LMFDB - Embedded newform 459.2.y.a.368.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,2,Mod(44,459)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([40, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("459.44"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	459.y (of order $48$, degree $16$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			368.14
Character	$\chi$	$=$	459.368
Dual form			459.2.y.a.116.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.19811 - 0.289387i) q^{2} +(2.81610 - 0.754572i) q^{4} +(0.864950 + 1.75395i) q^{5} +(0.161377 + 0.0795822i) q^{7} +(1.87511 - 0.776696i) q^{8} +(2.40883 + 3.60506i) q^{10} +(2.43861 - 0.827795i) q^{11} +(-0.292855 - 1.09295i) q^{13} +(0.377754 + 0.128230i) q^{14} +(-1.15275 + 0.665543i) q^{16} +(4.05247 + 0.759899i) q^{17} +(-5.72485 - 2.37131i) q^{19} +(3.75926 + 4.28662i) q^{20} +(5.12077 - 2.52529i) q^{22} +(-2.32784 + 2.65439i) q^{23} +(0.715622 - 0.932617i) q^{25} +(-0.960014 - 2.31768i) q^{26} +(0.514504 + 0.102341i) q^{28} +(0.409431 - 6.24671i) q^{29} +(-1.63425 + 4.81435i) q^{31} +(-5.56167 + 4.26762i) q^{32} +(9.12770 + 0.497610i) q^{34} +0.351881i q^{35} +(-1.71395 - 8.61661i) q^{37} +(-13.2701 - 3.55571i) q^{38} +(2.98416 + 2.61704i) q^{40} +(-7.19745 + 0.471746i) q^{41} +(1.48672 + 1.14080i) q^{43} +(6.24273 - 4.17126i) q^{44} +(-4.34870 + 6.50829i) q^{46} +(-0.219953 + 0.820877i) q^{47} +(-4.24162 - 5.52779i) q^{49} +(1.30313 - 2.25709i) q^{50} +(-1.64942 - 2.85688i) q^{52} +(-4.44864 + 10.7400i) q^{53} +(3.56118 + 3.56118i) q^{55} +(0.364411 + 0.0238847i) q^{56} +(-0.907741 - 13.8494i) q^{58} +(-0.412757 + 3.13520i) q^{59} +(4.80101 - 9.73548i) q^{61} +(-2.19906 + 11.0554i) q^{62} +(-9.10774 + 9.10774i) q^{64} +(1.66367 - 1.45900i) q^{65} +(-9.11090 - 5.26018i) q^{67} +(11.9856 - 0.917931i) q^{68} +(0.101830 + 0.773473i) q^{70} +(12.6361 - 2.51348i) q^{71} +(8.59520 + 5.74313i) q^{73} +(-6.26099 - 18.4443i) q^{74} +(-17.9111 - 2.35804i) q^{76} +(0.459412 + 0.0604827i) q^{77} +(2.06175 + 6.07373i) q^{79} +(-2.16440 - 1.44621i) q^{80} +(-15.6843 + 3.11980i) q^{82} +(1.21897 + 9.25898i) q^{83} +(2.17237 + 7.76509i) q^{85} +(3.59810 + 2.07737i) q^{86} +(3.92971 - 3.44626i) q^{88} +(-10.2745 + 10.2745i) q^{89} +(0.0397194 - 0.199683i) q^{91} +(-4.55250 + 9.23155i) q^{92} +(-0.245931 + 1.86803i) q^{94} +(-0.792561 - 12.0921i) q^{95} +(2.64284 + 0.173221i) q^{97} +(-10.9232 - 10.9232i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 24 q^{2} - 8 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 24 q^{11} - 8 q^{13} + 24 q^{14} - 32 q^{19} + 24 q^{20} - 8 q^{22} + 24 q^{23} - 8 q^{25} - 32 q^{28} + 24 q^{29} - 8 q^{31} + 24 q^{32} - 56 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) $ 256 * q + 24 * q^2 - 8 * q^4 + 24 * q^5 - 8 * q^7 - 32 * q^10 + 24 * q^11 - 8 * q^13 + 24 * q^14 - 32 * q^19 + 24 * q^20 - 8 * q^22 + 24 * q^23 - 8 * q^25 - 32 * q^28 + 24 * q^29 - 8 * q^31 + 24 * q^32 - 56 * q^34 - 32 * q^37 - 8 * q^40 + 24 * q^41 + 16 * q^43 - 32 * q^46 - 96 * q^47 - 8 * q^49 - 16 * q^52 - 32 * q^55 - 216 * q^56 - 8 * q^58 + 24 * q^59 - 8 * q^61 - 96 * q^64 - 24 * q^65 + 24 * q^68 + 8 * q^70 - 32 * q^73 + 24 * q^74 - 8 * q^76 + 24 * q^77 - 8 * q^79 + 160 * q^82 + 24 * q^83 - 8 * q^85 - 192 * q^86 - 8 * q^88 - 128 * q^91 + 24 * q^92 - 8 * q^94 - 216 * q^95 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{16}\right)$

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 $

$2$	2.19811	−	0.289387i	1.55430	−	0.204627i	0.696101	−	0.717944i	$-0.254917\pi$
$2$	2.19811	−	0.289387i	1.55430	−	0.204627i	0.858199	+	0.513317i	$0.171583\pi$
$3$		0			0
$3$		0			0
$4$	2.81610	−	0.754572i	1.40805	−	0.377286i
$5$	0.864950	+	1.75395i	0.386817	+	0.784388i	0.999985	−	0.00556511i	$-0.00177144\pi$
$5$	0.864950	+	1.75395i	0.386817	+	0.784388i	−0.613167	+	0.789953i	$0.710105\pi$
$6$		0			0
$7$	0.161377	+	0.0795822i	0.0609947	+	0.0300793i	0.472530	−	0.881314i	$-0.343341\pi$
$7$	0.161377	+	0.0795822i	0.0609947	+	0.0300793i	−0.411536	+	0.911394i	$0.635007\pi$
$8$	1.87511	−	0.776696i	0.662952	−	0.274604i
$9$		0			0
$10$	2.40883	+	3.60506i	0.761738	+	1.14002i
$11$	2.43861	−	0.827795i	0.735267	−	0.249590i	0.0714080	−	0.997447i	$-0.477251\pi$
$11$	2.43861	−	0.827795i	0.735267	−	0.249590i	0.663859	+	0.747858i	$0.268917\pi$
$12$		0			0
$13$	−0.292855	−	1.09295i	−0.0812234	−	0.303130i	0.913349	−	0.407178i	$-0.133487\pi$
$13$	−0.292855	−	1.09295i	−0.0812234	−	0.303130i	−0.994572	+	0.104048i	$0.966820\pi$
$14$	0.377754	+	0.128230i	0.100959	+	0.0342710i
$15$		0			0
$16$	−1.15275	+	0.665543i	−0.288188	+	0.166386i
$17$	4.05247	+	0.759899i	0.982870	+	0.184303i
$17$	4.05247	+	0.759899i	0.982870	+	0.184303i
$18$		0			0
$19$	−5.72485	−	2.37131i	−1.31337	−	0.544016i	−0.387505	−	0.921868i	$-0.626663\pi$
$19$	−5.72485	−	2.37131i	−1.31337	−	0.544016i	−0.925866	+	0.377852i	$0.876663\pi$
$20$	3.75926	+	4.28662i	0.840597	+	0.958517i
$21$		0			0
$22$	5.12077	−	2.52529i	1.09175	−	0.538393i
$23$	−2.32784	+	2.65439i	−0.485388	+	0.553479i	−0.941749	−	0.336316i	$-0.890819\pi$
$23$	−2.32784	+	2.65439i	−0.485388	+	0.553479i	0.456361	+	0.889794i	$0.349152\pi$
$24$		0			0
$25$	0.715622	−	0.932617i	0.143124	−	0.186523i
$26$	−0.960014	−	2.31768i	−0.188274	−	0.454534i
$27$		0			0
$28$	0.514504	+	0.102341i	0.0972320	+	0.0193407i
$29$	0.409431	−	6.24671i	0.0760294	−	1.15998i	−0.773978	−	0.633213i	$-0.781736\pi$
$29$	0.409431	−	6.24671i	0.0760294	−	1.15998i	0.850007	−	0.526772i	$-0.176598\pi$
$30$		0			0
$31$	−1.63425	+	4.81435i	−0.293521	+	0.864684i	0.695711	+	0.718322i	$0.255090\pi$
$31$	−1.63425	+	4.81435i	−0.293521	+	0.864684i	−0.989231	+	0.146361i	$0.953244\pi$
$32$	−5.56167	+	4.26762i	−0.983174	+	0.754416i
$33$		0			0
$34$	9.12770	+	0.497610i	1.56539	+	0.0853394i
$35$			0.351881i			0.0594787i
$36$		0			0
$37$	−1.71395	−	8.61661i	−0.281772	−	1.41656i	−0.819324	−	0.573331i	$-0.805651\pi$
$37$	−1.71395	−	8.61661i	−0.281772	−	1.41656i	0.537552	−	0.843230i	$-0.319349\pi$
$38$	−13.2701	−	3.55571i	−2.15269	−	0.576812i
$39$		0			0
$40$	2.98416	+	2.61704i	0.471837	+	0.413790i
$41$	−7.19745	+	0.471746i	−1.12405	+	0.0736743i	−0.616069	−	0.787693i	$-0.711276\pi$
$41$	−7.19745	+	0.471746i	−1.12405	+	0.0736743i	−0.507984	+	0.861367i	$0.669609\pi$
$42$		0			0
$43$	1.48672	+	1.14080i	0.226722	+	0.173970i	0.715876	−	0.698227i	$-0.246028\pi$
$43$	1.48672	+	1.14080i	0.226722	+	0.173970i	−0.489154	+	0.872198i	$0.662694\pi$
$44$	6.24273	−	4.17126i	0.941126	−	0.628840i
$45$		0			0
$46$	−4.34870	+	6.50829i	−0.641181	+	0.959596i
$47$	−0.219953	+	0.820877i	−0.0320835	+	0.119737i	−0.980110	−	0.198453i	$-0.936408\pi$
$47$	−0.219953	+	0.820877i	−0.0320835	+	0.119737i	0.948027	+	0.318190i	$0.103075\pi$
$48$		0			0
$49$	−4.24162	−	5.52779i	−0.605946	−	0.789684i
$50$	1.30313	−	2.25709i	0.184290	−	0.319200i
$51$		0			0
$52$	−1.64942	−	2.85688i	−0.228733	−	0.396178i
$53$	−4.44864	+	10.7400i	−0.611068	+	1.47525i	0.250761	+	0.968049i	$0.419319\pi$
$53$	−4.44864	+	10.7400i	−0.611068	+	1.47525i	−0.861829	+	0.507199i	$0.830681\pi$
$54$		0			0
$55$	3.56118	+	3.56118i	0.480189	+	0.480189i
$56$	0.364411	+	0.0238847i	0.0486964	+	0.00319173i
$57$		0			0
$58$	−0.907741	−	13.8494i	−0.119192	−	1.81852i
$59$	−0.412757	+	3.13520i	−0.0537364	+	0.408169i	0.943344	+	0.331815i	$0.107661\pi$
$59$	−0.412757	+	3.13520i	−0.0537364	+	0.408169i	−0.997081	+	0.0763535i	$0.975672\pi$
$60$		0			0
$61$	4.80101	−	9.73548i	0.614706	−	1.24650i	−0.337581	−	0.941297i	$-0.609609\pi$
$61$	4.80101	−	9.73548i	0.614706	−	1.24650i	0.952287	−	0.305204i	$-0.0987248\pi$
$62$	−2.19906	+	11.0554i	−0.279281	+	1.40404i
$63$		0			0
$64$	−9.10774	+	9.10774i	−1.13847	+	1.13847i
$65$	1.66367	−	1.45900i	0.206353	−	0.180967i
$66$		0			0
$67$	−9.11090	−	5.26018i	−1.11307	−	0.642633i	−0.173450	−	0.984843i	$-0.555492\pi$
$67$	−9.11090	−	5.26018i	−1.11307	−	0.642633i	−0.939624	+	0.342209i	$0.888825\pi$
