LMFDB - Embedded newform 222.2.j.b.85.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [222,2,Mod(85,222)] 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("222.85"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(222, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 222 = 2 \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	222.j (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.77267892487$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.303595776.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.3
Root			$-1.26217 + 1.18614i$ of defining polynomial
Character	$\chi$	$=$	222.85
Dual form			222.2.j.b.175.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.05446 - 1.18614i) q^{5} -1.00000i q^{6} +(0.762169 - 1.32012i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -2.37228 q^{10} -0.152056 q^{11} +(-0.500000 - 0.866025i) q^{12} +(2.41819 + 1.39614i) q^{13} -1.52434i q^{14} +(-2.05446 + 1.18614i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.454090 - 0.262169i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(4.24060 + 2.44831i) q^{19} +(-2.05446 + 1.18614i) q^{20} +(-0.762169 - 1.32012i) q^{21} +(-0.131685 + 0.0760282i) q^{22} +4.63325i q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.313859 + 0.543620i) q^{25} +2.79229 q^{26} -1.00000 q^{27} +(-0.762169 - 1.32012i) q^{28} +2.90818i q^{29} +(-1.18614 + 2.05446i) q^{30} +1.35977i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.0760282 + 0.131685i) q^{33} +(0.262169 - 0.454090i) q^{34} +(-3.13168 + 1.80808i) q^{35} -1.00000 q^{36} +(1.62194 + 5.86253i) q^{37} +4.89662 q^{38} +(2.41819 - 1.39614i) q^{39} +(-1.18614 + 2.05446i) q^{40} +(2.91819 - 5.05446i) q^{41} +(-1.32012 - 0.762169i) q^{42} -6.73758i q^{43} +(-0.0760282 + 0.131685i) q^{44} +2.37228i q^{45} +(2.31662 + 4.01251i) q^{46} -5.72747 q^{47} -1.00000 q^{48} +(2.33820 + 4.04988i) q^{49} +(0.543620 + 0.313859i) q^{50} -0.524338i q^{51} +(2.41819 - 1.39614i) q^{52} +(-1.57999 - 2.73663i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.312393 + 0.180360i) q^{55} +(-1.32012 - 0.762169i) q^{56} +(4.24060 - 2.44831i) q^{57} +(1.45409 + 2.51856i) q^{58} +(-7.21324 + 4.16457i) q^{59} +2.37228i q^{60} +(7.35494 + 4.24638i) q^{61} +(0.679885 + 1.17759i) q^{62} -1.52434 q^{63} -1.00000 q^{64} +(-3.31205 - 5.73663i) q^{65} +0.152056i q^{66} +(-5.92674 + 10.2654i) q^{67} -0.524338i q^{68} +(4.01251 + 2.31662i) q^{69} +(-1.80808 + 3.13168i) q^{70} +(-2.29625 + 3.97723i) q^{71} +(-0.866025 + 0.500000i) q^{72} +7.25181 q^{73} +(4.33591 + 4.26613i) q^{74} +0.627719 q^{75} +(4.24060 - 2.44831i) q^{76} +(-0.115893 + 0.200732i) q^{77} +(1.39614 - 2.41819i) q^{78} +(-11.2944 - 6.52085i) q^{79} +2.37228i q^{80} +(-0.500000 + 0.866025i) q^{81} -5.83638i q^{82} +(-6.31662 - 10.9407i) q^{83} -1.52434 q^{84} -1.24388 q^{85} +(-3.36879 - 5.83492i) q^{86} +(2.51856 + 1.45409i) q^{87} +0.152056i q^{88} +(11.2358 - 6.48697i) q^{89} +(1.18614 + 2.05446i) q^{90} +(3.68614 - 2.12819i) q^{91} +(4.01251 + 2.31662i) q^{92} +(1.17759 + 0.679885i) q^{93} +(-4.96014 + 2.86374i) q^{94} +(-5.80808 - 10.0599i) q^{95} +(-0.866025 + 0.500000i) q^{96} -13.9407i q^{97} +(4.04988 + 2.33820i) q^{98} +(0.0760282 + 0.131685i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{7} - 4 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} - 6 q^{13} - 4 q^{16} + 6 q^{17} + 6 q^{19} + 4 q^{21} - 6 q^{22} + 14 q^{25} + 16 q^{26} - 8 q^{27} + 4 q^{28} + 2 q^{30} - 2 q^{33}+ \cdots + 2 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^7 - 4 * q^9 + 4 * q^10 - 4 * q^11 - 4 * q^12 - 6 * q^13 - 4 * q^16 + 6 * q^17 + 6 * q^19 + 4 * q^21 - 6 * q^22 + 14 * q^25 + 16 * q^26 - 8 * q^27 + 4 * q^28 + 2 * q^30 - 2 * q^33 - 8 * q^34 - 30 * q^35 - 8 * q^36 + 12 * q^37 - 4 * q^38 - 6 * q^39 + 2 * q^40 - 2 * q^41 - 6 * q^42 - 2 * q^44 - 8 * q^46 - 28 * q^47 - 8 * q^48 + 10 * q^49 - 6 * q^52 + 4 * q^53 + 30 * q^55 - 6 * q^56 + 6 * q^57 + 14 * q^58 + 12 * q^59 - 36 * q^61 + 10 * q^62 + 8 * q^63 - 8 * q^64 + 4 * q^65 - 8 * q^67 - 2 * q^70 + 6 * q^71 + 20 * q^73 + 24 * q^74 + 28 * q^75 + 6 * q^76 - 12 * q^77 + 8 * q^78 - 24 * q^79 - 4 * q^81 - 24 * q^83 + 8 * q^84 - 8 * q^85 + 18 * q^86 - 24 * q^87 - 42 * q^89 - 2 * q^90 + 18 * q^91 + 12 * q^93 - 30 * q^94 - 34 * q^95 + 12 * q^98 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/222\mathbb{Z}\right)^\times$.

$n$	$149$	$187$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.05446	−	1.18614i	−0.918781	−	0.530458i	−0.0355348	−	0.999368i	$-0.511313\pi$
$5$	−2.05446	−	1.18614i	−0.918781	−	0.530458i	−0.883246	+	0.468910i	$0.844647\pi$
$6$		−	1.00000i		−	0.408248i
$7$	0.762169	−	1.32012i	0.288073	−	0.498957i	−0.685277	−	0.728283i	$-0.740319\pi$
$7$	0.762169	−	1.32012i	0.288073	−	0.498957i	0.973350	+	0.229326i	$0.0736522\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−2.37228			−0.750181
$11$	−0.152056			−0.0458468			−0.0229234	−	0.999737i	$-0.507297\pi$
$11$	−0.152056			−0.0458468			−0.0229234	+	0.999737i	$0.507297\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	2.41819	+	1.39614i	0.670686	+	0.387221i	0.796336	−	0.604854i	$-0.206769\pi$
$13$	2.41819	+	1.39614i	0.670686	+	0.387221i	−0.125651	+	0.992075i	$0.540102\pi$
$14$		−	1.52434i		−	0.407396i
$15$	−2.05446	+	1.18614i	−0.530458	+	0.306260i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.454090	−	0.262169i	0.110133	−	0.0635853i	−0.443922	−	0.896066i	$-0.646413\pi$
$17$	0.454090	−	0.262169i	0.110133	−	0.0635853i	0.554055	+	0.832480i	$0.313080\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	4.24060	+	2.44831i	0.972860	+	0.561681i	0.900107	−	0.435669i	$-0.143488\pi$
$19$	4.24060	+	2.44831i	0.972860	+	0.561681i	0.0727528	+	0.997350i	$0.476822\pi$
$20$	−2.05446	+	1.18614i	−0.459390	+	0.265229i
$21$	−0.762169	−	1.32012i	−0.166319	−	0.288073i
$22$	−0.131685	+	0.0760282i	−0.0280753	+	0.0162093i
$23$			4.63325i			0.966099i	0.875593	+	0.483050i	$0.160471\pi$
$23$			4.63325i			0.966099i	−0.875593	+	0.483050i	$0.839529\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	0.313859	+	0.543620i	0.0627719	+	0.108724i
$26$	2.79229			0.547613
$27$	−1.00000			−0.192450
$28$	−0.762169	−	1.32012i	−0.144036	−	0.249478i
$29$			2.90818i			0.540035i	0.962855	+	0.270018i	$0.0870296\pi$
$29$			2.90818i			0.540035i	−0.962855	+	0.270018i	$0.912970\pi$
$30$	−1.18614	+	2.05446i	−0.216559	+	0.375091i
$31$			1.35977i			0.244222i	0.992516	+	0.122111i	$0.0389664\pi$
$31$			1.35977i			0.244222i	−0.992516	+	0.122111i	$0.961034\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−0.0760282	+	0.131685i	−0.0132348	+	0.0229234i
$34$	0.262169	−	0.454090i	0.0449616	−	0.0778758i
$35$	−3.13168	+	1.80808i	−0.529351	+	0.305621i
$36$	−1.00000			−0.166667
$37$	1.62194	+	5.86253i	0.266645	+	0.963795i
$37$	1.62194	+	5.86253i	0.266645	+	0.963795i
$38$	4.89662			0.794337
$39$	2.41819	−	1.39614i	0.387221	−	0.223562i
$40$	−1.18614	+	2.05446i	−0.187545	+	0.324838i
$41$	2.91819	−	5.05446i	0.455745	−	0.789373i	−0.542986	−	0.839742i	$-0.682706\pi$
$41$	2.91819	−	5.05446i	0.455745	−	0.789373i	0.998731	+	0.0503685i	$0.0160396\pi$
$42$	−1.32012	−	0.762169i	−0.203698	−	0.117605i
$43$		−	6.73758i		−	1.02747i	−0.857948	−	0.513736i	$-0.828261\pi$
$43$		−	6.73758i		−	1.02747i	0.857948	−	0.513736i	$-0.171739\pi$
$44$	−0.0760282	+	0.131685i	−0.0114617	+	0.0198522i
$45$			2.37228i			0.353639i
$46$	2.31662	+	4.01251i	0.341568	+	0.591613i
$47$	−5.72747			−0.835438			−0.417719	−	0.908576i	$-0.637170\pi$
$47$	−5.72747			−0.835438			−0.417719	+	0.908576i	$0.637170\pi$
$48$	−1.00000			−0.144338
$49$	2.33820	+	4.04988i	0.334028	+	0.578554i
$50$	0.543620	+	0.313859i	0.0768795	+	0.0443864i
$51$		−	0.524338i		−	0.0734220i
$52$	2.41819	−	1.39614i	0.335343	−	0.193610i
$53$	−1.57999	−	2.73663i	−0.217029	−	0.375905i	0.736869	−	0.676035i	$-0.236303\pi$
$53$	−1.57999	−	2.73663i	−0.217029	−	0.375905i	−0.953898	+	0.300130i	$0.902970\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	0.312393	+	0.180360i	0.0421231	+	0.0243198i
$56$	−1.32012	−	0.762169i	−0.176408	−	0.101849i
$57$	4.24060	−	2.44831i	0.561681	−	0.324287i
$58$	1.45409	+	2.51856i	0.190931	+	0.330703i
$59$	−7.21324	+	4.16457i	−0.939084	+	0.542181i	−0.889673	−	0.456598i	$-0.849068\pi$
$59$	−7.21324	+	4.16457i	−0.939084	+	0.542181i	−0.0494112	+	0.998779i	$0.515734\pi$
$60$			2.37228i			0.306260i
$61$	7.35494	+	4.24638i	0.941704	+	0.543693i	0.890494	−	0.454995i	$-0.150359\pi$
$61$	7.35494	+	4.24638i	0.941704	+	0.543693i	0.0512097	+	0.998688i	$0.483692\pi$
$62$	0.679885	+	1.17759i	0.0863454	+	0.149555i
$63$	−1.52434			−0.192049
$64$	−1.00000			−0.125000
$65$	−3.31205	−	5.73663i	−0.410809	−	0.711541i
$66$			0.152056i			0.0187169i
