LMFDB - Embedded newform 552.2.bb.a.469.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [552,2,Mod(13,552)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(552, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 11, 0, 14])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("552.13"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			469.4
Character	$\chi$	$=$	552.469
Dual form			552.2.bb.a.133.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37210 - 0.342538i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(1.76533 + 0.939996i) q^{4} +(2.07717 - 0.298651i) q^{5} +(1.26128 - 0.639663i) q^{6} +(1.51486 - 3.31707i) q^{7} +(-2.10024 - 1.89447i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-2.95239 - 0.301729i) q^{10} +(1.05293 - 3.58595i) q^{11} +(-1.94972 + 0.445647i) q^{12} +(-1.79893 + 0.821544i) q^{13} +(-3.21477 + 4.03247i) q^{14} +(-1.37424 + 1.58596i) q^{15} +(2.23282 + 3.31882i) q^{16} +(-5.87350 - 3.77467i) q^{17} +(-0.534322 + 1.30939i) q^{18} +(0.728744 + 1.13395i) q^{19} +(3.94763 + 1.42531i) q^{20} +(1.02737 + 3.49890i) q^{21} +(-2.67305 + 4.55962i) q^{22} +(-1.06231 - 4.67670i) q^{23} +(2.82787 + 0.0563794i) q^{24} +(-0.572037 + 0.167965i) q^{25} +(2.74973 - 0.511041i) q^{26} +(0.540641 + 0.841254i) q^{27} +(5.79227 - 4.43179i) q^{28} +(-4.71795 + 7.34128i) q^{29} +(2.42886 - 1.70537i) q^{30} +(2.50820 - 2.89462i) q^{31} +(-1.92683 - 5.31858i) q^{32} +(1.55254 + 3.39960i) q^{33} +(6.76608 + 7.19114i) q^{34} +(2.15596 - 7.34253i) q^{35} +(1.18166 - 1.61359i) q^{36} +(6.24565 + 0.897989i) q^{37} +(-0.611492 - 1.80552i) q^{38} +(0.821544 - 1.79893i) q^{39} +(-4.92833 - 3.30788i) q^{40} +(-0.777487 - 5.40754i) q^{41} +(-0.211150 - 5.15276i) q^{42} +(3.65456 - 3.16669i) q^{43} +(5.22955 - 5.34065i) q^{44} -2.09853i q^{45} +(-0.144351 + 6.78079i) q^{46} -4.13018 q^{47} +(-3.86081 - 1.04601i) q^{48} +(-4.12417 - 4.75954i) q^{49} +(0.842428 - 0.0345210i) q^{50} +(6.91078 - 0.993620i) q^{51} +(-3.94796 - 0.240687i) q^{52} +(-6.04491 - 2.76062i) q^{53} +(-0.453653 - 1.33948i) q^{54} +(1.11616 - 7.76307i) q^{55} +(-9.46565 + 4.09680i) q^{56} +(-1.29333 - 0.379755i) q^{57} +(8.98819 - 8.45691i) q^{58} +(3.91018 - 1.78572i) q^{59} +(-3.91680 + 1.50797i) q^{60} +(-3.49243 - 3.02621i) q^{61} +(-4.43304 + 3.11256i) q^{62} +(-3.06772 - 1.97151i) q^{63} +(0.821993 + 7.95766i) q^{64} +(-3.49132 + 2.24374i) q^{65} +(-0.965759 - 5.19641i) q^{66} +(1.71718 + 5.84817i) q^{67} +(-6.82053 - 12.1846i) q^{68} +(3.86542 + 2.83875i) q^{69} +(-5.47330 + 9.33621i) q^{70} +(8.60887 - 2.52779i) q^{71} +(-2.17408 + 1.80925i) q^{72} +(12.0605 - 7.75082i) q^{73} +(-8.26208 - 3.37151i) q^{74} +(0.322323 - 0.501544i) q^{75} +(0.220571 + 2.68681i) q^{76} +(-10.2998 - 8.92484i) q^{77} +(-1.74345 + 2.18691i) q^{78} +(0.356204 + 0.779979i) q^{79} +(5.62910 + 6.22690i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-0.785497 + 7.68602i) q^{82} +(9.02183 + 1.29714i) q^{83} +(-1.47530 + 7.14245i) q^{84} +(-13.3276 - 6.08649i) q^{85} +(-6.09914 + 3.09320i) q^{86} +(-1.24192 - 8.63777i) q^{87} +(-9.00486 + 5.53660i) q^{88} +(9.92930 + 11.4590i) q^{89} +(-0.718826 + 2.87940i) q^{90} +7.21171i q^{91} +(2.52075 - 9.25450i) q^{92} +3.83013i q^{93} +(5.66704 + 1.41475i) q^{94} +(1.85238 + 2.13776i) q^{95} +(4.93913 + 2.75771i) q^{96} +(1.57487 + 10.9534i) q^{97} +(4.02846 + 7.94327i) q^{98} +(-3.39960 - 1.55254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32}+ \cdots - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.37210	−	0.342538i	−0.970224	−	0.242211i
$2$	−1.37210	−	0.342538i	−0.970224	−	0.242211i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$4$	1.76533	+	0.939996i	0.882667	+	0.469998i
$5$	2.07717	−	0.298651i	0.928937	−	0.133561i	0.338795	−	0.940860i	$-0.389981\pi$
$5$	2.07717	−	0.298651i	0.928937	−	0.133561i	0.590142	+	0.807299i	$0.299072\pi$
$6$	1.26128	−	0.639663i	0.514916	−	0.261141i
$7$	1.51486	−	3.31707i	0.572562	−	1.25374i	−0.372860	−	0.927888i	$-0.621623\pi$
$7$	1.51486	−	3.31707i	0.572562	−	1.25374i	0.945422	−	0.325849i	$-0.105650\pi$
$8$	−2.10024	−	1.89447i	−0.742546	−	0.669795i
$9$	0.142315	−	0.989821i	0.0474383	−	0.329940i
$10$	−2.95239	−	0.301729i	−0.933627	−	0.0954149i
$11$	1.05293	−	3.58595i	0.317470	−	1.08120i	−0.633967	−	0.773360i	$-0.718575\pi$
$11$	1.05293	−	3.58595i	0.317470	−	1.08120i	0.951437	−	0.307843i	$-0.0996073\pi$
$12$	−1.94972	+	0.445647i	−0.562835	+	0.128647i
$13$	−1.79893	+	0.821544i	−0.498934	+	0.227855i	−0.648954	−	0.760828i	$-0.724793\pi$
$13$	−1.79893	+	0.821544i	−0.498934	+	0.227855i	0.150020	+	0.988683i	$0.452066\pi$
$14$	−3.21477	+	4.03247i	−0.859182	+	1.07772i
$15$	−1.37424	+	1.58596i	−0.354828	+	0.409493i
$16$	2.23282	+	3.31882i	0.558204	+	0.829704i
$17$	−5.87350	−	3.77467i	−1.42453	−	0.915492i	−0.999949	−	0.0101043i	$-0.996784\pi$
$17$	−5.87350	−	3.77467i	−1.42453	−	0.915492i	−0.424585	−	0.905388i	$-0.639580\pi$
$18$	−0.534322	+	1.30939i	−0.125941	+	0.308626i
$19$	0.728744	+	1.13395i	0.167185	+	0.260146i	0.914730	−	0.404067i	$-0.132404\pi$
$19$	0.728744	+	1.13395i	0.167185	+	0.260146i	−0.747544	+	0.664212i	$0.768767\pi$
$20$	3.94763	+	1.42531i	0.882716	+	0.318709i
$21$	1.02737	+	3.49890i	0.224190	+	0.763522i
$22$	−2.67305	+	4.55962i	−0.569896	+	0.972114i
$23$	−1.06231	−	4.67670i	−0.221507	−	0.975159i
$23$	−1.06231	−	4.67670i	−0.221507	−	0.975159i
$24$	2.82787	+	0.0563794i	0.577236	+	0.0115084i
$25$	−0.572037	+	0.167965i	−0.114407	+	0.0335930i
$26$	2.74973	−	0.511041i	0.539266	−	0.100223i
$27$	0.540641	+	0.841254i	0.104046	+	0.161899i
$28$	5.79227	−	4.43179i	1.09464	−	0.837529i
$29$	−4.71795	+	7.34128i	−0.876102	+	1.36324i	0.0550021	+	0.998486i	$0.482483\pi$
$29$	−4.71795	+	7.34128i	−0.876102	+	1.36324i	−0.931104	+	0.364755i	$0.881153\pi$
$30$	2.42886	−	1.70537i	0.443446	−	0.311357i
$31$	2.50820	−	2.89462i	0.450487	−	0.519890i	−0.484395	−	0.874850i	$-0.660960\pi$
$31$	2.50820	−	2.89462i	0.450487	−	0.519890i	0.934881	+	0.354960i	$0.115506\pi$
$32$	−1.92683	−	5.31858i	−0.340619	−	0.940201i
$33$	1.55254	+	3.39960i	0.270263	+	0.591794i
$34$	6.76608	+	7.19114i	1.16037	+	1.23327i
$35$	2.15596	−	7.34253i	0.364424	−	1.24111i
$36$	1.18166	−	1.61359i	0.196944	−	0.268932i
$37$	6.24565	+	0.897989i	1.02678	+	0.147628i	0.635065	−	0.772459i	$-0.280973\pi$
$37$	6.24565	+	0.897989i	1.02678	+	0.147628i	0.391713	+	0.920087i	$0.371882\pi$
$38$	−0.611492	−	1.80552i	−0.0991970	−	0.292893i
$39$	0.821544	−	1.79893i	0.131552	−	0.288060i
$40$	−4.92833	−	3.30788i	−0.779237	−	0.523022i
$41$	−0.777487	−	5.40754i	−0.121423	−	0.844516i	−0.955946	−	0.293543i	$-0.905166\pi$
$41$	−0.777487	−	5.40754i	−0.121423	−	0.844516i	0.834523	−	0.550973i	$-0.185743\pi$
$42$	−0.211150	−	5.15276i	−0.0325811	−	0.795089i
$43$	3.65456	−	3.16669i	0.557315	−	0.482916i	−0.330063	−	0.943959i	$-0.607070\pi$
$43$	3.65456	−	3.16669i	0.557315	−	0.482916i	0.887378	+	0.461043i	$0.152525\pi$
$44$	5.22955	−	5.34065i	0.788384	−	0.805133i
$45$		−	2.09853i		−	0.312830i
$46$	−0.144351	+	6.78079i	−0.0212834	+	0.999773i
$47$	−4.13018			−0.602449			−0.301225	−	0.953553i	$-0.597395\pi$
$47$	−4.13018			−0.602449			−0.301225	+	0.953553i	$0.597395\pi$
$48$	−3.86081	−	1.04601i	−0.557260	−	0.150979i
$49$	−4.12417	−	4.75954i	−0.589167	−	0.679934i
$50$	0.842428	−	0.0345210i	0.119137	−	0.00488201i
$51$	6.91078	−	0.993620i	0.967703	−	0.139135i
$52$	−3.94796	−	0.240687i	−0.547484	−	0.0333773i
$53$	−6.04491	−	2.76062i	−0.830332	−	0.379200i	−0.0455428	−	0.998962i	$-0.514502\pi$
$53$	−6.04491	−	2.76062i	−0.830332	−	0.379200i	−0.784790	+	0.619762i	$0.787229\pi$
$54$	−0.453653	−	1.33948i	−0.0617344	−	0.182280i
$55$	1.11616	−	7.76307i	0.150503	−	1.04677i
$56$	−9.46565	+	4.09680i	−1.26490	+	0.547458i
$57$	−1.29333	−	0.379755i	−0.171305	−	0.0502998i
$58$	8.98819	−	8.45691i	1.18021	−	1.11045i
$59$	3.91018	−	1.78572i	0.509061	−	0.232481i	−0.144290	−	0.989535i	$-0.546090\pi$
$59$	3.91018	−	1.78572i	0.509061	−	0.232481i	0.653351	+	0.757055i	$0.273362\pi$
$60$	−3.91680	+	1.50797i	−0.505656	+	0.194678i
$61$	−3.49243	−	3.02621i	−0.447160	−	0.387466i	0.401968	−	0.915654i	$-0.368326\pi$
$61$	−3.49243	−	3.02621i	−0.447160	−	0.387466i	−0.849128	+	0.528187i	$0.822872\pi$
$62$	−4.43304	+	3.11256i	−0.562996	+	0.395296i
$63$	−3.06772	−	1.97151i	−0.386497	−	0.248387i
$64$	0.821993	+	7.95766i	0.102749	+	0.994707i
$65$	−3.49132	+	2.24374i	−0.433045	+	0.278301i
$66$	−0.965759	−	5.19641i	−0.118877	−	0.639634i
$67$	1.71718	+	5.84817i	0.209787	+	0.714468i	0.995405	+	0.0957564i	$0.0305270\pi$
$67$	1.71718	+	5.84817i	0.209787	+	0.714468i	−0.785618	+	0.618712i	$0.787655\pi$
$68$	−6.82053	−	12.1846i	−0.827110	−	1.47760i
$69$	3.86542	+	2.83875i	0.465342	+	0.341745i
$70$	−5.47330	+	9.33621i	−0.654184	+	1.11589i
$71$	8.60887	−	2.52779i	1.02169	−	0.299994i	0.272360	−	0.962196i	$-0.412196\pi$
$71$	8.60887	−	2.52779i	1.02169	−	0.299994i	0.749326	+	0.662202i	$0.230378\pi$
$72$	−2.17408	+	1.80925i	−0.256218	+	0.213222i
$73$	12.0605	−	7.75082i	1.41158	−	0.907165i	0.411585	−	0.911371i	$-0.364975\pi$
$73$	12.0605	−	7.75082i	1.41158	−	0.907165i	0.999991	+	0.00420642i	$0.00133895\pi$
$74$	−8.26208	−	3.37151i	−0.960447	−	0.391930i
$75$	0.322323	−	0.501544i	0.0372186	−	0.0579133i
