LMFDB - Embedded newform 558.2.g.a.211.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(211,558)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(558, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("558.211"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.45565243279$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.4
Character	$\chi$	$=$	558.211
Dual form			558.2.g.a.439.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.35283 - 1.08159i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.281395 + 0.487391i) q^{5} +(-0.260271 + 1.71238i) q^{6} +(0.502527 - 0.870402i) q^{7} +1.00000 q^{8} +(0.660311 + 2.92643i) q^{9} +(0.281395 - 0.487391i) q^{10} -0.144503 q^{11} +(1.61310 - 0.630790i) q^{12} +(2.35820 + 4.08453i) q^{13} -1.00505 q^{14} +(0.146478 - 0.963713i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.900123 + 1.55906i) q^{17} +(2.20421 - 2.03506i) q^{18} +(1.19266 + 2.06575i) q^{19} -0.562790 q^{20} +(-1.62126 + 0.633978i) q^{21} +(0.0722513 + 0.125143i) q^{22} +(1.87458 - 3.24686i) q^{23} +(-1.35283 - 1.08159i) q^{24} +(2.34163 - 4.05583i) q^{25} +(2.35820 - 4.08453i) q^{26} +(2.27192 - 4.67316i) q^{27} +(0.502527 + 0.870402i) q^{28} +(-0.145225 - 0.251538i) q^{29} +(-0.907839 + 0.355003i) q^{30} +(4.75181 + 2.90177i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.195488 + 0.156293i) q^{33} +(0.900123 - 1.55906i) q^{34} +0.565634 q^{35} +(-2.86452 - 0.891369i) q^{36} +(1.95794 + 3.39125i) q^{37} +(1.19266 - 2.06575i) q^{38} +(1.22755 - 8.07630i) q^{39} +(0.281395 + 0.487391i) q^{40} +(-0.763164 - 1.32184i) q^{41} +(1.35967 + 1.08706i) q^{42} +(4.55551 - 7.89038i) q^{43} +(0.0722513 - 0.125143i) q^{44} +(-1.24051 + 1.14531i) q^{45} -3.74915 q^{46} +(-5.11631 - 8.86171i) q^{47} +(-0.260271 + 1.71238i) q^{48} +(2.99493 + 5.18738i) q^{49} -4.68327 q^{50} +(0.468552 - 3.08271i) q^{51} -4.71641 q^{52} +(2.18202 - 3.77937i) q^{53} +(-5.18303 + 0.369040i) q^{54} +(-0.0406623 - 0.0704292i) q^{55} +(0.502527 - 0.870402i) q^{56} +(0.620830 - 4.08459i) q^{57} +(-0.145225 + 0.251538i) q^{58} -1.17214 q^{59} +(0.761361 + 0.608710i) q^{60} +(1.68911 + 2.92562i) q^{61} +(0.137103 - 5.56608i) q^{62} +(2.87899 + 0.895874i) q^{63} +1.00000 q^{64} +(-1.32717 + 2.29873i) q^{65} +(0.0376099 - 0.247444i) q^{66} +(5.87033 + 10.1677i) q^{67} -1.80025 q^{68} +(-6.04777 + 2.36493i) q^{69} +(-0.282817 - 0.489854i) q^{70} +(2.93897 - 5.09045i) q^{71} +(0.660311 + 2.92643i) q^{72} +(2.10808 - 3.65130i) q^{73} +(1.95794 - 3.39125i) q^{74} +(-7.55460 + 2.95416i) q^{75} -2.38532 q^{76} +(-0.0726165 + 0.125775i) q^{77} +(-7.60806 + 2.97507i) q^{78} +(-2.92516 + 5.06652i) q^{79} +(0.281395 - 0.487391i) q^{80} +(-8.12798 + 3.86471i) q^{81} +(-0.763164 + 1.32184i) q^{82} +6.17525 q^{83} +(0.261587 - 1.72104i) q^{84} +(-0.506580 + 0.877423i) q^{85} -9.11103 q^{86} +(-0.0755959 + 0.497363i) q^{87} -0.144503 q^{88} -6.44167 q^{89} +(1.61212 + 0.501653i) q^{90} +4.74024 q^{91} +(1.87458 + 3.24686i) q^{92} +(-3.28987 - 9.06514i) q^{93} +(-5.11631 + 8.86171i) q^{94} +(-0.671217 + 1.16258i) q^{95} +(1.61310 - 0.630790i) q^{96} +(2.71229 + 4.69783i) q^{97} +(2.99493 - 5.18738i) q^{98} +(-0.0954167 - 0.422877i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} + 4 q^{3} - 16 q^{4} - q^{5} - 2 q^{6} + q^{7} + 32 q^{8} + 12 q^{9} - q^{10} + 4 q^{11} - 2 q^{12} - 10 q^{13} - 2 q^{14} - 13 q^{15} - 16 q^{16} - 4 q^{17} - 6 q^{18} + 4 q^{19} + 2 q^{20}+ \cdots + 19 q^{99}+O(q^{100}) $ 32 * q - 16 * q^2 + 4 * q^3 - 16 * q^4 - q^5 - 2 * q^6 + q^7 + 32 * q^8 + 12 * q^9 - q^10 + 4 * q^11 - 2 * q^12 - 10 * q^13 - 2 * q^14 - 13 * q^15 - 16 * q^16 - 4 * q^17 - 6 * q^18 + 4 * q^19 + 2 * q^20 + 10 * q^21 - 2 * q^22 - q^23 + 4 * q^24 - 19 * q^25 - 10 * q^26 + 7 * q^27 + q^28 - 3 * q^29 + 14 * q^30 - q^31 - 16 * q^32 - 7 * q^33 - 4 * q^34 - 6 * q^36 - 19 * q^37 + 4 * q^38 + 19 * q^39 - q^40 + 10 * q^41 - 11 * q^42 - 13 * q^43 - 2 * q^44 + 14 * q^45 + 2 * q^46 - 6 * q^47 - 2 * q^48 - 13 * q^49 + 38 * q^50 + 20 * q^51 + 20 * q^52 - 7 * q^53 - 17 * q^54 - 11 * q^55 + q^56 - 5 * q^57 - 3 * q^58 + 12 * q^59 - q^60 + 7 * q^61 + 11 * q^62 - 42 * q^63 + 32 * q^64 - 8 * q^65 + 5 * q^66 - 8 * q^67 + 8 * q^68 + 43 * q^69 + 7 * q^71 + 12 * q^72 + 7 * q^73 - 19 * q^74 - 41 * q^75 - 8 * q^76 - q^77 - 11 * q^78 - 34 * q^79 - q^80 + 10 * q^82 - 28 * q^83 + q^84 + 13 * q^85 + 26 * q^86 - 54 * q^87 + 4 * q^88 + 2 * q^89 - 19 * q^90 + 24 * q^91 - q^92 - 15 * q^93 - 6 * q^94 + 21 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + 19 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.35283	−	1.08159i	−0.781058	−	0.624458i
$3$	−1.35283	−	1.08159i	−0.781058	−	0.624458i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.281395	+	0.487391i	0.125844	+	0.217968i	0.922062	−	0.387041i	$-0.126503\pi$
$5$	0.281395	+	0.487391i	0.125844	+	0.217968i	−0.796219	+	0.605009i	$0.793170\pi$
$6$	−0.260271	+	1.71238i	−0.106255	+	0.699078i
$7$	0.502527	−	0.870402i	0.189937	−	0.328981i	−0.755292	−	0.655389i	$-0.772505\pi$
$7$	0.502527	−	0.870402i	0.189937	−	0.328981i	0.945229	+	0.326408i	$0.105838\pi$
$8$	1.00000			0.353553
$9$	0.660311	+	2.92643i	0.220104	+	0.975476i
$10$	0.281395	−	0.487391i	0.0889849	−	0.154126i
$11$	−0.144503			−0.0435692			−0.0217846	−	0.999763i	$-0.506935\pi$
$11$	−0.144503			−0.0435692			−0.0217846	+	0.999763i	$0.506935\pi$
$12$	1.61310	−	0.630790i	0.465663	−	0.182094i
$13$	2.35820	+	4.08453i	0.654048	+	1.13284i	0.982132	+	0.188196i	$0.0602640\pi$
$13$	2.35820	+	4.08453i	0.654048	+	1.13284i	−0.328083	+	0.944649i	$0.606403\pi$
$14$	−1.00505			−0.268612
$15$	0.146478	−	0.963713i	0.0378205	−	0.248830i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.900123	+	1.55906i	0.218312	+	0.378127i	0.954292	−	0.298876i	$-0.0966117\pi$
$17$	0.900123	+	1.55906i	0.218312	+	0.378127i	−0.735980	+	0.677003i	$0.763278\pi$
$18$	2.20421	−	2.03506i	0.519537	−	0.479668i
$19$	1.19266	+	2.06575i	0.273615	+	0.473915i	0.969785	−	0.243962i	$-0.0784472\pi$
$19$	1.19266	+	2.06575i	0.273615	+	0.473915i	−0.696170	+	0.717877i	$0.745114\pi$
$20$	−0.562790			−0.125844
$21$	−1.62126	+	0.633978i	−0.353787	+	0.138345i
$22$	0.0722513	+	0.125143i	0.0154040	+	0.0266806i
$23$	1.87458	−	3.24686i	0.390876	−	0.677017i	−0.601689	−	0.798730i	$-0.705505\pi$
$23$	1.87458	−	3.24686i	0.390876	−	0.677017i	0.992565	+	0.121713i	$0.0388387\pi$
$24$	−1.35283	−	1.08159i	−0.276146	−	0.220779i
$25$	2.34163	−	4.05583i	0.468327	−	0.811166i
$26$	2.35820	−	4.08453i	0.462482	−	0.801042i
$27$	2.27192	−	4.67316i	0.437231	−	0.899349i
$28$	0.502527	+	0.870402i	0.0949687	+	0.164491i
$29$	−0.145225	−	0.251538i	−0.0269677	−	0.0467093i	0.852227	−	0.523173i	$-0.175252\pi$
$29$	−0.145225	−	0.251538i	−0.0269677	−	0.0467093i	−0.879194	+	0.476463i	$0.841918\pi$
$30$	−0.907839	+	0.355003i	−0.165748	+	0.0648143i
$31$	4.75181	+	2.90177i	0.853451	+	0.521174i
$31$	4.75181	+	2.90177i	0.853451	+	0.521174i
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.195488	+	0.156293i	0.0340301	+	0.0272071i
$34$	0.900123	−	1.55906i	0.154370	−	0.267376i
$35$	0.565634			0.0956097
$36$	−2.86452	−	0.891369i	−0.477420	−	0.148561i
$37$	1.95794	+	3.39125i	0.321883	+	0.557518i	0.980877	−	0.194631i	$-0.0623509\pi$
$37$	1.95794	+	3.39125i	0.321883	+	0.557518i	−0.658994	+	0.752149i	$0.729018\pi$
$38$	1.19266	−	2.06575i	0.193475	−	0.335109i
$39$	1.22755	−	8.07630i	0.196565	−	1.29324i
$40$	0.281395	+	0.487391i	0.0444925	+	0.0770632i
$41$	−0.763164	−	1.32184i	−0.119186	−	0.206437i	0.800259	−	0.599654i	$-0.204695\pi$
$41$	−0.763164	−	1.32184i	−0.119186	−	0.206437i	−0.919445	+	0.393218i	$0.871362\pi$
$42$	1.35967	+	1.08706i	0.209802	+	0.167737i
$43$	4.55551	−	7.89038i	0.694709	−	1.20327i	−0.275569	−	0.961281i	$-0.588866\pi$
$43$	4.55551	−	7.89038i	0.694709	−	1.20327i	0.970279	−	0.241991i	$-0.0778004\pi$
$44$	0.0722513	−	0.125143i	0.0108923	−	0.0188660i
$45$	−1.24051	+	1.14531i	−0.184924	+	0.170733i
$46$	−3.74915			−0.552782
$47$	−5.11631	−	8.86171i	−0.746291	−	1.29261i	−0.949589	−	0.313496i	$-0.898500\pi$
$47$	−5.11631	−	8.86171i	−0.746291	−	1.29261i	0.203299	−	0.979117i	$-0.434834\pi$
$48$	−0.260271	+	1.71238i	−0.0375669	+	0.247161i
$49$	2.99493	+	5.18738i	0.427848	+	0.741054i
$50$	−4.68327			−0.662314
$51$	0.468552	−	3.08271i	0.0656104	−	0.431666i
$52$	−4.71641			−0.654048
$53$	2.18202	−	3.77937i	0.299723	−	0.519136i	−0.676349	−	0.736581i	$-0.736439\pi$
$53$	2.18202	−	3.77937i	0.299723	−	0.519136i	0.976073	+	0.217445i	$0.0697723\pi$
$54$	−5.18303	+	0.369040i	−0.705321	+	0.0502200i
$55$	−0.0406623	−	0.0704292i	−0.00548291	−	0.00949667i
$56$	0.502527	−	0.870402i	0.0671530	−	0.116312i
$57$	0.620830	−	4.08459i	0.0822310	−	0.541017i
$58$	−0.145225	+	0.251538i	−0.0190690	+	0.0330285i
$59$	−1.17214			−0.152600			−0.0762998	−	0.997085i	$-0.524311\pi$
$59$	−1.17214			−0.152600			−0.0762998	+	0.997085i	$0.524311\pi$
$60$	0.761361	+	0.608710i	0.0982912	+	0.0785841i
$61$	1.68911	+	2.92562i	0.216268	+	0.374588i	0.953664	−	0.300873i	$-0.0972781\pi$
$61$	1.68911	+	2.92562i	0.216268	+	0.374588i	−0.737396	+	0.675461i	$0.763945\pi$
