LMFDB - Embedded newform 180.2.n.d.119.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [180,2,Mod(59,180)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("180.59"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			119.1
Character	$\chi$	$=$	180.119
Dual form			180.2.n.d.59.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41350 - 0.0449209i) q^{2} +(1.62879 - 0.589100i) q^{3} +(1.99596 + 0.126991i) q^{4} +(-1.91817 - 1.14918i) q^{5} +(-2.32876 + 0.759526i) q^{6} +(1.44473 - 2.50234i) q^{7} +(-2.81559 - 0.269163i) q^{8} +(2.30592 - 1.91904i) q^{9} +(2.65972 + 1.71053i) q^{10} +(0.395318 - 0.684712i) q^{11} +(3.32582 - 0.968981i) q^{12} +(-4.04214 + 2.33373i) q^{13} +(-2.15453 + 3.47216i) q^{14} +(-3.80129 - 0.741776i) q^{15} +(3.96775 + 0.506941i) q^{16} +5.89560 q^{17} +(-3.34563 + 2.60898i) q^{18} -4.55505i q^{19} +(-3.68267 - 2.53731i) q^{20} +(0.879030 - 4.92689i) q^{21} +(-0.589540 + 0.950082i) q^{22} +(-1.15468 + 0.666656i) q^{23} +(-4.74457 + 1.22026i) q^{24} +(2.35878 + 4.40865i) q^{25} +(5.81840 - 3.11715i) q^{26} +(2.62536 - 4.48414i) q^{27} +(3.20140 - 4.81112i) q^{28} +(2.29484 + 1.32492i) q^{29} +(5.33980 + 1.21926i) q^{30} +(2.26893 - 1.30997i) q^{31} +(-5.58564 - 0.894795i) q^{32} +(0.240527 - 1.34813i) q^{33} +(-8.33343 - 0.264836i) q^{34} +(-5.64688 + 3.13968i) q^{35} +(4.84624 - 3.53751i) q^{36} +7.44000i q^{37} +(-0.204617 + 6.43857i) q^{38} +(-5.20900 + 6.18239i) q^{39} +(5.09147 + 3.75192i) q^{40} +(-5.91566 + 3.41541i) q^{41} +(-1.46383 + 6.92467i) q^{42} +(-5.95249 + 10.3100i) q^{43} +(0.875994 - 1.31646i) q^{44} +(-6.62848 + 1.03114i) q^{45} +(1.66209 - 0.890449i) q^{46} +(2.60947 + 1.50658i) q^{47} +(6.76127 - 1.51170i) q^{48} +(-0.674484 - 1.16824i) q^{49} +(-3.13609 - 6.33758i) q^{50} +(9.60270 - 3.47310i) q^{51} +(-8.36434 + 4.14473i) q^{52} +1.70763 q^{53} +(-3.91237 + 6.22040i) q^{54} +(-1.54515 + 0.859104i) q^{55} +(-4.74130 + 6.65671i) q^{56} +(-2.68338 - 7.41923i) q^{57} +(-3.18423 - 1.97587i) q^{58} +(5.29436 + 9.17010i) q^{59} +(-7.49303 - 1.96329i) q^{60} +(-0.869749 + 1.50645i) q^{61} +(-3.26598 + 1.74972i) q^{62} +(-1.47067 - 8.54271i) q^{63} +(7.85510 + 1.51570i) q^{64} +(10.4354 + 0.168643i) q^{65} +(-0.400545 + 1.89478i) q^{66} +(-3.76721 - 6.52500i) q^{67} +(11.7674 + 0.748690i) q^{68} +(-1.48801 + 1.76607i) q^{69} +(8.12290 - 4.18427i) q^{70} -2.88566 q^{71} +(-7.00907 + 4.78257i) q^{72} -6.50847i q^{73} +(0.334212 - 10.5164i) q^{74} +(6.43909 + 5.79121i) q^{75} +(0.578452 - 9.09172i) q^{76} +(-1.14226 - 1.97845i) q^{77} +(7.64065 - 8.50481i) q^{78} +(-3.30854 - 1.91019i) q^{79} +(-7.02826 - 5.53205i) q^{80} +(1.63455 - 8.85032i) q^{81} +(8.51521 - 4.56194i) q^{82} +(8.33679 + 4.81325i) q^{83} +(2.38019 - 9.72226i) q^{84} +(-11.3088 - 6.77510i) q^{85} +(8.87697 - 14.3058i) q^{86} +(4.51832 + 0.806137i) q^{87} +(-1.29735 + 1.82146i) q^{88} -0.00741921i q^{89} +(9.41568 - 1.15976i) q^{90} +13.4864i q^{91} +(-2.38937 + 1.18399i) q^{92} +(2.92391 - 3.47029i) q^{93} +(-3.62081 - 2.24677i) q^{94} +(-5.23457 + 8.73738i) q^{95} +(-9.62496 + 1.83307i) q^{96} +(5.74925 + 3.31933i) q^{97} +(0.900905 + 1.68161i) q^{98} +(-0.402417 - 2.33752i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{4} - 18 q^{5} - 12 q^{9} - 16 q^{10} - 42 q^{14} + 30 q^{16} - 12 q^{21} - 6 q^{24} - 26 q^{25} - 12 q^{30} - 4 q^{34} + 96 q^{36} + 10 q^{40} + 96 q^{41} - 66 q^{45} + 4 q^{46} + 32 q^{49}+ \cdots + 54 q^{96}+O(q^{100}) $ 48 * q - 2 * q^4 - 18 * q^5 - 12 * q^9 - 16 * q^10 - 42 * q^14 + 30 * q^16 - 12 * q^21 - 6 * q^24 - 26 * q^25 - 12 * q^30 - 4 * q^34 + 96 * q^36 + 10 * q^40 + 96 * q^41 - 66 * q^45 + 4 * q^46 + 32 * q^49 - 90 * q^50 - 30 * q^54 + 6 * q^56 - 42 * q^60 + 8 * q^61 - 20 * q^64 - 6 * q^65 + 36 * q^66 - 96 * q^69 + 4 * q^70 + 72 * q^74 + 36 * q^81 - 6 * q^84 - 4 * q^85 + 108 * q^86 - 6 * q^90 - 62 * q^94 + 54 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.41350	−	0.0449209i	−0.999495	−	0.0317639i
$2$	−1.41350	−	0.0449209i	−0.999495	−	0.0317639i
$3$	1.62879	−	0.589100i	0.940383	−	0.340117i
$3$	1.62879	−	0.589100i	0.940383	−	0.340117i
$4$	1.99596	+	0.126991i	0.997982	+	0.0634957i
$5$	−1.91817	−	1.14918i	−0.857833	−	0.513928i
$5$	−1.91817	−	1.14918i	−0.857833	−	0.513928i
$6$	−2.32876	+	0.759526i	−0.950712	+	0.310075i
$7$	1.44473	−	2.50234i	0.546056	−	0.945797i	−0.452483	−	0.891773i	$-0.649462\pi$
$7$	1.44473	−	2.50234i	0.546056	−	0.945797i	0.998540	−	0.0540243i	$-0.0172049\pi$
$8$	−2.81559	−	0.269163i	−0.995462	−	0.0951634i
$9$	2.30592	−	1.91904i	0.768641	−	0.639681i
$10$	2.65972	+	1.71053i	0.841076	+	0.540917i
$11$	0.395318	−	0.684712i	0.119193	−	0.206448i	−0.800255	−	0.599660i	$-0.795303\pi$
$11$	0.395318	−	0.684712i	0.119193	−	0.206448i	0.919448	+	0.393211i	$0.128636\pi$
$12$	3.32582	−	0.968981i	0.960081	−	0.279721i
$13$	−4.04214	+	2.33373i	−1.12109	+	0.647261i	−0.941679	−	0.336514i	$-0.890752\pi$
$13$	−4.04214	+	2.33373i	−1.12109	+	0.647261i	−0.179410	+	0.983774i	$0.557419\pi$
$14$	−2.15453	+	3.47216i	−0.575823	+	0.927975i
$15$	−3.80129	−	0.741776i	−0.981488	−	0.191526i
$16$	3.96775	+	0.506941i	0.991937	+	0.126735i
$17$	5.89560			1.42989			0.714946	−	0.699179i	$-0.246451\pi$
$17$	5.89560			1.42989			0.714946	+	0.699179i	$0.246451\pi$
$18$	−3.34563	+	2.60898i	−0.788571	+	0.614943i
$19$		−	4.55505i		−	1.04500i	−0.852639	−	0.522500i	$-0.824999\pi$
$19$		−	4.55505i		−	1.04500i	0.852639	−	0.522500i	$-0.175001\pi$
$20$	−3.68267	−	2.53731i	−0.823470	−	0.567360i
$21$	0.879030	−	4.92689i	0.191820	−	1.07513i
$22$	−0.589540	+	0.950082i	−0.125690	+	0.202558i
$23$	−1.15468	+	0.666656i	−0.240768	+	0.139007i	−0.615530	−	0.788114i	$-0.711058\pi$
$23$	−1.15468	+	0.666656i	−0.240768	+	0.139007i	0.374762	+	0.927121i	$0.377725\pi$
$24$	−4.74457	+	1.22026i	−0.968482	+	0.249084i
$25$	2.35878	+	4.40865i	0.471755	+	0.881730i
$26$	5.81840	−	3.11715i	1.14108	−	0.611324i
$27$	2.62536	−	4.48414i	0.505250	−	0.862973i
$28$	3.20140	−	4.81112i	0.605008	−	0.909216i
$29$	2.29484	+	1.32492i	0.426140	+	0.246032i	0.697701	−	0.716389i	$-0.254206\pi$
$29$	2.29484	+	1.32492i	0.426140	+	0.246032i	−0.271561	+	0.962421i	$0.587540\pi$
$30$	5.33980	+	1.21926i	0.974909	+	0.222605i
$31$	2.26893	−	1.30997i	0.407512	−	0.235277i	−0.282208	−	0.959353i	$-0.591067\pi$
$31$	2.26893	−	1.30997i	0.407512	−	0.235277i	0.689720	+	0.724076i	$0.257734\pi$
$32$	−5.58564	−	0.894795i	−0.987410	−	0.158179i
$33$	0.240527	−	1.34813i	0.0418704	−	0.234680i
$34$	−8.33343	−	0.264836i	−1.42917	−	0.0454189i
$35$	−5.64688	+	3.13968i	−0.954497	+	0.530702i
$36$	4.84624	−	3.53751i	0.807707	−	0.589585i
$37$			7.44000i			1.22313i	0.791195	+	0.611564i	$0.209459\pi$
$37$			7.44000i			1.22313i	−0.791195	+	0.611564i	$0.790541\pi$
$38$	−0.204617	+	6.43857i	−0.0331933	+	1.04447i
$39$	−5.20900	+	6.18239i	−0.834108	+	0.989975i
$40$	5.09147	+	3.75192i	0.805033	+	0.593230i
$41$	−5.91566	+	3.41541i	−0.923871	+	0.533397i	−0.884868	−	0.465842i	$-0.845751\pi$
$41$	−5.91566	+	3.41541i	−0.923871	+	0.533397i	−0.0390029	+	0.999239i	$0.512418\pi$
$42$	−1.46383	+	6.92467i	−0.225874	+	1.06850i
$43$	−5.95249	+	10.3100i	−0.907746	+	1.57226i	−0.0905567	+	0.995891i	$0.528865\pi$
$43$	−5.95249	+	10.3100i	−0.907746	+	1.57226i	−0.817189	+	0.576370i	$0.804469\pi$
$44$	0.875994	−	1.31646i	0.132061	−	0.198463i
$45$	−6.62848	+	1.03114i	−0.988115	+	0.153713i
$46$	1.66209	−	0.890449i	0.245062	−	0.131290i
$47$	2.60947	+	1.50658i	0.380631	+	0.219757i	0.678093	−	0.734976i	$-0.262807\pi$
$47$	2.60947	+	1.50658i	0.380631	+	0.219757i	−0.297462	+	0.954734i	$0.596140\pi$
$48$	6.76127	−	1.51170i	0.975905	−	0.218195i
$49$	−0.674484	−	1.16824i	−0.0963548	−	0.166891i
$50$	−3.13609	−	6.33758i	−0.443510	−	0.896269i
$51$	9.60270	−	3.47310i	1.34465	−	0.486331i
$52$	−8.36434	+	4.14473i	−1.15992	+	0.574770i
$53$	1.70763			0.234561			0.117281	−	0.993099i	$-0.462582\pi$
$53$	1.70763			0.234561			0.117281	+	0.993099i	$0.462582\pi$
$54$	−3.91237	+	6.22040i	−0.532406	+	0.846489i
$55$	−1.54515	+	0.859104i	−0.208347	+	0.115842i
$56$	−4.74130	+	6.65671i	−0.633583	+	0.889540i
$57$	−2.68338	−	7.41923i	−0.355423	−	0.982701i
$58$	−3.18423	−	1.97587i	−0.418111	−	0.259444i
$59$	5.29436	+	9.17010i	0.689267	+	1.19385i	0.972075	+	0.234669i	$0.0754007\pi$
$59$	5.29436	+	9.17010i	0.689267	+	1.19385i	−0.282808	+	0.959176i	$0.591266\pi$
$60$	−7.49303	−	1.96329i	−0.967346	−	0.253460i
$61$	−0.869749	+	1.50645i	−0.111360	+	0.192881i	−0.916319	−	0.400450i	$-0.868854\pi$
$61$	−0.869749	+	1.50645i	−0.111360	+	0.192881i	0.804959	+	0.593331i	$0.202187\pi$
$62$	−3.26598	+	1.74972i	−0.414779	+	0.222214i
$63$	−1.47067	−	8.54271i	−0.185287	−	1.07628i
$64$	7.85510	+	1.51570i	0.981888	+	0.189463i
$65$	10.4354	+	0.168643i	1.29435	+	0.0209175i
$66$	−0.400545	+	1.89478i	−0.0493037	+	0.233232i
$67$	−3.76721	−	6.52500i	−0.460238	−	0.797155i	0.538735	−	0.842476i	$-0.318903\pi$
$67$	−3.76721	−	6.52500i	−0.460238	−	0.797155i	−0.998973	+	0.0453201i	$0.985569\pi$
$68$	11.7674	+	0.748690i	1.42701	+	0.0907920i
$69$	−1.48801	+	1.76607i	−0.179135	+	0.212610i
$70$	8.12290	−	4.18427i	0.970873	−	0.500116i
$71$	−2.88566			−0.342465			−0.171233	−	0.985231i	$-0.554775\pi$
$71$	−2.88566			−0.342465			−0.171233	+	0.985231i	$0.554775\pi$
$72$	−7.00907	+	4.78257i	−0.826026	+	0.563631i
$73$		−	6.50847i		−	0.761759i	−0.924625	−	0.380880i	$-0.875621\pi$
