LMFDB - Embedded newform 2160.2.q.k.1441.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2160,2,Mod(721,2160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2160, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2160.721");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2160 = 2^{4} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2160.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$17.2476868366$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1441.3
Root			$1.71903 - 0.211943i$ of defining polynomial
Character	$\chi$	$=$	2160.1441
Dual form			2160.2.q.k.721.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{5} +(2.04307 + 3.53869i) q^{7} +O(q^{10})$	$q+(0.500000 - 0.866025i) q^{5} +(2.04307 + 3.53869i) q^{7} +(0.675970 + 1.17081i) q^{11} +(-0.324030 + 0.561237i) q^{13} +1.35194 q^{17} -0.648061 q^{19} +(-2.39500 + 4.14827i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(1.93807 + 3.35683i) q^{29} +(-3.84823 + 6.66533i) q^{31} +4.08613 q^{35} +7.52420 q^{37} +(-0.0898394 + 0.155606i) q^{41} +(-0.410161 - 0.710419i) q^{43} +(-5.45323 - 9.44526i) q^{47} +(-4.84823 + 8.39738i) q^{49} -4.17226 q^{53} +1.35194 q^{55} +(-2.08613 + 3.61328i) q^{59} +(1.91016 + 3.30850i) q^{61} +(0.324030 + 0.561237i) q^{65} +(4.07097 - 7.05113i) q^{67} -6.11644 q^{71} -12.3445 q^{73} +(-2.76210 + 4.78410i) q^{77} +(5.17226 + 8.95862i) q^{79} +(6.12920 + 10.6161i) q^{83} +(0.675970 - 1.17081i) q^{85} +3.00000 q^{89} -2.64806 q^{91} +(-0.324030 + 0.561237i) q^{95} +(6.79001 + 11.7606i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} + 5 q^{7}+O(q^{10}) $ 6 * q + 3 * q^5 + 5 * q^7	$ 6 q + 3 q^{5} + 5 q^{7} + 2 q^{11} - 4 q^{13} + 4 q^{17} - 8 q^{19} - 3 q^{23} - 3 q^{25} - 7 q^{29} + 8 q^{31} + 10 q^{35} + 12 q^{37} - 13 q^{41} + 10 q^{43} - 13 q^{47} + 2 q^{49} + 4 q^{53} + 4 q^{55} + 2 q^{59} - q^{61} + 4 q^{65} + 11 q^{67} - 20 q^{71} - 16 q^{73} + 2 q^{79} + 15 q^{83} + 2 q^{85} + 18 q^{89} - 20 q^{91} - 4 q^{95} + 18 q^{97}+O(q^{100}) $ 6 * q + 3 * q^5 + 5 * q^7 + 2 * q^11 - 4 * q^13 + 4 * q^17 - 8 * q^19 - 3 * q^23 - 3 * q^25 - 7 * q^29 + 8 * q^31 + 10 * q^35 + 12 * q^37 - 13 * q^41 + 10 * q^43 - 13 * q^47 + 2 * q^49 + 4 * q^53 + 4 * q^55 + 2 * q^59 - q^61 + 4 * q^65 + 11 * q^67 - 20 * q^71 - 16 * q^73 + 2 * q^79 + 15 * q^83 + 2 * q^85 + 18 * q^89 - 20 * q^91 - 4 * q^95 + 18 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2160\mathbb{Z}\right)^\times$.

$n$	$271$	$1297$	$1621$	$2081$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	2.04307	+	3.53869i	0.772206	+	1.33750i	0.936351	+	0.351064i	$0.114180\pi$
$7$	2.04307	+	3.53869i	0.772206	+	1.33750i	−0.164145	+	0.986436i	$0.552487\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.675970	+	1.17081i	0.203813	+	0.353014i	0.949754	−	0.312998i	$-0.101333\pi$
$11$	0.675970	+	1.17081i	0.203813	+	0.353014i	−0.745941	+	0.666012i	$0.768000\pi$
$12$		0			0
$13$	−0.324030	+	0.561237i	−0.0898699	+	0.155659i	−0.907456	−	0.420147i	$-0.861978\pi$
$13$	−0.324030	+	0.561237i	−0.0898699	+	0.155659i	0.817586	+	0.575806i	$0.195312\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.35194			0.327893			0.163947	−	0.986469i	$-0.447577\pi$
$17$	1.35194			0.327893			0.163947	+	0.986469i	$0.447577\pi$
$18$		0			0
$19$	−0.648061			−0.148675			−0.0743377	−	0.997233i	$-0.523684\pi$
$19$	−0.648061			−0.148675			−0.0743377	+	0.997233i	$0.523684\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.39500	+	4.14827i	−0.499393	+	0.864974i	−1.00000		0.000700856i	$-0.999777\pi$
$23$	−2.39500	+	4.14827i	−0.499393	+	0.864974i	0.500607	+	0.865675i	$0.333110\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.93807	+	3.35683i	0.359890	+	0.623349i	0.987942	−	0.154823i	$-0.0494807\pi$
$29$	1.93807	+	3.35683i	0.359890	+	0.623349i	−0.628052	+	0.778172i	$0.716147\pi$
$30$		0			0
$31$	−3.84823	+	6.66533i	−0.691163	+	1.19713i	0.280295	+	0.959914i	$0.409568\pi$
$31$	−3.84823	+	6.66533i	−0.691163	+	1.19713i	−0.971457	+	0.237215i	$0.923766\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.08613			0.690682
$36$		0			0
$37$	7.52420			1.23697			0.618485	−	0.785796i	$-0.287747\pi$
$37$	7.52420			1.23697			0.618485	+	0.785796i	$0.287747\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.0898394	+	0.155606i	−0.0140306	+	0.0243016i	−0.872955	−	0.487800i	$-0.837800\pi$
$41$	−0.0898394	+	0.155606i	−0.0140306	+	0.0243016i	0.858925	+	0.512102i	$0.171133\pi$
$42$		0			0
$43$	−0.410161	−	0.710419i	−0.0625489	−	0.108338i	0.833055	−	0.553190i	$-0.186590\pi$
$43$	−0.410161	−	0.710419i	−0.0625489	−	0.108338i	−0.895604	+	0.444852i	$0.853256\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.45323	−	9.44526i	−0.795435	−	1.37773i	−0.922563	−	0.385847i	$-0.873909\pi$
$47$	−5.45323	−	9.44526i	−0.795435	−	1.37773i	0.127128	−	0.991886i	$-0.459424\pi$
$48$		0			0
$49$	−4.84823	+	8.39738i	−0.692604	+	1.19963i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.17226			−0.573104			−0.286552	−	0.958065i	$-0.592509\pi$
$53$	−4.17226			−0.573104			−0.286552	+	0.958065i	$0.592509\pi$
$54$		0			0
$55$	1.35194			0.182295
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.08613	+	3.61328i	−0.271591	+	0.470409i	−0.969269	−	0.246002i	$-0.920883\pi$
$59$	−2.08613	+	3.61328i	−0.271591	+	0.470409i	0.697678	+	0.716411i	$0.254216\pi$
$60$		0			0
$61$	1.91016	+	3.30850i	0.244571	+	0.423609i	0.962011	−	0.273011i	$-0.0880195\pi$
$61$	1.91016	+	3.30850i	0.244571	+	0.423609i	−0.717440	+	0.696620i	$0.754686\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.324030	+	0.561237i	0.0401910	+	0.0696129i
$66$		0			0
$67$	4.07097	−	7.05113i	0.497349	−	0.861433i	−0.502647	−	0.864492i	$-0.667640\pi$
$67$	4.07097	−	7.05113i	0.497349	−	0.861433i	0.999995	+	0.00305885i	$0.000973664\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−6.11644			−0.725888			−0.362944	−	0.931811i	$-0.618228\pi$
$71$	−6.11644			−0.725888			−0.362944	+	0.931811i	$0.618228\pi$
$72$		0			0
$73$	−12.3445			−1.44482			−0.722408	−	0.691467i	$-0.756965\pi$
