LMFDB - Embedded newform 1260.2.s.h.541.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1260,2,Mod(361,1260)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1260.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1260, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [6,0,0,0,3,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.4406832.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 6x^{4} + 7x^{3} + 24x^{2} + 5x + 1 $ x^6 - x^5 + 6x^4 + 7x^3 + 24x^2 + 5x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.2
Root			$-0.105378 + 0.182520i$ of defining polynomial
Character	$\chi$	$=$	1260.541
Dual form			1260.2.s.h.361.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{5} +(-1.16166 - 2.37709i) q^{7} +(-0.661657 - 1.14602i) q^{11} +0.323314 q^{13} +(-3.13945 - 5.43768i) q^{17} +(-1.97779 + 3.42563i) q^{19} +(-1.81613 + 3.14564i) q^{23} +(-0.500000 - 0.866025i) q^{25} -5.23448 q^{29} +(0.500000 + 0.866025i) q^{31} +(-2.63945 - 0.182520i) q^{35} +(2.31613 - 4.01166i) q^{37} -8.58785 q^{41} +5.27890 q^{43} +(-1.95558 + 3.38717i) q^{47} +(-4.30111 + 5.52273i) q^{49} +(-6.27890 - 10.8754i) q^{53} -1.32331 q^{55} +(-3.66166 - 6.34218i) q^{59} +(1.47779 - 2.55961i) q^{61} +(0.161657 - 0.279998i) q^{65} +(-0.161657 - 0.279998i) q^{67} +4.67669 q^{71} +(1.68387 + 2.91654i) q^{73} +(-1.95558 + 2.90410i) q^{77} +(-5.25669 + 9.10485i) q^{79} -8.92552 q^{83} -6.27890 q^{85} +(6.94055 - 12.0214i) q^{89} +(-0.375580 - 0.768547i) q^{91} +(1.97779 + 3.42563i) q^{95} +3.60221 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} - q^{7} + 2 q^{11} - 10 q^{13} - 2 q^{17} - q^{19} - 6 q^{23} - 3 q^{25} + 24 q^{29} + 3 q^{31} + q^{35} + 9 q^{37} - 20 q^{41} - 2 q^{43} + 10 q^{47} - 3 q^{49} - 4 q^{53} + 4 q^{55} - 16 q^{59}+ \cdots - 24 q^{97}+O(q^{100}) $ 6 * q + 3 * q^5 - q^7 + 2 * q^11 - 10 * q^13 - 2 * q^17 - q^19 - 6 * q^23 - 3 * q^25 + 24 * q^29 + 3 * q^31 + q^35 + 9 * q^37 - 20 * q^41 - 2 * q^43 + 10 * q^47 - 3 * q^49 - 4 * q^53 + 4 * q^55 - 16 * q^59 - 2 * q^61 - 5 * q^65 + 5 * q^67 + 40 * q^71 + 15 * q^73 + 10 * q^77 + 13 * q^79 + 4 * q^83 - 4 * q^85 + 2 * q^89 - 37 * q^91 + q^95 - 24 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−1.16166	−	2.37709i	−0.439065	−	0.898455i
$7$	−1.16166	−	2.37709i	−0.439065	−	0.898455i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.661657	−	1.14602i	−0.199497	−	0.345539i	0.748868	−	0.662719i	$-0.230598\pi$
$11$	−0.661657	−	1.14602i	−0.199497	−	0.345539i	−0.948365	+	0.317180i	$0.897264\pi$
$12$		0			0
$13$	0.323314			0.0896713			0.0448356	−	0.998994i	$-0.485724\pi$
$13$	0.323314			0.0896713			0.0448356	+	0.998994i	$0.485724\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.13945	−	5.43768i	−0.761428	−	1.31883i	−0.942115	−	0.335291i	$-0.891165\pi$
$17$	−3.13945	−	5.43768i	−0.761428	−	1.31883i	0.180687	−	0.983541i	$-0.442168\pi$
$18$		0			0
$19$	−1.97779	+	3.42563i	−0.453736	+	0.785894i	−0.998615	−	0.0526208i	$-0.983243\pi$
$19$	−1.97779	+	3.42563i	−0.453736	+	0.785894i	0.544878	+	0.838515i	$0.316576\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.81613	+	3.14564i	−0.378690	+	0.655910i	−0.990872	−	0.134807i	$-0.956959\pi$
$23$	−1.81613	+	3.14564i	−0.378690	+	0.655910i	0.612182	+	0.790717i	$0.290292\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.23448			−0.972018			−0.486009	−	0.873954i	$-0.661548\pi$
$29$	−5.23448			−0.972018			−0.486009	+	0.873954i	$0.661548\pi$
$30$		0			0
$31$	0.500000	+	0.866025i	0.0898027	+	0.155543i	0.907428	−	0.420208i	$-0.138043\pi$
$31$	0.500000	+	0.866025i	0.0898027	+	0.155543i	−0.817625	+	0.575751i	$0.804710\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.63945	−	0.182520i	−0.446148	−	0.0308515i
$36$		0			0
$37$	2.31613	−	4.01166i	0.380770	−	0.659513i	−0.610402	−	0.792091i	$-0.708992\pi$
$37$	2.31613	−	4.01166i	0.380770	−	0.659513i	0.991173	+	0.132578i	$0.0423256\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−8.58785			−1.34120			−0.670598	−	0.741821i	$-0.733963\pi$
$41$	−8.58785			−1.34120			−0.670598	+	0.741821i	$0.733963\pi$
$42$		0			0
$43$	5.27890			0.805024			0.402512	−	0.915415i	$-0.368137\pi$
$43$	5.27890			0.805024			0.402512	+	0.915415i	$0.368137\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.95558	+	3.38717i	−0.285251	+	0.494069i	−0.972670	−	0.232192i	$-0.925410\pi$
$47$	−1.95558	+	3.38717i	−0.285251	+	0.494069i	0.687419	+	0.726261i	$0.258744\pi$
$48$		0			0
$49$	−4.30111	+	5.52273i	−0.614444	+	0.788961i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.27890	−	10.8754i	−0.862473	−	1.49385i	−0.869535	−	0.493872i	$-0.835581\pi$
$53$	−6.27890	−	10.8754i	−0.862473	−	1.49385i	0.00706215	−	0.999975i	$-0.497752\pi$
$54$		0			0
$55$	−1.32331			−0.178436
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.66166	−	6.34218i	−0.476707	−	0.825681i	0.522937	−	0.852372i	$-0.324836\pi$
$59$	−3.66166	−	6.34218i	−0.476707	−	0.825681i	−0.999644	+	0.0266906i	$0.991503\pi$
$60$		0			0
$61$	1.47779	−	2.55961i	0.189212	−	0.327724i	−0.755776	−	0.654830i	$-0.772740\pi$
$61$	1.47779	−	2.55961i	0.189212	−	0.327724i	0.944988	+	0.327106i	$0.106073\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.161657	−	0.279998i	0.0200511	−	0.0347295i
$66$		0			0
$67$	−0.161657	−	0.279998i	−0.0197496	−	0.0342073i	0.855982	−	0.517006i	$-0.172954\pi$
$67$	−0.161657	−	0.279998i	−0.0197496	−	0.0342073i	−0.875731	+	0.482799i	$0.839620\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.67669			0.555020			0.277510	−	0.960723i	$-0.410491\pi$
