LMFDB - Embedded newform 1600.2.l.i.401.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(401,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("1600.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$12.7760643234$
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			401.5
Root			$-0.966675 + 1.03225i$ of defining polynomial
Character	$\chi$	$=$	1600.401
Dual form			1600.2.l.i.1201.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.209571 + 0.209571i) q^{3} +1.73696i q^{7} -2.91216i q^{9} +O(q^{10})$	$q+(0.209571 + 0.209571i) q^{3} +1.73696i q^{7} -2.91216i q^{9} +(-0.505430 + 0.505430i) q^{11} +(1.88750 + 1.88750i) q^{13} -4.53524 q^{17} +(3.22022 + 3.22022i) q^{19} +(-0.364018 + 0.364018i) q^{21} +8.85045i q^{23} +(1.23902 - 1.23902i) q^{27} +(-2.44059 - 2.44059i) q^{29} +5.70401 q^{31} -0.211847 q^{33} +(5.35670 - 5.35670i) q^{37} +0.791130i q^{39} +10.0343i q^{41} +(-2.10564 + 2.10564i) q^{43} +4.32303 q^{47} +3.98295 q^{49} +(-0.950456 - 0.950456i) q^{51} +(1.37458 - 1.37458i) q^{53} +1.34973i q^{57} +(-6.64140 + 6.64140i) q^{59} +(5.26208 + 5.26208i) q^{61} +5.05832 q^{63} +(-10.5578 - 10.5578i) q^{67} +(-1.85480 + 1.85480i) q^{69} +14.0437i q^{71} +6.63830i q^{73} +(-0.877914 - 0.877914i) q^{77} -4.27297 q^{79} -8.21715 q^{81} +(9.15483 + 9.15483i) q^{83} -1.02295i q^{87} +3.23826i q^{89} +(-3.27852 + 3.27852i) q^{91} +(1.19540 + 1.19540i) q^{93} -1.94129 q^{97} +(1.47189 + 1.47189i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 8 q^{11} + 8 q^{19} + 24 q^{27} - 16 q^{29} + 16 q^{37} + 8 q^{43} - 40 q^{47} - 16 q^{49} + 32 q^{51} - 16 q^{53} + 8 q^{59} + 16 q^{61} + 40 q^{63} + 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}+O(q^{100}) $ 16 * q + 8 * q^11 + 8 * q^19 + 24 * q^27 - 16 * q^29 + 16 * q^37 + 8 * q^43 - 40 * q^47 - 16 * q^49 + 32 * q^51 - 16 * q^53 + 8 * q^59 + 16 * q^61 + 40 * q^63 + 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$577$	$901$	$1151$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$		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
$7$			1.73696i			0.656511i	0.944589	+	0.328255i	$0.106461\pi$
$7$			1.73696i			0.656511i	−0.944589	+	0.328255i	$0.893539\pi$
$8$		0			0
$9$		−	2.91216i		−	0.970720i
$10$		0			0
$11$	−0.505430	+	0.505430i	−0.152393	+	0.152393i	−0.779186	−	0.626793i	$-0.784367\pi$
$11$	−0.505430	+	0.505430i	−0.152393	+	0.152393i	0.626793	+	0.779186i	$0.284367\pi$
$12$		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
$17$	−4.53524			−1.09996			−0.549979	−	0.835178i	$-0.685364\pi$
$17$	−4.53524			−1.09996			−0.549979	+	0.835178i	$0.685364\pi$
$18$		0			0
$19$	3.22022	+	3.22022i	0.738768	+	0.738768i	0.972340	−	0.233571i	$-0.0750413\pi$
$19$	3.22022	+	3.22022i	0.738768	+	0.738768i	−0.233571	+	0.972340i	$0.575041\pi$
$20$		0			0
$21$	−0.364018	+	0.364018i	−0.0794352	+	0.0794352i
$22$		0			0
$23$			8.85045i			1.84545i	0.385463	+	0.922723i	$0.374042\pi$
$23$			8.85045i			1.84545i	−0.385463	+	0.922723i	$0.625958\pi$
$24$		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	$-0.353839\pi$
$29$	−2.44059	−	2.44059i	−0.453205	−	0.453205i	−0.896417	+	0.443212i	$0.853839\pi$
$30$		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
$33$	−0.211847			−0.0368779
$34$		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	$0.286591\pi$
$41$			10.0343i			1.56709i	−0.621335	+	0.783545i	$0.713409\pi$
$42$		0			0
$43$	−2.10564	+	2.10564i	−0.321107	+	0.321107i	−0.849192	−	0.528085i	$-0.822910\pi$
$43$	−2.10564	+	2.10564i	−0.321107	+	0.321107i	0.528085	+	0.849192i	$0.322910\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.32303			0.630578			0.315289	−	0.948996i	$-0.397899\pi$
$47$	4.32303			0.630578			0.315289	+	0.948996i	$0.397899\pi$
$48$		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	−0.606369	−	0.795183i	$-0.707375\pi$
$53$	1.37458	−	1.37458i	0.188814	−	0.188814i	0.795183	+	0.606369i	$0.207375\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			1.34973i			0.178776i
$58$		0			0
$59$	−6.64140	+	6.64140i	−0.864637	+	0.864637i	−0.991872	−	0.127236i	$-0.959389\pi$
$59$	−6.64140	+	6.64140i	−0.864637	+	0.864637i	0.127236	+	0.991872i	$0.459389\pi$
$60$		0			0
$61$	5.26208	+	5.26208i	0.673741	+	0.673741i	0.958576	−	0.284836i	$-0.0919391\pi$
