LMFDB - Embedded newform 2916.2.e.d.1945.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2916,2,Mod(973,2916)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2916, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2916.973");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2916 = 2^{2} \cdot 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2916.e (of order $3$, degree $2$, not 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:	$23.2843772294$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 24 x^{16} - 66 x^{15} + 153 x^{14} - 315 x^{13} + 651 x^{12} - 1350 x^{11} + \cdots + 19683 $ x^18 - 6x^17 + 24x^16 - 66x^15 + 153x^14 - 315x^13 + 651x^12 - 1350x^11 + 2700x^10 - 4941x^9 + 8100x^8 - 12150x^7 + 17577x^6 - 25515x^5 + 37179x^4 - 48114x^3 + 52488x^2 - 39366*x + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1945.4
Root			$0.960398 + 1.44140i$ of defining polynomial
Character	$\chi$	$=$	2916.1945
Dual form			2916.2.e.d.973.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.296957 - 0.514344i) q^{5} +(-1.42798 + 2.47334i) q^{7} +O(q^{10})$	$q+(-0.296957 - 0.514344i) q^{5} +(-1.42798 + 2.47334i) q^{7} +(0.204120 - 0.353547i) q^{11} +(-0.0971750 - 0.168312i) q^{13} -7.33071 q^{17} -4.13172 q^{19} +(2.03741 + 3.52890i) q^{23} +(2.32363 - 4.02465i) q^{25} +(5.14422 - 8.91005i) q^{29} +(3.12032 + 5.40455i) q^{31} +1.69620 q^{35} +5.76698 q^{37} +(-4.21674 - 7.30361i) q^{41} +(2.99454 - 5.18669i) q^{43} +(5.62919 - 9.75005i) q^{47} +(-0.578282 - 1.00161i) q^{49} +3.42431 q^{53} -0.242459 q^{55} +(2.34268 + 4.05764i) q^{59} +(-2.18398 + 3.78276i) q^{61} +(-0.0577135 + 0.0999628i) q^{65} +(-6.07727 - 10.5261i) q^{67} +8.18817 q^{71} -3.93875 q^{73} +(0.582961 + 1.00972i) q^{77} +(-4.51141 + 7.81400i) q^{79} +(4.21400 - 7.29885i) q^{83} +(2.17690 + 3.77051i) q^{85} +4.76935 q^{89} +0.555058 q^{91} +(1.22694 + 2.12512i) q^{95} +(-3.86924 + 6.70172i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{5}+O(q^{10}) $ 18 * q + 6 * q^5	$ 18 q + 6 q^{5} + 6 q^{11} - 24 q^{17} + 3 q^{23} - 9 q^{25} + 24 q^{29} - 42 q^{35} + 33 q^{41} + 9 q^{47} - 9 q^{49} - 66 q^{53} + 30 q^{59} + 9 q^{61} + 39 q^{65} + 9 q^{67} - 24 q^{71} - 18 q^{73} + 39 q^{77} + 36 q^{83} - 96 q^{89} - 18 q^{91} + 12 q^{95}+O(q^{100}) $ 18 * q + 6 * q^5 + 6 * q^11 - 24 * q^17 + 3 * q^23 - 9 * q^25 + 24 * q^29 - 42 * q^35 + 33 * q^41 + 9 * q^47 - 9 * q^49 - 66 * q^53 + 30 * q^59 + 9 * q^61 + 39 * q^65 + 9 * q^67 - 24 * q^71 - 18 * q^73 + 39 * q^77 + 36 * q^83 - 96 * q^89 - 18 * q^91 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2916\mathbb{Z}\right)^\times$.

$n$	$1459$	$2189$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.296957	−	0.514344i	−0.132803	−	0.230022i	0.791953	−	0.610582i	$-0.209064\pi$
$5$	−0.296957	−	0.514344i	−0.132803	−	0.230022i	−0.924756	+	0.380560i	$0.875731\pi$
$6$		0			0
$7$	−1.42798	+	2.47334i	−0.539728	+	0.934836i	0.459191	+	0.888338i	$0.348139\pi$
$7$	−1.42798	+	2.47334i	−0.539728	+	0.934836i	−0.998918	+	0.0464979i	$0.985194\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.204120	−	0.353547i	0.0615445	−	0.106598i	−0.833611	−	0.552351i	$-0.813731\pi$
$11$	0.204120	−	0.353547i	0.0615445	−	0.106598i	0.895156	+	0.445753i	$0.147064\pi$
$12$		0			0
$13$	−0.0971750	−	0.168312i	−0.0269515	−	0.0466814i	0.852235	−	0.523159i	$-0.175247\pi$
$13$	−0.0971750	−	0.168312i	−0.0269515	−	0.0466814i	−0.879187	+	0.476478i	$0.841913\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−7.33071			−1.77796			−0.888980	−	0.457947i	$-0.848585\pi$
$17$	−7.33071			−1.77796			−0.888980	+	0.457947i	$0.848585\pi$
$18$		0			0
$19$	−4.13172			−0.947880			−0.473940	−	0.880557i	$-0.657169\pi$
$19$	−4.13172			−0.947880			−0.473940	+	0.880557i	$0.657169\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.03741	+	3.52890i	0.424830	+	0.735827i	0.996405	−	0.0847231i	$-0.0270006\pi$
$23$	2.03741	+	3.52890i	0.424830	+	0.735827i	−0.571575	+	0.820550i	$0.693667\pi$
$24$		0			0
$25$	2.32363	−	4.02465i	0.464727	−	0.804930i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	5.14422	−	8.91005i	0.955258	−	1.65455i	0.221480	−	0.975165i	$-0.428911\pi$
$29$	5.14422	−	8.91005i	0.955258	−	1.65455i	0.733777	−	0.679390i	$-0.237756\pi$
$30$		0			0
$31$	3.12032	+	5.40455i	0.560426	+	0.970686i	0.997459	+	0.0712410i	$0.0226960\pi$
$31$	3.12032	+	5.40455i	0.560426	+	0.970686i	−0.437033	+	0.899445i	$0.643971\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.69620			0.286710
$36$		0			0
$37$	5.76698			0.948085			0.474043	−	0.880502i	$-0.342794\pi$
$37$	5.76698			0.948085			0.474043	+	0.880502i	$0.342794\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.21674	−	7.30361i	−0.658544	−	1.14063i	−0.980993	−	0.194045i	$-0.937839\pi$
$41$	−4.21674	−	7.30361i	−0.658544	−	1.14063i	0.322448	−	0.946587i	$-0.395494\pi$
$42$		0			0
$43$	2.99454	−	5.18669i	0.456662	−	0.790962i	−0.542120	−	0.840301i	$-0.682378\pi$
$43$	2.99454	−	5.18669i	0.456662	−	0.790962i	0.998782	+	0.0493389i	$0.0157114\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.62919	−	9.75005i	0.821102	−	1.42219i	−0.0837596	−	0.996486i	$-0.526693\pi$
$47$	5.62919	−	9.75005i	0.821102	−	1.42219i	0.904862	−	0.425705i	$-0.139974\pi$
$48$		0			0
$49$	−0.578282	−	1.00161i	−0.0826118	−	0.143088i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.42431			0.470365			0.235183	−	0.971951i	$-0.424431\pi$
$53$	3.42431			0.470365			0.235183	+	0.971951i	$0.424431\pi$
$54$		0			0
$55$	−0.242459			−0.0326932
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.34268	+	4.05764i	0.304991	+	0.528259i	0.977259	−	0.212048i	$-0.0680133\pi$
$59$	2.34268	+	4.05764i	0.304991	+	0.528259i	−0.672269	+	0.740307i	$0.734680\pi$
$60$		0			0
$61$	−2.18398	+	3.78276i	−0.279630	+	0.484333i	−0.971293	−	0.237888i	$-0.923545\pi$
$61$	−2.18398	+	3.78276i	−0.279630	+	0.484333i	0.691663	+	0.722220i	$0.256878\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.0577135	+	0.0999628i	−0.00715848	+	0.0123989i
$66$		0			0