$73$		−	6.50847i		−	0.761759i	0.924625	−	0.380880i	$-0.124379\pi$
$74$	0.334212	−	10.5164i	0.0388513	−	1.22251i
$75$	6.43909	+	5.79121i	0.743522	+	0.668711i
$76$	0.578452	−	9.09172i	0.0663530	−	1.04289i
$77$	−1.14226	−	1.97845i	−0.130172	−	0.225465i
$78$	7.64065	−	8.50481i	0.865133	−	0.962981i
$79$	−3.30854	−	1.91019i	−0.372240	−	0.214913i	0.302197	−	0.953246i	$-0.402280\pi$
$79$	−3.30854	−	1.91019i	−0.372240	−	0.214913i	−0.674436	+	0.738333i	$0.735613\pi$
$80$	−7.02826	−	5.53205i	−0.785783	−	0.618502i
$81$	1.63455	−	8.85032i	0.181617	−	0.983369i
$82$	8.51521	−	4.56194i	0.940347	−	0.503782i
$83$	8.33679	+	4.81325i	0.915081	+	0.528322i	0.882063	−	0.471132i	$-0.156155\pi$
$83$	8.33679	+	4.81325i	0.915081	+	0.528322i	0.0330187	+	0.999455i	$0.489488\pi$
$84$	2.38019	−	9.72226i	0.259699	−	1.06079i
$85$	−11.3088	−	6.77510i	−1.22661	−	0.734862i
$86$	8.87697	−	14.3058i	0.957229	−	1.54263i
$87$	4.51832	+	0.806137i	0.484415	+	0.0864269i
$88$	−1.29735	+	1.82146i	−0.138298	+	0.194169i
$89$		−	0.00741921i		−	0.000786434i	−1.00000		0.000393217i	$-0.999875\pi$
$89$		−	0.00741921i		−	0.000786434i	1.00000		0.000393217i	$-0.000125165\pi$
$90$	9.41568	−	1.15976i	0.992499	−	0.122249i
$91$			13.4864i			1.41376i
$92$	−2.38937	+	1.18399i	−0.249109	+	0.123439i
$93$	2.92391	−	3.47029i	0.303195	−	0.359852i
$94$	−3.62081	−	2.24677i	−0.373459	−	0.231737i
$95$	−5.23457	+	8.73738i	−0.537055	+	0.896436i
$96$	−9.62496	+	1.83307i	−0.982343	+	0.187087i
$97$	5.74925	+	3.31933i	0.583748	+	0.337027i	0.762621	−	0.646845i	$-0.223912\pi$
$97$	5.74925	+	3.31933i	0.583748	+	0.337027i	−0.178874	+	0.983872i	$0.557245\pi$
$98$	0.900905	+	1.68161i	0.0910051	+	0.169868i
$99$	−0.402417	−	2.33752i	−0.0404445	−	0.234930i
$100$	4.14817	+	9.09905i	0.414817	+	0.909905i
$101$	−2.20027	−	1.27033i	−0.218935	−	0.126402i	0.386522	−	0.922280i	$-0.373676\pi$
$101$	−2.20027	−	1.27033i	−0.218935	−	0.126402i	−0.605457	+	0.795878i	$0.707010\pi$
$102$	−13.7294	+	4.47786i	−1.35942	+	0.443374i
$103$	−3.82824	−	6.63071i	−0.377208	−	0.653343i	0.613447	−	0.789736i	$-0.289782\pi$
$103$	−3.82824	−	6.63071i	−0.377208	−	0.653343i	−0.990655	+	0.136393i	$0.956449\pi$
$104$	12.0092	−	5.48284i	1.17760	−	0.537637i
$105$	−7.34801	+	8.44046i	−0.717092	+	0.823704i
$106$	−2.41374	−	0.0767084i	−0.234443	−	0.00745058i
$107$		−	13.7118i		−	1.32557i	−0.748808	−	0.662787i	$-0.769374\pi$
$107$		−	13.7118i		−	1.32557i	0.748808	−	0.662787i	$-0.230626\pi$
$108$	5.80956	−	8.61678i	0.559026	−	0.829150i
$109$	−13.2664			−1.27069			−0.635347	−	0.772227i	$-0.719143\pi$
$109$	−13.2664			−1.27069			−0.635347	+	0.772227i	$0.719143\pi$
$110$	2.22265	−	1.14493i	0.211922	−	0.109165i
$111$	4.38291	+	12.1182i	0.416007	+	1.15021i
$112$	7.00086	−	9.19627i	0.661519	−	0.868966i
$113$	4.62487	+	8.01051i	0.435071	+	0.753565i	0.997301	−	0.0734153i	$-0.0233899\pi$
$113$	4.62487	+	8.01051i	0.435071	+	0.753565i	−0.562230	+	0.826981i	$0.690057\pi$
$114$	3.45968	+	10.6076i	0.324029	+	0.993495i
$115$	2.98099	+	0.0481746i	0.277979	+	0.00449231i
$116$	4.41216	+	2.93593i	0.409659	+	0.272594i
$117$	−4.84233	+	13.1384i	−0.447674	+	1.21465i
$118$	−7.07165	−	13.1998i	−0.650998	−	1.21514i
$119$	8.51754	−	14.7528i	0.780802	−	1.35239i
$120$	10.5032	+	3.11170i	0.958807	+	0.284058i
$121$	5.18745	+	8.98492i	0.471586	+	0.816811i
$122$	1.29706	−	2.09030i	0.117430	−	0.189247i
$123$	−7.62336	+	9.04790i	−0.687375	+	0.815822i
$124$	4.69506	−	2.32651i	0.421628	−	0.208927i
$125$	0.541784	−	11.1672i	0.0484587	−	0.998825i
$126$	1.69505	+	12.1412i	0.151007	+	1.08162i
$127$	9.77239			0.867159			0.433580	−	0.901115i	$-0.357250\pi$
$127$	9.77239			0.867159			0.433580	+	0.901115i	$0.357250\pi$
$128$	−11.0351	−	2.49531i	−0.975374	−	0.220556i
$129$	−3.62173	+	20.2995i	−0.318875	+	1.78727i
$130$	−14.7429	−	0.707144i	−1.29304	−	0.0620206i
$131$	−6.61827	−	11.4632i	−0.578241	−	1.00154i	−0.995681	−	0.0928382i	$-0.970406\pi$
$131$	−6.61827	−	11.4632i	−0.578241	−	1.00154i	0.417440	−	0.908704i	$-0.362927\pi$
$132$	0.651285	−	2.66028i	0.0566871	−	0.231548i
$133$	−11.3983	−	6.58082i	−0.988359	−	0.570629i
$134$	5.03184	+	9.39231i	0.434685	+	0.811372i
$135$	−10.1890	+	5.58435i	−0.876927	+	0.480624i
$136$	−16.5996	−	1.58688i	−1.42340	−	0.136073i
$137$	1.57622	−	2.73010i	0.134666	−	0.233248i	−0.790804	−	0.612069i	$-0.790337\pi$
$137$	1.57622	−	2.73010i	0.134666	−	0.233248i	0.925470	+	0.378822i	$0.123671\pi$
$138$	2.18264	−	2.42949i	0.185798	−	0.206812i
$139$	2.22556	−	1.28493i	0.188770	−	0.108986i	−0.402637	−	0.915360i	$-0.631906\pi$
$139$	2.22556	−	1.28493i	0.188770	−	0.108986i	0.591407	+	0.806374i	$0.298573\pi$
$140$	−11.6697	+	5.54958i	−0.986268	+	0.469025i
$141$	5.13782	+	0.916663i	0.432682	+	0.0771970i
$142$	4.07889	+	0.129627i	0.342293	+	0.0108780i
$143$			3.69027i			0.308596i
$144$	10.1222	−	6.44531i	0.843513	−	0.537109i
$145$	−2.87932	−	5.17861i	−0.239114	−	0.430060i
$146$	−0.292366	+	9.19973i	−0.0241964	+	0.761375i
$147$	−1.78680	−	1.50548i	−0.147373	−	0.124170i
$148$	−0.944816	+	14.8500i	−0.0776634	+	1.22066i
$149$	8.52719	−	4.92318i	0.698575	−	0.403322i	−0.108242	−	0.994125i	$-0.534522\pi$
$149$	8.52719	−	4.92318i	0.698575	−	0.403322i	0.806816	+	0.590802i	$0.201189\pi$
$150$	−8.84151	−	8.47513i	−0.721906	−	0.691991i
$151$	−9.24153	−	5.33560i	−0.752065	−	0.434205i	0.0743744	−	0.997230i	$-0.476304\pi$
$151$	−9.24153	−	5.33560i	−0.752065	−	0.434205i	−0.826440	+	0.563025i	$0.809637\pi$
$152$	−1.22605	+	12.8252i	−0.0994458	+	1.04026i
$153$	13.5948	−	11.3139i	1.09907	−	0.914675i
$154$	1.52571	+	2.84784i	0.122945	+	0.229486i
$155$	−5.85758	−	0.0946622i	−0.470493	−	0.00760345i
$156$	−11.1821	+	11.6783i	−0.895284	+	0.935015i
$157$	12.9992	−	7.50509i	1.03745	−	0.598972i	0.118340	−	0.992973i	$-0.462243\pi$
$157$	12.9992	−	7.50509i	1.03745	−	0.598972i	0.919110	+	0.394001i	$0.128909\pi$
$158$	4.59081	+	2.84867i	0.365225	+	0.226628i
$159$	2.78138	−	1.00597i	0.220577	−	0.0797783i
$160$	9.68594	+	8.13527i	0.765741	+	0.643149i
$161$			3.85255i			0.303624i
$162$	−2.70800	+	12.4365i	−0.212761	+	0.977104i
$163$	4.15873			0.325737			0.162869	−	0.986648i	$-0.447925\pi$
$163$	4.15873			0.325737			0.162869	+	0.986648i	$0.447925\pi$
$164$	−12.2412	+	6.06579i	−0.955875	+	0.473659i
$165$	−2.01062	+	2.30955i	−0.156527	+	0.179798i
$166$	−11.5678	−	7.17802i	−0.897838	−	0.557122i
$167$	−0.0288855	+	0.0166770i	−0.00223522	+	0.00129051i	−0.501117	−	0.865379i	$-0.667077\pi$
$167$	−0.0288855	+	0.0166770i	−0.00223522	+	0.00129051i	0.498882	+	0.866670i	$0.333744\pi$
$168$	−3.80112	+	13.6355i	−0.293263	+	1.05200i
$169$	4.39261	−	7.60822i	0.337893	−	0.585248i
$170$	15.6806	+	10.0846i	1.20265	+	0.773453i
$171$	−8.74134	−	10.5036i	−0.668467	−	0.803230i
$172$	−13.1902	+	19.8225i	−1.00575	+	1.51145i
$173$	−11.9161	+	20.6392i	−0.905962	+	1.56917i	−0.0863411	+	0.996266i	$0.527517\pi$
$173$	−11.9161	+	20.6392i	−0.905962	+	1.56917i	−0.819621	+	0.572906i	$0.805816\pi$
$174$	−6.35044	−	1.34244i	−0.481425	−	0.101770i
$175$	14.4397	+	0.466832i	1.09154	+	0.0352892i
$176$	1.91563	−	2.51636i	0.144396	−	0.189678i
$177$	14.0255	+	11.8173i	1.05422	+	0.888241i
$178$	−0.000333277		0.0104870i	−2.49802e−5		0.000786037i
$179$	−25.5288			−1.90811			−0.954055	−	0.299631i	$-0.903136\pi$
$179$	−25.5288			−1.90811			−0.954055	+	0.299631i	$0.903136\pi$
$180$	−13.3612	+	1.21636i	−0.995882	+	0.0906620i
$181$	25.6109			1.90364			0.951821	−	0.306653i	$-0.0992092\pi$
$181$	25.6109			1.90364			0.951821	+	0.306653i	$0.0992092\pi$
$182$	0.605823	−	19.0631i	0.0449066	−	1.41305i
$183$	−0.529190	+	2.96606i	−0.0391188	+	0.219258i
$184$	3.43055	−	1.56623i	0.252904	−	0.115464i
$185$	8.54989	−	14.2712i	0.628601	−	1.04924i
$186$	−4.28883	+	4.77391i	−0.314473	+	0.350040i
$187$	2.33064	−	4.03678i	0.170433	−	0.295199i
$188$	5.01709	+	3.33846i	0.365909	+	0.243482i
$189$	−7.42793	−	13.0479i	−0.540302	−	0.949096i
$190$	7.79155	−	12.1151i	0.565259	−	0.878925i
$191$	3.85863	−	6.68334i	0.279200	−	0.483589i	−0.691986	−	0.721911i	$-0.743264\pi$
$191$	3.85863	−	6.68334i	0.279200	−	0.483589i	0.971186	+	0.238322i	$0.0765973\pi$
$192$	13.6872	−	2.15868i	0.987790	−	0.155789i
$193$	4.47373	−	2.58291i	0.322026	−	0.185922i	−0.330269	−	0.943887i	$-0.607139\pi$
$193$	4.47373	−	2.58291i	0.322026	−	0.185922i	0.652295	+	0.757965i	$0.273806\pi$
$194$	−7.97745	−	4.95013i	−0.572748	−	0.355399i
$195$	17.0964	−	5.87282i	1.22430	−	0.420561i
$196$	−1.19789	−	2.41742i	−0.0855635	−	0.172673i
$197$	−8.47116			−0.603545			−0.301773	−	0.953380i	$-0.597578\pi$
$197$	−8.47116			−0.603545			−0.301773	+	0.953380i	$0.597578\pi$
$198$	0.463813	+	3.32217i	0.0329618	+	0.236096i
$199$		−	0.555967i		−	0.0394115i	−0.999806	−	0.0197057i	$-0.993727\pi$
$199$		−	0.555967i		−	0.0394115i	0.999806	−	0.0197057i	$-0.00627293\pi$
$200$	−5.45470	−	13.0478i	−0.385706	−	0.922622i
$201$	−9.97988	−	8.40860i	−0.703926	−	0.593097i
$202$	3.05302	+	1.89444i	0.214809	+	0.133293i
$203$	6.63083	−	3.82831i	0.465393	−	0.268695i
$204$	19.6077	−	5.71272i	1.37281	−	0.399970i
$205$	15.2722	+	0.246808i	1.06665	+	0.0172378i
$206$	5.11336	+	9.54447i	0.356265	+	0.664995i
$207$	−1.38327	+	3.75314i	−0.0961436	+	0.260861i
$208$	−17.2213	+	7.21053i	−1.19408	+	0.499960i
$209$	−3.11890	−	1.80070i	−0.215739	−	0.124557i
$210$	10.7656	−	11.6005i	0.742894	−	0.800511i
$211$	−21.0649	+	12.1618i	−1.45016	+	0.837253i	−0.998490	−	0.0549298i	$-0.982507\pi$
