LMFDB - Embedded newform 1260.2.bm.d.109.2

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			109.2
Root			$1.51479 - 1.11371i$ of defining polynomial
Character	$\chi$	$=$	1260.109
Dual form			1260.2.bm.d.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70325 - 1.44877i) q^{5} +(0.308646 - 2.62769i) q^{7} +(0.919382 - 1.59242i) q^{11} -0.356394i q^{13} +(-3.16793 - 1.82901i) q^{17} +(0.936492 + 1.62205i) q^{19} +(-5.76833 + 3.33035i) q^{23} +(0.802121 + 4.93524i) q^{25} -2.37383 q^{29} +(3.37298 - 5.84218i) q^{31} +(-4.33262 + 4.02845i) q^{35} +(-3.66455 + 2.11573i) q^{37} +1.83876 q^{41} +2.80588i q^{43} +(-7.63606 + 4.40868i) q^{47} +(-6.80948 - 1.62205i) q^{49} +(-8.93627 - 5.15936i) q^{53} +(-3.87298 + 1.38031i) q^{55} +(4.86444 - 8.42546i) q^{59} +(-0.436492 - 0.756026i) q^{61} +(-0.516333 + 0.607028i) q^{65} +(-10.0285 - 5.78996i) q^{67} -10.7990 q^{71} +(7.90719 + 4.56522i) q^{73} +(-3.90061 - 2.90734i) q^{77} +(2.93649 + 5.08615i) q^{79} +9.66339i q^{83} +(2.74597 + 7.70486i) q^{85} +(-3.29321 - 5.70402i) q^{89} +(-0.936492 - 0.110000i) q^{91} +(0.754902 - 4.11952i) q^{95} -12.2474i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.70325	−	1.44877i	−0.761717	−	0.647910i
$5$	−1.70325	−	1.44877i	−0.761717	−	0.647910i
$6$		0			0
$7$	0.308646	−	2.62769i	0.116657	−	0.993172i
$7$	0.308646	−	2.62769i	0.116657	−	0.993172i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.919382	−	1.59242i	0.277204	−	0.480131i	−0.693485	−	0.720471i	$-0.743926\pi$
$11$	0.919382	−	1.59242i	0.277204	−	0.480131i	0.970689	+	0.240340i	$0.0772589\pi$
$12$		0			0
$13$		−	0.356394i		−	0.0988459i	−0.998778	−	0.0494229i	$-0.984262\pi$
$13$		−	0.356394i		−	0.0988459i	0.998778	−	0.0494229i	$-0.0157382\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.16793	−	1.82901i	−0.768336	−	0.443599i	0.0639446	−	0.997953i	$-0.479632\pi$
$17$	−3.16793	−	1.82901i	−0.768336	−	0.443599i	−0.832281	+	0.554354i	$0.812965\pi$
$18$		0			0
$19$	0.936492	+	1.62205i	0.214846	+	0.372124i	0.953225	−	0.302262i	$-0.0977417\pi$
$19$	0.936492	+	1.62205i	0.214846	+	0.372124i	−0.738379	+	0.674386i	$0.764408\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.76833	+	3.33035i	−1.20278	+	0.694426i	−0.961173	−	0.275948i	$-0.911008\pi$
$23$	−5.76833	+	3.33035i	−1.20278	+	0.694426i	−0.241608	+	0.970374i	$0.577675\pi$
$24$		0			0
$25$	0.802121	+	4.93524i	0.160424	+	0.987048i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.37383			−0.440810			−0.220405	−	0.975408i	$-0.570738\pi$
$29$	−2.37383			−0.440810			−0.220405	+	0.975408i	$0.570738\pi$
$30$		0			0
$31$	3.37298	−	5.84218i	0.605806	−	1.04929i	−0.386118	−	0.922449i	$-0.626184\pi$
$31$	3.37298	−	5.84218i	0.605806	−	1.04929i	0.991924	−	0.126837i	$-0.0404825\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.33262	+	4.02845i	−0.732346	+	0.680932i
$36$		0			0
$37$	−3.66455	+	2.11573i	−0.602449	+	0.347824i	−0.770004	−	0.638039i	$-0.779746\pi$
$37$	−3.66455	+	2.11573i	−0.602449	+	0.347824i	0.167556	+	0.985863i	$0.446413\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.83876			0.287167			0.143583	−	0.989638i	$-0.454138\pi$
$41$	1.83876			0.287167			0.143583	+	0.989638i	$0.454138\pi$
$42$		0			0
$43$			2.80588i			0.427893i	0.976845	+	0.213947i	$0.0686319\pi$
$43$			2.80588i			0.427893i	−0.976845	+	0.213947i	$0.931368\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.63606	+	4.40868i	−1.11383	+	0.643073i	−0.939820	−	0.341670i	$-0.889007\pi$
$47$	−7.63606	+	4.40868i	−1.11383	+	0.643073i	−0.174015	+	0.984743i	$0.555674\pi$
$48$		0			0
$49$	−6.80948	−	1.62205i	−0.972782	−	0.231722i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−8.93627	−	5.15936i	−1.22749	−	0.708692i	−0.260986	−	0.965343i	$-0.584048\pi$
$53$	−8.93627	−	5.15936i	−1.22749	−	0.708692i	−0.966504	+	0.256651i	$0.917381\pi$
$54$		0			0
$55$	−3.87298	+	1.38031i	−0.522233	+	0.186121i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.86444	−	8.42546i	0.633297	−	1.09690i	−0.353577	−	0.935405i	$-0.615035\pi$
$59$	4.86444	−	8.42546i	0.633297	−	1.09690i	0.986873	−	0.161496i	$-0.0516320\pi$
$60$		0			0
$61$	−0.436492	−	0.756026i	−0.0558870	−	0.0967992i	0.836728	−	0.547618i	$-0.184465\pi$
$61$	−0.436492	−	0.756026i	−0.0558870	−	0.0967992i	−0.892615	+	0.450819i	$0.851132\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.516333	+	0.607028i	−0.0640433	+	0.0752926i
$66$		0			0
$67$	−10.0285	−	5.78996i	−1.22518	−	0.707357i	−0.259161	−	0.965834i	$-0.583446\pi$
$67$	−10.0285	−	5.78996i	−1.22518	−	0.707357i	−0.966017	+	0.258478i	$0.916779\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−10.7990			−1.28161			−0.640804	−	0.767704i	$-0.721399\pi$
$71$	−10.7990			−1.28161			−0.640804	+	0.767704i	$0.721399\pi$
$72$		0			0
$73$	7.90719	+	4.56522i	0.925467	+	0.534319i	0.885375	−	0.464877i	$-0.153902\pi$
$73$	7.90719	+	4.56522i	0.925467	+	0.534319i	0.0400918	+	0.999196i	$0.487235\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.90061	−	2.90734i	−0.444515	−	0.331322i
$78$		0			0
$79$	2.93649	+	5.08615i	0.330381	+	0.572237i	0.982587	−	0.185805i	$-0.0594894\pi$
$79$	2.93649	+	5.08615i	0.330381	+	0.572237i	−0.652205	+	0.758042i	$0.726156\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			9.66339i			1.06069i	0.847781	+	0.530347i	$0.177938\pi$
$83$			9.66339i			1.06069i	−0.847781	+	0.530347i	$0.822062\pi$
$84$		0			0
$85$	2.74597	+	7.70486i	0.297842	+	0.835710i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.29321	−	5.70402i	−0.349080	−	0.604624i	0.637006	−	0.770859i	$-0.280173\pi$
$89$	−3.29321	−	5.70402i	−0.349080	−	0.604624i	−0.986086	+	0.166234i	$0.946839\pi$
$90$		0			0
$91$	−0.936492	−	0.110000i	−0.0981710	−	0.0115311i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.754902	−	4.11952i	0.0774513	−	0.422654i
