LMFDB - Embedded newform 1260.2.bm.d.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(109,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))

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

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

chi := DirichletCharacter("1260.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.bm (of order $6$, degree $2$, 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:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 4 x^{14} + 12 x^{13} + 162 x^{12} - 524 x^{11} - 88 x^{10} + 1492 x^{9} + \cdots + 1521 $ x^16 - 4x^15 - 4x^14 + 12x^13 + 162x^12 - 524x^11 - 88x^10 + 1492x^9 + 6266x^8 - 41348x^7 + 103092x^6 - 152724x^5 + 148342x^4 - 96348x^3 + 41016x^2 - 10764*x + 1521
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.1
Root			$1.45942 + 0.551253i$ of defining polynomial
Character	$\chi$	$=$	1260.109
Dual form			1260.2.bm.d.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.19944 + 0.403048i) q^{5} +(2.42997 + 1.04655i) q^{7} +(-2.57968 + 4.46813i) q^{11} -2.80588i q^{13} +(5.24063 + 3.02568i) q^{17} +(-2.93649 - 5.08615i) q^{19} +(-2.05580 + 1.18692i) q^{23} +(4.67510 - 1.77296i) q^{25} -6.66070 q^{29} +(-4.37298 + 7.57423i) q^{31} +(-5.76638 - 1.32243i) q^{35} +(-10.0285 + 5.78996i) q^{37} -5.15936 q^{41} +0.356394i q^{43} +(6.83305 - 3.94506i) q^{47} +(4.80948 + 5.08615i) q^{49} +(3.18483 + 1.83876i) q^{53} +(3.87298 - 10.8671i) q^{55} +(-6.98836 + 12.1042i) q^{59} +(3.43649 + 5.95218i) q^{61} +(1.13091 + 6.17138i) q^{65} +(-3.66455 - 2.11573i) q^{67} -9.66339 q^{71} +(5.78587 + 3.34047i) q^{73} +(-10.9446 + 8.15766i) q^{77} +(-0.936492 - 1.62205i) q^{79} +10.7990i q^{83} +(-12.7460 - 4.54259i) q^{85} +(-4.08102 - 7.06854i) q^{89} +(2.93649 - 6.81820i) q^{91} +(8.50861 + 10.0032i) q^{95} +12.2474i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{19} - 8 q^{31} - 16 q^{49} + 24 q^{61} + 16 q^{79} - 80 q^{85} + 16 q^{91}+O(q^{100}) $ 16 * q - 16 * q^19 - 8 * q^31 - 16 * q^49 + 24 * q^61 + 16 * q^79 - 80 * q^85 + 16 * q^91

Character values

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

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.19944	+	0.403048i	−0.983621	+	0.180249i
$5$	−2.19944	+	0.403048i	−0.983621	+	0.180249i
$6$		0			0
$7$	2.42997	+	1.04655i	0.918441	+	0.395558i
$7$	2.42997	+	1.04655i	0.918441	+	0.395558i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.57968	+	4.46813i	−0.777802	+	1.34719i	0.155404	+	0.987851i	$0.450332\pi$
$11$	−2.57968	+	4.46813i	−0.777802	+	1.34719i	−0.933206	+	0.359342i	$0.883001\pi$
$12$		0			0
$13$		−	2.80588i		−	0.778212i	−0.921193	−	0.389106i	$-0.872784\pi$
$13$		−	2.80588i		−	0.778212i	0.921193	−	0.389106i	$-0.127216\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.24063	+	3.02568i	1.27104	+	0.733835i	0.975184	−	0.221397i	$-0.0710618\pi$
$17$	5.24063	+	3.02568i	1.27104	+	0.733835i	0.295856	+	0.955233i	$0.404395\pi$
$18$		0			0
$19$	−2.93649	−	5.08615i	−0.673677	−	1.16684i	−0.976854	−	0.213909i	$-0.931380\pi$
$19$	−2.93649	−	5.08615i	−0.673677	−	1.16684i	0.303176	−	0.952935i	$-0.401953\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.05580	+	1.18692i	−0.428664	+	0.247489i	−0.698777	−	0.715339i	$-0.746272\pi$
$23$	−2.05580	+	1.18692i	−0.428664	+	0.247489i	0.270113	+	0.962829i	$0.412939\pi$
$24$		0			0
$25$	4.67510	−	1.77296i	0.935021	−	0.354593i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−6.66070			−1.23686			−0.618430	−	0.785840i	$-0.712231\pi$
$29$	−6.66070			−1.23686			−0.618430	+	0.785840i	$0.712231\pi$
$30$		0			0
$31$	−4.37298	+	7.57423i	−0.785411	+	1.36037i	0.143342	+	0.989673i	$0.454215\pi$
$31$	−4.37298	+	7.57423i	−0.785411	+	1.36037i	−0.928753	+	0.370699i	$0.879118\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.76638	−	1.32243i	−0.974697	−	0.223531i
$36$		0			0
$37$	−10.0285	+	5.78996i	−1.64868	+	0.951864i	−0.671079	+	0.741386i	$0.734169\pi$
$37$	−10.0285	+	5.78996i	−1.64868	+	0.951864i	−0.977599	+	0.210478i	$0.932498\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.15936			−0.805756			−0.402878	−	0.915254i	$-0.631990\pi$
$41$	−5.15936			−0.805756			−0.402878	+	0.915254i	$0.631990\pi$
$42$		0			0
$43$			0.356394i			0.0543496i	0.999631	+	0.0271748i	$0.00865107\pi$
$43$			0.356394i			0.0543496i	−0.999631	+	0.0271748i	$0.991349\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.83305	−	3.94506i	0.996702	−	0.575446i	0.0894314	−	0.995993i	$-0.471495\pi$
$47$	6.83305	−	3.94506i	0.996702	−	0.575446i	0.907271	+	0.420547i	$0.138162\pi$
$48$		0			0
$49$	4.80948	+	5.08615i	0.687068	+	0.726593i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.18483	+	1.83876i	0.437470	+	0.252574i	0.702524	−	0.711660i	$-0.252056\pi$
$53$	3.18483	+	1.83876i	0.437470	+	0.252574i	−0.265054	+	0.964234i	$0.585390\pi$
$54$		0			0
$55$	3.87298	−	10.8671i	0.522233	−	1.46532i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.98836	+	12.1042i	−0.909807	+	1.57583i	−0.0954760	+	0.995432i	$0.530437\pi$
$59$	−6.98836	+	12.1042i	−0.909807	+	1.57583i	−0.814331	+	0.580401i	$0.802896\pi$
$60$		0			0
$61$	3.43649	+	5.95218i	0.439998	+	0.762098i	0.997689	−	0.0679503i	$-0.0216459\pi$
$61$	3.43649	+	5.95218i	0.439998	+	0.762098i	−0.557691	+	0.830049i	$0.688313\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.13091	+	6.17138i	0.140272	+	0.765466i
$66$		0			0
$67$	−3.66455	−	2.11573i	−0.447696	−	0.258478i	0.259161	−	0.965834i	$-0.416554\pi$
$67$	−3.66455	−	2.11573i	−0.447696	−	0.258478i	−0.706857	+	0.707357i	$0.749887\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−9.66339			−1.14683			−0.573417	−	0.819264i	$-0.694382\pi$
$71$	−9.66339			−1.14683			−0.573417	+	0.819264i	$0.694382\pi$
$72$		0			0
$73$	5.78587	+	3.34047i	0.677185	+	0.390973i	0.798794	−	0.601605i	$-0.205472\pi$
$73$	5.78587	+	3.34047i	0.677185	+	0.390973i	−0.121609	+	0.992578i	$0.538805\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−10.9446	+	8.15766i	−1.24726	+	0.929651i
