LMFDB - Embedded newform 630.2.bi.b.509.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(479,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.479"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,48] 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.3
Character	$\chi$	$=$	630.509
Dual form			630.2.bi.b.479.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(-1.55560 - 0.761652i) q^{3} +1.00000 q^{4} +(-1.55089 + 1.61082i) q^{5} +(-1.55560 - 0.761652i) q^{6} +(-0.405354 - 2.61451i) q^{7} +1.00000 q^{8} +(1.83977 + 2.36965i) q^{9} +(-1.55089 + 1.61082i) q^{10} +(0.922101 + 0.532375i) q^{11} +(-1.55560 - 0.761652i) q^{12} +(2.83827 - 4.91604i) q^{13} +(-0.405354 - 2.61451i) q^{14} +(3.63945 - 1.32454i) q^{15} +1.00000 q^{16} +(1.18969 - 0.686867i) q^{17} +(1.83977 + 2.36965i) q^{18} +(-5.87638 - 3.39273i) q^{19} +(-1.55089 + 1.61082i) q^{20} +(-1.36078 + 4.37587i) q^{21} +(0.922101 + 0.532375i) q^{22} +(-2.24743 - 3.89266i) q^{23} +(-1.55560 - 0.761652i) q^{24} +(-0.189463 - 4.99641i) q^{25} +(2.83827 - 4.91604i) q^{26} +(-1.05710 - 5.08749i) q^{27} +(-0.405354 - 2.61451i) q^{28} +(4.67691 - 2.70021i) q^{29} +(3.63945 - 1.32454i) q^{30} -7.52185i q^{31} +1.00000 q^{32} +(-1.02893 - 1.53048i) q^{33} +(1.18969 - 0.686867i) q^{34} +(4.84017 + 3.40188i) q^{35} +(1.83977 + 2.36965i) q^{36} +(7.42263 + 4.28546i) q^{37} +(-5.87638 - 3.39273i) q^{38} +(-8.15952 + 5.48560i) q^{39} +(-1.55089 + 1.61082i) q^{40} +(1.21989 - 2.11292i) q^{41} +(-1.36078 + 4.37587i) q^{42} +(-4.89080 + 2.82370i) q^{43} +(0.922101 + 0.532375i) q^{44} +(-6.67036 - 0.711534i) q^{45} +(-2.24743 - 3.89266i) q^{46} +8.75012i q^{47} +(-1.55560 - 0.761652i) q^{48} +(-6.67138 + 2.11961i) q^{49} +(-0.189463 - 4.99641i) q^{50} +(-2.37383 + 0.162361i) q^{51} +(2.83827 - 4.91604i) q^{52} +(-2.29752 - 3.97942i) q^{53} +(-1.05710 - 5.08749i) q^{54} +(-2.28764 + 0.659679i) q^{55} +(-0.405354 - 2.61451i) q^{56} +(6.55721 + 9.75348i) q^{57} +(4.67691 - 2.70021i) q^{58} +9.70296 q^{59} +(3.63945 - 1.32454i) q^{60} +9.92998i q^{61} -7.52185i q^{62} +(5.44972 - 5.77066i) q^{63} +1.00000 q^{64} +(3.51697 + 12.1962i) q^{65} +(-1.02893 - 1.53048i) q^{66} -0.0645415i q^{67} +(1.18969 - 0.686867i) q^{68} +(0.531244 + 7.76717i) q^{69} +(4.84017 + 3.40188i) q^{70} -6.07978i q^{71} +(1.83977 + 2.36965i) q^{72} +(-4.78305 - 8.28448i) q^{73} +(7.42263 + 4.28546i) q^{74} +(-3.51080 + 7.91671i) q^{75} +(-5.87638 - 3.39273i) q^{76} +(1.01813 - 2.62665i) q^{77} +(-8.15952 + 5.48560i) q^{78} +7.34722 q^{79} +(-1.55089 + 1.61082i) q^{80} +(-2.23047 + 8.71923i) q^{81} +(1.21989 - 2.11292i) q^{82} +(-7.57279 + 4.37215i) q^{83} +(-1.36078 + 4.37587i) q^{84} +(-0.738663 + 2.98163i) q^{85} +(-4.89080 + 2.82370i) q^{86} +(-9.33201 + 0.638273i) q^{87} +(0.922101 + 0.532375i) q^{88} +(5.74422 - 9.94928i) q^{89} +(-6.67036 - 0.711534i) q^{90} +(-14.0036 - 5.42798i) q^{91} +(-2.24743 - 3.89266i) q^{92} +(-5.72903 + 11.7010i) q^{93} +8.75012i q^{94} +(14.5787 - 4.20401i) q^{95} +(-1.55560 - 0.761652i) q^{96} +(6.25791 + 10.8390i) q^{97} +(-6.67138 + 2.11961i) q^{98} +(0.434914 + 3.16451i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8} + 6 q^{11} + 3 q^{14} - 4 q^{15} + 48 q^{16} + 8 q^{21} + 6 q^{22} + 3 q^{23} - 18 q^{25} + 3 q^{28} - 3 q^{29} - 4 q^{30} + 48 q^{32} - 12 q^{35} - 18 q^{39}+ \cdots - 26 q^{99}+O(q^{100}) $ 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8 + 6 * q^11 + 3 * q^14 - 4 * q^15 + 48 * q^16 + 8 * q^21 + 6 * q^22 + 3 * q^23 - 18 * q^25 + 3 * q^28 - 3 * q^29 - 4 * q^30 + 48 * q^32 - 12 * q^35 - 18 * q^39 - 3 * q^41 + 8 * q^42 + 6 * q^44 - 39 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 - 42 * q^55 + 3 * q^56 - 22 * q^57 - 3 * q^58 - 4 * q^60 - 43 * q^63 + 48 * q^64 + 12 * q^65 - 42 * q^69 - 12 * q^70 - 18 * q^73 + 18 * q^75 - 12 * q^77 - 18 * q^78 + 8 * q^81 - 3 * q^82 + 9 * q^83 + 8 * q^84 - 33 * q^85 - 15 * q^87 + 6 * q^88 - 33 * q^89 - 39 * q^90 + 3 * q^92 - 8 * q^93 - 24 * q^97 + 3 * q^98 - 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.55560	−	0.761652i	−0.898125	−	0.439740i
$3$	−1.55560	−	0.761652i	−0.898125	−	0.439740i
$4$	1.00000			0.500000
$5$	−1.55089	+	1.61082i	−0.693580	+	0.720379i
$5$	−1.55089	+	1.61082i	−0.693580	+	0.720379i
$6$	−1.55560	−	0.761652i	−0.635070	−	0.310943i
$7$	−0.405354	−	2.61451i	−0.153209	−	0.988194i
$7$	−0.405354	−	2.61451i	−0.153209	−	0.988194i
$8$	1.00000			0.353553
$9$	1.83977	+	2.36965i	0.613258	+	0.789883i
$10$	−1.55089	+	1.61082i	−0.490435	+	0.509385i
$11$	0.922101	+	0.532375i	0.278024	+	0.160517i	0.632528	−	0.774537i	$-0.282017\pi$
$11$	0.922101	+	0.532375i	0.278024	+	0.160517i	−0.354505	+	0.935054i	$0.615350\pi$
$12$	−1.55560	−	0.761652i	−0.449063	−	0.219870i
$13$	2.83827	−	4.91604i	0.787196	−	1.36346i	−0.140483	−	0.990083i	$-0.544866\pi$
$13$	2.83827	−	4.91604i	0.787196	−	1.36346i	0.927679	−	0.373380i	$-0.121801\pi$
$14$	−0.405354	−	2.61451i	−0.108335	−	0.698759i
$15$	3.63945	−	1.32454i	0.939701	−	0.341996i
$16$	1.00000			0.250000
$17$	1.18969	−	0.686867i	0.288542	−	0.166590i	−0.348742	−	0.937219i	$-0.613391\pi$
$17$	1.18969	−	0.686867i	0.288542	−	0.166590i	0.637284	+	0.770629i	$0.280058\pi$
$18$	1.83977	+	2.36965i	0.433639	+	0.558532i
$19$	−5.87638	−	3.39273i	−1.34813	−	0.778345i	−0.360148	−	0.932895i	$-0.617274\pi$
$19$	−5.87638	−	3.39273i	−1.34813	−	0.778345i	−0.987985	+	0.154550i	$0.950607\pi$
$20$	−1.55089	+	1.61082i	−0.346790	+	0.360190i
$21$	−1.36078	+	4.37587i	−0.296947	+	0.954894i
$22$	0.922101	+	0.532375i	0.196593	+	0.113503i
$23$	−2.24743	−	3.89266i	−0.468621	−	0.811676i	0.530736	−	0.847537i	$-0.321916\pi$
$23$	−2.24743	−	3.89266i	−0.468621	−	0.811676i	−0.999357	+	0.0358617i	$0.988582\pi$
$24$	−1.55560	−	0.761652i	−0.317535	−	0.155472i
$25$	−0.189463	−	4.99641i	−0.0378926	−	0.999282i
$26$	2.83827	−	4.91604i	0.556631	−	0.964114i
$27$	−1.05710	−	5.08749i	−0.203439	−	0.979088i
$28$	−0.405354	−	2.61451i	−0.0766046	−	0.494097i
$29$	4.67691	−	2.70021i	0.868480	−	0.501417i	0.00163724	−	0.999999i	$-0.499479\pi$
$29$	4.67691	−	2.70021i	0.868480	−	0.501417i	0.866843	+	0.498581i	$0.166146\pi$
$30$	3.63945	−	1.32454i	0.664469	−	0.241828i
$31$		−	7.52185i		−	1.35096i	−0.737376	−	0.675482i	$-0.763936\pi$
$31$		−	7.52185i		−	1.35096i	0.737376	−	0.675482i	$-0.236064\pi$
$32$	1.00000			0.176777
$33$	−1.02893	−	1.53048i	−0.179114	−	0.266423i
$34$	1.18969	−	0.686867i	0.204030	−	0.117797i
$35$	4.84017	+	3.40188i	0.818137	+	0.575023i
$36$	1.83977	+	2.36965i	0.306629	+	0.394941i
$37$	7.42263	+	4.28546i	1.22027	+	0.704525i	0.964976	−	0.262338i	$-0.0844934\pi$
$37$	7.42263	+	4.28546i	1.22027	+	0.704525i	0.255297	+	0.966863i	$0.417827\pi$
$38$	−5.87638	−	3.39273i	−0.953274	−	0.550373i
$39$	−8.15952	+	5.48560i	−1.30657	+	0.878399i
$40$	−1.55089	+	1.61082i	−0.245218	+	0.254693i
$41$	1.21989	−	2.11292i	0.190515	−	0.329982i	−0.754906	−	0.655833i	$-0.772317\pi$
$41$	1.21989	−	2.11292i	0.190515	−	0.329982i	0.945421	+	0.325851i	$0.105651\pi$
$42$	−1.36078	+	4.37587i	−0.209973	+	0.675212i
$43$	−4.89080	+	2.82370i	−0.745840	+	0.430611i	−0.824189	−	0.566315i	$-0.808368\pi$
$43$	−4.89080	+	2.82370i	−0.745840	+	0.430611i	0.0783491	+	0.996926i	$0.475035\pi$
$44$	0.922101	+	0.532375i	0.139012	+	0.0802586i
$45$	−6.67036	−	0.711534i	−0.994359	−	0.106069i
$46$	−2.24743	−	3.89266i	−0.331365	−	0.573941i
$47$			8.75012i			1.27634i	0.769897	+	0.638168i	$0.220308\pi$
$47$			8.75012i			1.27634i	−0.769897	+	0.638168i	$0.779692\pi$
$48$	−1.55560	−	0.761652i	−0.224531	−	0.109935i
$49$	−6.67138	+	2.11961i	−0.953054	+	0.302801i
$50$	−0.189463	−	4.99641i	−0.0267941	−	0.706599i
$51$	−2.37383	+	0.162361i	−0.332403	+	0.0227351i
$52$	2.83827	−	4.91604i	0.393598	−	0.681731i
$53$	−2.29752	−	3.97942i	−0.315589	−	0.546615i	0.663974	−	0.747756i	$-0.268869\pi$
$53$	−2.29752	−	3.97942i	−0.315589	−	0.546615i	−0.979562	+	0.201140i	$0.935535\pi$
$54$	−1.05710	−	5.08749i	−0.143853	−	0.692319i
$55$	−2.28764	+	0.659679i	−0.308465	+	0.0889511i
$56$	−0.405354	−	2.61451i	−0.0541676	−	0.349379i
$57$	6.55721	+	9.75348i	0.868523	+	1.29188i
$58$	4.67691	−	2.70021i	0.614108	−	0.354556i
$59$	9.70296			1.26322			0.631609	−	0.775287i	$-0.282395\pi$
$59$	9.70296			1.26322			0.631609	+	0.775287i	$0.282395\pi$
$60$	3.63945	−	1.32454i	0.469851	−	0.170998i
$61$			9.92998i			1.27140i	0.771935	+	0.635702i	$0.219289\pi$
$61$			9.92998i			1.27140i	−0.771935	+	0.635702i	$0.780711\pi$
$62$		−	7.52185i		−	0.955276i
$63$	5.44972	−	5.77066i	0.686601	−	0.727035i
$64$	1.00000			0.125000
$65$	3.51697	+	12.1962i	0.436227	+	1.51275i
$66$	−1.02893	−	1.53048i	−0.126653	−	0.188389i
$67$		−	0.0645415i		−	0.00788500i	−0.999992	−	0.00394250i	$-0.998745\pi$
$67$		−	0.0645415i		−	0.00788500i	0.999992	−	0.00394250i	$-0.00125494\pi$
$68$	1.18969	−	0.686867i	0.144271	−	0.0832949i
$69$	0.531244	+	7.76717i	0.0639543	+	0.935058i
$70$	4.84017	+	3.40188i	0.578510	+	0.406603i
$71$		−	6.07978i		−	0.721537i	−0.932655	−	0.360768i	$-0.882514\pi$
$71$		−	6.07978i		−	0.721537i	0.932655	−	0.360768i	$-0.117486\pi$
$72$	1.83977	+	2.36965i	0.216819	+	0.279266i
$73$	−4.78305	−	8.28448i	−0.559813	−	0.969625i	−0.997512	−	0.0705034i	$-0.977539\pi$
