LMFDB - Embedded newform 372.2.p.a.191.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [372,2,Mod(191,372)] 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("372.191"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(372, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 372 = 2^{2} \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	372.p (of order $6$, degree $2$, 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:	$2.97043495519$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$60$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.12
Character	$\chi$	$=$	372.191
Dual form			372.2.p.a.335.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.09739 + 0.892042i) q^{2} +(-1.68099 - 0.417450i) q^{3} +(0.408523 - 1.95783i) q^{4} +(0.0699686 - 0.0403964i) q^{5} +(2.21708 - 1.04141i) q^{6} +(-0.885120 - 0.511024i) q^{7} +(1.29816 + 2.51292i) q^{8} +(2.65147 + 1.40346i) q^{9} +(-0.0407475 + 0.106745i) q^{10} +(1.66026 + 2.87565i) q^{11} +(-1.50402 + 3.12056i) q^{12} +(-2.04134 - 3.53571i) q^{13} +(1.42717 - 0.228772i) q^{14} +(-0.134480 + 0.0386976i) q^{15} +(-3.66622 - 1.59964i) q^{16} +(-4.25631 - 2.45738i) q^{17} +(-4.16164 + 0.825081i) q^{18} +(-1.55179 - 0.895926i) q^{19} +(-0.0505056 - 0.153490i) q^{20} +(1.27455 + 1.22852i) q^{21} +(-4.38715 - 1.67469i) q^{22} -3.92474 q^{23} +(-1.13318 - 4.76612i) q^{24} +(-2.49674 + 4.32447i) q^{25} +(5.39414 + 2.05908i) q^{26} +(-3.87123 - 3.46606i) q^{27} +(-1.36209 + 1.52415i) q^{28} -4.36102i q^{29} +(0.113057 - 0.162428i) q^{30} +(-3.43111 - 4.38491i) q^{31} +(5.45021 - 1.51499i) q^{32} +(-1.59044 - 5.52702i) q^{33} +(6.86291 - 1.10010i) q^{34} -0.0825741 q^{35} +(3.83093 - 4.61779i) q^{36} +(4.39260 - 7.60821i) q^{37} +(2.50212 - 0.401082i) q^{38} +(1.95550 + 6.79566i) q^{39} +(0.192343 + 0.123385i) q^{40} +(-9.29867 + 5.36859i) q^{41} +(-2.49457 - 0.211211i) q^{42} +(0.921465 + 0.532008i) q^{43} +(6.30830 - 2.07574i) q^{44} +(0.242214 - 0.00891169i) q^{45} +(4.30696 - 3.50103i) q^{46} -6.73110 q^{47} +(5.49511 + 4.21945i) q^{48} +(-2.97771 - 5.15754i) q^{49} +(-1.11772 - 6.97282i) q^{50} +(6.12899 + 5.90763i) q^{51} +(-7.75626 + 2.55219i) q^{52} +(-5.15428 + 2.97582i) q^{53} +(7.34011 + 0.350321i) q^{54} +(0.232332 + 0.134137i) q^{55} +(0.135137 - 2.88763i) q^{56} +(2.23454 + 2.15384i) q^{57} +(3.89021 + 4.78574i) q^{58} +(-0.988055 + 1.71136i) q^{59} +(0.0208252 + 0.279098i) q^{60} +5.22147 q^{61} +(7.67679 + 1.75126i) q^{62} +(-1.62967 - 2.59720i) q^{63} +(-4.62956 + 6.52435i) q^{64} +(-0.285660 - 0.164926i) q^{65} +(6.67567 + 4.64655i) q^{66} +(-2.80149 + 1.61744i) q^{67} +(-6.54994 + 7.32924i) q^{68} +(6.59745 + 1.63838i) q^{69} +(0.0906158 - 0.0736595i) q^{70} +(-0.617822 - 1.07010i) q^{71} +(-0.0847550 + 8.48486i) q^{72} +(0.663259 + 1.14880i) q^{73} +(1.96645 + 12.2675i) q^{74} +(6.00225 - 6.22715i) q^{75} +(-2.38802 + 2.67214i) q^{76} -3.39373i q^{77} +(-8.20795 - 5.71309i) q^{78} +(13.1653 + 7.60097i) q^{79} +(-0.321140 + 0.0361774i) q^{80} +(5.06060 + 7.44247i) q^{81} +(5.41525 - 14.1862i) q^{82} +(-4.14834 - 7.18513i) q^{83} +(2.92592 - 1.99348i) q^{84} -0.397077 q^{85} +(-1.48578 + 0.238166i) q^{86} +(-1.82051 + 7.33084i) q^{87} +(-5.07101 + 7.90516i) q^{88} +4.85111i q^{89} +(-0.257854 + 0.225845i) q^{90} +4.17270i q^{91} +(-1.60335 + 7.68398i) q^{92} +(3.93719 + 8.80333i) q^{93} +(7.38663 - 6.00442i) q^{94} -0.144769 q^{95} +(-9.79420 + 0.271500i) q^{96} -8.59029 q^{97} +(7.86845 + 3.00359i) q^{98} +(0.366263 + 9.95482i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 12 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} - 4 q^{16} - 2 q^{18} - 14 q^{21} - 6 q^{22} - 4 q^{24} + 48 q^{25} + 6 q^{28} - 48 q^{30} + 4 q^{33} + 28 q^{34} + 2 q^{36} - 8 q^{37} + 36 q^{40} - 4 q^{42}+ \cdots + 48 q^{96}+O(q^{100}) $ 120 * q - 12 * q^4 - 2 * q^9 + 4 * q^10 - 4 * q^12 - 4 * q^16 - 2 * q^18 - 14 * q^21 - 6 * q^22 - 4 * q^24 + 48 * q^25 + 6 * q^28 - 48 * q^30 + 4 * q^33 + 28 * q^34 + 2 * q^36 - 8 * q^37 + 36 * q^40 - 4 * q^42 - 34 * q^45 - 48 * q^46 + 10 * q^48 + 60 * q^49 + 8 * q^52 - 84 * q^54 - 14 * q^57 - 28 * q^58 - 60 * q^60 - 64 * q^61 + 84 * q^64 - 132 * q^66 - 4 * q^69 - 120 * q^70 + 44 * q^72 + 28 * q^76 + 20 * q^78 - 2 * q^81 + 48 * q^82 - 8 * q^84 + 8 * q^85 - 10 * q^88 + 24 * q^90 - 78 * q^93 - 88 * q^94 + 48 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/372\mathbb{Z}\right)^\times$.

$n$	$125$	$187$	$313$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.09739	+	0.892042i	−0.775971	+	0.630769i
$2$	−1.09739	+	0.892042i	−0.775971	+	0.630769i
$3$	−1.68099	−	0.417450i	−0.970521	−	0.241015i
$3$	−1.68099	−	0.417450i	−0.970521	−	0.241015i
$4$	0.408523	−	1.95783i	0.204262	−	0.978916i
$5$	0.0699686	−	0.0403964i	0.0312909	−	0.0180658i	−0.484273	−	0.874917i	$-0.660916\pi$
$5$	0.0699686	−	0.0403964i	0.0312909	−	0.0180658i	0.515564	+	0.856851i	$0.327582\pi$
$6$	2.21708	−	1.04141i	0.905121	−	0.425154i
$7$	−0.885120	−	0.511024i	−0.334544	−	0.193149i	0.323313	−	0.946292i	$-0.395203\pi$
$7$	−0.885120	−	0.511024i	−0.334544	−	0.193149i	−0.657857	+	0.753143i	$0.728537\pi$
$8$	1.29816	+	2.51292i	0.458969	+	0.888452i
$9$	2.65147	+	1.40346i	0.883824	+	0.467820i
$10$	−0.0407475	+	0.106745i	−0.0128855	+	0.0337559i
$11$	1.66026	+	2.87565i	0.500587	+	0.867042i	1.00000		0.000677716i	$0.000215724\pi$
$11$	1.66026	+	2.87565i	0.500587	+	0.867042i	−0.499413	+	0.866364i	$0.666451\pi$
$12$	−1.50402	+	3.12056i	−0.434174	+	0.900829i
$13$	−2.04134	−	3.53571i	−0.566166	−	0.980629i	−0.996940	−	0.0781689i	$-0.975093\pi$
$13$	−2.04134	−	3.53571i	−0.566166	−	0.980629i	0.430774	−	0.902460i	$-0.358241\pi$
$14$	1.42717	−	0.228772i	0.381429	−	0.0611418i
$15$	−0.134480	+	0.0386976i	−0.0347226	+	0.00999168i
$16$	−3.66622	−	1.59964i	−0.916554	−	0.399910i
$17$	−4.25631	−	2.45738i	−1.03231	−	0.596002i	−0.114662	−	0.993405i	$-0.536578\pi$
$17$	−4.25631	−	2.45738i	−1.03231	−	0.596002i	−0.917645	+	0.397402i	$0.869912\pi$
$18$	−4.16164	+	0.825081i	−0.980908	+	0.194474i
$19$	−1.55179	−	0.895926i	−0.356005	−	0.205540i	0.311322	−	0.950305i	$-0.399228\pi$
$19$	−1.55179	−	0.895926i	−0.356005	−	0.205540i	−0.667327	+	0.744765i	$0.732562\pi$
$20$	−0.0505056	−	0.153490i	−0.0112934	−	0.0343213i
$21$	1.27455	+	1.22852i	0.278130	+	0.268085i
$22$	−4.38715	−	1.67469i	−0.935344	−	0.357045i
$23$	−3.92474			−0.818364			−0.409182	−	0.912453i	$-0.634186\pi$
$23$	−3.92474			−0.818364			−0.409182	+	0.912453i	$0.634186\pi$
$24$	−1.13318	−	4.76612i	−0.231309	−	0.972880i
$25$	−2.49674	+	4.32447i	−0.499347	+	0.864895i
$26$	5.39414	+	2.05908i	1.05788	+	0.403819i
$27$	−3.87123	−	3.46606i	−0.745018	−	0.667044i
$28$	−1.36209	+	1.52415i	−0.257411	+	0.288037i
$29$		−	4.36102i		−	0.809821i	−0.914356	−	0.404911i	$-0.867303\pi$
$29$		−	4.36102i		−	0.809821i	0.914356	−	0.404911i	$-0.132697\pi$
$30$	0.113057	−	0.162428i	0.0206413	−	0.0296552i
$31$	−3.43111	−	4.38491i	−0.616246	−	0.787554i
$31$	−3.43111	−	4.38491i	−0.616246	−	0.787554i
$32$	5.45021	−	1.51499i	0.963470	−	0.267815i
$33$	−1.59044	−	5.52702i	−0.276860	−	0.962131i
$34$	6.86291	−	1.10010i	1.17698	−	0.188666i
$35$	−0.0825741			−0.0139576
$36$	3.83093	−	4.61779i	0.638488	−	0.769632i
$37$	4.39260	−	7.60821i	0.722139	−	1.25078i	−0.238001	−	0.971265i	$-0.576492\pi$
$37$	4.39260	−	7.60821i	0.722139	−	1.25078i	0.960141	−	0.279517i	$-0.0901744\pi$
$38$	2.50212	−	0.401082i	0.405897	−	0.0650641i
$39$	1.95550	+	6.79566i	0.313130	+	1.08818i
$40$	0.192343	+	0.123385i	0.0304122	+	0.0195088i
$41$	−9.29867	+	5.36859i	−1.45221	+	0.838433i	−0.998607	−	0.0527710i	$-0.983195\pi$
$41$	−9.29867	+	5.36859i	−1.45221	+	0.838433i	−0.453602	+	0.891204i	$0.649861\pi$
$42$	−2.49457	−	0.211211i	−0.384921	−	0.0325905i
$43$	0.921465	+	0.532008i	0.140522	+	0.0811305i	0.568613	−	0.822605i	$-0.307480\pi$
$43$	0.921465	+	0.532008i	0.140522	+	0.0811305i	−0.428091	+	0.903736i	$0.640814\pi$
$44$	6.30830	−	2.07574i	0.951012	−	0.312929i
$45$	0.242214	−	0.00891169i	0.0361072	−	0.00132848i
$46$	4.30696	−	3.50103i	0.635027	−	0.516199i
$47$	−6.73110			−0.981832			−0.490916	−	0.871207i	$-0.663338\pi$
$47$	−6.73110			−0.981832			−0.490916	+	0.871207i	$0.663338\pi$
$48$	5.49511	+	4.21945i	0.793151	+	0.609024i
$49$	−2.97771	−	5.15754i	−0.425387	−	0.736792i
$50$	−1.11772	−	6.97282i	−0.158070	−	0.986106i
$51$	6.12899	+	5.90763i	0.858230	+	0.827234i
$52$	−7.75626	+	2.55219i	−1.07560	+	0.353925i
$53$	−5.15428	+	2.97582i	−0.707994	+	0.408761i	−0.810318	−	0.585990i	$-0.800706\pi$
$53$	−5.15428	+	2.97582i	−0.707994	+	0.408761i	0.102324	+	0.994751i	$0.467372\pi$
$54$	7.34011	+	0.350321i	0.998863	+	0.0476726i
$55$	0.232332	+	0.134137i	0.0313276	+	0.0180870i
$56$	0.135137	−	2.88763i	0.0180585	−	0.385876i
$57$	2.23454	+	2.15384i	0.295972	+	0.285283i
$58$	3.89021	+	4.78574i	0.510810	+	0.628398i
$59$	−0.988055	+	1.71136i	−0.128634	+	0.222800i	−0.923148	−	0.384446i	$-0.874393\pi$
$59$	−0.988055	+	1.71136i	−0.128634	+	0.222800i	0.794514	+	0.607246i	$0.207726\pi$
$60$	0.0208252	+	0.279098i	0.00268852	+	0.0360314i
$61$	5.22147			0.668541			0.334270	−	0.942477i	$-0.391510\pi$
$61$	5.22147			0.668541			0.334270	+	0.942477i	$0.391510\pi$
$62$	7.67679	+	1.75126i	0.974953	+	0.222410i
$63$	−1.62967	−	2.59720i	−0.205319	−	0.327216i
$64$	−4.62956	+	6.52435i	−0.578695	+	0.815544i
$65$	−0.285660	−	0.164926i	−0.0354317	−	0.0204565i
