LMFDB - Embedded newform 740.2.ce.b.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [740,2,Mod(3,740)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(740, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 26]))

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

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

chi := DirichletCharacter("740.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.ce (of order $36$, degree $12$, 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:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{36}]$

Embedding invariants

Embedding label			3.1
Root			$0.642788 - 0.766044i$ of defining polynomial
Character	$\chi$	$=$	740.3
Dual form			740.2.ce.b.247.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.123257 - 1.40883i) q^{2} +(-1.96962 + 0.347296i) q^{4} +(1.53737 - 1.62373i) q^{5} +(0.732051 + 2.73205i) q^{8} +(2.95442 + 0.520945i) q^{9} +O(q^{10})$	\(q+(-0.123257 - 1.40883i) q^{2} +(-1.96962 + 0.347296i) q^{4} +(1.53737 - 1.62373i) q^{5} +(0.732051 + 2.73205i) q^{8} +(2.95442 + 0.520945i) q^{9} +(-2.47706 - 1.96575i) q^{10} +(4.43703 + 3.10684i) q^{13} +(3.75877 - 1.36808i) q^{16} +(1.28470 - 0.899557i) q^{17} +(0.369771 - 4.22650i) q^{18} +(-2.46410 + 3.73205i) q^{20} +(-0.273017 - 4.99254i) q^{25} +(3.83013 - 6.63397i) q^{26} +(-1.10137 + 1.90764i) q^{29} +(-2.39069 - 5.12685i) q^{32} +(-1.42567 - 1.69905i) q^{34} -6.00000 q^{36} +(-0.0570813 - 6.08249i) q^{37} +(5.56155 + 3.01150i) q^{40} +(0.711496 + 4.03509i) q^{41} +(5.38790 - 3.99631i) q^{45} +(4.49951 - 5.36231i) q^{49} +(-7.00000 + 1.00000i) q^{50} +(-9.81825 - 4.57832i) q^{52} +(-13.1942 - 6.15258i) q^{53} +(2.82329 + 1.31652i) q^{58} +(9.92806 - 1.75058i) q^{61} +(-6.92820 + 4.00000i) q^{64} +(11.8660 - 2.42820i) q^{65} +(-2.21795 + 2.21795i) q^{68} +(0.739541 + 8.45299i) q^{72} +(-7.02628 - 7.02628i) q^{73} +(-8.56218 + 0.830127i) q^{74} +(3.55721 - 8.20648i) q^{80} +(8.45723 + 3.07818i) q^{81} +(5.59707 - 1.49973i) q^{82} +(0.514414 - 3.46896i) q^{85} +(-13.9725 + 5.08558i) q^{89} +(-6.29423 - 7.09808i) q^{90} +(-0.976048 + 3.64266i) q^{97} +(-8.10919 - 5.67812i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{8}+O(q^{10}) $ 12 * q - 12 * q^8	$ 12 q - 12 q^{8} - 6 q^{17} + 12 q^{20} - 6 q^{26} - 30 q^{34} - 72 q^{36} + 24 q^{41} - 84 q^{50} - 18 q^{58} + 72 q^{61} + 132 q^{65} + 30 q^{73} - 30 q^{74} - 42 q^{85} - 60 q^{89} + 18 q^{90}+O(q^{100}) $ 12 * q - 12 * q^8 - 6 * q^17 + 12 * q^20 - 6 * q^26 - 30 * q^34 - 72 * q^36 + 24 * q^41 - 84 * q^50 - 18 * q^58 + 72 * q^61 + 132 * q^65 + 30 * q^73 - 30 * q^74 - 42 * q^85 - 60 * q^89 + 18 * q^90

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.123257	−	1.40883i	−0.0871557	−	0.996195i
$2$	−0.123257	−	1.40883i	−0.0871557	−	0.996195i
$3$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$3$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$4$	−1.96962	+	0.347296i	−0.984808	+	0.173648i
$5$	1.53737	−	1.62373i	0.687531	−	0.726155i
$5$	1.53737	−	1.62373i	0.687531	−	0.726155i
$6$		0			0
$7$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$7$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$8$	0.732051	+	2.73205i	0.258819	+	0.965926i
$9$	2.95442	+	0.520945i	0.984808	+	0.173648i
$10$	−2.47706	−	1.96575i	−0.783314	−	0.621626i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$		0			0
$13$	4.43703	+	3.10684i	1.23061	+	0.861684i	0.993942	−	0.109907i	$-0.0350552\pi$
$13$	4.43703	+	3.10684i	1.23061	+	0.861684i	0.236670	+	0.971590i	$0.423944\pi$
$14$		0			0
$15$		0			0
$16$	3.75877	−	1.36808i	0.939693	−	0.342020i
$17$	1.28470	−	0.899557i	0.311586	−	0.218175i	−0.407314	−	0.913288i	$-0.633535\pi$
$17$	1.28470	−	0.899557i	0.311586	−	0.218175i	0.718900	+	0.695113i	$0.244646\pi$
$18$	0.369771	−	4.22650i	0.0871557	−	0.996195i
$19$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$19$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$20$	−2.46410	+	3.73205i	−0.550990	+	0.834512i
$21$		0			0
$22$		0			0
$23$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$23$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$24$		0			0
$25$	−0.273017	−	4.99254i	−0.0546034	−	0.998508i
$26$	3.83013	−	6.63397i	0.751150	−	1.30103i
$27$		0			0
$28$		0			0
$29$	−1.10137	+	1.90764i	−0.204520	+	0.354239i	−0.949980	−	0.312312i	$-0.898897\pi$
$29$	−1.10137	+	1.90764i	−0.204520	+	0.354239i	0.745460	+	0.666551i	$0.232230\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−2.39069	−	5.12685i	−0.422618	−	0.906308i
$33$		0			0
$34$	−1.42567	−	1.69905i	−0.244501	−	0.291385i
$35$		0			0
$36$	−6.00000			−1.00000
$37$	−0.0570813	−	6.08249i	−0.00938411	−	0.999956i
$37$	−0.0570813	−	6.08249i	−0.00938411	−	0.999956i
$38$		0			0
$39$		0			0
$40$	5.56155	+	3.01150i	0.879358	+	0.476161i
$41$	0.711496	+	4.03509i	0.111117	+	0.630175i	0.988600	+	0.150567i	$0.0481100\pi$
$41$	0.711496	+	4.03509i	0.111117	+	0.630175i	−0.877483	+	0.479608i	$0.840779\pi$
$42$		0			0
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$		0			0
$45$	5.38790	−	3.99631i	0.803181	−	0.595735i
$46$		0			0
$47$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$47$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$48$		0			0
$49$	4.49951	−	5.36231i	0.642788	−	0.766044i
$50$	−7.00000	+	1.00000i	−0.989949	+	0.141421i
$51$		0			0
$52$	−9.81825	−	4.57832i	−1.36155	−	0.634899i
$53$	−13.1942	−	6.15258i	−1.81237	−	0.845121i	−0.913157	−	0.407607i	$-0.866363\pi$
$53$	−13.1942	−	6.15258i	−1.81237	−	0.845121i	−0.899211	−	0.437514i	$-0.855859\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	2.82329	+	1.31652i	0.370716	+	0.172868i