$68$	11.9856	−	0.917931i	1.45346	−	0.111315i
$69$		0			0
$70$	0.101830	+	0.773473i	0.0121710	+	0.0924477i
$71$	12.6361	−	2.51348i	1.49963	−	0.298295i	0.624056	−	0.781380i	$-0.285484\pi$
$71$	12.6361	−	2.51348i	1.49963	−	0.298295i	0.875574	+	0.483085i	$0.160484\pi$
$72$		0			0
$73$	8.59520	+	5.74313i	1.00599	+	0.672182i	0.945377	−	0.325979i	$-0.105694\pi$
$73$	8.59520	+	5.74313i	1.00599	+	0.672182i	0.0606148	+	0.998161i	$0.480694\pi$
$74$	−6.26099	−	18.4443i	−0.727825	−	2.14410i
$75$		0			0
$76$	−17.9111	−	2.35804i	−2.05454	−	0.270485i
$77$	0.459412	+	0.0604827i	0.0523549	+	0.00689265i
$78$		0			0
$79$	2.06175	+	6.07373i	0.231965	+	0.683348i	0.999122	+	0.0418883i	$0.0133374\pi$
$79$	2.06175	+	6.07373i	0.231965	+	0.683348i	−0.767157	+	0.641459i	$0.778329\pi$
$80$	−2.16440	−	1.44621i	−0.241987	−	0.161691i
$81$		0			0
$82$	−15.6843	+	3.11980i	−1.73204	+	0.344524i
$83$	1.21897	+	9.25898i	0.133799	+	1.01630i	0.918219	+	0.396074i	$0.129628\pi$
$83$	1.21897	+	9.25898i	0.133799	+	1.01630i	−0.784419	+	0.620231i	$0.787039\pi$
$84$		0			0
$85$	2.17237	+	7.76509i	0.235626	+	0.842243i
$86$	3.59810	+	2.07737i	0.387994	+	0.224008i
$87$		0			0
$88$	3.92971	−	3.44626i	0.418909	−	0.367373i
$89$	−10.2745	+	10.2745i	−1.08909	+	1.08909i	−0.0934682	+	0.995622i	$0.529795\pi$
$89$	−10.2745	+	10.2745i	−1.08909	+	1.08909i	−0.995622	+	0.0934682i	$0.970205\pi$
$90$		0			0
$91$	0.0397194	−	0.199683i	0.00416373	−	0.0209325i
$92$	−4.55250	+	9.23155i	−0.474631	+	0.962456i
$93$		0			0
$94$	−0.245931	+	1.86803i	−0.0253658	+	0.192673i
$95$	−0.792561	−	12.0921i	−0.0813150	−	1.24063i
$96$		0			0
$97$	2.64284	+	0.173221i	0.268340	+	0.0175879i	0.198979	−	0.980004i	$-0.436237\pi$
$97$	2.64284	+	0.173221i	0.268340	+	0.0175879i	0.0693606	+	0.997592i	$0.477904\pi$
$98$	−10.9232	−	10.9232i	−1.10341	−	1.10341i
$99$		0			0
$100$	1.31154	−	3.16633i	0.131154	−	0.316633i
$101$	−1.04532	−	1.81054i	−0.104013	−	0.180155i	0.809322	−	0.587366i	$-0.199835\pi$
$101$	−1.04532	−	1.81054i	−0.104013	−	0.180155i	−0.913334	+	0.407210i	$0.866502\pi$
$102$		0			0
$103$	−1.50429	+	2.60551i	−0.148222	+	0.256728i	−0.930570	−	0.366113i	$-0.880688\pi$
$103$	−1.50429	+	2.60551i	−0.148222	+	0.256728i	0.782348	+	0.622841i	$0.214022\pi$
$104$	−1.39803	−	1.82194i	−0.137088	−	0.178656i
$105$		0			0
$106$	−6.67060	+	24.8950i	−0.647906	+	2.41802i
$107$	4.92541	−	7.37140i	0.476158	−	0.712620i	−0.513177	−	0.858283i	$-0.671531\pi$
$107$	4.92541	−	7.37140i	0.476158	−	0.712620i	0.989334	+	0.145663i	$0.0465314\pi$
$108$		0			0
$109$	7.29495	−	4.87433i	0.698729	−	0.466876i	−0.154783	−	0.987948i	$-0.549468\pi$
$109$	7.29495	−	4.87433i	0.698729	−	0.466876i	0.853512	+	0.521073i	$0.174468\pi$
$110$	8.85843	+	6.79731i	0.844618	+	0.648098i
$111$		0			0
$112$	−0.238993	+	0.0156644i	−0.0225827	+	0.00148015i
$113$	−5.88634	−	5.16218i	−0.553741	−	0.485617i	0.336139	−	0.941812i	$-0.390879\pi$
$113$	−5.88634	−	5.16218i	−0.553741	−	0.485617i	−0.889880	+	0.456195i	$0.849212\pi$
$114$		0			0
$115$	−6.66912	−	1.78699i	−0.621899	−	0.166637i
$116$	−3.56059	−	17.9003i	−0.330593	−	1.66200i
$117$		0			0
$118$			7.01098i			0.645413i
$119$	0.593501	+	0.445135i	0.0544061	+	0.0408055i
$120$		0			0
$121$	−3.46534	+	2.65905i	−0.315030	+	0.241731i
$122$	7.73583	−	22.7890i	0.700370	−	2.06322i
$123$		0			0
$124$	−0.969444	+	14.7909i	−0.0870587	+	1.32826i
$125$	11.8450	+	2.35611i	1.05945	+	0.210737i
$126$		0			0
$127$	0.494267	+	1.19327i	0.0438591	+	0.105885i	0.944291	−	0.329112i	$-0.106749\pi$
$127$	0.494267	+	1.19327i	0.0438591	+	0.105885i	−0.900432	+	0.434997i	$0.856749\pi$
$128$	−8.84894	+	11.5322i	−0.782143	+	1.01931i
$129$		0			0
$130$	3.23472	−	3.68849i	0.283704	−	0.323502i
$131$	−13.1067	+	6.46352i	−1.14514	+	0.564720i	−0.912999	−	0.407962i	$-0.866239\pi$
$131$	−13.1067	+	6.46352i	−1.14514	+	0.564720i	−0.232140	+	0.972682i	$0.574573\pi$
$132$		0			0
$133$	−0.735144	−	0.838271i	−0.0637451	−	0.0726873i
$134$	−21.5490	−	8.92589i	−1.86155	−	0.771080i
$135$		0			0
$136$	8.18905	−	1.72265i	0.702205	−	0.147716i
$137$	15.0426	−	8.68484i	1.28517	−	0.741996i	0.307385	−	0.951585i	$-0.400546\pi$
$137$	15.0426	−	8.68484i	1.28517	−	0.741996i	0.977789	+	0.209589i	$0.0672127\pi$
$138$		0			0
$139$	19.6370	+	6.66587i	1.66559	+	0.565392i	0.985787	−	0.168002i	$-0.0537314\pi$
$139$	19.6370	+	6.66587i	1.66559	+	0.565392i	0.679804	+	0.733394i	$0.262065\pi$
$140$	0.265519	+	0.990931i	0.0224405	+	0.0837490i
$141$		0			0
$142$	27.0482	−	9.18163i	2.26983	−	0.770505i
$143$	−1.61890	−	2.42285i	−0.135379	−	0.202609i
$144$		0			0
$145$	11.3105	−	4.68497i	0.939288	−	0.389066i
$146$	20.5552	+	10.1367i	1.70116	+	0.838919i
$147$		0			0
$148$	−11.3285	−	22.9719i	−0.931197	−	1.88828i
$149$	16.6569	−	4.46321i	1.36459	−	0.365640i	0.499089	−	0.866551i	$-0.333668\pi$
$149$	16.6569	−	4.46321i	1.36459	−	0.365640i	0.865499	+	0.500911i	$0.167001\pi$
$150$		0			0
$151$	−15.8401	+	2.08539i	−1.28905	+	0.169706i	−0.743706	−	0.668507i	$-0.766934\pi$
$151$	−15.8401	+	2.08539i	−1.28905	+	0.169706i	−0.545343	+	0.838213i	$0.683600\pi$
$152$	−12.5765			−1.02009
$153$		0			0
$154$	1.02734			0.0827856
$155$	−9.85766	+	1.29779i	−0.791786	+	0.104241i
$156$		0			0
$157$	11.2723	−	3.02040i	0.899625	−	0.241054i	0.220770	−	0.975326i	$-0.429143\pi$
$157$	11.2723	−	3.02040i	0.899625	−	0.241054i	0.678855	+	0.734272i	$0.262476\pi$
$158$	6.28962	+	12.7541i	0.500375	+	1.01466i
$159$		0			0
$160$	−12.2957	−	6.06359i	−0.972064	−	0.479369i
$161$	−0.586901	+	0.243102i	−0.0462543	+	0.0191592i
$162$		0			0
$163$	−6.58170	−	9.85021i	−0.515518	−	0.771528i	0.478806	−	0.877921i	$-0.341070\pi$
$163$	−6.58170	−	9.85021i	−0.515518	−	0.771528i	−0.994324	+	0.106393i	$0.966070\pi$
$164$	−19.9128	+	6.75947i	−1.55493	+	0.527826i
$165$		0			0
$166$	5.35885	+	19.9995i	0.415928	+	1.55226i
$167$	4.14842	+	1.40820i	0.321014	+	0.108970i	0.477295	−	0.878743i	$-0.341617\pi$
$167$	4.14842	+	1.40820i	0.321014	+	0.108970i	−0.156281	+	0.987713i	$0.549951\pi$
$168$		0			0
$169$	10.1496	−	5.85985i	0.780735	−	0.450757i
$170$	7.02222	+	16.4399i	0.538580	+	1.26088i
$171$		0			0
$172$	5.04756	+	2.09077i	0.384873	+	0.159420i
$173$	7.01864	+	8.00322i	0.533617	+	0.608474i	0.954343	−	0.298714i	$-0.0965578\pi$
$173$	7.01864	+	8.00322i	0.533617	+	0.608474i	−0.420725	+	0.907188i	$0.638224\pi$
$174$		0			0
$175$	0.189704	−	0.0935519i	0.0143403	−	0.00707186i
$176$	−2.26018	+	2.57724i	−0.170367	+	0.194267i
$177$		0			0
$178$	−19.6111	+	25.5577i	−1.46992	+	1.91563i
$179$	2.62459	+	6.33632i	0.196171	+	0.473599i	0.991103	−	0.133100i	$-0.0424932\pi$
$179$	2.62459	+	6.33632i	0.196171	+	0.473599i	−0.794931	+	0.606699i	$0.792493\pi$
$180$		0			0
$181$	3.12720	+	0.622039i	0.232443	+	0.0462358i	0.309937	−	0.950757i	$-0.399692\pi$
$181$	3.12720	+	0.622039i	0.232443	+	0.0462358i	−0.0774943	+	0.996993i	$0.524692\pi$
$182$	0.0295221	−	0.450420i	0.00218832	−	0.0333873i
$183$		0			0
$184$	−2.30330	+	6.78530i	−0.169801	+	0.500219i
$185$	13.6306	−	10.4591i	1.00214	−	0.768969i
$186$		0			0
$187$	10.5114	−	1.50152i	0.768672	−	0.109802i
$188$			2.47764i			0.180701i
$189$		0			0
$190$	−5.24144	−	26.3505i	−0.380254	−	1.91167i
$191$	−1.67016	−	0.447519i	−0.120849	−	0.0323814i	0.197888	−	0.980225i	$-0.436592\pi$
$191$	−1.67016	−	0.447519i	−0.120849	−	0.0323814i	−0.318737	+	0.947843i	$0.603259\pi$
$192$		0			0
$193$	0.801167	+	0.702605i	0.0576693	+	0.0505746i	0.687695	−	0.725999i	$-0.258622\pi$
$193$	0.801167	+	0.702605i	0.0576693	+	0.0505746i	−0.630026	+	0.776574i	$0.716956\pi$
$194$	5.85939	−	0.384044i	0.420679	−	0.0275728i
$195$		0			0
$196$	−16.1159	−	12.3662i	−1.15114	−	0.883300i
$197$	7.44534	−	4.97482i	0.530459	−	0.354441i	−0.261317	−	0.965253i	$-0.584157\pi$
$197$	7.44534	−	4.97482i	0.530459	−	0.354441i	0.791776	+	0.610812i	$0.209157\pi$
$198$		0			0
$199$	−9.78402	+	14.6428i	−0.693571	+	1.03800i	0.302814	+	0.953050i	$0.402074\pi$