$76$	0.220571	+	2.68681i	0.0253012	+	0.308199i
$77$	−10.2998	−	8.92484i	−1.17377	−	1.01708i
$78$	−1.74345	+	2.18691i	−0.197406	+	0.247619i
$79$	0.356204	+	0.779979i	0.0400761	+	0.0877545i	0.928611	−	0.371054i	$-0.121004\pi$
$79$	0.356204	+	0.779979i	0.0400761	+	0.0877545i	−0.888535	+	0.458809i	$0.848276\pi$
$80$	5.62910	+	6.22690i	0.629352	+	0.696188i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−0.785497	+	7.68602i	−0.0867437	+	0.848779i
$83$	9.02183	+	1.29714i	0.990275	+	0.142380i	0.618367	−	0.785890i	$-0.287795\pi$
$83$	9.02183	+	1.29714i	0.990275	+	0.142380i	0.371908	+	0.928270i	$0.378704\pi$
$84$	−1.47530	+	7.14245i	−0.160968	+	0.779305i
$85$	−13.3276	−	6.08649i	−1.44558	−	0.660173i
$86$	−6.09914	+	3.09320i	−0.657687	+	0.333549i
$87$	−1.24192	−	8.63777i	−0.133148	−	0.926066i
$88$	−9.00486	+	5.53660i	−0.959921	+	0.590203i
$89$	9.92930	+	11.4590i	1.05250	+	1.21465i	0.976042	+	0.217582i	$0.0698168\pi$
$89$	9.92930	+	11.4590i	1.05250	+	1.21465i	0.0764617	+	0.997073i	$0.475638\pi$
$90$	−0.718826	+	2.87940i	−0.0757709	+	0.303515i
$91$			7.21171i			0.755993i
$92$	2.52075	−	9.25450i	0.262806	−	0.964849i
$93$			3.83013i			0.397166i
$94$	5.66704	+	1.41475i	0.584510	+	0.145920i
$95$	1.85238	+	2.13776i	0.190050	+	0.219329i
$96$	4.93913	+	2.75771i	0.504098	+	0.281458i
$97$	1.57487	+	10.9534i	0.159903	+	1.11215i	0.898808	+	0.438343i	$0.144434\pi$
$97$	1.57487	+	10.9534i	0.159903	+	1.11215i	−0.738904	+	0.673810i	$0.764657\pi$
$98$	4.02846	+	7.94327i	0.406936	+	0.802391i
$99$	−3.39960	−	1.55254i	−0.341673	−	0.156037i
$100$	−1.16772	−	0.241198i	−0.116772	−	0.0241198i
$101$	13.6909	+	1.96845i	1.36230	+	0.195869i	0.784407	−	0.620247i	$-0.212968\pi$
$101$	13.6909	+	1.96845i	1.36230	+	0.195869i	0.577889	+	0.816115i	$0.303877\pi$
$102$	−9.82266	−	1.00386i	−0.972588	−	0.0993968i
$103$	−7.03922	−	2.06690i	−0.693595	−	0.203658i	−0.0841111	−	0.996456i	$-0.526805\pi$
$103$	−7.03922	−	2.06690i	−0.693595	−	0.203658i	−0.609484	+	0.792799i	$0.708623\pi$
$104$	5.33457	+	1.68258i	0.523098	+	0.164990i
$105$	3.17897	+	6.96097i	0.310236	+	0.679321i
$106$	7.34862	+	5.85847i	0.713761	+	0.569025i
$107$	1.25824	+	1.09027i	0.121639	+	0.105401i	0.713556	−	0.700598i	$-0.247083\pi$
$107$	1.25824	+	1.09027i	0.121639	+	0.105401i	−0.591917	+	0.805999i	$0.701629\pi$
$108$	0.163637	+	1.99329i	0.0157460	+	0.191805i
$109$	−5.07710	+	7.90013i	−0.486298	+	0.756695i	−0.994522	−	0.104530i	$-0.966666\pi$
$109$	−5.07710	+	7.90013i	−0.486298	+	0.756695i	0.508223	+	0.861225i	$0.330302\pi$
$110$	−4.19064	+	10.2694i	−0.399561	+	0.979149i
$111$	−5.30820	+	3.41138i	−0.503832	+	0.323793i
$112$	14.3912	−	2.37888i	1.35984	−	0.224783i
$113$	9.85550	−	2.89384i	0.927127	−	0.272229i	0.216894	−	0.976195i	$-0.430407\pi$
$113$	9.85550	−	2.89384i	0.927127	−	0.272229i	0.710234	+	0.703966i	$0.248589\pi$
$114$	1.64450	+	0.964077i	0.154021	+	0.0902940i
$115$	−3.60329	−	9.39702i	−0.336009	−	0.876277i
$116$	−15.2295	+	8.52496i	−1.41403	+	0.791522i
$117$	0.557168	+	1.89754i	0.0515102	+	0.175427i
$118$	−5.97684	+	1.11080i	−0.550213	+	0.102258i
$119$	−21.4184	+	13.7648i	−1.96342	+	1.26181i
$120$	5.89078	−	0.727437i	0.537753	−	0.0664056i
$121$	−2.49656	−	1.60444i	−0.226960	−	0.145858i
$122$	3.75539	+	5.34856i	0.339997	+	0.484236i
$123$	4.12877	+	3.57760i	0.372279	+	0.322581i
$124$	7.14875	−	2.75228i	0.641977	−	0.247162i
$125$	−10.6825	+	4.87853i	−0.955471	+	0.436349i
$126$	3.53392	+	3.75592i	0.314826	+	0.334604i
$127$	−6.31413	−	1.85399i	−0.560288	−	0.164515i	−0.0106874	−	0.999943i	$-0.503402\pi$
$127$	−6.31413	−	1.85399i	−0.560288	−	0.164515i	−0.549601	+	0.835427i	$0.685220\pi$
$128$	1.59794	−	11.2003i	0.141240	−	0.989975i
$129$	−0.688188	+	4.78645i	−0.0605916	+	0.421424i
$130$	5.55902	−	1.88273i	0.487559	−	0.165126i
$131$	9.04610	+	4.13122i	0.790362	+	0.360946i	0.769345	−	0.638833i	$-0.220583\pi$
$131$	9.04610	+	4.13122i	0.790362	+	0.360946i	0.0210164	+	0.999779i	$0.493310\pi$
$132$	−0.454848	+	7.46082i	−0.0395894	+	0.649381i
$133$	4.86533	−	0.699529i	0.421878	−	0.0606569i
$134$	−0.352923	−	8.61250i	−0.0304879	−	0.744007i
$135$	1.37424	+	1.58596i	0.118276	+	0.136498i
$136$	5.18476	+	19.0549i	0.444590	+	1.63394i
$137$	15.7724			1.34753			0.673763	−	0.738948i	$-0.264677\pi$
$137$	15.7724			1.34753			0.673763	+	0.738948i	$0.264677\pi$
$138$	−4.33138	−	5.21911i	−0.368712	−	0.444280i
$139$		−	12.2360i		−	1.03784i	−0.854822	−	0.518922i	$-0.826334\pi$
$139$		−	12.2360i		−	1.03784i	0.854822	−	0.518922i	$-0.173666\pi$
$140$	10.7079	−	10.9354i	0.904986	−	0.924213i
$141$	3.12138	−	2.70470i	0.262868	−	0.227776i
$142$	−12.6781	+	0.519524i	−1.06392	+	0.0435975i
$143$	1.05187	+	7.31590i	0.0879616	+	0.611786i
$144$	3.60280	−	1.73777i	0.300233	−	0.144814i
$145$	−7.60749	+	16.6581i	−0.631768	+	1.38338i
$146$	−19.2032	+	6.50374i	−1.58927	+	0.538253i
$147$	6.23367	+	0.896267i	0.514145	+	0.0739229i
$148$	10.1816	+	7.45614i	0.836919	+	0.612891i
$149$	5.16996	−	17.6073i	0.423539	−	1.44244i	−0.421055	−	0.907035i	$-0.638340\pi$
$149$	5.16996	−	17.6073i	0.423539	−	1.44244i	0.844594	−	0.535407i	$-0.179842\pi$
$150$	−0.614058	+	0.577762i	−0.0501376	+	0.0471741i
$151$	4.41411	+	9.66554i	0.359215	+	0.786571i	0.999825	+	0.0187046i	$0.00595420\pi$
$151$	4.41411	+	9.66554i	0.359215	+	0.786571i	−0.640610	+	0.767866i	$0.721319\pi$
$152$	0.617691	−	3.76214i	0.0501014	−	0.305150i
$153$	−4.57214	+	5.27653i	−0.369635	+	0.426582i
$154$	11.0753	+	15.7739i	0.892474	+	1.27110i
$155$	4.34548	−	6.76169i	0.349037	−	0.543112i
$156$	3.14129	−	2.40347i	0.251504	−	0.192431i
$157$	2.86137	+	4.45238i	0.228362	+	0.355339i	0.936459	−	0.350777i	$-0.114082\pi$
$157$	2.86137	+	4.45238i	0.228362	+	0.355339i	−0.708097	+	0.706115i	$0.750446\pi$
$158$	−0.221577	−	1.19223i	−0.0176277	−	0.0948484i
$159$	6.37626	−	1.87224i	0.505670	−	0.148478i
$160$	−5.59075	−	10.4721i	−0.441988	−	0.827895i
$161$	−17.1222	−	3.56077i	−1.34942	−	0.280628i
$162$	1.22002	+	0.715229i	0.0958538	+	0.0561937i
$163$	−5.37814	−	18.3162i	−0.421248	−	1.43464i	−0.847868	−	0.530208i	$-0.822114\pi$
$163$	−5.37814	−	18.3162i	−0.421248	−	1.43464i	0.426619	−	0.904431i	$-0.359704\pi$
$164$	3.71054	−	10.2770i	0.289745	−	0.802495i
$165$	4.24019	+	6.59786i	0.330098	+	0.513643i
$166$	−11.9346	−	4.87014i	−0.926302	−	0.377996i
$167$	−1.20042	−	0.771465i	−0.0928915	−	0.0596977i	0.493370	−	0.869819i	$-0.335765\pi$
$167$	−1.20042	−	0.771465i	−0.0928915	−	0.0596977i	−0.586262	+	0.810122i	$0.699401\pi$
$168$	4.47083	−	9.29483i	0.344932	−	0.717112i
$169$	−5.95197	+	6.86894i	−0.457844	+	0.528380i
$170$	16.2019	+	12.9165i	1.24263	+	0.990650i
$171$	1.22612	−	0.559949i	0.0937635	−	0.0428204i
$172$	9.42819	−	2.15500i	0.718893	−	0.164317i
$173$	−5.38933	+	18.3544i	−0.409743	+	1.39546i	0.453764	+	0.891122i	$0.350081\pi$
$173$	−5.38933	+	18.3544i	−0.409743	+	1.39546i	−0.863507	+	0.504336i	$0.831737\pi$
$174$	−1.25472	+	12.2773i	−0.0951200	+	0.930741i
$175$	−0.309401	+	2.15193i	−0.0233885	+	0.162671i
$176$	14.2521	−	4.51228i	1.07429	−	0.340126i
$177$	−1.78572	+	3.91018i	−0.134223	+	0.293907i
$178$	−9.69887	−	19.1241i	−0.726961	−	1.43341i
$179$	−18.5492	+	2.66698i	−1.38644	+	0.199339i	−0.794803	−	0.606868i	$-0.792426\pi$
$179$	−18.5492	+	2.66698i	−1.38644	+	0.199339i	−0.591633	+	0.806207i	$0.701517\pi$
$180$	1.97261	−	3.70460i	0.147029	−	0.276125i
$181$	2.31209	−	2.00344i	0.171857	−	0.148915i	−0.564686	−	0.825306i	$-0.691003\pi$
$181$	2.31209	−	2.00344i	0.171857	−	0.148915i	0.736542	+	0.676391i	$0.236457\pi$
$182$	2.47029	−	9.89521i	0.183110	−	0.733482i
$183$	4.62115			0.341605
$184$	−6.62875	+	11.8347i	−0.488678	+	0.872464i
$185$	13.2414			0.973530
$186$	1.31197	−	5.25534i	0.0961982	−	0.385340i
$187$	−19.7202	+	17.0876i	−1.44208	+	1.24957i
$188$	−7.29116	−	3.88236i	−0.531762	−	0.283150i
$189$	3.60949	−	0.518967i	0.262552	−	0.0377493i
$190$	−1.80939	−	3.56774i	−0.131267	−	0.258831i
$191$	−9.84554	+	21.5587i	−0.712399	+	1.55994i	0.111862	+	0.993724i	$0.464319\pi$
$191$	−9.84554	+	21.5587i	−0.712399	+	1.55994i	−0.824260	+	0.566211i	$0.808409\pi$
$192$	−5.83238	−	5.47571i	−0.420916	−	0.395175i
$193$	0.802977	−	5.58482i	0.0577995	−	0.402004i	−0.940298	−	0.340352i	$-0.889454\pi$
$193$	0.802977	−	5.58482i	0.0577995	−	0.402004i	0.998098	−	0.0616526i	$-0.0196371\pi$
$194$	1.59109	−	15.5687i	0.114234	−	1.11777i
$195$	1.16923	−	3.98203i	0.0837304	−	0.285159i
$196$	−2.80658	−	12.2789i	−0.200470	−	0.877063i
$197$	−24.5690	+	11.2203i	−1.75047	+	0.799413i	−0.762079	+	0.647484i	$0.775821\pi$
$197$	−24.5690	+	11.2203i	−1.75047	+	0.799413i	−0.988391	+	0.151929i	$0.951452\pi$
$198$	4.13279	+	3.29474i	0.293705	+	0.234147i
$199$	4.59056	−	5.29779i	0.325416	−	0.375550i	−0.569342	−	0.822101i	$-0.692802\pi$
$199$	4.59056	−	5.29779i	0.325416	−	0.375550i	0.894759	+	0.446550i	$0.147348\pi$
$200$	1.51962	+	0.730938i	0.107453	+	0.0516851i
$201$	−5.12750	−	3.29524i	−0.361666	−	0.232428i
$202$	−18.1111	−	7.39058i	−1.27429	−	0.519999i
$203$	17.2045	+	26.7708i	1.20752	+	1.87894i
$204$	13.1338	+	4.74203i	0.919553	+	0.332009i
$205$	−3.22994	−	11.0002i	−0.225589	−	0.768285i
$206$	8.95054	+	5.24720i	0.623614	+	0.365590i
$207$	−4.78028	+	0.385932i	−0.332252	+	0.0268242i
$208$	−6.74323	−	4.13596i	−0.467559	−	0.286778i
$209$	4.83359	−	1.41927i	0.334347	−	0.0981730i
