LMFDB - Embedded newform 378.2.z.a.83.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,2,Mod(41,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.41"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([17, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.z (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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			83.11
Character	$\chi$	$=$	378.83
Dual form			378.2.z.a.41.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.984808 - 0.173648i) q^{2} +(1.56441 - 0.743380i) q^{3} +(0.939693 + 0.342020i) q^{4} +(0.941136 - 0.789707i) q^{5} +(-1.66973 + 0.460429i) q^{6} +(2.22826 - 1.42648i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(1.89477 - 2.32590i) q^{9} +(-1.06397 + 0.614283i) q^{10} +(-1.50712 + 1.79612i) q^{11} +(1.72432 - 0.163488i) q^{12} +(-0.429778 + 0.0757815i) q^{13} +(-2.44212 + 1.01787i) q^{14} +(0.885273 - 1.93505i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-1.74272 - 3.01848i) q^{17} +(-2.26988 + 1.96155i) q^{18} +(1.97392 + 1.13964i) q^{19} +(1.15447 - 0.420194i) q^{20} +(2.42551 - 3.88805i) q^{21} +(1.79612 - 1.50712i) q^{22} +(-1.85030 + 5.08367i) q^{23} +(-1.72651 - 0.138421i) q^{24} +(-0.606141 + 3.43760i) q^{25} +0.436408 q^{26} +(1.23518 - 5.04721i) q^{27} +(2.58177 - 0.578340i) q^{28} +(-2.08501 - 0.367644i) q^{29} +(-1.20784 + 1.75193i) q^{30} +(2.87174 - 7.89005i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(-1.02256 + 3.93024i) q^{33} +(1.19209 + 3.27524i) q^{34} +(0.970599 - 3.10219i) q^{35} +(2.57601 - 1.53759i) q^{36} +(2.71169 + 4.69678i) q^{37} +(-1.74604 - 1.46510i) q^{38} +(-0.616016 + 0.438042i) q^{39} +(-1.20990 + 0.213338i) q^{40} +(-0.273818 - 1.55290i) q^{41} +(-3.06381 + 3.40779i) q^{42} +(-1.56927 - 1.31677i) q^{43} +(-2.03054 + 1.17233i) q^{44} +(-0.0535437 - 3.68531i) q^{45} +(2.70496 - 4.68513i) q^{46} +(-4.45922 + 1.62303i) q^{47} +(1.67624 + 0.436123i) q^{48} +(2.93032 - 6.35714i) q^{49} +(1.19386 - 3.28012i) q^{50} +(-4.97020 - 3.42664i) q^{51} +(-0.429778 - 0.0757815i) q^{52} +0.117957i q^{53} +(-2.09285 + 4.75605i) q^{54} +2.88058i q^{55} +(-2.64297 + 0.121235i) q^{56} +(3.93522 + 0.315500i) q^{57} +(1.98950 + 0.724117i) q^{58} +(9.22472 - 7.74046i) q^{59} +(1.49371 - 1.51557i) q^{60} +(3.82461 + 10.5080i) q^{61} +(-4.19821 + 7.27151i) q^{62} +(0.904201 - 7.88558i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.344635 + 0.410720i) q^{65} +(1.68951 - 3.69296i) q^{66} +(1.46744 + 8.32229i) q^{67} +(-0.605240 - 3.43248i) q^{68} +(0.884457 + 9.32843i) q^{69} +(-1.49454 + 2.88651i) q^{70} +(-1.77135 + 1.02269i) q^{71} +(-2.80387 + 1.06691i) q^{72} +(-6.00651 - 3.46786i) q^{73} +(-1.85490 - 5.09631i) q^{74} +(1.60718 + 5.82841i) q^{75} +(1.46510 + 1.74604i) q^{76} +(-0.796142 + 6.15211i) q^{77} +(0.682723 - 0.324417i) q^{78} +(-0.916064 + 5.19526i) q^{79} +1.22857 q^{80} +(-1.81967 - 8.81413i) q^{81} +1.57686i q^{82} +(-1.50719 + 8.54769i) q^{83} +(3.60902 - 2.82400i) q^{84} +(-4.02385 - 1.46456i) q^{85} +(1.31677 + 1.56927i) q^{86} +(-3.53512 + 0.974809i) q^{87} +(2.20327 - 0.801923i) q^{88} +(-7.35317 + 12.7361i) q^{89} +(-0.587217 + 3.63862i) q^{90} +(-0.849559 + 0.781931i) q^{91} +(-3.47743 + 4.14424i) q^{92} +(-1.37271 - 14.4781i) q^{93} +(4.67331 - 0.824031i) q^{94} +(2.75771 - 0.486259i) q^{95} +(-1.57505 - 0.720574i) q^{96} +(-9.82215 + 11.7056i) q^{97} +(-3.98971 + 5.75172i) q^{98} +(1.32195 + 6.90866i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57}+ \cdots + 144 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$

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 $

$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$3$	1.56441	−	0.743380i	0.903214	−	0.429190i
$3$	1.56441	−	0.743380i	0.903214	−	0.429190i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	0.941136	−	0.789707i	0.420889	−	0.353168i	−0.407612	−	0.913155i	$-0.633638\pi$
$5$	0.941136	−	0.789707i	0.420889	−	0.353168i	0.828501	+	0.559987i	$0.189194\pi$
$6$	−1.66973	+	0.460429i	−0.681665	+	0.187969i
$7$	2.22826	−	1.42648i	0.842205	−	0.539158i
$7$	2.22826	−	1.42648i	0.842205	−	0.539158i
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	1.89477	−	2.32590i	0.631591	−	0.775302i
$10$	−1.06397	+	0.614283i	−0.336457	+	0.194253i
$11$	−1.50712	+	1.79612i	−0.454415	+	0.541550i	−0.943800	−	0.330517i	$-0.892777\pi$
$11$	−1.50712	+	1.79612i	−0.454415	+	0.541550i	0.489385	+	0.872068i	$0.337221\pi$
$12$	1.72432	−	0.163488i	0.497768	−	0.0471949i
$13$	−0.429778	+	0.0757815i	−0.119199	+	0.0210180i	−0.232929	−	0.972494i	$-0.574831\pi$
$13$	−0.429778	+	0.0757815i	−0.119199	+	0.0210180i	0.113730	+	0.993512i	$0.463720\pi$
$14$	−2.44212	+	1.01787i	−0.652683	+	0.272038i
$15$	0.885273	−	1.93505i	0.228577	−	0.499627i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−1.74272	−	3.01848i	−0.422671	−	0.732088i	0.573529	−	0.819186i	$-0.305574\pi$
$17$	−1.74272	−	3.01848i	−0.422671	−	0.732088i	−0.996200	+	0.0870975i	$0.972241\pi$
$18$	−2.26988	+	1.96155i	−0.535015	+	0.462341i
$19$	1.97392	+	1.13964i	0.452849	+	0.261452i	0.709032	−	0.705176i	$-0.249132\pi$
$19$	1.97392	+	1.13964i	0.452849	+	0.261452i	−0.256184	+	0.966628i	$0.582465\pi$
$20$	1.15447	−	0.420194i	0.258148	−	0.0939583i
$21$	2.42551	−	3.88805i	0.529289	−	0.848441i
$22$	1.79612	−	1.50712i	0.382934	−	0.321320i
$23$	−1.85030	+	5.08367i	−0.385815	+	1.06002i	0.583052	+	0.812435i	$0.301858\pi$
$23$	−1.85030	+	5.08367i	−0.385815	+	1.06002i	−0.968867	+	0.247583i	$0.920364\pi$
$24$	−1.72651	−	0.138421i	−0.352423	−	0.0282550i
$25$	−0.606141	+	3.43760i	−0.121228	+	0.687519i
$26$	0.436408			0.0855867
$27$	1.23518	−	5.04721i	0.237710	−	0.971336i
$28$	2.58177	−	0.578340i	0.487908	−	0.109296i
$29$	−2.08501	−	0.367644i	−0.387177	−	0.0682698i	−0.0233285	−	0.999728i	$-0.507426\pi$
$29$	−2.08501	−	0.367644i	−0.387177	−	0.0682698i	−0.363849	+	0.931458i	$0.618537\pi$
$30$	−1.20784	+	1.75193i	−0.220521	+	0.319856i
$31$	2.87174	−	7.89005i	0.515780	−	1.41709i	−0.359348	−	0.933203i	$-0.617001\pi$
$31$	2.87174	−	7.89005i	0.515780	−	1.41709i	0.875129	−	0.483891i	$-0.160777\pi$
$32$	−0.642788	−	0.766044i	−0.113630	−	0.135419i
$33$	−1.02256	+	3.93024i	−0.178005	+	0.684166i
$34$	1.19209	+	3.27524i	0.204442	+	0.561699i
$35$	0.970599	−	3.10219i	0.164061	−	0.524365i
$36$	2.57601	−	1.53759i	0.429335	−	0.256264i
$37$	2.71169	+	4.69678i	0.445799	+	0.772146i	0.998107	−	0.0614933i	$-0.0195863\pi$
$37$	2.71169	+	4.69678i	0.445799	+	0.772146i	−0.552309	+	0.833640i	$0.686253\pi$
$38$	−1.74604	−	1.46510i	−0.283244	−	0.237670i
$39$	−0.616016	+	0.438042i	−0.0986416	+	0.0701429i
$40$	−1.20990	+	0.213338i	−0.191302	+	0.0337317i
$41$	−0.273818	−	1.55290i	−0.0427632	−	0.242522i	0.955932	−	0.293588i	$-0.0948494\pi$
$41$	−0.273818	−	1.55290i	−0.0427632	−	0.242522i	−0.998695	+	0.0510656i	$0.983738\pi$
$42$	−3.06381	+	3.40779i	−0.472756	+	0.525834i
$43$	−1.56927	−	1.31677i	−0.239311	−	0.200806i	0.515242	−	0.857045i	$-0.327702\pi$
$43$	−1.56927	−	1.31677i	−0.239311	−	0.200806i	−0.754553	+	0.656239i	$0.772146\pi$
$44$	−2.03054	+	1.17233i	−0.306116	+	0.176736i
$45$	−0.0535437	−	3.68531i	−0.00798183	−	0.549373i
$46$	2.70496	−	4.68513i	0.398825	−	0.690785i
$47$	−4.45922	+	1.62303i	−0.650445	+	0.236743i	−0.646106	−	0.763248i	$-0.723603\pi$
$47$	−4.45922	+	1.62303i	−0.650445	+	0.236743i	−0.00433921	+	0.999991i	$0.501381\pi$
$48$	1.67624	+	0.436123i	0.241945	+	0.0629490i
$49$	2.93032	−	6.35714i	0.418617	−	0.908163i
$50$	1.19386	−	3.28012i	0.168838	−	0.463878i
$51$	−4.97020	−	3.42664i	−0.695968	−	0.479826i
$52$	−0.429778	−	0.0757815i	−0.0595995	−	0.0105090i
$53$			0.117957i			0.0162026i	0.999967	+	0.00810130i	$0.00257875\pi$
$53$			0.117957i			0.0162026i	−0.999967	+	0.00810130i	$0.997421\pi$
$54$	−2.09285	+	4.75605i	−0.284801	+	0.647216i
$55$			2.88058i			0.388417i
$56$	−2.64297	+	0.121235i	−0.353182	+	0.0162007i
$57$	3.93522	+	0.315500i	0.521232	+	0.0417890i
$58$	1.98950	+	0.724117i	0.261234	+	0.0950813i
$59$	9.22472	−	7.74046i	1.20096	−	1.00772i	0.201354	−	0.979519i	$-0.435466\pi$
$59$	9.22472	−	7.74046i	1.20096	−	1.00772i	0.999602	−	0.0282033i	$-0.00897857\pi$
$60$	1.49371	−	1.51557i	0.192837	−	0.195659i
$61$	3.82461	+	10.5080i	0.489691	+	1.34542i	0.900960	+	0.433902i	$0.142864\pi$
$61$	3.82461	+	10.5080i	0.489691	+	1.34542i	−0.411269	+	0.911514i	$0.634914\pi$
$62$	−4.19821	+	7.27151i	−0.533173	+	0.923482i
$63$	0.904201	−	7.88558i	0.113919	−	0.993490i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−0.344635	+	0.410720i	−0.0427467	+	0.0509435i
$66$	1.68951	−	3.69296i	0.207964	−	0.454572i
$67$	1.46744	+	8.32229i	0.179277	+	1.01673i	0.933091	+	0.359641i	$0.117101\pi$
$67$	1.46744	+	8.32229i	0.179277	+	1.01673i	−0.753814	+	0.657088i	$0.771788\pi$
$68$	−0.605240	−	3.43248i	−0.0733961	−	0.416250i
$69$	0.884457	+	9.32843i	0.106476	+	1.12301i
$70$	−1.49454	+	2.88651i	−0.178632	+	0.345004i
$71$	−1.77135	+	1.02269i	−0.210220	+	0.121371i	−0.601414	−	0.798938i	$-0.705396\pi$
$71$	−1.77135	+	1.02269i	−0.210220	+	0.121371i	0.391194	+	0.920308i	$0.372062\pi$
$72$	−2.80387	+	1.06691i	−0.330440	+	0.125736i
$73$	−6.00651	−	3.46786i	−0.703009	−	0.405882i	0.105458	−	0.994424i	$-0.466369\pi$
$73$	−6.00651	−	3.46786i	−0.703009	−	0.405882i	−0.808467	+	0.588541i	$0.799702\pi$
