LMFDB - Embedded newform 567.2.u.a.361.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(100,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16, 6]))

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

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

chi := DirichletCharacter("567.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.u (of order $9$, degree $6$, not 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			361.18
Character	$\chi$	$=$	567.361
Dual form			567.2.u.a.289.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.82816 + 0.665398i) q^{2} +(1.36734 + 1.14734i) q^{4} +(-2.57005 - 2.15653i) q^{5} +(-1.50198 - 2.17808i) q^{7} +(-0.209199 - 0.362343i) q^{8} +O(q^{10})$	\(q+(1.82816 + 0.665398i) q^{2} +(1.36734 + 1.14734i) q^{4} +(-2.57005 - 2.15653i) q^{5} +(-1.50198 - 2.17808i) q^{7} +(-0.209199 - 0.362343i) q^{8} +(-3.26352 - 5.65259i) q^{10} +(3.43544 - 2.88268i) q^{11} +(2.58000 + 2.16488i) q^{13} +(-1.29658 - 4.98131i) q^{14} +(-0.761251 - 4.31727i) q^{16} +(-1.98260 - 3.43397i) q^{17} +(-2.48870 + 4.31055i) q^{19} +(-1.03987 - 5.89742i) q^{20} +(8.19868 - 2.98408i) q^{22} +(2.08727 - 0.759706i) q^{23} +(1.08630 + 6.16070i) q^{25} +(3.27617 + 5.67449i) q^{26} +(0.445273 - 4.70147i) q^{28} +(3.26643 - 2.74086i) q^{29} +(-1.78723 - 1.49966i) q^{31} +(1.33570 - 7.57513i) q^{32} +(-1.33957 - 7.59708i) q^{34} +(-0.836932 + 8.83684i) q^{35} -2.99931 q^{37} +(-7.41798 + 6.22442i) q^{38} +(-0.243751 + 1.38238i) q^{40} +(-0.219856 - 0.184481i) q^{41} +(9.46658 + 3.44555i) q^{43} +8.00483 q^{44} +4.32139 q^{46} +(-4.14512 + 3.47817i) q^{47} +(-2.48810 + 6.54288i) q^{49} +(-2.11338 + 11.9856i) q^{50} +(1.04390 + 5.92027i) q^{52} +(-5.11933 + 8.86693i) q^{53} -15.0458 q^{55} +(-0.475001 + 0.999885i) q^{56} +(7.79533 - 2.83727i) q^{58} +(-0.580445 + 3.29187i) q^{59} +(7.93772 - 6.66054i) q^{61} +(-2.26947 - 3.93084i) q^{62} +(3.09848 - 5.36673i) q^{64} +(-1.96211 - 11.1277i) q^{65} +(11.9337 - 4.34350i) q^{67} +(1.22902 - 6.97013i) q^{68} +(-7.41006 + 15.5983i) q^{70} +(-2.77738 + 4.81056i) q^{71} +4.60079 q^{73} +(-5.48323 - 1.99573i) q^{74} +(-8.34856 + 3.03863i) q^{76} +(-11.4387 - 3.15295i) q^{77} +(-1.16530 - 0.424136i) q^{79} +(-7.35385 + 12.7372i) q^{80} +(-0.279180 - 0.483554i) q^{82} +(8.72055 - 7.31741i) q^{83} +(-2.31006 + 13.1010i) q^{85} +(15.0138 + 12.5981i) q^{86} +(-1.76321 - 0.641755i) q^{88} +(6.13111 - 10.6194i) q^{89} +(0.840175 - 8.87108i) q^{91} +(3.72566 + 1.35603i) q^{92} +(-9.89232 + 3.60051i) q^{94} +(15.6919 - 5.71138i) q^{95} +(10.3763 + 3.77665i) q^{97} +(-8.90228 + 10.3059i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) $ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8	$ 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} + 3 q^{10} + 15 q^{11} - 12 q^{13} + 30 q^{14} + 9 q^{16} - 27 q^{17} + 3 q^{19} + 18 q^{20} - 12 q^{22} + 36 q^{23} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} + 75 q^{32} - 18 q^{34} - 15 q^{35} - 6 q^{37} - 69 q^{38} + 51 q^{40} - 12 q^{43} + 6 q^{44} - 6 q^{46} + 21 q^{47} - 42 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 111 q^{56} - 3 q^{58} - 27 q^{59} - 21 q^{61} - 75 q^{62} - 30 q^{64} + 90 q^{65} - 3 q^{67} + 30 q^{68} + 39 q^{70} + 18 q^{71} - 42 q^{73} - 51 q^{74} - 24 q^{76} - 15 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} + 93 q^{86} - 51 q^{88} - 75 q^{89} - 21 q^{91} + 66 q^{92} + 33 q^{94} - 15 q^{95} - 12 q^{97} + 36 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 + 3 * q^10 + 15 * q^11 - 12 * q^13 + 30 * q^14 + 9 * q^16 - 27 * q^17 + 3 * q^19 + 18 * q^20 - 12 * q^22 + 36 * q^23 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 + 75 * q^32 - 18 * q^34 - 15 * q^35 - 6 * q^37 - 69 * q^38 + 51 * q^40 - 12 * q^43 + 6 * q^44 - 6 * q^46 + 21 * q^47 - 42 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 111 * q^56 - 3 * q^58 - 27 * q^59 - 21 * q^61 - 75 * q^62 - 30 * q^64 + 90 * q^65 - 3 * q^67 + 30 * q^68 + 39 * q^70 + 18 * q^71 - 42 * q^73 - 51 * q^74 - 24 * q^76 - 15 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 + 93 * q^86 - 51 * q^88 - 75 * q^89 - 21 * q^91 + 66 * q^92 + 33 * q^94 - 15 * q^95 - 12 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{9}\right)$

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	$-0.147450\pi$
$2$	1.82816	+	0.665398i	1.29271	+	0.470507i	0.398093	+	0.917345i	$0.369672\pi$
$3$		0			0
$3$		0			0
$4$	1.36734	+	1.14734i	0.683672	+	0.573669i
$5$	−2.57005	−	2.15653i	−1.14936	−	0.964427i	−0.149655	−	0.988738i	$-0.547816\pi$
$5$	−2.57005	−	2.15653i	−1.14936	−	0.964427i	−0.999704	+	0.0243109i	$0.992261\pi$
$6$		0			0
$7$	−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
$9$		0			0
$10$	−3.26352	−	5.65259i	−1.03202	−	1.78750i
$11$	3.43544	−	2.88268i	1.03582	−	0.869160i	0.0442922	−	0.999019i	$-0.485897\pi$
$11$	3.43544	−	2.88268i	1.03582	−	0.869160i	0.991533	+	0.129858i	$0.0414523\pi$
$12$		0			0
$13$	2.58000	+	2.16488i	0.715564	+	0.600430i	0.926154	−	0.377145i	$-0.123094\pi$
$13$	2.58000	+	2.16488i	0.715564	+	0.600430i	−0.210590	+	0.977574i	$0.567538\pi$
$14$	−1.29658	−	4.98131i	−0.346525	−	1.33131i
$15$		0			0
$16$	−0.761251	−	4.31727i	−0.190313	−	1.07932i
$17$	−1.98260	−	3.43397i	−0.480852	−	0.832860i	0.518907	−	0.854831i	$-0.326339\pi$
$17$	−1.98260	−	3.43397i	−0.480852	−	0.832860i	−0.999759	+	0.0219708i	$0.993006\pi$
$18$		0			0
$19$	−2.48870	+	4.31055i	−0.570946	+	0.988908i	0.425523	+	0.904948i	$0.360090\pi$
$19$	−2.48870	+	4.31055i	−0.570946	+	0.988908i	−0.996469	+	0.0839604i	$0.973243\pi$
$20$	−1.03987	−	5.89742i	−0.232523	−	1.31870i
$21$		0			0
$22$	8.19868	−	2.98408i	1.74796	−	0.636207i
$23$	2.08727	−	0.759706i	0.435227	−	0.158410i	−0.115109	−	0.993353i	$-0.536722\pi$
$23$	2.08727	−	0.759706i	0.435227	−	0.158410i	0.550336	+	0.834943i	$0.314500\pi$
$24$		0			0
$25$	1.08630	+	6.16070i	0.217260	+	1.23214i
$26$	3.27617	+	5.67449i	0.642509	+	1.11286i
$27$		0			0
$28$	0.445273	−	4.70147i	0.0841488	−	0.888494i
$29$	3.26643	−	2.74086i	0.606561	−	0.508965i	−0.286986	−	0.957935i	$-0.592653\pi$
$29$	3.26643	−	2.74086i	0.606561	−	0.508965i	0.893547	+	0.448970i	$0.148209\pi$
$30$		0			0
$31$	−1.78723	−	1.49966i	−0.320995	−	0.269347i	0.468024	−	0.883716i	$-0.344966\pi$
$31$	−1.78723	−	1.49966i	−0.320995	−	0.269347i	−0.789019	+	0.614369i	$0.789411\pi$
$32$	1.33570	−	7.57513i	0.236121	−	1.33911i
$33$		0			0
$34$	−1.33957	−	7.59708i	−0.229734	−	1.30289i
$35$	−0.836932	+	8.83684i	−0.141467	+	1.49370i
$36$		0			0
$37$	−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
$39$		0			0
$40$	−0.243751	+	1.38238i	−0.0385404	+	0.218574i
$41$	−0.219856	−	0.184481i	−0.0343358	−	0.0288112i	0.625458	−	0.780258i	$-0.284912\pi$
$41$	−0.219856	−	0.184481i	−0.0343358	−	0.0288112i	−0.659794	+	0.751446i	$0.729356\pi$
$42$		0			0
$43$	9.46658	+	3.44555i	1.44364	+	0.525442i	0.940807	−	0.338942i	$-0.110069\pi$
$43$	9.46658	+	3.44555i	1.44364	+	0.525442i	0.502833	+	0.864384i	$0.332291\pi$
$44$	8.00483			1.20677
$45$		0			0
$46$	4.32139			0.637154
$47$	−4.14512	+	3.47817i	−0.604628	+	0.507343i	−0.892929	−	0.450197i	$-0.851354\pi$
$47$	−4.14512	+	3.47817i	−0.604628	+	0.507343i	0.288302	+	0.957540i	$0.406909\pi$
$48$		0			0
$49$	−2.48810	+	6.54288i	−0.355443	+	0.934698i
$50$	−2.11338	+	11.9856i	−0.298878	+	1.69502i
$51$		0			0
$52$	1.04390	+	5.92027i	0.144763	+	0.820994i
$53$	−5.11933	+	8.86693i	−0.703194	+	1.21797i	0.264146	+	0.964483i	$0.414910\pi$
$53$	−5.11933	+	8.86693i	−0.703194	+	1.21797i	−0.967340	+	0.253484i	$0.918423\pi$
$54$		0			0
$55$	−15.0458			−2.02878
$56$	−0.475001	+	0.999885i	−0.0634747	+	0.133615i
$57$		0			0
$58$	7.79533	−	2.83727i	1.02358	−	0.372552i
$59$	−0.580445	+	3.29187i	−0.0755675	+	0.428564i	0.923429	+	0.383770i	$0.125374\pi$
