LMFDB - Embedded newform 2916.2.e.c.973.6

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			973.6
Root			$0.960398 - 1.44140i$ of defining polynomial
Character	$\chi$	$=$	2916.973
Dual form			2916.2.e.c.1945.6

$q$-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 $\left(\mathbb{Z}/2916\mathbb{Z}\right)^\times$.

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

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	$-0.790936\pi$
$5$	0.296957	−	0.514344i	0.132803	−	0.230022i	0.924756	+	0.380560i	$0.124269\pi$
$6$		0			0
$7$	−1.42798	−	2.47334i	−0.539728	−	0.934836i	−0.998918	−	0.0464979i	$-0.985194\pi$
$7$	−1.42798	−	2.47334i	−0.539728	−	0.934836i	0.459191	−	0.888338i	$-0.348139\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.204120	−	0.353547i	−0.0615445	−	0.106598i	0.833611	−	0.552351i	$-0.186269\pi$
$11$	−0.204120	−	0.353547i	−0.0615445	−	0.106598i	−0.895156	+	0.445753i	$0.852936\pi$
$12$		0			0
$13$	−0.0971750	+	0.168312i	−0.0269515	+	0.0466814i	−0.879187	−	0.476478i	$-0.841913\pi$
$13$	−0.0971750	+	0.168312i	−0.0269515	+	0.0466814i	0.852235	+	0.523159i	$0.175247\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	7.33071			1.77796			0.888980	−	0.457947i	$-0.151415\pi$
$17$	7.33071			1.77796			0.888980	+	0.457947i	$0.151415\pi$
$18$		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	$-0.972999\pi$
$23$	−2.03741	+	3.52890i	−0.424830	+	0.735827i	0.571575	+	0.820550i	$0.306333\pi$
$24$		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	−0.733777	−	0.679390i	$-0.762244\pi$
$29$	−5.14422	−	8.91005i	−0.955258	−	1.65455i	−0.221480	−	0.975165i	$-0.571089\pi$
$30$		0			0
$31$	3.12032	−	5.40455i	0.560426	−	0.970686i	−0.437033	−	0.899445i	$-0.643971\pi$
$31$	3.12032	−	5.40455i	0.560426	−	0.970686i	0.997459	−	0.0712410i	$-0.0226960\pi$
$32$		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	−0.322448	−	0.946587i	$-0.604506\pi$
$41$	4.21674	−	7.30361i	0.658544	−	1.14063i	0.980993	−	0.194045i	$-0.0621608\pi$
$42$		0			0
$43$	2.99454	+	5.18669i	0.456662	+	0.790962i	0.998782	−	0.0493389i	$-0.0157114\pi$
$43$	2.99454	+	5.18669i	0.456662	+	0.790962i	−0.542120	+	0.840301i	$0.682378\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.62919	−	9.75005i	−0.821102	−	1.42219i	−0.904862	−	0.425705i	$-0.860026\pi$
$47$	−5.62919	−	9.75005i	−0.821102	−	1.42219i	0.0837596	−	0.996486i	$-0.473307\pi$
$48$		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	$-0.575569\pi$
$53$	−3.42431			−0.470365			−0.235183	+	0.971951i	$0.575569\pi$
$54$		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	$-0.931987\pi$
$59$	−2.34268	+	4.05764i	−0.304991	+	0.528259i	0.672269	+	0.740307i	$0.265320\pi$
$60$		0			0
$61$	−2.18398	−	3.78276i	−0.279630	−	0.484333i	0.691663	−	0.722220i	$-0.256878\pi$
$61$	−2.18398	−	3.78276i	−0.279630	−	0.484333i	−0.971293	+	0.237888i	$0.923545\pi$
$62$		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	0.208917	+	0.977933i	$0.433006\pi$
$67$	−6.07727	+	10.5261i	−0.742457	+	1.28597i	−0.951374	+	0.308039i	$0.900327\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.18817			−0.971757			−0.485879	−	0.874026i	$-0.661500\pi$
$71$	−8.18817			−0.971757			−0.485879	+	0.874026i	$0.661500\pi$
$72$		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	−0.999962	−	0.00876750i	$-0.997209\pi$