$73$	−12.3445			−1.44482			−0.722408	+	0.691467i	$0.756965\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.76210	+	4.78410i	−0.314770	+	0.545198i
$78$		0			0
$79$	5.17226	+	8.95862i	0.581925	+	1.00792i	0.995251	+	0.0973403i	$0.0310335\pi$
$79$	5.17226	+	8.95862i	0.581925	+	1.00792i	−0.413326	+	0.910583i	$0.635633\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.12920	+	10.6161i	0.672767	+	1.16527i	0.977116	+	0.212706i	$0.0682275\pi$
$83$	6.12920	+	10.6161i	0.672767	+	1.16527i	−0.304350	+	0.952560i	$0.598439\pi$
$84$		0			0
$85$	0.675970	−	1.17081i	0.0733192	−	0.126993i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.00000			0.317999			0.159000	−	0.987279i	$-0.449173\pi$
$89$	3.00000			0.317999			0.159000	+	0.987279i	$0.449173\pi$
$90$		0			0
$91$	−2.64806			−0.277592
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.324030	+	0.561237i	−0.0332448	+	0.0575817i
$96$		0			0
$97$	6.79001	+	11.7606i	0.689421	+	1.19411i	0.972025	+	0.234876i	$0.0754683\pi$
$97$	6.79001	+	11.7606i	0.689421	+	1.19411i	−0.282605	+	0.959237i	$0.591198\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.734191	−	1.27166i	−0.0730547	−	0.126535i	0.827184	−	0.561931i	$-0.189941\pi$
$101$	−0.734191	−	1.27166i	−0.0730547	−	0.126535i	−0.900239	+	0.435397i	$0.856608\pi$
$102$		0			0
$103$	3.76210	−	6.51615i	0.370691	−	0.642055i	−0.618981	−	0.785406i	$-0.712454\pi$
$103$	3.76210	−	6.51615i	0.370691	−	0.642055i	0.989672	+	0.143351i	$0.0457877\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.20999			0.116974			0.0584871	−	0.998288i	$-0.481372\pi$
$107$	1.20999			0.116974			0.0584871	+	0.998288i	$0.481372\pi$
$108$		0			0
$109$	14.1042			1.35094			0.675469	−	0.737388i	$-0.263941\pi$
$109$	14.1042			1.35094			0.675469	+	0.737388i	$0.263941\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.96227	+	10.3270i	−0.560883	+	0.971478i	0.436537	+	0.899687i	$0.356205\pi$
$113$	−5.96227	+	10.3270i	−0.560883	+	0.971478i	−0.997420	+	0.0717915i	$0.977128\pi$
$114$		0			0
$115$	2.39500	+	4.14827i	0.223335	+	0.386828i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.76210	+	4.78410i	0.253201	+	0.438557i
$120$		0			0
$121$	4.58613	−	7.94341i	0.416921	−	0.722128i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	7.07871			0.628134			0.314067	−	0.949401i	$-0.398308\pi$
$127$	7.07871			0.628134			0.314067	+	0.949401i	$0.398308\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	−0.704692	−	0.709514i	$-0.748915\pi$
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	0.966803	+	0.255524i	$0.0822479\pi$
$132$		0			0
$133$	−1.32403	−	2.29329i	−0.114808	−	0.198853i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.73419	−	6.46781i	−0.319033	−	0.552582i	0.661253	−	0.750163i	$-0.270025\pi$
$137$	−3.73419	−	6.46781i	−0.319033	−	0.552582i	−0.980287	+	0.197581i	$0.936692\pi$
$138$		0			0
$139$	4.00000	−	6.92820i	0.339276	−	0.587643i	−0.645021	−	0.764165i	$-0.723151\pi$
$139$	4.00000	−	6.92820i	0.339276	−	0.587643i	0.984297	+	0.176522i	$0.0564848\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.876139			−0.0732664
$144$		0			0
$145$	3.87614			0.321896
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.29241	+	9.16673i	−0.433571	+	0.750968i	−0.997178	−	0.0750759i	$-0.976080\pi$
$149$	−5.29241	+	9.16673i	−0.433571	+	0.750968i	0.563607	+	0.826043i	$0.309413\pi$
$150$		0			0
$151$	8.84823	+	15.3256i	0.720059	+	1.24718i	0.960976	+	0.276633i	$0.0892185\pi$
$151$	8.84823	+	15.3256i	0.720059	+	1.24718i	−0.240917	+	0.970546i	$0.577448\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.84823	+	6.66533i	0.309097	+	0.535372i
$156$		0			0
$157$	1.26581	−	2.19245i	0.101023	−	0.174976i	−0.811084	−	0.584930i	$-0.801122\pi$
$157$	1.26581	−	2.19245i	0.101023	−	0.174976i	0.912106	+	0.409954i	$0.134455\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−19.5726			−1.54254
$162$		0			0
$163$	−8.47580			−0.663876			−0.331938	−	0.943301i	$-0.607702\pi$
$163$	−8.47580			−0.663876			−0.331938	+	0.943301i	$0.607702\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.36710	+	11.0281i	−0.492701	+	0.853383i	−0.999965	−	0.00840816i	$-0.997324\pi$
$167$	−6.36710	+	11.0281i	−0.492701	+	0.853383i	0.507264	+	0.861791i	$0.330657\pi$
$168$		0			0
$169$	6.29001	+	10.8946i	0.483847	+	0.838047i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	11.5242	+	19.9605i	0.876169	+	1.51757i	0.855513	+	0.517782i	$0.173242\pi$
$173$	11.5242	+	19.9605i	0.876169	+	1.51757i	0.0206561	+	0.999787i	$0.493424\pi$
$174$		0			0
$175$	2.04307	−	3.53869i	0.154441	−	0.267500i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	2.22808			0.166534			0.0832672	−	0.996527i	$-0.473465\pi$
$179$	2.22808			0.166534			0.0832672	+	0.996527i	$0.473465\pi$
$180$		0			0
$181$	0.468382			0.0348146			0.0174073	−	0.999848i	$-0.494459\pi$
$181$	0.468382			0.0348146			0.0174073	+	0.999848i	$0.494459\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.76210	−	6.51615i	0.276595	−	0.479077i
$186$		0			0
$187$	0.913870	+	1.58287i	0.0668288	+	0.115751i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	10.1140	+	17.5180i	0.731826	+	1.26756i	0.956102	+	0.293034i	$0.0946650\pi$
$191$	10.1140	+	17.5180i	0.731826	+	1.26756i	−0.224276	+	0.974526i	$0.572002\pi$
$192$		0			0
$193$	9.96467	−	17.2593i	0.717273	−	1.24235i	−0.244804	−	0.969573i	$-0.578723\pi$
$193$	9.96467	−	17.2593i	0.717273	−	1.24235i	0.962076	−	0.272780i	$-0.0879432\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	15.5800			1.11003			0.555015	−	0.831840i	$-0.312712\pi$
$197$	15.5800			1.11003			0.555015	+	0.831840i	$0.312712\pi$
$198$		0			0
$199$	−3.58482			−0.254121			−0.127061	−	0.991895i	$-0.540554\pi$
$199$	−3.58482			−0.254121			−0.127061	+	0.991895i	$0.540554\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−7.91920	+	13.7165i	−0.555819	+	0.962707i
$204$		0			0
$205$	0.0898394	+	0.155606i	0.00627466	+	0.0108680i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.438069	−	0.758758i	−0.0303019	−	0.0524844i
$210$		0			0
