LMFDB - Embedded newform 3997.1.cz.a.279.1

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			279.1
Root			$0.997024 + 0.0770854i$ of defining polynomial
Character	$\chi$	$=$	3997.279
Dual form			3997.1.cz.a.3338.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.98014 - 0.219162i) q^{2} +(2.89711 - 0.649259i) q^{4} +(-0.627176 - 0.778877i) q^{7} +(3.71011 - 1.27368i) q^{8} +(0.528360 + 0.849020i) q^{9} +O(q^{10})$	\(q+(1.98014 - 0.219162i) q^{2} +(2.89711 - 0.649259i) q^{4} +(-0.627176 - 0.778877i) q^{7} +(3.71011 - 1.27368i) q^{8} +(0.528360 + 0.849020i) q^{9} +(-1.16504 - 1.21088i) q^{11} +(-1.41260 - 1.40483i) q^{14} +(4.38236 - 2.06809i) q^{16} +(1.23230 + 1.56538i) q^{18} +(-2.57231 - 2.14237i) q^{22} +(-1.14126 + 1.51740i) q^{23} +(0.761300 + 0.648400i) q^{25} +(-2.32269 - 1.84930i) q^{28} +(-0.752996 - 0.914313i) q^{29} +(4.88266 - 3.00136i) q^{32} +(2.08195 + 2.11667i) q^{36} +(-0.451469 + 1.63085i) q^{37} +(-0.260921 - 0.309796i) q^{43} +(-4.16142 - 2.75163i) q^{44} +(-1.92729 + 3.25478i) q^{46} +(-0.213300 + 0.976987i) q^{49} +(1.64958 + 1.11707i) q^{50} +(-0.818541 + 0.466589i) q^{53} +(-3.31893 - 2.09089i) q^{56} +(-1.69142 - 1.64544i) q^{58} +(0.329907 - 0.944013i) q^{63} +(5.18650 - 4.03682i) q^{64} +(0.0109562 - 1.98783i) q^{67} +(1.10809 + 1.23066i) q^{71} +(3.04165 + 2.47699i) q^{72} +(-0.536551 + 3.32826i) q^{74} +(-0.212440 + 1.66685i) q^{77} +(1.71518 + 0.0189074i) q^{79} +(-0.441671 + 0.897177i) q^{81} +(-0.584555 - 0.556254i) q^{86} +(-5.86468 - 3.00859i) q^{88} +(-2.32117 + 5.13706i) q^{92} +(-0.208245 + 1.98131i) q^{98} +(0.412498 - 1.62892i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3997\mathbb{Z}\right)^\times$.

$n$	$1716$	$2285$
$\chi(n)$	$e\left(\frac{46}{285}\right)$	$-1$

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 $

$2$	1.98014	−	0.219162i	1.98014	−	0.219162i	0.980380	−	0.197117i	$-0.0631579\pi$
$2$	1.98014	−	0.219162i	1.98014	−	0.219162i	0.999757	−	0.0220445i	$-0.00701754\pi$
$3$		0			0		−0.874174	−	0.485613i	$-0.838596\pi$
$3$		0			0		0.874174	+	0.485613i	$0.161404\pi$
$4$	2.89711	−	0.649259i	2.89711	−	0.649259i
$5$		0			0		−0.938430	−	0.345471i	$-0.887719\pi$
$5$		0			0		0.938430	+	0.345471i	$0.112281\pi$
$6$		0			0
$7$	−0.627176	−	0.778877i	−0.627176	−	0.778877i
$7$	−0.627176	−	0.778877i	−0.627176	−	0.778877i
$8$	3.71011	−	1.27368i	3.71011	−	1.27368i
$9$	0.528360	+	0.849020i	0.528360	+	0.849020i
$10$		0			0
$11$	−1.16504	−	1.21088i	−1.16504	−	1.21088i	−0.973327	−	0.229424i	$-0.926316\pi$
$11$	−1.16504	−	1.21088i	−1.16504	−	1.21088i	−0.191711	−	0.981451i	$-0.561404\pi$
$12$		0			0
$13$		0			0		0.834139	−	0.551554i	$-0.185965\pi$
$13$		0			0		−0.834139	+	0.551554i	$0.814035\pi$
$14$	−1.41260	−	1.40483i	−1.41260	−	1.40483i
$15$		0			0
$16$	4.38236	−	2.06809i	4.38236	−	2.06809i
$17$		0			0		0.480787	−	0.876837i	$-0.340351\pi$
$17$		0			0		−0.480787	+	0.876837i	$0.659649\pi$
$18$	1.23230	+	1.56538i	1.23230	+	1.56538i
$19$		0			0		0.731980	−	0.681326i	$-0.238596\pi$
$19$		0			0		−0.731980	+	0.681326i	$0.761404\pi$
$20$		0			0
$21$		0			0
$22$	−2.57231	−	2.14237i	−2.57231	−	2.14237i
$23$	−1.14126	+	1.51740i	−1.14126	+	1.51740i	−0.319482	+	0.947592i	$0.603509\pi$
$23$	−1.14126	+	1.51740i	−1.14126	+	1.51740i	−0.821778	+	0.569808i	$0.807018\pi$
$24$		0			0
$25$	0.761300	+	0.648400i	0.761300	+	0.648400i
$26$		0			0
$27$		0			0
$28$	−2.32269	−	1.84930i	−2.32269	−	1.84930i
$29$	−0.752996	−	0.914313i	−0.752996	−	0.914313i	0.245485	−	0.969400i	$-0.421053\pi$
$29$	−0.752996	−	0.914313i	−0.752996	−	0.914313i	−0.998482	+	0.0550878i	$0.982456\pi$
$30$		0			0
$31$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$31$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$32$	4.88266	−	3.00136i	4.88266	−	3.00136i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	2.08195	+	2.11667i	2.08195	+	2.11667i
$37$	−0.451469	+	1.63085i	−0.451469	+	1.63085i	0.287976	+	0.957638i	$0.407018\pi$
$37$	−0.451469	+	1.63085i	−0.451469	+	1.63085i	−0.739446	+	0.673216i	$0.764912\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.962268	−	0.272103i	$-0.0877193\pi$
$41$		0			0		−0.962268	+	0.272103i	$0.912281\pi$
$42$		0			0
$43$	−0.260921	−	0.309796i	−0.260921	−	0.309796i	0.618553	−	0.785743i	$-0.287719\pi$
$43$	−0.260921	−	0.309796i	−0.260921	−	0.309796i	−0.879474	+	0.475947i	$0.842105\pi$
$44$	−4.16142	−	2.75163i	−4.16142	−	2.75163i
$45$		0			0
$46$	−1.92729	+	3.25478i	−1.92729	+	3.25478i
$47$		0			0		−0.821778	−	0.569808i	$-0.807018\pi$
$47$		0			0		0.821778	+	0.569808i	$0.192982\pi$
$48$		0			0
$49$	−0.213300	+	0.976987i	−0.213300	+	0.976987i
$50$	1.64958	+	1.11707i	1.64958	+	1.11707i
$51$		0			0
$52$		0			0
$53$	−0.818541	+	0.466589i	−0.818541	+	0.466589i	−0.846095	−	0.533032i	$-0.821053\pi$
$53$	−0.818541	+	0.466589i	−0.818541	+	0.466589i	0.0275543	+	0.999620i	$0.491228\pi$
$54$		0			0
$55$		0			0
$56$	−3.31893	−	2.09089i	−3.31893	−	2.09089i
$57$		0			0
$58$	−1.69142	−	1.64544i	−1.69142	−	1.64544i
$59$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$59$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$60$		0			0
$61$		0			0		0.949339	−	0.314254i	$-0.101754\pi$
$61$		0			0		−0.949339	+	0.314254i	$0.898246\pi$
$62$		0			0
$63$	0.329907	−	0.944013i	0.329907	−	0.944013i
$64$	5.18650	−	4.03682i	5.18650	−	4.03682i
$65$		0			0
$66$		0			0
$67$	0.0109562	−	1.98783i	0.0109562	−	1.98783i	−0.104528	−	0.994522i	$-0.533333\pi$
