LMFDB - Embedded newform 180.2.n.d.59.17

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			59.17
Character	$\chi$	$=$	180.59
Dual form			180.2.n.d.119.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.745653 - 1.20167i) q^{2} +(-1.62879 - 0.589100i) q^{3} +(-0.888004 - 1.79205i) q^{4} +(-1.91817 + 1.14918i) q^{5} +(-1.92241 + 1.51800i) q^{6} +(-1.44473 - 2.50234i) q^{7} +(-2.81559 - 0.269163i) q^{8} +(2.30592 + 1.91904i) q^{9} +(-0.0493612 + 3.16189i) q^{10} +(-0.395318 - 0.684712i) q^{11} +(0.390676 + 3.44200i) q^{12} +(-4.04214 - 2.33373i) q^{13} +(-4.08425 - 0.129797i) q^{14} +(3.80129 - 0.741776i) q^{15} +(-2.42290 + 3.18270i) q^{16} +5.89560 q^{17} +(4.02547 - 1.34001i) q^{18} -4.55505i q^{19} +(3.76273 + 2.41699i) q^{20} +(0.879030 + 4.92689i) q^{21} +(-1.11756 - 0.0355161i) q^{22} +(1.15468 + 0.666656i) q^{23} +(4.42745 + 2.09708i) 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} +(1.94307 - 5.12098i) q^{30} +(-2.26893 - 1.30997i) q^{31} +(2.01790 + 5.28470i) q^{32} +(0.240527 + 1.34813i) q^{33} +(4.39607 - 7.08454i) q^{34} +(5.64688 + 3.13968i) q^{35} +(1.39135 - 5.83645i) q^{36} -7.44000i q^{37} +(-5.47365 - 3.39649i) q^{38} +(5.20900 + 6.18239i) q^{39} +(5.71011 - 2.71932i) q^{40} +(-5.91566 - 3.41541i) q^{41} +(6.57593 + 2.61744i) 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} +(5.82132 - 3.75662i) q^{48} +(-0.674484 + 1.16824i) q^{49} +(-3.53890 - 6.12178i) q^{50} +(-9.60270 - 3.47310i) q^{51} +(-0.592728 + 9.31609i) q^{52} +1.70763 q^{53} +(-7.34604 - 0.188808i) q^{54} +(1.54515 + 0.859104i) q^{55} +(3.39423 + 7.43444i) q^{56} +(-2.68338 + 7.41923i) q^{57} +(0.119034 - 3.74556i) q^{58} +(-5.29436 + 9.17010i) q^{59} +(-4.70486 - 6.15340i) 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} +(1.79936 + 0.716206i) q^{66} +(3.76721 - 6.52500i) q^{67} +(-5.23532 - 10.5652i) q^{68} +(-1.48801 - 1.76607i) q^{69} +(7.98346 - 4.44456i) q^{70} +2.88566 q^{71} +(-5.97600 - 6.02391i) q^{72} +6.50847i q^{73} +(-8.94040 - 5.54766i) q^{74} +(-6.43909 + 5.79121i) q^{75} +(-8.16289 + 4.04491i) q^{76} +(-1.14226 + 1.97845i) q^{77} +(11.3133 - 1.64957i) q^{78} +(3.30854 - 1.91019i) q^{79} +(0.990045 - 8.88931i) q^{80} +(1.63455 + 8.85032i) q^{81} +(-8.51521 + 4.56194i) q^{82} +(-8.33679 + 4.81325i) q^{83} +(8.04865 - 5.95036i) q^{84} +(-11.3088 + 6.77510i) q^{85} +(16.8277 + 0.534782i) q^{86} +(-4.51832 + 0.806137i) q^{87} +(0.928756 + 2.03427i) q^{88} +0.00741921i q^{89} +(-6.18163 + 7.19635i) q^{90} +13.4864i q^{91} +(0.169319 - 2.66124i) q^{92} +(2.92391 + 3.47029i) q^{93} +(-0.135354 + 4.25910i) q^{94} +(5.23457 + 8.73738i) q^{95} +(-0.173524 - 9.79642i) 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 $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.745653	−	1.20167i	0.527256	−	0.849706i
$2$	0.745653	−	1.20167i	0.527256	−	0.849706i
$3$	−1.62879	−	0.589100i	−0.940383	−	0.340117i
$3$	−1.62879	−	0.589100i	−0.940383	−	0.340117i
$4$	−0.888004	−	1.79205i	−0.444002	−	0.896026i
$5$	−1.91817	+	1.14918i	−0.857833	+	0.513928i
$5$	−1.91817	+	1.14918i	−0.857833	+	0.513928i
$6$	−1.92241	+	1.51800i	−0.784822	+	0.619721i
$7$	−1.44473	−	2.50234i	−0.546056	−	0.945797i	−0.998540	−	0.0540243i	$-0.982795\pi$
$7$	−1.44473	−	2.50234i	−0.546056	−	0.945797i	0.452483	−	0.891773i	$-0.350538\pi$
$8$	−2.81559	−	0.269163i	−0.995462	−	0.0951634i
$9$	2.30592	+	1.91904i	0.768641	+	0.639681i
$10$	−0.0493612	+	3.16189i	−0.0156094	+	0.999878i
$11$	−0.395318	−	0.684712i	−0.119193	−	0.206448i	0.800255	−	0.599660i	$-0.204697\pi$
$11$	−0.395318	−	0.684712i	−0.119193	−	0.206448i	−0.919448	+	0.393211i	$0.871364\pi$
$12$	0.390676	+	3.44200i	0.112778	+	0.993620i
$13$	−4.04214	−	2.33373i	−1.12109	−	0.647261i	−0.179410	−	0.983774i	$-0.557419\pi$
$13$	−4.04214	−	2.33373i	−1.12109	−	0.647261i	−0.941679	+	0.336514i	$0.890752\pi$
$14$	−4.08425	−	0.129797i	−1.09156	−	0.0346897i
$15$	3.80129	−	0.741776i	0.981488	−	0.191526i
$16$	−2.42290	+	3.18270i	−0.605724	+	0.795675i
$17$	5.89560			1.42989			0.714946	−	0.699179i	$-0.246451\pi$
$17$	5.89560			1.42989			0.714946	+	0.699179i	$0.246451\pi$
$18$	4.02547	−	1.34001i	0.948811	−	0.315843i
$19$		−	4.55505i		−	1.04500i	−0.852639	−	0.522500i	$-0.824999\pi$
$19$		−	4.55505i		−	1.04500i	0.852639	−	0.522500i	$-0.175001\pi$
$20$	3.76273	+	2.41699i	0.841373	+	0.540455i
$21$	0.879030	+	4.92689i	0.191820	+	1.07513i
$22$	−1.11756	−	0.0355161i	−0.238266	−	0.00757206i
$23$	1.15468	+	0.666656i	0.240768	+	0.139007i	0.615530	−	0.788114i	$-0.288942\pi$
$23$	1.15468	+	0.666656i	0.240768	+	0.139007i	−0.374762	+	0.927121i	$0.622275\pi$
$24$	4.42745	+	2.09708i	0.903749	+	0.428064i
$25$	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	−0.271561	−	0.962421i	$-0.587540\pi$
$29$	2.29484	−	1.32492i	0.426140	−	0.246032i	0.697701	+	0.716389i	$0.254206\pi$
$30$	1.94307	−	5.12098i	0.354755	−	0.934959i
$31$	−2.26893	−	1.30997i	−0.407512	−	0.235277i	0.282208	−	0.959353i	$-0.408933\pi$
$31$	−2.26893	−	1.30997i	−0.407512	−	0.235277i	−0.689720	+	0.724076i	$0.742266\pi$
$32$	2.01790	+	5.28470i	0.356718	+	0.934212i
$33$	0.240527	+	1.34813i	0.0418704	+	0.234680i
$34$	4.39607	−	7.08454i	0.753919	−	1.21499i
$35$	5.64688	+	3.13968i	0.954497	+	0.530702i
$36$	1.39135	−	5.83645i	0.231892	−	0.972741i
$37$		−	7.44000i		−	1.22313i	−0.791195	−	0.611564i	$-0.790541\pi$
$37$		−	7.44000i		−	1.22313i	0.791195	−	0.611564i	$-0.209459\pi$
$38$	−5.47365	−	3.39649i	−0.887944	−	0.550983i
$39$	5.20900	+	6.18239i	0.834108	+	0.989975i
$40$	5.71011	−	2.71932i	0.902847	−	0.429962i
$41$	−5.91566	−	3.41541i	−0.923871	−	0.533397i	−0.0390029	−	0.999239i	$-0.512418\pi$
$41$	−5.91566	−	3.41541i	−0.923871	−	0.533397i	−0.884868	+	0.465842i	$0.845751\pi$
$42$	6.57593	+	2.61744i	1.01469	+	0.403880i
$43$	5.95249	+	10.3100i	0.907746	+	1.57226i	0.817189	+	0.576370i	$0.195531\pi$
$43$	5.95249	+	10.3100i	0.907746	+	1.57226i	0.0905567	+	0.995891i	$0.471135\pi$
$44$	−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	$-0.737193\pi$
$47$	−2.60947	+	1.50658i	−0.380631	+	0.219757i	0.297462	+	0.954734i	$0.403860\pi$
$48$	5.82132	−	3.75662i	0.840235	−	0.542222i
$49$	−0.674484	+	1.16824i	−0.0963548	+	0.166891i
$50$	−3.53890	−	6.12178i	−0.500476	−	0.865751i
$51$	−9.60270	−	3.47310i	−1.34465	−	0.486331i
$52$	−0.592728	+	9.31609i	−0.0821965	+	1.29191i
$53$	1.70763			0.234561			0.117281	−	0.993099i	$-0.462582\pi$
$53$	1.70763			0.234561			0.117281	+	0.993099i	$0.462582\pi$
$54$	−7.34604	−	0.188808i	−0.999670	−	0.0256935i
$55$	1.54515	+	0.859104i	0.208347	+	0.115842i
$56$	3.39423	+	7.43444i	0.453573	+	0.993469i
$57$	−2.68338	+	7.41923i	−0.355423	+	0.982701i
$58$	0.119034	−	3.74556i	0.0156299	−	0.491816i
$59$	−5.29436	+	9.17010i	−0.689267	+	1.19385i	0.282808	+	0.959176i	$0.408734\pi$
$59$	−5.29436	+	9.17010i	−0.689267	+	1.19385i	−0.972075	+	0.234669i	$0.924599\pi$
$60$	−4.70486	−	6.15340i	−0.607395	−	0.794400i
$61$	−0.869749	−	1.50645i	−0.111360	−	0.192881i	0.804959	−	0.593331i	$-0.202187\pi$
$61$	−0.869749	−	1.50645i	−0.111360	−	0.192881i	−0.916319	+	0.400450i	$0.868854\pi$
$62$	−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
$66$	1.79936	+	0.716206i	0.221486	+	0.0881589i
$67$	3.76721	−	6.52500i	0.460238	−	0.797155i	−0.538735	−	0.842476i	$-0.681097\pi$
$67$	3.76721	−	6.52500i	0.460238	−	0.797155i	0.998973	+	0.0453201i	$0.0144308\pi$
$68$	−5.23532	−	10.5652i	−0.634875	−	1.28122i
$69$	−1.48801	−	1.76607i	−0.179135	−	0.212610i
$70$	7.98346	−	4.44456i	0.954206	−	0.531226i
$71$	2.88566			0.342465			0.171233	−	0.985231i	$-0.445225\pi$
$71$	2.88566			0.342465			0.171233	+	0.985231i	$0.445225\pi$
$72$	−5.97600	−	6.02391i	−0.704278	−	0.709924i
$73$			6.50847i			0.761759i	0.924625	+	0.380880i	$0.124379\pi$
$73$			6.50847i			0.761759i	−0.924625	+	0.380880i	$0.875621\pi$
$74$	−8.94040	−	5.54766i	−1.03930	−	0.644902i
$75$	−6.43909	+	5.79121i	−0.743522	+	0.668711i
$76$	−8.16289	+	4.04491i	−0.936347	+	0.463983i
$77$	−1.14226	+	1.97845i	−0.130172	+	0.225465i
$78$	11.3133	−	1.64957i	1.28098	−	0.186777i
$79$	3.30854	−	1.91019i	0.372240	−	0.214913i	−0.302197	−	0.953246i	$-0.597720\pi$
$79$	3.30854	−	1.91019i	0.372240	−	0.214913i	0.674436	+	0.738333i	$0.264387\pi$
$80$	0.990045	−	8.88931i	0.110690	−	0.993855i
