LMFDB - Embedded newform 3997.1.cz.a.482.1

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			482.1
Root			$-0.0935596 + 0.995614i$ of defining polynomial
Character	$\chi$	$=$	3997.482
Dual form			3997.1.cz.a.2778.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.660728 - 1.76473i) q^{2} +(-1.92359 + 1.67525i) q^{4} +(0.652586 + 0.757715i) q^{7} +(2.57009 + 1.39086i) q^{8} +(-0.709053 - 0.705155i) q^{9} +O(q^{10})$	\(q+(-0.660728 - 1.76473i) q^{2} +(-1.92359 + 1.67525i) q^{4} +(0.652586 + 0.757715i) q^{7} +(2.57009 + 1.39086i) q^{8} +(-0.709053 - 0.705155i) q^{9} +(0.574517 + 1.48443i) q^{11} +(0.905977 - 1.65228i) q^{14} +(0.405997 - 2.92784i) q^{16} +(-0.775915 + 1.71720i) q^{18} +(2.24001 - 1.99467i) q^{22} +(-0.0523201 + 0.109303i) q^{23} +(-0.917973 - 0.396642i) q^{25} +(-2.52467 - 0.364284i) q^{28} +(-1.22347 + 0.345965i) q^{29} +(-2.58351 + 0.578979i) q^{32} +(2.54524 + 0.168585i) q^{36} +(0.188416 + 0.382735i) q^{37} +(-0.265516 + 1.64701i) q^{43} +(-3.59193 - 1.89296i) q^{44} +(0.227460 + 0.0201107i) q^{46} +(-0.148264 + 0.988948i) q^{49} +(-0.0934337 + 1.88204i) q^{50} +(-0.511814 - 0.0225818i) q^{53} +(0.623326 + 2.85505i) q^{56} +(1.41892 + 1.93051i) q^{58} +(0.0715891 - 0.997434i) q^{63} +(1.11204 + 1.70210i) q^{64} +(-0.377066 + 0.591276i) q^{67} +(-0.0103658 - 0.0986243i) q^{71} +(-0.841553 - 2.79850i) q^{72} +(0.550931 - 0.585387i) q^{74} +(-0.749851 + 1.40404i) q^{77} +(0.514455 + 1.10590i) q^{79} +(0.00551154 + 0.999985i) q^{81} +(3.08196 - 0.619665i) q^{86} +(-0.588074 + 4.61418i) q^{88} +(-0.0824688 - 0.297904i) q^{92} +(1.84318 - 0.391781i) q^{98} +(0.639389 - 1.45766i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3997\mathbb{Z}\right)^\times$.

$n$	$1716$	$2285$
$\chi(n)$	$e\left(\frac{178}{285}\right)$	$-1$

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 $

$2$	−0.660728	−	1.76473i	−0.660728	−	1.76473i	−0.644194	−	0.764862i	$-0.722807\pi$
$2$	−0.660728	−	1.76473i	−0.660728	−	1.76473i	−0.0165339	−	0.999863i	$-0.505263\pi$
$3$		0			0		0.381410	−	0.924406i	$-0.375439\pi$
$3$		0			0		−0.381410	+	0.924406i	$0.624561\pi$
$4$	−1.92359	+	1.67525i	−1.92359	+	1.67525i
$5$		0			0		0.202517	−	0.979279i	$-0.435088\pi$
$5$		0			0		−0.202517	+	0.979279i	$0.564912\pi$
$6$		0			0
$7$	0.652586	+	0.757715i	0.652586	+	0.757715i
$7$	0.652586	+	0.757715i	0.652586	+	0.757715i
$8$	2.57009	+	1.39086i	2.57009	+	1.39086i
$9$	−0.709053	−	0.705155i	−0.709053	−	0.705155i
$10$		0			0
$11$	0.574517	+	1.48443i	0.574517	+	1.48443i	0.851919	+	0.523673i	$0.175439\pi$
$11$	0.574517	+	1.48443i	0.574517	+	1.48443i	−0.277403	+	0.960754i	$0.589474\pi$
$12$		0			0
$13$		0			0		0.884667	−	0.466224i	$-0.154386\pi$
$13$		0			0		−0.884667	+	0.466224i	$0.845614\pi$
$14$	0.905977	−	1.65228i	0.905977	−	1.65228i
$15$		0			0
$16$	0.405997	−	2.92784i	0.405997	−	2.92784i
$17$		0			0		0.984487	−	0.175457i	$-0.0561404\pi$
$17$		0			0		−0.984487	+	0.175457i	$0.943860\pi$
$18$	−0.775915	+	1.71720i	−0.775915	+	1.71720i
$19$		0			0		−0.234785	−	0.972047i	$-0.575439\pi$
$19$		0			0		0.234785	+	0.972047i	$0.424561\pi$
$20$		0			0
$21$		0			0
$22$	2.24001	−	1.99467i	2.24001	−	1.99467i
$23$	−0.0523201	+	0.109303i	−0.0523201	+	0.109303i	−0.926494	−	0.376309i	$-0.877193\pi$
$23$	−0.0523201	+	0.109303i	−0.0523201	+	0.109303i	0.874174	+	0.485613i	$0.161404\pi$
$24$		0			0
$25$	−0.917973	−	0.396642i	−0.917973	−	0.396642i
$26$		0			0
$27$		0			0
$28$	−2.52467	−	0.364284i	−2.52467	−	0.364284i
$29$	−1.22347	+	0.345965i	−1.22347	+	0.345965i	−0.821778	−	0.569808i	$-0.807018\pi$
$29$	−1.22347	+	0.345965i	−1.22347	+	0.345965i	−0.401695	+	0.915773i	$0.631579\pi$
$30$		0			0
$31$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$31$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$32$	−2.58351	+	0.578979i	−2.58351	+	0.578979i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	2.54524	+	0.168585i	2.54524	+	0.168585i
$37$	0.188416	+	0.382735i	0.188416	+	0.382735i	0.970739	−	0.240139i	$-0.0771930\pi$
$37$	0.188416	+	0.382735i	0.188416	+	0.382735i	−0.782322	+	0.622874i	$0.785965\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.993931	−	0.110008i	$-0.0350877\pi$
$41$		0			0		−0.993931	+	0.110008i	$0.964912\pi$
$42$		0			0
$43$	−0.265516	+	1.64701i	−0.265516	+	1.64701i	0.411766	+	0.911290i	$0.364912\pi$
$43$	−0.265516	+	1.64701i	−0.265516	+	1.64701i	−0.677282	+	0.735724i	$0.736842\pi$
$44$	−3.59193	−	1.89296i	−3.59193	−	1.89296i
$45$		0			0
$46$	0.227460	+	0.0201107i	0.227460	+	0.0201107i
$47$		0			0		0.926494	−	0.376309i	$-0.122807\pi$
$47$		0			0		−0.926494	+	0.376309i	$0.877193\pi$
$48$		0			0
$49$	−0.148264	+	0.988948i	−0.148264	+	0.988948i
$50$	−0.0934337	+	1.88204i	−0.0934337	+	1.88204i
$51$		0			0
$52$		0			0
$53$	−0.511814	−	0.0225818i	−0.511814	−	0.0225818i	−0.213300	−	0.976987i	$-0.568421\pi$
$53$	−0.511814	−	0.0225818i	−0.511814	−	0.0225818i	−0.298515	+	0.954405i	$0.596491\pi$
$54$		0			0
$55$		0			0
$56$	0.623326	+	2.85505i	0.623326	+	2.85505i
$57$		0			0
$58$	1.41892	+	1.93051i	1.41892	+	1.93051i
$59$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$59$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$60$		0			0
$61$		0			0		0.0605901	−	0.998163i	$-0.480702\pi$
$61$		0			0		−0.0605901	+	0.998163i	$0.519298\pi$
$62$		0			0
$63$	0.0715891	−	0.997434i	0.0715891	−	0.997434i
$64$	1.11204	+	1.70210i	1.11204	+	1.70210i
$65$		0			0
$66$		0			0
$67$	−0.377066	+	0.591276i	−0.377066	+	0.591276i	−0.978148	−	0.207912i	$-0.933333\pi$