$66$	6.67567	+	4.64655i	0.821718	+	0.571951i
$67$	−2.80149	+	1.61744i	−0.342256	+	0.197602i	−0.661269	−	0.750149i	$-0.729982\pi$
$67$	−2.80149	+	1.61744i	−0.342256	+	0.197602i	0.319013	+	0.947750i	$0.396649\pi$
$68$	−6.54994	+	7.32924i	−0.794297	+	0.888801i
$69$	6.59745	+	1.63838i	0.794240	+	0.197238i
$70$	0.0906158	−	0.0736595i	0.0108307	−	0.00880400i
$71$	−0.617822	−	1.07010i	−0.0733219	−	0.126997i	0.827033	−	0.562153i	$-0.190027\pi$
$71$	−0.617822	−	1.07010i	−0.0733219	−	0.126997i	−0.900355	+	0.435156i	$0.856693\pi$
$72$	−0.0847550	+	8.48486i	−0.00998847	+	0.999950i
$73$	0.663259	+	1.14880i	0.0776286	+	0.134457i	0.902226	−	0.431263i	$-0.141932\pi$
$73$	0.663259	+	1.14880i	0.0776286	+	0.134457i	−0.824598	+	0.565719i	$0.808599\pi$
$74$	1.96645	+	12.2675i	0.228595	+	1.42607i
$75$	6.00225	−	6.22715i	0.693080	−	0.719049i
$76$	−2.38802	+	2.67214i	−0.273924	+	0.306515i
$77$		−	3.39373i		−	0.386751i
$78$	−8.20795	−	5.71309i	−0.929367	−	0.646880i
$79$	13.1653	+	7.60097i	1.48121	+	0.855176i	0.999773	−	0.0213047i	$-0.00678202\pi$
$79$	13.1653	+	7.60097i	1.48121	+	0.855176i	0.481436	+	0.876481i	$0.340115\pi$
$80$	−0.321140	+	0.0361774i	−0.0359045	+	0.00404475i
$81$	5.06060	+	7.44247i	0.562289	+	0.826941i
$82$	5.41525	−	14.1862i	0.598014	−	1.56661i
$83$	−4.14834	−	7.18513i	−0.455339	−	0.788670i	0.543369	−	0.839494i	$-0.317149\pi$
$83$	−4.14834	−	7.18513i	−0.455339	−	0.788670i	−0.998708	+	0.0508239i	$0.983815\pi$
$84$	2.92592	−	1.99348i	0.319244	−	0.217507i
$85$	−0.397077			−0.0430691
$86$	−1.48578	+	0.238166i	−0.160216	+	0.0256821i
$87$	−1.82051	+	7.33084i	−0.195179	+	0.785949i
$88$	−5.07101	+	7.90516i	−0.540572	+	0.842693i
$89$			4.85111i			0.514217i	0.966383	+	0.257108i	$0.0827697\pi$
$89$			4.85111i			0.514217i	−0.966383	+	0.257108i	$0.917230\pi$
$90$	−0.257854	+	0.225845i	−0.0271802	+	0.0238061i
$91$			4.17270i			0.437418i
$92$	−1.60335	+	7.68398i	−0.167160	+	0.801110i
$93$	3.93719	+	8.80333i	0.408267	+	0.912862i
$94$	7.38663	−	6.00442i	0.761873	−	0.619309i
$95$	−0.144769			−0.0148530
$96$	−9.79420	+	0.271500i	−0.999616	+	0.0277099i
$97$	−8.59029			−0.872212			−0.436106	−	0.899895i	$-0.643643\pi$
$97$	−8.59029			−0.872212			−0.436106	+	0.899895i	$0.643643\pi$
$98$	7.86845	+	3.00359i	0.794833	+	0.303408i
$99$	0.366263	+	9.95482i	0.0368108	+	1.00050i
$100$	7.44662	+	6.65484i	0.744662	+	0.665484i
$101$			3.70165i			0.368328i	0.982896	+	0.184164i	$0.0589578\pi$
$101$			3.70165i			0.368328i	−0.982896	+	0.184164i	$0.941042\pi$
$102$	−11.9957	−	1.01566i	−1.18776	−	0.100565i
$103$	−7.04197	+	4.06568i	−0.693865	+	0.400603i	−0.805059	−	0.593195i	$-0.797866\pi$
$103$	−7.04197	+	4.06568i	−0.693865	+	0.400603i	0.111193	+	0.993799i	$0.464533\pi$
$104$	6.23497	−	9.71965i	0.611389	−	0.953090i
$105$	0.138806	+	0.0344705i	0.0135461	+	0.00336398i
$106$	3.00169	−	7.86346i	0.291549	−	0.763767i
$107$	9.88250	−	17.1170i	0.955378	−	1.65476i	0.221876	−	0.975075i	$-0.428782\pi$
$107$	9.88250	−	17.1170i	0.955378	−	1.65476i	0.733501	−	0.679688i	$-0.237885\pi$
$108$	−8.36746	+	6.16325i	−0.805159	+	0.593059i
$109$	−4.40708			−0.422121			−0.211061	−	0.977473i	$-0.567692\pi$
$109$	−4.40708			−0.422121			−0.211061	+	0.977473i	$0.567692\pi$
$110$	−0.374614	+	0.0600494i	−0.0357180	+	0.00572549i
$111$	−10.5600	+	10.9557i	−1.00231	+	1.03986i
$112$	2.42759	+	3.28940i	0.229385	+	0.310819i
$113$	12.1445	−	7.01163i	1.14246	−	0.659598i	0.195420	−	0.980720i	$-0.437393\pi$
$113$	12.1445	−	7.01163i	1.14246	−	0.659598i	0.947038	+	0.321121i	$0.104060\pi$
$114$	−4.37348	−	0.370294i	−0.409614	−	0.0346812i
$115$	−0.274608	+	0.158545i	−0.0256074	+	0.0147844i
$116$	−8.53815	−	1.78158i	−0.792747	−	0.165415i
$117$	−0.450332	−	12.2398i	−0.0416332	−	1.13157i
$118$	−0.442326	−	2.75942i	−0.0407194	−	0.254025i
$119$	2.51156	+	4.35015i	0.230234	+	0.398778i
$120$	−0.271821	−	0.287702i	−0.0248137	−	0.0262635i
$121$	−0.0129173	+	0.0223734i	−0.00117430	+	0.00203394i
$122$	−5.72998	+	4.65777i	−0.518768	+	0.421695i
$123$	17.8721	−	5.14283i	1.61147	−	0.463713i
$124$	−9.98662	+	4.92620i	−0.896825	+	0.442386i
$125$			0.807400i			0.0722161i
$126$	4.10519	+	1.39640i	0.365719	+	0.124401i
$127$	4.72831	+	2.72989i	0.419570	+	0.242239i	0.694893	−	0.719113i	$-0.255452\pi$
$127$	4.72831	+	2.72989i	0.419570	+	0.242239i	−0.275323	+	0.961352i	$0.588785\pi$
$128$	−0.739564	−	11.2895i	−0.0653689	−	0.997861i
$129$	−1.32689	−	1.27897i	−0.116826	−	0.112607i
$130$	0.460600	−	0.0738327i	0.0403973	−	0.00647556i
$131$	−3.36161	+	5.82249i	−0.293706	+	0.508713i	−0.974683	−	0.223591i	$-0.928222\pi$
$131$	−3.36161	+	5.82249i	−0.293706	+	0.508713i	0.680977	+	0.732304i	$0.261555\pi$
$132$	−11.4707	+	0.855900i	−0.998398	+	0.0744965i
$133$	0.915680	+	1.58600i	0.0793995	+	0.137524i
$134$	1.63150	−	4.27400i	0.140940	−	0.369217i
$135$	−0.410881	−	0.0861319i	−0.0353630	−	0.00741305i
$136$	0.649840	−	13.8858i	0.0557233	−	1.19070i
$137$	−5.44953	+	3.14628i	−0.465584	+	0.268805i	−0.714389	−	0.699748i	$-0.753295\pi$
$137$	−5.44953	+	3.14628i	−0.465584	+	0.268805i	0.248805	+	0.968554i	$0.419962\pi$
$138$	−8.70147	+	4.08726i	−0.740719	+	0.347931i
$139$		−	17.2738i		−	1.46515i	−0.680688	−	0.732574i	$-0.738319\pi$
$139$		−	17.2738i		−	1.46515i	0.680688	−	0.732574i	$-0.261681\pi$
$140$	−0.0337334	+	0.161666i	−0.00285099	+	0.0136633i
$141$	11.3149	+	2.80990i	0.952889	+	0.236636i
$142$	1.63256	+	0.623191i	0.137002	+	0.0522970i
$143$	6.77831	−	11.7404i	0.566831	−	0.981780i
$144$	−7.47584	−	9.38679i	−0.622987	−	0.782233i
$145$	−0.176169	−	0.305134i	−0.0146301	−	0.0253400i
$146$	−1.75263	−	0.669023i	−0.145049	−	0.0553687i
$147$	2.85249	+	9.91283i	0.235269	+	0.817597i
$148$	−13.1011	−	11.7081i	−1.07691	−	0.962401i
$149$	4.74707	+	2.74072i	0.388895	+	0.224529i	0.681681	−	0.731649i	$-0.261249\pi$
$149$	4.74707	+	2.74072i	0.388895	+	0.224529i	−0.292786	+	0.956178i	$0.594582\pi$
$150$	−1.03192	+	12.1879i	−0.0842561	+	0.995134i
$151$			6.03289i			0.490950i	0.969403	+	0.245475i	$0.0789439\pi$
$151$			6.03289i			0.490950i	−0.969403	+	0.245475i	$0.921056\pi$
$152$	0.236922	−	5.06258i	0.0192170	−	0.410630i
$153$	−7.83664	−	12.4892i	−0.633555	−	1.00969i
$154$	3.02735	+	3.72424i	0.243951	+	0.300108i
$155$	−0.417205	−	0.168202i	−0.0335107	−	0.0135103i
$156$	14.1036	−	1.05236i	1.12919	−	0.0842560i
$157$	19.3755			1.54633			0.773165	−	0.634205i	$-0.218673\pi$
$157$	19.3755			1.54633			0.773165	+	0.634205i	$0.218673\pi$
$158$	−21.2278	+	3.40275i	−1.68879	+	0.270708i
$159$	9.90656	−	2.85068i	0.785641	−	0.226074i
$160$	0.320143	−	0.326171i	0.0253095	−	0.0257860i
$161$	3.47386	+	2.00564i	0.273779	+	0.158066i
$162$	−12.1924	−	3.65302i	−0.957928	−	0.287008i
$163$			6.97002i			0.545934i	0.962023	+	0.272967i	$0.0880050\pi$
$163$			6.97002i			0.545934i	−0.962023	+	0.272967i	$0.911995\pi$
$164$	6.71208	+	20.3984i	0.524125	+	1.59285i
$165$	−0.334553	−	0.322470i	−0.0260449	−	0.0251043i
$166$	10.9618	+	4.18439i	0.850798	+	0.324772i
$167$	7.92451	−	13.7256i	0.613217	−	1.06212i	−0.377478	−	0.926019i	$-0.623209\pi$
$167$	7.92451	−	13.7256i	0.613217	−	1.06212i	0.990695	−	0.136104i	$-0.0434581\pi$
$168$	−1.43261	+	4.79767i	−0.110528	+	0.370148i
$169$	−1.83415	+	3.17684i	−0.141089	+	0.244373i
$170$	0.435748	−	0.354209i	0.0334203	−	0.0271666i
$171$	−2.85713	−	4.55340i	−0.218490	−	0.348207i
$172$	1.41802	−	1.58674i	0.108123	−	0.120988i
$173$	−4.94753	+	2.85646i	−0.376154	+	0.217172i	−0.676143	−	0.736770i	$-0.736350\pi$
$173$	−4.94753	+	2.85646i	−0.376154	+	0.217172i	0.299990	+	0.953942i	$0.403017\pi$
$174$	−4.54161	−	9.66875i	−0.344299	−	0.732986i
$175$	4.41982	−	2.55178i	0.334107	−	0.192897i
$176$	−1.48686	−	13.1986i	−0.112076	−	0.994881i
$177$	2.37532	−	2.46432i	0.178540	−	0.185230i
$178$	−4.32739	−	5.32355i	−0.324352	−	0.399017i
$179$	11.0582	−	19.1534i	0.826530	−	1.43159i	−0.0742136	−	0.997242i	$-0.523645\pi$
$179$	11.0582	−	19.1534i	0.826530	−	1.43159i	0.900744	−	0.434350i	$-0.143022\pi$
$180$	0.0815026	−	0.477856i	0.00607484	−	0.0356173i
$181$	1.87663	+	3.25041i	0.139489	+	0.241601i	0.927303	−	0.374311i	$-0.122121\pi$
$181$	1.87663	+	3.25041i	0.139489	+	0.241601i	−0.787815	+	0.615913i	$0.788787\pi$
$182$	−3.72222	−	4.57907i	−0.275909	−	0.339423i
$183$	−8.77725	−	2.17970i	−0.648833	−	0.161128i
$184$	−5.09494	−	9.86256i	−0.375604	−	0.727078i
$185$		−	0.709781i		−	0.0521841i
$186$	−12.1736	−	6.14853i	−0.892609	−	0.450832i
$187$		−	16.3196i		−	1.19340i
$188$	−2.74981	+	13.1784i	−0.200551	+	0.961132i
$189$	1.65526	+	5.04617i	0.120402	+	0.367055i
$190$	0.158867	−	0.129140i	0.0115255	−	0.00936878i
$191$	−7.07279	−	12.2504i	−0.511769	−	0.886411i	−0.999907	−	0.0136440i	$-0.995657\pi$
$191$	−7.07279	−	12.2504i	−0.511769	−	0.886411i	0.488137	−	0.872767i	$-0.337676\pi$
$192$	10.5058	−	9.03477i	0.758194	−	0.652029i
$193$	−12.8446	+	22.2476i	−0.924578	+	1.60142i	−0.132338	+	0.991205i	$0.542249\pi$
$193$	−12.8446	+	22.2476i	−0.924578	+	1.60142i	−0.792239	+	0.610211i	$0.791085\pi$
$194$	9.42689	−	7.66290i	0.676811	−	0.550164i
$195$	0.411343	+	0.396487i	0.0294569	+	0.0283930i
$196$	−11.3141	+	3.72288i	−0.808148	+	0.265920i
$197$	−9.12501	+	5.26833i	−0.650130	+	0.375353i	−0.788506	−	0.615027i	$-0.789145\pi$
$197$	−9.12501	+	5.26833i	−0.650130	+	0.375353i	0.138376	+	0.990380i	$0.455812\pi$
$198$	−9.28204	−	10.5976i	−0.659646	−	0.753137i
$199$	2.14743	−	1.23982i	0.152227	−	0.0878885i	−0.421951	−	0.906618i	$-0.638655\pi$