$59$	−0.580445	+	3.29187i	−0.0755675	+	0.428564i	−0.998996	+	0.0447945i	$0.985737\pi$
$60$		0			0
$61$	7.93772	−	6.66054i	1.01632	−	0.852795i	0.0271605	−	0.999631i	$-0.491353\pi$
$61$	7.93772	−	6.66054i	1.01632	−	0.852795i	0.989161	+	0.146836i	$0.0469090\pi$
$62$	−2.26947	−	3.93084i	−0.288223	−	0.499218i
$63$		0			0
$64$	3.09848	−	5.36673i	0.387310	−	0.670841i
$65$	−1.96211	−	11.1277i	−0.243370	−	1.38022i
$66$		0			0
$67$	11.9337	−	4.34350i	1.45793	−	0.530643i	0.513135	−	0.858308i	$-0.328484\pi$
$67$	11.9337	−	4.34350i	1.45793	−	0.530643i	0.944794	+	0.327665i	$0.106262\pi$
$68$	1.22902	−	6.97013i	0.149041	−	0.845253i
$69$		0			0
$70$	−7.41006	+	15.5983i	−0.885672	+	1.86435i
$71$	−2.77738	+	4.81056i	−0.329614	+	0.570908i	−0.982435	−	0.186604i	$-0.940252\pi$
$71$	−2.77738	+	4.81056i	−0.329614	+	0.570908i	0.652821	+	0.757512i	$0.273585\pi$
$72$		0			0
$73$	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
$75$		0			0
$76$	−8.34856	+	3.03863i	−0.957646	+	0.348554i
$77$	−11.4387	−	3.15295i	−1.30356	−	0.359313i
$78$		0			0
$79$	−1.16530	−	0.424136i	−0.131107	−	0.0477190i	0.275633	−	0.961263i	$-0.411112\pi$
$79$	−1.16530	−	0.424136i	−0.131107	−	0.0477190i	−0.406740	+	0.913544i	$0.633335\pi$
$80$	−7.35385	+	12.7372i	−0.822185	+	1.42407i
$81$		0			0
$82$	−0.279180	−	0.483554i	−0.0308303	−	0.0533996i
$83$	8.72055	−	7.31741i	0.957205	−	0.803190i	−0.0232914	−	0.999729i	$-0.507415\pi$
$83$	8.72055	−	7.31741i	0.957205	−	0.803190i	0.980496	+	0.196539i	$0.0629701\pi$
$84$		0			0
$85$	−2.31006	+	13.1010i	−0.250561	+	1.42100i
$86$	15.0138	+	12.5981i	1.61898	+	1.35849i
$87$		0			0
$88$	−1.76321	−	0.641755i	−0.187959	−	0.0684114i
$89$	6.13111	−	10.6194i	0.649896	−	1.12565i	−0.333251	−	0.942838i	$-0.608146\pi$
$89$	6.13111	−	10.6194i	0.649896	−	1.12565i	0.983147	−	0.182815i	$-0.0585209\pi$
$90$		0			0
$91$	0.840175	−	8.87108i	0.0880743	−	0.929942i
$92$	3.72566	+	1.35603i	0.388427	+	0.141376i
$93$		0			0
$94$	−9.89232	+	3.60051i	−1.02032	+	0.371364i
$95$	15.6919	−	5.71138i	1.60995	−	0.585975i
$96$		0			0
$97$	10.3763	+	3.77665i	1.05355	+	0.383461i	0.810001	−	0.586428i	$-0.199466\pi$
$97$	10.3763	+	3.77665i	1.05355	+	0.383461i	0.243548	+	0.969889i	$0.421689\pi$
$98$	−8.90228	+	10.3059i	−0.899266	+	1.04105i
$99$		0			0
$100$	−5.58306	+	9.67014i	−0.558306	+	0.967014i
$101$	0.802721	+	0.292167i	0.0798737	+	0.0290717i	0.381648	−	0.924308i	$-0.375357\pi$
$101$	0.802721	+	0.292167i	0.0798737	+	0.0290717i	−0.301774	+	0.953379i	$0.597579\pi$
$102$		0			0
$103$	−0.555280	−	0.465935i	−0.0547133	−	0.0459099i	0.615021	−	0.788511i	$-0.289148\pi$
$103$	−0.555280	−	0.465935i	−0.0547133	−	0.0459099i	−0.669734	+	0.742601i	$0.733592\pi$
$104$	0.244695	−	1.38774i	0.0239944	−	0.136079i
$105$		0			0
$106$	−15.2590	+	12.8038i	−1.48209	+	1.24362i
$107$	−6.26413	−	10.8498i	−0.605577	−	1.04889i	−0.991960	−	0.126551i	$-0.959609\pi$
$107$	−6.26413	−	10.8498i	−0.605577	−	1.04889i	0.386384	−	0.922338i	$-0.373724\pi$
$108$		0			0
$109$	2.45242	−	4.24772i	0.234899	−	0.406857i	−0.724344	−	0.689439i	$-0.757857\pi$
$109$	2.45242	−	4.24772i	0.234899	−	0.406857i	0.959243	+	0.282581i	$0.0911906\pi$
$110$	−27.5062	−	10.0114i	−2.62262	−	0.954554i
$111$		0			0
$112$	−8.25999	+	8.14253i	−0.780496	+	0.769396i
$113$	4.66204	−	1.69685i	0.438568	−	0.159626i	−0.113293	−	0.993562i	$-0.536140\pi$
$113$	4.66204	−	1.69685i	0.438568	−	0.159626i	0.551861	+	0.833936i	$0.313918\pi$
$114$		0			0
$115$	−7.00272	−	2.54878i	−0.653007	−	0.237675i
$116$	7.61102			0.706665
$117$		0			0
$118$	−3.25155	+	5.63185i	−0.299329	+	0.518454i
$119$	−4.50164	+	9.47604i	−0.412665	+	0.868667i
$120$		0			0
$121$	1.58230	−	8.97366i	0.143845	−	0.815787i
$122$	18.9434	−	6.89482i	1.71505	−	0.624228i
$123$		0			0
$124$	−0.723135	−	4.10110i	−0.0649395	−	0.368290i
$125$	2.10648	−	3.64853i	0.188409	−	0.326334i
$126$		0			0
$127$	−0.898740	−	1.55666i	−0.0797503	−	0.138132i	0.823392	−	0.567473i	$-0.192079\pi$
$127$	−0.898740	−	1.55666i	−0.0797503	−	0.138132i	−0.903142	+	0.429342i	$0.858746\pi$
$128$	−2.54927	+	2.13909i	−0.225325	+	0.189070i
$129$		0			0
$130$	3.81727	−	21.6488i	0.334797	−	1.89873i
$131$	−8.38840	+	3.05313i	−0.732898	+	0.266753i	−0.681391	−	0.731919i	$-0.738625\pi$
$131$	−8.38840	+	3.05313i	−0.732898	+	0.266753i	−0.0515071	+	0.998673i	$0.516402\pi$
$132$		0			0
$133$	13.1267	−	1.05377i	1.13823	−	0.0913737i
$134$	24.7069			2.13435
$135$		0			0
$136$	−0.829517	+	1.43676i	−0.0711305	+	0.123202i
$137$	3.26623	+	18.5237i	0.279053	+	1.58259i	0.725787	+	0.687920i	$0.241476\pi$
$137$	3.26623	+	18.5237i	0.279053	+	1.58259i	−0.446734	+	0.894667i	$0.647413\pi$
$138$		0			0
$139$	2.88707	−	16.3734i	0.244878	−	1.38877i	−0.575899	−	0.817521i	$-0.695348\pi$
$139$	2.88707	−	16.3734i	0.244878	−	1.38877i	0.820777	−	0.571249i	$-0.193541\pi$
$140$	−11.2832	+	11.1227i	−0.953605	+	0.940044i
$141$		0			0
$142$	−8.27844	+	6.94643i	−0.694711	+	0.582932i
$143$	15.1041			1.26307
$144$		0			0
$145$	−14.3056			−1.18802
$146$	8.41101	+	3.06136i	0.696100	+	0.253360i
$147$		0			0
$148$	−4.10108	−	3.44122i	−0.337107	−	0.282866i
$149$	−0.159252	+	0.903164i	−0.0130464	+	0.0739900i	−0.990636	−	0.136531i	$-0.956405\pi$
$149$	−0.159252	+	0.903164i	−0.0130464	+	0.0739900i	0.977589	+	0.210521i	$0.0675159\pi$
$150$		0			0
$151$	−7.81741	+	6.55958i	−0.636172	+	0.533811i	−0.902840	−	0.429977i	$-0.858522\pi$
$151$	−7.81741	+	6.55958i	−0.636172	+	0.533811i	0.266668	+	0.963788i	$0.414077\pi$
$152$	2.08253			0.168916
$153$		0			0
$154$	−18.8138	−	13.3754i	−1.51606	−	1.07782i
$155$	1.35920	+	7.70840i	0.109173	+	0.619153i
$156$		0			0
$157$	−0.726950	+	4.12274i	−0.0580169	+	0.329030i	−0.999978	−	0.00669296i	$-0.997870\pi$
$157$	−0.726950	+	4.12274i	−0.0580169	+	0.329030i	0.941961	+	0.335723i	$0.108981\pi$
$158$	−1.84815	−	1.55078i	−0.147031	−	0.123373i
$159$		0			0
$160$	−19.7688	+	16.5880i	−1.56286	+	1.31139i
$161$	−4.78975	−	3.40520i	−0.377485	−	0.268367i
$162$		0			0
$163$	5.01262	+	8.68211i	0.392619	+	0.680036i	0.992794	−	0.119833i	$-0.0382359\pi$
$163$	5.01262	+	8.68211i	0.392619	+	0.680036i	−0.600175	+	0.799868i	$0.704903\pi$
$164$	−0.0889567	−	0.504499i	−0.00694635	−	0.0393947i
$165$		0			0
$166$	20.8116	−	7.57480i	1.61529	−	0.587918i
$167$	14.3390	−	5.21896i	1.10958	−	0.403855i	0.278743	−	0.960366i	$-0.410082\pi$
$167$	14.3390	−	5.21896i	1.10958	−	0.403855i	0.830841	+	0.556510i	$0.187860\pi$
$168$		0			0
$169$	−0.287712	−	1.63170i	−0.0221317	−	0.125515i
$170$	−12.9405	+	22.4137i	−0.992494	+	1.71905i
$171$		0			0
$172$	8.99085	+	15.5726i	0.685546	+	1.18740i
$173$	1.63308	+	9.26168i	0.124161	+	0.704152i	0.981803	+	0.189904i	$0.0608178\pi$
$173$	1.63308	+	9.26168i	0.124161	+	0.704152i	−0.857642	+	0.514248i	$0.828071\pi$
$174$		0			0
$175$	11.7869	−	11.6193i	0.891008	−	0.878337i
$176$	−15.0605	−	12.6373i	−1.13523	−	0.952571i
$177$		0			0
$178$	18.2748	−	15.3344i	1.36975	−	1.14936i
$179$	1.43683	+	2.48866i	0.107394	+	0.186011i	0.914714	−	0.404103i	$-0.132416\pi$
$179$	1.43683	+	2.48866i	0.107394	+	0.186011i	−0.807320	+	0.590114i	$0.799083\pi$
$180$		0			0
$181$	−2.27490	−	3.94025i	−0.169092	−	0.292876i	0.769009	−	0.639238i	$-0.220750\pi$
$181$	−2.27490	−	3.94025i	−0.169092	−	0.292876i	−0.938101	+	0.346362i	$0.887417\pi$
$182$	7.43877	−	15.6587i	0.551398	−	1.16070i
$183$		0			0
$184$	−0.711929	−	0.597379i	−0.0524841	−	0.0440394i
$185$	7.70836	+	6.46808i	0.566730	+	0.475543i
$186$		0			0
$187$	−16.7102	−	6.08200i	−1.22197	−	0.444760i
$188$	−9.65843			−0.704414
$189$		0			0
$190$	32.4877			2.35690
$191$	−16.6574	−	6.06279i	−1.20529	−	0.438688i	−0.340219	−	0.940346i	$-0.610501\pi$
$191$	−16.6574	−	6.06279i	−1.20529	−	0.438688i	−0.865066	+	0.501658i	$0.832724\pi$
$192$		0			0
