LMFDB - Embedded newform 3997.1.cz.a.244.1

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			244.1
Root			$0.782322 + 0.622874i$ of defining polynomial
Character	$\chi$	$=$	3997.244
Dual form			3997.1.cz.a.3653.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.75911 + 0.714490i) q^{2} +(1.86720 + 1.81644i) q^{4} +(-0.956036 + 0.293250i) q^{7} +(1.22410 + 2.79067i) q^{8} +(0.509516 - 0.860461i) q^{9} +O(q^{10})$	\(q+(1.75911 + 0.714490i) q^{2} +(1.86720 + 1.81644i) q^{4} +(-0.956036 + 0.293250i) q^{7} +(1.22410 + 2.79067i) q^{8} +(0.509516 - 0.860461i) q^{9} +(1.42569 - 1.01200i) q^{11} +(-1.89130 - 0.167218i) q^{14} +(0.0876484 + 3.17972i) q^{16} +(1.51109 - 1.14961i) q^{18} +(3.23101 - 0.761584i) q^{22} +(0.295776 + 1.35476i) q^{23} +(-0.834139 + 0.551554i) q^{25} +(-2.31778 - 1.18903i) q^{28} +(-0.274290 - 0.0151330i) q^{29} +(-1.04919 + 2.80225i) q^{32} +(2.51435 - 0.681149i) q^{36} +(-0.925435 - 0.920349i) q^{37} +(-1.78222 - 0.770071i) q^{43} +(4.50028 + 0.700067i) q^{44} +(-0.447658 + 2.59451i) q^{46} +(0.828009 - 0.560715i) q^{49} +(-1.86143 + 0.374262i) q^{50} +(1.28831 + 1.52963i) q^{53} +(-1.98865 - 2.30901i) q^{56} +(-0.471695 - 0.222598i) q^{58} +(-0.234785 + 0.972047i) q^{63} +(-1.69344 + 1.83956i) q^{64} +(-1.82424 + 0.325120i) q^{67} +(-0.204955 - 1.95002i) q^{71} +(3.02496 + 0.368598i) q^{72} +(-0.970366 - 2.28021i) q^{74} +(-1.06624 + 1.38559i) q^{77} +(0.0103444 - 0.00380815i) q^{79} +(-0.480787 - 0.876837i) q^{81} +(-2.58493 - 2.62803i) q^{86} +(4.56934 + 2.73982i) q^{88} +(-1.90857 + 3.06687i) q^{92} +(1.85719 - 0.394757i) q^{98} +(-0.144377 - 1.74238i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3997\mathbb{Z}\right)^\times$.

$n$	$1716$	$2285$
$\chi(n)$	$e\left(\frac{238}{285}\right)$	$-1$

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 $

$2$	1.75911	+	0.714490i	1.75911	+	0.714490i	0.997814	+	0.0660906i	$0.0210526\pi$
$2$	1.75911	+	0.714490i	1.75911	+	0.714490i	0.761300	+	0.648400i	$0.224561\pi$
$3$		0			0		0.868768	−	0.495219i	$-0.164912\pi$
$3$		0			0		−0.868768	+	0.495219i	$0.835088\pi$
$4$	1.86720	+	1.81644i	1.86720	+	1.81644i
$5$		0			0		−0.287976	−	0.957638i	$-0.592982\pi$
$5$		0			0		0.287976	+	0.957638i	$0.407018\pi$
$6$		0			0
$7$	−0.956036	+	0.293250i	−0.956036	+	0.293250i
$7$	−0.956036	+	0.293250i	−0.956036	+	0.293250i
$8$	1.22410	+	2.79067i	1.22410	+	2.79067i
$9$	0.509516	−	0.860461i	0.509516	−	0.860461i
$10$		0			0
$11$	1.42569	−	1.01200i	1.42569	−	1.01200i	0.431754	−	0.901991i	$-0.357895\pi$
$11$	1.42569	−	1.01200i	1.42569	−	1.01200i	0.993931	−	0.110008i	$-0.0350877\pi$
$12$		0			0
$13$		0			0		0.988116	−	0.153712i	$-0.0491228\pi$
$13$		0			0		−0.988116	+	0.153712i	$0.950877\pi$
$14$	−1.89130	−	0.167218i	−1.89130	−	0.167218i
$15$		0			0
$16$	0.0876484	+	3.17972i	0.0876484	+	3.17972i
$17$		0			0		0.942181	−	0.335105i	$-0.108772\pi$
$17$		0			0		−0.942181	+	0.335105i	$0.891228\pi$
$18$	1.51109	−	1.14961i	1.51109	−	1.14961i
$19$		0			0		0.411766	−	0.911290i	$-0.364912\pi$
$19$		0			0		−0.411766	+	0.911290i	$0.635088\pi$
$20$		0			0
$21$		0			0
$22$	3.23101	−	0.761584i	3.23101	−	0.761584i
$23$	0.295776	+	1.35476i	0.295776	+	1.35476i	0.851919	+	0.523673i	$0.175439\pi$
$23$	0.295776	+	1.35476i	0.295776	+	1.35476i	−0.556143	+	0.831087i	$0.687719\pi$
$24$		0			0
$25$	−0.834139	+	0.551554i	−0.834139	+	0.551554i
$26$		0			0
$27$		0			0
$28$	−2.31778	−	1.18903i	−2.31778	−	1.18903i
$29$	−0.274290	−	0.0151330i	−0.274290	−	0.0151330i	−0.0825793	−	0.996584i	$-0.526316\pi$
$29$	−0.274290	−	0.0151330i	−0.274290	−	0.0151330i	−0.191711	+	0.981451i	$0.561404\pi$
$30$		0			0
$31$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$31$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$32$	−1.04919	+	2.80225i	−1.04919	+	2.80225i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	2.51435	−	0.681149i	2.51435	−	0.681149i
$37$	−0.925435	−	0.920349i	−0.925435	−	0.920349i	0.0715891	−	0.997434i	$-0.477193\pi$
$37$	−0.925435	−	0.920349i	−0.925435	−	0.920349i	−0.997024	+	0.0770854i	$0.975439\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.821778	−	0.569808i	$-0.192982\pi$
$41$		0			0		−0.821778	+	0.569808i	$0.807018\pi$
$42$		0			0
$43$	−1.78222	−	0.770071i	−1.78222	−	0.770071i	−0.986361	−	0.164595i	$-0.947368\pi$
$43$	−1.78222	−	0.770071i	−1.78222	−	0.770071i	−0.795863	−	0.605477i	$-0.792982\pi$
$44$	4.50028	+	0.700067i	4.50028	+	0.700067i
$45$		0			0
$46$	−0.447658	+	2.59451i	−0.447658	+	2.59451i
$47$		0			0		0.851919	−	0.523673i	$-0.175439\pi$
$47$		0			0		−0.851919	+	0.523673i	$0.824561\pi$
$48$		0			0
$49$	0.828009	−	0.560715i	0.828009	−	0.560715i
$50$	−1.86143	+	0.374262i	−1.86143	+	0.374262i
$51$		0			0
$52$		0			0
$53$	1.28831	+	1.52963i	1.28831	+	1.52963i	0.652586	+	0.757715i	$0.273684\pi$
$53$	1.28831	+	1.52963i	1.28831	+	1.52963i	0.635724	+	0.771917i	$0.280702\pi$
$54$		0			0
$55$		0			0
$56$	−1.98865	−	2.30901i	−1.98865	−	2.30901i
$57$		0			0
$58$	−0.471695	−	0.222598i	−0.471695	−	0.222598i
$59$		0			0		−0.945817	−	0.324699i	$-0.894737\pi$
$59$		0			0		0.945817	+	0.324699i	$0.105263\pi$
$60$		0			0
$61$		0			0		−0.693336	−	0.720615i	$-0.743860\pi$
$61$		0			0		0.693336	+	0.720615i	$0.256140\pi$
$62$		0			0
$63$	−0.234785	+	0.972047i	−0.234785	+	0.972047i
$64$	−1.69344	+	1.83956i	−1.69344	+	1.83956i
$65$		0			0
$66$		0			0
$67$	−1.82424	+	0.325120i	−1.82424	+	0.325120i	−0.978148	−	0.207912i	$-0.933333\pi$