$199$	2.14743	−	1.23982i	0.152227	−	0.0878885i	0.574179	+	0.818730i	$0.305321\pi$
$200$	−14.1082	−	0.660247i	−0.997603	−	0.0466865i
$201$	5.38448	−	1.54942i	0.379792	−	0.109288i
$202$	−3.30203	−	4.06215i	−0.232330	−	0.285812i
$203$	−2.22859	+	3.86003i	−0.156416	+	0.270921i
$204$	14.0700	−	9.58613i	0.985097	−	0.671163i
$205$	−0.433743	+	0.751265i	−0.0302939	+	0.0524707i
$206$	4.10102	−	10.7434i	0.285731	−	0.748525i
$207$	−10.4063	−	5.50821i	−0.723290	−	0.382847i
$208$	1.82814	+	16.2281i	0.126759	+	1.12522i
$209$		−	5.94988i		−	0.411562i
$210$	−0.183074	+	0.0859935i	−0.0126333	+	0.00593412i
$211$	−9.11022	−	5.25979i	−0.627173	−	0.362099i	0.152483	−	0.988306i	$-0.451273\pi$
$211$	−9.11022	−	5.25979i	−0.627173	−	0.362099i	−0.779657	+	0.626207i	$0.784606\pi$
$212$	3.72052	+	11.3069i	0.255526	+	0.776561i
$213$	0.591841	+	2.05674i	0.0405523	+	0.140925i
$214$	4.42413	+	27.5996i	0.302427	+	1.88667i
$215$	0.0859648			0.00586275
$216$	3.68448	−	14.2276i	0.250697	−	0.968066i
$217$	0.796147	+	5.63455i	0.0540460	+	0.382498i
$218$	4.83627	−	3.93130i	0.327554	−	0.266261i
$219$	−0.635367	−	2.20800i	−0.0429341	−	0.149203i
$220$	0.357530	−	0.400069i	0.0241047	−	0.0269726i
$221$			20.0654i			1.34975i
$222$	1.81550	−	21.4425i	0.121848	−	1.43913i
$223$	−1.91744	−	1.10704i	−0.128401	−	0.0741326i	0.434423	−	0.900709i	$-0.356952\pi$
$223$	−1.91744	−	1.10704i	−0.128401	−	0.0741326i	−0.562825	+	0.826576i	$0.690285\pi$
$224$	−5.59829	−	1.44424i	−0.374051	−	0.0964973i
$225$	−12.6893	+	7.96215i	−0.845950	+	0.530810i
$226$	−7.07256	+	18.5279i	−0.470460	+	1.23246i
$227$	7.15749	+	12.3971i	0.475059	+	0.822827i	0.999592	−	0.0285633i	$-0.00909322\pi$
$227$	7.15749	+	12.3971i	0.475059	+	0.822827i	−0.524533	+	0.851390i	$0.675760\pi$
$228$	5.12972	−	3.49497i	0.339724	−	0.231460i
$229$	10.1538	−	17.5869i	0.670983	−	1.16218i	−0.306643	−	0.951825i	$-0.599206\pi$
$229$	10.1538	−	17.5869i	0.670983	−	1.16218i	0.977626	−	0.210352i	$-0.0674609\pi$
$230$	0.159923	−	0.418948i	0.0105450	−	0.0276246i
$231$	−1.41671	+	5.70483i	−0.0932128	+	0.375350i
$232$	10.9589	−	5.66130i	0.719488	−	0.371683i
$233$		−	0.148084i		−	0.00970132i	−0.999988	−	0.00485066i	$-0.998456\pi$
$233$		−	0.148084i		−	0.00970132i	0.999988	−	0.00485066i	$-0.00154402\pi$
$234$	11.4126	+	13.0301i	0.746063	+	0.851802i
$235$	−0.470966	+	0.271912i	−0.0307224	+	0.0177376i
$236$	2.94692	+	2.63358i	0.191828	+	0.171431i
$237$	−18.9577	−	18.2730i	−1.23143	−	1.18696i
$238$	−6.63668	−	2.53339i	−0.430192	−	0.164215i
$239$	11.3395	+	19.6407i	0.733494	+	1.27045i	0.955381	+	0.295377i	$0.0954451\pi$
$239$	11.3395	+	19.6407i	0.733494	+	1.27045i	−0.221887	+	0.975072i	$0.571222\pi$
$240$	0.554936	+	0.0732459i	0.0358209	+	0.00472800i
$241$	−10.8876	+	18.8580i	−0.701335	+	1.21475i	0.266663	+	0.963790i	$0.414079\pi$
$241$	−10.8876	+	18.8580i	−0.701335	+	1.21475i	−0.967998	+	0.250958i	$0.919254\pi$
$242$	−0.00578272	−	0.0360750i	−0.000371727	−	0.00231899i
$243$	−5.39997	−	14.6233i	−0.346408	−	0.938084i
$244$	2.13309	−	10.2228i	0.136557	−	0.654446i
$245$	−0.416692	−	0.240577i	−0.0266215	−	0.0153699i
$246$	−15.0250	+	21.5864i	−0.957962	+	1.37630i
$247$			7.31557i			0.465478i
$248$	6.56482	−	14.3144i	0.416867	−	0.908968i
$249$	3.97389	+	13.8099i	0.251835	+	0.875165i
$250$	−0.720235	−	0.886032i	−0.0455516	−	0.0560376i
$251$	−6.68695	+	11.5821i	−0.422076	+	0.731058i	−0.996142	−	0.0877514i	$-0.972032\pi$
$251$	−6.68695	+	11.5821i	−0.422076	+	0.731058i	0.574066	+	0.818809i	$0.305365\pi$
$252$	−5.75063	+	2.12960i	−0.362256	+	0.134152i
$253$	−6.51608	−	11.2862i	−0.409662	−	0.709556i
$254$	−7.62397	+	1.22210i	−0.478371	+	0.0766813i
$255$	0.667484	+	0.165760i	0.0417994	+	0.0103803i
$256$	10.8823	+	11.7293i	0.680144	+	0.733079i
$257$	−18.3163	+	10.5749i	−1.14254	+	0.659646i	−0.947058	−	0.321062i	$-0.895960\pi$
$257$	−18.3163	+	10.5749i	−1.14254	+	0.659646i	−0.195482	+	0.980707i	$0.562627\pi$
$258$	2.59701	+	0.219884i	0.161683	+	0.0136894i
$259$	−7.77596	+	4.48945i	−0.483175	+	0.278961i
$260$	−0.439595	+	0.491898i	−0.0272625	+	0.0305062i
$261$	6.12052	−	11.5631i	0.378851	−	0.715739i
$262$	−1.50490	−	9.38823i	−0.0929733	−	0.580007i
$263$	−17.4368			−1.07520			−0.537600	−	0.843200i	$-0.680669\pi$
$263$	−17.4368			−1.07520			−0.537600	+	0.843200i	$0.680669\pi$
$264$	11.8243	−	11.1716i	0.727738	−	0.687565i
$265$	−0.240425	+	0.416428i	−0.0147692	+	0.0255810i
$266$	−2.41964	−	0.923638i	−0.148358	−	0.0566319i
$267$	2.02510	−	8.15468i	0.123934	−	0.499058i
$268$	2.02220	+	6.14560i	0.123526	+	0.375402i
$269$	21.9565	−	12.6766i	1.33871	−	0.772905i	0.352094	−	0.935965i	$-0.385470\pi$
$269$	21.9565	−	12.6766i	1.33871	−	0.772905i	0.986616	+	0.163060i	$0.0521364\pi$
$270$	0.527729	−	0.272003i	0.0321166	−	0.0165535i
$271$		−	25.6530i		−	1.55831i	−0.626833	−	0.779153i	$-0.715649\pi$
$271$		−	25.6530i		−	1.55831i	0.626833	−	0.779153i	$-0.284351\pi$
$272$	11.6736	+	15.8179i	0.707818	+	0.959098i
$273$	1.74189	−	7.01428i	0.105424	−	0.424523i
$274$	3.17363	−	8.31390i	0.191726	−	0.502261i
$275$	−16.5809			−0.999867
$276$	5.90289	−	12.2474i	0.355312	−	0.737206i
$277$	0.843413			0.0506758			0.0253379	−	0.999679i	$-0.491934\pi$
$277$	0.843413			0.0506758			0.0253379	+	0.999679i	$0.491934\pi$
$278$	15.4090	+	18.9561i	0.924169	+	1.13691i
$279$	−2.94344	−	16.4419i	−0.176219	−	0.984351i
$280$	−0.107194	−	0.207502i	−0.00640609	−	0.0124006i
$281$		−	22.4299i		−	1.33806i	−0.743237	−	0.669028i	$-0.766711\pi$
$281$		−	22.4299i		−	1.33806i	0.743237	−	0.669028i	$-0.233289\pi$
$282$	−14.9234	+	7.00984i	−0.888677	+	0.417430i
$283$			28.8219i			1.71329i	0.515909	+	0.856643i	$0.327454\pi$
$283$			28.8219i			1.71329i	−0.515909	+	0.856643i	$0.672546\pi$
$284$	−2.34747	+	0.772431i	−0.139297	+	0.0458354i
$285$	0.243355	+	0.0604337i	0.0144151	+	0.00357978i
$286$	3.03447	+	18.9303i	0.179432	+	1.11937i
$287$	10.9739			0.647770
$288$	16.5773	+	3.63220i	0.976827	+	0.214029i
$289$	3.57744	+	6.19631i	0.210438	+	0.364489i
$290$	0.465519	+	0.177701i	0.0273362	+	0.0104349i
$291$	14.4402	+	3.58602i	0.846500	+	0.210216i
$292$	2.52011	−	0.829239i	0.147478	−	0.0485275i
$293$	27.2558	+	15.7361i	1.59230	+	0.919314i	0.992912	+	0.118855i	$0.0379225\pi$
$293$	27.2558	+	15.7361i	1.59230	+	0.919314i	0.599388	+	0.800459i	$0.295411\pi$
$294$	−11.9730	−	8.33369i	−0.698277	−	0.486031i
$295$			0.159655i			0.00929550i
$296$	24.8211	+	1.16160i	1.44270	+	0.0675165i
$297$	3.53995	−	16.8869i	0.205409	−	0.979875i
$298$	−7.65422	+	1.22695i	−0.443397	+	0.0710752i
$299$	8.01173	+	13.8767i	0.463330	+	0.802512i
$300$	−9.73965	−	14.2953i	−0.562319	−	0.825341i
$301$	−0.543738	−	0.941782i	−0.0313405	−	0.0542834i
$302$	−5.38159	−	6.62042i	−0.309676	−	0.380963i
$303$	1.54526	−	6.22245i	0.0887726	−	0.357470i
$304$	4.25604	+	5.76697i	0.244101	+	0.330758i
$305$	0.365339	−	0.210928i	0.0209192	−	0.0120777i
$306$	19.7408	+	6.71493i	1.12850	+	0.383867i
$307$	4.19427	+	2.42156i	0.239380	+	0.138206i	0.614892	−	0.788612i	$-0.289200\pi$
$307$	4.19427	+	2.42156i	0.239380	+	0.138206i	−0.375512	+	0.926818i	$0.622533\pi$
$308$	−6.64435	−	1.38642i	−0.378597	−	0.0789984i
$309$	13.5347	−	3.89471i	0.769963	−	0.221562i
$310$	0.607879	−	0.187581i	0.0345252	−	0.0106539i
$311$	−18.9460			−1.07433			−0.537166	−	0.843477i	$-0.680505\pi$
$311$	−18.9460			−1.07433			−0.537166	+	0.843477i	$0.680505\pi$
$312$	−14.5384	+	13.7359i	−0.823075	+	0.777640i
$313$	−12.9513	+	22.4322i	−0.732048	+	1.26794i	0.223958	+	0.974599i	$0.428102\pi$
$313$	−12.9513	+	22.4322i	−0.732048	+	1.26794i	−0.956006	+	0.293346i	$0.905231\pi$
$314$	−21.2624	+	17.2837i	−1.19991	+	0.975376i
$315$	−0.218943	−	0.115889i	−0.0123360	−	0.00652963i
$316$	20.2598	−	22.6702i	1.13970	−	1.27530i
$317$	−24.9534	−	14.4069i	−1.40152	−	0.809170i	−0.406974	−	0.913440i	$-0.633416\pi$
$317$	−24.9534	−	14.4069i	−1.40152	−	0.809170i	−0.994549	+	0.104270i	$0.966750\pi$
$318$	−8.32841	+	11.9654i	−0.467034	+	0.670985i
$319$	12.5408	−	7.24042i	0.702149	−	0.405386i
$320$	−0.0603638	+	0.643517i	−0.00337444	+	0.0359737i
$321$	−23.7579	+	24.6481i	−1.32604	+	1.37572i
$322$	−5.60129	+	0.897869i	−0.312148	+	0.0500363i
$323$	4.40326	+	7.62668i	0.245004	+	0.424360i
$324$	16.6385	−	6.86738i	0.924360	−	0.381521i
$325$	20.3868			1.13085
$326$	−6.21755	−	7.64882i	−0.344358	−	0.423629i
$327$	7.40826	+	1.83973i	0.409678	+	0.101738i
$328$	−25.5620	−	16.3976i	−1.41143	−	0.905404i
$329$	5.95783	+	3.43976i	0.328466	+	0.189640i
$330$	0.654791	+	0.0554399i	0.0360451	+	0.00305187i
$331$	−8.45629	+	4.88224i	−0.464800	+	0.268352i	−0.714060	−	0.700084i	$-0.753146\pi$
$331$	−8.45629	+	4.88224i	−0.464800	+	0.268352i	0.249260	+	0.968436i	$0.419812\pi$
$332$	−15.7620	+	5.18646i	−0.865051	+	0.284644i
$333$	22.3247	−	14.0081i	1.22339	−	0.767640i
$334$	3.54759	+	22.1314i	0.194115	+	1.21097i
$335$	−0.130677	+	0.226340i	−0.00713966	+	0.0123663i
$336$	−2.70760	−	6.54285i	−0.147711	−	0.356942i
$337$	12.0538			0.656615			0.328307	−	0.944571i	$-0.393522\pi$
$337$	12.0538			0.656615			0.328307	+	0.944571i	$0.393522\pi$
$338$	−0.821100	−	5.12237i	−0.0446620	−	0.278620i
$339$	−23.3418	+	6.71677i	−1.26775	+	0.364805i
$340$	−0.162215	+	0.777411i	−0.00879735	+	0.0421610i
$341$	6.91296	−	17.1468i	0.374358	−	0.928550i
$342$	7.19720	+	2.44817i	0.389180	+	0.132382i
$343$			13.2411i			0.714950i
$344$	−0.140687	+	3.00620i	−0.00758531	+	0.162084i