$67$	−5.92674	+	10.2654i	−0.724066	+	1.25412i	0.235291	+	0.971925i	$0.424396\pi$
$67$	−5.92674	+	10.2654i	−0.724066	+	1.25412i	−0.959357	+	0.282194i	$0.908938\pi$
$68$		−	0.524338i		−	0.0635853i
$69$	4.01251	+	2.31662i	0.483050	+	0.278889i
$70$	−1.80808	+	3.13168i	−0.216107	+	0.374308i
$71$	−2.29625	+	3.97723i	−0.272515	+	0.472010i	−0.969505	−	0.245071i	$-0.921189\pi$
$71$	−2.29625	+	3.97723i	−0.272515	+	0.472010i	0.696990	+	0.717081i	$0.254522\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	7.25181			0.848760			0.424380	−	0.905484i	$-0.360492\pi$
$73$	7.25181			0.848760			0.424380	+	0.905484i	$0.360492\pi$
$74$	4.33591	+	4.26613i	0.504039	+	0.495928i
$75$	0.627719			0.0724827
$76$	4.24060	−	2.44831i	0.486430	−	0.280840i
$77$	−0.115893	+	0.200732i	−0.0132072	+	0.0228755i
$78$	1.39614	−	2.41819i	0.158082	−	0.273806i
$79$	−11.2944	−	6.52085i	−1.27072	−	0.733653i	−0.295599	−	0.955312i	$-0.595519\pi$
$79$	−11.2944	−	6.52085i	−1.27072	−	0.733653i	−0.975124	+	0.221659i	$0.928853\pi$
$80$			2.37228i			0.265229i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		−	5.83638i		−	0.644521i
$83$	−6.31662	−	10.9407i	−0.693340	−	1.20090i	−0.970737	−	0.240144i	$-0.922805\pi$
$83$	−6.31662	−	10.9407i	−0.693340	−	1.20090i	0.277398	−	0.960755i	$-0.410528\pi$
$84$	−1.52434			−0.166319
$85$	−1.24388			−0.134917
$86$	−3.36879	−	5.83492i	−0.363266	−	0.629195i
$87$	2.51856	+	1.45409i	0.270018	+	0.155895i
$88$			0.152056i			0.0162093i
$89$	11.2358	−	6.48697i	1.19099	−	0.687618i	0.232458	−	0.972606i	$-0.425323\pi$
$89$	11.2358	−	6.48697i	1.19099	−	0.687618i	0.958531	+	0.284989i	$0.0919898\pi$
$90$	1.18614	+	2.05446i	0.125030	+	0.216559i
$91$	3.68614	−	2.12819i	0.386413	−	0.223095i
$92$	4.01251	+	2.31662i	0.418333	+	0.241525i
$93$	1.17759	+	0.679885i	0.122111	+	0.0705008i
$94$	−4.96014	+	2.86374i	−0.511599	+	0.295372i
$95$	−5.80808	−	10.0599i	−0.595896	−	1.03212i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$		−	13.9407i		−	1.41547i	−0.706480	−	0.707733i	$-0.749718\pi$
$97$		−	13.9407i		−	1.41547i	0.706480	−	0.707733i	$-0.250282\pi$
$98$	4.04988	+	2.33820i	0.409099	+	0.236194i
$99$	0.0760282	+	0.131685i	0.00764113	+	0.0132348i
$100$	0.627719			0.0627719
$101$	−2.85347			−0.283931			−0.141966	−	0.989872i	$-0.545342\pi$
$101$	−2.85347			−0.283931			−0.141966	+	0.989872i	$0.545342\pi$
$102$	−0.262169	−	0.454090i	−0.0259586	−	0.0449616i
$103$		−	2.77615i		−	0.273542i	−0.990603	−	0.136771i	$-0.956328\pi$
$103$		−	2.77615i		−	0.273542i	0.990603	−	0.136771i	$-0.0436724\pi$
$104$	1.39614	−	2.41819i	0.136903	−	0.237123i
$105$			3.61616i			0.352901i
$106$	−2.73663	−	1.57999i	−0.265805	−	0.153463i
$107$	−9.49241	+	16.4413i	−0.917665	+	1.58944i	−0.114714	+	0.993399i	$0.536595\pi$
$107$	−9.49241	+	16.4413i	−0.917665	+	1.58944i	−0.802951	+	0.596045i	$0.796738\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−12.3011	+	7.10204i	−1.17823	+	0.680252i	−0.955605	−	0.294651i	$-0.904796\pi$
$109$	−12.3011	+	7.10204i	−1.17823	+	0.680252i	−0.222627	+	0.974904i	$0.571463\pi$
$110$	0.360721			0.0343934
$111$	5.88807	+	1.52663i	0.558871	+	0.144901i
$112$	−1.52434			−0.144036
$113$	17.1962	−	9.92820i	1.61768	−	0.933967i	0.630159	−	0.776466i	$-0.282990\pi$
$113$	17.1962	−	9.92820i	1.61768	−	0.933967i	0.987519	−	0.157501i	$-0.0503437\pi$
$114$	2.44831	−	4.24060i	0.229305	−	0.397168i
$115$	5.49569	−	9.51881i	0.512475	−	0.887633i
$116$	2.51856	+	1.45409i	0.233842	+	0.135009i
$117$		−	2.79229i		−	0.258147i
$118$	−4.16457	+	7.21324i	−0.383380	+	0.664033i
$119$		−	0.799268i		−	0.0732688i
$120$	1.18614	+	2.05446i	0.108279	+	0.187545i
$121$	−10.9769			−0.997898
$122$	8.49275			0.768898
$123$	−2.91819	−	5.05446i	−0.263124	−	0.455745i
$124$	1.17759	+	0.679885i	0.105751	+	0.0610555i
$125$			10.3723i			0.927725i
$126$	−1.32012	+	0.762169i	−0.117605	+	0.0678994i
$127$	−9.52710	−	16.5014i	−0.845394	−	1.46426i	−0.885279	−	0.465061i	$-0.846033\pi$
$127$	−9.52710	−	16.5014i	−0.845394	−	1.46426i	0.0398851	−	0.999204i	$-0.487301\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−5.83492	−	3.36879i	−0.513736	−	0.296605i
$130$	−5.73663	−	3.31205i	−0.503136	−	0.290486i
$131$	12.3894	−	7.15301i	1.08246	−	0.624961i	0.150904	−	0.988548i	$-0.451781\pi$
$131$	12.3894	−	7.15301i	1.08246	−	0.624961i	0.931560	+	0.363587i	$0.118448\pi$
$132$	0.0760282	+	0.131685i	0.00661741	+	0.0114617i
$133$	6.46410	−	3.73205i	0.560509	−	0.323610i
$134$			11.8535i			1.02398i
$135$	2.05446	+	1.18614i	0.176819	+	0.102087i
$136$	−0.262169	−	0.454090i	−0.0224808	−	0.0389379i
$137$	−6.34916			−0.542445			−0.271223	−	0.962517i	$-0.587428\pi$
$137$	−6.34916			−0.542445			−0.271223	+	0.962517i	$0.587428\pi$
$138$	4.63325			0.394408
$139$	−1.77796	−	3.07952i	−0.150805	−	0.261201i	0.780719	−	0.624882i	$-0.214853\pi$
$139$	−1.77796	−	3.07952i	−0.150805	−	0.261201i	−0.931524	+	0.363681i	$0.881520\pi$
$140$			3.61616i			0.305621i
$141$	−2.86374	+	4.96014i	−0.241170	+	0.417719i
$142$			4.59251i			0.385395i
$143$	−0.367702	−	0.212293i	−0.0307488	−	0.0177528i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	3.44951	−	5.97473i	0.286466	−	0.496174i
$146$	6.28025	−	3.62590i	0.519757	−	0.300082i
$147$	4.67639			0.385702
$148$	5.88807	+	1.52663i	0.483997	+	0.125488i
$149$	0.964787			0.0790385			0.0395192	−	0.999219i	$-0.487417\pi$
$149$	0.964787			0.0790385			0.0395192	+	0.999219i	$0.487417\pi$
$150$	0.543620	−	0.313859i	0.0443864	−	0.0256265i
$151$	−4.21506	+	7.30069i	−0.343017	+	0.594122i	−0.984991	−	0.172604i	$-0.944782\pi$
$151$	−4.21506	+	7.30069i	−0.343017	+	0.594122i	0.641975	+	0.766726i	$0.278115\pi$
$152$	2.44831	−	4.24060i	0.198584	−	0.343958i
$153$	−0.454090	−	0.262169i	−0.0367110	−	0.0211951i
$154$			0.231785i			0.0186778i
$155$	1.61288	−	2.79359i	0.129549	−	0.224386i
$156$		−	2.79229i		−	0.223562i
$157$	−3.25242	−	5.63336i	−0.259572	−	0.449591i	0.706556	−	0.707658i	$-0.250248\pi$
$157$	−3.25242	−	5.63336i	−0.259572	−	0.449591i	−0.966127	+	0.258066i	$0.916915\pi$
$158$	−13.0417			−1.03754
$159$	−3.15999			−0.250603
$160$	1.18614	+	2.05446i	0.0937727	+	0.162419i
$161$	6.11642	+	3.53132i	0.482042	+	0.278307i
$162$			1.00000i			0.0785674i
$163$	5.88834	−	3.39963i	0.461210	−	0.266280i	−0.251343	−	0.967898i	$-0.580872\pi$
$163$	5.88834	−	3.39963i	0.461210	−	0.266280i	0.712553	+	0.701618i	$0.247539\pi$
$164$	−2.91819	−	5.05446i	−0.227872	−	0.394687i
$165$	0.312393	−	0.180360i	0.0243198	−	0.0140410i
$166$	−10.9407	−	6.31662i	−0.849164	−	0.490265i
$167$	−0.339746	−	0.196152i	−0.0262903	−	0.0151787i	0.486797	−	0.873515i	$-0.338165\pi$
$167$	−0.339746	−	0.196152i	−0.0262903	−	0.0151787i	−0.513088	+	0.858336i	$0.671498\pi$
$168$	−1.32012	+	0.762169i	−0.101849	+	0.0588026i
$169$	−2.60157	−	4.50605i	−0.200121	−	0.346619i
$170$	−1.07723	+	0.621938i	−0.0826197	+	0.0477005i
$171$		−	4.89662i		−	0.374454i
$172$	−5.83492	−	3.36879i	−0.444908	−	0.256868i
$173$	6.66603	+	11.5459i	0.506809	+	0.877819i	0.999969	+	0.00788052i	$0.00250847\pi$
$173$	6.66603	+	11.5459i	0.506809	+	0.877819i	−0.493160	+	0.869939i	$0.664158\pi$
$174$	2.90818			0.220469
$175$	0.956855			0.0723315
$176$	0.0760282	+	0.131685i	0.00573084	+	0.00992611i
$177$			8.32914i			0.626056i
$178$	6.48697	−	11.2358i	0.486219	−	0.842156i
$179$			20.4173i			1.52606i	0.646361	+	0.763031i	$0.276290\pi$
$179$			20.4173i			1.52606i	−0.646361	+	0.763031i	$0.723710\pi$
$180$	2.05446	+	1.18614i	0.153130	+	0.0884097i
$181$	−0.931218	+	1.61292i	−0.0692169	+	0.119887i	−0.898557	−	0.438857i	$-0.855383\pi$
$181$	−0.931218	+	1.61292i	−0.0692169	+	0.119887i	0.829340	+	0.558744i	$0.188717\pi$
$182$	2.12819	−	3.68614i	0.157752	−	0.273235i
$183$	7.35494	−	4.24638i	0.543693	−	0.313901i
$184$	4.63325			0.341568
$185$	3.62159	−	13.9682i	0.266265	−	1.02696i
$186$	1.35977			0.0997031
$187$	−0.0690473	+	0.0398645i	−0.00504924	+	0.00291518i
$188$	−2.86374	+	4.96014i	−0.208859	+	0.361755i
$189$	−0.762169	+	1.32012i	−0.0554396	+	0.0960243i
$190$	−10.0599	−	5.80808i	−0.729821	−	0.421362i
$191$			14.6101i			1.05715i	0.848886	+	0.528576i	$0.177274\pi$
$191$			14.6101i			1.05715i	−0.848886	+	0.528576i	$0.822726\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$			3.61158i			0.259967i	0.991516	+	0.129984i	$0.0414925\pi$
$193$			3.61158i			0.259967i	−0.991516	+	0.129984i	$0.958508\pi$
$194$	−6.97036	−	12.0730i	−0.500443	−	0.866792i
$195$	−6.62409			−0.474361
$196$	4.67639			0.334028
$197$	9.07155	+	15.7124i	0.646321	+	1.11946i	0.983995	+	0.178198i	$0.0570266\pi$
$197$	9.07155	+	15.7124i	0.646321	+	1.11946i	−0.337674	+	0.941263i	$0.609640\pi$
$198$	0.131685	+	0.0760282i	0.00935843	+	0.00540309i
$199$			13.0557i			0.925491i	0.886491	+	0.462745i	$0.153136\pi$
$199$			13.0557i			0.925491i	−0.886491	+	0.462745i	$0.846864\pi$