$74$	−1.85490	−	5.09631i	−0.215628	−	0.592434i
$75$	1.60718	+	5.82841i	0.185582	+	0.673007i
$76$	1.46510	+	1.74604i	0.168058	+	0.200284i
$77$	−0.796142	+	6.15211i	−0.0907288	+	0.701098i
$78$	0.682723	−	0.324417i	0.0773031	−	0.0367330i
$79$	−0.916064	+	5.19526i	−0.103065	+	0.584512i	0.888910	+	0.458081i	$0.151463\pi$
$79$	−0.916064	+	5.19526i	−0.103065	+	0.584512i	−0.991975	+	0.126431i	$0.959648\pi$
$80$	1.22857			0.137358
$81$	−1.81967	−	8.81413i	−0.202185	−	0.979347i
$82$			1.57686i			0.174135i
$83$	−1.50719	+	8.54769i	−0.165435	+	0.938231i	0.783179	+	0.621797i	$0.213597\pi$
$83$	−1.50719	+	8.54769i	−0.165435	+	0.938231i	−0.948614	+	0.316435i	$0.897514\pi$
$84$	3.60902	−	2.82400i	0.393777	−	0.308123i
$85$	−4.02385	−	1.46456i	−0.436447	−	0.158854i
$86$	1.31677	+	1.56927i	0.141991	+	0.169219i
$87$	−3.53512	+	0.974809i	−0.379005	+	0.104511i
$88$	2.20327	−	0.801923i	0.234869	−	0.0854853i
$89$	−7.35317	+	12.7361i	−0.779434	+	1.35002i	0.152834	+	0.988252i	$0.451160\pi$
$89$	−7.35317	+	12.7361i	−0.779434	+	1.35002i	−0.932268	+	0.361768i	$0.882173\pi$
$90$	−0.587217	+	3.63862i	−0.0618981	+	0.383544i
$91$	−0.849559	+	0.781931i	−0.0890580	+	0.0819686i
$92$	−3.47743	+	4.14424i	−0.362548	+	0.432067i
$93$	−1.37271	−	14.4781i	−0.142343	−	1.50131i
$94$	4.67331	−	0.824031i	0.482016	−	0.0849924i
$95$	2.75771	−	0.486259i	0.282935	−	0.0498891i
$96$	−1.57505	−	0.720574i	−0.160753	−	0.0735433i
$97$	−9.82215	+	11.7056i	−0.997288	+	1.18852i	−0.0152411	+	0.999884i	$0.504852\pi$
$97$	−9.82215	+	11.7056i	−0.997288	+	1.18852i	−0.982047	+	0.188638i	$0.939593\pi$
$98$	−3.98971	+	5.75172i	−0.403021	+	0.581011i
$99$	1.32195	+	6.90866i	0.132861	+	0.694347i
$100$	−1.74531	+	3.02297i	−0.174531	+	0.302297i
$101$	−11.7582	+	4.27964i	−1.16999	+	0.425840i	−0.852654	−	0.522475i	$-0.825009\pi$
$101$	−11.7582	+	4.27964i	−1.16999	+	0.425840i	−0.317331	+	0.948315i	$0.602787\pi$
$102$	4.29967	+	4.23765i	0.425730	+	0.419590i
$103$	−4.48548	−	5.34559i	−0.441967	−	0.526716i	0.498368	−	0.866966i	$-0.333933\pi$
$103$	−4.48548	−	5.34559i	−0.441967	−	0.526716i	−0.940335	+	0.340249i	$0.889489\pi$
$104$	0.410090	+	0.149260i	0.0402126	+	0.0146362i
$105$	−0.787684	−	5.57462i	−0.0768701	−	0.544027i
$106$	0.0204830	−	0.116165i	0.00198948	−	0.0112829i
$107$			3.92045i			0.379004i	0.981880	+	0.189502i	$0.0606874\pi$
$107$			3.92045i			0.379004i	−0.981880	+	0.189502i	$0.939313\pi$
$108$	2.88693	−	4.32037i	0.277795	−	0.415728i
$109$	−14.6558			−1.40377			−0.701885	−	0.712290i	$-0.747658\pi$
$109$	−14.6558			−1.40377			−0.701885	+	0.712290i	$0.747658\pi$
$110$	0.500207	−	2.83682i	0.0476929	−	0.270480i
$111$	7.73369	+	5.33189i	0.734050	+	0.506081i
$112$	2.62387	+	0.339554i	0.247933	+	0.0320849i
$113$	2.86487	+	3.41422i	0.269504	+	0.321183i	0.883775	−	0.467913i	$-0.154994\pi$
$113$	2.86487	+	3.41422i	0.269504	+	0.321183i	−0.614270	+	0.789096i	$0.710549\pi$
$114$	−3.82064	−	0.994050i	−0.357836	−	0.0931013i
$115$	2.27322	+	6.24562i	0.211979	+	0.582407i
$116$	−1.83353	−	1.05859i	−0.170239	−	0.0982875i
$117$	−0.638072	+	1.14321i	−0.0589898	+	0.105690i
$118$	−10.4287	+	6.02101i	−0.960039	+	0.554279i
$119$	−8.18903	−	4.24001i	−0.750687	−	0.388681i
$120$	−1.73419	+	1.23316i	−0.158309	+	0.112572i
$121$	0.955505	+	5.41894i	0.0868641	+	0.492631i
$122$	−1.94181	−	11.0125i	−0.175803	−	0.997028i
$123$	−1.58276	−	2.22583i	−0.142713	−	0.200696i
$124$	5.39711	−	6.43202i	0.484675	−	0.577613i
$125$	5.21565	+	9.03376i	0.466502	+	0.808004i
$126$	−2.25978	+	7.60877i	−0.201317	+	0.677843i
$127$	0.559717	−	0.969458i	0.0496668	−	0.0860255i	−0.840123	−	0.542396i	$-0.817517\pi$
$127$	0.559717	−	0.969458i	0.0496668	−	0.0860255i	0.889790	+	0.456370i	$0.150851\pi$
$128$	−0.342020	−	0.939693i	−0.0302306	−	0.0830579i
$129$	−3.43385	−	0.893414i	−0.302333	−	0.0786607i
$130$	0.410720	−	0.344635i	0.0360225	−	0.0302265i
$131$	16.4598	+	5.99087i	1.43810	+	0.523425i	0.939241	−	0.343260i	$-0.111531\pi$
$131$	16.4598	+	5.99087i	1.43810	+	0.523425i	0.498857	+	0.866684i	$0.333753\pi$
$132$	−2.30512	+	3.34348i	−0.200635	+	0.291012i
$133$	6.02409	−	0.276329i	0.522355	−	0.0239608i
$134$		−	8.45068i		−	0.730027i
$135$	−2.82335	−	5.72554i	−0.242995	−	0.492776i
$136$			3.48544i			0.298874i
$137$	22.1177	+	3.89995i	1.88965	+	0.333196i	0.993801	−	0.111172i	$-0.0354605\pi$
$137$	22.1177	+	3.89995i	1.88965	+	0.333196i	0.895845	+	0.444368i	$0.146572\pi$
$138$	0.748845	−	9.34030i	0.0637459	−	0.795099i
$139$	6.05302	−	16.6305i	0.513411	−	1.41058i	−0.364250	−	0.931301i	$-0.618675\pi$
$139$	6.05302	−	16.6305i	0.513411	−	1.41058i	0.877660	−	0.479283i	$-0.159103\pi$
$140$	1.97307	−	2.58314i	0.166755	−	0.218315i
$141$	−5.76954	+	5.85398i	−0.485883	+	0.492994i
$142$	1.92202	−	0.699559i	0.161293	−	0.0587057i
$143$	0.511616	−	0.886145i	0.0427835	−	0.0741032i
$144$	2.94654	−	0.563810i	0.245545	−	0.0469841i
$145$	−2.25261	+	1.30055i	−0.187069	+	0.108004i
$146$	5.31307	+	4.45820i	0.439713	+	0.368963i
$147$	−0.141543	−	12.1235i	−0.0116743	−	0.999932i
$148$	0.941760	+	5.34098i	0.0774122	+	0.439026i
$149$	11.4259	−	2.01470i	0.936049	−	0.165051i	0.315239	−	0.949012i	$-0.397915\pi$
$149$	11.4259	−	2.01470i	0.936049	−	0.165051i	0.620809	+	0.783962i	$0.286804\pi$
$150$	−0.570675	−	6.01895i	−0.0465954	−	0.491445i
$151$	−8.42543	−	7.06977i	−0.685652	−	0.575330i	0.232000	−	0.972716i	$-0.425473\pi$
$151$	−8.42543	−	7.06977i	−0.685652	−	0.575330i	−0.917652	+	0.397386i	$0.869918\pi$
$152$	−1.13964	−	1.97392i	−0.0924373	−	0.160106i
$153$	−10.3227	−	1.66593i	−0.834545	−	0.134683i
$154$	1.85235	−	5.92039i	0.149267	−	0.477079i
$155$	−3.52812	−	9.69344i	−0.283386	−	0.778596i
$156$	−0.728685	+	0.200935i	−0.0583415	+	0.0160877i
$157$	−9.34321	−	11.1348i	−0.745669	−	0.888654i	0.251183	−	0.967940i	$-0.419180\pi$
$157$	−9.34321	−	11.1348i	−0.745669	−	0.888654i	−0.996852	+	0.0792859i	$0.974736\pi$
$158$	1.80429	−	4.95726i	0.143542	−	0.394378i
$159$	0.0876867	+	0.184533i	0.00695400	+	0.0146344i
$160$	−1.20990	−	0.213338i	−0.0956511	−	0.0168659i
$161$	3.12878	+	13.9672i	0.246582	+	1.10077i
$162$	0.261466	+	8.99620i	0.0205427	+	0.706808i
$163$	3.92430			0.307375			0.153687	−	0.988120i	$-0.450885\pi$
$163$	3.92430			0.307375			0.153687	+	0.988120i	$0.450885\pi$
$164$	0.273818	−	1.55290i	0.0213816	−	0.121261i
$165$	2.14136	+	4.50641i	0.166705	+	0.350824i
$166$	2.96858	−	8.15611i	0.230407	−	0.633037i
$167$	4.67824	−	3.92551i	0.362013	−	0.303765i	−0.443579	−	0.896235i	$-0.646292\pi$
$167$	4.67824	−	3.92551i	0.362013	−	0.303765i	0.805592	+	0.592470i	$0.201847\pi$
$168$	−4.04458	+	2.15439i	−0.312046	+	0.166215i
$169$	−12.0370	+	4.38112i	−0.925926	+	0.337009i
$170$	3.70840	+	2.14104i	0.284421	+	0.164211i
$171$	6.39084	−	2.43179i	0.488719	−	0.185963i
$172$	−1.02427	−	1.77408i	−0.0780997	−	0.135273i
$173$	−18.9535	−	15.9039i	−1.44101	−	1.20915i	−0.938829	−	0.344384i	$-0.888088\pi$
$173$	−18.9535	−	15.9039i	−1.44101	−	1.20915i	−0.502178	−	0.864764i	$-0.667468\pi$
$174$	3.65069	−	0.346133i	0.276758	−	0.0262403i
$175$	3.55301	+	8.52452i	0.268583	+	0.644393i
$176$	−2.30905	+	0.407147i	−0.174051	+	0.0306899i
$177$	8.67717	−	18.9667i	0.652216	−	1.42563i
$178$	9.45305	−	11.2657i	0.708536	−	0.844401i
$179$	15.9501	−	9.20879i	1.19217	−	0.688297i	0.233369	−	0.972388i	$-0.425025\pi$
$179$	15.9501	−	9.20879i	1.19217	−	0.688297i	0.958797	+	0.284091i	$0.0916918\pi$
$180$	1.21014	−	3.48137i	0.0901981	−	0.259486i
$181$	4.81715	+	2.78118i	0.358056	+	0.206724i	0.668228	−	0.743957i	$-0.267053\pi$
$181$	4.81715	+	2.78118i	0.358056	+	0.206724i	−0.310172	+	0.950681i	$0.600387\pi$
$182$	0.972433	−	0.622527i	0.0720815	−	0.0461448i
$183$	13.7947	+	13.5958i	1.01974	+	1.00503i
$184$	4.14424	−	3.47743i	0.305518	−	0.256360i
$185$	6.26115	+	2.27887i	0.460329	+	0.167546i
$186$	−1.16224	+	14.4965i	−0.0852193	+	1.06293i
$187$	8.04804	+	1.41909i	0.588531	+	0.103774i
$188$	−4.74541			−0.346094
$189$	−4.44744	−	13.0085i	−0.323504	−	0.946227i
$190$	−2.80026			−0.203152
$191$	9.01172	+	1.58901i	0.652065	+	0.114977i	0.489888	−	0.871785i	$-0.337038\pi$
$191$	9.01172	+	1.58901i	0.652065	+	0.114977i	0.162176	+	0.986762i	$0.448149\pi$
$192$	1.42599	+	0.983131i	0.102912	+	0.0709514i
$193$	−25.3984	−	9.24425i	−1.82821	−	0.665416i	−0.993374	−	0.114923i	$-0.963338\pi$
$193$	−25.3984	−	9.24425i	−1.82821	−	0.665416i	−0.834840	−	0.550492i	$-0.814440\pi$
$194$	11.7056	−	9.82215i	0.840412	−	0.705189i
$195$	−0.233830	+	0.898730i	−0.0167449	+	0.0643594i
$196$	4.92787	−	4.97153i	0.351991	−	0.355109i
$197$	−9.39441	−	5.42386i	−0.669324	−	0.386434i	0.126497	−	0.991967i	$-0.459627\pi$
$197$	−9.39441	−	5.42386i	−0.669324	−	0.386434i	−0.795820	+	0.605533i	$0.792960\pi$
$198$	−0.102186	−	7.03326i	−0.00726204	−	0.499832i
$199$	−4.71281	+	2.72094i	−0.334082	+	0.192882i	−0.657652	−	0.753322i	$-0.728450\pi$
$199$	−4.71281	+	2.72094i	−0.334082	+	0.192882i	0.323570	+	0.946204i	$0.395117\pi$
$200$	2.24373	−	2.67397i	0.158656	−	0.189079i
$201$	8.48231	+	11.9286i	0.598296	+	0.841381i
$202$	12.3227	−	2.17283i	0.867024	−	0.152880i
$203$	−5.17040	+	2.15502i	−0.362891	+	0.151253i
$204$	−3.49848	−	4.91990i	−0.244943	−	0.344462i
$205$	−1.48404	−	1.24525i	−0.103650	−	0.0869724i
$206$	3.48908	+	6.04327i	0.243096	+	0.421055i
$207$	8.31822	+	13.9360i	0.578156	+	0.968621i
