LMFDB - Embedded newform 483.2.v.a.41.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(41,483)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 12]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("483.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.v (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$600$
Relative dimension:	$60$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			41.48
Character	$\chi$	$=$	483.41
Dual form			483.2.v.a.377.48

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.493988 - 1.68237i) q^{2} +(1.68620 - 0.395912i) q^{3} +(-0.903836 - 0.580860i) q^{4} +(-0.558871 + 3.88703i) q^{5} +(0.166890 - 3.03238i) q^{6} +(-0.0105749 - 2.64573i) q^{7} +(1.22655 - 1.06281i) q^{8} +(2.68651 - 1.33517i) q^{9} +(6.26335 + 2.86037i) q^{10} +(1.22718 + 4.17938i) q^{11} +(-1.75401 - 0.621604i) q^{12} +(1.88613 + 0.861367i) q^{13} +(-4.45632 - 1.28917i) q^{14} +(0.596557 + 6.77556i) q^{15} +(-2.07478 - 4.54313i) q^{16} +(-1.78108 + 1.14463i) q^{17} +(-0.919146 - 5.17926i) q^{18} +(1.42444 - 2.21647i) q^{19} +(2.76295 - 3.18861i) q^{20} +(-1.06531 - 4.45703i) q^{21} +7.63748 q^{22} +(-4.27389 - 2.17574i) q^{23} +(1.64742 - 2.27771i) q^{24} +(-9.99921 - 2.93603i) q^{25} +(2.38086 - 2.74766i) q^{26} +(4.00137 - 3.31498i) q^{27} +(-1.52724 + 2.39745i) q^{28} +(0.621661 + 0.967323i) q^{29} +(11.6937 + 2.34342i) q^{30} +(-0.602646 + 0.522195i) q^{31} +(-5.45526 + 0.784348i) q^{32} +(3.72393 + 6.56140i) q^{33} +(1.04586 + 3.56187i) q^{34} +(10.2899 + 1.43752i) q^{35} +(-3.20371 - 0.353710i) q^{36} +(-1.02173 - 7.10631i) q^{37} +(-3.02527 - 3.49135i) q^{38} +(3.52141 + 0.705691i) q^{39} +(3.44569 + 5.36161i) q^{40} +(0.650274 - 4.52275i) q^{41} +(-8.02462 - 0.409480i) q^{42} +(-5.13293 + 5.92372i) q^{43} +(1.31847 - 4.49029i) q^{44} +(3.68844 + 11.1887i) q^{45} +(-5.77165 + 6.11548i) q^{46} -9.37202 q^{47} +(-5.29716 - 6.83917i) q^{48} +(-6.99978 + 0.0559564i) q^{49} +(-9.87898 + 15.3720i) q^{50} +(-2.55007 + 2.63522i) q^{51} +(-1.20442 - 1.87411i) q^{52} +(8.95765 - 4.09082i) q^{53} +(-3.60039 - 8.36934i) q^{54} +(-16.9312 + 2.43434i) q^{55} +(-2.82488 - 3.23388i) q^{56} +(1.52436 - 4.30136i) q^{57} +(1.93449 - 0.568017i) q^{58} +(-4.97577 + 10.8954i) q^{59} +(3.39646 - 6.47051i) q^{60} +(-3.12603 + 2.70872i) q^{61} +(0.580826 + 1.27183i) q^{62} +(-3.56091 - 7.09365i) q^{63} +(0.0463023 - 0.322040i) q^{64} +(-4.40226 + 6.85005i) q^{65} +(12.8783 - 3.02377i) q^{66} +(7.89696 + 2.31876i) q^{67} +2.27467 q^{68} +(-8.06802 - 1.97664i) q^{69} +(7.50155 - 16.6014i) q^{70} +(0.509646 - 1.73569i) q^{71} +(1.87610 - 4.49290i) q^{72} +(-0.202891 + 0.315705i) q^{73} +(-12.4602 - 1.79150i) q^{74} +(-18.0230 - 0.991917i) q^{75} +(-2.57492 + 1.17593i) q^{76} +(11.0445 - 3.29098i) q^{77} +(2.92677 - 5.57571i) q^{78} +(-0.623336 + 1.36491i) q^{79} +(18.8188 - 5.52570i) q^{80} +(5.43464 - 7.17389i) q^{81} +(-7.28772 - 3.32819i) q^{82} +(2.36036 + 16.4166i) q^{83} +(-1.62605 + 4.64722i) q^{84} +(-3.45382 - 7.56281i) q^{85} +(7.43027 + 11.5617i) q^{86} +(1.43122 + 1.38497i) q^{87} +(5.94708 + 3.82196i) q^{88} +(-6.73704 + 7.77495i) q^{89} +(20.6456 - 0.678214i) q^{90} +(2.25900 - 4.99930i) q^{91} +(2.59910 + 4.44904i) q^{92} +(-0.809435 + 1.11912i) q^{93} +(-4.62967 + 15.7672i) q^{94} +(7.81942 + 6.77557i) q^{95} +(-8.88810 + 3.48237i) q^{96} +(1.26788 + 0.182293i) q^{97} +(-3.36367 + 11.8039i) q^{98} +(8.87700 + 9.58945i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 600 q + 20 q^{4} - 18 q^{7} - 26 q^{9} - 14 q^{15} - 116 q^{16} - 46 q^{18} - 50 q^{21} - 104 q^{22} - 88 q^{25} - 26 q^{28} + 26 q^{30} - 26 q^{36} - 56 q^{37} - 14 q^{39} + 5 q^{42} - 40 q^{43} - 44 q^{46}+ \cdots - 250 q^{99}+O(q^{100}) $ 600 * q + 20 * q^4 - 18 * q^7 - 26 * q^9 - 14 * q^15 - 116 * q^16 - 46 * q^18 - 50 * q^21 - 104 * q^22 - 88 * q^25 - 26 * q^28 + 26 * q^30 - 26 * q^36 - 56 * q^37 - 14 * q^39 + 5 * q^42 - 40 * q^43 - 44 * q^46 + 74 * q^49 + 14 * q^51 - 66 * q^57 - 76 * q^58 + 22 * q^60 - 44 * q^63 + 44 * q^64 - 92 * q^67 - 92 * q^70 + 178 * q^72 - 182 * q^78 + 68 * q^79 + 106 * q^81 - 87 * q^84 - 4 * q^85 - 220 * q^88 - 24 * q^91 - 44 * q^93 - 250 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{6}{11}\right)$

Coefficient data

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

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

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

$2$	0.493988	−	1.68237i	0.349302	−	1.18961i	−0.578230	−	0.815873i	$-0.696257\pi$
$2$	0.493988	−	1.68237i	0.349302	−	1.18961i	0.927533	−	0.373741i	$-0.121925\pi$
$3$	1.68620	−	0.395912i	0.973525	−	0.228580i
$3$	1.68620	−	0.395912i	0.973525	−	0.228580i
$4$	−0.903836	−	0.580860i	−0.451918	−	0.290430i
$5$	−0.558871	+	3.88703i	−0.249935	+	1.73833i	0.348632	+	0.937260i	$0.386646\pi$
$5$	−0.558871	+	3.88703i	−0.249935	+	1.73833i	−0.598566	+	0.801073i	$0.704263\pi$
$6$	0.166890	−	3.03238i	0.0681327	−	1.23796i
$7$	−0.0105749	−	2.64573i	−0.00399692	−	0.999992i
$7$	−0.0105749	−	2.64573i	−0.00399692	−	0.999992i
$8$	1.22655	−	1.06281i	0.433650	−	0.375760i
$9$	2.68651	−	1.33517i	0.895502	−	0.445057i
$10$	6.26335	+	2.86037i	1.98064	+	0.904530i
$11$	1.22718	+	4.17938i	0.370008	+	1.26013i	0.908637	+	0.417588i	$0.137124\pi$
$11$	1.22718	+	4.17938i	0.370008	+	1.26013i	−0.538629	+	0.842543i	$0.681057\pi$
$12$	−1.75401	−	0.621604i	−0.506340	−	0.179442i
$13$	1.88613	+	0.861367i	0.523118	+	0.238900i	0.659430	−	0.751766i	$-0.270798\pi$
$13$	1.88613	+	0.861367i	0.523118	+	0.238900i	−0.136312	+	0.990666i	$0.543525\pi$
$14$	−4.45632	−	1.28917i	−1.19100	−	0.344545i
$15$	0.596557	+	6.77556i	0.154030	+	1.74944i
$16$	−2.07478	−	4.54313i	−0.518694	−	1.13578i
$17$	−1.78108	+	1.14463i	−0.431975	+	0.277613i	−0.738506	−	0.674247i	$-0.764468\pi$
$17$	−1.78108	+	1.14463i	−0.431975	+	0.277613i	0.306531	+	0.951861i	$0.400832\pi$
$18$	−0.919146	−	5.17926i	−0.216645	−	1.22076i
$19$	1.42444	−	2.21647i	0.326789	−	0.508494i	−0.638519	−	0.769606i	$-0.720453\pi$
$19$	1.42444	−	2.21647i	0.326789	−	0.508494i	0.965309	+	0.261112i	$0.0840892\pi$
$20$	2.76295	−	3.18861i	0.617814	−	0.712995i
$21$	−1.06531	−	4.45703i	−0.232469	−	0.972604i
$22$	7.63748			1.62832
$23$	−4.27389	−	2.17574i	−0.891168	−	0.453673i
$23$	−4.27389	−	2.17574i	−0.891168	−	0.453673i
$24$	1.64742	−	2.27771i	0.336278	−	0.464936i
$25$	−9.99921	−	2.93603i	−1.99984	−	0.587206i
$26$	2.38086	−	2.74766i	0.466926	−	0.538861i
$27$	4.00137	−	3.31498i	0.770063	−	0.637968i
$28$	−1.52724	+	2.39745i	−0.288621	+	0.453075i
$29$	0.621661	+	0.967323i	0.115439	+	0.179627i	0.894165	−	0.447737i	$-0.147770\pi$
$29$	0.621661	+	0.967323i	0.115439	+	0.179627i	−0.778726	+	0.627365i	$0.784134\pi$
$30$	11.6937	+	2.34342i	2.13496	+	0.427847i
$31$	−0.602646	+	0.522195i	−0.108238	+	0.0937891i	−0.707299	−	0.706915i	$-0.750086\pi$
$31$	−0.602646	+	0.522195i	−0.108238	+	0.0937891i	0.599060	+	0.800704i	$0.295541\pi$
$32$	−5.45526	+	0.784348i	−0.964363	+	0.138654i
$33$	3.72393	+	6.56140i	0.648253	+	1.14219i
$34$	1.04586	+	3.56187i	0.179363	+	0.610855i
$35$	10.2899	+	1.43752i	1.73932	+	0.242985i
$36$	−3.20371	−	0.353710i	−0.533951	−	0.0589517i
$37$	−1.02173	−	7.10631i	−0.167972	−	1.16827i	−0.883068	−	0.469245i	$-0.844526\pi$
$37$	−1.02173	−	7.10631i	−0.167972	−	1.16827i	0.715096	−	0.699026i	$-0.246383\pi$
$38$	−3.02527	−	3.49135i	−0.490764	−	0.566371i
$39$	3.52141	+	0.705691i	0.563877	+	0.113001i
$40$	3.44569	+	5.36161i	0.544812	+	0.847744i
$41$	0.650274	−	4.52275i	0.101556	−	0.706336i	−0.873895	−	0.486116i	$-0.838413\pi$
$41$	0.650274	−	4.52275i	0.101556	−	0.706336i	0.975450	−	0.220220i	$-0.0706775\pi$
$42$	−8.02462	−	0.409480i	−1.23823	−	0.0631841i
$43$	−5.13293	+	5.92372i	−0.782764	+	0.903358i	−0.997306	−	0.0733566i	$-0.976629\pi$
$43$	−5.13293	+	5.92372i	−0.782764	+	0.903358i	0.214541	+	0.976715i	$0.431174\pi$
$44$	1.31847	−	4.49029i	0.198767	−	0.676937i
$45$	3.68844	+	11.1887i	0.549840	+	1.66792i
$46$	−5.77165	+	6.11548i	−0.850983	+	0.901678i
$47$	−9.37202			−1.36705			−0.683525	−	0.729927i	$-0.739554\pi$
$47$	−9.37202			−1.36705			−0.683525	+	0.729927i	$0.739554\pi$
$48$	−5.29716	−	6.83917i	−0.764579	−	0.987149i
$49$	−6.99978	+	0.0559564i	−0.999968	+	0.00799377i
$50$	−9.87898	+	15.3720i	−1.39710	+	2.17393i
$51$	−2.55007	+	2.63522i	−0.357082	+	0.369004i
$52$	−1.20442	−	1.87411i	−0.167023	−	0.259893i
$53$	8.95765	−	4.09082i	1.23043	−	0.561917i	0.309220	−	0.950990i	$-0.399932\pi$
$53$	8.95765	−	4.09082i	1.23043	−	0.561917i	0.921207	+	0.389073i	$0.127205\pi$
$54$	−3.60039	−	8.36934i	−0.489951	−	1.13892i
$55$	−16.9312	+	2.43434i	−2.28300	+	0.328247i
$56$	−2.82488	−	3.23388i	−0.377490	−	0.432145i
$57$	1.52436	−	4.30136i	0.201906	−	0.569729i
$58$	1.93449	−	0.568017i	0.254011	−	0.0745843i
$59$	−4.97577	+	10.8954i	−0.647790	+	1.41846i	0.245685	+	0.969350i	$0.420987\pi$
$59$	−4.97577	+	10.8954i	−0.647790	+	1.41846i	−0.893475	+	0.449113i	$0.851740\pi$
$60$	3.39646	−	6.47051i	0.438481	−	0.835339i
$61$	−3.12603	+	2.70872i	−0.400247	+	0.346816i	−0.831608	−	0.555363i	$-0.812579\pi$
$61$	−3.12603	+	2.70872i	−0.400247	+	0.346816i	0.431361	+	0.902180i	$0.358034\pi$
$62$	0.580826	+	1.27183i	0.0737650	+	0.161523i
$63$	−3.56091	−	7.09365i	−0.448632	−	0.893716i
$64$	0.0463023	−	0.322040i	0.00578779	−	0.0402550i
$65$	−4.40226	+	6.85005i	−0.546033	+	0.849644i
$66$	12.8783	−	3.02377i	1.58521	−	0.372200i
$67$	7.89696	+	2.31876i	0.964767	+	0.283281i	0.725922	−	0.687777i	$-0.241413\pi$