$199$	−9.78402	+	14.6428i	−0.693571	+	1.03800i	−0.996385	+	0.0849521i	$0.972926\pi$
$200$	0.617511	−	2.30458i	0.0436646	−	0.162958i
$201$		0			0
$202$	−2.82167	−	3.67727i	−0.198532	−	0.258732i
$203$	0.563200	−	0.975490i	0.0395289	−	0.0684660i
$204$		0			0
$205$	−7.05285	−	12.2159i	−0.492592	−	0.853195i
$206$	−2.55260	+	6.16252i	−0.177848	+	0.429363i
$207$		0			0
$208$	1.06500	+	1.06500i	0.0738442	+	0.0738442i
$209$	−15.9236	−	1.04369i	−1.10146	−	0.0721935i
$210$		0			0
$211$	0.703329	+	10.7307i	0.0484192	+	0.738734i	0.951189	+	0.308609i	$0.0998636\pi$
$211$	0.703329	+	10.7307i	0.0484192	+	0.738734i	−0.902770	+	0.430124i	$0.858470\pi$
$212$	−4.42374	+	33.6016i	−0.303824	+	2.30777i
$213$		0			0
$214$	8.69342	−	17.6285i	0.594270	−	1.20506i
$215$	−0.714962	+	3.59436i	−0.0487600	+	0.245133i
$216$		0			0
$217$	−0.646868	+	0.646868i	−0.0439122	+	0.0439122i
$218$	14.6245	−	12.8254i	0.990499	−	0.868644i
$219$		0			0
$220$	12.7158	+	7.34147i	0.857299	+	0.494962i
$221$	−0.356256	−	4.65170i	−0.0239644	−	0.312907i
$222$		0			0
$223$	−2.11273	−	16.0478i	−0.141479	−	1.07464i	−0.903956	−	0.427625i	$-0.859350\pi$
$223$	−2.11273	−	16.0478i	−0.141479	−	1.07464i	0.762477	−	0.647015i	$-0.223983\pi$
$224$	−1.23715	+	0.246085i	−0.0826606	+	0.0164422i
$225$		0			0
$226$	−14.4327	−	9.64363i	−0.960050	−	0.641485i
$227$	2.08697	+	6.14800i	0.138517	+	0.408057i	0.993947	−	0.109861i	$-0.0350405\pi$
$227$	2.08697	+	6.14800i	0.138517	+	0.408057i	−0.855430	+	0.517918i	$0.826707\pi$
$228$		0			0
$229$	11.6792	+	1.53759i	0.771782	+	0.101607i	0.506124	−	0.862460i	$-0.331078\pi$
$229$	11.6792	+	1.53759i	0.771782	+	0.101607i	0.265658	+	0.964067i	$0.414411\pi$
$230$	−15.1766	−	1.99804i	−1.00072	−	0.131747i
$231$		0			0
$232$	−4.08407	−	12.0313i	−0.268132	−	0.789892i
$233$	−6.04447	−	4.03878i	−0.395986	−	0.264589i	0.341596	−	0.939847i	$-0.389033\pi$
$233$	−6.04447	−	4.03878i	−0.395986	−	0.264589i	−0.737582	+	0.675257i	$0.764033\pi$
$234$		0			0
$235$	−1.63002	+	0.324231i	−0.106331	+	0.0211505i
$236$	1.20337	+	9.14050i	0.0783327	+	0.594996i
$237$		0			0
$238$	1.43340	+	0.806705i	0.0929134	+	0.0522909i
$239$	−10.7534	−	6.20850i	−0.695582	−	0.401595i	0.110118	−	0.993919i	$-0.464877\pi$
$239$	−10.7534	−	6.20850i	−0.695582	−	0.401595i	−0.805700	+	0.592324i	$0.798211\pi$
$240$		0			0
$241$	1.29871	−	1.13894i	0.0836572	−	0.0733654i	−0.616496	−	0.787358i	$-0.711448\pi$
$241$	1.29871	−	1.13894i	0.0836572	−	0.0733654i	0.700153	+	0.713993i	$0.253115\pi$
$242$	−6.84770	+	6.84770i	−0.440187	+	0.440187i
$243$		0			0
$244$	6.17400	−	31.0388i	0.395250	−	1.98706i
$245$	6.02665	−	12.2208i	0.385028	−	0.780760i
$246$		0			0
$247$	−0.915173	+	6.95143i	−0.0582311	+	0.442309i
$248$	0.674886	+	10.2968i	0.0428553	+	0.653845i
$249$		0			0
$250$	26.7184	+	1.75122i	1.68982	+	0.110757i
$251$	−9.98125	−	9.98125i	−0.630011	−	0.630011i	0.318060	−	0.948071i	$-0.396969\pi$
$251$	−9.98125	−	9.98125i	−0.630011	−	0.630011i	−0.948071	+	0.318060i	$0.896969\pi$
$252$		0			0
$253$	−3.47939	+	8.39998i	−0.218747	+	0.528102i
$254$	1.43177	+	2.47990i	0.0898372	+	0.155603i
$255$		0			0
$256$	−3.23340	+	5.60042i	−0.202088	+	0.350026i
$257$	−13.2480	−	17.2651i	−0.826387	−	1.07697i	−0.995812	−	0.0914251i	$-0.970858\pi$
$257$	−13.2480	−	17.2651i	−0.826387	−	1.07697i	0.169425	−	0.985543i	$-0.445809\pi$
$258$		0			0
$259$	0.409137	−	1.52692i	0.0254225	−	0.0948782i
$260$	3.58414	−	5.36405i	0.222279	−	0.332664i
$261$		0			0
$262$	−26.9396	+	18.0004i	−1.66433	+	1.11207i
$263$	1.00443	+	0.770729i	0.0619360	+	0.0475252i	0.639265	−	0.768986i	$-0.279238\pi$
$263$	1.00443	+	0.770729i	0.0619360	+	0.0475252i	−0.577329	+	0.816511i	$0.695905\pi$
$264$		0			0
$265$	−22.6852	+	1.48686i	−1.39354	+	0.0913374i
$266$	−1.85851	−	1.62987i	−0.113953	−	0.0999339i
$267$		0			0
$268$	−29.6264	−	7.93837i	−1.80972	−	0.484913i
$269$	1.32171	+	6.64467i	0.0805859	+	0.405133i	0.999932	+	0.0116823i	$0.00371868\pi$
$269$	1.32171	+	6.64467i	0.0805859	+	0.405133i	−0.919346	+	0.393450i	$0.871281\pi$
$270$		0			0
$271$			2.35757i			0.143212i	0.997433	+	0.0716060i	$0.0228124\pi$
$271$			2.35757i			0.143212i	−0.997433	+	0.0716060i	$0.977188\pi$
$272$	−5.17725	+	1.82112i	−0.313917	+	0.110422i
$273$		0			0
$274$	30.5520	−	23.4434i	1.84571	−	1.41627i
$275$	0.973104	−	2.86667i	0.0586804	−	0.172867i
$276$		0			0
$277$	−1.23062	+	18.7756i	−0.0739408	+	1.12812i	0.786170	+	0.618011i	$0.212061\pi$
$277$	−1.23062	+	18.7756i	−0.0739408	+	1.12812i	−0.860110	+	0.510108i	$0.829605\pi$
$278$	45.0934	+	8.96964i	2.70452	+	0.537963i
$279$		0			0
$280$	0.273304	+	0.659815i	0.0163331	+	0.0394315i
$281$	−11.9830	+	15.6166i	−0.714848	+	0.931608i	−0.999636	−	0.0269828i	$-0.991410\pi$
$281$	−11.9830	+	15.6166i	−0.714848	+	0.931608i	0.284788	+	0.958590i	$0.408077\pi$
$282$		0			0
$283$	−10.0416	+	11.4502i	−0.596909	+	0.680644i	−0.968860	−	0.247608i	$-0.920355\pi$
$283$	−10.0416	+	11.4502i	−0.596909	+	0.680644i	0.371951	+	0.928252i	$0.378689\pi$
$284$	33.6879	−	16.6130i	1.99901	−	0.985803i
$285$		0			0
$286$	−4.25966	−	4.85721i	−0.251879	−	0.287213i
$287$	−1.19904	−	0.496660i	−0.0707773	−	0.0293169i
$288$		0			0
$289$	15.8451	+	6.15894i	0.932065	+	0.362291i
$290$	23.5060	−	13.5712i	1.38032	−	0.796929i
$291$		0			0
$292$	28.5385	+	9.68753i	1.67009	+	0.566920i
$293$	8.61931	+	32.1677i	0.503545	+	1.87926i	0.475628	+	0.879646i	$0.342221\pi$
$293$	8.61931	+	32.1677i	0.503545	+	1.87926i	0.0279169	+	0.999610i	$0.491113\pi$
$294$		0			0
$295$	−5.85599	+	1.98784i	−0.340949	+	0.115737i
$296$	−9.90633	−	14.8259i	−0.575794	−	0.861736i
$297$		0			0
$298$	35.3222	−	14.6309i	2.04616	−	0.847547i
$299$	3.58284	+	1.76686i	0.207201	+	0.102180i
$300$		0			0
$301$	0.149134	+	0.302415i	0.00859597	+	0.0174309i
$302$	−34.2148	+	9.16783i	−1.96884	+	0.527550i
$303$		0			0
$304$	8.17755	−	1.07660i	0.469015	−	0.0617470i
$305$	21.2281			1.21552
$306$		0			0
$307$	30.4740			1.73925			0.869623	−	0.493717i	$-0.164362\pi$
$307$	30.4740			1.73925			0.869623	+	0.493717i	$0.164362\pi$
$308$	1.33939	−	0.176334i	0.0763188	−	0.0100476i
$309$		0			0
$310$	−21.2927	+	5.70536i	−1.20934	+	0.324042i
$311$	10.9790	+	22.2632i	0.622561	+	1.26243i	0.948422	+	0.317012i	$0.102679\pi$
$311$	10.9790	+	22.2632i	0.622561	+	1.26243i	−0.325860	+	0.945418i	$0.605654\pi$
$312$		0			0
$313$	−8.39428	−	4.13960i	−0.474473	−	0.233984i	0.189299	−	0.981920i	$-0.439379\pi$
$313$	−8.39428	−	4.13960i	−0.474473	−	0.233984i	−0.663771	+	0.747935i	$0.731045\pi$
$314$	23.9037	−	9.90122i	1.34896	−	0.558758i
$315$		0			0
$316$	10.3892	+	15.5485i	0.584436	+	0.874670i
$317$	19.6083	−	6.65612i	1.10131	−	0.373845i	0.289154	−	0.957283i	$-0.406626\pi$
$317$	19.6083	−	6.65612i	1.10131	−	0.373845i	0.812158	+	0.583437i	$0.198293\pi$
$318$		0			0
$319$	−4.17255	−	15.5722i	−0.233618	−	0.871875i
$320$	−23.8522	−	8.09674i	−1.33338	−	0.452622i
$321$		0			0
$322$	−1.21972	+	0.704208i	−0.0679726	+	0.0392440i
$323$	−21.3979	−	13.9600i	−1.19061	−	0.776754i
$324$		0			0
$325$	−1.22888	−	0.509018i	−0.0681659	−	0.0282352i
$326$	−17.3178	−	19.7472i	−0.959146	−	1.09370i
$327$		0			0
$328$	−13.1296	+	6.47481i	−0.724961	+	0.357511i
$329$	−0.100823	+	0.114966i	−0.00555853	+	0.00633829i
$330$		0			0
$331$	−5.08307	+	6.62438i	−0.279391	+	0.364109i	−0.911878	−	0.410462i	$-0.865367\pi$
$331$	−5.08307	+	6.62438i	−0.279391	+	0.364109i	0.632487	+	0.774571i	$0.282034\pi$
$332$	10.4193	+	25.1544i	0.571833	+	1.38053i
$333$		0			0
$334$	9.52621	+	1.89488i	0.521251	+	0.103683i
$335$	1.34560	−	20.5298i	0.0735177	−	1.12166i
$336$		0			0
$337$	9.04236	−	26.6379i	0.492569	−	1.45106i	−0.362224	−	0.932091i	$-0.617982\pi$
$337$	9.04236	−	26.6379i	0.492569	−	1.45106i	0.854793	−	0.518970i	$-0.173684\pi$
$338$	20.6141	−	15.8177i	1.12126	−	0.860372i
$339$		0			0
$340$	11.9769	+	20.2281i	0.649540	+	1.09702i
$341$			13.0931i			0.709033i
$342$		0			0
$343$	−0.490307	−	2.46494i	−0.0264741	−	0.133094i
