	663.220i	0.0767752	−	0.764079i
$869$	−760.983	+	276.975i	−0.875700	+	0.318729i
$870$	12.1174	−	141.993i	0.0139280	−	0.163210i
$871$	−43.0779	−	51.3383i	−0.0494580	−	0.0589418i
$872$	−55.5908	+	96.2861i	−0.0637509	+	0.110420i
$873$	201.899	+	72.5107i	0.231270	+	0.0830592i
$874$	−490.291	−	283.070i	−0.560974	−	0.323878i
$875$	−196.864	−	774.468i	−0.224988	−	0.885106i
$876$	335.907	+	477.552i	0.383456	+	0.545151i
$877$	908.967	−	330.837i	1.03645	−	0.377237i	0.232917	−	0.972497i	$-0.425173\pi$
$877$	908.967	−	330.837i	1.03645	−	0.377237i	0.803533	+	0.595260i	$0.202951\pi$
$878$	−301.546	−	53.1706i	−0.343446	−	0.0605588i
$879$	−508.416	−	722.804i	−0.578403	−	0.822303i
$880$	133.734	+	159.378i	0.151970	+	0.181111i
$881$	−619.823	−	357.855i	−0.703545	−	0.406192i	0.105122	−	0.994459i	$-0.466477\pi$
$881$	−619.823	−	357.855i	−0.703545	−	0.406192i	−0.808666	+	0.588268i	$0.799810\pi$
$882$	−95.0776	−	616.378i	−0.107798	−	0.698842i
$883$	−37.0022	−	64.0897i	−0.0419051	−	0.0725818i	0.844312	−	0.535852i	$-0.180009\pi$
$883$	−37.0022	−	64.0897i	−0.0419051	−	0.0725818i	−0.886217	+	0.463270i	$0.846676\pi$
$884$	62.3505	+	22.6937i	0.0705322	+	0.0256716i
$885$	1227.08	+	104.717i	1.38653	+	0.118324i
$886$	−136.574	−	114.599i	−0.154147	−	0.129345i
$887$	−907.985	+	1082.09i	−1.02366	+	1.21995i	−0.0484125	+	0.998827i	$0.515416\pi$
$887$	−907.985	+	1082.09i	−1.02366	+	1.21995i	−0.975246	+	0.221122i	$0.929028\pi$
$888$	88.4503	−	23.9027i	0.0996062	−	0.0269174i
$889$	−133.361	+	473.246i	−0.150012	+	0.532336i
$890$	−636.262			−0.714901
$891$	143.204	+	773.474i	0.160723	+	0.868096i
$892$	−564.411	+	325.863i	−0.632748	+	0.365317i
$893$	315.958	+	114.999i	0.353816	+	0.128778i
$894$	−241.560	+	909.275i	−0.270202	+	1.01709i
$895$	−1533.41	−	270.381i	−1.71331	−	0.302102i
$896$	32.5426	+	72.2010i	0.0363198	+	0.0805814i
$897$	175.560	+	122.371i	0.195719	+	0.136422i
$898$	607.934	+	221.270i	0.676987	+	0.246403i
$899$	−258.591	−	149.297i	−0.287643	−	0.166071i
$900$	−0.283236	−	66.3454i	−0.000314706	−	0.0737171i
$901$	14.1439	−	8.16596i	0.0156980	−	0.00906322i
$902$	−354.116	+	972.926i	−0.392590	+	1.07863i
$903$	25.6544	−	68.1962i	0.0284102	−	0.0755218i
$904$	401.862	+	337.202i	0.444537	+	0.373011i
$905$	1539.15	−	560.205i	1.70072	−	0.619011i
$906$	193.964	+	89.9433i	0.214088	+	0.0992752i
$907$	−211.673	−	1200.46i	−0.233377	−	1.32355i	−0.846004	−	0.533176i	$-0.820998\pi$
$907$	−211.673	−	1200.46i	−0.233377	−	1.32355i	0.612627	−	0.790372i	$-0.290113\pi$
$908$	−162.186	+	93.6381i	−0.178619	+	0.103126i