$81$	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	$-0.843845\pi$
$83$	−8.33679	+	4.81325i	−0.915081	+	0.528322i	−0.0330187	+	0.999455i	$0.510512\pi$
$84$	8.04865	−	5.95036i	0.878180	−	0.649238i
$85$	−11.3088	+	6.77510i	−1.22661	+	0.734862i
$86$	16.8277	+	0.534782i	1.81457	+	0.0576670i
$87$	−4.51832	+	0.806137i	−0.484415	+	0.0864269i
$88$	0.928756	+	2.03427i	0.0990057	+	0.216854i
$89$			0.00741921i			0.000786434i	1.00000		0.000393217i	$0.000125165\pi$
$89$			0.00741921i			0.000786434i	−1.00000		0.000393217i	$0.999875\pi$
$90$	−6.18163	+	7.19635i	−0.651601	+	0.758562i
$91$			13.4864i			1.41376i
$92$	0.169319	−	2.66124i	0.0176528	−	0.277454i
$93$	2.92391	+	3.47029i	0.303195	+	0.359852i
$94$	−0.135354	+	4.25910i	−0.0139607	+	0.439293i
$95$	5.23457	+	8.73738i	0.537055	+	0.896436i
$96$	−0.173524	−	9.79642i	−0.0177102	−	0.999843i
$97$	5.74925	−	3.31933i	0.583748	−	0.337027i	−0.178874	−	0.983872i	$-0.557245\pi$
$97$	5.74925	−	3.31933i	0.583748	−	0.337027i	0.762621	+	0.646845i	$0.223912\pi$
$98$	0.900905	+	1.68161i	0.0910051	+	0.169868i
$99$	0.402417	−	2.33752i	0.0404445	−	0.234930i
$100$	−9.99513	−	0.312149i	−0.999513	−	0.0312149i
$101$	−2.20027	+	1.27033i	−0.218935	+	0.126402i	−0.605457	−	0.795878i	$-0.707010\pi$
$101$	−2.20027	+	1.27033i	−0.218935	+	0.126402i	0.386522	+	0.922280i	$0.373676\pi$
$102$	−11.3338	+	8.94952i	−1.12221	+	0.886134i
$103$	3.82824	−	6.63071i	0.377208	−	0.653343i	−0.613447	−	0.789736i	$-0.710218\pi$
$103$	3.82824	−	6.63071i	0.377208	−	0.653343i	0.990655	+	0.136393i	$0.0435509\pi$
$104$	10.7529	+	7.65883i	1.05441	+	0.751010i
$105$	−7.34801	−	8.44046i	−0.717092	−	0.823704i
$106$	1.27330	−	2.05200i	0.123674	−	0.199308i
$107$		−	13.7118i		−	1.32557i	−0.748808	−	0.662787i	$-0.769374\pi$
$107$		−	13.7118i		−	1.32557i	0.748808	−	0.662787i	$-0.230626\pi$
$108$	−5.70448	+	8.68671i	−0.548914	+	0.835879i
$109$	−13.2664			−1.27069			−0.635347	−	0.772227i	$-0.719143\pi$
$109$	−13.2664			−1.27069			−0.635347	+	0.772227i	$0.719143\pi$
$110$	2.18450	−	1.21616i	0.208284	−	0.115956i
$111$	−4.38291	+	12.1182i	−0.416007	+	1.15021i
$112$	11.4646	+	1.46478i	1.08331	+	0.138409i
$113$	4.62487	−	8.01051i	0.435071	−	0.753565i	−0.562230	−	0.826981i	$-0.690057\pi$
$113$	4.62487	−	8.01051i	0.435071	−	0.753565i	0.997301	+	0.0734153i	$0.0233899\pi$
$114$	6.91457	+	8.75670i	0.647609	+	0.820140i
$115$	−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
$120$	−10.9025	+	1.06537i	−0.995260	+	0.0972548i
$121$	5.18745	−	8.98492i	0.471586	−	0.816811i
$122$	−2.45878	−	0.0781398i	−0.222608	−	0.00707445i
$123$	7.62336	+	9.04790i	0.687375	+	0.815822i
$124$	−0.332709	+	5.22929i	−0.0298781	+	0.469604i
$125$	0.541784	+	11.1672i	0.0484587	+	0.998825i
$126$	−9.16887	−	8.13715i	−0.816828	−	0.724915i
$127$	−9.77239			−0.867159			−0.433580	−	0.901115i	$-0.642750\pi$
$127$	−9.77239			−0.867159			−0.433580	+	0.901115i	$0.642750\pi$
$128$	7.67855	−	8.30902i	0.678694	−	0.734421i
$129$	−3.62173	−	20.2995i	−0.318875	−	1.78727i
$130$	7.57853	−	12.6656i	0.664681	−	1.11085i
$131$	6.61827	−	11.4632i	0.578241	−	1.00154i	−0.417440	−	0.908704i	$-0.637073\pi$
$131$	6.61827	−	11.4632i	0.578241	−	1.00154i	0.995681	−	0.0928382i	$-0.0295939\pi$
$132$	2.20234	−	1.62819i	0.191689	−	0.141715i
$133$	−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	0.925470	−	0.378822i	$-0.123671\pi$
$137$	1.57622	+	2.73010i	0.134666	+	0.233248i	−0.790804	+	0.612069i	$0.790337\pi$
$138$	−3.23176	+	0.471218i	−0.275106	+	0.0401127i
$139$	−2.22556	−	1.28493i	−0.188770	−	0.108986i	0.402637	−	0.915360i	$-0.368094\pi$
$139$	−2.22556	−	1.28493i	−0.188770	−	0.108986i	−0.591407	+	0.806374i	$0.701427\pi$
$140$	0.612008	−	12.9075i	0.0517241	−	1.09089i
$141$	5.13782	−	0.916663i	0.432682	−	0.0771970i
$142$	2.15170	−	3.46761i	0.180567	−	0.290995i
$143$			3.69027i			0.308596i
$144$	−11.6947	+	2.68941i	−0.974562	+	0.224118i
$145$	−2.87932	+	5.17861i	−0.239114	+	0.430060i
$146$	7.82101	+	4.85306i	0.647272	+	0.401642i
$147$	1.78680	−	1.50548i	0.147373	−	0.124170i
$148$	−13.3329	+	6.60675i	−1.09595	+	0.543072i
$149$	8.52719	+	4.92318i	0.698575	+	0.403322i	0.806816	−	0.590802i	$-0.201189\pi$
$149$	8.52719	+	4.92318i	0.698575	+	0.403322i	−0.108242	+	0.994125i	$0.534522\pi$
$150$	2.15778	+	12.0559i	0.176182	+	0.984358i
$151$	9.24153	−	5.33560i	0.752065	−	0.434205i	−0.0743744	−	0.997230i	$-0.523696\pi$
$151$	9.24153	−	5.33560i	0.752065	−	0.434205i	0.826440	+	0.563025i	$0.190363\pi$
$152$	−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
$156$	6.45354	−	14.8248i	0.516697	−	1.18693i
$157$	12.9992	+	7.50509i	1.03745	+	0.598972i	0.919110	−	0.394001i	$-0.128909\pi$
$157$	12.9992	+	7.50509i	1.03745	+	0.598972i	0.118340	+	0.992973i	$0.462243\pi$
$158$	0.171614	−	5.40009i	0.0136529	−	0.429608i
$159$	−2.78138	−	1.00597i	−0.220577	−	0.0797783i
$160$	−9.94375	−	7.81804i	−0.786123	−	0.618070i
$161$		−	3.85255i		−	0.303624i
$162$	11.8539	+	4.63508i	0.931334	+	0.364167i
$163$	−4.15873			−0.325737			−0.162869	−	0.986648i	$-0.552075\pi$
$163$	−4.15873			−0.325737			−0.162869	+	0.986648i	$0.552075\pi$
$164$	−0.867455	+	13.6341i	−0.0677368	+	1.06464i
$165$	−2.01062	−	2.30955i	−0.156527	−	0.179798i
$166$	−0.432431	+	13.6070i	−0.0335631	+	1.05611i
$167$	0.0288855	+	0.0166770i	0.00223522	+	0.00129051i	0.501117	−	0.865379i	$-0.332923\pi$
$167$	0.0288855	+	0.0166770i	0.00223522	+	0.00129051i	−0.498882	+	0.866670i	$0.666256\pi$
$168$	−1.14885	−	14.1087i	−0.0886361	−	1.08851i
$169$	4.39261	+	7.60822i	0.337893	+	0.585248i
$170$	−0.291014	+	18.6412i	−0.0223197	+	1.42972i
$171$	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	−0.819621	−	0.572906i	$-0.805816\pi$
$173$	−11.9161	−	20.6392i	−0.905962	−	1.56917i	−0.0863411	−	0.996266i	$-0.527517\pi$
$174$	−2.40039	+	6.03062i	−0.181973	+	0.457180i
$175$	−14.4397	+	0.466832i	−1.09154	+	0.0352892i
$176$	3.13705	+	0.400806i	0.236464	+	0.0302119i
$177$	14.0255	−	11.8173i	1.05422	−	0.888241i
$178$	0.00891541	+	0.00553215i	0.000668238	+	0.000414652i
$179$	25.5288			1.90811			0.954055	−	0.299631i	$-0.0968635\pi$
$179$	25.5288			1.90811			0.954055	+	0.299631i	$0.0968635\pi$
$180$	4.03826	+	12.7942i	0.300994	+	0.953626i
$181$	25.6109			1.90364			0.951821	−	0.306653i	$-0.0992092\pi$
$181$	25.6109			1.90364			0.951821	+	0.306653i	$0.0992092\pi$
$182$	16.2062	+	10.0562i	1.20128	+	0.745415i
$183$	0.529190	+	2.96606i	0.0391188	+	0.219258i
$184$	−3.07168	−	2.18783i	−0.226447	−	0.161289i
$185$	8.54989	+	14.2712i	0.628601	+	1.04924i
$186$	6.35035	−	0.925934i	0.465630	−	0.0678928i
$187$	−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
$190$	14.4026	+	0.224843i	1.04487	+	0.0163118i
$191$	−3.85863	−	6.68334i	−0.279200	−	0.483589i	0.691986	−	0.721911i	$-0.256736\pi$
$191$	−3.85863	−	6.68334i	−0.279200	−	0.483589i	−0.971186	+	0.238322i	$0.923403\pi$
$192$	−11.9014	−	7.09621i	−0.858911	−	0.512125i
$193$	4.47373	+	2.58291i	0.322026	+	0.185922i	0.652295	−	0.757965i	$-0.273806\pi$
$193$	4.47373	+	2.58291i	0.322026	+	0.185922i	−0.330269	+	0.943887i	$0.607139\pi$
$194$	0.298215	−	9.38374i	0.0214106	−	0.673714i
$195$	−17.0964	−	5.87282i	−1.22430	−	0.420561i
$196$	2.69249	+	0.171307i	0.192321	+	0.0122362i
$197$	−8.47116			−0.603545			−0.301773	−	0.953380i	$-0.597578\pi$
$197$	−8.47116			−0.603545			−0.301773	+	0.953380i	$0.597578\pi$
$198$	−2.50886	−	2.22655i	−0.178297	−	0.158234i
$199$		−	0.555967i		−	0.0394115i	−0.999806	−	0.0197057i	$-0.993727\pi$
$199$		−	0.555967i		−	0.0394115i	0.999806	−	0.0197057i	$-0.00627293\pi$
$200$	−7.82799	+	11.7781i	−0.553523	+	0.832834i
$201$	−9.97988	+	8.40860i	−0.703926	+	0.593097i
$202$	−0.114128	+	3.59121i	−0.00803004	+	0.252677i
$203$	−6.63083	−	3.82831i	−0.465393	−	0.268695i
$204$	2.30327	+	20.2927i	0.161261	+	1.42077i
$205$	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
$210$	−15.6217	+	2.53620i	−1.07800	+	0.175015i
$211$	21.0649	+	12.1618i	1.45016	+	0.837253i	0.998490	−	0.0549298i	$-0.0174935\pi$
$211$	21.0649	+	12.1618i	1.45016	+	0.837253i	0.451675	+	0.892183i	$0.350827\pi$
$212$	−1.51638	−	3.06016i	−0.104146	−	0.210173i
$213$	−4.70015	−	1.69995i	−0.322049	−	0.116478i
$214$	−16.4771	−	10.2243i	−1.12635	−	0.698917i
$215$	−23.2659	−	12.9359i	−1.58672	−	0.882222i