$59$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$59$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$60$		0			0
$61$	9.92806	−	1.75058i	1.27116	−	0.224139i	0.502936	−	0.864324i	$-0.332253\pi$
$61$	9.92806	−	1.75058i	1.27116	−	0.224139i	0.768221	+	0.640184i	$0.221142\pi$
$62$		0			0
$63$		0			0
$64$	−6.92820	+	4.00000i	−0.866025	+	0.500000i
$65$	11.8660	−	2.42820i	1.47180	−	0.301182i
$66$		0			0
$67$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$67$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$68$	−2.21795	+	2.21795i	−0.268966	+	0.268966i
$69$		0			0
$70$		0			0
$71$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$71$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$72$	0.739541	+	8.45299i	0.0871557	+	0.996195i
$73$	−7.02628	−	7.02628i	−0.822364	−	0.822364i	0.164083	−	0.986447i	$-0.447534\pi$
$73$	−7.02628	−	7.02628i	−0.822364	−	0.822364i	−0.986447	+	0.164083i	$0.947534\pi$
$74$	−8.56218	+	0.830127i	−0.995333	+	0.0965003i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$79$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$80$	3.55721	−	8.20648i	0.397708	−	0.917512i
$81$	8.45723	+	3.07818i	0.939693	+	0.342020i
$82$	5.59707	−	1.49973i	0.618093	−	0.165618i
$83$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$83$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$84$		0			0
$85$	0.514414	−	3.46896i	0.0557960	−	0.376262i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−13.9725	+	5.08558i	−1.48108	+	0.539071i	−0.951086	−	0.308928i	$-0.900030\pi$
$89$	−13.9725	+	5.08558i	−1.48108	+	0.539071i	−0.529999	+	0.847998i	$0.677808\pi$
$90$	−6.29423	−	7.09808i	−0.663470	−	0.748203i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.976048	+	3.64266i	−0.0991026	+	0.369856i	−0.997610	−	0.0691034i	$-0.977986\pi$
$97$	−0.976048	+	3.64266i	−0.0991026	+	0.369856i	0.898507	+	0.438959i	$0.144653\pi$
$98$	−8.10919	−	5.67812i	−0.819152	−	0.573576i
$99$		0			0
$100$	2.27163	+	9.73857i	0.227163	+	0.973857i
$101$	10.0217	+	17.3581i	0.997199	+	1.72720i	0.563373	+	0.826202i	$0.309503\pi$
$101$	10.0217	+	17.3581i	0.997199	+	1.72720i	0.433826	+	0.900997i	$0.357163\pi$
$102$		0			0
$103$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$103$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$104$	−5.23992	+	14.3966i	−0.513817	+	1.41170i
$105$		0			0
$106$	−7.04167	+	19.3468i	−0.683947	+	1.87913i
$107$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$107$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$108$		0			0
$109$	15.9689	+	13.3995i	1.52955	+	1.28344i	0.801784	+	0.597615i	$0.203885\pi$
$109$	15.9689	+	13.3995i	1.52955	+	1.28344i	0.727764	+	0.685828i	$0.240560\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−19.0057	+	1.66278i	−1.78790	+	0.156421i	−0.932413	−	0.361396i	$-0.882300\pi$
$113$	−19.0057	+	1.66278i	−1.78790	+	0.156421i	−0.855491	+	0.517817i	$0.826745\pi$
$114$		0			0
$115$		0			0
$116$	1.50677	−	4.13981i	0.139900	−	0.384372i
$117$	11.4904	+	11.4904i	1.06229	+	1.06229i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−5.50000	−	9.52628i	−0.500000	−	0.866025i
$122$	−3.68998	−	13.7712i	−0.334075	−	1.24679i
$123$		0			0
$124$		0			0
$125$	−8.52628	−	7.23205i	−0.762614	−	0.646854i
$126$		0			0
$127$		0			0		0.422618	−	0.906308i	$-0.361111\pi$
$127$		0			0		−0.422618	+	0.906308i	$0.638889\pi$
$128$	6.48928	+	9.26765i	0.573576	+	0.819152i
$129$		0			0
$130$	−4.88350	−	16.4179i	−0.428311	−	1.43995i
$131$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$131$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	3.39810	+	2.85135i	0.291385	+	0.244501i
$137$	2.55894	+	9.55009i	0.218625	+	0.815920i	0.984859	+	0.173358i	$0.0554617\pi$
$137$	2.55894	+	9.55009i	0.218625	+	0.815920i	−0.766234	+	0.642562i	$0.777872\pi$
$138$		0			0
$139$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$139$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	11.8177	−	2.08378i	0.984808	−	0.173648i
$145$	1.40428	+	4.72107i	0.116619	+	0.392064i
$146$	−9.03281	+	10.7649i	−0.747561	+	0.890908i
$147$		0			0
$148$	2.22486	+	11.9604i	0.182882	+	0.983135i
$149$			2.13113i			0.174589i	0.996183	+	0.0872945i	$0.0278221\pi$
$149$			2.13113i			0.174589i	−0.996183	+	0.0872945i	$0.972178\pi$
$150$		0			0
$151$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$151$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$152$		0			0
$153$	4.26417	−	1.98842i	0.344738	−	0.160754i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.905156	+	1.29270i	0.0722393	+	0.103168i	0.853646	−	0.520854i	$-0.174386\pi$
$157$	0.905156	+	1.29270i	0.0722393	+	0.103168i	−0.781407	+	0.624022i	$0.785497\pi$
$158$		0			0
$159$		0			0
$160$	−12.0000	−	4.00000i	−0.948683	−	0.316228i
$161$		0			0
$162$	3.29423	−	12.2942i	0.258819	−	0.965926i
$163$		0			0		0.422618	−	0.906308i	$-0.361111\pi$
$163$		0			0		−0.422618	+	0.906308i	$0.638889\pi$
$164$	−2.80275	−	7.70048i	−0.218858	−	0.601306i
$165$		0			0
$166$		0			0
$167$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$167$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$168$		0			0
$169$	5.58852	+	15.3543i	0.429886	+	1.18110i
$170$	−4.95059	−	0.297150i	−0.379693	−	0.0227903i
$171$		0			0
$172$		0			0
$173$	−2.28781	−	26.1498i	−0.173939	−	1.98813i	−0.152057	−	0.988372i	$-0.548590\pi$
$173$	−2.28781	−	26.1498i	−0.173939	−	1.98813i	−0.0218819	−	0.999761i	$-0.506966\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	8.88694	+	19.0581i	0.666104	+	1.42847i
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$	−9.22419	+	9.74240i	−0.687531	+	0.726155i
$181$	4.62678	+	26.2398i	0.343906	+	1.95039i	0.309229	+	0.950988i	$0.399929\pi$