$67$	−0.377066	+	0.591276i	−0.377066	+	0.591276i	0.601081	+	0.799188i	$0.294737\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.0103658	−	0.0986243i	−0.0103658	−	0.0986243i	0.988116	−	0.153712i	$-0.0491228\pi$
$71$	−0.0103658	−	0.0986243i	−0.0103658	−	0.0986243i	−0.998482	+	0.0550878i	$0.982456\pi$
$72$	−0.841553	−	2.79850i	−0.841553	−	2.79850i
$73$		0			0		0.556143	−	0.831087i	$-0.312281\pi$
$73$		0			0		−0.556143	+	0.831087i	$0.687719\pi$
$74$	0.550931	−	0.585387i	0.550931	−	0.585387i
$75$		0			0
$76$		0			0
$77$	−0.749851	+	1.40404i	−0.749851	+	1.40404i
$78$		0			0
$79$	0.514455	+	1.10590i	0.514455	+	1.10590i	0.975796	+	0.218681i	$0.0701754\pi$
$79$	0.514455	+	1.10590i	0.514455	+	1.10590i	−0.461341	+	0.887223i	$0.652632\pi$
$80$		0			0
$81$	0.00551154	+	0.999985i	0.00551154	+	0.999985i
$82$		0			0
$83$		0			0		0.528360	−	0.849020i	$-0.322807\pi$
$83$		0			0		−0.528360	+	0.849020i	$0.677193\pi$
$84$		0			0
$85$		0			0
$86$	3.08196	−	0.619665i	3.08196	−	0.619665i
$87$		0			0
$88$	−0.588074	+	4.61418i	−0.588074	+	4.61418i
$89$		0			0		−0.471093	−	0.882084i	$-0.656140\pi$
$89$		0			0		0.471093	+	0.882084i	$0.343860\pi$
$90$		0			0
$91$		0			0
$92$	−0.0824688	−	0.297904i	−0.0824688	−	0.297904i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.391577	−	0.920146i	$-0.628070\pi$
$97$		0			0		0.391577	+	0.920146i	$0.371930\pi$
$98$	1.84318	−	0.391781i	1.84318	−	0.391781i
$99$	0.639389	−	1.45766i	0.639389	−	1.45766i
$100$	2.43028	−	0.774863i	2.43028	−	0.774863i
$101$		0			0		0.857640	−	0.514250i	$-0.171930\pi$
$101$		0			0		−0.857640	+	0.514250i	$0.828070\pi$
$102$		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
$106$	0.298319	+	0.918132i	0.298319	+	0.918132i
$107$	0.253360	+	1.82710i	0.253360	+	1.82710i	0.509516	+	0.860461i	$0.329825\pi$
$107$	0.253360	+	1.82710i	0.253360	+	1.82710i	−0.256156	+	0.966635i	$0.582456\pi$
$108$		0			0
$109$	−0.894729	+	1.54972i	−0.894729	+	1.54972i	−0.0605901	+	0.998163i	$0.519298\pi$
$109$	−0.894729	+	1.54972i	−0.894729	+	1.54972i	−0.834139	+	0.551554i	$0.814035\pi$
$110$		0			0
$111$		0			0
$112$	2.48341	−	1.60303i	2.48341	−	1.60303i
$113$	−0.334782	−	1.94030i	−0.334782	−	1.94030i	−0.340293	−	0.940319i	$-0.610526\pi$
$113$	−0.334782	−	1.94030i	−0.334782	−	1.94030i	0.00551154	−	0.999985i	$-0.498246\pi$
$114$		0			0
$115$		0			0
$116$	1.77388	−	2.71512i	1.77388	−	2.71512i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−1.13401	+	1.03244i	−1.13401	+	1.03244i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−1.80750	+	0.532697i	−1.80750	+	0.532697i
$127$	−0.163769	+	0.162869i	−0.163769	+	0.162869i	−0.782322	−	0.622874i	$-0.785965\pi$
$127$	−0.163769	+	0.162869i	−0.163769	+	0.162869i	0.618553	+	0.785743i	$0.287719\pi$
$128$	0.700990	−	0.953731i	0.700990	−	0.953731i
$129$		0			0
$130$		0			0
$131$		0			0		−0.945817	−	0.324699i	$-0.894737\pi$
$131$		0			0		0.945817	+	0.324699i	$0.105263\pi$
$132$		0			0
$133$		0			0
$134$	1.29258	+	0.274746i	1.29258	+	0.274746i
$135$		0			0
$136$		0			0
$137$	0.882700	−	0.381401i	0.882700	−	0.381401i	0.0935596	−	0.995614i	$-0.470175\pi$
$137$	0.882700	−	0.381401i	0.882700	−	0.381401i	0.789141	+	0.614213i	$0.210526\pi$
$138$		0			0
$139$		0			0		−0.256156	−	0.966635i	$-0.582456\pi$
$139$		0			0		0.256156	+	0.966635i	$0.417544\pi$
$140$		0			0
$141$		0			0
$142$	−0.167196	+	0.0834566i	−0.167196	+	0.0834566i
$143$		0			0
$144$	−2.35245	+	1.78970i	−2.35245	+	1.78970i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−1.00361	−	0.420579i	−1.00361	−	0.420579i
$149$	−0.800036	−	1.67138i	−0.800036	−	1.67138i	−0.739446	−	0.673216i	$-0.764912\pi$
$149$	−0.800036	−	1.67138i	−0.800036	−	1.67138i	−0.0605901	−	0.998163i	$-0.519298\pi$
$150$		0			0
$151$	1.44657	+	1.31701i	1.44657	+	1.31701i	0.863256	+	0.504766i	$0.168421\pi$
$151$	1.44657	+	1.31701i	1.44657	+	1.31701i	0.583317	+	0.812244i	$0.301754\pi$
$152$		0			0
$153$		0			0
$154$	2.97318	+	0.395596i	2.97318	+	0.395596i
$155$		0			0
$156$		0			0
$157$		0			0		−0.644194	−	0.764862i	$-0.722807\pi$
$157$		0			0		0.644194	+	0.764862i	$0.277193\pi$
$158$	1.61170	−	1.63857i	1.61170	−	1.63857i
$159$		0			0
$160$		0			0
$161$	−0.116964	+	0.0316862i	−0.116964	+	0.0316862i
$162$	1.76106	−	0.670444i	1.76106	−	0.670444i
$163$	−1.21977	+	1.41627i	−1.21977	+	1.41627i	−0.340293	+	0.940319i	$0.610526\pi$
$163$	−1.21977	+	1.41627i	−1.21977	+	1.41627i	−0.879474	+	0.475947i	$0.842105\pi$
$164$		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
$169$	0.565270	−	0.824906i	0.565270	−	0.824906i
$170$		0			0
$171$		0			0
$172$	−2.24842	−	3.61298i	−2.24842	−	3.61298i
$173$		0			0		0.999757	−	0.0220445i	$-0.00701754\pi$
$173$		0			0		−0.999757	+	0.0220445i	$0.992982\pi$
$174$		0			0
$175$	−0.298515	−	0.954405i	−0.298515	−	0.954405i
$176$	4.57941	−	1.07942i	4.57941	−	1.07942i
$177$		0			0
$178$		0			0
$179$	1.12814	−	1.49996i	1.12814	−	1.49996i	0.287976	−	0.957638i	$-0.407018\pi$
$179$	1.12814	−	1.49996i	1.12814	−	1.49996i	0.840168	−	0.542326i	$-0.182456\pi$
$180$		0			0
$181$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$181$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$182$		0			0
$183$		0			0
$184$	−0.286493	+	0.208149i	−0.286493	+	0.208149i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.17481	−	1.09351i	1.17481	−	1.09351i	0.180881	−	0.983505i	$-0.442105\pi$
$191$	1.17481	−	1.09351i	1.17481	−	1.09351i	0.993931	−	0.110008i	$-0.0350877\pi$
$192$		0			0
$193$	−0.0984852	+	0.937024i	−0.0984852	+	0.937024i	0.828009	+	0.560715i	$0.189474\pi$
