LMFDB - Embedded newform 567.2.u.a.478.13

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			478.13
Character	$\chi$	$=$	567.478
Dual form			567.2.u.a.172.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.372124 + 0.312249i) q^{2} +(-0.306320 - 1.73722i) q^{4} +(0.266880 + 1.51355i) q^{5} +(-2.38579 - 1.14369i) q^{7} +(0.914231 - 1.58349i) q^{8} +O(q^{10})$	\(q+(0.372124 + 0.312249i) q^{2} +(-0.306320 - 1.73722i) q^{4} +(0.266880 + 1.51355i) q^{5} +(-2.38579 - 1.14369i) q^{7} +(0.914231 - 1.58349i) q^{8} +(-0.373293 + 0.646562i) q^{10} +(0.379279 - 2.15100i) q^{11} +(-1.09206 - 6.19341i) q^{13} +(-0.530692 - 1.17055i) q^{14} +(-2.48063 + 0.902875i) q^{16} +(-2.64457 + 4.58053i) q^{17} +(-1.16718 - 2.02162i) q^{19} +(2.54763 - 0.927262i) q^{20} +(0.812787 - 0.682009i) q^{22} +(2.20637 - 1.85136i) q^{23} +(2.47885 - 0.902227i) q^{25} +(1.52750 - 2.64571i) q^{26} +(-1.25603 + 4.49498i) q^{28} +(1.64020 - 9.30205i) q^{29} +(0.463969 + 2.63130i) q^{31} +(-4.64141 - 1.68933i) q^{32} +(-2.41438 + 0.878761i) q^{34} +(1.09431 - 3.91624i) q^{35} +0.458521 q^{37} +(0.196913 - 1.11675i) q^{38} +(2.64069 + 0.961133i) q^{40} +(-0.513695 - 2.91331i) q^{41} +(-4.87748 - 4.09269i) q^{43} -3.85295 q^{44} +1.39913 q^{46} +(-1.15593 + 6.55559i) q^{47} +(4.38395 + 5.45720i) q^{49} +(1.20416 + 0.438277i) q^{50} +(-10.4248 + 3.79432i) q^{52} +(4.80829 + 8.32820i) q^{53} +3.35687 q^{55} +(-3.99219 + 2.73228i) q^{56} +(3.51491 - 2.94936i) q^{58} +(-9.19604 - 3.34708i) q^{59} +(0.973943 - 5.52351i) q^{61} +(-0.648966 + 1.12404i) q^{62} +(1.44015 + 2.49441i) q^{64} +(9.08259 - 3.30579i) q^{65} +(6.94417 - 5.82685i) q^{67} +(8.76750 + 3.19111i) q^{68} +(1.63006 - 1.11563i) q^{70} +(1.42313 + 2.46494i) q^{71} +5.46594 q^{73} +(0.170627 + 0.143173i) q^{74} +(-3.15448 + 2.64693i) q^{76} +(-3.36496 + 4.69805i) q^{77} +(-2.45123 - 2.05682i) q^{79} +(-2.02858 - 3.51360i) q^{80} +(0.718519 - 1.24451i) q^{82} +(0.920085 - 5.21806i) q^{83} +(-7.63866 - 2.78025i) q^{85} +(-0.537088 - 3.04598i) q^{86} +(-3.05935 - 2.56710i) q^{88} +(8.98709 + 15.5661i) q^{89} +(-4.47790 + 16.0251i) q^{91} +(-3.89209 - 3.26585i) q^{92} +(-2.47713 + 2.07856i) q^{94} +(2.74833 - 2.30613i) q^{95} +(10.6549 + 8.94050i) q^{97} +(-0.0726314 + 3.39964i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.372124	+	0.312249i	0.263131	+	0.220793i	0.764802	−	0.644265i	$-0.222837\pi$
$2$	0.372124	+	0.312249i	0.263131	+	0.220793i	−0.501671	+	0.865059i	$0.667281\pi$
$3$		0			0
$3$		0			0
$4$	−0.306320	−	1.73722i	−0.153160	−	0.868612i
$5$	0.266880	+	1.51355i	0.119352	+	0.676881i	0.984503	+	0.175369i	$0.0561118\pi$
$5$	0.266880	+	1.51355i	0.119352	+	0.676881i	−0.865150	+	0.501512i	$0.832777\pi$
$6$		0			0
$7$	−2.38579	−	1.14369i	−0.901742	−	0.432274i
$7$	−2.38579	−	1.14369i	−0.901742	−	0.432274i
$8$	0.914231	−	1.58349i	0.323229	−	0.559850i
$9$		0			0
$10$	−0.373293	+	0.646562i	−0.118046	+	0.204461i
$11$	0.379279	−	2.15100i	0.114357	−	0.648551i	−0.872709	−	0.488240i	$-0.837639\pi$
$11$	0.379279	−	2.15100i	0.114357	−	0.648551i	0.987067	−	0.160311i	$-0.0512498\pi$
$12$		0			0
$13$	−1.09206	−	6.19341i	−0.302884	−	1.71774i	−0.633300	−	0.773906i	$-0.718300\pi$
$13$	−1.09206	−	6.19341i	−0.302884	−	1.71774i	0.330416	−	0.943835i	$-0.392811\pi$
$14$	−0.530692	−	1.17055i	−0.141833	−	0.312844i
$15$		0			0
$16$	−2.48063	+	0.902875i	−0.620157	+	0.225719i
$17$	−2.64457	+	4.58053i	−0.641403	+	1.11094i	0.343717	+	0.939073i	$0.388314\pi$
$17$	−2.64457	+	4.58053i	−0.641403	+	1.11094i	−0.985120	+	0.171869i	$0.945019\pi$
$18$		0			0
$19$	−1.16718	−	2.02162i	−0.267771	−	0.463792i	0.700515	−	0.713637i	$-0.252954\pi$
$19$	−1.16718	−	2.02162i	−0.267771	−	0.463792i	−0.968286	+	0.249845i	$0.919620\pi$
$20$	2.54763	−	0.927262i	0.569667	−	0.207342i
$21$		0			0
$22$	0.812787	−	0.682009i	0.173287	−	0.145405i
$23$	2.20637	−	1.85136i	0.460060	−	0.386036i	−0.383093	−	0.923710i	$-0.625141\pi$
$23$	2.20637	−	1.85136i	0.460060	−	0.386036i	0.843153	+	0.537674i	$0.180697\pi$
$24$		0			0
$25$	2.47885	−	0.902227i	0.495769	−	0.180445i
$26$	1.52750	−	2.64571i	0.299568	−	0.518866i
$27$		0			0
$28$	−1.25603	+	4.49498i	−0.237368	+	0.849472i
$29$	1.64020	−	9.30205i	0.304578	−	1.72735i	−0.320907	−	0.947111i	$-0.603988\pi$
$29$	1.64020	−	9.30205i	0.304578	−	1.72735i	0.625485	−	0.780237i	$-0.284901\pi$
$30$		0			0
$31$	0.463969	+	2.63130i	0.0833313	+	0.472595i	0.997704	+	0.0677222i	$0.0215732\pi$
$31$	0.463969	+	2.63130i	0.0833313	+	0.472595i	−0.914373	+	0.404873i	$0.867316\pi$
$32$	−4.64141	−	1.68933i	−0.820493	−	0.298635i
$33$		0			0
$34$	−2.41438	+	0.878761i	−0.414062	+	0.150706i
$35$	1.09431	−	3.91624i	0.184973	−	0.661965i
$36$		0			0
$37$	0.458521			0.0753804			0.0376902	−	0.999289i	$-0.488000\pi$
$37$	0.458521			0.0753804			0.0376902	+	0.999289i	$0.488000\pi$
$38$	0.196913	−	1.11675i	0.0319434	−	0.181160i
$39$		0			0
$40$	2.64069	+	0.961133i	0.417530	+	0.151969i
$41$	−0.513695	−	2.91331i	−0.0802256	−	0.454982i	−0.998285	−	0.0585394i	$-0.981356\pi$
$41$	−0.513695	−	2.91331i	−0.0802256	−	0.454982i	0.918059	−	0.396443i	$-0.129755\pi$
$42$		0			0
$43$	−4.87748	−	4.09269i	−0.743809	−	0.624130i	0.190049	−	0.981775i	$-0.439135\pi$
$43$	−4.87748	−	4.09269i	−0.743809	−	0.624130i	−0.933858	+	0.357645i	$0.883580\pi$
$44$	−3.85295			−0.580854
$45$		0			0
$46$	1.39913			0.206290
$47$	−1.15593	+	6.55559i	−0.168609	+	0.956232i	0.776655	+	0.629926i	$0.216915\pi$
$47$	−1.15593	+	6.55559i	−0.168609	+	0.956232i	−0.945264	+	0.326305i	$0.894196\pi$
$48$		0			0
$49$	4.38395	+	5.45720i	0.626279	+	0.779599i
$50$	1.20416	+	0.438277i	0.170294	+	0.0619818i
$51$		0			0
$52$	−10.4248	+	3.79432i	−1.44566	+	0.526178i
$53$	4.80829	+	8.32820i	0.660469	+	1.14397i	0.980492	+	0.196557i	$0.0629760\pi$
$53$	4.80829	+	8.32820i	0.660469	+	1.14397i	−0.320023	+	0.947410i	$0.603691\pi$
$54$		0			0
$55$	3.35687			0.452641
$56$	−3.99219	+	2.73228i	−0.533478	+	0.365117i
$57$		0			0
$58$	3.51491	−	2.94936i	0.461531	−	0.387270i
$59$	−9.19604	−	3.34708i	−1.19722	−	0.435753i	−0.334968	−	0.942229i	$-0.608726\pi$
$59$	−9.19604	−	3.34708i	−1.19722	−	0.435753i	−0.862254	+	0.506476i	$0.830948\pi$
$60$		0			0
$61$	0.973943	−	5.52351i	0.124701	−	0.707213i	−0.856785	−	0.515675i	$-0.827541\pi$
$61$	0.973943	−	5.52351i	0.124701	−	0.707213i	0.981485	−	0.191538i	$-0.0613475\pi$
$62$	−0.648966	+	1.12404i	−0.0824188	+	0.142754i
$63$		0			0
$64$	1.44015	+	2.49441i	0.180018	+	0.311801i
$65$	9.08259	−	3.30579i	1.12656	−	0.410033i
$66$		0			0
$67$	6.94417	−	5.82685i	0.848365	−	0.711863i	−0.111064	−	0.993813i	$-0.535426\pi$
$67$	6.94417	−	5.82685i	0.848365	−	0.711863i	0.959429	+	0.281950i	$0.0909813\pi$
$68$	8.76750	+	3.19111i	1.06322	+	0.386979i
$69$		0			0
$70$	1.63006	−	1.11563i	0.194830	−	0.133343i
$71$	1.42313	+	2.46494i	0.168895	+	0.292535i	0.938032	−	0.346550i	$-0.112647\pi$
$71$	1.42313	+	2.46494i	0.168895	+	0.292535i	−0.769137	+	0.639084i	$0.779313\pi$
$72$		0			0
$73$	5.46594			0.639740			0.319870	−	0.947461i	$-0.396361\pi$
$73$	5.46594			0.639740			0.319870	+	0.947461i	$0.396361\pi$
$74$	0.170627	+	0.143173i	0.0198349	+	0.0166435i
$75$		0			0
$76$	−3.15448	+	2.64693i	−0.361844	+	0.303623i
$77$	−3.36496	+	4.69805i	−0.383472	+	0.535392i
$78$		0			0
$79$	−2.45123	−	2.05682i	−0.275785	−	0.231411i	0.494396	−	0.869237i	$-0.335389\pi$
$79$	−2.45123	−	2.05682i	−0.275785	−	0.231411i	−0.770180	+	0.637826i	$0.779834\pi$
$80$	−2.02858	−	3.51360i	−0.226802	−	0.392833i
$81$		0			0
$82$	0.718519	−	1.24451i	0.0793471	−	0.137433i