$909$	−246.151	+	208.342i	−0.270793	+	0.229200i
$910$	−19.8907	−	266.896i	−0.0218579	−	0.293293i
$911$	163.379	+	926.570i	0.179341	+	1.01709i	0.933013	+	0.359842i	$0.117169\pi$
$911$	163.379	+	926.570i	0.179341	+	1.01709i	−0.753673	+	0.657250i	$0.771720\pi$
$912$	28.9043	−	338.703i	0.0316933	−	0.371385i
$913$	308.266	−	367.377i	0.337641	−	0.402385i
$914$	861.595	−	313.595i	0.942665	−	0.343102i
$915$	−580.503	+	156.874i	−0.634429	+	0.171447i
$916$	303.759	+	362.006i	0.331615	+	0.395204i
$917$	781.532	−	58.2444i	0.852271	−	0.0635162i
$918$	142.626	−	206.492i	0.155365	−	0.224937i
$919$	−274.558	+	475.548i	−0.298757	+	0.517462i	−0.975852	−	0.218433i	$-0.929905\pi$
$919$	−274.558	+	475.548i	−0.298757	+	0.517462i	0.677095	+	0.735896i	$0.263239\pi$
$920$	73.2193	−	201.168i	0.0795862	−	0.218661i
$921$	−360.354	−	1333.47i	−0.391264	−	1.44785i
$922$	167.483	−	199.599i	0.181652	−	0.216484i
$923$	−8.04279	−	22.0974i	−0.00871375	−	0.0239408i
$924$	355.402	−	200.132i	0.384634	−	0.216593i
$925$	6.91116	+	39.1951i	0.00747152	+	0.0423731i
$926$	−854.817			−0.923128
$927$	−34.8963	+	202.970i	−0.0376444	+	0.218954i
$928$	35.4769			0.0382295
$929$	−482.265	−	574.741i	−0.519123	−	0.618667i	0.441250	−	0.897384i	$-0.354535\pi$
$929$	−482.265	−	574.741i	−0.519123	−	0.618667i	−0.960373	+	0.278718i	$0.910091\pi$
$930$	−981.496	−	455.131i	−1.05537	−	0.489388i
$931$	1387.60	+	35.7473i	1.49045	+	0.0383967i
$932$	−195.485	−	164.031i	−0.209748	−	0.175999i
$933$	−912.192	−	1296.85i	−0.977698	−	1.38997i
$934$	−367.176	+	64.7430i	−0.393122	+	0.0693180i
$935$	−341.853			−0.365618
$936$	−21.7725	+	126.637i	−0.0232612	+	0.135296i
$937$	936.231	−	540.533i	0.999179	−	0.576876i	0.0911736	−	0.995835i	$-0.470938\pi$
$937$	936.231	−	540.533i	0.999179	−	0.576876i	0.908005	+	0.418959i	$0.137605\pi$
$938$	91.7322	+	94.1259i	0.0977956	+	0.100347i
$939$	−32.9594	+	386.221i	−0.0351005	+	0.411311i
$940$	−22.0782	+	125.212i	−0.0234874	+	0.133204i
$941$	13.8159	+	37.9588i	0.0146821	+	0.0403388i	0.946817	−	0.321772i	$-0.104278\pi$
$941$	13.8159	+	37.9588i	0.0146821	+	0.0403388i	−0.932135	+	0.362111i	$0.882056\pi$
$942$	−273.466	−	1011.95i	−0.290304	−	1.07425i
$943$	1049.17	−	184.997i	1.11259	−	0.196179i
$944$			306.587i			0.324775i
$945$	−995.731	−	182.229i	−1.05368	−	0.192835i
$946$	47.6515			0.0503715
$947$	200.626	+	1137.80i	0.211854	+	1.20148i	0.886283	+	0.463143i	$0.153278\pi$
$947$	200.626	+	1137.80i	0.211854	+	1.20148i	−0.674430	+	0.738339i	$0.735610\pi$
