LMFDB - Embedded newform 735.2.m.c.538.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(97,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("735.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.m (of order $4$, degree $2$, 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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			538.6
Character	$\chi$	$=$	735.538
Dual form			735.2.m.c.97.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09556 + 1.09556i) q^{2} +(0.707107 - 0.707107i) q^{3} -0.400511i q^{4} +(0.531984 + 2.17186i) q^{5} +1.54936i q^{6} +(-1.75234 - 1.75234i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.09556 + 1.09556i) q^{2} +(0.707107 - 0.707107i) q^{3} -0.400511i q^{4} +(0.531984 + 2.17186i) q^{5} +1.54936i q^{6} +(-1.75234 - 1.75234i) q^{8} -1.00000i q^{9} +(-2.96223 - 1.79659i) q^{10} +5.18923 q^{11} +(-0.283204 - 0.283204i) q^{12} +(3.30901 - 3.30901i) q^{13} +(1.91191 + 1.15957i) q^{15} +4.64061 q^{16} +(-0.0142038 - 0.0142038i) q^{17} +(1.09556 + 1.09556i) q^{18} +2.48097 q^{19} +(0.869856 - 0.213066i) q^{20} +(-5.68512 + 5.68512i) q^{22} +(1.64418 + 1.64418i) q^{23} -2.47818 q^{24} +(-4.43399 + 2.31079i) q^{25} +7.25046i q^{26} +(-0.707107 - 0.707107i) q^{27} +10.2081i q^{29} +(-3.36500 + 0.824234i) q^{30} -6.57334i q^{31} +(-1.57940 + 1.57940i) q^{32} +(3.66934 - 3.66934i) q^{33} +0.0311223 q^{34} -0.400511 q^{36} +(-1.95145 + 1.95145i) q^{37} +(-2.71805 + 2.71805i) q^{38} -4.67965i q^{39} +(2.87363 - 4.73806i) q^{40} +3.68910i q^{41} +(-2.79725 - 2.79725i) q^{43} -2.07835i q^{44} +(2.17186 - 0.531984i) q^{45} -3.60260 q^{46} +(0.828330 + 0.828330i) q^{47} +(3.28141 - 3.28141i) q^{48} +(2.32609 - 7.38932i) q^{50} -0.0200872 q^{51} +(-1.32530 - 1.32530i) q^{52} +(3.37433 + 3.37433i) q^{53} +1.54936 q^{54} +(2.76059 + 11.2703i) q^{55} +(1.75431 - 1.75431i) q^{57} +(-11.1836 - 11.1836i) q^{58} -0.445177 q^{59} +(0.464421 - 0.765741i) q^{60} +1.36997i q^{61} +(7.20150 + 7.20150i) q^{62} +5.82056i q^{64} +(8.94707 + 5.42639i) q^{65} +8.03998i q^{66} +(-4.17856 + 4.17856i) q^{67} +(-0.00568879 + 0.00568879i) q^{68} +2.32522 q^{69} -2.14741 q^{71} +(-1.75234 + 1.75234i) q^{72} +(5.23877 - 5.23877i) q^{73} -4.27586i q^{74} +(-1.50132 + 4.76928i) q^{75} -0.993655i q^{76} +(5.12685 + 5.12685i) q^{78} +4.00779i q^{79} +(2.46873 + 10.0788i) q^{80} -1.00000 q^{81} +(-4.04164 - 4.04164i) q^{82} +(3.77525 - 3.77525i) q^{83} +(0.0232926 - 0.0384050i) q^{85} +6.12911 q^{86} +(7.21821 + 7.21821i) q^{87} +(-9.09329 - 9.09329i) q^{88} +3.83884 q^{89} +(-1.79659 + 2.96223i) q^{90} +(0.658512 - 0.658512i) q^{92} +(-4.64805 - 4.64805i) q^{93} -1.81497 q^{94} +(1.31983 + 5.38832i) q^{95} +2.23361i q^{96} +(-10.5936 - 10.5936i) q^{97} -5.18923i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 24 q^{8}+O(q^{10}) $ 32 * q - 24 * q^8	$ 32 q - 24 q^{8} + 16 q^{11} - 8 q^{15} - 8 q^{22} + 16 q^{23} - 24 q^{25} - 16 q^{30} - 48 q^{32} - 32 q^{36} - 8 q^{37} + 40 q^{43} + 80 q^{46} + 72 q^{50} + 16 q^{51} + 48 q^{53} + 16 q^{57} - 8 q^{58} - 40 q^{60} + 8 q^{65} - 16 q^{67} - 16 q^{71} - 24 q^{72} + 80 q^{78} - 32 q^{81} - 72 q^{85} + 32 q^{86} + 64 q^{88} - 56 q^{92} + 48 q^{93} + 24 q^{95}+O(q^{100}) $ 32 * q - 24 * q^8 + 16 * q^11 - 8 * q^15 - 8 * q^22 + 16 * q^23 - 24 * q^25 - 16 * q^30 - 48 * q^32 - 32 * q^36 - 8 * q^37 + 40 * q^43 + 80 * q^46 + 72 * q^50 + 16 * q^51 + 48 * q^53 + 16 * q^57 - 8 * q^58 - 40 * q^60 + 8 * q^65 - 16 * q^67 - 16 * q^71 - 24 * q^72 + 80 * q^78 - 32 * q^81 - 72 * q^85 + 32 * q^86 + 64 * q^88 - 56 * q^92 + 48 * q^93 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.09556	+	1.09556i	−0.774679	+	0.774679i	−0.978921	−	0.204241i	$-0.934527\pi$
$2$	−1.09556	+	1.09556i	−0.774679	+	0.774679i	0.204241	+	0.978921i	$0.434527\pi$
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		−	0.400511i		−	0.200256i
$5$	0.531984	+	2.17186i	0.237910	+	0.971287i
$5$	0.531984	+	2.17186i	0.237910	+	0.971287i
$6$			1.54936i			0.632523i
$7$		0			0
$7$		0			0
$8$	−1.75234	−	1.75234i	−0.619545	−	0.619545i
$9$		−	1.00000i		−	0.333333i
$10$	−2.96223	−	1.79659i	−0.936740	−	0.568132i
$11$	5.18923			1.56461			0.782306	−	0.622895i	$-0.214043\pi$
$11$	5.18923			1.56461			0.782306	+	0.622895i	$0.214043\pi$
$12$	−0.283204	−	0.283204i	−0.0817540	−	0.0817540i
$13$	3.30901	−	3.30901i	0.917755	−	0.917755i	−0.0791106	−	0.996866i	$-0.525208\pi$
$13$	3.30901	−	3.30901i	0.917755	−	0.917755i	0.996866	+	0.0791106i	$0.0252080\pi$
$14$		0			0
$15$	1.91191	+	1.15957i	0.493653	+	0.299400i
$16$	4.64061			1.16015
$17$	−0.0142038	−	0.0142038i	−0.00344493	−	0.00344493i	0.705382	−	0.708827i	$-0.250775\pi$
$17$	−0.0142038	−	0.0142038i	−0.00344493	−	0.00344493i	−0.708827	+	0.705382i	$0.750775\pi$
$18$	1.09556	+	1.09556i	0.258226	+	0.258226i
$19$	2.48097			0.569173			0.284586	−	0.958650i	$-0.408144\pi$
$19$	2.48097			0.569173			0.284586	+	0.958650i	$0.408144\pi$
$20$	0.869856	−	0.213066i	0.194506	−	0.0476429i
$21$		0			0
$22$	−5.68512	+	5.68512i	−1.21207	+	1.21207i
$23$	1.64418	+	1.64418i	0.342835	+	0.342835i	0.857432	−	0.514597i	$-0.172059\pi$
$23$	1.64418	+	1.64418i	0.342835	+	0.342835i	−0.514597	+	0.857432i	$0.672059\pi$
$24$	−2.47818			−0.505857
$25$	−4.43399	+	2.31079i	−0.886797	+	0.462159i
$26$			7.25046i			1.42193i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$			10.2081i			1.89559i	0.318874	+	0.947797i	$0.396695\pi$
$29$			10.2081i			1.89559i	−0.318874	+	0.947797i	$0.603305\pi$
$30$	−3.36500	+	0.824234i	−0.614361	+	0.150484i
$31$		−	6.57334i		−	1.18061i	−0.807182	−	0.590303i	$-0.799008\pi$
$31$		−	6.57334i		−	1.18061i	0.807182	−	0.590303i	$-0.200992\pi$
$32$	−1.57940	+	1.57940i	−0.279201	+	0.279201i
$33$	3.66934	−	3.66934i	0.638750	−	0.638750i
$34$	0.0311223			0.00533744
$35$		0			0
$36$	−0.400511			−0.0667519
$37$	−1.95145	+	1.95145i	−0.320816	+	0.320816i	−0.849080	−	0.528264i	$-0.822843\pi$
$37$	−1.95145	+	1.95145i	−0.320816	+	0.320816i	0.528264	+	0.849080i	$0.322843\pi$
$38$	−2.71805	+	2.71805i	−0.440926	+	0.440926i
$39$		−	4.67965i		−	0.749344i
$40$	2.87363	−	4.73806i	0.454360	−	0.749153i
$41$			3.68910i			0.576141i	0.957609	+	0.288070i	$0.0930137\pi$
$41$			3.68910i			0.576141i	−0.957609	+	0.288070i	$0.906986\pi$
$42$		0			0
$43$	−2.79725	−	2.79725i	−0.426576	−	0.426576i	0.460884	−	0.887460i	$-0.347532\pi$
$43$	−2.79725	−	2.79725i	−0.426576	−	0.426576i	−0.887460	+	0.460884i	$0.847532\pi$
$44$		−	2.07835i		−	0.313322i
$45$	2.17186	−	0.531984i	0.323762	−	0.0793035i
$46$	−3.60260			−0.531174
$47$	0.828330	+	0.828330i	0.120824	+	0.120824i	0.764934	−	0.644109i	$-0.222772\pi$
$47$	0.828330	+	0.828330i	0.120824	+	0.120824i	−0.644109	+	0.764934i	$0.722772\pi$
$48$	3.28141	−	3.28141i	0.473631	−	0.473631i
$49$		0			0
$50$	2.32609	−	7.38932i	0.328959	−	1.04501i
$51$	−0.0200872			−0.00281278
$52$	−1.32530	−	1.32530i	−0.183786	−	0.183786i
$53$	3.37433	+	3.37433i	0.463500	+	0.463500i	0.899801	−	0.436301i	$-0.143712\pi$
$53$	3.37433	+	3.37433i	0.463500	+	0.463500i	−0.436301	+	0.899801i	$0.643712\pi$
$54$	1.54936			0.210841
$55$	2.76059	+	11.2703i	0.372237	+	1.51969i
$56$		0			0
$57$	1.75431	−	1.75431i	0.232364	−	0.232364i
$58$	−11.1836	−	11.1836i	−1.46848	−	1.46848i
$59$	−0.445177			−0.0579571			−0.0289786	−	0.999580i	$-0.509225\pi$
$59$	−0.445177			−0.0579571			−0.0289786	+	0.999580i	$0.509225\pi$
$60$	0.464421	−	0.765741i	0.0599565	−	0.0988568i
$61$			1.36997i			0.175406i	0.996147	+	0.0877032i	$0.0279527\pi$
$61$			1.36997i			0.175406i	−0.996147	+	0.0877032i	$0.972047\pi$
$62$	7.20150	+	7.20150i	0.914591	+	0.914591i
$63$		0			0
$64$			5.82056i			0.727570i
$65$	8.94707	+	5.42639i	1.10975	+	0.673060i
$66$			8.03998i			0.989653i
$67$	−4.17856	+	4.17856i	−0.510492	+	0.510492i	−0.914677	−	0.404185i	$-0.867555\pi$
$67$	−4.17856	+	4.17856i	−0.510492	+	0.510492i	0.404185	+	0.914677i	$0.367555\pi$
$68$	−0.00568879	+	0.00568879i	−0.000689868	+	0.000689868i
$69$	2.32522			0.279923