$96$		0			0
$97$		−	12.2474i		−	1.24354i	−0.783200	−	0.621770i	$-0.786414\pi$
$97$		−	12.2474i		−	1.24354i	0.783200	−	0.621770i	$-0.213586\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.39951	−	9.35223i	0.537272	−	0.930582i	−0.461778	−	0.886995i	$-0.652788\pi$
$101$	5.39951	−	9.35223i	0.537272	−	0.930582i	0.999050	−	0.0435862i	$-0.0138783\pi$
$102$		0			0
$103$	−2.42997	+	1.40294i	−0.239432	+	0.138236i	−0.614916	−	0.788593i	$-0.710810\pi$
$103$	−2.42997	+	1.40294i	−0.239432	+	0.138236i	0.375484	+	0.926829i	$0.377477\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.06854	+	4.08102i	−0.683341	+	0.394527i	−0.801113	−	0.598513i	$-0.795758\pi$
$107$	−7.06854	+	4.08102i	−0.683341	+	0.394527i	0.117771	+	0.993041i	$0.462425\pi$
$108$		0			0
$109$	2.93649	−	5.08615i	0.281265	−	0.487165i	−0.690432	−	0.723398i	$-0.742579\pi$
$109$	2.93649	−	5.08615i	0.281265	−	0.487165i	0.971697	+	0.236233i	$0.0759127\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	6.00538i		−	0.564938i	−0.959276	−	0.282469i	$-0.908847\pi$
$113$		−	6.00538i		−	0.564938i	0.959276	−	0.282469i	$-0.0911535\pi$
$114$		0			0
$115$	14.6498	+	2.68458i	1.36610	+	0.250339i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−5.78382	+	7.75981i	−0.530202	+	0.711341i
$120$		0			0
$121$	3.80948	+	6.59820i	0.346316	+	0.599837i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	5.78382	−	9.56804i	0.517321	−	0.855791i
$126$		0			0
$127$		−	14.3405i		−	1.27252i	−0.771476	−	0.636259i	$-0.780481\pi$
$127$		−	14.3405i		−	1.27252i	0.771476	−	0.636259i	$-0.219519\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.94506	−	6.83305i	−0.344682	−	0.597006i	0.640614	−	0.767863i	$-0.278680\pi$
$131$	−3.94506	−	6.83305i	−0.344682	−	0.597006i	−0.985296	+	0.170857i	$0.945346\pi$
$132$		0			0
$133$	4.55129	−	1.96017i	0.394647	−	0.169968i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	10.8040	+	6.23769i	0.923048	+	0.532922i	0.884606	−	0.466339i	$-0.154427\pi$
$137$	10.8040	+	6.23769i	0.923048	+	0.532922i	0.0384415	+	0.999261i	$0.487761\pi$
$138$		0			0
$139$	−1.87298			−0.158864			−0.0794322	−	0.996840i	$-0.525311\pi$
$139$	−1.87298			−0.158864			−0.0794322	+	0.996840i	$0.525311\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.567527	−	0.327662i	−0.0474590	−	0.0274005i
$144$		0			0
$145$	4.04323	+	3.43914i	0.335772	+	0.285605i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	9.99642	+	17.3143i	0.818939	+	1.41844i	0.906465	+	0.422281i	$0.138771\pi$
$149$	9.99642	+	17.3143i	0.818939	+	1.41844i	−0.0875262	+	0.996162i	$0.527896\pi$
$150$		0			0
$151$	−3.43649	+	5.95218i	−0.279658	+	0.484381i	−0.971300	−	0.237859i	$-0.923554\pi$
$151$	−3.43649	+	5.95218i	−0.279658	+	0.484381i	0.691642	+	0.722241i	$0.256888\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−14.2090	+	5.06401i	−1.14130	+	0.406751i
$156$		0			0
$157$	−18.8224	−	10.8671i	−1.50219	−	0.867292i	−0.999997	−	0.00253929i	$-0.999192\pi$
$157$	−18.8224	−	10.8671i	−1.50219	−	0.867292i	−0.502197	−	0.864753i	$-0.667475\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.97074	+	16.1853i	0.549371	+	1.27558i
$162$		0			0
$163$	−2.39076	+	1.38031i	−0.187259	+	0.108114i	−0.590699	−	0.806892i	$-0.701148\pi$
$163$	−2.39076	+	1.38031i	−0.187259	+	0.108114i	0.403440	+	0.915006i	$0.367815\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			5.15936i			0.399243i	0.979873	+	0.199621i	$0.0639712\pi$
$167$			5.15936i			0.399243i	−0.979873	+	0.199621i	$0.936029\pi$
$168$		0			0
$169$	12.8730			0.990229
$170$		0			0
$171$		0			0
$172$		0			0
$173$	12.8369	−	7.41137i	0.975969	−	0.563476i	0.0749185	−	0.997190i	$-0.476130\pi$
$173$	12.8369	−	7.41137i	0.975969	−	0.563476i	0.901051	+	0.433714i	$0.142797\pi$
$174$		0			0
$175$	13.2158	−	0.584480i	0.999023	−	0.0441825i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	2.37383	−	4.11160i	0.177429	−	0.307315i	−0.763570	−	0.645725i	$-0.776555\pi$
$179$	2.37383	−	4.11160i	0.177429	−	0.307315i	0.940999	+	0.338409i	$0.109889\pi$
$180$		0			0
$181$	−7.87298			−0.585194			−0.292597	−	0.956236i	$-0.594519\pi$
$181$	−7.87298			−0.585194			−0.292597	+	0.956236i	$0.594519\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	9.30686	+	1.70548i	0.684254	+	0.125390i
$186$		0			0
$187$	−5.82508	+	3.36311i	−0.425972	+	0.245935i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.58643	+	11.4080i	0.476577	+	0.825456i	0.999640	−	0.0268382i	$-0.00854390\pi$
$191$	6.58643	+	11.4080i	0.476577	+	0.825456i	−0.523062	+	0.852294i	$0.675211\pi$
$192$		0			0
$193$	10.2980	+	5.94553i	0.741263	+	0.427968i	0.822528	−	0.568724i	$-0.192563\pi$
$193$	10.2980	+	5.94553i	0.741263	+	0.427968i	−0.0812653	+	0.996693i	$0.525896\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	21.4834i		−	1.53063i	−0.643655	−	0.765316i	$-0.722583\pi$
$197$		−	21.4834i		−	1.53063i	0.643655	−	0.765316i	$-0.277417\pi$
$198$		0			0
$199$	−2.56351	+	4.44013i	−0.181722	+	0.314752i	−0.942467	−	0.334299i	$-0.891501\pi$
$199$	−2.56351	+	4.44013i	−0.181722	+	0.314752i	0.760745	+	0.649051i	$0.224834\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.732675	+	6.23769i	−0.0514237	+	0.437800i
$204$		0			0
$205$	−3.13187	−	2.66395i	−0.218740	−	0.186058i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.44397			0.238225
$210$		0			0
$211$	−14.6190			−1.00641			−0.503205	−	0.864167i	$-0.667846\pi$
$211$	−14.6190			−1.00641			−0.503205	+	0.864167i	$0.667846\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	4.06508	−	4.77912i	0.277236	−	0.325933i
$216$		0			0
$217$	−14.3104	−	10.6663i	−0.971450	−	0.724076i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.651847	+	1.12903i	−0.0438480	+	0.0759469i