$193$	15.0845	+	12.6574i	1.08580	+	0.911097i	0.996390	−	0.0848971i	$-0.0270561\pi$
$193$	15.0845	+	12.6574i	1.08580	+	0.911097i	0.0894140	+	0.995995i	$0.471501\pi$
$194$	16.4565	+	13.8087i	1.18151	+	0.991405i
$195$		0			0
$196$	−10.9090	+	6.09167i	−0.779213	+	0.435120i
$197$	−9.63644	−	16.6908i	−0.686568	−	1.18917i	−0.972941	−	0.231052i	$-0.925783\pi$
$197$	−9.63644	−	16.6908i	−0.686568	−	1.18917i	0.286373	−	0.958118i	$-0.407550\pi$
$198$		0			0
$199$	5.78264	+	10.0158i	0.409921	+	0.710003i	0.994880	−	0.101059i	$-0.0322231\pi$
$199$	5.78264	+	10.0158i	0.409921	+	0.710003i	−0.584960	+	0.811062i	$0.698890\pi$
$200$	2.00503	−	1.68242i	0.141777	−	0.118965i
$201$		0			0
$202$	1.27310	+	1.06826i	0.0895750	+	0.0751623i
$203$	−10.8759	−	2.99784i	−0.763341	−	0.210407i
$204$		0			0
$205$	0.167202	+	0.948251i	0.0116779	+	0.0662288i
$206$	−0.705111	−	1.22129i	−0.0491274	−	0.0850911i
$207$		0			0
$208$	7.38234	−	12.7866i	0.511873	−	0.886590i
$209$	3.87615	+	21.9828i	0.268119	+	1.52058i
$210$		0			0
$211$	−20.8302	+	7.58159i	−1.43401	+	0.521938i	−0.938079	−	0.346422i	$-0.887397\pi$
$211$	−20.8302	+	7.58159i	−1.43401	+	0.521938i	−0.495934	+	0.868360i	$0.665174\pi$
$212$	−17.1732	+	6.25055i	−1.17946	+	0.429289i
$213$		0			0
$214$	−4.23244	−	24.0034i	−0.289324	−	1.64084i
$215$	−16.8991	−	29.2701i	−1.15251	−	1.99621i
$216$		0			0
$217$	−0.582008	+	6.14519i	−0.0395093	+	0.417163i
$218$	7.30985	−	6.13369i	0.495085	−	0.415426i
$219$		0			0
$220$	−20.5728	−	17.2626i	−1.38702	−	1.16385i
$221$	2.31901	−	13.1518i	0.155993	−	0.884683i
$222$		0			0
$223$	−3.09264	−	17.5392i	−0.207098	−	1.17451i	−0.894104	−	0.447860i	$-0.852186\pi$
$223$	−3.09264	−	17.5392i	−0.207098	−	1.17451i	0.687005	−	0.726652i	$-0.258925\pi$
$224$	−18.5055	+	8.46844i	−1.23645	+	0.565821i
$225$		0			0
$226$	9.65206			0.642046
$227$	−2.45756	+	2.06214i	−0.163114	+	0.136869i	−0.720691	−	0.693256i	$-0.756175\pi$
$227$	−2.45756	+	2.06214i	−0.163114	+	0.136869i	0.557577	+	0.830125i	$0.311731\pi$
$228$		0			0
$229$	−0.702262	+	3.98273i	−0.0464068	+	0.263186i	−0.999180	−	0.0404979i	$-0.987106\pi$
$229$	−0.702262	+	3.98273i	−0.0464068	+	0.263186i	0.952773	+	0.303684i	$0.0982167\pi$
$230$	−11.1062	−	9.31918i	−0.732319	−	0.614489i
$231$		0			0
$232$	−1.67646	−	0.610183i	−0.110065	−	0.0400605i
$233$	15.3473			1.00543			0.502717	−	0.864451i	$-0.332334\pi$
$233$	15.3473			1.00543			0.502717	+	0.864451i	$0.332334\pi$
$234$		0			0
$235$	18.1539			1.18423
$236$	−4.57055	+	3.83515i	−0.297517	+	0.249647i
$237$		0			0
$238$	−14.5351	+	14.3284i	−0.942169	+	0.928771i
$239$	0.262379	−	1.48803i	0.0169719	−	0.0962524i	−0.975145	−	0.221567i	$-0.928883\pi$
$239$	0.262379	−	1.48803i	0.0169719	−	0.0962524i	0.992117	+	0.125315i	$0.0399940\pi$
$240$		0			0
$241$	3.33261	+	18.9002i	0.214672	+	1.21747i	0.881474	+	0.472232i	$0.156551\pi$
$241$	3.33261	+	18.9002i	0.214672	+	1.21747i	−0.666802	+	0.745235i	$0.732337\pi$
$242$	8.86376	−	15.3525i	0.569784	−	0.986894i
$243$		0			0
$244$	18.4955			1.18405
$245$	20.5044	−	11.4499i	1.30998	−	0.731505i
$246$		0			0
$247$	−15.7527	+	5.73351i	−1.00232	+	0.364814i
$248$	−0.169506	+	0.961316i	−0.0107636	+	0.0610436i
$249$		0			0
$250$	6.27871	−	5.26846i	0.397100	−	0.333207i
$251$	−4.44988	−	7.70741i	−0.280874	−	0.486488i	0.690726	−	0.723116i	$-0.257291\pi$
$251$	−4.44988	−	7.70741i	−0.280874	−	0.486488i	−0.971600	+	0.236629i	$0.923958\pi$
$252$		0			0
$253$	4.98072	−	8.62686i	0.313135	−	0.542366i
$254$	−0.607245	−	3.44386i	−0.0381019	−	0.216087i
$255$		0			0
$256$	−17.7303	+	6.45330i	−1.10814	+	0.403331i
$257$	−1.70465	+	9.66754i	−0.106333	+	0.603045i	0.884346	+	0.466831i	$0.154604\pi$
$257$	−1.70465	+	9.66754i	−0.106333	+	0.603045i	−0.990680	+	0.136213i	$0.956507\pi$
$258$		0			0
$259$	4.50490	+	6.53274i	0.279921	+	0.405925i
$260$	10.0843	−	17.4666i	0.625404	−	1.08323i
$261$		0			0
$262$	−17.3669			−1.07293
$263$	7.00430	+	2.54936i	0.431904	+	0.157200i	0.548818	−	0.835942i	$-0.315078\pi$
$263$	7.00430	+	2.54936i	0.431904	+	0.157200i	−0.116914	+	0.993142i	$0.537300\pi$
$264$		0			0
$265$	32.2787	−	11.7485i	1.98286	−	0.721703i
$266$	24.6990	+	6.80802i	1.51439	+	0.417426i
$267$		0			0
$268$	21.3009	+	7.75288i	1.30116	+	0.473583i
$269$	−8.61215	+	14.9167i	−0.525092	+	0.909486i	0.474481	+	0.880266i	$0.342636\pi$
$269$	−8.61215	+	14.9167i	−0.525092	+	0.909486i	−0.999573	+	0.0292204i	$0.990698\pi$
$270$		0			0
$271$	0.412552	+	0.714562i	0.0250608	+	0.0434065i	0.878284	−	0.478140i	$-0.158689\pi$
$271$	0.412552	+	0.714562i	0.0250608	+	0.0434065i	−0.853223	+	0.521546i	$0.825355\pi$
$272$	−13.3161	+	11.1735i	−0.807408	+	0.677496i
$273$		0			0
$274$	−6.35442	+	36.0377i	−0.383885	+	2.17712i
$275$	21.4912	+	18.0333i	1.29597	+	1.08745i
$276$		0			0
$277$	−10.8150	−	3.93635i	−0.649812	−	0.236512i	−0.00398024	−	0.999992i	$-0.501267\pi$
$277$	−10.8150	−	3.93635i	−0.649812	−	0.236512i	−0.645832	+	0.763480i	$0.723489\pi$
$278$	16.1728	−	28.0122i	0.969981	−	1.68006i
$279$		0			0
$280$	3.37705	−	1.54540i	0.201817	−	0.0923553i
$281$	22.9354	+	8.34780i	1.36821	+	0.497988i	0.918583	−	0.395228i	$-0.129334\pi$
$281$	22.9354	+	8.34780i	1.36821	+	0.497988i	0.449628	+	0.893216i	$0.351557\pi$
$282$		0			0
$283$	−0.563076	+	0.204943i	−0.0334714	+	0.0121826i	−0.358702	−	0.933452i	$-0.616780\pi$
$283$	−0.563076	+	0.204943i	−0.0334714	+	0.0121826i	0.325230	+	0.945635i	$0.394558\pi$
$284$	−9.31696	+	3.39110i	−0.552860	+	0.201225i
$285$		0			0
$286$	27.6128	+	10.0502i	1.63278	+	0.594283i
$287$	−0.0715959	+	0.755953i	−0.00422617	+	0.0446225i
$288$		0			0
$289$	0.638564	−	1.10602i	0.0375626	−	0.0650603i
$290$	−26.1530	−	9.51891i	−1.53576	−	0.558970i
$291$		0			0
$292$	6.29086	+	5.27866i	0.368145	+	0.308910i
$293$	−1.42904	+	8.10449i	−0.0834854	+	0.473469i	0.914188	+	0.405291i	$0.132830\pi$
$293$	−1.42904	+	8.10449i	−0.0834854	+	0.473469i	−0.997673	+	0.0681782i	$0.978281\pi$
$294$		0			0
$295$	8.59076	−	7.20851i	0.500174	−	0.419695i
$296$	0.627451	+	1.08678i	0.0364699	+	0.0631677i
$297$		0			0
$298$	−0.892102	+	1.54517i	−0.0516781	+	0.0895091i
$299$	7.02985	+	2.55866i	0.406547	+	0.147971i
$300$		0			0
$301$	−6.71392	−	25.7942i	−0.386984	−	1.48675i
$302$	−18.6562	+	6.79032i	−1.07355	+	0.390739i
$303$		0			0
$304$	20.5043	+	7.46297i	1.17600	+	0.428030i
$305$	−34.7639			−1.99058
$306$		0			0
$307$	−11.6784	+	20.2276i	−0.666521	+	1.15445i	0.312349	+	0.949967i	$0.398884\pi$
$307$	−11.6784	+	20.2276i	−0.666521	+	1.15445i	−0.978870	+	0.204482i	$0.934449\pi$
$308$	−12.0231	−	17.4352i	−0.685080	−	0.993463i
$309$		0			0
$310$	−2.64431	+	14.9966i	−0.150187	+	0.851751i
$311$	−23.4170	+	8.52309i	−1.32786	+	0.483300i	−0.905967	−	0.423348i	$-0.860855\pi$
$311$	−23.4170	+	8.52309i	−1.32786	+	0.483300i	−0.421888	+	0.906648i	$0.638633\pi$
$312$		0			0
$313$	−4.09384	−	23.2173i	−0.231398	−	1.31232i	−0.850069	−	0.526671i	$-0.823440\pi$
$313$	−4.09384	−	23.2173i	−0.231398	−	1.31232i	0.618671	−	0.785650i	$-0.287671\pi$
$314$	−4.07224	+	7.05333i	−0.229810	+	0.398042i
$315$		0			0
$316$	−1.10674	−	1.91694i	−0.0622592	−	0.107836i
$317$	11.6162	−	9.74716i	0.652431	−	0.547455i	−0.255376	−	0.966842i	$-0.582199\pi$
$317$	11.6162	−	9.74716i	0.652431	−	0.547455i	0.907808	+	0.419387i	$0.137755\pi$
$318$		0			0
$319$	3.32061	−	18.8321i	0.185919	−	1.05440i
$320$	−19.5367	+	7.11079i	−1.09214	+	0.397505i
$321$		0			0
$322$	−6.49064	−	9.41235i	−0.361709	−	0.524530i
$323$	19.7364			1.09816
$324$		0			0
$325$	−10.5345	+	18.2463i	−0.584351	+	1.01212i
$326$	3.38684	+	19.2077i	0.187580	+	1.06382i
$327$		0			0
$328$	−0.0208518	+	0.118257i	−0.00115135	+	0.00652963i
$329$	13.8016	+	3.80428i	0.760909	+	0.209737i
$330$		0			0
$331$	−12.4997	+	10.4885i	−0.687048	+	0.576501i	−0.918056	−	0.396450i	$-0.870242\pi$
$331$	−12.4997	+	10.4885i	−0.687048	+	0.576501i	0.231009	+	0.972952i	$0.425797\pi$