$208$	−0.377941	−	0.218204i	−0.0262055	−	0.0151297i
$209$	−5.02188	+	1.82781i	−0.347371	+	0.126433i
$210$	−0.192306	+	5.62671i	−0.0132704	+	0.388280i
$211$	17.8538	−	14.9811i	1.22911	−	1.03134i	0.230809	−	0.972999i	$-0.425863\pi$
$211$	17.8538	−	14.9811i	1.22911	−	1.03134i	0.998297	−	0.0583429i	$-0.0185817\pi$
$212$	−0.0403436	+	0.110843i	−0.00277081	+	0.00761273i
$213$	−2.01087	+	2.91669i	−0.137783	+	0.199848i
$214$	0.680779	−	3.86089i	0.0465371	−	0.263925i
$215$	−2.51676			−0.171642
$216$	−3.59330	+	3.75342i	−0.244493	+	0.255388i
$217$	−4.85598	−	21.6776i	−0.329646	−	1.47157i
$218$	14.4331	+	2.54495i	0.977536	+	0.172366i
$219$	−11.9746	−	0.960047i	−0.809168	−	0.0648739i
$220$	−0.985216	+	2.70686i	−0.0664232	+	0.182496i
$221$	0.977727	+	1.16521i	0.0657691	+	0.0783805i
$222$	−6.69033	−	6.59383i	−0.449025	−	0.442549i
$223$	2.24207	+	6.16004i	0.150140	+	0.412507i	0.991848	−	0.127426i	$-0.0406717\pi$
$223$	2.24207	+	6.16004i	0.150140	+	0.412507i	−0.841708	+	0.539933i	$0.818449\pi$
$224$	−2.52505	−	0.790026i	−0.168712	−	0.0527859i
$225$	6.84702	+	7.92329i	0.456468	+	0.528219i
$226$	−2.22847	−	3.85983i	−0.148236	−	0.256752i
$227$	−4.62522	−	3.88102i	−0.306986	−	0.257592i	0.476259	−	0.879305i	$-0.341993\pi$
$227$	−4.62522	−	3.88102i	−0.306986	−	0.257592i	−0.783245	+	0.621713i	$0.786437\pi$
$228$	3.58999	+	1.64240i	0.237753	+	0.108770i
$229$	−19.5706	+	3.45082i	−1.29326	+	0.228037i	−0.777602	−	0.628757i	$-0.783564\pi$
$229$	−19.5706	+	3.45082i	−1.29326	+	0.228037i	−0.515659	+	0.856794i	$0.672453\pi$
$230$	−1.15414	−	6.54548i	−0.0761020	−	0.431596i
$231$	3.32786	+	10.2163i	0.218957	+	0.672181i
$232$	1.62185	+	1.36090i	0.106480	+	0.0893472i
$233$	3.33964	−	1.92814i	0.218787	−	0.126317i	−0.386601	−	0.922247i	$-0.626351\pi$
$233$	3.33964	−	1.92814i	0.218787	−	0.126317i	0.605389	+	0.795930i	$0.293018\pi$
$234$	0.826895	−	1.01504i	0.0540558	−	0.0663555i
$235$	−2.91502	+	5.04897i	−0.190155	+	0.329358i
$236$	11.3158	−	4.11861i	0.736595	−	0.268099i
$237$	2.42895	+	8.80851i	0.157777	+	0.572174i
$238$	7.32835	+	5.59761i	0.475026	+	0.362839i
$239$	3.12052	−	8.57356i	0.201850	−	0.554578i	−0.796924	−	0.604079i	$-0.793541\pi$
$239$	3.12052	−	8.57356i	0.201850	−	0.554578i	0.998774	+	0.0495016i	$0.0157633\pi$
$240$	1.92198	−	0.913291i	0.124064	−	0.0589527i
$241$	27.7998	+	4.90186i	1.79074	+	0.315757i	0.967678	−	0.252188i	$-0.0811503\pi$
$241$	27.7998	+	4.90186i	1.79074	+	0.315757i	0.823066	+	0.567945i	$0.192261\pi$
$242$		−	5.50254i		−	0.353716i
$243$	−9.39895	−	12.4362i	−0.602943	−	0.797784i
$244$			11.1824i			0.715881i
$245$	−2.26245	−	8.29703i	−0.144543	−	0.530078i
$246$	1.17220	+	2.46685i	0.0747369	+	0.157281i
$247$	−0.934713	−	0.340208i	−0.0594743	−	0.0216469i
$248$	−6.43202	+	5.39711i	−0.408434	+	0.342717i
$249$	3.99632	+	14.4925i	0.253256	+	0.918427i
$250$	−3.56771	−	9.80221i	−0.225642	−	0.619946i
$251$	5.07709	−	8.79378i	0.320463	−	0.555058i	−0.660121	−	0.751160i	$-0.729495\pi$
$251$	5.07709	−	8.79378i	0.320463	−	0.555058i	0.980584	+	0.196101i	$0.0628282\pi$
$252$	3.54670	−	7.10077i	0.223421	−	0.447306i
$253$	−6.34224	−	10.9851i	−0.398733	−	0.690626i
$254$	−0.719558	+	0.857536i	−0.0451491	+	0.0538066i
$255$	−7.38368	+	0.700069i	−0.462384	+	0.0438400i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	2.19809	+	12.4660i	0.137113	+	0.777607i	0.973365	+	0.229261i	$0.0736310\pi$
$257$	2.19809	+	12.4660i	0.137113	+	0.777607i	−0.836252	+	0.548346i	$0.815258\pi$
$258$	3.22654	+	1.47612i	0.200876	+	0.0918994i
$259$	12.7422	+	6.59751i	0.791763	+	0.409949i
$260$	−0.464325	+	0.268078i	−0.0287962	+	0.0166255i
$261$	−4.80573	+	4.15294i	−0.297467	+	0.257061i
$262$	−15.1694	−	8.75806i	−0.937169	−	0.541075i
$263$	−9.71268	−	26.6854i	−0.598909	−	1.64549i	−0.753451	−	0.657504i	$-0.771612\pi$
$263$	−9.71268	−	26.6854i	−0.598909	−	1.64549i	0.154542	−	0.987986i	$-0.450610\pi$
$264$	2.85068	−	2.89240i	0.175447	−	0.178015i
$265$	0.0931513	+	0.111013i	0.00572224	+	0.00681950i
$266$	−5.98056	−	0.773942i	−0.366692	−	0.0474534i
$267$	−2.03566	+	25.3907i	−0.124580	+	1.55388i
$268$	−1.46744	+	8.32229i	−0.0896384	+	0.508365i
$269$	12.8796			0.785282			0.392641	−	0.919692i	$-0.371562\pi$
$269$	12.8796			0.785282			0.392641	+	0.919692i	$0.371562\pi$
$270$	1.78623	+	6.12883i	0.108706	+	0.372988i
$271$			23.3304i			1.41722i	0.705601	+	0.708610i	$0.250677\pi$
$271$			23.3304i			1.41722i	−0.705601	+	0.708610i	$0.749323\pi$
$272$	0.605240	−	3.43248i	0.0366980	−	0.208125i
$273$	−0.747789	+	1.85481i	−0.0452583	+	0.112258i
$274$	−21.1045	−	7.68141i	−1.27497	−	0.464051i
$275$	−5.26080	−	6.26958i	−0.317238	−	0.378070i
$276$	−2.35939	+	9.06836i	−0.142019	+	0.545851i
$277$	−20.8905	+	7.60350i	−1.25519	+	0.456850i	−0.882151	−	0.470967i	$-0.843905\pi$
$277$	−20.8905	+	7.60350i	−1.25519	+	0.456850i	−0.373035	+	0.927817i	$0.621683\pi$
$278$	−8.84893	+	15.3268i	−0.530723	+	0.919240i
$279$	−12.9102	−	21.6292i	−0.772913	−	1.29491i
$280$	−2.39166	+	2.20127i	−0.142929	+	0.131551i
$281$	−6.37582	+	7.59841i	−0.380350	+	0.453283i	−0.921925	−	0.387369i	$-0.873384\pi$
$281$	−6.37582	+	7.59841i	−0.380350	+	0.453283i	0.541575	+	0.840653i	$0.317828\pi$
$282$	6.69842	−	4.76317i	0.398885	−	0.283643i
$283$	−7.82006	+	1.37889i	−0.464855	+	0.0819664i	−0.401170	−	0.916004i	$-0.631396\pi$
$283$	−7.82006	+	1.37889i	−0.464855	+	0.0819664i	−0.0636847	+	0.997970i	$0.520285\pi$
$284$	−2.01430	+	0.355176i	−0.119527	+	0.0210758i
$285$	3.95273	−	2.81074i	0.234139	−	0.166494i
$286$	−0.657721	+	0.783842i	−0.0388919	+	0.0463495i
$287$	−2.82532	−	3.06968i	−0.166773	−	0.181197i
$288$	−2.99968	+	0.0435823i	−0.176758	+	0.00256811i
$289$	2.42587	−	4.20172i	0.142698	−	0.247160i
$290$	2.44423	−	0.889626i	0.143530	−	0.0522406i
$291$	−6.66420	+	25.6139i	−0.390662	+	1.50152i
$292$	−4.45820	−	5.31307i	−0.260896	−	0.310924i
$293$	−11.8053	−	4.29677i	−0.689672	−	0.251020i	−0.0266772	−	0.999644i	$-0.508493\pi$
$293$	−11.8053	−	4.29677i	−0.689672	−	0.251020i	−0.662995	+	0.748624i	$0.730715\pi$
$294$	−1.96584	+	11.9639i	−0.114650	+	0.697750i
$295$	2.56902	−	14.5696i	0.149574	−	0.848278i
$296$		−	5.42338i		−	0.315227i
$297$	7.20383	+	9.82529i	0.418009	+	0.570121i
$298$	−11.6022			−0.672097
$299$	0.409972	−	2.32507i	0.0237093	−	0.134462i
$300$	−0.483175	+	6.02660i	−0.0278961	+	0.347946i
$301$	−5.37510	−	0.695589i	−0.309815	−	0.0400931i
$302$	7.06977	+	8.42543i	0.406820	+	0.484829i
$303$	−15.2133	+	15.4359i	−0.873981	+	0.886771i
$304$	0.779562	+	2.14183i	0.0447110	+	0.122842i
$305$	11.8977	+	6.86917i	0.681263	+	0.393327i
$306$	9.87663	+	3.43315i	0.564610	+	0.196260i
$307$	7.67098	−	4.42884i	0.437806	−	0.252767i	−0.264861	−	0.964287i	$-0.585326\pi$
$307$	7.67098	−	4.42884i	0.437806	−	0.252767i	0.702667	+	0.711519i	$0.251993\pi$
$308$	−2.85227	+	5.50879i	−0.162523	+	0.313893i
$309$	−10.9909	−	5.02829i	−0.625253	−	0.286049i
$310$	1.79128	+	10.1588i	0.101738	+	0.576983i
$311$	3.63244	+	20.6006i	0.205977	+	1.16815i	0.895895	+	0.444266i	$0.146535\pi$
$311$	3.63244	+	20.6006i	0.205977	+	1.16815i	−0.689918	+	0.723887i	$0.742353\pi$
$312$	0.752507	−	0.0713474i	0.0426023	−	0.00403925i
$313$	8.13089	−	9.69001i	0.459585	−	0.547712i	−0.485628	−	0.874165i	$-0.661409\pi$
$313$	8.13089	−	9.69001i	0.459585	−	0.547712i	0.945213	+	0.326453i	$0.105854\pi$
$314$	7.26772	+	12.5881i	0.410141	+	0.710386i
$315$	−5.37632	−	8.13546i	−0.302921	−	0.458381i
$316$	−2.63770	+	4.56863i	−0.148382	+	0.257006i
$317$	1.60647	+	4.41375i	0.0902285	+	0.247901i	0.976596	−	0.215081i	$-0.0690017\pi$
$317$	1.60647	+	4.41375i	0.0902285	+	0.247901i	−0.886368	+	0.462982i	$0.846779\pi$
$318$	−0.0543107	−	0.196956i	−0.00304559	−	0.0110448i
$319$	3.80270	−	3.19085i	0.212911	−	0.178653i
$320$	1.15447	+	0.420194i	0.0645371	+	0.0234896i
$321$	2.91438	+	6.13320i	0.162665	+	0.342322i
$322$	−0.655871	−	14.2983i	−0.0365503	−	0.796812i
$323$		−	7.94431i		−	0.442033i
$324$	1.30468	−	8.90493i	0.0724822	−	0.494718i
$325$		−	1.52334i		−	0.0844996i
$326$	−3.86468	−	0.681447i	−0.214045	−	0.0377419i
$327$	−22.9277	+	10.8948i	−1.26791	+	0.602485i
$328$	−0.539317	+	1.48176i	−0.0297788	+	0.0818165i
$329$	−7.62112	+	9.97752i	−0.420166	+	0.550078i
$330$	−1.32630	−	4.80979i	−0.0730105	−	0.264770i
$331$	9.76080	−	3.55264i	0.536502	−	0.195271i	−0.0595370	−	0.998226i	$-0.518962\pi$
$331$	9.76080	−	3.55264i	0.536502	−	0.195271i	0.596039	+	0.802955i	$0.296740\pi$
$332$	−4.33978	+	7.51671i	−0.238176	+	0.412533i
$333$	16.0623	+	2.59221i	0.880209	+	0.142052i
$334$	−5.28882	+	3.05350i	−0.289392	+	0.167080i
$335$	7.95324	+	6.67356i	0.434532	+	0.364615i
$336$	4.35724	−	1.41933i	0.237707	−	0.0774308i
$337$	−0.683890	−	3.87853i	−0.0372538	−	0.211277i	0.960499	−	0.278285i	$-0.0897659\pi$
$337$	−0.683890	−	3.87853i	−0.0372538	−	0.211277i	−0.997752	+	0.0670077i	$0.978655\pi$
$338$	12.6149	−	2.22435i	0.686162	−	0.120989i
$339$	7.01990	+	3.21156i	0.381269	+	0.174428i
$340$	−3.28027	−	2.75247i	−0.177898	−	0.149274i
$341$	9.84340	+	17.0493i	0.533050	+	0.923269i
$342$	−6.71602	+	1.28508i	−0.363161	+	0.0694894i
$343$	−2.53880	−	18.3454i	−0.137083	−	0.990560i
$344$	0.700641	+	1.92499i	0.0377760	+	0.103789i
$345$	8.19912	+	8.08086i	0.441426	+	0.435059i
$346$	15.9039	+	18.9535i	0.854997	+	1.01895i
$347$	9.50367	−	26.1111i	0.510184	−	1.40172i	−0.370862	−	0.928688i	$-0.620938\pi$