$70$		0			0
$71$	−2.14741			−0.254850			−0.127425	−	0.991848i	$-0.540671\pi$
$71$	−2.14741			−0.254850			−0.127425	+	0.991848i	$0.540671\pi$
$72$	−1.75234	+	1.75234i	−0.206515	+	0.206515i
$73$	5.23877	−	5.23877i	0.613151	−	0.613151i	−0.330615	−	0.943766i	$-0.607256\pi$
$73$	5.23877	−	5.23877i	0.613151	−	0.613151i	0.943766	+	0.330615i	$0.107256\pi$
$74$		−	4.27586i		−	0.497059i
$75$	−1.50132	+	4.76928i	−0.173358	+	0.550709i
$76$		−	0.993655i		−	0.113980i
$77$		0			0
$78$	5.12685	+	5.12685i	0.580501	+	0.580501i
$79$			4.00779i			0.450911i	0.974253	+	0.225456i	$0.0723871\pi$
$79$			4.00779i			0.450911i	−0.974253	+	0.225456i	$0.927613\pi$
$80$	2.46873	+	10.0788i	0.276013	+	1.12684i
$81$	−1.00000			−0.111111
$82$	−4.04164	−	4.04164i	−0.446324	−	0.446324i
$83$	3.77525	−	3.77525i	0.414387	−	0.414387i	−0.468876	−	0.883264i	$-0.655341\pi$
$83$	3.77525	−	3.77525i	0.414387	−	0.414387i	0.883264	+	0.468876i	$0.155341\pi$
$84$		0			0
$85$	0.0232926	−	0.0384050i	0.00252643	−	0.00416561i
$86$	6.12911			0.660919
$87$	7.21821	+	7.21821i	0.773873	+	0.773873i
$88$	−9.09329	−	9.09329i	−0.969348	−	0.969348i
$89$	3.83884			0.406916			0.203458	−	0.979084i	$-0.434782\pi$
$89$	3.83884			0.406916			0.203458	+	0.979084i	$0.434782\pi$
$90$	−1.79659	+	2.96223i	−0.189377	+	0.312247i
$91$		0			0
$92$	0.658512	−	0.658512i	0.0686546	−	0.0686546i
$93$	−4.64805	−	4.64805i	−0.481981	−	0.481981i
$94$	−1.81497			−0.187200
$95$	1.31983	+	5.38832i	0.135412	+	0.552830i
$96$			2.23361i			0.227967i
$97$	−10.5936	−	10.5936i	−1.07561	−	1.07561i	−0.996897	−	0.0787167i	$-0.974918\pi$
$97$	−10.5936	−	10.5936i	−1.07561	−	1.07561i	−0.0787167	−	0.996897i	$-0.525082\pi$
$98$		0			0
$99$		−	5.18923i		−	0.521537i
$100$	0.925499	+	1.77586i	0.0925499	+	0.177586i
$101$			6.78565i			0.675198i	0.941290	+	0.337599i	$0.109615\pi$
$101$			6.78565i			0.675198i	−0.941290	+	0.337599i	$0.890385\pi$
$102$	0.0220068	−	0.0220068i	0.00217900	−	0.00217900i
$103$	6.65628	−	6.65628i	0.655863	−	0.655863i	−0.298536	−	0.954399i	$-0.596498\pi$
$103$	6.65628	−	6.65628i	0.655863	−	0.655863i	0.954399	+	0.298536i	$0.0964981\pi$
$104$	−11.5970			−1.13718
$105$		0			0
$106$	−7.39357			−0.718127
$107$	−8.79648	+	8.79648i	−0.850388	+	0.850388i	−0.990181	−	0.139793i	$-0.955356\pi$
$107$	−8.79648	+	8.79648i	−0.850388	+	0.850388i	0.139793	+	0.990181i	$0.455356\pi$
$108$	−0.283204	+	0.283204i	−0.0272513	+	0.0272513i
$109$			8.72881i			0.836068i	0.908431	+	0.418034i	$0.137281\pi$
$109$			8.72881i			0.836068i	−0.908431	+	0.418034i	$0.862719\pi$
$110$	−15.3717	−	9.32292i	−1.46563	−	0.888905i
$111$			2.75976i			0.261945i
$112$		0			0
$113$	−2.80125	−	2.80125i	−0.263519	−	0.263519i	0.562963	−	0.826482i	$-0.309661\pi$
$113$	−2.80125	−	2.80125i	−0.263519	−	0.263519i	−0.826482	+	0.562963i	$0.809661\pi$
$114$			3.84391i			0.360015i
$115$	−2.69625	+	4.44561i	−0.251427	+	0.414555i
$116$	4.08845			0.379603
$117$	−3.30901	−	3.30901i	−0.305918	−	0.305918i
$118$	0.487719	−	0.487719i	0.0448982	−	0.0448982i
$119$		0			0
$120$	−1.31835	−	5.38227i	−0.120349	−	0.491332i
$121$	15.9281			1.44801
$122$	−1.50088	−	1.50088i	−0.135884	−	0.135884i
$123$	2.60859	+	2.60859i	0.235208	+	0.235208i
$124$	−2.63270			−0.236423
$125$	−7.37754	−	8.40071i	−0.659867	−	0.751382i
$126$		0			0
$127$	2.63342	−	2.63342i	0.233679	−	0.233679i	−0.580548	−	0.814226i	$-0.697162\pi$
$127$	2.63342	−	2.63342i	0.233679	−	0.233679i	0.814226	+	0.580548i	$0.197162\pi$
$128$	−9.53559	−	9.53559i	−0.842835	−	0.842835i
$129$	−3.95590			−0.348298
$130$	−15.7470	+	3.85713i	−1.38110	+	0.338292i
$131$			3.00874i			0.262875i	0.991324	+	0.131437i	$0.0419592\pi$
$131$			3.00874i			0.262875i	−0.991324	+	0.131437i	$0.958041\pi$
$132$	−1.46961	−	1.46961i	−0.127913	−	0.127913i
$133$		0			0
$134$		−	9.15574i		−	0.790936i
$135$	1.15957	−	1.91191i	0.0997999	−	0.164551i
$136$			0.0497798i			0.00426858i
$137$	7.46715	−	7.46715i	0.637962	−	0.637962i	−0.312090	−	0.950052i	$-0.601029\pi$
$137$	7.46715	−	7.46715i	0.637962	−	0.637962i	0.950052	+	0.312090i	$0.101029\pi$
$138$	−2.54742	+	2.54742i	−0.216851	+	0.216851i
$139$	1.76721			0.149893			0.0749465	−	0.997188i	$-0.476121\pi$
$139$	1.76721			0.149893			0.0749465	+	0.997188i	$0.476121\pi$
$140$		0			0
$141$	1.17144			0.0986527
$142$	2.35262	−	2.35262i	0.197427	−	0.197427i
$143$	17.1712	−	17.1712i	1.43593	−	1.43593i
$144$		−	4.64061i		−	0.386718i
$145$	−22.1706	+	5.43054i	−1.84117	+	0.450981i
$146$			11.4788i			0.949991i
$147$		0			0
$148$	0.781577	+	0.781577i	0.0642452	+	0.0642452i
$149$		−	7.37301i		−	0.604020i	−0.953305	−	0.302010i	$-0.902342\pi$
$149$		−	7.37301i		−	0.604020i	0.953305	−	0.302010i	$-0.0976577\pi$
$150$	−3.58025	−	6.86983i	−0.292326	−	0.560920i
$151$	16.3565			1.33107			0.665535	−	0.746367i	$-0.268203\pi$
$151$	16.3565			1.33107			0.665535	+	0.746367i	$0.268203\pi$
$152$	−4.34749	−	4.34749i	−0.352628	−	0.352628i
$153$	−0.0142038	+	0.0142038i	−0.00114831	+	0.00114831i
$154$		0			0
$155$	14.2764	−	3.49691i	1.14671	−	0.280878i
$156$	−1.87425			−0.150060
$157$	−16.2132	−	16.2132i	−1.29395	−	1.29395i	−0.932321	−	0.361633i	$-0.882219\pi$
$157$	−16.2132	−	16.2132i	−1.29395	−	1.29395i	−0.361633	−	0.932321i	$-0.617781\pi$
$158$	−4.39078	−	4.39078i	−0.349312	−	0.349312i
$159$	4.77202			0.378446
$160$	−4.27046	−	2.59003i	−0.337610	−	0.204760i
$161$		0			0
$162$	1.09556	−	1.09556i	0.0860755	−	0.0860755i
$163$	10.7937	+	10.7937i	0.845429	+	0.845429i	0.989559	−	0.144129i	$-0.0460382\pi$
$163$	10.7937	+	10.7937i	0.845429	+	0.845429i	−0.144129	+	0.989559i	$0.546038\pi$
$164$	1.47753			0.115375
$165$	9.92133	+	6.01728i	0.772375	+	0.468444i
$166$			8.27204i			0.642034i
$167$	−8.60951	−	8.60951i	−0.666224	−	0.666224i	0.290616	−	0.956840i	$-0.406140\pi$
$167$	−8.60951	−	8.60951i	−0.666224	−	0.666224i	−0.956840	+	0.290616i	$0.906140\pi$
$168$		0			0
$169$		−	8.89914i		−	0.684550i
$170$	0.0165566	+	0.0675935i	0.00126983	+	0.00518418i
$171$		−	2.48097i		−	0.189724i
$172$	−1.12033	+	1.12033i	−0.0854243	+	0.0854243i
$173$	−2.55690	+	2.55690i	−0.194397	+	0.194397i	−0.797593	−	0.603196i	$-0.793894\pi$
$173$	−2.55690	+	2.55690i	−0.194397	+	0.194397i	0.603196	+	0.797593i	$0.293894\pi$
$174$	−15.8160			−1.19901
$175$		0			0
$176$	24.0812			1.81519
$177$	−0.314788	+	0.314788i	−0.0236609	+	0.0236609i
$178$	−4.20569	+	4.20569i	−0.315229	+	0.315229i
$179$		−	13.8904i		−	1.03822i	−0.854708	−	0.519108i	$-0.826264\pi$
$179$		−	13.8904i		−	1.03822i	0.854708	−	0.519108i	$-0.173736\pi$
$180$	−0.213066	−	0.869856i	−0.0158810	−	0.0648353i
$181$		−	15.4270i		−	1.14668i	−0.819318	−	0.573339i	$-0.805648\pi$
$181$		−	15.4270i		−	1.14668i	0.819318	−	0.573339i	$-0.194352\pi$
$182$		0			0
$183$	0.968714	+	0.968714i	0.0716094	+	0.0716094i
$184$		−	5.76231i		−	0.424803i
$185$	−5.27642	−	3.20014i	−0.387930	−	0.235279i
$186$	10.1845			0.746761
$187$	−0.0737069	−	0.0737069i	−0.00538998	−	0.00538998i
$188$	0.331756	−	0.331756i	0.0241958	−	0.0241958i
$189$		0			0
$190$	−7.34920	−	4.45728i	−0.533167	−	0.323365i
$191$	−0.0567941			−0.00410948			−0.00205474	−	0.999998i	$-0.500654\pi$
$191$	−0.0567941			−0.00410948			−0.00205474	+	0.999998i	$0.500654\pi$
$192$	4.11576	+	4.11576i	0.297029	+	0.297029i
$193$	1.68049	+	1.68049i	0.120964	+	0.120964i	0.764997	−	0.644033i	$-0.222740\pi$
$193$	1.68049	+	1.68049i	0.120964	+	0.120964i	−0.644033	+	0.764997i	$0.722740\pi$
$194$	23.2118			1.66651
$195$	10.1636	−	2.48950i	0.727828	−	0.178277i
$196$		0			0
$197$	0.251120	−	0.251120i	0.0178916	−	0.0178916i	−0.698104	−	0.715996i	$-0.745973\pi$
$197$	0.251120	−	0.251120i	0.0178916	−	0.0178916i	0.715996	+	0.698104i	$0.245973\pi$
$198$	5.68512	+	5.68512i	0.404024	+	0.404024i
$199$	25.1076			1.77983			0.889917	−	0.456123i	$-0.150762\pi$
$199$	25.1076			1.77983			0.889917	+	0.456123i	$0.150762\pi$
$200$	11.8191	+	3.72055i	0.835739	+	0.263083i
$201$			5.90938i			0.416815i
$202$	−7.43410	−	7.43410i	−0.523062	−	0.523062i
$203$		0			0
