LMFDB - Embedded newform 189.2.u.a.16.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(4,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2, 12]))

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

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

chi := DirichletCharacter("189.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.u (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			16.5
Character	$\chi$	$=$	189.16
Dual form			189.2.u.a.130.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.82816 + 0.665398i) q^{2} +(-0.461596 - 1.66941i) q^{3} +(1.36734 - 1.14734i) q^{4} +(2.57005 - 2.15653i) q^{5} +(1.95469 + 2.74481i) q^{6} +(-1.50198 + 2.17808i) q^{7} +(0.209199 - 0.362343i) q^{8} +(-2.57386 + 1.54119i) q^{9} +O(q^{10})$	\(q+(-1.82816 + 0.665398i) q^{2} +(-0.461596 - 1.66941i) q^{3} +(1.36734 - 1.14734i) q^{4} +(2.57005 - 2.15653i) q^{5} +(1.95469 + 2.74481i) q^{6} +(-1.50198 + 2.17808i) q^{7} +(0.209199 - 0.362343i) q^{8} +(-2.57386 + 1.54119i) q^{9} +(-3.26352 + 5.65259i) q^{10} +(-3.43544 - 2.88268i) q^{11} +(-2.54654 - 1.75305i) q^{12} +(2.58000 - 2.16488i) q^{13} +(1.29658 - 4.98131i) q^{14} +(-4.78645 - 3.29502i) q^{15} +(-0.761251 + 4.31727i) q^{16} +(1.98260 - 3.43397i) q^{17} +(3.67994 - 4.53018i) q^{18} +(-2.48870 - 4.31055i) q^{19} +(1.03987 - 5.89742i) q^{20} +(4.32942 + 1.50203i) q^{21} +(8.19868 + 2.98408i) q^{22} +(-2.08727 - 0.759706i) q^{23} +(-0.701464 - 0.181983i) q^{24} +(1.08630 - 6.16070i) q^{25} +(-3.27617 + 5.67449i) q^{26} +(3.76095 + 3.58542i) q^{27} +(0.445273 + 4.70147i) q^{28} +(-3.26643 - 2.74086i) q^{29} +(10.9429 + 2.83895i) q^{30} +(-1.78723 + 1.49966i) q^{31} +(-1.33570 - 7.57513i) q^{32} +(-3.22659 + 7.06579i) q^{33} +(-1.33957 + 7.59708i) q^{34} +(0.836932 + 8.83684i) q^{35} +(-1.75109 + 5.06041i) q^{36} -2.99931 q^{37} +(7.41798 + 6.22442i) q^{38} +(-4.80499 - 3.30778i) q^{39} +(-0.243751 - 1.38238i) q^{40} +(0.219856 - 0.184481i) q^{41} +(-8.91435 + 0.134834i) q^{42} +(9.46658 - 3.44555i) q^{43} -8.00483 q^{44} +(-3.29133 + 9.51151i) q^{45} +4.32139 q^{46} +(4.14512 + 3.47817i) q^{47} +(7.55868 - 0.721993i) q^{48} +(-2.48810 - 6.54288i) q^{49} +(2.11338 + 11.9856i) q^{50} +(-6.64787 - 1.72467i) q^{51} +(1.04390 - 5.92027i) q^{52} +(5.11933 + 8.86693i) q^{53} +(-9.26137 - 4.05221i) q^{54} -15.0458 q^{55} +(0.475001 + 0.999885i) q^{56} +(-6.04730 + 6.14439i) q^{57} +(7.79533 + 2.83727i) q^{58} +(0.580445 + 3.29187i) q^{59} +(-10.3252 + 0.986248i) q^{60} +(7.93772 + 6.66054i) q^{61} +(2.26947 - 3.93084i) q^{62} +(0.509055 - 7.92091i) q^{63} +(3.09848 + 5.36673i) q^{64} +(1.96211 - 11.1277i) q^{65} +(1.19717 - 15.0644i) q^{66} +(11.9337 + 4.34350i) q^{67} +(-1.22902 - 6.97013i) q^{68} +(-0.304783 + 3.83519i) q^{69} +(-7.41006 - 15.5983i) q^{70} +(2.77738 + 4.81056i) q^{71} +(0.0199895 + 1.25503i) q^{72} +4.60079 q^{73} +(5.48323 - 1.99573i) q^{74} +(-10.7862 + 1.03028i) q^{75} +(-8.34856 - 3.03863i) q^{76} +(11.4387 - 3.15295i) q^{77} +(10.9853 + 2.84994i) q^{78} +(-1.16530 + 0.424136i) q^{79} +(7.35385 + 12.7372i) q^{80} +(4.24950 - 7.93359i) q^{81} +(-0.279180 + 0.483554i) q^{82} +(-8.72055 - 7.31741i) q^{83} +(7.64314 - 2.91352i) q^{84} +(-2.31006 - 13.1010i) q^{85} +(-15.0138 + 12.5981i) q^{86} +(-3.06785 + 6.71818i) q^{87} +(-1.76321 + 0.641755i) q^{88} +(-6.13111 - 10.6194i) q^{89} +(-0.311839 - 19.5786i) q^{90} +(0.840175 + 8.87108i) q^{91} +(-3.72566 + 1.35603i) q^{92} +(3.32853 + 2.29138i) q^{93} +(-9.89232 - 3.60051i) q^{94} +(-15.6919 - 5.71138i) q^{95} +(-12.0294 + 5.72648i) q^{96} +(10.3763 - 3.77665i) q^{97} +(8.90228 + 10.3059i) q^{98} +(13.2851 + 2.12495i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.82816	+	0.665398i	−1.29271	+	0.470507i	−0.894615	−	0.446838i	$-0.852550\pi$
$2$	−1.82816	+	0.665398i	−1.29271	+	0.470507i	−0.398093	+	0.917345i	$0.630328\pi$
$3$	−0.461596	−	1.66941i	−0.266502	−	0.963834i
$3$	−0.461596	−	1.66941i	−0.266502	−	0.963834i
$4$	1.36734	−	1.14734i	0.683672	−	0.573669i
$5$	2.57005	−	2.15653i	1.14936	−	0.964427i	0.149655	−	0.988738i	$-0.452184\pi$
$5$	2.57005	−	2.15653i	1.14936	−	0.964427i	0.999704	+	0.0243109i	$0.00773915\pi$
$6$	1.95469	+	2.74481i	0.798001	+	1.12056i
$7$	−1.50198	+	2.17808i	−0.567696	+	0.823239i
$7$	−1.50198	+	2.17808i	−0.567696	+	0.823239i
$8$	0.209199	−	0.362343i	0.0739629	−	0.128108i
$9$	−2.57386	+	1.54119i	−0.857953	+	0.513728i
$10$	−3.26352	+	5.65259i	−1.03202	+	1.78750i
$11$	−3.43544	−	2.88268i	−1.03582	−	0.869160i	−0.0442922	−	0.999019i	$-0.514103\pi$
$11$	−3.43544	−	2.88268i	−1.03582	−	0.869160i	−0.991533	+	0.129858i	$0.958548\pi$
$12$	−2.54654	−	1.75305i	−0.735122	−	0.506062i
$13$	2.58000	−	2.16488i	0.715564	−	0.600430i	−0.210590	−	0.977574i	$-0.567538\pi$
$13$	2.58000	−	2.16488i	0.715564	−	0.600430i	0.926154	+	0.377145i	$0.123094\pi$
$14$	1.29658	−	4.98131i	0.346525	−	1.33131i
$15$	−4.78645	−	3.29502i	−1.23586	−	0.850770i
$16$	−0.761251	+	4.31727i	−0.190313	+	1.07932i
$17$	1.98260	−	3.43397i	0.480852	−	0.832860i	−0.518907	−	0.854831i	$-0.673661\pi$
$17$	1.98260	−	3.43397i	0.480852	−	0.832860i	0.999759	+	0.0219708i	$0.00699407\pi$
$18$	3.67994	−	4.53018i	0.867369	−	1.06777i
$19$	−2.48870	−	4.31055i	−0.570946	−	0.988908i	−0.996469	−	0.0839604i	$-0.973243\pi$
$19$	−2.48870	−	4.31055i	−0.570946	−	0.988908i	0.425523	−	0.904948i	$-0.360090\pi$
$20$	1.03987	−	5.89742i	0.232523	−	1.31870i
$21$	4.32942	+	1.50203i	0.944758	+	0.327769i
$22$	8.19868	+	2.98408i	1.74796	+	0.636207i
$23$	−2.08727	−	0.759706i	−0.435227	−	0.158410i	0.115109	−	0.993353i	$-0.463278\pi$
$23$	−2.08727	−	0.759706i	−0.435227	−	0.158410i	−0.550336	+	0.834943i	$0.685500\pi$
$24$	−0.701464	−	0.181983i	−0.143186	−	0.0371470i
$25$	1.08630	−	6.16070i	0.217260	−	1.23214i
$26$	−3.27617	+	5.67449i	−0.642509	+	1.11286i
$27$	3.76095	+	3.58542i	0.723796	+	0.690014i
$28$	0.445273	+	4.70147i	0.0841488	+	0.888494i
$29$	−3.26643	−	2.74086i	−0.606561	−	0.508965i	0.286986	−	0.957935i	$-0.407347\pi$
$29$	−3.26643	−	2.74086i	−0.606561	−	0.508965i	−0.893547	+	0.448970i	$0.851791\pi$
$30$	10.9429	+	2.83895i	1.99789	+	0.518318i
$31$	−1.78723	+	1.49966i	−0.320995	+	0.269347i	−0.789019	−	0.614369i	$-0.789411\pi$
$31$	−1.78723	+	1.49966i	−0.320995	+	0.269347i	0.468024	+	0.883716i	$0.344966\pi$
$32$	−1.33570	−	7.57513i	−0.236121	−	1.33911i
$33$	−3.22659	+	7.06579i	−0.561676	+	1.23000i
$34$	−1.33957	+	7.59708i	−0.229734	+	1.30289i
$35$	0.836932	+	8.83684i	0.141467	+	1.49370i
$36$	−1.75109	+	5.06041i	−0.291848	+	0.843402i
$37$	−2.99931			−0.493083			−0.246541	−	0.969132i	$-0.579294\pi$
$37$	−2.99931			−0.493083			−0.246541	+	0.969132i	$0.579294\pi$
$38$	7.41798	+	6.22442i	1.20336	+	1.00973i
$39$	−4.80499	−	3.30778i	−0.769415	−	0.529669i
$40$	−0.243751	−	1.38238i	−0.0385404	−	0.218574i
$41$	0.219856	−	0.184481i	0.0343358	−	0.0288112i	−0.625458	−	0.780258i	$-0.715088\pi$
$41$	0.219856	−	0.184481i	0.0343358	−	0.0288112i	0.659794	+	0.751446i	$0.270644\pi$
$42$	−8.91435	+	0.134834i	−1.37551	+	0.0208054i
$43$	9.46658	−	3.44555i	1.44364	−	0.525442i	0.502833	−	0.864384i	$-0.332291\pi$
$43$	9.46658	−	3.44555i	1.44364	−	0.525442i	0.940807	+	0.338942i	$0.110069\pi$
$44$	−8.00483			−1.20677
$45$	−3.29133	+	9.51151i	−0.490643	+	1.41789i
$46$	4.32139			0.637154
$47$	4.14512	+	3.47817i	0.604628	+	0.507343i	0.892929	−	0.450197i	$-0.148646\pi$
$47$	4.14512	+	3.47817i	0.604628	+	0.507343i	−0.288302	+	0.957540i	$0.593091\pi$
$48$	7.55868	−	0.721993i	1.09100	−	0.104211i
$49$	−2.48810	−	6.54288i	−0.355443	−	0.934698i
$50$	2.11338	+	11.9856i	0.298878	+	1.69502i
$51$	−6.64787	−	1.72467i	−0.930887	−	0.241502i
$52$	1.04390	−	5.92027i	0.144763	−	0.820994i
$53$	5.11933	+	8.86693i	0.703194	+	1.21797i	0.967340	+	0.253484i	$0.0815766\pi$
$53$	5.11933	+	8.86693i	0.703194	+	1.21797i	−0.264146	+	0.964483i	$0.585090\pi$
$54$	−9.26137	−	4.05221i	−1.26031	−	0.551436i
$55$	−15.0458			−2.02878
$56$	0.475001	+	0.999885i	0.0634747	+	0.133615i
$57$	−6.04730	+	6.14439i	−0.800985	+	0.813844i
$58$	7.79533	+	2.83727i	1.02358	+	0.372552i
$59$	0.580445	+	3.29187i	0.0755675	+	0.428564i	0.998996	+	0.0447945i	$0.0142633\pi$
$59$	0.580445	+	3.29187i	0.0755675	+	0.428564i	−0.923429	+	0.383770i	$0.874626\pi$
$60$	−10.3252	+	0.986248i	−1.33298	+	0.127324i
$61$	7.93772	+	6.66054i	1.01632	+	0.852795i	0.989161	−	0.146836i	$-0.0469090\pi$
$61$	7.93772	+	6.66054i	1.01632	+	0.852795i	0.0271605	+	0.999631i	$0.491353\pi$
$62$	2.26947	−	3.93084i	0.288223	−	0.499218i
$63$	0.509055	−	7.92091i	0.0641350	−	0.997941i
$64$	3.09848	+	5.36673i	0.387310	+	0.670841i
$65$	1.96211	−	11.1277i	0.243370	−	1.38022i
$66$	1.19717	−	15.0644i	0.147361	−	1.85430i
$67$	11.9337	+	4.34350i	1.45793	+	0.530643i	0.944794	−	0.327665i	$-0.106262\pi$
$67$	11.9337	+	4.34350i	1.45793	+	0.530643i	0.513135	+	0.858308i	$0.328484\pi$
$68$	−1.22902	−	6.97013i	−0.149041	−	0.845253i
$69$	−0.304783	+	3.83519i	−0.0366916	+	0.461703i
$70$	−7.41006	−	15.5983i	−0.885672	−	1.86435i
$71$	2.77738	+	4.81056i	0.329614	+	0.570908i	0.982435	−	0.186604i	$-0.0597480\pi$
$71$	2.77738	+	4.81056i	0.329614	+	0.570908i	−0.652821	+	0.757512i	$0.726415\pi$
$72$	0.0199895	+	1.25503i	0.00235579	+	0.147907i
$73$	4.60079			0.538482			0.269241	−	0.963073i	$-0.413227\pi$