$211$	−21.0649	+	12.1618i	−1.45016	+	0.837253i	−0.451675	+	0.892183i	$0.649173\pi$
$212$	3.40837	+	0.216855i	0.234088	+	0.0148936i
$213$	−4.70015	+	1.69995i	−0.322049	+	0.116478i
$214$	−0.615948	+	19.3817i	−0.0421054	+	1.32490i
$215$	23.2659	−	12.9359i	1.58672	−	0.882222i
$216$	−8.59889	+	11.9189i	−0.585081	+	0.810975i
$217$		−	7.57019i		−	0.513898i
$218$	18.7521	+	0.595940i	1.27005	+	0.0403622i
$219$	−3.83414	−	10.6009i	−0.259087	−	0.716345i
$220$	−3.19315	+	1.51852i	−0.215282	+	0.102379i
$221$	−23.8308	+	13.7587i	−1.60304	+	0.925513i
$222$	−5.65088	−	17.3260i	−0.379262	−	1.16284i
$223$	0.169636	−	0.293817i	0.0113596	−	0.0196755i	−0.860290	−	0.509805i	$-0.829717\pi$
$223$	0.169636	−	0.293817i	0.0113596	−	0.0196755i	0.871649	+	0.490130i	$0.163051\pi$
$224$	−10.3088	+	12.6844i	−0.688787	+	0.847515i
$225$	13.8995	+	5.63940i	0.926636	+	0.375960i
$226$	−6.17741	−	11.5306i	−0.410915	−	0.767005i
$227$	−7.45137	−	4.30205i	−0.494565	−	0.285537i	0.231902	−	0.972739i	$-0.425505\pi$
$227$	−7.45137	−	4.30205i	−0.494565	−	0.285537i	−0.726466	+	0.687202i	$0.758839\pi$
$228$	−4.41376	−	15.1493i	−0.292308	−	1.00329i
$229$	0.358866	+	0.621574i	0.0237145	+	0.0410748i	0.877639	−	0.479322i	$-0.159117\pi$
$229$	0.358866	+	0.621574i	0.0237145	+	0.0410748i	−0.853925	+	0.520397i	$0.825784\pi$
$230$	−4.21146	−	0.202004i	−0.277696	−	0.0133197i
$231$	−3.02600	−	2.54957i	−0.199096	−	0.167749i
$232$	−6.10470	−	4.34813i	−0.400793	−	0.285469i
$233$	−13.8379			−0.906553			−0.453276	−	0.891370i	$-0.649745\pi$
$233$	−13.8379			−0.906553			−0.453276	+	0.891370i	$0.649745\pi$
$234$	7.43483	−	18.3537i	0.486030	−	1.19982i
$235$	−3.27409	−	5.88864i	−0.213578	−	0.384132i
$236$	9.40283	+	18.9755i	0.612072	+	1.23520i
$237$	−6.51421	−	1.16223i	−0.423143	−	0.0754951i
$238$	−12.7023	+	20.4705i	−0.823365	+	1.32690i
$239$	13.8553	+	23.9980i	0.896223	+	1.55230i	0.832284	+	0.554350i	$0.187033\pi$
$239$	13.8553	+	23.9980i	0.896223	+	1.55230i	0.0639388	+	0.997954i	$0.479634\pi$
$240$	−14.7065	−	4.87020i	−0.949300	−	0.314370i
$241$	−5.71303	+	9.89526i	−0.368009	+	0.637410i	−0.989254	−	0.146206i	$-0.953294\pi$
$241$	−5.71303	+	9.89526i	−0.368009	+	0.637410i	0.621245	+	0.783616i	$0.286627\pi$
$242$	−6.92884	−	12.9332i	−0.445403	−	0.831378i
$243$	−2.55139	−	15.3782i	−0.163672	−	0.986515i
$244$	−1.92729	+	2.89637i	−0.123382	+	0.185421i
$245$	−0.0487403	+	3.01599i	−0.00311390	+	0.192685i
$246$	11.1821	−	12.4468i	0.712942	−	0.793576i
$247$	10.6303	+	18.4122i	0.676388	+	1.17154i
$248$	−6.74097	+	3.07762i	−0.428052	+	0.195429i
$249$	16.4144	+	2.92857i	1.04022	+	0.185591i
$250$	−1.26745	+	15.7605i	−0.0801608	+	0.996782i
$251$	−5.05161			−0.318855			−0.159427	−	0.987210i	$-0.550965\pi$
$251$	−5.05161			−0.318855			−0.159427	+	0.987210i	$0.550965\pi$
$252$	−1.85056	−	17.2377i	−0.116574	−	1.08587i
$253$			1.05417i			0.0662749i
$254$	−13.8133	−	0.438985i	−0.866722	−	0.0275443i
$255$	−22.4108	−	4.37321i	−1.40342	−	0.273861i
$256$	15.4860	+	4.02282i	0.967876	+	0.251426i
$257$	−1.32366	−	2.29265i	−0.0825679	−	0.143012i	0.821784	−	0.569799i	$-0.192979\pi$
$257$	−1.32366	−	2.29265i	−0.0825679	−	0.143012i	−0.904352	+	0.426787i	$0.859645\pi$
$258$	6.03118	−	28.5306i	0.375485	−	1.77624i
$259$	18.6174	+	10.7488i	1.15683	+	0.667897i
$260$	20.8073	+	1.66181i	1.29041	+	0.103061i
$261$	7.83430	−	1.34872i	0.484931	−	0.0834835i
$262$	8.83999	+	16.5005i	0.546136	+	1.01940i
$263$	2.19210	+	1.26561i	0.135171	+	0.0780408i	0.566060	−	0.824364i	$-0.308467\pi$
$263$	2.19210	+	1.26561i	0.135171	+	0.0780408i	−0.430890	+	0.902405i	$0.641800\pi$
$264$	−1.04009	+	3.73105i	−0.0640134	+	0.229630i
$265$	−3.27553	−	1.96237i	−0.201214	−	0.120548i
$266$	15.8159	+	9.81401i	0.969734	+	0.601735i
$267$	−0.00437066	−	0.0120843i	−0.000267480	−	0.000739549i
$268$	−6.69060	−	13.5021i	−0.408693	−	0.824770i
$269$		−	5.26469i		−	0.320994i	−0.987036	−	0.160497i	$-0.948690\pi$
$269$		−	5.26469i		−	0.320994i	0.987036	−	0.160497i	$-0.0513097\pi$
$270$	14.6530	−	7.43578i	0.891751	−	0.452527i
$271$		−	16.6468i		−	1.01122i	−0.862761	−	0.505612i	$-0.831267\pi$
$271$		−	16.6468i		−	1.01122i	0.862761	−	0.505612i	$-0.168733\pi$
$272$	23.3922	+	2.98872i	1.41836	+	0.181218i
$273$	7.94487	+	21.9666i	0.480845	+	1.32948i
$274$	−2.35063	+	3.78819i	−0.142007	+	0.228853i
$275$	3.95112	+	0.127738i	0.238261	+	0.00770292i
$276$	−3.19429	+	3.33604i	−0.192274	+	0.200806i
$277$	−22.8566	−	13.1963i	−1.37332	−	0.792888i	−0.381978	−	0.924171i	$-0.624757\pi$
$277$	−22.8566	−	13.1963i	−1.37332	−	0.792888i	−0.991345	+	0.131283i	$0.958090\pi$
$278$	−3.20355	+	1.71627i	−0.192136	+	0.102935i
$279$	2.71809	−	7.37485i	0.162728	−	0.441521i
$280$	16.7444	−	7.32012i	1.00067	−	0.437461i
$281$	−19.8511	−	11.4611i	−1.18422	−	0.683710i	−0.227233	−	0.973840i	$-0.572968\pi$
$281$	−19.8511	−	11.4611i	−1.18422	−	0.683710i	−0.956987	+	0.290131i	$0.906301\pi$
$282$	−7.22113	−	1.52650i	−0.430012	−	0.0909017i
$283$	3.25733	+	5.64186i	0.193628	+	0.335374i	0.946450	−	0.322851i	$-0.104641\pi$
$283$	3.25733	+	5.64186i	0.193628	+	0.335374i	−0.752822	+	0.658224i	$0.771308\pi$
$284$	−5.75968	−	0.366455i	−0.341774	−	0.0217451i
$285$	−3.37883	+	17.3151i	−0.200145	+	1.02566i
$286$	0.165770	−	5.21619i	0.00980220	−	0.308440i
$287$			19.7374i			1.16506i
$288$	−14.5972	+	8.65575i	−0.860148	+	0.510045i
$289$	17.7581			1.04459
$290$	3.83729	+	7.44931i	0.225333	+	0.437439i
$291$	11.3197	+	2.01961i	0.663575	+	0.118392i
$292$	0.826520	−	12.9907i	0.0483684	−	0.760222i
$293$	−8.37272	−	14.5020i	−0.489140	−	0.847215i	0.510782	−	0.859710i	$-0.329356\pi$
$293$	−8.37272	−	14.5020i	−0.489140	−	0.847215i	−0.999922	+	0.0124952i	$0.996023\pi$
$294$	2.45802	+	2.20826i	0.143355	+	0.128788i
$295$	0.382587	−	23.6740i	0.0222751	−	1.37835i
$296$	2.00257	−	20.9480i	0.116397	−	1.21758i
$297$	−2.03249	−	3.57027i	−0.117937	−	0.207168i
$298$	−12.2743	+	6.57586i	−0.711033	+	0.380929i
$299$	3.11159	−	5.38944i	0.179948	−	0.311679i
$300$	12.1168	+	12.3768i	0.699561	+	0.714573i
$301$	17.1995	+	29.7903i	0.991360	+	1.71709i
$302$	12.8232	+	7.95701i	0.737894	+	0.457874i
$303$	−4.33213	−	0.772916i	−0.248874	−	0.0444029i
$304$	2.30914	−	18.0733i	0.132438	−	1.03657i
$305$	3.39951	−	1.89013i	0.194655	−	0.108229i
$306$	−19.7245	+	15.3815i	−1.12757	+	0.879303i
$307$	−24.2759			−1.38550			−0.692749	−	0.721179i	$-0.743600\pi$
$307$	−24.2759			−1.38550			−0.692749	+	0.721179i	$0.743600\pi$
$308$	−2.02866	−	4.09396i	−0.115593	−	0.233275i
$309$	−10.1416	−	8.54482i	−0.576933	−	0.486098i
$310$	8.27544	+	0.396933i	0.470014	+	0.0225443i
$311$	3.81664	+	6.61061i	0.216422	+	0.374853i	0.953711	−	0.300723i	$-0.0972281\pi$
$311$	3.81664	+	6.61061i	0.216422	+	0.374853i	−0.737290	+	0.675577i	$0.763895\pi$
$312$	16.3305	−	16.0050i	0.924532	−	0.906105i
$313$	−3.85836	−	2.22762i	−0.218087	−	0.125913i	0.386977	−	0.922089i	$-0.373519\pi$
$313$	−3.85836	−	2.22762i	−0.218087	−	0.125913i	−0.605064	+	0.796177i	$0.706853\pi$
$314$	−18.7115	+	10.0245i	−1.05595	+	0.565716i
$315$	−6.99609	+	18.0765i	−0.394185	+	1.01849i
$316$	−6.36115	−	4.23282i	−0.357842	−	0.238115i
$317$	−2.47795	+	4.29194i	−0.139176	+	0.241059i	−0.927185	−	0.374604i	$-0.877779\pi$
$317$	−2.47795	+	4.29194i	−0.139176	+	0.241059i	0.788009	+	0.615663i	$0.211112\pi$
$318$	−3.97666	+	1.29699i	−0.223000	+	0.0727317i
$319$	1.81438	−	1.04753i	0.101586	−	0.0586506i
$320$	−13.3256	−	11.9343i	−0.744925	−	0.667148i
$321$	−8.07765	−	22.3337i	−0.450850	−	1.24655i
$322$	0.173060	−	5.44558i	0.00964426	−	0.303470i
$323$		−	26.8548i		−	1.49424i
$324$	4.38642	−	17.4574i	0.243690	−	0.969853i
$325$	−19.8231	−	12.3156i	−1.09959	−	0.683148i
$326$	−5.87837	−	0.186814i	−0.325573	−	0.0103467i
$327$	−21.6082	+	7.81526i	−1.19494	+	0.432185i
$328$	17.5754	−	8.02411i	0.970438	−	0.443058i
$329$	7.53997	−	4.35320i	0.415692	−	0.240000i
$330$	2.94576	−	3.17422i	0.162159	−	0.174735i
$331$	23.0250	+	13.2935i	1.26557	+	0.730676i	0.974146	−	0.225918i	$-0.0725382\pi$
$331$	23.0250	+	13.2935i	1.26557	+	0.730676i	0.291422	+	0.956594i	$0.405871\pi$
$332$	16.0287	+	10.6658i	0.879689	+	0.585360i
$333$	14.2777	+	17.1561i	0.782412	+	0.940146i
$334$	0.0415787	−	0.0222754i	0.00227509	−	0.00121886i
$335$	−0.272230	+	16.8453i	−0.0148735	+	0.920356i
$336$	5.98541	−	19.1030i	0.326531	−	1.04216i
$337$	−10.7769	+	6.22205i	−0.587056	+	0.338937i	−0.763933	−	0.645296i	$-0.776734\pi$
$337$	−10.7769	+	6.22205i	−0.587056	+	0.338937i	0.176877	+	0.984233i	$0.443401\pi$
$338$	−6.55072	+	10.5569i	−0.356312	+	0.574220i
$339$	12.2519	+	10.3229i	0.665434	+	0.560665i
$340$	−21.7115	−	14.9590i	−1.17747	−	0.811264i
$341$		−	2.07142i		−	0.112173i
$342$	11.8841	+	15.2395i	0.642616	+	0.824058i
$343$	16.3284			0.881652
$344$	19.5348	−	27.4266i	1.05325	−	1.47874i
$345$	4.88379	−	1.67764i	0.262934	−	0.0903208i
$346$	17.7705	−	28.6383i	0.955348	−	1.53960i
$347$	−14.6546	+	8.46084i	−0.786701	+	0.454202i	−0.838800	−	0.544440i	$-0.816742\pi$
$347$	−14.6546	+	8.46084i	−0.786701	+	0.454202i	0.0520991	+	0.998642i	$0.483409\pi$
$348$	8.91604	+	2.18281i	0.477950	+	0.117011i
$349$	−0.955553	+	1.65507i	−0.0511496	+	0.0885937i	−0.890467	−	0.455049i	$-0.849622\pi$
$349$	−0.955553	+	1.65507i	−0.0511496	+	0.0885937i	0.839317	+	0.543642i	$0.182955\pi$
$350$	−20.3896	−	1.30851i	−1.08987	−	0.0699430i
$351$	−0.147285	+	24.2524i	−0.00786147	+	1.29450i
$352$	−2.82078	+	3.47082i	−0.150348	+	0.184995i