$67$	0.0109562	−	1.98783i	0.0109562	−	1.98783i	0.115485	−	0.993309i	$-0.463158\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.10809	+	1.23066i	1.10809	+	1.23066i	0.970739	+	0.240139i	$0.0771930\pi$
$71$	1.10809	+	1.23066i	1.10809	+	1.23066i	0.137354	+	0.990522i	$0.456140\pi$
$72$	3.04165	+	2.47699i	3.04165	+	2.47699i
$73$		0			0		0.968033	−	0.250825i	$-0.0807018\pi$
$73$		0			0		−0.968033	+	0.250825i	$0.919298\pi$
$74$	−0.536551	+	3.32826i	−0.536551	+	3.32826i
$75$		0			0
$76$		0			0
$77$	−0.212440	+	1.66685i	−0.212440	+	1.66685i
$78$		0			0
$79$	1.71518	+	0.0189074i	1.71518	+	0.0189074i	0.863256	−	0.504766i	$-0.168421\pi$
$79$	1.71518	+	0.0189074i	1.71518	+	0.0189074i	0.851919	+	0.523673i	$0.175439\pi$
$80$		0			0
$81$	−0.441671	+	0.897177i	−0.441671	+	0.897177i
$82$		0			0
$83$		0			0		0.795863	−	0.605477i	$-0.207018\pi$
$83$		0			0		−0.795863	+	0.605477i	$0.792982\pi$
$84$		0			0
$85$		0			0
$86$	−0.584555	−	0.556254i	−0.584555	−	0.556254i
$87$		0			0
$88$	−5.86468	−	3.00859i	−5.86468	−	3.00859i
$89$		0			0		−0.126427	−	0.991976i	$-0.540351\pi$
$89$		0			0		0.126427	+	0.991976i	$0.459649\pi$
$90$		0			0
$91$		0			0
$92$	−2.32117	+	5.13706i	−2.32117	+	5.13706i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.917973	−	0.396642i	$-0.870175\pi$
$97$		0			0		0.917973	+	0.396642i	$0.129825\pi$
$98$	−0.208245	+	1.98131i	−0.208245	+	1.98131i
$99$	0.412498	−	1.62892i	0.412498	−	1.62892i
$100$	2.62655	+	1.38421i	2.62655	+	1.38421i
$101$		0			0		−0.660898	−	0.750475i	$-0.729825\pi$
$101$		0			0		0.660898	+	0.750475i	$0.270175\pi$
$102$		0			0
$103$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$103$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$104$		0			0
$105$		0			0
$106$	−1.51856	+	1.10330i	−1.51856	+	1.10330i
$107$	0.0896828	+	0.0423224i	0.0896828	+	0.0423224i	0.471093	−	0.882084i	$-0.343860\pi$
$107$	0.0896828	+	0.0423224i	0.0896828	+	0.0423224i	−0.381410	+	0.924406i	$0.624561\pi$
$108$		0			0
$109$	−0.746821	+	1.29353i	−0.746821	+	1.29353i	0.202517	+	0.979279i	$0.435088\pi$
$109$	−0.746821	+	1.29353i	−0.746821	+	1.29353i	−0.949339	+	0.314254i	$0.898246\pi$
$110$		0			0
$111$		0			0
$112$	−4.35930	−	2.11627i	−4.35930	−	2.11627i
$113$	−0.960640	−	0.0423845i	−0.960640	−	0.0423845i	−0.441671	−	0.897177i	$-0.645614\pi$
$113$	−0.960640	−	0.0423845i	−0.960640	−	0.0423845i	−0.518970	+	0.854793i	$0.673684\pi$
$114$		0			0
$115$		0			0
$116$	−2.77514	−	2.15998i	−2.77514	−	2.15998i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.0703361	+	1.82217i	−0.0703361	+	1.82217i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	0.446371	−	1.94158i	0.446371	−	1.94158i
$127$	0.191140	−	0.307142i	0.191140	−	0.307142i	−0.739446	−	0.673216i	$-0.764912\pi$
$127$	0.191140	−	0.307142i	0.191140	−	0.307142i	0.930586	+	0.366074i	$0.119298\pi$
$128$	5.27714	−	5.13368i	5.27714	−	5.13368i
$129$		0			0
$130$		0			0
$131$		0			0		−0.677282	−	0.735724i	$-0.736842\pi$
$131$		0			0		0.677282	+	0.735724i	$0.263158\pi$
$132$		0			0
$133$		0			0
$134$	−0.413961	−	3.93858i	−0.413961	−	3.93858i
$135$		0			0
$136$		0			0
$137$	−1.07960	+	0.919499i	−1.07960	+	0.919499i	−0.997024	−	0.0770854i	$-0.975439\pi$
$137$	−1.07960	+	0.919499i	−1.07960	+	0.919499i	−0.0825793	+	0.996584i	$0.526316\pi$
$138$		0			0
$139$		0			0		−0.471093	−	0.882084i	$-0.656140\pi$
$139$		0			0		0.471093	+	0.882084i	$0.343860\pi$
$140$		0			0
$141$		0			0
$142$	2.46389	+	2.19403i	2.46389	+	2.19403i
$143$		0			0
$144$	4.07132	+	2.62802i	4.07132	+	2.62802i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−0.249112	+	5.01789i	−0.249112	+	5.01789i
$149$	−0.987910	−	1.31351i	−0.987910	−	1.31351i	−0.949339	−	0.314254i	$-0.898246\pi$
$149$	−0.987910	−	1.31351i	−0.987910	−	1.31351i	−0.0385714	−	0.999256i	$-0.512281\pi$
$150$		0			0
$151$	0.00806362	+	0.208901i	0.00806362	+	0.208901i	0.997814	+	0.0660906i	$0.0210526\pi$
$151$	0.00806362	+	0.208901i	0.00806362	+	0.208901i	−0.989750	+	0.142811i	$0.954386\pi$
$152$		0			0
$153$		0			0
$154$	−0.0553493	+	3.34716i	−0.0553493	+	3.34716i
$155$		0			0
$156$		0			0
$157$		0			0		0.999757	−	0.0220445i	$-0.00701754\pi$
$157$		0			0		−0.999757	+	0.0220445i	$0.992982\pi$
$158$	3.40043	−	0.338461i	3.40043	−	0.338461i
$159$		0			0
$160$		0			0
$161$	1.89764	−	0.0627767i	1.89764	−	0.0627767i
$162$	−0.677942	+	1.87333i	−0.677942	+	1.87333i
$163$	0.426848	−	0.530093i	0.426848	−	0.530093i	−0.518970	−	0.854793i	$-0.673684\pi$
$163$	0.426848	−	0.530093i	0.426848	−	0.530093i	0.945817	+	0.324699i	$0.105263\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$167$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$168$		0			0
$169$	0.391577	−	0.920146i	0.391577	−	0.920146i
$170$		0			0
$171$		0			0
$172$	−0.957056	−	0.728109i	−0.957056	−	0.728109i
$173$		0			0		0.256156	−	0.966635i	$-0.417544\pi$
$173$		0			0		−0.256156	+	0.966635i	$0.582456\pi$
$174$		0			0
$175$	0.0275543	−	0.999620i	0.0275543	−	0.999620i
$176$	−7.60981	−	2.89710i	−7.60981	−	2.89710i
$177$		0			0
$178$		0			0
$179$	−0.124189	−	1.06818i	−0.124189	−	1.06818i	−0.899598	−	0.436719i	$-0.856140\pi$
$179$	−0.124189	−	1.06818i	−0.124189	−	1.06818i	0.775409	−	0.631460i	$-0.217544\pi$
$180$		0			0
$181$		0			0		−0.986361	−	0.164595i	$-0.947368\pi$
$181$		0			0		0.986361	+	0.164595i	$0.0526316\pi$
$182$		0			0
$183$		0			0
$184$	−2.30151	+	7.08332i	−2.30151	+	7.08332i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.53660	+	1.09073i	−1.53660	+	1.09073i	−0.574329	+	0.818625i	$0.694737\pi$
$191$	−1.53660	+	1.09073i	−1.53660	+	1.09073i	−0.962268	+	0.272103i	$0.912281\pi$
$192$		0			0