$67$	7.89696	+	2.31876i	0.964767	+	0.283281i	0.238845	+	0.971058i	$0.423231\pi$
$68$	2.27467			0.275845
$69$	−8.06802	−	1.97664i	−0.971275	−	0.237959i
$70$	7.50155	−	16.6014i	0.896606	−	1.98424i
$71$	0.509646	−	1.73569i	0.0604838	−	0.205989i	−0.923707	−	0.383099i	$-0.874857\pi$
$71$	0.509646	−	1.73569i	0.0604838	−	0.205989i	0.984191	+	0.177110i	$0.0566749\pi$
$72$	1.87610	−	4.49290i	0.221100	−	0.529493i
$73$	−0.202891	+	0.315705i	−0.0237466	+	0.0369505i	−0.852924	−	0.522035i	$-0.825173\pi$
$73$	−0.202891	+	0.315705i	−0.0237466	+	0.0369505i	0.829177	+	0.558986i	$0.188809\pi$
$74$	−12.4602	−	1.79150i	−1.44847	−	0.208258i
$75$	−18.0230	−	0.991917i	−2.08112	−	0.114537i
$76$	−2.57492	+	1.17593i	−0.295364	+	0.134888i
$77$	11.0445	−	3.29098i	1.25864	−	0.375042i
$78$	2.92677	−	5.57571i	0.331391	−	0.631325i
$79$	−0.623336	+	1.36491i	−0.0701307	+	0.153565i	−0.941451	−	0.337150i	$-0.890537\pi$
$79$	−0.623336	+	1.36491i	−0.0701307	+	0.153565i	0.871320	+	0.490715i	$0.163264\pi$
$80$	18.8188	−	5.52570i	2.10401	−	0.617792i
$81$	5.43464	−	7.17389i	0.603849	−	0.797099i
$82$	−7.28772	−	3.32819i	−0.804794	−	0.367537i
$83$	2.36036	+	16.4166i	0.259083	+	1.80196i	0.539397	+	0.842052i	$0.318652\pi$
$83$	2.36036	+	16.4166i	0.259083	+	1.80196i	−0.280314	+	0.959908i	$0.590439\pi$
$84$	−1.62605	+	4.64722i	−0.177416	+	0.507053i
$85$	−3.45382	−	7.56281i	−0.374619	−	0.820302i
$86$	7.43027	+	11.5617i	0.801227	+	1.24673i
$87$	1.43122	+	1.38497i	0.153442	+	0.148485i
$88$	5.94708	+	3.82196i	0.633961	+	0.407422i
$89$	−6.73704	+	7.77495i	−0.714124	+	0.824143i	−0.990587	−	0.136881i	$-0.956292\pi$
$89$	−6.73704	+	7.77495i	−0.714124	+	0.824143i	0.276463	+	0.961025i	$0.410838\pi$
$90$	20.6456	−	0.678214i	2.17624	−	0.0714900i
$91$	2.25900	−	4.99930i	0.236807	−	0.524069i
$92$	2.59910	+	4.44904i	0.270975	+	0.463845i
$93$	−0.809435	+	1.11912i	−0.0839345	+	0.116047i
$94$	−4.62967	+	15.7672i	−0.477514	+	1.62626i
$95$	7.81942	+	6.77557i	0.802256	+	0.695158i
$96$	−8.88810	+	3.48237i	−0.907138	+	0.355417i
$97$	1.26788	+	0.182293i	0.128734	+	0.0185091i	0.206380	−	0.978472i	$-0.433832\pi$
$97$	1.26788	+	0.182293i	0.128734	+	0.0185091i	−0.0776468	+	0.996981i	$0.524741\pi$
$98$	−3.36367	+	11.8039i	−0.339782	+	1.19237i
$99$	8.87700	+	9.58945i	0.892172	+	0.963776i
$100$	7.33222	+	8.46183i	0.733222	+	0.846183i
$101$	−2.57556	−	17.9134i	−0.256278	−	1.78245i	−0.558795	−	0.829306i	$-0.688736\pi$
$101$	−2.57556	−	17.9134i	−0.256278	−	1.78245i	0.302518	−	0.953144i	$-0.402173\pi$
$102$	3.17371	+	5.59193i	0.314244	+	0.553684i
$103$	−0.229998	−	0.783301i	−0.0226624	−	0.0771810i	0.947385	−	0.320095i	$-0.103715\pi$
$103$	−0.229998	−	0.783301i	−0.0226624	−	0.0771810i	−0.970048	+	0.242914i	$0.921897\pi$
$104$	3.22890	−	0.948090i	0.316620	−	0.0929679i
$105$	17.9200	−	1.64998i	1.74881	−	0.161022i
$106$	−2.45730	−	17.0909i	−0.238674	−	1.66001i
$107$	−11.0719	+	9.59384i	−1.07036	+	0.927471i	−0.997556	−	0.0698749i	$-0.977740\pi$
$107$	−11.0719	+	9.59384i	−1.07036	+	0.927471i	−0.0728033	+	0.997346i	$0.523195\pi$
$108$	−5.54212	+	0.671962i	−0.533290	+	0.0646596i
$109$	−5.12509	+	3.29369i	−0.490894	+	0.315479i	−0.762565	−	0.646912i	$-0.776060\pi$
$109$	−5.12509	+	3.29369i	−0.490894	+	0.315479i	0.271671	+	0.962390i	$0.412424\pi$
$110$	−4.26836	+	29.6871i	−0.406972	+	2.83055i
$111$	−4.53632	−	11.5781i	−0.430568	−	1.09895i
$112$	−11.9979	+	5.53734i	−1.13370	+	0.523230i
$113$	1.53221	−	5.21824i	0.144138	−	0.490890i	−0.855499	−	0.517804i	$-0.826750\pi$
$113$	1.53221	−	5.21824i	0.144138	−	0.490890i	0.999638	+	0.0269135i	$0.00856788\pi$
$114$	−6.48346	−	4.68935i	−0.607232	−	0.439198i
$115$	10.8457	−	15.3968i	1.01137	−	1.43576i
$116$		−	1.23540i		−	0.114704i
$117$	6.21717	−	0.204236i	0.574778	−	0.0188816i
$118$	15.8721	+	13.7533i	1.46115	+	1.26609i
$119$	3.04722	+	4.70015i	0.279338	+	0.430862i
$120$	7.93284	+	7.67652i	0.724166	+	0.700767i
$121$	−6.70748	+	4.31063i	−0.609771	+	0.391876i
$122$	3.01285	+	6.59721i	0.272770	+	0.597284i
$123$	−0.694124	−	7.88370i	−0.0625871	−	0.710849i
$124$	0.848015	−	0.121926i	0.0761540	−	0.0109493i
$125$	8.84403	−	19.3657i	0.791035	−	1.73212i
$126$	−13.6932	+	2.48658i	−1.21989	+	0.221522i
$127$	11.0189	−	3.23544i	0.977770	−	0.287099i	0.246467	−	0.969151i	$-0.420730\pi$
$127$	11.0189	−	3.23544i	0.977770	−	0.287099i	0.731304	+	0.682052i	$0.238912\pi$
$128$	−10.5455	−	4.81598i	−0.932102	−	0.425677i
$129$	−6.30985	+	12.0207i	−0.555551	+	1.05837i
$130$	9.34965	+	10.7901i	0.820019	+	0.946352i
$131$	−2.12230	−	4.64719i	−0.185426	−	0.406027i	0.793975	−	0.607950i	$-0.208008\pi$
$131$	−2.12230	−	4.64719i	−0.185426	−	0.406027i	−0.979401	+	0.201923i	$0.935281\pi$
$132$	0.445435	−	8.09351i	0.0387701	−	0.704449i
$133$	−5.87925	−	3.74525i	−0.509796	−	0.324754i
$134$	7.80201	−	12.1402i	0.673991	−	1.04875i
$135$	10.6492	+	17.4061i	0.916535	+	1.49808i
$136$	−0.968055	+	3.29689i	−0.0830100	+	0.282706i
$137$		−	22.1754i		−	1.89457i	−0.320390	−	0.947286i	$-0.603814\pi$
$137$		−	22.1754i		−	1.89457i	0.320390	−	0.947286i	$-0.396186\pi$
$138$	−7.31094	+	12.5970i	−0.622348	+	1.07232i
$139$			13.0848i			1.10984i	0.831904	+	0.554920i	$0.187251\pi$
$139$			13.0848i			1.10984i	−0.831904	+	0.554920i	$0.812749\pi$
$140$	−8.46543	−	7.27630i	−0.715459	−	0.614959i
$141$	−15.8031	+	3.71050i	−1.33086	+	0.312480i
$142$	−2.66832	−	1.71483i	−0.223921	−	0.143905i
$143$	−1.28536	+	8.93991i	−0.107488	+	0.747592i
$144$	−11.6397	−	9.43496i	−0.969979	−	0.786247i
$145$	−4.10744	+	1.87581i	−0.341104	+	0.155777i
$146$	0.430906	+	0.497293i	0.0356621	+	0.0411562i
$147$	−11.7808	+	2.86565i	−0.971667	+	0.236355i
$148$	−3.20429	+	7.01643i	−0.263391	+	0.576747i
$149$	−1.76192	−	6.00055i	−0.144342	−	0.491584i	0.855306	−	0.518124i	$-0.173369\pi$
$149$	−1.76192	−	6.00055i	−0.144342	−	0.491584i	−0.999648	+	0.0265395i	$0.991551\pi$
$150$	−10.5719	+	29.8314i	−0.863195	+	2.43572i
$151$	3.59727	−	7.87693i	0.292742	−	0.641015i	−0.704925	−	0.709282i	$-0.749020\pi$
$151$	3.59727	−	7.87693i	0.292742	−	0.641015i	0.997667	+	0.0682664i	$0.0217468\pi$
$152$	−0.608545	−	4.23252i	−0.0493595	−	0.343303i
$153$	−3.25661	+	5.45310i	−0.263281	+	0.440857i
$154$	−0.0807652	−	20.2067i	−0.00650824	−	1.62830i
$155$	−1.69299	−	2.63434i	−0.135984	−	0.211595i
$156$	−2.77287	−	2.68327i	−0.222007	−	0.214834i
$157$	7.69133	−	11.9679i	0.613835	−	0.955145i	−0.385637	−	0.922651i	$-0.626018\pi$
$157$	7.69133	−	11.9679i	0.613835	−	0.955145i	0.999472	−	0.0324950i	$-0.0103453\pi$
$158$	1.98837	+	1.72293i	0.158186	+	0.137069i
$159$	13.4847	−	10.4444i	1.06941	−	0.828292i
$160$		−	21.6431i		−	1.71104i
$161$	−5.71122	+	11.3306i	−0.450107	+	0.892974i
$162$	−9.38448	−	12.6869i	−0.737314	−	0.996777i
$163$	10.7895	+	3.16808i	0.845099	+	0.248144i	0.675491	−	0.737368i	$-0.263932\pi$
$163$	10.7895	+	3.16808i	0.845099	+	0.248144i	0.169608	+	0.985512i	$0.445750\pi$
$164$	−3.21483	+	3.71011i	−0.251036	+	0.289711i
$165$	−27.5856	+	10.8080i	−2.14753	+	0.841405i
$166$	28.7848	+	4.13864i	2.23414	+	0.321220i
$167$	−1.45120	+	0.932628i	−0.112297	+	0.0721689i	−0.595584	−	0.803293i	$-0.703079\pi$
$167$	−1.45120	+	0.932628i	−0.112297	+	0.0721689i	0.483287	+	0.875462i	$0.339443\pi$
$168$	−6.04363	−	4.33454i	−0.466276	−	0.334417i
$169$	−5.69766	−	6.57545i	−0.438281	−	0.505804i
$170$	−14.4296	+	2.07466i	−1.10670	+	0.159119i
$171$	0.867403	−	7.85644i	0.0663319	−	0.600797i
$172$	8.08018	−	2.37255i	0.616108	−	0.180906i
$173$	−5.13414	+	1.50752i	−0.390341	+	0.114615i	−0.471013	−	0.882126i	$-0.656112\pi$
$173$	−5.13414	+	1.50752i	−0.390341	+	0.114615i	0.0806719	+	0.996741i	$0.474293\pi$
$174$	3.03704	−	1.72367i	0.230237	−	0.130671i
$175$	−7.66221	+	26.4863i	−0.579209	+	2.00217i
$176$	16.4413	−	14.2465i	1.23931	−	1.07387i
$177$	−4.07649	+	20.3418i	−0.306408	+	1.52898i
$178$	9.75233	+	15.1749i	0.730968	+	1.13741i
$179$	12.1613	+	1.74853i	0.908977	+	0.130691i	0.580914	−	0.813965i	$-0.302695\pi$
$179$	12.1613	+	1.74853i	0.908977	+	0.130691i	0.328063	+	0.944656i	$0.393604\pi$
$180$	3.16534	−	12.2552i	0.235931	−	0.913451i
$181$	4.36980	+	3.78646i	0.324805	+	0.281445i	0.801965	−	0.597371i	$-0.203788\pi$
$181$	4.36980	+	3.78646i	0.324805	+	0.281445i	−0.477160	+	0.878817i	$0.658334\pi$
$182$	−7.29475	−	6.27007i	−0.540723	−	0.464768i
$183$	−4.19868	+	5.80506i	−0.310375	+	0.429123i
$184$	−7.55453	+	1.87369i	−0.556928	+	0.138130i
$185$	28.1935			2.07283
$186$	1.48292	+	1.91460i	0.108733	+	0.140385i
$187$	−6.96954	−	6.03914i	−0.509663	−	0.441626i
$188$	8.47077	+	5.44383i	0.617794	+	0.397032i
$189$	−8.81285	−	10.5515i	−0.641040	−	0.767507i
$190$	15.2617	−	9.80810i	1.10720	−	0.711555i
$191$	−16.5976	+	7.57986i	−1.20096	+	0.548459i	−0.912517	−	0.409039i	$-0.865864\pi$
$191$	−16.5976	+	7.57986i	−1.20096	+	0.548459i	−0.288441	+	0.957498i	$0.593137\pi$
$192$	−0.0494246	−	0.561353i	−0.00356692	−	0.0405122i
$193$	1.11914	+	7.78381i	0.0805577	+	0.560291i	0.989629	+	0.143650i	$0.0458839\pi$
$193$	1.11914	+	7.78381i	0.0805577	+	0.560291i	−0.909071	+	0.416641i	$0.863207\pi$
$194$	0.933002	−	2.04299i	0.0669857	−	0.146678i
$195$	−4.71105	+	13.2934i	−0.337366	+	0.951962i
$196$	6.35915	+	4.01532i	0.454225	+	0.286808i
$197$	24.6341	+	11.2500i	1.75511	+	0.801530i	0.986901	+	0.161328i	$0.0515777\pi$
$197$	24.6341	+	11.2500i	1.75511	+	0.801530i	0.768206	+	0.640203i	$0.221150\pi$
$198$	20.5181	−	10.1973i	1.45816	−	0.724692i
$199$	−19.5803	+	16.9664i	−1.38801	+	1.20272i	−0.434757	+	0.900548i	$0.643166\pi$