$948$	−128.464	+	483.562i	−0.135511	+	0.510087i
$949$	461.572	−	167.998i	0.486377	−	0.177027i
$950$	145.419	+	25.6414i	0.153073	+	0.0269909i
$951$	−625.552	−	1334.06i	−0.657783	−	1.40280i
$952$	−125.249	−	35.2953i	−0.131565	−	0.0370749i
$953$	−42.3220	−	73.3038i	−0.0444092	−	0.0769190i	0.842966	−	0.537966i	$-0.180807\pi$
$953$	−42.3220	−	73.3038i	−0.0444092	−	0.0769190i	−0.887376	+	0.461047i	$0.847474\pi$
$954$	20.4332	+	24.1413i	0.0214184	+	0.0253053i
$955$			1276.61i			1.33676i
$956$	136.327	+	773.152i	0.142602	+	0.808736i
$957$	−16.3131	−	181.984i	−0.0170460	−	0.190161i
$958$	−287.284	+	342.372i	−0.299879	+	0.357382i
$959$	−564.408	−	1252.23i	−0.588538	−	1.30577i
$960$	128.029	−	11.4765i	0.133363	−	0.0119547i
$961$	−1000.34	+	839.383i	−1.04093	+	0.873448i
$962$		−	77.0817i		−	0.0801265i
$963$	−566.663	−	323.946i	−0.588436	−	0.336392i
$964$		−	860.582i		−	0.892720i
$965$	−1803.32	+	317.974i	−1.86873	+	0.329507i
$966$	−361.187	−	213.738i	−0.373900	−	0.221261i
$967$	−439.297	+	159.891i	−0.454288	+	0.165347i	−0.559022	−	0.829153i	$-0.688823\pi$
$967$	−439.297	+	159.891i	−0.454288	+	0.165347i	0.104734	+	0.994500i	$0.466601\pi$
$968$	−57.8288	−	48.5241i	−0.0597405	−	0.0501282i
$969$	395.796	+	394.110i	0.408458	+	0.406718i
$970$	−169.657	−	61.7500i	−0.174904	−	0.0636597i
$971$	627.605	+	362.348i	0.646349	+	0.373170i	0.787056	−	0.616881i	$-0.211604\pi$
$971$	627.605	+	362.348i	0.646349	+	0.373170i	−0.140707	+	0.990051i	$0.544937\pi$
$972$	442.633	+	200.680i	0.455383	+	0.206461i
$973$	517.611	+	759.867i	0.531974	+	0.780953i
$974$	−632.782	+	530.967i	−0.649673	+	0.545141i
$975$	−53.9451	−	14.3312i	−0.0553284	−	0.0146987i
$976$	−51.1995	−	140.670i	−0.0524585	−	0.144129i
$977$	−1014.95	−	851.641i	−1.03884	−	0.871690i	−0.0469631	−	0.998897i	$-0.514954\pi$
$977$	−1014.95	−	851.641i	−1.03884	−	0.871690i	−0.991876	+	0.127207i	$0.959399\pi$
$978$	196.356	+	418.751i	0.200773	+	0.428171i
$979$	−803.374	+	141.657i	−0.820607	+	0.144695i
$980$	77.8022	+	519.082i	0.0793900	+	0.529675i
$981$	305.623	−	178.195i	0.311542	−	0.181646i
$982$	16.5970	+	28.7469i	0.0169012	+	0.0292738i
$983$	895.048	−	157.821i	0.910527	−	0.160550i	0.301284	−	0.953534i	$-0.402585\pi$
$983$	895.048	−	157.821i	0.910527	−	0.160550i	0.609243	+	0.792984i	$0.291474\pi$
$984$	368.026	+	523.214i	0.374010	+	0.531722i
$985$	209.129	+	574.577i	0.212314	+	0.583327i
$986$	−37.4697	+	44.6546i	−0.0380017	+	0.0452886i
$987$	233.296	+	87.7626i	0.236369	+	0.0889185i
$988$	−268.737	−	97.8123i	−0.272001	−	0.0990003i
