LMFDB - Embedded newform 1260.2.cg.a.521.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1260,2,Mod(341,1260)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1260.341"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1260, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.cg (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 9 x^{10} + 58 x^{9} - 78 x^{8} - 298 x^{7} + 1341 x^{6} - 2086 x^{5} - 3822 x^{4} + \cdots + 117649 $ x^12 - 2x^11 - 9x^10 + 58x^9 - 78x^8 - 298x^7 + 1341x^6 - 2086x^5 - 3822x^4 + 19894x^3 - 21609x^2 - 33614*x + 117649
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.3
Root			$0.260926 + 2.63285i$ of defining polynomial
Character	$\chi$	$=$	1260.521
Dual form			1260.2.cg.a.341.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{5} +(0.260926 + 2.63285i) q^{7} +(-3.06024 - 1.76683i) q^{11} -0.599777i q^{13} +(0.849017 - 1.47054i) q^{17} +(-6.74071 + 3.89175i) q^{19} +(-2.86931 + 1.65660i) q^{23} +(-0.500000 + 0.866025i) q^{25} +0.456069i q^{29} +(-0.914390 - 0.527923i) q^{31} +(2.14966 - 1.54239i) q^{35} +(0.193124 + 0.334501i) q^{37} -0.478149 q^{41} -4.21237 q^{43} +(-4.27902 - 7.41148i) q^{47} +(-6.86384 + 1.37396i) q^{49} +(-3.45520 - 1.99486i) q^{53} +3.53366i q^{55} +(1.30307 - 2.25698i) q^{59} +(-9.60378 + 5.54474i) q^{61} +(-0.519422 + 0.299889i) q^{65} +(-1.43711 + 2.48915i) q^{67} -0.336875i q^{71} +(2.67151 + 1.54239i) q^{73} +(3.85331 - 8.51816i) q^{77} +(6.80447 + 11.7857i) q^{79} -16.2901 q^{83} -1.69803 q^{85} +(5.34822 + 9.26339i) q^{89} +(1.57913 - 0.156497i) q^{91} +(6.74071 + 3.89175i) q^{95} -2.18092i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{5} + 2 q^{7} + 12 q^{11} - 6 q^{19} - 12 q^{23} - 6 q^{25} - 6 q^{31} + 2 q^{35} - 2 q^{37} - 8 q^{41} + 36 q^{43} - 16 q^{47} + 22 q^{49} + 12 q^{53} - 6 q^{65} + 2 q^{67} + 6 q^{73} + 28 q^{77}+ \cdots + 6 q^{95}+O(q^{100}) $ 12 * q - 6 * q^5 + 2 * q^7 + 12 * q^11 - 6 * q^19 - 12 * q^23 - 6 * q^25 - 6 * q^31 + 2 * q^35 - 2 * q^37 - 8 * q^41 + 36 * q^43 - 16 * q^47 + 22 * q^49 + 12 * q^53 - 6 * q^65 + 2 * q^67 + 6 * q^73 + 28 * q^77 + 14 * q^79 + 40 * q^83 - 20 * q^89 + 10 * q^91 + 6 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	0.260926	+	2.63285i	0.0986206	+	0.995125i
$7$	0.260926	+	2.63285i	0.0986206	+	0.995125i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.06024	−	1.76683i	−0.922696	−	0.532719i	−0.0382018	−	0.999270i	$-0.512163\pi$
$11$	−3.06024	−	1.76683i	−0.922696	−	0.532719i	−0.884494	+	0.466551i	$0.845496\pi$
$12$		0			0
$13$		−	0.599777i		−	0.166348i	−0.996535	−	0.0831742i	$-0.973494\pi$
$13$		−	0.599777i		−	0.166348i	0.996535	−	0.0831742i	$-0.0265058\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.849017	−	1.47054i	0.205917	−	0.356658i	−0.744508	−	0.667614i	$-0.767316\pi$
$17$	0.849017	−	1.47054i	0.205917	−	0.356658i	0.950424	+	0.310955i	$0.100649\pi$
$18$		0			0
$19$	−6.74071	+	3.89175i	−1.54642	+	0.892829i	−0.548014	+	0.836469i	$0.684616\pi$
$19$	−6.74071	+	3.89175i	−1.54642	+	0.892829i	−0.998411	+	0.0563594i	$0.982051\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.86931	+	1.65660i	−0.598292	+	0.345424i	−0.768369	−	0.640007i	$-0.778932\pi$
$23$	−2.86931	+	1.65660i	−0.598292	+	0.345424i	0.170077	+	0.985431i	$0.445598\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$			0.456069i			0.0846898i	0.999103	+	0.0423449i	$0.0134828\pi$
$29$			0.456069i			0.0846898i	−0.999103	+	0.0423449i	$0.986517\pi$
$30$		0			0
$31$	−0.914390	−	0.527923i	−0.164229	−	0.0948178i	0.415633	−	0.909533i	$-0.363560\pi$
$31$	−0.914390	−	0.527923i	−0.164229	−	0.0948178i	−0.579862	+	0.814715i	$0.696894\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.14966	−	1.54239i	0.363358	−	0.260712i
$36$		0			0
$37$	0.193124	+	0.334501i	0.0317494	+	0.0549917i	0.881464	−	0.472252i	$-0.156559\pi$
$37$	0.193124	+	0.334501i	0.0317494	+	0.0549917i	−0.849714	+	0.527244i	$0.823225\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.478149			−0.0746743			−0.0373372	−	0.999303i	$-0.511888\pi$
$41$	−0.478149			−0.0746743			−0.0373372	+	0.999303i	$0.511888\pi$
$42$		0			0
$43$	−4.21237			−0.642381			−0.321190	−	0.947015i	$-0.604083\pi$
$43$	−4.21237			−0.642381			−0.321190	+	0.947015i	$0.604083\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.27902	−	7.41148i	−0.624159	−	1.08108i	−0.988703	−	0.149889i	$-0.952108\pi$
$47$	−4.27902	−	7.41148i	−0.624159	−	1.08108i	0.364544	−	0.931186i	$-0.381225\pi$
$48$		0			0
$49$	−6.86384	+	1.37396i	−0.980548	+	0.196280i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.45520	−	1.99486i	−0.474609	−	0.274015i	0.243558	−	0.969886i	$-0.421685\pi$
$53$	−3.45520	−	1.99486i	−0.474609	−	0.274015i	−0.718167	+	0.695871i	$0.755019\pi$
$54$		0			0
$55$			3.53366i			0.476478i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.30307	−	2.25698i	0.169645	−	0.293834i	−0.768650	−	0.639669i	$-0.779071\pi$
$59$	1.30307	−	2.25698i	0.169645	−	0.293834i	0.938295	+	0.345836i	$0.112405\pi$
$60$		0			0
$61$	−9.60378	+	5.54474i	−1.22964	+	0.709932i	−0.966954	−	0.254950i	$-0.917941\pi$
$61$	−9.60378	+	5.54474i	−1.22964	+	0.709932i	−0.262684	+	0.964882i	$0.584608\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.519422	+	0.299889i	−0.0644264	+	0.0371966i
$66$		0			0
$67$	−1.43711	+	2.48915i	−0.175571	+	0.304097i	−0.940359	−	0.340185i	$-0.889510\pi$
$67$	−1.43711	+	2.48915i	−0.175571	+	0.304097i	0.764788	+	0.644282i	$0.222844\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	0.336875i		−	0.0399797i	−0.999800	−	0.0199898i	$-0.993637\pi$
$71$		−	0.336875i		−	0.0399797i	0.999800	−	0.0199898i	$-0.00636339\pi$
$72$		0			0
$73$	2.67151	+	1.54239i	0.312676	+	0.180524i	0.648123	−	0.761535i	$-0.275554\pi$
$73$	2.67151	+	1.54239i	0.312676	+	0.180524i	−0.335447	+	0.942059i	$0.608887\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.85331	−	8.51816i	0.439125	−	0.970735i
$78$		0			0
$79$	6.80447	+	11.7857i	0.765562	+	1.32599i	0.939949	+	0.341316i	$0.110873\pi$