$193$	−0.0984852	+	0.937024i	−0.0984852	+	0.937024i	−0.926494	+	0.376309i	$0.877193\pi$
$194$		0			0
$195$		0			0
$196$	−1.37154	−	2.15071i	−1.37154	−	2.15071i
$197$	−0.665175	+	0.844968i	−0.665175	+	0.844968i	−0.995083	−	0.0990455i	$-0.968421\pi$
$197$	−0.665175	+	0.844968i	−0.665175	+	0.844968i	0.329907	+	0.944013i	$0.392982\pi$
$198$	−2.99483	−	0.165229i	−2.99483	−	0.165229i
$199$		0			0		0.329907	−	0.944013i	$-0.392982\pi$
$199$		0			0		−0.329907	+	0.944013i	$0.607018\pi$
$200$	−1.80760	−	2.29618i	−1.80760	−	2.29618i
$201$		0			0
$202$		0			0
$203$	−1.06056	−	0.701272i	−1.06056	−	0.701272i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.114174	−	0.0406081i	0.114174	−	0.0406081i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	1.74155	−	0.153978i	1.74155	−	0.153978i	0.828009	−	0.560715i	$-0.189474\pi$
$211$	1.74155	−	0.153978i	1.74155	−	0.153978i	0.913545	+	0.406737i	$0.133333\pi$
$212$	1.02235	−	0.813981i	1.02235	−	0.813981i
$213$		0			0
$214$	3.05692	−	1.65432i	3.05692	−	1.65432i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	3.32600	+	0.555011i	3.32600	+	0.555011i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.565270	−	0.824906i	$-0.691228\pi$
$223$		0			0		0.565270	+	0.824906i	$0.308772\pi$
$224$	−2.12466	−	1.57973i	−2.12466	−	1.57973i
$225$	0.371197	+	0.928554i	0.371197	+	0.928554i
$226$	−3.20290	+	1.87281i	−3.20290	+	1.87281i
$227$		0			0		0.609854	−	0.792514i	$-0.291228\pi$
$227$		0			0		−0.609854	+	0.792514i	$0.708772\pi$
$228$		0			0
$229$		0			0		−0.982493	−	0.186298i	$-0.940351\pi$
$229$		0			0		0.982493	+	0.186298i	$0.0596491\pi$
$230$		0			0
$231$		0			0
$232$	−3.62562	−	0.812521i	−3.62562	−	0.812521i
$233$	0.952146	+	0.235539i	0.952146	+	0.235539i	0.685350	−	0.728214i	$-0.259649\pi$
$233$	0.952146	+	0.235539i	0.952146	+	0.235539i	0.266796	+	0.963753i	$0.414035\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.228160	+	1.41529i	0.228160	+	1.41529i	0.802489	+	0.596667i	$0.203509\pi$
$239$	0.228160	+	1.41529i	0.228160	+	1.41529i	−0.574329	+	0.818625i	$0.694737\pi$
$240$		0			0
$241$		0			0		0.991264	−	0.131892i	$-0.0421053\pi$
$241$		0			0		−0.991264	+	0.131892i	$0.957895\pi$
$242$	2.57124	+	1.31905i	2.57124	+	1.31905i
$243$		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		0.930586	−	0.366074i	$-0.119298\pi$
$251$		0			0		−0.930586	+	0.366074i	$0.880702\pi$
$252$	1.53325	+	2.03858i	1.53325	+	2.03858i
$253$	−0.192312	−	0.0148687i	−0.192312	−	0.0148687i
$254$	0.395627	+	0.181396i	0.395627	+	0.181396i
$255$		0			0
$256$	−0.189782	−	0.0536651i	−0.189782	−	0.0536651i
$257$		0			0		0.490424	−	0.871484i	$-0.336842\pi$
$257$		0			0		−0.490424	+	0.871484i	$0.663158\pi$
$258$		0			0
$259$	−0.167046	+	0.392533i	−0.167046	+	0.392533i
$260$		0			0
$261$	1.11147	+	0.617431i	1.11147	+	0.617431i
$262$		0			0
$263$	−0.344330	−	1.49773i	−0.344330	−	1.49773i	−0.795863	−	0.605477i	$-0.792982\pi$
$263$	−0.344330	−	1.49773i	−0.344330	−	1.49773i	0.451533	−	0.892254i	$-0.350877\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.265218	−	1.76905i	−0.265218	−	1.76905i
$269$		0			0		0.371197	−	0.928554i	$-0.378947\pi$
$269$		0			0		−0.371197	+	0.928554i	$0.621053\pi$
$270$		0			0
$271$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$271$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$272$		0			0
$273$		0			0
$274$	−1.25629	−	1.30572i	−1.25629	−	1.30572i
$275$	0.0613951	−	1.59054i	0.0613951	−	1.59054i
$276$		0			0
$277$	0.358601	−	1.94983i	0.358601	−	1.94983i	0.0495838	−	0.998770i	$-0.484211\pi$
$277$	0.358601	−	1.94983i	0.358601	−	1.94983i	0.309017	−	0.951057i	$-0.400000\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.81095	+	0.830325i	−1.81095	+	0.830325i	−0.868768	+	0.495219i	$0.835088\pi$
$281$	−1.81095	+	0.830325i	−1.81095	+	0.830325i	−0.942181	+	0.335105i	$0.891228\pi$
$282$		0			0
$283$		0			0		−0.846095	−	0.533032i	$-0.821053\pi$
$283$		0			0		0.846095	+	0.533032i	$0.178947\pi$
$284$	0.185160	+	0.172347i	0.185160	+	0.172347i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	2.24012	+	1.41125i	2.24012	+	1.41125i
$289$	0.938430	−	0.345471i	0.938430	−	0.345471i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.815447	−	0.578832i	$-0.196491\pi$
$293$		0			0		−0.815447	+	0.578832i	$0.803509\pi$
$294$		0			0
$295$		0			0
$296$	−0.0480851	+	1.24572i	−0.0480851	+	1.24572i
$297$		0			0
$298$	−2.42092	+	2.51617i	−2.42092	+	2.51617i
$299$		0			0
$300$		0			0
$301$	−1.42124	+	0.873632i	−1.42124	+	0.873632i
$302$	1.36837	−	3.42299i	1.36837	−	3.42299i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.868768	−	0.495219i	$-0.835088\pi$
$307$		0			0		0.868768	+	0.495219i	$0.164912\pi$
$308$	−0.909712	−	3.95698i	−0.909712	−	3.95698i
$309$		0			0
$310$		0			0
$311$		0			0		−0.840168	−	0.542326i	$-0.817544\pi$
$311$		0			0		0.840168	+	0.542326i	$0.182456\pi$
$312$		0			0
$313$		0			0		0.191711	−	0.981451i	$-0.438596\pi$
$313$		0			0		−0.191711	+	0.981451i	$0.561404\pi$
$314$		0			0
$315$		0			0
$316$	−2.84227	−	1.26546i	−2.84227	−	1.26546i
$317$	1.75990	+	0.806917i	1.75990	+	0.806917i	0.984487	+	0.175457i	$0.0561404\pi$
$317$	1.75990	+	0.806917i	1.75990	+	0.806917i	0.775409	+	0.631460i	$0.217544\pi$
$318$		0			0
$319$	−1.21647	−	1.61739i	−1.21647	−	1.61739i
$320$		0			0
$321$		0			0
$322$	0.133199	+	0.185474i	0.133199	+	0.185474i
$323$		0			0
$324$	−1.68583	−	1.91433i	−1.68583	−	1.91433i
$325$		0			0
$326$	3.30526	+	1.21679i	3.30526	+	1.21679i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.969470	+	1.07671i	−0.969470	+	1.07671i	0.0275543	+	0.999620i	$0.491228\pi$
