LMFDB - Embedded newform 2268.2.bm.g.1025.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2268,2,Mod(593,2268)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2268.593"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2268, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 1, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.bm (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,0,0,-10,0,0,0,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1025.1
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2268.1025
Dual form			2268.2.bm.g.593.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44949 q^{5} +(-2.50000 + 0.866025i) q^{7} -4.24264i q^{11} +(-1.50000 - 0.866025i) q^{13} +(-2.44949 + 4.24264i) q^{17} +(4.50000 - 2.59808i) q^{19} +1.00000 q^{25} +(-7.34847 + 4.24264i) q^{29} +(1.50000 - 0.866025i) q^{31} +(6.12372 - 2.12132i) q^{35} +(2.50000 + 4.33013i) q^{37} +(6.12372 - 10.6066i) q^{41} +(5.50000 + 9.52628i) q^{43} +(1.22474 - 2.12132i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-7.34847 - 4.24264i) q^{53} +10.3923i q^{55} +(2.44949 + 4.24264i) q^{59} +(3.00000 + 1.73205i) q^{61} +(3.67423 + 2.12132i) q^{65} +(3.50000 + 6.06218i) q^{67} -12.7279i q^{71} +(13.5000 + 7.79423i) q^{73} +(3.67423 + 10.6066i) q^{77} +(-5.50000 + 9.52628i) q^{79} +(6.12372 + 10.6066i) q^{83} +(6.00000 - 10.3923i) q^{85} +(7.34847 + 12.7279i) q^{89} +(4.50000 + 0.866025i) q^{91} +(-11.0227 + 6.36396i) q^{95} +(3.00000 - 1.73205i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 10 q^{7} - 6 q^{13} + 18 q^{19} + 4 q^{25} + 6 q^{31} + 10 q^{37} + 22 q^{43} + 22 q^{49} + 12 q^{61} + 14 q^{67} + 54 q^{73} - 22 q^{79} + 24 q^{85} + 18 q^{91} + 12 q^{97}+O(q^{100}) $ 4 * q - 10 * q^7 - 6 * q^13 + 18 * q^19 + 4 * q^25 + 6 * q^31 + 10 * q^37 + 22 * q^43 + 22 * q^49 + 12 * q^61 + 14 * q^67 + 54 * q^73 - 22 * q^79 + 24 * q^85 + 18 * q^91 + 12 * q^97

Character values

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

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$5$	−2.44949			−1.09545			−0.547723	−	0.836660i	$-0.684505\pi$
$5$	−2.44949			−1.09545			−0.547723	+	0.836660i	$0.684505\pi$
$6$		0			0
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	4.24264i		−	1.27920i	−0.768706	−	0.639602i	$-0.779099\pi$
$11$		−	4.24264i		−	1.27920i	0.768706	−	0.639602i	$-0.220901\pi$
$12$		0			0
$13$	−1.50000	−	0.866025i	−0.416025	−	0.240192i	0.277350	−	0.960769i	$-0.410544\pi$
$13$	−1.50000	−	0.866025i	−0.416025	−	0.240192i	−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.44949	+	4.24264i	−0.594089	+	1.02899i	0.399586	+	0.916696i	$0.369154\pi$
$17$	−2.44949	+	4.24264i	−0.594089	+	1.02899i	−0.993675	+	0.112296i	$0.964180\pi$
$18$		0			0
$19$	4.50000	−	2.59808i	1.03237	−	0.596040i	0.114708	−	0.993399i	$-0.463407\pi$
$19$	4.50000	−	2.59808i	1.03237	−	0.596040i	0.917663	+	0.397360i	$0.130073\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−7.34847	+	4.24264i	−1.36458	+	0.787839i	−0.990229	−	0.139450i	$-0.955467\pi$
$29$	−7.34847	+	4.24264i	−1.36458	+	0.787839i	−0.374347	+	0.927289i	$0.622133\pi$
$30$		0			0
$31$	1.50000	−	0.866025i	0.269408	−	0.155543i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	1.50000	−	0.866025i	0.269408	−	0.155543i	0.628619	+	0.777714i	$0.283621\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	6.12372	−	2.12132i	1.03510	−	0.358569i
$36$		0			0
$37$	2.50000	+	4.33013i	0.410997	+	0.711868i	0.994999	−	0.0998840i	$-0.0318472\pi$
$37$	2.50000	+	4.33013i	0.410997	+	0.711868i	−0.584002	+	0.811752i	$0.698514\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	6.12372	−	10.6066i	0.956365	−	1.65647i	0.225152	−	0.974324i	$-0.427712\pi$
$41$	6.12372	−	10.6066i	0.956365	−	1.65647i	0.731213	−	0.682149i	$-0.238955\pi$
$42$		0			0
$43$	5.50000	+	9.52628i	0.838742	+	1.45274i	0.890947	+	0.454108i	$0.150042\pi$
$43$	5.50000	+	9.52628i	0.838742	+	1.45274i	−0.0522047	+	0.998636i	$0.516625\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.22474	−	2.12132i	0.178647	−	0.309426i	−0.762770	−	0.646670i	$-0.776161\pi$
$47$	1.22474	−	2.12132i	0.178647	−	0.309426i	0.941417	+	0.337243i	$0.109495\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−7.34847	−	4.24264i	−1.00939	−	0.582772i	−0.0983769	−	0.995149i	$-0.531365\pi$
$53$	−7.34847	−	4.24264i	−1.00939	−	0.582772i	−0.911013	+	0.412378i	$0.864698\pi$
$54$		0			0
$55$			10.3923i			1.40130i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.44949	+	4.24264i	0.318896	+	0.552345i	0.980258	−	0.197722i	$-0.0633545\pi$
$59$	2.44949	+	4.24264i	0.318896	+	0.552345i	−0.661362	+	0.750067i	$0.730021\pi$
$60$		0			0
$61$	3.00000	+	1.73205i	0.384111	+	0.221766i	0.679605	−	0.733578i	$-0.262151\pi$
$61$	3.00000	+	1.73205i	0.384111	+	0.221766i	−0.295495	+	0.955344i	$0.595484\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.67423	+	2.12132i	0.455733	+	0.263117i
$66$		0			0
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	0.996659	−	0.0816792i	$-0.0260283\pi$
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	−0.569066	+	0.822292i	$0.692695\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	12.7279i		−	1.51053i	−0.655422	−	0.755263i	$-0.727509\pi$
$71$		−	12.7279i		−	1.51053i	0.655422	−	0.755263i	$-0.272491\pi$
$72$		0			0
$73$	13.5000	+	7.79423i	1.58006	+	0.912245i	0.994850	+	0.101361i	$0.0323196\pi$
$73$	13.5000	+	7.79423i	1.58006	+	0.912245i	0.585206	+	0.810885i	$0.301014\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.67423	+	10.6066i	0.418718	+	1.20873i
$78$		0			0
$79$	−5.50000	+	9.52628i	−0.618798	+	1.07179i	0.370907	+	0.928670i	$0.379047\pi$
$79$	−5.50000	+	9.52628i	−0.618798	+	1.07179i	−0.989705	+	0.143120i	$0.954286\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.12372	+	10.6066i	0.672166	+	1.16423i	0.977289	+	0.211913i	$0.0679692\pi$