$83$	0.920085	−	5.21806i	0.100992	−	0.572757i	−0.891753	−	0.452522i	$-0.850524\pi$
$83$	0.920085	−	5.21806i	0.100992	−	0.572757i	0.992746	−	0.120234i	$-0.0383646\pi$
$84$		0			0
$85$	−7.63866	−	2.78025i	−0.828529	−	0.301560i
$86$	−0.537088	−	3.04598i	−0.0579157	−	0.328456i
$87$		0			0
$88$	−3.05935	−	2.56710i	−0.326128	−	0.273654i
$89$	8.98709	+	15.5661i	0.952629	+	1.65000i	0.739702	+	0.672934i	$0.234966\pi$
$89$	8.98709	+	15.5661i	0.952629	+	1.65000i	0.212927	+	0.977068i	$0.431700\pi$
$90$		0			0
$91$	−4.47790	+	16.0251i	−0.469411	+	1.67989i
$92$	−3.89209	−	3.26585i	−0.405779	−	0.340489i
$93$		0			0
$94$	−2.47713	+	2.07856i	−0.255496	+	0.214387i
$95$	2.74833	−	2.30613i	0.281973	−	0.236604i
$96$		0			0
$97$	10.6549	+	8.94050i	1.08184	+	0.907771i	0.996072	−	0.0885447i	$-0.0282216\pi$
$97$	10.6549	+	8.94050i	1.08184	+	0.907771i	0.0857666	+	0.996315i	$0.472666\pi$
$98$	−0.0726314	+	3.39964i	−0.00733688	+	0.343415i
$99$		0			0
$100$	−2.32669	−	4.02995i	−0.232669	−	0.402995i
$101$	11.1457	+	9.35234i	1.10904	+	0.930593i	0.997999	−	0.0632237i	$-0.0201382\pi$
$101$	11.1457	+	9.35234i	1.10904	+	0.930593i	0.111038	+	0.993816i	$0.464583\pi$
$102$		0			0
$103$	−0.282132	−	1.60005i	−0.0277993	−	0.157658i	0.967748	−	0.251920i	$-0.0810619\pi$
$103$	−0.282132	−	1.60005i	−0.0277993	−	0.157658i	−0.995547	+	0.0942622i	$0.969951\pi$
$104$	−10.8056	−	3.93293i	−1.05958	−	0.385655i
$105$		0			0
$106$	−0.811193	+	4.60051i	−0.0787901	+	0.446841i
$107$	−5.06054	+	8.76511i	−0.489221	+	0.847356i	−0.999923	−	0.0124021i	$-0.996052\pi$
$107$	−5.06054	+	8.76511i	−0.489221	+	0.847356i	0.510702	+	0.859758i	$0.329386\pi$
$108$		0			0
$109$	−2.46881	−	4.27611i	−0.236469	−	0.409577i	0.723229	−	0.690608i	$-0.242657\pi$
$109$	−2.46881	−	4.27611i	−0.236469	−	0.409577i	−0.959699	+	0.281031i	$0.909324\pi$
$110$	1.24917	+	1.04818i	0.119104	+	0.0999401i
$111$		0			0
$112$	6.95086	+	0.683002i	0.656795	+	0.0645376i
$113$	−3.75536	+	3.15112i	−0.353274	+	0.296432i	−0.802103	−	0.597185i	$-0.796286\pi$
$113$	−3.75536	+	3.15112i	−0.353274	+	0.296432i	0.448829	+	0.893618i	$0.351841\pi$
$114$		0			0
$115$	3.39097	+	2.84536i	0.316210	+	0.265332i
$116$	−16.6622			−1.54704
$117$		0			0
$118$	−2.37694	−	4.11698i	−0.218815	−	0.378999i
$119$	11.5481	−	7.90360i	1.05861	−	0.724522i
$120$		0			0
$121$	5.85367	+	2.13056i	0.532152	+	0.193687i
$122$	2.08714	−	1.75132i	0.188961	−	0.158557i
$123$		0			0
$124$	4.42904	−	1.61204i	0.397739	−	0.144765i
$125$	5.86938	+	10.1661i	0.524973	+	0.909280i
$126$		0			0
$127$	1.46479	−	2.53708i	0.129979	−	0.225130i	−0.793689	−	0.608323i	$-0.791842\pi$
$127$	1.46479	−	2.53708i	0.129979	−	0.225130i	0.923668	+	0.383194i	$0.125176\pi$
$128$	−1.95836	+	11.1064i	−0.173096	+	0.981676i
$129$		0			0
$130$	4.41208	+	1.60587i	0.386965	+	0.140844i
$131$	3.49122	−	2.92948i	0.305030	−	0.255950i	−0.477404	−	0.878684i	$-0.658422\pi$
$131$	3.49122	−	2.92948i	0.305030	−	0.255950i	0.782434	+	0.622733i	$0.213978\pi$
$132$		0			0
$133$	0.472544	+	6.15806i	0.0409748	+	0.533971i
$134$	4.40352			0.380406
$135$		0			0
$136$	4.83550	+	8.37533i	0.414641	+	0.718179i
$137$	−4.51883	+	1.64472i	−0.386070	+	0.140518i	−0.527761	−	0.849393i	$-0.676968\pi$
$137$	−4.51883	+	1.64472i	−0.386070	+	0.140518i	0.141691	+	0.989911i	$0.454746\pi$
$138$		0			0
$139$	−2.85026	−	1.03741i	−0.241756	−	0.0879919i	0.218301	−	0.975882i	$-0.429949\pi$
$139$	−2.85026	−	1.03741i	−0.241756	−	0.0879919i	−0.460057	+	0.887890i	$0.652171\pi$
$140$	−7.13860	−	0.701450i	−0.603322	−	0.0592833i
$141$		0			0
$142$	−0.240093	+	1.36164i	−0.0201482	+	0.114266i
$143$	−13.7362			−1.14868
$144$		0			0
$145$	14.5169			1.20556
$146$	2.03401	+	1.70673i	0.168336	+	0.141250i
$147$		0			0
$148$	−0.140454	−	0.796554i	−0.0115453	−	0.0654764i
$149$	−13.9966	−	5.09435i	−1.14665	−	0.417346i	−0.302338	−	0.953201i	$-0.597767\pi$
$149$	−13.9966	−	5.09435i	−1.14665	−	0.417346i	−0.844310	+	0.535855i	$0.819989\pi$
$150$		0			0
$151$	1.66468	−	9.44086i	0.135470	−	0.768286i	−0.839062	−	0.544036i	$-0.816896\pi$
$151$	1.66468	−	9.44086i	0.135470	−	0.768286i	0.974532	−	0.224250i	$-0.0719933\pi$
$152$	−4.26831			−0.346205
$153$		0			0
$154$	−2.71914	+	0.697552i	−0.219115	+	0.0562104i
$155$	−3.85878	+	1.40448i	−0.309945	+	0.112811i
$156$		0			0
$157$	−8.76252	−	3.18930i	−0.699325	−	0.254534i	−0.0322024	−	0.999481i	$-0.510252\pi$
$157$	−8.76252	−	3.18930i	−0.699325	−	0.254534i	−0.667123	+	0.744948i	$0.732474\pi$
$158$	−0.269919	−	1.53079i	−0.0214736	−	0.121783i
$159$		0			0
$160$	1.31820	−	7.47586i	0.104213	−	0.591019i
$161$	−7.38131	+	1.89356i	−0.581729	+	0.149233i
$162$		0			0
$163$	−8.18715	+	14.1806i	−0.641267	+	1.11071i	0.343883	+	0.939012i	$0.388257\pi$
$163$	−8.18715	+	14.1806i	−0.641267	+	1.11071i	−0.985150	+	0.171694i	$0.945076\pi$
$164$	−4.90371	+	1.78481i	−0.382916	+	0.139370i
$165$		0			0
$166$	1.97172	−	1.65447i	0.153035	−	0.128412i
$167$	−0.526404	+	0.441705i	−0.0407344	+	0.0341802i	−0.662928	−	0.748684i	$-0.730686\pi$
$167$	−0.526404	+	0.441705i	−0.0407344	+	0.0341802i	0.622193	+	0.782864i	$0.286242\pi$
$168$		0			0
$169$	−24.9497	+	9.08094i	−1.91921	+	0.698534i
$170$	−1.97440	−	3.41976i	−0.151429	−	0.262284i
$171$		0			0
$172$	−5.61586	+	9.72695i	−0.428205	+	0.741673i
$173$	7.76214	−	2.82519i	0.590145	−	0.214795i	−0.0296484	−	0.999560i	$-0.509439\pi$
$173$	7.76214	−	2.82519i	0.590145	−	0.214795i	0.619793	+	0.784765i	$0.287217\pi$
$174$		0			0
$175$	−6.94587	−	0.682511i	−0.525058	−	0.0515930i
$176$	1.00123	+	5.67828i	0.0754708	+	0.428016i
$177$		0			0
$178$	−1.51619	+	8.59872i	−0.113643	+	0.644501i
$179$	11.9946	−	20.7753i	0.896521	−	1.55282i	0.0646105	−	0.997911i	$-0.479419\pi$
$179$	11.9946	−	20.7753i	0.896521	−	1.55282i	0.831911	−	0.554910i	$-0.187247\pi$
$180$		0			0
$181$	1.13840	−	1.97177i	0.0846166	−	0.146560i	−0.820611	−	0.571487i	$-0.806367\pi$
$181$	1.13840	−	1.97177i	0.0846166	−	0.146560i	0.905228	+	0.424927i	$0.139700\pi$
$182$	−6.67016	+	4.56511i	−0.494425	+	0.338389i
$183$		0			0
$184$	−0.914494	−	5.18635i	−0.0674174	−	0.382343i
$185$	0.122370	+	0.693996i	0.00899684	+	0.0510236i
$186$		0			0
$187$	8.84970	+	7.42578i	0.647154	+	0.543027i
$188$	11.7426			0.856419
$189$		0			0
$190$	1.74281			0.126436
$191$	−13.7718	−	11.5559i	−0.996495	−	0.836158i	−0.00999987	−	0.999950i	$-0.503183\pi$
$191$	−13.7718	−	11.5559i	−0.996495	−	0.836158i	−0.986495	+	0.163792i	$0.947628\pi$
$192$		0			0
$193$	−0.0163345	−	0.0926376i	−0.00117578	−	0.00666820i	0.984214	−	0.176981i	$-0.0566332\pi$
$193$	−0.0163345	−	0.0926376i	−0.00117578	−	0.00666820i	−0.985390	+	0.170313i	$0.945522\pi$
$194$	1.17327	+	6.65395i	0.0842359	+	0.477726i
$195$		0			0
$196$	8.13749	−	9.28755i	0.581249	−	0.663397i
$197$	12.1146	−	20.9832i	0.863132	−	1.49499i	−0.00575743	−	0.999983i	$-0.501833\pi$
$197$	12.1146	−	20.9832i	0.863132	−	1.49499i	0.868890	−	0.495006i	$-0.164834\pi$
$198$		0			0
$199$	5.71198	−	9.89345i	0.404912	−	0.701328i	−0.589399	−	0.807842i	$-0.700636\pi$
$199$	5.71198	−	9.89345i	0.404912	−	0.701328i	0.994311	+	0.106514i	$0.0339689\pi$
$200$	0.837568	−	4.75008i	0.0592250	−	0.335882i
$201$		0			0
$202$	1.22732	+	6.96046i	0.0863537	+	0.489736i
$203$	−14.5518	+	20.3168i	−1.02134	+	1.42596i
$204$		0			0
$205$	4.27235	−	1.55501i	0.298394	−	0.108606i
$206$	0.394626	−	0.683512i	0.0274949	−	0.0476225i
$207$		0			0
$208$	8.30088	+	14.3775i	0.575563	+	0.996904i
$209$	−4.79120	+	1.74386i	−0.331414	+	0.120625i
$210$		0			0
$211$	18.8128	−	15.7858i	1.29513	−	1.08674i	0.304165	−	0.952619i	$-0.401623\pi$