$200$	0.543620	−	0.313859i	0.0384398	−	0.0221932i
$201$	5.92674	+	10.2654i	0.418040	+	0.724066i
$202$	−2.47118	+	1.42674i	−0.173872	+	0.100385i
$203$	3.83913	+	2.21652i	0.269454	+	0.155569i
$204$	−0.454090	−	0.262169i	−0.0317926	−	0.0183555i
$205$	−11.9906	+	6.92277i	−0.837459	+	0.483507i
$206$	−1.38807	−	2.40421i	−0.0967117	−	0.167509i
$207$	4.01251	−	2.31662i	0.278889	−	0.161017i
$208$		−	2.79229i		−	0.193610i
$209$	−0.644810	−	0.372281i	−0.0446025	−	0.0257512i
$210$	1.80808	+	3.13168i	0.124769	+	0.216107i
$211$	0.157587			0.0108488			0.00542438	−	0.999985i	$-0.498273\pi$
$211$	0.157587			0.0108488			0.00542438	+	0.999985i	$0.498273\pi$
$212$	−3.15999			−0.217029
$213$	2.29625	+	3.97723i	0.157337	+	0.272515i
$214$			18.9848i			1.29777i
$215$	−7.99172	+	13.8421i	−0.545031	+	0.944021i
$216$			1.00000i			0.0680414i
$217$	1.79505	+	1.03637i	0.121856	+	0.0703537i
$218$	−7.10204	+	12.3011i	−0.481011	+	0.833135i
$219$	3.62590	−	6.28025i	0.245016	−	0.424380i
$220$	0.312393	−	0.180360i	0.0210616	−	0.0121599i
$221$	1.46410			0.0984861
$222$	5.86253	−	1.62194i	0.393468	−	0.108857i
$223$	−13.5578			−0.907899			−0.453950	−	0.891027i	$-0.649985\pi$
$223$	−13.5578			−0.907899			−0.453950	+	0.891027i	$0.649985\pi$
$224$	−1.32012	+	0.762169i	−0.0882039	+	0.0509246i
$225$	0.313859	−	0.543620i	0.0209240	−	0.0362414i
$226$	9.92820	−	17.1962i	0.660414	−	1.14387i
$227$	15.7297	+	9.08156i	1.04402	+	0.602764i	0.920969	−	0.389636i	$-0.127399\pi$
$227$	15.7297	+	9.08156i	1.04402	+	0.602764i	0.123049	+	0.992401i	$0.460733\pi$
$228$		−	4.89662i		−	0.324287i
$229$	−11.3206	+	19.6078i	−0.748086	+	1.29572i	0.200653	+	0.979662i	$0.435693\pi$
$229$	−11.3206	+	19.6078i	−0.748086	+	1.29572i	−0.948739	+	0.316060i	$0.897640\pi$
$230$		−	10.9914i		−	0.724750i
$231$	0.115893	+	0.200732i	0.00762518	+	0.0132072i
$232$	2.90818			0.190931
$233$	2.26097			0.148121			0.0740605	−	0.997254i	$-0.476404\pi$
$233$	2.26097			0.148121			0.0740605	+	0.997254i	$0.476404\pi$
$234$	−1.39614	−	2.41819i	−0.0912688	−	0.158082i
$235$	11.7668	+	6.79359i	0.767584	+	0.443165i
$236$			8.32914i			0.542181i
$237$	−11.2944	+	6.52085i	−0.733653	+	0.423575i
$238$	−0.399634	−	0.692186i	−0.0259044	−	0.0448678i
$239$	−6.90085	+	3.98421i	−0.446379	+	0.257717i	−0.706300	−	0.707913i	$-0.749637\pi$
$239$	−6.90085	+	3.98421i	−0.446379	+	0.257717i	0.259921	+	0.965630i	$0.416304\pi$
$240$	2.05446	+	1.18614i	0.132615	+	0.0765651i
$241$	8.51459	+	4.91590i	0.548473	+	0.316661i	0.748506	−	0.663128i	$-0.230772\pi$
$241$	8.51459	+	4.91590i	0.548473	+	0.316661i	−0.200033	+	0.979789i	$0.564105\pi$
$242$	−9.50626	+	5.48844i	−0.611085	+	0.352810i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	7.35494	−	4.24638i	0.470852	−	0.271846i
$245$		−	11.0937i		−	0.708752i
$246$	−5.05446	−	2.91819i	−0.322260	−	0.186057i
$247$	6.83638	+	11.8410i	0.434989	+	0.753422i
$248$	1.35977			0.0863454
$249$	−12.6332			−0.800600
$250$	5.18614	+	8.98266i	0.328000	+	0.568113i
$251$		−	9.34623i		−	0.589929i	−0.955508	−	0.294964i	$-0.904692\pi$
$251$		−	9.34623i		−	0.589929i	0.955508	−	0.294964i	$-0.0953078\pi$
$252$	−0.762169	+	1.32012i	−0.0480121	+	0.0831594i
$253$		−	0.704516i		−	0.0442925i
$254$	−16.5014	−	9.52710i	−1.03539	−	0.597784i
$255$	−0.621938	+	1.07723i	−0.0389473	+	0.0674587i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.7762	+	6.79902i	−0.734582	+	0.424111i	−0.820096	−	0.572226i	$-0.806080\pi$
$257$	−11.7762	+	6.79902i	−0.734582	+	0.424111i	0.0855141	+	0.996337i	$0.472747\pi$
$258$	−6.73758			−0.419464
$259$	8.97541	+	2.32710i	0.557705	+	0.144599i
$260$	−6.62409			−0.410809
$261$	2.51856	−	1.45409i	0.155895	−	0.0900059i
$262$	7.15301	−	12.3894i	0.441914	−	0.765418i
$263$	6.83638	−	11.8410i	0.421549	−	0.730145i	−0.574542	−	0.818475i	$-0.694820\pi$
$263$	6.83638	−	11.8410i	0.421549	−	0.730145i	0.996091	+	0.0883302i	$0.0281531\pi$
$264$	0.131685	+	0.0760282i	0.00810464	+	0.00467921i
$265$			7.49638i			0.460499i
$266$	3.73205	−	6.46410i	0.228827	−	0.396339i
$267$		−	12.9739i		−	0.793993i
$268$	5.92674	+	10.2654i	0.362033	+	0.627060i
$269$	1.21729			0.0742197			0.0371098	−	0.999311i	$-0.488185\pi$
$269$	1.21729			0.0742197			0.0371098	+	0.999311i	$0.488185\pi$
$270$	2.37228			0.144372
$271$	−2.08337	−	3.60851i	−0.126556	−	0.219201i	0.795784	−	0.605580i	$-0.207059\pi$
$271$	−2.08337	−	3.60851i	−0.126556	−	0.219201i	−0.922340	+	0.386379i	$0.873726\pi$
$272$	−0.454090	−	0.262169i	−0.0275332	−	0.0158963i
$273$		−	4.25639i		−	0.257608i
$274$	−5.49853	+	3.17458i	−0.332179	+	0.191783i
$275$	−0.0477243	−	0.0826610i	−0.00287789	−	0.00498465i
$276$	4.01251	−	2.31662i	0.241525	−	0.139444i
$277$	−23.7472	−	13.7105i	−1.42683	−	0.823783i	−0.429964	−	0.902846i	$-0.641474\pi$
$277$	−23.7472	−	13.7105i	−1.42683	−	0.823783i	−0.996870	+	0.0790632i	$0.974807\pi$
$278$	−3.07952	−	1.77796i	−0.184697	−	0.106635i
$279$	1.17759	−	0.679885i	0.0705008	−	0.0407036i
$280$	1.80808	+	3.13168i	0.108053	+	0.187154i
$281$	13.3823	−	7.72627i	0.798321	−	0.460911i	−0.0445629	−	0.999007i	$-0.514190\pi$
$281$	13.3823	−	7.72627i	0.798321	−	0.460911i	0.842884	+	0.538096i	$0.180856\pi$
$282$			5.72747i			0.341066i
$283$	16.2940	+	9.40736i	0.968579	+	0.559209i	0.898803	−	0.438353i	$-0.144438\pi$
$283$	16.2940	+	9.40736i	0.968579	+	0.559209i	0.0697762	+	0.997563i	$0.477771\pi$
$284$	2.29625	+	3.97723i	0.136258	+	0.236005i
$285$	−11.6162			−0.688082
$286$	−0.424585			−0.0251063
$287$	−4.44831	−	7.70470i	−0.262575	−	0.454794i
$288$			1.00000i			0.0589256i
$289$	−8.36253	+	14.4843i	−0.491914	+	0.852020i
$290$		−	6.89902i		−	0.405124i
$291$	−12.0730	−	6.97036i	−0.707733	−	0.408610i
$292$	3.62590	−	6.28025i	0.212190	−	0.367524i
$293$	13.4468	−	23.2905i	0.785568	−	1.36064i	−0.143091	−	0.989710i	$-0.545704\pi$
$293$	13.4468	−	23.2905i	0.785568	−	1.36064i	0.928659	−	0.370934i	$-0.120963\pi$
$294$	4.04988	−	2.33820i	0.236194	−	0.136366i
$295$	19.7591			1.15042
$296$	5.86253	−	1.62194i	0.340753	−	0.0942733i
$297$	0.152056			0.00882321
$298$	0.835530	−	0.482394i	0.0484010	−	0.0279443i
$299$	−6.46868	+	11.2041i	−0.374093	+	0.647949i
$300$	0.313859	−	0.543620i	0.0181207	−	0.0313859i
$301$	−8.89438	−	5.13518i	−0.512664	−	0.295987i
$302$			8.43012i			0.485099i
$303$	−1.42674	+	2.47118i	−0.0819639	+	0.141966i
$304$		−	4.89662i		−	0.280840i
$305$	−10.0736	−	17.4480i	−0.576813	−	0.999069i
$306$	−0.524338			−0.0299744
$307$	−16.6954			−0.952856			−0.476428	−	0.879213i	$-0.658069\pi$
$307$	−16.6954			−0.952856			−0.476428	+	0.879213i	$0.658069\pi$
$308$	0.115893	+	0.200732i	0.00660360	+	0.0114378i
$309$	−2.40421	−	1.38807i	−0.136771	−	0.0789647i
$310$		−	3.22576i		−	0.183211i
$311$	17.0507	−	9.84424i	0.966858	−	0.558216i	0.0685812	−	0.997646i	$-0.478153\pi$
$311$	17.0507	−	9.84424i	0.966858	−	0.558216i	0.898277	+	0.439430i	$0.144819\pi$
$312$	−1.39614	−	2.41819i	−0.0790411	−	0.136903i
$313$	15.0851	−	8.70939i	0.852661	−	0.492284i	−0.00888711	−	0.999961i	$-0.502829\pi$
$313$	15.0851	−	8.70939i	0.852661	−	0.492284i	0.861548	+	0.507677i	$0.169496\pi$
$314$	−5.63336	−	3.25242i	−0.317909	−	0.183545i
$315$	3.13168	+	1.80808i	0.176450	+	0.101874i
$316$	−11.2944	+	6.52085i	−0.635362	+	0.366826i
$317$	−11.1703	−	19.3476i	−0.627389	−	1.08667i	−0.988074	−	0.153982i	$-0.950790\pi$
$317$	−11.1703	−	19.3476i	−0.627389	−	1.08667i	0.360684	−	0.932688i	$-0.382543\pi$
$318$	−2.73663	+	1.57999i	−0.153463	+	0.0886017i
$319$		−	0.442208i		−	0.0247589i
$320$	2.05446	+	1.18614i	0.114848	+	0.0663073i
$321$	9.49241	+	16.4413i	0.529814	+	0.917665i
$322$	7.06264			0.393585
$323$	2.56748			0.142859
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$			1.75277i			0.0972262i
$326$	3.39963	−	5.88834i	0.188288	−	0.326125i
$327$			14.2041i			0.785488i
$328$	−5.05446	−	2.91819i	−0.279086	−	0.161130i
$329$	−4.36530	+	7.56092i	−0.240667	+	0.416847i
$330$	0.180360	−	0.312393i	0.00992851	−	0.0171967i
$331$	−10.0322	+	5.79208i	−0.551418	+	0.318361i	−0.749694	−	0.661785i	$-0.769799\pi$
$331$	−10.0322	+	5.79208i	−0.551418	+	0.318361i	0.198276	+	0.980146i	$0.436466\pi$
$332$	−12.6332			−0.693340
$333$	4.26613	−	4.33591i	0.233783	−	0.237606i
$334$	−0.392305			−0.0214660
$335$	24.3524	−	14.0599i	1.33052	−	0.768174i
$336$	−0.762169	+	1.32012i	−0.0415797	+	0.0720182i
$337$	16.9410	−	29.3426i	0.922834	−	1.59840i	0.127826	−	0.991797i	$-0.459200\pi$
$337$	16.9410	−	29.3426i	0.922834	−	1.59840i	0.795008	−	0.606599i	$-0.207467\pi$
$338$	−4.50605	−	2.60157i	−0.245097	−	0.141507i
$339$		−	19.8564i		−	1.07845i
$340$	−0.621938	+	1.07723i	−0.0337293	+	0.0584209i
$341$		−	0.206762i		−	0.0111968i
$342$	−2.44831	−	4.24060i	−0.132389	−	0.229305i
$343$	17.7988			0.961043
$344$	−6.73758			−0.363266
$345$	−5.49569	−	9.51881i	−0.295878	−	0.512475i