$73$	4.60079			0.538482			0.269241	+	0.963073i	$0.413227\pi$
$74$	5.48323	−	1.99573i	0.637412	−	0.231999i
$75$	−10.7862	+	1.03028i	−1.24548	+	0.118966i
$76$	−8.34856	−	3.03863i	−0.957646	−	0.348554i
$77$	11.4387	−	3.15295i	1.30356	−	0.359313i
$78$	10.9853	+	2.84994i	1.24384	+	0.322693i
$79$	−1.16530	+	0.424136i	−0.131107	+	0.0477190i	−0.406740	−	0.913544i	$-0.633335\pi$
$79$	−1.16530	+	0.424136i	−0.131107	+	0.0477190i	0.275633	+	0.961263i	$0.411112\pi$
$80$	7.35385	+	12.7372i	0.822185	+	1.42407i
$81$	4.24950	−	7.93359i	0.472166	−	0.881510i
$82$	−0.279180	+	0.483554i	−0.0308303	+	0.0533996i
$83$	−8.72055	−	7.31741i	−0.957205	−	0.803190i	0.0232914	−	0.999729i	$-0.492585\pi$
$83$	−8.72055	−	7.31741i	−0.957205	−	0.803190i	−0.980496	+	0.196539i	$0.937030\pi$
$84$	7.64314	−	2.91352i	0.833935	−	0.317891i
$85$	−2.31006	−	13.1010i	−0.250561	−	1.42100i
$86$	−15.0138	+	12.5981i	−1.61898	+	1.35849i
$87$	−3.06785	+	6.71818i	−0.328908	+	0.720264i
$88$	−1.76321	+	0.641755i	−0.187959	+	0.0684114i
$89$	−6.13111	−	10.6194i	−0.649896	−	1.12565i	−0.983147	−	0.182815i	$-0.941479\pi$
$89$	−6.13111	−	10.6194i	−0.649896	−	1.12565i	0.333251	−	0.942838i	$-0.391854\pi$
$90$	−0.311839	−	19.5786i	−0.0328707	−	2.06377i
$91$	0.840175	+	8.87108i	0.0880743	+	0.929942i
$92$	−3.72566	+	1.35603i	−0.388427	+	0.141376i
$93$	3.32853	+	2.29138i	0.345152	+	0.237605i
$94$	−9.89232	−	3.60051i	−1.02032	−	0.371364i
$95$	−15.6919	−	5.71138i	−1.60995	−	0.585975i
$96$	−12.0294	+	5.72648i	−1.22775	+	0.584456i
$97$	10.3763	−	3.77665i	1.05355	−	0.383461i	0.243548	−	0.969889i	$-0.421689\pi$
$97$	10.3763	−	3.77665i	1.05355	−	0.383461i	0.810001	+	0.586428i	$0.199466\pi$
$98$	8.90228	+	10.3059i	0.899266	+	1.04105i
$99$	13.2851	+	2.12495i	1.33520	+	0.213566i
$100$	−5.58306	−	9.67014i	−0.558306	−	0.967014i
$101$	−0.802721	+	0.292167i	−0.0798737	+	0.0290717i	−0.381648	−	0.924308i	$-0.624643\pi$
$101$	−0.802721	+	0.292167i	−0.0798737	+	0.0290717i	0.301774	+	0.953379i	$0.402421\pi$
$102$	13.3010	−	1.27049i	1.31699	−	0.125797i
$103$	−0.555280	+	0.465935i	−0.0547133	+	0.0459099i	−0.669734	−	0.742601i	$-0.733592\pi$
$103$	−0.555280	+	0.465935i	−0.0547133	+	0.0459099i	0.615021	+	0.788511i	$0.289148\pi$
$104$	−0.244695	−	1.38774i	−0.0239944	−	0.136079i
$105$	14.3660	−	5.47623i	1.40198	−	0.534425i
$106$	−15.2590	−	12.8038i	−1.48209	−	1.24362i
$107$	6.26413	−	10.8498i	0.605577	−	1.04889i	−0.386384	−	0.922338i	$-0.626276\pi$
$107$	6.26413	−	10.8498i	0.605577	−	1.04889i	0.991960	−	0.126551i	$-0.0403908\pi$
$108$	9.25620	+	0.587419i	0.890678	+	0.0565244i
$109$	2.45242	+	4.24772i	0.234899	+	0.406857i	0.959243	−	0.282581i	$-0.0911906\pi$
$109$	2.45242	+	4.24772i	0.234899	+	0.406857i	−0.724344	+	0.689439i	$0.757857\pi$
$110$	27.5062	−	10.0114i	2.62262	−	0.954554i
$111$	1.38447	+	5.00707i	0.131408	+	0.475250i
$112$	−8.25999	−	8.14253i	−0.780496	−	0.769396i
$113$	−4.66204	−	1.69685i	−0.438568	−	0.159626i	0.113293	−	0.993562i	$-0.463860\pi$
$113$	−4.66204	−	1.69685i	−0.438568	−	0.159626i	−0.551861	+	0.833936i	$0.686082\pi$
$114$	6.96701	−	15.2568i	0.652520	−	1.42893i
$115$	−7.00272	+	2.54878i	−0.653007	+	0.237675i
$116$	−7.61102			−0.706665
$117$	−3.30408	+	9.54836i	−0.305463	+	0.882746i
$118$	−3.25155	−	5.63185i	−0.299329	−	0.518454i
$119$	4.50164	+	9.47604i	0.412665	+	0.868667i
$120$	−2.19525	+	1.04502i	−0.200398	+	0.0953970i
$121$	1.58230	+	8.97366i	0.143845	+	0.815787i
$122$	−18.9434	−	6.89482i	−1.71505	−	0.624228i
$123$	−0.409460	−	0.281875i	−0.0369197	−	0.0254158i
$124$	−0.723135	+	4.10110i	−0.0649395	+	0.368290i
$125$	−2.10648	−	3.64853i	−0.188409	−	0.326334i
$126$	4.33992	+	14.8195i	0.386631	+	1.32022i
$127$	−0.898740	+	1.55666i	−0.0797503	+	0.138132i	−0.903142	−	0.429342i	$-0.858746\pi$
$127$	−0.898740	+	1.55666i	−0.0797503	+	0.138132i	0.823392	+	0.567473i	$0.192079\pi$
$128$	2.54927	+	2.13909i	0.225325	+	0.189070i
$129$	−10.1218	−	14.2131i	−0.891173	−	1.25140i
$130$	3.81727	+	21.6488i	0.334797	+	1.89873i
$131$	8.38840	+	3.05313i	0.732898	+	0.266753i	0.681391	−	0.731919i	$-0.261375\pi$
$131$	8.38840	+	3.05313i	0.732898	+	0.266753i	0.0515071	+	0.998673i	$0.483598\pi$
$132$	3.69500	+	13.3633i	0.321608	+	1.16313i
$133$	13.1267	+	1.05377i	1.13823	+	0.0913737i
$134$	−24.7069			−2.13435
$135$	17.3979	+	1.10411i	1.49737	+	0.0950265i
$136$	−0.829517	−	1.43676i	−0.0711305	−	0.123202i
$137$	−3.26623	+	18.5237i	−0.279053	+	1.58259i	0.446734	+	0.894667i	$0.352587\pi$
$137$	−3.26623	+	18.5237i	−0.279053	+	1.58259i	−0.725787	+	0.687920i	$0.758524\pi$
$138$	−1.99473	−	7.21417i	−0.169803	−	0.614111i
$139$	2.88707	+	16.3734i	0.244878	+	1.38877i	0.820777	+	0.571249i	$0.193541\pi$
$139$	2.88707	+	16.3734i	0.244878	+	1.38877i	−0.575899	+	0.817521i	$0.695348\pi$
$140$	11.2832	+	11.1227i	0.953605	+	0.940044i
$141$	3.89312	−	8.52541i	0.327860	−	0.717969i
$142$	−8.27844	−	6.94643i	−0.694711	−	0.582932i
$143$	−15.1041			−1.26307
$144$	−4.69436	−	12.2853i	−0.391197	−	1.02377i
$145$	−14.3056			−1.18802
$146$	−8.41101	+	3.06136i	−0.696100	+	0.253360i
$147$	−9.77426	+	7.17383i	−0.806167	+	0.591688i
$148$	−4.10108	+	3.44122i	−0.337107	+	0.282866i
$149$	0.159252	+	0.903164i	0.0130464	+	0.0739900i	0.990636	−	0.136531i	$-0.0435952\pi$
$149$	0.159252	+	0.903164i	0.0130464	+	0.0739900i	−0.977589	+	0.210521i	$0.932484\pi$
$150$	19.0333	−	9.06061i	1.55407	−	0.739795i
$151$	−7.81741	−	6.55958i	−0.636172	−	0.533811i	0.266668	−	0.963788i	$-0.414077\pi$
$151$	−7.81741	−	6.55958i	−0.636172	−	0.533811i	−0.902840	+	0.429977i	$0.858522\pi$
$152$	−2.08253			−0.168916
$153$	0.189443	+	11.8941i	0.0153156	+	0.961582i
$154$	−18.8138	+	13.3754i	−1.51606	+	1.07782i
$155$	−1.35920	+	7.70840i	−0.109173	+	0.619153i
$156$	−10.3652	+	0.990070i	−0.829882	+	0.0792690i
$157$	−0.726950	−	4.12274i	−0.0580169	−	0.329030i	0.941961	−	0.335723i	$-0.108981\pi$
$157$	−0.726950	−	4.12274i	−0.0580169	−	0.329030i	−0.999978	+	0.00669296i	$0.997870\pi$
$158$	1.84815	−	1.55078i	0.147031	−	0.123373i
$159$	12.4395	−	12.6392i	0.986515	−	1.00235i
$160$	−19.7688	−	16.5880i	−1.56286	−	1.31139i
$161$	4.78975	−	3.40520i	0.377485	−	0.268367i
$162$	−2.48979	+	17.3315i	−0.195616	+	1.36169i
$163$	5.01262	−	8.68211i	0.392619	−	0.680036i	−0.600175	−	0.799868i	$-0.704903\pi$
$163$	5.01262	−	8.68211i	0.392619	−	0.680036i	0.992794	+	0.119833i	$0.0382359\pi$
$164$	0.0889567	−	0.504499i	0.00694635	−	0.0393947i
$165$	6.94509	+	25.1176i	0.540674	+	1.95540i
$166$	20.8116	+	7.57480i	1.61529	+	0.587918i
$167$	−14.3390	−	5.21896i	−1.10958	−	0.403855i	−0.278743	−	0.960366i	$-0.589918\pi$
$167$	−14.3390	−	5.21896i	−1.10958	−	0.403855i	−0.830841	+	0.556510i	$0.812140\pi$
$168$	1.44996	−	1.25451i	0.111867	−	0.0967878i
$169$	−0.287712	+	1.63170i	−0.0221317	+	0.125515i
$170$	12.9405	+	22.4137i	0.992494	+	1.71905i
$171$	13.0489	+	7.25920i	0.997875	+	0.555125i
$172$	8.99085	−	15.5726i	0.685546	−	1.18740i
$173$	−1.63308	+	9.26168i	−0.124161	+	0.704152i	0.857642	+	0.514248i	$0.171929\pi$
$173$	−1.63308	+	9.26168i	−0.124161	+	0.704152i	−0.981803	+	0.189904i	$0.939182\pi$
$174$	1.13827	−	14.3233i	0.0862921	−	1.08584i
$175$	11.7869	+	11.6193i	0.891008	+	0.878337i
$176$	15.0605	−	12.6373i	1.13523	−	0.952571i
$177$	5.22754	−	2.48851i	0.392926	−	0.187048i
$178$	18.2748	+	15.3344i	1.36975	+	1.14936i
$179$	−1.43683	+	2.48866i	−0.107394	+	0.186011i	−0.914714	−	0.404103i	$-0.867584\pi$
$179$	−1.43683	+	2.48866i	−0.107394	+	0.186011i	0.807320	+	0.590114i	$0.200917\pi$
$180$	6.41253	+	16.7818i	0.477962	+	1.25084i
$181$	−2.27490	+	3.94025i	−0.169092	+	0.292876i	−0.938101	−	0.346362i	$-0.887417\pi$
$181$	−2.27490	+	3.94025i	−0.169092	+	0.292876i	0.769009	+	0.639238i	$0.220750\pi$
$182$	−7.43877	−	15.6587i	−0.551398	−	1.16070i
$183$	7.45515	−	16.3258i	0.551101	−	1.20684i
$184$	−0.711929	+	0.597379i	−0.0524841	+	0.0440394i
$185$	−7.70836	+	6.46808i	−0.566730	+	0.475543i
$186$	−7.60977	−	1.97422i	−0.557975	−	0.144757i
$187$	−16.7102	+	6.08200i	−1.22197	+	0.444760i
$188$	9.65843			0.704414
$189$	−13.4582	+	2.80644i	−0.978942	+	0.204138i
$190$	32.4877			2.35690
$191$	16.6574	−	6.06279i	1.20529	−	0.438688i	0.340219	−	0.940346i	$-0.389499\pi$
$191$	16.6574	−	6.06279i	1.20529	−	0.438688i	0.865066	+	0.501658i	$0.167276\pi$
$192$	7.52902	−	7.64990i	0.543360	−	0.552084i
$193$	15.0845	−	12.6574i	1.08580	−	0.911097i	0.0894140	−	0.995995i	$-0.471501\pi$
$193$	15.0845	−	12.6574i	1.08580	−	0.911097i	0.996390	+	0.0848971i	$0.0270561\pi$
$194$	−16.4565	+	13.8087i	−1.18151	+	0.991405i
$195$	−19.4824	+	1.86093i	−1.39516	+	0.133264i
$196$	−10.9090	−	6.09167i	−0.779213	−	0.435120i
$197$	9.63644	−	16.6908i	0.686568	−	1.18917i	−0.286373	−	0.958118i	$-0.592450\pi$
$197$	9.63644	−	16.6908i	0.686568	−	1.18917i	0.972941	−	0.231052i	$-0.0742169\pi$
$198$	−25.7013	+	4.95510i	−1.82651	+	0.352143i
$199$	5.78264	−	10.0158i	0.409921	−	0.710003i	−0.584960	−	0.811062i	$-0.698890\pi$
$199$	5.78264	−	10.0158i	0.409921	−	0.710003i	0.994880	+	0.101059i	$0.0322231\pi$
$200$	−2.00503	−	1.68242i	−0.141777	−	0.118965i
$201$	1.74255	−	21.9271i	0.122910	−	1.54662i
$202$	1.27310	−	1.06826i	0.0895750	−	0.0751623i
$203$	10.8759	−	2.99784i	0.763341	−	0.210407i
$204$	−11.0687	+	5.26913i	−0.774964	+	0.368913i
$205$	0.167202	−	0.948251i	0.0116779	−	0.0662288i