$61$	5.26208	+	5.26208i	0.673741	+	0.673741i	−0.284836	+	0.958576i	$0.591939\pi$
$62$		0			0
$63$	5.05832			0.637288
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−10.5578	−	10.5578i	−1.28984	−	1.28984i	−0.934884	−	0.354954i	$-0.884497\pi$
$67$	−10.5578	−	10.5578i	−1.28984	−	1.28984i	−0.354954	−	0.934884i	$-0.615503\pi$
$68$		0			0
$69$	−1.85480	+	1.85480i	−0.223292	+	0.223292i
$70$		0			0
$71$			14.0437i			1.66668i	0.552764	+	0.833338i	$0.313573\pi$
$71$			14.0437i			1.66668i	−0.552764	+	0.833338i	$0.686427\pi$
$72$		0			0
$73$			6.63830i			0.776954i	0.921458	+	0.388477i	$0.126999\pi$
$73$			6.63830i			0.776954i	−0.921458	+	0.388477i	$0.873001\pi$
$74$		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	$-0.577270\pi$
$79$	−4.27297			−0.480746			−0.240373	+	0.970681i	$0.577270\pi$
$80$		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
$87$		−	1.02295i		−	0.109672i
$88$		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
$97$	−1.94129			−0.197108			−0.0985541	−	0.995132i	$-0.531422\pi$
$97$	−1.94129			−0.197108			−0.0985541	+	0.995132i	$0.531422\pi$
$98$		0			0
$99$	1.47189	+	1.47189i	0.147931	+	0.147931i
$100$		0			0
$101$	10.3395	−	10.3395i	1.02882	−	1.02882i	0.0292464	−	0.999572i	$-0.490689\pi$
$101$	10.3395	−	10.3395i	1.02882	−	1.02882i	0.999572	−	0.0292464i	$-0.00931074\pi$
$102$		0			0
$103$		−	4.96401i		−	0.489118i	−0.969634	−	0.244559i	$-0.921357\pi$
$103$		−	4.96401i		−	0.489118i	0.969634	−	0.244559i	$-0.0786433\pi$
$104$		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	$-0.0927837\pi$
$109$	6.99959	+	6.99959i	0.670439	+	0.670439i	−0.287378	+	0.957817i	$0.592784\pi$
$110$		0			0
$111$	2.24522			0.213107
$112$		0			0
$113$	6.53194			0.614474			0.307237	−	0.951633i	$-0.400596\pi$
$113$	6.53194			0.614474			0.307237	+	0.951633i	$0.400596\pi$
$114$		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
$127$	−2.50861			−0.222603			−0.111302	−	0.993787i	$-0.535502\pi$
$127$	−2.50861			−0.222603			−0.111302	+	0.993787i	$0.535502\pi$
$128$		0			0
$129$	−0.882562			−0.0777053
$130$		0			0
$131$	−8.55783	−	8.55783i	−0.747701	−	0.747701i	0.226346	−	0.974047i	$-0.427322\pi$
$131$	−8.55783	−	8.55783i	−0.747701	−	0.747701i	−0.974047	+	0.226346i	$0.927322\pi$
$132$		0			0
$133$	−5.59340	+	5.59340i	−0.485009	+	0.485009i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			6.47131i			0.552881i	0.961031	+	0.276440i	$0.0891549\pi$
$137$			6.47131i			0.552881i	−0.961031	+	0.276440i	$0.910845\pi$
$138$		0			0
$139$	16.4430	−	16.4430i	1.39468	−	1.39468i	0.580223	−	0.814458i	$-0.302965\pi$
$139$	16.4430	−	16.4430i	1.39468	−	1.39468i	0.814458	−	0.580223i	$-0.197035\pi$
$140$		0			0
$141$	0.905982	+	0.905982i	0.0762974	+	0.0762974i
$142$		0			0
$143$	−1.90800			−0.159555
$144$		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	$-0.800514\pi$
$149$	−2.72803	+	2.72803i	−0.223489	+	0.223489i	0.586477	+	0.809966i	$0.300514\pi$
$150$		0			0
$151$			11.5196i			0.937453i	0.883343	+	0.468726i	$0.155287\pi$
$151$			11.5196i			0.937453i	−0.883343	+	0.468726i	$0.844713\pi$
$152$		0			0
$153$			13.2074i			1.06775i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−3.28013	−	3.28013i	−0.261783	−	0.261783i	0.563995	−	0.825778i	$-0.309264\pi$
$157$	−3.28013	−	3.28013i	−0.261783	−	0.261783i	−0.825778	+	0.563995i	$0.809264\pi$
$158$		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
$167$			7.08065i			0.547917i	0.961742	+	0.273958i	$0.0883331\pi$
$167$			7.08065i			0.547917i	−0.961742	+	0.273958i	$0.911667\pi$
$168$		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
$177$	−2.78369			−0.209235
$178$		0			0
$179$	−6.32196	−	6.32196i	−0.472525	−	0.472525i	0.430206	−	0.902731i	$-0.358441\pi$
$179$	−6.32196	−	6.32196i	−0.472525	−	0.472525i	−0.902731	+	0.430206i	$0.858441\pi$
$180$		0			0
$181$	13.0695	−	13.0695i	0.971448	−	0.971448i	−0.0281553	−	0.999604i	$-0.508963\pi$
$181$	13.0695	−	13.0695i	0.971448	−	0.971448i	0.999604	+	0.0281553i	$0.00896329\pi$
$182$		0			0
$183$			2.20556i			0.163040i
$184$		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
$193$	−7.97695			−0.574193			−0.287097	−	0.957902i	$-0.592690\pi$
$193$	−7.97695			−0.574193			−0.287097	+	0.957902i	$0.592690\pi$
$194$		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