$73$	−4.78305	−	8.28448i	−0.559813	−	0.969625i	0.437698	−	0.899122i	$-0.355794\pi$
$74$	7.42263	+	4.28546i	0.862863	+	0.498174i
$75$	−3.51080	+	7.91671i	−0.405392	+	0.914143i
$76$	−5.87638	−	3.39273i	−0.674067	−	0.389173i
$77$	1.01813	−	2.62665i	0.116026	−	0.299334i
$78$	−8.15952	+	5.48560i	−0.923884	+	0.621122i
$79$	7.34722			0.826627			0.413314	−	0.910589i	$-0.364371\pi$
$79$	7.34722			0.826627			0.413314	+	0.910589i	$0.364371\pi$
$80$	−1.55089	+	1.61082i	−0.173395	+	0.180095i
$81$	−2.23047	+	8.71923i	−0.247830	+	0.968803i
$82$	1.21989	−	2.11292i	0.134715	−	0.233332i
$83$	−7.57279	+	4.37215i	−0.831222	+	0.479906i	−0.854271	−	0.519828i	$-0.825996\pi$
$83$	−7.57279	+	4.37215i	−0.831222	+	0.479906i	0.0230489	+	0.999734i	$0.492663\pi$
$84$	−1.36078	+	4.37587i	−0.148474	+	0.477447i
$85$	−0.738663	+	2.98163i	−0.0801192	+	0.323403i
$86$	−4.89080	+	2.82370i	−0.527388	+	0.304488i
$87$	−9.33201	+	0.638273i	−1.00050	+	0.0684301i
$88$	0.922101	+	0.532375i	0.0982963	+	0.0567514i
$89$	5.74422	−	9.94928i	0.608886	−	1.05462i	−0.382538	−	0.923940i	$-0.624950\pi$
$89$	5.74422	−	9.94928i	0.608886	−	1.05462i	0.991424	−	0.130682i	$-0.0417166\pi$
$90$	−6.67036	−	0.711534i	−0.703118	−	0.0750023i
$91$	−14.0036	−	5.42798i	−1.46797	−	0.569007i
$92$	−2.24743	−	3.89266i	−0.234311	−	0.405838i
$93$	−5.72903	+	11.7010i	−0.594073	+	1.21333i
$94$			8.75012i			0.902506i
$95$	14.5787	−	4.20401i	1.49574	−	0.431322i
$96$	−1.55560	−	0.761652i	−0.158768	−	0.0777358i
$97$	6.25791	+	10.8390i	0.635394	+	1.10054i	0.986431	+	0.164174i	$0.0524957\pi$
$97$	6.25791	+	10.8390i	0.635394	+	1.10054i	−0.351037	+	0.936361i	$0.614171\pi$
$98$	−6.67138	+	2.11961i	−0.673911	+	0.214113i
$99$	0.434914	+	3.16451i	0.0437105	+	0.318045i
$100$	−0.189463	−	4.99641i	−0.0189463	−	0.499641i
$101$	−4.13794	+	7.16712i	−0.411740	+	0.713155i	−0.995080	−	0.0990729i	$-0.968412\pi$
$101$	−4.13794	+	7.16712i	−0.411740	+	0.713155i	0.583340	+	0.812228i	$0.301746\pi$
$102$	−2.37383	+	0.162361i	−0.235044	+	0.0160761i
$103$	0.0267719	+	0.0463704i	0.00263792	+	0.00456901i	0.867341	−	0.497714i	$-0.165827\pi$
$103$	0.0267719	+	0.0463704i	0.00263792	+	0.00456901i	−0.864703	+	0.502283i	$0.832494\pi$
$104$	2.83827	−	4.91604i	0.278316	−	0.482057i
$105$	−4.93830	−	8.97848i	−0.481929	−	0.876210i
$106$	−2.29752	−	3.97942i	−0.223155	−	0.386515i
$107$	−4.10444	+	7.10909i	−0.396791	+	0.687262i	−0.993328	−	0.115323i	$-0.963210\pi$
$107$	−4.10444	+	7.10909i	−0.396791	+	0.687262i	0.596537	+	0.802586i	$0.296543\pi$
$108$	−1.05710	−	5.08749i	−0.101720	−	0.489544i
$109$	6.86529	+	11.8910i	0.657575	+	1.13895i	0.981241	+	0.192783i	$0.0617512\pi$
$109$	6.86529	+	11.8910i	0.657575	+	1.13895i	−0.323666	+	0.946171i	$0.604915\pi$
$110$	−2.28764	+	0.659679i	−0.218118	+	0.0628979i
$111$	−8.28261	−	12.3199i	−0.786150	−	1.16935i
$112$	−0.405354	−	2.61451i	−0.0383023	−	0.247048i
$113$	0.256031	−	0.443458i	0.0240853	−	0.0417170i	−0.853732	−	0.520713i	$-0.825666\pi$
$113$	0.256031	−	0.443458i	0.0240853	−	0.0417170i	0.877817	+	0.478996i	$0.158999\pi$
$114$	6.55721	+	9.75348i	0.614139	+	0.913497i
$115$	9.75588	+	2.41690i	0.909741	+	0.225377i
$116$	4.67691	−	2.70021i	0.434240	−	0.250709i
$117$	16.8711	−	2.31867i	1.55973	−	0.214362i
$118$	9.70296			0.893230
$119$	−2.27807	−	2.83204i	−0.208830	−	0.259612i
$120$	3.63945	−	1.32454i	0.332235	−	0.120914i
$121$	−4.93315	−	8.54447i	−0.448468	−	0.776770i
$122$			9.92998i			0.899018i
$123$	−3.50697	+	2.35771i	−0.316213	+	0.212588i
$124$		−	7.52185i		−	0.675482i
$125$	8.34214	+	7.44371i	0.746143	+	0.665785i
$126$	5.44972	−	5.77066i	0.485500	−	0.514091i
$127$		−	4.60873i		−	0.408959i	−0.978871	−	0.204480i	$-0.934450\pi$
$127$		−	4.60873i		−	0.408959i	0.978871	−	0.204480i	$-0.0655502\pi$
$128$	1.00000			0.0883883
$129$	9.75880	−	0.667463i	0.859214	−	0.0587669i
$130$	3.51697	+	12.1962i	0.308459	+	1.06968i
$131$	2.65642	+	4.60106i	0.232093	+	0.401996i	0.958424	−	0.285349i	$-0.0921094\pi$
$131$	2.65642	+	4.60106i	0.232093	+	0.401996i	−0.726331	+	0.687345i	$0.758776\pi$
$132$	−1.02893	−	1.53048i	−0.0895572	−	0.133211i
$133$	−6.48833	+	16.7391i	−0.562609	+	1.45147i
$134$		−	0.0645415i		−	0.00557554i
$135$	9.83446	+	6.18735i	0.846416	+	0.532523i
$136$	1.18969	−	0.686867i	0.102015	−	0.0588984i
$137$	−0.0371922	+	0.0644188i	−0.00317754	+	0.00550367i	−0.867610	−	0.497246i	$-0.834345\pi$
$137$	−0.0371922	+	0.0644188i	−0.00317754	+	0.00550367i	0.864432	+	0.502749i	$0.167678\pi$
$138$	0.531244	+	7.76717i	0.0452225	+	0.661186i
$139$	−14.6763	−	8.47337i	−1.24483	−	0.718702i	−0.274755	−	0.961514i	$-0.588597\pi$
$139$	−14.6763	−	8.47337i	−1.24483	−	0.718702i	−0.970073	+	0.242812i	$0.921930\pi$
$140$	4.84017	+	3.40188i	0.409069	+	0.287512i
$141$	6.66455	−	13.6117i	0.561256	−	1.14631i
$142$		−	6.07978i		−	0.510203i
$143$	5.23435	−	3.02205i	0.437718	−	0.252717i
$144$	1.83977	+	2.36965i	0.153314	+	0.197471i
$145$	−2.90383	+	11.7214i	−0.241150	+	0.973408i
$146$	−4.78305	−	8.28448i	−0.395848	−	0.685629i
$147$	11.9924	+	1.78401i	0.989115	+	0.147143i
$148$	7.42263	+	4.28546i	0.610137	+	0.352263i
$149$	−14.4973	+	8.37004i	−1.18767	+	0.685700i	−0.957776	−	0.287516i	$-0.907171\pi$
$149$	−14.4973	+	8.37004i	−1.18767	+	0.685700i	−0.229892	+	0.973216i	$0.573837\pi$
$150$	−3.51080	+	7.91671i	−0.286655	+	0.646397i
$151$	3.00497	−	5.20476i	0.244541	−	0.423557i	−0.717462	−	0.696598i	$-0.754696\pi$
$151$	3.00497	−	5.20476i	0.244541	−	0.423557i	0.962002	+	0.273041i	$0.0880294\pi$
$152$	−5.87638	−	3.39273i	−0.476637	−	0.275187i
$153$	3.81639	+	1.55547i	0.308537	+	0.125752i
$154$	1.01813	−	2.62665i	0.0820429	−	0.211661i
$155$	12.1163	+	11.6656i	0.973207	+	0.937002i
$156$	−8.15952	+	5.48560i	−0.653285	+	0.439199i
$157$	−9.02952			−0.720634			−0.360317	−	0.932830i	$-0.617332\pi$
$157$	−9.02952			−0.720634			−0.360317	+	0.932830i	$0.617332\pi$
$158$	7.34722			0.584514
$159$	0.543084	+	7.94029i	0.0430694	+	0.629706i
$160$	−1.55089	+	1.61082i	−0.122609	+	0.127346i
$161$	−9.26641	+	7.45384i	−0.730296	+	0.587445i
$162$	−2.23047	+	8.71923i	−0.175242	+	0.685048i
$163$	8.62716	+	4.98089i	0.675731	+	0.390134i	0.798245	−	0.602333i	$-0.205762\pi$
$163$	8.62716	+	4.98089i	0.675731	+	0.390134i	−0.122514	+	0.992467i	$0.539095\pi$
$164$	1.21989	−	2.11292i	0.0952576	−	0.164991i
$165$	4.06109	+	0.716189i	0.316156	+	0.0557552i
$166$	−7.57279	+	4.37215i	−0.587763	+	0.339345i
$167$	16.2295	+	9.37008i	1.25587	+	0.725078i	0.972269	−	0.233863i	$-0.0751368\pi$
$167$	16.2295	+	9.37008i	1.25587	+	0.725078i	0.283603	+	0.958942i	$0.408470\pi$
$168$	−1.36078	+	4.37587i	−0.104987	+	0.337606i
$169$	−9.61160	−	16.6478i	−0.739354	−	1.28060i
$170$	−0.738663	+	2.98163i	−0.0566528	+	0.228680i
$171$	−2.77163	−	20.1668i	−0.211951	−	1.54219i
$172$	−4.89080	+	2.82370i	−0.372920	+	0.215305i
$173$			22.1147i			1.68135i	0.541538	+	0.840676i	$0.317842\pi$
$173$			22.1147i			1.68135i	−0.541538	+	0.840676i	$0.682158\pi$
$174$	−9.33201	+	0.638273i	−0.707458	+	0.0483874i
$175$	−12.9864	+	2.52067i	−0.981679	+	0.190544i
$176$	0.922101	+	0.532375i	0.0695060	+	0.0401293i
$177$	−15.0939	−	7.39028i	−1.13453	−	0.555488i
$178$	5.74422	−	9.94928i	0.430547	−	0.745730i
$179$	9.16532	−	5.29160i	0.685048	−	0.395513i	−0.116706	−	0.993166i	$-0.537234\pi$
$179$	9.16532	−	5.29160i	0.685048	−	0.395513i	0.801754	+	0.597654i	$0.203900\pi$
$180$	−6.67036	−	0.711534i	−0.497179	−	0.0530346i
$181$		−	6.54895i		−	0.486780i	−0.969929	−	0.243390i	$-0.921741\pi$
$181$		−	6.54895i		−	0.486780i	0.969929	−	0.243390i	$-0.0782594\pi$
$182$	−14.0036	−	5.42798i	−1.03801	−	0.402349i
$183$	7.56319	−	15.4471i	0.559087	−	1.14188i
$184$	−2.24743	−	3.89266i	−0.165683	−	0.286971i
$185$	−18.4148	+	5.31021i	−1.35388	+	0.390415i
$186$	−5.72903	+	11.7010i	−0.420073	+	0.857957i
$187$	1.46268			0.106962
$188$			8.75012i			0.638168i
$189$	−12.8728	+	4.82604i	−0.936360	+	0.351042i
$190$	14.5787	−	4.20401i	1.05765	−	0.304991i
$191$		−	6.43820i		−	0.465852i	−0.972495	−	0.232926i	$-0.925170\pi$
$191$		−	6.43820i		−	0.465852i	0.972495	−	0.232926i	$-0.0748299\pi$
$192$	−1.55560	−	0.761652i	−0.112266	−	0.0549675i
$193$		−	23.2031i		−	1.67019i	−0.550103	−	0.835097i	$-0.685411\pi$
$193$		−	23.2031i		−	1.67019i	0.550103	−	0.835097i	$-0.314589\pi$
$194$	6.25791	+	10.8390i	0.449292	+	0.778196i
$195$	3.81825	−	21.6511i	0.273430	−	1.55047i
$196$	−6.67138	+	2.11961i	−0.476527	+	0.151400i
$197$	−2.32392			−0.165572			−0.0827861	−	0.996567i	$-0.526382\pi$
$197$	−2.32392			−0.165572			−0.0827861	+	0.996567i	$0.526382\pi$
$198$	0.434914	+	3.16451i	0.0309080	+	0.224892i
$199$	−10.1070	+	5.83527i	−0.716465	+	0.413651i	−0.813450	−	0.581635i	$-0.802413\pi$
$199$	−10.1070	+	5.83527i	−0.716465	+	0.413651i	0.0969854	+	0.995286i	$0.469080\pi$
$200$	−0.189463	−	4.99641i	−0.0133970	−	0.353299i
$201$	−0.0491582	+	0.100401i	−0.00346735	+	0.00708172i
$202$	−4.13794	+	7.16712i	−0.291144	+	0.504277i
$203$	−8.95555	−	11.1333i	−0.628557	−	0.781405i
$204$	−2.37383	+	0.162361i	−0.166201	+	0.0113675i
$205$	1.51160	+	5.24193i	0.105575	+	0.366112i
$206$	0.0267719	+	0.0463704i	0.00186529	+	0.00323078i
$207$	5.08948	−	12.4872i	0.353743	−	0.867922i
