LMFDB - Embedded newform 2268.2.i.k.2053.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(865,2268)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2268, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 4]))

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

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

chi := DirichletCharacter("2268.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.i (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:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 756)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2053.2
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	2268.2053
Dual form			2268.2.i.k.865.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.433463 - 0.750780i) q^{5} +(2.32383 + 1.26483i) q^{7} +O(q^{10})$	$q+(-0.433463 - 0.750780i) q^{5} +(2.32383 + 1.26483i) q^{7} +(-1.75729 + 3.04372i) q^{11} +(0.933463 - 1.61680i) q^{13} +(-3.25729 - 5.64180i) q^{17} +(2.69076 - 4.66053i) q^{19} +(4.32383 + 7.48910i) q^{23} +(2.12422 - 3.67926i) q^{25} +(1.75729 + 3.04372i) q^{29} -1.86693 q^{31} +(-0.0576828 - 2.29294i) q^{35} +(1.39037 - 2.40819i) q^{37} +(5.19076 - 8.99066i) q^{41} +(2.89037 + 5.00627i) q^{43} -6.16225 q^{47} +(3.80039 + 5.87852i) q^{49} +(2.80039 + 4.85041i) q^{53} +3.04689 q^{55} +5.64766 q^{59} +10.2953 q^{61} -1.61849 q^{65} -1.35234 q^{67} -2.08619 q^{71} +(-3.62422 - 6.27733i) q^{73} +(-7.93346 + 4.85041i) q^{77} +11.6768 q^{79} +(3.43346 + 5.94693i) q^{83} +(-2.82383 + 4.89102i) q^{85} +(-3.28074 + 5.68240i) q^{89} +(4.21420 - 2.57651i) q^{91} -4.66537 q^{95} +(1.64766 + 2.85384i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{5} + 2 q^{7}+O(q^{10}) $ 6 * q + q^5 + 2 * q^7	$ 6 q + q^{5} + 2 q^{7} + 5 q^{11} + 2 q^{13} - 4 q^{17} - 3 q^{19} + 14 q^{23} - 10 q^{25} - 5 q^{29} - 4 q^{31} + 26 q^{35} + 12 q^{41} + 9 q^{43} + 18 q^{47} + 12 q^{49} + 6 q^{53} + 16 q^{55} + 10 q^{59} + 14 q^{61} - 48 q^{65} - 32 q^{67} - 22 q^{71} + q^{73} - 44 q^{77} - 16 q^{79} + 17 q^{83} - 5 q^{85} - 3 q^{89} + 5 q^{91} - 64 q^{95} - 14 q^{97}+O(q^{100}) $ 6 * q + q^5 + 2 * q^7 + 5 * q^11 + 2 * q^13 - 4 * q^17 - 3 * q^19 + 14 * q^23 - 10 * q^25 - 5 * q^29 - 4 * q^31 + 26 * q^35 + 12 * q^41 + 9 * q^43 + 18 * q^47 + 12 * q^49 + 6 * q^53 + 16 * q^55 + 10 * q^59 + 14 * q^61 - 48 * q^65 - 32 * q^67 - 22 * q^71 + q^73 - 44 * q^77 - 16 * q^79 + 17 * q^83 - 5 * q^85 - 3 * q^89 + 5 * q^91 - 64 * q^95 - 14 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	−0.433463	−	0.750780i	−0.193850	−	0.335759i	0.752673	−	0.658395i	$-0.228764\pi$
$5$	−0.433463	−	0.750780i	−0.193850	−	0.335759i	−0.946523	+	0.322636i	$0.895431\pi$
$6$		0			0
$7$	2.32383	+	1.26483i	0.878326	+	0.478062i
$7$	2.32383	+	1.26483i	0.878326	+	0.478062i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.75729	+	3.04372i	−0.529844	+	0.917717i	0.469550	+	0.882906i	$0.344416\pi$
$11$	−1.75729	+	3.04372i	−0.529844	+	0.917717i	−0.999394	+	0.0348111i	$0.988917\pi$
$12$		0			0
$13$	0.933463	−	1.61680i	0.258896	−	0.448421i	−0.707050	−	0.707163i	$-0.749975\pi$
$13$	0.933463	−	1.61680i	0.258896	−	0.448421i	0.965946	+	0.258742i	$0.0833080\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.25729	−	5.64180i	−0.790010	−	1.36834i	−0.925960	−	0.377622i	$-0.876742\pi$
$17$	−3.25729	−	5.64180i	−0.790010	−	1.36834i	0.135950	−	0.990716i	$-0.456591\pi$
$18$		0			0
$19$	2.69076	−	4.66053i	0.617302	−	1.06920i	−0.372674	−	0.927962i	$-0.621559\pi$
$19$	2.69076	−	4.66053i	0.617302	−	1.06920i	0.989976	−	0.141236i	$-0.0451077\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.32383	+	7.48910i	0.901581	+	1.56158i	0.825442	+	0.564487i	$0.190926\pi$
$23$	4.32383	+	7.48910i	0.901581	+	1.56158i	0.0761395	+	0.997097i	$0.475741\pi$
$24$		0			0
$25$	2.12422	−	3.67926i	0.424844	−	0.735851i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.75729	+	3.04372i	0.326321	+	0.565205i	0.981779	−	0.190027i	$-0.0608575\pi$
$29$	1.75729	+	3.04372i	0.326321	+	0.565205i	−0.655457	+	0.755232i	$0.727524\pi$
$30$		0			0
$31$	−1.86693			−0.335310			−0.167655	−	0.985846i	$-0.553619\pi$
$31$	−1.86693			−0.335310			−0.167655	+	0.985846i	$0.553619\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.0576828	−	2.29294i	−0.00975018	−	0.387578i
$36$		0			0
$37$	1.39037	−	2.40819i	0.228575	−	0.395904i	−0.728811	−	0.684715i	$-0.759927\pi$
$37$	1.39037	−	2.40819i	0.228575	−	0.395904i	0.957386	+	0.288811i	$0.0932600\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.19076	−	8.99066i	0.810660	−	1.40410i	−0.101743	−	0.994811i	$-0.532442\pi$
$41$	5.19076	−	8.99066i	0.810660	−	1.40410i	0.912403	−	0.409294i	$-0.134225\pi$
$42$		0			0
$43$	2.89037	+	5.00627i	0.440777	+	0.763448i	0.997747	−	0.0670841i	$-0.0213696\pi$
$43$	2.89037	+	5.00627i	0.440777	+	0.763448i	−0.556970	+	0.830532i	$0.688036\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.16225			−0.898857			−0.449428	−	0.893316i	$-0.648372\pi$
$47$	−6.16225			−0.898857			−0.449428	+	0.893316i	$0.648372\pi$
$48$		0			0
$49$	3.80039	+	5.87852i	0.542913	+	0.839789i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.80039	+	4.85041i	0.384663	+	0.666256i	0.991722	−	0.128401i	$-0.0409844\pi$
$53$	2.80039	+	4.85041i	0.384663	+	0.666256i	−0.607059	+	0.794656i	$0.707651\pi$
$54$		0			0
$55$	3.04689			0.410842
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.64766			0.735263			0.367632	−	0.929972i	$-0.380169\pi$
$59$	5.64766			0.735263			0.367632	+	0.929972i	$0.380169\pi$
$60$		0			0
$61$	10.2953			1.31818			0.659091	−	0.752063i	$-0.270941\pi$
$61$	10.2953			1.31818			0.659091	+	0.752063i	$0.270941\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.61849			−0.200748
$66$		0			0
$67$	−1.35234			−0.165214			−0.0826071	−	0.996582i	$-0.526325\pi$
$67$	−1.35234			−0.165214			−0.0826071	+	0.996582i	$0.526325\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.08619			−0.247585			−0.123792	−	0.992308i	$-0.539506\pi$
$71$	−2.08619			−0.247585			−0.123792	+	0.992308i	$0.539506\pi$