$210$	−1.97747	−	10.6401i	−0.136459	−	0.734236i
$211$	−9.61288	−	14.9579i	−0.661778	−	1.02975i	−0.996181	−	0.0873162i	$-0.972171\pi$
$211$	−9.61288	−	14.9579i	−0.661778	−	1.02975i	0.334403	−	0.942430i	$-0.391465\pi$
$212$	−8.07632	−	10.5556i	−0.554684	−	0.724962i
$213$	−4.85080	+	7.54799i	−0.332371	+	0.517180i
$214$	−1.35298	−	1.92696i	−0.0924875	−	0.131724i
$215$	6.64539	−	7.66918i	0.453212	−	0.523034i
$216$	0.458253	−	2.79106i	0.0311801	−	0.189907i
$217$	−5.80211	−	12.7048i	−0.393873	−	0.862461i
$218$	9.67241	−	9.10069i	0.655098	−	0.616376i
$219$	−4.03902	+	13.7556i	−0.272932	+	0.929520i
$220$	9.26765	−	12.6552i	0.624825	−	0.853215i
$221$	13.6671	+	1.96503i	0.919348	+	0.132182i
$222$	8.45193	−	2.86250i	0.567256	−	0.192118i
$223$	11.3900	−	24.9406i	0.762730	−	1.67014i	0.0206927	−	0.999786i	$-0.493413\pi$
$223$	11.3900	−	24.9406i	0.762730	−	1.67014i	0.742037	−	0.670359i	$-0.233860\pi$
$224$	−20.5610	−	1.66545i	−1.37379	−	0.111278i
$225$	0.0848462	+	0.590118i	0.00565641	+	0.0393412i
$226$	−14.5140	+	0.594755i	−0.965458	+	0.0395625i
$227$	1.86788	−	1.61852i	0.123975	−	0.107425i	−0.590667	−	0.806916i	$-0.701135\pi$
$227$	1.86788	−	1.61852i	0.123975	−	0.107425i	0.714642	+	0.699491i	$0.246590\pi$
$228$	−1.92619	−	1.88612i	−0.127565	−	0.124911i
$229$			6.36601i			0.420678i	0.977629	+	0.210339i	$0.0674568\pi$
$229$			6.36601i			0.420678i	−0.977629	+	0.210339i	$0.932543\pi$
$230$	1.72525	+	14.1279i	0.113760	+	0.931569i
$231$	13.6286			0.896697
$232$	23.8166	−	6.48042i	1.56364	−	0.425460i
$233$	−0.474324	−	0.547399i	−0.0310740	−	0.0358613i	0.740000	−	0.672607i	$-0.234826\pi$
$233$	−0.474324	−	0.547399i	−0.0310740	−	0.0358613i	−0.771074	+	0.636746i	$0.780280\pi$
$234$	−0.114512	−	2.79447i	−0.00748587	−	0.182680i
$235$	−8.57908	+	1.23349i	−0.559637	+	0.0804637i
$236$	8.58134	+	0.523160i	0.558597	+	0.0340548i
$237$	−0.779979	−	0.356204i	−0.0506651	−	0.0231380i
$238$	34.1032	−	11.5501i	2.21058	−	0.748679i
$239$	−2.86899	+	19.9543i	−0.185579	+	1.29073i	0.657709	+	0.753272i	$0.271526\pi$
$239$	−2.86899	+	19.9543i	−0.185579	+	1.29073i	−0.843289	+	0.537461i	$0.819383\pi$
$240$	−8.33194	−	1.01970i	−0.537824	−	0.0658214i
$241$	24.8930	+	7.30925i	1.60350	+	0.470830i	0.956518	−	0.291674i	$-0.0942122\pi$
$241$	24.8930	+	7.30925i	1.60350	+	0.470830i	0.646983	+	0.762504i	$0.276030\pi$
$242$	2.87596	+	3.05663i	0.184874	+	0.196488i
$243$	0.909632	−	0.415415i	0.0583529	−	0.0266489i
$244$	−3.32069	−	8.62515i	−0.212585	−	0.552168i
$245$	−9.98802	−	8.65467i	−0.638111	−	0.552927i
$246$	−4.43964	−	6.32310i	−0.283061	−	0.403146i
$247$	−2.24255	−	1.44120i	−0.142690	−	0.0917013i
$248$	−10.7516	+	1.32768i	−0.682727	+	0.0843080i
$249$	−7.66769	+	4.92773i	−0.485920	+	0.312282i
$250$	16.3286	−	3.03468i	1.03271	−	0.191930i
$251$	4.74717	+	16.1674i	0.299638	+	1.02047i	0.962398	+	0.271643i	$0.0875669\pi$
$251$	4.74717	+	16.1674i	0.299638	+	1.02047i	−0.662760	+	0.748832i	$0.730615\pi$
$252$	−3.56235	−	6.36402i	−0.224407	−	0.400896i
$253$	−17.8889	−	1.11485i	−1.12467	−	0.0700899i
$254$	8.02857	+	4.70670i	0.503757	+	0.295325i
$255$	14.0581	−	4.12783i	0.880352	−	0.258495i
$256$	−6.02907	+	14.8206i	−0.376817	+	0.926288i
$257$	3.49386	−	2.24537i	0.217941	−	0.140062i	−0.427116	−	0.904197i	$-0.640470\pi$
$257$	3.49386	−	2.24537i	0.217941	−	0.140062i	0.645056	+	0.764135i	$0.276834\pi$
$258$	2.58381	−	6.33177i	0.160861	−	0.394199i
$259$	12.4400	−	19.3570i	0.772982	−	1.20278i
$260$	−8.27246	+	0.679118i	−0.513036	+	0.0421171i
$261$	6.59512	+	5.71470i	0.408228	+	0.353731i
$262$	−10.9971	−	8.76709i	−0.679402	−	0.541633i
$263$	−3.83821	−	8.40452i	−0.236674	−	0.518245i	0.753607	−	0.657326i	$-0.228312\pi$
$263$	−3.83821	−	8.40452i	−0.236674	−	0.518245i	−0.990281	+	0.139081i	$0.955585\pi$
$264$	3.17971	−	10.0812i	0.195698	−	0.620456i
$265$	−13.3807	−	3.92894i	−0.821973	−	0.241353i
$266$	−6.91536	−	0.706737i	−0.424008	−	0.0433328i
$267$	−15.0081	−	2.15784i	−0.918483	−	0.132058i
$268$	−2.46586	+	11.9381i	−0.150627	+	0.729237i
$269$	3.29888	+	1.50655i	0.201136	+	0.0918558i	0.513436	−	0.858128i	$-0.328372\pi$
$269$	3.29888	+	1.50655i	0.201136	+	0.0918558i	−0.312300	+	0.949983i	$0.601099\pi$
$270$	−1.34235	−	2.64683i	−0.0816929	−	0.161081i
$271$	−3.06787	−	21.3375i	−0.186360	−	1.29616i	−0.841337	−	0.540511i	$-0.818231\pi$
$271$	−3.06787	−	21.3375i	−0.186360	−	1.29616i	0.654977	−	0.755648i	$-0.272678\pi$
$272$	−0.587009	−	27.9212i	−0.0355926	−	1.69297i
$273$	−4.72267	−	5.45025i	−0.285829	−	0.329864i
$274$	−21.6413	−	5.40265i	−1.30740	−	0.326386i
$275$			2.22815i			0.134362i
$276$	4.15536	+	8.64483i	0.250123	+	0.520357i
$277$			5.79483i			0.348178i	0.984730	+	0.174089i	$0.0556980\pi$
$277$			5.79483i			0.348178i	−0.984730	+	0.174089i	$0.944302\pi$
$278$	−4.19130	+	16.7891i	−0.251377	+	1.00694i
$279$	−2.50820	−	2.89462i	−0.150162	−	0.173297i
$280$	−18.4382	+	11.3367i	−1.10189	+	0.677495i
$281$	−4.41773	−	30.7260i	−0.263540	−	1.83296i	−0.505684	−	0.862719i	$-0.668760\pi$
$281$	−4.41773	−	30.7260i	−0.263540	−	1.83296i	0.242144	−	0.970240i	$-0.422149\pi$
$282$	−5.20932	+	2.64193i	−0.310211	+	0.157324i
$283$	1.23064	+	0.562013i	0.0731538	+	0.0334082i	0.451656	−	0.892192i	$-0.350833\pi$
$283$	1.23064	+	0.562013i	0.0731538	+	0.0334082i	−0.378502	+	0.925600i	$0.623561\pi$
$284$	17.5737	+	3.62990i	1.04280	+	0.215395i
$285$	−2.79987	−	0.402560i	−0.165850	−	0.0238456i
$286$	1.06270	−	10.3985i	0.0628391	−	0.614875i
$287$	−19.1150	−	5.61267i	−1.12832	−	0.331305i
$288$	−5.53866	+	1.15031i	−0.326369	+	0.0677824i
$289$	13.1878	+	28.8774i	0.775756	+	1.69867i
$290$	16.1443	−	20.2507i	0.948025	−	1.18916i
$291$	−8.36318	−	7.24674i	−0.490258	−	0.424811i
$292$	28.5766	−	2.34596i	1.67232	−	0.137287i
$293$	−2.70820	+	4.21404i	−0.158215	+	0.246187i	−0.911306	−	0.411729i	$-0.864925\pi$
$293$	−2.70820	+	4.21404i	−0.158215	+	0.246187i	0.753092	+	0.657915i	$0.228562\pi$
$294$	−8.24624	−	3.36504i	−0.480930	−	0.196253i
$295$	7.58878	−	4.87701i	0.441836	−	0.283951i
$296$	−11.4161	−	13.7182i	−0.663549	−	0.797352i
$297$	3.58595	−	1.05293i	0.208078	−	0.0610971i
$298$	−13.1249	+	22.3881i	−0.760303	+	1.29691i
$299$	5.75313	+	7.54032i	0.332712	+	0.436068i
$300$	1.04046	−	0.582411i	0.0600708	−	0.0336255i
$301$	−4.96802	−	16.9195i	−0.286352	−	0.975225i
$302$	−2.74579	−	14.7741i	−0.158002	−	0.850155i
$303$	−11.6360	+	7.47797i	−0.668468	+	0.429598i
$304$	−2.13621	+	4.95046i	−0.122520	+	0.283929i
$305$	−8.15815	−	5.24292i	−0.467134	−	0.300209i
$306$	8.08086	−	5.67381i	0.461952	−	0.324350i
$307$	−6.08620	−	5.27372i	−0.347358	−	0.300987i	0.463655	−	0.886016i	$-0.346538\pi$
$307$	−6.08620	−	5.27372i	−0.347358	−	0.300987i	−0.811013	+	0.585029i	$0.801083\pi$
$308$	−9.79331	−	25.4371i	−0.558026	−	1.44941i
$309$	6.67342	−	3.04765i	0.379638	−	0.173375i
$310$	−8.27858	+	7.78925i	−0.470192	+	0.442400i
$311$	16.3214	+	4.79241i	0.925504	+	0.271753i	0.709553	−	0.704652i	$-0.248897\pi$
$311$	16.3214	+	4.79241i	0.925504	+	0.271753i	0.215951	+	0.976404i	$0.430715\pi$
$312$	−5.13345	+	2.22179i	−0.290625	+	0.125784i
$313$	−4.96522	+	34.5338i	−0.280651	+	1.95197i	0.0246057	+	0.999697i	$0.492167\pi$
$313$	−4.96522	+	34.5338i	−0.280651	+	1.95197i	−0.305256	+	0.952270i	$0.598742\pi$
$314$	−2.40099	−	7.08926i	−0.135495	−	0.400070i
$315$	−6.96097	−	3.17897i	−0.392206	−	0.179115i
$316$	−0.104357	+	1.71175i	−0.00587054	+	0.0962937i
$317$	23.5618	−	3.38767i	1.32336	−	0.190270i	0.555837	−	0.831292i	$-0.312398\pi$
$317$	23.5618	−	3.38767i	1.32336	−	0.190270i	0.767523	+	0.641021i	$0.221489\pi$
$318$	−9.39020	+	0.384792i	−0.526576	+	0.0215780i
$319$	21.3578	+	24.6482i	1.19580	+	1.38003i
$320$	4.08398	+	16.2839i	0.228302	+	0.910297i
$321$	−1.66489			−0.0929251
$322$	22.2737	+	10.7508i	1.24127	+	0.599116i
$323$		−	9.41102i		−	0.523643i
$324$	−1.42900	−	1.39927i	−0.0793888	−	0.0777373i
$325$	0.891064	−	0.772111i	0.0494273	−	0.0428290i
$326$	1.10534	+	26.9740i	0.0612191	+	1.49395i
$327$	−1.33646	−	9.29531i	−0.0739066	−	0.514032i
$328$	−8.61150	+	12.8300i	−0.475490	+	0.708420i
$329$	−6.25664	+	13.7001i	−0.344940	+	0.755312i
$330$	−3.55796	−	10.5054i	−0.195859	−	0.578302i
$331$	9.66776	+	1.39001i	0.531388	+	0.0764021i	0.402786	−	0.915294i	$-0.368042\pi$
$331$	9.66776	+	1.39001i	0.531388	+	0.0764021i	0.128602	+	0.991696i	$0.458951\pi$
$332$	14.7072	+	10.7704i	0.807165	+	0.591101i
$333$	1.77770	−	6.05428i	0.0974172	−	0.331773i
$334$	1.38285	+	1.46972i	0.0756660	+	0.0804195i
$335$	5.31343	+	11.6348i	0.290304	+	0.635677i
$336$	−9.31827	+	11.2220i	−0.508353	+	0.612213i
$337$	13.1502	−	15.1761i	0.716335	−	0.826694i	−0.274526	−	0.961580i	$-0.588521\pi$
$337$	13.1502	−	15.1761i	0.716335	−	0.826694i	0.990861	+	0.134885i	$0.0430665\pi$
$338$	10.5196	−	7.38612i	0.572191	−	0.401752i
$339$	−5.55323	+	8.64100i	−0.301610	+	0.469314i
$340$	−17.8063	−	23.2725i	−0.965684	−	1.26213i
$341$	−7.73900	−	12.0421i	−0.419090	−	0.652117i
$342$	−1.87416	+	0.348316i	−0.101343	+	0.0188348i
$343$	2.45701	−	0.721444i	0.132666	−	0.0389543i
$344$	−13.6746	−	0.272632i	−0.737286	−	0.0146993i
$345$	8.87693	+	4.74214i	0.477918	+	0.255308i
$346$	13.6818	−	23.3381i	0.735538	−	1.25466i
$347$	−4.18947	−	14.2680i	−0.224903	−	0.765948i	−0.992200	−	0.124656i	$-0.960217\pi$
$347$	−4.18947	−	14.2680i	−0.224903	−	0.765948i	0.767297	−	0.641291i	$-0.221601\pi$
