LMFDB - Embedded newform 666.2.k.a.175.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(175,666)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("666.175"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			175.6
Character	$\chi$	$=$	666.175
Dual form			666.2.k.a.529.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(-0.831290 - 1.51953i) q^{3} -1.00000 q^{4} +0.827506i q^{5} +(-1.51953 + 0.831290i) q^{6} +(0.240855 - 0.417173i) q^{7} +1.00000i q^{8} +(-1.61792 + 2.52633i) q^{9} +0.827506 q^{10} +(2.72061 + 4.71223i) q^{11} +(0.831290 + 1.51953i) q^{12} +3.26345i q^{13} +(-0.417173 - 0.240855i) q^{14} +(1.25742 - 0.687897i) q^{15} +1.00000 q^{16} +(1.88641 + 1.08912i) q^{17} +(2.52633 + 1.61792i) q^{18} +(-6.41844 + 3.70569i) q^{19} -0.827506i q^{20} +(-0.834125 - 0.0191936i) q^{21} +(4.71223 - 2.72061i) q^{22} +(-4.52141 - 2.61044i) q^{23} +(1.51953 - 0.831290i) q^{24} +4.31523 q^{25} +3.26345 q^{26} +(5.18378 + 0.358350i) q^{27} +(-0.240855 + 0.417173i) q^{28} +(2.63163 - 1.51937i) q^{29} +(-0.687897 - 1.25742i) q^{30} +(5.50394 + 3.17770i) q^{31} -1.00000i q^{32} +(4.89874 - 8.05126i) q^{33} +(1.08912 - 1.88641i) q^{34} +(0.345213 + 0.199309i) q^{35} +(1.61792 - 2.52633i) q^{36} +(-5.94806 + 1.27302i) q^{37} +(3.70569 + 6.41844i) q^{38} +(4.95889 - 2.71287i) q^{39} -0.827506 q^{40} +10.3395 q^{41} +(-0.0191936 + 0.834125i) q^{42} +(-8.44579 + 4.87618i) q^{43} +(-2.72061 - 4.71223i) q^{44} +(-2.09055 - 1.33883i) q^{45} +(-2.61044 + 4.52141i) q^{46} +(-6.31576 - 10.9392i) q^{47} +(-0.831290 - 1.51953i) q^{48} +(3.38398 + 5.86122i) q^{49} -4.31523i q^{50} +(0.0867912 - 3.77181i) q^{51} -3.26345i q^{52} +(-0.0933100 + 0.161618i) q^{53} +(0.358350 - 5.18378i) q^{54} +(-3.89940 + 2.25132i) q^{55} +(0.417173 + 0.240855i) q^{56} +(10.9665 + 6.67248i) q^{57} +(-1.51937 - 2.63163i) q^{58} +(-3.50847 + 2.02562i) q^{59} +(-1.25742 + 0.687897i) q^{60} +(6.66181 + 3.84620i) q^{61} +(3.17770 - 5.50394i) q^{62} +(0.664234 + 1.28343i) q^{63} -1.00000 q^{64} -2.70052 q^{65} +(-8.05126 - 4.89874i) q^{66} +9.91978 q^{67} +(-1.88641 - 1.08912i) q^{68} +(-0.208024 + 9.04042i) q^{69} +(0.199309 - 0.345213i) q^{70} +(-3.12277 - 5.40879i) q^{71} +(-2.52633 - 1.61792i) q^{72} -11.1839 q^{73} +(1.27302 + 5.94806i) q^{74} +(-3.58721 - 6.55711i) q^{75} +(6.41844 - 3.70569i) q^{76} +2.62109 q^{77} +(-2.71287 - 4.95889i) q^{78} +(10.8506 + 6.26459i) q^{79} +0.827506i q^{80} +(-3.76470 - 8.17478i) q^{81} -10.3395i q^{82} +9.76840 q^{83} +(0.834125 + 0.0191936i) q^{84} +(-0.901251 + 1.56101i) q^{85} +(4.87618 + 8.44579i) q^{86} +(-4.49636 - 2.73579i) q^{87} +(-4.71223 + 2.72061i) q^{88} +(-1.91605 - 1.10623i) q^{89} +(-1.33883 + 2.09055i) q^{90} +(1.36142 + 0.786017i) q^{91} +(4.52141 + 2.61044i) q^{92} +(0.253229 - 11.0050i) q^{93} +(-10.9392 + 6.31576i) q^{94} +(-3.06648 - 5.31130i) q^{95} +(-1.51953 + 0.831290i) q^{96} +(-12.7209 + 7.34441i) q^{97} +(5.86122 - 3.38398i) q^{98} +(-16.3064 - 0.750832i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) $ 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.831290	−	1.51953i	−0.479945	−	0.877298i
$3$	−0.831290	−	1.51953i	−0.479945	−	0.877298i
$4$	−1.00000			−0.500000
$5$			0.827506i			0.370072i	0.982732	+	0.185036i	$0.0592402\pi$
$5$			0.827506i			0.370072i	−0.982732	+	0.185036i	$0.940760\pi$
$6$	−1.51953	+	0.831290i	−0.620344	+	0.339373i
$7$	0.240855	−	0.417173i	0.0910346	−	0.157677i	−0.816912	−	0.576762i	$-0.804316\pi$
$7$	0.240855	−	0.417173i	0.0910346	−	0.157677i	0.907947	+	0.419086i	$0.137649\pi$
$8$			1.00000i			0.353553i
$9$	−1.61792	+	2.52633i	−0.539305	+	0.842111i
$10$	0.827506			0.261680
$11$	2.72061	+	4.71223i	0.820294	+	1.42079i	0.905463	+	0.424424i	$0.139523\pi$
$11$	2.72061	+	4.71223i	0.820294	+	1.42079i	−0.0851696	+	0.996366i	$0.527143\pi$
$12$	0.831290	+	1.51953i	0.239973	+	0.438649i
$13$			3.26345i			0.905117i	0.891735	+	0.452559i	$0.149489\pi$
$13$			3.26345i			0.905117i	−0.891735	+	0.452559i	$0.850511\pi$
$14$	−0.417173	−	0.240855i	−0.111494	−	0.0643712i
$15$	1.25742	−	0.687897i	0.324663	−	0.177614i
$16$	1.00000			0.250000
$17$	1.88641	+	1.08912i	0.457521	+	0.264150i	0.711001	−	0.703191i	$-0.248242\pi$
$17$	1.88641	+	1.08912i	0.457521	+	0.264150i	−0.253481	+	0.967340i	$0.581575\pi$
$18$	2.52633	+	1.61792i	0.595462	+	0.381346i
$19$	−6.41844	+	3.70569i	−1.47249	+	0.850143i	−0.999521	−	0.0309358i	$-0.990151\pi$
$19$	−6.41844	+	3.70569i	−1.47249	+	0.850143i	−0.472969	+	0.881079i	$0.656818\pi$
$20$		−	0.827506i		−	0.185036i
$21$	−0.834125	−	0.0191936i	−0.182021	−	0.00418839i
$22$	4.71223	−	2.72061i	1.00465	−	0.580035i
$23$	−4.52141	−	2.61044i	−0.942779	−	0.544314i	−0.0519484	−	0.998650i	$-0.516543\pi$
$23$	−4.52141	−	2.61044i	−0.942779	−	0.544314i	−0.890830	+	0.454336i	$0.849876\pi$
$24$	1.51953	−	0.831290i	0.310172	−	0.169686i
$25$	4.31523			0.863047
$26$	3.26345			0.640015
$27$	5.18378	+	0.358350i	0.997619	+	0.0689644i
$28$	−0.240855	+	0.417173i	−0.0455173	+	0.0788383i
$29$	2.63163	−	1.51937i	0.488681	−	0.282140i	−0.235346	−	0.971912i	$-0.575622\pi$
$29$	2.63163	−	1.51937i	0.488681	−	0.282140i	0.724027	+	0.689772i	$0.242289\pi$
$30$	−0.687897	−	1.25742i	−0.125592	−	0.229572i
$31$	5.50394	+	3.17770i	0.988536	+	0.570732i	0.904836	−	0.425759i	$-0.139993\pi$
$31$	5.50394	+	3.17770i	0.988536	+	0.570732i	0.0836997	+	0.996491i	$0.473326\pi$
$32$		−	1.00000i		−	0.176777i
$33$	4.89874	−	8.05126i	0.852761	−	1.40154i
$34$	1.08912	−	1.88641i	0.186782	−	0.323516i
$35$	0.345213	+	0.199309i	0.0583517	+	0.0336894i
$36$	1.61792	−	2.52633i	0.269653	−	0.421055i
$37$	−5.94806	+	1.27302i	−0.977855	+	0.209284i
$37$	−5.94806	+	1.27302i	−0.977855	+	0.209284i
$38$	3.70569	+	6.41844i	0.601142	+	1.04121i
$39$	4.95889	−	2.71287i	0.794058	−	0.434407i
$40$	−0.827506			−0.130840
$41$	10.3395			1.61475			0.807377	−	0.590037i	$-0.200887\pi$
$41$	10.3395			1.61475			0.807377	+	0.590037i	$0.200887\pi$
$42$	−0.0191936	+	0.834125i	−0.00296164	+	0.128708i
$43$	−8.44579	+	4.87618i	−1.28797	+	0.743611i	−0.978292	−	0.207230i	$-0.933555\pi$
$43$	−8.44579	+	4.87618i	−1.28797	+	0.743611i	−0.309679	+	0.950841i	$0.600222\pi$
$44$	−2.72061	−	4.71223i	−0.410147	−	0.710395i
$45$	−2.09055	−	1.33883i	−0.311641	−	0.199582i
$46$	−2.61044	+	4.52141i	−0.384888	+	0.666645i
$47$	−6.31576	−	10.9392i	−0.921248	−	1.59565i	−0.797487	−	0.603337i	$-0.793838\pi$
$47$	−6.31576	−	10.9392i	−0.921248	−	1.59565i	−0.123762	−	0.992312i	$-0.539496\pi$
$48$	−0.831290	−	1.51953i	−0.119986	−	0.219325i
$49$	3.38398	+	5.86122i	0.483425	+	0.837317i
$50$		−	4.31523i		−	0.610266i
$51$	0.0867912	−	3.77181i	0.0121532	−	0.528160i
$52$		−	3.26345i		−	0.452559i
$53$	−0.0933100	+	0.161618i	−0.0128171	+	0.0221999i	−0.872363	−	0.488859i	$-0.837413\pi$
$53$	−0.0933100	+	0.161618i	−0.0128171	+	0.0221999i	0.859546	+	0.511059i	$0.170747\pi$
$54$	0.358350	−	5.18378i	0.0487652	−	0.705423i
$55$	−3.89940	+	2.25132i	−0.525795	+	0.303568i
$56$	0.417173	+	0.240855i	0.0557471	+	0.0321856i
$57$	10.9665	+	6.67248i	1.45254	+	0.883792i
$58$	−1.51937	−	2.63163i	−0.199503	−	0.345549i
$59$	−3.50847	+	2.02562i	−0.456764	+	0.263713i	−0.710683	−	0.703513i	$-0.751614\pi$
$59$	−3.50847	+	2.02562i	−0.456764	+	0.263713i	0.253919	+	0.967226i	$0.418280\pi$
$60$	−1.25742	+	0.687897i	−0.162332	+	0.0888071i
$61$	6.66181	+	3.84620i	0.852958	+	0.492455i	0.861648	−	0.507507i	$-0.169433\pi$
$61$	6.66181	+	3.84620i	0.852958	+	0.492455i	−0.00869000	+	0.999962i	$0.502766\pi$
$62$	3.17770	−	5.50394i	0.403568	−	0.699001i
$63$	0.664234	+	1.28343i	0.0836857	+	0.161697i
$64$	−1.00000			−0.125000
$65$	−2.70052			−0.334958
$66$	−8.05126	−	4.89874i	−0.991042	−	0.602993i
$67$	9.91978			1.21189			0.605947	−	0.795505i	$-0.292794\pi$
$67$	9.91978			1.21189			0.605947	+	0.795505i	$0.292794\pi$
$68$	−1.88641	−	1.08912i	−0.228760	−	0.132075i
$69$	−0.208024	+	9.04042i	−0.0250432	+	1.08834i
$70$	0.199309	−	0.345213i	0.0238220	−	0.0412609i
$71$	−3.12277	−	5.40879i	−0.370604	−	0.641906i	0.619054	−	0.785348i	$-0.287516\pi$
$71$	−3.12277	−	5.40879i	−0.370604	−	0.641906i	−0.989659	+	0.143443i	$0.954183\pi$
$72$	−2.52633	−	1.61792i	−0.297731	−	0.190673i
$73$	−11.1839			−1.30898			−0.654489	−	0.756072i	$-0.727116\pi$
$73$	−11.1839			−1.30898			−0.654489	+	0.756072i	$0.727116\pi$
$74$	1.27302	+	5.94806i	0.147986	+	0.691448i
$75$	−3.58721	−	6.55711i	−0.414215	−	0.757150i
$76$	6.41844	−	3.70569i	0.736245	−	0.425071i
$77$	2.62109			0.298701
$78$	−2.71287	−	4.95889i	−0.307172	−	0.561484i
$79$	10.8506	+	6.26459i	1.22079	+	0.704821i	0.965086	−	0.261935i	$-0.0843606\pi$
$79$	10.8506	+	6.26459i	1.22079	+	0.704821i	0.255700	+	0.966756i	$0.417694\pi$
$80$			0.827506i			0.0925180i
$81$	−3.76470	−	8.17478i	−0.418300	−	0.908309i