$347$	9.50367	−	26.1111i	0.510184	−	1.40172i	0.881046	−	0.473030i	$-0.156840\pi$
$348$	−3.65533	−	0.293061i	−0.195946	−	0.0157097i
$349$	−16.5657	−	2.92098i	−0.886740	−	0.156356i	−0.288316	−	0.957535i	$-0.593095\pi$
$349$	−16.5657	−	2.92098i	−0.886740	−	0.156356i	−0.598425	+	0.801179i	$0.704206\pi$
$350$	−2.01877	−	9.01198i	−0.107908	−	0.481711i
$351$	−0.148367	+	2.26279i	−0.00791924	+	0.120779i
$352$	2.34467			0.124971
$353$	0.293221	−	1.66294i	0.0156066	−	0.0885094i	−0.976010	−	0.217727i	$-0.930136\pi$
$353$	0.293221	−	1.66294i	0.0156066	−	0.0885094i	0.991616	+	0.129218i	$0.0412467\pi$
$354$	−11.8389	+	17.1718i	−0.629229	+	0.912672i
$355$	−0.859455	+	2.36133i	−0.0456151	+	0.125327i
$356$	−11.2657	+	9.45305i	−0.597081	+	0.501011i
$357$	−15.9630	−	0.545571i	−0.844849	−	0.0288747i
$358$	−17.3069	+	6.29918i	−0.914696	+	0.332922i
$359$	−10.5518	−	6.09211i	−0.556905	−	0.321529i	0.194997	−	0.980804i	$-0.437530\pi$
$359$	−10.5518	−	6.09211i	−0.556905	−	0.321529i	−0.751902	+	0.659274i	$0.770864\pi$
$360$	−1.79628	+	3.21834i	−0.0946725	+	0.169622i
$361$	−6.90242	−	11.9553i	−0.363285	−	0.629229i
$362$	−4.26102	−	3.57542i	−0.223954	−	0.187920i
$363$	5.52313	+	7.76715i	0.289889	+	0.407670i
$364$	−1.06576	+	0.444208i	−0.0558610	+	0.0232828i
$365$	−8.39154	+	1.47965i	−0.439233	+	0.0774486i
$366$	−11.2243	−	15.7846i	−0.586702	−	0.825076i
$367$	−13.7838	+	16.4269i	−0.719507	+	0.857475i	−0.994583	−	0.103948i	$-0.966853\pi$
$367$	−13.7838	+	16.4269i	−0.719507	+	0.857475i	0.275076	+	0.961423i	$0.411297\pi$
$368$	−4.68513	+	2.70496i	−0.244229	+	0.141006i
$369$	−4.13072	−	2.30552i	−0.215037	−	0.120021i
$370$	−5.77031	−	3.33149i	−0.299984	−	0.173196i
$371$	0.168263	+	0.262839i	0.00873577	+	0.0136459i
$372$	3.66187	−	14.0744i	0.189859	−	0.729726i
$373$	15.0931	−	12.6646i	0.781491	−	0.655749i	−0.162133	−	0.986769i	$-0.551837\pi$
$373$	15.0931	−	12.6646i	0.781491	−	0.655749i	0.943624	+	0.331020i	$0.107393\pi$
$374$	−7.67935	−	2.79505i	−0.397090	−	0.144529i
$375$	14.8749	+	10.2553i	0.768139	+	0.529583i
$376$	4.67331	+	0.824031i	0.241008	+	0.0424962i
$377$	0.923954			0.0475861
$378$	2.12097	+	13.5831i	0.109091	+	0.698641i
$379$	24.8328			1.27558			0.637788	−	0.770212i	$-0.279849\pi$
$379$	24.8328			1.27558			0.637788	+	0.770212i	$0.279849\pi$
$380$	2.75771	+	0.486259i	0.141468	+	0.0249446i
$381$	0.154953	−	1.93271i	0.00793847	−	0.0990160i
$382$	−8.59888	−	3.12974i	−0.439957	−	0.160131i
$383$	7.41782	−	6.22429i	0.379033	−	0.318047i	−0.433290	−	0.901255i	$-0.642647\pi$
$383$	7.41782	−	6.22429i	0.379033	−	0.318047i	0.812323	+	0.583208i	$0.198203\pi$
$384$	−1.23361	−	1.21582i	−0.0629523	−	0.0620444i
$385$	4.10908	+	6.41869i	0.209418	+	0.327127i
$386$	23.4073	+	13.5142i	1.19140	+	0.687854i
$387$	−6.03610	+	1.15498i	−0.306832	+	0.0587112i
$388$	−13.2333	+	7.64027i	−0.671821	+	0.387876i
$389$	19.7679	−	23.5584i	1.00227	−	1.19446i	0.0214059	−	0.999771i	$-0.493186\pi$
$389$	19.7679	−	23.5584i	1.00227	−	1.19446i	0.980865	−	0.194689i	$-0.0623698\pi$
$390$	0.386341	−	0.844472i	0.0195631	−	0.0427615i
$391$	18.5695	−	3.27430i	0.939099	−	0.165589i
$392$	−5.71630	+	4.04029i	−0.288717	+	0.204065i
$393$	30.2034	−	2.86367i	1.52356	−	0.144453i
$394$	8.30984	+	6.97278i	0.418644	+	0.351284i
$395$	3.24059	+	5.61286i	0.163052	+	0.282414i
$396$	−1.12068	+	6.94415i	−0.0563162	+	0.348957i
$397$	7.92617	+	4.57618i	0.397803	+	0.229672i	0.685536	−	0.728039i	$-0.259568\pi$
$397$	7.92617	+	4.57618i	0.397803	+	0.229672i	−0.287732	+	0.957711i	$0.592901\pi$
$398$	5.11369	−	1.86123i	0.256326	−	0.0932952i
$399$	9.21875	−	4.91048i	0.461515	−	0.245832i
$400$	−2.67397	+	2.24373i	−0.133699	+	0.112187i
$401$	−11.1932	+	30.7530i	−0.558961	+	1.53573i	0.262187	+	0.965017i	$0.415556\pi$
$401$	−11.1932	+	30.7530i	−0.558961	+	1.53573i	−0.821148	+	0.570715i	$0.806666\pi$
$402$	−6.28206	−	13.2203i	−0.313321	−	0.659371i
$403$	−0.636293	+	3.60860i	−0.0316960	+	0.179757i
$404$	−12.5128			−0.622536
$405$	−8.67313	−	6.85829i	−0.430971	−	0.340791i
$406$	5.46606	−	1.22445i	0.271276	−	0.0607684i
$407$	−12.5228	−	2.20811i	−0.620734	−	0.109452i
$408$	2.59100	+	5.45266i	0.128274	+	0.269947i
$409$	−2.40239	+	6.60050i	−0.118790	+	0.326374i	−0.984810	−	0.173637i	$-0.944448\pi$
$409$	−2.40239	+	6.60050i	−0.118790	+	0.326374i	0.866020	+	0.500010i	$0.166670\pi$
$410$	1.24525	+	1.48404i	0.0614987	+	0.0732913i
$411$	37.5004	−	10.3407i	1.84976	−	0.510071i
$412$	−2.38667	−	6.55733i	−0.117583	−	0.323057i
$413$	9.51351	−	30.4066i	0.468129	−	1.49621i
$414$	−5.77188	−	15.1688i	−0.283673	−	0.745504i
$415$	5.33170	+	9.23478i	0.261723	+	0.453317i
$416$	0.334308	+	0.280518i	0.0163908	+	0.0137535i
$417$	−2.89338	−	30.5167i	−0.141690	−	1.49441i
$418$	5.26298	−	0.928006i	0.257421	−	0.0453902i
$419$	−5.62520	−	31.9021i	−0.274809	−	1.55852i	−0.739568	−	0.673082i	$-0.764970\pi$
$419$	−5.62520	−	31.9021i	−0.274809	−	1.55852i	0.464759	−	0.885437i	$-0.346141\pi$
$420$	1.16645	−	5.50783i	0.0569170	−	0.268755i
$421$	7.36408	+	6.17920i	0.358903	+	0.301156i	0.804353	−	0.594151i	$-0.202512\pi$
$421$	7.36408	+	6.17920i	0.358903	+	0.301156i	−0.445450	+	0.895307i	$0.646956\pi$
$422$	−20.1840	+	11.6532i	−0.982541	+	0.567271i
$423$	−4.67422	+	13.4470i	−0.227268	+	0.653815i
$424$	0.0589784	−	0.102154i	0.00286424	−	0.00496101i
$425$	11.4326	−	4.16114i	0.554564	−	0.201845i
$426$	2.48680	−	2.52319i	0.120486	−	0.122249i
$427$	23.5117	+	17.9589i	1.13781	+	0.869094i
$428$	−1.34087	+	3.68402i	−0.0648135	+	0.178074i
$429$	0.141636	−	1.76662i	0.00683827	−	0.0852933i
$430$	2.47853	+	0.437031i	0.119525	+	0.0210755i
$431$		−	1.82273i		−	0.0877979i	−0.999036	−	0.0438989i	$-0.986022\pi$
$431$		−	1.82273i		−	0.0877979i	0.999036	−	0.0438989i	$-0.0139780\pi$
$432$	4.19048	−	3.07243i	0.201615	−	0.147822i
$433$		−	32.5239i		−	1.56300i	−0.623906	−	0.781499i	$-0.714455\pi$
$433$		−	32.5239i		−	1.56300i	0.623906	−	0.781499i	$-0.285545\pi$
$434$	1.01794	+	22.1915i	0.0488626	+	1.06523i
$435$	−2.55722	+	3.70914i	−0.122609	+	0.177840i
$436$	−13.7719	−	5.01258i	−0.659556	−	0.240059i
$437$	−9.44592	+	7.92607i	−0.451860	+	0.379155i
$438$	11.6260	+	3.02483i	0.555510	+	0.144532i
$439$	−10.8479	−	29.8044i	−0.517743	−	1.42249i	−0.873001	−	0.487719i	$-0.837829\pi$
$439$	−10.8479	−	29.8044i	−0.517743	−	1.42249i	0.355257	−	0.934768i	$-0.384393\pi$
$440$	1.44029	−	2.49465i	0.0686631	−	0.118928i
$441$	−9.23382	−	18.8610i	−0.439706	−	0.898142i
$442$	−0.760537	−	1.31729i	−0.0361751	−	0.0626570i
$443$	−22.8370	+	27.2161i	−1.08502	+	1.29307i	−0.131640	+	0.991298i	$0.542024\pi$
$443$	−22.8370	+	27.2161i	−1.08502	+	1.29307i	−0.953379	+	0.301777i	$0.902420\pi$
$444$	5.44368	+	7.65542i	0.258346	+	0.363310i
$445$	3.13742	+	17.7932i	0.148728	+	0.843479i
$446$	−1.13833	−	6.45579i	−0.0539015	−	0.305690i
$447$	16.3772	−	11.6456i	0.774614	−	0.550819i
$448$	2.34950	+	1.21649i	0.111003	+	0.0574739i
$449$	−5.81350	+	3.35643i	−0.274356	+	0.158400i	−0.630866	−	0.775892i	$-0.717300\pi$
$449$	−5.81350	+	3.35643i	−0.274356	+	0.158400i	0.356509	+	0.934292i	$0.383967\pi$
$450$	−5.36713	−	8.99189i	−0.253009	−	0.423882i
$451$	3.20187	+	1.84860i	0.150770	+	0.0870473i
$452$	1.52437	+	4.18816i	0.0717002	+	0.196995i
$453$	−18.4364	−	4.79675i	−0.866216	−	0.225371i
$454$	3.88102	+	4.62522i	0.182145	+	0.217072i
$455$	−0.182054	+	1.40681i	−0.00853484	+	0.0659521i
$456$	−3.25025	−	2.24084i	−0.152207	−	0.104937i
$457$	0.292432	−	1.65846i	0.0136794	−	0.0775796i	−0.977204	−	0.212303i	$-0.931904\pi$
$457$	0.292432	−	1.65846i	0.0136794	−	0.0775796i	0.990883	+	0.134724i	$0.0430147\pi$
$458$	19.8725			0.928580
$459$	−17.3875	+	5.06751i	−0.811577	+	0.236531i
$460$			6.64645i			0.309892i
$461$	−0.201902	+	1.14505i	−0.00940353	+	0.0533301i	−0.989148	−	0.146919i	$-0.953064\pi$
$461$	−0.201902	+	1.14505i	−0.00940353	+	0.0533301i	0.979745	+	0.200250i	$0.0641753\pi$
$462$	−1.50326	−	10.6389i	−0.0699381	−	0.494968i
$463$	−0.00916975	−	0.00333751i	−0.000426154	−	0.000155107i	0.341807	−	0.939770i	$-0.388961\pi$
$463$	−0.00916975	−	0.00333751i	−0.000426154	−	0.000155107i	−0.342233	+	0.939615i	$0.611183\pi$
$464$	−1.36090	−	1.62185i	−0.0631780	−	0.0752926i
$465$	−12.7253	−	12.5418i	−0.590124	−	0.581612i
$466$	−3.62372	+	1.31893i	−0.167866	+	0.0610981i
$467$	−4.32870	+	7.49752i	−0.200308	+	0.346944i	−0.948628	−	0.316394i	$-0.897528\pi$
$467$	−4.32870	+	7.49752i	−0.200308	+	0.346944i	0.748320	+	0.663338i	$0.230861\pi$
$468$	−0.990593	+	0.856035i	−0.0457902	+	0.0395702i
$469$	15.1414	+	16.4510i	0.699166	+	0.759636i
$470$	3.74748	−	4.46607i	0.172858	−	0.206005i
$471$	−22.8940	−	10.4739i	−1.05490	−	0.482610i
$472$	−11.8591	+	2.09107i	−0.545858	+	0.0962495i
$473$	4.73017	−	0.834056i	0.217493	−	0.0383499i
$474$	−0.862464	−	9.09647i	−0.0396143	−	0.417815i
$475$	−5.11411	+	6.09476i	−0.234651	+	0.279647i
$476$	−6.24500	−	6.78512i	−0.286239	−	0.310995i
$477$	0.274356	+	0.223501i	0.0125619	+	0.0102334i
$478$	−4.56190	+	7.90144i	−0.208656	+	0.361403i
$479$	−29.2874	+	10.6598i	−1.33818	+	0.487056i	−0.909238	−	0.416277i	$-0.863335\pi$
$479$	−29.2874	+	10.6598i	−1.33818	+	0.487056i	−0.428939	+	0.903334i	$0.641112\pi$
$480$	−2.05138	+	0.565667i	−0.0936321	+	0.0258190i
$481$	−1.52135	−	1.81308i	−0.0693678	−	0.0826693i
