LMFDB - Embedded newform 3997.1.cz.a.223.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3997,1,Mod(13,3997)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3997, base_ring=CyclotomicField(570))

chi = DirichletCharacter(H, H._module([285, 352]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("3997.13");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3997 = 7 \cdot 571 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3997.cz (of order $570$, degree $144$, 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:	$1.99476285549$
Analytic rank:	$0$
Dimension:	$144$
Coefficient field:	$\Q(\zeta_{570})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{144} - x^{143} + x^{142} + x^{139} - x^{138} + x^{137} - x^{129} + x^{128} - x^{127} + x^{125} + \cdots + 1 $ x^144 - x^143 + x^142 + x^139 - x^138 + x^137 - x^129 + x^128 - x^127 + x^125 - 2x^124 + 2x^123 - x^122 + x^120 - x^119 + x^118 + x^114 - x^113 + x^112 - x^110 + 2x^109 - 2x^108 + x^107 - x^105 + x^104 - x^103 - x^99 + x^98 - x^97 + x^95 - 2x^94 + 2x^93 - x^92 + x^90 - x^89 + x^88 - x^87 + x^86 - x^85 + x^84 - x^83 + x^81 - 2x^80 + 2x^79 - 2x^78 + x^77 - x^75 + x^74 - x^73 + x^72 - x^71 + x^70 - x^69 + x^67 - 2x^66 + 2x^65 - 2x^64 + x^63 - x^61 + x^60 - x^59 + x^58 - x^57 + x^56 - x^55 + x^54 - x^52 + 2x^51 - 2x^50 + x^49 - x^47 + x^46 - x^45 - x^41 + x^40 - x^39 + x^37 - 2x^36 + 2x^35 - x^34 + x^32 - x^31 + x^30 + x^26 - x^25 + x^24 - x^22 + 2x^21 - 2x^20 + x^19 - x^17 + x^16 - x^15 + x^7 - x^6 + x^5 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{285}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{285} - \cdots)$

Embedding invariants

Embedding label			223.1
Root			$-0.999028 + 0.0440782i$ of defining polynomial
Character	$\chi$	$=$	3997.223
Dual form			3997.1.cz.a.1882.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08088 + 0.439016i) q^{2} +(0.258785 - 0.251750i) q^{4} +(-0.574329 + 0.818625i) q^{7} +(0.299439 - 0.682651i) q^{8} +(0.0935596 - 0.995614i) q^{9} +O(q^{10})$	\(q+(-1.08088 + 0.439016i) q^{2} +(0.258785 - 0.251750i) q^{4} +(-0.574329 + 0.818625i) q^{7} +(0.299439 - 0.682651i) q^{8} +(0.0935596 - 0.995614i) q^{9} +(1.98519 - 0.0218840i) q^{11} +(0.261391 - 1.13697i) q^{14} +(-0.0339108 + 1.23022i) q^{16} +(0.335963 + 1.11721i) q^{18} +(-2.13615 + 0.895185i) q^{22} +(0.813348 + 0.475583i) q^{23} +(0.266796 - 0.963753i) q^{25} +(0.0574611 + 0.356435i) q^{28} +(-0.274290 + 0.0151330i) q^{29} +(-0.242055 - 0.646500i) q^{32} +(-0.226434 - 0.281203i) q^{36} +(-1.02560 + 0.159544i) q^{37} +(-0.698385 - 0.793043i) q^{43} +(0.508229 - 0.505436i) q^{44} +(-1.08792 - 0.156976i) q^{46} +(-0.340293 - 0.940319i) q^{49} +(0.134728 + 1.15883i) q^{50} +(0.116754 - 1.62671i) q^{53} +(0.386859 + 0.637194i) q^{56} +(0.289831 - 0.136775i) q^{58} +(0.761300 + 0.648400i) q^{63} +(-0.288067 - 0.312924i) q^{64} +(1.66694 - 0.809235i) q^{67} +(0.211001 + 0.0939437i) q^{71} +(-0.651641 - 0.361994i) q^{72} +(1.03851 - 0.622704i) q^{74} +(-1.12224 + 1.63770i) q^{77} +(1.17865 - 1.49723i) q^{79} +(-0.982493 - 0.186298i) q^{81} +(1.10303 + 0.550583i) q^{86} +(0.579505 - 1.36175i) q^{88} +(0.330210 - 0.0816865i) q^{92} +(0.780631 + 0.866979i) q^{98} +(0.163946 - 1.97853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9}+O(q^{10}) $ 144 * q + q^2 + 5 * q^4 + 2 * q^7 + 21 * q^8 - q^9	$ 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9} + 6 q^{11} + q^{14} + 6 q^{16} - 9 q^{18} + 21 q^{22} + 3 q^{23} - q^{25} - 10 q^{28} - 4 q^{29} - 5 q^{32} - 2 q^{37} - 9 q^{43} - 20 q^{44} - 34 q^{46} + 2 q^{49} - 2 q^{50} + 6 q^{53} - 8 q^{56} - q^{58} - q^{63} + 11 q^{64} + 20 q^{67} + 3 q^{71} + 23 q^{72} - 31 q^{74} + q^{77} + 6 q^{79} - q^{81} + 7 q^{86} - 9 q^{88} + 9 q^{92} + 6 q^{98} - 2 q^{99}+O(q^{100}) $ 144 * q + q^2 + 5 * q^4 + 2 * q^7 + 21 * q^8 - q^9 + 6 * q^11 + q^14 + 6 * q^16 - 9 * q^18 + 21 * q^22 + 3 * q^23 - q^25 - 10 * q^28 - 4 * q^29 - 5 * q^32 - 2 * q^37 - 9 * q^43 - 20 * q^44 - 34 * q^46 + 2 * q^49 - 2 * q^50 + 6 * q^53 - 8 * q^56 - q^58 - q^63 + 11 * q^64 + 20 * q^67 + 3 * q^71 + 23 * q^72 - 31 * q^74 + q^77 + 6 * q^79 - q^81 + 7 * q^86 - 9 * q^88 + 9 * q^92 + 6 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3997\mathbb{Z}\right)^\times$.