$79$	6.80447	+	11.7857i	0.765562	+	1.32599i	−0.174386	+	0.984677i	$0.555794\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−16.2901			−1.78807			−0.894036	−	0.447996i	$-0.852138\pi$
$83$	−16.2901			−1.78807			−0.894036	+	0.447996i	$0.852138\pi$
$84$		0			0
$85$	−1.69803			−0.184178
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.34822	+	9.26339i	0.566910	+	0.981918i	0.996869	+	0.0790691i	$0.0251948\pi$
$89$	5.34822	+	9.26339i	0.566910	+	0.981918i	−0.429959	+	0.902849i	$0.641472\pi$
$90$		0			0
$91$	1.57913	−	0.156497i	0.165537	−	0.0164054i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	6.74071	+	3.89175i	0.691582	+	0.399285i
$96$		0			0
$97$		−	2.18092i		−	0.221439i	−0.993852	−	0.110719i	$-0.964685\pi$
$97$		−	2.18092i		−	0.221439i	0.993852	−	0.110719i	$-0.0353155\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.85417	+	6.67563i	−0.383505	+	0.664250i	−0.991561	−	0.129645i	$-0.958616\pi$
$101$	−3.85417	+	6.67563i	−0.383505	+	0.664250i	0.608056	+	0.793894i	$0.291950\pi$
$102$		0			0
$103$	−0.636149	+	0.367281i	−0.0626816	+	0.0361893i	−0.531013	−	0.847363i	$-0.678189\pi$
$103$	−0.636149	+	0.367281i	−0.0626816	+	0.0361893i	0.468332	+	0.883553i	$0.344855\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−17.3009	+	9.98870i	−1.67255	+	0.965645i	−0.706339	+	0.707873i	$0.749655\pi$
$107$	−17.3009	+	9.98870i	−1.67255	+	0.965645i	−0.966206	+	0.257771i	$0.917012\pi$
$108$		0			0
$109$	0.221512	−	0.383671i	0.0212170	−	0.0367490i	−0.855222	−	0.518262i	$-0.826579\pi$
$109$	0.221512	−	0.383671i	0.0212170	−	0.0367490i	0.876439	+	0.481513i	$0.159913\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	14.6235i		−	1.37566i	−0.725871	−	0.687830i	$-0.758563\pi$
$113$		−	14.6235i		−	1.37566i	0.725871	−	0.687830i	$-0.241437\pi$
$114$		0			0
$115$	2.86931	+	1.65660i	0.267564	+	0.154478i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	4.09325	+	1.85164i	0.375227	+	0.169739i
$120$		0			0
$121$	0.743363	+	1.28754i	0.0675785	+	0.117049i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	0.961155			0.0852887			0.0426444	−	0.999090i	$-0.486422\pi$
$127$	0.961155			0.0852887			0.0426444	+	0.999090i	$0.486422\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.99734	−	13.8518i	−0.698731	−	1.21024i	−0.968907	−	0.247427i	$-0.920415\pi$
$131$	−7.99734	−	13.8518i	−0.698731	−	1.21024i	0.270175	−	0.962811i	$-0.412918\pi$
$132$		0			0
$133$	−12.0052	−	16.7318i	−1.04099	−	1.45083i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.31358	+	4.79985i	0.710277	+	0.410078i	0.811163	−	0.584819i	$-0.198835\pi$
$137$	8.31358	+	4.79985i	0.710277	+	0.410078i	−0.100887	+	0.994898i	$0.532168\pi$
$138$		0			0
$139$			9.13902i			0.775162i	0.921836	+	0.387581i	$0.126689\pi$
$139$			9.13902i			0.775162i	−0.921836	+	0.387581i	$0.873311\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.05970	+	1.83546i	−0.0886169	+	0.153489i
$144$		0			0
$145$	0.394967	−	0.228034i	0.0328002	−	0.0189372i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	17.5541	−	10.1349i	1.43809	−	0.830279i	0.440369	−	0.897817i	$-0.354847\pi$
$149$	17.5541	−	10.1349i	1.43809	−	0.830279i	0.997717	+	0.0675373i	$0.0215142\pi$
$150$		0			0
$151$	4.00516	−	6.93714i	0.325935	−	0.564536i	−0.655766	−	0.754964i	$-0.727654\pi$
$151$	4.00516	−	6.93714i	0.325935	−	0.564536i	0.981701	+	0.190428i	$0.0609876\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			1.05585i			0.0848076i
$156$		0			0
$157$	−8.08163	−	4.66593i	−0.644984	−	0.372382i	0.141548	−	0.989931i	$-0.454792\pi$
$157$	−8.08163	−	4.66593i	−0.644984	−	0.372382i	−0.786532	+	0.617550i	$0.788125\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−5.11025	−	7.12222i	−0.402744	−	0.561309i
$162$		0			0
$163$	6.82685	+	11.8245i	0.534720	+	0.926163i	0.999177	+	0.0405668i	$0.0129163\pi$
$163$	6.82685	+	11.8245i	0.534720	+	0.926163i	−0.464457	+	0.885596i	$0.653750\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.94429			0.769512			0.384756	−	0.923018i	$-0.374286\pi$
$167$	9.94429			0.769512			0.384756	+	0.923018i	$0.374286\pi$
$168$		0			0
$169$	12.6403			0.972328
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−4.96550	−	8.60049i	−0.377520	−	0.653883i	0.613181	−	0.789942i	$-0.289890\pi$
$173$	−4.96550	−	8.60049i	−0.377520	−	0.653883i	−0.990701	+	0.136059i	$0.956556\pi$
$174$		0			0
$175$	−2.41058	−	1.09046i	−0.182223	−	0.0824309i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	16.3233	+	9.42424i	1.22006	+	0.704400i	0.964930	−	0.262507i	$-0.0845493\pi$
$179$	16.3233	+	9.42424i	1.22006	+	0.704400i	0.255127	+	0.966907i	$0.417883\pi$
$180$		0			0
$181$		−	20.0424i		−	1.48974i	−0.667211	−	0.744869i	$-0.732512\pi$
$181$		−	20.0424i		−	1.48974i	0.667211	−	0.744869i	$-0.267488\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.193124	−	0.334501i	0.0141988	−	0.0245930i
$186$		0			0
$187$	−5.19639	+	3.00013i	−0.379997	+	0.219392i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−7.99103	+	4.61363i	−0.578211	+	0.333830i	−0.760422	−	0.649429i	$-0.775008\pi$
$191$	−7.99103	+	4.61363i	−0.578211	+	0.333830i	0.182211	+	0.983259i	$0.441675\pi$
$192$		0			0
$193$	13.0173	−	22.5467i	0.937007	−	1.62294i	0.165992	−	0.986127i	$-0.446917\pi$
$193$	13.0173	−	22.5467i	0.937007	−	1.62294i	0.771015	−	0.636817i	$-0.219749\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			15.6156i			1.11256i	0.830994	+	0.556282i	$0.187772\pi$
$197$			15.6156i			1.11256i	−0.830994	+	0.556282i	$0.812228\pi$
$198$		0			0
$199$	5.29961	+	3.05973i	0.375679	+	0.216899i	0.675937	−	0.736960i	$-0.263739\pi$
$199$	5.29961	+	3.05973i	0.375679	+	0.216899i	−0.300257	+	0.953858i	$0.597073\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.20076	+	0.119000i	−0.0842770	+	0.00835216i
$204$		0			0
$205$	0.239074	+	0.414089i	0.0166977	+	0.0289212i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	27.5042			1.90251
$210$		0			0
$211$	26.7224			1.83964			0.919822	−	0.392337i	$-0.128333\pi$