$83$	6.12372	+	10.6066i	0.672166	+	1.16423i	−0.305123	+	0.952313i	$0.598697\pi$
$84$		0			0
$85$	6.00000	−	10.3923i	0.650791	−	1.12720i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.34847	+	12.7279i	0.778936	+	1.34916i	0.932555	+	0.361027i	$0.117574\pi$
$89$	7.34847	+	12.7279i	0.778936	+	1.34916i	−0.153619	+	0.988130i	$0.549093\pi$
$90$		0			0
$91$	4.50000	+	0.866025i	0.471728	+	0.0907841i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−11.0227	+	6.36396i	−1.13091	+	0.652929i
$96$		0			0
$97$	3.00000	−	1.73205i	0.304604	−	0.175863i	−0.339905	−	0.940460i	$-0.610395\pi$
$97$	3.00000	−	1.73205i	0.304604	−	0.175863i	0.644509	+	0.764597i	$0.277062\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.34847			0.731200			0.365600	−	0.930772i	$-0.380864\pi$
$101$	7.34847			0.731200			0.365600	+	0.930772i	$0.380864\pi$
$102$		0			0
$103$			8.66025i			0.853320i	0.904412	+	0.426660i	$0.140310\pi$
$103$			8.66025i			0.853320i	−0.904412	+	0.426660i	$0.859690\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.34847	+	4.24264i	−0.710403	+	0.410152i	−0.811210	−	0.584754i	$-0.801191\pi$
$107$	−7.34847	+	4.24264i	−0.710403	+	0.410152i	0.100807	+	0.994906i	$0.467858\pi$
$108$		0			0
$109$	2.50000	−	4.33013i	0.239457	−	0.414751i	−0.721102	−	0.692829i	$-0.756364\pi$
$109$	2.50000	−	4.33013i	0.239457	−	0.414751i	0.960558	+	0.278078i	$0.0896974\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.67423	−	2.12132i	−0.345643	−	0.199557i	0.317122	−	0.948385i	$-0.397284\pi$
$113$	−3.67423	−	2.12132i	−0.345643	−	0.199557i	−0.662765	+	0.748828i	$0.730617\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.44949	−	12.7279i	0.224544	−	1.16677i
$120$		0			0
$121$	−7.00000			−0.636364
$122$		0			0
$123$		0			0
$124$		0			0
$125$	9.79796			0.876356
$126$		0			0
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.34847			−0.642039			−0.321019	−	0.947073i	$-0.604025\pi$
$131$	−7.34847			−0.642039			−0.321019	+	0.947073i	$0.604025\pi$
$132$		0			0
$133$	−9.00000	+	10.3923i	−0.780399	+	0.901127i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$		0			0
$139$	1.50000	+	0.866025i	0.127228	+	0.0734553i	0.562263	−	0.826958i	$-0.309931\pi$
$139$	1.50000	+	0.866025i	0.127228	+	0.0734553i	−0.435035	+	0.900414i	$0.643264\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.67423	+	6.36396i	−0.307255	+	0.532181i
$144$		0			0
$145$	18.0000	−	10.3923i	1.49482	−	0.863034i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			16.9706i			1.39028i	0.718873	+	0.695141i	$0.244658\pi$
$149$			16.9706i			1.39028i	−0.718873	+	0.695141i	$0.755342\pi$
$150$		0			0
$151$	−2.00000			−0.162758			−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000			−0.162758			−0.0813788	+	0.996683i	$0.525932\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.67423	+	2.12132i	−0.295122	+	0.170389i
$156$		0			0
$157$	9.00000	−	5.19615i	0.718278	−	0.414698i	−0.0958404	−	0.995397i	$-0.530554\pi$
$157$	9.00000	−	5.19615i	0.718278	−	0.414698i	0.814119	+	0.580699i	$0.197221\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	11.0000	+	19.0526i	0.861586	+	1.49231i	0.870397	+	0.492350i	$0.163862\pi$
$163$	11.0000	+	19.0526i	0.861586	+	1.49231i	−0.00881059	+	0.999961i	$0.502805\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.57321	−	14.8492i	0.663415	−	1.14907i	−0.316297	−	0.948660i	$-0.602440\pi$
$167$	8.57321	−	14.8492i	0.663415	−	1.14907i	0.979712	−	0.200409i	$-0.0642270\pi$
$168$		0			0
$169$	−5.00000	−	8.66025i	−0.384615	−	0.666173i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$		0			0
$175$	−2.50000	+	0.866025i	−0.188982	+	0.0654654i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	11.0227	+	6.36396i	0.823876	+	0.475665i	0.851751	−	0.523947i	$-0.175541\pi$
$179$	11.0227	+	6.36396i	0.823876	+	0.475665i	−0.0278755	+	0.999611i	$0.508874\pi$
$180$		0			0
$181$		−	5.19615i		−	0.386227i	−0.981176	−	0.193113i	$-0.938141\pi$
$181$		−	5.19615i		−	0.386227i	0.981176	−	0.193113i	$-0.0618586\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.12372	−	10.6066i	−0.450225	−	0.779813i
$186$		0			0
$187$	18.0000	+	10.3923i	1.31629	+	0.759961i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.67423	+	2.12132i	0.265858	+	0.153493i	0.627004	−	0.779016i	$-0.284281\pi$
$191$	3.67423	+	2.12132i	0.265858	+	0.153493i	−0.361146	+	0.932509i	$0.617614\pi$
$192$		0			0
$193$	−9.50000	−	16.4545i	−0.683825	−	1.18442i	−0.973805	−	0.227387i	$-0.926982\pi$
$193$	−9.50000	−	16.4545i	−0.683825	−	1.18442i	0.289980	−	0.957033i	$-0.406351\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	8.48528i		−	0.604551i	−0.953221	−	0.302276i	$-0.902254\pi$
$197$		−	8.48528i		−	0.604551i	0.953221	−	0.302276i	$-0.0977463\pi$
$198$		0			0
$199$	−12.0000	−	6.92820i	−0.850657	−	0.491127i	0.0102152	−	0.999948i	$-0.496748\pi$
$199$	−12.0000	−	6.92820i	−0.850657	−	0.491127i	−0.860873	+	0.508821i	$0.830082\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	14.6969	−	16.9706i	1.03152	−	1.19110i
$204$		0			0
$205$	−15.0000	+	25.9808i	−1.04765	+	1.81458i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−11.0227	−	19.0919i	−0.762456	−	1.32061i
$210$		0			0
$211$	1.00000	−	1.73205i	0.0688428	−	0.119239i	−0.829549	−	0.558433i	$-0.811403\pi$
$211$	1.00000	−	1.73205i	0.0688428	−	0.119239i	0.898392	+	0.439194i	$0.144736\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−13.4722	−	23.3345i	−0.918796	−	1.59140i
$216$		0			0
$217$	−3.00000	+	3.46410i	−0.203653	+	0.235159i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.34847	−	4.24264i	0.494312	−	0.285391i
$222$		0			0
$223$	18.0000	−	10.3923i	1.20537	−	0.695920i	0.243625	−	0.969870i	$-0.421663\pi$
$223$	18.0000	−	10.3923i	1.20537	−	0.695920i	0.961744	+	0.273949i	$0.0883300\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−22.0454			−1.46321			−0.731603	−	0.681731i	$-0.761227\pi$
$227$	−22.0454			−1.46321			−0.731603	+	0.681731i	$0.761227\pi$