$79$	−4.51141	−	7.81400i	−0.507574	−	0.879143i	0.492388	−	0.870376i	$-0.336124\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.21400	−	7.29885i	−0.462546	−	0.801153i	0.536541	−	0.843874i	$-0.319731\pi$
$83$	−4.21400	−	7.29885i	−0.462546	−	0.801153i	−0.999087	+	0.0427209i	$0.986397\pi$
$84$		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	$-0.581343\pi$
$89$	−4.76935			−0.505550			−0.252775	+	0.967525i	$0.581343\pi$
$90$		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	0.599964	−	0.800027i	$-0.295182\pi$
$97$	−3.86924	−	6.70172i	−0.392862	−	0.680456i	−0.992826	+	0.119571i	$0.961848\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.94201	−	10.2919i	−0.591252	−	1.02408i	−0.994064	−	0.108796i	$-0.965300\pi$
$101$	−5.94201	−	10.2919i	−0.591252	−	1.02408i	0.402812	−	0.915283i	$-0.368033\pi$
$102$		0			0
$103$	1.83427	−	3.17706i	0.180736	−	0.313045i	−0.761395	−	0.648288i	$-0.775485\pi$
$103$	1.83427	−	3.17706i	0.180736	−	0.313045i	0.942132	+	0.335243i	$0.108819\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.24784			−0.507328			−0.253664	−	0.967292i	$-0.581636\pi$
$107$	−5.24784			−0.507328			−0.253664	+	0.967292i	$0.581636\pi$
$108$		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	$-0.818799\pi$
$113$	0.485215	−	0.840417i	0.0456452	−	0.0790598i	0.887945	+	0.459949i	$0.152132\pi$
$114$		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	$-0.766348\pi$
$131$	2.39085	−	4.14108i	0.208890	−	0.361808i	0.951365	+	0.308066i	$0.0996816\pi$
$132$		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	−0.989367	−	0.145439i	$-0.953541\pi$
$137$	−7.26437	−	12.5823i	−0.620637	−	1.07498i	0.368730	−	0.929537i	$-0.379793\pi$
$138$		0			0
$139$	−7.50274	+	12.9951i	−0.636374	+	1.10223i	0.349848	+	0.936806i	$0.386233\pi$
$139$	−7.50274	+	12.9951i	−0.636374	+	1.10223i	−0.986222	+	0.165426i	$0.947100\pi$
$140$		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	$-0.887688\pi$
$149$	−2.07426	+	3.59273i	−0.169930	+	0.294328i	0.768465	+	0.639892i	$0.221021\pi$
$150$		0			0
$151$	2.26787	+	3.92807i	0.184557	+	0.319662i	0.943427	−	0.331580i	$-0.107582\pi$
$151$	2.26787	+	3.92807i	0.184557	+	0.319662i	−0.758870	+	0.651242i	$0.774248\pi$
$152$		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	0.457092	+	0.889420i	$0.348891\pi$
$157$	−6.78766	+	11.7566i	−0.541714	+	0.938276i	−0.998806	+	0.0488567i	$0.984442\pi$
$158$		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	$-0.691136\pi$
$167$	5.58285	−	9.66978i	0.432014	−	0.748270i	0.997047	+	0.0767984i	$0.0244698\pi$
$168$		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	−0.905472	−	0.424406i	$-0.860483\pi$
$173$	−10.7891	−	18.6873i	−0.820282	−	1.42077i	0.0851896	−	0.996365i	$-0.472850\pi$
$174$		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	$-0.694347\pi$
$179$	−15.3411			−1.14665			−0.573325	+	0.819328i	$0.694347\pi$
$180$		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	$-0.0189215\pi$
$191$	6.18689	+	10.7160i	0.447667	+	0.775383i	−0.550566	+	0.834791i	$0.685588\pi$
$192$		0			0
$193$	−7.79606	+	13.5032i	−0.561173	+	0.971980i	0.436222	+	0.899839i	$0.356316\pi$