$n$	$1716$	$2285$
$\chi(n)$	$e\left(\frac{218}{285}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.08088	+	0.439016i	−1.08088	+	0.439016i	−0.846095	−	0.533032i	$-0.821053\pi$
$2$	−1.08088	+	0.439016i	−1.08088	+	0.439016i	−0.234785	+	0.972047i	$0.575439\pi$
$3$		0			0		0.739446	−	0.673216i	$-0.235088\pi$
$3$		0			0		−0.739446	+	0.673216i	$0.764912\pi$
$4$	0.258785	−	0.251750i	0.258785	−	0.251750i
$5$		0			0		0.795863	−	0.605477i	$-0.207018\pi$
$5$		0			0		−0.795863	+	0.605477i	$0.792982\pi$
$6$		0			0
$7$	−0.574329	+	0.818625i	−0.574329	+	0.818625i
$7$	−0.574329	+	0.818625i	−0.574329	+	0.818625i
$8$	0.299439	−	0.682651i	0.299439	−	0.682651i
$9$	0.0935596	−	0.995614i	0.0935596	−	0.995614i
$10$		0			0
$11$	1.98519	−	0.0218840i	1.98519	−	0.0218840i	0.991264	−	0.131892i	$-0.0421053\pi$
$11$	1.98519	−	0.0218840i	1.98519	−	0.0218840i	0.993931	+	0.110008i	$0.0350877\pi$
$12$		0			0
$13$		0			0		−0.709053	−	0.705155i	$-0.750877\pi$
$13$		0			0		0.709053	+	0.705155i	$0.249123\pi$
$14$	0.261391	−	1.13697i	0.261391	−	1.13697i
$15$		0			0
$16$	−0.0339108	+	1.23022i	−0.0339108	+	1.23022i
$17$		0			0		0.959210	−	0.282694i	$-0.0912281\pi$
$17$		0			0		−0.959210	+	0.282694i	$0.908772\pi$
$18$	0.335963	+	1.11721i	0.335963	+	1.11721i
$19$		0			0		0.202517	−	0.979279i	$-0.435088\pi$
$19$		0			0		−0.202517	+	0.979279i	$0.564912\pi$
$20$		0			0
$21$		0			0
$22$	−2.13615	+	0.895185i	−2.13615	+	0.895185i
$23$	0.813348	+	0.475583i	0.813348	+	0.475583i	0.851919	−	0.523673i	$-0.175439\pi$
$23$	0.813348	+	0.475583i	0.813348	+	0.475583i	−0.0385714	+	0.999256i	$0.512281\pi$
$24$		0			0
$25$	0.266796	−	0.963753i	0.266796	−	0.963753i
$26$		0			0
$27$		0			0
$28$	0.0574611	+	0.356435i	0.0574611	+	0.356435i
$29$	−0.274290	+	0.0151330i	−0.274290	+	0.0151330i	−0.191711	−	0.981451i	$-0.561404\pi$
$29$	−0.274290	+	0.0151330i	−0.274290	+	0.0151330i	−0.0825793	+	0.996584i	$0.526316\pi$
$30$		0			0
$31$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$31$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$32$	−0.242055	−	0.646500i	−0.242055	−	0.646500i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.226434	−	0.281203i	−0.226434	−	0.281203i
$37$	−1.02560	+	0.159544i	−1.02560	+	0.159544i	−0.644194	−	0.764862i	$-0.722807\pi$
$37$	−1.02560	+	0.159544i	−1.02560	+	0.159544i	−0.381410	+	0.924406i	$0.624561\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.821778	−	0.569808i	$-0.807018\pi$
$41$		0			0		0.821778	+	0.569808i	$0.192982\pi$
$42$		0			0
$43$	−0.698385	−	0.793043i	−0.698385	−	0.793043i	0.287976	−	0.957638i	$-0.407018\pi$
$43$	−0.698385	−	0.793043i	−0.698385	−	0.793043i	−0.986361	+	0.164595i	$0.947368\pi$
$44$	0.508229	−	0.505436i	0.508229	−	0.505436i
$45$		0			0
$46$	−1.08792	−	0.156976i	−1.08792	−	0.156976i
$47$		0			0		−0.851919	−	0.523673i	$-0.824561\pi$
$47$		0			0		0.851919	+	0.523673i	$0.175439\pi$
$48$		0			0
$49$	−0.340293	−	0.940319i	−0.340293	−	0.940319i
$50$	0.134728	+	1.15883i	0.134728	+	1.15883i
$51$		0			0
$52$		0			0
$53$	0.116754	−	1.62671i	0.116754	−	1.62671i	−0.518970	−	0.854793i	$-0.673684\pi$
$53$	0.116754	−	1.62671i	0.116754	−	1.62671i	0.635724	−	0.771917i	$-0.280702\pi$
$54$		0			0
$55$		0			0
$56$	0.386859	+	0.637194i	0.386859	+	0.637194i
$57$		0			0
$58$	0.289831	−	0.136775i	0.289831	−	0.136775i
$59$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$59$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$60$		0			0
$61$		0			0		−0.471093	−	0.882084i	$-0.656140\pi$
$61$		0			0		0.471093	+	0.882084i	$0.343860\pi$
$62$		0			0
$63$	0.761300	+	0.648400i	0.761300	+	0.648400i
$64$	−0.288067	−	0.312924i	−0.288067	−	0.312924i
$65$		0			0
$66$		0			0
$67$	1.66694	−	0.809235i	1.66694	−	0.809235i	0.669131	−	0.743145i	$-0.266667\pi$
$67$	1.66694	−	0.809235i	1.66694	−	0.809235i	0.997814	−	0.0660906i	$-0.0210526\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.211001	+	0.0939437i	0.211001	+	0.0939437i	0.509516	−	0.860461i	$-0.329825\pi$
$71$	0.211001	+	0.0939437i	0.211001	+	0.0939437i	−0.298515	+	0.954405i	$0.596491\pi$
$72$	−0.651641	−	0.361994i	−0.651641	−	0.361994i
$73$		0			0		0.360939	−	0.932589i	$-0.382456\pi$
$73$		0			0		−0.360939	+	0.932589i	$0.617544\pi$
$74$	1.03851	−	0.622704i	1.03851	−	0.622704i
$75$		0			0
$76$		0			0
$77$	−1.12224	+	1.63770i	−1.12224	+	1.63770i
$78$		0			0
$79$	1.17865	−	1.49723i	1.17865	−	1.49723i	0.350638	−	0.936511i	$-0.385965\pi$
$79$	1.17865	−	1.49723i	1.17865	−	1.49723i	0.828009	−	0.560715i	$-0.189474\pi$
$80$		0			0
$81$	−0.982493	−	0.186298i	−0.982493	−	0.186298i
$82$		0			0
$83$		0			0		0.997024	−	0.0770854i	$-0.0245614\pi$
$83$		0			0		−0.997024	+	0.0770854i	$0.975439\pi$
$84$		0			0
$85$		0			0
$86$	1.10303	+	0.550583i	1.10303	+	0.550583i
$87$		0			0
$88$	0.579505	−	1.36175i	0.579505	−	1.36175i
$89$		0			0		−0.565270	−	0.824906i	$-0.691228\pi$
$89$		0			0		0.565270	+	0.824906i	$0.308772\pi$
$90$		0			0
$91$		0			0
$92$	0.330210	−	0.0816865i	0.330210	−	0.0816865i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.441671	−	0.897177i	$-0.645614\pi$
$97$		0			0		0.441671	+	0.897177i	$0.354386\pi$
$98$	0.780631	+	0.866979i	0.780631	+	0.866979i
$99$	0.163946	−	1.97853i	0.163946	−	1.97853i
$100$	−0.173582	−	0.316570i	−0.173582	−	0.316570i
$101$		0			0		0.884667	−	0.466224i	$-0.154386\pi$
$101$		0			0		−0.884667	+	0.466224i	$0.845614\pi$
$102$		0			0
$103$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$103$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$104$		0			0
$105$		0			0
$106$	0.587954	+	1.80953i	0.587954	+	1.80953i
$107$	0.0331248	+	1.20171i	0.0331248	+	1.20171i	0.815447	+	0.578832i	$0.196491\pi$
$107$	0.0331248	+	1.20171i	0.0331248	+	1.20171i	−0.782322	+	0.622874i	$0.785965\pi$
$108$		0			0
$109$	0.999453	+	1.73110i	0.999453	+	1.73110i	0.528360	+	0.849020i	$0.322807\pi$
$109$	0.999453	+	1.73110i	0.999453	+	1.73110i	0.471093	+	0.882084i	$0.343860\pi$
$110$		0			0
$111$		0			0
$112$	−0.987614	−	0.734312i	−0.987614	−	0.734312i
$113$	−1.70692	+	0.875652i	−1.70692	+	0.875652i	−0.724425	+	0.689353i	$0.757895\pi$
$113$	−1.70692	+	0.875652i	−1.70692	+	0.875652i	−0.982493	+	0.186298i	$0.940351\pi$
$114$		0			0
$115$		0			0