$67$	−6.07727	−	10.5261i	−0.742457	−	1.28597i	−0.951374	−	0.308039i	$-0.900327\pi$
$67$	−6.07727	−	10.5261i	−0.742457	−	1.28597i	0.208917	−	0.977933i	$-0.433006\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	8.18817			0.971757			0.485879	−	0.874026i	$-0.338500\pi$
$71$	8.18817			0.971757			0.485879	+	0.874026i	$0.338500\pi$
$72$		0			0
$73$	−3.93875			−0.460996			−0.230498	−	0.973073i	$-0.574035\pi$
$73$	−3.93875			−0.460996			−0.230498	+	0.973073i	$0.574035\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.582961	+	1.00972i	0.0664346	+	0.115068i
$78$		0			0
$79$	−4.51141	+	7.81400i	−0.507574	+	0.879143i	0.492388	+	0.870376i	$0.336124\pi$
$79$	−4.51141	+	7.81400i	−0.507574	+	0.879143i	−0.999962	+	0.00876750i	$0.997209\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.21400	−	7.29885i	0.462546	−	0.801153i	−0.536541	−	0.843874i	$-0.680269\pi$
$83$	4.21400	−	7.29885i	0.462546	−	0.801153i	0.999087	+	0.0427209i	$0.0136026\pi$
$84$		0			0
$85$	2.17690	+	3.77051i	0.236118	+	0.408969i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.76935			0.505550			0.252775	−	0.967525i	$-0.418657\pi$
$89$	4.76935			0.505550			0.252775	+	0.967525i	$0.418657\pi$
$90$		0			0
$91$	0.555058			0.0581859
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.22694	+	2.12512i	0.125881	+	0.218033i
$96$		0			0
$97$	−3.86924	+	6.70172i	−0.392862	+	0.680456i	−0.992826	−	0.119571i	$-0.961848\pi$
$97$	−3.86924	+	6.70172i	−0.392862	+	0.680456i	0.599964	+	0.800027i	$0.295182\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.94201	−	10.2919i	0.591252	−	1.02408i	−0.402812	−	0.915283i	$-0.631967\pi$
$101$	5.94201	−	10.2919i	0.591252	−	1.02408i	0.994064	−	0.108796i	$-0.0346996\pi$
$102$		0			0
$103$	1.83427	+	3.17706i	0.180736	+	0.313045i	0.942132	−	0.335243i	$-0.108819\pi$
$103$	1.83427	+	3.17706i	0.180736	+	0.313045i	−0.761395	+	0.648288i	$0.775485\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.24784			0.507328			0.253664	−	0.967292i	$-0.418364\pi$
$107$	5.24784			0.507328			0.253664	+	0.967292i	$0.418364\pi$
$108$		0			0
$109$	−7.04007			−0.674316			−0.337158	−	0.941448i	$-0.609466\pi$
$109$	−7.04007			−0.674316			−0.337158	+	0.941448i	$0.609466\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.485215	−	0.840417i	−0.0456452	−	0.0790598i	0.842300	−	0.539009i	$-0.181201\pi$
$113$	−0.485215	−	0.840417i	−0.0456452	−	0.0790598i	−0.887945	+	0.459949i	$0.847868\pi$
$114$		0			0
$115$	1.21005	−	2.09586i	0.112837	−	0.195440i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	10.4681	−	18.1314i	0.959614	−	1.66210i
$120$		0			0
$121$	5.41667	+	9.38195i	0.492425	+	0.852904i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−5.72964			−0.512475
$126$		0			0
$127$	8.81076			0.781829			0.390914	−	0.920427i	$-0.372159\pi$
$127$	8.81076			0.781829			0.390914	+	0.920427i	$0.372159\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.39085	−	4.14108i	−0.208890	−	0.361808i	0.742475	−	0.669874i	$-0.233652\pi$
$131$	−2.39085	−	4.14108i	−0.208890	−	0.361808i	−0.951365	+	0.308066i	$0.900318\pi$
$132$		0			0
$133$	5.90003	−	10.2191i	0.511597	−	0.886112i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.26437	−	12.5823i	0.620637	−	1.07498i	−0.368730	−	0.929537i	$-0.620207\pi$
$137$	7.26437	−	12.5823i	0.620637	−	1.07498i	0.989367	−	0.145439i	$-0.0464594\pi$
$138$		0			0
$139$	−7.50274	−	12.9951i	−0.636374	−	1.10223i	−0.986222	−	0.165426i	$-0.947100\pi$
$139$	−7.50274	−	12.9951i	−0.636374	−	1.10223i	0.349848	−	0.936806i	$-0.386233\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.0793415			−0.00663487
$144$		0			0
$145$	−6.11044			−0.507444
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.07426	+	3.59273i	0.169930	+	0.294328i	0.938395	−	0.345564i	$-0.112312\pi$
$149$	2.07426	+	3.59273i	0.169930	+	0.294328i	−0.768465	+	0.639892i	$0.778979\pi$
$150$		0			0
$151$	2.26787	−	3.92807i	0.184557	−	0.319662i	−0.758870	−	0.651242i	$-0.774248\pi$
$151$	2.26787	−	3.92807i	0.184557	−	0.319662i	0.943427	+	0.331580i	$0.107582\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.85320	−	3.20984i	0.148853	−	0.257820i
$156$		0			0
$157$	−6.78766	−	11.7566i	−0.541714	−	0.938276i	−0.998806	−	0.0488567i	$-0.984442\pi$
$157$	−6.78766	−	11.7566i	−0.541714	−	0.938276i	0.457092	−	0.889420i	$-0.348891\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−11.6376			−0.917170
$162$		0			0
$163$	19.9421			1.56199			0.780994	−	0.624539i	$-0.214713\pi$
$163$	19.9421			1.56199			0.780994	+	0.624539i	$0.214713\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.58285	−	9.66978i	−0.432014	−	0.748270i	0.565033	−	0.825069i	$-0.308864\pi$
$167$	−5.58285	−	9.66978i	−0.432014	−	0.748270i	−0.997047	+	0.0767984i	$0.975530\pi$
$168$		0			0
$169$	6.48111	−	11.2256i	0.498547	−	0.863509i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.7891	−	18.6873i	0.820282	−	1.42077i	−0.0851896	−	0.996365i	$-0.527150\pi$
$173$	10.7891	−	18.6873i	0.820282	−	1.42077i	0.905472	−	0.424406i	$-0.139517\pi$
$174$		0			0
$175$	6.63623	+	11.4943i	0.501652	+	0.868886i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	15.3411			1.14665			0.573325	−	0.819328i	$-0.305653\pi$
$179$	15.3411			1.14665			0.573325	+	0.819328i	$0.305653\pi$
$180$		0			0
$181$	7.39841			0.549920			0.274960	−	0.961456i	$-0.411335\pi$
$181$	7.39841			0.549920			0.274960	+	0.961456i	$0.411335\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.71254	−	2.96621i	−0.125909	−	0.218080i
$186$		0			0
$187$	−1.49635	+	2.59175i	−0.109424	+	0.189527i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−6.18689	+	10.7160i	−0.447667	+	0.775383i	−0.998234	−	0.0594088i	$-0.981078\pi$
$191$	−6.18689	+	10.7160i	−0.447667	+	0.775383i	0.550566	+	0.834791i	$0.314412\pi$
$192$		0			0
$193$	−7.79606	−	13.5032i	−0.561173	−	0.971980i	−0.997394	−	0.0721405i	$-0.977017\pi$
$193$	−7.79606	−	13.5032i	−0.561173	−	0.971980i	0.436222	−	0.899839i	$-0.356316\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−17.1990			−1.22538			−0.612688	−	0.790325i	$-0.709912\pi$