$222$		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
$227$	21.2056	+	12.2431i	1.40747	+	0.812601i	0.995143	−	0.0984372i	$-0.0313844\pi$
$227$	21.2056	+	12.2431i	1.40747	+	0.812601i	0.412323	+	0.911038i	$0.364718\pi$
$228$		0			0
$229$	−12.3730	−	21.4306i	−0.817630	−	1.41618i	−0.907424	−	0.420216i	$-0.861954\pi$
$229$	−12.3730	−	21.4306i	−0.817630	−	1.41618i	0.0897944	−	0.995960i	$-0.471379\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	11.3715	−	6.56535i	0.744973	−	0.430110i	−0.0789015	−	0.996882i	$-0.525141\pi$
$233$	11.3715	−	6.56535i	0.744973	−	0.430110i	0.823875	+	0.566772i	$0.191808\pi$
$234$		0			0
$235$	19.3933	+	3.55382i	1.26508	+	0.231826i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−29.4882			−1.90743			−0.953716	−	0.300710i	$-0.902776\pi$
$239$	−29.4882			−1.90743			−0.953716	+	0.300710i	$0.902776\pi$
$240$		0			0
$241$	−4.30948	+	7.46423i	−0.277598	+	0.480813i	−0.970787	−	0.239942i	$-0.922872\pi$
$241$	−4.30948	+	7.46423i	−0.277598	+	0.480813i	0.693190	+	0.720755i	$0.256205\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	9.24826	+	12.6281i	0.590849	+	0.806782i
$246$		0			0
$247$	0.578089	−	0.333760i	0.0367829	−	0.0212366i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	15.0116			0.947525			0.473763	−	0.880653i	$-0.342895\pi$
$251$	15.0116			0.947525			0.473763	+	0.880653i	$0.342895\pi$
$252$		0			0
$253$			12.2474i			0.769991i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	21.2056	−	12.2431i	1.32277	−	0.763701i	0.338600	−	0.940930i	$-0.390047\pi$
$257$	21.2056	−	12.2431i	1.32277	−	0.763701i	0.984170	+	0.177229i	$0.0567133\pi$
$258$		0			0
$259$	4.42843	+	10.2823i	0.275169	+	0.638911i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	21.7731	+	12.5707i	1.34259	+	0.775144i	0.987187	−	0.159569i	$-0.0510105\pi$
$263$	21.7731	+	12.5707i	1.34259	+	0.775144i	0.355402	+	0.934713i	$0.384344\pi$
$264$		0			0
$265$	7.74597	+	21.7343i	0.475831	+	1.33513i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	14.7441	−	25.5375i	0.898963	−	1.55705i	0.0701407	−	0.997537i	$-0.477655\pi$
$269$	14.7441	−	25.5375i	0.898963	−	1.55705i	0.828822	−	0.559512i	$-0.189011\pi$
$270$		0			0
$271$	7.30948	+	12.6604i	0.444019	+	0.769063i	0.997983	−	0.0634770i	$-0.0202189\pi$
$271$	7.30948	+	12.6604i	0.444019	+	0.769063i	−0.553964	+	0.832540i	$0.686886\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.59641	+	3.26006i	0.518383	+	0.196589i
$276$		0			0
$277$	−19.4005	−	11.2009i	−1.16566	−	0.672997i	−0.213010	−	0.977050i	$-0.568327\pi$
$277$	−19.4005	−	11.2009i	−1.16566	−	0.672997i	−0.952655	+	0.304053i	$0.901660\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−23.6704			−1.41206			−0.706028	−	0.708184i	$-0.749515\pi$
$281$	−23.6704			−1.41206			−0.706028	+	0.708184i	$0.749515\pi$
$282$		0			0
$283$	−2.42997	−	1.40294i	−0.144447	−	0.0833962i	0.426035	−	0.904707i	$-0.359910\pi$
$283$	−2.42997	−	1.40294i	−0.144447	−	0.0833962i	−0.570481	+	0.821310i	$0.693243\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.567527	−	4.83169i	0.0335001	−	0.285206i
$288$		0			0
$289$	−1.80948	−	3.13410i	−0.106440	−	0.184359i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	14.8227i		−	0.865954i	−0.901405	−	0.432977i	$-0.857463\pi$
$293$		−	14.8227i		−	0.865954i	0.901405	−	0.432977i	$-0.142537\pi$
$294$		0			0
$295$	−20.4919	+	7.30320i	−1.19309	+	0.425209i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.18692	+	2.05580i	0.0686412	+	0.118890i
$300$		0			0
$301$	7.37298	+	0.866025i	0.424972	+	0.0499169i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.351854	+	1.92008i	−0.0201471	+	0.109943i
$306$		0			0
$307$		−	26.9897i		−	1.54038i	−0.637814	−	0.770190i	$-0.720161\pi$
$307$		−	26.9897i		−	1.54038i	0.637814	−	0.770190i	$-0.279839\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.56075	−	6.16740i	0.201912	−	0.349721i	−0.747233	−	0.664562i	$-0.768618\pi$
$311$	3.56075	−	6.16740i	0.201912	−	0.349721i	0.949144	+	0.314841i	$0.101951\pi$
$312$		0			0
$313$	18.8616	−	10.8898i	1.06612	−	0.615526i	0.139003	−	0.990292i	$-0.455610\pi$
$313$	18.8616	−	10.8898i	1.06612	−	0.615526i	0.927120	+	0.374765i	$0.122277\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.1042	−	6.98836i	0.679839	−	0.392505i	−0.119955	−	0.992779i	$-0.538275\pi$
$317$	12.1042	−	6.98836i	0.679839	−	0.392505i	0.799795	+	0.600274i	$0.204942\pi$
$318$		0			0
$319$	−2.18246	+	3.78013i	−0.122194	+	0.211647i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	6.85140i		−	0.381222i
$324$		0			0
$325$	1.75889	−	0.285871i	0.0975657	−	0.0158573i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	9.22780	+	21.4259i	0.508745	+	1.18125i
$330$		0			0
$331$	−11.1190	−	19.2586i	−0.611153	−	1.05855i	−0.991046	−	0.133517i	$-0.957373\pi$
$331$	−11.1190	−	19.2586i	−0.611153	−	1.05855i	0.379894	−	0.925030i	$-0.375961\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	8.69273	+	24.3908i	0.474934	+	1.33261i
$336$		0			0
$337$		−	19.2395i		−	1.04804i	−0.851705	−	0.524022i	$-0.824431\pi$
$337$		−	19.2395i		−	1.04804i	0.851705	−	0.524022i	$-0.175569\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−6.20212	−	10.7424i	−0.335863	−	0.581733i
$342$		0			0
$343$	−6.36396	+	17.3925i	−0.343622	+	0.939108i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.13505	−	0.655324i	−0.0609329	−	0.0351796i	0.469224	−	0.883079i	$-0.344534\pi$
$347$	−1.13505	−	0.655324i	−0.0609329	−	0.0351796i	−0.530157	+	0.847900i	$0.677867\pi$
$348$		0			0
$349$	13.7460			0.735805			0.367902	−	0.929864i	$-0.380076\pi$
$349$	13.7460			0.735805			0.367902	+	0.929864i	$0.380076\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	30.1419	+	17.4024i	1.60429	+	0.926237i	0.990615	+	0.136678i	$0.0436427\pi$