$211$	18.8128	−	15.7858i	1.29513	−	1.08674i	0.990965	−	0.134123i	$-0.0428218\pi$
$212$	12.9951	−	10.9042i	0.892506	−	0.748902i
$213$		0			0
$214$	−4.62005	+	1.68156i	−0.315820	+	0.114949i
$215$	4.89280	−	8.47458i	0.333686	−	0.577962i
$216$		0			0
$217$	1.90246	−	6.80835i	0.129147	−	0.462181i
$218$	0.416507	−	2.36213i	0.0282094	−	0.159983i
$219$		0			0
$220$	−1.02828	−	5.83165i	−0.0693264	−	0.393169i
$221$	31.2571	+	11.3767i	2.10258	+	0.765278i
$222$		0			0
$223$	14.7349	−	5.36308i	0.986724	−	0.359138i	0.202273	−	0.979329i	$-0.435167\pi$
$223$	14.7349	−	5.36308i	0.986724	−	0.359138i	0.784451	+	0.620191i	$0.212945\pi$
$224$	9.14133	+	9.33872i	0.610781	+	0.623969i
$225$		0			0
$226$	−2.38139			−0.158408
$227$	0.421725	−	2.39172i	0.0279909	−	0.158744i	−0.967609	−	0.252455i	$-0.918762\pi$
$227$	0.421725	−	2.39172i	0.0279909	−	0.158744i	0.995599	+	0.0937111i	$0.0298730\pi$
$228$		0			0
$229$	0.665578	+	0.242251i	0.0439826	+	0.0160084i	0.363918	−	0.931431i	$-0.381439\pi$
$229$	0.665578	+	0.242251i	0.0439826	+	0.0160084i	−0.319935	+	0.947439i	$0.603661\pi$
$230$	0.373400	+	2.11766i	0.0246213	+	0.139634i
$231$		0			0
$232$	−13.2302	−	11.1015i	−0.868607	−	0.728847i
$233$	0.237608			0.0155662			0.00778310	−	0.999970i	$-0.497523\pi$
$233$	0.237608			0.0155662			0.00778310	+	0.999970i	$0.497523\pi$
$234$		0			0
$235$	−10.2307			−0.667379
$236$	−2.99771	+	17.0009i	−0.195134	+	1.10666i
$237$		0			0
$238$	6.76521	+	0.664760i	0.438524	+	0.0430900i
$239$	1.95296	+	0.710821i	0.126327	+	0.0459792i	0.404410	−	0.914578i	$-0.367477\pi$
$239$	1.95296	+	0.710821i	0.126327	+	0.0459792i	−0.278083	+	0.960557i	$0.589699\pi$
$240$		0			0
$241$	16.2363	−	5.90953i	1.04587	−	0.380667i	0.238769	−	0.971076i	$-0.423256\pi$
$241$	16.2363	−	5.90953i	1.04587	−	0.380667i	0.807104	+	0.590410i	$0.201034\pi$
$242$	1.51302	+	2.62063i	0.0972609	+	0.168461i
$243$		0			0
$244$	−9.89391			−0.633393
$245$	−7.08976	+	8.09175i	−0.452948	+	0.516963i
$246$		0			0
$247$	−11.2461	+	9.43659i	−0.715572	+	0.600436i
$248$	4.59082	+	1.67092i	0.291517	+	0.106104i
$249$		0			0
$250$	−0.990206	+	5.61574i	−0.0626261	+	0.355170i
$251$	3.32513	−	5.75929i	0.209880	−	0.363523i	−0.741796	−	0.670625i	$-0.766026\pi$
$251$	3.32513	−	5.75929i	0.209880	−	0.363523i	0.951677	+	0.307102i	$0.0993593\pi$
$252$		0			0
$253$	−3.14546	−	5.44809i	−0.197753	−	0.342518i
$254$	1.33728	−	0.486731i	0.0839086	−	0.0305402i
$255$		0			0
$256$	0.216149	−	0.181370i	0.0135093	−	0.0113356i
$257$	−5.60352	−	2.03952i	−0.349538	−	0.127221i	0.161284	−	0.986908i	$-0.448437\pi$
$257$	−5.60352	−	2.03952i	−0.349538	−	0.127221i	−0.510822	+	0.859687i	$0.670659\pi$
$258$		0			0
$259$	−1.09393	−	0.524406i	−0.0679737	−	0.0325850i
$260$	−8.52508	−	14.7659i	−0.528703	−	0.915741i
$261$		0			0
$262$	2.21390			0.136775
$263$	8.41519	+	7.06118i	0.518903	+	0.435411i	0.864249	−	0.503064i	$-0.167794\pi$
$263$	8.41519	+	7.06118i	0.518903	+	0.435411i	−0.345346	+	0.938475i	$0.612239\pi$
$264$		0			0
$265$	−11.3219	+	9.50023i	−0.695501	+	0.583594i
$266$	−1.74700	+	2.43911i	−0.107116	+	0.149552i
$267$		0			0
$268$	−12.2497	−	10.2787i	−0.748269	−	0.627872i
$269$	−6.36322	−	11.0214i	−0.387972	−	0.671988i	0.604204	−	0.796829i	$-0.293491\pi$
$269$	−6.36322	−	11.0214i	−0.387972	−	0.671988i	−0.992177	+	0.124841i	$0.960158\pi$
$270$		0			0
$271$	8.08647	−	14.0062i	0.491218	−	0.850815i	−0.508731	−	0.860926i	$-0.669885\pi$
$271$	8.08647	−	14.0062i	0.491218	−	0.850815i	0.999949	+	0.0101110i	$0.00321849\pi$
$272$	2.42455	−	13.7503i	0.147010	−	0.833736i
$273$		0			0
$274$	−2.19513	−	0.798961i	−0.132612	−	0.0482670i
$275$	−1.00051	−	5.67420i	−0.0603333	−	0.342167i
$276$		0			0
$277$	14.5287	+	12.1910i	0.872946	+	0.732488i	0.964716	−	0.263292i	$-0.0848082\pi$
$277$	14.5287	+	12.1910i	0.872946	+	0.732488i	−0.0917706	+	0.995780i	$0.529253\pi$
$278$	−0.736719	−	1.27604i	−0.0441855	−	0.0765315i
$279$		0			0
$280$	−5.20089	−	5.31319i	−0.310813	−	0.317524i
$281$	−2.90607	−	2.43848i	−0.173361	−	0.145467i	0.551979	−	0.833858i	$-0.313873\pi$
$281$	−2.90607	−	2.43848i	−0.173361	−	0.145467i	−0.725340	+	0.688391i	$0.758317\pi$
$282$		0			0
$283$	−24.6974	+	20.7236i	−1.46811	+	1.23189i	−0.550237	+	0.835009i	$0.685462\pi$
$283$	−24.6974	+	20.7236i	−1.46811	+	1.23189i	−0.917871	+	0.396879i	$0.870093\pi$
$284$	3.84622	−	3.22736i	0.228231	−	0.191509i
$285$		0			0
$286$	−5.11157	−	4.28912i	−0.302254	−	0.253621i
$287$	−2.10635	+	7.53803i	−0.124334	+	0.444956i
$288$		0			0
$289$	−5.48752	−	9.50467i	−0.322796	−	0.559098i
$290$	5.40208	+	4.53288i	0.317221	+	0.266180i
$291$		0			0
$292$	−1.67433	−	9.49557i	−0.0979825	−	0.555686i
$293$	−1.19797	−	0.436026i	−0.0699863	−	0.0254729i	0.306790	−	0.951777i	$-0.400745\pi$
$293$	−1.19797	−	0.436026i	−0.0699863	−	0.0254729i	−0.376776	+	0.926304i	$0.622967\pi$
$294$		0			0
$295$	2.61175	−	14.8120i	0.152062	−	0.862385i
$296$	0.419194	−	0.726066i	0.0243652	−	0.0422017i
$297$		0			0
$298$	−3.61777	−	6.26616i	−0.209572	−	0.362989i
$299$	−13.8758	−	11.6431i	−0.802455	−	0.673340i
$300$		0			0
$301$	6.95586	+	15.3426i	0.400929	+	0.884334i
$302$	3.56736	−	2.99337i	0.205279	−	0.172249i
$303$		0			0
$304$	4.72063	+	3.96108i	0.270747	+	0.227183i
$305$	8.62004			0.493582
$306$		0			0
$307$	−6.90602	−	11.9616i	−0.394147	−	0.682683i	0.598845	−	0.800865i	$-0.295627\pi$
$307$	−6.90602	−	11.9616i	−0.394147	−	0.682683i	−0.992992	+	0.118182i	$0.962293\pi$
$308$	9.19232	+	4.40658i	0.523781	+	0.251088i
$309$		0			0
$310$	−1.87449	−	0.682260i	−0.106464	−	0.0387498i
$311$	18.1868	−	15.2605i	1.03128	−	0.865344i	0.0402750	−	0.999189i	$-0.487177\pi$
$311$	18.1868	−	15.2605i	1.03128	−	0.865344i	0.991002	+	0.133844i	$0.0427322\pi$
$312$		0			0
$313$	−10.6398	+	3.87257i	−0.601398	+	0.218891i	−0.624735	−	0.780837i	$-0.714793\pi$
$313$	−10.6398	+	3.87257i	−0.601398	+	0.218891i	0.0233374	+	0.999728i	$0.492571\pi$
$314$	−2.26489	−	3.92290i	−0.127815	−	0.221382i
$315$		0			0
$316$	−2.82231	+	4.88838i	−0.158767	+	0.274993i
$317$	1.58069	−	8.96453i	0.0887803	−	0.503498i	−0.907696	−	0.419628i	$-0.862161\pi$
$317$	1.58069	−	8.96453i	0.0887803	−	0.503498i	0.996477	−	0.0838705i	$-0.0267282\pi$
$318$		0			0
$319$	−19.3866	−	7.05615i	−1.08544	−	0.395069i
$320$	−3.39107	+	2.84544i	−0.189566	+	0.159065i
$321$		0			0
$322$	−3.33802	−	1.60017i	−0.186021	−	0.0891740i
$323$	12.3468			0.686995
$324$		0			0
$325$	−8.29492	−	14.3672i	−0.460119	−	0.796950i
$326$	−7.47450	+	2.72049i	−0.413974	+	0.150674i
$327$		0			0
$328$	−5.08284	−	1.85000i	−0.280653	−	0.102149i
$329$	10.2554	−	14.3182i	0.565396	−	0.789389i
$330$		0			0
$331$	0.244768	−	1.38815i	0.0134536	−	0.0762994i	−0.977342	−	0.211668i	$-0.932111\pi$
$331$	0.244768	−	1.38815i	0.0134536	−	0.0762994i	0.990795	+	0.135368i	$0.0432217\pi$
$332$	−9.34679			−0.512972
$333$		0			0
$334$	−0.333809			−0.0182652
$335$	10.6725	+	8.95529i	0.583101	+	0.489280i
$336$		0			0
$337$	−4.68879	−	26.5914i	−0.255414	−	1.44853i	−0.795007	−	0.606601i	$-0.792533\pi$
$337$	−4.68879	−	26.5914i	−0.255414	−	1.44853i	0.539592	−	0.841926i	$-0.318578\pi$
$338$	−12.1199	−	4.41127i	−0.659234	−	0.239942i
$339$		0			0
$340$	−2.49004	+	14.1217i	−0.135041	+	0.765858i
$341$	5.83590			0.316032
$342$		0			0
$343$	−4.21783	−	18.0336i	−0.227741	−	0.973722i
$344$	−10.9399	+	3.98180i	−0.589840	+	0.214684i
$345$		0			0
$346$	3.77064	+	1.37240i	0.202711	+	0.0737807i
$347$	1.13843	+	6.45637i	0.0611143	+	0.346596i	0.999997	+	0.00235969i	$0.000751115\pi$
$347$	1.13843	+	6.45637i	0.0611143	+	0.346596i	−0.938883	+	0.344237i	$0.888138\pi$
$348$		0			0