$211$	26.7224			1.83964			0.919822	+	0.392337i	$0.128333\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.10619	+	3.64802i	0.143641	+	0.248793i
$216$		0			0
$217$	1.15136	−	2.54520i	0.0781592	−	0.172780i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.881997	−	0.509221i	−0.0593295	−	0.0342539i
$222$		0			0
$223$		−	20.3668i		−	1.36386i	−0.731416	−	0.681932i	$-0.761140\pi$
$223$		−	20.3668i		−	1.36386i	0.731416	−	0.681932i	$-0.238860\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.96949	+	17.2677i	−0.661698	+	1.14609i	0.318471	+	0.947933i	$0.396831\pi$
$227$	−9.96949	+	17.2677i	−0.661698	+	1.14609i	−0.980169	+	0.198162i	$0.936503\pi$
$228$		0			0
$229$	−16.4015	+	9.46944i	−1.08384	+	0.625758i	−0.931931	−	0.362636i	$-0.881877\pi$
$229$	−16.4015	+	9.46944i	−1.08384	+	0.625758i	−0.151914	+	0.988394i	$0.548544\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−22.9956	+	13.2765i	−1.50650	+	0.869775i	−0.506524	+	0.862226i	$0.669070\pi$
$233$	−22.9956	+	13.2765i	−1.50650	+	0.869775i	−0.999972	+	0.00754927i	$0.997597\pi$
$234$		0			0
$235$	−4.27902	+	7.41148i	−0.279133	+	0.483472i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			6.76076i			0.437317i	0.975801	+	0.218659i	$0.0701681\pi$
$239$			6.76076i			0.437317i	−0.975801	+	0.218659i	$0.929832\pi$
$240$		0			0
$241$	−10.4654	−	6.04219i	−0.674134	−	0.389211i	0.123507	−	0.992344i	$-0.460586\pi$
$241$	−10.4654	−	6.04219i	−0.674134	−	0.389211i	−0.797641	+	0.603132i	$0.793919\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	4.62180	+	5.25728i	0.295276	+	0.335875i
$246$		0			0
$247$	2.33418	+	4.04292i	0.148521	+	0.257245i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	17.3410			1.09455			0.547276	−	0.836952i	$-0.315665\pi$
$251$	17.3410			1.09455			0.547276	+	0.836952i	$0.315665\pi$
$252$		0			0
$253$	11.7077			0.736055
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.17127	−	7.22486i	−0.260197	−	0.450674i	0.706097	−	0.708115i	$-0.250454\pi$
$257$	−4.17127	−	7.22486i	−0.260197	−	0.450674i	−0.966294	+	0.257441i	$0.917121\pi$
$258$		0			0
$259$	−0.830302	+	0.595748i	−0.0515924	+	0.0370180i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	11.6209	+	6.70936i	0.716578	+	0.413717i	0.813492	−	0.581576i	$-0.197564\pi$
$263$	11.6209	+	6.70936i	0.716578	+	0.413717i	−0.0969137	+	0.995293i	$0.530897\pi$
$264$		0			0
$265$			3.98973i			0.245087i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.98145	−	6.89607i	0.242753	−	0.420461i	−0.718744	−	0.695274i	$-0.755283\pi$
$269$	3.98145	−	6.89607i	0.242753	−	0.420461i	0.961497	+	0.274814i	$0.0886162\pi$
$270$		0			0
$271$	−6.46871	+	3.73471i	−0.392946	+	0.226867i	−0.683436	−	0.730011i	$-0.739515\pi$
$271$	−6.46871	+	3.73471i	−0.392946	+	0.226867i	0.290490	+	0.956878i	$0.406182\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.06024	−	1.76683i	0.184539	−	0.106544i
$276$		0			0
$277$	15.6308	−	27.0734i	0.939166	−	1.62668i	0.172135	−	0.985073i	$-0.444933\pi$
$277$	15.6308	−	27.0734i	0.939166	−	1.62668i	0.767031	−	0.641610i	$-0.221733\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			23.4956i			1.40163i	0.713343	+	0.700815i	$0.247180\pi$
$281$			23.4956i			1.40163i	−0.713343	+	0.700815i	$0.752820\pi$
$282$		0			0
$283$	16.0325	+	9.25634i	0.953030	+	0.550232i	0.894021	−	0.448025i	$-0.147873\pi$
$283$	16.0325	+	9.25634i	0.953030	+	0.550232i	0.0590093	+	0.998257i	$0.481206\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.124761	−	1.25890i	−0.00736442	−	0.0743103i
$288$		0			0
$289$	7.05834	+	12.2254i	0.415196	+	0.719141i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−14.7388			−0.861048			−0.430524	−	0.902579i	$-0.641671\pi$
$293$	−14.7388			−0.861048			−0.430524	+	0.902579i	$0.641671\pi$
$294$		0			0
$295$	−2.60613			−0.151735
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.993588	+	1.72095i	0.0574607	+	0.0995248i
$300$		0			0
$301$	−1.09912	−	11.0906i	−0.0633520	−	0.639249i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	9.60378	+	5.54474i	0.549911	+	0.317491i
$306$		0			0
$307$		−	17.6583i		−	1.00781i	−0.863758	−	0.503906i	$-0.831896\pi$
$307$		−	17.6583i		−	1.00781i	0.863758	−	0.503906i	$-0.168104\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.43782	+	2.49037i	−0.0815310	+	0.141216i	−0.903908	−	0.427727i	$-0.859314\pi$
$311$	−1.43782	+	2.49037i	−0.0815310	+	0.141216i	0.822377	+	0.568943i	$0.192648\pi$
$312$		0			0
$313$	17.3539	−	10.0193i	0.980901	−	0.566324i	0.0783592	−	0.996925i	$-0.475032\pi$
$313$	17.3539	−	10.0193i	0.980901	−	0.566324i	0.902542	+	0.430602i	$0.141699\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	17.8323	−	10.2955i	1.00156	−	0.578252i	0.0928516	−	0.995680i	$-0.470402\pi$
$317$	17.8323	−	10.2955i	1.00156	−	0.578252i	0.908710	+	0.417428i	$0.137068\pi$
$318$		0			0
$319$	0.805795	−	1.39568i	0.0451159	−	0.0781430i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			13.2166i			0.735394i
$324$		0			0
$325$	0.519422	+	0.299889i	0.0288124	+	0.0166348i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	18.3968	−	13.1999i	1.01425	−	0.727733i
$330$		0			0
$331$	11.4497	+	19.8315i	0.629335	+	1.09004i	0.987685	+	0.156453i	$0.0500060\pi$
$331$	11.4497	+	19.8315i	0.629335	+	1.09004i	−0.358350	+	0.933587i	$0.616661\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.87422			0.157035
$336$		0			0
$337$	17.7305			0.965840			0.482920	−	0.875664i	$-0.339576\pi$
$337$	17.7305			0.965840			0.482920	+	0.875664i	$0.339576\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.86550	+	3.23114i	0.101022	+	0.174976i
$342$		0			0
$343$	−5.40838	−	17.7130i	−0.292025	−	0.956411i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−15.7529	−	9.09495i	−0.845661	−	0.488243i	0.0135233	−	0.999909i	$-0.495695\pi$
$347$	−15.7529	−	9.09495i	−0.845661	−	0.488243i	−0.859185	+	0.511666i	$0.829029\pi$
$348$		0			0
$349$			4.44213i			0.237782i	0.992907	+	0.118891i	$0.0379339\pi$