$348$	5.92706	−	16.4160i	0.317724	−	0.879988i
$349$	−1.68245	−	2.61794i	−0.0900593	−	0.140135i	0.793301	−	0.608830i	$-0.208361\pi$
$349$	−1.68245	−	2.61794i	−0.0900593	−	0.140135i	−0.883360	+	0.468695i	$0.844724\pi$
$350$	1.16165	−	2.84669i	0.0620928	−	0.152162i
$351$	−1.66370	−	1.06920i	−0.0888019	−	0.0570695i
$352$	−21.1010	+	1.30942i	−1.12469	+	0.0697926i
$353$	−7.02308	+	8.10507i	−0.373801	+	0.431389i	−0.911216	−	0.411928i	$-0.864855\pi$
$353$	−7.02308	+	8.10507i	−0.373801	+	0.431389i	0.537415	+	0.843318i	$0.319401\pi$
$354$	3.78957	−	4.75349i	0.201414	−	0.252645i
$355$	17.1271	−	7.82170i	0.909014	−	0.415133i
$356$	6.75711	+	29.5625i	0.358126	+	1.56681i
$357$	7.17293	−	24.4288i	0.379632	−	1.29291i
$358$	26.3650	+	2.69446i	1.39344	+	0.142407i
$359$	−3.63013	+	25.2481i	−0.191591	+	1.33254i	0.636207	+	0.771518i	$0.280502\pi$
$359$	−3.63013	+	25.2481i	−0.191591	+	1.33254i	−0.827798	+	0.561026i	$0.810407\pi$
$360$	−3.97559	+	4.40740i	−0.209532	+	0.232291i
$361$	7.13812	−	15.6303i	0.375690	−	0.822647i
$362$	−3.85869	+	1.95695i	−0.202808	+	0.102855i
$363$	2.93746	−	0.422343i	0.154177	−	0.0221673i
$364$	−6.77898	+	12.7311i	−0.355315	+	0.667290i
$365$	22.7369	−	19.7016i	1.19010	−	1.03123i
$366$	−6.34070	−	1.58292i	−0.331433	−	0.0827406i
$367$	−3.60232			−0.188040			−0.0940199	−	0.995570i	$-0.529972\pi$
$367$	−3.60232			−0.188040			−0.0940199	+	0.995570i	$0.529972\pi$
$368$	13.1492	−	13.9678i	0.685447	−	0.728122i
$369$	−5.46315			−0.284400
$370$	−18.1686	−	4.53570i	−0.944542	−	0.235800i
$371$	−18.3144	+	15.8695i	−0.950834	+	0.823902i
$372$	−3.60031	+	6.76147i	−0.186667	+	0.350566i
$373$	−16.0267	+	2.30429i	−0.829829	+	0.119311i	−0.544122	−	0.839006i	$-0.683137\pi$
$373$	−16.0267	+	2.30429i	−0.829829	+	0.119311i	−0.285706	+	0.958317i	$0.592228\pi$
$374$	32.9112	−	16.6911i	1.70180	−	0.863074i
$375$	4.87853	−	10.6825i	0.251926	−	0.551641i
$376$	8.67437	+	7.82449i	0.447346	+	0.403518i
$377$	2.45609	−	17.0825i	0.126495	−	0.879791i
$378$	−5.13037	−	0.524314i	−0.263878	−	0.0269678i
$379$	−8.12830	+	27.6824i	−0.417523	+	1.42195i	0.435553	+	0.900163i	$0.356553\pi$
$379$	−8.12830	+	27.6824i	−0.417523	+	1.42195i	−0.853075	+	0.521788i	$0.825265\pi$
$380$	1.26058	+	5.51509i	0.0646666	+	0.282918i
$381$	5.98601	−	2.73372i	0.306672	−	0.140053i
$382$	20.8938	−	26.2083i	1.06902	−	1.34093i
$383$	8.96817	−	10.3498i	0.458252	−	0.528851i	−0.478855	−	0.877894i	$-0.658948\pi$
$383$	8.96817	−	10.3498i	0.458252	−	0.528851i	0.937107	+	0.349043i	$0.113493\pi$
$384$	6.12699	+	9.51105i	0.312667	+	0.485359i
$385$	−24.0598	−	15.4623i	−1.22620	−	0.788033i
$386$	−3.01478	+	7.38791i	−0.153448	+	0.376035i
$387$	−2.61436	−	4.06803i	−0.132895	−	0.206789i
$388$	−7.51602	+	20.8169i	−0.381568	+	1.05682i
$389$	1.29339	+	4.40489i	0.0655775	+	0.223337i	0.985761	−	0.168150i	$-0.0537792\pi$
$389$	1.29339	+	4.40489i	0.0655775	+	0.223337i	−0.920184	+	0.391486i	$0.871961\pi$
$390$	−2.96831	+	5.06326i	−0.150306	+	0.256388i
$391$	−11.4135	+	31.4785i	−0.577207	+	1.59193i
$392$	−0.355065	+	17.8093i	−0.0179335	+	0.899504i
$393$	−9.54196	+	2.80177i	−0.481328	+	0.141331i
$394$	37.5546	−	6.97957i	1.89197	−	0.351626i
$395$	0.972838	+	1.51377i	0.0489488	+	0.0761658i
$396$	−4.54205	−	5.93637i	−0.228246	−	0.298314i
$397$	−8.34277	+	12.9816i	−0.418712	+	0.651528i	−0.984975	−	0.172696i	$-0.944752\pi$
$397$	−8.34277	+	12.9816i	−0.418712	+	0.651528i	0.566264	+	0.824224i	$0.308388\pi$
$398$	−8.11342	+	5.69667i	−0.406689	+	0.285548i
$399$	−3.21888	+	3.71478i	−0.161146	+	0.185972i
$400$	−1.83470	−	1.52345i	−0.0917349	−	0.0761725i
$401$	−15.0175	−	32.8837i	−0.749936	−	1.64213i	−0.766480	−	0.642268i	$-0.777994\pi$
$401$	−15.0175	−	32.8837i	−0.749936	−	1.64213i	0.0165436	−	0.999863i	$-0.494734\pi$
$402$	5.90671	+	6.27778i	0.294600	+	0.313107i
$403$	−2.13403	+	7.26783i	−0.106303	+	0.362036i
$404$	22.3187	+	16.3444i	1.11040	+	0.813163i
$405$	−2.07717	−	0.298651i	−0.103215	−	0.0148401i
$406$	−14.4364	−	42.6255i	−0.716466	−	2.11547i
$407$	9.79636	−	21.4510i	0.485588	−	1.06329i
$408$	−16.3967	−	11.0054i	−0.811756	−	0.544849i
$409$	−2.22987	−	15.5091i	−0.110260	−	0.766876i	−0.967666	−	0.252235i	$-0.918834\pi$
$409$	−2.22987	−	15.5091i	−0.110260	−	0.766876i	0.857406	−	0.514641i	$-0.172075\pi$
$410$	0.663833	+	16.1997i	0.0327844	+	0.800048i
$411$	−11.9200	+	10.3287i	−0.587969	+	0.509478i
$412$	−10.4837	−	10.2656i	−0.516495	−	0.505750i
$413$		−	15.6754i		−	0.771338i
$414$	6.69123	+	1.10789i	0.328856	+	0.0544498i
$415$	19.1272			0.938919
$416$	7.83569	+	7.98479i	0.384176	+	0.391486i
$417$	8.01287	+	9.24735i	0.392392	+	0.452845i
$418$	−7.11834	+	0.291695i	−0.348169	+	0.0142673i
$419$	26.7921	−	3.85212i	1.30888	−	0.188188i	0.547670	−	0.836694i	$-0.315515\pi$
$419$	26.7921	−	3.85212i	1.30888	−	0.188188i	0.761210	+	0.648506i	$0.224606\pi$
$420$	−0.931340	+	15.2767i	−0.0454447	+	0.745425i
$421$	21.0302	+	9.60419i	1.02495	+	0.468079i	0.855688	−	0.517491i	$-0.173134\pi$
$421$	21.0302	+	9.60419i	1.02495	+	0.468079i	0.169263	+	0.985571i	$0.445861\pi$
$422$	8.06620	+	23.8166i	0.392656	+	1.15937i
$423$	−0.587786	+	4.08814i	−0.0285792	+	0.198772i
$424$	7.46585	+	17.2498i	0.362574	+	0.837726i
$425$	3.99387	+	1.17271i	0.193731	+	0.0568846i
$426$	9.24127	−	8.69504i	0.447741	−	0.421276i
$427$	−15.3287	+	7.00038i	−0.741808	+	0.338772i
$428$	1.19637	+	3.10744i	0.0578285	+	0.150204i
$429$	−5.58584	−	4.84016i	−0.269687	−	0.233685i
$430$	−11.7451	+	8.24661i	−0.566401	+	0.397687i
$431$	8.24561	+	5.29913i	0.397177	+	0.255250i	0.723950	−	0.689853i	$-0.242325\pi$
$431$	8.24561	+	5.29913i	0.397177	+	0.255250i	−0.326773	+	0.945103i	$0.605961\pi$
$432$	−1.58481	+	3.67265i	−0.0762494	+	0.176700i
$433$	−10.7138	+	6.88534i	−0.514872	+	0.330888i	−0.772141	−	0.635452i	$-0.780814\pi$
$433$	−10.7138	+	6.88534i	−0.514872	+	0.330888i	0.257268	+	0.966340i	$0.417178\pi$
$434$	3.60919	+	19.4198i	0.173247	+	0.932180i
$435$	−5.15936	−	17.5712i	−0.247373	−	0.842474i
$436$	−16.3889	+	9.17391i	−0.784885	+	0.439351i
$437$	4.52898	−	4.61272i	0.216651	−	0.220656i
$438$	10.2538	−	17.4906i	0.489945	−	0.835735i
$439$	−25.9070	+	7.60699i	−1.23647	+	0.363062i	−0.833690	−	0.552233i	$-0.813776\pi$
$439$	−25.9070	+	7.60699i	−1.23647	+	0.363062i	−0.402785	+	0.915295i	$0.631958\pi$
$440$	−17.0511	+	14.1898i	−0.812878	+	0.676470i
$441$	−5.29803	+	3.40483i	−0.252287	+	0.162135i
$442$	−18.0796	−	7.37773i	−0.859957	−	0.350923i
$443$	−3.83695	+	5.97042i	−0.182299	+	0.283663i	−0.920361	−	0.391070i	$-0.872105\pi$
$443$	−3.83695	+	5.97042i	−0.182299	+	0.283663i	0.738062	+	0.674733i	$0.235741\pi$
$444$	−12.5774	+	1.03253i	−0.596899	+	0.0490017i
$445$	24.0471	+	20.8369i	1.13994	+	0.987764i
$446$	−24.1713	+	30.3195i	−1.14455	+	1.43567i
$447$	7.62311	+	16.6923i	0.360561	+	0.789518i
$448$	27.6413	+	9.32810i	1.30593	+	0.440711i
$449$	32.3620	+	9.50233i	1.52726	+	0.448443i	0.934209	−	0.356726i	$-0.116107\pi$
$449$	32.3620	+	9.50233i	1.52726	+	0.448443i	0.593046	+	0.805168i	$0.297925\pi$
$450$	0.0857204	−	0.838766i	0.00404090	−	0.0395398i
$451$	−20.2098	−	2.90573i	−0.951642	−	0.136825i
$452$	20.1185	+	4.15554i	0.946292	+	0.195460i
$453$	−9.66554	−	4.41411i	−0.454127	−	0.207393i
$454$	−3.11732	+	1.58096i	−0.146303	+	0.0741982i
$455$	2.15379	+	14.9799i	0.100971	+	0.702270i
$456$	1.99686	+	3.24774i	0.0935115	+	0.152089i
$457$	−13.4495	−	15.5216i	−0.629142	−	0.726068i	0.348274	−	0.937393i	$-0.386768\pi$
$457$	−13.4495	−	15.5216i	−0.629142	−	0.726068i	−0.977416	+	0.211325i	$0.932222\pi$
$458$	2.18060	−	8.73483i	0.101893	−	0.408152i
$459$		−	6.98185i		−	0.325885i
$460$	2.47214	−	19.9760i	0.115264	−	0.931384i
$461$			26.9010i			1.25290i	0.779460	+	0.626452i	$0.215493\pi$
$461$			26.9010i			1.25290i	−0.779460	+	0.626452i	$0.784507\pi$
$462$	−18.6999	−	4.66832i	−0.869996	−	0.217190i
$463$	5.92620	+	6.83920i	0.275414	+	0.317845i	0.876558	−	0.481296i	$-0.159834\pi$
$463$	5.92620	+	6.83920i	0.275414	+	0.317845i	−0.601144	+	0.799141i	$0.705288\pi$
$464$	−34.8987	+	0.733700i	−1.62013	+	0.0340612i
$465$	1.14388	+	7.95583i	0.0530459	+	0.368943i
$466$	0.463316	+	0.913562i	0.0214627	+	0.0423200i
$467$	16.8182	+	7.68062i	0.778254	+	0.355417i	0.764612	−	0.644490i	$-0.222930\pi$
$467$	16.8182	+	7.68062i	0.778254	+	0.355417i	0.0136414	+	0.999907i	$0.495658\pi$
$468$	−0.800091	+	3.87353i	−0.0369842	+	0.179054i
$469$	22.0001	+	3.16314i	1.01587	+	0.146060i
$470$	12.1939	+	1.24619i	0.562463	+	0.0574827i
$471$	−5.07817	−	1.49109i	−0.233990	−	0.0687056i
$472$	−11.5953	−	3.65727i	−0.533716	−	0.168339i
$473$	−7.50760	−	16.4393i	−0.345200	−	0.755882i
$474$	0.948198	+	0.755922i	0.0435522	+	0.0347206i
$475$	−0.607332	−	0.526256i	−0.0278663	−	0.0241463i
$476$	−50.7494	+	4.16622i	−2.32610	+	0.190958i
$477$	−3.59280	+	5.59051i	−0.164503	+	0.255972i
$478$	10.7716	−	26.3966i	0.492684	−	1.20735i
$479$	−7.19782	+	4.62576i	−0.328877	+	0.211356i	−0.694650	−	0.719348i	$-0.744441\pi$
$479$	−7.19782	+	4.62576i	−0.328877	+	0.211356i	0.365773	+	0.930704i	$0.380805\pi$
$480$	11.0830	+	4.25314i	0.505867	+	0.194129i
$481$	−11.9732	+	3.51566i	−0.545932	+	0.160300i
$482$	−31.6521	−	18.5559i	−1.44171	−	0.845197i
$483$	15.2719	−	8.52160i	0.694896	−	0.387746i
$484$	−2.89910	−	5.17914i	−0.131777	−	0.235415i