$228$		0			0
$229$			1.73205i			0.114457i	0.998361	+	0.0572286i	$0.0182264\pi$
$229$			1.73205i			0.114457i	−0.998361	+	0.0572286i	$0.981774\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.67423	+	2.12132i	−0.240707	+	0.138972i	−0.615502	−	0.788136i	$-0.711047\pi$
$233$	−3.67423	+	2.12132i	−0.240707	+	0.138972i	0.374795	+	0.927108i	$0.377713\pi$
$234$		0			0
$235$	−3.00000	+	5.19615i	−0.195698	+	0.338960i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−3.67423	−	2.12132i	−0.237666	−	0.137217i	0.376437	−	0.926442i	$-0.377149\pi$
$239$	−3.67423	−	2.12132i	−0.237666	−	0.137217i	−0.614104	+	0.789225i	$0.710482\pi$
$240$		0			0
$241$		−	13.8564i		−	0.892570i	−0.894891	−	0.446285i	$-0.852747\pi$
$241$		−	13.8564i		−	0.892570i	0.894891	−	0.446285i	$-0.147253\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−13.4722	+	10.6066i	−0.860707	+	0.677631i
$246$		0			0
$247$	−9.00000			−0.572656
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−9.79796			−0.618442			−0.309221	−	0.950990i	$-0.600068\pi$
$251$	−9.79796			−0.618442			−0.309221	+	0.950990i	$0.600068\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.34847			0.458385			0.229192	−	0.973381i	$-0.426391\pi$
$257$	7.34847			0.458385			0.229192	+	0.973381i	$0.426391\pi$
$258$		0			0
$259$	−10.0000	−	8.66025i	−0.621370	−	0.538122i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			25.4558i			1.56967i	0.619702	+	0.784837i	$0.287254\pi$
$263$			25.4558i			1.56967i	−0.619702	+	0.784837i	$0.712746\pi$
$264$		0			0
$265$	18.0000	+	10.3923i	1.10573	+	0.638394i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	6.12372	−	10.6066i	0.373370	−	0.646696i	−0.616712	−	0.787189i	$-0.711536\pi$
$269$	6.12372	−	10.6066i	0.373370	−	0.646696i	0.990082	+	0.140493i	$0.0448688\pi$
$270$		0			0
$271$	−24.0000	+	13.8564i	−1.45790	+	0.841717i	−0.998908	−	0.0467255i	$-0.985121\pi$
$271$	−24.0000	+	13.8564i	−1.45790	+	0.841717i	−0.458988	+	0.888442i	$0.651788\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	4.24264i		−	0.255841i
$276$		0			0
$277$	11.0000			0.660926			0.330463	−	0.943819i	$-0.392795\pi$
$277$	11.0000			0.660926			0.330463	+	0.943819i	$0.392795\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	14.6969	−	8.48528i	0.876746	−	0.506189i	0.00716177	−	0.999974i	$-0.497720\pi$
$281$	14.6969	−	8.48528i	0.876746	−	0.506189i	0.869584	+	0.493785i	$0.164387\pi$
$282$		0			0
$283$	7.50000	−	4.33013i	0.445829	−	0.257399i	−0.260238	−	0.965544i	$-0.583801\pi$
$283$	7.50000	−	4.33013i	0.445829	−	0.257399i	0.706067	+	0.708145i	$0.250468\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.12372	+	31.8198i	−0.361472	+	1.87826i
$288$		0			0
$289$	−3.50000	−	6.06218i	−0.205882	−	0.356599i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−12.2474	+	21.2132i	−0.715504	+	1.23929i	0.247261	+	0.968949i	$0.420469\pi$
$293$	−12.2474	+	21.2132i	−0.715504	+	1.23929i	−0.962765	+	0.270340i	$0.912864\pi$
$294$		0			0
$295$	−6.00000	−	10.3923i	−0.349334	−	0.605063i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−22.0000	−	19.0526i	−1.26806	−	1.09817i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−7.34847	−	4.24264i	−0.420772	−	0.242933i
$306$		0			0
$307$		−	19.0526i		−	1.08739i	−0.839284	−	0.543693i	$-0.817025\pi$
$307$		−	19.0526i		−	1.08739i	0.839284	−	0.543693i	$-0.182975\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.57321	+	14.8492i	0.486142	+	0.842023i	0.999873	−	0.0159282i	$-0.00507031\pi$
$311$	8.57321	+	14.8492i	0.486142	+	0.842023i	−0.513731	+	0.857951i	$0.671737\pi$
$312$		0			0
$313$	13.5000	+	7.79423i	0.763065	+	0.440556i	0.830395	−	0.557175i	$-0.188115\pi$
$313$	13.5000	+	7.79423i	0.763065	+	0.440556i	−0.0673300	+	0.997731i	$0.521448\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.34847	−	4.24264i	−0.412731	−	0.238290i	0.279231	−	0.960224i	$-0.409920\pi$
$317$	−7.34847	−	4.24264i	−0.412731	−	0.238290i	−0.691963	+	0.721933i	$0.743254\pi$
$318$		0			0
$319$	18.0000	+	31.1769i	1.00781	+	1.74557i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			25.4558i			1.41640i
$324$		0			0
$325$	−1.50000	−	0.866025i	−0.0832050	−	0.0480384i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.22474	+	6.36396i	−0.0675224	+	0.350857i
$330$		0			0
$331$	2.50000	−	4.33013i	0.137412	−	0.238005i	−0.789104	−	0.614260i	$-0.789455\pi$
$331$	2.50000	−	4.33013i	0.137412	−	0.238005i	0.926516	+	0.376254i	$0.122788\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−8.57321	−	14.8492i	−0.468405	−	0.811301i
$336$		0			0
$337$	−3.50000	+	6.06218i	−0.190657	+	0.330228i	−0.945468	−	0.325714i	$-0.894395\pi$
$337$	−3.50000	+	6.06218i	−0.190657	+	0.330228i	0.754811	+	0.655942i	$0.227729\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−3.67423	−	6.36396i	−0.198971	−	0.344628i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.34847	+	4.24264i	−0.394486	+	0.227757i	−0.684102	−	0.729386i	$-0.739806\pi$
$347$	−7.34847	+	4.24264i	−0.394486	+	0.227757i	0.289616	+	0.957143i	$0.406472\pi$
$348$		0			0
$349$	−21.0000	+	12.1244i	−1.12410	+	0.649002i	−0.942446	−	0.334360i	$-0.891480\pi$
$349$	−21.0000	+	12.1244i	−1.12410	+	0.649002i	−0.181659	+	0.983362i	$0.558147\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	26.9444			1.43411			0.717053	−	0.697019i	$-0.245491\pi$
$353$	26.9444			1.43411			0.717053	+	0.697019i	$0.245491\pi$
$354$		0			0
$355$			31.1769i			1.65470i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	14.6969	−	8.48528i	0.775675	−	0.447836i	−0.0592205	−	0.998245i	$-0.518862\pi$
$359$	14.6969	−	8.48528i	0.775675	−	0.447836i	0.834895	+	0.550409i	$0.185528\pi$
$360$		0			0
$361$	4.00000	−	6.92820i	0.210526	−	0.364642i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−33.0681	−	19.0919i	−1.73086	−	0.999315i
$366$		0			0
$367$		−	25.9808i		−	1.35618i	−0.734977	−	0.678092i	$-0.762807\pi$