$346$	11.5459	+	6.66603i	0.620712	+	0.358368i
$347$			11.3278i			0.608106i	0.952655	+	0.304053i	$0.0983400\pi$
$347$			11.3278i			0.608106i	−0.952655	+	0.304053i	$0.901660\pi$
$348$	2.51856	−	1.45409i	0.135009	−	0.0779474i
$349$	7.39515	+	12.8088i	0.395853	+	0.685638i	0.993210	−	0.116338i	$-0.0371155\pi$
$349$	7.39515	+	12.8088i	0.395853	+	0.685638i	−0.597356	+	0.801976i	$0.703782\pi$
$350$	0.828661	−	0.478428i	0.0442938	−	0.0255730i
$351$	−2.41819	−	1.39614i	−0.129074	−	0.0745206i
$352$	0.131685	+	0.0760282i	0.00701882	+	0.00405232i
$353$	3.88859	−	2.24508i	0.206969	−	0.119493i	−0.392933	−	0.919567i	$-0.628540\pi$
$353$	3.88859	−	2.24508i	0.206969	−	0.119493i	0.599902	+	0.800074i	$0.295206\pi$
$354$	4.16457	+	7.21324i	0.221344	+	0.383380i
$355$	9.43510	−	5.44736i	0.500763	−	0.289116i
$356$		−	12.9739i		−	0.687618i
$357$	−0.692186	−	0.399634i	−0.0366344	−	0.0211509i
$358$	10.2087	+	17.6819i	0.539545	+	0.934519i
$359$	−18.2810			−0.964834			−0.482417	−	0.875942i	$-0.660241\pi$
$359$	−18.2810			−0.964834			−0.482417	+	0.875942i	$0.660241\pi$
$360$	2.37228			0.125030
$361$	2.48844	+	4.31010i	0.130970	+	0.226848i
$362$			1.86244i			0.0978875i
$363$	−5.48844	+	9.50626i	−0.288068	+	0.498949i
$364$		−	4.25639i		−	0.223095i
$365$	−14.8985	−	8.60167i	−0.779824	−	0.450232i
$366$	4.24638	−	7.35494i	0.221962	−	0.384449i
$367$	14.1001	−	24.4221i	0.736020	−	1.27482i	−0.218254	−	0.975892i	$-0.570036\pi$
$367$	14.1001	−	24.4221i	0.736020	−	1.27482i	0.954274	−	0.298932i	$-0.0966305\pi$
$368$	4.01251	−	2.31662i	0.209167	−	0.120762i
$369$	−5.83638			−0.303830
$370$	−3.84769	−	13.9076i	−0.200032	−	0.723021i
$371$	−4.81689			−0.250080
$372$	1.17759	−	0.679885i	0.0610555	−	0.0352504i
$373$	15.0743	−	26.1095i	0.780518	−	1.35190i	−0.151122	−	0.988515i	$-0.548289\pi$
$373$	15.0743	−	26.1095i	0.780518	−	1.35190i	0.931640	−	0.363382i	$-0.118378\pi$
$374$	−0.0398645	+	0.0690473i	−0.00206134	+	0.00357035i
$375$	8.98266	+	5.18614i	0.463863	+	0.267811i
$376$			5.72747i			0.295372i
$377$	−4.06024	+	7.03254i	−0.209113	+	0.362194i
$378$			1.52434i			0.0784035i
$379$	−9.46082	−	16.3866i	−0.485970	−	0.841724i	0.513900	−	0.857850i	$-0.328200\pi$
$379$	−9.46082	−	16.3866i	−0.485970	−	0.841724i	−0.999870	+	0.0161257i	$0.994867\pi$
$380$	−11.6162			−0.595896
$381$	−19.0542			−0.976177
$382$	7.30506	+	12.6527i	0.373760	+	0.647371i
$383$	−19.7343	−	11.3936i	−1.00838	−	0.582186i	−0.0976600	−	0.995220i	$-0.531136\pi$
$383$	−19.7343	−	11.3936i	−1.00838	−	0.582186i	−0.910716	+	0.413034i	$0.864469\pi$
$384$			1.00000i			0.0510310i
$385$	0.476193	−	0.274930i	0.0242690	−	0.0140117i
$386$	1.80579	+	3.12772i	0.0919123	+	0.159197i
$387$	−5.83492	+	3.36879i	−0.296605	+	0.171245i
$388$	−12.0730	−	6.97036i	−0.612914	−	0.353866i
$389$	−13.2506	−	7.65024i	−0.671833	−	0.387883i	0.124938	−	0.992165i	$-0.460127\pi$
$389$	−13.2506	−	7.65024i	−0.671833	−	0.387883i	−0.796771	+	0.604282i	$0.793460\pi$
$390$	−5.73663	+	3.31205i	−0.290486	+	0.167712i
$391$	1.21469	+	2.10391i	0.0614297	+	0.106399i
$392$	4.04988	−	2.33820i	0.204550	−	0.118097i
$393$		−	14.3060i		−	0.721643i
$394$	15.7124	+	9.07155i	0.791578	+	0.457018i
$395$	15.4693	+	26.7936i	0.778344	+	1.34813i
$396$	0.152056			0.00764113
$397$	22.5549			1.13200			0.565999	−	0.824406i	$-0.308491\pi$
$397$	22.5549			1.13200			0.565999	+	0.824406i	$0.308491\pi$
$398$	6.52783	+	11.3065i	0.327210	+	0.566745i
$399$		−	7.46410i		−	0.373672i
$400$	0.313859	−	0.543620i	0.0156930	−	0.0271810i
$401$		−	25.1619i		−	1.25652i	−0.778001	−	0.628262i	$-0.783766\pi$
$401$		−	25.1619i		−	1.25652i	0.778001	−	0.628262i	$-0.216234\pi$
$402$	10.2654	+	5.92674i	0.511992	+	0.295599i
$403$	−1.89843	+	3.28818i	−0.0945677	+	0.163796i
$404$	−1.42674	+	2.47118i	−0.0709828	+	0.122946i
$405$	2.05446	−	1.18614i	0.102087	−	0.0589398i
$406$	4.43305			0.220008
$407$	−0.246626	−	0.891436i	−0.0122248	−	0.0441869i
$408$	−0.524338			−0.0259586
$409$	−19.4532	+	11.2313i	−0.961900	+	0.555353i	−0.896757	−	0.442523i	$-0.854084\pi$
$409$	−19.4532	+	11.2313i	−0.961900	+	0.555353i	−0.0651428	+	0.997876i	$0.520750\pi$
$410$	−6.92277	+	11.9906i	−0.341891	+	0.592173i
$411$	−3.17458	+	5.49853i	−0.156590	+	0.271223i
$412$	−2.40421	−	1.38807i	−0.118447	−	0.0683855i
$413$			12.6964i			0.624750i
$414$	2.31662	−	4.01251i	0.113856	−	0.197204i
$415$			29.9696i			1.47115i
$416$	−1.39614	−	2.41819i	−0.0684516	−	0.118562i
$417$	−3.55592			−0.174134
$418$	−0.744563			−0.0364177
$419$	−11.1688	−	19.3449i	−0.545632	−	0.945062i	−0.998567	−	0.0535182i	$-0.982956\pi$
$419$	−11.1688	−	19.3449i	−0.545632	−	0.945062i	0.452935	−	0.891543i	$-0.350377\pi$
$420$	3.13168	+	1.80808i	0.152811	+	0.0882252i
$421$			24.3202i			1.18529i	0.805463	+	0.592646i	$0.201917\pi$
$421$			24.3202i			1.18529i	−0.805463	+	0.592646i	$0.798083\pi$
$422$	0.136475	−	0.0787937i	0.00664348	−	0.00383562i
$423$	2.86374	+	4.96014i	0.139240	+	0.241170i
$424$	−2.73663	+	1.57999i	−0.132903	+	0.0767313i
$425$	0.285041	+	0.164568i	0.0138265	+	0.00798274i
$426$	3.97723	+	2.29625i	0.192697	+	0.111254i
$427$	11.2114	−	6.47291i	0.542558	−	0.313246i
$428$	9.49241	+	16.4413i	0.458833	+	0.794722i
$429$	−0.367702	+	0.212293i	−0.0177528	+	0.0102496i
$430$			15.9834i			0.770790i
$431$	6.55482	+	3.78443i	0.315735	+	0.182289i	0.649490	−	0.760370i	$-0.274983\pi$
$431$	6.55482	+	3.78443i	0.315735	+	0.182289i	−0.333755	+	0.942660i	$0.608316\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−8.13134			−0.390767			−0.195384	−	0.980727i	$-0.562595\pi$
$433$	−8.13134			−0.390767			−0.195384	+	0.980727i	$0.562595\pi$
$434$	2.07275			0.0994951
$435$	−3.44951	−	5.97473i	−0.165391	−	0.286466i
$436$			14.2041i			0.680252i
$437$	−11.3436	+	19.6477i	−0.542639	+	0.939879i
$438$		−	7.25181i		−	0.346505i
$439$	−13.7934	−	7.96363i	−0.658323	−	0.380083i	0.133315	−	0.991074i	$-0.457438\pi$
$439$	−13.7934	−	7.96363i	−0.658323	−	0.380083i	−0.791638	+	0.610991i	$0.790771\pi$
$440$	0.180360	−	0.312393i	0.00859834	−	0.0148928i
$441$	2.33820	−	4.04988i	0.111343	−	0.192851i
$442$	1.26795	−	0.732051i	0.0603102	−	0.0348201i
$443$	24.9624			1.18600			0.592999	−	0.805203i	$-0.297944\pi$
$443$	24.9624			1.18600			0.592999	+	0.805203i	$0.297944\pi$
$444$	4.26613	−	4.33591i	0.202462	−	0.205773i
$445$	−30.7779			−1.45901
$446$	−11.7414	+	6.77891i	−0.555972	+	0.320991i
$447$	0.482394	−	0.835530i	0.0228164	−	0.0395192i
$448$	−0.762169	+	1.32012i	−0.0360091	+	0.0623696i
$449$	6.72747	+	3.88411i	0.317489	+	0.183302i	0.650273	−	0.759701i	$-0.274655\pi$
$449$	6.72747	+	3.88411i	0.317489	+	0.183302i	−0.332784	+	0.943003i	$0.607988\pi$
$450$		−	0.627719i		−	0.0295909i
$451$	−0.443730	+	0.768563i	−0.0208944	+	0.0361902i
$452$		−	19.8564i		−	0.933967i
$453$	4.21506	+	7.30069i	0.198041	+	0.343017i
$454$	18.1631			0.852437
$455$	−10.0974			−0.473371
$456$	−2.44831	−	4.24060i	−0.114653	−	0.198584i
$457$	−31.5579	−	18.2200i	−1.47622	−	0.852295i	−0.476578	−	0.879132i	$-0.658123\pi$
$457$	−31.5579	−	18.2200i	−1.47622	−	0.852295i	−0.999640	+	0.0268379i	$0.991456\pi$
$458$			22.6412i			1.05795i
$459$	−0.454090	+	0.262169i	−0.0211951	+	0.0122370i
$460$	−5.49569	−	9.51881i	−0.256238	−	0.443817i
$461$	−24.3130	+	14.0371i	−1.13237	+	0.653774i	−0.944530	−	0.328426i	$-0.893482\pi$
$461$	−24.3130	+	14.0371i	−1.13237	+	0.653774i	−0.187839	+	0.982200i	$0.560148\pi$
$462$	0.200732	+	0.115893i	0.00933890	+	0.00539182i
$463$	14.7427	+	8.51169i	0.685150	+	0.395572i	0.801793	−	0.597602i	$-0.203880\pi$
$463$	14.7427	+	8.51169i	0.685150	+	0.395572i	−0.116642	+	0.993174i	$0.537213\pi$
$464$	2.51856	−	1.45409i	0.116921	−	0.0675044i
$465$	−1.61288	−	2.79359i	−0.0747954	−	0.129549i
$466$	1.95806	−	1.13048i	0.0907052	−	0.0523687i
$467$			39.1619i			1.81220i	0.423068	+	0.906098i	$0.360953\pi$
$467$			39.1619i			1.81220i	−0.423068	+	0.906098i	$0.639047\pi$
$468$	−2.41819	−	1.39614i	−0.111781	−	0.0645368i
$469$	9.03435	+	15.6480i	0.417168	+	0.722555i
$470$	13.5872			0.626730
$471$	−6.50485			−0.299727
$472$	4.16457	+	7.21324i	0.191690	+	0.332016i
$473$			1.02449i			0.0471062i
$474$	−6.52085	+	11.2944i	−0.299512	+	0.518771i
$475$			3.07370i			0.141031i
$476$	−0.692186	−	0.399634i	−0.0317263	−	0.0183172i
$477$	−1.57999	+	2.73663i	−0.0723430	+	0.125302i
$478$	−3.98421	+	6.90085i	−0.182233	+	0.315638i
$479$	5.29255	−	3.05566i	0.241823	−	0.139617i	−0.374191	−	0.927352i	$-0.622080\pi$
$479$	5.29255	−	3.05566i	0.241823	−	0.139617i	0.616014	+	0.787735i	$0.288746\pi$
$480$	2.37228			0.108279
$481$	−4.26278	+	16.4412i	−0.194366	+	0.749654i
$482$	9.83180			0.447826
$483$	6.11642	−	3.53132i	0.278307	−	0.160681i
$484$	−5.48844	+	9.50626i	−0.249475	+	0.432103i
$485$	−16.5356	+	28.6406i	−0.750845	+	1.30050i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$			27.0737i			1.22683i	0.789762	+	0.613413i	$0.210204\pi$