$216$	6.18497	+	13.3321i	0.420834	+	0.907138i
$217$			7.57019i			0.513898i
$218$	−9.89215	+	15.9418i	−0.669981	+	1.07972i
$219$	3.83414	−	10.6009i	0.259087	−	0.716345i
$220$	0.167462	−	3.53187i	0.0112903	−	0.238118i
$221$	−23.8308	−	13.7587i	−1.60304	−	0.925513i
$222$	11.2939	+	14.3028i	0.757998	+	0.959939i
$223$	−0.169636	−	0.293817i	−0.0113596	−	0.0196755i	0.860290	−	0.509805i	$-0.170283\pi$
$223$	−0.169636	−	0.293817i	−0.0113596	−	0.0196755i	−0.871649	+	0.490130i	$0.836949\pi$
$224$	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	$-0.574495\pi$
$227$	7.45137	−	4.30205i	0.494565	−	0.285537i	0.726466	+	0.687202i	$0.241161\pi$
$228$	15.6785	−	1.77955i	1.03833	−	0.117853i
$229$	0.358866	−	0.621574i	0.0237145	−	0.0410748i	−0.853925	−	0.520397i	$-0.825784\pi$
$229$	0.358866	−	0.621574i	0.0237145	−	0.0410748i	0.877639	+	0.479322i	$0.159117\pi$
$230$	−2.16489	+	3.61808i	−0.142749	+	0.238569i
$231$	3.02600	−	2.54957i	0.199096	−	0.167749i
$232$	−6.81794	+	3.11276i	−0.447620	+	0.204363i
$233$	−13.8379			−0.906553			−0.453276	−	0.891370i	$-0.649745\pi$
$233$	−13.8379			−0.906553			−0.453276	+	0.891370i	$0.649745\pi$
$234$	−19.3987	−	3.97785i	−1.26813	−	0.260040i
$235$	3.27409	−	5.88864i	0.213578	−	0.384132i
$236$	21.1347	+	1.34468i	1.37575	+	0.0875310i
$237$	−6.51421	+	1.16223i	−0.423143	+	0.0754951i
$238$	−24.0791	−	0.765231i	−1.56082	−	0.0496026i
$239$	−13.8553	+	23.9980i	−0.896223	+	1.55230i	−0.0639388	+	0.997954i	$0.520366\pi$
$239$	−13.8553	+	23.9980i	−0.896223	+	1.55230i	−0.832284	+	0.554350i	$0.812967\pi$
$240$	−6.84927	+	13.8956i	−0.442119	+	0.896957i
$241$	−5.71303	−	9.89526i	−0.368009	−	0.637410i	0.621245	−	0.783616i	$-0.286627\pi$
$241$	−5.71303	−	9.89526i	−0.368009	−	0.637410i	−0.989254	+	0.146206i	$0.953294\pi$
$242$	−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
$246$	16.5569	−	2.41414i	1.05563	−	0.153920i
$247$	−10.6303	+	18.4122i	−0.676388	+	1.17154i
$248$	6.03578	+	4.29904i	0.383272	+	0.272989i
$249$	16.4144	−	2.92857i	1.04022	−	0.185591i
$250$	13.8232	+	7.67581i	0.874258	+	0.485461i
$251$	5.05161			0.318855			0.159427	−	0.987210i	$-0.449035\pi$
$251$	5.05161			0.318855			0.159427	+	0.987210i	$0.449035\pi$
$252$	−16.6149	+	4.95044i	−1.04664	+	0.311848i
$253$		−	1.05417i		−	0.0662749i
$254$	−7.28681	+	11.7432i	−0.457215	+	0.736831i
$255$	22.4108	−	4.37321i	1.40342	−	0.273861i
$256$	−4.25914	−	15.4227i	−0.266197	−	0.963919i
$257$	−1.32366	+	2.29265i	−0.0825679	+	0.143012i	−0.904352	−	0.426787i	$-0.859645\pi$
$257$	−1.32366	+	2.29265i	−0.0825679	+	0.143012i	0.821784	+	0.569799i	$0.192979\pi$
$258$	−27.0937	−	10.7842i	−1.68678	−	0.671397i
$259$	−18.6174	+	10.7488i	−1.15683	+	0.667897i
$260$	−9.56890	−	18.5510i	−0.593438	−	1.15049i
$261$	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	$-0.691533\pi$
$263$	−2.19210	+	1.26561i	−0.135171	+	0.0780408i	0.430890	+	0.902405i	$0.358200\pi$
$264$	−0.314359	−	3.86054i	−0.0193475	−	0.237600i
$265$	−3.27553	+	1.96237i	−0.201214	+	0.120548i
$266$	−0.591232	+	18.6040i	−0.0362508	+	1.14068i
$267$	0.00437066	−	0.0120843i	0.000267480	−	0.000739549i
$268$	−15.0384	−	0.956806i	−0.918618	−	0.0584462i
$269$			5.26469i			0.320994i	0.987036	+	0.160497i	$0.0513097\pi$
$269$			5.26469i			0.320994i	−0.987036	+	0.160497i	$0.948690\pi$
$270$	14.3080	−	8.07975i	0.870754	−	0.491718i
$271$		−	16.6468i		−	1.01122i	−0.862761	−	0.505612i	$-0.831267\pi$
$271$		−	16.6468i		−	1.01122i	0.862761	−	0.505612i	$-0.168733\pi$
$272$	−14.2844	+	18.7639i	−0.866120	+	1.13773i
$273$	7.94487	−	21.9666i	0.480845	−	1.32948i
$274$	4.45598	+	0.141611i	0.269196	+	0.00855501i
$275$	−3.95112	+	0.127738i	−0.238261	+	0.00770292i
$276$	−1.84353	+	4.23487i	−0.110967	+	0.254909i
$277$	−22.8566	+	13.1963i	−1.37332	+	0.792888i	−0.991345	−	0.131283i	$-0.958090\pi$
$277$	−22.8566	+	13.1963i	−1.37332	+	0.792888i	−0.381978	+	0.924171i	$0.624757\pi$
$278$	−3.20355	+	1.71627i	−0.192136	+	0.102935i
$279$	−2.71809	−	7.37485i	−0.162728	−	0.441521i
$280$	−15.0542	−	10.3600i	−0.899662	−	0.619127i
$281$	−19.8511	+	11.4611i	−1.18422	+	0.683710i	−0.956987	−	0.290131i	$-0.906301\pi$
$281$	−19.8511	+	11.4611i	−1.18422	+	0.683710i	−0.227233	+	0.973840i	$0.572968\pi$
$282$	2.72950	−	6.85745i	0.162540	−	0.408355i
$283$	−3.25733	+	5.64186i	−0.193628	+	0.335374i	−0.946450	−	0.322851i	$-0.895359\pi$
$283$	−3.25733	+	5.64186i	−0.193628	+	0.335374i	0.752822	+	0.658224i	$0.228692\pi$
$284$	−2.56248	−	5.17126i	−0.152055	−	0.306858i
$285$	−3.37883	−	17.3151i	−0.200145	−	1.02566i
$286$	4.43447	+	2.75166i	0.262216	+	0.162709i
$287$			19.7374i			1.16506i
$288$	−5.48844	+	16.0585i	−0.323409	+	0.946259i
$289$	17.7581			1.04459
$290$	4.07599	+	7.32143i	0.239351	+	0.429929i
$291$	−11.3197	+	2.01961i	−0.663575	+	0.118392i
$292$	11.6635	−	5.77955i	0.682556	−	0.338223i
$293$	−8.37272	+	14.5020i	−0.489140	+	0.847215i	−0.999922	−	0.0124952i	$-0.996023\pi$
$293$	−8.37272	+	14.5020i	−0.489140	+	0.847215i	0.510782	+	0.859710i	$0.329356\pi$
$294$	−0.476751	−	3.26971i	−0.0278047	−	0.190693i
$295$	−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
$300$	16.0961	+	6.39656i	0.929308	+	0.369305i
$301$	17.1995	−	29.7903i	0.991360	−	1.71709i
$302$	0.479360	−	15.0837i	0.0275841	−	0.867972i
$303$	4.33213	−	0.772916i	0.248874	−	0.0444029i
$304$	14.4974	+	11.0364i	0.831481	+	0.632982i
$305$	3.39951	+	1.89013i	0.194655	+	0.108229i
$306$	23.7325	−	7.90016i	1.35670	−	0.451622i
$307$	24.2759			1.38550			0.692749	−	0.721179i	$-0.256400\pi$
$307$	24.2759			1.38550			0.692749	+	0.721179i	$0.256400\pi$
$308$	4.55980	+	0.290113i	0.259819	+	0.0165307i
$309$	−10.1416	+	8.54482i	−0.576933	+	0.486098i
$310$	4.25397	−	7.10945i	0.241609	−	0.403790i
$311$	−3.81664	+	6.61061i	−0.216422	+	0.374853i	−0.953711	−	0.300723i	$-0.902772\pi$
$311$	−3.81664	+	6.61061i	−0.216422	+	0.374853i	0.737290	+	0.675577i	$0.236105\pi$
$312$	−13.0024	−	18.8091i	−0.736113	−	1.06486i
$313$	−3.85836	+	2.22762i	−0.218087	+	0.125913i	−0.605064	−	0.796177i	$-0.706853\pi$
$313$	−3.85836	+	2.22762i	−0.218087	+	0.125913i	0.386977	+	0.922089i	$0.373519\pi$
$314$	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	0.788009	−	0.615663i	$-0.211112\pi$
$317$	−2.47795	−	4.29194i	−0.139176	−	0.241059i	−0.927185	+	0.374604i	$0.877779\pi$
$318$	−3.28278	+	2.59218i	−0.184089	+	0.145362i
$319$	−1.81438	−	1.04753i	−0.101586	−	0.0586506i
$320$	−16.8093	+	6.11953i	−0.939666	+	0.342092i
$321$	−8.07765	+	22.3337i	−0.450850	+	1.24655i
$322$	−4.62948	−	2.87267i	−0.257991	−	0.160087i
$323$		−	26.8548i		−	1.49424i
$324$	14.4087	−	10.7883i	0.800486	−	0.599351i
$325$	−19.8231	+	12.3156i	−1.09959	+	0.683148i
$326$	−3.10097	+	4.99741i	−0.171747	+	0.276781i
$327$	21.6082	+	7.81526i	1.19494	+	0.432185i
$328$	15.7368	+	11.2087i	0.868918	+	0.618895i
$329$	7.53997	+	4.35320i	0.415692	+	0.240000i
$330$	−4.27453	+	0.693976i	−0.235305	+	0.0382021i
$331$	−23.0250	+	13.2935i	−1.26557	+	0.730676i	−0.974146	−	0.225918i	$-0.927462\pi$
$331$	−23.0250	+	13.2935i	−1.26557	+	0.730676i	−0.291422	+	0.956594i	$0.594129\pi$
$332$	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
$336$	−17.8106	−	9.13965i	−0.971648	−	0.498609i
$337$	−10.7769	−	6.22205i	−0.587056	−	0.338937i	0.176877	−	0.984233i	$-0.443401\pi$
$337$	−10.7769	−	6.22205i	−0.587056	−	0.338937i	−0.763933	+	0.645296i	$0.776734\pi$
$338$	12.4179	+	0.394640i	0.675445	+	0.0214656i
$339$	−12.2519	+	10.3229i	−0.665434	+	0.560665i
$340$	22.1836	+	14.2496i	1.20307	+	0.772793i
$341$			2.07142i			0.112173i
$342$	−6.10381	−	18.3362i	−0.330056	−	0.991508i
$343$	−16.3284			−0.881652
$344$	−13.9847	−	30.6309i	−0.754004	−	1.65151i
$345$	4.88379	+	1.67764i	0.262934	+	0.0903208i
$346$	−33.6867	−	1.07056i	−1.81101	−	0.0575537i
$347$	14.6546	+	8.46084i	0.786701	+	0.454202i	0.838800	−	0.544440i	$-0.183258\pi$
$347$	14.6546	+	8.46084i	0.786701	+	0.454202i	−0.0520991	+	0.998642i	$0.516591\pi$
$348$	5.45693	+	7.38122i	0.292522	+	0.395675i
$349$	−0.955553	−	1.65507i	−0.0511496	−	0.0885937i	0.839317	−	0.543642i	$-0.182955\pi$
$349$	−0.955553	−	1.65507i	−0.0511496	−	0.0885937i	−0.890467	+	0.455049i	$0.849622\pi$
$350$	−10.2061	+	17.6999i	−0.545537	+	0.946097i
$351$	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	0.994435	+	0.105355i	$0.0335978\pi$