$206$	0.705111	−	1.22129i	0.0491274	−	0.0850911i
$207$	6.54320	−	1.26150i	0.454784	−	0.0876804i
$208$	7.38234	+	12.7866i	0.511873	+	0.886590i
$209$	−3.87615	+	21.9828i	−0.268119	+	1.52058i
$210$	−22.6195	+	19.5705i	−1.56089	+	1.35050i
$211$	−20.8302	−	7.58159i	−1.43401	−	0.521938i	−0.495934	−	0.868360i	$-0.665174\pi$
$211$	−20.8302	−	7.58159i	−1.43401	−	0.521938i	−0.938079	+	0.346422i	$0.887397\pi$
$212$	17.1732	+	6.25055i	1.17946	+	0.429289i
$213$	6.74877	−	6.85712i	0.462418	−	0.469842i
$214$	−4.23244	+	24.0034i	−0.289324	+	1.64084i
$215$	16.8991	−	29.2701i	1.15251	−	1.99621i
$216$	2.08594	−	0.612689i	0.141930	−	0.0416882i
$217$	−0.582008	−	6.14519i	−0.0395093	−	0.417163i
$218$	−7.30985	−	6.13369i	−0.495085	−	0.415426i
$219$	−2.12371	−	7.68061i	−0.143507	−	0.519008i
$220$	−20.5728	+	17.2626i	−1.38702	+	1.16385i
$221$	−2.31901	−	13.1518i	−0.155993	−	0.884683i
$222$	−5.86273	−	8.23253i	−0.393481	−	0.552531i
$223$	−3.09264	+	17.5392i	−0.207098	+	1.17451i	0.687005	+	0.726652i	$0.258925\pi$
$223$	−3.09264	+	17.5392i	−0.207098	+	1.17451i	−0.894104	+	0.447860i	$0.852186\pi$
$224$	18.5055	+	8.46844i	1.23645	+	0.565821i
$225$	6.69881	+	17.5310i	0.446587	+	1.16873i
$226$	9.65206			0.642046
$227$	2.45756	+	2.06214i	0.163114	+	0.136869i	0.720691	−	0.693256i	$-0.243825\pi$
$227$	2.45756	+	2.06214i	0.163114	+	0.136869i	−0.557577	+	0.830125i	$0.688269\pi$
$228$	−1.21905	+	15.3398i	−0.0807338	+	1.01590i
$229$	−0.702262	−	3.98273i	−0.0464068	−	0.263186i	0.952773	−	0.303684i	$-0.0982167\pi$
$229$	−0.702262	−	3.98273i	−0.0464068	−	0.263186i	−0.999180	+	0.0404979i	$0.987106\pi$
$230$	11.1062	−	9.31918i	0.732319	−	0.614489i
$231$	−10.5436	−	17.6405i	−0.693720	−	1.16066i
$232$	−1.67646	+	0.610183i	−0.110065	+	0.0400605i
$233$	−15.3473			−1.00543			−0.502717	−	0.864451i	$-0.667666\pi$
$233$	−15.3473			−1.00543			−0.502717	+	0.864451i	$0.667666\pi$
$234$	−0.313047	−	19.6545i	−0.0204645	−	1.28486i
$235$	18.1539			1.18423
$236$	4.57055	+	3.83515i	0.297517	+	0.249647i
$237$	1.24596	+	1.74959i	0.0809335	+	0.113648i
$238$	−14.5351	−	14.3284i	−0.942169	−	0.928771i
$239$	−0.262379	−	1.48803i	−0.0169719	−	0.0962524i	0.975145	−	0.221567i	$-0.0711171\pi$
$239$	−0.262379	−	1.48803i	−0.0169719	−	0.0962524i	−0.992117	+	0.125315i	$0.960006\pi$
$240$	17.8692	−	18.1560i	1.15345	−	1.17197i
$241$	3.33261	−	18.9002i	0.214672	−	1.21747i	−0.666802	−	0.745235i	$-0.732337\pi$
$241$	3.33261	−	18.9002i	0.214672	−	1.21747i	0.881474	−	0.472232i	$-0.156551\pi$
$242$	−8.86376	−	15.3525i	−0.569784	−	0.986894i
$243$	−15.2060	−	3.43204i	−0.975463	−	0.220165i
$244$	18.4955			1.18405
$245$	−20.5044	−	11.4499i	−1.30998	−	0.731505i
$246$	0.936119	+	0.242859i	0.0596847	+	0.0154842i
$247$	−15.7527	−	5.73351i	−1.00232	−	0.364814i
$248$	0.169506	+	0.961316i	0.0107636	+	0.0610436i
$249$	−8.19039	+	17.9359i	−0.519045	+	1.13664i
$250$	6.27871	+	5.26846i	0.397100	+	0.333207i
$251$	4.44988	−	7.70741i	0.280874	−	0.486488i	−0.690726	−	0.723116i	$-0.742709\pi$
$251$	4.44988	−	7.70741i	0.280874	−	0.486488i	0.971600	+	0.236629i	$0.0760424\pi$
$252$	−8.39191	−	11.4147i	−0.528640	−	0.719056i
$253$	4.98072	+	8.62686i	0.313135	+	0.542366i
$254$	0.607245	−	3.44386i	0.0381019	−	0.216087i
$255$	−20.8046	+	9.90380i	−1.30284	+	0.620200i
$256$	−17.7303	−	6.45330i	−1.10814	−	0.403331i
$257$	1.70465	+	9.66754i	0.106333	+	0.603045i	0.990680	+	0.136213i	$0.0434933\pi$
$257$	1.70465	+	9.66754i	0.106333	+	0.603045i	−0.884346	+	0.466831i	$0.845396\pi$
$258$	27.9617	+	19.2490i	1.74082	+	1.19839i
$259$	4.50490	−	6.53274i	0.279921	−	0.405925i
$260$	−10.0843	−	17.4666i	−0.625404	−	1.08323i
$261$	12.6315	+	2.02041i	0.781870	+	0.125060i
$262$	−17.3669			−1.07293
$263$	−7.00430	+	2.54936i	−0.431904	+	0.157200i	−0.548818	−	0.835942i	$-0.684922\pi$
$263$	−7.00430	+	2.54936i	−0.431904	+	0.157200i	0.116914	+	0.993142i	$0.462700\pi$
$264$	1.88524	+	2.64729i	0.116029	+	0.162929i
$265$	32.2787	+	11.7485i	1.98286	+	0.721703i
$266$	−24.6990	+	6.80802i	−1.51439	+	0.417426i
$267$	−14.8980	+	15.1372i	−0.911744	+	0.926381i
$268$	21.3009	−	7.75288i	1.30116	−	0.473583i
$269$	8.61215	+	14.9167i	0.525092	+	0.909486i	0.999573	+	0.0292204i	$0.00930245\pi$
$269$	8.61215	+	14.9167i	0.525092	+	0.909486i	−0.474481	+	0.880266i	$0.657364\pi$
$270$	−32.5408	+	9.55801i	−1.98037	+	0.581682i
$271$	0.412552	−	0.714562i	0.0250608	−	0.0434065i	−0.853223	−	0.521546i	$-0.825355\pi$
$271$	0.412552	−	0.714562i	0.0250608	−	0.0434065i	0.878284	+	0.478140i	$0.158689\pi$
$272$	13.3161	+	11.1735i	0.807408	+	0.677496i
$273$	14.4216	−	5.49745i	0.872838	−	0.332721i
$274$	−6.35442	−	36.0377i	−0.383885	−	2.17712i
$275$	−21.4912	+	18.0333i	−1.29597	+	1.08745i
$276$	3.98352	+	5.59371i	0.239780	+	0.336702i
$277$	−10.8150	+	3.93635i	−0.649812	+	0.236512i	−0.645832	−	0.763480i	$-0.723489\pi$
$277$	−10.8150	+	3.93635i	−0.649812	+	0.236512i	−0.00398024	+	0.999992i	$0.501267\pi$
$278$	−16.1728	−	28.0122i	−0.969981	−	1.68006i
$279$	2.28881	−	6.61436i	0.137028	−	0.395992i
$280$	3.37705	+	1.54540i	0.201817	+	0.0923553i
$281$	−22.9354	+	8.34780i	−1.36821	+	0.497988i	−0.918583	−	0.395228i	$-0.870666\pi$
$281$	−22.9354	+	8.34780i	−1.36821	+	0.497988i	−0.449628	+	0.893216i	$0.648443\pi$
$282$	−1.44447	+	18.1763i	−0.0860171	+	1.08238i
$283$	−0.563076	−	0.204943i	−0.0334714	−	0.0121826i	0.325230	−	0.945635i	$-0.394558\pi$
$283$	−0.563076	−	0.204943i	−0.0334714	−	0.0121826i	−0.358702	+	0.933452i	$0.616780\pi$
$284$	9.31696	+	3.39110i	0.552860	+	0.201225i
$285$	−2.29132	+	28.8325i	−0.135726	+	1.70789i
$286$	27.6128	−	10.0502i	1.63278	−	0.594283i
$287$	0.0715959	+	0.755953i	0.00422617	+	0.0446225i
$288$	15.1126	+	17.4388i	0.890517	+	1.02759i
$289$	0.638564	+	1.10602i	0.0375626	+	0.0650603i
$290$	26.1530	−	9.51891i	1.53576	−	0.558970i
$291$	−11.0944	−	15.5789i	−0.650366	−	0.913254i
$292$	6.29086	−	5.27866i	0.368145	−	0.308910i
$293$	1.42904	+	8.10449i	0.0834854	+	0.473469i	0.997673	+	0.0681782i	$0.0217187\pi$
$293$	1.42904	+	8.10449i	0.0834854	+	0.473469i	−0.914188	+	0.405291i	$0.867170\pi$
$294$	13.0955	−	19.6187i	0.763745	−	1.14419i
$295$	8.59076	+	7.20851i	0.500174	+	0.419695i
$296$	−0.627451	+	1.08678i	−0.0364699	+	0.0631677i
$297$	−2.58492	−	23.1591i	−0.149992	−	1.34383i
$298$	−0.892102	−	1.54517i	−0.0516781	−	0.0895091i
$299$	−7.02985	+	2.55866i	−0.406547	+	0.147971i
$300$	−13.5663	+	13.7841i	−0.783252	+	0.795826i
$301$	−6.71392	+	25.7942i	−0.386984	+	1.48675i
$302$	18.6562	+	6.79032i	1.07355	+	0.390739i
$303$	0.858279	+	1.20521i	0.0493068	+	0.0692374i
$304$	20.5043	−	7.46297i	1.17600	−	0.428030i
$305$	34.7639			1.99058
$306$	−8.26065	−	21.6183i	−0.472230	−	1.23584i
$307$	−11.6784	−	20.2276i	−0.666521	−	1.15445i	−0.978870	−	0.204482i	$-0.934449\pi$
$307$	−11.6784	−	20.2276i	−0.666521	−	1.15445i	0.312349	−	0.949967i	$-0.398884\pi$
$308$	12.0231	−	17.4352i	0.685080	−	0.993463i
$309$	1.03415	+	0.711916i	0.0588308	+	0.0404995i
$310$	−2.64431	−	14.9966i	−0.150187	−	0.851751i
$311$	23.4170	+	8.52309i	1.32786	+	0.483300i	0.905967	−	0.423348i	$-0.139145\pi$
$311$	23.4170	+	8.52309i	1.32786	+	0.483300i	0.421888	+	0.906648i	$0.361367\pi$
$312$	−2.20375	+	1.04907i	−0.124763	+	0.0593919i
$313$	−4.09384	+	23.2173i	−0.231398	+	1.31232i	0.618671	+	0.785650i	$0.287671\pi$
$313$	−4.09384	+	23.2173i	−0.231398	+	1.31232i	−0.850069	+	0.526671i	$0.823440\pi$
$314$	4.07224	+	7.05333i	0.229810	+	0.398042i
$315$	−15.7734	−	21.4549i	−0.888728	−	1.20885i
$316$	−1.10674	+	1.91694i	−0.0622592	+	0.107836i
$317$	−11.6162	−	9.74716i	−0.652431	−	0.547455i	0.255376	−	0.966842i	$-0.417801\pi$
$317$	−11.6162	−	9.74716i	−0.652431	−	0.547455i	−0.907808	+	0.419387i	$0.862245\pi$
$318$	−14.3313	+	31.3837i	−0.803662	+	1.75991i
$319$	3.32061	+	18.8321i	0.185919	+	1.05440i
$320$	19.5367	+	7.11079i	1.09214	+	0.397505i
$321$	−21.0043	−	5.44918i	−1.17234	−	0.304144i
$322$	−6.49064	+	9.41235i	−0.361709	+	0.524530i
$323$	−19.7364			−1.09816
$324$	−3.29198	−	15.7235i	−0.182888	−	0.873530i
$325$	−10.5345	−	18.2463i	−0.584351	−	1.01212i
$326$	−3.38684	+	19.2077i	−0.187580	+	1.06382i
$327$	5.95915	−	6.05482i	0.329542	−	0.334832i
$328$	−0.0208518	−	0.118257i	−0.00115135	−	0.00652963i
$329$	−13.8016	+	3.80428i	−0.760909	+	0.209737i
$330$	−29.4100	−	41.2979i	−1.61897	−	2.27338i
$331$	−12.4997	−	10.4885i	−0.687048	−	0.576501i	0.231009	−	0.972952i	$-0.425797\pi$
$331$	−12.4997	−	10.4885i	−0.687048	−	0.576501i	−0.918056	+	0.396450i	$0.870242\pi$
$332$	−20.3195			−1.11518
$333$	7.71979	−	4.62249i	0.423042	−	0.253311i
$334$	29.6867			1.62438
$335$	40.0369	−	14.5723i	2.18745	−	0.796167i
$336$	−9.78043	+	17.5479i	−0.533566	+	0.957315i
$337$	0.0798940	−	0.0670390i	0.00435210	−	0.00365185i	−0.640609	−	0.767867i	$-0.721318\pi$
$337$	0.0798940	−	0.0670390i	0.00435210	−	0.00365185i	0.644961	+	0.764215i	$0.276874\pi$
$338$	−0.559742	−	3.17446i	−0.0304460	−	0.172668i
$339$	−0.680750	+	8.56612i	−0.0369733	+	0.465248i
$340$	−18.1899	−	15.2631i	−0.986486	−	0.827760i
$341$	10.4630			0.566601
$342$	−28.6858	−	4.58830i	−1.55115	−	0.248107i
$343$	17.9880	+	4.40799i	0.971263	+	0.238009i
$344$	0.731925	−	4.15095i	0.0394628	−	0.223804i
$345$	7.48738	+	10.5139i	0.403107	+	0.566049i
$346$	−3.17715	−	18.0185i	−0.170805	−	0.968682i