$332$	20.3195			1.11518
$333$		0			0
$334$	29.6867			1.62438
$335$	−40.0369	−	14.5723i	−2.18745	−	0.796167i
$336$		0			0
$337$	0.0798940	+	0.0670390i	0.00435210	+	0.00365185i	0.644961	−	0.764215i	$-0.276874\pi$
$337$	0.0798940	+	0.0670390i	0.00435210	+	0.00365185i	−0.640609	+	0.767867i	$0.721318\pi$
$338$	0.559742	−	3.17446i	0.0304460	−	0.172668i
$339$		0			0
$340$	−18.1899	+	15.2631i	−0.986486	+	0.827760i
$341$	−10.4630			−0.566601
$342$		0			0
$343$	17.9880	−	4.40799i	0.971263	−	0.238009i
$344$	−0.731925	−	4.15095i	−0.0394628	−	0.223804i
$345$		0			0
$346$	−3.17715	+	18.0185i	−0.170805	+	0.968682i
$347$	−19.1112	−	16.0362i	−1.02594	−	0.860869i	−0.0355809	−	0.999367i	$-0.511328\pi$
$347$	−19.1112	−	16.0362i	−1.02594	−	0.860869i	−0.990363	+	0.138498i	$0.955773\pi$
$348$		0			0
$349$	22.2592	−	18.6777i	1.19151	−	0.999793i	0.191675	−	0.981458i	$-0.438608\pi$
$349$	22.2592	−	18.6777i	1.19151	−	0.999793i	0.999832	−	0.0183346i	$-0.00583640\pi$
$350$	29.2799	−	13.3990i	1.56508	−	0.716207i
$351$		0			0
$352$	−17.2479	−	29.8743i	−0.919318	−	1.59231i
$353$	0.762326	+	4.32337i	0.0405745	+	0.230110i	0.998351	−	0.0574043i	$-0.0182824\pi$
$353$	0.762326	+	4.32337i	0.0405745	+	0.230110i	−0.957776	+	0.287514i	$0.907171\pi$
$354$		0			0
$355$	17.5121	−	6.37388i	0.929445	−	0.338290i
$356$	20.5673	−	7.48590i	1.09007	−	0.396752i
$357$		0			0
$358$	0.970810	+	5.50574i	0.0513089	+	0.290987i
$359$	3.36744	−	5.83257i	0.177727	−	0.307831i	−0.763375	−	0.645956i	$-0.776459\pi$
$359$	3.36744	−	5.83257i	0.177727	−	0.307831i	0.941101	+	0.338124i	$0.109792\pi$
$360$		0			0
$361$	−2.88723	−	5.00083i	−0.151960	−	0.263202i
$362$	−1.53707	−	8.71714i	−0.0807865	−	0.458163i
$363$		0			0
$364$	11.3269	−	11.1658i	0.593692	−	0.585249i
$365$	−11.8243	−	9.92173i	−0.618910	−	0.519327i
$366$		0			0
$367$	6.35341	−	5.33114i	0.331645	−	0.278283i	−0.461725	−	0.887023i	$-0.652769\pi$
$367$	6.35341	−	5.33114i	0.331645	−	0.278283i	0.793370	+	0.608740i	$0.208325\pi$
$368$	−4.86879	−	8.43300i	−0.253803	−	0.439600i
$369$		0			0
$370$	9.78830	+	16.9538i	0.508870	+	0.881388i
$371$	27.0021	−	2.16764i	1.40188	−	0.112538i
$372$		0			0
$373$	8.96660	+	7.52387i	0.464273	+	0.389571i	0.844700	−	0.535239i	$-0.179779\pi$
$373$	8.96660	+	7.52387i	0.464273	+	0.389571i	−0.380427	+	0.924811i	$0.624223\pi$
$374$	−26.5020	−	22.2378i	−1.37038	−	1.14989i
$375$		0			0
$376$	2.12744	+	0.774326i	0.109715	+	0.0399328i
$377$	14.3610			0.739631
$378$		0			0
$379$	−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
$381$		0			0
$382$	−26.4183	−	22.1676i	−1.35168	−	1.13419i
$383$	−12.8174	−	10.7551i	−0.654938	−	0.549559i	0.253626	−	0.967302i	$-0.418377\pi$
$383$	−12.8174	−	10.7551i	−0.654938	−	0.549559i	−0.908565	+	0.417744i	$0.862821\pi$
$384$		0			0
$385$	22.5985	+	32.7711i	1.15173	+	1.67017i
$386$	19.1547	+	33.1769i	0.974949	+	1.68866i
$387$		0			0
$388$	9.85482	+	17.0691i	0.500303	+	0.866550i
$389$	−1.22668	+	1.02931i	−0.0621953	+	0.0521880i	−0.673355	−	0.739319i	$-0.735148\pi$
$389$	−1.22668	+	1.02931i	−0.0621953	+	0.0521880i	0.611160	+	0.791507i	$0.290703\pi$
$390$		0			0
$391$	−6.74704	−	5.66144i	−0.341213	−	0.286311i
$392$	2.89128	−	0.467216i	0.146032	−	0.0235980i
$393$		0			0
$394$	−6.51098	−	36.9256i	−0.328018	−	1.86028i
$395$	2.08022	+	3.60305i	0.104667	+	0.181289i
$396$		0			0
$397$	−5.92068	+	10.2549i	−0.297150	+	0.514679i	−0.975483	−	0.220076i	$-0.929370\pi$
$397$	−5.92068	+	10.2549i	−0.297150	+	0.514679i	0.678333	+	0.734755i	$0.262703\pi$
$398$	3.90711	+	22.1583i	0.195846	+	1.11070i
$399$		0			0
$400$	25.7705	−	9.37968i	1.28852	−	0.468984i
$401$	0.147208	−	0.0535792i	0.00735120	−	0.00267562i	−0.338342	−	0.941023i	$-0.609866\pi$
$401$	0.147208	−	0.0535792i	0.00735120	−	0.00267562i	0.345693	+	0.938348i	$0.387644\pi$
$402$		0			0
$403$	−1.36446	−	7.73826i	−0.0679688	−	0.385470i
$404$	0.762382	+	1.32048i	0.0379299	+	0.0656965i
$405$		0			0
$406$	−17.8882	−	12.7174i	−0.887779	−	0.631152i
$407$	−10.3039	+	8.64603i	−0.510748	+	0.428568i
$408$		0			0
$409$	−20.5877	−	17.2751i	−1.01799	−	0.854198i	−0.0286198	−	0.999590i	$-0.509111\pi$
$409$	−20.5877	−	17.2751i	−1.01799	−	0.854198i	−0.989374	+	0.145392i	$0.953556\pi$
$410$	−0.325291	+	1.84482i	−0.0160650	+	0.0911090i
$411$		0			0
$412$	−0.224673	−	1.27419i	−0.0110689	−	0.0627747i
$413$	8.04178	−	3.68006i	0.395710	−	0.181084i
$414$		0			0
$415$	−38.1924			−1.87479
$416$	19.8454	−	16.6522i	0.972999	−	0.816443i
$417$		0			0
$418$	−7.54103	+	42.7673i	−0.368844	+	2.09182i
$419$	18.4551	+	15.4857i	0.901593	+	0.756526i	0.970501	−	0.241097i	$-0.0775072\pi$
$419$	18.4551	+	15.4857i	0.901593	+	0.756526i	−0.0689084	+	0.997623i	$0.521952\pi$
$420$		0			0
$421$	−3.47375	−	1.26434i	−0.169300	−	0.0616202i	0.255980	−	0.966682i	$-0.417602\pi$
$421$	−3.47375	−	1.26434i	−0.169300	−	0.0616202i	−0.425280	+	0.905062i	$0.639824\pi$
$422$	−43.1259			−2.09934
$423$		0			0
$424$	4.28383			0.208041
$425$	19.0020	−	15.9445i	0.921731	−	0.773424i
$426$		0			0
$427$	−26.4295	−	7.28502i	−1.27901	−	0.352547i
$428$	3.88316	−	22.0225i	0.187699	−	1.06450i
$429$		0			0
$430$	−11.4181	−	64.7553i	−0.550630	−	3.12278i
$431$	−1.18001	+	2.04383i	−0.0568390	+	0.0984480i	−0.893045	−	0.449968i	$-0.851436\pi$
$431$	−1.18001	+	2.04383i	−0.0568390	+	0.0984480i	0.836206	+	0.548416i	$0.184769\pi$
$432$		0			0
$433$	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
$435$		0			0
$436$	8.22686	−	2.99433i	0.393995	−	0.143403i
$437$	−1.91984	+	10.8880i	−0.0918386	+	0.520843i
$438$		0			0
$439$	30.1791	−	25.3233i	1.44037	−	1.20861i	0.501122	−	0.865376i	$-0.332921\pi$
$439$	30.1791	−	25.3233i	1.44037	−	1.20861i	0.939248	−	0.343238i	$-0.111524\pi$
$440$	3.14757	+	5.45174i	0.150054	+	0.259902i
$441$		0			0
$442$	12.9907	−	22.5005i	0.617904	−	1.07024i
$443$	0.540539	+	3.06555i	0.0256818	+	0.145649i	0.994952	−	0.100348i	$-0.0319958\pi$
$443$	0.540539	+	3.06555i	0.0256818	+	0.145649i	−0.969271	+	0.245997i	$0.920885\pi$
$444$		0			0
$445$	−38.6582	+	14.0704i	−1.83257	+	0.667003i
$446$	6.01670	−	34.1224i	0.284899	−	1.61574i
$447$		0			0
$448$	−16.3431	+	1.31197i	−0.772137	+	0.0619848i
$449$	7.45557	−	12.9134i	0.351850	−	0.609422i	−0.634724	−	0.772739i	$-0.718886\pi$
$449$	7.45557	−	12.9134i	0.351850	−	0.609422i	0.986574	+	0.163317i	$0.0522194\pi$
$450$		0			0
$451$	−1.28710			−0.0606074
$452$	8.32147	+	3.02877i	0.391409	+	0.142461i
$453$		0			0
$454$	−5.86496	+	2.13467i	−0.275256	+	0.100185i
$455$	−21.2900	+	20.9872i	−0.998090	+	0.983896i
$456$		0			0
$457$	26.0018	+	9.46387i	1.21631	+	0.442701i	0.868889	−	0.495007i	$-0.164835\pi$
$457$	26.0018	+	9.46387i	1.21631	+	0.442701i	0.347423	+	0.937709i	$0.387057\pi$
$458$	−3.93395	+	6.81380i	−0.183821	+	0.318388i
$459$		0			0
$460$	−6.65081	−	11.5195i	−0.310095	−	0.537101i
$461$	26.9668	−	22.6278i	1.25597	−	1.05388i	0.259868	−	0.965644i	$-0.416321\pi$
$461$	26.9668	−	22.6278i	1.25597	−	1.05388i	0.996099	−	0.0882379i	$-0.0281236\pi$
$462$		0			0
$463$	−3.64646	+	20.6801i	−0.169465	+	0.961086i	0.774874	+	0.632115i	$0.217813\pi$
$463$	−3.64646	+	20.6801i	−0.169465	+	0.961086i	−0.944340	+	0.328971i	$0.893298\pi$
$464$	−14.3196	−	12.0156i	−0.664770	−	0.557809i
$465$		0			0
$466$	28.0574	+	10.2120i	1.29973	+	0.473064i
$467$	−18.1184	+	31.3819i	−0.838418	+	1.45218i	0.0527986	+	0.998605i	$0.483186\pi$
$467$	−18.1184	+	31.3819i	−0.838418	+	1.45218i	−0.891217	+	0.453578i	$0.850147\pi$
$468$		0			0
$469$	−27.3846	−	19.4687i	−1.26451	−	0.898980i
$470$	33.1883	+	12.0796i	1.53086	+	0.557189i
$471$		0			0
$472$	1.31421	−	0.478334i	0.0604915	−	0.0220171i
$473$	42.4543	−	15.4521i	1.95205	−	0.710488i
$474$		0			0
$475$	−29.2595	−	10.6496i	−1.34252	−	0.488636i
$476$	−17.0275	+	7.79209i	−0.780454	+	0.357150i