$78$		0			0
$79$	−0.936492	−	1.62205i	−0.105364	−	0.182495i	0.808523	−	0.588464i	$-0.200267\pi$
$79$	−0.936492	−	1.62205i	−0.105364	−	0.182495i	−0.913887	+	0.405969i	$0.866934\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			10.7990i			1.18535i	0.805443	+	0.592674i	$0.201928\pi$
$83$			10.7990i			1.18535i	−0.805443	+	0.592674i	$0.798072\pi$
$84$		0			0
$85$	−12.7460	−	4.54259i	−1.38249	−	0.492713i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.08102	−	7.06854i	−0.432587	−	0.749263i	0.564508	−	0.825428i	$-0.309066\pi$
$89$	−4.08102	−	7.06854i	−0.432587	−	0.749263i	−0.997095	+	0.0761643i	$0.975733\pi$
$90$		0			0
$91$	2.93649	−	6.81820i	0.307828	−	0.714742i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8.50861	+	10.0032i	0.872965	+	1.02630i
$96$		0			0
$97$			12.2474i			1.24354i	0.783200	+	0.621770i	$0.213586\pi$
$97$			12.2474i			1.24354i	−0.783200	+	0.621770i	$0.786414\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.83169	−	8.36874i	0.480771	−	0.832721i	−0.518985	−	0.854783i	$-0.673690\pi$
$101$	4.83169	−	8.36874i	0.480771	−	0.832721i	0.999757	+	0.0220627i	$0.00702333\pi$
$102$		0			0
$103$	−0.308646	+	0.178197i	−0.0304118	+	0.0175583i	−0.515129	−	0.857113i	$-0.672256\pi$
$103$	−0.308646	+	0.178197i	−0.0304118	+	0.0175583i	0.484717	+	0.874671i	$0.338923\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.70402	+	3.29321i	−0.551428	+	0.318367i	−0.749698	−	0.661780i	$-0.769801\pi$
$107$	−5.70402	+	3.29321i	−0.551428	+	0.318367i	0.198270	+	0.980147i	$0.436468\pi$
$108$		0			0
$109$	−0.936492	+	1.62205i	−0.0896996	+	0.155364i	−0.907384	−	0.420302i	$-0.861924\pi$
$109$	−0.936492	+	1.62205i	−0.0896996	+	0.155364i	0.817685	+	0.575667i	$0.195257\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	16.8504i		−	1.58515i	−0.609774	−	0.792575i	$-0.708740\pi$
$113$		−	16.8504i		−	1.58515i	0.609774	−	0.792575i	$-0.291260\pi$
$114$		0			0
$115$	4.04323	−	3.43914i	0.377033	−	0.320702i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	9.56804	+	12.8369i	0.877101	+	1.17675i
$120$		0			0
$121$	−7.80948	−	13.5264i	−0.709952	−	1.22967i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.56804	+	5.78382i	−0.855791	+	0.517321i
$126$		0			0
$127$			17.5028i			1.55312i	0.630041	+	0.776562i	$0.283038\pi$
$127$			17.5028i			1.55312i	−0.630041	+	0.776562i	$0.716962\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.40868	+	7.63606i	0.385188	+	0.667166i	0.991795	−	0.127836i	$-0.0408031\pi$
$131$	4.40868	+	7.63606i	0.385188	+	0.667166i	−0.606607	+	0.795002i	$0.707470\pi$
$132$		0			0
$133$	−1.81267	−	15.4324i	−0.157179	−	1.33816i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−12.0737	−	6.97074i	−1.03152	−	0.595551i	−0.114103	−	0.993469i	$-0.536399\pi$
$137$	−12.0737	−	6.97074i	−1.03152	−	0.595551i	−0.917421	+	0.397918i	$0.869733\pi$
$138$		0			0
$139$	5.87298			0.498140			0.249070	−	0.968485i	$-0.419875\pi$
$139$	5.87298			0.498140			0.249070	+	0.968485i	$0.419875\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	12.5371	+	7.23828i	1.04840	+	0.605295i
$144$		0			0
$145$	14.6498	−	2.68458i	1.21660	−	0.222942i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−8.06670	−	13.9719i	−0.660849	−	1.14462i	−0.980393	−	0.197053i	$-0.936863\pi$
$149$	−8.06670	−	13.9719i	−0.660849	−	1.14462i	0.319543	−	0.947572i	$-0.396470\pi$
$150$		0			0
$151$	0.436492	−	0.756026i	0.0355212	−	0.0615245i	−0.847718	−	0.530447i	$-0.822024\pi$
$151$	0.436492	−	0.756026i	0.0355212	−	0.0615245i	0.883239	+	0.468922i	$0.155358\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	6.56535	−	18.4216i	0.527342	−	1.47966i
$156$		0			0
$157$	2.39076	+	1.38031i	0.190804	+	0.110161i	0.592359	−	0.805674i	$-0.298197\pi$
$157$	2.39076	+	1.38031i	0.190804	+	0.110161i	−0.401555	+	0.915835i	$0.631530\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−6.23769	+	0.732675i	−0.491599	+	0.0577428i
$162$		0			0
$163$	18.8224	−	10.8671i	1.47429	−	0.851180i	0.474707	−	0.880144i	$-0.342554\pi$
$163$	18.8224	−	10.8671i	1.47429	−	0.851180i	0.999580	+	0.0289638i	$0.00922076\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	1.83876i		−	0.142288i	−0.997466	−	0.0711439i	$-0.977335\pi$
$167$		−	1.83876i		−	0.142288i	0.997466	−	0.0711439i	$-0.0226649\pi$
$168$		0			0
$169$	5.12702			0.394386
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.75981	−	4.48013i	0.589968	−	0.340618i	−0.175117	−	0.984548i	$-0.556030\pi$
$173$	7.75981	−	4.48013i	0.589968	−	0.340618i	0.765085	+	0.643930i	$0.222697\pi$
$174$		0			0
$175$	13.2158	+	0.584480i	0.999023	+	0.0441825i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	6.66070	−	11.5367i	0.497844	−	0.862291i	−0.502153	−	0.864779i	$-0.667459\pi$
$179$	6.66070	−	11.5367i	0.497844	−	0.862291i	0.999997	+	0.00248769i	$0.000791858\pi$
$180$		0			0
$181$	−0.127017			−0.00944107			−0.00472054	−	0.999989i	$-0.501503\pi$
$181$	−0.127017			−0.00944107			−0.00472054	+	0.999989i	$0.501503\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	19.7235	−	16.7767i	1.45010	−	1.23345i
$186$		0			0
$187$	−27.0383	+	15.6106i	−1.97723	+	1.14156i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.16204	+	14.1371i	0.590585	+	1.02292i	0.994154	+	0.107974i	$0.0344362\pi$
$191$	8.16204	+	14.1371i	0.590585	+	1.02292i	−0.403569	+	0.914949i	$0.632230\pi$
$192$		0			0
$193$	−13.0366	−	7.52667i	−0.938393	−	0.541781i	−0.0489366	−	0.998802i	$-0.515583\pi$
$193$	−13.0366	−	7.52667i	−0.938393	−	0.541781i	−0.889456	+	0.457021i	$0.848917\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	11.3341i		−	0.807521i	−0.914865	−	0.403760i	$-0.867703\pi$
$197$		−	11.3341i		−	0.807521i	0.914865	−	0.403760i	$-0.132297\pi$
$198$		0			0
$199$	−6.43649	+	11.1483i	−0.456271	+	0.790284i	−0.998760	−	0.0497784i	$-0.984148\pi$