$193$	−0.169192	+	0.187907i	−0.169192	+	0.187907i	−0.821778	−	0.569808i	$-0.807018\pi$
$193$	−0.169192	+	0.187907i	−0.169192	+	0.187907i	0.652586	+	0.757715i	$0.273684\pi$
$194$		0			0
$195$		0			0
$196$	0.0163636	+	2.96893i	0.0163636	+	2.96893i
$197$	0.0102579	−	0.00403526i	0.0102579	−	0.00403526i	−0.360939	−	0.932589i	$-0.617544\pi$
$197$	0.0102579	−	0.00403526i	0.0102579	−	0.00403526i	0.371197	+	0.928554i	$0.378947\pi$
$198$	0.459807	−	3.31589i	0.459807	−	3.31589i
$199$		0			0		0.360939	−	0.932589i	$-0.382456\pi$
$199$		0			0		−0.360939	+	0.932589i	$0.617544\pi$
$200$	3.65036	+	1.43598i	3.65036	+	1.43598i
$201$		0			0
$202$		0			0
$203$	−0.239876	+	1.15993i	−0.239876	+	1.15993i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.89130	−	0.167218i	−1.89130	−	0.167218i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.325562	−	0.549803i	−0.325562	−	0.549803i	0.652586	−	0.757715i	$-0.273684\pi$
$211$	−0.325562	−	0.549803i	−0.325562	−	0.549803i	−0.978148	+	0.207912i	$0.933333\pi$
$212$	−2.06847	+	1.88321i	−2.06847	+	1.88321i
$213$		0			0
$214$	0.186860	+	0.0641490i	0.186860	+	0.0641490i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−1.19532	+	2.72505i	−1.19532	+	2.72505i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.391577	−	0.920146i	$-0.628070\pi$
$223$		0			0		0.391577	+	0.920146i	$0.371930\pi$
$224$	−5.39998	−	1.92061i	−5.39998	−	1.92061i
$225$	−0.148264	+	0.988948i	−0.148264	+	0.988948i
$226$	−1.91149	+	0.126608i	−1.91149	+	0.126608i
$227$		0			0		−0.857640	−	0.514250i	$-0.828070\pi$
$227$		0			0		0.857640	+	0.514250i	$0.171930\pi$
$228$		0			0
$229$		0			0		−0.988116	−	0.153712i	$-0.950877\pi$
$229$		0			0		0.988116	+	0.153712i	$0.0491228\pi$
$230$		0			0
$231$		0			0
$232$	−3.95824	−	2.43312i	−3.95824	−	2.43312i
$233$	0.570921	−	1.89854i	0.570921	−	1.89854i	0.159156	−	0.987253i	$-0.449123\pi$
$233$	0.570921	−	1.89854i	0.570921	−	1.89854i	0.411766	−	0.911290i	$-0.364912\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.451757	+	0.536379i	−0.451757	+	0.536379i	−0.942181	−	0.335105i	$-0.891228\pi$
$239$	−0.451757	+	0.536379i	−0.451757	+	0.536379i	0.490424	+	0.871484i	$0.336842\pi$
$240$		0			0
$241$		0			0		−0.0165339	−	0.999863i	$-0.505263\pi$
$241$		0			0		0.0165339	+	0.999863i	$0.494737\pi$
$242$	0.260075	+	3.62357i	0.260075	+	3.62357i
$243$		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		0.952745	−	0.303771i	$-0.0982456\pi$
$251$		0			0		−0.952745	+	0.303771i	$0.901754\pi$
$252$	0.342871	−	2.94911i	0.342871	−	2.94911i
$253$	3.16699	−	0.385905i	3.16699	−	0.385905i
$254$	0.311170	−	0.650075i	0.311170	−	0.650075i
$255$		0			0
$256$	5.14615	−	6.24862i	5.14615	−	6.24862i
$257$		0			0		0.991264	−	0.131892i	$-0.0421053\pi$
$257$		0			0		−0.991264	+	0.131892i	$0.957895\pi$
$258$		0			0
$259$	1.55339	−	0.671194i	1.55339	−	0.671194i
$260$		0			0
$261$	0.378417	−	1.12240i	0.378417	−	1.12240i
$262$		0			0
$263$	−0.0863258	−	0.918635i	−0.0863258	−	0.918635i	−0.926494	−	0.376309i	$-0.877193\pi$
$263$	−0.0863258	−	0.918635i	−0.0863258	−	0.918635i	0.840168	−	0.542326i	$-0.182456\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−1.25887	−	5.76609i	−1.25887	−	5.76609i
$269$		0			0		−0.148264	−	0.988948i	$-0.547368\pi$
$269$		0			0		0.148264	+	0.988948i	$0.452632\pi$
$270$		0			0
$271$		0			0		−0.546948	−	0.837166i	$-0.684211\pi$
$271$		0			0		0.546948	+	0.837166i	$0.315789\pi$
$272$		0			0
$273$		0			0
$274$	−1.93624	+	2.05734i	−1.93624	+	2.05734i
$275$	−0.101812	−	1.67725i	−0.101812	−	1.67725i
$276$		0			0
$277$	0.0189918	−	0.0270702i	0.0189918	−	0.0270702i	−0.809017	−	0.587785i	$-0.800000\pi$
$277$	0.0189918	−	0.0270702i	0.0189918	−	0.0270702i	0.828009	+	0.560715i	$0.189474\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.439971	+	0.919157i	0.439971	+	0.919157i	0.996114	+	0.0880708i	$0.0280702\pi$
$281$	0.439971	+	0.919157i	0.439971	+	0.919157i	−0.556143	+	0.831087i	$0.687719\pi$
$282$		0			0
$283$		0			0		−0.894729	−	0.446609i	$-0.852632\pi$
$283$		0			0		0.894729	+	0.446609i	$0.147368\pi$
$284$	4.00929	+	2.84593i	4.00929	+	2.84593i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	5.12802	+	2.55968i	5.12802	+	2.55968i
$289$	−0.537687	−	0.843145i	−0.537687	−	0.843145i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.565270	−	0.824906i	$-0.691228\pi$
$293$		0			0		0.565270	+	0.824906i	$0.308772\pi$
$294$		0			0
$295$		0			0
$296$	0.402189	+	6.62567i	0.402189	+	6.62567i
$297$		0			0
$298$	−2.24407	−	2.38442i	−2.24407	−	2.38442i
$299$		0			0
$300$		0			0
$301$	−0.0776495	+	0.397522i	−0.0776495	+	0.397522i
$302$	0.0617502	+	0.411886i	0.0617502	+	0.411886i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.556143	−	0.831087i	$-0.687719\pi$
$307$		0			0		0.556143	+	0.831087i	$0.312281\pi$
$308$	0.466757	+	4.96699i	0.466757	+	4.96699i
$309$		0			0
$310$		0			0
$311$		0			0		0.899598	−	0.436719i	$-0.143860\pi$
$311$		0			0		−0.899598	+	0.436719i	$0.856140\pi$
$312$		0			0
$313$		0			0		−0.298515	−	0.954405i	$-0.596491\pi$
$313$		0			0		0.298515	+	0.954405i	$0.403509\pi$
$314$		0			0
$315$		0			0
$316$	4.98134	−	1.05882i	4.98134	−	1.05882i
$317$	0.503700	−	1.05229i	0.503700	−	1.05229i	−0.480787	−	0.876837i	$-0.659649\pi$
$317$	0.503700	−	1.05229i	0.503700	−	1.05229i	0.984487	−	0.175457i	$-0.0561404\pi$
$318$		0			0
$319$	−0.229850	+	1.97699i	−0.229850	+	1.97699i
$320$		0			0
$321$		0			0
$322$	3.74383	−	0.540196i	3.74383	−	0.540196i
$323$		0			0
$324$	−0.697070	+	2.88598i	−0.697070	+	2.88598i
$325$		0			0