$199$	−19.5803	+	16.9664i	−1.38801	+	1.20272i	−0.953254	+	0.302171i	$0.902289\pi$
$200$	−15.3850	+	7.02608i	−1.08788	+	0.496819i
$201$	14.2338	+	0.783375i	1.00398	+	0.0552550i
$202$	−31.4092	−	4.51597i	−2.20995	−	0.317742i
$203$	2.55270	−	1.65498i	0.179165	−	0.116157i
$204$	3.83554	−	0.900570i	0.268542	−	0.0630525i
$205$	17.2167	+	5.05527i	1.20246	+	0.353075i
$206$	−1.43142			−0.0997317
$207$	−14.3868	−	0.138768i	−0.999953	−	0.00964503i
$208$		−	10.3561i		−	0.718064i
$209$	11.0115	+	3.23328i	0.761683	+	0.223650i
$210$	6.07639	−	30.9631i	0.419310	−	2.13666i
$211$	3.28049	+	2.10825i	0.225839	+	0.145138i	0.648668	−	0.761072i	$-0.275327\pi$
$211$	3.28049	+	2.10825i	0.225839	+	0.145138i	−0.422829	+	0.906209i	$0.638963\pi$
$212$	−10.4724	−	1.50571i	−0.719250	−	0.103413i
$213$	0.172180	−	3.12849i	0.0117976	−	0.214361i
$214$	10.6710	+	23.3662i	0.729455	+	1.59728i
$215$	−20.1570	−	23.2624i	−1.37470	−	1.58649i
$216$	1.38468	−	8.31867i	0.0942153	−	0.566014i
$217$	1.38796	+	1.58892i	0.0942210	+	0.107863i
$218$	3.00948	+	10.2493i	0.203827	+	0.694173i
$219$	−0.217123	+	0.612667i	−0.0146718	+	0.0414002i
$220$	16.7171	+	7.63442i	1.12706	+	0.514713i
$221$	−4.34529	+	0.624758i	−0.292296	+	0.0420258i
$222$	−21.7196	+	1.91231i	−1.45772	+	0.128346i
$223$	25.3693	−	11.5858i	1.69886	−	0.775842i	0.700811	−	0.713347i	$-0.252821\pi$
$223$	25.3693	−	11.5858i	1.69886	−	0.775842i	0.998045	−	0.0624952i	$-0.0199058\pi$
$224$	2.13286	+	14.4248i	0.142508	+	0.963801i
$225$	−30.7830	+	5.46297i	−2.05220	+	0.364198i
$226$	−8.02211	−	5.15549i	−0.533623	−	0.342938i
$227$	12.4325	−	14.3479i	0.825176	−	0.952304i	−0.174299	−	0.984693i	$-0.555766\pi$
$227$	12.4325	−	14.3479i	0.825176	−	0.952304i	0.999475	+	0.0323885i	$0.0103114\pi$
$228$	−3.87626	+	3.00228i	−0.256711	+	0.198831i
$229$		−	7.77742i		−	0.513946i	−0.966419	−	0.256973i	$-0.917275\pi$
$229$		−	7.77742i		−	0.513946i	0.966419	−	0.256973i	$-0.0827252\pi$
$230$	−20.5454	−	25.8523i	−1.35473	−	1.70465i
$231$	17.3203	−	9.92189i	1.13959	−	0.652813i
$232$	1.79058	+	0.525761i	0.117557	+	0.0345179i
$233$	3.92459	+	3.40068i	0.257108	+	0.222786i	0.773871	−	0.633343i	$-0.218318\pi$
$233$	3.92459	+	3.40068i	0.257108	+	0.222786i	−0.516763	+	0.856129i	$0.672863\pi$
$234$	2.72761	−	10.5605i	0.178309	−	0.690360i
$235$	5.23775	−	36.4293i	0.341673	−	2.37639i
$236$	10.8260	−	6.95744i	0.704712	−	0.452891i
$237$	−0.510679	+	2.54830i	−0.0331722	+	0.165530i
$238$	9.41268	−	2.80472i	0.610133	−	0.181803i
$239$	−3.27363	+	0.470677i	−0.211753	+	0.0304455i	−0.247375	−	0.968920i	$-0.579568\pi$
$239$	−3.27363	+	0.470677i	−0.211753	+	0.0304455i	0.0356216	+	0.999365i	$0.488659\pi$
$240$	29.5445	−	16.7680i	1.90709	−	1.08237i
$241$	1.26913	+	4.32227i	0.0817520	+	0.278422i	0.990216	−	0.139541i	$-0.0445626\pi$
$241$	1.26913	+	4.32227i	0.0817520	+	0.278422i	−0.908464	+	0.417962i	$0.862744\pi$
$242$	3.93866	+	13.4139i	0.253187	+	0.862275i
$243$	6.32364	−	14.2482i	0.405662	−	0.914023i
$244$	4.39881	−	0.632453i	0.281605	−	0.0404886i
$245$	3.69447	−	27.2396i	0.236031	−	1.74028i
$246$	−13.6062	−	2.72668i	−0.867499	−	0.173847i
$247$	4.59588	−	2.95359i	0.292429	−	0.187932i
$248$	−0.184179	+	1.28100i	−0.0116954	+	0.0813433i
$249$	10.4796	+	26.7472i	0.664115	+	1.69503i
$250$	−28.2115	−	24.4454i	−1.78425	−	1.54606i
$251$	−13.6253	−	4.00076i	−0.860023	−	0.252526i	−0.178157	−	0.984002i	$-0.557013\pi$
$251$	−13.6253	−	4.00076i	−0.860023	−	0.252526i	−0.681867	+	0.731477i	$0.738832\pi$
$252$	−0.901944	+	8.47989i	−0.0568171	+	0.534183i
$253$	3.84842	−	20.5322i	0.241948	−	1.29085i
$254$		−	20.1362i		−	1.26345i
$255$	−8.81802	−	11.3850i	−0.552206	−	0.712954i
$256$	−12.8855	+	14.8707i	−0.805344	+	0.929417i
$257$	−9.40755	−	6.04587i	−0.586827	−	0.377131i	0.213277	−	0.976992i	$-0.431586\pi$
$257$	−9.40755	−	6.04587i	−0.586827	−	0.377131i	−0.800104	+	0.599861i	$0.795223\pi$
$258$	17.1063	+	16.5536i	1.06499	+	1.03058i
$259$	−18.7906	+	2.77838i	−1.16759	+	0.172640i
$260$	7.95784	−	3.63423i	0.493525	−	0.225385i
$261$	2.96164	+	1.76870i	0.183321	+	0.109480i
$262$	−8.86669	+	1.27484i	−0.547786	+	0.0787597i
$263$	2.44888	+	1.11837i	0.151004	+	0.0689613i	0.489484	−	0.872012i	$-0.337185\pi$
$263$	2.44888	+	1.11837i	0.151004	+	0.0689613i	−0.338479	+	0.940974i	$0.609913\pi$
$264$	11.5411	+	4.09004i	0.710306	+	0.251725i
$265$	10.8950	+	37.1049i	0.669273	+	2.27933i
$266$	−9.20517	+	8.04097i	−0.564405	+	0.493023i
$267$	−8.28176	+	15.7774i	−0.506835	+	0.965559i
$268$	−5.79068	−	6.68280i	−0.353722	−	0.408217i
$269$	−7.85971	−	17.2104i	−0.479215	−	1.04933i	−0.982679	−	0.185318i	$-0.940668\pi$
$269$	−7.85971	−	17.2104i	−0.479215	−	1.04933i	0.503463	−	0.864017i	$-0.332059\pi$
$270$	34.5440	−	9.31745i	2.10228	−	0.567042i
$271$	−17.6181	−	2.53310i	−1.07022	−	0.153875i	−0.415387	−	0.909645i	$-0.636354\pi$
$271$	−17.6181	−	2.53310i	−1.07022	−	0.153875i	−0.654838	+	0.755770i	$0.727263\pi$
$272$	8.89553	+	5.71681i	0.539371	+	0.346633i
$273$	1.82983	−	9.32416i	0.110746	−	0.564324i
$274$	−37.3072	−	10.9544i	−2.25381	−	0.661778i
$275$		−	45.3935i		−	2.73733i
$276$	6.14402	+	6.47294i	0.369826	+	0.389625i
$277$	1.25766			0.0755653			0.0377827	−	0.999286i	$-0.487971\pi$
$277$	1.25766			0.0755653			0.0377827	+	0.999286i	$0.487971\pi$
$278$	22.0135	+	6.46375i	1.32028	+	0.387670i
$279$	−0.921793	+	2.20752i	−0.0551863	+	0.132161i
$280$	14.1489	−	9.17308i	0.845560	−	0.548196i
$281$	−11.0464	−	1.58824i	−0.658975	−	0.0947463i	−0.195289	−	0.980746i	$-0.562564\pi$
$281$	−11.0464	−	1.58824i	−0.658975	−	0.0947463i	−0.463686	+	0.886000i	$0.653473\pi$
$282$	−1.56410	+	28.4195i	−0.0931407	+	1.69236i
$283$	23.8672	−	10.8998i	1.41876	−	0.647926i	0.449346	−	0.893358i	$-0.351657\pi$
$283$	23.8672	−	10.8998i	1.41876	−	0.647926i	0.969414	+	0.245432i	$0.0789299\pi$
$284$	−1.46883	+	1.27275i	−0.0871591	+	0.0755238i
$285$	15.8676	+	8.32912i	0.939915	+	0.493375i
$286$	14.4053	+	6.57867i	0.851801	+	0.389005i
$287$	−11.9729	−	1.67262i	−0.706736	−	0.0987318i
$288$	−13.6084	+	9.39085i	−0.801880	+	0.553361i
$289$	−5.19999	+	11.3864i	−0.305882	+	0.669788i
$290$	1.12677	+	7.83686i	0.0661662	+	0.460196i
$291$	2.21006	−	0.194586i	0.129556	−	0.0114068i
$292$	0.366761	−	0.167494i	0.0214630	−	0.00980185i
$293$	−9.74317	+	6.26156i	−0.569202	+	0.365804i	−0.793364	−	0.608748i	$-0.791672\pi$
$293$	−9.74317	+	6.26156i	−0.569202	+	0.365804i	0.224161	+	0.974552i	$0.428036\pi$
$294$	−0.998513	+	21.2353i	−0.0582345	+	1.23847i
$295$	−39.5700	−	25.4301i	−2.30385	−	1.48060i
$296$	−8.80587	−	7.63033i	−0.511831	−	0.443504i
$297$	18.7649	+	12.6552i	1.08885	+	0.734327i
$298$	−10.9655			−0.635215
$299$	−6.18701	−	7.78512i	−0.357804	−	0.450225i
$300$	15.7137	+	11.3654i	0.907230	+	0.656181i
$301$	15.7268	+	13.5177i	0.906480	+	0.779147i
$302$	−11.4749	−	9.94305i	−0.660306	−	0.572158i
$303$	−11.4350	−	29.1858i	−0.656925	−	1.67668i
$304$	−13.0251	−	1.87273i	−0.747041	−	0.107408i
$305$	−8.78183	−	13.6648i	−0.502846	−	0.782444i
$306$	7.56540	+	8.17258i	0.432485	+	0.467195i
$307$	−9.17327	+	7.94868i	−0.523546	+	0.453655i	−0.876095	−	0.482138i	$-0.839860\pi$
$307$	−9.17327	+	7.94868i	−0.523546	+	0.453655i	0.352549	+	0.935793i	$0.385315\pi$
$308$	−11.8940	−	3.44083i	−0.677726	−	0.196059i
$309$	−0.697940	−	1.22974i	−0.0397044	−	0.0699575i
$310$	−5.26825	+	1.54690i	−0.299217	+	0.0878580i
$311$	20.6264	−	6.05646i	1.16962	−	0.343431i	0.361454	−	0.932390i	$-0.382280\pi$
$311$	20.6264	−	6.05646i	1.16962	−	0.343431i	0.808163	+	0.588959i	$0.200462\pi$
$312$	5.06919	−	2.87703i	0.286987	−	0.162879i
$313$	11.0776	−	1.59272i	0.626142	−	0.0900256i	0.178062	−	0.984019i	$-0.443017\pi$
$313$	11.0776	−	1.59272i	0.626142	−	0.0900256i	0.448080	+	0.893994i	$0.352108\pi$
$314$	−16.3351	−	18.8517i	−0.921841	−	1.06386i
$315$	29.5633	−	9.87693i	1.66571	−	0.556502i
$316$	1.35622	−	0.871588i	0.0762932	−	0.0490307i
$317$	23.8175	+	3.42443i	1.33772	+	0.192335i	0.773767	−	0.633470i	$-0.218370\pi$
$317$	23.8175	+	3.42443i	1.33772	+	0.192335i	0.563955	+	0.825806i	$0.309279\pi$
$318$	−10.9100	−	27.8457i	−0.611801	−	1.56151i
$319$	−3.27992	+	3.78523i	−0.183640	+	0.211932i
$320$	1.22590	+	0.359957i	0.0685300	+	0.0201222i
$321$	−14.8710	+	20.5606i	−0.830020	+	1.14758i
$322$	16.2409	+	15.2056i	0.905072	+	0.847373i
$323$			5.57817i			0.310378i
$324$	−9.07905	+	3.32725i	−0.504392	+	0.184847i
$325$	−16.3308	−	14.1507i	−0.905870	−	0.784941i
$326$	10.6598	−	16.5869i	0.590391	−	0.918666i
$327$	−7.33788	+	7.58289i	−0.405786	+	0.419335i
$328$	−4.00924	−	6.23850i	−0.221373	−	0.344463i
$329$	0.0991077	+	24.7958i	0.00546399	+	1.36704i
$330$	4.55619	+	51.7481i	0.250810	+	2.84864i
$331$	−0.557892	−	3.88022i	−0.0306645	−	0.213276i	0.968728	−	0.248125i	$-0.0798143\pi$
$331$	−0.557892	−	3.88022i	−0.0306645	−	0.213276i	−0.999393	+	0.0348483i	$0.988905\pi$
$332$	7.40239	−	16.2090i	0.406259	−	0.889584i
$333$	−12.2330	−	17.7270i	−0.670366	−	0.971432i
$334$	0.852150	+	2.90216i	0.0466276	+	0.158799i
$335$	−13.4265	+	29.3998i	−0.733566	+	1.60629i
$336$	−18.0386	+	14.0872i	−0.984085	+	0.768518i
$337$	−4.53815	−	5.23730i	−0.247209	−	0.285294i	0.618561	−	0.785737i	$-0.287716\pi$
$337$	−4.53815	−	5.23730i	−0.247209	−	0.285294i	−0.865770	+	0.500443i	$0.833171\pi$
$338$	−13.8769	+	6.33737i	−0.754804	+	0.344708i
$339$	0.517646	−	9.40558i	0.0281147	−	0.510841i
$340$	−1.27125	+	8.84172i	−0.0689431	+	0.479510i
$341$	−2.92201	−	1.87786i	−0.158236	−	0.101692i
$342$	−12.7890	−	5.34028i	−0.691547	−	0.288769i
$343$	0.222067	+	18.5189i	0.0119905	+	0.999928i
$344$			12.7211i			0.685873i