$199$	−6.43649	+	11.1483i	−0.456271	+	0.790284i	0.542489	+	0.840063i	$0.317482\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−16.1853	−	6.97074i	−1.13598	−	0.489250i
$204$		0			0
$205$	11.3477	−	2.07947i	0.792559	−	0.145236i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	30.3008			2.09595
$210$		0			0
$211$	8.61895			0.593353			0.296676	−	0.954978i	$-0.404122\pi$
$211$	8.61895			0.593353			0.296676	+	0.954978i	$0.404122\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.143644	−	0.783868i	−0.00979643	−	0.0534594i
$216$		0			0
$217$	−18.5530	+	13.8286i	−1.25946	+	0.938746i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	8.48971	−	14.7046i	0.571079	−	0.989138i
$222$		0			0
$223$			12.6491i			0.847047i	0.905885	+	0.423524i	$0.139207\pi$
$223$			12.6491i			0.847047i	−0.905885	+	0.423524i	$0.860793\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	17.1120	+	9.87964i	1.13577	+	0.655735i	0.945379	−	0.325974i	$-0.105692\pi$
$227$	17.1120	+	9.87964i	1.13577	+	0.655735i	0.190388	+	0.981709i	$0.439026\pi$
$228$		0			0
$229$	−4.62702	−	8.01423i	−0.305762	−	0.529595i	0.671669	−	0.740852i	$-0.265578\pi$
$229$	−4.62702	−	8.01423i	−0.305762	−	0.529595i	−0.977431	+	0.211256i	$0.932244\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−24.6107	+	14.2090i	−1.61230	+	0.930864i	−0.623468	+	0.781849i	$0.714277\pi$
$233$	−24.6107	+	14.2090i	−1.61230	+	0.930864i	−0.988835	+	0.149015i	$0.952390\pi$
$234$		0			0
$235$	−13.4389	+	11.4310i	−0.876654	+	0.745675i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−10.5094			−0.679797			−0.339899	−	0.940462i	$-0.610393\pi$
$239$	−10.5094			−0.679797			−0.339899	+	0.940462i	$0.610393\pi$
$240$		0			0
$241$	7.30948	−	12.6604i	0.470845	−	0.815527i	−0.528599	−	0.848872i	$-0.677283\pi$
$241$	7.30948	−	12.6604i	0.470845	−	0.815527i	0.999444	+	0.0333446i	$0.0106159\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−12.6281	−	9.24826i	−0.806782	−	0.590849i
$246$		0			0
$247$	−14.2712	+	8.23945i	−0.908052	+	0.524264i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	11.1647			0.704712			0.352356	−	0.935866i	$-0.385381\pi$
$251$	11.1647			0.704712			0.352356	+	0.935866i	$0.385381\pi$
$252$		0			0
$253$		−	12.2474i		−	0.769991i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	17.1120	−	9.87964i	1.06742	−	0.616275i	0.139945	−	0.990159i	$-0.455308\pi$
$257$	17.1120	−	9.87964i	1.06742	−	0.616275i	0.927475	+	0.373884i	$0.121974\pi$
$258$		0			0
$259$	−30.4284	+	3.57410i	−1.89073	+	0.222084i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.57498	+	2.64137i	0.282106	+	0.162874i	0.634376	−	0.773024i	$-0.281257\pi$
$263$	4.57498	+	2.64137i	0.282106	+	0.162874i	−0.352271	+	0.935898i	$0.614590\pi$
$264$		0			0
$265$	−7.74597	−	2.76062i	−0.475831	−	0.169583i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	5.25470	−	9.10141i	0.320385	−	0.554923i	−0.660183	−	0.751105i	$-0.729521\pi$
$269$	5.25470	−	9.10141i	0.320385	−	0.554923i	0.980567	+	0.196182i	$0.0628544\pi$
$270$		0			0
$271$	−4.30948	−	7.46423i	−0.261782	−	0.453420i	0.704934	−	0.709273i	$-0.250977\pi$
$271$	−4.30948	−	7.46423i	−0.261782	−	0.453420i	−0.966716	+	0.255854i	$0.917643\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.13843	+	25.4627i	−0.249557	+	1.53546i
$276$		0			0
$277$	16.6619	+	9.61976i	1.00112	+	0.577995i	0.908579	−	0.417714i	$-0.137168\pi$
$277$	16.6619	+	9.61976i	1.00112	+	0.577995i	0.0925388	+	0.995709i	$0.470502\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	26.4521			1.57800			0.789000	−	0.614393i	$-0.210599\pi$
$281$	26.4521			1.57800			0.789000	+	0.614393i	$0.210599\pi$
$282$		0			0
$283$	−0.308646	−	0.178197i	−0.0183471	−	0.0105927i	0.490798	−	0.871273i	$-0.336705\pi$
$283$	−0.308646	−	0.178197i	−0.0183471	−	0.0105927i	−0.509146	+	0.860680i	$0.670038\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−12.5371	−	5.39951i	−0.740039	−	0.318723i
$288$		0			0
$289$	9.80948	+	16.9905i	0.577028	+	0.999442i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	8.96026i		−	0.523464i	−0.965141	−	0.261732i	$-0.915706\pi$
$293$		−	8.96026i		−	0.523464i	0.965141	−	0.261732i	$-0.0842937\pi$
$294$		0			0
$295$	10.4919	−	29.4391i	0.610864	−	1.71401i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.33035	+	5.76833i	0.192599	+	0.333591i
$300$		0			0
$301$	−0.372983	+	0.866025i	−0.0214984	+	0.0499169i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−9.95738	−	11.7064i	−0.570158	−	0.670307i
$306$		0			0
$307$			4.85371i			0.277016i	0.990361	+	0.138508i	$0.0442307\pi$
$307$			4.85371i			0.277016i	−0.990361	+	0.138508i	$0.955769\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	9.99105	−	17.3050i	0.566540	−	0.981277i	−0.430364	−	0.902655i	$-0.641615\pi$
$311$	9.99105	−	17.3050i	0.566540	−	0.981277i	0.996905	−	0.0786214i	$-0.0250518\pi$
$312$		0			0
$313$	16.7403	−	9.66503i	0.946219	−	0.546300i	0.0543146	−	0.998524i	$-0.482703\pi$
$313$	16.7403	−	9.66503i	0.946219	−	0.546300i	0.891904	+	0.452224i	$0.149369\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.42546	+	4.86444i	−0.473221	+	0.273214i	−0.717587	−	0.696469i	$-0.754753\pi$
$317$	−8.42546	+	4.86444i	−0.473221	+	0.273214i	0.244366	+	0.969683i	$0.421420\pi$
$318$		0			0
$319$	17.1825	−	29.7609i	0.962033	−	1.66629i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	35.5395i		−	1.97747i
$324$		0			0
$325$	−4.97473	−	13.1178i	−0.275948	−	0.727645i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	20.7328	−	2.43526i	1.14303	−	0.134260i
$330$		0			0
$331$	12.1190	+	20.9906i	0.666118	+	1.15375i	0.978981	+	0.203952i	$0.0653785\pi$
$331$	12.1190	+	20.9906i	0.666118	+	1.15375i	−0.312863	+	0.949798i	$0.601288\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	8.91272	+	3.17644i	0.486954	+	0.173547i
$336$		0			0
$337$			22.4018i			1.22030i	0.792284	+	0.610152i	$0.208892\pi$
$337$			22.4018i			1.22030i	−0.792284	+	0.610152i	$0.791108\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−22.5618	−	39.0781i	−1.22179	−	2.11620i