$353$	11.0561	+	19.1497i	0.588457	+	1.01924i	−0.405978	+	0.913883i	$0.633069\pi$
$354$	−3.74225	−	25.6656i	−0.198899	−	1.36411i
$355$	−5.53520	+	3.31614i	−0.293778	+	0.176003i
$356$	0.0132956	−	0.00658829i	0.000704665	−	0.000349178i
$357$	5.18241	+	29.0469i	0.274282	+	1.53733i
$358$	19.0356	−	30.6771i	1.00606	−	1.62133i
$359$	1.48034			0.0781296			0.0390648	−	0.999237i	$-0.487562\pi$
$359$	1.48034			0.0781296			0.0390648	+	0.999237i	$0.487562\pi$
$360$	18.3855	+	4.68741i	0.969003	+	0.247048i
$361$	−1.74850			−0.0920262
$362$	19.0968	−	30.7757i	1.00371	−	1.61754i
$363$	−13.7423	+	11.5786i	−0.721283	+	0.607721i
$364$	24.1684	−	11.9760i	1.26677	−	0.627714i
$365$	−7.47940	−	12.4844i	−0.391490	−	0.653462i
$366$	3.95881	+	1.57574i	0.206930	+	0.0823653i
$367$	−0.0631149	−	0.109318i	−0.00329457	−	0.00570636i	0.864373	−	0.502850i	$-0.167715\pi$
$367$	−0.0631149	−	0.109318i	−0.00329457	−	0.00570636i	−0.867668	+	0.497144i	$0.834382\pi$
$368$	−4.91944	+	2.05977i	−0.256444	+	0.107373i
$369$	−7.08673	−	19.2281i	−0.368921	−	1.00097i
$370$	23.5245	+	0.367247i	1.22298	+	0.0190923i
$371$	−2.46707	−	4.27308i	−0.128084	−	0.221847i
$372$	3.62249	−	8.32143i	0.187817	−	0.431446i
$373$	19.8527	+	11.4620i	1.02794	+	0.593479i	0.916393	−	0.400280i	$-0.131087\pi$
$373$	19.8527	+	11.4620i	1.02794	+	0.593479i	0.111543	+	0.993760i	$0.464421\pi$
$374$	−6.58871	−	0.209389i	−0.340694	−	0.0108272i
$375$	5.69615	−	18.5082i	0.294148	−	0.955760i
$376$	7.75273	−	3.53954i	0.399816	−	0.182538i
$377$	−12.3681			−0.636988
$378$	10.1406	+	18.6551i	0.521575	+	0.959515i
$379$			27.5123i			1.41321i	0.707608	+	0.706605i	$0.249774\pi$
$379$			27.5123i			1.41321i	−0.707608	+	0.706605i	$0.750226\pi$
$380$	11.0095	−	17.1394i	0.564776	−	0.879235i
$381$	15.9172	+	5.75692i	0.815462	+	0.294936i
$382$	−10.9083	−	0.346666i	−0.558119	−	0.0177370i
$383$	20.5507	+	11.8649i	1.05009	+	0.606270i	0.922675	−	0.385579i	$-0.125998\pi$
$383$	20.5507	+	11.8649i	1.05009	+	0.606270i	0.127416	+	0.991849i	$0.459332\pi$
$384$	−17.4016	+	9.01023i	−0.888022	+	0.459801i
$385$	−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	−0.539551	−	0.841953i	$-0.681406\pi$
$389$	−1.58128	+	0.912954i	−0.0801742	+	0.0462886i	0.459377	+	0.888241i	$0.348073\pi$
$390$	−19.8052	+	16.1651i	−1.00287	+	0.818554i
$391$	6.80755	+	3.93034i	0.344272	+	0.198766i
$392$	2.21352	−	3.10774i	0.111800	−	0.156965i
$393$	−17.5327	+	14.7723i	−0.884410	+	0.745164i
$394$	−6.31654	+	10.1795i	−0.318223	+	0.512836i
$395$	−4.15120	+	7.46617i	−0.208870	+	0.375664i
$396$	−4.54631	+	1.35458i	−0.228461	+	0.0680701i
$397$		−	19.0828i		−	0.957737i	−0.877887	−	0.478868i	$-0.841047\pi$
$397$		−	19.0828i		−	0.957737i	0.877887	−	0.478868i	$-0.158953\pi$
$398$	−0.668087	−	0.414558i	−0.0334882	−	0.0207799i
$399$	22.4422	−	4.00403i	1.12352	−	0.200452i
$400$	8.31633	+	18.1890i	0.415816	+	0.909449i
$401$	−15.1375	−	8.73963i	−0.755930	−	0.436436i	0.0719025	−	0.997412i	$-0.477093\pi$
$401$	−15.1375	−	8.73963i	−0.755930	−	0.436436i	−0.827833	+	0.560975i	$0.810426\pi$
$402$	2.66281	+	18.2624i	0.132809	+	0.910844i
$403$	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
$408$	26.1024	+	12.3635i	1.29226	+	0.612085i
$409$	−8.17716	+	14.1633i	−0.404335	+	0.700328i	−0.994244	−	0.107142i	$-0.965830\pi$
$409$	−8.17716	+	14.1633i	−0.404335	+	0.700328i	0.589909	+	0.807470i	$0.299164\pi$
$410$	11.0912	−	18.5361i	0.547753	−	0.915432i
$411$	−0.959036	−	5.37531i	−0.0473057	−	0.265144i
$412$	−15.2821	−	0.972307i	−0.752893	−	0.0479021i
$413$	30.5957			1.50551
$414$	5.54146	+	1.13632i	0.272348	+	0.0558469i
$415$	10.4601	−	18.8131i	0.513467	−	0.923499i
$416$	4.17642	−	26.0708i	0.204766	−	1.27822i
$417$	2.86803	+	3.40396i	0.140448	+	0.166693i
$418$	−0.161778	+	5.09057i	−0.00791281	+	0.248988i
$419$	12.3846	−	21.4508i	0.605029	−	1.04794i	−0.387018	−	0.922072i	$-0.626495\pi$
$419$	12.3846	−	21.4508i	0.605029	−	1.04794i	0.992047	−	0.125869i	$-0.0401720\pi$
$420$	−8.60067	+	20.6632i	−0.419670	+	1.00826i
$421$	8.38623	+	14.5254i	0.408720	+	0.707923i	0.994747	−	0.102368i	$-0.0326420\pi$
$421$	8.38623	+	14.5254i	0.408720	+	0.707923i	−0.586027	+	0.810292i	$0.699309\pi$
$422$	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
$426$	−5.54744	+	4.38044i	−0.268775	+	0.212233i
$427$	−2.51310	+	4.35282i	−0.121618	+	0.210648i
$428$	−24.5723	+	12.1762i	−1.18775	+	0.588558i
$429$	2.17394	−	6.01068i	0.104959	−	0.290198i
$430$	−32.8930	+	18.3122i	−1.58624	+	0.883093i
$431$	−15.2488			−0.734510			−0.367255	−	0.930120i	$-0.619702\pi$
$431$	−15.2488			−0.734510			−0.367255	+	0.930120i	$0.619702\pi$
$432$	20.6326	+	2.50889i	0.992688	+	0.120709i
$433$		−	23.5695i		−	1.13268i	−0.824172	−	0.566340i	$-0.808359\pi$
$433$		−	23.5695i		−	1.13268i	0.824172	−	0.566340i	$-0.191641\pi$
$434$	9.09684	+	5.64473i	0.436662	+	0.270956i
$435$	7.74053	−	6.73867i	0.371130	−	0.323095i
$436$	11.7806	+	23.7741i	0.564191	+	1.13857i
$437$	3.03665	−	5.25964i	0.145263	−	0.251603i
$438$	−9.87986	−	12.5120i	−0.472078	−	0.597846i
$439$	12.8688	−	7.42979i	0.614193	−	0.354605i	−0.160412	−	0.987050i	$-0.551282\pi$
$439$	12.8688	−	7.42979i	0.614193	−	0.354605i	0.774605	+	0.632446i	$0.217949\pi$
$440$	−4.11926	−	2.83478i	−0.196378	−	0.135143i
$441$	−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	$-0.443611\pi$
$443$	23.5062	−	13.5713i	1.11681	−	0.644791i	0.940585	+	0.339558i	$0.110278\pi$
$444$	25.6085	−	2.90663i	1.21533	−	0.137942i
$445$	−0.00852599	−	0.0142313i	−0.000404171	−	0.000674629i
$446$	−0.479560	−	0.0152404i	−0.0227078	−	0.000721652i
$447$	−10.9888	−	13.0422i	−0.519751	−	0.616875i
$448$	−7.55568	−	21.8460i	−0.356972	−	1.03212i
$449$		−	17.4879i		−	0.825304i	−0.910889	−	0.412652i	$-0.864602\pi$
$449$		−	17.4879i		−	0.825304i	0.910889	−	0.412652i	$-0.135398\pi$
$450$	3.58754	−	20.9076i	0.169118	−	0.985596i
$451$			5.40069i			0.254309i
$452$	−18.4622	−	1.17464i	−0.868386	−	0.0552503i
$453$	−18.1957	+	3.24639i	−0.854910	+	0.152529i
$454$	0.386504	−	12.1619i	0.0181395	−	0.570786i
$455$	−15.4983	−	25.8693i	−0.726573	−	1.21277i
$456$	9.55229	−	20.1672i	0.447327	−	0.944418i
$457$	5.10627	−	2.94811i	0.238861	−	0.137907i	−0.375792	−	0.926704i	$-0.622629\pi$
$457$	5.10627	−	2.94811i	0.238861	−	0.137907i	0.614653	+	0.788797i	$0.289296\pi$
$458$	−0.479335	−	0.894715i	−0.0223979	−	0.0418073i
$459$	−15.4780	−	26.4367i	−0.722453	−	1.23396i
$460$	2.73346	+	5.29931i	0.127448	+	0.247081i
$461$	30.5948	−	17.6639i	1.42494	−	0.822691i	0.428227	−	0.903671i	$-0.359138\pi$
$461$	30.5948	−	17.6639i	1.42494	−	0.822691i	0.996716	+	0.0809799i	$0.0258050\pi$
$462$	−0.807390	−	5.53734i	−0.0375632	−	0.257620i
$463$	18.6175	−	32.2464i	0.865227	−	1.49862i	−0.00159457	−	0.999999i	$-0.500508\pi$
$463$	18.6175	−	32.2464i	0.865227	−	1.49862i	0.866822	−	0.498618i	$-0.166159\pi$
$464$	−1.34332	+	10.5139i	−0.0623619	+	0.488097i
$465$	−9.59655	−	3.29652i	−0.445029	−	0.152872i
$466$	−10.3183	+	16.6286i	−0.477985	+	0.770304i
$467$			6.98334i			0.323151i	0.986860	+	0.161575i	$0.0516575\pi$
$467$			6.98334i			0.323151i	−0.986860	+	0.161575i	$0.948343\pi$
$468$	−19.2448	+	20.3447i	−0.889589	+	0.940434i
$469$	−21.7704			−1.00526
$470$	−4.63484	−	8.32524i	−0.213789	−	0.384015i
$471$	−16.7517	−	19.8821i	−0.771879	−	0.916117i
$472$	17.3750	−	24.3942i	0.799749	−	1.12283i
$473$	4.70625	−	8.15147i	0.216394	−	0.374805i
$474$	−3.46072	+	8.69453i	−0.158956	+	0.399353i
$475$	−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	$-0.0121958\pi$
$479$	10.2090	+	17.6825i	0.466460	+	0.807932i	−0.532806	+	0.846237i	$0.678863\pi$
$480$	11.5907	+	18.5918i	0.529040	+	0.848597i
$481$	−17.3630	+	30.0735i	−0.791683	+	1.37124i
$482$	−16.1507	−	0.513269i	−0.735646	−	0.0233788i
$483$	−2.26954	+	6.27500i	−0.103268	+	0.285522i
$484$	−20.7079	−	1.31752i	−0.941269	−	0.0598874i
$485$	−7.21355	+	12.9740i	−0.327550	+	0.589117i
$486$	−16.5771	−	14.5327i	−0.751951	−	0.659219i
$487$	20.8264			0.943735			0.471868	−	0.881669i	$-0.343580\pi$
$487$	20.8264			0.943735			0.471868	+	0.881669i	$0.343580\pi$
$488$	2.04338	+	4.47565i	0.0924993	+	0.202603i
$489$	6.77371	+	2.44991i	0.306318	+	0.110789i
$490$	−3.66056	−	2.19031i	−0.165367	−	0.0989482i