$67$	−1.82424	+	0.325120i	−1.82424	+	0.325120i	−0.846095	+	0.533032i	$0.821053\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.204955	−	1.95002i	−0.204955	−	1.95002i	−0.298515	−	0.954405i	$-0.596491\pi$
$71$	−0.204955	−	1.95002i	−0.204955	−	1.95002i	0.0935596	−	0.995614i	$-0.470175\pi$
$72$	3.02496	+	0.368598i	3.02496	+	0.368598i
$73$		0			0		0.256156	−	0.966635i	$-0.417544\pi$
$73$		0			0		−0.256156	+	0.966635i	$0.582456\pi$
$74$	−0.970366	−	2.28021i	−0.970366	−	2.28021i
$75$		0			0
$76$		0			0
$77$	−1.06624	+	1.38559i	−1.06624	+	1.38559i
$78$		0			0
$79$	0.0103444	−	0.00380815i	0.0103444	−	0.00380815i	−0.340293	−	0.940319i	$-0.610526\pi$
$79$	0.0103444	−	0.00380815i	0.0103444	−	0.00380815i	0.350638	+	0.936511i	$0.385965\pi$
$80$		0			0
$81$	−0.480787	−	0.876837i	−0.480787	−	0.876837i
$82$		0			0
$83$		0			0		0.381410	−	0.924406i	$-0.375439\pi$
$83$		0			0		−0.381410	+	0.924406i	$0.624561\pi$
$84$		0			0
$85$		0			0
$86$	−2.58493	−	2.62803i	−2.58493	−	2.62803i
$87$		0			0
$88$	4.56934	+	2.73982i	4.56934	+	2.73982i
$89$		0			0		−0.609854	−	0.792514i	$-0.708772\pi$
$89$		0			0		0.609854	+	0.792514i	$0.291228\pi$
$90$		0			0
$91$		0			0
$92$	−1.90857	+	3.06687i	−1.90857	+	3.06687i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.884667	−	0.466224i	$-0.154386\pi$
$97$		0			0		−0.884667	+	0.466224i	$0.845614\pi$
$98$	1.85719	−	0.394757i	1.85719	−	0.394757i
$99$	−0.144377	−	1.74238i	−0.144377	−	1.74238i
$100$	−2.55937	−	0.485303i	−2.55937	−	0.485303i
$101$		0			0		−0.441671	−	0.897177i	$-0.645614\pi$
$101$		0			0		0.441671	+	0.897177i	$0.354386\pi$
$102$		0			0
$103$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$103$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$104$		0			0
$105$		0			0
$106$	1.17338	+	3.61128i	1.17338	+	3.61128i
$107$	−0.000911164		0.0330553i	−0.000911164		0.0330553i	−0.999939	−	0.0110229i	$-0.996491\pi$
$107$	−0.000911164		0.0330553i	−0.000911164		0.0330553i	0.999028	+	0.0440782i	$0.0140351\pi$
$108$		0			0
$109$	0.277403	−	0.480476i	0.277403	−	0.480476i	−0.693336	−	0.720615i	$-0.743860\pi$
$109$	0.277403	−	0.480476i	0.277403	−	0.480476i	0.970739	+	0.240139i	$0.0771930\pi$
$110$		0			0
$111$		0			0
$112$	−1.01625	−	3.01423i	−1.01625	−	3.01423i
$113$	−0.299907	+	1.86034i	−0.299907	+	1.86034i	0.180881	+	0.983505i	$0.442105\pi$
$113$	−0.299907	+	1.86034i	−0.299907	+	1.86034i	−0.480787	+	0.876837i	$0.659649\pi$
$114$		0			0
$115$		0			0
$116$	−0.484667	−	0.526488i	−0.484667	−	0.526488i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.678527	−	1.94157i	0.678527	−	1.94157i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−1.10753	+	1.54219i	−1.10753	+	1.54219i
$127$	0.911757	+	1.53976i	0.911757	+	1.53976i	0.840168	+	0.542326i	$0.182456\pi$
$127$	0.911757	+	1.53976i	0.911757	+	1.53976i	0.0715891	+	0.997434i	$0.477193\pi$
$128$	−1.58726	+	0.749044i	−1.58726	+	0.749044i
$129$		0			0
$130$		0			0
$131$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$131$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$132$		0			0
$133$		0			0
$134$	−3.44135	−	0.731481i	−3.44135	−	0.731481i
$135$		0			0
$136$		0			0
$137$	−1.66180	−	1.09882i	−1.66180	−	1.09882i	−0.879474	−	0.475947i	$-0.842105\pi$
$137$	−1.66180	−	1.09882i	−1.66180	−	1.09882i	−0.782322	−	0.622874i	$-0.785965\pi$
$138$		0			0
$139$		0			0		0.999939	−	0.0110229i	$-0.00350877\pi$
$139$		0			0		−0.999939	+	0.0110229i	$0.996491\pi$
$140$		0			0
$141$		0			0
$142$	1.03273	−	3.57674i	1.03273	−	3.57674i
$143$		0			0
$144$	2.78069	+	1.54470i	2.78069	+	1.54470i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−0.0562145	−	3.39948i	−0.0562145	−	3.39948i
$149$	−0.363428	+	1.66463i	−0.363428	+	1.66463i	0.329907	+	0.944013i	$0.392982\pi$
$149$	−0.363428	+	1.66463i	−0.363428	+	1.66463i	−0.693336	+	0.720615i	$0.743860\pi$
$150$		0			0
$151$	−0.645396	−	1.84677i	−0.645396	−	1.84677i	−0.518970	−	0.854793i	$-0.673684\pi$
$151$	−0.645396	−	1.84677i	−0.645396	−	1.84677i	−0.126427	−	0.991976i	$-0.540351\pi$
$152$		0			0
$153$		0			0
$154$	−2.86562	+	1.67559i	−2.86562	+	1.67559i
$155$		0			0
$156$		0			0
$157$		0			0		−0.761300	−	0.648400i	$-0.775439\pi$
$157$		0			0		0.761300	+	0.648400i	$0.224561\pi$
$158$	0.0209178		0.000691992i	0.0209178		0.000691992i
$159$		0			0
$160$		0			0
$161$	−0.680056	−	1.20846i	−0.680056	−	1.20846i
$162$	−0.219268	−	1.88597i	−0.219268	−	1.88597i
$163$	−0.220815	−	0.0677317i	−0.220815	−	0.0677317i	0.180881	−	0.983505i	$-0.442105\pi$
$163$	−0.220815	−	0.0677317i	−0.220815	−	0.0677317i	−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
$169$	0.952745	−	0.303771i	0.952745	−	0.303771i
$170$		0			0
$171$		0			0
$172$	−1.92898	−	4.67519i	−1.92898	−	4.67519i
$173$		0			0		−0.421786	−	0.906696i	$-0.638596\pi$
$173$		0			0		0.421786	+	0.906696i	$0.361404\pi$
$174$		0			0
$175$	0.635724	−	0.771917i	0.635724	−	0.771917i
$176$	3.34284	+	4.44458i	3.34284	+	4.44458i
$177$		0			0
$178$		0			0
$179$	−1.31214	−	0.826635i	−1.31214	−	0.826635i	−0.319482	−	0.947592i	$-0.603509\pi$
$179$	−1.31214	−	0.826635i	−1.31214	−	0.826635i	−0.992658	+	0.120958i	$0.961404\pi$
$180$		0			0
$181$		0			0		−0.546948	−	0.837166i	$-0.684211\pi$
$181$		0			0		0.546948	+	0.837166i	$0.315789\pi$
$182$		0			0
$183$		0			0
$184$	−3.41862	+	2.48378i	−3.41862	+	2.48378i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.0749563	−	0.0952165i	−0.0749563	−	0.0952165i	0.746821	−	0.665025i	$-0.231579\pi$
$191$	−0.0749563	−	0.0952165i	−0.0749563	−	0.0952165i	−0.821778	+	0.569808i	$0.807018\pi$
$192$		0			0