$71$	4.67669			0.555020			0.277510	+	0.960723i	$0.410491\pi$
$72$		0			0
$73$	1.68387	+	2.91654i	0.197082	+	0.341355i	0.947581	−	0.319516i	$-0.103520\pi$
$73$	1.68387	+	2.91654i	0.197082	+	0.341355i	−0.750499	+	0.660871i	$0.770187\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.95558	+	2.90410i	−0.222859	+	0.330953i
$78$		0			0
$79$	−5.25669	+	9.10485i	−0.591424	+	1.02438i	0.402617	+	0.915368i	$0.368101\pi$
$79$	−5.25669	+	9.10485i	−0.591424	+	1.02438i	−0.994041	+	0.109007i	$0.965233\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.92552			−0.979704			−0.489852	−	0.871806i	$-0.662949\pi$
$83$	−8.92552			−0.979704			−0.489852	+	0.871806i	$0.662949\pi$
$84$		0			0
$85$	−6.27890			−0.681042
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.94055	−	12.0214i	0.735697	−	1.27426i	−0.218720	−	0.975788i	$-0.570188\pi$
$89$	6.94055	−	12.0214i	0.735697	−	1.27426i	0.954417	−	0.298477i	$-0.0964787\pi$
$90$		0			0
$91$	−0.375580	−	0.768547i	−0.0393715	−	0.0805656i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.97779	+	3.42563i	0.202917	+	0.351463i
$96$		0			0
$97$	3.60221			0.365749			0.182875	−	0.983136i	$-0.441460\pi$
$97$	3.60221			0.365749			0.182875	+	0.983136i	$0.441460\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.98497	−	8.63422i	−0.496023	−	0.859137i	0.503966	−	0.863723i	$-0.331874\pi$
$101$	−4.98497	−	8.63422i	−0.496023	−	0.859137i	−0.999989	+	0.00458594i	$0.998540\pi$
$102$		0			0
$103$	8.59503	−	14.8870i	0.846893	−	1.46686i	−0.0370732	−	0.999313i	$-0.511803\pi$
$103$	8.59503	−	14.8870i	0.846893	−	1.46686i	0.883967	−	0.467550i	$-0.154863\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.18387	+	2.05052i	−0.114449	+	0.198231i	−0.917559	−	0.397599i	$-0.869843\pi$
$107$	−1.18387	+	2.05052i	−0.114449	+	0.198231i	0.803111	+	0.595830i	$0.203177\pi$
$108$		0			0
$109$	−1.34552	−	2.33051i	−0.128878	−	0.223223i	0.794364	−	0.607442i	$-0.207804\pi$
$109$	−1.34552	−	2.33051i	−0.128878	−	0.223223i	−0.923242	+	0.384219i	$0.874471\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	14.6466			1.37784			0.688919	−	0.724838i	$-0.258085\pi$
$113$	14.6466			1.37784			0.688919	+	0.724838i	$0.258085\pi$
$114$		0			0
$115$	1.81613	+	3.14564i	0.169355	+	0.293332i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−9.27890	+	13.7795i	−0.850595	+	1.26316i
$120$		0			0
$121$	4.62442	−	8.00973i	0.420402	−	0.728157i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−3.58785			−0.318370			−0.159185	−	0.987249i	$-0.550887\pi$
$127$	−3.58785			−0.318370			−0.159185	+	0.987249i	$0.550887\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.67669	−	2.90410i	0.146493	−	0.253733i	−0.783436	−	0.621472i	$-0.786535\pi$
$131$	1.67669	−	2.90410i	0.146493	−	0.253733i	0.929929	+	0.367739i	$0.119868\pi$
$132$		0			0
$133$	10.4406	+	0.721973i	0.905311	+	0.0626030i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.81613	−	8.34179i	−0.411470	−	0.712687i	0.583581	−	0.812055i	$-0.301651\pi$
$137$	−4.81613	−	8.34179i	−0.411470	−	0.712687i	−0.995051	+	0.0993681i	$0.968318\pi$
$138$		0			0
$139$	−21.1600			−1.79477			−0.897384	−	0.441250i	$-0.854535\pi$
$139$	−21.1600			−1.79477			−0.897384	+	0.441250i	$0.854535\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.213923	−	0.370526i	−0.0178892	−	0.0309849i
$144$		0			0
$145$	−2.61724	+	4.53319i	−0.217350	+	0.376461i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	2.16884	+	3.75654i	0.176498	+	0.305703i	0.940678	−	0.339299i	$-0.110190\pi$
$151$	2.16884	+	3.75654i	0.176498	+	0.305703i	−0.764181	+	0.645002i	$0.776857\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.00000			0.0803219
$156$		0			0
$157$	5.27890	+	9.14332i	0.421302	+	0.729716i	0.996067	−	0.0886022i	$-0.0282400\pi$
$157$	5.27890	+	9.14332i	0.421302	+	0.729716i	−0.574765	+	0.818318i	$0.694907\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	9.58718	+	0.662961i	0.755576	+	0.0522487i
$162$		0			0
$163$	7.23448	−	12.5305i	0.566648	−	0.981463i	−0.430246	−	0.902712i	$-0.641573\pi$
$163$	7.23448	−	12.5305i	0.566648	−	0.981463i	0.996894	−	0.0787517i	$-0.0250934\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.36773			−0.183221			−0.0916103	−	0.995795i	$-0.529201\pi$
$167$	−2.36773			−0.183221			−0.0916103	+	0.995795i	$0.529201\pi$
$168$		0			0
$169$	−12.8955			−0.991959
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.95558	+	3.38717i	−0.148680	+	0.257522i	−0.930740	−	0.365682i	$-0.880836\pi$
$173$	−1.95558	+	3.38717i	−0.148680	+	0.257522i	0.782060	+	0.623203i	$0.214169\pi$
$174$		0			0
$175$	−1.47779	+	2.19457i	−0.111710	+	0.165894i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.60221	+	13.1674i	0.568216	+	0.984179i	0.996743	+	0.0806496i	$0.0256995\pi$
$179$	7.60221	+	13.1674i	0.568216	+	0.984179i	−0.428527	+	0.903529i	$0.640967\pi$
$180$		0			0
$181$	7.30895			0.543270			0.271635	−	0.962400i	$-0.412436\pi$
$181$	7.30895			0.543270			0.271635	+	0.962400i	$0.412436\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.31613	−	4.01166i	−0.170286	−	0.294943i
$186$		0			0
$187$	−4.15448	+	7.19576i	−0.303805	+	0.526206i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−13.6022	+	23.5597i	−0.984221	+	1.70472i	−0.338875	+	0.940831i	$0.610046\pi$
$191$	−13.6022	+	23.5597i	−0.984221	+	1.70472i	−0.645346	+	0.763890i	$0.723287\pi$
$192$		0			0
$193$	−4.94840	−	8.57088i	−0.356194	−	0.616946i	0.631128	−	0.775679i	$-0.282592\pi$
$193$	−4.94840	−	8.57088i	−0.356194	−	0.616946i	−0.987322	+	0.158733i	$0.949259\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	24.2789			1.72980			0.864900	−	0.501944i	$-0.167382\pi$
