LMFDB - Embedded newform 2592.2.s.j.863.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2592,2,Mod(863,2592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2592, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("2592.863");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2592 = 2^{5} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2592.s (of order $6$, 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:	$20.6972242039$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 49x^{12} - 12x^{10} - 600x^{8} + 108x^{6} + 4057x^{4} + 18252x^{2} + 28561 $ x^16 - 12x^14 + 49x^12 - 12x^10 - 600x^8 + 108x^6 + 4057x^4 + 18252*x^2 + 28561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			863.6
Root			$2.39101 - 0.123030i$ of defining polynomial
Character	$\chi$	$=$	2592.863
Dual form			2592.2.s.j.1727.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.25522 + 1.30205i) q^{5} +(-0.301361 + 0.173991i) q^{7} +O(q^{10})$	$q+(2.25522 + 1.30205i) q^{5} +(-0.301361 + 0.173991i) q^{7} +(-0.336125 - 0.582186i) q^{11} +(-1.04002 + 1.80136i) q^{13} -0.0255169i q^{17} -5.29869i q^{19} +(4.44589 - 7.70051i) q^{23} +(0.890673 + 1.54269i) q^{25} +(0.133898 - 0.0773060i) q^{29} +(6.82333 + 3.93945i) q^{31} -0.906181 q^{35} +5.34798 q^{37} +(5.89358 + 3.40266i) q^{41} +(9.76546 - 5.63809i) q^{43} +(1.28134 + 2.21934i) q^{47} +(-3.43945 + 5.95731i) q^{49} -3.97689i q^{53} -1.75061i q^{55} +(-3.07449 + 5.32517i) q^{59} +(6.26546 + 10.8521i) q^{61} +(-4.69093 + 2.70831i) q^{65} +(-4.80941 - 2.77671i) q^{67} -6.82123 q^{71} +7.21865 q^{73} +(0.202590 + 0.116966i) q^{77} +(2.94213 - 1.69864i) q^{79} +(6.87226 + 11.9031i) q^{83} +(0.0332243 - 0.0575462i) q^{85} -10.6435i q^{89} -0.723815i q^{91} +(6.89916 - 11.9497i) q^{95} +(8.89016 + 15.3982i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{7}+O(q^{10}) $ 16 * q + 12 * q^7	$ 16 q + 12 q^{7} + 4 q^{13} + 24 q^{25} + 72 q^{31} + 72 q^{37} + 84 q^{43} + 24 q^{49} + 28 q^{61} + 36 q^{67} + 96 q^{73} + 12 q^{79} + 12 q^{85} + 16 q^{97}+O(q^{100}) $ 16 * q + 12 * q^7 + 4 * q^13 + 24 * q^25 + 72 * q^31 + 72 * q^37 + 84 * q^43 + 24 * q^49 + 28 * q^61 + 36 * q^67 + 96 * q^73 + 12 * q^79 + 12 * q^85 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times$.

$n$	$325$	$1217$	$2431$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	2.25522	+	1.30205i	1.00856	+	0.582295i	0.910771	−	0.412912i	$-0.135488\pi$
$5$	2.25522	+	1.30205i	1.00856	+	0.582295i	0.0977933	+	0.995207i	$0.468822\pi$
$6$		0			0
$7$	−0.301361	+	0.173991i	−0.113904	+	0.0657625i	−0.555870	−	0.831269i	$-0.687615\pi$
$7$	−0.301361	+	0.173991i	−0.113904	+	0.0657625i	0.441966	+	0.897032i	$0.354281\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.336125	−	0.582186i	−0.101346	−	0.175536i	0.810894	−	0.585193i	$-0.198981\pi$
$11$	−0.336125	−	0.582186i	−0.101346	−	0.175536i	−0.912239	+	0.409658i	$0.865648\pi$
$12$		0			0
$13$	−1.04002	+	1.80136i	−0.288449	+	0.499608i	−0.973440	−	0.228944i	$-0.926473\pi$
$13$	−1.04002	+	1.80136i	−0.288449	+	0.499608i	0.684991	+	0.728552i	$0.259806\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	0.0255169i		−	0.00618876i	−0.999995	−	0.00309438i	$-0.999015\pi$
$17$		−	0.0255169i		−	0.00618876i	0.999995	−	0.00309438i	$-0.000984973\pi$
$18$		0			0
$19$		−	5.29869i		−	1.21560i	−0.794089	−	0.607801i	$-0.792052\pi$
$19$		−	5.29869i		−	1.21560i	0.794089	−	0.607801i	$-0.207948\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.44589	−	7.70051i	0.927032	−	1.60567i	0.138772	−	0.990324i	$-0.455685\pi$
$23$	4.44589	−	7.70051i	0.927032	−	1.60567i	0.788260	−	0.615342i	$-0.210982\pi$
$24$		0			0
$25$	0.890673	+	1.54269i	0.178135	+	0.308538i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.133898	−	0.0773060i	0.0248642	−	0.0143554i	−0.487516	−	0.873114i	$-0.662097\pi$
$29$	0.133898	−	0.0773060i	0.0248642	−	0.0143554i	0.512381	+	0.858758i	$0.328764\pi$
$30$		0			0
$31$	6.82333	+	3.93945i	1.22551	+	0.707547i	0.966087	−	0.258218i	$-0.0831352\pi$
$31$	6.82333	+	3.93945i	1.22551	+	0.707547i	0.259420	+	0.965765i	$0.416469\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.906181			−0.153173
$36$		0			0
$37$	5.34798			0.879203			0.439601	−	0.898193i	$-0.355120\pi$
$37$	5.34798			0.879203			0.439601	+	0.898193i	$0.355120\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.89358	+	3.40266i	0.920422	+	0.531406i	0.883770	−	0.467922i	$-0.154997\pi$
$41$	5.89358	+	3.40266i	0.920422	+	0.531406i	0.0366522	+	0.999328i	$0.488331\pi$
$42$		0			0
$43$	9.76546	−	5.63809i	1.48922	−	0.859801i	0.489295	−	0.872118i	$-0.337254\pi$
$43$	9.76546	−	5.63809i	1.48922	−	0.859801i	0.999924	+	0.0123173i	$0.00392080\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.28134	+	2.21934i	0.186902	+	0.323724i	0.944216	−	0.329327i	$-0.106822\pi$
$47$	1.28134	+	2.21934i	0.186902	+	0.323724i	−0.757314	+	0.653051i	$0.773489\pi$
$48$		0			0
$49$	−3.43945	+	5.95731i	−0.491351	+	0.851044i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	3.97689i		−	0.546267i	−0.961976	−	0.273134i	$-0.911940\pi$
$53$		−	3.97689i		−	0.546267i	0.961976	−	0.273134i	$-0.0880602\pi$
$54$		0			0
$55$		−	1.75061i		−	0.236052i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.07449	+	5.32517i	−0.400264	+	0.693278i	−0.993758	−	0.111561i	$-0.964415\pi$
$59$	−3.07449	+	5.32517i	−0.400264	+	0.693278i	0.593493	+	0.804839i	$0.297748\pi$
$60$		0			0
$61$	6.26546	+	10.8521i	0.802210	+	1.38947i	0.918158	+	0.396214i	$0.129676\pi$
$61$	6.26546	+	10.8521i	0.802210	+	1.38947i	−0.115948	+	0.993255i	$0.536991\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.69093	+	2.70831i	−0.581838	+	0.335924i
$66$		0			0
$67$	−4.80941	−	2.77671i	−0.587563	−	0.339230i	0.176570	−	0.984288i	$-0.443500\pi$
$67$	−4.80941	−	2.77671i	−0.587563	−	0.339230i	−0.764133	+	0.645058i	$0.776833\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−6.82123			−0.809531			−0.404765	−	0.914421i	$-0.632647\pi$