$208$	2.83827	−	4.91604i	0.196799	−	0.340866i
$209$	−3.61241	−	6.25688i	−0.249876	−	0.432797i
$210$	−4.93830	−	8.97848i	−0.340775	−	0.619574i
$211$	7.82600	−	13.5550i	0.538764	−	0.933167i	−0.460207	−	0.887812i	$-0.652225\pi$
$211$	7.82600	−	13.5550i	0.538764	−	0.933167i	0.998971	−	0.0453551i	$-0.0144419\pi$
$212$	−2.29752	−	3.97942i	−0.157794	−	0.273308i
$213$	−4.63067	+	9.45769i	−0.317288	+	0.648030i
$214$	−4.10444	+	7.10909i	−0.280574	+	0.485968i
$215$	3.03663	−	12.2574i	0.207097	−	0.835951i
$216$	−1.05710	−	5.08749i	−0.0719266	−	0.346160i
$217$	−19.6660	+	3.04901i	−1.33501	+	0.206980i
$218$	6.86529	+	11.8910i	0.464976	+	0.805362i
$219$	1.13061	+	16.5303i	0.0763996	+	1.11702i
$220$	−2.28764	+	0.659679i	−0.154233	+	0.0444755i
$221$		−	7.79807i		−	0.524555i
$222$	−8.28261	−	12.3199i	−0.555892	−	0.826858i
$223$	−6.52152	−	11.2956i	−0.436714	−	0.756410i	0.560720	−	0.828005i	$-0.310524\pi$
$223$	−6.52152	−	11.2956i	−0.436714	−	0.756410i	−0.997434	+	0.0715953i	$0.977191\pi$
$224$	−0.405354	−	2.61451i	−0.0270838	−	0.174690i
$225$	11.4912	−	9.64122i	0.766078	−	0.642748i
$226$	0.256031	−	0.443458i	0.0170309	−	0.0294984i
$227$	24.8272	+	14.3340i	1.64784	+	0.951380i	0.977929	+	0.208936i	$0.0670001\pi$
$227$	24.8272	+	14.3340i	1.64784	+	0.951380i	0.669909	+	0.742444i	$0.266333\pi$
$228$	6.55721	+	9.75348i	0.434262	+	0.645940i
$229$	3.57358	−	2.06321i	0.236149	−	0.136341i	−0.377257	−	0.926109i	$-0.623133\pi$
$229$	3.57358	−	2.06321i	0.236149	−	0.136341i	0.613405	+	0.789768i	$0.289799\pi$
$230$	9.75588	+	2.41690i	0.643284	+	0.159366i
$231$	−3.58439	+	3.31055i	−0.235835	+	0.217818i
$232$	4.67691	−	2.70021i	0.307054	−	0.177278i
$233$	0.859394	−	1.48851i	0.0563008	−	0.0975158i	−0.836501	−	0.547965i	$-0.815403\pi$
$233$	0.859394	−	1.48851i	0.0563008	−	0.0975158i	0.892802	+	0.450449i	$0.148736\pi$
$234$	16.8711	−	2.31867i	1.10290	−	0.151576i
$235$	−14.0948	−	13.5705i	−0.919447	−	0.885242i
$236$	9.70296			0.631609
$237$	−11.4293	−	5.59603i	−0.742415	−	0.363501i
$238$	−2.27807	−	2.83204i	−0.147665	−	0.183574i
$239$	7.92591	+	4.57603i	0.512684	+	0.295999i	0.733936	−	0.679218i	$-0.237681\pi$
$239$	7.92591	+	4.57603i	0.512684	+	0.295999i	−0.221252	+	0.975217i	$0.571014\pi$
$240$	3.63945	−	1.32454i	0.234925	−	0.0854989i
$241$	−0.696421	−	0.402079i	−0.0448605	−	0.0259002i	0.477402	−	0.878685i	$-0.341579\pi$
$241$	−0.696421	−	0.402079i	−0.0448605	−	0.0259002i	−0.522262	+	0.852785i	$0.674912\pi$
$242$	−4.93315	−	8.54447i	−0.317115	−	0.549259i
$243$	10.1107	−	11.8648i	0.648604	−	0.761126i
$244$			9.92998i			0.635702i
$245$	6.93229	−	14.0336i	0.442888	−	0.896577i
$246$	−3.50697	+	2.35771i	−0.223596	+	0.150322i
$247$	−33.3575	+	19.2590i	−2.12249	+	1.22542i
$248$		−	7.52185i		−	0.477638i
$249$	15.1103	−	1.03348i	0.957575	−	0.0654944i
$250$	8.34214	+	7.44371i	0.527603	+	0.470781i
$251$	−19.6454			−1.24001			−0.620004	−	0.784599i	$-0.712869\pi$
$251$	−19.6454			−1.24001			−0.620004	+	0.784599i	$0.712869\pi$
$252$	5.44972	−	5.77066i	0.343300	−	0.363517i
$253$		−	4.78590i		−	0.300887i
$254$		−	4.60873i		−	0.289178i
$255$	3.42003	−	4.07561i	0.214170	−	0.255225i
$256$	1.00000			0.0625000
$257$	14.3279	−	8.27221i	0.893749	−	0.516006i	0.0185820	−	0.999827i	$-0.494085\pi$
$257$	14.3279	−	8.27221i	0.893749	−	0.516006i	0.875167	+	0.483821i	$0.160752\pi$
$258$	9.75880	−	0.667463i	0.607556	−	0.0415544i
$259$	8.19560	−	21.1437i	0.509250	−	1.31381i
$260$	3.51697	+	12.1962i	0.218113	+	0.756375i
$261$	15.0030	+	6.11485i	0.928663	+	0.378500i
$262$	2.65642	+	4.60106i	0.164114	+	0.284254i
$263$	1.01677	−	1.76111i	0.0626970	−	0.108594i	−0.832973	−	0.553313i	$-0.813363\pi$
$263$	1.01677	−	1.76111i	0.0626970	−	0.108594i	0.895670	+	0.444719i	$0.146696\pi$
$264$	−1.02893	−	1.53048i	−0.0633265	−	0.0941947i
$265$	9.97332	+	2.47077i	0.612656	+	0.151778i
$266$	−6.48833	+	16.7391i	−0.397825	+	1.02634i
$267$	−16.5136	+	11.1020i	−1.01061	+	0.679430i
$268$		−	0.0645415i		−	0.00394250i
$269$	11.6388	+	20.1590i	0.709631	+	1.22912i	0.964994	+	0.262272i	$0.0844718\pi$
$269$	11.6388	+	20.1590i	0.709631	+	1.22912i	−0.255363	+	0.966845i	$0.582195\pi$
$270$	9.83446	+	6.18735i	0.598506	+	0.376550i
$271$	21.0788	+	12.1699i	1.28045	+	0.739266i	0.976930	−	0.213560i	$-0.0685059\pi$
$271$	21.0788	+	12.1699i	1.28045	+	0.739266i	0.303517	+	0.952826i	$0.401839\pi$
$272$	1.18969	−	0.686867i	0.0721355	−	0.0416474i
$273$	17.6497	+	19.1096i	1.06821	+	1.15656i
$274$	−0.0371922	+	0.0644188i	−0.00224686	+	0.00389168i
$275$	2.48526	−	4.70806i	0.149867	−	0.283907i
$276$	0.531244	+	7.76717i	0.0319771	+	0.467529i
$277$	−7.08143	−	4.08846i	−0.425482	−	0.245652i	0.271938	−	0.962315i	$-0.412335\pi$
$277$	−7.08143	−	4.08846i	−0.425482	−	0.245652i	−0.697420	+	0.716663i	$0.745669\pi$
$278$	−14.6763	−	8.47337i	−0.880227	−	0.508199i
$279$	17.8241	−	13.8385i	1.06710	−	0.828489i
$280$	4.84017	+	3.40188i	0.289255	+	0.203301i
$281$	−4.54162	+	2.62210i	−0.270930	+	0.156422i	−0.629310	−	0.777154i	$-0.716663\pi$
$281$	−4.54162	+	2.62210i	−0.270930	+	0.156422i	0.358380	+	0.933576i	$0.383329\pi$
$282$	6.66455	−	13.6117i	0.396868	−	0.810564i
$283$	16.8827			1.00357			0.501785	−	0.864992i	$-0.332677\pi$
$283$	16.8827			1.00357			0.501785	+	0.864992i	$0.332677\pi$
$284$		−	6.07978i		−	0.360768i
$285$	−25.8806	−	4.56414i	−1.53303	−	0.270356i
$286$	5.23435	−	3.02205i	0.309514	−	0.178698i
$287$	−6.01874	−	2.33295i	−0.355275	−	0.137710i
$288$	1.83977	+	2.36965i	0.108410	+	0.139633i
$289$	−7.55643	+	13.0881i	−0.444496	+	0.769889i
$290$	−2.90383	+	11.7214i	−0.170519	+	0.688304i
$291$	−1.47924	−	21.6275i	−0.0867143	−	1.26783i
$292$	−4.78305	−	8.28448i	−0.279907	−	0.484813i
$293$	−25.5501	−	14.7514i	−1.49265	−	0.861783i	−0.492688	−	0.870206i	$-0.663986\pi$
$293$	−25.5501	−	14.7514i	−1.49265	−	0.861783i	−0.999965	+	0.00842274i	$0.997319\pi$
$294$	11.9924	+	1.78401i	0.699410	+	0.104046i
$295$	−15.0483	+	15.6297i	−0.876143	+	0.909996i
$296$	7.42263	+	4.28546i	0.431432	+	0.249087i
$297$	1.73370	−	5.25395i	0.100599	−	0.304865i
$298$	−14.4973	+	8.37004i	−0.839808	+	0.484863i
$299$	−25.5153			−1.47559
$300$	−3.51080	+	7.91671i	−0.202696	+	0.457072i
$301$	9.36512	+	11.6425i	0.539796	+	0.671061i
$302$	3.00497	−	5.20476i	0.172917	−	0.299500i
$303$	11.8958	−	7.99749i	0.683397	−	0.459444i
$304$	−5.87638	−	3.39273i	−0.337033	−	0.194586i
$305$	−15.9954	−	15.4003i	−0.915893	−	0.881821i
$306$	3.81639	+	1.55547i	0.218169	+	0.0889200i
$307$	10.7900			0.615818			0.307909	−	0.951416i	$-0.400371\pi$
$307$	10.7900			0.615818			0.307909	+	0.951416i	$0.400371\pi$
$308$	1.01813	−	2.62665i	0.0580131	−	0.149667i
$309$	−0.00632831	−	0.0925246i	−0.000360005	−	0.00526354i
$310$	12.1163	+	11.6656i	0.688161	+	0.662561i
$311$	−6.78533			−0.384761			−0.192380	−	0.981320i	$-0.561621\pi$
$311$	−6.78533			−0.384761			−0.192380	+	0.981320i	$0.561621\pi$
$312$	−8.15952	+	5.48560i	−0.461942	+	0.310561i
$313$	22.5896			1.27684			0.638419	−	0.769689i	$-0.279589\pi$
$313$	22.5896			1.27684			0.638419	+	0.769689i	$0.279589\pi$
$314$	−9.02952			−0.509565
$315$	0.843538	+	17.7282i	0.0475280	+	0.998870i
$316$	7.34722			0.413314
$317$	−27.0432			−1.51890			−0.759449	−	0.650567i	$-0.774531\pi$
$317$	−27.0432			−1.51890			−0.759449	+	0.650567i	$0.774531\pi$
$318$	0.543084	+	7.94029i	0.0304547	+	0.445269i
$319$	5.75011			0.321944
$320$	−1.55089	+	1.61082i	−0.0866975	+	0.0900474i
$321$	11.7995	−	7.93274i	0.658585	−	0.442763i
$322$	−9.26641	+	7.45384i	−0.516397	+	0.415386i
$323$	−9.32142			−0.518657
$324$	−2.23047	+	8.71923i	−0.123915	+	0.484402i
$325$	−25.1003	−	13.2498i	−1.39231	−	0.734965i
$326$	8.62716	+	4.98089i	0.477814	+	0.275866i
$327$	−1.62281	−	23.7266i	−0.0897415	−	1.31209i
$328$	1.21989	−	2.11292i	0.0673573	−	0.116666i
$329$	22.8773	−	3.54689i	1.26127	−	0.195547i
$330$	4.06109	+	0.716189i	0.223556	+	0.0394249i
$331$	6.03337			0.331624			0.165812	−	0.986157i	$-0.446976\pi$
$331$	6.03337			0.331624			0.165812	+	0.986157i	$0.446976\pi$
$332$	−7.57279	+	4.37215i	−0.415611	+	0.239953i
$333$	3.50092	+	25.4733i	0.191849	+	1.39593i
$334$	16.2295	+	9.37008i	0.888036	+	0.512708i
$335$	0.103965	+	0.100097i	0.00568019	+	0.00546888i
$336$	−1.36078	+	4.37587i	−0.0742368	+	0.238723i
$337$	14.4392	+	8.33650i	0.786555	+	0.454118i	0.838748	−	0.544519i	$-0.183288\pi$
$337$	14.4392	+	8.33650i	0.786555	+	0.454118i	−0.0521932	+	0.998637i	$0.516621\pi$
$338$	−9.61160	−	16.6478i	−0.522802	−	0.905520i
$339$	−0.736041	+	0.494836i	−0.0399763	+	0.0268758i
$340$	−0.738663	+	2.98163i	−0.0400596	+	0.161702i
$341$	4.00445	−	6.93591i	0.216853	−	0.375600i
$342$	−2.77163	−	20.1668i	−0.149872	−	1.09050i
$343$	8.24601	+	16.5832i	0.445243	+	0.895410i
$344$	−4.89080	+	2.82370i	−0.263694	+	0.152244i
$345$	−13.3354	−	11.1903i	−0.717954	−	0.602466i
$346$			22.1147i			1.18890i
$347$	33.0004			1.77156			0.885778	−	0.464108i	$-0.153625\pi$
$347$	33.0004			1.77156			0.885778	+	0.464108i	$0.153625\pi$
$348$	−9.33201	+	0.638273i	−0.500248	+	0.0342150i
$349$	−9.69567	+	5.59780i	−0.518998	+	0.299643i	−0.736524	−	0.676411i	$-0.763534\pi$
$349$	−9.69567	+	5.59780i	−0.518998	+	0.299643i	0.217527	+	0.976054i	$0.430201\pi$
$350$	−12.9864	+	2.52067i	−0.694152	+	0.134735i