$207$	25.7739			1.79141
$208$		0			0
$209$	−3.25519			−0.225166
$210$		0			0
$211$	−10.7547	−	10.7547i	−0.740384	−	0.740384i	0.232268	−	0.972652i	$-0.425385\pi$
$211$	−10.7547	−	10.7547i	−0.740384	−	0.740384i	−0.972652	+	0.232268i	$0.925385\pi$
$212$		0			0
$213$	−2.94315	+	2.94315i	−0.201661	+	0.201661i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			9.90766i			0.672576i
$218$		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
$223$	−3.98714			−0.266998			−0.133499	−	0.991049i	$-0.542621\pi$
$223$	−3.98714			−0.266998			−0.133499	+	0.991049i	$0.542621\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.82103	−	3.82103i	−0.253611	−	0.253611i	0.568839	−	0.822449i	$-0.307393\pi$
$227$	−3.82103	−	3.82103i	−0.253611	−	0.253611i	−0.822449	+	0.568839i	$0.807393\pi$
$228$		0			0
$229$	−8.80687	+	8.80687i	−0.581974	+	0.581974i	−0.935445	−	0.353471i	$-0.885001\pi$
$229$	−8.80687	+	8.80687i	−0.581974	+	0.581974i	0.353471	+	0.935445i	$0.385001\pi$
$230$		0			0
$231$		−	0.367971i		−	0.0242107i
$232$		0			0
$233$		−	16.6042i		−	1.08778i	−0.839157	−	0.543889i	$-0.816951\pi$
$233$		−	16.6042i		−	1.08778i	0.839157	−	0.543889i	$-0.183049\pi$
$234$		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	$-0.539348\pi$
$239$	−3.81234			−0.246600			−0.123300	+	0.992369i	$0.539348\pi$
$240$		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
$247$			12.1563i			0.773487i
$248$		0			0
$249$			3.83718i			0.243171i
$250$		0			0
$251$	−11.9933	+	11.9933i	−0.757010	+	0.757010i	−0.975777	−	0.218767i	$-0.929797\pi$
$251$	−11.9933	+	11.9933i	−0.757010	+	0.757010i	0.218767	+	0.975777i	$0.429797\pi$
$252$		0			0
$253$	−4.47328	−	4.47328i	−0.281233	−	0.281233i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−18.8752			−1.17740			−0.588702	−	0.808350i	$-0.700361\pi$
$257$	−18.8752			−1.17740			−0.588702	+	0.808350i	$0.700361\pi$
$258$		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
$263$		−	23.1398i		−	1.42686i	−0.700727	−	0.713429i	$-0.747141\pi$
$263$		−	23.1398i		−	1.42686i	0.700727	−	0.713429i	$-0.252859\pi$
$264$		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	$-0.401644\pi$
$269$	−10.6368	−	10.6368i	−0.648539	−	0.648539i	−0.952640	+	0.304101i	$0.901644\pi$
$270$		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
$273$	−1.37417			−0.0831683
$274$		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	$-0.909192\pi$
$281$		−	9.43520i		−	0.562857i	0.959582	−	0.281429i	$-0.0908082\pi$
$282$		0			0
$283$	8.71287	−	8.71287i	0.517926	−	0.517926i	−0.399017	−	0.916943i	$-0.630649\pi$
$283$	8.71287	−	8.71287i	0.517926	−	0.517926i	0.916943	+	0.399017i	$0.130649\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−17.4292			−1.02881
$288$		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	−0.303957	−	0.952686i	$-0.598308\pi$
$293$	11.1045	−	11.1045i	0.648729	−	0.648729i	0.952686	+	0.303957i	$0.0983079\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$			1.25247i			0.0726759i
$298$		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
$303$	4.33372			0.248966
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−2.99854	−	2.99854i	−0.171136	−	0.171136i	0.616343	−	0.787478i	$-0.288614\pi$
$307$	−2.99854	−	2.99854i	−0.171136	−	0.171136i	−0.787478	+	0.616343i	$0.788614\pi$
$308$		0			0
$309$	1.04031	−	1.04031i	0.0591814	−	0.0591814i
$310$		0			0
$311$		−	9.06099i		−	0.513802i	−0.966438	−	0.256901i	$-0.917299\pi$
$311$		−	9.06099i		−	0.513802i	0.966438	−	0.256901i	$-0.0827014\pi$
$312$		0			0
$313$		−	19.5699i		−	1.10616i	−0.833129	−	0.553078i	$-0.813453\pi$
$313$		−	19.5699i		−	1.10616i	0.833129	−	0.553078i	$-0.186547\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.1019	+	11.1019i	0.623546	+	0.623546i	0.946436	−	0.322890i	$-0.104654\pi$
$317$	11.1019	+	11.1019i	0.623546	+	0.623546i	−0.322890	+	0.946436i	$0.604654\pi$
$318$		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
$327$			2.93382i			0.162241i
$328$		0			0
$329$			7.50894i			0.413981i
$330$		0			0
$331$	8.14718	−	8.14718i	0.447810	−	0.447810i	−0.446816	−	0.894626i	$-0.647442\pi$
$331$	8.14718	−	8.14718i	0.447810	−	0.447810i	0.894626	+	0.446816i	$0.147442\pi$
$332$		0			0
$333$	−15.5996	−	15.5996i	−0.854851	−	0.854851i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	25.1380			1.36935			0.684677	−	0.728847i	$-0.259943\pi$