$331$	−0.969470	+	1.07671i	−0.969470	+	1.07671i	−0.997024	+	0.0770854i	$0.975439\pi$
$332$		0			0
$333$	0.136291	−	0.404242i	0.136291	−	0.404242i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.00867518	−	0.142915i	−0.00867518	−	0.142915i	−0.999939	−	0.0110229i	$-0.996491\pi$
$337$	−0.00867518	−	0.142915i	−0.00867518	−	0.142915i	0.991264	−	0.131892i	$-0.0421053\pi$
$338$	−1.82922	−	0.452508i	−1.82922	−	0.452508i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.846095	+	0.533032i	−0.846095	+	0.533032i
$344$	−2.97317	+	3.86367i	−2.97317	+	3.86367i
$345$		0			0
$346$		0			0
$347$	−1.41154	−	1.04951i	−1.41154	−	1.04951i	−0.989750	−	0.142811i	$-0.954386\pi$
$347$	−1.41154	−	1.04951i	−1.41154	−	1.04951i	−0.421786	−	0.906696i	$-0.638596\pi$
$348$		0			0
$349$		0			0		−0.411766	−	0.911290i	$-0.635088\pi$
$349$		0			0		0.411766	+	0.911290i	$0.364912\pi$
$350$	−1.48703	+	1.15740i	−1.48703	+	1.15740i
$351$		0			0
$352$	−2.34372	−	3.50240i	−2.34372	−	3.50240i
$353$		0			0		−0.986361	−	0.164595i	$-0.947368\pi$
$353$		0			0		0.986361	+	0.164595i	$0.0526316\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−3.39242	−	0.999798i	−3.39242	−	0.999798i
$359$	−1.09719	+	0.873564i	−1.09719	+	0.873564i	−0.992658	−	0.120958i	$-0.961404\pi$
$359$	−1.09719	+	0.873564i	−1.09719	+	0.873564i	−0.104528	+	0.994522i	$0.533333\pi$
$360$		0			0
$361$	−0.889752	+	0.456444i	−0.889752	+	0.456444i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.480787	−	0.876837i	$-0.659649\pi$
$367$		0			0		0.480787	+	0.876837i	$0.340351\pi$
$368$	0.298781	+	0.197562i	0.298781	+	0.197562i
$369$		0			0
$370$		0			0
$371$	−0.316892	−	0.402546i	−0.316892	−	0.402546i
$372$		0			0
$373$	−0.361212	−	0.0199286i	−0.361212	−	0.0199286i	−0.126427	−	0.991976i	$-0.540351\pi$
$373$	−0.361212	−	0.0199286i	−0.361212	−	0.0199286i	−0.234785	+	0.972047i	$0.575439\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.96451	+	0.372506i	−1.96451	+	0.372506i	−0.978148	+	0.207912i	$0.933333\pi$
$379$	−1.96451	+	0.372506i	−1.96451	+	0.372506i	−0.986361	+	0.164595i	$0.947368\pi$
$380$		0			0
$381$		0			0
$382$	−2.70598	−	1.35070i	−2.70598	−	1.35070i
$383$		0			0		0.451533	−	0.892254i	$-0.350877\pi$
$383$		0			0		−0.451533	+	0.892254i	$0.649123\pi$
$384$		0			0
$385$		0			0
$386$	1.71866	−	0.445319i	1.71866	−	0.445319i
$387$	1.34967	−	0.980589i	1.34967	−	0.980589i
$388$		0			0
$389$	−0.0269651	+	1.63067i	−0.0269651	+	1.63067i	0.565270	+	0.824906i	$0.308772\pi$
$389$	−0.0269651	+	1.63067i	−0.0269651	+	1.63067i	−0.592235	+	0.805765i	$0.701754\pi$
$390$		0			0
$391$		0			0
$392$	−1.75654	+	2.33547i	−1.75654	+	2.33547i
$393$		0			0
$394$	1.93064	+	0.615558i	1.93064	+	0.615558i
$395$		0			0
$396$	1.21203	+	3.87508i	1.21203	+	3.87508i
$397$		0			0		0.970739	−	0.240139i	$-0.0771930\pi$
$397$		0			0		−0.970739	+	0.240139i	$0.922807\pi$
$398$		0			0
$399$		0			0
$400$	−1.53400	+	2.52664i	−1.53400	+	2.52664i
$401$	−0.362646	+	0.124497i	−0.362646	+	0.124497i	−0.500000	−	0.866025i	$-0.666667\pi$
$401$	−0.362646	+	0.124497i	−0.362646	+	0.124497i	0.137354	+	0.990522i	$0.456140\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−0.536808	+	2.33495i	−0.536808	+	2.33495i
$407$	−0.459894	+	0.499578i	−0.459894	+	0.499578i
$408$		0			0
$409$		0			0		0.934564	−	0.355794i	$-0.115789\pi$
$409$		0			0		−0.934564	+	0.355794i	$0.884211\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−0.147100	−	0.174654i	−0.147100	−	0.174654i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.256156	−	0.966635i	$-0.417544\pi$
$419$		0			0		−0.256156	+	0.966635i	$0.582456\pi$
$420$		0			0
$421$	1.11879	+	0.527967i	1.11879	+	0.527967i	0.894729	−	0.446609i	$-0.147368\pi$
$421$	1.11879	+	0.527967i	1.11879	+	0.527967i	0.224056	+	0.974576i	$0.428070\pi$
$422$	−1.42242	−	2.97163i	−1.42242	−	2.97163i
$423$		0			0
$424$	−1.28400	−	0.769900i	−1.28400	−	0.769900i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−3.54821	−	3.09014i	−3.54821	−	3.09014i
$429$		0			0
$430$		0			0
$431$	0.678561	−	1.87504i	0.678561	−	1.87504i	0.266796	−	0.963753i	$-0.414035\pi$
$431$	0.678561	−	1.87504i	0.678561	−	1.87504i	0.411766	−	0.911290i	$-0.364912\pi$
$432$		0			0
$433$		0			0		0.461341	−	0.887223i	$-0.347368\pi$
$433$		0			0		−0.461341	+	0.887223i	$0.652632\pi$
$434$		0			0
$435$		0			0
$436$	−0.875079	−	4.47992i	−0.875079	−	4.47992i
$437$		0			0
$438$		0			0
$439$		0			0		0.768401	−	0.639969i	$-0.221053\pi$
$439$		0			0		−0.768401	+	0.639969i	$0.778947\pi$
$440$		0			0
$441$	0.802489	−	0.596667i	0.802489	−	0.596667i
$442$		0			0
$443$	0.973372	−	1.32432i	0.973372	−	1.32432i	0.0275543	−	0.999620i	$-0.491228\pi$
$443$	0.973372	−	1.32432i	0.973372	−	1.32432i	0.945817	−	0.324699i	$-0.105263\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.564007	+	1.95338i	−0.564007	+	1.95338i
$449$	1.72010	−	0.527614i	1.72010	−	0.527614i	0.731980	−	0.681326i	$-0.238596\pi$
$449$	1.72010	−	0.527614i	1.72010	−	0.527614i	0.988116	+	0.153712i	$0.0491228\pi$
$450$	1.39338	−	1.26858i	1.39338	−	1.26858i
$451$		0			0
$452$	3.89449	+	3.17150i	3.89449	+	3.17150i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.349649	+	1.69074i	0.349649	+	1.69074i	0.669131	+	0.743145i	$0.266667\pi$
$457$	0.349649	+	1.69074i	0.349649	+	1.69074i	−0.319482	+	0.947592i	$0.603509\pi$
$458$		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
$463$	0.523146	−	1.06268i	0.523146	−	1.06268i	−0.461341	−	0.887223i	$-0.652632\pi$