$345$	0.527799	−	0.151878i	0.0284157	−	0.00817684i
$346$	2.88128	−	7.54804i	0.154899	−	0.405785i
$347$	−15.6929	+	27.1809i	−0.842439	+	1.45915i	0.0453882	+	0.998969i	$0.485548\pi$
$347$	−15.6929	+	27.1809i	−0.842439	+	1.45915i	−0.887827	+	0.460177i	$0.847786\pi$
$348$	13.6088	+	6.55907i	0.729511	+	0.351603i
$349$	−19.7618			−1.05783			−0.528913	−	0.848676i	$-0.677400\pi$
$349$	−19.7618			−1.05783			−0.528913	+	0.848676i	$0.677400\pi$
$350$	−2.57396	+	6.74296i	−0.137584	+	0.360427i
$351$	−4.35249	+	20.7629i	−0.232318	+	1.10824i
$352$	13.4054	+	13.1576i	0.714508	+	0.701304i
$353$	−3.68299	−	2.12638i	−0.196026	−	0.113176i	0.398774	−	0.917049i	$-0.369436\pi$
$353$	−3.68299	−	2.12638i	−0.196026	−	0.113176i	−0.594801	+	0.803873i	$0.702769\pi$
$354$	−0.408372	+	4.82321i	−0.0217047	+	0.256350i
$355$	−0.0864562	−	0.0499155i	−0.00458862	−	0.00264924i
$356$	9.49766	+	1.98179i	0.503375	+	0.105035i
$357$	−2.40595	−	8.36102i	−0.127336	−	0.442512i
$358$	4.95047	+	30.8831i	0.261640	+	1.63222i
$359$	7.55155	+	13.0797i	0.398556	+	0.690319i	0.993548	−	0.113413i	$-0.0361782\pi$
$359$	7.55155	+	13.0797i	0.398556	+	0.690319i	−0.594992	+	0.803731i	$0.702845\pi$
$360$	0.336827	+	0.597097i	0.0177524	+	0.0314698i
$361$	−7.89463	−	13.6739i	−0.415507	−	0.719679i
$362$	−4.95890	−	1.89294i	−0.260634	−	0.0994906i
$363$	0.0310536	−	0.0322172i	0.00162989	−	0.00169096i
$364$	8.16945	+	1.70464i	0.428195	+	0.0893476i
$365$	0.0928145	+	0.0535865i	0.00485813	+	0.00280485i
$366$	11.5764	−	5.43769i	0.605110	−	0.284233i
$367$	12.7335	−	7.35166i	0.664681	−	0.383754i	−0.129377	−	0.991595i	$-0.541298\pi$
$367$	12.7335	−	7.35166i	0.664681	−	0.383754i	0.794058	+	0.607842i	$0.207965\pi$
$368$	14.3889	+	6.27817i	0.750075	+	0.327272i
$369$	−32.1898	+	1.18434i	−1.67573	+	0.0616545i
$370$	0.633154	+	0.778905i	0.0329161	+	0.0404934i
$371$	6.08287			0.315807
$372$	18.8439	−	4.11199i	0.977009	−	0.213197i
$373$	37.9735			1.96619			0.983097	−	0.183086i	$-0.0586086\pi$
$373$	37.9735			1.96619			0.983097	+	0.183086i	$0.0586086\pi$
$374$	14.5577	+	17.9089i	0.752762	+	0.926047i
$375$	0.337049	−	1.35723i	0.0174051	−	0.0700872i
$376$	−8.73805	−	16.9147i	−0.450630	−	0.872311i
$377$	−15.4193	+	8.90234i	−0.794134	+	0.458494i
$378$	−6.31786	−	4.06105i	−0.324955	−	0.208878i
$379$	7.52182	+	4.34273i	0.386370	+	0.223071i	0.680586	−	0.732668i	$-0.261725\pi$
$379$	7.52182	+	4.34273i	0.386370	+	0.223071i	−0.294216	+	0.955739i	$0.595059\pi$
$380$	−0.0591414	+	0.283433i	−0.00303389	+	0.0145398i
$381$	−6.80866	−	6.56276i	−0.348818	−	0.336221i
$382$	18.6895	+	7.13426i	0.956238	+	0.365021i
$383$	4.15974	+	7.20489i	0.212553	+	0.368152i	0.952513	−	0.304499i	$-0.0984889\pi$
$383$	4.15974	+	7.20489i	0.212553	+	0.368152i	−0.739960	+	0.672651i	$0.765156\pi$
$384$	−3.46960	+	19.2863i	−0.177057	+	0.984201i
$385$	−0.137094	−	0.237454i	−0.00698697	−	0.0121018i
$386$	−5.75020	−	35.8722i	−0.292677	−	1.82585i
$387$	1.69659	+	2.70384i	0.0862423	+	0.137444i
$388$	−3.50933	+	16.8184i	−0.178159	+	0.853823i
$389$	−19.4738	−	11.2432i	−0.987363	−	0.570054i	−0.0828777	−	0.996560i	$-0.526411\pi$
$389$	−19.4738	−	11.2432i	−0.987363	−	0.570054i	−0.904485	+	0.426506i	$0.859744\pi$
$390$	−0.805087	−	0.0681652i	−0.0407671	−	0.00345168i
$391$	16.7049	+	9.64457i	0.844803	+	0.487747i
$392$	9.09497	−	14.1781i	0.459365	−	0.716101i
$393$	8.08144	−	8.38425i	0.407655	−	0.422929i
$394$	5.31411	−	13.9213i	0.267721	−	0.701345i
$395$	1.22821			0.0617978
$396$	19.6395	+	3.34969i	0.986922	+	0.168328i
$397$	0.935306	−	1.62000i	0.0469417	−	0.0813053i	−0.841600	−	0.540101i	$-0.818386\pi$
$397$	0.935306	−	1.62000i	0.0469417	−	0.0813053i	0.888542	+	0.458796i	$0.151719\pi$
$398$	−1.25060	+	3.27616i	−0.0626867	+	0.164219i
$399$	−0.877173	−	3.04831i	−0.0439136	−	0.152606i
$400$	16.0712	−	11.8606i	0.803559	−	0.593029i
$401$		−	11.0158i		−	0.550104i	−0.961429	−	0.275052i	$-0.911305\pi$
$401$		−	11.0158i		−	0.550104i	0.961429	−	0.275052i	$-0.0886950\pi$
$402$	−4.52671	+	6.50349i	−0.225772	+	0.324365i
$403$	−8.49971	+	21.0825i	−0.423401	+	1.05019i
$404$	7.24722	+	1.51221i	0.360563	+	0.0752353i
$405$	0.654732	+	0.316309i	0.0325339	+	0.0157175i
$406$	−0.997678	−	6.22394i	−0.0495139	−	0.308889i
$407$	29.1714			1.44597
$408$	−6.88902	+	23.0707i	−0.341057	+	1.14217i
$409$	15.6324	−	27.0761i	0.772972	−	1.33883i	−0.162956	−	0.986633i	$-0.552103\pi$
$409$	15.6324	−	27.0761i	0.772972	−	1.33883i	0.935927	−	0.352193i	$-0.114564\pi$
$410$	−0.194175	−	1.21135i	−0.00958963	−	0.0598242i
$411$	10.4740	−	3.01398i	0.516646	−	0.148669i
$412$	5.08312	+	15.4479i	0.250427	+	0.761064i
$413$	1.74909	−	1.00984i	0.0860673	−	0.0496910i
$414$	16.3333	−	3.23823i	0.802740	−	0.159150i
$415$	−0.580506	−	0.335155i	−0.0284959	−	0.0164521i
$416$	−16.4823	−	16.1777i	−0.808112	−	0.793179i
$417$	−7.21096	+	29.0372i	−0.353122	+	1.42196i
$418$	5.30754	+	6.52933i	0.259600	+	0.319360i
$419$	−20.7520			−1.01380			−0.506900	−	0.862005i	$-0.669209\pi$
$419$	−20.7520			−1.01380			−0.506900	+	0.862005i	$0.669209\pi$
$420$	0.124193	−	0.257678i	0.00606001	−	0.0125734i
$421$	−10.9124	−	18.9009i	−0.531839	−	0.921172i	−0.999309	−	0.0371630i	$-0.988168\pi$
$421$	−10.9124	−	18.9009i	−0.531839	−	0.921172i	0.467470	−	0.884009i	$-0.345165\pi$
$422$	14.6894	−	2.35467i	0.715069	−	0.114623i
$423$	−17.8473	−	9.44684i	−0.867767	−	0.459321i
$424$	−14.1691	−	9.08920i	−0.688112	−	0.441411i
$425$	21.2538	−	12.2709i	1.03096	−	0.595224i
$426$	−2.48417	−	1.72909i	−0.120359	−	0.0837748i
$427$	−4.62163	−	2.66830i	−0.223656	−	0.129128i
$428$	−29.4750	−	26.3410i	−1.42473	−	1.27324i
$429$	−16.2953	+	16.9059i	−0.786745	+	0.816224i
$430$	−0.0943368	+	0.0766842i	−0.00454932	+	0.00369804i
$431$	−11.8952	+	20.6031i	−0.572973	+	0.992418i	0.423286	+	0.905996i	$0.360877\pi$
$431$	−11.8952	+	20.6031i	−0.572973	+	0.992418i	−0.996259	+	0.0864220i	$0.972457\pi$
$432$	8.64831	+	18.8999i	0.416092	+	0.909322i
$433$	13.6603			0.656475			0.328237	−	0.944595i	$-0.393545\pi$
$433$	13.6603			0.656475			0.328237	+	0.944595i	$0.393545\pi$
$434$	−5.89994	−	5.47310i	−0.283206	−	0.262717i
$435$	0.168761	+	0.586471i	0.00809148	+	0.0281191i
$436$	−1.80039	+	8.62832i	−0.0862232	+	0.413221i
$437$	6.09037	+	3.51628i	0.291342	+	0.168206i
$438$	2.66687	+	1.85626i	0.127428	+	0.0886954i
$439$	15.7938	−	9.11854i	0.753796	−	0.435204i	−0.0732681	−	0.997312i	$-0.523343\pi$
$439$	15.7938	−	9.11854i	0.753796	−	0.435204i	0.827064	+	0.562108i	$0.190010\pi$
$440$	−0.0354717	+	0.757963i	−0.00169105	+	0.0361345i
$441$	−0.656901	−	17.8542i	−0.0312810	−	0.850199i
$442$	−17.8992	−	22.0196i	−0.851378	−	1.04736i
$443$	−19.1175	−	33.1125i	−0.908301	−	1.57322i	−0.816424	−	0.577454i	$-0.804046\pi$
$443$	−19.1175	−	33.1125i	−0.908301	−	1.57322i	−0.0918776	−	0.995770i	$-0.529287\pi$
$444$	17.1353	+	25.1503i	0.813207	+	1.19358i
$445$	0.195967	+	0.339425i	0.00928974	+	0.0160903i
$446$	3.09170	−	0.495590i	0.146396	−	0.0234669i
$447$	−6.83568	−	6.58880i	−0.323316	−	0.311640i
$448$	7.43182	−	3.40901i	0.351120	−	0.161061i
$449$		−	34.4583i		−	1.62619i	−0.582132	−	0.813094i	$-0.697781\pi$
$449$		−	34.4583i		−	1.62619i	0.582132	−	0.813094i	$-0.302219\pi$
$450$	6.82247	−	20.0569i	0.321614	−	0.945492i
$451$	−30.8764	−	17.8265i	−1.45391	−	0.839417i
$452$	−8.76628	−	26.6413i	−0.412331	−	1.25310i
$453$	2.51843	−	10.1412i	0.118326	−	0.476477i
$454$	−18.9133	−	7.21970i	−0.887646	−	0.338837i
$455$	0.168562	+	0.291958i	0.00790230	+	0.0136872i
$456$	−2.51164	+	8.41126i	−0.117618	+	0.393893i
$457$	3.26828			0.152884			0.0764419	−	0.997074i	$-0.475644\pi$
$457$	3.26828			0.152884			0.0764419	+	0.997074i	$0.475644\pi$
$458$	4.54559	+	28.3573i	0.212401	+	1.32505i
$459$	7.95970	+	24.2657i	0.371527	+	1.13263i
$460$	0.198221	+	0.602406i	0.00924210	+	0.0280873i
$461$			22.8221i			1.06293i	0.847080	+	0.531466i	$0.178359\pi$
$461$			22.8221i			1.06293i	−0.847080	+	0.531466i	$0.821641\pi$
$462$	−3.53426	−	7.52418i	−0.164429	−	0.350057i
$463$		−	37.8612i		−	1.75956i	−0.475382	−	0.879779i	$-0.657690\pi$
$463$		−	37.8612i		−	1.75956i	0.475382	−	0.879779i	$-0.342310\pi$
$464$	−6.97607	+	15.9885i	−0.323856	+	0.742245i
$465$	0.631102	+	0.456908i	0.0292666	+	0.0211886i
$466$	0.132097	+	0.162506i	0.00611929	+	0.00752794i
$467$	0.601903			0.0278527			0.0139264	−	0.999903i	$-0.495567\pi$
$467$	0.601903			0.0278527			0.0139264	+	0.999903i	$0.495567\pi$
$468$	−24.1474	−	4.11855i	−1.11621	−	0.190380i
$469$	3.30620			0.152666
$470$	0.274275	−	0.718514i	0.0126514	−	0.0331426i
$471$	−32.5700	−	8.08828i	−1.50075	−	0.372688i
$472$	−5.58317	−	0.261285i	−0.256986	−	0.0120266i
$473$			3.53309i			0.162451i
$474$	37.1043	+	3.14155i	1.70426	+	0.144296i
$475$	7.74882	−	4.47378i	0.355540	−	0.205271i
$476$	9.54290	−	3.14008i	0.437398	−	0.143925i
$477$	−17.8429	+	0.656485i	−0.816969	+	0.0300584i
$478$	−29.9642	−	11.4381i	−1.37053	−	0.523166i
$479$	−11.7014	+	20.2675i	−0.534653	+	0.926046i	0.464527	+	0.885559i	$0.346224\pi$
$479$	−11.7014	+	20.2675i	−0.534653	+	0.926046i	−0.999180	+	0.0404870i	$0.987109\pi$
$480$	−0.674318	+	0.414646i	−0.0307783	+	0.0189259i
$481$	−35.8672			−1.63540
$482$	−4.87411	−	30.4067i	−0.222009	−	1.38499i
$483$	−5.00228	−	4.82162i	−0.227612	−	0.219391i
$484$	0.0385263	+	0.0344299i	0.00175120	+	0.00156500i
$485$	−0.601050	+	0.347017i	−0.0272923	+	0.0157572i
$486$	18.9704	+	11.2304i	0.860517	+	0.509422i
$487$	−14.6297	+	8.44648i	−0.662936	+	0.382747i	−0.793395	−	0.608707i	$-0.791688\pi$
