LMFDB - Embedded newform 1600.2.q.h.49.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1600,2,Mod(49,1600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1600.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1600, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.q (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			49.5
Root			$-0.966675 + 1.03225i$ of defining polynomial
Character	$\chi$	$=$	1600.49
Dual form			1600.2.q.h.849.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.209571 + 0.209571i) q^{3} -1.73696 q^{7} -2.91216i q^{9} +(-0.505430 - 0.505430i) q^{11} +(1.88750 + 1.88750i) q^{13} +4.53524i q^{17} +(-3.22022 + 3.22022i) q^{19} +(-0.364018 - 0.364018i) q^{21} +8.85045 q^{23} +(1.23902 - 1.23902i) q^{27} +(2.44059 - 2.44059i) q^{29} +5.70401 q^{31} -0.211847i q^{33} +(5.35670 - 5.35670i) q^{37} +0.791130i q^{39} -10.0343i q^{41} +(2.10564 - 2.10564i) q^{43} -4.32303i q^{47} -3.98295 q^{49} +(-0.950456 + 0.950456i) q^{51} +(-1.37458 + 1.37458i) q^{53} -1.34973 q^{57} +(6.64140 + 6.64140i) q^{59} +(5.26208 - 5.26208i) q^{61} +5.05832i q^{63} +(10.5578 + 10.5578i) q^{67} +(1.85480 + 1.85480i) q^{69} -14.0437i q^{71} +6.63830 q^{73} +(0.877914 + 0.877914i) q^{77} +4.27297 q^{79} -8.21715 q^{81} +(9.15483 + 9.15483i) q^{83} +1.02295 q^{87} +3.23826i q^{89} +(-3.27852 - 3.27852i) q^{91} +(1.19540 + 1.19540i) q^{93} +1.94129i q^{97} +(-1.47189 + 1.47189i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7} + 8 q^{11} - 8 q^{19} + 24 q^{23} + 24 q^{27} + 16 q^{29} + 16 q^{37} - 8 q^{43} + 16 q^{49} + 32 q^{51} + 16 q^{53} - 8 q^{59} + 16 q^{61} - 40 q^{67} - 16 q^{69} + 16 q^{77} + 16 q^{79}+ \cdots - 8 q^{99}+O(q^{100}) $ 16 * q + 8 * q^7 + 8 * q^11 - 8 * q^19 + 24 * q^23 + 24 * q^27 + 16 * q^29 + 16 * q^37 - 8 * q^43 + 16 * q^49 + 32 * q^51 + 16 * q^53 - 8 * q^59 + 16 * q^61 - 40 * q^67 - 16 * q^69 + 16 * q^77 + 16 * q^79 - 16 * q^81 + 40 * q^83 - 32 * q^91 + 48 * q^93 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.209571	+	0.209571i	0.120996	+	0.120996i	0.765012	−	0.644016i	$-0.222733\pi$
$3$	0.209571	+	0.209571i	0.120996	+	0.120996i	−0.644016	+	0.765012i	$0.722733\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.73696			−0.656511			−0.328255	−	0.944589i	$-0.606461\pi$
$7$	−1.73696			−0.656511			−0.328255	+	0.944589i	$0.606461\pi$
$8$		0			0
$9$		−	2.91216i		−	0.970720i
$10$		0			0
$11$	−0.505430	−	0.505430i	−0.152393	−	0.152393i	0.626793	−	0.779186i	$-0.284367\pi$
$11$	−0.505430	−	0.505430i	−0.152393	−	0.152393i	−0.779186	+	0.626793i	$0.784367\pi$
$12$		0			0
$13$	1.88750	+	1.88750i	0.523498	+	0.523498i	0.918626	−	0.395128i	$-0.129300\pi$
$13$	1.88750	+	1.88750i	0.523498	+	0.523498i	−0.395128	+	0.918626i	$0.629300\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			4.53524i			1.09996i	0.835178	+	0.549979i	$0.185364\pi$
$17$			4.53524i			1.09996i	−0.835178	+	0.549979i	$0.814636\pi$
$18$		0			0
$19$	−3.22022	+	3.22022i	−0.738768	+	0.738768i	−0.972340	−	0.233571i	$-0.924959\pi$
$19$	−3.22022	+	3.22022i	−0.738768	+	0.738768i	0.233571	+	0.972340i	$0.424959\pi$
$20$		0			0
$21$	−0.364018	−	0.364018i	−0.0794352	−	0.0794352i
$22$		0			0
$23$	8.85045			1.84545			0.922723	−	0.385463i	$-0.125958\pi$
$23$	8.85045			1.84545			0.922723	+	0.385463i	$0.125958\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.23902	−	1.23902i	0.238449	−	0.238449i
$28$		0			0
$29$	2.44059	−	2.44059i	0.453205	−	0.453205i	−0.443212	−	0.896417i	$-0.646161\pi$
$29$	2.44059	−	2.44059i	0.453205	−	0.453205i	0.896417	+	0.443212i	$0.146161\pi$
$30$		0			0
$31$	5.70401			1.02447			0.512235	−	0.858845i	$-0.328818\pi$
$31$	5.70401			1.02447			0.512235	+	0.858845i	$0.328818\pi$
$32$		0			0
$33$		−	0.211847i		−	0.0368779i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	5.35670	−	5.35670i	0.880636	−	0.880636i	−0.112963	−	0.993599i	$-0.536034\pi$
$37$	5.35670	−	5.35670i	0.880636	−	0.880636i	0.993599	+	0.112963i	$0.0360342\pi$
$38$		0			0
$39$			0.791130i			0.126682i
$40$		0			0
$41$		−	10.0343i		−	1.56709i	−0.621335	−	0.783545i	$-0.713409\pi$
$41$		−	10.0343i		−	1.56709i	0.621335	−	0.783545i	$-0.286591\pi$
$42$		0			0
$43$	2.10564	−	2.10564i	0.321107	−	0.321107i	−0.528085	−	0.849192i	$-0.677090\pi$
$43$	2.10564	−	2.10564i	0.321107	−	0.321107i	0.849192	+	0.528085i	$0.177090\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	4.32303i		−	0.630578i	−0.948996	−	0.315289i	$-0.897899\pi$
$47$		−	4.32303i		−	0.630578i	0.948996	−	0.315289i	$-0.102101\pi$
$48$		0			0
$49$	−3.98295			−0.568993
$50$		0			0
$51$	−0.950456	+	0.950456i	−0.133091	+	0.133091i
$52$		0			0
$53$	−1.37458	+	1.37458i	−0.188814	+	0.188814i	−0.795183	−	0.606369i	$-0.792625\pi$
$53$	−1.37458	+	1.37458i	−0.188814	+	0.188814i	0.606369	+	0.795183i	$0.292625\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.34973			−0.178776
$58$		0			0
$59$	6.64140	+	6.64140i	0.864637	+	0.864637i	0.991872	−	0.127236i	$-0.0406105\pi$
$59$	6.64140	+	6.64140i	0.864637	+	0.864637i	−0.127236	+	0.991872i	$0.540611\pi$
$60$		0			0
$61$	5.26208	−	5.26208i	0.673741	−	0.673741i	−0.284836	−	0.958576i	$-0.591939\pi$
$61$	5.26208	−	5.26208i	0.673741	−	0.673741i	0.958576	+	0.284836i	$0.0919391\pi$
$62$		0			0
$63$			5.05832i			0.637288i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	10.5578	+	10.5578i	1.28984	+	1.28984i	0.934884	+	0.354954i	$0.115503\pi$
$67$	10.5578	+	10.5578i	1.28984	+	1.28984i	0.354954	+	0.934884i	$0.384497\pi$
$68$		0			0
$69$	1.85480	+	1.85480i	0.223292	+	0.223292i
$70$		0			0
$71$		−	14.0437i		−	1.66668i	−0.552764	−	0.833338i	$-0.686427\pi$
$71$		−	14.0437i		−	1.66668i	0.552764	−	0.833338i	$-0.313573\pi$
$72$		0			0
$73$	6.63830			0.776954			0.388477	−	0.921458i	$-0.373001\pi$
$73$	6.63830			0.776954			0.388477	+	0.921458i	$0.373001\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.877914	+	0.877914i	0.100048	+	0.100048i
$78$		0			0
$79$	4.27297			0.480746			0.240373	−	0.970681i	$-0.422730\pi$