$344$	3.67382	+	0.984396i	0.198079	+	0.0530751i
$345$		0			0
$346$	17.7438	+	15.5609i	0.953911	+	0.836558i
$347$	−20.4266	+	1.33883i	−1.09656	+	0.0718721i	−0.602924	−	0.797799i	$-0.705998\pi$
$347$	−20.4266	+	1.33883i	−1.09656	+	0.0718721i	−0.493632	+	0.869671i	$0.664331\pi$
$348$		0			0
$349$	3.01429	+	2.31295i	0.161351	+	0.123809i	0.686281	−	0.727336i	$-0.259242\pi$
$349$	3.01429	+	2.31295i	0.161351	+	0.123809i	−0.524930	+	0.851145i	$0.675909\pi$
$350$	0.389919	−	0.260536i	0.0208420	−	0.0139262i
$351$		0			0
$352$	−10.0300	+	15.0110i	−0.534601	+	0.800087i
$353$	−0.702285	+	2.62096i	−0.0373789	+	0.139500i	−0.982094	−	0.188393i	$-0.939672\pi$
$353$	−0.702285	+	2.62096i	−0.0373789	+	0.139500i	0.944715	+	0.327893i	$0.106339\pi$
$354$		0			0
$355$	15.3381	+	19.9890i	0.814062	+	1.06091i
$356$	−21.1811	+	36.6867i	−1.12260	+	1.94439i
$357$		0			0
$358$	7.60279	+	13.1684i	0.401820	+	0.695973i
$359$	9.40229	−	22.6991i	0.496234	−	1.19802i	−0.455263	−	0.890357i	$-0.650455\pi$
$359$	9.40229	−	22.6991i	0.496234	−	1.19802i	0.951497	−	0.307658i	$-0.0995453\pi$
$360$		0			0
$361$	13.7158	+	13.7158i	0.721883	+	0.721883i
$362$	7.05395	+	0.462340i	0.370747	+	0.0243001i
$363$		0			0
$364$	−0.0388213	−	0.592298i	−0.00203479	−	0.0310449i
$365$	−2.63871	+	20.0430i	−0.138117	+	1.04910i
$366$		0			0
$367$	−1.53717	+	3.11708i	−0.0802397	+	0.162710i	−0.933295	−	0.359110i	$-0.883080\pi$
$367$	−1.53717	+	3.11708i	−0.0802397	+	0.162710i	0.853055	+	0.521820i	$0.174747\pi$
$368$	0.916814	−	4.60914i	0.0477922	−	0.240268i
$369$		0			0
$370$	26.9348	−	26.9348i	1.40027	−	1.40027i
$371$	−1.57262	+	1.37915i	−0.0816463	+	0.0716018i
$372$		0			0
$373$	−26.9296	−	15.5478i	−1.39436	−	0.805035i	−0.400567	−	0.916267i	$-0.631187\pi$
$373$	−26.9296	−	15.5478i	−1.39436	−	0.805035i	−0.993794	+	0.111232i	$0.964520\pi$
$374$	22.6708	−	6.34239i	1.17228	−	0.327957i
$375$		0			0
$376$	0.225135	+	1.71007i	0.0116105	+	0.0881902i
$377$	−6.94725	+	1.38189i	−0.357802	+	0.0711711i
$378$		0			0
$379$	−21.4947	−	14.3623i	−1.10411	−	0.737740i	−0.136610	−	0.990625i	$-0.543621\pi$
$379$	−21.4947	−	14.3623i	−1.10411	−	0.737740i	−0.967496	+	0.252885i	$0.918621\pi$
$380$	−11.3563	−	33.4546i	−0.582567	−	1.71619i
$381$		0			0
$382$	−3.80071	−	0.500374i	−0.194461	−	0.0256013i
$383$	2.08664	+	0.274712i	0.106622	+	0.0140371i	0.183649	−	0.982992i	$-0.441209\pi$
$383$	2.08664	+	0.274712i	0.106622	+	0.0140371i	−0.0770261	+	0.997029i	$0.524542\pi$
$384$		0			0
$385$	0.291285	+	0.858098i	0.0148453	+	0.0437327i
$386$	1.96438	+	1.31256i	0.0999843	+	0.0668074i
$387$		0			0
$388$	7.57321	−	1.50640i	0.384471	−	0.0764761i
$389$	−0.136798	−	1.03908i	−0.00693592	−	0.0526836i	0.987627	−	0.156822i	$-0.0501249\pi$
$389$	−0.136798	−	1.03908i	−0.00693592	−	0.0526836i	−0.994563	+	0.104138i	$0.966792\pi$
$390$		0			0
$391$	−11.4506	+	8.98793i	−0.579080	+	0.454539i
$392$	−12.2469	−	7.07076i	−0.618563	−	0.357128i
$393$		0			0
$394$	14.9260	−	13.0898i	0.751963	−	0.659454i
$395$	−8.86967	+	8.86967i	−0.446282	+	0.446282i
$396$		0			0
$397$	−2.28690	+	11.4970i	−0.114776	+	0.577020i	0.880003	+	0.474969i	$0.157541\pi$
$397$	−2.28690	+	11.4970i	−0.114776	+	0.577020i	−0.994779	+	0.102051i	$0.967459\pi$
$398$	−17.2689	+	35.0179i	−0.865613	+	1.75529i
$399$		0			0
$400$	−0.204240	+	1.55135i	−0.0102120	+	0.0775677i
$401$	0.554616	+	8.46180i	0.0276962	+	0.422562i	0.989083	+	0.147361i	$0.0470779\pi$
$401$	0.554616	+	8.46180i	0.0276962	+	0.422562i	−0.961387	+	0.275201i	$0.911255\pi$
$402$		0			0
$403$	5.74045	+	0.376249i	0.285952	+	0.0187423i
$404$	−4.30989	−	4.30989i	−0.214425	−	0.214425i
$405$		0			0
$406$	0.955682	−	2.30722i	0.0474297	−	0.114505i
$407$	−11.3124	−	19.5937i	−0.560736	−	0.971224i
$408$		0			0
$409$	−17.0137	+	29.4686i	−0.841274	+	1.45713i	0.0475435	+	0.998869i	$0.484861\pi$
$409$	−17.0137	+	29.4686i	−0.841274	+	1.45713i	−0.888818	+	0.458261i	$0.848473\pi$
$410$	−19.0381	−	24.8109i	−0.940223	−	1.22532i
$411$		0			0
$412$	−2.27019	+	8.47247i	−0.111844	+	0.417408i
$413$	−0.316116	+	0.473101i	−0.0155550	+	0.0232798i
$414$		0			0
$415$	−15.1854	+	10.1466i	−0.745422	+	0.498075i
$416$	6.29306	+	4.82884i	0.308543	+	0.236753i
$417$		0			0
$418$	−35.3039	+	2.31394i	−1.72677	+	0.113179i
$419$	−8.42903	−	7.39206i	−0.411785	−	0.361126i	0.428248	−	0.903661i	$-0.359131\pi$
$419$	−8.42903	−	7.39206i	−0.411785	−	0.361126i	−0.840033	+	0.542536i	$0.817464\pi$
$420$		0			0
$421$	−32.7112	−	8.76493i	−1.59424	−	0.427176i	−0.650946	−	0.759124i	$-0.725628\pi$
$421$	−32.7112	−	8.76493i	−1.59424	−	0.427176i	−0.943298	+	0.331948i	$0.892294\pi$
$422$	4.65133	+	23.3838i	0.226423	+	1.13831i
$423$		0			0
$424$			23.5939i			1.14582i
$425$	3.60874	−	3.23561i	0.175049	−	0.156950i
$426$		0			0
$427$	1.54954	−	1.18901i	0.0749876	−	0.0575400i
$428$	8.30820	−	24.4752i	0.401592	−	1.18305i
$429$		0			0
$430$	−0.531406	+	8.10770i	−0.0256267	+	0.390988i
$431$	−7.57077	−	1.50592i	−0.364671	−	0.0725376i	0.00935382	−	0.999956i	$-0.497023\pi$
$431$	−7.57077	−	1.50592i	−0.364671	−	0.0725376i	−0.374025	+	0.927419i	$0.622023\pi$
$432$		0			0
$433$	−9.03116	−	21.8032i	−0.434010	−	1.04779i	−0.977982	−	0.208689i	$-0.933080\pi$
$433$	−9.03116	−	21.8032i	−0.434010	−	1.04779i	0.543972	−	0.839103i	$-0.316920\pi$
$434$	−1.23469	+	1.60908i	−0.0592671	+	0.0772384i
$435$		0			0
$436$	16.8653	−	19.2312i	0.807700	−	0.921005i
$437$	19.6209	−	9.67596i	0.938596	−	0.462864i
$438$		0			0
$439$	−0.220862	−	0.251845i	−0.0105412	−	0.0120199i	0.746545	−	0.665335i	$-0.231711\pi$
$439$	−0.220862	−	0.251845i	−0.0105412	−	0.0120199i	−0.757086	+	0.653315i	$0.773378\pi$
$440$	9.44356	+	3.91165i	0.450204	+	0.186481i
$441$		0			0
$442$	−2.12923	−	10.1219i	−0.101277	−	0.481447i
$443$	0.140494	−	0.0811141i	0.00667506	−	0.00385385i	−0.496659	−	0.867946i	$-0.665440\pi$
$443$	0.140494	−	0.0811141i	0.00667506	−	0.00385385i	0.503334	+	0.864092i	$0.332107\pi$
$444$		0			0
$445$	−26.9077	−	9.13394i	−1.27555	−	0.432990i
$446$	−9.28804	−	34.6635i	−0.439802	−	1.64136i
$447$		0			0
$448$	−2.19459	+	0.744964i	−0.103685	+	0.0351962i
$449$	−7.85643	−	11.7580i	−0.370768	−	0.554893i	0.598431	−	0.801175i	$-0.295791\pi$
$449$	−7.85643	−	11.7580i	−0.370768	−	0.554893i	−0.969198	+	0.246282i	$0.920791\pi$
$450$		0			0
$451$	−17.1612	+	7.10841i	−0.808090	+	0.334722i
$452$	−20.4718	−	10.0956i	−0.962911	−	0.474855i
$453$		0			0
$454$	6.36654	+	12.9101i	0.298796	+	0.605899i
$455$	0.384588	−	0.103050i	0.0180298	−	0.00483106i
$456$		0			0
$457$	−17.4023	+	2.29106i	−0.814045	+	0.107171i	−0.526042	−	0.850459i	$-0.676325\pi$
$457$	−17.4023	+	2.29106i	−0.814045	+	0.107171i	−0.288003	+	0.957630i	$0.592991\pi$
$458$	26.1171			1.22037
$459$		0			0
$460$	−20.1293			−0.938534
$461$	−17.5825	+	2.31478i	−0.818900	+	0.107810i	−0.528325	−	0.849042i	$-0.677180\pi$
$461$	−17.5825	+	2.31478i	−0.818900	+	0.107810i	−0.290575	+	0.956852i	$0.593846\pi$
$462$		0			0
$463$	18.1457	−	4.86211i	0.843300	−	0.225962i	0.188792	−	0.982017i	$-0.439543\pi$
$463$	18.1457	−	4.86211i	0.843300	−	0.225962i	0.654508	+	0.756056i	$0.272876\pi$
$464$	3.68548	+	7.47341i	0.171094	+	0.346944i
$465$		0			0
$466$	−14.4552	−	7.12851i	−0.669623	−	0.330222i
$467$	−24.8403	+	10.2892i	−1.14947	+	0.476127i	−0.874357	−	0.485284i	$-0.838716\pi$
$467$	−24.8403	+	10.2892i	−1.14947	+	0.476127i	−0.275116	+	0.961411i	$0.588716\pi$
$468$		0			0
$469$	−1.05167	−	1.57394i	−0.0485617	−	0.0726777i
$470$	−3.48914	+	1.18440i	−0.160942	+	0.0546325i
$471$		0			0
$472$	1.66114	+	6.19944i	0.0764600	+	0.285352i
$473$	4.56987	+	1.55126i	0.210123	+	0.0713270i
$474$		0			0
$475$	−6.30835	+	3.64213i	−0.289447	+	0.167112i
$476$	2.00724	+	0.805706i	0.0920019	+	0.0369295i
$477$		0			0
$478$	−25.4339	−	10.5351i	−1.16332	−	0.481863i
$479$	−7.85185	−	8.95332i	−0.358760	−	0.409088i	0.544101	−	0.839020i	$-0.316871\pi$
$479$	−7.85185	−	8.95332i	−0.358760	−	0.409088i	−0.902861	+	0.429932i	$0.858538\pi$
