LMFDB - Embedded newform 552.2.bb.a.133.44

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			133.44
Character	$\chi$	$=$	552.133
Dual form			552.2.bb.a.469.44

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.33377 - 0.470182i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(1.55786 - 1.25422i) q^{4} +(4.05863 + 0.583543i) q^{5} +(-1.31590 - 0.518091i) q^{6} +(-1.78354 - 3.90540i) q^{7} +(1.48810 - 2.40532i) q^{8} +(0.142315 + 0.989821i) q^{9} +(5.68763 - 1.12998i) q^{10} +(1.14978 + 3.91580i) q^{11} +(-1.99869 - 0.0723017i) q^{12} +(-1.92706 - 0.880060i) q^{13} +(-4.21507 - 4.37030i) q^{14} +(-2.68517 - 3.09885i) q^{15} +(0.853847 - 3.90781i) q^{16} +(-5.02005 + 3.22619i) q^{17} +(0.655210 + 1.25328i) q^{18} +(1.02677 - 1.59769i) q^{19} +(7.05467 - 4.18135i) q^{20} +(-1.20959 + 4.11947i) q^{21} +(3.37468 + 4.68215i) q^{22} +(-0.488059 + 4.77093i) q^{23} +(-2.69978 + 0.843315i) q^{24} +(11.3345 + 3.32811i) q^{25} +(-2.98404 - 0.267724i) q^{26} +(0.540641 - 0.841254i) q^{27} +(-7.67674 - 3.84711i) q^{28} +(2.79446 + 4.34826i) q^{29} +(-5.03841 - 2.87062i) q^{30} +(-4.76520 - 5.49933i) q^{31} +(-0.698546 - 5.61356i) q^{32} +(1.69536 - 3.71231i) q^{33} +(-5.17867 + 6.66331i) q^{34} +(-4.95975 - 16.8914i) q^{35} +(1.46316 + 1.36351i) q^{36} +(5.40131 - 0.776591i) q^{37} +(0.618270 - 2.61371i) q^{38} +(0.880060 + 1.92706i) q^{39} +(7.44327 - 8.89392i) q^{40} +(-0.231664 + 1.61126i) q^{41} +(0.323596 + 6.06314i) q^{42} +(-6.36528 - 5.51555i) q^{43} +(6.70249 + 4.65818i) q^{44} +4.10037i q^{45} +(1.59225 + 6.59278i) q^{46} +1.49751 q^{47} +(-3.20436 + 2.39417i) q^{48} +(-7.48713 + 8.64061i) q^{49} +(16.6824 - 0.890356i) q^{50} +(5.90660 + 0.849241i) q^{51} +(-4.10588 + 1.04596i) q^{52} +(-0.541617 + 0.247348i) q^{53} +(0.325546 - 1.37623i) q^{54} +(2.38151 + 16.5637i) q^{55} +(-12.0478 - 1.52168i) q^{56} +(-1.82225 + 0.535061i) q^{57} +(5.77163 + 4.48566i) q^{58} +(8.89448 + 4.06197i) q^{59} +(-8.06976 - 1.45977i) q^{60} +(0.615311 - 0.533170i) q^{61} +(-8.94134 - 5.09431i) q^{62} +(3.61183 - 2.32118i) q^{63} +(-3.57109 - 7.15872i) q^{64} +(-7.30768 - 4.69636i) q^{65} +(0.515746 - 5.74848i) q^{66} +(-3.24059 + 11.0364i) q^{67} +(-3.77416 + 11.3222i) q^{68} +(3.49315 - 3.28602i) q^{69} +(-14.5571 - 20.1971i) q^{70} +(1.90309 + 0.558799i) q^{71} +(2.59261 + 1.13065i) q^{72} +(-1.88366 - 1.21055i) q^{73} +(6.83894 - 3.57539i) q^{74} +(-6.38659 - 9.93773i) q^{75} +(-0.404293 - 3.77678i) q^{76} +(13.2421 - 11.4743i) q^{77} +(2.07986 + 2.15646i) q^{78} +(-2.87414 + 6.29348i) q^{79} +(5.74582 - 15.3621i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(0.448598 + 2.25796i) q^{82} +(-1.11770 + 0.160701i) q^{83} +(3.28237 + 7.93465i) q^{84} +(-22.2571 + 10.1645i) q^{85} +(-11.0831 - 4.36361i) q^{86} +(0.735596 - 5.11618i) q^{87} +(11.1297 + 3.06153i) q^{88} +(-3.54339 + 4.08929i) q^{89} +(1.92792 + 5.46893i) q^{90} +9.09557i q^{91} +(5.22349 + 8.04457i) q^{92} +7.27666i q^{93} +(1.99733 - 0.704101i) q^{94} +(5.09962 - 5.88527i) q^{95} +(-3.14817 + 4.69989i) q^{96} +(0.310739 - 2.16124i) q^{97} +(-5.92342 + 15.0448i) q^{98} +(-3.71231 + 1.69536i) 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 $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{6}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	1.33377	−	0.470182i	0.943114	−	0.332469i
$2$	1.33377	−	0.470182i	0.943114	−	0.332469i
$3$	−0.755750	−	0.654861i	−0.436332	−	0.378084i
$3$	−0.755750	−	0.654861i	−0.436332	−	0.378084i
$4$	1.55786	−	1.25422i	0.778929	−	0.627112i
$5$	4.05863	+	0.583543i	1.81507	+	0.260968i	0.964348	−	0.264639i	$-0.0852528\pi$
$5$	4.05863	+	0.583543i	1.81507	+	0.260968i	0.850727	+	0.525607i	$0.176162\pi$
$6$	−1.31590	−	0.518091i	−0.537212	−	0.211510i
$7$	−1.78354	−	3.90540i	−0.674114	−	1.47610i	−0.868762	−	0.495230i	$-0.835084\pi$
$7$	−1.78354	−	3.90540i	−0.674114	−	1.47610i	0.194648	−	0.980873i	$-0.437643\pi$
$8$	1.48810	−	2.40532i	0.526125	−	0.850408i
$9$	0.142315	+	0.989821i	0.0474383	+	0.329940i
$10$	5.68763	−	1.12998i	1.79859	−	0.357332i
$11$	1.14978	+	3.91580i	0.346673	+	1.18066i	0.929734	+	0.368231i	$0.120036\pi$
$11$	1.14978	+	3.91580i	0.346673	+	1.18066i	−0.583062	+	0.812428i	$0.698145\pi$
$12$	−1.99869	−	0.0723017i	−0.576973	−	0.0208717i
$13$	−1.92706	−	0.880060i	−0.534471	−	0.244085i	0.129848	−	0.991534i	$-0.458551\pi$
$13$	−1.92706	−	0.880060i	−0.534471	−	0.244085i	−0.664319	+	0.747449i	$0.731278\pi$
$14$	−4.21507	−	4.37030i	−1.12652	−	1.16801i
$15$	−2.68517	−	3.09885i	−0.693308	−	0.800120i
$16$	0.853847	−	3.90781i	0.213462	−	0.976951i
$17$	−5.02005	+	3.22619i	−1.21754	+	0.782466i	−0.981905	−	0.189376i	$-0.939354\pi$
$17$	−5.02005	+	3.22619i	−1.21754	+	0.782466i	−0.235636	+	0.971841i	$0.575717\pi$
$18$	0.655210	+	1.25328i	0.154435	+	0.295400i
$19$	1.02677	−	1.59769i	0.235558	−	0.366535i	−0.703269	−	0.710923i	$-0.748277\pi$
$19$	1.02677	−	1.59769i	0.235558	−	0.366535i	0.938827	+	0.344388i	$0.111914\pi$
$20$	7.05467	−	4.18135i	1.57747	−	0.934979i
$21$	−1.20959	+	4.11947i	−0.263953	+	0.898943i
$22$	3.37468	+	4.68215i	0.719484	+	0.998238i
$23$	−0.488059	+	4.77093i	−0.101767	+	0.994808i
$23$	−0.488059	+	4.77093i	−0.101767	+	0.994808i
$24$	−2.69978	+	0.843315i	−0.551091	+	0.172141i
$25$	11.3345	+	3.32811i	2.26690	+	0.665622i
$26$	−2.98404	−	0.267724i	−0.585218	−	0.0525050i
$27$	0.540641	−	0.841254i	0.104046	−	0.161899i
$28$	−7.67674	−	3.84711i	−1.45077	−	0.727035i
$29$	2.79446	+	4.34826i	0.518918	+	0.807453i	0.997506	−	0.0705874i	$-0.0224874\pi$
$29$	2.79446	+	4.34826i	0.518918	+	0.807453i	−0.478587	+	0.878040i	$0.658851\pi$
$30$	−5.03841	−	2.87062i	−0.919883	−	0.524101i
$31$	−4.76520	−	5.49933i	−0.855855	−	0.987709i	0.144144	−	0.989557i	$-0.453957\pi$
$31$	−4.76520	−	5.49933i	−0.855855	−	0.987709i	−0.999998	+	0.00184791i	$0.999412\pi$
$32$	−0.698546	−	5.61356i	−0.123487	−	0.992346i
$33$	1.69536	−	3.71231i	0.295124	−	0.646231i
$34$	−5.17867	+	6.66331i	−0.888135	+	1.14275i
$35$	−4.95975	−	16.8914i	−0.838350	−	2.85516i
$36$	1.46316	+	1.36351i	0.243861	+	0.227251i
$37$	5.40131	−	0.776591i	0.887970	−	0.127671i	0.316790	−	0.948496i	$-0.397395\pi$
$37$	5.40131	−	0.776591i	0.887970	−	0.127671i	0.571180	+	0.820825i	$0.306486\pi$
$38$	0.618270	−	2.61371i	0.100297	−	0.424001i
$39$	0.880060	+	1.92706i	0.140922	+	0.308577i
$40$	7.44327	−	8.89392i	1.17688	−	1.40625i
$41$	−0.231664	+	1.61126i	−0.0361798	+	0.251636i	−0.999882	−	0.0153425i	$-0.995116\pi$
$41$	−0.231664	+	1.61126i	−0.0361798	+	0.251636i	0.963703	+	0.266978i	$0.0860252\pi$
$42$	0.323596	+	6.06314i	0.0499319	+	0.935562i
$43$	−6.36528	−	5.51555i	−0.970697	−	0.841114i	0.0166223	−	0.999862i	$-0.494709\pi$
$43$	−6.36528	−	5.51555i	−0.970697	−	0.841114i	−0.987319	+	0.158748i	$0.949254\pi$
$44$	6.70249	+	4.65818i	1.01044	+	0.702247i
$45$			4.10037i			0.611247i
$46$	1.59225	+	6.59278i	0.234764	+	0.972052i
$47$	1.49751			0.218434			0.109217	−	0.994018i	$-0.465166\pi$
$47$	1.49751			0.218434			0.109217	+	0.994018i	$0.465166\pi$
$48$	−3.20436	+	2.39417i	−0.462510	+	0.345569i
$49$	−7.48713	+	8.64061i	−1.06959	+	1.23437i
$50$	16.6824	−	0.890356i	2.35924	−	0.125915i
$51$	5.90660	+	0.849241i	0.827090	+	0.118918i
$52$	−4.10588	+	1.04596i	−0.569383	+	0.145048i
$53$	−0.541617	+	0.247348i	−0.0743968	+	0.0339759i	−0.452266	−	0.891883i	$-0.649384\pi$
$53$	−0.541617	+	0.247348i	−0.0743968	+	0.0339759i	0.377869	+	0.925859i	$0.376657\pi$
$54$	0.325546	−	1.37623i	0.0443012	−	0.187282i
$55$	2.38151	+	16.5637i	0.321122	+	2.23345i
$56$	−12.0478	−	1.52168i	−1.60996	−	0.203343i
$57$	−1.82225	+	0.535061i	−0.241363	+	0.0708705i
$58$	5.77163	+	4.48566i	0.757852	+	0.588996i
$59$	8.89448	+	4.06197i	1.15796	+	0.528824i	0.899381	−	0.437166i	$-0.144018\pi$
$59$	8.89448	+	4.06197i	1.15796	+	0.528824i	0.258581	+	0.965989i	$0.416745\pi$
$60$	−8.06976	−	1.45977i	−1.04180	−	0.188455i
$61$	0.615311	−	0.533170i	0.0787824	−	0.0682654i	−0.614579	−	0.788855i	$-0.710674\pi$
$61$	0.615311	−	0.533170i	0.0787824	−	0.0682654i	0.693362	+	0.720590i	$0.256129\pi$
$62$	−8.94134	−	5.09431i	−1.13555	−	0.646978i
$63$	3.61183	−	2.32118i	0.455047	−	0.292441i
$64$	−3.57109	−	7.15872i	−0.446386	−	0.894841i
$65$	−7.30768	−	4.69636i	−0.906406	−	0.582512i
$66$	0.515746	−	5.74848i	0.0634840	−	0.707589i
$67$	−3.24059	+	11.0364i	−0.395901	+	1.34831i	0.484794	+	0.874628i	$0.338895\pi$
$67$	−3.24059	+	11.0364i	−0.395901	+	1.34831i	−0.880694	+	0.473685i	$0.842924\pi$
$68$	−3.77416	+	11.3222i	−0.457685	+	1.37302i
$69$	3.49315	−	3.28602i	0.420525	−	0.395590i
$70$	−14.5571	−	20.1971i	−1.73991	−	2.41402i
$71$	1.90309	+	0.558799i	0.225856	+	0.0663172i	0.392702	−	0.919666i	$-0.371540\pi$
$71$	1.90309	+	0.558799i	0.225856	+	0.0663172i	−0.166847	+	0.985983i	$0.553358\pi$
$72$	2.59261	+	1.13065i	0.305542	+	0.133248i
$73$	−1.88366	−	1.21055i	−0.220465	−	0.141684i	0.425747	−	0.904842i	$-0.360011\pi$
$73$	−1.88366	−	1.21055i	−0.220465	−	0.141684i	−0.646212	+	0.763158i	$0.723648\pi$
$74$	6.83894	−	3.57539i	0.795011	−	0.415630i
$75$	−6.38659	−	9.93773i	−0.737460	−	1.14751i
$76$	−0.404293	−	3.77678i	−0.0463756	−	0.433226i
$77$	13.2421	−	11.4743i	1.50908	−	1.30762i
$78$	2.07986	+	2.15646i	0.235498	+	0.244171i