$72$		0			0
$73$	−3.62422	−	6.27733i	−0.424183	−	0.734706i	0.572161	−	0.820141i	$-0.306105\pi$
$73$	−3.62422	−	6.27733i	−0.424183	−	0.734706i	−0.996344	+	0.0854351i	$0.972772\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.93346	+	4.85041i	−0.904102	+	0.552756i
$78$		0			0
$79$	11.6768			1.31375			0.656874	−	0.754001i	$-0.271878\pi$
$79$	11.6768			1.31375			0.656874	+	0.754001i	$0.271878\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.43346	+	5.94693i	0.376871	+	0.652761i	0.990605	−	0.136752i	$-0.0436665\pi$
$83$	3.43346	+	5.94693i	0.376871	+	0.652761i	−0.613734	+	0.789513i	$0.710333\pi$
$84$		0			0
$85$	−2.82383	+	4.89102i	−0.306288	+	0.530506i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.28074	+	5.68240i	−0.347758	+	0.602334i	−0.985851	−	0.167625i	$-0.946390\pi$
$89$	−3.28074	+	5.68240i	−0.347758	+	0.602334i	0.638093	+	0.769959i	$0.279723\pi$
$90$		0			0
$91$	4.21420	−	2.57651i	0.441768	−	0.270091i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.66537			−0.478657
$96$		0			0
$97$	1.64766	+	2.85384i	0.167295	+	0.289763i	0.937468	−	0.348072i	$-0.113163\pi$
$97$	1.64766	+	2.85384i	0.167295	+	0.289763i	−0.770173	+	0.637835i	$0.779830\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.948052	−	1.64207i	0.0943347	−	0.163392i	−0.814996	−	0.579467i	$-0.803261\pi$
$101$	0.948052	−	1.64207i	0.0943347	−	0.163392i	0.909331	+	0.416074i	$0.136594\pi$
$102$		0			0
$103$	3.50000	+	6.06218i	0.344865	+	0.597324i	0.985329	−	0.170664i	$-0.0545913\pi$
$103$	3.50000	+	6.06218i	0.344865	+	0.597324i	−0.640464	+	0.767988i	$0.721258\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.69076	−	16.7849i	0.936841	−	1.62266i	0.165523	−	0.986206i	$-0.447069\pi$
$107$	9.69076	−	16.7849i	0.936841	−	1.62266i	0.771318	−	0.636450i	$-0.219598\pi$
$108$		0			0
$109$	−4.51459	−	7.81950i	−0.432419	−	0.748972i	0.564662	−	0.825322i	$-0.309007\pi$
$109$	−4.51459	−	7.81950i	−0.432419	−	0.748972i	−0.997081	+	0.0763503i	$0.975673\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.233851	+	0.405042i	−0.0219989	+	0.0381031i	−0.876815	−	0.480827i	$-0.840336\pi$
$113$	−0.233851	+	0.405042i	−0.0219989	+	0.0381031i	0.854816	+	0.518931i	$0.173670\pi$
$114$		0			0
$115$	3.74844	−	6.49249i	0.349544	−	0.605428i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.433463	−	17.2305i	−0.0397355	−	1.57952i
$120$		0			0
$121$	−0.676168	−	1.17116i	−0.0614698	−	0.106469i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−8.01771			−0.717126
$126$		0			0
$127$	14.6768			1.30236			0.651180	−	0.758924i	$-0.274274\pi$
$127$	14.6768			1.30236			0.651180	+	0.758924i	$0.274274\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.12422	−	12.3395i	−0.622446	−	1.07811i	−0.989029	−	0.147723i	$-0.952806\pi$
$131$	−7.12422	−	12.3395i	−0.622446	−	1.07811i	0.366583	−	0.930385i	$-0.380528\pi$
$132$		0			0
$133$	12.1477	−	7.42692i	1.05334	−	0.643996i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.64766	−	14.9782i	0.738820	−	1.27967i	−0.214207	−	0.976788i	$-0.568717\pi$
$137$	8.64766	−	14.9782i	0.738820	−	1.27967i	0.953027	−	0.302885i	$-0.0979499\pi$
$138$		0			0
$139$	6.06654	−	10.5076i	0.514557	−	0.891239i	−0.485300	−	0.874348i	$-0.661290\pi$
$139$	6.06654	−	10.5076i	0.514557	−	0.891239i	0.999857	−	0.0168913i	$-0.00537693\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.28074	+	5.68240i	0.274349	+	0.475187i
$144$		0			0
$145$	1.52344	−	2.63868i	0.126515	−	0.219131i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.47150	−	4.28076i	−0.202473	−	0.350693i	0.746852	−	0.664991i	$-0.231564\pi$
$149$	−2.47150	−	4.28076i	−0.202473	−	0.350693i	−0.949325	+	0.314297i	$0.898231\pi$
$150$		0			0
$151$	−8.12422	+	14.0716i	−0.661140	+	1.14513i	0.319177	+	0.947695i	$0.396594\pi$
$151$	−8.12422	+	14.0716i	−0.661140	+	1.14513i	−0.980317	+	0.197432i	$0.936740\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.809243	+	1.40165i	0.0649999	+	0.112583i
$156$		0			0
$157$	−1.39922			−0.111670			−0.0558351	−	0.998440i	$-0.517782\pi$
$157$	−1.39922			−0.111670			−0.0558351	+	0.998440i	$0.517782\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.575392	+	22.8723i	0.0453472	+	1.80259i
$162$		0			0
$163$	10.0723	−	17.4457i	0.788921	−	1.36645i	−0.137707	−	0.990473i	$-0.543973\pi$
$163$	10.0723	−	17.4457i	0.788921	−	1.36645i	0.926628	−	0.375979i	$-0.122693\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.09572	+	8.82604i	−0.394318	+	0.682979i	−0.993014	−	0.117997i	$-0.962353\pi$
$167$	−5.09572	+	8.82604i	−0.394318	+	0.682979i	0.598696	+	0.800977i	$0.295686\pi$
$168$		0			0
$169$	4.75729	+	8.23988i	0.365946	+	0.633837i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	20.8099			1.58215			0.791074	−	0.611720i	$-0.209522\pi$
$173$	20.8099			1.58215			0.791074	+	0.611720i	$0.209522\pi$
$174$		0			0
$175$	9.58998	−	5.86319i	0.724934	−	0.443215i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	11.6819	+	20.2336i	0.873146	+	1.51233i	0.858724	+	0.512438i	$0.171258\pi$
$179$	11.6819	+	20.2336i	0.873146	+	1.51233i	0.0144222	+	0.999896i	$0.495409\pi$
$180$		0			0
$181$	9.33463			0.693837			0.346919	−	0.937895i	$-0.387228\pi$
$181$	9.33463			0.693837			0.346919	+	0.937895i	$0.387228\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.41069			−0.177238
$186$		0			0
$187$	22.8961			1.67433
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−24.9823			−1.80766			−0.903828	−	0.427897i	$-0.859255\pi$
$191$	−24.9823			−1.80766			−0.903828	+	0.427897i	$0.859255\pi$
$192$		0			0
$193$	−23.9430			−1.72345			−0.861727	−	0.507372i	$-0.830617\pi$
$193$	−23.9430			−1.72345			−0.861727	+	0.507372i	$0.830617\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.13307			0.365716			0.182858	−	0.983139i	$-0.441465\pi$
$197$	5.13307			0.365716			0.182858	+	0.983139i	$0.441465\pi$
$198$		0			0
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	0.963001	−	0.269498i	$-0.0868577\pi$