$487$	−14.6297	+	8.44648i	−0.662936	+	0.382747i	0.130458	+	0.991454i	$0.458355\pi$
$488$	6.77830	+	13.1212i	0.306839	+	0.593967i
$489$	2.90964	−	11.7166i	0.131578	−	0.529841i
$490$	0.671878	−	0.107700i	0.0303524	−	0.00486539i
$491$	4.85488	+	8.40890i	0.219098	+	0.379488i	0.954532	−	0.298107i	$-0.0963554\pi$
$491$	4.85488	+	8.40890i	0.219098	+	0.379488i	−0.735435	+	0.677596i	$0.763022\pi$
$492$	−2.76763	−	37.0916i	−0.124774	−	1.67222i
$493$	−10.7167	+	18.5619i	−0.482656	+	0.835984i
$494$	−6.52579	−	8.02802i	−0.293609	−	0.361198i
$495$	0.427765	+	0.681729i	0.0192266	+	0.0306414i
$496$	5.56491	+	21.5646i	0.249872	+	0.968279i
$497$			1.26289i			0.0566482i
$498$	−16.6799	−	11.6099i	−0.747443	−	0.520253i
$499$	14.7796	+	8.53303i	0.661627	+	0.381991i	0.792897	−	0.609356i	$-0.208572\pi$
$499$	14.7796	+	8.53303i	0.661627	+	0.381991i	−0.131269	+	0.991347i	$0.541905\pi$
$500$	1.58075	+	0.329842i	0.0706935	+	0.0147510i
$501$	−19.0508	+	19.7646i	−0.851127	+	0.883018i
$502$	−2.99357	−	18.6751i	−0.133609	−	0.833512i
$503$	12.7348	−	22.0573i	0.567815	−	0.983484i	−0.428967	−	0.903320i	$-0.641122\pi$
$503$	12.7348	−	22.0573i	0.567815	−	0.983484i	0.996782	−	0.0801640i	$-0.0255444\pi$
$504$	4.41099	−	7.46680i	0.196481	−	0.332598i
$505$	0.149533	+	0.258999i	0.00665415	+	0.0115253i
$506$	17.2184	+	6.57271i	0.765452	+	0.292193i
$507$	4.40937	−	4.57458i	0.195827	−	0.203164i
$508$	7.27630	−	8.14202i	0.322834	−	0.361244i
$509$	25.3287	−	14.6236i	1.12268	−	0.648178i	0.180594	−	0.983558i	$-0.442198\pi$
$509$	25.3287	−	14.6236i	1.12268	−	0.648178i	0.942083	+	0.335380i	$0.108865\pi$
$510$	−0.880354	+	0.413520i	−0.0389827	+	0.0183110i
$511$		−	1.35576i		−	0.0599755i
$512$	−22.4051	−	3.16408i	−0.990175	−	0.139834i
$513$	2.90200	+	8.84694i	0.128126	+	0.390602i
$514$	10.6668	−	27.9437i	0.470494	−	1.23254i
$515$	−0.328478	+	0.568940i	−0.0144744	+	0.0250705i
$516$	−3.04607	+	2.07534i	−0.134096	+	0.0913617i
$517$	−11.1754	−	19.3563i	−0.491492	−	0.851289i
$518$	4.52847	−	11.8632i	0.198970	−	0.521237i
$519$	9.50919	−	2.73634i	0.417407	−	0.120112i
$520$	0.0436136	−	0.931940i	0.00191258	−	0.0408683i
$521$	18.6471	+	10.7659i	0.816942	+	0.471662i	0.849361	−	0.527813i	$-0.176988\pi$
$521$	18.6471	+	10.7659i	0.816942	+	0.471662i	−0.0324186	+	0.999474i	$0.510321\pi$
$522$	3.59820	+	18.1490i	0.157489	+	0.794360i
$523$		−	18.9660i		−	0.829324i	−0.909975	−	0.414662i	$-0.863900\pi$
$523$		−	18.9660i		−	0.829324i	0.909975	−	0.414662i	$-0.136100\pi$
$524$	10.0262	+	8.96010i	0.437995	+	0.391424i
$525$	−8.49493	+	2.44448i	−0.370749	+	0.106686i
$526$	19.1350	−	15.5544i	0.834324	−	0.678203i
$527$	3.82846	+	27.0951i	0.166770	+	1.18028i
$528$	−3.01035	+	22.8074i	−0.131009	+	0.992565i
$529$	−7.59644			−0.330280
$530$	−0.107632	−	0.671452i	−0.00467522	−	0.0291660i
$531$	−5.02163	+	3.15093i	−0.217920	+	0.136739i
$532$	3.47921	−	1.14483i	0.150843	−	0.0496346i
$533$	37.9635	+	21.9183i	1.64438	+	0.949385i
$534$	5.05200	+	10.7553i	0.218621	+	0.465428i
$535$		−	1.59687i		−	0.0690387i
$536$	−7.70127	−	4.94022i	−0.332644	−	0.213385i
$537$	−26.5844	+	27.5805i	−1.14720	+	1.19019i
$538$	−12.7868	+	33.4972i	−0.551276	+	1.44417i
$539$	9.88753	−	17.1257i	0.425886	−	0.737657i
$540$	−0.336486	+	0.769249i	−0.0144801	+	0.0331032i
$541$	−11.2369	+	19.4629i	−0.483114	+	0.836777i	−0.999812	−	0.0193902i	$-0.993828\pi$
$541$	−11.2369	+	19.4629i	−0.483114	+	0.836777i	0.516698	+	0.856167i	$0.327161\pi$
$542$	22.8835	+	28.1513i	0.982931	+	1.20920i
$543$	−1.79771	−	6.24732i	−0.0771472	−	0.268098i
$544$	−26.9207	−	6.94497i	−1.15422	−	0.297763i
$545$	−0.308357	+	0.178030i	−0.0132086	+	0.00762596i
$546$	4.34549	+	9.25123i	0.185970	+	0.395916i
$547$	−31.4063	+	18.1324i	−1.34284	+	0.775287i	−0.987223	−	0.159346i	$-0.949061\pi$
$547$	−31.4063	+	18.1324i	−1.34284	+	0.775287i	−0.355614	+	0.934633i	$0.615728\pi$
$548$	3.93364	+	11.9546i	0.168037	+	0.510675i
$549$	13.8446	+	7.32813i	0.590872	+	0.312757i
$550$	18.1957	−	14.7909i	0.775867	−	0.630685i
$551$	−3.90715	+	6.76739i	−0.166450	+	0.288300i
$552$	4.44742	+	18.7058i	0.189295	+	0.796171i
$553$	−7.76856	−	13.4555i	−0.330353	−	0.572188i
$554$	−0.925551	+	0.752359i	−0.0393229	+	0.0319647i
$555$	−0.296298	+	1.19314i	−0.0125771	+	0.0506458i
$556$	−33.8193	−	7.05676i	−1.43426	−	0.299273i
$557$		−	0.794621i		−	0.0336692i	−0.999858	−	0.0168346i	$-0.994641\pi$
$557$		−	0.794621i		−	0.0336692i	0.999858	−	0.0168346i	$-0.00535887\pi$
$558$	17.8970	+	15.4175i	0.757639	+	0.652674i
$559$		−	4.34404i		−	0.183733i
$560$	0.302735	+	0.132089i	0.0127929	+	0.00558177i
$561$	−6.81260	+	27.4330i	−0.287628	+	1.15822i
$562$	20.0084	+	24.6143i	0.844004	+	1.03829i
$563$	−21.4293	−	37.1166i	−0.903136	−	1.56428i	−0.823399	−	0.567462i	$-0.807925\pi$
$563$	−21.4293	−	37.1166i	−0.903136	−	1.56428i	−0.0797369	−	0.996816i	$-0.525408\pi$
$564$	10.1237	−	21.0048i	0.426286	−	0.884463i
$565$	0.566489	−	0.981187i	0.0238324	−	0.0412788i
$566$	−25.7104	−	31.6289i	−1.08069	−	1.32946i
$567$	−0.675953	−	9.17356i	−0.0283874	−	0.385253i
$568$	1.88704	−	2.94170i	0.0791786	−	0.123431i
$569$	−4.24433	+	2.45047i	−0.177932	+	0.102729i	−0.586320	−	0.810079i	$-0.699424\pi$
$569$	−4.24433	+	2.45047i	−0.177932	+	0.102729i	0.408389	+	0.912808i	$0.366091\pi$
$570$	−0.320964	+	0.150764i	−0.0134437	+	0.00631479i
$571$	−34.8301	+	20.1092i	−1.45759	+	0.841542i	−0.998893	−	0.0470485i	$-0.985018\pi$
$571$	−34.8301	+	20.1092i	−1.45759	+	0.841542i	−0.458701	+	0.888591i	$0.651685\pi$
$572$	−20.2166	−	18.0670i	−0.845298	−	0.755420i
$573$	6.77537	+	23.5454i	0.283045	+	0.983625i
$574$	−12.0427	+	9.78919i	−0.502651	+	0.408593i
$575$	9.79903	−	16.9724i	0.408648	−	0.707799i
$576$	−21.4318	+	10.8017i	−0.892992	+	0.450072i
$577$	−6.28874	+	10.8924i	−0.261804	+	0.453458i	−0.966721	−	0.255832i	$-0.917651\pi$
$577$	−6.28874	+	10.8924i	−0.261804	+	0.453458i	0.704917	+	0.709289i	$0.250984\pi$
$578$	−9.45321	−	3.60853i	−0.393202	−	0.150095i
$579$	30.8790	−	32.0360i	1.28329	−	1.33137i
$580$	−0.669372	+	0.220256i	−0.0277941	+	0.00914563i
$581$			8.47960i			0.351793i
$582$	−19.0454	+	8.94602i	−0.789457	+	0.370824i
$583$	−17.1149	−	9.88127i	−0.708825	−	0.409240i
$584$	−2.02582	+	3.15804i	−0.0838292	+	0.130681i
$585$	−0.525951	−	0.838207i	−0.0217454	−	0.0346556i
$586$	−43.9475	+	7.04464i	−1.81545	+	0.291011i
$587$	24.1342			0.996124			0.498062	−	0.867141i	$-0.334045\pi$
$587$	24.1342			0.996124			0.498062	+	0.867141i	$0.334045\pi$
$588$	20.5730	−	1.53507i	0.848415	−	0.0633054i
$589$	1.39580	+	9.87849i	0.0575131	+	0.407036i
$590$	−0.142419	−	0.175204i	−0.00586331	−	0.00721303i
$591$	17.5383	−	5.04678i	0.721431	−	0.207597i
$592$	−28.2746	+	20.8668i	−1.16208	+	0.857619i
$593$		−	4.37509i		−	0.179663i	−0.995957	−	0.0898317i	$-0.971367\pi$
$593$		−	4.37509i		−	0.179663i	0.995957	−	0.0898317i	$-0.0286329\pi$
$594$	11.1791	+	21.6892i	0.458683	+	0.889920i
$595$	0.351461	+	0.202916i	0.0144085	+	0.00831874i
$596$	7.30517	−	8.17432i	0.299231	−	0.334833i
$597$	−4.12738	+	1.18768i	−0.168922	+	0.0486086i
$598$	−21.1706	−	8.08136i	−0.865730	−	0.330471i
$599$	−1.95479	−	3.38580i	−0.0798707	−	0.138340i	0.823323	−	0.567573i	$-0.192117\pi$
$599$	−1.95479	−	3.38580i	−0.0798707	−	0.138340i	−0.903194	+	0.429233i	$0.858784\pi$
$600$	23.4402	+	6.99935i	0.956943	+	0.285747i
$601$	12.6427	−	21.8978i	0.515707	−	0.893231i	−0.484127	−	0.874998i	$-0.660863\pi$
$601$	12.6427	−	21.8978i	0.515707	−	0.893231i	0.999834	−	0.0182330i	$-0.00580408\pi$
$602$	1.43680	+	0.548464i	0.0585596	+	0.0223537i
$603$	−9.69807	+	0.356817i	−0.394936	+	0.0145307i
$604$	11.8114	+	2.46458i	0.480599	+	0.100282i
$605$			0.00208724i			8.48585e-5i
$606$	3.85494	+	8.20688i	0.156596	+	0.333382i
$607$	23.6101	−	13.6313i	0.958305	−	0.553278i	0.0626540	−	0.998035i	$-0.480044\pi$
$607$	23.6101	−	13.6313i	0.958305	−	0.553278i	0.895651	+	0.444758i	$0.146710\pi$
$608$	−9.81490	−	2.53204i	−0.398047	−	0.102688i
$609$	5.35761	−	5.55835i	0.217101	−	0.225236i
$610$	−0.212762	+	0.557368i	−0.00861447	+	0.0225672i
$611$	13.7405	+	23.7992i	0.555880	+	0.962813i
$612$	−27.6533	+	10.2407i	−1.11782	+	0.413955i
$613$	18.1150	−	31.3762i	0.731660	−	1.26727i	−0.224513	−	0.974471i	$-0.572079\pi$
$613$	18.1150	−	31.3762i	0.731660	−	1.26727i	0.956173	−	0.292801i	$-0.0945874\pi$
$614$	−6.76288	+	1.08407i	−0.272928	+	0.0437494i
$615$	1.04273	−	1.08181i	0.0420471	−	0.0436226i
$616$	8.52818	−	4.40560i	0.343610	−	0.177507i
$617$	37.6305	+	21.7260i	1.51495	+	0.874655i	0.999846	+	0.0175254i	$0.00557879\pi$
$617$	37.6305	+	21.7260i	1.51495	+	0.874655i	0.515101	+	0.857130i	$0.327755\pi$
$618$	−11.3786	+	16.3475i	−0.457714	+	0.657594i
$619$		−	13.6863i		−	0.550098i	−0.961430	−	0.275049i	$-0.911306\pi$
$619$		−	13.6863i		−	0.550098i	0.961430	−	0.275049i	$-0.0886941\pi$
$620$	−0.499749	+	0.748102i	−0.0200704	+	0.0300445i
$621$	15.1936	+	13.6034i	0.609696	+	0.545885i
$622$	20.7912	−	16.9007i	0.833650	−	0.677655i
$623$	2.47903	−	4.29381i	0.0993204	−	0.172028i
$624$	3.70132	−	28.0424i	0.148171	−	1.12260i
$625$	−12.4511	−	21.5659i	−0.498043	−	0.862635i
$626$	−5.79793	−	36.1699i	−0.231732	−	1.44564i
$627$	−2.48378	+	10.0017i	−0.0991925	+	0.399429i
$628$	7.91532	−	37.9339i	0.315856	−	1.51373i
$629$	−37.3925	+	21.5886i	−1.49094	+	0.860794i
$630$	0.343644	−	0.0681303i	0.0136911	−	0.00271438i