$211$	7.49629	−	12.9840i	0.516066	−	0.893852i	−0.483760	−	0.875201i	$-0.660729\pi$
$211$	7.49629	−	12.9840i	0.516066	−	0.893852i	0.999826	−	0.0186518i	$-0.00593739\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.820321			−0.0559454
$216$		0			0
$217$	−31.4487			−2.13488
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.438069	+	0.758758i	−0.0294677	+	0.0510396i
$222$		0			0
$223$	−13.4155	−	23.2363i	−0.898368	−	1.55602i	−0.829580	−	0.558388i	$-0.811420\pi$
$223$	−13.4155	−	23.2363i	−0.898368	−	1.55602i	−0.0687878	−	0.997631i	$-0.521913\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.675970	−	1.17081i	−0.0448657	−	0.0777096i	0.842721	−	0.538351i	$-0.180953\pi$
$227$	−0.675970	−	1.17081i	−0.0448657	−	0.0777096i	−0.887586	+	0.460642i	$0.847619\pi$
$228$		0			0
$229$	4.11775	−	7.13215i	0.272108	−	0.471306i	−0.697293	−	0.716786i	$-0.745612\pi$
$229$	4.11775	−	7.13215i	0.272108	−	0.471306i	0.969402	+	0.245480i	$0.0789457\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−8.58744			−0.562582			−0.281291	−	0.959623i	$-0.590763\pi$
$233$	−8.58744			−0.562582			−0.281291	+	0.959623i	$0.590763\pi$
$234$		0			0
$235$	−10.9065			−0.711458
$236$		0			0
$237$		0			0
$238$		0			0
$239$	11.9623	−	20.7193i	0.773775	−	1.34022i	−0.161706	−	0.986839i	$-0.551700\pi$
$239$	11.9623	−	20.7193i	0.773775	−	1.34022i	0.935480	−	0.353378i	$-0.114967\pi$
$240$		0			0
$241$	3.12015	+	5.40426i	0.200987	+	0.348119i	0.948847	−	0.315737i	$-0.102252\pi$
$241$	3.12015	+	5.40426i	0.200987	+	0.348119i	−0.747860	+	0.663857i	$0.768919\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	4.84823	+	8.39738i	0.309742	+	0.536489i
$246$		0			0
$247$	0.209991	−	0.363716i	0.0133614	−	0.0231427i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−28.5726			−1.80349			−0.901743	−	0.432272i	$-0.857712\pi$
$251$	−28.5726			−1.80349			−0.901743	+	0.432272i	$0.857712\pi$
$252$		0			0
$253$	−6.47580			−0.407130
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	0.435970	+	0.899961i	$0.356405\pi$
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	−0.997374	+	0.0724199i	$0.976928\pi$
$258$		0			0
$259$	15.3724	+	26.6258i	0.955196	+	1.65445i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−15.9344	−	27.5991i	−0.982555	−	1.70183i	−0.652335	−	0.757931i	$-0.726211\pi$
$263$	−15.9344	−	27.5991i	−0.982555	−	1.70183i	−0.330220	−	0.943904i	$-0.607123\pi$
$264$		0			0
$265$	−2.08613	+	3.61328i	−0.128150	+	0.221962i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	31.4971			1.92041			0.960207	−	0.279289i	$-0.0900987\pi$
$269$	31.4971			1.92041			0.960207	+	0.279289i	$0.0900987\pi$
$270$		0			0
$271$	3.24030			0.196834			0.0984172	−	0.995145i	$-0.468622\pi$
$271$	3.24030			0.196834			0.0984172	+	0.995145i	$0.468622\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.675970	−	1.17081i	0.0407625	−	0.0706027i
$276$		0			0
$277$	2.79241	+	4.83660i	0.167780	+	0.290603i	0.937639	−	0.347611i	$-0.113007\pi$
$277$	2.79241	+	4.83660i	0.167780	+	0.290603i	−0.769859	+	0.638214i	$0.779674\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−12.0521	−	20.8749i	−0.718969	−	1.24529i	−0.961409	−	0.275124i	$-0.911281\pi$
$281$	−12.0521	−	20.8749i	−0.718969	−	1.24529i	0.242440	−	0.970166i	$-0.422052\pi$
$282$		0			0
$283$	−5.27114	+	9.12989i	−0.313337	+	0.542715i	−0.979083	−	0.203463i	$-0.934780\pi$
$283$	−5.27114	+	9.12989i	−0.313337	+	0.542715i	0.665746	+	0.746179i	$0.268114\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.734191			−0.0433379
$288$		0			0
$289$	−15.1723			−0.892486
$290$		0			0
$291$		0			0
$292$		0			0
$293$	9.49629	−	16.4481i	0.554779	−	0.960906i	−0.443141	−	0.896452i	$-0.646136\pi$
$293$	9.49629	−	16.4481i	0.554779	−	0.960906i	0.997921	−	0.0644541i	$-0.0205306\pi$
$294$		0			0
$295$	2.08613	+	3.61328i	0.121459	+	0.210373i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.55211	−	2.68833i	−0.0897607	−	0.155470i
$300$		0			0
$301$	1.67597	−	2.90286i	0.0966013	−	0.167318i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	3.82032			0.218751
$306$		0			0
$307$	−29.4791			−1.68246			−0.841229	−	0.540679i	$-0.818167\pi$
$307$	−29.4791			−1.68246			−0.841229	+	0.540679i	$0.818167\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.70628	−	8.15152i	0.266869	−	0.462230i	−0.701183	−	0.712982i	$-0.747344\pi$
$311$	4.70628	−	8.15152i	0.266869	−	0.462230i	0.968052	+	0.250751i	$0.0806776\pi$
$312$		0			0
$313$	−5.81050	−	10.0641i	−0.328429	−	0.568855i	0.653771	−	0.756692i	$-0.273186\pi$
$313$	−5.81050	−	10.0641i	−0.328429	−	0.568855i	−0.982200	+	0.187837i	$0.939852\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.58984	−	7.94984i	−0.257791	−	0.446507i	0.707859	−	0.706354i	$-0.249661\pi$
$317$	−4.58984	−	7.94984i	−0.257791	−	0.446507i	−0.965650	+	0.259847i	$0.916328\pi$
$318$		0			0
$319$	−2.62015	+	4.53824i	−0.146700	+	0.254092i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.876139			−0.0487497
$324$		0			0
$325$	0.648061			0.0359479
$326$		0			0
$327$		0			0
$328$		0			0
$329$	22.2826	−	38.5946i	1.22848	−	2.12779i
$330$		0			0
$331$	−3.61033	−	6.25327i	−0.198442	−	0.343711i	0.749582	−	0.661912i	$-0.230255\pi$
$331$	−3.61033	−	6.25327i	−0.198442	−	0.343711i	−0.948023	+	0.318201i	$0.896921\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−4.07097	−	7.05113i	−0.222421	−	0.385245i
$336$		0			0
$337$	−1.14195	+	1.97791i	−0.0622059	+	0.107744i	−0.895451	−	0.445160i	$-0.853147\pi$
$337$	−1.14195	+	1.97791i	−0.0622059	+	0.107744i	0.833245	+	0.552904i	$0.186480\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−10.4051			−0.563470
$342$		0			0
$343$	−11.0181			−0.594921
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.354343	−	0.613740i	0.0190221	−	0.0329473i	−0.856358	−	0.516383i	$-0.827278\pi$
$347$	0.354343	−	0.613740i	0.0190221	−	0.0329473i	0.875380	+	0.483436i	$0.160611\pi$
$348$		0			0
$349$	10.6723	+	18.4849i	0.571273	+	0.989474i	0.996436	+	0.0843569i	$0.0268836\pi$