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	−0.714893	+	0.699234i	$0.753524\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.233851	+	9.29579i	0.0164131	+	0.652436i
$204$		0			0
$205$	−9.00000			−0.628587
$206$		0			0
$207$		0			0
$208$		0			0
$209$	9.45691	+	16.3798i	0.654148	+	1.13302i
$210$		0			0
$211$	2.77188	−	4.80104i	0.190824	−	0.330517i	−0.754699	−	0.656071i	$-0.772217\pi$
$211$	2.77188	−	4.80104i	0.190824	−	0.330517i	0.945524	+	0.325553i	$0.105551\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.50573	−	4.34006i	0.170890	−	0.295990i
$216$		0			0
$217$	−4.33842	−	2.36135i	−0.294511	−	0.160299i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−12.1623			−0.818122
$222$		0			0
$223$	−9.80039	−	16.9748i	−0.656283	−	1.13671i	−0.981571	−	0.191100i	$-0.938795\pi$
$223$	−9.80039	−	16.9748i	−0.656283	−	1.13671i	0.325288	−	0.945615i	$-0.394539\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.07227	+	13.9816i	−0.535776	+	0.927990i	0.463350	+	0.886175i	$0.346647\pi$
$227$	−8.07227	+	13.9816i	−0.535776	+	0.927990i	−0.999125	+	0.0418150i	$0.986686\pi$
$228$		0			0
$229$	11.3384	+	19.6387i	0.749264	+	1.29776i	0.948176	+	0.317746i	$0.102926\pi$
$229$	11.3384	+	19.6387i	0.749264	+	1.29776i	−0.198912	+	0.980017i	$0.563741\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.85234	−	3.20834i	0.121351	−	0.210185i	−0.798950	−	0.601398i	$-0.794611\pi$
$233$	1.85234	−	3.20834i	0.121351	−	0.210185i	0.920301	+	0.391212i	$0.127944\pi$
$234$		0			0
$235$	2.67111	+	4.62649i	0.174244	+	0.301799i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.809243	−	1.40165i	0.0523456	−	0.0906652i	−0.838665	−	0.544647i	$-0.816664\pi$
$239$	0.809243	−	1.40165i	0.0523456	−	0.0906652i	0.891011	+	0.453982i	$0.149997\pi$
$240$		0			0
$241$	−2.10078	+	3.63865i	−0.135323	+	0.234386i	−0.925721	−	0.378208i	$-0.876541\pi$
$241$	−2.10078	+	3.63865i	−0.135323	+	0.234386i	0.790398	+	0.612594i	$0.209874\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.76615	−	5.40138i	0.176723	−	0.345081i
$246$		0			0
$247$	−5.02344	−	8.70086i	−0.319634	−	0.553622i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−19.5438			−1.23359			−0.616796	−	0.787123i	$-0.711570\pi$
$251$	−19.5438			−1.23359			−0.616796	+	0.787123i	$0.711570\pi$
$252$		0			0
$253$	−30.3930			−1.91079
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.28074	+	5.68240i	0.204647	+	0.354459i	0.950020	−	0.312189i	$-0.101062\pi$
$257$	3.28074	+	5.68240i	0.204647	+	0.354459i	−0.745373	+	0.666647i	$0.767729\pi$
$258$		0			0
$259$	6.27694	−	3.83764i	0.390030	−	0.238459i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	9.69076	−	16.7849i	0.597558	−	1.03500i	−0.395623	−	0.918413i	$-0.629471\pi$
$263$	9.69076	−	16.7849i	0.597558	−	1.03500i	0.993180	−	0.116587i	$-0.0371954\pi$
$264$		0			0
$265$	2.42773	−	4.20495i	0.149134	−	0.258308i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.24271	−	12.5447i	−0.441596	−	0.764866i	0.556213	−	0.831040i	$-0.312254\pi$
$269$	−7.24271	−	12.5447i	−0.441596	−	0.764866i	−0.997808	+	0.0661742i	$0.978921\pi$
$270$		0			0
$271$	−2.67617	+	4.63526i	−0.162566	+	0.281572i	−0.935788	−	0.352563i	$-0.885310\pi$
$271$	−2.67617	+	4.63526i	−0.162566	+	0.281572i	0.773222	+	0.634135i	$0.218644\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	7.46576	+	12.9311i	0.450202	+	0.779773i
$276$		0			0
$277$	−6.10963	+	10.5822i	−0.367092	+	0.635822i	−0.989110	−	0.147181i	$-0.952980\pi$
$277$	−6.10963	+	10.5822i	−0.367092	+	0.635822i	0.622017	+	0.783003i	$0.286313\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−4.55768	−	7.89414i	−0.271889	−	0.470925i	0.697457	−	0.716627i	$-0.254315\pi$
$281$	−4.55768	−	7.89414i	−0.271889	−	0.470925i	−0.969345	+	0.245702i	$0.920982\pi$
$282$		0			0
$283$	13.8099			0.820914			0.410457	−	0.911880i	$-0.365369\pi$
$283$	13.8099			0.820914			0.410457	+	0.911880i	$0.365369\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	23.4341	−	14.3273i	1.38327	−	0.845715i
$288$		0			0
$289$	−12.7199	+	22.0316i	−0.748231	+	1.29597i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	14.0723	−	24.3739i	0.822111	−	1.42394i	−0.0819965	−	0.996633i	$-0.526130\pi$
$293$	14.0723	−	24.3739i	0.822111	−	1.42394i	0.904107	−	0.427305i	$-0.140537\pi$
$294$		0			0
$295$	−2.44805	−	4.24015i	−0.142531	−	0.246871i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	16.1445			0.933663
$300$		0			0
$301$	0.384634	+	15.2896i	0.0221700	+	0.881275i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−4.46264	−	7.72952i	−0.255530	−	0.442591i
$306$		0			0
$307$	7.24844			0.413690			0.206845	−	0.978374i	$-0.433680\pi$
$307$	7.24844			0.413690			0.206845	+	0.978374i	$0.433680\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−7.73385			−0.438546			−0.219273	−	0.975663i	$-0.570369\pi$
$311$	−7.73385			−0.438546			−0.219273	+	0.975663i	$0.570369\pi$
$312$		0			0
$313$	−9.85680			−0.557139			−0.278570	−	0.960416i	$-0.589860\pi$
$313$	−9.85680			−0.557139			−0.278570	+	0.960416i	$0.589860\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−18.7237			−1.05163			−0.525815	−	0.850599i	$-0.676239\pi$
$317$	−18.7237			−1.05163			−0.525815	+	0.850599i	$0.676239\pi$
$318$		0			0
$319$	−12.3523			−0.691598
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−35.0584			−1.95070
$324$		0			0
$325$	−3.96576	−	6.86890i	−0.219981	−	0.381018i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−14.3200	−	7.79423i	−0.789489	−	0.429710i
$330$		0			0
$331$	−18.9253			−1.04023			−0.520114	−	0.854097i	$-0.674110\pi$
$331$	−18.9253			−1.04023			−0.520114	+	0.854097i	$0.674110\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.586187	+	1.01531i	0.0320268	+	0.0554721i
$336$		0			0
$337$	−14.6388	+	25.3552i	−0.797427	+	1.38118i	0.123860	+	0.992300i	$0.460473\pi$
$337$	−14.6388	+	25.3552i	−0.797427	+	1.38118i	−0.921287	+	0.388884i	$0.872861\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	3.28074	−	5.68240i	0.177662	−	0.307719i
$342$		0			0
$343$	1.39610	+	18.4676i	0.0753825	+	0.997155i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	21.0875			1.13204			0.566019	−	0.824392i	$-0.308483\pi$