$79$	4.27297			0.480746			0.240373	+	0.970681i	$0.422730\pi$
$80$		0			0
$81$	−8.21715			−0.913017
$82$		0			0
$83$	9.15483	+	9.15483i	1.00487	+	1.00487i	0.999988	+	0.00488547i	$0.00155510\pi$
$83$	9.15483	+	9.15483i	1.00487	+	1.00487i	0.00488547	+	0.999988i	$0.498445\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.02295			0.109672
$88$		0			0
$89$			3.23826i			0.343255i	0.985162	+	0.171627i	$0.0549025\pi$
$89$			3.23826i			0.343255i	−0.985162	+	0.171627i	$0.945097\pi$
$90$		0			0
$91$	−3.27852	−	3.27852i	−0.343682	−	0.343682i
$92$		0			0
$93$	1.19540	+	1.19540i	0.123957	+	0.123957i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			1.94129i			0.197108i	0.995132	+	0.0985541i	$0.0314217\pi$
$97$			1.94129i			0.197108i	−0.995132	+	0.0985541i	$0.968578\pi$
$98$		0			0
$99$	−1.47189	+	1.47189i	−0.147931	+	0.147931i
$100$		0			0
$101$	10.3395	+	10.3395i	1.02882	+	1.02882i	0.999572	+	0.0292464i	$0.00931074\pi$
$101$	10.3395	+	10.3395i	1.02882	+	1.02882i	0.0292464	+	0.999572i	$0.490689\pi$
$102$		0			0
$103$	−4.96401			−0.489118			−0.244559	−	0.969634i	$-0.578643\pi$
$103$	−4.96401			−0.489118			−0.244559	+	0.969634i	$0.578643\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.74631	+	2.74631i	−0.265496	+	0.265496i	−0.827282	−	0.561787i	$-0.810114\pi$
$107$	−2.74631	+	2.74631i	−0.265496	+	0.265496i	0.561787	+	0.827282i	$0.310114\pi$
$108$		0			0
$109$	−6.99959	+	6.99959i	−0.670439	+	0.670439i	−0.957817	−	0.287378i	$-0.907216\pi$
$109$	−6.99959	+	6.99959i	−0.670439	+	0.670439i	0.287378	+	0.957817i	$0.407216\pi$
$110$		0			0
$111$	2.24522			0.213107
$112$		0			0
$113$			6.53194i			0.614474i	0.951633	+	0.307237i	$0.0994044\pi$
$113$			6.53194i			0.614474i	−0.951633	+	0.307237i	$0.900596\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	5.49670	−	5.49670i	0.508170	−	0.508170i
$118$		0			0
$119$		−	7.87756i		−	0.722134i
$120$		0			0
$121$		−	10.4891i		−	0.953553i
$122$		0			0
$123$	2.10289	−	2.10289i	0.189612	−	0.189612i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			2.50861i			0.222603i	0.993787	+	0.111302i	$0.0355020\pi$
$127$			2.50861i			0.222603i	−0.993787	+	0.111302i	$0.964498\pi$
$128$		0			0
$129$	0.882562			0.0777053
$130$		0			0
$131$	−8.55783	+	8.55783i	−0.747701	+	0.747701i	−0.974047	−	0.226346i	$-0.927322\pi$
$131$	−8.55783	+	8.55783i	−0.747701	+	0.747701i	0.226346	+	0.974047i	$0.427322\pi$
$132$		0			0
$133$	5.59340	−	5.59340i	0.485009	−	0.485009i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.47131			−0.552881			−0.276440	−	0.961031i	$-0.589155\pi$
$137$	−6.47131			−0.552881			−0.276440	+	0.961031i	$0.589155\pi$
$138$		0			0
$139$	−16.4430	−	16.4430i	−1.39468	−	1.39468i	−0.814458	−	0.580223i	$-0.802965\pi$
$139$	−16.4430	−	16.4430i	−1.39468	−	1.39468i	−0.580223	−	0.814458i	$-0.697035\pi$
$140$		0			0
$141$	0.905982	−	0.905982i	0.0762974	−	0.0762974i
$142$		0			0
$143$		−	1.90800i		−	0.159555i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.834712	−	0.834712i	−0.0688459	−	0.0688459i
$148$		0			0
$149$	2.72803	+	2.72803i	0.223489	+	0.223489i	0.809966	−	0.586477i	$-0.199486\pi$
$149$	2.72803	+	2.72803i	0.223489	+	0.223489i	−0.586477	+	0.809966i	$0.699486\pi$
$150$		0			0
$151$		−	11.5196i		−	0.937453i	−0.883343	−	0.468726i	$-0.844713\pi$
$151$		−	11.5196i		−	0.937453i	0.883343	−	0.468726i	$-0.155287\pi$
$152$		0			0
$153$	13.2074			1.06775
$154$		0			0
$155$		0			0
$156$		0			0
$157$	3.28013	+	3.28013i	0.261783	+	0.261783i	0.825778	−	0.563995i	$-0.190736\pi$
$157$	3.28013	+	3.28013i	0.261783	+	0.261783i	−0.563995	+	0.825778i	$0.690736\pi$
$158$		0			0
$159$	−0.576147			−0.0456914
$160$		0			0
$161$	−15.3729			−1.21156
$162$		0			0
$163$	−9.27367	−	9.27367i	−0.726370	−	0.726370i	0.243525	−	0.969895i	$-0.421696\pi$
$163$	−9.27367	−	9.27367i	−0.726370	−	0.726370i	−0.969895	+	0.243525i	$0.921696\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.08065			−0.547917			−0.273958	−	0.961742i	$-0.588333\pi$
$167$	−7.08065			−0.547917			−0.273958	+	0.961742i	$0.588333\pi$
$168$		0			0
$169$		−	5.87470i		−	0.451900i
$170$		0			0
$171$	9.37778	+	9.37778i	0.717137	+	0.717137i
$172$		0			0
$173$	5.21471	+	5.21471i	0.396467	+	0.396467i	0.876985	−	0.480518i	$-0.159551\pi$
$173$	5.21471	+	5.21471i	0.396467	+	0.396467i	−0.480518	+	0.876985i	$0.659551\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			2.78369i			0.209235i
$178$		0			0
$179$	6.32196	−	6.32196i	0.472525	−	0.472525i	−0.430206	−	0.902731i	$-0.641559\pi$
$179$	6.32196	−	6.32196i	0.472525	−	0.472525i	0.902731	+	0.430206i	$0.141559\pi$
$180$		0			0
$181$	13.0695	+	13.0695i	0.971448	+	0.971448i	0.999604	−	0.0281553i	$-0.00896329\pi$
$181$	13.0695	+	13.0695i	0.971448	+	0.971448i	−0.0281553	+	0.999604i	$0.508963\pi$
$182$		0			0
$183$	2.20556			0.163040
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.29225	−	2.29225i	0.167626	−	0.167626i
$188$		0			0
$189$	−2.15213	+	2.15213i	−0.156545	+	0.156545i
$190$		0			0
$191$	22.1722			1.60433			0.802164	−	0.597104i	$-0.203682\pi$
$191$	22.1722			1.60433			0.802164	+	0.597104i	$0.203682\pi$
$192$		0			0
$193$		−	7.97695i		−	0.574193i	−0.957902	−	0.287097i	$-0.907310\pi$
$193$		−	7.97695i		−	0.574193i	0.957902	−	0.287097i	$-0.0926901\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.76327	+	5.76327i	−0.410616	+	0.410616i	−0.881953	−	0.471337i	$-0.843772\pi$
$197$	−5.76327	+	5.76327i	−0.410616	+	0.410616i	0.471337	+	0.881953i	$0.343772\pi$
$198$		0			0
$199$			5.38869i			0.381994i	0.981591	+	0.190997i	$0.0611721\pi$
$199$			5.38869i			0.381994i	−0.981591	+	0.190997i	$0.938828\pi$
$200$		0			0
$201$			4.42521i			0.312130i
$202$		0			0
$203$	−4.23921	+	4.23921i	−0.297534	+	0.297534i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	25.7739i		−	1.79141i
$208$		0			0
$209$	3.25519			0.225166
$210$		0			0
$211$	−10.7547	+	10.7547i	−0.740384	+	0.740384i	−0.972652	−	0.232268i	$-0.925385\pi$
$211$	−10.7547	+	10.7547i	−0.740384	+	0.740384i	0.232268	+	0.972652i	$0.425385\pi$