$353$	11.0561	−	19.1497i	0.588457	−	1.01924i	−0.405978	−	0.913883i	$-0.633069\pi$
$353$	11.0561	−	19.1497i	0.588457	−	1.01924i	0.994435	−	0.105355i	$-0.0335978\pi$
$354$	−19.2942	−	17.3338i	−1.02548	−	0.921279i
$355$	5.53520	+	3.31614i	0.293778	+	0.176003i
$356$	0.000942175	−	0.0148085i	4.99352e−5	−	0.000784847i
$357$	5.18241	−	29.0469i	0.274282	−	1.53733i
$358$	36.0849	+	1.14678i	1.90715	+	0.0606090i
$359$	−1.48034			−0.0781296			−0.0390648	−	0.999237i	$-0.512438\pi$
$359$	−1.48034			−0.0781296			−0.0390648	+	0.999237i	$0.512438\pi$
$360$	18.9406	−	1.11913i	0.998259	−	0.0589832i
$361$	−1.74850			−0.0920262
$362$	−36.2010	−	1.15046i	−1.90268	−	0.0604671i
$363$	13.7423	+	11.5786i	0.721283	+	0.607721i
$364$	−1.71266	+	26.9185i	−0.0897679	+	1.41091i
$365$	−7.47940	+	12.4844i	−0.391490	+	0.653462i
$366$	0.881248	−	4.16876i	0.0460636	−	0.217904i
$367$	0.0631149	−	0.109318i	0.00329457	−	0.00570636i	−0.864373	−	0.502850i	$-0.832285\pi$
$367$	0.0631149	−	0.109318i	0.00329457	−	0.00570636i	0.867668	+	0.497144i	$0.165618\pi$
$368$	−4.91944	+	2.05977i	−0.256444	+	0.107373i
$369$	−7.08673	+	19.2281i	−0.368921	+	1.00097i
$370$	−12.7263	+	19.7883i	−0.661611	+	1.02874i
$371$	2.46707	−	4.27308i	0.128084	−	0.221847i
$372$	6.27672	−	6.55526i	0.325433	−	0.339874i
$373$	19.8527	−	11.4620i	1.02794	−	0.593479i	0.111543	−	0.993760i	$-0.464421\pi$
$373$	19.8527	−	11.4620i	1.02794	−	0.593479i	0.916393	+	0.400280i	$0.131087\pi$
$374$	−3.47569	+	5.60130i	−0.179724	+	0.289636i
$375$	−5.69615	−	18.5082i	−0.294148	−	0.955760i
$376$	−6.94170	−	4.94429i	−0.357991	−	0.254982i
$377$	−12.3681			−0.636988
$378$	9.91326	+	18.7769i	0.509883	+	0.965779i
$379$			27.5123i			1.41321i	0.707608	+	0.706605i	$0.249774\pi$
$379$			27.5123i			1.41321i	−0.707608	+	0.706605i	$0.750226\pi$
$380$	−11.5576	+	16.7747i	−0.592892	+	0.860526i
$381$	15.9172	−	5.75692i	0.815462	−	0.294936i
$382$	−5.75439	+	9.27357i	−0.294420	+	0.474477i
$383$	−20.5507	+	11.8649i	−1.05009	+	0.606270i	−0.922675	−	0.385579i	$-0.874002\pi$
$383$	−20.5507	+	11.8649i	−1.05009	+	0.606270i	−0.127416	+	0.991849i	$0.540668\pi$
$384$	−19.4439	+	2.43645i	−0.992240	+	0.124334i
$385$	−0.0825429	+	5.10766i	−0.00420678	+	0.260310i
$386$	−6.43965	+	3.44998i	−0.327770	+	0.175599i
$387$	6.05938	+	35.1971i	0.308016	+	1.78917i
$388$	11.0538	+	7.35537i	0.561170	+	0.373412i
$389$	−1.58128	−	0.912954i	−0.0801742	−	0.0462886i	0.459377	−	0.888241i	$-0.348073\pi$
$389$	−1.58128	−	0.912954i	−0.0801742	−	0.0462886i	−0.539551	+	0.841953i	$0.681406\pi$
$390$	−24.4296	+	7.53324i	−1.23704	+	0.381460i
$391$	−6.80755	+	3.93034i	−0.344272	+	0.198766i
$392$	1.58462	+	3.47083i	0.0800356	+	0.175304i
$393$	−17.5327	−	14.7723i	−0.884410	−	0.745164i
$394$	11.9740	+	0.380532i	0.603241	+	0.0191709i
$395$	4.15120	+	7.46617i	0.208870	+	0.375664i
$396$	−0.506366	−	4.71672i	−0.0254458	−	0.237024i
$397$			19.0828i			0.957737i	0.877887	+	0.478868i	$0.158953\pi$
$397$			19.0828i			0.957737i	−0.877887	+	0.478868i	$0.841047\pi$
$398$	−0.0249745	+	0.785859i	−0.00125186	+	0.0393916i
$399$	−22.4422	−	4.00403i	−1.12352	−	0.200452i
$400$	7.12410	+	18.6882i	0.356205	+	0.934408i
$401$	−15.1375	+	8.73963i	−0.755930	+	0.436436i	−0.827833	−	0.560975i	$-0.810426\pi$
$401$	−15.1375	+	8.73963i	−0.755930	+	0.436436i	0.0719025	+	0.997412i	$0.477093\pi$
$402$	13.7288	+	12.3339i	0.684732	+	0.615157i
$403$	−6.11422	+	10.5901i	−0.304571	+	0.527533i
$404$	−4.23034	−	2.81494i	−0.210467	−	0.140048i
$405$	−13.3060	+	15.0981i	−0.661178	+	0.750229i
$406$	−9.54466	+	5.11346i	−0.473693	+	0.253777i
$407$	5.09425	+	2.94117i	0.252513	+	0.145788i
$408$	−27.9721	+	7.19413i	−1.38483	+	0.356163i
$409$	−8.17716	−	14.1633i	−0.404335	−	0.700328i	0.589909	−	0.807470i	$-0.299164\pi$
$409$	−8.17716	−	14.1633i	−0.404335	−	0.700328i	−0.994244	+	0.107142i	$0.965830\pi$
$410$	−21.5761	−	1.03490i	−1.06557	−	0.0511102i
$411$	0.959036	−	5.37531i	0.0473057	−	0.265144i
$412$	−6.79899	−	13.7208i	−0.334962	−	0.675976i
$413$	30.5957			1.50551
$414$	2.12384	−	5.24293i	0.104381	−	0.257676i
$415$	−10.4601	−	18.8131i	−0.513467	−	0.923499i
$416$	24.6662	−	9.41849i	1.20936	−	0.461779i
$417$	2.86803	−	3.40396i	0.140448	−	0.166693i
$418$	4.32767	+	2.68539i	0.211673	+	0.131347i
$419$	−12.3846	−	21.4508i	−0.605029	−	1.04794i	−0.992047	−	0.125869i	$-0.959828\pi$
$419$	−12.3846	−	21.4508i	−0.605029	−	1.04794i	0.387018	−	0.922072i	$-0.373505\pi$
$420$	−15.7382	+	15.9137i	−0.767947	+	0.776510i
$421$	8.38623	−	14.5254i	0.408720	−	0.707923i	−0.586027	−	0.810292i	$-0.699309\pi$
$421$	8.38623	−	14.5254i	0.408720	−	0.707923i	0.994747	+	0.102368i	$0.0326420\pi$
$422$	30.3215	−	16.2445i	1.47603	−	0.790768i
$423$	8.90844	−	1.53364i	0.433143	−	0.0745679i
$424$	−4.80799	−	0.459631i	−0.233497	−	0.0223217i
$425$	13.9064	+	25.9916i	0.674559	+	1.26078i
$426$	6.72002	−	2.19174i	0.325586	−	0.106190i
$427$	2.51310	+	4.35282i	0.121618	+	0.210648i
$428$	1.74129	−	27.3683i	0.0841682	−	1.32290i
$429$	2.17394	+	6.01068i	0.104959	+	0.290198i
$430$	−33.4675	+	17.2398i	−1.61395	+	0.831376i
$431$	15.2488			0.734510			0.367255	−	0.930120i	$-0.380298\pi$
$431$	15.2488			0.734510			0.367255	+	0.930120i	$0.380298\pi$
$432$	12.6899	−	16.4610i	0.610545	−	0.791982i
$433$			23.5695i			1.13268i	0.824172	+	0.566340i	$0.191641\pi$
$433$			23.5695i			1.13268i	−0.824172	+	0.566340i	$0.808359\pi$
$434$	−0.340060	+	10.7005i	−0.0163234	+	0.513639i
$435$	−7.74053	−	6.73867i	−0.371130	−	0.323095i
$436$	−26.4793	−	1.68472i	−1.26813	−	0.0806836i
$437$	3.03665	+	5.25964i	0.145263	+	0.251603i
$438$	4.94336	+	15.1567i	0.236203	+	0.724214i
$439$	−12.8688	−	7.42979i	−0.614193	−	0.354605i	0.160412	−	0.987050i	$-0.448718\pi$
$439$	−12.8688	−	7.42979i	−0.614193	−	0.354605i	−0.774605	+	0.632446i	$0.782051\pi$
$440$	4.58173	−	2.00299i	0.218426	−	0.0954887i
$441$	−3.79721	−	1.39951i	−0.180820	−	0.0666432i
$442$	34.3030	−	18.3775i	1.63163	−	0.874128i
$443$	−23.5062	−	13.5713i	−1.11681	−	0.644791i	−0.176226	−	0.984350i	$-0.556389\pi$
$443$	−23.5062	−	13.5713i	−1.11681	−	0.644791i	−0.940585	+	0.339558i	$0.889722\pi$
$444$	7.20922	+	24.7441i	0.342134	+	1.17430i
$445$	−0.00852599	+	0.0142313i	−0.000404171	+	0.000674629i
$446$	−0.252978	+	0.407691i	−0.0119789	+	0.0193047i
$447$	10.9888	−	13.0422i	0.519751	−	0.616875i
$448$	15.1413	−	17.4664i	0.715360	−	0.825209i
$449$			17.4879i			0.825304i	0.910889	+	0.412652i	$0.135398\pi$
$449$			17.4879i			0.825304i	−0.910889	+	0.412652i	$0.864602\pi$
$450$	−19.3937	−	8.59568i	−0.914226	−	0.405204i
$451$			5.40069i			0.254309i
$452$	8.21381	+	16.5760i	0.386345	+	0.779670i
$453$	−18.1957	−	3.24639i	−0.854910	−	0.152529i
$454$	10.3393	+	6.41567i	0.485245	+	0.301102i
$455$	15.4983	−	25.8693i	0.726573	−	1.21277i
$456$	5.55833	+	21.6118i	0.260292	+	1.01206i
$457$	5.10627	+	2.94811i	0.238861	+	0.137907i	0.614653	−	0.788797i	$-0.289296\pi$
$457$	5.10627	+	2.94811i	0.238861	+	0.137907i	−0.375792	+	0.926704i	$0.622629\pi$
$458$	−0.479335	−	0.894715i	−0.0223979	−	0.0418073i
$459$	15.4780	−	26.4367i	0.722453	−	1.23396i
$460$	5.94383	+	0.474715i	0.277132	+	0.0221337i
$461$	30.5948	+	17.6639i	1.42494	+	0.822691i	0.996716	−	0.0809799i	$-0.0258050\pi$
$461$	30.5948	+	17.6639i	1.42494	+	0.822691i	0.428227	+	0.903671i	$0.359138\pi$
$462$	4.16272	+	3.73975i	0.193667	+	0.173989i
$463$	−18.6175	−	32.2464i	−0.865227	−	1.49862i	−0.866822	−	0.498618i	$-0.833841\pi$
$463$	−18.6175	−	32.2464i	−0.865227	−	1.49862i	0.00159457	−	0.999999i	$-0.499492\pi$
$464$	8.43367	+	6.42031i	0.391523	+	0.298055i
$465$	−9.59655	+	3.29652i	−0.445029	+	0.152872i
$466$	19.5599	+	0.621612i	0.906095	+	0.0287956i
$467$			6.98334i			0.323151i	0.986860	+	0.161575i	$0.0516575\pi$
$467$			6.98334i			0.323151i	−0.986860	+	0.161575i	$0.948343\pi$
$468$	−11.3336	+	25.6089i	−0.523895	+	1.18377i
$469$	−21.7704			−1.00526
$470$	4.36341	+	8.47066i	0.201269	+	0.390722i
$471$	16.7517	−	19.8821i	0.771879	−	0.916117i
$472$	−12.4385	−	27.2443i	−0.572529	−	1.25402i
$473$	4.70625	+	8.15147i	0.216394	+	0.374805i
$474$	9.15562	+	1.93544i	0.420532	+	0.0888977i
$475$	20.0816	−	10.7443i	0.921408	−	0.492984i
$476$	18.8742	−	28.3644i	0.865097	−	1.30008i
$477$	3.93767	−	3.27702i	0.180293	−	0.150044i
$478$	−18.5064	−	34.5436i	−0.846463	−	1.57999i
$479$	−10.2090	+	17.6825i	−0.466460	+	0.807932i	−0.999266	−	0.0383050i	$-0.987804\pi$
$479$	−10.2090	+	17.6825i	−0.466460	+	0.807932i	0.532806	+	0.846237i	$0.321137\pi$
$480$	20.5689	+	7.54466i	0.938836	+	0.344365i
$481$	−17.3630	−	30.0735i	−0.791683	−	1.37124i
$482$	8.51987	−	13.7303i	0.388070	−	0.625399i
$483$	2.26954	+	6.27500i	0.103268	+	0.285522i
$484$	9.21295	+	18.5923i	0.418770	+	0.845106i
$485$	−7.21355	−	12.9740i	−0.327550	−	0.589117i
$486$	2.91558	+	21.8518i	0.132254	+	0.991216i
$487$	−20.8264			−0.943735			−0.471868	−	0.881669i	$-0.656420\pi$
$487$	−20.8264			−0.943735			−0.471868	+	0.881669i	$0.656420\pi$
$488$	2.85434	−	4.00744i	0.129210	−	0.181408i
$489$	6.77371	−	2.44991i	0.306318	−	0.110789i
$490$	0.204375	−	4.26091i	0.00923274	−	0.192488i
$491$	−9.31608	−	16.1359i	−0.420429	−	0.728204i	0.575552	−	0.817765i	$-0.304787\pi$
$491$	−9.31608	−	16.1359i	−0.420429	−	0.728204i	−0.995981	+	0.0895606i	$0.971454\pi$
$492$	−16.3650	+	17.0912i	−0.737789	+	0.770530i
$493$	13.5294	+	7.81122i	0.609335	+	0.351800i
$494$	−14.1988	−	26.5031i	−0.638834	−	1.19243i
$495$	−1.91433	+	4.94623i	−0.0860426	+	0.222316i