$487$			27.0737i			1.22683i	−0.789762	+	0.613413i	$0.789796\pi$
$488$	4.24638	−	7.35494i	0.192224	−	0.332943i
$489$		−	6.79927i		−	0.307474i
$490$	−5.54686	−	9.60745i	−0.250582	−	0.434020i
$491$	5.55299			0.250603			0.125301	−	0.992119i	$-0.460010\pi$
$491$	5.55299			0.250603			0.125301	+	0.992119i	$0.460010\pi$
$492$	−5.83638			−0.263124
$493$	0.762434	+	1.32057i	0.0343383	+	0.0594757i
$494$	11.8410	+	6.83638i	0.532750	+	0.307583i
$495$		−	0.360721i		−	0.0162132i
$496$	1.17759	−	0.679885i	0.0528756	−	0.0305277i
$497$	3.50027	+	6.06264i	0.157008	+	0.271946i
$498$	−10.9407	+	6.31662i	−0.490265	+	0.283055i
$499$	−10.1425	−	5.85580i	−0.454043	−	0.262142i	0.255493	−	0.966811i	$-0.417762\pi$
$499$	−10.1425	−	5.85580i	−0.454043	−	0.262142i	−0.709536	+	0.704669i	$0.751095\pi$
$500$	8.98266	+	5.18614i	0.401717	+	0.231931i
$501$	−0.339746	+	0.196152i	−0.0151787	+	0.00876344i
$502$	−4.67311	−	8.09407i	−0.208571	−	0.361256i
$503$	17.4955	−	10.1011i	0.780087	−	0.450384i	−0.0563739	−	0.998410i	$-0.517954\pi$
$503$	17.4955	−	10.1011i	0.780087	−	0.450384i	0.836461	+	0.548026i	$0.184621\pi$
$504$			1.52434i			0.0678994i
$505$	5.86234	+	3.38462i	0.260871	+	0.150614i
$506$	−0.352258	−	0.610128i	−0.0156598	−	0.0271235i
$507$	−5.20313			−0.231079
$508$	−19.0542			−0.845394
$509$	−2.03496	−	3.52466i	−0.0901982	−	0.156228i	0.817396	−	0.576076i	$-0.195417\pi$
$509$	−2.03496	−	3.52466i	−0.0901982	−	0.156228i	−0.907594	+	0.419848i	$0.862083\pi$
$510$			1.24388i			0.0550798i
$511$	5.52710	−	9.57322i	0.244505	−	0.423494i
$512$			1.00000i			0.0441942i
$513$	−4.24060	−	2.44831i	−0.187227	−	0.108096i
$514$	−6.79902	+	11.7762i	−0.299892	+	0.519428i
$515$	−3.29290	+	5.70347i	−0.145103	+	0.251325i
$516$	−5.83492	+	3.36879i	−0.256868	+	0.148303i
$517$	0.870899			0.0383021
$518$	8.93648	−	2.47238i	0.392647	−	0.108630i
$519$	13.3321			0.585213
$520$	−5.73663	+	3.31205i	−0.251568	+	0.145243i
$521$	10.4812	−	18.1540i	0.459189	−	0.795339i	−0.539729	−	0.841839i	$-0.681473\pi$
$521$	10.4812	−	18.1540i	0.459189	−	0.795339i	0.998918	+	0.0464995i	$0.0148066\pi$
$522$	1.45409	−	2.51856i	0.0636438	−	0.110234i
$523$	−28.7804	−	16.6164i	−1.25848	−	0.726583i	−0.285700	−	0.958319i	$-0.592226\pi$
$523$	−28.7804	−	16.6164i	−1.25848	−	0.726583i	−0.972779	+	0.231736i	$0.925559\pi$
$524$		−	14.3060i		−	0.624961i
$525$	0.478428	−	0.828661i	0.0208803	−	0.0361657i
$526$		−	13.6728i		−	0.596161i
$527$	0.356489	+	0.617458i	0.0155289	+	0.0268969i
$528$	0.152056			0.00661741
$529$	1.53300			0.0666521
$530$	3.74819	+	6.49206i	0.162811	+	0.281997i
$531$	7.21324	+	4.16457i	0.313028	+	0.180727i
$532$		−	7.46410i		−	0.323610i
$533$	14.1135	−	8.14843i	0.611323	−	0.352948i
$534$	−6.48697	−	11.2358i	−0.280719	−	0.486219i
$535$	39.0035	−	22.5187i	1.68627	−	0.973566i
$536$	10.2654	+	5.92674i	0.443398	+	0.255996i
$537$	17.6819	+	10.2087i	0.763031	+	0.440536i
$538$	1.05421	−	0.608646i	0.0454501	−	0.0262406i
$539$	−0.355538	−	0.615810i	−0.0153141	−	0.0265248i
$540$	2.05446	−	1.18614i	0.0884097	−	0.0510434i
$541$			10.0546i			0.432282i	0.976362	+	0.216141i	$0.0693471\pi$
$541$			10.0546i			0.432282i	−0.976362	+	0.216141i	$0.930653\pi$
$542$	−3.60851	−	2.08337i	−0.154999	−	0.0894885i
$543$	0.931218	+	1.61292i	0.0399624	+	0.0692169i
$544$	−0.524338			−0.0224808
$545$	33.6961			1.44338
$546$	−2.12819	−	3.68614i	−0.0910783	−	0.157752i
$547$		−	32.4214i		−	1.38624i	−0.720823	−	0.693120i	$-0.756236\pi$
$547$		−	32.4214i		−	1.38624i	0.720823	−	0.693120i	$-0.243764\pi$
$548$	−3.17458	+	5.49853i	−0.135611	+	0.234886i
$549$		−	8.49275i		−	0.362462i
$550$	−0.0826610	−	0.0477243i	−0.00352468	−	0.00203497i
$551$	−7.12012	+	12.3324i	−0.303327	+	0.525379i
$552$	2.31662	−	4.01251i	0.0986021	−	0.170784i
$553$	−17.2165	+	9.93997i	−0.732122	+	0.422691i
$554$	−27.4210			−1.16500
$555$	−10.2860	−	10.1205i	−0.436616	−	0.429590i
$556$	−3.55592			−0.150805
$557$	29.8236	−	17.2187i	1.26367	−	0.729579i	0.289885	−	0.957061i	$-0.406383\pi$
$557$	29.8236	−	17.2187i	1.26367	−	0.729579i	0.973782	+	0.227483i	$0.0730495\pi$
$558$	0.679885	−	1.17759i	0.0287818	−	0.0498516i
$559$	9.40663	−	16.2928i	0.397858	−	0.689110i
$560$	3.13168	+	1.80808i	0.132338	+	0.0764053i
$561$			0.0797290i			0.00336616i
$562$	7.72627	−	13.3823i	0.325913	−	0.564498i
$563$		−	34.2679i		−	1.44422i	−0.691779	−	0.722109i	$-0.743173\pi$
$563$		−	34.2679i		−	1.44422i	0.691779	−	0.722109i	$-0.256827\pi$
$564$	2.86374	+	4.96014i	0.120585	+	0.208859i
$565$	−47.1050			−1.98172
$566$	18.8147			0.790841
$567$	0.762169	+	1.32012i	0.0320081	+	0.0554396i
$568$	3.97723	+	2.29625i	0.166881	+	0.0963486i
$569$			27.3089i			1.14485i	0.819957	+	0.572425i	$0.193997\pi$
$569$			27.3089i			1.14485i	−0.819957	+	0.572425i	$0.806003\pi$
$570$	−10.0599	+	5.80808i	−0.421362	+	0.243274i
$571$	−3.98663	−	6.90504i	−0.166835	−	0.288967i	0.770470	−	0.637476i	$-0.220021\pi$
$571$	−3.98663	−	6.90504i	−0.166835	−	0.288967i	−0.937305	+	0.348509i	$0.886688\pi$
$572$	−0.367702	+	0.212293i	−0.0153744	+	0.00887640i
$573$	12.6527	+	7.30506i	0.528576	+	0.305173i
$574$	−7.70470	−	4.44831i	−0.321588	−	0.185669i
$575$	−2.51873	+	1.45419i	−0.105038	+	0.0606439i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	23.7725	−	13.7251i	0.989663	−	0.571382i	0.0844894	−	0.996424i	$-0.473074\pi$
$577$	23.7725	−	13.7251i	0.989663	−	0.571382i	0.905174	+	0.425042i	$0.139741\pi$
$578$			16.7251i			0.695671i
$579$	3.12772	+	1.80579i	0.129984	+	0.0750460i
$580$	−3.44951	−	5.97473i	−0.143233	−	0.248087i
$581$	−19.2573			−0.798929
$582$	−13.9407			−0.577861
$583$	0.240248	+	0.416122i	0.00995007	+	0.0172340i
$584$		−	7.25181i		−	0.300082i
$585$	−3.31205	+	5.73663i	−0.136936	+	0.237180i
$586$		−	26.8935i		−	1.11096i
$587$	11.9115	+	6.87713i	0.491642	+	0.283849i	0.725255	−	0.688480i	$-0.241722\pi$
$587$	11.9115	+	6.87713i	0.491642	+	0.283849i	−0.233614	+	0.972329i	$0.575055\pi$
$588$	2.33820	−	4.04988i	0.0964256	−	0.167014i
$589$	−3.32914	+	5.76623i	−0.137175	+	0.237594i
$590$	17.1118	−	9.87953i	0.704483	−	0.406734i
$591$	18.1431			0.746307
$592$	4.26613	−	4.33591i	0.175337	−	0.178205i
$593$	−24.2749			−0.996852			−0.498426	−	0.866932i	$-0.666088\pi$
$593$	−24.2749			−0.996852			−0.498426	+	0.866932i	$0.666088\pi$
$594$	0.131685	−	0.0760282i	0.00540309	−	0.00311948i
$595$	−0.948044	+	1.64206i	−0.0388660	+	0.0673179i
$596$	0.482394	−	0.835530i	0.0197596	−	0.0342247i
$597$	11.3065	+	6.52783i	0.462745	+	0.267166i
$598$			12.9374i			0.529048i
$599$	2.92397	−	5.06447i	0.119470	−	0.206929i	−0.800088	−	0.599883i	$-0.795214\pi$
$599$	2.92397	−	5.06447i	0.119470	−	0.206929i	0.919558	+	0.392955i	$0.128547\pi$
$600$		−	0.627719i		−	0.0256265i
$601$	1.45926	+	2.52751i	0.0595243	+	0.103099i	0.894252	−	0.447564i	$-0.147708\pi$
$601$	1.45926	+	2.52751i	0.0595243	+	0.103099i	−0.834728	+	0.550663i	$0.814375\pi$
$602$	−10.2704			−0.418588
$603$	11.8535			0.482711
$604$	4.21506	+	7.30069i	0.171508	+	0.297061i
$605$	22.5515	+	13.0201i	0.916849	+	0.529343i
$606$			2.85347i			0.115914i
$607$	16.3859	−	9.46040i	0.665083	−	0.383986i	−0.129128	−	0.991628i	$-0.541218\pi$
$607$	16.3859	−	9.46040i	0.665083	−	0.383986i	0.794211	+	0.607642i	$0.207884\pi$
$608$	−2.44831	−	4.24060i	−0.0992921	−	0.171979i
$609$	3.83913	−	2.21652i	0.155569	−	0.0898181i
$610$	−17.4480	−	10.0736i	−0.706448	−	0.407868i
$611$	−13.8501	−	7.99637i	−0.560316	−	0.323499i
$612$	−0.454090	+	0.262169i	−0.0183555	+	0.0105975i
$613$	14.3118	+	24.7888i	0.578048	+	1.00121i	0.995703	+	0.0926029i	$0.0295187\pi$
$613$	14.3118	+	24.7888i	0.578048	+	1.00121i	−0.417655	+	0.908606i	$0.637148\pi$
$614$	−14.4586	+	8.34769i	−0.583503	+	0.336886i
$615$			13.8455i			0.558306i
$616$	0.200732	+	0.115893i	0.00808773	+	0.00466945i
$617$	3.21229	+	5.56385i	0.129322	+	0.223992i	0.923414	−	0.383805i	$-0.125387\pi$
$617$	3.21229	+	5.56385i	0.129322	+	0.223992i	−0.794092	+	0.607797i	$0.792053\pi$
$618$	−2.77615			−0.111673
$619$	−4.19657			−0.168675			−0.0843373	−	0.996437i	$-0.526877\pi$
$619$	−4.19657			−0.168675			−0.0843373	+	0.996437i	$0.526877\pi$
$620$	−1.61288	−	2.79359i	−0.0647747	−	0.112193i
$621$		−	4.63325i		−	0.185926i
$622$	9.84424	−	17.0507i	0.394718	−	0.683672i
$623$		−	19.7767i		−	0.792336i
$624$	−2.41819	−	1.39614i	−0.0968051	−	0.0558905i
$625$	13.8723	−	24.0275i	0.554891	−	0.961100i
$626$	8.70939	−	15.0851i	0.348097	−	0.602922i
$627$	−0.644810	+	0.372281i	−0.0257512	+	0.0148675i
$628$	−6.50485			−0.259572
$629$	2.27348	+	2.23690i	0.0906496	+	0.0891909i
$630$	3.61616			0.144071
$631$	−27.0283	+	15.6048i	−1.07598	+	0.621218i	−0.929809	−	0.368042i	$-0.880028\pi$
$631$	−27.0283	+	15.6048i	−1.07598	+	0.621218i	−0.146171	+	0.989259i	$0.546695\pi$