$204$			0.00804517i			0.000563274i
$205$	−8.01222	+	1.96254i	−0.559598	+	0.137070i
$206$			14.5847i			1.01617i
$207$	1.64418	−	1.64418i	0.114278	−	0.114278i
$208$	15.3559	−	15.3559i	1.06474	−	1.06474i
$209$	12.8743			0.890534
$210$		0			0
$211$	−15.2060			−1.04682			−0.523411	−	0.852080i	$-0.675341\pi$
$211$	−15.2060			−1.04682			−0.523411	+	0.852080i	$0.675341\pi$
$212$	1.35146	−	1.35146i	0.0928184	−	0.0928184i
$213$	−1.51845	+	1.51845i	−0.104042	+	0.104042i
$214$		−	19.2742i		−	1.31756i
$215$	4.58715	−	7.56333i	0.312841	−	0.515815i
$216$			2.47818i			0.168619i
$217$		0			0
$218$	−9.56295	−	9.56295i	−0.647685	−	0.647685i
$219$		−	7.40874i		−	0.500636i
$220$	4.51388	−	1.10565i	0.304326	−	0.0745426i
$221$	−0.0940013			−0.00632321
$222$	−3.02349	−	3.02349i	−0.202923	−	0.202923i
$223$	−3.59679	+	3.59679i	−0.240859	+	0.240859i	−0.817205	−	0.576346i	$-0.804478\pi$
$223$	−3.59679	+	3.59679i	−0.240859	+	0.240859i	0.576346	+	0.817205i	$0.304478\pi$
$224$		0			0
$225$	2.31079	+	4.43399i	0.154053	+	0.295599i
$226$	6.13788			0.408285
$227$	5.33517	+	5.33517i	0.354108	+	0.354108i	0.861635	−	0.507528i	$-0.169440\pi$
$227$	5.33517	+	5.33517i	0.354108	+	0.354108i	−0.507528	+	0.861635i	$0.669440\pi$
$228$	−0.702620	−	0.702620i	−0.0465322	−	0.0465322i
$229$	−25.7256			−1.70000			−0.849998	−	0.526786i	$-0.823397\pi$
$229$	−25.7256			−1.70000			−0.849998	+	0.526786i	$0.823397\pi$
$230$	−1.91652	−	7.82435i	−0.126372	−	0.515922i
$231$		0			0
$232$	17.8880	−	17.8880i	1.17441	−	1.17441i
$233$	−18.9657	−	18.9657i	−1.24249	−	1.24249i	−0.958966	−	0.283521i	$-0.908498\pi$
$233$	−18.9657	−	18.9657i	−1.24249	−	1.24249i	−0.283521	−	0.958966i	$-0.591502\pi$
$234$	7.25046			0.473977
$235$	−1.35836	+	2.23968i	−0.0886098	+	0.146101i
$236$			0.178299i			0.0116062i
$237$	2.83393	+	2.83393i	0.184084	+	0.184084i
$238$		0			0
$239$			19.0811i			1.23425i	0.786863	+	0.617127i	$0.211704\pi$
$239$			19.0811i			1.23425i	−0.786863	+	0.617127i	$0.788296\pi$
$240$	8.87243	+	5.38112i	0.572713	+	0.347350i
$241$		−	12.2495i		−	0.789063i	−0.918882	−	0.394531i	$-0.870907\pi$
$241$		−	12.2495i		−	0.789063i	0.918882	−	0.394531i	$-0.129093\pi$
$242$	−17.4502	+	17.4502i	−1.12174	+	1.12174i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	0.548688			0.0351261
$245$		0			0
$246$	−5.71574			−0.364422
$247$	8.20955	−	8.20955i	0.522361	−	0.522361i
$248$	−11.5187	+	11.5187i	−0.731439	+	0.731439i
$249$		−	5.33901i		−	0.338346i
$250$	17.2860	+	1.12095i	1.09327	+	0.0708952i
$251$		−	24.6455i		−	1.55561i	−0.628505	−	0.777806i	$-0.716333\pi$
$251$		−	24.6455i		−	1.55561i	0.628505	−	0.777806i	$-0.283667\pi$
$252$		0			0
$253$	8.53201	+	8.53201i	0.536403	+	0.536403i
$254$			5.77016i			0.362052i
$255$	−0.0106861	−	0.0436268i	−0.000669189	−	0.00273201i
$256$	9.25253			0.578283
$257$	−6.00685	−	6.00685i	−0.374697	−	0.374697i	0.494488	−	0.869185i	$-0.335356\pi$
$257$	−6.00685	−	6.00685i	−0.374697	−	0.374697i	−0.869185	+	0.494488i	$0.835356\pi$
$258$	4.33394	−	4.33394i	0.269819	−	0.269819i
$259$		0			0
$260$	2.17333	−	3.58340i	0.134784	−	0.222233i
$261$	10.2081			0.631865
$262$	−3.29626	−	3.29626i	−0.203643	−	0.203643i
$263$	−17.3987	−	17.3987i	−1.07285	−	1.07285i	−0.997129	−	0.0757235i	$-0.975873\pi$
$263$	−17.3987	−	17.3987i	−1.07285	−	1.07285i	−0.0757235	−	0.997129i	$-0.524127\pi$
$264$	−12.8598			−0.791469
$265$	−5.53349	+	9.12367i	−0.339920	+	0.560463i
$266$		0			0
$267$	2.71447	−	2.71447i	0.166123	−	0.166123i
$268$	1.67356	+	1.67356i	0.102229	+	0.102229i
$269$	−19.9339			−1.21539			−0.607696	−	0.794170i	$-0.707906\pi$
$269$	−19.9339			−1.21539			−0.607696	+	0.794170i	$0.707906\pi$
$270$	0.824234	+	3.36500i	0.0501613	+	0.204787i
$271$			28.2586i			1.71659i	0.513160	+	0.858293i	$0.328475\pi$
$271$			28.2586i			1.71659i	−0.513160	+	0.858293i	$0.671525\pi$
$272$	−0.0659145	−	0.0659145i	−0.00399665	−	0.00399665i
$273$		0			0
$274$			16.3615i			0.988432i
$275$	−23.0090	+	11.9912i	−1.38749	+	0.723099i
$276$		−	0.931276i		−	0.0560562i
$277$	21.1186	−	21.1186i	1.26889	−	1.26889i	0.322231	−	0.946661i	$-0.395567\pi$
$277$	21.1186	−	21.1186i	1.26889	−	1.26889i	0.946661	−	0.322231i	$-0.104433\pi$
$278$	−1.93609	+	1.93609i	−0.116119	+	0.116119i
$279$	−6.57334			−0.393535
$280$		0			0
$281$	−17.9592			−1.07135			−0.535677	−	0.844423i	$-0.679944\pi$
$281$	−17.9592			−1.07135			−0.535677	+	0.844423i	$0.679944\pi$
$282$	−1.28338	+	1.28338i	−0.0764242	+	0.0764242i
$283$	−16.1181	+	16.1181i	−0.958123	+	0.958123i	−0.999158	−	0.0410343i	$-0.986935\pi$
$283$	−16.1181	+	16.1181i	−0.958123	+	0.958123i	0.0410343	+	0.999158i	$0.486935\pi$
$284$			0.860060i			0.0510352i
$285$	4.74338	+	2.87685i	0.280974	+	0.170410i
$286$			37.6243i			2.22477i
$287$		0			0
$288$	1.57940	+	1.57940i	0.0930671	+	0.0930671i
$289$		−	16.9996i		−	0.999976i
$290$	18.3397	−	30.2387i	1.07695	−	1.77568i
$291$	−14.9816			−0.878235
$292$	−2.09819	−	2.09819i	−0.122787	−	0.122787i
$293$	−17.3271	+	17.3271i	−1.01226	+	1.01226i	−0.0123342	+	0.999924i	$0.503926\pi$
$293$	−17.3271	+	17.3271i	−1.01226	+	1.01226i	−0.999924	+	0.0123342i	$0.996074\pi$
$294$		0			0
$295$	−0.236827	−	0.966865i	−0.0137886	−	0.0562930i
$296$	6.83919			0.397520
$297$	−3.66934	−	3.66934i	−0.212917	−	0.212917i
$298$	8.07759	+	8.07759i	0.467922	+	0.467922i
$299$	10.8812			0.629277
$300$	1.91015	+	0.601298i	0.110283	+	0.0347159i
$301$		0			0
$302$	−17.9195	+	17.9195i	−1.03115	+	1.03115i
$303$	4.79818	+	4.79818i	0.275648	+	0.275648i
$304$	11.5132			0.660328
$305$	−2.97538	+	0.728801i	−0.170370	+	0.0417310i
$306$		−	0.0311223i		−	0.00177915i
$307$	7.07730	+	7.07730i	0.403923	+	0.403923i	0.879613	−	0.475690i	$-0.157802\pi$
$307$	7.07730	+	7.07730i	0.403923	+	0.403923i	−0.475690	+	0.879613i	$0.657802\pi$
$308$		0			0
$309$		−	9.41340i		−	0.535510i
$310$	−11.8096	+	19.4718i	−0.670740	+	1.10592i
$311$		−	4.98885i		−	0.282892i	−0.989946	−	0.141446i	$-0.954825\pi$
$311$		−	4.98885i		−	0.282892i	0.989946	−	0.141446i	$-0.0451751\pi$
$312$	−8.20034	+	8.20034i	−0.464253	+	0.464253i
$313$	4.17161	−	4.17161i	0.235794	−	0.235794i	−0.579312	−	0.815106i	$-0.696679\pi$
$313$	4.17161	−	4.17161i	0.235794	−	0.235794i	0.815106	+	0.579312i	$0.196679\pi$
$314$	35.5251			2.00480
$315$		0			0
$316$	1.60516			0.0902975
$317$	−0.623714	+	0.623714i	−0.0350313	+	0.0350313i	−0.724405	−	0.689374i	$-0.757886\pi$
$317$	−0.623714	+	0.623714i	−0.0350313	+	0.0350313i	0.689374	+	0.724405i	$0.257886\pi$
$318$	−5.22804	+	5.22804i	−0.293174	+	0.293174i
$319$			52.9721i			2.96587i
$320$	−12.6415	+	3.09645i	−0.706680	+	0.173097i
$321$			12.4401i			0.694339i
$322$		0			0
$323$	−0.0352392	−	0.0352392i	−0.00196076	−	0.00196076i
$324$			0.400511i			0.0222506i
$325$	−7.02568	+	22.3186i	−0.389714	+	1.23801i
$326$	−23.6504			−1.30987
$327$	6.17220	+	6.17220i	0.341323	+	0.341323i
$328$	6.46455	−	6.46455i	0.356945	−	0.356945i
$329$		0			0
$330$	−17.4617	+	4.27714i	−0.961237	+	0.235449i
$331$	−23.9584			−1.31687			−0.658435	−	0.752637i	$-0.728781\pi$
$331$	−23.9584			−1.31687			−0.658435	+	0.752637i	$0.728781\pi$
$332$	−1.51203	−	1.51203i	−0.0829834	−	0.0829834i
$333$	1.95145	+	1.95145i	0.106939	+	0.106939i
$334$	18.8645			1.03222
$335$	−11.2982	−	6.85234i	−0.617286	−	0.374383i
$336$		0			0
$337$	−2.18043	+	2.18043i	−0.118776	+	0.118776i	−0.763996	−	0.645221i	$-0.776765\pi$
$337$	−2.18043	+	2.18043i	−0.118776	+	0.118776i	0.645221	+	0.763996i	$0.276765\pi$
$338$	9.74956	+	9.74956i	0.530306	+	0.530306i
$339$	−3.96156			−0.215162
$340$	−0.0153816	−	0.00932894i	−0.000834186	−	0.000505933i
$341$		−	34.1106i		−	1.84719i
$342$	2.71805	+	2.71805i	0.146975	+	0.146975i
$343$		0			0
$344$			9.80345i			0.528567i
$345$	1.23698	+	5.05006i	0.0665967	+	0.271886i
$346$		−	5.60248i		−	0.301191i
$347$	−11.0281	+	11.0281i	−0.592019	+	0.592019i	−0.938176	−	0.346158i	$-0.887486\pi$
$347$	−11.0281	+	11.0281i	−0.592019	+	0.592019i	0.346158	+	0.938176i	$0.387486\pi$
$348$	2.89097	−	2.89097i	0.154972	−	0.154972i