$193$	−7.79606	+	13.5032i	−0.561173	+	0.971980i	−0.997394	+	0.0721405i	$0.977017\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	17.1990			1.22538			0.612688	−	0.790325i	$-0.290088\pi$
$197$	17.1990			1.22538			0.612688	+	0.790325i	$0.290088\pi$
$198$		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	−0.333240	−	0.942842i	$-0.608142\pi$
$211$	9.44042	−	16.3513i	0.649905	−	1.12567i	0.983145	−	0.182827i	$-0.0585247\pi$
$212$		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	0.889939	−	0.456079i	$-0.150747\pi$
$223$	0.746560	+	1.29308i	0.0499933	+	0.0865910i	−0.839946	+	0.542670i	$0.817413\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.75075	−	16.8888i	−0.647180	−	1.12095i	−0.983793	−	0.179306i	$-0.942615\pi$
$227$	−9.75075	−	16.8888i	−0.647180	−	1.12095i	0.336613	−	0.941643i	$-0.390719\pi$
$228$		0			0
$229$	0.0158446	−	0.0274437i	0.00104704	−	0.00181353i	−0.865501	−	0.500906i	$-0.833000\pi$
$229$	0.0158446	−	0.0274437i	0.00104704	−	0.00181353i	0.866548	+	0.499093i	$0.166333\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	13.4318			0.879949			0.439975	−	0.898010i	$-0.354987\pi$
$233$	13.4318			0.879949			0.439975	+	0.898010i	$0.354987\pi$
$234$		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	−0.498755	−	0.866743i	$-0.666209\pi$
$239$	7.74905	−	13.4217i	0.501244	−	0.868181i	0.999999	−	0.00143735i	$-0.000457522\pi$
$240$		0			0
$241$	−11.7474	−	20.3471i	−0.756717	−	1.31067i	−0.944516	−	0.328465i	$-0.893469\pi$
$241$	−11.7474	−	20.3471i	−0.756717	−	1.31067i	0.187799	−	0.982208i	$-0.439865\pi$
$242$		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	$-0.391803\pi$
$251$	10.5642			0.666805			0.333403	+	0.942785i	$0.391803\pi$
$252$		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	$-0.710820\pi$
$257$	6.01899	−	10.4252i	0.375454	−	0.650306i	0.990395	+	0.138268i	$0.0441534\pi$
$258$		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	$-0.201617\pi$
$263$	−1.77710	−	3.07802i	−0.109580	−	0.189799i	−0.915600	+	0.402090i	$0.868284\pi$
$264$		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	$-0.210948\pi$
$269$	25.8590			1.57665			0.788327	+	0.615257i	$0.210948\pi$
$270$		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	0.984457	−	0.175628i	$-0.0561957\pi$
$277$	5.66088	+	9.80494i	0.340130	+	0.589122i	−0.644327	+	0.764750i	$0.722862\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	10.3420	+	17.9128i	0.616951	+	1.06859i	0.990039	+	0.140794i	$0.0449656\pi$
$281$	10.3420	+	17.9128i	0.616951	+	1.06859i	−0.373088	+	0.927796i	$0.621701\pi$
$282$		0			0
$283$	0.770226	−	1.33407i	0.0457852	−	0.0793023i	−0.842225	−	0.539127i	$-0.818754\pi$
$283$	0.770226	−	1.33407i	0.0457852	−	0.0793023i	0.888010	+	0.459825i	$0.152088\pi$
$284$		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	$-0.883877\pi$
$293$	−2.70662	+	4.68800i	−0.158122	+	0.273876i	0.776069	+	0.630648i	$0.217211\pi$
$294$		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	$-0.721499\pi$
$311$	6.06925	−	10.5123i	0.344156	−	0.596095i	0.985200	+	0.171409i	$0.0548318\pi$
$312$		0			0
$313$	−0.519495	−	0.899791i	−0.0293636	−	0.0508592i	0.850970	−	0.525214i	$-0.176015\pi$
$313$	−0.519495	−	0.899791i	−0.0293636	−	0.0508592i	−0.880334	+	0.474355i	$0.842681\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.68112	−	15.0361i	−0.487580	−	0.844514i	0.512318	−	0.858796i	$-0.328787\pi$