$212$		0			0
$213$	2.94315	−	2.94315i	0.201661	−	0.201661i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−9.90766			−0.672576
$218$		0			0
$219$	1.39120	+	1.39120i	0.0940084	+	0.0940084i
$220$		0			0
$221$	−8.56026	+	8.56026i	−0.575826	+	0.575826i
$222$		0			0
$223$		−	3.98714i		−	0.266998i	−0.991049	−	0.133499i	$-0.957379\pi$
$223$		−	3.98714i		−	0.266998i	0.991049	−	0.133499i	$-0.0426214\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.82103	+	3.82103i	0.253611	+	0.253611i	0.822449	−	0.568839i	$-0.192607\pi$
$227$	3.82103	+	3.82103i	0.253611	+	0.253611i	−0.568839	+	0.822449i	$0.692607\pi$
$228$		0			0
$229$	8.80687	+	8.80687i	0.581974	+	0.581974i	0.935445	−	0.353471i	$-0.114999\pi$
$229$	8.80687	+	8.80687i	0.581974	+	0.581974i	−0.353471	+	0.935445i	$0.614999\pi$
$230$		0			0
$231$			0.367971i			0.0242107i
$232$		0			0
$233$	−16.6042			−1.08778			−0.543889	−	0.839157i	$-0.683049\pi$
$233$	−16.6042			−1.08778			−0.543889	+	0.839157i	$0.683049\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.895491	+	0.895491i	0.0581684	+	0.0581684i
$238$		0			0
$239$	3.81234			0.246600			0.123300	−	0.992369i	$-0.460652\pi$
$239$	3.81234			0.246600			0.123300	+	0.992369i	$0.460652\pi$
$240$		0			0
$241$	9.54985			0.615160			0.307580	−	0.951522i	$-0.400481\pi$
$241$	9.54985			0.615160			0.307580	+	0.951522i	$0.400481\pi$
$242$		0			0
$243$	−5.43913	−	5.43913i	−0.348921	−	0.348921i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−12.1563			−0.773487
$248$		0			0
$249$			3.83718i			0.243171i
$250$		0			0
$251$	−11.9933	−	11.9933i	−0.757010	−	0.757010i	0.218767	−	0.975777i	$-0.429797\pi$
$251$	−11.9933	−	11.9933i	−0.757010	−	0.757010i	−0.975777	+	0.218767i	$0.929797\pi$
$252$		0			0
$253$	−4.47328	−	4.47328i	−0.281233	−	0.281233i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			18.8752i			1.17740i	0.808350	+	0.588702i	$0.200361\pi$
$257$			18.8752i			1.17740i	−0.808350	+	0.588702i	$0.799639\pi$
$258$		0			0
$259$	−9.30440	+	9.30440i	−0.578147	+	0.578147i
$260$		0			0
$261$	−7.10738	−	7.10738i	−0.439936	−	0.439936i
$262$		0			0
$263$	−23.1398			−1.42686			−0.713429	−	0.700727i	$-0.752859\pi$
$263$	−23.1398			−1.42686			−0.713429	+	0.700727i	$0.752859\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.678646	+	0.678646i	−0.0415325	+	0.0415325i
$268$		0			0
$269$	10.6368	−	10.6368i	0.648539	−	0.648539i	−0.304101	−	0.952640i	$-0.598356\pi$
$269$	10.6368	−	10.6368i	0.648539	−	0.648539i	0.952640	+	0.304101i	$0.0983560\pi$
$270$		0			0
$271$	−19.9763			−1.21348			−0.606738	−	0.794902i	$-0.707522\pi$
$271$	−19.9763			−1.21348			−0.606738	+	0.794902i	$0.707522\pi$
$272$		0			0
$273$		−	1.37417i		−	0.0831683i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	16.1534	−	16.1534i	0.970563	−	0.970563i	−0.0290160	−	0.999579i	$-0.509237\pi$
$277$	16.1534	−	16.1534i	0.970563	−	0.970563i	0.999579	+	0.0290160i	$0.00923738\pi$
$278$		0			0
$279$		−	16.6110i		−	0.994474i
$280$		0			0
$281$			9.43520i			0.562857i	0.959582	+	0.281429i	$0.0908082\pi$
$281$			9.43520i			0.562857i	−0.959582	+	0.281429i	$0.909192\pi$
$282$		0			0
$283$	−8.71287	+	8.71287i	−0.517926	+	0.517926i	−0.916943	−	0.399017i	$-0.869351\pi$
$283$	−8.71287	+	8.71287i	−0.517926	+	0.517926i	0.399017	+	0.916943i	$0.369351\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			17.4292i			1.02881i
$288$		0			0
$289$	−3.56843			−0.209908
$290$		0			0
$291$	−0.406838	+	0.406838i	−0.0238493	+	0.0238493i
$292$		0			0
$293$	−11.1045	+	11.1045i	−0.648729	+	0.648729i	−0.952686	−	0.303957i	$-0.901692\pi$
$293$	−11.1045	+	11.1045i	−0.648729	+	0.648729i	0.303957	+	0.952686i	$0.401692\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.25247			−0.0726759
$298$		0			0
$299$	16.7052	+	16.7052i	0.966087	+	0.966087i
$300$		0			0
$301$	−3.65742	+	3.65742i	−0.210810	+	0.210810i
$302$		0			0
$303$			4.33372i			0.248966i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	2.99854	+	2.99854i	0.171136	+	0.171136i	0.787478	−	0.616343i	$-0.211386\pi$
$307$	2.99854	+	2.99854i	0.171136	+	0.171136i	−0.616343	+	0.787478i	$0.711386\pi$
$308$		0			0
$309$	−1.04031	−	1.04031i	−0.0591814	−	0.0591814i
$310$		0			0
$311$			9.06099i			0.513802i	0.966438	+	0.256901i	$0.0827014\pi$
$311$			9.06099i			0.513802i	−0.966438	+	0.256901i	$0.917299\pi$
$312$		0			0
$313$	−19.5699			−1.10616			−0.553078	−	0.833129i	$-0.686547\pi$
$313$	−19.5699			−1.10616			−0.553078	+	0.833129i	$0.686547\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.1019	−	11.1019i	−0.623546	−	0.623546i	0.322890	−	0.946436i	$-0.395346\pi$
$317$	−11.1019	−	11.1019i	−0.623546	−	0.623546i	−0.946436	+	0.322890i	$0.895346\pi$
$318$		0			0
$319$	−2.46709			−0.138131
$320$		0			0
$321$	−1.15109			−0.0642478
$322$		0			0
$323$	−14.6045	−	14.6045i	−0.812614	−	0.812614i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−2.93382			−0.162241
$328$		0			0
$329$			7.50894i			0.413981i
$330$		0			0
$331$	8.14718	+	8.14718i	0.447810	+	0.447810i	0.894626	−	0.446816i	$-0.147442\pi$
$331$	8.14718	+	8.14718i	0.447810	+	0.447810i	−0.446816	+	0.894626i	$0.647442\pi$
$332$		0			0
$333$	−15.5996	−	15.5996i	−0.854851	−	0.854851i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	25.1380i		−	1.36935i	−0.728847	−	0.684677i	$-0.759943\pi$
$337$		−	25.1380i		−	1.36935i	0.728847	−	0.684677i	$-0.240057\pi$
$338$		0			0
$339$	−1.36891	+	1.36891i	−0.0743488	+	0.0743488i
$340$		0			0
$341$	−2.88298	−	2.88298i	−0.156122	−	0.156122i
$342$		0			0
$343$	19.0770			1.03006
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.36719	−	7.36719i	0.395491	−	0.395491i	−0.481148	−	0.876639i	$-0.659780\pi$
$347$	7.36719	−	7.36719i	0.395491	−	0.395491i	0.876639	+	0.481148i	$0.159780\pi$
$348$		0			0
$349$	3.25982	−	3.25982i	0.174494	−	0.174494i	−0.614457	−	0.788951i	$-0.710625\pi$
$349$	3.25982	−	3.25982i	0.174494	−	0.174494i	0.788951	+	0.614457i	$0.210625\pi$
$350$		0			0
$351$	4.67729			0.249655
$352$		0			0