$62$	0.137103	−	5.56608i	0.0174121	−	0.706892i
$63$	2.87899	+	0.895874i	0.362719	+	0.112869i
$64$	1.00000			0.125000
$65$	−1.32717	+	2.29873i	−0.164616	+	0.285123i
$66$	0.0376099	−	0.247444i	0.00462946	−	0.0304582i
$67$	5.87033	+	10.1677i	0.717176	+	1.24218i	0.962114	+	0.272646i	$0.0878988\pi$
$67$	5.87033	+	10.1677i	0.717176	+	1.24218i	−0.244939	+	0.969539i	$0.578768\pi$
$68$	−1.80025			−0.218312
$69$	−6.04777	+	2.36493i	−0.728066	+	0.284704i
$70$	−0.282817	−	0.489854i	−0.0338031	−	0.0585487i
$71$	2.93897	−	5.09045i	0.348792	−	0.604125i	−0.637243	−	0.770663i	$-0.719925\pi$
$71$	2.93897	−	5.09045i	0.348792	−	0.604125i	0.986035	+	0.166537i	$0.0532587\pi$
$72$	0.660311	+	2.92643i	0.0778184	+	0.344883i
$73$	2.10808	−	3.65130i	0.246732	−	0.427352i	−0.715885	−	0.698218i	$-0.753977\pi$
$73$	2.10808	−	3.65130i	0.246732	−	0.427352i	0.962617	+	0.270866i	$0.0873099\pi$
$74$	1.95794	−	3.39125i	0.227606	−	0.394225i
$75$	−7.55460	+	2.95416i	−0.872330	+	0.341117i
$76$	−2.38532			−0.273615
$77$	−0.0726165	+	0.125775i	−0.00827541	+	0.0143334i
$78$	−7.60806	+	2.97507i	−0.861443	+	0.336860i
$79$	−2.92516	+	5.06652i	−0.329106	+	0.570028i	−0.982335	−	0.187132i	$-0.940081\pi$
$79$	−2.92516	+	5.06652i	−0.329106	+	0.570028i	0.653229	+	0.757161i	$0.273414\pi$
$80$	0.281395	−	0.487391i	0.0314609	−	0.0544919i
$81$	−8.12798	+	3.86471i	−0.903109	+	0.429412i
$82$	−0.763164	+	1.32184i	−0.0842774	+	0.145973i
$83$	6.17525			0.677822			0.338911	−	0.940818i	$-0.389941\pi$
$83$	6.17525			0.677822			0.338911	+	0.940818i	$0.389941\pi$
$84$	0.261587	−	1.72104i	0.0285414	−	0.187781i
$85$	−0.506580	+	0.877423i	−0.0549463	+	0.0951698i
$86$	−9.11103			−0.982468
$87$	−0.0755959	+	0.497363i	−0.00810473	+	0.0533229i
$88$	−0.144503			−0.0154040
$89$	−6.44167			−0.682815			−0.341408	−	0.939915i	$-0.610904\pi$
$89$	−6.44167			−0.682815			−0.341408	+	0.939915i	$0.610904\pi$
$90$	1.61212	+	0.501653i	0.169933	+	0.0528789i
$91$	4.74024			0.496913
$92$	1.87458	+	3.24686i	0.195438	+	0.338509i
$93$	−3.28987	−	9.06514i	−0.341143	−	0.940011i
$94$	−5.11631	+	8.86171i	−0.527707	+	0.914016i
$95$	−0.671217	+	1.16258i	−0.0688655	+	0.119278i
$96$	1.61310	−	0.630790i	0.164637	−	0.0643798i
$97$	2.71229	+	4.69783i	0.275392	+	0.476992i	0.970234	−	0.242170i	$-0.0778592\pi$
$97$	2.71229	+	4.69783i	0.275392	+	0.476992i	−0.694842	+	0.719162i	$0.744526\pi$
$98$	2.99493	−	5.18738i	0.302534	−	0.524004i
$99$	−0.0954167	−	0.422877i	−0.00958974	−	0.0425007i
$100$	2.34163	+	4.05583i	0.234163	+	0.405583i
$101$	5.63378	+	9.75799i	0.560582	+	0.970956i	0.997446	+	0.0714286i	$0.0227558\pi$
$101$	5.63378	+	9.75799i	0.560582	+	0.970956i	−0.436864	+	0.899528i	$0.643911\pi$
$102$	−2.90398	+	1.13558i	−0.287537	+	0.112439i
$103$	5.67780	+	9.83424i	0.559450	+	0.968996i	0.997542	+	0.0700660i	$0.0223210\pi$
$103$	5.67780	+	9.83424i	0.559450	+	0.968996i	−0.438092	+	0.898930i	$0.644346\pi$
$104$	2.35820	+	4.08453i	0.231241	+	0.400521i
$105$	−0.765209	−	0.611787i	−0.0746767	−	0.0597043i
$106$	−4.36404			−0.423873
$107$	7.45699	+	12.9159i	0.720895	+	1.24863i	0.960642	+	0.277791i	$0.0896023\pi$
$107$	7.45699	+	12.9159i	0.720895	+	1.24863i	−0.239747	+	0.970835i	$0.577064\pi$
$108$	2.91111	+	4.30412i	0.280122	+	0.414164i
$109$	−3.27184			−0.313386			−0.156693	−	0.987647i	$-0.550083\pi$
$109$	−3.27184			−0.313386			−0.156693	+	0.987647i	$0.550083\pi$
$110$	−0.0406623	+	0.0704292i	−0.00387700	+	0.00671516i
$111$	1.01919	−	6.70548i	0.0967372	−	0.636456i
$112$	−1.00505			−0.0949687
$113$	3.10728	+	5.38197i	0.292308	+	0.506293i	0.974355	−	0.225016i	$-0.0722433\pi$
$113$	3.10728	+	5.38197i	0.292308	+	0.506293i	−0.682047	+	0.731309i	$0.738910\pi$
$114$	−3.84777	+	1.50464i	−0.360377	+	0.140922i
$115$	2.10999			0.196757
$116$	0.290450			0.0269677
$117$	−10.3959	+	9.59818i	−0.961105	+	0.887352i
$118$	0.586070	+	1.01510i	0.0539521	+	0.0934477i
$119$	1.80934			0.165862
$120$	0.146478	−	0.963713i	0.0133716	−	0.0879745i
$121$	−10.9791			−0.998102
$122$	1.68911	−	2.92562i	0.152925	−	0.264874i
$123$	−0.397259	+	2.61366i	−0.0358197	+	0.235666i
$124$	−4.88891	+	2.66430i	−0.439038	+	0.239261i
$125$	5.44965			0.487431
$126$	−0.663648	−	2.94122i	−0.0591225	−	0.262025i
$127$	1.36027	+	2.35605i	0.120704	+	0.209066i	0.920046	−	0.391812i	$-0.128151\pi$
$127$	1.36027	+	2.35605i	0.120704	+	0.209066i	−0.799341	+	0.600877i	$0.794818\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−14.6970	+	5.74715i	−1.29400	+	0.506008i
$130$	2.65435			0.232802
$131$	−12.6041			−1.10123			−0.550613	−	0.834761i	$-0.685606\pi$
$131$	−12.6041			−1.10123			−0.550613	+	0.834761i	$0.685606\pi$
$132$	−0.233098	+	0.0911509i	−0.0202886	+	0.00793367i
$133$	2.39738			0.207879
$134$	5.87033	−	10.1677i	0.507120	−	0.878357i
$135$	2.91696	−	0.207692i	0.251052	−	0.0178753i
$136$	0.900123	+	1.55906i	0.0771849	+	0.133688i
$137$	6.37264			0.544451			0.272226	−	0.962233i	$-0.412240\pi$
$137$	6.37264			0.544451			0.272226	+	0.962233i	$0.412240\pi$
$138$	5.07198	+	4.05506i	0.431755	+	0.345190i
$139$	2.25964	−	3.91382i	0.191660	−	0.331966i	−0.754140	−	0.656713i	$-0.771946\pi$
$139$	2.25964	−	3.91382i	0.191660	−	0.331966i	0.945801	+	0.324748i	$0.105279\pi$
$140$	−0.282817	+	0.489854i	−0.0239024	+	0.0414002i
$141$	−2.66326	+	17.5222i	−0.224287	+	1.47563i
$142$	−5.87794			−0.493266
$143$	−0.340767	−	0.590225i	−0.0284963	−	0.0493571i
$144$	2.20421	−	2.03506i	0.183684	−	0.169588i
$145$	0.0817313	−	0.141563i	0.00678742	−	0.0117562i
$146$	−4.21616			−0.348932
$147$	1.55899	−	10.2570i	0.128583	−	0.845979i
$148$	−3.91588			−0.321883
$149$	4.89186			0.400757			0.200378	−	0.979719i	$-0.435783\pi$
$149$	4.89186			0.400757			0.200378	+	0.979719i	$0.435783\pi$
$150$	6.33568	+	5.06539i	0.517306	+	0.413587i
$151$	−12.0587	−	20.8862i	−0.981320	−	1.69970i	−0.657269	−	0.753656i	$-0.728288\pi$
$151$	−12.0587	−	20.8862i	−0.981320	−	1.69970i	−0.324051	−	0.946039i	$-0.605045\pi$
$152$	1.19266	+	2.06575i	0.0967375	+	0.167554i
$153$	−3.96811	+	3.66361i	−0.320803	+	0.296185i
$154$	0.145233			0.0117032
$155$	−0.0771603	+	3.13253i	−0.00619766	+	0.251611i
$156$	6.38051	+	5.10124i	0.510850	+	0.408426i
$157$	−2.71077	+	4.69520i	−0.216343	+	0.374717i	−0.953687	−	0.300800i	$-0.902746\pi$
$157$	−2.71077	+	4.69520i	−0.216343	+	0.374717i	0.737344	+	0.675517i	$0.236080\pi$
$158$	5.85031			0.465426
$159$	−7.03965	+	2.75279i	−0.558280	+	0.218311i
$160$	−0.562790			−0.0444925
$161$	−1.88405	−	3.26327i	−0.148484	−	0.257182i
$162$	7.41092	+	5.10668i	0.582257	+	0.401219i
$163$	12.9586			1.01500			0.507498	−	0.861653i	$-0.330571\pi$
$163$	12.9586			1.01500			0.507498	+	0.861653i	$0.330571\pi$
$164$	1.52633			0.119186
$165$	−0.0211665	+	0.139259i	−0.00164781	+	0.0108413i
$166$	−3.08762	−	5.34792i	−0.239646	−	0.415079i
$167$	5.26551			0.407457			0.203729	−	0.979027i	$-0.434694\pi$
$167$	5.26551			0.407457			0.203729	+	0.979027i	$0.434694\pi$
$168$	−1.62126	+	0.633978i	−0.125083	+	0.0489125i
$169$	−4.62225	+	8.00598i	−0.355558	+	0.615844i
$170$	1.01316			0.0777059
$171$	−5.25774	+	4.85427i	−0.402069	+	0.371216i
$172$	4.55551	+	7.89038i	0.347355	+	0.601636i
$173$	−11.9797			−0.910797			−0.455398	−	0.890288i	$-0.650503\pi$
$173$	−11.9797			−0.910797			−0.455398	+	0.890288i	$0.650503\pi$
$174$	0.468527	−	0.183213i	0.0355189	−	0.0138894i
$175$	−2.35347	−	4.07633i	−0.177905	−	0.308141i
$176$	0.0722513	+	0.125143i	0.00544615	+	0.00943300i
$177$	1.58571	+	1.26778i	0.119189	+	0.0952920i
$178$	3.22083	+	5.57865i	0.241412	+	0.418137i
$179$	−6.85731	−	11.8772i	−0.512539	−	0.887744i	−0.999894	−	0.0145400i	$-0.995372\pi$
$179$	−6.85731	−	11.8772i	−0.512539	−	0.887744i	0.487355	−	0.873204i	$-0.337962\pi$
$180$	−0.371616	−	1.64697i	−0.0276987	−	0.122758i
$181$	11.0891	−	19.2069i	0.824247	−	1.42764i	−0.0782463	−	0.996934i	$-0.524932\pi$
$181$	11.0891	−	19.2069i	0.824247	−	1.42764i	0.902493	−	0.430704i	$-0.141735\pi$
$182$	−2.37012	−	4.10517i	−0.175685	−	0.304296i
$183$	0.879254	−	5.78481i	0.0649963	−	0.427625i
$184$	1.87458	−	3.24686i	0.138196	−	0.239362i
$185$	−1.10191	+	1.90856i	−0.0810139	+	0.140320i
$186$	−6.20571	+	7.38168i	−0.455025	+	0.541251i
$187$	−0.130070	−	0.225288i	−0.00951167	−	0.0164747i
$188$	10.2326			0.746291
$189$	−2.92583	−	4.32587i	−0.212823	−	0.314661i
$190$	1.34243			0.0973905
$191$	−14.8837			−1.07695			−0.538473	−	0.842643i	$-0.680999\pi$
$191$	−14.8837			−1.07695			−0.538473	+	0.842643i	$0.680999\pi$
$192$	−1.35283	−	1.08159i	−0.0976323	−	0.0780573i
$193$	−18.7119			−1.34691			−0.673455	−	0.739228i	$-0.735190\pi$
$193$	−18.7119			−1.34691			−0.673455	+	0.739228i	$0.735190\pi$
$194$	2.71229	−	4.69783i	0.194731	−	0.337284i
$195$	4.28174	−	1.67434i	0.306622	−	0.119902i
$196$	−5.98987			−0.427848
$197$	−7.08002	+	12.2629i	−0.504430	+	0.873699i	0.495557	+	0.868576i	$0.334964\pi$
$197$	−7.08002	+	12.2629i	−0.504430	+	0.873699i	−0.999987	+	0.00512323i	$0.998369\pi$
$198$	−0.318514	+	0.294072i	−0.0226358	+	0.0208988i
$199$	−4.65872	+	8.06915i	−0.330248	+	0.572007i	−0.982560	−	0.185944i	$-0.940466\pi$