$482$	−26.5263	−	9.65478i	−1.20824	−	0.439763i
$483$	15.2776	+	19.5245i	0.695155	+	0.888398i
$484$	−0.955505	+	5.41894i	−0.0434321	+	0.246315i
$485$			18.7732i			0.852445i
$486$	7.09663	+	13.8794i	0.321910	+	0.629582i
$487$	−1.34497			−0.0609466			−0.0304733	−	0.999536i	$-0.509701\pi$
$487$	−1.34497			−0.0609466			−0.0304733	+	0.999536i	$0.509701\pi$
$488$	1.94181	−	11.0125i	0.0879014	−	0.498514i
$489$	6.13922	−	2.91724i	0.277625	−	0.131922i
$490$	0.787315	+	8.56385i	0.0355673	+	0.386875i
$491$	−4.22823	−	5.03901i	−0.190818	−	0.227407i	0.662150	−	0.749371i	$-0.269644\pi$
$491$	−4.22823	−	5.03901i	−0.190818	−	0.227407i	−0.852968	+	0.521964i	$0.825200\pi$
$492$	−0.726030	−	2.63293i	−0.0327320	−	0.118702i
$493$	2.52387	+	6.93426i	0.113669	+	0.312304i
$494$	0.861436	+	0.497350i	0.0387578	+	0.0223768i
$495$	6.69995	+	5.45804i	0.301140	+	0.245321i
$496$	7.27151	−	4.19821i	0.326500	−	0.188505i
$497$	−2.48819	+	4.80560i	−0.111610	+	0.215561i
$498$	−1.41900	−	14.9663i	−0.0635870	−	0.670656i
$499$	5.69767	+	32.3131i	0.255063	+	1.44653i	0.795911	+	0.605413i	$0.206992\pi$
$499$	5.69767	+	32.3131i	0.255063	+	1.44653i	−0.540848	+	0.841120i	$0.681897\pi$
$500$	1.81138	+	10.2728i	0.0810072	+	0.459414i
$501$	4.40055	−	9.61883i	0.196602	−	0.429737i
$502$	−6.52698	+	7.77855i	−0.291313	+	0.347174i
$503$	−16.8167	−	29.1274i	−0.749821	−	1.29873i	−0.947908	−	0.318544i	$-0.896806\pi$
$503$	−16.8167	−	29.1274i	−0.749821	−	1.29873i	0.198087	−	0.980185i	$-0.436527\pi$
$504$	−4.72585	+	6.37701i	−0.210506	+	0.284055i
$505$	−7.68641	+	13.3133i	−0.342041	+	0.592432i
$506$	4.33835	+	11.9195i	0.192863	+	0.529887i
$507$	−15.5741	+	15.8020i	−0.691668	+	0.701790i
$508$	0.857536	−	0.719558i	0.0380470	−	0.0319252i
$509$	1.94816	+	0.709073i	0.0863508	+	0.0314291i	0.384834	−	0.922986i	$-0.374259\pi$
$509$	1.94816	+	0.709073i	0.0863508	+	0.0314291i	−0.298484	+	0.954415i	$0.596481\pi$
$510$	7.39307	+	0.592729i	0.327371	+	0.0262465i
$511$	−18.3309	+	0.840851i	−0.810912	+	0.0371971i
$512$		−	1.00000i		−	0.0441942i
$513$	8.19016	−	8.55513i	0.361605	−	0.377718i
$514$		−	12.6583i		−	0.558333i
$515$	−8.44289	−	1.48871i	−0.372038	−	0.0656004i
$516$	−2.92120	−	2.01398i	−0.128598	−	0.0886605i
$517$	3.80545	−	10.4554i	0.167364	−	0.459828i
$518$	−11.4030	−	8.70994i	−0.501019	−	0.382693i
$519$	−41.4737	−	10.7906i	−1.82049	−	0.473653i
$520$	0.503822	−	0.183376i	0.0220941	−	0.00804158i
$521$	17.6685	−	30.6027i	0.774069	−	1.34073i	−0.161247	−	0.986914i	$-0.551551\pi$
$521$	17.6685	−	30.6027i	0.774069	−	1.34073i	0.935316	−	0.353813i	$-0.115115\pi$
$522$	5.45387	−	3.25534i	0.238710	−	0.142482i
$523$	0.666516	−	0.384813i	0.0291447	−	0.0168267i	−0.485357	−	0.874316i	$-0.661310\pi$
$523$	0.666516	−	0.384813i	0.0291447	−	0.0168267i	0.514502	+	0.857489i	$0.327977\pi$
$524$	13.4181	+	11.2592i	0.586174	+	0.491858i
$525$	11.8953	+	10.6946i	0.519155	+	0.466752i
$526$	4.93126	+	27.9665i	0.215013	+	1.21940i
$527$	−28.8206	+	5.08184i	−1.25544	+	0.221368i
$528$	−3.30964	+	2.35344i	−0.144033	+	0.102421i
$529$	−4.80103	−	4.02854i	−0.208741	−	0.175154i
$530$	−0.0724588	−	0.125502i	−0.00314741	−	0.00545147i
$531$	−0.524819	−	36.1222i	−0.0227752	−	1.56757i
$532$	5.75531	+	1.80070i	0.249524	+	0.0780701i
$533$	0.235362	+	0.646653i	0.0101947	+	0.0280096i
$534$	6.41378	−	24.6514i	0.277551	−	1.06677i
$535$	3.09601	+	3.68968i	0.133852	+	0.159519i
$536$	2.89030	−	7.94104i	0.124842	−	0.343001i
$537$	18.1069	−	26.2633i	0.781370	−	1.13335i
$538$	−12.6839	−	2.23651i	−0.546842	−	0.0964230i
$539$	7.00183	+	14.8442i	0.301590	+	0.639385i
$540$	−0.694829	−	6.34589i	−0.0299007	−	0.273084i
$541$	28.0848			1.20746			0.603731	−	0.797188i	$-0.293680\pi$
$541$	28.0848			1.20746			0.603731	+	0.797188i	$0.293680\pi$
$542$	4.05128	−	22.9759i	0.174017	−	0.986901i
$543$	9.60348	+	0.769946i	0.412125	+	0.0330415i
$544$	−1.19209	+	3.27524i	−0.0511104	+	0.140425i
$545$	−13.7931	+	11.5738i	−0.590831	+	0.495766i
$546$	1.05851	−	1.69678i	0.0453001	−	0.0726153i
$547$	30.8451	−	11.2267i	1.31884	−	0.480019i	0.415754	−	0.909477i	$-0.363518\pi$
$547$	30.8451	−	11.2267i	1.31884	−	0.480019i	0.903087	+	0.429458i	$0.141295\pi$
$548$	19.4500	+	11.2295i	0.830863	+	0.479699i
$549$	31.6875	+	11.0147i	1.35239	+	0.470094i
$550$	4.09218	+	7.08786i	0.174491	+	0.302227i
$551$	−3.69667	−	3.10187i	−0.157483	−	0.132144i
$552$	3.89825	−	8.52089i	0.165921	−	0.362673i
$553$	5.36969	+	12.8831i	0.228342	+	0.547847i
$554$	21.8934	−	3.86040i	0.930162	−	0.164013i
$555$	11.4891	−	1.08932i	0.487685	−	0.0462389i
$556$	11.3760	−	13.5573i	0.482448	−	0.574959i
$557$	19.8930	−	11.4852i	0.842895	−	0.486645i	−0.0153525	−	0.999882i	$-0.504887\pi$
$557$	19.8930	−	11.4852i	0.842895	−	0.486645i	0.858247	+	0.513237i	$0.171554\pi$
$558$	8.95818	+	23.5425i	0.379230	+	0.996633i
$559$	0.774225	+	0.446999i	0.0327462	+	0.0189061i
$560$	2.73757	−	1.75252i	0.115683	−	0.0740576i
$561$	13.6454	−	3.76271i	0.576108	−	0.158862i
$562$	7.59841	−	6.37582i	0.320520	−	0.268948i
$563$	18.1788	+	6.61655i	0.766146	+	0.278854i	0.695384	−	0.718639i	$-0.255235\pi$
$563$	18.1788	+	6.61655i	0.766146	+	0.278854i	0.0707626	+	0.997493i	$0.477457\pi$
$564$	−7.42378	+	3.52764i	−0.312597	+	0.148540i
$565$	5.39247	+	0.950837i	0.226863	+	0.0400020i
$566$	7.94070			0.333773
$567$	−16.6279	−	17.0445i	−0.698305	−	0.715801i
$568$	2.04537			0.0858220
$569$	−13.7869	−	2.43100i	−0.577976	−	0.101913i	−0.122985	−	0.992409i	$-0.539247\pi$
$569$	−13.7869	−	2.43100i	−0.577976	−	0.101913i	−0.454992	+	0.890496i	$0.650358\pi$
$570$	−4.38075	+	2.08165i	−0.183490	+	0.0871908i
$571$	−25.4729	−	9.27136i	−1.06601	−	0.387994i	−0.251324	−	0.967903i	$-0.580866\pi$
$571$	−25.4729	−	9.27136i	−1.06601	−	0.387994i	−0.814682	+	0.579909i	$0.803088\pi$
$572$	0.783842	−	0.657721i	0.0327741	−	0.0275007i
$573$	15.2793	−	4.21326i	0.638301	−	0.176012i
$574$	2.24935	+	3.51365i	0.0938862	+	0.146657i
$575$	−16.3540	−	9.44201i	−0.682011	−	0.393759i
$576$	2.96168	+	0.477969i	0.123403	+	0.0199154i
$577$	23.7587	−	13.7171i	0.989089	−	0.571051i	0.0840869	−	0.996458i	$-0.473203\pi$
$577$	23.7587	−	13.7171i	0.989089	−	0.571051i	0.905002	+	0.425408i	$0.139869\pi$
$578$	−3.11863	+	3.71664i	−0.129718	+	0.154592i
$579$	−46.6055	+	4.41881i	−1.93686	+	0.183639i
$580$	−2.56158	+	0.451675i	−0.106364	+	0.0187548i
$581$	8.83469	+	21.1965i	0.366525	+	0.879378i
$582$	11.0108	−	24.0676i	0.456411	−	0.997633i
$583$	−0.211864	−	0.177775i	−0.00877453	−	0.00736270i
$584$	3.46786	+	6.00651i	0.143501	+	0.248551i
$585$	0.302290	+	1.57981i	0.0124982	+	0.0653170i
$586$	10.8798	+	6.28146i	0.449441	+	0.259485i
$587$	41.8734	−	15.2407i	1.72830	−	0.629050i	0.729792	−	0.683669i	$-0.239617\pi$
$587$	41.8734	−	15.2407i	1.72830	−	0.629050i	0.998507	+	0.0546196i	$0.0173946\pi$
$588$	4.01348	−	11.4408i	0.165513	−	0.471811i
$589$	14.6604	−	12.3016i	0.604073	−	0.506877i
$590$	−5.05999	+	13.9022i	−0.208316	+	0.572344i
$591$	−18.7287	−	1.50155i	−0.770397	−	0.0617655i
$592$	−0.941760	+	5.34098i	−0.0387061	+	0.219513i
$593$	−15.7583			−0.647115			−0.323558	−	0.946209i	$-0.604879\pi$
$593$	−15.7583			−0.647115			−0.323558	+	0.946209i	$0.604879\pi$
$594$	−5.38824	−	10.9270i	−0.221082	−	0.448338i
$595$	−11.0554	+	2.47650i	−0.453225	+	0.101527i
$596$	11.4259	+	2.01470i	0.468024	+	0.0825253i
$597$	−5.35008	+	7.76008i	−0.218964	+	0.317599i
$598$	−0.807488	+	2.21856i	−0.0330206	+	0.0907235i
$599$	13.2291	+	15.7658i	0.540525	+	0.644173i	0.965305	−	0.261124i	$-0.0840931\pi$
$599$	13.2291	+	15.7658i	0.540525	+	0.644173i	−0.424780	+	0.905296i	$0.639649\pi$
$600$	1.52234	−	5.85114i	0.0621494	−	0.238872i
$601$	2.58497	+	7.10215i	0.105443	+	0.289703i	0.981183	−	0.193081i	$-0.0618480\pi$
$601$	2.58497	+	7.10215i	0.105443	+	0.289703i	−0.875740	+	0.482784i	$0.839626\pi$
$602$	5.17265	+	1.61840i	0.210821	+	0.0659610i
$603$	22.1373	+	12.3557i	0.901502	+	0.503164i
$604$	−5.49931	−	9.52508i	−0.223764	−	0.387570i
$605$	5.17863	+	4.34539i	0.210541	+	0.176665i
$606$	17.6626	−	12.5597i	0.717493	−	0.510201i
$607$	−25.2819	+	4.45788i	−1.02616	+	0.180940i	−0.661299	−	0.750122i	$-0.729995\pi$
$607$	−25.2819	+	4.45788i	−1.02616	+	0.180940i	−0.364861	+	0.931062i	$0.618884\pi$
$608$	−0.395794	−	2.24466i	−0.0160516	−	0.0910330i
$609$	−6.48663	+	7.21491i	−0.262852	+	0.292363i
$610$	−10.5242	−	8.83083i	−0.426111	−	0.357550i
$611$	1.79348	−	1.03547i	0.0725566	−	0.0418906i
$612$	−9.13043	−	5.09605i	−0.369076	−	0.205996i
$613$	−10.0628	+	17.4293i	−0.406433	+	0.703962i	−0.994487	−	0.104859i	$-0.966561\pi$
$613$	−10.0628	+	17.4293i	−0.406433	+	0.703962i	0.588054	+	0.808821i	$0.299894\pi$
$614$	−8.32350	+	3.02951i	−0.335909	+	0.122261i
$615$	−3.24734	−	0.844889i	−0.130945	−	0.0340692i
$616$	3.76553	−	4.92981i	0.151718	−	0.198628i
$617$	3.08423	−	8.47385i	0.124166	−	0.341145i	−0.861999	−	0.506911i	$-0.830787\pi$
$617$	3.08423	−	8.47385i	0.124166	−	0.341145i	0.986165	+	0.165766i	$0.0530097\pi$
$618$	9.95081	+	6.86045i	0.400280	+	0.275968i
$619$	−10.9095	−	1.92363i	−0.438488	−	0.0773173i	−0.0499538	−	0.998752i	$-0.515907\pi$
$619$	−10.9095	−	1.92363i	−0.438488	−	0.0773173i	−0.388534	+	0.921434i	$0.627019\pi$
$620$		−	10.3155i		−	0.414282i
$621$	23.3729	+	15.6181i	0.937922	+	0.626733i
$622$		−	20.9184i		−	0.838752i
$623$	1.78292	+	38.8684i	0.0714312	+	1.55723i