$351$	−28.0106	−	9.24295i	−1.49510	−	0.493352i
$352$	0.922101	+	0.532375i	0.0491481	+	0.0283757i
$353$	12.5080	+	7.22147i	0.665731	+	0.384360i	0.794457	−	0.607320i	$-0.207755\pi$
$353$	12.5080	+	7.22147i	0.665731	+	0.384360i	−0.128726	+	0.991680i	$0.541089\pi$
$354$	−15.0939	−	7.39028i	−0.802233	−	0.392789i
$355$	9.79341	+	9.42908i	0.519780	+	0.500444i
$356$	5.74422	−	9.94928i	0.304443	−	0.527311i
$357$	1.38674	+	6.14061i	0.0733938	+	0.324995i
$358$	9.16532	−	5.29160i	0.484402	−	0.279670i
$359$	−18.4344	−	10.6431i	−0.972931	−	0.561722i	−0.0728028	−	0.997346i	$-0.523194\pi$
$359$	−18.4344	−	10.6431i	−0.972931	−	0.561722i	−0.900129	+	0.435624i	$0.856528\pi$
$360$	−6.67036	−	0.711534i	−0.351559	−	0.0375011i
$361$	13.5212	+	23.4194i	0.711643	+	1.23260i
$362$		−	6.54895i		−	0.344205i
$363$	1.16609	+	17.0491i	0.0612040	+	0.894846i
$364$	−14.0036	−	5.42798i	−0.733986	−	0.284503i
$365$	20.7628	+	5.14373i	1.08677	+	0.269235i
$366$	7.56319	−	15.4471i	0.395334	−	0.807431i
$367$	8.90707	−	15.4275i	0.464945	−	0.805309i	−0.534254	−	0.845324i	$-0.679407\pi$
$367$	8.90707	−	15.4275i	0.464945	−	0.805309i	0.999199	+	0.0400151i	$0.0127406\pi$
$368$	−2.24743	−	3.89266i	−0.117155	−	0.202919i
$369$	7.25119	−	0.996568i	0.377482	−	0.0518793i
$370$	−18.4148	+	5.31021i	−0.957340	+	0.276065i
$371$	−9.47295	+	7.61997i	−0.491811	+	0.395609i
$372$	−5.72903	+	11.7010i	−0.297036	+	0.606667i
$373$	15.5268	−	8.96439i	0.803946	−	0.464159i	−0.0409028	−	0.999163i	$-0.513023\pi$
$373$	15.5268	−	8.96439i	0.803946	−	0.464159i	0.844849	+	0.535004i	$0.179690\pi$
$374$	1.46268			0.0756336
$375$	−7.30750	−	17.9332i	−0.377358	−	0.926068i
$376$			8.75012i			0.451253i
$377$		−	30.6558i		−	1.57885i
$378$	−12.8728	+	4.82604i	−0.662106	+	0.248224i
$379$	−0.162766			−0.00836075			−0.00418037	−	0.999991i	$-0.501331\pi$
$379$	−0.162766			−0.00836075			−0.00418037	+	0.999991i	$0.501331\pi$
$380$	14.5787	−	4.20401i	0.747871	−	0.215661i
$381$	−3.51025	+	7.16934i	−0.179836	+	0.367296i
$382$		−	6.43820i		−	0.329407i
$383$	−8.64195	+	4.98943i	−0.441583	+	0.254948i	−0.704269	−	0.709933i	$-0.748725\pi$
$383$	−8.64195	+	4.98943i	−0.441583	+	0.254948i	0.262686	+	0.964881i	$0.415392\pi$
$384$	−1.55560	−	0.761652i	−0.0793838	−	0.0388679i
$385$	2.65204	+	5.71366i	0.135161	+	0.291195i
$386$		−	23.2031i		−	1.18101i
$387$	−15.6891	−	6.39450i	−0.797524	−	0.325051i
$388$	6.25791	+	10.8390i	0.317697	+	0.550268i
$389$	20.5762	+	11.8797i	1.04326	+	0.602325i	0.920754	−	0.390144i	$-0.127575\pi$
$389$	20.5762	+	11.8797i	1.04326	+	0.602325i	0.122503	+	0.992468i	$0.460908\pi$
$390$	3.81825	−	21.6511i	0.193344	−	1.09634i
$391$	−5.34748	−	3.08737i	−0.270434	−	0.156135i
$392$	−6.67138	+	2.11961i	−0.336955	+	0.107056i
$393$	−0.627921	−	9.18066i	−0.0316744	−	0.463103i
$394$	−2.32392			−0.117077
$395$	−11.3948	+	11.8350i	−0.573332	+	0.595485i
$396$	0.434914	+	3.16451i	0.0218552	+	0.159022i
$397$	10.9098	−	18.8963i	0.547547	−	0.948379i	−0.450895	−	0.892577i	$-0.648895\pi$
$397$	10.9098	−	18.8963i	0.547547	−	0.948379i	0.998442	−	0.0558021i	$-0.0177716\pi$
$398$	−10.1070	+	5.83527i	−0.506617	+	0.292495i
$399$	22.8426	−	21.0975i	1.14356	−	1.05620i
$400$	−0.189463	−	4.99641i	−0.00947314	−	0.249820i
$401$	−2.29120	+	1.32282i	−0.114417	+	0.0660587i	−0.556116	−	0.831104i	$-0.687709\pi$
$401$	−2.29120	+	1.32282i	−0.114417	+	0.0660587i	0.441699	+	0.897163i	$0.354376\pi$
$402$	−0.0491582	+	0.100401i	−0.00245179	+	0.00500753i
$403$	−36.9777	−	21.3491i	−1.84199	−	1.06347i
$404$	−4.13794	+	7.16712i	−0.205870	+	0.356578i
$405$	−10.5859	−	17.1155i	−0.526016	−	0.850475i
$406$	−8.95555	−	11.1333i	−0.444457	−	0.552537i
$407$	4.56294	+	7.90325i	0.226177	+	0.391750i
$408$	−2.37383	+	0.162361i	−0.117522	+	0.00803806i
$409$		−	17.4968i		−	0.865163i	−0.901595	−	0.432582i	$-0.857603\pi$
$409$		−	17.4968i		−	0.865163i	0.901595	−	0.432582i	$-0.142397\pi$
$410$	1.51160	+	5.24193i	0.0746525	+	0.258880i
$411$	0.106921	−	0.0718823i	0.00527402	−	0.00354569i
$412$	0.0267719	+	0.0463704i	0.00131896	+	0.00228450i
$413$	−3.93313	−	25.3685i	−0.193537	−	1.24830i
$414$	5.08948	−	12.4872i	0.250134	−	0.613714i
$415$	4.70185	−	18.9791i	0.230805	−	0.931649i
$416$	2.83827	−	4.91604i	0.139158	−	0.241028i
$417$	16.3767	+	24.3594i	0.801970	+	1.19289i
$418$	−3.61241	−	6.25688i	−0.176689	−	0.306034i
$419$	−4.87854	+	8.44988i	−0.238332	+	0.412804i	−0.960236	−	0.279190i	$-0.909934\pi$
$419$	−4.87854	+	8.44988i	−0.238332	+	0.412804i	0.721904	+	0.691994i	$0.243267\pi$
$420$	−4.93830	−	8.97848i	−0.240965	−	0.438105i
$421$	15.0741	+	26.1091i	0.734667	+	1.27248i	0.954869	+	0.297027i	$0.0959951\pi$
$421$	15.0741	+	26.1091i	0.734667	+	1.27248i	−0.220202	+	0.975454i	$0.570672\pi$
$422$	7.82600	−	13.5550i	0.380964	−	0.659849i
$423$	−20.7347	+	16.0982i	−1.00816	+	0.782723i
$424$	−2.29752	−	3.97942i	−0.111577	−	0.193258i
$425$	−3.65727	−	5.81404i	−0.177404	−	0.282022i
$426$	−4.63067	+	9.45769i	−0.224357	+	0.458227i
$427$	25.9621	−	4.02515i	1.25639	−	0.194791i
$428$	−4.10444	+	7.10909i	−0.198395	+	0.343631i
$429$	−10.4443	+	0.714349i	−0.504256	+	0.0344891i
$430$	3.03663	−	12.2574i	0.146439	−	0.591106i
$431$	−30.1386	+	17.4005i	−1.45172	+	0.838153i	−0.998579	−	0.0532842i	$-0.983031\pi$
$431$	−30.1386	+	17.4005i	−1.45172	+	0.838153i	−0.453144	+	0.891437i	$0.649698\pi$
$432$	−1.05710	−	5.08749i	−0.0508598	−	0.244772i
$433$	36.5774			1.75780			0.878899	−	0.477008i	$-0.158279\pi$
$433$	36.5774			1.75780			0.878899	+	0.477008i	$0.158279\pi$
$434$	−19.6660	+	3.04901i	−0.943998	+	0.146357i
$435$	13.4448	−	16.0221i	0.644629	−	0.768199i
$436$	6.86529	+	11.8910i	0.328788	+	0.569477i
$437$			30.4997i			1.45900i
$438$	1.13061	+	16.5303i	0.0540227	+	0.789851i
$439$			1.51393i			0.0722559i	0.999347	+	0.0361280i	$0.0115024\pi$
$439$			1.51393i			0.0722559i	−0.999347	+	0.0361280i	$0.988498\pi$
$440$	−2.28764	+	0.659679i	−0.109059	+	0.0314490i
$441$	−17.2965	−	11.9092i	−0.823645	−	0.567106i
$442$		−	7.79807i		−	0.370916i
$443$	−22.5770			−1.07267			−0.536333	−	0.844006i	$-0.680191\pi$
$443$	−22.5770			−1.07267			−0.536333	+	0.844006i	$0.680191\pi$
$444$	−8.28261	−	12.3199i	−0.393075	−	0.584677i
$445$	7.11780	+	24.6831i	0.337416	+	1.17009i
$446$	−6.52152	−	11.2956i	−0.308803	−	0.534863i
$447$	28.9271	−	1.97850i	1.36820	−	0.0935798i
$448$	−0.405354	−	2.61451i	−0.0191512	−	0.123524i
$449$		−	6.39415i		−	0.301758i	−0.988552	−	0.150879i	$-0.951790\pi$
$449$		−	6.39415i		−	0.301758i	0.988552	−	0.150879i	$-0.0482105\pi$
$450$	11.4912	−	9.64122i	0.541699	−	0.454491i
$451$	2.24973	−	1.29888i	0.105936	−	0.0611619i
$452$	0.256031	−	0.443458i	0.0120427	−	0.0208585i
$453$	−8.63874	+	5.80778i	−0.405883	+	0.272873i
$454$	24.8272	+	14.3340i	1.16520	+	0.672727i
$455$	30.4615	−	14.1389i	1.42806	−	0.662844i
$456$	6.55721	+	9.75348i	0.307069	+	0.456748i
$457$			1.55320i			0.0726557i	0.999340	+	0.0363278i	$0.0115661\pi$
$457$			1.55320i			0.0726557i	−0.999340	+	0.0363278i	$0.988434\pi$
$458$	3.57358	−	2.06321i	0.166982	−	0.0964073i
$459$	−4.75205	−	5.32644i	−0.221807	−	0.248617i
$460$	9.75588	+	2.41690i	0.454870	+	0.112689i
$461$	−7.34634	−	12.7242i	−0.342153	−	0.592626i	0.642679	−	0.766135i	$-0.277823\pi$
$461$	−7.34634	−	12.7242i	−0.342153	−	0.592626i	−0.984832	+	0.173509i	$0.944489\pi$
$462$	−3.58439	+	3.31055i	−0.166761	+	0.154021i
$463$	1.02891	+	0.594041i	0.0478174	+	0.0276074i	0.523718	−	0.851892i	$-0.324545\pi$
$463$	1.02891	+	0.594041i	0.0478174	+	0.0276074i	−0.475901	+	0.879499i	$0.657878\pi$
$464$	4.67691	−	2.70021i	0.217120	−	0.125354i
$465$	−9.96302	−	27.3754i	−0.462024	−	1.26950i
$466$	0.859394	−	1.48851i	0.0398107	−	0.0689541i
$467$	29.2203	+	16.8704i	1.35216	+	0.780667i	0.988551	−	0.150886i	$-0.0482128\pi$
$467$	29.2203	+	16.8704i	1.35216	+	0.780667i	0.363604	+	0.931554i	$0.381546\pi$
$468$	16.8711	−	2.31867i	0.779865	−	0.107181i
$469$	−0.168745	+	0.0261621i	−0.00779191	+	0.00120806i
$470$	−14.0948	−	13.5705i	−0.650147	−	0.625961i
$471$	14.0463	+	6.87735i	0.647220	+	0.316892i
$472$	9.70296			0.446615
$473$	−6.01308			−0.276482
$474$	−11.4293	−	5.59603i	−0.524967	−	0.257034i
$475$	−15.8381	+	30.0036i	−0.726702	+	1.37666i
$476$	−2.27807	−	2.83204i	−0.104415	−	0.129806i
$477$	5.20291	−	12.7655i	0.238225	−	0.584494i
$478$	7.92591	+	4.57603i	0.362523	+	0.209303i
$479$	3.15505	−	5.46471i	0.144158	−	0.249689i	−0.784901	−	0.619622i	$-0.787286\pi$
$479$	3.15505	−	5.46471i	0.144158	−	0.249689i	0.929058	+	0.369933i	$0.120619\pi$
$480$	3.63945	−	1.32454i	0.166117	−	0.0604569i
$481$	42.1349	−	24.3266i	1.92119	−	1.10920i
$482$	−0.696421	−	0.402079i	−0.0317211	−	0.0183142i
$483$	20.0921	−	4.53740i	0.914220	−	0.206459i
$484$	−4.93315	−	8.54447i	−0.224234	−	0.388385i
$485$	−27.1650	−	6.72980i	−1.23350	−	0.305585i
$486$	10.1107	−	11.8648i	0.458632	−	0.538197i
$487$	−29.8197	+	17.2164i	−1.35126	+	0.780149i	−0.988426	−	0.151705i	$-0.951524\pi$
$487$	−29.8197	+	17.2164i	−1.35126	+	0.780149i	−0.362833	+	0.931854i	$0.618190\pi$
$488$			9.92998i			0.449509i
$489$	−9.62669	−	14.3192i	−0.435334	−	0.647535i
$490$	6.93229	−	14.0336i	0.313169	−	0.633976i
$491$	0.145232	+	0.0838499i	0.00655424	+	0.00378409i	0.503274	−	0.864127i	$-0.332129\pi$