$71$	−6.82123			−0.809531			−0.404765	+	0.914421i	$0.632647\pi$
$72$		0			0
$73$	7.21865			0.844880			0.422440	−	0.906391i	$-0.361174\pi$
$73$	7.21865			0.844880			0.422440	+	0.906391i	$0.361174\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.202590	+	0.116966i	0.0230873	+	0.0133295i
$78$		0			0
$79$	2.94213	−	1.69864i	0.331015	−	0.191112i	−0.325276	−	0.945619i	$-0.605457\pi$
$79$	2.94213	−	1.69864i	0.331015	−	0.191112i	0.656292	+	0.754507i	$0.272124\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.87226	+	11.9031i	0.754328	+	1.30654i	0.945707	+	0.325019i	$0.105371\pi$
$83$	6.87226	+	11.9031i	0.754328	+	1.30654i	−0.191379	+	0.981516i	$0.561296\pi$
$84$		0			0
$85$	0.0332243	−	0.0575462i	0.00360368	−	0.00624176i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	10.6435i		−	1.12821i	−0.825703	−	0.564104i	$-0.809222\pi$
$89$		−	10.6435i		−	1.12821i	0.825703	−	0.564104i	$-0.190778\pi$
$90$		0			0
$91$		−	0.723815i		−	0.0758764i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	6.89916	−	11.9497i	0.707839	−	1.22601i
$96$		0			0
$97$	8.89016	+	15.3982i	0.902659	+	1.56345i	0.824029	+	0.566547i	$0.191721\pi$
$97$	8.89016	+	15.3982i	0.902659	+	1.56345i	0.0786296	+	0.996904i	$0.474946\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−13.3239	+	7.69255i	−1.32578	+	0.765437i	−0.984643	−	0.174578i	$-0.944144\pi$
$101$	−13.3239	+	7.69255i	−1.32578	+	0.765437i	−0.341133	+	0.940015i	$0.610811\pi$
$102$		0			0
$103$	8.53590	+	4.92820i	0.841067	+	0.485590i	0.857627	−	0.514273i	$-0.171938\pi$
$103$	8.53590	+	4.92820i	0.841067	+	0.485590i	−0.0165597	+	0.999863i	$0.505271\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−13.7051			−1.32493			−0.662463	−	0.749095i	$-0.730489\pi$
$107$	−13.7051			−1.32493			−0.662463	+	0.749095i	$0.730489\pi$
$108$		0			0
$109$	−3.19080			−0.305624			−0.152812	−	0.988255i	$-0.548833\pi$
$109$	−3.19080			−0.305624			−0.152812	+	0.988255i	$0.548833\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.36402	−	4.25162i	−0.692748	−	0.399959i	0.111892	−	0.993720i	$-0.464309\pi$
$113$	−7.36402	−	4.25162i	−0.692748	−	0.399959i	−0.804641	+	0.593762i	$0.797642\pi$
$114$		0			0
$115$	20.0529	−	11.5775i	1.86994	−	1.07961i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.00443971	+	0.00768981i	0.000406988	+	0.000704924i
$120$		0			0
$121$	5.27404	−	9.13491i	0.479458	−	0.830446i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	8.38170i		−	0.749682i
$126$		0			0
$127$		−	16.4816i		−	1.46251i	−0.682105	−	0.731254i	$-0.738935\pi$
$127$		−	16.4816i		−	1.46251i	0.682105	−	0.731254i	$-0.261065\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.45444	+	12.9115i	−0.651298	+	1.12808i	0.331510	+	0.943452i	$0.392442\pi$
$131$	−7.45444	+	12.9115i	−0.651298	+	1.12808i	−0.982808	+	0.184629i	$0.940892\pi$
$132$		0			0
$133$	0.921925	+	1.59682i	0.0799410	+	0.138462i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.60966	+	3.81609i	−0.564701	+	0.326030i	−0.755030	−	0.655690i	$-0.772378\pi$
$137$	−6.60966	+	3.81609i	−0.564701	+	0.326030i	0.190329	+	0.981720i	$0.439045\pi$
$138$		0			0
$139$	−2.42015	−	1.39728i	−0.205275	−	0.118515i	0.393839	−	0.919180i	$-0.371147\pi$
$139$	−2.42015	−	1.39728i	−0.205275	−	0.118515i	−0.599114	+	0.800664i	$0.704480\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.39830			0.116932
$144$		0			0
$145$	0.402625			0.0334362
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.61746	+	3.24324i	0.460200	+	0.265697i	0.712128	−	0.702049i	$-0.247731\pi$
$149$	5.61746	+	3.24324i	0.460200	+	0.265697i	−0.251928	+	0.967746i	$0.581065\pi$
$150$		0			0
$151$	8.57487	−	4.95071i	0.697813	−	0.402883i	−0.108719	−	0.994073i	$-0.534675\pi$
$151$	8.57487	−	4.95071i	0.697813	−	0.402883i	0.806532	+	0.591190i	$0.201342\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	10.2587	+	17.7687i	0.824002	+	1.42721i
$156$		0			0
$157$	−5.56415	+	9.63739i	−0.444068	+	0.769148i	−0.997987	−	0.0634229i	$-0.979798\pi$
$157$	−5.56415	+	9.63739i	−0.444068	+	0.769148i	0.553919	+	0.832570i	$0.313132\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			3.09418i			0.243856i
$162$		0			0
$163$			16.7085i			1.30871i	0.756186	+	0.654356i	$0.227060\pi$
$163$			16.7085i			1.30871i	−0.756186	+	0.654356i	$0.772940\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.13667	−	7.16491i	0.320105	−	0.554438i	−0.660405	−	0.750910i	$-0.729615\pi$
$167$	4.13667	−	7.16491i	0.320105	−	0.554438i	0.980509	+	0.196472i	$0.0629486\pi$
$168$		0			0
$169$	4.33673	+	7.51144i	0.333595	+	0.577803i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.0903	−	5.82561i	0.767148	−	0.442913i	−0.0647086	−	0.997904i	$-0.520612\pi$
$173$	10.0903	−	5.82561i	0.767148	−	0.442913i	0.831856	+	0.554991i	$0.187278\pi$
$174$		0			0
$175$	−0.536829	−	0.309938i	−0.0405805	−	0.0234291i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−17.1651			−1.28298			−0.641490	−	0.767131i	$-0.721683\pi$
$179$	−17.1651			−1.28298			−0.641490	+	0.767131i	$0.721683\pi$
$180$		0			0
$181$	17.5256			1.30267			0.651333	−	0.758792i	$-0.274210\pi$
$181$	17.5256			1.30267			0.651333	+	0.758792i	$0.274210\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	12.0609	+	6.96334i	0.886733	+	0.511955i
$186$		0			0
$187$	−0.0148556	+	0.00857687i	−0.00108635	+	0.000627203i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−7.58354	−	13.1351i	−0.548726	−	0.950421i	−0.998362	−	0.0572092i	$-0.981780\pi$
$191$	−7.58354	−	13.1351i	−0.548726	−	0.950421i	0.449637	−	0.893212i	$-0.351554\pi$
$192$		0			0
$193$	−11.4229	+	19.7850i	−0.822235	+	1.42415i	0.0817791	+	0.996650i	$0.473940\pi$
$193$	−11.4229	+	19.7850i	−0.822235	+	1.42415i	−0.904014	+	0.427502i	$0.859394\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			2.08719i			0.148706i	0.997232	+	0.0743531i	$0.0236892\pi$
$197$			2.08719i			0.148706i	−0.997232	+	0.0743531i	$0.976311\pi$
$198$		0			0
$199$		−	21.1497i		−	1.49927i	−0.661854	−	0.749633i	$-0.730230\pi$