$349$	−1.35955	+	7.71038i	−0.0727749	+	0.412727i	0.926556	+	0.376156i	$0.122754\pi$
$349$	−1.35955	+	7.71038i	−0.0727749	+	0.412727i	−0.999331	+	0.0365706i	$0.988357\pi$
$350$	−2.37161	−	2.42282i	−0.126768	−	0.129505i
$351$		0			0
$352$	−5.39415	+	9.34294i	−0.287509	+	0.497980i
$353$	−30.2455	+	11.0085i	−1.60981	+	0.585921i	−0.981402	−	0.191966i	$-0.938514\pi$
$353$	−30.2455	+	11.0085i	−1.60981	+	0.585921i	−0.628404	+	0.777887i	$0.716292\pi$
$354$		0			0
$355$	−3.35101	+	2.81183i	−0.177853	+	0.149237i
$356$	24.2889	−	20.3808i	1.28731	−	1.08018i
$357$		0			0
$358$	10.9506	−	3.98568i	0.578755	−	0.210650i
$359$	7.62445	+	13.2059i	0.402403	+	0.696983i	0.994015	−	0.109240i	$-0.0348416\pi$
$359$	7.62445	+	13.2059i	0.402403	+	0.696983i	−0.591612	+	0.806223i	$0.701508\pi$
$360$		0			0
$361$	6.77536	−	11.7353i	0.356598	−	0.617646i
$362$	1.03931	−	0.378277i	0.0546248	−	0.0198818i
$363$		0			0
$364$	29.2109	+	2.87031i	1.53107	+	0.150445i
$365$	1.45875	+	8.27299i	0.0763545	+	0.433028i
$366$		0			0
$367$	−2.14975	+	12.1918i	−0.112216	+	0.636409i	0.875875	+	0.482538i	$0.160285\pi$
$367$	−2.14975	+	12.1918i	−0.112216	+	0.636409i	−0.988091	+	0.153871i	$0.950826\pi$
$368$	−3.80164	+	6.58463i	−0.198174	+	0.343247i
$369$		0			0
$370$	−0.171163	+	0.296462i	−0.00889832	+	0.0154123i
$371$	−1.94668	−	25.3685i	−0.101066	−	1.31707i
$372$		0			0
$373$	4.06024	+	23.0268i	0.210231	+	1.19228i	0.888992	+	0.457922i	$0.151406\pi$
$373$	4.06024	+	23.0268i	0.210231	+	1.19228i	−0.678761	+	0.734359i	$0.737483\pi$
$374$	0.974492	+	5.52662i	0.0503898	+	0.285775i
$375$		0			0
$376$	9.32396	+	7.82373i	0.480847	+	0.403478i
$377$	−59.4026			−3.05939
$378$		0			0
$379$	0.0616475			0.00316662			0.00158331	−	0.999999i	$-0.499496\pi$
$379$	0.0616475			0.00316662			0.00158331	+	0.999999i	$0.499496\pi$
$380$	−4.84813	−	4.06806i	−0.248704	−	0.208687i
$381$		0			0
$382$	−1.51650	−	8.60048i	−0.0775907	−	0.440039i
$383$	0.278612	+	1.58008i	0.0142364	+	0.0807386i	0.991098	−	0.133133i	$-0.0425037\pi$
$383$	0.278612	+	1.58008i	0.0142364	+	0.0807386i	−0.976862	+	0.213871i	$0.931393\pi$
$384$		0			0
$385$	−8.00878	−	3.83922i	−0.408165	−	0.195665i
$386$	0.0228475	−	0.0395731i	0.00116291	−	0.00201422i
$387$		0			0
$388$	12.2679	−	21.2486i	0.622807	−	1.07873i
$389$	2.40650	−	13.6479i	0.122014	−	0.691978i	−0.861022	−	0.508568i	$-0.830175\pi$
$389$	2.40650	−	13.6479i	0.122014	−	0.691978i	0.983036	−	0.183411i	$-0.0587138\pi$
$390$		0			0
$391$	2.64533	+	15.0024i	0.133780	+	0.758705i
$392$	12.6494	−	1.95282i	0.638890	−	0.0986325i
$393$		0			0
$394$	11.0601	−	4.02555i	0.557201	−	0.202804i
$395$	2.45893	−	4.25899i	0.123722	−	0.214293i
$396$		0			0
$397$	3.04239	+	5.26958i	0.152693	+	0.264473i	0.932217	−	0.361901i	$-0.117872\pi$
$397$	3.04239	+	5.26958i	0.152693	+	0.264473i	−0.779523	+	0.626373i	$0.784539\pi$
$398$	5.21478	−	1.89803i	0.261393	−	0.0951394i
$399$		0			0
$400$	−5.33450	+	4.47618i	−0.266725	+	0.223809i
$401$	−17.9862	+	15.0922i	−0.898186	+	0.753667i	−0.969835	−	0.243763i	$-0.921618\pi$
$401$	−17.9862	+	15.0922i	−0.898186	+	0.753667i	0.0716492	+	0.997430i	$0.477174\pi$
$402$		0			0
$403$	15.7900	−	5.74710i	0.786557	−	0.286283i
$404$	12.8330	−	22.2274i	0.638464	−	1.10585i
$405$		0			0
$406$	−11.7590	+	3.01658i	−0.583589	+	0.149710i
$407$	0.173908	−	0.986279i	0.00862028	−	0.0488881i
$408$		0			0
$409$	−0.315413	−	1.78880i	−0.0155962	−	0.0884503i	0.976016	−	0.217698i	$-0.0698548\pi$
$409$	−0.315413	−	1.78880i	−0.0155962	−	0.0884503i	−0.991612	+	0.129248i	$0.958744\pi$
$410$	2.07539	+	0.755381i	0.102496	+	0.0373056i
$411$		0			0
$412$	−2.69322	+	0.980253i	−0.132686	+	0.0482936i
$413$	18.1118	+	18.5028i	0.891221	+	0.910465i
$414$		0			0
$415$	8.14336			0.399742
$416$	−5.39402	+	30.5910i	−0.264463	+	1.49985i
$417$		0			0
$418$	−2.32744	−	0.847118i	−0.113839	−	0.0414339i
$419$	−0.303043	−	1.71864i	−0.0148046	−	0.0839611i	0.976510	−	0.215471i	$-0.0691286\pi$
$419$	−0.303043	−	1.71864i	−0.0148046	−	0.0839611i	−0.991315	+	0.131510i	$0.958018\pi$
$420$		0			0
$421$	10.8495	+	9.10383i	0.528773	+	0.443693i	0.867678	−	0.497127i	$-0.165612\pi$
$421$	10.8495	+	9.10383i	0.528773	+	0.443693i	−0.338904	+	0.940821i	$0.610056\pi$
$422$	11.9298			0.580735
$423$		0			0
$424$	17.5836			0.853933
$425$	−2.42281	+	13.7404i	−0.117524	+	0.666510i
$426$		0			0
$427$	−8.64080	+	12.0640i	−0.418157	+	0.583819i
$428$	16.7771	+	6.10637i	0.810953	+	0.295163i
$429$		0			0
$430$	4.46691	−	1.62582i	0.215413	−	0.0784041i
$431$	−5.63358	−	9.75765i	−0.271360	−	0.470009i	0.697850	−	0.716244i	$-0.254140\pi$
$431$	−5.63358	−	9.75765i	−0.271360	−	0.470009i	−0.969210	+	0.246234i	$0.920807\pi$
$432$		0			0
$433$	11.4819			0.551785			0.275892	−	0.961189i	$-0.411027\pi$
$433$	11.4819			0.551785			0.275892	+	0.961189i	$0.411027\pi$
$434$	2.83385	−	1.93951i	0.136029	−	0.0930994i
$435$		0			0
$436$	−6.67232	+	5.59874i	−0.319546	+	0.268131i
$437$	−6.31800	−	2.29957i	−0.302231	−	0.110003i
$438$		0			0
$439$	2.99246	−	16.9711i	0.142822	−	0.809985i	−0.826268	−	0.563277i	$-0.809540\pi$
$439$	2.99246	−	16.9711i	0.142822	−	0.809985i	0.969090	−	0.246707i	$-0.0793486\pi$
$440$	3.06896	−	5.31559i	0.146307	−	0.253411i
$441$		0			0
$442$	8.07917	+	13.9935i	0.384287	+	0.665605i
$443$	33.7445	−	12.2820i	1.60325	−	0.583535i	0.623159	−	0.782095i	$-0.285849\pi$
$443$	33.7445	−	12.2820i	1.60325	−	0.583535i	0.980089	+	0.198560i	$0.0636265\pi$
$444$		0			0
$445$	−21.1616	+	17.7567i	−1.00316	+	0.841749i
$446$	7.15784	+	2.60524i	0.338933	+	0.123362i
$447$		0			0
$448$	−0.583055	−	7.59820i	−0.0275467	−	0.358981i
$449$	−8.11520	−	14.0559i	−0.382980	−	0.663341i	0.608507	−	0.793549i	$-0.291769\pi$
$449$	−8.11520	−	14.0559i	−0.382980	−	0.663341i	−0.991487	+	0.130208i	$0.958435\pi$
$450$		0			0
$451$	−6.46136			−0.304253
$452$	6.62454	+	5.55865i	0.311592	+	0.261457i
$453$		0			0
$454$	0.903747	−	0.758334i	0.0424150	−	0.0355904i
$455$	−25.4499	−	2.50075i	−1.19311	−	0.117237i
$456$		0			0
$457$	13.7786	+	11.5616i	0.644535	+	0.540829i	0.905407	−	0.424544i	$-0.139566\pi$
$457$	13.7786	+	11.5616i	0.644535	+	0.540829i	−0.260872	+	0.965373i	$0.584010\pi$
$458$	0.172035	+	0.297973i	0.00803866	+	0.0139234i
$459$		0			0
$460$	3.90432	−	6.76247i	0.182040	−	0.315302i
$461$	−6.39959	+	36.2939i	−0.298059	+	1.69037i	0.356445	+	0.934316i	$0.383989\pi$
$461$	−6.39959	+	36.2939i	−0.298059	+	1.69037i	−0.654504	+	0.756059i	$0.727122\pi$
$462$		0			0
$463$	31.3099	+	11.3959i	1.45509	+	0.529611i	0.944009	−	0.329920i	$-0.107022\pi$
$463$	31.3099	+	11.3959i	1.45509	+	0.529611i	0.511084	+	0.859531i	$0.329244\pi$
$464$	4.32986	+	24.5558i	0.201009	+	1.13998i
$465$		0			0
$466$	0.0884195	+	0.0741928i	0.00409595	+	0.00343691i
$467$	−13.1357	−	22.7518i	−0.607850	−	1.05283i	−0.991594	−	0.129387i	$-0.958699\pi$
$467$	−13.1357	−	22.7518i	−0.607850	−	1.05283i	0.383744	−	0.923439i	$-0.374634\pi$
$468$		0			0
$469$	−23.2314	+	5.95965i	−1.07273	+	0.275191i
$470$	−3.80710	−	3.19453i	−0.175608	−	0.147353i
$471$		0			0
$472$	−13.7074	+	11.5019i	−0.630934	+	0.529416i
$473$	−10.6533	+	8.93919i	−0.489840	+	0.411024i
$474$		0			0
$475$	−4.71724	−	3.95823i	−0.216442	−	0.181616i
$476$	−17.2677	−	17.6406i	−0.791466	−	0.808556i
$477$		0			0
$478$	0.504791	+	0.874324i	0.0230886	+	0.0399907i
$479$	−5.89925	−	4.95006i	−0.269544	−	0.226174i	0.497990	−	0.867183i	$-0.334072\pi$
$479$	−5.89925	−	4.95006i	−0.269544	−	0.226174i	−0.767533	+	0.641009i	$0.778516\pi$
$480$		0			0
$481$	−0.500735	−	2.83981i	−0.0228315	−	0.129484i
$482$	7.88716	+	2.87069i	0.359250	+	0.130756i
$483$		0			0