$197$	−17.1990			−1.22538			−0.612688	+	0.790325i	$0.709912\pi$
$198$		0			0
$199$	−17.7777			−1.26023			−0.630114	−	0.776503i	$-0.716992\pi$
$199$	−17.7777			−1.26023			−0.630114	+	0.776503i	$0.716992\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	14.6917	+	25.4468i	1.03116	+	1.78602i
$204$		0			0
$205$	−2.50438	+	4.33771i	−0.174913	+	0.302959i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.843366	+	1.46075i	−0.0583369	+	0.101042i
$210$		0			0
$211$	9.44042	+	16.3513i	0.649905	+	1.12567i	0.983145	+	0.182827i	$0.0585247\pi$
$211$	9.44042	+	16.3513i	0.649905	+	1.12567i	−0.333240	+	0.942842i	$0.608142\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.55699			−0.242585
$216$		0			0
$217$	−17.8231			−1.20991
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.712362	+	1.23385i	0.0479187	+	0.0829976i
$222$		0			0
$223$	0.746560	−	1.29308i	0.0499933	−	0.0865910i	−0.839946	−	0.542670i	$-0.817413\pi$
$223$	0.746560	−	1.29308i	0.0499933	−	0.0865910i	0.889939	+	0.456079i	$0.150747\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.75075	−	16.8888i	0.647180	−	1.12095i	−0.336613	−	0.941643i	$-0.609281\pi$
$227$	9.75075	−	16.8888i	0.647180	−	1.12095i	0.983793	−	0.179306i	$-0.0573852\pi$
$228$		0			0
$229$	0.0158446	+	0.0274437i	0.00104704	+	0.00181353i	0.866548	−	0.499093i	$-0.166333\pi$
$229$	0.0158446	+	0.0274437i	0.00104704	+	0.00181353i	−0.865501	+	0.500906i	$0.833000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−13.4318			−0.879949			−0.439975	−	0.898010i	$-0.645013\pi$
$233$	−13.4318			−0.879949			−0.439975	+	0.898010i	$0.645013\pi$
$234$		0			0
$235$	−6.68651			−0.436180
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.74905	−	13.4217i	−0.501244	−	0.868181i	−0.999999	−	0.00143735i	$-0.999542\pi$
$239$	−7.74905	−	13.4217i	−0.501244	−	0.868181i	0.498755	−	0.866743i	$-0.333791\pi$
$240$		0			0
$241$	−11.7474	+	20.3471i	−0.756717	+	1.31067i	0.187799	+	0.982208i	$0.439865\pi$
$241$	−11.7474	+	20.3471i	−0.756717	+	1.31067i	−0.944516	+	0.328465i	$0.893469\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.343449	+	0.594872i	−0.0219422	+	0.0380050i
$246$		0			0
$247$	0.401500	+	0.695418i	0.0255468	+	0.0442484i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−10.5642			−0.666805			−0.333403	−	0.942785i	$-0.608197\pi$
$251$	−10.5642			−0.666805			−0.333403	+	0.942785i	$0.608197\pi$
$252$		0			0
$253$	1.66351			0.104584
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.01899	−	10.4252i	−0.375454	−	0.650306i	0.614941	−	0.788573i	$-0.289180\pi$
$257$	−6.01899	−	10.4252i	−0.375454	−	0.650306i	−0.990395	+	0.138268i	$0.955847\pi$
$258$		0			0
$259$	−8.23516	+	14.2637i	−0.511708	+	0.886304i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.77710	−	3.07802i	0.109580	−	0.189799i	−0.806020	−	0.591888i	$-0.798383\pi$
$263$	1.77710	−	3.07802i	0.109580	−	0.189799i	0.915600	+	0.402090i	$0.131716\pi$
$264$		0			0
$265$	−1.01687	−	1.76127i	−0.0624659	−	0.108194i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−25.8590			−1.57665			−0.788327	−	0.615257i	$-0.789052\pi$
$269$	−25.8590			−1.57665			−0.788327	+	0.615257i	$0.789052\pi$
$270$		0			0
$271$	−2.86426			−0.173991			−0.0869957	−	0.996209i	$-0.527727\pi$
$271$	−2.86426			−0.173991			−0.0869957	+	0.996209i	$0.527727\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.948601	−	1.64303i	−0.0572028	−	0.0990781i
$276$		0			0
$277$	5.66088	−	9.80494i	0.340130	−	0.589122i	−0.644327	−	0.764750i	$-0.722862\pi$
$277$	5.66088	−	9.80494i	0.340130	−	0.589122i	0.984457	+	0.175628i	$0.0561957\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−10.3420	+	17.9128i	−0.616951	+	1.06859i	0.373088	+	0.927796i	$0.378299\pi$
$281$	−10.3420	+	17.9128i	−0.616951	+	1.06859i	−0.990039	+	0.140794i	$0.955034\pi$
$282$		0			0
$283$	0.770226	+	1.33407i	0.0457852	+	0.0793023i	0.888010	−	0.459825i	$-0.152088\pi$
$283$	0.770226	+	1.33407i	0.0457852	+	0.0793023i	−0.842225	+	0.539127i	$0.818754\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	24.0858			1.42174
$288$		0			0
$289$	36.7394			2.16114
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.70662	+	4.68800i	0.158122	+	0.273876i	0.934192	−	0.356772i	$-0.116123\pi$
$293$	2.70662	+	4.68800i	0.158122	+	0.273876i	−0.776069	+	0.630648i	$0.782789\pi$
$294$		0			0
$295$	1.39135	−	2.40988i	0.0810074	−	0.140309i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.395971	−	0.685842i	0.0228996	−	0.0396633i
$300$		0			0
$301$	8.55230	+	14.8130i	0.492947	+	0.853808i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.59419			0.148543
$306$		0			0
$307$	12.1406			0.692899			0.346449	−	0.938069i	$-0.387387\pi$
$307$	12.1406			0.692899			0.346449	+	0.938069i	$0.387387\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−6.06925	−	10.5123i	−0.344156	−	0.596095i	0.641044	−	0.767504i	$-0.278501\pi$
$311$	−6.06925	−	10.5123i	−0.344156	−	0.596095i	−0.985200	+	0.171409i	$0.945168\pi$
$312$		0			0
$313$	−0.519495	+	0.899791i	−0.0293636	+	0.0508592i	−0.880334	−	0.474355i	$-0.842681\pi$
$313$	−0.519495	+	0.899791i	−0.0293636	+	0.0508592i	0.850970	+	0.525214i	$0.176015\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.68112	−	15.0361i	0.487580	−	0.844514i	−0.512318	−	0.858796i	$-0.671213\pi$
$317$	8.68112	−	15.0361i	0.487580	−	0.844514i	0.999898	+	0.0142823i	$0.00454636\pi$
$318$		0			0
$319$	−2.10008	−	3.63744i	−0.117582	−	0.203658i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	30.2884			1.68529
$324$		0			0
$325$	−0.903197			−0.0501003
$326$		0			0
$327$		0			0
$328$		0			0
$329$	16.0768	+	27.8459i	0.886343	+	1.53519i
$330$		0			0
$331$	−1.16710	+	2.02148i	−0.0641496	+	0.111110i	−0.896316	−	0.443415i	$-0.853767\pi$
$331$	−1.16710	+	2.02148i	−0.0641496	+	0.111110i	0.832167	+	0.554525i	$0.187100\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3.60937	+	6.25161i	−0.197201	+	0.341562i
$336$		0			0
$337$	2.54360	+	4.40565i	0.138559	+	0.239991i	0.926951	−	0.375182i	$-0.122420\pi$