$82$		−	10.3395i		−	1.14180i
$83$	9.76840			1.07222			0.536111	−	0.844148i	$-0.319893\pi$
$83$	9.76840			1.07222			0.536111	+	0.844148i	$0.319893\pi$
$84$	0.834125	+	0.0191936i	0.0910105	+	0.00209419i
$85$	−0.901251	+	1.56101i	−0.0977544	+	0.169316i
$86$	4.87618	+	8.44579i	0.525812	+	0.910733i
$87$	−4.49636	−	2.73579i	−0.482061	−	0.293307i
$88$	−4.71223	+	2.72061i	−0.502325	+	0.290018i
$89$	−1.91605	−	1.10623i	−0.203100	−	0.117260i	0.395000	−	0.918681i	$-0.370744\pi$
$89$	−1.91605	−	1.10623i	−0.203100	−	0.117260i	−0.598101	+	0.801421i	$0.704078\pi$
$90$	−1.33883	+	2.09055i	−0.141126	+	0.220364i
$91$	1.36142	+	0.786017i	0.142716	+	0.0823970i
$92$	4.52141	+	2.61044i	0.471389	+	0.272157i
$93$	0.253229	−	11.0050i	0.0262586	−	1.14116i
$94$	−10.9392	+	6.31576i	−1.12829	+	0.651421i
$95$	−3.06648	−	5.31130i	−0.314614	−	0.544927i
$96$	−1.51953	+	0.831290i	−0.155086	+	0.0848431i
$97$	−12.7209	+	7.34441i	−1.29161	+	0.745712i	−0.978940	−	0.204149i	$-0.934557\pi$
$97$	−12.7209	+	7.34441i	−1.29161	+	0.745712i	−0.312672	+	0.949861i	$0.601224\pi$
$98$	5.86122	−	3.38398i	0.592073	−	0.341833i
$99$	−16.3064	−	0.750832i	−1.63885	−	0.0754614i
$100$	−4.31523			−0.431523
$101$	5.93768	+	10.2844i	0.590821	+	1.02333i	0.994122	+	0.108265i	$0.0345295\pi$
$101$	5.93768	+	10.2844i	0.590821	+	1.02333i	−0.403301	+	0.915067i	$0.632137\pi$
$102$	−3.77181	−	0.0867912i	−0.373465	−	0.00859361i
$103$	−4.56507	−	2.63564i	−0.449809	−	0.259698i	0.257940	−	0.966161i	$-0.416956\pi$
$103$	−4.56507	−	2.63564i	−0.449809	−	0.259698i	−0.707750	+	0.706463i	$0.750290\pi$
$104$	−3.26345			−0.320007
$105$	0.0158828	−	0.690244i	0.00155001	−	0.0673609i
$106$	0.161618	+	0.0933100i	0.0156977	+	0.00906307i
$107$	−0.109836	−	0.190242i	−0.0106183	−	0.0183913i	0.860667	−	0.509167i	$-0.170047\pi$
$107$	−0.109836	−	0.190242i	−0.0106183	−	0.0183913i	−0.871286	+	0.490776i	$0.836713\pi$
$108$	−5.18378	−	0.358350i	−0.498810	−	0.0344822i
$109$	3.30742	+	1.90954i	0.316794	+	0.182901i	0.649963	−	0.759966i	$-0.274785\pi$
$109$	3.30742	+	1.90954i	0.316794	+	0.182901i	−0.333169	+	0.942867i	$0.608118\pi$
$110$	2.25132	+	3.89940i	0.214655	+	0.371793i
$111$	6.87895	+	7.97998i	0.652921	+	0.757426i
$112$	0.240855	−	0.417173i	0.0227587	−	0.0394191i
$113$	−1.19818	+	0.691770i	−0.112715	+	0.0650762i	−0.555298	−	0.831652i	$-0.687396\pi$
$113$	−1.19818	+	0.691770i	−0.112715	+	0.0650762i	0.442582	+	0.896728i	$0.354062\pi$
$114$	6.67248	−	10.9665i	0.624935	−	1.02710i
$115$	2.16015	−	3.74149i	0.201435	−	0.348896i
$116$	−2.63163	+	1.51937i	−0.244340	+	0.141070i
$117$	−8.24455	−	5.27998i	−0.762209	−	0.488134i
$118$	2.02562	+	3.50847i	0.186473	+	0.322981i
$119$	0.908700	−	0.524638i	0.0833004	−	0.0480935i
$120$	0.687897	+	1.25742i	0.0627961	+	0.114786i
$121$	−9.30341	+	16.1140i	−0.845764	+	1.46491i
$122$	3.84620	−	6.66181i	0.348219	−	0.603132i
$123$	−8.59509	−	15.7111i	−0.774993	−	1.41662i
$124$	−5.50394	−	3.17770i	−0.494268	−	0.285366i
$125$			7.70841i			0.689461i
$126$	1.28343	−	0.664234i	0.114337	−	0.0591747i
$127$	−9.97994	+	17.2858i	−0.885576	+	1.53386i	−0.0405249	+	0.999179i	$0.512903\pi$
$127$	−9.97994	+	17.2858i	−0.885576	+	1.53386i	−0.845052	+	0.534685i	$0.820430\pi$
$128$			1.00000i			0.0883883i
$129$	14.4304	+	8.78008i	1.27052	+	0.773043i
$130$			2.70052i			0.236851i
$131$	7.75504	−	4.47737i	0.677561	−	0.391190i	−0.121374	−	0.992607i	$-0.538730\pi$
$131$	7.75504	−	4.47737i	0.677561	−	0.391190i	0.798935	+	0.601417i	$0.205397\pi$
$132$	−4.89874	+	8.05126i	−0.426381	+	0.700772i
$133$			3.57013i			0.309570i
$134$		−	9.91978i		−	0.856938i
$135$	−0.296537	+	4.28961i	−0.0255218	+	0.369191i
$136$	−1.08912	+	1.88641i	−0.0933910	+	0.161758i
$137$	6.51114	+	11.2776i	0.556284	+	0.963513i	0.997802	+	0.0662604i	$0.0211068\pi$
$137$	6.51114	+	11.2776i	0.556284	+	0.963513i	−0.441518	+	0.897252i	$0.645560\pi$
$138$	9.04042	+	0.208024i	0.769572	+	0.0177082i
$139$	−10.2192	−	17.7002i	−0.866782	−	1.50131i	−0.865267	−	0.501311i	$-0.832851\pi$
$139$	−10.2192	−	17.7002i	−0.866782	−	1.50131i	−0.00151499	−	0.999999i	$-0.500482\pi$
$140$	−0.345213	−	0.199309i	−0.0291758	−	0.0168447i
$141$	−11.3722	+	18.6906i	−0.957711	+	1.57403i
$142$	−5.40879	+	3.12277i	−0.453896	+	0.262057i
$143$	−15.3781	+	8.87856i	−1.28598	+	0.742462i
$144$	−1.61792	+	2.52633i	−0.134826	+	0.210528i
$145$	1.25729	+	2.17769i	0.104412	+	0.180847i
$146$			11.1839i			0.925587i
$147$	6.09321	−	10.0144i	0.502559	−	0.825975i
$148$	5.94806	−	1.27302i	0.488927	−	0.104642i
$149$	−8.64800	+	14.9788i	−0.708472	+	1.22711i	0.256952	+	0.966424i	$0.417282\pi$
$149$	−8.64800	+	14.9788i	−0.708472	+	1.22711i	−0.965424	+	0.260685i	$0.916052\pi$
$150$	−6.55711	+	3.58721i	−0.535386	+	0.292894i
$151$	2.30926	−	3.99975i	0.187925	−	0.325495i	−0.756634	−	0.653839i	$-0.773157\pi$
$151$	2.30926	−	3.99975i	0.187925	−	0.325495i	0.944558	+	0.328344i	$0.106491\pi$
$152$	−3.70569	−	6.41844i	−0.300571	−	0.520604i
$153$	−5.80351	+	3.00359i	−0.469186	+	0.242826i
$154$		−	2.62109i		−	0.211213i
$155$	−2.62956	+	4.55454i	−0.211212	+	0.365829i
$156$	−4.95889	+	2.71287i	−0.397029	+	0.217203i
$157$	−0.631378	−	1.09358i	−0.0503894	−	0.0872771i	0.839731	−	0.543003i	$-0.182713\pi$
$157$	−0.631378	−	1.09358i	−0.0503894	−	0.0872771i	−0.890120	+	0.455726i	$0.849380\pi$
$158$	6.26459	−	10.8506i	0.498384	−	0.863226i
$159$	0.323150	+	0.00743583i	0.0256275	+	0.000589700i
$160$	0.827506			0.0654201
$161$	−2.17801	+	1.25747i	−0.171651	+	0.0991027i
$162$	−8.17478	+	3.76470i	−0.642271	+	0.295783i
$163$	−1.05113	−	0.606868i	−0.0823305	−	0.0475335i	0.458270	−	0.888813i	$-0.348469\pi$
$163$	−1.05113	−	0.606868i	−0.0823305	−	0.0475335i	−0.540600	+	0.841280i	$0.681803\pi$
$164$	−10.3395			−0.807377
$165$	6.66246	+	4.05374i	0.518672	+	0.315583i
$166$		−	9.76840i		−	0.758175i
$167$		−	23.1203i		−	1.78910i	−0.446966	−	0.894551i	$-0.647495\pi$
$167$		−	23.1203i		−	1.78910i	0.446966	−	0.894551i	$-0.352505\pi$
$168$	0.0191936	−	0.834125i	0.00148082	−	0.0643542i
$169$	2.34991			0.180763
$170$	1.56101	+	0.901251i	0.119724	+	0.0691228i
$171$	1.02269	−	22.2106i	0.0782073	−	1.69849i
$172$	8.44579	−	4.87618i	0.643986	−	0.371805i
$173$	12.2176			0.928884			0.464442	−	0.885603i	$-0.346255\pi$
$173$	12.2176			0.928884			0.464442	+	0.885603i	$0.346255\pi$
$174$	−2.73579	+	4.49636i	−0.207399	+	0.340868i
$175$	1.03935	−	1.80020i	0.0785671	−	0.136082i
$176$	2.72061	+	4.71223i	0.205073	+	0.355198i
$177$	5.99453	+	3.64734i	0.450577	+	0.274151i
$178$	−1.10623	+	1.91605i	−0.0829154	+	0.143614i
$179$			8.21539i			0.614047i	0.951702	+	0.307024i	$0.0993331\pi$
$179$			8.21539i			0.614047i	−0.951702	+	0.307024i	$0.900667\pi$
$180$	2.09055	+	1.33883i	0.155821	+	0.0997908i
$181$	−11.2683	−	19.5172i	−0.837565	−	1.45071i	−0.891925	−	0.452184i	$-0.850645\pi$
$181$	−11.2683	−	19.5172i	−0.837565	−	1.45071i	0.0543600	−	0.998521i	$-0.482688\pi$
$182$	0.786017	−	1.36142i	0.0582635	−	0.100915i
$183$	0.306502	−	13.3201i	0.0226573	−	0.984650i
$184$	2.61044	−	4.52141i	0.192444	−	0.333323i
$185$	−1.05343	−	4.92205i	−0.0774500	−	0.361877i
$186$	−11.0050	−	0.253229i	−0.806923	−	0.0185677i
$187$			11.8522i			0.866721i
$188$	6.31576	+	10.9392i	0.460624	+	0.797824i
$189$	1.39803	−	2.07622i	0.101692	−	0.151023i
$190$	−5.31130	+	3.06648i	−0.385322	+	0.222466i
$191$	6.56807	−	3.79207i	0.475249	−	0.274385i	−0.243186	−	0.969980i	$-0.578192\pi$
$191$	6.56807	−	3.79207i	0.475249	−	0.274385i	0.718434	+	0.695595i	$0.244859\pi$
$192$	0.831290	+	1.51953i	0.0599932	+	0.109662i
$193$	4.70640	+	2.71724i	0.338774	+	0.195591i	0.659730	−	0.751503i	$-0.270671\pi$
$193$	4.70640	+	2.71724i	0.338774	+	0.195591i	−0.320956	+	0.947094i	$0.604004\pi$
$194$	7.34441	+	12.7209i	0.527298	+	0.913307i
$195$	2.24492	+	4.10351i	0.160762	+	0.293859i
$196$	−3.38398	−	5.86122i	−0.241713	−	0.418659i
$197$	12.1777	−	21.0925i	0.867628	−	1.50278i	0.00321437	−	0.999995i	$-0.498977\pi$
$197$	12.1777	−	21.0925i	0.867628	−	1.50278i	0.864414	−	0.502781i	$-0.167690\pi$
$198$	−0.750832	+	16.3064i	−0.0533593	+	1.15884i
$199$		−	1.75902i		−	0.124694i	−0.998055	−	0.0623470i	$-0.980141\pi$
$199$		−	1.75902i		−	0.124694i	0.998055	−	0.0623470i	$-0.0198585\pi$
$200$			4.31523i			0.305133i
$201$	−8.24621	−	15.0734i	−0.581643	−	1.06319i
$202$	10.2844	−	5.93768i	0.723605	−	0.417774i
$203$		−	1.46379i		−	0.102738i
$204$	−0.0867912	+	3.77181i	−0.00607660	+	0.264080i
$205$			8.55597i			0.597575i
$206$	−2.63564	+	4.56507i	−0.183634	+	0.318063i
$207$	13.9101	−	7.19911i	0.966817	−	0.500373i
$208$			3.26345i			0.226279i
$209$	−34.9241	−	20.1634i	−2.41575	−	1.39473i
$210$	−0.690244	−	0.0158828i	−0.0476313	−	0.00109602i
$211$	−8.19737	+	14.1983i	−0.564330	+	0.977448i	0.432782	+	0.901499i	$0.357532\pi$