$484$	1.90817	−	10.8218i	0.0867350	−	0.491899i
$485$	−10.6883	+	18.5128i	−0.485333	+	0.840621i
$486$		0			0
$487$	−14.0607	−	24.3538i	−0.637150	−	1.10358i	−0.986055	−	0.166418i	$-0.946780\pi$
$487$	−14.0607	−	24.3538i	−0.637150	−	1.10358i	0.348906	−	0.937158i	$-0.386553\pi$
$488$	−7.85604	−	6.59200i	−0.355626	−	0.298406i
$489$		0			0
$490$	−5.16491	+	0.797364i	−0.233327	+	0.0360212i
$491$	−29.8391	+	25.0380i	−1.34662	+	1.12995i	−0.366747	+	0.930321i	$0.619529\pi$
$491$	−29.8391	+	25.0380i	−1.34662	+	1.12995i	−0.979872	+	0.199627i	$0.936027\pi$
$492$		0			0
$493$	38.2707	+	32.1129i	1.72363	+	1.44629i
$494$	−7.13151			−0.320862
$495$		0			0
$496$	−3.52667	−	6.10837i	−0.158352	−	0.274274i
$497$	−0.576167	−	7.50844i	−0.0258446	−	0.336800i
$498$		0			0
$499$	13.9446	+	5.07541i	0.624245	+	0.227206i	0.634724	−	0.772739i	$-0.281114\pi$
$499$	13.9446	+	5.07541i	0.624245	+	0.227206i	−0.0104798	+	0.999945i	$0.503336\pi$
$500$	15.8628	−	13.3105i	0.709407	−	0.595263i
$501$		0			0
$502$	3.03569	−	1.10490i	0.135490	−	0.0493142i
$503$	13.9372	+	24.1400i	0.621430	+	1.07635i	0.989220	+	0.146439i	$0.0467812\pi$
$503$	13.9372	+	24.1400i	0.621430	+	1.07635i	−0.367790	+	0.929909i	$0.619886\pi$
$504$		0			0
$505$	−11.1807	+	19.3655i	−0.497534	+	0.861755i
$506$	0.530661	−	3.00953i	0.0235908	−	0.133790i
$507$		0			0
$508$	−4.85618	−	1.76750i	−0.215458	−	0.0784203i
$509$	19.0971	−	16.0244i	0.846464	−	0.710268i	−0.112544	−	0.993647i	$-0.535900\pi$
$509$	19.0971	−	16.0244i	0.846464	−	0.710268i	0.959008	+	0.283379i	$0.0914555\pi$
$510$		0			0
$511$	−13.0406	−	6.25134i	−0.576881	−	0.276543i
$512$	22.6925			1.00288
$513$		0			0
$514$	−1.44837	−	2.50865i	−0.0638848	−	0.110652i
$515$	2.34646	−	0.854043i	0.103397	−	0.0376336i
$516$		0			0
$517$	13.6627	+	4.97280i	0.600884	+	0.218704i
$518$	−0.243334	−	0.536723i	−0.0106915	−	0.0235823i
$519$		0			0
$520$	3.06888	−	17.4045i	0.134579	−	0.763238i
$521$	−10.7084			−0.469143			−0.234572	−	0.972099i	$-0.575369\pi$
$521$	−10.7084			−0.469143			−0.234572	+	0.972099i	$0.575369\pi$
$522$		0			0
$523$	−6.73986			−0.294713			−0.147357	−	0.989083i	$-0.547077\pi$
$523$	−6.73986			−0.294713			−0.147357	+	0.989083i	$0.547077\pi$
$524$	−6.15860	−	5.16768i	−0.269040	−	0.225751i
$525$		0			0
$526$	0.926646	+	5.25527i	0.0404037	+	0.229141i
$527$	−13.2798	−	4.83343i	−0.578475	−	0.210548i
$528$		0			0
$529$	−2.55339	+	14.4810i	−0.111017	+	0.629608i
$530$	−7.17960			−0.311862
$531$		0			0
$532$	10.5532	−	2.70725i	0.457538	−	0.117374i
$533$	−17.4823	+	6.36304i	−0.757243	+	0.275614i
$534$		0			0
$535$	−14.6170	−	5.32016i	−0.631949	−	0.230011i
$536$	−2.87821	−	16.3231i	−0.124320	−	0.705052i
$537$		0			0
$538$	1.07352	−	6.08824i	0.0462828	−	0.262483i
$539$	13.4012	−	7.36008i	0.577229	−	0.317021i
$540$		0			0
$541$	9.86926	−	17.0941i	0.424312	−	0.734931i	−0.572043	−	0.820223i	$-0.693849\pi$
$541$	9.86926	−	17.0941i	0.424312	−	0.734931i	0.996356	+	0.0852926i	$0.0271825\pi$
$542$	7.38258	−	2.68704i	0.317109	−	0.115418i
$543$		0			0
$544$	20.0126	−	16.7926i	0.858033	−	0.719975i
$545$	5.81324	−	4.87789i	0.249012	−	0.208946i
$546$		0			0
$547$	−33.7755	+	12.2933i	−1.44413	+	0.525622i	−0.940947	−	0.338555i	$-0.890062\pi$
$547$	−33.7755	+	12.2933i	−1.44413	+	0.525622i	−0.503188	+	0.864177i	$0.667840\pi$
$548$	4.24145	+	7.34642i	0.181186	+	0.313823i
$549$		0			0
$550$	1.39945	−	2.42391i	0.0596726	−	0.103356i
$551$	−20.7197	+	7.54134i	−0.882687	+	0.321272i
$552$		0			0
$553$	3.49574	+	7.71058i	0.148654	+	0.327887i
$554$	1.59984	+	9.07315i	0.0679707	+	0.385481i
$555$		0			0
$556$	−0.929124	+	5.26932i	−0.0394036	+	0.223469i
$557$	−9.58345	+	16.5990i	−0.406064	+	0.703323i	−0.994445	−	0.105261i	$-0.966432\pi$
$557$	−9.58345	+	16.5990i	−0.406064	+	0.703323i	0.588381	+	0.808584i	$0.299766\pi$
$558$		0			0
$559$	−20.0212	+	34.6777i	−0.846806	+	1.46671i
$560$	0.821287	+	10.7028i	0.0347057	+	0.452275i
$561$		0			0
$562$	−0.320004	−	1.81483i	−0.0134986	−	0.0765541i
$563$	5.86715	+	33.2743i	0.247271	+	1.40234i	0.815159	+	0.579237i	$0.196650\pi$
$563$	5.86715	+	33.2743i	0.247271	+	1.40234i	−0.567888	+	0.823106i	$0.692239\pi$
$564$		0			0
$565$	−5.77161	−	4.84296i	−0.242814	−	0.203745i
$566$	−15.6614			−0.658298
$567$		0			0
$568$	5.20429			0.218367
$569$	24.3822	+	20.4591i	1.02215	+	0.857688i	0.989897	−	0.141791i	$-0.0452862\pi$
$569$	24.3822	+	20.4591i	1.02215	+	0.857688i	0.0322566	+	0.999480i	$0.489731\pi$
$570$		0			0
$571$	2.91425	+	16.5275i	0.121958	+	0.691656i	0.983068	+	0.183239i	$0.0586582\pi$
$571$	2.91425	+	16.5275i	0.121958	+	0.691656i	−0.861111	+	0.508417i	$0.830231\pi$
$572$	4.20767	+	23.8629i	0.175932	+	0.997758i
$573$		0			0
$574$	−3.13757	+	2.14738i	−0.130960	+	0.0896297i
$575$	3.79891	−	6.57990i	0.158425	−	0.274401i
$576$		0			0
$577$	−1.05080	+	1.82003i	−0.0437453	+	0.0757690i	−0.887069	−	0.461637i	$-0.847262\pi$
$577$	−1.05080	+	1.82003i	−0.0437453	+	0.0757690i	0.843324	+	0.537406i	$0.180596\pi$
$578$	0.925785	−	5.25039i	0.0385076	−	0.218387i
$579$		0			0
$580$	−4.44680	−	25.2191i	−0.184644	−	1.04717i
$581$	−8.16297	+	11.3969i	−0.338657	+	0.472823i
$582$		0			0
$583$	19.7377	−	7.18392i	0.817450	−	0.297528i
$584$	4.99713	−	8.65529i	0.206783	−	0.358158i
$585$		0			0
$586$	−0.309645	−	0.536321i	−0.0127913	−	0.0221552i
$587$	−11.2216	+	4.08433i	−0.463165	+	0.168578i	−0.563054	−	0.826420i	$-0.690374\pi$
$587$	−11.2216	+	4.08433i	−0.463165	+	0.168578i	0.0998888	+	0.994999i	$0.468151\pi$
$588$		0			0
$589$	4.77796	−	4.00918i	0.196872	−	0.165195i
$590$	5.59691	−	4.69637i	0.230421	−	0.193346i
$591$		0			0
$592$	−1.13742	+	0.413988i	−0.0467477	+	0.0170148i
$593$	−13.9411	+	24.1467i	−0.572493	+	0.991587i	0.423816	+	0.905748i	$0.360690\pi$
$593$	−13.9411	+	24.1467i	−0.572493	+	0.991587i	−0.996309	+	0.0858390i	$0.972643\pi$
$594$		0			0
$595$	15.0445	+	15.3693i	0.616763	+	0.630081i
$596$	−4.56260	+	25.8758i	−0.186891	+	1.05991i
$597$		0			0
$598$	−1.52794	−	8.66538i	−0.0624821	−	0.354354i
$599$	−5.38142	−	1.95868i	−0.219879	−	0.0800294i	0.229732	−	0.973254i	$-0.426215\pi$
$599$	−5.38142	−	1.95868i	−0.219879	−	0.0800294i	−0.449611	+	0.893225i	$0.648437\pi$
$600$		0			0
$601$	−10.6243	+	3.86694i	−0.433375	+	0.157736i	−0.549490	−	0.835500i	$-0.685178\pi$
$601$	−10.6243	+	3.86694i	−0.433375	+	0.157736i	0.116115	+	0.993236i	$0.462956\pi$
$602$	−2.20227	+	7.88131i	−0.0897580	+	0.321218i
$603$		0			0
$604$	−16.9108			−0.688091
$605$	−1.66249	+	9.42844i	−0.0675897	+	0.383320i
$606$		0			0
$607$	−35.9408	−	13.0814i	−1.45879	−	0.530957i	−0.513761	−	0.857933i	$-0.671748\pi$
$607$	−35.9408	−	13.0814i	−1.45879	−	0.530957i	−0.945033	+	0.326976i	$0.893970\pi$
$608$	2.00218	+	11.3549i	0.0811992	+	0.460504i
$609$		0			0
$610$	3.20772	+	2.69160i	0.129877	+	0.108980i
$611$	41.8638			1.69363
$612$		0			0
$613$	19.2932			0.779243			0.389622	−	0.920975i	$-0.372606\pi$
$613$	19.2932			0.779243			0.389622	+	0.920975i	$0.372606\pi$
$614$	1.16510	−	6.60758i	0.0470194	−	0.266660i
$615$		0			0
$616$	4.36299	+	9.62349i	0.175790	+	0.387742i
$617$	22.5923	+	8.22291i	0.909531	+	0.331042i	0.754065	−	0.656799i	$-0.228090\pi$
$617$	22.5923	+	8.22291i	0.909531	+	0.331042i	0.155465	+	0.987841i	$0.450312\pi$
$618$		0			0
$619$	−34.8954	+	12.7009i	−1.40257	+	0.510492i	−0.928939	−	0.370233i	$-0.879278\pi$
$619$	−34.8954	+	12.7009i	−1.40257	+	0.510492i	−0.473627	+	0.880725i	$0.657056\pi$
$620$	3.62192	+	6.27336i	0.145460	+	0.251944i
$621$		0			0
$622$	11.5328			0.462424
$623$	−3.63850	−	47.4158i	−0.145773	−	1.89967i
$624$		0			0