$349$	10.6723	+	18.4849i	0.571273	+	0.989474i	−0.425163	+	0.905117i	$0.639783\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.04840	−	8.74408i	−0.268699	−	0.465401i	0.699827	−	0.714312i	$-0.253260\pi$
$353$	−5.04840	−	8.74408i	−0.268699	−	0.465401i	−0.968526	+	0.248912i	$0.919927\pi$
$354$		0			0
$355$	−3.05822	+	5.29699i	−0.162314	+	0.281135i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	30.5578			1.61278			0.806388	−	0.591386i	$-0.201419\pi$
$359$	30.5578			1.61278			0.806388	+	0.591386i	$0.201419\pi$
$360$		0			0
$361$	−18.5800			−0.977896
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−6.17226	+	10.6907i	−0.323071	+	0.559575i
$366$		0			0
$367$	−3.58984	−	6.21778i	−0.187388	−	0.324566i	0.756991	−	0.653426i	$-0.226669\pi$
$367$	−3.58984	−	6.21778i	−0.187388	−	0.324566i	−0.944379	+	0.328860i	$0.893336\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−8.52420	−	14.7643i	−0.442554	−	0.766527i
$372$		0			0
$373$	10.9623	−	18.9872i	0.567605	−	0.983120i	−0.429197	−	0.903211i	$-0.641204\pi$
$373$	10.9623	−	18.9872i	0.567605	−	0.983120i	0.996802	−	0.0799096i	$-0.0254632\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.51197			−0.129373
$378$		0			0
$379$	17.3929			0.893414			0.446707	−	0.894680i	$-0.352597\pi$
$379$	17.3929			0.893414			0.446707	+	0.894680i	$0.352597\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.237900	+	0.412055i	−0.0121561	+	0.0210550i	−0.872039	−	0.489436i	$-0.837203\pi$
$383$	−0.237900	+	0.412055i	−0.0121561	+	0.0210550i	0.859883	+	0.510491i	$0.170536\pi$
$384$		0			0
$385$	2.76210	+	4.78410i	0.140770	+	0.243820i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−2.79372	−	4.83886i	−0.141647	−	0.245340i	0.786470	−	0.617629i	$-0.211906\pi$
$389$	−2.79372	−	4.83886i	−0.141647	−	0.245340i	−0.928117	+	0.372289i	$0.878573\pi$
$390$		0			0
$391$	−3.23790	+	5.60821i	−0.163748	+	0.283619i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	10.3445			0.520489
$396$		0			0
$397$	3.75228			0.188321			0.0941607	−	0.995557i	$-0.469983\pi$
$397$	3.75228			0.188321			0.0941607	+	0.995557i	$0.469983\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.7826	−	20.4080i	0.588394	−	1.01913i	−0.406048	−	0.913852i	$-0.633094\pi$
$401$	11.7826	−	20.4080i	0.588394	−	1.01913i	0.994443	−	0.105278i	$-0.0335731\pi$
$402$		0			0
$403$	−2.49389	−	4.31954i	−0.124229	−	0.215172i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	5.08613	+	8.80944i	0.252110	+	0.436668i
$408$		0			0
$409$	−0.524200	+	0.907940i	−0.0259200	+	0.0448948i	−0.878694	−	0.477385i	$-0.841585\pi$
$409$	−0.524200	+	0.907940i	−0.0259200	+	0.0448948i	0.852774	+	0.522279i	$0.174918\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−17.0484			−0.838897
$414$		0			0
$415$	12.2584			0.601741
$416$		0			0
$417$		0			0
$418$		0			0
$419$	12.9599	−	22.4471i	0.633131	−	1.09661i	−0.353777	−	0.935330i	$-0.615103\pi$
$419$	12.9599	−	22.4471i	0.633131	−	1.09661i	0.986908	−	0.161285i	$-0.0515638\pi$
$420$		0			0
$421$	−3.82032	−	6.61699i	−0.186191	−	0.322492i	0.757786	−	0.652503i	$-0.226281\pi$
$421$	−3.82032	−	6.61699i	−0.186191	−	0.322492i	−0.943977	+	0.330011i	$0.892948\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.675970	−	1.17081i	−0.0327893	−	0.0567928i
$426$		0			0
$427$	−7.80516	+	13.5189i	−0.377718	+	0.654227i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	7.98516			0.384632			0.192316	−	0.981333i	$-0.438400\pi$
$431$	7.98516			0.384632			0.192316	+	0.981333i	$0.438400\pi$
$432$		0			0
$433$	−12.5120			−0.601287			−0.300644	−	0.953737i	$-0.597201\pi$
$433$	−12.5120			−0.601287			−0.300644	+	0.953737i	$0.597201\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.55211	−	2.68833i	0.0742474	−	0.128600i
$438$		0			0
$439$	−4.38225	−	7.59028i	−0.209153	−	0.362264i	0.742295	−	0.670074i	$-0.233737\pi$
$439$	−4.38225	−	7.59028i	−0.209153	−	0.362264i	−0.951448	+	0.307809i	$0.900404\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.83548	−	3.17914i	−0.0872062	−	0.151046i	0.819123	−	0.573618i	$-0.194461\pi$
$443$	−1.83548	−	3.17914i	−0.0872062	−	0.151046i	−0.906329	+	0.422572i	$0.861127\pi$
$444$		0			0
$445$	1.50000	−	2.59808i	0.0711068	−	0.123161i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−28.1723			−1.32953			−0.664766	−	0.747052i	$-0.731469\pi$
$449$	−28.1723			−1.32953			−0.664766	+	0.747052i	$0.731469\pi$
$450$		0			0
$451$	−0.242915			−0.0114384
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.32403	+	2.29329i	−0.0620715	+	0.107511i
$456$		0			0
$457$	−17.6308	−	30.5375i	−0.824735	−	1.42848i	−0.902122	−	0.431482i	$-0.857991\pi$
$457$	−17.6308	−	30.5375i	−0.824735	−	1.42848i	0.0773867	−	0.997001i	$-0.475342\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	17.3384	+	30.0310i	0.807530	+	1.39868i	0.914570	+	0.404428i	$0.132530\pi$
$461$	17.3384	+	30.0310i	0.807530	+	1.39868i	−0.107039	+	0.994255i	$0.534137\pi$
$462$		0			0
$463$	3.72437	−	6.45080i	0.173086	−	0.299794i	−0.766411	−	0.642350i	$-0.777959\pi$
$463$	3.72437	−	6.45080i	0.173086	−	0.299794i	0.939497	+	0.342556i	$0.111293\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	29.9655			1.38664			0.693319	−	0.720630i	$-0.256148\pi$
$467$	29.9655			1.38664			0.693319	+	0.720630i	$0.256148\pi$
$468$		0			0
$469$	33.2691			1.53622
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.554512	−	0.960443i	0.0254965	−	0.0441612i
$474$		0			0
$475$	0.324030	+	0.561237i	0.0148675	+	0.0257513i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.99258	+	6.91535i	0.182426	+	0.315971i	0.942706	−	0.333625i	$-0.108272\pi$
$479$	3.99258	+	6.91535i	0.182426	+	0.315971i	−0.760280	+	0.649595i	$0.774938\pi$
$480$		0			0
$481$	−2.43807	+	4.22286i	−0.111166	+	0.192546i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	13.5800			0.616637
$486$		0			0
$487$	11.9442			0.541243			0.270621	−	0.962686i	$-0.412771\pi$
$487$	11.9442			0.541243			0.270621	+	0.962686i	$0.412771\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	4.61033	−	7.98533i	0.208061	−	0.360373i	−0.743042	−	0.669244i	$-0.766618\pi$
$491$	4.61033	−	7.98533i	0.208061	−	0.360373i	0.951104	+	0.308872i	$0.0999513\pi$