$624$	−0.753464	−	0.0604079i	−0.0301627	−	0.00241825i
$625$	−4.35792	−	1.58615i	−0.174317	−	0.0634461i
$626$	−9.69001	+	8.13089i	−0.387291	+	0.324976i
$627$	−6.49753	+	6.59262i	−0.259486	+	0.263284i
$628$	−4.97142	−	13.6589i	−0.198381	−	0.545048i
$629$	9.45142	−	16.3703i	0.376853	−	0.652728i
$630$	3.88194	+	8.94545i	0.154660	+	0.356395i
$631$	−8.40768	−	14.5625i	−0.334704	−	0.579725i	0.648724	−	0.761024i	$-0.275303\pi$
$631$	−8.40768	−	14.5625i	−0.334704	−	0.579725i	−0.983428	+	0.181299i	$0.941970\pi$
$632$	3.39096	−	4.04119i	0.134885	−	0.160750i
$633$	16.7940	−	36.7088i	0.667503	−	1.45904i
$634$	−0.815627	−	4.62565i	−0.0323927	−	0.183708i
$635$	−0.238818	−	1.35440i	−0.00947720	−	0.0537479i
$636$	0.0192845	+	0.203395i	0.000764680	+	0.00806513i
$637$	−0.777634	+	2.95423i	−0.0308110	+	0.117051i
$638$	−4.29902	+	2.48204i	−0.170200	+	0.0982649i
$639$	−0.977626	+	6.05774i	−0.0386743	+	0.239641i
$640$	−1.06397	−	0.614283i	−0.0420571	−	0.0242817i
$641$	13.6635	+	37.5403i	0.539677	+	1.48275i	0.847233	+	0.531221i	$0.178267\pi$
$641$	13.6635	+	37.5403i	0.539677	+	1.48275i	−0.307556	+	0.951530i	$0.599511\pi$
$642$	−1.80509	−	6.54610i	−0.0712411	−	0.258354i
$643$	9.74558	+	11.6143i	0.384328	+	0.458025i	0.923175	−	0.384379i	$-0.125584\pi$
$643$	9.74558	+	11.6143i	0.384328	+	0.458025i	−0.538847	+	0.842404i	$0.681140\pi$
$644$	−1.83696	+	14.1950i	−0.0723865	+	0.559359i
$645$	−3.93725	+	1.87091i	−0.155029	+	0.0736670i
$646$	−1.37952	+	7.82362i	−0.0542763	+	0.307816i
$647$	−39.1958			−1.54094			−0.770472	−	0.637473i	$-0.779980\pi$
$647$	−39.1958			−1.54094			−0.770472	+	0.637473i	$0.779980\pi$
$648$	−2.83118	+	8.54309i	−0.111219	+	0.335604i
$649$			28.2345i			1.10830i
$650$	−0.264525	+	1.50020i	−0.0103755	+	0.0588425i
$651$	−23.7114	−	30.3028i	−0.929324	−	1.18766i
$652$	3.68764	+	1.34219i	0.144419	+	0.0525642i
$653$	−25.1406	−	29.9614i	−0.983829	−	1.17248i	−0.985013	−	0.172482i	$-0.944821\pi$
$653$	−25.1406	−	29.9614i	−0.983829	−	1.17248i	0.00118396	−	0.999999i	$-0.499623\pi$
$654$	24.4713	−	6.74795i	0.956902	−	0.263866i
$655$	20.2219	−	7.36018i	0.790136	−	0.287586i
$656$	0.788428	−	1.36560i	0.0307830	−	0.0533176i
$657$	−19.4469	+	7.39976i	−0.758695	+	0.288692i
$658$	9.23791	−	8.50254i	0.360131	−	0.331464i
$659$	8.02297	−	9.56140i	0.312531	−	0.372459i	−0.586798	−	0.809734i	$-0.699612\pi$
$659$	8.02297	−	9.56140i	0.312531	−	0.372459i	0.899328	+	0.437274i	$0.144056\pi$
$660$	0.470939	+	4.96703i	0.0183313	+	0.193341i
$661$	−27.8439	+	4.90963i	−1.08300	+	0.190963i	−0.686543	−	0.727090i	$-0.740873\pi$
$661$	−27.8439	+	4.90963i	−1.08300	+	0.190963i	−0.396460	+	0.918052i	$0.629761\pi$
$662$	−10.2294	+	1.80372i	−0.397578	+	0.0701037i
$663$	2.39576	+	1.09605i	0.0930437	+	0.0425669i
$664$	5.57911	−	6.64892i	0.216511	−	0.258028i
$665$	5.45127	−	5.01733i	0.211391	−	0.194564i
$666$	−15.3682	−	5.34202i	−0.595504	−	0.206999i
$667$	5.72689	−	9.91926i	0.221746	−	0.384075i
$668$	5.73871	−	2.08872i	0.222037	−	0.0808150i
$669$	8.08677	+	7.97013i	0.312653	+	0.308143i
$670$	−6.67356	−	7.95324i	−0.257822	−	0.307260i
$671$	−24.6378	−	8.96744i	−0.951133	−	0.346184i
$672$	−4.53750	+	0.641141i	−0.175038	+	0.0247326i
$673$	−1.02565	+	5.81673i	−0.0395358	+	0.224219i	−0.998174	−	0.0604101i	$-0.980759\pi$
$673$	−1.02565	+	5.81673i	−0.0395358	+	0.224219i	0.958638	+	0.284629i	$0.0918703\pi$
$674$			3.93836i			0.151700i
$675$	16.6016	+	7.30536i	0.638995	+	0.281183i
$676$	−12.8095			−0.492675
$677$	6.20980	−	35.2175i	0.238662	−	1.35352i	−0.596101	−	0.802910i	$-0.703284\pi$
$677$	6.20980	−	35.2175i	0.238662	−	1.35352i	0.834763	−	0.550610i	$-0.185605\pi$
$678$	−6.35557	−	4.38177i	−0.244084	−	0.168281i
$679$	−5.18858	+	40.0942i	−0.199119	+	1.53867i
$680$	2.75247	+	3.28027i	0.105553	+	0.125793i
$681$	−10.1208	−	2.63322i	−0.387831	−	0.100905i
$682$	−6.73328	−	18.4995i	−0.257831	−	0.708384i
$683$	−37.1567	−	21.4524i	−1.42176	−	0.820855i	−0.425313	−	0.905046i	$-0.639836\pi$
$683$	−37.1567	−	21.4524i	−1.42176	−	0.820855i	−0.996450	+	0.0841913i	$0.973169\pi$
$684$	6.83714	−	0.0993366i	0.261425	−	0.00379823i
$685$	23.8956	−	13.7961i	0.913005	−	0.527123i
$686$	−0.685416	+	18.5076i	−0.0261693	+	0.706622i
$687$	−28.0512	+	19.9469i	−1.07022	+	0.761021i
$688$	−0.355725	−	2.01741i	−0.0135619	−	0.0769132i
$689$	−0.00893894	−	0.0506953i	−0.000340547	−	0.00193134i
$690$	−6.67133	−	9.38186i	−0.253973	−	0.357161i
$691$	22.9322	−	27.3296i	0.872383	−	1.03967i	−0.126479	−	0.991969i	$-0.540368\pi$
$691$	22.9322	−	27.3296i	0.872383	−	1.03967i	0.998862	−	0.0476960i	$-0.0151879\pi$
$692$	−12.3710	−	21.4272i	−0.470275	−	0.814541i
$693$	12.8007	+	13.5086i	0.486259	+	0.513149i
$694$	−13.8934	+	24.0641i	−0.527388	+	0.913462i
$695$	−7.43654	−	20.4317i	−0.282084	−	0.775019i
$696$	3.54891	+	0.923350i	0.134521	+	0.0349995i
$697$	−4.21021	+	3.53278i	−0.159473	+	0.133814i
$698$	15.8068	+	5.75320i	0.598296	+	0.217762i
$699$	3.79123	−	5.49903i	0.143398	−	0.207992i
$700$	0.423185	+	9.22563i	0.0159949	+	0.348696i
$701$			22.7597i			0.859624i	0.902918	+	0.429812i	$0.141420\pi$
$701$			22.7597i			0.859624i	−0.902918	+	0.429812i	$0.858580\pi$
$702$	0.539042	−	2.20265i	0.0203448	−	0.0831335i
$703$			12.3614i			0.466221i
$704$	−2.30905	−	0.407147i	−0.0870255	−	0.0153449i
$705$	−0.806999	+	10.0656i	−0.0303933	+	0.379094i
$706$	−0.577533	+	1.58676i	−0.0217358	+	0.0597185i
$707$	−20.0956	+	26.3090i	−0.755772	+	0.989451i
$708$	14.6409	−	14.8551i	0.550238	−	0.558290i
$709$	42.5614	−	15.4911i	1.59843	−	0.581780i	0.619323	−	0.785136i	$-0.287407\pi$
$709$	42.5614	−	15.4911i	1.59843	−	0.581780i	0.979105	+	0.203356i	$0.0651848\pi$
$710$	1.25644	−	2.17622i	0.0471533	−	0.0816719i
$711$	10.3479	+	11.9745i	0.388078	+	0.449079i
$712$	12.7361	−	7.35317i	0.477304	−	0.275572i
$713$	34.7968	+	29.1980i	1.30315	+	1.09347i
$714$	15.6257	+	3.30922i	0.584777	+	0.123844i
$715$	−0.218295	−	1.23801i	−0.00816376	−	0.0462990i
$716$	18.1378	−	3.19818i	0.677840	−	0.119522i
$717$	−1.49163	−	15.7323i	−0.0557059	−	0.587534i
$718$	9.33366	+	7.83187i	0.348329	+	0.292283i
$719$	−0.807602	−	1.39881i	−0.0301185	−	0.0521667i	0.850573	−	0.525857i	$-0.176255\pi$
$719$	−0.807602	−	1.39881i	−0.0301185	−	0.0521667i	−0.880692	+	0.473690i	$0.842922\pi$
$720$	2.32785	−	2.85753i	0.0867540	−	0.106494i
$721$	−17.6202	−	5.51294i	−0.656210	−	0.205312i
$722$	4.72154	+	12.9723i	0.175717	+	0.482780i
$723$	47.1344	−	12.9973i	1.75295	−	0.483375i
$724$	3.57542	+	4.26102i	0.132879	+	0.158359i
$725$	2.52762	−	6.94459i	0.0938736	−	0.257916i
$726$	−4.09047	−	8.60824i	−0.151812	−	0.319482i
$727$	−48.1472	−	8.48966i	−1.78568	−	0.314864i	−0.819569	−	0.572981i	$-0.805787\pi$
$727$	−48.1472	−	8.48966i	−1.78568	−	0.314864i	−0.966114	+	0.258117i	$0.916898\pi$
$728$	1.12671	−	0.252393i	0.0417585	−	0.00935429i
$729$	−23.9487	−	12.4684i	−0.886988	−	0.461792i
$730$	8.52099			0.315376
$731$	−1.23986	+	7.03157i	−0.0458577	+	0.260072i
$732$	8.31278	+	17.4939i	0.307249	+	0.646594i
$733$	−0.0218471	+	0.0600243i	−0.000806939	+	0.00221705i	−0.940095	−	0.340911i	$-0.889264\pi$
$733$	−0.0218471	+	0.0600243i	−0.000806939	+	0.00221705i	0.939288	+	0.343128i	$0.111487\pi$
$734$	16.4269	−	13.7838i	0.606326	−	0.508768i
$735$	−9.70725	−	11.2981i	−0.358057	−	0.416737i
$736$	5.08367	−	1.85030i	0.187386	−	0.0682031i
$737$	−17.1594	−	9.90701i	−0.632076	−	0.364929i
$738$	3.66762	+	2.98779i	0.135007	+	0.109982i
$739$	11.3282	+	19.6211i	0.416715	+	0.721772i	0.995607	−	0.0936324i	$-0.0298478\pi$
$739$	11.3282	+	19.6211i	0.416715	+	0.721772i	−0.578891	+	0.815405i	$0.696514\pi$
$740$	5.10414	+	4.28288i	0.187632	+	0.157442i
$741$	−1.71518	+	0.162621i	−0.0630087	+	0.00597405i
$742$	−0.120065	−	0.288064i	−0.00440773	−	0.0105752i
$743$	−28.1945	+	4.97145i	−1.03436	+	0.182385i	−0.664954	−	0.746885i	$-0.731549\pi$
$743$	−28.1945	+	4.97145i	−1.03436	+	0.182385i	−0.369402	+	0.929270i	$0.620438\pi$
$744$	−6.05024	+	13.2247i	−0.221812	+	0.484843i
$745$	9.16233	−	10.9192i	0.335682	−	0.400050i
$746$	−17.0630	+	9.85132i	−0.624720	+	0.360682i
$747$	17.0253	+	19.7015i	0.622925	+	0.720841i
$748$	7.07732	+	4.08609i	0.258773	+	0.149402i
$749$	5.59244	+	8.73580i	0.204343	+	0.319199i
$750$	−12.8681	−	12.6825i	−0.469878	−	0.463101i
$751$	33.1976	−	27.8561i	1.21140	−	1.01648i	0.212169	−	0.977233i	$-0.431947\pi$
$751$	33.1976	−	27.8561i	1.21140	−	1.01648i	0.999229	−	0.0392509i	$-0.0124972\pi$
$752$	−4.45922	−	1.62303i	−0.162611	−	0.0591856i
$753$	1.40555	−	17.5313i	0.0512210	−	0.638876i
$754$	−0.909917	−	0.160443i	−0.0331372	−	0.00584299i
$755$	−13.5125			−0.491771
$756$	0.269934	−	13.7451i	0.00981739	−	0.499904i
$757$	24.6013			0.894149			0.447075	−	0.894497i	$-0.352466\pi$
$757$	24.6013			0.894149			0.447075	+	0.894497i	$0.352466\pi$
$758$	−24.4556	−	4.31218i	−0.888266	−	0.156625i
$759$	−18.0880	−	12.4705i	−0.656551	−	0.452651i
$760$	−2.63138	−	0.957744i	−0.0954501	−	0.0347410i
$761$	−0.393164	+	0.329903i	−0.0142522	+	0.0119590i	−0.649886	−	0.760032i	$-0.725183\pi$
$761$	−0.393164	+	0.329903i	−0.0142522	+	0.0119590i	0.635634	+	0.771991i	$0.280739\pi$
$762$	−0.488211	+	1.87644i	−0.0176860	+	0.0679764i
$763$	−32.6570	+	20.9062i	−1.18226	+	0.756854i
$764$	7.92477	+	4.57537i	0.286708	+	0.165531i
$765$	−11.0307	+	6.58408i	−0.398816	+	0.238048i
$766$	−8.38597	+	4.84164i	−0.302997	+	0.174936i