$342$		0			0
$343$	6.36396	+	17.3925i	0.343622	+	0.939108i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	25.0741	+	14.4766i	1.34605	+	0.777142i	0.987687	−	0.156441i	$-0.0500020\pi$
$347$	25.0741	+	14.4766i	1.34605	+	0.777142i	0.358362	+	0.933583i	$0.383335\pi$
$348$		0			0
$349$	−1.74597			−0.0934595			−0.0467297	−	0.998908i	$-0.514880\pi$
$349$	−1.74597			−0.0934595			−0.0467297	+	0.998908i	$0.514880\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	13.9272	+	8.04088i	0.741271	+	0.427973i	0.822531	−	0.568720i	$-0.192561\pi$
$353$	13.9272	+	8.04088i	0.741271	+	0.427973i	−0.0812604	+	0.996693i	$0.525895\pi$
$354$		0			0
$355$	21.2541	−	3.89481i	1.12805	−	0.206715i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.17368	+	2.03288i	0.0619446	+	0.107291i	0.895335	−	0.445394i	$-0.146936\pi$
$359$	1.17368	+	2.03288i	0.0619446	+	0.107291i	−0.833390	+	0.552685i	$0.813603\pi$
$360$		0			0
$361$	−7.74597	+	13.4164i	−0.407682	+	0.706127i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−14.0721	−	5.01520i	−0.736566	−	0.262508i
$366$		0			0
$367$	−14.6190	−	8.44029i	−0.763106	−	0.440579i	0.0673040	−	0.997733i	$-0.478560\pi$
$367$	−14.6190	−	8.44029i	−0.763106	−	0.440579i	−0.830410	+	0.557153i	$0.811894\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	5.81468	+	7.80121i	0.301883	+	0.405019i
$372$		0			0
$373$	0.0392032	−	0.0226340i	0.00202987	−	0.00117194i	−0.498985	−	0.866611i	$-0.666294\pi$
$373$	0.0392032	−	0.0226340i	0.00202987	−	0.00117194i	0.501015	+	0.865439i	$0.332960\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			18.6891i			0.962540i
$378$		0			0
$379$	17.0000			0.873231			0.436616	−	0.899648i	$-0.356177\pi$
$379$	17.0000			0.873231			0.436616	+	0.899648i	$0.356177\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	3.18483	−	1.83876i	0.162737	−	0.0939564i	−0.416420	−	0.909173i	$-0.636715\pi$
$383$	3.18483	−	1.83876i	0.162737	−	0.0939564i	0.579157	+	0.815216i	$0.303382\pi$
$384$		0			0
$385$	20.7842	−	22.3535i	1.05926	−	1.13924i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	0.327662	−	0.567527i	0.0166131	−	0.0287748i	−0.857599	−	0.514318i	$-0.828045\pi$
$389$	0.327662	−	0.567527i	0.0166131	−	0.0287748i	0.874212	+	0.485544i	$0.161378\pi$
$390$		0			0
$391$	−14.3649			−0.726465
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.71353	+	3.19016i	0.136532	+	0.160514i
$396$		0			0
$397$	−10.0285	+	5.78996i	−0.503317	+	0.290590i	−0.730082	−	0.683359i	$-0.760518\pi$
$397$	−10.0285	+	5.78996i	−0.503317	+	0.290590i	0.226766	+	0.973949i	$0.427185\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.50403	+	7.80121i	0.224921	+	0.389574i	0.956296	−	0.292402i	$-0.0944544\pi$
$401$	4.50403	+	7.80121i	0.224921	+	0.389574i	−0.731375	+	0.681976i	$0.761121\pi$
$402$		0			0
$403$	21.2524	+	12.2701i	1.05866	+	0.611216i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	59.7450i		−	2.96145i
$408$		0			0
$409$	−0.754033	+	1.30602i	−0.0372845	+	0.0645787i	−0.884066	−	0.467363i	$-0.845204\pi$
$409$	−0.754033	+	1.30602i	−0.0372845	+	0.0645787i	0.846781	+	0.531942i	$0.178537\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−29.6491	+	22.0991i	−1.45894	+	1.08743i
$414$		0			0
$415$	−4.35253	−	23.7518i	−0.213657	−	1.16593i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	3.00269			0.146691			0.0733454	−	0.997307i	$-0.476632\pi$
$419$	3.00269			0.146691			0.0733454	+	0.997307i	$0.476632\pi$
$420$		0			0
$421$	−33.3649			−1.62611			−0.813053	−	0.582189i	$-0.802196\pi$
$421$	−33.3649			−1.62611			−0.813053	+	0.582189i	$0.802196\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	29.8649	+	4.85392i	1.44866	+	0.235450i
$426$		0			0
$427$	2.12132	+	18.0600i	0.102658	+	0.873987i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−6.56535	+	11.3715i	−0.316242	+	0.547747i	−0.979701	−	0.200466i	$-0.935754\pi$
$431$	−6.56535	+	11.3715i	−0.316242	+	0.547747i	0.663459	+	0.748213i	$0.269088\pi$
$432$		0			0
$433$		−	34.3381i		−	1.65018i	−0.564998	−	0.825092i	$-0.691123\pi$
$433$		−	34.3381i		−	1.65018i	0.564998	−	0.825092i	$-0.308877\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	12.0737	+	6.97074i	0.577562	+	0.333456i
$438$		0			0
$439$	−3.69052	−	6.39218i	−0.176139	−	0.305082i	0.764416	−	0.644724i	$-0.223028\pi$
$439$	−3.69052	−	6.39218i	−0.176139	−	0.305082i	−0.940555	+	0.339642i	$0.889694\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	17.3143	−	9.99642i	0.822628	−	0.474944i	−0.0286941	−	0.999588i	$-0.509135\pi$
$443$	17.3143	−	9.99642i	0.822628	−	0.474944i	0.851322	+	0.524644i	$0.175802\pi$
$444$		0			0
$445$	11.8249	+	13.9020i	0.560556	+	0.659018i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−16.3241			−0.770381			−0.385191	−	0.922837i	$-0.625864\pi$
$449$	−16.3241			−0.770381			−0.385191	+	0.922837i	$0.625864\pi$
$450$		0			0
$451$	13.3095	−	23.0527i	0.626719	−	1.08551i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.71058	+	16.1798i	−0.173955	+	0.758521i
$456$		0			0
$457$	−17.0098	+	9.82059i	−0.795683	+	0.459388i	−0.841960	−	0.539541i	$-0.818598\pi$
$457$	−17.0098	+	9.82059i	−0.795683	+	0.459388i	0.0462762	+	0.998929i	$0.485265\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	8.16204			0.380144			0.190072	−	0.981770i	$-0.439128\pi$
$461$	8.16204			0.380144			0.190072	+	0.981770i	$0.439128\pi$
$462$		0			0
$463$		−	9.84323i		−	0.457454i	−0.973491	−	0.228727i	$-0.926544\pi$
$463$		−	9.84323i		−	0.457454i	0.973491	−	0.228727i	$-0.0734562\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−17.7777	+	10.2640i	−0.822653	+	0.474959i	−0.851331	−	0.524630i	$-0.824204\pi$
$467$	−17.7777	+	10.2640i	−0.822653	+	0.474959i	0.0286772	+	0.999589i	$0.490871\pi$
$468$		0			0
$469$	−6.69052	−	8.97628i	−0.308940	−	0.414486i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.59242	−	0.919382i	−0.0732193	−	0.0422732i