$197$	24.2789			1.72980			0.864900	+	0.501944i	$0.167382\pi$
$198$		0			0
$199$	−4.16884	−	7.22064i	−0.295521	−	0.511858i	0.679585	−	0.733597i	$-0.262160\pi$
$199$	−4.16884	−	7.22064i	−0.295521	−	0.511858i	−0.975106	+	0.221739i	$0.928827\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	6.08067	+	12.4428i	0.426779	+	0.873315i
$204$		0			0
$205$	−4.29392	+	7.43730i	−0.299901	+	0.519443i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	5.23448			0.362076
$210$		0			0
$211$	25.5134			1.75641			0.878207	−	0.478282i	$-0.158740\pi$
$211$	25.5134			1.75641			0.878207	+	0.478282i	$0.158740\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.63945	−	4.57166i	0.180009	−	0.311785i
$216$		0			0
$217$	1.47779	−	2.19457i	0.100319	−	0.148977i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.01503	−	1.75808i	−0.0682782	−	0.118261i
$222$		0			0
$223$	21.1156			1.41400			0.707002	−	0.707211i	$-0.250047\pi$
$223$	21.1156			1.41400			0.707002	+	0.707211i	$0.250047\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.904970	−	1.56745i	−0.0600650	−	0.104036i	0.834429	−	0.551115i	$-0.185797\pi$
$227$	−0.904970	−	1.56745i	−0.0600650	−	0.104036i	−0.894494	+	0.447079i	$0.852464\pi$
$228$		0			0
$229$	−9.05779	+	15.6886i	−0.598556	+	1.03673i	0.394479	+	0.918905i	$0.370925\pi$
$229$	−9.05779	+	15.6886i	−0.598556	+	1.03673i	−0.993034	+	0.117824i	$0.962408\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.23448	−	3.87023i	0.146386	−	0.253547i	−0.783503	−	0.621387i	$-0.786569\pi$
$233$	2.23448	−	3.87023i	0.146386	−	0.253547i	0.929889	+	0.367840i	$0.119903\pi$
$234$		0			0
$235$	1.95558	+	3.38717i	0.127568	+	0.220954i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	25.8223			1.67031			0.835154	−	0.550017i	$-0.185379\pi$
$239$	25.8223			1.67031			0.835154	+	0.550017i	$0.185379\pi$
$240$		0			0
$241$	−9.75669	−	16.8991i	−0.628483	−	1.08857i	−0.987856	−	0.155371i	$-0.950343\pi$
$241$	−9.75669	−	16.8991i	−0.628483	−	1.08857i	0.359373	−	0.933194i	$-0.382991\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.63227	+	6.48623i	0.168169	+	0.414390i
$246$		0			0
$247$	−0.639448	+	1.10756i	−0.0406871	+	0.0704721i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	21.7034			1.36991			0.684954	−	0.728586i	$-0.259822\pi$
$251$	21.7034			1.36991			0.684954	+	0.728586i	$0.259822\pi$
$252$		0			0
$253$	4.80663			0.302190
$254$		0			0
$255$		0			0
$256$		0			0
$257$	8.72730	−	15.1161i	0.544394	−	0.942918i	−0.454251	−	0.890874i	$-0.650093\pi$
$257$	8.72730	−	15.1161i	0.544394	−	0.942918i	0.998645	−	0.0520441i	$-0.0165736\pi$
$258$		0			0
$259$	−12.2266	−	0.845481i	−0.759726	−	0.0525356i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	6.91116	+	11.9705i	0.426161	+	0.738132i	0.996528	−	0.0832578i	$-0.0265325\pi$
$263$	6.91116	+	11.9705i	0.426161	+	0.738132i	−0.570367	+	0.821390i	$0.693199\pi$
$264$		0			0
$265$	−12.5578			−0.771419
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−6.63227	−	11.4874i	−0.404376	−	0.700401i	0.589872	−	0.807497i	$-0.299178\pi$
$269$	−6.63227	−	11.4874i	−0.404376	−	0.700401i	−0.994249	+	0.107096i	$0.965845\pi$
$270$		0			0
$271$	−8.84552	+	15.3209i	−0.537327	+	0.930678i	0.461720	+	0.887026i	$0.347233\pi$
$271$	−8.84552	+	15.3209i	−0.537327	+	0.930678i	−0.999047	+	0.0436522i	$0.986101\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.661657	+	1.14602i	−0.0398994	+	0.0691078i
$276$		0			0
$277$	6.63945	+	11.4999i	0.398926	+	0.690960i	0.993594	−	0.113012i	$-0.0360498\pi$
$277$	6.63945	+	11.4999i	0.398926	+	0.690960i	−0.594668	+	0.803971i	$0.702716\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	27.9112			1.66504			0.832520	−	0.553995i	$-0.186897\pi$
$281$	27.9112			1.66504			0.832520	+	0.553995i	$0.186897\pi$
$282$		0			0
$283$	1.05160	+	1.82142i	0.0625110	+	0.108272i	0.895587	−	0.444886i	$-0.146756\pi$
$283$	1.05160	+	1.82142i	0.0625110	+	0.108272i	−0.833076	+	0.553158i	$0.813422\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	9.97614	+	20.4141i	0.588873	+	1.20501i
$288$		0			0
$289$	−11.2123	+	19.4202i	−0.659545	+	1.14237i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5.44221			−0.317937			−0.158969	−	0.987284i	$-0.550817\pi$
$293$	−5.44221			−0.317937			−0.158969	+	0.987284i	$0.550817\pi$
$294$		0			0
$295$	−7.32331			−0.426380
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.587182	+	1.01703i	−0.0339576	+	0.0588163i
$300$		0			0
$301$	−6.13227	−	12.5484i	−0.353458	−	0.723278i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.47779	−	2.55961i	−0.0846181	−	0.146563i
$306$		0			0
$307$	2.41215			0.137669			0.0688343	−	0.997628i	$-0.478072\pi$
$307$	2.41215			0.137669			0.0688343	+	0.997628i	$0.478072\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.38276	−	5.85911i	−0.191819	−	0.332240i	0.754034	−	0.656835i	$-0.228105\pi$
$311$	−3.38276	−	5.85911i	−0.191819	−	0.332240i	−0.945853	+	0.324595i	$0.894772\pi$
$312$		0			0
$313$	15.9183	−	27.5714i	0.899758	−	1.55843i	0.0719549	−	0.997408i	$-0.477076\pi$
$313$	15.9183	−	27.5714i	0.899758	−	1.55843i	0.827803	−	0.561019i	$-0.189590\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−14.0950	+	24.4133i	−0.791656	+	1.37119i	0.133285	+	0.991078i	$0.457447\pi$
$317$	−14.0950	+	24.4133i	−0.791656	+	1.37119i	−0.924941	+	0.380110i	$0.875886\pi$
$318$		0			0
$319$	3.46343	+	5.99884i	0.193915	+	0.335870i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	24.8367			1.38195
$324$		0			0