$193$	0.127494	−	1.21303i	0.127494	−	1.21303i	−0.724425	−	0.689353i	$-0.757895\pi$
$193$	0.127494	−	1.21303i	0.127494	−	1.21303i	0.851919	−	0.523673i	$-0.175439\pi$
$194$		0			0
$195$		0			0
$196$	2.56457	+	0.457062i	2.56457	+	0.457062i
$197$	1.65427	−	1.06783i	1.65427	−	1.06783i	0.731980	−	0.681326i	$-0.238596\pi$
$197$	1.65427	−	1.06783i	1.65427	−	1.06783i	0.922290	−	0.386499i	$-0.126316\pi$
$198$	0.990935	−	3.16819i	0.990935	−	3.16819i
$199$		0			0		−0.731980	−	0.681326i	$-0.761404\pi$
$199$		0			0		0.731980	+	0.681326i	$0.238596\pi$
$200$	−2.56027	−	1.65265i	−2.56027	−	1.65265i
$201$		0			0
$202$		0			0
$203$	0.266669	−	0.0659679i	0.266669	−	0.0659679i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.31642	+	0.435767i	1.31642	+	0.435767i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.189120	+	1.09609i	0.189120	+	1.09609i	0.913545	+	0.406737i	$0.133333\pi$
$211$	0.189120	+	1.09609i	0.189120	+	1.09609i	−0.724425	+	0.689353i	$0.757895\pi$
$212$	−0.372953	+	5.19627i	−0.372953	+	5.19627i
$213$		0			0
$214$	−0.0252206	+	0.0574971i	−0.0252206	+	0.0574971i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.831279	−	0.647010i	0.831279	−	0.647010i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.952745	−	0.303771i	$-0.901754\pi$
$223$		0			0		0.952745	+	0.303771i	$0.0982456\pi$
$224$	0.181299	−	2.98673i	0.181299	−	2.98673i
$225$	0.0495838	+	0.998770i	0.0495838	+	0.998770i
$226$	−1.85677	+	3.05827i	−1.85677	+	3.05827i
$227$		0			0		−0.00551154	−	0.999985i	$-0.501754\pi$
$227$		0			0		0.00551154	+	0.999985i	$0.498246\pi$
$228$		0			0
$229$		0			0		−0.224056	−	0.974576i	$-0.571930\pi$
$229$		0			0		0.224056	+	0.974576i	$0.428070\pi$
$230$		0			0
$231$		0			0
$232$	−0.293527	−	0.783977i	−0.293527	−	0.783977i
$233$	0.919937	+	0.0711253i	0.919937	+	0.0711253i	0.528360	−	0.849020i	$-0.322807\pi$
$233$	0.919937	+	0.0711253i	0.919937	+	0.0711253i	0.391577	+	0.920146i	$0.371930\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.828991	+	0.358194i	−0.828991	+	0.358194i	−0.768401	−	0.639969i	$-0.778947\pi$
$239$	−0.828991	+	0.358194i	−0.828991	+	0.358194i	−0.0605901	+	0.998163i	$0.519298\pi$
$240$		0			0
$241$		0			0		−0.863256	−	0.504766i	$-0.831579\pi$
$241$		0			0		0.863256	+	0.504766i	$0.168421\pi$
$242$	2.58084	−	2.93064i	2.58084	−	2.93064i
$243$		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		−0.899598	−	0.436719i	$-0.856140\pi$
$251$		0			0		0.899598	+	0.436719i	$0.143860\pi$
$252$	−2.20406	+	1.38854i	−2.20406	+	1.38854i
$253$	1.79270	+	1.63213i	1.79270	+	1.63213i
$254$	0.503741	+	3.36005i	0.503741	+	3.36005i
$255$		0			0
$256$	−0.830802	+	0.0458366i	−0.830802	+	0.0458366i
$257$		0			0		−0.461341	−	0.887223i	$-0.652632\pi$
$257$		0			0		0.461341	+	0.887223i	$0.347368\pi$
$258$		0			0
$259$	1.15464	+	0.608502i	1.15464	+	0.608502i
$260$		0			0
$261$	−0.152776	+	0.228305i	−0.152776	+	0.228305i
$262$		0			0
$263$	1.84997	−	0.266932i	1.84997	−	0.266932i	0.874174	−	0.485613i	$-0.161404\pi$
$263$	1.84997	−	0.266932i	1.84997	−	0.266932i	0.975796	+	0.218681i	$0.0701754\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−3.99679	−	2.70657i	−3.99679	−	2.70657i
$269$		0			0		0.0495838	−	0.998770i	$-0.484211\pi$
$269$		0			0		−0.0495838	+	0.998770i	$0.515789\pi$
$270$		0			0
$271$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$271$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$272$		0			0
$273$		0			0
$274$	−2.13819	−	3.12029i	−2.13819	−	3.12029i
$275$	−0.631048	+	1.63049i	−0.631048	+	1.63049i
$276$		0			0
$277$	1.28940	−	1.14817i	1.28940	−	1.14817i	0.309017	−	0.951057i	$-0.400000\pi$
$277$	1.28940	−	1.14817i	1.28940	−	1.14817i	0.980380	−	0.197117i	$-0.0631579\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.0504181	−	0.336299i	0.0504181	−	0.336299i	−0.949339	−	0.314254i	$-0.898246\pi$
$281$	0.0504181	−	0.336299i	0.0504181	−	0.336299i	0.999757	−	0.0220445i	$-0.00701754\pi$
$282$		0			0
$283$		0			0		−0.627176	−	0.778877i	$-0.715789\pi$
$283$		0			0		0.627176	+	0.778877i	$0.284211\pi$
$284$	3.15940	−	4.01337i	3.15940	−	4.01337i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	1.87665	+	2.33058i	1.87665	+	2.33058i
$289$	0.775409	−	0.631460i	0.775409	−	0.631460i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.930586	−	0.366074i	$-0.880702\pi$
$293$		0			0		0.930586	+	0.366074i	$0.119298\pi$
$294$		0			0
$295$		0			0
$296$	1.43556	−	3.70918i	1.43556	−	3.70918i
$297$		0			0
$298$	−1.82867	+	2.66860i	−1.82867	+	2.66860i
$299$		0			0
$300$		0			0
$301$	1.92969	+	0.213578i	1.92969	+	0.213578i
$302$	0.184173	−	3.70981i	0.184173	−	3.70981i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.999757	−	0.0220445i	$-0.992982\pi$
$307$		0			0		0.999757	+	0.0220445i	$0.00701754\pi$
$308$	−4.50772	+	0.650418i	−4.50772	+	0.650418i
$309$		0			0
$310$		0			0
$311$		0			0		0.319482	−	0.947592i	$-0.396491\pi$
$311$		0			0		−0.319482	+	0.947592i	$0.603509\pi$
$312$		0			0
$313$		0			0		−0.962268	−	0.272103i	$-0.912281\pi$
$313$		0			0		0.962268	+	0.272103i	$0.0877193\pi$
$314$		0			0
$315$		0			0
$316$	0.0262323	+	0.0116794i	0.0262323	+	0.0116794i
$317$	−0.139692	−	0.931773i	−0.139692	−	0.931773i	−0.942181	−	0.335105i	$-0.891228\pi$
$317$	−0.139692	−	0.931773i	−0.139692	−	0.931773i	0.802489	−	0.596667i	$-0.203509\pi$
$318$		0			0
$319$	−0.406366	+	0.256006i	−0.406366	+	0.256006i
$320$		0			0
$321$		0			0
$322$	−0.332862	−	2.61172i	−0.332862	−	2.61172i
$323$		0			0
$324$	0.694997	−	2.51056i	0.694997	−	2.51056i
$325$		0			0