$349$	34.9635			1.87155			0.935776	−	0.352596i	$-0.114701\pi$
$349$	34.9635			1.87155			0.935776	+	0.352596i	$0.114701\pi$
$350$		0			0
$351$	−4.67965			−0.249781
$352$	−8.19588	+	8.19588i	−0.436842	+	0.436842i
$353$	−2.59387	+	2.59387i	−0.138058	+	0.138058i	−0.772758	−	0.634700i	$-0.781123\pi$
$353$	−2.59387	+	2.59387i	−0.138058	+	0.138058i	0.634700	+	0.772758i	$0.281123\pi$
$354$		−	0.689739i		−	0.0366592i
$355$	−1.14239	−	4.66387i	−0.0606315	−	0.247533i
$356$		−	1.53750i		−	0.0814873i
$357$		0			0
$358$	15.2178	+	15.2178i	0.804285	+	0.804285i
$359$		−	16.1113i		−	0.850324i	−0.905117	−	0.425162i	$-0.860217\pi$
$359$		−	16.1113i		−	0.850324i	0.905117	−	0.425162i	$-0.139783\pi$
$360$	−4.73806	−	2.87363i	−0.249718	−	0.151453i
$361$	−12.8448			−0.676043
$362$	16.9012	+	16.9012i	0.888307	+	0.888307i
$363$	11.2629	−	11.2629i	0.591147	−	0.591147i
$364$		0			0
$365$	14.1648	+	8.59095i	0.741421	+	0.449671i
$366$	−2.12257			−0.110949
$367$	20.8870	+	20.8870i	1.09029	+	1.09029i	0.995497	+	0.0947935i	$0.0302191\pi$
$367$	20.8870	+	20.8870i	1.09029	+	1.09029i	0.0947935	+	0.995497i	$0.469781\pi$
$368$	7.62999	+	7.62999i	0.397741	+	0.397741i
$369$	3.68910			0.192047
$370$	9.28659	−	2.27469i	0.482787	−	0.118255i
$371$		0			0
$372$	−1.86160	+	1.86160i	−0.0965193	+	0.0965193i
$373$	5.36302	+	5.36302i	0.277687	+	0.277687i	0.832185	−	0.554498i	$-0.187090\pi$
$373$	5.36302	+	5.36302i	0.277687	+	0.277687i	−0.554498	+	0.832185i	$0.687090\pi$
$374$	0.161501			0.00835101
$375$	−11.1569	−	0.723494i	−0.576140	−	0.0373611i
$376$		−	2.90303i		−	0.149712i
$377$	33.7787	+	33.7787i	1.73969	+	1.73969i
$378$		0			0
$379$		−	17.5078i		−	0.899317i	−0.893201	−	0.449658i	$-0.851546\pi$
$379$		−	17.5078i		−	0.899317i	0.893201	−	0.449658i	$-0.148454\pi$
$380$	2.15808	−	0.528608i	0.110707	−	0.0271170i
$381$		−	3.72422i		−	0.190798i
$382$	0.0622215	−	0.0622215i	0.00318353	−	0.00318353i
$383$	−8.40518	+	8.40518i	−0.429485	+	0.429485i	−0.888453	−	0.458968i	$-0.848219\pi$
$383$	−8.40518	+	8.40518i	−0.429485	+	0.429485i	0.458968	+	0.888453i	$0.348219\pi$
$384$	−13.4854			−0.688172
$385$		0			0
$386$	−3.68216			−0.187417
$387$	−2.79725	+	2.79725i	−0.142192	+	0.142192i
$388$	−4.24284	+	4.24284i	−0.215398	+	0.215398i
$389$			8.66261i			0.439212i	0.975589	+	0.219606i	$0.0704771\pi$
$389$			8.66261i			0.439212i	−0.975589	+	0.219606i	$0.929523\pi$
$390$	−8.40742	+	13.8622i	−0.425726	+	0.701941i
$391$		−	0.0467072i		−	0.00236209i
$392$		0			0
$393$	2.12750	+	2.12750i	0.107318	+	0.107318i
$394$			0.550235i			0.0277204i
$395$	−8.70437	+	2.13208i	−0.437964	+	0.107276i
$396$	−2.07835			−0.104441
$397$	−1.85222	−	1.85222i	−0.0929600	−	0.0929600i	0.659097	−	0.752058i	$-0.270938\pi$
$397$	−1.85222	−	1.85222i	−0.0929600	−	0.0929600i	−0.752058	+	0.659097i	$0.770938\pi$
$398$	−27.5070	+	27.5070i	−1.37880	+	1.37880i
$399$		0			0
$400$	−20.5764	+	10.7235i	−1.02882	+	0.536175i
$401$	9.96036			0.497396			0.248698	−	0.968581i	$-0.419997\pi$
$401$	9.96036			0.497396			0.248698	+	0.968581i	$0.419997\pi$
$402$	−6.47409	−	6.47409i	−0.322898	−	0.322898i
$403$	−21.7513	−	21.7513i	−1.08351	−	1.08351i
$404$	2.71773			0.135212
$405$	−0.531984	−	2.17186i	−0.0264345	−	0.107921i
$406$		0			0
$407$	−10.1265	+	10.1265i	−0.501952	+	0.501952i
$408$	0.0351997	+	0.0351997i	0.00174264	+	0.00174264i
$409$	−8.06563			−0.398820			−0.199410	−	0.979916i	$-0.563903\pi$
$409$	−8.06563			−0.398820			−0.199410	+	0.979916i	$0.563903\pi$
$410$	6.62780	−	10.9280i	0.327324	−	0.539694i
$411$		−	10.5602i		−	0.520894i
$412$	−2.66592	−	2.66592i	−0.131340	−	0.131340i
$413$		0			0
$414$			3.60260i			0.177058i
$415$	10.2077	+	6.19095i	0.501076	+	0.303902i
$416$			10.4525i			0.512477i
$417$	1.24961	−	1.24961i	0.0611935	−	0.0611935i
$418$	−14.1046	+	14.1046i	−0.689878	+	0.689878i
$419$	1.30845			0.0639222			0.0319611	−	0.999489i	$-0.489825\pi$
$419$	1.30845			0.0639222			0.0319611	+	0.999489i	$0.489825\pi$
$420$		0			0
$421$	2.88085			0.140404			0.0702020	−	0.997533i	$-0.477636\pi$
$421$	2.88085			0.140404			0.0702020	+	0.997533i	$0.477636\pi$
$422$	16.6591	−	16.6591i	0.810951	−	0.810951i
$423$	0.828330	−	0.828330i	0.0402748	−	0.0402748i
$424$		−	11.8259i		−	0.574318i
$425$	0.0958017	+	0.0301575i	0.00464706	+	0.00146285i
$426$		−	3.32710i		−	0.161199i
$427$		0			0
$428$	3.52309	+	3.52309i	0.170295	+	0.170295i
$429$		−	24.2838i		−	1.17243i
$430$	3.26059	+	13.3116i	0.157240	+	0.641943i
$431$	20.8325			1.00347			0.501734	−	0.865022i	$-0.332696\pi$
$431$	20.8325			1.00347			0.501734	+	0.865022i	$0.332696\pi$
$432$	−3.28141	−	3.28141i	−0.157877	−	0.157877i
$433$	−5.72121	+	5.72121i	−0.274944	+	0.274944i	−0.831087	−	0.556143i	$-0.812281\pi$
$433$	−5.72121	+	5.72121i	−0.274944	+	0.274944i	0.556143	+	0.831087i	$0.312281\pi$
$434$		0			0
$435$	−11.8370	+	19.5169i	−0.567540	+	0.935765i
$436$	3.49599			0.167427
$437$	4.07915	+	4.07915i	0.195132	+	0.195132i
$438$	8.11673	+	8.11673i	0.387832	+	0.387832i
$439$	8.63928			0.412330			0.206165	−	0.978517i	$-0.433902\pi$
$439$	8.63928			0.412330			0.206165	+	0.978517i	$0.433902\pi$
$440$	14.9119	−	24.5869i	0.710897	−	1.17213i
$441$		0			0
$442$	0.102984	−	0.102984i	0.00489846	−	0.00489846i
$443$	22.0087	+	22.0087i	1.04567	+	1.04567i	0.998906	+	0.0467589i	$0.0148893\pi$
$443$	22.0087	+	22.0087i	1.04567	+	1.04567i	0.0467589	+	0.998906i	$0.485111\pi$
$444$	1.10532			0.0524560
$445$	2.04220	+	8.33744i	0.0968096	+	0.395232i
$446$		−	7.88102i		−	0.373177i
$447$	−5.21350	−	5.21350i	−0.246590	−	0.246590i
$448$		0			0
$449$		−	40.3196i		−	1.90280i	−0.307962	−	0.951399i	$-0.599647\pi$
$449$		−	40.3196i		−	1.90280i	0.307962	−	0.951399i	$-0.400353\pi$
$450$	−7.38932	−	2.32609i	−0.348336	−	0.109653i
$451$			19.1436i			0.901436i
$452$	−1.12193	+	1.12193i	−0.0527712	+	0.0527712i
$453$	11.5658	−	11.5658i	0.543407	−	0.543407i
$454$	−11.6900			−0.548640
$455$		0			0
$456$	−6.14828			−0.287920
$457$	−9.46669	+	9.46669i	−0.442833	+	0.442833i	−0.892963	−	0.450130i	$-0.851378\pi$
$457$	−9.46669	+	9.46669i	−0.442833	+	0.442833i	0.450130	+	0.892963i	$0.351378\pi$
$458$	28.1840	−	28.1840i	1.31695	−	1.31695i
$459$			0.0200872i			0.000937592i
$460$	1.78052	+	1.07988i	0.0830170	+	0.0503497i
$461$		−	2.07258i		−	0.0965298i	−0.998835	−	0.0482649i	$-0.984631\pi$
$461$		−	2.07258i		−	0.0965298i	0.998835	−	0.0482649i	$-0.0153692\pi$
$462$		0			0
$463$	12.9744	+	12.9744i	0.602971	+	0.602971i	0.941100	−	0.338129i	$-0.109794\pi$
$463$	12.9744	+	12.9744i	0.602971	+	0.602971i	−0.338129	+	0.941100i	$0.609794\pi$
$464$			47.3718i			2.19918i
$465$	7.62225	−	12.5676i	0.353473	−	0.582810i
$466$	41.5563			1.92506
$467$	18.2080	+	18.2080i	0.842565	+	0.842565i	0.989192	−	0.146626i	$-0.0468415\pi$
$467$	18.2080	+	18.2080i	0.842565	+	0.842565i	−0.146626	+	0.989192i	$0.546842\pi$
$468$	−1.32530	+	1.32530i	−0.0612619	+	0.0612619i
$469$		0			0
$470$	−0.965537	−	3.94188i	−0.0445369	−	0.181825i
$471$	−22.9289			−1.05651
$472$	0.780101	+	0.780101i	0.0359071	+	0.0359071i
$473$	−14.5156	−	14.5156i	−0.667426	−	0.667426i
$474$	−6.20950			−0.285212
$475$	−11.0006	+	5.73300i	−0.504741	+	0.263048i
$476$		0			0
$477$	3.37433	−	3.37433i	0.154500	−	0.154500i
$478$	−20.9045	−	20.9045i	−0.956151	−	0.956151i
$479$	−24.9999			−1.14228			−0.571138	−	0.820854i	$-0.693498\pi$
$479$	−24.9999			−1.14228			−0.571138	+	0.820854i	$0.693498\pi$
$480$	−4.85110	+	1.18824i	−0.221421	+	0.0542357i
$481$			12.9147i			0.588861i
$482$	13.4201	+	13.4201i	0.611271	+	0.611271i
$483$		0			0
$484$		−	6.37938i		−	0.289972i
$485$	17.3722	−	28.6434i	0.788830	−	1.30063i
$486$		−	1.54936i		−	0.0702803i
$487$	19.2891	−	19.2891i	0.874073	−	0.874073i	−0.118840	−	0.992913i	$-0.537918\pi$
$487$	19.2891	−	19.2891i	0.874073	−	0.874073i	0.992913	+	0.118840i	$0.0379176\pi$
$488$	2.40065	−	2.40065i	0.108672	−	0.108672i
$489$	15.2646			0.690290
$490$		0			0
$491$	−23.4800			−1.05964			−0.529820	−	0.848110i	$-0.677740\pi$
$491$	−23.4800			−1.05964			−0.529820	+	0.848110i	$0.677740\pi$