$199$	−4.65872	+	8.06915i	−0.330248	+	0.572007i	0.652312	+	0.757950i	$0.273799\pi$
$200$	2.34163	−	4.05583i	0.165579	−	0.286790i
$201$	3.05576	−	20.1045i	0.215537	−	1.41806i
$202$	5.63378	−	9.75799i	0.396391	−	0.686570i
$203$	−0.291918			−0.0204887
$204$	2.43543	+	1.94713i	0.170514	+	0.136327i
$205$	0.429501	−	0.743918i	0.0299977	−	0.0519575i
$206$	5.67780	−	9.83424i	0.395591	−	0.685184i
$207$	10.7395	+	3.34188i	0.746448	+	0.232277i
$208$	2.35820	−	4.08453i	0.163512	−	0.283211i
$209$	−0.172343	−	0.298506i	−0.0119212	−	0.0206481i
$210$	−0.147218	+	0.968583i	−0.0101590	+	0.0668386i
$211$	−8.02459			−0.552436			−0.276218	−	0.961095i	$-0.589081\pi$
$211$	−8.02459			−0.552436			−0.276218	+	0.961095i	$0.589081\pi$
$212$	2.18202	+	3.77937i	0.149862	+	0.259568i
$213$	−9.48173	+	3.70775i	−0.649678	+	0.254051i
$214$	7.45699	−	12.9159i	0.509750	−	0.882912i
$215$	5.12760			0.349699
$216$	2.27192	−	4.67316i	0.154584	−	0.317968i
$217$	4.91362	−	2.67777i	0.333558	−	0.181779i
$218$	1.63592	+	2.83350i	0.110799	+	0.191909i
$219$	−6.80110	+	2.65951i	−0.459576	+	0.179713i
$220$	0.0813246			0.00548291
$221$	−4.24535	+	7.35316i	−0.285573	+	0.494627i
$222$	−6.31671	+	2.47010i	−0.423950	+	0.165782i
$223$	7.26363	−	12.5810i	0.486409	−	0.842485i	−0.513469	−	0.858108i	$-0.671640\pi$
$223$	7.26363	−	12.5810i	0.486409	−	0.842485i	0.999878	+	0.0156234i	$0.00497329\pi$
$224$	0.502527	+	0.870402i	0.0335765	+	0.0581562i
$225$	13.4153	+	4.17452i	0.894353	+	0.278301i
$226$	3.10728	−	5.38197i	0.206693	−	0.358003i
$227$	18.8216			1.24923			0.624616	−	0.780932i	$-0.285255\pi$
$227$	18.8216			1.24923			0.624616	+	0.780932i	$0.285255\pi$
$228$	3.22694	+	2.57995i	0.213709	+	0.170861i
$229$	1.75878			0.116224			0.0581119	−	0.998310i	$-0.481492\pi$
$229$	1.75878			0.116224			0.0581119	+	0.998310i	$0.481492\pi$
$230$	−1.05499	−	1.82730i	−0.0695642	−	0.120489i
$231$	0.234276	−	0.0916116i	0.0154142	−	0.00602760i
$232$	−0.145225	−	0.251538i	−0.00953450	−	0.0165142i
$233$	−23.2370			−1.52231			−0.761154	−	0.648571i	$-0.775367\pi$
$233$	−23.2370			−1.52231			−0.761154	+	0.648571i	$0.775367\pi$
$234$	13.5102	+	4.20406i	0.883192	+	0.274828i
$235$	2.87941	−	4.98728i	0.187832	−	0.325334i
$236$	0.586070	−	1.01510i	0.0381499	−	0.0660775i
$237$	9.43716	−	3.69032i	0.613010	−	0.239712i
$238$	−0.904672	−	1.56694i	−0.0586412	−	0.101570i
$239$	−4.44457	−	7.69823i	−0.287496	−	0.497957i	0.685716	−	0.727870i	$-0.259489\pi$
$239$	−4.44457	−	7.69823i	−0.287496	−	0.497957i	−0.973211	+	0.229912i	$0.926156\pi$
$240$	−0.907839	+	0.355003i	−0.0586007	+	0.0229153i
$241$	7.36589	−	12.7581i	0.474479	−	0.821821i	−0.525094	−	0.851044i	$-0.675970\pi$
$241$	7.36589	−	12.7581i	0.474479	−	0.821821i	0.999573	+	0.0292228i	$0.00930324\pi$
$242$	5.48956	+	9.50820i	0.352882	+	0.611210i
$243$	15.1758	+	3.56287i	0.973530	+	0.228558i
$244$	−3.37822			−0.216268
$245$	−1.68552	+	2.91940i	−0.107684	+	0.186514i
$246$	2.46213	−	0.962793i	0.156979	−	0.0613855i
$247$	−5.62507	+	9.74291i	−0.357915	+	0.619927i
$248$	4.75181	+	2.90177i	0.301740	+	0.184263i
$249$	−8.35408	−	6.67911i	−0.529418	−	0.423271i
$250$	−2.72482	−	4.71953i	−0.172333	−	0.298489i
$251$	1.91785	+	3.32181i	0.121053	+	0.209671i	0.920183	−	0.391488i	$-0.128039\pi$
$251$	1.91785	+	3.32181i	0.121053	+	0.209671i	−0.799130	+	0.601158i	$0.794706\pi$
$252$	−2.21535	+	2.04535i	−0.139554	+	0.128845i
$253$	−0.270881	+	0.469180i	−0.0170302	+	0.0294971i
$254$	1.36027	−	2.35605i	0.0853506	−	0.147832i
$255$	1.63433	−	0.639092i	0.102346	−	0.0400215i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.31303	+	7.47039i	0.269039	+	0.465990i	0.968614	−	0.248570i	$-0.0799605\pi$
$257$	4.31303	+	7.47039i	0.269039	+	0.465990i	−0.699575	+	0.714560i	$0.746627\pi$
$258$	12.3257	+	9.85443i	0.767364	+	0.613510i
$259$	3.93567			0.244550
$260$	−1.32717	−	2.29873i	−0.0823078	−	0.142561i
$261$	0.640213	−	0.591084i	0.0396282	−	0.0365872i
$262$	6.30206	+	10.9155i	0.389342	+	0.674361i
$263$	−11.0513	−	19.1415i	−0.681455	−	1.18031i	−0.974537	−	0.224227i	$-0.928014\pi$
$263$	−11.0513	−	19.1415i	−0.681455	−	1.18031i	0.293082	−	0.956087i	$-0.405319\pi$
$264$	0.195488	+	0.156293i	0.0120314	+	0.00961918i
$265$	2.45604			0.150873
$266$	−1.19869	−	2.07619i	−0.0734963	−	0.127299i
$267$	8.71449	+	6.96726i	0.533318	+	0.426390i
$268$	−11.7407			−0.717176
$269$	−7.76488	+	13.4492i	−0.473433	+	0.820010i	−0.999538	−	0.0304096i	$-0.990319\pi$
$269$	−7.76488	+	13.4492i	−0.473433	+	0.820010i	0.526104	+	0.850420i	$0.323652\pi$
$270$	−1.63835	−	2.42231i	−0.0997066	−	0.147417i
$271$	−24.5909			−1.49379			−0.746894	−	0.664943i	$-0.768456\pi$
$271$	−24.5909			−1.49379			−0.746894	+	0.664943i	$0.768456\pi$
$272$	0.900123	−	1.55906i	0.0545780	−	0.0945318i
$273$	−6.41276	−	5.12702i	−0.388118	−	0.310301i
$274$	−3.18632	−	5.51886i	−0.192492	−	0.333407i
$275$	−0.338372	+	0.586078i	−0.0204046	+	0.0353418i
$276$	0.975797	−	6.41999i	0.0587361	−	0.386438i
$277$	−2.42178	−	4.19464i	−0.145510	−	0.252031i	0.784053	−	0.620694i	$-0.213149\pi$
$277$	−2.42178	−	4.19464i	−0.145510	−	0.252031i	−0.929563	+	0.368663i	$0.879816\pi$
$278$	−4.51929			−0.271049
$279$	−5.35416	+	15.8219i	−0.320545	+	0.947233i
$280$	0.565634			0.0338031
$281$	1.76336	+	3.05424i	0.105194	+	0.182201i	0.913817	−	0.406126i	$-0.133120\pi$
$281$	1.76336	+	3.05424i	0.105194	+	0.182201i	−0.808624	+	0.588326i	$0.799787\pi$
$282$	16.5063	−	6.45464i	0.982935	−	0.384368i
$283$	−0.972049	+	1.68364i	−0.0577823	+	0.100082i	−0.893470	−	0.449124i	$-0.851736\pi$
$283$	−0.972049	+	1.68364i	−0.0577823	+	0.100082i	0.835687	+	0.549206i	$0.185070\pi$
$284$	2.93897	+	5.09045i	0.174396	+	0.302063i
$285$	2.16549	−	0.846795i	0.128272	−	0.0501598i
$286$	−0.340767	+	0.590225i	−0.0201500	+	0.0349007i
$287$	−1.53404			−0.0905517
$288$	−2.86452	−	0.891369i	−0.168793	−	0.0525244i
$289$	6.87956	−	11.9157i	0.404680	−	0.700926i
$290$	−0.163463			−0.00959886
$291$	1.41186	−	9.28897i	0.0827649	−	0.544529i
$292$	2.10808	+	3.65130i	0.123366	+	0.213676i
$293$	22.0735			1.28955			0.644773	−	0.764374i	$-0.276952\pi$
$293$	22.0735			1.28955			0.644773	+	0.764374i	$0.276952\pi$
$294$	−9.66228	+	3.77835i	−0.563515	+	0.220358i
$295$	−0.329834	−	0.571289i	−0.0192037	−	0.0332618i
$296$	1.95794	+	3.39125i	0.113803	+	0.197112i
$297$	−0.328298	+	0.675283i	−0.0190498	+	0.0391839i
$298$	−2.44593	−	4.23647i	−0.141689	−	0.245412i
$299$	17.6825			1.02261
$300$	1.21892	−	8.01955i	0.0703744	−	0.463009i
$301$	−4.57854	−	7.93026i	−0.263903	−	0.457093i
$302$	−12.0587	+	20.8862i	−0.693898	+	1.20187i
$303$	2.93262	−	19.2944i	0.168475	−	1.10843i
$304$	1.19266	−	2.06575i	0.0684038	−	0.118479i
$305$	−0.950614	+	1.64651i	−0.0544320	+	0.0942790i
$306$	5.15684	+	1.60468i	0.294797	+	0.0917336i
$307$	−8.51193	−	14.7431i	−0.485801	−	0.841433i	0.514066	−	0.857751i	$-0.328139\pi$
$307$	−8.51193	−	14.7431i	−0.485801	−	0.841433i	−0.999867	+	0.0163183i	$0.994805\pi$
$308$	−0.0726165	−	0.125775i	−0.00413771	−	0.00716672i
$309$	2.95554	−	19.4451i	0.168135	−	1.10620i
$310$	2.75143	−	1.49944i	0.156271	−	0.0851627i
$311$	4.84163	−	8.38595i	0.274544	−	0.475523i	−0.695476	−	0.718549i	$-0.744807\pi$
$311$	4.84163	−	8.38595i	0.274544	−	0.475523i	0.970020	+	0.243026i	$0.0781399\pi$
$312$	1.22755	−	8.07630i	0.0694961	−	0.457231i
$313$	−0.386686	+	0.669760i	−0.0218568	+	0.0378571i	−0.876747	−	0.480952i	$-0.840291\pi$
$313$	−0.386686	+	0.669760i	−0.0218568	+	0.0378571i	0.854890	+	0.518809i	$0.173624\pi$
$314$	5.42155			0.305955
$315$	0.373495	+	1.65529i	0.0210440	+	0.0932650i
$316$	−2.92516	−	5.06652i	−0.164553	−	0.285014i
$317$	−7.24340	+	12.5459i	−0.406830	+	0.704650i	−0.994533	−	0.104427i	$-0.966699\pi$
$317$	−7.24340	+	12.5459i	−0.406830	+	0.704650i	0.587703	+	0.809077i	$0.300033\pi$
$318$	5.90381	+	4.72012i	0.331069	+	0.264691i
$319$	0.0209854	+	0.0363478i	0.00117496	+	0.00203509i
$320$	0.281395	+	0.487391i	0.0157305	+	0.0272460i
$321$	3.88168	−	25.5385i	0.216654	−	1.42542i
$322$	−1.88405	+	3.26327i	−0.104994	+	0.181855i
$323$	−2.14708	+	3.71885i	−0.119467	+	0.206923i
$324$	0.717055	−	8.97139i	0.0398364	−	0.498411i
$325$	22.0882			1.22523
$326$	−6.47930	−	11.2225i	−0.358855	−	0.621555i
$327$	4.42625	+	3.53880i	0.244772	+	0.195696i
$328$	−0.763164	−	1.32184i	−0.0421387	−	0.0729864i
$329$	−10.2843			−0.566994
$330$	0.131185	−	0.0512988i	0.00722150	−	0.00282391i
$331$	−21.8175			−1.19920			−0.599600	−	0.800300i	$-0.704674\pi$
$331$	−21.8175			−1.19920			−0.599600	+	0.800300i	$0.704674\pi$
$332$	−3.08762	+	5.34792i	−0.169455	+	0.293505i
$333$	−8.63140	+	7.96905i	−0.472998	+	0.436701i
$334$	−2.63275	−	4.56006i	−0.144058	−	0.249516i
$335$	−3.30377	+	5.72229i	−0.180504	+	0.312642i
$336$	1.35967	+	1.08706i	0.0741761	+	0.0593040i
$337$	6.85960	−	11.8812i	0.373666	−	0.647209i	−0.616460	−	0.787386i	$-0.711434\pi$
$337$	6.85960	−	11.8812i	0.373666	−	0.647209i	0.990126	+	0.140177i	$0.0447673\pi$
$338$	9.24451			0.502835
$339$	1.61747	−	10.6417i	0.0878490	−	0.577979i
$340$	−0.506580	−	0.877423i	−0.0274732	−	0.0475849i
$341$	−0.686649	−	0.419314i	−0.0371841	−	0.0227071i
$342$	6.83279	+	2.12620i	0.369475	+	0.114972i