$491$	0.145232	+	0.0838499i	0.00655424	+	0.00378409i	−0.496719	+	0.867911i	$0.665462\pi$
$492$	−3.50697	+	2.35771i	−0.158106	+	0.106294i
$493$	3.70938	−	6.42483i	0.167062	−	0.289360i
$494$	−33.3575	+	19.2590i	−1.50083	+	0.866503i
$495$	−5.77194	−	4.20724i	−0.259430	−	0.189101i
$496$		−	7.52185i		−	0.337741i
$497$	−15.8957	+	2.46446i	−0.713018	+	0.110546i
$498$	15.1103	−	1.03348i	0.677108	−	0.0463115i
$499$	1.46377	+	2.53532i	0.0655272	+	0.113496i	0.896928	−	0.442177i	$-0.145794\pi$
$499$	1.46377	+	2.53532i	0.0655272	+	0.113496i	−0.831401	+	0.555674i	$0.812460\pi$
$500$	8.34214	+	7.44371i	0.373072	+	0.332893i
$501$	−18.1098	−	26.9373i	−0.809085	−	1.20347i
$502$	−19.6454			−0.876818
$503$			14.0715i			0.627418i	0.949519	+	0.313709i	$0.101572\pi$
$503$			14.0715i			0.627418i	−0.949519	+	0.313709i	$0.898428\pi$
$504$	5.44972	−	5.77066i	0.242750	−	0.257046i
$505$	−5.12742	−	17.7809i	−0.228167	−	0.791240i
$506$		−	4.78590i		−	0.212759i
$507$	2.27198	+	33.2180i	0.100902	+	1.47526i
$508$		−	4.60873i		−	0.204480i
$509$	−13.8664	−	24.0173i	−0.614616	−	1.06455i	−0.990452	−	0.137860i	$-0.955978\pi$
$509$	−13.8664	−	24.0173i	−0.614616	−	1.06455i	0.375836	−	0.926686i	$-0.377356\pi$
$510$	3.42003	−	4.07561i	0.151441	−	0.180471i
$511$	−19.7211	+	15.8635i	−0.872409	+	0.701760i
$512$	1.00000			0.0441942
$513$	−11.0485	+	33.4825i	−0.487805	+	1.47829i
$514$	14.3279	−	8.27221i	0.631976	−	0.364871i
$515$	−0.116215	−	0.0287908i	−0.00512103	−	0.00126867i
$516$	9.75880	−	0.667463i	0.429607	−	0.0293834i
$517$	−4.65835	+	8.06850i	−0.204874	+	0.354852i
$518$	8.19560	−	21.1437i	0.360094	−	0.929001i
$519$	16.8437	−	34.4017i	0.739358	−	1.51007i
$520$	3.51697	+	12.1962i	0.154230	+	0.534838i
$521$	12.4542	+	21.5713i	0.545627	+	0.945054i	0.998567	+	0.0535127i	$0.0170418\pi$
$521$	12.4542	+	21.5713i	0.545627	+	0.945054i	−0.452940	+	0.891541i	$0.649625\pi$
$522$	15.0030	+	6.11485i	0.656664	+	0.267640i
$523$	−9.31147	+	16.1279i	−0.407162	+	0.705226i	−0.994570	−	0.104065i	$-0.966815\pi$
$523$	−9.31147	+	16.1279i	−0.407162	+	0.705226i	0.587408	+	0.809291i	$0.300148\pi$
$524$	2.65642	+	4.60106i	0.116046	+	0.200998i
$525$	22.1215	+	5.96996i	0.965460	+	0.260551i
$526$	1.01677	−	1.76111i	0.0443335	−	0.0767878i
$527$	−5.16651	−	8.94866i	−0.225057	−	0.389810i
$528$	−1.02893	−	1.53048i	−0.0447786	−	0.0666057i
$529$	1.39813	−	2.42164i	0.0607883	−	0.105289i
$530$	9.97332	+	2.47077i	0.433213	+	0.107323i
$531$	17.8513	+	22.9926i	0.774678	+	0.997795i
$532$	−6.48833	+	16.7391i	−0.281305	+	0.725733i
$533$	−6.92478	−	11.9941i	−0.299945	−	0.519521i
$534$	−16.5136	+	11.1020i	−0.714613	+	0.480430i
$535$	−5.08591	−	17.6369i	−0.219883	−	0.762512i
$536$		−	0.0645415i		−	0.00278777i
$537$	−18.2879	+	1.25082i	−0.789182	+	0.0539769i
$538$	11.6388	+	20.1590i	0.501785	+	0.869117i
$539$	−7.28011	−	1.59719i	−0.313577	−	0.0687956i
$540$	9.83446	+	6.18735i	0.423208	+	0.266261i
$541$	−8.55300	+	14.8142i	−0.367722	+	0.636913i	−0.989209	−	0.146511i	$-0.953196\pi$
$541$	−8.55300	+	14.8142i	−0.367722	+	0.636913i	0.621487	+	0.783425i	$0.286529\pi$
$542$	21.0788	+	12.1699i	0.905412	+	0.522740i
$543$	−4.98802	+	10.1875i	−0.214056	+	0.437189i
$544$	1.18969	−	0.686867i	0.0510075	−	0.0294492i
$545$	−29.8016	−	7.38299i	−1.27656	−	0.316252i
$546$	17.6497	+	19.1096i	0.755336	+	0.817815i
$547$	−10.4426	+	6.02903i	−0.446493	+	0.257783i	−0.706348	−	0.707865i	$-0.749658\pi$
$547$	−10.4426	+	6.02903i	−0.446493	+	0.257783i	0.259855	+	0.965648i	$0.416325\pi$
$548$	−0.0371922	+	0.0644188i	−0.00158877	+	0.00275183i
$549$	−23.5306	+	18.2689i	−1.00426	+	0.779698i
$550$	2.48526	−	4.70806i	0.105972	−	0.200752i
$551$	−36.6444			−1.56110
$552$	0.531244	+	7.76717i	0.0226112	+	0.330593i
$553$	−2.97822	−	19.2094i	−0.126647	−	0.816868i
$554$	−7.08143	−	4.08846i	−0.300861	−	0.173702i
$555$	32.6906	+	5.76510i	1.38764	+	0.244715i
$556$	−14.6763	−	8.47337i	−0.622414	−	0.359351i
$557$	−5.85535	−	10.1418i	−0.248099	−	0.429720i	0.714899	−	0.699227i	$-0.246472\pi$
$557$	−5.85535	−	10.1418i	−0.248099	−	0.429720i	−0.962998	+	0.269507i	$0.913139\pi$
$558$	17.8241	−	13.8385i	0.754556	−	0.585830i
$559$			32.0578i			1.35590i
$560$	4.84017	+	3.40188i	0.204534	+	0.143756i
$561$	−2.27535	−	1.11406i	−0.0960653	−	0.0470355i
$562$	−4.54162	+	2.62210i	−0.191577	+	0.110607i
$563$		−	28.8230i		−	1.21474i	−0.794417	−	0.607372i	$-0.792224\pi$
$563$		−	28.8230i		−	1.21474i	0.794417	−	0.607372i	$-0.207776\pi$
$564$	6.66455	−	13.6117i	0.280628	−	0.573155i
$565$	0.317254	+	1.10017i	0.0133470	+	0.0462847i
$566$	16.8827			0.709632
$567$	23.7007	+	2.29723i	0.995335	+	0.0964746i
$568$		−	6.07978i		−	0.255102i
$569$		−	44.5037i		−	1.86569i	−0.360273	−	0.932847i	$-0.617316\pi$
$569$		−	44.5037i		−	1.86569i	0.360273	−	0.932847i	$-0.382684\pi$
$570$	−25.8806	−	4.56414i	−1.08402	−	0.191171i
$571$	19.7658			0.827175			0.413587	−	0.910464i	$-0.364276\pi$
$571$	19.7658			0.827175			0.413587	+	0.910464i	$0.364276\pi$
$572$	5.23435	−	3.02205i	0.218859	−	0.126358i
$573$	−4.90366	+	10.0152i	−0.204854	+	0.418393i
$574$	−6.01874	−	2.33295i	−0.251217	−	0.0973754i
$575$	−19.0235	+	11.9666i	−0.793336	+	0.499041i
$576$	1.83977	+	2.36965i	0.0766572	+	0.0987354i
$577$	13.6853	+	23.7036i	0.569726	+	0.986795i	0.996593	+	0.0824802i	$0.0262841\pi$
$577$	13.6853	+	23.7036i	0.569726	+	0.986795i	−0.426866	+	0.904315i	$0.640383\pi$
$578$	−7.55643	+	13.0881i	−0.314306	+	0.544394i
$579$	−17.6727	+	36.0947i	−0.734451	+	1.50004i
$580$	−2.90383	+	11.7214i	−0.120575	+	0.486704i
$581$	14.5007	+	18.0269i	0.601591	+	0.747882i
$582$	−1.47924	−	21.6275i	−0.0613163	−	0.896489i
$583$		−	4.89257i		−	0.202630i
$584$	−4.78305	−	8.28448i	−0.197924	−	0.342814i
$585$	−22.4302	+	30.7722i	−0.927376	+	1.27227i
$586$	−25.5501	−	14.7514i	−1.05546	−	0.609373i
$587$	−22.8974	+	13.2198i	−0.945077	+	0.545641i	−0.891548	−	0.452926i	$-0.850380\pi$
$587$	−22.8974	+	13.2198i	−0.945077	+	0.545641i	−0.0535291	+	0.998566i	$0.517047\pi$
$588$	11.9924	+	1.78401i	0.494558	+	0.0735714i
$589$	−25.5196	+	44.2012i	−1.05152	+	1.82128i
$590$	−15.0483	+	15.6297i	−0.619527	+	0.643465i
$591$	3.61508	+	1.77002i	0.148705	+	0.0728087i
$592$	7.42263	+	4.28546i	0.305068	+	0.176131i
$593$	1.24355	+	0.717964i	0.0510665	+	0.0294832i	0.525316	−	0.850907i	$-0.323947\pi$
$593$	1.24355	+	0.717964i	0.0510665	+	0.0294832i	−0.474249	+	0.880391i	$0.657280\pi$
$594$	1.73370	−	5.25395i	0.0711346	−	0.215572i
$595$	8.09493	+	0.722631i	0.331860	+	0.0296250i
$596$	−14.4973	+	8.37004i	−0.593834	+	0.342850i
$597$	20.1668	−	1.37933i	0.825374	−	0.0564523i
$598$	−25.5153			−1.04340
$599$			25.1094i			1.02594i	0.858406	+	0.512972i	$0.171455\pi$
$599$			25.1094i			1.02594i	−0.858406	+	0.512972i	$0.828545\pi$
$600$	−3.51080	+	7.91671i	−0.143328	+	0.323198i
$601$	18.4357	−	10.6439i	0.752009	−	0.434173i	−0.0744104	−	0.997228i	$-0.523707\pi$
$601$	18.4357	−	10.6439i	0.752009	−	0.434173i	0.826419	+	0.563055i	$0.190374\pi$
$602$	9.36512	+	11.6425i	0.381694	+	0.474511i
$603$	0.152941	−	0.118742i	0.00622823	−	0.00483554i
$604$	3.00497	−	5.20476i	0.122270	−	0.211779i
$605$	21.4144	+	5.30515i	0.870618	+	0.215685i
$606$	11.8958	−	7.99749i	0.483235	−	0.324876i
$607$	10.6016	+	18.3625i	0.430306	+	0.745311i	0.996899	−	0.0786859i	$-0.0250724\pi$
$607$	10.6016	+	18.3625i	0.430306	+	0.745311i	−0.566594	+	0.823997i	$0.691739\pi$
$608$	−5.87638	−	3.39273i	−0.238319	−	0.137593i
$609$	5.45154	+	24.1400i	0.220908	+	0.978201i
$610$	−15.9954	−	15.4003i	−0.647634	−	0.623542i
$611$	43.0159	+	24.8353i	1.74024	+	1.00473i
$612$	3.81639	+	1.55547i	0.154268	+	0.0628760i
$613$	15.9028	−	9.18146i	0.642306	−	0.370836i	−0.143196	−	0.989694i	$-0.545738\pi$
$613$	15.9028	−	9.18146i	0.642306	−	0.370836i	0.785502	+	0.618859i	$0.212405\pi$
$614$	10.7900			0.435449
$615$	1.64109	−	9.30565i	0.0661750	−	0.375240i
$616$	1.01813	−	2.62665i	0.0410215	−	0.105831i
$617$	−4.58356	+	7.93896i	−0.184527	+	0.319610i	−0.943417	−	0.331609i	$-0.892409\pi$
$617$	−4.58356	+	7.93896i	−0.184527	+	0.319610i	0.758890	+	0.651219i	$0.225742\pi$
$618$	−0.00632831	−	0.0925246i	−0.000254562	−	0.00372188i
$619$	28.7858	+	16.6195i	1.15700	+	0.667993i	0.950583	−	0.310472i	$-0.100487\pi$
$619$	28.7858	+	16.6195i	1.15700	+	0.667993i	0.206415	+	0.978465i	$0.433820\pi$
$620$	12.1163	+	11.6656i	0.486603	+	0.468501i
$621$	−17.4281	+	15.5487i	−0.699366	+	0.623948i
$622$	−6.78533			−0.272067
$623$	−28.3410	−	10.9854i	−1.13546	−	0.440120i
$624$	−8.15952	+	5.48560i	−0.326642	+	0.219600i
$625$	−24.9282	+	1.89327i	−0.997128	+	0.0757307i
$626$	22.5896			0.902860
$627$	0.853896	+	12.4846i	0.0341013	+	0.498586i
$628$	−9.02952			−0.360317
$629$	11.7742			0.469467
$630$	0.843538	+	17.7282i	0.0336074	+	0.706308i
$631$	−33.5594			−1.33598			−0.667989	−	0.744171i	$-0.732845\pi$
$631$	−33.5594			−1.33598			−0.667989	+	0.744171i	$0.732845\pi$
$632$	7.34722			0.292257
$633$	−22.4983	+	15.1255i	−0.894228	+	0.601185i
$634$	−27.0432			−1.07402
$635$	7.42383	+	7.14765i	0.294606	+	0.283646i
$636$	0.543084	+	7.94029i	0.0215347	+	0.314853i
$637$	−8.51514	+	38.8127i	−0.337382	+	1.53782i
$638$	5.75011			0.227649
$639$	14.4069	−	11.1854i	0.569930	−	0.442488i