$631$	9.02299	−	5.20942i	0.359199	−	0.207384i	−0.309530	−	0.950890i	$-0.600172\pi$
$631$	9.02299	−	5.20942i	0.359199	−	0.207384i	0.668730	+	0.743506i	$0.266838\pi$
$632$	−2.01003	+	42.9506i	−0.0799548	+	1.70848i
$633$	13.1185	+	12.6447i	0.521414	+	0.502583i
$634$	40.2351	−	6.44956i	1.59794	−	0.256145i
$635$	0.441111			0.0175050
$636$	−1.53410	−	20.5599i	−0.0608311	−	0.815255i
$637$	−12.1570	+	21.0566i	−0.481680	+	0.834293i
$638$	−7.30335	+	19.1325i	−0.289142	+	0.757461i
$639$	−0.136295	−	3.70442i	−0.00539176	−	0.146545i
$640$	−0.507802	−	0.760035i	−0.0200726	−	0.0300430i
$641$	−5.03342	+	2.90605i	−0.198808	+	0.114782i	−0.596099	−	0.802911i	$-0.703284\pi$
$641$	−5.03342	+	2.90605i	−0.198808	+	0.114782i	0.397291	+	0.917693i	$0.369950\pi$
$642$	4.08452	−	48.2416i	0.161203	−	1.90394i
$643$			9.21443i			0.363381i	0.983356	+	0.181691i	$0.0581570\pi$
$643$			9.21443i			0.363381i	−0.983356	+	0.181691i	$0.941843\pi$
$644$	5.34585	−	5.98189i	0.210656	−	0.235720i
$645$	−0.144506	−	0.0358860i	−0.00568993	−	0.00141301i
$646$	−11.6354	−	4.44153i	−0.457789	−	0.174750i
$647$	−35.1923			−1.38355			−0.691776	−	0.722112i	$-0.743171\pi$
$647$	−35.1923			−1.38355			−0.691776	+	0.722112i	$0.743171\pi$
$648$	−12.1329	+	22.3784i	−0.476625	+	0.879107i
$649$	−6.56171			−0.257570
$650$	−22.3722	+	18.1858i	−0.877510	+	0.713308i
$651$	1.01383	−	9.80400i	0.0397350	−	0.384249i
$652$	13.6461	+	2.84742i	0.534424	+	0.111513i
$653$		−	32.8983i		−	1.28741i	−0.765274	−	0.643704i	$-0.777397\pi$
$653$		−	32.8983i		−	1.28741i	0.765274	−	0.643704i	$-0.222603\pi$
$654$	−9.77086	+	4.58958i	−0.382071	+	0.179467i
$655$			0.543188i			0.0212241i
$656$	42.6788	−	4.80790i	1.66633	−	0.187717i
$657$	0.146319	+	3.97686i	0.00570844	+	0.155152i
$658$	−9.60646	+	1.53989i	−0.374499	+	0.0600310i
$659$	19.2546			0.750051			0.375026	−	0.927014i	$-0.377634\pi$
$659$	19.2546			0.750051			0.375026	+	0.927014i	$0.377634\pi$
$660$	−0.768015	+	0.523262i	−0.0298949	+	0.0203679i
$661$	−3.37424	−	5.84435i	−0.131243	−	0.227319i	0.792913	−	0.609335i	$-0.208563\pi$
$661$	−3.37424	−	5.84435i	−0.131243	−	0.227319i	−0.924156	+	0.382016i	$0.875230\pi$
$662$	4.92468	−	12.9011i	0.191403	−	0.501415i
$663$	8.37631	−	33.7298i	0.325309	−	1.30996i
$664$	12.6705	−	19.7519i	0.491710	−	0.766522i
$665$	0.128138	+	0.0739803i	0.00496896	+	0.00286883i
$666$	−12.0030	+	35.2869i	−0.465108	+	1.36734i
$667$			17.1159i			0.662729i
$668$	−23.6352	−	21.1221i	−0.914473	−	0.817239i
$669$	2.76107	+	2.66135i	0.106749	+	0.102894i
$670$	−0.0585007	−	0.364952i	−0.00226008	−	0.0140993i
$671$	8.66899	+	15.0151i	0.334663	+	0.579653i
$672$	8.80778	+	4.76476i	0.339767	+	0.183805i
$673$	9.49453	+	16.4450i	0.365987	+	0.633908i	0.988934	−	0.148356i	$-0.0473981\pi$
$673$	9.49453	+	16.4450i	0.365987	+	0.633908i	−0.622947	+	0.782264i	$0.714065\pi$
$674$	−13.2277	+	10.7525i	−0.509514	+	0.414172i
$675$	24.6543	−	8.08718i	0.948946	−	0.311276i
$676$	5.47043	+	4.88878i	0.210401	+	0.188030i
$677$	1.98973	−	1.14877i	0.0764716	−	0.0441509i	−0.461277	−	0.887256i	$-0.652608\pi$
$677$	1.98973	−	1.14877i	0.0764716	−	0.0441509i	0.537748	+	0.843105i	$0.319275\pi$
$678$	19.6234	−	28.1928i	0.753632	−	1.08274i
$679$	7.60344	+	4.38985i	0.291793	+	0.168467i
$680$	−0.515470	−	0.997824i	−0.0197674	−	0.0382648i
$681$	−6.85650	−	23.8274i	−0.262742	−	0.913068i
$682$	7.70944	+	24.9833i	0.295210	+	0.956661i
$683$	15.6597			0.599203			0.299601	−	0.954064i	$-0.403146\pi$
$683$	15.6597			0.599203			0.299601	+	0.954064i	$0.403146\pi$
$684$	−10.0820	+	3.73361i	−0.385495	+	0.142758i
$685$	−0.254197	+	0.440282i	−0.00971237	+	0.0168223i
$686$	−11.8116	−	14.5306i	−0.450968	−	0.554780i
$687$	−24.4101	+	25.3248i	−0.931305	+	0.966200i
$688$	−2.52727	−	3.42447i	−0.0963513	−	0.130557i
$689$	21.0433	+	12.1493i	0.801685	+	0.462853i
$690$	−0.443719	+	0.637488i	−0.0168921	+	0.0242688i
$691$	−20.0278	+	11.5631i	−0.761894	+	0.439880i	−0.829975	−	0.557800i	$-0.811646\pi$
$691$	−20.0278	+	11.5631i	−0.761894	+	0.439880i	0.0680814	+	0.997680i	$0.478312\pi$
$692$	3.57128	+	10.8534i	0.135760	+	0.412583i
$693$	4.76296	−	8.99837i	0.180930	−	0.341820i
$694$	−7.02529	−	43.8267i	−0.266676	−	1.66364i
$695$	−0.697800	−	1.20863i	−0.0264691	−	0.0458458i
$696$	−20.7852	+	4.94181i	−0.787859	+	0.187319i
$697$	52.7707			1.99883
$698$	21.6864	−	17.6284i	0.820842	−	0.667244i
$699$	−0.0618177	+	0.248928i	−0.00233816	+	0.00941534i
$700$	−3.19037	−	9.69573i	−0.120585	−	0.366464i
$701$	−13.6460	−	7.87850i	−0.515401	−	0.297567i	0.219650	−	0.975579i	$-0.429508\pi$
$701$	−13.6460	−	7.87850i	−0.515401	−	0.297567i	−0.735051	+	0.678012i	$0.762842\pi$
$702$	−13.7450	−	26.6676i	−0.518773	−	1.00650i
$703$	−13.6328	+	7.87090i	−0.514170	+	0.296856i
$704$	−26.4480	−	2.48090i	−0.996798	−	0.0935025i
$705$	0.905199	−	0.260478i	0.0340918	−	0.00981015i
$706$	5.93849	−	0.951922i	0.223498	−	0.0358261i
$707$	1.89163	−	3.27641i	0.0711422	−	0.123222i
$708$	−3.85436	−	5.65721i	−0.144856	−	0.212611i
$709$	−12.5259			−0.470419			−0.235210	−	0.971945i	$-0.575578\pi$
$709$	−12.5259			−0.470419			−0.235210	+	0.971945i	$0.575578\pi$
$710$	0.139403	−	0.0223458i	0.00523169	−	0.000838624i
$711$	24.2397	+	38.6307i	0.909059	+	1.44876i
$712$	−12.1905	+	6.29752i	−0.456857	+	0.236009i
$713$	13.4662	+	17.2096i	0.504314	+	0.644506i
$714$	10.0986	+	7.02909i	0.377932	+	0.263057i
$715$		−	1.09528i		−	0.0409610i
$716$	−32.9816	−	29.4748i	−1.23258	−	1.10152i
$717$	−10.8627	−	37.7495i	−0.405675	−	1.40978i
$718$	−19.9546	−	7.61718i	−0.744699	−	0.284271i
$719$	22.8221	−	39.5291i	0.851122	−	1.47419i	−0.0290748	−	0.999577i	$-0.509256\pi$
$719$	22.8221	−	39.5291i	0.851122	−	1.47419i	0.880197	−	0.474609i	$-0.157411\pi$
$720$	−0.902266	−	0.354784i	−0.0336255	−	0.0132220i
$721$	8.31064			0.309505
$722$	20.8612	+	7.96324i	0.776372	+	0.296361i
$723$	26.1743	−	27.1550i	0.973433	−	1.00991i
$724$	7.13041	−	2.34625i	0.265000	−	0.0871978i
$725$	18.8591	+	10.8883i	0.700410	+	0.404382i
$726$	−0.00533882	+	0.0630558i	−0.000198142	+	0.00234022i
$727$	29.8806	+	17.2515i	1.10821	+	0.639825i	0.938365	−	0.345646i	$-0.112340\pi$
$727$	29.8806	+	17.2515i	1.10821	+	0.639825i	0.169844	+	0.985471i	$0.445674\pi$
$728$	−10.4857	+	5.41683i	−0.388625	+	0.200761i
$729$	2.97281	+	26.8358i	0.110104	+	0.993920i
$730$	−0.149655	+	0.0239892i	−0.00553898	+	0.000887881i
$731$	−2.61469	−	4.52878i	−0.0967080	−	0.167503i
$732$	−7.85321	+	16.2939i	−0.290263	+	0.602241i
$733$	0.491806	+	0.851832i	0.0181653	+	0.0314631i	0.874965	−	0.484186i	$-0.160884\pi$
$733$	0.491806	+	0.851832i	0.0181653	+	0.0314631i	−0.856800	+	0.515649i	$0.827551\pi$
$734$	−7.41555	+	19.4264i	−0.273713	+	0.717041i
$735$	0.600027	+	0.578357i	0.0221323	+	0.0213330i
$736$	−21.3906	+	5.94595i	−0.788470	+	0.219171i
$737$	−9.30238	−	5.37073i	−0.342658	−	0.197833i
$738$	34.2682	−	30.0143i	1.26143	−	1.10484i
$739$	−3.06507	+	1.76962i	−0.112750	+	0.0650964i	−0.555315	−	0.831640i	$-0.687402\pi$
$739$	−3.06507	+	1.76962i	−0.112750	+	0.0650964i	0.442564	+	0.896737i	$0.354069\pi$
$740$	−1.38963	−	0.289962i	−0.0510839	−	0.0106592i
$741$	3.05388	−	12.2974i	0.112187	−	0.451757i
$742$	−6.67527	+	5.42617i	−0.245057	+	0.199201i
$743$	0.154441			0.00566589			0.00283294	−	0.999996i	$-0.499098\pi$
$743$	0.154441			0.00566589			0.00283294	+	0.999996i	$0.499098\pi$
$744$	−17.0110	+	21.3220i	−0.623653	+	0.781702i
$745$	0.442861			0.0162252
$746$	−41.6717	+	33.8740i	−1.52571	+	1.24021i
$747$	−0.915148	−	24.8732i	−0.0334835	−	0.910062i
$748$	−31.9510	−	6.66692i	−1.16824	−	0.243767i
$749$	−17.4944	+	10.1004i	−0.639231	+	0.369060i
$750$	0.840835	+	1.79007i	0.0307030	+	0.0653643i
$751$	20.1225	+	11.6177i	0.734280	+	0.423937i	0.819986	−	0.572384i	$-0.193981\pi$
$751$	20.1225	+	11.6177i	0.734280	+	0.423937i	−0.0857061	+	0.996320i	$0.527315\pi$
$752$	24.6777	+	10.7673i	0.899903	+	0.392645i
$753$	16.0757	−	16.6780i	0.585830	−	0.607780i
$754$	8.97971	−	23.5240i	0.327022	−	0.856693i
$755$	0.243707	+	0.422113i	0.00886940	+	0.0153623i
$756$	10.5558	−	1.17924i	0.383910	−	0.0428886i
$757$	−6.61265	−	11.4534i	−0.240341	−	0.416283i	0.720470	−	0.693486i	$-0.243926\pi$
$757$	−6.61265	−	11.4534i	−0.240341	−	0.416283i	−0.960811	+	0.277203i	$0.910593\pi$
$758$	−12.1283	+	1.94412i	−0.440518	+	0.0706137i
$759$	6.24206	+	21.6921i	0.226573	+	0.787374i
$760$	−0.187933	−	0.363793i	−0.00681704	−	0.0131961i
$761$	−17.4065	−	10.0497i	−0.630987	−	0.364300i	0.150147	−	0.988664i	$-0.452025\pi$
$761$	−17.4065	−	10.0497i	−0.630987	−	0.364300i	−0.781134	+	0.624363i	$0.785359\pi$
$762$	13.3260	+	1.12829i	0.482750	+	0.0408736i
$763$	3.90079	+	2.25212i	0.141218	+	0.0815323i
$764$	−26.8737	+	8.84276i	−0.972257	+	0.319920i
$765$	−1.05284	−	0.557282i	−0.0380655	−	0.0201486i
$766$	−10.9919	−	4.19589i	−0.397154	−	0.151604i
$767$	8.06783			0.291313
$768$	−13.3967	−	24.2596i	−0.483411	−	0.875393i
$769$	−17.5536	+	30.4038i	−0.633000	+	1.09639i	0.353935	+	0.935270i	$0.384843\pi$
$769$	−17.5536	+	30.4038i	−0.633000	+	1.09639i	−0.986935	+	0.161118i	$0.948490\pi$
$770$	0.362265	+	0.138286i	0.0130551	+	0.00498347i
$771$	35.2041	−	10.1302i	1.26784	−	0.364831i
$772$	38.3097	+	34.2363i	1.37880	+	1.23219i
$773$		−	51.9636i		−	1.86900i	−0.355962	−	0.934500i	$-0.615847\pi$
$773$		−	51.9636i		−	1.86900i	0.355962	−	0.934500i	$-0.384153\pi$
$774$	−4.27376	−	1.45374i	−0.153617	−	0.0522537i
$775$	27.5290	−	3.88978i	0.988872	−	0.139725i
$776$	−11.1516	−	21.5867i	−0.400318	−	0.774919i