$632$	−6.52085	+	11.2944i	−0.259385	+	0.449269i
$633$	0.0787937	−	0.136475i	0.00313177	−	0.00542438i
$634$	−19.3476	−	11.1703i	−0.768392	−	0.443631i
$635$			45.2019i			1.79378i
$636$	−1.57999	+	2.73663i	−0.0626509	+	0.108514i
$637$			13.0578i			0.517370i
$638$	−0.221104	−	0.382963i	−0.00875358	−	0.0151616i
$639$	4.59251			0.181677
$640$	2.37228			0.0937727
$641$	−19.2278	−	33.3036i	−0.759454	−	1.31541i	−0.943129	−	0.332426i	$-0.892133\pi$
$641$	−19.2278	−	33.3036i	−0.759454	−	1.31541i	0.183676	−	0.982987i	$-0.441200\pi$
$642$	16.4413	+	9.49241i	0.648887	+	0.374635i
$643$		−	5.45712i		−	0.215208i	−0.994194	−	0.107604i	$-0.965682\pi$
$643$		−	5.45712i		−	0.215208i	0.994194	−	0.107604i	$-0.0343178\pi$
$644$	6.11642	−	3.53132i	0.241021	−	0.139153i
$645$	7.99172	+	13.8421i	0.314674	+	0.545031i
$646$	2.22351	−	1.28374i	0.0874826	−	0.0505081i
$647$	0.158434	+	0.0914721i	0.00622870	+	0.00359614i	0.503111	−	0.864222i	$-0.332189\pi$
$647$	0.158434	+	0.0914721i	0.00622870	+	0.00359614i	−0.496882	+	0.867818i	$0.665522\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	1.09682	−	0.633250i	0.0430540	−	0.0248572i
$650$	0.876385	+	1.51794i	0.0343747	+	0.0595387i
$651$	1.79505	−	1.03637i	0.0703537	−	0.0406187i
$652$		−	6.79927i		−	0.266280i
$653$	−19.7364	−	11.3948i	−0.772344	−	0.445913i	0.0613660	−	0.998115i	$-0.480454\pi$
$653$	−19.7364	−	11.3948i	−0.772344	−	0.445913i	−0.833710	+	0.552202i	$0.813788\pi$
$654$	7.10204	+	12.3011i	0.277712	+	0.481011i
$655$	−33.9379			−1.32606
$656$	−5.83638			−0.227872
$657$	−3.62590	−	6.28025i	−0.141460	−	0.245016i
$658$			8.73060i			0.340354i
$659$	−2.75154	+	4.76581i	−0.107185	+	0.185650i	−0.914629	−	0.404295i	$-0.867517\pi$
$659$	−2.75154	+	4.76581i	−0.107185	+	0.185650i	0.807444	+	0.589944i	$0.200850\pi$
$660$		−	0.360721i		−	0.0140410i
$661$	−2.60158	−	1.50202i	−0.101190	−	0.0584220i	0.448551	−	0.893757i	$-0.351940\pi$
$661$	−2.60158	−	1.50202i	−0.101190	−	0.0584220i	−0.549741	+	0.835335i	$0.685274\pi$
$662$	−5.79208	+	10.0322i	−0.225115	+	0.389911i
$663$	0.732051	−	1.26795i	0.0284305	−	0.0492431i
$664$	−10.9407	+	6.31662i	−0.424582	+	0.245133i
$665$	−17.7069			−0.686646
$666$	1.52663	−	5.88807i	0.0591556	−	0.228158i
$667$	−13.4743			−0.521728
$668$	−0.339746	+	0.196152i	−0.0131452	+	0.00758937i
$669$	−6.77891	+	11.7414i	−0.262088	+	0.453950i
$670$	14.0599	−	24.3524i	0.543181	−	0.940817i
$671$	−1.11837	−	0.645689i	−0.0431741	−	0.0249266i
$672$			1.52434i			0.0588026i
$673$	13.1248	−	22.7328i	0.505923	−	0.876284i	−0.494054	−	0.869431i	$-0.664485\pi$
$673$	13.1248	−	22.7328i	0.505923	−	0.876284i	0.999977	−	0.00685278i	$-0.00218132\pi$
$674$		−	33.8820i		−	1.30508i
$675$	−0.313859	−	0.543620i	−0.0120805	−	0.0209240i
$676$	−5.20313			−0.200121
$677$	−11.4415			−0.439732			−0.219866	−	0.975530i	$-0.570562\pi$
$677$	−11.4415			−0.439732			−0.219866	+	0.975530i	$0.570562\pi$
$678$	−9.92820	−	17.1962i	−0.381290	−	0.660414i
$679$	−18.4034	−	10.6252i	−0.706256	−	0.407757i
$680$			1.24388i			0.0477005i
$681$	15.7297	−	9.08156i	0.602764	−	0.348006i
$682$	−0.103381	−	0.179061i	−0.00395866	−	0.00685660i
$683$	−29.6345	+	17.1095i	−1.13393	+	0.654677i	−0.944921	−	0.327297i	$-0.893862\pi$
$683$	−29.6345	+	17.1095i	−1.13393	+	0.654677i	−0.189013	+	0.981975i	$0.560529\pi$
$684$	−4.24060	−	2.44831i	−0.162143	−	0.0936135i
$685$	13.0441	+	7.53100i	0.498388	+	0.287745i
$686$	15.4142	−	8.89938i	0.588516	−	0.339780i
$687$	11.3206	+	19.6078i	0.431907	+	0.748086i
$688$	−5.83492	+	3.36879i	−0.222454	+	0.128434i
$689$		−	8.82360i		−	0.336152i
$690$	−9.51881	−	5.49569i	−0.362375	−	0.209217i
$691$	−22.1159	−	38.3059i	−0.841329	−	1.45722i	−0.888772	−	0.458350i	$-0.848441\pi$
$691$	−22.1159	−	38.3059i	−0.841329	−	1.45722i	0.0474428	−	0.998874i	$-0.484893\pi$
$692$	13.3321			0.506809
$693$	0.231785			0.00880480
$694$	5.66388	+	9.81013i	0.214998	+	0.372388i
$695$			8.43565i			0.319982i
$696$	1.45409	−	2.51856i	0.0551171	−	0.0954657i
$697$		−	3.06024i		−	0.115915i
$698$	12.8088	+	7.39515i	0.484820	+	0.279911i
$699$	1.13048	−	1.95806i	0.0427588	−	0.0740605i
$700$	0.478428	−	0.828661i	0.0180829	−	0.0313204i
$701$	13.9703	−	8.06577i	0.527652	−	0.304640i	−0.212408	−	0.977181i	$-0.568131\pi$
$701$	13.9703	−	8.06577i	0.527652	−	0.304640i	0.740060	+	0.672541i	$0.234797\pi$
$702$	−2.79229			−0.105388
$703$	−7.47531	+	28.8317i	−0.281937	+	1.08741i
$704$	0.152056			0.00573084
$705$	11.7668	−	6.79359i	0.443165	−	0.255861i
$706$	2.24508	−	3.88859i	0.0844946	−	0.146349i
$707$	−2.17483	+	3.76692i	−0.0817929	+	0.141669i
$708$	7.21324	+	4.16457i	0.271090	+	0.156514i
$709$		−	8.49924i		−	0.319196i	−0.987182	−	0.159598i	$-0.948980\pi$
$709$		−	8.49924i		−	0.319196i	0.987182	−	0.159598i	$-0.0510197\pi$
$710$	5.44736	−	9.43510i	0.204436	−	0.354093i
$711$			13.0417i			0.489102i
$712$	−6.48697	−	11.2358i	−0.243110	−	0.421078i
$713$	−6.30015			−0.235943
$714$	−0.799268			−0.0299119
$715$	0.503618	+	0.872292i	0.0188342	+	0.0326219i
$716$	17.6819	+	10.2087i	0.660805	+	0.381516i
$717$			7.96842i			0.297586i
$718$	−15.8318	+	9.14050i	−0.590838	+	0.341120i
$719$	−18.3222	−	31.7349i	−0.683301	−	1.18351i	−0.973967	−	0.226688i	$-0.927210\pi$
$719$	−18.3222	−	31.7349i	−0.683301	−	1.18351i	0.290666	−	0.956824i	$-0.406123\pi$
$720$	2.05446	−	1.18614i	0.0765651	−	0.0442049i
$721$	−3.66483	−	2.11589i	−0.136486	−	0.0788000i
$722$	4.31010	+	2.48844i	0.160405	+	0.0926101i
$723$	8.51459	−	4.91590i	0.316661	−	0.182824i
$724$	0.931218	+	1.61292i	0.0346084	+	0.0599436i
$725$	−1.58095	+	0.912759i	−0.0587148	+	0.0338990i
$726$			10.9769i			0.407390i
$727$	40.6251	+	23.4549i	1.50670	+	0.869895i	0.999970	+	0.00779216i	$0.00248035\pi$
$727$	40.6251	+	23.4549i	1.50670	+	0.869895i	0.506733	+	0.862103i	$0.330853\pi$
$728$	−2.12819	−	3.68614i	−0.0788761	−	0.136617i
$729$	1.00000			0.0370370
$730$	−17.2033			−0.636724
$731$	−1.76638	−	3.05947i	−0.0653321	−	0.113158i
$732$		−	8.49275i		−	0.313901i
$733$	−1.39577	+	2.41754i	−0.0515538	+	0.0892938i	−0.890651	−	0.454688i	$-0.849751\pi$
$733$	−1.39577	+	2.41754i	−0.0515538	+	0.0892938i	0.839097	+	0.543982i	$0.183084\pi$
$734$		−	28.2002i		−	1.04089i
$735$	−9.60745	−	5.54686i	−0.354376	−	0.204599i
$736$	2.31662	−	4.01251i	0.0853919	−	0.147903i
$737$	0.901199	−	1.56092i	0.0331961	−	0.0574973i
$738$	−5.05446	+	2.91819i	−0.186057	+	0.107420i
$739$	22.7056			0.835238			0.417619	−	0.908622i	$-0.362865\pi$
$739$	22.7056			0.835238			0.417619	+	0.908622i	$0.362865\pi$
$740$	−10.2860	−	10.1205i	−0.378121	−	0.372036i
$741$	13.6728			0.502282
$742$	−4.17155	+	2.40845i	−0.153142	+	0.0884168i
$743$	−15.9018	+	27.5427i	−0.583381	+	1.01044i	0.411695	+	0.911322i	$0.364937\pi$
$743$	−15.9018	+	27.5427i	−0.583381	+	1.01044i	−0.995075	+	0.0991229i	$0.968396\pi$
$744$	0.679885	−	1.17759i	0.0249258	−	0.0431727i
$745$	−1.98211	−	1.14437i	−0.0726190	−	0.0419266i
$746$		−	30.1486i		−	1.10382i
$747$	−6.31662	+	10.9407i	−0.231113	+	0.400300i
$748$			0.0797290i			0.00291518i
$749$	14.4696	+	25.0621i	0.528709	+	0.915751i
$750$	10.3723			0.378742
$751$	9.70072			0.353984			0.176992	−	0.984212i	$-0.443363\pi$
$751$	9.70072			0.353984			0.176992	+	0.984212i	$0.443363\pi$
$752$	2.86374	+	4.96014i	0.104430	+	0.180878i
$753$	−8.09407	−	4.67311i	−0.294964	−	0.170298i
$754$			8.12047i			0.295730i
$755$	17.3193	−	9.99930i	0.630314	−	0.363912i
$756$	0.762169	+	1.32012i	0.0277198	+	0.0480121i
$757$	34.7640	−	20.0710i	1.26352	−	0.729493i	0.289765	−	0.957098i	$-0.406423\pi$
$757$	34.7640	−	20.0710i	1.26352	−	0.729493i	0.973753	+	0.227605i	$0.0730896\pi$
$758$	−16.3866	−	9.46082i	−0.595189	−	0.343633i
$759$	−0.610128	−	0.352258i	−0.0221463	−	0.0127861i
$760$	−10.0599	+	5.80808i	−0.364910	+	0.210681i
$761$	6.32370	+	10.9530i	0.229234	+	0.397045i	0.957581	−	0.288163i	$-0.0930445\pi$
$761$	6.32370	+	10.9530i	0.229234	+	0.397045i	−0.728347	+	0.685208i	$0.759711\pi$
$762$	−16.5014	+	9.52710i	−0.597784	+	0.345131i
$763$			21.6518i			0.783849i
$764$	12.6527	+	7.30506i	0.457760	+	0.264288i
$765$	0.621938	+	1.07723i	0.0224862	+	0.0389473i
$766$	−22.7872			−0.823335
$767$	−23.2573			−0.839774
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$			24.5374i			0.884841i	0.896808	+	0.442420i	$0.145880\pi$
$769$			24.5374i			0.884841i	−0.896808	+	0.442420i	$0.854120\pi$
$770$	0.274930	−	0.476193i	0.00990779	−	0.0171608i
$771$			13.5980i			0.489721i
$772$	3.12772	+	1.80579i	0.112569	+	0.0649918i
$773$	19.9882	−	34.6206i	0.718925	−	1.24522i	−0.242501	−	0.970151i	$-0.577968\pi$
$773$	19.9882	−	34.6206i	0.718925	−	1.24522i	0.961426	−	0.275064i	$-0.0886990\pi$
$774$	−3.36879	+	5.83492i	−0.121089	+	0.209732i
$775$	−0.739198	+	0.426776i	−0.0265528	+	0.0153303i
$776$	−13.9407			−0.500443
$777$	6.50303	−	6.60939i	0.233295	−	0.237110i
