LMFDB - Embedded newform 3997.1.cz.a.321.1

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			321.1
Root			$-0.988116 + 0.153712i$ of defining polynomial
Character	$\chi$	$=$	3997.321
Dual form			3997.1.cz.a.3611.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.92132 + 0.430577i) q^{2} +(2.60171 + 1.22778i) q^{4} +(-0.213300 - 0.976987i) q^{7} +(2.91626 + 2.26982i) q^{8} +(-0.441671 - 0.897177i) q^{9} +O(q^{10})$	\(q+(1.92132 + 0.430577i) q^{2} +(2.60171 + 1.22778i) q^{4} +(-0.213300 - 0.976987i) q^{7} +(2.91626 + 2.26982i) q^{8} +(-0.441671 - 0.897177i) q^{9} +(-0.0317647 - 0.822918i) q^{11} +(0.0108521 - 1.96894i) q^{14} +(2.79684 + 3.39602i) q^{16} +(-0.462286 - 1.91394i) q^{18} +(0.293300 - 1.59476i) q^{22} +(-0.445225 + 1.54199i) q^{23} +(0.159156 - 0.987253i) q^{25} +(0.644577 - 2.80372i) q^{28} +(0.114457 + 0.585956i) q^{29} +(2.24274 + 4.43177i) q^{32} +(-0.0475658 - 2.87647i) q^{36} +(-0.740580 + 0.444060i) q^{37} +(0.312163 + 1.80921i) q^{43} +(0.927716 - 2.17999i) q^{44} +(-1.51936 + 2.77095i) q^{46} +(-0.909007 + 0.416782i) q^{49} +(0.730878 - 1.82830i) q^{50} +(-0.566727 - 0.957079i) q^{53} +(1.59554 - 3.33330i) q^{56} +(-0.0323911 + 1.17509i) q^{58} +(-0.782322 + 0.622874i) q^{63} +(1.32079 + 5.21567i) q^{64} +(-1.95147 + 0.0215122i) q^{67} +(-0.0776014 - 0.738328i) q^{71} +(0.748401 - 3.61891i) q^{72} +(-1.61409 + 0.534303i) q^{74} +(-0.797205 + 0.206562i) q^{77} +(0.941957 - 0.0207700i) q^{79} +(-0.609854 + 0.792514i) q^{81} +(-0.179242 + 3.61049i) q^{86} +(1.77524 - 2.47194i) q^{88} +(-3.05156 + 3.46517i) q^{92} +(-1.92595 + 0.409373i) q^{98} +(-0.724274 + 0.391957i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3997\mathbb{Z}\right)^\times$.

$n$	$1716$	$2285$
$\chi(n)$	$e\left(\frac{193}{285}\right)$	$-1$

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 $

$2$	1.92132	+	0.430577i	1.92132	+	0.430577i	0.999028	+	0.0440782i	$0.0140351\pi$
$2$	1.92132	+	0.430577i	1.92132	+	0.430577i	0.922290	+	0.386499i	$0.126316\pi$
$3$		0			0		0.528360	−	0.849020i	$-0.322807\pi$
$3$		0			0		−0.528360	+	0.849020i	$0.677193\pi$
$4$	2.60171	+	1.22778i	2.60171	+	1.22778i
$5$		0			0		0.761300	−	0.648400i	$-0.224561\pi$
$5$		0			0		−0.761300	+	0.648400i	$0.775439\pi$
$6$		0			0
$7$	−0.213300	−	0.976987i	−0.213300	−	0.976987i
$7$	−0.213300	−	0.976987i	−0.213300	−	0.976987i
$8$	2.91626	+	2.26982i	2.91626	+	2.26982i
$9$	−0.441671	−	0.897177i	−0.441671	−	0.897177i
$10$		0			0
$11$	−0.0317647	−	0.822918i	−0.0317647	−	0.822918i	−0.926494	−	0.376309i	$-0.877193\pi$
$11$	−0.0317647	−	0.822918i	−0.0317647	−	0.822918i	0.894729	−	0.446609i	$-0.147368\pi$
$12$		0			0
$13$		0			0		−0.391577	−	0.920146i	$-0.628070\pi$
$13$		0			0		0.391577	+	0.920146i	$0.371930\pi$
$14$	0.0108521	−	1.96894i	0.0108521	−	1.96894i
$15$		0			0
$16$	2.79684	+	3.39602i	2.79684	+	3.39602i
$17$		0			0		0.537687	−	0.843145i	$-0.319298\pi$
$17$		0			0		−0.537687	+	0.843145i	$0.680702\pi$
$18$	−0.462286	−	1.91394i	−0.462286	−	1.91394i
$19$		0			0		−0.0715891	−	0.997434i	$-0.522807\pi$
$19$		0			0		0.0715891	+	0.997434i	$0.477193\pi$
$20$		0			0
$21$		0			0
$22$	0.293300	−	1.59476i	0.293300	−	1.59476i
$23$	−0.445225	+	1.54199i	−0.445225	+	1.54199i	0.350638	+	0.936511i	$0.385965\pi$
$23$	−0.445225	+	1.54199i	−0.445225	+	1.54199i	−0.795863	+	0.605477i	$0.792982\pi$
$24$		0			0
$25$	0.159156	−	0.987253i	0.159156	−	0.987253i
$26$		0			0
$27$		0			0
$28$	0.644577	−	2.80372i	0.644577	−	2.80372i
$29$	0.114457	+	0.585956i	0.114457	+	0.585956i	0.993931	+	0.110008i	$0.0350877\pi$
$29$	0.114457	+	0.585956i	0.114457	+	0.585956i	−0.879474	+	0.475947i	$0.842105\pi$
$30$		0			0
$31$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$31$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$32$	2.24274	+	4.43177i	2.24274	+	4.43177i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.0475658	−	2.87647i	−0.0475658	−	2.87647i
$37$	−0.740580	+	0.444060i	−0.740580	+	0.444060i	−0.834139	−	0.551554i	$-0.814035\pi$
$37$	−0.740580	+	0.444060i	−0.740580	+	0.444060i	0.0935596	+	0.995614i	$0.470175\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.851919	−	0.523673i	$-0.824561\pi$
$41$		0			0		0.851919	+	0.523673i	$0.175439\pi$
$42$		0			0
$43$	0.312163	+	1.80921i	0.312163	+	1.80921i	0.546948	+	0.837166i	$0.315789\pi$
$43$	0.312163	+	1.80921i	0.312163	+	1.80921i	−0.234785	+	0.972047i	$0.575439\pi$
$44$	0.927716	−	2.17999i	0.927716	−	2.17999i
$45$		0			0
$46$	−1.51936	+	2.77095i	−1.51936	+	2.77095i
$47$		0			0		0.350638	−	0.936511i	$-0.385965\pi$
$47$		0			0		−0.350638	+	0.936511i	$0.614035\pi$
$48$		0			0
$49$	−0.909007	+	0.416782i	−0.909007	+	0.416782i
$50$	0.730878	−	1.82830i	0.730878	−	1.82830i
$51$		0			0
$52$		0			0
$53$	−0.566727	−	0.957079i	−0.566727	−	0.957079i	−0.998482	−	0.0550878i	$-0.982456\pi$
$53$	−0.566727	−	0.957079i	−0.566727	−	0.957079i	0.431754	−	0.901991i	$-0.357895\pi$
$54$		0			0
$55$		0			0
$56$	1.59554	−	3.33330i	1.59554	−	3.33330i
$57$		0			0
$58$	−0.0323911	+	1.17509i	−0.0323911	+	1.17509i
$59$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$59$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$60$		0			0
$61$		0			0		−0.802489	−	0.596667i	$-0.796491\pi$
$61$		0			0		0.802489	+	0.596667i	$0.203509\pi$
$62$		0			0
$63$	−0.782322	+	0.622874i	−0.782322	+	0.622874i
$64$	1.32079	+	5.21567i	1.32079	+	5.21567i
$65$		0			0
$66$		0			0
$67$	−1.95147	+	0.0215122i	−1.95147	+	0.0215122i	−0.978148	−	0.207912i	$-0.933333\pi$