$116$	−0.0671724	+	0.0729686i	−0.0671724	+	0.0729686i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	2.94076	−	0.0648433i	2.94076	−	0.0648433i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−1.10753	−	0.366620i	−1.10753	−	0.366620i
$127$	0.131215	+	1.39632i	0.131215	+	1.39632i	0.775409	+	0.631460i	$0.217544\pi$
$127$	0.131215	+	1.39632i	0.131215	+	1.39632i	−0.644194	+	0.764862i	$0.722807\pi$
$128$	1.07305	+	0.506383i	1.07305	+	0.506383i
$129$		0			0
$130$		0			0
$131$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$131$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$132$		0			0
$133$		0			0
$134$	−1.44650	+	1.60650i	−1.44650	+	1.60650i
$135$		0			0
$136$		0			0
$137$	0.119554	+	0.431869i	0.119554	+	0.431869i	0.999028	−	0.0440782i	$-0.0140351\pi$
$137$	0.119554	+	0.431869i	0.119554	+	0.431869i	−0.879474	+	0.475947i	$0.842105\pi$
$138$		0			0
$139$		0			0		0.815447	−	0.578832i	$-0.196491\pi$
$139$		0			0		−0.815447	+	0.578832i	$0.803509\pi$
$140$		0			0
$141$		0			0
$142$	−0.269309	−	0.00890915i	−0.269309	−	0.00890915i
$143$		0			0
$144$	1.22165	+	0.148861i	1.22165	+	0.148861i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−0.225246	+	0.299483i	−0.225246	+	0.299483i
$149$	1.47085	−	0.860039i	1.47085	−	0.860039i	0.471093	−	0.882084i	$-0.343860\pi$
$149$	1.47085	−	0.860039i	1.47085	−	0.860039i	0.999757	+	0.0220445i	$0.00701754\pi$
$150$		0			0
$151$	1.33794	+	0.0295013i	1.33794	+	0.0295013i	0.685350	−	0.728214i	$-0.259649\pi$
$151$	1.33794	+	0.0295013i	1.33794	+	0.0295013i	0.652586	+	0.757715i	$0.273684\pi$
$152$		0			0
$153$		0			0
$154$	0.494031	−	2.26284i	0.494031	−	2.26284i
$155$		0			0
$156$		0			0
$157$		0			0		0.234785	−	0.972047i	$-0.424561\pi$
$157$		0			0		−0.234785	+	0.972047i	$0.575439\pi$
$158$	−0.616670	+	2.13577i	−0.616670	+	2.13577i
$159$		0			0
$160$		0			0
$161$	−0.856453	+	0.392686i	−0.856453	+	0.392686i
$162$	1.14375	−	0.229964i	1.14375	−	0.229964i
$163$	−1.12612	−	1.60513i	−1.12612	−	1.60513i	−0.724425	−	0.689353i	$-0.757895\pi$
$163$	−1.12612	−	1.60513i	−1.12612	−	1.60513i	−0.401695	−	0.915773i	$-0.631579\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$167$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$168$		0			0
$169$	0.00551154	+	0.999985i	0.00551154	+	0.999985i
$170$		0			0
$171$		0			0
$172$	−0.380380	−	0.0294092i	−0.380380	−	0.0294092i
$173$		0			0		−0.731980	−	0.681326i	$-0.761404\pi$
$173$		0			0		0.731980	+	0.681326i	$0.238596\pi$
$174$		0			0
$175$	0.635724	+	0.771917i	0.635724	+	0.771917i
$176$	−0.0403975	+	2.44297i	−0.0403975	+	2.44297i
$177$		0			0
$178$		0			0
$179$	1.67666	+	0.111054i	1.67666	+	0.111054i	0.874174	−	0.485613i	$-0.161404\pi$
$179$	1.67666	+	0.111054i	1.67666	+	0.111054i	0.802489	+	0.596667i	$0.203509\pi$
$180$		0			0
$181$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$181$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$182$		0			0
$183$		0			0
$184$	0.568205	−	0.412825i	0.568205	−	0.412825i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.81686	−	0.668854i	−1.81686	−	0.668854i	−0.995083	−	0.0990455i	$-0.968421\pi$
$191$	−1.81686	−	0.668854i	−1.81686	−	0.668854i	−0.821778	−	0.569808i	$-0.807018\pi$
$192$		0			0
$193$	1.03280	−	0.459832i	1.03280	−	0.459832i	0.180881	−	0.983505i	$-0.442105\pi$
$193$	1.03280	−	0.459832i	1.03280	−	0.459832i	0.851919	+	0.523673i	$0.175439\pi$
$194$		0			0
$195$		0			0
$196$	−0.324788	−	0.157672i	−0.324788	−	0.157672i
$197$	−1.39511	+	1.13612i	−1.39511	+	1.13612i	−0.421786	+	0.906696i	$0.638596\pi$
$197$	−1.39511	+	1.13612i	−1.39511	+	1.13612i	−0.973327	+	0.229424i	$0.926316\pi$
$198$	0.691401	+	2.21053i	0.691401	+	2.21053i
$199$		0			0		−0.421786	−	0.906696i	$-0.638596\pi$
$199$		0			0		0.421786	+	0.906696i	$0.361404\pi$
$200$	−0.578018	−	0.470713i	−0.578018	−	0.470713i
$201$		0			0
$202$		0			0
$203$	0.145144	−	0.233232i	0.145144	−	0.233232i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.549593	−	0.765285i	0.549593	−	0.765285i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.0763521	−	0.0110168i	0.0763521	−	0.0110168i	−0.104528	−	0.994522i	$-0.533333\pi$
$211$	0.0763521	−	0.0110168i	0.0763521	−	0.0110168i	0.180881	+	0.983505i	$0.442105\pi$
$212$	−0.379309	−	0.450361i	−0.379309	−	0.450361i
$213$		0			0
$214$	−0.563372	−	1.28436i	−0.563372	−	1.28436i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−1.84027	−	1.43234i	−1.84027	−	1.43234i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.00551154	−	0.999985i	$-0.498246\pi$
$223$		0			0		−0.00551154	+	0.999985i	$0.501754\pi$
$224$	0.668260	+	0.173151i	0.668260	+	0.173151i
$225$	−0.934564	−	0.355794i	−0.934564	−	0.355794i
$226$	1.46055	−	1.69584i	1.46055	−	1.69584i
$227$		0			0		0.952745	−	0.303771i	$-0.0982456\pi$
$227$		0			0		−0.952745	+	0.303771i	$0.901754\pi$
$228$		0			0
$229$		0			0		0.996114	−	0.0880708i	$-0.0280702\pi$
$229$		0			0		−0.996114	+	0.0880708i	$0.971930\pi$
$230$		0			0
$231$		0			0
$232$	−0.0718024	+	0.191776i	−0.0718024	+	0.191776i
$233$	0.113098	+	0.274112i	0.113098	+	0.274112i	0.970739	−	0.240139i	$-0.0771930\pi$
$233$	0.113098	+	0.274112i	0.113098	+	0.274112i	−0.857640	+	0.514250i	$0.828070\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.596835	+	0.677729i	−0.596835	+	0.677729i	−0.968033	−	0.250825i	$-0.919298\pi$
$239$	−0.596835	+	0.677729i	−0.596835	+	0.677729i	0.371197	+	0.928554i	$0.378947\pi$
$240$		0			0
$241$		0			0		−0.213300	−	0.976987i	$-0.568421\pi$
$241$		0			0		0.213300	+	0.976987i	$0.431579\pi$
$242$	−3.15014	+	1.36113i	−3.15014	+	1.36113i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		−0.984487	−	0.175457i	$-0.943860\pi$
$251$		0			0		0.984487	+	0.175457i	$0.0561404\pi$
$252$	0.360247	−	0.0238611i	0.360247	−	0.0238611i
$253$	1.62506	+	0.926325i	1.62506	+	0.926325i
$254$	−0.754835	−	1.45165i	−0.754835	−	1.45165i
$255$		0			0
$256$	−0.957464	−	0.0528248i	−0.957464	−	0.0528248i
$257$		0			0		−0.148264	−	0.988948i	$-0.547368\pi$
$257$		0			0		0.148264	+	0.988948i	$0.452632\pi$
$258$		0			0
$259$	0.458427	−	0.931215i	0.458427	−	0.931215i
$260$		0			0
$261$	−0.0105958	+	0.274503i	−0.0105958	+	0.274503i
$262$		0			0
$263$	−0.0168613	−	0.0977235i	−0.0168613	−	0.0977235i	0.975796	−	0.218681i	$-0.0701754\pi$
$263$	−0.0168613	−	0.0977235i	−0.0168613	−	0.0977235i	−0.992658	+	0.120958i	$0.961404\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	0.227655	−	0.629071i	0.227655	−	0.629071i