$211$	−8.19737	+	14.1983i	−0.564330	+	0.977448i	−0.997112	+	0.0759493i	$0.975801\pi$
$212$	0.0933100	−	0.161618i	0.00640856	−	0.0110999i
$213$	−5.62287	+	9.24140i	−0.385273	+	0.633210i
$214$	−0.190242	+	0.109836i	−0.0130046	+	0.00750824i
$215$	−4.03507	−	6.98894i	−0.275189	−	0.476642i
$216$	−0.358350	+	5.18378i	−0.0243826	+	0.352712i
$217$	2.65130	−	1.53073i	0.179982	−	0.103913i
$218$	1.90954	−	3.30742i	0.129330	−	0.224007i
$219$	9.29707	+	16.9942i	0.628238	+	1.14836i
$220$	3.89940	−	2.25132i	0.262897	−	0.151784i
$221$	−3.55428	+	6.15619i	−0.239086	+	0.414110i
$222$	7.97998	−	6.87895i	0.535581	−	0.461685i
$223$	5.57093	+	9.64914i	0.373057	+	0.646154i	0.990034	−	0.140827i	$-0.0449761\pi$
$223$	5.57093	+	9.64914i	0.373057	+	0.646154i	−0.616977	+	0.786981i	$0.711643\pi$
$224$	−0.417173	−	0.240855i	−0.0278735	−	0.0160928i
$225$	−6.98168	+	10.9017i	−0.465445	+	0.726781i
$226$	0.691770	+	1.19818i	0.0460158	+	0.0797018i
$227$	6.41562	+	3.70406i	0.425820	+	0.245847i	0.697564	−	0.716522i	$-0.254267\pi$
$227$	6.41562	+	3.70406i	0.425820	+	0.245847i	−0.271745	+	0.962369i	$0.587601\pi$
$228$	−10.9665	−	6.67248i	−0.726272	−	0.441896i
$229$	20.7317			1.36999			0.684996	−	0.728547i	$-0.259804\pi$
$229$	20.7317			1.36999			0.684996	+	0.728547i	$0.259804\pi$
$230$	−3.74149	−	2.16015i	−0.246707	−	0.142436i
$231$	−2.17888	−	3.98281i	−0.143360	−	0.262050i
$232$	1.51937	+	2.63163i	0.0997515	+	0.172775i
$233$	15.3633			1.00648			0.503242	−	0.864146i	$-0.332141\pi$
$233$	15.3633			1.00648			0.503242	+	0.864146i	$0.332141\pi$
$234$	−5.27998	+	8.24455i	−0.345163	+	0.538963i
$235$	9.05227	−	5.22633i	0.590505	−	0.340928i
$236$	3.50847	−	2.02562i	0.228382	−	0.131856i
$237$	0.499222	−	21.6954i	0.0324279	−	1.40927i
$238$	−0.524638	−	0.908700i	−0.0340073	−	0.0589023i
$239$	−6.90954	+	3.98923i	−0.446941	+	0.258042i	−0.706538	−	0.707676i	$-0.749744\pi$
$239$	−6.90954	+	3.98923i	−0.446941	+	0.258042i	0.259596	+	0.965717i	$0.416411\pi$
$240$	1.25742	−	0.687897i	0.0811659	−	0.0444036i
$241$	−17.4526	−	10.0763i	−1.12422	−	0.649069i	−0.181746	−	0.983346i	$-0.558175\pi$
$241$	−17.4526	−	10.0763i	−1.12422	−	0.649069i	−0.942475	+	0.334276i	$0.891508\pi$
$242$	16.1140	+	9.30341i	1.03585	+	0.598046i
$243$	−9.29223	+	12.5162i	−0.596097	+	0.802913i
$244$	−6.66181	−	3.84620i	−0.426479	−	0.246228i
$245$	−4.85020	+	2.80026i	−0.309868	+	0.178902i
$246$	−15.7111	+	8.59509i	−1.00170	+	0.548003i
$247$	−12.0933	−	20.9462i	−0.769479	−	1.33278i
$248$	−3.17770	+	5.50394i	−0.201784	+	0.349500i
$249$	−8.12037	−	14.8433i	−0.514608	−	0.940658i
$250$	7.70841			0.487523
$251$		−	1.32517i		−	0.0836437i	−0.999125	−	0.0418219i	$-0.986684\pi$
$251$		−	1.32517i		−	0.0836437i	0.999125	−	0.0418219i	$-0.0133162\pi$
$252$	−0.664234	−	1.28343i	−0.0418428	−	0.0808485i
$253$		−	28.4079i		−	1.78599i
$254$	17.2858	+	9.97994i	1.08461	+	0.626197i
$255$	3.12120	+	0.0718202i	0.195457	+	0.00449756i
$256$	1.00000			0.0625000
$257$	−19.9455	+	11.5155i	−1.24416	+	0.718318i	−0.969939	−	0.243348i	$-0.921754\pi$
$257$	−19.9455	+	11.5155i	−1.24416	+	0.718318i	−0.274224	+	0.961666i	$0.588421\pi$
$258$	8.78008	−	14.4304i	0.546624	−	0.898396i
$259$	−0.901548	+	2.78798i	−0.0560195	+	0.173237i
$260$	2.70052			0.167479
$261$	−0.419315	+	9.10657i	−0.0259549	+	0.563682i
$262$	−4.47737	−	7.75504i	−0.276613	−	0.479108i
$263$	6.49001	−	11.2410i	0.400191	−	0.693151i	−0.593558	−	0.804792i	$-0.702277\pi$
$263$	6.49001	−	11.2410i	0.400191	−	0.693151i	0.993749	+	0.111640i	$0.0356104\pi$
$264$	8.05126	+	4.89874i	0.495521	+	0.301497i
$265$	−0.133740	−	0.0772146i	−0.00821556	−	0.00474326i
$266$	3.57013			0.218899
$267$	−0.0881549	+	3.83108i	−0.00539499	+	0.234458i
$268$	−9.91978			−0.605947
$269$	−11.1365			−0.679002			−0.339501	−	0.940606i	$-0.610258\pi$
$269$	−11.1365			−0.679002			−0.339501	+	0.940606i	$0.610258\pi$
$270$	4.28961	+	0.296537i	0.261057	+	0.0180466i
$271$	7.92308	−	13.7232i	0.481293	−	0.833623i	−0.518477	−	0.855092i	$-0.673501\pi$
$271$	7.92308	−	13.7232i	0.481293	−	0.833623i	0.999770	+	0.0214684i	$0.00683412\pi$
$272$	1.88641	+	1.08912i	0.114380	+	0.0660374i
$273$	0.0626373	−	2.72212i	0.00379098	−	0.164750i
$274$	11.2776	−	6.51114i	0.681306	−	0.393352i
$275$	11.7401	+	20.3344i	0.707952	+	1.22621i
$276$	0.208024	−	9.04042i	0.0125216	−	0.544169i
$277$	25.5354	+	14.7429i	1.53428	+	0.885814i	0.999158	+	0.0410364i	$0.0130659\pi$
$277$	25.5354	+	14.7429i	1.53428	+	0.885814i	0.535117	+	0.844778i	$0.320267\pi$
$278$	−17.7002	+	10.2192i	−1.06159	+	0.612907i
$279$	−16.9328	+	8.76352i	−1.01374	+	0.524658i
$280$	−0.199309	+	0.345213i	−0.0119110	+	0.0206304i
$281$		−	24.8867i		−	1.48461i	−0.670060	−	0.742307i	$-0.733732\pi$
$281$		−	24.8867i		−	1.48461i	0.670060	−	0.742307i	$-0.266268\pi$
$282$	18.6906	+	11.3722i	1.11301	+	0.677204i
$283$		−	21.7190i		−	1.29106i	−0.763735	−	0.645530i	$-0.776637\pi$
$283$		−	21.7190i		−	1.29106i	0.763735	−	0.645530i	$-0.223363\pi$
$284$	3.12277	+	5.40879i	0.185302	+	0.320953i
$285$	−5.52152	+	9.07482i	−0.327066	+	0.537546i
$286$	8.87856	+	15.3781i	0.525000	+	0.909327i
$287$	2.49031	−	4.31335i	0.146998	−	0.254609i
$288$	2.52633	+	1.61792i	0.148866	+	0.0953366i
$289$	−6.12765	−	10.6134i	−0.360450	−	0.624318i
$290$	2.17769	−	1.25729i	0.127878	−	0.0738304i
$291$	21.7348	+	13.2244i	1.27412	+	0.775228i
$292$	11.1839			0.654489
$293$	7.90816			0.462000			0.231000	−	0.972954i	$-0.425800\pi$
$293$	7.90816			0.462000			0.231000	+	0.972954i	$0.425800\pi$
$294$	−10.0144	−	6.09321i	−0.584052	−	0.355363i
$295$	−1.67621	−	2.90328i	−0.0975927	−	0.169036i
$296$	−1.27302	−	5.94806i	−0.0739930	−	0.345724i
$297$	12.4144	+	25.4021i	0.720357	+	1.47398i
$298$	14.9788	+	8.64800i	0.867697	+	0.500965i
$299$	8.51902	−	14.7554i	0.492668	−	0.853325i
$300$	3.58721	+	6.55711i	0.207108	+	0.378575i
$301$			4.69781i			0.270777i
$302$	−3.99975	−	2.30926i	−0.230160	−	0.132883i
$303$	10.6914	−	17.5717i	0.614206	−	1.00947i
$304$	−6.41844	+	3.70569i	−0.368123	+	0.212536i
$305$	−3.18275	+	5.51269i	−0.182244	+	0.315656i
$306$	3.00359	+	5.80351i	0.171704	+	0.331765i
$307$	−10.3177			−0.588860			−0.294430	−	0.955673i	$-0.595130\pi$
$307$	−10.3177			−0.588860			−0.294430	+	0.955673i	$0.595130\pi$
$308$	−2.62109			−0.149350
$309$	−0.210033	+	9.12771i	−0.0119484	+	0.519258i
$310$	4.55454	+	2.62956i	0.258680	+	0.149349i
$311$	8.94124	−	5.16223i	0.507011	−	0.292723i	−0.224593	−	0.974453i	$-0.572105\pi$
$311$	8.94124	−	5.16223i	0.507011	−	0.292723i	0.731604	+	0.681730i	$0.238772\pi$
$312$	2.71287	+	4.95889i	0.153586	+	0.280742i
$313$		−	26.6770i		−	1.50787i	−0.656947	−	0.753937i	$-0.728152\pi$
$313$		−	26.6770i		−	1.50787i	0.656947	−	0.753937i	$-0.271848\pi$
$314$	−1.09358	+	0.631378i	−0.0617142	+	0.0356307i
$315$	−1.06205	+	0.549658i	−0.0598395	+	0.0309697i
$316$	−10.8506	−	6.26459i	−0.610393	−	0.352411i
$317$	−1.26263			−0.0709162			−0.0354581	−	0.999371i	$-0.511289\pi$
$317$	−1.26263			−0.0709162			−0.0354581	+	0.999371i	$0.511289\pi$
$318$	0.00743583	−	0.323150i	0.000416981	−	0.0181213i
$319$	14.3192	+	8.26721i	0.801723	+	0.462875i
$320$		−	0.827506i		−	0.0462590i
$321$	−0.197771	+	0.325045i	−0.0110385	+	0.0181422i
$322$	1.25747	+	2.17801i	0.0700762	+	0.121376i
$323$	−16.1437			−0.898260
$324$	3.76470	+	8.17478i	0.209150	+	0.454154i
$325$			14.0825i			0.781159i
$326$	−0.606868	+	1.05113i	−0.0336113	+	0.0582165i
$327$	0.152170	−	6.61310i	0.00841504	−	0.365705i
$328$			10.3395i			0.570901i
$329$	−6.08473			−0.335462
$330$	4.05374	−	6.66246i	0.223151	−	0.366757i
$331$			20.1907i			1.10978i	0.831923	+	0.554891i	$0.187240\pi$
$331$			20.1907i			1.10978i	−0.831923	+	0.554891i	$0.812760\pi$
$332$	−9.76840			−0.536111
$333$	6.40737	−	17.0864i	0.351122	−	0.936330i
$334$	−23.1203			−1.26509
$335$			8.20867i			0.448488i
$336$	−0.834125	−	0.0191936i	−0.0455053	−	0.00104710i
$337$	29.1975			1.59049			0.795245	−	0.606288i	$-0.207342\pi$
$337$	29.1975			1.59049			0.795245	+	0.606288i	$0.207342\pi$
$338$		−	2.34991i		−	0.127818i
$339$	2.04720	+	1.24560i	0.111188	+	0.0676519i
$340$	0.901251	−	1.56101i	0.0488772	−	0.0846578i
$341$			34.5811i			1.87267i
$342$	−22.2106	−	1.02269i	−1.20101	−	0.0553009i
$343$	6.63216			0.358103
$344$	−4.87618	−	8.44579i	−0.262906	−	0.455367i
$345$	−7.48100	−	0.172141i	−0.402764	−	0.00926778i
$346$		−	12.2176i		−	0.656821i
$347$	−27.1596	−	15.6806i	−1.45800	−	0.841779i	−0.459090	−	0.888390i	$-0.651825\pi$
$347$	−27.1596	−	15.6806i	−1.45800	−	0.841779i	−0.998913	+	0.0466109i	$0.985158\pi$
$348$	4.49636	+	2.73579i	0.241030	+	0.146653i
$349$	9.65184			0.516651			0.258325	−	0.966058i	$-0.416829\pi$
$349$	9.65184			0.516651			0.258325	+	0.966058i	$0.416829\pi$
$350$	−1.80020	−	1.03935i	−0.0962247	−	0.0555554i
$351$	−1.16946	+	16.9170i	−0.0624209	+	0.902962i