$485$	6.54252	+	22.2818i	0.297081	+	1.01176i
$486$	−1.39040	+	0.258408i	−0.0630700	+	0.0117216i
$487$	−19.4757	+	12.5163i	−0.882527	+	0.567166i	−0.901561	−	0.432653i	$-0.857578\pi$
$487$	−19.4757	+	12.5163i	−0.882527	+	0.567166i	0.0190332	+	0.999819i	$0.493941\pi$
$488$	1.60188	+	12.9721i	0.0725139	+	0.587217i
$489$	16.0591	+	10.3206i	0.726218	+	0.466712i
$490$	10.7400	+	15.2964i	0.485186	+	0.691020i
$491$	−11.6453	−	10.0907i	−0.525544	−	0.455387i	0.351230	−	0.936289i	$-0.385764\pi$
$491$	−11.6453	−	10.0907i	−0.525544	−	0.455387i	−0.876774	+	0.480903i	$0.840309\pi$
$492$	3.92573	+	10.1967i	0.176986	+	0.459702i
$493$	55.4218	−	25.3103i	2.49607	−	1.13992i
$494$	2.58334	+	2.74563i	0.116230	+	0.123532i
$495$	−7.52520	−	2.20960i	−0.338233	−	0.0993141i
$496$	15.2071	+	1.86111i	0.682818	+	0.0835664i
$497$	4.65633	−	32.3855i	0.208865	−	1.45269i
$498$	12.2088	−	4.13487i	0.547090	−	0.185288i
$499$	27.5643	+	12.5882i	1.23395	+	0.563524i	0.922226	−	0.386650i	$-0.126368\pi$
$499$	27.5643	+	12.5882i	1.23395	+	0.563524i	0.311719	+	0.950174i	$0.399095\pi$
$500$	−23.4440	−	1.42926i	−1.04845	−	0.0639184i
$501$	1.41242	−	0.203075i	0.0631023	−	0.00907274i
$502$	−0.975660	−	23.8094i	−0.0435459	−	1.06266i
$503$	20.2874	+	23.4129i	0.904571	+	1.04393i	0.998829	+	0.0483830i	$0.0154068\pi$
$503$	20.2874	+	23.4129i	0.904571	+	1.04393i	−0.0942576	+	0.995548i	$0.530048\pi$
$504$	2.70800	+	9.95233i	0.120624	+	0.443312i
$505$	29.0262			1.29165
$506$	24.1636	+	7.65733i	1.07420	+	0.340410i
$507$		−	9.08891i		−	0.403653i
$508$	−9.40380	−	9.20818i	−0.417226	−	0.408547i
$509$	−7.64208	+	6.62190i	−0.338729	+	0.293510i	−0.807569	−	0.589772i	$-0.799217\pi$
$509$	−7.64208	+	6.62190i	−0.338729	+	0.293510i	0.468840	+	0.883283i	$0.344672\pi$
$510$	−20.7031	+	0.848372i	−0.916749	+	0.0375665i
$511$	−7.44010	−	51.7470i	−0.329130	−	2.28915i
$512$	13.3491	−	18.2702i	0.589954	−	0.807437i
$513$	−0.559949	+	1.22612i	−0.0247223	+	0.0541344i
$514$	−5.56306	+	1.88409i	−0.245376	+	0.0831038i
$515$	−15.2389	−	2.19103i	−0.671507	−	0.0965481i
$516$	−5.71413	+	7.80280i	−0.251550	+	0.343499i
$517$	−4.34879	+	14.8106i	−0.191260	+	0.651370i
$518$	−23.6994	+	22.2986i	−1.04129	+	0.979743i
$519$	−7.94658	−	17.4006i	−0.348816	−	0.763801i
$520$	11.5833	+	1.90181i	0.507961	+	0.0834001i
$521$	−13.9910	+	16.1465i	−0.612956	+	0.707389i	−0.974354	−	0.225023i	$-0.927754\pi$
$521$	−13.9910	+	16.1465i	−0.612956	+	0.707389i	0.361397	+	0.932412i	$0.382300\pi$
$522$	−7.09168	−	10.1002i	−0.310394	−	0.442076i
$523$	−19.8358	+	30.8652i	−0.867360	+	1.34964i	0.0686407	+	0.997641i	$0.478134\pi$
$523$	−19.8358	+	30.8652i	−0.867360	+	1.34964i	−0.936001	+	0.351997i	$0.885503\pi$
$524$	12.0861	+	15.7963i	0.527983	+	0.690064i
$525$	−1.17539	−	1.82894i	−0.0512980	−	0.0798213i
$526$	2.38756	+	12.8466i	0.104102	+	0.560138i
$527$	−25.6582	+	7.53393i	−1.11769	+	0.328183i
$528$	−7.81610	+	12.7433i	−0.340152	+	0.554580i
$529$	−20.7430	+	9.93619i	−0.901870	+	0.432008i
$530$	17.0140	+	9.97433i	0.739039	+	0.433257i
$531$	−1.21107	−	4.12451i	−0.0525558	−	0.178988i
$532$	9.24650	+	3.33849i	0.400887	+	0.144742i
$533$	5.84118	+	9.08905i	0.253010	+	0.393691i
$534$	19.8536	+	8.10164i	0.859148	+	0.350592i
$535$	2.93919	+	1.88890i	0.127072	+	0.0816643i
$536$	7.47269	−	15.5357i	0.322771	−	0.671040i
$537$	12.2721	−	14.1627i	0.529580	−	0.611167i
$538$	−4.01035	−	3.19713i	−0.172899	−	0.137838i
$539$	−21.4099	+	9.77758i	−0.922190	+	0.421150i
$540$	0.935202	+	4.09153i	0.0402447	+	0.176072i
$541$	0.783676	−	2.66896i	0.0336929	−	0.114747i	−0.940930	−	0.338602i	$-0.890046\pi$
$541$	0.783676	−	2.66896i	0.0336929	−	0.114747i	0.974623	+	0.223855i	$0.0718641\pi$
$542$	−3.09947	+	30.3281i	−0.133134	+	1.30270i
$543$	−0.435389	+	3.02820i	−0.0186843	+	0.129952i
$544$	−8.75865	+	38.5119i	−0.375524	+	1.65118i
$545$	−8.18660	+	17.9262i	−0.350676	+	0.767872i
$546$	4.61307	+	9.09600i	0.197421	+	0.389273i
$547$	14.0838	−	2.02495i	0.602182	−	0.0865806i	0.165520	−	0.986206i	$-0.447070\pi$
$547$	14.0838	−	2.02495i	0.602182	−	0.0865806i	0.436662	+	0.899626i	$0.356161\pi$
$548$	27.8435	+	14.8260i	1.18942	+	0.633334i
$549$	−3.49243	+	3.02621i	−0.149053	+	0.129155i
$550$	0.763226	−	3.05725i	0.0325441	−	0.130362i
$551$	−11.7628			−0.501112
$552$	−2.74040	−	13.2850i	−0.116639	−	0.565446i
$553$	3.12685			0.132967
$554$	1.98495	−	7.95111i	0.0843326	−	0.337810i
$555$	−10.0072	+	8.67130i	−0.424782	+	0.368076i
$556$	11.5018	−	21.6006i	0.487785	−	0.916071i
$557$	0.611977	−	0.0879890i	0.0259303	−	0.00372822i	−0.129337	−	0.991601i	$-0.541285\pi$
$557$	0.611977	−	0.0879890i	0.0259303	−	0.00372822i	0.155268	+	0.987872i	$0.450376\pi$
$558$	2.45000	+	4.83088i	0.103717	+	0.204507i
$559$	−3.97272	+	8.69904i	−0.168028	+	0.367930i
$560$	29.1824	−	9.23927i	1.23318	−	0.390431i
$561$	3.71349	−	25.8279i	0.156784	−	1.09045i
$562$	−4.46325	+	43.6725i	−0.188271	+	1.84221i
$563$	4.72207	−	16.0819i	0.199012	−	0.677772i	−0.798148	−	0.602461i	$-0.794187\pi$
$563$	4.72207	−	16.0819i	0.199012	−	0.677772i	0.997160	−	0.0753107i	$-0.0239949\pi$
$564$	8.05269	−	1.84060i	0.339079	−	0.0775034i
$565$	19.6073	−	8.95434i	0.824884	−	0.376712i
$566$	−1.49605	−	1.19268i	−0.0628837	−	0.0501321i
$567$	−2.38802	+	2.75593i	−0.100288	+	0.115738i
$568$	−22.8695	−	11.0003i	−0.959583	−	0.461560i
$569$	−17.5729	−	11.2934i	−0.736693	−	0.473444i	0.117714	−	0.993048i	$-0.462443\pi$
$569$	−17.5729	−	11.2934i	−0.736693	−	0.473444i	−0.854408	+	0.519603i	$0.826080\pi$
$570$	3.70382	+	1.51142i	0.155136	+	0.0633063i
$571$	−10.8401	−	16.8675i	−0.453643	−	0.705883i	0.536814	−	0.843700i	$-0.319628\pi$
$571$	−10.8401	−	16.8675i	−0.453643	−	0.705883i	−0.990458	+	0.137818i	$0.955991\pi$
$572$	−5.02002	+	13.9038i	−0.209897	+	0.581345i
$573$	−6.67720	−	22.7405i	−0.278944	−	0.949996i
$574$	24.3052	+	14.2488i	1.01448	+	0.594733i
$575$	1.39320	+	2.49681i	0.0581005	+	0.104124i
$576$	7.99364	+	0.318866i	0.333068	+	0.0132861i
$577$	29.2827	−	8.59819i	1.21906	−	0.357947i	0.391947	−	0.919988i	$-0.371802\pi$
$577$	29.2827	−	8.59819i	1.21906	−	0.357947i	0.827110	+	0.562041i	$0.189984\pi$
$578$	−8.20349	−	44.1401i	−0.341220	−	1.83598i
$579$	3.05043	+	4.74657i	0.126772	+	0.197261i
$580$	−29.0883	+	22.2561i	−1.20783	+	0.924133i
$581$	17.9695	−	27.9611i	0.745501	−	1.16002i
$582$	8.99286	+	12.8080i	0.372766	+	0.530908i
$583$	−16.2643	+	18.7700i	−0.673598	+	0.777374i
$584$	−40.0136	−	6.56967i	−1.65577	−	0.271855i
$585$	1.72403	+	3.77510i	0.0712800	+	0.156081i
$586$	5.15939	−	4.85443i	0.213133	−	0.200535i
$587$	−4.63139	+	15.7731i	−0.191158	+	0.651024i	0.807011	+	0.590536i	$0.201084\pi$
$587$	−4.63139	+	15.7731i	−0.191158	+	0.651024i	−0.998169	+	0.0604879i	$0.980734\pi$
$588$	10.1620	+	7.44184i	0.419075	+	0.306896i
$589$	5.11019	+	0.734734i	0.210562	+	0.0302742i
$590$	−12.0832	+	4.09232i	−0.497455	+	0.168478i
$591$	11.2203	−	24.5690i	0.461541	−	1.01063i
$592$	10.9651	+	22.7332i	0.450664	+	0.934329i
$593$	−0.781532	−	5.43567i	−0.0320937	−	0.223216i	0.967462	−	0.253015i	$-0.0814223\pi$
$593$	−0.781532	−	5.43567i	−0.0320937	−	0.223216i	−0.999556	+	0.0297991i	$0.990513\pi$
$594$	−5.28096	+	0.216403i	−0.216680	+	0.00887912i
$595$	−40.3787	+	34.9883i	−1.65536	+	1.43438i
$596$	25.6775	−	26.2230i	1.05179	−	1.07413i
$597$			7.00998i			0.286899i
$598$	−5.31104	−	12.3168i	−0.217185	−	0.503670i
$599$	11.3925			0.465485			0.232743	−	0.972538i	$-0.425230\pi$
$599$	11.3925			0.465485			0.232743	+	0.972538i	$0.425230\pi$
$600$	−1.62711	+	0.442732i	−0.0664266	+	0.0180744i
$601$	−2.36217	−	2.72609i	−0.0963549	−	0.111200i	0.705524	−	0.708686i	$-0.250712\pi$
$601$	−2.36217	−	2.72609i	−0.0963549	−	0.111200i	−0.801879	+	0.597486i	$0.796166\pi$
$602$	1.02105	+	24.9171i	0.0416149	+	1.01554i
$603$	6.03303	−	0.867419i	0.245684	−	0.0353240i
$604$	−1.29320	+	21.2122i	−0.0526194	+	0.863111i
$605$	−5.66494	−	2.58709i	−0.230313	−	0.105180i
$606$	18.5272	−	6.27479i	0.752617	−	0.254896i
$607$	4.62288	−	32.1528i	0.187637	−	1.30504i	−0.650468	−	0.759534i	$-0.725427\pi$
$607$	4.62288	−	32.1528i	0.187637	−	1.30504i	0.838105	−	0.545510i	$-0.183664\pi$
$608$	4.62683	−	6.06081i	0.187643	−	0.245798i
$609$	−30.5335	−	8.96543i	−1.23728	−	0.363298i
$610$	9.39792	+	9.98831i	0.380511	+	0.404415i
$611$	7.42992	−	3.39313i	0.300582	−	0.137271i
$612$	−13.0313	+	5.01705i	−0.526758	+	0.202802i
$613$	−30.5477	−	26.4697i	−1.23381	−	1.06910i	−0.995188	−	0.0979888i	$-0.968759\pi$
$613$	−30.5477	−	26.4697i	−1.23381	−	1.06910i	−0.238621	−	0.971113i	$-0.576695\pi$
$614$	6.54444	+	9.32085i	0.264112	+	0.376159i
$615$	9.64460	+	6.19821i	0.388908	+	0.249936i
$616$	4.72424	+	38.2569i	0.190345	+	1.54142i
$617$	−17.1084	+	10.9949i	−0.688757	+	0.442637i	−0.837644	−	0.546217i	$-0.816067\pi$
$617$	−17.1084	+	10.9949i	−0.688757	+	0.442637i	0.148887	+	0.988854i	$0.452431\pi$
$618$	−10.2006	+	1.89579i	−0.410327	+	0.0762597i
$619$	−5.83062	−	19.8573i	−0.234353	−	0.798132i	−0.989743	−	0.142857i	$-0.954371\pi$
$619$	−5.83062	−	19.8573i	−0.234353	−	0.798132i	0.755391	−	0.655275i	$-0.227447\pi$
$620$	14.0272	−	7.85192i	0.563345	−	0.315341i
$621$	3.35996	−	3.42208i	0.134831	−	0.137324i
$622$	−20.7531	−	12.1664i	−0.832125	−	0.487828i
$623$	53.0519	−	15.5774i	2.12548	−	0.624097i
$624$	7.80468	−	1.29013i	0.312437	−	0.0516464i