$317$	−8.68112	−	15.0361i	−0.487580	−	0.844514i	−0.999898	+	0.0142823i	$0.995454\pi$
$318$		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	0.832167	−	0.554525i	$-0.187100\pi$
$331$	−1.16710	−	2.02148i	−0.0641496	−	0.111110i	−0.896316	+	0.443415i	$0.853767\pi$
$332$		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	−0.788393	−	0.615173i	$-0.789086\pi$
$337$	2.54360	−	4.40565i	0.138559	−	0.239991i	0.926951	+	0.375182i	$0.122420\pi$
$338$		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	$-0.785011\pi$
$347$	2.81702	−	4.87922i	0.151225	−	0.261930i	0.931678	+	0.363285i	$0.118345\pi$
$348$		0			0
$349$	5.93484	+	10.2795i	0.317685	+	0.550246i	0.980005	−	0.198975i	$-0.0637612\pi$
$349$	5.93484	+	10.2795i	0.317685	+	0.550246i	−0.662320	+	0.749221i	$0.730428\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2.08959	+	3.61928i	0.111218	+	0.192635i	0.916261	−	0.400581i	$-0.131192\pi$
$353$	2.08959	+	3.61928i	0.111218	+	0.192635i	−0.805044	+	0.593215i	$0.797858\pi$
$354$		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	$-0.758419\pi$
$359$	−27.4948			−1.45112			−0.725559	+	0.688160i	$0.758419\pi$
$360$		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	0.929772	+	0.368137i	$0.120004\pi$
$367$	15.0136	+	26.0042i	0.783701	+	1.35741i	−0.146070	+	0.989274i	$0.546663\pi$
$368$		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	−0.702645	−	0.711540i	$-0.747998\pi$
$373$	5.11587	−	8.86094i	0.264889	−	0.458802i	0.967535	+	0.252738i	$0.0813312\pi$
$374$		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	−0.456905	−	0.889515i	$-0.651042\pi$
$383$	10.6050	−	18.3684i	0.541890	−	0.938581i	0.998796	−	0.0490661i	$-0.0156245\pi$
$384$		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	$-0.124492\pi$
$389$	2.60555	+	4.51295i	0.132107	+	0.228816i	−0.792382	+	0.610026i	$0.791159\pi$
$390$		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	0.357070	+	0.934078i	$0.383776\pi$
$401$	−12.6238	+	21.8650i	−0.630400	+	1.09189i	−0.987470	+	0.157807i	$0.949557\pi$
$402$		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	−0.693953	−	0.720020i	$-0.744133\pi$
$409$	5.59347	−	9.68817i	0.276579	−	0.479049i	0.970532	+	0.240971i	$0.0774659\pi$
$410$		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	$-0.821502\pi$
$419$	0.760652	−	1.31749i	0.0371603	−	0.0643635i	0.884007	+	0.467473i	$0.154835\pi$
$420$		0			0
$421$	3.15729	+	5.46859i	0.153877	+	0.266523i	0.932650	−	0.360784i	$-0.117491\pi$
$421$	3.15729	+	5.46859i	0.153877	+	0.266523i	−0.778772	+	0.627306i	$0.784157\pi$
$422$		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	$-0.685143\pi$
$431$	−22.8116			−1.09880			−0.549398	+	0.835561i	$0.685143\pi$
$432$		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	0.832823	−	0.553540i	$-0.186723\pi$
$439$	−1.31933	−	2.28514i	−0.0629679	−	0.109064i	−0.895791	+	0.444476i	$0.853390\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	14.7604	+	25.5657i	0.701286	+	1.21466i	0.968015	+	0.250891i	$0.0807235\pi$
$443$	14.7604	+	25.5657i	0.701286	+	1.21466i	−0.266730	+	0.963771i	$0.585943\pi$
$444$		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	$-0.230169\pi$
$449$	31.7742			1.49952			0.749759	+	0.661711i	$0.230169\pi$