$349$			4.44213i			0.237782i	−0.992907	+	0.118891i	$0.962066\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2.59135	−	4.48835i	0.137924	−	0.238891i	−0.788787	−	0.614667i	$-0.789290\pi$
$353$	2.59135	−	4.48835i	0.137924	−	0.238891i	0.926711	+	0.375776i	$0.122624\pi$
$354$		0			0
$355$	−0.291742	+	0.168437i	−0.0154841	+	0.00893973i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−15.7893	+	9.11596i	−0.833327	+	0.481122i	−0.854991	−	0.518644i	$-0.826437\pi$
$359$	−15.7893	+	9.11596i	−0.833327	+	0.481122i	0.0216632	+	0.999765i	$0.493104\pi$
$360$		0			0
$361$	20.7914	−	36.0118i	1.09429	−	1.89536i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	3.08479i		−	0.161465i
$366$		0			0
$367$	17.3722	+	10.0298i	0.906821	+	0.523553i	0.879407	−	0.476071i	$-0.157939\pi$
$367$	17.3722	+	10.0298i	0.906821	+	0.523553i	0.0274140	+	0.999624i	$0.491273\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	4.35063	−	9.61755i	0.225873	−	0.499319i
$372$		0			0
$373$	−13.2945	−	23.0267i	−0.688361	−	1.19228i	−0.972368	−	0.233454i	$-0.924997\pi$
$373$	−13.2945	−	23.0267i	−0.688361	−	1.19228i	0.284007	−	0.958822i	$-0.408336\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.273540			0.0140880
$378$		0			0
$379$	−18.3623			−0.943210			−0.471605	−	0.881810i	$-0.656325\pi$
$379$	−18.3623			−0.943210			−0.471605	+	0.881810i	$0.656325\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−18.4049	−	31.8783i	−0.940449	−	1.62891i	−0.764617	−	0.644485i	$-0.777072\pi$
$383$	−18.4049	−	31.8783i	−0.940449	−	1.62891i	−0.175832	−	0.984420i	$-0.556262\pi$
$384$		0			0
$385$	−9.30360	+	0.922021i	−0.474155	+	0.0469906i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	27.4003	+	15.8196i	1.38925	+	0.802084i	0.993231	−	0.116157i	$-0.0370577\pi$
$389$	27.4003	+	15.8196i	1.38925	+	0.802084i	0.396020	+	0.918242i	$0.370391\pi$
$390$		0			0
$391$			5.62591i			0.284515i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	6.80447	−	11.7857i	0.342370	−	0.593002i
$396$		0			0
$397$	−23.3704	+	13.4929i	−1.17293	+	0.677190i	−0.954368	−	0.298634i	$-0.903469\pi$
$397$	−23.3704	+	13.4929i	−1.17293	+	0.677190i	−0.218560	+	0.975824i	$0.570136\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8.48970	+	4.90153i	−0.423956	+	0.244771i	−0.696768	−	0.717296i	$-0.745379\pi$
$401$	−8.48970	+	4.90153i	−0.423956	+	0.244771i	0.272813	+	0.962067i	$0.412046\pi$
$402$		0			0
$403$	−0.316636	+	0.548430i	−0.0157728	+	0.0273193i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	1.36487i		−	0.0676541i
$408$		0			0
$409$	7.43046	+	4.28998i	0.367413	+	0.212126i	0.672328	−	0.740254i	$-0.265295\pi$
$409$	7.43046	+	4.28998i	0.367413	+	0.212126i	−0.304915	+	0.952380i	$0.598628\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	6.28230	+	2.84188i	0.309132	+	0.139840i
$414$		0			0
$415$	8.14505	+	14.1076i	0.399825	+	0.692517i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	21.7882			1.06443			0.532213	−	0.846611i	$-0.321361\pi$
$419$	21.7882			1.06443			0.532213	+	0.846611i	$0.321361\pi$
$420$		0			0
$421$	−24.2280			−1.18080			−0.590400	−	0.807111i	$-0.701030\pi$
$421$	−24.2280			−1.18080			−0.590400	+	0.807111i	$0.701030\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.849017	+	1.47054i	0.0411834	+	0.0713317i
$426$		0			0
$427$	−17.1044	−	23.8386i	−0.827738	−	1.15363i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−20.6400	−	11.9165i	−0.994194	−	0.573998i	−0.0876688	−	0.996150i	$-0.527942\pi$
$431$	−20.6400	−	11.9165i	−0.994194	−	0.573998i	−0.906525	+	0.422151i	$0.861275\pi$
$432$		0			0
$433$			1.39596i			0.0670855i	0.999437	+	0.0335427i	$0.0106790\pi$
$433$			1.39596i			0.0670855i	−0.999437	+	0.0335427i	$0.989321\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	12.8941	−	22.3333i	0.616809	−	1.06834i
$438$		0			0
$439$	−10.2953	+	5.94397i	−0.491366	+	0.283690i	−0.725141	−	0.688600i	$-0.758225\pi$
$439$	−10.2953	+	5.94397i	−0.491366	+	0.283690i	0.233775	+	0.972291i	$0.424892\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−23.1578	+	13.3701i	−1.10026	+	0.635235i	−0.936289	−	0.351230i	$-0.885763\pi$
$443$	−23.1578	+	13.3701i	−1.10026	+	0.635235i	−0.163970	+	0.986465i	$0.552430\pi$
$444$		0			0
$445$	5.34822	−	9.26339i	0.253530	−	0.439127i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			32.8394i			1.54979i	0.632091	+	0.774895i	$0.282197\pi$
$449$			32.8394i			1.54979i	−0.632091	+	0.774895i	$0.717803\pi$
$450$		0			0
$451$	1.46325	+	0.844807i	0.0689017	+	0.0397804i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.925094	−	1.28931i	−0.0433691	−	0.0604440i
$456$		0			0
$457$	17.5227	+	30.3502i	0.819677	+	1.41972i	0.905920	+	0.423448i	$0.139180\pi$
$457$	17.5227	+	30.3502i	0.819677	+	1.41972i	−0.0862436	+	0.996274i	$0.527486\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−8.90991			−0.414976			−0.207488	−	0.978238i	$-0.566529\pi$
$461$	−8.90991			−0.414976			−0.207488	+	0.978238i	$0.566529\pi$
$462$		0			0
$463$	−10.2000			−0.474036			−0.237018	−	0.971505i	$-0.576170\pi$
$463$	−10.2000			−0.474036			−0.237018	+	0.971505i	$0.576170\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	8.41916	+	14.5824i	0.389592	+	0.674794i	0.992395	−	0.123097i	$-0.0392826\pi$
$467$	8.41916	+	14.5824i	0.389592	+	0.674794i	−0.602802	+	0.797891i	$0.705949\pi$
$468$		0			0
$469$	−6.92853	−	3.13421i	−0.319930	−	0.144725i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	12.8909	+	7.44254i	0.592722	+	0.342208i
$474$		0			0
$475$		−	7.78350i		−	0.357131i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−9.18515	+	15.9091i	−0.419680	+	0.726907i	−0.995907	−	0.0903824i	$-0.971191\pi$
$479$	−9.18515	+	15.9091i	−0.419680	+	0.726907i	0.576227	+	0.817290i	$0.304524\pi$
$480$		0			0
$481$	0.200626	−	0.115832i	0.00914777	−	0.00528147i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.88873	+	1.09046i	−0.0857628	+	0.0495152i
$486$		0			0
$487$	5.83194	−	10.1012i	0.264270	−	0.457729i	−0.703102	−	0.711089i	$-0.748202\pi$