$326$	0.729041	−	1.14321i	0.729041	−	1.14321i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.74676	−	0.777710i	−1.74676	−	0.777710i	−0.992658	−	0.120958i	$-0.961404\pi$
$331$	−1.74676	−	0.777710i	−1.74676	−	0.777710i	−0.754107	−	0.656752i	$-0.771930\pi$
$332$		0			0
$333$	−1.62317	+	0.478372i	−1.62317	+	0.478372i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.626388	−	0.207350i	−0.626388	−	0.207350i	−0.0165339	−	0.999863i	$-0.505263\pi$
$337$	−0.626388	−	0.207350i	−0.626388	−	0.207350i	−0.609854	+	0.792514i	$0.708772\pi$
$338$	0.573715	−	1.90783i	0.573715	−	1.90783i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.894729	−	0.446609i	0.894729	−	0.446609i
$344$	−1.36263	−	0.817046i	−1.36263	−	0.817046i
$345$		0			0
$346$		0			0
$347$	−1.78226	−	0.633897i	−1.78226	−	0.633897i	−0.999939	−	0.0110229i	$-0.996491\pi$
$347$	−1.78226	−	0.633897i	−1.78226	−	0.633897i	−0.782322	−	0.622874i	$-0.785965\pi$
$348$		0			0
$349$		0			0		0.618553	−	0.785743i	$-0.287719\pi$
$349$		0			0		−0.618553	+	0.785743i	$0.712281\pi$
$350$	−0.164517	−	1.98542i	−0.164517	−	1.98542i
$351$		0			0
$352$	−9.32275	−	2.41560i	−9.32275	−	2.41560i
$353$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$353$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−0.480015	−	2.08792i	−0.480015	−	2.08792i
$359$	1.47162	−	1.33981i	1.47162	−	1.33981i	0.669131	−	0.743145i	$-0.266667\pi$
$359$	1.47162	−	1.33981i	1.47162	−	1.33981i	0.802489	−	0.596667i	$-0.203509\pi$
$360$		0			0
$361$	0.0715891	−	0.997434i	0.0715891	−	0.997434i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.709053	−	0.705155i	$-0.249123\pi$
$367$		0			0		−0.709053	+	0.705155i	$0.750877\pi$
$368$	−1.86330	+	9.01003i	−1.86330	+	9.01003i
$369$		0			0
$370$		0			0
$371$	0.876785	+	0.344910i	0.876785	+	0.344910i
$372$		0			0
$373$	−0.157772	+	1.13777i	−0.157772	+	1.13777i	0.731980	+	0.681326i	$0.238596\pi$
$373$	−0.157772	+	1.13777i	−0.157772	+	1.13777i	−0.889752	+	0.456444i	$0.849123\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.506224	+	0.0787486i	−0.506224	+	0.0787486i	−0.401695	−	0.915773i	$-0.631579\pi$
$379$	−0.506224	+	0.0787486i	−0.506224	+	0.0787486i	−0.104528	+	0.994522i	$0.533333\pi$
$380$		0			0
$381$		0			0
$382$	−2.80363	+	2.49655i	−2.80363	+	2.49655i
$383$		0			0		−0.926494	−	0.376309i	$-0.877193\pi$
$383$		0			0		0.926494	+	0.376309i	$0.122807\pi$
$384$		0			0
$385$		0			0
$386$	−0.293841	+	0.409162i	−0.293841	+	0.409162i
$387$	0.125163	−	0.385211i	0.125163	−	0.385211i
$388$		0			0
$389$	1.10836	+	0.222849i	1.10836	+	0.222849i	0.716783	−	0.697297i	$-0.245614\pi$
$389$	1.10836	+	0.222849i	1.10836	+	0.222849i	0.391577	+	0.920146i	$0.371930\pi$
$390$		0			0
$391$		0			0
$392$	0.453005	+	3.89640i	0.453005	+	3.89640i
$393$		0			0
$394$	0.0194277	−	0.0102385i	0.0194277	−	0.0102385i
$395$		0			0
$396$	0.137465	−	4.98698i	0.137465	−	4.98698i
$397$		0			0		−0.287976	−	0.957638i	$-0.592982\pi$
$397$		0			0		0.287976	+	0.957638i	$0.407018\pi$
$398$		0			0
$399$		0			0
$400$	4.67724	+	1.26709i	4.67724	+	1.26709i
$401$	0.404357	−	0.439249i	0.404357	−	0.439249i	−0.500000	−	0.866025i	$-0.666667\pi$
$401$	0.404357	−	0.439249i	0.404357	−	0.439249i	0.904357	+	0.426776i	$0.140351\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−0.220776	+	2.34939i	−0.220776	+	2.34939i
$407$	2.50074	−	1.35333i	2.50074	−	1.35333i
$408$		0			0
$409$		0			0		0.340293	−	0.940319i	$-0.389474\pi$
$409$		0			0		−0.340293	+	0.940319i	$0.610526\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−3.78168	+	0.0833854i	−3.78168	+	0.0833854i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.471093	−	0.882084i	$-0.343860\pi$
$419$		0			0		−0.471093	+	0.882084i	$0.656140\pi$
$420$		0			0
$421$	0.840381	+	1.66064i	0.840381	+	1.66064i	0.746821	+	0.665025i	$0.231579\pi$
$421$	0.840381	+	1.66064i	0.840381	+	1.66064i	0.0935596	+	0.995614i	$0.470175\pi$
$422$	−0.765153	−	1.01733i	−0.765153	−	1.01733i
$423$		0			0
$424$	−2.44259	+	2.77365i	−2.44259	+	2.77365i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.287300	+	0.0643853i	0.287300	+	0.0643853i
$429$		0			0
$430$		0			0
$431$	1.03032	+	1.69703i	1.03032	+	1.69703i	0.618553	+	0.785743i	$0.287719\pi$
$431$	1.03032	+	1.69703i	1.03032	+	1.69703i	0.411766	+	0.911290i	$0.364912\pi$
$432$		0			0
$433$		0			0		0.863256	−	0.504766i	$-0.168421\pi$
$433$		0			0		−0.863256	+	0.504766i	$0.831579\pi$
$434$		0			0
$435$		0			0
$436$	−1.32379	+	4.23239i	−1.32379	+	4.23239i
$437$		0			0
$438$		0			0
$439$		0			0		−0.461341	−	0.887223i	$-0.652632\pi$
$439$		0			0		0.461341	+	0.887223i	$0.347368\pi$
$440$		0			0
$441$	−0.942181	+	0.335105i	−0.942181	+	0.335105i
$442$		0			0
$443$	−1.43139	+	1.39248i	−1.43139	+	1.39248i	−0.677282	+	0.735724i	$0.736842\pi$
$443$	−1.43139	+	1.39248i	−1.43139	+	1.39248i	−0.754107	+	0.656752i	$0.771930\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−6.39704	−	1.50785i	−6.39704	−	1.50785i
$449$	1.78619	−	0.818971i	1.78619	−	0.818971i	0.815447	−	0.578832i	$-0.196491\pi$
$449$	1.78619	−	0.818971i	1.78619	−	0.818971i	0.970739	−	0.240139i	$-0.0771930\pi$
$450$	−0.0768430	+	1.99075i	−0.0768430	+	1.99075i
$451$		0			0
$452$	−2.81060	+	0.500911i	−2.81060	+	0.500911i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.87276	−	0.689431i	1.87276	−	0.689431i	0.913545	−	0.406737i	$-0.133333\pi$
$457$	1.87276	−	0.689431i	1.87276	−	0.689431i	0.959210	−	0.282694i	$-0.0912281\pi$
$458$		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
$463$	0.382469	+	1.38160i	0.382469	+	1.38160i	0.863256	+	0.504766i	$0.168421\pi$