$450$		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	0.960049	−	0.279833i	$-0.0902790\pi$
$457$	5.08107	+	8.80066i	0.237682	+	0.411678i	−0.722367	+	0.691510i	$0.756946\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	10.5991	+	18.3581i	0.493648	+	0.855023i	0.999973	−	0.00731950i	$-0.00232989\pi$
$461$	10.5991	+	18.3581i	0.493648	+	0.855023i	−0.506325	+	0.862342i	$0.668997\pi$
$462$		0			0
$463$	2.42933	−	4.20772i	0.112900	−	0.195549i	−0.804038	−	0.594578i	$-0.797319\pi$
$463$	2.42933	−	4.20772i	0.112900	−	0.195549i	0.916939	+	0.399029i	$0.130653\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−29.6157			−1.37045			−0.685225	−	0.728332i	$-0.740296\pi$
$467$	−29.6157			−1.37045			−0.685225	+	0.728332i	$0.740296\pi$
$468$		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	0.987146	+	0.159821i	$0.0510917\pi$
$479$	13.8316	+	23.9570i	0.631982	+	1.09463i	−0.355164	+	0.934804i	$0.615575\pi$
$480$		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	$-0.881995\pi$
$491$	−3.37429	+	5.84444i	−0.152280	+	0.263756i	0.779786	+	0.626047i	$0.215328\pi$
$492$		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	−0.354201	−	0.935169i	$-0.615247\pi$
$499$	14.1352	−	24.4829i	0.632780	−	1.09601i	0.986981	−	0.160837i	$-0.0514195\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	29.2222			1.30295			0.651476	−	0.758669i	$-0.274150\pi$
$503$	29.2222			1.30295			0.651476	+	0.758669i	$0.274150\pi$
$504$		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	$-0.868931\pi$
$509$	−2.51782	+	4.36100i	−0.111601	+	0.193298i	0.804815	+	0.593525i	$0.202264\pi$
$510$		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	$-0.483723\pi$
$521$	2.33341			0.102229			0.0511143	+	0.998693i	$0.483723\pi$
$522$		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	0.833150	−	0.553047i	$-0.186535\pi$
$547$	−1.45889	−	2.52688i	−0.0623778	−	0.108042i	−0.895528	+	0.445006i	$0.853202\pi$
$548$		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	$-0.400699\pi$
$557$	14.4875			0.613857			0.306928	+	0.951733i	$0.400699\pi$
$558$		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	0.244946	+	0.969537i	$0.421230\pi$
$563$	−17.0168	+	29.4739i	−0.717171	+	1.24218i	−0.962116	+	0.272639i	$0.912103\pi$
$564$		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	$-0.196104\pi$
$569$	−2.20287	−	3.81548i	−0.0923490	−	0.159953i	−0.908499	+	0.417887i	$0.862771\pi$
$570$		0			0
$571$	18.2452	−	31.6016i	0.763539	−	1.32249i	−0.177477	−	0.984125i	$-0.556794\pi$
$571$	18.2452	−	31.6016i	0.763539	−	1.32249i	0.941016	−	0.338363i	$-0.109873\pi$
$572$		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	$-0.182412\pi$
$587$	−1.19798	−	2.07496i	−0.0494458	−	0.0856427i	−0.889689	+	0.456567i	$0.849079\pi$
$588$		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	$-0.460447\pi$
$593$	6.03623			0.247878			0.123939	+	0.992290i	$0.460447\pi$
$594$		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	0.448195	+	0.893936i	$0.352067\pi$
$599$	−13.4628	+	23.3182i	−0.550073	+	0.952755i	−0.998269	+	0.0588191i	$0.981266\pi$
$600$		0			0
$601$	17.1496	+	29.7040i	0.699547	+	1.21165i	0.968623	+	0.248533i	$0.0799484\pi$
$601$	17.1496	+	29.7040i	0.699547	+	1.21165i	−0.269076	+	0.963119i	$0.586718\pi$