$269$		0			0		0.934564	−	0.355794i	$-0.115789\pi$
$269$		0			0		−0.934564	+	0.355794i	$0.884211\pi$
$270$		0			0
$271$		0			0		−0.945817	−	0.324699i	$-0.894737\pi$
$271$		0			0		0.945817	+	0.324699i	$0.105263\pi$
$272$		0			0
$273$		0			0
$274$	−0.318821	−	0.414313i	−0.318821	−	0.414313i
$275$	0.508551	−	1.91908i	0.508551	−	1.91908i
$276$		0			0
$277$	0.424502	+	0.0422528i	0.424502	+	0.0422528i	0.309017	−	0.951057i	$-0.400000\pi$
$277$	0.424502	+	0.0422528i	0.424502	+	0.0422528i	0.115485	+	0.993309i	$0.463158\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.913225	−	1.75626i	0.913225	−	1.75626i	0.329907	−	0.944013i	$-0.392982\pi$
$281$	0.913225	−	1.75626i	0.913225	−	1.75626i	0.583317	−	0.812244i	$-0.301754\pi$
$282$		0			0
$283$		0			0		0.965209	−	0.261480i	$-0.0842105\pi$
$283$		0			0		−0.965209	+	0.261480i	$0.915789\pi$
$284$	0.0782541	−	0.0288082i	0.0782541	−	0.0288082i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.666311	+	0.180507i	−0.666311	+	0.180507i
$289$	0.840168	−	0.542326i	0.840168	−	0.542326i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.537687	−	0.843145i	$-0.319298\pi$
$293$		0			0		−0.537687	+	0.843145i	$0.680702\pi$
$294$		0			0
$295$		0			0
$296$	−0.198193	+	0.747903i	−0.198193	+	0.747903i
$297$		0			0
$298$	−1.21224	+	1.57533i	−1.21224	+	1.57533i
$299$		0			0
$300$		0			0
$301$	1.05031	−	0.116248i	1.05031	−	0.116248i
$302$	−1.45910	+	0.555487i	−1.45910	+	0.555487i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.329907	−	0.944013i	$-0.607018\pi$
$307$		0			0		0.329907	+	0.944013i	$0.392982\pi$
$308$	0.121872	+	0.706335i	0.121872	+	0.706335i
$309$		0			0
$310$		0			0
$311$		0			0		0.802489	−	0.596667i	$-0.203509\pi$
$311$		0			0		−0.802489	+	0.596667i	$0.796491\pi$
$312$		0			0
$313$		0			0		0.962268	−	0.272103i	$-0.0877193\pi$
$313$		0			0		−0.962268	+	0.272103i	$0.912281\pi$
$314$		0			0
$315$		0			0
$316$	−0.0719106	−	0.684183i	−0.0719106	−	0.684183i
$317$	0.639729	+	1.23029i	0.639729	+	1.23029i	0.959210	+	0.282694i	$0.0912281\pi$
$317$	0.639729	+	1.23029i	0.639729	+	1.23029i	−0.319482	+	0.947592i	$0.603509\pi$
$318$		0			0
$319$	−0.544188	+	0.0360445i	−0.544188	+	0.0360445i
$320$		0			0
$321$		0			0
$322$	0.753328	−	0.800443i	0.753328	−	0.800443i
$323$		0			0
$324$	−0.301155	+	0.199131i	−0.301155	+	0.199131i
$325$		0			0
$326$	1.92188	+	1.24057i	1.92188	+	1.24057i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.46100	−	0.310546i	−1.46100	−	0.310546i	−0.592235	−	0.805765i	$-0.701754\pi$
$331$	−1.46100	−	0.310546i	−1.46100	−	0.310546i	−0.868768	+	0.495219i	$0.835088\pi$
$332$		0			0
$333$	0.0628888	+	1.03603i	0.0628888	+	1.03603i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.717286	−	1.34306i	0.717286	−	1.34306i	−0.213300	−	0.976987i	$-0.568421\pi$
$337$	0.717286	−	1.34306i	0.717286	−	1.34306i	0.930586	−	0.366074i	$-0.119298\pi$
$338$	−0.444966	−	1.07844i	−0.444966	−	1.07844i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.965209	+	0.261480i	0.965209	+	0.261480i
$344$	−0.750495	+	0.239286i	−0.750495	+	0.239286i
$345$		0			0
$346$		0			0
$347$	0.777708	+	0.201510i	0.777708	+	0.201510i	0.618553	−	0.785743i	$-0.287719\pi$
$347$	0.777708	+	0.201510i	0.777708	+	0.201510i	0.159156	+	0.987253i	$0.449123\pi$
$348$		0			0
$349$		0			0		0.287976	−	0.957638i	$-0.407018\pi$
$349$		0			0		−0.287976	+	0.957638i	$0.592982\pi$
$350$	−1.02602	−	0.555257i	−1.02602	−	0.555257i
$351$		0			0
$352$	−0.494674	−	1.27813i	−0.494674	−	1.27813i
$353$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$353$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.86103	+	0.616045i	−1.86103	+	0.616045i
$359$	0.357403	+	0.424350i	0.357403	+	0.424350i	0.913545	−	0.406737i	$-0.133333\pi$
$359$	0.357403	+	0.424350i	0.357403	+	0.424350i	−0.556143	+	0.831087i	$0.687719\pi$
$360$		0			0
$361$	−0.917973	−	0.396642i	−0.917973	−	0.396642i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.224056	−	0.974576i	$-0.571930\pi$
$367$		0			0		0.224056	+	0.974576i	$0.428070\pi$
$368$	−0.612654	+	0.984471i	−0.612654	+	0.984471i
$369$		0			0
$370$		0			0
$371$	1.26461	+	1.02984i	1.26461	+	1.02984i
$372$		0			0
$373$	0.594094	+	1.89942i	0.594094	+	1.89942i	0.391577	+	0.920146i	$0.371930\pi$
$373$	0.594094	+	1.89942i	0.594094	+	1.89942i	0.202517	+	0.979279i	$0.435088\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.45827	+	0.128932i	1.45827	+	0.128932i	0.789141	−	0.614213i	$-0.210526\pi$
$379$	1.45827	+	0.128932i	1.45827	+	0.128932i	0.669131	+	0.743145i	$0.266667\pi$
$380$		0			0
$381$		0			0
$382$	2.25745	−	0.0746796i	2.25745	−	0.0746796i
$383$		0			0		0.975796	−	0.218681i	$-0.0701754\pi$
$383$		0			0		−0.975796	+	0.218681i	$0.929825\pi$
$384$		0			0
$385$		0			0
$386$	−0.914460	+	0.950439i	−0.914460	+	0.950439i
$387$	−0.854905	+	0.621125i	−0.854905	+	0.621125i
$388$		0			0
$389$	0.909869	−	0.573208i	0.909869	−	0.573208i	0.00551154	−	0.999985i	$-0.498246\pi$
$389$	0.909869	−	0.573208i	0.909869	−	0.573208i	0.904357	+	0.426776i	$0.140351\pi$
$390$		0			0
$391$		0			0
$392$	−0.743807	−	0.0492664i	−0.743807	−	0.0492664i
$393$		0			0
$394$	1.00917	−	1.84049i	1.00917	−	1.84049i
$395$		0			0
$396$	−0.455669	−	0.553288i	−0.455669	−	0.553288i
$397$		0			0		0.381410	−	0.924406i	$-0.375439\pi$
$397$		0			0		−0.381410	+	0.924406i	$0.624561\pi$
$398$		0			0
$399$		0			0
$400$	1.17658	+	0.360900i	1.17658	+	0.360900i
$401$	−0.472446	+	1.86565i	−0.472446	+	1.86565i	0.0275543	+	0.999620i	$0.491228\pi$
$401$	−0.472446	+	1.86565i	−0.472446	+	1.86565i	−0.500000	+	0.866025i	$0.666667\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−0.0544912	+	0.315816i	−0.0544912	+	0.315816i
$407$	−2.03253	+	0.339170i	−2.03253	+	0.339170i
$408$		0			0
$409$		0			0		0.980380	−	0.197117i	$-0.0631579\pi$
$409$		0			0		−0.980380	+	0.197117i	$0.936842\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−0.258073	+	1.06846i	−0.258073	+	1.06846i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.815447	−	0.578832i	$-0.803509\pi$
$419$		0			0		0.815447	+	0.578832i	$0.196491\pi$
$420$		0			0
$421$	−1.16948	−	1.01850i	−1.16948	−	1.01850i	−0.999453	−	0.0330634i	$-0.989474\pi$
$421$	−1.16948	−	1.01850i	−1.16948	−	1.01850i	−0.170028	−	0.985439i	$-0.554386\pi$