$181$	4.62678	+	26.2398i	0.343906	+	1.95039i	0.0346764	+	0.999399i	$0.488960\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−9.96410	−	9.25833i	−0.732575	−	0.680686i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$		0			0
$193$	3.00996	+	11.2333i	0.216661	+	0.808591i	0.985575	+	0.169239i	$0.0541309\pi$
$193$	3.00996	+	11.2333i	0.216661	+	0.808591i	−0.768914	+	0.639353i	$0.779202\pi$
$194$	5.25220	+	0.926105i	0.377086	+	0.0664904i
$195$		0			0
$196$	−7.00000	+	12.1244i	−0.500000	+	0.866025i
$197$	13.5940	−	1.18932i	0.968532	−	0.0847356i	0.408101	−	0.912937i	$-0.366191\pi$
$197$	13.5940	−	1.18932i	0.968532	−	0.0847356i	0.560431	+	0.828201i	$0.310635\pi$
$198$		0			0
$199$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$199$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$200$	13.4400	−	4.40069i	0.950352	−	0.311176i
$201$		0			0
$202$	23.2195	−	16.2584i	1.63372	−	1.14394i
$203$		0			0
$204$		0			0
$205$	7.64574	+	5.04813i	0.534002	+	0.352577i
$206$		0			0
$207$		0			0
$208$	20.9282	+	5.60770i	1.45111	+	0.388824i
$209$		0			0
$210$		0			0
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$	28.1244	+	7.53590i	1.93159	+	0.517568i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	16.9094	−	24.1491i	1.14525	−	1.63559i
$219$		0			0
$220$		0			0
$221$	8.49505			0.571439
$222$		0			0
$223$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$223$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$224$		0			0
$225$	1.79423	−	14.8923i	0.119615	−	0.992820i
$226$	4.68516	+	26.5709i	0.311652	+	1.76747i
$227$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$227$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$228$		0			0
$229$	−9.86716	+	27.1098i	−0.652040	+	1.79147i	−0.0419691	+	0.999119i	$0.513363\pi$
$229$	−9.86716	+	27.1098i	−0.652040	+	1.79147i	−0.610071	+	0.792347i	$0.708859\pi$
$230$		0			0
$231$		0			0
$232$	−6.01802	−	1.61252i	−0.395103	−	0.105867i
$233$	13.2072	−	3.53885i	0.865230	−	0.231838i	0.201206	−	0.979549i	$-0.435514\pi$
$233$	13.2072	−	3.53885i	0.865230	−	0.231838i	0.664024	+	0.747711i	$0.268847\pi$
$234$	14.7717	−	17.6043i	0.965659	−	1.15083i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$239$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$240$		0			0
$241$	−14.0952	−	16.7980i	−0.907950	−	1.08205i	−0.996298	−	0.0859632i	$-0.972603\pi$
$241$	−14.0952	−	16.7980i	−0.907950	−	1.08205i	0.0883481	−	0.996090i	$-0.471841\pi$
$242$	−12.7430	+	8.92276i	−0.819152	+	0.573576i
$243$		0			0
$244$	−18.9465	+	6.89595i	−1.21292	+	0.441468i
$245$	−1.78957	−	15.5498i	−0.114331	−	0.993443i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−9.13782	+	12.9035i	−0.577927	+	0.816089i
$251$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$251$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	12.2567	−	10.2846i	0.766044	−	0.642788i
$257$	−1.45691	−	16.6525i	−0.0908794	−	1.03876i	−0.895528	−	0.445005i	$-0.853202\pi$
$257$	−1.45691	−	16.6525i	−0.0908794	−	1.03876i	0.804649	−	0.593751i	$-0.202354\pi$
$258$		0			0
$259$		0			0
$260$	−22.5282	+	8.90365i	−1.39714	+	0.552181i
$261$	−4.24770	+	5.06221i	−0.262926	+	0.313343i
$262$		0			0
$263$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$263$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$264$		0			0
$265$	−30.2745	+	11.9652i	−1.85975	+	0.735015i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−26.2583	+	15.1603i	−1.60100	+	0.924337i	−0.609711	+	0.792624i	$0.708714\pi$
$269$	−26.2583	+	15.1603i	−1.60100	+	0.924337i	−0.991288	+	0.131713i	$0.957952\pi$
$270$		0			0
$271$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$271$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$272$	3.59823	−	5.13880i	0.218175	−	0.311586i
$273$		0			0
$274$	13.1391	−	4.78223i	0.793760	−	0.288905i
$275$		0			0
$276$		0			0
$277$	−29.3501	−	2.56780i	−1.76348	−	0.154284i	−0.841178	−	0.540758i	$-0.818138\pi$
$277$	−29.3501	−	2.56780i	−1.76348	−	0.154284i	−0.922301	+	0.386473i	$0.873693\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.65511	−	26.5272i	−0.575975	−	1.58248i	−0.794902	−	0.606738i	$-0.792478\pi$
$281$	−9.65511	−	26.5272i	−0.575975	−	1.58248i	0.218926	−	0.975741i	$-0.429745\pi$
$282$		0			0
$283$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$283$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−4.39230	−	16.3923i	−0.258819	−	0.965926i
$289$	−4.97309	+	13.6634i	−0.292535	+	0.803732i
$290$	6.47811	−	2.56030i	0.380408	−	0.150346i
$291$		0			0
$292$	16.2793	+	11.3989i	0.952672	+	0.667068i
$293$	−30.0308	−	2.62735i	−1.75442	−	0.153492i	−0.835902	−	0.548879i	$-0.815055\pi$
$293$	−30.0308	−	2.62735i	−1.75442	−	0.153492i	−0.918514	+	0.395388i	$0.870610\pi$
$294$		0			0
$295$		0			0
$296$	16.5759	−	4.60864i	0.963455	−	0.267872i
$297$		0			0
$298$	3.00240	−	0.262676i	0.173925	−	0.0152164i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	12.4206	−	18.8118i	0.711199	−	1.07716i
$306$	−3.32693	−	5.76241i	−0.190188	−	0.329415i
$307$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$307$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$311$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$312$		0			0
$313$	13.6565	+	19.5035i	0.771909	+	1.10240i	0.991915	+	0.126902i	$0.0405034\pi$
$313$	13.6565	+	19.5035i	0.771909	+	1.10240i	−0.220006	+	0.975499i	$0.570608\pi$
$314$	1.70963	−	1.43455i	0.0964798	−	0.0809562i
$315$		0			0
$316$		0			0
$317$	−14.6540	+	31.4255i	−0.823048	+	1.76503i	−0.205227	+	0.978714i	$0.565793\pi$
$317$	−14.6540	+	31.4255i	−0.823048	+	1.76503i	−0.617822	+	0.786318i	$0.711985\pi$
$318$		0			0
$319$		0			0
$320$	−4.15625	+	17.3990i	−0.232341	+	0.972634i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−17.7265	−	3.12567i	−0.984808	−	0.173648i