$367$		−	25.9808i		−	1.35618i	0.734977	−	0.678092i	$-0.237193\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	22.0454	+	4.24264i	1.14454	+	0.220267i
$372$		0			0
$373$	−7.00000			−0.362446			−0.181223	−	0.983442i	$-0.558006\pi$
$373$	−7.00000			−0.362446			−0.181223	+	0.983442i	$0.558006\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	14.6969			0.756931
$378$		0			0
$379$	−5.00000			−0.256833			−0.128416	−	0.991720i	$-0.540989\pi$
$379$	−5.00000			−0.256833			−0.128416	+	0.991720i	$0.540989\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.79796			0.500652			0.250326	−	0.968162i	$-0.419462\pi$
$383$	9.79796			0.500652			0.250326	+	0.968162i	$0.419462\pi$
$384$		0			0
$385$	−9.00000	−	25.9808i	−0.458682	−	1.32410i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	4.24264i		−	0.215110i	−0.994199	−	0.107555i	$-0.965698\pi$
$389$		−	4.24264i		−	0.215110i	0.994199	−	0.107555i	$-0.0343022\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$	13.4722	−	23.3345i	0.677860	−	1.17409i
$396$		0			0
$397$	7.50000	−	4.33013i	0.376414	−	0.217323i	−0.299843	−	0.953989i	$-0.596934\pi$
$397$	7.50000	−	4.33013i	0.376414	−	0.217323i	0.676257	+	0.736666i	$0.263601\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	8.48528i		−	0.423735i	−0.977298	−	0.211867i	$-0.932046\pi$
$401$		−	8.48528i		−	0.423735i	0.977298	−	0.211867i	$-0.0679545\pi$
$402$		0			0
$403$	−3.00000			−0.149441
$404$		0			0
$405$		0			0
$406$		0			0
$407$	18.3712	−	10.6066i	0.910625	−	0.525750i
$408$		0			0
$409$	7.50000	−	4.33013i	0.370851	−	0.214111i	−0.302979	−	0.952997i	$-0.597981\pi$
$409$	7.50000	−	4.33013i	0.370851	−	0.214111i	0.673830	+	0.738886i	$0.264648\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−9.79796	−	8.48528i	−0.482126	−	0.417533i
$414$		0			0
$415$	−15.0000	−	25.9808i	−0.736321	−	1.27535i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−13.4722	+	23.3345i	−0.658160	+	1.13997i	0.322932	+	0.946422i	$0.395332\pi$
$419$	−13.4722	+	23.3345i	−0.658160	+	1.13997i	−0.981092	+	0.193544i	$0.938002\pi$
$420$		0			0
$421$	−17.5000	−	30.3109i	−0.852898	−	1.47726i	−0.878582	−	0.477592i	$-0.841510\pi$
$421$	−17.5000	−	30.3109i	−0.852898	−	1.47726i	0.0256838	−	0.999670i	$-0.491824\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.44949	+	4.24264i	−0.118818	+	0.205798i
$426$		0			0
$427$	−9.00000	−	1.73205i	−0.435541	−	0.0838198i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	18.3712	+	10.6066i	0.884908	+	0.510902i	0.872274	−	0.489018i	$-0.162645\pi$
$431$	18.3712	+	10.6066i	0.884908	+	0.510902i	0.0126347	+	0.999920i	$0.495978\pi$
$432$		0			0
$433$		−	12.1244i		−	0.582659i	−0.956623	−	0.291330i	$-0.905902\pi$
$433$		−	12.1244i		−	0.582659i	0.956623	−	0.291330i	$-0.0940977\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	36.0000	+	20.7846i	1.71819	+	0.991995i	0.922231	+	0.386640i	$0.126365\pi$
$439$	36.0000	+	20.7846i	1.71819	+	0.991995i	0.795956	+	0.605355i	$0.206969\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$443$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$444$		0			0
$445$	−18.0000	−	31.1769i	−0.853282	−	1.47793i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			12.7279i			0.600668i	0.953834	+	0.300334i	$0.0970981\pi$
$449$			12.7279i			0.600668i	−0.953834	+	0.300334i	$0.902902\pi$
$450$		0			0
$451$	−45.0000	−	25.9808i	−2.11897	−	1.22339i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−11.0227	−	2.12132i	−0.516752	−	0.0994490i
$456$		0			0
$457$	−6.50000	+	11.2583i	−0.304057	+	0.526642i	−0.977051	−	0.213006i	$-0.931675\pi$
$457$	−6.50000	+	11.2583i	−0.304057	+	0.526642i	0.672994	+	0.739648i	$0.265008\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.44949	+	4.24264i	0.114084	+	0.197599i	0.917413	−	0.397936i	$-0.130273\pi$
$461$	2.44949	+	4.24264i	0.114084	+	0.197599i	−0.803329	+	0.595535i	$0.796940\pi$
$462$		0			0
$463$	−14.5000	+	25.1147i	−0.673872	+	1.16718i	0.302925	+	0.953014i	$0.402037\pi$
$463$	−14.5000	+	25.1147i	−0.673872	+	1.16718i	−0.976797	+	0.214166i	$0.931297\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.67423	+	6.36396i	0.170023	+	0.294489i	0.938428	−	0.345476i	$-0.112282\pi$
$467$	3.67423	+	6.36396i	0.170023	+	0.294489i	−0.768404	+	0.639965i	$0.778949\pi$
$468$		0			0
$469$	−14.0000	−	12.1244i	−0.646460	−	0.559851i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	40.4166	−	23.3345i	1.85836	−	1.07292i
$474$		0			0
$475$	4.50000	−	2.59808i	0.206474	−	0.119208i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−4.89898			−0.223840			−0.111920	−	0.993717i	$-0.535700\pi$
$479$	−4.89898			−0.223840			−0.111920	+	0.993717i	$0.535700\pi$
$480$		0			0
$481$		−	8.66025i		−	0.394874i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−7.34847	+	4.24264i	−0.333677	+	0.192648i
$486$		0			0
$487$	−3.50000	+	6.06218i	−0.158600	+	0.274703i	−0.934364	−	0.356320i	$-0.884031\pi$
$487$	−3.50000	+	6.06218i	−0.158600	+	0.274703i	0.775764	+	0.631023i	$0.217365\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	29.3939	+	16.9706i	1.32653	+	0.765871i	0.984761	−	0.173914i	$-0.0556415\pi$
$491$	29.3939	+	16.9706i	1.32653	+	0.765871i	0.341766	+	0.939785i	$0.388975\pi$
$492$		0			0
$493$		−	41.5692i		−	1.87218i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	11.0227	+	31.8198i	0.494436	+	1.42731i
$498$		0			0
$499$	−35.0000			−1.56682			−0.783408	−	0.621508i	$-0.786520\pi$
$499$	−35.0000			−1.56682			−0.783408	+	0.621508i	$0.786520\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	2.44949			0.109217			0.0546087	−	0.998508i	$-0.482609\pi$
$503$	2.44949			0.109217			0.0546087	+	0.998508i	$0.482609\pi$
$504$		0			0
$505$	−18.0000			−0.800989
$506$		0			0
$507$		0			0
$508$		0			0
$509$	17.1464			0.760002			0.380001	−	0.924986i	$-0.375924\pi$
$509$	17.1464			0.760002			0.380001	+	0.924986i	$0.375924\pi$
$510$		0			0
