LMFDB - Embedded newform 189.2.be.a.104.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,2,Mod(20,189)] 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("189.20"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.be (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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			104.1
Character	$\chi$	$=$	189.104
Dual form			189.2.be.a.20.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.878867 + 2.41467i) q^{2} +(-1.25404 + 1.19473i) q^{3} +(-3.52612 - 2.95877i) q^{4} +(-0.588152 + 3.33557i) q^{5} +(-1.78274 - 4.07810i) q^{6} +(-0.566293 + 2.58444i) q^{7} +(5.79269 - 3.34441i) q^{8} +(0.145238 - 2.99648i) q^{9} +(-7.53740 - 4.35172i) q^{10} +(4.55474 - 0.803123i) q^{11} +(7.95683 - 0.502350i) q^{12} +(-0.619664 - 1.70251i) q^{13} +(-5.74286 - 3.63879i) q^{14} +(-3.24755 - 4.88563i) q^{15} +(1.38602 + 7.86054i) q^{16} +(-1.40471 + 2.43302i) q^{17} +(7.10786 + 2.98421i) q^{18} +(0.586660 - 0.338709i) q^{19} +(11.9431 - 10.0214i) q^{20} +(-2.37755 - 3.91756i) q^{21} +(-2.06373 + 11.7040i) q^{22} +(-2.29937 + 2.74028i) q^{23} +(-3.26860 + 11.1147i) q^{24} +(-6.08167 - 2.21355i) q^{25} +4.65561 q^{26} +(3.39786 + 3.93123i) q^{27} +(9.64357 - 7.43751i) q^{28} +(-0.546385 + 1.50118i) q^{29} +(14.6513 - 3.54793i) q^{30} +(1.99247 - 2.37454i) q^{31} +(-7.02429 - 1.23857i) q^{32} +(-4.75231 + 6.44883i) q^{33} +(-4.64039 - 5.53021i) q^{34} +(-8.28751 - 3.40895i) q^{35} +(-9.37802 + 10.1362i) q^{36} +(-0.898066 + 1.55550i) q^{37} +(0.302272 + 1.71427i) q^{38} +(2.81113 + 1.39469i) q^{39} +(7.74856 + 21.2890i) q^{40} +(-11.6140 + 4.22715i) q^{41} +(11.5491 - 2.29798i) q^{42} +(-0.0534327 - 0.303032i) q^{43} +(-18.4368 - 10.6445i) q^{44} +(9.90957 + 2.24684i) q^{45} +(-4.59602 - 7.96055i) q^{46} +(2.22186 - 1.86436i) q^{47} +(-11.1294 - 8.20151i) q^{48} +(-6.35862 - 2.92710i) q^{49} +(10.6900 - 12.7398i) q^{50} +(-1.14525 - 4.72936i) q^{51} +(-2.85233 + 7.83672i) q^{52} +4.31910i q^{53} +(-12.4789 + 4.74966i) q^{54} +15.6650i q^{55} +(5.36306 + 16.8648i) q^{56} +(-0.331031 + 1.12566i) q^{57} +(-3.14465 - 2.63868i) q^{58} +(1.34243 - 7.61331i) q^{59} +(-3.00420 + 26.8361i) q^{60} +(-0.783123 - 0.933289i) q^{61} +(3.98260 + 6.89806i) q^{62} +(7.66197 + 2.07224i) q^{63} +(1.18236 - 2.04791i) q^{64} +(6.04332 - 1.06560i) q^{65} +(-11.3951 - 17.1429i) q^{66} +(0.826896 - 0.300966i) q^{67} +(12.1519 - 4.42294i) q^{68} +(-0.390395 - 6.18355i) q^{69} +(15.5151 - 17.0156i) q^{70} +(11.6410 + 6.72094i) q^{71} +(-9.18016 - 17.8434i) q^{72} +(11.2992 - 6.52362i) q^{73} +(-2.96672 - 3.53560i) q^{74} +(10.2713 - 4.49008i) q^{75} +(-3.07080 - 0.541464i) q^{76} +(-0.503696 + 12.2262i) q^{77} +(-5.83832 + 5.56220i) q^{78} +(13.7757 + 5.01396i) q^{79} -27.0346 q^{80} +(-8.95781 - 0.870403i) q^{81} -31.7590i q^{82} +(-6.55767 - 2.38680i) q^{83} +(-3.20761 + 20.8484i) q^{84} +(-7.28935 - 6.11649i) q^{85} +(0.778681 + 0.137302i) q^{86} +(-1.10832 - 2.53533i) q^{87} +(23.6982 - 19.8852i) q^{88} +(8.53240 + 14.7785i) q^{89} +(-14.1346 + 21.9536i) q^{90} +(4.75095 - 0.637362i) q^{91} +(16.2157 - 2.85927i) q^{92} +(0.338289 + 5.35823i) q^{93} +(2.54910 + 7.00358i) q^{94} +(0.784742 + 2.15606i) q^{95} +(10.2885 - 6.83891i) q^{96} +(-5.81042 + 1.02453i) q^{97} +(12.6564 - 12.7814i) q^{98} +(-1.74502 - 13.7648i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30}+ \cdots - 192 q^{99}+O(q^{100}) $ 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.878867	+	2.41467i	−0.621453	+	1.70743i	0.0819501	+	0.996636i	$0.473885\pi$
$2$	−0.878867	+	2.41467i	−0.621453	+	1.70743i	−0.703403	+	0.710791i	$0.748337\pi$
$3$	−1.25404	+	1.19473i	−0.724021	+	0.689778i
$3$	−1.25404	+	1.19473i	−0.724021	+	0.689778i
$4$	−3.52612	−	2.95877i	−1.76306	−	1.47938i
$5$	−0.588152	+	3.33557i	−0.263029	+	1.49171i	0.511559	+	0.859248i	$0.329068\pi$
$5$	−0.588152	+	3.33557i	−0.263029	+	1.49171i	−0.774588	+	0.632466i	$0.782043\pi$
$6$	−1.78274	−	4.07810i	−0.727801	−	1.66488i
$7$	−0.566293	+	2.58444i	−0.214039	+	0.976825i
$7$	−0.566293	+	2.58444i	−0.214039	+	0.976825i
$8$	5.79269	−	3.34441i	2.04803	−	1.18243i
$9$	0.145238	−	2.99648i	0.0484125	−	0.998827i
$10$	−7.53740	−	4.35172i	−2.38353	−	1.37613i
$11$	4.55474	−	0.803123i	1.37330	−	0.242151i	0.562176	−	0.827018i	$-0.309965\pi$
$11$	4.55474	−	0.803123i	1.37330	−	0.242151i	0.811129	+	0.584867i	$0.198853\pi$
$12$	7.95683	−	0.502350i	2.29694	−	0.145016i
$13$	−0.619664	−	1.70251i	−0.171864	−	0.472192i	0.823618	−	0.567145i	$-0.191952\pi$
$13$	−0.619664	−	1.70251i	−0.171864	−	0.472192i	−0.995482	+	0.0949528i	$0.969730\pi$
$14$	−5.74286	−	3.63879i	−1.53484	−	0.972506i
$15$	−3.24755	−	4.88563i	−0.838513	−	1.26146i
$16$	1.38602	+	7.86054i	0.346506	+	1.96513i
$17$	−1.40471	+	2.43302i	−0.340692	+	0.590095i	−0.984561	−	0.175040i	$-0.943995\pi$
$17$	−1.40471	+	2.43302i	−0.340692	+	0.590095i	0.643870	+	0.765135i	$0.277328\pi$
$18$	7.10786	+	2.98421i	1.67534	+	0.703385i
$19$	0.586660	−	0.338709i	0.134589	−	0.0777051i	−0.431194	−	0.902259i	$-0.641907\pi$
$19$	0.586660	−	0.338709i	0.134589	−	0.0777051i	0.565783	+	0.824554i	$0.308574\pi$
$20$	11.9431	−	10.0214i	2.67056	−	2.24086i
$21$	−2.37755	−	3.91756i	−0.518824	−	0.854881i
$22$	−2.06373	+	11.7040i	−0.439989	+	2.49530i
$23$	−2.29937	+	2.74028i	−0.479451	+	0.571388i	−0.950502	−	0.310718i	$-0.899430\pi$
$23$	−2.29937	+	2.74028i	−0.479451	+	0.571388i	0.471051	+	0.882106i	$0.343875\pi$
$24$	−3.26860	+	11.1147i	−0.667201	+	2.26879i
$25$	−6.08167	−	2.21355i	−1.21633	−	0.442709i
$26$	4.65561			0.913040
$27$	3.39786	+	3.93123i	0.653918	+	0.756566i
$28$	9.64357	−	7.43751i	1.82246	−	1.40556i
$29$	−0.546385	+	1.50118i	−0.101461	+	0.278762i	−0.980029	−	0.198856i	$-0.936277\pi$
$29$	−0.546385	+	1.50118i	−0.101461	+	0.278762i	0.878568	+	0.477618i	$0.158500\pi$
$30$	14.6513	−	3.54793i	2.67496	−	0.647760i
$31$	1.99247	−	2.37454i	0.357859	−	0.426479i	−0.556838	−	0.830621i	$-0.687985\pi$
$31$	1.99247	−	2.37454i	0.357859	−	0.426479i	0.914696	+	0.404142i	$0.132430\pi$
$32$	−7.02429	−	1.23857i	−1.24173	−	0.218951i
$33$	−4.75231	+	6.44883i	−0.827271	+	1.12260i
$34$	−4.64039	−	5.53021i	−0.795821	−	0.948423i
$35$	−8.28751	−	3.40895i	−1.40085	−	0.576218i
$36$	−9.37802	+	10.1362i	−1.56300	+	1.68937i
$37$	−0.898066	+	1.55550i	−0.147641	+	0.255722i	−0.930355	−	0.366660i	$-0.880501\pi$
$37$	−0.898066	+	1.55550i	−0.147641	+	0.255722i	0.782714	+	0.622381i	$0.213835\pi$
$38$	0.302272	+	1.71427i	0.0490350	+	0.278091i
$39$	2.81113	+	1.39469i	0.450141	+	0.223329i
$40$	7.74856	+	21.2890i	1.22515	+	3.36608i
$41$	−11.6140	+	4.22715i	−1.81380	+	0.660169i	−0.817335	+	0.576163i	$0.804549\pi$
$41$	−11.6140	+	4.22715i	−1.81380	+	0.660169i	−0.996465	+	0.0840066i	$0.973228\pi$
$42$	11.5491	−	2.29798i	1.78207	−	0.354586i
$43$	−0.0534327	−	0.303032i	−0.00814840	−	0.0462119i	0.980462	−	0.196706i	$-0.0630246\pi$
$43$	−0.0534327	−	0.303032i	−0.00814840	−	0.0462119i	−0.988611	+	0.150494i	$0.951913\pi$
$44$	−18.4368	−	10.6445i	−2.77945	−	1.60472i
$45$	9.90957	+	2.24684i	1.47723	+	0.334939i
$46$	−4.59602	−	7.96055i	−0.677647	−	1.17372i
$47$	2.22186	−	1.86436i	0.324092	−	0.271945i	−0.466196	−	0.884682i	$-0.654376\pi$
$47$	2.22186	−	1.86436i	0.324092	−	0.271945i	0.790287	+	0.612736i	$0.209931\pi$
$48$	−11.1294	−	8.20151i	−1.60638	−	1.18379i
$49$	−6.35862	−	2.92710i	−0.908375	−	0.418157i
$50$	10.6900	−	12.7398i	1.51179	−	1.80168i
$51$	−1.14525	−	4.72936i	−0.160367	−	0.662243i
$52$	−2.85233	+	7.83672i	−0.395547	+	1.08676i
$53$			4.31910i			0.593273i	0.954990	+	0.296637i	$0.0958650\pi$
$53$			4.31910i			0.593273i	−0.954990	+	0.296637i	$0.904135\pi$
$54$	−12.4789	+	4.74966i	−1.69816	+	0.646347i
$55$			15.6650i			2.11227i
$56$	5.36306	+	16.8648i	0.716669	+	2.25365i
$57$	−0.331031	+	1.12566i	−0.0438461	+	0.149097i
$58$	−3.14465	−	2.63868i	−0.412913	−	0.346475i
$59$	1.34243	−	7.61331i	0.174770	−	0.991168i	−0.763640	−	0.645643i	$-0.776590\pi$
$59$	1.34243	−	7.61331i	0.174770	−	0.991168i	0.938409	−	0.345525i	$-0.112299\pi$
$60$	−3.00420	+	26.8361i	−0.387840	+	3.46452i
$61$	−0.783123	−	0.933289i	−0.100269	−	0.119495i	0.713577	−	0.700577i	$-0.247074\pi$
$61$	−0.783123	−	0.933289i	−0.100269	−	0.119495i	−0.813845	+	0.581082i	$0.802630\pi$
$62$	3.98260	+	6.89806i	0.505790	+	0.876055i
$63$	7.66197	+	2.07224i	0.965318	+	0.261078i
$64$	1.18236	−	2.04791i	0.147795	−	0.255988i
$65$	6.04332	−	1.06560i	0.749582	−	0.132171i
$66$	−11.3951	−	17.1429i	−1.40264	−	2.11015i
$67$	0.826896	−	0.300966i	0.101021	−	0.0367688i	−0.291015	−	0.956719i	$-0.593993\pi$
$67$	0.826896	−	0.300966i	0.101021	−	0.0367688i	0.392036	+	0.919950i	$0.371771\pi$
$68$	12.1519	−	4.42294i	1.47364	−	0.536360i
$69$	−0.390395	−	6.18355i	−0.0469980	−	0.744411i
$70$	15.5151	−	17.0156i	1.85441	−	2.03375i
$71$	11.6410	+	6.72094i	1.38153	+	0.797629i	0.992341	−	0.123527i	$-0.0394205\pi$
$71$	11.6410	+	6.72094i	1.38153	+	0.797629i	0.389193	+	0.921156i	$0.372754\pi$
$72$	−9.18016	−	17.8434i	−1.08189	−	2.10287i
$73$	11.2992	−	6.52362i	1.32248	−	0.763532i	0.338354	−	0.941019i	$-0.390130\pi$
$73$	11.2992	−	6.52362i	1.32248	−	0.763532i	0.984123	+	0.177487i	$0.0567966\pi$
$74$	−2.96672	−	3.53560i	−0.344875	−	0.411006i