$487$	5.83194	−	10.1012i	0.264270	−	0.457729i	0.967372	+	0.253360i	$0.0815356\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	21.4694i		−	0.968902i	−0.874818	−	0.484451i	$-0.839019\pi$
$491$		−	21.4694i		−	0.968902i	0.874818	−	0.484451i	$-0.160981\pi$
$492$		0			0
$493$	0.670668	+	0.387210i	0.0302054	+	0.0174391i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.886942	−	0.0878993i	0.0397848	−	0.00394282i
$498$		0			0
$499$	7.41090	+	12.8361i	0.331757	+	0.574621i	0.982857	−	0.184372i	$-0.0590251\pi$
$499$	7.41090	+	12.8361i	0.331757	+	0.574621i	−0.651099	+	0.758993i	$0.725692\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−28.9563			−1.29110			−0.645548	−	0.763719i	$-0.723371\pi$
$503$	−28.9563			−1.29110			−0.645548	+	0.763719i	$0.723371\pi$
$504$		0			0
$505$	7.70835			0.343017
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−14.5897	−	25.2700i	−0.646675	−	1.12007i	−0.983912	−	0.178654i	$-0.942826\pi$
$509$	−14.5897	−	25.2700i	−0.646675	−	1.12007i	0.337237	−	0.941420i	$-0.390508\pi$
$510$		0			0
$511$	−3.36384	+	7.43614i	−0.148807	+	0.328955i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.636149	+	0.367281i	0.0280321	+	0.0161843i
$516$		0			0
$517$			30.2412i			1.33001i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−15.3104	+	26.5184i	−0.670761	+	1.16179i	0.306928	+	0.951733i	$0.400699\pi$
$521$	−15.3104	+	26.5184i	−0.670761	+	1.16179i	−0.977689	+	0.210059i	$0.932635\pi$
$522$		0			0
$523$	−10.4636	+	6.04118i	−0.457542	+	0.264162i	−0.711010	−	0.703182i	$-0.751762\pi$
$523$	−10.4636	+	6.04118i	−0.457542	+	0.264162i	0.253468	+	0.967344i	$0.418429\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.55266	+	0.896431i	−0.0676351	+	0.0390492i
$528$		0			0
$529$	−6.01138	+	10.4120i	−0.261365	+	0.452697i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			0.286783i			0.0124219i
$534$		0			0
$535$	17.3009	+	9.98870i	0.747985	+	0.431849i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	23.4325	+	7.92258i	1.00931	+	0.341250i
$540$		0			0
$541$	−2.77440	−	4.80539i	−0.119281	−	0.206600i	0.800202	−	0.599730i	$-0.204725\pi$
$541$	−2.77440	−	4.80539i	−0.119281	−	0.206600i	−0.919483	+	0.393130i	$0.871392\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.443025			−0.0189771
$546$		0			0
$547$	4.60440			0.196870			0.0984349	−	0.995143i	$-0.468616\pi$
$547$	4.60440			0.196870			0.0984349	+	0.995143i	$0.468616\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.77491	−	3.07423i	−0.0756135	−	0.130966i
$552$		0			0
$553$	−29.2545	+	20.9904i	−1.24403	+	0.892601i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−13.5974	−	7.85045i	−0.576139	−	0.332634i	0.183458	−	0.983028i	$-0.441271\pi$
$557$	−13.5974	−	7.85045i	−0.576139	−	0.332634i	−0.759598	+	0.650393i	$0.774604\pi$
$558$		0			0
$559$			2.52649i			0.106859i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	16.3425	−	28.3061i	0.688756	−	1.19296i	−0.283485	−	0.958977i	$-0.591491\pi$
$563$	16.3425	−	28.3061i	0.688756	−	1.19296i	0.972241	−	0.233983i	$-0.0751761\pi$
$564$		0			0
$565$	−12.6643	+	7.31174i	−0.532791	+	0.307607i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−20.0566	+	11.5797i	−0.840817	+	0.485446i	−0.857542	−	0.514414i	$-0.828009\pi$
$569$	−20.0566	+	11.5797i	−0.840817	+	0.485446i	0.0167248	+	0.999860i	$0.494676\pi$
$570$		0			0
$571$	1.95247	−	3.38177i	0.0817083	−	0.141523i	−0.822276	−	0.569090i	$-0.807296\pi$
$571$	1.95247	−	3.38177i	0.0817083	−	0.141523i	0.903984	+	0.427567i	$0.140629\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	3.31319i		−	0.138170i
$576$		0			0
$577$	−6.65040	−	3.83961i	−0.276860	−	0.159845i	0.355141	−	0.934813i	$-0.384433\pi$
$577$	−6.65040	−	3.83961i	−0.276860	−	0.159845i	−0.632001	+	0.774968i	$0.717766\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−4.25050	−	42.8895i	−0.176341	−	1.77935i
$582$		0			0
$583$	7.04916	+	12.2095i	0.291946	+	0.505666i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.375586			−0.0155021			−0.00775105	−	0.999970i	$-0.502467\pi$
$587$	−0.375586			−0.0155021			−0.00775105	+	0.999970i	$0.502467\pi$
$588$		0			0
$589$	8.21818			0.338624
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−11.5202	−	19.9536i	−0.473078	−	0.819396i	0.526447	−	0.850208i	$-0.323524\pi$
$593$	−11.5202	−	19.9536i	−0.473078	−	0.819396i	−0.999525	+	0.0308124i	$0.990191\pi$
$594$		0			0
$595$	−0.443060	−	4.47068i	−0.0181637	−	0.183280i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	7.46233	+	4.30838i	0.304902	+	0.176036i	0.644643	−	0.764484i	$-0.277006\pi$
$599$	7.46233	+	4.30838i	0.304902	+	0.176036i	−0.339741	+	0.940519i	$0.610339\pi$
$600$		0			0
$601$			27.4954i			1.12156i	0.827965	+	0.560780i	$0.189499\pi$
$601$			27.4954i			1.12156i	−0.827965	+	0.560780i	$0.810501\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.743363	−	1.28754i	0.0302220	−	0.0523461i
$606$		0			0
$607$	−31.1143	+	17.9638i	−1.26289	+	0.729130i	−0.973633	−	0.228121i	$-0.926742\pi$
$607$	−31.1143	+	17.9638i	−1.26289	+	0.729130i	−0.289257	+	0.957251i	$0.593408\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.44524	+	2.56646i	−0.179835	+	0.103828i
$612$		0			0
$613$	−20.9271	+	36.2468i	−0.845238	+	1.46400i	0.0401755	+	0.999193i	$0.487208\pi$
$613$	−20.9271	+	36.2468i	−0.845238	+	1.46400i	−0.885414	+	0.464803i	$0.846125\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	27.6411i		−	1.11279i	−0.830918	−	0.556395i	$-0.812184\pi$
$617$		−	27.6411i		−	1.11279i	0.830918	−	0.556395i	$-0.187816\pi$
$618$		0			0
$619$	−11.4818	−	6.62901i	−0.461492	−	0.266442i	0.251179	−	0.967941i	$-0.419182\pi$
$619$	−11.4818	−	6.62901i	−0.461492	−	0.266442i	−0.712671	+	0.701498i	$0.752515\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−22.9937	+	16.4981i	−0.921222	+	0.660984i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	0.655863			0.0261510
$630$		0			0
$631$	−12.2455			−0.487485			−0.243742	−	0.969840i	$-0.578375\pi$
$631$	−12.2455			−0.487485			−0.243742	+	0.969840i	$0.578375\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.480578	−	0.832385i	−0.0190711	−	0.0330322i