$337$	2.54360	+	4.40565i	0.138559	+	0.239991i	−0.788393	+	0.615173i	$0.789086\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.54768			0.137965
$342$		0			0
$343$	−16.6887			−0.901104
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.81702	−	4.87922i	−0.151225	−	0.261930i	0.780453	−	0.625215i	$-0.214989\pi$
$347$	−2.81702	−	4.87922i	−0.151225	−	0.261930i	−0.931678	+	0.363285i	$0.881655\pi$
$348$		0			0
$349$	5.93484	−	10.2795i	0.317685	−	0.550246i	−0.662320	−	0.749221i	$-0.730428\pi$
$349$	5.93484	−	10.2795i	0.317685	−	0.550246i	0.980005	+	0.198975i	$0.0637612\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−2.08959	+	3.61928i	−0.111218	+	0.192635i	−0.916261	−	0.400581i	$-0.868808\pi$
$353$	−2.08959	+	3.61928i	−0.111218	+	0.192635i	0.805044	+	0.593215i	$0.202142\pi$
$354$		0			0
$355$	−2.43153	−	4.21154i	−0.129052	−	0.223525i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	27.4948			1.45112			0.725559	−	0.688160i	$-0.241581\pi$
$359$	27.4948			1.45112			0.725559	+	0.688160i	$0.241581\pi$
$360$		0			0
$361$	−1.92893			−0.101523
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.16964	+	2.02587i	0.0612216	+	0.106039i
$366$		0			0
$367$	15.0136	−	26.0042i	0.783701	−	1.35741i	−0.146070	−	0.989274i	$-0.546663\pi$
$367$	15.0136	−	26.0042i	0.783701	−	1.35741i	0.929772	−	0.368137i	$-0.120004\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.88986	+	8.46949i	−0.253869	+	0.439714i
$372$		0			0
$373$	5.11587	+	8.86094i	0.264889	+	0.458802i	0.967535	−	0.252738i	$-0.0813312\pi$
$373$	5.11587	+	8.86094i	0.264889	+	0.458802i	−0.702645	+	0.711540i	$0.747998\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.99956			−0.102983
$378$		0			0
$379$	−12.4688			−0.640478			−0.320239	−	0.947337i	$-0.603763\pi$
$379$	−12.4688			−0.640478			−0.320239	+	0.947337i	$0.603763\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−10.6050	−	18.3684i	−0.541890	−	0.938581i	−0.998796	−	0.0490661i	$-0.984375\pi$
$383$	−10.6050	−	18.3684i	−0.541890	−	0.938581i	0.456905	−	0.889515i	$-0.348958\pi$
$384$		0			0
$385$	0.346228	−	0.599685i	0.0176454	−	0.0305628i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−2.60555	+	4.51295i	−0.132107	+	0.228816i	−0.924489	−	0.381210i	$-0.875508\pi$
$389$	−2.60555	+	4.51295i	−0.132107	+	0.228816i	0.792382	+	0.610026i	$0.208841\pi$
$390$		0			0
$391$	−14.9357	−	25.8694i	−0.755330	−	1.30827i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	5.35878			0.269629
$396$		0			0
$397$	−31.5370			−1.58280			−0.791399	−	0.611300i	$-0.790647\pi$
$397$	−31.5370			−1.58280			−0.791399	+	0.611300i	$0.790647\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	12.6238	+	21.8650i	0.630400	+	1.09189i	0.987470	+	0.157807i	$0.0504425\pi$
$401$	12.6238	+	21.8650i	0.630400	+	1.09189i	−0.357070	+	0.934078i	$0.616224\pi$
$402$		0			0
$403$	0.606435	−	1.05038i	0.0302087	−	0.0523229i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.17716	−	2.03889i	0.0583495	−	0.101064i
$408$		0			0
$409$	5.59347	+	9.68817i	0.276579	+	0.479049i	0.970532	−	0.240971i	$-0.0774659\pi$
$409$	5.59347	+	9.68817i	0.276579	+	0.479049i	−0.693953	+	0.720020i	$0.744133\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−13.3812			−0.658448
$414$		0			0
$415$	−5.00550			−0.245710
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.760652	−	1.31749i	−0.0371603	−	0.0643635i	0.846847	−	0.531836i	$-0.178498\pi$
$419$	−0.760652	−	1.31749i	−0.0371603	−	0.0643635i	−0.884007	+	0.467473i	$0.845165\pi$
$420$		0			0
$421$	3.15729	−	5.46859i	0.153877	−	0.266523i	−0.778772	−	0.627306i	$-0.784157\pi$
$421$	3.15729	−	5.46859i	0.153877	−	0.266523i	0.932650	+	0.360784i	$0.117491\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−17.0339	+	29.5036i	−0.826265	+	1.43113i
$426$		0			0
$427$	−6.23737	−	10.8034i	−0.301848	−	0.522815i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	22.8116			1.09880			0.549398	−	0.835561i	$-0.314857\pi$
$431$	22.8116			1.09880			0.549398	+	0.835561i	$0.314857\pi$
$432$		0			0
$433$	30.2232			1.45243			0.726216	−	0.687466i	$-0.241277\pi$
$433$	30.2232			1.45243			0.726216	+	0.687466i	$0.241277\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−8.41801	−	14.5804i	−0.402688	−	0.697476i
$438$		0			0
$439$	−1.31933	+	2.28514i	−0.0629679	+	0.109064i	−0.895791	−	0.444476i	$-0.853390\pi$
$439$	−1.31933	+	2.28514i	−0.0629679	+	0.109064i	0.832823	+	0.553540i	$0.186723\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−14.7604	+	25.5657i	−0.701286	+	1.21466i	0.266730	+	0.963771i	$0.414057\pi$
$443$	−14.7604	+	25.5657i	−0.701286	+	1.21466i	−0.968015	+	0.250891i	$0.919276\pi$
$444$		0			0
$445$	−1.41629	−	2.45309i	−0.0671386	−	0.116287i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−31.7742			−1.49952			−0.749759	−	0.661711i	$-0.769831\pi$
$449$	−31.7742			−1.49952			−0.749759	+	0.661711i	$0.769831\pi$
$450$		0			0
$451$	−3.44289			−0.162119
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.164828	−	0.285491i	−0.00772726	−	0.0133840i
$456$		0			0
$457$	5.08107	−	8.80066i	0.237682	−	0.411678i	−0.722367	−	0.691510i	$-0.756946\pi$
$457$	5.08107	−	8.80066i	0.237682	−	0.411678i	0.960049	+	0.279833i	$0.0902790\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.5991	+	18.3581i	−0.493648	+	0.855023i	−0.999973	−	0.00731950i	$-0.997670\pi$
$461$	−10.5991	+	18.3581i	−0.493648	+	0.855023i	0.506325	+	0.862342i	$0.331003\pi$
$462$		0			0
$463$	2.42933	+	4.20772i	0.112900	+	0.195549i	0.916939	−	0.399029i	$-0.130653\pi$
$463$	2.42933	+	4.20772i	0.112900	+	0.195549i	−0.804038	+	0.594578i	$0.797319\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	29.6157			1.37045			0.685225	−	0.728332i	$-0.259704\pi$
$467$	29.6157			1.37045			0.685225	+	0.728332i	$0.259704\pi$
$468$		0			0
$469$	34.7130			1.60290
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.22249	−	2.11741i	−0.0562102	−	0.0973588i
$474$		0			0
$475$	−9.60059	+	16.6287i	−0.440505	+	0.762978i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−13.8316	+	23.9570i	−0.631982	+	1.09463i	0.355164	+	0.934804i	$0.384425\pi$