$67$	−1.95147	+	0.0215122i	−1.95147	+	0.0215122i	−0.973327	+	0.229424i	$0.926316\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.0776014	−	0.738328i	−0.0776014	−	0.738328i	−0.962268	−	0.272103i	$-0.912281\pi$
$71$	−0.0776014	−	0.738328i	−0.0776014	−	0.738328i	0.884667	−	0.466224i	$-0.154386\pi$
$72$	0.748401	−	3.61891i	0.748401	−	3.61891i
$73$		0			0		−0.874174	−	0.485613i	$-0.838596\pi$
$73$		0			0		0.874174	+	0.485613i	$0.161404\pi$
$74$	−1.61409	+	0.534303i	−1.61409	+	0.534303i
$75$		0			0
$76$		0			0
$77$	−0.797205	+	0.206562i	−0.797205	+	0.206562i
$78$		0			0
$79$	0.941957	−	0.0207700i	0.941957	−	0.0207700i	0.451533	−	0.892254i	$-0.350877\pi$
$79$	0.941957	−	0.0207700i	0.941957	−	0.0207700i	0.490424	+	0.871484i	$0.336842\pi$
$80$		0			0
$81$	−0.609854	+	0.792514i	−0.609854	+	0.792514i
$82$		0			0
$83$		0			0		−0.266796	−	0.963753i	$-0.585965\pi$
$83$		0			0		0.266796	+	0.963753i	$0.414035\pi$
$84$		0			0
$85$		0			0
$86$	−0.179242	+	3.61049i	−0.179242	+	3.61049i
$87$		0			0
$88$	1.77524	−	2.47194i	1.77524	−	2.47194i
$89$		0			0		−0.968033	−	0.250825i	$-0.919298\pi$
$89$		0			0		0.968033	+	0.250825i	$0.0807018\pi$
$90$		0			0
$91$		0			0
$92$	−3.05156	+	3.46517i	−3.05156	+	3.46517i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.685350	−	0.728214i	$-0.259649\pi$
$97$		0			0		−0.685350	+	0.728214i	$0.740351\pi$
$98$	−1.92595	+	0.409373i	−1.92595	+	0.409373i
$99$	−0.724274	+	0.391957i	−0.724274	+	0.391957i
$100$	1.62620	−	2.37314i	1.62620	−	2.37314i
$101$		0			0		−0.126427	−	0.991976i	$-0.540351\pi$
$101$		0			0		0.126427	+	0.991976i	$0.459649\pi$
$102$		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
$106$	−0.676766	−	2.08287i	−0.676766	−	2.08287i
$107$	−1.26520	+	1.53624i	−1.26520	+	1.53624i	−0.556143	+	0.831087i	$0.687719\pi$
$107$	−1.26520	+	1.53624i	−1.26520	+	1.53624i	−0.709053	+	0.705155i	$0.750877\pi$
$108$		0			0
$109$	−0.115485	+	0.200025i	−0.115485	+	0.200025i	−0.917973	−	0.396642i	$-0.870175\pi$
$109$	−0.115485	+	0.200025i	−0.115485	+	0.200025i	0.802489	+	0.596667i	$0.203509\pi$
$110$		0			0
$111$		0			0
$112$	2.72130	−	3.45685i	2.72130	−	3.45685i
$113$	−1.07120	+	0.0947090i	−1.07120	+	0.0947090i	−0.609854	−	0.792514i	$-0.708772\pi$
$113$	−1.07120	+	0.0947090i	−1.07120	+	0.0947090i	−0.461341	+	0.887223i	$0.652632\pi$
$114$		0			0
$115$		0			0
$116$	−0.421639	+	1.66501i	−0.421639	+	1.66501i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.320839	−	0.0248058i	0.320839	−	0.0248058i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−1.77128	+	0.859889i	−1.77128	+	0.859889i
$127$	0.825539	−	1.67694i	0.825539	−	1.67694i	0.0935596	−	0.995614i	$-0.470175\pi$
$127$	0.825539	−	1.67694i	0.825539	−	1.67694i	0.731980	−	0.681326i	$-0.238596\pi$
$128$	0.155041	+	5.62461i	0.155041	+	5.62461i
$129$		0			0
$130$		0			0
$131$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$131$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$132$		0			0
$133$		0			0
$134$	−3.75866	−	0.798929i	−3.75866	−	0.798929i
$135$		0			0
$136$		0			0
$137$	0.00175439	+	0.0108826i	0.00175439	+	0.0108826i	0.988116	−	0.153712i	$-0.0491228\pi$
$137$	0.00175439	+	0.0108826i	0.00175439	+	0.0108826i	−0.986361	+	0.164595i	$0.947368\pi$
$138$		0			0
$139$		0			0		−0.556143	−	0.831087i	$-0.687719\pi$
$139$		0			0		0.556143	+	0.831087i	$0.312281\pi$
$140$		0			0
$141$		0			0
$142$	0.168810	−	1.45198i	0.168810	−	1.45198i
$143$		0			0
$144$	1.81155	−	4.00918i	1.81155	−	4.00918i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−2.47198	+	0.246048i	−2.47198	+	0.246048i
$149$	−0.194536	−	0.673753i	−0.194536	−	0.673753i	−0.997024	−	0.0770854i	$-0.975439\pi$
$149$	−0.194536	−	0.673753i	−0.194536	−	0.673753i	0.802489	−	0.596667i	$-0.203509\pi$
$150$		0			0
$151$	1.95047	+	0.150802i	1.95047	+	0.150802i	0.991264	−	0.131892i	$-0.0421053\pi$
$151$	1.95047	+	0.150802i	1.95047	+	0.150802i	0.959210	+	0.282694i	$0.0912281\pi$
$152$		0			0
$153$		0			0
$154$	−1.62062	+	0.0536126i	−1.62062	+	0.0536126i
$155$		0			0
$156$		0			0
$157$		0			0		−0.999028	−	0.0440782i	$-0.985965\pi$
$157$		0			0		0.999028	+	0.0440782i	$0.0140351\pi$
$158$	1.81874	+	0.365680i	1.81874	+	0.365680i
$159$		0			0
$160$		0			0
$161$	1.60147	+	0.106074i	1.60147	+	0.106074i
$162$	−1.51296	+	1.26008i	−1.51296	+	1.26008i
$163$	0.327799	−	1.50144i	0.327799	−	1.50144i	−0.461341	−	0.887223i	$-0.652632\pi$
$163$	0.327799	−	1.50144i	0.327799	−	1.50144i	0.789141	−	0.614213i	$-0.210526\pi$
$164$		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
$169$	−0.693336	+	0.720615i	−0.693336	+	0.720615i
$170$		0			0
$171$		0			0
$172$	−1.40915	+	5.09031i	−1.40915	+	5.09031i
$173$		0			0		0.868768	−	0.495219i	$-0.164912\pi$
$173$		0			0		−0.868768	+	0.495219i	$0.835088\pi$
$174$		0			0
$175$	−0.998482	+	0.0550878i	−0.998482	+	0.0550878i
$176$	2.70580	−	2.40944i	2.70580	−	2.40944i
$177$		0			0
$178$		0			0
$179$	0.821070	+	0.193535i	0.821070	+	0.193535i	0.618553	−	0.785743i	$-0.287719\pi$
$179$	0.821070	+	0.193535i	0.821070	+	0.193535i	0.202517	+	0.979279i	$0.435088\pi$
$180$		0			0
$181$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$181$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$182$		0			0
$183$		0			0
$184$	−4.79842	+	3.48626i	−4.79842	+	3.48626i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.511626	+	1.46399i	0.511626	+	1.46399i	0.851919	+	0.523673i	$0.175439\pi$
$191$	0.511626	+	1.46399i	0.511626	+	1.46399i	−0.340293	+	0.940319i	$0.610526\pi$
$192$		0			0