$511$	−40.5000	−	7.79423i	−1.79161	−	0.344796i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	21.2132i		−	0.934765i
$516$		0			0
$517$	−9.00000	−	5.19615i	−0.395820	−	0.228527i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2.44949	−	4.24264i	0.107314	−	0.185873i	−0.807367	−	0.590049i	$-0.799108\pi$
$521$	2.44949	−	4.24264i	0.107314	−	0.185873i	0.914681	+	0.404176i	$0.132442\pi$
$522$		0			0
$523$	−7.50000	+	4.33013i	−0.327952	+	0.189343i	−0.654932	−	0.755688i	$-0.727303\pi$
$523$	−7.50000	+	4.33013i	−0.327952	+	0.189343i	0.326979	+	0.945031i	$0.393969\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			8.48528i			0.369625i
$528$		0			0
$529$	23.0000			1.00000
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−18.3712	+	10.6066i	−0.795744	+	0.459423i
$534$		0			0
$535$	18.0000	−	10.3923i	0.778208	−	0.449299i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−18.3712	−	23.3345i	−0.791302	−	1.00509i
$540$		0			0
$541$	9.50000	+	16.4545i	0.408437	+	0.707433i	0.994715	−	0.102677i	$-0.0327407\pi$
$541$	9.50000	+	16.4545i	0.408437	+	0.707433i	−0.586278	+	0.810110i	$0.699407\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−6.12372	+	10.6066i	−0.262312	+	0.454337i
$546$		0			0
$547$	−1.00000	−	1.73205i	−0.0427569	−	0.0740571i	0.843855	−	0.536571i	$-0.180281\pi$
$547$	−1.00000	−	1.73205i	−0.0427569	−	0.0740571i	−0.886612	+	0.462514i	$0.846947\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−22.0454	+	38.1838i	−0.939166	+	1.62668i
$552$		0			0
$553$	5.50000	−	28.5788i	0.233884	−	1.21530i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−18.3712	−	10.6066i	−0.778412	−	0.449416i	0.0574555	−	0.998348i	$-0.481701\pi$
$557$	−18.3712	−	10.6066i	−0.778412	−	0.449416i	−0.835867	+	0.548932i	$0.815035\pi$
$558$		0			0
$559$		−	19.0526i		−	0.805837i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−3.67423	−	6.36396i	−0.154851	−	0.268209i	0.778154	−	0.628073i	$-0.216156\pi$
$563$	−3.67423	−	6.36396i	−0.154851	−	0.268209i	−0.933005	+	0.359864i	$0.882823\pi$
$564$		0			0
$565$	9.00000	+	5.19615i	0.378633	+	0.218604i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−18.3712	−	10.6066i	−0.770160	−	0.444652i	0.0627719	−	0.998028i	$-0.480006\pi$
$569$	−18.3712	−	10.6066i	−0.770160	−	0.444652i	−0.832932	+	0.553376i	$0.813339\pi$
$570$		0			0
$571$	3.50000	+	6.06218i	0.146470	+	0.253694i	0.929921	−	0.367760i	$-0.119875\pi$
$571$	3.50000	+	6.06218i	0.146470	+	0.253694i	−0.783450	+	0.621455i	$0.786542\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−34.5000	−	19.9186i	−1.43625	−	0.829222i	−0.438667	−	0.898650i	$-0.644549\pi$
$577$	−34.5000	−	19.9186i	−1.43625	−	0.829222i	−0.997587	+	0.0694283i	$0.977883\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−24.4949	−	21.2132i	−1.01622	−	0.880072i
$582$		0			0
$583$	−18.0000	+	31.1769i	−0.745484	+	1.29122i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	7.34847	+	12.7279i	0.303304	+	0.525338i	0.976882	−	0.213778i	$-0.0685770\pi$
$587$	7.34847	+	12.7279i	0.303304	+	0.525338i	−0.673578	+	0.739116i	$0.735244\pi$
$588$		0			0
$589$	4.50000	−	7.79423i	0.185419	−	0.321156i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.22474	−	2.12132i	−0.0502942	−	0.0871122i	0.839782	−	0.542923i	$-0.182683\pi$
$593$	−1.22474	−	2.12132i	−0.0502942	−	0.0871122i	−0.890077	+	0.455811i	$0.849349\pi$
$594$		0			0
$595$	−6.00000	+	31.1769i	−0.245976	+	1.27813i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−14.6969	+	8.48528i	−0.600501	+	0.346699i	−0.769238	−	0.638962i	$-0.779364\pi$
$599$	−14.6969	+	8.48528i	−0.600501	+	0.346699i	0.168738	+	0.985661i	$0.446031\pi$
$600$		0			0
$601$	37.5000	−	21.6506i	1.52966	−	0.883148i	0.530281	−	0.847822i	$-0.322086\pi$
$601$	37.5000	−	21.6506i	1.52966	−	0.883148i	0.999376	−	0.0353259i	$-0.0112469\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	17.1464			0.697101
$606$		0			0
$607$			25.9808i			1.05453i	0.849702	+	0.527263i	$0.176782\pi$
$607$			25.9808i			1.05453i	−0.849702	+	0.527263i	$0.823218\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3.67423	+	2.12132i	−0.148644	+	0.0858194i
$612$		0			0
$613$	−4.00000	+	6.92820i	−0.161558	+	0.279827i	−0.935428	−	0.353518i	$-0.884985\pi$
$613$	−4.00000	+	6.92820i	−0.161558	+	0.279827i	0.773869	+	0.633345i	$0.218319\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	18.3712	+	10.6066i	0.739596	+	0.427006i	0.821922	−	0.569600i	$-0.192902\pi$
$617$	18.3712	+	10.6066i	0.739596	+	0.427006i	−0.0823267	+	0.996605i	$0.526235\pi$
$618$		0			0
$619$		−	8.66025i		−	0.348085i	−0.984738	−	0.174042i	$-0.944317\pi$
$619$		−	8.66025i		−	0.348085i	0.984738	−	0.174042i	$-0.0556830\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−29.3939	−	25.4558i	−1.17764	−	1.01987i
$624$		0			0
$625$	−29.0000			−1.16000
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−24.4949			−0.976676
$630$		0			0
$631$	−22.0000			−0.875806			−0.437903	−	0.899022i	$-0.644279\pi$
$631$	−22.0000			−0.875806			−0.437903	+	0.899022i	$0.644279\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−12.2474			−0.486025
$636$		0			0
$637$	−12.0000	+	1.73205i	−0.475457	+	0.0686264i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	8.48528i		−	0.335148i	−0.985859	−	0.167574i	$-0.946407\pi$
$641$		−	8.48528i		−	0.335148i	0.985859	−	0.167574i	$-0.0535934\pi$
$642$		0			0
$643$	28.5000	+	16.4545i	1.12393	+	0.648901i	0.942401	−	0.334484i	$-0.108562\pi$
$643$	28.5000	+	16.4545i	1.12393	+	0.648901i	0.181529	+	0.983386i	$0.441895\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−11.0227	+	19.0919i	−0.433347	+	0.750579i	−0.997159	−	0.0753238i	$-0.976001\pi$
$647$	−11.0227	+	19.0919i	−0.433347	+	0.750579i	0.563812	+	0.825903i	$0.309334\pi$
$648$		0			0
$649$	18.0000	−	10.3923i	0.706562	−	0.407934i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	21.2132i		−	0.830137i	−0.909790	−	0.415068i	$-0.863758\pi$