$480$		0			0
$481$	−8.91559	+	4.39668i	−0.406516	+	0.200471i
$482$	2.52512	−	2.87934i	0.115016	−	0.131150i
$483$		0			0
$484$	−7.75229	+	10.1030i	−0.352377	+	0.459226i
$485$	1.98210	+	4.78522i	0.0900027	+	0.217286i
$486$		0			0
$487$	−15.6673	−	3.11643i	−0.709955	−	0.141219i	−0.173113	−	0.984902i	$-0.555383\pi$
$487$	−15.6673	−	3.11643i	−0.709955	−	0.141219i	−0.536842	+	0.843683i	$0.680383\pi$
$488$	1.44091	−	21.9840i	0.0652269	−	0.995171i
$489$		0			0
$490$	9.71070	−	28.6068i	0.438685	−	1.29232i
$491$	−8.05433	+	6.18031i	−0.363487	+	0.278913i	−0.774316	−	0.632799i	$-0.781906\pi$
$491$	−8.05433	+	6.18031i	−0.363487	+	0.278913i	0.410829	+	0.911712i	$0.365239\pi$
$492$		0			0
$493$	6.40608	−	25.0035i	0.288515	−	1.12610i
$494$			15.5449i			0.699396i
$495$		0			0
$496$	−1.32027	−	6.63743i	−0.0592818	−	0.298029i
$497$	2.23920	+	0.599992i	0.100442	+	0.0269133i
$498$		0			0
$499$	9.25912	+	8.12003i	0.414495	+	0.363502i	0.841048	−	0.540960i	$-0.181939\pi$
$499$	9.25912	+	8.12003i	0.414495	+	0.363502i	−0.426553	+	0.904462i	$0.640272\pi$
$500$	35.1345	−	2.30283i	1.57126	−	0.102986i
$501$		0			0
$502$	−24.8283	−	19.0515i	−1.10814	−	0.850308i
$503$	−16.6358	+	11.1157i	−0.741753	+	0.495623i	−0.868116	−	0.496361i	$-0.834669\pi$
$503$	−16.6358	+	11.1157i	−0.741753	+	0.495623i	0.126364	+	0.991984i	$0.459669\pi$
$504$		0			0
$505$	2.27144	−	3.39945i	0.101078	−	0.151274i
$506$	−5.21724	+	19.4710i	−0.231934	+	0.865591i
$507$		0			0
$508$	2.29231	+	2.98739i	0.101705	+	0.132544i
$509$	10.4673	−	18.1299i	0.463956	−	0.803596i	−0.535198	−	0.844727i	$-0.679763\pi$
$509$	10.4673	−	18.1299i	0.463956	−	0.803596i	0.999154	+	0.0411314i	$0.0130962\pi$
$510$		0			0
$511$	0.930014	+	1.61083i	0.0411414	+	0.0712590i
$512$	5.63865	−	13.6129i	0.249196	−	0.601611i
$513$		0			0
$514$	−34.1169	−	34.1169i	−1.50483	−	1.50483i
$515$	−5.87106	−	0.384809i	−0.258710	−	0.0169567i
$516$		0			0
$517$	0.143138	+	2.18387i	0.00629522	+	0.0960465i
$518$	0.457458	−	3.47474i	0.0200996	−	0.152671i
$519$		0			0
$520$	1.98637	−	4.02795i	0.0871080	−	0.176637i
$521$	−3.88666	+	19.5396i	−0.170278	+	0.856044i	0.797322	+	0.603554i	$0.206249\pi$
$521$	−3.88666	+	19.5396i	−0.170278	+	0.856044i	−0.967600	+	0.252490i	$0.918751\pi$
$522$		0			0
$523$	14.6139	−	14.6139i	0.639022	−	0.639022i	−0.311292	−	0.950314i	$-0.600762\pi$
$523$	14.6139	−	14.6139i	0.639022	−	0.639022i	0.950314	+	0.311292i	$0.100762\pi$
$524$	−32.0326	+	28.0919i	−1.39935	+	1.22720i
$525$		0			0
$526$	2.43090	+	1.40348i	0.105992	+	0.0611946i
$527$	−10.2812	+	18.2682i	−0.447856	+	0.795775i
$528$		0			0
$529$	1.37514	+	10.4452i	0.0597888	+	0.454141i
$530$	−49.4343	+	9.83309i	−2.14729	+	0.427122i
$531$		0			0
$532$	−2.70277	−	1.80594i	−0.117180	−	0.0782972i
$533$	2.62340	+	7.72830i	0.113632	+	0.334750i
$534$		0			0
$535$	17.1893	+	2.26301i	0.743157	+	0.0978385i
$536$	−21.1695	−	2.78702i	−0.914384	−	0.120381i
$537$		0			0
$538$	4.82814	+	14.2232i	0.208156	+	0.613208i
$539$	−14.9195	−	9.96890i	−0.642629	−	0.429391i
$540$		0			0
$541$	33.0365	−	6.57136i	1.42035	−	0.282525i	0.575619	−	0.817718i	$-0.304761\pi$
$541$	33.0365	−	6.57136i	1.42035	−	0.282525i	0.844730	+	0.535193i	$0.179761\pi$
$542$	0.682249	+	5.18220i	0.0293051	+	0.222594i
$543$		0			0
$544$	−25.7815	+	13.0681i	−1.10537	+	0.560291i
$545$	14.8591	+	8.57889i	0.636492	+	0.367479i
$546$		0			0
$547$	−22.9071	+	20.0890i	−0.979438	+	0.858944i	−0.990010	−	0.141000i	$-0.954968\pi$
$547$	−22.9071	+	20.0890i	−0.979438	+	0.858944i	0.0105719	+	0.999944i	$0.496635\pi$
$548$	35.8081	−	35.8081i	1.52965	−	1.52965i
$549$		0			0
$550$	1.30941	−	6.58287i	0.0558336	−	0.280695i
$551$	−17.1568	+	34.7906i	−0.730905	+	1.48213i
$552$		0			0
$553$	−0.150642	+	1.14424i	−0.00640594	+	0.0486579i
$554$	2.72838	+	41.6271i	0.115918	+	1.76856i
$555$		0			0
$556$	60.3297	+	3.95422i	2.55855	+	0.167696i
$557$	−13.7661	−	13.7661i	−0.583287	−	0.583287i	0.352518	−	0.935805i	$-0.385325\pi$
$557$	−13.7661	−	13.7661i	−0.583287	−	0.583287i	−0.935805	+	0.352518i	$0.885325\pi$
$558$		0			0
$559$	0.811444	−	1.95900i	0.0343204	−	0.0828568i
$560$	−0.234192	−	0.405632i	−0.00989640	−	0.0171411i
$561$		0			0
$562$	−21.8208	+	37.7947i	−0.920455	+	1.59428i
$563$	−6.21454	−	8.09895i	−0.261912	−	0.341330i	0.643823	−	0.765174i	$-0.277347\pi$
$563$	−6.21454	−	8.09895i	−0.261912	−	0.341330i	−0.905735	+	0.423844i	$0.860680\pi$
$564$		0			0
$565$	3.96280	−	14.7894i	0.166716	−	0.622193i
$566$	−18.7589	+	28.0747i	−0.788497	+	1.18007i
$567$		0			0
$568$	21.7419	−	14.5275i	0.912269	−	0.609559i
$569$	−18.6620	−	14.3199i	−0.782353	−	0.600321i	0.138441	−	0.990371i	$-0.455791\pi$
$569$	−18.6620	−	14.3199i	−0.782353	−	0.600321i	−0.920794	+	0.390050i	$0.872458\pi$
$570$		0			0
$571$	6.45258	−	0.422924i	0.270032	−	0.0176988i	0.0702143	−	0.997532i	$-0.477632\pi$
$571$	6.45258	−	0.422924i	0.270032	−	0.0176988i	0.199818	+	0.979833i	$0.435965\pi$
$572$	−6.38719	−	5.60142i	−0.267062	−	0.234207i
$573$		0			0
$574$	−2.77936	−	0.744727i	−0.116008	−	0.0310843i
$575$	0.809677	+	4.07052i	0.0337659	+	0.169752i
$576$		0			0
$577$		−	18.2911i		−	0.761468i	−0.924685	−	0.380734i	$-0.875671\pi$
$577$		−	18.2911i		−	0.761468i	0.924685	−	0.380734i	$-0.124329\pi$
$578$	36.6116	+	8.95268i	1.52284	+	0.372383i
$579$		0			0
$580$	28.3164	−	21.7279i	1.17577	−	0.902204i
$581$	−0.540137	+	1.59119i	−0.0224087	+	0.0660138i
$582$		0			0
$583$	−1.95799	+	29.8731i	−0.0810915	+	1.23722i
$584$	20.5776	+	4.09314i	0.851508	+	0.169375i
$585$		0			0
$586$	28.2551	+	68.2139i	1.16721	+	2.81789i
$587$	15.0635	−	19.6311i	0.621736	−	0.810262i	−0.371245	−	0.928535i	$-0.621069\pi$
$587$	15.0635	−	19.6311i	0.621736	−	0.810262i	0.992981	+	0.118273i	$0.0377358\pi$
$588$		0			0
$589$	20.7722	−	23.6861i	0.855903	−	0.975970i
$590$	−12.2969	+	6.06414i	−0.506254	+	0.249657i
$591$		0			0
$592$	7.71048	+	8.79212i	0.316899	+	0.361354i
$593$	12.7576	+	5.28436i	0.523890	+	0.217003i	0.628925	−	0.777466i	$-0.283495\pi$
$593$	12.7576	+	5.28436i	0.523890	+	0.217003i	−0.105034	+	0.994469i	$0.533495\pi$
$594$		0			0
$595$	−0.267394	+	1.42599i	−0.0109621	+	0.0584598i
$596$	43.5397	−	25.1377i	1.78346	−	1.02968i
$597$		0			0
$598$	8.38679	+	2.84693i	0.342961	+	0.116420i
$599$	2.34742	+	8.76070i	0.0959130	+	0.357952i	0.997156	−	0.0753612i	$-0.0240110\pi$
$599$	2.34742	+	8.76070i	0.0959130	+	0.357952i	−0.901243	+	0.433313i	$0.857344\pi$
$600$		0			0
$601$	6.20233	−	2.10541i	0.252998	−	0.0858813i	−0.192059	−	0.981383i	$-0.561517\pi$
$601$	6.20233	−	2.10541i	0.252998	−	0.0858813i	0.445057	+	0.895502i	$0.353183\pi$
$602$	0.415329	+	0.621584i	0.0169275	+	0.0253339i
$603$		0			0
$604$	−43.0337	+	17.8251i	−1.75102	+	0.725295i
$605$	−7.66116	−	3.77807i	−0.311471	−	0.153600i
$606$		0			0
$607$	−8.97229	−	18.1940i	−0.364174	−	0.738472i	0.635253	−	0.772304i	$-0.280896\pi$
$607$	−8.97229	−	18.1940i	−0.364174	−	0.738472i	−0.999428	+	0.0338318i	$0.989229\pi$
$608$	41.9596	−	11.2430i	1.70169	−	0.455965i
$609$		0			0
$610$	46.6618	−	6.14315i	1.88928	−	0.248729i
$611$	0.961592			0.0389019
$612$		0			0
$613$	29.3144			1.18400			0.591998	−	0.805939i	$-0.298339\pi$
$613$	29.3144			1.18400			0.591998	+	0.805939i	$0.298339\pi$
$614$	66.9854	−	8.81879i	2.70331	−	0.355897i
$615$		0			0
$616$	0.908425	−	0.243412i	0.0366015	−	0.00980734i
$617$	−7.32525	−	14.8541i	−0.294903	−	0.598005i	0.698112	−	0.715988i	$-0.254024\pi$
$617$	−7.32525	−	14.8541i	−0.294903	−	0.598005i	−0.993016	+	0.117983i	$0.962357\pi$
$618$		0			0
$619$	35.3429	+	17.4292i	1.42055	+	0.700538i	0.980332	−	0.197353i	$-0.0632345\pi$
$619$	35.3429	+	17.4292i	1.42055	+	0.700538i	0.440218	+	0.897891i	$0.354901\pi$
$620$	−26.7809	+	11.0930i	−1.07555	+	0.445506i
$621$		0			0
$622$	30.5757	+	45.7598i	1.22597	+	1.83480i
$623$	−2.47572	+	0.840395i	−0.0991878	+	0.0336697i
$624$		0			0
$625$	4.59156	+	17.1359i	0.183662	+	0.685437i
$626$	−19.6495	−	6.67011i	−0.785353	−	0.266591i