$193$	0.202374	−	1.92546i	0.202374	−	1.92546i	−0.148264	−	0.988948i	$-0.547368\pi$
$193$	0.202374	−	1.92546i	0.202374	−	1.92546i	0.350638	−	0.936511i	$-0.385965\pi$
$194$		0			0
$195$		0			0
$196$	−2.87668	−	0.0317114i	−2.87668	−	0.0317114i
$197$	−1.46387	−	1.36257i	−1.46387	−	1.36257i	−0.739446	−	0.673216i	$-0.764912\pi$
$197$	−1.46387	−	1.36257i	−1.46387	−	1.36257i	−0.724425	−	0.689353i	$-0.757895\pi$
$198$	−1.56033	+	0.441219i	−1.56033	+	0.441219i
$199$		0			0		0.739446	−	0.673216i	$-0.235088\pi$
$199$		0			0		−0.739446	+	0.673216i	$0.764912\pi$
$200$	2.70502	−	2.51783i	2.70502	−	2.51783i
$201$		0			0
$202$		0			0
$203$	0.548057	−	0.236807i	0.548057	−	0.236807i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.58008	−	0.281605i	1.58008	−	0.281605i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.765282	+	1.39568i	0.765282	+	1.39568i	0.913545	+	0.406737i	$0.133333\pi$
$211$	0.765282	+	1.39568i	0.765282	+	1.39568i	−0.148264	+	0.988948i	$0.547368\pi$
$212$	−0.299380	−	3.18585i	−0.299380	−	3.18585i
$213$		0			0
$214$	−3.09231	+	2.40684i	−3.09231	+	2.40684i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.308009	+	0.334587i	−0.308009	+	0.334587i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.693336	−	0.720615i	$-0.743860\pi$
$223$		0			0		0.693336	+	0.720615i	$0.256140\pi$
$224$	3.85140	−	3.13642i	3.85140	−	3.13642i
$225$	−0.956036	+	0.293250i	−0.956036	+	0.293250i
$226$	−2.09889	−	0.279266i	−2.09889	−	0.279266i
$227$		0			0		0.471093	−	0.882084i	$-0.343860\pi$
$227$		0			0		−0.471093	+	0.882084i	$0.656140\pi$
$228$		0			0
$229$		0			0		0.952745	−	0.303771i	$-0.0982456\pi$
$229$		0			0		−0.952745	+	0.303771i	$0.901754\pi$
$230$		0			0
$231$		0			0
$232$	−0.996225	+	1.96859i	−0.996225	+	1.96859i
$233$	−1.61024	+	1.06473i	−1.61024	+	1.06473i	−0.660898	+	0.750475i	$0.729825\pi$
$233$	−1.61024	+	1.06473i	−1.61024	+	1.06473i	−0.949339	+	0.314254i	$0.898246\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.256439	−	1.48625i	0.256439	−	1.48625i	−0.518970	−	0.854793i	$-0.673684\pi$
$239$	0.256439	−	1.48625i	0.256439	−	1.48625i	0.775409	−	0.631460i	$-0.217544\pi$
$240$		0			0
$241$		0			0		−0.999453	−	0.0330634i	$-0.989474\pi$
$241$		0			0		0.999453	+	0.0330634i	$0.0105263\pi$
$242$	0.627115	+	0.0904862i	0.627115	+	0.0904862i
$243$		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		−0.815447	−	0.578832i	$-0.803509\pi$
$251$		0			0		0.815447	+	0.578832i	$0.196491\pi$
$252$	−2.80012	+	0.660020i	−2.80012	+	0.660020i
$253$	1.28307	+	0.317403i	1.28307	+	0.317403i
$254$	2.30818	−	2.86648i	2.30818	−	2.86648i
$255$		0			0
$256$	−1.09249	+	5.59292i	−1.09249	+	5.59292i
$257$		0			0		−0.965209	−	0.261480i	$-0.915789\pi$
$257$		0			0		0.965209	+	0.261480i	$0.0842105\pi$
$258$		0			0
$259$	0.591806	+	0.628819i	0.591806	+	0.628819i
$260$		0			0
$261$	0.475154	−	0.361488i	0.475154	−	0.361488i
$262$		0			0
$263$	1.12855	+	0.213993i	1.12855	+	0.213993i	0.716783	−	0.697297i	$-0.245614\pi$
$263$	1.12855	+	0.213993i	1.12855	+	0.213993i	0.411766	+	0.911290i	$0.364912\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−5.10358	−	2.34000i	−5.10358	−	2.34000i
$269$		0			0		−0.956036	−	0.293250i	$-0.905263\pi$
$269$		0			0		0.956036	+	0.293250i	$0.0947368\pi$
$270$		0			0
$271$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$271$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$272$		0			0
$273$		0			0
$274$	−0.00131506	+	0.0216643i	−0.00131506	+	0.0216643i
$275$	−0.817484	−	0.0996123i	−0.817484	−	0.0996123i
$276$		0			0
$277$	0.680214	−	1.87961i	0.680214	−	1.87961i	0.309017	−	0.951057i	$-0.400000\pi$
$277$	0.680214	−	1.87961i	0.680214	−	1.87961i	0.371197	−	0.928554i	$-0.378947\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.603077	+	0.748949i	0.603077	+	0.748949i	0.984487	−	0.175457i	$-0.0561404\pi$
$281$	0.603077	+	0.748949i	0.603077	+	0.748949i	−0.381410	+	0.924406i	$0.624561\pi$
$282$		0			0
$283$		0			0		0.601081	−	0.799188i	$-0.294737\pi$
$283$		0			0		−0.601081	+	0.799188i	$0.705263\pi$
$284$	0.704605	−	2.01619i	0.704605	−	2.01619i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	2.98553	−	3.96951i	2.98553	−	3.96951i
$289$	−0.421786	−	0.906696i	−0.421786	−	0.906696i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.360939	−	0.932589i	$-0.617544\pi$
$293$		0			0		0.360939	+	0.932589i	$0.382456\pi$
$294$		0			0
$295$		0			0
$296$	−3.16766	−	0.385986i	−3.16766	−	0.385986i
$297$		0			0
$298$	−0.0836623	−	1.37826i	−0.0836623	−	1.37826i
$299$		0			0
$300$		0			0
$301$	1.70099	−	0.690884i	1.70099	−	0.690884i
$302$	3.68255	+	1.12957i	3.68255	+	1.12957i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.381410	−	0.924406i	$-0.624561\pi$
$307$		0			0		0.381410	+	0.924406i	$0.375439\pi$
$308$	−2.32771	−	0.441375i	−2.32771	−	0.441375i
$309$		0			0
$310$		0			0
$311$		0			0		−0.618553	−	0.785743i	$-0.712281\pi$
$311$		0			0		0.618553	+	0.785743i	$0.287719\pi$
$312$		0			0
$313$		0			0		−0.821778	−	0.569808i	$-0.807018\pi$
$313$		0			0		0.821778	+	0.569808i	$0.192982\pi$
$314$		0			0
$315$		0			0
$316$	2.47620	+	1.10247i	2.47620	+	1.10247i
$317$	0.400743	−	0.497674i	0.400743	−	0.497674i	−0.537687	−	0.843145i	$-0.680702\pi$
$317$	0.400743	−	0.497674i	0.400743	−	0.497674i	0.938430	+	0.345471i	$0.112281\pi$
$318$		0			0
$319$	0.478558	−	0.112801i	0.478558	−	0.112801i
$320$		0			0
$321$		0			0
$322$	3.03126	+	0.893358i	3.03126	+	0.893358i
$323$		0			0
$324$	−2.55969	+	1.31313i	−2.55969	+	1.31313i
$325$		0			0