$343$	13.0555			0.704932
$344$	4.55551	−	7.89038i	0.245617	−	0.425421i
$345$	−2.85446	−	2.28215i	−0.153679	−	0.122867i
$346$	5.98983	+	10.3747i	0.322015	+	0.557747i
$347$	14.3323			0.769399			0.384700	−	0.923042i	$-0.374305\pi$
$347$	14.3323			0.769399			0.384700	+	0.923042i	$0.374305\pi$
$348$	−0.392931	−	0.314149i	−0.0210633	−	0.0168402i
$349$	7.33248	+	12.7002i	0.392498	+	0.679827i	0.992778	−	0.119963i	$-0.0382775\pi$
$349$	7.33248	+	12.7002i	0.392498	+	0.679827i	−0.600280	+	0.799790i	$0.704944\pi$
$350$	−2.35347	+	4.07633i	−0.125798	+	0.217889i
$351$	24.4453	−	1.74054i	1.30479	−	0.0929034i
$352$	0.0722513	−	0.125143i	0.00385101	−	0.00667014i
$353$	6.25046	−	10.8261i	0.332678	−	0.576216i	−0.650358	−	0.759628i	$-0.725381\pi$
$353$	6.25046	−	10.8261i	0.332678	−	0.576216i	0.983036	+	0.183412i	$0.0587144\pi$
$354$	0.305074	−	2.00715i	0.0162145	−	0.106679i
$355$	3.30805			0.175573
$356$	3.22083	−	5.57865i	0.170704	−	0.295668i
$357$	−2.44774	−	1.95697i	−0.129548	−	0.103574i
$358$	−6.85731	+	11.8772i	−0.362420	+	0.627730i
$359$	−16.2102	+	28.0769i	−0.855543	+	1.48184i	0.0205965	+	0.999788i	$0.493443\pi$
$359$	−16.2102	+	28.0769i	−0.855543	+	1.48184i	−0.876140	+	0.482057i	$0.839890\pi$
$360$	−1.24051	+	1.14531i	−0.0653804	+	0.0603632i
$361$	6.65512	−	11.5270i	0.350270	−	0.606685i
$362$	−22.1782			−1.16566
$363$	14.8529	+	11.8749i	0.779575	+	0.623273i
$364$	−2.37012	+	4.10517i	−0.124228	+	0.215169i
$365$	2.37281			0.124199
$366$	−5.44942	+	2.13095i	−0.284846	+	0.111386i
$367$	−7.75185			−0.404643			−0.202322	−	0.979319i	$-0.564849\pi$
$367$	−7.75185			−0.404643			−0.202322	+	0.979319i	$0.564849\pi$
$368$	−3.74915			−0.195438
$369$	3.36434	−	3.10617i	0.175141	−	0.161701i
$370$	2.20382			0.114571
$371$	−2.19305	−	3.79847i	−0.113857	−	0.197207i
$372$	9.49558	+	1.68346i	0.492323	+	0.0872835i
$373$	4.35411	−	7.54154i	0.225447	−	0.390486i	−0.731006	−	0.682371i	$-0.760949\pi$
$373$	4.35411	−	7.54154i	0.225447	−	0.390486i	0.956454	+	0.291885i	$0.0942823\pi$
$374$	−0.130070	+	0.225288i	−0.00672577	+	0.0116494i
$375$	−7.37246	−	5.89430i	−0.380712	−	0.304380i
$376$	−5.11631	−	8.86171i	−0.263854	−	0.457008i
$377$	0.684942	−	1.18635i	0.0352763	−	0.0611003i
$378$	−2.28340	+	4.69677i	−0.117445	+	0.241576i
$379$	12.2708	+	21.2536i	0.630307	+	1.09172i	0.987489	+	0.157688i	$0.0504041\pi$
$379$	12.2708	+	21.2536i	0.630307	+	1.09172i	−0.357182	+	0.934035i	$0.616263\pi$
$380$	−0.671217	−	1.16258i	−0.0344327	−	0.0596392i
$381$	0.708076	−	4.65859i	0.0362758	−	0.238667i
$382$	7.44184	+	12.8897i	0.380758	+	0.659492i
$383$	−5.96267	−	10.3276i	−0.304678	−	0.527718i	0.672511	−	0.740087i	$-0.265216\pi$
$383$	−5.96267	−	10.3276i	−0.304678	−	0.527718i	−0.977190	+	0.212369i	$0.931882\pi$
$384$	−0.260271	+	1.71238i	−0.0132819	+	0.0873847i
$385$	−0.0817357			−0.00416563
$386$	9.35593	+	16.2050i	0.476204	+	0.824810i
$387$	26.0987	+	8.12129i	1.32667	+	0.412828i
$388$	−5.42458			−0.275392
$389$	−17.6419	+	30.5566i	−0.894478	+	1.54928i	−0.0600277	+	0.998197i	$0.519119\pi$
$389$	−17.6419	+	30.5566i	−0.894478	+	1.54928i	−0.834450	+	0.551084i	$0.814214\pi$
$390$	−3.59089	−	2.87093i	−0.181832	−	0.145375i
$391$	6.74940			0.341332
$392$	2.99493	+	5.18738i	0.151267	+	0.262002i
$393$	17.0512	+	13.6325i	0.860122	+	0.687670i
$394$	14.1600			0.713372
$395$	−3.29250			−0.165664
$396$	0.413930	+	0.128805i	0.0208008	+	0.00647270i
$397$	−5.24729	−	9.08858i	−0.263354	−	0.456143i	0.703777	−	0.710421i	$-0.251495\pi$
$397$	−5.24729	−	9.08858i	−0.263354	−	0.456143i	−0.967131	+	0.254278i	$0.918162\pi$
$398$	9.31745			0.467041
$399$	−3.24325	−	2.59299i	−0.162365	−	0.129812i
$400$	−4.68327			−0.234163
$401$	17.4404	−	30.2077i	0.870933	−	1.50850i	0.00989984	−	0.999951i	$-0.496849\pi$
$401$	17.4404	−	30.2077i	0.870933	−	1.50850i	0.861033	−	0.508549i	$-0.169818\pi$
$402$	−18.9389	+	7.40590i	−0.944587	+	0.369373i
$403$	−0.646634	+	26.2519i	−0.0322111	+	1.30770i
$404$	−11.2676			−0.560582
$405$	−4.17079	−	2.87399i	−0.207248	−	0.142810i
$406$	0.145959	+	0.252809i	0.00724383	+	0.0125467i
$407$	−0.282927	−	0.490044i	−0.0140242	−	0.0242906i
$408$	0.468552	−	3.08271i	0.0231968	−	0.152617i
$409$	−4.12542			−0.203989			−0.101994	−	0.994785i	$-0.532522\pi$
$409$	−4.12542			−0.203989			−0.101994	+	0.994785i	$0.532522\pi$
$410$	−0.859003			−0.0424231
$411$	−8.62111	−	6.89260i	−0.425248	−	0.339987i
$412$	−11.3556			−0.559450
$413$	−0.589032	+	1.02023i	−0.0289843	+	0.0502024i
$414$	−2.47561	−	10.9716i	−0.121669	−	0.539226i
$415$	1.73768	+	3.00976i	0.0852996	+	0.147743i
$416$	−4.71641			−0.231241
$417$	−7.29008	+	2.85072i	−0.356997	+	0.139601i
$418$	−0.172343	+	0.298506i	−0.00842955	+	0.0146004i
$419$	−4.66325	+	8.07699i	−0.227815	+	0.394587i	−0.957160	−	0.289559i	$-0.906491\pi$
$419$	−4.66325	+	8.07699i	−0.227815	+	0.394587i	0.729345	+	0.684146i	$0.239825\pi$
$420$	0.912427	−	0.356797i	0.0445219	−	0.0174099i
$421$	−27.1655			−1.32396			−0.661982	−	0.749519i	$-0.730285\pi$
$421$	−27.1655			−1.32396			−0.661982	+	0.749519i	$0.730285\pi$
$422$	4.01230	+	6.94950i	0.195315	+	0.338296i
$423$	22.5548	−	20.8240i	1.09665	−	1.01250i
$424$	2.18202	−	3.77937i	0.105968	−	0.183542i
$425$	8.43103			0.408965
$426$	7.95187	+	6.35755i	0.385270	+	0.308024i
$427$	3.39529			0.164310
$428$	−14.9140			−0.720895
$429$	−0.177384	+	1.16705i	−0.00856416	+	0.0563456i
$430$	−2.56380	−	4.44063i	−0.123637	−	0.214146i
$431$	−12.0917	−	20.9434i	−0.582435	−	1.00881i	−0.995190	−	0.0979652i	$-0.968767\pi$
$431$	−12.0917	−	20.9434i	−0.582435	−	1.00881i	0.412755	−	0.910842i	$-0.364567\pi$
$432$	−5.18303	+	0.369040i	−0.249369	+	0.0177555i
$433$	−12.9103			−0.620429			−0.310215	−	0.950667i	$-0.600401\pi$
$433$	−12.9103			−0.620429			−0.310215	+	0.950667i	$0.600401\pi$
$434$	−4.77583	−	2.91644i	−0.229247	−	0.139994i
$435$	−0.263682	+	0.103111i	−0.0126426	+	0.00494378i
$436$	1.63592	−	2.83350i	0.0783464	−	0.135700i
$437$	8.94293			0.427798
$438$	5.70376	+	4.56017i	0.272536	+	0.217893i
$439$	4.28157			0.204348			0.102174	−	0.994767i	$-0.467420\pi$
$439$	4.28157			0.204348			0.102174	+	0.994767i	$0.467420\pi$
$440$	−0.0406623	−	0.0704292i	−0.00193850	−	0.00335758i
$441$	−13.2029	+	12.1897i	−0.628710	+	0.580464i
$442$	8.49069			0.403861
$443$	−23.0099			−1.09323			−0.546616	−	0.837383i	$-0.684084\pi$
$443$	−23.0099			−1.09323			−0.546616	+	0.837383i	$0.684084\pi$
$444$	5.29752	+	4.23539i	0.251409	+	0.201003i
$445$	−1.81265	−	3.13961i	−0.0859280	−	0.148832i
$446$	−14.5273			−0.687886
$447$	−6.61787	−	5.29100i	−0.313014	−	0.250256i
$448$	0.502527	−	0.870402i	0.0237422	−	0.0411226i
$449$	−0.738049			−0.0348307			−0.0174153	−	0.999848i	$-0.505544\pi$
$449$	−0.738049			−0.0348307			−0.0174153	+	0.999848i	$0.505544\pi$
$450$	−3.09241	−	13.7053i	−0.145778	−	0.646072i
$451$	0.110279	+	0.191009i	0.00519285	+	0.00899427i
$452$	−6.21456			−0.292308
$453$	−6.27705	+	41.2981i	−0.294921	+	1.94035i
$454$	−9.41079	−	16.3000i	−0.441670	−	0.764995i
$455$	1.33388	+	2.31035i	0.0625333	+	0.108311i
$456$	0.620830	−	4.08459i	0.0290731	−	0.191278i
$457$	−18.3750	−	31.8265i	−0.859548	−	1.48878i	−0.872361	−	0.488863i	$-0.837412\pi$
$457$	−18.3750	−	31.8265i	−0.859548	−	1.48878i	0.0128131	−	0.999918i	$-0.495921\pi$
$458$	−0.879392	−	1.52315i	−0.0410913	−	0.0711722i
$459$	9.33073	−	0.664363i	0.435521	−	0.0310098i
$460$	−1.05499	+	1.82730i	−0.0491893	+	0.0851984i
$461$	12.6047	+	21.8321i	0.587062	+	1.01682i	0.994615	+	0.103639i	$0.0330487\pi$
$461$	12.6047	+	21.8321i	0.587062	+	1.01682i	−0.407553	+	0.913181i	$0.633618\pi$
$462$	−0.196476	−	0.157083i	−0.00914088	−	0.00730816i
$463$	1.36131	−	2.35786i	0.0632655	−	0.109579i	−0.832658	−	0.553788i	$-0.813182\pi$
$463$	1.36131	−	2.35786i	0.0632655	−	0.109579i	0.895923	+	0.444209i	$0.146515\pi$
$464$	−0.145225	+	0.251538i	−0.00674191	+	0.0116773i
$465$	3.49251	−	4.15434i	0.161961	−	0.192653i
$466$	11.6185	+	20.1239i	0.538217	+	0.932219i
$467$	2.41485			0.111746			0.0558730	−	0.998438i	$-0.482206\pi$
$467$	2.41485			0.111746			0.0558730	+	0.998438i	$0.482206\pi$
$468$	−3.11430	−	13.8022i	−0.143958	−	0.638009i
$469$	11.8000			0.544874
$470$	−5.75882			−0.265634
$471$	8.74551	−	3.41986i	0.402972	−	0.157579i
$472$	−1.17214			−0.0539521
$473$	−0.658284	+	1.14018i	−0.0302679	+	0.0524256i
$474$	−7.91449	−	6.32766i	−0.363525	−	0.290639i
$475$	11.1711			0.512565
$476$	−0.904672	+	1.56694i	−0.0414656	+	0.0718205i
$477$	12.5009	+	3.88997i	0.572375	+	0.178109i
$478$	−4.44457	+	7.69823i	−0.203290	+	0.352109i
$479$	−16.3308	+	28.2858i	−0.746173	+	1.29241i	0.203472	+	0.979081i	$0.434778\pi$
$479$	−16.3308	+	28.2858i	−0.746173	+	1.29241i	−0.949645	+	0.313329i	$0.898556\pi$
$480$	0.761361	+	0.608710i	0.0347512	+	0.0277837i
$481$	−9.23444	+	15.9945i	−0.421054	+	0.729287i
$482$	−14.7318			−0.671014
$483$	−0.980728	+	6.45244i	−0.0446247	+	0.293596i
$484$	5.48956	−	9.50820i	0.249525	−	0.432191i
$485$	−1.52645	+	2.64389i	−0.0693126	+	0.120053i
$486$	−4.50238	−	14.9241i	−0.204232	−	0.676971i
$487$	−18.4595	+	31.9728i	−0.836480	+	1.44883i	0.0563390	+	0.998412i	$0.482057\pi$