$345$	12.1922	−	30.2560i	0.656407	−	1.62893i
$346$			9.38221i			0.504391i
$347$	−5.04853	+	17.1937i	−0.271019	+	0.923006i	0.705705	+	0.708506i	$0.250631\pi$
$347$	−5.04853	+	17.1937i	−0.271019	+	0.923006i	−0.976724	+	0.214500i	$0.931188\pi$
$348$	−0.489109	−	2.08312i	−0.0262190	−	0.111667i
$349$	0.297783	−	0.463360i	0.0159400	−	0.0248031i	−0.833192	−	0.552984i	$-0.813489\pi$
$349$	0.297783	−	0.463360i	0.0159400	−	0.0248031i	0.849132	+	0.528181i	$0.177126\pi$
$350$	40.7746	+	25.9746i	2.17950	+	1.38840i
$351$	10.4025	−	2.80583i	0.555245	−	0.149764i
$352$	−9.97266	−	21.8371i	−0.531544	−	1.16392i
$353$	4.78208	+	5.51881i	0.254524	+	0.293737i	0.868604	−	0.495508i	$-0.165018\pi$
$353$	4.78208	+	5.51881i	0.254524	+	0.293737i	−0.614079	+	0.789244i	$0.710472\pi$
$354$	32.2086	+	16.9068i	1.71187	+	0.898584i
$355$	6.46187	+	2.95104i	0.342961	+	0.156625i
$356$	10.6053	−	3.11401i	0.562082	−	0.165042i
$357$	6.99904	+	6.71894i	0.370429	+	0.355604i
$358$	8.94920	−	19.5960i	0.472980	−	1.03568i
$359$	26.4331	−	3.80050i	1.39509	−	0.200583i	0.596572	−	0.802560i	$-0.296529\pi$
$359$	26.4331	−	3.80050i	1.39509	−	0.200583i	0.798513	+	0.601977i	$0.205620\pi$
$360$	16.4155	+	9.80340i	0.865175	+	0.516685i
$361$	5.00916	+	10.9685i	0.263640	+	0.577292i
$362$	8.52885	−	5.48116i	0.448267	−	0.288083i
$363$	−9.60348	+	9.92414i	−0.504052	+	0.520882i
$364$	−4.94566	+	3.20638i	−0.259223	+	0.168060i
$365$	−1.11376	−	0.965083i	−0.0582971	−	0.0505147i
$366$	7.69216	+	9.93137i	0.402076	+	0.519121i
$367$			15.3991i			0.803826i	0.915678	+	0.401913i	$0.131655\pi$
$367$			15.3991i			0.803826i	−0.915678	+	0.401913i	$0.868345\pi$
$368$	−1.01729	+	23.9310i	−0.0530298	+	1.24749i
$369$	−4.29168	−	13.0186i	−0.223416	−	0.677723i
$370$	13.9272	−	47.4319i	0.724043	−	2.46586i
$371$	−10.9179	−	23.6563i	−0.566831	−	1.22817i
$372$	1.38165	−	0.541331i	0.0716351	−	0.0280667i
$373$	−0.615332	+	4.27973i	−0.0318607	+	0.221596i	−0.999531	−	0.0306224i	$-0.990251\pi$
$373$	−0.615332	+	4.27973i	−0.0318607	+	0.221596i	0.967670	+	0.252218i	$0.0811602\pi$
$374$	−13.6029	+	8.74208i	−0.703391	+	0.452042i
$375$	7.24564	−	36.1559i	0.374163	−	1.86708i
$376$	−11.4952	+	9.96068i	−0.592822	+	0.513683i
$377$	0.339313	+	2.35997i	0.0174755	+	0.121545i
$378$	−22.1049	+	9.61416i	−1.13695	+	0.494499i
$379$	2.97530	−	0.873626i	0.152831	−	0.0448751i	−0.204422	−	0.978883i	$-0.565532\pi$
$379$	2.97530	−	0.873626i	0.152831	−	0.0448751i	0.357253	+	0.934008i	$0.383713\pi$
$380$	−3.13182	−	10.6660i	−0.160659	−	0.547154i
$381$	17.2991	−	9.81811i	0.886259	−	0.502997i
$382$	4.55311	+	31.6676i	0.232958	+	1.62026i
$383$	5.13446	+	5.92548i	0.262359	+	0.302778i	0.871611	−	0.490198i	$-0.163076\pi$
$383$	5.13446	+	5.92548i	0.262359	+	0.302778i	−0.609252	+	0.792977i	$0.708530\pi$
$384$	−19.6885	−	3.94558i	−1.00473	−	0.201347i
$385$	6.61966	+	44.7697i	0.337369	+	2.28167i
$386$	13.6481	+	1.96230i	0.694670	+	0.0998784i
$387$	−5.88049	+	22.7674i	−0.298922	+	1.15733i
$388$	−1.04007	−	0.901224i	−0.0528014	−	0.0457527i
$389$	−3.67734	+	12.5239i	−0.186449	+	0.634986i	0.812218	+	0.583355i	$0.198260\pi$
$389$	−3.67734	+	12.5239i	−0.186449	+	0.634986i	−0.998666	+	0.0516310i	$0.983558\pi$
$390$	20.0373	+	14.4925i	1.01463	+	0.733858i
$391$	10.1026	−	1.01686i	0.510908	−	0.0514249i
$392$	−8.52609	+	7.50807i	−0.430633	+	0.379215i
$393$	−5.41849	−	6.99583i	−0.273327	−	0.352893i
$394$	31.0956	−	35.8863i	1.56658	−	1.80792i
$395$	−4.95710	−	3.18574i	−0.249419	−	0.160292i
$396$	−2.45323	−	13.8236i	−0.123279	−	0.694661i
$397$	−6.27655	−	9.76650i	−0.315011	−	0.490166i	0.647256	−	0.762272i	$-0.275916\pi$
$397$	−6.27655	−	9.76650i	−0.315011	−	0.490166i	−0.962267	+	0.272106i	$0.912280\pi$
$398$	18.8714	+	41.3225i	0.945936	+	2.07131i
$399$	−11.3964	−	3.98755i	−0.570531	−	0.199627i
$400$	7.40735	+	51.5193i	0.370368	+	2.57596i
$401$	14.2020	+	6.48583i	0.709213	+	0.323887i	0.737156	−	0.675723i	$-0.236168\pi$
$401$	14.2020	+	6.48583i	0.709213	+	0.323887i	−0.0279428	+	0.999610i	$0.508896\pi$
$402$	8.34928	−	23.5596i	0.416424	−	1.17505i
$403$	−1.58647	+	0.465830i	−0.0790277	+	0.0232046i
$404$	−8.07729	+	17.6868i	−0.401860	+	0.879951i
$405$	24.8479	+	25.1339i	1.23470	+	1.24891i
$406$	−1.52328	−	5.11213i	−0.0755989	−	0.253711i
$407$	28.4461	−	12.9909i	1.41002	−	0.643936i
$408$	−0.327050	+	5.94247i	−0.0161914	+	0.294196i
$409$	28.4293	+	4.08751i	1.40574	+	0.202114i	0.803073	−	0.595881i	$-0.203197\pi$
$409$	28.4293	+	4.08751i	1.40574	+	0.202114i	0.602664	+	0.797995i	$0.294106\pi$
$410$	17.0097	−	26.4676i	0.840047	−	1.30714i
$411$	−8.77950	−	37.3920i	−0.433061	−	1.84441i
$412$	−0.247108	+	0.841573i	−0.0121741	+	0.0414613i
$413$	28.8789	+	13.0493i	1.42104	+	0.642115i
$414$	−7.34038	+	24.1354i	−0.360760	+	1.18619i
$415$	−65.1311			−3.19716
$416$	−10.9649	−	3.21960i	−0.537600	−	0.157854i
$417$	5.18044	+	22.0636i	0.253687	+	1.08046i
$418$	10.8791	−	16.9283i	0.532116	−	0.827988i
$419$	0.0885265	−	0.615715i	0.00432480	−	0.0300797i	−0.987545	−	0.157338i	$-0.949709\pi$
$419$	0.0885265	−	0.615715i	0.00432480	−	0.0300797i	0.991870	+	0.127259i	$0.0406178\pi$
$420$	−17.1551	−	8.91769i	−0.837085	−	0.435139i
$421$	2.67110	+	5.84889i	0.130181	+	0.285057i	0.963487	−	0.267755i	$-0.0862818\pi$
$421$	2.67110	+	5.84889i	0.130181	+	0.285057i	−0.833306	+	0.552813i	$0.813555\pi$
$422$	5.16737	−	4.47756i	0.251544	−	0.217964i
$423$	−25.1780	+	12.5132i	−1.22420	+	0.608415i
$424$	6.63922	−	14.5379i	0.322429	−	0.706021i
$425$	21.1700	−	6.21609i	1.02690	−	0.301524i
$426$	−5.17823	−	1.83511i	−0.250886	−	0.0889114i
$427$	7.19960	+	8.24199i	0.348413	+	0.398858i
$428$	15.5798	−	2.24004i	0.753080	−	0.108277i
$429$	1.37204	+	15.5833i	0.0662428	+	0.752370i
$430$	−49.0934	+	22.4202i	−2.36749	+	1.08120i
$431$	−12.6882	−	19.7432i	−0.611168	−	0.950997i	−0.999565	−	0.0295041i	$-0.990607\pi$
$431$	−12.6882	−	19.7432i	−0.611168	−	0.950997i	0.388396	−	0.921492i	$-0.373029\pi$
$432$	−23.3623	−	11.3009i	−1.12402	−	0.543713i
$433$	1.58321	−	2.46352i	0.0760842	−	0.118389i	−0.801126	−	0.598495i	$-0.795765\pi$
$433$	1.58321	−	2.46352i	0.0760842	−	0.118389i	0.877210	+	0.480106i	$0.159402\pi$
$434$	3.35878	−	1.55016i	0.161227	−	0.0744100i
$435$	−6.18329	+	4.78916i	−0.296466	+	0.229623i
$436$	6.54541			0.313468
$437$	−10.9104	+	6.37376i	−0.521914	+	0.304898i
$438$	0.923476	+	0.667931i	0.0441254	+	0.0319150i
$439$	−2.49644	+	8.50209i	−0.119148	+	0.405782i	−0.997371	−	0.0724706i	$-0.976912\pi$
$439$	−2.49644	+	8.50209i	−0.119148	+	0.405782i	0.878222	+	0.478253i	$0.158730\pi$
$440$	−18.1797	+	20.9805i	−0.866684	+	1.00021i
$441$	−18.7302	+	9.49622i	−0.891916	+	0.452201i
$442$	−1.09545	+	7.61901i	−0.0521051	+	0.362399i
$443$	7.85509	+	12.2228i	0.373206	+	0.580721i	0.976159	−	0.217056i	$-0.0696456\pi$
$443$	7.85509	+	12.2228i	0.373206	+	0.580721i	−0.602953	+	0.797777i	$0.706009\pi$
$444$	−2.62518	+	13.0997i	−0.124585	+	0.621683i
$445$	−26.4564	−	30.5323i	−1.25415	−	1.44737i
$446$	−6.95942	−	48.4038i	−0.329538	−	2.29199i
$447$	−5.34663	−	9.42054i	−0.252887	−	0.445576i
$448$	−0.852520	−	0.119098i	−0.0402778	−	0.00562685i
$449$	8.47484	+	28.8626i	0.399952	+	1.36211i	0.875838	+	0.482605i	$0.160309\pi$
$449$	8.47484	+	28.8626i	0.399952	+	1.36211i	−0.475886	+	0.879507i	$0.657872\pi$
$450$	−6.01573	+	54.4871i	−0.283584	+	2.56855i
$451$	19.7003	−	2.83248i	0.927652	−	0.133376i
$452$	−4.41593	+	3.82643i	−0.207708	+	0.179980i
$453$	2.94713	−	14.7062i	0.138468	−	0.690959i
$454$	−17.9970	−	28.0038i	−0.844639	−	1.31428i
$455$	18.1699	+	11.5748i	0.851820	+	0.542633i
$456$	−2.70183	−	6.89593i	−0.126525	−	0.322931i
$457$	11.6126	−	13.4017i	0.543215	−	0.626903i	−0.416074	−	0.909331i	$-0.636594\pi$
$457$	11.6126	−	13.4017i	0.543215	−	0.626903i	0.959289	+	0.282427i	$0.0911396\pi$
$458$	−13.0845	−	3.84195i	−0.611398	−	0.179523i
$459$	−3.33232	+	10.4843i	−0.155540	+	0.489366i
$460$	−18.7461	+	7.61633i	−0.874043	+	0.355113i
$461$	−11.0014			−0.512384			−0.256192	−	0.966626i	$-0.582468\pi$
$461$	−11.0014			−0.512384			−0.256192	+	0.966626i	$0.582468\pi$
$462$	−8.13626	−	34.0405i	−0.378533	−	1.58371i
$463$	−0.248210	+	0.286449i	−0.0115353	+	0.0133124i	−0.761488	−	0.648179i	$-0.775531\pi$
$463$	−0.248210	+	0.286449i	−0.0115353	+	0.0133124i	0.749953	+	0.661492i	$0.230076\pi$
$464$	3.10486	−	4.83126i	0.144140	−	0.224286i
$465$	−3.89768	−	3.77174i	−0.180750	−	0.174910i
$466$	7.65989	−	4.92271i	0.354838	−	0.228040i
$467$	4.74878	+	10.3984i	0.219747	+	0.481179i	0.987112	−	0.160032i	$-0.0511596\pi$
$467$	4.74878	+	10.3984i	0.219747	+	0.481179i	−0.767365	+	0.641211i	$0.778432\pi$
$468$	−5.73794	−	3.42671i	−0.265236	−	0.158400i
$469$	6.05130	−	20.9177i	0.279423	−	0.965892i
$470$	−58.7002	−	26.8075i	−2.70764	−	1.23654i
$471$	8.23083	−	23.2254i	0.379256	−	1.07017i
$472$	5.47674	+	18.6521i	0.252087	+	0.858530i
$473$	−31.0565	−	14.1830i	−1.42798	−	0.652136i
$474$	4.03491	+	2.11798i	0.185330	+	0.0972821i
$475$	−20.7509	+	17.9808i	−0.952117	+	0.825014i
$476$	−0.0240543	−	6.01817i	−0.00110253	−	0.275842i
$477$	18.6028	−	22.9500i	0.851766	−	1.05081i
$478$	−0.825282	+	5.73996i	−0.0377475	+	0.262540i
$479$	−24.9843	−	16.0564i	−1.14156	−	0.733638i	−0.173621	−	0.984813i	$-0.555547\pi$
$479$	−24.9843	−	16.0564i	−1.14156	−	0.733638i	−0.967942	+	0.251175i	$0.919183\pi$
$480$	−8.56877	−	36.4945i	−0.391109	−	1.66574i
$481$	4.19402	−	14.2835i	0.191231	−	0.651272i
$482$	7.89859			0.359771
$483$	−5.14433	+	21.3667i	−0.234075	+	0.972219i
$484$	8.56633			0.389379