$326$	1.27629	−	2.74359i	1.27629	−	2.74359i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.10809	−	1.23066i	1.10809	−	1.23066i	0.137354	−	0.990522i	$-0.456140\pi$
$331$	1.10809	−	1.23066i	1.10809	−	1.23066i	0.970739	−	0.240139i	$-0.0771930\pi$
$332$		0			0
$333$	0.725493	+	0.468303i	0.725493	+	0.468303i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.25561	+	0.933572i	−1.25561	+	0.933572i	−0.999453	−	0.0330634i	$-0.989474\pi$
$337$	−1.25561	+	0.933572i	−1.25561	+	0.933572i	−0.256156	+	0.966635i	$0.582456\pi$
$338$	−1.64240	+	1.08600i	−1.64240	+	1.08600i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.601081	+	0.799188i	0.601081	+	0.799188i
$344$	−3.19623	+	5.98469i	−3.19623	+	5.98469i
$345$		0			0
$346$		0			0
$347$	1.22381	−	0.996621i	1.22381	−	0.996621i	0.224056	−	0.974576i	$-0.428070\pi$
$347$	1.22381	−	0.996621i	1.22381	−	0.996621i	0.999757	−	0.0220445i	$-0.00701754\pi$
$348$		0			0
$349$		0			0		0.234785	−	0.972047i	$-0.424561\pi$
$349$		0			0		−0.234785	+	0.972047i	$0.575439\pi$
$350$	−1.94212	−	0.324082i	−1.94212	−	0.324082i
$351$		0			0
$352$	3.57574	−	1.98636i	3.57574	−	1.98636i
$353$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$353$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	1.49420	+	0.725377i	1.49420	+	0.725377i
$359$	0.183448	+	1.95216i	0.183448	+	1.95216i	0.287976	+	0.957638i	$0.407018\pi$
$359$	0.183448	+	1.95216i	0.183448	+	1.95216i	−0.104528	+	0.994522i	$0.533333\pi$
$360$		0			0
$361$	−0.989750	+	0.142811i	−0.989750	+	0.142811i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.00551154	−	0.999985i	$-0.501754\pi$
$367$		0			0		0.00551154	+	0.999985i	$0.498246\pi$
$368$	−6.48184	+	2.80070i	−6.48184	+	2.80070i
$369$		0			0
$370$		0			0
$371$	−0.814171	+	0.757830i	−0.814171	+	0.757830i
$372$		0			0
$373$	0.654906	−	0.185190i	0.654906	−	0.185190i	0.0715891	−	0.997434i	$-0.477193\pi$
$373$	0.654906	−	0.185190i	0.654906	−	0.185190i	0.583317	+	0.812244i	$0.301754\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.65543	−	0.527812i	−1.65543	−	0.527812i	−0.677282	−	0.735724i	$-0.736842\pi$
$379$	−1.65543	−	0.527812i	−1.65543	−	0.527812i	−0.978148	+	0.207912i	$0.933333\pi$
$380$		0			0
$381$		0			0
$382$	0.352635	+	3.03309i	0.352635	+	3.03309i
$383$		0			0		0.716783	−	0.697297i	$-0.245614\pi$
$383$		0			0		−0.716783	+	0.697297i	$0.754386\pi$
$384$		0			0
$385$		0			0
$386$	1.21788	−	3.61228i	1.21788	−	3.61228i
$387$	1.48531	−	1.07914i	1.48531	−	1.07914i
$388$		0			0
$389$	−0.665781	+	0.279006i	−0.665781	+	0.279006i	−0.693336	−	0.720615i	$-0.743860\pi$
$389$	−0.665781	+	0.279006i	−0.665781	+	0.279006i	0.0275543	+	0.999620i	$0.491228\pi$
$390$		0			0
$391$		0			0
$392$	−3.59692	−	0.847833i	−3.59692	−	0.847833i
$393$		0			0
$394$	−2.22587	−	3.24824i	−2.22587	−	3.24824i
$395$		0			0
$396$	−2.36559	+	0.130513i	−2.36559	+	0.130513i
$397$		0			0		−0.834139	−	0.551554i	$-0.814035\pi$
$397$		0			0		0.834139	+	0.551554i	$0.185965\pi$
$398$		0			0
$399$		0			0
$400$	3.79786	−	2.22070i	3.79786	−	2.22070i
$401$	0.135724	−	1.63794i	0.135724	−	1.63794i	−0.500000	−	0.866025i	$-0.666667\pi$
$401$	0.135724	−	1.63794i	0.135724	−	1.63794i	0.635724	−	0.771917i	$-0.280702\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	1.15496	−	0.219000i	1.15496	−	0.219000i
$407$	0.388949	+	0.595331i	0.388949	+	0.595331i
$408$		0			0
$409$		0			0		0.768401	−	0.639969i	$-0.221053\pi$
$409$		0			0		−0.768401	+	0.639969i	$0.778947\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	3.15709	+	0.139294i	3.15709	+	0.139294i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.556143	−	0.831087i	$-0.312281\pi$
$419$		0			0		−0.556143	+	0.831087i	$0.687719\pi$
$420$		0			0
$421$	−0.867009	−	1.17961i	−0.867009	−	1.17961i	−0.982493	−	0.186298i	$-0.940351\pi$
$421$	−0.867009	−	1.17961i	−0.867009	−	1.17961i	0.115485	−	0.993309i	$-0.463158\pi$
$422$	0.869399	+	3.01107i	0.869399	+	3.01107i
$423$		0			0
$424$	0.519669	−	4.07746i	0.519669	−	4.07746i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−5.17783	+	2.44348i	−5.17783	+	2.44348i
$429$		0			0
$430$		0			0
$431$	−0.895683	−	1.72252i	−0.895683	−	1.72252i	−0.660898	−	0.750475i	$-0.729825\pi$
$431$	−0.895683	−	1.72252i	−0.895683	−	1.72252i	−0.234785	−	0.972047i	$-0.575439\pi$
$432$		0			0
$433$		0			0		−0.490424	−	0.871484i	$-0.663158\pi$
$433$		0			0		0.490424	+	0.871484i	$0.336842\pi$
$434$		0			0
$435$		0			0
$436$	−0.546043	+	0.378618i	−0.546043	+	0.378618i
$437$		0			0
$438$		0			0
$439$		0			0		−0.574329	−	0.818625i	$-0.694737\pi$
$439$		0			0		0.574329	+	0.818625i	$0.305263\pi$
$440$		0			0
$441$	0.775409	+	0.631460i	0.775409	+	0.631460i
$442$		0			0
$443$	0.0547742	+	1.98711i	0.0547742	+	1.98711i	0.137354	+	0.990522i	$0.456140\pi$
$443$	0.0547742	+	1.98711i	0.0547742	+	1.98711i	−0.0825793	+	0.996584i	$0.526316\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	4.81392	−	2.40289i	4.81392	−	2.40289i
$449$	1.21457	+	1.41024i	1.21457	+	1.41024i	0.884667	+	0.466224i	$0.154386\pi$
$449$	1.21457	+	1.41024i	1.21457	+	1.41024i	0.329907	+	0.944013i	$0.392982\pi$
$450$	−1.96312	+	0.151779i	−1.96312	+	0.151779i
$451$		0			0
$452$	−2.90322	−	1.06878i	−2.90322	−	1.06878i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.50930	+	1.28547i	1.50930	+	1.28547i	0.840168	+	0.542326i	$0.182456\pi$
$457$	1.50930	+	1.28547i	1.50930	+	1.28547i	0.669131	+	0.743145i	$0.266667\pi$
$458$		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
$463$	−0.0472634	−	0.0283397i	−0.0472634	−	0.0283397i	0.490424	−	0.871484i	$-0.336842\pi$