$325$	−0.161657	−	0.279998i	−0.00896713	−	0.0155315i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	10.3233	+	0.713865i	0.569143	+	0.0393567i
$330$		0			0
$331$	7.41116	−	12.8365i	0.407354	−	0.705559i	−0.587238	−	0.809414i	$-0.699785\pi$
$331$	7.41116	−	12.8365i	0.407354	−	0.705559i	0.994592	+	0.103856i	$0.0331181\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.323314			−0.0176645
$336$		0			0
$337$	20.1456			1.09740			0.548702	−	0.836018i	$-0.315122\pi$
$337$	20.1456			1.09740			0.548702	+	0.836018i	$0.315122\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.661657	−	1.14602i	0.0358307	−	0.0620607i
$342$		0			0
$343$	18.1244	+	3.80860i	0.978627	+	0.205645i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.9556	+	18.9756i	0.588126	+	1.01866i	0.994478	+	0.104948i	$0.0334676\pi$
$347$	10.9556	+	18.9756i	0.588126	+	1.01866i	−0.406351	+	0.913717i	$0.633199\pi$
$348$		0			0
$349$	−10.5578			−0.565146			−0.282573	−	0.959246i	$-0.591188\pi$
$349$	−10.5578			−0.565146			−0.282573	+	0.959246i	$0.591188\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−4.81613	−	8.34179i	−0.256337	−	0.443989i	0.708921	−	0.705288i	$-0.249182\pi$
$353$	−4.81613	−	8.34179i	−0.256337	−	0.443989i	−0.965258	+	0.261299i	$0.915849\pi$
$354$		0			0
$355$	2.33834	−	4.05013i	0.124106	−	0.214959i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−4.70608	+	8.15116i	−0.248377	+	0.430202i	−0.963076	−	0.269231i	$-0.913231\pi$
$359$	−4.70608	+	8.15116i	−0.248377	+	0.430202i	0.714699	+	0.699433i	$0.246564\pi$
$360$		0			0
$361$	1.67669	+	2.90410i	0.0882466	+	0.152848i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	3.36773			0.176275
$366$		0			0
$367$	−16.0728	−	27.8389i	−0.838994	−	1.45318i	−0.890736	−	0.454520i	$-0.849811\pi$
$367$	−16.0728	−	27.8389i	−0.838994	−	1.45318i	0.0517419	−	0.998660i	$-0.483523\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−18.5578	+	27.5589i	−0.963473	+	1.43079i
$372$		0			0
$373$	0.749507	−	1.29818i	0.0388080	−	0.0672174i	−0.845969	−	0.533232i	$-0.820977\pi$
$373$	0.749507	−	1.29818i	0.0388080	−	0.0672174i	0.884777	+	0.466015i	$0.154311\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.69238			−0.0871621
$378$		0			0
$379$	−27.3801			−1.40642			−0.703211	−	0.710981i	$-0.748251\pi$
$379$	−27.3801			−1.40642			−0.703211	+	0.710981i	$0.748251\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.63227	−	16.6836i	0.492186	−	0.852491i	−0.507774	−	0.861491i	$-0.669531\pi$
$383$	9.63227	−	16.6836i	0.492186	−	0.852491i	0.999960	+	0.00899958i	$0.00286469\pi$
$384$		0			0
$385$	1.53724	+	3.14564i	0.0783449	+	0.160316i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−12.3083	−	21.3186i	−0.624055	−	1.08089i	−0.988723	−	0.149757i	$-0.952151\pi$
$389$	−12.3083	−	21.3186i	−0.624055	−	1.08089i	0.364668	−	0.931138i	$-0.381183\pi$
$390$		0			0
$391$	22.8066			1.15338
$392$		0			0
$393$		0			0
$394$		0			0
$395$	5.25669	+	9.10485i	0.264493	+	0.458115i
$396$		0			0
$397$	6.22730	−	10.7860i	0.312539	−	0.541334i	−0.666372	−	0.745619i	$-0.732154\pi$
$397$	6.22730	−	10.7860i	0.312539	−	0.541334i	0.978911	+	0.204286i	$0.0654871\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	10.1901	−	17.6497i	0.508867	−	0.881384i	−0.491080	−	0.871115i	$-0.663398\pi$
$401$	10.1901	−	17.6497i	0.508867	−	0.881384i	0.999947	−	0.0102695i	$-0.00326896\pi$
$402$		0			0
$403$	0.161657	+	0.279998i	0.00805272	+	0.0139477i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.12995			−0.303850
$408$		0			0
$409$	7.69006	+	13.3196i	0.380249	+	0.658611i	0.991098	−	0.133137i	$-0.0425050\pi$
$409$	7.69006	+	13.3196i	0.380249	+	0.658611i	−0.610849	+	0.791747i	$0.709172\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−10.8223	+	16.0715i	−0.532532	+	0.790828i
$414$		0			0
$415$	−4.46276	+	7.72973i	−0.219068	+	0.379438i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−19.2645			−0.941134			−0.470567	−	0.882364i	$-0.655951\pi$
$419$	−19.2645			−0.941134			−0.470567	+	0.882364i	$0.655951\pi$
$420$		0			0
$421$	−5.13128			−0.250083			−0.125042	−	0.992151i	$-0.539906\pi$
$421$	−5.13128			−0.250083			−0.125042	+	0.992151i	$0.539906\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.13945	+	5.43768i	−0.152286	+	0.263766i
$426$		0			0
$427$	−7.80111	−	0.539453i	−0.377522	−	0.0261059i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.632268	−	1.09512i	−0.0304553	−	0.0527501i	0.850396	−	0.526143i	$-0.176362\pi$
$431$	−0.632268	−	1.09512i	−0.0304553	−	0.0527501i	−0.880851	+	0.473393i	$0.843029\pi$
$432$		0			0
$433$	8.96994			0.431068			0.215534	−	0.976496i	$-0.430851\pi$
$433$	8.96994			0.431068			0.215534	+	0.976496i	$0.430851\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.18387	−	12.4428i	−0.343651	−	0.595221i
$438$		0			0
$439$	−14.0212	+	24.2855i	−0.669196	+	1.15908i	0.308933	+	0.951084i	$0.400028\pi$
$439$	−14.0212	+	24.2855i	−0.669196	+	1.15908i	−0.978129	+	0.207998i	$0.933305\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−12.9112	+	22.3628i	−0.613428	+	1.06249i	0.377230	+	0.926120i	$0.376877\pi$
$443$	−12.9112	+	22.3628i	−0.613428	+	1.06249i	−0.990658	+	0.136369i	$0.956457\pi$
$444$		0			0
$445$	−6.94055	−	12.0214i	−0.329014	−	0.569869i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	39.2044			1.85017			0.925086	−	0.379759i	$-0.123993\pi$
$449$	39.2044			1.85017			0.925086	+	0.379759i	$0.123993\pi$
$450$		0			0
$451$	5.68221	+	9.84188i	0.267565	+	0.463436i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.853371	−	0.0590113i	−0.0400067	−	0.00276649i