$602$		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	−0.959497	−	0.281720i	$-0.909095\pi$
$607$	−5.80879	+	10.0611i	−0.235772	+	0.408368i	0.723725	+	0.690088i	$0.242428\pi$
$608$		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	$-0.701302\pi$
$617$	10.0102	−	17.3382i	0.402996	−	0.698009i	0.994086	+	0.108596i	$0.0346356\pi$
$618$		0			0
$619$	10.1728	+	17.6198i	0.408879	+	0.708200i	0.994764	−	0.102194i	$-0.0325864\pi$
$619$	10.1728	+	17.6198i	0.408879	+	0.708200i	−0.585885	+	0.810394i	$0.699253\pi$
$620$		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	$-0.0203542\pi$
$641$	11.2320	+	19.4544i	0.443638	+	0.768404i	−0.554318	+	0.832305i	$0.687021\pi$
$642$		0			0
$643$	1.90280	−	3.29574i	0.0750390	−	0.129971i	−0.826064	−	0.563576i	$-0.809425\pi$
$643$	1.90280	−	3.29574i	0.0750390	−	0.129971i	0.901103	+	0.433605i	$0.142759\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	19.6269			0.771613			0.385807	−	0.922580i	$-0.373923\pi$
$647$	19.6269			0.771613			0.385807	+	0.922580i	$0.373923\pi$
$648$		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	−0.168028	−	0.985782i	$-0.553740\pi$
$653$	19.6688	−	34.0673i	0.769699	−	1.33316i	0.937726	−	0.347375i	$-0.112927\pi$
$654$		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	$-0.0232708\pi$
$659$	11.1774	+	19.3598i	0.435408	+	0.754149i	−0.561921	+	0.827191i	$0.689937\pi$
$660$		0			0
$661$	−16.2314	+	28.1137i	−0.631330	+	1.09350i	0.355951	+	0.934505i	$0.384157\pi$
$661$	−16.2314	+	28.1137i	−0.631330	+	1.09350i	−0.987280	+	0.158990i	$0.949176\pi$
$662$		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	0.571420	−	0.820658i	$-0.306393\pi$
$673$	−11.0255	−	19.0967i	−0.425000	−	0.736122i	−0.996420	+	0.0845357i	$0.973059\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	16.5730	+	28.7053i	0.636952	+	1.10323i	0.986098	+	0.166165i	$0.0531385\pi$
$677$	16.5730	+	28.7053i	0.636952	+	1.10323i	−0.349146	+	0.937068i	$0.613528\pi$
$678$		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	$-0.402405\pi$
$683$	15.7757			0.603642			0.301821	+	0.953365i	$0.402405\pi$
$684$		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	0.913415	+	0.407031i	$0.133436\pi$
$691$	21.2715	+	36.8433i	0.809206	+	1.40159i	−0.104208	+	0.994555i	$0.533231\pi$
$692$		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	$-0.476328\pi$
$701$	3.93434			0.148598			0.0742990	+	0.997236i	$0.476328\pi$
$702$		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	0.988380	+	0.152006i	$0.0485734\pi$
$709$	16.6640	+	28.8630i	0.625831	+	1.08397i	−0.362549	+	0.931965i	$0.618093\pi$
$710$		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	$-0.708540\pi$
$719$	−32.6745			−1.21855			−0.609277	+	0.792957i	$0.708540\pi$
$720$		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	0.500486	−	0.865744i	$-0.333155\pi$
$727$	−13.4684	−	23.3279i	−0.499514	−	0.865183i	−1.00000		0.000561643i	$0.999821\pi$
$728$		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	−0.271779	−	0.962360i	$-0.587612\pi$
$733$	18.8851	−	32.7100i	0.697538	−	1.20817i	0.969317	−	0.245812i	$-0.0790546\pi$
$734$		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	$-0.787515\pi$
$743$	3.91007	−	6.77243i	0.143446	−	0.248456i	0.928792	+	0.370601i	$0.120848\pi$
$744$		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	0.227770	+	0.973715i	$0.426857\pi$