$353$	30.1419	+	17.4024i	1.60429	+	0.926237i	0.613675	+	0.789559i	$0.289691\pi$
$354$		0			0
$355$	18.3934	+	15.6453i	0.976222	+	0.830367i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	11.4509	+	19.8335i	0.604354	+	1.04677i	0.992153	+	0.125028i	$0.0399020\pi$
$359$	11.4509	+	19.8335i	0.604354	+	1.04677i	−0.387799	+	0.921744i	$0.626765\pi$
$360$		0			0
$361$	7.74597	−	13.4164i	0.407682	−	0.706127i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−6.85396	−	19.2314i	−0.358753	−	1.00662i
$366$		0			0
$367$	−20.9830	−	12.1145i	−1.09530	−	0.632373i	−0.160319	−	0.987065i	$-0.551252\pi$
$367$	−20.9830	−	12.1145i	−1.09530	−	0.632373i	−0.934983	+	0.354693i	$0.884586\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−16.3153	+	21.8893i	−0.847049	+	1.13644i
$372$		0			0
$373$	19.1311	−	11.0453i	0.990570	−	0.571906i	0.0851254	−	0.996370i	$-0.472871\pi$
$373$	19.1311	−	11.0453i	0.990570	−	0.571906i	0.905445	+	0.424464i	$0.139538\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			0.846020i			0.0435722i
$378$		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
$383$	−8.93627	+	5.15936i	−0.456622	+	0.263631i	−0.710623	−	0.703573i	$-0.751587\pi$
$383$	−8.93627	+	5.15936i	−0.456622	+	0.263631i	0.254001	+	0.967204i	$0.418253\pi$
$384$		0			0
$385$	2.43163	+	10.6030i	0.123928	+	0.540380i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−7.23828	+	12.5371i	−0.366995	+	0.635654i	−0.989094	−	0.147284i	$-0.952947\pi$
$389$	−7.23828	+	12.5371i	−0.366995	+	0.635654i	0.622099	+	0.782939i	$0.286280\pi$
$390$		0			0
$391$	24.3649			1.23219
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.36709	−	12.9173i	0.119101	−	0.649940i
$396$		0			0
$397$	−3.66455	+	2.11573i	−0.183919	+	0.106185i	−0.589132	−	0.808036i	$-0.700530\pi$
$397$	−3.66455	+	2.11573i	−0.183919	+	0.106185i	0.405214	+	0.914222i	$0.367197\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	12.6378	+	21.8893i	0.631101	+	1.09310i	0.987327	+	0.158699i	$0.0507300\pi$
$401$	12.6378	+	21.8893i	0.631101	+	1.09310i	−0.356226	+	0.934400i	$0.615937\pi$
$402$		0			0
$403$	−2.08212	−	1.20211i	−0.103718	−	0.0598814i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			7.78065i			0.385673i
$408$		0			0
$409$	−16.2460	+	28.1388i	−0.803311	+	1.39138i	0.114114	+	0.993468i	$0.463597\pi$
$409$	−16.2460	+	28.1388i	−0.803311	+	1.39138i	−0.917425	+	0.397908i	$0.869736\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−20.6381	−	15.3827i	−1.01553	−	0.756934i
$414$		0			0
$415$	14.0000	−	16.4592i	0.687235	−	0.807949i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	8.42519			0.411598			0.205799	−	0.978594i	$-0.434021\pi$
$419$	8.42519			0.411598			0.205799	+	0.978594i	$0.434021\pi$
$420$		0			0
$421$	5.36492			0.261470			0.130735	−	0.991417i	$-0.458266\pi$
$421$	5.36492			0.261470			0.130735	+	0.991417i	$0.458266\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.48552	−	17.1016i	0.314594	−	0.829549i
$426$		0			0
$427$	−2.12132	+	0.913619i	−0.102658	+	0.0442131i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	14.2090	−	24.6107i	0.684424	−	1.18546i	−0.289193	−	0.957271i	$-0.593387\pi$
$431$	14.2090	−	24.6107i	0.684424	−	1.18546i	0.973617	−	0.228187i	$-0.0732797\pi$
$432$		0			0
$433$			12.2022i			0.586399i	0.956051	+	0.293200i	$0.0947201\pi$
$433$			12.2022i			0.586399i	−0.956051	+	0.293200i	$0.905280\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.8040	−	6.23769i	−0.516825	−	0.298389i
$438$		0			0
$439$	−15.3095	−	26.5168i	−0.730681	−	1.26558i	−0.956592	−	0.291429i	$-0.905869\pi$
$439$	−15.3095	−	26.5168i	−0.730681	−	1.26558i	0.225911	−	0.974148i	$-0.427464\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−13.9719	+	8.06670i	−0.663826	+	0.383260i	−0.793733	−	0.608266i	$-0.791865\pi$
$443$	−13.9719	+	8.06670i	−0.663826	+	0.383260i	0.129907	+	0.991526i	$0.458532\pi$
$444$		0			0
$445$	−2.65465	+	14.4865i	−0.125842	+	0.686725i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−13.1729			−0.621666			−0.310833	−	0.950465i	$-0.600608\pi$
$449$	−13.1729			−0.621666			−0.310833	+	0.950465i	$0.600608\pi$
$450$		0			0
$451$	1.69052	−	2.92808i	0.0796037	−	0.137878i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.43572	+	1.54412i	0.0673074	+	0.0723894i
$456$		0			0
$457$	−2.16052	+	1.24738i	−0.101065	+	0.0583499i	−0.549681	−	0.835375i	$-0.685251\pi$
$457$	−2.16052	+	1.24738i	−0.101065	+	0.0583499i	0.448616	+	0.893725i	$0.351917\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	6.58643			0.306761			0.153380	−	0.988167i	$-0.450984\pi$
$461$	6.58643			0.306761			0.153380	+	0.988167i	$0.450984\pi$
$462$		0			0
$463$		−	12.2927i		−	0.571291i	−0.958335	−	0.285645i	$-0.907792\pi$
$463$		−	12.2927i		−	0.571291i	0.958335	−	0.285645i	$-0.0922080\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.73546	−	2.15667i	0.172856	−	0.0997987i	−0.411076	−	0.911601i	$-0.634847\pi$
$467$	3.73546	−	2.15667i	0.172856	−	0.0997987i	0.583932	+	0.811803i	$0.301513\pi$
$468$		0			0
$469$	−18.3095	+	24.5647i	−0.845453	+	1.13429i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.46813	+	2.57968i	0.205445	+	0.118614i
$474$		0			0
$475$	−7.25403	+	5.92289i	−0.332838	+	0.271761i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	6.31889	−	10.9446i	0.288718	−	0.500074i	−0.684786	−	0.728744i	$-0.740104\pi$
$479$	6.31889	−	10.9446i	0.288718	−	0.500074i	0.973504	+	0.228670i	$0.0734378\pi$
$480$		0			0
$481$	0.754033	+	1.30602i	0.0343810	+	0.0595496i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−17.7438	+	20.8605i	−0.805703	+	0.947225i
$486$		0			0
$487$	−6.40316	−	3.69687i	−0.290155	−	0.167521i	0.347857	−	0.937548i	$-0.386910\pi$