$778$	−15.3005			−0.548549
$779$	24.7497	−	14.2893i	0.886752	−	0.511966i
$780$	−3.31205	+	5.73663i	−0.118590	+	0.205404i
$781$	0.349160	−	0.604763i	0.0124939	−	0.0216401i
$782$	2.10391	+	1.21469i	0.0752357	+	0.0434374i
$783$		−	2.90818i		−	0.103930i
$784$	2.33820	−	4.04988i	0.0835070	−	0.144638i
$785$			15.4313i			0.550768i
$786$	−7.15301	−	12.3894i	−0.255139	−	0.441914i
$787$	−2.64358			−0.0942336			−0.0471168	−	0.998889i	$-0.515003\pi$
$787$	−2.64358			−0.0942336			−0.0471168	+	0.998889i	$0.515003\pi$
$788$	18.1431			0.646321
$789$	−6.83638	−	11.8410i	−0.243382	−	0.421549i
$790$	26.7936	+	15.4693i	0.953273	+	0.550372i
$791$		−	30.2679i		−	1.07620i
$792$	0.131685	−	0.0760282i	0.00467921	−	0.00270155i
$793$	11.8571	+	20.5371i	0.421058	+	0.729294i
$794$	19.5331	−	11.2774i	0.693204	−	0.400222i
$795$	6.49206	+	3.74819i	0.230250	+	0.132935i
$796$	11.3065	+	6.52783i	0.400749	+	0.231373i
$797$	12.0375	−	6.94987i	0.426391	−	0.246177i	−0.271417	−	0.962462i	$-0.587492\pi$
$797$	12.0375	−	6.94987i	0.426391	−	0.246177i	0.697808	+	0.716285i	$0.254159\pi$
$798$	−3.73205	−	6.46410i	−0.132113	−	0.228827i
$799$	−2.60079	+	1.50156i	−0.0920092	+	0.0531215i
$800$		−	0.627719i		−	0.0221932i
$801$	−11.2358	−	6.48697i	−0.396996	−	0.229206i
$802$	−12.5809	−	21.7908i	−0.444249	−	0.769461i
$803$	−1.10268			−0.0389129
$804$	11.8535			0.418040
$805$	−8.37728	−	14.5099i	−0.295260	−	0.511406i
$806$			3.79687i			0.133739i
$807$	0.608646	−	1.05421i	0.0214254	−	0.0371098i
$808$			2.85347i			0.100385i
$809$	40.2508	+	23.2388i	1.41514	+	0.817033i	0.995867	−	0.0908265i	$-0.0289509\pi$
$809$	40.2508	+	23.2388i	1.41514	+	0.817033i	0.419275	+	0.907859i	$0.362284\pi$
$810$	1.18614	−	2.05446i	0.0416767	−	0.0721862i
$811$	−17.5523	+	30.4015i	−0.616344	+	1.06754i	0.373803	+	0.927508i	$0.378054\pi$
$811$	−17.5523	+	30.4015i	−0.616344	+	1.06754i	−0.990147	+	0.140032i	$0.955280\pi$
$812$	3.83913	−	2.21652i	0.134727	−	0.0777847i
$813$	−4.16675			−0.146134
$814$	−0.659303	−	0.648693i	−0.0231086	−	0.0227367i
$815$	−16.1298			−0.565001
$816$	−0.454090	+	0.262169i	−0.0158963	+	0.00917775i
$817$	16.4957	−	28.5714i	0.577111	−	0.999586i
$818$	−11.2313	+	19.4532i	−0.392694	+	0.680166i
$819$	−3.68614	−	2.12819i	−0.128804	−	0.0743651i
$820$			13.8455i			0.483507i
$821$	−26.8474	+	46.5011i	−0.936982	+	1.62290i	−0.165922	+	0.986139i	$0.553060\pi$
$821$	−26.8474	+	46.5011i	−0.936982	+	1.62290i	−0.771060	+	0.636762i	$0.780273\pi$
$822$			6.34916i			0.221452i
$823$	12.9401	+	22.4130i	0.451065	+	0.781267i	0.998452	−	0.0556124i	$-0.0177111\pi$
$823$	12.9401	+	22.4130i	0.451065	+	0.781267i	−0.547388	+	0.836879i	$0.684378\pi$
$824$	−2.77615			−0.0967117
$825$	−0.0954487			−0.00332310
$826$	6.34821	+	10.9954i	0.220882	+	0.382580i
$827$	16.1665	+	9.33372i	0.562163	+	0.324565i	0.754013	−	0.656859i	$-0.228115\pi$
$827$	16.1665	+	9.33372i	0.562163	+	0.324565i	−0.191850	+	0.981424i	$0.561449\pi$
$828$		−	4.63325i		−	0.161017i
$829$	45.3789	−	26.1995i	1.57607	−	0.909946i	0.580673	−	0.814137i	$-0.302790\pi$
$829$	45.3789	−	26.1995i	1.57607	−	0.909946i	0.995400	−	0.0958090i	$-0.0305438\pi$
$830$	14.9848	+	25.9545i	0.520130	+	0.900892i
$831$	−23.7472	+	13.7105i	−0.823783	+	0.475611i
$832$	−2.41819	−	1.39614i	−0.0838357	−	0.0484026i
$833$	2.12350	+	1.22601i	0.0735750	+	0.0424786i
$834$	−3.07952	+	1.77796i	−0.106635	+	0.0615658i
$835$	0.465329	+	0.805973i	0.0161034	+	0.0278918i
$836$	−0.644810	+	0.372281i	−0.0223012	+	0.0128756i
$837$		−	1.35977i		−	0.0470005i
$838$	−19.3449	−	11.1688i	−0.668259	−	0.385820i
$839$	−10.7130	−	18.5554i	−0.369853	−	0.640604i	0.619689	−	0.784847i	$-0.287259\pi$
$839$	−10.7130	−	18.5554i	−0.369853	−	0.640604i	−0.989542	+	0.144243i	$0.953925\pi$
$840$	3.61616			0.124769
$841$	20.5425			0.708362
$842$	12.1601	+	21.0619i	0.419064	+	0.725841i
$843$		−	15.4525i		−	0.532214i
$844$	0.0787937	−	0.136475i	0.00271219	−	0.00469765i
$845$			12.3433i			0.424622i
$846$	4.96014	+	2.86374i	0.170533	+	0.0984573i
$847$	−8.36624	+	14.4907i	−0.287467	+	0.497908i
$848$	−1.57999	+	2.73663i	−0.0542572	+	0.0939763i
$849$	16.2940	−	9.40736i	0.559209	−	0.322860i
$850$	0.329137			0.0112893
$851$	−27.1626	+	7.51485i	−0.931122	+	0.257606i
$852$	4.59251			0.157337
$853$	−10.8579	+	6.26880i	−0.371767	+	0.214640i	−0.674230	−	0.738521i	$-0.735524\pi$
$853$	−10.8579	+	6.26880i	−0.371767	+	0.214640i	0.302463	+	0.953161i	$0.402191\pi$
$854$	6.47291	−	11.2114i	0.221499	−	0.383647i
$855$	−5.80808	+	10.0599i	−0.198632	+	0.344041i
$856$	16.4413	+	9.49241i	0.561953	+	0.324444i
$857$		−	9.15278i		−	0.312653i	−0.987705	−	0.156327i	$-0.950035\pi$
$857$		−	9.15278i		−	0.312653i	0.987705	−	0.156327i	$-0.0499652\pi$
$858$	−0.212293	+	0.367702i	−0.00724755	+	0.0125531i
$859$			47.3135i			1.61432i	0.590335	+	0.807158i	$0.298996\pi$
$859$			47.3135i			1.61432i	−0.590335	+	0.807158i	$0.701004\pi$
$860$	7.99172	+	13.8421i	0.272515	+	0.472010i
$861$	−8.89662			−0.303196
$862$	7.56885			0.257796
$863$	−25.9200	−	44.8947i	−0.882327	−	1.52824i	−0.848747	−	0.528799i	$-0.822643\pi$
$863$	−25.9200	−	44.8947i	−0.882327	−	1.52824i	−0.0335798	−	0.999436i	$-0.510691\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$		−	31.6274i		−	1.07536i
$866$	−7.04194	+	4.06567i	−0.239295	+	0.138157i
$867$	8.36253	+	14.4843i	0.284007	+	0.491914i
$868$	1.79505	−	1.03637i	0.0609280	−	0.0351768i
$869$	1.71739	+	0.991537i	0.0582586	+	0.0336356i
$870$	−5.97473	−	3.44951i	−0.202562	−	0.116949i
$871$	−28.6640	+	16.5492i	−0.971242	+	0.560747i
$872$	7.10204	+	12.3011i	0.240506	+	0.416568i
$873$	−12.0730	+	6.97036i	−0.408610	+	0.235911i
$874$			22.6873i			0.767408i
$875$	13.6926	+	7.90543i	0.462895	+	0.267252i
$876$	−3.62590	−	6.28025i	−0.122508	−	0.212190i
$877$	−12.1192			−0.409238			−0.204619	−	0.978842i	$-0.565596\pi$
$877$	−12.1192			−0.409238			−0.204619	+	0.978842i	$0.565596\pi$
$878$	−15.9273			−0.537519
$879$	−13.4468	−	23.2905i	−0.453548	−	0.785568i
$880$		−	0.360721i		−	0.0121599i
$881$	−19.5794	+	33.9125i	−0.659647	+	1.14254i	0.321060	+	0.947059i	$0.395961\pi$
$881$	−19.5794	+	33.9125i	−0.659647	+	1.14254i	−0.980707	+	0.195483i	$0.937373\pi$
$882$		−	4.67639i		−	0.157462i
$883$	−36.4841	−	21.0641i	−1.22779	−	0.708864i	−0.261222	−	0.965279i	$-0.584125\pi$
$883$	−36.4841	−	21.0641i	−1.22779	−	0.708864i	−0.966567	+	0.256415i	$0.917459\pi$
$884$	0.732051	−	1.26795i	0.0246215	−	0.0426457i
$885$	9.87953	−	17.1118i	0.332097	−	0.575208i
$886$	21.6181	−	12.4812i	0.726273	−	0.419314i
$887$	25.2033			0.846245			0.423123	−	0.906072i	$-0.360934\pi$
$887$	25.2033			0.846245			0.423123	+	0.906072i	$0.360934\pi$
$888$	1.52663	−	5.88807i	0.0512303	−	0.197591i
$889$	−29.0450			−0.974140
$890$	−26.6544	+	15.3889i	−0.893458	+	0.515838i
$891$	0.0760282	−	0.131685i	0.00254704	−	0.00441161i
$892$	−6.77891	+	11.7414i	−0.226975	+	0.393132i
$893$	−24.2879	−	14.0226i	−0.812763	−	0.469249i
$894$		−	0.964787i		−	0.0322673i
$895$	24.2178	−	41.9465i	0.809513	−	1.40212i
$896$			1.52434i			0.0509246i
$897$	6.46868	+	11.2041i	0.215983	+	0.374093i
$898$	7.76821			0.259229
$899$	−3.95445			−0.131888
$900$	−0.313859	−	0.543620i	−0.0104620	−	0.0181207i
$901$	−1.43492	−	0.828451i	−0.0478041	−	0.0275997i
$902$			0.887460i			0.0295492i
$903$	−8.89438	+	5.13518i	−0.295987	+	0.170888i
$904$	−9.92820	−	17.1962i	−0.330207	−	0.571936i
$905$	3.82629	−	2.20911i	0.127190	−	0.0734333i
$906$	7.30069	+	4.21506i	0.242549	+	0.140036i
$907$	7.27399	+	4.19964i	0.241529	+	0.139447i	0.615879	−	0.787841i	$-0.288801\pi$
$907$	7.27399	+	4.19964i	0.241529	+	0.139447i	−0.374350	+	0.927287i	$0.622134\pi$
$908$	15.7297	−	9.08156i	0.522009	−	0.301382i
$909$	1.42674	+	2.47118i	0.0473219	+	0.0819639i
$910$	−8.74456	+	5.04868i	−0.289879	+	0.167362i
$911$		−	22.4588i		−	0.744092i	−0.928214	−	0.372046i	$-0.878656\pi$
$911$		−	22.4588i		−	0.744092i	0.928214	−	0.372046i	$-0.121344\pi$
$912$	−4.24060	−	2.44831i	−0.140420	−	0.0810716i
$913$	0.960484	+	1.66361i	0.0317874	+	0.0550573i
$914$	−36.4400			−1.20533
$915$	−20.1472			−0.666046
$916$	11.3206	+	19.6078i	0.374043	+	0.647861i
$917$		−	21.8072i		−	0.720137i
$918$	−0.262169	+	0.454090i	−0.00865286	+	0.0149872i
$919$			18.5374i			0.611492i	0.952113	+	0.305746i	$0.0989058\pi$
$919$			18.5374i			0.611492i	−0.952113	+	0.305746i	$0.901094\pi$
$920$	−9.51881	−	5.49569i	−0.313826	−	0.181187i
$921$	−8.34769	+	14.4586i	−0.275066	+	0.476428i
$922$	−14.0371	+	24.3130i	−0.462288	+	0.800706i
$923$	−11.1056	+	6.41180i	−0.365544	+	0.211047i
$924$	0.231785			0.00762518
$925$	−2.67793	+	2.72173i	−0.0880499	+	0.0894899i
$926$	17.0234			0.559423
$927$	−2.40421	+	1.38807i	−0.0789647	+	0.0455903i
$928$	1.45409	−	2.51856i	0.0477328	−	0.0826757i
$929$	−12.6898	+	21.9793i	−0.416337	+	0.721118i	−0.995568	−	0.0940462i	$-0.970020\pi$