$463$	0.523146	−	1.06268i	0.523146	−	1.06268i	0.984487	−	0.175457i	$-0.0561404\pi$
$464$	0.516204	+	3.72259i	0.516204	+	3.72259i
$465$		0			0
$466$	−0.213447	−	1.83590i	−0.213447	−	1.83590i
$467$		0			0		−0.999939	−	0.0110229i	$-0.996491\pi$
$467$		0			0		0.999939	+	0.0110229i	$0.00350877\pi$
$468$		0			0
$469$	−0.694087	+	0.100150i	−0.694087	+	0.100150i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.59741	+	0.552097i	−2.59741	+	0.552097i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.346980	+	0.376920i	0.346980	+	0.376920i
$478$	2.34685	−	1.33776i	2.34685	−	1.33776i
$479$		0			0		−0.266796	−	0.963753i	$-0.585965\pi$
$479$		0			0		0.266796	+	0.963753i	$0.414035\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.451766	−	3.88574i	0.451766	−	3.88574i
$485$		0			0
$486$		0			0
$487$	0.439971	−	0.743016i	0.439971	−	0.743016i	−0.556143	−	0.831087i	$-0.687719\pi$
$487$	0.439971	−	0.743016i	0.439971	−	0.743016i	0.996114	+	0.0880708i	$0.0280702\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.87510	+	0.666915i	1.87510	+	0.666915i	0.970739	+	0.240139i	$0.0771930\pi$
$491$	1.87510	+	0.666915i	1.87510	+	0.666915i	0.904357	+	0.426776i	$0.140351\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.0679645	−	0.0722151i	0.0679645	−	0.0722151i
$498$		0			0
$499$	0.394729	+	1.31263i	0.394729	+	1.31263i	0.894729	+	0.446609i	$0.147368\pi$
$499$	0.394729	+	1.31263i	0.394729	+	1.31263i	−0.500000	+	0.866025i	$0.666667\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.627176	−	0.778877i	$-0.284211\pi$
$503$		0			0		−0.627176	+	0.778877i	$0.715789\pi$
$504$	1.57128	−	2.46392i	1.57128	−	2.46392i
$505$		0			0
$506$	0.100827	+	0.349202i	0.100827	+	0.349202i
$507$		0			0
$508$	0.0421774	−	0.587649i	0.0421774	−	0.587649i
$509$		0			0		0.298515	−	0.954405i	$-0.403509\pi$
$509$		0			0		−0.298515	+	0.954405i	$0.596491\pi$
$510$		0			0
$511$		0			0
$512$	−0.0670539	−	0.809220i	−0.0670539	−	0.809220i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	0.803086	+	0.0354331i	0.803086	+	0.0354331i
$519$		0			0
$520$		0			0
$521$		0			0		0.0495838	−	0.998770i	$-0.484211\pi$
$521$		0			0		−0.0495838	+	0.998770i	$0.515789\pi$
$522$	0.355220	−	2.36939i	0.355220	−	2.36939i
$523$		0			0		−0.863256	−	0.504766i	$-0.831579\pi$
$523$		0			0		0.863256	+	0.504766i	$0.168421\pi$
$524$		0			0
$525$		0			0
$526$	−2.41558	+	1.59724i	−2.41558	+	1.59724i
$527$		0			0
$528$		0			0
$529$	0.617967	+	0.767440i	0.617967	+	0.767440i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−1.79148	+	0.995184i	−1.79148	+	0.995184i
$537$		0			0
$538$		0			0
$539$	−1.55320	+	0.348080i	−1.55320	+	0.348080i
$540$		0			0
$541$	−0.458205	+	1.89704i	−0.458205	+	1.89704i	−0.0165339	+	0.999863i	$0.505263\pi$
$541$	−0.458205	+	1.89704i	−0.458205	+	1.89704i	−0.441671	+	0.897177i	$0.645614\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.479229	−	0.390264i	0.479229	−	0.390264i	−0.360939	−	0.932589i	$-0.617544\pi$
$547$	0.479229	−	0.390264i	0.479229	−	0.390264i	0.840168	+	0.542326i	$0.182456\pi$
$548$	−1.05901	+	2.21241i	−1.05901	+	2.21241i
$549$		0			0
$550$	−2.84743	+	0.942570i	−2.84743	+	0.942570i
$551$		0			0
$552$		0			0
$553$	−0.502234	+	1.11151i	−0.502234	+	1.11151i
$554$	−3.67785	+	0.655473i	−3.67785	+	0.655473i
$555$		0			0
$556$		0			0
$557$	0.752261	−	1.37194i	0.752261	−	1.37194i	−0.170028	−	0.985439i	$-0.554386\pi$
$557$	0.752261	−	1.37194i	0.752261	−	1.37194i	0.922290	−	0.386499i	$-0.126316\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	2.66184	+	2.64721i	2.66184	+	2.64721i
$563$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$563$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.754107	+	0.656752i	−0.754107	+	0.656752i
$568$	0.110532	−	0.267890i	0.110532	−	0.267890i
$569$	0.0656110	+	0.175239i	0.0656110	+	0.175239i	0.965209	−	0.261480i	$-0.0842105\pi$
$569$	0.0656110	+	0.175239i	0.0656110	+	0.175239i	−0.899598	+	0.436719i	$0.856140\pi$
$570$		0			0
$571$	0.137354	−	0.990522i	0.137354	−	0.990522i
$571$	0.137354	−	0.990522i	0.137354	−	0.990522i
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.0913828	−	0.0795853i	0.0913828	−	0.0795853i
$576$	0.411752	−	1.99104i	0.411752	−	1.99104i
$577$		0			0		−0.999453	−	0.0330634i	$-0.989474\pi$
$577$		0			0		0.999453	+	0.0330634i	$0.0105263\pi$
$578$	−1.22971	−	1.42781i	−1.22971	−	1.42781i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.260525	−	0.772725i	−0.260525	−	0.772725i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.137354	−	0.990522i	$-0.456140\pi$
$587$		0			0		−0.137354	+	0.990522i	$0.543860\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	1.19708	−	0.396263i	1.19708	−	0.396263i
$593$		0			0		0.746821	−	0.665025i	$-0.231579\pi$
$593$		0			0		−0.746821	+	0.665025i	$0.768421\pi$
$594$		0			0
$595$		0			0
$596$	4.33892	+	1.87478i	4.33892	+	1.87478i
$597$		0			0
$598$		0			0
$599$	−1.95598	−	0.282227i	−1.95598	−	0.282227i	−0.956036	−	0.293250i	$-0.905263\pi$
$599$	−1.95598	−	0.282227i	−1.95598	−	0.282227i	−0.999939	+	0.0110229i	$0.996491\pi$
$600$		0			0
$601$		0			0		0.234785	−	0.972047i	$-0.424561\pi$
$601$		0			0		−0.234785	+	0.972047i	$0.575439\pi$
$602$	2.48077	+	1.93086i	2.48077	+	1.93086i
$603$	0.684302	−	0.153356i	0.684302	−	0.153356i
$604$	−4.98894	−	0.110005i	−4.98894	−	0.110005i
$605$		0			0
$606$		0			0
$607$		0			0		−0.997814	−	0.0660906i	$-0.978947\pi$
$607$		0			0		0.997814	+	0.0660906i	$0.0210526\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.0207394	+	0.0257558i	0.0207394	+	0.0257558i	0.789141	−	0.614213i	$-0.210526\pi$