$625$	−18.2246	+	11.7122i	−0.728984	+	0.468490i
$626$	18.6419	−	45.6832i	0.745082	−	1.82587i
$627$	−2.72356	+	4.23794i	−0.108769	+	0.169247i
$628$	0.866059	+	10.5496i	0.0345595	+	0.420976i
$629$	−33.2942	−	28.8496i	−1.32753	−	1.15031i
$630$	8.46225	+	6.74627i	0.337144	+	0.268778i
$631$	−8.51827	−	18.6524i	−0.339107	−	0.742541i	0.660861	−	0.750508i	$-0.270191\pi$
$631$	−8.51827	−	18.6524i	−0.339107	−	0.742541i	−0.999968	+	0.00796742i	$0.997464\pi$
$632$	0.729530	−	2.31296i	0.0290192	−	0.0920045i
$633$	17.0603	+	5.00935i	0.678086	+	0.199104i
$634$	−33.4896	−	3.42257i	−1.33004	−	0.135928i
$635$	−13.6692	−	1.96533i	−0.542445	−	0.0779919i
$636$	13.0161	+	2.68853i	0.516123	+	0.106607i
$637$	11.3293	+	5.17390i	0.448882	+	0.204997i
$638$	−20.8621	−	41.1357i	−0.825939	−	1.62858i
$639$	−1.27689	−	8.88099i	−0.0505131	−	0.351326i
$640$	−0.0257890	−	23.7421i	−0.00101940	−	0.938489i
$641$	−3.46270	−	3.99617i	−0.136768	−	0.157839i	0.683234	−	0.730200i	$-0.260573\pi$
$641$	−3.46270	−	3.99617i	−0.136768	−	0.157839i	−0.820002	+	0.572361i	$0.806028\pi$
$642$	2.28440	+	0.570289i	0.0901582	+	0.0225075i
$643$			22.9385i			0.904606i	0.891864	+	0.452303i	$0.149398\pi$
$643$			22.9385i			0.904606i	−0.891864	+	0.452303i	$0.850602\pi$
$644$	−26.8793	−	22.3808i	−1.05919	−	0.881925i
$645$			10.1478i			0.399569i
$646$	−3.22363	+	12.9129i	−0.126832	+	0.508051i
$647$	−14.1937	−	16.3804i	−0.558011	−	0.643979i	0.404720	−	0.914441i	$-0.367369\pi$
$647$	−14.1937	−	16.3804i	−0.558011	−	0.643979i	−0.962731	+	0.270462i	$0.912824\pi$
$648$	1.48143	+	2.40943i	0.0581961	+	0.0946514i
$649$	−2.28635	−	15.9019i	−0.0897471	−	0.624205i
$650$	−1.48711	+	0.754193i	−0.0583292	+	0.0295819i
$651$	12.7048	+	5.80211i	0.497942	+	0.227402i
$652$	7.72299	−	37.3897i	0.302456	−	1.46430i
$653$	−13.4236	−	1.93003i	−0.525307	−	0.0755278i	−0.125441	−	0.992101i	$-0.540034\pi$
$653$	−13.4236	−	1.93003i	−0.525307	−	0.0755278i	−0.399867	+	0.916573i	$0.630944\pi$
$654$	−1.35023	+	13.2119i	−0.0527983	+	0.516627i
$655$	20.0241	+	5.87959i	0.782405	+	0.229735i
$656$	16.2106	−	14.6544i	0.632919	−	0.572157i
$657$	−5.95554	−	13.0408i	−0.232348	−	0.508770i
$658$	13.2776	−	16.6549i	0.517614	−	0.649274i
$659$	−27.6403	−	23.9504i	−1.07671	−	0.932976i	−0.0787564	−	0.996894i	$-0.525095\pi$
$659$	−27.6403	−	23.9504i	−1.07671	−	0.932976i	−0.997955	+	0.0639180i	$0.979640\pi$
$660$	1.28339	+	15.6332i	0.0499559	+	0.608521i
$661$	15.9584	−	24.8317i	0.620709	−	0.965842i	−0.378481	−	0.925609i	$-0.623554\pi$
$661$	15.9584	−	24.8317i	0.620709	−	0.965842i	0.999190	−	0.0402332i	$-0.0128101\pi$
$662$	−12.7890	−	5.21882i	−0.497060	−	0.202835i
$663$	−11.6157	+	7.46497i	−0.451117	+	0.289915i
$664$	−16.4906	−	19.8159i	−0.639959	−	0.769005i
$665$	9.89719	−	2.90608i	0.383797	−	0.112693i
$666$	−4.51301	+	7.69817i	−0.174875	+	0.298298i
$667$	39.3448	+	14.2657i	1.52344	+	0.552371i
$668$	−1.39397	−	2.49029i	−0.0539345	−	0.0963521i
$669$	7.72463	+	26.3077i	0.298652	+	1.01711i
$670$	−3.30521	−	17.7842i	−0.127692	−	0.687063i
$671$	−14.5291	+	9.33729i	−0.560890	+	0.360462i
$672$	16.6296	−	12.2059i	0.641501	−	0.470854i
$673$	−1.07753	−	0.692485i	−0.0415357	−	0.0266934i	0.519708	−	0.854344i	$-0.326041\pi$
$673$	−1.07753	−	0.692485i	−0.0415357	−	0.0266934i	−0.561244	+	0.827650i	$0.689677\pi$
$674$	−23.2418	+	16.3187i	−0.895240	+	0.628574i
$675$	−0.450568	−	0.390419i	−0.0173424	−	0.0150272i
$676$	−16.9640	+	6.53115i	−0.652462	+	0.251198i
$677$	−15.6100	+	7.12884i	−0.599940	+	0.273983i	−0.692147	−	0.721756i	$-0.743335\pi$
$677$	−15.6100	+	7.12884i	−0.599940	+	0.273983i	0.0922071	+	0.995740i	$0.470608\pi$
$678$	10.5795	−	9.95414i	0.406302	−	0.382287i
$679$	38.7191	+	11.3689i	1.48590	+	0.436300i
$680$	16.4604	+	38.0317i	0.631227	+	1.45845i
$681$	−0.351739	+	2.44640i	−0.0134787	+	0.0937461i
$682$	6.49382	+	19.1739i	0.248661	+	0.734208i
$683$	29.6326	+	13.5328i	1.13386	+	0.517817i	0.891794	−	0.452443i	$-0.149447\pi$
$683$	29.6326	+	13.5328i	1.13386	+	0.517817i	0.242067	+	0.970259i	$0.422175\pi$
$684$	2.69086	+	0.164048i	0.102887	+	0.00627252i
$685$	32.7619	−	4.71044i	1.25177	−	0.179977i
$686$	−3.61840	+	0.148275i	−0.138151	+	0.00566115i
$687$	−4.16885	−	4.81111i	−0.159052	−	0.183555i
$688$	18.6696	+	5.05816i	0.711772	+	0.192841i
$689$	13.1423			0.500684
$690$	−10.5557	−	9.54739i	−0.401849	−	0.363463i
$691$		−	24.8938i		−	0.947006i	−0.880792	−	0.473503i	$-0.842989\pi$
$691$		−	24.8938i		−	0.947006i	0.880792	−	0.473503i	$-0.157011\pi$
$692$	−26.7670	+	27.3357i	−1.01753	+	1.03915i
$693$	−10.2998	+	8.92484i	−0.391258	+	0.339027i
$694$	0.861040	+	21.0123i	0.0326846	+	0.797615i
$695$	−3.65430	−	25.4162i	−0.138615	−	0.964092i
$696$	−13.7556	+	20.4941i	−0.521406	+	0.776829i
$697$	−15.8451	+	34.6960i	−0.600177	+	1.31420i
$698$	1.41175	+	4.16838i	0.0534354	+	0.157776i
$699$	0.716940	+	0.103080i	0.0271172	+	0.00389886i
$700$	−2.56900	+	3.50804i	−0.0970992	+	0.132592i
$701$	3.16909	−	10.7929i	0.119695	−	0.407643i	−0.877747	−	0.479124i	$-0.840954\pi$
$701$	3.16909	−	10.7929i	0.119695	−	0.407643i	0.997442	+	0.0714812i	$0.0227726\pi$
$702$	1.91653	+	2.03693i	0.0723348	+	0.0768790i
$703$	3.53321	+	7.73665i	0.133257	+	0.291793i
$704$	29.4012	+	5.43122i	1.10810	+	0.204697i
$705$	5.67587	−	6.55031i	0.213766	−	0.246699i
$706$	12.4127	−	8.71532i	0.467158	−	0.328005i
$707$	27.2693	−	42.4318i	1.02557	−	1.59581i
$708$	−6.82794	+	5.22420i	−0.256610	+	0.196338i
$709$	10.5335	+	16.3904i	0.395594	+	0.615556i	0.980727	−	0.195381i	$-0.0625943\pi$
$709$	10.5335	+	16.3904i	0.395594	+	0.615556i	−0.585134	+	0.810937i	$0.698958\pi$
$710$	−26.1794	+	4.86548i	−0.982496	+	0.182598i
$711$	0.822733	−	0.241576i	0.0308549	−	0.00905982i
$712$	0.854850	−	42.8774i	0.0320369	−	1.60690i
$713$	−16.2018	−	8.65513i	−0.606761	−	0.324137i
$714$	−18.2098	+	31.0618i	−0.681485	+	1.16246i
$715$	4.36981	+	14.8822i	0.163422	+	0.556563i
$716$	−35.2526	−	12.7281i	−1.31745	−	0.475672i
$717$	−10.8990	−	16.9592i	−0.407031	−	0.633353i
$718$	13.6294	−	33.3996i	0.508643	−	1.24646i
$719$	−17.1967	−	11.0516i	−0.641328	−	0.412156i	0.179160	−	0.983820i	$-0.442662\pi$
$719$	−17.1967	−	11.0516i	−0.641328	−	0.412156i	−0.820488	+	0.571664i	$0.806298\pi$
$720$	6.96462	−	4.68562i	0.259556	−	0.174623i
$721$	−17.5195	+	20.2186i	−0.652459	+	0.752978i
$722$	−15.1482	+	19.0013i	−0.563758	+	0.707155i
$723$	−23.5994	+	10.7775i	−0.877673	+	0.400820i
$724$	5.96485	−	1.36339i	0.221682	−	0.0506698i
$725$	1.46576	−	4.99193i	0.0544371	−	0.185396i
$726$	−4.17517	−	0.426695i	−0.154955	−	0.0158361i
$727$	2.76632	−	19.2402i	0.102597	−	0.713578i	−0.871983	−	0.489537i	$-0.837166\pi$
$727$	2.76632	−	19.2402i	0.102597	−	0.713578i	0.974580	−	0.224041i	$-0.0719250\pi$
$728$	13.6623	−	15.1463i	0.506360	−	0.561359i
$729$	−0.415415	+	0.909632i	−0.0153857	+	0.0336901i
$730$	−37.9459	+	19.2444i	−1.40444	+	0.712268i
$731$	−33.4183	+	4.80482i	−1.23602	+	0.177713i
$732$	8.15788	+	4.34386i	0.301524	+	0.160554i
$733$	6.63410	−	5.74848i	0.245036	−	0.212325i	−0.523680	−	0.851915i	$-0.675441\pi$
$733$	6.63410	−	5.74848i	0.245036	−	0.212325i	0.768716	+	0.639590i	$0.220896\pi$
$734$	4.94276	+	1.23393i	0.182441	+	0.0455453i
$735$	13.2160			0.487481
$736$	−22.8265	+	14.6612i	−0.841396	+	0.540418i
$737$	22.7793			0.839086
$738$	7.49600	+	1.87134i	0.275932	+	0.0688849i
$739$	39.3785	−	34.1217i	1.44856	−	1.25519i	0.537281	−	0.843403i	$-0.319452\pi$
$739$	39.3785	−	34.1217i	1.44856	−	1.25519i	0.911282	−	0.411783i	$-0.135094\pi$
$740$	23.3756	+	12.4469i	0.859303	+	0.457557i
$741$	2.63859	−	0.379372i	0.0969310	−	0.0139366i
$742$	30.5651	−	15.5012i	1.12208	−	0.569067i
$743$	−0.0328285	+	0.0718843i	−0.00120436	+	0.00263718i	−0.910233	−	0.414096i	$-0.864098\pi$
$743$	−0.0328285	+	0.0718843i	−0.00120436	+	0.00263718i	0.909029	+	0.416733i	$0.136825\pi$
$744$	7.25606	−	8.04419i	0.266020	−	0.294914i
$745$	5.48043	−	38.1172i	0.200787	−	1.39651i
$746$	22.7795	+	2.32803i	0.834018	+	0.0852351i
$747$	2.56788	−	8.74540i	0.0939538	−	0.319977i
$748$	−50.8750	+	11.6285i	−1.86017	+	0.425180i
$749$	5.52257	−	2.52207i	0.201790	−	0.0921545i
$750$	−10.3530	+	12.9864i	−0.378038	+	0.474196i
$751$	−23.3462	+	26.9429i	−0.851914	+	0.983161i	−0.999983	−	0.00581582i	$-0.998149\pi$
$751$	−23.3462	+	26.9429i	−0.851914	+	0.983161i	0.148069	+	0.988977i	$0.452694\pi$
$752$	−9.22194	−	13.7073i	−0.336289	−	0.499854i
$753$	−14.1750	−	9.10974i	−0.516567	−	0.331978i
$754$	−9.22140	+	22.5976i	−0.335824	+	0.822956i
$755$	12.0555	+	18.7587i	0.438743	+	0.682698i
$756$	6.85979	+	2.47676i	0.249488	+	0.0900789i
$757$	−0.867516	−	2.95449i	−0.0315304	−	0.107383i	0.942224	−	0.334982i	$-0.108730\pi$
$757$	−0.867516	−	2.95449i	−0.0315304	−	0.107383i	−0.973755	+	0.227600i	$0.926912\pi$
$758$	20.6352	−	35.1989i	0.749503	−	1.27848i
$759$	14.2496	−	10.8722i	0.517228	−	0.394636i
$760$	0.159478	−	7.99907i	0.00578488	−	0.290157i
$761$	24.6005	−	7.22335i	0.891767	−	0.261846i	0.196419	−	0.980520i	$-0.437069\pi$
$761$	24.6005	−	7.22335i	0.891767	−	0.261846i	0.695347	+	0.718674i	$0.255250\pi$
$762$	−9.14982	+	1.70051i	−0.331463	+	0.0616028i
$763$	18.5142	+	28.8087i	0.670260	+	1.04294i
$764$	−37.6458	+	28.8036i	−1.36198	+	1.04208i
$765$	−7.92125	+	12.3257i	−0.286393	+	0.445637i
$766$	−15.8505	+	11.1291i	−0.572701	+	0.402110i