$989$	−24.5158	−	42.4627i	−0.0247885	−	0.0429349i
$990$	−117.741	−	651.466i	−0.118930	−	0.658046i
$991$	121.771	−	210.914i	0.122877	−	0.212830i	−0.798024	−	0.602626i	$-0.794121\pi$
$991$	121.771	−	210.914i	0.122877	−	0.212830i	0.920901	+	0.389796i	$0.127454\pi$
$992$	92.1166	−	253.088i	0.0928595	−	0.255129i
$993$	−103.402	−	220.516i	−0.104131	−	0.222070i
$994$	18.9504	+	42.0446i	0.0190648	+	0.0422984i
$995$	−286.465	+	1624.62i	−0.287905	+	1.63279i
$996$	−77.2985	−	286.038i	−0.0776090	−	0.287187i
$997$	−637.080	+	1750.36i	−0.638997	+	1.75563i	0.0158552	+	0.999874i	$0.494953\pi$
$997$	−637.080	+	1750.36i	−0.638997	+	1.75563i	−0.654853	+	0.755757i	$0.727269\pi$
$998$	−484.517	−	839.207i	−0.485487	−	0.840889i
$999$	−282.086	−	73.6520i	−0.282369	−	0.0737257i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.x.a.103.42	✓	288
7.3	odd	6		378.3.be.a.157.12	yes	288
27.16	even	9		378.3.be.a.313.12	yes	288
189.178	odd	18	inner	378.3.x.a.367.42	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.3.x.a.103.42	✓	288	1.1	even	1	trivial
378.3.x.a.367.42	yes	288	189.178	odd	18	inner
378.3.be.a.157.12	yes	288	7.3	odd	6
378.3.be.a.313.12	yes	288	27.16	even	9

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.245576 + 1.39273i) q^{2} +(2.12584 + 2.11679i) q^{3} +(-1.87939 + 0.684040i) q^{4} +(-5.27455 - 0.930046i) q^{5} +(-2.42605 + 3.48055i) q^{6} +(-4.88560 - 5.01308i) q^{7} +(-1.41421 - 2.44949i) q^{8} +(0.0384216 + 8.99992i) q^{9} -7.57442i q^{10} +(-1.68636 - 9.56381i) q^{11} +(-5.44325 - 2.52410i) q^{12} +(-3.24463 + 3.86680i) q^{13} +(5.78207 - 8.03540i) q^{14} +(-9.24416 - 13.1422i) q^{15} +(3.06418 - 2.57115i) q^{16} +6.57243i q^{17} +(-12.5250 + 2.26367i) q^{18} -28.3279i q^{19} +(10.5491 - 1.86009i) q^{20} +(0.225611 - 20.9988i) q^{21} +(12.9057 - 4.69728i) q^{22} +(-10.8255 - 9.08369i) q^{23} +(2.17865 - 8.20082i) q^{24} +(3.46360 + 1.26065i) q^{25} +(-6.18221 - 3.56930i) q^{26} +(-18.9692 + 19.2137i) q^{27} +(12.6111 + 6.07956i) q^{28} +(4.80424 - 4.03124i) q^{29} +(16.0334 - 16.1020i) q^{30} +(-16.2841 - 44.7401i) q^{31} +(4.33340 + 3.63616i) q^{32} +(16.6596 - 23.9008i) q^{33} +(-9.15361 + 1.61403i) q^{34} +(21.1069 + 30.9856i) q^{35} +(-6.22852 - 16.8880i) q^{36} +(5.39894 + 9.35124i) q^{37} +(39.4530 - 6.95663i) q^{38} +(-15.0828 + 1.35202i) q^{39} +(5.18121 + 14.2352i) q^{40} +(-48.4582 + 57.7502i) q^{41} +(29.3010 - 4.84258i) q^{42} +(3.26038 + 1.18668i) q^{43} +(9.71135 + 16.8205i) q^{44} +(8.16768 - 47.5063i) q^{45} +(9.99263 - 17.3077i) q^{46} +(-4.05958 + 11.1536i) q^{47} +(11.9565 + 1.02035i) q^{48} +(-1.26191 + 48.9837i) q^{49} +(-0.905164 + 5.13344i) q^{50} +(-13.9124 + 13.9720i) q^{51} +(3.45286 - 9.48667i) q^{52} +(-1.24246 - 2.15200i) q^{53} +(-31.4179 - 21.7006i) q^{54} +52.0132i q^{55} +(-5.37021 + 19.0568i) q^{56} +(59.9640 - 60.2206i) q^{57} +(6.79423 + 5.70103i) q^{58} +(-49.2676 + 58.7149i) q^{59} +(26.3632 + 18.3759i) q^{60} +(12.7999 - 35.1674i) q^{61} +(58.3119 - 33.6664i) q^{62} +(44.9296 - 44.1626i) q^{63} +(-4.00000 + 6.92820i) q^{64} +(20.7103 - 17.3780i) q^{65} +(37.3785 + 17.3329i) q^{66} +(-2.30547 + 13.0750i) q^{67} +(-4.49581 - 12.3521i) q^{68} +(-3.78512 - 42.2258i) q^{69} +(-37.9711 + 37.0055i) q^{70} +(-2.32931 + 4.03448i) q^{71} +(21.9909 - 12.8219i) q^{72} +(-84.2726 - 48.6548i) q^{73} +(-11.6979 + 9.81570i) q^{74} +(4.69455 + 10.0116i) q^{75} +(19.3774 + 53.2389i) q^{76} +(-39.7053 + 55.1787i) q^{77} +(-5.58696 - 20.6742i) q^{78} +(-14.4804 - 82.1223i) q^{79} +(-18.5535 + 10.7118i) q^{80} +(-80.9970 + 0.691583i) q^{81} +(-92.3305 - 53.3070i) q^{82} +(31.7429 + 37.8297i) q^{83} +(13.9400 + 39.6191i) q^{84} +(6.11266 - 34.6666i) q^{85} +(-0.852054 + 4.83224i) q^{86} +(18.7463 + 1.59978i) q^{87} +(-21.0416 + 17.6560i) q^{88} -84.0015i q^{89} +(68.1691 - 0.291021i) q^{90} +(35.2365 - 2.62603i) q^{91} +(26.5589 + 9.66666i) q^{92} +(60.0879 - 129.580i) q^{93} +(-16.5309 - 2.91484i) q^{94} +(-26.3462 + 149.417i) q^{95} +(1.51517 + 16.9028i) q^{96} +(8.15244 - 22.3986i) q^{97} +(-68.5310 + 10.2717i) q^{98} +(86.0087 - 15.5445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 36 q^{6} - 12 q^{9} + 36 q^{11} + 36 q^{14} - 24 q^{15} + 186 q^{21} + 126 q^{23} + 36 q^{29} - 72 q^{30} + 162 q^{35} - 48 q^{36} + 246 q^{39} - 48 q^{42} + 324 q^{47} - 72 q^{49} + 288 q^{50}+ \cdots - 216 q^{99}+O(q^{100}) \) 288 * q - 36 * q^6 - 12 * q^9 + 36 * q^11 + 36 * q^14 - 24 * q^15 + 186 * q^21 + 126 * q^23 + 36 * q^29 - 72 * q^30 + 162 * q^35 - 48 * q^36 + 246 * q^39 - 48 * q^42 + 324 * q^47 - 72 * q^49 + 288 * q^50 - 198 * q^51 + 270 * q^53 + 432 * q^54 - 144 * q^56 + 354 * q^57 + 270 * q^59 + 72 * q^60 + 138 * q^63 - 1152 * q^64 - 360 * q^65 + 72 * q^69 + 180 * q^70 + 216 * q^71 - 96 * q^72 + 216 * q^74 - 1170 * q^75 + 234 * q^77 - 96 * q^78 - 36 * q^79 + 324 * q^81 - 24 * q^84 - 360 * q^85 + 144 * q^86 - 990 * q^87 - 198 * q^91 - 180 * q^92 + 168 * q^93 - 72 * q^95 + 216 * q^98 - 216 * q^99

Introduction

L-functions

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