$326$	−0.340045	−	0.276918i	−0.340045	−	0.276918i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.33168	+	1.47898i	−1.33168	+	1.47898i	−0.592235	+	0.805765i	$0.701754\pi$
$331$	−1.33168	+	1.47898i	−1.33168	+	1.47898i	−0.739446	+	0.673216i	$0.764912\pi$
$332$		0			0
$333$	−1.26345	+	0.327369i	−1.26345	+	0.327369i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.325570	−	0.338379i	0.325570	−	0.338379i	−0.537687	−	0.843145i	$-0.680702\pi$
$337$	0.325570	−	0.338379i	0.325570	−	0.338379i	0.863256	+	0.504766i	$0.168421\pi$
$338$	1.89303	+	0.146360i	1.89303	+	0.146360i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.627176	+	0.778877i	−0.627176	+	0.778877i
$344$	−0.0326081	−	5.91624i	−0.0326081	−	5.91624i
$345$		0			0
$346$		0			0
$347$	0.0486775	−	0.801915i	0.0486775	−	0.801915i	−0.889752	−	0.456444i	$-0.849123\pi$
$347$	0.0486775	−	0.801915i	0.0486775	−	0.801915i	0.938430	−	0.345471i	$-0.112281\pi$
$348$		0			0
$349$		0			0		−0.795863	−	0.605477i	$-0.792982\pi$
$349$		0			0		0.795863	+	0.605477i	$0.207018\pi$
$350$	1.66984	−	0.903671i	1.66984	−	0.903671i
$351$		0			0
$352$	1.34007	+	5.05691i	1.34007	+	5.05691i
$353$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$353$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.71758	−	2.39166i	−1.71758	−	2.39166i
$359$	−0.143100	+	1.99378i	−0.143100	+	1.99378i	−0.0385714	+	0.999256i	$0.512281\pi$
$359$	−0.143100	+	1.99378i	−0.143100	+	1.99378i	−0.104528	+	0.994522i	$0.533333\pi$
$360$		0			0
$361$	−0.660898	−	0.750475i	−0.660898	−	0.750475i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.996114	−	0.0880708i	$-0.0280702\pi$
$367$		0			0		−0.996114	+	0.0880708i	$0.971930\pi$
$368$	−4.28184	+	1.05923i	−4.28184	+	1.05923i
$369$		0			0
$370$		0			0
$371$	−1.68023	−	1.08459i	−1.68023	−	1.08459i
$372$		0			0
$373$	−0.445875	+	1.42554i	−0.445875	+	1.42554i	0.411766	+	0.911290i	$0.364912\pi$
$373$	−0.445875	+	1.42554i	−0.445875	+	1.42554i	−0.857640	+	0.514250i	$0.828070\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.189007	+	0.822124i	−0.189007	+	0.822124i	0.789141	+	0.614213i	$0.210526\pi$
$379$	−0.189007	+	0.822124i	−0.189007	+	0.822124i	−0.978148	+	0.207912i	$0.933333\pi$
$380$		0			0
$381$		0			0
$382$	−0.0638255	−	0.221052i	−0.0638255	−	0.221052i
$383$		0			0		−0.975796	−	0.218681i	$-0.929825\pi$
$383$		0			0		0.975796	+	0.218681i	$0.0701754\pi$
$384$		0			0
$385$		0			0
$386$	1.09097	−	2.04276i	1.09097	−	2.04276i
$387$	−1.57069	+	1.14117i	−1.57069	+	1.14117i
$388$		0			0
$389$	1.85710	−	0.123006i	1.85710	−	0.123006i	0.904357	−	0.426776i	$-0.140351\pi$
$389$	1.85710	−	0.123006i	1.85710	−	0.123006i	0.952745	+	0.303771i	$0.0982456\pi$
$390$		0			0
$391$		0			0
$392$	2.57834	+	1.62433i	2.57834	+	1.62433i
$393$		0			0
$394$	3.67300	−	0.696467i	3.67300	−	0.696467i
$395$		0			0
$396$	2.89534	−	3.51562i	2.89534	−	3.51562i
$397$		0			0		0.997024	−	0.0770854i	$-0.0245614\pi$
$397$		0			0		−0.997024	+	0.0770854i	$0.975439\pi$
$398$		0			0
$399$		0			0
$400$	−1.82690	−	2.60399i	−1.82690	−	2.60399i
$401$	−0.472446	−	1.86565i	−0.472446	−	1.86565i	−0.500000	−	0.866025i	$-0.666667\pi$
$401$	−0.472446	−	1.86565i	−0.472446	−	1.86565i	0.0275543	−	0.999620i	$-0.491228\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	0.516234	+	0.0744873i	0.516234	+	0.0744873i
$407$	−2.25077	−	0.375587i	−2.25077	−	0.375587i
$408$		0			0
$409$		0			0		−0.115485	−	0.993309i	$-0.536842\pi$
$409$		0			0		0.115485	+	0.993309i	$0.463158\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	2.00438	+	1.70713i	2.00438	+	1.70713i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.999939	−	0.0110229i	$-0.996491\pi$
$419$		0			0		0.999939	+	0.0110229i	$0.00350877\pi$
$420$		0			0
$421$	−1.26715	+	1.10356i	−1.26715	+	1.10356i	−0.277403	+	0.960754i	$0.589474\pi$
$421$	−1.26715	+	1.10356i	−1.26715	+	1.10356i	−0.989750	+	0.142811i	$0.954386\pi$
$422$	−0.450462	+	2.06327i	−0.450462	+	2.06327i
$423$		0			0
$424$	−2.69167	+	5.46767i	−2.69167	+	5.46767i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.0617444	+	0.0600659i	−0.0617444	+	0.0600659i
$429$		0			0
$430$		0			0
$431$	−0.267503	+	1.45450i	−0.267503	+	1.45450i	0.528360	+	0.849020i	$0.322807\pi$
$431$	−0.267503	+	1.45450i	−0.267503	+	1.45450i	−0.795863	+	0.605477i	$0.792982\pi$
$432$		0			0
$433$		0			0		−0.340293	−	0.940319i	$-0.610526\pi$
$433$		0			0		0.340293	+	0.940319i	$0.389474\pi$
$434$		0			0
$435$		0			0
$436$	1.39072	−	0.393259i	1.39072	−	0.393259i
$437$		0			0
$438$		0			0
$439$		0			0		0.934564	−	0.355794i	$-0.115789\pi$
$439$		0			0		−0.934564	+	0.355794i	$0.884211\pi$
$440$		0			0
$441$	−0.0605901	−	0.998163i	−0.0605901	−	0.998163i
$442$		0			0
$443$	−0.346750	+	0.163635i	−0.346750	+	0.163635i	−0.592235	−	0.805765i	$-0.701754\pi$
$443$	−0.346750	+	0.163635i	−0.346750	+	0.163635i	0.245485	+	0.969400i	$0.421053\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	1.07953	−	2.25529i	1.07953	−	2.25529i
$449$	0.712112	+	1.78136i	0.712112	+	1.78136i	0.618553	+	0.785743i	$0.287719\pi$
$449$	0.712112	+	1.78136i	0.712112	+	1.78136i	0.0935596	+	0.995614i	$0.470175\pi$
$450$	−0.626388	+	1.79238i	−0.626388	+	1.79238i
$451$		0			0
$452$	−3.93919	+	2.92887i	−3.93919	+	2.92887i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.298902	+	0.993969i	−0.298902	+	0.993969i	0.669131	+	0.743145i	$0.266667\pi$
$457$	−0.298902	+	0.993969i	−0.298902	+	0.993969i	−0.968033	+	0.250825i	$0.919298\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$461$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$462$		0			0