$487$	−6.40316	−	3.69687i	−0.290155	−	0.167521i	−0.638012	+	0.770027i	$0.720243\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−30.5583			−1.37908			−0.689539	−	0.724249i	$-0.742187\pi$
$491$	−30.5583			−1.37908			−0.689539	+	0.724249i	$0.742187\pi$
$492$		0			0
$493$	7.52014	+	4.34175i	0.338690	+	0.195543i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.33308	+	28.3765i	−0.149509	+	1.27286i
$498$		0			0
$499$	−0.372983	−	0.646026i	−0.0166970	−	0.0289201i	0.857556	−	0.514390i	$-0.171982\pi$
$499$	−0.372983	−	0.646026i	−0.0166970	−	0.0289201i	−0.874253	+	0.485470i	$0.838648\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	14.6320i		−	0.652411i	−0.945299	−	0.326205i	$-0.894230\pi$
$503$		−	14.6320i		−	0.652411i	0.945299	−	0.326205i	$-0.105770\pi$
$504$		0			0
$505$	−22.7460	+	8.10653i	−1.01218	+	0.360736i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−16.8504	−	29.1857i	−0.746880	−	1.29363i	−0.949311	−	0.314338i	$-0.898218\pi$
$509$	−16.8504	−	29.1857i	−0.746880	−	1.29363i	0.202431	−	0.979297i	$-0.435116\pi$
$510$		0			0
$511$	14.4365	−	19.3686i	0.638633	−	0.856816i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	6.17138	+	1.13091i	0.271944	+	0.0498337i
$516$		0			0
$517$			16.2131i			0.713049i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	18.1541	−	31.4438i	0.795345	−	1.37758i	−0.127276	−	0.991867i	$-0.540623\pi$
$521$	18.1541	−	31.4438i	0.795345	−	1.37758i	0.922620	−	0.385710i	$-0.126043\pi$
$522$		0			0
$523$	−37.9535	+	21.9125i	−1.65959	+	0.958166i	−0.686689	+	0.726951i	$0.740937\pi$
$523$	−37.9535	+	21.9125i	−1.65959	+	0.958166i	−0.972903	+	0.231215i	$0.925730\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−21.3708	+	12.3384i	−0.930925	+	0.537470i
$528$		0			0
$529$	10.6825	−	18.5026i	0.464455	−	0.804459i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	0.655324i		−	0.0283852i
$534$		0			0
$535$	17.9520	+	3.28970i	0.776131	+	0.142226i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−8.84349	+	9.35223i	−0.380916	+	0.402829i
$540$		0			0
$541$	−7.24597	−	12.5504i	−0.311528	−	0.539583i	0.667165	−	0.744910i	$-0.267508\pi$
$541$	−7.24597	−	12.5504i	−0.311528	−	0.539583i	−0.978693	+	0.205327i	$0.934174\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−12.3703	+	4.40868i	−0.529883	+	0.188847i
$546$		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
$551$	−2.22307	−	3.85048i	−0.0947062	−	0.164036i
$552$		0			0
$553$	14.2712	−	6.14636i	0.606871	−	0.261370i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−37.0453	−	21.3881i	−1.56966	−	0.906243i	−0.996208	−	0.0870022i	$-0.972271\pi$
$557$	−37.0453	−	21.3881i	−1.56966	−	0.906243i	−0.573450	−	0.819240i	$-0.694395\pi$
$558$		0			0
$559$	1.00000			0.0422955
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−12.6717	−	7.31602i	−0.534050	−	0.308334i	0.208614	−	0.977998i	$-0.433105\pi$
$563$	−12.6717	−	7.31602i	−0.534050	−	0.308334i	−0.742664	+	0.669664i	$0.766438\pi$
$564$		0			0
$565$	−8.70042	+	10.2287i	−0.366029	+	0.430323i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.43567	−	11.1469i	−0.269797	−	0.467303i	0.699012	−	0.715110i	$-0.253623\pi$
$569$	−6.43567	−	11.1469i	−0.269797	−	0.467303i	−0.968809	+	0.247807i	$0.920290\pi$
$570$		0			0
$571$	−8.93649	+	15.4785i	−0.373981	+	0.647753i	−0.990174	−	0.139842i	$-0.955341\pi$
$571$	−8.93649	+	15.4785i	−0.373981	+	0.647753i	0.616193	+	0.787595i	$0.288674\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−21.0630	−	25.7968i	−0.878387	−	1.07580i
$576$		0			0
$577$	−14.2712	−	8.23945i	−0.594116	−	0.343013i	0.172607	−	0.984991i	$-0.444781\pi$
$577$	−14.2712	−	8.23945i	−0.594116	−	0.343013i	−0.766723	+	0.641978i	$0.778114\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	25.3924	+	2.98257i	1.05345	+	0.123738i
$582$		0			0
$583$	−16.4317	+	9.48683i	−0.680531	+	0.392904i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			6.85140i			0.282787i	0.989953	+	0.141394i	$0.0451583\pi$
$587$			6.85140i			0.282787i	−0.989953	+	0.141394i	$0.954842\pi$
$588$		0			0
$589$	12.6351			0.520620
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−23.4757	+	13.5537i	−0.964032	+	0.556584i	−0.897412	−	0.441194i	$-0.854555\pi$
$593$	−23.4757	+	13.5537i	−0.964032	+	0.556584i	−0.0666206	+	0.997778i	$0.521222\pi$
$594$		0			0
$595$	21.0935	−	4.83746i	0.864749	−	0.198317i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	22.6342	−	39.2036i	0.924809	−	1.60182i	0.132940	−	0.991124i	$-0.457558\pi$
$599$	22.6342	−	39.2036i	0.924809	−	1.60182i	0.791869	−	0.610692i	$-0.209108\pi$
$600$		0			0
$601$	−15.6190			−0.637110			−0.318555	−	0.947904i	$-0.603198\pi$
$601$	−15.6190			−0.637110			−0.318555	+	0.947904i	$0.603198\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	3.07080	−	16.7575i	0.124846	−	0.681287i
$606$		0			0
$607$	11.8804	−	6.85915i	0.482210	−	0.278404i	−0.239127	−	0.970988i	$-0.576861\pi$
$607$	11.8804	−	6.85915i	0.482210	−	0.278404i	0.721337	+	0.692584i	$0.243528\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.57123	+	2.72145i	0.0635651	+	0.110098i
$612$		0			0
$613$	27.0383	+	15.6106i	1.09207	+	0.630504i	0.934126	−	0.356944i	$-0.116181\pi$
$613$	27.0383	+	15.6106i	1.09207	+	0.630504i	0.157940	+	0.987449i	$0.449515\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			17.6347i			0.709948i	0.934876	+	0.354974i	$0.115510\pi$
$617$			17.6347i			0.709948i	−0.934876	+	0.354974i	$0.884490\pi$
$618$		0			0
$619$	−7.62702	+	13.2104i	−0.306556	+	0.530970i	−0.977606	−	0.210441i	$-0.932510\pi$
$619$	−7.62702	+	13.2104i	−0.306556	+	0.530970i	0.671051	+	0.741411i	$0.265843\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−16.0048	+	6.89301i	−0.641219	+	0.276163i
$624$		0			0