$347$	21.0875			1.13204			0.566019	+	0.824392i	$0.308483\pi$
$348$		0			0
$349$	−16.5957	−	28.7446i	−0.888348	−	1.53866i	−0.841827	−	0.539747i	$-0.818520\pi$
$349$	−16.5957	−	28.7446i	−0.888348	−	1.53866i	−0.0465210	−	0.998917i	$-0.514813\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−10.8619	+	18.8133i	−0.578119	+	1.00133i	0.417576	+	0.908642i	$0.362880\pi$
$353$	−10.8619	+	18.8133i	−0.578119	+	1.00133i	−0.995695	+	0.0926892i	$0.970454\pi$
$354$		0			0
$355$	0.904285	+	1.56627i	0.0479944	+	0.0831288i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	3.37578	−	5.84702i	0.178167	−	0.308594i	−0.763086	−	0.646297i	$-0.776317\pi$
$359$	3.37578	−	5.84702i	0.178167	−	0.308594i	0.941253	+	0.337703i	$0.109650\pi$
$360$		0			0
$361$	−4.98035	−	8.62622i	−0.262124	−	0.454012i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.14193	+	5.44198i	−0.164456	+	0.284846i
$366$		0			0
$367$	−17.5438	+	30.3867i	−0.915777	+	1.58617i	−0.110018	+	0.993930i	$0.535091\pi$
$367$	−17.5438	+	30.3867i	−0.915777	+	1.58617i	−0.805759	+	0.592243i	$0.798243\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.372660	+	14.8136i	0.0193476	+	0.769083i
$372$		0			0
$373$	−8.73385	−	15.1275i	−0.452222	−	0.783271i	0.546302	−	0.837588i	$-0.316035\pi$
$373$	−8.73385	−	15.1275i	−0.452222	−	0.783271i	−0.998524	+	0.0543173i	$0.982702\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.56148			0.337933
$378$		0			0
$379$	2.86693			0.147264			0.0736320	−	0.997285i	$-0.476541\pi$
$379$	2.86693			0.147264			0.0736320	+	0.997285i	$0.476541\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.42461	+	4.19954i	0.123892	+	0.214587i	0.921299	−	0.388855i	$-0.127129\pi$
$383$	2.42461	+	4.19954i	0.123892	+	0.214587i	−0.797407	+	0.603441i	$0.793796\pi$
$384$		0			0
$385$	7.08045	+	3.85381i	0.360853	+	0.196408i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−13.2053	+	22.8723i	−0.669538	+	1.15967i	0.308496	+	0.951226i	$0.400174\pi$
$389$	−13.2053	+	22.8723i	−0.669538	+	1.15967i	−0.978034	+	0.208448i	$0.933159\pi$
$390$		0			0
$391$	28.1680	−	48.7884i	1.42452	−	2.46733i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−5.06148	−	8.76673i	−0.254670	−	0.441102i
$396$		0			0
$397$	−14.5095	+	25.1312i	−0.728212	+	1.26130i	0.229426	+	0.973326i	$0.426315\pi$
$397$	−14.5095	+	25.1312i	−0.728212	+	1.26130i	−0.957638	+	0.287975i	$0.907018\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	16.9538	+	29.3648i	0.846632	+	1.46641i	0.884197	+	0.467115i	$0.154707\pi$
$401$	16.9538	+	29.3648i	0.846632	+	1.46641i	−0.0375649	+	0.999294i	$0.511960\pi$
$402$		0			0
$403$	−1.74271	+	3.01845i	−0.0868103	+	0.150360i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.88658	+	8.46380i	0.242219	+	0.419535i
$408$		0			0
$409$	−36.2675			−1.79331			−0.896656	−	0.442728i	$-0.854011\pi$
$409$	−36.2675			−1.79331			−0.896656	+	0.442728i	$0.854011\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	13.1242	+	7.14336i	0.645801	+	0.351502i
$414$		0			0
$415$	2.97656	−	5.15555i	0.146113	−	0.253076i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	11.0615	−	19.1590i	0.540388	−	0.935980i	−0.458493	−	0.888698i	$-0.651611\pi$
$419$	11.0615	−	19.1590i	0.540388	−	0.935980i	0.998882	−	0.0472823i	$-0.0150560\pi$
$420$		0			0
$421$	−3.23764	−	5.60776i	−0.157793	−	0.273306i	0.776279	−	0.630389i	$-0.217105\pi$
$421$	−3.23764	−	5.60776i	−0.157793	−	0.273306i	−0.934073	+	0.357083i	$0.883771\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−27.6768			−1.34252
$426$		0			0
$427$	23.9246	+	13.0219i	1.15779	+	0.630173i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.99115	−	3.44877i	−0.0959101	−	0.166121i	0.814078	−	0.580756i	$-0.197243\pi$
$431$	−1.99115	−	3.44877i	−0.0959101	−	0.166121i	−0.909988	+	0.414634i	$0.863909\pi$
$432$		0			0
$433$	−26.4690			−1.27202			−0.636011	−	0.771680i	$-0.719417\pi$
$433$	−26.4690			−1.27202			−0.636011	+	0.771680i	$0.719417\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	46.5375			2.22619
$438$		0			0
$439$	−10.7922			−0.515084			−0.257542	−	0.966267i	$-0.582913\pi$
$439$	−10.7922			−0.515084			−0.257542	+	0.966267i	$0.582913\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	0.277618			0.0131900			0.00659502	−	0.999978i	$-0.497901\pi$
$443$	0.277618			0.0131900			0.00659502	+	0.999978i	$0.497901\pi$
$444$		0			0
$445$	5.68831			0.269652
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.277618			−0.0131016			−0.00655081	−	0.999979i	$-0.502085\pi$
$449$	−0.277618			−0.0131016			−0.00655081	+	0.999979i	$0.502085\pi$
$450$		0			0
$451$	18.2434	+	31.5985i	0.859047	+	1.48791i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.76109	−	2.04712i	−0.176323	−	0.0959703i
$456$		0			0
$457$	−37.6768			−1.76245			−0.881224	−	0.472699i	$-0.843280\pi$
$457$	−37.6768			−1.76245			−0.881224	+	0.472699i	$0.843280\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−3.92461	−	6.79762i	−0.182787	−	0.316597i	0.760041	−	0.649875i	$-0.225179\pi$
$461$	−3.92461	−	6.79762i	−0.182787	−	0.316597i	−0.942829	+	0.333278i	$0.891845\pi$
$462$		0			0
$463$	0.266149	−	0.460984i	0.0123690	−	0.0214237i	−0.859775	−	0.510674i	$-0.829396\pi$
$463$	0.266149	−	0.460984i	0.0123690	−	0.0214237i	0.872144	+	0.489250i	$0.162729\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.84348	+	6.65711i	−0.177855	+	0.308054i	−0.941146	−	0.338001i	$-0.890249\pi$
$467$	−3.84348	+	6.65711i	−0.177855	+	0.308054i	0.763291	+	0.646055i	$0.223583\pi$
$468$		0			0
$469$	−3.14260	−	1.71048i	−0.145112	−	0.0789827i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−20.3169			−0.934173
$474$		0			0
$475$	−11.4315	−	19.8000i	−0.524514	−	0.908485i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	11.0957	−	19.2183i	0.506976	−	0.878108i	−0.492991	−	0.870034i	$-0.664097\pi$
$479$	11.0957	−	19.2183i	0.506976	−	0.878108i	0.999967	−	0.00807422i	$-0.00257013\pi$
$480$		0			0