$79$	−2.87414	+	6.29348i	−0.323366	+	0.708072i	−0.999590	−	0.0286233i	$-0.990888\pi$
$79$	−2.87414	+	6.29348i	−0.323366	+	0.708072i	0.676224	+	0.736696i	$0.263615\pi$
$80$	5.74582	−	15.3621i	0.642403	−	1.71753i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	0.448598	+	2.25796i	0.0495393	+	0.249350i
$83$	−1.11770	+	0.160701i	−0.122684	+	0.0176393i	−0.203383	−	0.979099i	$-0.565194\pi$
$83$	−1.11770	+	0.160701i	−0.122684	+	0.0176393i	0.0806994	+	0.996738i	$0.474285\pi$
$84$	3.28237	+	7.93465i	0.358136	+	0.865741i
$85$	−22.2571	+	10.1645i	−2.41413	+	1.10249i
$86$	−11.0831	−	4.36361i	−1.19512	−	0.470540i
$87$	0.735596	−	5.11618i	0.0788642	−	0.548512i
$88$	11.1297	+	3.06153i	1.18643	+	0.326360i
$89$	−3.54339	+	4.08929i	−0.375598	+	0.433464i	−0.911805	−	0.410623i	$-0.865311\pi$
$89$	−3.54339	+	4.08929i	−0.375598	+	0.433464i	0.536207	+	0.844087i	$0.319857\pi$
$90$	1.92792	+	5.46893i	0.203220	+	0.576475i
$91$			9.09557i			0.953475i
$92$	5.22349	+	8.04457i	0.544586	+	0.838705i
$93$			7.27666i			0.754554i
$94$	1.99733	−	0.704101i	0.206008	−	0.0726225i
$95$	5.09962	−	5.88527i	0.523210	−	0.603816i
$96$	−3.14817	+	4.69989i	−0.321309	+	0.479681i
$97$	0.310739	−	2.16124i	0.0315508	−	0.219440i	−0.967946	−	0.251158i	$-0.919189\pi$
$97$	0.310739	−	2.16124i	0.0315508	−	0.219440i	0.999497	+	0.0317176i	$0.0100977\pi$
$98$	−5.92342	+	15.0448i	−0.598355	+	1.51976i
$99$	−3.71231	+	1.69536i	−0.373101	+	0.170390i
$100$	21.8317	−	9.03127i	2.18317	−	0.903127i
$101$	4.50140	−	0.647204i	0.447906	−	0.0643992i	0.0853288	−	0.996353i	$-0.472806\pi$
$101$	4.50140	−	0.647204i	0.447906	−	0.0643992i	0.362577	+	0.931954i	$0.381897\pi$
$102$	8.27732	−	1.64449i	0.819577	−	0.162829i
$103$	9.78518	−	2.87319i	0.964162	−	0.283104i	0.238491	−	0.971145i	$-0.423347\pi$
$103$	9.78518	−	2.87319i	0.964162	−	0.283104i	0.725672	+	0.688041i	$0.241529\pi$
$104$	−4.98449	+	3.32557i	−0.488770	+	0.326099i
$105$	−7.31316	+	16.0136i	−0.713691	+	1.56277i
$106$	−0.606091	+	0.584563i	−0.0588688	+	0.0567778i
$107$	−5.58925	+	4.84311i	−0.540333	+	0.468201i	−0.881754	−	0.471709i	$-0.843637\pi$
$107$	−5.58925	+	4.84311i	−0.540333	+	0.468201i	0.341421	+	0.939910i	$0.389092\pi$
$108$	−0.212878	−	1.98864i	−0.0204842	−	0.191357i
$109$	6.21752	+	9.67465i	0.595530	+	0.926663i	0.999927	+	0.0120795i	$0.00384510\pi$
$109$	6.21752	+	9.67465i	0.595530	+	0.926663i	−0.404397	+	0.914584i	$0.632519\pi$
$110$	10.9643	+	20.9724i	1.04541	+	1.99964i
$111$	−4.59060	−	2.95020i	−0.435720	−	0.280020i
$112$	−16.7844	+	3.63510i	−1.58598	+	0.343485i
$113$	−16.7095	−	4.90635i	−1.57190	−	0.461550i	−0.624343	−	0.781150i	$-0.714633\pi$
$113$	−16.7095	−	4.90635i	−1.57190	−	0.461550i	−0.947553	+	0.319600i	$0.896452\pi$
$114$	−2.17888	+	1.57043i	−0.204070	+	0.147085i
$115$	−4.76489	+	19.0787i	−0.444329	+	1.77909i
$116$	9.80707	+	3.26910i	0.910564	+	0.303529i
$117$	0.596853	−	2.03269i	0.0551790	−	0.187923i
$118$	13.7730	+	1.23570i	1.26791	+	0.113755i
$119$	21.5530	+	13.8513i	1.97576	+	1.26974i
$120$	−11.4495	+	1.84726i	−1.04519	+	0.168631i
$121$	−4.75771	+	3.05759i	−0.432519	+	0.277963i
$122$	0.569993	−	1.00043i	0.0516048	−	0.0905747i
$123$	1.23023	−	1.06600i	0.110926	−	0.0961178i
$124$	−14.3209	−	2.59056i	−1.28605	−	0.232639i
$125$	25.4113	+	11.6050i	2.27286	+	1.03798i
$126$	3.72595	−	4.79412i	0.331934	−	0.427094i
$127$	4.51942	−	1.32702i	0.401033	−	0.117754i	−0.0749951	−	0.997184i	$-0.523894\pi$
$127$	4.51942	−	1.32702i	0.401033	−	0.117754i	0.476028	+	0.879430i	$0.342076\pi$
$128$	−8.12889	−	7.86900i	−0.718499	−	0.695528i
$129$	1.19864	+	8.33675i	0.105535	+	0.734010i
$130$	−11.9549	−	2.82791i	−1.04851	−	0.248024i
$131$	−12.1999	+	5.57151i	−1.06591	+	0.486785i	−0.869600	−	0.493757i	$-0.835623\pi$
$131$	−12.1999	+	5.57151i	−1.06591	+	0.486785i	−0.196310	+	0.980542i	$0.562896\pi$
$132$	−2.01494	−	7.90961i	−0.175378	−	0.688444i
$133$	−8.07091	−	1.16042i	−0.699837	−	0.100621i
$134$	0.866941	+	16.2437i	0.0748923	+	1.40324i
$135$	2.68517	−	3.09885i	0.231103	−	0.266707i
$136$	0.289645	+	16.8757i	0.0248368	+	1.44708i
$137$	2.67095			0.228194			0.114097	−	0.993470i	$-0.463602\pi$
$137$	2.67095			0.228194			0.114097	+	0.993470i	$0.463602\pi$
$138$	3.11401	−	6.02519i	0.265082	−	0.512898i
$139$		−	8.25598i		−	0.700263i	−0.936701	−	0.350131i	$-0.886137\pi$
$139$		−	8.25598i		−	0.700263i	0.936701	−	0.350131i	$-0.113863\pi$
$140$	−28.9121	−	20.0937i	−2.44352	−	1.69823i
$141$	−1.13174	−	0.980660i	−0.0953099	−	0.0825865i
$142$	2.80102	−	0.149493i	0.235056	−	0.0125452i
$143$	1.23044	−	8.55787i	0.102894	−	0.715645i
$144$	3.98954	+	0.289018i	0.332462	+	0.0240848i
$145$	8.80428	+	19.2787i	0.731156	+	1.60101i
$146$	−3.08153	−	0.728932i	−0.255030	−	0.0603268i
$147$	11.3168	−	1.62711i	0.933393	−	0.134202i
$148$	7.44046	−	7.98427i	0.611602	−	0.656303i
$149$	−3.24541	−	11.0528i	−0.265874	−	0.905484i	−0.978899	−	0.204345i	$-0.934493\pi$
$149$	−3.24541	−	11.0528i	−0.265874	−	0.905484i	0.713025	−	0.701139i	$-0.247325\pi$
$150$	−13.1908	−	10.2517i	−1.07702	−	0.837051i
$151$	−3.98019	+	8.71540i	−0.323903	+	0.709249i	−0.999610	−	0.0279212i	$-0.991111\pi$
$151$	−3.98019	+	8.71540i	−0.323903	+	0.709249i	0.675707	+	0.737170i	$0.263839\pi$
$152$	−2.31500	−	4.84725i	−0.187772	−	0.393164i
$153$	−3.90778	−	4.50982i	−0.315925	−	0.364597i
$154$	12.2668	−	21.5303i	0.988489	−	1.73496i
$155$	−16.1311	−	25.1004i	−1.29568	−	2.01612i
$156$	3.78798	+	1.89830i	0.303281	+	0.151986i
$157$	0.916790	−	1.42655i	0.0731678	−	0.113851i	−0.802741	−	0.596327i	$-0.796626\pi$
$157$	0.916790	−	1.42655i	0.0731678	−	0.113851i	0.875909	+	0.482476i	$0.160262\pi$
$158$	−0.874345	+	9.74540i	−0.0695592	+	0.775302i
$159$	0.571306	+	0.167750i	0.0453075	+	0.0133035i
$160$	0.440612	−	23.1910i	0.0348335	−	1.83341i
$161$	19.5029	−	6.60307i	1.53704	−	0.520395i
$162$	−1.14727	+	0.826901i	−0.0901383	+	0.0649675i
$163$	1.97390	−	6.72249i	0.154608	−	0.526546i	−0.845363	−	0.534192i	$-0.820616\pi$
$163$	1.97390	−	6.72249i	0.154608	−	0.526546i	0.999971	+	0.00764655i	$0.00243400\pi$
$164$	1.65998	+	2.80067i	0.129622	+	0.218695i
$165$	9.04712	−	14.0776i	0.704317	−	1.09594i
$166$	−1.41519	+	0.739861i	−0.109840	+	0.0574244i
$167$	−16.0524	+	10.3163i	−1.24217	+	0.798297i	−0.985742	−	0.168265i	$-0.946183\pi$
$167$	−16.0524	+	10.3163i	−1.24217	+	0.798297i	−0.256433	+	0.966562i	$0.582547\pi$
$168$	8.10864	+	9.03965i	0.625595	+	0.697424i
$169$	−5.57413	−	6.43288i	−0.428779	−	0.494837i
$170$	−24.9066	+	24.0219i	−1.91025	+	1.84240i
$171$	1.72755	+	0.788948i	0.132109	+	0.0603323i
$172$	−16.8339	−	0.608960i	−1.28358	−	0.0464327i
$173$	−4.13510	−	14.0829i	−0.314386	−	1.07070i	−0.953451	−	0.301547i	$-0.902497\pi$
$173$	−4.13510	−	14.0829i	−0.314386	−	1.07070i	0.639065	−	0.769152i	$-0.279321\pi$
$174$	−1.42442	−	7.16965i	−0.107985	−	0.543530i
$175$	−7.21789	−	50.2016i	−0.545622	−	3.79488i
$176$	16.2839	−	1.14963i	1.22745	−	0.0866567i
$177$	−4.06197	−	8.89448i	−0.305317	−	0.668550i
$178$	−2.80334	+	7.12018i	−0.210119	+	0.533680i
$179$	7.99911	+	1.15010i	0.597882	+	0.0859624i	0.434610	−	0.900619i	$-0.356886\pi$
$179$	7.99911	+	1.15010i	0.597882	+	0.0859624i	0.163272	+	0.986581i	$0.447795\pi$
$180$	5.14278	+	6.38779i	0.383320	+	0.476118i
$181$	6.42976	+	5.57142i	0.477920	+	0.414120i	0.860224	−	0.509917i	$-0.170324\pi$
$181$	6.42976	+	5.57142i	0.477920	+	0.414120i	−0.382304	+	0.924037i	$0.624869\pi$
$182$	4.27657	+	12.1314i	0.317000	+	0.899236i
$183$	−0.814173			−0.0601854
$184$	10.7493	+	8.27358i	0.792450	+	0.609937i
$185$	22.3751			1.64505
$186$	3.42135	+	9.70535i	0.250866	+	0.711631i
$187$	−18.4051	−	15.9481i	−1.34591	−	1.16624i
$188$	2.33291	−	1.87821i	0.170145	−	0.136983i
$189$	−4.24969	−	0.611012i	−0.309119	−	0.0444446i
$190$	4.03455	−	10.2473i	0.292697	−	0.743418i
$191$	8.64634	+	18.9328i	0.625627	+	1.36993i	0.911355	+	0.411621i	$0.135037\pi$
$191$	8.64634	+	18.9328i	0.625627	+	1.36993i	−0.285728	+	0.958311i	$0.592235\pi$
$192$	−1.98912	+	7.74877i	−0.143552	+	0.559219i
$193$	−3.38006	−	23.5088i	−0.243302	−	1.69220i	−0.635323	−	0.772247i	$-0.719133\pi$
$193$	−3.38006	−	23.5088i	−0.243302	−	1.69220i	0.392020	−	0.919957i	$-0.371776\pi$
$194$	−0.601721	−	3.02869i	−0.0432010	−	0.217447i
$195$	2.44731	+	8.33479i	0.175256	+	0.596867i
$196$	−0.826637	+	22.8514i	−0.0590455	+	1.63224i
$197$	−3.97409	−	1.81491i	−0.283142	−	0.129307i	0.268782	−	0.963201i	$-0.413379\pi$
$197$	−3.97409	−	1.81491i	−0.283142	−	0.129307i	−0.551924	+	0.833894i	$0.686106\pi$
$198$	−4.15423	+	4.00667i	−0.295228	+	0.284742i
$199$	7.77730	+	8.97548i	0.551318	+	0.636255i	0.961190	−	0.275888i	$-0.0889719\pi$
$199$	7.77730	+	8.97548i	0.551318	+	0.636255i	−0.409872	+	0.912143i	$0.634426\pi$
$200$	24.8721	−	22.3105i	1.75872	−	1.57759i
$201$	9.67639	−	6.21864i	0.682520	−	0.438629i
$202$	5.69951	−	2.97969i	0.401016	−	0.209651i
$203$	11.9977	−	18.6688i	0.842073	−	1.31029i
$204$	10.2668	−	6.08520i	0.718819	−	0.426049i
$205$	−1.88047	+	6.40431i	−0.131338	+	0.447296i
$206$	11.7002	−	8.43297i	0.815192	−	0.587553i
$207$	−4.79183	+	0.195884i	−0.333055	+	0.0136149i
$208$	−5.08452	+	6.77915i	−0.352548	+	0.470049i
$209$	7.43681	+	2.18364i	0.514415	+	0.151046i
$210$	−2.22474	+	24.7969i	−0.153522	+	1.71115i
$211$	−7.79792	+	12.1338i	−0.536831	+	0.835325i	−0.998666	−	0.0516409i	$-0.983555\pi$