$463$	−1.28247	+	1.27542i	−1.28247	+	1.27542i	−0.340293	+	0.940319i	$0.610526\pi$
$463$	−1.28247	+	1.27542i	−1.28247	+	1.27542i	−0.942181	+	0.335105i	$0.891228\pi$
$464$	0.0240777	−	0.873492i	0.0240777	−	0.873492i
$465$		0			0
$466$	1.56746	+	0.782403i	1.56746	+	0.782403i
$467$		0			0		−0.537687	−	0.843145i	$-0.680702\pi$
$467$		0			0		0.537687	+	0.843145i	$0.319298\pi$
$468$		0			0
$469$	1.64870	−	0.845786i	1.64870	−	0.845786i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.32020	+	0.705731i	−3.32020	+	0.705731i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.97260	−	0.329169i	1.97260	−	0.329169i
$478$	−1.71422	+	0.0377982i	−1.71422	+	0.0377982i
$479$		0			0		0.528360	−	0.849020i	$-0.322807\pi$
$479$		0			0		−0.528360	+	0.849020i	$0.677193\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	4.79370	−	2.39280i	4.79370	−	2.39280i
$485$		0			0
$486$		0			0
$487$	−0.426185	+	0.0188037i	−0.426185	+	0.0188037i	−0.256156	−	0.966635i	$-0.582456\pi$
$487$	−0.426185	+	0.0188037i	−0.426185	+	0.0188037i	−0.170028	+	0.985439i	$0.554386\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.75113	+	0.579667i	−1.75113	+	0.579667i	−0.997024	−	0.0770854i	$-0.975439\pi$
$491$	−1.75113	+	0.579667i	−1.75113	+	0.579667i	−0.754107	+	0.656752i	$0.771930\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.767788	+	1.80418i	0.767788	+	1.80418i
$498$		0			0
$499$	−0.777403	−	0.0947283i	−0.777403	−	0.0947283i	−0.277403	−	0.960754i	$-0.589474\pi$
$499$	−0.777403	−	0.0947283i	−0.777403	−	0.0947283i	−0.500000	+	0.866025i	$0.666667\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.909007	−	0.416782i	$-0.863158\pi$
$503$		0			0		0.909007	+	0.416782i	$0.136842\pi$
$504$	−3.00006	+	0.534677i	−3.00006	+	0.534677i
$505$		0			0
$506$	1.98742	+	4.15198i	1.98742	+	4.15198i
$507$		0			0
$508$	−1.09445	+	4.53120i	−1.09445	+	4.53120i
$509$		0			0		−0.635724	−	0.771917i	$-0.719298\pi$
$509$		0			0		0.635724	+	0.771917i	$0.280702\pi$
$510$		0			0
$511$		0			0
$512$	0.165799	+	0.0569188i	0.165799	+	0.0569188i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	1.59638	+	1.89541i	1.59638	+	1.89541i
$519$		0			0
$520$		0			0
$521$		0			0		0.980380	−	0.197117i	$-0.0631579\pi$
$521$		0			0		−0.980380	+	0.197117i	$0.936842\pi$
$522$	−0.431873	+	0.292458i	−0.431873	+	0.292458i
$523$		0			0		−0.518970	−	0.854793i	$-0.673684\pi$
$523$		0			0		0.518970	+	0.854793i	$0.326316\pi$
$524$		0			0
$525$		0			0
$526$	3.44503	+	0.852223i	3.44503	+	0.852223i
$527$		0			0
$528$		0			0
$529$	−0.838883	+	0.384630i	−0.838883	+	0.384630i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−3.14036	−	4.69288i	−3.14036	−	4.69288i
$537$		0			0
$538$		0			0
$539$	0.613036	−	1.63735i	0.613036	−	1.63735i
$540$		0			0
$541$	0.288761	+	0.639065i	0.288761	+	0.639065i	0.997814	−	0.0660906i	$-0.0210526\pi$
$541$	0.288761	+	0.639065i	0.288761	+	0.639065i	−0.709053	+	0.705155i	$0.750877\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.495965	+	0.368761i	0.495965	+	0.368761i	0.815447	−	0.578832i	$-0.196491\pi$
$547$	0.495965	+	0.368761i	0.495965	+	0.368761i	−0.319482	+	0.947592i	$0.603509\pi$
$548$	−1.10696	−	5.07028i	−1.10696	−	5.07028i
$549$		0			0
$550$	−2.27505	+	2.41734i	−2.27505	+	2.41734i
$551$		0			0
$552$		0			0
$553$	−0.00877286	+	0.00667422i	−0.00877286	+	0.00667422i
$554$	3.08855	−	1.09851i	3.08855	−	1.09851i
$555$		0			0
$556$		0			0
$557$	0.142622	+	0.0126098i	0.142622	+	0.0126098i	0.159156	−	0.987253i	$-0.449123\pi$
$557$	0.142622	+	0.0126098i	0.142622	+	0.0126098i	−0.0165339	+	0.999863i	$0.505263\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.328973	−	0.555564i	0.328973	−	0.555564i
$563$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$563$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.716783	+	0.697297i	0.716783	+	0.697297i
$568$	5.19097	−	2.95898i	5.19097	−	2.95898i
$569$	1.44963	+	0.588790i	1.44963	+	0.588790i	0.959210	−	0.282694i	$-0.0912281\pi$
$569$	1.44963	+	0.588790i	1.44963	+	0.588790i	0.490424	+	0.871484i	$0.336842\pi$
$570$		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
$575$	−0.993942	−	0.966921i	−0.993942	−	0.966921i
$576$	0.720040	+	2.39442i	0.720040	+	2.39442i
$577$		0			0		0.991264	−	0.131892i	$-0.0421053\pi$
$577$		0			0		−0.991264	+	0.131892i	$0.957895\pi$
$578$	1.81520	−	0.556787i	1.81520	−	0.556787i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	3.38471	+	0.877004i	3.38471	+	0.877004i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.0275543	−	0.999620i	$-0.508772\pi$
$587$		0			0		0.0275543	+	0.999620i	$0.491228\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	2.84534	−	3.02329i	2.84534	−	3.02329i
$593$		0			0		0.973327	−	0.229424i	$-0.0736842\pi$
$593$		0			0		−0.973327	+	0.229424i	$0.926316\pi$
$594$		0			0
$595$		0			0
$596$	−3.70230	+	2.44805i	−3.70230	+	2.44805i
$597$		0			0
$598$		0			0
$599$	−0.166490	−	0.0854095i	−0.166490	−	0.0854095i	0.371197	−	0.928554i	$-0.378947\pi$
$599$	−0.166490	−	0.0854095i	−0.166490	−	0.0854095i	−0.537687	+	0.843145i	$0.680702\pi$
$600$		0			0
$601$		0			0		−0.411766	−	0.911290i	$-0.635088\pi$
$601$		0			0		0.411766	+	0.911290i	$0.364912\pi$
$602$	3.24195	+	1.75446i	3.24195	+	1.75446i
$603$	−0.649727	+	1.73534i	−0.649727	+	1.73534i
$604$	2.14946	−	4.62062i	2.14946	−	4.62062i
$605$		0			0
$606$		0			0
$607$		0			0		0.965209	−	0.261480i	$-0.0842105\pi$
$607$		0			0		−0.965209	+	0.261480i	$0.915789\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.81404	+	0.831741i	−1.81404	+	0.831741i	−0.879474	+	0.475947i	$0.842105\pi$