$481$	−2.59572	−	4.49591i	−0.118354	−	0.204996i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.42840	−	2.47406i	0.0648604	−	0.112341i
$486$		0			0
$487$	3.99115	+	6.91287i	0.180856	+	0.313252i	0.942172	−	0.335129i	$-0.108780\pi$
$487$	3.99115	+	6.91287i	0.180856	+	0.313252i	−0.761316	+	0.648381i	$0.775447\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	19.0526	−	33.0001i	0.859833	−	1.48927i	−0.0122552	−	0.999925i	$-0.503901\pi$
$491$	19.0526	−	33.0001i	0.859833	−	1.48927i	0.872088	−	0.489349i	$-0.162766\pi$
$492$		0			0
$493$	11.4481	−	19.8286i	0.515594	−	0.893036i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.84795	−	2.63868i	−0.217460	−	0.118361i
$498$		0			0
$499$	−7.72500	−	13.3801i	−0.345818	−	0.598975i	0.639684	−	0.768638i	$-0.279065\pi$
$499$	−7.72500	−	13.3801i	−0.345818	−	0.598975i	−0.985502	+	0.169663i	$0.945732\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.78074			0.0793992			0.0396996	−	0.999212i	$-0.487360\pi$
$503$	1.78074			0.0793992			0.0396996	+	0.999212i	$0.487360\pi$
$504$		0			0
$505$	−1.64378			−0.0731473
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3.89037	−	6.73832i	−0.172438	−	0.298671i	0.766834	−	0.641846i	$-0.221831\pi$
$509$	−3.89037	−	6.73832i	−0.172438	−	0.298671i	−0.939272	+	0.343175i	$0.888498\pi$
$510$		0			0
$511$	−0.482291	−	19.1715i	−0.0213353	−	0.848097i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.03424	−	5.25546i	0.133705	−	0.231583i
$516$		0			0
$517$	10.8289	−	18.7562i	0.476254	−	0.824896i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−2.10963	−	3.65399i	−0.0924246	−	0.160084i	0.816106	−	0.577902i	$-0.196128\pi$
$521$	−2.10963	−	3.65399i	−0.0924246	−	0.160084i	−0.908531	+	0.417818i	$0.862795\pi$
$522$		0			0
$523$	1.02850	−	1.78142i	0.0449734	−	0.0778962i	−0.842662	−	0.538442i	$-0.819013\pi$
$523$	1.02850	−	1.78142i	0.0449734	−	0.0778962i	0.887636	+	0.460546i	$0.152346\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.08113	+	10.5328i	0.264898	+	0.458817i
$528$		0			0
$529$	−25.8910	+	44.8446i	−1.12570	+	1.94977i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−9.69076	−	16.7849i	−0.419753	−	0.727034i
$534$		0			0
$535$	−16.8023			−0.726428
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−24.5710	+	1.23703i	−1.05835	+	0.0532827i
$540$		0			0
$541$	−8.63881	+	14.9629i	−0.371411	+	0.643303i	−0.989783	−	0.142582i	$-0.954459\pi$
$541$	−8.63881	+	14.9629i	−0.371411	+	0.643303i	0.618372	+	0.785886i	$0.287793\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.91381	+	6.77892i	−0.167649	+	0.290377i
$546$		0			0
$547$	10.4246	+	18.0560i	0.445724	+	0.772017i	0.998102	−	0.0615768i	$-0.0196129\pi$
$547$	10.4246	+	18.0560i	0.445724	+	0.772017i	−0.552378	+	0.833594i	$0.686280\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	18.9138			0.805756
$552$		0			0
$553$	27.1350	+	14.7693i	1.15390	+	0.628053i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−6.64387	−	11.5075i	−0.281510	−	0.487589i	0.690247	−	0.723574i	$-0.257502\pi$
$557$	−6.64387	−	11.5075i	−0.281510	−	0.487589i	−0.971757	+	0.235985i	$0.924169\pi$
$558$		0			0
$559$	10.7922			0.456462
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−30.3930			−1.28091			−0.640456	−	0.767995i	$-0.721255\pi$
$563$	−30.3930			−1.28091			−0.640456	+	0.767995i	$0.721255\pi$
$564$		0			0
$565$	0.405463			0.0170580
$566$		0			0
$567$		0			0
$568$		0			0
$569$	43.7060			1.83225			0.916126	−	0.400891i	$-0.131299\pi$
$569$	43.7060			1.83225			0.916126	+	0.400891i	$0.131299\pi$
$570$		0			0
$571$	−38.2130			−1.59917			−0.799583	−	0.600556i	$-0.794946\pi$
$571$	−38.2130			−1.59917			−0.799583	+	0.600556i	$0.794946\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	36.7391			1.53213
$576$		0			0
$577$	−16.5957	−	28.7446i	−0.690889	−	1.19665i	−0.971547	−	0.236847i	$-0.923886\pi$
$577$	−16.5957	−	28.7446i	−0.690889	−	1.19665i	0.280658	−	0.959808i	$-0.409447\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.456906	+	18.1624i	0.0189557	+	0.753505i
$582$		0			0
$583$	−19.6844			−0.815246
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.89610	+	3.28415i	0.0782606	+	0.135551i	0.902500	−	0.430691i	$-0.141730\pi$
$587$	1.89610	+	3.28415i	0.0782606	+	0.135551i	−0.824239	+	0.566242i	$0.808397\pi$
$588$		0			0
$589$	−5.02344	+	8.70086i	−0.206987	+	0.358513i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.81810	−	3.14904i	0.0746603	−	0.129315i	−0.826278	−	0.563262i	$-0.809546\pi$
$593$	1.81810	−	3.14904i	0.0746603	−	0.129315i	0.900938	+	0.433947i	$0.142879\pi$
$594$		0			0
$595$	−12.7484	+	7.79423i	−0.522635	+	0.319532i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−38.8506			−1.58739			−0.793696	−	0.608315i	$-0.791846\pi$
$599$	−38.8506			−1.58739			−0.793696	+	0.608315i	$0.791846\pi$
$600$		0			0
$601$	−16.3619	−	28.3396i	−0.667414	−	1.15600i	−0.978625	−	0.205655i	$-0.934068\pi$
$601$	−16.3619	−	28.3396i	−0.667414	−	1.15600i	0.311210	−	0.950341i	$-0.399266\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.586187	+	1.01531i	−0.0238319	+	0.0412781i
$606$		0			0
$607$	13.9050	+	24.0841i	0.564385	+	0.977543i	0.997107	+	0.0760157i	$0.0242199\pi$
$607$	13.9050	+	24.0841i	0.564385	+	0.977543i	−0.432722	+	0.901528i	$0.642447\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.75223	+	9.96316i	−0.232710	+	0.403066i
$612$		0			0
$613$	14.9684	+	25.9260i	0.604567	+	1.04714i	0.992120	+	0.125293i	$0.0399872\pi$
$613$	14.9684	+	25.9260i	0.604567	+	1.04714i	−0.387553	+	0.921848i	$0.626680\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−15.2091	+	26.3430i	−0.612297	+	1.06053i	0.378555	+	0.925579i	$0.376421\pi$
$617$	−15.2091	+	26.3430i	−0.612297	+	1.06053i	−0.990852	+	0.134951i	$0.956912\pi$
$618$		0			0
$619$	−11.6527	+	20.1831i	−0.468363	+	0.811228i	−0.999346	−	0.0361543i	$-0.988489\pi$
$619$	−11.6527	+	20.1831i	−0.468363	+	0.811228i	0.530984	+	0.847382i	$0.321823\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−14.8112	+	9.05536i	−0.593398	+	0.362795i
$624$		0			0