$485$	−1.41716	+	4.82641i	−0.0643500	+	0.219156i
$486$	−20.8470	−	17.6772i	−0.945637	−	0.801852i
$487$	10.5736	+	6.79527i	0.479137	+	0.307923i	0.757824	−	0.652459i	$-0.226263\pi$
$487$	10.5736	+	6.79527i	0.479137	+	0.307923i	−0.278686	+	0.960382i	$0.589899\pi$
$488$	−0.955371	+	6.64475i	−0.0432476	+	0.300794i
$489$	19.4475	+	1.07031i	0.879446	+	0.0484013i
$490$	−44.0021	−	19.6715i	−1.98781	−	0.888668i
$491$	6.94084	−	6.01427i	0.313236	−	0.271420i	−0.484027	−	0.875053i	$-0.660826\pi$
$491$	6.94084	−	6.01427i	0.313236	−	0.271420i	0.797262	+	0.603633i	$0.206281\pi$
$492$	−3.95195	+	7.52876i	−0.178168	+	0.339423i
$493$	−2.21445	−	1.01131i	−0.0997339	−	0.0455470i
$494$	−2.69872	−	9.19100i	−0.121421	−	0.413523i
$495$	−42.2356	+	29.1459i	−1.89835	+	1.31001i
$496$	3.62275	+	1.65446i	0.162666	+	0.0742873i
$497$	−4.59757	−	1.33003i	−0.206229	−	0.0596600i
$498$	50.1754	−	4.41772i	2.24841	−	0.197963i
$499$	3.13363	+	6.86169i	0.140281	+	0.307171i	0.966712	−	0.255865i	$-0.0823603\pi$
$499$	3.13363	+	6.86169i	0.140281	+	0.307171i	−0.826432	+	0.563037i	$0.809633\pi$
$500$	−19.2423	+	12.3663i	−0.860544	+	0.553038i
$501$	−2.07776	+	2.14714i	−0.0928276	+	0.0959271i
$502$	−13.4615	+	20.9465i	−0.600817	+	0.934889i
$503$	7.65259	−	8.83156i	0.341212	−	0.393780i	−0.559046	−	0.829137i	$-0.688832\pi$
$503$	7.65259	−	8.83156i	0.341212	−	0.393780i	0.900258	+	0.435357i	$0.143378\pi$
$504$	−11.9068	−	4.91614i	−0.530373	−	0.218982i
$505$	71.0693			3.16254
$506$	−32.6417	−	16.6172i	−1.45110	−	0.738723i
$507$	−12.2107	−	8.83171i	−0.542294	−	0.392230i
$508$	−11.8386	−	3.47614i	−0.525254	−	0.154229i
$509$	2.96390	−	3.42052i	0.131372	−	0.151612i	−0.686252	−	0.727364i	$-0.740745\pi$
$509$	2.96390	−	3.42052i	0.131372	−	0.151612i	0.817624	+	0.575752i	$0.195291\pi$
$510$	−23.5097	+	9.21113i	−1.04103	+	0.407876i
$511$	0.837415	+	0.533457i	0.0370451	+	0.0235987i
$512$	6.11718	+	9.51851i	0.270344	+	0.420663i
$513$	−1.64785	−	13.5909i	−0.0727543	−	0.600053i
$514$	−14.8186	+	12.8404i	−0.653620	+	0.566365i
$515$	3.17326	−	0.456245i	0.139830	−	0.0201046i
$516$	12.6854	−	7.19963i	0.558445	−	0.316946i
$517$	−11.5011	−	39.1693i	−0.505819	−	1.72266i
$518$	−4.60807	+	32.9852i	−0.202467	+	1.44929i
$519$	−8.06031	+	4.57464i	−0.353809	+	0.200804i
$520$	1.88072	+	13.0807i	0.0824750	+	0.573626i
$521$	25.7972	+	29.7716i	1.13020	+	1.30432i	0.946998	+	0.321239i	$0.104099\pi$
$521$	25.7972	+	29.7716i	1.13020	+	1.30432i	0.183198	+	0.983076i	$0.441355\pi$
$522$	4.43862	−	4.10885i	0.194273	−	0.179840i
$523$	3.27180	+	5.09103i	0.143066	+	0.222615i	0.905390	−	0.424580i	$-0.139578\pi$
$523$	3.27180	+	5.09103i	0.143066	+	0.222615i	−0.762324	+	0.647195i	$0.775942\pi$
$524$	−0.781156	+	5.43306i	−0.0341250	+	0.237344i
$525$	−2.43375	+	47.6946i	−0.106218	+	2.08156i
$526$	3.09122	−	3.56746i	0.134784	−	0.155549i
$527$	0.475639	−	1.61988i	0.0207192	−	0.0705630i
$528$	22.0829	−	30.5317i	0.961037	−	1.32872i
$529$	13.5323	+	18.5978i	0.588362	+	0.808598i
$530$	67.8061			2.94531
$531$	1.17979	+	35.9141i	0.0511984	+	1.55854i
$532$	3.13842	+	6.80011i	0.136068	+	0.294822i
$533$	5.12225	−	7.97038i	0.221869	−	0.345235i
$534$	22.4523	+	21.7268i	0.971604	+	0.940211i
$535$	−31.1038	−	48.3985i	−1.34473	−	2.09245i
$536$	12.1504	−	5.54890i	0.524817	−	0.239676i
$537$	21.1986	−	1.86644i	0.914786	−	0.0805428i
$538$	−32.8368	+	4.72122i	−1.41570	+	0.203546i
$539$	−8.82383	−	29.1861i	−0.380069	−	1.25713i
$540$	0.485389	−	21.9179i	0.0208878	−	0.943197i
$541$	23.0596	−	6.77089i	0.991407	−	0.291104i	0.254482	−	0.967078i	$-0.418095\pi$
$541$	23.0596	−	6.77089i	0.991407	−	0.291104i	0.736925	+	0.675974i	$0.236277\pi$
$542$	−12.9648	+	28.3889i	−0.556884	+	1.21941i
$543$	8.86745	+	4.65465i	0.380539	+	0.199750i
$544$	8.81845	−	7.64123i	0.378088	−	0.327615i
$545$	−9.93843	−	21.7621i	−0.425715	−	0.932187i
$546$	−14.7828	−	7.68447i	−0.632644	−	0.328865i
$547$	−4.43844	+	30.8701i	−0.189774	+	1.31991i	0.642817	+	0.766020i	$0.277766\pi$
$547$	−4.43844	+	30.8701i	−0.189774	+	1.31991i	−0.832591	+	0.553888i	$0.813143\pi$
$548$	−12.8808	+	20.0429i	−0.550240	+	0.856191i
$549$	−4.78150	+	11.4508i	−0.204070	+	0.488707i
$550$	−76.3687	−	22.4239i	−3.25637	−	0.956157i
$551$	3.02956			0.129064
$552$	−11.9966	+	6.15033i	−0.510609	+	0.261776i
$553$	3.61779	+	1.63474i	0.153844	+	0.0695164i
$554$	0.621268	−	2.11585i	0.0263952	−	0.0898937i
$555$	47.5397	−	11.1621i	2.01795	−	0.473806i
$556$	7.60045	−	11.8265i	0.322331	−	0.501557i
$557$	−9.76400	−	1.40385i	−0.413714	−	0.0594831i	−0.0676845	−	0.997707i	$-0.521561\pi$
$557$	−9.76400	−	1.40385i	−0.413714	−	0.0594831i	−0.346029	+	0.938224i	$0.612470\pi$
$558$	3.25850	+	2.64128i	0.137943	+	0.111814i
$559$	−14.7839	+	6.75156i	−0.625291	+	0.285561i
$560$	−14.8185	−	49.7310i	−0.626197	−	2.10152i
$561$	−14.1430	−	7.42385i	−0.597117	−	0.313435i
$562$	−8.12881	+	17.7996i	−0.342893	+	0.750831i
$563$	−38.5829	+	11.3290i	−1.62608	+	0.477459i	−0.962642	−	0.270776i	$-0.912720\pi$
$563$	−38.5829	+	11.3290i	−1.62608	+	0.477459i	−0.663433	+	0.748235i	$0.730901\pi$
$564$	16.4386	+	5.82568i	0.692192	+	0.245306i
$565$	19.4271	+	8.87208i	0.817306	+	0.373251i
$566$	−6.54736	−	45.5379i	−0.275206	−	1.91410i
$567$	−19.0376	−	14.3027i	−0.799506	−	0.600659i
$568$	−1.21961	−	2.67057i	−0.0511736	−	0.112055i
$569$	−5.27101	−	8.20185i	−0.220972	−	0.343839i	0.713013	−	0.701151i	$-0.247330\pi$
$569$	−5.27101	−	8.20185i	−0.220972	−	0.343839i	−0.933985	+	0.357311i	$0.883694\pi$
$570$	21.8511	−	22.5807i	0.915241	−	0.945800i
$571$	21.8008	+	14.0105i	0.912335	+	0.586322i	0.910424	−	0.413676i	$-0.135755\pi$
$571$	21.8008	+	14.0105i	0.912335	+	0.586322i	0.00191087	+	0.999998i	$0.499392\pi$
$572$	6.35459	−	7.33359i	0.265699	−	0.306633i
$573$	−24.9858	+	19.3523i	−1.04380	+	0.808454i
$574$	−8.72842	+	19.3165i	−0.364317	+	0.806256i
$575$	36.3475	+	34.3040i	1.51580	+	1.43057i
$576$	−0.305586	−	0.926983i	−0.0127328	−	0.0386243i
$577$	−3.19919	+	10.8954i	−0.133184	+	0.453583i	−0.998897	−	0.0469579i	$-0.985047\pi$
$577$	−3.19919	+	10.8954i	−0.133184	+	0.453583i	0.865713	+	0.500541i	$0.166866\pi$
$578$	16.5874	+	14.3731i	0.689944	+	0.597840i
$579$	4.96880	+	12.6819i	0.206496	+	0.527044i
$580$	4.80203	+	0.690428i	0.199394	+	0.0286685i
$581$	43.4090	−	6.41847i	1.80091	−	0.266283i
$582$	0.764380	−	3.81427i	0.0316846	−	0.158106i
$583$	28.0897	+	32.4173i	1.16336	+	1.34259i
$584$	0.0866785	+	0.602862i	0.00358678	+	0.0249466i
$585$	−2.68072	+	24.2805i	−0.110834	+	1.00387i
$586$	5.72124	+	19.4848i	0.236342	+	0.804908i
$587$	−1.69326	+	0.497186i	−0.0698884	+	0.0205211i	−0.316490	−	0.948596i	$-0.602504\pi$
$587$	−1.69326	+	0.497186i	−0.0698884	+	0.0205211i	0.246601	+	0.969117i	$0.420686\pi$
$588$	12.3125	+	4.25294i	0.507758	+	0.175388i
$589$	0.298999	+	2.07958i	0.0123200	+	0.0856878i
$590$	−62.3299	+	54.0092i	−2.56608	+	2.22352i
$591$	45.9919	+	9.21679i	1.89185	+	0.379128i
$592$	−30.1650	+	19.3859i	−1.23977	+	0.796755i
$593$	4.26622	−	29.6722i	0.175192	−	1.21849i	−0.692511	−	0.721408i	$-0.743495\pi$
$593$	4.26622	−	29.6722i	0.175192	−	1.21849i	0.867703	−	0.497083i	$-0.165595\pi$
$594$	30.5603	−	25.3181i	1.25391	−	1.03881i
$595$	−19.9726	+	9.21785i	−0.818798	+	0.377895i
$596$	−1.89299	+	6.44695i	−0.0775401	+	0.264077i
$597$	−26.2990	+	36.3608i	−1.07635	+	1.48815i
$598$	−16.1538	+	6.56308i	−0.660576	+	0.268384i
$599$			7.98304i			0.326178i	0.986611	+	0.163089i	$0.0521458\pi$
$599$			7.98304i			0.326178i	−0.986611	+	0.163089i	$0.947854\pi$
$600$	−23.1603	+	17.9384i	−0.945517	+	0.732333i
$601$	12.9208	+	11.1959i	0.527049	+	0.456691i	0.877284	−	0.479971i	$-0.159353\pi$
$601$	12.9208	+	11.1959i	0.527049	+	0.456691i	−0.350235	+	0.936662i	$0.613898\pi$
$602$	30.5106	−	19.7808i	1.24352	−	0.806204i
$603$	24.3112	−	4.31443i	0.990028	−	0.175697i
$604$	−7.82673	+	5.02994i	−0.318465	+	0.204665i
$605$	−13.0070	−	28.4813i	−0.528808	−	1.15793i
$606$	−54.7500	+	4.82049i	−2.22407	+	0.195819i
$607$	34.0039	−	4.88902i	1.38017	−	0.198439i	0.588063	−	0.808815i	$-0.299891\pi$
$607$	34.0039	−	4.88902i	1.38017	−	0.198439i	0.792112	+	0.610376i	$0.208982\pi$
$608$	−6.03221	+	13.2087i	−0.244638	+	0.535683i
$609$	3.64913	−	3.80126i	0.147870	−	0.154035i
$610$	−27.3274	+	8.02404i	−1.10645	+	0.324884i
$611$	−17.6768	−	8.07275i	−0.715129	−	0.326588i
$612$	6.11092	−	3.03707i	0.247019	−	0.122766i
$613$	20.0784	+	23.1717i	0.810960	+	0.935898i	0.998929	−	0.0462772i	$-0.0147358\pi$
$613$	20.0784	+	23.1717i	0.810960	+	0.935898i	−0.187969	+	0.982175i	$0.560190\pi$
$614$	8.84113	+	19.3594i	0.356799	+	0.781281i
$615$	31.0321	+	1.70789i	1.25134	+	0.0688686i
$616$	10.0490	−	15.7748i	0.404885	−	0.635584i
$617$	21.6893	−	33.7491i	0.873177	−	1.35869i	−0.0595955	−	0.998223i	$-0.518981\pi$
$617$	21.6893	−	33.7491i	0.873177	−	1.35869i	0.932772	−	0.360467i	$-0.117383\pi$
$618$	−2.41365	+	0.566716i	−0.0970913	+	0.0227967i
$619$	7.07086	−	24.0812i	0.284202	−	0.967903i	−0.686402	−	0.727222i	$-0.740811\pi$
$619$	7.07086	−	24.0812i	0.284202	−	0.967903i	0.970604	−	0.240681i	$-0.0773708\pi$
$620$			3.36440i			0.135118i
$621$	−24.3139	+	5.46193i	−0.975685	+	0.219180i
$622$		−	37.6931i		−	1.51135i
$623$	20.6417	+	17.7422i	0.826991	+	0.710825i
$624$	−4.10009	−	17.4624i	−0.164135	−	0.699054i
$625$	26.4976	+	17.0290i	1.05990	+	0.681158i
$626$	2.79266	−	19.4234i	0.111617	−	0.776314i
$627$	19.8477	+	1.09234i	0.792640	+	0.0436238i
$628$	−13.9034	+	6.34947i	−0.554806	+	0.253371i
$629$	9.95388	+	11.4874i	0.396887	+	0.458032i
$630$	−2.01269	−	54.6156i	−0.0801877	−	2.17594i