$337$	25.1380			1.36935			0.684677	+	0.728847i	$0.259943\pi$
$338$		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
$343$			19.0770i			1.03006i
$344$		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	$-0.289375\pi$
$349$	−3.25982	−	3.25982i	−0.174494	−	0.174494i	−0.788951	+	0.614457i	$0.789375\pi$
$350$		0			0
$351$	4.67729			0.249655
$352$		0			0
$353$	−0.502832			−0.0267630			−0.0133815	−	0.999910i	$-0.504260\pi$
$353$	−0.502832			−0.0267630			−0.0133815	+	0.999910i	$0.504260\pi$
$354$		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
$367$	1.95365			0.101980			0.0509898	−	0.998699i	$-0.483762\pi$
$367$	1.95365			0.101980			0.0509898	+	0.998699i	$0.483762\pi$
$368$		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	−0.0337233	−	0.999431i	$-0.510736\pi$
$373$	18.6509	−	18.6509i	0.965708	−	0.965708i	0.999431	+	0.0337233i	$0.0107365\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	9.21320i		−	0.474504i
$378$		0			0
$379$	3.85143	−	3.85143i	0.197835	−	0.197835i	−0.601236	−	0.799071i	$-0.705325\pi$
$379$	3.85143	−	3.85143i	0.197835	−	0.197835i	0.799071	+	0.601236i	$0.205325\pi$
$380$		0			0
$381$	−0.525732	−	0.525732i	−0.0269341	−	0.0269341i
$382$		0			0
$383$	2.29258			0.117145			0.0585726	−	0.998283i	$-0.481345\pi$
$383$	2.29258			0.117145			0.0585726	+	0.998283i	$0.481345\pi$
$384$		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	$-0.693732\pi$
$389$	4.90500	−	4.90500i	0.248693	−	0.248693i	0.820434	+	0.571741i	$0.193732\pi$
$390$		0			0
$391$		−	40.1389i		−	2.02991i
$392$		0			0
$393$		−	3.58695i		−	0.180938i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	10.8616	+	10.8616i	0.545126	+	0.545126i	0.925027	−	0.379901i	$-0.124042\pi$
$397$	10.8616	+	10.8616i	0.545126	+	0.545126i	−0.379901	+	0.925027i	$0.624042\pi$
$398$		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
$407$			5.41487i			0.268405i
$408$		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
$417$	6.89198			0.337502
$418$		0			0
$419$	−3.06616	−	3.06616i	−0.149792	−	0.149792i	0.628233	−	0.778025i	$-0.283778\pi$
$419$	−3.06616	−	3.06616i	−0.149792	−	0.149792i	−0.778025	+	0.628233i	$0.783778\pi$
$420$		0			0
$421$	−0.532242	+	0.532242i	−0.0259399	+	0.0259399i	−0.719958	−	0.694018i	$-0.755839\pi$
$421$	−0.532242	+	0.532242i	−0.0259399	+	0.0259399i	0.694018	+	0.719958i	$0.255839\pi$
$422$		0			0
$423$		−	12.5893i		−	0.612115i
$424$		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
$433$	−28.3675			−1.36326			−0.681628	−	0.731699i	$-0.738728\pi$
$433$	−28.3675			−1.36326			−0.681628	+	0.731699i	$0.738728\pi$
$434$		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	−0.896630	−	0.442780i	$-0.853992\pi$
$443$	−9.55246	+	9.55246i	−0.453851	+	0.453851i	0.442780	+	0.896630i	$0.353992\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−1.14343			−0.0540824
$448$		0			0
$449$	−9.35573			−0.441524			−0.220762	−	0.975328i	$-0.570854\pi$
$449$	−9.35573			−0.441524			−0.220762	+	0.975328i	$0.570854\pi$
$450$		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
$457$			6.84779i			0.320326i	0.987091	+	0.160163i	$0.0512020\pi$
$457$			6.84779i			0.320326i	−0.987091	+	0.160163i	$0.948798\pi$
$458$		0			0
$459$	−5.61925	+	5.61925i	−0.262284	+	0.262284i
$460$		0			0
$461$	−11.7403	−	11.7403i	−0.546801	−	0.546801i	0.378713	−	0.925514i	$-0.376367\pi$
$461$	−11.7403	−	11.7403i	−0.546801	−	0.546801i	−0.925514	+	0.378713i	$0.876367\pi$
$462$		0			0
$463$	−26.6096			−1.23665			−0.618326	−	0.785922i	$-0.712189\pi$
$463$	−26.6096			−1.23665			−0.618326	+	0.785922i	$0.712189\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.47583	+	1.47583i	0.0682933	+	0.0682933i	0.740428	−	0.672135i	$-0.234623\pi$
$467$	1.47583	+	1.47583i	0.0682933	+	0.0682933i	−0.672135	+	0.740428i	$0.734623\pi$
$468$		0			0
$469$	18.3385	−	18.3385i	0.846792	−	0.846792i
$470$		0			0
$471$		−	1.37484i		−	0.0633494i
$472$		0			0
$473$		−	2.12851i		−	0.0978688i
$474$		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	$-0.479727\pi$
$479$	2.78600			0.127296			0.0636479	+	0.997972i	$0.479727\pi$
$480$		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
$487$		−	16.9499i		−	0.768073i	−0.923318	−	0.384036i	$-0.874534\pi$