$474$		0			0
$475$	−22.7460	−	18.5720i	−1.04366	−	0.852142i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.25202	−	3.90061i	0.102897	−	0.178223i	−0.809980	−	0.586458i	$-0.800522\pi$
$479$	2.25202	−	3.90061i	0.102897	−	0.178223i	0.912877	+	0.408234i	$0.133855\pi$
$480$		0			0
$481$	16.2460	+	28.1388i	0.740752	+	1.28302i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.93631	−	26.9376i	−0.224146	−	1.22317i
$486$		0			0
$487$	−12.7671	−	7.37110i	−0.578534	−	0.334017i	0.182017	−	0.983295i	$-0.441737\pi$
$487$	−12.7671	−	7.37110i	−0.578534	−	0.334017i	−0.760550	+	0.649279i	$0.775071\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−34.1495			−1.54115			−0.770573	−	0.637352i	$-0.780030\pi$
$491$	−34.1495			−1.54115			−0.770573	+	0.637352i	$0.780030\pi$
$492$		0			0
$493$	−34.9063	−	20.1531i	−1.57210	−	0.907652i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−23.4817	−	10.1132i	−1.05330	−	0.453639i
$498$		0			0
$499$	7.37298	+	12.7704i	0.330060	+	0.571681i	0.982523	−	0.186140i	$-0.0595977\pi$
$499$	7.37298	+	12.7704i	0.330060	+	0.571681i	−0.652463	+	0.757820i	$0.726264\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			24.2054i			1.07927i	0.841900	+	0.539634i	$0.181437\pi$
$503$			24.2054i			1.07927i	−0.841900	+	0.539634i	$0.818563\pi$
$504$		0			0
$505$	−7.25403	+	20.3540i	−0.322800	+	0.905740i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−6.00538	−	10.4016i	−0.266184	−	0.461043i	0.701689	−	0.712483i	$-0.252429\pi$
$509$	−6.00538	−	10.4016i	−0.266184	−	0.461043i	−0.967873	+	0.251439i	$0.919096\pi$
$510$		0			0
$511$	10.5635	+	14.1724i	0.467302	+	0.626952i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.607028	−	0.516333i	0.0267489	−	0.0227524i
$516$		0			0
$517$			40.7079i			1.79033i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−10.9740	+	19.0076i	−0.480781	+	0.832737i	−0.999757	−	0.0220516i	$-0.992980\pi$
$521$	−10.9740	+	19.0076i	−0.480781	+	0.832737i	0.518976	+	0.854789i	$0.326314\pi$
$522$		0			0
$523$	2.35156	−	1.35767i	0.102827	−	0.0593669i	−0.447705	−	0.894181i	$-0.647758\pi$
$523$	2.35156	−	1.35767i	0.102827	−	0.0593669i	0.550531	+	0.834814i	$0.314425\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−45.8344	+	26.4625i	−1.99658	+	1.15272i
$528$		0			0
$529$	−8.68246	+	15.0385i	−0.377498	+	0.653846i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			14.4766i			0.627049i
$534$		0			0
$535$	11.2183	−	9.54223i	0.485011	−	0.412547i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−35.1325	+	8.36874i	−1.51326	+	0.360467i
$540$		0			0
$541$	8.24597	+	14.2824i	0.354522	+	0.614050i	0.987036	−	0.160499i	$-0.0513103\pi$
$541$	8.24597	+	14.2824i	0.354522	+	0.614050i	−0.632514	+	0.774549i	$0.717977\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.40600	−	3.94506i	0.0602263	−	0.168988i
$546$		0			0
$547$		−	12.6491i		−	0.540837i	−0.962743	−	0.270418i	$-0.912838\pi$
$547$		−	12.6491i		−	0.540837i	0.962743	−	0.270418i	$-0.0871621\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	19.5591	+	33.8773i	0.833245	+	1.44322i
$552$		0			0
$553$	−0.578089	−	4.92161i	−0.0245829	−	0.209288i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.09111	+	5.24875i	0.385203	+	0.222397i	0.680079	−	0.733138i	$-0.261945\pi$
$557$	9.09111	+	5.24875i	0.385203	+	0.222397i	−0.294877	+	0.955535i	$0.595279\pi$
$558$		0			0
$559$	1.00000			0.0422955
$560$		0			0
$561$		0			0
$562$		0			0
$563$	20.9625	+	12.1027i	0.883465	+	0.510069i	0.871799	−	0.489863i	$-0.162953\pi$
$563$	20.9625	+	12.1027i	0.883465	+	0.510069i	0.0116657	+	0.999932i	$0.496287\pi$
$564$		0			0
$565$	6.79152	+	37.0615i	0.285721	+	1.55919i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	18.0577	+	31.2769i	0.757020	+	1.31120i	0.944364	+	0.328903i	$0.106679\pi$
$569$	18.0577	+	31.2769i	0.757020	+	1.31120i	−0.187344	+	0.982294i	$0.559988\pi$
$570$		0			0
$571$	−5.06351	+	8.77025i	−0.211901	+	0.367024i	−0.952310	−	0.305134i	$-0.901299\pi$
$571$	−5.06351	+	8.77025i	−0.211901	+	0.367024i	0.740408	+	0.672157i	$0.234632\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−7.50672	+	9.19382i	−0.313052	+	0.383409i
$576$		0			0
$577$	0.578089	+	0.333760i	0.0240662	+	0.0138946i	0.511985	−	0.858994i	$-0.328910\pi$
$577$	0.578089	+	0.333760i	0.0240662	+	0.0138946i	−0.487919	+	0.872889i	$0.662244\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−11.3017	+	26.2413i	−0.468873	+	1.08867i
$582$		0			0
$583$	−16.4317	+	9.48683i	−0.680531	+	0.392904i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			35.5395i			1.46687i	0.679758	+	0.733437i	$0.262085\pi$
$587$			35.5395i			1.46687i	−0.679758	+	0.733437i	$0.737915\pi$
$588$		0			0
$589$	51.3649			2.11645
$590$		0			0
$591$		0			0
$592$		0			0
$593$	33.0362	−	19.0735i	1.35663	−	0.783253i	0.367466	−	0.930037i	$-0.380226\pi$
$593$	33.0362	−	19.0735i	1.35663	−	0.783253i	0.989169	+	0.146784i	$0.0468922\pi$
$594$		0			0
$595$	−26.2182	−	24.3776i	−1.07484	−	0.999384i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−3.56266	+	6.17071i	−0.145567	+	0.252129i	−0.929584	−	0.368610i	$-0.879834\pi$
$599$	−3.56266	+	6.17071i	−0.145567	+	0.252129i	0.784018	+	0.620739i	$0.213167\pi$
$600$		0			0
$601$	7.61895			0.310783			0.155392	−	0.987853i	$-0.450336\pi$
$601$	7.61895			0.310783			0.155392	+	0.987853i	$0.450336\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	22.6283	+	26.6030i	0.919971	+	1.08156i
$606$		0			0
$607$	18.2444	−	10.5334i	0.740515	−	0.427537i	−0.0817413	−	0.996654i	$-0.526048\pi$
$607$	18.2444	−	10.5334i	0.740515	−	0.427537i	0.822257	+	0.569117i	$0.192715\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−11.0694	−	19.1727i	−0.447819	−	0.775646i
$612$		0			0
$613$	5.82508	+	3.36311i	0.235273	+	0.135835i	0.613002	−	0.790081i	$-0.289962\pi$
$613$	5.82508	+	3.36311i	0.235273	+	0.135835i	−0.377729	+	0.925916i	$0.623295\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	15.7802i		−	0.635289i	−0.948210	−	0.317644i	$-0.897108\pi$