$613$	−1.81404	+	0.831741i	−1.81404	+	0.831741i	−0.934564	+	0.355794i	$0.884211\pi$
$614$		0			0
$615$		0			0
$616$	−5.17190	−	1.27941i	−5.17190	−	1.27941i
$617$	0.283655	−	1.64399i	0.283655	−	1.64399i	−0.401695	−	0.915773i	$-0.631579\pi$
$617$	0.283655	−	1.64399i	0.283655	−	1.64399i	0.685350	−	0.728214i	$-0.259649\pi$
$618$		0			0
$619$		0			0		−0.518970	−	0.854793i	$-0.673684\pi$
$619$		0			0		0.518970	+	0.854793i	$0.326316\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.391577	−	0.920146i	0.391577	−	0.920146i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.0172843	−	0.447778i	−0.0172843	−	0.447778i	−0.982493	−	0.186298i	$-0.940351\pi$
$631$	−0.0172843	−	0.447778i	−0.0172843	−	0.447778i	0.965209	−	0.261480i	$-0.0842105\pi$
$632$	0.0232898	+	0.0242062i	0.0232898	+	0.0242062i
$633$		0			0
$634$	0.420009	−	1.73890i	0.420009	−	1.73890i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−0.897758	+	0.160000i	−0.897758	+	0.160000i
$639$	−1.78234	−	0.817209i	−1.78234	−	0.817209i
$640$		0			0
$641$	−0.239876	−	1.15993i	−0.239876	−	1.15993i	−0.909007	−	0.416782i	$-0.863158\pi$
$641$	−0.239876	−	1.15993i	−0.239876	−	1.15993i	0.669131	−	0.743145i	$-0.266667\pi$
$642$		0			0
$643$		0			0		−0.992658	−	0.120958i	$-0.961404\pi$
$643$		0			0		0.992658	+	0.120958i	$0.0385965\pi$
$644$	0.925300	−	3.49173i	0.925300	−	3.49173i
$645$		0			0
$646$		0			0
$647$		0			0		0.930586	−	0.366074i	$-0.119298\pi$
$647$		0			0		−0.930586	+	0.366074i	$0.880702\pi$
$648$	1.85843	−	2.41506i	1.85843	−	2.41506i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.289275	−	0.527566i	−0.289275	−	0.527566i
$653$	0.520677	−	0.116686i	0.520677	−	0.116686i	0.0495838	−	0.998770i	$-0.484211\pi$
$653$	0.520677	−	0.116686i	0.520677	−	0.116686i	0.471093	+	0.882084i	$0.343860\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.671663	−	0.402737i	−0.671663	−	0.402737i	0.137354	−	0.990522i	$-0.456140\pi$
$659$	−0.671663	−	0.402737i	−0.671663	−	0.402737i	−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	$0.200000\pi$
$662$	−3.39930	+	1.65022i	−3.39930	+	1.65022i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−2.45645	−	0.326842i	−2.45645	−	0.326842i
$667$	−0.0606269	−	0.376073i	−0.0606269	−	0.376073i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.531208	−	0.272511i	0.531208	−	0.272511i	−0.170028	−	0.985439i	$-0.554386\pi$
$673$	0.531208	−	0.272511i	0.531208	−	0.272511i	0.701237	+	0.712928i	$0.252632\pi$
$674$	0.814482	−	0.362631i	0.814482	−	0.362631i
$675$		0			0
$676$	2.33075	+	1.16341i	2.33075	+	1.16341i
$677$		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
$683$	−0.635085	−	1.88368i	−0.635085	−	1.88368i	−0.421786	−	0.906696i	$-0.638596\pi$
$683$	−0.635085	−	1.88368i	−0.635085	−	1.88368i	−0.213300	−	0.976987i	$-0.568421\pi$
$684$		0			0
$685$		0			0
$686$	−1.65977	+	0.922022i	−1.65977	+	0.922022i
$687$		0			0
$688$	2.29240	−	5.73447i	2.29240	−	5.73447i
$689$		0			0
$690$		0			0
$691$		0			0		0.340293	−	0.940319i	$-0.389474\pi$
$691$		0			0		−0.340293	+	0.940319i	$0.610526\pi$
$692$		0			0
$693$	0.648982	+	1.62344i	0.648982	+	1.62344i
$694$	0.658590	−	1.37588i	0.658590	−	1.37588i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	2.58917	−	0.286569i	2.58917	−	0.286569i
$701$	0.0948019	+	1.56177i	0.0948019	+	1.56177i	0.669131	+	0.743145i	$0.266667\pi$
$701$	0.0948019	+	1.56177i	0.0948019	+	1.56177i	−0.574329	+	0.818625i	$0.694737\pi$
$702$		0			0
$703$		0			0
$704$	−0.552671	+	4.33639i	−0.552671	+	4.33639i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.658830	+	1.82052i	0.658830	+	1.82052i	0.565270	+	0.824906i	$0.308772\pi$
$709$	0.658830	+	1.82052i	0.658830	+	1.82052i	0.0935596	+	0.995614i	$0.470175\pi$
$710$		0			0
$711$	0.00199386	−	0.0108413i	0.00199386	−	0.0108413i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.948495	−	3.92692i	−0.948495	−	3.92692i
$717$		0			0
$718$	−1.67626	+	3.40504i	−1.67626	+	3.40504i
$719$		0			0		−0.0165339	−	0.999863i	$-0.505263\pi$
$719$		0			0		0.0165339	+	0.999863i	$0.494737\pi$
$720$		0			0
$721$		0			0
$722$	−0.626388	−	1.79238i	−0.626388	−	1.79238i
$723$		0			0
$724$		0			0
$725$	0.237143	−	0.138663i	0.237143	−	0.138663i
$726$		0			0
$727$		0			0		−0.995083	−	0.0990455i	$-0.968421\pi$
$727$		0			0		0.995083	+	0.0990455i	$0.0315789\pi$
$728$		0			0
$729$	−0.999453	−	0.0330634i	−0.999453	−	0.0330634i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.115485	−	0.993309i	$-0.536842\pi$
$733$		0			0		0.115485	+	0.993309i	$0.463158\pi$
$734$		0			0
$735$		0			0
$736$	−4.10670	−	0.592555i	−4.10670	−	0.592555i
$737$	−2.27177	+	2.30965i	−2.27177	+	2.30965i
$738$		0			0
$739$	1.88150	+	0.669193i	1.88150	+	0.669193i	0.959210	+	0.282694i	$0.0912281\pi$
$739$	1.88150	+	0.669193i	1.88150	+	0.669193i	0.922290	+	0.386499i	$0.126316\pi$
$740$		0			0
$741$		0			0
$742$	−2.18080	−	3.10842i	−2.18080	−	3.10842i
$743$	0.586152	+	1.42063i	0.586152	+	1.42063i	0.884667	+	0.466224i	$0.154386\pi$
$743$	0.586152	+	1.42063i	0.586152	+	1.42063i	−0.298515	+	0.954405i	$0.596491\pi$
$744$		0			0
$745$		0			0
$746$	−1.80288	+	2.18911i	−1.80288	+	2.18911i
$747$		0			0
$748$		0			0
$749$	−0.00882237	−	0.0318693i	−0.00882237	−	0.0318693i
$750$		0			0
$751$	0.577971	+	0.928740i	0.577971	+	0.928740i	0.999757	+	0.0220445i	$0.00701754\pi$
$751$	0.577971	+	0.928740i	0.577971	+	0.928740i	−0.421786	+	0.906696i	$0.638596\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.17227	+	0.446291i	1.17227	+	0.446291i	0.863256	−	0.504766i	$-0.168421\pi$