$777$	14.9454	−	4.30066i	0.536165	−	0.154285i
$778$	31.3998	−	5.03329i	1.12574	−	0.180452i
$779$	19.2395			0.689325
$780$	0.944299	−	0.643367i	0.0338113	−	0.0230362i
$781$	2.05149	−	3.55328i	0.0734080	−	0.127146i
$782$	−26.9351	+	4.31762i	−0.963198	+	0.154398i
$783$	−15.1156	+	16.8825i	−0.540187	+	0.603332i
$784$	2.66672	+	23.6719i	0.0952399	+	0.845426i
$785$	1.35567	−	0.782698i	0.0483860	−	0.0279357i
$786$	−1.38938	+	16.4098i	−0.0495577	+	0.585317i
$787$	12.9345	+	7.46774i	0.461066	+	0.266196i	0.712492	−	0.701680i	$-0.247566\pi$
$787$	12.9345	+	7.46774i	0.461066	+	0.266196i	−0.251427	+	0.967876i	$0.580900\pi$
$788$	6.58673	+	20.0175i	0.234642	+	0.713093i
$789$	29.3112	+	7.27900i	1.04350	+	0.259139i
$790$	−1.34782	+	1.09561i	−0.0479533	+	0.0389801i
$791$	−14.3324			−0.509603
$792$	−24.5402	+	13.8433i	−0.871999	+	0.491901i
$793$	−10.6588	−	18.4616i	−0.378505	−	0.655590i
$794$	0.418711	+	2.61210i	0.0148595	+	0.0926999i
$795$	0.577990	−	0.599647i	0.0204992	−	0.0212673i
$796$	−1.55009	−	4.71081i	−0.0549413	−	0.166970i
$797$	21.3976	−	12.3539i	0.757942	−	0.437598i	−0.0706146	−	0.997504i	$-0.522496\pi$
$797$	21.3976	−	12.3539i	0.757942	−	0.437598i	0.828556	+	0.559906i	$0.189163\pi$
$798$	3.68182	+	2.56271i	0.130335	+	0.0907188i
$799$	28.6496	+	16.5409i	1.01355	+	0.585174i
$800$	−7.05619	+	27.3518i	−0.249474	+	0.967033i
$801$	−6.80834	+	12.8626i	−0.240561	+	0.454477i
$802$	9.82657	+	12.0886i	0.346988	+	0.426865i
$803$	−2.20236	+	3.81460i	−0.0777197	+	0.134614i
$804$	−0.833825	−	11.1749i	−0.0294067	−	0.394107i
$805$	0.324082			0.0114224
$806$	−9.47900	−	30.7178i	−0.333884	−	1.08199i
$807$	−42.2005	+	12.1435i	−1.48553	+	0.427472i
$808$	−9.30197	+	4.80534i	−0.327242	+	0.169051i
$809$	−21.2672	−	12.2786i	−0.747715	−	0.431693i	0.0771528	−	0.997019i	$-0.475417\pi$
$809$	−21.2672	−	12.2786i	−0.747715	−	0.431693i	−0.824868	+	0.565326i	$0.808750\pi$
$810$	−1.00066	+	0.236934i	−0.0351595	+	0.00832500i
$811$	26.4024	−	15.2435i	0.927115	−	0.535270i	0.0412170	−	0.999150i	$-0.486877\pi$
$811$	26.4024	−	15.2435i	0.927115	−	0.535270i	0.885898	+	0.463880i	$0.153543\pi$
$812$	6.64686	+	5.94011i	0.233259	+	0.208457i
$813$	−10.7088	+	43.1224i	−0.375575	+	1.51237i
$814$	−32.0124	+	26.0221i	−1.12203	+	0.912075i
$815$	0.281564	+	0.487683i	0.00986275	+	0.0170828i
$816$	−13.0201	−	31.4629i	−0.455795	−	1.10142i
$817$	−0.953280	−	1.65113i	−0.0333511	−	0.0577657i
$818$	6.99820	+	43.6577i	0.244686	+	1.52646i
$819$	−5.85622	+	11.0638i	−0.204633	+	0.386600i
$820$	1.29366	+	1.15611i	0.0451765	+	0.0403730i
$821$		−	19.8630i		−	0.693222i	−0.938009	−	0.346611i	$-0.887332\pi$
$821$		−	19.8630i		−	0.693222i	0.938009	−	0.346611i	$-0.112668\pi$
$822$	−8.80548	+	12.6508i	−0.307127	+	0.441246i
$823$	−24.1583	−	13.9478i	−0.842105	−	0.486190i	0.0158740	−	0.999874i	$-0.494947\pi$
$823$	−24.1583	−	13.9478i	−0.842105	−	0.486190i	−0.857979	+	0.513684i	$0.828280\pi$
$824$	−19.3583	−	12.4180i	−0.674380	−	0.432602i
$825$	27.8724	+	6.92170i	0.970392	+	0.240983i
$826$	−1.01862	+	2.66845i	−0.0354422	+	0.0928473i
$827$	16.0552	+	27.8083i	0.558292	+	0.966991i	0.997639	+	0.0686733i	$0.0218766\pi$
$827$	16.0552	+	27.8083i	0.558292	+	0.966991i	−0.439347	+	0.898318i	$0.644790\pi$
$828$	−15.0354	+	18.1236i	−0.522516	+	0.629839i
$829$	−27.3120			−0.948586			−0.474293	−	0.880367i	$-0.657296\pi$
$829$	−27.3120			−0.948586			−0.474293	+	0.880367i	$0.657296\pi$
$830$	0.936014	−	0.150040i	0.0324895	−	0.00520797i
$831$	−1.41777	−	0.352083i	−0.0491819	−	0.0122136i
$832$	32.5187	+	3.05035i	1.12738	+	0.105752i
$833$			29.2695i			1.01413i
$834$	−17.9891	−	38.2975i	−0.622913	−	1.32614i
$835$		−	1.28049i		−	0.0443130i
$836$	−11.6489	−	2.43066i	−0.402884	−	0.0840662i
$837$	−1.91578	+	28.8675i	−0.0662189	+	0.997805i
$838$	22.7730	−	18.5116i	0.786679	−	0.639473i
$839$	40.4207			1.39548			0.697738	−	0.716353i	$-0.254190\pi$
$839$	40.4207			1.39548			0.697738	+	0.716353i	$0.254190\pi$
$840$	0.0935711	+	0.393558i	0.00322851	+	0.0135790i
$841$	9.98149			0.344189
$842$	28.8355	+	11.0073i	0.993738	+	0.379335i
$843$	−9.36337	+	37.7045i	−0.322491	+	1.29861i
$844$	−14.0195	+	15.6875i	−0.482572	+	0.539987i
$845$			0.296372i			0.0101955i
$846$	28.0124	−	5.55371i	0.963087	−	0.190940i
$847$	0.0228667	−	0.0132021i	0.000785708	−	0.000453629i
$848$	23.6569	−	2.66503i	0.812383	−	0.0915174i
$849$	12.0317	−	48.4495i	0.412928	−	1.66278i
$850$	−12.3775	+	32.4251i	−0.424545	+	1.11217i
$851$	−17.2398	+	29.8602i	−0.590973	+	1.02360i
$852$	4.26853	−	0.318501i	0.146237	−	0.0109117i
$853$	−8.59082			−0.294144			−0.147072	−	0.989126i	$-0.546985\pi$
$853$	−8.59082			−0.294144			−0.147072	+	0.989126i	$0.546985\pi$
$854$	7.45195	−	1.19452i	0.255001	−	0.0408758i
$855$	−0.383850	−	0.203177i	−0.0131274	−	0.00694851i
$856$	55.8428	+	2.61337i	1.90867	+	0.0893232i
$857$	26.4438	−	15.2674i	0.903304	−	0.521523i	0.0250335	−	0.999687i	$-0.492031\pi$
$857$	26.4438	−	15.2674i	0.903304	−	0.521523i	0.878271	+	0.478164i	$0.158697\pi$
$858$	2.80153	−	33.0884i	0.0956428	−	1.12962i
$859$	−17.7968	+	10.2750i	−0.607218	+	0.350577i	−0.771876	−	0.635773i	$-0.780681\pi$
$859$	−17.7968	+	10.2750i	−0.607218	+	0.350577i	0.164658	+	0.986351i	$0.447348\pi$
$860$	0.0351186	−	0.168305i	0.00119754	−	0.00573914i
$861$	−18.4471	−	4.58106i	−0.628675	−	0.156122i
$862$	−5.32517	−	33.2207i	−0.181376	−	1.13150i
$863$	−19.8583	−	34.3956i	−0.675984	−	1.17084i	−0.976180	−	0.216961i	$-0.930386\pi$
$863$	−19.8583	−	34.3956i	−0.675984	−	1.17084i	0.300196	−	0.953877i	$-0.402948\pi$
$864$	−26.3501	−	13.0259i	−0.896448	−	0.443150i
$865$	−0.230781	+	0.399724i	−0.00784679	+	0.0135910i
$866$	−14.9907	+	12.1856i	−0.509405	+	0.414084i
$867$	−3.42700	−	11.9094i	−0.116387	−	0.404463i
$868$	11.3568	+	0.743124i	0.385474	+	0.0252233i
$869$			50.4783i			1.71236i
$870$	−0.708353	−	0.493044i	−0.0240154	−	0.0167158i
$871$	11.4376	+	6.60349i	0.387548	+	0.223751i
$872$	−5.72109	−	11.0746i	−0.193741	−	0.375035i
$873$	−22.7769	−	12.0561i	−0.770882	−	0.408038i
$874$	−9.82016	+	1.57414i	−0.332172	+	0.0532461i
$875$	0.412601	−	0.714646i	0.0139485	−	0.0241594i
$876$	−4.58245	+	0.341925i	−0.154827	+	0.0115526i
$877$	12.2789	+	21.2676i	0.414628	+	0.718157i	0.995389	−	0.0959170i	$-0.0305783\pi$
$877$	12.2789	+	21.2676i	0.414628	+	0.718157i	−0.580761	+	0.814074i	$0.697245\pi$
$878$	−9.19779	+	24.0953i	−0.310410	+	0.813176i
$879$	−39.2477	−	37.8302i	−1.32379	−	1.27598i
$880$	−0.637208	−	0.863422i	−0.0214803	−	0.0291060i
$881$	−34.8684	+	20.1313i	−1.17475	+	0.678240i	−0.954793	−	0.297270i	$-0.903924\pi$
$881$	−34.8684	+	20.1313i	−1.17475	+	0.678240i	−0.219953	+	0.975510i	$0.570590\pi$
$882$	16.6475	+	19.0070i	0.560552	+	0.639998i
$883$			14.4272i			0.485514i	0.970087	+	0.242757i	$0.0780517\pi$
$883$			14.4272i			0.485514i	−0.970087	+	0.242757i	$0.921948\pi$
$884$	39.2847	+	8.19719i	1.32129	+	0.275701i
$885$	0.0666481	−	0.268380i	0.00224035	−	0.00902148i
$886$	50.5171	+	19.2837i	1.69716	+	0.647848i
$887$	−23.3628	+	40.4655i	−0.784445	+	1.35870i	0.144886	+	0.989448i	$0.453719\pi$
$887$	−23.3628	+	40.4655i	−0.784445	+	1.35870i	−0.929330	+	0.369249i	$0.879615\pi$
$888$	−41.2393	−	12.3142i	−1.38390	−	0.413238i
$889$	−2.79008	−	4.83256i	−0.0935763	−	0.162079i
$890$	−0.517834	−	0.197670i	−0.0173578	−	0.00662593i
$891$	−13.0001	+	26.9089i	−0.435518	+	0.901483i
$892$	−2.95071	+	3.30178i	−0.0987971	+	0.110552i
$893$	10.4453	+	6.03057i	0.349537	+	0.201805i
$894$	13.3789	+	1.13276i	0.447457	+	0.0378853i
$895$		−	1.78685i		−	0.0597278i
$896$	−5.11461	+	10.3705i	−0.170867	+	0.346454i
$897$	−7.67482	−	26.6712i	−0.256255	−	0.890524i
$898$	30.7383	+	37.8142i	1.02575	+	1.26187i
$899$	−19.1227	+	14.9632i	−0.637778	+	0.499049i
$900$	10.4047	+	28.0962i	0.346823	+	0.936538i
$901$	29.2509			0.974489
$902$	49.7854	−	7.98044i	1.65767	−	0.265720i
$903$	0.520873	+	1.81011i	0.0173336	+	0.0602368i
$904$	33.3852	+	21.4160i	1.11037	+	0.712284i
$905$	0.262610	+	0.151618i	0.00872945	+	0.00503995i
$906$	6.28272	+	13.3754i	0.208729	+	0.444369i
$907$		−	44.6132i		−	1.48136i	−0.671860	−	0.740678i	$-0.734505\pi$
$907$		−	44.6132i		−	1.48136i	0.671860	−	0.740678i	$-0.265495\pi$
$908$	27.1955	−	8.94865i	0.902515	−	0.296971i
$909$	−5.19512	+	9.81483i	−0.172311	+	0.325537i
$910$	−0.445416	−	0.170027i	−0.0147654	−	0.00563634i
$911$	11.4024	−	19.7495i	0.377777	−	0.654329i	−0.612962	−	0.790113i	$-0.710022\pi$
$911$	11.4024	−	19.7495i	0.377777	−	0.654329i	0.990738	+	0.135784i	$0.0433553\pi$
$912$	−4.74695	−	11.4709i	−0.157187	−	0.379840i
$913$	13.7746	−	23.8583i	0.455873	−	0.789596i
$914$	−3.58657	+	2.91544i	−0.118633	+	0.0964343i
$915$	−0.702184	+	0.202058i	−0.0232135	+	0.00667985i
$916$	−30.2842	−	27.0641i	−1.00062	−	0.894224i
$917$	5.95086	−	3.43573i	0.196515	−	0.113458i
$918$	−30.3809	−	19.5285i	−1.00272	−	0.644538i
$919$	−26.3724	+	15.2261i	−0.869946	+	0.502264i	−0.867330	−	0.497733i	$-0.834166\pi$
$919$	−26.3724	+	15.2261i	−0.869946	+	0.502264i	−0.00261593	+	0.999997i	$0.500833\pi$
$920$	−0.754897	−	0.484252i	−0.0248882	−	0.0159653i
$921$	−6.03965	−	5.82153i	−0.199013	−	0.191826i
$922$	−20.3583	−	25.0447i	−0.670464	−	0.824804i
$923$	−2.52237	+	4.36887i	−0.0830248	+	0.143803i
$924$	10.5903	+	5.10424i	0.348397	+	0.167917i
$925$	21.9343	+	37.9914i	0.721197	+	1.24915i
$926$	33.7738	+	41.5484i	1.10987	+	1.36537i
$927$	−24.3776	+	0.896914i	−0.800665	+	0.0294585i