$487$	−18.4595	+	31.9728i	−0.836480	+	1.44883i	−0.892819	+	0.450415i	$0.851276\pi$
$488$	1.68911	+	2.92562i	0.0764624	+	0.132437i
$489$	−17.5308	−	14.0159i	−0.792771	−	0.633822i
$490$	3.37104			0.152288
$491$	−7.05101	−	12.2127i	−0.318207	−	0.551152i	0.661907	−	0.749586i	$-0.269748\pi$
$491$	−7.05101	−	12.2127i	−0.318207	−	0.551152i	−0.980114	+	0.198435i	$0.936414\pi$
$492$	−2.06487	−	1.65087i	−0.0930914	−	0.0744268i
$493$	0.261441	−	0.452829i	0.0117747	−	0.0203944i
$494$	11.2501			0.506168
$495$	0.179256	−	0.165501i	0.00805697	−	0.00743870i
$496$	0.137103	−	5.56608i	0.00615611	−	0.249924i
$497$	−2.95383	−	5.11618i	−0.132497	−	0.229492i
$498$	−1.60724	+	10.5744i	−0.0720221	+	0.473850i
$499$	−34.2964			−1.53532			−0.767659	−	0.640859i	$-0.778579\pi$
$499$	−34.2964			−1.53532			−0.767659	+	0.640859i	$0.778579\pi$
$500$	−2.72482	+	4.71953i	−0.121858	+	0.211064i
$501$	−7.12335	−	5.69514i	−0.318248	−	0.254440i
$502$	1.91785	−	3.32181i	0.0855977	−	0.148260i
$503$	9.19335	+	15.9234i	0.409911	+	0.709987i	0.994879	−	0.101069i	$-0.0322263\pi$
$503$	9.19335	+	15.9234i	0.409911	+	0.709987i	−0.584968	+	0.811056i	$0.698893\pi$
$504$	2.87899	+	0.895874i	0.128241	+	0.0399054i
$505$	−3.17063	+	5.49170i	−0.141091	+	0.244377i
$506$	0.541762			0.0240843
$507$	14.9123	−	5.83135i	0.662281	−	0.258979i
$508$	−2.72053			−0.120704
$509$	13.1934	+	22.8516i	0.584786	+	1.01288i	0.994902	+	0.100846i	$0.0321549\pi$
$509$	13.1934	+	22.8516i	0.584786	+	1.01288i	−0.410116	+	0.912033i	$0.634512\pi$
$510$	−1.37064	−	1.09583i	−0.0606928	−	0.0485241i
$511$	−2.11873	−	3.66975i	−0.0937273	−	0.162340i
$512$	1.00000			0.0441942
$513$	12.3632	−	0.880280i	0.545848	−	0.0388653i
$514$	4.31303	−	7.47039i	0.190240	−	0.329505i
$515$	−3.19541	+	5.53461i	−0.140807	+	0.243884i
$516$	2.37134	−	15.6016i	0.104392	−	0.686821i
$517$	0.739320	+	1.28054i	0.0325153	+	0.0563181i
$518$	−1.96783	−	3.40839i	−0.0864616	−	0.149756i
$519$	16.2065	+	12.9571i	0.711385	+	0.568755i
$520$	−1.32717	+	2.29873i	−0.0582004	+	0.100806i
$521$	16.4542	+	28.4995i	0.720871	+	1.24859i	0.960651	+	0.277758i	$0.0895913\pi$
$521$	16.4542	+	28.4995i	0.720871	+	1.24859i	−0.239780	+	0.970827i	$0.577075\pi$
$522$	−0.832001	−	0.258898i	−0.0364157	−	0.0113317i
$523$	−22.4005			−0.979506			−0.489753	−	0.871861i	$-0.662913\pi$
$523$	−22.4005			−0.979506			−0.489753	+	0.871861i	$0.662913\pi$
$524$	6.30206	−	10.9155i	0.275307	−	0.476845i
$525$	−1.22508	+	8.06008i	−0.0534669	+	0.351771i
$526$	−11.0513	+	19.1415i	−0.481861	+	0.834608i
$527$	−0.246819	+	10.0203i	−0.0107516	+	0.436491i
$528$	0.0376099	−	0.247444i	0.00163676	−	0.0107686i
$529$	4.47193	+	7.74560i	0.194432	+	0.336765i
$530$	−1.22802	−	2.12699i	−0.0533417	−	0.0923906i
$531$	−0.773976	−	3.43018i	−0.0335877	−	0.148857i
$532$	−1.19869	+	2.07619i	−0.0519697	+	0.0900142i
$533$	3.59939	−	6.23433i	0.155907	−	0.270039i
$534$	1.67658	−	11.0306i	0.0725527	−	0.477341i
$535$	−4.19672	+	7.26894i	−0.181440	+	0.314264i
$536$	5.87033	+	10.1677i	0.253560	+	0.439179i
$537$	−3.56952	+	23.4847i	−0.154036	+	1.01344i
$538$	15.5298			0.669536
$539$	−0.432776	−	0.749590i	−0.0186410	−	0.0322871i
$540$	−1.27861	+	2.63001i	−0.0550227	+	0.113177i
$541$	7.32005	+	12.6787i	0.314714	+	0.545100i	0.979377	−	0.202043i	$-0.0647582\pi$
$541$	7.32005	+	12.6787i	0.314714	+	0.545100i	−0.664663	+	0.747143i	$0.731425\pi$
$542$	12.2954	+	21.2963i	0.528134	+	0.914755i
$543$	−35.7758	+	13.9898i	−1.53529	+	0.600360i
$544$	−1.80025			−0.0771849
$545$	−0.920680	−	1.59466i	−0.0394376	−	0.0683079i
$546$	−1.23375	+	8.11712i	−0.0527996	+	0.347381i
$547$	−10.5410			−0.450700			−0.225350	−	0.974278i	$-0.572353\pi$
$547$	−10.5410			−0.450700			−0.225350	+	0.974278i	$0.572353\pi$
$548$	−3.18632	+	5.51886i	−0.136113	+	0.235754i
$549$	−7.44630	+	6.87488i	−0.317800	+	0.293413i
$550$	0.676744			0.0288565
$551$	0.346409	−	0.599998i	0.0147575	−	0.0255608i
$552$	−6.04777	+	2.36493i	−0.257410	+	0.100658i
$553$	2.93994	+	5.09213i	0.125019	+	0.216539i
$554$	−2.42178	+	4.19464i	−0.102891	+	0.178213i
$555$	3.55498	−	1.39015i	0.150901	−	0.0590084i
$556$	2.25964	+	3.91382i	0.0958302	+	0.165983i
$557$	−20.9081			−0.885905			−0.442952	−	0.896545i	$-0.646069\pi$
$557$	−20.9081			−0.885905			−0.442952	+	0.896545i	$0.646069\pi$
$558$	16.3793	−	3.27412i	0.693389	−	0.138604i
$559$	42.9713			1.81749
$560$	−0.282817	−	0.489854i	−0.0119512	−	0.0207001i
$561$	−0.0677070	+	0.445460i	−0.00285859	+	0.0188073i
$562$	1.76336	−	3.05424i	0.0743830	−	0.128835i
$563$	−11.8782	−	20.5737i	−0.500608	−	0.867079i	−1.00000		0.000702709i	$-0.999776\pi$
$563$	−11.8782	−	20.5737i	−0.500608	−	0.867079i	0.499391	−	0.866377i	$-0.333557\pi$
$564$	−13.8430	−	11.0675i	−0.582896	−	0.466027i
$565$	−1.74875	+	3.02892i	−0.0735703	+	0.127428i
$566$	1.94410			0.0817165
$567$	−0.720679	+	9.01673i	−0.0302657	+	0.378667i
$568$	2.93897	−	5.09045i	0.123317	−	0.213591i
$569$	34.4043			1.44230			0.721152	−	0.692777i	$-0.243613\pi$
$569$	34.4043			1.44230			0.721152	+	0.692777i	$0.243613\pi$
$570$	−1.81609	−	1.45197i	−0.0760676	−	0.0608163i
$571$	−1.90725	−	3.30345i	−0.0798159	−	0.138245i	0.823355	−	0.567527i	$-0.192100\pi$
$571$	−1.90725	−	3.30345i	−0.0798159	−	0.138245i	−0.903170	+	0.429282i	$0.858767\pi$
$572$	0.681533			0.0284963
$573$	20.1351	+	16.0981i	0.841157	+	0.672508i
$574$	0.767021	+	1.32852i	0.0320148	+	0.0554513i
$575$	−8.77914	−	15.2059i	−0.366116	−	0.634131i
$576$	0.660311	+	2.92643i	0.0275130	+	0.121935i
$577$	−15.1861	−	26.3032i	−0.632207	−	1.09502i	−0.987100	−	0.160108i	$-0.948816\pi$
$577$	−15.1861	−	26.3032i	−0.632207	−	1.09502i	0.354892	−	0.934907i	$-0.384518\pi$
$578$	−13.7591			−0.572304
$579$	25.3140	+	20.2386i	1.05201	+	0.841089i
$580$	0.0817313	+	0.141563i	0.00339371	+	0.00587808i
$581$	3.10323	−	5.37495i	0.128744	−	0.222991i
$582$	−8.75042	+	3.42178i	−0.362716	+	0.141837i
$583$	−0.315308	+	0.546129i	−0.0130587	+	0.0226183i
$584$	2.10808	−	3.65130i	0.0872330	−	0.151092i
$585$	−7.60343	−	2.36600i	−0.314363	−	0.0978222i
$586$	−11.0367	−	19.1162i	−0.455923	−	0.789682i
$587$	5.22247	+	9.04558i	0.215554	+	0.373351i	0.953444	−	0.301570i	$-0.0975108\pi$
$587$	5.22247	+	9.04558i	0.215554	+	0.373351i	−0.737890	+	0.674921i	$0.764178\pi$
$588$	8.10329	+	6.47860i	0.334174	+	0.267173i
$589$	−0.327035	+	13.2769i	−0.0134752	+	0.547064i
$590$	−0.329834	+	0.571289i	−0.0135791	+	0.0235196i
$591$	22.8416	−	8.93201i	0.939578	−	0.367414i
$592$	1.95794	−	3.39125i	0.0804708	−	0.139379i
$593$	−37.7447			−1.54999			−0.774995	−	0.631968i	$-0.782247\pi$
$593$	−37.7447			−1.54999			−0.774995	+	0.631968i	$0.782247\pi$
$594$	0.748962	−	0.0533273i	0.0307303	−	0.00218805i
$595$	0.509140	+	0.881857i	0.0208727	+	0.0361526i
$596$	−2.44593	+	4.23647i	−0.100189	+	0.173533i
$597$	15.0300	−	5.87736i	0.615137	−	0.240544i
$598$	−8.84127	−	15.3135i	−0.361546	−	0.626217i
$599$	−19.4496	−	33.6877i	−0.794690	−	1.37644i	−0.923036	−	0.384714i	$-0.874300\pi$
$599$	−19.4496	−	33.6877i	−0.794690	−	1.37644i	0.128346	−	0.991729i	$-0.459033\pi$
$600$	−7.55460	+	2.95416i	−0.308415	+	0.120603i
$601$	9.99816	−	17.3173i	0.407834	−	0.706388i	−0.586813	−	0.809722i	$-0.699618\pi$
$601$	9.99816	−	17.3173i	0.407834	−	0.706388i	0.994647	+	0.103334i	$0.0329510\pi$
$602$	−4.57854	+	7.93026i	−0.186607	+	0.323213i
$603$	−25.8789	+	23.8930i	−1.05387	+	0.972997i
$604$	24.1173			0.981320
$605$	−3.08947	−	5.35112i	−0.125605	−	0.217554i
$606$	−18.1757	+	7.10747i	−0.738339	+	0.288721i
$607$	13.4027	+	23.2142i	0.544000	+	0.942236i	0.998669	+	0.0515758i	$0.0164244\pi$
$607$	13.4027	+	23.2142i	0.544000	+	0.942236i	−0.454669	+	0.890661i	$0.650242\pi$
$608$	−2.38532			−0.0967375
$609$	0.394917	+	0.315737i	0.0160028	+	0.0127943i
$610$	1.90123			0.0769785
$611$	24.1306	−	41.7954i	0.976220	−	1.69086i
$612$	−1.18872	−	5.26829i	−0.0480512	−	0.212958i
$613$	−0.164854	−	0.285536i	−0.00665840	−	0.0115327i	0.862677	−	0.505755i	$-0.168786\pi$
$613$	−0.164854	−	0.285536i	−0.00665840	−	0.0115327i	−0.869335	+	0.494223i	$0.835453\pi$
$614$	−8.51193	+	14.7431i	−0.343513	+	0.594983i
$615$	−1.38566	+	0.541851i	−0.0558752	+	0.0218495i
$616$	−0.0726165	+	0.125775i	−0.00292580	+	0.00506764i
$617$	−34.0625			−1.37130			−0.685652	−	0.727930i	$-0.740483\pi$
$617$	−34.0625			−1.37130			−0.685652	+	0.727930i	$0.740483\pi$
$618$	−18.3178	+	7.16300i	−0.736848	+	0.288138i
$619$	10.7938	+	18.6954i	0.433838	+	0.751430i	0.997200	−	0.0747805i	$-0.0238256\pi$
$619$	10.7938	+	18.6954i	0.433838	+	0.751430i	−0.563362	+	0.826210i	$0.690492\pi$
$620$	−2.67427	−	1.63309i	−0.107401	−	0.0655864i
$621$	−10.9142	−	16.1368i	−0.437972	−	0.647547i
$622$	−9.68326			−0.388263
$623$	−3.23711	+	5.60684i	−0.129692	+	0.224633i
$624$	−7.60806	+	2.97507i	−0.304566	+	0.119098i
$625$	−10.1747	−	17.6230i	−0.406987	−	0.704921i
$626$	0.773372			0.0309102
$627$	−0.0897116	+	0.590233i	−0.00358274	+	0.0235716i
$628$	−2.71077	−	4.69520i	−0.108172	−	0.187359i
$629$	−3.52477	+	6.10508i	−0.140542	+	0.243425i
$630$	1.24678	−	1.15110i	0.0496727	−	0.0458609i
$631$	−1.47927	+	2.56218i	−0.0588889	+	0.101999i	−0.893967	−	0.448133i	$-0.852089\pi$