$199$		−	21.1497i		−	1.49927i	0.661854	−	0.749633i	$-0.269770\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.0269011	+	0.0465941i	−0.00188809	+	0.00327026i
$204$		0			0
$205$	8.86087	+	15.3475i	0.618870	+	1.07191i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.08482	+	1.78102i	−0.213381	+	0.123196i
$210$		0			0
$211$	9.09685	+	5.25207i	0.626253	+	0.361567i	0.779299	−	0.626652i	$-0.215575\pi$
$211$	9.09685	+	5.25207i	0.626253	+	0.361567i	−0.153047	+	0.988219i	$0.548908\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	29.3643			2.00263
$216$		0			0
$217$	−2.74172			−0.186120
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.0459652	+	0.0265380i	0.00309195	+	0.00178514i
$222$		0			0
$223$	−4.87530	+	2.81476i	−0.326474	+	0.188490i	−0.654275	−	0.756257i	$-0.727026\pi$
$223$	−4.87530	+	2.81476i	−0.326474	+	0.188490i	0.327800	+	0.944747i	$0.393693\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.55153	−	2.68733i	−0.102979	−	0.178364i	0.809932	−	0.586524i	$-0.199504\pi$
$227$	−1.55153	−	2.68733i	−0.102979	−	0.178364i	−0.912911	+	0.408160i	$0.866171\pi$
$228$		0			0
$229$	3.77011	−	6.53002i	0.249136	−	0.431516i	−0.714150	−	0.699992i	$-0.753187\pi$
$229$	3.77011	−	6.53002i	0.249136	−	0.431516i	0.963286	+	0.268476i	$0.0865201\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	15.8911i		−	1.04106i	−0.853843	−	0.520530i	$-0.825734\pi$
$233$		−	15.8911i		−	1.04106i	0.853843	−	0.520530i	$-0.174266\pi$
$234$		0			0
$235$			6.67346i			0.435329i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	12.9356	−	22.4051i	0.836735	−	1.44927i	−0.0558749	−	0.998438i	$-0.517795\pi$
$239$	12.9356	−	22.4051i	0.836735	−	1.44927i	0.892610	−	0.450830i	$-0.148872\pi$
$240$		0			0
$241$	−8.45215	−	14.6396i	−0.544451	−	0.943016i	−0.998641	−	0.0521118i	$-0.983405\pi$
$241$	−8.45215	−	14.6396i	−0.544451	−	0.943016i	0.454190	−	0.890905i	$-0.349929\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−15.5134	+	8.95669i	−0.991117	+	0.572222i
$246$		0			0
$247$	9.54485	+	5.51072i	0.607324	+	0.350639i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−4.32123			−0.272754			−0.136377	−	0.990657i	$-0.543546\pi$
$251$	−4.32123			−0.272754			−0.136377	+	0.990657i	$0.543546\pi$
$252$		0			0
$253$	−5.97750			−0.375802
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.92234	+	4.57396i	0.494182	+	0.285316i	0.726308	−	0.687370i	$-0.241235\pi$
$257$	7.92234	+	4.57396i	0.494182	+	0.285316i	−0.232126	+	0.972686i	$0.574568\pi$
$258$		0			0
$259$	−1.61168	+	0.930501i	−0.100145	+	0.0578185i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−7.61044	−	13.1817i	−0.469280	−	0.812817i	0.530103	−	0.847933i	$-0.322153\pi$
$263$	−7.61044	−	13.1817i	−0.469280	−	0.812817i	−0.999383	+	0.0351164i	$0.988820\pi$
$264$		0			0
$265$	5.17811	−	8.96875i	0.318089	−	0.550946i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			6.95993i			0.424354i	0.977231	+	0.212177i	$0.0680554\pi$
$269$			6.95993i			0.424354i	−0.977231	+	0.212177i	$0.931945\pi$
$270$		0			0
$271$		−	16.9229i		−	1.02799i	−0.857793	−	0.513995i	$-0.828165\pi$
$271$		−	16.9229i		−	1.02799i	0.857793	−	0.513995i	$-0.171835\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.598755	−	1.03707i	0.0361063	−	0.0625379i
$276$		0			0
$277$	−9.62417	−	16.6695i	−0.578260	−	1.00158i	−0.995679	−	0.0928618i	$-0.970399\pi$
$277$	−9.62417	−	16.6695i	−0.578260	−	1.00158i	0.417419	−	0.908714i	$-0.362935\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	24.3687	−	14.0693i	1.45371	−	0.839302i	0.455025	−	0.890479i	$-0.349630\pi$
$281$	24.3687	−	14.0693i	1.45371	−	0.839302i	0.998690	+	0.0511767i	$0.0162972\pi$
$282$		0			0
$283$	−5.39728	−	3.11612i	−0.320835	−	0.185234i	0.330930	−	0.943655i	$-0.392638\pi$
$283$	−5.39728	−	3.11612i	−0.320835	−	0.185234i	−0.651765	+	0.758421i	$0.725971\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.36813			−0.139786
$288$		0			0
$289$	16.9993			0.999962
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.81239	+	1.04638i	0.105881	+	0.0611304i	0.552005	−	0.833841i	$-0.313863\pi$
$293$	1.81239	+	1.04638i	0.105881	+	0.0611304i	−0.446124	+	0.894971i	$0.647196\pi$
$294$		0			0
$295$	−13.8673	+	8.00628i	−0.807384	+	0.466144i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	9.24760	+	16.0173i	0.534802	+	0.926305i
$300$		0			0
$301$	−1.96196	+	3.39821i	−0.113085	+	0.195869i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			32.6318i			1.86849i
$306$		0			0
$307$			8.57487i			0.489394i	0.969600	+	0.244697i	$0.0786885\pi$
$307$			8.57487i			0.489394i	−0.969600	+	0.244697i	$0.921312\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.23922	−	14.2707i	0.467203	−	0.809220i	−0.532095	−	0.846685i	$-0.678595\pi$
$311$	8.23922	−	14.2707i	0.467203	−	0.809220i	0.999298	+	0.0374650i	$0.0119283\pi$
$312$		0			0
$313$	−2.67132	−	4.62686i	−0.150992	−	0.261525i	0.780601	−	0.625030i	$-0.214913\pi$
$313$	−2.67132	−	4.62686i	−0.150992	−	0.261525i	−0.931592	+	0.363505i	$0.881580\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	22.7954	−	13.1610i	1.28032	−	0.739193i	0.303413	−	0.952859i	$-0.401874\pi$
$317$	22.7954	−	13.1610i	1.28032	−	0.739193i	0.976907	+	0.213666i	$0.0685405\pi$
$318$		0			0
$319$	−0.0900129	−	0.0519689i	−0.00503975	−	0.00290970i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.135206			−0.00752307
$324$		0			0
$325$	−3.70526			−0.205531
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.772291	−	0.445882i	−0.0425778	−	0.0245823i
$330$		0			0
$331$	2.94213	−	1.69864i	0.161714	−	0.0933656i	−0.416959	−	0.908925i	$-0.636904\pi$
$331$	2.94213	−	1.69864i	0.161714	−	0.0933656i	0.578673	+	0.815560i	$0.303571\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−7.23085	−	12.5242i	−0.395063	−	0.684270i
$336$		0			0
$337$	−1.43141	+	2.47927i	−0.0779736	+	0.135054i	−0.902376	−	0.430951i	$-0.858178\pi$
$337$	−1.43141	+	2.47927i	−0.0779736	+	0.135054i	0.824402	+	0.566005i	$0.191512\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	5.29660i		−	0.286827i