$325$	14.2997	−	23.0003i	0.793202	−	1.27583i
$326$		0			0
$327$		0			0
$328$	−10.5032	+	4.89773i	−0.579944	+	0.270432i
$329$		0			0
$330$		0			0
$331$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$331$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$332$		0			0
$333$	3.00000	−	18.0000i	0.164399	−	0.986394i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−13.0151	−	9.11326i	−0.708977	−	0.496431i	0.162598	−	0.986692i	$-0.448012\pi$
$337$	−13.0151	−	9.11326i	−0.708977	−	0.496431i	−0.871576	+	0.490261i	$0.836901\pi$
$338$	20.9429	−	9.76582i	1.13914	−	0.531190i
$339$		0			0
$340$	0.191560	+	7.01117i	0.0103888	+	0.380234i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−36.5587	+	6.44628i	−1.96541	+	0.346554i
$347$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$347$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$348$		0			0
$349$	1.23016	+	3.37983i	0.0658489	+	0.180918i	0.968253	−	0.249973i	$-0.0804216\pi$
$349$	1.23016	+	3.37983i	0.0658489	+	0.180918i	−0.902404	+	0.430891i	$0.858199\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−21.2386	−	30.3319i	−1.13042	−	1.61440i	−0.704620	−	0.709585i	$-0.748883\pi$
$353$	−21.2386	−	30.3319i	−1.13042	−	1.61440i	−0.425797	−	0.904819i	$-0.640006\pi$
$354$		0			0
$355$		0			0
$356$	25.7543	−	14.8692i	1.36497	−	0.788069i
$357$		0			0
$358$		0			0
$359$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$359$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$360$	14.8623	+	11.7945i	0.783314	+	0.621626i
$361$	3.29932	−	18.7113i	0.173648	−	0.984808i
$362$	36.3971	−	9.75258i	1.91299	−	0.512584i
$363$		0			0
$364$		0			0
$365$	−22.2108	+	0.606844i	−1.16256	+	0.0317637i
$366$		0			0
$367$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$367$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$368$		0			0
$369$			12.2920i			0.639897i
$370$	−11.8153	+	15.1789i	−0.614248	+	0.789113i
$371$		0			0
$372$		0			0
$373$	−27.7964	−	2.43187i	−1.43924	−	0.125917i	−0.659352	−	0.751834i	$-0.729169\pi$
$373$	−27.7964	−	2.43187i	−1.43924	−	0.125917i	−0.779890	+	0.625917i	$0.784725\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.8136	+	5.04245i	−0.556927	+	0.259699i
$378$		0			0
$379$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$379$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$383$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$384$		0			0
$385$		0			0
$386$	15.4549	−	5.62511i	0.786631	−	0.286310i
$387$		0			0
$388$	0.657356	−	7.51362i	0.0333722	−	0.381446i
$389$	−5.00525	+	4.19990i	−0.253776	+	0.212944i	−0.760796	−	0.648991i	$-0.775191\pi$
$389$	−5.00525	+	4.19990i	−0.253776	+	0.212944i	0.507020	+	0.861934i	$0.330747\pi$
$390$		0			0
$391$		0			0
$392$	17.9440	+	8.36741i	0.906308	+	0.422618i
$393$		0			0
$394$	−3.35111	−	19.0051i	−0.168826	−	0.957462i
$395$		0			0
$396$		0			0
$397$	37.5757	+	10.0684i	1.88587	+	0.505318i	0.999068	+	0.0431736i	$0.0137468\pi$
$397$	37.5757	+	10.0684i	1.88587	+	0.505318i	0.886805	+	0.462144i	$0.152920\pi$
$398$		0			0
$399$		0			0
$400$	−7.85641	−	18.3923i	−0.392820	−	0.919615i
$401$		−	18.2679i		−	0.912258i	−0.889914	−	0.456129i	$-0.849236\pi$
$401$		−	18.2679i		−	0.912258i	0.889914	−	0.456129i	$-0.150764\pi$
$402$		0			0
$403$		0			0
$404$	−25.7674	−	30.7083i	−1.28197	−	1.52780i
$405$	18.0000	−	9.00000i	0.894427	−	0.447214i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−26.4274	−	22.1752i	−1.30675	−	1.09649i	−0.988936	−	0.148340i	$-0.952607\pi$
$409$	−26.4274	−	22.1752i	−1.30675	−	1.09649i	−0.317814	−	0.948153i	$-0.602949\pi$
$410$	6.16958	−	11.3938i	0.304694	−	0.562699i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	5.32076	−	30.1755i	0.260872	−	1.47948i
$417$		0			0
$418$		0			0
$419$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$419$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$420$		0			0
$421$	16.1204	−	9.30711i	0.785659	−	0.453601i	−0.0527728	−	0.998607i	$-0.516806\pi$
$421$	16.1204	−	9.30711i	0.785659	−	0.453601i	0.838432	+	0.545006i	$0.183473\pi$
$422$		0			0
$423$		0			0
$424$	7.15030	−	40.5513i	0.347249	−	1.96935i
$425$	−4.84182	−	6.16833i	−0.234863	−	0.299208i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$431$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$432$		0			0
$433$	7.13082	−	1.91070i	0.342685	−	0.0918222i	−0.0833719	−	0.996519i	$-0.526569\pi$
$433$	7.13082	−	1.91070i	0.342685	−	0.0918222i	0.426057	+	0.904696i	$0.359902\pi$
$434$		0			0
$435$		0			0
$436$	−36.1063	−	20.8460i	−1.72918	−	0.998341i
$437$		0			0
$438$		0			0
$439$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$439$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$440$		0			0
$441$	16.0869	−	13.4985i	0.766044	−	0.642788i
$442$	−1.04707	−	11.9681i	−0.0498042	−	0.569264i
$443$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$443$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$444$		0			0
$445$	−13.2232	+	30.5060i	−0.626842	+	1.44613i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	7.40068	+	2.69363i	0.349260	+	0.127120i	0.510692	−	0.859764i	$-0.329389\pi$
$449$	7.40068	+	2.69363i	0.349260	+	0.127120i	−0.161432	+	0.986884i	$0.551611\pi$
$450$	−21.2019	−	0.692188i	−0.999467	−	0.0326301i
$451$		0			0
$452$	36.8564	−	9.87564i	1.73358	−	0.464511i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−19.8939	+	28.4115i	−0.930598	+	1.32903i	0.0136882	+	0.999906i	$0.495643\pi$
$457$	−19.8939	+	28.4115i	−0.930598	+	1.32903i	−0.944286	+	0.329125i	$0.893246\pi$
$458$	39.4093	+	10.5597i	1.84148	+	0.493422i
$459$		0			0
$460$		0			0
$461$	22.5609	+	3.97810i	1.05077	+	0.185279i	0.672256	−	0.740318i	$-0.265325\pi$