$422$	−0.0776909	+	0.0454276i	−0.0776909	+	0.0454276i
$423$		0			0
$424$	−1.07551	−	0.566802i	−1.07551	−	0.566802i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.311101	+	0.302644i	0.311101	+	0.302644i
$429$		0			0
$430$		0			0
$431$	1.25871	+	1.19778i	1.25871	+	1.19778i	0.970739	+	0.240139i	$0.0771930\pi$
$431$	1.25871	+	1.19778i	1.25871	+	1.19778i	0.287976	+	0.957638i	$0.407018\pi$
$432$		0			0
$433$		0			0		0.828009	−	0.560715i	$-0.189474\pi$
$433$		0			0		−0.828009	+	0.560715i	$0.810526\pi$
$434$		0			0
$435$		0			0
$436$	0.694448	+	0.196371i	0.694448	+	0.196371i
$437$		0			0
$438$		0			0
$439$		0			0		0.0495838	−	0.998770i	$-0.484211\pi$
$439$		0			0		−0.0495838	+	0.998770i	$0.515789\pi$
$440$		0			0
$441$	−0.968033	+	0.250825i	−0.968033	+	0.250825i
$442$		0			0
$443$	−0.346750	−	0.163635i	−0.346750	−	0.163635i	0.245485	−	0.969400i	$-0.421053\pi$
$443$	−0.346750	−	0.163635i	−0.346750	−	0.163635i	−0.592235	+	0.805765i	$0.701754\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.421613	−	0.0560975i	0.421613	−	0.0560975i
$449$	1.44795	+	1.20593i	1.44795	+	1.20593i	0.938430	+	0.345471i	$0.112281\pi$
$449$	1.44795	+	1.20593i	1.44795	+	1.20593i	0.509516	+	0.860461i	$0.329825\pi$
$450$	1.16635	−	0.0257179i	1.16635	−	0.0257179i
$451$		0			0
$452$	−0.221279	+	0.656322i	−0.221279	+	0.656322i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.03874	−	0.790251i	−1.03874	−	0.790251i	−0.0605901	−	0.998163i	$-0.519298\pi$
$457$	−1.03874	−	0.790251i	−1.03874	−	0.790251i	−0.978148	+	0.207912i	$0.933333\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$461$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$462$		0			0
$463$	1.78722	+	0.278021i	1.78722	+	0.278021i	0.959210	−	0.282694i	$-0.0912281\pi$
$463$	1.78722	+	0.278021i	1.78722	+	0.278021i	0.828009	+	0.560715i	$0.189474\pi$
$464$	−0.00931555	−	0.337951i	−0.00931555	−	0.337951i
$465$		0			0
$466$	−0.242585	−	0.246630i	−0.242585	−	0.246630i
$467$		0			0		0.930586	−	0.366074i	$-0.119298\pi$
$467$		0			0		−0.930586	+	0.366074i	$0.880702\pi$
$468$		0			0
$469$	−0.294914	+	1.82937i	−0.294914	+	1.82937i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.40379	−	1.55906i	−1.40379	−	1.55906i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.60865	−	0.268436i	−1.60865	−	0.268436i
$478$	0.347574	−	0.994564i	0.347574	−	0.994564i
$479$		0			0		0.970739	−	0.240139i	$-0.0771930\pi$
$479$		0			0		−0.970739	+	0.240139i	$0.922807\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.744700	−	0.757117i	0.744700	−	0.757117i
$485$		0			0
$486$		0			0
$487$	−1.35069	−	1.07540i	−1.35069	−	1.07540i	−0.989750	−	0.142811i	$-0.954386\pi$
$487$	−1.35069	−	1.07540i	−1.35069	−	1.07540i	−0.360939	−	0.932589i	$-0.617544\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.13552	−	1.58116i	−1.13552	−	1.58116i	−0.754107	−	0.656752i	$-0.771930\pi$
$491$	−1.13552	−	1.58116i	−1.13552	−	1.58116i	−0.381410	−	0.924406i	$-0.624561\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.198088	+	0.118776i	−0.198088	+	0.118776i
$498$		0			0
$499$	−1.49945	−	0.832962i	−1.49945	−	0.832962i	−0.500000	−	0.866025i	$-0.666667\pi$
$499$	−1.49945	−	0.832962i	−1.49945	−	0.832962i	−0.999453	+	0.0330634i	$0.989474\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.490424	−	0.871484i	$-0.336842\pi$
$503$		0			0		−0.490424	+	0.871484i	$0.663158\pi$
$504$	0.670593	−	0.325547i	0.670593	−	0.325547i
$505$		0			0
$506$	−2.16317	−	0.287819i	−2.16317	−	0.287819i
$507$		0			0
$508$	0.385480	+	0.328314i	0.385480	+	0.328314i
$509$		0			0		0.635724	−	0.771917i	$-0.280702\pi$
$509$		0			0		−0.635724	+	0.771917i	$0.719298\pi$
$510$		0			0
$511$		0			0
$512$	−0.0641469	+	0.0220217i	−0.0641469	+	0.0220217i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−0.0866869	+	1.20779i	−0.0866869	+	1.20779i
$519$		0			0
$520$		0			0
$521$		0			0		−0.115485	−	0.993309i	$-0.536842\pi$
$521$		0			0		0.115485	+	0.993309i	$0.463158\pi$
$522$	−0.109058	−	0.301356i	−0.109058	−	0.301356i
$523$		0			0		−0.652586	−	0.757715i	$-0.726316\pi$
$523$		0			0		0.652586	+	0.757715i	$0.273684\pi$
$524$		0			0
$525$		0			0
$526$	0.0611272	+	0.0982251i	0.0611272	+	0.0982251i
$527$		0			0
$528$		0			0
$529$	−0.0550676	−	0.0978554i	−0.0550676	−	0.0978554i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−0.0532781	−	1.38026i	−0.0532781	−	1.38026i
$537$		0			0
$538$		0			0
$539$	−0.696126	−	1.85927i	−0.696126	−	1.85927i
$540$		0			0
$541$	0.142020	+	0.686744i	0.142020	+	0.686744i	0.988116	+	0.153712i	$0.0491228\pi$
$541$	0.142020	+	0.686744i	0.142020	+	0.686744i	−0.846095	+	0.533032i	$0.821053\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.197451	−	0.585644i	−0.197451	−	0.585644i	0.802489	−	0.596667i	$-0.203509\pi$
$547$	−0.197451	−	0.585644i	−0.197451	−	0.585644i	−0.999939	+	0.0110229i	$0.996491\pi$
$548$	0.139662	+	0.0816634i	0.139662	+	0.0816634i
$549$		0			0
$550$	0.292822	+	2.29755i	0.292822	+	2.29755i
$551$		0			0
$552$		0			0
$553$	0.548736	+	1.82477i	0.548736	+	1.82477i
$554$	−0.477385	+	0.140693i	−0.477385	+	0.140693i
$555$		0			0
$556$		0			0
$557$	−0.288671	+	1.25563i	−0.288671	+	1.25563i	0.601081	+	0.799188i	$0.294737\pi$
$557$	−0.288671	+	1.25563i	−0.288671	+	1.25563i	−0.889752	+	0.456444i	$0.849123\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.216062	+	2.29922i	−0.216062	+	2.29922i
$563$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$563$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.716783	−	0.697297i	0.716783	−	0.697297i
$568$	0.127313	−	0.115910i	0.127313	−	0.115910i
$569$	−1.85119	+	0.751887i	−1.85119	+	0.751887i	−0.909007	+	0.416782i	$0.863158\pi$
$569$	−1.85119	+	0.751887i	−1.85119	+	0.751887i	−0.942181	+	0.335105i	$0.891228\pi$
$570$		0			0
$571$	0.0275543	−	0.999620i	0.0275543	−	0.999620i
$571$	0.0275543	−	0.999620i	0.0275543	−	0.999620i
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.675342	−	0.656983i	0.675342	−	0.656983i
$576$	−0.338503	+	0.257526i	−0.338503	+	0.257526i
$577$		0			0		0.431754	−	0.901991i	$-0.357895\pi$
$577$		0			0		−0.431754	+	0.901991i	$0.642105\pi$
$578$	−0.670032	+	0.955036i	−0.670032	+	0.955036i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.196181	−	3.23189i	0.196181	−	3.23189i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.0275543	−	0.999620i	$-0.491228\pi$