$456$		0			0
$457$	−1.20608	+	2.08898i	−0.0564178	+	0.0977185i	−0.892855	−	0.450344i	$-0.851301\pi$
$457$	−1.20608	+	2.08898i	−0.0564178	+	0.0977185i	0.836437	+	0.548063i	$0.184635\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−29.0855			−1.35465			−0.677324	−	0.735685i	$-0.736860\pi$
$461$	−29.0855			−1.35465			−0.677324	+	0.735685i	$0.736860\pi$
$462$		0			0
$463$	−24.2345			−1.12627			−0.563136	−	0.826364i	$-0.690405\pi$
$463$	−24.2345			−1.12627			−0.563136	+	0.826364i	$0.690405\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	12.2789	−	21.2677i	0.568200	−	0.984151i	−0.428545	−	0.903521i	$-0.640973\pi$
$467$	12.2789	−	21.2677i	0.568200	−	0.984151i	0.996744	−	0.0806299i	$-0.0256932\pi$
$468$		0			0
$469$	−0.477791	+	0.709536i	−0.0220623	+	0.0327633i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.49282	−	6.04974i	−0.160600	−	0.278167i
$474$		0			0
$475$	3.95558			0.181495
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−1.73546	−	3.00591i	−0.0792954	−	0.137344i	0.823651	−	0.567097i	$-0.191934\pi$
$479$	−1.73546	−	3.00591i	−0.0792954	−	0.137344i	−0.902946	+	0.429754i	$0.858600\pi$
$480$		0			0
$481$	0.748839	−	1.29703i	0.0341441	−	0.0591394i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.80111	−	3.11961i	0.0817840	−	0.141654i
$486$		0			0
$487$	−16.3517	−	28.3220i	−0.740967	−	1.28339i	−0.952055	−	0.305926i	$-0.901034\pi$
$487$	−16.3517	−	28.3220i	−0.740967	−	1.28339i	0.211088	−	0.977467i	$-0.432299\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.26454			−0.0570677			−0.0285338	−	0.999593i	$-0.509084\pi$
$491$	−1.26454			−0.0570677			−0.0285338	+	0.999593i	$0.509084\pi$
$492$		0			0
$493$	16.4334	+	28.4634i	0.740122	+	1.28193i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.43271	−	11.1169i	−0.243690	−	0.498661i
$498$		0			0
$499$	−5.77890	+	10.0093i	−0.258699	+	0.448080i	−0.965894	−	0.258939i	$-0.916627\pi$
$499$	−5.77890	+	10.0093i	−0.258699	+	0.448080i	0.707195	+	0.707019i	$0.249960\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	−9.96994			−0.443657
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−13.5434	+	23.4579i	−0.600302	+	1.03975i	0.392473	+	0.919764i	$0.371620\pi$
$509$	−13.5434	+	23.4579i	−0.600302	+	1.03975i	−0.992775	+	0.119990i	$0.961714\pi$
$510$		0			0
$511$	4.97680	−	7.39072i	0.220161	−	0.326946i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−8.59503	−	14.8870i	−0.378742	−	0.656001i
$516$		0			0
$517$	5.17570			0.227627
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−8.58785	−	14.8746i	−0.376241	−	0.651668i	0.614271	−	0.789095i	$-0.289450\pi$
$521$	−8.58785	−	14.8746i	−0.376241	−	0.651668i	−0.990512	+	0.137427i	$0.956117\pi$
$522$		0			0
$523$	16.7939	−	29.0879i	0.734347	−	1.27193i	−0.220662	−	0.975350i	$-0.570822\pi$
$523$	16.7939	−	29.0879i	0.734347	−	1.27193i	0.955009	−	0.296576i	$-0.0958448\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.13945	−	5.43768i	0.136757	−	0.236869i
$528$		0			0
$529$	4.90332	+	8.49279i	0.213188	+	0.369252i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.77657			−0.120267
$534$		0			0
$535$	1.18387	+	2.05052i	0.0511830	+	0.0886516i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	9.17503	+	1.27502i	0.395197	+	0.0549189i
$540$		0			0
$541$	−4.38111	+	7.58830i	−0.188358	+	0.326246i	−0.944703	−	0.327927i	$-0.893650\pi$
$541$	−4.38111	+	7.58830i	−0.188358	+	0.326246i	0.756345	+	0.654173i	$0.226983\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.69105			−0.115272
$546$		0			0
$547$	12.6179			0.539503			0.269751	−	0.962930i	$-0.413058\pi$
$547$	12.6179			0.539503			0.269751	+	0.962930i	$0.413058\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	10.3527	−	17.9314i	0.441040	−	0.763904i
$552$		0			0
$553$	27.7495	+	1.91890i	1.18003	+	0.0816000i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−11.6466	−	20.1726i	−0.493483	−	0.854738i	0.506488	−	0.862247i	$-0.330943\pi$
$557$	−11.6466	−	20.1726i	−0.493483	−	0.854738i	−0.999972	+	0.00750834i	$0.997610\pi$
$558$		0			0
$559$	1.70674			0.0721875
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−22.5277	−	39.0192i	−0.949431	−	1.64446i	−0.746627	−	0.665243i	$-0.768328\pi$
$563$	−22.5277	−	39.0192i	−0.949431	−	1.64446i	−0.202804	−	0.979219i	$-0.565005\pi$
$564$		0			0
$565$	7.32331	−	12.6844i	0.308094	−	0.533635i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−15.2495	+	26.4129i	−0.639293	+	1.10729i	0.346296	+	0.938125i	$0.387439\pi$
$569$	−15.2495	+	26.4129i	−0.639293	+	1.10729i	−0.985588	+	0.169162i	$0.945894\pi$
$570$		0			0
$571$	10.0222	+	17.3590i	0.419416	+	0.726451i	0.995881	−	0.0906717i	$-0.0289014\pi$
$571$	10.0222	+	17.3590i	0.419416	+	0.726451i	−0.576464	+	0.817122i	$0.695568\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	3.63227			0.151476
$576$		0			0
$577$	−7.07282	−	12.2505i	−0.294445	−	0.509994i	0.680410	−	0.732831i	$-0.261802\pi$
$577$	−7.07282	−	12.2505i	−0.294445	−	0.509994i	−0.974856	+	0.222837i	$0.928468\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	10.3684	+	21.2168i	0.430154	+	0.880220i
$582$		0			0
$583$	−8.30895	+	14.3915i	−0.344122	+	0.596036i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−25.3945			−1.04814			−0.524071	−	0.851674i	$-0.675587\pi$
$587$	−25.3945			−1.04814			−0.524071	+	0.851674i	$0.675587\pi$
$588$		0			0
$589$	−3.95558			−0.162987
$590$		0			0
$591$		0			0
$592$		0			0
$593$	14.0206	−	24.2843i	0.575755	−	0.997237i	−0.420204	−	0.907430i	$-0.638041\pi$