$479$	−13.8316	+	23.9570i	−0.631982	+	1.09463i	−0.987146	+	0.159821i	$0.948908\pi$
$480$		0			0
$481$	−0.560406	−	0.970652i	−0.0255523	−	0.0442579i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.59598			0.208693
$486$		0			0
$487$	16.7022			0.756847			0.378423	−	0.925633i	$-0.376466\pi$
$487$	16.7022			0.756847			0.378423	+	0.925633i	$0.376466\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	3.37429	+	5.84444i	0.152280	+	0.263756i	0.932065	−	0.362291i	$-0.118005\pi$
$491$	3.37429	+	5.84444i	0.152280	+	0.263756i	−0.779786	+	0.626047i	$0.784672\pi$
$492$		0			0
$493$	−37.7108	+	65.3170i	−1.69841	+	2.94173i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−11.6926	+	20.2522i	−0.524484	+	0.908433i
$498$		0			0
$499$	14.1352	+	24.4829i	0.632780	+	1.09601i	0.986981	+	0.160837i	$0.0514195\pi$
$499$	14.1352	+	24.4829i	0.632780	+	1.09601i	−0.354201	+	0.935169i	$0.615247\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−29.2222			−1.30295			−0.651476	−	0.758669i	$-0.725850\pi$
$503$	−29.2222			−1.30295			−0.651476	+	0.758669i	$0.725850\pi$
$504$		0			0
$505$	−7.05808			−0.314080
$506$		0			0
$507$		0			0
$508$		0			0
$509$	2.51782	+	4.36100i	0.111601	+	0.193298i	0.916416	−	0.400228i	$-0.131069\pi$
$509$	2.51782	+	4.36100i	0.111601	+	0.193298i	−0.804815	+	0.593525i	$0.797736\pi$
$510$		0			0
$511$	5.62448	−	9.74188i	0.248812	−	0.430955i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.08940	−	1.88690i	0.0480047	−	0.0831466i
$516$		0			0
$517$	−2.29806	−	3.98036i	−0.101069	−	0.175056i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−2.33341			−0.102229			−0.0511143	−	0.998693i	$-0.516277\pi$
$521$	−2.33341			−0.102229			−0.0511143	+	0.998693i	$0.516277\pi$
$522$		0			0
$523$	−0.651260			−0.0284776			−0.0142388	−	0.999899i	$-0.504533\pi$
$523$	−0.651260			−0.0284776			−0.0142388	+	0.999899i	$0.504533\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−22.8742	−	39.6192i	−0.996415	−	1.72584i
$528$		0			0
$529$	3.19790	−	5.53892i	0.139039	−	0.240823i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.819524	+	1.41946i	−0.0354975	+	0.0614835i
$534$		0			0
$535$	−1.55838	−	2.69919i	−0.0673747	−	0.116696i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.472156			−0.0203372
$540$		0			0
$541$	−12.1207			−0.521111			−0.260555	−	0.965459i	$-0.583906\pi$
$541$	−12.1207			−0.521111			−0.260555	+	0.965459i	$0.583906\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2.09060	+	3.62102i	0.0895513	+	0.155107i
$546$		0			0
$547$	−1.45889	+	2.52688i	−0.0623778	+	0.108042i	−0.895528	−	0.445006i	$-0.853202\pi$
$547$	−1.45889	+	2.52688i	−0.0623778	+	0.108042i	0.833150	+	0.553047i	$0.186535\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−21.2545	+	36.8138i	−0.905470	+	1.56832i
$552$		0			0
$553$	−12.8845	−	22.3165i	−0.547903	−	0.948996i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−14.4875			−0.613857			−0.306928	−	0.951733i	$-0.599301\pi$
$557$	−14.4875			−0.613857			−0.306928	+	0.951733i	$0.599301\pi$
$558$		0			0
$559$	−1.16398			−0.0492310
$560$		0			0
$561$		0			0
$562$		0			0
$563$	17.0168	+	29.4739i	0.717171	+	1.24218i	0.962116	+	0.272639i	$0.0878965\pi$
$563$	17.0168	+	29.4739i	0.717171	+	1.24218i	−0.244946	+	0.969537i	$0.578770\pi$
$564$		0			0
$565$	−0.288176	+	0.499135i	−0.0121236	+	0.0209988i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2.20287	−	3.81548i	0.0923490	−	0.159953i	−0.816150	−	0.577840i	$-0.803896\pi$
$569$	2.20287	−	3.81548i	0.0923490	−	0.159953i	0.908499	+	0.417887i	$0.137229\pi$
$570$		0			0
$571$	18.2452	+	31.6016i	0.763539	+	1.32249i	0.941016	+	0.338363i	$0.109873\pi$
$571$	18.2452	+	31.6016i	0.763539	+	1.32249i	−0.177477	+	0.984125i	$0.556794\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	18.9368			0.789719
$576$		0			0
$577$	−30.4917			−1.26939			−0.634693	−	0.772765i	$-0.718873\pi$
$577$	−30.4917			−1.26939			−0.634693	+	0.772765i	$0.718873\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	12.0350	+	20.8453i	0.499298	+	0.864809i
$582$		0			0
$583$	0.698971	−	1.21065i	0.0289484	−	0.0501401i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.19798	−	2.07496i	0.0494458	−	0.0856427i	−0.840243	−	0.542210i	$-0.817588\pi$
$587$	1.19798	−	2.07496i	0.0494458	−	0.0856427i	0.889689	+	0.456567i	$0.150921\pi$
$588$		0			0
$589$	−12.8923	−	22.3301i	−0.531217	−	0.920095i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−6.03623			−0.247878			−0.123939	−	0.992290i	$-0.539553\pi$
$593$	−6.03623			−0.247878			−0.123939	+	0.992290i	$0.539553\pi$
$594$		0			0
$595$	−12.4343			−0.509758
$596$		0			0
$597$		0			0
$598$		0			0
$599$	13.4628	+	23.3182i	0.550073	+	0.952755i	0.998269	+	0.0588191i	$0.0187335\pi$
$599$	13.4628	+	23.3182i	0.550073	+	0.952755i	−0.448195	+	0.893936i	$0.647933\pi$
$600$		0			0
$601$	17.1496	−	29.7040i	0.699547	−	1.21165i	−0.269076	−	0.963119i	$-0.586718\pi$
$601$	17.1496	−	29.7040i	0.699547	−	1.21165i	0.968623	−	0.248533i	$-0.0799484\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	3.21703	−	5.57206i	0.130791	−	0.226537i
$606$		0			0
$607$	−5.80879	−	10.0611i	−0.235772	−	0.408368i	0.723725	−	0.690088i	$-0.242428\pi$
$607$	−5.80879	−	10.0611i	−0.235772	−	0.408368i	−0.959497	+	0.281720i	$0.909095\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.18807			−0.0885198
$612$		0			0
$613$	−36.6099			−1.47866			−0.739330	−	0.673343i	$-0.764858\pi$
$613$	−36.6099			−1.47866			−0.739330	+	0.673343i	$0.764858\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−10.0102	−	17.3382i	−0.402996	−	0.698009i	0.591090	−	0.806605i	$-0.298698\pi$
$617$	−10.0102	−	17.3382i	−0.402996	−	0.698009i	−0.994086	+	0.108596i	$0.965364\pi$
$618$		0			0
$619$	10.1728	−	17.6198i	0.408879	−	0.708200i	−0.585885	−	0.810394i	$-0.699253\pi$
$619$	10.1728	−	17.6198i	0.408879	−	0.708200i	0.994764	+	0.102194i	$0.0325864\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−6.81056	+	11.7962i	−0.272859	+	0.472606i
$624$		0			0