$757$	1.17227	+	0.446291i	1.17227	+	0.446291i	0.309017	+	0.951057i	$0.400000\pi$
$758$	−0.919885	+	1.31117i	−0.919885	+	1.31117i
$759$		0			0
$760$		0			0
$761$		0			0		−0.868768	−	0.495219i	$-0.835088\pi$
$761$		0			0		0.868768	+	0.495219i	$0.164912\pi$
$762$		0			0
$763$	−0.124308	+	0.540701i	−0.124308	+	0.540701i
$764$	0.0329967	−	0.313942i	0.0329967	−	0.313942i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.298515	−	0.954405i	$-0.403509\pi$
$769$		0			0		−0.298515	+	0.954405i	$0.596491\pi$
$770$		0			0
$771$		0			0
$772$	2.44145	−	2.03338i	2.44145	−	2.03338i
$773$		0			0		−0.0715891	−	0.997434i	$-0.522807\pi$
$773$		0			0		0.0715891	+	0.997434i	$0.477193\pi$
$774$	−3.57837	+	0.885209i	−3.57837	+	0.885209i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	3.35474	+	1.11050i	3.35474	+	1.11050i
$779$		0			0
$780$		0			0
$781$	−2.26562	−	2.57270i	−2.26562	−	2.57270i
$782$		0			0
$783$		0			0
$784$	1.85549	+	2.58369i	1.85549	+	2.58369i
$785$		0			0
$786$		0			0
$787$		0			0		0.922290	−	0.386499i	$-0.126316\pi$
$787$		0			0		−0.922290	+	0.386499i	$0.873684\pi$
$788$	5.02850	+	1.01104i	5.02850	+	1.01104i
$789$		0			0
$790$		0			0
$791$	−0.258824	−	1.86650i	−0.258824	−	1.86650i
$792$	4.68566	−	2.53575i	4.68566	−	2.53575i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.518970	−	0.854793i	$-0.326316\pi$
$797$		0			0		−0.518970	+	0.854793i	$0.673684\pi$
$798$		0			0
$799$		0			0
$800$	−0.670426	−	2.91615i	−0.670426	−	2.91615i
$801$		0			0
$802$	0.501900	−	3.61944i	0.501900	−	3.61944i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.77726	−	0.460501i	1.77726	−	0.460501i	0.789141	−	0.614213i	$-0.210526\pi$
$809$	1.77726	−	0.460501i	1.77726	−	0.460501i	0.988116	+	0.153712i	$0.0491228\pi$
$810$		0			0
$811$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$811$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$812$	0.617751	+	0.361213i	0.617751	+	0.361213i
$813$		0			0
$814$	−3.69101	−	2.26886i	−3.69101	−	2.26886i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.903754	+	1.69221i	0.903754	+	1.69221i	0.701237	+	0.712928i	$0.252632\pi$
$821$	0.903754	+	1.69221i	0.903754	+	1.69221i	0.202517	+	0.979279i	$0.435088\pi$
$822$		0			0
$823$	1.25128	−	0.788296i	1.25128	−	0.788296i	0.266796	−	0.963753i	$-0.414035\pi$
$823$	1.25128	−	0.788296i	1.25128	−	0.788296i	0.984487	+	0.175457i	$0.0561404\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.28643	−	0.0709744i	1.28643	−	0.0709744i	0.601081	−	0.799188i	$-0.294737\pi$
$827$	1.28643	−	0.0709744i	1.28643	−	0.0709744i	0.685350	+	0.728214i	$0.259649\pi$
$828$	1.66648	+	3.20487i	1.66648	+	3.20487i
$829$		0			0		−0.962268	−	0.272103i	$-0.912281\pi$
$829$		0			0		0.962268	+	0.272103i	$0.0877193\pi$
$830$		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		−0.828009	−	0.560715i	$-0.810526\pi$
$839$		0			0		0.828009	+	0.560715i	$0.189474\pi$
$840$		0			0
$841$	−0.918925	−	0.101707i	−0.918925	−	0.101707i
$842$	−3.01755	+	1.03593i	−3.01755	+	1.03593i
$843$		0			0
$844$	−1.63786	+	2.39015i	−1.63786	+	2.39015i
$845$		0			0
$846$		0			0
$847$	−0.0793306	+	2.05519i	−0.0793306	+	2.05519i
$848$	−4.75089	+	4.23054i	−4.75089	+	4.23054i
$849$		0			0
$850$		0			0
$851$	0.973129	−	1.52596i	0.973129	−	1.52596i
$852$		0			0
$853$		0			0		0.775409	−	0.631460i	$-0.217544\pi$
$853$		0			0		−0.775409	+	0.631460i	$0.782456\pi$
$854$		0			0
$855$		0			0
$856$	−0.0933618	+	0.0379203i	−0.0933618	+	0.0379203i
$857$		0			0		0.926494	−	0.376309i	$-0.122807\pi$
$857$		0			0		−0.926494	+	0.376309i	$0.877193\pi$
$858$		0			0
$859$		0			0		−0.627176	−	0.778877i	$-0.715789\pi$
$859$		0			0		0.627176	+	0.778877i	$0.284211\pi$
$860$		0			0
$861$		0			0
$862$	−1.50979	+	2.36750i	−1.50979	+	2.36750i
$863$	−1.60967	+	0.965176i	−1.60967	+	0.965176i	−0.627176	+	0.778877i	$0.715789\pi$
$863$	−1.60967	+	0.965176i	−1.60967	+	0.965176i	−0.982493	+	0.186298i	$0.940351\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.0108940	−	0.0158977i	0.0108940	−	0.0158977i
$870$		0			0
$871$		0			0
$872$	1.68042	+	0.185989i	1.68042	+	0.185989i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.268536	−	0.411024i	0.268536	−	0.411024i	−0.677282	−	0.735724i	$-0.736842\pi$
$877$	0.268536	−	0.411024i	0.268536	−	0.411024i	0.945817	+	0.324699i	$0.105263\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.556143	−	0.831087i	$-0.312281\pi$
$881$		0			0		−0.556143	+	0.831087i	$0.687719\pi$
$882$	0.606593	−	1.79917i	0.606593	−	1.79917i
$883$	1.18392	+	0.623930i	1.18392	+	0.623930i	0.938430	−	0.345471i	$-0.112281\pi$
$883$	1.18392	+	0.623930i	1.18392	+	0.623930i	0.245485	+	0.969400i	$0.421053\pi$
$884$		0			0
$885$		0			0
$886$	−0.726888	+	0.0401035i	−0.726888	+	0.0401035i
$887$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$887$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$888$		0			0
$889$	−1.32321	−	1.20469i	−1.32321	−	1.20469i
$890$		0			0
$891$	−1.57281	−	0.763537i	−1.57281	−	0.763537i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	1.29782	−	1.18158i	1.29782	−	1.18158i
$897$		0			0
$898$	−0.0200756	+	3.64241i	−0.0200756	+	3.64241i
$899$		0			0
$900$	−1.72163	+	1.95497i	−1.72163	+	1.95497i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−5.55871	+	1.44031i	−5.55871	+	1.44031i
$905$		0			0
$906$		0			0
$907$	−1.22744	−	1.09300i	−1.22744	−	1.09300i	−0.992658	−	0.120958i	$-0.961404\pi$