$627$		0			0
$628$	29.4647	−	17.0115i	1.17577	−	0.678832i
$629$	−0.397986	−	36.2210i	−0.0158687	−	1.44423i
$630$		0			0
$631$	−29.7616	−	12.3276i	−1.18479	−	0.490756i	−0.298735	−	0.954336i	$-0.596565\pi$
$631$	−29.7616	−	12.3276i	−1.18479	−	0.490756i	−0.886055	+	0.463580i	$0.846565\pi$
$632$	8.58346	+	9.78756i	0.341432	+	0.389328i
$633$		0			0
$634$	41.1751	−	20.3053i	1.63527	−	0.806426i
$635$	−1.66541	+	1.89903i	−0.0660896	+	0.0753608i
$636$		0			0
$637$	−4.79942	+	6.25472i	−0.190160	+	0.247821i
$638$	−13.6781	−	33.0219i	−0.541522	−	1.30735i
$639$		0			0
$640$	−27.8807	−	5.54581i	−1.10208	−	0.219217i
$641$	−2.55496	+	38.9812i	−0.100915	+	1.53966i	0.584430	+	0.811444i	$0.301318\pi$
$641$	−2.55496	+	38.9812i	−0.100915	+	1.53966i	−0.685345	+	0.728219i	$0.740348\pi$
$642$		0			0
$643$	7.24768	−	21.3510i	0.285821	−	0.842000i	−0.705285	−	0.708924i	$-0.749181\pi$
$643$	7.24768	−	21.3510i	0.285821	−	0.842000i	0.991106	−	0.133077i	$-0.0424857\pi$
$644$	−1.46933	+	1.12746i	−0.0578999	+	0.0444281i
$645$		0			0
$646$	−51.0747	−	24.4934i	−2.00951	−	0.963678i
$647$			16.3636i			0.643321i	0.946855	+	0.321661i	$0.104241\pi$
$647$			16.3636i			0.643321i	−0.946855	+	0.321661i	$0.895759\pi$
$648$		0			0
$649$	1.58875	+	7.98720i	0.0623640	+	0.313525i
$650$	−2.84851	−	0.763257i	−0.111728	−	0.0299374i
$651$		0			0
$652$	−25.9674	−	22.7728i	−1.01696	−	0.891852i
$653$	11.0667	−	0.725348i	0.433072	−	0.0283851i	0.152692	−	0.988274i	$-0.451206\pi$
$653$	11.0667	−	0.725348i	0.433072	−	0.0283851i	0.280381	+	0.959889i	$0.409539\pi$
$654$		0			0
$655$	−22.6733	−	17.3978i	−0.885919	−	0.679790i
$656$	7.98292	−	5.33401i	0.311681	−	0.208258i
$657$		0			0
$658$	−0.188350	+	0.281885i	−0.00734263	+	0.0109890i
$659$	−8.98545	+	33.5342i	−0.350023	+	1.30631i	0.536609	+	0.843831i	$0.319705\pi$
$659$	−8.98545	+	33.5342i	−0.350023	+	1.30631i	−0.886633	+	0.462474i	$0.846962\pi$
$660$		0			0
$661$	−1.21720	−	1.58629i	−0.0473437	−	0.0616995i	0.769081	−	0.639151i	$-0.220714\pi$
$661$	−1.21720	−	1.58629i	−0.0473437	−	0.0616995i	−0.816425	+	0.577451i	$0.804047\pi$
$662$	−9.25614	+	16.0321i	−0.359750	+	0.623106i
$663$		0			0
$664$	9.47711	+	16.4148i	0.367783	+	0.637019i
$665$	0.834418	−	2.01446i	0.0323574	−	0.0781176i
$666$		0			0
$667$	15.6281	+	15.6281i	0.605123	+	0.605123i
$668$	12.7450	+	0.835348i	0.493117	+	0.0323206i
$669$		0			0
$670$	−2.98329	−	45.5162i	−0.115255	−	1.75845i
$671$	3.64878	−	27.7153i	0.140860	−	1.06994i
$672$		0			0
$673$	−0.285317	+	0.578565i	−0.0109981	+	0.0223020i	−0.902302	−	0.431103i	$-0.858124\pi$
$673$	−0.285317	+	0.578565i	−0.0109981	+	0.0223020i	0.891304	+	0.453406i	$0.149791\pi$
$674$	12.1675	−	61.1699i	0.468673	−	2.35618i
$675$		0			0
$676$	24.1605	−	24.1605i	0.929249	−	0.929249i
$677$	14.0720	−	12.3408i	0.540831	−	0.474296i	−0.344806	−	0.938674i	$-0.612055\pi$
$677$	14.0720	−	12.3408i	0.540831	−	0.474296i	0.885637	+	0.464378i	$0.153722\pi$
$678$		0			0
$679$	0.412708	+	0.238277i	0.0158383	+	0.00914423i
$680$	10.1045	+	12.8731i	0.387492	+	0.493662i
$681$		0			0
$682$	3.78898	+	28.7802i	0.145088	+	1.10205i
$683$	11.2368	−	2.23513i	0.429962	−	0.0855248i	0.0246352	−	0.999697i	$-0.492158\pi$
$683$	11.2368	−	2.23513i	0.429962	−	0.0855248i	0.405327	+	0.914172i	$0.367158\pi$
$684$		0			0
$685$	28.2438	+	18.8719i	1.07914	+	0.721059i
$686$	−1.79107	−	5.27633i	−0.0683835	−	0.201451i
$687$		0			0
$688$	−2.47307	−	0.325586i	−0.0942849	−	0.0124128i
$689$	13.0411	+	1.71689i	0.496825	+	0.0654083i
$690$		0			0
$691$	−15.9052	−	46.8552i	−0.605063	−	1.78246i	−0.622513	−	0.782609i	$-0.713888\pi$
$691$	−15.9052	−	46.8552i	−0.605063	−	1.78246i	0.0174504	−	0.999848i	$-0.494445\pi$
$692$	25.8042	+	17.2418i	0.980928	+	0.655435i
$693$		0			0
$694$	−44.5125	+	8.85408i	−1.68967	+	0.336096i
$695$	5.29347	+	40.2079i	0.200793	+	1.52517i
$696$		0			0
$697$	−29.5259	−	3.55760i	−1.11837	−	0.134754i
$698$	7.29509	+	4.21182i	0.276123	+	0.159420i
$699$		0			0
$700$	0.463635	−	0.406597i	0.0175238	−	0.0153679i
$701$	34.6398	−	34.6398i	1.30833	−	1.30833i	0.385706	−	0.922622i	$-0.373958\pi$
$701$	34.6398	−	34.6398i	1.30833	−	1.30833i	0.922622	−	0.385706i	$-0.126042\pi$
$702$		0			0
$703$	−10.6205	+	53.3931i	−0.400561	+	2.01376i
$704$	−14.6708	+	29.7495i	−0.552928	+	1.12123i
$705$		0			0
$706$	−0.785229	+	5.96441i	−0.0295525	+	0.224473i
$707$	−0.0246029	−	0.375368i	−0.000925287	−	0.0141171i
$708$		0			0
$709$	29.7155	+	1.94766i	1.11599	+	0.0731458i	0.612216	−	0.790690i	$-0.290278\pi$
$709$	29.7155	+	1.94766i	1.11599	+	0.0731458i	0.503773	+	0.863836i	$0.331945\pi$
$710$	39.4994	+	39.4994i	1.48239	+	1.48239i
$711$		0			0
$712$	−11.2856	+	27.2459i	−0.422946	+	1.02108i
$713$	−8.97490	−	15.5450i	−0.336113	−	0.582164i
$714$		0			0
$715$	2.84928	−	4.93510i	0.106557	−	0.184562i
$716$	12.1723	+	15.8633i	0.454901	+	0.592838i
$717$		0			0
$718$	14.0985	−	52.6162i	0.526150	−	1.96362i
$719$	11.7055	−	17.5185i	0.436541	−	0.653330i	−0.546342	−	0.837562i	$-0.683980\pi$
$719$	11.7055	−	17.5185i	0.436541	−	0.653330i	0.982883	+	0.184233i	$0.0589800\pi$
$720$		0			0
$721$	−0.450110	+	0.300754i	−0.0167630	+	0.0112007i
$722$	34.1180	+	26.1796i	1.26974	+	0.974305i
$723$		0			0
$724$	9.27588	−	0.607973i	0.344735	−	0.0225952i
$725$	−5.53279	−	4.85212i	−0.205483	−	0.180203i
$726$		0			0
$727$	38.7252	+	10.3764i	1.43624	+	0.384838i	0.891214	−	0.453583i	$-0.149854\pi$
$727$	38.7252	+	10.3764i	1.43624	+	0.384838i	0.545022	+	0.838421i	$0.316521\pi$
$728$	−0.0806147	−	0.405278i	−0.00298778	−	0.0150206i
$729$		0			0
$730$			44.8204i			1.65888i
$731$	5.15799	+	5.75281i	0.190775	+	0.212776i
$732$		0			0
$733$	−17.6990	+	13.5809i	−0.653728	+	0.501623i	−0.881557	−	0.472078i	$-0.843504\pi$
$733$	−17.6990	+	13.5809i	−0.653728	+	0.501623i	0.227829	+	0.973701i	$0.426837\pi$
$734$	−2.47683	+	7.29652i	−0.0914216	+	0.269319i
$735$		0			0
$736$	1.61874	−	24.6972i	0.0596675	−	0.910350i
$737$	−26.5722	−	5.28555i	−0.978801	−	0.194696i
$738$		0			0
$739$	−14.4782	−	34.9535i	−0.532590	−	1.28579i	−0.929803	−	0.368059i	$-0.880023\pi$
$739$	−14.4782	−	34.9535i	−0.532590	−	1.28579i	0.397213	−	0.917727i	$-0.369977\pi$
$740$	30.4929	−	39.7391i	1.12094	−	1.46084i
$741$		0			0
$742$	−3.05768	+	3.48662i	−0.112251	+	0.127998i
$743$	−9.54668	+	4.70790i	−0.350234	+	0.172716i	−0.608893	−	0.793252i	$-0.708386\pi$
$743$	−9.54668	+	4.70790i	−0.350234	+	0.172716i	0.258659	+	0.965969i	$0.416719\pi$
$744$		0			0
$745$	22.2356	+	25.3549i	0.814650	+	0.928931i
$746$	−63.6936	−	26.3828i	−2.33199	−	0.965941i
$747$		0			0
$748$	28.4682	−	12.1601i	1.04090	−	0.444616i
$749$	1.38148	−	0.797598i	0.0504782	−	0.0291436i
$750$		0			0
$751$	38.2405	+	12.9809i	1.39542	+	0.473680i	0.915033	−	0.403378i	$-0.132164\pi$
$751$	38.2405	+	12.9809i	1.39542	+	0.473680i	0.480384	+	0.877058i	$0.340497\pi$
$752$	−0.292777	−	1.09266i	−0.0106765	−	0.0398451i
$753$		0			0
$754$	−14.8709	+	5.04800i	−0.541567	+	0.183837i
$755$	−17.3585	−	25.9789i	−0.631742	−	0.945469i
$756$		0			0
$757$	−19.5481	+	8.09711i	−0.710489	+	0.294294i	−0.708507	−	0.705704i	$-0.750631\pi$
$757$	−19.5481	+	8.09711i	−0.710489	+	0.294294i	−0.00198230	+	0.999998i	$0.500631\pi$
$758$	−51.4039	−	25.3496i	−1.86707	−	0.920739i
$759$		0			0
$760$	−10.8781	−	22.0585i	−0.394589	−	0.800147i
$761$	6.79443	−	1.82056i	0.246298	−	0.0659953i	−0.133558	−	0.991041i	$-0.542640\pi$
$761$	6.79443	−	1.82056i	0.246298	−	0.0659953i	0.379856	+	0.925046i	$0.375974\pi$
$762$		0			0
$763$	1.56514	−	0.206055i	0.0566620	−	0.00745970i
$764$	−5.04104			−0.182378
$765$		0			0
$766$	4.66617			0.168596
$767$	3.54750	−	0.467037i	0.128093	−	0.0168637i
$768$		0			0
$769$	−13.2740	+	3.55676i	−0.478673	+	0.128260i	−0.490085	−	0.871675i	$-0.663034\pi$
$769$	−13.2740	+	3.55676i	−0.478673	+	0.128260i	0.0114118	+	0.999935i	$0.496367\pi$
$770$	0.888599	+	1.80190i	0.0320229	+	0.0649360i
$771$		0			0
$772$	2.78633	+	1.37407i	0.100282	+	0.0494538i