$492$	1.04477	−	1.04477i	0.0471018	−	0.0471018i
$493$	0.144994	−	0.144994i	0.00653020	−	0.00653020i
$494$			17.9881i			0.809325i
$495$	11.2703	−	2.76059i	0.506562	−	0.124079i
$496$		−	30.5043i		−	1.36968i
$497$		0			0
$498$	5.84921	+	5.84921i	0.262109	+	0.262109i
$499$			28.6587i			1.28294i	0.767148	+	0.641470i	$0.221675\pi$
$499$			28.6587i			1.28294i	−0.767148	+	0.641470i	$0.778325\pi$
$500$	−3.36458	+	2.95479i	−0.150469	+	0.132142i
$501$	−12.1757			−0.543969
$502$	27.0007	+	27.0007i	1.20510	+	1.20510i
$503$	−7.43731	+	7.43731i	−0.331613	+	0.331613i	−0.853199	−	0.521586i	$-0.825341\pi$
$503$	−7.43731	+	7.43731i	−0.331613	+	0.331613i	0.521586	+	0.853199i	$0.325341\pi$
$504$		0			0
$505$	−14.7375	+	3.60986i	−0.655811	+	0.160637i
$506$	−18.6947			−0.831081
$507$	−6.29265	−	6.29265i	−0.279466	−	0.279466i
$508$	−1.05472	−	1.05472i	−0.0467955	−	0.0467955i
$509$	−10.1664			−0.450618			−0.225309	−	0.974287i	$-0.572339\pi$
$509$	−10.1664			−0.450618			−0.225309	+	0.974287i	$0.572339\pi$
$510$	0.0595031	+	0.0360885i	0.00263484	+	0.00159803i
$511$		0			0
$512$	8.93446	−	8.93446i	0.394851	−	0.394851i
$513$	−1.75431	−	1.75431i	−0.0774546	−	0.0774546i
$514$	13.1617			0.580540
$515$	17.9976	+	10.9155i	0.793068	+	0.480995i
$516$			1.58438i			0.0697487i
$517$	4.29840	+	4.29840i	0.189043	+	0.189043i
$518$		0			0
$519$			3.61600i			0.158725i
$520$	−6.16943	−	25.1872i	−0.270547	−	1.10453i
$521$		−	27.0511i		−	1.18513i	−0.805523	−	0.592565i	$-0.798115\pi$
$521$		−	27.0511i		−	1.18513i	0.805523	−	0.592565i	$-0.201885\pi$
$522$	−11.1836	+	11.1836i	−0.489492	+	0.489492i
$523$	−4.08066	+	4.08066i	−0.178435	+	0.178435i	−0.790673	−	0.612238i	$-0.790269\pi$
$523$	−4.08066	+	4.08066i	−0.178435	+	0.178435i	0.612238	+	0.790673i	$0.290269\pi$
$524$	1.20503			0.0526421
$525$		0			0
$526$	38.1228			1.66223
$527$	−0.0933665	+	0.0933665i	−0.00406711	+	0.00406711i
$528$	17.0280	−	17.0280i	0.741048	−	0.741048i
$529$		−	17.5934i		−	0.764929i
$530$	−3.93326	−	16.0578i	−0.170850	−	0.697508i
$531$			0.445177i			0.0193190i
$532$		0			0
$533$	12.2073	+	12.2073i	0.528756	+	0.528756i
$534$			5.94774i			0.257384i
$535$	−23.7843	−	14.4252i	−1.02829	−	0.623655i
$536$	14.6445			0.632546
$537$	−9.82199	−	9.82199i	−0.423850	−	0.423850i
$538$	21.8388	−	21.8388i	0.941539	−	0.941539i
$539$		0			0
$540$	−0.765741	−	0.464421i	−0.0329523	−	0.0199855i
$541$	−22.0309			−0.947181			−0.473590	−	0.880745i	$-0.657042\pi$
$541$	−22.0309			−0.947181			−0.473590	+	0.880745i	$0.657042\pi$
$542$	−30.9590	−	30.9590i	−1.32980	−	1.32980i
$543$	−10.9085	−	10.9085i	−0.468129	−	0.468129i
$544$	0.0448671			0.00192366
$545$	−18.9578	+	4.64358i	−0.812062	+	0.198909i
$546$		0			0
$547$	19.7018	−	19.7018i	0.842388	−	0.842388i	−0.146781	−	0.989169i	$-0.546891\pi$
$547$	19.7018	−	19.7018i	0.842388	−	0.842388i	0.989169	+	0.146781i	$0.0468913\pi$
$548$	−2.99068	−	2.99068i	−0.127756	−	0.127756i
$549$	1.36997			0.0584688
$550$	12.0706	−	38.3449i	0.514693	−	1.63503i
$551$			25.3259i			1.07892i
$552$	−4.07457	−	4.07457i	−0.173425	−	0.173425i
$553$		0			0
$554$			46.2734i			1.96597i
$555$	−5.99383	+	1.46815i	−0.254424	+	0.0623195i
$556$		−	0.707788i		−	0.0300169i
$557$	−11.3143	+	11.3143i	−0.479401	+	0.479401i	−0.904940	−	0.425539i	$-0.860084\pi$
$557$	−11.3143	+	11.3143i	−0.479401	+	0.479401i	0.425539	+	0.904940i	$0.360084\pi$
$558$	7.20150	−	7.20150i	0.304864	−	0.304864i
$559$	−18.5123			−0.782985
$560$		0			0
$561$	−0.104237			−0.00440090
$562$	19.6754	−	19.6754i	0.829956	−	0.829956i
$563$	11.3323	−	11.3323i	0.477599	−	0.477599i	−0.426764	−	0.904363i	$-0.640346\pi$
$563$	11.3323	−	11.3323i	0.477599	−	0.477599i	0.904363	+	0.426764i	$0.140346\pi$
$564$		−	0.469173i		−	0.0197558i
$565$	4.59371	−	7.57414i	0.193259	−	0.318647i
$566$		−	35.3168i		−	1.48448i
$567$		0			0
$568$	3.76298	+	3.76298i	0.157891	+	0.157891i
$569$		−	25.6356i		−	1.07470i	−0.843360	−	0.537350i	$-0.819426\pi$
$569$		−	25.6356i		−	1.07470i	0.843360	−	0.537350i	$-0.180574\pi$
$570$	−8.34844	+	2.04490i	−0.349678	+	0.0856512i
$571$	−16.6649			−0.697406			−0.348703	−	0.937233i	$-0.613378\pi$
$571$	−16.6649			−0.697406			−0.348703	+	0.937233i	$0.613378\pi$
$572$	−6.87727	−	6.87727i	−0.287553	−	0.287553i
$573$	−0.0401595	+	0.0401595i	−0.00167769	+	0.00167769i
$574$		0			0
$575$	−11.0896	−	3.49091i	−0.462469	−	0.145581i
$576$	5.82056			0.242523
$577$	−3.11451	−	3.11451i	−0.129659	−	0.129659i	0.639299	−	0.768958i	$-0.279225\pi$
$577$	−3.11451	−	3.11451i	−0.129659	−	0.129659i	−0.768958	+	0.639299i	$0.779225\pi$
$578$	18.6241	+	18.6241i	0.774661	+	0.774661i
$579$	2.37657			0.0987669
$580$	2.17499	+	8.87957i	0.0903116	+	0.368704i
$581$		0			0
$582$	16.4132	−	16.4132i	0.680350	−	0.680350i
$583$	17.5102	+	17.5102i	0.725197	+	0.725197i
$584$	−18.3602			−0.759750
$585$	5.42639	−	8.94707i	0.224353	−	0.369916i
$586$		−	37.9657i		−	1.56835i
$587$	−25.1535	−	25.1535i	−1.03820	−	1.03820i	−0.999241	−	0.0389571i	$-0.987596\pi$
$587$	−25.1535	−	25.1535i	−1.03820	−	1.03820i	−0.0389571	−	0.999241i	$-0.512404\pi$
$588$		0			0
$589$		−	16.3082i		−	0.671969i
$590$	1.31872	+	0.799801i	0.0542908	+	0.0329273i
$591$		−	0.355137i		−	0.0146084i
$592$	−9.05591	+	9.05591i	−0.372196	+	0.372196i
$593$	−30.0891	+	30.0891i	−1.23561	+	1.23561i	−0.273833	+	0.961777i	$0.588292\pi$
$593$	−30.0891	+	30.0891i	−1.23561	+	1.23561i	−0.961777	+	0.273833i	$0.911708\pi$
$594$	8.03998			0.329884
$595$		0			0
$596$	−2.95297			−0.120959
$597$	17.7538	−	17.7538i	0.726614	−	0.726614i
$598$	−11.9210	+	11.9210i	−0.487488	+	0.487488i
$599$		−	18.4501i		−	0.753852i	−0.926243	−	0.376926i	$-0.876981\pi$
$599$		−	18.4501i		−	0.753852i	0.926243	−	0.376926i	$-0.123019\pi$
$600$	10.9882	−	5.72656i	0.448592	−	0.233786i
$601$		−	4.13978i		−	0.168865i	−0.996429	−	0.0844326i	$-0.973092\pi$
$601$		−	4.13978i		−	0.168865i	0.996429	−	0.0844326i	$-0.0269078\pi$
$602$		0			0
$603$	4.17856	+	4.17856i	0.170164	+	0.170164i
$604$		−	6.55095i		−	0.266554i
$605$	8.47349	+	34.5937i	0.344496	+	1.40643i
$606$	−10.5134			−0.427078
$607$	−17.4597	−	17.4597i	−0.708667	−	0.708667i	0.257587	−	0.966255i	$-0.417072\pi$
$607$	−17.4597	−	17.4597i	−0.708667	−	0.708667i	−0.966255	+	0.257587i	$0.917072\pi$
$608$	−3.91844	+	3.91844i	−0.158914	+	0.158914i
$609$		0			0
$610$	2.46127	−	4.05816i	0.0996539	−	0.164310i
$611$	5.48191			0.221774
$612$	0.00568879	+	0.00568879i	0.000229956	+	0.000229956i
$613$	34.2874	+	34.2874i	1.38486	+	1.38486i	0.835757	+	0.549099i	$0.185029\pi$
$613$	34.2874	+	34.2874i	1.38486	+	1.38486i	0.549099	+	0.835757i	$0.314971\pi$
$614$	−15.5072			−0.625821
$615$	−4.27777	+	7.05322i	−0.172496	+	0.284413i
$616$		0			0
$617$	−9.77318	+	9.77318i	−0.393453	+	0.393453i	−0.875916	−	0.482463i	$-0.839742\pi$
$617$	−9.77318	+	9.77318i	−0.393453	+	0.393453i	0.482463	+	0.875916i	$0.339742\pi$
$618$	10.3130	+	10.3130i	0.414848	+	0.414848i
$619$	27.7798			1.11656			0.558281	−	0.829652i	$-0.311461\pi$
$619$	27.7798			1.11656			0.558281	+	0.829652i	$0.311461\pi$
$620$	−1.40055	−	5.71786i	−0.0562475	−	0.229635i
$621$		−	2.32522i		−	0.0933078i
$622$	5.46559	+	5.46559i	0.219150	+	0.219150i
$623$		0			0
$624$		−	21.7165i		−	0.869354i
$625$	14.3205	−	20.4920i	0.572819	−	0.819682i
$626$			9.14052i			0.365329i
$627$	9.10351	−	9.10351i	0.363559	−	0.363559i
$628$	−6.49357	+	6.49357i	−0.259122	+	0.259122i
$629$	0.0554360			0.00221038
$630$		0			0
$631$	15.9169			0.633641			0.316821	−	0.948486i	$-0.397385\pi$
$631$	15.9169			0.633641			0.316821	+	0.948486i	$0.397385\pi$
$632$	7.02300	−	7.02300i	0.279360	−	0.279360i
$633$	−10.7522	+	10.7522i	−0.427363	+	0.427363i
$634$		−	1.36663i		−	0.0542760i
$635$	7.12038	+	4.31850i	0.282563	+	0.171374i
$636$		−	1.91125i		−	0.0757859i
$637$		0			0
$638$	−58.0342	−	58.0342i	−2.29760	−	2.29760i
$639$			2.14741i			0.0849501i
$640$	15.6372	−	25.7828i	0.618116	−	1.01915i
$641$	−29.5822			−1.16843			−0.584214	−	0.811600i	$-0.698597\pi$