$653$		−	21.2132i		−	0.830137i	0.909790	−	0.415068i	$-0.136242\pi$
$654$		0			0
$655$	18.0000			0.703318
$656$		0			0
$657$		0			0
$658$		0			0
$659$	14.6969	−	8.48528i	0.572511	−	0.330540i	−0.185640	−	0.982618i	$-0.559436\pi$
$659$	14.6969	−	8.48528i	0.572511	−	0.330540i	0.758152	+	0.652078i	$0.226103\pi$
$660$		0			0
$661$	−4.50000	+	2.59808i	−0.175030	+	0.101053i	−0.584955	−	0.811065i	$-0.698888\pi$
$661$	−4.50000	+	2.59808i	−0.175030	+	0.101053i	0.409926	+	0.912119i	$0.365555\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	22.0454	−	25.4558i	0.854884	−	0.987135i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$	7.34847	−	12.7279i	0.283685	−	0.491356i
$672$		0			0
$673$	−9.50000	−	16.4545i	−0.366198	−	0.634274i	0.622770	−	0.782405i	$-0.286007\pi$
$673$	−9.50000	−	16.4545i	−0.366198	−	0.634274i	−0.988968	+	0.148132i	$0.952674\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	14.6969	−	25.4558i	0.564849	−	0.978348i	−0.432214	−	0.901771i	$-0.642268\pi$
$677$	14.6969	−	25.4558i	0.564849	−	0.978348i	0.997064	−	0.0765767i	$-0.0243990\pi$
$678$		0			0
$679$	−6.00000	+	6.92820i	−0.230259	+	0.265880i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−7.34847	−	4.24264i	−0.281181	−	0.162340i	0.352777	−	0.935708i	$-0.385238\pi$
$683$	−7.34847	−	4.24264i	−0.281181	−	0.162340i	−0.633958	+	0.773367i	$0.718571\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.34847	+	12.7279i	0.279954	+	0.484895i
$690$		0			0
$691$	−16.5000	−	9.52628i	−0.627690	−	0.362397i	0.152167	−	0.988355i	$-0.451375\pi$
$691$	−16.5000	−	9.52628i	−0.627690	−	0.362397i	−0.779857	+	0.625958i	$0.784708\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.67423	−	2.12132i	−0.139372	−	0.0804663i
$696$		0			0
$697$	30.0000	+	51.9615i	1.13633	+	1.96818i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			33.9411i			1.28194i	0.767567	+	0.640969i	$0.221467\pi$
$701$			33.9411i			1.28194i	−0.767567	+	0.640969i	$0.778533\pi$
$702$		0			0
$703$	22.5000	+	12.9904i	0.848604	+	0.489942i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−18.3712	+	6.36396i	−0.690919	+	0.239341i
$708$		0			0
$709$	−8.00000	+	13.8564i	−0.300446	+	0.520388i	−0.976237	−	0.216705i	$-0.930469\pi$
$709$	−8.00000	+	13.8564i	−0.300446	+	0.520388i	0.675791	+	0.737093i	$0.263802\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$	9.00000	−	15.5885i	0.336581	−	0.582975i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	13.4722	+	23.3345i	0.502428	+	0.870231i	0.999996	+	0.00280593i	$0.000893157\pi$
$719$	13.4722	+	23.3345i	0.502428	+	0.870231i	−0.497568	+	0.867425i	$0.665774\pi$
$720$		0			0
$721$	−7.50000	−	21.6506i	−0.279315	−	0.806312i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−7.34847	+	4.24264i	−0.272915	+	0.157568i
$726$		0			0
$727$	34.5000	−	19.9186i	1.27953	−	0.738739i	0.302772	−	0.953063i	$-0.402088\pi$
$727$	34.5000	−	19.9186i	1.27953	−	0.738739i	0.976763	+	0.214324i	$0.0687548\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−53.8888			−1.99315
$732$		0			0
$733$			8.66025i			0.319874i	0.987127	+	0.159937i	$0.0511291\pi$
$733$			8.66025i			0.319874i	−0.987127	+	0.159937i	$0.948871\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	25.7196	−	14.8492i	0.947395	−	0.546979i
$738$		0			0
$739$	9.50000	−	16.4545i	0.349463	−	0.605288i	−0.636691	−	0.771119i	$-0.719697\pi$
$739$	9.50000	−	16.4545i	0.349463	−	0.605288i	0.986154	+	0.165831i	$0.0530307\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	11.0227	+	6.36396i	0.404384	+	0.233471i	0.688374	−	0.725356i	$-0.258325\pi$
$743$	11.0227	+	6.36396i	0.404384	+	0.233471i	−0.283990	+	0.958827i	$0.591658\pi$
$744$		0			0
$745$		−	41.5692i		−	1.52298i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	14.6969	−	16.9706i	0.537014	−	0.620091i
$750$		0			0
$751$	−5.00000			−0.182453			−0.0912263	−	0.995830i	$-0.529079\pi$
$751$	−5.00000			−0.182453			−0.0912263	+	0.995830i	$0.529079\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	4.89898			0.178292
$756$		0			0
$757$	−14.0000			−0.508839			−0.254419	−	0.967094i	$-0.581884\pi$
$757$	−14.0000			−0.508839			−0.254419	+	0.967094i	$0.581884\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−34.2929			−1.24312			−0.621558	−	0.783369i	$-0.713500\pi$
$761$	−34.2929			−1.24312			−0.621558	+	0.783369i	$0.713500\pi$
$762$		0			0
$763$	−2.50000	+	12.9904i	−0.0905061	+	0.470283i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	8.48528i		−	0.306386i
$768$		0			0
$769$	13.5000	+	7.79423i	0.486822	+	0.281067i	0.723255	−	0.690581i	$-0.242645\pi$
$769$	13.5000	+	7.79423i	0.486822	+	0.281067i	−0.236433	+	0.971648i	$0.575978\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−20.8207	+	36.0624i	−0.748867	+	1.29708i	0.199499	+	0.979898i	$0.436069\pi$
$773$	−20.8207	+	36.0624i	−0.748867	+	1.29708i	−0.948366	+	0.317178i	$0.897265\pi$
$774$		0			0
$775$	1.50000	−	0.866025i	0.0538816	−	0.0311086i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	63.6396i		−	2.28013i
$780$		0			0
$781$	−54.0000			−1.93227
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−22.0454	+	12.7279i	−0.786834	+	0.454279i
$786$		0			0
$787$	−15.0000	+	8.66025i	−0.534692	+	0.308705i	−0.742925	−	0.669375i	$-0.766562\pi$
$787$	−15.0000	+	8.66025i	−0.534692	+	0.308705i	0.208233	+	0.978079i	$0.433229\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	11.0227	+	2.12132i	0.391922	+	0.0754255i
$792$		0			0
$793$	−3.00000	−	5.19615i	−0.106533	−	0.184521i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$797$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$798$		0			0
$799$	6.00000	+	10.3923i	0.212265	+	0.367653i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	33.0681	−	57.2756i	1.16695	−	2.02121i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	18.3712	+	10.6066i	0.645896	+	0.372908i	0.786882	−	0.617103i	$-0.211694\pi$