$353$		−	0.502832i		−	0.0267630i	−0.999910	−	0.0133815i	$-0.995740\pi$
$353$		−	0.502832i		−	0.0267630i	0.999910	−	0.0133815i	$-0.00425960\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	1.65091	−	1.65091i	0.0873754	−	0.0873754i
$358$		0			0
$359$			5.95161i			0.314114i	0.987590	+	0.157057i	$0.0502007\pi$
$359$			5.95161i			0.314114i	−0.987590	+	0.157057i	$0.949799\pi$
$360$		0			0
$361$		−	1.73958i		−	0.0915571i
$362$		0			0
$363$	2.19821	−	2.19821i	0.115376	−	0.115376i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		−	1.95365i		−	0.101980i	−0.998699	−	0.0509898i	$-0.983762\pi$
$367$		−	1.95365i		−	0.101980i	0.998699	−	0.0509898i	$-0.0162376\pi$
$368$		0			0
$369$	−29.2214			−1.52121
$370$		0			0
$371$	2.38760	−	2.38760i	0.123958	−	0.123958i
$372$		0			0
$373$	−18.6509	+	18.6509i	−0.965708	+	0.965708i	−0.999431	−	0.0337233i	$-0.989264\pi$
$373$	−18.6509	+	18.6509i	−0.965708	+	0.965708i	0.0337233	+	0.999431i	$0.489264\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	9.21320			0.474504
$378$		0			0
$379$	−3.85143	−	3.85143i	−0.197835	−	0.197835i	0.601236	−	0.799071i	$-0.294675\pi$
$379$	−3.85143	−	3.85143i	−0.197835	−	0.197835i	−0.799071	+	0.601236i	$0.794675\pi$
$380$		0			0
$381$	−0.525732	+	0.525732i	−0.0269341	+	0.0269341i
$382$		0			0
$383$			2.29258i			0.117145i	0.998283	+	0.0585726i	$0.0186549\pi$
$383$			2.29258i			0.117145i	−0.998283	+	0.0585726i	$0.981345\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−6.13195	−	6.13195i	−0.311705	−	0.311705i
$388$		0			0
$389$	−4.90500	−	4.90500i	−0.248693	−	0.248693i	0.571741	−	0.820434i	$-0.306268\pi$
$389$	−4.90500	−	4.90500i	−0.248693	−	0.248693i	−0.820434	+	0.571741i	$0.806268\pi$
$390$		0			0
$391$			40.1389i			2.02991i
$392$		0			0
$393$	−3.58695			−0.180938
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−10.8616	−	10.8616i	−0.545126	−	0.545126i	0.379901	−	0.925027i	$-0.375958\pi$
$397$	−10.8616	−	10.8616i	−0.545126	−	0.545126i	−0.925027	+	0.379901i	$0.875958\pi$
$398$		0			0
$399$	2.34443			0.117368
$400$		0			0
$401$	−7.10783			−0.354948			−0.177474	−	0.984125i	$-0.556793\pi$
$401$	−7.10783			−0.354948			−0.177474	+	0.984125i	$0.556793\pi$
$402$		0			0
$403$	10.7663	+	10.7663i	0.536308	+	0.536308i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.41487			−0.268405
$408$		0			0
$409$		−	29.1697i		−	1.44235i	−0.692752	−	0.721176i	$-0.743602\pi$
$409$		−	29.1697i		−	1.44235i	0.692752	−	0.721176i	$-0.256398\pi$
$410$		0			0
$411$	−1.35620	−	1.35620i	−0.0668964	−	0.0668964i
$412$		0			0
$413$	−11.5359	−	11.5359i	−0.567643	−	0.567643i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	6.89198i		−	0.337502i
$418$		0			0
$419$	3.06616	−	3.06616i	0.149792	−	0.149792i	−0.628233	−	0.778025i	$-0.716222\pi$
$419$	3.06616	−	3.06616i	0.149792	−	0.149792i	0.778025	+	0.628233i	$0.216222\pi$
$420$		0			0
$421$	−0.532242	−	0.532242i	−0.0259399	−	0.0259399i	0.694018	−	0.719958i	$-0.255839\pi$
$421$	−0.532242	−	0.532242i	−0.0259399	−	0.0259399i	−0.719958	+	0.694018i	$0.755839\pi$
$422$		0			0
$423$	−12.5893			−0.612115
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−9.14005	+	9.14005i	−0.442318	+	0.442318i
$428$		0			0
$429$	0.399861	−	0.399861i	0.0193055	−	0.0193055i
$430$		0			0
$431$	−16.7237			−0.805555			−0.402777	−	0.915298i	$-0.631955\pi$
$431$	−16.7237			−0.805555			−0.402777	+	0.915298i	$0.631955\pi$
$432$		0			0
$433$		−	28.3675i		−	1.36326i	−0.731699	−	0.681628i	$-0.761272\pi$
$433$		−	28.3675i		−	1.36326i	0.731699	−	0.681628i	$-0.238728\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−28.5004	+	28.5004i	−1.36336	+	1.36336i
$438$		0			0
$439$			13.5018i			0.644405i	0.946671	+	0.322203i	$0.104423\pi$
$439$			13.5018i			0.644405i	−0.946671	+	0.322203i	$0.895577\pi$
$440$		0			0
$441$			11.5990i			0.552333i
$442$		0			0
$443$	9.55246	−	9.55246i	0.453851	−	0.453851i	−0.442780	−	0.896630i	$-0.646008\pi$
$443$	9.55246	−	9.55246i	0.453851	−	0.453851i	0.896630	+	0.442780i	$0.146008\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			1.14343i			0.0540824i
$448$		0			0
$449$	9.35573			0.441524			0.220762	−	0.975328i	$-0.429146\pi$
$449$	9.35573			0.441524			0.220762	+	0.975328i	$0.429146\pi$
$450$		0			0
$451$	−5.07162	+	5.07162i	−0.238813	+	0.238813i
$452$		0			0
$453$	2.41418	−	2.41418i	0.113428	−	0.113428i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−6.84779			−0.320326			−0.160163	−	0.987091i	$-0.551202\pi$
$457$	−6.84779			−0.320326			−0.160163	+	0.987091i	$0.551202\pi$
$458$		0			0
$459$	5.61925	+	5.61925i	0.262284	+	0.262284i
$460$		0			0
$461$	−11.7403	+	11.7403i	−0.546801	+	0.546801i	−0.925514	−	0.378713i	$-0.876367\pi$
$461$	−11.7403	+	11.7403i	−0.546801	+	0.546801i	0.378713	+	0.925514i	$0.376367\pi$
$462$		0			0
$463$		−	26.6096i		−	1.23665i	−0.785922	−	0.618326i	$-0.787811\pi$
$463$		−	26.6096i		−	1.23665i	0.785922	−	0.618326i	$-0.212189\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.47583	−	1.47583i	−0.0682933	−	0.0682933i	0.672135	−	0.740428i	$-0.265377\pi$
$467$	−1.47583	−	1.47583i	−0.0682933	−	0.0682933i	−0.740428	+	0.672135i	$0.765377\pi$
$468$		0			0
$469$	−18.3385	−	18.3385i	−0.846792	−	0.846792i
$470$		0			0
$471$			1.37484i			0.0633494i
$472$		0			0
$473$	−2.12851			−0.0978688
$474$		0			0
$475$		0			0
$476$		0			0
$477$	4.00301	+	4.00301i	0.183285	+	0.183285i
$478$		0			0
$479$	−2.78600			−0.127296			−0.0636479	−	0.997972i	$-0.520273\pi$
$479$	−2.78600			−0.127296			−0.0636479	+	0.997972i	$0.520273\pi$
$480$		0			0
$481$	20.2215			0.922022
$482$		0			0
$483$	−3.22172	−	3.22172i	−0.146593	−	0.146593i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	16.9499			0.768073			0.384036	−	0.923318i	$-0.374534\pi$
$487$	16.9499			0.768073			0.384036	+	0.923318i	$0.374534\pi$
$488$		0			0
$489$		−	3.88699i		−	0.175776i
$490$		0			0
$491$	22.8390	+	22.8390i	1.03071	+	1.03071i	0.999513	+	0.0311972i	$0.00993197\pi$
$491$	22.8390	+	22.8390i	1.03071	+	1.03071i	0.0311972	+	0.999513i	$0.490068\pi$
$492$		0			0