$75$	10.2713	−	4.49008i	1.18602	−	0.518470i
$76$	−3.07080	−	0.541464i	−0.352244	−	0.0621102i
$77$	−0.503696	+	12.2262i	−0.0574014	+	1.39331i
$78$	−5.83832	+	5.56220i	−0.661060	+	0.629795i
$79$	13.7757	+	5.01396i	1.54989	+	0.564115i	0.968392	−	0.249432i	$-0.0802438\pi$
$79$	13.7757	+	5.01396i	1.54989	+	0.564115i	0.581500	+	0.813546i	$0.302466\pi$
$80$	−27.0346			−3.02256
$81$	−8.95781	−	0.870403i	−0.995312	−	0.0967115i
$82$		−	31.7590i		−	3.50720i
$83$	−6.55767	−	2.38680i	−0.719798	−	0.261985i	−0.0439581	−	0.999033i	$-0.513997\pi$
$83$	−6.55767	−	2.38680i	−0.719798	−	0.261985i	−0.675840	+	0.737048i	$0.736219\pi$
$84$	−3.20761	+	20.8484i	−0.349979	+	2.27475i
$85$	−7.28935	−	6.11649i	−0.790642	−	0.663427i
$86$	0.778681	+	0.137302i	0.0839673	+	0.0148057i
$87$	−1.10832	−	2.53533i	−0.118824	−	0.271816i
$88$	23.6982	−	19.8852i	2.52624	−	2.11977i
$89$	8.53240	+	14.7785i	0.904432	+	1.56652i	0.821678	+	0.569952i	$0.193038\pi$
$89$	8.53240	+	14.7785i	0.904432	+	1.56652i	0.0827545	+	0.996570i	$0.473628\pi$
$90$	−14.1346	+	21.9536i	−1.48991	+	2.31412i
$91$	4.75095	−	0.637362i	0.498035	−	0.0668136i
$92$	16.2157	−	2.85927i	1.69060	−	0.298099i
$93$	0.338289	+	5.35823i	0.0350789	+	0.555623i
$94$	2.54910	+	7.00358i	0.262919	+	0.722364i
$95$	0.784742	+	2.15606i	0.0805128	+	0.221207i
$96$	10.2885	−	6.83891i	1.05007	−	0.697994i
$97$	−5.81042	+	1.02453i	−0.589959	+	0.104026i	−0.460655	−	0.887579i	$-0.652385\pi$
$97$	−5.81042	+	1.02453i	−0.589959	+	0.104026i	−0.129304	+	0.991605i	$0.541274\pi$
$98$	12.6564	−	12.7814i	1.27848	−	1.29112i
$99$	−1.74502	−	13.7648i	−0.175382	−	1.38342i
$100$	14.8953	+	25.7995i	1.48953	+	2.57995i
$101$	−4.44425	+	3.72917i	−0.442219	+	0.371066i	−0.836539	−	0.547907i	$-0.815425\pi$
$101$	−4.44425	+	3.72917i	−0.442219	+	0.371066i	0.394320	+	0.918973i	$0.370980\pi$
$102$	12.4264	+	1.39108i	1.23039	+	0.137738i
$103$	1.31146	+	0.231246i	0.129222	+	0.0227853i	0.237885	−	0.971293i	$-0.423546\pi$
$103$	1.31146	+	0.231246i	0.129222	+	0.0227853i	−0.108663	+	0.994079i	$0.534657\pi$
$104$	−9.28344	−	7.78973i	−0.910316	−	0.763846i
$105$	14.4657	−	5.62638i	1.41170	−	0.549078i
$106$	−10.4292	−	3.79591i	−1.01297	−	0.368691i
$107$			5.37579i			0.519697i	0.965649	+	0.259848i	$0.0836726\pi$
$107$			5.37579i			0.519697i	−0.965649	+	0.259848i	$0.916327\pi$
$108$	−0.349653	−	23.9155i	−0.0336453	−	2.30127i
$109$	−8.37864			−0.802529			−0.401264	−	0.915962i	$-0.631429\pi$
$109$	−8.37864			−0.802529			−0.401264	+	0.915962i	$0.631429\pi$
$110$	−37.8258	−	13.7675i	−3.60655	−	1.31268i
$111$	−0.732187	−	3.02360i	−0.0694961	−	0.286988i
$112$	−21.1000	−	0.869275i	−1.99376	−	0.0821387i
$113$	−11.4667	−	2.02188i	−1.07869	−	0.190203i	−0.394056	−	0.919086i	$-0.628929\pi$
$113$	−11.4667	−	2.02188i	−1.07869	−	0.190203i	−0.684638	+	0.728883i	$0.740040\pi$
$114$	−2.42715	−	1.78863i	−0.227324	−	0.167521i
$115$	−7.78803	−	9.28141i	−0.726237	−	0.865496i
$116$	6.36827	−	3.67672i	0.591279	−	0.341375i
$117$	−5.19155	+	1.60954i	−0.479959	+	0.148802i
$118$	17.2038	+	9.93261i	1.58374	+	0.914371i
$119$	−5.49252	−	5.00818i	−0.503499	−	0.459099i
$120$	−35.1516	−	17.4398i	−3.20889	−	1.59203i
$121$	9.76399	−	3.55380i	0.887636	−	0.323073i
$122$	2.94184	−	1.07074i	0.266342	−	0.0969406i
$123$	9.51412	−	19.1766i	0.857859	−	1.72910i
$124$	−14.0514	+	2.47764i	−1.26185	+	0.222499i
$125$	2.49282	−	4.31769i	0.222964	−	0.386186i
$126$	−11.7376	+	16.6799i	−1.04567	+	1.48596i
$127$	6.11354	+	10.5890i	0.542489	+	0.939618i	0.998760	+	0.0497777i	$0.0158513\pi$
$127$	6.11354	+	10.5890i	0.542489	+	0.939618i	−0.456271	+	0.889841i	$0.650815\pi$
$128$	−5.26368	−	6.27301i	−0.465248	−	0.554461i
$129$	0.429048	+	0.316176i	0.0377756	+	0.0278378i
$130$	−2.73820	+	15.5291i	−0.240156	+	1.36199i
$131$	9.11926	+	7.65197i	0.796753	+	0.668556i	0.947407	−	0.320031i	$-0.103693\pi$
$131$	9.11926	+	7.65197i	0.796753	+	0.668556i	−0.150654	+	0.988587i	$0.548138\pi$
$132$	35.8378	−	8.67839i	3.11928	−	0.755357i
$133$	0.543149	+	1.70799i	0.0470970	+	0.148102i
$134$			2.26119i			0.195337i
$135$	−15.1114	+	9.02164i	−1.30058	+	0.776459i
$136$			18.7917i			1.61137i
$137$	2.07270	−	5.69469i	0.177082	−	0.486530i	−0.819118	−	0.573626i	$-0.805536\pi$
$137$	2.07270	−	5.69469i	0.177082	−	0.486530i	0.996200	+	0.0870958i	$0.0277586\pi$
$138$	15.2743	+	4.49184i	1.30024	+	0.382371i
$139$	3.77560	−	4.49958i	0.320242	−	0.381650i	−0.581775	−	0.813350i	$-0.697642\pi$
$139$	3.77560	−	4.49958i	0.320242	−	0.381650i	0.902017	+	0.431700i	$0.142086\pi$
$140$	19.1365	+	36.5412i	1.61733	+	3.08830i
$141$	−0.558893	+	4.99251i	−0.0470673	+	0.420445i
$142$	−26.4597	+	22.2024i	−2.22045	+	1.86318i
$143$	−4.18974	−	7.25684i	−0.350363	−	0.606847i
$144$	23.7553	−	3.01155i	1.97960	−	0.250963i
$145$	−4.68594	−	2.70543i	−0.389147	−	0.224674i
$146$	5.82184	+	33.0173i	0.481819	+	2.73253i
$147$	11.4711	−	3.92614i	0.946118	−	0.323823i
$148$	7.76904	−	2.82770i	0.638611	−	0.232435i
$149$	−3.41781	−	9.39037i	−0.279998	−	0.769289i	−0.997362	−	0.0725900i	$-0.976874\pi$
$149$	−3.41781	−	9.39037i	−0.279998	−	0.769289i	0.717364	−	0.696699i	$-0.245349\pi$
$150$	1.81498	+	28.7479i	0.148192	+	2.34725i
$151$	1.48657	+	8.43073i	0.120975	+	0.686083i	0.983617	+	0.180269i	$0.0576968\pi$
$151$	1.48657	+	8.43073i	0.120975	+	0.686083i	−0.862642	+	0.505814i	$0.831192\pi$
$152$	2.26556	−	3.92407i	0.183761	−	0.318284i
$153$	7.08650	+	4.56255i	0.572910	+	0.368860i
$154$	−29.0796	−	11.9615i	−2.34330	−	0.963884i
$155$	6.74857	+	8.04263i	0.542058	+	0.645999i
$156$	−5.78583	−	13.2353i	−0.463237	−	1.05967i
$157$	0.122753	+	0.0216446i	0.00979672	+	0.00172743i	0.178544	−	0.983932i	$-0.442861\pi$
$157$	0.122753	+	0.0216446i	0.00979672	+	0.00172743i	−0.168748	+	0.985659i	$0.553972\pi$
$158$	−24.2141	+	28.8572i	−1.92637	+	2.29576i
$159$	−5.16016	−	5.41632i	−0.409227	−	0.429542i
$160$	8.26270	−	22.7016i	0.653224	−	1.79472i
$161$	−5.77996	−	7.49437i	−0.455525	−	0.590639i
$162$	9.97446	−	20.8652i	0.783668	−	1.63932i
$163$	−11.4176			−0.894293			−0.447146	−	0.894461i	$-0.647560\pi$
$163$	−11.4176			−0.894293			−0.447146	+	0.894461i	$0.647560\pi$
$164$	53.4595	+	19.4577i	4.17448	+	1.51939i
$165$	−18.7155	−	19.6446i	−1.45700	−	1.52933i
$166$	11.5266	−	13.7369i	0.894641	−	1.06619i
$167$	−1.76953	+	10.0355i	−0.136930	+	0.776570i	0.836566	+	0.547866i	$0.184560\pi$
$167$	−1.76953	+	10.0355i	−0.136930	+	0.776570i	−0.973496	+	0.228703i	$0.926551\pi$
$168$	−26.8744	−	14.7417i	−2.07340	−	1.13735i
$169$	7.44401	−	6.24626i	0.572616	−	0.480482i
$170$	21.1757	−	12.2258i	1.62410	−	0.937675i
$171$	−0.929729	−	1.80711i	−0.0710982	−	0.138193i
$172$	−0.708190	+	1.22662i	−0.0539990	+	0.0935290i
$173$	−3.27964	−	18.5997i	−0.249346	−	1.41411i	−0.810179	−	0.586183i	$-0.800630\pi$
$173$	−3.27964	−	18.5997i	−0.249346	−	1.41411i	0.560832	−	0.827929i	$-0.310481\pi$
$174$	7.09603	−	0.448004i	0.537949	−	0.0339631i
$175$	9.16478	−	14.4642i	0.692792	−	1.09339i
$176$	12.6260	+	34.6895i	0.951717	+	2.61482i
$177$	7.41239	+	11.1512i	0.557149	+	0.838179i
$178$	−43.1841	+	7.61452i	−3.23679	+	0.570733i
$179$	−4.68484	−	2.70479i	−0.350161	−	0.202166i	0.314595	−	0.949226i	$-0.398131\pi$
$179$	−4.68484	−	2.70479i	−0.350161	−	0.202166i	−0.664756	+	0.747060i	$0.731465\pi$
$180$	−28.2945	−	37.2427i	−2.10895	−	2.77591i
$181$	1.56807	−	0.905328i	0.116554	−	0.0672925i	−0.440590	−	0.897709i	$-0.645231\pi$
$181$	1.56807	−	0.905328i	0.116554	−	0.0672925i	0.557144	+	0.830416i	$0.311897\pi$
$182$	−2.63644	+	12.0321i	−0.195426	+	0.891880i
$183$	2.09710	+	0.234762i	0.155022	+	0.0173541i
$184$	−4.15490	+	23.5636i	−0.306304	+	1.73713i
$185$	−4.66027	−	3.91043i	−0.342630	−	0.287501i
$186$	−13.2357	−	3.89232i	−0.970486	−	0.285399i
$187$	−4.44405	+	12.2099i	−0.324981	+	0.892879i
$188$	−13.3508			−0.973705
$189$	−12.0842	+	6.55531i	−0.878996	+	0.476829i
$190$	−5.89585			−0.427730
$191$	−4.04999	+	11.1272i	−0.293047	+	0.805139i	0.702570	+	0.711614i	$0.252036\pi$
$191$	−4.04999	+	11.1272i	−0.293047	+	0.805139i	−0.995617	+	0.0935249i	$0.970187\pi$
$192$	0.963970	+	3.98076i	0.0695685	+	0.287287i
$193$	13.2951	+	11.1559i	0.957000	+	0.803018i	0.980462	−	0.196707i	$-0.0630247\pi$
$193$	13.2951	+	11.1559i	0.957000	+	0.803018i	−0.0234627	+	0.999725i	$0.507469\pi$
$194$	2.63268	−	14.9307i	0.189015	−	1.07196i
$195$	−6.30546	+	8.55645i	−0.451544	+	0.612740i
$196$	13.7607	+	29.1350i	0.982906	+	2.08107i
$197$	14.3984	−	8.31290i	1.02584	−	0.592270i	0.110051	−	0.993926i	$-0.464899\pi$
$197$	14.3984	−	8.31290i	1.02584	−	0.592270i	0.915791	+	0.401656i	$0.131565\pi$
$198$	34.7711	+	7.88380i	2.47108	+	0.560277i
$199$	19.4018	+	11.2016i	1.37536	+	0.794062i	0.991596	−	0.129371i	$-0.0412957\pi$
$199$	19.4018	+	11.2016i	1.37536	+	0.794062i	0.383760	+	0.923433i	$0.374629\pi$
$200$	−42.6323	+	7.51722i	−3.01456	+	0.531548i
$201$	−0.677389	+	1.36534i	−0.0477793	+	0.0963038i
$202$	−5.09879	−	14.0088i	−0.358750	−	0.985657i
$203$	−3.57029	−	2.26221i	−0.250585	−	0.158776i
$204$	−9.95479	+	20.0648i	−0.696975	+	1.40482i
$205$	−7.26917	−	41.2255i	−0.507701	−	2.87932i
$206$	−1.71098	+	2.96350i	−0.119210	+	0.206477i
$207$	7.87724	+	7.28800i	0.547506	+	0.506551i
$208$	12.5238	−	7.23062i	0.868369	−	0.501353i