$625$	−23.7132	+	7.91732i	−0.948528	+	0.316693i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	15.4787			0.617177
$630$		0			0
$631$	−2.50807			−0.0998446			−0.0499223	−	0.998753i	$-0.515897\pi$
$631$	−2.50807			−0.0998446			−0.0499223	+	0.998753i	$0.515897\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−20.7762	+	24.4255i	−0.824477	+	0.969298i
$636$		0			0
$637$	−0.578089	+	2.42686i	−0.0229047	+	0.0961555i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−17.7698	+	30.7781i	−0.701864	+	1.21566i	0.265948	+	0.963987i	$0.414315\pi$
$641$	−17.7698	+	30.7781i	−0.701864	+	1.21566i	−0.967812	+	0.251676i	$0.919018\pi$
$642$		0			0
$643$		−	15.0533i		−	0.593645i	−0.954933	−	0.296823i	$-0.904073\pi$
$643$		−	15.0533i		−	0.593645i	0.954933	−	0.296823i	$-0.0959271\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.46813	−	2.57968i	−0.175660	−	0.101418i	0.409592	−	0.912269i	$-0.365671\pi$
$647$	−4.46813	−	2.57968i	−0.175660	−	0.101418i	−0.585252	+	0.810851i	$0.699004\pi$
$648$		0			0
$649$	−8.94456	−	15.4924i	−0.351105	−	0.608131i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−16.1700	+	9.33573i	−0.632779	+	0.365335i	−0.781828	−	0.623495i	$-0.785712\pi$
$653$	−16.1700	+	9.33573i	−0.632779	+	0.365335i	0.149049	+	0.988830i	$0.452379\pi$
$654$		0			0
$655$	−3.18010	+	17.3539i	−0.124257	+	0.678072i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−32.6306			−1.27111			−0.635554	−	0.772056i	$-0.719228\pi$
$659$	−32.6306			−1.27111			−0.635554	+	0.772056i	$0.719228\pi$
$660$		0			0
$661$	8.93649	−	15.4785i	0.347589	−	0.602042i	−0.638231	−	0.769845i	$-0.720334\pi$
$661$	8.93649	−	15.4785i	0.347589	−	0.602042i	0.985821	+	0.167802i	$0.0536670\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−10.5918	−	3.25512i	−0.410733	−	0.126228i
$666$		0			0
$667$	13.6931	−	7.90569i	0.530198	−	0.306110i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.60521			−0.0619684
$672$		0			0
$673$			0.356394i			0.0137380i	0.999976	+	0.00686899i	$0.00218648\pi$
$673$			0.356394i			0.0137380i	−0.999976	+	0.00686899i	$0.997814\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−14.7046	+	8.48971i	−0.565144	+	0.326286i	−0.755207	−	0.655486i	$-0.772464\pi$
$677$	−14.7046	+	8.48971i	−0.565144	+	0.326286i	0.190064	+	0.981772i	$0.439131\pi$
$678$		0			0
$679$	−32.1825	−	3.78013i	−1.23505	−	0.145068i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−10.8040	−	6.23769i	−0.413403	−	0.238679i	0.278848	−	0.960335i	$-0.410048\pi$
$683$	−10.8040	−	6.23769i	−0.413403	−	0.238679i	−0.692251	+	0.721657i	$0.743381\pi$
$684$		0			0
$685$	−9.36492	−	26.2769i	−0.357815	−	1.00399i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.83876	+	3.18483i	−0.0700513	+	0.121332i
$690$		0			0
$691$	7.24597	+	12.5504i	0.275650	+	0.477439i	0.970299	−	0.241910i	$-0.0777737\pi$
$691$	7.24597	+	12.5504i	0.275650	+	0.477439i	−0.694649	+	0.719349i	$0.744440\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	3.19016	+	2.71353i	0.121010	+	0.102930i
$696$		0			0
$697$	−5.82508	−	3.36311i	−0.220640	−	0.127387i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	4.44615			0.167929			0.0839644	−	0.996469i	$-0.473242\pi$
$701$	4.44615			0.167929			0.0839644	+	0.996469i	$0.473242\pi$
$702$		0			0
$703$	−6.86364	−	3.96273i	−0.258867	−	0.149457i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−22.9082	−	17.0748i	−0.861551	−	0.642162i
$708$		0			0
$709$	25.8014	+	44.6894i	0.968992	+	1.67834i	0.698483	+	0.715626i	$0.253859\pi$
$709$	25.8014	+	44.6894i	0.968992	+	1.67834i	0.270509	+	0.962717i	$0.412808\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			44.9329i			1.68275i
$714$		0			0
$715$	0.491933	+	1.38031i	0.0183973	+	0.0516206i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	3.94506	+	6.83305i	0.147126	+	0.254830i	0.930164	−	0.367144i	$-0.119664\pi$
$719$	3.94506	+	6.83305i	0.147126	+	0.254830i	−0.783038	+	0.621974i	$0.786331\pi$
$720$		0			0
$721$	2.93649	+	6.81820i	0.109361	+	0.253923i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.90410	−	11.7154i	−0.0707166	−	0.435100i
$726$		0			0
$727$			14.7422i			0.546758i	0.961906	+	0.273379i	$0.0881413\pi$
$727$			14.7422i			0.546758i	−0.961906	+	0.273379i	$0.911859\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	5.13198	−	8.88885i	0.189813	−	0.328766i
$732$		0			0
$733$	40.3443	−	23.2928i	1.49015	−	0.860339i	0.490214	−	0.871602i	$-0.336919\pi$
$733$	40.3443	−	23.2928i	1.49015	−	0.860339i	0.999937	+	0.0112635i	$0.00358537\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−18.4401	+	10.6464i	−0.679248	+	0.392164i
$738$		0			0
$739$	23.6825	−	41.0192i	0.871173	−	1.50892i	0.0103893	−	0.999946i	$-0.496693\pi$
$739$	23.6825	−	41.0192i	0.871173	−	1.50892i	0.860784	−	0.508970i	$-0.169974\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	24.4861i		−	0.898309i	−0.893454	−	0.449154i	$-0.851725\pi$
$743$		−	24.4861i		−	0.898309i	0.893454	−	0.449154i	$-0.148275\pi$
$744$		0			0
$745$	8.05808	−	43.9731i	0.295225	−	1.61105i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	8.54197	+	19.8335i	0.312117	+	0.724700i
$750$		0			0
$751$	14.9919	+	25.9668i	0.547063	+	0.947542i	0.998474	+	0.0552252i	$0.0175877\pi$
$751$	14.9919	+	25.9668i	0.547063	+	0.947542i	−0.451411	+	0.892316i	$0.649079\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	14.4766	−	5.15936i	0.526856	−	0.187768i
$756$		0			0
$757$			21.7343i			0.789946i	0.918693	+	0.394973i	$0.129246\pi$
$757$			21.7343i			0.789946i	−0.918693	+	0.394973i	$0.870754\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−13.2896	−	23.0183i	−0.481749	−	0.834414i	0.518032	−	0.855361i	$-0.326665\pi$
$761$	−13.2896	−	23.0183i	−0.481749	−	0.834414i	−0.999781	+	0.0209479i	$0.993332\pi$
$762$		0			0