$929$	−12.6898	+	21.9793i	−0.416337	+	0.721118i	0.579230	+	0.815164i	$0.303353\pi$
$930$	−2.79359	−	1.61288i	−0.0916053	−	0.0528883i
$931$			22.8985i			0.750469i
$932$	1.13048	−	1.95806i	0.0370302	−	0.0641383i
$933$		−	19.6885i		−	0.644572i
$934$	19.5809	+	33.9152i	0.640708	+	1.10974i
$935$	0.189140			0.00618552
$936$	−2.79229			−0.0912688
$937$	1.35088	+	2.33979i	0.0441312	+	0.0764374i	0.887247	−	0.461294i	$-0.152615\pi$
$937$	1.35088	+	2.33979i	0.0441312	+	0.0764374i	−0.843116	+	0.537732i	$0.819281\pi$
$938$	15.6480	+	9.03435i	0.510924	+	0.294982i
$939$		−	17.4188i		−	0.568440i
$940$	11.7668	−	6.79359i	0.383792	−	0.221582i
$941$	21.6831	+	37.5563i	0.706850	+	1.22430i	0.966020	+	0.258468i	$0.0832176\pi$
$941$	21.6831	+	37.5563i	0.706850	+	1.22430i	−0.259170	+	0.965832i	$0.583449\pi$
$942$	−5.63336	+	3.25242i	−0.183545	+	0.105970i
$943$	23.4186	+	13.5207i	0.762613	+	0.440295i
$944$	7.21324	+	4.16457i	0.234771	+	0.135545i
$945$	3.13168	−	1.80808i	0.101874	−	0.0588168i
$946$	0.512246	+	0.887237i	0.0166546	+	0.0288466i
$947$	−22.9311	+	13.2393i	−0.745162	+	0.430219i	−0.823943	−	0.566673i	$-0.808230\pi$
$947$	−22.9311	+	13.2393i	−0.745162	+	0.430219i	0.0787813	+	0.996892i	$0.474897\pi$
$948$			13.0417i			0.423575i
$949$	17.5363	+	10.1246i	0.569251	+	0.328657i
$950$	1.53685	+	2.66190i	0.0498620	+	0.0863635i
$951$	−22.3407			−0.724447
$952$	−0.799268			−0.0259044
$953$	−19.5299	−	33.8267i	−0.632635	−	1.09576i	−0.987011	−	0.160652i	$-0.948640\pi$
$953$	−19.5299	−	33.8267i	−0.632635	−	1.09576i	0.354377	−	0.935103i	$-0.384693\pi$
$954$			3.15999i			0.102308i
$955$	17.3297	−	30.0159i	0.560775	−	0.971291i
$956$			7.96842i			0.257717i
$957$	−0.382963	−	0.221104i	−0.0123794	−	0.00714727i
$958$	3.05566	−	5.29255i	0.0987238	−	0.170995i
$959$	−4.83913	+	8.38162i	−0.156264	+	0.270657i
$960$	2.05446	−	1.18614i	0.0663073	−	0.0382825i
$961$	29.1510			0.940356
$962$	4.52892	+	16.3699i	0.146018	+	0.527786i
$963$	18.9848			0.611777
$964$	8.51459	−	4.91590i	0.274237	−	0.158331i
$965$	4.28384	−	7.41983i	0.137902	−	0.238853i
$966$	3.53132	−	6.11642i	0.113618	−	0.196793i
$967$	−12.8538	−	7.42117i	−0.413352	−	0.238649i	0.278877	−	0.960327i	$-0.410038\pi$
$967$	−12.8538	−	7.42117i	−0.413352	−	0.238649i	−0.692229	+	0.721678i	$0.743371\pi$
$968$			10.9769i			0.352810i
$969$	1.28374	−	2.22351i	0.0412397	−	0.0714293i
$970$			33.0713i			1.06186i
$971$	0.0922408	+	0.159766i	0.00296015	+	0.00512713i	0.867502	−	0.497434i	$-0.165724\pi$
$971$	0.0922408	+	0.159766i	0.00296015	+	0.00512713i	−0.864542	+	0.502561i	$0.832391\pi$
$972$	1.00000			0.0320750
$973$	−5.42043			−0.173771
$974$	13.5368	+	23.4465i	0.433749	+	0.751275i
$975$	1.51794	+	0.876385i	0.0486131	+	0.0280668i
$976$		−	8.49275i		−	0.271846i
$977$	−48.9527	+	28.2629i	−1.56614	+	0.904209i	−0.569524	+	0.821975i	$0.692872\pi$
$977$	−48.9527	+	28.2629i	−1.56614	+	0.904209i	−0.996613	+	0.0822343i	$0.973794\pi$
$978$	−3.39963	−	5.88834i	−0.108708	−	0.188288i
$979$	−1.70847	+	0.986386i	−0.0546030	+	0.0315250i
$980$	−9.60745	−	5.54686i	−0.306899	−	0.177188i
$981$	12.3011	+	7.10204i	0.392744	+	0.226751i
$982$	4.80903	−	2.77649i	0.153462	−	0.0886015i
$983$	−22.8146	−	39.5160i	−0.727671	−	1.26036i	−0.957865	−	0.287219i	$-0.907269\pi$
$983$	−22.8146	−	39.5160i	−0.727671	−	1.26036i	0.230193	−	0.973145i	$-0.426064\pi$
$984$	−5.05446	+	2.91819i	−0.161130	+	0.0930285i
$985$		−	43.0405i		−	1.37139i
$986$	1.32057	+	0.762434i	0.0420557	+	0.0242809i
$987$	4.36530	+	7.56092i	0.138949	+	0.240667i
$988$	13.6728			0.434989
$989$	31.2169			0.992640
$990$	−0.180360	−	0.312393i	−0.00573223	−	0.00992851i
$991$			54.7351i			1.73872i	0.494181	+	0.869359i	$0.335468\pi$
$991$			54.7351i			1.73872i	−0.494181	+	0.869359i	$0.664532\pi$
$992$	0.679885	−	1.17759i	0.0215864	−	0.0373887i
$993$			11.5842i			0.367612i
$994$	6.06264	+	3.50027i	0.192295	+	0.111022i
$995$	15.4858	−	26.8223i	0.490934	−	0.850323i
$996$	−6.31662	+	10.9407i	−0.200150	+	0.346670i
$997$	−25.4594	+	14.6990i	−0.806309	+	0.465523i	−0.845672	−	0.533702i	$-0.820800\pi$
$997$	−25.4594	+	14.6990i	−0.806309	+	0.465523i	0.0393637	+	0.999225i	$0.487467\pi$
$998$	−11.7116			−0.370724
$999$	−1.62194	−	5.86253i	−0.0513159	−	0.185482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	222.2.j.b.85.3	✓	8
3.2	odd	2		666.2.s.f.307.2		8
4.3	odd	2		1776.2.bz.i.529.2		8
37.8	odd	12		8214.2.a.ba.1.1		4
37.27	even	6	inner	222.2.j.b.175.3	yes	8
37.29	odd	12		8214.2.a.z.1.3		4
111.101	odd	6		666.2.s.f.397.2		8
148.27	odd	6		1776.2.bz.i.1729.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
222.2.j.b.85.3	✓	8	1.1	even	1	trivial
222.2.j.b.175.3	yes	8	37.27	even	6	inner
666.2.s.f.307.2		8	3.2	odd	2
666.2.s.f.397.2		8	111.101	odd	6
1776.2.bz.i.529.2		8	4.3	odd	2
1776.2.bz.i.1729.2		8	148.27	odd	6
8214.2.a.z.1.3		4	37.29	odd	12
8214.2.a.ba.1.1		4	37.8	odd	12

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:	\( N \)	\(=\)	\( 222 = 2 \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	222.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.05446 - 1.18614i) q^{5} -1.00000i q^{6} +(0.762169 - 1.32012i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -2.37228 q^{10} -0.152056 q^{11} +(-0.500000 - 0.866025i) q^{12} +(2.41819 + 1.39614i) q^{13} -1.52434i q^{14} +(-2.05446 + 1.18614i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.454090 - 0.262169i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(4.24060 + 2.44831i) q^{19} +(-2.05446 + 1.18614i) q^{20} +(-0.762169 - 1.32012i) q^{21} +(-0.131685 + 0.0760282i) q^{22} +4.63325i q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.313859 + 0.543620i) q^{25} +2.79229 q^{26} -1.00000 q^{27} +(-0.762169 - 1.32012i) q^{28} +2.90818i q^{29} +(-1.18614 + 2.05446i) q^{30} +1.35977i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.0760282 + 0.131685i) q^{33} +(0.262169 - 0.454090i) q^{34} +(-3.13168 + 1.80808i) q^{35} -1.00000 q^{36} +(1.62194 + 5.86253i) q^{37} +4.89662 q^{38} +(2.41819 - 1.39614i) q^{39} +(-1.18614 + 2.05446i) q^{40} +(2.91819 - 5.05446i) q^{41} +(-1.32012 - 0.762169i) q^{42} -6.73758i q^{43} +(-0.0760282 + 0.131685i) q^{44} +2.37228i q^{45} +(2.31662 + 4.01251i) q^{46} -5.72747 q^{47} -1.00000 q^{48} +(2.33820 + 4.04988i) q^{49} +(0.543620 + 0.313859i) q^{50} -0.524338i q^{51} +(2.41819 - 1.39614i) q^{52} +(-1.57999 - 2.73663i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.312393 + 0.180360i) q^{55} +(-1.32012 - 0.762169i) q^{56} +(4.24060 - 2.44831i) q^{57} +(1.45409 + 2.51856i) q^{58} +(-7.21324 + 4.16457i) q^{59} +2.37228i q^{60} +(7.35494 + 4.24638i) q^{61} +(0.679885 + 1.17759i) q^{62} -1.52434 q^{63} -1.00000 q^{64} +(-3.31205 - 5.73663i) q^{65} +0.152056i q^{66} +(-5.92674 + 10.2654i) q^{67} -0.524338i q^{68} +(4.01251 + 2.31662i) q^{69} +(-1.80808 + 3.13168i) q^{70} +(-2.29625 + 3.97723i) q^{71} +(-0.866025 + 0.500000i) q^{72} +7.25181 q^{73} +(4.33591 + 4.26613i) q^{74} +0.627719 q^{75} +(4.24060 - 2.44831i) q^{76} +(-0.115893 + 0.200732i) q^{77} +(1.39614 - 2.41819i) q^{78} +(-11.2944 - 6.52085i) q^{79} +2.37228i q^{80} +(-0.500000 + 0.866025i) q^{81} -5.83638i q^{82} +(-6.31662 - 10.9407i) q^{83} -1.52434 q^{84} -1.24388 q^{85} +(-3.36879 - 5.83492i) q^{86} +(2.51856 + 1.45409i) q^{87} +0.152056i q^{88} +(11.2358 - 6.48697i) q^{89} +(1.18614 + 2.05446i) q^{90} +(3.68614 - 2.12819i) q^{91} +(4.01251 + 2.31662i) q^{92} +(1.17759 + 0.679885i) q^{93} +(-4.96014 + 2.86374i) q^{94} +(-5.80808 - 10.0599i) q^{95} +(-0.866025 + 0.500000i) q^{96} -13.9407i q^{97} +(4.04988 + 2.33820i) q^{98} +(0.0760282 + 0.131685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{7} - 4 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} - 6 q^{13} - 4 q^{16} + 6 q^{17} + 6 q^{19} + 4 q^{21} - 6 q^{22} + 14 q^{25} + 16 q^{26} - 8 q^{27} + 4 q^{28} + 2 q^{30} - 2 q^{33}+ \cdots + 2 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^7 - 4 * q^9 + 4 * q^10 - 4 * q^11 - 4 * q^12 - 6 * q^13 - 4 * q^16 + 6 * q^17 + 6 * q^19 + 4 * q^21 - 6 * q^22 + 14 * q^25 + 16 * q^26 - 8 * q^27 + 4 * q^28 + 2 * q^30 - 2 * q^33 - 8 * q^34 - 30 * q^35 - 8 * q^36 + 12 * q^37 - 4 * q^38 - 6 * q^39 + 2 * q^40 - 2 * q^41 - 6 * q^42 - 2 * q^44 - 8 * q^46 - 28 * q^47 - 8 * q^48 + 10 * q^49 - 6 * q^52 + 4 * q^53 + 30 * q^55 - 6 * q^56 + 6 * q^57 + 14 * q^58 + 12 * q^59 - 36 * q^61 + 10 * q^62 + 8 * q^63 - 8 * q^64 + 4 * q^65 - 8 * q^67 - 2 * q^70 + 6 * q^71 + 20 * q^73 + 24 * q^74 + 28 * q^75 + 6 * q^76 - 12 * q^77 + 8 * q^78 - 24 * q^79 - 4 * q^81 - 24 * q^83 + 8 * q^84 - 8 * q^85 + 18 * q^86 - 24 * q^87 - 42 * q^89 - 2 * q^90 + 18 * q^91 + 12 * q^93 - 30 * q^94 - 34 * q^95 + 12 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more