$625$	−9.91671	−	17.1763i	−0.396669	−	0.687050i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−42.2761			−1.68566
$630$		0			0
$631$	41.9747			1.67099			0.835493	−	0.549501i	$-0.185182\pi$
$631$	41.9747			1.67099			0.835493	+	0.549501i	$0.185182\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.61641	−	4.53176i	−0.103829	−	0.179837i
$636$		0			0
$637$	−0.112389	+	0.194664i	−0.00445302	+	0.00771286i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−11.2320	+	19.4544i	−0.443638	+	0.768404i	−0.997956	−	0.0639012i	$-0.979646\pi$
$641$	−11.2320	+	19.4544i	−0.443638	+	0.768404i	0.554318	+	0.832305i	$0.312979\pi$
$642$		0			0
$643$	1.90280	+	3.29574i	0.0750390	+	0.129971i	0.901103	−	0.433605i	$-0.142759\pi$
$643$	1.90280	+	3.29574i	0.0750390	+	0.129971i	−0.826064	+	0.563576i	$0.809425\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−19.6269			−0.771613			−0.385807	−	0.922580i	$-0.626077\pi$
$647$	−19.6269			−0.771613			−0.385807	+	0.922580i	$0.626077\pi$
$648$		0			0
$649$	1.91275			0.0750821
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−19.6688	−	34.0673i	−0.769699	−	1.33316i	−0.937726	−	0.347375i	$-0.887073\pi$
$653$	−19.6688	−	34.0673i	−0.769699	−	1.33316i	0.168028	−	0.985782i	$-0.446260\pi$
$654$		0			0
$655$	−1.41996	+	2.45944i	−0.0554824	+	0.0960984i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−11.1774	+	19.3598i	−0.435408	+	0.754149i	−0.997329	−	0.0730422i	$-0.976729\pi$
$659$	−11.1774	+	19.3598i	−0.435408	+	0.754149i	0.561921	+	0.827191i	$0.310063\pi$
$660$		0			0
$661$	−16.2314	−	28.1137i	−0.631330	−	1.09350i	−0.987280	−	0.158990i	$-0.949176\pi$
$661$	−16.2314	−	28.1137i	−0.631330	−	1.09350i	0.355951	−	0.934505i	$-0.384157\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−7.00821			−0.271767
$666$		0			0
$667$	41.9236			1.62329
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.891588	+	1.54427i	0.0344194	+	0.0596161i
$672$		0			0
$673$	−11.0255	+	19.0967i	−0.425000	+	0.736122i	−0.996420	−	0.0845357i	$-0.973059\pi$
$673$	−11.0255	+	19.0967i	−0.425000	+	0.736122i	0.571420	+	0.820658i	$0.306393\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.5730	+	28.7053i	−0.636952	+	1.10323i	0.349146	+	0.937068i	$0.386472\pi$
$677$	−16.5730	+	28.7053i	−0.636952	+	1.10323i	−0.986098	+	0.166165i	$0.946862\pi$
$678$		0			0
$679$	−11.0504	−	19.1399i	−0.424077	−	0.734522i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−15.7757			−0.603642			−0.301821	−	0.953365i	$-0.597595\pi$
$683$	−15.7757			−0.603642			−0.301821	+	0.953365i	$0.597595\pi$
$684$		0			0
$685$	−8.62882			−0.329690
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.332758	−	0.576353i	−0.0126771	−	0.0219573i
$690$		0			0
$691$	21.2715	−	36.8433i	0.809206	−	1.40159i	−0.104208	−	0.994555i	$-0.533231\pi$
$691$	21.2715	−	36.8433i	0.809206	−	1.40159i	0.913415	−	0.407031i	$-0.133436\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.45598	+	7.71798i	−0.169025	+	0.292759i
$696$		0			0
$697$	30.9117	+	53.5407i	1.17086	+	2.02800i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−3.93434			−0.148598			−0.0742990	−	0.997236i	$-0.523672\pi$
$701$	−3.93434			−0.148598			−0.0742990	+	0.997236i	$0.523672\pi$
$702$		0			0
$703$	−23.8275			−0.898672
$704$		0			0
$705$		0			0
$706$		0			0
$707$	16.9702	+	29.3933i	0.638230	+	1.10545i
$708$		0			0
$709$	16.6640	−	28.8630i	0.625831	−	1.08397i	−0.362549	−	0.931965i	$-0.618093\pi$
$709$	16.6640	−	28.8630i	0.625831	−	1.08397i	0.988380	−	0.152006i	$-0.0485734\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−12.7148	+	22.0226i	−0.476172	+	0.824753i
$714$		0			0
$715$	0.0235610	+	0.0408088i	0.000881131	+	0.00152616i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	32.6745			1.21855			0.609277	−	0.792957i	$-0.291460\pi$
$719$	32.6745			1.21855			0.609277	+	0.792957i	$0.291460\pi$
$720$		0			0
$721$	−10.4773			−0.390194
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−23.9066	−	41.4074i	−0.887868	−	1.53783i
$726$		0			0
$727$	−13.4684	+	23.3279i	−0.499514	+	0.865183i	−1.00000		0.000561643i	$-0.999821\pi$
$727$	−13.4684	+	23.3279i	−0.499514	+	0.865183i	0.500486	+	0.865744i	$0.333155\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−21.9521	+	38.0221i	−0.811927	+	1.40630i
$732$		0			0
$733$	18.8851	+	32.7100i	0.697538	+	1.20817i	0.969317	+	0.245812i	$0.0790546\pi$
$733$	18.8851	+	32.7100i	0.697538	+	1.20817i	−0.271779	+	0.962360i	$0.587612\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.96197			−0.182777
$738$		0			0
$739$	−2.90122			−0.106723			−0.0533615	−	0.998575i	$-0.516994\pi$
$739$	−2.90122			−0.106723			−0.0533615	+	0.998575i	$0.516994\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−3.91007	−	6.77243i	−0.143446	−	0.248456i	0.785346	−	0.619057i	$-0.212485\pi$
$743$	−3.91007	−	6.77243i	−0.143446	−	0.248456i	−0.928792	+	0.370601i	$0.879152\pi$
$744$		0			0
$745$	1.23193	−	2.13377i	0.0451345	−	0.0781753i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−7.49383	+	12.9797i	−0.273819	+	0.474268i
$750$		0			0
$751$	−19.9881	−	34.6204i	−0.729377	−	1.26332i	−0.957147	−	0.289603i	$-0.906477\pi$
$751$	−19.9881	−	34.6204i	−0.729377	−	1.26332i	0.227770	−	0.973715i	$-0.426857\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−2.69384			−0.0980389
$756$		0			0
$757$	29.6529			1.07775			0.538877	−	0.842384i	$-0.318849\pi$
$757$	29.6529			1.07775			0.538877	+	0.842384i	$0.318849\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.883575	+	1.53040i	0.0320296	+	0.0554768i	0.881596	−	0.472005i	$-0.156470\pi$
$761$	0.883575	+	1.53040i	0.0320296	+	0.0554768i	−0.849566	+	0.527482i	$0.823136\pi$
$762$		0			0
$763$	10.0531	−	17.4125i	0.363947	−	0.630375i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.455300	−	0.788602i	0.0164399	−	0.0284748i
$768$		0			0
$769$	23.8606	+	41.3277i	0.860434	+	1.49031i	0.871511	+	0.490376i	$0.163141\pi$
$769$	23.8606	+	41.3277i	0.860434	+	1.49031i	−0.0110770	+	0.999939i	$0.503526\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	29.4741			1.06011			0.530054	−	0.847964i	$-0.322172\pi$