$347$	19.1112	−	16.0362i	1.02594	−	0.860869i	0.0355809	−	0.999367i	$-0.488672\pi$
$347$	19.1112	−	16.0362i	1.02594	−	0.860869i	0.990363	+	0.138498i	$0.0442274\pi$
$348$	3.51321	+	12.7059i	0.188328	+	0.681108i
$349$	22.2592	+	18.6777i	1.19151	+	0.999793i	0.999832	+	0.0183346i	$0.00583640\pi$
$349$	22.2592	+	18.6777i	1.19151	+	0.999793i	0.191675	+	0.981458i	$0.438608\pi$
$350$	−29.2799	−	13.3990i	−1.56508	−	0.716207i
$351$	17.4653	+	1.10839i	0.932228	+	0.0591613i
$352$	−17.2479	+	29.8743i	−0.919318	+	1.59231i
$353$	−0.762326	+	4.32337i	−0.0405745	+	0.230110i	−0.998351	−	0.0574043i	$-0.981718\pi$
$353$	−0.762326	+	4.32337i	−0.0405745	+	0.230110i	0.957776	+	0.287514i	$0.0928287\pi$
$354$	−7.90096	+	8.02780i	−0.419931	+	0.426673i
$355$	17.5121	+	6.37388i	0.929445	+	0.338290i
$356$	−20.5673	−	7.48590i	−1.09007	−	0.396752i
$357$	13.7415	−	11.8892i	0.727275	−	0.629243i
$358$	0.970810	−	5.50574i	0.0513089	−	0.290987i
$359$	−3.36744	−	5.83257i	−0.177727	−	0.307831i	0.763375	−	0.645956i	$-0.223541\pi$
$359$	−3.36744	−	5.83257i	−0.177727	−	0.307831i	−0.941101	+	0.338124i	$0.890208\pi$
$360$	2.75789	+	3.18239i	0.145353	+	0.167727i
$361$	−2.88723	+	5.00083i	−0.151960	+	0.263202i
$362$	1.53707	−	8.71714i	0.0807865	−	0.458163i
$363$	14.2503	−	6.78371i	0.747949	−	0.356052i
$364$	11.3269	+	11.1658i	0.593692	+	0.585249i
$365$	11.8243	−	9.92173i	0.618910	−	0.519327i
$366$	−2.76610	+	34.8069i	−0.144587	+	1.81938i
$367$	6.35341	+	5.33114i	0.331645	+	0.278283i	0.793370	−	0.608740i	$-0.208325\pi$
$367$	6.35341	+	5.33114i	0.331645	+	0.278283i	−0.461725	+	0.887023i	$0.652769\pi$
$368$	4.86879	−	8.43300i	0.253803	−	0.439600i
$369$	−0.281559	+	0.813668i	−0.0146574	+	0.0423579i
$370$	9.78830	−	16.9538i	0.508870	−	0.881388i
$371$	−27.0021	−	2.16764i	−1.40188	−	0.112538i
$372$	7.18022	−	0.685843i	0.372277	−	0.0355593i
$373$	8.96660	−	7.52387i	0.464273	−	0.389571i	−0.380427	−	0.924811i	$-0.624223\pi$
$373$	8.96660	−	7.52387i	0.464273	−	0.389571i	0.844700	+	0.535239i	$0.179779\pi$
$374$	26.5020	−	22.2378i	1.37038	−	1.14989i
$375$	−5.11854	+	5.20072i	−0.264320	+	0.268564i
$376$	2.12744	−	0.774326i	0.109715	−	0.0399328i
$377$	−14.3610			−0.739631
$378$	22.7365	−	14.0857i	1.16944	−	0.724490i
$379$	−26.9202			−1.38280			−0.691398	−	0.722474i	$-0.743005\pi$
$379$	−26.9202			−1.38280			−0.691398	+	0.722474i	$0.743005\pi$
$380$	−28.0091	+	10.1945i	−1.43683	+	0.522965i
$381$	3.01356	+	0.781816i	0.154390	+	0.0400536i
$382$	−26.4183	+	22.1676i	−1.35168	+	1.13419i
$383$	12.8174	−	10.7551i	0.654938	−	0.549559i	−0.253626	−	0.967302i	$-0.581623\pi$
$383$	12.8174	−	10.7551i	0.654938	−	0.549559i	0.908565	+	0.417744i	$0.137179\pi$
$384$	2.39428	−	5.24316i	0.122183	−	0.267564i
$385$	22.5985	−	32.7711i	1.15173	−	1.67017i
$386$	−19.1547	+	33.1769i	−0.974949	+	1.68866i
$387$	−19.0554	+	23.4581i	−0.968640	+	1.19244i
$388$	9.85482	−	17.0691i	0.500303	−	0.866550i
$389$	1.22668	+	1.02931i	0.0621953	+	0.0521880i	0.673355	−	0.739319i	$-0.264852\pi$
$389$	1.22668	+	1.02931i	0.0621953	+	0.0521880i	−0.611160	+	0.791507i	$0.709297\pi$
$390$	34.3787	−	16.3656i	1.74083	−	0.828705i
$391$	−6.74704	+	5.66144i	−0.341213	+	0.286311i
$392$	−2.89128	−	0.467216i	−0.146032	−	0.0235980i
$393$	1.22487	−	15.4130i	0.0617866	−	0.777483i
$394$	−6.51098	+	36.9256i	−0.328018	+	1.86028i
$395$	−2.08022	+	3.60305i	−0.104667	+	0.181289i
$396$	20.6033	−	12.3369i	1.03536	−	0.619954i
$397$	−5.92068	−	10.2549i	−0.297150	−	0.514679i	0.678333	−	0.734755i	$-0.262703\pi$
$397$	−5.92068	−	10.2549i	−0.297150	−	0.514679i	−0.975483	+	0.220076i	$0.929370\pi$
$398$	−3.90711	+	22.1583i	−0.195846	+	1.11070i
$399$	−4.30006	−	22.4003i	−0.215272	−	1.12142i
$400$	25.7705	+	9.37968i	1.28852	+	0.468984i
$401$	−0.147208	−	0.0535792i	−0.00735120	−	0.00267562i	0.338342	−	0.941023i	$-0.390134\pi$
$401$	−0.147208	−	0.0535792i	−0.00735120	−	0.00267562i	−0.345693	+	0.938348i	$0.612356\pi$
$402$	11.4046	+	41.2459i	0.568809	+	2.05716i
$403$	−1.36446	+	7.73826i	−0.0679688	+	0.385470i
$404$	−0.762382	+	1.32048i	−0.0379299	+	0.0656965i
$405$	−6.18758	−	29.5538i	−0.307463	−	1.46854i
$406$	−17.8882	+	12.7174i	−0.887779	+	0.631152i
$407$	10.3039	+	8.64603i	0.510748	+	0.428568i
$408$	−2.01565	+	2.04801i	−0.0997895	+	0.101392i
$409$	−20.5877	+	17.2751i	−1.01799	+	0.854198i	−0.989374	−	0.145392i	$-0.953556\pi$
$409$	−20.5877	+	17.2751i	−1.01799	+	0.854198i	−0.0286198	+	0.999590i	$0.509111\pi$
$410$	0.325291	+	1.84482i	0.0160650	+	0.0911090i
$411$	32.4313	−	3.09779i	1.59972	−	0.152803i
$412$	−0.224673	+	1.27419i	−0.0110689	+	0.0627747i
$413$	−8.04178	−	3.68006i	−0.395710	−	0.181084i
$414$	−11.1226	+	6.66006i	−0.546648	+	0.327324i
$415$	−38.1924			−1.87479
$416$	−19.8454	−	16.6522i	−0.972999	−	0.816443i
$417$	26.0012	−	12.3776i	1.27328	−	0.606132i
$418$	−7.54103	−	42.7673i	−0.368844	−	2.09182i
$419$	−18.4551	+	15.4857i	−0.901593	+	0.756526i	−0.970501	−	0.241097i	$-0.922493\pi$
$419$	−18.4551	+	15.4857i	−0.901593	+	0.756526i	0.0689084	+	0.997623i	$0.478048\pi$
$420$	13.3601	−	23.9705i	0.651908	−	1.16964i
$421$	−3.47375	+	1.26434i	−0.169300	+	0.0616202i	−0.425280	−	0.905062i	$-0.639824\pi$
$421$	−3.47375	+	1.26434i	−0.169300	+	0.0616202i	0.255980	+	0.966682i	$0.417602\pi$
$422$	43.1259			2.09934
$423$	−16.0294	−	2.56392i	−0.779379	−	0.124662i
$424$	4.28383			0.208041
$425$	−19.0020	−	15.9445i	−0.921731	−	0.773424i
$426$	−7.77515	+	17.0266i	−0.376707	+	0.824939i
$427$	−26.4295	+	7.28502i	−1.27901	+	0.352547i
$428$	−3.88316	−	22.0225i	−0.187699	−	1.06450i
$429$	6.97199	+	25.2149i	0.336611	+	1.21739i
$430$	−11.4181	+	64.7553i	−0.550630	+	3.12278i
$431$	1.18001	+	2.04383i	0.0568390	+	0.0984480i	0.893045	−	0.449968i	$-0.148564\pi$
$431$	1.18001	+	2.04383i	0.0568390	+	0.0984480i	−0.836206	+	0.548416i	$0.815231\pi$
$432$	−18.3422	+	13.5076i	−0.882492	+	0.649886i
$433$	15.5635			0.747935			0.373968	−	0.927442i	$-0.377997\pi$
$433$	15.5635			0.747935			0.373968	+	0.927442i	$0.377997\pi$
$434$	5.15300	+	10.8472i	0.247352	+	0.520680i
$435$	6.60341	+	23.8819i	0.316609	+	1.14505i
$436$	8.22686	+	2.99433i	0.393995	+	0.143403i
$437$	1.91984	+	10.8880i	0.0918386	+	0.520843i
$438$	8.99315	+	12.6283i	0.429709	+	0.603404i
$439$	30.1791	+	25.3233i	1.44037	+	1.20861i	0.939248	+	0.343238i	$0.111524\pi$
$439$	30.1791	+	25.3233i	1.44037	+	1.20861i	0.501122	+	0.865376i	$0.332921\pi$
$440$	−3.14757	+	5.45174i	−0.150054	+	0.259902i
$441$	16.4878	+	13.0058i	0.785135	+	0.619325i
$442$	12.9907	+	22.5005i	0.617904	+	1.07024i
$443$	−0.540539	+	3.06555i	−0.0256818	+	0.145649i	−0.994952	−	0.100348i	$-0.968004\pi$
$443$	−0.540539	+	3.06555i	−0.0256818	+	0.145649i	0.969271	+	0.245997i	$0.0791154\pi$
$444$	7.63784	+	5.25794i	0.362476	+	0.249531i
$445$	−38.6582	−	14.0704i	−1.83257	−	0.667003i
$446$	−6.01670	−	34.1224i	−0.284899	−	1.61574i
$447$	1.43424	−	0.682754i	0.0678372	−	0.0322931i
$448$	−16.3431	−	1.31197i	−0.772137	−	0.0619848i
$449$	−7.45557	−	12.9134i	−0.351850	−	0.609422i	0.634724	−	0.772739i	$-0.281114\pi$
$449$	−7.45557	−	12.9134i	−0.351850	−	0.609422i	−0.986574	+	0.163317i	$0.947781\pi$
$450$	−23.9116	−	27.5921i	−1.12720	−	1.30070i
$451$	−1.28710			−0.0606074
$452$	−8.32147	+	3.02877i	−0.391409	+	0.142461i
$453$	−7.34215	+	16.0783i	−0.344964	+	0.755426i
$454$	−5.86496	−	2.13467i	−0.275256	−	0.100185i
$455$	21.2900	+	20.9872i	0.998090	+	0.983896i
$456$	0.961287	+	3.47660i	0.0450164	+	0.162807i
$457$	26.0018	−	9.46387i	1.21631	−	0.442701i	0.347423	−	0.937709i	$-0.387057\pi$
$457$	26.0018	−	9.46387i	1.21631	−	0.442701i	0.868889	+	0.495007i	$0.164835\pi$
$458$	3.93395	+	6.81380i	0.183821	+	0.318388i
$459$	19.7687	−	5.80653i	0.922724	−	0.271026i
$460$	−6.65081	+	11.5195i	−0.310095	+	0.537101i
$461$	−26.9668	−	22.6278i	−1.25597	−	1.05388i	−0.996099	−	0.0882379i	$-0.971876\pi$
$461$	−26.9668	−	22.6278i	−1.25597	−	1.05388i	−0.259868	−	0.965644i	$-0.583679\pi$
$462$	31.0134	+	25.2340i	1.44287	+	1.17399i
$463$	−3.64646	−	20.6801i	−0.169465	−	0.961086i	−0.944340	−	0.328971i	$-0.893298\pi$
$463$	−3.64646	−	20.6801i	−0.169465	−	0.961086i	0.774874	−	0.632115i	$-0.217813\pi$
$464$	14.3196	−	12.0156i	0.664770	−	0.557809i
$465$	13.4959	−	1.28911i	0.625856	−	0.0597808i
$466$	28.0574	−	10.2120i	1.29973	−	0.473064i
$467$	18.1184	+	31.3819i	0.838418	+	1.45218i	0.891217	+	0.453578i	$0.149853\pi$
$467$	18.1184	+	31.3819i	0.838418	+	1.45218i	−0.0527986	+	0.998605i	$0.516814\pi$
$468$	6.43737	+	16.8468i	0.297568	+	0.778743i
$469$	−27.3846	+	19.4687i	−1.26451	+	0.898980i
$470$	−33.1883	+	12.0796i	−1.53086	+	0.557189i
$471$	−6.54698	+	3.11662i	−0.301669	+	0.143606i
$472$	1.31421	+	0.478334i	0.0604915	+	0.0220171i
$473$	−42.4543	−	15.4521i	−1.95205	−	0.710488i
$474$	−3.44198	−	2.36948i	−0.158096	−	0.108834i
$475$	−29.2595	+	10.6496i	−1.34252	+	0.488636i
$476$	17.0275	+	7.79209i	0.780454	+	0.357150i
$477$	−26.8420	−	14.9324i	−1.22901	−	0.683708i
$478$	1.46980	+	2.54577i	0.0672271	+	0.116441i
$479$	30.6419	−	11.1527i	1.40006	−	0.509582i	0.471867	−	0.881670i	$-0.343580\pi$
$479$	30.6419	−	11.1527i	1.40006	−	0.509582i	0.928198	+	0.372088i	$0.121358\pi$
$480$	−18.5669	+	40.6591i	−0.847461	+	1.85583i
$481$	−7.73822	+	6.49314i	−0.352833	+	0.296062i
$482$	6.48356	+	36.7701i	0.295318	+	1.67483i
$483$	−7.89560	−	6.42423i	−0.359262	−	0.292313i