$487$		−	16.9499i		−	0.768073i	0.923318	−	0.384036i	$-0.125466\pi$
$488$		0			0
$489$		−	3.88699i		−	0.175776i
$490$		0			0
$491$	22.8390	−	22.8390i	1.03071	−	1.03071i	0.0311972	−	0.999513i	$-0.490068\pi$
$491$	22.8390	−	22.8390i	1.03071	−	1.03071i	0.999513	−	0.0311972i	$-0.00993197\pi$
$492$		0			0
$493$	11.0687	+	11.0687i	0.498507	+	0.498507i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−24.3933			−1.09419
$498$		0			0
$499$	−2.33906	−	2.33906i	−0.104711	−	0.104711i	0.652811	−	0.757521i	$-0.273590\pi$
$499$	−2.33906	−	2.33906i	−0.104711	−	0.104711i	−0.757521	+	0.652811i	$0.773590\pi$
$500$		0			0
$501$	−1.48390	+	1.48390i	−0.0662958	+	0.0662958i
$502$		0			0
$503$			1.58801i			0.0708057i	0.999373	+	0.0354029i	$0.0112714\pi$
$503$			1.58801i			0.0708057i	−0.999373	+	0.0354029i	$0.988729\pi$
$504$		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	$-0.286154\pi$
$509$	−3.61613	−	3.61613i	−0.160282	−	0.160282i	−0.782692	+	0.622410i	$0.786154\pi$
$510$		0			0
$511$	−11.5305			−0.510079
$512$		0			0
$513$	7.97981			0.352317
$514$		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	$-0.937327\pi$
$521$		−	8.93031i		−	0.391244i	0.980679	−	0.195622i	$-0.0626725\pi$
$522$		0			0
$523$	15.0355	−	15.0355i	0.657455	−	0.657455i	−0.297323	−	0.954777i	$-0.596094\pi$
$523$	15.0355	−	15.0355i	0.657455	−	0.657455i	0.954777	+	0.297323i	$0.0960937\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−25.8691			−1.12687
$528$		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
$537$		−	2.64980i		−	0.114347i
$538$		0			0
$539$	−2.01310	+	2.01310i	−0.0867106	+	0.0867106i
$540$		0			0
$541$	5.57591	+	5.57591i	0.239727	+	0.239727i	0.816737	−	0.577010i	$-0.195781\pi$
$541$	5.57591	+	5.57591i	0.239727	+	0.239727i	−0.577010	+	0.816737i	$0.695781\pi$
$542$		0			0
$543$	5.47798			0.235083
$544$		0			0
$545$		0			0
$546$		0			0
$547$	32.8366	+	32.8366i	1.40399	+	1.40399i	0.786856	+	0.617136i	$0.211707\pi$
$547$	32.8366	+	32.8366i	1.40399	+	1.40399i	0.617136	+	0.786856i	$0.288293\pi$
$548$		0			0
$549$	15.3240	−	15.3240i	0.654013	−	0.654013i
$550$		0			0
$551$		−	15.7184i		−	0.669628i
$552$		0			0
$553$		−	7.42199i		−	0.315615i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−24.2077	−	24.2077i	−1.02571	−	1.02571i	−0.999661	−	0.0260537i	$-0.991706\pi$
$557$	−24.2077	−	24.2077i	−1.02571	−	1.02571i	−0.0260537	−	0.999661i	$-0.508294\pi$
$558$		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
$567$		−	14.2729i		−	0.599406i
$568$		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	−0.00410070	+	0.999992i	$0.501305\pi$
$571$	−23.9934	+	23.9934i	−1.00409	+	1.00409i	−0.999992	+	0.00410070i	$0.998695\pi$
$572$		0			0
$573$	4.64666	+	4.64666i	0.194117	+	0.194117i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	31.9232			1.32898			0.664490	−	0.747297i	$-0.268649\pi$
$577$	31.9232			1.32898			0.664490	+	0.747297i	$0.268649\pi$
$578$		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
$583$			1.38951i			0.0575477i
$584$		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
$593$	38.2085			1.56904			0.784518	−	0.620106i	$-0.212910\pi$
$593$	38.2085			1.56904			0.784518	+	0.620106i	$0.212910\pi$
$594$		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	$-0.850417\pi$
$601$		−	22.2022i		−	0.905647i	0.891600	−	0.452823i	$-0.149583\pi$
$602$		0			0
$603$	−30.7459	+	30.7459i	−1.25207	+	1.25207i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	12.9648			0.526226			0.263113	−	0.964765i	$-0.415251\pi$
$607$	12.9648			0.526226			0.263113	+	0.964765i	$0.415251\pi$
$608$		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	−0.841020	−	0.541004i	$-0.818044\pi$
$613$	−7.42804	+	7.42804i	−0.300016	+	0.300016i	0.541004	+	0.841020i	$0.318044\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	23.2743i		−	0.936989i	−0.883467	−	0.468494i	$-0.844797\pi$
$617$		−	23.2743i		−	0.936989i	0.883467	−	0.468494i	$-0.155203\pi$
$618$		0			0
$619$	31.6213	−	31.6213i	1.27097	−	1.27097i	0.325386	−	0.945581i	$-0.394506\pi$
$619$	31.6213	−	31.6213i	1.27097	−	1.27097i	0.945581	−	0.325386i	$-0.105494\pi$
$620$		0			0
$621$	10.9659	+	10.9659i	0.440045	+	0.440045i
$622$		0			0
$623$	−5.62474			−0.225351
$624$		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	$0.203111\pi$