$496$	9.66661	−	4.04740i	0.434044	−	0.181734i
$497$	−4.16900	+	7.22093i	−0.187005	+	0.323903i
$498$	−23.0702	−	4.87688i	−1.03380	−	0.218538i
$499$	−4.48667	+	2.59038i	−0.200851	+	0.115961i	−0.597052	−	0.802202i	$-0.703662\pi$
$499$	−4.48667	+	2.59038i	−0.200851	+	0.115961i	0.396201	+	0.918164i	$0.370328\pi$
$500$	2.49952	−	22.2205i	0.111782	−	0.993733i
$501$	−0.0372239	+	0.0441798i	−0.00166304	+	0.00197381i
$502$	7.14045	+	0.226923i	0.318694	+	0.0101281i
$503$			27.8846i			1.24331i	0.783290	+	0.621657i	$0.213540\pi$
$503$			27.8846i			1.24331i	−0.783290	+	0.621657i	$0.786460\pi$
$504$	1.84144	+	24.4486i	0.0820241	+	1.08903i
$505$	2.76066	+	4.96521i	0.122848	+	0.220949i
$506$	0.0473541	−	1.49006i	0.00210515	−	0.0662414i
$507$	2.67264	−	14.9799i	0.118696	−	0.665281i
$508$	19.5053	+	1.24101i	0.865410	+	0.0550609i
$509$	18.6724	−	10.7805i	0.827640	−	0.477838i	−0.0254039	−	0.999677i	$-0.508087\pi$
$509$	18.6724	−	10.7805i	0.827640	−	0.477838i	0.853044	+	0.521839i	$0.174754\pi$
$510$	31.4813	+	7.18825i	1.39401	+	0.318301i
$511$	−16.2864	−	9.40298i	−0.720470	−	0.415963i
$512$	−21.7088	−	6.38191i	−0.959402	−	0.282043i
$513$	−20.4255	−	11.9586i	−0.901807	−	0.527987i
$514$	1.76801	+	3.30013i	0.0779837	+	0.145562i
$515$	−0.276640	+	17.1182i	−0.0121902	+	0.754317i
$516$	−9.80670	+	40.0571i	−0.431716	+	1.76341i
$517$	2.06315	−	1.19116i	0.0907371	−	0.0523871i
$518$	−25.8329	−	16.0297i	−1.13503	−	0.704306i
$519$	−7.25021	+	40.6368i	−0.318249	+	1.78376i
$520$	−29.3364	−	3.28365i	−1.28649	−	0.143998i
$521$		−	19.9411i		−	0.873633i	−0.899551	−	0.436817i	$-0.856106\pi$
$521$		−	19.9411i		−	0.873633i	0.899551	−	0.436817i	$-0.143894\pi$
$522$	−11.1344	+	1.55449i	−0.487338	+	0.0680381i
$523$	18.9360			0.828013			0.414006	−	0.910274i	$-0.364129\pi$
$523$	18.9360			0.828013			0.414006	+	0.910274i	$0.364129\pi$
$524$	−11.7541	−	23.7206i	−0.513480	−	1.03624i
$525$	23.7943	−	7.74609i	1.03847	−	0.338067i
$526$	−3.04168	−	1.88741i	−0.132624	−	0.0822950i
$527$	13.3767	−	7.72304i	0.582698	−	0.336421i
$528$	1.63778	−	5.22712i	0.0712750	−	0.227481i
$529$	−10.6111	+	18.3790i	−0.461354	+	0.799088i
$530$	4.54182	+	2.92096i	0.197284	+	0.126878i
$531$	29.8062	+	10.9854i	1.29348	+	0.476727i
$532$	−21.9149	−	14.5826i	−0.950132	−	0.632234i
$533$	15.9413	−	27.6111i	0.690494	−	1.19597i
$534$	0.00563508	+	0.0172775i	0.000243854	+	0.000747672i
$535$	−15.7574	+	26.3017i	−0.681250	+	1.13712i
$536$	8.85063	+	19.3857i	0.382289	+	0.837335i
$537$	−41.5810	+	15.0390i	−1.79435	+	0.648981i
$538$	−0.236495	+	7.44164i	−0.0101960	+	0.320832i
$539$	−1.06654			−0.0459393
$540$	−21.0460	+	9.85225i	−0.905675	+	0.423974i
$541$	−13.2697			−0.570511			−0.285255	−	0.958452i	$-0.592078\pi$
$541$	−13.2697			−0.570511			−0.285255	+	0.958452i	$0.592078\pi$
$542$	−0.747791	+	23.5303i	−0.0321204	+	1.01071i
$543$	41.7148	−	15.0874i	1.79015	−	0.647462i
$544$	−32.9307	−	5.27535i	−1.41189	−	0.226179i
$545$	25.4473	+	15.2455i	1.09004	+	0.653046i
$546$	−10.2433	−	31.4067i	−0.438373	−	1.34408i
$547$	−4.51377	+	7.81809i	−0.192995	+	0.334277i	−0.946241	−	0.323461i	$-0.895153\pi$
$547$	−4.51377	+	7.81809i	−0.192995	+	0.334277i	0.753246	+	0.657738i	$0.228487\pi$
$548$	3.49278	−	5.24901i	0.149204	−	0.224227i
$549$	0.885368	+	5.14284i	0.0377866	+	0.219491i
$550$	−5.57917	−	0.358046i	−0.237897	−	0.0152671i
$551$	6.03510	−	10.4531i	0.257104	−	0.445317i
$552$	4.66499	−	4.57201i	0.198555	−	0.194598i
$553$	−9.55988	+	5.51940i	−0.406527	+	0.234709i
$554$	31.7151	+	19.6797i	1.34744	+	0.836110i
$555$	5.51882	−	28.2816i	0.234261	−	1.20049i
$556$	4.60532	−	2.28205i	0.195309	−	0.0967803i
$557$	30.4174			1.28883			0.644414	−	0.764677i	$-0.277101\pi$
$557$	30.4174			1.28883			0.644414	+	0.764677i	$0.277101\pi$
$558$	−4.17331	+	10.3023i	−0.176670	+	0.436129i
$559$		−	55.5660i		−	2.35019i
$560$	−23.9970	+	9.59481i	−1.01406	+	0.405455i
$561$	1.41805	−	7.94806i	0.0598702	−	0.335567i
$562$	27.5448	+	17.0919i	1.16191	+	0.720980i
$563$	39.1934	−	22.6283i	1.65180	−	0.953669i	0.675473	−	0.737385i	$-0.263940\pi$
$563$	39.1934	−	22.6283i	1.65180	−	0.953669i	0.976330	−	0.216284i	$-0.0693938\pi$
$564$	10.1385	+	2.48209i	0.426907	+	0.104515i
$565$	0.334207	−	20.6803i	0.0140602	−	0.870029i
$566$	−4.35080	−	8.12109i	−0.182878	−	0.341355i
$567$	−19.7851	−	16.8765i	−0.830895	−	0.708747i
$568$	8.12485	+	0.776714i	0.340911	+	0.0325902i
$569$	−4.42750	−	2.55622i	−0.185610	−	0.107162i	0.404316	−	0.914620i	$-0.367510\pi$
$569$	−4.42750	−	2.55622i	−0.185610	−	0.107162i	−0.589926	+	0.807457i	$0.700843\pi$
$570$	5.55378	−	24.3230i	0.232622	−	1.01878i
$571$	30.6553	−	17.6989i	1.28289	−	0.740675i	0.305511	−	0.952189i	$-0.401173\pi$
$571$	30.6553	−	17.6989i	1.28289	−	0.740675i	0.977375	+	0.211514i	$0.0678394\pi$
$572$	−0.468632	+	7.36564i	−0.0195945	+	0.307973i
$573$	2.34774	−	13.1589i	0.0980783	−	0.549720i
$574$	0.886620	−	27.8987i	0.0370068	−	1.16447i
$575$	−5.66269	−	3.51810i	−0.236151	−	0.146715i
$576$	21.0220	−	11.5792i	0.875915	−	0.482466i
$577$		−	30.4257i		−	1.26664i	−0.773890	−	0.633320i	$-0.781692\pi$
$577$		−	30.4257i		−	1.26664i	0.773890	−	0.633320i	$-0.218308\pi$
$578$	−25.1010	−	0.797709i	−1.04407	−	0.0331803i
$579$	5.76519	−	6.84250i	0.239593	−	0.284365i
$580$	−5.08938	−	10.7020i	−0.211325	−	0.444375i
$581$	24.0888	−	13.9077i	0.999372	−	0.576987i
$582$	−15.9097	−	3.36321i	−0.659480	−	0.139410i
$583$	0.675058	−	1.16924i	0.0279581	−	0.0484248i
$584$	−1.75184	+	18.3252i	−0.0724916	+	0.758302i
$585$	24.3869	−	19.6371i	1.00827	−	0.811895i
$586$	11.1834	+	20.8747i	0.461982	+	0.862324i
$587$	25.3201	+	14.6186i	1.04507	+	0.603372i	0.921265	−	0.388934i	$-0.127157\pi$
$587$	25.3201	+	14.6186i	1.04507	+	0.603372i	0.123806	+	0.992306i	$0.460490\pi$
$588$	−3.37521	−	3.23179i	−0.139191	−	0.133277i
$589$	−5.96697	−	10.3351i	−0.245865	−	0.425850i
$590$	−1.60424	+	33.4460i	−0.0660457	+	1.37695i
$591$	−13.7978	+	4.99036i	−0.567564	+	0.205276i
$592$	−3.77164	+	29.5200i	−0.155013	+	1.21327i
$593$	−1.73460			−0.0712314			−0.0356157	−	0.999366i	$-0.511339\pi$
$593$	−1.73460			−0.0712314			−0.0356157	+	0.999366i	$0.511339\pi$
$594$	2.71254	+	5.13788i	0.111297	+	0.210810i
$595$	−33.2917	+	18.5103i	−1.36483	+	0.758847i
$596$	17.6452	−	8.74360i	0.722774	−	0.358152i
$597$	−0.327520	−	0.905554i	−0.0134045	−	0.0370619i
$598$	−4.64034	+	7.47820i	−0.189758	+	0.305806i
$599$	−1.94974	−	3.37704i	−0.0796641	−	0.137982i	0.823441	−	0.567402i	$-0.192051\pi$
$599$	−1.94974	−	3.37704i	−0.0796641	−	0.137982i	−0.903105	+	0.429420i	$0.858718\pi$
$600$	−16.5711	−	18.0388i	−0.676511	−	0.736433i
$601$	2.16133	−	3.74354i	0.0881625	−	0.152702i	−0.818572	−	0.574404i	$-0.805234\pi$
$601$	2.16133	−	3.74354i	0.0881625	−	0.152702i	0.906734	+	0.421702i	$0.138567\pi$
$602$	−22.9732	−	42.8812i	−0.936319	−	1.74771i
$603$	−21.2086	−	7.81670i	−0.863683	−	0.318321i
$604$	−17.7682	−	11.8233i	−0.722978	−	0.481082i
$605$	0.374861	−	23.1959i	0.0152403	−	0.943049i
$606$	6.08874	+	1.28712i	0.247338	+	0.0522857i
$607$	6.33497	+	10.9725i	0.257128	+	0.445360i	0.965471	−	0.260509i	$-0.0838903\pi$
$607$	6.33497	+	10.9725i	0.257128	+	0.445360i	−0.708343	+	0.705868i	$0.750557\pi$
$608$	−4.07584	+	25.4429i	−0.165297	+	1.03184i
$609$	8.54498	−	10.1418i	0.346260	−	0.410964i
$610$	−4.89011	+	2.51899i	−0.197995	+	0.101991i
$611$	−14.0638			−0.568961
$612$	28.5715	−	20.8557i	1.15493	−	0.843043i
$613$			47.3059i			1.91067i	0.295527	+	0.955334i	$0.404505\pi$
$613$			47.3059i			1.91067i	−0.295527	+	0.955334i	$0.595495\pi$
$614$	34.3139	+	1.09049i	1.38480	+	0.0440088i
$615$	25.0206	−	8.59484i	1.00893	−	0.346578i
$616$	2.68360	+	5.87794i	0.108125	+	0.236829i
$617$	−3.48880	−	6.04277i	−0.140454	−	0.243273i	0.787214	−	0.616680i	$-0.211523\pi$
$617$	−3.48880	−	6.04277i	−0.140454	−	0.243273i	−0.927668	+	0.373407i	$0.878189\pi$
$618$	13.9512	+	12.5337i	0.561202	+	0.504178i
$619$	−24.9827	−	14.4238i	−1.00414	−	0.579741i	−0.0946695	−	0.995509i	$-0.530179\pi$
$619$	−24.9827	−	14.4238i	−1.00414	−	0.579741i	−0.909471	+	0.415768i	$0.863513\pi$
$620$	−11.6795	−	0.932805i	−0.469060	−	0.0374624i
$621$	−0.0420735	+	6.92797i	−0.00168835	+	0.278010i
$622$	−5.09786	−	9.51554i	−0.204406	−	0.381538i
$623$	−0.0185654	−	0.0107187i	−0.000743807	−	0.000429437i
$624$	−23.8021	+	21.8895i	−0.952847	+	0.876281i
$625$	−13.8724	+	20.7980i	−0.554894	+	0.831921i
$626$	5.35372	+	3.32207i	0.213978	+	0.132777i
$627$	−6.14082	−	1.09561i	−0.245241	−	0.0437546i
$628$	26.8990	−	13.3291i	1.07339	−	0.531890i
$629$			43.8633i			1.74894i
$630$	10.7010	−	25.2368i	0.426337	−	1.00546i
$631$			31.3427i			1.24774i	0.781530	+	0.623868i	$0.214440\pi$
$631$			31.3427i			1.24774i	−0.781530	+	0.623868i	$0.785560\pi$
$632$	8.80134	+	6.26884i	0.350098	+	0.249361i
$633$	−27.1457	+	32.2184i	−1.07895	+	1.28056i
$634$	3.69538	−	5.95534i	0.146762	−	0.236517i
$635$	−18.7451	−	11.2302i	−0.743878	−	0.445658i
$636$	5.67928	−	1.65466i	0.225198	−	0.0656116i
$637$	5.45272	+	3.14813i	0.216045	+	0.124733i
$638$	−2.61169	+	1.39919i	−0.103398	+	0.0553943i
$639$	−6.65412	+	5.53771i	−0.263233	+	0.219069i
$640$	18.2997	+	17.4677i	0.723358	+	0.690473i
$641$	−17.6686	−	10.2010i	−0.697869	−	0.402915i	0.108684	−	0.994076i	$-0.465336\pi$
$641$	−17.6686	−	10.2010i	−0.697869	−	0.402915i	−0.806553	+	0.591162i	$0.798670\pi$
$642$	10.4145	+	31.9316i	0.411028	+	1.26024i