$641$	−29.5822			−1.16843			−0.584214	+	0.811600i	$0.698597\pi$
$642$	−13.6289	−	13.6289i	−0.537890	−	0.537890i
$643$	−23.0451	+	23.0451i	−0.908809	+	0.908809i	−0.996176	−	0.0873668i	$-0.972155\pi$
$643$	−23.0451	+	23.0451i	−0.908809	+	0.908809i	0.0873668	+	0.996176i	$0.472155\pi$
$644$		0			0
$645$	−2.10448	−	8.59169i	−0.0828637	−	0.338297i
$646$	0.0772135			0.00303792
$647$	19.4197	+	19.4197i	0.763466	+	0.763466i	0.976947	−	0.213481i	$-0.0684802\pi$
$647$	19.4197	+	19.4197i	0.763466	+	0.763466i	−0.213481	+	0.976947i	$0.568480\pi$
$648$	1.75234	+	1.75234i	0.0688384	+	0.0688384i
$649$	−2.31013			−0.0906804
$650$	−16.7543	−	32.1484i	−0.657158	−	1.26097i
$651$		0			0
$652$	4.32301	−	4.32301i	0.169302	−	0.169302i
$653$	23.0544	+	23.0544i	0.902188	+	0.902188i	0.995625	−	0.0934368i	$-0.0297853\pi$
$653$	23.0544	+	23.0544i	0.902188	+	0.902188i	−0.0934368	+	0.995625i	$0.529785\pi$
$654$	−13.5241			−0.528832
$655$	−6.53457	+	1.60060i	−0.255327	+	0.0625406i
$656$			17.1197i			0.668411i
$657$	−5.23877	−	5.23877i	−0.204384	−	0.204384i
$658$		0			0
$659$		−	4.16401i		−	0.162207i	−0.996706	−	0.0811034i	$-0.974156\pi$
$659$		−	4.16401i		−	0.162207i	0.996706	−	0.0811034i	$-0.0258444\pi$
$660$	2.40999	−	3.97361i	0.0938086	−	0.154672i
$661$			11.7820i			0.458266i	0.973395	+	0.229133i	$0.0735891\pi$
$661$			11.7820i			0.458266i	−0.973395	+	0.229133i	$0.926411\pi$
$662$	26.2479	−	26.2479i	1.02015	−	1.02015i
$663$	−0.0664690	+	0.0664690i	−0.00258144	+	0.00258144i
$664$	−13.2310			−0.513463
$665$		0			0
$666$	−4.27586			−0.165686
$667$	−16.7839	+	16.7839i	−0.649875	+	0.649875i
$668$	−3.44820	+	3.44820i	−0.133415	+	0.133415i
$669$			5.08663i			0.196661i
$670$	19.8850	−	4.87071i	0.768226	−	0.188172i
$671$			7.10908i			0.274443i
$672$		0			0
$673$	−7.90660	−	7.90660i	−0.304777	−	0.304777i	0.538102	−	0.842879i	$-0.319141\pi$
$673$	−7.90660	−	7.90660i	−0.304777	−	0.304777i	−0.842879	+	0.538102i	$0.819141\pi$
$674$		−	4.77759i		−	0.184026i
$675$	4.76928	+	1.50132i	0.183570	+	0.0577860i
$676$	−3.56421			−0.137085
$677$	−5.82700	−	5.82700i	−0.223950	−	0.223950i	0.586210	−	0.810159i	$-0.300619\pi$
$677$	−5.82700	−	5.82700i	−0.223950	−	0.223950i	−0.810159	+	0.586210i	$0.800619\pi$
$678$	4.34013	−	4.34013i	0.166682	−	0.166682i
$679$		0			0
$680$	−0.108115	+	0.0264821i	−0.00414602	+	0.00101554i
$681$	7.54507			0.289128
$682$	37.3702	+	37.3702i	1.43098	+	1.43098i
$683$	15.3662	+	15.3662i	0.587973	+	0.587973i	0.937082	−	0.349109i	$-0.113516\pi$
$683$	15.3662	+	15.3662i	0.587973	+	0.587973i	−0.349109	+	0.937082i	$0.613516\pi$
$684$	−0.993655			−0.0379934
$685$	20.1900	+	12.2452i	0.771422	+	0.467867i
$686$		0			0
$687$	−18.1908	+	18.1908i	−0.694020	+	0.694020i
$688$	−12.9809	−	12.9809i	−0.494894	−	0.494894i
$689$	22.3314			0.850759
$690$	−6.88784	−	4.17746i	−0.262215	−	0.159033i
$691$		−	28.8290i		−	1.09671i	−0.836247	−	0.548353i	$-0.815255\pi$
$691$		−	28.8290i		−	1.09671i	0.836247	−	0.548353i	$-0.184745\pi$
$692$	1.02407	+	1.02407i	0.0389292	+	0.0389292i
$693$		0			0
$694$		−	24.1639i		−	0.917249i
$695$	0.940128	+	3.83814i	0.0356611	+	0.145589i
$696$		−	25.2975i		−	0.958899i
$697$	0.0523993	−	0.0523993i	0.00198477	−	0.00198477i
$698$	−38.3046	+	38.3046i	−1.44985	+	1.44985i
$699$	−26.8216			−1.01449
$700$		0			0
$701$	48.9967			1.85058			0.925290	−	0.379259i	$-0.123821\pi$
$701$	48.9967			1.85058			0.925290	+	0.379259i	$0.123821\pi$
$702$	5.12685	−	5.12685i	0.193500	−	0.193500i
$703$	−4.84147	+	4.84147i	−0.182600	+	0.182600i
$704$			30.2042i			1.13836i
$705$	0.623185	+	2.54420i	0.0234705	+	0.0958201i
$706$		−	5.68349i		−	0.213901i
$707$		0			0
$708$	0.126076	+	0.126076i	0.00473823	+	0.00473823i
$709$			21.2029i			0.796292i	0.917322	+	0.398146i	$0.130346\pi$
$709$			21.2029i			0.796292i	−0.917322	+	0.398146i	$0.869654\pi$
$710$	6.36112	+	3.85801i	0.238728	+	0.144788i
$711$	4.00779			0.150304
$712$	−6.72695	−	6.72695i	−0.252103	−	0.252103i
$713$	10.8077	−	10.8077i	0.404753	−	0.404753i
$714$		0			0
$715$	46.4284	+	28.1588i	1.73632	+	1.05308i
$716$	−5.56326			−0.207909
$717$	13.4924	+	13.4924i	0.503882	+	0.503882i
$718$	17.6510	+	17.6510i	0.658728	+	0.658728i
$719$	15.9329			0.594198			0.297099	−	0.954847i	$-0.403981\pi$
$719$	15.9329			0.594198			0.297099	+	0.954847i	$0.403981\pi$
$720$	10.0788	−	2.46873i	0.375614	−	0.0920042i
$721$		0			0
$722$	14.0723	−	14.0723i	0.523716	−	0.523716i
$723$	−8.66174	−	8.66174i	−0.322134	−	0.322134i
$724$	−6.17868			−0.229629
$725$	−23.5888	−	45.2625i	−0.876065	−	1.68101i
$726$			24.6783i			0.915899i
$727$	−20.1000	−	20.1000i	−0.745467	−	0.745467i	0.228157	−	0.973624i	$-0.426730\pi$
$727$	−20.1000	−	20.1000i	−0.745467	−	0.745467i	−0.973624	+	0.228157i	$0.926730\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$	−24.9304	+	6.10653i	−0.922714	+	0.226013i
$731$			0.0794632i			0.00293905i
$732$	0.387981	−	0.387981i	0.0143402	−	0.0143402i
$733$	10.2702	−	10.2702i	0.379337	−	0.379337i	−0.491526	−	0.870863i	$-0.663561\pi$
$733$	10.2702	−	10.2702i	0.379337	−	0.379337i	0.870863	+	0.491526i	$0.163561\pi$
$734$	−45.7659			−1.68925
$735$		0			0
$736$	−5.19363			−0.191440
$737$	−21.6835	+	21.6835i	−0.798722	+	0.798722i
$738$	−4.04164	+	4.04164i	−0.148775	+	0.148775i
$739$		−	13.0334i		−	0.479442i	−0.970842	−	0.239721i	$-0.922944\pi$
$739$		−	13.0334i		−	0.479442i	0.970842	−	0.239721i	$-0.0770560\pi$
$740$	−1.28169	+	2.11326i	−0.0471159	+	0.0776852i
$741$		−	11.6101i		−	0.426506i
$742$		0			0
$743$	−18.6181	−	18.6181i	−0.683031	−	0.683031i	0.277651	−	0.960682i	$-0.410444\pi$
$743$	−18.6181	−	18.6181i	−0.683031	−	0.683031i	−0.960682	+	0.277651i	$0.910444\pi$
$744$			16.2899i			0.597218i
$745$	16.0132	−	3.92232i	0.586677	−	0.143703i
$746$	−11.7510			−0.430237
$747$	−3.77525	−	3.77525i	−0.138129	−	0.138129i
$748$	−0.0295205	+	0.0295205i	−0.00107937	+	0.00107937i
$749$		0			0
$750$	13.0157	−	11.4304i	0.475267	−	0.417381i
$751$	−29.4801			−1.07574			−0.537872	−	0.843026i	$-0.680772\pi$
$751$	−29.4801			−1.07574			−0.537872	+	0.843026i	$0.680772\pi$
$752$	3.84396	+	3.84396i	0.140175	+	0.140175i
$753$	−17.4270	−	17.4270i	−0.635076	−	0.635076i
$754$	−74.0133			−2.69541
$755$	8.70137	+	35.5240i	0.316675	+	1.29285i
$756$		0			0
$757$	5.70030	−	5.70030i	0.207181	−	0.207181i	−0.595887	−	0.803068i	$-0.703199\pi$
$757$	5.70030	−	5.70030i	0.207181	−	0.207181i	0.803068	+	0.595887i	$0.203199\pi$
$758$	19.1809	+	19.1809i	0.696682	+	0.696682i
$759$	12.0661			0.437971
$760$	7.12937	−	11.7550i	0.258609	−	0.426397i
$761$		−	54.7241i		−	1.98375i	−0.127226	−	0.991874i	$-0.540607\pi$
$761$		−	54.7241i		−	1.98375i	0.127226	−	0.991874i	$-0.459393\pi$
$762$	4.08012	+	4.08012i	0.147807	+	0.147807i
$763$		0			0
$764$			0.0227467i			0.000822947i
$765$	−0.0384050	−	0.0232926i	−0.00138854	−	0.000842145i
$766$		−	18.4168i		−	0.665426i
$767$	−1.47310	+	1.47310i	−0.0531905	+	0.0531905i
$768$	6.54253	−	6.54253i	0.236083	−	0.236083i
$769$	−42.0339			−1.51578			−0.757891	−	0.652381i	$-0.773770\pi$
$769$	−42.0339			−1.51578			−0.757891	+	0.652381i	$0.773770\pi$
$770$		0			0
$771$	−8.49497			−0.305939
$772$	0.673055	−	0.673055i	0.0242238	−	0.0242238i
$773$	−20.1963	+	20.1963i	−0.726410	+	0.726410i	−0.969903	−	0.243493i	$-0.921707\pi$
$773$	−20.1963	+	20.1963i	−0.726410	+	0.726410i	0.243493	+	0.969903i	$0.421707\pi$
$774$		−	6.12911i		−	0.220306i
$775$	15.1896	+	29.1461i	0.545627	+	1.04696i
$776$			37.1270i			1.33278i
$777$		0			0
$778$	−9.49042	−	9.49042i	−0.340248	−	0.340248i
$779$			9.15253i			0.327923i
$780$	−0.997073	−	4.07062i	−0.0357009	−	0.145752i
$781$	−11.1434			−0.398742
$782$	0.0511707	+	0.0511707i	0.00182986	+	0.00182986i
$783$	7.21821	−	7.21821i	0.257958	−	0.257958i
$784$		0			0
$785$	26.5877	−	43.8380i	0.948955	−	1.56465i
$786$	−4.66161			−0.166274
$787$	−11.7505	−	11.7505i	−0.418859	−	0.418859i	0.465951	−	0.884810i	$-0.345712\pi$
$787$	−11.7505	−	11.7505i	−0.418859	−	0.418859i	−0.884810	+	0.465951i	$0.845712\pi$