$342$		0			0
$343$		−	4.82961i		−	0.260775i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.2717	+	22.9873i	−0.712464	+	1.23402i	0.251465	+	0.967866i	$0.419088\pi$
$347$	−13.2717	+	22.9873i	−0.712464	+	1.23402i	−0.963930	+	0.266158i	$0.914246\pi$
$348$		0			0
$349$	−4.87263	−	8.43964i	−0.260826	−	0.451764i	0.705636	−	0.708575i	$-0.250662\pi$
$349$	−4.87263	−	8.43964i	−0.260826	−	0.451764i	−0.966462	+	0.256811i	$0.917328\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−15.4889	+	8.94255i	−0.824393	+	0.475964i	−0.851929	−	0.523657i	$-0.824567\pi$
$353$	−15.4889	+	8.94255i	−0.824393	+	0.475964i	0.0275358	+	0.999621i	$0.491234\pi$
$354$		0			0
$355$	−15.3834	−	8.88158i	−0.816464	−	0.471385i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.29070			−0.0681204			−0.0340602	−	0.999420i	$-0.510844\pi$
$359$	−1.29070			−0.0681204			−0.0340602	+	0.999420i	$0.510844\pi$
$360$		0			0
$361$	−9.07609			−0.477689
$362$		0			0
$363$		0			0
$364$		0			0
$365$	16.2796	+	9.39906i	0.852115	+	0.491969i
$366$		0			0
$367$	−10.2874	+	5.93945i	−0.537000	+	0.310037i	−0.743862	−	0.668333i	$-0.767008\pi$
$367$	−10.2874	+	5.93945i	−0.537000	+	0.310037i	0.206862	+	0.978370i	$0.433675\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.691943	+	1.19848i	0.0359239	+	0.0622220i
$372$		0			0
$373$	−3.16541	+	5.48266i	−0.163899	+	0.283881i	−0.936264	−	0.351298i	$-0.885740\pi$
$373$	−3.16541	+	5.48266i	−0.163899	+	0.283881i	0.772365	+	0.635179i	$0.219074\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			0.321598i			0.0165631i
$378$		0			0
$379$			19.5588i			1.00467i	0.864674	+	0.502333i	$0.167525\pi$
$379$			19.5588i			1.00467i	−0.864674	+	0.502333i	$0.832475\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−11.5642	+	20.0298i	−0.590903	+	1.02347i	0.403208	+	0.915109i	$0.367895\pi$
$383$	−11.5642	+	20.0298i	−0.590903	+	1.02347i	−0.994111	+	0.108366i	$0.965438\pi$
$384$		0			0
$385$	0.304590	+	0.527566i	0.0155234	+	0.0268872i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−5.86602	+	3.38675i	−0.297419	+	0.171715i	−0.641283	−	0.767305i	$-0.721597\pi$
$389$	−5.86602	+	3.38675i	−0.297419	+	0.171715i	0.343864	+	0.939019i	$0.388264\pi$
$390$		0			0
$391$	−0.196493	−	0.113445i	−0.00993708	−	0.00573718i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	8.84686			0.445134
$396$		0			0
$397$	−14.8843			−0.747019			−0.373510	−	0.927626i	$-0.621846\pi$
$397$	−14.8843			−0.747019			−0.373510	+	0.927626i	$0.621846\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−28.8288	−	16.6443i	−1.43964	−	0.831179i	−0.441819	−	0.897104i	$-0.645667\pi$
$401$	−28.8288	−	16.6443i	−1.43964	−	0.831179i	−0.997825	+	0.0659256i	$0.979000\pi$
$402$		0			0
$403$	−14.1928	+	8.19419i	−0.706992	+	0.408182i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.79759	−	3.11352i	−0.0891033	−	0.154331i
$408$		0			0
$409$	13.2583	−	22.9641i	0.655582	−	1.13550i	−0.326165	−	0.945313i	$-0.605757\pi$
$409$	13.2583	−	22.9641i	0.655582	−	1.13550i	0.981747	−	0.190189i	$-0.0609101\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	2.13973i		−	0.105289i
$414$		0			0
$415$			35.7921i			1.75697i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−4.15323	+	7.19361i	−0.202899	+	0.351431i	−0.949461	−	0.313884i	$-0.898370\pi$
$419$	−4.15323	+	7.19361i	−0.202899	+	0.351431i	0.746562	+	0.665315i	$0.231703\pi$
$420$		0			0
$421$	−5.41283	−	9.37530i	−0.263805	−	0.456924i	0.703445	−	0.710750i	$-0.251644\pi$
$421$	−5.41283	−	9.37530i	−0.263805	−	0.456924i	−0.967250	+	0.253826i	$0.918311\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.0393647	−	0.0227272i	0.00190947	−	0.00110243i
$426$		0			0
$427$	−3.77634	−	2.18027i	−0.182750	−	0.105511i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	22.5582			1.08659			0.543296	−	0.839541i	$-0.317176\pi$
$431$	22.5582			1.08659			0.543296	+	0.839541i	$0.317176\pi$
$432$		0			0
$433$	−17.8521			−0.857918			−0.428959	−	0.903324i	$-0.641120\pi$
$433$	−17.8521			−0.857918			−0.428959	+	0.903324i	$0.641120\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−40.8026	−	23.5574i	−1.95185	−	1.12690i
$438$		0			0
$439$	−25.9613	+	14.9887i	−1.23906	+	0.715374i	−0.968903	−	0.247441i	$-0.920410\pi$
$439$	−25.9613	+	14.9887i	−1.23906	+	0.715374i	−0.270161	+	0.962815i	$0.587077\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−19.3306	−	33.4817i	−0.918427	−	1.59076i	−0.801805	−	0.597585i	$-0.796127\pi$
$443$	−19.3306	−	33.4817i	−0.918427	−	1.59076i	−0.116621	−	0.993176i	$-0.537206\pi$
$444$		0			0
$445$	13.8584	−	24.0034i	0.656950	−	1.13787i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	17.1197i		−	0.807926i	−0.914775	−	0.403963i	$-0.867632\pi$
$449$		−	17.1197i		−	0.807926i	0.914775	−	0.403963i	$-0.132368\pi$
$450$		0			0
$451$		−	4.57487i		−	0.215422i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.942443	−	1.63236i	0.0441824	−	0.0765262i
$456$		0			0
$457$	2.24475	+	3.88801i	0.105005	+	0.181874i	0.913740	−	0.406299i	$-0.133181\pi$
$457$	2.24475	+	3.88801i	0.105005	+	0.181874i	−0.808735	+	0.588173i	$0.799848\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	15.2312	−	8.79376i	0.709389	−	0.409566i	−0.101446	−	0.994841i	$-0.532347\pi$
$461$	15.2312	−	8.79376i	0.709389	−	0.409566i	0.810835	+	0.585275i	$0.199013\pi$
$462$		0			0
$463$	13.4743	+	7.77939i	0.626204	+	0.361539i	0.779280	−	0.626675i	$-0.215585\pi$
$463$	13.4743	+	7.77939i	0.626204	+	0.361539i	−0.153077	+	0.988214i	$0.548918\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	17.5198			0.810721			0.405360	−	0.914157i	$-0.367146\pi$
$467$	17.5198			0.810721			0.405360	+	0.914157i	$0.367146\pi$
$468$		0			0
$469$	1.93249			0.0892343
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−6.56483	−	3.79021i	−0.301851	−	0.174274i
$474$		0			0
$475$	8.17424	−	4.71940i	0.375060	−	0.216541i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	8.00973	+	13.8733i	0.365974	+	0.633885i	0.988932	−	0.148370i	$-0.0474026\pi$