$631$	−1.47927	+	2.56218i	−0.0588889	+	0.101999i	0.835078	+	0.550132i	$0.185422\pi$
$632$	−2.92516	+	5.06652i	−0.116357	+	0.201535i
$633$	10.8559	+	8.67935i	0.431484	+	0.344973i
$634$	14.4868			0.575345
$635$	−0.765544	+	1.32596i	−0.0303797	+	0.0526192i
$636$	1.13583	−	7.47291i	0.0450387	−	0.296320i
$637$	−14.1253	+	24.4658i	−0.559666	+	0.969370i
$638$	0.0209854	−	0.0363478i	0.000830821	−	0.00143902i
$639$	16.8375	+	5.23942i	0.666080	+	0.207268i
$640$	0.281395	−	0.487391i	0.0111231	−	0.0192658i
$641$	27.1398			1.07196			0.535978	−	0.844232i	$-0.319943\pi$
$641$	27.1398			1.07196			0.535978	+	0.844232i	$0.319943\pi$
$642$	−24.0578	+	9.40760i	−0.949486	+	0.371288i
$643$	21.2148	−	36.7450i	0.836628	−	1.44908i	−0.0560698	−	0.998427i	$-0.517857\pi$
$643$	21.2148	−	36.7450i	0.836628	−	1.44908i	0.892698	−	0.450656i	$-0.148810\pi$
$644$	3.76810			0.148484
$645$	−6.93678	−	5.54598i	−0.273135	−	0.218373i
$646$	4.29416			0.168952
$647$	−23.6612			−0.930219			−0.465109	−	0.885253i	$-0.653985\pi$
$647$	−23.6612			−0.930219			−0.465109	+	0.885253i	$0.653985\pi$
$648$	−8.12798	+	3.86471i	−0.319297	+	0.151820i
$649$	0.169377			0.00664864
$650$	−11.0441	−	19.1289i	−0.433185	−	0.750299i
$651$	−9.54357	−	1.69197i	−0.374042	−	0.0663136i
$652$	−6.47930	+	11.2225i	−0.253749	+	0.439506i
$653$	21.6145	−	37.4374i	0.845840	−	1.46504i	−0.0390505	−	0.999237i	$-0.512433\pi$
$653$	21.6145	−	37.4374i	0.845840	−	1.46504i	0.884890	−	0.465800i	$-0.154233\pi$
$654$	0.851566	−	5.60265i	0.0332989	−	0.219081i
$655$	−3.54673	−	6.14312i	−0.138582	−	0.240032i
$656$	−0.763164	+	1.32184i	−0.0297966	+	0.0516092i
$657$	12.0773	+	3.75815i	0.471179	+	0.146619i
$658$	5.14217	+	8.90650i	0.200463	+	0.347211i
$659$	−11.6466	−	20.1725i	−0.453686	−	0.785807i	0.544925	−	0.838485i	$-0.316558\pi$
$659$	−11.6466	−	20.1725i	−0.453686	−	0.785807i	−0.998612	+	0.0526770i	$0.983225\pi$
$660$	−0.110019	−	0.0879602i	−0.00428247	−	0.00342385i
$661$	−8.59534	−	14.8876i	−0.334320	−	0.579059i	0.649034	−	0.760759i	$-0.275173\pi$
$661$	−8.59534	−	14.8876i	−0.334320	−	0.579059i	−0.983354	+	0.181700i	$0.941840\pi$
$662$	10.9088	+	18.8945i	0.423981	+	0.734357i
$663$	13.6964	−	5.35585i	0.531923	−	0.208004i
$664$	6.17525			0.239646
$665$	0.674610	+	1.16846i	0.0261602	+	0.0453109i
$666$	11.2171	+	3.49049i	0.434654	+	0.135254i
$667$	−1.08894			−0.0421641
$668$	−2.63275	+	4.56006i	−0.101864	+	0.176434i
$669$	−23.4340	+	9.16366i	−0.906010	+	0.354287i
$670$	6.60753			0.255271
$671$	−0.244081	−	0.422760i	−0.00942264	−	0.0163205i
$672$	0.261587	−	1.72104i	0.0100909	−	0.0663905i
$673$	42.3826			1.63373			0.816865	−	0.576829i	$-0.195710\pi$
$673$	42.3826			1.63373			0.816865	+	0.576829i	$0.195710\pi$
$674$	−13.7192			−0.528444
$675$	−13.6335	−	20.1573i	−0.524755	−	0.775856i
$676$	−4.62225	−	8.00598i	−0.177779	−	0.307922i
$677$	42.3470			1.62753			0.813764	−	0.581195i	$-0.197415\pi$
$677$	42.3470			1.62753			0.813764	+	0.581195i	$0.197415\pi$
$678$	−10.0247	+	3.92009i	−0.384998	+	0.150550i
$679$	5.45200			0.209229
$680$	−0.506580	+	0.877423i	−0.0194265	+	0.0336476i
$681$	−25.4624	−	20.3573i	−0.975723	−	0.780093i
$682$	−0.0198118	+	0.804313i	−0.000758631	+	0.0307987i
$683$	7.88799			0.301825			0.150913	−	0.988547i	$-0.451779\pi$
$683$	7.88799			0.301825			0.150913	+	0.988547i	$0.451779\pi$
$684$	−1.57505	−	6.98047i	−0.0602237	−	0.266905i
$685$	1.79323	+	3.10596i	0.0685157	+	0.118673i
$686$	−6.52776	−	11.3064i	−0.249231	−	0.431681i
$687$	−2.37934	−	1.90229i	−0.0907775	−	0.0725769i
$688$	−9.11103			−0.347355
$689$	20.5826			0.784134
$690$	−0.549169	+	3.61311i	−0.0209065	+	0.137549i
$691$	−43.8693			−1.66887			−0.834433	−	0.551109i	$-0.814205\pi$
$691$	−43.8693			−1.66887			−0.834433	+	0.551109i	$0.814205\pi$
$692$	5.98983	−	10.3747i	0.227699	−	0.394387i
$693$	−0.416022	−	0.129456i	−0.0158034	−	0.00491763i
$694$	−7.16616	−	12.4122i	−0.272024	−	0.471159i
$695$	2.54341			0.0964770
$696$	−0.0755959	+	0.497363i	−0.00286546	+	0.0188525i
$697$	1.37388	−	2.37964i	0.0520395	−	0.0901351i
$698$	7.33248	−	12.7002i	0.277538	−	0.480710i
$699$	31.4358	+	25.1330i	1.18901	+	0.950618i
$700$	4.70694			0.177905
$701$	−0.0214641	−	0.0371768i	−0.000810686	−	0.00140415i	0.865620	−	0.500702i	$-0.166925\pi$
$701$	−0.0214641	−	0.0371768i	−0.000810686	−	0.00140415i	−0.866430	+	0.499298i	$0.833591\pi$
$702$	−13.7300	−	20.3000i	−0.518205	−	0.766173i
$703$	−4.67031	+	8.08922i	−0.176144	+	0.305091i
$704$	−0.144503			−0.00544615
$705$	−9.28957	+	3.63261i	−0.349865	+	0.136812i
$706$	−12.5009			−0.470478
$707$	11.3245			0.425902
$708$	−1.89078	+	0.739374i	−0.0710599	+	0.0277874i
$709$	−14.5464	−	25.1950i	−0.546300	−	0.946220i	−0.998524	−	0.0543151i	$-0.982702\pi$
$709$	−14.5464	−	25.1950i	−0.546300	−	0.946220i	0.452224	−	0.891905i	$-0.350631\pi$
$710$	−1.65402	−	2.86485i	−0.0620744	−	0.107516i
$711$	−16.7583	−	5.21479i	−0.628486	−	0.195570i
$712$	−6.44167			−0.241412
$713$	18.3293	−	9.98888i	0.686437	−	0.374087i
$714$	−0.470920	+	3.09829i	−0.0176237	+	0.115951i
$715$	0.191780	−	0.332173i	0.00717217	−	0.0124226i
$716$	13.7146			0.512539
$717$	−2.31359	+	15.2216i	−0.0864026	+	0.568462i
$718$	32.4205			1.20992
$719$	−2.08236	−	3.60676i	−0.0776590	−	0.134509i	0.824580	−	0.565745i	$-0.191411\pi$
$719$	−2.08236	−	3.60676i	−0.0776590	−	0.134509i	−0.902240	+	0.431235i	$0.858078\pi$
$720$	1.61212	+	0.501653i	0.0600802	+	0.0186955i
$721$	11.4130			0.425042
$722$	−13.3102			−0.495356
$723$	−23.7639	+	9.29267i	−0.883789	+	0.345598i
$724$	11.0891	+	19.2069i	0.412124	+	0.713819i
$725$	−1.36026			−0.0505187
$726$	2.85755	−	18.8005i	0.106054	−	0.697751i
$727$	1.22498	−	2.12173i	0.0454320	−	0.0786906i	−0.842415	−	0.538829i	$-0.818867\pi$
$727$	1.22498	−	2.12173i	0.0454320	−	0.0786906i	0.887847	+	0.460138i	$0.152200\pi$
$728$	4.74024			0.175685
$729$	−16.6768	−	21.2340i	−0.617659	−	0.786446i
$730$	−1.18641	−	2.05492i	−0.0439109	−	0.0760559i
$731$	16.4021			0.606653
$732$	4.57017	+	3.65386i	0.168918	+	0.135051i
$733$	−6.03051	−	10.4452i	−0.222742	−	0.385801i	0.732898	−	0.680339i	$-0.238167\pi$
$733$	−6.03051	−	10.4452i	−0.222742	−	0.385801i	−0.955640	+	0.294538i	$0.904834\pi$
$734$	3.87593	+	6.71330i	0.143063	+	0.247792i
$735$	5.43783	−	2.12642i	0.200577	−	0.0784341i
$736$	1.87458	+	3.24686i	0.0690978	+	0.119681i
$737$	−0.848279	−	1.46926i	−0.0312468	−	0.0541210i
$738$	−4.37220	−	1.36052i	−0.160943	−	0.0500815i
$739$	−22.3007	+	38.6259i	−0.820343	+	1.42088i	0.0850836	+	0.996374i	$0.472884\pi$
$739$	−22.3007	+	38.6259i	−0.820343	+	1.42088i	−0.905427	+	0.424502i	$0.860449\pi$
$740$	−1.10191	−	1.90856i	−0.0405070	−	0.0701601i
$741$	18.1477	−	7.09648i	0.666671	−	0.260696i
$742$	−2.19305	+	3.79847i	−0.0805093	+	0.139446i
$743$	4.26426	−	7.38592i	0.156441	−	0.270963i	−0.777142	−	0.629325i	$-0.783331\pi$
$743$	4.26426	−	7.38592i	0.156441	−	0.270963i	0.933583	+	0.358362i	$0.116665\pi$
$744$	−3.28987	−	9.06514i	−0.120612	−	0.332344i
$745$	1.37654	+	2.38425i	0.0504327	+	0.0873520i
$746$	−8.70822			−0.318831
$747$	4.07758	+	18.0714i	0.149191	+	0.661199i
$748$	0.260140			0.00951167
$749$	14.9894			0.547699
$750$	−1.41839	+	9.33189i	−0.0517922	+	0.340752i
$751$	−24.8545			−0.906955			−0.453477	−	0.891268i	$-0.649817\pi$
$751$	−24.8545			−0.906955			−0.453477	+	0.891268i	$0.649817\pi$
$752$	−5.11631	+	8.86171i	−0.186573	+	0.323153i
$753$	0.998321	−	6.56818i	0.0363808	−	0.239358i
$754$	−1.36988			−0.0498882
$755$	6.78649	−	11.7546i	0.246986	−	0.427792i
$756$	5.20923	−	0.370905i	0.189458	−	0.0134897i
$757$	−0.273055	+	0.472945i	−0.00992435	+	0.0171895i	−0.870945	−	0.491381i	$-0.836492\pi$
$757$	−0.273055	+	0.472945i	−0.00992435	+	0.0171895i	0.861021	+	0.508570i	$0.169826\pi$
$758$	12.2708	−	21.2536i	0.445694	−	0.771965i
$759$	0.873919	−	0.341739i	0.0317213	−	0.0124043i
$760$	−0.671217	+	1.16258i	−0.0243476	+	0.0421713i
$761$	−22.0763			−0.800265			−0.400133	−	0.916457i	$-0.631036\pi$
$761$	−22.0763			−0.800265			−0.400133	+	0.916457i	$0.631036\pi$
$762$	−4.38850	+	1.71608i	−0.158979	+	0.0621672i
$763$	−1.64419	+	2.84782i	−0.0595236	+	0.103098i
$764$	7.44184	−	12.8897i	0.269236	−	0.466331i
$765$	−2.90222	−	0.903099i	−0.104930	−	0.0326516i
$766$	−5.96267	+	10.3276i	−0.215440	+	0.373153i
$767$	−2.76414	−	4.78764i	−0.0998074	−	0.172872i
$768$	1.61310	−	0.630790i	0.0582079	−	0.0227617i
$769$	41.9949			1.51438			0.757188	−	0.653197i	$-0.226573\pi$
$769$	41.9949			1.51438			0.757188	+	0.653197i	$0.226573\pi$
$770$	0.0408678	+	0.0707852i	0.00147277	+	0.00255092i
$771$	2.24512	−	14.7711i	0.0808559	−	0.531969i
$772$	9.35593	−	16.2050i	0.336727	−	0.583229i
$773$	46.8946			1.68668			0.843341	−	0.537379i	$-0.180585\pi$
$773$	46.8946			1.68668			0.843341	+	0.537379i	$0.180585\pi$
$774$	−6.01611	−	26.6628i	−0.216245	−	0.958374i
$775$	22.8961	−	12.4776i	0.822452	−	0.448210i
$776$	2.71229	+	4.69783i	0.0973656	+	0.168642i
$777$	−5.32430	−	4.25679i	−0.191008	−	0.152712i
$778$	35.2837			1.26498
$779$	1.82039	−	3.15301i	0.0652223	−	0.112968i
$780$	−0.690850	+	4.54526i	−0.0247364	+	0.162747i
$781$	−0.424689	+	0.735583i	−0.0151966	+	0.0263212i