$493$	11.0687	+	11.0687i	0.498507	+	0.498507i
$494$		0			0
$495$		0			0
$496$		0			0
$497$			24.3933i			1.09419i
$498$		0			0
$499$	2.33906	−	2.33906i	0.104711	−	0.104711i	−0.652811	−	0.757521i	$-0.726410\pi$
$499$	2.33906	−	2.33906i	0.104711	−	0.104711i	0.757521	+	0.652811i	$0.226410\pi$
$500$		0			0
$501$	−1.48390	−	1.48390i	−0.0662958	−	0.0662958i
$502$		0			0
$503$	1.58801			0.0708057			0.0354029	−	0.999373i	$-0.488729\pi$
$503$	1.58801			0.0708057			0.0354029	+	0.999373i	$0.488729\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.23117	−	1.23117i	0.0546781	−	0.0546781i
$508$		0			0
$509$	3.61613	−	3.61613i	0.160282	−	0.160282i	−0.622410	−	0.782692i	$-0.713846\pi$
$509$	3.61613	−	3.61613i	0.160282	−	0.160282i	0.782692	+	0.622410i	$0.213846\pi$
$510$		0			0
$511$	−11.5305			−0.510079
$512$		0			0
$513$			7.97981i			0.352317i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−2.18499	+	2.18499i	−0.0960956	+	0.0960956i
$518$		0			0
$519$			2.18571i			0.0959419i
$520$		0			0
$521$			8.93031i			0.391244i	0.980679	+	0.195622i	$0.0626725\pi$
$521$			8.93031i			0.391244i	−0.980679	+	0.195622i	$0.937327\pi$
$522$		0			0
$523$	−15.0355	+	15.0355i	−0.657455	+	0.657455i	−0.954777	−	0.297323i	$-0.903906\pi$
$523$	−15.0355	+	15.0355i	−0.657455	+	0.657455i	0.297323	+	0.954777i	$0.403906\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			25.8691i			1.12687i
$528$		0			0
$529$	55.3305			2.40567
$530$		0			0
$531$	19.3408	−	19.3408i	0.839320	−	0.839320i
$532$		0			0
$533$	18.9397	−	18.9397i	0.820368	−	0.820368i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	2.64980			0.114347
$538$		0			0
$539$	2.01310	+	2.01310i	0.0867106	+	0.0867106i
$540$		0			0
$541$	5.57591	−	5.57591i	0.239727	−	0.239727i	−0.577010	−	0.816737i	$-0.695781\pi$
$541$	5.57591	−	5.57591i	0.239727	−	0.239727i	0.816737	+	0.577010i	$0.195781\pi$
$542$		0			0
$543$			5.47798i			0.235083i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−32.8366	−	32.8366i	−1.40399	−	1.40399i	−0.786856	−	0.617136i	$-0.788293\pi$
$547$	−32.8366	−	32.8366i	−1.40399	−	1.40399i	−0.617136	−	0.786856i	$-0.711707\pi$
$548$		0			0
$549$	−15.3240	−	15.3240i	−0.654013	−	0.654013i
$550$		0			0
$551$			15.7184i			0.669628i
$552$		0			0
$553$	−7.42199			−0.315615
$554$		0			0
$555$		0			0
$556$		0			0
$557$	24.2077	+	24.2077i	1.02571	+	1.02571i	0.999661	+	0.0260537i	$0.00829408\pi$
$557$	24.2077	+	24.2077i	1.02571	+	1.02571i	0.0260537	+	0.999661i	$0.491706\pi$
$558$		0			0
$559$	7.94877			0.336197
$560$		0			0
$561$	0.960778			0.0405641
$562$		0			0
$563$	22.3407	+	22.3407i	0.941547	+	0.941547i	0.998384	−	0.0568365i	$-0.0181014\pi$
$563$	22.3407	+	22.3407i	0.941547	+	0.941547i	−0.0568365	+	0.998384i	$0.518101\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	14.2729			0.599406
$568$		0			0
$569$			29.3339i			1.22974i	0.788629	+	0.614870i	$0.210791\pi$
$569$			29.3339i			1.22974i	−0.788629	+	0.614870i	$0.789209\pi$
$570$		0			0
$571$	−23.9934	−	23.9934i	−1.00409	−	1.00409i	−0.999992	−	0.00410070i	$-0.998695\pi$
$571$	−23.9934	−	23.9934i	−1.00409	−	1.00409i	−0.00410070	−	0.999992i	$-0.501305\pi$
$572$		0			0
$573$	4.64666	+	4.64666i	0.194117	+	0.194117i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	31.9232i		−	1.32898i	−0.747297	−	0.664490i	$-0.768649\pi$
$577$		−	31.9232i		−	1.32898i	0.747297	−	0.664490i	$-0.231351\pi$
$578$		0			0
$579$	1.67174	−	1.67174i	0.0694751	−	0.0694751i
$580$		0			0
$581$	−15.9016	−	15.9016i	−0.659710	−	0.659710i
$582$		0			0
$583$	1.38951			0.0575477
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−26.2847	+	26.2847i	−1.08488	+	1.08488i	−0.0888379	+	0.996046i	$0.528315\pi$
$587$	−26.2847	+	26.2847i	−1.08488	+	1.08488i	−0.996046	+	0.0888379i	$0.971685\pi$
$588$		0			0
$589$	−18.3681	+	18.3681i	−0.756846	+	0.756846i
$590$		0			0
$591$	−2.41563			−0.0993658
$592$		0			0
$593$			38.2085i			1.56904i	0.620106	+	0.784518i	$0.287090\pi$
$593$			38.2085i			1.56904i	−0.620106	+	0.784518i	$0.712910\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.12931	+	1.12931i	−0.0462197	+	0.0462197i
$598$		0			0
$599$			25.1150i			1.02617i	0.858337	+	0.513086i	$0.171498\pi$
$599$			25.1150i			1.02617i	−0.858337	+	0.513086i	$0.828502\pi$
$600$		0			0
$601$			22.2022i			0.905647i	0.891600	+	0.452823i	$0.149583\pi$
$601$			22.2022i			0.905647i	−0.891600	+	0.452823i	$0.850417\pi$
$602$		0			0
$603$	30.7459	−	30.7459i	1.25207	−	1.25207i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		−	12.9648i		−	0.526226i	−0.964765	−	0.263113i	$-0.915251\pi$
$607$		−	12.9648i		−	0.526226i	0.964765	−	0.263113i	$-0.0847492\pi$
$608$		0			0
$609$	−1.77683			−0.0720009
$610$		0			0
$611$	8.15970	−	8.15970i	0.330106	−	0.330106i
$612$		0			0
$613$	7.42804	−	7.42804i	0.300016	−	0.300016i	−0.541004	−	0.841020i	$-0.681956\pi$
$613$	7.42804	−	7.42804i	0.300016	−	0.300016i	0.841020	+	0.541004i	$0.181956\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	23.2743			0.936989			0.468494	−	0.883467i	$-0.344797\pi$
$617$	23.2743			0.936989			0.468494	+	0.883467i	$0.344797\pi$
$618$		0			0
$619$	−31.6213	−	31.6213i	−1.27097	−	1.27097i	−0.945581	−	0.325386i	$-0.894506\pi$
$619$	−31.6213	−	31.6213i	−1.27097	−	1.27097i	−0.325386	−	0.945581i	$-0.605494\pi$
$620$		0			0
$621$	10.9659	−	10.9659i	0.440045	−	0.440045i
$622$		0			0
$623$		−	5.62474i		−	0.225351i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	0.682194	+	0.682194i	0.0272442	+	0.0272442i
$628$		0			0
$629$	24.2939	+	24.2939i	0.968663	+	0.968663i
$630$		0			0
$631$		−	29.9258i		−	1.19133i	−0.803234	−	0.595663i	$-0.796889\pi$
$631$		−	29.9258i		−	1.19133i	0.803234	−	0.595663i	$-0.203111\pi$
$632$		0			0
$633$	−4.50775			−0.179167
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−7.51782	−	7.51782i	−0.297867	−	0.297867i
$638$		0			0
$639$	−40.8974			−1.61788
$640$		0			0
$641$	10.2240			0.403825			0.201912	−	0.979404i	$-0.435284\pi$
$641$	10.2240			0.403825			0.201912	+	0.979404i	$0.435284\pi$