$640$	−1.55089	+	1.61082i	−0.0613044	+	0.0636731i
$641$	24.6820	+	14.2502i	0.974881	+	0.562848i	0.900721	−	0.434398i	$-0.143039\pi$
$641$	24.6820	+	14.2502i	0.974881	+	0.562848i	0.0741605	+	0.997246i	$0.476372\pi$
$642$	11.7995	−	7.93274i	0.465690	−	0.313080i
$643$	1.28905	−	2.23270i	0.0508352	−	0.0880491i	−0.839488	−	0.543378i	$-0.817145\pi$
$643$	1.28905	−	2.23270i	0.0508352	−	0.0880491i	0.890323	+	0.455329i	$0.150478\pi$
$644$	−9.26641	+	7.45384i	−0.365148	+	0.293722i
$645$	−14.0597	+	16.7548i	−0.553600	+	0.659720i
$646$	−9.32142			−0.366746
$647$	6.52143	−	3.76515i	0.256384	−	0.148023i	−0.366300	−	0.930497i	$-0.619376\pi$
$647$	6.52143	−	3.76515i	0.256384	−	0.148023i	0.622684	+	0.782473i	$0.286042\pi$
$648$	−2.23047	+	8.71923i	−0.0876212	+	0.342524i
$649$	8.94711	+	5.16562i	0.351205	+	0.202768i
$650$	−25.1003	−	13.2498i	−0.984514	−	0.519699i
$651$	32.9147	+	10.2356i	1.29003	+	0.401165i
$652$	8.62716	+	4.98089i	0.337866	+	0.195067i
$653$	16.9498	+	29.3579i	0.663296	+	1.14886i	0.979744	+	0.200252i	$0.0641762\pi$
$653$	16.9498	+	29.3579i	0.663296	+	1.14886i	−0.316449	+	0.948610i	$0.602491\pi$
$654$	−1.62281	−	23.7266i	−0.0634568	−	0.927784i
$655$	−11.5313	−	2.85674i	−0.450565	−	0.111622i
$656$	1.21989	−	2.11292i	0.0476288	−	0.0824955i
$657$	10.8316	−	26.5757i	0.422581	−	1.03682i
$658$	22.8773	−	3.54689i	0.891851	−	0.138272i
$659$	5.47266	−	3.15964i	0.213185	−	0.123082i	−0.389606	−	0.920982i	$-0.627389\pi$
$659$	5.47266	−	3.15964i	0.213185	−	0.123082i	0.602791	+	0.797899i	$0.294055\pi$
$660$	4.06109	+	0.716189i	0.158078	+	0.0278776i
$661$			22.2173i			0.864155i	0.901837	+	0.432077i	$0.142219\pi$
$661$			22.2173i			0.864155i	−0.901837	+	0.432077i	$0.857781\pi$
$662$	6.03337			0.234493
$663$	−5.93942	+	12.1307i	−0.230668	+	0.471116i
$664$	−7.57279	+	4.37215i	−0.293881	+	0.169672i
$665$	−16.9010	−	36.4121i	−0.655392	−	1.41200i
$666$	3.50092	+	25.4733i	0.135658	+	0.987070i
$667$	−21.0220	−	12.1371i	−0.813976	−	0.469949i
$668$	16.2295	+	9.37008i	0.627936	+	0.362539i
$669$	1.54155	+	22.5386i	0.0595997	+	0.871391i
$670$	0.103965	+	0.100097i	0.00401650	+	0.00386708i
$671$	−5.28648	+	9.15645i	−0.204082	+	0.353481i
$672$	−1.36078	+	4.37587i	−0.0524933	+	0.168803i
$673$	12.4379	−	7.18105i	0.479447	−	0.276809i	−0.240739	−	0.970590i	$-0.577390\pi$
$673$	12.4379	−	7.18105i	0.479447	−	0.276809i	0.720186	+	0.693781i	$0.244056\pi$
$674$	14.4392	+	8.33650i	0.556179	+	0.321110i
$675$	−25.2189	+	6.24559i	−0.970676	+	0.240393i
$676$	−9.61160	−	16.6478i	−0.369677	−	0.640299i
$677$		−	37.5022i		−	1.44132i	−0.693286	−	0.720662i	$-0.743838\pi$
$677$		−	37.5022i		−	1.44132i	0.693286	−	0.720662i	$-0.256162\pi$
$678$	−0.736041	+	0.494836i	−0.0282675	+	0.0190041i
$679$	25.8021	−	20.7550i	0.990194	−	0.796505i
$680$	−0.738663	+	2.98163i	−0.0283264	+	0.114340i
$681$	−27.7036	−	41.2076i	−1.06161	−	1.57908i
$682$	4.00445	−	6.93591i	0.153338	−	0.265590i
$683$	2.22205	+	3.84871i	0.0850245	+	0.147267i	0.905402	−	0.424556i	$-0.139570\pi$
$683$	2.22205	+	3.84871i	0.0850245	+	0.147267i	−0.820377	+	0.571823i	$0.806236\pi$
$684$	−2.77163	−	20.1668i	−0.105976	−	0.771097i
$685$	−0.0460858	−	0.159816i	−0.00176085	−	0.00610627i
$686$	8.24601	+	16.5832i	0.314834	+	0.633150i
$687$	−7.13050	+	0.487698i	−0.272046	+	0.0186068i
$688$	−4.89080	+	2.82370i	−0.186460	+	0.107653i
$689$	−26.0840			−0.993720
$690$	−13.3354	−	11.1903i	−0.507670	−	0.426008i
$691$			41.5004i			1.57875i	0.613912	+	0.789374i	$0.289595\pi$
$691$			41.5004i			1.57875i	−0.613912	+	0.789374i	$0.710405\pi$
$692$			22.1147i			0.840676i
$693$	8.09735	−	2.41983i	0.307593	−	0.0919218i
$694$	33.0004			1.25268
$695$	36.4104	−	10.4996i	1.38113	−	0.398271i
$696$	−9.33201	+	0.638273i	−0.353729	+	0.0241937i
$697$		−	3.35162i		−	0.126952i
$698$	−9.69567	+	5.59780i	−0.366987	+	0.211880i
$699$	−2.47060	+	1.66097i	−0.0934468	+	0.0628237i
$700$	−12.9864	+	2.52067i	−0.490839	+	0.0952722i
$701$			26.9990i			1.01974i	0.860252	+	0.509869i	$0.170306\pi$
$701$			26.9990i			1.01974i	−0.860252	+	0.509869i	$0.829694\pi$
$702$	−28.0106	−	9.24295i	−1.05719	−	0.348853i
$703$	−29.0788	−	50.3659i	−1.09673	−	1.89959i
$704$	0.922101	+	0.532375i	0.0347530	+	0.0200646i
$705$	11.5899	+	31.8456i	0.436502	+	1.19938i
$706$	12.5080	+	7.22147i	0.470743	+	0.271784i
$707$	20.4159	+	7.91349i	0.767818	+	0.297617i
$708$	−15.0939	−	7.39028i	−0.567264	−	0.277744i
$709$	37.9992			1.42709			0.713545	−	0.700610i	$-0.247089\pi$
$709$	37.9992			1.42709			0.713545	+	0.700610i	$0.247089\pi$
$710$	9.79341	+	9.42908i	0.367540	+	0.353867i
$711$	13.5172	+	17.4103i	0.506935	+	0.652939i
$712$	5.74422	−	9.94928i	0.215274	−	0.372865i
$713$	−29.2800	+	16.9048i	−1.09654	+	0.633090i
$714$	1.38674	+	6.14061i	0.0518973	+	0.229806i
$715$	−3.24994	+	13.1185i	−0.121541	+	0.490603i
$716$	9.16532	−	5.29160i	0.342524	−	0.197756i
$717$	−8.84419	−	13.1552i	−0.330292	−	0.491292i
$718$	−18.4344	−	10.6431i	−0.687966	−	0.397198i
$719$	5.43173	−	9.40802i	0.202569	−	0.350860i	−0.746786	−	0.665064i	$-0.768404\pi$
$719$	5.43173	−	9.40802i	0.202569	−	0.350860i	0.949356	+	0.314204i	$0.101738\pi$
$720$	−6.67036	−	0.711534i	−0.248590	−	0.0265173i
$721$	0.110384	−	0.0887920i	0.00411091	−	0.00330679i
$722$	13.5212	+	23.4194i	0.503207	+	0.871581i
$723$	0.777108	+	1.15590i	0.0289010	+	0.0429885i
$724$		−	6.54895i		−	0.243390i
$725$	−14.3775	−	22.8562i	−0.533966	−	0.848856i
$726$	1.16609	+	17.0491i	0.0432777	+	0.632752i
$727$	16.6696	+	28.8726i	0.618242	+	1.07083i	0.989806	+	0.142419i	$0.0454881\pi$
$727$	16.6696	+	28.8726i	0.618242	+	1.07083i	−0.371565	+	0.928407i	$0.621179\pi$
$728$	−14.0036	−	5.42798i	−0.519006	−	0.201174i
$729$	−24.7651	+	10.7560i	−0.917225	+	0.398369i
$730$	20.7628	+	5.14373i	0.768465	+	0.190378i
$731$	−3.87902	+	6.71866i	−0.143471	+	0.248499i
$732$	7.56319	−	15.4471i	0.279544	−	0.570940i
$733$	0.906200	+	1.56958i	0.0334713	+	0.0579739i	0.882276	−	0.470733i	$-0.156010\pi$
$733$	0.906200	+	1.56958i	0.0334713	+	0.0579739i	−0.848805	+	0.528707i	$0.822677\pi$
$734$	8.90707	−	15.4275i	0.328766	−	0.569440i
$735$	−21.4726	+	16.5507i	−0.792030	+	0.610483i
$736$	−2.24743	−	3.89266i	−0.0828413	−	0.143485i
$737$	0.0343603	−	0.0595138i	0.00126568	−	0.00219222i
$738$	7.25119	−	0.996568i	0.266920	−	0.0366842i
$739$	−5.23342	−	9.06456i	−0.192515	−	0.333445i	0.753568	−	0.657370i	$-0.228331\pi$
$739$	−5.23342	−	9.06456i	−0.192515	−	0.333445i	−0.946083	+	0.323924i	$0.894998\pi$
$740$	−18.4148	+	5.31021i	−0.676941	+	0.195207i
$741$	66.5596	−	4.55241i	2.44513	−	0.167237i
$742$	−9.47295	+	7.61997i	−0.347763	+	0.279738i
$743$	−8.55060	+	14.8101i	−0.313691	+	0.543329i	−0.979158	−	0.203098i	$-0.934899\pi$
$743$	−8.55060	+	14.8101i	−0.313691	+	0.543329i	0.665467	+	0.746427i	$0.268232\pi$
$744$	−5.72903	+	11.7010i	−0.210036	+	0.428979i
$745$	9.00121	−	36.3336i	0.329779	−	1.33116i
$746$	15.5268	−	8.96439i	0.568476	−	0.328210i
$747$	−24.2927	−	9.90109i	−0.888823	−	0.362262i
$748$	1.46268			0.0534810
$749$	20.2506	+	7.84942i	0.739940	+	0.286811i
$750$	−7.30750	−	17.9332i	−0.266832	−	0.654829i
$751$	−3.02573	−	5.24072i	−0.110410	−	0.191237i	0.805525	−	0.592561i	$-0.201883\pi$
$751$	−3.02573	−	5.24072i	−0.110410	−	0.191237i	−0.915936	+	0.401325i	$0.868550\pi$
$752$			8.75012i			0.319084i
$753$	30.5604	+	14.9630i	1.11368	+	0.545281i
$754$		−	30.6558i		−	1.11642i
$755$	3.72353	+	12.9125i	0.135513	+	0.469933i
$756$	−12.8728	+	4.82604i	−0.468180	+	0.175521i
$757$		−	29.0415i		−	1.05553i	−0.849390	−	0.527765i	$-0.823030\pi$
$757$		−	29.0415i		−	1.05553i	0.849390	−	0.527765i	$-0.176970\pi$
$758$	−0.162766			−0.00591194
$759$	−3.64519	+	7.44494i	−0.132312	+	0.270234i
$760$	14.5787	−	4.20401i	0.528825	−	0.152496i
$761$	15.7946	+	27.3571i	0.572555	+	0.991694i	0.996303	+	0.0859137i	$0.0273809\pi$
$761$	15.7946	+	27.3571i	0.572555	+	0.991694i	−0.423748	+	0.905780i	$0.639286\pi$
$762$	−3.51025	+	7.16934i	−0.127163	+	0.259718i
$763$	28.3064	−	22.7695i	1.02476	−	0.824310i
$764$		−	6.43820i		−	0.232926i
$765$	−8.42439	+	3.73515i	−0.304584	+	0.135045i
$766$	−8.64195	+	4.98943i	−0.312246	+	0.180276i
$767$	27.5397	−	47.7001i	0.994400	−	1.72235i
$768$	−1.55560	−	0.761652i	−0.0561328	−	0.0274837i
$769$	−45.0333	−	26.0000i	−1.62394	−	0.937583i	−0.985851	−	0.167622i	$-0.946391\pi$
$769$	−45.0333	−	26.0000i	−1.62394	−	0.937583i	−0.638090	−	0.769961i	$-0.720275\pi$
$770$	2.65204	+	5.71366i	0.0955730	+	0.205906i
$771$	−28.5890	+	1.95537i	−1.02961	+	0.0704210i
$772$		−	23.2031i		−	0.835097i
$773$	−1.80797	+	1.04383i	−0.0650283	+	0.0375441i	−0.532162	−	0.846643i	$-0.678620\pi$
$773$	−1.80797	+	1.04383i	−0.0650283	+	0.0375441i	0.467133	+	0.884187i	$0.345287\pi$
$774$	−15.6891	−	6.39450i	−0.563935	−	0.229846i
$775$	−37.5822	+	1.42511i	−1.34999	+	0.0511915i
$776$	6.25791	+	10.8390i	0.224646	+	0.389098i
$777$	−28.8532	+	26.6489i	−1.03510	+	0.956025i
$778$	20.5762	+	11.8797i	0.737694	+	0.425908i
$779$	−14.3371	+	8.27753i	−0.513680	+	0.296573i
$780$	3.81825	−	21.6511i	0.136715	−	0.775233i
$781$	3.23672	−	5.60617i	0.115819	−	0.200604i
$782$	−5.34748	−	3.08737i	−0.191226	−	0.110404i
$783$	−18.6813	−	20.9393i	−0.667614	−	0.748310i