$593$	14.0206	−	24.2843i	0.575755	−	0.997237i	0.995959	−	0.0898075i	$-0.0286252\pi$
$594$		0			0
$595$	7.29392	+	14.9255i	0.299022	+	0.611886i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−9.83669	−	17.0376i	−0.401916	−	0.696139i	0.592041	−	0.805908i	$-0.298322\pi$
$599$	−9.83669	−	17.0376i	−0.401916	−	0.696139i	−0.993957	+	0.109769i	$0.964989\pi$
$600$		0			0
$601$	−21.0424			−0.858339			−0.429170	−	0.903224i	$-0.641194\pi$
$601$	−21.0424			−0.858339			−0.429170	+	0.903224i	$0.641194\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.62442	−	8.00973i	−0.188009	−	0.325642i
$606$		0			0
$607$	−12.4406	+	21.5477i	−0.504946	+	0.874593i	0.495037	+	0.868872i	$0.335154\pi$
$607$	−12.4406	+	21.5477i	−0.504946	+	0.874593i	−0.999984	+	0.00572116i	$0.998179\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.632268	+	1.09512i	−0.0255788	+	0.0443038i
$612$		0			0
$613$	−8.84552	−	15.3209i	−0.357267	−	0.618805i	0.630236	−	0.776404i	$-0.282958\pi$
$613$	−8.84552	−	15.3209i	−0.357267	−	0.618805i	−0.987503	+	0.157599i	$0.949625\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	22.5865			0.909299			0.454649	−	0.890670i	$-0.349765\pi$
$617$	22.5865			0.909299			0.454649	+	0.890670i	$0.349765\pi$
$618$		0			0
$619$	−0.469943	−	0.813965i	−0.0188886	−	0.0327160i	0.856427	−	0.516269i	$-0.172679\pi$
$619$	−0.469943	−	0.813965i	−0.0188886	−	0.0327160i	−0.875315	+	0.483553i	$0.839346\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−36.6385	−	2.53358i	−1.46789	−	0.101506i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−29.0855			−1.15972
$630$		0			0
$631$	44.9980			1.79134			0.895672	−	0.444716i	$-0.146695\pi$
$631$	44.9980			1.79134			0.895672	+	0.444716i	$0.146695\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.79392	+	3.10717i	−0.0711897	+	0.123304i
$636$		0			0
$637$	−1.39061	+	1.78558i	−0.0550979	+	0.0707471i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−4.07381	−	7.05604i	−0.160906	−	0.278697i	0.774288	−	0.632833i	$-0.218108\pi$
$641$	−4.07381	−	7.05604i	−0.160906	−	0.278697i	−0.935194	+	0.354136i	$0.884775\pi$
$642$		0			0
$643$	−27.5878			−1.08796			−0.543979	−	0.839099i	$-0.683083\pi$
$643$	−27.5878			−1.08796			−0.543979	+	0.839099i	$0.683083\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−19.9618	−	34.5748i	−0.784778	−	1.35928i	−0.929131	−	0.369750i	$-0.879443\pi$
$647$	−19.9618	−	34.5748i	−0.784778	−	1.35928i	0.144353	−	0.989526i	$-0.453890\pi$
$648$		0			0
$649$	−4.84552	+	8.39269i	−0.190203	+	0.329442i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8.37393	+	14.5041i	−0.327697	+	0.567588i	−0.982054	−	0.188597i	$-0.939606\pi$
$653$	−8.37393	+	14.5041i	−0.327697	+	0.567588i	0.654357	+	0.756185i	$0.272939\pi$
$654$		0			0
$655$	−1.67669	−	2.90410i	−0.0655135	−	0.113473i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−27.6447			−1.07688			−0.538441	−	0.842663i	$-0.680987\pi$
$659$	−27.6447			−1.07688			−0.538441	+	0.842663i	$0.680987\pi$
$660$		0			0
$661$	−21.8589	−	37.8607i	−0.850213	−	1.47261i	−0.881016	−	0.473086i	$-0.843140\pi$
$661$	−21.8589	−	37.8607i	−0.850213	−	1.47261i	0.0308037	−	0.999525i	$-0.490193\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	5.84552	−	8.68080i	0.226680	−	0.336627i
$666$		0			0
$667$	9.50651	−	16.4658i	0.368094	−	0.637557i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3.91116			−0.150989
$672$		0			0
$673$	−17.1189			−0.659885			−0.329942	−	0.944001i	$-0.607029\pi$
$673$	−17.1189			−0.659885			−0.329942	+	0.944001i	$0.607029\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−18.2851	+	31.6707i	−0.702753	+	1.21720i	0.264743	+	0.964319i	$0.414713\pi$
$677$	−18.2851	+	31.6707i	−0.702753	+	1.21720i	−0.967496	+	0.252885i	$0.918621\pi$
$678$		0			0
$679$	−4.18453	−	8.56278i	−0.160588	−	0.328609i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	9.83049	+	17.0269i	0.376153	+	0.651517i	0.990499	−	0.137520i	$-0.0439132\pi$
$683$	9.83049	+	17.0269i	0.376153	+	0.651517i	−0.614346	+	0.789037i	$0.710580\pi$
$684$		0			0
$685$	−9.63227			−0.368030
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2.03006	−	3.51616i	−0.0773390	−	0.133955i
$690$		0			0
$691$	−12.1910	+	21.1155i	−0.463769	+	0.803272i	−0.999145	−	0.0413420i	$-0.986837\pi$
$691$	−12.1910	+	21.1155i	−0.463769	+	0.803272i	0.535376	+	0.844614i	$0.320170\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−10.5800	+	18.3251i	−0.401322	+	0.695111i
$696$		0			0
$697$	26.9611	+	46.6980i	1.02122	+	1.76881i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−19.6146			−0.740833			−0.370417	−	0.928866i	$-0.620785\pi$
$701$	−19.6146			−0.740833			−0.370417	+	0.928866i	$0.620785\pi$
$702$		0			0
$703$	9.16166	+	15.8685i	0.345538	+	0.598490i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−14.7335	+	21.8797i	−0.554110	+	0.822872i
$708$		0			0
$709$	20.3145	−	35.1857i	0.762926	−	1.32143i	−0.178410	−	0.983956i	$-0.557095\pi$
$709$	20.3145	−	35.1857i	0.762926	−	1.32143i	0.941336	−	0.337471i	$-0.109571\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.63227			−0.136029
$714$		0			0
$715$	−0.427846			−0.0160006
$716$		0			0
$717$		0			0
$718$		0			0
$719$	14.2345	−	24.6548i	0.530856	−	0.919470i	−0.468495	−	0.883466i	$-0.655204\pi$
$719$	14.2345	−	24.6548i	0.530856	−	0.919470i	0.999352	−	0.0360043i	$-0.0114630\pi$
$720$		0			0
$721$	−45.3723	−	3.13753i	−1.68975	−	0.116848i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.61724	+	4.53319i	0.0972018	+	0.168358i
$726$		0			0
$727$	−14.9523			−0.554549			−0.277275	−	0.960791i	$-0.589431\pi$