$625$	−7.14572	−	12.3768i	−0.285829	−	0.495070i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−18.1154			−0.722307
$630$		0			0
$631$	4.60078			0.183154			0.0915770	−	0.995798i	$-0.470809\pi$
$631$	4.60078			0.183154			0.0915770	+	0.995798i	$0.470809\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−6.36186	−	11.0191i	−0.252463	−	0.437279i
$636$		0			0
$637$	13.0519	−	0.657103i	0.517137	−	0.0260354i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	2.33269	−	4.04033i	0.0921356	−	0.159583i	−0.816274	−	0.577665i	$-0.803964\pi$
$641$	2.33269	−	4.04033i	0.0921356	−	0.159583i	0.908410	+	0.418081i	$0.137297\pi$
$642$		0			0
$643$	11.1996	−	19.3983i	0.441670	−	0.764994i	−0.556144	−	0.831086i	$-0.687720\pi$
$643$	11.1996	−	19.3983i	0.441670	−	0.764994i	0.997814	+	0.0660918i	$0.0210530\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	19.8619	+	34.4018i	0.780850	+	1.35247i	0.931447	+	0.363877i	$0.118547\pi$
$647$	19.8619	+	34.4018i	0.780850	+	1.35247i	−0.150596	+	0.988595i	$0.548119\pi$
$648$		0			0
$649$	−9.92461	+	17.1899i	−0.389575	+	0.674764i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−19.0526	−	33.0001i	−0.745587	−	1.29139i	−0.949920	−	0.312493i	$-0.898836\pi$
$653$	−19.0526	−	33.0001i	−0.745587	−	1.29139i	0.204333	−	0.978901i	$-0.434497\pi$
$654$		0			0
$655$	−6.17617	+	10.6974i	−0.241323	+	0.417983i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	14.1660	+	24.5363i	0.551831	+	0.955799i	0.998143	+	0.0609214i	$0.0194039\pi$
$659$	14.1660	+	24.5363i	0.551831	+	0.955799i	−0.446312	+	0.894878i	$0.647263\pi$
$660$		0			0
$661$	43.0774			1.67552			0.837759	−	0.546041i	$-0.183866\pi$
$661$	43.0774			1.67552			0.837759	+	0.546041i	$0.183866\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−10.8415	−	5.90092i	−0.420417	−	0.228828i
$666$		0			0
$667$	−15.1965	+	26.3211i	−0.588411	+	1.01916i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−18.0919	+	31.3361i	−0.698431	+	1.20972i
$672$		0			0
$673$	−11.3815	−	19.7134i	−0.438725	−	0.759894i	0.558866	−	0.829258i	$-0.311236\pi$
$673$	−11.3815	−	19.7134i	−0.438725	−	0.759894i	−0.997591	+	0.0693635i	$0.977903\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−38.8506			−1.49315			−0.746574	−	0.665302i	$-0.768303\pi$
$677$	−38.8506			−1.49315			−0.746574	+	0.665302i	$0.768303\pi$
$678$		0			0
$679$	0.219262	+	8.71586i	0.00841450	+	0.334484i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.328893	−	0.569659i	−0.0125847	−	0.0217974i	0.859664	−	0.510859i	$-0.170673\pi$
$683$	−0.328893	−	0.569659i	−0.0125847	−	0.0217974i	−0.872249	+	0.489062i	$0.837339\pi$
$684$		0			0
$685$	−14.9938			−0.572882
$686$		0			0
$687$		0			0
$688$		0			0
$689$	10.4562			0.398351
$690$		0			0
$691$	−4.72373			−0.179699			−0.0898496	−	0.995955i	$-0.528639\pi$
$691$	−4.72373			−0.179699			−0.0898496	+	0.995955i	$0.528639\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−10.5185			−0.398988
$696$		0			0
$697$	−67.6313			−2.56172
$698$		0			0
$699$		0			0
$700$		0			0
$701$	48.1560			1.81883			0.909414	−	0.415893i	$-0.136531\pi$
$701$	48.1560			1.81883			0.909414	+	0.415893i	$0.136531\pi$
$702$		0			0
$703$	−7.48229	−	12.9597i	−0.282200	−	0.488785i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.28006	−	2.61678i	0.160968	−	0.0984140i
$708$		0			0
$709$	0.543767			0.0204216			0.0102108	−	0.999948i	$-0.496750\pi$
$709$	0.543767			0.0204216			0.0102108	+	0.999948i	$0.496750\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−8.07227	−	13.9816i	−0.302309	−	0.523614i
$714$		0			0
$715$	2.84416	−	4.92622i	0.106365	−	0.184230i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−25.3068	+	43.8327i	−0.943784	+	1.63468i	−0.185617	+	0.982622i	$0.559428\pi$
$719$	−25.3068	+	43.8327i	−0.943784	+	1.63468i	−0.758167	+	0.652060i	$0.773905\pi$
$720$		0			0
$721$	0.465761	+	18.5144i	0.0173458	+	0.689512i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	14.9315			0.554543
$726$		0			0
$727$	−11.6527	−	20.1831i	−0.432176	−	0.748550i	0.564885	−	0.825170i	$-0.308921\pi$
$727$	−11.6527	−	20.1831i	−0.432176	−	0.748550i	−0.997060	+	0.0766196i	$0.975587\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	18.8296	−	32.6138i	0.696437	−	1.20626i
$732$		0			0
$733$	22.3061	+	38.6353i	0.823895	+	1.42703i	0.902761	+	0.430143i	$0.141537\pi$
$733$	22.3061	+	38.6353i	0.823895	+	1.42703i	−0.0788651	+	0.996885i	$0.525130\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.37645	−	4.11614i	0.0875378	−	0.151620i
$738$		0			0
$739$	−18.9392	−	32.8037i	−0.696690	−	1.20670i	−0.969608	−	0.244665i	$-0.921322\pi$
$739$	−18.9392	−	32.8037i	−0.696690	−	1.20670i	0.272918	−	0.962037i	$-0.412011\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	8.02850	−	13.9058i	0.294537	−	0.510154i	−0.680340	−	0.732897i	$-0.738168\pi$
$743$	8.02850	−	13.9058i	0.294537	−	0.510154i	0.974877	+	0.222743i	$0.0715012\pi$
$744$		0			0
$745$	−2.14260	+	3.71110i	−0.0784989	+	0.135964i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	43.7498	−	26.7480i	1.59858	−	0.977352i
$750$		0			0
$751$	−4.86693	−	8.42976i	−0.177597	−	0.307606i	0.763460	−	0.645855i	$-0.223499\pi$
$751$	−4.86693	−	8.42976i	−0.177597	−	0.307606i	−0.941057	+	0.338248i	$0.890166\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	14.0862			0.512649
$756$		0			0
$757$	−16.7922			−0.610323			−0.305162	−	0.952301i	$-0.598710\pi$
$757$	−16.7922			−0.610323			−0.305162	+	0.952301i	$0.598710\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	9.64387	+	16.7037i	0.349590	+	0.605508i	0.986177	−	0.165698i	$-0.0529875\pi$
$761$	9.64387	+	16.7037i	0.349590	+	0.605508i	−0.636587	+	0.771205i	$0.719654\pi$
$762$		0			0
$763$	−0.600777	−	23.8814i	−0.0217496	−	0.864565i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	5.27188	−	9.13117i	0.190357	−	0.329707i
$768$		0			0
$769$	0.794654	−	1.37638i	0.0286559	−	0.0496335i	−0.851342	−	0.524611i	$-0.824211\pi$
$769$	0.794654	−	1.37638i	0.0286559	−	0.0496335i	0.879998	+	0.474978i	$0.157544\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	10.2769	+	17.8002i	0.369636	+	0.640228i	0.989509	−	0.144474i	$-0.0461491\pi$