$587$		0			0		−0.0275543	+	0.999620i	$0.508772\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.161495	−	1.26713i	−0.161495	−	1.26713i
$593$		0			0		0.922290	−	0.386499i	$-0.126316\pi$
$593$		0			0		−0.922290	+	0.386499i	$0.873684\pi$
$594$		0			0
$595$		0			0
$596$	0.164119	−	0.592851i	0.164119	−	0.592851i
$597$		0			0
$598$		0			0
$599$	0.162185	+	1.00604i	0.162185	+	1.00604i	0.930586	+	0.366074i	$0.119298\pi$
$599$	0.162185	+	1.00604i	0.162185	+	1.00604i	−0.768401	+	0.639969i	$0.778947\pi$
$600$		0			0
$601$		0			0		−0.202517	−	0.979279i	$-0.564912\pi$
$601$		0			0		0.202517	+	0.979279i	$0.435088\pi$
$602$	−1.08422	+	0.586751i	−1.08422	+	0.586751i
$603$	−0.649727	−	1.73534i	−0.649727	−	1.73534i
$604$	0.353664	−	0.329191i	0.353664	−	0.329191i
$605$		0			0
$606$		0			0
$607$		0			0		−0.627176	−	0.778877i	$-0.715789\pi$
$607$		0			0		0.627176	+	0.778877i	$0.284211\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.829890	−	1.47472i	−0.829890	−	1.47472i	−0.879474	−	0.475947i	$-0.842105\pi$
$613$	−0.829890	−	1.47472i	−0.829890	−	1.47472i	0.0495838	−	0.998770i	$-0.484211\pi$
$614$		0			0
$615$		0			0
$616$	0.781935	+	1.25649i	0.781935	+	1.25649i
$617$	−0.528122	−	0.0762026i	−0.528122	−	0.0762026i	−0.126427	−	0.991976i	$-0.540351\pi$
$617$	−0.528122	−	0.0762026i	−0.528122	−	0.0762026i	−0.401695	+	0.915773i	$0.631579\pi$
$618$		0			0
$619$		0			0		−0.652586	−	0.757715i	$-0.726316\pi$
$619$		0			0		0.652586	+	0.757715i	$0.273684\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.857640	−	0.514250i	−0.857640	−	0.514250i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−1.10796	−	1.65571i	−1.10796	−	1.65571i	−0.627176	−	0.778877i	$-0.715789\pi$
$631$	−1.10796	−	1.65571i	−1.10796	−	1.65571i	−0.480787	−	0.876837i	$-0.659649\pi$
$632$	−0.669151	−	1.25293i	−0.669151	−	1.25293i
$633$		0			0
$634$	−1.23158	−	1.04894i	−1.23158	−	1.04894i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	0.572378	−	0.277867i	0.572378	−	0.277867i
$639$	0.113273	−	0.201286i	0.113273	−	0.201286i
$640$		0			0
$641$	−0.487724	−	1.07940i	−0.487724	−	1.07940i	−0.978148	−	0.207912i	$-0.933333\pi$
$641$	−0.487724	−	1.07940i	−0.487724	−	1.07940i	0.490424	−	0.871484i	$-0.336842\pi$
$642$		0			0
$643$		0			0		−0.874174	−	0.485613i	$-0.838596\pi$
$643$		0			0		0.874174	+	0.485613i	$0.161404\pi$
$644$	−0.122778	+	0.317233i	−0.122778	+	0.317233i
$645$		0			0
$646$		0			0
$647$		0			0		−0.537687	−	0.843145i	$-0.680702\pi$
$647$		0			0		0.537687	+	0.843145i	$0.319298\pi$
$648$	−0.421373	+	0.614915i	−0.421373	+	0.614915i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.695513	−	0.131882i	−0.695513	−	0.131882i
$653$	−1.62790	−	0.364821i	−1.62790	−	0.364821i	−0.693336	−	0.720615i	$-0.743860\pi$
$653$	−1.62790	−	0.364821i	−1.62790	−	0.364821i	−0.934564	+	0.355794i	$0.884211\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.671663	+	1.57831i	−0.671663	+	1.57831i	0.137354	+	0.990522i	$0.456140\pi$
$659$	−0.671663	+	1.57831i	−0.671663	+	1.57831i	−0.809017	+	0.587785i	$0.800000\pi$
$660$		0			0
$661$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$661$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$662$	1.71550	−	0.305740i	1.71550	−	0.305740i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.522810	−	1.09222i	−0.522810	−	1.09222i
$667$	−0.230290	−	0.118139i	−0.230290	−	0.118139i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.0950207	+	0.589420i	−0.0950207	+	0.589420i	0.894729	+	0.446609i	$0.147368\pi$
$673$	−0.0950207	+	0.589420i	−0.0950207	+	0.589420i	−0.989750	+	0.142811i	$0.954386\pi$
$674$	−0.185676	+	1.76659i	−0.185676	+	1.76659i
$675$		0			0
$676$	0.253172	+	0.257393i	0.253172	+	0.257393i
$677$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$677$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.59524	+	1.18609i	1.59524	+	1.18609i	0.863256	+	0.504766i	$0.168421\pi$
$683$	1.59524	+	1.18609i	1.59524	+	1.18609i	0.731980	+	0.681326i	$0.238596\pi$
$684$		0			0
$685$		0			0
$686$	−1.15807	+	0.141113i	−1.15807	+	0.141113i
$687$		0			0
$688$	0.999302	−	0.832276i	0.999302	−	0.832276i
$689$		0			0
$690$		0			0
$691$		0			0		−0.828009	−	0.560715i	$-0.810526\pi$
$691$		0			0		0.828009	+	0.560715i	$0.189474\pi$
$692$		0			0
$693$	1.52552	+	1.27054i	1.52552	+	1.27054i
$694$	−0.929076	+	0.123618i	−0.929076	+	0.123618i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.358845	+	0.0397170i	0.358845	+	0.0397170i
$701$	−1.93418	+	0.501162i	−1.93418	+	0.501162i	−0.956036	+	0.293250i	$0.905263\pi$
$701$	−1.93418	+	0.501162i	−1.93418	+	0.501162i	−0.978148	+	0.207912i	$0.933333\pi$
$702$		0			0
$703$		0			0
$704$	−0.578717	−	0.614912i	−0.578717	−	0.614912i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.100338	+	0.0679476i	−0.100338	+	0.0679476i	−0.609854	−	0.792514i	$-0.708772\pi$
$709$	−0.100338	+	0.0679476i	−0.100338	+	0.0679476i	0.509516	+	0.860461i	$0.329825\pi$
$710$		0			0
$711$	−1.38039	−	1.31356i	−1.38039	−	1.31356i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.461853	−	0.393360i	0.461853	−	0.393360i
$717$		0			0
$718$	−0.572606	−	0.301766i	−0.572606	−	0.301766i
$719$		0			0		0.601081	−	0.799188i	$-0.294737\pi$
$719$		0			0		−0.601081	+	0.799188i	$0.705263\pi$
$720$		0			0
$721$		0			0
$722$	1.16635	+	0.0257179i	1.16635	+	0.0257179i
$723$		0			0
$724$		0			0
$725$	−0.0585949	+	0.268385i	−0.0585949	+	0.268385i
$726$		0			0
$727$		0			0		0.746821	−	0.665025i	$-0.231579\pi$
$727$		0			0		−0.746821	+	0.665025i	$0.768421\pi$
$728$		0			0
$729$	−0.277403	+	0.960754i	−0.277403	+	0.960754i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.980380	−	0.197117i	$-0.0631579\pi$
$733$		0			0		−0.980380	+	0.197117i	$0.936842\pi$
$734$		0			0
$735$		0			0
$736$	0.110589	−	0.640947i	0.110589	−	0.640947i
$737$	3.29150	−	1.64297i	3.29150	−	1.64297i
$738$		0			0
$739$	−1.91551	−	0.564529i	−1.91551	−	0.564529i	−0.973327	−	0.229424i	$-0.926316\pi$
$739$	−1.91551	−	0.564529i	−1.91551	−	0.564529i	−0.942181	−	0.335105i	$-0.891228\pi$
$740$		0			0
$741$		0			0
$742$	−1.81901	−	0.557954i	−1.81901	−	0.557954i
$743$	−0.740185	−	0.0572278i	−0.740185	−	0.0572278i	−0.298515	−	0.954405i	$-0.596491\pi$