$492$		0			0
$493$	2.62015	+	4.53824i	0.118006	+	0.204392i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−12.4963	−	21.6442i	−0.560535	−	0.970876i
$498$		0			0
$499$	15.0861	−	26.1299i	0.675348	−	1.16974i	−0.301019	−	0.953618i	$-0.597327\pi$
$499$	15.0861	−	26.1299i	0.675348	−	1.16974i	0.976367	−	0.216119i	$-0.0693399\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−10.5981			−0.472546			−0.236273	−	0.971687i	$-0.575926\pi$
$503$	−10.5981			−0.472546			−0.236273	+	0.971687i	$0.575926\pi$
$504$		0			0
$505$	−1.46838			−0.0653421
$506$		0			0
$507$		0			0
$508$		0			0
$509$	14.3761	−	24.9002i	0.637211	−	1.10368i	−0.348831	−	0.937186i	$-0.613421\pi$
$509$	14.3761	−	24.9002i	0.637211	−	1.10368i	0.986042	−	0.166496i	$-0.0532454\pi$
$510$		0			0
$511$	−25.2207	−	43.6835i	−1.11570	−	1.93244i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−3.76210	−	6.51615i	−0.165778	−	0.287136i
$516$		0			0
$517$	7.37243	−	12.7694i	0.324239	−	0.561599i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	36.0942			1.58132			0.790658	−	0.612259i	$-0.209739\pi$
$521$	36.0942			1.58132			0.790658	+	0.612259i	$0.209739\pi$
$522$		0			0
$523$	−11.1297			−0.486669			−0.243334	−	0.969942i	$-0.578241\pi$
$523$	−11.1297			−0.486669			−0.243334	+	0.969942i	$0.578241\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.20257	+	9.01112i	−0.226628	+	0.392531i
$528$		0			0
$529$	0.0279088	+	0.0483395i	0.00121343	+	0.00210172i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.0582214	−	0.100842i	−0.00252185	−	0.00436797i
$534$		0			0
$535$	0.604996	−	1.04788i	0.0261562	−	0.0453039i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−13.1090			−0.564646
$540$		0			0
$541$	−34.7374			−1.49348			−0.746740	−	0.665116i	$-0.768382\pi$
$541$	−34.7374			−1.49348			−0.746740	+	0.665116i	$0.768382\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	7.05211	−	12.2146i	0.302079	−	0.523216i
$546$		0			0
$547$	−1.35727	−	2.35087i	−0.0580328	−	0.100516i	0.835549	−	0.549415i	$-0.185149\pi$
$547$	−1.35727	−	2.35087i	−0.0580328	−	0.100516i	−0.893582	+	0.448899i	$0.851816\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.25599	−	2.17543i	−0.0535068	−	0.0926766i
$552$		0			0
$553$	−21.1345	+	36.6061i	−0.898732	+	1.55665i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	8.93676			0.378663			0.189331	−	0.981913i	$-0.439368\pi$
$557$	8.93676			0.378663			0.189331	+	0.981913i	$0.439368\pi$
$558$		0			0
$559$	0.531618			0.0224850
$560$		0			0
$561$		0			0
$562$		0			0
$563$	4.68130	−	8.10826i	0.197293	−	0.341722i	−0.750357	−	0.661033i	$-0.770118\pi$
$563$	4.68130	−	8.10826i	0.197293	−	0.341722i	0.947650	+	0.319311i	$0.103451\pi$
$564$		0			0
$565$	5.96227	+	10.3270i	0.250835	+	0.434458i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	17.9368	+	31.0674i	0.751948	+	1.30241i	0.946877	+	0.321595i	$0.104219\pi$
$569$	17.9368	+	31.0674i	0.751948	+	1.30241i	−0.194929	+	0.980817i	$0.562448\pi$
$570$		0			0
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	−0.577301	−	0.816532i	$-0.695894\pi$
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	0.995788	+	0.0916910i	$0.0292272\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.79001			0.199757
$576$		0			0
$577$	1.35675			0.0564821			0.0282411	−	0.999601i	$-0.491009\pi$
$577$	1.35675			0.0564821			0.0282411	+	0.999601i	$0.491009\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−25.0447	+	43.3787i	−1.03903	+	1.79965i
$582$		0			0
$583$	−2.82032	−	4.88494i	−0.116806	−	0.202314i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−14.3950	−	24.9329i	−0.594145	−	1.02909i	−0.993667	−	0.112366i	$-0.964157\pi$
$587$	−14.3950	−	24.9329i	−0.594145	−	1.02909i	0.399521	−	0.916724i	$-0.369176\pi$
$588$		0			0
$589$	2.49389	−	4.31954i	0.102759	−	0.177984i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−30.9171			−1.26961			−0.634807	−	0.772671i	$-0.718920\pi$
$593$	−30.9171			−1.26961			−0.634807	+	0.772671i	$0.718920\pi$
$594$		0			0
$595$	5.52420			0.226470
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−0.696460	+	1.20630i	−0.0284566	+	0.0492882i	−0.879903	−	0.475153i	$-0.842393\pi$
$599$	−0.696460	+	1.20630i	−0.0284566	+	0.0492882i	0.851446	+	0.524442i	$0.175726\pi$
$600$		0			0
$601$	−4.41256	−	7.64279i	−0.179992	−	0.311756i	0.761885	−	0.647712i	$-0.224274\pi$
$601$	−4.41256	−	7.64279i	−0.179992	−	0.311756i	−0.941878	+	0.335956i	$0.890941\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.58613	−	7.94341i	−0.186453	−	0.322946i
$606$		0			0
$607$	−1.07839	+	1.86783i	−0.0437706	+	0.0758129i	−0.887081	−	0.461614i	$-0.847270\pi$
$607$	−1.07839	+	1.86783i	−0.0437706	+	0.0758129i	0.843310	+	0.537427i	$0.180604\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	7.06804			0.285942
$612$		0			0
$613$	−9.57521			−0.386739			−0.193370	−	0.981126i	$-0.561942\pi$
$613$	−9.57521			−0.386739			−0.193370	+	0.981126i	$0.561942\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−18.8384	+	32.6291i	−0.758406	+	1.31360i	0.185258	+	0.982690i	$0.440688\pi$
$617$	−18.8384	+	32.6291i	−0.758406	+	1.31360i	−0.943663	+	0.330907i	$0.892645\pi$
$618$		0			0
$619$	8.55211	+	14.8127i	0.343738	+	0.595372i	0.985124	−	0.171847i	$-0.0549734\pi$
$619$	8.55211	+	14.8127i	0.343738	+	0.595372i	−0.641385	+	0.767219i	$0.721640\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	6.12920	+	10.6161i	0.245561	+	0.425324i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	10.1723			0.405595
$630$		0			0
$631$	−33.1090			−1.31805			−0.659025	−	0.752121i	$-0.729031\pi$
$631$	−33.1090			−1.31805			−0.659025	+	0.752121i	$0.729031\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	3.53936	−	6.13034i	0.140455	−	0.243275i
$636$		0			0
$637$	−3.14195	−	5.44201i	−0.124489	−	0.215620i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−11.5763	−	20.0508i	−0.457237	−	0.791957i	0.541577	−	0.840651i	$-0.317827\pi$
$641$	−11.5763	−	20.0508i	−0.457237	−	0.791957i	−0.998814	+	0.0486939i	$0.984494\pi$
$642$		0			0