$636$		0			0
$637$	0.824069	+	4.11677i	0.0326508	+	0.163112i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−10.7315	−	6.19582i	−0.423868	−	0.244720i	0.272863	−	0.962053i	$-0.412029\pi$
$641$	−10.7315	−	6.19582i	−0.423868	−	0.244720i	−0.696731	+	0.717333i	$0.745363\pi$
$642$		0			0
$643$		−	42.8847i		−	1.69121i	−0.533811	−	0.845604i	$-0.679241\pi$
$643$		−	42.8847i		−	1.69121i	0.533811	−	0.845604i	$-0.320759\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.4350	+	23.2701i	−0.528185	+	0.914843i	0.471275	+	0.881986i	$0.343794\pi$
$647$	−13.4350	+	23.2701i	−0.528185	+	0.914843i	−0.999460	+	0.0328565i	$0.989540\pi$
$648$		0			0
$649$	−7.97539	+	4.60459i	−0.313061	+	0.180746i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.538748	+	0.311046i	−0.0210828	+	0.0121722i	−0.510504	−	0.859875i	$-0.670541\pi$
$653$	−0.538748	+	0.311046i	−0.0210828	+	0.0121722i	0.489422	+	0.872047i	$0.337208\pi$
$654$		0			0
$655$	−7.99734	+	13.8518i	−0.312482	+	0.541235i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		−	17.9996i		−	0.701167i	−0.936532	−	0.350583i	$-0.885983\pi$
$659$		−	17.9996i		−	0.701167i	0.936532	−	0.350583i	$-0.114017\pi$
$660$		0			0
$661$	−26.0446	−	15.0369i	−1.01302	−	0.584866i	−0.100944	−	0.994892i	$-0.532186\pi$
$661$	−26.0446	−	15.0369i	−1.01302	−	0.584866i	−0.912074	+	0.410026i	$0.865519\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−8.48758	+	18.7628i	−0.329134	+	0.727588i
$666$		0			0
$667$	−0.755521	−	1.30860i	−0.0292539	−	0.0506693i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	39.1864			1.51278
$672$		0			0
$673$	39.4637			1.52121			0.760606	−	0.649213i	$-0.224902\pi$
$673$	39.4637			1.52121			0.760606	+	0.649213i	$0.224902\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−9.83874	−	17.0412i	−0.378134	−	0.654947i	0.612657	−	0.790349i	$-0.290101\pi$
$677$	−9.83874	−	17.0412i	−0.378134	−	0.654947i	−0.990791	+	0.135402i	$0.956767\pi$
$678$		0			0
$679$	5.74204	−	0.569057i	0.220359	−	0.0218384i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	15.6077	+	9.01113i	0.597213	+	0.344801i	0.767945	−	0.640516i	$-0.221280\pi$
$683$	15.6077	+	9.01113i	0.597213	+	0.344801i	−0.170731	+	0.985318i	$0.554613\pi$
$684$		0			0
$685$		−	9.59969i		−	0.366785i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.19647	+	2.07235i	−0.0455820	+	0.0789503i
$690$		0			0
$691$	−23.5609	+	13.6029i	−0.896298	+	0.517478i	−0.875997	−	0.482316i	$-0.839796\pi$
$691$	−23.5609	+	13.6029i	−0.896298	+	0.517478i	−0.0203004	+	0.999794i	$0.506462\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	7.91463	−	4.56951i	0.300219	−	0.173331i
$696$		0			0
$697$	−0.405957	+	0.703137i	−0.0153767	+	0.0266332i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			33.1556i			1.25227i	0.779715	+	0.626134i	$0.215364\pi$
$701$			33.1556i			1.25227i	−0.779715	+	0.626134i	$0.784636\pi$
$702$		0			0
$703$	−2.60359	−	1.50318i	−0.0981962	−	0.0566936i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−18.5816	−	8.40563i	−0.698833	−	0.316126i
$708$		0			0
$709$	−0.989596	−	1.71403i	−0.0371650	−	0.0643717i	0.846845	−	0.531840i	$-0.178499\pi$
$709$	−0.989596	−	1.71403i	−0.0371650	−	0.0643717i	−0.884010	+	0.467469i	$0.845166\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	3.49822			0.131009
$714$		0			0
$715$	2.11941			0.0792613
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−15.1795	−	26.2916i	−0.566098	−	0.980510i	−0.996947	−	0.0780862i	$-0.975119\pi$
$719$	−15.1795	−	26.2916i	−0.566098	−	0.980510i	0.430849	−	0.902424i	$-0.358214\pi$
$720$		0			0
$721$	−1.13298	−	1.57905i	−0.0421945	−	0.0588071i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.394967	−	0.228034i	−0.0146687	−	0.00846898i
$726$		0			0
$727$		−	17.5883i		−	0.652313i	−0.945316	−	0.326156i	$-0.894246\pi$
$727$		−	17.5883i		−	0.652313i	0.945316	−	0.326156i	$-0.105754\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−3.57638	+	6.19446i	−0.132277	+	0.229111i
$732$		0			0
$733$	−31.9948	+	18.4722i	−1.18176	+	0.682287i	−0.956420	−	0.291994i	$-0.905681\pi$
$733$	−31.9948	+	18.4722i	−1.18176	+	0.682287i	−0.225336	+	0.974281i	$0.572348\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8.79578	−	5.07825i	0.323997	−	0.187060i
$738$		0			0
$739$	2.52958	−	4.38136i	0.0930520	−	0.161171i	−0.815742	−	0.578416i	$-0.803671\pi$
$739$	2.52958	−	4.38136i	0.0930520	−	0.161171i	0.908794	+	0.417245i	$0.137004\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	6.19725i		−	0.227355i	−0.993518	−	0.113678i	$-0.963737\pi$
$743$		−	6.19725i		−	0.227355i	0.993518	−	0.113678i	$-0.0362631\pi$
$744$		0			0
$745$	−17.5541	−	10.1349i	−0.643132	−	0.371312i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−30.8131	−	42.9445i	−1.12588	−	1.56916i
$750$		0			0
$751$	18.9100	+	32.7531i	0.690037	+	1.19518i	0.971825	+	0.235703i	$0.0757392\pi$
$751$	18.9100	+	32.7531i	0.690037	+	1.19518i	−0.281788	+	0.959477i	$0.590928\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−8.01031			−0.291525
$756$		0			0
$757$	−13.7436			−0.499519			−0.249760	−	0.968308i	$-0.580352\pi$
$757$	−13.7436			−0.499519			−0.249760	+	0.968308i	$0.580352\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.19974	−	2.07800i	−0.0434904	−	0.0753275i	0.843461	−	0.537191i	$-0.180514\pi$
$761$	−1.19974	−	2.07800i	−0.0434904	−	0.0753275i	−0.886951	+	0.461863i	$0.847181\pi$
$762$		0			0
$763$	1.06795	+	0.483100i	0.0386623	+	0.0174894i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.35368	−	0.781550i	−0.0488787	−	0.0282201i
$768$		0			0
$769$			9.42300i			0.339802i	0.985461	+	0.169901i	$0.0543448\pi$
$769$			9.42300i			0.339802i	−0.985461	+	0.169901i	$0.945655\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	11.2838	−	19.5441i	0.405850	−	0.702953i	−0.588570	−	0.808446i	$-0.700309\pi$
$773$	11.2838	−	19.5441i	0.405850	−	0.702953i	0.994420	+	0.105493i	$0.0336421\pi$
$774$		0			0