$767$	−5.56709	+	6.42476i	−0.201016	+	0.231985i
$768$	−5.14896	−	15.1489i	−0.185797	−	0.546638i
$769$	−0.617441	−	1.35201i	−0.0222655	−	0.0487546i	0.898173	−	0.439643i	$-0.144895\pi$
$769$	−0.617441	−	1.35201i	−0.0222655	−	0.0487546i	−0.920438	+	0.390888i	$0.872168\pi$
$770$	27.7162	+	29.4573i	0.998821	+	1.06157i
$771$	−1.17008	+	3.98492i	−0.0421394	+	0.143514i
$772$	6.66724	−	9.10429i	0.239959	−	0.327671i
$773$	−15.6491	−	2.25000i	−0.562858	−	0.0809267i	−0.144988	−	0.989433i	$-0.546314\pi$
$773$	−15.6491	−	2.25000i	−0.562858	−	0.0809267i	−0.417870	+	0.908507i	$0.637223\pi$
$774$	2.19372	+	6.47727i	0.0788516	+	0.232821i
$775$	−0.948590	+	2.07712i	−0.0340743	+	0.0746124i
$776$	17.4433	−	25.9883i	0.626179	−	0.932927i
$777$	3.27462	+	22.7755i	0.117476	+	0.817065i
$778$	−0.265824	−	6.48700i	−0.00953025	−	0.232570i
$779$	5.56528	−	4.82234i	0.199397	−	0.172778i
$780$	5.80718	−	5.93055i	0.207930	−	0.212348i
$781$		−	33.5325i		−	1.19989i
$782$	26.4431	−	39.2821i	0.945604	−	1.40473i
$783$	−8.72659			−0.311863
$784$	6.58754	−	24.3145i	0.235269	−	0.868376i
$785$	7.27326	+	8.39378i	0.259594	+	0.299587i
$786$	14.0523	−	0.575834i	0.501228	−	0.0205393i
$787$	22.2291	−	3.19606i	0.792381	−	0.113927i	0.265773	−	0.964036i	$-0.414373\pi$
$787$	22.2291	−	3.19606i	0.792381	−	0.113927i	0.526608	+	0.850108i	$0.323464\pi$
$788$	−53.9196	−	3.28720i	−1.92081	−	0.117102i
$789$	8.40452	+	3.83821i	0.299209	+	0.136644i
$790$	−0.816311	−	2.41028i	−0.0290431	−	0.0857538i
$791$	5.33061	−	37.0752i	0.189535	−	1.31824i
$792$	4.19872	+	9.70114i	0.149195	+	0.344715i
$793$	8.76881	+	2.57476i	0.311390	+	0.0914322i
$794$	15.8938	−	14.9544i	0.564051	−	0.530711i
$795$	12.6854	−	5.79323i	0.449905	−	0.205465i
$796$	13.0838	−	5.03726i	0.463742	−	0.178541i
$797$	24.3951	+	21.1385i	0.864120	+	0.748764i	0.969350	−	0.245684i	$-0.0790125\pi$
$797$	24.3951	+	21.1385i	0.864120	+	0.748764i	−0.105230	+	0.994448i	$0.533558\pi$
$798$	5.68909	−	3.99448i	0.201392	−	0.141403i
$799$	24.2586	+	15.5901i	0.858209	+	0.551538i
$800$	1.99555	+	2.71878i	0.0705535	+	0.0961235i
$801$	12.7555	−	8.19745i	0.450693	−	0.289643i
$802$	9.34160	+	50.2638i	0.329863	+	1.77488i
$803$	−15.0952	−	51.4094i	−0.532697	−	1.81420i
$804$	−5.95424	−	10.6370i	−0.209990	−	0.375139i
$805$	−36.6291	−	2.28275i	−1.29101	−	0.0804562i
$806$	5.41761	−	9.24122i	0.190827	−	0.325508i
$807$	−3.47970	+	1.02173i	−0.122491	+	0.0359667i
$808$	−25.0250	−	30.0712i	−0.880375	−	1.05790i
$809$	3.12638	−	2.00920i	0.109918	−	0.0706399i	−0.484527	−	0.874776i	$-0.661008\pi$
$809$	3.12638	−	2.00920i	0.109918	−	0.0706399i	0.594445	+	0.804136i	$0.297372\pi$
$810$	2.74779	+	1.12129i	0.0965474	+	0.0393981i
$811$	−1.50862	+	2.34746i	−0.0529749	+	0.0824305i	−0.866731	−	0.498776i	$-0.833783\pi$
$811$	−1.50862	+	2.34746i	−0.0529749	+	0.0824305i	0.813756	+	0.581207i	$0.197419\pi$
$812$	5.20734	+	63.4316i	0.182742	+	2.22601i
$813$	16.2916	+	14.1168i	0.571372	+	0.495096i
$814$	−20.7894	+	26.0774i	−0.728669	+	0.914013i
$815$	−16.6415	−	36.4397i	−0.582925	−	1.27643i
$816$	18.7281	+	20.7170i	0.655616	+	0.725241i
$817$	6.25410	+	1.83637i	0.218803	+	0.0642464i
$818$	−2.25285	+	22.0439i	−0.0787690	+	0.770747i
$819$	7.13831	+	1.02633i	0.249433	+	0.0358630i
$820$	4.63818	−	22.4551i	0.161972	−	0.784166i
$821$	−33.5713	−	15.3315i	−1.17165	−	0.535073i	−0.268029	−	0.963411i	$-0.586372\pi$
$821$	−33.5713	−	15.3315i	−1.17165	−	0.535073i	−0.903619	+	0.428338i	$0.859099\pi$
$822$	19.8934	−	10.0890i	0.693862	−	0.351895i
$823$	3.60760	+	25.0914i	0.125753	+	0.874632i	0.950853	+	0.309644i	$0.100210\pi$
$823$	3.60760	+	25.0914i	0.125753	+	0.874632i	−0.825099	+	0.564988i	$0.808881\pi$
$824$	10.8684	+	17.6765i	0.378617	+	0.615792i
$825$	−1.45913	−	1.68392i	−0.0508003	−	0.0586266i
$826$	−5.36944	+	21.5083i	−0.186827	+	0.748371i
$827$			37.9478i			1.31958i	0.751452	+	0.659788i	$0.229354\pi$
$827$			37.9478i			1.31958i	−0.751452	+	0.659788i	$0.770646\pi$
$828$	−8.80157	−	3.81214i	−0.305876	−	0.132481i
$829$			4.21000i			0.146219i	0.997324	+	0.0731097i	$0.0232923\pi$
$829$			4.21000i			0.146219i	−0.997324	+	0.0731097i	$0.976708\pi$
$830$	−26.2445	−	6.55181i	−0.910962	−	0.227417i
$831$	−3.79481	−	4.37944i	−0.131640	−	0.151921i
$832$	−8.01628	−	13.6400i	−0.277914	−	0.472881i
$833$	6.25760	+	43.5226i	0.216813	+	1.50797i
$834$	−7.82692	−	15.4330i	−0.271024	−	0.534402i
$835$	−2.72388	−	1.24395i	−0.0942636	−	0.0430488i
$836$	9.86702	+	2.03807i	0.341258	+	0.0704881i
$837$	3.79115	+	0.545085i	0.131041	+	0.0188409i
$838$	−38.0810	−	3.89181i	−1.31549	−	0.134440i
$839$	1.01472	+	0.297949i	0.0350321	+	0.0102863i	0.299202	−	0.954190i	$-0.403280\pi$
$839$	1.01472	+	0.297949i	0.0350321	+	0.0102863i	−0.264170	+	0.964476i	$0.585098\pi$
$840$	6.51074	−	20.6421i	0.224642	−	0.712221i
$841$	−19.5882	−	42.8922i	−0.675456	−	1.47904i
$842$	−25.5659	−	20.3816i	−0.881058	−	0.702396i
$843$	23.4599	+	20.3282i	0.808003	+	0.700139i
$844$	−2.90956	−	35.4418i	−0.100151	−	1.21996i
$845$	−10.3118	+	16.0455i	−0.354737	+	0.551982i
$846$	2.20685	−	5.40802i	0.0758731	−	0.185931i
$847$	−9.10399	+	5.85078i	−0.312817	+	0.201035i
$848$	−4.33518	−	26.2259i	−0.148871	−	0.900601i
$849$	−1.29809	+	0.381155i	−0.0445505	+	0.0130812i
$850$	−5.07831	−	2.97713i	−0.174185	−	0.102115i
$851$	−2.43519	−	30.1630i	−0.0834771	−	1.03397i
$852$	−15.6584	+	8.76500i	−0.536447	+	0.300284i
$853$	9.78337	+	33.3191i	0.334976	+	1.14082i	0.939017	+	0.343871i	$0.111738\pi$
$853$	9.78337	+	33.3191i	0.334976	+	1.14082i	−0.604041	+	0.796953i	$0.706444\pi$
$854$	23.4305	−	4.35458i	0.801774	−	0.149011i
$855$	2.37962	−	1.52929i	0.0813813	−	0.0523006i
$856$	−0.577121	−	4.67352i	−0.0197256	−	0.159738i
$857$	26.3419	+	16.9289i	0.899821	+	0.578280i	0.906737	−	0.421696i	$-0.138565\pi$
$857$	26.3419	+	16.9289i	0.899821	+	0.578280i	−0.00691590	+	0.999976i	$0.502201\pi$
$858$	6.00641	+	8.55456i	0.205056	+	0.292048i
$859$	3.72304	+	3.22604i	0.127029	+	0.110071i	0.716058	−	0.698040i	$-0.245944\pi$
$859$	3.72304	+	3.22604i	0.127029	+	0.110071i	−0.589030	+	0.808111i	$0.700490\pi$
$860$	18.9403	−	7.29204i	0.645860	−	0.248657i
$861$	18.1217	−	8.27589i	0.617585	−	0.282041i
$862$	−9.49867	−	10.0954i	−0.323526	−	0.343850i
$863$	−9.86156	−	2.89562i	−0.335692	−	0.0985679i	0.109543	−	0.993982i	$-0.465061\pi$
$863$	−9.86156	−	2.89562i	−0.335692	−	0.0985679i	−0.445234	+	0.895414i	$0.646880\pi$
$864$	3.43255	−	4.49640i	0.116778	−	0.152971i
$865$	−5.71298	+	39.7346i	−0.194247	+	1.35102i
$866$	17.0589	−	5.77751i	0.579686	−	0.196328i
$867$	−28.8774	−	13.1878i	−0.980726	−	0.447883i
$868$	1.69984	−	27.8823i	0.0576963	−	0.946385i
$869$	3.17202	−	0.456068i	0.107603	−	0.0154710i
$870$	1.06038	+	25.8768i	0.0359502	+	0.877304i
$871$	−7.89362	−	9.10972i	−0.267465	−	0.308671i
$872$	25.6296	−	6.97374i	0.867929	−	0.236161i
$873$	11.0661			0.374530
$874$	−7.79426	+	4.77778i	−0.263645	+	0.161611i
$875$			42.8249i			1.44775i
$876$	−20.0605	+	20.4866i	−0.677780	+	0.692179i
$877$	−33.4529	+	28.9871i	−1.12962	+	0.978825i	−0.999919	−	0.0127275i	$-0.995949\pi$
$877$	−33.4529	+	28.9871i	−1.12962	+	0.978825i	−0.129705	+	0.991553i	$0.541403\pi$
$878$	38.1528	−	1.56343i	1.28759	−	0.0527630i
$879$	−0.712888	−	4.95825i	−0.0240451	−	0.167238i
$880$	28.2564	−	13.6292i	0.952522	−	0.459439i
$881$	11.4675	−	25.1104i	0.386351	−	0.845991i	−0.612123	−	0.790763i	$-0.709684\pi$
$881$	11.4675	−	25.1104i	0.386351	−	0.845991i	0.998474	−	0.0552281i	$-0.0175886\pi$
$882$	8.43573	−	2.85701i	0.284046	−	0.0962005i
$883$	−39.2369	−	5.64142i	−1.32043	−	0.189849i	−0.554182	−	0.832396i	$-0.686969\pi$
$883$	−39.2369	−	5.64142i	−1.32043	−	0.189849i	−0.766246	+	0.642547i	$0.777878\pi$
$884$	22.2799	+	16.3159i	0.749353	+	0.548765i
$885$	−2.54145	+	8.65539i	−0.0854300	+	0.290948i
$886$	7.30979	−	6.87772i	0.245577	−	0.231062i
$887$	22.7302	+	49.7721i	0.763204	+	1.67118i	0.741070	+	0.671428i	$0.234319\pi$
$887$	22.7302	+	49.7721i	0.763204	+	1.67118i	0.0221342	+	0.999755i	$0.492954\pi$
$888$	17.6112	+	2.89152i	0.590994	+	0.0970330i
$889$	−15.7148	+	18.1359i	−0.527059	+	0.608258i
$890$	−25.8576	−	36.8274i	−0.866749	−	1.23446i
$891$	−2.02056	+	3.14405i	−0.0676912	+	0.105329i
$892$	43.5512	−	33.3219i	1.45820	−	1.11570i
$893$	−3.00985	−	4.68341i	−0.100721	−	0.156724i
$894$	−4.74195	−	25.5147i	−0.158594	−	0.853340i
$895$	−37.7334	+	11.0795i	−1.26129	+	0.370348i
$896$	−34.7316	−	22.2673i	−1.16030	−	0.743900i
$897$	−9.28579	−	1.93109i	−0.310044	−	0.0644774i
$898$	−41.1490	−	24.1234i	−1.37316	−	0.805008i
$899$	9.41663	+	32.0701i	0.314062	+	1.06960i
$900$	−0.404927	+	1.12151i	−0.0134976	+	0.0373837i
$901$	25.0844	+	39.0321i	0.835682	+	1.30035i
$902$	26.7346	+	10.9096i	0.890164	+	0.363249i
$903$	14.8345	+	9.53356i	0.493662	+	0.317257i
$904$	−26.1812	−	12.5932i	−0.870773	−	0.418843i
$905$	4.20427	−	4.85199i	0.139755	−	0.161286i
$906$	11.7501	+	9.36743i	0.390372	+	0.311212i
$907$	28.9846	−	13.2368i	0.962418	−	0.439521i	0.128682	−	0.991686i	$-0.458925\pi$
$907$	28.9846	−	13.2368i	0.962418	−	0.439521i	0.833735	+	0.552164i	$0.186198\pi$
$908$	4.81883	−	1.10144i	0.159919	−	0.0365526i
$909$	3.89684	−	13.2714i	0.129250	−	0.440185i
$910$	2.17598	−	21.2918i	0.0721330	−	0.705815i
$911$	−0.916055	+	6.37130i	−0.0303503	+	0.211091i	−0.999353	−	0.0359581i	$-0.988552\pi$