$625$	−3.71656	+	3.11857i	−0.148663	+	0.124743i
$626$	−5.16853	−	1.88119i	−0.206576	−	0.0751876i
$627$		0			0
$628$	−2.85639	+	16.1994i	−0.113982	+	0.646427i
$629$	−1.21259	+	2.10027i	−0.0483492	+	0.0837433i
$630$		0			0
$631$	20.4388	+	35.4011i	0.813656	+	1.40929i	0.910289	+	0.413974i	$0.135859\pi$
$631$	20.4388	+	35.4011i	0.813656	+	1.40929i	−0.0966327	+	0.995320i	$0.530807\pi$
$632$	−5.49796	+	2.00109i	−0.218697	+	0.0795992i
$633$		0			0
$634$	3.38738	−	2.84235i	0.134530	−	0.112884i
$635$	4.23093	+	1.53993i	0.167899	+	0.0611104i
$636$		0			0
$637$	29.0111	−	33.1112i	1.14946	−	1.31191i
$638$	−5.01095	−	8.67921i	−0.198385	−	0.343613i
$639$		0			0
$640$	−17.3328			−0.685138
$641$	−10.1753	−	8.53811i	−0.401901	−	0.337235i	0.419327	−	0.907835i	$-0.362266\pi$
$641$	−10.1753	−	8.53811i	−0.401901	−	0.337235i	−0.821228	+	0.570600i	$0.806711\pi$
$642$		0			0
$643$	10.9753	−	9.20939i	0.432825	−	0.363183i	−0.400192	−	0.916431i	$-0.631056\pi$
$643$	10.9753	−	9.20939i	0.432825	−	0.363183i	0.833016	+	0.553248i	$0.186612\pi$
$644$	5.55058	+	12.2430i	0.218723	+	0.482441i
$645$		0			0
$646$	4.59455	+	3.85528i	0.180770	+	0.151684i
$647$	2.12844	+	3.68657i	0.0836777	+	0.144934i	0.904827	−	0.425779i	$-0.140000\pi$
$647$	2.12844	+	3.68657i	0.0836777	+	0.144934i	−0.821149	+	0.570713i	$0.806667\pi$
$648$		0			0
$649$	−10.6874	+	18.5112i	−0.419519	+	0.726628i
$650$	1.39941	−	7.93646i	0.0548895	−	0.311294i
$651$		0			0
$652$	27.1427	+	9.87913i	1.06299	+	0.386897i
$653$	2.07085	+	11.7444i	0.0810385	+	0.459592i	0.998141	+	0.0609415i	$0.0194103\pi$
$653$	2.07085	+	11.7444i	0.0810385	+	0.459592i	−0.917103	+	0.398651i	$0.869479\pi$
$654$		0			0
$655$	5.36567	+	4.50233i	0.209654	+	0.175921i
$656$	3.90464	+	6.76303i	0.152451	+	0.264052i
$657$		0			0
$658$	8.28711	−	2.12593i	0.323065	−	0.0828772i
$659$	−23.1573	−	19.4313i	−0.902082	−	0.756936i	0.0685145	−	0.997650i	$-0.478174\pi$
$659$	−23.1573	−	19.4313i	−0.902082	−	0.756936i	−0.970596	+	0.240714i	$0.922619\pi$
$660$		0			0
$661$	38.4579	−	32.2700i	1.49584	−	1.25516i	0.608919	−	0.793233i	$-0.291604\pi$
$661$	38.4579	−	32.2700i	1.49584	−	1.25516i	0.886919	−	0.461924i	$-0.152841\pi$
$662$	0.524531	−	0.440134i	0.0203865	−	0.0171063i
$663$		0			0
$664$	−7.42160	−	6.22746i	−0.288014	−	0.241672i
$665$	−9.19443	+	2.35868i	−0.356545	+	0.0914658i
$666$		0			0
$667$	−13.6026	−	23.5604i	−0.526694	−	0.912262i
$668$	0.928589	+	0.779179i	0.0359282	+	0.0301473i
$669$		0			0
$670$	1.17521	+	6.66496i	0.0454024	+	0.257490i
$671$	−11.5117	−	4.18991i	−0.444403	−	0.161750i
$672$		0			0
$673$	−6.51850	+	36.9682i	−0.251270	+	1.42502i	0.554200	+	0.832384i	$0.313024\pi$
$673$	−6.51850	+	36.9682i	−0.251270	+	1.42502i	−0.805470	+	0.592637i	$0.798087\pi$
$674$	6.55834	−	11.3594i	0.252618	−	0.437547i
$675$		0			0
$676$	23.4182	+	40.5615i	0.900700	+	1.56006i
$677$	11.8071	+	9.90735i	0.453785	+	0.380771i	0.840838	−	0.541287i	$-0.182063\pi$
$677$	11.8071	+	9.90735i	0.453785	+	0.380771i	−0.387053	+	0.922057i	$0.626507\pi$
$678$		0			0
$679$	−15.1951	−	33.5160i	−0.583134	−	1.28623i
$680$	−11.3860	+	9.55399i	−0.436633	+	0.366379i
$681$		0			0
$682$	2.17168	+	1.82225i	0.0831578	+	0.0697777i
$683$	−11.0380			−0.422357			−0.211178	−	0.977448i	$-0.567730\pi$
$683$	−11.0380			−0.422357			−0.211178	+	0.977448i	$0.567730\pi$
$684$		0			0
$685$	−3.69536	−	6.40054i	−0.141192	−	0.244552i
$686$	4.06141	−	8.02774i	0.155065	−	0.306500i
$687$		0			0
$688$	15.7944	+	5.74870i	0.602157	+	0.219167i
$689$	46.3290	−	38.8746i	1.76499	−	1.48101i
$690$		0			0
$691$	−41.3237	+	15.0406i	−1.57203	+	0.572172i	−0.973452	−	0.228893i	$-0.926489\pi$
$691$	−41.3237	+	15.0406i	−1.57203	+	0.572172i	−0.598577	+	0.801065i	$0.704267\pi$
$692$	−7.28568	−	12.6192i	−0.276960	−	0.479709i
$693$		0			0
$694$	−1.59236	+	2.75804i	−0.0604451	+	0.104694i
$695$	0.809496	−	4.59088i	0.0307059	−	0.174142i
$696$		0			0
$697$	14.7030	+	5.35145i	0.556916	+	0.202701i
$698$	−2.91348	+	2.44470i	−0.110277	+	0.0925332i
$699$		0			0
$700$	0.941980	+	12.2756i	0.0356035	+	0.463974i
$701$	38.0205			1.43601			0.718007	−	0.696036i	$-0.245055\pi$
$701$	38.0205			1.43601			0.718007	+	0.696036i	$0.245055\pi$
$702$		0			0
$703$	−0.535179	−	0.926957i	−0.0201847	−	0.0349609i
$704$	5.91169	−	2.15168i	0.222805	−	0.0810944i
$705$		0			0
$706$	−14.6925	−	5.34762i	−0.552958	−	0.201260i
$707$	−15.8950	−	35.0599i	−0.597795	−	1.31856i
$708$		0			0
$709$	7.05221	−	39.9951i	0.264851	−	1.50205i	−0.504607	−	0.863349i	$-0.668363\pi$
$709$	7.05221	−	39.9951i	0.264851	−	1.50205i	0.769458	−	0.638697i	$-0.220526\pi$
$710$	−2.12498			−0.0797492
$711$		0			0
$712$	32.8651			1.23167
$713$	5.89518	+	4.94664i	0.220776	+	0.185253i
$714$		0			0
$715$	−3.66592	−	20.7905i	−0.137098	−	0.777520i
$716$	−39.7656	−	14.4735i	−1.48611	−	0.540900i
$717$		0			0
$718$	−1.28630	+	7.29497i	−0.0480043	+	0.272246i
$719$	−3.58576			−0.133726			−0.0668631	−	0.997762i	$-0.521299\pi$
$719$	−3.58576			−0.133726			−0.0668631	+	0.997762i	$0.521299\pi$
$720$		0			0
$721$	−1.15685	+	4.14005i	−0.0430834	+	0.154183i
$722$	6.18560	−	2.25137i	0.230204	−	0.0837874i
$723$		0			0
$724$	−3.77412	−	1.37367i	−0.140264	−	0.0510519i
$725$	−4.32675	−	24.5382i	−0.160691	−	0.911326i
$726$		0			0
$727$	1.66588	−	9.44768i	0.0617841	−	0.350395i	−0.938207	−	0.346076i	$-0.887514\pi$
$727$	1.66588	−	9.44768i	0.0617841	−	0.350395i	0.999991	−	0.00431931i	$-0.00137488\pi$
$728$	21.2819	+	21.7414i	0.788758	+	0.805790i
$729$		0			0
$730$	−2.04040	+	3.53407i	−0.0755185	+	0.130802i
$731$	31.6456	−	11.5180i	1.17045	−	0.426010i
$732$		0			0
$733$	−25.8318	+	21.6755i	−0.954119	+	0.800601i	−0.979986	−	0.199064i	$-0.936210\pi$
$733$	−25.8318	+	21.6755i	−0.954119	+	0.800601i	0.0258671	+	0.999665i	$0.491765\pi$
$734$	−4.60686	+	3.86562i	−0.170042	+	0.142683i
$735$		0			0
$736$	−13.3682	+	4.86564i	−0.492760	+	0.179350i
$737$	−9.89978	−	17.1469i	−0.364663	−	0.631615i
$738$		0			0
$739$	5.05405	−	8.75387i	0.185916	−	0.322016i	−0.757969	−	0.652291i	$-0.773808\pi$
$739$	5.05405	−	8.75387i	0.185916	−	0.322016i	0.943885	+	0.330275i	$0.107141\pi$
$740$	1.16814	−	0.425169i	0.0429418	−	0.0156295i
$741$		0			0
$742$	7.19688	−	10.0481i	0.264206	−	0.368876i
$743$	−0.817980	−	4.63899i	−0.0300088	−	0.170188i	0.966120	−	0.258093i	$-0.0830940\pi$
$743$	−0.817980	−	4.63899i	−0.0300088	−	0.170188i	−0.996129	+	0.0879046i	$0.971983\pi$
$744$		0			0
$745$	3.97515	−	22.5442i	0.145638	−	0.825956i
$746$	−5.67917	+	9.83661i	−0.207929	+	0.360144i
$747$		0			0
$748$	10.1894	−	17.6486i	0.372562	−	0.645296i
$749$	22.0979	−	15.1240i	0.807441	−	0.552619i
$750$		0			0
$751$	2.54023	+	14.4063i	0.0926942	+	0.525695i	0.995430	+	0.0954987i	$0.0304446\pi$
$751$	2.54023	+	14.4063i	0.0926942	+	0.525695i	−0.902735	+	0.430196i	$0.858444\pi$
$752$	−3.05146	−	17.3057i	−0.111275	−	0.631073i
$753$		0			0
$754$	−22.1051	−	18.5484i	−0.805021	−	0.675493i
$755$	14.7335			0.536207
$756$		0			0
$757$	50.4233			1.83266			0.916332	−	0.400419i	$-0.131135\pi$
$757$	50.4233			1.83266			0.916332	+	0.400419i	$0.131135\pi$
$758$	0.0229405	+	0.0192494i	0.000833236	+	0.000699168i
$759$		0			0
$760$	−1.13913	−	6.46031i	−0.0413204	−	0.234340i
$761$	−8.56094	−	48.5515i	−0.310334	−	1.75999i	−0.597269	−	0.802041i	$-0.703747\pi$
$761$	−8.56094	−	48.5515i	−0.310334	−	1.75999i	0.286935	−	0.957950i	$-0.407364\pi$
$762$		0			0
$763$	0.999519	+	13.0254i	0.0361850	+	0.471552i
$764$	−15.8567	+	27.4646i	−0.573675	+	0.993634i
$765$		0			0
$766$	−0.389702	+	0.674983i	−0.0140805	+	0.0243881i
$767$	−10.6872	+	60.6100i	−0.385892	+	2.18850i