$643$	21.5319	−	37.2944i	0.849137	−	1.47075i	−0.0328430	−	0.999461i	$-0.510456\pi$
$643$	21.5319	−	37.2944i	0.849137	−	1.47075i	0.881980	−	0.471287i	$-0.156211\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−20.6439			−0.811595			−0.405798	−	0.913963i	$-0.633006\pi$
$647$	−20.6439			−0.811595			−0.405798	+	0.913963i	$0.633006\pi$
$648$		0			0
$649$	−5.64064			−0.221415
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.41758	−	5.91942i	0.133740	−	0.231645i	−0.791375	−	0.611331i	$-0.790635\pi$
$653$	3.41758	−	5.91942i	0.133740	−	0.231645i	0.925116	+	0.379686i	$0.123968\pi$
$654$		0			0
$655$	−3.00000	−	5.19615i	−0.117220	−	0.203030i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	13.4307	+	23.2626i	0.523184	+	0.906181i	0.999636	+	0.0269806i	$0.00858924\pi$
$659$	13.4307	+	23.2626i	0.523184	+	0.906181i	−0.476452	+	0.879200i	$0.658077\pi$
$660$		0			0
$661$	1.06063	−	1.83706i	0.0412535	−	0.0714532i	−0.844661	−	0.535301i	$-0.820198\pi$
$661$	1.06063	−	1.83706i	0.0412535	−	0.0714532i	0.885915	+	0.463848i	$0.153532\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−2.64806			−0.102687
$666$		0			0
$667$	−18.5667			−0.718907
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2.58242	+	4.47288i	−0.0996933	+	0.172674i
$672$		0			0
$673$	−17.4102	−	30.1553i	−0.671112	−	1.16240i	−0.977589	−	0.210523i	$-0.932483\pi$
$673$	−17.4102	−	30.1553i	−0.671112	−	1.16240i	0.306477	−	0.951878i	$-0.400850\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−12.3421	−	21.3772i	−0.474346	−	0.821592i	0.525222	−	0.850965i	$-0.323982\pi$
$677$	−12.3421	−	21.3772i	−0.474346	−	0.821592i	−0.999569	+	0.0293735i	$0.990649\pi$
$678$		0			0
$679$	−27.7449	+	48.0555i	−1.06475	+	1.84420i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−38.4610			−1.47167			−0.735834	−	0.677162i	$-0.763210\pi$
$683$	−38.4610			−1.47167			−0.735834	+	0.677162i	$0.763210\pi$
$684$		0			0
$685$	−7.46838			−0.285352
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.35194	−	2.34163i	0.0515048	−	0.0892089i
$690$		0			0
$691$	0.240304	+	0.416219i	0.00914159	+	0.0158337i	0.870560	−	0.492062i	$-0.163757\pi$
$691$	0.240304	+	0.416219i	0.00914159	+	0.0158337i	−0.861418	+	0.507896i	$0.830423\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.00000	−	6.92820i	−0.151729	−	0.262802i
$696$		0			0
$697$	−0.121457	+	0.210370i	−0.00460053	+	0.00796835i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	18.1797			0.686637			0.343318	−	0.939219i	$-0.388449\pi$
$701$	18.1797			0.686637			0.343318	+	0.939219i	$0.388449\pi$
$702$		0			0
$703$	−4.87614			−0.183907
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3.00000	−	5.19615i	0.112827	−	0.195421i
$708$		0			0
$709$	−3.59355	−	6.22421i	−0.134959	−	0.233755i	0.790623	−	0.612303i	$-0.209757\pi$
$709$	−3.59355	−	6.22421i	−0.134959	−	0.233755i	−0.925582	+	0.378548i	$0.876423\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−18.4331	−	31.9270i	−0.690323	−	1.19568i
$714$		0			0
$715$	−0.438069	+	0.758758i	−0.0163829	+	0.0283760i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	12.5168			0.466797			0.233399	−	0.972381i	$-0.425015\pi$
$719$	12.5168			0.466797			0.233399	+	0.972381i	$0.425015\pi$
$720$		0			0
$721$	30.7449			1.14500
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.93807	−	3.35683i	0.0719781	−	0.124670i
$726$		0			0
$727$	4.21292	+	7.29699i	0.156249	+	0.270631i	0.933513	−	0.358544i	$-0.116727\pi$
$727$	4.21292	+	7.29699i	0.156249	+	0.270631i	−0.777264	+	0.629174i	$0.783393\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.554512	−	0.960443i	−0.0205094	−	0.0355233i
$732$		0			0
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	11.0074			0.405463
$738$		0			0
$739$	1.81290			0.0666887			0.0333444	−	0.999444i	$-0.489384\pi$
$739$	1.81290			0.0666887			0.0333444	+	0.999444i	$0.489384\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−10.0686	+	17.4393i	−0.369380	+	0.639785i	−0.989469	−	0.144747i	$-0.953763\pi$
$743$	−10.0686	+	17.4393i	−0.369380	+	0.639785i	0.620089	+	0.784532i	$0.287097\pi$
$744$		0			0
$745$	5.29241	+	9.16673i	0.193899	+	0.335843i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.47209	+	4.28179i	0.0903282	+	0.156453i
$750$		0			0
$751$	6.10662	−	10.5770i	0.222834	−	0.385959i	−0.732834	−	0.680408i	$-0.761803\pi$
$751$	6.10662	−	10.5770i	0.222834	−	0.385959i	0.955667	+	0.294449i	$0.0951360\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	17.6965			0.644040
$756$		0			0
$757$	52.9533			1.92462			0.962310	−	0.271955i	$-0.0876701\pi$
$757$	52.9533			1.92462			0.962310	+	0.271955i	$0.0876701\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−9.22677	+	15.9812i	−0.334470	+	0.579319i	−0.983383	−	0.181543i	$-0.941891\pi$
$761$	−9.22677	+	15.9812i	−0.334470	+	0.579319i	0.648913	+	0.760863i	$0.275224\pi$
$762$		0			0
$763$	28.8158	+	49.9105i	1.04320	+	1.80688i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.35194	−	2.34163i	−0.0488157	−	0.0845513i
$768$		0			0
$769$	2.22677	−	3.85688i	0.0802995	−	0.139083i	−0.823079	−	0.567927i	$-0.807746\pi$
$769$	2.22677	−	3.85688i	0.0802995	−	0.139083i	0.903379	+	0.428844i	$0.141079\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−38.9368			−1.40046			−0.700229	−	0.713918i	$-0.746919\pi$
$773$	−38.9368			−1.40046			−0.700229	+	0.713918i	$0.746919\pi$
$774$		0			0
$775$	7.69646			0.276465
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.0582214	−	0.100842i	0.00208600	−	0.00361305i
$780$		0			0
$781$	−4.13453	−	7.16121i	−0.147945	−	0.256248i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.26581	−	2.19245i	−0.0451787	−	0.0782517i
$786$		0			0
$787$	17.1140	−	29.6424i	0.610050	−	1.05664i	−0.381182	−	0.924500i	$-0.624483\pi$
$787$	17.1140	−	29.6424i	0.610050	−	1.05664i	0.991231	−	0.132137i	$-0.0421838\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−48.7252			−1.73247
$792$		0			0
$793$	−2.47580			−0.0879183
$794$		0			0
$795$		0			0
$796$		0			0
$797$	11.9828	−	20.7547i	0.424451	−	0.735171i	−0.571918	−	0.820311i	$-0.693800\pi$