$773$	29.4741			1.06011			0.530054	+	0.847964i	$0.322172\pi$
$774$		0			0
$775$	29.0019			1.04178
$776$		0			0
$777$		0			0
$778$		0			0
$779$	17.4224	+	30.1764i	0.624221	+	1.08118i
$780$		0			0
$781$	1.67137	−	2.89490i	0.0598064	−	0.103588i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−4.03128	+	6.98238i	−0.143883	+	0.249212i
$786$		0			0
$787$	9.28601	+	16.0838i	0.331010	+	0.573327i	0.982710	−	0.185150i	$-0.0592771\pi$
$787$	9.28601	+	16.0838i	0.331010	+	0.573327i	−0.651700	+	0.758477i	$0.725944\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	2.77152			0.0985439
$792$		0			0
$793$	0.848912			0.0301458
$794$		0			0
$795$		0			0
$796$		0			0
$797$	10.0551	+	17.4160i	0.356172	+	0.616907i	0.987318	−	0.158757i	$-0.0507485\pi$
$797$	10.0551	+	17.4160i	0.356172	+	0.616907i	−0.631146	+	0.775664i	$0.717415\pi$
$798$		0			0
$799$	−41.2660	+	71.4748i	−1.45989	+	2.52860i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.803978	+	1.39253i	−0.0283718	+	0.0491414i
$804$		0			0
$805$	3.45586	+	5.98572i	0.121803	+	0.210969i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−36.1888			−1.27233			−0.636165	−	0.771553i	$-0.719480\pi$
$809$	−36.1888			−1.27233			−0.636165	+	0.771553i	$0.719480\pi$
$810$		0			0
$811$	−10.3479			−0.363364			−0.181682	−	0.983357i	$-0.558154\pi$
$811$	−10.3479			−0.363364			−0.181682	+	0.983357i	$0.558154\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5.92195	−	10.2571i	−0.207437	−	0.359291i
$816$		0			0
$817$	−12.3726	+	21.4299i	−0.432861	+	0.749738i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.935060	+	1.61957i	−0.0326338	+	0.0565234i	−0.881881	−	0.471472i	$-0.843723\pi$
$821$	−0.935060	+	1.61957i	−0.0326338	+	0.0565234i	0.849247	+	0.527995i	$0.177056\pi$
$822$		0			0
$823$	11.2665	+	19.5141i	0.392725	+	0.680219i	0.992808	−	0.119718i	$-0.0381991\pi$
$823$	11.2665	+	19.5141i	0.392725	+	0.680219i	−0.600083	+	0.799938i	$0.704866\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	24.3227			0.845784			0.422892	−	0.906180i	$-0.361015\pi$
$827$	24.3227			0.845784			0.422892	+	0.906180i	$0.361015\pi$
$828$		0			0
$829$	29.9201			1.03917			0.519584	−	0.854420i	$-0.326087\pi$
$829$	29.9201			1.03917			0.519584	+	0.854420i	$0.326087\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	4.23922	+	7.34255i	0.146880	+	0.254404i
$834$		0			0
$835$	−3.31573	+	5.74301i	−0.114746	+	0.198745i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	12.1053	−	20.9670i	0.417921	−	0.723861i	−0.577809	−	0.816172i	$-0.696092\pi$
$839$	12.1053	−	20.9670i	0.417921	−	0.723861i	0.995730	+	0.0923111i	$0.0294254\pi$
$840$		0			0
$841$	−38.4260	−	66.5558i	−1.32503	−	2.29503i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−7.69844			−0.264834
$846$		0			0
$847$	−30.9397			−1.06310
$848$		0			0
$849$		0			0
$850$		0			0
$851$	11.7497	+	20.3511i	0.402775	+	0.697627i
$852$		0			0
$853$	9.88865	−	17.1277i	0.338581	−	0.586440i	−0.645585	−	0.763688i	$-0.723386\pi$
$853$	9.88865	−	17.1277i	0.338581	−	0.586440i	0.984166	+	0.177249i	$0.0567197\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−8.34675	+	14.4570i	−0.285119	+	0.493841i	−0.972638	−	0.232325i	$-0.925367\pi$
$857$	−8.34675	+	14.4570i	−0.285119	+	0.493841i	0.687519	+	0.726167i	$0.258700\pi$
$858$		0			0
$859$	−2.88183	−	4.99148i	−0.0983268	−	0.170307i	0.812665	−	0.582731i	$-0.198016\pi$
$859$	−2.88183	−	4.99148i	−0.0983268	−	0.170307i	−0.910992	+	0.412424i	$0.864682\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	56.2504			1.91478			0.957392	−	0.288791i	$-0.0932531\pi$
$863$	56.2504			1.91478			0.957392	+	0.288791i	$0.0932531\pi$
$864$		0			0
$865$	−12.8156			−0.435744
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.84174	+	3.18999i	0.0624768	+	0.108213i
$870$		0			0
$871$	−1.18112	+	2.04576i	−0.0400207	+	0.0693178i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	8.18184	−	14.1714i	0.276597	−	0.479079i
$876$		0			0
$877$	7.32359	+	12.6848i	0.247300	+	0.428336i	0.962776	−	0.270301i	$-0.0871234\pi$
$877$	7.32359	+	12.6848i	0.247300	+	0.428336i	−0.715476	+	0.698637i	$0.753790\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.564576			0.0190211			0.00951053	−	0.999955i	$-0.496973\pi$
$881$	0.564576			0.0190211			0.00951053	+	0.999955i	$0.496973\pi$
$882$		0			0
$883$	−21.5529			−0.725312			−0.362656	−	0.931923i	$-0.618130\pi$
$883$	−21.5529			−0.725312			−0.362656	+	0.931923i	$0.618130\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−24.7932	−	42.9431i	−0.832474	−	1.44189i	−0.896071	−	0.443911i	$-0.853591\pi$
$887$	−24.7932	−	42.9431i	−0.832474	−	1.44189i	0.0635974	−	0.997976i	$-0.479743\pi$
$888$		0			0
$889$	−12.5816	+	21.7920i	−0.421975	+	0.730881i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−23.2582	+	40.2844i	−0.778307	+	1.34807i
$894$		0			0
$895$	−4.55565	−	7.89062i	−0.152279	−	0.263754i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	64.2065			2.14141
$900$		0			0
$901$	−25.1026			−0.836290
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.19701	−	3.80533i	−0.0730310	−	0.126493i
$906$		0			0
$907$	−10.7173	+	18.5629i	−0.355861	+	0.616370i	−0.987265	−	0.159084i	$-0.949146\pi$
$907$	−10.7173	+	18.5629i	−0.355861	+	0.616370i	0.631404	+	0.775454i	$0.282479\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.71527	+	2.97094i	−0.0568295	+	0.0984316i	−0.893041	−	0.449976i	$-0.851432\pi$
$911$	−1.71527	+	2.97094i	−0.0568295	+	0.0984316i	0.836211	+	0.548408i	$0.184766\pi$
$912$		0			0
$913$	−1.72032	−	2.97969i	−0.0569344	−	0.0986132i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	13.6564			0.450975
$918$		0			0
$919$	−23.1771			−0.764542			−0.382271	−	0.924050i	$-0.624858\pi$
$919$	−23.1771			−0.764542			−0.382271	+	0.924050i	$0.624858\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.795686	−	1.37817i	−0.0261903	−	0.0453630i
$924$		0			0
$925$	13.4003	−	23.2101i	0.440601	−	0.763143i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	28.9721	−	50.1812i	0.950545	−	1.64639i	0.206295	−	0.978490i	$-0.433859\pi$