$784$	−6.67138	+	2.11961i	−0.238263	+	0.0757002i
$785$	14.0038	−	14.5449i	0.499818	−	0.519130i
$786$	−0.627921	−	9.18066i	−0.0223972	−	0.327463i
$787$	26.9597			0.961010			0.480505	−	0.876992i	$-0.340453\pi$
$787$	26.9597			0.961010			0.480505	+	0.876992i	$0.340453\pi$
$788$	−2.32392			−0.0827861
$789$	−2.92304	+	1.96514i	−0.104063	+	0.0699610i
$790$	−11.3948	+	11.8350i	−0.405407	+	0.421072i
$791$	−1.26321	−	0.489638i	−0.0449146	−	0.0174095i
$792$	0.434914	+	3.16451i	0.0154540	+	0.112446i
$793$	48.8161	+	28.1840i	1.73351	+	1.00084i
$794$	10.9098	−	18.8963i	0.387174	−	0.670605i
$795$	−13.6326	−	11.4397i	−0.483499	−	0.405725i
$796$	−10.1070	+	5.83527i	−0.358232	+	0.206826i
$797$	−6.03754	−	3.48577i	−0.213861	−	0.123472i	0.389244	−	0.921135i	$-0.372736\pi$
$797$	−6.03754	−	3.48577i	−0.213861	−	0.123472i	−0.603104	+	0.797662i	$0.706070\pi$
$798$	22.8426	−	21.0975i	0.808620	−	0.746844i
$799$	6.01017	+	10.4099i	0.212625	+	0.368277i
$800$	−0.189463	−	4.99641i	−0.00669852	−	0.176650i
$801$	34.1444	−	4.69263i	1.20643	−	0.165806i
$802$	−2.29120	+	1.32282i	−0.0809051	+	0.0467106i
$803$		−	10.1855i		−	0.359439i
$804$	−0.0491582	+	0.100401i	−0.00173368	+	0.00354086i
$805$	2.36445	−	26.4866i	0.0833358	−	0.933530i
$806$	−36.9777	−	21.3491i	−1.30248	−	0.751989i
$807$	−2.75117	−	40.2241i	−0.0968457	−	1.41595i
$808$	−4.13794	+	7.16712i	−0.145572	+	0.252138i
$809$	9.53225	−	5.50345i	0.335136	−	0.193491i	−0.322983	−	0.946405i	$-0.604686\pi$
$809$	9.53225	−	5.50345i	0.335136	−	0.193491i	0.658119	+	0.752914i	$0.271352\pi$
$810$	−10.5859	−	17.1155i	−0.371949	−	0.601377i
$811$		−	44.4197i		−	1.55979i	−0.625913	−	0.779893i	$-0.715273\pi$
$811$		−	44.4197i		−	1.55979i	0.625913	−	0.779893i	$-0.284727\pi$
$812$	−8.95555	−	11.1333i	−0.314278	−	0.390702i
$813$	−23.5210	−	34.9861i	−0.824916	−	1.22702i
$814$	4.56294	+	7.90325i	0.159931	+	0.277009i
$815$	−21.4031	+	6.17194i	−0.749718	+	0.216194i
$816$	−2.37383	+	0.162361i	−0.0831007	+	0.00568376i
$817$	38.3202			1.34066
$818$		−	17.4968i		−	0.611763i
$819$	−12.9010	−	43.1697i	−0.450796	−	1.50847i
$820$	1.51160	+	5.24193i	0.0527873	+	0.183056i
$821$		−	5.01695i		−	0.175093i	−0.996160	−	0.0875464i	$-0.972097\pi$
$821$		−	5.01695i		−	0.175093i	0.996160	−	0.0875464i	$-0.0279026\pi$
$822$	0.106921	−	0.0718823i	0.00372929	−	0.00250718i
$823$		−	22.3769i		−	0.780008i	−0.920813	−	0.390004i	$-0.872474\pi$
$823$		−	22.3769i		−	0.780008i	0.920813	−	0.390004i	$-0.127526\pi$
$824$	0.0267719	+	0.0463704i	0.000932645	+	0.00161539i
$825$	−7.45197	+	5.43095i	−0.259444	+	0.189081i
$826$	−3.93313	−	25.3685i	−0.136851	−	0.882685i
$827$	4.65264			0.161788			0.0808940	−	0.996723i	$-0.474222\pi$
$827$	4.65264			0.161788			0.0808940	+	0.996723i	$0.474222\pi$
$828$	5.08948	−	12.4872i	0.176872	−	0.433961i
$829$	25.1125	−	14.4987i	0.872192	−	0.503561i	0.00411622	−	0.999992i	$-0.498690\pi$
$829$	25.1125	−	14.4987i	0.872192	−	0.503561i	0.868076	+	0.496431i	$0.165356\pi$
$830$	4.70185	−	18.9791i	0.163204	−	0.658775i
$831$	7.90187	+	11.7536i	0.274113	+	0.407728i
$832$	2.83827	−	4.91604i	0.0983995	−	0.170433i
$833$	−6.48098	+	7.10402i	−0.224553	+	0.246140i
$834$	16.3767	+	24.3594i	0.567078	+	0.843497i
$835$	−40.2636	+	11.6107i	−1.39338	+	0.401804i
$836$	−3.61241	−	6.25688i	−0.124938	−	0.216399i
$837$	−38.2673	+	7.95135i	−1.32271	+	0.274839i
$838$	−4.87854	+	8.44988i	−0.168526	+	0.291896i
$839$	24.3540	+	42.1824i	0.840793	+	1.45630i	0.889225	+	0.457470i	$0.151244\pi$
$839$	24.3540	+	42.1824i	0.840793	+	1.45630i	−0.0484316	+	0.998827i	$0.515422\pi$
$840$	−4.93830	−	8.97848i	−0.170388	−	0.309787i
$841$	0.0823151	−	0.142574i	0.00283845	−	0.00491634i
$842$	15.0741	+	26.1091i	0.519488	+	0.899780i
$843$	9.06206	−	0.619809i	0.312114	−	0.0213474i
$844$	7.82600	−	13.5550i	0.269382	−	0.466583i
$845$	41.7231	+	10.3364i	1.43532	+	0.355583i
$846$	−20.7347	+	16.0982i	−0.712874	+	0.553469i
$847$	−20.3400	+	16.3613i	−0.698890	+	0.562182i
$848$	−2.29752	−	3.97942i	−0.0788971	−	0.136654i
$849$	−26.2627	−	12.8587i	−0.901332	−	0.441310i
$850$	−3.65727	−	5.81404i	−0.125443	−	0.199420i
$851$		−	38.5250i		−	1.32062i
$852$	−4.63067	+	9.45769i	−0.158644	+	0.324015i
$853$	6.96876	+	12.0702i	0.238606	+	0.413277i	0.960314	−	0.278920i	$-0.0899763\pi$
$853$	6.96876	+	12.0702i	0.238606	+	0.413277i	−0.721709	+	0.692197i	$0.756643\pi$
$854$	25.9621	−	4.02515i	0.888404	−	0.137738i
$855$	36.7835	+	26.8120i	1.25797	+	0.916950i
$856$	−4.10444	+	7.10909i	−0.140287	+	0.242984i
$857$	−5.89936	−	3.40600i	−0.201518	−	0.116347i	0.395845	−	0.918317i	$-0.370452\pi$
$857$	−5.89936	−	3.40600i	−0.201518	−	0.116347i	−0.597363	+	0.801971i	$0.703785\pi$
$858$	−10.4443	+	0.714349i	−0.356563	+	0.0243875i
$859$	−21.8561	+	12.6186i	−0.745721	+	0.430542i	−0.824146	−	0.566378i	$-0.808344\pi$
$859$	−21.8561	+	12.6186i	−0.745721	+	0.430542i	0.0784245	+	0.996920i	$0.475011\pi$
$860$	3.03663	−	12.2574i	0.103548	−	0.417975i
$861$	7.58584	+	8.21331i	0.258525	+	0.279909i
$862$	−30.1386	+	17.4005i	−1.02652	+	0.592664i
$863$	5.87923	−	10.1831i	0.200131	−	0.346638i	−0.748439	−	0.663203i	$-0.769196\pi$
$863$	5.87923	−	10.1831i	0.200131	−	0.346638i	0.948571	+	0.316566i	$0.102530\pi$
$864$	−1.05710	−	5.08749i	−0.0359633	−	0.173080i
$865$	−35.6228	−	34.2976i	−1.21121	−	1.16615i
$866$	36.5774			1.24295
$867$	21.7234	−	14.6045i	0.737764	−	0.495994i
$868$	−19.6660	+	3.04901i	−0.667507	+	0.103490i
$869$	6.77488	+	3.91148i	0.229822	+	0.132688i
$870$	13.4448	−	16.0221i	0.455822	−	0.543199i
$871$	−0.317288	−	0.183187i	−0.0107509	−	0.00620704i
$872$	6.86529	+	11.8910i	0.232488	+	0.402681i
$873$	−14.1715	+	34.7704i	−0.479634	+	1.17680i
$874$			30.4997i			1.03167i
$875$	16.0802	−	24.8280i	0.543609	−	0.839339i
$876$	1.13061	+	16.5303i	0.0381998	+	0.558509i
$877$	−6.11879	+	3.53268i	−0.206617	+	0.119290i	−0.599738	−	0.800196i	$-0.704729\pi$
$877$	−6.11879	+	3.53268i	−0.206617	+	0.119290i	0.393121	+	0.919487i	$0.371395\pi$
$878$			1.51393i			0.0510927i
$879$	28.5103	+	42.4075i	0.961628	+	1.43037i
$880$	−2.28764	+	0.659679i	−0.0771163	+	0.0222378i
$881$	−15.3713			−0.517872			−0.258936	−	0.965895i	$-0.583372\pi$
$881$	−15.3713			−0.517872			−0.258936	+	0.965895i	$0.583372\pi$
$882$	−17.2965	−	11.9092i	−0.582405	−	0.401005i
$883$		−	29.3232i		−	0.986803i	−0.869802	−	0.493401i	$-0.835753\pi$
$883$		−	29.3232i		−	0.986803i	0.869802	−	0.493401i	$-0.164247\pi$
$884$		−	7.79807i		−	0.262278i
$885$	35.3134	−	12.8520i	1.18705	−	0.432015i
$886$	−22.5770			−0.758490
$887$	−33.5481	+	19.3690i	−1.12644	+	0.650348i	−0.943036	−	0.332691i	$-0.892044\pi$
$887$	−33.5481	+	19.3690i	−1.12644	+	0.650348i	−0.183400	+	0.983038i	$0.558710\pi$
$888$	−8.28261	−	12.3199i	−0.277946	−	0.413429i
$889$	−12.0496	+	1.86817i	−0.404131	+	0.0626563i
$890$	7.11780	+	24.6831i	0.238589	+	0.827381i
$891$	−6.69862	+	6.85256i	−0.224412	+	0.229570i
$892$	−6.52152	−	11.2956i	−0.218357	−	0.378205i
$893$	29.6868	−	51.4190i	0.993431	−	1.72067i
$894$	28.9271	−	1.97850i	0.967466	−	0.0661709i
$895$	−5.69063	+	22.9704i	−0.190217	+	0.767814i
$896$	−0.405354	−	2.61451i	−0.0135419	−	0.0873448i
$897$	39.6915	+	19.4338i	1.32526	+	0.648874i
$898$		−	6.39415i		−	0.213375i
$899$	−20.3106	−	35.1790i	−0.677397	−	1.17329i
$900$	11.4912	−	9.64122i	0.383039	−	0.321374i
$901$	−5.46667	−	3.15618i	−0.182121	−	0.105148i
$902$	2.24973	−	1.29888i	0.0749077	−	0.0432480i
$903$	−5.70085	−	25.2440i	−0.189713	−	0.840066i
$904$	0.256031	−	0.443458i	0.00851545	−	0.0147492i
$905$	10.5492	+	10.1567i	0.350666	+	0.337621i
$906$	−8.63874	+	5.80778i	−0.287003	+	0.192950i
$907$	−34.3857	−	19.8526i	−1.14176	−	0.659194i	−0.194893	−	0.980825i	$-0.562436\pi$
$907$	−34.3857	−	19.8526i	−1.14176	−	0.659194i	−0.946865	+	0.321630i	$0.895769\pi$
$908$	24.8272	+	14.3340i	0.823919	+	0.475690i
$909$	−24.5964	+	3.38041i	−0.815812	+	0.112121i
$910$	30.4615	−	14.1389i	1.00979	−	0.468702i
$911$	27.2064	−	15.7076i	0.901388	−	0.520417i	0.0237377	−	0.999718i	$-0.492443\pi$
$911$	27.2064	−	15.7076i	0.901388	−	0.520417i	0.877650	+	0.479302i	$0.159110\pi$
$912$	6.55721	+	9.75348i	0.217131	+	0.322970i
$913$	−9.31051			−0.308133
$914$			1.55320i			0.0513753i
$915$	13.1527	+	36.1397i	0.434815	+	1.19474i
$916$	3.57358	−	2.06321i	0.118074	−	0.0681703i
$917$	10.9527	−	8.81031i	0.361691	−	0.290942i
$918$	−4.75205	−	5.32644i	−0.156841	−	0.175799i
$919$	15.2764	−	26.4595i	0.503921	−	0.872818i	−0.496068	−	0.868284i	$-0.665223\pi$
$919$	15.2764	−	26.4595i	0.503921	−	0.872818i	0.999990	−	0.00453405i	$-0.00144324\pi$
$920$	9.75588	+	2.41690i	0.321642	+	0.0796829i
$921$	−16.7849	−	8.21823i	−0.553082	−	0.270800i
$922$	−7.34634	−	12.7242i	−0.241939	−	0.419050i
$923$	−29.8884	−	17.2561i	−0.983788	−	0.567991i
$924$	−3.58439	+	3.31055i	−0.117918	+	0.108909i
$925$	20.0056	−	37.8984i	0.657780	−	1.24609i
$926$	1.02891	+	0.594041i	0.0338120	+	0.0195214i
$927$	−0.0606272	+	0.148751i	−0.00199126	+	0.00488562i
$928$	4.67691	−	2.70021i	0.153527	−	0.0886389i
$929$	−36.6852			−1.20360			−0.601801	−	0.798646i	$-0.705550\pi$
$929$	−36.6852			−1.20360			−0.601801	+	0.798646i	$0.705550\pi$
$930$	−9.96302	−	27.3754i	−0.326700	−	0.897674i
$931$	46.3948	+	10.1786i	1.52053	+	0.333589i