$352$	4.71223	−	2.72061i	0.251163	−	0.145009i
$353$		−	3.53077i		−	0.187924i	−0.995576	−	0.0939620i	$-0.970047\pi$
$353$		−	3.53077i		−	0.187924i	0.995576	−	0.0939620i	$-0.0299532\pi$
$354$	3.64734	−	5.99453i	0.193854	−	0.318606i
$355$	4.47581	−	2.58411i	0.237551	−	0.137150i
$356$	1.91605	+	1.10623i	0.101550	+	0.0586301i
$357$	−1.55259	−	0.944667i	−0.0821720	−	0.0499971i
$358$	8.21539			0.434197
$359$	6.08563			0.321187			0.160594	−	0.987021i	$-0.448659\pi$
$359$	6.08563			0.321187			0.160594	+	0.987021i	$0.448659\pi$
$360$	1.33883	−	2.09055i	0.0705628	−	0.110182i
$361$	17.9642	−	31.1150i	0.945486	−	1.63763i
$362$	−19.5172	+	11.2683i	−1.02580	+	0.592248i
$363$	32.2194	+	0.741384i	1.69108	+	0.0389126i
$364$	−1.36142	−	0.786017i	−0.0713579	−	0.0411985i
$365$		−	9.25475i		−	0.484416i
$366$	−13.3201	−	0.306502i	−0.696253	−	0.0160211i
$367$	5.79164	−	10.0314i	0.302321	−	0.523635i	−0.674340	−	0.738421i	$-0.735572\pi$
$367$	5.79164	−	10.0314i	0.302321	−	0.523635i	0.976661	+	0.214785i	$0.0689052\pi$
$368$	−4.52141	−	2.61044i	−0.235695	−	0.136078i
$369$	−16.7284	+	26.1209i	−0.870844	+	1.35980i
$370$	−4.92205	+	1.05343i	−0.255885	+	0.0547655i
$371$	0.0449484	+	0.0778529i	0.00233360	+	0.00404192i
$372$	−0.253229	+	11.0050i	−0.0131293	+	0.570581i
$373$	−10.9534			−0.567148			−0.283574	−	0.958950i	$-0.591520\pi$
$373$	−10.9534			−0.567148			−0.283574	+	0.958950i	$0.591520\pi$
$374$	11.8522			0.612865
$375$	11.7131	−	6.40792i	0.604863	−	0.330904i
$376$	10.9392	−	6.31576i	0.564147	−	0.325710i
$377$	4.95838	+	8.58817i	0.255370	+	0.442313i
$378$	−2.07622	−	1.39803i	−0.106789	−	0.0719071i
$379$	−5.66267	+	9.80803i	−0.290872	+	0.503805i	−0.974016	−	0.226479i	$-0.927279\pi$
$379$	−5.66267	+	9.80803i	−0.290872	+	0.503805i	0.683144	+	0.730283i	$0.260612\pi$
$380$	3.06648	+	5.31130i	0.157307	+	0.272464i
$381$	34.5624	+	0.795296i	1.77068	+	0.0407443i
$382$	−3.79207	−	6.56807i	−0.194019	−	0.336051i
$383$		−	8.96064i		−	0.457867i	−0.973442	−	0.228934i	$-0.926476\pi$
$383$		−	8.96064i		−	0.457867i	0.973442	−	0.228934i	$-0.0735239\pi$
$384$	1.51953	−	0.831290i	0.0775430	−	0.0424216i
$385$			2.16896i			0.110541i
$386$	2.71724	−	4.70640i	0.138304	−	0.239549i
$387$	1.34573	−	29.2261i	0.0684071	−	1.48565i
$388$	12.7209	−	7.34441i	0.645806	−	0.372856i
$389$	−12.0175	−	6.93830i	−0.609311	−	0.351786i	0.163385	−	0.986562i	$-0.447759\pi$
$389$	−12.0175	−	6.93830i	−0.609311	−	0.351786i	−0.772696	+	0.634777i	$0.781092\pi$
$390$	4.10351	−	2.24492i	0.207789	−	0.113676i
$391$	−5.68614	−	9.84868i	−0.287560	−	0.498069i
$392$	−5.86122	+	3.38398i	−0.296036	+	0.170917i
$393$	−13.2502	−	8.06199i	−0.668383	−	0.406673i
$394$	−21.0925	−	12.1777i	−1.06262	−	0.613506i
$395$	−5.18398	+	8.97892i	−0.260834	+	0.451779i
$396$	16.3064	+	0.750832i	0.819426	+	0.0377307i
$397$	5.30259			0.266130			0.133065	−	0.991107i	$-0.457518\pi$
$397$	5.30259			0.266130			0.133065	+	0.991107i	$0.457518\pi$
$398$	−1.75902			−0.0881719
$399$	5.42491	−	2.96781i	0.271585	−	0.148577i
$400$	4.31523			0.215762
$401$	19.8525	+	11.4618i	0.991386	+	0.572377i	0.905688	−	0.423944i	$-0.139355\pi$
$401$	19.8525	+	11.4618i	0.991386	+	0.572377i	0.0856977	+	0.996321i	$0.472688\pi$
$402$	−15.0734	+	8.24621i	−0.751791	+	0.411283i
$403$	−10.3703	+	17.9618i	−0.516579	+	0.894741i
$404$	−5.93768	−	10.2844i	−0.295411	−	0.511666i
$405$	6.76468	−	3.11531i	0.336140	−	0.154801i
$406$	−1.46379			−0.0726467
$407$	−22.1811	−	24.5652i	−1.09948	−	1.21765i
$408$	3.77181	+	0.0867912i	0.186733	+	0.00429680i
$409$	−15.7855	+	9.11374i	−0.780541	+	0.450646i	−0.836622	−	0.547781i	$-0.815473\pi$
$409$	−15.7855	+	9.11374i	−0.780541	+	0.450646i	0.0560810	+	0.998426i	$0.482139\pi$
$410$	8.55597			0.422549
$411$	11.7240	−	19.2688i	0.578302	−	0.950461i
$412$	4.56507	+	2.63564i	0.224905	+	0.129849i
$413$			1.95152i			0.0960280i
$414$	−7.19911	−	13.9101i	−0.353817	−	0.683643i
$415$			8.08341i			0.396799i
$416$	3.26345			0.160004
$417$	−18.4008	+	30.2423i	−0.901089	+	1.48097i
$418$	−20.1634	+	34.9241i	−0.986226	+	1.70819i
$419$	−4.92526	−	8.53080i	−0.240615	−	0.416757i	0.720275	−	0.693689i	$-0.244016\pi$
$419$	−4.92526	−	8.53080i	−0.240615	−	0.416757i	−0.960890	+	0.276932i	$0.910682\pi$
$420$	−0.0158828	+	0.690244i	−0.000775003	+	0.0336804i
$421$	6.37750	−	3.68205i	0.310820	−	0.179452i	−0.336473	−	0.941693i	$-0.609234\pi$
$421$	6.37750	−	3.68205i	0.310820	−	0.179452i	0.647294	+	0.762241i	$0.275901\pi$
$422$	14.1983	+	8.19737i	0.691160	+	0.399041i
$423$	37.8544	+	1.74302i	1.84055	+	0.0847485i
$424$	−0.161618	−	0.0933100i	−0.00784885	−	0.00453154i
$425$	8.14028	+	4.69979i	0.394862	+	0.227974i
$426$	9.24140	+	5.62287i	0.447747	+	0.272429i
$427$	3.20906	−	1.85275i	0.155297	−	0.0896610i
$428$	0.109836	+	0.190242i	0.00530913	+	0.00919567i
$429$	26.2749	+	15.9868i	1.26856	+	0.771849i
$430$	−6.98894	+	4.03507i	−0.337037	+	0.194588i
$431$	13.5809	−	7.84093i	0.654169	−	0.377684i	−0.135883	−	0.990725i	$-0.543387\pi$
$431$	13.5809	−	7.84093i	0.654169	−	0.377684i	0.790052	+	0.613040i	$0.210054\pi$
$432$	5.18378	+	0.358350i	0.249405	+	0.0172411i
$433$	−6.31571			−0.303514			−0.151757	−	0.988418i	$-0.548493\pi$
$433$	−6.31571			−0.303514			−0.151757	+	0.988418i	$0.548493\pi$
$434$	−1.53073	−	2.65130i	−0.0734773	−	0.127266i
$435$	2.26388	−	3.72077i	0.108545	−	0.178397i
$436$	−3.30742	−	1.90954i	−0.158397	−	0.0914505i
$437$	38.6938			1.85098
$438$	16.9942	−	9.29707i	0.812016	−	0.444231i
$439$	3.61499	+	2.08711i	0.172534	+	0.0996125i	0.583780	−	0.811912i	$-0.301573\pi$
$439$	3.61499	+	2.08711i	0.172534	+	0.0996125i	−0.411246	+	0.911524i	$0.634906\pi$
$440$	−2.25132	−	3.89940i	−0.107327	−	0.185896i
$441$	−20.2824	−	0.933908i	−0.965827	−	0.0444718i
$442$	6.15619	+	3.55428i	0.292820	+	0.169060i
$443$	−14.4440	−	25.0178i	−0.686257	−	1.18863i	−0.973040	−	0.230636i	$-0.925919\pi$
$443$	−14.4440	−	25.0178i	−0.686257	−	1.18863i	0.286783	−	0.957996i	$-0.407414\pi$
$444$	−6.87895	−	7.97998i	−0.326461	−	0.378713i
$445$	0.915412	−	1.58554i	0.0433947	−	0.0751618i
$446$	9.64914	−	5.57093i	0.456900	−	0.263791i
$447$	29.9496	+	0.689155i	1.41657	+	0.0325959i
$448$	−0.240855	+	0.417173i	−0.0113793	+	0.0197096i
$449$	−4.05881	+	2.34336i	−0.191547	+	0.110590i	−0.592707	−	0.805418i	$-0.701941\pi$
$449$	−4.05881	+	2.34336i	−0.191547	+	0.110590i	0.401159	+	0.916008i	$0.368607\pi$
$450$	10.9017	+	6.98168i	0.513912	+	0.329120i
$451$	28.1296	+	48.7219i	1.32457	+	2.29423i
$452$	1.19818	−	0.691770i	0.0563577	−	0.0325381i
$453$	−7.99738	−	0.184023i	−0.375750	−	0.00864617i
$454$	3.70406	−	6.41562i	0.173840	−	0.301100i
$455$	−0.650434	+	1.12658i	−0.0304928	+	0.0528151i
$456$	−6.67248	+	10.9665i	−0.312468	+	0.513552i
$457$	5.62118	+	3.24539i	0.262948	+	0.151813i	0.625678	−	0.780081i	$-0.284822\pi$
$457$	5.62118	+	3.24539i	0.262948	+	0.151813i	−0.362731	+	0.931894i	$0.618156\pi$
$458$		−	20.7317i		−	0.968731i
$459$	9.38843	+	6.32174i	0.438214	+	0.295073i
$460$	−2.16015	+	3.74149i	−0.100718	+	0.174448i
$461$			4.65733i			0.216914i	0.994101	+	0.108457i	$0.0345909\pi$
$461$			4.65733i			0.216914i	−0.994101	+	0.108457i	$0.965409\pi$
$462$	−3.98281	+	2.17888i	−0.185297	+	0.101371i
$463$			15.7233i			0.730725i	0.930865	+	0.365363i	$0.119055\pi$
$463$			15.7233i			0.730725i	−0.930865	+	0.365363i	$0.880945\pi$
$464$	2.63163	−	1.51937i	0.122170	−	0.0705350i
$465$	9.10667	+	0.209549i	0.422312	+	0.00971759i
$466$		−	15.3633i		−	0.711691i
$467$			13.1700i			0.609437i	0.952443	+	0.304718i	$0.0985623\pi$
$467$			13.1700i			0.609437i	−0.952443	+	0.304718i	$0.901438\pi$
$468$	8.24455	+	5.27998i	0.381104	+	0.244067i
$469$	2.38923	−	4.13826i	0.110324	−	0.191087i
$470$	−5.22633	−	9.05227i	−0.241073	−	0.417550i
$471$	−1.13686	+	1.86848i	−0.0523839	+	0.0860948i
$472$	−2.02562	−	3.50847i	−0.0932366	−	0.161490i
$473$	−45.9554	−	26.5323i	−2.11303	−	1.21996i
$474$	−21.6954	−	0.499222i	−0.996504	−	0.0229300i
$475$	−27.6971	+	15.9909i	−1.27083	+	0.733713i
$476$	−0.908700	+	0.524638i	−0.0416502	+	0.0240468i
$477$	−0.257332	−	0.497216i	−0.0117824	−	0.0227659i
$478$	3.98923	+	6.90954i	0.182463	+	0.316035i
$479$			3.06704i			0.140137i	0.997542	+	0.0700683i	$0.0223217\pi$
$479$			3.06704i			0.140137i	−0.997542	+	0.0700683i	$0.977678\pi$
$480$	−0.687897	−	1.25742i	−0.0313981	−	0.0573929i
$481$	−4.15445	−	19.4112i	−0.189426	−	0.885073i
$482$	−10.0763	+	17.4526i	−0.458961	+	0.794944i
$483$	3.72132	+	2.26421i	0.169326	+	0.103025i
$484$	9.30341	−	16.1140i	0.422882	−	0.732453i
$485$	−6.07755	−	10.5266i	−0.275967	−	0.477989i
$486$	12.5162	+	9.29223i	0.567745	+	0.421504i
$487$		−	18.6022i		−	0.842945i	−0.906841	−	0.421473i	$-0.861513\pi$
$487$		−	18.6022i		−	0.842945i	0.906841	−	0.421473i	$-0.138487\pi$