$631$			29.9258i			1.19133i	−0.803234	+	0.595663i	$0.796889\pi$
$632$		0			0
$633$		−	4.50775i		−	0.179167i
$634$		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
$647$		−	18.6767i		−	0.734255i	−0.930171	−	0.367128i	$-0.880341\pi$
$647$		−	18.6767i		−	0.734255i	0.930171	−	0.367128i	$-0.119659\pi$
$648$		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
$657$	19.3318			0.754205
$658$		0			0
$659$	−12.3193	−	12.3193i	−0.479893	−	0.479893i	0.425204	−	0.905097i	$-0.360202\pi$
$659$	−12.3193	−	12.3193i	−0.479893	−	0.479893i	−0.905097	+	0.425204i	$0.860202\pi$
$660$		0			0
$661$	−24.0352	+	24.0352i	−0.934862	+	0.934862i	−0.998005	−	0.0631421i	$-0.979888\pi$
$661$	−24.0352	+	24.0352i	−0.934862	+	0.934862i	0.0631421	+	0.998005i	$0.479888\pi$
$662$		0			0
$663$		−	3.58797i		−	0.139345i
$664$		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
$673$	21.5360			0.830150			0.415075	−	0.909787i	$-0.363755\pi$
$673$	21.5360			0.830150			0.415075	+	0.909787i	$0.363755\pi$
$674$		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	$-0.439499\pi$
$683$	30.6011	−	30.6011i	1.17092	−	1.17092i	0.981991	−	0.188926i	$-0.0605008\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−3.69133			−0.140833
$688$		0			0
$689$	5.18905			0.197687
$690$		0			0
$691$	25.2675	+	25.2675i	0.961220	+	0.961220i	0.999276	−	0.0380558i	$-0.0121165\pi$
$691$	25.2675	+	25.2675i	0.961220	+	0.961220i	−0.0380558	+	0.999276i	$0.512116\pi$
$692$		0			0
$693$	−2.55663	+	2.55663i	−0.0971182	+	0.0971182i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		−	45.5079i		−	1.72373i
$698$		0			0
$699$	3.47976	−	3.47976i	0.131617	−	0.131617i
$700$		0			0
$701$	18.5583	+	18.5583i	0.700937	+	0.700937i	0.964612	−	0.263675i	$-0.0849345\pi$
$701$	18.5583	+	18.5583i	0.700937	+	0.700937i	−0.263675	+	0.964612i	$0.584935\pi$
$702$		0			0
$703$	34.4995			1.30117
$704$		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	$-0.712884\pi$
$709$	4.38093	−	4.38093i	0.164529	−	0.164529i	0.784570	+	0.620040i	$0.212884\pi$
$710$		0			0
$711$			12.4436i			0.466670i
$712$		0			0
$713$			50.4831i			1.89061i
$714$		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	$-0.509599\pi$
$719$	−1.61691			−0.0603007			−0.0301503	+	0.999545i	$0.509599\pi$
$720$		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
$727$		−	39.3600i		−	1.45978i	−0.683563	−	0.729891i	$-0.739571\pi$
$727$		−	39.3600i		−	1.45978i	0.683563	−	0.729891i	$-0.260429\pi$
$728$		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
$737$	10.6724			0.393124
$738$		0			0
$739$	−15.4278	−	15.4278i	−0.567520	−	0.567520i	0.363913	−	0.931433i	$-0.381441\pi$
$739$	−15.4278	−	15.4278i	−0.567520	−	0.567520i	−0.931433	+	0.363913i	$0.881441\pi$
$740$		0			0
$741$	−2.54761	+	2.54761i	−0.0935888	+	0.0935888i
$742$		0			0
$743$		−	23.5004i		−	0.862147i	−0.902317	−	0.431074i	$-0.858135\pi$
$743$		−	23.5004i		−	0.862147i	0.902317	−	0.431074i	$-0.141865\pi$
$744$		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
$753$	−5.02690			−0.183190
$754$		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	$0.132343\pi$
$761$			22.2837i			0.807783i	−0.914807	+	0.403891i	$0.867657\pi$
$762$		0			0
$763$	−12.1580	+	12.1580i	−0.440151	+	0.440151i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−25.0713			−0.905271
$768$		0			0
$769$	10.5399			0.380077			0.190039	−	0.981777i	$-0.439139\pi$
$769$	10.5399			0.380077			0.190039	+	0.981777i	$0.439139\pi$
$770$		0			0
$771$	−3.95571	−	3.95571i	−0.142461	−	0.142461i
$772$		0			0
$773$	−4.07768	+	4.07768i	−0.146664	+	0.146664i	−0.776626	−	0.629962i	$-0.783070\pi$
$773$	−4.07768	+	4.07768i	−0.146664	+	0.146664i	0.629962	+	0.776626i	$0.283070\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$			3.89987i			0.139907i
$778$		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
$783$	−6.04786			−0.216133
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−8.16669	−	8.16669i	−0.291111	−	0.291111i	0.546408	−	0.837519i	$-0.315995\pi$
$787$	−8.16669	−	8.16669i	−0.291111	−	0.291111i	−0.837519	+	0.546408i	$0.815995\pi$
$788$		0			0
$789$	4.84943	−	4.84943i	0.172644	−	0.172644i
$790$		0			0
$791$			11.3458i			0.403409i
$792$		0			0
$793$			19.8643i			0.705403i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−17.9971	−	17.9971i	−0.637491	−	0.637491i	0.312445	−	0.949936i	$-0.398852\pi$