$461$	22.5609	+	3.97810i	1.05077	+	0.185279i	0.378511	+	0.925597i	$0.376436\pi$
$462$		0			0
$463$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$463$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$464$	−1.53001	+	8.67714i	−0.0710291	+	0.402826i
$465$		0			0
$466$	−6.61352	−	18.1705i	−0.306365	−	0.841732i
$467$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$467$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$468$	−26.6222	−	18.6411i	−1.23061	−	0.861684i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−35.7762	−	25.0508i	−1.63808	−	1.14700i
$478$		0			0
$479$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$479$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$480$		0			0
$481$	18.6441	−	27.1656i	0.850097	−	1.23864i
$482$	−21.9282	+	21.9282i	−0.998802	+	0.998802i
$483$		0			0
$484$	14.1413	+	16.8530i	0.642788	+	0.766044i
$485$	4.41417	+	7.18494i	0.200437	+	0.326251i
$486$		0			0
$487$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$487$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$488$	12.0505	+	25.8424i	0.545502	+	1.16983i
$489$		0			0
$490$	−21.6865	+	4.43782i	−0.979698	+	0.200480i
$491$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$491$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$492$		0			0
$493$	0.301092	+	3.44149i	0.0135605	+	0.154997i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$499$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$500$	19.3052	+	11.2832i	0.863353	+	0.504601i
$501$		0			0
$502$		0			0
$503$		0			0		0.422618	−	0.906308i	$-0.361111\pi$
$503$		0			0		−0.422618	+	0.906308i	$0.638889\pi$
$504$		0			0
$505$	43.5920	+	10.4132i	1.93982	+	0.463381i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	26.8637	+	4.73679i	1.19071	+	0.209954i	0.733679	−	0.679496i	$-0.237801\pi$
$509$	26.8637	+	4.73679i	1.19071	+	0.209954i	0.457032	+	0.889450i	$0.348913\pi$
$510$		0			0
$511$		0			0
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$		0			0
$514$	−23.2810	+	4.10508i	−1.02688	+	0.181067i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	15.3205	+	30.6410i	0.671849	+	1.34370i
$521$	−18.1101	+	15.1962i	−0.793417	+	0.665756i	−0.946589	−	0.322444i	$-0.895496\pi$
$521$	−18.1101	+	15.1962i	−0.793417	+	0.665756i	0.153172	+	0.988200i	$0.451051\pi$
$522$	7.65536	+	5.36034i	0.335066	+	0.234616i
$523$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$523$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	19.9186	+	11.5000i	0.866025	+	0.500000i
$530$	20.5885	+	41.1769i	0.894305	+	1.78861i
$531$		0			0
$532$		0			0
$533$	−9.37947	+	20.1143i	−0.406270	+	0.871249i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	24.5948	+	35.1250i	1.06036	+	1.51435i
$539$		0			0
$540$		0			0
$541$	−3.83563	+	2.21450i	−0.164907	+	0.0952089i	−0.580182	−	0.814487i	$-0.697019\pi$
$541$	−3.83563	+	2.21450i	−0.164907	+	0.0952089i	0.415275	+	0.909696i	$0.363685\pi$
$542$		0			0
$543$		0			0
$544$	−7.68322	−	4.43591i	−0.329415	−	0.190188i
$545$	46.3074	−	5.32932i	1.98359	−	0.228283i
$546$		0			0
$547$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$547$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$548$	−8.35684	−	17.9213i	−0.356987	−	0.765560i
$549$	30.2436			1.29077
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$			41.6659i			1.77022i
$555$		0			0
$556$		0			0
$557$	4.03296	+	46.0969i	0.170882	+	1.95319i	0.282079	+	0.959391i	$0.408976\pi$
$557$	4.03296	+	46.0969i	0.170882	+	1.95319i	−0.111198	+	0.993798i	$0.535469\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−36.1823	+	16.8721i	−1.52626	+	0.711706i
$563$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$563$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$564$		0			0
$565$	−26.5188	+	33.4165i	−1.11565	+	1.40584i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−16.2755	−	28.1899i	−0.682303	−	1.18178i	−0.974276	−	0.225357i	$-0.927645\pi$
$569$	−16.2755	−	28.1899i	−0.682303	−	1.18178i	0.291973	−	0.956426i	$-0.405688\pi$
$570$		0			0
$571$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$571$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−22.5526	+	8.20848i	−0.939693	+	0.342020i
$577$	13.0102	+	6.06676i	0.541622	+	0.252562i	0.674121	−	0.738621i	$-0.264523\pi$
$577$	13.0102	+	6.06676i	0.541622	+	0.252562i	−0.132500	+	0.991183i	$0.542300\pi$
$578$	19.8625	+	5.32213i	0.826170	+	0.221372i
$579$		0			0
$580$	−4.40550	−	8.81100i	−0.182928	−	0.365857i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	14.0526	−	24.3397i	0.581499	−	1.00719i
$585$	36.3222	−	0.992399i	1.50174	−	0.0410307i
$586$			42.6321i			1.76112i
$587$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$587$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−8.53590	−	22.7846i	−0.350823	−	0.936442i
$593$	−33.1338	−	33.1338i	−1.36064	−	1.36064i	−0.873101	−	0.487540i	$-0.837894\pi$
$593$	−33.1338	−	33.1338i	−1.36064	−	1.36064i	−0.487540	−	0.873101i	$-0.662106\pi$
$594$		0			0
$595$		0			0
$596$	−0.740134	−	4.19751i	−0.0303171	−	0.171937i
$597$		0			0
$598$		0			0
$599$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$599$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$600$		0			0
$601$	3.15748	−	17.9069i	0.128796	−	0.730440i	−0.850184	−	0.526485i	$-0.823510\pi$
$601$	3.15748	−	17.9069i	0.128796	−	0.730440i	0.978980	−	0.203954i	$-0.0653794\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−23.9236	−	5.71484i	−0.972634	−	0.232341i
$606$		0			0
$607$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$607$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$608$		0			0
$609$		0			0
$610$	−28.0336	−	15.1798i	−1.13505	−	0.614612i