$631$	7.70840	−	16.8791i	0.306867	−	0.671944i	−0.691879	−	0.722013i	$-0.743217\pi$
$631$	7.70840	−	16.8791i	0.306867	−	0.671944i	0.998746	+	0.0500690i	$0.0159441\pi$
$632$	0.686094	+	2.33662i	0.0272914	+	0.0929458i
$633$	6.36623	+	2.25613i	0.253035	+	0.0896730i
$634$	17.5267	−	38.3781i	0.696074	−	1.52419i
$635$	6.41813	+	44.6391i	0.254696	+	1.77145i
$636$	−18.2547	+	1.60724i	−0.723846	+	0.0637314i
$637$	−13.2507	−	5.92383i	−0.525011	−	0.234711i
$638$	4.74792	+	7.38790i	0.187972	+	0.292490i
$639$	−0.948279	−	5.34342i	−0.0375134	−	0.211382i
$640$	24.6135	−	38.2993i	0.972932	−	1.51391i
$641$	−17.4903	−	15.1554i	−0.690826	−	0.598604i	0.237048	−	0.971498i	$-0.423820\pi$
$641$	−17.4903	−	15.1554i	−0.690826	−	0.598604i	−0.927874	+	0.372894i	$0.878366\pi$
$642$	27.2444	+	35.1753i	1.07525	+	1.38826i
$643$		−	26.5828i		−	1.04832i	−0.851619	−	0.524162i	$-0.824379\pi$
$643$		−	26.5828i		−	1.04832i	0.851619	−	0.524162i	$-0.175621\pi$
$644$	11.7435	−	6.92356i	0.462758	−	0.272826i
$645$	−43.1986	−	31.2446i	−1.70094	−	1.23026i
$646$	9.38454	+	2.75555i	0.369230	+	0.108416i
$647$	−14.4258	+	16.6483i	−0.567137	+	0.654511i	−0.964789	−	0.263025i	$-0.915280\pi$
$647$	−14.4258	+	16.6483i	−0.567137	+	0.654511i	0.397652	+	0.917536i	$0.369825\pi$
$648$	−0.958627	−	14.5751i	−0.0376584	−	0.572565i
$649$	−51.6422	−	7.42503i	−2.02714	−	0.291458i
$650$	−31.8740	+	20.4842i	−1.25020	+	0.803455i
$651$	2.96944	+	2.12971i	0.116382	+	0.0834700i
$652$	−7.91173	−	9.13062i	−0.309847	−	0.357583i
$653$	−20.6295	+	2.96607i	−0.807293	+	0.116071i	−0.533590	−	0.845743i	$-0.679158\pi$
$653$	−20.6295	+	2.96607i	−0.807293	+	0.116071i	−0.273703	+	0.961814i	$0.588248\pi$
$654$	9.13240	+	16.0909i	0.357105	+	0.629204i
$655$	19.2499	−	5.65227i	0.752155	−	0.220853i
$656$	−21.8966	+	6.42943i	−0.854919	+	0.251027i
$657$	−0.123549	+	1.11904i	−0.00482011	+	0.0436578i
$658$	41.7647	+	12.0821i	1.62816	+	0.471010i
$659$	−28.8363	+	24.9868i	−1.12330	+	0.973347i	−0.999819	−	0.0189995i	$-0.993952\pi$
$659$	−28.8363	+	24.9868i	−1.12330	+	0.973347i	−0.123483	+	0.992347i	$0.539406\pi$
$660$	31.2108	+	6.25464i	1.21488	+	0.243462i
$661$	−12.1371	−	18.8857i	−0.472078	−	0.734568i	0.520803	−	0.853677i	$-0.325633\pi$
$661$	−12.1371	−	18.8857i	−0.472078	−	0.734568i	−0.992881	+	0.119109i	$0.961996\pi$
$662$	−6.80356	−	0.978205i	−0.264428	−	0.0380190i
$663$	−7.07966	+	2.77382i	−0.274951	+	0.107726i
$664$	20.3429	+	17.6272i	0.789456	+	0.684068i
$665$	17.8436	−	20.7597i	0.691946	−	0.805028i
$666$	−35.8663	+	11.8236i	−1.38979	+	0.458154i
$667$	−0.552268	−	5.48681i	−0.0213839	−	0.212450i
$668$	1.85337			0.0717090
$669$	38.1907	−	29.5799i	1.47654	−	1.14363i
$670$	42.8289	+	37.1114i	1.65462	+	1.43374i
$671$	−15.1570	−	9.74079i	−0.585128	−	0.376039i
$672$	9.30739	+	23.4787i	0.359040	+	0.905710i
$673$	−0.390287	+	0.250822i	−0.0150445	+	0.00966849i	−0.548141	−	0.836386i	$-0.684664\pi$
$673$	−0.390287	+	0.250822i	−0.0150445	+	0.00966849i	0.533097	+	0.846054i	$0.321028\pi$
$674$	−11.0529	+	5.04767i	−0.425740	+	0.194429i
$675$	−49.7434	+	21.3990i	−1.91462	+	0.823648i
$676$	1.33033	+	9.25266i	0.0511666	+	0.355872i
$677$	−13.6329	+	29.8518i	−0.523954	+	1.14730i	0.443967	+	0.896043i	$0.353571\pi$
$677$	−13.6329	+	29.8518i	−0.523954	+	1.14730i	−0.967921	+	0.251256i	$0.919156\pi$
$678$	−15.5680	−	5.51712i	−0.597884	−	0.211884i
$679$	0.468892	−	3.35639i	0.0179944	−	0.128807i
$680$	−12.2741	−	5.60540i	−0.470690	−	0.214957i
$681$	15.2832	−	29.1156i	0.585652	−	1.11571i
$682$	−4.60269	+	3.98826i	−0.176246	+	0.152718i
$683$	17.3463	−	7.92179i	0.663738	−	0.303119i	−0.0549120	−	0.998491i	$-0.517488\pi$
$683$	17.3463	−	7.92179i	0.663738	−	0.303119i	0.718650	+	0.695372i	$0.244761\pi$
$684$	−5.34748	+	6.59709i	−0.204466	+	0.252246i
$685$	86.1964	+	12.3932i	3.29340	+	0.473519i
$686$	31.2654	+	8.77453i	1.19372	+	0.335013i
$687$	−3.07917	−	13.1142i	−0.117478	−	0.500339i
$688$	37.5619	+	11.0292i	1.43203	+	0.420483i
$689$	20.4190			0.777901
$690$	−44.8789	−	35.4579i	−1.70851	−	1.34986i
$691$		−	38.1537i		−	1.45144i	−0.687992	−	0.725718i	$-0.741508\pi$
$691$		−	38.1537i		−	1.45144i	0.687992	−	0.725718i	$-0.258492\pi$
$692$	5.51608	+	1.61967i	0.209690	+	0.0615705i
$693$	25.2772	−	23.5876i	0.960202	−	0.896017i
$694$	26.4323	+	16.9870i	1.00335	+	0.644817i
$695$	−50.8611	−	7.31272i	−1.92927	−	0.277387i
$696$	3.22742	+	0.177624i	0.122335	+	0.00673284i
$697$	4.01869	+	8.79970i	0.152219	+	0.333313i
$698$	−0.632441	−	0.729876i	−0.0239382	−	0.0276262i
$699$	7.96399	+	4.18041i	0.301226	+	0.158118i
$700$	22.3102	−	19.4886i	0.843246	−	0.736598i
$701$	4.73080	+	16.1116i	0.178680	+	0.608528i	0.999313	+	0.0370718i	$0.0118030\pi$
$701$	4.73080	+	16.1116i	0.178680	+	0.608528i	−0.820633	+	0.571456i	$0.806379\pi$
$702$	0.418265	−	18.8869i	0.0157864	−	0.712840i
$703$	−17.2064	−	7.85788i	−0.648950	−	0.296365i
$704$	1.40275	−	0.201685i	0.0528680	−	0.00760128i
$705$	−5.59095	−	63.5007i	−0.210567	−	2.39157i
$706$	11.6470	−	5.31900i	0.438340	−	0.200183i
$707$	−47.3668	+	7.00366i	−1.78141	+	0.263400i
$708$	15.5002	−	16.0177i	0.582533	−	0.601984i
$709$	−37.5606	−	24.1388i	−1.41062	−	0.906550i	−0.410633	−	0.911801i	$-0.634692\pi$
$709$	−37.5606	−	24.1388i	−1.41062	−	0.906550i	−0.999986	+	0.00525099i	$0.998329\pi$
$710$	8.15683	−	9.41348i	0.306120	−	0.353282i
$711$	0.147797	+	4.49911i	0.00554282	+	0.168730i
$712$			16.6965i			0.625730i
$713$	3.71180	−	0.920607i	0.139008	−	0.0344770i
$714$	14.7612	−	8.45590i	0.552423	−	0.316454i
$715$	−34.0313	−	9.99250i	−1.27270	−	0.373698i
$716$	−9.97616	−	8.64439i	−0.372826	−	0.323056i
$717$	−5.33363	+	2.08972i	−0.199188	+	0.0780421i
$718$	6.66378	−	46.3476i	0.248690	−	1.72968i
$719$	21.4250	−	13.7690i	0.799018	−	0.513498i	−0.0762773	−	0.997087i	$-0.524303\pi$
$719$	21.4250	−	13.7690i	0.799018	−	0.513498i	0.875295	+	0.483589i	$0.160667\pi$
$720$	43.1791	−	39.9711i	1.60919	−	1.48964i
$721$	−2.06997	+	0.616796i	−0.0770898	+	0.0229707i
$722$	20.9276	−	3.00894i	0.778845	−	0.111981i
$723$	3.85124	+	6.78573i	0.143229	+	0.252364i
$724$	−1.75018	−	5.96058i	−0.0650451	−	0.221523i
$725$	−3.37602	−	11.4977i	−0.125382	−	0.427013i
$726$	11.9521	+	21.0590i	0.443583	+	0.781573i
$727$	−25.0116	+	3.59613i	−0.927630	+	0.133373i	−0.589538	−	0.807740i	$-0.700690\pi$
$727$	−25.0116	+	3.59613i	−0.927630	+	0.133373i	−0.338091	+	0.941113i	$0.609781\pi$
$728$	−2.54254	−	8.53277i	−0.0942327	−	0.316245i
$729$	5.02185	−	26.5289i	0.185995	−	0.982551i
$730$	−2.17381	+	1.39702i	−0.0804564	+	0.0517062i
$731$	2.36169	−	16.4259i	0.0873502	−	0.607534i
$732$	7.16685	−	2.80798i	0.264894	−	0.103786i
$733$	14.2923	+	12.3844i	0.527899	+	0.457427i	0.877572	−	0.479445i	$-0.159162\pi$
$733$	14.2923	+	12.3844i	0.527899	+	0.457427i	−0.349673	+	0.936872i	$0.613707\pi$
$734$	25.9070	+	7.60697i	0.956243	+	0.280778i
$735$	−4.55490	−	47.3940i	−0.168010	−	1.74815i
$736$	25.0217	+	8.51700i	0.922313	+	0.313941i
$737$			35.8499i			1.32055i
$738$	−24.0222	+	0.789136i	−0.884270	+	0.0290485i
$739$	−25.1922	+	29.0734i	−0.926711	+	1.06948i	0.0706952	+	0.997498i	$0.477478\pi$
$739$	−25.1922	+	29.0734i	−0.926711	+	1.06948i	−0.997406	+	0.0719832i	$0.977067\pi$
$740$	−25.4823	−	16.3765i	−0.936747	−	0.602011i
$741$	6.58018	−	6.79989i	0.241729	−	0.249800i
$742$	−45.1919	+	6.68208i	−1.65905	+	0.245307i
$743$	−46.1236	+	21.0639i	−1.69211	+	0.772761i	−0.693479	+	0.720477i	$0.743923\pi$
$743$	−46.1236	+	21.0639i	−1.69211	+	0.772761i	−0.998632	+	0.0522843i	$0.983350\pi$
$744$	0.196599	+	2.23293i	0.00720768	+	0.0818631i
$745$	24.3090	−	3.49511i	0.890614	−	0.128051i
$746$	6.89612	+	3.14935i	0.252485	+	0.115306i
$747$	28.2601	+	40.9519i	1.03398	+	1.49835i
$748$	2.79143	+	9.50672i	0.102065	+	0.347600i
$749$	25.4998	+	29.1918i	0.931742	+	1.06664i
$750$	−57.2483	−	30.0504i	−2.09041	−	1.09729i
$751$	−10.2690	−	11.8511i	−0.374721	−	0.432451i	0.536797	−	0.843711i	$-0.319634\pi$
$751$	−10.2690	−	11.8511i	−0.374721	−	0.432451i	−0.911518	+	0.411260i	$0.865089\pi$
$752$	19.4448	+	42.5783i	0.709081	+	1.55267i
$753$	−24.5589	−	1.35163i	−0.894977	−	0.0492560i
$754$	4.13797	+	0.594950i	0.150696	+	0.0216668i
$755$	28.6074	+	18.3849i	1.04113	+	0.669095i
$756$	1.83644	+	14.6558i	0.0667906	+	0.533028i
$757$	7.43347	+	2.18266i	0.270174	+	0.0793303i	0.414013	−	0.910271i	$-0.364127\pi$
$757$	7.43347	+	2.18266i	0.270174	+	0.0793303i	−0.143839	+	0.989601i	$0.545945\pi$
$758$		−	5.43711i		−	0.197485i
$759$	−1.63977	−	36.1450i	−0.0595200	−	1.31198i
$760$	16.7920			0.609111
$761$	−36.8409	−	10.8175i	−1.33548	−	0.392133i	−0.465427	−	0.885086i	$-0.654099\pi$
$761$	−36.8409	−	10.8175i	−1.33548	−	0.392133i	−0.870056	+	0.492953i	$0.835917\pi$
$762$	−7.97215	−	33.9535i	−0.288800	−	1.23001i
$763$	8.76842	+	13.5248i	0.317438	+	0.489629i
$764$	19.4043	+	2.78992i	0.702023	+	0.100936i
$765$	−19.3763	−	15.7061i	−0.700553	−	0.567855i
$766$	12.5052	−	5.71094i	0.451832	−	0.206345i
$767$	−18.7699	+	16.2642i	−0.677742	+	0.587266i
$768$	−15.8400	+	30.1764i	−0.571577	+	1.08890i
$769$	−40.9640	−	18.7076i	−1.47720	−	0.674614i	−0.496125	−	0.868251i	$-0.665244\pi$
$769$	−40.9640	−	18.7076i	−1.47720	−	0.674614i	−0.981073	+	0.193637i	$0.937972\pi$
$770$	78.5892	+	10.9790i	2.83216	+	0.395656i
$771$	−18.2566	−	6.46995i	−0.657495	−	0.233009i
$772$	3.50978	−	7.68536i	0.126320	−	0.276602i
$773$	1.71668	+	11.9398i	0.0617446	+	0.429443i	0.997123	+	0.0757956i	$0.0241496\pi$
$773$	1.71668	+	11.9398i	0.0617446	+	0.429443i	−0.935379	+	0.353647i	$0.884941\pi$