$788$	−0.100576	−	0.100576i	−0.00358289	−	0.00358289i
$789$	−24.6055			−0.875980
$790$	7.20035	−	11.8720i	0.256177	−	0.422387i
$791$		0			0
$792$	−9.09329	+	9.09329i	−0.323116	+	0.323116i
$793$	4.53324	+	4.53324i	0.160980	+	0.160980i
$794$	4.05843			0.144028
$795$	2.53864	+	10.3642i	0.0900362	+	0.367580i
$796$		−	10.0559i		−	0.356422i
$797$	18.2572	+	18.2572i	0.646702	+	0.646702i	0.952194	−	0.305492i	$-0.0988211\pi$
$797$	18.2572	+	18.2572i	0.646702	+	0.646702i	−0.305492	+	0.952194i	$0.598821\pi$
$798$		0			0
$799$		−	0.0235309i		−	0.000832464i
$800$	3.35338	−	10.6527i	0.118560	−	0.376630i
$801$		−	3.83884i		−	0.135639i
$802$	−10.9122	+	10.9122i	−0.385323	+	0.385323i
$803$	27.1852	−	27.1852i	0.959344	−	0.959344i
$804$	2.36677			0.0834696
$805$		0			0
$806$	47.6597			1.67874
$807$	−14.0954	+	14.0954i	−0.496182	+	0.496182i
$808$	11.8908	−	11.8908i	0.418316	−	0.418316i
$809$			27.3427i			0.961317i	0.876908	+	0.480658i	$0.159602\pi$
$809$			27.3427i			0.961317i	−0.876908	+	0.480658i	$0.840398\pi$
$810$	2.96223	+	1.79659i	0.104082	+	0.0631257i
$811$			23.3175i			0.818788i	0.912358	+	0.409394i	$0.134260\pi$
$811$			23.3175i			0.818788i	−0.912358	+	0.409394i	$0.865740\pi$
$812$		0			0
$813$	19.9818	+	19.9818i	0.700793	+	0.700793i
$814$		−	22.1884i		−	0.777704i
$815$	−17.7004	+	29.1846i	−0.620018	+	1.02229i
$816$	−0.0932171			−0.00326325
$817$	−6.93988	−	6.93988i	−0.242796	−	0.242796i
$818$	8.83640	−	8.83640i	0.308958	−	0.308958i
$819$		0			0
$820$	0.786020	+	3.20899i	0.0274490	+	0.112063i
$821$	−6.41412			−0.223855			−0.111927	−	0.993716i	$-0.535702\pi$
$821$	−6.41412			−0.223855			−0.111927	+	0.993716i	$0.535702\pi$
$822$	11.5693	+	11.5693i	0.403526	+	0.403526i
$823$	−4.49148	−	4.49148i	−0.156563	−	0.156563i	0.624479	−	0.781042i	$-0.285311\pi$
$823$	−4.49148	−	4.49148i	−0.156563	−	0.156563i	−0.781042	+	0.624479i	$0.785311\pi$
$824$	−23.3281			−0.812674
$825$	−7.79072	+	24.7489i	−0.271238	+	0.861646i
$826$		0			0
$827$	−31.0388	+	31.0388i	−1.07932	+	1.07932i	−0.0827533	+	0.996570i	$0.526371\pi$
$827$	−31.0388	+	31.0388i	−1.07932	+	1.07932i	−0.996570	+	0.0827533i	$0.973629\pi$
$828$	−0.658512	−	0.658512i	−0.0228849	−	0.0228849i
$829$	−50.9245			−1.76868			−0.884340	−	0.466844i	$-0.845391\pi$
$829$	−50.9245			−1.76868			−0.884340	+	0.466844i	$0.845391\pi$
$830$	−17.9657	+	4.40059i	−0.623600	+	0.152747i
$831$		−	29.8662i		−	1.03605i
$832$	19.2603	+	19.2603i	0.667732	+	0.667732i
$833$		0			0
$834$			2.73804i			0.0948107i
$835$	14.1186	−	23.2788i	0.488593	−	0.805596i
$836$		−	5.15630i		−	0.178334i
$837$	−4.64805	+	4.64805i	−0.160660	+	0.160660i
$838$	−1.43349	+	1.43349i	−0.0495192	+	0.0495192i
$839$	46.0999			1.59155			0.795773	−	0.605596i	$-0.207065\pi$
$839$	46.0999			1.59155			0.795773	+	0.605596i	$0.207065\pi$
$840$		0			0
$841$	−75.2050			−2.59328
$842$	−3.15615	+	3.15615i	−0.108768	+	0.108768i
$843$	−12.6991	+	12.6991i	−0.437379	+	0.437379i
$844$			6.09016i			0.209632i
$845$	19.3277	−	4.73420i	0.664894	−	0.162861i
$846$			1.81497i			0.0624001i
$847$		0			0
$848$	15.6590	+	15.6590i	0.537731	+	0.537731i
$849$			22.7945i			0.782305i
$850$	−0.137996	+	0.0719173i	−0.00473322	+	0.00246674i
$851$	−6.41705			−0.219974
$852$	0.608155	+	0.608155i	0.0208350	+	0.0208350i
$853$	6.59157	−	6.59157i	0.225691	−	0.225691i	−0.585199	−	0.810890i	$-0.698983\pi$
$853$	6.59157	−	6.59157i	0.225691	−	0.225691i	0.810890	+	0.585199i	$0.198983\pi$
$854$		0			0
$855$	5.38832	−	1.31983i	0.184277	−	0.0451374i
$856$	30.8288			1.05371
$857$	7.71768	+	7.71768i	0.263631	+	0.263631i	0.826527	−	0.562897i	$-0.190313\pi$
$857$	7.71768	+	7.71768i	0.263631	+	0.263631i	−0.562897	+	0.826527i	$0.690313\pi$
$858$	26.6044	+	26.6044i	0.908259	+	0.908259i
$859$	13.4236			0.458009			0.229004	−	0.973425i	$-0.426453\pi$
$859$	13.4236			0.458009			0.229004	+	0.973425i	$0.426453\pi$
$860$	−3.02920	−	1.83721i	−0.103295	−	0.0626482i
$861$		0			0
$862$	−22.8233	+	22.8233i	−0.777365	+	0.777365i
$863$	−38.4338	−	38.4338i	−1.30830	−	1.30830i	−0.922641	−	0.385660i	$-0.873974\pi$
$863$	−38.4338	−	38.4338i	−1.30830	−	1.30830i	−0.385660	−	0.922641i	$-0.626026\pi$
$864$	2.23361			0.0759890
$865$	−6.91346	−	4.19301i	−0.235065	−	0.142566i
$866$		−	12.5359i		−	0.425986i
$867$	−12.0205	−	12.0205i	−0.408239	−	0.408239i
$868$		0			0
$869$			20.7973i			0.705501i
$870$	−8.41385	−	34.3502i	−0.285256	−	1.16458i
$871$			27.6538i			0.937014i
$872$	15.2958	−	15.2958i	0.517982	−	0.517982i
$873$	−10.5936	+	10.5936i	−0.358538	+	0.358538i
$874$	−8.93792			−0.302330
$875$		0			0
$876$	−2.96728			−0.100255
$877$	17.4124	−	17.4124i	0.587976	−	0.587976i	−0.349107	−	0.937083i	$-0.613515\pi$
$877$	17.4124	−	17.4124i	0.587976	−	0.587976i	0.937083	+	0.349107i	$0.113515\pi$
$878$	−9.46486	+	9.46486i	−0.319424	+	0.319424i
$879$			24.5042i			0.826505i
$880$	12.8108	+	52.3011i	0.431852	+	1.76307i
$881$		−	16.1540i		−	0.544243i	−0.962263	−	0.272121i	$-0.912275\pi$
$881$		−	16.1540i		−	0.544243i	0.962263	−	0.272121i	$-0.0877253\pi$
$882$		0			0
$883$	−34.4853	−	34.4853i	−1.16052	−	1.16052i	−0.984361	−	0.176161i	$-0.943632\pi$
$883$	−34.4853	−	34.4853i	−1.16052	−	1.16052i	−0.176161	−	0.984361i	$-0.556368\pi$
$884$			0.0376486i			0.00126626i
$885$	−0.851139	−	0.516214i	−0.0286107	−	0.0173524i
$886$	−48.2238			−1.62011
$887$	11.1720	+	11.1720i	0.375120	+	0.375120i	0.869338	−	0.494218i	$-0.164545\pi$
$887$	11.1720	+	11.1720i	0.375120	+	0.375120i	−0.494218	+	0.869338i	$0.664545\pi$
$888$	4.83604	−	4.83604i	0.162287	−	0.162287i
$889$		0			0
$890$	−11.3715	−	6.89682i	−0.381175	−	0.231182i
$891$	−5.18923			−0.173846
$892$	1.44056	+	1.44056i	0.0482334	+	0.0482334i
$893$	2.05506	+	2.05506i	0.0687699	+	0.0687699i
$894$	11.4234			0.382057
$895$	30.1680	−	7.38946i	1.00841	−	0.247003i
$896$		0			0
$897$	7.69418	−	7.69418i	0.256901	−	0.256901i
$898$	44.1726	+	44.1726i	1.47406	+	1.47406i
$899$	67.1012			2.23795
$900$	1.77586	−	0.925499i	0.0591954	−	0.0308500i
$901$		−	0.0958567i		−	0.00319345i
$902$	−20.9730	−	20.9730i	−0.698324	−	0.698324i
$903$		0			0
$904$			9.81746i			0.326524i
$905$	33.5053	−	8.20690i	1.11375	−	0.272807i
$906$			25.3420i			0.841932i
$907$	−25.9994	+	25.9994i	−0.863295	+	0.863295i	−0.991719	−	0.128424i	$-0.959008\pi$
$907$	−25.9994	+	25.9994i	−0.863295	+	0.863295i	0.128424	+	0.991719i	$0.459008\pi$
$908$	2.13680	−	2.13680i	0.0709121	−	0.0709121i
$909$	6.78565			0.225066
$910$		0			0
$911$	30.1482			0.998856			0.499428	−	0.866355i	$-0.333544\pi$
$911$	30.1482			0.998856			0.499428	+	0.866355i	$0.333544\pi$
$912$	8.14106	−	8.14106i	0.269578	−	0.269578i
$913$	19.5906	−	19.5906i	0.648355	−	0.648355i
$914$		−	20.7427i		−	0.686107i
$915$	−1.58857	+	2.61925i	−0.0525166	+	0.0865899i
$916$			10.3034i			0.340434i
$917$		0			0
$918$	−0.0220068	−	0.0220068i	−0.000726333	−	0.000726333i
$919$		−	1.19428i		−	0.0393955i	−0.999806	−	0.0196978i	$-0.993730\pi$
$919$		−	1.19428i		−	0.0393955i	0.999806	−	0.0196978i	$-0.00627039\pi$
$920$	12.5150	−	3.06546i	0.412606	−	0.101065i
$921$	10.0088			0.329801
$922$	2.27064	+	2.27064i	0.0747796	+	0.0747796i
$923$	−7.10580	+	7.10580i	−0.233890	+	0.233890i
$924$		0			0
$925$	4.14330	−	13.1621i	0.136231	−	0.432767i
$926$	−28.4285			−0.934217
$927$	−6.65628	−	6.65628i	−0.218621	−	0.218621i
$928$	−16.1227	−	16.1227i	−0.529252	−	0.529252i
$929$	12.4626			0.408886			0.204443	−	0.978879i	$-0.434462\pi$
$929$	12.4626			0.408886			0.204443	+	0.978879i	$0.434462\pi$
$930$	5.41797	+	22.1193i	0.177662	+	0.725319i
$931$		0			0
$932$	−7.59599	+	7.59599i	−0.248815	+	0.248815i
$933$	−3.52765	−	3.52765i	−0.115490	−	0.115490i
$934$	−39.8960			−1.30544
$935$	0.120870	−	0.199292i	0.00395289	−	0.00651755i
$936$			11.5970i			0.379061i
$937$	−34.0770	−	34.0770i	−1.11325	−	1.11325i	−0.992709	−	0.120539i	$-0.961538\pi$
$937$	−34.0770	−	34.0770i	−1.11325	−	1.11325i	−0.120539	−	0.992709i	$-0.538462\pi$
$938$		0			0
$939$		−	5.89955i		−	0.192525i
$940$	0.897017	+	0.544040i	0.0292575	+	0.0177446i