$491$	9.31608	−	16.1359i	0.420429	−	0.728204i	−0.575552	−	0.817765i	$-0.695213\pi$
$491$	9.31608	−	16.1359i	0.420429	−	0.728204i	0.995981	+	0.0895606i	$0.0285463\pi$
$492$	9.44473	−	21.6960i	0.425801	−	0.978132i
$493$	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
$498$	8.72025	−	21.9083i	0.390764	−	0.981734i
$499$	4.48667	+	2.59038i	0.200851	+	0.115961i	0.597052	−	0.802202i	$-0.296338\pi$
$499$	4.48667	+	2.59038i	0.200851	+	0.115961i	−0.396201	+	0.918164i	$0.629672\pi$
$500$	19.5311	−	10.8874i	0.873457	−	0.486901i
$501$	−0.0372239	−	0.0441798i	−0.00166304	−	0.00197381i
$502$	3.76675	−	6.07035i	0.168118	−	0.270933i
$503$			27.8846i			1.24331i	0.783290	+	0.621657i	$0.213540\pi$
$503$			27.8846i			1.24331i	−0.783290	+	0.621657i	$0.786460\pi$
$504$	−6.44019	+	23.6569i	−0.286869	+	1.05376i
$505$	2.76066	−	4.96521i	0.122848	−	0.220949i
$506$	−1.26676	−	0.786042i	−0.0563142	−	0.0349438i
$507$	−2.67264	−	14.9799i	−0.118696	−	0.665281i
$508$	8.67792	+	17.5126i	0.385021	+	0.776997i
$509$	18.6724	+	10.7805i	0.827640	+	0.477838i	0.853044	−	0.521839i	$-0.174754\pi$
$509$	18.6724	+	10.7805i	0.827640	+	0.477838i	−0.0254039	+	0.999677i	$0.508087\pi$
$510$	11.4556	−	30.1913i	0.507261	−	1.33689i
$511$	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
$516$	−33.1616	+	24.5163i	−1.45986	+	1.07927i
$517$	2.06315	+	1.19116i	0.0907371	+	0.0523871i
$518$	−0.965690	+	30.3868i	−0.0424300	+	1.33512i
$519$	7.25021	+	40.6368i	0.318249	+	1.78376i
$520$	−29.4272	−	2.33399i	−1.29047	−	0.102352i
$521$			19.9411i			0.873633i	0.899551	+	0.436817i	$0.143894\pi$
$521$			19.9411i			0.873633i	−0.899551	+	0.436817i	$0.856106\pi$
$522$	7.46238	−	8.40854i	0.326619	−	0.368032i
$523$	−18.9360			−0.828013			−0.414006	−	0.910274i	$-0.635871\pi$
$523$	−18.9360			−0.828013			−0.414006	+	0.910274i	$0.635871\pi$
$524$	−26.4197	−	1.68093i	−1.15415	−	0.0734316i
$525$	23.7943	+	7.74609i	1.03847	+	0.338067i
$526$	−0.113705	+	3.57788i	−0.00495776	+	0.156003i
$527$	−13.3767	−	7.72304i	−0.582698	−	0.336421i
$528$	−4.87348	−	2.50086i	−0.212091	−	0.108836i
$529$	−10.6111	−	18.3790i	−0.461354	−	0.799088i
$530$	−0.0842907	+	5.39935i	−0.00366135	+	0.234533i
$531$	−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
$534$	−0.0112624	−	0.0142628i	−0.000487370	−	0.000617211i
$535$	15.7574	+	26.3017i	0.681250	+	1.13712i
$536$	−12.3632	+	17.3577i	−0.534009	+	0.749740i
$537$	−41.5810	−	15.0390i	−1.79435	−	0.648981i
$538$	6.32640	+	3.92563i	0.272751	+	0.169246i
$539$	1.06654			0.0459393
$540$	0.959599	−	23.2181i	0.0412946	−	0.999147i
$541$	−13.2697			−0.570511			−0.285255	−	0.958452i	$-0.592078\pi$
$541$	−13.2697			−0.570511			−0.285255	+	0.958452i	$0.592078\pi$
$542$	−20.0039	−	12.4128i	−0.859243	−	0.533174i
$543$	−41.7148	−	15.0874i	−1.79015	−	0.647462i
$544$	11.8967	+	31.1565i	0.510069	+	1.33582i
$545$	25.4473	−	15.2455i	1.09004	−	0.653046i
$546$	−20.4724	−	25.9265i	−0.876138	−	1.10955i
$547$	4.51377	+	7.81809i	0.192995	+	0.334277i	0.946241	−	0.323461i	$-0.104847\pi$
$547$	4.51377	+	7.81809i	0.192995	+	0.334277i	−0.753246	+	0.657738i	$0.771513\pi$
$548$	3.49278	−	5.24901i	0.149204	−	0.224227i
$549$	0.885368	−	5.14284i	0.0377866	−	0.219491i
$550$	−2.79266	+	4.84318i	−0.119080	+	0.206514i
$551$	−6.03510	−	10.4531i	−0.257104	−	0.445317i
$552$	3.71427	+	5.37304i	0.158090	+	0.228692i
$553$	−9.55988	−	5.51940i	−0.406527	−	0.234709i
$554$	−1.18558	+	37.3059i	−0.0503704	+	1.58498i
$555$	−5.51882	−	28.2816i	−0.234261	−	1.20049i
$556$	−0.326350	+	5.12935i	−0.0138403	+	0.217533i
$557$	30.4174			1.28883			0.644414	−	0.764677i	$-0.277101\pi$
$557$	30.4174			1.28883			0.644414	+	0.764677i	$0.277101\pi$
$558$	−10.8889	−	2.23284i	−0.460962	−	0.0945237i
$559$		−	55.5660i		−	2.35019i
$560$	−23.6745	+	10.3652i	−1.00043	+	0.438010i
$561$	1.41805	+	7.94806i	0.0598702	+	0.335567i
$562$	−1.02968	+	32.4004i	−0.0434345	+	1.36673i
$563$	−39.1934	−	22.6283i	−1.65180	−	0.953669i	−0.976330	−	0.216284i	$-0.930606\pi$
$563$	−39.1934	−	22.6283i	−1.65180	−	0.953669i	−0.675473	−	0.737385i	$-0.736060\pi$
$564$	−6.20511	−	8.39323i	−0.261282	−	0.353419i
$565$	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	−0.589926	−	0.807457i	$-0.700843\pi$
$569$	−4.42750	+	2.55622i	−0.185610	+	0.107162i	0.404316	+	0.914620i	$0.367510\pi$
$570$	−23.3263	−	8.85079i	−0.977033	−	0.370719i
$571$	−30.6553	−	17.6989i	−1.28289	−	0.740675i	−0.305511	−	0.952189i	$-0.598827\pi$
$571$	−30.6553	−	17.6989i	−1.28289	−	0.740675i	−0.977375	+	0.211514i	$0.932161\pi$
$572$	6.61315	−	3.27697i	0.276510	−	0.137017i
$573$	2.34774	+	13.1589i	0.0980783	+	0.549720i
$574$	23.7177	+	14.7172i	0.989958	+	0.614284i
$575$	5.66269	−	3.51810i	0.236151	−	0.146715i
$576$	15.2045	+	18.5694i	0.633523	+	0.773724i
$577$			30.4257i			1.26664i	0.773890	+	0.633320i	$0.218308\pi$
$577$			30.4257i			1.26664i	−0.773890	+	0.633320i	$0.781692\pi$
$578$	13.2414	−	21.3393i	0.550768	−	0.887597i
$579$	−5.76519	−	6.84250i	−0.239593	−	0.284365i
$580$	11.8372	+	0.561257i	0.491512	+	0.0233049i
$581$	24.0888	+	13.9077i	0.999372	+	0.576987i
$582$	−6.01370	+	15.1085i	−0.249276	+	0.626267i
$583$	−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	$-0.872843\pi$
$587$	−25.3201	+	14.6186i	−1.04507	+	0.603372i	−0.123806	+	0.992306i	$0.539510\pi$
$588$	−4.28459	−	1.86517i	−0.176693	−	0.0769184i
$589$	−5.96697	+	10.3351i	−0.245865	+	0.425850i
$590$	−28.7335	−	17.1928i	−1.18294	−	0.707818i
$591$	13.7978	+	4.99036i	0.567564	+	0.205276i
$592$	23.6793	+	18.0264i	0.973213	+	0.740879i
$593$	−1.73460			−0.0712314			−0.0356157	−	0.999366i	$-0.511339\pi$
$593$	−1.73460			−0.0712314			−0.0356157	+	0.999366i	$0.511339\pi$
$594$	2.77475	+	5.10456i	0.113849	+	0.209443i
$595$	33.2917	+	18.5103i	1.36483	+	0.758847i
$596$	1.25040	−	19.6530i	0.0512185	−	0.805017i
$597$	−0.327520	+	0.905554i	−0.0134045	+	0.0370619i
$598$	−8.79648	−	0.279551i	−0.359715	−	0.0114317i
$599$	1.94974	−	3.37704i	0.0796641	−	0.137982i	−0.823441	−	0.567402i	$-0.807949\pi$
$599$	1.94974	−	3.37704i	0.0796641	−	0.137982i	0.903105	+	0.429420i	$0.141282\pi$
$600$	19.6886	−	14.5725i	0.803785	−	0.594921i
$601$	2.16133	+	3.74354i	0.0881625	+	0.152702i	0.906734	−	0.421702i	$-0.138567\pi$
$601$	2.16133	+	3.74354i	0.0881625	+	0.152702i	−0.818572	+	0.574404i	$0.805234\pi$
$602$	−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
$606$	2.30147	−	5.78210i	0.0934910	−	0.234882i
$607$	−6.33497	+	10.9725i	−0.257128	+	0.445360i	−0.965471	−	0.260509i	$-0.916110\pi$
$607$	−6.33497	+	10.9725i	−0.257128	+	0.445360i	0.708343	+	0.705868i	$0.249443\pi$
$608$	24.0721	−	9.19165i	0.976252	−	0.372771i
$609$	8.54498	+	10.1418i	0.346260	+	0.410964i
$610$	4.80616	−	2.67569i	0.194596	−	0.108336i
$611$	14.0638			0.568961
$612$	8.20287	−	34.4094i	0.331581	−	1.39092i
$613$		−	47.3059i		−	1.91067i	−0.295527	−	0.955334i	$-0.595495\pi$
$613$		−	47.3059i		−	1.91067i	0.295527	−	0.955334i	$-0.404505\pi$
$614$	18.1014	−	29.1715i	0.730512	−	1.17727i
$615$	−25.0206	−	8.59484i	−1.00893	−	0.346578i
$616$	3.74865	−	5.26304i	0.151037	−	0.212054i
$617$	−3.48880	+	6.04277i	−0.140454	+	0.243273i	−0.927668	−	0.373407i	$-0.878189\pi$
$617$	−3.48880	+	6.04277i	−0.140454	+	0.243273i	0.787214	+	0.616680i	$0.211523\pi$
$618$	2.70595	+	18.5582i	0.108849	+	0.746522i
$619$	24.9827	−	14.4238i	1.00414	−	0.579741i	0.0946695	−	0.995509i	$-0.469821\pi$
$619$	24.9827	−	14.4238i	1.00414	−	0.579741i	0.909471	+	0.415768i	$0.136487\pi$
$620$	−5.37120	−	10.4130i	−0.215713	−	0.418197i
$621$	−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
$624$	−32.2976	+	1.59940i	−1.29294	+	0.0640273i
$625$	−13.8724	−	20.7980i	−0.554894	−	0.831921i
$626$	−0.200134	+	6.29750i	−0.00799896	+	0.251699i
$627$	6.14082	−	1.09561i	0.245241	−	0.0437546i
$628$	1.90616	−	29.9598i	0.0760643	−	1.19553i
$629$		−	43.8633i		−	1.74894i
$630$	26.9385	+	5.07179i	1.07326	+	0.202065i
$631$			31.3427i			1.24774i	0.781530	+	0.623868i	$0.214440\pi$
$631$			31.3427i			1.24774i	−0.781530	+	0.623868i	$0.785560\pi$
$632$	−9.82964	+	4.48776i	−0.391002	+	0.178514i
$633$	−27.1457	−	32.2184i	−1.07895	−	1.28056i
$634$	−7.00517	−	0.222624i	−0.278211	−	0.00884151i
$635$	18.7451	−	11.2302i	0.743878	−	0.445658i
$636$	0.667130	+	5.87767i	0.0264534	+	0.233065i
$637$	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