$209$	2.40006	−	2.01389i	0.166016	−	0.139304i
$210$	0.872439	+	39.8746i	0.0602040	+	2.75161i
$211$	1.47800	−	8.38217i	0.101750	−	0.577052i	−0.890719	−	0.454554i	$-0.849798\pi$
$211$	1.47800	−	8.38217i	0.101750	−	0.577052i	0.992469	−	0.122498i	$-0.0390904\pi$
$212$	12.7792	−	15.2297i	0.877679	−	1.04598i
$213$	−22.6280	+	5.47954i	−1.55045	+	0.375452i
$214$	−12.9807	−	4.72460i	−0.887345	−	0.322967i
$215$	1.04221			0.0710782
$216$	32.8304	+	11.4086i	2.23383	+	0.776256i
$217$	5.00851	+	6.49410i	0.340000	+	0.440848i
$218$	7.36371	−	20.2316i	0.498734	−	1.37026i
$219$	−6.37575	+	21.6804i	−0.430833	+	1.46503i
$220$	46.3492	−	55.2368i	3.12486	−	3.72406i
$221$	5.01271	+	0.883876i	0.337191	+	0.0594559i
$222$	7.94449	+	0.889356i	0.533199	+	0.0596897i
$223$	−1.93481	−	2.30582i	−0.129565	−	0.154409i	0.697362	−	0.716719i	$-0.254357\pi$
$223$	−1.93481	−	2.30582i	−0.129565	−	0.154409i	−0.826926	+	0.562310i	$0.809913\pi$
$224$	7.17882	−	17.4524i	0.479655	−	1.16609i
$225$	−7.51614	+	17.9021i	−0.501076	+	1.19348i
$226$	14.9599	−	25.9112i	0.995115	−	1.72359i
$227$	−1.74616	−	9.90298i	−0.115897	−	0.657284i	−0.986302	−	0.164948i	$-0.947254\pi$
$227$	−1.74616	−	9.90298i	−0.115897	−	0.657284i	0.870405	−	0.492336i	$-0.163857\pi$
$228$	4.49781	−	2.98976i	0.297875	−	0.198001i
$229$	8.78597	+	24.1392i	0.580593	+	1.59517i	0.787170	+	0.616736i	$0.211545\pi$
$229$	8.78597	+	24.1392i	0.580593	+	1.59517i	−0.206577	+	0.978430i	$0.566232\pi$
$230$	29.2562	−	10.6484i	1.92909	−	0.702133i
$231$	−13.9754	−	15.9340i	−0.919513	−	1.04838i
$232$	1.85553	+	10.5232i	0.121821	+	0.690884i
$233$	0.222223	+	0.128301i	0.0145583	+	0.00840525i	0.507261	−	0.861792i	$-0.330658\pi$
$233$	0.222223	+	0.128301i	0.0145583	+	0.00840525i	−0.492703	+	0.870197i	$0.663991\pi$
$234$	0.676169	−	13.9504i	0.0442025	−	0.911969i
$235$	4.91193	+	8.50771i	0.320419	+	0.554982i
$236$	−27.2596	+	22.8735i	−1.77445	+	1.48894i
$237$	−23.2657	+	10.1706i	−1.51127	+	0.660651i
$238$	16.9203	−	8.86109i	1.09678	−	0.574379i
$239$	8.49409	−	10.1229i	0.549437	−	0.654794i	−0.417838	−	0.908521i	$-0.637212\pi$
$239$	8.49409	−	10.1229i	0.549437	−	0.654794i	0.967276	+	0.253727i	$0.0816566\pi$
$240$	33.9025	−	32.2991i	2.18840	−	2.08490i
$241$	−4.64833	+	12.7712i	−0.299425	+	0.822664i	0.695171	+	0.718844i	$0.255329\pi$
$241$	−4.64833	+	12.7712i	−0.299425	+	0.822664i	−0.994596	+	0.103820i	$0.966894\pi$
$242$			26.7001i			1.71635i
$243$	12.2734	−	9.61065i	0.787336	−	0.616524i
$244$			5.60797i			0.359014i
$245$	13.5034	−	19.4881i	0.862700	−	1.24505i
$246$	37.9435	+	39.8271i	2.41919	+	2.53928i
$247$	−0.940189	−	0.788912i	−0.0598228	−	0.0501973i
$248$	3.60035	−	20.4186i	0.228623	−	1.29658i
$249$	11.0752	−	4.84151i	0.701861	−	0.306818i
$250$	8.23493	+	9.81400i	0.520822	+	0.620692i
$251$	−11.8874	−	20.5896i	−0.750326	−	1.29960i	−0.947665	−	0.319268i	$-0.896563\pi$
$251$	−11.8874	−	20.5896i	−0.750326	−	1.29960i	0.197338	−	0.980335i	$-0.436770\pi$
$252$	−20.8858	−	29.9770i	−1.31568	−	1.88837i
$253$	−8.27223	+	14.3279i	−0.520071	+	0.900789i
$254$	−30.9418	+	5.45588i	−1.94146	+	0.342332i
$255$	16.4487	−	1.03848i	1.03006	−	0.0650321i
$256$	24.2175	−	8.81446i	1.51360	−	0.550904i
$257$	−9.29984	+	3.38487i	−0.580108	+	0.211142i	−0.615373	−	0.788236i	$-0.710995\pi$
$257$	−9.29984	+	3.38487i	−0.580108	+	0.211142i	0.0352650	+	0.999378i	$0.488772\pi$
$258$	−1.14054	+	0.758131i	−0.0710067	+	0.0471992i
$259$	−3.51151	−	3.20186i	−0.218195	−	0.198954i
$260$	−24.4623	−	14.1233i	−1.51709	−	0.875893i
$261$	4.41891	+	1.85526i	0.273524	+	0.114838i
$262$	−26.4916	+	15.2949i	−1.63665	+	0.944923i
$263$	6.43655	+	7.67078i	0.396895	+	0.473001i	0.927070	−	0.374887i	$-0.122319\pi$
$263$	6.43655	+	7.67078i	0.396895	+	0.473001i	−0.530176	+	0.847888i	$0.677874\pi$
$264$	−5.96112	+	53.2498i	−0.366882	+	3.27730i
$265$	−14.4067	−	2.54028i	−0.884994	−	0.156048i
$266$	−4.60159	−	0.189576i	−0.282142	−	0.0116237i
$267$	−28.3564	−	8.33898i	−1.73538	−	0.510338i
$268$	−3.80623	−	1.38535i	−0.232502	−	0.0846239i
$269$	14.5115			0.884779			0.442389	−	0.896823i	$-0.354131\pi$
$269$	14.5115			0.884779			0.442389	+	0.896823i	$0.354131\pi$
$270$	−8.50337	−	44.4178i	−0.517499	−	2.70318i
$271$			0.249134i			0.0151338i	0.999971	+	0.00756690i	$0.00240864\pi$
$271$			0.249134i			0.0151338i	−0.999971	+	0.00756690i	$0.997591\pi$
$272$	−21.0718	−	7.66952i	−1.27767	−	0.465033i
$273$	−5.19641	+	6.47538i	−0.314501	+	0.391908i
$274$	11.9292	+	10.0097i	0.720666	+	0.604711i
$275$	−29.4782	−	5.19779i	−1.77760	−	0.313439i
$276$	−16.9191	+	22.9590i	−1.01841	+	1.38197i
$277$	−11.2035	+	9.40083i	−0.673151	+	0.564841i	−0.913996	−	0.405723i	$-0.867020\pi$
$277$	−11.2035	+	9.40083i	−0.673151	+	0.564841i	0.240845	+	0.970564i	$0.422575\pi$
$278$	7.54675	+	13.0714i	0.452624	+	0.783967i
$279$	−6.82587	−	6.31528i	−0.408654	−	0.378086i
$280$	−59.4080	+	7.96985i	−3.55031	+	0.476290i
$281$	−23.4578	+	4.13624i	−1.39937	+	0.246747i	−0.821886	−	0.569652i	$-0.807078\pi$
$281$	−23.4578	+	4.13624i	−1.39937	+	0.246747i	−0.577488	+	0.816399i	$0.695967\pi$
$282$	−11.5641	−	5.73730i	−0.688630	−	0.341651i
$283$	−6.60507	−	18.1473i	−0.392630	−	1.07874i	−0.965796	−	0.259303i	$-0.916507\pi$
$283$	−6.60507	−	18.1473i	−0.392630	−	1.07874i	0.573166	−	0.819440i	$-0.305715\pi$
$284$	−21.1619	−	58.1419i	−1.25573	−	3.45009i
$285$	−3.56001	−	1.76623i	−0.210877	−	0.104623i
$286$	21.2051	−	3.73903i	1.25388	−	0.221093i
$287$	−4.34787	−	32.4094i	−0.256647	−	1.91307i
$288$	−4.73155	+	20.8683i	−0.278809	+	1.22967i
$289$	4.55359	+	7.88705i	0.267858	+	0.463944i
$290$	10.6510	−	8.93728i	0.625451	−	0.524815i
$291$	6.06246	−	8.22670i	0.355388	−	0.482257i
$292$	−59.1444	−	10.4288i	−3.46117	−	0.610297i
$293$	17.3375	+	14.5479i	1.01287	+	0.849899i	0.988715	−	0.149810i	$-0.0478661\pi$
$293$	17.3375	+	14.5479i	1.01287	+	0.849899i	0.0241549	+	0.999708i	$0.492310\pi$
$294$	−0.601213	+	31.1494i	−0.0350635	+	1.81667i
$295$	24.6052	+	8.95556i	1.43257	+	0.521413i
$296$			12.0140i			0.698301i
$297$	18.6336	+	15.1768i	1.08123	+	0.880649i
$298$	25.6784			1.48751
$299$	6.09020	+	2.21665i	0.352205	+	0.128192i
$300$	−49.5028	−	14.5577i	−2.85805	−	0.840489i
$301$	0.813425	+	0.0335114i	0.0468850	+	0.00193157i
$302$	−21.6639	−	3.81993i	−1.24662	−	0.219812i
$303$	1.11792	−	9.98621i	0.0642228	−	0.573693i
$304$	3.47556	+	4.14201i	0.199337	+	0.237560i
$305$	3.57365	−	2.06325i	0.204627	−	0.118141i
$306$	−17.2451	+	13.1017i	−0.985838	+	0.748972i
$307$	3.45170	+	1.99284i	0.196999	+	0.113737i	0.595255	−	0.803537i	$-0.297051\pi$
$307$	3.45170	+	1.99284i	0.196999	+	0.113737i	−0.398256	+	0.917274i	$0.630384\pi$
$308$	37.9507	−	41.6209i	2.16244	−	2.37157i
$309$	−1.92090	+	1.27685i	−0.109276	+	0.0726374i
$310$	−25.3514	+	9.22714i	−1.43986	+	0.524066i
$311$	−2.45813	+	0.894685i	−0.139388	+	0.0507329i	−0.410772	−	0.911738i	$-0.634741\pi$
$311$	−2.45813	+	0.894685i	−0.139388	+	0.0507329i	0.271384	+	0.962471i	$0.412519\pi$
$312$	20.9484	−	1.32257i	1.18597	−	0.0748757i
$313$	25.8005	−	4.54932i	1.45833	−	0.257143i	0.612446	−	0.790512i	$-0.290186\pi$
$313$	25.8005	−	4.54932i	1.45833	−	0.257143i	0.845882	+	0.533369i	$0.179074\pi$
$314$	−0.160148	+	0.277384i	−0.00903765	+	0.0156537i
$315$	−11.4185	+	24.3383i	−0.643361	+	1.37131i
$316$	−33.7398	−	58.4391i	−1.89801	−	3.28746i
$317$	−3.22194	−	3.83976i	−0.180962	−	0.215662i	0.667936	−	0.744219i	$-0.267178\pi$
$317$	−3.22194	−	3.83976i	−0.180962	−	0.215662i	−0.848898	+	0.528556i	$0.822734\pi$
$318$	17.6137	−	7.69983i	0.987728	−	0.431785i
$319$	−1.28301	+	7.27630i	−0.0718347	+	0.407395i
$320$	6.13554	+	5.14833i	0.342987	+	0.287800i
$321$	−6.42262	−	6.74146i	−0.358476	−	0.376271i
$322$	23.1762	−	7.37013i	1.29156	−	0.410721i
$323$			1.90315i			0.105894i
$324$	29.0110	+	29.5732i	1.61172	+	1.64296i
$325$			11.7258i			0.650430i
$326$	10.0345	−	27.5696i	0.555761	−	1.52694i
$327$	10.5072	−	10.0102i	0.581047	−	0.553567i
$328$	−53.1390	+	63.3286i	−2.93411	+	3.49673i
$329$	3.56010	+	6.79803i	0.196275	+	0.374788i
$330$	63.8835	−	27.9267i	3.51667	−	1.53731i
$331$	5.54912	−	4.65626i	0.305007	−	0.255931i	−0.477418	−	0.878677i	$-0.658427\pi$
$331$	5.54912	−	4.65626i	0.305007	−	0.255931i	0.782425	+	0.622745i	$0.213983\pi$
$332$	16.0612	+	27.8188i	0.881472	+	1.52675i
$333$	4.53058	+	2.91695i	0.248274	+	0.159848i
$334$	−22.6772	−	13.0927i	−1.24084	−	0.716400i
$335$	0.517553	+	2.93519i	0.0282769	+	0.160366i
$336$	27.4988	−	24.1187i	1.50018	−	1.31578i
$337$	0.545928	−	0.198702i	0.0297386	−	0.0108240i	−0.327108	−	0.944987i	$-0.606074\pi$
$337$	0.545928	−	0.198702i	0.0297386	−	0.0108240i	0.356847	+	0.934163i	$0.383852\pi$
$338$	8.54036	+	23.4644i	0.464534	+	1.27630i
$339$	16.7953	−	11.1641i	0.912195	−	0.606349i
$340$	7.60587	+	43.1350i	0.412486	+	2.33932i
$341$	7.16814	−	12.4156i	0.388177	−	0.672342i
$342$	5.18068	−	0.656776i	0.280139	−	0.0355144i
$343$	11.1657	−	14.7759i	0.602893	−	0.797822i
$344$	−1.32298	−	1.57667i	−0.0713304	−	0.0850083i
$345$	20.8553	+	2.33467i	1.12281	+	0.125695i
$346$	47.7946	+	8.42747i	2.56945	+	0.453064i
$347$	2.56214	−	3.05344i	0.137543	−	0.163917i	−0.692876	−	0.721057i	$-0.743657\pi$
$347$	2.56214	−	3.05344i	0.137543	−	0.163917i	0.830419	+	0.557140i	$0.188101\pi$