$484$	12.4594	+	10.4546i	0.566335	+	0.475211i
$485$	18.5230	−	32.0828i	0.841088	−	1.45681i
$486$	30.0827	−	3.84367i	1.36458	−	0.174353i
$487$	−15.5004	−	26.8476i	−0.702392	−	1.21658i	−0.967624	−	0.252394i	$-0.918782\pi$
$487$	−15.5004	−	26.8476i	−0.702392	−	1.21658i	0.265232	−	0.964185i	$-0.414551\pi$
$488$	4.07396	−	1.48280i	0.184420	−	0.0671232i
$489$	−16.8078	−	4.36049i	−0.760076	−	0.197188i
$490$	45.1042	+	7.28862i	2.03760	+	0.329266i
$491$	39.1653	+	14.2550i	1.76751	+	0.643320i	0.999997	+	0.00228119i	$0.000726125\pi$
$491$	39.1653	+	14.2550i	1.76751	+	0.643320i	0.767509	+	0.641038i	$0.221496\pi$
$492$	−0.883277	+	0.0843693i	−0.0398212	+	0.00380366i
$493$	−15.8881	+	5.78278i	−0.715562	+	0.260443i
$494$	32.6136			1.46735
$495$	38.7258	−	23.1884i	1.74060	−	1.04224i
$496$	−5.11391	−	8.85756i	−0.229621	−	0.397716i
$497$	−14.6494	−	1.17601i	−0.657114	−	0.0527511i
$498$	3.03890	−	38.2396i	0.136176	−	1.71356i
$499$	3.09411	+	17.5476i	0.138512	+	0.785538i	0.972350	+	0.233529i	$0.0750274\pi$
$499$	3.09411	+	17.5476i	0.138512	+	0.785538i	−0.833838	+	0.552009i	$0.813861\pi$
$500$	−7.06637	−	2.57195i	−0.316018	−	0.115021i
$501$	−2.09377	+	26.3467i	−0.0935429	+	1.17708i
$502$	−3.00661	+	17.0514i	−0.134192	+	0.761039i
$503$	13.0372	+	22.5811i	0.581300	+	1.00684i	0.995326	+	0.0965762i	$0.0307891\pi$
$503$	13.0372	+	22.5811i	0.581300	+	1.00684i	−0.414025	+	0.910265i	$0.635878\pi$
$504$	−2.76359	−	1.84150i	−0.123100	−	0.0820268i
$505$	−1.43297	+	2.48197i	−0.0637662	+	0.110446i
$506$	−14.8459	−	12.4572i	−0.659980	−	0.553789i
$507$	2.85678	−	0.272875i	0.126874	−	0.0121188i
$508$	0.557132	+	3.15965i	0.0247187	+	0.140187i
$509$	−4.93449	−	1.79601i	−0.218717	−	0.0796066i	0.230338	−	0.973111i	$-0.426017\pi$
$509$	−4.93449	−	1.79601i	−0.218717	−	0.0796066i	−0.449055	+	0.893504i	$0.648239\pi$
$510$	31.4443	−	31.9491i	1.39238	−	1.41473i
$511$	−6.91031	+	10.0209i	−0.305694	+	0.443299i
$512$	30.0523			1.32814
$513$	6.09526	−	25.1348i	0.269112	−	1.10973i
$514$	−9.54914	−	16.5396i	−0.421194	−	0.729530i
$515$	−0.422294	+	2.39495i	−0.0186085	+	0.105534i
$516$	−30.1472	−	7.82116i	−1.32716	−	0.344308i
$517$	−4.21388	−	23.8981i	−0.185326	−	1.05104i
$518$	−3.88883	+	14.9405i	−0.170865	+	0.656447i
$519$	16.2154	−	1.54887i	0.711775	−	0.0679877i
$520$	−3.62157	−	3.03886i	−0.158816	−	0.133263i
$521$	−27.4421			−1.20226			−0.601130	−	0.799151i	$-0.705283\pi$
$521$	−27.4421			−1.20226			−0.601130	+	0.799151i	$0.705283\pi$
$522$	−24.4368	+	4.71132i	−1.06957	+	0.206209i
$523$	−15.8772			−0.694262			−0.347131	−	0.937817i	$-0.612844\pi$
$523$	−15.8772			−0.694262			−0.347131	+	0.937817i	$0.612844\pi$
$524$	14.9728	−	5.44965i	0.654090	−	0.238069i
$525$	13.9566	−	25.0406i	0.609115	−	1.09286i
$526$	11.1087	−	9.32129i	0.484362	−	0.406428i
$527$	1.60643	+	9.11052i	0.0699772	+	0.396860i
$528$	−28.0487	−	19.3089i	−1.22066	−	0.840311i
$529$	−13.8395	−	11.6127i	−0.601716	−	0.504899i
$530$	−66.8281			−2.90283
$531$	−6.56736	−	7.57822i	−0.284999	−	0.328867i
$532$	19.1578	−	13.6199i	0.830595	−	0.590498i
$533$	0.167850	−	0.951925i	0.00727040	−	0.0412325i
$534$	17.1638	−	37.5864i	0.742749	−	1.62652i
$535$	−7.29875	−	41.3932i	−0.315552	−	1.78959i
$536$	4.07034	−	3.41542i	0.175812	−	0.147524i
$537$	4.81782	+	1.24990i	0.207904	+	0.0539372i
$538$	−25.6700	−	21.5396i	−1.10671	−	0.928640i
$539$	−10.3133	+	29.6501i	−0.444225	+	1.27712i
$540$	25.0556	−	18.4515i	1.07822	−	0.794028i
$541$	7.33572	−	12.7058i	0.315387	−	0.546267i	−0.664133	−	0.747615i	$-0.731199\pi$
$541$	7.33572	−	12.7058i	0.315387	−	0.546267i	0.979520	+	0.201348i	$0.0645323\pi$
$542$	−0.278746	+	1.58085i	−0.0119732	+	0.0679032i
$543$	7.62798	+	1.97894i	0.327348	+	0.0849246i
$544$	−28.6609	−	10.4317i	−1.22883	−	0.447257i
$545$	15.4631	+	5.62812i	0.662368	+	0.241082i
$546$	−22.7071	+	19.6464i	−0.971776	+	0.840787i
$547$	−0.350819	+	1.98960i	−0.0150000	+	0.0850690i	−0.991389	−	0.130952i	$-0.958197\pi$
$547$	−0.350819	+	1.98960i	−0.0150000	+	0.0850690i	0.976389	+	0.216021i	$0.0693078\pi$
$548$	16.7869	+	29.0757i	0.717100	+	1.24205i
$549$	−30.6957	−	4.90979i	−1.31006	−	0.209545i
$550$	27.2902	−	47.2680i	1.16366	−	2.01552i
$551$	−3.68546	+	20.9013i	−0.157006	+	0.890424i
$552$	1.32589	+	0.912754i	0.0564338	+	0.0388494i
$553$	0.826460	−	3.17517i	0.0351447	−	0.135022i
$554$	17.1524	−	14.3926i	0.728736	−	0.611482i
$555$	14.3560	+	9.88277i	0.609379	+	0.419500i
$556$	22.7334	+	19.0756i	0.964110	+	0.808984i
$557$	6.42943	−	11.1361i	0.272424	−	0.471852i	−0.697058	−	0.717015i	$-0.745508\pi$
$557$	6.42943	−	11.1361i	0.272424	−	0.471852i	0.969482	+	0.245163i	$0.0788414\pi$
$558$	0.216855	+	13.6151i	0.00918019	+	0.576374i
$559$	16.9646	−	29.3836i	0.717526	−	1.24279i
$560$	−38.7881	−	3.11379i	−1.63910	−	0.131582i
$561$	17.8667	+	25.0887i	0.754332	+	1.05924i
$562$	36.3751	−	30.5223i	1.53439	−	1.28751i
$563$	1.92912	−	1.61873i	0.0813029	−	0.0682212i	−0.601230	−	0.799076i	$-0.705323\pi$
$563$	1.92912	−	1.61873i	0.0813029	−	0.0682212i	0.682533	+	0.730854i	$0.260878\pi$
$564$	−4.45829	−	16.1239i	−0.187728	−	0.678938i
$565$	−15.6410	+	5.69284i	−0.658020	+	0.239500i
$566$	1.16576			0.0490007
$567$	10.8974	+	21.1719i	0.457646	+	0.889134i
$568$	2.32410			0.0975169
$569$	−33.3079	+	12.1231i	−1.39634	+	0.508225i	−0.927089	−	0.374841i	$-0.877697\pi$
$569$	−33.3079	+	12.1231i	−1.39634	+	0.508225i	−0.469249	+	0.883066i	$0.655475\pi$
$570$	−14.9962	−	54.2353i	−0.628121	−	2.27166i
$571$	−1.00671	+	0.844734i	−0.0421297	+	0.0353510i	−0.663609	−	0.748079i	$-0.730976\pi$
$571$	−1.00671	+	0.844734i	−0.0421297	+	0.0353510i	0.621480	+	0.783430i	$0.286532\pi$
$572$	−20.6525	+	17.3295i	−0.863525	+	0.724583i
$573$	−17.8103	−	25.0094i	−0.744034	−	1.04478i
$574$	−0.633899	−	1.33437i	−0.0264584	−	0.0556954i
$575$	−6.94772	+	12.0338i	−0.289740	+	0.501844i
$576$	−16.2462	−	9.03787i	−0.676924	−	0.376578i
$577$	3.16099	−	5.47499i	0.131594	−	0.227927i	−0.792697	−	0.609615i	$-0.791324\pi$
$577$	3.16099	−	5.47499i	0.131594	−	0.227927i	0.924291	+	0.381688i	$0.124657\pi$
$578$	−1.90335	−	1.59710i	−0.0791688	−	0.0664305i
$579$	−28.0933	−	19.3396i	−1.16752	−	0.803725i
$580$	−19.5607	+	16.4134i	−0.812213	+	0.681527i
$581$	29.0360	−	8.00348i	1.20462	−	0.332040i
$582$	30.6486	+	21.0987i	1.27043	+	0.874569i
$583$	7.97337	−	45.2192i	0.330223	−	1.87279i
$584$	0.962480	−	1.66706i	0.0398277	−	0.0689836i
$585$	12.0996	+	31.6651i	0.500258	+	1.30919i
$586$	−8.00522	−	13.8655i	−0.330693	−	0.572777i
$587$	1.97608	−	11.2069i	0.0815614	−	0.462558i	−0.916484	−	0.400071i	$-0.868986\pi$
$587$	1.97608	−	11.2069i	0.0815614	−	0.462558i	0.998046	−	0.0624873i	$-0.0199033\pi$
$588$	−5.13396	+	21.0235i	−0.211721	+	0.866993i
$589$	10.9122	+	3.97173i	0.449631	+	0.163652i
$590$	−20.5019	−	7.46206i	−0.844048	−	0.307208i
$591$	−32.3119	−	8.38276i	−1.32914	−	0.344821i
$592$	2.28322	−	12.9488i	0.0938400	−	0.532193i
$593$	−22.5967	+	39.1386i	−0.927935	+	1.60723i	−0.141162	+	0.989986i	$0.545084\pi$
$593$	−22.5967	+	39.1386i	−0.927935	+	1.60723i	−0.786772	+	0.617243i	$0.788249\pi$
$594$	20.1357	+	40.6187i	0.826177	+	1.66660i
$595$	32.0048	+	14.6460i	1.31207	+	0.600425i
$596$	1.25399	+	1.05222i	0.0513653	+	0.0431006i
$597$	−19.3898	−	5.03033i	−0.793570	−	0.205878i
$598$	11.1492	−	9.35529i	0.455925	−	0.382566i
$599$	2.60661	+	14.7828i	0.106503	+	0.604009i	0.990609	+	0.136723i	$0.0436570\pi$
$599$	2.60661	+	14.7828i	0.106503	+	0.604009i	−0.884106	+	0.467286i	$0.845232\pi$
$600$	−1.88314	+	4.12382i	−0.0768788	+	0.168354i
$601$	8.02293	−	45.5003i	0.327262	−	1.85600i	−0.166014	−	0.986123i	$-0.553090\pi$
$601$	8.02293	−	45.5003i	0.327262	−	1.85600i	0.493276	−	0.869873i	$-0.335799\pi$
$602$	−4.88922	−	51.6234i	−0.199270	−	2.10401i
$603$	−37.4097	+	7.21244i	−1.52344	+	0.293713i
$604$	−18.2151			−0.741163
$605$	23.4185	+	19.6505i	0.952098	+	0.798905i
$606$	−2.37102	−	1.63222i	−0.0963160	−	0.0663045i
$607$	−6.31688	−	35.8248i	−0.256394	−	1.45408i	−0.792468	−	0.609913i	$-0.791204\pi$
$607$	−6.31688	−	35.8248i	−0.256394	−	1.45408i	0.536074	−	0.844171i	$-0.319907\pi$
$608$	−29.3288	+	24.6098i	−1.18944	+	0.998060i
$609$	−10.0249	−	16.7726i	−0.406230	−	0.679660i
$610$	−63.5542	+	23.1318i	−2.57323	+	0.936581i
$611$	18.2242			0.737274
$612$	13.9056	+	16.0460i	0.562100	+	0.648620i
$613$	−16.1729			−0.653215			−0.326608	−	0.945160i	$-0.605906\pi$
$613$	−16.1729			−0.653215			−0.326608	+	0.945160i	$0.605906\pi$
$614$	34.8094	+	29.2086i	1.40479	+	1.17876i
$615$	−1.66020	+	0.158580i	−0.0669457	+	0.00639455i
$616$	1.25051	−	4.80432i	0.0503844	−	0.193572i
$617$	8.46705	+	48.0190i	0.340871	+	1.93317i	0.359000	+	0.933338i	$0.383118\pi$
$617$	8.46705	+	48.0190i	0.340871	+	1.93317i	−0.0181293	+	0.999836i	$0.505771\pi$
$618$	−2.36431	−	0.613378i	−0.0951063	−	0.0246737i
$619$	1.46954	−	8.33416i	0.0590657	−	0.334978i	−0.940928	−	0.338608i	$-0.890044\pi$
$619$	1.46954	−	8.33416i	0.0590657	−	0.334978i	0.999993	+	0.00362926i	$0.00115523\pi$
$620$	6.98564	+	12.0995i	0.280550	+	0.485927i
$621$	−5.12627	−	10.3410i	−0.205710	−	0.414969i
$622$	−48.4813			−1.94392
$623$	32.3387	+	2.59605i	1.29562	+	0.104009i
$624$	17.9384	−	18.2264i	0.718111	−	0.729639i
$625$	16.1105	+	5.86374i	0.644419	+	0.234549i
$626$	−7.96454	−	45.1691i	−0.318327	−	1.80532i