$611$		0			0
$612$	−7.70821	+	5.39734i	−0.311586	+	0.218175i
$613$	35.1886	+	16.4087i	1.42125	+	0.662741i	0.972924	−	0.231127i	$-0.0742412\pi$
$613$	35.1886	+	16.4087i	1.42125	+	0.662741i	0.448330	+	0.893868i	$0.352019\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−20.9943	+	1.83676i	−0.845199	+	0.0739453i	−0.501524	−	0.865143i	$-0.667227\pi$
$617$	−20.9943	+	1.83676i	−0.845199	+	0.0739453i	−0.343675	+	0.939089i	$0.611672\pi$
$618$		0			0
$619$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$619$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−24.8509	+	2.72610i	−0.994037	+	0.109044i
$626$	25.7938	−	21.6436i	1.03093	−	0.865052i
$627$		0			0
$628$	−2.23176	−	2.23176i	−0.0890569	−	0.0890569i
$629$	−5.54489	−	7.76284i	−0.221089	−	0.309525i
$630$		0			0
$631$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$631$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$632$		0			0
$633$		0			0
$634$	46.0795	+	16.7716i	1.83005	+	0.666084i
$635$		0			0
$636$		0			0
$637$	36.6244	−	9.81347i	1.45111	−	0.388824i
$638$		0			0
$639$		0			0
$640$	25.0246	+	3.71091i	0.989183	+	0.146686i
$641$	29.3148	+	24.5980i	1.15786	+	0.971564i	0.999874	−	0.0158770i	$-0.00505402\pi$
$641$	29.3148	+	24.5980i	1.15786	+	0.971564i	0.157991	+	0.987441i	$0.449498\pi$
$642$		0			0
$643$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$643$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$647$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$648$	−2.21862	+	25.3590i	−0.0871557	+	0.996195i
$649$		0			0
$650$	−34.1661	−	17.3109i	−1.34010	−	0.678988i
$651$		0			0
$652$		0			0
$653$	−23.6649	−	16.5703i	−0.926078	−	0.648447i	0.0101092	−	0.999949i	$-0.496782\pi$
$653$	−23.6649	−	16.5703i	−0.926078	−	0.648447i	−0.936187	+	0.351502i	$0.885671\pi$
$654$		0			0
$655$		0			0
$656$	8.19468	+	14.1936i	0.319948	+	0.554167i
$657$	−17.0983	−	24.4189i	−0.667068	−	0.952672i
$658$		0			0
$659$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$659$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$660$		0			0
$661$	−15.7383	+	43.2406i	−0.612148	+	1.68186i	0.113277	+	0.993563i	$0.463865\pi$
$661$	−15.7383	+	43.2406i	−0.612148	+	1.68186i	−0.725426	+	0.688301i	$0.758357\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−25.7287	−	2.00787i	−0.996969	−	0.0778035i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−4.76567	−	10.2200i	−0.183703	−	0.393953i	0.792792	−	0.609492i	$-0.208627\pi$
$673$	−4.76567	−	10.2200i	−0.183703	−	0.393953i	−0.976495	+	0.215540i	$0.930849\pi$
$674$	−11.2349	+	19.4593i	−0.432751	+	0.749546i
$675$		0			0
$676$	−16.3397	−	28.3013i	−0.628452	−	1.08851i
$677$	11.3215	+	42.2526i	0.435122	+	1.62390i	0.740774	+	0.671754i	$0.234459\pi$
$677$	11.3215	+	42.2526i	0.435122	+	1.62390i	−0.305652	+	0.952143i	$0.598874\pi$
$678$		0			0
$679$		0			0
$680$	9.85395	−	1.13405i	0.377882	−	0.0434888i
$681$		0			0
$682$		0			0
$683$		0			0		−0.573576	−	0.819152i	$-0.694444\pi$
$683$		0			0		0.573576	+	0.819152i	$0.305556\pi$
$684$		0			0
$685$	19.4408	+	10.5269i	0.742796	+	0.402214i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−39.4282	−	68.2917i	−1.50209	−	2.60170i
$690$		0			0
$691$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$691$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$692$	13.5878	+	50.7105i	0.516532	+	1.92772i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	4.54386	+	4.54386i	0.172111	+	0.172111i
$698$	4.60999	−	2.14967i	0.174491	−	0.0813664i
$699$		0			0
$700$		0			0
$701$	−32.1608	+	38.3277i	−1.21470	+	1.44762i	−0.356502	+	0.934295i	$0.616031\pi$
$701$	−32.1608	+	38.3277i	−1.21470	+	1.44762i	−0.858195	+	0.513324i	$0.828414\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−40.1147	+	33.6603i	−1.50974	+	1.26682i
$707$		0			0
$708$		0			0
$709$	30.0000			1.12667			0.563337	−	0.826227i	$-0.309517\pi$
$709$	30.0000			1.12667			0.563337	+	0.826227i	$0.309517\pi$
$710$		0			0
$711$		0			0
$712$	−24.1227	−	34.4507i	−0.904035	−	1.29110i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$719$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$720$	14.7846	−	22.3923i	0.550990	−	0.834512i
$721$		0			0
$722$	−26.7678	−	2.34188i	−0.996195	−	0.0871557i
$723$		0			0
$724$	−18.2259	−	50.0754i	−0.677362	−	1.86104i
$725$	9.82465	+	4.97784i	0.364878	+	0.184872i
$726$		0			0
$727$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$727$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$728$		0			0
$729$	23.3827	+	13.5000i	0.866025	+	0.500000i
$730$	3.59257	+	31.2164i	0.132967	+	1.15537i
$731$		0			0
$732$		0			0
$733$	7.53948	+	16.1685i	0.278477	+	0.597196i	0.994945	−	0.100424i	$-0.0320200\pi$
$733$	7.53948	+	16.1685i	0.278477	+	0.597196i	−0.716468	+	0.697620i	$0.754242\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	17.3174	−	1.51508i	0.637462	−	0.0557707i
$739$		0			0			−	1.00000i	$-0.5\pi$
$739$		0			0				1.00000i	$0.5\pi$
$740$	22.8408	+	14.7749i	0.839646	+	0.543134i
$741$		0			0
$742$		0			0
$743$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$743$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$744$		0			0
$745$	3.46039	+	3.27632i	0.126779	+	0.120035i
$746$			39.4602i			1.44474i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$751$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$752$		0			0
$753$		0			0
$754$	8.43681	+	14.6130i	0.307250	+	0.532173i
$755$		0			0
$756$		0			0
$757$	36.5102	−	25.5647i	1.32699	−	0.929165i	0.327111	−	0.944986i	$-0.393925\pi$
$757$	36.5102	−	25.5647i	1.32699	−	0.929165i	0.999875	+	0.0158209i	$0.00503616\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	3.19325	−	1.16225i	0.115755	−	0.0421314i	−0.283493	−	0.958974i	$-0.591493\pi$