$479$	8.00973	+	13.8733i	0.365974	+	0.633885i	−0.622958	+	0.782255i	$0.714069\pi$
$480$		0			0
$481$	−5.56199	+	9.63365i	−0.253605	+	0.439257i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			46.3018i			2.10245i
$486$		0			0
$487$			17.9668i			0.814154i	0.913394	+	0.407077i	$0.133452\pi$
$487$			17.9668i			0.814154i	−0.913394	+	0.407077i	$0.866548\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−17.4671	+	30.2539i	−0.788280	+	1.36534i	0.138739	+	0.990329i	$0.455695\pi$
$491$	−17.4671	+	30.2539i	−0.788280	+	1.36534i	−0.927020	+	0.375013i	$0.877638\pi$
$492$		0			0
$493$	−0.00197261	−	0.00341666i	−8.88418e−5	−	0.000153879i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.05565	−	1.18683i	0.0922087	−	0.0532367i
$498$		0			0
$499$	−30.5018	−	17.6102i	−1.36545	−	0.788343i	−0.375107	−	0.926982i	$-0.622394\pi$
$499$	−30.5018	−	17.6102i	−1.36545	−	0.788343i	−0.990343	+	0.138639i	$0.955727\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−33.7941			−1.50681			−0.753403	−	0.657559i	$-0.771589\pi$
$503$	−33.7941			−1.50681			−0.753403	+	0.657559i	$0.771589\pi$
$504$		0			0
$505$	−40.0644			−1.78284
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−10.6994	−	6.17728i	−0.474241	−	0.273803i	0.243772	−	0.969832i	$-0.421615\pi$
$509$	−10.6994	−	6.17728i	−0.474241	−	0.273803i	−0.718013	+	0.696029i	$0.754948\pi$
$510$		0			0
$511$	−2.17542	+	1.25598i	−0.0962351	+	0.0555614i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	12.8335	+	22.2283i	0.565513	+	0.979498i
$516$		0			0
$517$	0.861379	−	1.49195i	0.0378834	−	0.0656160i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	4.04053i		−	0.177019i	−0.996075	−	0.0885095i	$-0.971790\pi$
$521$		−	4.04053i		−	0.177019i	0.996075	−	0.0885095i	$-0.0282104\pi$
$522$		0			0
$523$		−	11.8961i		−	0.520178i	−0.965585	−	0.260089i	$-0.916248\pi$
$523$		−	11.8961i		−	0.520178i	0.965585	−	0.260089i	$-0.0837520\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.100523	−	0.174110i	0.00437884	−	0.00758437i
$528$		0			0
$529$	−28.0319	−	48.5526i	−1.21878	−	2.11098i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−12.2588	+	7.07764i	−0.530989	+	0.306567i
$534$		0			0
$535$	−30.9081	−	17.8448i	−1.33627	−	0.771497i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	4.62435			0.199185
$540$		0			0
$541$	−19.3509			−0.831959			−0.415979	−	0.909374i	$-0.636561\pi$
$541$	−19.3509			−0.831959			−0.415979	+	0.909374i	$0.636561\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−7.19596	−	4.15459i	−0.308241	−	0.177963i
$546$		0			0
$547$	−0.784360	+	0.452851i	−0.0335368	+	0.0193625i	−0.516675	−	0.856182i	$-0.672830\pi$
$547$	−0.784360	+	0.452851i	−0.0335368	+	0.0193625i	0.483138	+	0.875544i	$0.339497\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.409620	−	0.709483i	−0.0174504	−	0.0302250i
$552$		0			0
$553$	−0.591096	+	1.02381i	−0.0251360	+	0.0435368i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	28.5142i		−	1.20818i	−0.796914	−	0.604092i	$-0.793536\pi$
$557$		−	28.5142i		−	1.20818i	0.796914	−	0.604092i	$-0.206464\pi$
$558$		0			0
$559$			23.4548i			0.992034i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−16.9087	+	29.2868i	−0.712617	+	1.23429i	0.251254	+	0.967921i	$0.419157\pi$
$563$	−16.9087	+	29.2868i	−0.712617	+	1.23429i	−0.963871	+	0.266368i	$0.914176\pi$
$564$		0			0
$565$	−11.0716	−	19.1767i	−0.465788	−	0.806768i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	26.3071	−	15.1884i	1.10285	−	0.636732i	0.165884	−	0.986145i	$-0.446952\pi$
$569$	26.3071	−	15.1884i	1.10285	−	0.636732i	0.936969	+	0.349413i	$0.113619\pi$
$570$		0			0
$571$	−14.1835	−	8.18885i	−0.593561	−	0.342693i	0.172943	−	0.984932i	$-0.444672\pi$
$571$	−14.1835	−	8.18885i	−0.593561	−	0.342693i	−0.766504	+	0.642239i	$0.778006\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	15.8393			0.660546
$576$		0			0
$577$	24.0287			1.00033			0.500163	−	0.865931i	$-0.333273\pi$
$577$	24.0287			1.00033			0.500163	+	0.865931i	$0.333273\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−4.14207	−	2.39142i	−0.171842	−	0.0992130i
$582$		0			0
$583$	−2.31529	+	1.33673i	−0.0958894	+	0.0553618i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−10.2121	−	17.6880i	−0.421500	−	0.730060i	0.574586	−	0.818444i	$-0.305163\pi$
$587$	−10.2121	−	17.6880i	−0.421500	−	0.730060i	−0.996086	+	0.0883841i	$0.971830\pi$
$588$		0			0
$589$	20.8739	−	36.1547i	0.860096	−	1.48973i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			40.9983i			1.68360i	0.539790	+	0.841800i	$0.318504\pi$
$593$			40.9983i			1.68360i	−0.539790	+	0.841800i	$0.681496\pi$
$594$		0			0
$595$			0.0231229i			0.000947948i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−13.9395	+	24.1440i	−0.569554	+	0.986497i	0.427056	+	0.904225i	$0.359551\pi$
$599$	−13.9395	+	24.1440i	−0.569554	+	0.986497i	−0.996610	+	0.0822717i	$0.973782\pi$
$600$		0			0
$601$	−1.32333	−	2.29208i	−0.0539800	−	0.0934960i	0.837773	−	0.546019i	$-0.183857\pi$
$601$	−1.32333	−	2.29208i	−0.0539800	−	0.0934960i	−0.891753	+	0.452523i	$0.850524\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	23.7882	−	13.7341i	0.967129	−	0.558372i
$606$		0			0
$607$	8.36912	+	4.83191i	0.339692	+	0.196121i	0.660136	−	0.751146i	$-0.270499\pi$
$607$	8.36912	+	4.83191i	0.339692	+	0.196121i	−0.320444	+	0.947268i	$0.603832\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.33045			−0.215647
$612$		0			0
$613$	−11.7228			−0.473478			−0.236739	−	0.971573i	$-0.576079\pi$
$613$	−11.7228			−0.473478			−0.236739	+	0.971573i	$0.576079\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	7.16189	+	4.13492i	0.288327	+	0.166466i	0.637187	−	0.770709i	$-0.280098\pi$
$617$	7.16189	+	4.13492i	0.288327	+	0.166466i	−0.348860	+	0.937175i	$0.613431\pi$
$618$		0			0
$619$	−30.0281	+	17.3367i	−1.20693	+	0.696822i	−0.962088	−	0.272741i	$-0.912070\pi$