$809$	18.3712	+	10.6066i	0.645896	+	0.372908i	−0.140986	+	0.990012i	$0.545027\pi$
$810$		0			0
$811$			31.1769i			1.09477i	0.836881	+	0.547385i	$0.184377\pi$
$811$			31.1769i			1.09477i	−0.836881	+	0.547385i	$0.815623\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−26.9444	−	46.6690i	−0.943821	−	1.63475i
$816$		0			0
$817$	49.5000	+	28.5788i	1.73179	+	0.999847i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	18.3712	+	10.6066i	0.641158	+	0.370173i	0.785061	−	0.619419i	$-0.212632\pi$
$821$	18.3712	+	10.6066i	0.641158	+	0.370173i	−0.143902	+	0.989592i	$0.545965\pi$
$822$		0			0
$823$	−13.0000	−	22.5167i	−0.453152	−	0.784881i	0.545428	−	0.838157i	$-0.316367\pi$
$823$	−13.0000	−	22.5167i	−0.453152	−	0.784881i	−0.998580	+	0.0532760i	$0.983034\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	29.6985i		−	1.03272i	−0.856372	−	0.516359i	$-0.827287\pi$
$827$		−	29.6985i		−	1.03272i	0.856372	−	0.516359i	$-0.172713\pi$
$828$		0			0
$829$	31.5000	+	18.1865i	1.09404	+	0.631644i	0.934649	−	0.355571i	$-0.115714\pi$
$829$	31.5000	+	18.1865i	1.09404	+	0.631644i	0.159391	+	0.987216i	$0.449047\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	4.89898	+	33.9411i	0.169740	+	1.17599i
$834$		0			0
$835$	−21.0000	+	36.3731i	−0.726735	+	1.25874i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	26.9444	+	46.6690i	0.930224	+	1.61119i	0.782937	+	0.622101i	$0.213720\pi$
$839$	26.9444	+	46.6690i	0.930224	+	1.61119i	0.147286	+	0.989094i	$0.452946\pi$
$840$		0			0
$841$	21.5000	−	37.2391i	0.741379	−	1.28411i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	12.2474	+	21.2132i	0.421325	+	0.729756i
$846$		0			0
$847$	17.5000	−	6.06218i	0.601307	−	0.208299i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−22.5000	+	12.9904i	−0.770385	+	0.444782i	−0.833012	−	0.553255i	$-0.813386\pi$
$853$	−22.5000	+	12.9904i	−0.770385	+	0.444782i	0.0626267	+	0.998037i	$0.480052\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−39.1918			−1.33877			−0.669384	−	0.742917i	$-0.733442\pi$
$857$	−39.1918			−1.33877			−0.669384	+	0.742917i	$0.733442\pi$
$858$		0			0
$859$			45.0333i			1.53652i	0.640140	+	0.768259i	$0.278876\pi$
$859$			45.0333i			1.53652i	−0.640140	+	0.768259i	$0.721124\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	33.0681	−	19.0919i	1.12565	−	0.649895i	0.182814	−	0.983148i	$-0.441479\pi$
$863$	33.0681	−	19.0919i	1.12565	−	0.649895i	0.942838	+	0.333252i	$0.108146\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	40.4166	+	23.3345i	1.37104	+	0.791570i
$870$		0			0
$871$		−	12.1244i		−	0.410818i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−24.4949	+	8.48528i	−0.828079	+	0.286855i
$876$		0			0
$877$	−28.0000			−0.945493			−0.472746	−	0.881199i	$-0.656737\pi$
$877$	−28.0000			−0.945493			−0.472746	+	0.881199i	$0.656737\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−29.3939			−0.990305			−0.495152	−	0.868806i	$-0.664888\pi$
$881$	−29.3939			−0.990305			−0.495152	+	0.868806i	$0.664888\pi$
$882$		0			0
$883$	1.00000			0.0336527			0.0168263	−	0.999858i	$-0.494644\pi$
$883$	1.00000			0.0336527			0.0168263	+	0.999858i	$0.494644\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	56.3383			1.89165			0.945827	−	0.324671i	$-0.105254\pi$
$887$	56.3383			1.89165			0.945827	+	0.324671i	$0.105254\pi$
$888$		0			0
$889$	−12.5000	+	4.33013i	−0.419237	+	0.145228i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	12.7279i		−	0.425924i
$894$		0			0
$895$	−27.0000	−	15.5885i	−0.902510	−	0.521065i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−7.34847	+	12.7279i	−0.245085	+	0.424500i
$900$		0			0
$901$	36.0000	−	20.7846i	1.19933	−	0.692436i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			12.7279i			0.423090i
$906$		0			0
$907$	7.00000			0.232431			0.116216	−	0.993224i	$-0.462924\pi$
$907$	7.00000			0.232431			0.116216	+	0.993224i	$0.462924\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	7.34847	−	4.24264i	0.243466	−	0.140565i	−0.373303	−	0.927710i	$-0.621775\pi$
$911$	7.34847	−	4.24264i	0.243466	−	0.140565i	0.616769	+	0.787145i	$0.288441\pi$
$912$		0			0
$913$	45.0000	−	25.9808i	1.48928	−	0.859838i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	18.3712	−	6.36396i	0.606670	−	0.210157i
$918$		0			0
$919$	20.5000	+	35.5070i	0.676233	+	1.17127i	0.976107	+	0.217291i	$0.0697219\pi$
$919$	20.5000	+	35.5070i	0.676233	+	1.17127i	−0.299874	+	0.953979i	$0.596945\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−11.0227	+	19.0919i	−0.362817	+	0.628417i
$924$		0			0
$925$	2.50000	+	4.33013i	0.0821995	+	0.142374i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−13.4722	+	23.3345i	−0.442008	+	0.765581i	−0.997838	−	0.0657150i	$-0.979067\pi$
$929$	−13.4722	+	23.3345i	−0.442008	+	0.765581i	0.555830	+	0.831296i	$0.312401\pi$
$930$		0			0
$931$	13.5000	−	33.7750i	0.442445	−	1.10693i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−44.0908	−	25.4558i	−1.44192	−	0.832495i
$936$		0			0
$937$			19.0526i			0.622420i	0.950341	+	0.311210i	$0.100734\pi$
$937$			19.0526i			0.622420i	−0.950341	+	0.311210i	$0.899266\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	9.79796	+	16.9706i	0.319404	+	0.553225i	0.980364	−	0.197197i	$-0.0631839\pi$
$941$	9.79796	+	16.9706i	0.319404	+	0.553225i	−0.660960	+	0.750422i	$0.729851\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	47.7650	+	27.5772i	1.55216	+	0.896137i	0.997966	+	0.0637469i	$0.0203050\pi$
$947$	47.7650	+	27.5772i	1.55216	+	0.896137i	0.554189	+	0.832391i	$0.313028\pi$
$948$		0			0
$949$	−13.5000	−	23.3827i	−0.438229	−	0.759034i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	33.9411i		−	1.09946i	−0.835342	−	0.549730i	$-0.814730\pi$
$953$		−	33.9411i		−	1.09946i	0.835342	−	0.549730i	$-0.185270\pi$
$954$		0			0