$761$	3.19325	−	1.16225i	0.115755	−	0.0421314i	0.399248	+	0.916843i	$0.369271\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	3.32693	−	9.98079i	0.120285	−	0.360856i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	25.0000	−	43.3013i	0.901523	−	1.56148i	0.0760054	−	0.997107i	$-0.475783\pi$
$769$	25.0000	−	43.3013i	0.901523	−	1.56148i	0.825518	−	0.564376i	$-0.190883\pi$
$770$		0			0
$771$		0			0
$772$	−9.82974	−	21.0800i	−0.353780	−	0.758684i
$773$	−30.4503	+	43.4876i	−1.09522	+	1.56414i	−0.303937	+	0.952692i	$0.598301\pi$
$773$	−30.4503	+	43.4876i	−1.09522	+	1.56414i	−0.791285	+	0.611448i	$0.790588\pi$
$774$		0			0
$775$		0			0
$776$	−10.6664			−0.382903
$777$		0			0
$778$	6.53389	+	6.53389i	0.234251	+	0.234251i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	9.57656	−	26.3114i	0.342020	−	0.939693i
$785$	3.49055	+	0.517615i	0.124583	+	0.0184745i
$786$		0			0
$787$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$787$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$788$	−26.3619	+	7.06365i	−0.939104	+	0.251632i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	49.4899	+	23.0775i	1.75744	+	0.819507i
$794$	9.55320	−	54.1789i	0.339030	−	1.92274i
$795$		0			0
$796$		0			0
$797$	42.8629	−	30.0129i	1.51828	−	1.06311i	0.543645	−	0.839315i	$-0.317044\pi$
$797$	42.8629	−	30.0129i	1.51828	−	1.06311i	0.974636	−	0.223796i	$-0.0718450\pi$
$798$		0			0
$799$		0			0
$800$	−24.9433	+	13.3353i	−0.881879	+	0.471475i
$801$	−43.9301	+	7.74605i	−1.55219	+	0.273693i
$802$	−25.7365	+	2.25165i	−0.908786	+	0.0795085i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−40.0869	+	40.0869i	−1.41025	+	1.41025i
$809$	40.8742	+	14.8770i	1.43706	+	0.523047i	0.938946	−	0.344064i	$-0.111804\pi$
$809$	40.8742	+	14.8770i	1.43706	+	0.523047i	0.498114	+	0.867111i	$0.334026\pi$
$810$	−14.8981	−	24.2497i	−0.523466	−	0.852046i
$811$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$811$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−27.9838	+	39.9650i	−0.978430	+	1.39734i
$819$		0			0
$820$	−16.8124	−	7.28754i	−0.587113	−	0.254492i
$821$	−53.8456	−	19.5982i	−1.87922	−	0.683981i	−0.944096	−	0.329671i	$-0.893062\pi$
$821$	−53.8456	−	19.5982i	−1.87922	−	0.683981i	−0.935128	−	0.354310i	$-0.884716\pi$
$822$		0			0
$823$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$823$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$827$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$828$		0			0
$829$	18.7939	−	6.84040i	0.652737	−	0.237577i	0.00563977	−	0.999984i	$-0.498205\pi$
$829$	18.7939	−	6.84040i	0.652737	−	0.237577i	0.647098	+	0.762407i	$0.275983\pi$
$830$		0			0
$831$		0			0
$832$	−43.1680	−	3.77671i	−1.49658	−	0.130934i
$833$	0.956823	−	10.9365i	0.0331520	−	0.378929i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$839$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$840$		0			0
$841$	12.0739	+	20.9127i	0.416343	+	0.721127i
$842$	−15.0991	−	21.5637i	−0.520349	−	0.743136i
$843$		0			0
$844$		0			0
$845$	33.5229	+	14.5310i	1.15322	+	0.499880i
$846$		0			0
$847$		0			0
$848$	−58.0114	−	5.07534i	−1.99212	−	0.174288i
$849$		0			0
$850$	−8.09335	+	7.58160i	−0.277600	+	0.260047i
$851$		0			0
$852$		0			0
$853$	51.8694	−	4.53798i	1.77597	−	0.155378i	0.848483	−	0.529223i	$-0.177516\pi$
$853$	51.8694	−	4.53798i	1.77597	−	0.155378i	0.927491	+	0.373845i	$0.121961\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	9.20978	+	9.20978i	0.314600	+	0.314600i	0.846689	−	0.532089i	$-0.178593\pi$
$857$	9.20978	+	9.20978i	0.314600	+	0.314600i	−0.532089	+	0.846689i	$0.678593\pi$
$858$		0			0
$859$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$859$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.0871557	−	0.996195i	$-0.527778\pi$
$863$		0			0		0.0871557	+	0.996195i	$0.472222\pi$
$864$		0			0
$865$	−45.9775	−	36.4870i	−1.56328	−	1.24059i
$866$	−3.57077	−	9.81062i	−0.121340	−	0.333378i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−24.9181	+	53.4371i	−0.843834	+	1.80961i
$873$	−4.78128	+	10.2535i	−0.161822	+	0.347028i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	10.5153	+	39.2435i	0.355076	+	1.32516i	0.880389	+	0.474252i	$0.157281\pi$
$877$	10.5153	+	39.2435i	0.355076	+	1.32516i	−0.525314	+	0.850909i	$0.676052\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−41.0492	−	14.9407i	−1.38298	−	0.503365i	−0.459902	−	0.887970i	$-0.652115\pi$
$881$	−41.0492	−	14.9407i	−1.38298	−	0.503365i	−0.923081	+	0.384605i	$0.874338\pi$
$882$	−21.0000	−	21.0000i	−0.707107	−	0.707107i
$883$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$883$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$884$	−16.7320	+	2.95030i	−0.562757	+	0.0992293i
$885$		0			0
$886$		0			0
$887$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$887$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$888$		0			0
$889$		0			0
$890$	44.6077	+	14.8692i	1.49526	+	0.498418i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	2.88269	−	10.7583i	0.0961965	−	0.359010i
$899$		0			0
$900$	1.63810	+	29.9552i	0.0546034	+	0.998508i
$901$	−22.4853	+	3.96476i	−0.749093	+	0.132085i
$902$		0			0
$903$		0			0
$904$	−18.4559	−	50.7072i	−0.613835	−	1.68650i
$905$	49.7194	+	32.8274i	1.65273	+	1.09122i
$906$		0			0
$907$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$907$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$908$		0			0
$909$	20.5658	+	56.5041i	0.682124	+	1.87412i
$910$		0			0
$911$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$911$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$912$		0			0
$913$		0			0
$914$	42.4790	+	24.5253i	1.40508	+	0.811224i
$915$		0			0