$797$	−17.9971	−	17.9971i	−0.637491	−	0.637491i	−0.949936	+	0.312445i	$0.898852\pi$
$798$		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
$807$		−	4.45835i		−	0.156941i
$808$		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	−0.955086	−	0.296329i	$-0.904238\pi$
$811$	−18.7601	+	18.7601i	−0.658757	+	0.658757i	0.296329	+	0.955086i	$0.404238\pi$
$812$		0			0
$813$	−4.18646	−	4.18646i	−0.146826	−	0.146826i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−13.5612			−0.474447
$818$		0			0
$819$	9.54757	+	9.54757i	0.333619	+	0.333619i
$820$		0			0
$821$	−21.4050	+	21.4050i	−0.747038	+	0.747038i	−0.973922	−	0.226884i	$-0.927146\pi$
$821$	−21.4050	+	21.4050i	−0.747038	+	0.747038i	0.226884	+	0.973922i	$0.427146\pi$
$822$		0			0
$823$			43.7323i			1.52441i	0.647334	+	0.762206i	$0.275884\pi$
$823$			43.7323i			1.52441i	−0.647334	+	0.762206i	$0.724116\pi$
$824$		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	0.995516	+	0.0945964i	$0.0301561\pi$
$829$	31.3869	+	31.3869i	1.09011	+	1.09011i	0.0945964	+	0.995516i	$0.469844\pi$
$830$		0			0
$831$	6.77057			0.234868
$832$		0			0
$833$	−18.0637			−0.625869
$834$		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
$847$	−18.2192			−0.626018
$848$		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	−0.972449	−	0.233114i	$-0.925109\pi$
$853$	−21.5932	+	21.5932i	−0.739336	+	0.739336i	0.233114	+	0.972449i	$0.425109\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			41.3609i			1.41286i	0.707782	+	0.706431i	$0.249696\pi$
$857$			41.3609i			1.41286i	−0.707782	+	0.706431i	$0.750304\pi$
$858$		0			0
$859$	0.700596	−	0.700596i	0.0239040	−	0.0239040i	−0.695054	−	0.718958i	$-0.744619\pi$
$859$	0.700596	−	0.700596i	0.0239040	−	0.0239040i	0.718958	+	0.695054i	$0.244619\pi$
$860$		0			0
$861$	−3.65265	−	3.65265i	−0.124482	−	0.124482i
$862$		0			0
$863$	55.0780			1.87488			0.937439	−	0.348150i	$-0.113190\pi$
$863$	55.0780			1.87488			0.937439	+	0.348150i	$0.113190\pi$
$864$		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
$873$			5.65335i			0.191337i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	36.5100	+	36.5100i	1.23285	+	1.23285i	0.962863	+	0.269992i	$0.0870211\pi$
$877$	36.5100	+	36.5100i	1.23285	+	1.23285i	0.269992	+	0.962863i	$0.412979\pi$
$878$		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
$887$		−	0.817003i		−	0.0274323i	−0.999906	−	0.0137161i	$-0.995634\pi$
$887$		−	0.817003i		−	0.0274323i	0.999906	−	0.0137161i	$-0.00436612\pi$
$888$		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
$897$	−7.00186			−0.233785
$898$		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
$903$		−	1.53298i		−	0.0510144i
$904$		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
$913$	−9.25426			−0.306271
$914$		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
$927$	−14.4560			−0.474797
$928$		0			0
$929$	3.16600			0.103873			0.0519366	−	0.998650i	$-0.483461\pi$
$929$	3.16600			0.103873			0.0519366	+	0.998650i	$0.483461\pi$
$930$		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
$937$		−	23.4847i		−	0.767211i	−0.923497	−	0.383606i	$-0.874682\pi$
$937$		−	23.4847i		−	0.767211i	0.923497	−	0.383606i	$-0.125318\pi$
$938$		0			0
$939$	4.10129	−	4.10129i	0.133840	−	0.133840i
$940$		0			0
$941$	27.7583	+	27.7583i	0.904896	+	0.904896i	0.995855	−	0.0909585i	$-0.0289931\pi$
$941$	27.7583	+	27.7583i	0.904896	+	0.904896i	−0.0909585	+	0.995855i	$0.528993\pi$
$942$		0			0
$943$	−88.8078			−2.89198
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−27.2916	−	27.2916i	−0.886857	−	0.886857i	0.107363	−	0.994220i	$-0.465759\pi$
$947$	−27.2916	−	27.2916i	−0.886857	−	0.886857i	−0.994220	+	0.107363i	$0.965759\pi$
$948$		0			0
$949$	−12.5298	+	12.5298i	−0.406734	+	0.406734i
$950$		0			0
$951$			4.65329i			0.150893i
$952$		0			0
$953$			12.1516i			0.393630i	0.980441	+	0.196815i	$0.0630598\pi$
$953$			12.1516i			0.393630i	−0.980441	+	0.196815i	$0.936940\pi$
$954$		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
$967$			48.2694i			1.55224i	0.630585	+	0.776120i	$0.282815\pi$
$967$			48.2694i			1.55224i	−0.630585	+	0.776120i	$0.717185\pi$
$968$		0			0
$969$		−	6.12135i		−	0.196646i
$970$		0			0