$488$	−3.84620	+	6.66181i	−0.174109	+	0.301566i
$489$	−0.0483610	+	2.10169i	−0.00218696	+	0.0950419i
$490$	2.80026	+	4.85020i	0.126503	+	0.219109i
$491$	−4.77501	+	8.27056i	−0.215493	+	0.373245i	−0.953425	−	0.301630i	$-0.902469\pi$
$491$	−4.77501	+	8.27056i	−0.215493	+	0.373245i	0.737932	+	0.674875i	$0.235803\pi$
$492$	8.59509	+	15.7111i	0.387497	+	0.708310i
$493$	6.61908			0.298109
$494$	−20.9462	+	12.0933i	−0.942416	+	0.544104i
$495$	0.621318	−	13.4936i	0.0279262	−	0.606493i
$496$	5.50394	+	3.17770i	0.247134	+	0.142683i
$497$	−3.00854			−0.134951
$498$	−14.8433	+	8.12037i	−0.665146	+	0.363883i
$499$		−	3.02563i		−	0.135446i	−0.997704	−	0.0677229i	$-0.978427\pi$
$499$		−	3.02563i		−	0.135446i	0.997704	−	0.0677229i	$-0.0215734\pi$
$500$		−	7.70841i		−	0.344731i
$501$	−35.1319	+	19.2197i	−1.56958	+	0.858671i
$502$	−1.32517			−0.0591450
$503$	−15.6359	−	9.02738i	−0.697169	−	0.402511i	0.109123	−	0.994028i	$-0.465196\pi$
$503$	−15.6359	−	9.02738i	−0.697169	−	0.402511i	−0.806292	+	0.591517i	$0.798529\pi$
$504$	−1.28343	+	0.664234i	−0.0571685	+	0.0295874i
$505$	−8.51037	+	4.91347i	−0.378707	+	0.218646i
$506$	−28.4079			−1.26288
$507$	−1.95346	−	3.57075i	−0.0867561	−	0.158583i
$508$	9.97994	−	17.2858i	0.442788	−	0.766932i
$509$	4.19494	+	7.26584i	0.185937	+	0.322053i	0.943892	−	0.330254i	$-0.107135\pi$
$509$	4.19494	+	7.26584i	0.185937	+	0.322053i	−0.757955	+	0.652307i	$0.773801\pi$
$510$	0.0718202	−	3.12120i	0.00318025	−	0.138209i
$511$	−2.69370	+	4.66563i	−0.119162	+	0.206395i
$512$		−	1.00000i		−	0.0441942i
$513$	−34.5997	+	16.9094i	−1.52761	+	0.746569i
$514$	11.5155	+	19.9455i	0.507928	+	0.879756i
$515$	2.18101	−	3.77762i	0.0961067	−	0.166462i
$516$	−14.4304	−	8.78008i	−0.635262	−	0.386521i
$517$	34.3654	−	59.5226i	1.51139	−	2.61780i
$518$	2.78798	+	0.901548i	0.122497	+	0.0396118i
$519$	−10.1563	−	18.5649i	−0.445814	−	0.814909i
$520$		−	2.70052i		−	0.118426i
$521$	4.34319	+	7.52262i	0.190278	+	0.329572i	0.945342	−	0.326079i	$-0.105728\pi$
$521$	4.34319	+	7.52262i	0.190278	+	0.329572i	−0.755064	+	0.655651i	$0.772394\pi$
$522$	9.10657	+	0.419315i	0.398584	+	0.0183529i
$523$	3.35614	−	1.93767i	0.146754	−	0.0847284i	−0.424825	−	0.905275i	$-0.639664\pi$
$523$	3.35614	−	1.93767i	0.146754	−	0.0847284i	0.571579	+	0.820547i	$0.306331\pi$
$524$	−7.75504	+	4.47737i	−0.338781	+	0.195595i
$525$	−3.59945	−	0.0828249i	−0.157093	−	0.00361478i
$526$	−11.2410	−	6.49001i	−0.490132	−	0.282978i
$527$	6.92177	+	11.9889i	0.301517	+	0.522243i
$528$	4.89874	−	8.05126i	0.213190	−	0.350386i
$529$	2.12875	+	3.68710i	0.0925544	+	0.160309i
$530$	−0.0772146	+	0.133740i	−0.00335399	+	0.00580928i
$531$	0.559029	−	12.1408i	0.0242598	−	0.526867i
$532$		−	3.57013i		−	0.154785i
$533$			33.7423i			1.46154i
$534$	3.83108	+	0.0881549i	0.165787	+	0.00381484i
$535$	0.157426	−	0.0908900i	0.00680612	−	0.00392952i
$536$			9.91978i			0.428469i
$537$	12.4835	−	6.82937i	0.538703	−	0.294709i
$538$			11.1365i			0.480127i
$539$	−18.4129	+	31.8922i	−0.793102	+	1.37369i
$540$	0.296537	−	4.28961i	0.0127609	−	0.184595i
$541$			10.2285i			0.439759i	0.975527	+	0.219879i	$0.0705663\pi$
$541$			10.2285i			0.439759i	−0.975527	+	0.219879i	$0.929434\pi$
$542$	−13.7232	−	7.92308i	−0.589461	−	0.340325i
$543$	−20.2897	+	33.3469i	−0.870716	+	1.43105i
$544$	1.08912	−	1.88641i	0.0466955	−	0.0808790i
$545$	−1.58016	+	2.73691i	−0.0676865	+	0.117236i
$546$	−2.72212	−	0.0626373i	−0.116496	−	0.00268063i
$547$	6.45613	−	3.72745i	0.276044	−	0.159374i	−0.355587	−	0.934643i	$-0.615719\pi$
$547$	6.45613	−	3.72745i	0.276044	−	0.159374i	0.631631	+	0.775269i	$0.282386\pi$
$548$	−6.51114	−	11.2776i	−0.278142	−	0.481756i
$549$	−20.4950	+	10.6071i	−0.874706	+	0.452701i
$550$	20.3344	−	11.7401i	0.867061	−	0.500598i
$551$	−11.2606	+	19.5040i	−0.479718	+	0.830897i
$552$	−9.04042	−	0.208024i	−0.384786	−	0.00885410i
$553$	5.22683	−	3.01771i	0.222268	−	0.128326i
$554$	14.7429	−	25.5354i	0.626365	−	1.08490i
$555$	−6.60348	+	5.69237i	−0.280302	+	0.241628i
$556$	10.2192	+	17.7002i	0.433391	+	0.750655i
$557$	36.0732	+	20.8269i	1.52847	+	0.882464i	0.999426	+	0.0338700i	$0.0107832\pi$
$557$	36.0732	+	20.8269i	1.52847	+	0.882464i	0.529045	+	0.848594i	$0.322550\pi$
$558$	8.76352	+	16.9328i	0.370989	+	0.716823i
$559$	−15.9132	−	27.5624i	−0.673055	−	1.16577i
$560$	0.345213	+	0.199309i	0.0145879	+	0.00842234i
$561$	18.0098	−	9.85264i	0.760373	−	0.415979i
$562$	−24.8867			−1.04978
$563$	−29.9714	−	17.3040i	−1.26314	−	0.729276i	−0.289461	−	0.957190i	$-0.593476\pi$
$563$	−29.9714	−	17.3040i	−1.26314	−	0.729276i	−0.973681	+	0.227914i	$0.926810\pi$
$564$	11.3722	−	18.6906i	0.478856	−	0.787017i
$565$	−0.572443	−	0.991501i	−0.0240829	−	0.0417128i
$566$	−21.7190			−0.912917
$567$	−4.31704	−	0.398404i	−0.181299	−	0.0167314i
$568$	5.40879	−	3.12277i	0.226948	−	0.131028i
$569$	7.87957	−	4.54927i	0.330329	−	0.190715i	−0.325658	−	0.945487i	$-0.605586\pi$
$569$	7.87957	−	4.54927i	0.330329	−	0.190715i	0.655987	+	0.754772i	$0.272253\pi$
$570$	9.07482	+	5.52152i	0.380102	+	0.231271i
$571$	18.1776	+	31.4845i	0.760707	+	1.31758i	0.942487	+	0.334244i	$0.108481\pi$
$571$	18.1776	+	31.4845i	0.760707	+	1.31758i	−0.181779	+	0.983339i	$0.558186\pi$
$572$	15.3781	−	8.87856i	0.642991	−	0.371231i
$573$	−11.2221	−	6.82803i	−0.468811	−	0.285245i
$574$	−4.31335	−	2.49031i	−0.180036	−	0.103944i
$575$	−19.5109	−	11.2646i	−0.813662	−	0.469768i
$576$	1.61792	−	2.52633i	0.0674131	−	0.105264i
$577$	7.08022	+	4.08776i	0.294753	+	0.170176i	0.640083	−	0.768305i	$-0.278900\pi$
$577$	7.08022	+	4.08776i	0.294753	+	0.170176i	−0.345330	+	0.938481i	$0.612233\pi$
$578$	−10.6134	+	6.12765i	−0.441459	+	0.254877i
$579$	0.216535	−	9.41030i	0.00899890	−	0.391079i
$580$	−1.25729	−	2.17769i	−0.0522060	−	0.0904235i
$581$	2.35277	−	4.07511i	0.0976093	−	0.169064i
$582$	13.2244	−	21.7348i	0.548169	−	0.900935i
$583$	−1.01544			−0.0420552
$584$		−	11.1839i		−	0.462794i
$585$	4.36921	−	6.82241i	0.180645	−	0.282072i
$586$		−	7.90816i		−	0.326683i
$587$	15.9348	+	9.19993i	0.657698	+	0.379722i	0.791399	−	0.611300i	$-0.209353\pi$
$587$	15.9348	+	9.19993i	0.657698	+	0.379722i	−0.133702	+	0.991022i	$0.542686\pi$
$588$	−6.09321	+	10.0144i	−0.251280	+	0.412987i
$589$	−47.1022			−1.94081
$590$	−2.90328	+	1.67621i	−0.119526	+	0.0690085i
$591$	−42.1738	−	0.970438i	−1.73480	−	0.0399185i
$592$	−5.94806	+	1.27302i	−0.244464	+	0.0523209i
$593$	2.48249			0.101944			0.0509719	−	0.998700i	$-0.483768\pi$
$593$	2.48249			0.101944			0.0509719	+	0.998700i	$0.483768\pi$
$594$	25.4021	−	12.4144i	1.04226	−	0.509369i
$595$	0.434141	+	0.751955i	0.0177981	+	0.0308271i
$596$	8.64800	−	14.9788i	0.354236	−	0.613554i
$597$	−2.67288	+	1.46226i	−0.109394	+	0.0598463i
$598$	−14.7554	−	8.51902i	−0.603392	−	0.348369i
$599$	−28.2575			−1.15457			−0.577284	−	0.816543i	$-0.695888\pi$
$599$	−28.2575			−1.15457			−0.577284	+	0.816543i	$0.695888\pi$
$600$	6.55711	−	3.58721i	0.267693	−	0.146447i
$601$	−27.7718			−1.13284			−0.566419	−	0.824118i	$-0.691671\pi$
$601$	−27.7718			−1.13284			−0.566419	+	0.824118i	$0.691671\pi$
$602$	4.69781			0.191468
$603$	−16.0494	+	25.0606i	−0.653580	+	1.02055i
$604$	−2.30926	+	3.99975i	−0.0939623	+	0.162747i
$605$	−13.3344	−	7.69862i	−0.542121	−	0.312994i
$606$	−17.5717	−	10.6914i	−0.713803	−	0.434309i
$607$	14.4771	−	8.35837i	0.587608	−	0.339256i	−0.176543	−	0.984293i	$-0.556491\pi$
$607$	14.4771	−	8.35837i	0.587608	−	0.339256i	0.764151	+	0.645037i	$0.223158\pi$
$608$	3.70569	+	6.41844i	0.150285	+	0.260302i
$609$	−2.22427	+	1.21683i	−0.0901318	+	0.0493086i
$610$	5.51269	+	3.18275i	0.223202	+	0.128866i
$611$	35.6996	−	20.6111i	1.44425	−	0.833838i
$612$	5.80351	−	3.00359i	0.234593	−	0.121413i
$613$	−9.31314	+	16.1308i	−0.376154	+	0.651518i	−0.990499	−	0.137519i	$-0.956087\pi$
$613$	−9.31314	+	16.1308i	−0.376154	+	0.651518i	0.614345	+	0.789038i	$0.289420\pi$
$614$			10.3177i			0.416387i
$615$	13.0010	−	7.11249i	0.524251	−	0.286803i
$616$			2.62109i			0.105607i
$617$	10.9347	+	18.9394i	0.440212	+	0.762470i	0.997705	−	0.0677116i	$-0.0215698\pi$
$617$	10.9347	+	18.9394i	0.440212	+	0.762470i	−0.557492	+	0.830182i	$0.688236\pi$
$618$	9.12771	+	0.210033i	0.367171	+	0.00844877i
$619$	−4.76840	−	8.25912i	−0.191658	−	0.331962i	0.754142	−	0.656712i	$-0.228053\pi$
$619$	−4.76840	−	8.25912i	−0.191658	−	0.331962i	−0.945800	+	0.324750i	$0.894720\pi$
$620$	2.62956	−	4.55454i	0.105606	−	0.182915i
$621$	−22.5025	−	15.1522i	−0.902996	−	0.608036i
$622$	−5.16223	−	8.94124i	−0.206986	−	0.358511i
$623$	−0.922978	+	0.532882i	−0.0369783	+	0.0213495i
$624$	4.95889	−	2.71287i	0.198515	−	0.108602i
$625$	15.1974			0.607897
$626$	−26.6770			−1.06623
$627$	−1.60681	+	69.8297i	−0.0641700	+	2.78873i
$628$	0.631378	+	1.09358i	0.0251947	+	0.0436385i