$916$	10.0194	−	56.8227i	0.331049	−	1.87747i
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$	2.82369	−	32.2749i	0.0929932	−	1.06292i
$923$		0			0
$924$		0			0
$925$	−30.3515	+	1.94561i	−0.997952	+	0.0639711i
$926$		0			0
$927$		0			0
$928$	12.4132	+	1.08602i	0.407484	+	0.0356502i
$929$	60.0236	−	10.5838i	1.96931	−	0.347242i	0.981597	−	0.190965i	$-0.0611616\pi$
$929$	60.0236	−	10.5838i	1.96931	−	0.347242i	0.987713	−	0.156278i	$-0.0499495\pi$
$930$		0			0
$931$		0			0
$932$	−24.7840	+	11.5570i	−0.811827	+	0.378561i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−22.9808	+	39.8038i	−0.751150	+	1.30103i
$937$	−58.4362	+	5.11251i	−1.90903	+	0.167018i	−0.979461	−	0.201634i	$-0.935375\pi$
$937$	−58.4362	+	5.11251i	−1.90903	+	0.167018i	−0.929567	+	0.368652i	$0.879819\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	57.6432	−	20.9804i	1.87911	−	0.683941i	0.933740	−	0.357951i	$-0.116524\pi$
$941$	57.6432	−	20.9804i	1.87911	−	0.683941i	0.945373	−	0.325991i	$-0.105698\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$947$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$948$		0			0
$949$	−9.34628	−	53.0054i	−0.303393	−	1.72063i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−49.8218	+	34.8856i	−1.61389	+	1.13005i	−0.708281	+	0.705931i	$0.750529\pi$
$953$	−49.8218	+	34.8856i	−1.61389	+	1.13005i	−0.905604	+	0.424124i	$0.860582\pi$
$954$	−30.8827	+	53.4904i	−0.999864	+	1.73182i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−31.0000			−1.00000
$962$	−40.5697	−	22.9181i	−1.30802	−	0.738908i
$963$		0			0
$964$	33.5960	+	28.1904i	1.08205	+	0.907950i
$965$	22.8673	+	12.3823i	0.736124	+	0.398601i
$966$		0			0
$967$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$967$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$968$	22.0000	−	22.0000i	0.707107	−	0.707107i
$969$		0			0
$970$	9.57830	−	7.10441i	0.307541	−	0.228109i
$971$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$971$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	34.9223	−	20.1624i	1.11784	−	0.645383i
$977$	−56.1530	−	26.1846i	−1.79649	−	0.837718i	−0.954489	−	0.298248i	$-0.903598\pi$
$977$	−56.1530	−	26.1846i	−1.79649	−	0.837718i	−0.842004	−	0.539471i	$-0.818624\pi$
$978$		0			0
$979$		0			0
$980$	8.92516	+	30.0057i	0.285104	+	0.958497i
$981$	40.1986	+	47.9068i	1.28344	+	1.52955i
$982$		0			0
$983$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$983$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$984$		0			0
$985$	18.9678	−	23.9014i	0.604364	−	0.761563i
$986$	4.81137	−	0.848375i	0.153225	−	0.0270178i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$991$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−4.56050	−	52.1268i	−0.144433	−	1.65087i	−0.629943	−	0.776641i	$-0.716922\pi$
$997$	−4.56050	−	52.1268i	−0.144433	−	1.65087i	0.485511	−	0.874231i	$-0.338634\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.ce.b.3.1	yes	12
4.3	odd	2	CM	740.2.ce.b.3.1	yes	12
5.2	odd	4		740.2.ce.a.447.1	✓	12
20.7	even	4		740.2.ce.a.447.1	✓	12
37.25	even	18		740.2.ce.a.543.1	yes	12
148.99	odd	18		740.2.ce.a.543.1	yes	12
185.62	odd	36	inner	740.2.ce.b.247.1	yes	12
740.247	even	36	inner	740.2.ce.b.247.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.ce.a.447.1	✓	12	5.2	odd	4
740.2.ce.a.447.1	✓	12	20.7	even	4
740.2.ce.a.543.1	yes	12	37.25	even	18
740.2.ce.a.543.1	yes	12	148.99	odd	18
740.2.ce.b.3.1	yes	12	1.1	even	1	trivial
740.2.ce.b.3.1	yes	12	4.3	odd	2	CM
740.2.ce.b.247.1	yes	12	185.62	odd	36	inner
740.2.ce.b.247.1	yes	12	740.247	even	36	inner

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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.ce (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.123257 - 1.40883i) q^{2} +(-1.96962 + 0.347296i) q^{4} +(1.53737 - 1.62373i) q^{5} +(0.732051 + 2.73205i) q^{8} +(2.95442 + 0.520945i) q^{9} +O(q^{10})\)	\(q+(-0.123257 - 1.40883i) q^{2} +(-1.96962 + 0.347296i) q^{4} +(1.53737 - 1.62373i) q^{5} +(0.732051 + 2.73205i) q^{8} +(2.95442 + 0.520945i) q^{9} +(-2.47706 - 1.96575i) q^{10} +(4.43703 + 3.10684i) q^{13} +(3.75877 - 1.36808i) q^{16} +(1.28470 - 0.899557i) q^{17} +(0.369771 - 4.22650i) q^{18} +(-2.46410 + 3.73205i) q^{20} +(-0.273017 - 4.99254i) q^{25} +(3.83013 - 6.63397i) q^{26} +(-1.10137 + 1.90764i) q^{29} +(-2.39069 - 5.12685i) q^{32} +(-1.42567 - 1.69905i) q^{34} -6.00000 q^{36} +(-0.0570813 - 6.08249i) q^{37} +(5.56155 + 3.01150i) q^{40} +(0.711496 + 4.03509i) q^{41} +(5.38790 - 3.99631i) q^{45} +(4.49951 - 5.36231i) q^{49} +(-7.00000 + 1.00000i) q^{50} +(-9.81825 - 4.57832i) q^{52} +(-13.1942 - 6.15258i) q^{53} +(2.82329 + 1.31652i) q^{58} +(9.92806 - 1.75058i) q^{61} +(-6.92820 + 4.00000i) q^{64} +(11.8660 - 2.42820i) q^{65} +(-2.21795 + 2.21795i) q^{68} +(0.739541 + 8.45299i) q^{72} +(-7.02628 - 7.02628i) q^{73} +(-8.56218 + 0.830127i) q^{74} +(3.55721 - 8.20648i) q^{80} +(8.45723 + 3.07818i) q^{81} +(5.59707 - 1.49973i) q^{82} +(0.514414 - 3.46896i) q^{85} +(-13.9725 + 5.08558i) q^{89} +(-6.29423 - 7.09808i) q^{90} +(-0.976048 + 3.64266i) q^{97} +(-8.10919 - 5.67812i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{8}+O(q^{10}) \) 12 * q - 12 * q^8	\( 12 q - 12 q^{8} - 6 q^{17} + 12 q^{20} - 6 q^{26} - 30 q^{34} - 72 q^{36} + 24 q^{41} - 84 q^{50} - 18 q^{58} + 72 q^{61} + 132 q^{65} + 30 q^{73} - 30 q^{74} - 42 q^{85} - 60 q^{89} + 18 q^{90}+O(q^{100}) \) 12 * q - 12 * q^8 - 6 * q^17 + 12 * q^20 - 6 * q^26 - 30 * q^34 - 72 * q^36 + 24 * q^41 - 84 * q^50 - 18 * q^58 + 72 * q^61 + 132 * q^65 + 30 * q^73 - 30 * q^74 - 42 * q^85 - 60 * q^89 + 18 * q^90

Introduction

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