$348$	−3.59338	+	12.2191i	−0.192625	+	0.655014i
$349$	4.94233	−	13.5789i	0.264557	−	0.726863i	−0.734289	−	0.678837i	$-0.762484\pi$
$349$	4.94233	−	13.5789i	0.264557	−	0.726863i	0.998846	−	0.0480269i	$-0.0152933\pi$
$350$	26.8715	+	34.8420i	1.43634	+	1.86238i
$351$	4.58745	−	8.22094i	0.244860	−	0.438801i
$352$	−32.9885			−1.75829
$353$	5.93484	+	2.16010i	0.315880	+	0.114971i	0.495094	−	0.868839i	$-0.335133\pi$
$353$	5.93484	+	2.16010i	0.315880	+	0.114971i	−0.179215	+	0.983810i	$0.557356\pi$
$354$	−33.4410	+	8.09799i	−1.77737	+	0.430403i
$355$	−29.2649	+	34.8765i	−1.55322	+	1.85105i
$356$	13.6400	−	77.3563i	0.722919	−	4.09988i
$357$	12.8713	−	0.281618i	0.681220	−	0.0149048i
$358$	10.6485	−	8.93517i	0.562792	−	0.472238i
$359$	−28.2385	+	16.3035i	−1.49037	+	0.860467i	−0.999939	−	0.0110119i	$-0.996495\pi$
$359$	−28.2385	+	16.3035i	−1.49037	+	0.860467i	−0.490433	+	0.871479i	$0.663161\pi$
$360$	64.9175	−	20.1265i	3.42145	−	1.06076i
$361$	−9.27055	+	16.0571i	−0.487924	+	0.845109i
$362$	0.807937	+	4.58204i	0.0424642	+	0.240827i
$363$	−7.99861	+	16.1220i	−0.419818	+	0.846183i
$364$	−18.6382	−	11.8095i	−0.976909	−	0.618989i
$365$	15.1144	+	41.5264i	0.791122	+	2.17359i
$366$	−2.40994	+	4.85747i	−0.125970	+	0.253904i
$367$	28.3869	−	5.00537i	1.48178	−	0.261278i	0.626492	−	0.779428i	$-0.284490\pi$
$367$	28.3869	−	5.00537i	1.48178	−	0.261278i	0.855290	+	0.518150i	$0.173379\pi$
$368$	−24.7270	−	14.2762i	−1.28899	−	0.744196i
$369$	10.9798	+	35.4151i	0.571585	+	1.84363i
$370$	13.5382	−	7.81626i	0.703815	−	0.406348i
$371$	−11.1624	−	2.44587i	−0.579524	−	0.126983i
$372$	14.6609	−	19.8947i	0.760133	−	1.03149i
$373$	0.466317	−	2.64461i	0.0241450	−	0.136933i	−0.970352	−	0.241694i	$-0.922297\pi$
$373$	0.466317	−	2.64461i	0.0241450	−	0.136933i	0.994497	+	0.104762i	$0.0334079\pi$
$374$	−25.5772	−	21.4618i	−1.32257	−	1.10976i
$375$	2.03238	+	8.39280i	0.104952	+	0.433403i
$376$	6.63536	−	18.2305i	0.342193	−	0.940167i
$377$	2.89436			0.149067
$378$	−5.20849	−	34.9406i	−0.267896	−	1.79715i
$379$	14.7592			0.758131			0.379066	−	0.925370i	$-0.376245\pi$
$379$	14.7592			0.758131			0.379066	+	0.925370i	$0.376245\pi$
$380$	3.61219	−	9.92441i	0.185301	−	0.509111i
$381$	−20.3176	−	5.97496i	−1.04090	−	0.306106i
$382$	−23.3092	−	19.5587i	−1.19260	−	1.00071i
$383$	−5.10475	+	28.9505i	−0.260841	+	1.47930i	0.519783	+	0.854298i	$0.326013\pi$
$383$	−5.10475	+	28.9505i	−0.260841	+	1.47930i	−0.780623	+	0.625002i	$0.785098\pi$
$384$	14.0954	+	1.57793i	0.719304	+	0.0805235i
$385$	−40.4852	−	8.87099i	−2.06332	−	0.452108i
$386$	−38.6223	+	22.2986i	−1.96583	+	1.13497i
$387$	−0.915789	+	0.116098i	−0.0465522	+	0.00590162i
$388$	23.5196	+	13.5791i	1.19403	+	0.689372i
$389$	33.7474	−	5.95059i	1.71106	−	0.301707i	0.769526	−	0.638615i	$-0.220492\pi$
$389$	33.7474	−	5.95059i	1.71106	−	0.301707i	0.941537	+	0.336909i	$0.109381\pi$
$390$	−15.1193	−	22.7456i	−0.765596	−	1.15177i
$391$	−3.43723	−	9.44371i	−0.173828	−	0.477589i
$392$	−46.6230	+	4.31009i	−2.35482	+	0.217692i
$393$	−20.5780	+	1.29918i	−1.03802	+	0.0655349i
$394$	7.41864	+	42.0732i	0.373746	+	2.11962i
$395$	−24.8267	+	43.0011i	−1.24917	+	2.16362i
$396$	−34.5738	+	53.6996i	−1.73740	+	2.69851i
$397$	20.6504	−	11.9225i	1.03642	−	0.598375i	0.117600	−	0.993061i	$-0.462480\pi$
$397$	20.6504	−	11.9225i	1.03642	−	0.598375i	0.918816	+	0.394686i	$0.129147\pi$
$398$	−44.0998	+	37.0041i	−2.21052	+	1.85485i
$399$	−2.72172	−	1.49298i	−0.136257	−	0.0747424i
$400$	8.97032	−	50.8732i	0.448516	−	2.54366i
$401$	16.1656	−	19.2654i	0.807269	−	0.962066i	−0.192546	−	0.981288i	$-0.561674\pi$
$401$	16.1656	−	19.2654i	0.807269	−	0.962066i	0.999815	+	0.0192219i	$0.00611890\pi$
$402$	−2.70151	−	2.83562i	−0.134739	−	0.141428i
$403$	−5.27735	−	1.92080i	−0.262883	−	0.0956817i
$404$	26.7047			1.32861
$405$	8.17185	−	29.3675i	0.406062	−	1.45928i
$406$	8.60029	−	6.63289i	0.426825	−	0.329185i
$407$	−2.84120	+	7.80613i	−0.140833	+	0.386935i
$408$	−22.4510	−	23.5656i	−1.11149	−	1.16667i
$409$	−0.228603	+	0.272438i	−0.0113037	+	0.0134712i	−0.771667	−	0.636027i	$-0.780577\pi$
$409$	−0.228603	+	0.272438i	−0.0113037	+	0.0134712i	0.760363	+	0.649498i	$0.225021\pi$
$410$	105.935	+	18.6791i	5.23174	+	0.922496i
$411$	4.20437	+	9.61768i	0.207386	+	0.474405i
$412$	−3.94016	−	4.69570i	−0.194118	−	0.231341i
$413$	18.9159	+	7.78079i	0.930791	+	0.382868i
$414$	−24.5212	+	12.6157i	−1.20515	+	0.620030i
$415$	11.8182	−	20.4698i	0.580135	−	1.00482i
$416$	2.24402	+	12.7265i	0.110022	+	0.623966i
$417$	0.641034	+	10.1535i	0.0313916	+	0.497218i
$418$	2.75354	+	7.56528i	0.134680	+	0.370030i
$419$	25.0271	−	9.10912i	1.22265	−	0.445010i	0.351578	−	0.936159i	$-0.385645\pi$
$419$	25.0271	−	9.10912i	1.22265	−	0.445010i	0.871076	+	0.491149i	$0.163423\pi$
$420$	−67.6549	−	22.9612i	−3.30122	−	1.12039i
$421$	−4.94818	−	28.0625i	−0.241160	−	1.36768i	−0.829245	−	0.558885i	$-0.811229\pi$
$421$	−4.94818	−	28.0625i	−0.241160	−	1.36768i	0.588085	−	0.808799i	$-0.299882\pi$
$422$	18.9412	+	10.9357i	0.922042	+	0.532341i
$423$	−5.26383	−	6.92854i	−0.255936	−	0.336877i
$424$	14.4448	+	25.0192i	0.701504	+	1.21504i
$425$	13.9286	−	11.6875i	0.675636	−	0.566926i
$426$	6.65576	−	59.4549i	0.322473	−	2.88060i
$427$	2.85550	−	1.49542i	0.138188	−	0.0723682i
$428$	15.9057	−	18.9557i	0.768831	−	0.916258i
$429$	13.9241	+	4.09476i	0.672260	+	0.197697i
$430$	−0.915965	+	2.51659i	−0.0441718	+	0.121361i
$431$		−	26.0928i		−	1.25684i	−0.777872	−	0.628422i	$-0.783701\pi$
$431$		−	26.0928i		−	1.25684i	0.777872	−	0.628422i	$-0.216299\pi$
$432$	−26.1921	+	32.1577i	−1.26017	+	1.54719i
$433$		−	21.3082i		−	1.02401i	−0.858983	−	0.512004i	$-0.828903\pi$
$433$		−	21.3082i		−	1.02401i	0.858983	−	0.512004i	$-0.171097\pi$
$434$	−20.0829	+	6.38645i	−0.964011	+	0.306559i
$435$	9.10863	−	2.20572i	0.436725	−	0.105756i
$436$	29.5441	+	24.7905i	1.41491	+	1.18725i
$437$	−0.420792	+	2.38643i	−0.0201292	+	0.114158i
$438$	−46.7476	−	34.4495i	−2.23369	−	1.64606i
$439$	1.15331	+	1.37446i	0.0550444	+	0.0655994i	0.792864	−	0.609398i	$-0.208589\pi$
$439$	1.15331	+	1.37446i	0.0550444	+	0.0655994i	−0.737820	+	0.674998i	$0.764145\pi$
$440$	52.3903	+	90.7427i	2.49761	+	4.32599i
$441$	−9.69451	+	18.6284i	−0.461643	+	0.887066i
$442$	−6.53977	+	11.3272i	−0.311065	+	0.538781i
$443$	19.7101	−	3.47542i	0.936454	−	0.165122i	0.315461	−	0.948938i	$-0.397841\pi$
$443$	19.7101	−	3.47542i	0.936454	−	0.165122i	0.620993	+	0.783816i	$0.286730\pi$
$444$	−6.36436	+	12.8280i	−0.302039	+	0.608788i
$445$	−54.3133	+	19.7684i	−2.57470	+	0.937113i
$446$	7.26823	−	2.64542i	0.344160	−	0.125264i
$447$	15.5050	+	7.69254i	0.733363	+	0.363845i
$448$	4.62313	+	4.21545i	0.218422	+	0.199161i
$449$	−0.145244	−	0.0838569i	−0.00685451	−	0.00395745i	0.496569	−	0.867997i	$-0.334593\pi$
$449$	−0.145244	−	0.0838569i	−0.00685451	−	0.00395745i	−0.503423	+	0.864040i	$0.667926\pi$
$450$	−36.6220	−	33.8826i	−1.72638	−	1.59724i
$451$	−49.5037	+	28.5810i	−2.33104	+	1.34583i
$452$	34.4506	+	41.0567i	1.62042	+	1.93114i
$453$	−11.9367	−	8.79644i	−0.560833	−	0.413293i
$454$	25.4471	+	4.48700i	1.19429	+	0.210585i
$455$	−0.668314	+	16.2220i	−0.0313310	+	0.760500i
$456$	1.84710	+	7.62768i	0.0864983	+	0.357199i
$457$	19.2205	+	6.99570i	0.899099	+	0.327245i	0.749892	−	0.661561i	$-0.230106\pi$
$457$	19.2205	+	6.99570i	0.899099	+	0.327245i	0.149207	+	0.988806i	$0.452328\pi$
$458$	−66.0099			−3.08444
$459$	−14.3378	+	2.74484i	−0.669230	+	0.128118i
$460$			55.7704i			2.60031i
$461$	1.81793	+	0.661673i	0.0846695	+	0.0308172i	0.384008	−	0.923330i	$-0.374544\pi$
$461$	1.81793	+	0.661673i	0.0846695	+	0.0308172i	−0.299338	+	0.954147i	$0.596766\pi$
$462$	50.7578	−	19.7421i	2.36146	−	0.918485i
$463$	−30.6253	−	25.6977i	−1.42328	−	1.19427i	−0.949555	−	0.313599i	$-0.898465\pi$
$463$	−30.6253	−	25.6977i	−1.42328	−	1.19427i	−0.473724	−	0.880674i	$-0.657090\pi$
$464$	−12.5574	−	2.21421i	−0.582962	−	0.102792i
$465$	−18.0718	−	2.02307i	−0.838057	−	0.0938175i
$466$	−0.505108	+	0.423836i	−0.0233987	+	0.0196338i
$467$	0.858878	+	1.48762i	0.0397442	+	0.0688389i	0.885213	−	0.465186i	$-0.154012\pi$
$467$	0.858878	+	1.48762i	0.0397442	+	0.0688389i	−0.845469	+	0.534024i	$0.820679\pi$
$468$	23.0683	+	9.68515i	1.06633	+	0.447696i
$469$	0.309561	+	2.30750i	0.0142942	+	0.106550i
$470$	−24.8602	+	4.38353i	−1.14672	+	0.202197i
$471$	−0.179796	+	0.119513i	−0.00828457	+	0.00550687i
$472$	−17.6858	−	48.5912i	−0.814053	−	2.23659i
$473$	−0.486743	−	1.33732i	−0.0223805	−	0.0614899i
$474$	−4.11116	−	65.1175i	−0.188832	−	2.99095i
$475$	−4.31762	+	0.761313i	−0.198106	+	0.0349314i
$476$	4.54925	+	33.9106i	0.208515	+	1.55429i
$477$	12.9421	+	0.627295i	0.592578	+	0.0287219i
$478$	16.9782	+	29.4071i	0.776564	+	1.34505i
$479$	22.9906	−	19.2914i	1.05047	−	0.881447i	0.0573246	−	0.998356i	$-0.481743\pi$
$479$	22.9906	−	19.2914i	1.05047	−	0.881447i	0.993143	+	0.116909i	$0.0372985\pi$
$480$	16.7605	+	38.3404i	0.765009	+	1.74999i
$481$	3.20475	+	0.565084i	0.146124	+	0.0257656i
$482$	−26.7529	−	22.4483i	−1.21856	−	1.02249i
$483$	16.2021	+	2.49275i	0.737219	+	0.113424i
$484$	−44.9439	−	16.3582i	−2.04291	−	0.743557i
$485$		−	19.9837i		−	0.907412i