$797$	11.9828	−	20.7547i	0.424451	−	0.735171i	0.996369	+	0.0851400i	$0.0271337\pi$
$798$		0			0
$799$	−7.37243	−	12.7694i	−0.260818	−	0.451750i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−8.34452	−	14.4531i	−0.294472	−	0.510040i
$804$		0			0
$805$	−9.78630	+	16.9504i	−0.344922	+	0.597422i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.283896			0.00998124			0.00499062	−	0.999988i	$-0.498411\pi$
$809$	0.283896			0.00998124			0.00499062	+	0.999988i	$0.498411\pi$
$810$		0			0
$811$	−32.4413			−1.13917			−0.569584	−	0.821933i	$-0.692896\pi$
$811$	−32.4413			−1.13917			−0.569584	+	0.821933i	$0.692896\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−4.23790	+	7.34026i	−0.148447	+	0.257118i
$816$		0			0
$817$	0.265809	+	0.460395i	0.00929948	+	0.0161072i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	20.8347	+	36.0868i	0.727136	+	1.25944i	0.958089	+	0.286472i	$0.0924824\pi$
$821$	20.8347	+	36.0868i	0.727136	+	1.25944i	−0.230953	+	0.972965i	$0.574184\pi$
$822$		0			0
$823$	−9.68130	+	16.7685i	−0.337469	+	0.584514i	−0.983956	−	0.178412i	$-0.942904\pi$
$823$	−9.68130	+	16.7685i	−0.337469	+	0.584514i	0.646487	+	0.762925i	$0.276237\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	18.8097			0.654076			0.327038	−	0.945011i	$-0.393950\pi$
$827$	18.8097			0.654076			0.327038	+	0.945011i	$0.393950\pi$
$828$		0			0
$829$	−33.1016			−1.14967			−0.574833	−	0.818271i	$-0.694933\pi$
$829$	−33.1016			−1.14967			−0.574833	+	0.818271i	$0.694933\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−6.55451	+	11.3527i	−0.227100	+	0.393349i
$834$		0			0
$835$	6.36710	+	11.0281i	0.220342	+	0.381644i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	19.8482	+	34.3781i	0.685237	+	1.18687i	0.973362	+	0.229273i	$0.0736347\pi$
$839$	19.8482	+	34.3781i	0.685237	+	1.18687i	−0.288125	+	0.957593i	$0.593032\pi$
$840$		0			0
$841$	6.98777	−	12.1032i	0.240958	−	0.417351i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	12.5800			0.432766
$846$		0			0
$847$	37.4791			1.28780
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−18.0205	+	31.2124i	−0.617734	+	1.06995i
$852$		0			0
$853$	2.05822	+	3.56494i	0.0704722	+	0.122061i	0.899108	−	0.437726i	$-0.144216\pi$
$853$	2.05822	+	3.56494i	0.0704722	+	0.122061i	−0.828636	+	0.559788i	$0.810883\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.37243	+	12.7694i	0.251837	+	0.436195i	0.964032	−	0.265787i	$-0.0856319\pi$
$857$	7.37243	+	12.7694i	0.251837	+	0.436195i	−0.712194	+	0.701982i	$0.752299\pi$
$858$		0			0
$859$	−18.9269	+	32.7824i	−0.645779	+	1.11852i	0.338342	+	0.941023i	$0.390134\pi$
$859$	−18.9269	+	32.7824i	−0.645779	+	1.11852i	−0.984121	+	0.177499i	$0.943199\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	26.7704			0.911274			0.455637	−	0.890166i	$-0.349412\pi$
$863$	26.7704			0.911274			0.455637	+	0.890166i	$0.349412\pi$
$864$		0			0
$865$	23.0484			0.783669
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−6.99258	+	12.1115i	−0.237207	+	0.410855i
$870$		0			0
$871$	2.63824	+	4.56956i	0.0893933	+	0.154834i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.04307	−	3.53869i	−0.0690682	−	0.119630i
$876$		0			0
$877$	23.4841	−	40.6756i	0.793001	−	1.37352i	−0.131101	−	0.991369i	$-0.541851\pi$
$877$	23.4841	−	40.6756i	0.793001	−	1.37352i	0.924101	−	0.382148i	$-0.124816\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	19.8055			0.667264			0.333632	−	0.942703i	$-0.391726\pi$
$881$	19.8055			0.667264			0.333632	+	0.942703i	$0.391726\pi$
$882$		0			0
$883$	6.20257			0.208733			0.104367	−	0.994539i	$-0.466718\pi$
$883$	6.20257			0.208733			0.104367	+	0.994539i	$0.466718\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−6.71370	+	11.6285i	−0.225424	+	0.390446i	−0.956447	−	0.291907i	$-0.905710\pi$
$887$	−6.71370	+	11.6285i	−0.225424	+	0.390446i	0.731023	+	0.682353i	$0.239043\pi$
$888$		0			0
$889$	14.4623	+	25.0494i	0.485049	+	0.840129i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3.53402	+	6.12111i	0.118262	+	0.204835i
$894$		0			0
$895$	1.11404	−	1.92957i	0.0372382	−	0.0644985i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−29.8325			−0.994971
$900$		0			0
$901$	−5.64064			−0.187917
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.234191	−	0.405631i	0.00778477	−	0.0134836i
$906$		0			0
$907$	0.336783	+	0.583325i	0.0111827	+	0.0193690i	0.871563	−	0.490284i	$-0.163107\pi$
$907$	0.336783	+	0.583325i	0.0111827	+	0.0193690i	−0.860380	+	0.509653i	$0.829774\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	3.95485	+	6.85000i	0.131030	+	0.226951i	0.924074	−	0.382214i	$-0.124838\pi$
$911$	3.95485	+	6.85000i	0.131030	+	0.226951i	−0.793044	+	0.609165i	$0.791505\pi$
$912$		0			0
$913$	−8.28630	+	14.3523i	−0.274236	+	0.474992i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	24.5168			0.809615
$918$		0			0
$919$	8.58263			0.283115			0.141557	−	0.989930i	$-0.454789\pi$
$919$	8.58263			0.283115			0.141557	+	0.989930i	$0.454789\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.98191	−	3.43277i	0.0652355	−	0.112991i
$924$		0			0
$925$	−3.76210	−	6.51615i	−0.123697	−	0.214250i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	14.8081	+	25.6484i	0.485838	+	0.841496i	0.999868	−	0.0162766i	$-0.00518122\pi$
$929$	14.8081	+	25.6484i	0.485838	+	0.841496i	−0.514030	+	0.857772i	$0.671848\pi$
$930$		0			0
$931$	3.14195	−	5.44201i	0.102973	−	0.178355i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.82774			0.0597735
$936$		0			0
$937$	−15.2058			−0.496753			−0.248376	−	0.968664i	$-0.579897\pi$
$937$	−15.2058			−0.496753			−0.248376	+	0.968664i	$0.579897\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	2.82643	−	4.89553i	0.0921391	−	0.159590i	−0.816272	−	0.577668i	$-0.803963\pi$
$941$	2.82643	−	4.89553i	0.0921391	−	0.159590i	0.908411	+	0.418078i	$0.137296\pi$
$942$		0			0
$943$	−0.430332	−	0.745356i	−0.0140135	−	0.0242721i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	20.1981	+	34.9841i	0.656350	+	1.13683i	0.981554	+	0.191187i	$0.0612337\pi$