$463$	−0.0472634	−	0.0283397i	−0.0472634	−	0.0283397i	−0.537687	+	0.843145i	$0.680702\pi$
$464$	−1.66980	+	2.02752i	−1.66980	+	2.02752i
$465$		0			0
$466$	−3.55223	+	1.35235i	−3.55223	+	1.35235i
$467$		0			0		0.256156	−	0.966635i	$-0.417544\pi$
$467$		0			0		−0.256156	+	0.966635i	$0.582456\pi$
$468$		0			0
$469$	0.437266	+	1.90198i	0.437266	+	1.90198i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.47892	−	0.314354i	1.47892	−	0.314354i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.608363	+	0.931168i	−0.608363	+	0.931168i
$478$	1.13265	−	2.74515i	1.13265	−	2.74515i
$479$		0			0		0.660898	−	0.750475i	$-0.270175\pi$
$479$		0			0		−0.660898	+	0.750475i	$0.729825\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.865186	+	0.329381i	0.865186	+	0.329381i
$485$		0			0
$486$		0			0
$487$	0.393387	+	0.391224i	0.393387	+	0.391224i	0.874174	−	0.485613i	$-0.161404\pi$
$487$	0.393387	+	0.391224i	0.393387	+	0.391224i	−0.480787	+	0.876837i	$0.659649\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.42637	−	0.254211i	−1.42637	−	0.254211i	−0.592235	−	0.805765i	$-0.701754\pi$
$491$	−1.42637	−	0.254211i	−1.42637	−	0.254211i	−0.834139	+	0.551554i	$0.814035\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.704784	+	0.233301i	−0.704784	+	0.233301i
$498$		0			0
$499$	−0.384515	+	1.85933i	−0.384515	+	1.85933i	0.115485	+	0.993309i	$0.463158\pi$
$499$	−0.384515	+	1.85933i	−0.384515	+	1.85933i	−0.500000	+	0.866025i	$0.666667\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.846095	−	0.533032i	$-0.178947\pi$
$503$		0			0		−0.846095	+	0.533032i	$0.821053\pi$
$504$	−3.69526	+	0.0407350i	−3.69526	+	0.0407350i
$505$		0			0
$506$	2.32852	+	1.16229i	2.32852	+	1.16229i
$507$		0			0
$508$	4.20672	−	3.34933i	4.20672	−	3.34933i
$509$		0			0		−0.998482	−	0.0550878i	$-0.982456\pi$
$509$		0			0		0.998482	+	0.0550878i	$0.0175439\pi$
$510$		0			0
$511$		0			0
$512$	−2.24696	+	5.12254i	−2.24696	+	5.12254i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	0.866292	+	1.46298i	0.866292	+	1.46298i
$519$		0			0
$520$		0			0
$521$		0			0		0.371197	−	0.928554i	$-0.378947\pi$
$521$		0			0		−0.371197	+	0.928554i	$0.621053\pi$
$522$	1.06857	−	0.489942i	1.06857	−	0.489942i
$523$		0			0		0.991264	−	0.131892i	$-0.0421053\pi$
$523$		0			0		−0.991264	+	0.131892i	$0.957895\pi$
$524$		0			0
$525$		0			0
$526$	2.07616	+	0.897076i	2.07616	+	0.897076i
$527$		0			0
$528$		0			0
$529$	−1.33341	−	0.840033i	−1.33341	−	0.840033i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−5.73983	−	4.36675i	−5.73983	−	4.36675i
$537$		0			0
$538$		0			0
$539$	0.371852	+	0.734799i	0.371852	+	0.734799i
$540$		0			0
$541$	0.0646497	−	0.900750i	0.0646497	−	0.900750i	−0.857640	−	0.514250i	$-0.828070\pi$
$541$	0.0646497	−	0.900750i	0.0646497	−	0.900750i	0.922290	−	0.386499i	$-0.126316\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.579981	−	0.213513i	0.579981	−	0.213513i	−0.0385714	−	0.999256i	$-0.512281\pi$
$547$	0.579981	−	0.213513i	0.579981	−	0.213513i	0.618553	+	0.785743i	$0.287719\pi$
$548$	−0.00879696	+	0.0304673i	−0.00879696	+	0.0304673i
$549$		0			0
$550$	−1.52776	−	0.543377i	−1.52776	−	0.543377i
$551$		0			0
$552$		0			0
$553$	−0.221211	−	0.915849i	−0.221211	−	0.915849i
$554$	2.11623	−	3.31844i	2.11623	−	3.31844i
$555$		0			0
$556$		0			0
$557$	0.00103131	−	0.187116i	0.00103131	−	0.187116i	−0.995083	−	0.0990455i	$-0.968421\pi$
$557$	0.00103131	−	0.187116i	0.00103131	−	0.187116i	0.996114	−	0.0880708i	$-0.0280702\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.836222	+	1.69864i	0.836222	+	1.69864i
$563$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$563$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.904357	+	0.426776i	0.904357	+	0.426776i
$568$	1.44956	−	2.32929i	1.44956	−	2.32929i
$569$	1.92840	+	0.432164i	1.92840	+	0.432164i	0.997814	+	0.0660906i	$0.0210526\pi$
$569$	1.92840	+	0.432164i	1.92840	+	0.432164i	0.930586	+	0.366074i	$0.119298\pi$
$570$		0			0
$571$	0.635724	+	0.771917i	0.635724	+	0.771917i
$571$	0.635724	+	0.771917i	0.635724	+	0.771917i
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.45147	+	0.684967i	1.45147	+	0.684967i
$576$	4.09603	−	3.48859i	4.09603	−	3.48859i
$577$		0			0		0.701237	−	0.712928i	$-0.252632\pi$
$577$		0			0		−0.701237	+	0.712928i	$0.747368\pi$
$578$	−0.419981	−	1.92366i	−0.419981	−	1.92366i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.769596	+	0.496771i	−0.769596	+	0.496771i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.635724	−	0.771917i	$-0.719298\pi$
$587$		0			0		0.635724	+	0.771917i	$0.280702\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−3.57932	−	1.27306i	−3.57932	−	1.27306i
$593$		0			0		0.180881	−	0.983505i	$-0.442105\pi$
$593$		0			0		−0.180881	+	0.983505i	$0.557895\pi$
$594$		0			0
$595$		0			0
$596$	0.321092	−	1.99175i	0.321092	−	1.99175i
$597$		0			0
$598$		0			0
$599$	0.396430	−	1.72435i	0.396430	−	1.72435i	−0.256156	−	0.966635i	$-0.582456\pi$
$599$	0.396430	−	1.72435i	0.396430	−	1.72435i	0.652586	−	0.757715i	$-0.273684\pi$
$600$		0			0
$601$		0			0		0.0715891	−	0.997434i	$-0.477193\pi$
$601$		0			0		−0.0715891	+	0.997434i	$0.522807\pi$
$602$	3.56563	−	0.594998i	3.56563	−	0.594998i
$603$	0.881209	+	1.74132i	0.881209	+	1.74132i
$604$	4.88941	+	2.78709i	4.88941	+	2.78709i
$605$		0			0
$606$		0			0
$607$		0			0		−0.0165339	−	0.999863i	$-0.505263\pi$
$607$		0			0		0.0165339	+	0.999863i	$0.494737\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.56069	−	0.983219i	−1.56069	−	0.983219i	−0.986361	−	0.164595i	$-0.947368\pi$