$774$	35.3984	+	21.1400i	1.27237	+	0.759862i
$775$	7.55916	−	3.45215i	0.271533	−	0.124005i
$776$	1.74886	−	1.12392i	0.0627804	−	0.0403465i
$777$	−30.5846	+	12.1243i	−1.09722	+	0.434957i
$778$	19.2532	+	12.3733i	0.690261	+	0.443604i
$779$	−9.09829	−	7.88371i	−0.325980	−	0.282463i
$780$	11.9796	−	9.27862i	0.428940	−	0.332228i
$781$	7.87956			0.281953
$782$	3.27981	−	17.4985i	0.117286	−	0.625747i
$783$	5.69414	+	1.80982i	0.203492	+	0.0646777i
$784$	14.7772	+	31.6848i	0.527757	+	1.13160i
$785$	42.2213	+	36.5850i	1.50694	+	1.30577i
$786$	−14.4462	+	5.66005i	−0.515280	+	0.201887i
$787$	49.9200	+	7.17741i	1.77946	+	0.255847i	0.952090	−	0.305817i	$-0.0989294\pi$
$787$	49.9200	+	7.17741i	1.77946	+	0.255847i	0.827366	+	0.561664i	$0.189839\pi$
$788$	−15.7305	−	24.4771i	−0.560376	−	0.871962i
$789$	4.57206	+	0.916241i	0.162770	+	0.0326191i
$790$	−7.80834	+	6.76596i	−0.277808	+	0.240722i
$791$	−13.8222	−	3.99864i	−0.491463	−	0.142175i
$792$	21.0798	+	2.32735i	0.749040	+	0.0826989i
$793$	−8.22930	+	2.41634i	−0.292231	+	0.0858068i
$794$	−19.5314	+	5.73494i	−0.693143	+	0.203525i
$795$	33.0613	+	58.2526i	1.17256	+	2.06601i
$796$	27.5525	−	3.96145i	0.976573	−	0.140410i
$797$	−24.4018	−	28.1611i	−0.864355	−	0.997518i	−0.999977	−	0.00675771i	$-0.997849\pi$
$797$	−24.4018	−	28.1611i	−0.864355	−	0.997518i	0.135623	−	0.990761i	$-0.456697\pi$
$798$	−12.3382	+	17.2031i	−0.436767	+	0.608982i
$799$	16.6923	−	10.7275i	0.590531	−	0.379511i
$800$	56.8511	+	8.17396i	2.00999	+	0.288993i
$801$	−7.71821	+	29.8826i	−0.272710	+	1.05585i
$802$	17.9272	−	20.6891i	0.633030	−	0.730556i
$803$	−1.56843	−	0.460534i	−0.0553489	−	0.0162519i
$804$	−12.4100	−	8.97591i	−0.437668	−	0.316556i
$805$	−40.8505	−	28.5320i	−1.43979	−	1.00562i
$806$			2.89914i			0.102118i
$807$	−20.0668	−	25.9083i	−0.706385	−	0.912015i
$808$	−22.1976	−	19.2343i	−0.780908	−	0.676661i
$809$	−4.79537	+	7.46175i	−0.168596	+	0.262341i	−0.915263	−	0.402858i	$-0.868017\pi$
$809$	−4.79537	+	7.46175i	−0.168596	+	0.262341i	0.746666	+	0.665199i	$0.231653\pi$
$810$	54.5591	−	29.3874i	1.91701	−	1.03257i
$811$	14.3655	+	22.3532i	0.504441	+	0.784926i	0.996318	−	0.0857393i	$-0.0273252\pi$
$811$	14.3655	+	22.3532i	0.504441	+	0.784926i	−0.491877	+	0.870665i	$0.663689\pi$
$812$	−3.26853	+	0.0130642i	−0.114703	+	0.000458462i
$813$	−30.7105	+	2.70392i	−1.07706	+	0.0948306i
$814$	−7.80347	−	54.2743i	−0.273511	−	1.90231i
$815$	−18.3444	+	40.1686i	−0.642576	+	1.40704i
$816$	17.2630	+	6.11781i	0.604325	+	0.214166i
$817$	5.81820	+	19.8150i	0.203553	+	0.693238i
$818$	20.9204	−	45.8093i	0.731465	−	1.60169i
$819$	−0.606098	−	16.4468i	−0.0211788	−	0.574698i
$820$	−12.6246	−	14.5696i	−0.440872	−	0.508793i
$821$	39.6203	−	18.0940i	1.38276	−	0.631485i	0.421423	−	0.906864i	$-0.361531\pi$
$821$	39.6203	−	18.0940i	1.38276	−	0.631485i	0.961336	+	0.275380i	$0.0888036\pi$
$822$	−67.2442	−	3.70086i	−2.34541	−	0.129082i
$823$	7.44774	−	51.8002i	0.259612	−	1.80564i	−0.275981	−	0.961163i	$-0.589003\pi$
$823$	7.44774	−	51.8002i	0.259612	−	1.80564i	0.535592	−	0.844477i	$-0.320088\pi$
$824$	−1.11460	−	0.716313i	−0.0388291	−	0.0249539i
$825$	−17.9718	−	76.5424i	−0.625699	−	2.66486i
$826$	36.2197	−	42.1389i	1.26024	−	1.46620i
$827$			1.94824i			0.0677468i	0.999426	+	0.0338734i	$0.0107843\pi$
$827$			1.94824i			0.0677468i	−0.999426	+	0.0338734i	$0.989216\pi$
$828$	12.9227	+	8.48216i	0.449096	+	0.294775i
$829$		−	3.09702i		−	0.107564i	−0.998553	−	0.0537820i	$-0.982872\pi$
$829$		−	3.09702i		−	0.107564i	0.998553	−	0.0537820i	$-0.0171276\pi$
$830$	−32.1740	+	109.575i	−1.11678	+	3.80339i
$831$	2.12066	−	0.497922i	0.0735648	−	0.0172727i
$832$	0.364726	−	0.567525i	0.0126446	−	0.0196754i
$833$	12.4031	−	8.11181i	0.429742	−	0.281058i
$834$	39.6781	+	2.18373i	1.37394	+	0.0756164i
$835$	−2.81412	−	6.16207i	−0.0973867	−	0.213247i
$836$	−8.07453	−	9.31851i	−0.279264	−	0.322287i
$837$	−0.680340	+	4.08725i	−0.0235160	+	0.141276i
$838$	−0.992130	−	0.453090i	−0.0342725	−	0.0156517i
$839$	43.7662	−	12.8509i	1.51098	−	0.443663i	0.581812	−	0.813324i	$-0.302344\pi$
$839$	43.7662	−	12.8509i	1.51098	−	0.443663i	0.929167	+	0.369660i	$0.120526\pi$
$840$	20.2261	−	21.0693i	0.697867	−	0.726961i
$841$	11.4978	−	25.1766i	0.396475	−	0.868160i
$842$	11.1595	−	1.60449i	0.384581	−	0.0552944i
$843$	−19.2552	+	1.69534i	−0.663186	+	0.0583905i
$844$	−1.74043	−	3.81102i	−0.0599082	−	0.131181i
$845$	28.7432	−	18.4721i	0.988797	−	0.635461i
$846$	8.61425	+	48.5401i	0.296164	+	1.66884i
$847$	11.4757	+	17.7006i	0.394310	+	0.608199i
$848$	−37.1702	−	32.2082i	−1.27643	−	1.10603i
$849$	35.9294	−	27.8285i	1.23310	−	0.955072i
$850$		−	38.6865i		−	1.32694i
$851$	−11.0947	+	32.5946i	−0.380322	+	1.11733i
$852$	−1.97284	+	2.72763i	−0.0675884	+	0.0934472i
$853$	5.36448	−	18.2697i	0.183676	−	0.625544i	−0.815245	−	0.579116i	$-0.803398\pi$
$853$	5.36448	−	18.2697i	0.183676	−	0.625544i	0.998922	−	0.0464284i	$-0.0147839\pi$
$854$	17.4226	−	8.04094i	0.596189	−	0.275155i
$855$	30.0535	+	7.76236i	1.02781	+	0.265467i
$856$	−3.38377	+	23.5346i	−0.115655	+	0.804397i
$857$	17.2739	−	11.1013i	0.590065	−	0.379212i	−0.211270	−	0.977428i	$-0.567760\pi$
$857$	17.2739	−	11.1013i	0.590065	−	0.379212i	0.801335	+	0.598216i	$0.204124\pi$
$858$	26.8947	+	5.38970i	0.918169	+	0.184001i
$859$	38.0162	−	32.9412i	1.29710	−	1.12394i	0.312346	−	0.949968i	$-0.398885\pi$
$859$	38.0162	−	32.9412i	1.29710	−	1.12394i	0.984751	−	0.173972i	$-0.0556603\pi$
$860$	4.70642	+	32.7338i	0.160487	+	1.11621i
$861$	−20.8508	+	1.91983i	−0.710593	+	0.0654278i
$862$	−39.4832	+	11.5933i	−1.34480	+	0.394870i
$863$	−12.4734	−	42.4804i	−0.424598	−	1.44605i	−0.843063	−	0.537815i	$-0.819250\pi$
$863$	−12.4734	−	42.4804i	−0.424598	−	1.44605i	0.418464	−	0.908233i	$-0.362568\pi$
$864$	−19.2284	+	21.2225i	−0.654163	+	0.722005i
$865$	−2.99045	−	20.7991i	−0.101678	−	0.707189i
$866$	−3.36247	−	3.88049i	−0.114261	−	0.131865i
$867$	−4.26019	+	21.2584i	−0.144684	+	0.721974i
$868$	−0.331551	−	2.24233i	−0.0112536	−	0.0761097i
$869$	−6.46944	−	0.930165i	−0.219461	−	0.0315537i
$870$	5.00266	+	12.7684i	0.169606	+	0.432888i
$871$	12.8974	+	11.1757i	0.437011	+	0.378673i
$872$	−2.78560	+	9.48687i	−0.0943322	+	0.321266i
$873$	3.64956	−	1.20310i	0.123519	−	0.0407188i
$874$	5.33342	+	21.5038i	0.180405	+	0.727378i
$875$	−51.3300	−	23.1941i	−1.73527	−	0.784105i
$876$	0.552117	−	0.427633i	0.0186543	−	0.0144484i
$877$	−32.1374	+	37.0886i	−1.08520	+	1.25239i	−0.119476	+	0.992837i	$0.538122\pi$
$877$	−32.1374	+	37.0886i	−1.08520	+	1.25239i	−0.965728	+	0.259556i	$0.916424\pi$
$878$	13.0704	+	8.39986i	0.441106	+	0.283482i
$879$	−13.9499	+	14.4156i	−0.470517	+	0.486228i
$880$	46.1880	+	71.8699i	1.55700	+	2.42274i
$881$	2.73515	+	5.98913i	0.0921494	+	0.201779i	0.950094	−	0.311962i	$-0.100986\pi$
$881$	2.73515	+	5.98913i	0.0921494	+	0.201779i	−0.857945	+	0.513741i	$0.828259\pi$
$882$	6.72363	+	36.2022i	0.226396	+	1.21899i
$883$	4.37601	+	30.4358i	0.147264	+	1.02425i	0.920672	+	0.390337i	$0.127642\pi$
$883$	4.37601	+	30.4358i	0.147264	+	1.02425i	−0.773407	+	0.633909i	$0.781449\pi$
$884$	4.29033	+	1.95933i	0.144299	+	0.0658993i
$885$	−76.7908	−	27.2139i	−2.58130	−	0.914784i
$886$	24.4435	−	7.17726i	0.821196	−	0.241125i
$887$	1.14580	−	2.50896i	0.0384724	−	0.0842427i	−0.889420	−	0.457091i	$-0.848891\pi$
$887$	1.14580	−	2.50896i	0.0384724	−	0.0842427i	0.927892	+	0.372848i	$0.121619\pi$
$888$	−17.8694	−	9.37987i	−0.599656	−	0.314768i
$889$	−8.67664	−	29.1189i	−0.291005	−	0.976615i
$890$	−64.4357	+	29.4268i	−2.15989	+	0.986388i
$891$	36.6517	+	13.9098i	1.22788	+	0.465996i
$892$	−29.6594	−	4.26438i	−0.993072	−	0.142782i
$893$	−13.3499	+	20.7728i	−0.446737	+	0.695136i
$894$	−18.4900	+	4.34138i	−0.618398	+	0.145197i
$895$	−13.5932	+	46.2941i	−0.454370	+	1.54744i
$896$	−12.6303	+	27.9516i	−0.421948	+	0.933796i
$897$	−13.5147	−	10.6777i	−0.451243	−	0.356518i
$898$	52.7441			1.76009
$899$	−0.879773	−	0.258325i	−0.0293421	−	0.00861561i
$900$	30.9960	+	12.9430i	1.03320	+	0.431434i
$901$	−11.2718	+	17.5393i	−0.375518	+	0.584317i
$902$	4.96645	−	34.5424i	0.165365	−	1.15014i
$903$	31.8703	+	16.5670i	1.06058	+	0.551317i
$904$	−3.66666	−	8.02887i	−0.121951	−	0.267036i
$905$	−17.1602	+	14.8694i	−0.570425	+	0.494276i
$906$	−23.2855	−	12.2229i	−0.773608	−	0.406078i
$907$	−6.97995	+	15.2840i	−0.231766	+	0.507496i	−0.989406	−	0.145177i	$-0.953625\pi$
$907$	−6.97995	+	15.2840i	−0.231766	+	0.507496i	0.757640	+	0.652672i	$0.226352\pi$
$908$	−19.5711	+	5.74659i	−0.649490	+	0.190707i
$909$	−30.8367	−	44.6857i	−1.02279	−	1.48213i
$910$	28.4488	−	24.8508i	0.943067	−	0.823795i
$911$	54.5086	−	7.83716i	1.80595	−	0.259657i	0.844683	−	0.535267i	$-0.179789\pi$
$911$	54.5086	−	7.83716i	1.80595	−	0.259657i	0.961269	+	0.275611i	$0.0888801\pi$
$912$	−22.7043	+	1.99901i	−0.751815	+	0.0661939i
$913$	−65.7148	+	30.0110i	−2.17484	+	0.993218i
$914$	−16.8101	−	26.1570i	−0.556027	−	0.865196i
$915$	−20.2179	−	19.5647i	−0.668385	−	0.646789i
$916$	−4.51759	+	7.02951i	−0.149265	+	0.232261i
$917$	−12.2728	+	5.66418i	−0.405283	+	0.187048i
$918$	15.9924	+	10.7853i	0.527827	+	0.355969i
$919$	−18.3790			−0.606268			−0.303134	−	0.952948i	$-0.598033\pi$
$919$	−18.3790			−0.606268			−0.303134	+	0.952948i	$0.598033\pi$
$920$	−3.06107	−	30.4119i	−0.100921	−	1.00265i
$921$	−12.3209	+	17.0348i	−0.405989	+	0.561317i
$922$	−5.43454	+	18.5084i	−0.178977	+	0.609540i
$923$	2.45633	−	2.83475i	0.0808510	−	0.0933070i
$924$	−21.4179	−	1.09291i	−0.704599	−	0.0359542i