$773$	10.2769	+	17.8002i	0.369636	+	0.640228i	−0.619873	+	0.784702i	$0.712816\pi$
$774$		0			0
$775$	−3.96576	+	6.86890i	−0.142454	+	0.246738i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−27.9341	−	48.3833i	−1.00084	−	1.73351i
$780$		0			0
$781$	3.66605	−	6.34978i	0.131181	−	0.227213i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.606511	+	1.05051i	0.0216473	+	0.0374942i
$786$		0			0
$787$	−30.3891			−1.08325			−0.541627	−	0.840619i	$-0.682192\pi$
$787$	−30.3891			−1.08325			−0.541627	+	0.840619i	$0.682192\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.05574	+	0.645466i	−0.0375378	+	0.0229501i
$792$		0			0
$793$	9.61030	−	16.6455i	0.341272	−	0.591100i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−22.7060	+	39.3280i	−0.804288	+	1.39307i	0.112482	+	0.993654i	$0.464120\pi$
$797$	−22.7060	+	39.3280i	−0.804288	+	1.39307i	−0.916770	+	0.399415i	$0.869213\pi$
$798$		0			0
$799$	20.0723	+	34.7662i	0.710106	+	1.22994i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	25.4753			0.899003
$804$		0			0
$805$	16.9227	−	10.3463i	0.596446	−	0.364659i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	7.50953	+	13.0069i	0.264021	+	0.457298i	0.967307	−	0.253610i	$-0.0816179\pi$
$809$	7.50953	+	13.0069i	0.264021	+	0.457298i	−0.703286	+	0.710907i	$0.748285\pi$
$810$		0			0
$811$	23.3930			0.821439			0.410719	−	0.911762i	$-0.365278\pi$
$811$	23.3930			0.821439			0.410719	+	0.911762i	$0.365278\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−17.4638			−0.611731
$816$		0			0
$817$	31.1091			1.08837
$818$		0			0
$819$		0			0
$820$		0			0
$821$	29.1547			1.01750			0.508752	−	0.860913i	$-0.330107\pi$
$821$	29.1547			1.01750			0.508752	+	0.860913i	$0.330107\pi$
$822$		0			0
$823$	3.19143			0.111246			0.0556231	−	0.998452i	$-0.482285\pi$
$823$	3.19143			0.111246			0.0556231	+	0.998452i	$0.482285\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−34.5654			−1.20196			−0.600978	−	0.799266i	$-0.705222\pi$
$827$	−34.5654			−1.20196			−0.600978	+	0.799266i	$0.705222\pi$
$828$		0			0
$829$	11.7111	+	20.2842i	0.406743	+	0.704499i	0.994523	−	0.104522i	$-0.0333312\pi$
$829$	11.7111	+	20.2842i	0.406743	+	0.704499i	−0.587780	+	0.809021i	$0.699998\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	20.7865	−	40.5891i	0.720209	−	1.40633i
$834$		0			0
$835$	8.83521			0.305755
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−12.5488	−	21.7352i	−0.433234	−	0.750383i	0.563916	−	0.825832i	$-0.309294\pi$
$839$	−12.5488	−	21.7352i	−0.433234	−	0.750383i	−0.997150	+	0.0754495i	$0.975961\pi$
$840$		0			0
$841$	8.32383	−	14.4173i	0.287029	−	0.497148i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	4.12422	−	7.14336i	0.141877	−	0.245739i
$846$		0			0
$847$	−0.0899807	−	3.57681i	−0.00309177	−	0.122901i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	24.0469			0.824317
$852$		0			0
$853$	5.97150	+	10.3429i	0.204460	+	0.354135i	0.949961	−	0.312370i	$-0.101123\pi$
$853$	5.97150	+	10.3429i	0.204460	+	0.354135i	−0.745500	+	0.666505i	$0.767789\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−5.10963	+	8.85014i	−0.174542	+	0.302315i	−0.940003	−	0.341167i	$-0.889178\pi$
$857$	−5.10963	+	8.85014i	−0.174542	+	0.302315i	0.765461	+	0.643482i	$0.222511\pi$
$858$		0			0
$859$	5.97150	+	10.3429i	0.203745	+	0.352896i	0.949732	−	0.313064i	$-0.101355\pi$
$859$	5.97150	+	10.3429i	0.203745	+	0.352896i	−0.745987	+	0.665960i	$0.768022\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−7.93346	+	13.7412i	−0.270058	+	0.467755i	−0.968876	−	0.247545i	$-0.920376\pi$
$863$	−7.93346	+	13.7412i	−0.270058	+	0.467755i	0.698818	+	0.715299i	$0.253710\pi$
$864$		0			0
$865$	−9.02032	−	15.6237i	−0.306700	−	0.531220i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−20.5197	+	35.5411i	−0.696081	+	1.20565i
$870$		0			0
$871$	−1.26236	+	2.18646i	−0.0427733	+	0.0740855i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−18.6318	−	10.1411i	−0.629870	−	0.342831i
$876$		0			0
$877$	15.5907	+	27.0038i	0.526459	+	0.911854i	0.999525	+	0.0308266i	$0.00981396\pi$
$877$	15.5907	+	27.0038i	0.526459	+	0.911854i	−0.473066	+	0.881027i	$0.656853\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	33.1623			1.11726			0.558632	−	0.829415i	$-0.311326\pi$
$881$	33.1623			1.11726			0.558632	+	0.829415i	$0.311326\pi$
$882$		0			0
$883$	19.5045			0.656378			0.328189	−	0.944612i	$-0.393562\pi$
$883$	19.5045			0.656378			0.328189	+	0.944612i	$0.393562\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.7630	+	25.5703i	0.495694	+	0.858567i	0.999988	−	0.00496501i	$-0.00158042\pi$
$887$	14.7630	+	25.5703i	0.495694	+	0.858567i	−0.504294	+	0.863532i	$0.668247\pi$
$888$		0			0
$889$	34.1065	+	18.5638i	1.14390	+	0.622609i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−16.5811	+	28.7194i	−0.554866	+	0.961057i
$894$		0			0
$895$	10.1273	−	17.5411i	0.338520	−	0.586333i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−3.28074	−	5.68240i	−0.109419	−	0.189519i
$900$		0			0
$901$	18.2434	−	31.5985i	0.607775	−	1.05270i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−4.04621	−	7.00825i	−0.134501	−	0.232962i
$906$		0			0
$907$	−16.2091	+	28.0751i	−0.538216	+	0.932217i	0.460785	+	0.887512i	$0.347568\pi$
$907$	−16.2091	+	28.0751i	−0.538216	+	0.932217i	−0.999000	+	0.0447048i	$0.985765\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	15.2915	+	26.4857i	0.506631	+	0.877511i	0.999971	+	0.00767396i	$0.00244272\pi$
$911$	15.2915	+	26.4857i	0.506631	+	0.877511i	−0.493339	+	0.869837i	$0.664224\pi$
$912$		0			0
$913$	−24.1344			−0.798733
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.948052	−	37.6859i	−0.0313074	−	1.24450i
$918$		0			0
$919$	24.1477	−	41.8250i	0.796558	−	1.37968i	−0.125287	−	0.992121i	$-0.539985\pi$
$919$	24.1477	−	41.8250i	0.796558	−	1.37968i	0.921845	−	0.387558i	$-0.126681\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1.94738	+	3.37296i	−0.0640987	+	0.111022i