$640$	−5.18023	+	24.7622i	−0.204767	+	0.978811i
$641$	−17.6686	+	10.2010i	−0.697869	+	0.402915i	−0.806553	−	0.591162i	$-0.798670\pi$
$641$	−17.6686	+	10.2010i	−0.697869	+	0.402915i	0.108684	+	0.994076i	$0.465336\pi$
$642$	20.8146	+	26.3598i	0.821485	+	1.04034i
$643$	14.8702	−	25.7560i	0.586424	−	1.01572i	−0.408272	−	0.912860i	$-0.633869\pi$
$643$	14.8702	−	25.7560i	0.586424	−	1.01572i	0.994696	−	0.102856i	$-0.0327981\pi$
$644$	−6.90397	+	3.42108i	−0.272055	+	0.134810i
$645$	30.2748	+	34.7759i	1.19207	+	1.36930i
$646$	−32.2705	−	20.0243i	−1.26966	−	0.787846i
$647$			7.37854i			0.290081i	0.989426	+	0.145040i	$0.0463312\pi$
$647$			7.37854i			0.290081i	−0.989426	+	0.145040i	$0.953669\pi$
$648$	−2.22004	−	25.3589i	−0.0872116	−	0.996190i
$649$	8.37183			0.328623
$650$	0.0181262	+	33.0039i	0.000710968	+	1.29452i
$651$	4.45960	−	12.3303i	0.174786	−	0.483261i
$652$	3.69297	+	7.45266i	0.144628	+	0.291869i
$653$	−7.32692	+	12.6906i	−0.286724	+	0.496621i	−0.973026	−	0.230696i	$-0.925900\pi$
$653$	−7.32692	+	12.6906i	−0.286724	+	0.496621i	0.686301	+	0.727317i	$0.259233\pi$
$654$	25.5036	−	20.1384i	0.997269	−	0.787475i
$655$	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	$-0.207281\pi$
$659$	−3.26655	−	5.65782i	−0.127247	−	0.220398i	−0.922609	+	0.385737i	$0.873947\pi$
$660$	−2.35339	+	5.65402i	−0.0916054	+	0.220083i
$661$	13.4007	−	23.2106i	0.521225	−	0.902788i	−0.478470	−	0.878104i	$-0.658809\pi$
$661$	13.4007	−	23.2106i	0.521225	−	0.902788i	0.999695	−	0.0246846i	$-0.00785816\pi$
$662$	−1.19431	+	37.5807i	−0.0464182	+	1.46062i
$663$	30.7102	+	36.4489i	1.19269	+	1.41556i
$664$	24.7685	−	11.3082i	0.961205	−	0.438842i
$665$	14.3014	−	25.7218i	0.554584	−	0.997450i
$666$	−9.96967	−	29.9495i	−0.386317	−	1.16052i
$667$	3.53308			0.136801
$668$	0.00423568	−	0.0665735i	0.000163883	−	0.00257581i
$669$	0.103213	+	0.578500i	0.00399044	+	0.0223661i
$670$	20.4454	+	12.2336i	0.789874	+	0.472625i
$671$	−0.687656	+	1.19105i	−0.0265466	+	0.0459801i
$672$	−24.2633	+	14.5874i	−0.935978	+	0.562721i
$673$	16.3504	−	9.43992i	0.630262	−	0.363882i	−0.150591	−	0.988596i	$-0.548118\pi$
$673$	16.3504	−	9.43992i	0.630262	−	0.363882i	0.780854	+	0.624714i	$0.214784\pi$
$674$	−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	0.992288	−	0.123950i	$-0.0395564\pi$
$677$	10.1163	+	17.5219i	0.388800	+	0.673421i	−0.603488	+	0.797372i	$0.706223\pi$
$678$	3.26903	+	22.4201i	0.125546	+	0.861038i
$679$	−16.6122	−	9.59106i	−0.637518	−	0.368071i
$680$	33.6645	−	16.0320i	1.29097	−	0.614799i
$681$	−14.6711	+	2.61754i	−0.562196	+	0.100304i
$682$	2.48915	+	1.54456i	0.0953145	+	0.0591441i
$683$			15.3795i			0.588481i	0.955731	+	0.294241i	$0.0950667\pi$
$683$			15.3795i			0.588481i	−0.955731	+	0.294241i	$0.904933\pi$
$684$	−26.5853	−	6.33769i	−1.01652	−	0.242328i
$685$	−6.16084	−	3.42544i	−0.235393	−	0.130879i
$686$	−12.1753	+	19.6213i	−0.464856	+	0.749145i
$687$	−0.950687	+	0.801006i	−0.0362710	+	0.0305603i
$688$	−47.2359	−	6.03511i	−1.80085	−	0.230086i
$689$	−6.90249	−	3.98516i	−0.262964	−	0.151822i
$690$	5.65757	−	4.61775i	0.215380	−	0.175795i
$691$	13.7773	−	7.95434i	0.524114	−	0.302598i	−0.214502	−	0.976724i	$-0.568813\pi$
$691$	13.7773	−	7.95434i	0.524114	−	0.302598i	0.738616	+	0.674126i	$0.235480\pi$
$692$	−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
$696$	12.9387	−	1.05359i	0.490441	−	0.0399361i
$697$	−34.8763	−	20.1359i	−1.32104	−	0.762700i
$698$	−2.70135	−	0.0858486i	−0.102248	−	0.00324942i
$699$	22.5391	+	8.15193i	0.852507	+	0.308334i
$700$	13.6591	+	25.4622i	0.516267	+	0.962381i
$701$		−	38.9767i		−	1.47213i	−0.676912	−	0.736064i	$-0.736682\pi$
$701$		−	38.9767i		−	1.47213i	0.676912	−	0.736064i	$-0.263318\pi$
$702$	29.2531	+	17.9069i	1.10409	+	0.675852i
$703$	−33.8896			−1.27817
$704$	−2.06745	−	5.97767i	−0.0779198	−	0.225292i
$705$	−8.80181	+	7.66259i	−0.331495	+	0.288590i
$706$	31.2556	+	0.993301i	1.17632	+	0.0373834i
$707$	6.35758	+	3.67055i	0.239102	+	0.138045i
$708$	−33.6319	−	14.6407i	−1.26396	−	0.550230i
$709$	−6.59388	−	11.4209i	−0.247638	−	0.428922i	0.715232	−	0.698887i	$-0.246321\pi$
$709$	−6.59388	−	11.4209i	−0.247638	−	0.428922i	−0.962870	+	0.269965i	$0.912988\pi$
$710$	−0.142440	+	9.12416i	−0.00534567	+	0.342424i
$711$	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
$714$	38.7690	+	15.4314i	1.45089	+	0.577506i
$715$	−4.24078	−	7.07857i	−0.158596	−	0.264724i
$716$	−22.6697	−	45.7489i	−0.847205	−	1.70972i
$717$	36.7046	−	30.9256i	1.37076	−	1.15494i
$718$	1.10382	−	1.77888i	0.0411943	−	0.0663872i
$719$	−43.7650			−1.63216			−0.816079	−	0.577940i	$-0.803857\pi$
$719$	−43.7650			−1.63216			−0.816079	+	0.577940i	$0.803857\pi$
$720$	19.3419	−	18.5981i	0.720831	−	0.693111i
$721$	−22.1231			−0.823907
$722$	−1.30377	+	2.10111i	−0.0485214	+	0.0781953i
$723$	3.47603	+	19.4829i	0.129275	+	0.724575i
$724$	−22.7426	−	45.8960i	−0.845221	−	1.70571i
$725$	−0.428120	−	13.2423i	−0.0159000	−	0.491808i
$726$	3.66668	+	25.1473i	0.136083	+	0.933303i
$727$	−4.95811	−	8.58770i	−0.183886	−	0.318500i	0.759314	−	0.650724i	$-0.225534\pi$
$727$	−4.95811	−	8.58770i	−0.183886	−	0.318500i	−0.943201	+	0.332224i	$0.892201\pi$
$728$	3.63005	−	37.9723i	0.134539	−	1.40735i
$729$	−13.2150	+	23.5449i	−0.489445	+	0.872034i
$730$	−20.5791	−	0.321266i	−0.761666	−	0.0118906i
$731$	35.0935	+	60.7837i	1.29798	+	2.24816i
$732$	4.84541	−	3.58221i	0.179092	−	0.132402i
$733$	24.2247	+	13.9862i	0.894761	+	0.516591i	0.875497	−	0.483224i	$-0.160534\pi$
$733$	24.2247	+	13.9862i	0.894761	+	0.516591i	0.0192642	+	0.999814i	$0.493868\pi$
$734$	−0.178426	−	0.00567035i	−0.00658581	−	0.000209297i
$735$	−1.69733	+	4.94113i	−0.0626071	+	0.182256i
$736$	−1.19304	+	7.44740i	−0.0439761	+	0.274515i
$737$	−5.95699			−0.219428
$738$	−28.3900	−	5.82157i	−1.04505	−	0.214295i
$739$			24.2237i			0.891082i	0.895262	+	0.445541i	$0.146989\pi$
$739$			24.2237i			0.891082i	−0.895262	+	0.445541i	$0.853011\pi$
$740$	17.9824	−	27.9947i	0.661046	−	1.02911i
$741$	28.1611	−	23.7273i	1.03452	−	0.871644i
$742$	−6.97439	−	0.221646i	−0.256038	−	0.00813687i
$743$	43.9304	+	25.3632i	1.61165	+	0.930486i	0.988988	+	0.147993i	$0.0472814\pi$
$743$	43.9304	+	25.3632i	1.61165	+	0.930486i	0.622660	+	0.782492i	$0.286052\pi$
$744$	−7.29846	−	10.5579i	−0.267575	−	0.387072i
$745$	−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
$750$	−17.9933	−	20.6456i	−0.657024	−	0.753870i
$751$	0.581286	+	0.335605i	0.0212114	+	0.0122464i	0.510568	−	0.859837i	$-0.329435\pi$
$751$	0.581286	+	0.335605i	0.0212114	+	0.0122464i	−0.489357	+	0.872084i	$0.662768\pi$
$752$	1.52749	−	11.9555i	0.0557020	−	0.435971i
$753$	−8.22802	−	2.97591i	−0.299846	−	0.108448i
$754$	−9.22229	+	14.8623i	−0.335856	+	0.541253i
$755$	−11.5953	+	20.8548i	−0.421996	+	0.758983i
$756$	29.9786	+	1.72463i	1.09031	+	0.0627243i
$757$			17.0611i			0.620095i	0.950721	+	0.310048i	$0.100345\pi$
$757$			17.0611i			0.620095i	−0.950721	+	0.310048i	$0.899655\pi$
$758$	33.0606	+	20.5146i	1.20081	+	0.745123i
$759$	−0.621010	+	1.71702i	−0.0225412	+	0.0623238i
$760$	−12.3866	−	26.0098i	−0.449310	−	0.943476i
$761$	6.74677	+	3.89525i	0.244570	+	0.141203i	0.617275	−	0.786747i	$-0.288236\pi$
$761$	6.74677	+	3.89525i	0.244570	+	0.141203i	−0.372705	+	0.927950i	$0.621570\pi$
$762$	18.7866	−	14.8345i	0.680566	−	0.537397i
$763$	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
$768$	−2.14826	+	27.6294i	−0.0775187	+	0.996991i
$769$	4.58773	−	7.94618i	0.165438	−	0.286546i	−0.771373	−	0.636383i	$-0.780430\pi$
$769$	4.58773	−	7.94618i	0.165438	−	0.286546i	0.936811	+	0.349837i	$0.113763\pi$
$770$	−6.19925	−	3.70935i	−0.223405	−	0.133676i
$771$	3.50658	−	2.95448i	0.126286	−	0.106403i
$772$	0.656015	−	10.3108i	0.0236105	−	0.371094i
$773$	−32.0512			−1.15280			−0.576401	−	0.817167i	$-0.695543\pi$
$773$	−32.0512			−1.15280			−0.576401	+	0.817167i	$0.695543\pi$
$774$	37.7770	+	33.5262i	1.35787	+	1.20507i
$775$	−11.1271	+	6.91299i	−0.399696	+	0.248322i
$776$	−17.0810	+	7.79839i	−0.613171	+	0.279946i
$777$	36.6560	−	6.53999i	1.31503	−	0.234621i
$778$	−0.0820214	+	2.58092i	−0.00294061	+	0.0925305i
$779$	−15.5574	+	26.9461i	−0.557400	+	0.965445i
$780$	4.65733	+	35.8528i	0.166759	+	1.28374i