$463$	0.382469	+	1.38160i	0.382469	+	1.38160i	−0.480787	+	0.876837i	$0.659649\pi$
$464$	−5.19078	−	2.44959i	−5.19078	−	2.44959i
$465$		0			0
$466$	0.714415	−	3.88450i	0.714415	−	3.88450i
$467$		0			0		0.609854	−	0.792514i	$-0.291228\pi$
$467$		0			0		−0.609854	+	0.792514i	$0.708772\pi$
$468$		0			0
$469$	−1.55515	+	1.23819i	−1.55515	+	1.23819i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.0711415	+	0.676867i	−0.0711415	+	0.676867i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.828628	−	0.448431i	−0.828628	−	0.448431i
$478$	−0.776987	+	1.16111i	−0.776987	+	1.16111i
$479$		0			0		0.411766	−	0.911290i	$-0.364912\pi$
$479$		0			0		−0.411766	+	0.911290i	$0.635088\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.979290	+	5.32471i	0.979290	+	5.32471i
$485$		0			0
$486$		0			0
$487$	−0.458517	−	1.11129i	−0.458517	−	1.11129i	−0.968033	−	0.250825i	$-0.919298\pi$
$487$	−0.458517	−	1.11129i	−0.458517	−	1.11129i	0.509516	−	0.860461i	$-0.329825\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.739510	−	0.0653833i	0.739510	−	0.0653833i	0.287976	−	0.957638i	$-0.407018\pi$
$491$	0.739510	−	0.0653833i	0.739510	−	0.0653833i	0.451533	+	0.892254i	$0.350877\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.263565	−	1.63491i	0.263565	−	1.63491i
$498$		0			0
$499$	0.246821	+	0.201001i	0.246821	+	0.201001i	0.746821	−	0.665025i	$-0.231579\pi$
$499$	0.246821	+	0.201001i	0.246821	+	0.201001i	−0.500000	+	0.866025i	$0.666667\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.277403	−	0.960754i	$-0.410526\pi$
$503$		0			0		−0.277403	+	0.960754i	$0.589474\pi$
$504$	0.0216198	−	3.92259i	0.0216198	−	3.92259i
$505$		0			0
$506$	6.18650	−	1.45823i	6.18650	−	1.45823i
$507$		0			0
$508$	0.354340	−	1.01393i	0.354340	−	1.01393i
$509$		0			0		−0.0275543	−	0.999620i	$-0.508772\pi$
$509$		0			0		0.0275543	+	0.999620i	$0.491228\pi$
$510$		0			0
$511$		0			0
$512$	4.79385	−	7.33754i	4.79385	−	7.33754i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	2.92882	−	1.66950i	2.92882	−	1.66950i
$519$		0			0
$520$		0			0
$521$		0			0		−0.828009	−	0.560715i	$-0.810526\pi$
$521$		0			0		0.828009	+	0.560715i	$0.189474\pi$
$522$	0.503331	−	2.30543i	0.503331	−	2.30543i
$523$		0			0		−0.997814	−	0.0660906i	$-0.978947\pi$
$523$		0			0		0.997814	+	0.0660906i	$0.0210526\pi$
$524$		0			0
$525$		0			0
$526$	−0.372266	−	1.80010i	−0.372266	−	1.80010i
$527$		0			0
$528$		0			0
$529$	−0.722628	−	2.50274i	−0.722628	−	2.50274i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−2.49121	−	7.38902i	−2.49121	−	7.38902i
$537$		0			0
$538$		0			0
$539$	1.43151	−	0.879947i	1.43151	−	0.879947i
$540$		0			0
$541$	1.24718	+	1.16087i	1.24718	+	1.16087i	0.980380	+	0.197117i	$0.0631579\pi$
$541$	1.24718	+	1.16087i	1.24718	+	1.16087i	0.266796	+	0.963753i	$0.414035\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.59293	−	0.283896i	−1.59293	−	0.283896i	−0.693336	−	0.720615i	$-0.743860\pi$
$547$	−1.59293	−	0.283896i	−1.59293	−	0.283896i	−0.899598	+	0.436719i	$0.856140\pi$
$548$	−2.53074	+	3.36484i	−2.53074	+	3.36484i
$549$		0			0
$550$	−0.569190	−	3.29887i	−0.569190	−	3.29887i
$551$		0			0
$552$		0			0
$553$	−1.06099	−	1.34777i	−1.06099	−	1.34777i
$554$	0.0316737	−	0.0577650i	0.0316737	−	0.0577650i
$555$		0			0
$556$		0			0
$557$	1.04861	+	1.04285i	1.04861	+	1.04285i	0.999028	+	0.0440782i	$0.0140351\pi$
$557$	1.04861	+	1.04285i	1.04861	+	1.04285i	0.0495838	+	0.998770i	$0.484211\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	1.07265	+	1.72363i	1.07265	+	1.72363i
$563$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$563$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.975796	−	0.218681i	0.975796	−	0.218681i
$568$	5.67861	+	3.15453i	5.67861	+	3.15453i
$569$	−1.98195	+	0.219362i	−1.98195	+	0.219362i	−0.982493	+	0.186298i	$0.940351\pi$
$569$	−1.98195	+	0.219362i	−1.98195	+	0.219362i	−0.999453	+	0.0330634i	$0.989474\pi$
$570$		0			0
$571$	0.904357	−	0.426776i	0.904357	−	0.426776i
$571$	0.904357	−	0.426776i	0.904357	−	0.426776i
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.85272	+	0.415205i	−1.85272	+	0.415205i
$576$	6.16768	+	2.27055i	6.16768	+	2.27055i
$577$		0			0		−0.922290	−	0.386499i	$-0.873684\pi$
$577$		0			0		0.922290	+	0.386499i	$0.126316\pi$
$578$	−1.24948	−	1.55170i	−1.24948	−	1.55170i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.51861	+	0.447558i	1.51861	+	0.447558i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.904357	−	0.426776i	$-0.140351\pi$
$587$		0			0		−0.904357	+	0.426776i	$0.859649\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	1.39425	+	8.08067i	1.39425	+	8.08067i
$593$		0			0		−0.768401	−	0.639969i	$-0.778947\pi$
$593$		0			0		0.768401	+	0.639969i	$0.221053\pi$
$594$		0			0
$595$		0			0
$596$	−3.71490	−	3.16398i	−3.71490	−	3.16398i
$597$		0			0
$598$		0			0
$599$	−1.51886	−	1.20930i	−1.51886	−	1.20930i	−0.909007	−	0.416782i	$-0.863158\pi$
$599$	−1.51886	−	1.20930i	−1.51886	−	1.20930i	−0.609854	−	0.792514i	$-0.708772\pi$
$600$		0			0
$601$		0			0		−0.731980	−	0.681326i	$-0.761404\pi$
$601$		0			0		0.731980	+	0.681326i	$0.238596\pi$
$602$	−0.0666351	+	0.804166i	−0.0666351	+	0.804166i
$603$	1.69350	−	1.04099i	1.69350	−	1.04099i
$604$	0.158992	+	0.599976i	0.158992	+	0.599976i
$605$		0			0
$606$		0			0
$607$		0			0		−0.701237	−	0.712928i	$-0.747368\pi$
$607$		0			0		0.701237	+	0.712928i	$0.252632\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.543921	−	1.88381i	−0.543921	−	1.88381i	−0.461341	−	0.887223i	$-0.652632\pi$