$763$	−12.4585	−	9.28600i	−0.451027	−	0.336176i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.00278	−	1.73366i	−0.108424	−	0.0625988i
$768$		0			0
$769$	19.6190			0.707477			0.353739	−	0.935344i	$-0.384910\pi$
$769$	19.6190			0.707477			0.353739	+	0.935344i	$0.384910\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−36.3126	−	20.9651i	−1.30607	−	0.754062i	−0.324635	−	0.945839i	$-0.605241\pi$
$773$	−36.3126	−	20.9651i	−1.30607	−	0.754062i	−0.981438	+	0.191778i	$0.938575\pi$
$774$		0			0
$775$	31.5381	+	11.9604i	1.13288	+	0.429628i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.72199	+	2.98257i	0.0616966	+	0.106862i
$780$		0			0
$781$	−9.92843	+	17.1965i	−0.355267	+	0.615340i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	16.3153	+	45.7789i	0.582319	+	1.63392i
$786$		0			0
$787$	35.2541	+	20.3540i	1.25667	+	0.725541i	0.972426	−	0.233210i	$-0.0749230\pi$
$787$	35.2541	+	20.3540i	1.25667	+	0.725541i	0.284247	+	0.958751i	$0.408256\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−15.7802	−	1.85354i	−0.561081	−	0.0659042i
$792$		0			0
$793$	−0.269443	+	0.155563i	−0.00956820	+	0.00552420i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	11.1647i		−	0.395475i	−0.980255	−	0.197738i	$-0.936641\pi$
$797$		−	11.1647i		−	0.395475i	0.980255	−	0.197738i	$-0.0633594\pi$
$798$		0			0
$799$	32.2540			1.14107
$800$		0			0
$801$		0			0
$802$		0			0
$803$	14.5395	−	8.39436i	0.513086	−	0.296230i
$804$		0			0
$805$	11.5759	−	37.6666i	0.407995	−	1.32757i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−9.22780	+	15.9830i	−0.324432	+	0.561933i	−0.981397	−	0.191988i	$-0.938507\pi$
$809$	−9.22780	+	15.9830i	−0.324432	+	0.561933i	0.656965	+	0.753921i	$0.271840\pi$
$810$		0			0
$811$	−39.6028			−1.39064			−0.695321	−	0.718699i	$-0.744738\pi$
$811$	−39.6028			−1.39064			−0.695321	+	0.718699i	$0.744738\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.07182	+	1.11266i	0.212687	+	0.0389748i
$816$		0			0
$817$	−4.55129	+	2.62769i	−0.159229	+	0.0919311i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−13.5572	−	23.4817i	−0.473149	−	0.819517i	0.526379	−	0.850250i	$-0.323549\pi$
$821$	−13.5572	−	23.4817i	−0.473149	−	0.819517i	−0.999528	+	0.0307327i	$0.990216\pi$
$822$		0			0
$823$	−45.8607	−	26.4777i	−1.59860	−	0.922955i	−0.991757	−	0.128136i	$-0.959100\pi$
$823$	−45.8607	−	26.4777i	−1.59860	−	0.922955i	−0.606848	−	0.794818i	$-0.707566\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	29.4548i		−	1.02424i	−0.858913	−	0.512122i	$-0.828860\pi$
$827$		−	29.4548i		−	1.02424i	0.858913	−	0.512122i	$-0.171140\pi$
$828$		0			0
$829$	−6.31754	+	10.9423i	−0.219417	+	0.380042i	−0.954630	−	0.297795i	$-0.903749\pi$
$829$	−6.31754	+	10.9423i	−0.219417	+	0.380042i	0.735213	+	0.677836i	$0.237082\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	18.6052	+	17.5931i	0.644632	+	0.609565i
$834$		0			0
$835$	7.47473	−	8.78767i	0.258674	−	0.304110i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	22.9017			0.790656			0.395328	−	0.918540i	$-0.370631\pi$
$839$	22.9017			0.790656			0.395328	+	0.918540i	$0.370631\pi$
$840$		0			0
$841$	−23.3649			−0.805687
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−21.9259	−	18.6500i	−0.754274	−	0.641580i
$846$		0			0
$847$	18.5138	−	7.97360i	0.636141	−	0.273976i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	14.0922	−	24.4085i	0.483076	−	0.836712i
$852$		0			0
$853$		−	28.1041i		−	0.962266i	−0.876648	−	0.481133i	$-0.840225\pi$
$853$		−	28.1041i		−	0.962266i	0.876648	−	0.481133i	$-0.159775\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	32.7423	+	18.9038i	1.11845	+	0.645740i	0.941006	−	0.338390i	$-0.109882\pi$
$857$	32.7423	+	18.9038i	1.11845	+	0.645740i	0.177449	+	0.984130i	$0.443216\pi$
$858$		0			0
$859$	−17.5635	−	30.4209i	−0.599259	−	1.03795i	−0.992931	−	0.118696i	$-0.962129\pi$
$859$	−17.5635	−	30.4209i	−0.599259	−	1.03795i	0.393671	−	0.919251i	$-0.371205\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.43526	−	1.40600i	0.0828971	−	0.0478607i	−0.457978	−	0.888963i	$-0.651426\pi$
$863$	2.43526	−	1.40600i	0.0828971	−	0.0478607i	0.540876	+	0.841103i	$0.318093\pi$
$864$		0			0
$865$	−32.6018	−	5.97428i	−1.10849	−	0.203132i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	10.7990			0.366332
$870$		0			0
$871$	−2.06351	+	3.57410i	−0.0699193	+	0.121104i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−23.3567	−	18.1512i	−0.789599	−	0.613623i
$876$		0			0
$877$	−34.5584	+	19.9523i	−1.16695	+	0.673742i	−0.952961	−	0.303093i	$-0.901981\pi$
$877$	−34.5584	+	19.9523i	−1.16695	+	0.673742i	−0.213994	+	0.976835i	$0.568647\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−27.3479			−0.921374			−0.460687	−	0.887563i	$-0.652397\pi$
$881$	−27.3479			−0.921374			−0.460687	+	0.887563i	$0.652397\pi$
$882$		0			0
$883$			35.1414i			1.18260i	0.806450	+	0.591302i	$0.201386\pi$
$883$			35.1414i			1.18260i	−0.806450	+	0.591302i	$0.798614\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	13.4044	−	7.73903i	0.450076	−	0.259851i	−0.257786	−	0.966202i	$-0.582993\pi$
$887$	13.4044	−	7.73903i	0.450076	−	0.259851i	0.707862	+	0.706351i	$0.249660\pi$
$888$		0			0
$889$	−37.6825	−	4.42615i	−1.26383	−	0.148448i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−14.3022	−	8.25739i	−0.478606	−	0.276323i
$894$		0			0
$895$	−10.0000	+	3.56394i	−0.334263	+	0.119129i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−8.00690	+	13.8684i	−0.267045	+	0.462536i
$900$		0			0
$901$	18.8730	+	32.6890i	0.628750	+	1.08903i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	13.4097	+	11.4062i	0.445752	+	0.379153i
$906$		0			0
$907$	35.8322	+	20.6877i	1.18979	+	0.686925i	0.958259	−	0.285903i	$-0.0922934\pi$