$773$	0.300425	−	0.124440i	0.0108055	−	0.00447580i	−0.377274	−	0.926102i	$-0.623139\pi$
$773$	0.300425	−	0.124440i	0.0108055	−	0.00447580i	0.388080	+	0.921626i	$0.373139\pi$
$774$		0			0
$775$	3.32044	+	4.96939i	0.119274	+	0.178506i
$776$	5.09016	−	1.72788i	0.182726	−	0.0620271i
$777$		0			0
$778$	−0.601394	−	2.24443i	−0.0215610	−	0.0804668i
$779$	42.3230	+	14.3667i	1.51638	+	0.514741i
$780$		0			0
$781$	28.7338	−	16.5895i	1.02818	−	0.593618i
$782$	−22.5687	+	23.0701i	−0.807054	+	0.824986i
$783$		0			0
$784$	8.56852	+	3.54920i	0.306019	+	0.126757i
$785$	15.0476	+	17.1585i	0.537071	+	0.612412i
$786$		0			0
$787$	25.8447	−	12.7452i	0.921264	−	0.454317i	0.0811346	−	0.996703i	$-0.474146\pi$
$787$	25.8447	−	12.7452i	0.921264	−	0.454317i	0.840129	+	0.542386i	$0.182479\pi$
$788$	17.2130	−	19.6276i	0.613187	−	0.699205i
$789$		0			0
$790$	−16.9298	+	22.0633i	−0.602334	+	0.784977i
$791$	−0.539101	−	1.30150i	−0.0191682	−	0.0462762i
$792$		0			0
$793$	−12.0464	−	2.39618i	−0.427780	−	0.0850908i
$794$	−1.69978	+	25.9336i	−0.0603228	+	0.920349i
$795$		0			0
$796$	−16.5037	+	48.6184i	−0.584959	+	1.72323i
$797$	7.65465	−	5.87362i	0.271142	−	0.208054i	−0.464237	−	0.885711i	$-0.653671\pi$
$797$	7.65465	−	5.87362i	0.271142	−	0.208054i	0.735378	+	0.677657i	$0.237005\pi$
$798$		0			0
$799$	−1.51514	+	3.15944i	−0.0536018	+	0.111773i
$800$			8.24091i			0.291360i
$801$		0			0
$802$	3.66784	+	18.4395i	0.129516	+	0.651121i
$803$	25.7144	+	6.89016i	0.907442	+	0.243148i
$804$		0			0
$805$	−0.934029	−	0.819121i	−0.0329202	−	0.0288702i
$806$	12.7270	−	0.834174i	0.448291	−	0.0293825i
$807$		0			0
$808$	−3.36632	−	2.58307i	−0.118427	−	0.0908721i
$809$	7.78611	−	5.20251i	0.273745	−	0.182911i	−0.411119	−	0.911582i	$-0.634862\pi$
$809$	7.78611	−	5.20251i	0.273745	−	0.182911i	0.684864	+	0.728671i	$0.259862\pi$
$810$		0			0
$811$	−15.7832	+	23.6213i	−0.554225	+	0.829456i	−0.997767	−	0.0667978i	$-0.978722\pi$
$811$	−15.7832	+	23.6213i	−0.554225	+	0.829456i	0.443542	+	0.896254i	$0.353722\pi$
$812$	0.849949	−	3.17205i	0.0298274	−	0.111317i
$813$		0			0
$814$	−30.5361	−	39.7955i	−1.07029	−	1.39483i
$815$	11.5839	−	20.0639i	0.405766	−	0.702807i
$816$		0			0
$817$	−5.80605	−	10.0564i	−0.203128	−	0.351828i
$818$	−28.8702	+	69.6989i	−1.00942	+	2.43696i
$819$		0			0
$820$	−29.0793	−	29.0793i	−1.01549	−	1.01549i
$821$	32.1567	+	2.10766i	1.12228	+	0.0735579i	0.615221	−	0.788355i	$-0.289067\pi$
$821$	32.1567	+	2.10766i	1.12228	+	0.0735579i	0.507056	+	0.861913i	$0.330734\pi$
$822$		0			0
$823$	−0.751231	−	11.4616i	−0.0261863	−	0.399525i	−0.990752	−	0.135684i	$-0.956677\pi$
$823$	−0.751231	−	11.4616i	−0.0261863	−	0.399525i	0.964566	−	0.263842i	$-0.0849897\pi$
$824$	−0.797023	+	6.05399i	−0.0277656	+	0.210901i
$825$		0			0
$826$	−0.557949	+	1.13141i	−0.0194135	+	0.0393667i
$827$	−5.08115	+	25.5447i	−0.176689	+	0.888275i	0.786116	+	0.618079i	$0.212089\pi$
$827$	−5.08115	+	25.5447i	−0.176689	+	0.888275i	−0.962805	+	0.270196i	$0.912911\pi$
$828$		0			0
$829$	5.16068	−	5.16068i	0.179238	−	0.179238i	−0.611786	−	0.791023i	$-0.709549\pi$
$829$	5.16068	−	5.16068i	0.179238	−	0.179238i	0.791023	+	0.611786i	$0.209549\pi$
$830$	−30.4429	+	26.6977i	−1.05669	+	0.926691i
$831$		0			0
$832$	12.6216	+	7.28706i	0.437574	+	0.252634i
$833$	−12.9885	−	25.6244i	−0.450025	−	0.887834i
$834$		0			0
$835$	1.11827	+	8.49413i	0.0386994	+	0.293951i
$836$	−45.6300	+	9.07637i	−1.57815	+	0.313913i
$837$		0			0
$838$	−20.6671	−	13.8093i	−0.713934	−	0.477035i
$839$	−1.48606	−	4.37779i	−0.0513045	−	0.151138i	0.918258	−	0.395983i	$-0.129596\pi$
$839$	−1.48606	−	4.37779i	−0.0513045	−	0.151138i	−0.969562	+	0.244845i	$0.921263\pi$
$840$		0			0
$841$	−10.1018	−	1.32993i	−0.348339	−	0.0458597i
$842$	−74.4392	−	9.80011i	−2.56535	−	0.337734i
$843$		0			0
$844$	10.0777	+	29.6881i	0.346890	+	1.02191i
$845$	19.0567	+	12.7333i	0.655571	+	0.438038i
$846$		0			0
$847$	−0.770837	+	0.153329i	−0.0264863	+	0.00526845i
$848$	−2.01972	−	15.3413i	−0.0693575	−	0.526822i
$849$		0			0
$850$	6.99606	−	8.15654i	0.239963	−	0.279767i
$851$	26.8616	+	15.5086i	0.920805	+	0.531627i
$852$		0			0
$853$	18.8057	−	16.4922i	0.643895	−	0.564681i	−0.273889	−	0.961761i	$-0.588310\pi$
$853$	18.8057	−	16.4922i	0.643895	−	0.564681i	0.917784	+	0.397081i	$0.129977\pi$
$854$	3.06199	−	3.06199i	0.104779	−	0.104779i
$855$		0			0
$856$	3.51035	−	17.6477i	0.119981	−	0.603187i
$857$	2.78614	−	5.64973i	0.0951727	−	0.192991i	−0.844080	−	0.536217i	$-0.819853\pi$
$857$	2.78614	−	5.64973i	0.0951727	−	0.192991i	0.939253	+	0.343226i	$0.111520\pi$
$858$		0			0
$859$	4.78059	−	36.3122i	0.163112	−	1.23896i	−0.692530	−	0.721389i	$-0.743504\pi$
$859$	4.78059	−	36.3122i	0.163112	−	1.23896i	0.855642	−	0.517568i	$-0.173163\pi$
$860$	0.698795	+	10.6616i	0.0238287	+	0.363556i
$861$		0			0
$862$	−17.0772	−	1.11930i	−0.581651	−	0.0381234i
$863$	33.6934	+	33.6934i	1.14694	+	1.14694i	0.987152	+	0.159784i	$0.0510798\pi$
$863$	33.6934	+	33.6934i	1.14694	+	1.14694i	0.159784	+	0.987152i	$0.448920\pi$
$864$		0			0
$865$	−7.96644	+	19.2327i	−0.270867	+	0.653931i
$866$	−26.1610	−	45.3123i	−0.888989	−	1.53977i
$867$		0			0
$868$	−1.33354	+	2.30975i	−0.0452631	+	0.0783981i
$869$	10.0556	+	13.1047i	0.341113	+	0.444547i
$870$		0			0
$871$	−3.08094	+	11.4982i	−0.104394	+	0.389603i
$872$	9.89296	−	14.8059i	0.335018	−	0.501390i
$873$		0			0
$874$	40.3289	−	26.9469i	1.36414	−	0.911492i
$875$	1.72400	+	1.32287i	0.0582818	+	0.0447212i
$876$		0			0
$877$	10.9320	−	0.716523i	0.369148	−	0.0241953i	0.120300	−	0.992738i	$-0.461614\pi$
$877$	10.9320	−	0.716523i	0.369148	−	0.0241953i	0.248849	+	0.968542i	$0.419948\pi$
$878$	−0.558361	−	0.489670i	−0.0188438	−	0.0165255i
$879$		0			0
$880$	−6.47528	−	1.73505i	−0.218282	−	0.0584884i
$881$	2.51851	+	12.6614i	0.0848506	+	0.426573i	0.999739	+	0.0228649i	$0.00727877\pi$
$881$	2.51851	+	12.6614i	0.0848506	+	0.426573i	−0.914888	+	0.403708i	$0.867721\pi$
$882$		0			0
$883$		−	57.1259i		−	1.92244i	−0.275781	−	0.961220i	$-0.588937\pi$
$883$		−	57.1259i		−	1.92244i	0.275781	−	0.961220i	$-0.411063\pi$
$884$	−4.51329	−	12.8308i	−0.151798	−	0.431547i
$885$		0			0
$886$	0.285348	−	0.218955i	0.00958645	−	0.00735594i
$887$	11.6789	−	34.4050i	0.392139	−	1.15521i	−0.554298	−	0.832318i	$-0.687013\pi$
$887$	11.6789	−	34.4050i	0.392139	−	1.15521i	0.946437	−	0.322887i	$-0.104653\pi$
$888$		0			0
$889$	−0.0151995	+	0.231900i	−0.000509776	+	0.00777768i
$890$	−61.7895	−	12.2907i	−2.07119	−	0.411985i
$891$		0			0
$892$	−18.0589	−	43.5980i	−0.604656	−	1.45977i
$893$	3.20575	−	4.17782i	0.107276	−	0.139805i
$894$		0			0
$895$	−8.84342	+	10.0840i	−0.295603	+	0.337071i
$896$	−2.34577	+	1.15680i	−0.0783666	+	0.0386461i
$897$		0			0
$898$	−20.6719	−	23.5718i	−0.689830	−	0.786601i
$899$	29.4048	+	12.1798i	0.980703	+	0.406221i
$900$		0			0
$901$	−26.1893	+	40.1429i	−0.872492	+	1.33736i
$902$	−35.6652	+	20.5913i	−1.18752	+	0.685616i
$903$		0			0
$904$	−15.0470	−	5.10777i	−0.500456	−	0.169882i
$905$	1.61385	+	6.02297i	0.0536462	+	0.200210i
$906$		0			0
$907$	−2.45193	+	0.832316i	−0.0814148	+	0.0276366i	−0.361850	−	0.932236i	$-0.617855\pi$
$907$	−2.45193	+	0.832316i	−0.0814148	+	0.0276366i	0.280435	+	0.959873i	$0.409521\pi$
$908$	10.5162	+	15.7386i	0.348993	+	0.522305i
$909$		0			0
$910$	0.815547	−	0.337810i	0.0270351	−	0.0111983i
$911$	−40.9359	−	20.1873i	−1.35627	−	0.668836i	−0.388679	−	0.921373i	$-0.627068\pi$
$911$	−40.9359	−	20.1873i	−1.35627	−	0.668836i	−0.967587	+	0.252537i	$0.918735\pi$
$912$		0			0
$913$	10.6371	+	21.5699i	0.352037	+	0.713861i
$914$	−37.5892	+	10.0720i	−1.24334	+	0.333152i
$915$		0			0
$916$	34.0500	−	4.48276i	1.12504	−	0.148115i
$917$	−2.62950			−0.0868337
$918$		0			0
$919$	12.2132			0.402876			0.201438	−	0.979501i	$-0.435439\pi$
$919$	12.2132			0.402876			0.201438	+	0.979501i	$0.435439\pi$
$920$	−13.8933	+	1.82909i	−0.458048	+	0.0603032i
$921$		0			0