$486$	12.4199	+	38.0826i	0.563377	+	1.72746i
$487$	−37.1109			−1.68165			−0.840827	−	0.541304i	$-0.817931\pi$
$487$	−37.1109			−1.68165			−0.840827	+	0.541304i	$0.817931\pi$
$488$	−7.65770	−	2.78717i	−0.346648	−	0.126169i
$489$	14.3181	−	13.6409i	0.647487	−	0.616864i
$490$	35.1896	+	49.7336i	1.58970	+	2.24674i
$491$	−33.6615	−	5.93543i	−1.51912	−	0.267862i	−0.649034	−	0.760759i	$-0.724827\pi$
$491$	−33.6615	−	5.93543i	−1.51912	−	0.267862i	−0.870088	+	0.492897i	$0.835938\pi$
$492$	−90.2871	+	39.4690i	−4.07045	+	1.77940i
$493$	−2.88490	−	3.43809i	−0.129929	−	0.154844i
$494$	2.73126	−	1.57689i	0.122885	−	0.0709478i
$495$	46.9400	+	2.27515i	2.10979	+	0.102260i
$496$	21.4267	+	12.3707i	0.962089	+	0.555462i
$497$	−23.9621	+	26.2794i	−1.07485	+	1.17879i
$498$	1.95703	+	30.9979i	0.0876968	+	1.38905i
$499$	22.0595	−	8.02898i	0.987517	−	0.359427i	0.202759	−	0.979229i	$-0.435009\pi$
$499$	22.0595	−	8.02898i	0.987517	−	0.359427i	0.784758	+	0.619802i	$0.212787\pi$
$500$	−21.5650	+	7.84903i	−0.964417	+	0.351019i
$501$	−9.77065	−	14.6990i	−0.436520	−	0.656704i
$502$	60.1644	−	10.6086i	2.68527	−	0.473486i
$503$	−8.06083	+	13.9618i	−0.359415	+	0.622524i	−0.987863	−	0.155327i	$-0.950357\pi$
$503$	−8.06083	+	13.9618i	−0.359415	+	0.622524i	0.628449	+	0.777851i	$0.283690\pi$
$504$	51.3139	−	13.6209i	2.28570	−	0.606724i
$505$	−9.82502	−	17.0174i	−0.437208	−	0.757266i
$506$	−27.3270	−	32.5670i	−1.21483	−	1.44778i
$507$	−1.87249	+	16.7267i	−0.0831601	+	0.742857i
$508$	9.77319	−	55.4265i	0.433615	−	2.45915i
$509$	−25.7566	−	21.6124i	−1.14164	−	0.957952i	−0.142151	−	0.989845i	$-0.545402\pi$
$509$	−25.7566	−	21.6124i	−1.14164	−	0.957952i	−0.999491	+	0.0318930i	$0.989846\pi$
$510$	−11.9486	+	40.6309i	−0.529095	+	1.79916i
$511$	10.4612	+	32.8965i	0.462776	+	1.45525i
$512$			49.8464i			2.20292i
$513$	3.32493	+	1.15541i	0.146799	+	0.0510128i
$514$		−	25.4309i		−	1.12171i
$515$	−1.54267	+	4.23846i	−0.0679783	+	0.186769i
$516$	−0.577383	−	2.38433i	−0.0254179	−	0.104964i
$517$	8.62268	−	10.2761i	0.379225	−	0.451943i
$518$	10.8176	−	5.66512i	0.475297	−	0.248911i
$519$	26.3345	+	19.4066i	1.15596	+	0.851853i
$520$	31.4433	−	26.3841i	1.37888	−	1.15702i
$521$	−5.45369	−	9.44606i	−0.238930	−	0.413839i	0.721477	−	0.692438i	$-0.243463\pi$
$521$	−5.45369	−	9.44606i	−0.238930	−	0.413839i	−0.960408	+	0.278599i	$0.910130\pi$
$522$	−8.36347	+	9.03966i	−0.366059	+	0.395655i
$523$	−23.6689	−	13.6653i	−1.03497	−	0.597541i	−0.116566	−	0.993183i	$-0.537189\pi$
$523$	−23.6689	−	13.6653i	−1.03497	−	0.597541i	−0.918405	+	0.395642i	$0.870522\pi$
$524$	−9.51523	−	53.9636i	−0.415675	−	2.35741i
$525$	5.78778	+	29.0881i	0.252600	+	1.26951i
$526$	−24.1793	+	8.80053i	−1.05427	+	0.383721i
$527$	2.97846	+	8.18326i	0.129744	+	0.356469i
$528$	−57.2781	−	28.4175i	−2.49271	−	1.23671i
$529$	1.77187	+	10.0488i	0.0770378	+	0.436903i
$530$	18.7955	−	32.5547i	0.816424	−	1.41409i
$531$	−22.6182	−	5.12831i	−0.981545	−	0.222550i
$532$	3.13835	−	7.62965i	0.136065	−	0.330787i
$533$	14.3936	+	17.1536i	0.623454	+	0.743004i
$534$	45.0573	−	61.1423i	1.94982	−	2.64589i
$535$	−17.9313	−	3.16178i	−0.775239	−	0.136696i
$536$	3.78340	−	4.50889i	0.163418	−	0.194754i
$537$	9.10647	−	2.20520i	0.392973	−	0.0951613i
$538$	−12.7536	+	35.0403i	−0.549848	+	1.51070i
$539$	−31.3127	−	8.22540i	−1.34873	−	0.354293i
$540$	79.9775	+	12.8996i	3.44168	+	0.555112i
$541$	−27.4497			−1.18015			−0.590076	−	0.807347i	$-0.700902\pi$
$541$	−27.4497			−1.18015			−0.590076	+	0.807347i	$0.700902\pi$
$542$	−0.601575	−	0.218955i	−0.0258399	−	0.00940494i
$543$	−0.884806	+	3.00874i	−0.0379707	+	0.129118i
$544$	12.8806	−	15.3504i	0.552249	−	0.658145i
$545$	4.92791	−	27.9476i	0.211089	−	1.19714i
$546$	−11.0689	−	18.2386i	−0.473707	−	0.780540i
$547$	−32.0533	+	26.8959i	−1.37050	+	1.14999i	−0.397921	+	0.917420i	$0.630268\pi$
$547$	−32.0533	+	26.8959i	−1.37050	+	1.14999i	−0.972580	+	0.232568i	$0.925287\pi$
$548$	−24.1578	+	13.9475i	−1.03197	+	0.595809i
$549$	−2.91032	+	2.21106i	−0.124210	+	0.0943659i
$550$	38.4583	−	66.6118i	1.63987	−	2.84034i
$551$	0.187920	+	1.06575i	0.00800567	+	0.0454024i
$552$	−22.9418	−	34.5138i	−0.976467	−	1.46900i
$553$	−20.7594	+	32.7632i	−0.882778	+	1.39323i
$554$	−12.8535	−	35.3147i	−0.546093	−	1.50038i
$555$	10.5161	−	0.663927i	0.446383	−	0.0281821i
$556$	−26.6264	+	4.69496i	−1.12921	+	0.199111i
$557$	27.5246	+	15.8913i	1.16625	+	0.673337i	0.952795	−	0.303616i	$-0.0981938\pi$
$557$	27.5246	+	15.8913i	1.16625	+	0.673337i	0.213459	+	0.976952i	$0.431527\pi$
$558$	21.2483	−	10.9319i	0.899514	−	0.462785i
$559$	−0.482805	+	0.278748i	−0.0204205	+	0.0117898i
$560$	15.3095	−	69.8692i	0.646945	−	2.95251i
$561$	−9.01456	−	20.6212i	−0.380595	−	0.870628i
$562$	10.6286	−	60.2779i	0.448342	−	2.54267i
$563$	6.98724	+	5.86299i	0.294477	+	0.247095i	0.778041	−	0.628214i	$-0.216214\pi$
$563$	6.98724	+	5.86299i	0.294477	+	0.247095i	−0.483564	+	0.875309i	$0.660658\pi$
$564$	16.7424	−	15.9506i	0.704983	−	0.671640i
$565$	13.4883	−	37.0588i	0.567457	−	1.55907i
$566$	49.6246			2.08588
$567$	7.32225	−	22.6580i	0.307506	−	0.951546i
$568$	89.9105			3.77256
$569$	−4.11399	+	11.3031i	−0.172468	+	0.473851i	−0.995568	−	0.0940452i	$-0.970020\pi$
$569$	−4.11399	+	11.3031i	−0.172468	+	0.473851i	0.823100	+	0.567896i	$0.192242\pi$
$570$	7.39364	−	7.04396i	0.309686	−	0.295039i
$571$	22.3766	+	18.7762i	0.936433	+	0.785761i	0.976961	−	0.213417i	$-0.0684594\pi$
$571$	22.3766	+	18.7762i	0.936433	+	0.785761i	−0.0405277	+	0.999178i	$0.512904\pi$
$572$	−6.69777	+	37.9850i	−0.280048	+	1.58823i
$573$	−8.21521	−	18.7927i	−0.343195	−	0.785075i
$574$	82.0792	+	17.9849i	3.42592	+	0.750676i
$575$	20.0497	−	11.5757i	0.836131	−	0.482741i
$576$	−5.96480	−	3.84035i	−0.248533	−	0.160015i
$577$	−12.2130	−	7.05117i	−0.508433	−	0.293544i	0.223756	−	0.974645i	$-0.428168\pi$
$577$	−12.2130	−	7.05117i	−0.508433	−	0.293544i	−0.732189	+	0.681101i	$0.761501\pi$
$578$	−23.0466	+	4.06374i	−0.958613	+	0.169029i
$579$	−30.0008	+	1.89409i	−1.24679	+	0.0787155i
$580$	8.51847	+	23.4043i	0.353710	+	0.971811i
$581$	9.88209	−	15.5963i	0.409978	−	0.647042i
$582$	14.5366	+	21.8690i	0.602563	+	0.906500i
$583$	3.46876	+	19.6723i	0.143662	+	0.814745i
$584$	43.6354	−	75.5787i	1.80565	−	3.12747i
$585$	−2.31534	−	18.2635i	−0.0957274	−	0.755101i
$586$	−50.3658	+	29.0787i	−2.08059	+	1.20123i
$587$	0.422612	−	0.354614i	0.0174431	−	0.0146365i	−0.634024	−	0.773313i	$-0.718598\pi$
$587$	0.422612	−	0.354614i	0.0174431	−	0.0146365i	0.651467	+	0.758677i	$0.274154\pi$
$588$	−52.0649	−	20.0962i	−2.14712	−	0.828752i
$589$	0.364629	−	2.06791i	0.0150243	−	0.0852069i
$590$	−43.2494	+	51.5426i	−1.78055	+	2.12198i
$591$	−8.12447	+	27.6269i	−0.334196	+	1.13642i
$592$	−13.4718	−	4.90332i	−0.553686	−	0.201525i
$593$	−24.4959			−1.00593			−0.502964	−	0.864307i	$-0.667757\pi$
$593$	−24.4959			−1.00593			−0.502964	+	0.864307i	$0.667757\pi$
$594$	−53.0234	+	31.6555i	−2.17558	+	1.29884i
$595$	19.9356	−	15.3751i	0.817280	−	0.630320i
$596$	−15.7323	+	43.2241i	−0.644420	+	1.77053i
$597$	−37.7136	+	9.13261i	−1.54351	+	0.373773i
$598$	−10.7050	+	12.7577i	−0.437758	+	0.521700i
$599$	5.18052	+	0.913465i	0.211670	+	0.0373232i	0.278478	−	0.960443i	$-0.410170\pi$
$599$	5.18052	+	0.913465i	0.211670	+	0.0373232i	−0.0668074	+	0.997766i	$0.521281\pi$
$600$	44.4816	−	60.3610i	1.81595	−	2.46423i
$601$	−17.5340	−	20.8963i	−0.715228	−	0.852376i	0.278930	−	0.960312i	$-0.410020\pi$
$601$	−17.5340	−	20.8963i	−0.715228	−	0.852376i	−0.994158	+	0.107936i	$0.965576\pi$
$602$	−0.795811	+	1.93470i	−0.0324348	+	0.0788524i
$603$	−0.781742	−	2.52149i	−0.0318350	−	0.102683i
$604$	19.7028	−	34.1262i	0.801694	−	1.38857i
$605$	6.11126	+	34.6587i	0.248458	+	1.40908i
$606$	23.1309	+	11.4760i	0.939627	+	0.466179i
$607$	−4.85192	−	13.3305i	−0.196933	−	0.541069i	0.801441	−	0.598074i	$-0.204067\pi$
$607$	−4.85192	−	13.3305i	−0.196933	−	0.541069i	−0.998374	+	0.0570048i	$0.981845\pi$
$608$	−4.54039	+	1.65257i	−0.184137	+	0.0670204i
$609$	7.18002	−	1.42864i	0.290949	−	0.0578914i
$610$	1.84129	+	10.4425i	0.0745518	+	0.422804i
$611$	−4.55091	−	2.62747i	−0.184110	−	0.106296i
$612$	−11.4883	−	37.0554i	−0.464389	−	1.49788i
$613$	−2.75943	−	4.77947i	−0.111452	−	0.193041i	0.804904	−	0.593405i	$-0.202217\pi$
$613$	−2.75943	−	4.77947i	−0.111452	−	0.193041i	−0.916356	+	0.400364i	$0.868884\pi$
$614$	−7.84563	+	6.58326i	−0.316624	+	0.265679i
$615$	58.3692	+	43.0138i	2.35367	+	1.73448i
$616$	37.9718	+	72.5074i	1.52993	+	2.92141i
$617$	25.0437	−	29.8460i	1.00822	−	1.20155i	0.0288310	−	0.999584i	$-0.490822\pi$
$617$	25.0437	−	29.8460i	1.00822	−	1.20155i	0.979392	−	0.201969i	$-0.0647340\pi$
$618$	−1.39495	−	5.76051i	−0.0561131	−	0.231722i
$619$	4.01593	−	11.0337i	0.161414	−	0.443481i	−0.832449	−	0.554102i	$-0.813062\pi$
$619$	4.01593	−	11.0337i	0.161414	−	0.443481i	0.993863	+	0.110621i	$0.0352840\pi$
$620$		−	48.3267i		−	1.94085i
$621$	−18.5856	+	0.271728i	−0.745814	+	0.0109041i
$622$		−	6.72187i		−	0.269522i
$623$	−43.0260	+	13.6824i	−1.72380	+	0.548176i
$624$	−7.06672	+	24.0301i	−0.282895	+	0.961972i
$625$	−11.8533	−	9.94610i	−0.474132	−	0.397844i
$626$	−11.6901	+	66.2978i	−0.467230	+	2.64979i