$768$		0			0
$769$	5.95324	+	33.7625i	0.214679	+	1.21751i	0.881462	+	0.472255i	$0.156560\pi$
$769$	5.95324	+	33.7625i	0.214679	+	1.21751i	−0.666783	+	0.745252i	$0.732329\pi$
$770$	−1.78147	−	3.92940i	−0.0641996	−	0.141606i
$771$		0			0
$772$	−0.155929	+	0.0567534i	−0.00561200	+	0.00204260i
$773$	7.66073	−	13.2688i	0.275537	−	0.477245i	−0.694733	−	0.719267i	$-0.744478\pi$
$773$	7.66073	−	13.2688i	0.275537	−	0.477245i	0.970271	+	0.242023i	$0.0778109\pi$
$774$		0			0
$775$	3.52414	+	6.10398i	0.126591	+	0.219262i
$776$	23.8983	−	8.69825i	0.857897	−	0.312249i
$777$		0			0
$778$	5.15707	−	4.32730i	0.184890	−	0.155141i
$779$	−5.29003	+	4.43886i	−0.189535	+	0.159039i
$780$		0			0
$781$	5.84185	−	2.12626i	0.209038	−	0.0760836i
$782$	−3.70010	+	6.40876i	−0.132315	+	0.229177i
$783$		0			0
$784$	−15.8021	−	9.57912i	−0.564362	−	0.342111i
$785$	2.48862	−	14.1137i	0.0888228	−	0.503739i
$786$		0			0
$787$	−0.589959	−	3.34583i	−0.0210298	−	0.119266i	0.972486	−	0.232962i	$-0.0748419\pi$
$787$	−0.589959	−	3.34583i	−0.0210298	−	0.119266i	−0.993516	+	0.113697i	$0.963731\pi$
$788$	−40.1634	−	14.6183i	−1.43076	−	0.520755i
$789$		0			0
$790$	2.24489	−	0.817073i	0.0798696	−	0.0290701i
$791$	12.5634	−	3.22293i	0.446702	−	0.114594i
$792$		0			0
$793$	−35.2729			−1.25258
$794$	−0.513274	+	2.91092i	−0.0182154	+	0.103305i
$795$		0			0
$796$	−18.9368	−	6.89244i	−0.671198	−	0.244296i
$797$	2.86495	+	16.2480i	0.101482	+	0.575532i	0.992567	+	0.121697i	$0.0388335\pi$
$797$	2.86495	+	16.2480i	0.101482	+	0.575532i	−0.891086	+	0.453835i	$0.850055\pi$
$798$		0			0
$799$	−26.9712	−	22.6315i	−0.954172	−	0.800645i
$800$	−13.0295			−0.460663
$801$		0			0
$802$	−11.4056			−0.402746
$803$	2.07312	−	11.7572i	0.0731588	−	0.414904i
$804$		0			0
$805$	−4.83592	−	10.6667i	−0.170444	−	0.375950i
$806$	7.67037	+	2.79178i	0.270177	+	0.0983364i
$807$		0			0
$808$	24.9991	−	9.09893i	0.879466	−	0.320099i
$809$	−10.8360	−	18.7686i	−0.380975	−	0.659868i	0.610227	−	0.792227i	$-0.291078\pi$
$809$	−10.8360	−	18.7686i	−0.380975	−	0.659868i	−0.991202	+	0.132359i	$0.957745\pi$
$810$		0			0
$811$	−23.1731			−0.813716			−0.406858	−	0.913491i	$-0.633376\pi$
$811$	−23.1731			−0.813716			−0.406858	+	0.913491i	$0.633376\pi$
$812$	39.7524	+	19.0564i	1.39504	+	0.668747i
$813$		0			0
$814$	0.372680	−	0.312716i	0.0130624	−	0.0109607i
$815$	−23.6480	−	8.60717i	−0.828353	−	0.301496i
$816$		0			0
$817$	−2.58096	+	14.6374i	−0.0902964	+	0.512096i
$818$	0.441177	−	0.764142i	0.0154254	−	0.0267176i
$819$		0			0
$820$	−4.01010	−	6.94570i	−0.140039	−	0.242554i
$821$	−23.1015	+	8.40827i	−0.806249	+	0.293451i	−0.712074	−	0.702105i	$-0.752244\pi$
$821$	−23.1015	+	8.40827i	−0.806249	+	0.293451i	−0.0941758	+	0.995556i	$0.530022\pi$
$822$		0			0
$823$	16.8351	−	14.1263i	0.586835	−	0.492413i	−0.300349	−	0.953829i	$-0.597103\pi$
$823$	16.8351	−	14.1263i	0.586835	−	0.492413i	0.887184	+	0.461417i	$0.152659\pi$
$824$	−2.79160	−	1.01606i	−0.0972501	−	0.0353961i
$825$		0			0
$826$	0.962324	+	12.5407i	0.0334835	+	0.436348i
$827$	18.1708	+	31.4727i	0.631860	+	1.09441i	0.987171	+	0.159666i	$0.0510416\pi$
$827$	18.1708	+	31.4727i	0.631860	+	1.09441i	−0.355311	+	0.934748i	$0.615625\pi$
$828$		0			0
$829$	38.8890			1.35067			0.675336	−	0.737510i	$-0.263999\pi$
$829$	38.8890			1.35067			0.675336	+	0.737510i	$0.263999\pi$
$830$	3.03034	+	2.54276i	0.105185	+	0.0882604i
$831$		0			0
$832$	13.8761	−	11.6435i	0.481068	−	0.403664i
$833$	−36.5905	+	5.64888i	−1.26779	+	0.195722i
$834$		0			0
$835$	−0.809031	−	0.678857i	−0.0279977	−	0.0234928i
$836$	4.49711	+	7.78922i	0.155536	+	0.269396i
$837$		0			0
$838$	0.423874	−	0.734172i	0.0146425	−	0.0253615i
$839$	1.84595	−	10.4689i	0.0637293	−	0.361427i	−0.936221	−	0.351413i	$-0.885701\pi$
$839$	1.84595	−	10.4689i	0.0637293	−	0.361427i	0.999950	−	0.0100140i	$-0.00318760\pi$
$840$		0			0
$841$	−56.5868	−	20.5959i	−1.95127	−	0.710204i
$842$	1.19470	+	6.77550i	0.0411722	+	0.233499i
$843$		0			0
$844$	−33.1863	−	27.8466i	−1.14232	−	0.958520i
$845$	−20.4030	−	35.3391i	−0.701886	−	1.21570i
$846$		0			0
$847$	−11.5289	−	11.7778i	−0.396138	−	0.404691i
$848$	−19.4469	−	16.3179i	−0.667810	−	0.560359i
$849$		0			0
$850$	−5.19203	+	4.35663i	−0.178085	+	0.149431i
$851$	1.01167	−	0.848890i	0.0346795	−	0.0290996i
$852$		0			0
$853$	23.3312	+	19.5772i	0.798847	+	0.670312i	0.947918	−	0.318515i	$-0.103184\pi$
$853$	23.3312	+	19.5772i	0.798847	+	0.670312i	−0.149071	+	0.988826i	$0.547628\pi$
$854$	−6.98242	+	1.79123i	−0.238934	+	0.0612946i
$855$		0			0
$856$	9.25301	+	16.0267i	0.316261	+	0.547781i
$857$	24.9976	+	20.9755i	0.853902	+	0.716509i	0.960645	−	0.277778i	$-0.0895979\pi$
$857$	24.9976	+	20.9755i	0.853902	+	0.716509i	−0.106743	+	0.994287i	$0.534042\pi$
$858$		0			0
$859$	−4.11077	−	23.3133i	−0.140258	−	0.795441i	−0.971053	−	0.238863i	$-0.923225\pi$
$859$	−4.11077	−	23.3133i	−0.140258	−	0.795441i	0.830795	−	0.556578i	$-0.187886\pi$
$860$	−16.2210	−	5.90397i	−0.553132	−	0.201324i
$861$		0			0
$862$	0.950426	−	5.39013i	0.0323716	−	0.183589i
$863$	−12.7899	+	22.1527i	−0.435372	+	0.754087i	−0.997326	−	0.0730817i	$-0.976717\pi$
$863$	−12.7899	+	22.1527i	−0.435372	+	0.754087i	0.561954	+	0.827169i	$0.310050\pi$
$864$		0			0
$865$	6.34763	+	10.9944i	0.215826	+	0.373821i
$866$	4.27269	+	3.58521i	0.145192	+	0.121830i
$867$		0			0
$868$	−12.4104	−	1.21946i	−0.421236	−	0.0413913i
$869$	−5.35393	+	4.49248i	−0.181620	+	0.152397i
$870$		0			0
$871$	−43.6715	−	36.6448i	−1.47975	−	1.24166i
$872$	−9.02826			−0.305736
$873$		0			0
$874$	−1.63304	−	2.82851i	−0.0552385	−	0.0956759i
$875$	−2.37626	−	30.9668i	−0.0803324	−	1.04687i
$876$		0			0
$877$	−12.2919	−	4.47389i	−0.415069	−	0.151073i	0.126040	−	0.992025i	$-0.459773\pi$
$877$	−12.2919	−	4.47389i	−0.415069	−	0.151073i	−0.541109	+	0.840952i	$0.681995\pi$
$878$	6.41276	−	5.38095i	0.216420	−	0.181598i
$879$		0			0
$880$	−8.32716	+	3.03084i	−0.280709	+	0.102170i
$881$	10.1622	+	17.6014i	0.342373	+	0.593007i	0.984873	−	0.173279i	$-0.0554362\pi$
$881$	10.1622	+	17.6014i	0.342373	+	0.593007i	−0.642500	+	0.766285i	$0.722103\pi$
$882$		0			0
$883$	−11.6233	+	20.1321i	−0.391155	+	0.677500i	−0.992602	−	0.121412i	$-0.961258\pi$
$883$	−11.6233	+	20.1321i	−0.391155	+	0.677500i	0.601447	+	0.798913i	$0.294591\pi$
$884$	10.1892	−	57.7856i	0.342698	−	1.94354i
$885$		0			0
$886$	16.3922	+	5.96626i	0.550705	+	0.200440i
$887$	15.0975	−	12.6683i	0.506926	−	0.425361i	−0.353120	−	0.935578i	$-0.614879\pi$
$887$	15.0975	−	12.6683i	0.506926	−	0.425361i	0.860046	+	0.510217i	$0.170435\pi$
$888$		0			0
$889$	−6.39630	+	4.37768i	−0.214525	+	0.146823i
$890$	−13.4193			−0.449814
$891$		0			0
$892$	−13.8305	−	23.9551i	−0.463078	−	0.802075i
$893$	14.6021	−	5.31474i	0.488642	−	0.177851i
$894$		0			0
$895$	34.6457	+	12.6100i	1.15808	+	0.421505i
$896$	17.3745	−	24.2577i	0.580441	−	0.810394i
$897$		0			0
$898$	1.36909	−	7.76451i	0.0456872	−	0.259105i
$899$	25.2375			0.841717
$900$		0			0
$901$	−50.8635			−1.69451
$902$	−2.40443	−	2.01755i	−0.0800586	−	0.0671771i
$903$		0			0
$904$	1.55652	+	8.82744i	0.0517689	+	0.293596i
$905$	3.28819	+	1.19680i	0.109303	+	0.0397831i
$906$		0			0
$907$	−2.27886	+	12.9240i	−0.0756682	+	0.429136i	0.923315	+	0.384044i	$0.125469\pi$
$907$	−2.27886	+	12.9240i	−0.0756682	+	0.429136i	−0.998983	+	0.0450915i	$0.985642\pi$
$908$	−4.28414			−0.142174
$909$		0			0
$910$	−8.68967	−	8.87730i	−0.288060	−	0.294280i
$911$	−13.1943	+	4.80232i	−0.437145	+	0.159108i	−0.551212	−	0.834365i	$-0.685834\pi$