$627$	38.4875	−	3.67626i	1.53704	−	0.146816i
$628$	−5.72416	−	4.80314i	−0.228419	−	0.191666i
$629$	−5.94644	+	10.2995i	−0.237100	+	0.410669i
$630$	43.1123	+	28.7276i	1.71764	+	1.14453i
$631$	17.6216	+	30.5215i	0.701505	+	1.21504i	0.967938	+	0.251189i	$0.0808216\pi$
$631$	17.6216	+	30.5215i	0.701505	+	1.21504i	−0.266433	+	0.963853i	$0.585845\pi$
$632$	−0.0900975	+	0.510968i	−0.00358388	+	0.0203252i
$633$	−3.04162	+	38.2738i	−0.120894	+	1.52125i
$634$	27.7221	+	10.0900i	1.10098	+	0.400726i
$635$	1.04718	+	5.93885i	0.0415561	+	0.235676i
$636$	2.50763	−	31.5544i	0.0994340	−	1.25121i
$637$	−20.5839	−	11.4942i	−0.815563	−	0.455418i
$638$	−18.6015	−	32.2187i	−0.736439	−	1.27555i
$639$	−14.5625	−	8.10125i	−0.576085	−	0.320480i
$640$	11.1647			0.441325
$641$	−5.44735	+	1.98267i	−0.215157	+	0.0783109i	−0.447350	−	0.894359i	$-0.647632\pi$
$641$	−5.44735	+	1.98267i	−0.215157	+	0.0783109i	0.232193	+	0.972670i	$0.425410\pi$
$642$	42.0251	−	4.01417i	1.65860	−	0.158427i
$643$	4.93946	+	1.79782i	0.194793	+	0.0708990i	0.437575	−	0.899182i	$-0.355838\pi$
$643$	4.93946	+	1.79782i	0.194793	+	0.0708990i	−0.242781	+	0.970081i	$0.578060\pi$
$644$	2.64232	−	10.1515i	0.104122	−	0.400026i
$645$	−56.6644	−	14.7006i	−2.23116	−	0.578835i
$646$	36.0814	−	13.1326i	1.41960	−	0.516694i
$647$	−9.29941	−	16.1071i	−0.365598	−	0.633234i	0.623274	−	0.782003i	$-0.285802\pi$
$647$	−9.29941	−	16.1071i	−0.365598	−	0.633234i	−0.988872	+	0.148770i	$0.952469\pi$
$648$	−1.98569	−	3.19947i	−0.0780053	−	0.125687i
$649$	7.49531	−	12.9823i	0.294217	−	0.509598i
$650$	31.3999	+	26.3477i	1.23161	+	1.03344i
$651$	−9.99019	+	3.80821i	−0.391547	+	0.149255i
$652$	−3.10734	−	17.6226i	−0.121693	−	0.690154i
$653$	15.0822	−	12.6554i	0.590210	−	0.495245i	−0.298072	−	0.954543i	$-0.596343\pi$
$653$	15.0822	−	12.6554i	0.590210	−	0.495245i	0.888282	+	0.459298i	$0.151899\pi$
$654$	−6.86545	+	15.0344i	−0.268460	+	0.587892i
$655$	28.1427	−	10.2431i	1.09963	−	0.400232i
$656$	0.629090	+	1.08962i	0.0245618	+	0.0425423i
$657$	−11.8418	+	7.09068i	−0.461992	+	0.276634i
$658$	22.7003	−	16.1384i	0.884950	−	0.629141i
$659$	39.3495	−	14.3220i	1.53284	−	0.557907i	0.568523	−	0.822667i	$-0.307515\pi$
$659$	39.3495	−	14.3220i	1.53284	−	0.557907i	0.964314	+	0.264760i	$0.0852929\pi$
$660$	38.3147	+	26.3761i	1.49140	+	1.02669i
$661$	34.5295	+	12.5677i	1.34304	+	0.488828i	0.910770	−	0.412915i	$-0.135489\pi$
$661$	34.5295	+	12.5677i	1.34304	+	0.488828i	0.432273	+	0.901743i	$0.357712\pi$
$662$	29.8306	+	10.8575i	1.15940	+	0.421987i
$663$	−20.8852	+	9.94218i	−0.811115	+	0.386122i
$664$	−4.47574	+	1.62904i	−0.173692	+	0.0632189i
$665$	36.0088	−	25.5999i	1.39636	−	0.992720i
$666$	−11.0373	+	13.5874i	−0.427685	+	0.526501i
$667$	4.73569	+	8.20245i	0.183366	+	0.317600i
$668$	−25.5942	+	9.31553i	−0.990270	+	0.360429i
$669$	30.7077	−	2.93315i	1.18723	−	0.113402i
$670$	−63.4978	+	53.2809i	−2.45313	+	2.05842i
$671$	−8.06939	−	45.7638i	−0.311515	−	1.76669i
$672$	5.59524	−	34.8022i	0.215841	−	1.34252i
$673$	−17.1674	−	14.4052i	−0.661756	−	0.555280i	0.248856	−	0.968540i	$-0.419945\pi$
$673$	−17.1674	−	14.4052i	−0.661756	−	0.555280i	−0.910613	+	0.413261i	$0.864390\pi$
$674$	−0.101452	+	0.175720i	−0.00390778	+	0.00676847i
$675$	26.1742	−	19.2753i	1.00745	−	0.741906i
$676$	1.47871	+	2.56120i	0.0568733	+	0.0985075i
$677$	15.7042	−	5.71587i	0.603563	−	0.219679i	−0.0221216	−	0.999755i	$-0.507042\pi$
$677$	15.7042	−	5.71587i	0.603563	−	0.219679i	0.625684	+	0.780076i	$0.284820\pi$
$678$	−4.45535	−	16.1132i	−0.171107	−	0.618826i
$679$	−7.35909	+	28.2728i	−0.282416	+	1.08501i
$680$	−5.23032	−	1.90368i	−0.200573	−	0.0730028i
$681$	2.30815	−	5.05454i	0.0884485	−	0.193691i
$682$	−19.1280	+	6.96202i	−0.732449	+	0.266590i
$683$	−23.5592			−0.901467			−0.450734	−	0.892659i	$-0.648838\pi$
$683$	−23.5592			−0.901467			−0.450734	+	0.892659i	$0.648838\pi$
$684$	26.1711	−	5.04568i	1.00068	−	0.192926i
$685$	31.5525	+	54.6505i	1.20556	+	2.08809i
$686$	−35.8182	+	3.91067i	−1.36754	+	0.149310i
$687$	−6.32464	+	3.01077i	−0.241300	+	0.114868i
$688$	7.66894	+	43.4927i	0.292375	+	1.65814i
$689$	32.4037	+	11.7940i	1.23448	+	0.449315i
$690$	−20.6841	−	14.2390i	−0.787430	−	0.542071i
$691$	−0.188059	+	1.06653i	−0.00715409	+	0.0405729i	−0.988176	−	0.153325i	$-0.951002\pi$
$691$	−0.188059	+	1.06653i	−0.00715409	+	0.0405729i	0.981022	+	0.193898i	$0.0621130\pi$
$692$	8.39328	+	14.5376i	0.319065	+	0.552636i
$693$	−24.5823	+	25.7444i	−0.933803	+	0.977949i
$694$	−24.2680	+	42.0334i	−0.921200	+	1.59557i
$695$	42.7295	+	35.8543i	1.62082	+	1.36003i
$696$	1.79249	+	2.51705i	0.0679443	+	0.0954084i
$697$	−0.197616	−	1.12073i	−0.00748522	−	0.0424508i
$698$	−53.1215	−	19.3347i	−2.01068	−	0.731828i
$699$	7.08425	+	25.6209i	0.267951	+	0.969072i
$700$	29.4480	+	2.36400i	1.11303	+	0.0893507i
$701$	39.4989			1.49185			0.745927	−	0.666028i	$-0.232007\pi$
$701$	39.4989			1.49185			0.745927	+	0.666028i	$0.232007\pi$
$702$	−32.6669	+	9.59504i	−1.23293	+	0.362142i
$703$	7.46437	+	12.9287i	0.281524	+	0.487614i
$704$	4.82590	−	27.3690i	0.181883	−	1.03151i
$705$	−8.37977	−	30.3063i	−0.315600	−	1.14140i
$706$	−1.48310	−	8.41107i	−0.0558172	−	0.316555i
$707$	0.569309	−	2.18722i	0.0214111	−	0.0822590i
$708$	4.29268	−	9.40041i	0.161329	−	0.353289i
$709$	−36.5821	−	30.6960i	−1.37387	−	1.15281i	−0.971419	−	0.237373i	$-0.923714\pi$
$709$	−36.5821	−	30.6960i	−1.37387	−	1.15281i	−0.402452	−	0.915441i	$-0.631842\pi$
$710$	−36.2561			−1.36067
$711$	2.34565	−	2.88761i	0.0879689	−	0.108294i
$712$	−5.13048			−0.192273
$713$	4.86973	−	1.77244i	0.182373	−	0.0663783i
$714$	−17.2106	+	30.8789i	−0.644090	+	1.15561i
$715$	−38.8183	+	32.5724i	−1.45172	+	1.21814i
$716$	0.890694	+	5.05138i	0.0332868	+	0.188779i
$717$	−2.36301	+	1.12488i	−0.0882483	+	0.0420096i
$718$	10.0372	+	8.42222i	0.374585	+	0.314314i
$719$	0.749777			0.0279620			0.0139810	−	0.999902i	$-0.495550\pi$
$719$	0.749777			0.0279620			0.0139810	+	0.999902i	$0.495550\pi$
$720$	−38.5582	−	21.4502i	−1.43698	−	0.799402i
$721$	−0.180826	−	1.90927i	−0.00673432	−	0.0711050i
$722$	1.95079	−	11.0635i	0.0726011	−	0.411741i
$723$	−33.0904	+	3.16075i	−1.23065	+	0.117549i
$724$	1.41022	+	7.99776i	0.0524104	+	0.297234i
$725$	−20.4339	+	17.1461i	−0.758897	+	0.636790i
$726$	−21.5381	+	21.8839i	−0.799354	+	0.812187i
$727$	33.4171	+	28.0403i	1.23937	+	1.03996i	0.997573	+	0.0696290i	$0.0221815\pi$
$727$	33.4171	+	28.0403i	1.23937	+	1.03996i	0.241798	+	0.970327i	$0.422263\pi$
$728$	3.39014	+	1.55139i	0.125647	+	0.0574982i
$729$	1.28953	+	26.9692i	0.0477602	+	0.998859i
$730$	−15.0148	+	26.0064i	−0.555722	+	0.962539i
$731$	6.93655	−	39.3391i	0.256558	−	1.45501i
$732$	−8.53744	−	30.8765i	−0.315553	−	1.14123i
$733$	20.6475	+	7.51509i	0.762634	+	0.277576i	0.693912	−	0.720060i	$-0.255886\pi$
$733$	20.6475	+	7.51509i	0.762634	+	0.277576i	0.0687222	+	0.997636i	$0.478108\pi$
$734$	−15.1624	−	5.51867i	−0.559655	−	0.203698i
$735$	−9.64974	+	39.5155i	−0.355936	+	1.45755i
$736$	−2.96690	+	16.8261i	−0.109361	+	0.620219i
$737$	−28.4765	−	49.3227i	−1.04895	−	1.81683i
$738$	−0.0266764	−	1.67487i	−0.000981974	−	0.0616528i
$739$	−20.0557	+	34.7375i	−0.737761	+	1.27784i	0.215740	+	0.976451i	$0.430784\pi$
$739$	−20.0557	+	34.7375i	−0.737761	+	1.27784i	−0.953501	+	0.301389i	$0.902550\pi$
$740$	−3.11890	+	17.6882i	−0.114653	+	0.650230i
$741$	−2.30020	+	28.9442i	−0.0845000	+	1.06329i
$742$	50.8066	−	14.0043i	1.86517	−	0.514114i
$743$	−6.31887	+	5.30216i	−0.231817	+	0.194518i	−0.751295	−	0.659966i	$-0.770571\pi$
$743$	−6.31887	+	5.30216i	−0.231817	+	0.194518i	0.519479	+	0.854484i	$0.326126\pi$
$744$	1.52659	−	0.726715i	0.0559674	−	0.0266426i
$745$	2.35698	+	1.97774i	0.0863531	+	0.0724588i
$746$	−11.3861	+	19.7212i	−0.416873	+	0.722046i
$747$	33.7229	+	5.39399i	1.23386	+	0.197356i
$748$	−15.8704	+	27.4884i	−0.580280	+	1.00507i
$749$	14.2232	+	29.9400i	0.519703	+	1.09398i
$750$	5.89700	−	12.9136i	0.215328	−	0.471539i
$751$	−18.8433	+	15.8114i	−0.687600	+	0.576965i	−0.918216	−	0.396080i	$-0.870370\pi$
$751$	−18.8433	+	15.8114i	−0.687600	+	0.576965i	0.230616	+	0.973045i	$0.425926\pi$
$752$	−18.1717	+	15.2478i	−0.662652	+	0.556031i
$753$	−14.9209	−	3.87096i	−0.543747	−	0.141066i
$754$	26.2543	−	9.55579i	0.956126	−	0.348002i
$755$	−34.2370			−1.24601
$756$	−15.1821	+	19.2785i	−0.552167	+	0.701152i
$757$	−20.6308			−0.749839			−0.374920	−	0.927057i	$-0.622330\pi$
$757$	−20.6308			−0.749839			−0.374920	+	0.927057i	$0.622330\pi$
$758$	49.2145	−	17.9126i	1.78755	−	0.650616i
$759$	12.1027	−	12.2970i	0.439300	−	0.446353i
$760$	−5.35220	+	4.49103i	−0.194145	+	0.162907i
$761$	−10.5292	+	8.83505i	−0.381683	+	0.320270i	−0.813363	−	0.581757i	$-0.802366\pi$
$761$	−10.5292	+	8.83505i	−0.381683	+	0.320270i	0.431680	+	0.902027i	$0.357921\pi$
$762$	−6.02951	+	0.575929i	−0.218426	+	0.0208637i
$763$	−12.9354	−	1.03841i	−0.468292	−	0.0375930i
$764$	15.8203	−	27.4015i	0.572358	−	0.991353i
$765$	26.1368	+	30.1599i	0.944979	+	1.09043i
$766$	−16.2759	+	28.1907i	−0.588073	+	1.01857i
$767$	8.62405	+	7.23644i	0.311396	+	0.261293i
$768$	−2.58897	+	32.5780i	−0.0934215	+	1.17556i
$769$	11.6423	−	9.76902i	0.419831	−	0.352280i	−0.408268	−	0.912862i	$-0.633867\pi$
$769$	11.6423	−	9.76902i	0.419831	−	0.352280i	0.828099	+	0.560582i	$0.189423\pi$