$477$		0			0
$478$	1.46980	−	2.54577i	0.0672271	−	0.116441i
$479$	−30.6419	−	11.1527i	−1.40006	−	0.509582i	−0.471867	−	0.881670i	$-0.656420\pi$
$479$	−30.6419	−	11.1527i	−1.40006	−	0.509582i	−0.928198	+	0.372088i	$0.878642\pi$
$480$		0			0
$481$	−7.73822	−	6.49314i	−0.352833	−	0.296062i
$482$	−6.48356	+	36.7701i	−0.295318	+	1.67483i
$483$		0			0
$484$	12.4594	−	10.4546i	0.566335	−	0.475211i
$485$	−18.5230	−	32.0828i	−0.841088	−	1.45681i
$486$		0			0
$487$	−15.5004	+	26.8476i	−0.702392	+	1.21658i	0.265232	+	0.964185i	$0.414551\pi$
$487$	−15.5004	+	26.8476i	−0.702392	+	1.21658i	−0.967624	+	0.252394i	$0.918782\pi$
$488$	−4.07396	−	1.48280i	−0.184420	−	0.0671232i
$489$		0			0
$490$	45.1042	−	7.28862i	2.03760	−	0.329266i
$491$	−39.1653	+	14.2550i	−1.76751	+	0.643320i	−0.767509	+	0.641038i	$0.778504\pi$
$491$	−39.1653	+	14.2550i	−1.76751	+	0.643320i	−0.999997	+	0.00228119i	$0.999274\pi$
$492$		0			0
$493$	−15.8881	−	5.78278i	−0.715562	−	0.260443i
$494$	−32.6136			−1.46735
$495$		0			0
$496$	−5.11391	+	8.85756i	−0.229621	+	0.397716i
$497$	14.6494	−	1.17601i	0.657114	−	0.0527511i
$498$		0			0
$499$	3.09411	−	17.5476i	0.138512	−	0.785538i	−0.833838	−	0.552009i	$-0.813861\pi$
$499$	3.09411	−	17.5476i	0.138512	−	0.785538i	0.972350	−	0.233529i	$-0.0750274\pi$
$500$	7.06637	−	2.57195i	0.316018	−	0.115021i
$501$		0			0
$502$	−3.00661	−	17.0514i	−0.134192	−	0.761039i
$503$	−13.0372	+	22.5811i	−0.581300	+	1.00684i	0.414025	+	0.910265i	$0.364122\pi$
$503$	−13.0372	+	22.5811i	−0.581300	+	1.00684i	−0.995326	+	0.0965762i	$0.969211\pi$
$504$		0			0
$505$	−1.43297	−	2.48197i	−0.0637662	−	0.110446i
$506$	14.8459	−	12.4572i	0.659980	−	0.553789i
$507$		0			0
$508$	0.557132	−	3.15965i	0.0247187	−	0.140187i
$509$	4.93449	−	1.79601i	0.218717	−	0.0796066i	−0.230338	−	0.973111i	$-0.573983\pi$
$509$	4.93449	−	1.79601i	0.218717	−	0.0796066i	0.449055	+	0.893504i	$0.351761\pi$
$510$		0			0
$511$	−6.91031	−	10.0209i	−0.305694	−	0.443299i
$512$	−30.0523			−1.32814
$513$		0			0
$514$	−9.54914	+	16.5396i	−0.421194	+	0.729530i
$515$	0.422294	+	2.39495i	0.0186085	+	0.105534i
$516$		0			0
$517$	−4.21388	+	23.8981i	−0.185326	+	1.05104i
$518$	3.88883	+	14.9405i	0.170865	+	0.656447i
$519$		0			0
$520$	−3.62157	+	3.03886i	−0.158816	+	0.133263i
$521$	27.4421			1.20226			0.601130	−	0.799151i	$-0.294717\pi$
$521$	27.4421			1.20226			0.601130	+	0.799151i	$0.294717\pi$
$522$		0			0
$523$	−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
$525$		0			0
$526$	11.1087	+	9.32129i	0.484362	+	0.406428i
$527$	−1.60643	+	9.11052i	−0.0699772	+	0.396860i
$528$		0			0
$529$	−13.8395	+	11.6127i	−0.601716	+	0.504899i
$530$	66.8281			2.90283
$531$		0			0
$532$	19.1578	+	13.6199i	0.830595	+	0.590498i
$533$	−0.167850	−	0.951925i	−0.00727040	−	0.0412325i
$534$		0			0
$535$	−7.29875	+	41.3932i	−0.315552	+	1.78959i
$536$	−4.07034	−	3.41542i	−0.175812	−	0.147524i
$537$		0			0
$538$	−25.6700	+	21.5396i	−1.10671	+	0.928640i
$539$	10.3133	+	29.6501i	0.444225	+	1.27712i
$540$		0			0
$541$	7.33572	+	12.7058i	0.315387	+	0.546267i	0.979520	−	0.201348i	$-0.0645323\pi$
$541$	7.33572	+	12.7058i	0.315387	+	0.546267i	−0.664133	+	0.747615i	$0.731199\pi$
$542$	0.278746	+	1.58085i	0.0119732	+	0.0679032i
$543$		0			0
$544$	−28.6609	+	10.4317i	−1.22883	+	0.447257i
$545$	−15.4631	+	5.62812i	−0.662368	+	0.241082i
$546$		0			0
$547$	−0.350819	−	1.98960i	−0.0150000	−	0.0850690i	0.976389	−	0.216021i	$-0.0693078\pi$
$547$	−0.350819	−	1.98960i	−0.0150000	−	0.0850690i	−0.991389	+	0.130952i	$0.958197\pi$
$548$	−16.7869	+	29.0757i	−0.717100	+	1.24205i
$549$		0			0
$550$	27.2902	+	47.2680i	1.16366	+	2.01552i
$551$	3.68546	+	20.9013i	0.157006	+	0.890424i
$552$		0			0
$553$	0.826460	+	3.17517i	0.0351447	+	0.135022i
$554$	−17.1524	−	14.3926i	−0.728736	−	0.611482i
$555$		0			0
$556$	22.7334	−	19.0756i	0.964110	−	0.808984i
$557$	−6.42943	−	11.1361i	−0.272424	−	0.471852i	0.697058	−	0.717015i	$-0.254492\pi$
$557$	−6.42943	−	11.1361i	−0.272424	−	0.471852i	−0.969482	+	0.245163i	$0.921159\pi$
$558$		0			0
$559$	16.9646	+	29.3836i	0.717526	+	1.24279i
$560$	38.7881	−	3.11379i	1.63910	−	0.131582i
$561$		0			0
$562$	36.3751	+	30.5223i	1.53439	+	1.28751i
$563$	−1.92912	−	1.61873i	−0.0813029	−	0.0682212i	0.601230	−	0.799076i	$-0.294677\pi$
$563$	−1.92912	−	1.61873i	−0.0813029	−	0.0682212i	−0.682533	+	0.730854i	$0.739122\pi$
$564$		0			0
$565$	−15.6410	−	5.69284i	−0.658020	−	0.239500i
$566$	−1.16576			−0.0490007
$567$		0			0
$568$	2.32410			0.0975169
$569$	33.3079	+	12.1231i	1.39634	+	0.508225i	0.927089	−	0.374841i	$-0.122303\pi$
$569$	33.3079	+	12.1231i	1.39634	+	0.508225i	0.469249	+	0.883066i	$0.344525\pi$
$570$		0			0
$571$	−1.00671	−	0.844734i	−0.0421297	−	0.0353510i	0.621480	−	0.783430i	$-0.286532\pi$
$571$	−1.00671	−	0.844734i	−0.0421297	−	0.0353510i	−0.663609	+	0.748079i	$0.730976\pi$
$572$	20.6525	+	17.3295i	0.863525	+	0.724583i
$573$		0			0
$574$	−0.633899	+	1.33437i	−0.0264584	+	0.0556954i
$575$	6.94772	+	12.0338i	0.289740	+	0.501844i
$576$		0			0
$577$	3.16099	+	5.47499i	0.131594	+	0.227927i	0.924291	−	0.381688i	$-0.124657\pi$
$577$	3.16099	+	5.47499i	0.131594	+	0.227927i	−0.792697	+	0.609615i	$0.791324\pi$
$578$	1.90335	−	1.59710i	0.0791688	−	0.0664305i
$579$		0			0
$580$	−19.5607	−	16.4134i	−0.812213	−	0.681527i
$581$	−29.0360	−	8.00348i	−1.20462	−	0.332040i
$582$		0			0
$583$	7.97337	+	45.2192i	0.330223	+	1.87279i
$584$	−0.962480	−	1.66706i	−0.0398277	−	0.0689836i
$585$		0			0
$586$	−8.00522	+	13.8655i	−0.330693	+	0.572777i
$587$	−1.97608	−	11.2069i	−0.0815614	−	0.462558i	−0.998046	−	0.0624873i	$-0.980097\pi$
$587$	−1.97608	−	11.2069i	−0.0815614	−	0.462558i	0.916484	−	0.400071i	$-0.131014\pi$
$588$		0			0
$589$	10.9122	−	3.97173i	0.449631	−	0.163652i
$590$	20.5019	−	7.46206i	0.844048	−	0.307208i
$591$		0			0
$592$	2.28322	+	12.9488i	0.0938400	+	0.532193i
$593$	22.5967	+	39.1386i	0.927935	+	1.60723i	0.786772	+	0.617243i	$0.211751\pi$
$593$	22.5967	+	39.1386i	0.927935	+	1.60723i	0.141162	+	0.989986i	$0.454916\pi$
$594$		0			0
$595$	32.0048	−	14.6460i	1.31207	−	0.600425i
$596$	−1.25399	+	1.05222i	−0.0513653	+	0.0431006i
$597$		0			0
$598$	11.1492	+	9.35529i	0.455925	+	0.382566i
$599$	−2.60661	+	14.7828i	−0.106503	+	0.604009i	0.884106	+	0.467286i	$0.154768\pi$
$599$	−2.60661	+	14.7828i	−0.106503	+	0.604009i	−0.990609	+	0.136723i	$0.956343\pi$
$600$		0			0
$601$	8.02293	+	45.5003i	0.327262	+	1.85600i	0.493276	+	0.869873i	$0.335799\pi$
$601$	8.02293	+	45.5003i	0.327262	+	1.85600i	−0.166014	+	0.986123i	$0.553090\pi$
$602$	4.88922	−	51.6234i	0.199270	−	2.10401i
$603$		0			0
$604$	−18.2151			−0.741163
$605$	−23.4185	+	19.6505i	−0.952098	+	0.798905i
$606$		0			0
$607$	−6.31688	+	35.8248i	−0.256394	+	1.45408i	0.536074	+	0.844171i	$0.319907\pi$
$607$	−6.31688	+	35.8248i	−0.256394	+	1.45408i	−0.792468	+	0.609913i	$0.791204\pi$
$608$	29.3288	+	24.6098i	1.18944	+	0.998060i
$609$		0			0
$610$	−63.5542	−	23.1318i	−2.57323	−	0.936581i
$611$	−18.2242			−0.737274
$612$		0			0
$613$	−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
$615$		0			0
$616$	1.25051	+	4.80432i	0.0503844	+	0.193572i
$617$	−8.46705	+	48.0190i	−0.340871	+	1.93317i	0.0181293	+	0.999836i	$0.494229\pi$
$617$	−8.46705	+	48.0190i	−0.340871	+	1.93317i	−0.359000	+	0.933338i	$0.616882\pi$
$618$		0			0
$619$	1.46954	+	8.33416i	0.0590657	+	0.334978i	0.999993	−	0.00362926i	$-0.00115523\pi$
$619$	1.46954	+	8.33416i	0.0590657	+	0.334978i	−0.940928	+	0.338608i	$0.890044\pi$
$620$	−6.98564	+	12.0995i	−0.280550	+	0.485927i
$621$		0			0
$622$	−48.4813			−1.94392
$623$	−32.3387	+	2.59605i	−1.29562	+	0.104009i
$624$		0			0
$625$	16.1105	−	5.86374i	0.644419	−	0.234549i
$626$	7.96454	−	45.1691i	0.318327	−	1.80532i
$627$		0			0
$628$	−5.72416	+	4.80314i	−0.228419	+	0.191666i