$767$	−3.37800	+	4.02575i	−0.121973	+	0.145361i
$768$	1.00374	+	1.41156i	0.0362195	+	0.0509353i
$769$	−16.7334	+	2.95055i	−0.603423	+	0.106400i	−0.467009	−	0.884252i	$-0.654669\pi$
$769$	−16.7334	+	2.95055i	−0.603423	+	0.106400i	−0.136413	+	0.990652i	$0.543557\pi$
$770$	−2.93206	−	7.03471i	−0.105664	−	0.253513i
$771$	12.7057	+	17.8679i	0.457584	+	0.643498i
$772$	−20.7049	−	17.3735i	−0.745187	−	0.625286i
$773$	−12.8605	−	22.2751i	−0.462561	−	0.801179i	0.536527	−	0.843883i	$-0.319736\pi$
$773$	−12.8605	−	22.2751i	−0.462561	−	0.801179i	−0.999088	+	0.0427040i	$0.986403\pi$
$774$	6.14496	−	0.0892799i	0.220876	−	0.00320910i
$775$	25.3821	+	14.6544i	0.911752	+	0.526400i
$776$	14.3590	−	5.22626i	0.515459	−	0.187612i
$777$	24.8385	+	0.848914i	0.891078	+	0.0304546i
$778$	−23.5584	+	19.7679i	−0.844611	+	0.708713i
$779$	1.22926	−	3.37736i	0.0440427	−	0.121006i
$780$	−0.527112	+	0.764555i	−0.0188736	+	0.0273755i
$781$	0.832769	−	4.72287i	0.0297988	−	0.168997i
$782$	−18.8560			−0.674288
$783$	−4.43094	+	10.0694i	−0.158349	+	0.359851i
$784$	6.33105	−	2.98628i	0.226109	−	0.106653i
$785$	−17.5865	−	3.10097i	−0.627688	−	0.110678i
$786$	−30.2418	−	2.42459i	−1.07869	−	0.0864824i
$787$	−7.98929	+	21.9504i	−0.284788	+	0.782448i	0.711987	+	0.702193i	$0.247796\pi$
$787$	−7.98929	+	21.9504i	−0.284788	+	0.782448i	−0.996774	+	0.0802546i	$0.974427\pi$
$788$	−6.97278	−	8.30984i	−0.248395	−	0.296026i
$789$	−35.0320	−	34.5267i	−1.24717	−	1.22918i
$790$	−2.21669	−	6.09032i	−0.0788664	−	0.216684i
$791$	11.2540	+	3.52111i	0.400146	+	0.125196i
$792$	2.30949	−	6.64405i	0.0820643	−	0.236086i
$793$	−2.44005	−	4.22629i	−0.0866487	−	0.150080i
$794$	−7.01111	−	5.88302i	−0.248815	−	0.208781i
$795$	0.228252	+	0.104424i	0.00809527	+	0.00370354i
$796$	−5.35921	+	0.944973i	−0.189952	+	0.0334937i
$797$	3.92923	+	22.2838i	0.139181	+	0.789332i	0.971857	+	0.235572i	$0.0756965\pi$
$797$	3.92923	+	22.2838i	0.139181	+	0.789332i	−0.832676	+	0.553760i	$0.813192\pi$
$798$	−9.93139	+	3.23506i	−0.351568	+	0.114520i
$799$	12.6702	+	10.6316i	0.448241	+	0.376119i
$800$	3.02297	−	1.74531i	0.106878	−	0.0617061i
$801$	15.6903	+	41.2347i	0.554389	+	1.45696i
$802$	16.3633	−	28.3421i	0.577810	−	1.00080i
$803$	15.2812	−	5.56192i	0.539263	−	0.196276i
$804$	3.89093	+	14.1104i	0.137223	+	0.497634i
$805$	13.9746	+	10.6742i	0.492539	+	0.376216i
$806$	1.25325	−	3.44328i	0.0441439	−	0.121284i
$807$	20.1490	−	9.57441i	0.709277	−	0.337035i
$808$	12.3227	+	2.17283i	0.433512	+	0.0764398i
$809$			11.9777i			0.421115i	0.977582	+	0.210557i	$0.0675279\pi$
$809$			11.9777i			0.421115i	−0.977582	+	0.210557i	$0.932472\pi$
$810$	7.35044	+	8.26017i	0.258268	+	0.290233i
$811$			7.72412i			0.271230i	0.990762	+	0.135615i	$0.0433011\pi$
$811$			7.72412i			0.271230i	−0.990762	+	0.135615i	$0.956699\pi$
$812$	−5.59564	+	0.256676i	−0.196369	+	0.00900755i
$813$	17.3433	+	36.4983i	0.608257	+	1.28005i
$814$	11.9491	+	4.34913i	0.418817	+	0.152437i
$815$	3.69330	−	3.09905i	0.129371	−	0.108555i
$816$	−1.60479	−	5.81975i	−0.0561791	−	0.203732i
$817$	−1.59696	−	4.38762i	−0.0558706	−	0.153503i
$818$	3.51205	−	6.08305i	0.122796	−	0.212689i
$819$	0.208975	+	3.45758i	0.00730219	+	0.120817i
$820$	−0.968636	−	1.67773i	−0.0338262	−	0.0585888i
$821$	−1.09508	+	1.30506i	−0.0382184	+	0.0455469i	−0.784815	−	0.619730i	$-0.787242\pi$
$821$	−1.09508	+	1.30506i	−0.0382184	+	0.0455469i	0.746597	+	0.665277i	$0.231687\pi$
$822$	−38.7263	+	3.67176i	−1.35074	+	0.128067i
$823$	1.25194	+	7.10010i	0.0436399	+	0.247494i	0.998822	−	0.0485248i	$-0.0154520\pi$
$823$	1.25194	+	7.10010i	0.0436399	+	0.247494i	−0.955182	+	0.296019i	$0.904341\pi$
$824$	1.21175	+	6.87215i	0.0422132	+	0.239403i
$825$	−12.8907	−	5.89744i	−0.448798	−	0.205322i
$826$	−14.6490	+	28.2927i	−0.509705	+	0.984429i
$827$	17.5393	−	10.1263i	0.609901	−	0.352126i	−0.163026	−	0.986622i	$-0.552125\pi$
$827$	17.5393	−	10.1263i	0.609901	−	0.352126i	0.772927	+	0.634495i	$0.218792\pi$
$828$	3.05017	+	15.9406i	0.106001	+	0.553974i
$829$	40.7465	+	23.5250i	1.41519	+	0.817058i	0.995871	−	0.0907826i	$-0.0289368\pi$
$829$	40.7465	+	23.5250i	1.41519	+	0.817058i	0.419315	+	0.907841i	$0.362270\pi$
$830$	−3.64710	−	10.0203i	−0.126593	−	0.347810i
$831$	−27.0290	+	27.4246i	−0.937626	+	0.951347i
$832$	−0.280518	−	0.334308i	−0.00972521	−	0.0115901i
$833$	−24.2956	+	2.23361i	−0.841793	+	0.0773900i
$834$	−2.44975	+	30.5555i	−0.0848278	+	1.05805i
$835$	1.30286	−	7.38888i	0.0450873	−	0.255703i
$836$	−5.34417			−0.184832
$837$	−36.2756	−	24.2399i	−1.25387	−	0.837853i
$838$			32.3942i			1.11904i
$839$	−5.25636	+	29.8103i	−0.181470	+	1.02917i	0.748938	+	0.662640i	$0.230564\pi$
$839$	−5.25636	+	29.8103i	−0.181470	+	1.02917i	−0.930408	+	0.366526i	$0.880547\pi$
$840$	−2.10516	+	5.22161i	−0.0726348	+	0.180163i
$841$	−23.0390	−	8.38550i	−0.794447	−	0.289155i
$842$	−6.17920	−	7.36408i	−0.212949	−	0.253783i
$843$	−4.32592	+	16.6267i	−0.148992	+	0.572654i
$844$	21.9009	−	7.97128i	0.753861	−	0.274383i
$845$	−7.86869	+	13.6290i	−0.270691	+	0.468851i
$846$	6.93825	−	12.4310i	0.238542	−	0.427388i
$847$	9.85912	+	10.7118i	0.338763	+	0.368062i
$848$	−0.0758211	+	0.0903601i	−0.00260371	+	0.00310298i
$849$	−11.2088	+	7.97043i	−0.384684	+	0.273544i
$850$	−11.9815	+	2.11267i	−0.410963	+	0.0724638i
$851$	−28.8943	+	5.09485i	−0.990485	+	0.174649i
$852$	−2.88717	+	2.05303i	−0.0989127	+	0.0703357i
$853$	−33.2273	+	39.5988i	−1.13768	+	1.35584i	−0.212120	+	0.977244i	$0.568037\pi$
$853$	−33.2273	+	39.5988i	−1.13768	+	1.35584i	−0.925563	+	0.378594i	$0.876408\pi$
$854$	−20.0360	−	21.7689i	−0.685618	−	0.744916i
$855$	4.09425	−	7.33553i	0.140020	−	0.250870i
$856$	1.96023	−	3.39521i	0.0669991	−	0.116046i
$857$	−2.22382	+	0.809405i	−0.0759643	+	0.0276487i	−0.379723	−	0.925100i	$-0.623981\pi$
$857$	−2.22382	+	0.809405i	−0.0759643	+	0.0276487i	0.303758	+	0.952749i	$0.401758\pi$
$858$	−0.446255	+	1.71519i	−0.0152349	+	0.0585556i
$859$	−13.6641	−	16.2842i	−0.466212	−	0.555610i	0.480791	−	0.876835i	$-0.340350\pi$
$859$	−13.6641	−	16.2842i	−0.466212	−	0.555610i	−0.947003	+	0.321225i	$0.895905\pi$
$860$	−2.36498	−	0.860783i	−0.0806452	−	0.0293525i
$861$	−6.70190	−	2.70196i	−0.228400	−	0.0920824i
$862$	−0.316514	+	1.79504i	−0.0107805	+	0.0611393i
$863$		−	13.3941i		−	0.455942i	−0.973668	−	0.227971i	$-0.926791\pi$
$863$		−	13.3941i		−	0.455942i	0.973668	−	0.227971i	$-0.0732092\pi$
$864$	−4.66034	+	2.29808i	−0.158548	+	0.0781824i
$865$	−30.3972			−1.03354
$866$	−5.64771	+	32.0298i	−0.191917	+	1.08842i
$867$	0.671580	−	8.37657i	0.0228080	−	0.284483i
$868$	2.85104	−	22.0311i	0.0967705	−	0.747784i
$869$	−7.95068	−	9.47525i	−0.269708	−	0.321426i
$870$	3.16245	−	3.20873i	0.107217	−	0.108786i
$871$	−1.26135	−	3.46554i	−0.0427393	−	0.117425i
$872$	12.6923	+	7.32790i	0.429815	+	0.248154i
$873$	8.61532	+	45.0248i	0.291584	+	1.52386i
$874$	10.6788	−	6.16539i	0.361215	−	0.208547i
$875$	24.5083	+	12.6896i	0.828532	+	0.428987i
$876$	−10.9241	−	4.99770i	−0.369091	−	0.168857i
$877$	−3.38439	−	19.1938i	−0.114283	−	0.648129i	−0.987103	−	0.160087i	$-0.948822\pi$
$877$	−3.38439	−	19.1938i	−0.114283	−	0.648129i	0.872820	−	0.488042i	$-0.162289\pi$
$878$	5.50764	+	31.2354i	0.185874	+	1.05414i
$879$	−21.6625	+	2.05388i	−0.730657	+	0.0692758i
$880$	−1.85160	+	2.20665i	−0.0624174	+	0.0743862i
$881$	−11.0298	−	19.1042i	−0.371604	−	0.643637i	0.618208	−	0.786014i	$-0.287859\pi$
$881$	−11.0298	−	19.1042i	−0.371604	−	0.643637i	−0.989812	+	0.142377i	$0.954525\pi$
$882$	5.81836	+	20.1779i	0.195914	+	0.679424i
$883$	−17.0509	+	29.5330i	−0.573808	+	0.993864i	0.422362	+	0.906427i	$0.361201\pi$
$883$	−17.0509	+	29.5330i	−0.573808	+	0.993864i	−0.996170	+	0.0874371i	$0.972132\pi$
$884$	0.520238	+	1.42934i	0.0174975	+	0.0480740i
$885$	−6.81177	−	24.7027i	−0.228975	−	0.830372i
$886$	27.2161	−	22.8370i	0.914342	−	0.767224i
$887$	19.4112	+	7.06510i	0.651765	+	0.237223i	0.646677	−	0.762764i	$-0.276158\pi$
$887$	19.4112	+	7.06510i	0.651765	+	0.237223i	0.00508786	+	0.999987i	$0.498380\pi$
$888$	−4.03163	−	8.48440i	−0.135293	−	0.284718i
$889$	−0.135714	−	2.95863i	−0.00455171	−	0.0992293i
$890$		−	18.0677i		−	0.605631i
$891$	18.5737	+	10.0156i	0.622242	+	0.335536i
$892$			6.55538i			0.219490i
$893$	−10.6518	−	1.87820i	−0.356450	−	0.0628517i
$894$	−18.1506	+	8.62484i	−0.607047	+	0.288458i
$895$	7.73896	−	21.2626i	0.258685	−	0.710731i
$896$	−2.10256	−	1.60600i	−0.0702417	−	0.0536526i
$897$	−1.08704	−	3.94213i	−0.0362953	−	0.131624i
$898$	6.30802	−	2.29593i	0.210501	−	0.0766162i
$899$	−8.88835	+	15.3951i	−0.296443	+	0.513454i
$900$	3.72417	+	9.78728i	0.124139	+	0.326243i
$901$	0.356050	−	0.205565i	0.0118617	−	0.00684838i
$902$	−2.83222	−	2.37652i	−0.0943027	−	0.0791294i
$903$	−8.92596	+	2.90755i	−0.297037	+	0.0967572i
$904$	−0.773941	−	4.38924i	−0.0257409	−	0.145984i
$905$	6.72991	−	1.18666i	0.223710	−	0.0394461i
$906$	17.3233	+	7.92532i	0.575529	+	0.263301i
$907$	−7.48056	−	6.27693i	−0.248388	−	0.208422i	0.510090	−	0.860121i	$-0.329612\pi$
$907$	−7.48056	−	6.27693i	−0.248388	−	0.208422i	−0.758478	+	0.651699i	$0.774057\pi$
$908$	−3.01890	−	5.22888i	−0.100186	−	0.173527i
$909$	−12.3251	+	35.4574i	−0.408798	+	1.17605i
$910$	0.423578	−	1.35382i	0.0140415	−	0.0448787i
$911$	1.54942	+	4.25699i	0.0513345	+	0.141040i	0.962710	−	0.270535i	$-0.0872007\pi$