$922$	−37.9785	+	10.1763i	−1.25075	+	0.335139i
$923$	−6.44766	−	13.0746i	−0.212227	−	0.430354i
$924$		0			0
$925$	−9.26253	−	4.56778i	−0.304550	−	0.150188i
$926$	38.4791	−	15.9386i	1.26450	−	0.523774i
$927$		0			0
$928$	24.3815	+	36.4894i	0.800361	+	1.19782i
$929$	−51.9532	+	17.6357i	−1.70453	+	0.578610i	−0.992358	−	0.123394i	$-0.960622\pi$
$929$	−51.9532	+	17.6357i	−1.70453	+	0.578610i	−0.712173	+	0.702004i	$0.752289\pi$
$930$		0			0
$931$	11.1745	+	41.7040i	0.366231	+	1.36679i
$932$	−20.0694	−	6.81263i	−0.657394	−	0.223155i
$933$		0			0
$934$	−51.6243	+	29.8053i	−1.68920	+	0.975258i
$935$	11.7255	+	17.1377i	0.383463	+	0.560464i
$936$		0			0
$937$	−42.4638	−	17.5891i	−1.38723	−	0.574610i	−0.440826	−	0.897593i	$-0.645314\pi$
$937$	−42.4638	−	17.5891i	−1.38723	−	0.574610i	−0.946405	+	0.322983i	$0.895314\pi$
$938$	−2.76717	−	3.15535i	−0.0903512	−	0.103026i
$939$		0			0
$940$	−4.34565	+	2.14304i	−0.141739	+	0.0698981i
$941$	−31.2184	+	35.5977i	−1.01769	+	1.16045i	−0.0307223	+	0.999528i	$0.509781\pi$
$941$	−31.2184	+	35.5977i	−1.01769	+	1.16045i	−0.986967	+	0.160924i	$0.948553\pi$
$942$		0			0
$943$	15.5023	−	20.2030i	0.504824	−	0.657900i
$944$	−1.61080	−	3.88883i	−0.0524272	−	0.126571i
$945$		0			0
$946$	10.4940	+	2.08738i	0.341189	+	0.0678667i
$947$	1.64772	−	25.1394i	0.0535438	−	0.816920i	−0.883658	−	0.468133i	$-0.844927\pi$
$947$	1.64772	−	25.1394i	0.0535438	−	0.816920i	0.937202	−	0.348787i	$-0.113406\pi$
$948$		0			0
$949$	3.75981	−	11.0760i	0.122048	−	0.359543i
$950$	−12.8125	+	9.83136i	−0.415692	+	0.318972i
$951$		0			0
$952$	1.45861	+	0.373708i	0.0472740	+	0.0121119i
$953$		−	8.03487i		−	0.260275i	−0.991496	−	0.130138i	$-0.958458\pi$
$953$		−	8.03487i		−	0.260275i	0.991496	−	0.130138i	$-0.0415419\pi$
$954$		0			0
$955$	−0.659685	−	3.31646i	−0.0213469	−	0.107318i
$956$	−34.9675	−	9.36952i	−1.13093	−	0.303032i
$957$		0			0
$958$	−19.8502	−	17.4082i	−0.641332	−	0.562433i
$959$	3.11868	−	0.204409i	0.100707	−	0.00660072i
$960$		0			0
$961$	4.08673	+	3.13586i	0.131830	+	0.101157i
$962$	−18.3251	+	12.2445i	−0.590825	+	0.394777i
$963$		0			0
$964$	2.79789	−	4.18733i	0.0901138	−	0.134865i
$965$	−0.539361	+	2.01292i	−0.0173626	+	0.0647982i
$966$		0			0
$967$	−17.9863	−	23.4401i	−0.578399	−	0.753784i	0.408914	−	0.912573i	$-0.365908\pi$
$967$	−17.9863	−	23.4401i	−0.578399	−	0.753784i	−0.987313	+	0.158789i	$0.949241\pi$
$968$	−4.43262	+	7.67752i	−0.142470	+	0.246765i
$969$		0			0
$970$	5.74167	+	9.94486i	0.184354	+	0.319310i
$971$	4.64743	−	11.2199i	0.149143	−	0.360064i	−0.831597	−	0.555379i	$-0.812573\pi$
$971$	4.64743	−	11.2199i	0.149143	−	0.360064i	0.980740	+	0.195316i	$0.0625731\pi$
$972$		0			0
$973$	2.63848	+	2.63848i	0.0845856	+	0.0845856i
$974$	−35.3404	−	2.31633i	−1.13238	−	0.0742201i
$975$		0			0
$976$	0.944999	+	14.4179i	0.0302487	+	0.461506i
$977$	−4.32703	+	32.8670i	−0.138434	+	1.05151i	0.771345	+	0.636417i	$0.219584\pi$
$977$	−4.32703	+	32.8670i	−0.138434	+	1.05151i	−0.909779	+	0.415093i	$0.863749\pi$
$978$		0			0
$979$	−16.5502	+	33.5605i	−0.528947	+	1.07260i
$980$	7.75015	−	38.9626i	0.247569	−	1.24462i
$981$		0			0
$982$	−15.9158	+	15.9158i	−0.507894	+	0.507894i
$983$	29.7343	−	26.0762i	0.948376	−	0.831703i	−0.0374805	−	0.999297i	$-0.511933\pi$
$983$	29.7343	−	26.0762i	0.948376	−	0.831703i	0.985856	+	0.167594i	$0.0535999\pi$
$984$		0			0
$985$	15.1654	+	8.75575i	0.483210	+	0.278981i
$986$	6.84559	−	56.8143i	0.218008	−	1.80934i
$987$		0			0
$988$	2.66813	+	20.2665i	0.0848846	+	0.644763i
$989$	−6.48896	+	1.29074i	−0.206337	+	0.0410430i
$990$		0			0
$991$	−39.0754	−	26.1093i	−1.24127	−	0.829390i	−0.250924	−	0.968007i	$-0.580734\pi$
$991$	−39.0754	−	26.1093i	−1.24127	−	0.829390i	−0.990346	+	0.138616i	$0.955734\pi$
$992$	−11.4567	−	33.7502i	−0.363749	−	1.07157i
$993$		0			0
$994$	5.09565	+	0.670854i	0.161624	+	0.0212782i
$995$	−34.1454	−	4.49532i	−1.08248	−	0.142511i
$996$		0			0
$997$	−7.65963	−	22.5645i	−0.242583	−	0.714626i	−0.998220	−	0.0596357i	$-0.981006\pi$
$997$	−7.65963	−	22.5645i	−0.242583	−	0.714626i	0.755637	−	0.654990i	$-0.227327\pi$
$998$	22.7024	+	15.1693i	0.718632	+	0.480175i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.y.a.368.14		256
3.2	odd	2		153.2.s.a.113.3	yes	256
9.2	odd	6	inner	459.2.y.a.62.14		256
9.7	even	3		153.2.s.a.11.3	✓	256
17.14	odd	16	inner	459.2.y.a.422.14		256
51.14	even	16		153.2.s.a.14.3	yes	256
153.65	even	48	inner	459.2.y.a.116.14		256
153.133	odd	48		153.2.s.a.65.3	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.3	✓	256	9.7	even	3
153.2.s.a.14.3	yes	256	51.14	even	16
153.2.s.a.65.3	yes	256	153.133	odd	48
153.2.s.a.113.3	yes	256	3.2	odd	2
459.2.y.a.62.14		256	9.2	odd	6	inner
459.2.y.a.116.14		256	153.65	even	48	inner
459.2.y.a.368.14		256	1.1	even	1	trivial
459.2.y.a.422.14		256	17.14	odd	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.y (of order \(48\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.19811 - 0.289387i) q^{2} +(2.81610 - 0.754572i) q^{4} +(0.864950 + 1.75395i) q^{5} +(0.161377 + 0.0795822i) q^{7} +(1.87511 - 0.776696i) q^{8} +(2.40883 + 3.60506i) q^{10} +(2.43861 - 0.827795i) q^{11} +(-0.292855 - 1.09295i) q^{13} +(0.377754 + 0.128230i) q^{14} +(-1.15275 + 0.665543i) q^{16} +(4.05247 + 0.759899i) q^{17} +(-5.72485 - 2.37131i) q^{19} +(3.75926 + 4.28662i) q^{20} +(5.12077 - 2.52529i) q^{22} +(-2.32784 + 2.65439i) q^{23} +(0.715622 - 0.932617i) q^{25} +(-0.960014 - 2.31768i) q^{26} +(0.514504 + 0.102341i) q^{28} +(0.409431 - 6.24671i) q^{29} +(-1.63425 + 4.81435i) q^{31} +(-5.56167 + 4.26762i) q^{32} +(9.12770 + 0.497610i) q^{34} +0.351881i q^{35} +(-1.71395 - 8.61661i) q^{37} +(-13.2701 - 3.55571i) q^{38} +(2.98416 + 2.61704i) q^{40} +(-7.19745 + 0.471746i) q^{41} +(1.48672 + 1.14080i) q^{43} +(6.24273 - 4.17126i) q^{44} +(-4.34870 + 6.50829i) q^{46} +(-0.219953 + 0.820877i) q^{47} +(-4.24162 - 5.52779i) q^{49} +(1.30313 - 2.25709i) q^{50} +(-1.64942 - 2.85688i) q^{52} +(-4.44864 + 10.7400i) q^{53} +(3.56118 + 3.56118i) q^{55} +(0.364411 + 0.0238847i) q^{56} +(-0.907741 - 13.8494i) q^{58} +(-0.412757 + 3.13520i) q^{59} +(4.80101 - 9.73548i) q^{61} +(-2.19906 + 11.0554i) q^{62} +(-9.10774 + 9.10774i) q^{64} +(1.66367 - 1.45900i) q^{65} +(-9.11090 - 5.26018i) q^{67} +(11.9856 - 0.917931i) q^{68} +(0.101830 + 0.773473i) q^{70} +(12.6361 - 2.51348i) q^{71} +(8.59520 + 5.74313i) q^{73} +(-6.26099 - 18.4443i) q^{74} +(-17.9111 - 2.35804i) q^{76} +(0.459412 + 0.0604827i) q^{77} +(2.06175 + 6.07373i) q^{79} +(-2.16440 - 1.44621i) q^{80} +(-15.6843 + 3.11980i) q^{82} +(1.21897 + 9.25898i) q^{83} +(2.17237 + 7.76509i) q^{85} +(3.59810 + 2.07737i) q^{86} +(3.92971 - 3.44626i) q^{88} +(-10.2745 + 10.2745i) q^{89} +(0.0397194 - 0.199683i) q^{91} +(-4.55250 + 9.23155i) q^{92} +(-0.245931 + 1.86803i) q^{94} +(-0.792561 - 12.0921i) q^{95} +(2.64284 + 0.173221i) q^{97} +(-10.9232 - 10.9232i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 24 q^{2} - 8 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 24 q^{11} - 8 q^{13} + 24 q^{14} - 32 q^{19} + 24 q^{20} - 8 q^{22} + 24 q^{23} - 8 q^{25} - 32 q^{28} + 24 q^{29} - 8 q^{31} + 24 q^{32} - 56 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) \) 256 * q + 24 * q^2 - 8 * q^4 + 24 * q^5 - 8 * q^7 - 32 * q^10 + 24 * q^11 - 8 * q^13 + 24 * q^14 - 32 * q^19 + 24 * q^20 - 8 * q^22 + 24 * q^23 - 8 * q^25 - 32 * q^28 + 24 * q^29 - 8 * q^31 + 24 * q^32 - 56 * q^34 - 32 * q^37 - 8 * q^40 + 24 * q^41 + 16 * q^43 - 32 * q^46 - 96 * q^47 - 8 * q^49 - 16 * q^52 - 32 * q^55 - 216 * q^56 - 8 * q^58 + 24 * q^59 - 8 * q^61 - 96 * q^64 - 24 * q^65 + 24 * q^68 + 8 * q^70 - 32 * q^73 + 24 * q^74 - 8 * q^76 + 24 * q^77 - 8 * q^79 + 160 * q^82 + 24 * q^83 - 8 * q^85 - 192 * q^86 - 8 * q^88 - 128 * q^91 + 24 * q^92 - 8 * q^94 - 216 * q^95 - 8 * q^97

Introduction

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