$627$	−0.603718	+	5.39292i	−0.0241102	+	0.215373i
$628$	−0.368799	−	0.439518i	−0.0147167	−	0.0175387i
$629$	−2.52304	−	4.37003i	−0.100600	−	0.174245i
$630$	−48.7335	−	48.9621i	−1.94159	−	1.95070i
$631$	13.6313	−	23.6101i	0.542654	−	0.939904i	−0.456097	−	0.889930i	$-0.650753\pi$
$631$	13.6313	−	23.6101i	0.542654	−	0.939904i	0.998751	−	0.0499740i	$-0.0159138\pi$
$632$	96.5675	−	17.0274i	3.84125	−	0.677315i
$633$	8.16096	+	12.2774i	0.324369	+	0.487983i
$634$	12.1034	−	4.40528i	0.480688	−	0.174956i
$635$	−38.9160	+	14.1642i	−1.54433	+	0.562091i
$636$	2.16970	+	34.3663i	0.0860341	+	1.36271i
$637$	−1.04321	+	12.6395i	−0.0413335	+	0.500794i
$638$	−16.4422	−	9.49294i	−0.650955	−	0.375829i
$639$	21.8299	−	33.9060i	0.863577	−	1.34130i
$640$	24.0199	−	13.8679i	0.949471	−	0.548178i
$641$	−13.0135	−	15.5088i	−0.514000	−	0.612562i	0.445151	−	0.895456i	$-0.353150\pi$
$641$	−13.0135	−	15.5088i	−0.514000	−	0.612562i	−0.959151	+	0.282894i	$0.908706\pi$
$642$	21.9230	−	9.58364i	0.865232	−	0.378236i
$643$	37.2220	+	6.56324i	1.46789	+	0.258829i	0.849729	−	0.527220i	$-0.176766\pi$
$643$	37.2220	+	6.56324i	1.46789	+	0.258829i	0.618164	+	0.786049i	$0.287877\pi$
$644$	−1.79325	+	43.5276i	−0.0706639	+	1.71523i
$645$	−1.30698	+	1.24516i	−0.0514621	+	0.0490282i
$646$	−4.59546	−	1.67261i	−0.180806	−	0.0658080i
$647$	23.4908			0.923517			0.461759	−	0.887006i	$-0.347219\pi$
$647$	23.4908			0.923517			0.461759	+	0.887006i	$0.347219\pi$
$648$	−54.8009	+	24.9167i	−2.15278	+	0.978819i
$649$		−	35.7547i		−	1.40350i
$650$	−28.3139	−	10.3054i	−1.11056	−	0.404211i
$651$	−14.0396	−	2.16004i	−0.550255	−	0.0846588i
$652$	40.2597	+	33.7819i	1.57669	+	1.32300i
$653$	−4.96907	−	0.876181i	−0.194455	−	0.0342876i	0.0755724	−	0.997140i	$-0.475922\pi$
$653$	−4.96907	−	0.876181i	−0.194455	−	0.0342876i	−0.270027	+	0.962853i	$0.587033\pi$
$654$	14.9370	+	34.1690i	0.584081	+	1.33611i
$655$	−30.8872	+	25.9175i	−1.20686	+	1.01268i
$656$	−49.3249	−	85.4332i	−1.92581	−	3.33561i
$657$	−17.9068	−	34.8055i	−0.698613	−	1.35789i
$658$	−19.5438	+	2.62190i	−0.761899	+	0.102212i
$659$	28.1030	−	4.95532i	1.09474	−	0.193032i	0.403014	−	0.915194i	$-0.367962\pi$
$659$	28.1030	−	4.95532i	1.09474	−	0.193032i	0.691724	+	0.722162i	$0.256851\pi$
$660$	7.86932	+	124.644i	0.306313	+	4.85176i
$661$	5.93347	+	16.3021i	0.230785	+	0.634077i	0.999988	−	0.00492766i	$-0.00156853\pi$
$661$	5.93347	+	16.3021i	0.230785	+	0.634077i	−0.769203	+	0.639005i	$0.779346\pi$
$662$	6.36639	+	17.4915i	0.247437	+	0.679827i
$663$	−7.34213	+	4.88042i	−0.285145	+	0.189540i
$664$	−45.9690	+	8.10558i	−1.78394	+	0.314558i
$665$	−6.01660	+	0.807154i	−0.233314	+	0.0313001i
$666$	−11.0253	+	8.37623i	−0.427220	+	0.324572i
$667$	−2.85732	−	4.94902i	−0.110636	−	0.191627i
$668$	35.9323	−	30.1508i	1.39026	−	1.16657i
$669$	5.18116	+	0.580012i	0.200315	+	0.0224246i
$670$	−7.54236	−	1.32992i	−0.291387	−	0.0513794i
$671$	−4.31646	−	3.62194i	−0.166635	−	0.139824i
$672$	11.8484	+	30.4628i	0.457063	+	1.17513i
$673$	−2.93848	−	1.06952i	−0.113270	−	0.0412270i	0.284763	−	0.958598i	$-0.408085\pi$
$673$	−2.93848	−	1.06952i	−0.113270	−	0.0412270i	−0.398034	+	0.917371i	$0.630307\pi$
$674$			1.49287i			0.0575031i
$675$	−11.9627	−	31.4298i	−0.460443	−	1.20973i
$676$	−44.7297			−1.72037
$677$	32.1288	+	11.6939i	1.23481	+	0.449434i	0.875242	−	0.483685i	$-0.160702\pi$
$677$	32.1288	+	11.6939i	1.23481	+	0.449434i	0.359568	+	0.933119i	$0.382924\pi$
$678$	12.1967	+	50.3668i	0.468410	+	1.93432i
$679$	0.642558	−	15.5969i	0.0246591	−	0.598552i
$680$	−62.6811	−	11.0524i	−2.40371	−	0.423839i
$681$	14.0212	+	10.3325i	0.537292	+	0.395944i
$682$	23.6797	+	28.2203i	0.906741	+	1.08061i
$683$	5.42717	−	3.13338i	0.207665	−	0.119895i	−0.392561	−	0.919726i	$-0.628411\pi$
$683$	5.42717	−	3.13338i	0.207665	−	0.119895i	0.600226	+	0.799831i	$0.295077\pi$
$684$	−2.06848	+	9.12295i	−0.0790904	+	0.348825i
$685$	17.7760	+	10.2630i	0.679186	+	0.392128i
$686$	25.8656	+	39.9476i	0.987553	+	1.52521i
$687$	−39.8579	−	19.7747i	−1.52067	−	0.754453i
$688$	2.30793	−	0.840019i	0.0879891	−	0.0320254i
$689$	7.35332	−	2.67639i	0.280139	−	0.101962i
$690$	−23.9665	+	48.3067i	−0.912389	+	1.83901i
$691$	22.6829	−	3.99961i	0.862898	−	0.152152i	0.275353	−	0.961343i	$-0.411205\pi$
$691$	22.6829	−	3.99961i	0.862898	−	0.152152i	0.587546	+	0.809191i	$0.300094\pi$
$692$	−43.4679	+	75.2887i	−1.65240	+	2.86205i
$693$	36.5625	+	3.28502i	1.38890	+	0.124788i
$694$	5.12126	+	8.87027i	0.194400	+	0.336711i
$695$	12.7881	+	15.2402i	0.485079	+	0.578095i
$696$	−14.8993	−	10.9797i	−0.564758	−	0.416184i
$697$	6.02951	−	34.1950i	0.228384	−	1.29523i
$698$	28.4450	+	23.8681i	1.07666	+	0.903423i
$699$	−0.431961	+	0.104603i	−0.0163383	+	0.00395643i
$700$	−75.1123	+	23.8860i	−2.83898	+	0.902806i
$701$			12.1725i			0.459751i	0.973220	+	0.229875i	$0.0738319\pi$
$701$			12.1725i			0.459751i	−0.973220	+	0.229875i	$0.926168\pi$
$702$	15.8191	+	18.3023i	0.597053	+	0.690775i
$703$			1.21673i			0.0458898i
$704$	3.74062	−	10.2773i	0.140980	−	0.387339i
$705$	−16.3242	−	4.80059i	−0.614804	−	0.180801i
$706$	−10.4319	+	12.4322i	−0.392609	+	0.467893i
$707$	−7.12105	−	13.5977i	−0.267815	−	0.511393i
$708$	6.85696	−	61.2522i	0.257700	−	2.30200i
$709$	10.1824	−	8.54408i	0.382410	−	0.320880i	−0.431238	−	0.902238i	$-0.641923\pi$
$709$	10.1824	−	8.54408i	0.382410	−	0.320880i	0.813648	+	0.581358i	$0.197479\pi$
$710$	−58.4953	−	101.317i	−2.19529	−	3.80235i
$711$	17.0250	−	40.5506i	0.638487	−	1.52076i
$712$	98.8511	+	57.0717i	3.70460	+	2.13885i
$713$	1.92547	+	10.9199i	0.0721093	+	0.408952i
$714$	−10.6321	+	31.3274i	−0.397897	+	1.17240i
$715$	26.6699	−	9.70706i	0.997398	−	0.363023i
$716$	8.51645	+	23.3988i	0.318275	+	0.874453i
$717$	1.44216	+	22.8426i	0.0538584	+	0.853074i
$718$	−14.5497	−	82.5153i	−0.542989	−	3.07944i
$719$	−5.03392	+	8.71901i	−0.187734	+	0.325164i	−0.944494	−	0.328528i	$-0.893447\pi$
$719$	−5.03392	+	8.71901i	−0.187734	+	0.325164i	0.756761	+	0.653692i	$0.226781\pi$
$720$	−3.92644	+	81.0087i	−0.146330	+	3.01902i
$721$	−1.34031	+	3.25843i	−0.0499157	+	0.121350i
$722$	−30.6249	−	36.4973i	−1.13974	−	1.35829i
$723$	−9.42892	−	21.5691i	−0.350665	−	0.802163i
$724$	−8.20787	−	1.44727i	−0.305043	−	0.0537874i
$725$	6.64587	−	7.92024i	0.246821	−	0.294150i
$726$	−31.8995	−	33.4830i	−1.18390	−	1.24267i
$727$	−7.35676	+	20.2125i	−0.272847	+	0.749641i	0.725279	+	0.688455i	$0.241711\pi$
$727$	−7.35676	+	20.2125i	−0.272847	+	0.749641i	−0.998126	+	0.0611864i	$0.980512\pi$
$728$	25.3892	−	19.5812i	0.940987	−	0.725727i
$729$	−3.90916	+	26.7155i	−0.144784	+	0.989463i
$730$	−113.556			−4.20289
$731$	0.812341	+	0.295668i	0.0300455	+	0.0109357i
$732$	−6.70001	−	7.03262i	−0.247640	−	0.259933i
$733$	10.3290	−	12.3096i	0.381510	−	0.454666i	−0.540780	−	0.841164i	$-0.681871\pi$
$733$	10.3290	−	12.3096i	0.381510	−	0.454666i	0.922290	+	0.386498i	$0.126315\pi$
$734$	−12.8620	+	72.9439i	−0.474744	+	2.69241i
$735$	6.34921	+	40.5718i	0.234194	+	1.49651i
$736$	19.5455	−	16.4006i	0.720455	−	0.604534i
$737$	3.52458	−	2.03492i	0.129830	−	0.0749572i
$738$	−95.1653	−	4.61260i	−3.50308	−	0.169792i
$739$	−14.4202	+	24.9765i	−0.530456	+	0.918777i	0.468912	+	0.883245i	$0.344646\pi$
$739$	−14.4202	+	24.9765i	−0.530456	+	0.918777i	−0.999369	+	0.0355323i	$0.988687\pi$
$740$	4.86263	+	27.5773i	0.178754	+	1.01376i
$741$	2.12157	−	0.133944i	0.0779379	−	0.00492057i
$742$	15.7163	−	24.8040i	0.576962	−	0.910582i
$743$	14.1355	+	38.8370i	0.518581	+	1.42479i	0.872084	+	0.489357i	$0.162768\pi$
$743$	14.1355	+	38.8370i	0.518581	+	1.42479i	−0.353502	+	0.935434i	$0.615009\pi$
$744$	19.8798	+	29.9072i	0.728827	+	1.09645i
$745$	33.3325	−	5.87741i	1.22121	−	0.215332i
$746$	5.97603	+	3.45026i	0.218798	+	0.126323i
$747$	−8.10442	+	19.3033i	−0.296525	+	0.706271i
$748$	51.7967	−	29.9048i	1.89387	−	1.09343i
$749$	−13.8934	−	3.04427i	−0.507653	−	0.111235i
$750$	−22.0520	−	2.46864i	−0.805226	−	0.0901421i
$751$	−4.57803	+	25.9633i	−0.167055	+	0.947415i	0.779866	+	0.625947i	$0.215287\pi$
$751$	−4.57803	+	25.9633i	−0.167055	+	0.947415i	−0.946920	+	0.321468i	$0.895824\pi$
$752$	17.7344	+	14.8810i	0.646709	+	0.542653i
$753$	39.5063	+	11.6179i	1.43969	+	0.423381i
$754$	−2.54376	+	6.98891i	−0.0926381	+	0.254521i
$755$	−28.9957			−1.05526
$756$	62.0060	+	12.6395i	2.25514	+	0.459695i
$757$	19.0655			0.692946			0.346473	−	0.938060i	$-0.387379\pi$
$757$	19.0655			0.692946			0.346473	+	0.938060i	$0.387379\pi$
$758$	−12.9714	+	35.6387i	−0.471143	+	1.29445i
$759$	−6.74429	−	27.8509i	−0.244802	−	1.01092i
$760$	11.7565	+	9.86490i	0.426454	+	0.357838i
$761$	8.16798	−	46.3229i	0.296089	−	1.67920i	−0.366654	−	0.930358i	$-0.619497\pi$
$761$	8.16798	−	46.3229i	0.296089	−	1.67920i	0.662743	−	0.748847i	$-0.269392\pi$
$762$	32.2840	−	43.8090i	1.16953	−	1.58703i
$763$	4.74477	−	21.6541i	0.171772	−	0.783930i
$764$	47.2037	−	27.2531i	1.70777	−	0.985981i
$765$	−19.3867	+	20.9541i	−0.700926	+	0.757596i
$766$	−65.4194	−	37.7699i	−2.36370	−	1.36468i
$767$	−13.7936	+	2.43219i	−0.498059	+	0.0878212i
$768$	−19.8389	+	39.9871i	−0.715874	+	1.44291i
$769$	−9.11120	−	25.0328i	−0.328558	−	0.902706i	−0.988477	−	0.151369i	$-0.951632\pi$
$769$	−9.11120	−	25.0328i	−0.328558	−	0.902706i	0.659919	−	0.751337i	$-0.270591\pi$