$775$	0.914390	−	0.527923i	0.0328458	−	0.0189636i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.22306	−	1.86084i	0.115478	−	0.0666714i
$780$		0			0
$781$	−0.595200	+	1.03092i	−0.0212979	+	0.0368891i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			9.33186i			0.333068i
$786$		0			0
$787$	−22.4427	−	12.9573i	−0.799997	−	0.461878i	0.0434733	−	0.999055i	$-0.486158\pi$
$787$	−22.4427	−	12.9573i	−0.799997	−	0.461878i	−0.843470	+	0.537176i	$0.819491\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	38.5015	−	3.81564i	1.36895	−	0.135668i
$792$		0			0
$793$	3.32561	+	5.76013i	0.118096	+	0.204548i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.94772			−0.246101			−0.123050	−	0.992400i	$-0.539268\pi$
$797$	−6.94772			−0.246101			−0.123050	+	0.992400i	$0.539268\pi$
$798$		0			0
$799$	−14.5318			−0.514100
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.45029	−	9.44019i	−0.192337	−	0.333137i
$804$		0			0
$805$	−3.61290	+	7.98671i	−0.127338	+	0.281495i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−28.9229	−	16.6986i	−1.01687	−	0.587093i	−0.103677	−	0.994611i	$-0.533061\pi$
$809$	−28.9229	−	16.6986i	−1.01687	−	0.587093i	−0.913197	+	0.407518i	$0.866394\pi$
$810$		0			0
$811$			28.9701i			1.01728i	0.860979	+	0.508640i	$0.169851\pi$
$811$			28.9701i			1.01728i	−0.860979	+	0.508640i	$0.830149\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.82685	−	11.8245i	0.239134	−	0.414193i
$816$		0			0
$817$	28.3944	−	16.3935i	0.993393	−	0.573536i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.25824	+	1.30380i	−0.0788132	+	0.0455028i	−0.538889	−	0.842377i	$-0.681156\pi$
$821$	−2.25824	+	1.30380i	−0.0788132	+	0.0455028i	0.460076	+	0.887880i	$0.347822\pi$
$822$		0			0
$823$	−4.22848	+	7.32393i	−0.147395	+	0.255296i	−0.930264	−	0.366891i	$-0.880422\pi$
$823$	−4.22848	+	7.32393i	−0.147395	+	0.255296i	0.782869	+	0.622187i	$0.213756\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			13.3362i			0.463744i	0.972746	+	0.231872i	$0.0744851\pi$
$827$			13.3362i			0.463744i	−0.972746	+	0.231872i	$0.925515\pi$
$828$		0			0
$829$	10.0783	+	5.81869i	0.350033	+	0.202091i	0.664700	−	0.747111i	$-0.268560\pi$
$829$	10.0783	+	5.81869i	0.350033	+	0.202091i	−0.314667	+	0.949202i	$0.601893\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3.80705	+	11.2601i	−0.131907	+	0.390138i
$834$		0			0
$835$	−4.97214	−	8.61201i	−0.172068	−	0.298031i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−19.9335			−0.688181			−0.344090	−	0.938937i	$-0.611813\pi$
$839$	−19.9335			−0.688181			−0.344090	+	0.938937i	$0.611813\pi$
$840$		0			0
$841$	28.7920			0.992828
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−6.32013	−	10.9468i	−0.217419	−	0.376581i
$846$		0			0
$847$	−3.19595	+	2.29312i	−0.109814	+	0.0787925i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.10827	−	0.639858i	−0.0379909	−	0.0219340i
$852$		0			0
$853$		−	2.08233i		−	0.0712975i	−0.999364	−	0.0356487i	$-0.988650\pi$
$853$		−	2.08233i		−	0.0712975i	0.999364	−	0.0356487i	$-0.0113498\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−23.2741	+	40.3119i	−0.795028	+	1.37703i	0.127793	+	0.991801i	$0.459211\pi$
$857$	−23.2741	+	40.3119i	−0.795028	+	1.37703i	−0.922821	+	0.385228i	$0.874123\pi$
$858$		0			0
$859$	4.62888	−	2.67248i	0.157935	−	0.0911840i	−0.418949	−	0.908010i	$-0.637602\pi$
$859$	4.62888	−	2.67248i	0.157935	−	0.0911840i	0.576885	+	0.816826i	$0.304268\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	11.5242	−	6.65350i	0.392288	−	0.226488i	−0.290863	−	0.956765i	$-0.593942\pi$
$863$	11.5242	−	6.65350i	0.392288	−	0.226488i	0.683151	+	0.730277i	$0.260609\pi$
$864$		0			0
$865$	−4.96550	+	8.60049i	−0.168832	+	0.292426i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		−	48.0893i		−	1.63132i
$870$		0			0
$871$	1.49293	+	0.861945i	0.0505861	+	0.0292059i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.260926	+	2.63285i	0.00882089	+	0.0890067i
$876$		0			0
$877$	9.89224	+	17.1339i	0.334037	+	0.578570i	0.983299	−	0.181995i	$-0.0582555\pi$
$877$	9.89224	+	17.1339i	0.334037	+	0.578570i	−0.649262	+	0.760565i	$0.724922\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−34.3203			−1.15628			−0.578141	−	0.815937i	$-0.696222\pi$
$881$	−34.3203			−1.15628			−0.578141	+	0.815937i	$0.696222\pi$
$882$		0			0
$883$	28.1109			0.946006			0.473003	−	0.881061i	$-0.343170\pi$
$883$	28.1109			0.946006			0.473003	+	0.881061i	$0.343170\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	20.8826	+	36.1697i	0.701169	+	1.21446i	0.968056	+	0.250732i	$0.0806714\pi$
$887$	20.8826	+	36.1697i	0.701169	+	1.21446i	−0.266888	+	0.963728i	$0.585995\pi$
$888$		0			0
$889$	0.250790	+	2.53058i	0.00841122	+	0.0848730i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	57.6873	+	33.3058i	1.93043	+	1.11453i
$894$		0			0
$895$		−	18.8485i		−	0.630035i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.240769	−	0.417025i	0.00803010	−	0.0139085i
$900$		0			0
$901$	−5.86705	+	3.38734i	−0.195460	+	0.112849i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−17.3572	+	10.0212i	−0.576973	+	0.333115i
$906$		0			0
$907$	3.96050	−	6.85979i	0.131506	−	0.227776i	−0.792751	−	0.609546i	$-0.791352\pi$
$907$	3.96050	−	6.85979i	0.131506	−	0.227776i	0.924257	+	0.381770i	$0.124685\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	49.9301i		−	1.65426i	−0.562012	−	0.827129i	$-0.689973\pi$
$911$		−	49.9301i		−	1.65426i	0.562012	−	0.827129i	$-0.310027\pi$
$912$		0			0
$913$	49.8516	+	28.7818i	1.64985	+	0.952539i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	34.3831	−	24.6701i	1.13543	−	0.814679i
$918$		0			0
$919$	0.132073	+	0.228757i	0.00435668	+	0.00754598i	0.868196	−	0.496222i	$-0.165280\pi$
$919$	0.132073	+	0.228757i	0.00435668	+	0.00754598i	−0.863839	+	0.503768i	$0.831947\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.202050			−0.00665055
$924$		0			0
$925$	−0.386249			−0.0126998
$926$		0			0
$927$		0			0
$928$		0			0
$929$	28.4346	+	49.2502i	0.932910	+	1.61585i	0.778320	+	0.627868i	$0.216072\pi$