$617$		−	15.7802i		−	0.635289i	0.948210	−	0.317644i	$-0.102892\pi$
$618$		0			0
$619$	−15.3730	+	26.6268i	−0.617892	+	1.07022i	0.371977	+	0.928242i	$0.378680\pi$
$619$	−15.3730	+	26.6268i	−0.617892	+	1.07022i	−0.989870	+	0.141979i	$0.954653\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−2.51918	−	21.4473i	−0.100929	−	0.859268i
$624$		0			0
$625$	18.7132	−	16.5776i	0.748528	−	0.663103i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−70.0743			−2.79405
$630$		0			0
$631$	−33.4919			−1.33329			−0.666646	−	0.745374i	$-0.732271\pi$
$631$	−33.4919			−1.33329			−0.666646	+	0.745374i	$0.732271\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−7.05448	−	38.4965i	−0.279948	−	1.52769i
$636$		0			0
$637$	14.2712	−	13.4948i	0.565444	−	0.534685i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.42570	+	5.93348i	−0.135307	+	0.234358i	−0.925715	−	0.378223i	$-0.876535\pi$
$641$	−3.42570	+	5.93348i	−0.135307	+	0.234358i	0.790408	+	0.612581i	$0.209869\pi$
$642$		0			0
$643$			11.8911i			0.468937i	0.972124	+	0.234469i	$0.0753350\pi$
$643$			11.8911i			0.468937i	−0.972124	+	0.234469i	$0.924665\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.59242	+	0.919382i	0.0626043	+	0.0361446i	0.530975	−	0.847387i	$-0.321826\pi$
$647$	1.59242	+	0.919382i	0.0626043	+	0.0361446i	−0.468371	+	0.883532i	$0.655159\pi$
$648$		0			0
$649$	−36.0554	−	62.4499i	−1.41530	−	2.45137i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−31.2415	+	18.0373i	−1.22258	+	0.705854i	−0.965466	−	0.260528i	$-0.916103\pi$
$653$	−31.2415	+	18.0373i	−1.22258	+	0.705854i	−0.257109	+	0.966382i	$0.582770\pi$
$654$		0			0
$655$	−12.7744	−	15.0182i	−0.499135	−	0.586809i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	11.6294			0.453016			0.226508	−	0.974009i	$-0.427269\pi$
$659$	11.6294			0.453016			0.226508	+	0.974009i	$0.427269\pi$
$660$		0			0
$661$	5.06351	−	8.77025i	0.196948	−	0.341123i	−0.750590	−	0.660769i	$-0.770230\pi$
$661$	5.06351	−	8.77025i	0.196948	−	0.341123i	0.947537	+	0.319645i	$0.103564\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	10.2069	+	33.2120i	0.395805	+	1.28791i
$666$		0			0
$667$	13.6931	−	7.90569i	0.530198	−	0.306110i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−35.4602			−1.36892
$672$		0			0
$673$			2.80588i			0.108159i	0.998537	+	0.0540794i	$0.0172224\pi$
$673$			2.80588i			0.108159i	−0.998537	+	0.0540794i	$0.982778\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1.12903	−	0.651847i	0.0433922	−	0.0250525i	−0.478147	−	0.878280i	$-0.658691\pi$
$677$	1.12903	−	0.651847i	0.0433922	−	0.0250525i	0.521539	+	0.853227i	$0.325358\pi$
$678$		0			0
$679$	−12.8175	+	29.7609i	−0.491892	+	1.14212i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	12.0737	+	6.97074i	0.461986	+	0.266728i	0.712879	−	0.701287i	$-0.247391\pi$
$683$	12.0737	+	6.97074i	0.461986	+	0.266728i	−0.250893	+	0.968015i	$0.580724\pi$
$684$		0			0
$685$	29.3649	+	10.4655i	1.12198	+	0.399865i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	5.15936	−	8.93627i	0.196556	−	0.340445i
$690$		0			0
$691$	−8.24597	−	14.2824i	−0.313691	−	0.543329i	0.665467	−	0.746427i	$-0.268232\pi$
$691$	−8.24597	−	14.2824i	−0.313691	−	0.543329i	−0.979158	+	0.203098i	$0.934899\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−12.9173	+	2.36709i	−0.489981	+	0.0897890i
$696$		0			0
$697$	−27.0383	−	15.6106i	−1.02415	−	0.591292i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−39.1182			−1.47747			−0.738737	−	0.673994i	$-0.764577\pi$
$701$	−39.1182			−1.47747			−0.738737	+	0.673994i	$0.764577\pi$
$702$		0			0
$703$	58.8973	+	34.0044i	2.22135	+	1.28250i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	20.4991	−	15.2792i	0.770949	−	0.574632i
$708$		0			0
$709$	−16.8014	−	29.1009i	−0.630990	−	1.09291i	−0.987350	−	0.158558i	$-0.949315\pi$
$709$	−16.8014	−	29.1009i	−0.630990	−	1.09291i	0.356360	−	0.934349i	$-0.384018\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	20.7615i		−	0.777523i
$714$		0			0
$715$	−30.4919	−	10.8671i	−1.14033	−	0.406408i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−4.40868	−	7.63606i	−0.164416	−	0.284777i	0.772032	−	0.635584i	$-0.219241\pi$
$719$	−4.40868	−	7.63606i	−0.164416	−	0.284777i	−0.936448	+	0.350807i	$0.885907\pi$
$720$		0			0
$721$	−0.936492	+	0.110000i	−0.0348768	+	0.00409660i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−31.1395	+	11.8092i	−1.15649	+	0.438582i
$726$		0			0
$727$			7.39374i			0.274219i	0.990556	+	0.137109i	$0.0437811\pi$
$727$			7.39374i			0.274219i	−0.990556	+	0.137109i	$0.956219\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.07833	+	1.86773i	−0.0398836	+	0.0690805i
$732$		0			0
$733$	−21.1740	+	12.2248i	−0.782080	+	0.451534i	−0.837167	−	0.546948i	$-0.815790\pi$
$733$	−21.1740	+	12.2248i	−0.782080	+	0.451534i	0.0550872	+	0.998482i	$0.482456\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	18.9067	−	10.9158i	0.696438	−	0.402089i
$738$		0			0
$739$	4.31754	−	7.47820i	0.158823	−	0.275090i	−0.775621	−	0.631199i	$-0.782563\pi$
$739$	4.31754	−	7.47820i	0.158823	−	0.275090i	0.934445	+	0.356108i	$0.115897\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	19.7593i		−	0.724898i	−0.932004	−	0.362449i	$-0.881941\pi$
$743$		−	19.7593i		−	0.724898i	0.932004	−	0.362449i	$-0.118059\pi$
$744$		0			0
$745$	23.3736	+	27.4792i	0.856342	+	1.00676i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−17.3071	+	2.03288i	−0.632387	+	0.0742797i
$750$		0			0
$751$	−15.9919	−	27.6988i	−0.583554	−	1.01075i	−0.995054	−	0.0993353i	$-0.968328\pi$
$751$	−15.9919	−	27.6988i	−0.583554	−	1.01075i	0.411500	−	0.911410i	$-0.365005\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−0.655324	+	1.83876i	−0.0238497	+	0.0669194i
$756$		0			0
$757$		−	2.76062i		−	0.100336i	−0.998741	−	0.0501681i	$-0.984024\pi$