$955$	−9.00000	−	5.19615i	−0.291233	−	0.168144i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−14.0000	+	24.2487i	−0.451613	+	0.782216i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	23.2702	+	40.3051i	0.749093	+	1.29747i
$966$		0			0
$967$	21.5000	−	37.2391i	0.691393	−	1.19753i	−0.279988	−	0.960003i	$-0.590331\pi$
$967$	21.5000	−	37.2391i	0.691393	−	1.19753i	0.971381	−	0.237525i	$-0.0763362\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−4.89898	−	8.48528i	−0.157216	−	0.272306i	0.776648	−	0.629935i	$-0.216918\pi$
$971$	−4.89898	−	8.48528i	−0.157216	−	0.272306i	−0.933864	+	0.357629i	$0.883585\pi$
$972$		0			0
$973$	−4.50000	−	0.866025i	−0.144263	−	0.0277635i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−33.0681	+	19.0919i	−1.05794	+	0.610803i	−0.924862	−	0.380302i	$-0.875820\pi$
$977$	−33.0681	+	19.0919i	−1.05794	+	0.610803i	−0.133080	+	0.991105i	$0.542487\pi$
$978$		0			0
$979$	54.0000	−	31.1769i	1.72585	−	0.996419i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	53.8888			1.71878			0.859392	−	0.511316i	$-0.170842\pi$
$983$	53.8888			1.71878			0.859392	+	0.511316i	$0.170842\pi$
$984$		0			0
$985$			20.7846i			0.662253i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−6.50000	+	11.2583i	−0.206479	+	0.357633i	−0.950603	−	0.310409i	$-0.899534\pi$
$991$	−6.50000	+	11.2583i	−0.206479	+	0.357633i	0.744124	+	0.668042i	$0.232867\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	29.3939	+	16.9706i	0.931849	+	0.538003i
$996$		0			0
$997$			50.2295i			1.59078i	0.606096	+	0.795392i	$0.292735\pi$
$997$			50.2295i			1.59078i	−0.606096	+	0.795392i	$0.707265\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.bm.g.1025.1		4
3.2	odd	2	inner	2268.2.bm.g.1025.2		4
7.5	odd	6		2268.2.w.h.1349.1		4
9.2	odd	6		2268.2.w.h.269.1		4
9.4	even	3		252.2.t.a.17.2	yes	4
9.5	odd	6		252.2.t.a.17.1	✓	4
9.7	even	3		2268.2.w.h.269.2		4
21.5	even	6		2268.2.w.h.1349.2		4
36.23	even	6		1008.2.bt.a.17.1		4
36.31	odd	6		1008.2.bt.a.17.2		4
45.4	even	6		6300.2.ch.a.4301.2		4
45.13	odd	12		6300.2.dd.a.4049.2		8
45.14	odd	6		6300.2.ch.a.4301.1		4
45.22	odd	12		6300.2.dd.a.4049.4		8
45.23	even	12		6300.2.dd.a.4049.1		8
45.32	even	12		6300.2.dd.a.4049.3		8
63.4	even	3		1764.2.f.a.881.1		4
63.5	even	6		252.2.t.a.89.2	yes	4
63.13	odd	6		1764.2.t.a.521.1		4
63.23	odd	6		1764.2.t.a.1097.1		4
63.31	odd	6		1764.2.f.a.881.3		4
63.32	odd	6		1764.2.f.a.881.4		4
63.40	odd	6		252.2.t.a.89.1	yes	4
63.41	even	6		1764.2.t.a.521.2		4
63.47	even	6	inner	2268.2.bm.g.593.1		4
63.58	even	3		1764.2.t.a.1097.2		4
63.59	even	6		1764.2.f.a.881.2		4
63.61	odd	6	inner	2268.2.bm.g.593.2		4
252.31	even	6		7056.2.k.a.881.4		4
252.59	odd	6		7056.2.k.a.881.1		4
252.67	odd	6		7056.2.k.a.881.2		4
252.95	even	6		7056.2.k.a.881.3		4
252.103	even	6		1008.2.bt.a.593.1		4
252.131	odd	6		1008.2.bt.a.593.2		4
315.68	odd	12		6300.2.dd.a.1349.4		8
315.103	even	12		6300.2.dd.a.1349.3		8
315.194	even	6		6300.2.ch.a.1601.2		4
315.229	odd	6		6300.2.ch.a.1601.1		4
315.257	odd	12		6300.2.dd.a.1349.2		8
315.292	even	12		6300.2.dd.a.1349.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.t.a.17.1	✓	4	9.5	odd	6
252.2.t.a.17.2	yes	4	9.4	even	3
252.2.t.a.89.1	yes	4	63.40	odd	6
252.2.t.a.89.2	yes	4	63.5	even	6
1008.2.bt.a.17.1		4	36.23	even	6
1008.2.bt.a.17.2		4	36.31	odd	6
1008.2.bt.a.593.1		4	252.103	even	6
1008.2.bt.a.593.2		4	252.131	odd	6
1764.2.f.a.881.1		4	63.4	even	3
1764.2.f.a.881.2		4	63.59	even	6
1764.2.f.a.881.3		4	63.31	odd	6
1764.2.f.a.881.4		4	63.32	odd	6
1764.2.t.a.521.1		4	63.13	odd	6
1764.2.t.a.521.2		4	63.41	even	6
1764.2.t.a.1097.1		4	63.23	odd	6
1764.2.t.a.1097.2		4	63.58	even	3
2268.2.w.h.269.1		4	9.2	odd	6
2268.2.w.h.269.2		4	9.7	even	3
2268.2.w.h.1349.1		4	7.5	odd	6
2268.2.w.h.1349.2		4	21.5	even	6
2268.2.bm.g.593.1		4	63.47	even	6	inner
2268.2.bm.g.593.2		4	63.61	odd	6	inner
2268.2.bm.g.1025.1		4	1.1	even	1	trivial
2268.2.bm.g.1025.2		4	3.2	odd	2	inner
6300.2.ch.a.1601.1		4	315.229	odd	6
6300.2.ch.a.1601.2		4	315.194	even	6
6300.2.ch.a.4301.1		4	45.14	odd	6
6300.2.ch.a.4301.2		4	45.4	even	6
6300.2.dd.a.1349.1		8	315.292	even	12
6300.2.dd.a.1349.2		8	315.257	odd	12
6300.2.dd.a.1349.3		8	315.103	even	12
6300.2.dd.a.1349.4		8	315.68	odd	12
6300.2.dd.a.4049.1		8	45.23	even	12
6300.2.dd.a.4049.2		8	45.13	odd	12
6300.2.dd.a.4049.3		8	45.32	even	12
6300.2.dd.a.4049.4		8	45.22	odd	12
7056.2.k.a.881.1		4	252.59	odd	6
7056.2.k.a.881.2		4	252.67	odd	6
7056.2.k.a.881.3		4	252.95	even	6
7056.2.k.a.881.4		4	252.31	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.44949 q^{5} +(-2.50000 + 0.866025i) q^{7} -4.24264i q^{11} +(-1.50000 - 0.866025i) q^{13} +(-2.44949 + 4.24264i) q^{17} +(4.50000 - 2.59808i) q^{19} +1.00000 q^{25} +(-7.34847 + 4.24264i) q^{29} +(1.50000 - 0.866025i) q^{31} +(6.12372 - 2.12132i) q^{35} +(2.50000 + 4.33013i) q^{37} +(6.12372 - 10.6066i) q^{41} +(5.50000 + 9.52628i) q^{43} +(1.22474 - 2.12132i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-7.34847 - 4.24264i) q^{53} +10.3923i q^{55} +(2.44949 + 4.24264i) q^{59} +(3.00000 + 1.73205i) q^{61} +(3.67423 + 2.12132i) q^{65} +(3.50000 + 6.06218i) q^{67} -12.7279i q^{71} +(13.5000 + 7.79423i) q^{73} +(3.67423 + 10.6066i) q^{77} +(-5.50000 + 9.52628i) q^{79} +(6.12372 + 10.6066i) q^{83} +(6.00000 - 10.3923i) q^{85} +(7.34847 + 12.7279i) q^{89} +(4.50000 + 0.866025i) q^{91} +(-11.0227 + 6.36396i) q^{95} +(3.00000 - 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 10 q^{7} - 6 q^{13} + 18 q^{19} + 4 q^{25} + 6 q^{31} + 10 q^{37} + 22 q^{43} + 22 q^{49} + 12 q^{61} + 14 q^{67} + 54 q^{73} - 22 q^{79} + 24 q^{85} + 18 q^{91} + 12 q^{97}+O(q^{100}) \) 4 * q - 10 * q^7 - 6 * q^13 + 18 * q^19 + 4 * q^25 + 6 * q^31 + 10 * q^37 + 22 * q^43 + 22 * q^49 + 12 * q^61 + 14 * q^67 + 54 * q^73 - 22 * q^79 + 24 * q^85 + 18 * q^91 + 12 * q^97

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