$941$		−	46.6066i		−	1.51933i	−0.650313	−	0.759666i	$-0.725362\pi$
$941$		−	46.6066i		−	1.51933i	0.650313	−	0.759666i	$-0.274638\pi$
$942$	25.1200	−	25.1200i	0.818455	−	0.818455i
$943$	−6.06553	+	6.06553i	−0.197521	+	0.197521i
$944$	−2.06590			−0.0672392
$945$		0			0
$946$	31.8054			1.03408
$947$	−8.34466	+	8.34466i	−0.271165	+	0.271165i	−0.829569	−	0.558404i	$-0.811414\pi$
$947$	−8.34466	+	8.34466i	−0.271165	+	0.271165i	0.558404	+	0.829569i	$0.311414\pi$
$948$	1.13502	−	1.13502i	0.0368638	−	0.0368638i
$949$		−	34.6703i		−	1.12545i
$950$	5.77095	−	18.3327i	0.187234	−	0.594790i
$951$			0.882064i			0.0286029i
$952$		0			0
$953$	−28.2281	−	28.2281i	−0.914399	−	0.914399i	0.0822160	−	0.996615i	$-0.473800\pi$
$953$	−28.2281	−	28.2281i	−0.914399	−	0.914399i	−0.996615	+	0.0822160i	$0.973800\pi$
$954$			7.39357i			0.239376i
$955$	−0.0302136	−	0.123349i	−0.000977688	−	0.00399148i
$956$	7.64220			0.247167
$957$	37.4569	+	37.4569i	1.21081	+	1.21081i
$958$	27.3890	−	27.3890i	0.884898	−	0.884898i
$959$		0			0
$960$	−6.74935	+	11.1284i	−0.217834	+	0.359167i
$961$	−12.2088			−0.393831
$962$	−14.1489	−	14.1489i	−0.456178	−	0.456178i
$963$	8.79648	+	8.79648i	0.283463	+	0.283463i
$964$	−4.90608			−0.158014
$965$	−2.75580	+	4.54379i	−0.0887123	+	0.146270i
$966$		0			0
$967$	−22.3045	+	22.3045i	−0.717263	+	0.717263i	−0.968044	−	0.250781i	$-0.919313\pi$
$967$	−22.3045	+	22.3045i	−0.717263	+	0.717263i	0.250781	+	0.968044i	$0.419313\pi$
$968$	−27.9114	−	27.9114i	−0.897107	−	0.897107i
$969$	−0.0498358			−0.00160096
$970$	12.3483	+	50.4129i	0.396480	+	1.61866i
$971$		−	29.4623i		−	0.945491i	−0.881199	−	0.472745i	$-0.843263\pi$
$971$		−	29.4623i		−	0.945491i	0.881199	−	0.472745i	$-0.156737\pi$
$972$	0.283204	+	0.283204i	0.00908378	+	0.00908378i
$973$		0			0
$974$			42.2648i			1.35425i
$975$	10.8137	+	20.7495i	0.346316	+	0.664516i
$976$			6.35749i			0.203498i
$977$	−2.95286	+	2.95286i	−0.0944703	+	0.0944703i	−0.752763	−	0.658292i	$-0.771279\pi$
$977$	−2.95286	+	2.95286i	−0.0944703	+	0.0944703i	0.658292	+	0.752763i	$0.271279\pi$
$978$	−16.7233	+	16.7233i	−0.534753	+	0.534753i
$979$	19.9206			0.636666
$980$		0			0
$981$	8.72881			0.278689
$982$	25.7238	−	25.7238i	0.820880	−	0.820880i
$983$	2.08536	−	2.08536i	0.0665128	−	0.0665128i	−0.673068	−	0.739581i	$-0.735024\pi$
$983$	2.08536	−	2.08536i	0.0665128	−	0.0665128i	0.739581	+	0.673068i	$0.235024\pi$
$984$		−	9.14226i		−	0.291444i
$985$	0.678991	+	0.411807i	0.0216344	+	0.0131213i
$986$			0.317700i			0.0101176i
$987$		0			0
$988$	−3.28802	−	3.28802i	−0.104606	−	0.104606i
$989$		−	9.19834i		−	0.292490i
$990$	−9.32292	+	15.3717i	−0.296302	+	0.488545i
$991$	−27.4337			−0.871459			−0.435729	−	0.900078i	$-0.643510\pi$
$991$	−27.4337			−0.871459			−0.435729	+	0.900078i	$0.643510\pi$
$992$	10.3819	+	10.3819i	0.329627	+	0.329627i
$993$	−16.9411	+	16.9411i	−0.537610	+	0.537610i
$994$		0			0
$995$	13.3569	+	54.5304i	0.423441	+	1.72873i
$996$	−2.13833			−0.0677557
$997$	−15.1033	−	15.1033i	−0.478327	−	0.478327i	0.426269	−	0.904596i	$-0.359828\pi$
$997$	−15.1033	−	15.1033i	−0.478327	−	0.478327i	−0.904596	+	0.426269i	$0.859828\pi$
$998$	−31.3974	−	31.3974i	−0.993868	−	0.993868i
$999$	2.75976			0.0873150

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.m.c.538.6		32
5.2	odd	4	inner	735.2.m.c.97.5		32
7.2	even	3		105.2.u.a.73.6	yes	32
7.3	odd	6		105.2.u.a.103.3	yes	32
7.4	even	3		735.2.v.b.313.3		32
7.5	odd	6		735.2.v.b.178.6		32
7.6	odd	2	inner	735.2.m.c.538.5		32
21.2	odd	6		315.2.bz.d.73.3		32
21.17	even	6		315.2.bz.d.208.6		32
35.2	odd	12		105.2.u.a.52.3	✓	32
35.3	even	12		525.2.bc.e.82.3		32
35.9	even	6		525.2.bc.e.493.3		32
35.12	even	12		735.2.v.b.472.3		32
35.17	even	12		105.2.u.a.82.6	yes	32
35.23	odd	12		525.2.bc.e.157.6		32
35.24	odd	6		525.2.bc.e.418.6		32
35.27	even	4	inner	735.2.m.c.97.6		32
35.32	odd	12		735.2.v.b.607.6		32
105.2	even	12		315.2.bz.d.262.6		32
105.17	odd	12		315.2.bz.d.82.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.u.a.52.3	✓	32	35.2	odd	12
105.2.u.a.73.6	yes	32	7.2	even	3
105.2.u.a.82.6	yes	32	35.17	even	12
105.2.u.a.103.3	yes	32	7.3	odd	6
315.2.bz.d.73.3		32	21.2	odd	6
315.2.bz.d.82.3		32	105.17	odd	12
315.2.bz.d.208.6		32	21.17	even	6
315.2.bz.d.262.6		32	105.2	even	12
525.2.bc.e.82.3		32	35.3	even	12
525.2.bc.e.157.6		32	35.23	odd	12
525.2.bc.e.418.6		32	35.24	odd	6
525.2.bc.e.493.3		32	35.9	even	6
735.2.m.c.97.5		32	5.2	odd	4	inner
735.2.m.c.97.6		32	35.27	even	4	inner
735.2.m.c.538.5		32	7.6	odd	2	inner
735.2.m.c.538.6		32	1.1	even	1	trivial
735.2.v.b.178.6		32	7.5	odd	6
735.2.v.b.313.3		32	7.4	even	3
735.2.v.b.472.3		32	35.12	even	12
735.2.v.b.607.6		32	35.32	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09556 + 1.09556i) q^{2} +(0.707107 - 0.707107i) q^{3} -0.400511i q^{4} +(0.531984 + 2.17186i) q^{5} +1.54936i q^{6} +(-1.75234 - 1.75234i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.09556 + 1.09556i) q^{2} +(0.707107 - 0.707107i) q^{3} -0.400511i q^{4} +(0.531984 + 2.17186i) q^{5} +1.54936i q^{6} +(-1.75234 - 1.75234i) q^{8} -1.00000i q^{9} +(-2.96223 - 1.79659i) q^{10} +5.18923 q^{11} +(-0.283204 - 0.283204i) q^{12} +(3.30901 - 3.30901i) q^{13} +(1.91191 + 1.15957i) q^{15} +4.64061 q^{16} +(-0.0142038 - 0.0142038i) q^{17} +(1.09556 + 1.09556i) q^{18} +2.48097 q^{19} +(0.869856 - 0.213066i) q^{20} +(-5.68512 + 5.68512i) q^{22} +(1.64418 + 1.64418i) q^{23} -2.47818 q^{24} +(-4.43399 + 2.31079i) q^{25} +7.25046i q^{26} +(-0.707107 - 0.707107i) q^{27} +10.2081i q^{29} +(-3.36500 + 0.824234i) q^{30} -6.57334i q^{31} +(-1.57940 + 1.57940i) q^{32} +(3.66934 - 3.66934i) q^{33} +0.0311223 q^{34} -0.400511 q^{36} +(-1.95145 + 1.95145i) q^{37} +(-2.71805 + 2.71805i) q^{38} -4.67965i q^{39} +(2.87363 - 4.73806i) q^{40} +3.68910i q^{41} +(-2.79725 - 2.79725i) q^{43} -2.07835i q^{44} +(2.17186 - 0.531984i) q^{45} -3.60260 q^{46} +(0.828330 + 0.828330i) q^{47} +(3.28141 - 3.28141i) q^{48} +(2.32609 - 7.38932i) q^{50} -0.0200872 q^{51} +(-1.32530 - 1.32530i) q^{52} +(3.37433 + 3.37433i) q^{53} +1.54936 q^{54} +(2.76059 + 11.2703i) q^{55} +(1.75431 - 1.75431i) q^{57} +(-11.1836 - 11.1836i) q^{58} -0.445177 q^{59} +(0.464421 - 0.765741i) q^{60} +1.36997i q^{61} +(7.20150 + 7.20150i) q^{62} +5.82056i q^{64} +(8.94707 + 5.42639i) q^{65} +8.03998i q^{66} +(-4.17856 + 4.17856i) q^{67} +(-0.00568879 + 0.00568879i) q^{68} +2.32522 q^{69} -2.14741 q^{71} +(-1.75234 + 1.75234i) q^{72} +(5.23877 - 5.23877i) q^{73} -4.27586i q^{74} +(-1.50132 + 4.76928i) q^{75} -0.993655i q^{76} +(5.12685 + 5.12685i) q^{78} +4.00779i q^{79} +(2.46873 + 10.0788i) q^{80} -1.00000 q^{81} +(-4.04164 - 4.04164i) q^{82} +(3.77525 - 3.77525i) q^{83} +(0.0232926 - 0.0384050i) q^{85} +6.12911 q^{86} +(7.21821 + 7.21821i) q^{87} +(-9.09329 - 9.09329i) q^{88} +3.83884 q^{89} +(-1.79659 + 2.96223i) q^{90} +(0.658512 - 0.658512i) q^{92} +(-4.64805 - 4.64805i) q^{93} -1.81497 q^{94} +(1.31983 + 5.38832i) q^{95} +2.23361i q^{96} +(-10.5936 - 10.5936i) q^{97} -5.18923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 24 q^{8}+O(q^{10}) \) 32 * q - 24 * q^8	\( 32 q - 24 q^{8} + 16 q^{11} - 8 q^{15} - 8 q^{22} + 16 q^{23} - 24 q^{25} - 16 q^{30} - 48 q^{32} - 32 q^{36} - 8 q^{37} + 40 q^{43} + 80 q^{46} + 72 q^{50} + 16 q^{51} + 48 q^{53} + 16 q^{57} - 8 q^{58} - 40 q^{60} + 8 q^{65} - 16 q^{67} - 16 q^{71} - 24 q^{72} + 80 q^{78} - 32 q^{81} - 72 q^{85} + 32 q^{86} + 64 q^{88} - 56 q^{92} + 48 q^{93} + 24 q^{95}+O(q^{100}) \) 32 * q - 24 * q^8 + 16 * q^11 - 8 * q^15 - 8 * q^22 + 16 * q^23 - 24 * q^25 - 16 * q^30 - 48 * q^32 - 32 * q^36 - 8 * q^37 + 40 * q^43 + 80 * q^46 + 72 * q^50 + 16 * q^51 + 48 * q^53 + 16 * q^57 - 8 * q^58 - 40 * q^60 + 8 * q^65 - 16 * q^67 - 16 * q^71 - 24 * q^72 + 80 * q^78 - 32 * q^81 - 72 * q^85 + 32 * q^86 + 64 * q^88 - 56 * q^92 + 48 * q^93 + 24 * q^95

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