$743$	−0.740185	−	0.0572278i	−0.740185	−	0.0572278i	−0.441671	+	0.897177i	$0.645614\pi$
$744$		0			0
$745$		0			0
$746$	−1.47602	−	1.79223i	−1.47602	−	1.79223i
$747$		0			0
$748$		0			0
$749$	−1.00277	−	0.663057i	−1.00277	−	0.663057i
$750$		0			0
$751$	1.06189	+	0.262687i	1.06189	+	0.262687i	0.731980	−	0.681326i	$-0.238596\pi$
$751$	1.06189	+	0.262687i	1.06189	+	0.262687i	0.329907	+	0.944013i	$0.392982\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.0957174	+	1.92804i	0.0957174	+	1.92804i	0.309017	+	0.951057i	$0.400000\pi$
$757$	0.0957174	+	1.92804i	0.0957174	+	1.92804i	−0.213300	+	0.976987i	$0.568421\pi$
$758$	−1.63282	+	0.500844i	−1.63282	+	0.500844i
$759$		0			0
$760$		0			0
$761$		0			0		−0.739446	−	0.673216i	$-0.764912\pi$
$761$		0			0		0.739446	+	0.673216i	$0.235088\pi$
$762$		0			0
$763$	−1.99114	−	0.176045i	−1.99114	−	0.176045i
$764$	−0.638560	+	0.284305i	−0.638560	+	0.284305i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		−0.298515	−	0.954405i	$-0.596491\pi$
$769$		0			0		0.298515	+	0.954405i	$0.403509\pi$
$770$		0			0
$771$		0			0
$772$	0.151510	−	0.379005i	0.151510	−	0.379005i
$773$		0			0		0.644194	−	0.764862i	$-0.277193\pi$
$773$		0			0		−0.644194	+	0.764862i	$0.722807\pi$
$774$	0.651366	−	1.04668i	0.651366	−	1.04668i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.731812	+	1.01902i	−0.731812	+	1.01902i
$779$		0			0
$780$		0			0
$781$	0.420934	+	0.181879i	0.420934	+	0.181879i
$782$		0			0
$783$		0			0
$784$	1.16834	−	0.386749i	1.16834	−	0.386749i
$785$		0			0
$786$		0			0
$787$		0			0		0.973327	−	0.229424i	$-0.0736842\pi$
$787$		0			0		−0.973327	+	0.229424i	$0.926316\pi$
$788$	−0.0750160	+	0.645230i	−0.0750160	+	0.645230i
$789$		0			0
$790$		0			0
$791$	0.263502	−	1.90024i	0.263502	−	1.90024i
$792$	−1.30156	−	0.704367i	−1.30156	−	0.704367i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.652586	−	0.757715i	$-0.273684\pi$
$797$		0			0		−0.652586	+	0.757715i	$0.726316\pi$
$798$		0			0
$799$		0			0
$800$	−0.687646	+	0.0607977i	−0.687646	+	0.0607977i
$801$		0			0
$802$	−0.308390	−	2.22395i	−0.308390	−	2.22395i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.0800878	+	1.31937i	0.0800878	+	1.31937i	0.789141	+	0.614213i	$0.210526\pi$
$809$	0.0800878	+	1.31937i	0.0800878	+	1.31937i	−0.709053	+	0.705155i	$0.750877\pi$
$810$		0			0
$811$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$811$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$812$	−0.0211549	−	0.0968969i	−0.0211549	−	0.0968969i
$813$		0			0
$814$	2.04802	−	1.25892i	2.04802	−	1.25892i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.30649	+	1.35790i	1.30649	+	1.35790i	0.894729	+	0.446609i	$0.147368\pi$
$821$	1.30649	+	1.35790i	1.30649	+	1.35790i	0.411766	+	0.911290i	$0.364912\pi$
$822$		0			0
$823$	−1.73374	+	0.114835i	−1.73374	+	0.114835i	−0.899598	−	0.436719i	$-0.856140\pi$
$823$	−1.73374	+	0.114835i	−1.73374	+	0.114835i	−0.834139	+	0.551554i	$0.814035\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.142961	−	0.00788736i	−0.142961	−	0.00788736i	−0.0165339	−	0.999863i	$-0.505263\pi$
$827$	−0.142961	−	0.00788736i	−0.142961	−	0.00788736i	−0.126427	+	0.991976i	$0.540351\pi$
$828$	−0.0504339	−	0.336404i	−0.0504339	−	0.336404i
$829$		0			0		0.962268	−	0.272103i	$-0.0877193\pi$
$829$		0			0		−0.962268	+	0.272103i	$0.912281\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.340293	−	0.940319i	$-0.389474\pi$
$839$		0			0		−0.340293	+	0.940319i	$0.610526\pi$
$840$		0			0
$841$	−0.918925	+	0.101707i	−0.918925	+	0.101707i
$842$	1.71121	+	0.587458i	1.71121	+	0.587458i
$843$		0			0
$844$	0.0169853	−	0.0220726i	0.0169853	−	0.0220726i
$845$		0			0
$846$		0			0
$847$	−1.63588	+	2.44462i	−1.63588	+	2.44462i
$848$	1.99725	+	0.198797i	1.99725	+	0.198797i
$849$		0			0
$850$		0			0
$851$	−0.910049	−	0.357995i	−0.910049	−	0.357995i
$852$		0			0
$853$		0			0		0.840168	−	0.542326i	$-0.182456\pi$
$853$		0			0		−0.840168	+	0.542326i	$0.817544\pi$
$854$		0			0
$855$		0			0
$856$	0.830265	+	0.337224i	0.830265	+	0.337224i
$857$		0			0		−0.926494	−	0.376309i	$-0.877193\pi$
$857$		0			0		0.926494	+	0.376309i	$0.122807\pi$
$858$		0			0
$859$		0			0		0.965209	−	0.261480i	$-0.0842105\pi$
$859$		0			0		−0.965209	+	0.261480i	$0.915789\pi$
$860$		0			0
$861$		0			0
$862$	−1.88636	−	0.742057i	−1.88636	−	0.742057i
$863$	0.484421	+	1.13832i	0.484421	+	1.13832i	0.965209	+	0.261480i	$0.0842105\pi$
$863$	0.484421	+	1.13832i	0.484421	+	1.13832i	−0.480787	+	0.876837i	$0.659649\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.30708	−	2.99808i	2.30708	−	2.99808i
$870$		0			0
$871$		0			0
$872$	1.48101	−	0.163919i	1.48101	−	0.163919i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.268536	+	0.411024i	0.268536	+	0.411024i	0.945817	−	0.324699i	$-0.105263\pi$
$877$	0.268536	+	0.411024i	0.268536	+	0.411024i	−0.677282	+	0.735724i	$0.736842\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.0385714	−	0.999256i	$-0.487719\pi$
$881$		0			0		−0.0385714	+	0.999256i	$0.512281\pi$
$882$	0.936211	−	0.696093i	0.936211	−	0.696093i
$883$	0.864038	−	1.75514i	0.864038	−	1.75514i	0.245485	−	0.969400i	$-0.421053\pi$
$883$	0.864038	−	1.75514i	0.864038	−	1.75514i	0.618553	−	0.785743i	$-0.287719\pi$
$884$		0			0
$885$		0			0
$886$	0.446633	+	0.0246414i	0.446633	+	0.0246414i
$887$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$887$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$888$		0			0
$889$	−1.21842	−	0.694532i	−1.21842	−	0.694532i
$890$		0			0
$891$	−1.95452	−	0.348338i	−1.95452	−	0.348338i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−1.03082	+	0.587593i	−1.03082	+	0.587593i
$897$		0			0
$898$	−2.09448	−	0.667797i	−2.09448	−	0.667797i
$899$		0			0
$900$	−0.331422	+	0.143202i	−0.331422	+	0.143202i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.0866475	+	1.42743i	0.0866475	+	1.42743i
$905$		0			0
$906$		0			0
$907$	1.63547	−	0.162787i	1.63547	−	0.162787i	0.761300	−	0.648400i	$-0.224561\pi$
$907$	1.63547	−	0.162787i	1.63547	−	0.162787i	0.874174	+	0.485613i	$0.161404\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.0762046	−	0.549547i	−0.0762046	−	0.549547i	−0.989750	−	0.142811i	$-0.954386\pi$
$911$	−0.0762046	−	0.549547i	−0.0762046	−	0.549547i	0.913545	−	0.406737i	$-0.133333\pi$