$642$		0			0
$643$	−13.7202	−	13.7202i	−0.541074	−	0.541074i	0.382770	−	0.923844i	$-0.374970\pi$
$643$	−13.7202	−	13.7202i	−0.541074	−	0.541074i	−0.923844	+	0.382770i	$0.874970\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	18.6767			0.734255			0.367128	−	0.930171i	$-0.380341\pi$
$647$	18.6767			0.734255			0.367128	+	0.930171i	$0.380341\pi$
$648$		0			0
$649$		−	6.71353i		−	0.263529i
$650$		0			0
$651$	−2.07636	−	2.07636i	−0.0813790	−	0.0813790i
$652$		0			0
$653$	−12.7935	−	12.7935i	−0.500647	−	0.500647i	0.410992	−	0.911639i	$-0.365183\pi$
$653$	−12.7935	−	12.7935i	−0.500647	−	0.500647i	−0.911639	+	0.410992i	$0.865183\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	19.3318i		−	0.754205i
$658$		0			0
$659$	12.3193	−	12.3193i	0.479893	−	0.479893i	−0.425204	−	0.905097i	$-0.639798\pi$
$659$	12.3193	−	12.3193i	0.479893	−	0.479893i	0.905097	+	0.425204i	$0.139798\pi$
$660$		0			0
$661$	−24.0352	−	24.0352i	−0.934862	−	0.934862i	0.0631421	−	0.998005i	$-0.479888\pi$
$661$	−24.0352	−	24.0352i	−0.934862	−	0.934862i	−0.998005	+	0.0631421i	$0.979888\pi$
$662$		0			0
$663$	−3.58797			−0.139345
$664$		0			0
$665$		0			0
$666$		0			0
$667$	21.6003	−	21.6003i	0.836367	−	0.836367i
$668$		0			0
$669$	0.835589	−	0.835589i	0.0323057	−	0.0323057i
$670$		0			0
$671$	−5.31923			−0.205347
$672$		0			0
$673$			21.5360i			0.830150i	0.909787	+	0.415075i	$0.136245\pi$
$673$			21.5360i			0.830150i	−0.909787	+	0.415075i	$0.863755\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−13.1852	+	13.1852i	−0.506750	+	0.506750i	−0.913527	−	0.406778i	$-0.866652\pi$
$677$	−13.1852	+	13.1852i	−0.506750	+	0.506750i	0.406778	+	0.913527i	$0.366652\pi$
$678$		0			0
$679$		−	3.37195i		−	0.129404i
$680$		0			0
$681$			1.60156i			0.0613717i
$682$		0			0
$683$	−30.6011	+	30.6011i	−1.17092	+	1.17092i	−0.188926	+	0.981991i	$0.560501\pi$
$683$	−30.6011	+	30.6011i	−1.17092	+	1.17092i	−0.981991	+	0.188926i	$0.939499\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			3.69133i			0.140833i
$688$		0			0
$689$	−5.18905			−0.197687
$690$		0			0
$691$	25.2675	−	25.2675i	0.961220	−	0.961220i	−0.0380558	−	0.999276i	$-0.512116\pi$
$691$	25.2675	−	25.2675i	0.961220	−	0.961220i	0.999276	+	0.0380558i	$0.0121165\pi$
$692$		0			0
$693$	2.55663	−	2.55663i	0.0971182	−	0.0971182i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	45.5079			1.72373
$698$		0			0
$699$	−3.47976	−	3.47976i	−0.131617	−	0.131617i
$700$		0			0
$701$	18.5583	−	18.5583i	0.700937	−	0.700937i	−0.263675	−	0.964612i	$-0.584935\pi$
$701$	18.5583	−	18.5583i	0.700937	−	0.700937i	0.964612	+	0.263675i	$0.0849345\pi$
$702$		0			0
$703$			34.4995i			1.30117i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−17.9593	−	17.9593i	−0.675431	−	0.675431i
$708$		0			0
$709$	−4.38093	−	4.38093i	−0.164529	−	0.164529i	0.620040	−	0.784570i	$-0.287116\pi$
$709$	−4.38093	−	4.38093i	−0.164529	−	0.164529i	−0.784570	+	0.620040i	$0.787116\pi$
$710$		0			0
$711$		−	12.4436i		−	0.466670i
$712$		0			0
$713$	50.4831			1.89061
$714$		0			0
$715$		0			0
$716$		0			0
$717$	0.798957	+	0.798957i	0.0298376	+	0.0298376i
$718$		0			0
$719$	1.61691			0.0603007			0.0301503	−	0.999545i	$-0.490401\pi$
$719$	1.61691			0.0603007			0.0301503	+	0.999545i	$0.490401\pi$
$720$		0			0
$721$	8.62231			0.321112
$722$		0			0
$723$	2.00137	+	2.00137i	0.0744319	+	0.0744319i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	39.3600			1.45978			0.729891	−	0.683563i	$-0.239571\pi$
$727$	39.3600			1.45978			0.729891	+	0.683563i	$0.239571\pi$
$728$		0			0
$729$			22.3717i			0.828581i
$730$		0			0
$731$	9.54958	+	9.54958i	0.353204	+	0.353204i
$732$		0			0
$733$	34.0787	+	34.0787i	1.25873	+	1.25873i	0.951701	+	0.307026i	$0.0993339\pi$
$733$	34.0787	+	34.0787i	1.25873	+	1.25873i	0.307026	+	0.951701i	$0.400666\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	10.6724i		−	0.393124i
$738$		0			0
$739$	15.4278	−	15.4278i	0.567520	−	0.567520i	−0.363913	−	0.931433i	$-0.618559\pi$
$739$	15.4278	−	15.4278i	0.567520	−	0.567520i	0.931433	+	0.363913i	$0.118559\pi$
$740$		0			0
$741$	−2.54761	−	2.54761i	−0.0935888	−	0.0935888i
$742$		0			0
$743$	−23.5004			−0.862147			−0.431074	−	0.902317i	$-0.641865\pi$
$743$	−23.5004			−0.862147			−0.431074	+	0.902317i	$0.641865\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	26.6603	−	26.6603i	0.975451	−	0.975451i
$748$		0			0
$749$	4.77024	−	4.77024i	0.174301	−	0.174301i
$750$		0			0
$751$	−10.8586			−0.396236			−0.198118	−	0.980178i	$-0.563483\pi$
$751$	−10.8586			−0.396236			−0.198118	+	0.980178i	$0.563483\pi$
$752$		0			0
$753$		−	5.02690i		−	0.183190i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−18.8434	+	18.8434i	−0.684874	+	0.684874i	−0.961094	−	0.276220i	$-0.910918\pi$
$757$	−18.8434	+	18.8434i	−0.684874	+	0.684874i	0.276220	+	0.961094i	$0.410918\pi$
$758$		0			0
$759$		−	1.87494i		−	0.0680561i
$760$		0			0
$761$		−	22.2837i		−	0.807783i	−0.914807	−	0.403891i	$-0.867657\pi$
$761$		−	22.2837i		−	0.807783i	0.914807	−	0.403891i	$-0.132343\pi$
$762$		0			0
$763$	12.1580	−	12.1580i	0.440151	−	0.440151i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			25.0713i			0.905271i
$768$		0			0
$769$	−10.5399			−0.380077			−0.190039	−	0.981777i	$-0.560861\pi$
$769$	−10.5399			−0.380077			−0.190039	+	0.981777i	$0.560861\pi$
$770$		0			0
$771$	−3.95571	+	3.95571i	−0.142461	+	0.142461i
$772$		0			0
$773$	4.07768	−	4.07768i	0.146664	−	0.146664i	−0.629962	−	0.776626i	$-0.716930\pi$
$773$	4.07768	−	4.07768i	0.146664	−	0.146664i	0.776626	+	0.629962i	$0.216930\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−3.89987			−0.139907
$778$		0			0
$779$	32.3125	+	32.3125i	1.15772	+	1.15772i
$780$		0			0
$781$	−7.09809	+	7.09809i	−0.253990	+	0.253990i
$782$		0			0
$783$		−	6.04786i		−	0.216133i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	8.16669	+	8.16669i	0.291111	+	0.291111i	0.837519	−	0.546408i	$-0.184005\pi$
$787$	8.16669	+	8.16669i	0.291111	+	0.291111i	−0.546408	+	0.837519i	$0.684005\pi$