$643$	−14.8702	−	25.7560i	−0.586424	−	1.01572i	−0.994696	−	0.102856i	$-0.967202\pi$
$643$	−14.8702	−	25.7560i	−0.586424	−	1.01572i	0.408272	−	0.912860i	$-0.366131\pi$
$644$	−0.489241	+	7.68956i	−0.0192788	+	0.303011i
$645$	30.2748	−	34.7759i	1.19207	−	1.36930i
$646$	−1.20634	+	37.9592i	−0.0474628	+	1.49348i
$647$			7.37854i			0.290081i	0.989426	+	0.145040i	$0.0463312\pi$
$647$			7.37854i			0.290081i	−0.989426	+	0.145040i	$0.953669\pi$
$648$	−6.98440	+	24.4789i	−0.274373	+	0.961623i
$649$	8.37183			0.328623
$650$	27.4667	+	18.2986i	1.07733	+	0.717731i
$651$	−4.45960	−	12.3303i	−0.174786	−	0.483261i
$652$	8.30068	+	0.528123i	0.325080	+	0.0206829i
$653$	−7.32692	−	12.6906i	−0.286724	−	0.496621i	0.686301	−	0.727317i	$-0.259233\pi$
$653$	−7.32692	−	12.6906i	−0.286724	−	0.496621i	−0.973026	+	0.230696i	$0.925900\pi$
$654$	30.8943	−	10.0762i	1.20806	−	0.394011i
$655$	−0.478256	+	29.5939i	−0.0186870	+	1.15633i
$656$	−25.2032	+	10.5526i	−0.984021	+	0.412009i
$657$	−12.4900	−	15.0080i	−0.487283	−	0.585519i
$658$	−10.8533	+	5.81455i	−0.423105	+	0.226675i
$659$	3.26655	−	5.65782i	0.127247	−	0.220398i	−0.795362	−	0.606134i	$-0.792719\pi$
$659$	3.26655	−	5.65782i	0.127247	−	0.220398i	0.922609	+	0.385737i	$0.126053\pi$
$660$	−4.30642	+	4.35444i	−0.167627	+	0.169496i
$661$	13.4007	+	23.2106i	0.521225	+	0.902788i	0.999695	+	0.0246846i	$0.00785816\pi$
$661$	13.4007	+	23.2106i	0.521225	+	0.902788i	−0.478470	+	0.878104i	$0.658809\pi$
$662$	−31.9487	−	19.8247i	−1.24172	−	0.770507i
$663$	−30.7102	+	36.4489i	−1.19269	+	1.41556i
$664$	−22.1774	−	15.7961i	−0.860651	−	0.613007i
$665$	14.3014	+	25.7218i	0.554584	+	0.997450i
$666$	−19.4108	−	24.8915i	−0.752155	−	0.964524i
$667$	−3.53308			−0.136801
$668$	−0.0597722	+	0.0296185i	−0.00231266	+	0.00114598i
$669$	0.103213	−	0.578500i	0.00399044	−	0.0223661i
$670$	1.14150	−	23.7986i	0.0441001	−	0.919419i
$671$	0.687656	+	1.19105i	0.0265466	+	0.0459801i
$672$	−9.31850	+	26.7332i	−0.359469	+	1.03126i
$673$	16.3504	+	9.43992i	0.630262	+	0.363882i	0.780854	−	0.624714i	$-0.214784\pi$
$673$	16.3504	+	9.43992i	0.630262	+	0.363882i	−0.150591	+	0.988596i	$0.548118\pi$
$674$	15.5127	−	8.31076i	0.597526	−	0.320119i
$675$	25.9616	+	0.997191i	0.999263	+	0.0383819i
$676$	9.73367	−	14.6279i	0.374372	−	0.562612i
$677$	10.1163	−	17.5219i	0.388800	−	0.673421i	−0.603488	−	0.797372i	$-0.706223\pi$
$677$	10.1163	−	17.5219i	0.388800	−	0.673421i	0.992288	+	0.123950i	$0.0395564\pi$
$678$	−16.8544	−	15.1418i	−0.647289	−	0.581519i
$679$	16.6122	−	9.59106i	0.637518	−	0.368071i
$680$	30.0173	+	22.1198i	1.15111	+	0.848256i
$681$	−14.6711	−	2.61754i	−0.562196	−	0.100304i
$682$	−0.0930499	+	2.92795i	−0.00356306	+	0.112117i
$683$			15.3795i			0.588481i	0.955731	+	0.294241i	$0.0950667\pi$
$683$			15.3795i			0.588481i	−0.955731	+	0.294241i	$0.904933\pi$
$684$	−16.1135	−	22.0749i	−0.616116	−	0.844054i
$685$	−6.16084	+	3.42544i	−0.235393	+	0.130879i
$686$	−23.0802	−	0.733487i	−0.881207	−	0.0280047i
$687$	0.950687	+	0.801006i	0.0362710	+	0.0305603i
$688$	−28.8445	+	37.8899i	−1.09969	+	1.44454i
$689$	−6.90249	+	3.98516i	−0.262964	+	0.151822i
$690$	−6.97860	+	2.15195i	−0.265671	+	0.0819234i
$691$	−13.7773	−	7.95434i	−0.524114	−	0.302598i	0.214502	−	0.976724i	$-0.431187\pi$
$691$	−13.7773	−	7.95434i	−0.524114	−	0.302598i	−0.738616	+	0.674126i	$0.764520\pi$
$692$	−26.4051	+	39.6819i	−1.00377	+	1.50848i
$693$	−6.43067	−	2.37010i	−0.244281	−	0.0900327i
$694$	21.0944	−	11.3011i	0.800731	−	0.428984i
$695$	−5.74563	−	0.0928530i	−0.217944	−	0.00352211i
$696$	−12.5048	−	3.48592i	−0.473992	−	0.132133i
$697$	−34.8763	+	20.1359i	−1.32104	+	0.762700i
$698$	1.42502	−	2.29651i	0.0539378	−	0.0869242i
$699$	−22.5391	+	8.15193i	−0.852507	+	0.308334i
$700$	28.7619	+	2.76550i	1.08710	+	0.104526i
$701$			38.9767i			1.47213i	0.676912	+	0.736064i	$0.263318\pi$
$701$			38.9767i			1.47213i	−0.676912	+	0.736064i	$0.736682\pi$
$702$	1.29763	−	34.2742i	0.0489758	−	1.29359i
$703$	33.8896			1.27817
$704$	4.14309	−	4.77929i	0.156148	−	0.180126i
$705$	−8.80181	−	7.66259i	−0.331495	−	0.288590i
$706$	−16.4880	+	26.5715i	−0.620535	+	1.00003i
$707$	−6.35758	+	3.67055i	−0.239102	+	0.138045i
$708$	26.4937	+	25.3680i	0.995696	+	0.953387i
$709$	−6.59388	+	11.4209i	−0.247638	+	0.428922i	−0.962870	−	0.269965i	$-0.912988\pi$
$709$	−6.59388	+	11.4209i	−0.247638	+	0.428922i	0.715232	+	0.698887i	$0.246321\pi$
$710$	−7.67505	−	4.93602i	−0.288039	−	0.185245i
$711$	−11.2950	+	1.94449i	−0.423594	+	0.0729240i
$712$	−0.00199697	+	0.0208894i	−7.48398e−5	+	0.000782865i
$713$	−1.74660	+	3.02519i	−0.0654105	+	0.113294i
$714$	−8.63015	+	40.8251i	−0.322975	+	1.52784i
$715$	4.24078	−	7.07857i	0.158596	−	0.264724i
$716$	−50.9545	−	3.24193i	−1.90426	−	0.121157i
$717$	36.7046	+	30.9256i	1.37076	+	1.15494i
$718$	2.09247	+	0.0664984i	0.0780902	+	0.00248170i
$719$	43.7650			1.63216			0.816079	−	0.577940i	$-0.196143\pi$
$719$	43.7650			1.63216			0.816079	+	0.577940i	$0.196143\pi$
$720$	−26.8229	+	0.731056i	−0.999629	+	0.0272449i
$721$	−22.1231			−0.823907
$722$	2.47150	+	0.0785441i	0.0919798	+	0.00292311i
$723$	−3.47603	+	19.4829i	−0.129275	+	0.724575i
$724$	51.1184	+	3.25236i	1.89980	+	0.120873i
$725$	−0.428120	+	13.2423i	−0.0159000	+	0.491808i
$726$	−18.9046	−	16.9837i	−0.701616	−	0.630325i
$727$	4.95811	−	8.58770i	0.183886	−	0.318500i	−0.759314	−	0.650724i	$-0.774466\pi$
$727$	4.95811	−	8.58770i	0.183886	−	0.318500i	0.943201	+	0.332224i	$0.107799\pi$
$728$	3.63005	−	37.9723i	0.134539	−	1.40735i
$729$	−13.2150	−	23.5449i	−0.489445	−	0.872034i
$730$	11.1329	−	17.3107i	0.412049	−	0.640697i
$731$	−35.0935	+	60.7837i	−1.29798	+	2.24816i
$732$	−1.43291	+	5.85295i	−0.0529618	+	0.216331i
$733$	24.2247	−	13.9862i	0.894761	−	0.516591i	0.0192642	−	0.999814i	$-0.493868\pi$
$733$	24.2247	−	13.9862i	0.894761	−	0.516591i	0.875497	+	0.483224i	$0.160534\pi$
$734$	−0.0941235	+	0.151686i	−0.00347416	+	0.00559883i
$735$	1.69733	+	4.94113i	0.0626071	+	0.182256i
$736$	7.04616	−	2.69050i	0.259725	−	0.0991730i
$737$	−5.95699			−0.219428
$738$	10.8808	−	26.8605i	0.400529	−	0.988750i
$739$			24.2237i			0.891082i	0.895262	+	0.445541i	$0.146989\pi$
$739$			24.2237i			0.891082i	−0.895262	+	0.445541i	$0.853011\pi$
$740$	18.8776	−	27.3991i	0.693954	−	1.00721i
$741$	28.1611	+	23.7273i	1.03452	+	0.871644i
$742$	−3.67915	+	5.92918i	−0.135066	+	0.217667i
$743$	−43.9304	+	25.3632i	−1.61165	+	0.930486i	−0.622660	+	0.782492i	$0.713948\pi$
$743$	−43.9304	+	25.3632i	−1.61165	+	0.930486i	−0.988988	+	0.147993i	$0.952719\pi$
$744$	−9.16661	+	8.98391i	−0.336064	+	0.329366i
$745$	−22.0142	−	0.355764i	−0.806539	−	0.0130342i
$746$	−28.5767	+	15.3097i	−1.04627	+	0.560528i
$747$	28.4608	−	4.89968i	1.04133	−	0.179270i
$748$	5.16451	−	7.76131i	0.188833	−	0.283781i
$749$	−34.3117	−	19.8099i	−1.25372	−	0.723838i
$750$	7.22010	+	26.4172i	0.263641	+	0.964621i
$751$	−0.581286	+	0.335605i	−0.0212114	+	0.0122464i	−0.510568	−	0.859837i	$-0.670565\pi$
$751$	−0.581286	+	0.335605i	−0.0212114	+	0.0122464i	0.489357	+	0.872084i	$0.337232\pi$
$752$	9.58999	+	7.30058i	0.349711	+	0.266225i
$753$	−8.22802	+	2.97591i	−0.299846	+	0.108448i
$754$	17.4823	+	0.555585i	0.636667	+	0.0202332i
$755$	11.5953	+	20.8548i	0.421996	+	0.758983i
$756$	−13.1689	−	26.9864i	−0.478949	−	0.981488i
$757$		−	17.0611i		−	0.620095i	−0.950721	−	0.310048i	$-0.899655\pi$
$757$		−	17.0611i		−	0.620095i	0.950721	−	0.310048i	$-0.100345\pi$
$758$	1.23588	−	38.8886i	0.0448890	−	1.41250i
$759$	0.621010	+	1.71702i	0.0225412	+	0.0623238i
$760$	17.0902	−	23.1919i	0.619926	−	0.841260i
$761$	6.74677	−	3.89525i	0.244570	−	0.141203i	−0.372705	−	0.927950i	$-0.621570\pi$
$761$	6.74677	−	3.89525i	0.244570	−	0.141203i	0.617275	+	0.786747i	$0.288236\pi$
$762$	−22.7575	+	7.42239i	−0.824419	+	0.268885i
$763$	−19.1664	+	33.1972i	−0.693870	+	1.20182i
$764$	8.55041	−	12.8497i	0.309343	−	0.464886i
$765$	−39.0789	+	6.07919i	−1.41290	+	0.219793i
$766$	29.5814	−	15.8479i	1.06882	−	0.572609i
$767$	−42.8011	−	24.7112i	−1.54546	−	0.892271i
$768$	27.5933	−	2.57048i	0.995689	−	0.0927543i
$769$	4.58773	+	7.94618i	0.165438	+	0.286546i	0.936811	−	0.349837i	$-0.113763\pi$
$769$	4.58773	+	7.94618i	0.165438	+	0.286546i	−0.771373	+	0.636383i	$0.780430\pi$
$770$	0.346115	−	7.21596i	0.0124731	−	0.260045i
$771$	−3.50658	−	2.95448i	−0.126286	−	0.106403i
$772$	9.25742	−	4.58727i	0.333182	−	0.165100i
$773$	−32.0512			−1.15280			−0.576401	−	0.817167i	$-0.695543\pi$
$773$	−32.0512			−1.15280			−0.576401	+	0.817167i	$0.695543\pi$
$774$	−6.98385	−	50.0234i	−0.251029	−	1.79805i
$775$	11.1271	+	6.91299i	0.399696	+	0.248322i
$776$	−15.2941	−	10.8934i	−0.549026	−	0.391049i
$777$	36.6560	+	6.53999i	1.31503	+	0.234621i
$778$	2.19413	+	1.36149i	0.0786634	+	0.0488119i
$779$	15.5574	+	26.9461i	0.557400	+	0.965445i
$780$	34.8697	−	9.55083i	1.24853	−	0.341975i
$781$	−1.14076	+	1.97585i	−0.0408195	+	0.0707014i
$782$	9.79902	−	5.24973i	0.350412	−	0.187730i
$783$	11.9659	−	6.81197i	0.427627	−	0.243440i
$784$	−2.08395	−	4.97720i	−0.0744269	−	0.177757i
$785$	−33.5594	−	0.542341i	−1.19779	−	0.0193570i
$786$	24.1189	+	21.6682i	0.860294	+	0.772880i
$787$	−1.97855	−	3.42695i	−0.0705276	−	0.122157i	0.828605	−	0.559834i	$-0.189135\pi$
$787$	−1.97855	−	3.42695i	−0.0705276	−	0.122157i	−0.899133	+	0.437676i	$0.855802\pi$
$788$	−16.9081	−	1.07576i	−0.602327	−	0.0383225i
$789$	4.31604	+	0.770047i	0.153655	+	0.0274144i