$613$	−0.543921	−	1.88381i	−0.543921	−	1.88381i	−0.0825793	−	0.996584i	$-0.526316\pi$
$614$		0			0
$615$		0			0
$616$	1.33487	+	6.45478i	1.33487	+	6.45478i
$617$	0.775789	−	1.31014i	0.775789	−	1.31014i	−0.170028	−	0.985439i	$-0.554386\pi$
$617$	0.775789	−	1.31014i	0.775789	−	1.31014i	0.945817	−	0.324699i	$-0.105263\pi$
$618$		0			0
$619$		0			0		−0.997814	−	0.0660906i	$-0.978947\pi$
$619$		0			0		0.997814	+	0.0660906i	$0.0210526\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.159156	+	0.987253i	0.159156	+	0.987253i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	1.58590	+	1.17915i	1.58590	+	1.17915i	0.884667	+	0.466224i	$0.154386\pi$
$631$	1.58590	+	1.17915i	1.58590	+	1.17915i	0.701237	+	0.712928i	$0.252632\pi$
$632$	6.38757	−	2.11444i	6.38757	−	2.11444i
$633$		0			0
$634$	0.766772	−	2.19408i	0.766772	−	2.19408i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−0.0218541	+	3.96509i	−0.0218541	+	3.96509i
$639$	−0.459384	+	1.59103i	−0.459384	+	1.59103i
$640$		0			0
$641$	0.636143	+	1.36749i	0.636143	+	1.36749i	0.913545	+	0.406737i	$0.133333\pi$
$641$	0.636143	+	1.36749i	0.636143	+	1.36749i	−0.277403	+	0.960754i	$0.589474\pi$
$642$		0			0
$643$		0			0		−0.775409	−	0.631460i	$-0.782456\pi$
$643$		0			0		0.775409	+	0.631460i	$0.217544\pi$
$644$	5.45692	−	1.41393i	5.45692	−	1.41393i
$645$		0			0
$646$		0			0
$647$		0			0		0.565270	−	0.824906i	$-0.308772\pi$
$647$		0			0		−0.565270	+	0.824906i	$0.691228\pi$
$648$	−0.495928	+	3.89117i	−0.495928	+	3.89117i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.892459	−	1.81288i	0.892459	−	1.81288i
$653$	0.435054	−	0.176704i	0.435054	−	0.176704i	−0.148264	−	0.988948i	$-0.547368\pi$
$653$	0.435054	−	0.176704i	0.435054	−	0.176704i	0.583317	+	0.812244i	$0.301754\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.283218	−	0.145291i	−0.283218	−	0.145291i	0.309017	−	0.951057i	$-0.400000\pi$
$659$	−0.283218	−	0.145291i	−0.283218	−	0.145291i	−0.592235	+	0.805765i	$0.701754\pi$
$660$		0			0
$661$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$661$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$662$	−3.62928	−	1.15715i	−3.62928	−	1.15715i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−3.10925	+	1.30298i	−3.10925	+	1.30298i
$667$	2.24674	−	0.0991288i	2.24674	−	0.0991288i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.214909	+	0.171108i	−0.214909	+	0.171108i	−0.724425	−	0.689353i	$-0.757895\pi$
$673$	−0.214909	+	0.171108i	−0.214909	+	0.171108i	0.509516	+	0.860461i	$0.329825\pi$
$674$	−1.28578	−	0.273300i	−1.28578	−	0.273300i
$675$		0			0
$676$	0.537030	−	2.92000i	0.537030	−	2.92000i
$677$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$677$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.344925	+	0.167447i	0.344925	+	0.167447i	0.601081	−	0.799188i	$-0.294737\pi$
$683$	0.344925	+	0.167447i	0.344925	+	0.167447i	−0.256156	+	0.966635i	$0.582456\pi$
$684$		0			0
$685$		0			0
$686$	1.67381	−	1.08044i	1.67381	−	1.08044i
$687$		0			0
$688$	−1.78414	−	0.818031i	−1.78414	−	0.818031i
$689$		0			0
$690$		0			0
$691$		0			0		−0.863256	−	0.504766i	$-0.831579\pi$
$691$		0			0		0.863256	+	0.504766i	$0.168421\pi$
$692$		0			0
$693$	−1.52744	+	0.700334i	−1.52744	+	0.700334i
$694$	−3.66805	−	0.864600i	−3.66805	−	0.864600i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.569184	−	2.91390i	−0.569184	−	2.91390i
$701$	1.87875	−	0.668217i	1.87875	−	0.668217i	0.913545	−	0.406737i	$-0.133333\pi$
$701$	1.87875	−	0.668217i	1.87875	−	0.668217i	0.965209	−	0.261480i	$-0.0842105\pi$
$702$		0			0
$703$		0			0
$704$	−10.9306	−	1.57717i	−10.9306	−	1.57717i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.65609	−	0.968352i	1.65609	−	0.968352i	0.685350	−	0.728214i	$-0.259649\pi$
$709$	1.65609	−	0.968352i	1.65609	−	0.968352i	0.970739	−	0.240139i	$-0.0771930\pi$
$710$		0			0
$711$	0.890178	+	1.46621i	0.890178	+	1.46621i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.05331	−	3.01401i	−1.05331	−	3.01401i
$717$		0			0
$718$	2.62037	−	2.97553i	2.62037	−	2.97553i
$719$		0			0		0.0495838	−	0.998770i	$-0.484211\pi$
$719$		0			0		−0.0495838	+	0.998770i	$0.515789\pi$
$720$		0			0
$721$		0			0
$722$	−0.0768430	−	1.99075i	−0.0768430	−	1.99075i
$723$		0			0
$724$		0			0
$725$	0.0195840	−	1.18431i	0.0195840	−	1.18431i
$726$		0			0
$727$		0			0		0.956036	−	0.293250i	$-0.0947368\pi$
$727$		0			0		−0.956036	+	0.293250i	$0.905263\pi$
$728$		0			0
$729$	−0.995083	+	0.0990455i	−0.995083	+	0.0990455i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.340293	−	0.940319i	$-0.389474\pi$
$733$		0			0		−0.340293	+	0.940319i	$0.610526\pi$
$734$		0			0
$735$		0			0
$736$	−1.01812	+	10.8343i	−1.01812	+	10.8343i
$737$	−2.41978	+	2.30263i	−2.41978	+	2.30263i
$738$		0			0
$739$	−0.611296	−	1.11485i	−0.611296	−	1.11485i	−0.982493	−	0.186298i	$-0.940351\pi$
$739$	−0.611296	−	1.11485i	−0.611296	−	1.11485i	0.371197	−	0.928554i	$-0.378947\pi$
$740$		0			0
$741$		0			0
$742$	1.81174	+	0.490811i	1.81174	+	0.490811i
$743$	−0.780620	−	0.593880i	−0.780620	−	0.593880i	0.137354	−	0.990522i	$-0.456140\pi$
$743$	−0.780620	−	0.593880i	−0.780620	−	0.593880i	−0.917973	+	0.396642i	$0.870175\pi$
$744$		0			0
$745$		0			0
$746$	−0.0630550	+	2.28752i	−0.0630550	+	2.28752i
$747$		0			0
$748$		0			0
$749$	−0.0232830	−	0.0963955i	−0.0232830	−	0.0963955i
$750$		0			0
$751$	−0.812299	−	1.79772i	−0.812299	−	1.79772i	−0.556143	−	0.831087i	$-0.687719\pi$