$629$	−12.6069	−	4.07669i	−0.502671	−	0.162548i
$630$	0.549658	+	1.06205i	0.0218989	+	0.0423129i
$631$	−38.3623	−	22.1485i	−1.52718	−	0.881718i	−0.999479	−	0.0322874i	$-0.989721\pi$
$631$	−38.3623	−	22.1485i	−1.52718	−	0.881718i	−0.527701	−	0.849430i	$-0.676946\pi$
$632$	−6.26459	+	10.8506i	−0.249192	+	0.431613i
$633$	28.3890	+	0.653244i	1.12836	+	0.0259641i
$634$			1.26263i			0.0501453i
$635$	−14.3041	−	8.25846i	−0.567640	−	0.327727i
$636$	−0.323150	−	0.00743583i	−0.0128137	−	0.000294850i
$637$	−19.1278	+	11.0434i	−0.757870	+	0.437557i
$638$	8.26721	−	14.3192i	0.327302	−	0.566904i
$639$	18.7168	+	0.861820i	0.740424	+	0.0340931i
$640$	−0.827506			−0.0327100
$641$	−6.14328			−0.242645			−0.121322	−	0.992613i	$-0.538714\pi$
$641$	−6.14328			−0.242645			−0.121322	+	0.992613i	$0.538714\pi$
$642$	0.325045	+	0.197771i	0.0128285	+	0.00780541i
$643$	12.4072	+	7.16331i	0.489293	+	0.282493i	0.724281	−	0.689505i	$-0.242172\pi$
$643$	12.4072	+	7.16331i	0.489293	+	0.282493i	−0.234988	+	0.971998i	$0.575505\pi$
$644$	2.17801	−	1.25747i	0.0858255	−	0.0495514i
$645$	−7.26557	+	11.9412i	−0.286081	+	0.470185i
$646$			16.1437i			0.635166i
$647$	0.406641	−	0.234774i	0.0159867	−	0.00922992i	−0.491985	−	0.870603i	$-0.663729\pi$
$647$	0.406641	−	0.234774i	0.0159867	−	0.00922992i	0.507972	+	0.861374i	$0.330395\pi$
$648$	8.17478	−	3.76470i	0.321136	−	0.147891i
$649$	−19.0903	−	11.0218i	−0.749361	−	0.432644i
$650$	14.0825			0.552363
$651$	−4.52998	−	2.75624i	−0.177544	−	0.108026i
$652$	1.05113	+	0.606868i	0.0411653	+	0.0237668i
$653$		−	6.34015i		−	0.248109i	−0.992275	−	0.124055i	$-0.960410\pi$
$653$		−	6.34015i		−	0.248109i	0.992275	−	0.124055i	$-0.0395898\pi$
$654$	−6.61310	−	0.152170i	−0.258593	−	0.00595034i
$655$	3.70505	+	6.41734i	0.144768	+	0.250746i
$656$	10.3395			0.403688
$657$	18.0946	−	28.2543i	0.705938	−	1.10230i
$658$			6.08473i			0.237207i
$659$	−10.0173	+	17.3505i	−0.390220	+	0.675880i	−0.992478	−	0.122421i	$-0.960934\pi$
$659$	−10.0173	+	17.3505i	−0.390220	+	0.675880i	0.602259	+	0.798301i	$0.294268\pi$
$660$	−6.66246	−	4.05374i	−0.259336	−	0.157791i
$661$			15.4270i			0.600040i	0.953933	+	0.300020i	$0.0969934\pi$
$661$			15.4270i			0.600040i	−0.953933	+	0.300020i	$0.903007\pi$
$662$	20.1907			0.784734
$663$	12.3091	+	0.283238i	0.478046	+	0.0110001i
$664$			9.76840i			0.379088i
$665$	−2.95431			−0.114563
$666$	−17.0864	−	6.40737i	−0.662085	−	0.248281i
$667$	−15.8649			−0.614290
$668$			23.1203i			0.894551i
$669$	10.0311	−	16.4864i	0.387823	−	0.637401i
$670$	8.20867			0.317129
$671$			41.8560i			1.61583i
$672$	−0.0191936	+	0.834125i	−0.000740410	+	0.0321771i
$673$	−1.78423	+	3.09037i	−0.0687768	+	0.119125i	−0.898363	−	0.439254i	$-0.855243\pi$
$673$	−1.78423	+	3.09037i	−0.0687768	+	0.119125i	0.829586	+	0.558379i	$0.188576\pi$
$674$		−	29.1975i		−	1.12465i
$675$	22.3692	+	1.54636i	0.860992	+	0.0595195i
$676$	−2.34991			−0.0903813
$677$	4.79345	+	8.30249i	0.184227	+	0.319091i	0.943316	−	0.331896i	$-0.107688\pi$
$677$	4.79345	+	8.30249i	0.184227	+	0.319091i	−0.759089	+	0.650987i	$0.774355\pi$
$678$	1.24560	−	2.04720i	0.0478371	−	0.0786221i
$679$			7.07575i			0.271543i
$680$	−1.56101	−	0.901251i	−0.0598621	−	0.0345614i
$681$	0.295175	−	12.8278i	0.0113111	−	0.491564i
$682$	34.5811			1.32418
$683$	17.1817	+	9.91989i	0.657441	+	0.379574i	0.791301	−	0.611426i	$-0.209404\pi$
$683$	17.1817	+	9.91989i	0.657441	+	0.379574i	−0.133860	+	0.991000i	$0.542737\pi$
$684$	−1.02269	+	22.2106i	−0.0391037	+	0.849243i
$685$	−9.33230	+	5.38801i	−0.356569	+	0.205865i
$686$		−	6.63216i		−	0.253217i
$687$	−17.2341	−	31.5024i	−0.657521	−	1.20189i
$688$	−8.44579	+	4.87618i	−0.321993	+	0.185903i
$689$	−0.527431	−	0.304512i	−0.0200935	−	0.0116010i
$690$	−0.172141	+	7.48100i	−0.00655331	+	0.284797i
$691$	−26.8328			−1.02077			−0.510384	−	0.859947i	$-0.670497\pi$
$691$	−26.8328			−1.02077			−0.510384	+	0.859947i	$0.670497\pi$
$692$	−12.2176			−0.464442
$693$	−4.24070	+	6.62173i	−0.161091	+	0.251539i
$694$	−15.6806	+	27.1596i	−0.595227	+	1.03096i
$695$	14.6470	−	8.45645i	0.555593	−	0.320772i
$696$	2.73579	−	4.49636i	0.103700	−	0.170434i
$697$	19.5044	+	11.2609i	0.738783	+	0.426536i
$698$		−	9.65184i		−	0.365327i
$699$	−12.7713	−	23.3449i	−0.483057	−	0.882986i
$700$	−1.03935	+	1.80020i	−0.0392836	+	0.0680411i
$701$	8.11479	+	4.68508i	0.306491	+	0.176953i	0.645355	−	0.763882i	$-0.276709\pi$
$701$	8.11479	+	4.68508i	0.306491	+	0.176953i	−0.338864	+	0.940835i	$0.610043\pi$
$702$	16.9170	+	1.16946i	0.638491	+	0.0441382i
$703$	33.4598	−	30.2125i	1.26196	−	1.13949i
$704$	−2.72061	−	4.71223i	−0.102537	−	0.177599i
$705$	−15.4666	−	9.41056i	−0.582506	−	0.354422i
$706$	−3.53077			−0.132882
$707$	5.72048			0.215141
$708$	−5.99453	−	3.64734i	−0.225288	−	0.137075i
$709$	1.46903	−	0.848144i	0.0551705	−	0.0318527i	−0.472161	−	0.881512i	$-0.656526\pi$
$709$	1.46903	−	0.848144i	0.0551705	−	0.0318527i	0.527332	+	0.849660i	$0.323193\pi$
$710$	−2.58411	−	4.47581i	−0.0969799	−	0.167974i
$711$	−33.3817	+	17.2766i	−1.25191	+	0.647923i
$712$	1.10623	−	1.91605i	0.0414577	−	0.0718069i
$713$	−16.5904	−	28.7353i	−0.621314	−	1.07615i
$714$	−0.944667	+	1.55259i	−0.0353533	+	0.0581044i
$715$	−7.34706	−	12.7255i	−0.274764	−	0.475906i
$716$		−	8.21539i		−	0.307024i
$717$	11.8056	+	7.18302i	0.440887	+	0.268255i
$718$		−	6.08563i		−	0.227114i
$719$	22.8072	−	39.5033i	0.850567	−	1.47322i	−0.0301313	−	0.999546i	$-0.509593\pi$
$719$	22.8072	−	39.5033i	0.850567	−	1.47322i	0.880698	−	0.473678i	$-0.157074\pi$
$720$	−2.09055	−	1.33883i	−0.0779104	−	0.0498954i
$721$	−2.19904	+	1.26961i	−0.0818964	+	0.0472829i
$722$	−31.1150	−	17.9642i	−1.15798	−	0.668560i
$723$	−0.802972	+	34.8960i	−0.0298629	+	1.29779i
$724$	11.2683	+	19.5172i	0.418782	+	0.725353i
$725$	11.3561	−	6.55643i	0.421754	−	0.243500i
$726$	0.741384	−	32.2194i	0.0275153	−	1.19577i
$727$	11.3467	+	6.55105i	0.420828	+	0.242965i	0.695431	−	0.718593i	$-0.255213\pi$
$727$	11.3467	+	6.55105i	0.420828	+	0.242965i	−0.274604	+	0.961557i	$0.588547\pi$
$728$	−0.786017	+	1.36142i	−0.0291317	+	0.0504577i
$729$	26.7432	+	3.71521i	0.990488	+	0.137600i
$730$	−9.25475			−0.342534
$731$	−21.2429			−0.785698
$732$	−0.306502	+	13.3201i	−0.0113286	+	0.492325i
$733$	−29.7773			−1.09985			−0.549925	−	0.835214i	$-0.685344\pi$
$733$	−29.7773			−1.09985			−0.549925	+	0.835214i	$0.685344\pi$
$734$	−10.0314	−	5.79164i	−0.370266	−	0.213773i
$735$	8.28699	+	5.04217i	0.305670	+	0.185983i
$736$	−2.61044	+	4.52141i	−0.0962219	+	0.166661i
$737$	26.9878	+	46.7443i	0.994109	+	1.72185i
$738$	26.1209	+	16.7284i	0.961524	+	0.615780i
$739$	25.4204			0.935106			0.467553	−	0.883965i	$-0.345136\pi$
$739$	25.4204			0.935106			0.467553	+	0.883965i	$0.345136\pi$
$740$	1.05343	+	4.92205i	0.0387250	+	0.180938i
$741$	−21.7753	+	35.7885i	−0.799935	+	1.31472i
$742$	0.0778529	−	0.0449484i	0.00285807	−	0.00165011i
$743$	−29.3040			−1.07506			−0.537530	−	0.843245i	$-0.680642\pi$
$743$	−29.3040			−1.07506			−0.537530	+	0.843245i	$0.680642\pi$
$744$	11.0050	+	0.253229i	0.403461	+	0.00928383i
$745$	−12.3950	−	7.15627i	−0.454118	−	0.262185i
$746$			10.9534i			0.401034i
$747$	−15.8044	+	24.6782i	−0.578254	+	0.902929i
$748$		−	11.8522i		−	0.433361i
$749$	−0.105818			−0.00386651
$750$	−6.40792	−	11.7131i	−0.233984	−	0.427703i
$751$	19.6400	−	34.0175i	0.716673	−	1.24131i	−0.245637	−	0.969362i	$-0.578997\pi$
$751$	19.6400	−	34.0175i	0.716673	−	1.24131i	0.962311	−	0.271953i	$-0.0876695\pi$
$752$	−6.31576	−	10.9392i	−0.230312	−	0.398912i
$753$	−2.01362	+	1.10160i	−0.0733805	+	0.0401444i
$754$	8.58817	−	4.95838i	0.312763	−	0.180574i
$755$	3.30981	+	1.91092i	0.120456	+	0.0695456i
$756$	−1.39803	+	2.07622i	−0.0508460	+	0.0755115i
$757$	−1.13752	−	0.656745i	−0.0413437	−	0.0238698i	0.479186	−	0.877714i	$-0.340932\pi$
$757$	−1.13752	−	0.656745i	−0.0413437	−	0.0238698i	−0.520529	+	0.853844i	$0.674265\pi$
$758$	9.80803	+	5.66267i	0.356244	+	0.205677i
$759$	−43.1665	+	23.6152i	−1.56684	+	0.857177i
$760$	5.31130	−	3.06648i	0.192661	−	0.111233i
$761$	−6.32778	−	10.9600i	−0.229382	−	0.397301i	0.728243	−	0.685319i	$-0.240337\pi$
$761$	−6.32778	−	10.9600i	−0.229382	−	0.397301i	−0.957625	+	0.288018i	$0.907004\pi$
$762$	0.795296	−	34.5624i	0.0288105	−	1.25206i
$763$	1.59322	−	0.919845i	0.0576784	−	0.0333006i
$764$	−6.56807	+	3.79207i	−0.237624	+	0.137192i
$765$	−2.48549	−	4.80244i	−0.0898630	−	0.173633i
$766$	−8.96064			−0.323761
$767$	−6.61049	−	11.4497i	−0.238691	−	0.413425i
$768$	−0.831290	−	1.51953i	−0.0299966	−	0.0548312i
$769$	−32.7030	−	18.8811i	−1.17930	−	0.680869i	−0.223448	−	0.974716i	$-0.571731\pi$
$769$	−32.7030	−	18.8811i	−1.17930	−	0.680869i	−0.955853	+	0.293846i	$0.905065\pi$
$770$	2.16896			0.0781641