$788$		0			0
$789$	−4.84943	−	4.84943i	−0.172644	−	0.172644i
$790$		0			0
$791$		−	11.3458i		−	0.403409i
$792$		0			0
$793$	19.8643			0.705403
$794$		0			0
$795$		0			0
$796$		0			0
$797$	17.9971	+	17.9971i	0.637491	+	0.637491i	0.949936	−	0.312445i	$-0.101148\pi$
$797$	17.9971	+	17.9971i	0.637491	+	0.637491i	−0.312445	+	0.949936i	$0.601148\pi$
$798$		0			0
$799$	19.6060			0.693609
$800$		0			0
$801$	9.43033			0.333204
$802$		0			0
$803$	−3.35520	−	3.35520i	−0.118402	−	0.118402i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	4.45835			0.156941
$808$		0			0
$809$			42.0296i			1.47768i	0.673879	+	0.738841i	$0.264627\pi$
$809$			42.0296i			1.47768i	−0.673879	+	0.738841i	$0.735373\pi$
$810$		0			0
$811$	−18.7601	−	18.7601i	−0.658757	−	0.658757i	0.296329	−	0.955086i	$-0.404238\pi$
$811$	−18.7601	−	18.7601i	−0.658757	−	0.658757i	−0.955086	+	0.296329i	$0.904238\pi$
$812$		0			0
$813$	−4.18646	−	4.18646i	−0.146826	−	0.146826i
$814$		0			0
$815$		0			0
$816$		0			0
$817$			13.5612i			0.474447i
$818$		0			0
$819$	−9.54757	+	9.54757i	−0.333619	+	0.333619i
$820$		0			0
$821$	−21.4050	−	21.4050i	−0.747038	−	0.747038i	0.226884	−	0.973922i	$-0.427146\pi$
$821$	−21.4050	−	21.4050i	−0.747038	−	0.747038i	−0.973922	+	0.226884i	$0.927146\pi$
$822$		0			0
$823$	43.7323			1.52441			0.762206	−	0.647334i	$-0.224116\pi$
$823$	43.7323			1.52441			0.762206	+	0.647334i	$0.224116\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−19.9621	+	19.9621i	−0.694149	+	0.694149i	−0.963142	−	0.268993i	$-0.913309\pi$
$827$	−19.9621	+	19.9621i	−0.694149	+	0.694149i	0.268993	+	0.963142i	$0.413309\pi$
$828$		0			0
$829$	−31.3869	+	31.3869i	−1.09011	+	1.09011i	−0.0945964	+	0.995516i	$0.530156\pi$
$829$	−31.3869	+	31.3869i	−1.09011	+	1.09011i	−0.995516	+	0.0945964i	$0.969844\pi$
$830$		0			0
$831$	6.77057			0.234868
$832$		0			0
$833$		−	18.0637i		−	0.625869i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	7.06737	−	7.06737i	0.244284	−	0.244284i
$838$		0			0
$839$		−	54.5335i		−	1.88271i	−0.337423	−	0.941353i	$-0.609555\pi$
$839$		−	54.5335i		−	1.88271i	0.337423	−	0.941353i	$-0.390445\pi$
$840$		0			0
$841$			17.0871i			0.589210i
$842$		0			0
$843$	−1.97735	+	1.97735i	−0.0681035	+	0.0681035i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			18.2192i			0.626018i
$848$		0			0
$849$	−3.65193			−0.125334
$850$		0			0
$851$	47.4092	−	47.4092i	1.62517	−	1.62517i
$852$		0			0
$853$	21.5932	−	21.5932i	0.739336	−	0.739336i	−0.233114	−	0.972449i	$-0.574891\pi$
$853$	21.5932	−	21.5932i	0.739336	−	0.739336i	0.972449	+	0.233114i	$0.0748914\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−41.3609			−1.41286			−0.706431	−	0.707782i	$-0.749696\pi$
$857$	−41.3609			−1.41286			−0.706431	+	0.707782i	$0.749696\pi$
$858$		0			0
$859$	−0.700596	−	0.700596i	−0.0239040	−	0.0239040i	0.695054	−	0.718958i	$-0.255381\pi$
$859$	−0.700596	−	0.700596i	−0.0239040	−	0.0239040i	−0.718958	+	0.695054i	$0.755381\pi$
$860$		0			0
$861$	−3.65265	+	3.65265i	−0.124482	+	0.124482i
$862$		0			0
$863$			55.0780i			1.87488i	0.348150	+	0.937439i	$0.386810\pi$
$863$			55.0780i			1.87488i	−0.348150	+	0.937439i	$0.613190\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−0.747840	−	0.747840i	−0.0253980	−	0.0253980i
$868$		0			0
$869$	−2.15969	−	2.15969i	−0.0732623	−	0.0732623i
$870$		0			0
$871$			39.8556i			1.35045i
$872$		0			0
$873$	5.65335			0.191337
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−36.5100	−	36.5100i	−1.23285	−	1.23285i	−0.962863	−	0.269992i	$-0.912979\pi$
$877$	−36.5100	−	36.5100i	−1.23285	−	1.23285i	−0.269992	−	0.962863i	$-0.587021\pi$
$878$		0			0
$879$	−4.65435			−0.156987
$880$		0			0
$881$	54.3503			1.83111			0.915554	−	0.402196i	$-0.131753\pi$
$881$	54.3503			1.83111			0.915554	+	0.402196i	$0.131753\pi$
$882$		0			0
$883$	35.5476	+	35.5476i	1.19627	+	1.19627i	0.975274	+	0.220999i	$0.0709319\pi$
$883$	35.5476	+	35.5476i	1.19627	+	1.19627i	0.220999	+	0.975274i	$0.429068\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.817003			0.0274323			0.0137161	−	0.999906i	$-0.495634\pi$
$887$	0.817003			0.0274323			0.0137161	+	0.999906i	$0.495634\pi$
$888$		0			0
$889$		−	4.35737i		−	0.146141i
$890$		0			0
$891$	4.15320	+	4.15320i	0.139137	+	0.139137i
$892$		0			0
$893$	13.9211	+	13.9211i	0.465851	+	0.465851i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			7.00186i			0.233785i
$898$		0			0
$899$	13.9211	−	13.9211i	0.464296	−	0.464296i
$900$		0			0
$901$	−6.23407	−	6.23407i	−0.207687	−	0.207687i
$902$		0			0
$903$	−1.53298			−0.0510144
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−3.36159	+	3.36159i	−0.111620	+	0.111620i	−0.760711	−	0.649091i	$-0.775149\pi$
$907$	−3.36159	+	3.36159i	−0.111620	+	0.111620i	0.649091	+	0.760711i	$0.275149\pi$
$908$		0			0
$909$	30.1103	−	30.1103i	0.998695	−	0.998695i
$910$		0			0
$911$	−34.6568			−1.14823			−0.574116	−	0.818774i	$-0.694654\pi$
$911$	−34.6568			−1.14823			−0.574116	+	0.818774i	$0.694654\pi$
$912$		0			0
$913$		−	9.25426i		−	0.306271i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	14.8646	−	14.8646i	0.490874	−	0.490874i
$918$		0			0
$919$			24.3452i			0.803074i	0.915843	+	0.401537i	$0.131524\pi$
$919$			24.3452i			0.803074i	−0.915843	+	0.401537i	$0.868476\pi$
$920$		0			0
$921$			1.25681i			0.0414135i
$922$		0			0
$923$	26.5074	−	26.5074i	0.872501	−	0.872501i
$924$		0			0
$925$		0			0
$926$		0			0
$927$			14.4560i			0.474797i
$928$		0			0
$929$	−3.16600			−0.103873			−0.0519366	−	0.998650i	$-0.516539\pi$
$929$	−3.16600			−0.103873			−0.0519366	+	0.998650i	$0.516539\pi$
$930$		0			0
$931$	12.8260	−	12.8260i	0.420354	−	0.420354i
$932$		0			0
$933$	−1.89892	+	1.89892i	−0.0621680	+	0.0621680i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	23.4847			0.767211			0.383606	−	0.923497i	$-0.374682\pi$
$937$	23.4847			0.767211			0.383606	+	0.923497i	$0.374682\pi$
$938$		0			0
$939$	−4.10129	−	4.10129i	−0.133840	−	0.133840i
$940$		0			0