$751$	−0.812299	−	1.79772i	−0.812299	−	1.79772i	−0.256156	−	0.966635i	$-0.582456\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−0.825551	+	1.58765i	−0.825551	+	1.58765i	−0.0165339	+	0.999863i	$0.505263\pi$
$757$	−0.825551	+	1.58765i	−0.825551	+	1.58765i	−0.809017	+	0.587785i	$0.800000\pi$
$758$	−0.985134	+	0.266878i	−0.985134	+	0.266878i
$759$		0			0
$760$		0			0
$761$		0			0		0.874174	−	0.485613i	$-0.161404\pi$
$761$		0			0		−0.874174	+	0.485613i	$0.838596\pi$
$762$		0			0
$763$	1.47589	−	0.229591i	1.47589	−	0.229591i
$764$	−3.74353	+	4.15761i	−3.74353	+	4.15761i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.137354	−	0.990522i	$-0.456140\pi$
$769$		0			0		−0.137354	+	0.990522i	$0.543860\pi$
$770$		0			0
$771$		0			0
$772$	−0.368169	+	0.654237i	−0.368169	+	0.654237i
$773$		0			0		−0.739446	−	0.673216i	$-0.764912\pi$
$773$		0			0		0.739446	+	0.673216i	$0.235088\pi$
$774$	0.163416	−	0.790201i	0.163416	−	0.790201i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	2.24354	+	0.198361i	2.24354	+	0.198361i
$779$		0			0
$780$		0			0
$781$	0.199209	−	2.77553i	0.199209	−	2.77553i
$782$		0			0
$783$		0			0
$784$	1.08574	+	4.72263i	1.08574	+	4.72263i
$785$		0			0
$786$		0			0
$787$		0			0		−0.371197	−	0.928554i	$-0.621053\pi$
$787$		0			0		0.371197	+	0.928554i	$0.378947\pi$
$788$	0.0270984	−	0.0183506i	0.0270984	−	0.0183506i
$789$		0			0
$790$		0			0
$791$	0.569479	+	0.774803i	0.569479	+	0.774803i
$792$	−0.544311	−	6.56885i	−0.544311	−	6.56885i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.997814	−	0.0660906i	$-0.0210526\pi$
$797$		0			0		−0.997814	+	0.0660906i	$0.978947\pi$
$798$		0			0
$799$		0			0
$800$	5.66325	+	0.880979i	5.66325	+	0.880979i
$801$		0			0
$802$	0.704416	−	0.958393i	0.704416	−	0.958393i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.23583	+	0.364219i	−1.23583	+	0.364219i	−0.834139	−	0.551554i	$-0.814035\pi$
$809$	−1.23583	+	0.364219i	−1.23583	+	0.364219i	−0.401695	+	0.915773i	$0.631579\pi$
$810$		0			0
$811$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$811$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$812$	0.0581443	+	3.51618i	0.0581443	+	3.51618i
$813$		0			0
$814$	4.65521	−	3.22785i	4.65521	−	3.22785i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.14621	−	1.59605i	−1.14621	−	1.59605i	−0.724425	−	0.689353i	$-0.757895\pi$
$821$	−1.14621	−	1.59605i	−1.14621	−	1.59605i	−0.421786	−	0.906696i	$-0.638596\pi$
$822$		0			0
$823$	−0.229273	+	1.97203i	−0.229273	+	1.97203i	0.00551154	+	0.999985i	$0.498246\pi$
$823$	−0.229273	+	1.97203i	−0.229273	+	1.97203i	−0.234785	+	0.972047i	$0.575439\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.10459	+	1.34123i	−1.10459	+	1.34123i	−0.170028	+	0.985439i	$0.554386\pi$
$827$	−1.10459	+	1.34123i	−1.10459	+	1.34123i	−0.934564	+	0.355794i	$0.884211\pi$
$828$	−5.58788	+	0.743493i	−5.58788	+	0.743493i
$829$		0			0		−0.298515	−	0.954405i	$-0.596491\pi$
$829$		0			0		0.298515	+	0.954405i	$0.403509\pi$
$830$		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		−0.213300	−	0.976987i	$-0.568421\pi$
$839$		0			0		0.213300	+	0.976987i	$0.431579\pi$
$840$		0			0
$841$	−0.0772537	+	0.395496i	−0.0772537	+	0.395496i
$842$	2.02802	+	3.10411i	2.02802	+	3.10411i
$843$		0			0
$844$	−1.30015	−	1.38147i	−1.30015	−	1.38147i
$845$		0			0
$846$		0			0
$847$	1.46336	−	1.08804i	1.46336	−	1.08804i
$848$	−2.62220	+	3.73758i	−2.62220	+	3.73758i
$849$		0			0
$850$		0			0
$851$	−1.95941	−	2.54629i	−1.95941	−	2.54629i
$852$		0			0
$853$		0			0		−0.537687	−	0.843145i	$-0.680702\pi$
$853$		0			0		0.537687	+	0.843145i	$0.319298\pi$
$854$		0			0
$855$		0			0
$856$	0.386638	+	0.0427931i	0.386638	+	0.0427931i
$857$		0			0		−0.993931	−	0.110008i	$-0.964912\pi$
$857$		0			0		0.993931	+	0.110008i	$0.0350877\pi$
$858$		0			0
$859$		0			0		−0.894729	−	0.446609i	$-0.852632\pi$
$859$		0			0		0.894729	+	0.446609i	$0.147368\pi$
$860$		0			0
$861$		0			0
$862$	2.41210	+	3.13455i	2.41210	+	3.13455i
$863$	1.77940	−	0.912833i	1.77940	−	0.912833i	0.884667	−	0.466224i	$-0.154386\pi$
$863$	1.77940	−	0.912833i	1.77940	−	0.912833i	0.894729	−	0.446609i	$-0.147368\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.97535	−	2.09889i	−1.97535	−	2.09889i
$870$		0			0
$871$		0			0
$872$	−1.12324	+	5.75036i	−1.12324	+	5.75036i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.33609	−	0.222954i	1.33609	−	0.222954i	0.546948	−	0.837166i	$-0.315789\pi$
$877$	1.33609	−	0.222954i	1.33609	−	0.222954i	0.789141	+	0.614213i	$0.210526\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.319482	−	0.947592i	$-0.396491\pi$
$881$		0			0		−0.319482	+	0.947592i	$0.603509\pi$
$882$	−1.79220	+	0.870044i	−1.79220	+	0.870044i
$883$	−1.67722	+	0.724701i	−1.67722	+	0.724701i	−0.999939	−	0.0110229i	$-0.996491\pi$
$883$	−1.67722	+	0.724701i	−1.67722	+	0.724701i	−0.677282	+	0.735724i	$0.736842\pi$
$884$		0			0
$885$		0			0
$886$	−2.52917	+	3.07100i	−2.52917	+	3.07100i
$887$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$887$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$888$		0			0
$889$	−0.359105	+	0.0437577i	−0.359105	+	0.0437577i
$890$		0			0
$891$	1.60093	−	0.510437i	1.60093	−	0.510437i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−7.30820	−	0.890520i	−7.30820	−	0.890520i
$897$		0			0
$898$	3.35741	−	2.01314i	3.35741	−	2.01314i
$899$		0			0
$900$	0.212546	+	2.96136i	0.212546	+	2.96136i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−3.61806	+	1.06630i	−3.61806	+	1.06630i
$905$		0			0
$906$		0			0
$907$	1.10532	+	1.57547i	1.10532	+	1.57547i	0.775409	+	0.631460i	$0.217544\pi$