$925$	−10.6478	+	74.0574i	−0.350099	+	2.43499i
$926$	0.359301	+	0.559083i	0.0118074	+	0.0183726i
$927$	−1.66373	−	1.79726i	−0.0546441	−	0.0590297i
$928$	−4.15004	−	4.78940i	−0.136232	−	0.157220i
$929$	0.701550	+	4.87939i	0.0230171	+	0.160088i	0.998088	−	0.0618050i	$-0.0196857\pi$
$929$	0.701550	+	4.87939i	0.0230171	+	0.160088i	−0.975071	+	0.221893i	$0.928777\pi$
$930$	−8.27087	+	4.69414i	−0.271212	+	0.153927i
$931$	−9.84674	+	15.5945i	−0.322714	+	0.511090i
$932$	−1.57187	−	5.35329i	−0.0514882	−	0.175353i
$933$	32.3823	−	18.3786i	1.06015	−	0.601689i
$934$	19.8397	−	2.85252i	0.649176	−	0.0933375i
$935$	27.3694	−	23.7157i	0.895075	−	0.775587i
$936$	7.40860	−	6.85818i	0.242158	−	0.224167i
$937$	−2.04590	−	3.18348i	−0.0668367	−	0.104000i	0.806227	−	0.591607i	$-0.201506\pi$
$937$	−2.04590	−	3.18348i	−0.0668367	−	0.104000i	−0.873063	+	0.487607i	$0.837870\pi$
$938$	−32.2021	−	20.5136i	−1.05144	−	0.669794i
$939$	18.0484	−	7.07137i	0.588987	−	0.230766i
$940$	−25.8944	+	29.8837i	−0.844583	+	0.974700i
$941$	−8.58808	−	2.52169i	−0.279964	−	0.0822047i	0.138736	−	0.990329i	$-0.455696\pi$
$941$	−8.58808	−	2.52169i	−0.279964	−	0.0822047i	−0.418700	+	0.908125i	$0.637514\pi$
$942$	−35.0077	−	25.3204i	−1.14061	−	0.824982i
$943$	−12.6195	+	17.9149i	−0.410949	+	0.583391i
$944$	59.8229			1.94707
$945$	45.9392	−	28.3589i	1.49440	−	0.922515i
$946$	−39.2026	+	45.2422i	−1.27459	+	1.47095i
$947$	−6.50255	+	10.1182i	−0.211304	+	0.328796i	−0.930686	−	0.365819i	$-0.880789\pi$
$947$	−6.50255	+	10.1182i	−0.211304	+	0.328796i	0.719382	+	0.694615i	$0.244425\pi$
$948$	1.94178	−	2.00661i	0.0630659	−	0.0651717i
$949$	−0.654617	+	0.420697i	−0.0212498	+	0.0136564i
$950$	19.9996	+	43.7930i	0.648872	+	1.42083i
$951$	41.5167	−	3.65536i	1.34627	−	0.118533i
$952$	8.73292	+	2.52635i	0.283036	+	0.0818794i
$953$	13.4021	+	6.12054i	0.434137	+	0.198264i	0.620482	−	0.784221i	$-0.286937\pi$
$953$	13.4021	+	6.12054i	0.434137	+	0.198264i	−0.186345	+	0.982484i	$0.559664\pi$
$954$	−29.4208	−	42.6339i	−0.952533	−	1.38032i
$955$	−20.1872	−	68.7514i	−0.653244	−	2.22474i
$956$	3.23222	+	1.47611i	0.104537	+	0.0477407i
$957$	−4.03197	+	7.68120i	−0.130335	+	0.248298i
$958$	−39.3548	+	34.1012i	−1.27150	+	1.10176i
$959$	−58.6701	+	0.234501i	−1.89456	+	0.00757245i
$960$	2.20962	+	0.121609i	0.0713152	+	0.00392491i
$961$	−4.32127	+	30.0551i	−0.139396	+	0.969518i
$962$	−21.9584	−	14.1118i	−0.707966	−	0.454982i
$963$	−16.9353	+	40.5568i	−0.545732	+	1.30692i
$964$	1.36355	−	4.64381i	0.0439169	−	0.149567i
$965$	−30.8814			−0.994107
$966$	33.4055	+	19.2096i	1.07480	+	0.618057i
$967$	22.5026			0.723634			0.361817	−	0.932249i	$-0.382156\pi$
$967$	22.5026			0.723634			0.361817	+	0.932249i	$0.382156\pi$
$968$	−3.64566	+	12.4160i	−0.117176	+	0.399065i
$969$	2.20846	+	9.40588i	0.0709461	+	0.302160i
$970$	7.41974	+	4.76838i	0.238233	+	0.153103i
$971$	−6.91398	+	48.0878i	−0.221880	+	1.54321i	0.509037	+	0.860745i	$0.330002\pi$
$971$	−6.91398	+	48.0878i	−0.221880	+	1.54321i	−0.730917	+	0.682466i	$0.760907\pi$
$972$	−13.9918	+	9.20490i	−0.448786	+	0.295247i
$973$	34.6189	−	0.138370i	1.10983	−	0.00443594i
$974$	16.6554	−	14.4320i	0.533674	−	0.462431i
$975$	−33.1394	−	17.3953i	−1.06131	−	0.557096i
$976$	18.7919	+	8.58196i	0.601513	+	0.274702i
$977$	−9.40825	−	32.0416i	−0.300997	−	1.02510i	−0.961620	−	0.274383i	$-0.911526\pi$
$977$	−9.40825	−	32.0416i	−0.300997	−	1.02510i	0.660624	−	0.750717i	$-0.270292\pi$
$978$	11.4075	−	32.1892i	0.364772	−	1.02930i
$979$	−40.7620	−	18.6154i	−1.30276	−	0.594951i
$980$	−19.1616	+	22.4742i	−0.612095	+	0.717911i
$981$	−9.37094	+	15.6914i	−0.299191	+	0.500988i
$982$	−6.68953	−	14.6480i	−0.213471	−	0.467437i
$983$	11.0831	−	7.12266i	0.353495	−	0.227178i	−0.351826	−	0.936065i	$-0.614439\pi$
$983$	11.0831	−	7.12266i	0.353495	−	0.227178i	0.705321	+	0.708888i	$0.250803\pi$
$984$	−9.23025	−	8.93201i	−0.294250	−	0.284742i
$985$	−57.4964	+	89.4662i	−1.83199	+	2.85063i
$986$	−2.79531	+	3.22595i	−0.0890207	+	0.102735i
$987$	9.98409	+	41.7714i	0.317797	+	1.32960i
$988$	−5.86954			−0.186735
$989$	34.8261	−	14.1494i	1.10740	−	0.449925i
$990$	28.1703	+	85.4536i	0.895312	+	2.71589i
$991$	−36.2824	−	10.6535i	−1.15255	−	0.338419i	−0.351016	−	0.936370i	$-0.614164\pi$
$991$	−36.2824	−	10.6535i	−1.15255	−	0.338419i	−0.801533	+	0.597951i	$0.795982\pi$
$992$	2.87801	−	3.32140i	0.0913768	−	0.105454i
$993$	−2.47694	−	6.32194i	−0.0786034	−	0.200621i
$994$	−4.50875	+	7.07779i	−0.143009	+	0.224494i
$995$	−55.0062	−	85.5913i	−1.74381	−	2.71343i
$996$	6.06455	−	30.2622i	0.192163	−	0.958895i
$997$	−40.7108	+	35.2761i	−1.28932	+	1.11720i	−0.302892	+	0.953025i	$0.597952\pi$
$997$	−40.7108	+	35.2761i	−1.28932	+	1.11720i	−0.986430	+	0.164179i	$0.947502\pi$
$998$	13.0919	−	1.88233i	0.414416	−	0.0595840i
$999$	−27.6456	−	25.0479i	−0.874668	−	0.792482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.v.a.41.48	yes	600
3.2	odd	2	inner	483.2.v.a.41.13	✓	600
7.6	odd	2	inner	483.2.v.a.41.47	yes	600
21.20	even	2	inner	483.2.v.a.41.14	yes	600
23.9	even	11	inner	483.2.v.a.377.14	yes	600
69.32	odd	22	inner	483.2.v.a.377.47	yes	600
161.55	odd	22	inner	483.2.v.a.377.13	yes	600
483.377	even	22	inner	483.2.v.a.377.48	yes	600

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.v.a.41.13	✓	600	3.2	odd	2	inner
483.2.v.a.41.14	yes	600	21.20	even	2	inner
483.2.v.a.41.47	yes	600	7.6	odd	2	inner
483.2.v.a.41.48	yes	600	1.1	even	1	trivial
483.2.v.a.377.13	yes	600	161.55	odd	22	inner
483.2.v.a.377.14	yes	600	23.9	even	11	inner
483.2.v.a.377.47	yes	600	69.32	odd	22	inner
483.2.v.a.377.48	yes	600	483.377	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.v (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.493988 - 1.68237i) q^{2} +(1.68620 - 0.395912i) q^{3} +(-0.903836 - 0.580860i) q^{4} +(-0.558871 + 3.88703i) q^{5} +(0.166890 - 3.03238i) q^{6} +(-0.0105749 - 2.64573i) q^{7} +(1.22655 - 1.06281i) q^{8} +(2.68651 - 1.33517i) q^{9} +(6.26335 + 2.86037i) q^{10} +(1.22718 + 4.17938i) q^{11} +(-1.75401 - 0.621604i) q^{12} +(1.88613 + 0.861367i) q^{13} +(-4.45632 - 1.28917i) q^{14} +(0.596557 + 6.77556i) q^{15} +(-2.07478 - 4.54313i) q^{16} +(-1.78108 + 1.14463i) q^{17} +(-0.919146 - 5.17926i) q^{18} +(1.42444 - 2.21647i) q^{19} +(2.76295 - 3.18861i) q^{20} +(-1.06531 - 4.45703i) q^{21} +7.63748 q^{22} +(-4.27389 - 2.17574i) q^{23} +(1.64742 - 2.27771i) q^{24} +(-9.99921 - 2.93603i) q^{25} +(2.38086 - 2.74766i) q^{26} +(4.00137 - 3.31498i) q^{27} +(-1.52724 + 2.39745i) q^{28} +(0.621661 + 0.967323i) q^{29} +(11.6937 + 2.34342i) q^{30} +(-0.602646 + 0.522195i) q^{31} +(-5.45526 + 0.784348i) q^{32} +(3.72393 + 6.56140i) q^{33} +(1.04586 + 3.56187i) q^{34} +(10.2899 + 1.43752i) q^{35} +(-3.20371 - 0.353710i) q^{36} +(-1.02173 - 7.10631i) q^{37} +(-3.02527 - 3.49135i) q^{38} +(3.52141 + 0.705691i) q^{39} +(3.44569 + 5.36161i) q^{40} +(0.650274 - 4.52275i) q^{41} +(-8.02462 - 0.409480i) q^{42} +(-5.13293 + 5.92372i) q^{43} +(1.31847 - 4.49029i) q^{44} +(3.68844 + 11.1887i) q^{45} +(-5.77165 + 6.11548i) q^{46} -9.37202 q^{47} +(-5.29716 - 6.83917i) q^{48} +(-6.99978 + 0.0559564i) q^{49} +(-9.87898 + 15.3720i) q^{50} +(-2.55007 + 2.63522i) q^{51} +(-1.20442 - 1.87411i) q^{52} +(8.95765 - 4.09082i) q^{53} +(-3.60039 - 8.36934i) q^{54} +(-16.9312 + 2.43434i) q^{55} +(-2.82488 - 3.23388i) q^{56} +(1.52436 - 4.30136i) q^{57} +(1.93449 - 0.568017i) q^{58} +(-4.97577 + 10.8954i) q^{59} +(3.39646 - 6.47051i) q^{60} +(-3.12603 + 2.70872i) q^{61} +(0.580826 + 1.27183i) q^{62} +(-3.56091 - 7.09365i) q^{63} +(0.0463023 - 0.322040i) q^{64} +(-4.40226 + 6.85005i) q^{65} +(12.8783 - 3.02377i) q^{66} +(7.89696 + 2.31876i) q^{67} +2.27467 q^{68} +(-8.06802 - 1.97664i) q^{69} +(7.50155 - 16.6014i) q^{70} +(0.509646 - 1.73569i) q^{71} +(1.87610 - 4.49290i) q^{72} +(-0.202891 + 0.315705i) q^{73} +(-12.4602 - 1.79150i) q^{74} +(-18.0230 - 0.991917i) q^{75} +(-2.57492 + 1.17593i) q^{76} +(11.0445 - 3.29098i) q^{77} +(2.92677 - 5.57571i) q^{78} +(-0.623336 + 1.36491i) q^{79} +(18.8188 - 5.52570i) q^{80} +(5.43464 - 7.17389i) q^{81} +(-7.28772 - 3.32819i) q^{82} +(2.36036 + 16.4166i) q^{83} +(-1.62605 + 4.64722i) q^{84} +(-3.45382 - 7.56281i) q^{85} +(7.43027 + 11.5617i) q^{86} +(1.43122 + 1.38497i) q^{87} +(5.94708 + 3.82196i) q^{88} +(-6.73704 + 7.77495i) q^{89} +(20.6456 - 0.678214i) q^{90} +(2.25900 - 4.99930i) q^{91} +(2.59910 + 4.44904i) q^{92} +(-0.809435 + 1.11912i) q^{93} +(-4.62967 + 15.7672i) q^{94} +(7.81942 + 6.77557i) q^{95} +(-8.88810 + 3.48237i) q^{96} +(1.26788 + 0.182293i) q^{97} +(-3.36367 + 11.8039i) q^{98} +(8.87700 + 9.58945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 600 q + 20 q^{4} - 18 q^{7} - 26 q^{9} - 14 q^{15} - 116 q^{16} - 46 q^{18} - 50 q^{21} - 104 q^{22} - 88 q^{25} - 26 q^{28} + 26 q^{30} - 26 q^{36} - 56 q^{37} - 14 q^{39} + 5 q^{42} - 40 q^{43} - 44 q^{46}+ \cdots - 250 q^{99}+O(q^{100}) \) 600 * q + 20 * q^4 - 18 * q^7 - 26 * q^9 - 14 * q^15 - 116 * q^16 - 46 * q^18 - 50 * q^21 - 104 * q^22 - 88 * q^25 - 26 * q^28 + 26 * q^30 - 26 * q^36 - 56 * q^37 - 14 * q^39 + 5 * q^42 - 40 * q^43 - 44 * q^46 + 74 * q^49 + 14 * q^51 - 66 * q^57 - 76 * q^58 + 22 * q^60 - 44 * q^63 + 44 * q^64 - 92 * q^67 - 92 * q^70 + 178 * q^72 - 182 * q^78 + 68 * q^79 + 106 * q^81 - 87 * q^84 - 4 * q^85 - 220 * q^88 - 24 * q^91 - 44 * q^93 - 250 * q^99

Introduction

L-functions

Modular forms

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