$727$	−14.9523			−0.554549			−0.277275	+	0.960791i	$0.589431\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−16.5728	−	28.7050i	−0.612968	−	1.06169i
$732$		0			0
$733$	7.92718	−	13.7303i	0.292797	−	0.507139i	−0.681673	−	0.731657i	$-0.738747\pi$
$733$	7.92718	−	13.7303i	0.292797	−	0.507139i	0.974470	+	0.224518i	$0.0720806\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.213923	+	0.370526i	−0.00787996	+	0.0136485i
$738$		0			0
$739$	−9.52122	−	16.4912i	−0.350244	−	0.606640i	0.636048	−	0.771649i	$-0.280568\pi$
$739$	−9.52122	−	16.4912i	−0.350244	−	0.606640i	−0.986292	+	0.165009i	$0.947235\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−42.5702			−1.56175			−0.780874	−	0.624688i	$-0.785226\pi$
$743$	−42.5702			−1.56175			−0.780874	+	0.624688i	$0.785226\pi$
$744$		0			0
$745$	3.00000	+	5.19615i	0.109911	+	0.190372i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	6.24951	+	0.432158i	0.228352	+	0.0157907i
$750$		0			0
$751$	10.1323	−	17.5496i	0.369732	−	0.640394i	−0.619792	−	0.784766i	$-0.712783\pi$
$751$	10.1323	−	17.5496i	0.369732	−	0.640394i	0.989523	+	0.144372i	$0.0461163\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	4.33768			0.157864
$756$		0			0
$757$	31.8510			1.15765			0.578823	−	0.815453i	$-0.303512\pi$
$757$	31.8510			1.15765			0.578823	+	0.815453i	$0.303512\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−3.38276	+	5.85911i	−0.122625	+	0.212393i	−0.920802	−	0.390030i	$-0.872465\pi$
$761$	−3.38276	+	5.85911i	−0.122625	+	0.212393i	0.798177	+	0.602423i	$0.205798\pi$
$762$		0			0
$763$	−3.97680	+	5.90569i	−0.143970	+	0.213800i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.18387	−	2.05052i	−0.0427469	−	0.0740399i
$768$		0			0
$769$	31.0424			1.11942			0.559710	−	0.828689i	$-0.310913\pi$
$769$	31.0424			1.11942			0.559710	+	0.828689i	$0.310913\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.08067	+	5.33588i	0.110804	+	0.191918i	0.916095	−	0.400962i	$-0.131324\pi$
$773$	3.08067	+	5.33588i	0.110804	+	0.191918i	−0.805291	+	0.592880i	$0.797991\pi$
$774$		0			0
$775$	0.500000	−	0.866025i	0.0179605	−	0.0311086i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	16.9850	−	29.4188i	0.608550	−	1.05404i
$780$		0			0
$781$	−3.09436	−	5.35959i	−0.110725	−	0.191781i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	10.5578			0.376824
$786$		0			0
$787$	1.94122	+	3.36229i	0.0691971	+	0.119853i	0.898548	−	0.438875i	$-0.144623\pi$
$787$	1.94122	+	3.36229i	0.0691971	+	0.119853i	−0.829351	+	0.558728i	$0.811290\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−17.0144	−	34.8163i	−0.604961	−	1.23793i
$792$		0			0
$793$	0.477791	−	0.827558i	0.0169669	−	0.0293875i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−15.0431			−0.532853			−0.266427	−	0.963855i	$-0.585843\pi$
$797$	−15.0431			−0.532853			−0.266427	+	0.963855i	$0.585843\pi$
$798$		0			0
$799$	24.5578			0.868792
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.22828	−	3.85950i	0.0786344	−	0.136199i
$804$		0			0
$805$	5.36773	−	7.97126i	0.189188	−	0.280950i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−17.8667	−	30.9461i	−0.628161	−	1.08801i	−0.987920	−	0.154962i	$-0.950474\pi$
$809$	−17.8667	−	30.9461i	−0.628161	−	1.08801i	0.359759	−	0.933045i	$-0.382859\pi$
$810$		0			0
$811$	28.6002			1.00429			0.502145	−	0.864783i	$-0.332544\pi$
$811$	28.6002			1.00429			0.502145	+	0.864783i	$0.332544\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−7.23448	−	12.5305i	−0.253413	−	0.438924i
$816$		0			0
$817$	−10.4406	+	18.0836i	−0.365269	+	0.632664i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−18.8818	+	32.7042i	−0.658978	+	1.14138i	0.321902	+	0.946773i	$0.395678\pi$
$821$	−18.8818	+	32.7042i	−0.658978	+	1.14138i	−0.980880	+	0.194611i	$0.937655\pi$
$822$		0			0
$823$	−2.92000	−	5.05759i	−0.101785	−	0.176296i	0.810635	−	0.585551i	$-0.199122\pi$
$823$	−2.92000	−	5.05759i	−0.101785	−	0.176296i	−0.912420	+	0.409255i	$0.865789\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	14.3801			0.500046			0.250023	−	0.968240i	$-0.419562\pi$
$827$	14.3801			0.500046			0.250023	+	0.968240i	$0.419562\pi$
$828$		0			0
$829$	−11.1979	−	19.3953i	−0.388919	−	0.673628i	0.603385	−	0.797450i	$-0.293818\pi$
$829$	−11.1979	−	19.3953i	−0.388919	−	0.673628i	−0.992304	+	0.123822i	$0.960485\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	43.5339	+	6.04974i	1.50836	+	0.209611i
$834$		0			0
$835$	−1.18387	+	2.05052i	−0.0409694	+	0.0709610i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	6.20773			0.214315			0.107157	−	0.994242i	$-0.465825\pi$
$839$	6.20773			0.214315			0.107157	+	0.994242i	$0.465825\pi$
$840$		0			0
$841$	−1.60024			−0.0551806
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−6.44773	+	11.1678i	−0.221809	+	0.384184i
$846$		0			0
$847$	−24.4118	−	1.68810i	−0.838800	−	0.0580037i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	8.41282	+	14.5714i	0.288388	+	0.499502i
$852$		0			0
$853$	−10.0431			−0.343869			−0.171934	−	0.985108i	$-0.555002\pi$
$853$	−10.0431			−0.343869			−0.171934	+	0.985108i	$0.555002\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	22.0506	+	38.1928i	0.753235	+	1.30464i	0.946247	+	0.323444i	$0.104841\pi$
$857$	22.0506	+	38.1928i	0.753235	+	1.30464i	−0.193013	+	0.981196i	$0.561826\pi$
$858$		0			0
$859$	18.0212	−	31.2137i	0.614876	−	1.06500i	−0.375530	−	0.926810i	$-0.622539\pi$
$859$	18.0212	−	31.2137i	0.614876	−	1.06500i	0.990406	−	0.138187i	$-0.0441274\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	14.4546	−	25.0361i	0.492040	−	0.852239i	−0.507918	−	0.861406i	$-0.669585\pi$