$613$	0.0207394	+	0.0257558i	0.0207394	+	0.0257558i	−0.768401	+	0.639969i	$0.778947\pi$
$614$		0			0
$615$		0			0
$616$	−3.88000	+	2.56555i	−3.88000	+	2.56555i
$617$	−1.82881	−	0.161693i	−1.82881	−	0.161693i	−0.879474	−	0.475947i	$-0.842105\pi$
$617$	−1.82881	−	0.161693i	−1.82881	−	0.161693i	−0.949339	+	0.314254i	$0.898246\pi$
$618$		0			0
$619$		0			0		−0.863256	−	0.504766i	$-0.831579\pi$
$619$		0			0		0.863256	+	0.504766i	$0.168421\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.685350	+	0.728214i	0.685350	+	0.728214i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	1.95056	−	0.237680i	1.95056	−	0.237680i	0.952745	−	0.303771i	$-0.0982456\pi$
$631$	1.95056	−	0.237680i	1.95056	−	0.237680i	0.997814	+	0.0660906i	$0.0210526\pi$
$632$	−0.215964	+	3.55780i	−0.215964	+	3.55780i
$633$		0			0
$634$	0.261175	−	3.63889i	0.261175	−	3.63889i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−2.05050	+	3.21538i	−2.05050	+	3.21538i
$639$	−0.0621955	+	0.0772393i	−0.0621955	+	0.0772393i
$640$		0			0
$641$	0.0419542	+	0.0357325i	0.0419542	+	0.0357325i	0.669131	−	0.743145i	$-0.266667\pi$
$641$	0.0419542	+	0.0357325i	0.0419542	+	0.0357325i	−0.627176	+	0.778877i	$0.715789\pi$
$642$		0			0
$643$		0			0		−0.287976	−	0.957638i	$-0.592982\pi$
$643$		0			0		0.287976	+	0.957638i	$0.407018\pi$
$644$	0.171909	−	0.256896i	0.171909	−	0.256896i
$645$		0			0
$646$		0			0
$647$		0			0		−0.815447	−	0.578832i	$-0.803509\pi$
$647$		0			0		0.815447	+	0.578832i	$0.196491\pi$
$648$	−1.37668	+	2.57771i	−1.37668	+	2.57771i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.0262779	−	4.76773i	−0.0262779	−	4.76773i
$653$	−0.596835	−	1.17938i	−0.596835	−	1.17938i	−0.968033	−	0.250825i	$-0.919298\pi$
$653$	−0.596835	−	1.17938i	−0.596835	−	1.17938i	0.371197	−	0.928554i	$-0.378947\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.173293	+	1.35970i	−0.173293	+	1.35970i	0.635724	+	0.771917i	$0.280702\pi$
$659$	−0.173293	+	1.35970i	−0.173293	+	1.35970i	−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	$0.200000\pi$
$662$	2.54065	+	0.999439i	2.54065	+	0.999439i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.803428	+	0.0265786i	−0.803428	+	0.0265786i
$667$	0.0261970	−	0.151831i	0.0261970	−	0.151831i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.97649	−	0.285188i	1.97649	−	0.285188i	0.980380	−	0.197117i	$-0.0631579\pi$
$673$	1.97649	−	0.285188i	1.97649	−	0.285188i	0.996114	−	0.0880708i	$-0.0280702\pi$
$674$	−0.246474	+	0.109737i	−0.246474	+	0.109737i
$675$		0			0
$676$	0.294580	+	2.53375i	0.294580	+	2.53375i
$677$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$677$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.43151	−	0.924036i	1.43151	−	0.924036i	0.431754	−	0.901991i	$-0.357895\pi$
$683$	1.43151	−	0.924036i	1.43151	−	0.924036i	0.999757	−	0.0220445i	$-0.00701754\pi$
$684$		0			0
$685$		0			0
$686$	1.49969	+	1.14094i	1.49969	+	1.14094i
$687$		0			0
$688$	4.71439	+	1.44607i	4.71439	+	1.44607i
$689$		0			0
$690$		0			0
$691$		0			0		−0.461341	−	0.887223i	$-0.652632\pi$
$691$		0			0		0.461341	+	0.887223i	$0.347368\pi$
$692$		0			0
$693$	1.52175	−	0.466774i	1.52175	−	0.466774i
$694$	−0.919450	+	3.18441i	−0.919450	+	3.18441i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	2.17309	+	1.33579i	2.17309	+	1.33579i
$701$	0.150161	−	0.111648i	0.150161	−	0.111648i	−0.518970	−	0.854793i	$-0.673684\pi$
$701$	0.150161	−	0.111648i	0.150161	−	0.111648i	0.669131	+	0.743145i	$0.266667\pi$
$702$		0			0
$703$		0			0
$704$	−1.88776	+	2.62863i	−1.88776	+	2.62863i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.294780	−	0.566903i	0.294780	−	0.566903i	−0.693336	−	0.720615i	$-0.743860\pi$
$709$	0.294780	−	0.566903i	0.294780	−	0.566903i	0.988116	+	0.153712i	$0.0491228\pi$
$710$		0			0
$711$	0.415058	−	1.14692i	0.415058	−	1.14692i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.342734	+	4.77524i	0.342734	+	4.77524i
$717$		0			0
$718$	2.26654	+	1.35904i	2.26654	+	1.35904i
$719$		0			0		−0.922290	−	0.386499i	$-0.873684\pi$
$719$		0			0		0.922290	+	0.386499i	$0.126316\pi$
$720$		0			0
$721$		0			0
$722$	1.39338	+	1.26858i	1.39338	+	1.26858i
$723$		0			0
$724$		0			0
$725$	1.26034	+	0.167694i	1.26034	+	0.167694i
$726$		0			0
$727$		0			0		−0.724425	−	0.689353i	$-0.757895\pi$
$727$		0			0		0.724425	+	0.689353i	$0.242105\pi$
$728$		0			0
$729$	0.701237	−	0.712928i	0.701237	−	0.712928i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.934564	−	0.355794i	$-0.115789\pi$
$733$		0			0		−0.934564	+	0.355794i	$0.884211\pi$
$734$		0			0
$735$		0			0
$736$	0.0718852	−	0.312679i	0.0718852	−	0.312679i
$737$	−1.09434	−	0.220029i	−1.09434	−	0.220029i
$738$		0			0
$739$	−1.89468	−	0.337674i	−1.89468	−	0.337674i	−0.899598	−	0.436719i	$-0.856140\pi$
$739$	−1.89468	−	0.337674i	−1.89468	−	0.337674i	−0.995083	+	0.0990455i	$0.968421\pi$
$740$		0			0
$741$		0			0
$742$	−0.501004	+	0.825201i	−0.501004	+	0.825201i
$743$	−0.606905	−	0.975233i	−0.606905	−	0.975233i	−0.998482	−	0.0550878i	$-0.982456\pi$
$743$	−0.606905	−	0.975233i	−0.606905	−	0.975233i	0.391577	−	0.920146i	$-0.371930\pi$
$744$		0			0
$745$		0			0
$746$	0.203494	+	0.650607i	0.203494	+	0.650607i
$747$		0			0
$748$		0			0
$749$	−1.21908	+	1.38431i	−1.21908	+	1.38431i
$750$		0			0
$751$	0.130989	−	0.473175i	0.130989	−	0.473175i	−0.868768	−	0.495219i	$-0.835088\pi$
$751$	0.130989	−	0.473175i	0.130989	−	0.473175i	0.999757	+	0.0220445i	$0.00701754\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.30028	+	1.08295i	1.30028	+	1.08295i	0.991264	+	0.131892i	$0.0421053\pi$