$932$	0.859394	−	1.48851i	0.0281504	−	0.0487579i
$933$	10.5552	+	5.16806i	0.345563	+	0.169195i
$934$	29.2203	+	16.8704i	0.956118	+	0.552015i
$935$	−2.26847	+	2.35612i	−0.0741868	+	0.0770533i
$936$	16.8711	−	2.31867i	0.551448	−	0.0757882i
$937$	−14.4145			−0.470900			−0.235450	−	0.971887i	$-0.575656\pi$
$937$	−14.4145			−0.470900			−0.235450	+	0.971887i	$0.575656\pi$
$938$	−0.168745	+	0.0261621i	−0.00550971	+	0.000854224i
$939$	−35.1403	−	17.2054i	−1.14676	−	0.561476i
$940$	−14.0948	−	13.5705i	−0.459723	−	0.442621i
$941$	5.61702			0.183110			0.0915548	−	0.995800i	$-0.470816\pi$
$941$	5.61702			0.183110			0.0915548	+	0.995800i	$0.470816\pi$
$942$	14.0463	+	6.87735i	0.457653	+	0.224076i
$943$	−10.9665			−0.357118
$944$	9.70296			0.315805
$945$	12.1905	−	28.2204i	0.396557	−	0.918010i
$946$	−6.01308			−0.195502
$947$	−56.8287			−1.84668			−0.923342	−	0.383979i	$-0.874554\pi$
$947$	−56.8287			−1.84668			−0.923342	+	0.383979i	$0.874554\pi$
$948$	−11.4293	−	5.59603i	−0.371207	−	0.181751i
$949$	−54.3024			−1.76273
$950$	−15.8381	+	30.0036i	−0.513856	+	0.973445i
$951$	42.0684	+	20.5975i	1.36416	+	0.667920i
$952$	−2.27807	−	2.83204i	−0.0738327	−	0.0917868i
$953$	−17.2680			−0.559366			−0.279683	−	0.960092i	$-0.590229\pi$
$953$	−17.2680			−0.559366			−0.279683	+	0.960092i	$0.590229\pi$
$954$	5.20291	−	12.7655i	0.168451	−	0.413300i
$955$	10.3708	+	9.98495i	0.335590	+	0.323105i
$956$	7.92591	+	4.57603i	0.256342	+	0.147999i
$957$	−8.94486	−	4.37958i	−0.289146	−	0.141572i
$958$	3.15505	−	5.46471i	0.101935	−	0.176557i
$959$	0.183500	+	0.0711272i	0.00592552	+	0.00229682i
$960$	3.63945	−	1.32454i	0.117463	−	0.0427495i
$961$	−25.5782			−0.825104
$962$	42.1349	−	24.3266i	1.35848	−	0.784321i
$963$	−24.3973	+	3.35304i	−0.786192	+	0.108050i
$964$	−0.696421	−	0.402079i	−0.0224302	−	0.0129501i
$965$	37.3759	+	35.9855i	1.20317	+	1.15841i
$966$	20.0921	−	4.53740i	0.646451	−	0.145988i
$967$	−21.1215	−	12.1945i	−0.679222	−	0.392149i	0.120340	−	0.992733i	$-0.461602\pi$
$967$	−21.1215	−	12.1945i	−0.679222	−	0.392149i	−0.799562	+	0.600584i	$0.794935\pi$
$968$	−4.93315	−	8.54447i	−0.158558	−	0.274630i
$969$	14.5004	+	7.09967i	0.465819	+	0.228074i
$970$	−27.1650	−	6.72980i	−0.872216	−	0.216081i
$971$	19.8177	−	34.3253i	0.635980	−	1.10155i	−0.350326	−	0.936628i	$-0.613929\pi$
$971$	19.8177	−	34.3253i	0.635980	−	1.10155i	0.986307	−	0.164923i	$-0.0527374\pi$
$972$	10.1107	−	11.8648i	0.324302	−	0.380563i
$973$	−16.2047	+	41.8062i	−0.519498	+	1.34024i
$974$	−29.8197	+	17.2164i	−0.955484	+	0.551649i
$975$	28.9542	+	39.7290i	0.927277	+	1.27235i
$976$			9.92998i			0.317851i
$977$	4.03312			0.129031			0.0645155	−	0.997917i	$-0.479450\pi$
$977$	4.03312			0.129031			0.0645155	+	0.997917i	$0.479450\pi$
$978$	−9.62669	−	14.3192i	−0.307828	−	0.457876i
$979$	10.5935	−	6.11616i	0.338570	−	0.195473i
$980$	6.93229	−	14.0336i	0.221444	−	0.448288i
$981$	−15.5470	+	38.1451i	−0.496377	+	1.21788i
$982$	0.145232	+	0.0838499i	0.00463455	+	0.00267576i
$983$	−11.2271	−	6.48198i	−0.358090	−	0.206743i	0.310153	−	0.950687i	$-0.399620\pi$
$983$	−11.2271	−	6.48198i	−0.358090	−	0.206743i	−0.668242	+	0.743944i	$0.732953\pi$
$984$	−3.50697	+	2.35771i	−0.111798	+	0.0751612i
$985$	3.60415	−	3.74340i	0.114838	−	0.119275i
$986$	3.70938	−	6.42483i	0.118131	−	0.204608i
$987$	−38.2894	−	11.9070i	−1.21877	−	0.379005i
$988$	−33.3575	+	19.2590i	−1.06124	+	0.612710i
$989$	21.9834	+	12.6921i	0.699032	+	0.403587i
$990$	−5.77194	−	4.20724i	−0.183444	−	0.133715i
$991$	5.51935	+	9.55980i	0.175328	+	0.303677i	0.940275	−	0.340417i	$-0.110568\pi$
$991$	5.51935	+	9.55980i	0.175328	+	0.303677i	−0.764947	+	0.644094i	$0.777235\pi$
$992$		−	7.52185i		−	0.238819i
$993$	−9.38549	−	4.59532i	−0.297840	−	0.145828i
$994$	−15.8957	+	2.46446i	−0.504180	+	0.0781679i
$995$	6.27529	−	25.3304i	0.198940	−	0.803027i
$996$	15.1103	−	1.03348i	0.478788	−	0.0327472i
$997$	12.2807	−	21.2708i	0.388934	−	0.673653i	−0.603373	−	0.797459i	$-0.706177\pi$
$997$	12.2807	−	21.2708i	0.388934	−	0.673653i	0.992306	+	0.123807i	$0.0395102\pi$
$998$	1.46377	+	2.53532i	0.0463347	+	0.0802540i
$999$	13.9558	−	42.2927i	0.441541	−	1.33808i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bi.b.509.3	yes	48
3.2	odd	2		1890.2.bi.a.719.18		48
5.4	even	2		630.2.bi.a.509.22	yes	48
7.3	odd	6		630.2.r.a.59.11	✓	48
9.2	odd	6		630.2.r.b.299.14	yes	48
9.7	even	3		1890.2.r.a.89.10		48
15.14	odd	2		1890.2.bi.b.719.2		48
21.17	even	6		1890.2.r.b.1529.10		48
35.24	odd	6		630.2.r.b.59.14	yes	48
45.29	odd	6		630.2.r.a.299.11	yes	48
45.34	even	6		1890.2.r.b.89.10		48
63.38	even	6		630.2.bi.a.479.22	yes	48
63.52	odd	6		1890.2.bi.b.899.2		48
105.59	even	6		1890.2.r.a.1529.10		48
315.164	even	6	inner	630.2.bi.b.479.3	yes	48
315.304	odd	6		1890.2.bi.a.899.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.11	✓	48	7.3	odd	6
630.2.r.a.299.11	yes	48	45.29	odd	6
630.2.r.b.59.14	yes	48	35.24	odd	6
630.2.r.b.299.14	yes	48	9.2	odd	6
630.2.bi.a.479.22	yes	48	63.38	even	6
630.2.bi.a.509.22	yes	48	5.4	even	2
630.2.bi.b.479.3	yes	48	315.164	even	6	inner
630.2.bi.b.509.3	yes	48	1.1	even	1	trivial
1890.2.r.a.89.10		48	9.7	even	3
1890.2.r.a.1529.10		48	105.59	even	6
1890.2.r.b.89.10		48	45.34	even	6
1890.2.r.b.1529.10		48	21.17	even	6
1890.2.bi.a.719.18		48	3.2	odd	2
1890.2.bi.a.899.18		48	315.304	odd	6
1890.2.bi.b.719.2		48	15.14	odd	2
1890.2.bi.b.899.2		48	63.52	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.55560 - 0.761652i) q^{3} +1.00000 q^{4} +(-1.55089 + 1.61082i) q^{5} +(-1.55560 - 0.761652i) q^{6} +(-0.405354 - 2.61451i) q^{7} +1.00000 q^{8} +(1.83977 + 2.36965i) q^{9} +(-1.55089 + 1.61082i) q^{10} +(0.922101 + 0.532375i) q^{11} +(-1.55560 - 0.761652i) q^{12} +(2.83827 - 4.91604i) q^{13} +(-0.405354 - 2.61451i) q^{14} +(3.63945 - 1.32454i) q^{15} +1.00000 q^{16} +(1.18969 - 0.686867i) q^{17} +(1.83977 + 2.36965i) q^{18} +(-5.87638 - 3.39273i) q^{19} +(-1.55089 + 1.61082i) q^{20} +(-1.36078 + 4.37587i) q^{21} +(0.922101 + 0.532375i) q^{22} +(-2.24743 - 3.89266i) q^{23} +(-1.55560 - 0.761652i) q^{24} +(-0.189463 - 4.99641i) q^{25} +(2.83827 - 4.91604i) q^{26} +(-1.05710 - 5.08749i) q^{27} +(-0.405354 - 2.61451i) q^{28} +(4.67691 - 2.70021i) q^{29} +(3.63945 - 1.32454i) q^{30} -7.52185i q^{31} +1.00000 q^{32} +(-1.02893 - 1.53048i) q^{33} +(1.18969 - 0.686867i) q^{34} +(4.84017 + 3.40188i) q^{35} +(1.83977 + 2.36965i) q^{36} +(7.42263 + 4.28546i) q^{37} +(-5.87638 - 3.39273i) q^{38} +(-8.15952 + 5.48560i) q^{39} +(-1.55089 + 1.61082i) q^{40} +(1.21989 - 2.11292i) q^{41} +(-1.36078 + 4.37587i) q^{42} +(-4.89080 + 2.82370i) q^{43} +(0.922101 + 0.532375i) q^{44} +(-6.67036 - 0.711534i) q^{45} +(-2.24743 - 3.89266i) q^{46} +8.75012i q^{47} +(-1.55560 - 0.761652i) q^{48} +(-6.67138 + 2.11961i) q^{49} +(-0.189463 - 4.99641i) q^{50} +(-2.37383 + 0.162361i) q^{51} +(2.83827 - 4.91604i) q^{52} +(-2.29752 - 3.97942i) q^{53} +(-1.05710 - 5.08749i) q^{54} +(-2.28764 + 0.659679i) q^{55} +(-0.405354 - 2.61451i) q^{56} +(6.55721 + 9.75348i) q^{57} +(4.67691 - 2.70021i) q^{58} +9.70296 q^{59} +(3.63945 - 1.32454i) q^{60} +9.92998i q^{61} -7.52185i q^{62} +(5.44972 - 5.77066i) q^{63} +1.00000 q^{64} +(3.51697 + 12.1962i) q^{65} +(-1.02893 - 1.53048i) q^{66} -0.0645415i q^{67} +(1.18969 - 0.686867i) q^{68} +(0.531244 + 7.76717i) q^{69} +(4.84017 + 3.40188i) q^{70} -6.07978i q^{71} +(1.83977 + 2.36965i) q^{72} +(-4.78305 - 8.28448i) q^{73} +(7.42263 + 4.28546i) q^{74} +(-3.51080 + 7.91671i) q^{75} +(-5.87638 - 3.39273i) q^{76} +(1.01813 - 2.62665i) q^{77} +(-8.15952 + 5.48560i) q^{78} +7.34722 q^{79} +(-1.55089 + 1.61082i) q^{80} +(-2.23047 + 8.71923i) q^{81} +(1.21989 - 2.11292i) q^{82} +(-7.57279 + 4.37215i) q^{83} +(-1.36078 + 4.37587i) q^{84} +(-0.738663 + 2.98163i) q^{85} +(-4.89080 + 2.82370i) q^{86} +(-9.33201 + 0.638273i) q^{87} +(0.922101 + 0.532375i) q^{88} +(5.74422 - 9.94928i) q^{89} +(-6.67036 - 0.711534i) q^{90} +(-14.0036 - 5.42798i) q^{91} +(-2.24743 - 3.89266i) q^{92} +(-5.72903 + 11.7010i) q^{93} +8.75012i q^{94} +(14.5787 - 4.20401i) q^{95} +(-1.55560 - 0.761652i) q^{96} +(6.25791 + 10.8390i) q^{97} +(-6.67138 + 2.11961i) q^{98} +(0.434914 + 3.16451i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8} + 6 q^{11} + 3 q^{14} - 4 q^{15} + 48 q^{16} + 8 q^{21} + 6 q^{22} + 3 q^{23} - 18 q^{25} + 3 q^{28} - 3 q^{29} - 4 q^{30} + 48 q^{32} - 12 q^{35} - 18 q^{39}+ \cdots - 26 q^{99}+O(q^{100}) \) 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8 + 6 * q^11 + 3 * q^14 - 4 * q^15 + 48 * q^16 + 8 * q^21 + 6 * q^22 + 3 * q^23 - 18 * q^25 + 3 * q^28 - 3 * q^29 - 4 * q^30 + 48 * q^32 - 12 * q^35 - 18 * q^39 - 3 * q^41 + 8 * q^42 + 6 * q^44 - 39 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 - 42 * q^55 + 3 * q^56 - 22 * q^57 - 3 * q^58 - 4 * q^60 - 43 * q^63 + 48 * q^64 + 12 * q^65 - 42 * q^69 - 12 * q^70 - 18 * q^73 + 18 * q^75 - 12 * q^77 - 18 * q^78 + 8 * q^81 - 3 * q^82 + 9 * q^83 + 8 * q^84 - 33 * q^85 - 15 * q^87 + 6 * q^88 - 33 * q^89 - 39 * q^90 + 3 * q^92 - 8 * q^93 - 24 * q^97 + 3 * q^98 - 26 * q^99

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