$629$	5.94644	+	10.2995i	0.237100	+	0.410669i
$630$		0			0
$631$	17.6216	−	30.5215i	0.701505	−	1.21504i	−0.266433	−	0.963853i	$-0.585845\pi$
$631$	17.6216	−	30.5215i	0.701505	−	1.21504i	0.967938	−	0.251189i	$-0.0808216\pi$
$632$	0.0900975	+	0.510968i	0.00358388	+	0.0203252i
$633$		0			0
$634$	27.7221	−	10.0900i	1.10098	−	0.400726i
$635$	−1.04718	+	5.93885i	−0.0415561	+	0.235676i
$636$		0			0
$637$	−20.5839	+	11.4942i	−0.815563	+	0.455418i
$638$	18.6015	−	32.2187i	0.736439	−	1.27555i
$639$		0			0
$640$	11.1647			0.441325
$641$	5.44735	+	1.98267i	0.215157	+	0.0783109i	0.447350	−	0.894359i	$-0.352368\pi$
$641$	5.44735	+	1.98267i	0.215157	+	0.0783109i	−0.232193	+	0.972670i	$0.574590\pi$
$642$		0			0
$643$	4.93946	−	1.79782i	0.194793	−	0.0708990i	−0.242781	−	0.970081i	$-0.578060\pi$
$643$	4.93946	−	1.79782i	0.194793	−	0.0708990i	0.437575	+	0.899182i	$0.355838\pi$
$644$	−2.64232	−	10.1515i	−0.104122	−	0.400026i
$645$		0			0
$646$	36.0814	+	13.1326i	1.41960	+	0.516694i
$647$	9.29941	−	16.1071i	0.365598	−	0.633234i	−0.623274	−	0.782003i	$-0.714198\pi$
$647$	9.29941	−	16.1071i	0.365598	−	0.633234i	0.988872	+	0.148770i	$0.0475313\pi$
$648$		0			0
$649$	7.49531	+	12.9823i	0.294217	+	0.509598i
$650$	−31.3999	+	26.3477i	−1.23161	+	1.03344i
$651$		0			0
$652$	−3.10734	+	17.6226i	−0.121693	+	0.690154i
$653$	−15.0822	−	12.6554i	−0.590210	−	0.495245i	0.298072	−	0.954543i	$-0.403657\pi$
$653$	−15.0822	−	12.6554i	−0.590210	−	0.495245i	−0.888282	+	0.459298i	$0.848101\pi$
$654$		0			0
$655$	28.1427	+	10.2431i	1.09963	+	0.400232i
$656$	−0.629090	+	1.08962i	−0.0245618	+	0.0425423i
$657$		0			0
$658$	22.7003	+	16.1384i	0.884950	+	0.629141i
$659$	−39.3495	−	14.3220i	−1.53284	−	0.557907i	−0.568523	−	0.822667i	$-0.692485\pi$
$659$	−39.3495	−	14.3220i	−1.53284	−	0.557907i	−0.964314	+	0.264760i	$0.914707\pi$
$660$		0			0
$661$	34.5295	−	12.5677i	1.34304	−	0.488828i	0.432273	−	0.901743i	$-0.357712\pi$
$661$	34.5295	−	12.5677i	1.34304	−	0.488828i	0.910770	+	0.412915i	$0.135489\pi$
$662$	−29.8306	+	10.8575i	−1.15940	+	0.421987i
$663$		0			0
$664$	−4.47574	−	1.62904i	−0.173692	−	0.0632189i
$665$	−36.0088	−	25.5999i	−1.39636	−	0.992720i
$666$		0			0
$667$	4.73569	−	8.20245i	0.183366	−	0.317600i
$668$	25.5942	+	9.31553i	0.990270	+	0.360429i
$669$		0			0
$670$	−63.4978	−	53.2809i	−2.45313	−	2.05842i
$671$	8.06939	−	45.7638i	0.311515	−	1.76669i
$672$		0			0
$673$	−17.1674	+	14.4052i	−0.661756	+	0.555280i	−0.910613	−	0.413261i	$-0.864390\pi$
$673$	−17.1674	+	14.4052i	−0.661756	+	0.555280i	0.248856	+	0.968540i	$0.419945\pi$
$674$	0.101452	+	0.175720i	0.00390778	+	0.00676847i
$675$		0			0
$676$	1.47871	−	2.56120i	0.0568733	−	0.0985075i
$677$	−15.7042	−	5.71587i	−0.603563	−	0.219679i	0.0221216	−	0.999755i	$-0.492958\pi$
$677$	−15.7042	−	5.71587i	−0.603563	−	0.219679i	−0.625684	+	0.780076i	$0.715180\pi$
$678$		0			0
$679$	−7.35909	−	28.2728i	−0.282416	−	1.08501i
$680$	5.23032	−	1.90368i	0.200573	−	0.0730028i
$681$		0			0
$682$	−19.1280	−	6.96202i	−0.732449	−	0.266590i
$683$	23.5592			0.901467			0.450734	−	0.892659i	$-0.351162\pi$
$683$	23.5592			0.901467			0.450734	+	0.892659i	$0.351162\pi$
$684$		0			0
$685$	31.5525	−	54.6505i	1.20556	−	2.08809i
$686$	35.8182	+	3.91067i	1.36754	+	0.149310i
$687$		0			0
$688$	7.66894	−	43.4927i	0.292375	−	1.65814i
$689$	−32.4037	+	11.7940i	−1.23448	+	0.449315i
$690$		0			0
$691$	−0.188059	−	1.06653i	−0.00715409	−	0.0405729i	0.981022	−	0.193898i	$-0.0621130\pi$
$691$	−0.188059	−	1.06653i	−0.00715409	−	0.0405729i	−0.988176	+	0.153325i	$0.951002\pi$
$692$	−8.39328	+	14.5376i	−0.319065	+	0.552636i
$693$		0			0
$694$	−24.2680	−	42.0334i	−0.921200	−	1.59557i
$695$	−42.7295	+	35.8543i	−1.62082	+	1.36003i
$696$		0			0
$697$	−0.197616	+	1.12073i	−0.00748522	+	0.0424508i
$698$	53.1215	−	19.3347i	2.01068	−	0.731828i
$699$		0			0
$700$	29.4480	−	2.36400i	1.11303	−	0.0893507i
$701$	−39.4989			−1.49185			−0.745927	−	0.666028i	$-0.767993\pi$
$701$	−39.4989			−1.49185			−0.745927	+	0.666028i	$0.767993\pi$
$702$		0			0
$703$	7.46437	−	12.9287i	0.281524	−	0.487614i
$704$	−4.82590	−	27.3690i	−0.181883	−	1.03151i
$705$		0			0
$706$	−1.48310	+	8.41107i	−0.0558172	+	0.316555i
$707$	−0.569309	−	2.18722i	−0.0214111	−	0.0822590i
$708$		0			0
$709$	−36.5821	+	30.6960i	−1.37387	+	1.15281i	−0.402452	+	0.915441i	$0.631842\pi$
$709$	−36.5821	+	30.6960i	−1.37387	+	1.15281i	−0.971419	+	0.237373i	$0.923714\pi$
$710$	36.2561			1.36067
$711$		0			0
$712$	−5.13048			−0.192273
$713$	−4.86973	−	1.77244i	−0.182373	−	0.0663783i
$714$		0			0
$715$	−38.8183	−	32.5724i	−1.45172	−	1.21814i
$716$	−0.890694	+	5.05138i	−0.0332868	+	0.188779i
$717$		0			0
$718$	10.0372	−	8.42222i	0.374585	−	0.314314i
$719$	−0.749777			−0.0279620			−0.0139810	−	0.999902i	$-0.504450\pi$
$719$	−0.749777			−0.0279620			−0.0139810	+	0.999902i	$0.504450\pi$
$720$		0			0
$721$	−0.180826	+	1.90927i	−0.00673432	+	0.0711050i
$722$	−1.95079	−	11.0635i	−0.0726011	−	0.411741i
$723$		0			0
$724$	1.41022	−	7.99776i	0.0524104	−	0.297234i
$725$	20.4339	+	17.1461i	0.758897	+	0.636790i
$726$		0			0
$727$	33.4171	−	28.0403i	1.23937	−	1.03996i	0.241798	−	0.970327i	$-0.422263\pi$
$727$	33.4171	−	28.0403i	1.23937	−	1.03996i	0.997573	−	0.0696290i	$-0.0221815\pi$
$728$	−3.39014	+	1.55139i	−0.125647	+	0.0574982i
$729$		0			0
$730$	−15.0148	−	26.0064i	−0.555722	−	0.962539i
$731$	−6.93655	−	39.3391i	−0.256558	−	1.45501i
$732$		0			0
$733$	20.6475	−	7.51509i	0.762634	−	0.277576i	0.0687222	−	0.997636i	$-0.478108\pi$
$733$	20.6475	−	7.51509i	0.762634	−	0.277576i	0.693912	+	0.720060i	$0.255886\pi$
$734$	15.1624	−	5.51867i	0.559655	−	0.203698i
$735$		0			0
$736$	−2.96690	−	16.8261i	−0.109361	−	0.620219i
$737$	28.4765	−	49.3227i	1.04895	−	1.81683i
$738$		0			0
$739$	−20.0557	−	34.7375i	−0.737761	−	1.27784i	−0.953501	−	0.301389i	$-0.902550\pi$
$739$	−20.0557	−	34.7375i	−0.737761	−	1.27784i	0.215740	−	0.976451i	$-0.430784\pi$
$740$	3.11890	+	17.6882i	0.114653	+	0.650230i
$741$		0			0
$742$	50.8066	+	14.0043i	1.86517	+	0.514114i
$743$	6.31887	+	5.30216i	0.231817	+	0.194518i	0.751295	−	0.659966i	$-0.229429\pi$
$743$	6.31887	+	5.30216i	0.231817	+	0.194518i	−0.519479	+	0.854484i	$0.673874\pi$
$744$		0			0
$745$	2.35698	−	1.97774i	0.0863531	−	0.0724588i
$746$	11.3861	+	19.7212i	0.416873	+	0.722046i
$747$		0			0
$748$	−15.8704	−	27.4884i	−0.580280	−	1.00507i
$749$	−14.2232	+	29.9400i	−0.519703	+	1.09398i
$750$		0			0
$751$	−18.8433	−	15.8114i	−0.687600	−	0.576965i	0.230616	−	0.973045i	$-0.425926\pi$
$751$	−18.8433	−	15.8114i	−0.687600	−	0.576965i	−0.918216	+	0.396080i	$0.870370\pi$
$752$	18.1717	+	15.2478i	0.662652	+	0.556031i
$753$		0			0
$754$	26.2543	+	9.55579i	0.956126	+	0.348002i
$755$	34.2370			1.24601
$756$		0			0
$757$	−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
$759$		0			0
$760$	−5.35220	−	4.49103i	−0.194145	−	0.162907i
$761$	10.5292	+	8.83505i	0.381683	+	0.320270i	0.813363	−	0.581757i	$-0.197634\pi$
$761$	10.5292	+	8.83505i	0.381683	+	0.320270i	−0.431680	+	0.902027i	$0.642079\pi$
$762$		0			0
$763$	−12.9354	+	1.03841i	−0.468292	+	0.0375930i
$764$	−15.8203	−	27.4015i	−0.572358	−	0.991353i
$765$		0			0
$766$	−16.2759	−	28.1907i	−0.588073	−	1.01857i
$767$	−8.62405	+	7.23644i	−0.311396	+	0.261293i
$768$		0			0
$769$	11.6423	+	9.76902i	0.419831	+	0.352280i	0.828099	−	0.560582i	$-0.189423\pi$
$769$	11.6423	+	9.76902i	0.419831	+	0.352280i	−0.408268	+	0.912862i	$0.633867\pi$
$770$	19.5081	+	74.9479i	0.703022	+	2.70093i
$771$		0			0
$772$	6.10337	+	34.6139i	0.219665	+	1.24578i
$773$	19.0197	+	32.9431i	0.684091	+	1.18488i	0.973722	+	0.227741i	$0.0731341\pi$
$773$	19.0197	+	32.9431i	0.684091	+	1.18488i	−0.289631	+	0.957138i	$0.593533\pi$
$774$		0			0