$929$	28.4346	+	49.2502i	0.932910	+	1.61585i	0.154590	+	0.987979i	$0.450594\pi$
$930$		0			0
$931$	40.9200	−	35.9738i	1.34110	−	1.17899i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	5.19639	+	3.00013i	0.169940	+	0.0981149i
$936$		0			0
$937$			37.3673i			1.22074i	0.792118	+	0.610369i	$0.208979\pi$
$937$			37.3673i			1.22074i	−0.792118	+	0.610369i	$0.791021\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−23.8667	+	41.3384i	−0.778033	+	1.34759i	0.155042	+	0.987908i	$0.450449\pi$
$941$	−23.8667	+	41.3384i	−0.778033	+	1.34759i	−0.933074	+	0.359684i	$0.882885\pi$
$942$		0			0
$943$	1.37196	−	0.792099i	0.0446770	−	0.0257943i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−28.7296	+	16.5870i	−0.933587	+	0.539006i	−0.887944	−	0.459951i	$-0.847867\pi$
$947$	−28.7296	+	16.5870i	−0.933587	+	0.539006i	−0.0456424	+	0.998958i	$0.514533\pi$
$948$		0			0
$949$	0.925094	−	1.60231i	0.0300298	−	0.0520131i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			28.1591i			0.912164i	0.889938	+	0.456082i	$0.150748\pi$
$953$			28.1591i			0.912164i	−0.889938	+	0.456082i	$0.849252\pi$
$954$		0			0
$955$	7.99103	+	4.61363i	0.258584	+	0.149293i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−10.4681	+	23.1408i	−0.338031	+	0.747256i
$960$		0			0
$961$	−14.9426	−	25.8813i	−0.482019	−	0.834882i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−26.0346			−0.838085
$966$		0			0
$967$	−53.8983			−1.73325			−0.866626	−	0.498959i	$-0.833716\pi$
$967$	−53.8983			−1.73325			−0.866626	+	0.498959i	$0.833716\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	20.5266	+	35.5531i	0.658729	+	1.14095i	0.980945	+	0.194286i	$0.0622390\pi$
$971$	20.5266	+	35.5531i	0.658729	+	1.14095i	−0.322216	+	0.946666i	$0.604428\pi$
$972$		0			0
$973$	−24.0617	+	2.38460i	−0.771383	+	0.0764469i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	25.0445	+	14.4594i	0.801244	+	0.462598i	0.843906	−	0.536491i	$-0.180251\pi$
$977$	25.0445	+	14.4594i	0.801244	+	0.462598i	−0.0426622	+	0.999090i	$0.513584\pi$
$978$		0			0
$979$		−	37.7976i		−	1.20802i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	18.1376	−	31.4152i	0.578499	−	1.00199i	−0.417153	−	0.908836i	$-0.636972\pi$
$983$	18.1376	−	31.4152i	0.578499	−	1.00199i	0.995652	−	0.0931532i	$-0.0296946\pi$
$984$		0			0
$985$	13.5235	−	7.80779i	0.430894	−	0.248777i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	12.0866	−	6.97820i	0.384331	−	0.221894i
$990$		0			0
$991$	19.6101	−	33.9656i	0.622934	−	1.07895i	−0.366002	−	0.930614i	$-0.619274\pi$
$991$	19.6101	−	33.9656i	0.622934	−	1.07895i	0.988936	−	0.148340i	$-0.0473930\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	6.11946i		−	0.194000i
$996$		0			0
$997$	−10.7505	−	6.20678i	−0.340471	−	0.196571i	0.320009	−	0.947414i	$-0.396314\pi$
$997$	−10.7505	−	6.20678i	−0.340471	−	0.196571i	−0.660480	+	0.750844i	$0.729647\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.cg.a.521.3	yes	12
3.2	odd	2		1260.2.cg.b.521.3	yes	12
5.2	odd	4		6300.2.dd.c.4049.1		24
5.3	odd	4		6300.2.dd.c.4049.12		24
5.4	even	2		6300.2.ch.c.4301.4		12
7.3	odd	6		8820.2.d.a.881.11		12
7.4	even	3		8820.2.d.b.881.11		12
7.5	odd	6		1260.2.cg.b.341.3	yes	12
15.2	even	4		6300.2.dd.b.4049.1		24
15.8	even	4		6300.2.dd.b.4049.12		24
15.14	odd	2		6300.2.ch.b.4301.4		12
21.5	even	6	inner	1260.2.cg.a.341.3	✓	12
21.11	odd	6		8820.2.d.a.881.2		12
21.17	even	6		8820.2.d.b.881.2		12
35.12	even	12		6300.2.dd.b.1349.12		24
35.19	odd	6		6300.2.ch.b.1601.4		12
35.33	even	12		6300.2.dd.b.1349.1		24
105.47	odd	12		6300.2.dd.c.1349.12		24
105.68	odd	12		6300.2.dd.c.1349.1		24
105.89	even	6		6300.2.ch.c.1601.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.cg.a.341.3	✓	12	21.5	even	6	inner
1260.2.cg.a.521.3	yes	12	1.1	even	1	trivial
1260.2.cg.b.341.3	yes	12	7.5	odd	6
1260.2.cg.b.521.3	yes	12	3.2	odd	2
6300.2.ch.b.1601.4		12	35.19	odd	6
6300.2.ch.b.4301.4		12	15.14	odd	2
6300.2.ch.c.1601.4		12	105.89	even	6
6300.2.ch.c.4301.4		12	5.4	even	2
6300.2.dd.b.1349.1		24	35.33	even	12
6300.2.dd.b.1349.12		24	35.12	even	12
6300.2.dd.b.4049.1		24	15.2	even	4
6300.2.dd.b.4049.12		24	15.8	even	4
6300.2.dd.c.1349.1		24	105.68	odd	12
6300.2.dd.c.1349.12		24	105.47	odd	12
6300.2.dd.c.4049.1		24	5.2	odd	4
6300.2.dd.c.4049.12		24	5.3	odd	4
8820.2.d.a.881.2		12	21.11	odd	6
8820.2.d.a.881.11		12	7.3	odd	6
8820.2.d.b.881.2		12	21.17	even	6
8820.2.d.b.881.11		12	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.cg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{5} +(0.260926 + 2.63285i) q^{7} +(-3.06024 - 1.76683i) q^{11} -0.599777i q^{13} +(0.849017 - 1.47054i) q^{17} +(-6.74071 + 3.89175i) q^{19} +(-2.86931 + 1.65660i) q^{23} +(-0.500000 + 0.866025i) q^{25} +0.456069i q^{29} +(-0.914390 - 0.527923i) q^{31} +(2.14966 - 1.54239i) q^{35} +(0.193124 + 0.334501i) q^{37} -0.478149 q^{41} -4.21237 q^{43} +(-4.27902 - 7.41148i) q^{47} +(-6.86384 + 1.37396i) q^{49} +(-3.45520 - 1.99486i) q^{53} +3.53366i q^{55} +(1.30307 - 2.25698i) q^{59} +(-9.60378 + 5.54474i) q^{61} +(-0.519422 + 0.299889i) q^{65} +(-1.43711 + 2.48915i) q^{67} -0.336875i q^{71} +(2.67151 + 1.54239i) q^{73} +(3.85331 - 8.51816i) q^{77} +(6.80447 + 11.7857i) q^{79} -16.2901 q^{83} -1.69803 q^{85} +(5.34822 + 9.26339i) q^{89} +(1.57913 - 0.156497i) q^{91} +(6.74071 + 3.89175i) q^{95} -2.18092i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{5} + 2 q^{7} + 12 q^{11} - 6 q^{19} - 12 q^{23} - 6 q^{25} - 6 q^{31} + 2 q^{35} - 2 q^{37} - 8 q^{41} + 36 q^{43} - 16 q^{47} + 22 q^{49} + 12 q^{53} - 6 q^{65} + 2 q^{67} + 6 q^{73} + 28 q^{77}+ \cdots + 6 q^{95}+O(q^{100}) \) 12 * q - 6 * q^5 + 2 * q^7 + 12 * q^11 - 6 * q^19 - 12 * q^23 - 6 * q^25 - 6 * q^31 + 2 * q^35 - 2 * q^37 - 8 * q^41 + 36 * q^43 - 16 * q^47 + 22 * q^49 + 12 * q^53 - 6 * q^65 + 2 * q^67 + 6 * q^73 + 28 * q^77 + 14 * q^79 + 40 * q^83 - 20 * q^89 + 10 * q^91 + 6 * q^95

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