$613$	−1.56069	−	0.983219i	−1.56069	−	0.983219i	−0.574329	−	0.818625i	$-0.694737\pi$
$614$		0			0
$615$		0			0
$616$	−2.79371	−	1.20712i	−2.79371	−	1.20712i
$617$	−0.153040	+	0.279107i	−0.153040	+	0.279107i	−0.942181	−	0.335105i	$-0.891228\pi$
$617$	−0.153040	+	0.279107i	−0.153040	+	0.279107i	0.789141	+	0.614213i	$0.210526\pi$
$618$		0			0
$619$		0			0		0.991264	−	0.131892i	$-0.0421053\pi$
$619$		0			0		−0.991264	+	0.131892i	$0.957895\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.949339	−	0.314254i	−0.949339	−	0.314254i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.548736	−	1.82477i	0.548736	−	1.82477i	−0.0165339	−	0.999863i	$-0.505263\pi$
$631$	0.548736	−	1.82477i	0.548736	−	1.82477i	0.565270	−	0.824906i	$-0.308772\pi$
$632$	2.79413	+	2.07750i	2.79413	+	2.07750i
$633$		0			0
$634$	0.984241	−	0.783639i	0.984241	−	0.783639i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	0.968031	−	0.0106712i	0.968031	−	0.0106712i
$639$	−0.628136	+	0.395720i	−0.628136	+	0.395720i
$640$		0			0
$641$	−0.176965	−	0.210113i	−0.176965	−	0.210113i	0.669131	−	0.743145i	$-0.266667\pi$
$641$	−0.176965	−	0.210113i	−0.176965	−	0.210113i	−0.846095	+	0.533032i	$0.821053\pi$
$642$		0			0
$643$		0			0		0.202517	−	0.979279i	$-0.435088\pi$
$643$		0			0		−0.202517	+	0.979279i	$0.564912\pi$
$644$	4.03632	+	2.24222i	4.03632	+	2.24222i
$645$		0			0
$646$		0			0
$647$		0			0		0.360939	−	0.932589i	$-0.382456\pi$
$647$		0			0		−0.360939	+	0.932589i	$0.617544\pi$
$648$	−3.57735	+	0.926919i	−3.57735	+	0.926919i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	2.69626	−	3.50383i	2.69626	−	3.50383i
$653$	−1.27552	−	1.24084i	−1.27552	−	1.24084i	−0.956036	−	0.293250i	$-0.905263\pi$
$653$	−1.27552	−	1.24084i	−1.27552	−	1.24084i	−0.319482	−	0.947592i	$-0.603509\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.10753	+	1.54219i	−1.10753	+	1.54219i	−0.298515	+	0.954405i	$0.596491\pi$
$659$	−1.10753	+	1.54219i	−1.10753	+	1.54219i	−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	$0.200000\pi$
$662$	2.65889	−	1.88737i	2.65889	−	1.88737i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	1.19226	+	1.21214i	1.19226	+	1.21214i
$667$	−0.954496	−	0.0843911i	−0.954496	−	0.0843911i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.431204	−	1.87561i	−0.431204	−	1.87561i	−0.480787	−	0.876837i	$-0.659649\pi$
$673$	−0.431204	−	1.87561i	−0.431204	−	1.87561i	0.0495838	−	0.998770i	$-0.484211\pi$
$674$	−2.81440	+	1.25305i	−2.81440	+	1.25305i
$675$		0			0
$676$	−2.68861	+	1.02357i	−2.68861	+	1.02357i
$677$		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
$683$	−1.14617	+	1.45597i	−1.14617	+	1.45597i	−0.277403	+	0.960754i	$0.589474\pi$
$683$	−1.14617	+	1.45597i	−1.14617	+	1.45597i	−0.868768	+	0.495219i	$0.835088\pi$
$684$		0			0
$685$		0			0
$686$	0.810756	+	1.79431i	0.810756	+	1.79431i
$687$		0			0
$688$	−5.27105	+	6.12019i	−5.27105	+	6.12019i
$689$		0			0
$690$		0			0
$691$		0			0		0.490424	−	0.871484i	$-0.336842\pi$
$691$		0			0		−0.490424	+	0.871484i	$0.663158\pi$
$692$		0			0
$693$	0.537425	+	0.624002i	0.537425	+	0.624002i
$694$	2.78046	−	1.38788i	2.78046	−	1.38788i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−2.66539	−	1.08259i	−2.66539	−	1.08259i
$701$	1.53239	+	1.24791i	1.53239	+	1.24791i	0.863256	+	0.504766i	$0.168421\pi$
$701$	1.53239	+	1.24791i	1.53239	+	1.24791i	0.669131	+	0.743145i	$0.266667\pi$
$702$		0			0
$703$		0			0
$704$	4.25012	−	1.25257i	4.25012	−	1.25257i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.824077	+	1.46439i	0.824077	+	1.46439i	0.884667	+	0.466224i	$0.154386\pi$
$709$	0.824077	+	1.46439i	0.824077	+	1.46439i	−0.0605901	+	0.998163i	$0.519298\pi$
$710$		0			0
$711$	−0.434669	−	0.835929i	−0.434669	−	0.835929i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.89857	+	1.51161i	1.89857	+	1.51161i
$717$		0			0
$718$	−0.488094	+	3.82971i	−0.488094	+	3.82971i
$719$		0			0		0.995083	−	0.0990455i	$-0.0315789\pi$
$719$		0			0		−0.995083	+	0.0990455i	$0.968421\pi$
$720$		0			0
$721$		0			0
$722$	−1.96312	−	0.151779i	−1.96312	−	0.151779i
$723$		0			0
$724$		0			0
$725$	0.596703	−	0.0197398i	0.596703	−	0.0197398i
$726$		0			0
$727$		0			0		−0.828009	−	0.560715i	$-0.810526\pi$
$727$		0			0		0.828009	+	0.560715i	$0.189474\pi$
$728$		0			0
$729$	0.980380	+	0.197117i	0.980380	+	0.197117i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.768401	−	0.639969i	$-0.221053\pi$
$733$		0			0		−0.768401	+	0.639969i	$0.778947\pi$
$734$		0			0
$735$		0			0
$736$	−7.83226	+	1.48514i	−7.83226	+	1.48514i
$737$	0.0796909	+	1.60522i	0.0796909	+	1.60522i
$738$		0			0
$739$	0.206161	+	0.323280i	0.206161	+	0.323280i	0.930586	−	0.366074i	$-0.119298\pi$
$739$	0.206161	+	0.323280i	0.206161	+	0.323280i	−0.724425	+	0.689353i	$0.757895\pi$
$740$		0			0
$741$		0			0
$742$	−1.89059	+	1.10547i	−1.89059	+	1.10547i
$743$	−0.276918	+	1.00032i	−0.276918	+	1.00032i	0.685350	+	0.728214i	$0.259649\pi$
$743$	−0.276918	+	1.00032i	−0.276918	+	1.00032i	−0.962268	+	0.272103i	$0.912281\pi$
$744$		0			0
$745$		0			0
$746$	1.33802	−	0.0738207i	1.33802	−	0.0738207i
$747$		0			0
$748$		0			0
$749$	1.77075	+	0.908400i	1.77075	+	0.908400i
$750$		0			0
$751$	−1.25018	−	1.41963i	−1.25018	−	1.41963i	−0.868768	−	0.495219i	$-0.835088\pi$
$751$	−1.25018	−	1.41963i	−1.25018	−	1.41963i	−0.381410	−	0.924406i	$-0.624561\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−0.690436	+	0.984120i	−0.690436	+	0.984120i	0.309017	+	0.951057i	$0.400000\pi$