$770$	57.0016	−	89.9620i	2.05420	−	3.24200i
$771$	7.61838	−	15.3556i	0.274369	−	0.553017i
$772$	−13.8724	−	78.6740i	−0.499277	−	2.83154i
$773$	−3.41916	+	5.92216i	−0.122979	+	0.213005i	−0.920941	−	0.389702i	$-0.872578\pi$
$773$	−3.41916	+	5.92216i	−0.122979	+	0.213005i	0.797962	+	0.602707i	$0.205911\pi$
$774$	0.524518	−	2.31336i	0.0188534	−	0.0831521i
$775$	−17.3737	+	10.0307i	−0.624082	+	0.360314i
$776$	−30.2315	+	25.3673i	−1.08525	+	0.910632i
$777$	8.22894	−	0.180046i	0.295212	−	0.00645910i
$778$	−15.2908	+	86.7186i	−0.548203	+	3.10901i
$779$	−5.38170	+	6.41366i	−0.192819	+	0.229793i
$780$	47.5504	−	11.5147i	1.70258	−	0.412291i
$781$	58.4195	+	21.2630i	2.09041	+	0.760848i
$782$	25.8243			0.923474
$783$	−7.75803	+	2.95283i	−0.277249	+	0.105526i
$784$	14.1953	−	54.0392i	0.506976	−	1.92997i
$785$	−0.144394	+	0.396720i	−0.00515365	+	0.0141595i
$786$	14.9482	−	50.8307i	0.533185	−	1.81307i
$787$	−23.0217	+	27.4362i	−0.820636	+	0.977996i	−0.999983	−	0.00579002i	$-0.998157\pi$
$787$	−23.0217	+	27.4362i	−0.820636	+	0.977996i	0.179347	+	0.983786i	$0.442601\pi$
$788$	−75.3664	−	13.2891i	−2.68482	−	0.473405i
$789$	−17.2362	−	1.92953i	−0.613625	−	0.0686931i
$790$	−82.0139	−	97.7404i	−2.91792	−	3.47745i
$791$	11.7189	−	28.4899i	0.416677	−	1.01298i
$792$	−56.1437	−	73.8994i	−1.99498	−	2.62590i
$793$	−1.10366	+	1.91160i	−0.0391923	+	0.0678830i
$794$	10.6400	+	60.3423i	0.377598	+	2.14147i
$795$	21.1015	−	14.0265i	0.748393	−	0.497467i
$796$	−35.2701	−	96.9037i	−1.25011	−	3.43466i
$797$	21.1088	−	7.68297i	0.747712	−	0.272145i	0.0600693	−	0.998194i	$-0.480868\pi$
$797$	21.1088	−	7.68297i	0.747712	−	0.272145i	0.687643	+	0.726049i	$0.258646\pi$
$798$	5.99708	−	5.25993i	0.212294	−	0.186199i
$799$	1.41498	+	8.02473i	0.0500583	+	0.283894i
$800$	39.9778	+	23.0812i	1.41343	+	0.816043i
$801$	45.5229	−	23.4208i	1.60847	−	0.827532i
$802$	32.3121	+	55.9661i	1.14098	+	1.97623i
$803$	46.2258	−	38.7881i	1.63127	−	1.36880i
$804$	6.42829	−	2.81013i	0.226708	−	0.0991055i
$805$	28.3975	−	14.8717i	1.00088	−	0.524157i
$806$	9.27617	−	11.0549i	0.326739	−	0.389393i
$807$	−18.1980	+	17.3373i	−0.640598	+	0.610301i
$808$	−13.2723	+	36.4653i	−0.466918	+	1.28285i
$809$			18.6798i			0.656746i	0.944548	+	0.328373i	$0.106500\pi$
$809$			18.6798i			0.656746i	−0.944548	+	0.328373i	$0.893500\pi$
$810$	63.7308	+	45.5424i	2.23927	+	1.60020i
$811$			45.1917i			1.58689i	0.608640	+	0.793447i	$0.291716\pi$
$811$			45.1917i			1.58689i	−0.608640	+	0.793447i	$0.708284\pi$
$812$	5.89595	+	18.5405i	0.206907	+	0.650644i
$813$	−0.297648	−	0.312424i	−0.0104390	−	0.0109572i
$814$	−16.3522	−	13.7211i	−0.573143	−	0.480924i
$815$	6.71526	−	38.0841i	0.235225	−	1.33403i
$816$	35.5880	−	15.5573i	1.24583	−	0.544614i
$817$	−0.133986	−	0.159679i	−0.00468758	−	0.00558645i
$818$	−0.456936	−	0.791436i	−0.0159764	−	0.0276719i
$819$	−1.21983	−	14.3287i	−0.0426242	−	0.500686i
$820$	−96.3448	+	166.874i	−3.36451	+	5.82749i
$821$	−20.6869	+	3.64765i	−0.721976	+	0.127304i	−0.522550	−	0.852609i	$-0.675019\pi$
$821$	−20.6869	+	3.64765i	−0.721976	+	0.127304i	−0.199427	+	0.979913i	$0.563908\pi$
$822$	−26.9186	+	1.69949i	−0.938894	+	0.0592765i
$823$	−22.7468	+	8.27916i	−0.792904	+	0.288593i	−0.706543	−	0.707671i	$-0.749746\pi$
$823$	−22.7468	+	8.27916i	−0.792904	+	0.288593i	−0.0863611	+	0.996264i	$0.527524\pi$
$824$	8.37026	−	3.04653i	0.291592	−	0.106131i
$825$	43.1768	−	28.7002i	1.50322	−	0.999213i
$826$	−35.4126	+	38.8373i	−1.23216	+	1.35132i
$827$	−5.68375	−	3.28152i	−0.197644	−	0.114110i	0.397912	−	0.917423i	$-0.369735\pi$
$827$	−5.68375	−	3.28152i	−0.197644	−	0.114110i	−0.595556	+	0.803314i	$0.703068\pi$
$828$	−6.21261	−	49.0053i	−0.215903	−	1.70305i
$829$	23.4539	−	13.5411i	0.814588	−	0.470303i	−0.0339585	−	0.999423i	$-0.510811\pi$
$829$	23.4539	−	13.5411i	0.814588	−	0.470303i	0.848547	+	0.529121i	$0.177478\pi$
$830$	39.0411	+	46.5274i	1.35514	+	1.61499i
$831$	2.81815	−	25.1741i	0.0977607	−	0.873282i
$832$	−4.21926	−	0.743969i	−0.146276	−	0.0257925i
$833$	16.0537	−	11.3590i	0.556228	−	0.393565i
$834$	−25.0807	−	7.37568i	−0.868473	−	0.255399i
$835$	−32.4334	−	11.8048i	−1.12240	−	0.408521i
$836$	−14.4215			−0.498779
$837$	16.1050	−	0.235461i	0.556670	−	0.00813871i
$838$			68.4378i			2.36415i
$839$	0.0158875	+	0.00578259i	0.000548499	+	0.000199637i	0.342294	−	0.939593i	$-0.388796\pi$
$839$	0.0158875	+	0.00578259i	0.000548499	+	0.000199637i	−0.341746	+	0.939792i	$0.611018\pi$
$840$	64.9782	−	80.9711i	2.24196	−	2.79377i
$841$	20.2603	+	17.0004i	0.698630	+	0.586220i
$842$	72.1105	+	12.7150i	2.48509	+	0.438189i
$843$	24.4753	−	33.2127i	0.842975	−	1.14391i
$844$	−30.0125	+	25.1835i	−1.03307	+	0.866851i
$845$	16.4567	+	28.5038i	0.566127	+	0.980560i
$846$	21.3563	−	6.62114i	0.734246	−	0.227639i
$847$	3.65530	+	27.2469i	0.125597	+	0.936215i
$848$	−33.9504	+	5.98637i	−1.16586	+	0.205573i
$849$	29.9641	+	14.8661i	1.02837	+	0.510205i
$850$	15.9800	+	43.9046i	0.548109	+	1.50592i
$851$	−2.19751	−	6.03761i	−0.0753296	−	0.206966i
$852$	96.0019	+	47.6296i	3.28897	+	1.63176i
$853$	−48.3871	+	8.53196i	−1.65674	+	0.292129i	−0.922281	−	0.386520i	$-0.873677\pi$
$853$	−48.3871	+	8.53196i	−1.65674	+	0.292129i	−0.734463	+	0.678649i	$0.762566\pi$
$854$	1.10132	+	8.20936i	0.0376865	+	0.280919i
$855$	6.57457	−	2.03832i	0.224846	−	0.0697092i
$856$	17.9789	+	31.1403i	0.614505	+	1.06435i
$857$	−39.9664	+	33.5358i	−1.36523	+	1.14556i	−0.390897	+	0.920434i	$0.627835\pi$
$857$	−39.9664	+	33.5358i	−1.36523	+	1.14556i	−0.974329	+	0.225127i	$0.927720\pi$
$858$	−22.1249	+	30.0232i	−0.755331	+	1.02498i
$859$	−13.3149	−	2.34777i	−0.454297	−	0.0801048i	−0.0581825	−	0.998306i	$-0.518531\pi$
$859$	−13.3149	−	2.34777i	−0.454297	−	0.0801048i	−0.396114	+	0.918201i	$0.629642\pi$
$860$	−3.67496	−	3.08366i	−0.125315	−	0.105152i
$861$	44.1729	+	35.4482i	1.50541	+	1.20807i
$862$	63.0054	+	22.9321i	2.14597	+	0.781070i
$863$			4.93737i			0.168070i	0.996463	+	0.0840349i	$0.0267807\pi$
$863$			4.93737i			0.168070i	−0.996463	+	0.0840349i	$0.973219\pi$
$864$	−18.9984	−	31.8226i	−0.646339	−	1.08263i
$865$	63.9698			2.17504
$866$	51.4523	+	18.7271i	1.74842	+	0.636373i
$867$	−15.1333	−	4.45037i	−0.513954	−	0.151143i
$868$	1.55391	−	37.7180i	0.0527430	−	1.28023i
$869$	66.7717	+	11.7737i	2.26508	+	0.399394i
$870$	−2.67919	+	23.9328i	−0.0908332	+	0.811399i
$871$	−1.02480	−	1.22131i	−0.0347239	−	0.0413823i
$872$	−48.5349	+	28.0217i	−1.64360	+	0.948933i
$873$	2.22611	+	17.5596i	0.0753423	+	0.594303i
$874$	−5.39261	−	3.11342i	−0.182408	−	0.105313i
$875$	9.74713	+	8.88761i	0.329513	+	0.300456i
$876$	86.6291	−	57.5836i	2.92693	−	1.94557i
$877$	−28.7212	+	10.4537i	−0.969847	+	0.352995i	−0.777885	−	0.628407i	$-0.783707\pi$
$877$	−28.7212	+	10.4537i	−0.969847	+	0.352995i	−0.191962	+	0.981402i	$0.561485\pi$
$878$	−4.33247	+	1.57689i	−0.146214	+	0.0532174i
$879$	−39.1228	+	2.47000i	−1.31958	+	0.0833110i
$880$	−123.135	+	21.7121i	−4.15089	+	0.731915i
$881$	18.8633	−	32.6722i	0.635521	−	1.10075i	−0.350883	−	0.936419i	$-0.614119\pi$
$881$	18.8633	−	32.6722i	0.635521	−	1.10075i	0.986404	−	0.164336i	$-0.0525481\pi$
$882$	−36.4612	−	39.7809i	−1.22771	−	1.33949i
$883$	−22.0384	−	38.1716i	−0.741651	−	1.28458i	−0.951743	−	0.306896i	$-0.900710\pi$
$883$	−22.0384	−	38.1716i	−0.741651	−	1.28458i	0.210092	−	0.977682i	$-0.432624\pi$
$884$	−15.0602	−	17.9481i	−0.506531	−	0.603660i
$885$	−41.5554	+	18.1659i	−1.39687	+	0.610642i
$886$	−8.93056	+	50.6477i	−0.300028	+	1.70154i
$887$	22.3368	+	18.7428i	0.749998	+	0.629323i	0.935502	−	0.353321i	$-0.114948\pi$
$887$	22.3368	+	18.7428i	0.749998	+	0.629323i	−0.185505	+	0.982643i	$0.559392\pi$
$888$	−14.3535	−	15.0661i	−0.481672	−	0.505584i
$889$	−30.8286	+	9.80360i	−1.03396	+	0.328802i
$890$		−	148.522i		−	4.97848i
$891$	−41.4995	+	3.22977i	−1.39029	+	0.108201i
$892$			13.8553i			0.463908i
$893$	0.672002	−	1.84631i	0.0224877	−	0.0617844i
$894$	−32.2018	+	30.6788i	−1.07699	+	1.02605i
$895$	11.7774	−	14.0358i	0.393676	−	0.469165i
$896$	19.1930	−	10.0513i	0.641193	−	0.335790i
$897$	−10.2857	+	4.49638i	−0.343428	+	0.150130i
$898$	0.330137	−	0.277018i	0.0110168	−	0.00924421i
$899$	2.47595	+	4.28847i	0.0825776	+	0.143029i
$900$	79.4711	−	40.8866i	2.64904	−	1.36289i
$901$	−10.5085	−	6.06707i	−0.350088	−	0.202123i
$902$	−25.5064	−	144.654i	−0.849270	−	4.81645i
$903$	−1.06010	+	0.929799i	−0.0352781	+	0.0309418i
$904$	−73.1850	+	26.6372i	−2.43410	+	0.885939i
$905$	2.09752	+	5.76290i	0.0697240	+	0.191565i
$906$	31.7312	−	21.0922i	1.05420	−	0.700741i
$907$	−6.57304	−	37.2776i	−0.218254	−	1.23778i	−0.875169	−	0.483817i	$-0.839250\pi$
$907$	−6.57304	−	37.2776i	−0.218254	−	1.23778i	0.656915	−	0.753964i	$-0.271861\pi$
$908$	−23.1434	+	40.0856i	−0.768042	+	1.33029i
$909$	10.5289	+	13.8587i	0.349222	+	0.459665i
$910$	−38.5834	−	15.8708i	−1.27903	−	0.526110i
$911$	−27.6782	−	32.9856i	−0.917021	−	1.09286i	−0.995387	−	0.0959383i	$-0.969415\pi$
$911$	−27.6782	−	32.9856i	−0.917021	−	1.09286i	0.0783664	−	0.996925i	$-0.475030\pi$
$912$	−9.30707	−	1.04189i	−0.308188	−	0.0345005i
$913$	−31.7854	−	5.60462i	−1.05194	−	0.185486i
$914$	−33.7846	+	40.2629i	−1.11750	+	1.33178i