$911$	1.54942	+	4.25699i	0.0513345	+	0.141040i	−0.911375	+	0.411576i	$0.864979\pi$
$912$	2.81175	+	2.77119i	0.0931063	+	0.0917634i
$913$	−13.0812	−	15.5895i	−0.432923	−	0.515938i
$914$	−0.575978	+	1.58249i	−0.0190517	+	0.0523440i
$915$	23.7194	+	1.90167i	0.784139	+	0.0628672i
$916$	−19.5706	−	3.45082i	−0.646630	−	0.114018i
$917$	45.2226	−	10.1303i	1.49338	−	0.334531i
$918$	18.0033	−	1.97123i	0.594196	−	0.0650602i
$919$	−6.66460			−0.219845			−0.109922	−	0.993940i	$-0.535060\pi$
$919$	−6.66460			−0.219845			−0.109922	+	0.993940i	$0.535060\pi$
$920$	1.15414	−	6.54548i	0.0380510	−	0.215798i
$921$	8.70827	−	12.6310i	0.286947	−	0.416205i
$922$	0.397670	−	1.09259i	0.0130966	−	0.0359825i
$923$	0.683786	−	0.573764i	0.0225071	−	0.0188857i
$924$	−0.367007	+	10.7383i	−0.0120737	+	0.353266i
$925$	−17.7893	+	6.47478i	−0.584909	+	0.212889i
$926$	0.00845088	+	0.00487912i	0.000277713	+	0.000160338i
$927$	−20.9323	+	0.304125i	−0.687507	+	0.00998877i
$928$	1.05859	+	1.83353i	0.0347499	+	0.0601886i
$929$	−40.4176	−	33.9144i	−1.32606	−	1.11270i	−0.984981	−	0.172662i	$-0.944763\pi$
$929$	−40.4176	−	33.9144i	−1.32606	−	1.11270i	−0.341079	−	0.940035i	$-0.610792\pi$
$930$	10.3542	+	14.5610i	0.339526	+	0.477474i
$931$	13.0291	−	9.20897i	0.427011	−	0.301812i
$932$	3.79770	−	0.669637i	0.124398	−	0.0219347i
$933$	20.9967	+	29.5276i	0.687401	+	0.966689i
$934$	5.56487	−	6.63195i	0.182088	−	0.217004i
$935$	8.69496	−	5.02004i	0.284356	−	0.164173i
$936$	1.12419	−	0.671015i	0.0367454	−	0.0219328i
$937$	24.6944	+	14.2573i	0.806732	+	0.465767i	0.845820	−	0.533469i	$-0.179112\pi$
$937$	24.6944	+	14.2573i	0.806732	+	0.465767i	−0.0390877	+	0.999236i	$0.512445\pi$
$938$	−12.0547	−	18.8303i	−0.393600	−	0.614832i
$939$	5.51670	−	21.2035i	0.180031	−	0.691950i
$940$	−4.46607	+	3.74748i	−0.145667	+	0.122229i
$941$	4.64598	+	1.69100i	0.151455	+	0.0551250i	0.416635	−	0.909074i	$-0.363209\pi$
$941$	4.64598	+	1.69100i	0.151455	+	0.0551250i	−0.265180	+	0.964199i	$0.585432\pi$
$942$	20.7274	+	14.2903i	0.675336	+	0.465602i
$943$	8.40108	+	1.48134i	0.273577	+	0.0482390i
$944$	12.0420			0.391934
$945$	−14.4585	−	8.73057i	−0.470336	−	0.284005i
$946$	−4.80314			−0.156163
$947$	20.0258	+	3.53109i	0.650752	+	0.114745i	0.489273	−	0.872131i	$-0.337262\pi$
$947$	20.0258	+	3.53109i	0.650752	+	0.114745i	0.161480	+	0.986876i	$0.448373\pi$
$948$	−0.730224	+	9.10804i	−0.0237166	+	0.295815i
$949$	2.84427	+	1.03523i	0.0923289	+	0.0336050i
$950$	6.09476	−	5.11411i	0.197740	−	0.165924i
$951$	5.79427	+	5.71070i	0.187892	+	0.185182i
$952$	4.97190	+	7.76647i	0.161140	+	0.251713i
$953$	21.1725	+	12.2240i	0.685846	+	0.395973i	0.802054	−	0.597252i	$-0.203741\pi$
$953$	21.1725	+	12.2240i	0.685846	+	0.395973i	−0.116208	+	0.993225i	$0.537074\pi$
$954$	−0.231378	−	0.267747i	−0.00749112	−	0.00866864i
$955$	9.73610	−	5.62114i	0.315053	−	0.181896i
$956$	5.86466	−	6.98923i	0.189677	−	0.226048i
$957$	3.57699	−	7.81866i	0.115628	−	0.252741i
$958$	30.6935	−	5.41210i	0.991663	−	0.174857i
$959$	54.8473	−	22.8604i	1.77111	−	0.738199i
$960$	2.11844	−	0.200855i	0.0683723	−	0.00648258i
$961$	−30.2585	−	25.3899i	−0.976082	−	0.819030i
$962$	1.18340	+	2.04972i	0.0381545	+	0.0660855i
$963$	9.11859	+	7.42836i	0.293843	+	0.239376i
$964$	24.4468	+	14.1143i	0.787377	+	0.454592i
$965$	−31.2036	+	11.3572i	−1.00448	+	0.365600i
$966$	−11.6551	−	21.8809i	−0.374997	−	0.704005i
$967$	−16.8178	+	14.1118i	−0.540823	+	0.453805i	−0.871819	−	0.489827i	$-0.837060\pi$
$967$	−16.8178	+	14.1118i	−0.540823	+	0.453805i	0.330996	+	0.943632i	$0.392615\pi$
$968$	1.88198	−	5.17069i	0.0604891	−	0.166192i
$969$	−5.90564	−	12.4282i	−0.189717	−	0.399251i
$970$	3.25992	−	18.4880i	0.104670	−	0.593612i
$971$	−17.7138			−0.568462			−0.284231	−	0.958756i	$-0.591738\pi$
$971$	−17.7138			−0.568462			−0.284231	+	0.958756i	$0.591738\pi$
$972$	−4.57869	−	14.9009i	−0.146861	−	0.477945i
$973$	−10.2354	−	45.6917i	−0.328131	−	1.46481i
$974$	1.32454	+	0.233552i	0.0424410	+	0.00748350i
$975$	−1.13242	−	2.38313i	−0.0362664	−	0.0763212i
$976$	−3.82461	+	10.5080i	−0.122423	+	0.336354i
$977$	28.9823	+	34.5397i	0.927225	+	1.10502i	0.994230	+	0.107271i	$0.0342112\pi$
$977$	28.9823	+	34.5397i	0.927225	+	1.10502i	−0.0670051	+	0.997753i	$0.521344\pi$
$978$	−6.55253	+	1.80686i	−0.209527	+	0.0577770i
$979$	−11.7934	−	32.4020i	−0.376917	−	1.03557i
$980$	0.711743	−	8.57046i	0.0227358	−	0.273773i
$981$	−27.7694	+	34.0880i	−0.886609	+	1.08835i
$982$	3.28898	+	5.69668i	0.104956	+	0.181789i
$983$	39.6733	+	33.2899i	1.26538	+	1.06178i	0.995087	+	0.0990054i	$0.0315661\pi$
$983$	39.6733	+	33.2899i	1.26538	+	1.06178i	0.270296	+	0.962777i	$0.412878\pi$
$984$	0.257797	+	2.71900i	0.00821826	+	0.0866786i
$985$	−13.1247	+	2.31423i	−0.418187	+	0.0737377i
$986$	−1.28140	−	7.26718i	−0.0408081	−	0.231434i
$987$	−4.50549	+	21.2743i	−0.143411	+	0.677170i
$988$	−0.761985	−	0.639381i	−0.0242420	−	0.0203414i
$989$	9.59767	−	5.54122i	0.305188	−	0.176200i
$990$	−5.65038	−	6.53856i	−0.179581	−	0.207809i
$991$	25.8908	−	44.8442i	0.822449	−	1.42452i	−0.0814048	−	0.996681i	$-0.525941\pi$
$991$	25.8908	−	44.8442i	0.822449	−	1.42452i	0.903854	−	0.427842i	$-0.140726\pi$
$992$	−7.89005	+	2.87174i	−0.250509	+	0.0911779i
$993$	12.6290	−	12.8138i	0.400768	−	0.406633i
$994$	3.28487	−	4.30053i	0.104190	−	0.136404i
$995$	−2.28665	+	6.28251i	−0.0724916	+	0.199169i
$996$	−1.20143	+	14.9853i	−0.0380687	+	0.474829i
$997$	−31.2822	−	5.51589i	−0.990717	−	0.174690i	−0.345277	−	0.938501i	$-0.612215\pi$
$997$	−31.2822	−	5.51589i	−0.990717	−	0.174690i	−0.645440	+	0.763811i	$0.723326\pi$
$998$		−	32.8116i		−	1.03863i
$999$	27.0551	−	7.88511i	0.855985	−	0.249474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.83.11	yes	144
7.6	odd	2	inner	378.2.z.a.83.2	yes	144
27.14	odd	18	inner	378.2.z.a.41.2	✓	144
189.41	even	18	inner	378.2.z.a.41.11	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.41.2	✓	144	27.14	odd	18	inner
378.2.z.a.41.11	yes	144	189.41	even	18	inner
378.2.z.a.83.2	yes	144	7.6	odd	2	inner
378.2.z.a.83.11	yes	144	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.984808 - 0.173648i) q^{2} +(1.56441 - 0.743380i) q^{3} +(0.939693 + 0.342020i) q^{4} +(0.941136 - 0.789707i) q^{5} +(-1.66973 + 0.460429i) q^{6} +(2.22826 - 1.42648i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(1.89477 - 2.32590i) q^{9} +(-1.06397 + 0.614283i) q^{10} +(-1.50712 + 1.79612i) q^{11} +(1.72432 - 0.163488i) q^{12} +(-0.429778 + 0.0757815i) q^{13} +(-2.44212 + 1.01787i) q^{14} +(0.885273 - 1.93505i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-1.74272 - 3.01848i) q^{17} +(-2.26988 + 1.96155i) q^{18} +(1.97392 + 1.13964i) q^{19} +(1.15447 - 0.420194i) q^{20} +(2.42551 - 3.88805i) q^{21} +(1.79612 - 1.50712i) q^{22} +(-1.85030 + 5.08367i) q^{23} +(-1.72651 - 0.138421i) q^{24} +(-0.606141 + 3.43760i) q^{25} +0.436408 q^{26} +(1.23518 - 5.04721i) q^{27} +(2.58177 - 0.578340i) q^{28} +(-2.08501 - 0.367644i) q^{29} +(-1.20784 + 1.75193i) q^{30} +(2.87174 - 7.89005i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(-1.02256 + 3.93024i) q^{33} +(1.19209 + 3.27524i) q^{34} +(0.970599 - 3.10219i) q^{35} +(2.57601 - 1.53759i) q^{36} +(2.71169 + 4.69678i) q^{37} +(-1.74604 - 1.46510i) q^{38} +(-0.616016 + 0.438042i) q^{39} +(-1.20990 + 0.213338i) q^{40} +(-0.273818 - 1.55290i) q^{41} +(-3.06381 + 3.40779i) q^{42} +(-1.56927 - 1.31677i) q^{43} +(-2.03054 + 1.17233i) q^{44} +(-0.0535437 - 3.68531i) q^{45} +(2.70496 - 4.68513i) q^{46} +(-4.45922 + 1.62303i) q^{47} +(1.67624 + 0.436123i) q^{48} +(2.93032 - 6.35714i) q^{49} +(1.19386 - 3.28012i) q^{50} +(-4.97020 - 3.42664i) q^{51} +(-0.429778 - 0.0757815i) q^{52} +0.117957i q^{53} +(-2.09285 + 4.75605i) q^{54} +2.88058i q^{55} +(-2.64297 + 0.121235i) q^{56} +(3.93522 + 0.315500i) q^{57} +(1.98950 + 0.724117i) q^{58} +(9.22472 - 7.74046i) q^{59} +(1.49371 - 1.51557i) q^{60} +(3.82461 + 10.5080i) q^{61} +(-4.19821 + 7.27151i) q^{62} +(0.904201 - 7.88558i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.344635 + 0.410720i) q^{65} +(1.68951 - 3.69296i) q^{66} +(1.46744 + 8.32229i) q^{67} +(-0.605240 - 3.43248i) q^{68} +(0.884457 + 9.32843i) q^{69} +(-1.49454 + 2.88651i) q^{70} +(-1.77135 + 1.02269i) q^{71} +(-2.80387 + 1.06691i) q^{72} +(-6.00651 - 3.46786i) q^{73} +(-1.85490 - 5.09631i) q^{74} +(1.60718 + 5.82841i) q^{75} +(1.46510 + 1.74604i) q^{76} +(-0.796142 + 6.15211i) q^{77} +(0.682723 - 0.324417i) q^{78} +(-0.916064 + 5.19526i) q^{79} +1.22857 q^{80} +(-1.81967 - 8.81413i) q^{81} +1.57686i q^{82} +(-1.50719 + 8.54769i) q^{83} +(3.60902 - 2.82400i) q^{84} +(-4.02385 - 1.46456i) q^{85} +(1.31677 + 1.56927i) q^{86} +(-3.53512 + 0.974809i) q^{87} +(2.20327 - 0.801923i) q^{88} +(-7.35317 + 12.7361i) q^{89} +(-0.587217 + 3.63862i) q^{90} +(-0.849559 + 0.781931i) q^{91} +(-3.47743 + 4.14424i) q^{92} +(-1.37271 - 14.4781i) q^{93} +(4.67331 - 0.824031i) q^{94} +(2.75771 - 0.486259i) q^{95} +(-1.57505 - 0.720574i) q^{96} +(-9.82215 + 11.7056i) q^{97} +(-3.98971 + 5.75172i) q^{98} +(1.32195 + 6.90866i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57}+ \cdots + 144 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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