$751$	−19.9881	+	34.6204i	−0.729377	+	1.26332i	−0.957147	+	0.289603i	$0.906477\pi$
$752$		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	$-0.843530\pi$
$761$	−0.883575	+	1.53040i	−0.0320296	+	0.0554768i	0.849566	+	0.527482i	$0.176864\pi$
$762$		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	−0.0110770	−	0.999939i	$-0.503526\pi$
$769$	23.8606	−	41.3277i	0.860434	−	1.49031i	0.871511	−	0.490376i	$-0.163141\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−29.4741			−1.06011			−0.530054	−	0.847964i	$-0.677828\pi$
$773$	−29.4741			−1.06011			−0.530054	+	0.847964i	$0.677828\pi$
$774$		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	−0.651700	−	0.758477i	$-0.725944\pi$
$787$	9.28601	−	16.0838i	0.331010	−	0.573327i	0.982710	+	0.185150i	$0.0592771\pi$
$788$		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	$-0.949251\pi$
$797$	−10.0551	+	17.4160i	−0.356172	+	0.616907i	0.631146	+	0.775664i	$0.282585\pi$
$798$		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	$-0.280520\pi$
$809$	36.1888			1.27233			0.636165	+	0.771553i	$0.280520\pi$
$810$		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	$-0.156277\pi$
$821$	0.935060	+	1.61957i	0.0326338	+	0.0565234i	−0.849247	+	0.527995i	$0.822944\pi$
$822$		0			0
$823$	11.2665	−	19.5141i	0.392725	−	0.680219i	−0.600083	−	0.799938i	$-0.704866\pi$
$823$	11.2665	−	19.5141i	0.392725	−	0.680219i	0.992808	+	0.119718i	$0.0381991\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−24.3227			−0.845784			−0.422892	−	0.906180i	$-0.638985\pi$
$827$	−24.3227			−0.845784			−0.422892	+	0.906180i	$0.638985\pi$
$828$		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	$-0.303908\pi$
$839$	−12.1053	−	20.9670i	−0.417921	−	0.723861i	−0.995730	+	0.0923111i	$0.970575\pi$
$840$		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	0.984166	−	0.177249i	$-0.0567197\pi$
$853$	9.88865	+	17.1277i	0.338581	+	0.586440i	−0.645585	+	0.763688i	$0.723386\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	8.34675	+	14.4570i	0.285119	+	0.493841i	0.972638	−	0.232325i	$-0.0746334\pi$
$857$	8.34675	+	14.4570i	0.285119	+	0.493841i	−0.687519	+	0.726167i	$0.741300\pi$
$858$		0			0
$859$	−2.88183	+	4.99148i	−0.0983268	+	0.170307i	−0.910992	−	0.412424i	$-0.864682\pi$
$859$	−2.88183	+	4.99148i	−0.0983268	+	0.170307i	0.812665	+	0.582731i	$0.198016\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−56.2504			−1.91478			−0.957392	−	0.288791i	$-0.906747\pi$
$863$	−56.2504			−1.91478			−0.957392	+	0.288791i	$0.906747\pi$
$864$		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	−0.715476	−	0.698637i	$-0.753790\pi$
$877$	7.32359	−	12.6848i	0.247300	−	0.428336i	0.962776	+	0.270301i	$0.0871234\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.564576			−0.0190211			−0.00951053	−	0.999955i	$-0.503027\pi$
$881$	−0.564576			−0.0190211			−0.00951053	+	0.999955i	$0.503027\pi$
$882$		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	−0.0635974	−	0.997976i	$-0.520257\pi$
$887$	24.7932	−	42.9431i	0.832474	−	1.44189i	0.896071	−	0.443911i	$-0.146409\pi$
$888$		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	0.631404	−	0.775454i	$-0.282479\pi$