$782$	−3.37470	−	5.84515i	−0.120679	−	0.209022i
$783$	−1.50541	+	0.107188i	−0.0537991	+	0.00383058i
$784$	2.99493	−	5.18738i	0.106962	−	0.185263i
$785$	−3.05119			−0.108902
$786$	3.28049	−	21.5831i	0.117011	−	0.769843i
$787$	−5.93761			−0.211653			−0.105826	−	0.994385i	$-0.533749\pi$
$787$	−5.93761			−0.211653			−0.105826	+	0.994385i	$0.533749\pi$
$788$	−7.08002	−	12.2629i	−0.252215	−	0.436849i
$789$	−5.75269	+	37.8483i	−0.204801	+	1.34743i
$790$	1.64625	+	2.85139i	0.0585709	+	0.101448i
$791$	6.24597			0.222081
$792$	−0.0954167	−	0.422877i	−0.00339048	−	0.0150263i
$793$	−7.96653	+	13.7984i	−0.282900	+	0.489997i
$794$	−5.24729	+	9.08858i	−0.186219	+	0.322541i
$795$	−3.32261	−	2.65643i	−0.117841	−	0.0942140i
$796$	−4.65872	−	8.06915i	−0.165124	−	0.286003i
$797$	−4.41797	−	7.65215i	−0.156492	−	0.271053i	0.777109	−	0.629366i	$-0.216685\pi$
$797$	−4.41797	−	7.65215i	−0.156492	−	0.271053i	−0.933601	+	0.358313i	$0.883352\pi$
$798$	−0.623968	+	4.10523i	−0.0220882	+	0.145324i
$799$	9.21062	−	15.9533i	0.325848	−	0.564386i
$800$	2.34163	+	4.05583i	0.0827893	+	0.143395i
$801$	−4.25350	−	18.8511i	−0.150290	−	0.666070i
$802$	−34.8808			−1.23169
$803$	−0.304623	+	0.527623i	−0.0107499	+	0.0186194i
$804$	15.8832	+	12.6986i	0.560156	+	0.447846i
$805$	1.06032	−	1.83654i	0.0373715	−	0.0647294i
$806$	23.0581	−	12.5659i	0.812188	−	0.442616i
$807$	25.0511	−	9.79603i	0.881841	−	0.344836i
$808$	5.63378	+	9.75799i	0.198196	+	0.343285i
$809$	0.882494	+	1.52852i	0.0310268	+	0.0537401i	0.881122	−	0.472889i	$-0.156789\pi$
$809$	0.882494	+	1.52852i	0.0310268	+	0.0537401i	−0.850095	+	0.526629i	$0.823456\pi$
$810$	−0.403552	+	5.04901i	−0.0141794	+	0.177404i
$811$	−7.05458	+	12.2189i	−0.247720	+	0.429063i	−0.962893	−	0.269884i	$-0.913015\pi$
$811$	−7.05458	+	12.2189i	−0.247720	+	0.429063i	0.715173	+	0.698947i	$0.246348\pi$
$812$	0.145959	−	0.252809i	0.00512216	−	0.00887185i
$813$	33.2673	+	26.5973i	1.16674	+	0.932809i
$814$	−0.282927	+	0.490044i	−0.00991659	+	0.0171760i
$815$	3.64649	+	6.31590i	0.127731	+	0.221236i
$816$	−2.90398	+	1.13558i	−0.101660	+	0.0397532i
$817$	21.7327			0.760332
$818$	2.06271	+	3.57272i	0.0721210	+	0.124917i
$819$	3.13004	+	13.8720i	0.109372	+	0.484727i
$820$	0.429501	+	0.743918i	0.0149988	+	0.0259787i
$821$	4.58364	+	7.93910i	0.159970	+	0.277076i	0.934858	−	0.355023i	$-0.115527\pi$
$821$	4.58364	+	7.93910i	0.159970	+	0.277076i	−0.774888	+	0.632099i	$0.782194\pi$
$822$	−1.65861	+	10.9124i	−0.0578508	+	0.380614i
$823$	36.6124			1.27623			0.638114	−	0.769942i	$-0.279715\pi$
$823$	36.6124			1.27623			0.638114	+	0.769942i	$0.279715\pi$
$824$	5.67780	+	9.83424i	0.197795	+	0.342592i
$825$	1.09166	−	0.426884i	0.0380067	−	0.0148622i
$826$	1.17806			0.0409901
$827$	23.9647	−	41.5081i	0.833335	−	1.44338i	−0.0620432	−	0.998073i	$-0.519762\pi$
$827$	23.9647	−	41.5081i	0.833335	−	1.44338i	0.895379	−	0.445306i	$-0.146905\pi$
$828$	−8.26391	+	7.62975i	−0.287191	+	0.265152i
$829$	−41.7758			−1.45093			−0.725467	−	0.688257i	$-0.758376\pi$
$829$	−41.7758			−1.45093			−0.725467	+	0.688257i	$0.758376\pi$
$830$	1.73768	−	3.00976i	0.0603159	−	0.104470i
$831$	−1.26064	+	8.29402i	−0.0437310	+	0.287716i
$832$	2.35820	+	4.08453i	0.0817560	+	0.141606i
$833$	−5.39162	+	9.33855i	−0.186808	+	0.323562i
$834$	6.11384	+	4.88803i	0.211705	+	0.169259i
$835$	1.48169	+	2.56636i	0.0512759	+	0.0888125i
$836$	0.344685			0.0119212
$837$	24.3562	−	15.6134i	0.841872	−	0.539677i
$838$	9.32651			0.322179
$839$	10.7603	+	18.6374i	0.371487	+	0.643435i	0.989795	−	0.142502i	$-0.0455146\pi$
$839$	10.7603	+	18.6374i	0.371487	+	0.643435i	−0.618307	+	0.785936i	$0.712181\pi$
$840$	−0.765209	−	0.611787i	−0.0264022	−	0.0211086i
$841$	14.4578	−	25.0417i	0.498545	−	0.863506i
$842$	13.5827	+	23.5260i	0.468092	+	0.810759i
$843$	0.917906	−	6.03911i	0.0316144	−	0.207998i
$844$	4.01230	−	6.94950i	0.138109	−	0.239212i
$845$	−5.20272			−0.178979
$846$	−29.3115	−	9.12104i	−1.00775	−	0.313588i
$847$	−5.51730	+	9.55625i	−0.189577	+	0.328357i
$848$	−4.36404			−0.149862
$849$	3.13603	−	1.22632i	0.107628	−	0.0420871i
$850$	−4.21552	−	7.30149i	−0.144591	−	0.250439i
$851$	14.6812			0.503266
$852$	1.52986	−	10.0653i	0.0524121	−	0.344831i
$853$	16.3170	+	28.2618i	0.558682	+	0.967666i	0.997607	+	0.0691423i	$0.0220263\pi$
$853$	16.3170	+	28.2618i	0.558682	+	0.967666i	−0.438924	+	0.898524i	$0.644640\pi$
$854$	−1.69765	−	2.94041i	−0.0580923	−	0.100619i
$855$	−3.84543	−	1.19660i	−0.131511	−	0.0409230i
$856$	7.45699	+	12.9159i	0.254875	+	0.441456i
$857$	53.3387			1.82201			0.911007	−	0.412390i	$-0.135306\pi$
$857$	53.3387			1.82201			0.911007	+	0.412390i	$0.135306\pi$
$858$	1.09938	−	0.429905i	0.0375324	−	0.0146767i
$859$	2.28897	+	3.96461i	0.0780985	+	0.135271i	0.902430	−	0.430838i	$-0.141782\pi$
$859$	2.28897	+	3.96461i	0.0780985	+	0.135271i	−0.824331	+	0.566108i	$0.808448\pi$
$860$	−2.56380	+	4.44063i	−0.0874248	+	0.151424i
$861$	2.07530	+	1.65921i	0.0707261	+	0.0565457i
$862$	−12.0917	+	20.9434i	−0.411844	+	0.713335i
$863$	25.5424	−	44.2408i	0.869475	−	1.50597i	0.00694067	−	0.999976i	$-0.497791\pi$
$863$	25.5424	−	44.2408i	0.869475	−	1.50597i	0.862534	−	0.505999i	$-0.168876\pi$
$864$	2.91111	+	4.30412i	0.0990381	+	0.146429i
$865$	−3.37102	−	5.83877i	−0.114618	−	0.198524i
$866$	6.45515	+	11.1806i	0.219355	+	0.379934i
$867$	−22.1949	+	8.67912i	−0.753778	+	0.294758i
$868$	−0.137796	+	5.59421i	−0.00467710	+	0.189880i
$869$	0.422693	−	0.732126i	0.0143389	−	0.0248357i
$870$	0.221138	+	0.176800i	0.00749727	+	0.00599409i
$871$	−27.6869	+	47.9551i	−0.938135	+	1.62490i
$872$	−3.27184			−0.110799
$873$	−11.9569	+	11.0394i	−0.404680	+	0.373626i
$874$	−4.47147	−	7.74481i	−0.151250	−	0.261972i
$875$	2.73859	−	4.74339i	0.0925814	−	0.160356i
$876$	1.09735	−	7.21968i	0.0370759	−	0.243931i
$877$	8.88493	+	15.3891i	0.300023	+	0.519654i	0.976141	−	0.217139i	$-0.0696724\pi$
$877$	8.88493	+	15.3891i	0.300023	+	0.519654i	−0.676118	+	0.736793i	$0.736339\pi$
$878$	−2.14079	−	3.70795i	−0.0722480	−	0.125137i
$879$	−29.8617	−	23.8745i	−1.00721	−	0.805268i
$880$	−0.0406623	+	0.0704292i	−0.00137073	+	0.00237417i
$881$	14.3083	−	24.7828i	0.482060	−	0.834952i	−0.517728	−	0.855545i	$-0.673222\pi$
$881$	14.3083	−	24.7828i	0.482060	−	0.834952i	0.999788	+	0.0205930i	$0.00655542\pi$
$882$	17.1581	+	5.33918i	0.577743	+	0.179780i
$883$	0.842196			0.0283421			0.0141711	−	0.999900i	$-0.495489\pi$
$883$	0.842196			0.0283421			0.0141711	+	0.999900i	$0.495489\pi$
$884$	−4.24535	−	7.35316i	−0.142786	−	0.247313i
$885$	−0.171693	+	1.12961i	−0.00577139	+	0.0379713i
$886$	11.5049	+	19.9272i	0.386516	+	0.669466i
$887$	−55.7510			−1.87194			−0.935968	−	0.352086i	$-0.885473\pi$
$887$	−55.7510			−1.87194			−0.935968	+	0.352086i	$0.885473\pi$
$888$	1.01919	−	6.70548i	0.0342018	−	0.225021i
$889$	2.73428			0.0917048
$890$	−1.81265	+	3.13961i	−0.0607603	+	0.105240i
$891$	1.17451	−	0.558460i	0.0393477	−	0.0187091i
$892$	7.26363	+	12.5810i	0.243204	+	0.421242i
$893$	12.2040	−	21.1380i	0.408393	−	0.707357i
$894$	−1.27321	+	8.37674i	−0.0425825	+	0.280160i
$895$	3.85922	−	6.68437i	0.129000	−	0.223434i
$896$	−1.00505			−0.0335765
$897$	−23.9215	−	19.1253i	−0.798716	−	0.638576i
$898$	0.369024	+	0.639169i	0.0123145	+	0.0213293i
$899$	0.0398217	−	1.61667i	0.00132813	−	0.0539189i
$900$	−10.3229	+	9.53073i	−0.344096	+	0.317691i
$901$	7.85634			0.261733
$902$	0.110279	−	0.191009i	0.00367190	−	0.00635991i
$903$	−2.38332	+	15.6804i	−0.0793121	+	0.521812i
$904$	3.10728	+	5.38197i	0.103347	+	0.179002i
$905$	12.4817			0.414905
$906$	38.9037	−	15.2130i	1.29249	−	0.505417i
$907$	−13.9039	−	24.0823i	−0.461672	−	0.799640i	0.537372	−	0.843345i	$-0.319417\pi$
$907$	−13.9039	−	24.0823i	−0.461672	−	0.799640i	−0.999044	+	0.0437054i	$0.986084\pi$
$908$	−9.41079	+	16.3000i	−0.312308	+	0.540933i
$909$	−24.8360	+	22.9302i	−0.823759	+	0.760545i
$910$	1.33388	−	2.31035i	0.0442177	−	0.0765874i
$911$	1.59600	−	2.76435i	0.0528778	−	0.0915870i	−0.838375	−	0.545094i	$-0.816494\pi$
$911$	1.59600	−	2.76435i	0.0528778	−	0.0915870i	0.891253	+	0.453507i	$0.149827\pi$
$912$	−3.84777	+	1.50464i	−0.127412	+	0.0498235i
$913$	−0.892340			−0.0295321
$914$	−18.3750	+	31.8265i	−0.607792	+	1.05273i
$915$	3.06688	−	1.19928i	0.101388	−	0.0396469i
$916$	−0.879392	+	1.52315i	−0.0290559	+	0.0503264i
$917$	−6.33391	+	10.9706i	−0.209164	+	0.362283i
$918$	−5.24072	−	7.74847i	−0.172970	−	0.255738i
$919$	−5.31857	+	9.21203i	−0.175443	+	0.303877i	−0.940315	−	0.340306i	$-0.889469\pi$
$919$	−5.31857	+	9.21203i	−0.175443	+	0.303877i	0.764871	+	0.644183i	$0.222803\pi$
$920$	2.10999			0.0695642
$921$	−4.43082	+	29.1514i	−0.146000	+	0.960570i
$922$	12.6047	−	21.8321i	0.415115	−	0.719001i
$923$	27.7228			0.912507
$924$	−0.0378000	+	0.248695i	−0.00124353	+	0.00818145i
$925$	18.3391			0.602986
$926$	−2.72262			−0.0894710
$927$	−25.0301	+	23.1093i	−0.822096	+	0.759010i
$928$	0.290450			0.00953450
$929$	−12.4243	−	21.5195i	−0.407628	−	0.706032i	0.586995	−	0.809590i	$-0.300311\pi$
$929$	−12.4243	−	21.5195i	−0.407628	−	0.706032i	−0.994623	+	0.103558i	$0.966977\pi$