$924$		0			0
$925$	−5.90690	−	10.2311i	−0.194218	−	0.336395i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−43.2193			−1.41798			−0.708989	−	0.705220i	$-0.750848\pi$
$929$	−43.2193			−1.41798			−0.708989	+	0.705220i	$0.750848\pi$
$930$		0			0
$931$	37.6230	−	1.89413i	1.23304	−	0.0620778i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−9.92461	−	17.1899i	−0.324569	−	0.562171i
$936$		0			0
$937$	37.3638			1.22062			0.610311	−	0.792162i	$-0.291044\pi$
$937$	37.3638			1.22062			0.610311	+	0.792162i	$0.291044\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−27.5146			−0.896950			−0.448475	−	0.893795i	$-0.648033\pi$
$941$	−27.5146			−0.896950			−0.448475	+	0.893795i	$0.648033\pi$
$942$		0			0
$943$	89.7758			2.92350
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−15.6768			−0.509429			−0.254714	−	0.967016i	$-0.581981\pi$
$947$	−15.6768			−0.509429			−0.254714	+	0.967016i	$0.581981\pi$
$948$		0			0
$949$	−13.5323			−0.439277
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−11.2268			−0.363673			−0.181837	−	0.983329i	$-0.558204\pi$
$953$	−11.2268			−0.363673			−0.181837	+	0.983329i	$0.558204\pi$
$954$		0			0
$955$	10.8289	+	18.7562i	0.350415	+	0.606936i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	39.0406	−	23.8689i	1.26069	−	0.770768i
$960$		0			0
$961$	−27.5146			−0.887567
$962$		0			0
$963$		0			0
$964$		0			0
$965$	10.3784	+	17.9759i	0.334092	+	0.578665i
$966$		0			0
$967$	−19.2434	+	33.3305i	−0.618825	+	1.07184i	0.370875	+	0.928683i	$0.379058\pi$
$967$	−19.2434	+	33.3305i	−0.618825	+	1.07184i	−0.989700	+	0.143154i	$0.954276\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	7.08998	−	12.2802i	0.227528	−	0.394091i	−0.729547	−	0.683931i	$-0.760269\pi$
$971$	7.08998	−	12.2802i	0.227528	−	0.394091i	0.957075	+	0.289840i	$0.0936022\pi$
$972$		0			0
$973$	27.3879	−	16.7446i	0.878016	−	0.536808i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	49.3943			1.58026			0.790132	−	0.612936i	$-0.210012\pi$
$977$	49.3943			1.58026			0.790132	+	0.612936i	$0.210012\pi$
$978$		0			0
$979$	−11.5304	−	19.9713i	−0.368515	−	0.638286i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	6.72812	−	11.6534i	0.214594	−	0.371687i	−0.738553	−	0.674195i	$-0.764491\pi$
$983$	6.72812	−	11.6534i	0.214594	−	0.371687i	0.953147	+	0.302508i	$0.0978240\pi$
$984$		0			0
$985$	−2.22500	−	3.85381i	−0.0708943	−	0.122793i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−24.9949	+	43.2925i	−0.794793	+	1.37662i
$990$		0			0
$991$	1.09884	+	1.90324i	0.0349056	+	0.0604584i	0.882950	−	0.469466i	$-0.155554\pi$
$991$	1.09884	+	1.90324i	0.0349056	+	0.0604584i	−0.848045	+	0.529924i	$0.822220\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	3.03424	−	5.25546i	0.0961919	−	0.166609i
$996$		0			0
$997$	24.9164	−	43.1565i	0.789111	−	1.36678i	−0.137401	−	0.990516i	$-0.543875\pi$
$997$	24.9164	−	43.1565i	0.789111	−	1.36678i	0.926512	−	0.376265i	$-0.122792\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.i.k.2053.2		6
3.2	odd	2		2268.2.i.j.2053.2		6
7.4	even	3		2268.2.l.j.109.2		6
9.2	odd	6		2268.2.l.k.541.2		6
9.4	even	3		756.2.k.f.541.2	yes	6
9.5	odd	6		756.2.k.e.541.2	yes	6
9.7	even	3		2268.2.l.j.541.2		6
21.11	odd	6		2268.2.l.k.109.2		6
63.4	even	3		756.2.k.f.109.2	yes	6
63.5	even	6		5292.2.a.v.1.2		3
63.11	odd	6		2268.2.i.j.865.2		6
63.23	odd	6		5292.2.a.x.1.2		3
63.25	even	3	inner	2268.2.i.k.865.2		6
63.32	odd	6		756.2.k.e.109.2	✓	6
63.40	odd	6		5292.2.a.w.1.2		3
63.58	even	3		5292.2.a.u.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.k.e.109.2	✓	6	63.32	odd	6
756.2.k.e.541.2	yes	6	9.5	odd	6
756.2.k.f.109.2	yes	6	63.4	even	3
756.2.k.f.541.2	yes	6	9.4	even	3
2268.2.i.j.865.2		6	63.11	odd	6
2268.2.i.j.2053.2		6	3.2	odd	2
2268.2.i.k.865.2		6	63.25	even	3	inner
2268.2.i.k.2053.2		6	1.1	even	1	trivial
2268.2.l.j.109.2		6	7.4	even	3
2268.2.l.j.541.2		6	9.7	even	3
2268.2.l.k.109.2		6	21.11	odd	6
2268.2.l.k.541.2		6	9.2	odd	6
5292.2.a.u.1.2		3	63.58	even	3
5292.2.a.v.1.2		3	63.5	even	6
5292.2.a.w.1.2		3	63.40	odd	6
5292.2.a.x.1.2		3	63.23	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:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.433463 - 0.750780i) q^{5} +(2.32383 + 1.26483i) q^{7} +O(q^{10})\)	\(q+(-0.433463 - 0.750780i) q^{5} +(2.32383 + 1.26483i) q^{7} +(-1.75729 + 3.04372i) q^{11} +(0.933463 - 1.61680i) q^{13} +(-3.25729 - 5.64180i) q^{17} +(2.69076 - 4.66053i) q^{19} +(4.32383 + 7.48910i) q^{23} +(2.12422 - 3.67926i) q^{25} +(1.75729 + 3.04372i) q^{29} -1.86693 q^{31} +(-0.0576828 - 2.29294i) q^{35} +(1.39037 - 2.40819i) q^{37} +(5.19076 - 8.99066i) q^{41} +(2.89037 + 5.00627i) q^{43} -6.16225 q^{47} +(3.80039 + 5.87852i) q^{49} +(2.80039 + 4.85041i) q^{53} +3.04689 q^{55} +5.64766 q^{59} +10.2953 q^{61} -1.61849 q^{65} -1.35234 q^{67} -2.08619 q^{71} +(-3.62422 - 6.27733i) q^{73} +(-7.93346 + 4.85041i) q^{77} +11.6768 q^{79} +(3.43346 + 5.94693i) q^{83} +(-2.82383 + 4.89102i) q^{85} +(-3.28074 + 5.68240i) q^{89} +(4.21420 - 2.57651i) q^{91} -4.66537 q^{95} +(1.64766 + 2.85384i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{5} + 2 q^{7}+O(q^{10}) \) 6 * q + q^5 + 2 * q^7	\( 6 q + q^{5} + 2 q^{7} + 5 q^{11} + 2 q^{13} - 4 q^{17} - 3 q^{19} + 14 q^{23} - 10 q^{25} - 5 q^{29} - 4 q^{31} + 26 q^{35} + 12 q^{41} + 9 q^{43} + 18 q^{47} + 12 q^{49} + 6 q^{53} + 16 q^{55} + 10 q^{59} + 14 q^{61} - 48 q^{65} - 32 q^{67} - 22 q^{71} + q^{73} - 44 q^{77} - 16 q^{79} + 17 q^{83} - 5 q^{85} - 3 q^{89} + 5 q^{91} - 64 q^{95} - 14 q^{97}+O(q^{100}) \) 6 * q + q^5 + 2 * q^7 + 5 * q^11 + 2 * q^13 - 4 * q^17 - 3 * q^19 + 14 * q^23 - 10 * q^25 - 5 * q^29 - 4 * q^31 + 26 * q^35 + 12 * q^41 + 9 * q^43 + 18 * q^47 + 12 * q^49 + 6 * q^53 + 16 * q^55 + 10 * q^59 + 14 * q^61 - 48 * q^65 - 32 * q^67 - 22 * q^71 + q^73 - 44 * q^77 - 16 * q^79 + 17 * q^83 - 5 * q^85 - 3 * q^89 + 5 * q^91 - 64 * q^95 - 14 * q^97

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