$971$	−5.92047	+	5.92047i	−0.189997	+	0.189997i	−0.795695	−	0.605698i	$-0.792894\pi$
$971$	−5.92047	+	5.92047i	−0.189997	+	0.189997i	0.605698	+	0.795695i	$0.292894\pi$
$972$		0			0
$973$	28.5610	+	28.5610i	0.915623	+	0.915623i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	27.7522			0.887872			0.443936	−	0.896059i	$-0.353582\pi$
$977$	27.7522			0.887872			0.443936	+	0.896059i	$0.353582\pi$
$978$		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
$983$			28.3604i			0.904556i	0.891877	+	0.452278i	$0.149389\pi$
$983$			28.3604i			0.904556i	−0.891877	+	0.452278i	$0.850611\pi$
$984$		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
$993$	3.41483			0.108366
$994$		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.l.i.401.5		16
4.3	odd	2		400.2.l.h.301.3		16
5.2	odd	4		1600.2.q.h.849.5		16
5.3	odd	4		1600.2.q.g.849.4		16
5.4	even	2		320.2.l.a.81.4		16
15.14	odd	2		2880.2.t.c.721.1		16
16.5	even	4	inner	1600.2.l.i.1201.5		16
16.11	odd	4		400.2.l.h.101.3		16
20.3	even	4		400.2.q.h.349.2		16
20.7	even	4		400.2.q.g.349.7		16
20.19	odd	2		80.2.l.a.61.6	yes	16
40.19	odd	2		640.2.l.b.161.4		16
40.29	even	2		640.2.l.a.161.5		16
60.59	even	2		720.2.t.c.541.3		16
80.19	odd	4		640.2.l.b.481.4		16
80.27	even	4		400.2.q.h.149.2		16
80.29	even	4		640.2.l.a.481.5		16
80.37	odd	4		1600.2.q.g.49.4		16
80.43	even	4		400.2.q.g.149.7		16
80.53	odd	4		1600.2.q.h.49.5		16
80.59	odd	4		80.2.l.a.21.6	✓	16
80.69	even	4		320.2.l.a.241.4		16
160.59	odd	8		5120.2.a.v.1.3		8
160.69	even	8		5120.2.a.t.1.6		8
160.139	odd	8		5120.2.a.s.1.6		8
160.149	even	8		5120.2.a.u.1.3		8
240.59	even	4		720.2.t.c.181.3		16
240.149	odd	4		2880.2.t.c.2161.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.6	✓	16	80.59	odd	4
80.2.l.a.61.6	yes	16	20.19	odd	2
320.2.l.a.81.4		16	5.4	even	2
320.2.l.a.241.4		16	80.69	even	4
400.2.l.h.101.3		16	16.11	odd	4
400.2.l.h.301.3		16	4.3	odd	2
400.2.q.g.149.7		16	80.43	even	4
400.2.q.g.349.7		16	20.7	even	4
400.2.q.h.149.2		16	80.27	even	4
400.2.q.h.349.2		16	20.3	even	4
640.2.l.a.161.5		16	40.29	even	2
640.2.l.a.481.5		16	80.29	even	4
640.2.l.b.161.4		16	40.19	odd	2
640.2.l.b.481.4		16	80.19	odd	4
720.2.t.c.181.3		16	240.59	even	4
720.2.t.c.541.3		16	60.59	even	2
1600.2.l.i.401.5		16	1.1	even	1	trivial
1600.2.l.i.1201.5		16	16.5	even	4	inner
1600.2.q.g.49.4		16	80.37	odd	4
1600.2.q.g.849.4		16	5.3	odd	4
1600.2.q.h.49.5		16	80.53	odd	4
1600.2.q.h.849.5		16	5.2	odd	4
2880.2.t.c.721.1		16	15.14	odd	2
2880.2.t.c.2161.4		16	240.149	odd	4
5120.2.a.s.1.6		8	160.139	odd	8
5120.2.a.t.1.6		8	160.69	even	8
5120.2.a.u.1.3		8	160.149	even	8
5120.2.a.v.1.3		8	160.59	odd	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.209571 + 0.209571i) q^{3} +1.73696i q^{7} -2.91216i q^{9} +O(q^{10})\)	\(q+(0.209571 + 0.209571i) q^{3} +1.73696i q^{7} -2.91216i q^{9} +(-0.505430 + 0.505430i) q^{11} +(1.88750 + 1.88750i) q^{13} -4.53524 q^{17} +(3.22022 + 3.22022i) q^{19} +(-0.364018 + 0.364018i) q^{21} +8.85045i q^{23} +(1.23902 - 1.23902i) q^{27} +(-2.44059 - 2.44059i) q^{29} +5.70401 q^{31} -0.211847 q^{33} +(5.35670 - 5.35670i) q^{37} +0.791130i q^{39} +10.0343i q^{41} +(-2.10564 + 2.10564i) q^{43} +4.32303 q^{47} +3.98295 q^{49} +(-0.950456 - 0.950456i) q^{51} +(1.37458 - 1.37458i) q^{53} +1.34973i q^{57} +(-6.64140 + 6.64140i) q^{59} +(5.26208 + 5.26208i) q^{61} +5.05832 q^{63} +(-10.5578 - 10.5578i) q^{67} +(-1.85480 + 1.85480i) q^{69} +14.0437i q^{71} +6.63830i q^{73} +(-0.877914 - 0.877914i) q^{77} -4.27297 q^{79} -8.21715 q^{81} +(9.15483 + 9.15483i) q^{83} -1.02295i q^{87} +3.23826i q^{89} +(-3.27852 + 3.27852i) q^{91} +(1.19540 + 1.19540i) q^{93} -1.94129 q^{97} +(1.47189 + 1.47189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 8 q^{11} + 8 q^{19} + 24 q^{27} - 16 q^{29} + 16 q^{37} + 8 q^{43} - 40 q^{47} - 16 q^{49} + 32 q^{51} - 16 q^{53} + 8 q^{59} + 16 q^{61} + 40 q^{63} + 40 q^{67} + 16 q^{69} - 16 q^{77} - 16 q^{79} - 16 q^{81} + 40 q^{83} - 32 q^{91} + 48 q^{93} + 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^11 + 8 * q^19 + 24 * q^27 - 16 * q^29 + 16 * q^37 + 8 * q^43 - 40 * q^47 - 16 * q^49 + 32 * q^51 - 16 * q^53 + 8 * q^59 + 16 * q^61 + 40 * q^63 + 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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