$790$	−5.53234	−	10.7399i	−0.196832	−	0.382109i
$791$	26.7267			0.950293
$792$	0.503868	+	6.68983i	0.0179042	+	0.237713i
$793$		−	8.11904i		−	0.288316i
$794$	0.857215	−	26.9735i	0.0304214	−	0.957253i
$795$	−6.49120	−	1.26668i	−0.230219	−	0.0449245i
$796$	0.0706030	−	1.10969i	0.00250246	−	0.0393319i
$797$	4.99178	+	8.64602i	0.176818	+	0.306258i	0.940789	−	0.338993i	$-0.110086\pi$
$797$	4.99178	+	8.64602i	0.176818	+	0.306258i	−0.763971	+	0.645251i	$0.776753\pi$
$798$	31.5422	+	6.66782i	1.11658	+	0.236038i
$799$	15.3844	+	8.88219i	0.544261	+	0.314229i
$800$	−9.23043	−	26.7357i	−0.326345	−	0.945251i
$801$	−0.0142378	−	0.0171081i	−0.000503067	−	0.000604485i
$802$	21.7894	−	11.6735i	0.769412	−	0.412205i
$803$	−4.45643	−	2.57292i	−0.157264	−	0.0907963i
$804$	−18.8517	−	18.0506i	−0.664847	−	0.636596i
$805$	4.42727	−	7.38986i	0.156041	−	0.260458i
$806$	9.11817	−	14.6945i	0.321174	−	0.517592i
$807$	−3.10143	−	8.57508i	−0.109176	−	0.301857i
$808$	5.85313	+	4.16895i	0.205912	+	0.146663i
$809$		−	37.9989i		−	1.33597i	−0.744174	−	0.667986i	$-0.767157\pi$
$809$		−	37.9989i		−	1.33597i	0.744174	−	0.667986i	$-0.232843\pi$
$810$	19.4862	−	20.7434i	0.684675	−	0.728849i
$811$		−	21.3193i		−	0.748622i	−0.927303	−	0.374311i	$-0.877879\pi$
$811$		−	21.3193i		−	0.748622i	0.927303	−	0.374311i	$-0.122121\pi$
$812$	13.7211	−	6.79912i	0.481515	−	0.238602i
$813$	−9.80666	−	27.1142i	−0.343934	−	0.950937i
$814$	−7.06861	−	4.38618i	−0.247755	−	0.153736i
$815$	−7.97717	−	4.77913i	−0.279428	−	0.167406i
$816$	39.8617	−	8.91238i	1.39544	−	0.311996i
$817$	46.9626	+	27.1139i	1.64301	+	0.948595i
$818$	10.9222	+	20.3871i	0.381885	+	0.712818i
$819$	25.8811	+	31.0987i	0.904357	+	1.08668i
$820$	30.4514	+	2.43205i	1.06341	+	0.0849310i
$821$	−4.11744	−	2.37721i	−0.143700	−	0.0829651i	0.426426	−	0.904522i	$-0.359772\pi$
$821$	−4.11744	−	2.37721i	−0.143700	−	0.0829651i	−0.570126	+	0.821557i	$0.693106\pi$
$822$	−1.59706	+	7.55492i	−0.0557039	+	0.263508i
$823$	−20.4702	−	35.4554i	−0.713546	−	1.23590i	−0.963518	−	0.267644i	$-0.913755\pi$
$823$	−20.4702	−	35.4554i	−0.713546	−	1.23590i	0.249972	−	0.968253i	$-0.419578\pi$
$824$	8.99402	+	19.6998i	0.313322	+	0.686274i
$825$	6.51080	−	2.11955i	0.226677	−	0.0737931i
$826$	−43.2470	−	1.37438i	−1.50475	−	0.0478210i
$827$		−	26.4974i		−	0.921406i	−0.887554	−	0.460703i	$-0.847597\pi$
$827$		−	26.4974i		−	0.921406i	0.887554	−	0.460703i	$-0.152403\pi$
$828$	−3.23757	+	7.31548i	−0.112513	+	0.254230i
$829$	38.1524			1.32509			0.662544	−	0.749023i	$-0.269477\pi$
$829$	38.1524			1.32509			0.662544	+	0.749023i	$0.269477\pi$
$830$	13.9403	+	27.0622i	0.483874	+	0.939342i
$831$	−45.0026	−	8.02915i	−1.56112	−	0.278528i
$832$	−35.2887	+	12.2050i	−1.22342	+	0.423133i
$833$	−3.97649	−	6.88748i	−0.137777	−	0.238637i
$834$	−4.20686	+	4.68267i	−0.145672	+	0.162147i
$835$	0.0745722	+	0.00120513i	0.00258068	+	4.17054e-5i
$836$	−5.99653	−	3.99020i	−0.207394	−	0.138004i
$837$	0.0826736	−	13.6133i	0.00285762	−	0.470545i
$838$	16.5421	+	30.8771i	0.571437	+	1.06663i
$839$	8.60385	−	14.9023i	0.297038	−	0.514485i	−0.678419	−	0.734675i	$-0.737335\pi$
$839$	8.60385	−	14.9023i	0.297038	−	0.514485i	0.975457	+	0.220190i	$0.0706679\pi$
$840$	22.9608	−	21.7871i	0.792224	−	0.751725i
$841$	−10.9891	−	19.0338i	−0.378936	−	0.656337i
$842$	−12.5064	+	20.1549i	−0.431000	+	0.694584i
$843$	−39.0851	−	6.97337i	−1.34616	−	0.240175i
$844$	−43.5892	+	21.5995i	−1.50040	+	0.743484i
$845$	−17.1690	+	9.54600i	−0.590631	+	0.328392i
$846$	−12.6610	+	1.76762i	−0.435293	+	0.0607720i
$847$	29.9778			1.03005
$848$	6.77545	+	0.865668i	0.232670	+	0.0297272i
$849$	8.62913	+	7.27052i	0.296151	+	0.249524i
$850$	−18.4891	−	37.3638i	−0.634172	−	1.28157i
$851$	−4.95992	−	8.59084i	−0.170024	−	0.294490i
$852$	−9.59720	+	2.79615i	−0.328795	+	0.0957946i
$853$	−37.6416	−	21.7324i	−1.28882	−	0.744102i	−0.310378	−	0.950613i	$-0.600456\pi$
$853$	−37.6416	−	21.7324i	−1.28882	−	0.744102i	−0.978444	+	0.206511i	$0.933789\pi$
$854$	−3.35674	−	6.26561i	−0.114865	−	0.214405i
$855$	4.69690	+	30.1931i	0.160630	+	1.03258i
$856$	−3.69072	+	38.6069i	−0.126146	+	1.31956i
$857$	−6.72648	+	11.6506i	−0.229772	+	0.397977i	−0.957741	−	0.287634i	$-0.907131\pi$
$857$	−6.72648	+	11.6506i	−0.229772	+	0.397977i	0.727968	+	0.685611i	$0.240465\pi$
$858$	−2.80286	−	8.59375i	−0.0956879	−	0.293386i
$859$	1.00899	−	0.582541i	0.0344263	−	0.0198760i	−0.482688	−	0.875792i	$-0.660340\pi$
$859$	1.00899	−	0.582541i	0.0344263	−	0.0198760i	0.517114	+	0.855916i	$0.327006\pi$
$860$	48.0807	−	22.8650i	1.63954	−	0.779691i
$861$	11.6273	+	32.1480i	0.396257	+	1.09560i
$862$	−21.5542	−	0.684991i	−0.734139	−	0.0233309i
$863$		−	0.0600669i		−	0.00204470i	−0.999999	−	0.00102235i	$-0.999675\pi$
$863$		−	0.0600669i		−	0.00204470i	0.999999	−	0.00102235i	$-0.000325424\pi$
$864$	−18.6767	+	22.6976i	−0.635393	+	0.772189i
$865$	46.5753	−	25.8959i	1.58361	−	0.880488i
$866$	1.05877	−	33.3156i	0.0359783	−	1.13211i
$867$	28.9242	−	10.4613i	0.982317	−	0.355284i
$868$	0.961349	−	15.1098i	0.0326303	−	0.512861i
$869$	−2.61585	+	1.51026i	−0.0887367	+	0.0512321i
$870$	10.6385	+	9.87282i	0.360680	+	0.334720i
$871$	30.4552	+	17.5833i	1.03193	+	0.595788i
$872$	37.3528	+	3.57083i	1.26493	+	0.120924i
$873$	19.6273	−	3.37894i	0.664282	−	0.114360i
$874$	−4.05604	−	7.57091i	−0.137198	−	0.256090i
$875$	−27.1615	−	17.4893i	−0.918225	−	0.591247i
$876$	−6.30658	−	21.6460i	−0.213080	−	0.731351i
$877$	−5.64252	+	3.25771i	−0.190534	+	0.110005i	−0.592233	−	0.805767i	$-0.701753\pi$
$877$	−5.64252	+	3.25771i	−0.190534	+	0.110005i	0.401698	+	0.915772i	$0.368420\pi$
$878$	17.8563	+	11.0801i	0.602620	+	0.373935i
$879$	−22.1805	−	18.6883i	−0.748131	−	0.630342i
$880$	−6.56626	+	2.62541i	−0.221349	+	0.0885025i
$881$			12.1468i			0.409237i	0.978842	+	0.204619i	$0.0655954\pi$
$881$			12.1468i			0.409237i	−0.978842	+	0.204619i	$0.934405\pi$
$882$	5.30449	+	2.14878i	0.178611	+	0.0723531i
$883$	30.7337			1.03427			0.517135	−	0.855904i	$-0.326998\pi$
$883$	30.7337			1.03427			0.517135	+	0.855904i	$0.326998\pi$
$884$	−49.3128	+	24.4357i	−1.65857	+	0.821860i
$885$	−13.3232	−	38.7854i	−0.447855	−	1.30376i
$886$	32.6163	+	20.2389i	1.09577	+	0.679940i
$887$	48.2108	−	27.8345i	1.61876	−	0.934592i	0.631519	−	0.775361i	$-0.282432\pi$
$887$	48.2108	−	27.8345i	1.61876	−	0.934592i	0.987241	−	0.159231i	$-0.0509014\pi$
$888$	−9.07870	−	35.2996i	−0.304661	−	1.18458i
$889$	14.1185	−	24.4539i	0.473518	−	0.820157i
$890$	0.0126908	−	0.0197330i	0.000425396	−	0.000661451i
$891$	−5.41375	−	4.61789i	−0.181368	−	0.154705i
$892$	0.375899	−	0.564907i	0.0125860	−	0.0189145i
$893$	6.86255	−	11.8863i	0.229647	−	0.397760i
$894$	−16.1185	+	17.9415i	−0.539083	+	0.600054i
$895$	48.9686	+	29.3371i	1.63684	+	0.980632i
$896$	−22.1868	+	24.0086i	−0.741211	+	0.802070i
$897$	1.89322	−	10.6113i	0.0632127	−	0.354301i
$898$	0.785572	−	24.7191i	0.0262149	−	0.824888i
$899$	6.94243			0.231543
$900$	27.0268	+	13.0212i	0.900894	+	0.434039i
$901$	10.0675			0.335397
$902$	0.242604	−	7.63388i	0.00807783	−	0.254180i
$903$	45.5638	+	38.3900i	1.51627	+	1.27754i
$904$	−10.8656	−	23.7992i	−0.361385	−	0.791548i
$905$	−49.1261	−	29.4315i	−1.63301	−	0.978336i
$906$	25.5738	+	5.40614i	0.849634	+	0.179607i
$907$	8.31258	−	14.3978i	0.276015	−	0.478072i	−0.694376	−	0.719612i	$-0.744319\pi$
$907$	8.31258	−	14.3978i	0.276015	−	0.478072i	0.970391	+	0.241541i	$0.0776528\pi$
$908$	−14.3263	−	9.53299i	−0.475436	−	0.316363i
$909$	−7.51146	+	1.29314i	−0.249139	+	0.0428907i
$910$	−23.0690	+	35.8701i	−0.764729	+	1.18908i
$911$	−9.29200	+	16.0942i	−0.307858	+	0.533225i	−0.977893	−	0.209104i	$-0.932945\pi$
$911$	−9.29200	+	16.0942i	−0.307858	+	0.533225i	0.670036	+	0.742329i	$0.266279\pi$
$912$	−6.88587	−	30.7979i	−0.228014	−	1.01982i
$913$	6.59137	−	3.80553i	0.218143	−	0.125945i
$914$	−7.08529	−	4.39653i	−0.234360	−	0.145424i
$915$	4.42361	−	5.08129i	0.146240	−	0.167982i
$916$	0.637349	+	1.28621i	0.0210586	+	0.0424977i
$917$	−38.2464			−1.26301
$918$	−23.0658	+	36.6730i	−0.761284	+	1.21039i
$919$			31.1617i			1.02793i	0.857811	+	0.513965i	$0.171824\pi$
$919$			31.1617i			1.02793i	−0.857811	+	0.513965i	$0.828176\pi$
$920$	−8.38028	−	0.938012i	−0.276290	−	0.0309253i
$921$	−39.5403	+	14.3009i	−1.30290	+	0.471231i
$922$	−42.4523	−	26.3423i	−1.39809	−	0.867538i
$923$	11.6643	−	6.73437i	0.383934	−	0.221664i
$924$	−5.71601	−	5.47313i	−0.188043	−	0.180053i
$925$	−32.8003	+	17.5493i	−1.07847	+	0.577017i
$926$	24.8672	+	46.4166i	0.817189	+	1.52534i
$927$	−21.5522	−	7.94333i	−0.707868	−	0.260893i
$928$	−11.6326	−	9.45396i	−0.381858	−	0.310341i
$929$	24.5849	+	14.1941i	0.806604	+	0.465693i	0.845775	−	0.533540i	$-0.179139\pi$
$929$	24.5849	+	14.1941i	0.806604	+	0.465693i	−0.0391715	+	0.999233i	$0.512472\pi$
$930$	13.7128	−	4.22855i	0.449661	−	0.138659i
$931$	−5.32140	+	3.07231i	−0.174402	+	0.100691i
$932$	−27.6200	−	1.75730i	−0.904723	−	0.0575622i
$933$	10.1108	+	8.51892i	0.331013	+	0.278897i
$934$	0.313698	−	9.87095i	0.0102645	−	0.322988i
$935$	−9.10955	+	5.06493i	−0.297914	+	0.165641i
$936$	17.1704	−	35.6891i	0.561232	−	1.16654i
$937$		−	25.1998i		−	0.823241i	−0.911355	−	0.411620i	$-0.864963\pi$
$937$		−	25.1998i		−	0.823241i	0.911355	−	0.411620i	$-0.135037\pi$
$938$	30.7724	+	0.977945i	1.00476	+	0.0319311i
$939$	−7.59676	−	1.35538i	−0.247911	−	0.0442310i