$619$	−30.0281	+	17.3367i	−1.20693	+	0.696822i	−0.244844	+	0.969563i	$0.578737\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.85187	+	3.20754i	0.0741938	+	0.128507i
$624$		0			0
$625$	15.3668	−	26.6160i	0.614671	−	1.06464i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	0.136464i		−	0.00544117i
$630$		0			0
$631$			37.8564i			1.50704i	0.657425	+	0.753520i	$0.271646\pi$
$631$			37.8564i			1.50704i	−0.657425	+	0.753520i	$0.728354\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	21.4599	−	37.1697i	0.851611	−	1.47503i
$636$		0			0
$637$	−7.15418	−	12.3914i	−0.283459	−	0.490965i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−28.5391	+	16.4771i	−1.12723	+	0.650805i	−0.943236	−	0.332123i	$-0.892235\pi$
$641$	−28.5391	+	16.4771i	−1.12723	+	0.650805i	−0.183991	+	0.982928i	$0.558902\pi$
$642$		0			0
$643$	24.2487	+	14.0000i	0.956276	+	0.552106i	0.895025	−	0.446016i	$-0.147158\pi$
$643$	24.2487	+	14.0000i	0.956276	+	0.552106i	0.0612510	+	0.998122i	$0.480491\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	27.3089			1.07362			0.536812	−	0.843702i	$-0.319628\pi$
$647$	27.3089			1.07362			0.536812	+	0.843702i	$0.319628\pi$
$648$		0			0
$649$	4.13365			0.162260
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.182876	−	0.105584i	−0.00715649	−	0.00413180i	0.496417	−	0.868084i	$-0.334649\pi$
$653$	−0.182876	−	0.105584i	−0.00715649	−	0.00413180i	−0.503574	+	0.863952i	$0.667982\pi$
$654$		0			0
$655$	−33.6228	+	19.4121i	−1.31375	+	0.758495i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−24.5976	−	42.6042i	−0.958185	−	1.65963i	−0.726904	−	0.686739i	$-0.759042\pi$
$659$	−24.5976	−	42.6042i	−0.958185	−	1.65963i	−0.231281	−	0.972887i	$-0.574292\pi$
$660$		0			0
$661$	−25.0292	+	43.3518i	−0.973522	+	1.68619i	−0.288795	+	0.957391i	$0.593255\pi$
$661$	−25.0292	+	43.3518i	−0.973522	+	1.68619i	−0.684727	+	0.728799i	$0.740079\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			4.80157i			0.186197i
$666$		0			0
$667$		−	1.37478i		−	0.0532315i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.21196	−	7.29533i	0.162601	−	0.281633i
$672$		0			0
$673$	2.07593	+	3.59562i	0.0800212	+	0.138601i	0.903259	−	0.429096i	$-0.141168\pi$
$673$	2.07593	+	3.59562i	0.0800212	+	0.138601i	−0.823238	+	0.567697i	$0.807835\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−23.6364	+	13.6465i	−0.908422	+	0.524478i	−0.879923	−	0.475116i	$-0.842406\pi$
$677$	−23.6364	+	13.6465i	−0.908422	+	0.524478i	−0.0284987	+	0.999594i	$0.509073\pi$
$678$		0			0
$679$	−5.35830	−	3.09362i	−0.205633	−	0.118722i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	33.8326			1.29457			0.647283	−	0.762249i	$-0.275905\pi$
$683$	33.8326			1.29457			0.647283	+	0.762249i	$0.275905\pi$
$684$		0			0
$685$	−19.8750			−0.759383
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.16381	+	4.13603i	0.272919	+	0.157570i
$690$		0			0
$691$	−38.7444	+	22.3691i	−1.47391	+	0.850961i	−0.999568	−	0.0293805i	$-0.990647\pi$
$691$	−38.7444	+	22.3691i	−1.47391	+	0.850961i	−0.474340	+	0.880342i	$0.657313\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.63865	−	6.30233i	−0.138022	−	0.239061i
$696$		0			0
$697$	0.0868253	−	0.150386i	0.00328874	−	0.00569627i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	9.06986i		−	0.342564i	−0.985222	−	0.171282i	$-0.945209\pi$
$701$		−	9.06986i		−	0.342564i	0.985222	−	0.171282i	$-0.0547909\pi$
$702$		0			0
$703$		−	28.3373i		−	1.06876i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.67687	−	4.63648i	0.100674	−	0.174373i
$708$		0			0
$709$	−8.22989	−	14.2546i	−0.309080	−	0.535342i	0.669081	−	0.743189i	$-0.266688\pi$
$709$	−8.22989	−	14.2546i	−0.309080	−	0.535342i	−0.978161	+	0.207847i	$0.933354\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	60.6716	−	35.0288i	2.27217	−	1.31184i
$714$		0			0
$715$	3.15348	+	1.82066i	0.117933	+	0.0680889i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−28.8873			−1.07732			−0.538658	−	0.842525i	$-0.681068\pi$
$719$	−28.8873			−1.07732			−0.538658	+	0.842525i	$0.681068\pi$
$720$		0			0
$721$	−3.42985			−0.127734
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.238518	+	0.137709i	0.00885835	+	0.00511437i
$726$		0			0
$727$	15.6497	−	9.03537i	0.580416	−	0.335103i	−0.180883	−	0.983505i	$-0.557895\pi$
$727$	15.6497	−	9.03537i	0.580416	−	0.335103i	0.761299	+	0.648401i	$0.224562\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.143867	−	0.249184i	−0.00532110	−	0.00921642i
$732$		0			0
$733$	0.762789	−	1.32119i	0.0281743	−	0.0487992i	−0.851594	−	0.524201i	$-0.824364\pi$
$733$	0.762789	−	1.32119i	0.0281743	−	0.0487992i	0.879769	+	0.475402i	$0.157697\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			3.73329i			0.137518i
$738$		0			0
$739$		−	29.6671i		−	1.09132i	−0.838007	−	0.545660i	$-0.816279\pi$
$739$		−	29.6671i		−	1.09132i	0.838007	−	0.545660i	$-0.183721\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.26921	+	2.19833i	−0.0465627	+	0.0806490i	−0.888367	−	0.459133i	$-0.848160\pi$
$743$	−1.26921	+	2.19833i	−0.0465627	+	0.0806490i	0.841805	+	0.539782i	$0.181493\pi$
$744$		0			0
$745$	8.44573	+	14.6284i	0.309428	+	0.535945i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	4.13020	−	2.38457i	0.150914	−	0.0871303i
$750$		0			0
$751$	−27.0402	−	15.6117i	−0.986711	−	0.569678i	−0.0824218	−	0.996598i	$-0.526265\pi$
$751$	−27.0402	−	15.6117i	−0.986711	−	0.569678i	−0.904290	+	0.426919i	$0.859599\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	25.7843			0.938386
$756$		0			0
$757$	29.4170			1.06918			0.534590	−	0.845111i	$-0.320466\pi$
$757$	29.4170			1.06918			0.534590	+	0.845111i	$0.320466\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−17.4083	−	10.0507i	−0.631050	−	0.364337i	0.150108	−	0.988670i	$-0.452038\pi$
$761$	−17.4083	−	10.0507i	−0.631050	−	0.364337i	−0.781159	+	0.624332i	$0.785371\pi$
$762$		0			0
$763$	0.961585	−	0.555172i	0.0348117	−	0.0200986i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.39504	−	11.0765i	−0.230911	−	0.399950i
$768$		0			0