$211$	−7.79792	+	12.1338i	−0.536831	+	0.835325i	0.461835	+	0.886966i	$0.347191\pi$
$212$	−0.533533	+	1.06464i	−0.0366432	+	0.0731199i
$213$	−1.07233	−	1.66857i	−0.0734746	−	0.114329i
$214$	−5.17760	+	9.08753i	−0.353934	+	0.621211i
$215$	−22.6158	−	26.1000i	−1.54238	−	1.78001i
$216$	−1.21895	−	2.55229i	−0.0829390	−	0.173661i
$217$	−12.9782	+	28.4183i	−0.881017	+	1.92916i
$218$	12.8415	+	9.98034i	0.869739	+	0.675954i
$219$	0.630829	+	2.14841i	0.0426275	+	0.145176i
$220$	24.4847	+	22.8170i	1.65076	+	1.53832i
$221$	12.5132	−	1.79912i	0.841728	−	0.121022i
$222$	−7.50991	−	1.77646i	−0.504032	−	0.119228i
$223$	−6.05232	−	13.2527i	−0.405293	−	0.887469i	−0.996706	−	0.0810996i	$-0.974157\pi$
$223$	−6.05232	−	13.2527i	−0.405293	−	0.887469i	0.591413	−	0.806369i	$-0.298570\pi$
$224$	−20.6773	+	12.7401i	−1.38156	+	0.851233i
$225$	−1.68117	+	11.6928i	−0.112078	+	0.779518i
$226$	−24.5934	+	1.31258i	−1.63593	+	0.0873112i
$227$	−7.90981	−	6.85389i	−0.524992	−	0.454908i	0.351594	−	0.936152i	$-0.385640\pi$
$227$	−7.90981	−	6.85389i	−0.524992	−	0.454908i	−0.876587	+	0.481244i	$0.840185\pi$
$228$	−2.16772	+	3.11906i	−0.143561	+	0.206565i
$229$		−	23.9691i		−	1.58392i	−0.610572	−	0.791960i	$-0.709061\pi$
$229$		−	23.9691i		−	1.58392i	0.610572	−	0.791960i	$-0.290939\pi$
$230$	2.61518	+	27.6868i	0.172440	+	1.82561i
$231$	−17.5218			−1.15285
$232$	14.6174	−	0.250884i	0.959679	−	0.0164714i
$233$	16.1604	−	18.6501i	1.05870	−	1.22181i	0.0844329	−	0.996429i	$-0.473092\pi$
$233$	16.1604	−	18.6501i	1.05870	−	1.22181i	0.974271	−	0.225380i	$-0.0723624\pi$
$234$	−0.159674	−	2.99176i	−0.0104382	−	0.195578i
$235$	6.07784	+	0.873861i	0.396474	+	0.0570044i
$236$	18.9510	−	4.82768i	1.23360	−	0.314255i
$237$	6.29348	−	2.87414i	0.408806	−	0.186695i
$238$	35.2593	+	8.34052i	2.28552	+	0.540636i
$239$	−1.99576	−	13.8808i	−0.129095	−	0.897877i	−0.946704	−	0.322103i	$-0.895610\pi$
$239$	−1.99576	−	13.8808i	−0.129095	−	0.897877i	0.817609	−	0.575773i	$-0.195299\pi$
$240$	−14.4024	+	7.84717i	−0.929673	+	0.506533i
$241$	−15.4360	+	4.53243i	−0.994322	+	0.291959i	−0.738124	−	0.674665i	$-0.764288\pi$
$241$	−15.4360	+	4.53243i	−0.994322	+	0.291959i	−0.256198	+	0.966624i	$0.582470\pi$
$242$	−4.90804	+	6.31510i	−0.315501	+	0.405950i
$243$	0.909632	+	0.415415i	0.0583529	+	0.0266489i
$244$	0.289853	−	1.60234i	0.0185559	−	0.102579i
$245$	−35.4297	+	30.7000i	−2.26352	+	1.96135i
$246$	1.13962	−	2.00022i	0.0726597	−	0.127529i
$247$	−3.38472	+	2.17523i	−0.215365	+	0.138406i
$248$	−20.3187	+	3.27822i	−1.29024	+	0.208167i
$249$	0.949940	+	0.610490i	0.0602000	+	0.0386882i
$250$	39.3492	+	3.53036i	2.48866	+	0.223280i
$251$	−0.225706	+	0.768686i	−0.0142465	+	0.0485190i	−0.966309	−	0.257383i	$-0.917140\pi$
$251$	−0.225706	+	0.768686i	−0.0142465	+	0.0485190i	0.952063	+	0.305902i	$0.0989580\pi$
$252$	2.71544	−	8.14611i	0.171056	−	0.513156i
$253$	−19.2432	+	3.57440i	−1.20981	+	0.224720i
$254$	5.40390	−	3.89488i	0.339071	−	0.244386i
$255$	23.4772	+	6.89352i	1.47020	+	0.431689i
$256$	−14.5419	−	6.67334i	−0.908868	−	0.417084i
$257$	−21.0034	−	13.4981i	−1.31015	−	0.841985i	−0.315876	−	0.948801i	$-0.602298\pi$
$257$	−21.0034	−	13.4981i	−1.31015	−	0.841985i	−0.994279	+	0.106815i	$0.965935\pi$
$258$	5.51849	+	10.5557i	0.343566	+	0.657168i
$259$	−12.6663	−	19.7092i	−0.787048	−	1.22467i
$260$	−17.2746	+	1.84920i	−1.07133	+	0.114682i
$261$	−3.90631	+	3.38484i	−0.241795	+	0.209516i
$262$	−13.6522	+	13.1672i	−0.843434	+	0.813475i
$263$	3.12639	−	6.84584i	0.192782	−	0.422133i	−0.788415	−	0.615144i	$-0.789098\pi$
$263$	3.12639	−	6.84584i	0.192782	−	0.422133i	0.981197	+	0.193011i	$0.0618253\pi$
$264$	−6.40642	−	9.60218i	−0.394288	−	0.590973i
$265$	−2.34256	+	0.687838i	−0.143902	+	0.0422536i
$266$	−11.3103	+	2.24706i	−0.693480	+	0.137776i
$267$	5.35583	−	0.770052i	0.327771	−	0.0471264i
$268$	8.79376	+	21.2576i	0.537165	+	1.29851i
$269$	10.7340	−	4.90204i	0.654461	−	0.298882i	−0.0603735	−	0.998176i	$-0.519229\pi$
$269$	10.7340	−	4.90204i	0.654461	−	0.298882i	0.714835	+	0.699293i	$0.246502\pi$
$270$	2.12436	−	5.39566i	0.129285	−	0.328369i
$271$	3.49467	−	24.3060i	0.212286	−	1.47648i	−0.553209	−	0.833042i	$-0.686597\pi$
$271$	3.49467	−	24.3060i	0.212286	−	1.47648i	0.765496	−	0.643441i	$-0.222494\pi$
$272$	8.32096	+	22.3720i	0.504533	+	1.35650i
$273$	5.95633	−	6.87397i	0.360494	−	0.416032i
$274$	3.56241	−	1.25583i	0.215213	−	0.0758674i
$275$			48.2102i			2.90719i
$276$	1.32043	−	9.50034i	0.0794803	−	0.571853i
$277$			16.7004i			1.00343i	0.865033	+	0.501716i	$0.167298\pi$
$277$			16.7004i			1.00343i	−0.865033	+	0.501716i	$0.832702\pi$
$278$	−3.88181	−	11.0115i	−0.232815	−	0.660428i
$279$	4.76520	−	5.49933i	0.285285	−	0.329236i
$280$	−48.0097	−	13.2063i	−2.86913	−	0.789230i
$281$	2.65267	−	18.4497i	0.158245	−	1.10062i	−0.743621	−	0.668601i	$-0.766893\pi$
$281$	2.65267	−	18.4497i	0.158245	−	1.10062i	0.901866	−	0.432016i	$-0.142198\pi$
$282$	−1.97057	−	0.775846i	−0.117346	−	0.0462010i
$283$	28.9092	−	13.2024i	1.71847	−	0.784800i	0.722884	−	0.690970i	$-0.242816\pi$
$283$	28.9092	−	13.2024i	1.71847	−	0.784800i	0.995588	−	0.0938302i	$-0.0299111\pi$
$284$	3.66561	−	1.51637i	0.217514	−	0.0899803i
$285$	−7.70807	+	1.10825i	−0.456586	+	0.0656472i
$286$	−2.38264	−	11.9927i	−0.140888	−	0.709144i
$287$	6.70578	−	1.96899i	0.395830	−	0.116226i
$288$	5.45701	−	1.49033i	0.321557	−	0.0878184i
$289$	7.73053	−	16.9275i	0.454737	−	0.995736i
$290$	20.8073	+	21.5736i	1.22185	+	1.26685i
$291$	−1.65015	+	1.42986i	−0.0967335	+	0.0838201i
$292$	−4.45277	+	0.476656i	−0.260579	+	0.0278942i
$293$	17.6018	+	27.3889i	1.02831	+	1.60008i	0.774239	+	0.632893i	$0.218133\pi$
$293$	17.6018	+	27.3889i	1.02831	+	1.60008i	0.254069	+	0.967186i	$0.418231\pi$
$294$	14.3289	−	7.49112i	0.835678	−	0.436891i
$295$	33.7291	+	21.6764i	1.96378	+	1.26205i
$296$	6.16977	−	14.1475i	0.358611	−	0.822307i
$297$	3.91580	+	1.14978i	0.227218	+	0.0667172i
$298$	−9.52545	−	13.2160i	−0.551795	−	0.765580i
$299$	5.13923	−	8.76436i	0.297209	−	0.506856i
$300$	−22.4135	−	7.47137i	−1.29405	−	0.431360i
$301$	−10.1877	+	34.6962i	−0.587210	+	1.99985i
$302$	−1.21082	+	13.4957i	−0.0696748	+	0.776591i
$303$	−3.82576	−	2.45867i	−0.219784	−	0.141247i
$304$	−5.36676	−	5.37662i	−0.307805	−	0.308370i
$305$	2.80845	−	1.80488i	0.160811	−	0.103347i
$306$	−7.33249	−	4.17767i	−0.419171	−	0.238822i
$307$	12.7793	−	11.0734i	0.729355	−	0.631990i	−0.208899	−	0.977937i	$-0.566988\pi$
$307$	12.7793	−	11.0734i	0.729355	−	0.631990i	0.938254	+	0.345947i	$0.112442\pi$
$308$	6.23793	−	34.4839i	0.355439	−	1.96490i
$309$	−9.27668	−	4.23652i	−0.527732	−	0.241007i
$310$	−33.3168	−	25.8936i	−1.89227	−	1.47066i
$311$	−7.98972	+	2.34599i	−0.453055	+	0.133029i	−0.500296	−	0.865854i	$-0.666775\pi$
$311$	−7.98972	+	2.34599i	−0.453055	+	0.133029i	0.0472406	+	0.998884i	$0.484957\pi$
$312$	5.94481	+	0.750849i	0.336559	+	0.0425085i
$313$	−1.11307	−	7.74156i	−0.0629144	−	0.437579i	−0.996795	−	0.0799948i	$-0.974510\pi$
$313$	−1.11307	−	7.74156i	−0.0629144	−	0.437579i	0.933881	−	0.357584i	$-0.116399\pi$
$314$	0.552044	−	2.33375i	0.0311536	−	0.131701i
$315$	16.0136	−	7.31316i	0.902263	−	0.412050i
$316$	3.41593	+	13.4092i	0.192161	+	0.754325i
$317$	−25.0902	−	3.60742i	−1.40921	−	0.202613i	−0.604650	−	0.796491i	$-0.706687\pi$
$317$	−25.0902	−	3.60742i	−1.40921	−	0.202613i	−0.804555	+	0.593878i	$0.797596\pi$
$318$	0.840860	−	0.0448776i	0.0471531	−	0.00251661i
$319$	−13.8139	+	15.9421i	−0.773431	+	0.892587i
$320$	−10.3163	−	31.1385i	−0.576699	−	1.74070i
$321$	7.39563			0.412784
$322$	22.9076	−	17.9768i	1.27659	−	1.00181i
$323$			11.3331i			0.630588i
$324$	−1.14140	+	1.64232i	−0.0634111	+	0.0912399i
$325$	−18.9133	−	16.3885i	−1.04912	−	0.909071i
$326$	−0.528070	−	9.89431i	−0.0292471	−	0.547995i
$327$	1.63666	−	11.3832i	0.0905075	−	0.629493i
$328$	3.53084	+	2.95494i	0.194958	+	0.163159i
$329$	−2.67086	−	5.84838i	−0.147249	−	0.322431i
$330$	5.44771	−	23.0300i	0.299887	−	1.26776i
$331$	−16.2483	+	2.33615i	−0.893087	+	0.128406i	−0.573553	−	0.819168i	$-0.694435\pi$
$331$	−16.2483	+	2.33615i	−0.893087	+	0.128406i	−0.319534	+	0.947575i	$0.603526\pi$
$332$	−1.53967	+	1.65220i	−0.0845002	+	0.0906762i
$333$	1.53737	+	5.23581i	0.0842476	+	0.286921i
$334$	−16.5597	+	21.3070i	−0.906104	+	1.16587i
$335$	−19.5926	+	42.9017i	−1.07046	+	2.34397i
$336$	15.0653	+	8.24423i	0.821879	+	0.449760i
$337$	12.4174	+	14.3305i	0.676421	+	0.780632i	0.985367	−	0.170448i	$-0.0545215\pi$
$337$	12.4174	+	14.3305i	0.676421	+	0.780632i	−0.308945	+	0.951080i	$0.599976\pi$
$338$	−10.4592	−	5.95911i	−0.568905	−	0.324133i
$339$	9.41521	+	14.6504i	0.511364	+	0.795698i
$340$	−21.9249	+	43.7503i	−1.18905	+	2.37269i
$341$	16.0553	−	24.9826i	0.869445	−	1.35288i
$342$	2.67510	+	0.240007i	0.144653	+	0.0129781i
$343$	18.2623	+	5.36229i	0.986071	+	0.289537i
$344$	−22.7389	+	7.10280i	−1.22600	+	0.382957i
$345$	16.0949	−	11.2983i	0.866522	−	0.608282i
$346$	−12.1368	−	16.8390i	−0.652476	−	0.905269i
$347$	−6.13184	+	20.8831i	−0.329175	+	1.12107i	0.614149	+	0.789190i	$0.289500\pi$
$347$	−6.13184	+	20.8831i	−0.329175	+	1.12107i	−0.943323	+	0.331875i	$0.892319\pi$
$348$	−5.27088	−	8.89289i	−0.282549	−	0.476709i