$940$	−5.78717	−	12.1693i	−0.188757	−	0.396918i
$941$	35.0946	−	20.2619i	1.14405	−	0.660519i	0.196622	−	0.980479i	$-0.437003\pi$
$941$	35.0946	−	20.2619i	1.14405	−	0.660519i	0.947431	+	0.319960i	$0.103670\pi$
$942$	−24.5717	+	27.3508i	−0.800589	+	0.891137i
$943$	4.55381	−	7.88742i	0.148292	−	0.256850i
$944$	16.3580	+	39.0686i	0.532407	+	1.27157i
$945$	−0.746326	+	33.5642i	−0.0242780	+	1.09184i
$946$	−6.28612	−	11.7335i	−0.204379	−	0.381489i
$947$	0.518242	+	0.299207i	0.0168406	+	0.00972293i	0.508397	−	0.861123i	$-0.330238\pi$
$947$	0.518242	+	0.299207i	0.0168406	+	0.00972293i	−0.491556	+	0.870846i	$0.663572\pi$
$948$	−12.8545	−	3.14702i	−0.417496	−	0.102211i
$949$	15.1890	+	26.3082i	0.493057	+	0.853999i
$950$	−28.8680	+	14.2850i	−0.936602	+	0.463468i
$951$	−1.50768	+	8.45043i	−0.0488900	+	0.274024i
$952$	−27.9528	+	39.2453i	−0.905956	+	1.27195i
$953$	−2.50405			−0.0811142			−0.0405571	−	0.999177i	$-0.512913\pi$
$953$	−2.50405			−0.0811142			−0.0405571	+	0.999177i	$0.512913\pi$
$954$	−5.71310	+	4.45518i	−0.184968	+	0.144242i
$955$	−15.0819	+	8.38555i	−0.488038	+	0.271350i
$956$	24.6071	+	49.6587i	0.795850	+	1.60608i
$957$	2.33815	−	2.77507i	0.0755816	−	0.0897052i
$958$	15.2247	−	24.5356i	0.491888	−	0.792708i
$959$	−4.55443	−	7.88850i	−0.147070	−	0.254733i
$960$	−28.7352	−	11.5884i	−0.927424	−	0.374012i
$961$	−12.0680	+	20.9023i	−0.389289	+	0.674269i
$962$	23.1916	+	43.2889i	0.747728	+	1.39569i
$963$	−26.3136	−	31.6184i	−0.847944	−	1.01889i
$964$	−12.6596	+	19.0251i	−0.407739	+	0.612756i
$965$	−11.5496	−	0.186649i	−0.371796	−	0.00600845i
$966$	−2.92612	−	8.97167i	−0.0941462	−	0.288659i
$967$	−18.5754	−	32.1736i	−0.597346	−	1.03463i	−0.993211	−	0.116325i	$-0.962889\pi$
$967$	−18.5754	−	32.1736i	−0.597346	−	1.03463i	0.395866	−	0.918308i	$-0.370445\pi$
$968$	−12.1873	−	26.6941i	−0.391715	−	0.857982i
$969$	−15.8201	−	43.7408i	−0.508216	−	1.40516i
$970$	9.61355	+	18.6627i	0.308672	+	0.599224i
$971$	14.7960			0.474826			0.237413	−	0.971409i	$-0.423701\pi$
$971$	14.7960			0.474826			0.237413	+	0.971409i	$0.423701\pi$
$972$	−3.13958	−	31.0184i	−0.100702	−	0.994917i
$973$		−	7.42550i		−	0.238051i
$974$	29.4381	+	0.935542i	0.943259	+	0.0299767i
$975$	−39.5429	−	8.38179i	−1.26638	−	0.268432i
$976$	−4.21462	+	5.53630i	−0.134907	+	0.177213i
$977$	16.1759	+	28.0175i	0.517514	+	0.896360i	0.999793	+	0.0203428i	$0.00647578\pi$
$977$	16.1759	+	28.0175i	0.517514	+	0.896360i	−0.482279	+	0.876018i	$0.660191\pi$
$978$	−9.68469	+	3.15867i	−0.309682	+	0.101003i
$979$	−0.00508002	−	0.00293295i	−0.000162358	−	9.37374e-5i
$980$	−0.480289	+	6.01362i	−0.0153423	+	0.192098i
$981$	−30.5913	+	25.4588i	−0.976707	+	0.812838i
$982$	12.4434	+	23.2266i	0.397086	+	0.741191i
$983$	2.93257	+	1.69312i	0.0935346	+	0.0540022i	0.546038	−	0.837761i	$-0.316136\pi$
$983$	2.93257	+	1.69312i	0.0935346	+	0.0540022i	−0.452503	+	0.891763i	$0.649469\pi$
$984$	23.8996	−	23.4233i	0.761892	−	0.746706i
$985$	16.2492	+	9.73488i	0.517741	+	0.310179i
$986$	−18.7730	−	11.6489i	−0.597853	−	0.370977i
$987$	9.71656	−	11.5323i	0.309281	−	0.367076i
$988$	18.8795	+	38.1000i	0.600635	+	1.21212i
$989$		−	15.8731i		−	0.504734i
$990$	2.92809	−	6.90550i	0.0930608	−	0.219471i
$991$		−	39.7022i		−	1.26118i	−0.776116	−	0.630591i	$-0.782813\pi$
$991$		−	39.7022i		−	1.26118i	0.776116	−	0.630591i	$-0.217187\pi$
$992$	−13.8456	+	5.28677i	−0.439597	+	0.167855i
$993$	45.3341	+	8.08829i	1.43864	+	0.256674i
$994$	6.21726	−	10.0195i	0.197199	−	0.317799i
$995$	−0.638906	+	1.06644i	−0.0202547	+	0.0338085i
$996$	32.3906	+	7.92980i	1.02634	+	0.251265i
$997$	17.8325	+	10.2956i	0.564760	+	0.326064i	0.755054	−	0.655663i	$-0.227611\pi$
$997$	17.8325	+	10.2956i	0.564760	+	0.326064i	−0.190294	+	0.981727i	$0.560944\pi$
$998$	6.45827	−	3.45995i	0.204433	−	0.109523i
$999$	33.3620	+	19.5327i	1.05553	+	0.617986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.2.n.d.119.1	yes	48
3.2	odd	2		540.2.n.d.359.24		48
4.3	odd	2	inner	180.2.n.d.119.17	yes	48
5.2	odd	4		900.2.r.g.551.13		48
5.3	odd	4		900.2.r.g.551.12		48
5.4	even	2	inner	180.2.n.d.119.24	yes	48
9.4	even	3		540.2.n.d.179.17		48
9.5	odd	6	inner	180.2.n.d.59.8	yes	48
12.11	even	2		540.2.n.d.359.8		48
15.14	odd	2		540.2.n.d.359.1		48
20.3	even	4		900.2.r.g.551.20		48
20.7	even	4		900.2.r.g.551.5		48
20.19	odd	2	inner	180.2.n.d.119.8	yes	48
36.23	even	6	inner	180.2.n.d.59.24	yes	48
36.31	odd	6		540.2.n.d.179.1		48
45.4	even	6		540.2.n.d.179.8		48
45.14	odd	6	inner	180.2.n.d.59.17	yes	48
45.23	even	12		900.2.r.g.851.20		48
45.32	even	12		900.2.r.g.851.5		48
60.59	even	2		540.2.n.d.359.17		48
180.23	odd	12		900.2.r.g.851.12		48
180.59	even	6	inner	180.2.n.d.59.1	✓	48
180.139	odd	6		540.2.n.d.179.24		48
180.167	odd	12		900.2.r.g.851.13		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.1	✓	48	180.59	even	6	inner
180.2.n.d.59.8	yes	48	9.5	odd	6	inner
180.2.n.d.59.17	yes	48	45.14	odd	6	inner
180.2.n.d.59.24	yes	48	36.23	even	6	inner
180.2.n.d.119.1	yes	48	1.1	even	1	trivial
180.2.n.d.119.8	yes	48	20.19	odd	2	inner
180.2.n.d.119.17	yes	48	4.3	odd	2	inner
180.2.n.d.119.24	yes	48	5.4	even	2	inner
540.2.n.d.179.1		48	36.31	odd	6
540.2.n.d.179.8		48	45.4	even	6
540.2.n.d.179.17		48	9.4	even	3
540.2.n.d.179.24		48	180.139	odd	6
540.2.n.d.359.1		48	15.14	odd	2
540.2.n.d.359.8		48	12.11	even	2
540.2.n.d.359.17		48	60.59	even	2
540.2.n.d.359.24		48	3.2	odd	2
900.2.r.g.551.5		48	20.7	even	4
900.2.r.g.551.12		48	5.3	odd	4
900.2.r.g.551.13		48	5.2	odd	4
900.2.r.g.551.20		48	20.3	even	4
900.2.r.g.851.5		48	45.32	even	12
900.2.r.g.851.12		48	180.23	odd	12
900.2.r.g.851.13		48	180.167	odd	12
900.2.r.g.851.20		48	45.23	even	12

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41350 - 0.0449209i) q^{2} +(1.62879 - 0.589100i) q^{3} +(1.99596 + 0.126991i) q^{4} +(-1.91817 - 1.14918i) q^{5} +(-2.32876 + 0.759526i) q^{6} +(1.44473 - 2.50234i) q^{7} +(-2.81559 - 0.269163i) q^{8} +(2.30592 - 1.91904i) q^{9} +(2.65972 + 1.71053i) q^{10} +(0.395318 - 0.684712i) q^{11} +(3.32582 - 0.968981i) q^{12} +(-4.04214 + 2.33373i) q^{13} +(-2.15453 + 3.47216i) q^{14} +(-3.80129 - 0.741776i) q^{15} +(3.96775 + 0.506941i) q^{16} +5.89560 q^{17} +(-3.34563 + 2.60898i) q^{18} -4.55505i q^{19} +(-3.68267 - 2.53731i) q^{20} +(0.879030 - 4.92689i) q^{21} +(-0.589540 + 0.950082i) q^{22} +(-1.15468 + 0.666656i) q^{23} +(-4.74457 + 1.22026i) q^{24} +(2.35878 + 4.40865i) q^{25} +(5.81840 - 3.11715i) q^{26} +(2.62536 - 4.48414i) q^{27} +(3.20140 - 4.81112i) q^{28} +(2.29484 + 1.32492i) q^{29} +(5.33980 + 1.21926i) q^{30} +(2.26893 - 1.30997i) q^{31} +(-5.58564 - 0.894795i) q^{32} +(0.240527 - 1.34813i) q^{33} +(-8.33343 - 0.264836i) q^{34} +(-5.64688 + 3.13968i) q^{35} +(4.84624 - 3.53751i) q^{36} +7.44000i q^{37} +(-0.204617 + 6.43857i) q^{38} +(-5.20900 + 6.18239i) q^{39} +(5.09147 + 3.75192i) q^{40} +(-5.91566 + 3.41541i) q^{41} +(-1.46383 + 6.92467i) q^{42} +(-5.95249 + 10.3100i) q^{43} +(0.875994 - 1.31646i) q^{44} +(-6.62848 + 1.03114i) q^{45} +(1.66209 - 0.890449i) q^{46} +(2.60947 + 1.50658i) q^{47} +(6.76127 - 1.51170i) q^{48} +(-0.674484 - 1.16824i) q^{49} +(-3.13609 - 6.33758i) q^{50} +(9.60270 - 3.47310i) q^{51} +(-8.36434 + 4.14473i) q^{52} +1.70763 q^{53} +(-3.91237 + 6.22040i) q^{54} +(-1.54515 + 0.859104i) q^{55} +(-4.74130 + 6.65671i) q^{56} +(-2.68338 - 7.41923i) q^{57} +(-3.18423 - 1.97587i) q^{58} +(5.29436 + 9.17010i) q^{59} +(-7.49303 - 1.96329i) q^{60} +(-0.869749 + 1.50645i) q^{61} +(-3.26598 + 1.74972i) q^{62} +(-1.47067 - 8.54271i) q^{63} +(7.85510 + 1.51570i) q^{64} +(10.4354 + 0.168643i) q^{65} +(-0.400545 + 1.89478i) q^{66} +(-3.76721 - 6.52500i) q^{67} +(11.7674 + 0.748690i) q^{68} +(-1.48801 + 1.76607i) q^{69} +(8.12290 - 4.18427i) q^{70} -2.88566 q^{71} +(-7.00907 + 4.78257i) q^{72} -6.50847i q^{73} +(0.334212 - 10.5164i) q^{74} +(6.43909 + 5.79121i) q^{75} +(0.578452 - 9.09172i) q^{76} +(-1.14226 - 1.97845i) q^{77} +(7.64065 - 8.50481i) q^{78} +(-3.30854 - 1.91019i) q^{79} +(-7.02826 - 5.53205i) q^{80} +(1.63455 - 8.85032i) q^{81} +(8.51521 - 4.56194i) q^{82} +(8.33679 + 4.81325i) q^{83} +(2.38019 - 9.72226i) q^{84} +(-11.3088 - 6.77510i) q^{85} +(8.87697 - 14.3058i) q^{86} +(4.51832 + 0.806137i) q^{87} +(-1.29735 + 1.82146i) q^{88} -0.00741921i q^{89} +(9.41568 - 1.15976i) q^{90} +13.4864i q^{91} +(-2.38937 + 1.18399i) q^{92} +(2.92391 - 3.47029i) q^{93} +(-3.62081 - 2.24677i) q^{94} +(-5.23457 + 8.73738i) q^{95} +(-9.62496 + 1.83307i) q^{96} +(5.74925 + 3.31933i) q^{97} +(0.900905 + 1.68161i) q^{98} +(-0.402417 - 2.33752i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} - 18 q^{5} - 12 q^{9} - 16 q^{10} - 42 q^{14} + 30 q^{16} - 12 q^{21} - 6 q^{24} - 26 q^{25} - 12 q^{30} - 4 q^{34} + 96 q^{36} + 10 q^{40} + 96 q^{41} - 66 q^{45} + 4 q^{46} + 32 q^{49}+ \cdots + 54 q^{96}+O(q^{100}) \) 48 * q - 2 * q^4 - 18 * q^5 - 12 * q^9 - 16 * q^10 - 42 * q^14 + 30 * q^16 - 12 * q^21 - 6 * q^24 - 26 * q^25 - 12 * q^30 - 4 * q^34 + 96 * q^36 + 10 * q^40 + 96 * q^41 - 66 * q^45 + 4 * q^46 + 32 * q^49 - 90 * q^50 - 30 * q^54 + 6 * q^56 - 42 * q^60 + 8 * q^61 - 20 * q^64 - 6 * q^65 + 36 * q^66 - 96 * q^69 + 4 * q^70 + 72 * q^74 + 36 * q^81 - 6 * q^84 - 4 * q^85 + 108 * q^86 - 6 * q^90 - 62 * q^94 + 54 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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