$929$	28.9721	−	50.1812i	0.950545	−	1.64639i	0.744250	−	0.667902i	$-0.232807\pi$
$930$		0			0
$931$	2.38930	+	4.13838i	0.0783061	+	0.135630i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.77740			0.0581272
$936$		0			0
$937$	26.7087			0.872534			0.436267	−	0.899817i	$-0.356300\pi$
$937$	26.7087			0.872534			0.436267	+	0.899817i	$0.356300\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−6.73633	−	11.6677i	−0.219598	−	0.380355i	0.735087	−	0.677973i	$-0.237141\pi$
$941$	−6.73633	−	11.6677i	−0.219598	−	0.380355i	−0.954685	+	0.297618i	$0.903808\pi$
$942$		0			0
$943$	17.1825	−	29.7609i	0.559539	−	0.969149i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.97908	−	3.42787i	0.0643115	−	0.111391i	−0.832077	−	0.554660i	$-0.812848\pi$
$947$	1.97908	−	3.42787i	0.0643115	−	0.111391i	0.896388	+	0.443270i	$0.146182\pi$
$948$		0			0
$949$	0.382748	+	0.662939i	0.0124245	+	0.0215199i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−11.0480			−0.357880			−0.178940	−	0.983860i	$-0.557267\pi$
$953$	−11.0480			−0.357880			−0.178940	+	0.983860i	$0.557267\pi$
$954$		0			0
$955$	7.34895			0.237806
$956$		0			0
$957$		0			0
$958$		0			0
$959$	20.7468	+	35.9346i	0.669950	+	1.16039i
$960$		0			0
$961$	−3.97280	+	6.88109i	−0.128155	+	0.221971i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−4.63018	+	8.01971i	−0.149051	+	0.258164i
$966$		0			0
$967$	10.8261	+	18.7514i	0.348145	+	0.603005i	0.985920	−	0.167218i	$-0.0534782\pi$
$967$	10.8261	+	18.7514i	0.348145	+	0.603005i	−0.637775	+	0.770223i	$0.720145\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	2.69387			0.0864503			0.0432252	−	0.999065i	$-0.486237\pi$
$971$	2.69387			0.0864503			0.0432252	+	0.999065i	$0.486237\pi$
$972$		0			0
$973$	42.8552			1.37387
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−20.5821	−	35.6492i	−0.658479	−	1.14052i	−0.981009	−	0.193960i	$-0.937867\pi$
$977$	−20.5821	−	35.6492i	−0.658479	−	1.14052i	0.322530	−	0.946559i	$-0.395467\pi$
$978$		0			0
$979$	0.973521	−	1.68619i	0.0311139	−	0.0538908i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	7.68409	−	13.3092i	0.245085	−	0.424499i	−0.717071	−	0.697000i	$-0.754518\pi$
$983$	7.68409	−	13.3092i	0.245085	−	0.424499i	0.962155	+	0.272501i	$0.0878509\pi$
$984$		0			0
$985$	5.10735	+	8.84619i	0.162734	+	0.281863i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	24.4044			0.776015
$990$		0			0
$991$	−11.5465			−0.366787			−0.183394	−	0.983040i	$-0.558708\pi$
$991$	−11.5465			−0.366787			−0.183394	+	0.983040i	$0.558708\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	5.27920	+	9.14385i	0.167362	+	0.289880i
$996$		0			0
$997$	2.18815	−	3.78999i	0.0692994	−	0.120030i	−0.829294	−	0.558813i	$-0.811257\pi$
$997$	2.18815	−	3.78999i	0.0692994	−	0.120030i	0.898593	+	0.438783i	$0.144590\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2916.2.e.d.1945.4		18
3.2	odd	2		2916.2.e.c.1945.6		18
9.2	odd	6		2916.2.a.d.1.4		9
9.4	even	3	inner	2916.2.e.d.973.4		18
9.5	odd	6		2916.2.e.c.973.6		18
9.7	even	3		2916.2.a.c.1.6		9
27.2	odd	18		972.2.i.c.109.2		18
27.4	even	9		324.2.i.a.181.2		18
27.5	odd	18		972.2.i.c.865.2		18
27.7	even	9		972.2.i.d.757.2		18
27.11	odd	18		108.2.i.a.85.2	yes	18
27.13	even	9		972.2.i.d.217.2		18
27.14	odd	18		972.2.i.a.217.2		18
27.16	even	9		324.2.i.a.145.2		18
27.20	odd	18		972.2.i.a.757.2		18
27.22	even	9		972.2.i.b.865.2		18
27.23	odd	18		108.2.i.a.61.2	✓	18
27.25	even	9		972.2.i.b.109.2		18
108.11	even	18		432.2.u.d.193.2		18
108.23	even	18		432.2.u.d.385.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.i.a.61.2	✓	18	27.23	odd	18
108.2.i.a.85.2	yes	18	27.11	odd	18
324.2.i.a.145.2		18	27.16	even	9
324.2.i.a.181.2		18	27.4	even	9
432.2.u.d.193.2		18	108.11	even	18
432.2.u.d.385.2		18	108.23	even	18
972.2.i.a.217.2		18	27.14	odd	18
972.2.i.a.757.2		18	27.20	odd	18
972.2.i.b.109.2		18	27.25	even	9
972.2.i.b.865.2		18	27.22	even	9
972.2.i.c.109.2		18	27.2	odd	18
972.2.i.c.865.2		18	27.5	odd	18
972.2.i.d.217.2		18	27.13	even	9
972.2.i.d.757.2		18	27.7	even	9
2916.2.a.c.1.6		9	9.7	even	3
2916.2.a.d.1.4		9	9.2	odd	6
2916.2.e.c.973.6		18	9.5	odd	6
2916.2.e.c.1945.6		18	3.2	odd	2
2916.2.e.d.973.4		18	9.4	even	3	inner
2916.2.e.d.1945.4		18	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2916 = 2^{2} \cdot 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2916.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.296957 - 0.514344i) q^{5} +(-1.42798 + 2.47334i) q^{7} +O(q^{10})\)	\(q+(-0.296957 - 0.514344i) q^{5} +(-1.42798 + 2.47334i) q^{7} +(0.204120 - 0.353547i) q^{11} +(-0.0971750 - 0.168312i) q^{13} -7.33071 q^{17} -4.13172 q^{19} +(2.03741 + 3.52890i) q^{23} +(2.32363 - 4.02465i) q^{25} +(5.14422 - 8.91005i) q^{29} +(3.12032 + 5.40455i) q^{31} +1.69620 q^{35} +5.76698 q^{37} +(-4.21674 - 7.30361i) q^{41} +(2.99454 - 5.18669i) q^{43} +(5.62919 - 9.75005i) q^{47} +(-0.578282 - 1.00161i) q^{49} +3.42431 q^{53} -0.242459 q^{55} +(2.34268 + 4.05764i) q^{59} +(-2.18398 + 3.78276i) q^{61} +(-0.0577135 + 0.0999628i) q^{65} +(-6.07727 - 10.5261i) q^{67} +8.18817 q^{71} -3.93875 q^{73} +(0.582961 + 1.00972i) q^{77} +(-4.51141 + 7.81400i) q^{79} +(4.21400 - 7.29885i) q^{83} +(2.17690 + 3.77051i) q^{85} +4.76935 q^{89} +0.555058 q^{91} +(1.22694 + 2.12512i) q^{95} +(-3.86924 + 6.70172i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{5}+O(q^{10}) \) 18 * q + 6 * q^5	\( 18 q + 6 q^{5} + 6 q^{11} - 24 q^{17} + 3 q^{23} - 9 q^{25} + 24 q^{29} - 42 q^{35} + 33 q^{41} + 9 q^{47} - 9 q^{49} - 66 q^{53} + 30 q^{59} + 9 q^{61} + 39 q^{65} + 9 q^{67} - 24 q^{71} - 18 q^{73} + 39 q^{77} + 36 q^{83} - 96 q^{89} - 18 q^{91} + 12 q^{95}+O(q^{100}) \) 18 * q + 6 * q^5 + 6 * q^11 - 24 * q^17 + 3 * q^23 - 9 * q^25 + 24 * q^29 - 42 * q^35 + 33 * q^41 + 9 * q^47 - 9 * q^49 - 66 * q^53 + 30 * q^59 + 9 * q^61 + 39 * q^65 + 9 * q^67 - 24 * q^71 - 18 * q^73 + 39 * q^77 + 36 * q^83 - 96 * q^89 - 18 * q^91 + 12 * q^95

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