$757$	1.30028	+	1.08295i	1.30028	+	1.08295i	0.309017	+	0.951057i	$0.400000\pi$
$758$	1.95538	+	3.22069i	1.95538	+	3.22069i
$759$		0			0
$760$		0			0
$761$		0			0		−0.381410	−	0.924406i	$-0.624561\pi$
$761$		0			0		0.381410	+	0.924406i	$0.375439\pi$
$762$		0			0
$763$	−1.75813	+	0.333373i	−1.75813	+	0.333373i
$764$	−0.427940	+	4.07158i	−0.427940	+	4.07158i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		−0.998482	−	0.0550878i	$-0.982456\pi$
$769$		0			0		0.998482	+	0.0550878i	$0.0175439\pi$
$770$		0			0
$771$		0			0
$772$	−1.38031	−	1.96744i	−1.38031	−	1.96744i
$773$		0			0		−0.782322	−	0.622874i	$-0.785965\pi$
$773$		0			0		0.782322	+	0.622874i	$0.214035\pi$
$774$	−2.62223	−	1.73389i	−2.62223	−	1.73389i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	2.89550	−	1.02984i	2.89550	−	1.02984i
$779$		0			0
$780$		0			0
$781$	0.140445	−	0.0720486i	0.140445	−	0.0720486i
$782$		0			0
$783$		0			0
$784$	2.83528	+	0.835602i	2.83528	+	0.835602i
$785$		0			0
$786$		0			0
$787$		0			0		−0.995083	−	0.0990455i	$-0.968421\pi$
$787$		0			0		0.995083	+	0.0990455i	$0.0315789\pi$
$788$	−0.136012	−	2.73971i	−0.136012	−	2.73971i
$789$		0			0
$790$		0			0
$791$	1.25172	−	1.51988i	1.25172	−	1.51988i
$792$	3.67069	−	2.85701i	3.67069	−	2.85701i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.863256	−	0.504766i	$-0.168421\pi$
$797$		0			0		−0.863256	+	0.504766i	$0.831579\pi$
$798$		0			0
$799$		0			0
$800$	2.60124	+	0.493242i	2.60124	+	0.493242i
$801$		0			0
$802$	0.459313	+	0.557713i	0.459313	+	0.557713i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.101695	+	0.301630i	−0.101695	+	0.301630i	−0.986361	−	0.164595i	$-0.947368\pi$
$809$	−0.101695	+	0.301630i	−0.101695	+	0.301630i	0.884667	+	0.466224i	$0.154386\pi$
$810$		0			0
$811$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$811$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$812$	3.21490	−	0.427757i	3.21490	−	0.427757i
$813$		0			0
$814$	1.18548	+	0.481501i	1.18548	+	0.481501i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.74168	+	0.451283i	1.74168	+	0.451283i	0.980380	−	0.197117i	$-0.0631579\pi$
$821$	1.74168	+	0.451283i	1.74168	+	0.451283i	0.761300	+	0.648400i	$0.224561\pi$
$822$		0			0
$823$	−1.19859	−	1.59362i	−1.19859	−	1.59362i	−0.660898	−	0.750475i	$-0.729825\pi$
$823$	−1.19859	−	1.59362i	−1.19859	−	1.59362i	−0.537687	−	0.843145i	$-0.680702\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.92267	−	0.543678i	−1.92267	−	0.543678i	−0.973327	−	0.229424i	$-0.926316\pi$
$827$	−1.92267	−	0.543678i	−1.92267	−	0.543678i	−0.949339	−	0.314254i	$-0.898246\pi$
$828$	−0.151594	+	0.269383i	−0.151594	+	0.269383i
$829$		0			0		0.191711	−	0.981451i	$-0.438596\pi$
$829$		0			0		−0.191711	+	0.981451i	$0.561404\pi$
$830$		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		−0.148264	−	0.988948i	$-0.547368\pi$
$839$		0			0		0.148264	+	0.988948i	$0.452632\pi$
$840$		0			0
$841$	0.525275	−	0.322886i	0.525275	−	0.322886i
$842$	0.192505	−	2.32319i	0.192505	−	2.32319i
$843$		0			0
$844$	−3.09208	+	3.21374i	−3.09208	+	3.21374i
$845$		0			0
$846$		0			0
$847$	−1.52233	−	0.185499i	−1.52233	−	0.185499i
$848$	−0.273911	+	1.48934i	−0.273911	+	1.48934i
$849$		0			0
$850$		0			0
$851$	−0.0516922		0.000569833i	−0.0516922		0.000569833i
$852$		0			0
$853$		0			0		0.938430	−	0.345471i	$-0.112281\pi$
$853$		0			0		−0.938430	+	0.345471i	$0.887719\pi$
$854$		0			0
$855$		0			0
$856$	−1.89008	+	5.04818i	−1.89008	+	5.04818i
$857$		0			0		0.350638	−	0.936511i	$-0.385965\pi$
$857$		0			0		−0.350638	+	0.936511i	$0.614035\pi$
$858$		0			0
$859$		0			0		−0.846095	−	0.533032i	$-0.821053\pi$
$859$		0			0		0.846095	+	0.533032i	$0.178947\pi$
$860$		0			0
$861$		0			0
$862$	−3.75728	+	0.0414187i	−3.75728	+	0.0414187i
$863$	0.106650	+	0.836802i	0.106650	+	0.836802i	0.952745	+	0.303771i	$0.0982456\pi$
$863$	0.106650	+	0.836802i	0.106650	+	0.836802i	−0.846095	+	0.533032i	$0.821053\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.34607	+	1.39903i	−1.34607	+	1.39903i
$870$		0			0
$871$		0			0
$872$	−4.45497	+	2.73846i	−4.45497	+	2.73846i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.464369	−	1.83375i	0.464369	−	1.83375i	−0.0825793	−	0.996584i	$-0.526316\pi$
$877$	0.464369	−	1.83375i	0.464369	−	1.83375i	0.546948	−	0.837166i	$-0.315789\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.874174	−	0.485613i	$-0.838596\pi$
$881$		0			0		0.874174	+	0.485613i	$0.161404\pi$
$882$	−1.58318	−	1.02194i	−1.58318	−	1.02194i
$883$	0.524032	−	1.23140i	0.524032	−	1.23140i	−0.421786	−	0.906696i	$-0.638596\pi$
$883$	0.524032	−	1.23140i	0.524032	−	1.23140i	0.945817	−	0.324699i	$-0.105263\pi$
$884$		0			0
$885$		0			0
$886$	−2.98019	−	0.842719i	−2.98019	−	0.842719i
$887$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$887$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$888$		0			0
$889$	−0.230282	−	0.0178044i	−0.230282	−	0.0178044i
$890$		0			0
$891$	−1.48124	+	0.582689i	−1.48124	+	0.582689i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	1.18011	−	0.0912408i	1.18011	−	0.0912408i
$897$		0			0
$898$	−2.06761	−	2.68689i	−2.06761	−	2.68689i
$899$		0			0
$900$	−2.26960	−	1.16431i	−2.26960	−	1.16431i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	1.83828	−	5.45238i	1.83828	−	5.45238i
$905$		0			0
$906$		0			0
$907$	0.359565	+	1.95507i	0.359565	+	1.95507i	0.287976	+	0.957638i	$0.407018\pi$