$349$	13.0248	−	20.2670i	0.697202	−	1.08487i	−0.294417	−	0.955677i	$-0.595126\pi$
$349$	13.0248	−	20.2670i	0.697202	−	1.08487i	0.991620	−	0.129191i	$-0.0412381\pi$
$350$	−33.2308	−	63.5634i	−1.77626	−	3.39760i
$351$	−1.78220	+	1.14535i	−0.0951269	+	0.0611344i
$352$	21.1784	−	9.18974i	1.12881	−	0.489815i
$353$	−16.0390	−	18.5100i	−0.853671	−	0.985188i	0.146321	−	0.989237i	$-0.453257\pi$
$353$	−16.0390	−	18.5100i	−0.853671	−	0.985188i	−0.999992	+	0.00404872i	$0.998711\pi$
$354$	−9.59974	−	9.95328i	−0.510220	−	0.529011i
$355$	7.39787	+	3.37849i	0.392638	+	0.179312i
$356$	−0.391217	+	10.8147i	−0.0207345	+	0.573180i
$357$	−7.21802	−	24.5823i	−0.382018	−	1.30103i
$358$	11.2097	−	2.22707i	0.592451	−	0.117704i
$359$	0.535900	+	3.72726i	0.0282837	+	0.196717i	0.999064	−	0.0432517i	$-0.0137718\pi$
$359$	0.535900	+	3.72726i	0.0282837	+	0.196717i	−0.970781	+	0.239969i	$0.922863\pi$
$360$	9.86268	+	6.10178i	0.519809	+	0.321592i
$361$	6.39453	+	14.0021i	0.336554	+	0.736951i
$362$	11.1954	+	4.40781i	0.588415	+	0.231669i
$363$	5.59794	+	0.804862i	0.293815	+	0.0422443i
$364$	11.4079	+	14.1696i	0.597935	+	0.742690i
$365$	−6.93865	−	6.01238i	−0.363186	−	0.314702i
$366$	−1.08591	+	0.382809i	−0.0567617	+	0.0200097i
$367$	18.7753			0.980061			0.490030	−	0.871705i	$-0.336986\pi$
$367$	18.7753			0.980061			0.490030	+	0.871705i	$0.336986\pi$
$368$	18.2271	+	5.98089i	0.950156	+	0.311775i
$369$	−1.62782			−0.0847412
$370$	29.8431	−	10.5204i	1.55147	−	0.546928i
$371$	1.93199	+	1.67408i	0.100304	+	0.0869138i
$372$	9.12655	+	11.3360i	0.473190	+	0.587744i
$373$	24.6557	+	3.54495i	1.27662	+	0.183550i	0.747080	−	0.664734i	$-0.231455\pi$
$373$	24.6557	+	3.54495i	1.27662	+	0.183550i	0.529541	+	0.848284i	$0.322364\pi$
$374$	−32.0466	−	12.6173i	−1.65709	−	0.652424i
$375$	−11.6050	−	25.4113i	−0.599278	−	1.31223i
$376$	2.22845	−	3.60198i	0.114924	−	0.185758i
$377$	−1.55837	−	10.8387i	−0.0802599	−	0.558220i
$378$	−5.95537	+	1.18318i	−0.306311	+	0.0608560i
$379$	−0.742356	−	2.52823i	−0.0381323	−	0.129867i	0.938227	−	0.346020i	$-0.112467\pi$
$379$	−0.742356	−	2.52823i	−0.0381323	−	0.129867i	−0.976359	+	0.216153i	$0.930649\pi$
$380$	0.563037	−	15.5645i	0.0288832	−	0.798441i
$381$	−4.28456	−	1.95669i	−0.219505	−	0.100244i
$382$	20.4341	+	21.1866i	1.04550	+	1.08400i
$383$	5.46575	+	6.30781i	0.279287	+	0.322314i	0.878010	−	0.478642i	$-0.158871\pi$
$383$	5.46575	+	6.30781i	0.279287	+	0.322314i	−0.598724	+	0.800956i	$0.704325\pi$
$384$	0.990309	+	11.2703i	0.0505365	+	0.575134i
$385$	60.4405	−	38.8428i	3.08034	−	1.97961i
$386$	−15.5616	−	29.7660i	−0.792066	−	1.51505i
$387$	4.55354	−	7.08544i	0.231469	−	0.360173i
$388$	−2.22659	−	3.75664i	−0.113038	−	0.190714i
$389$	−9.20803	+	31.3597i	−0.466866	+	1.59000i	0.303785	+	0.952741i	$0.401749\pi$
$389$	−9.20803	+	31.3597i	−0.466866	+	1.59000i	−0.770651	+	0.637258i	$0.780069\pi$
$390$	7.18301	+	9.96597i	0.363726	+	0.504646i
$391$	−12.9419	−	25.5249i	−0.654498	−	1.29085i
$392$	9.64175	+	30.8670i	0.486982	+	1.55902i
$393$	12.8686	+	3.77857i	0.649136	+	0.190604i
$394$	−6.15384	−	0.552115i	−0.310026	−	0.0278151i
$395$	−15.3376	+	23.8657i	−0.771718	+	1.20082i
$396$	−3.65690	+	7.29720i	−0.183766	+	0.366698i
$397$	3.19776	+	4.97581i	0.160491	+	0.249729i	0.912181	−	0.409788i	$-0.134397\pi$
$397$	3.19776	+	4.97581i	0.160491	+	0.249729i	−0.751690	+	0.659517i	$0.770761\pi$
$398$	14.5932	+	8.31444i	0.731491	+	0.416765i
$399$	5.33967	+	6.16231i	0.267318	+	0.308502i
$400$	22.6835	−	41.4513i	1.13418	−	2.07257i
$401$	−4.94507	+	10.8282i	−0.246945	+	0.540734i	−0.991995	−	0.126274i	$-0.959698\pi$
$401$	−4.94507	+	10.8282i	−0.246945	+	0.540734i	0.745050	+	0.667008i	$0.232425\pi$
$402$	9.98214	−	12.8439i	0.497864	−	0.640594i
$403$	4.34309	+	14.7912i	0.216345	+	0.736803i
$404$	6.20081	−	6.65402i	0.308502	−	0.331050i
$405$	−4.05863	+	0.583543i	−0.201675	+	0.0289965i
$406$	7.22439	−	30.5409i	0.358541	−	1.51572i
$407$	9.25131	+	20.2576i	0.458571	+	1.00413i
$408$	10.8323	−	12.9435i	0.536281	−	0.640798i
$409$	−2.22202	+	15.4545i	−0.109872	+	0.764175i	0.858166	+	0.513372i	$0.171604\pi$
$409$	−2.22202	+	15.4545i	−0.109872	+	0.764175i	−0.968038	+	0.250803i	$0.919305\pi$
$410$	0.503076	+	9.42600i	0.0248451	+	0.465517i
$411$	−2.01857	−	1.74910i	−0.0995685	−	0.0862766i
$412$	11.6403	−	16.7488i	0.573477	−	0.825155i
$413$		−	41.9812i		−	2.06576i
$414$	−6.29907	+	2.51429i	−0.309583	+	0.123571i
$415$	−4.63012			−0.227284
$416$	−3.59413	+	11.4324i	−0.176217	+	0.560521i
$417$	−5.40652	+	6.23945i	−0.264758	+	0.305547i
$418$	10.9457	−	0.584182i	0.535370	−	0.0285733i
$419$	8.54644	+	1.22879i	0.417521	+	0.0600304i	0.347874	−	0.937541i	$-0.386904\pi$
$419$	8.54644	+	1.22879i	0.417521	+	0.0600304i	0.0696467	+	0.997572i	$0.477813\pi$
$420$	8.69174	+	34.1192i	0.424113	+	1.66485i
$421$	28.5516	−	13.0391i	1.39152	−	0.635487i	0.428163	−	0.903702i	$-0.359161\pi$
$421$	28.5516	−	13.0391i	1.39152	−	0.635487i	0.963359	+	0.268215i	$0.0864336\pi$
$422$	−4.69550	+	19.8501i	−0.228574	+	0.966286i
$423$	0.213118	+	1.48227i	0.0103621	+	0.0720703i
$424$	−0.211032	+	1.67084i	−0.0102486	+	0.0811432i
$425$	−67.6368	+	19.8600i	−3.28087	+	0.963350i
$426$	−2.21476	−	1.72130i	−0.107306	−	0.0833971i
$427$	−3.17967	−	1.45211i	−0.153875	−	0.0702724i
$428$	−2.63292	+	14.5550i	−0.127267	+	0.703545i
$429$	−6.53412	+	5.66184i	−0.315470	+	0.273356i
$430$	−42.4359	−	24.1777i	−2.04644	−	1.16595i
$431$	−14.4303	+	9.27376i	−0.695081	+	0.446701i	−0.839889	−	0.542758i	$-0.817380\pi$
$431$	−14.4303	+	9.27376i	−0.695081	+	0.446701i	0.144808	+	0.989460i	$0.453744\pi$
$432$	−2.82583	−	2.83102i	−0.135958	−	0.136208i
$433$	−6.89298	−	4.42985i	−0.331256	−	0.212885i	0.364431	−	0.931230i	$-0.381263\pi$
$433$	−6.89298	−	4.42985i	−0.331256	−	0.212885i	−0.695687	+	0.718345i	$0.744900\pi$
$434$	−3.94811	+	44.0054i	−0.189515	+	2.11233i
$435$	5.97102	−	20.3354i	0.286289	−	0.975010i
$436$	21.8202	+	7.27358i	1.04500	+	0.348341i
$437$	7.12135	+	5.67844i	0.340660	+	0.271636i
$438$	1.85152	+	2.56887i	0.0884690	+	0.122745i
$439$	−36.9111	−	10.8381i	−1.76167	−	0.517273i	−0.769120	−	0.639104i	$-0.779305\pi$
$439$	−36.9111	−	10.8381i	−1.76167	−	0.517273i	−0.992551	+	0.121831i	$0.961123\pi$
$440$	43.3850	+	18.9203i	2.06830	+	0.901990i
$441$	−9.61819	−	6.18123i	−0.458009	−	0.294344i
$442$	15.8437	−	8.28308i	0.753610	−	0.393986i
$443$	4.53722	+	7.06005i	0.215570	+	0.335433i	0.932150	−	0.362071i	$-0.117930\pi$
$443$	4.53722	+	7.06005i	0.215570	+	0.335433i	−0.716581	+	0.697504i	$0.754294\pi$
$444$	−10.8517	+	1.16164i	−0.514999	+	0.0551292i
$445$	−16.7676	+	14.5292i	−0.794859	+	0.688749i
$446$	−14.3036	−	14.8303i	−0.677293	−	0.702237i
$447$	−4.78536	+	10.4785i	−0.226340	+	0.495615i
$448$	−21.5885	+	26.7144i	−1.01996	+	1.26214i
$449$	13.8010	−	4.05233i	0.651308	−	0.191241i	0.0606447	−	0.998159i	$-0.480684\pi$
$449$	13.8010	−	4.05233i	0.651308	−	0.191241i	0.590663	+	0.806918i	$0.298866\pi$
$450$	3.25544	+	16.3859i	0.153463	+	0.772437i
$451$	−6.57572	+	0.945446i	−0.309639	+	0.0445193i
$452$	−32.1847	+	13.3140i	−1.51384	+	0.626239i
$453$	8.71540	−	3.98019i	0.409485	−	0.187006i
$454$	−13.7724	−	5.42243i	−0.646371	−	0.254487i
$455$	−5.30766	+	36.9156i	−0.248827	+	1.73063i
$456$	−1.42471	+	5.17931i	−0.0667181	+	0.242543i
$457$	−16.8590	+	19.4563i	−0.788630	+	0.910128i	−0.997701	−	0.0677727i	$-0.978411\pi$
$457$	−16.8590	+	19.4563i	−0.788630	+	0.910128i	0.209070	+	0.977901i	$0.432956\pi$
$458$	−11.2698	−	31.9691i	−0.526604	−	1.49382i
$459$			5.96734i			0.278532i
$460$	16.5059	+	35.6981i	0.769590	+	1.66443i
$461$		−	34.1444i		−	1.59026i	−0.606437	−	0.795132i	$-0.707402\pi$
$461$		−	34.1444i		−	1.59026i	0.606437	−	0.795132i	$-0.292598\pi$
$462$	−23.3700	+	8.23843i	−1.08727	+	0.383286i
$463$	−6.72449	+	7.76048i	−0.312514	+	0.360660i	−0.890177	−	0.455615i	$-0.849419\pi$
$463$	−6.72449	+	7.76048i	−0.312514	+	0.360660i	0.577663	+	0.816275i	$0.303965\pi$
$464$	19.3782	−	7.20745i	0.899611	−	0.334598i
$465$	−4.24624	+	29.5333i	−0.196915	+	1.36957i
$466$	12.7853	−	32.4732i	0.592266	−	1.50429i
$467$	−35.3266	+	16.1331i	−1.63472	+	0.746551i	−0.999664	−	0.0259159i	$-0.991750\pi$
$467$	−35.3266	+	16.1331i	−1.63472	+	0.746551i	−0.635055	+	0.772467i	$0.719023\pi$
$468$	−1.61964	−	3.91524i	−0.0748679	−	0.180982i
$469$	48.8814	−	7.02808i	2.25713	−	0.324526i
$470$	8.51728	−	1.69216i	0.392873	−	0.0780536i
$471$	−1.62706	+	0.477747i	−0.0749709	+	0.0220134i
$472$	23.0062	−	15.3494i	1.05895	−	0.706513i
$473$	14.2791	−	31.2669i	0.656554	−	1.43765i
$474$	7.04266	−	6.79250i	0.323480	−	0.311990i
$475$	16.9553	−	14.6918i	0.777960	−	0.674107i
$476$	50.9491	−	5.45395i	2.33525	−	0.249982i
$477$	−0.321911	−	0.500903i	−0.0147393	−	0.0229348i
$478$	−9.18839	−	17.5754i	−0.420267	−	0.803880i
$479$	−26.2363	−	16.8611i	−1.19877	−	0.770402i	−0.220026	−	0.975494i	$-0.570614\pi$
$479$	−26.2363	−	16.8611i	−1.19877	−	0.770402i	−0.978743	+	0.205092i	$0.934251\pi$
$480$	−15.5199	+	17.2380i	−0.708382	+	0.786805i
$481$	−11.0921	−	3.25694i	−0.505757	−	0.148504i
$482$	−18.4570	+	13.3029i	−0.840692	+	0.605932i
$483$	−19.0634	−	7.78140i	−0.867414	−	0.354066i
$484$	−3.57693	+	10.7305i	−0.162588	+	0.487751i
$485$	2.52235	−	8.59033i	0.114534	−	0.390067i