$915$	−2.01648	+	6.85695i	−0.0666627	+	0.226684i
$916$	40.4420	−	111.114i	1.33624	−	3.67130i
$917$	−24.9402	+	19.2349i	−0.823598	+	0.635192i
$918$	5.97313	−	37.0333i	0.197143	−	1.22228i
$919$	30.6114			1.00978			0.504888	−	0.863185i	$-0.331534\pi$
$919$	30.6114			1.00978			0.504888	+	0.863185i	$0.331534\pi$
$920$	−76.1545	−	27.7180i	−2.51074	−	0.913835i
$921$	−6.70948	+	1.62475i	−0.221085	+	0.0535373i
$922$	−3.19544	+	3.80818i	−0.105236	+	0.125416i
$923$	4.22898	−	23.9837i	0.139198	−	0.789434i
$924$	2.13403	+	97.5351i	0.0702043	+	3.20867i
$925$	8.90490	−	7.47210i	0.292791	−	0.245681i
$926$	88.9670	−	51.3651i	2.92364	−	1.68796i
$927$	0.883396	−	3.89618i	0.0290145	−	0.127967i
$928$	5.69729	−	9.86800i	0.187023	−	0.323933i
$929$	−0.783935	−	4.44592i	−0.0257201	−	0.145866i	0.969243	−	0.246104i	$-0.0791506\pi$
$929$	−0.783935	−	4.44592i	−0.0257201	−	0.145866i	−0.994963	+	0.100238i	$0.968039\pi$
$930$	20.7677	−	41.8593i	0.681000	−	1.37262i
$931$	−4.72179	+	0.436508i	−0.154750	+	0.0143060i
$932$	−0.403974	−	1.10991i	−0.0132326	−	0.0363563i
$933$	2.01368	−	4.05877i	0.0659251	−	0.132878i
$934$	−4.34695	+	0.766485i	−0.142237	+	0.0250801i
$935$	−38.1134	−	22.0048i	−1.24644	−	0.719633i
$936$	−24.6901	+	26.6863i	−0.807021	+	0.872269i
$937$	4.61706	−	2.66566i	0.150833	−	0.0870833i	−0.422684	−	0.906277i	$-0.638912\pi$
$937$	4.61706	−	2.66566i	0.150833	−	0.0870833i	0.573517	+	0.819194i	$0.305579\pi$
$938$	−5.84390	−	1.28050i	−0.190810	−	0.0418097i
$939$	−26.9196	+	36.5296i	−0.878489	+	1.19210i
$940$	7.85228	−	44.5325i	0.256113	−	1.45249i
$941$	9.86127	+	8.27459i	0.321468	+	0.269744i	0.789213	−	0.614120i	$-0.210489\pi$
$941$	9.86127	+	8.27459i	0.321468	+	0.269744i	−0.467745	+	0.883864i	$0.654933\pi$
$942$	−0.130567	−	0.539184i	−0.00425411	−	0.0175676i
$943$	15.1213	−	41.5453i	0.492416	−	1.35290i
$944$	61.7053			2.00834
$945$	−14.7584	−	44.1633i	−0.480090	−	1.43663i
$946$	3.65696			0.118898
$947$	9.46635	−	26.0086i	0.307615	−	0.845165i	−0.685505	−	0.728068i	$-0.740419\pi$
$947$	9.46635	−	26.0086i	0.307615	−	0.845165i	0.993120	−	0.117098i	$-0.0373591\pi$
$948$	112.130	+	32.9750i	3.64182	+	1.07098i
$949$	−18.1083	−	15.1947i	−0.587820	−	0.493240i
$950$	1.95630	−	11.0947i	0.0634707	−	0.359960i
$951$	8.62793	+	0.965865i	0.279780	+	0.0313203i
$952$	−48.5659	−	10.6416i	−1.57403	−	0.344896i
$953$	−39.2760	+	22.6760i	−1.27227	+	0.734547i	−0.975415	−	0.220374i	$-0.929272\pi$
$953$	−39.2760	+	22.6760i	−1.27227	+	0.734547i	−0.296858	+	0.954922i	$0.595939\pi$
$954$	−12.8891	+	30.6995i	−0.417300	+	0.993934i
$955$	−34.7338	−	20.0535i	−1.12396	−	0.648917i
$956$	−59.9024	+	10.5624i	−1.93738	+	0.341613i
$957$	−7.08427	−	10.6576i	−0.229002	−	0.344512i
$958$	26.3766	+	72.4692i	0.852191	+	2.34137i
$959$	13.5438	+	8.58161i	0.437352	+	0.277115i
$960$	−13.8451	+	0.874102i	−0.446848	+	0.0282115i
$961$	3.71462	+	21.0666i	0.119826	+	0.679569i
$962$	−4.18104	+	7.24178i	−0.134802	+	0.233484i
$963$	16.1085	+	0.780766i	0.519088	+	0.0251598i
$964$	54.1775	−	31.2794i	1.74494	−	1.00744i
$965$	−45.0308	+	37.7853i	−1.44959	+	1.21635i
$966$	−20.2586	+	36.9318i	−0.651810	+	1.18826i
$967$	−2.82307	+	16.0104i	−0.0907838	+	0.514860i	0.905174	+	0.425041i	$0.139740\pi$
$967$	−2.82307	+	16.0104i	−0.0907838	+	0.514860i	−0.995958	+	0.0898197i	$0.971371\pi$
$968$	44.6745	−	53.2409i	1.43589	−	1.71123i
$969$	−2.27375	−	2.38662i	−0.0730433	−	0.0766694i
$970$	48.2539	+	17.5630i	1.54934	+	0.563914i
$971$	−38.7014			−1.24199			−0.620993	−	0.783816i	$-0.713270\pi$
$971$	−38.7014			−1.24199			−0.620993	+	0.783816i	$0.713270\pi$
$972$	−71.7131	−	2.42569i	−2.30020	−	0.0778042i
$973$	9.49079	+	12.3059i	0.304261	+	0.394508i
$974$	32.6155	−	89.6104i	1.04507	−	2.87130i
$975$	−14.0092	−	14.7046i	−0.448652	−	0.470925i
$976$	6.25073	−	7.44932i	0.200081	−	0.238447i
$977$	−30.7656	−	5.42481i	−0.984279	−	0.173555i	−0.341729	−	0.939799i	$-0.611012\pi$
$977$	−30.7656	−	5.42481i	−0.984279	−	0.173555i	−0.642550	+	0.766244i	$0.722124\pi$
$978$	20.3546	+	46.5620i	0.650867	+	1.48889i
$979$	50.7318	+	60.4598i	1.62140	+	1.93230i
$980$	−105.275	+	28.7640i	−3.36290	+	0.918832i
$981$	−1.21689	+	25.1065i	−0.0388524	+	0.801588i
$982$	43.9161	−	76.0649i	1.40142	−	2.42733i
$983$	−2.40791	−	13.6559i	−0.0768003	−	0.435556i	−0.998827	−	0.0484290i	$-0.984579\pi$
$983$	−2.40791	−	13.6559i	−0.0768003	−	0.435556i	0.922026	−	0.387127i	$-0.126533\pi$
$984$	−9.02212	−	142.903i	−0.287615	−	4.55559i
$985$	19.2599	+	52.9161i	0.613671	+	1.68605i
$986$	10.8373	−	3.94445i	0.345130	−	0.125617i
$987$	−12.5863	−	4.27165i	−0.400627	−	0.135968i
$988$	0.981013	+	5.56360i	0.0312102	+	0.177002i
$989$	0.953253	+	0.550361i	0.0303117	+	0.0175005i
$990$	−46.7477	+	111.345i	−1.48574	+	3.53877i
$991$	0.458511	+	0.794164i	0.0145651	+	0.0252275i	0.873216	−	0.487333i	$-0.162030\pi$
$991$	0.458511	+	0.794164i	0.0145651	+	0.0252275i	−0.858651	+	0.512561i	$0.828697\pi$
$992$	−16.9367	+	14.2116i	−0.537742	+	0.451219i
$993$	−1.39584	+	12.4688i	−0.0442957	+	0.395687i
$994$	−42.3966	−	80.9566i	−1.34474	−	2.56779i
$995$	−48.7751	+	58.1278i	−1.54627	+	1.84278i
$996$	−53.3773	−	15.6971i	−1.69133	−	0.497382i
$997$	−5.13116	+	14.0978i	−0.162506	+	0.446480i	−0.994043	−	0.108988i	$-0.965239\pi$
$997$	−5.13116	+	14.0978i	−0.162506	+	0.446480i	0.831537	+	0.555469i	$0.187461\pi$
$998$			60.3227i			1.90948i
$999$	−9.16651	+	1.75484i	−0.290016	+	0.0555208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.be.a.104.1	yes	132
3.2	odd	2		567.2.be.a.503.22		132
7.6	odd	2	inner	189.2.be.a.104.2	yes	132
21.20	even	2		567.2.be.a.503.21		132
27.7	even	9		567.2.be.a.62.21		132
27.20	odd	18	inner	189.2.be.a.20.2	yes	132
189.20	even	18	inner	189.2.be.a.20.1	✓	132
189.34	odd	18		567.2.be.a.62.22		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.1	✓	132	189.20	even	18	inner
189.2.be.a.20.2	yes	132	27.20	odd	18	inner
189.2.be.a.104.1	yes	132	1.1	even	1	trivial
189.2.be.a.104.2	yes	132	7.6	odd	2	inner
567.2.be.a.62.21		132	27.7	even	9
567.2.be.a.62.22		132	189.34	odd	18
567.2.be.a.503.21		132	21.20	even	2
567.2.be.a.503.22		132	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.878867 + 2.41467i) q^{2} +(-1.25404 + 1.19473i) q^{3} +(-3.52612 - 2.95877i) q^{4} +(-0.588152 + 3.33557i) q^{5} +(-1.78274 - 4.07810i) q^{6} +(-0.566293 + 2.58444i) q^{7} +(5.79269 - 3.34441i) q^{8} +(0.145238 - 2.99648i) q^{9} +(-7.53740 - 4.35172i) q^{10} +(4.55474 - 0.803123i) q^{11} +(7.95683 - 0.502350i) q^{12} +(-0.619664 - 1.70251i) q^{13} +(-5.74286 - 3.63879i) q^{14} +(-3.24755 - 4.88563i) q^{15} +(1.38602 + 7.86054i) q^{16} +(-1.40471 + 2.43302i) q^{17} +(7.10786 + 2.98421i) q^{18} +(0.586660 - 0.338709i) q^{19} +(11.9431 - 10.0214i) q^{20} +(-2.37755 - 3.91756i) q^{21} +(-2.06373 + 11.7040i) q^{22} +(-2.29937 + 2.74028i) q^{23} +(-3.26860 + 11.1147i) q^{24} +(-6.08167 - 2.21355i) q^{25} +4.65561 q^{26} +(3.39786 + 3.93123i) q^{27} +(9.64357 - 7.43751i) q^{28} +(-0.546385 + 1.50118i) q^{29} +(14.6513 - 3.54793i) q^{30} +(1.99247 - 2.37454i) q^{31} +(-7.02429 - 1.23857i) q^{32} +(-4.75231 + 6.44883i) q^{33} +(-4.64039 - 5.53021i) q^{34} +(-8.28751 - 3.40895i) q^{35} +(-9.37802 + 10.1362i) q^{36} +(-0.898066 + 1.55550i) q^{37} +(0.302272 + 1.71427i) q^{38} +(2.81113 + 1.39469i) q^{39} +(7.74856 + 21.2890i) q^{40} +(-11.6140 + 4.22715i) q^{41} +(11.5491 - 2.29798i) q^{42} +(-0.0534327 - 0.303032i) q^{43} +(-18.4368 - 10.6445i) q^{44} +(9.90957 + 2.24684i) q^{45} +(-4.59602 - 7.96055i) q^{46} +(2.22186 - 1.86436i) q^{47} +(-11.1294 - 8.20151i) q^{48} +(-6.35862 - 2.92710i) q^{49} +(10.6900 - 12.7398i) q^{50} +(-1.14525 - 4.72936i) q^{51} +(-2.85233 + 7.83672i) q^{52} +4.31910i q^{53} +(-12.4789 + 4.74966i) q^{54} +15.6650i q^{55} +(5.36306 + 16.8648i) q^{56} +(-0.331031 + 1.12566i) q^{57} +(-3.14465 - 2.63868i) q^{58} +(1.34243 - 7.61331i) q^{59} +(-3.00420 + 26.8361i) q^{60} +(-0.783123 - 0.933289i) q^{61} +(3.98260 + 6.89806i) q^{62} +(7.66197 + 2.07224i) q^{63} +(1.18236 - 2.04791i) q^{64} +(6.04332 - 1.06560i) q^{65} +(-11.3951 - 17.1429i) q^{66} +(0.826896 - 0.300966i) q^{67} +(12.1519 - 4.42294i) q^{68} +(-0.390395 - 6.18355i) q^{69} +(15.5151 - 17.0156i) q^{70} +(11.6410 + 6.72094i) q^{71} +(-9.18016 - 17.8434i) q^{72} +(11.2992 - 6.52362i) q^{73} +(-2.96672 - 3.53560i) q^{74} +(10.2713 - 4.49008i) q^{75} +(-3.07080 - 0.541464i) q^{76} +(-0.503696 + 12.2262i) q^{77} +(-5.83832 + 5.56220i) q^{78} +(13.7757 + 5.01396i) q^{79} -27.0346 q^{80} +(-8.95781 - 0.870403i) q^{81} -31.7590i q^{82} +(-6.55767 - 2.38680i) q^{83} +(-3.20761 + 20.8484i) q^{84} +(-7.28935 - 6.11649i) q^{85} +(0.778681 + 0.137302i) q^{86} +(-1.10832 - 2.53533i) q^{87} +(23.6982 - 19.8852i) q^{88} +(8.53240 + 14.7785i) q^{89} +(-14.1346 + 21.9536i) q^{90} +(4.75095 - 0.637362i) q^{91} +(16.2157 - 2.85927i) q^{92} +(0.338289 + 5.35823i) q^{93} +(2.54910 + 7.00358i) q^{94} +(0.784742 + 2.15606i) q^{95} +(10.2885 - 6.83891i) q^{96} +(-5.81042 + 1.02453i) q^{97} +(12.6564 - 12.7814i) q^{98} +(-1.74502 - 13.7648i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30}+ \cdots - 192 q^{99}+O(q^{100}) \) 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more