$775$	7.29750	−	12.6396i	0.262134	−	0.454030i
$776$	−0.802259	−	4.54984i	−0.0287994	−	0.163330i
$777$		0			0
$778$	−2.92748	+	1.06551i	−0.104955	+	0.0382005i
$779$	1.34237	−	0.488584i	0.0480955	−	0.0175053i
$780$		0			0
$781$	4.32577	+	24.5327i	0.154788	+	0.877849i
$782$	−8.56760	−	14.8395i	−0.306377	−	0.530660i
$783$		0			0
$784$	30.1415	+	5.76104i	1.07648	+	0.205751i
$785$	10.7591	−	9.02794i	0.384008	−	0.322221i
$786$		0			0
$787$	11.5764	+	9.71374i	0.412654	+	0.346258i	0.825360	−	0.564606i	$-0.190972\pi$
$787$	11.5764	+	9.71374i	0.412654	+	0.346258i	−0.412707	+	0.910864i	$0.635416\pi$
$788$	5.97366	−	33.8783i	0.212803	−	1.20686i
$789$		0			0
$790$	1.40553	+	7.97115i	0.0500065	+	0.283601i
$791$	−10.6982	−	7.60570i	−0.380383	−	0.270427i
$792$		0			0
$793$	34.8986			1.23929
$794$	−17.6476	+	14.8081i	−0.626289	+	0.525519i
$795$		0			0
$796$	−3.58468	+	20.3297i	−0.127056	+	0.720568i
$797$	0.774338	+	0.649747i	0.0274285	+	0.0230152i	0.656399	−	0.754414i	$-0.272079\pi$
$797$	0.774338	+	0.649747i	0.0274285	+	0.0230152i	−0.628970	+	0.777429i	$0.716523\pi$
$798$		0			0
$799$	20.1621	+	7.33839i	0.713282	+	0.259613i
$800$	48.1191			1.70127
$801$		0			0
$802$	0.304771			0.0107619
$803$	15.8058	−	13.2626i	0.557773	−	0.468027i
$804$		0			0
$805$	4.96649	+	19.0807i	0.175046	+	0.672507i
$806$	2.65456	−	15.0547i	0.0935027	−	0.530280i
$807$		0			0
$808$	−0.0620638	−	0.351981i	−0.00218340	−	0.0123827i
$809$	−1.37661	+	2.38435i	−0.0483989	+	0.0838293i	−0.889210	−	0.457499i	$-0.848745\pi$
$809$	−1.37661	+	2.38435i	−0.0483989	+	0.0838293i	0.840811	+	0.541329i	$0.182079\pi$
$810$		0			0
$811$	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
$813$		0			0
$814$	−24.5904	+	8.95016i	−0.861892	+	0.313703i
$815$	5.84053	−	33.1233i	0.204585	−	1.16026i
$816$		0			0
$817$	−38.4117	+	32.2312i	−1.34385	+	1.12763i
$818$	−26.1428	−	45.2807i	−0.914062	−	1.58320i
$819$		0			0
$820$	−0.859341	+	1.48842i	−0.0300095	+	0.0519780i
$821$	−3.24294	−	18.3916i	−0.113180	−	0.641873i	−0.987635	−	0.156768i	$-0.949892\pi$
$821$	−3.24294	−	18.3916i	−0.113180	−	0.641873i	0.874456	−	0.485105i	$-0.161219\pi$
$822$		0			0
$823$	−17.3503	+	6.31498i	−0.604792	+	0.220126i	−0.626223	−	0.779644i	$-0.715400\pi$
$823$	−17.3503	+	6.31498i	−0.604792	+	0.220126i	0.0214308	+	0.999770i	$0.493178\pi$
$824$	−0.0526644	+	0.298675i	−0.00183465	+	0.0104048i
$825$		0			0
$826$	17.1504	−	1.37678i	0.596739	−	0.0479044i
$827$	9.06140	−	15.6948i	0.315096	−	0.545762i	−0.664362	−	0.747411i	$-0.731297\pi$
$827$	9.06140	−	15.6948i	0.315096	−	0.545762i	0.979458	+	0.201649i	$0.0646300\pi$
$828$		0			0
$829$	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
$831$		0			0
$832$	19.6124	−	7.13834i	0.679939	−	0.247477i
$833$	27.4010	−	4.42787i	0.949388	−	0.153417i
$834$		0			0
$835$	−48.1067	−	17.5094i	−1.66480	−	0.605938i
$836$	−19.9216	+	34.5052i	−0.689003	+	1.19339i
$837$		0			0
$838$	23.4349	+	40.5904i	0.809545	+	1.40217i
$839$	24.2173	−	20.3207i	0.836073	−	0.701548i	−0.120604	−	0.992701i	$-0.538483\pi$
$839$	24.2173	−	20.3207i	0.836073	−	0.701548i	0.956677	+	0.291153i	$0.0940387\pi$
$840$		0			0
$841$	−1.87855	+	10.6538i	−0.0647776	+	0.367372i
$842$	−5.50929	−	4.62285i	−0.189863	−	0.159314i
$843$		0			0
$844$	−37.1807	−	13.5327i	−1.27981	−	0.465814i
$845$	−2.77936	+	4.81400i	−0.0956130	+	0.165607i
$846$		0			0
$847$	−21.9220	+	10.0319i	−0.753248	+	0.344700i
$848$	42.1780	+	15.3515i	1.44840	+	0.527174i
$849$		0			0
$850$	45.3482	−	16.5054i	1.55543	−	0.566130i
$851$	−6.26037	+	2.27859i	−0.214603	+	0.0781091i
$852$		0			0
$853$	−18.4639	−	6.72031i	−0.632192	−	0.230099i	0.00599331	−	0.999982i	$-0.498092\pi$
$853$	−18.4639	−	6.72031i	−0.632192	−	0.230099i	−0.638185	+	0.769883i	$0.720314\pi$
$854$	−43.4701	−	30.9044i	−1.48752	−	1.05753i
$855$		0			0
$856$	−2.62090	+	4.53953i	−0.0895804	+	0.155158i
$857$	1.46475	+	0.533127i	0.0500350	+	0.0182113i	0.366916	−	0.930254i	$-0.380413\pi$
$857$	1.46475	+	0.533127i	0.0500350	+	0.0182113i	−0.316881	+	0.948465i	$0.602636\pi$
$858$		0			0
$859$	−37.6422	−	31.5856i	−1.28434	−	1.07769i	−0.992631	−	0.121178i	$-0.961333\pi$
$859$	−37.6422	−	31.5856i	−1.28434	−	1.07769i	−0.291706	−	0.956508i	$-0.594223\pi$
$860$	10.4758	−	59.4113i	0.357223	−	2.02591i
$861$		0			0
$862$	−3.51721	+	2.95129i	−0.119797	+	0.100521i
$863$	−4.07047	−	7.05026i	−0.138560	−	0.239994i	0.788391	−	0.615174i	$-0.210914\pi$
$863$	−4.07047	−	7.05026i	−0.138560	−	0.239994i	−0.926952	+	0.375180i	$0.877581\pi$
$864$		0			0
$865$	15.7759	−	27.3247i	0.536398	−	0.929069i
$866$	28.4527	+	10.3559i	0.966862	+	0.351909i
$867$		0			0
$868$	−7.84641	+	7.73483i	−0.266325	+	0.262537i
$869$	−5.22598	+	1.90210i	−0.177279	+	0.0645243i
$870$		0			0
$871$	40.1921	+	14.6287i	1.36186	+	0.495675i
$872$	−2.05217			−0.0694954
$873$		0			0
$874$	−10.7546	+	18.6276i	−0.363781	+	0.630087i
$875$	−11.1107	+	0.891932i	−0.375610	+	0.0301528i
$876$		0			0
$877$	7.86491	−	44.6041i	0.265579	−	1.50617i	−0.501802	−	0.864983i	$-0.667329\pi$
$877$	7.86491	−	44.6041i	0.265579	−	1.50617i	0.767381	−	0.641192i	$-0.221560\pi$
$878$	72.0225	−	26.2140i	2.43064	−	0.884681i
$879$		0			0
$880$	11.4536	+	64.9568i	0.386102	+	2.18969i
$881$	−0.111855	+	0.193739i	−0.00376850	+	0.00652724i	−0.867904	−	0.496733i	$-0.834533\pi$
$881$	−0.111855	+	0.193739i	−0.00376850	+	0.00652724i	0.864135	+	0.503260i	$0.167866\pi$
$882$		0			0
$883$	28.2842	+	48.9896i	0.951838	+	1.64863i	0.741443	+	0.671016i	$0.234142\pi$
$883$	28.2842	+	48.9896i	0.951838	+	1.64863i	0.210396	+	0.977616i	$0.432525\pi$
$884$	18.2604	−	15.3223i	0.614163	−	0.515344i
$885$		0			0
$886$	−1.05161	+	5.96400i	−0.0353297	+	0.200365i
$887$	−1.02508	+	0.373100i	−0.0344190	+	0.0125275i	−0.359172	−	0.933271i	$-0.616941\pi$
$887$	−1.02508	+	0.373100i	−0.0344190	+	0.0125275i	0.324753	+	0.945799i	$0.394719\pi$
$888$		0			0
$889$	−2.04065	+	4.29561i	−0.0684413	+	0.144070i
$890$	−80.0360			−2.68281
$891$		0			0
$892$	15.8947	−	27.5304i	0.532194	−	0.921787i
$893$	−4.67687	−	26.5239i	−0.156506	−	0.887587i
$894$		0			0
$895$	1.67414	−	9.49452i	0.0559603	−	0.317367i
$896$	8.48806	+	2.33965i	0.283566	+	0.0781621i
$897$		0			0
$898$	22.2226	−	18.6469i	0.741576	−	0.622256i
$899$	−9.94821			−0.331791
$900$		0			0
$901$	40.5984			1.35253
$902$	−2.35304	−	0.856436i	−0.0783476	−	0.0285162i
$903$		0			0
$904$	−1.59013	−	1.33428i	−0.0528871	−	0.0443775i
$905$	−2.65064	+	15.0325i	−0.0881102	+	0.499698i
$906$		0			0
$907$	31.6864	−	26.5880i	1.05213	−	0.882841i	0.0588135	−	0.998269i	$-0.481268\pi$
$907$	31.6864	−	26.5880i	1.05213	−	0.882841i	0.993316	+	0.115428i	$0.0368238\pi$
$908$	−5.72629			−0.190034
$909$		0			0
$910$	−52.8865	+	24.2018i	−1.75317	+	0.802282i
$911$	6.65639	+	37.7502i	0.220536	+	1.25072i	0.871037	+	0.491217i	$0.163448\pi$
$911$	6.65639	+	37.7502i	0.220536	+	1.25072i	−0.650502	+	0.759505i	$0.725441\pi$
$912$		0			0
$913$	8.86521	−	50.2771i	0.293395	−	1.66393i
$914$	41.2383	+	34.6030i	1.36404	+	1.14457i
$915$		0			0
$916$	−5.52977	+	4.64003i	−0.182709	+	0.153311i
$917$	19.2492	+	13.6849i	0.635665	+	0.451916i
$918$		0			0
$919$	−2.47835	−	4.29263i	−0.0817533	−	0.141601i	0.822250	−	0.569127i	$-0.192719\pi$
$919$	−2.47835	−	4.29263i	−0.0817533	−	0.141601i	−0.904003	+	0.427526i	$0.859385\pi$
$920$	0.541427	+	3.07059i	0.0178503	+	0.101234i
$921$		0			0
$922$	64.3562	−	23.4237i	2.11946	−	0.771420i
$923$	−17.5799	+	6.39857i	−0.578651	+	0.210612i
$924$		0			0
$925$	−3.25814	−	18.4778i	−0.107127	−	0.607547i
$926$	−20.4268	+	35.3803i	−0.671267	+	1.16267i
$927$		0			0
$928$	−16.3994	−	28.4046i	−0.538336	−	0.932426i
$929$	−4.28226	−	24.2859i	−0.140496	−	0.796795i	−0.970873	−	0.239593i	$-0.922986\pi$
$929$	−4.28226	−	24.2859i	−0.140496	−	0.796795i	0.830377	−	0.557202i	$-0.188125\pi$
$930$		0			0