$486$	1.40856	+	0.126374i	0.0638934	+	0.00573244i
$487$	17.9507	+	11.5362i	0.813426	+	0.522757i	0.879972	−	0.475026i	$-0.157561\pi$
$487$	17.9507	+	11.5362i	0.813426	+	0.522757i	−0.0665456	+	0.997783i	$0.521198\pi$
$488$	−0.366795	−	2.27343i	−0.0166040	−	0.102913i
$489$	−5.89407	+	3.78789i	−0.266539	+	0.171294i
$490$	−32.8203	+	57.6049i	−1.48267	+	2.60232i
$491$	−2.00148	+	1.73430i	−0.0903257	+	0.0782676i	−0.698853	−	0.715265i	$-0.746306\pi$
$491$	−2.00148	+	1.73430i	−0.0903257	+	0.0782676i	0.608528	+	0.793533i	$0.291760\pi$
$492$	0.579521	−	3.20366i	0.0261268	−	0.144432i
$493$	−28.0567	−	12.8130i	−1.26361	−	0.577070i
$494$	−3.49167	+	4.49268i	−0.157098	+	0.202135i
$495$	−16.0562	+	4.71453i	−0.721673	+	0.211902i
$496$	−25.5591	+	13.9259i	−1.14764	+	0.625290i
$497$	−1.21190	−	8.42898i	−0.0543613	−	0.378091i
$498$	1.55404	+	0.367605i	0.0696381	+	0.0164728i
$499$	26.0006	−	11.8741i	1.16394	−	0.531556i	0.262705	−	0.964876i	$-0.415386\pi$
$499$	26.0006	−	11.8741i	1.16394	−	0.531556i	0.901240	+	0.433321i	$0.142658\pi$
$500$	54.1425	−	13.7926i	2.42132	−	0.616823i
$501$	18.8873	+	2.71559i	0.843824	+	0.121324i
$502$	0.0603824	+	1.13137i	0.00269500	+	0.0504955i
$503$	17.2362	−	19.8917i	0.768526	−	0.886927i	−0.227699	−	0.973732i	$-0.573120\pi$
$503$	17.2362	−	19.8917i	0.768526	−	0.886927i	0.996225	+	0.0868050i	$0.0276657\pi$
$504$	−0.208394	−	12.1417i	−0.00928259	−	0.540836i
$505$	18.6472			0.829789
$506$	−23.9853	+	13.8152i	−1.06628	+	0.614160i
$507$			8.51193i			0.378028i
$508$	5.37623	−	7.73567i	0.238532	−	0.343215i
$509$	1.47007	+	1.27382i	0.0651595	+	0.0564611i	0.686832	−	0.726816i	$-0.259001\pi$
$509$	1.47007	+	1.27382i	0.0651595	+	0.0564611i	−0.621672	+	0.783278i	$0.713546\pi$
$510$	34.5542	−	1.84419i	1.53009	−	0.0816623i
$511$	−1.36812	+	9.51550i	−0.0605221	+	0.420941i
$512$	−22.5331	−	2.06334i	−0.995834	−	0.0911876i
$513$	−0.788948	−	1.72755i	−0.0348329	−	0.0762734i
$514$	−34.3601	−	8.12783i	−1.51556	−	0.358503i
$515$	41.3911	−	5.95114i	1.82391	−	0.262238i
$516$	12.3235	+	11.4841i	0.542510	+	0.505560i
$517$	1.72181	+	5.86395i	0.0757252	+	0.257896i
$518$	−26.1608	−	20.3320i	−1.14944	−	0.893336i
$519$	−6.09721	+	13.3510i	−0.267638	+	0.586045i
$520$	−22.1708	+	10.5886i	−0.972255	+	0.464341i
$521$	−5.22381	−	6.02859i	−0.228859	−	0.264117i	0.629693	−	0.776844i	$-0.283181\pi$
$521$	−5.22381	−	6.02859i	−0.228859	−	0.264117i	−0.858552	+	0.512727i	$0.828635\pi$
$522$	−3.61861	+	6.35126i	−0.158382	+	0.277987i
$523$	7.80976	+	12.1522i	0.341497	+	0.531380i	0.968944	−	0.247279i	$-0.0795366\pi$
$523$	7.80976	+	12.1522i	0.341497	+	0.531380i	−0.627447	+	0.778659i	$0.715900\pi$
$524$	−12.0178	+	23.9810i	−0.525000	+	1.04762i
$525$	−27.4201	+	42.6665i	−1.19671	+	1.86212i
$526$	0.951083	−	10.6007i	0.0414692	−	0.462213i
$527$	41.6634	+	12.2335i	1.81489	+	0.532899i
$528$	−13.0594	−	9.79487i	−0.568338	−	0.426267i
$529$	−22.5236	−	4.65699i	−0.979287	−	0.202478i
$530$	−2.80102	+	2.01884i	−0.121668	+	0.0876930i
$531$	−2.75481	+	9.38202i	−0.119549	+	0.407145i
$532$	−14.0288	+	8.31495i	−0.608224	+	0.360499i
$533$	1.86443	−	2.90111i	0.0807575	−	0.125661i
$534$	6.78135	−	3.54528i	0.293458	−	0.153419i
$535$	−25.5109	+	16.3948i	−1.10293	+	0.708810i
$536$	21.7237	+	24.2180i	0.938323	+	1.04606i
$537$	−5.29217	−	6.10749i	−0.228374	−	0.263558i
$538$	12.0117	−	11.5851i	0.517863	−	0.499468i
$539$	−42.4435	−	19.3833i	−1.82817	−	0.834897i
$540$	0.296464	−	8.19537i	0.0127578	−	0.352673i
$541$	−7.64403	−	26.0332i	−0.328642	−	1.11925i	−0.943709	−	0.330778i	$-0.892689\pi$
$541$	−7.64403	−	26.0332i	−0.328642	−	1.11925i	0.615066	−	0.788475i	$-0.289129\pi$
$542$	−6.76715	−	34.0616i	−0.290674	−	1.46307i
$543$	−1.21078	−	8.42119i	−0.0519597	−	0.361388i
$544$	21.6171	+	25.9267i	0.926827	+	1.11160i
$545$	19.5890	+	42.8940i	0.839102	+	1.83738i
$546$	4.71233	−	11.9688i	0.201669	−	0.512218i
$547$	11.0170	+	1.58400i	0.471052	+	0.0677271i	0.373753	−	0.927528i	$-0.378071\pi$
$547$	11.0170	+	1.58400i	0.471052	+	0.0677271i	0.0972989	+	0.995255i	$0.468980\pi$
$548$	4.16096	−	3.34996i	0.177747	−	0.143103i
$549$	0.615311	+	0.533170i	0.0262608	+	0.0227551i
$550$	22.6676	+	64.3011i	0.966548	+	2.74181i
$551$	9.81646			0.418195
$552$	−2.70575	−	13.2921i	−0.115164	−	0.565748i
$553$	29.7047			1.26317
$554$	7.85223	+	22.2745i	0.333609	+	0.946351i
$555$	−16.9100	−	14.6526i	−0.717789	−	0.621967i
$556$	−10.3548	−	12.8616i	−0.439143	−	0.545455i
$557$	−15.9136	−	2.28803i	−0.674282	−	0.0969471i	−0.203336	−	0.979109i	$-0.565178\pi$
$557$	−15.9136	−	2.28803i	−0.674282	−	0.0969471i	−0.470946	+	0.882162i	$0.656087\pi$
$558$	3.76997	−	9.57532i	0.159596	−	0.405356i
$559$	7.41229	+	16.2306i	0.313506	+	0.686483i
$560$	−70.2430	+	4.95909i	−2.96831	+	0.209560i
$561$	3.46585	+	24.1055i	0.146328	+	1.01774i
$562$	−5.13668	−	25.8548i	−0.216678	−	1.09062i
$563$	2.72232	+	9.27137i	0.114732	+	0.390742i	0.996758	−	0.0804595i	$-0.0256388\pi$
$563$	2.72232	+	9.27137i	0.114732	+	0.390742i	−0.882026	+	0.471201i	$0.843821\pi$
$564$	−2.99306	−	0.108273i	−0.126031	−	0.00455909i
$565$	−64.9546	−	29.6638i	−2.73266	−	1.24796i
$566$	32.3505	−	31.2014i	1.35979	−	1.31149i
$567$	2.81157	+	3.24472i	0.118075	+	0.136266i
$568$	4.17609	−	3.74599i	0.175225	−	0.157178i
$569$	−1.22679	+	0.788408i	−0.0514295	+	0.0330518i	−0.566103	−	0.824335i	$-0.691550\pi$
$569$	−1.22679	+	0.788408i	−0.0514295	+	0.0330518i	0.514673	+	0.857386i	$0.327913\pi$
$570$	−9.75967	+	5.10234i	−0.408788	+	0.213713i
$571$	8.33740	−	12.9732i	0.348909	−	0.542913i	−0.621798	−	0.783177i	$-0.713598\pi$
$571$	8.33740	−	12.9732i	0.348909	−	0.542913i	0.970708	+	0.240264i	$0.0772340\pi$
$572$	−8.81664	−	14.8752i	−0.368642	−	0.621963i
$573$	5.86391	−	19.9706i	0.244968	−	0.834285i
$574$	8.01815	−	5.77911i	0.334671	−	0.241215i
$575$	−21.4101	+	52.4518i	−0.892862	+	2.18739i
$576$	6.57764	−	4.55353i	0.274068	−	0.189730i
$577$	−27.9718	−	8.21327i	−1.16448	−	0.341923i	−0.358310	−	0.933603i	$-0.616647\pi$
$577$	−27.9718	−	8.21327i	−1.16448	−	0.341923i	−0.806173	+	0.591680i	$0.798465\pi$
$578$	2.35172	−	26.2121i	0.0978185	−	1.09028i
$579$	−12.8405	+	19.9803i	−0.533635	+	0.830352i
$580$	37.8956	+	18.9909i	1.57353	+	0.788556i
$581$	2.62107	+	4.07846i	0.108740	+	0.169203i
$582$	−1.52862	+	2.68297i	−0.0633632	+	0.111213i
$583$	−1.59131	−	1.83647i	−0.0659053	−	0.0760587i
$584$	−5.71484	+	2.72936i	−0.236482	+	0.112942i
$585$	3.60857	−	7.90166i	0.149196	−	0.326694i
$586$	36.3544	+	28.2544i	1.50179	+	1.16718i
$587$	−6.65025	−	22.6487i	−0.274485	−	0.934811i	−0.975192	−	0.221361i	$-0.928950\pi$
$587$	−6.65025	−	22.6487i	−0.274485	−	0.934811i	0.700707	−	0.713450i	$-0.252868\pi$
$588$	15.5892	−	16.7286i	0.642888	−	0.689875i
$589$	−13.6790	+	1.96674i	−0.563634	+	0.0810383i
$590$	55.1785	+	13.0524i	2.27166	+	0.537358i
$591$	1.81491	+	3.97409i	0.0746552	+	0.163472i
$592$	1.57713	−	21.7704i	0.0648196	−	0.894757i
$593$	−4.93579	+	34.3292i	−0.202689	+	1.40973i	0.593575	+	0.804779i	$0.297716\pi$
$593$	−4.93579	+	34.3292i	−0.202689	+	1.40973i	−0.796263	+	0.604951i	$0.793193\pi$
$594$	5.76337	−	0.307597i	0.236474	−	0.0126209i
$595$	79.3929	+	68.7943i	3.25479	+	2.82029i
$596$	−18.9186	−	13.1483i	−0.774937	−	0.538575i
$597$		−	11.8763i		−	0.486063i
$598$	2.73368	−	14.1060i	0.111788	−	0.576836i
$599$	−9.86855			−0.403218			−0.201609	−	0.979466i	$-0.564617\pi$
$599$	−9.86855			−0.403218			−0.201609	+	0.979466i	$0.564617\pi$
$600$	−33.4073	+	0.573384i	−1.36385	+	0.0234083i
$601$	−11.3147	+	13.0579i	−0.461537	+	0.532642i	−0.938038	−	0.346532i	$-0.887359\pi$
$601$	−11.3147	+	13.0579i	−0.461537	+	0.532642i	0.476501	+	0.879174i	$0.341905\pi$
$602$	2.72548	+	51.0666i	0.111082	+	2.08132i
$603$	−11.3853	−	1.63695i	−0.463644	−	0.0666619i
$604$	4.73049	+	18.5694i	0.192481	+	0.755579i
$605$	−21.0940	+	9.63332i	−0.857594	+	0.391650i
$606$	−6.25869	−	1.48048i	−0.254242	−	0.0601405i
$607$	2.38459	+	16.5852i	0.0967877	+	0.673173i	0.979230	+	0.202753i	$0.0649887\pi$
$607$	2.38459	+	16.5852i	0.0967877	+	0.673173i	−0.882442	+	0.470421i	$0.844102\pi$
$608$	−9.68598	−	4.64779i	−0.392818	−	0.188493i
$609$	−21.2927	+	6.25210i	−0.862824	+	0.253348i
$610$	2.89719	−	3.72776i	0.117304	−	0.150933i
$611$	−2.88579	−	1.31790i	−0.116747	−	0.0533164i
$612$	−11.7441	−	2.12443i	−0.474726	−	0.0858750i
$613$	−10.6635	+	9.24000i	−0.430696	+	0.373200i	−0.843060	−	0.537819i	$-0.819248\pi$
$613$	−10.6635	+	9.24000i	−0.430696	+	0.373200i	0.412365	+	0.911019i	$0.364703\pi$
$614$	11.8381	−	20.7779i	0.477749	−	0.838526i
$615$	5.61510	−	3.60860i	0.226423	−	0.145513i
$616$	−7.89378	−	48.9264i	−0.318050	−	1.97130i
$617$	38.4279	+	24.6961i	1.54705	+	0.994229i	0.986057	+	0.166409i	$0.0532172\pi$
$617$	38.4279	+	24.6961i	1.54705	+	0.994229i	0.560994	+	0.827820i	$0.310419\pi$
$618$	−14.3648	−	1.28880i	−0.577839	−	0.0518430i
$619$	2.74758	−	9.35740i	0.110435	−	0.376106i	−0.885667	−	0.464321i	$-0.846298\pi$
$619$	2.74758	−	9.35740i	0.110435	−	0.376106i	0.996101	+	0.0882156i	$0.0281164\pi$
$620$	−56.6115	−	18.8710i	−2.27357	−	0.757877i
$621$	3.74970	+	2.98994i	0.150470	+	0.119982i
$622$	−9.55337	+	6.88562i	−0.383055	+	0.276088i
$623$	22.2901	+	6.54495i	0.893033	+	0.262218i
$624$	8.28202	−	1.79369i	0.331546	−	0.0718049i