$770$	−19.5081	+	74.9479i	−0.703022	+	2.70093i
$771$	15.3522	−	7.30825i	0.552897	−	0.263200i
$772$	6.10337	−	34.6139i	0.219665	−	1.24578i
$773$	−19.0197	+	32.9431i	−0.684091	+	1.18488i	0.289631	+	0.957138i	$0.406467\pi$
$773$	−19.0197	+	32.9431i	−0.684091	+	1.18488i	−0.973722	+	0.227741i	$0.926866\pi$
$774$	19.2274	−	55.5647i	0.691116	−	1.99723i
$775$	7.29750	+	12.6396i	0.262134	+	0.454030i
$776$	0.802259	−	4.54984i	0.0287994	−	0.163330i
$777$	−12.9853	−	4.50504i	−0.465844	−	0.161617i
$778$	−2.92748	−	1.06551i	−0.104955	−	0.0382005i
$779$	−1.34237	−	0.488584i	−0.0480955	−	0.0175053i
$780$	−24.5040	+	24.8974i	−0.877383	+	0.891469i
$781$	4.32577	−	24.5327i	0.154788	−	0.877849i
$782$	8.56760	−	14.8395i	0.306377	−	0.530660i
$783$	−2.45775	−	22.0198i	−0.0878329	−	0.786922i
$784$	30.1415	−	5.76104i	1.07648	−	0.205751i
$785$	−10.7591	−	9.02794i	−0.384008	−	0.322221i
$786$	8.01650	+	28.9925i	0.285939	+	1.03413i
$787$	11.5764	−	9.71374i	0.412654	−	0.346258i	−0.412707	−	0.910864i	$-0.635416\pi$
$787$	11.5764	−	9.71374i	0.412654	−	0.346258i	0.825360	+	0.564606i	$0.190972\pi$
$788$	−5.97366	−	33.8783i	−0.212803	−	1.20686i
$789$	7.48908	+	10.5163i	0.266618	+	0.374389i
$790$	1.40553	−	7.97115i	0.0500065	−	0.283601i
$791$	10.6982	−	7.60570i	0.380383	−	0.270427i
$792$	3.54918	−	4.36922i	0.126115	−	0.155253i
$793$	34.8986			1.23929
$794$	17.6476	+	14.8081i	0.626289	+	0.525519i
$795$	4.71332	−	59.3094i	0.167164	−	2.10349i
$796$	−3.58468	−	20.3297i	−0.127056	−	0.720568i
$797$	−0.774338	+	0.649747i	−0.0274285	+	0.0230152i	−0.656399	−	0.754414i	$-0.727921\pi$
$797$	−0.774338	+	0.649747i	−0.0274285	+	0.0230152i	0.628970	+	0.777429i	$0.283477\pi$
$798$	22.7663	+	38.0902i	0.805919	+	1.34838i
$799$	20.1621	−	7.33839i	0.713282	−	0.259613i
$800$	−48.1191			−1.70127
$801$	32.1470	+	17.8836i	1.13586	+	0.631887i
$802$	0.304771			0.0107619
$803$	−15.8058	−	13.2626i	−0.557773	−	0.468027i
$804$	−22.7751	−	31.9812i	−0.803217	−	1.12789i
$805$	4.96649	−	19.0807i	0.175046	−	0.672507i
$806$	−2.65456	−	15.0547i	−0.0935027	−	0.530280i
$807$	20.9267	−	21.2627i	0.736656	−	0.748482i
$808$	−0.0620638	+	0.351981i	−0.00218340	+	0.0123827i
$809$	1.37661	+	2.38435i	0.0483989	+	0.0838293i	0.889210	−	0.457499i	$-0.151255\pi$
$809$	1.37661	+	2.38435i	0.0483989	+	0.0838293i	−0.840811	+	0.541329i	$0.817921\pi$
$810$	30.9770	+	49.9121i	1.08842	+	1.75373i
$811$	33.2392			1.16718			0.583592	−	0.812047i	$-0.301647\pi$
$811$	33.2392			1.16718			0.583592	+	0.812047i	$0.301647\pi$
$812$	11.4316	−	16.5774i	0.401171	−	0.581754i
$813$	−1.38333	−	0.358880i	−0.0485155	−	0.0125865i
$814$	−24.5904	−	8.95016i	−0.861892	−	0.313703i
$815$	−5.84053	−	33.1233i	−0.204585	−	1.16026i
$816$	12.5066	−	27.3877i	0.437817	−	0.958762i
$817$	−38.4117	−	32.2312i	−1.34385	−	1.12763i
$818$	26.1428	−	45.2807i	0.914062	−	1.58320i
$819$	−15.8345	−	21.5380i	−0.553301	−	0.752600i
$820$	−0.859341	−	1.48842i	−0.0300095	−	0.0519780i
$821$	3.24294	−	18.3916i	0.113180	−	0.641873i	−0.874456	−	0.485105i	$-0.838781\pi$
$821$	3.24294	−	18.3916i	0.113180	−	0.641873i	0.987635	−	0.156768i	$-0.0501075\pi$
$822$	−57.2285	+	27.2430i	−1.99607	+	0.950209i
$823$	−17.3503	−	6.31498i	−0.604792	−	0.220126i	0.0214308	−	0.999770i	$-0.493178\pi$
$823$	−17.3503	−	6.31498i	−0.604792	−	0.220126i	−0.626223	+	0.779644i	$0.715400\pi$
$824$	0.0526644	+	0.298675i	0.00183465	+	0.0104048i
$825$	40.0252	+	27.5536i	1.39350	+	0.959293i
$826$	17.1504	+	1.37678i	0.596739	+	0.0479044i
$827$	−9.06140	−	15.6948i	−0.315096	−	0.545762i	0.664362	−	0.747411i	$-0.268703\pi$
$827$	−9.06140	−	15.6948i	−0.315096	−	0.545762i	−0.979458	+	0.201649i	$0.935370\pi$
$828$	7.49943	−	9.23216i	0.260623	−	0.320840i
$829$	8.52869			0.296214			0.148107	−	0.988971i	$-0.452682\pi$
$829$	8.52869			0.296214			0.148107	+	0.988971i	$0.452682\pi$
$830$	69.8220	−	25.4131i	2.42356	−	0.882103i
$831$	11.5635	+	16.2377i	0.401135	+	0.563280i
$832$	19.6124	+	7.13834i	0.679939	+	0.247477i
$833$	−27.4010	−	4.42787i	−0.949388	−	0.153417i
$834$	−39.2985	+	39.9294i	−1.36079	+	1.38264i
$835$	−48.1067	+	17.5094i	−1.66480	+	0.605938i
$836$	19.9216	+	34.5052i	0.689003	+	1.19339i
$837$	−12.0986	−	0.767804i	−0.418188	−	0.0265392i
$838$	23.4349	−	40.5904i	0.809545	−	1.40217i
$839$	−24.2173	−	20.3207i	−0.836073	−	0.701548i	0.120604	−	0.992701i	$-0.461517\pi$
$839$	−24.2173	−	20.3207i	−0.836073	−	0.701548i	−0.956677	+	0.291153i	$0.905961\pi$
$840$	1.02107	−	6.35103i	0.0352303	−	0.219131i
$841$	−1.87855	−	10.6538i	−0.0647776	−	0.367372i
$842$	5.50929	−	4.62285i	0.189863	−	0.159314i
$843$	24.5228	+	34.4353i	0.844610	+	1.18601i
$844$	−37.1807	+	13.5327i	−1.27981	+	0.465814i
$845$	2.77936	+	4.81400i	0.0956130	+	0.165607i
$846$	31.0105	−	5.97870i	1.06616	−	0.205552i
$847$	−21.9220	−	10.0319i	−0.753248	−	0.344700i
$848$	−42.1780	+	15.3515i	−1.44840	+	0.527174i
$849$	−0.0822201	+	1.03461i	−0.00282179	+	0.0355076i
$850$	45.3482	+	16.5054i	1.55543	+	0.566130i
$851$	6.26037	+	2.27859i	0.214603	+	0.0781091i
$852$	1.36046	−	17.1191i	0.0466086	−	0.586492i
$853$	−18.4639	+	6.72031i	−0.632192	+	0.230099i	−0.638185	−	0.769883i	$-0.720314\pi$
$853$	−18.4639	+	6.72031i	−0.632192	+	0.230099i	0.00599331	+	0.999982i	$0.498092\pi$
$854$	43.4701	−	30.9044i	1.48752	−	1.05753i
$855$	49.1910	−	9.48382i	1.68230	−	0.324340i
$856$	−2.62090	−	4.53953i	−0.0895804	−	0.155158i
$857$	−1.46475	+	0.533127i	−0.0500350	+	0.0182113i	−0.366916	−	0.930254i	$-0.619587\pi$
$857$	−1.46475	+	0.533127i	−0.0500350	+	0.0182113i	0.316881	+	0.948465i	$0.397364\pi$
$858$	−29.5239	−	41.4579i	−1.00793	−	1.41535i
$859$	−37.6422	+	31.5856i	−1.28434	+	1.07769i	−0.291706	+	0.956508i	$0.594223\pi$
$859$	−37.6422	+	31.5856i	−1.28434	+	1.07769i	−0.992631	+	0.121178i	$0.961333\pi$
$860$	−10.4758	−	59.4113i	−0.357223	−	2.02591i
$861$	1.22895	−	0.468468i	0.0418824	−	0.0159653i
$862$	−3.51721	−	2.95129i	−0.119797	−	0.100521i
$863$	4.07047	−	7.05026i	0.138560	−	0.239994i	−0.788391	−	0.615174i	$-0.789086\pi$
$863$	4.07047	−	7.05026i	0.138560	−	0.239994i	0.926952	+	0.375180i	$0.122419\pi$
$864$	22.1365	−	33.2787i	0.753100	−	1.13217i
$865$	15.7759	+	27.3247i	0.536398	+	0.929069i
$866$	−28.4527	+	10.3559i	−0.966862	+	0.351909i
$867$	1.55165	−	1.57656i	0.0526968	−	0.0535428i
$868$	−7.84641	−	7.73483i	−0.266325	−	0.262537i
$869$	5.22598	+	1.90210i	0.177279	+	0.0645243i
$870$	−27.9631	−	39.2662i	−0.948037	−	1.33125i
$871$	40.1921	−	14.6287i	1.36186	−	0.495675i
$872$	2.05217			0.0694954
$873$	−20.8865	+	25.7123i	−0.706901	+	0.870230i
$874$	−10.7546	−	18.6276i	−0.363781	−	0.630087i
$875$	11.1107	+	0.891932i	0.375610	+	0.0301528i
$876$	−11.7161	−	8.06542i	−0.395850	−	0.272505i
$877$	7.86491	+	44.6041i	0.265579	+	1.50617i	0.767381	+	0.641192i	$0.221560\pi$
$877$	7.86491	+	44.6041i	0.265579	+	1.50617i	−0.501802	+	0.864983i	$0.667329\pi$
$878$	−72.0225	−	26.2140i	−2.43064	−	0.884681i
$879$	12.8701	−	6.12665i	0.434097	−	0.206647i
$880$	11.4536	−	64.9568i	0.386102	−	2.18969i
$881$	0.111855	+	0.193739i	0.00376850	+	0.00652724i	0.867904	−	0.496733i	$-0.165467\pi$
$881$	0.111855	+	0.193739i	0.00376850	+	0.00652724i	−0.864135	+	0.503260i	$0.832134\pi$
$882$	−38.7965	−	12.8058i	−1.30635	−	0.431195i
$883$	28.2842	−	48.9896i	0.951838	−	1.64863i	0.210396	−	0.977616i	$-0.432525\pi$
$883$	28.2842	−	48.9896i	0.951838	−	1.64863i	0.741443	−	0.671016i	$-0.234142\pi$
$884$	−18.2604	−	15.3223i	−0.614163	−	0.515344i
$885$	8.06849	−	17.6689i	0.271219	−	0.593934i
$886$	−1.05161	−	5.96400i	−0.0353297	−	0.200365i
$887$	1.02508	+	0.373100i	0.0344190	+	0.0125275i	0.359172	−	0.933271i	$-0.383059\pi$
$887$	1.02508	+	0.373100i	0.0344190	+	0.0125275i	−0.324753	+	0.945799i	$0.605281\pi$
$888$	2.10391	+	0.545821i	0.0706025	+	0.0183166i
$889$	−2.04065	−	4.29561i	−0.0684413	−	0.144070i
$890$	80.0360			2.68281
$891$	−37.4689	+	15.0054i	−1.25525	+	0.502701i
$892$	15.8947	+	27.5304i	0.532194	+	0.921787i
$893$	4.67687	−	26.5239i	0.156506	−	0.887587i
$894$	−2.16772	+	2.20253i	−0.0724996	+	0.0736635i
$895$	1.67414	+	9.49452i	0.0559603	+	0.317367i
$896$	−8.48806	+	2.33965i	−0.283566	+	0.0781621i
$897$	7.51639	+	10.5546i	0.250965	+	0.352409i
$898$	22.2226	+	18.6469i	0.741576	+	0.622256i
$899$	9.94821			0.331791
$900$	29.2735	+	16.2851i	0.975783	+	0.542835i
$901$	40.5984			1.35253
$902$	2.35304	−	0.856436i	0.0783476	−	0.0285162i
$903$	46.1602	−	0.698197i	1.53611	−	0.0232346i
$904$	−1.59013	+	1.33428i	−0.0528871	+	0.0443775i
$905$	2.65064	+	15.0325i	0.0881102	+	0.499698i
$906$	2.72418	−	34.2793i	0.0905047	−	1.13885i
$907$	31.6864	+	26.5880i	1.05213	+	0.882841i	0.993316	−	0.115428i	$-0.0368238\pi$
$907$	31.6864	+	26.5880i	1.05213	+	0.882841i	0.0588135	+	0.998269i	$0.481268\pi$
$908$	5.72629			0.190034
$909$	1.61581	−	1.98914i	0.0535930	−	0.0659755i
$910$	−52.8865	−	24.2018i	−1.75317	−	0.802282i
$911$	−6.65639	+	37.7502i	−0.220536	+	1.25072i	0.650502	+	0.759505i	$0.274559\pi$
$911$	−6.65639	+	37.7502i	−0.220536	+	1.25072i	−0.871037	+	0.491217i	$0.836552\pi$
$912$	−21.9235	−	30.7853i	−0.725958	−	1.01940i
$913$	8.86521	+	50.2771i	0.293395	+	1.66393i
$914$	−41.2383	+	34.6030i	−1.36404	+	1.14457i
$915$	−16.0469	−	58.0353i	−0.530494	−	1.91859i
$916$	−5.52977	−	4.64003i	−0.182709	−	0.153311i
$917$	−19.2492	+	13.6849i	−0.635665	+	0.451916i