$907$	1.10532	+	1.57547i	1.10532	+	1.57547i	0.329907	+	0.944013i	$0.392982\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.17865	−	1.60361i	1.17865	−	1.60361i	0.509516	−	0.860461i	$-0.329825\pi$
$911$	1.17865	−	1.60361i	1.17865	−	1.60361i	0.669131	−	0.743145i	$-0.266667\pi$
$912$		0			0
$913$		0			0
$914$	3.55722	−	1.77560i	3.55722	−	1.77560i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.116113	−	0.272848i	−0.116113	−	0.272848i	0.851919	−	0.523673i	$-0.175439\pi$
$919$	−0.116113	−	0.272848i	−0.116113	−	0.272848i	−0.968033	+	0.250825i	$0.919298\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−1.40115	+	0.948837i	−1.40115	+	0.948837i
$926$	1.06014	+	2.65194i	1.06014	+	2.65194i
$927$		0			0
$928$	−6.42080	−	2.20426i	−6.42080	−	2.20426i
$929$		0			0		−0.224056	−	0.974576i	$-0.571930\pi$
$929$		0			0		0.224056	+	0.974576i	$0.428070\pi$
$930$		0			0
$931$		0			0
$932$	0.421379	−	5.87097i	0.421379	−	5.87097i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.997024	−	0.0770854i	$-0.975439\pi$
$937$		0			0		0.997024	+	0.0770854i	$0.0245614\pi$
$938$	−2.80804	+	2.79261i	−2.80804	+	2.79261i
$939$		0			0
$940$		0			0
$941$		0			0		0.490424	−	0.871484i	$-0.336842\pi$
$941$		0			0		−0.490424	+	0.871484i	$0.663158\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	0.00747310	+	1.35588i	0.00747310	+	1.35588i
$947$	0.327226	+	0.0925307i	0.327226	+	0.0925307i	0.431754	−	0.901991i	$-0.357895\pi$
$947$	0.327226	+	0.0925307i	0.327226	+	0.0925307i	−0.104528	+	0.994522i	$0.533333\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.0411563	−	0.0366486i	0.0411563	−	0.0366486i	−0.644194	−	0.764862i	$-0.722807\pi$
$953$	0.0411563	−	0.0366486i	0.0411563	−	0.0366486i	0.685350	+	0.728214i	$0.259649\pi$
$954$	−1.73908	−	0.706351i	−1.73908	−	0.706351i
$955$		0			0
$956$	−0.960544	+	1.84726i	−0.960544	+	1.84726i
$957$		0			0
$958$		0			0
$959$	1.39328	+	0.264191i	1.39328	+	0.264191i
$960$		0			0
$961$	−0.986361	−	0.164595i	−0.986361	−	0.164595i
$962$		0			0
$963$	0.0114523	+	0.0985040i	0.0114523	+	0.0985040i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.0539044	+	1.95555i	−0.0539044	+	1.95555i	0.180881	+	0.983505i	$0.442105\pi$
$967$	−0.0539044	+	1.95555i	−0.0539044	+	1.95555i	−0.234785	+	0.972047i	$0.575439\pi$
$968$	2.05991	+	6.85005i	2.05991	+	6.85005i
$969$		0			0
$970$		0			0
$971$		0			0		−0.965209	−	0.261480i	$-0.915789\pi$
$971$		0			0		0.965209	+	0.261480i	$0.0842105\pi$
$972$		0			0
$973$		0			0
$974$	−1.15148	−	2.10001i	−1.15148	−	2.10001i
$975$		0			0
$976$		0			0
$977$	−0.0399125	+	0.424728i	−0.0399125	+	0.424728i	0.952745	+	0.303771i	$0.0982456\pi$
$977$	−0.0399125	+	0.424728i	−0.0399125	+	0.424728i	−0.992658	+	0.120958i	$0.961404\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−1.49283	+	0.0493849i	−1.49283	+	0.0493849i
$982$	1.45000	−	0.291540i	1.45000	−	0.291540i
$983$		0			0		0.999939	−	0.0110229i	$-0.00350877\pi$
$983$		0			0		−0.999939	+	0.0110229i	$0.996491\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.767863	−	0.0423642i	0.767863	−	0.0423642i
$990$		0			0
$991$	−0.0348325	−	0.902395i	−0.0348325	−	0.902395i	−0.909007	−	0.416782i	$-0.863158\pi$
$991$	−0.0348325	−	0.902395i	−0.0348325	−	0.902395i	0.874174	−	0.485613i	$-0.161404\pi$
$992$		0			0
$993$		0			0
$994$	0.163585	−	3.29511i	0.163585	−	3.29511i
$995$		0			0
$996$		0			0
$997$		0			0		−0.329907	−	0.944013i	$-0.607018\pi$
$997$		0			0		0.329907	+	0.944013i	$0.392982\pi$
$998$	0.532792	+	0.343915i	0.532792	+	0.343915i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3997.1.cz.a.279.1	✓	144
7.6	odd	2	CM	3997.1.cz.a.279.1	✓	144
571.483	even	285	inner	3997.1.cz.a.3338.1	yes	144
3997.3338	odd	570	inner	3997.1.cz.a.3338.1	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3997.1.cz.a.279.1	✓	144	1.1	even	1	trivial
3997.1.cz.a.279.1	✓	144	7.6	odd	2	CM
3997.1.cz.a.3338.1	yes	144	571.483	even	285	inner
3997.1.cz.a.3338.1	yes	144	3997.3338	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)

\(f(q)\)	\(=\)	\(q+(1.98014 - 0.219162i) q^{2} +(2.89711 - 0.649259i) q^{4} +(-0.627176 - 0.778877i) q^{7} +(3.71011 - 1.27368i) q^{8} +(0.528360 + 0.849020i) q^{9} +O(q^{10})\)	\(q+(1.98014 - 0.219162i) q^{2} +(2.89711 - 0.649259i) q^{4} +(-0.627176 - 0.778877i) q^{7} +(3.71011 - 1.27368i) q^{8} +(0.528360 + 0.849020i) q^{9} +(-1.16504 - 1.21088i) q^{11} +(-1.41260 - 1.40483i) q^{14} +(4.38236 - 2.06809i) q^{16} +(1.23230 + 1.56538i) q^{18} +(-2.57231 - 2.14237i) q^{22} +(-1.14126 + 1.51740i) q^{23} +(0.761300 + 0.648400i) q^{25} +(-2.32269 - 1.84930i) q^{28} +(-0.752996 - 0.914313i) q^{29} +(4.88266 - 3.00136i) q^{32} +(2.08195 + 2.11667i) q^{36} +(-0.451469 + 1.63085i) q^{37} +(-0.260921 - 0.309796i) q^{43} +(-4.16142 - 2.75163i) q^{44} +(-1.92729 + 3.25478i) q^{46} +(-0.213300 + 0.976987i) q^{49} +(1.64958 + 1.11707i) q^{50} +(-0.818541 + 0.466589i) q^{53} +(-3.31893 - 2.09089i) q^{56} +(-1.69142 - 1.64544i) q^{58} +(0.329907 - 0.944013i) q^{63} +(5.18650 - 4.03682i) q^{64} +(0.0109562 - 1.98783i) q^{67} +(1.10809 + 1.23066i) q^{71} +(3.04165 + 2.47699i) q^{72} +(-0.536551 + 3.32826i) q^{74} +(-0.212440 + 1.66685i) q^{77} +(1.71518 + 0.0189074i) q^{79} +(-0.441671 + 0.897177i) q^{81} +(-0.584555 - 0.556254i) q^{86} +(-5.86468 - 3.00859i) q^{88} +(-2.32117 + 5.13706i) q^{92} +(-0.208245 + 1.98131i) q^{98} +(0.412498 - 1.62892i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9}+O(q^{10}) \) 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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