$625$	46.6745	+	29.9959i	1.86698	+	1.19984i
$626$	−5.12451	−	9.80208i	−0.204817	−	0.391770i
$627$	−4.19038	−	6.52036i	−0.167348	−	0.260398i
$628$	−0.360987	−	3.37223i	−0.0144050	−	0.134567i
$629$	−24.6094	+	21.3242i	−0.981242	+	0.850251i
$630$	17.9198	−	17.2833i	0.713943	−	0.688584i
$631$	−12.5276	+	27.4316i	−0.498716	+	1.09204i	0.478168	+	0.878268i	$0.341301\pi$
$631$	−12.5276	+	27.4316i	−0.498716	+	1.09204i	−0.976884	+	0.213768i	$0.931426\pi$
$632$	10.8608	+	16.2786i	0.432019	+	0.647527i
$633$	13.8392	−	4.06356i	0.550060	−	0.161512i
$634$	−35.1606	+	6.98549i	−1.39640	+	0.277429i
$635$	19.1170	−	2.74861i	0.758636	−	0.109075i
$636$	1.10041	−	0.455213i	0.0436341	−	0.0180504i
$637$	22.0324	−	10.0619i	0.872956	−	0.398666i
$638$	−10.9288	+	27.7581i	−0.432677	+	1.09895i
$639$	−0.282272	+	1.96325i	−0.0111665	+	0.0776649i
$640$	−28.4003	−	36.6809i	−1.12262	−	1.44994i
$641$	25.5079	−	29.4377i	1.00750	−	1.16272i	0.0208670	−	0.999782i	$-0.493357\pi$
$641$	25.5079	−	29.4377i	1.00750	−	1.16272i	0.986636	−	0.162938i	$-0.0520972\pi$
$642$	9.86404	−	3.47729i	0.389303	−	0.137238i
$643$			21.8080i			0.860025i	0.902823	+	0.430013i	$0.141491\pi$
$643$			21.8080i			0.860025i	−0.902823	+	0.430013i	$0.858509\pi$
$644$	22.1010	−	34.7476i	0.870901	−	1.36925i
$645$			34.5353i			1.35982i
$646$	5.32859	+	15.1156i	0.209651	+	0.594717i
$647$	31.4584	−	36.3050i	1.23676	−	1.42730i	0.369653	−	0.929170i	$-0.379476\pi$
$647$	31.4584	−	36.3050i	1.23676	−	1.42730i	0.867105	−	0.498125i	$-0.165978\pi$
$648$	−0.750170	+	2.72713i	−0.0294695	+	0.107132i
$649$	−5.67916	+	39.4994i	−0.222926	+	1.55049i
$650$	−32.9315	−	12.9657i	−1.29168	−	0.508557i
$651$	28.4183	−	12.9782i	1.11380	−	0.508655i
$652$	−5.35644	−	12.9484i	−0.209774	−	0.507098i
$653$	7.44886	−	1.07098i	0.291496	−	0.0419109i	0.00498464	−	0.999988i	$-0.498413\pi$
$653$	7.44886	−	1.07098i	0.291496	−	0.0419109i	0.286512	+	0.958077i	$0.407504\pi$
$654$	−3.16926	−	15.9521i	−0.123928	−	0.623775i
$655$	−52.7661	+	15.4935i	−2.06174	+	0.605382i
$656$	6.09867	+	2.28106i	0.238113	+	0.0890605i
$657$	0.930158	−	2.03676i	0.0362889	−	0.0794617i
$658$	−6.31210	−	6.54457i	−0.246071	−	0.255134i
$659$	−2.08487	+	1.80655i	−0.0812151	+	0.0703732i	−0.694522	−	0.719471i	$-0.744384\pi$
$659$	−2.08487	+	1.80655i	−0.0812151	+	0.0703732i	0.613307	+	0.789844i	$0.289839\pi$
$660$	−3.56231	−	33.2780i	−0.138663	−	1.29534i
$661$	1.39218	+	2.16627i	0.0541495	+	0.0842582i	0.867273	−	0.497833i	$-0.165871\pi$
$661$	1.39218	+	2.16627i	0.0541495	+	0.0842582i	−0.813123	+	0.582092i	$0.802235\pi$
$662$	−20.5730	+	10.7555i	−0.799592	+	0.418025i
$663$	−10.6350	−	6.83471i	−0.413030	−	0.265438i
$664$	−1.27672	+	2.92757i	−0.0495464	+	0.113612i
$665$	−32.0797	−	9.41945i	−1.24400	−	0.365271i
$666$	4.51228	+	6.26050i	0.174847	+	0.242590i
$667$	−22.1091	+	11.2100i	−0.856069	+	0.434052i
$668$	−12.0685	+	36.2046i	−0.466945	+	1.40080i
$669$	−4.10466	+	13.9792i	−0.158695	+	0.540466i
$670$	−5.96028	+	66.4329i	−0.230266	+	2.56653i
$671$	2.79526	+	1.79640i	0.107910	+	0.0693494i
$672$	23.9699	+	3.91244i	0.924657	+	0.150926i
$673$	4.49403	−	2.88814i	0.173232	−	0.111330i	−0.451151	−	0.892447i	$-0.648987\pi$
$673$	4.49403	−	2.88814i	0.173232	−	0.111330i	0.624384	+	0.781118i	$0.285350\pi$
$674$	23.2999	+	13.2751i	0.897478	+	0.511336i
$675$	8.92767	−	7.73587i	0.343626	−	0.297754i
$676$	−16.7520	−	3.03033i	−0.644307	−	0.116551i
$677$	−8.12669	−	3.71134i	−0.312334	−	0.142638i	0.253080	−	0.967445i	$-0.418556\pi$
$677$	−8.12669	−	3.71134i	−0.312334	−	0.142638i	−0.565414	+	0.824807i	$0.691284\pi$
$678$	19.4460	+	15.1133i	0.746819	+	0.580422i
$679$	−8.99471	+	2.64109i	−0.345185	+	0.101356i
$680$	−8.67214	+	68.6613i	−0.332561	+	2.63304i
$681$	1.48949	+	10.3596i	0.0570775	+	0.396982i
$682$	9.66770	−	40.8698i	0.370195	−	1.56499i
$683$	1.85560	−	0.847426i	0.0710027	−	0.0324259i	−0.379597	−	0.925152i	$-0.623937\pi$
$683$	1.85560	−	0.847426i	0.0710027	−	0.0324259i	0.450600	+	0.892726i	$0.351210\pi$
$684$	3.68080	−	0.937670i	0.140739	−	0.0358527i
$685$	10.8404	+	1.55861i	0.414190	+	0.0595515i
$686$	26.8789	−	1.43455i	1.02624	−	0.0547715i
$687$	−15.6964	+	18.1146i	−0.598855	+	0.691116i
$688$	−26.9887	+	20.1649i	−1.02893	+	0.768778i
$689$	1.26141			0.0480559
$690$	16.1546	−	22.6369i	0.614994	−	0.861771i
$691$			9.33086i			0.354963i	0.984124	+	0.177481i	$0.0567950\pi$
$691$			9.33086i			0.354963i	−0.984124	+	0.177481i	$0.943205\pi$
$692$	−24.1049	−	16.7528i	−0.916333	−	0.636844i
$693$	13.2421	+	11.4743i	0.503026	+	0.435874i
$694$	1.64043	+	30.7363i	0.0622698	+	1.16673i
$695$	4.81772	−	33.5080i	0.182746	−	1.27103i
$696$	−11.2114	−	9.38276i	−0.424967	−	0.355652i
$697$	−4.03525	−	8.83597i	−0.152846	−	0.334686i
$698$	7.84287	−	33.1555i	0.296857	−	1.25495i
$699$	−24.4264	+	3.51199i	−0.923893	+	0.132836i
$700$	−74.2084	−	69.1541i	−2.80481	−	2.61378i
$701$	2.55690	+	8.70802i	0.0965729	+	0.328897i	0.993582	−	0.113115i	$-0.0360829\pi$
$701$	2.55690	+	8.70802i	0.0965729	+	0.328897i	−0.897009	+	0.442012i	$0.854265\pi$
$702$	−1.83852	+	2.36559i	−0.0693903	+	0.0892834i
$703$	4.30517	−	9.42701i	0.162373	−	0.355547i
$704$	23.9262	−	22.2146i	0.901751	−	0.837246i
$705$	−4.02107	−	4.64056i	−0.151442	−	0.174774i
$706$	−30.0953	−	17.1468i	−1.13265	−	0.645327i
$707$	−10.5560	−	16.4255i	−0.396999	−	0.617743i
$708$	−17.4836	−	8.76172i	−0.657075	−	0.329286i
$709$	−5.56131	+	8.65357i	−0.208859	+	0.324992i	−0.929840	−	0.367963i	$-0.880055\pi$
$709$	−5.56131	+	8.65357i	−0.208859	+	0.324992i	0.720981	+	0.692955i	$0.243692\pi$
$710$	11.4555	+	1.02778i	0.429918	+	0.0385717i
$711$	−6.63846	−	1.94923i	−0.248962	−	0.0731017i
$712$	4.56309	+	14.6083i	0.171009	+	0.547467i
$713$	28.5626	−	20.0504i	1.06968	−	0.750895i
$714$	−21.1853	−	29.3933i	−0.792839	−	1.10001i
$715$	9.98777	−	34.0152i	0.373521	−	1.27210i
$716$	13.9040	−	8.24098i	0.519616	−	0.307980i
$717$	−7.58172	+	11.7974i	−0.283144	+	0.440581i
$718$	2.46725	+	4.71932i	0.0920771	+	0.176124i
$719$	17.2158	−	11.0639i	0.642040	−	0.412614i	−0.178710	−	0.983902i	$-0.557192\pi$
$719$	17.2158	−	11.0639i	0.642040	−	0.412614i	0.820750	+	0.571288i	$0.193556\pi$
$720$	16.0234	+	3.50109i	0.597158	+	0.130478i
$721$	−28.6732	−	33.0906i	−1.06785	−	1.23236i
$722$	15.1123	+	15.6689i	0.562422	+	0.583136i
$723$	14.6339	+	6.68307i	0.544240	+	0.248546i
$724$	17.0045	+	0.615128i	0.631966	+	0.0228610i
$725$	17.2023	+	58.5857i	0.638877	+	2.17582i
$726$	7.84476	−	1.55855i	0.291146	−	0.0578432i
$727$	−1.30362	−	9.06690i	−0.0483487	−	0.336273i	−0.999611	−	0.0278898i	$-0.991121\pi$
$727$	−1.30362	−	9.06690i	−0.0483487	−	0.336273i	0.951262	−	0.308383i	$-0.0997878\pi$
$728$	21.8777	+	13.5352i	0.810842	+	0.501647i
$729$	−0.415415	−	0.909632i	−0.0153857	−	0.0336901i
$730$	−12.0814	−	4.75667i	−0.447154	−	0.176052i
$731$	49.7482	+	7.15272i	1.84001	+	0.264553i
$732$	−1.26837	+	1.02115i	−0.0468801	+	0.0377429i
$733$	−31.8458	−	27.5946i	−1.17625	−	1.01923i	−0.999388	−	0.0349927i	$-0.988859\pi$
$733$	−31.8458	−	27.5946i	−1.17625	−	1.01923i	−0.176864	−	0.984235i	$-0.556595\pi$
$734$	25.0418	−	8.82778i	0.924309	−	0.325839i
$735$	46.8802			1.72920
$736$	27.1228	−	0.592970i	0.999761	−	0.0218572i
$737$	−46.9424			−1.72915
$738$	−2.17114	+	0.765373i	−0.0799206	+	0.0281738i
$739$	−2.56988	−	2.22681i	−0.0945345	−	0.0819146i	0.606311	−	0.795227i	$-0.292649\pi$
$739$	−2.56988	−	2.22681i	−0.0945345	−	0.0819146i	−0.700846	+	0.713313i	$0.747194\pi$
$740$	34.8573	−	28.0634i	1.28138	−	1.03163i
$741$	3.98247	+	0.572593i	0.146300	+	0.0210347i
$742$	3.36394	+	1.32444i	0.123494	+	0.0486217i
$743$	−9.14424	−	20.0231i	−0.335470	−	0.734576i	0.664449	−	0.747334i	$-0.268666\pi$
$743$	−9.14424	−	20.0231i	−0.335470	−	0.734576i	−0.999919	+	0.0127576i	$0.995939\pi$
$744$	17.5027	+	10.8284i	0.641679	+	0.396989i
$745$	−6.72210	−	46.7532i	−0.246279	−	1.71291i
$746$	34.5516	−	6.86451i	1.26503	−	0.251327i
$747$	−0.318131	−	1.08346i	−0.0116398	−	0.0396416i
$748$	−48.6750	−	1.76079i	−1.77973	−	0.0643810i
$749$	28.8829	+	13.1904i	1.05536	+	0.481966i
$750$	−27.4262	−	28.4363i	−1.00146	−	1.03835i
$751$	−14.4889	−	16.7211i	−0.528707	−	0.610161i	0.427082	−	0.904213i	$-0.359542\pi$
$751$	−14.4889	−	16.7211i	−0.528707	−	0.610161i	−0.955789	+	0.294052i	$0.904996\pi$
$752$	1.27864	−	5.85198i	0.0466274	−	0.213400i
$753$	0.673960	−	0.433127i	0.0245605	−	0.0157840i
$754$	−7.17464	−	13.7235i	−0.261285	−	0.499781i
$755$	−21.2399	+	33.0500i	−0.773000	+	1.20281i
$756$	−7.38676	+	4.37818i	−0.268654	+	0.159233i
$757$	7.60122	−	25.8874i	0.276271	−	0.940893i	−0.698110	−	0.715991i	$-0.745975\pi$
$757$	7.60122	−	25.8874i	0.276271	−	0.940893i	0.974381	−	0.224903i	$-0.0722065\pi$
$758$	−2.17886	−	3.02302i	−0.0791396	−	0.109801i
$759$	16.8838	+	9.90026i	0.612842	+	0.359357i
$760$	−6.56717	−	21.0241i	−0.238216	−	0.762624i
$761$	25.5203	+	7.49345i	0.925112	+	0.271637i	0.709389	−	0.704817i	$-0.248971\pi$
$761$	25.5203	+	7.49345i	0.925112	+	0.271637i	0.215723	+	0.976455i	$0.430789\pi$
$762$	−6.63460	−	0.595248i	−0.240346	−	0.0215636i
$763$	26.6942	−	41.5370i	0.966395	−	1.50374i
$764$	37.2158	+	18.6502i	1.34642	+	0.674742i
$765$	−13.2286	−	20.5840i	−0.478280	−	0.744218i
$766$	10.2558	+	5.84324i	0.370558	+	0.211125i