$781$	−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
$786$	4.67804	+	32.0835i	0.166860	+	1.14438i
$787$	1.97855	−	3.42695i	0.0705276	−	0.122157i	−0.828605	−	0.559834i	$-0.810865\pi$
$787$	1.97855	−	3.42695i	0.0705276	−	0.122157i	0.899133	+	0.437676i	$0.144198\pi$
$788$	7.52243	+	15.1808i	0.267975	+	0.540792i
$789$	4.31604	−	0.770047i	0.153655	−	0.0274144i
$790$	5.87649	+	10.5555i	0.209076	+	0.375549i
$791$	−26.7267			−0.950293
$792$	−1.76222	+	6.47320i	−0.0626177	+	0.230015i
$793$			8.11904i			0.288316i
$794$	−22.9311	−	14.2291i	−0.813795	−	0.504972i
$795$	6.49120	−	1.26668i	0.230219	−	0.0449245i
$796$	−0.996321	+	0.493701i	−0.0353137	+	0.0174988i
$797$	4.99178	−	8.64602i	0.176818	−	0.306258i	−0.763971	−	0.645251i	$-0.776753\pi$
$797$	4.99178	−	8.64602i	0.176818	−	0.306258i	0.940789	+	0.338993i	$0.110086\pi$
$798$	11.9226	−	29.9537i	0.422055	−	1.06035i
$799$	−15.3844	+	8.88219i	−0.544261	+	0.314229i
$800$	28.0582	+	3.56920i	0.992006	+	0.126190i
$801$	−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
$804$	23.9308	+	10.4176i	0.843975	+	0.367400i
$805$	4.42727	+	7.38986i	0.156041	+	0.260458i
$806$	17.2849	+	0.549313i	0.608835	+	0.0193487i
$807$	3.10143	−	8.57508i	0.109176	−	0.301857i
$808$	6.53698	−	2.98449i	0.229970	−	0.104994i
$809$			37.9989i			1.33597i	0.744174	+	0.667986i	$0.232843\pi$
$809$			37.9989i			1.33597i	−0.744174	+	0.667986i	$0.767157\pi$
$810$	−28.0645	+	4.73141i	−0.986085	+	0.166245i
$811$		−	21.3193i		−	0.748622i	−0.927303	−	0.374311i	$-0.877879\pi$
$811$		−	21.3193i		−	0.748622i	0.927303	−	0.374311i	$-0.122121\pi$
$812$	−0.972326	+	15.2824i	−0.0341219	+	0.536306i
$813$	−9.80666	+	27.1142i	−0.343934	+	0.950937i
$814$	−0.264240	+	8.31469i	−0.00926161	+	0.291430i
$815$	7.97717	−	4.77913i	0.279428	−	0.167406i
$816$	34.3202	−	22.1475i	1.20145	−	0.775319i
$817$	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
$820$	−14.0040	−	27.1494i	−0.489043	−	0.948096i
$821$	−4.11744	+	2.37721i	−0.143700	+	0.0829651i	−0.570126	−	0.821557i	$-0.693106\pi$
$821$	−4.11744	+	2.37721i	−0.143700	+	0.0829651i	0.426426	+	0.904522i	$0.359772\pi$
$822$	−7.17444	−	2.85567i	−0.250237	−	0.0996030i
$823$	20.4702	−	35.4554i	0.713546	−	1.23590i	−0.249972	−	0.968253i	$-0.580422\pi$
$823$	20.4702	−	35.4554i	0.713546	−	1.23590i	0.963518	−	0.267644i	$-0.0862452\pi$
$824$	−12.5635	+	17.6389i	−0.437670	+	0.614482i
$825$	6.51080	+	2.11955i	0.226677	+	0.0737931i
$826$	22.8137	−	36.7658i	0.793792	−	1.27925i
$827$		−	26.4974i		−	0.921406i	−0.887554	−	0.460703i	$-0.847597\pi$
$827$		−	26.4974i		−	0.921406i	0.887554	−	0.460703i	$-0.152403\pi$
$828$	5.49748	−	5.81169i	0.191051	−	0.201970i
$829$	38.1524			1.32509			0.662544	−	0.749023i	$-0.269477\pi$
$829$	38.1524			1.32509			0.662544	+	0.749023i	$0.269477\pi$
$830$	−14.8075	−	26.5976i	−0.513974	−	0.923217i
$831$	45.0026	−	8.02915i	1.56112	−	0.278528i
$832$	−28.2142	−	24.4584i	−0.978151	−	0.847942i
$833$	−3.97649	+	6.88748i	−0.137777	+	0.238637i
$834$	6.22898	−	0.908237i	0.215692	−	0.0314497i
$835$	−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	$-0.262665\pi$
$839$	−8.60385	−	14.9023i	−0.297038	−	0.514485i	−0.975457	+	0.220190i	$0.929332\pi$
$840$	18.4171	+	25.7427i	0.635451	+	0.888207i
$841$	−10.9891	+	19.0338i	−0.378936	+	0.656337i
$842$	23.7079	+	0.753434i	0.817027	+	0.0259650i
$843$	39.0851	−	6.97337i	1.34616	−	0.240175i
$844$	3.08889	−	48.5490i	0.106324	−	1.67113i
$845$	−17.1690	−	9.54600i	−0.590631	−	0.328392i
$846$	−8.48552	+	9.56141i	−0.291738	+	0.328728i
$847$	−29.9778			−1.03005
$848$	−4.13742	+	5.43488i	−0.142079	+	0.186634i
$849$	8.62913	−	7.27052i	0.296151	−	0.249524i
$850$	−20.8639	−	36.0916i	−0.715626	−	1.23793i
$851$	4.95992	−	8.59084i	0.170024	−	0.294490i
$852$	1.12736	+	9.93246i	0.0386227	+	0.340281i
$853$	−37.6416	+	21.7324i	−1.28882	+	0.744102i	−0.978444	−	0.206511i	$-0.933789\pi$
$853$	−37.6416	+	21.7324i	−1.28882	+	0.744102i	−0.310378	+	0.950613i	$0.600456\pi$
$854$	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	0.727968	−	0.685611i	$-0.240465\pi$
$857$	−6.72648	−	11.6506i	−0.229772	−	0.397977i	−0.957741	+	0.287634i	$0.907131\pi$
$858$	−5.60183	−	7.09423i	−0.191243	−	0.242193i
$859$	−1.00899	−	0.582541i	−0.0344263	−	0.0198760i	0.482688	−	0.875792i	$-0.339660\pi$
$859$	−1.00899	−	0.582541i	−0.0344263	−	0.0198760i	−0.517114	+	0.855916i	$0.672994\pi$
$860$	−2.52156	+	53.1809i	−0.0859844	+	1.81345i
$861$	11.6273	−	32.1480i	0.396257	−	1.09560i
$862$	−11.3703	+	18.3240i	−0.387275	+	0.624118i
$863$		−	0.0600669i		−	0.00204470i	−0.999999	−	0.00102235i	$-0.999675\pi$
$863$		−	0.0600669i		−	0.00204470i	0.999999	−	0.00102235i	$-0.000325424\pi$
$864$	18.3996	−	22.9228i	0.625968	−	0.779849i
$865$	46.5753	+	25.8959i	1.58361	+	0.880488i
$866$	−28.3227	−	17.5747i	−0.962446	−	0.597212i
$867$	−28.9242	−	10.4613i	−0.982317	−	0.355284i
$868$	13.5662	−	6.72236i	0.460466	−	0.228172i
$869$	−2.61585	−	1.51026i	−0.0887367	−	0.0512321i
$870$	−2.32589	−	14.3262i	−0.0788550	−	0.485705i
$871$	−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
$876$	−22.4022	+	2.54270i	−0.756899	+	0.0859099i
$877$	−5.64252	−	3.25771i	−0.190534	−	0.110005i	0.401698	−	0.915772i	$-0.368420\pi$
$877$	−5.64252	−	3.25771i	−0.190534	−	0.110005i	−0.592233	+	0.805767i	$0.701753\pi$
$878$	0.667506	−	21.0040i	0.0225272	−	0.708851i
$879$	22.1805	−	18.6883i	0.748131	−	0.630342i
$880$	−6.47799	+	2.83621i	−0.218373	+	0.0956087i
$881$		−	12.1468i		−	0.409237i	−0.978842	−	0.204619i	$-0.934405\pi$
$881$		−	12.1468i		−	0.409237i	0.978842	−	0.204619i	$-0.0655954\pi$
$882$	−1.14966	+	5.60653i	−0.0387110	+	0.188782i
$883$	−30.7337			−1.03427			−0.517135	−	0.855904i	$-0.673002\pi$
$883$	−30.7337			−1.03427			−0.517135	+	0.855904i	$0.673002\pi$
$884$	−3.49448	+	54.9239i	−0.117532	+	1.84729i
$885$	−13.3232	+	38.7854i	−0.447855	+	1.30376i
$886$	1.21927	−	38.3660i	0.0409621	−	1.28893i
$887$	−48.2108	−	27.8345i	−1.61876	−	0.934592i	−0.987241	−	0.159231i	$-0.949099\pi$
$887$	−48.2108	−	27.8345i	−1.61876	−	0.934592i	−0.631519	−	0.775361i	$-0.717568\pi$
$888$	15.6022	−	32.9402i	0.523577	−	1.10540i
$889$	14.1185	+	24.4539i	0.473518	+	0.820157i
$890$	−0.0234587		0.000366221i	−0.000786338		1.22757e-5i
$891$	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
$894$	−23.8662	+	3.47989i	−0.798204	+	0.116385i
$895$	−48.9686	+	29.3371i	−1.63684	+	0.980632i
$896$	−31.8855	−	7.21008i	−1.06522	−	0.240872i
$897$	1.89322	+	10.6113i	0.0632127	+	0.354301i
$898$	−21.0146	−	13.0399i	−0.701267	−	0.435147i
$899$	−6.94243			−0.231543
$900$	−22.4490	−	19.9009i	−0.748298	−	0.663362i
$901$	10.0675			0.335397
$902$	6.48983	+	4.02704i	0.216088	+	0.134086i
$903$	−45.5638	+	38.3900i	−1.51627	+	1.27754i
$904$	−15.1779	+	21.3095i	−0.504809	+	0.708743i
$905$	−49.1261	+	29.4315i	−1.63301	+	0.978336i
$906$	−9.66662	+	24.2859i	−0.321152	+	0.806844i
$907$	−8.31258	−	14.3978i	−0.276015	−	0.478072i	0.694376	−	0.719612i	$-0.255681\pi$
$907$	−8.31258	−	14.3978i	−0.276015	−	0.478072i	−0.970391	+	0.241541i	$0.922347\pi$
$908$	−14.3263	−	9.53299i	−0.475436	−	0.316363i
$909$	−7.51146	−	1.29314i	−0.249139	−	0.0428907i
$910$	−42.6427	−	0.665706i	−1.41359	−	0.0220680i
$911$	9.29200	+	16.0942i	0.307858	+	0.533225i	0.977893	−	0.209104i	$-0.0670546\pi$
$911$	9.29200	+	16.0942i	0.307858	+	0.533225i	−0.670036	+	0.742329i	$0.733721\pi$
$912$	−17.1116	−	26.5164i	−0.566622	−	0.878046i
$913$	6.59137	+	3.80553i	0.218143	+	0.125945i
$914$	0.264863	−	8.33430i	0.00876090	−	0.275674i
$915$	−4.42361	−	5.08129i	−0.146240	−	0.167982i
$916$	−1.43257	−	0.0911458i	−0.0473334	−	0.00301154i
$917$	−38.2464			−1.26301
$918$	−43.3093	−	1.11313i	−1.42942	−	0.0367389i
$919$			31.1617i			1.02793i	0.857811	+	0.513965i	$0.171824\pi$
$919$			31.1617i			1.02793i	−0.857811	+	0.513965i	$0.828176\pi$
$920$	8.40621	+	0.666731i	0.277145	+	0.0219815i
$921$	−39.5403	−	14.3009i	−1.30290	−	0.471231i
$922$	1.58696	−	49.9359i	0.0522637	−	1.64455i
$923$	−11.6643	−	6.73437i	−0.383934	−	0.221664i
$924$	−7.25606	−	3.15872i	−0.238707	−	0.103914i
$925$	−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	−0.0391715	−	0.999233i	$-0.512472\pi$
$929$	24.5849	−	14.1941i	0.806604	−	0.465693i	0.845775	+	0.533540i	$0.179139\pi$