$771$	34.0786	+	20.7349i	1.22731	+	0.746749i
$772$	−4.70640	−	2.71724i	−0.169387	−	0.0977956i
$773$	−14.3379	−	24.8339i	−0.515698	−	0.893215i	−0.999834	−	0.0182219i	$-0.994199\pi$
$773$	−14.3379	−	24.8339i	−0.515698	−	0.893215i	0.484136	−	0.874993i	$-0.339134\pi$
$774$	−29.2261	−	1.34573i	−1.05051	−	0.0483711i
$775$	23.7508	+	13.7125i	0.853153	+	0.492568i
$776$	−7.34441	−	12.7209i	−0.263649	−	0.456654i
$777$	4.98586	−	0.947696i	0.178867	−	0.0339984i
$778$	−6.93830	+	12.0175i	−0.248750	+	0.430848i
$779$	−66.3632	+	38.3148i	−2.37771	+	1.37277i
$780$	−2.24492	−	4.10351i	−0.0803809	−	0.146929i
$781$	16.9917	−	29.4304i	0.608009	−	1.05310i
$782$	−9.84868	+	5.68614i	−0.352188	+	0.203336i
$783$	14.1862	−	6.93304i	0.506975	−	0.247767i
$784$	3.38398	+	5.86122i	0.120856	+	0.209329i
$785$	0.904943	−	0.522469i	0.0322988	−	0.0186477i
$786$	−8.06199	+	13.2502i	−0.287562	+	0.472618i
$787$	−0.974155	+	1.68729i	−0.0347249	+	0.0601452i	−0.882866	−	0.469626i	$-0.844389\pi$
$787$	−0.974155	+	1.68729i	−0.0347249	+	0.0601452i	0.848141	+	0.529771i	$0.177722\pi$
$788$	−12.1777	+	21.0925i	−0.433814	+	0.751388i
$789$	−22.4761	−	0.517186i	−0.800170	−	0.0184123i
$790$	8.97892	+	5.18398i	0.319456	+	0.184438i
$791$			0.666465i			0.0236968i
$792$	0.750832	−	16.3064i	0.0266796	−	0.579421i
$793$	−12.5519	+	21.7405i	−0.445730	+	0.772027i
$794$		−	5.30259i		−	0.188182i
$795$	−0.00615319	+	0.267408i	−0.000218231	+	0.00948400i
$796$			1.75902i			0.0623470i
$797$	41.0328	−	23.6903i	1.45346	−	0.839154i	0.454782	−	0.890603i	$-0.349717\pi$
$797$	41.0328	−	23.6903i	1.45346	−	0.839154i	0.998676	+	0.0514487i	$0.0163839\pi$
$798$	−2.96781	−	5.42491i	−0.105059	−	0.192040i
$799$		−	27.5144i		−	0.973390i
$800$		−	4.31523i		−	0.152567i
$801$	5.89470	−	3.05078i	0.208279	−	0.107794i
$802$	11.4618	−	19.8525i	0.404732	−	0.701016i
$803$	−30.4270	−	52.7012i	−1.07375	−	1.85978i
$804$	8.24621	+	15.0734i	0.290821	+	0.531596i
$805$	−1.04057	−	1.80231i	−0.0366751	−	0.0635232i
$806$	17.9618	+	10.3703i	0.632678	+	0.365277i
$807$	9.25763	+	16.9221i	0.325884	+	0.595688i
$808$	−10.2844	+	5.93768i	−0.361803	+	0.208887i
$809$	18.0515	−	10.4220i	0.634657	−	0.366420i	−0.147896	−	0.989003i	$-0.547250\pi$
$809$	18.0515	−	10.4220i	0.634657	−	0.366420i	0.782554	+	0.622583i	$0.213917\pi$
$810$	−3.11531	−	6.76468i	−0.109461	−	0.237687i
$811$	10.0118	+	17.3410i	0.351563	+	0.608925i	0.986523	−	0.163620i	$-0.0523171\pi$
$811$	10.0118	+	17.3410i	0.351563	+	0.608925i	−0.634961	+	0.772544i	$0.718984\pi$
$812$			1.46379i			0.0513690i
$813$	−27.4391	−	0.631386i	−0.962331	−	0.0221437i
$814$	−24.5652	+	22.1811i	−0.861011	+	0.777448i
$815$	0.502187	−	0.869813i	0.0175908	−	0.0304682i
$816$	0.0867912	−	3.77181i	0.00303830	−	0.132040i
$817$	36.1392	−	62.5949i	1.26435	−	2.18992i
$818$	9.11374	+	15.7855i	0.318655	+	0.551926i
$819$	−4.18841	+	2.16769i	−0.146355	+	0.0757454i
$820$		−	8.55597i		−	0.298787i
$821$	22.4018	−	38.8011i	0.781829	−	1.35417i	−0.149046	−	0.988830i	$-0.547620\pi$
$821$	22.4018	−	38.8011i	0.781829	−	1.35417i	0.930875	−	0.365337i	$-0.119046\pi$
$822$	−19.2688	−	11.7240i	−0.672077	−	0.408921i
$823$	0.515712	+	0.893240i	0.0179766	+	0.0311364i	0.874874	−	0.484351i	$-0.160944\pi$
$823$	0.515712	+	0.893240i	0.0179766	+	0.0311364i	−0.856897	+	0.515487i	$0.827611\pi$
$824$	2.63564	−	4.56507i	0.0918169	−	0.159032i
$825$	21.1392	−	34.7431i	0.735973	−	1.20960i
$826$	1.95152			0.0679020
$827$	−4.33728	+	2.50413i	−0.150822	+	0.0870772i	−0.573512	−	0.819197i	$-0.694419\pi$
$827$	−4.33728	+	2.50413i	−0.150822	+	0.0870772i	0.422690	+	0.906274i	$0.361086\pi$
$828$	−13.9101	+	7.19911i	−0.483409	+	0.250186i
$829$	−12.3352	−	7.12174i	−0.428420	−	0.247348i	0.270253	−	0.962789i	$-0.412892\pi$
$829$	−12.3352	−	7.12174i	−0.428420	−	0.247348i	−0.698673	+	0.715441i	$0.746226\pi$
$830$	8.08341			0.280579
$831$	1.17485	−	51.0573i	0.0407552	−	1.77116i
$832$		−	3.26345i		−	0.113140i
$833$			14.7422i			0.510787i
$834$	30.2423	+	18.4008i	1.04721	+	0.637166i
$835$	19.1322			0.662096
$836$	34.9241	+	20.1634i	1.20788	+	0.697367i
$837$	27.3925	+	18.4448i	0.946822	+	0.637547i
$838$	−8.53080	+	4.92526i	−0.294692	+	0.170140i
$839$	55.9406			1.93128			0.965642	−	0.259876i	$-0.0836817\pi$
$839$	55.9406			1.93128			0.965642	+	0.259876i	$0.0836817\pi$
$840$	0.690244	+	0.0158828i	0.0238157	+	0.000548010i
$841$	−9.88303	+	17.1179i	−0.340794	+	0.590273i
$842$	−3.68205	−	6.37750i	−0.126892	−	0.219783i
$843$	−37.8159	+	20.6880i	−1.30245	+	0.712534i
$844$	8.19737	−	14.1983i	0.282165	−	0.488724i
$845$			1.94457i			0.0668951i
$846$	1.74302	−	37.8544i	0.0599263	−	1.30146i
$847$	4.48154	+	7.76226i	0.153988	+	0.266714i
$848$	−0.0933100	+	0.161618i	−0.00320428	+	0.00554997i
$849$	−33.0025	+	18.0548i	−1.13264	+	0.619638i
$850$	4.69979	−	8.14028i	0.161202	−	0.279209i
$851$	30.2167	+	9.77117i	1.03582	+	0.334951i
$852$	5.62287	−	9.24140i	0.192637	−	0.316605i
$853$			4.22015i			0.144495i	0.997387	+	0.0722476i	$0.0230172\pi$
$853$			4.22015i			0.144495i	−0.997387	+	0.0722476i	$0.976983\pi$
$854$	−1.85275	−	3.20906i	−0.0633999	−	0.109812i
$855$	18.3794	+	0.846285i	0.628562	+	0.0289423i
$856$	0.190242	−	0.109836i	0.00650232	−	0.00375412i
$857$	−9.35703	+	5.40229i	−0.319630	+	0.184539i	−0.651228	−	0.758882i	$-0.725746\pi$
$857$	−9.35703	+	5.40229i	−0.319630	+	0.184539i	0.331598	+	0.943421i	$0.392412\pi$
$858$	15.9868	−	26.2749i	0.545780	−	0.897009i
$859$	37.8229	+	21.8371i	1.29050	+	0.745071i	0.978743	−	0.205090i	$-0.0657488\pi$
$859$	37.8229	+	21.8371i	1.29050	+	0.745071i	0.311758	+	0.950161i	$0.399082\pi$
$860$	4.03507	+	6.98894i	0.137595	+	0.238321i
$861$	−8.62441	−	0.198452i	−0.293919	−	0.00676321i
$862$	−7.84093	−	13.5809i	−0.267063	−	0.462567i
$863$	−7.19089	+	12.4550i	−0.244781	+	0.423973i	−0.962070	−	0.272803i	$-0.912049\pi$
$863$	−7.19089	+	12.4550i	−0.244781	+	0.423973i	0.717289	+	0.696776i	$0.245383\pi$
$864$	0.358350	−	5.18378i	0.0121913	−	0.176356i
$865$			10.1101i			0.343754i
$866$			6.31571i			0.214617i
$867$	−11.0335	+	18.1339i	−0.374717	+	0.615860i
$868$	−2.65130	+	1.53073i	−0.0899910	+	0.0519563i
$869$			68.1739i			2.31264i
$870$	−3.72077	−	2.26388i	−0.126146	−	0.0767527i
$871$			32.3727i			1.09691i
$872$	−1.90954	+	3.30742i	−0.0646652	+	0.112003i
$873$	2.02691	−	44.0198i	0.0686004	−	1.48985i
$874$		−	38.6938i		−	1.30884i
$875$	3.21574	+	1.85661i	0.108712	+	0.0627648i
$876$	−9.29707	−	16.9942i	−0.314119	−	0.574182i
$877$	5.87463	−	10.1752i	0.198372	−	0.343591i	−0.749629	−	0.661859i	$-0.769768\pi$
$877$	5.87463	−	10.1752i	0.198372	−	0.343591i	0.948001	+	0.318268i	$0.103101\pi$
$878$	2.08711	−	3.61499i	0.0704366	−	0.122000i
$879$	−6.57397	−	12.0167i	−0.221735	−	0.405312i
$880$	−3.89940	+	2.25132i	−0.131449	+	0.0758919i
$881$	2.28562	+	3.95881i	0.0770045	+	0.133376i	0.901956	−	0.431828i	$-0.142131\pi$
$881$	2.28562	+	3.95881i	0.0770045	+	0.133376i	−0.824952	+	0.565203i	$0.808798\pi$
$882$	−0.933908	+	20.2824i	−0.0314463	+	0.682943i
$883$	7.53244	−	4.34886i	0.253487	−	0.146351i	−0.367873	−	0.929876i	$-0.619914\pi$
$883$	7.53244	−	4.34886i	0.253487	−	0.146351i	0.621360	+	0.783525i	$0.286581\pi$
$884$	3.55428	−	6.15619i	0.119543	−	0.207055i
$885$	−3.01819	+	4.96051i	−0.101455	+	0.166746i
$886$	−25.0178	+	14.4440i	−0.840490	+	0.485257i
$887$	−8.13785	+	14.0952i	−0.273242	+	0.473269i	−0.969690	−	0.244338i	$-0.921429\pi$
$887$	−8.13785	+	14.0952i	−0.273242	+	0.473269i	0.696448	+	0.717607i	$0.254763\pi$
$888$	−7.97998	+	6.87895i	−0.267790	+	0.230843i
$889$	4.80744	+	8.32672i	0.161236	+	0.279269i
$890$	−1.58554	−	0.915412i	−0.0531474	−	0.0306847i
$891$	28.2792	−	39.9805i	0.947388	−	1.33940i
$892$	−5.57093	−	9.64914i	−0.186529	−	0.323077i
$893$	81.0746	+	46.8085i	2.71306	+	1.56639i
$894$	0.689155	−	29.9496i	0.0230488	−	1.00166i
$895$	−6.79829			−0.227242
$896$	0.417173	+	0.240855i	0.0139368	+	0.00804640i
$897$	−29.5029	−	0.678876i	−0.985074	−	0.0226670i
$898$	2.34336	+	4.05881i	0.0781989	+	0.135444i
$899$	19.3124			0.644104
$900$	6.98168	−	10.9017i	0.232723	−	0.363390i
$901$	−0.352041	+	0.203251i	−0.0117282	+	0.00677127i
$902$	48.7219	−	28.1296i	1.62226	−	0.936614i
$903$	7.13844	−	3.90524i	0.237552	−	0.129958i
$904$	−0.691770	−	1.19818i	−0.0230079	−	0.0398509i
$905$	16.1506	−	9.32457i	0.536865	−	0.309959i
$906$	−0.184023	+	7.99738i	−0.00611377	+	0.265695i
$907$	12.7059	+	7.33576i	0.421893	+	0.243580i	0.695887	−	0.718151i	$-0.255011\pi$
$907$	12.7059	+	7.33576i	0.421893	+	0.243580i	−0.273994	+	0.961731i	$0.588345\pi$
$908$	−6.41562	−	3.70406i	−0.212910	−	0.122924i
$909$	−35.5884	−	1.63868i	−1.18039	−	0.0543515i
$910$	1.12658	+	0.650434i	0.0373459	+	0.0215617i
$911$	10.2660	−	5.92710i	0.340129	−	0.196374i	−0.320200	−	0.947350i	$-0.603750\pi$