$767$	−13.5654	−	15.6553i	−0.489819	−	0.565282i
$768$	6.61992	+	14.5663i	0.238876	+	0.525616i
$769$	1.75755	−	3.84850i	0.0633790	−	0.138781i	−0.875292	−	0.483595i	$-0.839331\pi$
$769$	1.75755	−	3.84850i	0.0633790	−	0.138781i	0.938671	+	0.344814i	$0.112058\pi$
$770$	62.3503	−	80.2252i	2.24695	−	2.89111i
$771$	7.03395	+	23.9554i	0.253322	+	0.862734i
$772$	−34.7510	−	32.3841i	−1.25072	−	1.16553i
$773$	3.40536	−	0.489616i	0.122482	−	0.0176103i	−0.0808011	−	0.996730i	$-0.525748\pi$
$773$	3.40536	−	0.489616i	0.122482	−	0.0176103i	0.203283	+	0.979120i	$0.434839\pi$
$774$	2.74190	−	11.5913i	0.0985557	−	0.416641i
$775$	−35.7087	−	78.1912i	−1.28270	−	2.80871i
$776$	−4.73605	−	3.96357i	−0.170014	−	0.142284i
$777$	−3.33421	+	23.1899i	−0.119614	+	0.831934i
$778$	2.46339	+	46.1559i	0.0883167	+	1.65477i
$779$	2.33642	+	2.02452i	0.0837110	+	0.0725360i
$780$	14.2663	+	9.91494i	0.510814	+	0.355012i
$781$			8.09463i			0.289649i
$782$	−29.2627	−	27.9592i	−1.04643	−	0.999818i
$783$	5.16879			0.184718
$784$	27.3729	+	36.6360i	0.977605	+	1.30843i
$785$	4.55337	−	5.25487i	0.162517	−	0.187554i
$786$	18.9403	−	1.01087i	0.675580	−	0.0360564i
$787$	3.73334	+	0.536773i	0.133079	+	0.0191339i	0.208532	−	0.978015i	$-0.433131\pi$
$787$	3.73334	+	0.536773i	0.133079	+	0.0191339i	−0.0754534	+	0.997149i	$0.524040\pi$
$788$	−8.46737	+	2.15703i	−0.301637	+	0.0768410i
$789$	−6.84584	+	3.12639i	−0.243718	+	0.111303i
$790$	−9.23550	+	39.0427i	−0.328584	+	1.38908i
$791$	10.6407	+	74.0079i	0.378341	+	2.63142i
$792$	−1.44644	+	11.4522i	−0.0513971	+	0.406935i
$793$	−1.65496	+	0.485941i	−0.0587695	+	0.0172563i
$794$	6.60459	+	5.13303i	0.234388	+	0.182164i
$795$	2.22083	+	1.01422i	0.0787647	+	0.0359706i
$796$	23.3732	+	4.22806i	0.828441	+	0.149860i
$797$	26.6313	−	23.0762i	0.943330	−	0.817401i	−0.0400052	−	0.999199i	$-0.512737\pi$
$797$	26.6313	−	23.0762i	0.943330	−	0.817401i	0.983336	+	0.181799i	$0.0581920\pi$
$798$	10.0193	+	5.70846i	0.354679	+	0.202077i
$799$	−7.51757	+	4.83125i	−0.265953	+	0.170917i
$800$	10.7649	−	65.9517i	0.380595	−	2.33174i
$801$	−4.55194	−	2.92535i	−0.160835	−	0.103362i
$802$	−1.50435	+	16.7673i	−0.0531203	+	0.592076i
$803$	2.57449	−	8.76789i	0.0908516	−	0.309412i
$804$	7.27489	−	21.8241i	0.256565	−	0.769677i
$805$	83.0081	−	15.4187i	2.92565	−	0.543436i
$806$	12.7472	+	17.6860i	0.449002	+	0.622961i
$807$	−11.3223	−	3.32454i	−0.398565	−	0.117029i
$808$	5.14183	−	11.7904i	0.180889	−	0.414785i
$809$	14.4940	+	9.31472i	0.509582	+	0.327488i	0.770039	−	0.637997i	$-0.220237\pi$
$809$	14.4940	+	9.31472i	0.509582	+	0.327488i	−0.260457	+	0.965485i	$0.583873\pi$
$810$	−5.13889	+	2.68660i	−0.180562	+	0.0943976i
$811$	−12.8128	−	19.9371i	−0.449918	−	0.700085i	0.540010	−	0.841658i	$-0.318420\pi$
$811$	−12.8128	−	19.9371i	−0.449918	−	0.700085i	−0.989928	+	0.141573i	$0.954784\pi$
$812$	−4.72410	−	44.1311i	−0.165784	−	1.54870i
$813$	−18.5581	+	16.0807i	−0.650862	+	0.563975i
$814$	21.8638	+	22.6690i	0.766326	+	0.794549i
$815$	11.9342	−	26.1322i	0.418037	−	0.915372i
$816$	8.36201	−	22.3567i	0.292729	−	0.782642i
$817$	−15.3479	+	4.50654i	−0.536953	+	0.157664i
$818$	4.30276	+	21.6574i	0.150442	+	0.757233i
$819$	−9.00299	+	1.29443i	−0.314590	+	0.0452312i
$820$	5.10292	+	12.3355i	0.178202	+	0.430776i
$821$	−6.29395	+	2.87435i	−0.219660	+	0.100316i	−0.522206	−	0.852819i	$-0.674891\pi$
$821$	−6.29395	+	2.87435i	−0.219660	+	0.100316i	0.302546	+	0.953135i	$0.402164\pi$
$822$	−3.51469	−	1.38379i	−0.122589	−	0.0482653i
$823$	−0.189308	+	1.31667i	−0.00659887	+	0.0458962i	−0.992855	−	0.119329i	$-0.961926\pi$
$823$	−0.189308	+	1.31667i	−0.00659887	+	0.0458962i	0.986256	+	0.165225i	$0.0528349\pi$
$824$	7.65045	−	27.8121i	0.266516	−	0.968879i
$825$	31.5710	−	36.4349i	1.09916	−	1.26850i
$826$	−19.7388	−	55.9930i	−0.686800	−	1.94825i
$827$		−	12.2272i		−	0.425183i	−0.977141	−	0.212592i	$-0.931810\pi$
$827$		−	12.2272i		−	0.425183i	0.977141	−	0.212592i	$-0.0681904\pi$
$828$	−7.21931	+	6.31518i	−0.250888	+	0.219468i
$829$		−	8.97402i		−	0.311681i	−0.987782	−	0.155840i	$-0.950191\pi$
$829$		−	8.97402i		−	0.311681i	0.987782	−	0.155840i	$-0.0498085\pi$
$830$	−6.17549	+	2.17700i	−0.214354	+	0.0755646i
$831$	10.9365	−	12.6213i	0.379381	−	0.437830i
$832$	0.581602	+	16.9381i	0.0201634	+	0.587222i
$833$	9.70951	−	67.5312i	0.336415	−	2.33982i
$834$	−4.27735	+	10.8640i	−0.148112	+	0.376190i
$835$	−71.1709	+	32.5026i	−2.46297	+	1.12480i
$836$	14.3243	−	5.92561i	0.495415	−	0.204941i
$837$	−7.20259	+	1.03558i	−0.248958	+	0.0357948i
$838$	11.9767	−	2.37946i	0.413728	−	0.0821970i
$839$	−50.3765	+	14.7919i	−1.73919	+	0.510672i	−0.988661	−	0.150165i	$-0.952020\pi$
$839$	−50.3765	+	14.7919i	−1.73919	+	0.510672i	−0.750529	+	0.660837i	$0.770201\pi$
$840$	27.6350	+	41.4203i	0.953497	+	1.42914i
$841$	0.948636	−	2.07722i	0.0327116	−	0.0716284i
$842$	31.9504	−	30.8156i	1.10109	−	1.06197i
$843$	−14.0867	+	12.2062i	−0.485173	+	0.420405i
$844$	3.07044	+	28.6831i	0.105689	+	0.987312i
$845$	−18.8695	−	29.3614i	−0.649129	−	1.01006i
$846$	0.981184	+	1.87679i	0.0337338	+	0.0645254i
$847$	20.4267	+	13.1274i	0.701869	+	0.451064i
$848$	0.504130	+	2.32773i	0.0173119	+	0.0799346i
$849$	−30.4938	−	8.95379i	−1.04654	−	0.307293i
$850$	−80.8739	+	58.2901i	−2.77395	+	1.99933i
$851$	1.06891	+	26.1483i	0.0366417	+	0.896353i
$852$	−3.76330	−	1.25446i	−0.128928	−	0.0429772i
$853$	4.75579	−	16.1967i	0.162835	−	0.554565i	−0.837136	−	0.546994i	$-0.815772\pi$
$853$	4.75579	−	16.1967i	0.162835	−	0.554565i	0.999971	−	0.00757096i	$-0.00240993\pi$
$854$	−4.92369	−	0.441747i	−0.168485	−	0.0151163i
$855$	6.55112	+	4.21015i	0.224044	+	0.143984i
$856$	3.33182	+	20.6510i	0.113879	+	0.705835i
$857$	−33.8546	+	21.7570i	−1.15645	+	0.743207i	−0.970914	−	0.239431i	$-0.923039\pi$
$857$	−33.8546	+	21.7570i	−1.15645	+	0.743207i	−0.185538	+	0.982637i	$0.559403\pi$
$858$	−6.05288	+	10.6238i	−0.206642	+	0.362690i
$859$	−3.19463	+	2.76816i	−0.108999	+	0.0944484i	−0.707655	−	0.706558i	$-0.750247\pi$
$859$	−3.19463	+	2.76816i	−0.108999	+	0.0944484i	0.598656	+	0.801006i	$0.295702\pi$
$860$	−67.9674	−	12.2949i	−2.31767	−	0.419252i
$861$	−6.35731	−	2.90329i	−0.216656	−	0.0989437i
$862$	−14.8862	+	19.1539i	−0.507027	+	0.652383i
$863$	23.4997	−	6.90015i	0.799940	−	0.234884i	0.143883	−	0.989595i	$-0.454041\pi$
$863$	23.4997	−	6.90015i	0.799940	−	0.234884i	0.656057	+	0.754711i	$0.272223\pi$
$864$	−5.10009	−	2.44726i	−0.173509	−	0.0832576i
$865$	−8.56489	−	59.5701i	−0.291215	−	2.02544i
$866$	−11.2765	−	2.66743i	−0.383190	−	0.0906429i
$867$	−16.9275	+	7.73053i	−0.574888	+	0.262543i
$868$	15.4247	+	60.5492i	0.523547	+	2.05517i
$869$	−27.9487	−	4.01841i	−0.948094	−	0.136315i
$870$	−1.59740	−	29.9302i	−0.0541571	−	1.01473i
$871$	15.9575	−	18.4160i	0.540700	−	0.624001i
$872$	32.5229	−	0.558204i	1.10136	−	0.0189032i
$873$	2.18346			0.0738990
$874$	12.1681	+	4.22537i	0.411592	+	0.142925i
$875$		−	119.939i		−	4.05469i
$876$	3.67732	+	2.55571i	0.124245	+	0.0863495i
$877$	29.5031	+	25.5646i	0.996250	+	0.863256i	0.990609	−	0.136728i	$-0.0436588\pi$
$877$	29.5031	+	25.5646i	0.996250	+	0.863256i	0.00564161	+	0.999984i	$0.498204\pi$
$878$	−54.3266	+	2.89947i	−1.83343	+	0.0978523i
$879$	4.63339	−	32.2259i	0.156280	−	1.08695i
$880$	66.7613	+	4.83644i	2.25052	+	0.163036i
$881$	19.4988	+	42.6965i	0.656932	+	1.43848i	0.885353	+	0.464919i	$0.153917\pi$
$881$	19.4988	+	42.6965i	0.656932	+	1.43848i	−0.228421	+	0.973562i	$0.573356\pi$
$882$	−15.7347	−	3.72202i	−0.529815	−	0.125327i
$883$	−14.9879	+	2.15494i	−0.504385	+	0.0725196i	−0.389810	−	0.920895i	$-0.627459\pi$
$883$	−14.9879	+	2.15494i	−0.504385	+	0.0725196i	−0.114574	+	0.993415i	$0.536550\pi$
$884$	17.2373	−	18.4971i	0.579752	−	0.622125i
$885$	−11.2957	−	38.4697i	−0.379702	−	1.29315i
$886$	9.37108	+	7.28313i	0.314828	+	0.244681i
$887$	3.09179	−	6.77006i	0.103812	−	0.227317i	−0.850597	−	0.525818i	$-0.823759\pi$
$887$	3.09179	−	6.77006i	0.103812	−	0.227317i	0.954409	+	0.298501i	$0.0964867\pi$
$888$	−13.9275	+	6.65163i	−0.467375	+	0.223214i
$889$	−13.2431	−	15.2833i	−0.444159	−	0.512587i
$890$	−15.5327	+	27.2623i	−0.520656	+	0.913835i
$891$	−2.20642	−	3.43325i	−0.0739178	−	0.115018i
$892$	−26.0505	−	13.0549i	−0.872237	−	0.437111i
$893$	1.53760	−	2.39256i	0.0514539	−	0.0800639i
$894$	−1.45576	+	16.2258i	−0.0486879	+	0.542672i
$895$	31.7943	+	9.33565i	1.06277	+	0.312056i
$896$	−16.2334	+	45.7812i	−0.542320	+	1.52944i
$897$	−9.62341	+	3.25819i	−0.321316	+	0.108788i
$898$	16.5019	−	11.8938i	0.550676	−	0.396902i
$899$	10.5964	−	36.0880i	0.353409	−	1.20360i
$900$	12.0463	+	20.3242i	0.401544	+	0.677475i
$901$	1.92095	−	2.98906i	0.0639962	−	0.0995800i
$902$	−8.32593	+	4.35278i	−0.277223	+	0.144932i
$903$	30.4205	−	19.5501i	1.01233	−	0.650586i
$904$	−36.6668	+	32.8904i	−1.21952	+	1.09392i
$905$	22.8448	+	26.3644i	0.759389	+	0.876381i
$906$	9.75289	−	9.40646i	0.324018	−	0.312509i
$907$	6.75744	+	3.08602i	0.224377	+	0.102470i	0.524432	−	0.851452i	$-0.324278\pi$
$907$	6.75744	+	3.08602i	0.224377	+	0.102470i	−0.300055	+	0.953922i	$0.597005\pi$
$908$	−20.9187	−	0.756722i	−0.694210	−	0.0251127i
$909$	1.28123	+	4.36348i	0.0424958	+	0.144727i
$910$	10.2778	+	51.7323i	0.340707	+	1.71491i
$911$	1.85060	+	12.8712i	0.0613130	+	0.426441i	0.997240	+	0.0742470i	$0.0236553\pi$