$907$	−1.22744	−	1.09300i	−1.22744	−	1.09300i	−0.234785	−	0.972047i	$-0.575439\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.274557	+	1.97996i	−0.274557	+	1.97996i	−0.104528	+	0.994522i	$0.533333\pi$
$911$	−0.274557	+	1.97996i	−0.274557	+	1.97996i	−0.170028	+	0.985439i	$0.554386\pi$
$912$		0			0
$913$		0			0
$914$	−1.23598	+	1.53494i	−1.23598	+	1.53494i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.0944814	+	0.0301242i	0.0944814	+	0.0301242i	0.350638	−	0.936511i	$-0.385965\pi$
$919$	0.0944814	+	0.0301242i	0.0944814	+	0.0301242i	−0.256156	+	0.966635i	$0.582456\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	1.27956	+	0.257272i	1.27956	+	0.257272i
$926$	−3.16730	+	1.32730i	−3.16730	+	1.32730i
$927$		0			0
$928$	0.330188	−	0.752753i	0.330188	−	0.752753i
$929$		0			0		−0.583317	−	0.812244i	$-0.698246\pi$
$929$		0			0		0.583317	+	0.812244i	$0.301754\pi$
$930$		0			0
$931$		0			0
$932$	1.58851	+	1.80382i	1.58851	+	1.80382i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.782322	−	0.622874i	$-0.785965\pi$
$937$		0			0		0.782322	+	0.622874i	$0.214035\pi$
$938$	3.50456	−	0.309853i	3.50456	−	0.309853i
$939$		0			0
$940$		0			0
$941$		0			0		0.768401	−	0.639969i	$-0.221053\pi$
$941$		0			0		−0.768401	+	0.639969i	$0.778947\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−6.34485	−	1.13079i	−6.34485	−	1.13079i
$947$	−1.12641	−	0.781036i	−1.12641	−	0.781036i	−0.148264	−	0.988948i	$-0.547368\pi$
$947$	−1.12641	−	0.781036i	−1.12641	−	0.781036i	−0.978148	+	0.207912i	$0.933333\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.352703	−	1.22155i	−0.352703	−	1.22155i	−0.917973	−	0.396642i	$-0.870175\pi$
$953$	−0.352703	−	1.22155i	−0.352703	−	1.22155i	0.565270	−	0.824906i	$-0.308772\pi$
$954$	3.70522	+	0.830359i	3.70522	+	0.830359i
$955$		0			0
$956$	−2.19853	−	0.836994i	−2.19853	−	0.836994i
$957$		0			0
$958$		0			0
$959$	1.91097	+	0.563191i	1.91097	+	0.563191i
$960$		0			0
$961$	0.546948	+	0.837166i	0.546948	+	0.837166i
$962$		0			0
$963$	0.0279786	+	0.0176262i	0.0279786	+	0.0176262i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1.16153	−	1.41036i	1.16153	−	1.41036i	0.266796	−	0.963753i	$-0.414035\pi$
$967$	1.16153	−	1.41036i	1.16153	−	1.41036i	0.894729	−	0.446609i	$-0.147368\pi$
$968$	6.24887	−	0.483134i	6.24887	−	0.483134i
$969$		0			0
$970$		0			0
$971$		0			0		−0.574329	−	0.818625i	$-0.694737\pi$
$971$		0			0		0.574329	+	0.818625i	$0.305263\pi$
$972$		0			0
$973$		0			0
$974$	−0.763142	−	0.271427i	−0.763142	−	0.271427i
$975$		0			0
$976$		0			0
$977$	−1.63904	−	0.236497i	−1.63904	−	0.236497i	−0.739446	−	0.673216i	$-0.764912\pi$
$977$	−1.63904	−	0.236497i	−1.63904	−	0.236497i	−0.899598	+	0.436719i	$0.856140\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−0.272090	−	0.483505i	−0.272090	−	0.483505i
$982$	−3.49460	−	0.231467i	−3.49460	−	0.231467i
$983$		0			0		−0.938430	−	0.345471i	$-0.887719\pi$
$983$		0			0		0.938430	+	0.345471i	$0.112281\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.516122	−	2.64225i	0.516122	−	2.64225i
$990$		0			0
$991$	−0.497571	−	1.42377i	−0.497571	−	1.42377i	−0.868768	−	0.495219i	$-0.835088\pi$
$991$	−0.497571	−	1.42377i	−0.497571	−	1.42377i	0.371197	−	0.928554i	$-0.378947\pi$
$992$		0			0
$993$		0			0
$994$	0.0615534	+	3.72234i	0.0615534	+	3.72234i
$995$		0			0
$996$		0			0
$997$		0			0		−0.234785	−	0.972047i	$-0.575439\pi$
$997$		0			0		0.234785	+	0.972047i	$0.424561\pi$
$998$	−1.29986	−	0.722085i	−1.29986	−	0.722085i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3997.1.cz.a.244.1	✓	144
7.6	odd	2	CM	3997.1.cz.a.244.1	✓	144
571.227	even	285	inner	3997.1.cz.a.3653.1	yes	144
3997.3653	odd	570	inner	3997.1.cz.a.3653.1	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3997.1.cz.a.244.1	✓	144	1.1	even	1	trivial
3997.1.cz.a.244.1	✓	144	7.6	odd	2	CM
3997.1.cz.a.3653.1	yes	144	571.227	even	285	inner
3997.1.cz.a.3653.1	yes	144	3997.3653	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)

\(f(q)\)	\(=\)	\(q+(1.75911 + 0.714490i) q^{2} +(1.86720 + 1.81644i) q^{4} +(-0.956036 + 0.293250i) q^{7} +(1.22410 + 2.79067i) q^{8} +(0.509516 - 0.860461i) q^{9} +O(q^{10})\)	\(q+(1.75911 + 0.714490i) q^{2} +(1.86720 + 1.81644i) q^{4} +(-0.956036 + 0.293250i) q^{7} +(1.22410 + 2.79067i) q^{8} +(0.509516 - 0.860461i) q^{9} +(1.42569 - 1.01200i) q^{11} +(-1.89130 - 0.167218i) q^{14} +(0.0876484 + 3.17972i) q^{16} +(1.51109 - 1.14961i) q^{18} +(3.23101 - 0.761584i) q^{22} +(0.295776 + 1.35476i) q^{23} +(-0.834139 + 0.551554i) q^{25} +(-2.31778 - 1.18903i) q^{28} +(-0.274290 - 0.0151330i) q^{29} +(-1.04919 + 2.80225i) q^{32} +(2.51435 - 0.681149i) q^{36} +(-0.925435 - 0.920349i) q^{37} +(-1.78222 - 0.770071i) q^{43} +(4.50028 + 0.700067i) q^{44} +(-0.447658 + 2.59451i) q^{46} +(0.828009 - 0.560715i) q^{49} +(-1.86143 + 0.374262i) q^{50} +(1.28831 + 1.52963i) q^{53} +(-1.98865 - 2.30901i) q^{56} +(-0.471695 - 0.222598i) q^{58} +(-0.234785 + 0.972047i) q^{63} +(-1.69344 + 1.83956i) q^{64} +(-1.82424 + 0.325120i) q^{67} +(-0.204955 - 1.95002i) q^{71} +(3.02496 + 0.368598i) q^{72} +(-0.970366 - 2.28021i) q^{74} +(-1.06624 + 1.38559i) q^{77} +(0.0103444 - 0.00380815i) q^{79} +(-0.480787 - 0.876837i) q^{81} +(-2.58493 - 2.62803i) q^{86} +(4.56934 + 2.73982i) q^{88} +(-1.90857 + 3.06687i) q^{92} +(1.85719 - 0.394757i) q^{98} +(-0.144377 - 1.74238i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9}+O(q^{10}) \) 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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