$769$	−1.84798	+	3.20080i	−0.0666399	+	0.115424i	−0.897420	−	0.441177i	$-0.854561\pi$
$769$	−1.84798	+	3.20080i	−0.0666399	+	0.115424i	0.830780	+	0.556600i	$0.187895\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			50.0604i			1.80055i	0.435323	+	0.900274i	$0.356634\pi$
$773$			50.0604i			1.80055i	−0.435323	+	0.900274i	$0.643366\pi$
$774$		0			0
$775$			14.0351i			0.504154i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	18.0296	−	31.2282i	0.645978	−	1.11887i
$780$		0			0
$781$	2.29278	+	3.97122i	0.0820423	+	0.142101i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−25.0967	+	14.4896i	−0.895741	+	0.517156i
$786$		0			0
$787$	13.0106	+	7.51165i	0.463777	+	0.267762i	0.713631	−	0.700522i	$-0.247049\pi$
$787$	13.0106	+	7.51165i	0.463777	+	0.267762i	−0.249854	+	0.968283i	$0.580383\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	2.95897			0.105209
$792$		0			0
$793$	−26.0647			−0.925586
$794$		0			0
$795$		0			0
$796$		0			0
$797$	37.6281	+	21.7246i	1.33285	+	0.769524i	0.985736	−	0.168298i	$-0.0538271\pi$
$797$	37.6281	+	21.7246i	1.33285	+	0.769524i	0.347118	+	0.937822i	$0.387160\pi$
$798$		0			0
$799$	0.0566307	−	0.0326957i	0.00200345	−	0.00115669i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.42637	−	4.20260i	−0.0856248	−	0.148306i
$804$		0			0
$805$	−4.02878	+	6.97805i	−0.141996	+	0.245944i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	3.02370i		−	0.106308i	−0.998586	−	0.0531538i	$-0.983073\pi$
$809$		−	3.02370i		−	0.106308i	0.998586	−	0.0531538i	$-0.0169274\pi$
$810$		0			0
$811$			16.8746i			0.592548i	0.955103	+	0.296274i	$0.0957441\pi$
$811$			16.8746i			0.592548i	−0.955103	+	0.296274i	$0.904256\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−21.7553	+	37.6814i	−0.762057	+	1.31992i
$816$		0			0
$817$	−29.8745	−	51.7441i	−1.04518	−	1.81030i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	45.6478	−	26.3548i	1.59312	−	0.919787i	0.600351	−	0.799737i	$-0.295028\pi$
$821$	45.6478	−	26.3548i	1.59312	−	0.919787i	0.992768	−	0.120050i	$-0.0383056\pi$
$822$		0			0
$823$	42.9969	+	24.8243i	1.49878	+	0.865319i	0.999999	−	0.00141010i	$-0.000448849\pi$
$823$	42.9969	+	24.8243i	1.49878	+	0.865319i	0.498778	+	0.866730i	$0.333782\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−16.3377			−0.568117			−0.284059	−	0.958807i	$-0.591681\pi$
$827$	−16.3377			−0.568117			−0.284059	+	0.958807i	$0.591681\pi$
$828$		0			0
$829$	20.6403			0.716866			0.358433	−	0.933555i	$-0.383311\pi$
$829$	20.6403			0.716866			0.358433	+	0.933555i	$0.383311\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.152012	+	0.0877642i	0.00526691	+	0.00304085i
$834$		0			0
$835$	18.6582	−	10.7723i	0.645692	−	0.372791i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	8.33205	+	14.4315i	0.287654	+	0.498232i	0.973249	−	0.229751i	$-0.0737912\pi$
$839$	8.33205	+	14.4315i	0.287654	+	0.498232i	−0.685595	+	0.727983i	$0.740458\pi$
$840$		0			0
$841$	−14.4880	+	25.0940i	−0.499588	+	0.865312i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			22.5866i			0.777002i
$846$		0			0
$847$			3.67054i			0.126121i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	23.7765	−	41.1822i	0.815049	−	1.41171i
$852$		0			0
$853$	−8.50308	−	14.7278i	−0.291140	−	0.504269i	0.682940	−	0.730475i	$-0.260701\pi$
$853$	−8.50308	−	14.7278i	−0.291140	−	0.504269i	−0.974080	+	0.226206i	$0.927368\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	21.0489	−	12.1526i	0.719016	−	0.415124i	−0.0953742	−	0.995441i	$-0.530405\pi$
$857$	21.0489	−	12.1526i	0.719016	−	0.415124i	0.814391	+	0.580317i	$0.197071\pi$
$858$		0			0
$859$	14.9570	+	8.63542i	0.510326	+	0.294637i	0.732968	−	0.680264i	$-0.238135\pi$
$859$	14.9570	+	8.63542i	0.510326	+	0.294637i	−0.222642	+	0.974900i	$0.571468\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.59381			0.0542540			0.0271270	−	0.999632i	$-0.491364\pi$
$863$	1.59381			0.0542540			0.0271270	+	0.999632i	$0.491364\pi$
$864$		0			0
$865$	30.3410			1.03162
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.97785	−	1.14191i	−0.0670938	−	0.0387366i
$870$		0			0
$871$	10.0037	−	5.77566i	0.338964	−	0.195701i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.45834	+	2.52592i	0.0493010	+	0.0853918i
$876$		0			0
$877$	14.6461	−	25.3679i	0.494565	−	0.856612i	−0.505415	−	0.862876i	$-0.668661\pi$
$877$	14.6461	−	25.3679i	0.494565	−	0.856612i	0.999980	+	0.00626442i	$0.00199404\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	18.3399i		−	0.617885i	−0.951081	−	0.308943i	$-0.900025\pi$
$881$		−	18.3399i		−	0.617885i	0.951081	−	0.308943i	$-0.0999751\pi$
$882$		0			0
$883$			38.1130i			1.28260i	0.767288	+	0.641302i	$0.221606\pi$
$883$			38.1130i			1.28260i	−0.767288	+	0.641302i	$0.778394\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−15.3137	+	26.5241i	−0.514184	+	0.890593i	0.485680	+	0.874136i	$0.338572\pi$
$887$	−15.3137	+	26.5241i	−0.514184	+	0.890593i	−0.999865	+	0.0164567i	$0.994761\pi$
$888$		0			0
$889$	2.86766	+	4.96693i	0.0961781	+	0.166585i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	11.7596	−	6.78940i	0.393520	−	0.227199i
$894$		0			0
$895$	−38.7111	−	22.3498i	−1.29397	−	0.747073i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.21817			0.0406284
$900$		0			0
$901$	−0.101478			−0.00338072
$902$		0			0
$903$		0			0
$904$		0			0
$905$	39.5240	+	22.8192i	1.31382	+	0.758536i
$906$		0			0
$907$	−37.8970	+	21.8798i	−1.25835	+	0.726508i	−0.972753	−	0.231842i	$-0.925525\pi$
$907$	−37.8970	+	21.8798i	−1.25835	+	0.726508i	−0.285596	+	0.958350i	$0.592191\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	8.20019	+	14.2031i	0.271684	+	0.470571i	0.969293	−	0.245908i	$-0.0790860\pi$
$911$	8.20019	+	14.2031i	0.271684	+	0.470571i	−0.697609	+	0.716479i	$0.745753\pi$
$912$		0			0
$913$	4.61988	−	8.00186i	0.152896	−	0.264823i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	5.18803i		−	0.171324i
$918$		0			0
$919$		−	58.3956i		−	1.92629i	−0.268977	−	0.963147i	$-0.586686\pi$