$757$	−0.690436	+	0.984120i	−0.690436	+	0.984120i	−0.999453	+	0.0330634i	$0.989474\pi$
$758$	−2.95334	−	1.72689i	−2.95334	−	1.72689i
$759$		0			0
$760$		0			0
$761$		0			0		−0.528360	−	0.849020i	$-0.677193\pi$
$761$		0			0		0.528360	+	0.849020i	$0.322807\pi$
$762$		0			0
$763$	0.220055	+	0.0701617i	0.220055	+	0.0701617i
$764$	−0.466352	+	4.43704i	−0.466352	+	4.43704i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.962268	−	0.272103i	$-0.0877193\pi$
$769$		0			0		−0.962268	+	0.272103i	$0.912281\pi$
$770$		0			0
$771$		0			0
$772$	2.89055	−	4.76101i	2.89055	−	4.76101i
$773$		0			0		0.0935596	−	0.995614i	$-0.470175\pi$
$773$		0			0		−0.0935596	+	0.995614i	$0.529825\pi$
$774$	3.31841	−	1.43383i	3.31841	−	1.43383i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.39931	+	0.249388i	−1.39931	+	0.249388i
$779$		0			0
$780$		0			0
$781$	−0.605118	+	0.0873123i	−0.605118	+	0.0873123i
$782$		0			0
$783$		0			0
$784$	−3.95774	−	1.92133i	−3.95774	−	1.92133i
$785$		0			0
$786$		0			0
$787$		0			0		−0.724425	−	0.689353i	$-0.757895\pi$
$787$		0			0		0.724425	+	0.689353i	$0.242105\pi$
$788$	−2.13563	−	5.34231i	−2.13563	−	5.34231i
$789$		0			0
$790$		0			0
$791$	0.321015	+	1.02634i	0.321015	+	1.02634i
$792$	−3.00184	−	0.500919i	−3.00184	−	0.500919i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.991264	−	0.131892i	$-0.957895\pi$
$797$		0			0		0.991264	+	0.131892i	$0.0421053\pi$
$798$		0			0
$799$		0			0
$800$	4.73222	−	1.50881i	4.73222	−	1.50881i
$801$		0			0
$802$	0.966029	−	3.08857i	0.966029	−	3.08857i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.285705	−	0.184422i	−0.285705	−	0.184422i	0.391577	−	0.920146i	$-0.371930\pi$
$809$	−0.285705	−	0.184422i	−0.285705	−	0.184422i	−0.677282	+	0.735724i	$0.736842\pi$
$810$		0			0
$811$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$811$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$812$	1.71663	+	0.0567887i	1.71663	+	0.0567887i
$813$		0			0
$814$	0.490959	+	1.31129i	0.490959	+	1.31129i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.594610	−	1.76363i	−0.594610	−	1.76363i	−0.644194	−	0.764862i	$-0.722807\pi$
$821$	−0.594610	−	1.76363i	−0.594610	−	1.76363i	0.0495838	−	0.998770i	$-0.484211\pi$
$822$		0			0
$823$	−1.88969	+	0.445421i	−1.88969	+	0.445421i	−0.999939	−	0.0110229i	$-0.996491\pi$
$823$	−1.88969	+	0.445421i	−1.88969	+	0.445421i	−0.889752	+	0.456444i	$0.849123\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.195359	+	1.00013i	−0.195359	+	1.00013i	0.746821	+	0.665025i	$0.231579\pi$
$827$	−0.195359	+	1.00013i	−0.195359	+	1.00013i	−0.942181	+	0.335105i	$0.891228\pi$
$828$	4.45665	+	1.20733i	4.45665	+	1.20733i
$829$		0			0		−0.821778	−	0.569808i	$-0.807018\pi$
$829$		0			0		0.821778	+	0.569808i	$0.192982\pi$
$830$		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		−0.909007	−	0.416782i	$-0.863158\pi$
$839$		0			0		0.909007	+	0.416782i	$0.136842\pi$
$840$		0			0
$841$	0.596250	−	0.242176i	0.596250	−	0.242176i
$842$	−1.15789	−	2.63972i	−1.15789	−	2.63972i
$843$		0			0
$844$	0.277452	+	4.57076i	0.277452	+	4.57076i
$845$		0			0
$846$		0			0
$847$	−0.0926698	−	0.308165i	−0.0926698	−	0.308165i
$848$	1.66521	−	4.60141i	1.66521	−	4.60141i
$849$		0			0
$850$		0			0
$851$	−0.355010	−	1.33967i	−0.355010	−	1.33967i
$852$		0			0
$853$		0			0		−0.421786	−	0.906696i	$-0.638596\pi$
$853$		0			0		0.421786	+	0.906696i	$0.361404\pi$
$854$		0			0
$855$		0			0
$856$	−7.17662	+	1.60832i	−7.17662	+	1.60832i
$857$		0			0		0.975796	−	0.218681i	$-0.0701754\pi$
$857$		0			0		−0.975796	+	0.218681i	$0.929825\pi$
$858$		0			0
$859$		0			0		0.601081	−	0.799188i	$-0.294737\pi$
$859$		0			0		−0.601081	+	0.799188i	$0.705263\pi$
$860$		0			0
$861$		0			0
$862$	−0.979213	−	3.69517i	−0.979213	−	3.69517i
$863$	1.16635	+	1.62409i	1.16635	+	1.62409i	0.601081	+	0.799188i	$0.294737\pi$
$863$	1.16635	+	1.62409i	1.16635	+	1.62409i	0.565270	+	0.824906i	$0.308772\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.0470130	−	0.774494i	−0.0470130	−	0.774494i
$870$		0			0
$871$		0			0
$872$	−0.790803	+	0.321197i	−0.790803	+	0.321197i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.156210	−	0.0536269i	−0.156210	−	0.0536269i	0.245485	−	0.969400i	$-0.421053\pi$
$877$	−0.156210	−	0.0536269i	−0.156210	−	0.0536269i	−0.401695	+	0.915773i	$0.631579\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.795863	−	0.605477i	$-0.207018\pi$
$881$		0			0		−0.795863	+	0.605477i	$0.792982\pi$
$882$	1.21791	+	1.54711i	1.21791	+	1.54711i
$883$	0.917178	+	0.974540i	0.917178	+	0.974540i	0.999757	−	0.0220445i	$-0.00701754\pi$
$883$	0.917178	+	0.974540i	0.917178	+	0.974540i	−0.0825793	+	0.996584i	$0.526316\pi$
$884$		0			0
$885$		0			0
$886$	−0.750365	+	3.84145i	−0.750365	+	3.84145i
$887$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$887$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$888$		0			0
$889$	−1.81444	−	0.448851i	−1.81444	−	0.448851i
$890$		0			0
$891$	0.671546	+	0.476686i	0.671546	+	0.476686i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	5.46210	−	1.35120i	5.46210	−	1.35120i
$897$		0			0
$898$	1.72637	+	3.23248i	1.72637	+	3.23248i
$899$		0			0
$900$	−2.84737	−	0.410846i	−2.84737	−	0.410846i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−3.33885	−	2.15522i	−3.33885	−	2.15522i
$905$		0			0
$906$		0			0
$907$	−0.579805	−	1.60215i	−0.579805	−	1.60215i	−0.782322	−	0.622874i	$-0.785965\pi$