$911$	1.85060	+	12.8712i	0.0613130	+	0.426441i	−0.935927	+	0.352194i	$0.885436\pi$
$912$	0.534990	+	7.57786i	0.0177153	+	0.250928i
$913$	−1.91439	−	4.19193i	−0.0633571	−	0.138733i
$914$	−13.3379	+	33.8769i	−0.441180	+	1.12055i
$915$	−3.30443	−	0.475105i	−0.109241	−	0.0157065i
$916$	−30.0626	−	37.3404i	−0.993295	−	1.23376i
$917$	43.5179	+	37.7085i	1.43709	+	1.24524i
$918$	2.80573	+	7.95903i	0.0926030	+	0.262687i
$919$	32.6514			1.07707			0.538535	−	0.842603i	$-0.318978\pi$
$919$	32.6514			1.07707			0.538535	+	0.842603i	$0.318978\pi$
$920$	38.7995	+	39.8521i	1.27918	+	1.31389i
$921$	−16.9095			−0.557186
$922$	−16.0541	−	45.5406i	−0.528712	−	1.49980i
$923$	−3.17560	−	2.75168i	−0.104526	−	0.0905725i
$924$	−27.2965	+	21.9763i	−0.897989	+	0.722966i
$925$	63.8057	+	9.17388i	2.09792	+	0.301635i
$926$	−5.32006	+	13.5124i	−0.174828	+	0.444045i
$927$	4.23652	+	9.27668i	0.139146	+	0.304686i
$928$	22.4572	−	18.7243i	0.737193	−	0.614656i
$929$	3.26445	+	22.7047i	0.107103	+	0.744918i	0.970623	+	0.240604i	$0.0773455\pi$
$929$	3.26445	+	22.7047i	0.107103	+	0.744918i	−0.863520	+	0.504314i	$0.831745\pi$
$930$	8.22250	+	41.3869i	0.269627	+	1.35713i
$931$	6.11743	+	20.8341i	0.200491	+	0.682809i
$932$	1.78424	−	49.3230i	0.0584446	−	1.61563i
$933$	7.57452	+	3.45917i	0.247979	+	0.113248i
$934$	−39.5319	+	38.1277i	−1.29352	+	1.24758i
$935$	−65.3930	−	75.4676i	−2.13858	−	2.46805i
$936$	−4.00109	−	4.46048i	−0.130780	−	0.145795i
$937$	16.9981	−	10.9240i	0.555303	−	0.356871i	−0.232695	−	0.972550i	$-0.574754\pi$
$937$	16.9981	−	10.9240i	0.555303	−	0.356871i	0.787998	+	0.615678i	$0.211118\pi$
$938$	61.8918	−	32.3569i	2.02084	−	1.05649i
$939$	−4.22844	+	6.57959i	−0.137990	+	0.214717i
$940$	10.5644	−	6.26161i	0.344574	−	0.204231i
$941$	−0.157131	+	0.535138i	−0.00512231	+	0.0174450i	−0.962014	−	0.272998i	$-0.911985\pi$
$941$	−0.157131	+	0.535138i	−0.00512231	+	0.0174450i	0.956892	+	0.290443i	$0.0938028\pi$
$942$	−1.94548	+	1.40222i	−0.0633873	+	0.0456866i
$943$	−7.57413	−	1.89164i	−0.246648	−	0.0616002i
$944$	23.4679	−	31.2896i	0.763816	−	1.01839i
$945$	−16.8914	−	4.95975i	−0.549476	−	0.161341i
$946$	4.34386	−	48.4164i	0.141231	−	1.57415i
$947$	−2.70348	+	4.20670i	−0.0878513	+	0.136699i	−0.882398	−	0.470504i	$-0.844072\pi$
$947$	−2.70348	+	4.20670i	−0.0878513	+	0.136699i	0.794547	+	0.607203i	$0.207709\pi$
$948$	6.19955	−	12.3709i	0.201352	−	0.401789i
$949$	2.56456	+	3.99054i	0.0832493	+	0.129538i
$950$	15.7065	−	27.5675i	0.509586	−	0.894407i
$951$	16.5995	+	19.1569i	0.538277	+	0.621205i
$952$	65.3898	−	31.2296i	2.11930	−	1.01216i
$953$	−5.96118	+	13.0532i	−0.193102	+	0.422834i	−0.981273	−	0.192622i	$-0.938301\pi$
$953$	−5.96118	+	13.0532i	−0.193102	+	0.422834i	0.788171	+	0.615456i	$0.211028\pi$
$954$	−0.664869	−	0.516730i	−0.0215259	−	0.0167298i
$955$	24.0442	+	81.8869i	0.778051	+	2.64980i
$956$	−20.5188	−	19.1213i	−0.663625	−	0.618426i
$957$	20.8797	−	3.00205i	0.674946	−	0.0970425i
$958$	−42.9209	−	10.1529i	−1.38671	−	0.328024i
$959$	−4.76373	−	10.4311i	−0.153829	−	0.336838i
$960$	−12.5948	+	30.2887i	−0.406497	+	0.977562i
$961$	−3.12377	+	21.7263i	−0.100767	+	0.700849i
$962$	−16.3256	+	0.871316i	−0.526359	+	0.0280923i
$963$	−5.58925	−	4.84311i	−0.180111	−	0.156067i
$964$	−18.3625	+	26.4211i	−0.591415	+	0.850966i
$965$		−	97.3861i		−	3.13497i
$966$	−29.0847	−	1.41531i	−0.935786	−	0.0455369i
$967$	−7.86825			−0.253026			−0.126513	−	0.991965i	$-0.540379\pi$
$967$	−7.86825			−0.253026			−0.126513	+	0.991965i	$0.540379\pi$
$968$	0.274508	+	15.9938i	0.00882304	+	0.514061i
$969$	7.42157	−	8.56495i	0.238415	−	0.275146i
$970$	−0.674794	−	12.6435i	−0.0216663	−	0.405957i
$971$	19.9507	+	2.86848i	0.640249	+	0.0920539i	0.454791	−	0.890598i	$-0.349714\pi$
$971$	19.9507	+	2.86848i	0.640249	+	0.0920539i	0.185458	+	0.982652i	$0.440623\pi$
$972$	1.93810	−	0.493724i	0.0621646	−	0.0158362i
$973$	−32.2429	+	14.7248i	−1.03366	+	0.472057i
$974$	29.3662	+	6.94653i	0.940954	+	0.222581i
$975$	3.56156	+	24.7712i	0.114061	+	0.793314i
$976$	−1.55814	−	2.85976i	−0.0498749	−	0.0915387i
$977$	−44.1194	+	12.9546i	−1.41150	+	0.414455i	−0.896618	−	0.442804i	$-0.853984\pi$
$977$	−44.1194	+	12.9546i	−1.41150	+	0.414455i	−0.514885	+	0.857259i	$0.672166\pi$
$978$	−6.08031	+	7.82343i	−0.194427	+	0.250166i
$979$	−20.0870	−	9.17341i	−0.641982	−	0.293183i
$980$	−16.6898	+	92.2629i	−0.533135	+	2.94723i
$981$	−8.69133	+	7.53108i	−0.277493	+	0.240449i
$982$	−1.85408	+	3.25420i	−0.0591659	+	0.103846i
$983$	38.9056	−	25.0031i	1.24090	−	0.797475i	0.255344	−	0.966850i	$-0.417811\pi$
$983$	38.9056	−	25.0031i	1.24090	−	0.797475i	0.985552	+	0.169375i	$0.0541748\pi$
$984$	−0.733355	−	4.54540i	−0.0233785	−	0.144902i
$985$	−15.0703	−	9.68508i	−0.480179	−	0.308592i
$986$	−43.4454	−	3.89787i	−1.38358	−	0.124134i
$987$	−1.81137	+	6.16895i	−0.0576565	+	0.196360i
$988$	−2.54470	+	7.63389i	−0.0809575	+	0.242867i
$989$	29.4210	−	27.6764i	0.935532	−	0.880059i
$990$	−19.1985	+	13.8374i	−0.610170	+	0.439782i
$991$	30.3080	+	8.89923i	0.962765	+	0.282693i	0.725092	−	0.688652i	$-0.241797\pi$
$991$	30.3080	+	8.89923i	0.962765	+	0.282693i	0.237673	+	0.971345i	$0.423615\pi$
$992$	−27.5421	+	30.5912i	−0.874463	+	0.971273i
$993$	13.8095	+	8.87482i	0.438231	+	0.281634i
$994$	−5.57955	−	10.6725i	−0.176972	−	0.338510i
$995$	26.3276	+	40.9666i	0.834641	+	1.29873i
$996$	2.24556	−	0.240381i	0.0711534	−	0.00761676i
$997$	−15.9712	+	13.8391i	−0.505811	+	0.438288i	−0.870011	−	0.493033i	$-0.835888\pi$
$997$	−15.9712	+	13.8391i	−0.505811	+	0.438288i	0.364199	+	0.931321i	$0.381343\pi$
$998$	29.0957	−	28.0622i	0.921007	−	0.888293i
$999$	2.26686	−	4.96373i	0.0717203	−	0.157045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.133.44	yes	480
8.5	even	2	inner	552.2.bb.a.133.34	✓	480
23.9	even	11	inner	552.2.bb.a.469.34	yes	480
184.101	even	22	inner	552.2.bb.a.469.44	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.133.34	✓	480	8.5	even	2	inner
552.2.bb.a.133.44	yes	480	1.1	even	1	trivial
552.2.bb.a.469.34	yes	480	23.9	even	11	inner
552.2.bb.a.469.44	yes	480	184.101	even	22	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+(1.33377 - 0.470182i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(1.55786 - 1.25422i) q^{4} +(4.05863 + 0.583543i) q^{5} +(-1.31590 - 0.518091i) q^{6} +(-1.78354 - 3.90540i) q^{7} +(1.48810 - 2.40532i) q^{8} +(0.142315 + 0.989821i) q^{9} +(5.68763 - 1.12998i) q^{10} +(1.14978 + 3.91580i) q^{11} +(-1.99869 - 0.0723017i) q^{12} +(-1.92706 - 0.880060i) q^{13} +(-4.21507 - 4.37030i) q^{14} +(-2.68517 - 3.09885i) q^{15} +(0.853847 - 3.90781i) q^{16} +(-5.02005 + 3.22619i) q^{17} +(0.655210 + 1.25328i) q^{18} +(1.02677 - 1.59769i) q^{19} +(7.05467 - 4.18135i) q^{20} +(-1.20959 + 4.11947i) q^{21} +(3.37468 + 4.68215i) q^{22} +(-0.488059 + 4.77093i) q^{23} +(-2.69978 + 0.843315i) q^{24} +(11.3345 + 3.32811i) q^{25} +(-2.98404 - 0.267724i) q^{26} +(0.540641 - 0.841254i) q^{27} +(-7.67674 - 3.84711i) q^{28} +(2.79446 + 4.34826i) q^{29} +(-5.03841 - 2.87062i) q^{30} +(-4.76520 - 5.49933i) q^{31} +(-0.698546 - 5.61356i) q^{32} +(1.69536 - 3.71231i) q^{33} +(-5.17867 + 6.66331i) q^{34} +(-4.95975 - 16.8914i) q^{35} +(1.46316 + 1.36351i) q^{36} +(5.40131 - 0.776591i) q^{37} +(0.618270 - 2.61371i) q^{38} +(0.880060 + 1.92706i) q^{39} +(7.44327 - 8.89392i) q^{40} +(-0.231664 + 1.61126i) q^{41} +(0.323596 + 6.06314i) q^{42} +(-6.36528 - 5.51555i) q^{43} +(6.70249 + 4.65818i) q^{44} +4.10037i q^{45} +(1.59225 + 6.59278i) q^{46} +1.49751 q^{47} +(-3.20436 + 2.39417i) q^{48} +(-7.48713 + 8.64061i) q^{49} +(16.6824 - 0.890356i) q^{50} +(5.90660 + 0.849241i) q^{51} +(-4.10588 + 1.04596i) q^{52} +(-0.541617 + 0.247348i) q^{53} +(0.325546 - 1.37623i) q^{54} +(2.38151 + 16.5637i) q^{55} +(-12.0478 - 1.52168i) q^{56} +(-1.82225 + 0.535061i) q^{57} +(5.77163 + 4.48566i) q^{58} +(8.89448 + 4.06197i) q^{59} +(-8.06976 - 1.45977i) q^{60} +(0.615311 - 0.533170i) q^{61} +(-8.94134 - 5.09431i) q^{62} +(3.61183 - 2.32118i) q^{63} +(-3.57109 - 7.15872i) q^{64} +(-7.30768 - 4.69636i) q^{65} +(0.515746 - 5.74848i) q^{66} +(-3.24059 + 11.0364i) q^{67} +(-3.77416 + 11.3222i) q^{68} +(3.49315 - 3.28602i) q^{69} +(-14.5571 - 20.1971i) q^{70} +(1.90309 + 0.558799i) q^{71} +(2.59261 + 1.13065i) q^{72} +(-1.88366 - 1.21055i) q^{73} +(6.83894 - 3.57539i) q^{74} +(-6.38659 - 9.93773i) q^{75} +(-0.404293 - 3.77678i) q^{76} +(13.2421 - 11.4743i) q^{77} +(2.07986 + 2.15646i) q^{78} +(-2.87414 + 6.29348i) q^{79} +(5.74582 - 15.3621i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(0.448598 + 2.25796i) q^{82} +(-1.11770 + 0.160701i) q^{83} +(3.28237 + 7.93465i) q^{84} +(-22.2571 + 10.1645i) q^{85} +(-11.0831 - 4.36361i) q^{86} +(0.735596 - 5.11618i) q^{87} +(11.1297 + 3.06153i) q^{88} +(-3.54339 + 4.08929i) q^{89} +(1.92792 + 5.46893i) q^{90} +9.09557i q^{91} +(5.22349 + 8.04457i) q^{92} +7.27666i q^{93} +(1.99733 - 0.704101i) q^{94} +(5.09962 - 5.88527i) q^{95} +(-3.14817 + 4.69989i) q^{96} +(0.310739 - 2.16124i) q^{97} +(-5.92342 + 15.0448i) q^{98} +(-3.71231 + 1.69536i) 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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