$919$		−	58.3956i		−	1.92629i	0.268977	−	0.963147i	$-0.413314\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	7.09419	−	12.2875i	0.233508	−	0.404448i
$924$		0			0
$925$	4.76330	+	8.25028i	0.156616	+	0.271268i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−49.5699	+	28.6192i	−1.62634	+	0.938966i	−0.641164	+	0.767404i	$0.721548\pi$
$929$	−49.5699	+	28.6192i	−1.62634	+	0.938966i	−0.985173	+	0.171562i	$0.945119\pi$
$930$		0			0
$931$	31.5659	+	18.2246i	1.03453	+	0.597287i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.0446701			−0.00146087
$936$		0			0
$937$	−24.2258			−0.791423			−0.395712	−	0.918375i	$-0.629502\pi$
$937$	−24.2258			−0.791423			−0.395712	+	0.918375i	$0.629502\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.560087	−	0.323367i	−0.0182583	−	0.0105414i	0.490843	−	0.871248i	$-0.336689\pi$
$941$	−0.560087	−	0.323367i	−0.0182583	−	0.0105414i	−0.509101	+	0.860707i	$0.670022\pi$
$942$		0			0
$943$	52.4044	−	30.2557i	1.70652	−	0.985260i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−5.61026	−	9.71726i	−0.182309	−	0.315768i	0.760357	−	0.649505i	$-0.225024\pi$
$947$	−5.61026	−	9.71726i	−0.182309	−	0.315768i	−0.942666	+	0.333736i	$0.891690\pi$
$948$		0			0
$949$	−7.50752	+	13.0034i	−0.243704	+	0.422108i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	6.15028i		−	0.199227i	−0.995026	−	0.0996135i	$-0.968239\pi$
$953$		−	6.15028i		−	0.199227i	0.995026	−	0.0996135i	$-0.0317606\pi$
$954$		0			0
$955$		−	39.4966i		−	1.27808i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.32793	−	2.30004i	0.0428811	−	0.0742723i
$960$		0			0
$961$	15.5386	+	26.9136i	0.501245	+	0.868182i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−51.5221	+	29.7463i	−1.65855	+	0.957567i
$966$		0			0
$967$	−37.8054	−	21.8269i	−1.21574	−	0.701907i	−0.251735	−	0.967796i	$-0.581001\pi$
$967$	−37.8054	−	21.8269i	−1.21574	−	0.701907i	−0.964004	+	0.265889i	$0.914334\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	0.282196			0.00905612			0.00452806	−	0.999990i	$-0.498559\pi$
$971$	0.282196			0.00905612			0.00452806	+	0.999990i	$0.498559\pi$
$972$		0			0
$973$	0.972455			0.0311755
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−32.6897	−	18.8734i	−1.04583	−	0.603813i	−0.124354	−	0.992238i	$-0.539686\pi$
$977$	−32.6897	−	18.8734i	−1.04583	−	0.603813i	−0.921480	+	0.388425i	$0.873019\pi$
$978$		0			0
$979$	−6.19649	+	3.57755i	−0.198041	+	0.114339i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−7.53515	−	13.0513i	−0.240334	−	0.416271i	0.720475	−	0.693480i	$-0.243924\pi$
$983$	−7.53515	−	13.0513i	−0.240334	−	0.416271i	−0.960809	+	0.277210i	$0.910590\pi$
$984$		0			0
$985$	−2.71763	+	4.70707i	−0.0865908	+	0.149980i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	100.265i		−	3.18825i
$990$		0			0
$991$			16.5127i			0.524544i	0.964994	+	0.262272i	$0.0844717\pi$
$991$			16.5127i			0.524544i	−0.964994	+	0.262272i	$0.915528\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	27.5380	−	47.6973i	0.873015	−	1.51211i
$996$		0			0
$997$	26.1507	+	45.2943i	0.828199	+	1.43448i	0.899449	+	0.437025i	$0.143968\pi$
$997$	26.1507	+	45.2943i	0.828199	+	1.43448i	−0.0712500	+	0.997458i	$0.522699\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2592.2.s.j.863.6		16
3.2	odd	2	inner	2592.2.s.j.863.3		16
4.3	odd	2		2592.2.s.i.863.6		16
9.2	odd	6		2592.2.s.i.1727.6		16
9.4	even	3		2592.2.c.b.2591.5	✓	16
9.5	odd	6		2592.2.c.b.2591.11	yes	16
9.7	even	3		2592.2.s.i.1727.3		16
12.11	even	2		2592.2.s.i.863.3		16
36.7	odd	6	inner	2592.2.s.j.1727.3		16
36.11	even	6	inner	2592.2.s.j.1727.6		16
36.23	even	6		2592.2.c.b.2591.12	yes	16
36.31	odd	6		2592.2.c.b.2591.6	yes	16
72.5	odd	6		5184.2.c.l.5183.5		16
72.13	even	6		5184.2.c.l.5183.11		16
72.59	even	6		5184.2.c.l.5183.6		16
72.67	odd	6		5184.2.c.l.5183.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2592.2.c.b.2591.5	✓	16	9.4	even	3
2592.2.c.b.2591.6	yes	16	36.31	odd	6
2592.2.c.b.2591.11	yes	16	9.5	odd	6
2592.2.c.b.2591.12	yes	16	36.23	even	6
2592.2.s.i.863.3		16	12.11	even	2
2592.2.s.i.863.6		16	4.3	odd	2
2592.2.s.i.1727.3		16	9.7	even	3
2592.2.s.i.1727.6		16	9.2	odd	6
2592.2.s.j.863.3		16	3.2	odd	2	inner
2592.2.s.j.863.6		16	1.1	even	1	trivial
2592.2.s.j.1727.3		16	36.7	odd	6	inner
2592.2.s.j.1727.6		16	36.11	even	6	inner
5184.2.c.l.5183.5		16	72.5	odd	6
5184.2.c.l.5183.6		16	72.59	even	6
5184.2.c.l.5183.11		16	72.13	even	6
5184.2.c.l.5183.12		16	72.67	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:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.25522 + 1.30205i) q^{5} +(-0.301361 + 0.173991i) q^{7} +O(q^{10})\)	\(q+(2.25522 + 1.30205i) q^{5} +(-0.301361 + 0.173991i) q^{7} +(-0.336125 - 0.582186i) q^{11} +(-1.04002 + 1.80136i) q^{13} -0.0255169i q^{17} -5.29869i q^{19} +(4.44589 - 7.70051i) q^{23} +(0.890673 + 1.54269i) q^{25} +(0.133898 - 0.0773060i) q^{29} +(6.82333 + 3.93945i) q^{31} -0.906181 q^{35} +5.34798 q^{37} +(5.89358 + 3.40266i) q^{41} +(9.76546 - 5.63809i) q^{43} +(1.28134 + 2.21934i) q^{47} +(-3.43945 + 5.95731i) q^{49} -3.97689i q^{53} -1.75061i q^{55} +(-3.07449 + 5.32517i) q^{59} +(6.26546 + 10.8521i) q^{61} +(-4.69093 + 2.70831i) q^{65} +(-4.80941 - 2.77671i) q^{67} -6.82123 q^{71} +7.21865 q^{73} +(0.202590 + 0.116966i) q^{77} +(2.94213 - 1.69864i) q^{79} +(6.87226 + 11.9031i) q^{83} +(0.0332243 - 0.0575462i) q^{85} -10.6435i q^{89} -0.723815i q^{91} +(6.89916 - 11.9497i) q^{95} +(8.89016 + 15.3982i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{7}+O(q^{10}) \) 16 * q + 12 * q^7	\( 16 q + 12 q^{7} + 4 q^{13} + 24 q^{25} + 72 q^{31} + 72 q^{37} + 84 q^{43} + 24 q^{49} + 28 q^{61} + 36 q^{67} + 96 q^{73} + 12 q^{79} + 12 q^{85} + 16 q^{97}+O(q^{100}) \) 16 * q + 12 * q^7 + 4 * q^13 + 24 * q^25 + 72 * q^31 + 72 * q^37 + 84 * q^43 + 24 * q^49 + 28 * q^61 + 36 * q^67 + 96 * q^73 + 12 * q^79 + 12 * q^85 + 16 * q^97

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