$930$	−5.34402	−	0.947436i	−0.175237	−	0.0310677i
$931$	−7.14388	+	12.3736i	−0.234131	+	0.405527i
$932$	11.6185	−	20.1239i	0.380577	−	0.659179i
$933$	−15.6201	+	6.10811i	−0.511379	+	0.199970i
$934$	−1.20742	−	2.09132i	−0.0395081	−	0.0684301i
$935$	0.0732022	−	0.126790i	0.00239397	−	0.00414647i
$936$	−10.3959	+	9.59818i	−0.339802	+	0.313726i
$937$	−18.2775	−	31.6576i	−0.597100	−	1.03421i	−0.993247	−	0.116020i	$-0.962986\pi$
$937$	−18.2775	−	31.6576i	−0.597100	−	1.03421i	0.396147	−	0.918187i	$-0.370347\pi$
$938$	−5.90000	−	10.2191i	−0.192642	−	0.333666i
$939$	1.24753	−	0.487836i	0.0407116	−	0.0159199i
$940$	2.87941	+	4.98728i	0.0939160	+	0.162667i
$941$	−4.39855	−	7.61851i	−0.143389	−	0.248356i	0.785382	−	0.619011i	$-0.212467\pi$
$941$	−4.39855	−	7.61851i	−0.143389	−	0.248356i	−0.928771	+	0.370655i	$0.879133\pi$
$942$	−7.33444	−	5.86391i	−0.238969	−	0.191056i
$943$	−5.72244			−0.186348
$944$	0.586070	+	1.01510i	0.0190749	+	0.0330388i
$945$	1.28507	−	2.64330i	0.0418035	−	0.0859865i
$946$	1.31657			0.0428053
$947$	6.05831	−	10.4933i	0.196869	−	0.340986i	−0.750643	−	0.660708i	$-0.770256\pi$
$947$	6.05831	−	10.4933i	0.196869	−	0.340986i	0.947511	+	0.319722i	$0.103589\pi$
$948$	−1.52267	+	10.0180i	−0.0494540	+	0.325369i
$949$	19.8851			0.645499
$950$	−5.58555	−	9.67445i	−0.181219	−	0.313881i
$951$	23.3687	−	9.13814i	0.757783	−	0.296324i
$952$	1.80934			0.0586412
$953$	−55.8909			−1.81048			−0.905242	−	0.424897i	$-0.860310\pi$
$953$	−55.8909			−1.81048			−0.905242	+	0.424897i	$0.860310\pi$
$954$	−2.88162	−	12.7711i	−0.0932960	−	0.413478i
$955$	−4.18820	−	7.25417i	−0.135527	−	0.234739i
$956$	8.88915			0.287496
$957$	0.0109238	−	0.0718702i	0.000353117	−	0.00232323i
$958$	32.6616			1.05525
$959$	3.20242	−	5.54676i	0.103412	−	0.179114i
$960$	0.146478	−	0.963713i	0.00472756	−	0.0311037i
$961$	14.1594	+	27.5774i	0.456756	+	0.889592i
$962$	18.4689			0.595460
$963$	−32.8735	+	30.3509i	−1.05933	+	0.978043i
$964$	7.36589	+	12.7581i	0.237239	+	0.410911i
$965$	−5.26543	−	9.11999i	−0.169500	−	0.293583i
$966$	6.07834	−	2.37688i	0.195567	−	0.0764749i
$967$	32.4407			1.04322			0.521611	−	0.853184i	$-0.325331\pi$
$967$	32.4407			1.04322			0.521611	+	0.853184i	$0.325331\pi$
$968$	−10.9791			−0.352882
$969$	6.92693	−	2.70872i	0.222525	−	0.0870165i
$970$	3.05290			0.0980228
$971$	22.2476	−	38.5340i	0.713960	−	1.23662i	−0.249399	−	0.968401i	$-0.580233\pi$
$971$	22.2476	−	38.5340i	0.713960	−	1.23662i	0.963359	−	0.268215i	$-0.0864337\pi$
$972$	−10.6735	+	11.3612i	−0.342351	+	0.364411i
$973$	−2.27106	−	3.93360i	−0.0728070	−	0.126105i
$974$	36.9190			1.18296
$975$	−29.8816	−	23.8905i	−0.956978	−	0.765107i
$976$	1.68911	−	2.92562i	0.0540671	−	0.0936470i
$977$	16.0697	−	27.8336i	0.514117	−	0.890476i	−0.485749	−	0.874098i	$-0.661453\pi$
$977$	16.0697	−	27.8336i	0.514117	−	0.890476i	0.999866	−	0.0163780i	$-0.00521352\pi$
$978$	−3.37275	+	22.1901i	−0.107849	+	0.709561i
$979$	0.930838			0.0297497
$980$	−1.68552	−	2.91940i	−0.0538419	−	0.0932569i
$981$	−2.16043	−	9.57481i	−0.0689773	−	0.305700i
$982$	−7.05101	+	12.2127i	−0.225007	+	0.389723i
$983$	−56.7703			−1.81069			−0.905345	−	0.424677i	$-0.860388\pi$
$983$	−56.7703			−1.81069			−0.905345	+	0.424677i	$0.860388\pi$
$984$	−0.397259	+	2.61366i	−0.0126642	+	0.0833205i
$985$	−7.96913			−0.253917
$986$	−0.522882			−0.0166520
$987$	13.9130	+	11.1235i	0.442855	+	0.354064i
$988$	−5.62507	−	9.74291i	−0.178957	−	0.309963i
$989$	−17.0793	−	29.5823i	−0.543091	−	0.940661i
$990$	−0.232956	−	0.0724902i	−0.00740382	−	0.00230389i
$991$	−39.3750			−1.25079			−0.625394	−	0.780309i	$-0.715062\pi$
$991$	−39.3750			−1.25079			−0.625394	+	0.780309i	$0.715062\pi$
$992$	−4.88891	+	2.66430i	−0.155223	+	0.0845917i
$993$	29.5155	+	23.5977i	0.936645	+	0.748850i
$994$	−2.95383	+	5.11618i	−0.0936897	+	0.162275i
$995$	−5.24377			−0.166239
$996$	9.96132	−	3.89529i	0.315636	−	0.123427i
$997$	58.5737			1.85505			0.927524	−	0.373764i	$-0.121933\pi$
$997$	58.5737			1.85505			0.927524	+	0.373764i	$0.121933\pi$
$998$	17.1482	+	29.7016i	0.542817	+	0.940186i
$999$	20.2961	−	1.44512i	0.642140	−	0.0457215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.g.a.211.4	✓	32
3.2	odd	2		1674.2.g.b.955.7		32
9.2	odd	6		1674.2.h.b.397.10		32
9.7	even	3		558.2.h.a.25.8	yes	32
31.5	even	3		558.2.h.a.67.8	yes	32
93.5	odd	6		1674.2.h.b.253.10		32
279.160	even	3	inner	558.2.g.a.439.4	yes	32
279.191	odd	6		1674.2.g.b.1369.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.g.a.211.4	✓	32	1.1	even	1	trivial
558.2.g.a.439.4	yes	32	279.160	even	3	inner
558.2.h.a.25.8	yes	32	9.7	even	3
558.2.h.a.67.8	yes	32	31.5	even	3
1674.2.g.b.955.7		32	3.2	odd	2
1674.2.g.b.1369.7		32	279.191	odd	6
1674.2.h.b.253.10		32	93.5	odd	6
1674.2.h.b.397.10		32	9.2	odd	6

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:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.35283 - 1.08159i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.281395 + 0.487391i) q^{5} +(-0.260271 + 1.71238i) q^{6} +(0.502527 - 0.870402i) q^{7} +1.00000 q^{8} +(0.660311 + 2.92643i) q^{9} +(0.281395 - 0.487391i) q^{10} -0.144503 q^{11} +(1.61310 - 0.630790i) q^{12} +(2.35820 + 4.08453i) q^{13} -1.00505 q^{14} +(0.146478 - 0.963713i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.900123 + 1.55906i) q^{17} +(2.20421 - 2.03506i) q^{18} +(1.19266 + 2.06575i) q^{19} -0.562790 q^{20} +(-1.62126 + 0.633978i) q^{21} +(0.0722513 + 0.125143i) q^{22} +(1.87458 - 3.24686i) q^{23} +(-1.35283 - 1.08159i) q^{24} +(2.34163 - 4.05583i) q^{25} +(2.35820 - 4.08453i) q^{26} +(2.27192 - 4.67316i) q^{27} +(0.502527 + 0.870402i) q^{28} +(-0.145225 - 0.251538i) q^{29} +(-0.907839 + 0.355003i) q^{30} +(4.75181 + 2.90177i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.195488 + 0.156293i) q^{33} +(0.900123 - 1.55906i) q^{34} +0.565634 q^{35} +(-2.86452 - 0.891369i) q^{36} +(1.95794 + 3.39125i) q^{37} +(1.19266 - 2.06575i) q^{38} +(1.22755 - 8.07630i) q^{39} +(0.281395 + 0.487391i) q^{40} +(-0.763164 - 1.32184i) q^{41} +(1.35967 + 1.08706i) q^{42} +(4.55551 - 7.89038i) q^{43} +(0.0722513 - 0.125143i) q^{44} +(-1.24051 + 1.14531i) q^{45} -3.74915 q^{46} +(-5.11631 - 8.86171i) q^{47} +(-0.260271 + 1.71238i) q^{48} +(2.99493 + 5.18738i) q^{49} -4.68327 q^{50} +(0.468552 - 3.08271i) q^{51} -4.71641 q^{52} +(2.18202 - 3.77937i) q^{53} +(-5.18303 + 0.369040i) q^{54} +(-0.0406623 - 0.0704292i) q^{55} +(0.502527 - 0.870402i) q^{56} +(0.620830 - 4.08459i) q^{57} +(-0.145225 + 0.251538i) q^{58} -1.17214 q^{59} +(0.761361 + 0.608710i) q^{60} +(1.68911 + 2.92562i) q^{61} +(0.137103 - 5.56608i) q^{62} +(2.87899 + 0.895874i) q^{63} +1.00000 q^{64} +(-1.32717 + 2.29873i) q^{65} +(0.0376099 - 0.247444i) q^{66} +(5.87033 + 10.1677i) q^{67} -1.80025 q^{68} +(-6.04777 + 2.36493i) q^{69} +(-0.282817 - 0.489854i) q^{70} +(2.93897 - 5.09045i) q^{71} +(0.660311 + 2.92643i) q^{72} +(2.10808 - 3.65130i) q^{73} +(1.95794 - 3.39125i) q^{74} +(-7.55460 + 2.95416i) q^{75} -2.38532 q^{76} +(-0.0726165 + 0.125775i) q^{77} +(-7.60806 + 2.97507i) q^{78} +(-2.92516 + 5.06652i) q^{79} +(0.281395 - 0.487391i) q^{80} +(-8.12798 + 3.86471i) q^{81} +(-0.763164 + 1.32184i) q^{82} +6.17525 q^{83} +(0.261587 - 1.72104i) q^{84} +(-0.506580 + 0.877423i) q^{85} -9.11103 q^{86} +(-0.0755959 + 0.497363i) q^{87} -0.144503 q^{88} -6.44167 q^{89} +(1.61212 + 0.501653i) q^{90} +4.74024 q^{91} +(1.87458 + 3.24686i) q^{92} +(-3.28987 - 9.06514i) q^{93} +(-5.11631 + 8.86171i) q^{94} +(-0.671217 + 1.16258i) q^{95} +(1.61310 - 0.630790i) q^{96} +(2.71229 + 4.69783i) q^{97} +(2.99493 - 5.18738i) q^{98} +(-0.0954167 - 0.422877i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} + 4 q^{3} - 16 q^{4} - q^{5} - 2 q^{6} + q^{7} + 32 q^{8} + 12 q^{9} - q^{10} + 4 q^{11} - 2 q^{12} - 10 q^{13} - 2 q^{14} - 13 q^{15} - 16 q^{16} - 4 q^{17} - 6 q^{18} + 4 q^{19} + 2 q^{20}+ \cdots + 19 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 + 4 * q^3 - 16 * q^4 - q^5 - 2 * q^6 + q^7 + 32 * q^8 + 12 * q^9 - q^10 + 4 * q^11 - 2 * q^12 - 10 * q^13 - 2 * q^14 - 13 * q^15 - 16 * q^16 - 4 * q^17 - 6 * q^18 + 4 * q^19 + 2 * q^20 + 10 * q^21 - 2 * q^22 - q^23 + 4 * q^24 - 19 * q^25 - 10 * q^26 + 7 * q^27 + q^28 - 3 * q^29 + 14 * q^30 - q^31 - 16 * q^32 - 7 * q^33 - 4 * q^34 - 6 * q^36 - 19 * q^37 + 4 * q^38 + 19 * q^39 - q^40 + 10 * q^41 - 11 * q^42 - 13 * q^43 - 2 * q^44 + 14 * q^45 + 2 * q^46 - 6 * q^47 - 2 * q^48 - 13 * q^49 + 38 * q^50 + 20 * q^51 + 20 * q^52 - 7 * q^53 - 17 * q^54 - 11 * q^55 + q^56 - 5 * q^57 - 3 * q^58 + 12 * q^59 - q^60 + 7 * q^61 + 11 * q^62 - 42 * q^63 + 32 * q^64 - 8 * q^65 + 5 * q^66 - 8 * q^67 + 8 * q^68 + 43 * q^69 + 7 * q^71 + 12 * q^72 + 7 * q^73 - 19 * q^74 - 41 * q^75 - 8 * q^76 - q^77 - 11 * q^78 - 34 * q^79 - q^80 + 10 * q^82 - 28 * q^83 + q^84 + 13 * q^85 + 26 * q^86 - 54 * q^87 + 4 * q^88 + 2 * q^89 - 19 * q^90 + 24 * q^91 - q^92 - 15 * q^93 - 6 * q^94 + 21 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + 19 * q^99

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