$928$	−6.60692	−	23.7685i	−0.216883	−	0.780239i
$929$			0.874659i			0.0286966i	0.999897	+	0.0143483i	$0.00456737\pi$
$929$			0.874659i			0.0286966i	−0.999897	+	0.0143483i	$0.995433\pi$
$930$	−1.10014	+	0.0615637i	−0.0360752	+	0.00201875i
$931$			10.6712i			0.349735i
$932$	−0.289924	−	0.0604958i	−0.00949678	−	0.00198161i
$933$	31.8482	+	7.90903i	1.04266	+	0.258930i
$934$	−0.660521	+	0.536922i	−0.0216129	+	0.0175686i
$935$	−0.659251	−	1.14186i	−0.0215598	−	0.0373427i
$936$	30.1730	−	17.0208i	0.986235	−	0.556343i
$937$	2.62942	−	4.55429i	0.0858995	−	0.148782i	−0.819875	−	0.572543i	$-0.805957\pi$
$937$	2.62942	−	4.55429i	0.0858995	−	0.148782i	0.905774	+	0.423761i	$0.139290\pi$
$938$	−3.62819	+	2.94927i	−0.118464	+	0.0962970i
$939$	31.1353	−	32.3019i	1.01606	−	1.05413i
$940$	0.339958	+	1.03315i	0.0110882	+	0.0336978i
$941$	−46.2357	+	26.6942i	−1.50724	+	0.870207i	−0.507278	+	0.861783i	$0.669348\pi$
$941$	−46.2357	+	26.6942i	−1.50724	+	0.870207i	−0.999965	+	0.00842400i	$0.997319\pi$
$942$	42.9570	−	20.1778i	1.39962	−	0.657428i
$943$	36.4949	−	21.0703i	1.18844	−	0.686144i
$944$	6.35999	−	4.69369i	0.207000	−	0.152767i
$945$	0.319663	+	0.286207i	0.0103986	+	0.00931031i
$946$	−3.15166	−	3.87717i	−0.102469	−	0.126058i
$947$	−8.15547	+	14.1257i	−0.265017	+	0.459023i	−0.967568	−	0.252610i	$-0.918711\pi$
$947$	−8.15547	+	14.1257i	−0.265017	+	0.459023i	0.702551	+	0.711633i	$0.252044\pi$
$948$	−43.5202	+	29.6511i	−1.41347	+	0.963021i
$949$	2.70788	−	4.69018i	0.0879014	−	0.152250i
$950$	−4.51266	+	11.8217i	−0.146410	+	0.383548i
$951$	35.9324	+	34.6346i	1.16519	+	1.12310i
$952$	−7.67119	+	11.9586i	−0.248625	+	0.387579i
$953$			31.2665i			1.01282i	0.862293	+	0.506410i	$0.169028\pi$
$953$			31.2665i			1.01282i	−0.862293	+	0.506410i	$0.830972\pi$
$954$	18.9949	−	16.6370i	0.614984	−	0.538643i
$955$	−0.989747	−	0.571431i	−0.0320274	−	0.0184911i
$956$	43.0856	−	14.1773i	1.39349	−	0.458525i
$957$	−24.1035	+	6.93595i	−0.779155	+	0.224207i
$958$	−5.23842	−	32.6795i	−0.169246	−	1.05583i
$959$	6.43131			0.207678
$960$	0.370107	−	1.05655i	0.0119452	−	0.0341000i
$961$	−7.45495	+	30.0903i	−0.240482	+	0.970654i
$962$	39.3603	−	31.9950i	1.26903	−	1.03156i
$963$	50.2262	−	31.5155i	1.61852	−	1.01557i
$964$	32.4729	+	29.0201i	1.04588	+	0.934675i
$965$			2.07551i			0.0668130i
$966$	9.79054	+	0.828946i	0.315005	+	0.0266709i
$967$	−37.7750	−	21.8094i	−1.21476	−	0.701343i	−0.250969	−	0.967995i	$-0.580749\pi$
$967$	−37.7750	−	21.8094i	−1.21476	−	0.701343i	−0.963793	+	0.266652i	$0.914083\pi$
$968$	−0.0729912	−	0.00341590i	−0.00234603	−	0.000109791i
$969$	−4.21810	−	14.6585i	−0.135505	−	0.470900i
$970$	0.350033	−	0.916974i	0.0112389	−	0.0294423i
$971$	−18.7230	−	32.4292i	−0.600850	−	1.04070i	−0.992693	−	0.120671i	$-0.961495\pi$
$971$	−18.7230	−	32.4292i	−0.600850	−	1.04070i	0.391842	−	0.920032i	$-0.371838\pi$
$972$	−30.8359	+	4.59828i	−0.989064	+	0.147490i
$973$	−8.82734	+	15.2894i	−0.282992	+	0.490156i
$974$	8.51989	−	22.3194i	0.272995	−	0.715160i
$975$	−34.2700	−	8.51046i	−1.09752	−	0.272553i
$976$	−19.1430	−	8.35247i	−0.612754	−	0.267356i
$977$			54.3939i			1.74022i	0.492861	+	0.870108i	$0.335951\pi$
$977$			54.3939i			1.74022i	−0.492861	+	0.870108i	$0.664049\pi$
$978$	7.25866	+	15.4531i	0.232106	+	0.494137i
$979$	−13.9501	+	8.05410i	−0.445847	+	0.257410i
$980$	−0.641238	+	0.717532i	−0.0204836	+	0.0229207i
$981$	−11.6852	−	6.18516i	−0.373081	−	0.197477i
$982$	−12.8288	−	4.89707i	−0.409383	−	0.156272i
$983$	−21.5667	−	37.3546i	−0.687871	−	1.19143i	−0.972525	−	0.232797i	$-0.925212\pi$
$983$	−21.5667	−	37.3546i	−0.687871	−	1.19143i	0.284654	−	0.958630i	$-0.408121\pi$
$984$	36.1244	+	38.2350i	1.15160	+	1.21889i
$985$	−0.425643	+	0.737235i	−0.0135621	+	0.0234902i
$986$	−4.79757	−	29.9293i	−0.152786	−	0.953143i
$987$	−8.57914	−	8.26930i	−0.273077	−	0.263215i
$988$	14.3227	+	2.98858i	0.455664	+	0.0950793i
$989$	−3.61651	−	2.08799i	−0.114998	−	0.0663943i
$990$	−1.07756	−	0.366537i	−0.0342469	−	0.0116493i
$991$			37.5010i			1.19126i	0.803259	+	0.595629i	$0.203097\pi$
$991$			37.5010i			1.19126i	−0.803259	+	0.595629i	$0.796903\pi$
$992$	−25.3434	−	18.7006i	−0.804653	−	0.593745i
$993$	16.2531	−	4.67693i	0.515775	−	0.148418i
$994$	−1.12655	−	1.38588i	−0.0357319	−	0.0439574i
$995$	0.100169	−	0.173497i	0.00317555	−	0.00550022i
$996$	28.6608	−	2.13856i	0.908153	−	0.0677628i
$997$	11.4294	+	19.7963i	0.361973	+	0.626956i	0.988286	−	0.152616i	$-0.0487699\pi$
$997$	11.4294	+	19.7963i	0.361973	+	0.626956i	−0.626312	+	0.779572i	$0.715437\pi$
$998$	−23.8308	+	3.82001i	−0.754351	+	0.120920i
$999$	−43.3753	+	14.2281i	−1.37233	+	0.450157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	372.2.p.a.191.12	yes	120
3.2	odd	2	inner	372.2.p.a.191.49	yes	120
4.3	odd	2	inner	372.2.p.a.191.50	yes	120
12.11	even	2	inner	372.2.p.a.191.11	✓	120
31.25	even	3	inner	372.2.p.a.335.12	yes	120
93.56	odd	6	inner	372.2.p.a.335.49	yes	120
124.87	odd	6	inner	372.2.p.a.335.50	yes	120
372.335	even	6	inner	372.2.p.a.335.11	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
372.2.p.a.191.11	✓	120	12.11	even	2	inner
372.2.p.a.191.12	yes	120	1.1	even	1	trivial
372.2.p.a.191.49	yes	120	3.2	odd	2	inner
372.2.p.a.191.50	yes	120	4.3	odd	2	inner
372.2.p.a.335.11	yes	120	372.335	even	6	inner
372.2.p.a.335.12	yes	120	31.25	even	3	inner
372.2.p.a.335.49	yes	120	93.56	odd	6	inner
372.2.p.a.335.50	yes	120	124.87	odd	6	inner

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:	\( N \)	\(=\)	\( 372 = 2^{2} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	372.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09739 + 0.892042i) q^{2} +(-1.68099 - 0.417450i) q^{3} +(0.408523 - 1.95783i) q^{4} +(0.0699686 - 0.0403964i) q^{5} +(2.21708 - 1.04141i) q^{6} +(-0.885120 - 0.511024i) q^{7} +(1.29816 + 2.51292i) q^{8} +(2.65147 + 1.40346i) q^{9} +(-0.0407475 + 0.106745i) q^{10} +(1.66026 + 2.87565i) q^{11} +(-1.50402 + 3.12056i) q^{12} +(-2.04134 - 3.53571i) q^{13} +(1.42717 - 0.228772i) q^{14} +(-0.134480 + 0.0386976i) q^{15} +(-3.66622 - 1.59964i) q^{16} +(-4.25631 - 2.45738i) q^{17} +(-4.16164 + 0.825081i) q^{18} +(-1.55179 - 0.895926i) q^{19} +(-0.0505056 - 0.153490i) q^{20} +(1.27455 + 1.22852i) q^{21} +(-4.38715 - 1.67469i) q^{22} -3.92474 q^{23} +(-1.13318 - 4.76612i) q^{24} +(-2.49674 + 4.32447i) q^{25} +(5.39414 + 2.05908i) q^{26} +(-3.87123 - 3.46606i) q^{27} +(-1.36209 + 1.52415i) q^{28} -4.36102i q^{29} +(0.113057 - 0.162428i) q^{30} +(-3.43111 - 4.38491i) q^{31} +(5.45021 - 1.51499i) q^{32} +(-1.59044 - 5.52702i) q^{33} +(6.86291 - 1.10010i) q^{34} -0.0825741 q^{35} +(3.83093 - 4.61779i) q^{36} +(4.39260 - 7.60821i) q^{37} +(2.50212 - 0.401082i) q^{38} +(1.95550 + 6.79566i) q^{39} +(0.192343 + 0.123385i) q^{40} +(-9.29867 + 5.36859i) q^{41} +(-2.49457 - 0.211211i) q^{42} +(0.921465 + 0.532008i) q^{43} +(6.30830 - 2.07574i) q^{44} +(0.242214 - 0.00891169i) q^{45} +(4.30696 - 3.50103i) q^{46} -6.73110 q^{47} +(5.49511 + 4.21945i) q^{48} +(-2.97771 - 5.15754i) q^{49} +(-1.11772 - 6.97282i) q^{50} +(6.12899 + 5.90763i) q^{51} +(-7.75626 + 2.55219i) q^{52} +(-5.15428 + 2.97582i) q^{53} +(7.34011 + 0.350321i) q^{54} +(0.232332 + 0.134137i) q^{55} +(0.135137 - 2.88763i) q^{56} +(2.23454 + 2.15384i) q^{57} +(3.89021 + 4.78574i) q^{58} +(-0.988055 + 1.71136i) q^{59} +(0.0208252 + 0.279098i) q^{60} +5.22147 q^{61} +(7.67679 + 1.75126i) q^{62} +(-1.62967 - 2.59720i) q^{63} +(-4.62956 + 6.52435i) q^{64} +(-0.285660 - 0.164926i) q^{65} +(6.67567 + 4.64655i) q^{66} +(-2.80149 + 1.61744i) q^{67} +(-6.54994 + 7.32924i) q^{68} +(6.59745 + 1.63838i) q^{69} +(0.0906158 - 0.0736595i) q^{70} +(-0.617822 - 1.07010i) q^{71} +(-0.0847550 + 8.48486i) q^{72} +(0.663259 + 1.14880i) q^{73} +(1.96645 + 12.2675i) q^{74} +(6.00225 - 6.22715i) q^{75} +(-2.38802 + 2.67214i) q^{76} -3.39373i q^{77} +(-8.20795 - 5.71309i) q^{78} +(13.1653 + 7.60097i) q^{79} +(-0.321140 + 0.0361774i) q^{80} +(5.06060 + 7.44247i) q^{81} +(5.41525 - 14.1862i) q^{82} +(-4.14834 - 7.18513i) q^{83} +(2.92592 - 1.99348i) q^{84} -0.397077 q^{85} +(-1.48578 + 0.238166i) q^{86} +(-1.82051 + 7.33084i) q^{87} +(-5.07101 + 7.90516i) q^{88} +4.85111i q^{89} +(-0.257854 + 0.225845i) q^{90} +4.17270i q^{91} +(-1.60335 + 7.68398i) q^{92} +(3.93719 + 8.80333i) q^{93} +(7.38663 - 6.00442i) q^{94} -0.144769 q^{95} +(-9.79420 + 0.271500i) q^{96} -8.59029 q^{97} +(7.86845 + 3.00359i) q^{98} +(0.366263 + 9.95482i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 12 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} - 4 q^{16} - 2 q^{18} - 14 q^{21} - 6 q^{22} - 4 q^{24} + 48 q^{25} + 6 q^{28} - 48 q^{30} + 4 q^{33} + 28 q^{34} + 2 q^{36} - 8 q^{37} + 36 q^{40} - 4 q^{42}+ \cdots + 48 q^{96}+O(q^{100}) \) 120 * q - 12 * q^4 - 2 * q^9 + 4 * q^10 - 4 * q^12 - 4 * q^16 - 2 * q^18 - 14 * q^21 - 6 * q^22 - 4 * q^24 + 48 * q^25 + 6 * q^28 - 48 * q^30 + 4 * q^33 + 28 * q^34 + 2 * q^36 - 8 * q^37 + 36 * q^40 - 4 * q^42 - 34 * q^45 - 48 * q^46 + 10 * q^48 + 60 * q^49 + 8 * q^52 - 84 * q^54 - 14 * q^57 - 28 * q^58 - 60 * q^60 - 64 * q^61 + 84 * q^64 - 132 * q^66 - 4 * q^69 - 120 * q^70 + 44 * q^72 + 28 * q^76 + 20 * q^78 - 2 * q^81 + 48 * q^82 - 8 * q^84 + 8 * q^85 - 10 * q^88 + 24 * q^90 - 78 * q^93 - 88 * q^94 + 48 * q^96

Introduction

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