$911$	−13.1943	+	4.80232i	−0.437145	+	0.159108i	0.114067	+	0.993473i	$0.463612\pi$
$912$		0			0
$913$	−10.8751	−	3.95821i	−0.359913	−	0.130998i
$914$	1.51724	+	8.60470i	0.0501859	+	0.284618i
$915$		0			0
$916$	0.216964	−	1.23046i	0.00716870	−	0.0406557i
$917$	−11.6797	+	2.99625i	−0.385699	+	0.0989448i
$918$		0			0
$919$	−23.0349	+	39.8977i	−0.759852	+	1.31610i	0.183074	+	0.983099i	$0.441395\pi$
$919$	−23.0349	+	39.8977i	−0.759852	+	1.31610i	−0.942926	+	0.333003i	$0.891938\pi$
$920$	7.60575	−	2.76827i	0.250754	−	0.0912671i
$921$		0			0
$922$	−13.7142	+	11.5076i	−0.451652	+	0.378981i
$923$	13.7122	−	11.5059i	0.451343	−	0.378722i
$924$		0			0
$925$	1.13660	−	0.413690i	0.0373713	−	0.0136020i
$926$	8.09280	+	14.0171i	0.265946	+	0.460632i
$927$		0			0
$928$	−23.3271	+	40.4038i	−0.765750	+	1.32632i
$929$	−19.2621	+	7.01083i	−0.631969	+	0.230018i	−0.638088	−	0.769963i	$-0.720274\pi$
$929$	−19.2621	+	7.01083i	−0.631969	+	0.230018i	0.00611906	+	0.999981i	$0.498052\pi$
$930$		0			0
$931$	5.91551	−	15.2323i	0.193873	−	0.499217i
$932$	−0.0727839	−	0.412778i	−0.00238412	−	0.0135210i
$933$		0			0
$934$	2.21610	−	12.5681i	0.0725128	−	0.411241i
$935$	−8.87750	+	15.3763i	−0.290325	+	0.502858i
$936$		0			0
$937$	23.3013	−	40.3591i	0.761222	−	1.31847i	−0.180999	−	0.983483i	$-0.557933\pi$
$937$	23.3013	−	40.3591i	0.761222	−	1.31847i	0.942221	−	0.334992i	$-0.108733\pi$
$938$	−10.5059	−	5.03626i	−0.343028	−	0.164440i
$939$		0			0
$940$	3.13387	+	17.7731i	0.102216	+	0.579694i
$941$	2.75204	+	15.6076i	0.0897140	+	0.508794i	0.996239	+	0.0866424i	$0.0276137\pi$
$941$	2.75204	+	15.6076i	0.0897140	+	0.508794i	−0.906525	+	0.422151i	$0.861275\pi$
$942$		0			0
$943$	−6.52699	−	5.47680i	−0.212548	−	0.178349i
$944$	25.8340			0.840824
$945$		0			0
$946$	−6.75561			−0.219644
$947$	11.8757	+	9.96486i	0.385907	+	0.323814i	0.815016	−	0.579438i	$-0.196728\pi$
$947$	11.8757	+	9.96486i	0.385907	+	0.323814i	−0.429109	+	0.903253i	$0.641172\pi$
$948$		0			0
$949$	−5.96916	−	33.8528i	−0.193767	−	1.09891i
$950$	−0.519442	−	2.94590i	−0.0168529	−	0.0955777i
$951$		0			0
$952$	−1.95769	−	25.5121i	−0.0634492	−	0.826851i
$953$	7.02346	−	12.1650i	0.227512	−	0.394062i	−0.729558	−	0.683919i	$-0.760274\pi$
$953$	7.02346	−	12.1650i	0.227512	−	0.394062i	0.957070	+	0.289856i	$0.0936076\pi$
$954$		0			0
$955$	13.8151	−	23.9284i	0.447046	−	0.774306i
$956$	0.636624	−	3.61048i	0.0205899	−	0.116771i
$957$		0			0
$958$	−0.649601	−	3.68407i	−0.0209877	−	0.119027i
$959$	12.6620	+	1.24419i	0.408878	+	0.0401769i
$960$		0			0
$961$	22.4220	−	8.16094i	0.723290	−	0.263256i
$962$	0.700392	−	1.21311i	0.0225815	−	0.0391124i
$963$		0			0
$964$	−15.2397	−	26.3959i	−0.490837	−	0.850155i
$965$	0.135853	−	0.0494463i	0.00437325	−	0.00159173i
$966$		0			0
$967$	32.5537	−	27.3158i	1.04686	−	0.878417i	0.0540975	−	0.998536i	$-0.482772\pi$
$967$	32.5537	−	27.3158i	1.04686	−	0.878417i	0.992760	+	0.120118i	$0.0383274\pi$
$968$	8.72534	−	7.32143i	0.280443	−	0.235320i
$969$		0			0
$970$	−9.75798	+	3.55161i	−0.313310	+	0.114035i
$971$	6.82904	−	11.8282i	0.219154	−	0.379586i	−0.735395	−	0.677638i	$-0.763004\pi$
$971$	6.82904	−	11.8282i	0.219154	−	0.379586i	0.954550	+	0.298052i	$0.0963369\pi$
$972$		0			0
$973$	5.61364	+	5.73485i	0.179965	+	0.183851i
$974$	2.37214	−	13.4531i	0.0760081	−	0.431064i
$975$		0			0
$976$	2.57105	+	14.5811i	0.0822972	+	0.466731i
$977$	22.4103	+	8.15667i	0.716968	+	0.260955i	0.674638	−	0.738149i	$-0.264300\pi$
$977$	22.4103	+	8.15667i	0.716968	+	0.260955i	0.0423301	+	0.999104i	$0.486522\pi$
$978$		0			0
$979$	36.8913	−	13.4273i	1.17905	−	0.429139i
$980$	16.2289	+	9.83785i	0.518414	+	0.314259i
$981$		0			0
$982$	−18.9219			−0.603822
$983$	0.830161	−	4.70808i	0.0264780	−	0.150164i	−0.968702	−	0.248225i	$-0.920153\pi$
$983$	0.830161	−	4.70808i	0.0264780	−	0.150164i	0.995180	+	0.0980606i	$0.0312639\pi$
$984$		0			0
$985$	34.9923	+	12.7361i	1.11495	+	0.405807i
$986$	4.21421	+	23.9000i	0.134208	+	0.761131i
$987$		0			0
$988$	19.8384	+	16.6464i	0.631143	+	0.529592i
$989$	−18.3386			−0.583133
$990$		0			0
$991$	9.05897			0.287768			0.143884	−	0.989595i	$-0.454041\pi$
$991$	9.05897			0.287768			0.143884	+	0.989595i	$0.454041\pi$
$992$	2.29167	−	12.9967i	0.0727607	−	0.412647i
$993$		0			0
$994$	2.13010	−	2.97398i	0.0675626	−	0.0943289i
$995$	16.4987	+	6.00502i	0.523043	+	0.190372i
$996$		0			0
$997$	−1.84870	+	0.672873i	−0.0585490	+	0.0213101i	−0.371129	−	0.928581i	$-0.621029\pi$
$997$	−1.84870	+	0.672873i	−0.0585490	+	0.0213101i	0.312580	+	0.949892i	$0.398807\pi$
$998$	3.60432	+	6.24286i	0.114093	+	0.197614i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.u.a.478.13		132
3.2	odd	2		189.2.u.a.79.10	yes	132
7.4	even	3		567.2.w.a.235.10		132
21.11	odd	6		189.2.w.a.25.13	yes	132
27.13	even	9		567.2.w.a.415.10		132
27.14	odd	18		189.2.w.a.121.13	yes	132
189.67	even	9	inner	567.2.u.a.172.13		132
189.95	odd	18		189.2.u.a.67.10	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.67.10	✓	132	189.95	odd	18
189.2.u.a.79.10	yes	132	3.2	odd	2
189.2.w.a.25.13	yes	132	21.11	odd	6
189.2.w.a.121.13	yes	132	27.14	odd	18
567.2.u.a.172.13		132	189.67	even	9	inner
567.2.u.a.478.13		132	1.1	even	1	trivial
567.2.w.a.235.10		132	7.4	even	3
567.2.w.a.415.10		132	27.13	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)

\(f(q)\)	\(=\)	\(q+(0.372124 + 0.312249i) q^{2} +(-0.306320 - 1.73722i) q^{4} +(0.266880 + 1.51355i) q^{5} +(-2.38579 - 1.14369i) q^{7} +(0.914231 - 1.58349i) q^{8} +O(q^{10})\)	\(q+(0.372124 + 0.312249i) q^{2} +(-0.306320 - 1.73722i) q^{4} +(0.266880 + 1.51355i) q^{5} +(-2.38579 - 1.14369i) q^{7} +(0.914231 - 1.58349i) q^{8} +(-0.373293 + 0.646562i) q^{10} +(0.379279 - 2.15100i) q^{11} +(-1.09206 - 6.19341i) q^{13} +(-0.530692 - 1.17055i) q^{14} +(-2.48063 + 0.902875i) q^{16} +(-2.64457 + 4.58053i) q^{17} +(-1.16718 - 2.02162i) q^{19} +(2.54763 - 0.927262i) q^{20} +(0.812787 - 0.682009i) q^{22} +(2.20637 - 1.85136i) q^{23} +(2.47885 - 0.902227i) q^{25} +(1.52750 - 2.64571i) q^{26} +(-1.25603 + 4.49498i) q^{28} +(1.64020 - 9.30205i) q^{29} +(0.463969 + 2.63130i) q^{31} +(-4.64141 - 1.68933i) q^{32} +(-2.41438 + 0.878761i) q^{34} +(1.09431 - 3.91624i) q^{35} +0.458521 q^{37} +(0.196913 - 1.11675i) q^{38} +(2.64069 + 0.961133i) q^{40} +(-0.513695 - 2.91331i) q^{41} +(-4.87748 - 4.09269i) q^{43} -3.85295 q^{44} +1.39913 q^{46} +(-1.15593 + 6.55559i) q^{47} +(4.38395 + 5.45720i) q^{49} +(1.20416 + 0.438277i) q^{50} +(-10.4248 + 3.79432i) q^{52} +(4.80829 + 8.32820i) q^{53} +3.35687 q^{55} +(-3.99219 + 2.73228i) q^{56} +(3.51491 - 2.94936i) q^{58} +(-9.19604 - 3.34708i) q^{59} +(0.973943 - 5.52351i) q^{61} +(-0.648966 + 1.12404i) q^{62} +(1.44015 + 2.49441i) q^{64} +(9.08259 - 3.30579i) q^{65} +(6.94417 - 5.82685i) q^{67} +(8.76750 + 3.19111i) q^{68} +(1.63006 - 1.11563i) q^{70} +(1.42313 + 2.46494i) q^{71} +5.46594 q^{73} +(0.170627 + 0.143173i) q^{74} +(-3.15448 + 2.64693i) q^{76} +(-3.36496 + 4.69805i) q^{77} +(-2.45123 - 2.05682i) q^{79} +(-2.02858 - 3.51360i) q^{80} +(0.718519 - 1.24451i) q^{82} +(0.920085 - 5.21806i) q^{83} +(-7.63866 - 2.78025i) q^{85} +(-0.537088 - 3.04598i) q^{86} +(-3.05935 - 2.56710i) q^{88} +(8.98709 + 15.5661i) q^{89} +(-4.47790 + 16.0251i) q^{91} +(-3.89209 - 3.26585i) q^{92} +(-2.47713 + 2.07856i) q^{94} +(2.74833 - 2.30613i) q^{95} +(10.6549 + 8.94050i) q^{97} +(-0.0726314 + 3.39964i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) 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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