$941$	27.7583	−	27.7583i	0.904896	−	0.904896i	−0.0909585	−	0.995855i	$-0.528993\pi$
$941$	27.7583	−	27.7583i	0.904896	−	0.904896i	0.995855	+	0.0909585i	$0.0289931\pi$
$942$		0			0
$943$		−	88.8078i		−	2.89198i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	27.2916	+	27.2916i	0.886857	+	0.886857i	0.994220	−	0.107363i	$-0.0342407\pi$
$947$	27.2916	+	27.2916i	0.886857	+	0.886857i	−0.107363	+	0.994220i	$0.534241\pi$
$948$		0			0
$949$	12.5298	+	12.5298i	0.406734	+	0.406734i
$950$		0			0
$951$		−	4.65329i		−	0.150893i
$952$		0			0
$953$	12.1516			0.393630			0.196815	−	0.980441i	$-0.436940\pi$
$953$	12.1516			0.393630			0.196815	+	0.980441i	$0.436940\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−0.517031	−	0.517031i	−0.0167132	−	0.0167132i
$958$		0			0
$959$	11.2404			0.362972
$960$		0			0
$961$	1.53571			0.0495392
$962$		0			0
$963$	7.99769	+	7.99769i	0.257722	+	0.257722i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−48.2694			−1.55224			−0.776120	−	0.630585i	$-0.782815\pi$
$967$	−48.2694			−1.55224			−0.776120	+	0.630585i	$0.782815\pi$
$968$		0			0
$969$		−	6.12135i		−	0.196646i
$970$		0			0
$971$	−5.92047	−	5.92047i	−0.189997	−	0.189997i	0.605698	−	0.795695i	$-0.292894\pi$
$971$	−5.92047	−	5.92047i	−0.189997	−	0.189997i	−0.795695	+	0.605698i	$0.792894\pi$
$972$		0			0
$973$	28.5610	+	28.5610i	0.915623	+	0.915623i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	27.7522i		−	0.887872i	−0.896059	−	0.443936i	$-0.853582\pi$
$977$		−	27.7522i		−	0.887872i	0.896059	−	0.443936i	$-0.146418\pi$
$978$		0			0
$979$	1.63671	−	1.63671i	0.0523096	−	0.0523096i
$980$		0			0
$981$	20.3839	+	20.3839i	0.650808	+	0.650808i
$982$		0			0
$983$	28.3604			0.904556			0.452278	−	0.891877i	$-0.350611\pi$
$983$	28.3604			0.904556			0.452278	+	0.891877i	$0.350611\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−1.57366	+	1.57366i	−0.0500901	+	0.0500901i
$988$		0			0
$989$	18.6358	−	18.6358i	0.592585	−	0.592585i
$990$		0			0
$991$	43.7506			1.38979			0.694893	−	0.719114i	$-0.255452\pi$
$991$	43.7506			1.38979			0.694893	+	0.719114i	$0.255452\pi$
$992$		0			0
$993$			3.41483i			0.108366i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−10.5572	+	10.5572i	−0.334349	+	0.334349i	−0.854235	−	0.519887i	$-0.825974\pi$
$997$	−10.5572	+	10.5572i	−0.334349	+	0.334349i	0.519887	+	0.854235i	$0.325974\pi$
$998$		0			0
$999$		−	13.2741i		−	0.419974i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.q.h.49.5		16
4.3	odd	2		400.2.q.g.149.7		16
5.2	odd	4		1600.2.l.i.1201.5		16
5.3	odd	4		320.2.l.a.241.4		16
5.4	even	2		1600.2.q.g.49.4		16
15.8	even	4		2880.2.t.c.2161.4		16
16.3	odd	4		400.2.q.h.349.2		16
16.13	even	4		1600.2.q.g.849.4		16
20.3	even	4		80.2.l.a.21.6	✓	16
20.7	even	4		400.2.l.h.101.3		16
20.19	odd	2		400.2.q.h.149.2		16
40.3	even	4		640.2.l.b.481.4		16
40.13	odd	4		640.2.l.a.481.5		16
60.23	odd	4		720.2.t.c.181.3		16
80.3	even	4		80.2.l.a.61.6	yes	16
80.13	odd	4		320.2.l.a.81.4		16
80.19	odd	4		400.2.q.g.349.7		16
80.29	even	4	inner	1600.2.q.h.849.5		16
80.43	even	4		640.2.l.b.161.4		16
80.53	odd	4		640.2.l.a.161.5		16
80.67	even	4		400.2.l.h.301.3		16
80.77	odd	4		1600.2.l.i.401.5		16
160.3	even	8		5120.2.a.s.1.6		8
160.13	odd	8		5120.2.a.t.1.6		8
160.83	even	8		5120.2.a.v.1.3		8
160.93	odd	8		5120.2.a.u.1.3		8
240.83	odd	4		720.2.t.c.541.3		16
240.173	even	4		2880.2.t.c.721.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.6	✓	16	20.3	even	4
80.2.l.a.61.6	yes	16	80.3	even	4
320.2.l.a.81.4		16	80.13	odd	4
320.2.l.a.241.4		16	5.3	odd	4
400.2.l.h.101.3		16	20.7	even	4
400.2.l.h.301.3		16	80.67	even	4
400.2.q.g.149.7		16	4.3	odd	2
400.2.q.g.349.7		16	80.19	odd	4
400.2.q.h.149.2		16	20.19	odd	2
400.2.q.h.349.2		16	16.3	odd	4
640.2.l.a.161.5		16	80.53	odd	4
640.2.l.a.481.5		16	40.13	odd	4
640.2.l.b.161.4		16	80.43	even	4
640.2.l.b.481.4		16	40.3	even	4
720.2.t.c.181.3		16	60.23	odd	4
720.2.t.c.541.3		16	240.83	odd	4
1600.2.l.i.401.5		16	80.77	odd	4
1600.2.l.i.1201.5		16	5.2	odd	4
1600.2.q.g.49.4		16	5.4	even	2
1600.2.q.g.849.4		16	16.13	even	4
1600.2.q.h.49.5		16	1.1	even	1	trivial
1600.2.q.h.849.5		16	80.29	even	4	inner
2880.2.t.c.721.1		16	240.173	even	4
2880.2.t.c.2161.4		16	15.8	even	4
5120.2.a.s.1.6		8	160.3	even	8
5120.2.a.t.1.6		8	160.13	odd	8
5120.2.a.u.1.3		8	160.93	odd	8
5120.2.a.v.1.3		8	160.83	even	8

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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.209571 + 0.209571i) q^{3} -1.73696 q^{7} -2.91216i q^{9} +(-0.505430 - 0.505430i) q^{11} +(1.88750 + 1.88750i) q^{13} +4.53524i q^{17} +(-3.22022 + 3.22022i) q^{19} +(-0.364018 - 0.364018i) q^{21} +8.85045 q^{23} +(1.23902 - 1.23902i) q^{27} +(2.44059 - 2.44059i) q^{29} +5.70401 q^{31} -0.211847i q^{33} +(5.35670 - 5.35670i) q^{37} +0.791130i q^{39} -10.0343i q^{41} +(2.10564 - 2.10564i) q^{43} -4.32303i q^{47} -3.98295 q^{49} +(-0.950456 + 0.950456i) q^{51} +(-1.37458 + 1.37458i) q^{53} -1.34973 q^{57} +(6.64140 + 6.64140i) q^{59} +(5.26208 - 5.26208i) q^{61} +5.05832i q^{63} +(10.5578 + 10.5578i) q^{67} +(1.85480 + 1.85480i) q^{69} -14.0437i q^{71} +6.63830 q^{73} +(0.877914 + 0.877914i) q^{77} +4.27297 q^{79} -8.21715 q^{81} +(9.15483 + 9.15483i) q^{83} +1.02295 q^{87} +3.23826i q^{89} +(-3.27852 - 3.27852i) q^{91} +(1.19540 + 1.19540i) q^{93} +1.94129i q^{97} +(-1.47189 + 1.47189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7} + 8 q^{11} - 8 q^{19} + 24 q^{23} + 24 q^{27} + 16 q^{29} + 16 q^{37} - 8 q^{43} + 16 q^{49} + 32 q^{51} + 16 q^{53} - 8 q^{59} + 16 q^{61} - 40 q^{67} - 16 q^{69} + 16 q^{77} + 16 q^{79}+ \cdots - 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^7 + 8 * q^11 - 8 * q^19 + 24 * q^23 + 24 * q^27 + 16 * q^29 + 16 * q^37 - 8 * q^43 + 16 * q^49 + 32 * q^51 + 16 * q^53 - 8 * q^59 + 16 * q^61 - 40 * q^67 - 16 * q^69 + 16 * q^77 + 16 * q^79 - 16 * q^81 + 40 * q^83 - 32 * q^91 + 48 * q^93 - 8 * q^99

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