$907$	0.359565	+	1.95507i	0.359565	+	1.95507i	0.0715891	+	0.997434i	$0.477193\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.891586	+	1.08259i	0.891586	+	1.08259i	0.996114	+	0.0880708i	$0.0280702\pi$
$911$	0.891586	+	1.08259i	0.891586	+	1.08259i	−0.104528	+	0.994522i	$0.533333\pi$
$912$		0			0
$913$		0			0
$914$	2.75266	−	1.73415i	2.75266	−	1.73415i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.419653	+	0.612406i	0.419653	+	0.612406i	0.975796	−	0.218681i	$-0.0701754\pi$
$919$	0.419653	+	0.612406i	0.419653	+	0.612406i	−0.556143	+	0.831087i	$0.687719\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.0211524	−	0.426075i	−0.0211524	−	0.426075i
$926$	−2.22100	−	0.221067i	−2.22100	−	0.221067i
$927$		0			0
$928$	2.96055	−	1.60217i	2.96055	−	1.60217i
$929$		0			0		−0.959210	−	0.282694i	$-0.908772\pi$
$929$		0			0		0.959210	+	0.282694i	$0.0912281\pi$
$930$		0			0
$931$		0			0
$932$	−2.22613	+	1.14201i	−2.22613	+	1.14201i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.0935596	−	0.995614i	$-0.470175\pi$
$937$		0			0		−0.0935596	+	0.995614i	$0.529825\pi$
$938$	0.635339	+	1.15870i	0.635339	+	1.15870i
$939$		0			0
$940$		0			0
$941$		0			0		−0.574329	−	0.818625i	$-0.694737\pi$
$941$		0			0		0.574329	+	0.818625i	$0.305263\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	2.69048	+	4.21894i	2.69048	+	4.21894i
$947$	−1.88715	−	0.208870i	−1.88715	−	0.208870i	−0.909007	−	0.416782i	$-0.863158\pi$
$947$	−1.88715	−	0.208870i	−1.88715	−	0.208870i	−0.978148	+	0.207912i	$0.933333\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.534180	−	0.266639i	−0.534180	−	0.266639i	0.159156	−	0.987253i	$-0.449123\pi$
$953$	−0.534180	−	0.266639i	−0.534180	−	0.266639i	−0.693336	+	0.720615i	$0.743860\pi$
$954$	0.435902	−	0.861366i	0.435902	−	0.861366i
$955$		0			0
$956$	−2.80986	−	2.34021i	−2.80986	−	2.34021i
$957$		0			0
$958$		0			0
$959$	0.865031	+	0.419938i	0.865031	+	0.419938i
$960$		0			0
$961$	0.245485	+	0.969400i	0.245485	+	0.969400i
$962$		0			0
$963$	1.10874	−	1.47417i	1.10874	−	1.47417i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.545414	−	1.74378i	−0.545414	−	1.74378i	−0.660898	−	0.750475i	$-0.729825\pi$
$967$	−0.545414	−	1.74378i	−0.545414	−	1.74378i	0.115485	−	0.993309i	$-0.463158\pi$
$968$	−4.35048	+	1.07621i	−4.35048	+	1.07621i
$969$		0			0
$970$		0			0
$971$		0			0		0.518970	−	0.854793i	$-0.326316\pi$
$971$		0			0		−0.518970	+	0.854793i	$0.673684\pi$
$972$		0			0
$973$		0			0
$974$	−1.60192	−	0.285497i	−1.60192	−	0.285497i
$975$		0			0
$976$		0			0
$977$	−0.0664387	+	0.288988i	−0.0664387	+	0.288988i	−0.997024	−	0.0770854i	$-0.975439\pi$
$977$	−0.0664387	+	0.288988i	−0.0664387	+	0.288988i	0.930586	+	0.366074i	$0.119298\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	1.72720	−	0.467908i	1.72720	−	0.467908i
$982$	−0.0620055	−	3.74968i	−0.0620055	−	3.74968i
$983$		0			0		0.421786	−	0.906696i	$-0.361404\pi$
$983$		0			0		−0.421786	+	0.906696i	$0.638596\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.166132	−	0.115194i	−0.166132	−	0.115194i
$990$		0			0
$991$	−1.33745	−	1.21766i	−1.33745	−	1.21766i	−0.956036	−	0.293250i	$-0.905263\pi$
$991$	−1.33745	−	1.21766i	−1.33745	−	1.21766i	−0.381410	−	0.924406i	$-0.624561\pi$
$992$		0			0
$993$		0			0
$994$	−0.172346	−	0.0722241i	−0.172346	−	0.0722241i
$995$		0			0
$996$		0			0
$997$		0			0		−0.0715891	−	0.997434i	$-0.522807\pi$
$997$		0			0		0.0715891	+	0.997434i	$0.477193\pi$
$998$	2.05563	−	1.56388i	2.05563	−	1.56388i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3997.1.cz.a.482.1	✓	144
7.6	odd	2	CM	3997.1.cz.a.482.1	✓	144
571.494	even	285	inner	3997.1.cz.a.2778.1	yes	144
3997.2778	odd	570	inner	3997.1.cz.a.2778.1	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3997.1.cz.a.482.1	✓	144	1.1	even	1	trivial
3997.1.cz.a.482.1	✓	144	7.6	odd	2	CM
3997.1.cz.a.2778.1	yes	144	571.494	even	285	inner
3997.1.cz.a.2778.1	yes	144	3997.2778	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)

\(f(q)\)	\(=\)	\(q+(-0.660728 - 1.76473i) q^{2} +(-1.92359 + 1.67525i) q^{4} +(0.652586 + 0.757715i) q^{7} +(2.57009 + 1.39086i) q^{8} +(-0.709053 - 0.705155i) q^{9} +O(q^{10})\)	\(q+(-0.660728 - 1.76473i) q^{2} +(-1.92359 + 1.67525i) q^{4} +(0.652586 + 0.757715i) q^{7} +(2.57009 + 1.39086i) q^{8} +(-0.709053 - 0.705155i) q^{9} +(0.574517 + 1.48443i) q^{11} +(0.905977 - 1.65228i) q^{14} +(0.405997 - 2.92784i) q^{16} +(-0.775915 + 1.71720i) q^{18} +(2.24001 - 1.99467i) q^{22} +(-0.0523201 + 0.109303i) q^{23} +(-0.917973 - 0.396642i) q^{25} +(-2.52467 - 0.364284i) q^{28} +(-1.22347 + 0.345965i) q^{29} +(-2.58351 + 0.578979i) q^{32} +(2.54524 + 0.168585i) q^{36} +(0.188416 + 0.382735i) q^{37} +(-0.265516 + 1.64701i) q^{43} +(-3.59193 - 1.89296i) q^{44} +(0.227460 + 0.0201107i) q^{46} +(-0.148264 + 0.988948i) q^{49} +(-0.0934337 + 1.88204i) q^{50} +(-0.511814 - 0.0225818i) q^{53} +(0.623326 + 2.85505i) q^{56} +(1.41892 + 1.93051i) q^{58} +(0.0715891 - 0.997434i) q^{63} +(1.11204 + 1.70210i) q^{64} +(-0.377066 + 0.591276i) q^{67} +(-0.0103658 - 0.0986243i) q^{71} +(-0.841553 - 2.79850i) q^{72} +(0.550931 - 0.585387i) q^{74} +(-0.749851 + 1.40404i) q^{77} +(0.514455 + 1.10590i) q^{79} +(0.00551154 + 0.999985i) q^{81} +(3.08196 - 0.619665i) q^{86} +(-0.588074 + 4.61418i) q^{88} +(-0.0824688 - 0.297904i) q^{92} +(1.84318 - 0.391781i) q^{98} +(0.639389 - 1.45766i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9}+O(q^{10}) \) 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

Introduction

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