$907$	−10.7173	−	18.5629i	−0.355861	−	0.616370i	−0.987265	+	0.159084i	$0.949146\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.71527	+	2.97094i	0.0568295	+	0.0984316i	0.893041	−	0.449976i	$-0.148568\pi$
$911$	1.71527	+	2.97094i	0.0568295	+	0.0984316i	−0.836211	+	0.548408i	$0.815234\pi$
$912$		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	−0.744250	−	0.667902i	$-0.767193\pi$
$929$	−28.9721	−	50.1812i	−0.950545	−	1.64639i	−0.206295	−	0.978490i	$-0.566141\pi$
$930$		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	$-0.762859\pi$
$941$	6.73633	−	11.6677i	0.219598	−	0.380355i	0.954685	+	0.297618i	$0.0961921\pi$
$942$		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	$-0.187152\pi$
$947$	−1.97908	−	3.42787i	−0.0643115	−	0.111391i	−0.896388	+	0.443270i	$0.853818\pi$
$948$		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	$-0.442733\pi$
$953$	11.0480			0.357880			0.178940	+	0.983860i	$0.442733\pi$
$954$		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	−0.637775	−	0.770223i	$-0.720145\pi$
$967$	10.8261	−	18.7514i	0.348145	−	0.603005i	0.985920	+	0.167218i	$0.0534782\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−2.69387			−0.0864503			−0.0432252	−	0.999065i	$-0.513763\pi$
$971$	−2.69387			−0.0864503			−0.0432252	+	0.999065i	$0.513763\pi$
$972$		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	−0.322530	−	0.946559i	$-0.604533\pi$
$977$	20.5821	−	35.6492i	0.658479	−	1.14052i	0.981009	−	0.193960i	$-0.0621332\pi$
$978$		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	$-0.245482\pi$
$983$	−7.68409	−	13.3092i	−0.245085	−	0.424499i	−0.962155	+	0.272501i	$0.912149\pi$
$984$		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	0.898593	−	0.438783i	$-0.144590\pi$
$997$	2.18815	+	3.78999i	0.0692994	+	0.120030i	−0.829294	+	0.558813i	$0.811257\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2916.2.e.c.973.6		18
3.2	odd	2		2916.2.e.d.973.4		18
9.2	odd	6		2916.2.e.d.1945.4		18
9.4	even	3		2916.2.a.d.1.4		9
9.5	odd	6		2916.2.a.c.1.6		9
9.7	even	3	inner	2916.2.e.c.1945.6		18
27.2	odd	18		972.2.i.d.757.2		18
27.4	even	9		972.2.i.a.217.2		18
27.5	odd	18		324.2.i.a.181.2		18
27.7	even	9		108.2.i.a.85.2	yes	18
27.11	odd	18		972.2.i.b.109.2		18
27.13	even	9		972.2.i.c.865.2		18
27.14	odd	18		972.2.i.b.865.2		18
27.16	even	9		972.2.i.c.109.2		18
27.20	odd	18		324.2.i.a.145.2		18
27.22	even	9		108.2.i.a.61.2	✓	18
27.23	odd	18		972.2.i.d.217.2		18
27.25	even	9		972.2.i.a.757.2		18
108.7	odd	18		432.2.u.d.193.2		18
108.103	odd	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	27.22	even	9
108.2.i.a.85.2	yes	18	27.7	even	9
324.2.i.a.145.2		18	27.20	odd	18
324.2.i.a.181.2		18	27.5	odd	18
432.2.u.d.193.2		18	108.7	odd	18
432.2.u.d.385.2		18	108.103	odd	18
972.2.i.a.217.2		18	27.4	even	9
972.2.i.a.757.2		18	27.25	even	9
972.2.i.b.109.2		18	27.11	odd	18
972.2.i.b.865.2		18	27.14	odd	18
972.2.i.c.109.2		18	27.16	even	9
972.2.i.c.865.2		18	27.13	even	9
972.2.i.d.217.2		18	27.23	odd	18
972.2.i.d.757.2		18	27.2	odd	18
2916.2.a.c.1.6		9	9.5	odd	6
2916.2.a.d.1.4		9	9.4	even	3
2916.2.e.c.973.6		18	1.1	even	1	trivial
2916.2.e.c.1945.6		18	9.7	even	3	inner
2916.2.e.d.973.4		18	3.2	odd	2
2916.2.e.d.1945.4		18	9.2	odd	6

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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