$907$	−0.579805	−	1.60215i	−0.579805	−	1.60215i	0.202517	−	0.979279i	$-0.435088\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.585316	+	1.87136i	−0.585316	+	1.87136i	−0.104528	+	0.994522i	$0.533333\pi$
$911$	−0.585316	+	1.87136i	−0.585316	+	1.87136i	−0.480787	+	0.876837i	$0.659649\pi$
$912$		0			0
$913$		0			0
$914$	2.34635	+	3.11967i	2.34635	+	3.11967i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	1.32571	+	1.37787i	1.32571	+	1.37787i	0.874174	+	0.485613i	$0.161404\pi$
$919$	1.32571	+	1.37787i	1.32571	+	1.37787i	0.451533	+	0.892254i	$0.350877\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.320532	+	0.801814i	0.320532	+	0.801814i
$926$	−0.0786056	−	0.0748001i	−0.0786056	−	0.0748001i
$927$		0			0
$928$	−2.34012	+	1.82139i	−2.34012	+	1.82139i
$929$		0			0		−0.899598	−	0.436719i	$-0.856140\pi$
$929$		0			0		0.899598	+	0.436719i	$0.143860\pi$
$930$		0			0
$931$		0			0
$932$	−5.49662	+	0.793105i	−5.49662	+	0.793105i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.988116	−	0.153712i	$-0.0491228\pi$
$937$		0			0		−0.988116	+	0.153712i	$0.950877\pi$
$938$	0.0211788	+	3.84258i	0.0211788	+	3.84258i
$939$		0			0
$940$		0			0
$941$		0			0		0.518970	−	0.854793i	$-0.326316\pi$
$941$		0			0		−0.518970	+	0.854793i	$0.673684\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	2.97683	+	0.0328153i	2.97683	+	0.0328153i
$947$	−1.60532	+	0.986789i	−1.60532	+	0.986789i	−0.627176	+	0.778877i	$0.715789\pi$
$947$	−1.60532	+	0.986789i	−1.60532	+	0.986789i	−0.978148	+	0.207912i	$0.933333\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.230619	−	1.98360i	−0.230619	−	1.98360i	−0.170028	−	0.985439i	$-0.554386\pi$
$953$	−0.230619	−	1.98360i	−0.230619	−	1.98360i	−0.0605901	−	0.998163i	$-0.519298\pi$
$954$	−1.56980	+	1.52712i	−1.56980	+	1.52712i
$955$		0			0
$956$	2.49196	−	3.55195i	2.49196	−	3.55195i
$957$		0			0
$958$		0			0
$959$	0.0102579	−	0.00403526i	0.0102579	−	0.00403526i
$960$		0			0
$961$	0.945817	−	0.324699i	0.945817	−	0.324699i
$962$		0			0
$963$	1.93708	+	0.456592i	1.93708	+	0.456592i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1.82432	+	0.100650i	−1.82432	+	0.100650i	−0.934564	−	0.355794i	$-0.884211\pi$
$967$	−1.82432	+	0.100650i	−1.82432	+	0.100650i	−0.889752	+	0.456444i	$0.849123\pi$
$968$	0.991955	+	0.655905i	0.991955	+	0.655905i
$969$		0			0
$970$		0			0
$971$		0			0		0.863256	−	0.504766i	$-0.168421\pi$
$971$		0			0		−0.863256	+	0.504766i	$0.831579\pi$
$972$		0			0
$973$		0			0
$974$	0.587368	+	0.921050i	0.587368	+	0.921050i
$975$		0			0
$976$		0			0
$977$	1.78619	−	0.338693i	1.78619	−	0.338693i	0.815447	−	0.578832i	$-0.196491\pi$
$977$	1.78619	−	0.338693i	1.78619	−	0.338693i	0.970739	+	0.240139i	$0.0771930\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.230464	+	0.0152649i	0.230464	+	0.0152649i
$982$	−2.63106	−	1.10259i	−2.63106	−	1.10259i
$983$		0			0		−0.999757	−	0.0220445i	$-0.992982\pi$
$983$		0			0		0.999757	+	0.0220445i	$0.00701754\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.92877	−	0.324156i	−2.92877	−	0.324156i
$990$		0			0
$991$	1.18095	+	0.0913054i	1.18095	+	0.0913054i	0.652586	−	0.757715i	$-0.273684\pi$
$991$	1.18095	+	0.0913054i	1.18095	+	0.0913054i	0.528360	+	0.849020i	$0.322807\pi$
$992$		0			0
$993$		0			0
$994$	−1.45457	+	0.144780i	−1.45457	+	0.144780i
$995$		0			0
$996$		0			0
$997$		0			0		−0.782322	−	0.622874i	$-0.785965\pi$
$997$		0			0		0.782322	+	0.622874i	$0.214035\pi$
$998$	−1.53936	+	3.40681i	−1.53936	+	3.40681i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3997.1.cz.a.321.1	✓	144
7.6	odd	2	CM	3997.1.cz.a.321.1	✓	144
571.185	even	285	inner	3997.1.cz.a.3611.1	yes	144
3997.3611	odd	570	inner	3997.1.cz.a.3611.1	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3997.1.cz.a.321.1	✓	144	1.1	even	1	trivial
3997.1.cz.a.321.1	✓	144	7.6	odd	2	CM
3997.1.cz.a.3611.1	yes	144	571.185	even	285	inner
3997.1.cz.a.3611.1	yes	144	3997.3611	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)

\(f(q)\)	\(=\)	\(q+(1.92132 + 0.430577i) q^{2} +(2.60171 + 1.22778i) q^{4} +(-0.213300 - 0.976987i) q^{7} +(2.91626 + 2.26982i) q^{8} +(-0.441671 - 0.897177i) q^{9} +O(q^{10})\)	\(q+(1.92132 + 0.430577i) q^{2} +(2.60171 + 1.22778i) q^{4} +(-0.213300 - 0.976987i) q^{7} +(2.91626 + 2.26982i) q^{8} +(-0.441671 - 0.897177i) q^{9} +(-0.0317647 - 0.822918i) q^{11} +(0.0108521 - 1.96894i) q^{14} +(2.79684 + 3.39602i) q^{16} +(-0.462286 - 1.91394i) q^{18} +(0.293300 - 1.59476i) q^{22} +(-0.445225 + 1.54199i) q^{23} +(0.159156 - 0.987253i) q^{25} +(0.644577 - 2.80372i) q^{28} +(0.114457 + 0.585956i) q^{29} +(2.24274 + 4.43177i) q^{32} +(-0.0475658 - 2.87647i) q^{36} +(-0.740580 + 0.444060i) q^{37} +(0.312163 + 1.80921i) q^{43} +(0.927716 - 2.17999i) q^{44} +(-1.51936 + 2.77095i) q^{46} +(-0.909007 + 0.416782i) q^{49} +(0.730878 - 1.82830i) q^{50} +(-0.566727 - 0.957079i) q^{53} +(1.59554 - 3.33330i) q^{56} +(-0.0323911 + 1.17509i) q^{58} +(-0.782322 + 0.622874i) q^{63} +(1.32079 + 5.21567i) q^{64} +(-1.95147 + 0.0215122i) q^{67} +(-0.0776014 - 0.738328i) q^{71} +(0.748401 - 3.61891i) q^{72} +(-1.61409 + 0.534303i) q^{74} +(-0.797205 + 0.206562i) q^{77} +(0.941957 - 0.0207700i) q^{79} +(-0.609854 + 0.792514i) q^{81} +(-0.179242 + 3.61049i) q^{86} +(1.77524 - 2.47194i) q^{88} +(-3.05156 + 3.46517i) q^{92} +(-1.92595 + 0.409373i) q^{98} +(-0.724274 + 0.391957i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9}+O(q^{10}) \) 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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