$930$	−11.1170	+	9.07379i	−0.364541	+	0.297541i
$931$	5.32140	+	3.07231i	0.174402	+	0.100691i
$932$	12.2881	+	24.7983i	0.402511	+	0.812295i
$933$	10.1108	−	8.51892i	0.331013	−	0.278897i
$934$	8.39165	+	5.20715i	0.274583	+	0.170383i
$935$	9.10955	+	5.06493i	0.297914	+	0.165641i
$936$	10.0976	+	38.2959i	0.330052	+	1.25174i
$937$			25.1998i			0.823241i	0.911355	+	0.411620i	$0.135037\pi$
$937$			25.1998i			0.823241i	−0.911355	+	0.411620i	$0.864963\pi$
$938$	−16.2331	+	26.1607i	−0.530031	+	0.854179i
$939$	7.59676	−	1.35538i	0.247911	−	0.0442310i
$940$	−13.4601	−	0.638209i	−0.439022	−	0.0208161i
$941$	35.0946	+	20.2619i	1.14405	+	0.660519i	0.947431	−	0.319960i	$-0.103670\pi$
$941$	35.0946	+	20.2619i	1.14405	+	0.660519i	0.196622	+	0.980479i	$0.437003\pi$
$942$	−36.3826	+	5.30488i	−1.18541	+	0.172842i
$943$	−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	$-0.669762\pi$
$947$	−0.518242	+	0.299207i	−0.0168406	+	0.00972293i	0.491556	+	0.870846i	$0.336428\pi$
$948$	7.86742	+	10.6417i	0.255522	+	0.345627i
$949$	15.1890	−	26.3082i	0.493057	−	0.853999i
$950$	−27.8850	+	16.1199i	−0.904710	+	0.522997i
$951$	1.50768	+	8.45043i	0.0488900	+	0.274024i
$952$	20.0110	+	43.8305i	0.648560	+	1.42055i
$953$	−2.50405			−0.0811142			−0.0405571	−	0.999177i	$-0.512913\pi$
$953$	−2.50405			−0.0811142			−0.0405571	+	0.999177i	$0.512913\pi$
$954$	6.87401	−	2.28824i	0.222554	−	0.0740846i
$955$	15.0819	+	8.38555i	0.488038	+	0.271350i
$956$	55.3092	+	3.51900i	1.78883	+	0.113813i
$957$	2.33815	+	2.77507i	0.0755816	+	0.0897052i
$958$	28.8608	+	0.917193i	0.932449	+	0.0296332i
$959$	4.55443	−	7.88850i	0.147070	−	0.254733i
$960$	30.9838	−	0.0651014i	0.999998	−	0.00210114i
$961$	−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
$966$	5.84817	+	7.40620i	0.188162	+	0.238291i
$967$	18.5754	−	32.1736i	0.597346	−	1.03463i	−0.395866	−	0.918308i	$-0.629555\pi$
$967$	18.5754	−	32.1736i	0.597346	−	1.03463i	0.993211	−	0.116325i	$-0.0371113\pi$
$968$	−17.0241	+	23.9016i	−0.547176	+	0.768226i
$969$	−15.8201	+	43.7408i	−0.508216	+	1.40516i
$970$	10.2116	+	18.3423i	0.327874	+	0.588937i
$971$	−14.7960			−0.474826			−0.237413	−	0.971409i	$-0.576299\pi$
$971$	−14.7960			−0.474826			−0.237413	+	0.971409i	$0.576299\pi$
$972$	−29.8243	+	9.08373i	−0.956613	+	0.291361i
$973$			7.42550i			0.238051i
$974$	15.5293	−	25.0264i	0.497590	−	0.801898i
$975$	39.5429	−	8.38179i	1.26638	−	0.268432i
$976$	6.90189	+	0.881822i	0.220924	+	0.0282264i
$977$	16.1759	−	28.0175i	0.517514	−	0.896360i	−0.482279	−	0.876018i	$-0.660191\pi$
$977$	16.1759	−	28.0175i	0.517514	−	0.896360i	0.999793	−	0.0203428i	$-0.00647578\pi$
$978$	7.99481	−	6.31295i	0.255646	−	0.201866i
$979$	0.00508002	−	0.00293295i	0.000162358	−	9.37374e-5i
$980$	−5.36153	+	2.76556i	−0.171268	+	0.0883425i
$981$	−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	$-0.683864\pi$
$983$	−2.93257	+	1.69312i	−0.0935346	+	0.0540022i	0.452503	+	0.891763i	$0.350531\pi$
$984$	−19.0289	−	27.5271i	−0.606619	−	0.877532i
$985$	16.2492	−	9.73488i	0.517741	−	0.310179i
$986$	0.701774	−	22.0823i	0.0223490	−	0.703245i
$987$	−9.71656	−	11.5323i	−0.309281	−	0.367076i
$988$	42.4353	+	2.69991i	1.35005	+	0.0858954i
$989$			15.8731i			0.504734i
$990$	7.37114	+	1.38778i	0.234270	+	0.0441067i
$991$		−	39.7022i		−	1.26118i	−0.776116	−	0.630591i	$-0.782813\pi$
$991$		−	39.7022i		−	1.26118i	0.776116	−	0.630591i	$-0.217187\pi$
$992$	2.34430	−	14.6340i	0.0744317	−	0.464630i
$993$	45.3341	−	8.08829i	1.43864	−	0.256674i
$994$	−11.7858	−	0.374551i	−0.373822	−	0.0118800i
$995$	0.638906	+	1.06644i	0.0202547	+	0.0338085i
$996$	−19.8242	−	26.8148i	−0.628153	−	0.849660i
$997$	17.8325	−	10.2956i	0.564760	−	0.326064i	−0.190294	−	0.981727i	$-0.560944\pi$
$997$	17.8325	−	10.2956i	0.564760	−	0.326064i	0.755054	+	0.655663i	$0.227611\pi$
$998$	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.59.17	yes	48
3.2	odd	2		540.2.n.d.179.8		48
4.3	odd	2	inner	180.2.n.d.59.1	✓	48
5.2	odd	4		900.2.r.g.851.20		48
5.3	odd	4		900.2.r.g.851.5		48
5.4	even	2	inner	180.2.n.d.59.8	yes	48
9.2	odd	6	inner	180.2.n.d.119.24	yes	48
9.7	even	3		540.2.n.d.359.1		48
12.11	even	2		540.2.n.d.179.24		48
15.14	odd	2		540.2.n.d.179.17		48
20.3	even	4		900.2.r.g.851.13		48
20.7	even	4		900.2.r.g.851.12		48
20.19	odd	2	inner	180.2.n.d.59.24	yes	48
36.7	odd	6		540.2.n.d.359.17		48
36.11	even	6	inner	180.2.n.d.119.8	yes	48
45.2	even	12		900.2.r.g.551.12		48
45.29	odd	6	inner	180.2.n.d.119.1	yes	48
45.34	even	6		540.2.n.d.359.24		48
45.38	even	12		900.2.r.g.551.13		48
60.59	even	2		540.2.n.d.179.1		48
180.47	odd	12		900.2.r.g.551.20		48
180.79	odd	6		540.2.n.d.359.8		48
180.83	odd	12		900.2.r.g.551.5		48
180.119	even	6	inner	180.2.n.d.119.17	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.1	✓	48	4.3	odd	2	inner
180.2.n.d.59.8	yes	48	5.4	even	2	inner
180.2.n.d.59.17	yes	48	1.1	even	1	trivial
180.2.n.d.59.24	yes	48	20.19	odd	2	inner
180.2.n.d.119.1	yes	48	45.29	odd	6	inner
180.2.n.d.119.8	yes	48	36.11	even	6	inner
180.2.n.d.119.17	yes	48	180.119	even	6	inner
180.2.n.d.119.24	yes	48	9.2	odd	6	inner
540.2.n.d.179.1		48	60.59	even	2
540.2.n.d.179.8		48	3.2	odd	2
540.2.n.d.179.17		48	15.14	odd	2
540.2.n.d.179.24		48	12.11	even	2
540.2.n.d.359.1		48	9.7	even	3
540.2.n.d.359.8		48	180.79	odd	6
540.2.n.d.359.17		48	36.7	odd	6
540.2.n.d.359.24		48	45.34	even	6
900.2.r.g.551.5		48	180.83	odd	12
900.2.r.g.551.12		48	45.2	even	12
900.2.r.g.551.13		48	45.38	even	12
900.2.r.g.551.20		48	180.47	odd	12
900.2.r.g.851.5		48	5.3	odd	4
900.2.r.g.851.12		48	20.7	even	4
900.2.r.g.851.13		48	20.3	even	4
900.2.r.g.851.20		48	5.2	odd	4

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+(0.745653 - 1.20167i) q^{2} +(-1.62879 - 0.589100i) q^{3} +(-0.888004 - 1.79205i) q^{4} +(-1.91817 + 1.14918i) q^{5} +(-1.92241 + 1.51800i) q^{6} +(-1.44473 - 2.50234i) q^{7} +(-2.81559 - 0.269163i) q^{8} +(2.30592 + 1.91904i) q^{9} +(-0.0493612 + 3.16189i) q^{10} +(-0.395318 - 0.684712i) q^{11} +(0.390676 + 3.44200i) q^{12} +(-4.04214 - 2.33373i) q^{13} +(-4.08425 - 0.129797i) q^{14} +(3.80129 - 0.741776i) q^{15} +(-2.42290 + 3.18270i) q^{16} +5.89560 q^{17} +(4.02547 - 1.34001i) q^{18} -4.55505i q^{19} +(3.76273 + 2.41699i) q^{20} +(0.879030 + 4.92689i) q^{21} +(-1.11756 - 0.0355161i) q^{22} +(1.15468 + 0.666656i) q^{23} +(4.42745 + 2.09708i) 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} +(1.94307 - 5.12098i) q^{30} +(-2.26893 - 1.30997i) q^{31} +(2.01790 + 5.28470i) q^{32} +(0.240527 + 1.34813i) q^{33} +(4.39607 - 7.08454i) q^{34} +(5.64688 + 3.13968i) q^{35} +(1.39135 - 5.83645i) q^{36} -7.44000i q^{37} +(-5.47365 - 3.39649i) q^{38} +(5.20900 + 6.18239i) q^{39} +(5.71011 - 2.71932i) q^{40} +(-5.91566 - 3.41541i) q^{41} +(6.57593 + 2.61744i) 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} +(5.82132 - 3.75662i) q^{48} +(-0.674484 + 1.16824i) q^{49} +(-3.53890 - 6.12178i) q^{50} +(-9.60270 - 3.47310i) q^{51} +(-0.592728 + 9.31609i) q^{52} +1.70763 q^{53} +(-7.34604 - 0.188808i) q^{54} +(1.54515 + 0.859104i) q^{55} +(3.39423 + 7.43444i) q^{56} +(-2.68338 + 7.41923i) q^{57} +(0.119034 - 3.74556i) q^{58} +(-5.29436 + 9.17010i) q^{59} +(-4.70486 - 6.15340i) 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} +(1.79936 + 0.716206i) q^{66} +(3.76721 - 6.52500i) q^{67} +(-5.23532 - 10.5652i) q^{68} +(-1.48801 - 1.76607i) q^{69} +(7.98346 - 4.44456i) q^{70} +2.88566 q^{71} +(-5.97600 - 6.02391i) q^{72} +6.50847i q^{73} +(-8.94040 - 5.54766i) q^{74} +(-6.43909 + 5.79121i) q^{75} +(-8.16289 + 4.04491i) q^{76} +(-1.14226 + 1.97845i) q^{77} +(11.3133 - 1.64957i) q^{78} +(3.30854 - 1.91019i) q^{79} +(0.990045 - 8.88931i) q^{80} +(1.63455 + 8.85032i) q^{81} +(-8.51521 + 4.56194i) q^{82} +(-8.33679 + 4.81325i) q^{83} +(8.04865 - 5.95036i) q^{84} +(-11.3088 + 6.77510i) q^{85} +(16.8277 + 0.534782i) q^{86} +(-4.51832 + 0.806137i) q^{87} +(0.928756 + 2.03427i) q^{88} +0.00741921i q^{89} +(-6.18163 + 7.19635i) q^{90} +13.4864i q^{91} +(0.169319 - 2.66124i) q^{92} +(2.92391 + 3.47029i) q^{93} +(-0.135354 + 4.25910i) q^{94} +(5.23457 + 8.73738i) q^{95} +(-0.173524 - 9.79642i) 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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