$757$		−	2.76062i		−	0.100336i	0.998741	−	0.0501681i	$-0.0159757\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	3.98567	+	6.90339i	0.144481	+	0.250248i	0.929179	−	0.369630i	$-0.120516\pi$
$761$	3.98567	+	6.90339i	0.144481	+	0.250248i	−0.784698	+	0.619878i	$0.787182\pi$
$762$		0			0
$763$	−3.97320	+	2.96145i	−0.143839	+	0.107212i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	33.9630	+	19.6085i	1.22633	+	0.708023i
$768$		0			0
$769$	−3.61895			−0.130503			−0.0652513	−	0.997869i	$-0.520785\pi$
$769$	−3.61895			−0.130503			−0.0652513	+	0.997869i	$0.520785\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	25.2764	+	14.5933i	0.909128	+	0.524886i	0.880151	−	0.474695i	$-0.157441\pi$
$773$	25.2764	+	14.5933i	0.909128	+	0.524886i	0.0289778	+	0.999580i	$0.490775\pi$
$774$		0			0
$775$	−7.01532	+	43.1635i	−0.251998	+	1.55048i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	15.1504	+	26.2413i	0.542820	+	0.940191i
$780$		0			0
$781$	24.9284	−	43.1773i	0.892009	−	1.54501i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−5.81468	−	2.07232i	−0.207535	−	0.0739642i
$786$		0			0
$787$	14.0409	+	8.10653i	0.500505	+	0.288966i	0.728922	−	0.684597i	$-0.240022\pi$
$787$	14.0409	+	8.10653i	0.500505	+	0.288966i	−0.228417	+	0.973563i	$0.573355\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	17.6347	−	40.9459i	0.627019	−	1.45587i
$792$		0			0
$793$	16.7011	−	9.64240i	0.593074	−	0.342412i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	15.0116i		−	0.531739i	−0.964009	−	0.265869i	$-0.914341\pi$
$797$		−	15.0116i		−	0.531739i	0.964009	−	0.265869i	$-0.0856590\pi$
$798$		0			0
$799$	47.7460			1.68913
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−29.8514	+	17.2347i	−1.05343	+	0.608199i
$804$		0			0
$805$	13.4241	−	4.12557i	0.473139	−	0.145407i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−20.7328	+	35.9102i	−0.728925	+	1.26254i	0.228412	+	0.973564i	$0.426647\pi$
$809$	−20.7328	+	35.9102i	−0.728925	+	1.26254i	−0.957338	+	0.288971i	$0.906687\pi$
$810$		0			0
$811$	45.6028			1.60133			0.800666	−	0.599111i	$-0.204479\pi$
$811$	45.6028			1.60133			0.800666	+	0.599111i	$0.204479\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−37.0189	+	31.4880i	−1.29672	+	1.10298i
$816$		0			0
$817$	1.81267	−	1.04655i	0.0634174	−	0.0366141i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.92435	−	3.33308i	−0.0671604	−	0.116325i	0.830490	−	0.557034i	$-0.188061\pi$
$821$	−1.92435	−	3.33308i	−0.0671604	−	0.116325i	−0.897650	+	0.440708i	$0.854727\pi$
$822$		0			0
$823$	−3.43431	−	1.98280i	−0.119713	−	0.0691161i	0.438948	−	0.898512i	$-0.355351\pi$
$823$	−3.43431	−	1.98280i	−0.119713	−	0.0691161i	−0.558661	+	0.829396i	$0.688685\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			15.2452i			0.530127i	0.964231	+	0.265063i	$0.0853929\pi$
$827$			15.2452i			0.530127i	−0.964231	+	0.265063i	$0.914607\pi$
$828$		0			0
$829$	−25.6825	+	44.4833i	−0.891989	+	1.54497i	−0.0545008	+	0.998514i	$0.517357\pi$
$829$	−25.6825	+	44.4833i	−0.891989	+	1.54497i	−0.837488	+	0.546456i	$0.815977\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	9.81561	+	41.2066i	0.340091	+	1.42772i
$834$		0			0
$835$	0.741110	+	4.04426i	0.0256472	+	0.139957i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	2.34736			0.0810400			0.0405200	−	0.999179i	$-0.487099\pi$
$839$	2.34736			0.0810400			0.0405200	+	0.999179i	$0.487099\pi$
$840$		0			0
$841$	15.3649			0.529825
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−11.2766	+	2.06643i	−0.387926	+	0.0710875i
$846$		0			0
$847$	−4.82073	−	41.0417i	−0.165642	−	1.41021i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	13.7444	−	23.8060i	0.471152	−	0.816060i
$852$		0			0
$853$		−	25.6546i		−	0.878397i	−0.898390	−	0.439199i	$-0.855262\pi$
$853$		−	25.6546i		−	0.878397i	0.898390	−	0.439199i	$-0.144738\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	21.2236	+	12.2535i	0.724986	+	0.418571i	0.816585	−	0.577225i	$-0.195865\pi$
$857$	21.2236	+	12.2535i	0.724986	+	0.418571i	−0.0915991	+	0.995796i	$0.529198\pi$
$858$		0			0
$859$	−21.4365	−	37.1291i	−0.731404	−	1.26683i	−0.956283	−	0.292442i	$-0.905532\pi$
$859$	−21.4365	−	37.1291i	−0.731404	−	1.26683i	0.224880	−	0.974387i	$-0.427801\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−21.4259	+	12.3703i	−0.729346	+	0.421088i	−0.818183	−	0.574958i	$-0.805018\pi$
$863$	−21.4259	+	12.3703i	−0.729346	+	0.421088i	0.0888366	+	0.996046i	$0.471685\pi$
$864$		0			0
$865$	−15.2616	+	12.9814i	−0.518909	+	0.441380i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	9.66339			0.327808
$870$		0			0
$871$	−5.93649	+	10.2823i	−0.201150	+	0.348403i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−29.3031	+	4.04109i	−0.990624	+	0.136614i
$876$		0			0
$877$	29.0812	−	16.7900i	0.982002	−	0.566959i	0.0791281	−	0.996864i	$-0.474786\pi$
$877$	29.0812	−	16.7900i	0.982002	−	0.566959i	0.902874	+	0.429905i	$0.141453\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	36.7708			1.23884			0.619420	−	0.785060i	$-0.287368\pi$
$881$	36.7708			1.23884			0.619420	+	0.785060i	$0.287368\pi$
$882$		0			0
$883$			37.5909i			1.26504i	0.774546	+	0.632518i	$0.217979\pi$
$883$			37.5909i			1.26504i	−0.774546	+	0.632518i	$0.782021\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−4.77725	+	2.75814i	−0.160404	+	0.0926094i	−0.578053	−	0.815999i	$-0.696187\pi$
$887$	−4.77725	+	2.75814i	−0.160404	+	0.0926094i	0.417649	+	0.908608i	$0.362854\pi$
$888$		0			0
$889$	−18.3175	+	42.5313i	−0.614351	+	1.42645i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−40.1304	−	23.1693i	−1.34291	−	0.775330i
$894$		0			0
$895$	−10.0000	+	28.0588i	−0.334263	+	0.937903i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	29.1271	−	50.4497i	0.971444	−	1.68259i
$900$		0			0
$901$	11.1270	+	19.2726i	0.370695	+	0.642062i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.279366	−	0.0511938i	0.00928644	−	0.00170174i