$918$	−32.2768	+	23.7693i	−1.06529	+	0.784505i
$919$	−2.47835	+	4.29263i	−0.0817533	+	0.141601i	−0.904003	−	0.427526i	$-0.859385\pi$
$919$	−2.47835	+	4.29263i	−0.0817533	+	0.141601i	0.822250	+	0.569127i	$0.192719\pi$
$920$	−0.541427	+	3.07059i	−0.0178503	+	0.101234i
$921$	−28.3774	+	28.8330i	−0.935068	+	0.950080i
$922$	64.3562	+	23.4237i	2.11946	+	0.771420i
$923$	17.5799	+	6.39857i	0.578651	+	0.210612i
$924$	−34.6563	−	12.0235i	−1.14011	−	0.395543i
$925$	−3.25814	+	18.4778i	−0.107127	+	0.607547i
$926$	20.4268	+	35.3803i	0.671267	+	1.16267i
$927$	0.711119	−	2.05504i	0.0233562	−	0.0674964i
$928$	−16.3994	+	28.4046i	−0.538336	+	0.932426i
$929$	4.28226	−	24.2859i	0.140496	−	0.796795i	−0.830377	−	0.557202i	$-0.811875\pi$
$929$	4.28226	−	24.2859i	0.140496	−	0.796795i	0.970873	−	0.239593i	$-0.0770139\pi$
$930$	−23.8149	+	11.3368i	−0.780922	+	0.371749i
$931$	−22.0113	+	27.0084i	−0.721391	+	0.885163i
$932$	−20.9850	+	17.6085i	−0.687387	+	0.576786i
$933$	3.41934	−	43.0268i	0.111944	−	1.40863i
$934$	−54.0048	−	45.3154i	−1.76709	−	1.48277i
$935$	−29.8299	+	51.6669i	−0.975542	+	1.68969i
$936$	2.76857	+	3.19472i	0.0904936	+	0.104423i
$937$	−20.2545	+	35.0818i	−0.661684	+	1.14607i	0.318488	+	0.947927i	$0.396825\pi$
$937$	−20.2545	+	35.0818i	−0.661684	+	1.14607i	−0.980173	+	0.198144i	$0.936509\pi$
$938$	37.1092	−	53.8136i	1.21166	−	1.75708i
$939$	40.6490	−	3.88272i	1.32653	−	0.126708i
$940$	24.8226	−	20.8287i	0.809625	−	0.679356i
$941$	−18.0273	+	15.1267i	−0.587675	+	0.493118i	−0.887457	−	0.460890i	$-0.847530\pi$
$941$	−18.0273	+	15.1267i	−0.587675	+	0.493118i	0.299783	+	0.954008i	$0.403086\pi$
$942$	9.89517	−	10.0540i	0.322402	−	0.327578i
$943$	−0.599052	+	0.218037i	−0.0195078	+	0.00710026i
$944$	−14.6537			−0.476938
$945$	−28.5361	+	36.2357i	−0.928280	+	1.17875i
$946$	87.8953			2.85772
$947$	−26.0978	+	9.49881i	−0.848063	+	0.308670i	−0.729250	−	0.684247i	$-0.760131\pi$
$947$	−26.0978	+	9.49881i	−0.848063	+	0.308670i	−0.118813	+	0.992917i	$0.537909\pi$
$948$	3.71102	+	0.962758i	0.120528	+	0.0312689i
$949$	11.8701	−	9.96017i	0.385319	−	0.323321i
$950$	46.4050	−	38.9384i	1.50558	−	1.26333i
$951$	−10.9100	+	23.8915i	−0.353781	+	0.774734i
$952$	4.37531	+	0.351237i	0.141805	+	0.0113836i
$953$	−21.0460	+	36.4528i	−0.681748	+	1.18082i	0.292699	+	0.956204i	$0.405446\pi$
$953$	−21.0460	+	36.4528i	−0.681748	+	1.18082i	−0.974447	+	0.224617i	$0.927887\pi$
$954$	59.0076	+	9.43828i	1.91044	+	0.305576i
$955$	29.7357	−	51.5037i	0.962224	−	1.66662i
$956$	−2.06603	−	1.73360i	−0.0668202	−	0.0560688i
$957$	29.9058	−	14.2363i	0.966716	−	0.460194i
$958$	−48.5975	+	40.7781i	−1.57011	+	1.31748i
$959$	−35.4404	−	34.9364i	−1.14443	−	1.12815i
$960$	2.85275	−	35.8971i	0.0920720	−	1.15857i
$961$	−4.43790	+	25.1686i	−0.143158	+	0.811889i
$962$	9.82623	−	17.0195i	0.316810	−	0.548731i
$963$	0.598555	+	37.5800i	0.0192882	+	1.21100i
$964$	−17.1280	−	29.6666i	−0.551657	−	0.955498i
$965$	11.4718	−	65.0601i	0.369292	−	2.09436i
$966$	18.7091	+	6.49084i	0.601956	+	0.208839i
$967$	45.8194	+	16.6769i	1.47345	+	0.536293i	0.949036	−	0.315168i	$-0.102061\pi$
$967$	45.8194	+	16.6769i	1.47345	+	0.536293i	0.524417	+	0.851461i	$0.324283\pi$
$968$	3.58256	+	1.30394i	0.115148	+	0.0419104i
$969$	9.11024	+	32.9482i	0.292663	+	1.05845i
$970$	−12.5153	+	70.9779i	−0.401843	+	2.27896i
$971$	−1.76073	+	3.04968i	−0.0565045	+	0.0978687i	−0.892894	−	0.450267i	$-0.851329\pi$
$971$	−1.76073	+	3.04968i	−0.0565045	+	0.0978687i	0.836390	+	0.548136i	$0.184662\pi$
$972$	−24.7295	+	12.7536i	−0.793198	+	0.409071i
$973$	−39.9989	−	18.3042i	−1.28231	−	0.586806i
$974$	46.2017	+	38.7678i	1.48040	+	1.24220i
$975$	−25.5979	+	26.0089i	−0.819790	+	0.832951i
$976$	−34.7979	+	29.1989i	−1.11385	+	0.934635i
$977$	0.611671	+	3.46896i	0.0195691	+	0.110982i	0.993028	−	0.117881i	$-0.0376103\pi$
$977$	0.611671	+	3.46896i	0.0195691	+	0.110982i	−0.973459	+	0.228863i	$0.926499\pi$
$978$	33.6289	−	3.21218i	1.07533	−	0.102714i
$979$	−9.54922	+	54.1563i	−0.305194	+	1.73084i
$980$	−41.1735	+	7.86962i	−1.31524	+	0.251386i
$981$	−12.8587	−	7.15339i	−0.410547	−	0.228390i
$982$	−81.0859			−2.58756
$983$	−19.7672	−	16.5867i	−0.630476	−	0.529032i	0.270601	−	0.962692i	$-0.412778\pi$
$983$	−19.7672	−	16.5867i	−0.630476	−	0.529032i	−0.901077	+	0.433659i	$0.857222\pi$
$984$	−0.187794	+	0.0893971i	−0.00598665	+	0.00284987i
$985$	−11.2280	−	63.6774i	−0.357755	−	2.02893i
$986$	25.1981	−	21.1438i	0.802472	−	0.673354i
$987$	12.7217	+	21.2845i	0.404935	+	0.677495i
$988$	−28.1176	+	10.2340i	−0.894540	+	0.325586i
$989$	−22.3770			−0.711546
$990$	−55.3676	+	68.1602i	−1.75970	+	2.16627i
$991$	−47.1097			−1.49649			−0.748244	−	0.663424i	$-0.769103\pi$
$991$	−47.1097			−1.49649			−0.748244	+	0.663424i	$0.769103\pi$
$992$	13.7473	+	11.5354i	0.436478	+	0.366249i
$993$	−11.7398	+	25.7086i	−0.372552	+	0.815839i
$994$	27.5640	−	7.59772i	0.874276	−	0.240985i
$995$	−6.73773	−	38.2116i	−0.213600	−	1.21139i
$996$	9.37941	+	33.9216i	0.297198	+	1.07485i
$997$	−0.0841224	+	0.477082i	−0.00266418	+	0.0151093i	−0.986111	−	0.166088i	$-0.946886\pi$
$997$	−0.0841224	+	0.477082i	−0.00266418	+	0.0151093i	0.983447	+	0.181198i	$0.0579974\pi$
$998$	−17.3327	−	30.0211i	−0.548656	−	0.950300i
$999$	−11.2802	−	10.7538i	−0.356891	−	0.340234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.u.a.16.5	✓	132
3.2	odd	2		567.2.u.a.289.18		132
7.4	even	3		189.2.w.a.151.18	yes	132
21.11	odd	6		567.2.w.a.46.5		132
27.5	odd	18		567.2.w.a.37.5		132
27.22	even	9		189.2.w.a.184.18	yes	132
189.32	odd	18		567.2.u.a.361.18		132
189.130	even	9	inner	189.2.u.a.130.5	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.16.5	✓	132	1.1	even	1	trivial
189.2.u.a.130.5	yes	132	189.130	even	9	inner
189.2.w.a.151.18	yes	132	7.4	even	3
189.2.w.a.184.18	yes	132	27.22	even	9
567.2.u.a.289.18		132	3.2	odd	2
567.2.u.a.361.18		132	189.32	odd	18
567.2.w.a.37.5		132	27.5	odd	18
567.2.w.a.46.5		132	21.11	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.82816 + 0.665398i) q^{2} +(-0.461596 - 1.66941i) q^{3} +(1.36734 - 1.14734i) q^{4} +(2.57005 - 2.15653i) q^{5} +(1.95469 + 2.74481i) q^{6} +(-1.50198 + 2.17808i) q^{7} +(0.209199 - 0.362343i) q^{8} +(-2.57386 + 1.54119i) q^{9} +O(q^{10})\)	\(q+(-1.82816 + 0.665398i) q^{2} +(-0.461596 - 1.66941i) q^{3} +(1.36734 - 1.14734i) q^{4} +(2.57005 - 2.15653i) q^{5} +(1.95469 + 2.74481i) q^{6} +(-1.50198 + 2.17808i) q^{7} +(0.209199 - 0.362343i) q^{8} +(-2.57386 + 1.54119i) q^{9} +(-3.26352 + 5.65259i) q^{10} +(-3.43544 - 2.88268i) q^{11} +(-2.54654 - 1.75305i) q^{12} +(2.58000 - 2.16488i) q^{13} +(1.29658 - 4.98131i) q^{14} +(-4.78645 - 3.29502i) q^{15} +(-0.761251 + 4.31727i) q^{16} +(1.98260 - 3.43397i) q^{17} +(3.67994 - 4.53018i) q^{18} +(-2.48870 - 4.31055i) q^{19} +(1.03987 - 5.89742i) q^{20} +(4.32942 + 1.50203i) q^{21} +(8.19868 + 2.98408i) q^{22} +(-2.08727 - 0.759706i) q^{23} +(-0.701464 - 0.181983i) q^{24} +(1.08630 - 6.16070i) q^{25} +(-3.27617 + 5.67449i) q^{26} +(3.76095 + 3.58542i) q^{27} +(0.445273 + 4.70147i) q^{28} +(-3.26643 - 2.74086i) q^{29} +(10.9429 + 2.83895i) q^{30} +(-1.78723 + 1.49966i) q^{31} +(-1.33570 - 7.57513i) q^{32} +(-3.22659 + 7.06579i) q^{33} +(-1.33957 + 7.59708i) q^{34} +(0.836932 + 8.83684i) q^{35} +(-1.75109 + 5.06041i) q^{36} -2.99931 q^{37} +(7.41798 + 6.22442i) q^{38} +(-4.80499 - 3.30778i) q^{39} +(-0.243751 - 1.38238i) q^{40} +(0.219856 - 0.184481i) q^{41} +(-8.91435 + 0.134834i) q^{42} +(9.46658 - 3.44555i) q^{43} -8.00483 q^{44} +(-3.29133 + 9.51151i) q^{45} +4.32139 q^{46} +(4.14512 + 3.47817i) q^{47} +(7.55868 - 0.721993i) q^{48} +(-2.48810 - 6.54288i) q^{49} +(2.11338 + 11.9856i) q^{50} +(-6.64787 - 1.72467i) q^{51} +(1.04390 - 5.92027i) q^{52} +(5.11933 + 8.86693i) q^{53} +(-9.26137 - 4.05221i) q^{54} -15.0458 q^{55} +(0.475001 + 0.999885i) q^{56} +(-6.04730 + 6.14439i) q^{57} +(7.79533 + 2.83727i) q^{58} +(0.580445 + 3.29187i) q^{59} +(-10.3252 + 0.986248i) q^{60} +(7.93772 + 6.66054i) q^{61} +(2.26947 - 3.93084i) q^{62} +(0.509055 - 7.92091i) q^{63} +(3.09848 + 5.36673i) q^{64} +(1.96211 - 11.1277i) q^{65} +(1.19717 - 15.0644i) q^{66} +(11.9337 + 4.34350i) q^{67} +(-1.22902 - 6.97013i) q^{68} +(-0.304783 + 3.83519i) q^{69} +(-7.41006 - 15.5983i) q^{70} +(2.77738 + 4.81056i) q^{71} +(0.0199895 + 1.25503i) q^{72} +4.60079 q^{73} +(5.48323 - 1.99573i) q^{74} +(-10.7862 + 1.03028i) q^{75} +(-8.34856 - 3.03863i) q^{76} +(11.4387 - 3.15295i) q^{77} +(10.9853 + 2.84994i) q^{78} +(-1.16530 + 0.424136i) q^{79} +(7.35385 + 12.7372i) q^{80} +(4.24950 - 7.93359i) q^{81} +(-0.279180 + 0.483554i) q^{82} +(-8.72055 - 7.31741i) q^{83} +(7.64314 - 2.91352i) q^{84} +(-2.31006 - 13.1010i) q^{85} +(-15.0138 + 12.5981i) q^{86} +(-3.06785 + 6.71818i) q^{87} +(-1.76321 + 0.641755i) q^{88} +(-6.13111 - 10.6194i) q^{89} +(-0.311839 - 19.5786i) q^{90} +(0.840175 + 8.87108i) q^{91} +(-3.72566 + 1.35603i) q^{92} +(3.32853 + 2.29138i) q^{93} +(-9.89232 - 3.60051i) q^{94} +(-15.6919 - 5.71138i) q^{95} +(-12.0294 + 5.72648i) q^{96} +(10.3763 - 3.77665i) q^{97} +(8.90228 + 10.3059i) q^{98} +(13.2851 + 2.12495i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Introduction

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