$947$	20.1981	+	34.9841i	0.656350	+	1.13683i	−0.325204	+	0.945644i	$0.605433\pi$
$948$		0			0
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	22.9320			0.742839			0.371419	−	0.928465i	$-0.378871\pi$
$953$	22.9320			0.742839			0.371419	+	0.928465i	$0.378871\pi$
$954$		0			0
$955$	20.2281			0.654565
$956$		0			0
$957$		0			0
$958$		0			0
$959$	15.2584	−	26.4283i	0.492719	−	0.853415i
$960$		0			0
$961$	−14.1177	−	24.4527i	−0.455411	−	0.788795i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−9.96467	−	17.2593i	−0.320774	−	0.555597i
$966$		0			0
$967$	5.18501	−	8.98071i	0.166739	−	0.288800i	−0.770533	−	0.637401i	$-0.780010\pi$
$967$	5.18501	−	8.98071i	0.166739	−	0.288800i	0.937271	+	0.348601i	$0.113343\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	48.0410			1.54171			0.770854	−	0.637012i	$-0.219830\pi$
$971$	48.0410			1.54171			0.770854	+	0.637012i	$0.219830\pi$
$972$		0			0
$973$	32.6890			1.04796
$974$		0			0
$975$		0			0
$976$		0			0
$977$	13.5266	−	23.4288i	0.432754	−	0.749553i	−0.564355	−	0.825532i	$-0.690875\pi$
$977$	13.5266	−	23.4288i	0.432754	−	0.749553i	0.997109	+	0.0759796i	$0.0242084\pi$
$978$		0			0
$979$	2.02791	+	3.51244i	0.0648122	+	0.112258i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	11.2408	+	19.4697i	0.358527	+	0.620987i	0.987715	−	0.156266i	$-0.0499458\pi$
$983$	11.2408	+	19.4697i	0.358527	+	0.620987i	−0.629188	+	0.777253i	$0.716612\pi$
$984$		0			0
$985$	7.79001	−	13.4927i	0.248210	−	0.429913i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.92935			0.124946
$990$		0			0
$991$	26.5316			0.842805			0.421402	−	0.906874i	$-0.361538\pi$
$991$	26.5316			0.842805			0.421402	+	0.906874i	$0.361538\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.79241	+	3.10455i	−0.0568233	+	0.0984208i
$996$		0			0
$997$	14.1829	+	24.5656i	0.449178	+	0.777999i	0.998333	−	0.0577217i	$-0.0183836\pi$
$997$	14.1829	+	24.5656i	0.449178	+	0.777999i	−0.549155	+	0.835721i	$0.685050\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2160.2.q.k.1441.3		6
3.2	odd	2		720.2.q.i.481.3		6
4.3	odd	2		135.2.e.b.91.1		6
9.2	odd	6		720.2.q.i.241.3		6
9.4	even	3		6480.2.a.bs.1.1		3
9.5	odd	6		6480.2.a.bv.1.1		3
9.7	even	3	inner	2160.2.q.k.721.3		6
12.11	even	2		45.2.e.b.31.3	yes	6
20.3	even	4		675.2.k.b.199.2		12
20.7	even	4		675.2.k.b.199.5		12
20.19	odd	2		675.2.e.b.226.3		6
36.7	odd	6		135.2.e.b.46.1		6
36.11	even	6		45.2.e.b.16.3	✓	6
36.23	even	6		405.2.a.j.1.1		3
36.31	odd	6		405.2.a.i.1.3		3
60.23	odd	4		225.2.k.b.49.5		12
60.47	odd	4		225.2.k.b.49.2		12
60.59	even	2		225.2.e.b.76.1		6
180.7	even	12		675.2.k.b.424.2		12
180.23	odd	12		2025.2.b.l.649.5		6
180.43	even	12		675.2.k.b.424.5		12
180.47	odd	12		225.2.k.b.124.5		12
180.59	even	6		2025.2.a.n.1.3		3
180.67	even	12		2025.2.b.m.649.5		6
180.79	odd	6		675.2.e.b.451.3		6
180.83	odd	12		225.2.k.b.124.2		12
180.103	even	12		2025.2.b.m.649.2		6
180.119	even	6		225.2.e.b.151.1		6
180.139	odd	6		2025.2.a.o.1.1		3
180.167	odd	12		2025.2.b.l.649.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.e.b.16.3	✓	6	36.11	even	6
45.2.e.b.31.3	yes	6	12.11	even	2
135.2.e.b.46.1		6	36.7	odd	6
135.2.e.b.91.1		6	4.3	odd	2
225.2.e.b.76.1		6	60.59	even	2
225.2.e.b.151.1		6	180.119	even	6
225.2.k.b.49.2		12	60.47	odd	4
225.2.k.b.49.5		12	60.23	odd	4
225.2.k.b.124.2		12	180.83	odd	12
225.2.k.b.124.5		12	180.47	odd	12
405.2.a.i.1.3		3	36.31	odd	6
405.2.a.j.1.1		3	36.23	even	6
675.2.e.b.226.3		6	20.19	odd	2
675.2.e.b.451.3		6	180.79	odd	6
675.2.k.b.199.2		12	20.3	even	4
675.2.k.b.199.5		12	20.7	even	4
675.2.k.b.424.2		12	180.7	even	12
675.2.k.b.424.5		12	180.43	even	12
720.2.q.i.241.3		6	9.2	odd	6
720.2.q.i.481.3		6	3.2	odd	2
2025.2.a.n.1.3		3	180.59	even	6
2025.2.a.o.1.1		3	180.139	odd	6
2025.2.b.l.649.2		6	180.167	odd	12
2025.2.b.l.649.5		6	180.23	odd	12
2025.2.b.m.649.2		6	180.103	even	12
2025.2.b.m.649.5		6	180.67	even	12
2160.2.q.k.721.3		6	9.7	even	3	inner
2160.2.q.k.1441.3		6	1.1	even	1	trivial
6480.2.a.bs.1.1		3	9.4	even	3
6480.2.a.bv.1.1		3	9.5	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:	\( N \)	\(=\)	\( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2160.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{5} +(2.04307 + 3.53869i) q^{7} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{5} +(2.04307 + 3.53869i) q^{7} +(0.675970 + 1.17081i) q^{11} +(-0.324030 + 0.561237i) q^{13} +1.35194 q^{17} -0.648061 q^{19} +(-2.39500 + 4.14827i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(1.93807 + 3.35683i) q^{29} +(-3.84823 + 6.66533i) q^{31} +4.08613 q^{35} +7.52420 q^{37} +(-0.0898394 + 0.155606i) q^{41} +(-0.410161 - 0.710419i) q^{43} +(-5.45323 - 9.44526i) q^{47} +(-4.84823 + 8.39738i) q^{49} -4.17226 q^{53} +1.35194 q^{55} +(-2.08613 + 3.61328i) q^{59} +(1.91016 + 3.30850i) q^{61} +(0.324030 + 0.561237i) q^{65} +(4.07097 - 7.05113i) q^{67} -6.11644 q^{71} -12.3445 q^{73} +(-2.76210 + 4.78410i) q^{77} +(5.17226 + 8.95862i) q^{79} +(6.12920 + 10.6161i) q^{83} +(0.675970 - 1.17081i) q^{85} +3.00000 q^{89} -2.64806 q^{91} +(-0.324030 + 0.561237i) q^{95} +(6.79001 + 11.7606i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} + 5 q^{7}+O(q^{10}) \) 6 * q + 3 * q^5 + 5 * q^7	\( 6 q + 3 q^{5} + 5 q^{7} + 2 q^{11} - 4 q^{13} + 4 q^{17} - 8 q^{19} - 3 q^{23} - 3 q^{25} - 7 q^{29} + 8 q^{31} + 10 q^{35} + 12 q^{37} - 13 q^{41} + 10 q^{43} - 13 q^{47} + 2 q^{49} + 4 q^{53} + 4 q^{55} + 2 q^{59} - q^{61} + 4 q^{65} + 11 q^{67} - 20 q^{71} - 16 q^{73} + 2 q^{79} + 15 q^{83} + 2 q^{85} + 18 q^{89} - 20 q^{91} - 4 q^{95} + 18 q^{97}+O(q^{100}) \) 6 * q + 3 * q^5 + 5 * q^7 + 2 * q^11 - 4 * q^13 + 4 * q^17 - 8 * q^19 - 3 * q^23 - 3 * q^25 - 7 * q^29 + 8 * q^31 + 10 * q^35 + 12 * q^37 - 13 * q^41 + 10 * q^43 - 13 * q^47 + 2 * q^49 + 4 * q^53 + 4 * q^55 + 2 * q^59 - q^61 + 4 * q^65 + 11 * q^67 - 20 * q^71 - 16 * q^73 + 2 * q^79 + 15 * q^83 + 2 * q^85 + 18 * q^89 - 20 * q^91 - 4 * q^95 + 18 * q^97

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