$911$	−0.916055	+	6.37130i	−0.0303503	+	0.211091i	0.969003	+	0.247049i	$0.0794608\pi$
$912$	−1.62742	−	5.14023i	−0.0538893	−	0.170210i
$913$	14.1508	−	30.9860i	0.468324	−	1.02549i
$914$	13.1374	+	25.9042i	0.434546	+	0.856833i
$915$	9.59890	−	1.38011i	0.317330	−	0.0456251i
$916$	−5.98403	+	11.2381i	−0.197718	+	0.371319i
$917$	27.4071	−	23.7484i	0.905063	−	0.784241i
$918$	−2.39155	+	9.57982i	−0.0789329	+	0.316181i
$919$	−7.99618			−0.263770			−0.131885	−	0.991265i	$-0.542103\pi$
$919$	−7.99618			−0.263770			−0.131885	+	0.991265i	$0.542103\pi$
$920$	−10.2346	+	26.5623i	−0.337424	+	0.875733i
$921$	8.05320			0.265362
$922$	9.21462	−	36.9109i	0.303467	−	1.21560i
$923$	−13.4101	+	11.6199i	−0.441398	+	0.382473i
$924$	24.0591	+	12.8108i	0.791485	+	0.421446i
$925$	−3.72357	+	0.535369i	−0.122430	+	0.0176028i
$926$	−5.78867	−	11.4140i	−0.190228	−	0.375089i
$927$	−3.04765	+	6.67342i	−0.100098	+	0.219184i
$928$	48.1359	+	10.9474i	1.58014	+	0.359367i
$929$	6.35342	−	44.1890i	0.208449	−	1.44979i	−0.569771	−	0.821803i	$-0.692968\pi$
$929$	6.35342	−	44.1890i	0.208449	−	1.44979i	0.778220	−	0.627991i	$-0.216123\pi$
$930$	1.15566	−	11.3080i	0.0378956	−	0.370805i
$931$	2.39161	−	8.14508i	0.0783819	−	0.266944i
$932$	−0.322788	−	1.41221i	−0.0105733	−	0.0462583i
$933$	−15.4733	+	7.06641i	−0.506573	+	0.231344i
$934$	−20.4454	−	16.2995i	−0.668994	−	0.533335i
$935$	−35.8588	+	41.3833i	−1.17271	+	1.35338i
$936$	2.42464	−	5.04082i	0.0792518	−	0.164764i
$937$	−13.1267	−	8.43603i	−0.428831	−	0.275593i	0.308370	−	0.951267i	$-0.400217\pi$
$937$	−13.1267	−	8.43603i	−0.428831	−	0.275593i	−0.737201	+	0.675674i	$0.763853\pi$
$938$	−29.1029	−	11.8760i	−0.950244	−	0.387766i
$939$	−18.8624	−	29.3505i	−0.615551	−	0.957816i
$940$	−16.3044	−	5.88679i	−0.531792	−	0.192006i
$941$	7.12248	+	24.2569i	0.232186	+	0.790753i	0.990338	+	0.138675i	$0.0442844\pi$
$941$	7.12248	+	24.2569i	0.232186	+	0.790753i	−0.758152	+	0.652078i	$0.773897\pi$
$942$	6.45702	+	3.78539i	0.210381	+	0.123335i
$943$	−24.4635	+	9.38055i	−0.796641	+	0.305473i
$944$	14.6572	+	8.98997i	0.477050	+	0.292599i
$945$	7.34253	−	2.15596i	0.238853	−	0.0701334i
$946$	4.67009	+	25.1281i	0.151838	+	0.816986i
$947$	−16.1416	−	25.1168i	−0.524531	−	0.816186i	0.473376	−	0.880861i	$-0.343035\pi$
$947$	−16.1416	−	25.1168i	−0.524531	−	0.816186i	−0.997906	+	0.0646749i	$0.979399\pi$
$948$	−1.04209	−	1.36200i	−0.0338456	−	0.0442356i
$949$	−15.3284	+	23.8514i	−0.497581	+	0.774250i
$950$	0.653060	+	0.930113i	0.0211880	+	0.0301768i
$951$	−15.5883	+	17.9899i	−0.505486	+	0.583362i
$952$	71.0606	+	11.6672i	2.30309	+	0.378135i
$953$	14.8585	+	32.5356i	0.481314	+	1.05393i	0.982100	+	0.188360i	$0.0603171\pi$
$953$	14.8585	+	32.5356i	0.481314	+	1.05393i	−0.500786	+	0.865571i	$0.666956\pi$
$954$	6.84465	−	6.44008i	0.221604	−	0.208505i
$955$	−14.0123	+	47.7215i	−0.453427	+	1.54423i
$956$	−23.8216	+	32.5291i	−0.770447	+	1.05207i
$957$	−32.2822	−	4.64148i	−1.04354	−	0.150038i
$958$	11.4607	−	3.88149i	0.370277	−	0.125405i
$959$	23.8929	−	52.3182i	0.771542	−	1.68944i
$960$	−13.7502	−	9.63210i	−0.443784	−	0.310875i
$961$	2.32401	+	16.1639i	0.0749681	+	0.521415i
$962$	17.6328	−	0.722555i	0.568503	−	0.0232961i
$963$	1.25824	−	1.09027i	0.0405462	−	0.0351335i
$964$	37.0739	+	36.3026i	1.19407	+	1.16923i
$965$		−	11.8404i		−	0.381157i
$966$	−23.8736	+	6.46131i	−0.768121	+	0.207889i
$967$	7.54595			0.242661			0.121331	−	0.992612i	$-0.461284\pi$
$967$	7.54595			0.242661			0.121331	+	0.992612i	$0.461284\pi$
$968$	2.20381	+	8.09936i	0.0708331	+	0.260323i
$969$	6.16291	+	7.11237i	0.197981	+	0.228482i
$970$	−1.34465	−	32.8140i	−0.0431741	−	1.05359i
$971$	−35.1886	+	5.05936i	−1.12926	+	0.162363i	−0.681518	−	0.731802i	$-0.738680\pi$
$971$	−35.1886	+	5.05936i	−1.12926	+	0.162363i	−0.447739	+	0.894164i	$0.647771\pi$
$972$	1.99629	+	0.121704i	0.0640311	+	0.00390365i
$973$	−40.5877	−	18.5358i	−1.30118	−	0.594230i
$974$	31.0099	−	10.5024i	0.993623	−	0.336520i
$975$	−0.167796	+	1.16705i	−0.00537377	+	0.0373754i
$976$	2.24548	−	18.3477i	0.0718760	−	0.587296i
$977$	−19.2117	−	5.64106i	−0.614637	−	0.180474i	−0.0404278	−	0.999182i	$-0.512872\pi$
$977$	−19.2117	−	5.64106i	−0.614637	−	0.180474i	−0.574209	+	0.818709i	$0.694690\pi$
$978$	−18.4996	−	19.6617i	−0.591551	−	0.628713i
$979$	51.5463	−	23.5404i	1.64743	−	0.752355i
$980$	−9.49685	−	24.6671i	−0.303366	−	0.787962i
$981$	7.09717	+	6.14973i	0.226595	+	0.196346i
$982$	12.5221	+	17.8344i	0.399596	+	0.569120i
$983$	−24.3020	−	15.6179i	−0.775112	−	0.498134i	0.0922960	−	0.995732i	$-0.470579\pi$
$983$	−24.3020	−	15.6179i	−0.775112	−	0.498134i	−0.867408	+	0.497597i	$0.834216\pi$
$984$	−1.89375	−	15.3356i	−0.0603707	−	0.488882i
$985$	−47.6830	+	30.6440i	−1.51931	+	0.976399i
$986$	−84.7142	+	15.7442i	−2.69785	+	0.501399i
$987$	−4.24322	−	14.4511i	−0.135063	−	0.459983i
$988$	−2.60413	−	4.65219i	−0.0828484	−	0.148006i
$989$	−18.6919	−	13.7273i	−0.594369	−	0.436501i
$990$	9.56848	+	5.60947i	0.304106	+	0.178281i
$991$	−41.5363	+	12.1961i	−1.31944	+	0.387423i	−0.864292	−	0.502991i	$-0.832233\pi$
$991$	−41.5363	+	12.1961i	−1.31944	+	0.387423i	−0.455151	+	0.890414i	$0.650415\pi$
$992$	−20.2282	−	7.76264i	−0.642245	−	0.246464i
$993$	−8.21667	+	5.28053i	−0.260748	+	0.167573i
$994$	−17.4823	+	42.8413i	−0.554503	+	1.35884i
$995$	7.95317	−	12.3754i	0.252132	−	0.392326i
$996$	−18.1681	+	1.49149i	−0.575678	+	0.0472596i
$997$	8.59699	+	7.44934i	0.272269	+	0.235923i	0.780284	−	0.625426i	$-0.215075\pi$
$997$	8.59699	+	7.44934i	0.272269	+	0.235923i	−0.508014	+	0.861349i	$0.669620\pi$
$998$	−33.5091	−	26.7141i	−1.06071	−	0.845620i
$999$	2.62122	+	5.73966i	0.0829316	+	0.181595i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.469.4	yes	480
8.5	even	2	inner	552.2.bb.a.469.12	yes	480
23.18	even	11	inner	552.2.bb.a.133.12	yes	480
184.133	even	22	inner	552.2.bb.a.133.4	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.133.4	✓	480	184.133	even	22	inner
552.2.bb.a.133.12	yes	480	23.18	even	11	inner
552.2.bb.a.469.4	yes	480	1.1	even	1	trivial
552.2.bb.a.469.12	yes	480	8.5	even	2	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37210 - 0.342538i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(1.76533 + 0.939996i) q^{4} +(2.07717 - 0.298651i) q^{5} +(1.26128 - 0.639663i) q^{6} +(1.51486 - 3.31707i) q^{7} +(-2.10024 - 1.89447i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-2.95239 - 0.301729i) q^{10} +(1.05293 - 3.58595i) q^{11} +(-1.94972 + 0.445647i) q^{12} +(-1.79893 + 0.821544i) q^{13} +(-3.21477 + 4.03247i) q^{14} +(-1.37424 + 1.58596i) q^{15} +(2.23282 + 3.31882i) q^{16} +(-5.87350 - 3.77467i) q^{17} +(-0.534322 + 1.30939i) q^{18} +(0.728744 + 1.13395i) q^{19} +(3.94763 + 1.42531i) q^{20} +(1.02737 + 3.49890i) q^{21} +(-2.67305 + 4.55962i) q^{22} +(-1.06231 - 4.67670i) q^{23} +(2.82787 + 0.0563794i) q^{24} +(-0.572037 + 0.167965i) q^{25} +(2.74973 - 0.511041i) q^{26} +(0.540641 + 0.841254i) q^{27} +(5.79227 - 4.43179i) q^{28} +(-4.71795 + 7.34128i) q^{29} +(2.42886 - 1.70537i) q^{30} +(2.50820 - 2.89462i) q^{31} +(-1.92683 - 5.31858i) q^{32} +(1.55254 + 3.39960i) q^{33} +(6.76608 + 7.19114i) q^{34} +(2.15596 - 7.34253i) q^{35} +(1.18166 - 1.61359i) q^{36} +(6.24565 + 0.897989i) q^{37} +(-0.611492 - 1.80552i) q^{38} +(0.821544 - 1.79893i) q^{39} +(-4.92833 - 3.30788i) q^{40} +(-0.777487 - 5.40754i) q^{41} +(-0.211150 - 5.15276i) q^{42} +(3.65456 - 3.16669i) q^{43} +(5.22955 - 5.34065i) q^{44} -2.09853i q^{45} +(-0.144351 + 6.78079i) q^{46} -4.13018 q^{47} +(-3.86081 - 1.04601i) q^{48} +(-4.12417 - 4.75954i) q^{49} +(0.842428 - 0.0345210i) q^{50} +(6.91078 - 0.993620i) q^{51} +(-3.94796 - 0.240687i) q^{52} +(-6.04491 - 2.76062i) q^{53} +(-0.453653 - 1.33948i) q^{54} +(1.11616 - 7.76307i) q^{55} +(-9.46565 + 4.09680i) q^{56} +(-1.29333 - 0.379755i) q^{57} +(8.98819 - 8.45691i) q^{58} +(3.91018 - 1.78572i) q^{59} +(-3.91680 + 1.50797i) q^{60} +(-3.49243 - 3.02621i) q^{61} +(-4.43304 + 3.11256i) q^{62} +(-3.06772 - 1.97151i) q^{63} +(0.821993 + 7.95766i) q^{64} +(-3.49132 + 2.24374i) q^{65} +(-0.965759 - 5.19641i) q^{66} +(1.71718 + 5.84817i) q^{67} +(-6.82053 - 12.1846i) q^{68} +(3.86542 + 2.83875i) q^{69} +(-5.47330 + 9.33621i) q^{70} +(8.60887 - 2.52779i) q^{71} +(-2.17408 + 1.80925i) q^{72} +(12.0605 - 7.75082i) q^{73} +(-8.26208 - 3.37151i) q^{74} +(0.322323 - 0.501544i) q^{75} +(0.220571 + 2.68681i) q^{76} +(-10.2998 - 8.92484i) q^{77} +(-1.74345 + 2.18691i) q^{78} +(0.356204 + 0.779979i) q^{79} +(5.62910 + 6.22690i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-0.785497 + 7.68602i) q^{82} +(9.02183 + 1.29714i) q^{83} +(-1.47530 + 7.14245i) q^{84} +(-13.3276 - 6.08649i) q^{85} +(-6.09914 + 3.09320i) q^{86} +(-1.24192 - 8.63777i) q^{87} +(-9.00486 + 5.53660i) q^{88} +(9.92930 + 11.4590i) q^{89} +(-0.718826 + 2.87940i) q^{90} +7.21171i q^{91} +(2.52075 - 9.25450i) q^{92} +3.83013i q^{93} +(5.66704 + 1.41475i) q^{94} +(1.85238 + 2.13776i) q^{95} +(4.93913 + 2.75771i) q^{96} +(1.57487 + 10.9534i) q^{97} +(4.02846 + 7.94327i) q^{98} +(-3.39960 - 1.55254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32}+ \cdots - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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