$911$	10.2660	−	5.92710i	0.340129	−	0.196374i	0.660329	+	0.750976i	$0.270417\pi$
$912$	10.9665	+	6.67248i	0.363136	+	0.220948i
$913$	26.5760	+	46.0310i	0.879537	+	1.52340i
$914$	3.24539	−	5.62118i	0.107348	−	0.185932i
$915$	11.0225	+	0.253632i	0.364391	+	0.00838481i
$916$	−20.7317			−0.684996
$917$		−	4.31359i		−	0.142447i
$918$	6.32174	−	9.38843i	0.208648	−	0.309864i
$919$			24.2859i			0.801120i	0.916271	+	0.400560i	$0.131184\pi$
$919$			24.2859i			0.801120i	−0.916271	+	0.400560i	$0.868816\pi$
$920$	3.74149	+	2.16015i	0.123353	+	0.0712181i
$921$	8.57697	+	15.6780i	0.282621	+	0.516606i
$922$	4.65733			0.153381
$923$	17.6513	−	10.1910i	0.581000	−	0.335441i
$924$	2.17888	+	3.98281i	0.0716800	+	0.131025i
$925$	−25.6673	+	5.49339i	−0.843935	+	0.180622i
$926$	15.7233			0.516701
$927$	14.0444	−	7.26862i	0.461278	−	0.238733i
$928$	−1.51937	−	2.63163i	−0.0498757	−	0.0863873i
$929$	−9.42834	+	16.3304i	−0.309334	+	0.535782i	−0.978217	−	0.207586i	$-0.933439\pi$
$929$	−9.42834	+	16.3304i	−0.309334	+	0.535782i	0.668883	+	0.743368i	$0.266773\pi$
$930$	0.209549	−	9.10667i	0.00687137	−	0.298619i
$931$	−43.4397	−	25.0799i	−1.42368	−	0.821961i
$932$	−15.3633			−0.503242
$933$	−15.2769	−	9.29513i	−0.500143	−	0.304309i
$934$	13.1700			0.430937
$935$	−9.80780			−0.320749
$936$	5.27998	−	8.24455i	0.172582	−	0.269482i
$937$	11.5374	−	19.9834i	0.376911	−	0.652829i	−0.613700	−	0.789539i	$-0.710320\pi$
$937$	11.5374	−	19.9834i	0.376911	−	0.652829i	0.990611	+	0.136710i	$0.0436530\pi$
$938$	−4.13826	−	2.38923i	−0.135119	−	0.0780110i
$939$	−40.5364	+	22.1763i	−1.32286	+	0.723697i
$940$	−9.05227	+	5.22633i	−0.295252	+	0.170464i
$941$	11.6265	+	20.1377i	0.379014	+	0.656471i	0.990919	−	0.134460i	$-0.0429300\pi$
$941$	11.6265	+	20.1377i	0.379014	+	0.656471i	−0.611905	+	0.790931i	$0.709597\pi$
$942$	1.86848	+	1.13686i	0.0608782	+	0.0370410i
$943$	−46.7489	−	26.9905i	−1.52235	−	0.878932i
$944$	−3.50847	+	2.02562i	−0.114191	+	0.0659282i
$945$	1.71809	+	1.15688i	0.0558894	+	0.0376333i
$946$	−26.5323	+	45.9554i	−0.862641	+	1.49414i
$947$			56.0463i			1.82126i	0.413224	+	0.910629i	$0.364403\pi$
$947$			56.0463i			1.82126i	−0.413224	+	0.910629i	$0.635597\pi$
$948$	−0.499222	+	21.6954i	−0.0162140	+	0.704635i
$949$		−	36.4981i		−	1.18478i
$950$	15.9909	+	27.6971i	0.518814	+	0.898611i
$951$	1.04961	+	1.91859i	0.0340359	+	0.0622147i
$952$	0.524638	+	0.908700i	0.0170036	+	0.0294511i
$953$	−1.46795	+	2.54256i	−0.0475515	+	0.0823616i	−0.888821	−	0.458254i	$-0.848475\pi$
$953$	−1.46795	+	2.54256i	−0.0475515	+	0.0823616i	0.841270	+	0.540615i	$0.181808\pi$
$954$	−0.497216	+	0.257332i	−0.0160980	+	0.00833144i
$955$	3.13796	+	5.43511i	0.101542	+	0.175876i
$956$	6.90954	−	3.98923i	0.223471	−	0.129021i
$957$	0.658810	−	28.6309i	0.0212963	−	0.925505i
$958$	3.06704			0.0990915
$959$	6.27296			0.202565
$960$	−1.25742	+	0.687897i	−0.0405829	+	0.0222018i
$961$	4.69554	+	8.13291i	0.151469	+	0.262352i
$962$	−19.4112	+	4.15445i	−0.625841	+	0.133945i
$963$	0.658319	+	0.0303125i	0.0212140	+	0.000976806i
$964$	17.4526	+	10.0763i	0.562110	+	0.324535i
$965$	−2.24853	+	3.89457i	−0.0723828	+	0.125371i
$966$	2.26421	−	3.72132i	0.0728498	−	0.119731i
$967$			25.9355i			0.834029i	0.908900	+	0.417015i	$0.136924\pi$
$967$			25.9355i			0.834029i	−0.908900	+	0.417015i	$0.863076\pi$
$968$	−16.1140	−	9.30341i	−0.517923	−	0.299023i
$969$	13.4201	+	24.5308i	0.431116	+	0.788042i
$970$	−10.5266	+	6.07755i	−0.337989	+	0.195138i
$971$	22.6856	−	39.2926i	0.728015	−	1.26096i	−0.229706	−	0.973260i	$-0.573776\pi$
$971$	22.6856	−	39.2926i	0.728015	−	1.26096i	0.957721	−	0.287699i	$-0.0928904\pi$
$972$	9.29223	−	12.5162i	0.298048	−	0.401456i
$973$	−9.84539			−0.315629
$974$	−18.6022			−0.596052
$975$	21.3988	−	11.7067i	0.685309	−	0.374913i
$976$	6.66181	+	3.84620i	0.213239	+	0.123114i
$977$	15.8937	−	9.17625i	0.508486	−	0.293574i	−0.223725	−	0.974652i	$-0.571822\pi$
$977$	15.8937	−	9.17625i	0.508486	−	0.293574i	0.732211	+	0.681078i	$0.238489\pi$
$978$	2.10169	+	0.0483610i	0.0672048	+	0.00154641i
$979$		−	12.0385i		−	0.384751i
$980$	4.85020	−	2.80026i	0.154934	−	0.0894511i
$981$	−10.1753	+	5.26617i	−0.324871	+	0.168136i
$982$	8.27056	+	4.77501i	0.263924	+	0.152377i
$983$	52.1907			1.66463			0.832313	−	0.554306i	$-0.187016\pi$
$983$	52.1907			1.66463			0.832313	+	0.554306i	$0.187016\pi$
$984$	15.7111	−	8.59509i	0.500851	−	0.274001i
$985$	17.4541	+	10.0772i	0.556135	+	0.321085i
$986$		−	6.61908i		−	0.210795i
$987$	5.05817	+	9.24590i	0.161003	+	0.294300i
$988$	12.0933	+	20.9462i	0.384740	+	0.666389i
$989$	50.9158			1.61903
$990$	−13.4936	−	0.621318i	−0.428855	−	0.0197468i
$991$			44.7085i			1.42021i	0.704094	+	0.710107i	$0.251353\pi$
$991$			44.7085i			1.42021i	−0.704094	+	0.710107i	$0.748647\pi$
$992$	3.17770	−	5.50394i	0.100892	−	0.174750i
$993$	30.6803	−	16.7843i	0.973609	−	0.532634i
$994$			3.00854i			0.0954250i
$995$	1.45560			0.0461457
$996$	8.12037	+	14.8433i	0.257304	+	0.470329i
$997$		−	51.0299i		−	1.61613i	−0.589091	−	0.808067i	$-0.700514\pi$
$997$		−	51.0299i		−	1.61613i	0.589091	−	0.808067i	$-0.299486\pi$
$998$	−3.02563			−0.0957747
$999$	−31.2896	+	4.46759i	−0.989960	+	0.141348i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.k.a.175.6	✓	76
3.2	odd	2		1998.2.k.a.1063.33		76
9.2	odd	6		1998.2.t.a.397.34		76
9.7	even	3		666.2.t.a.619.7	yes	76
37.11	even	6		666.2.t.a.85.7	yes	76
111.11	odd	6		1998.2.t.a.307.34		76
333.11	odd	6		1998.2.k.a.1639.6		76
333.196	even	6	inner	666.2.k.a.529.25	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.6	✓	76	1.1	even	1	trivial
666.2.k.a.529.25	yes	76	333.196	even	6	inner
666.2.t.a.85.7	yes	76	37.11	even	6
666.2.t.a.619.7	yes	76	9.7	even	3
1998.2.k.a.1063.33		76	3.2	odd	2
1998.2.k.a.1639.6		76	333.11	odd	6
1998.2.t.a.307.34		76	111.11	odd	6
1998.2.t.a.397.34		76	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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.831290 - 1.51953i) q^{3} -1.00000 q^{4} +0.827506i q^{5} +(-1.51953 + 0.831290i) q^{6} +(0.240855 - 0.417173i) q^{7} +1.00000i q^{8} +(-1.61792 + 2.52633i) q^{9} +0.827506 q^{10} +(2.72061 + 4.71223i) q^{11} +(0.831290 + 1.51953i) q^{12} +3.26345i q^{13} +(-0.417173 - 0.240855i) q^{14} +(1.25742 - 0.687897i) q^{15} +1.00000 q^{16} +(1.88641 + 1.08912i) q^{17} +(2.52633 + 1.61792i) q^{18} +(-6.41844 + 3.70569i) q^{19} -0.827506i q^{20} +(-0.834125 - 0.0191936i) q^{21} +(4.71223 - 2.72061i) q^{22} +(-4.52141 - 2.61044i) q^{23} +(1.51953 - 0.831290i) q^{24} +4.31523 q^{25} +3.26345 q^{26} +(5.18378 + 0.358350i) q^{27} +(-0.240855 + 0.417173i) q^{28} +(2.63163 - 1.51937i) q^{29} +(-0.687897 - 1.25742i) q^{30} +(5.50394 + 3.17770i) q^{31} -1.00000i q^{32} +(4.89874 - 8.05126i) q^{33} +(1.08912 - 1.88641i) q^{34} +(0.345213 + 0.199309i) q^{35} +(1.61792 - 2.52633i) q^{36} +(-5.94806 + 1.27302i) q^{37} +(3.70569 + 6.41844i) q^{38} +(4.95889 - 2.71287i) q^{39} -0.827506 q^{40} +10.3395 q^{41} +(-0.0191936 + 0.834125i) q^{42} +(-8.44579 + 4.87618i) q^{43} +(-2.72061 - 4.71223i) q^{44} +(-2.09055 - 1.33883i) q^{45} +(-2.61044 + 4.52141i) q^{46} +(-6.31576 - 10.9392i) q^{47} +(-0.831290 - 1.51953i) q^{48} +(3.38398 + 5.86122i) q^{49} -4.31523i q^{50} +(0.0867912 - 3.77181i) q^{51} -3.26345i q^{52} +(-0.0933100 + 0.161618i) q^{53} +(0.358350 - 5.18378i) q^{54} +(-3.89940 + 2.25132i) q^{55} +(0.417173 + 0.240855i) q^{56} +(10.9665 + 6.67248i) q^{57} +(-1.51937 - 2.63163i) q^{58} +(-3.50847 + 2.02562i) q^{59} +(-1.25742 + 0.687897i) q^{60} +(6.66181 + 3.84620i) q^{61} +(3.17770 - 5.50394i) q^{62} +(0.664234 + 1.28343i) q^{63} -1.00000 q^{64} -2.70052 q^{65} +(-8.05126 - 4.89874i) q^{66} +9.91978 q^{67} +(-1.88641 - 1.08912i) q^{68} +(-0.208024 + 9.04042i) q^{69} +(0.199309 - 0.345213i) q^{70} +(-3.12277 - 5.40879i) q^{71} +(-2.52633 - 1.61792i) q^{72} -11.1839 q^{73} +(1.27302 + 5.94806i) q^{74} +(-3.58721 - 6.55711i) q^{75} +(6.41844 - 3.70569i) q^{76} +2.62109 q^{77} +(-2.71287 - 4.95889i) q^{78} +(10.8506 + 6.26459i) q^{79} +0.827506i q^{80} +(-3.76470 - 8.17478i) q^{81} -10.3395i q^{82} +9.76840 q^{83} +(0.834125 + 0.0191936i) q^{84} +(-0.901251 + 1.56101i) q^{85} +(4.87618 + 8.44579i) q^{86} +(-4.49636 - 2.73579i) q^{87} +(-4.71223 + 2.72061i) q^{88} +(-1.91605 - 1.10623i) q^{89} +(-1.33883 + 2.09055i) q^{90} +(1.36142 + 0.786017i) q^{91} +(4.52141 + 2.61044i) q^{92} +(0.253229 - 11.0050i) q^{93} +(-10.9392 + 6.31576i) q^{94} +(-3.06648 - 5.31130i) q^{95} +(-1.51953 + 0.831290i) q^{96} +(-12.7209 + 7.34441i) q^{97} +(5.86122 - 3.38398i) q^{98} +(-16.3064 - 0.750832i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) \) 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

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