$912$		0			0
$913$		0			0
$914$	1.46968	+	0.398145i	1.46968	+	0.398145i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.0103018	+	1.86910i	−0.0103018	+	1.86910i	0.350638	+	0.936511i	$0.385965\pi$
$919$	−0.0103018	+	1.86910i	−0.0103018	+	1.86910i	−0.360939	+	0.932589i	$0.617544\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.119866	+	1.03099i	−0.119866	+	1.03099i
$926$	−2.05383	+	0.484109i	−2.05383	+	0.484109i
$927$		0			0
$928$	0.0761767	+	0.173665i	0.0761767	+	0.173665i
$929$		0			0		0.949339	−	0.314254i	$-0.101754\pi$
$929$		0			0		−0.949339	+	0.314254i	$0.898246\pi$
$930$		0			0
$931$		0			0
$932$	0.0982757	+	0.0424634i	0.0982757	+	0.0424634i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.999028	−	0.0440782i	$-0.0140351\pi$
$937$		0			0		−0.999028	+	0.0440782i	$0.985965\pi$
$938$	−0.484355	−	2.10680i	−0.484355	−	2.10680i
$939$		0			0
$940$		0			0
$941$		0			0		0.371197	−	0.928554i	$-0.378947\pi$
$941$		0			0		−0.371197	+	0.928554i	$0.621053\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	2.20178	+	1.06887i	2.20178	+	1.06887i
$947$	0.207789	−	0.144078i	0.207789	−	0.144078i	−0.461341	−	0.887223i	$-0.652632\pi$
$947$	0.207789	−	0.144078i	0.207789	−	0.144078i	0.669131	+	0.743145i	$0.266667\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.27075	+	0.0420383i	−1.27075	+	0.0420383i	−0.660898	−	0.750475i	$-0.729825\pi$
$953$	−1.27075	+	0.0420383i	−1.27075	+	0.0420383i	−0.609854	+	0.792514i	$0.708772\pi$
$954$	1.85661	−	0.416075i	1.85661	−	0.416075i
$955$		0			0
$956$	0.0161663	+	0.325639i	0.0161663	+	0.325639i
$957$		0			0
$958$		0			0
$959$	−0.422202	−	0.150165i	−0.422202	−	0.150165i
$960$		0			0
$961$	0.546948	−	0.837166i	0.546948	−	0.837166i
$962$		0			0
$963$	1.19953	+	0.0794516i	1.19953	+	0.0794516i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.132902	−	0.161375i	−0.132902	−	0.161375i	0.701237	−	0.712928i	$-0.252632\pi$
$967$	−0.132902	−	0.161375i	−0.132902	−	0.161375i	−0.834139	+	0.551554i	$0.814035\pi$
$968$	0.836312	−	2.02693i	0.836312	−	2.02693i
$969$		0			0
$970$		0			0
$971$		0			0		−0.956036	−	0.293250i	$-0.905263\pi$
$971$		0			0		0.956036	+	0.293250i	$0.0947368\pi$
$972$		0			0
$973$		0			0
$974$	1.93205	+	0.569405i	1.93205	+	0.569405i
$975$		0			0
$976$		0			0
$977$	0.115719	−	0.670676i	0.115719	−	0.670676i	−0.868768	−	0.495219i	$-0.835088\pi$
$977$	0.115719	−	0.670676i	0.115719	−	0.670676i	0.984487	−	0.175457i	$-0.0561404\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	1.81702	−	0.833108i	1.81702	−	0.833108i
$982$	1.92151	+	1.21053i	1.92151	+	1.21053i
$983$		0			0		−0.618553	−	0.785743i	$-0.712281\pi$
$983$		0			0		0.618553	+	0.785743i	$0.287719\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.190872	−	0.977160i	−0.190872	−	0.977160i
$990$		0			0
$991$	−1.50785	−	0.0332478i	−1.50785	−	0.0332478i	−0.739446	−	0.673216i	$-0.764912\pi$
$991$	−1.50785	−	0.0332478i	−1.50785	−	0.0332478i	−0.768401	+	0.639969i	$0.778947\pi$
$992$		0			0
$993$		0			0
$994$	0.161965	−	0.215347i	0.161965	−	0.215347i
$995$		0			0
$996$		0			0
$997$		0			0		0.761300	−	0.648400i	$-0.224561\pi$
$997$		0			0		−0.761300	+	0.648400i	$0.775439\pi$
$998$	1.98641	+	0.242049i	1.98641	+	0.242049i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3997.1.cz.a.223.1	✓	144
7.6	odd	2	CM	3997.1.cz.a.223.1	✓	144
571.169	even	285	inner	3997.1.cz.a.1882.1	yes	144
3997.1882	odd	570	inner	3997.1.cz.a.1882.1	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3997.1.cz.a.223.1	✓	144	1.1	even	1	trivial
3997.1.cz.a.223.1	✓	144	7.6	odd	2	CM
3997.1.cz.a.1882.1	yes	144	571.169	even	285	inner
3997.1.cz.a.1882.1	yes	144	3997.1882	odd	570	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3997 = 7 \cdot 571 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3997.cz (of order \(570\), degree \(144\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08088 + 0.439016i) q^{2} +(0.258785 - 0.251750i) q^{4} +(-0.574329 + 0.818625i) q^{7} +(0.299439 - 0.682651i) q^{8} +(0.0935596 - 0.995614i) q^{9} +O(q^{10})\)	\(q+(-1.08088 + 0.439016i) q^{2} +(0.258785 - 0.251750i) q^{4} +(-0.574329 + 0.818625i) q^{7} +(0.299439 - 0.682651i) q^{8} +(0.0935596 - 0.995614i) q^{9} +(1.98519 - 0.0218840i) q^{11} +(0.261391 - 1.13697i) q^{14} +(-0.0339108 + 1.23022i) q^{16} +(0.335963 + 1.11721i) q^{18} +(-2.13615 + 0.895185i) q^{22} +(0.813348 + 0.475583i) q^{23} +(0.266796 - 0.963753i) q^{25} +(0.0574611 + 0.356435i) q^{28} +(-0.274290 + 0.0151330i) q^{29} +(-0.242055 - 0.646500i) q^{32} +(-0.226434 - 0.281203i) q^{36} +(-1.02560 + 0.159544i) q^{37} +(-0.698385 - 0.793043i) q^{43} +(0.508229 - 0.505436i) q^{44} +(-1.08792 - 0.156976i) q^{46} +(-0.340293 - 0.940319i) q^{49} +(0.134728 + 1.15883i) q^{50} +(0.116754 - 1.62671i) q^{53} +(0.386859 + 0.637194i) q^{56} +(0.289831 - 0.136775i) q^{58} +(0.761300 + 0.648400i) q^{63} +(-0.288067 - 0.312924i) q^{64} +(1.66694 - 0.809235i) q^{67} +(0.211001 + 0.0939437i) q^{71} +(-0.651641 - 0.361994i) q^{72} +(1.03851 - 0.622704i) q^{74} +(-1.12224 + 1.63770i) q^{77} +(1.17865 - 1.49723i) q^{79} +(-0.982493 - 0.186298i) q^{81} +(1.10303 + 0.550583i) q^{86} +(0.579505 - 1.36175i) q^{88} +(0.330210 - 0.0816865i) q^{92} +(0.780631 + 0.866979i) q^{98} +(0.163946 - 1.97853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9}+O(q^{10}) \) 144 * q + q^2 + 5 * q^4 + 2 * q^7 + 21 * q^8 - q^9	\( 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9} + 6 q^{11} + q^{14} + 6 q^{16} - 9 q^{18} + 21 q^{22} + 3 q^{23} - q^{25} - 10 q^{28} - 4 q^{29} - 5 q^{32} - 2 q^{37} - 9 q^{43} - 20 q^{44} - 34 q^{46} + 2 q^{49} - 2 q^{50} + 6 q^{53} - 8 q^{56} - q^{58} - q^{63} + 11 q^{64} + 20 q^{67} + 3 q^{71} + 23 q^{72} - 31 q^{74} + q^{77} + 6 q^{79} - q^{81} + 7 q^{86} - 9 q^{88} + 9 q^{92} + 6 q^{98} - 2 q^{99}+O(q^{100}) \) 144 * q + q^2 + 5 * q^4 + 2 * q^7 + 21 * q^8 - q^9 + 6 * q^11 + q^14 + 6 * q^16 - 9 * q^18 + 21 * q^22 + 3 * q^23 - q^25 - 10 * q^28 - 4 * q^29 - 5 * q^32 - 2 * q^37 - 9 * q^43 - 20 * q^44 - 34 * q^46 + 2 * q^49 - 2 * q^50 + 6 * q^53 - 8 * q^56 - q^58 - q^63 + 11 * q^64 + 20 * q^67 + 3 * q^71 + 23 * q^72 - 31 * q^74 + q^77 + 6 * q^79 - q^81 + 7 * q^86 - 9 * q^88 + 9 * q^92 + 6 * q^98 - 2 * q^99

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