$906$		0			0
$907$	−0.230240	−	0.132929i	−0.00764499	−	0.00441384i	0.496173	−	0.868224i	$-0.334738\pi$
$907$	−0.230240	−	0.132929i	−0.00764499	−	0.00441384i	−0.503818	+	0.863810i	$0.668072\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−18.4808			−0.612295			−0.306147	−	0.951984i	$-0.599040\pi$
$911$	−18.4808			−0.612295			−0.306147	+	0.951984i	$0.599040\pi$
$912$		0			0
$913$	−48.2515	−	27.8580i	−1.59689	−	0.921965i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.72145	+	23.1693i	0.0898701	+	0.765117i
$918$		0			0
$919$	19.2460	+	33.3350i	0.634866	+	1.09962i	0.986544	+	0.163499i	$0.0522780\pi$
$919$	19.2460	+	33.3350i	0.634866	+	1.09962i	−0.351678	+	0.936121i	$0.614389\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			27.1143i			0.892479i
$924$		0			0
$925$	−36.6190	+	44.8489i	−1.20402	+	1.47462i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	18.0577	+	31.2769i	0.592455	+	1.02616i	0.993901	+	0.110280i	$0.0351747\pi$
$929$	18.0577	+	31.2769i	0.592455	+	1.02616i	−0.401445	+	0.915883i	$0.631492\pi$
$930$		0			0
$931$	11.7460	−	39.3972i	0.384959	−	1.29119i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	53.1774	−	45.2323i	1.73909	−	1.47925i
$936$		0			0
$937$		−	52.2879i		−	1.70817i	−0.520133	−	0.854085i	$-0.674118\pi$
$937$		−	52.2879i		−	1.70817i	0.520133	−	0.854085i	$-0.325882\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−8.48971	+	14.7046i	−0.276756	+	0.479356i	−0.970577	−	0.240792i	$-0.922593\pi$
$941$	−8.48971	+	14.7046i	−0.276756	+	0.479356i	0.693820	+	0.720148i	$0.255926\pi$
$942$		0			0
$943$	10.6066	−	6.12372i	0.345398	−	0.199416i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	39.0013	−	22.5174i	1.26737	−	0.731718i	0.292883	−	0.956148i	$-0.405385\pi$
$947$	39.0013	−	22.5174i	1.26737	−	0.731718i	0.974490	+	0.224430i	$0.0720520\pi$
$948$		0			0
$949$	9.37298	−	16.2345i	0.304260	−	0.526994i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	7.35505i		−	0.238254i	−0.992879	−	0.119127i	$-0.961991\pi$
$953$		−	7.35505i		−	0.238254i	0.992879	−	0.119127i	$-0.0380095\pi$
$954$		0			0
$955$	−23.6499	−	27.8040i	−0.765292	−	0.899716i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−22.0434	−	29.5743i	−0.711819	−	0.955006i
$960$		0			0
$961$	−22.7460	−	39.3972i	−0.733741	−	1.27088i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	31.7068	+	11.3001i	1.02068	+	0.363764i
$966$		0			0
$967$		−	10.7766i		−	0.346552i	−0.984873	−	0.173276i	$-0.944565\pi$
$967$		−	10.7766i		−	0.346552i	0.984873	−	0.173276i	$-0.0554353\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−3.56266	−	6.17071i	−0.114331	−	0.198028i	0.803181	−	0.595735i	$-0.203139\pi$
$971$	−3.56266	−	6.17071i	−0.114331	−	0.198028i	−0.917512	+	0.397708i	$0.869806\pi$
$972$		0			0
$973$	14.2712	+	6.14636i	0.457512	+	0.197043i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−25.2764	−	14.5933i	−0.808663	−	0.466882i	0.0378282	−	0.999284i	$-0.487956\pi$
$977$	−25.2764	−	14.5933i	−0.808663	−	0.466882i	−0.846491	+	0.532402i	$0.821289\pi$
$978$		0			0
$979$	42.1109			1.34587
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−47.6291	−	27.4987i	−1.51913	−	0.877071i	−0.999746	−	0.0225304i	$-0.992828\pi$
$983$	−47.6291	−	27.4987i	−1.51913	−	0.877071i	−0.519385	−	0.854540i	$-0.673839\pi$
$984$		0			0
$985$	4.56819	+	24.9287i	0.145554	+	0.794295i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.423010	−	0.732675i	−0.0134509	−	0.0232977i
$990$		0			0
$991$	−22.8095	+	39.5072i	−0.724567	+	1.25499i	0.234585	+	0.972096i	$0.424627\pi$
$991$	−22.8095	+	39.5072i	−0.724567	+	1.25499i	−0.959152	+	0.282891i	$0.908707\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	9.66339	−	27.1143i	0.306350	−	0.859582i
$996$		0			0
$997$	44.7437	+	25.8328i	1.41705	+	0.818133i	0.996039	−	0.0889226i	$-0.0283424\pi$
$997$	44.7437	+	25.8328i	1.41705	+	0.818133i	0.421010	+	0.907056i	$0.361676\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.bm.d.109.1	✓	16
3.2	odd	2	inner	1260.2.bm.d.109.8	yes	16
5.4	even	2	inner	1260.2.bm.d.109.6	yes	16
7.2	even	3	inner	1260.2.bm.d.289.6	yes	16
15.14	odd	2	inner	1260.2.bm.d.109.3	yes	16
21.2	odd	6	inner	1260.2.bm.d.289.3	yes	16
35.9	even	6	inner	1260.2.bm.d.289.1	yes	16
105.44	odd	6	inner	1260.2.bm.d.289.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.bm.d.109.1	✓	16	1.1	even	1	trivial
1260.2.bm.d.109.3	yes	16	15.14	odd	2	inner
1260.2.bm.d.109.6	yes	16	5.4	even	2	inner
1260.2.bm.d.109.8	yes	16	3.2	odd	2	inner
1260.2.bm.d.289.1	yes	16	35.9	even	6	inner
1260.2.bm.d.289.3	yes	16	21.2	odd	6	inner
1260.2.bm.d.289.6	yes	16	7.2	even	3	inner
1260.2.bm.d.289.8	yes	16	105.44	odd	6	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:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.19944 + 0.403048i) q^{5} +(2.42997 + 1.04655i) q^{7} +(-2.57968 + 4.46813i) q^{11} -2.80588i q^{13} +(5.24063 + 3.02568i) q^{17} +(-2.93649 - 5.08615i) q^{19} +(-2.05580 + 1.18692i) q^{23} +(4.67510 - 1.77296i) q^{25} -6.66070 q^{29} +(-4.37298 + 7.57423i) q^{31} +(-5.76638 - 1.32243i) q^{35} +(-10.0285 + 5.78996i) q^{37} -5.15936 q^{41} +0.356394i q^{43} +(6.83305 - 3.94506i) q^{47} +(4.80948 + 5.08615i) q^{49} +(3.18483 + 1.83876i) q^{53} +(3.87298 - 10.8671i) q^{55} +(-6.98836 + 12.1042i) q^{59} +(3.43649 + 5.95218i) q^{61} +(1.13091 + 6.17138i) q^{65} +(-3.66455 - 2.11573i) q^{67} -9.66339 q^{71} +(5.78587 + 3.34047i) q^{73} +(-10.9446 + 8.15766i) q^{77} +(-0.936492 - 1.62205i) q^{79} +10.7990i q^{83} +(-12.7460 - 4.54259i) q^{85} +(-4.08102 - 7.06854i) q^{89} +(2.93649 - 6.81820i) q^{91} +(8.50861 + 10.0032i) q^{95} +12.2474i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{19} - 8 q^{31} - 16 q^{49} + 24 q^{61} + 16 q^{79} - 80 q^{85} + 16 q^{91}+O(q^{100}) \) 16 * q - 16 * q^19 - 8 * q^31 - 16 * q^49 + 24 * q^61 + 16 * q^79 - 80 * q^85 + 16 * q^91

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