$931$	−22.0113	−	27.0084i	−0.721391	−	0.885163i
$932$	20.9850	+	17.6085i	0.687387	+	0.576786i
$933$		0			0
$934$	−54.0048	+	45.3154i	−1.76709	+	1.48277i
$935$	29.8299	+	51.6669i	0.975542	+	1.68969i
$936$		0			0
$937$	−20.2545	−	35.0818i	−0.661684	−	1.14607i	−0.980173	−	0.198144i	$-0.936509\pi$
$937$	−20.2545	−	35.0818i	−0.661684	−	1.14607i	0.318488	−	0.947927i	$-0.396825\pi$
$938$	−37.1092	−	53.8136i	−1.21166	−	1.75708i
$939$		0			0
$940$	24.8226	+	20.8287i	0.809625	+	0.679356i
$941$	18.0273	+	15.1267i	0.587675	+	0.493118i	0.887457	−	0.460890i	$-0.152470\pi$
$941$	18.0273	+	15.1267i	0.587675	+	0.493118i	−0.299783	+	0.954008i	$0.596914\pi$
$942$		0			0
$943$	−0.599052	−	0.218037i	−0.0195078	−	0.00710026i
$944$	14.6537			0.476938
$945$		0			0
$946$	87.8953			2.85772
$947$	26.0978	+	9.49881i	0.848063	+	0.308670i	0.729250	−	0.684247i	$-0.239869\pi$
$947$	26.0978	+	9.49881i	0.848063	+	0.308670i	0.118813	+	0.992917i	$0.462091\pi$
$948$		0			0
$949$	11.8701	+	9.96017i	0.385319	+	0.323321i
$950$	−46.4050	−	38.9384i	−1.50558	−	1.26333i
$951$		0			0
$952$	4.37531	−	0.351237i	0.141805	−	0.0113836i
$953$	21.0460	+	36.4528i	0.681748	+	1.18082i	0.974447	+	0.224617i	$0.0721131\pi$
$953$	21.0460	+	36.4528i	0.681748	+	1.18082i	−0.292699	+	0.956204i	$0.594554\pi$
$954$		0			0
$955$	29.7357	+	51.5037i	0.962224	+	1.66662i
$956$	2.06603	−	1.73360i	0.0668202	−	0.0560688i
$957$		0			0
$958$	−48.5975	−	40.7781i	−1.57011	−	1.31748i
$959$	35.4404	−	34.9364i	1.14443	−	1.12815i
$960$		0			0
$961$	−4.43790	−	25.1686i	−0.143158	−	0.811889i
$962$	−9.82623	−	17.0195i	−0.316810	−	0.548731i
$963$		0			0
$964$	−17.1280	+	29.6666i	−0.551657	+	0.955498i
$965$	−11.4718	−	65.0601i	−0.369292	−	2.09436i
$966$		0			0
$967$	45.8194	−	16.6769i	1.47345	−	0.536293i	0.524417	−	0.851461i	$-0.324283\pi$
$967$	45.8194	−	16.6769i	1.47345	−	0.536293i	0.949036	+	0.315168i	$0.102061\pi$
$968$	−3.58256	+	1.30394i	−0.115148	+	0.0419104i
$969$		0			0
$970$	−12.5153	−	70.9779i	−0.401843	−	2.27896i
$971$	1.76073	+	3.04968i	0.0565045	+	0.0978687i	0.892894	−	0.450267i	$-0.148671\pi$
$971$	1.76073	+	3.04968i	0.0565045	+	0.0978687i	−0.836390	+	0.548136i	$0.815338\pi$
$972$		0			0
$973$	−39.9989	+	18.3042i	−1.28231	+	0.586806i
$974$	−46.2017	+	38.7678i	−1.48040	+	1.24220i
$975$		0			0
$976$	−34.7979	−	29.1989i	−1.11385	−	0.934635i
$977$	−0.611671	+	3.46896i	−0.0195691	+	0.110982i	−0.993028	−	0.117881i	$-0.962390\pi$
$977$	−0.611671	+	3.46896i	−0.0195691	+	0.110982i	0.973459	+	0.228863i	$0.0735009\pi$
$978$		0			0
$979$	−9.54922	−	54.1563i	−0.305194	−	1.73084i
$980$	41.1735	+	7.86962i	1.31524	+	0.251386i
$981$		0			0
$982$	−81.0859			−2.58756
$983$	19.7672	−	16.5867i	0.630476	−	0.529032i	−0.270601	−	0.962692i	$-0.587222\pi$
$983$	19.7672	−	16.5867i	0.630476	−	0.529032i	0.901077	+	0.433659i	$0.142778\pi$
$984$		0			0
$985$	−11.2280	+	63.6774i	−0.357755	+	2.02893i
$986$	−25.1981	−	21.1438i	−0.802472	−	0.673354i
$987$		0			0
$988$	−28.1176	−	10.2340i	−0.894540	−	0.325586i
$989$	22.3770			0.711546
$990$		0			0
$991$	−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
$993$		0			0
$994$	27.5640	+	7.59772i	0.874276	+	0.240985i
$995$	6.73773	−	38.2116i	0.213600	−	1.21139i
$996$		0			0
$997$	−0.0841224	−	0.477082i	−0.00266418	−	0.0151093i	0.983447	−	0.181198i	$-0.0579974\pi$
$997$	−0.0841224	−	0.477082i	−0.00266418	−	0.0151093i	−0.986111	+	0.166088i	$0.946886\pi$
$998$	17.3327	−	30.0211i	0.548656	−	0.950300i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.u.a.361.18		132
3.2	odd	2		189.2.u.a.130.5	yes	132
7.2	even	3		567.2.w.a.37.5		132
21.2	odd	6		189.2.w.a.184.18	yes	132
27.11	odd	18		189.2.w.a.151.18	yes	132
27.16	even	9		567.2.w.a.46.5		132
189.16	even	9	inner	567.2.u.a.289.18		132
189.65	odd	18		189.2.u.a.16.5	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.16.5	✓	132	189.65	odd	18
189.2.u.a.130.5	yes	132	3.2	odd	2
189.2.w.a.151.18	yes	132	27.11	odd	18
189.2.w.a.184.18	yes	132	21.2	odd	6
567.2.u.a.289.18		132	189.16	even	9	inner
567.2.u.a.361.18		132	1.1	even	1	trivial
567.2.w.a.37.5		132	7.2	even	3
567.2.w.a.46.5		132	27.16	even	9

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.82816 + 0.665398i) q^{2} +(1.36734 + 1.14734i) q^{4} +(-2.57005 - 2.15653i) q^{5} +(-1.50198 - 2.17808i) q^{7} +(-0.209199 - 0.362343i) q^{8} +O(q^{10})\)	\(q+(1.82816 + 0.665398i) q^{2} +(1.36734 + 1.14734i) q^{4} +(-2.57005 - 2.15653i) q^{5} +(-1.50198 - 2.17808i) q^{7} +(-0.209199 - 0.362343i) q^{8} +(-3.26352 - 5.65259i) q^{10} +(3.43544 - 2.88268i) q^{11} +(2.58000 + 2.16488i) q^{13} +(-1.29658 - 4.98131i) q^{14} +(-0.761251 - 4.31727i) q^{16} +(-1.98260 - 3.43397i) q^{17} +(-2.48870 + 4.31055i) q^{19} +(-1.03987 - 5.89742i) q^{20} +(8.19868 - 2.98408i) q^{22} +(2.08727 - 0.759706i) q^{23} +(1.08630 + 6.16070i) q^{25} +(3.27617 + 5.67449i) q^{26} +(0.445273 - 4.70147i) q^{28} +(3.26643 - 2.74086i) q^{29} +(-1.78723 - 1.49966i) q^{31} +(1.33570 - 7.57513i) q^{32} +(-1.33957 - 7.59708i) q^{34} +(-0.836932 + 8.83684i) q^{35} -2.99931 q^{37} +(-7.41798 + 6.22442i) q^{38} +(-0.243751 + 1.38238i) q^{40} +(-0.219856 - 0.184481i) q^{41} +(9.46658 + 3.44555i) q^{43} +8.00483 q^{44} +4.32139 q^{46} +(-4.14512 + 3.47817i) q^{47} +(-2.48810 + 6.54288i) q^{49} +(-2.11338 + 11.9856i) q^{50} +(1.04390 + 5.92027i) q^{52} +(-5.11933 + 8.86693i) q^{53} -15.0458 q^{55} +(-0.475001 + 0.999885i) q^{56} +(7.79533 - 2.83727i) q^{58} +(-0.580445 + 3.29187i) q^{59} +(7.93772 - 6.66054i) q^{61} +(-2.26947 - 3.93084i) q^{62} +(3.09848 - 5.36673i) q^{64} +(-1.96211 - 11.1277i) q^{65} +(11.9337 - 4.34350i) q^{67} +(1.22902 - 6.97013i) q^{68} +(-7.41006 + 15.5983i) q^{70} +(-2.77738 + 4.81056i) q^{71} +4.60079 q^{73} +(-5.48323 - 1.99573i) q^{74} +(-8.34856 + 3.03863i) q^{76} +(-11.4387 - 3.15295i) q^{77} +(-1.16530 - 0.424136i) q^{79} +(-7.35385 + 12.7372i) q^{80} +(-0.279180 - 0.483554i) q^{82} +(8.72055 - 7.31741i) q^{83} +(-2.31006 + 13.1010i) q^{85} +(15.0138 + 12.5981i) q^{86} +(-1.76321 - 0.641755i) q^{88} +(6.13111 - 10.6194i) q^{89} +(0.840175 - 8.87108i) q^{91} +(3.72566 + 1.35603i) q^{92} +(-9.89232 + 3.60051i) q^{94} +(15.6919 - 5.71138i) q^{95} +(10.3763 + 3.77665i) q^{97} +(-8.90228 + 10.3059i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} + 3 q^{10} + 15 q^{11} - 12 q^{13} + 30 q^{14} + 9 q^{16} - 27 q^{17} + 3 q^{19} + 18 q^{20} - 12 q^{22} + 36 q^{23} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} + 75 q^{32} - 18 q^{34} - 15 q^{35} - 6 q^{37} - 69 q^{38} + 51 q^{40} - 12 q^{43} + 6 q^{44} - 6 q^{46} + 21 q^{47} - 42 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 111 q^{56} - 3 q^{58} - 27 q^{59} - 21 q^{61} - 75 q^{62} - 30 q^{64} + 90 q^{65} - 3 q^{67} + 30 q^{68} + 39 q^{70} + 18 q^{71} - 42 q^{73} - 51 q^{74} - 24 q^{76} - 15 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} + 93 q^{86} - 51 q^{88} - 75 q^{89} - 21 q^{91} + 66 q^{92} + 33 q^{94} - 15 q^{95} - 12 q^{97} + 36 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 + 3 * q^10 + 15 * q^11 - 12 * q^13 + 30 * q^14 + 9 * q^16 - 27 * q^17 + 3 * q^19 + 18 * q^20 - 12 * q^22 + 36 * q^23 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 + 75 * q^32 - 18 * q^34 - 15 * q^35 - 6 * q^37 - 69 * q^38 + 51 * q^40 - 12 * q^43 + 6 * q^44 - 6 * q^46 + 21 * q^47 - 42 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 111 * q^56 - 3 * q^58 - 27 * q^59 - 21 * q^61 - 75 * q^62 - 30 * q^64 + 90 * q^65 - 3 * q^67 + 30 * q^68 + 39 * q^70 + 18 * q^71 - 42 * q^73 - 51 * q^74 - 24 * q^76 - 15 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 + 93 * q^86 - 51 * q^88 - 75 * q^89 - 21 * q^91 + 66 * q^92 + 33 * q^94 - 15 * q^95 - 12 * q^97 + 36 * q^98

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