$907$	35.8322	+	20.6877i	1.18979	+	0.686925i	0.231530	+	0.972828i	$0.425627\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−2.90890			−0.0963763			−0.0481881	−	0.998838i	$-0.515345\pi$
$911$	−2.90890			−0.0963763			−0.0481881	+	0.998838i	$0.515345\pi$
$912$		0			0
$913$	15.3881	+	8.88434i	0.509273	+	0.294029i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−19.1727	+	8.25739i	−0.633139	+	0.272683i
$918$		0			0
$919$	3.75403	+	6.50218i	0.123834	+	0.214487i	0.921277	−	0.388908i	$-0.127148\pi$
$919$	3.75403	+	6.50218i	0.123834	+	0.214487i	−0.797442	+	0.603395i	$0.793814\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			3.84871i			0.126682i
$924$		0			0
$925$	−13.3810	−	16.3884i	−0.439966	−	0.538846i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−6.43567	−	11.1469i	−0.211148	−	0.365718i	0.740926	−	0.671586i	$-0.234387\pi$
$929$	−6.43567	−	11.1469i	−0.211148	−	0.365718i	−0.952074	+	0.305868i	$0.901053\pi$
$930$		0			0
$931$	−3.74597	−	12.5644i	−0.122769	−	0.411780i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	14.7939	+	2.71099i	0.483813	+	0.0886588i
$936$		0			0
$937$		−	20.4445i		−	0.667893i	−0.942592	−	0.333947i	$-0.891620\pi$
$937$		−	20.4445i		−	0.667893i	0.942592	−	0.333947i	$-0.108380\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.651847	−	1.12903i	0.0212496	−	0.0368054i	−0.855205	−	0.518290i	$-0.826569\pi$
$941$	0.651847	−	1.12903i	0.0212496	−	0.0368054i	0.876455	+	0.481484i	$0.159902\pi$
$942$		0			0
$943$	−10.6066	+	6.12372i	−0.345398	+	0.199416i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	29.0068	−	16.7471i	0.942595	−	0.544208i	0.0518222	−	0.998656i	$-0.483497\pi$
$947$	29.0068	−	16.7471i	0.942595	−	0.544208i	0.890773	+	0.454449i	$0.150164\pi$
$948$		0			0
$949$	1.62702	−	2.81808i	0.0528152	−	0.0914786i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			20.6374i			0.668512i	0.942482	+	0.334256i	$0.108485\pi$
$953$			20.6374i			0.668512i	−0.942482	+	0.334256i	$0.891515\pi$
$954$		0			0
$955$	5.30930	−	28.9730i	0.171805	−	0.937543i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	19.7253	−	26.4643i	0.636963	−	0.854576i
$960$		0			0
$961$	−7.25403	−	12.5644i	−0.234001	−	0.405302i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−8.92628	−	25.0461i	−0.287347	−	0.806263i
$966$		0			0
$967$			45.5617i			1.46516i	0.680679	+	0.732582i	$0.261685\pi$
$967$			45.5617i			1.46516i	−0.680679	+	0.732582i	$0.738315\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	22.6342	+	39.2036i	0.726366	+	1.25810i	0.958409	+	0.285398i	$0.0921257\pi$
$971$	22.6342	+	39.2036i	0.726366	+	1.25810i	−0.232043	+	0.972706i	$0.574541\pi$
$972$		0			0
$973$	−0.578089	+	4.92161i	−0.0185327	+	0.157780i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	36.3126	+	20.9651i	1.16174	+	0.670732i	0.951721	−	0.306964i	$-0.0993132\pi$
$977$	36.3126	+	20.9651i	1.16174	+	0.670732i	0.210022	+	0.977697i	$0.432647\pi$
$978$		0			0
$979$	−12.1109			−0.387066
$980$		0			0
$981$		0			0
$982$		0			0
$983$	18.2749	+	10.5510i	0.582879	+	0.336525i	0.762277	−	0.647251i	$-0.224082\pi$
$983$	18.2749	+	10.5510i	0.582879	+	0.336525i	−0.179398	+	0.983777i	$0.557415\pi$
$984$		0			0
$985$	−31.1246	+	36.5917i	−0.991712	+	1.16591i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−9.34457	−	16.1853i	−0.297140	−	0.514662i
$990$		0			0
$991$	−11.1905	+	19.3826i	−0.355479	+	0.615707i	−0.987200	−	0.159489i	$-0.949015\pi$
$991$	−11.1905	+	19.3826i	−0.355479	+	0.615707i	0.631721	+	0.775196i	$0.282349\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	10.7990	−	3.84871i	0.342352	−	0.122012i
$996$		0			0
$997$	51.1077	+	29.5070i	1.61860	+	0.934498i	0.987283	+	0.158970i	$0.0508173\pi$
$997$	51.1077	+	29.5070i	1.61860	+	0.934498i	0.631314	+	0.775527i	$0.282516\pi$
$998$		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.109.2	✓	16
3.2	odd	2	inner	1260.2.bm.d.109.7	yes	16
5.4	even	2	inner	1260.2.bm.d.109.4	yes	16
7.2	even	3	inner	1260.2.bm.d.289.4	yes	16
15.14	odd	2	inner	1260.2.bm.d.109.5	yes	16
21.2	odd	6	inner	1260.2.bm.d.289.5	yes	16
35.9	even	6	inner	1260.2.bm.d.289.2	yes	16
105.44	odd	6	inner	1260.2.bm.d.289.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.bm.d.109.2	✓	16	1.1	even	1	trivial
1260.2.bm.d.109.4	yes	16	5.4	even	2	inner
1260.2.bm.d.109.5	yes	16	15.14	odd	2	inner
1260.2.bm.d.109.7	yes	16	3.2	odd	2	inner
1260.2.bm.d.289.2	yes	16	35.9	even	6	inner
1260.2.bm.d.289.4	yes	16	7.2	even	3	inner
1260.2.bm.d.289.5	yes	16	21.2	odd	6	inner
1260.2.bm.d.289.7	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)

\(f(q)\)	\(=\)	\(q+(-1.70325 - 1.44877i) q^{5} +(0.308646 - 2.62769i) q^{7} +(0.919382 - 1.59242i) q^{11} -0.356394i q^{13} +(-3.16793 - 1.82901i) q^{17} +(0.936492 + 1.62205i) q^{19} +(-5.76833 + 3.33035i) q^{23} +(0.802121 + 4.93524i) q^{25} -2.37383 q^{29} +(3.37298 - 5.84218i) q^{31} +(-4.33262 + 4.02845i) q^{35} +(-3.66455 + 2.11573i) q^{37} +1.83876 q^{41} +2.80588i q^{43} +(-7.63606 + 4.40868i) q^{47} +(-6.80948 - 1.62205i) q^{49} +(-8.93627 - 5.15936i) q^{53} +(-3.87298 + 1.38031i) q^{55} +(4.86444 - 8.42546i) q^{59} +(-0.436492 - 0.756026i) q^{61} +(-0.516333 + 0.607028i) q^{65} +(-10.0285 - 5.78996i) q^{67} -10.7990 q^{71} +(7.90719 + 4.56522i) q^{73} +(-3.90061 - 2.90734i) q^{77} +(2.93649 + 5.08615i) q^{79} +9.66339i q^{83} +(2.74597 + 7.70486i) q^{85} +(-3.29321 - 5.70402i) q^{89} +(-0.936492 - 0.110000i) q^{91} +(0.754902 - 4.11952i) q^{95} -12.2474i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{19} - 8 q^{31} - 16 q^{49} + 24 q^{61} + 16 q^{79} - 80 q^{85} + 16 q^{91}+O(q^{100}) \) 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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