$863$	14.4546	−	25.0361i	0.492040	−	0.852239i	0.999958	+	0.00916698i	$0.00291798\pi$
$864$		0			0
$865$	1.95558	+	3.38717i	0.0664918	+	0.115167i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	13.9125			0.471949
$870$		0			0
$871$	−0.0522661	−	0.0905275i	−0.00177097	−	0.00306741i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.16166	+	2.37709i	0.0392712	+	0.0803603i
$876$		0			0
$877$	−12.2345	+	21.1907i	−0.413129	+	0.715560i	−0.995230	−	0.0975561i	$-0.968897\pi$
$877$	−12.2345	+	21.1907i	−0.413129	+	0.715560i	0.582101	+	0.813116i	$0.302231\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	7.11559			0.239730			0.119865	−	0.992790i	$-0.461754\pi$
$881$	7.11559			0.239730			0.119865	+	0.992790i	$0.461754\pi$
$882$		0			0
$883$	−55.6877			−1.87404			−0.937021	−	0.349274i	$-0.886428\pi$
$883$	−55.6877			−1.87404			−0.937021	+	0.349274i	$0.886428\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	6.19823	−	10.7356i	0.208116	−	0.360468i	−0.743005	−	0.669286i	$-0.766600\pi$
$887$	6.19823	−	10.7356i	0.208116	−	0.360468i	0.951121	+	0.308818i	$0.0999335\pi$
$888$		0			0
$889$	4.16785	+	8.52864i	0.139785	+	0.286041i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−7.73546	−	13.3982i	−0.258857	−	0.448354i
$894$		0			0
$895$	15.2044			0.508228
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.61724	−	4.53319i	−0.0872898	−	0.151190i
$900$		0			0
$901$	−39.4245	+	68.2853i	−1.31342	+	2.27491i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3.65448	−	6.32974i	0.121479	−	0.210408i
$906$		0			0
$907$	−0.683866	−	1.18449i	−0.0227074	−	0.0393304i	0.854448	−	0.519536i	$-0.173895\pi$
$907$	−0.683866	−	1.18449i	−0.0227074	−	0.0393304i	−0.877156	+	0.480206i	$0.840562\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	21.7034			0.719067			0.359533	−	0.933132i	$-0.382936\pi$
$911$	21.7034			0.719067			0.359533	+	0.933132i	$0.382936\pi$
$912$		0			0
$913$	5.90564	+	10.2289i	0.195448	+	0.338526i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−8.85105	−	0.612057i	−0.292287	−	0.0202119i
$918$		0			0
$919$	16.3367	−	28.2960i	0.538898	−	0.933398i	−0.460066	−	0.887885i	$-0.652174\pi$
$919$	16.3367	−	28.2960i	0.538898	−	0.933398i	0.998964	−	0.0455134i	$-0.0144924\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.51204			0.0497694
$924$		0			0
$925$	−4.63227			−0.152308
$926$		0			0
$927$		0			0
$928$		0			0
$929$	2.20509	−	3.81933i	0.0723466	−	0.125308i	−0.827583	−	0.561344i	$-0.810285\pi$
$929$	2.20509	−	3.81933i	0.0723466	−	0.125308i	0.899929	+	0.436036i	$0.143618\pi$
$930$		0			0
$931$	−10.4122	−	25.6568i	−0.341244	−	0.840868i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	4.15448	+	7.19576i	0.135866	+	0.235327i
$936$		0			0
$937$	5.83669			0.190676			0.0953382	−	0.995445i	$-0.469607\pi$
$937$	5.83669			0.190676			0.0953382	+	0.995445i	$0.469607\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	20.1306	+	34.8672i	0.656239	+	1.13664i	0.981582	+	0.191043i	$0.0611871\pi$
$941$	20.1306	+	34.8672i	0.656239	+	1.13664i	−0.325342	+	0.945596i	$0.605480\pi$
$942$		0			0
$943$	15.5967	−	27.0142i	0.507898	−	0.879705i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	12.6972	−	21.9923i	0.412605	−	0.714653i	−0.582569	−	0.812781i	$-0.697952\pi$
$947$	12.6972	−	21.9923i	0.412605	−	0.714653i	0.995174	+	0.0981287i	$0.0312857\pi$
$948$		0			0
$949$	0.544418	+	0.942960i	0.0176726	+	0.0306098i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	22.4690			0.727841			0.363920	−	0.931430i	$-0.381438\pi$
$953$	22.4690			0.727841			0.363920	+	0.931430i	$0.381438\pi$
$954$		0			0
$955$	13.6022	+	23.5597i	0.440157	+	0.762375i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−14.2345	+	21.1387i	−0.459655	+	0.682603i
$960$		0			0
$961$	15.0000	−	25.9808i	0.483871	−	0.838089i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−9.89680			−0.318589
$966$		0			0
$967$	−36.8634			−1.18545			−0.592724	−	0.805406i	$-0.701948\pi$
$967$	−36.8634			−1.18545			−0.592724	+	0.805406i	$0.701948\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	10.2645	−	17.7787i	0.329405	−	0.570546i	−0.652989	−	0.757367i	$-0.726485\pi$
$971$	10.2645	−	17.7787i	0.329405	−	0.570546i	0.982394	+	0.186822i	$0.0598187\pi$
$972$		0			0
$973$	24.5807	+	50.2992i	0.788020	+	1.61252i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.47846	−	2.56077i	−0.0473001	−	0.0819261i	0.841406	−	0.540403i	$-0.181728\pi$
$977$	−1.47846	−	2.56077i	−0.0473001	−	0.0819261i	−0.888706	+	0.458477i	$0.848395\pi$
$978$		0			0
$979$	−18.3691			−0.587078
$980$		0			0
$981$		0			0
$982$		0			0
$983$	3.49282	+	6.04974i	0.111404	+	0.192957i	0.916336	−	0.400409i	$-0.131132\pi$
$983$	3.49282	+	6.04974i	0.111404	+	0.192957i	−0.804933	+	0.593366i	$0.797799\pi$
$984$		0			0
$985$	12.1394	−	21.0261i	0.386795	−	0.669949i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−9.58718	+	16.6055i	−0.304855	+	0.528024i
$990$		0			0
$991$	27.0490	+	46.8502i	0.859238	+	1.48824i	0.872656	+	0.488335i	$0.162395\pi$
$991$	27.0490	+	46.8502i	0.859238	+	1.48824i	−0.0134179	+	0.999910i	$0.504271\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−8.33768			−0.264322
$996$		0			0
$997$	16.7550	+	29.0206i	0.530637	+	0.919091i	0.999361	+	0.0357458i	$0.0113807\pi$
$997$	16.7550	+	29.0206i	0.530637	+	0.919091i	−0.468724	+	0.883345i	$0.655286\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.s.h.541.2	yes	6
3.2	odd	2		1260.2.s.g.541.2	yes	6
7.2	even	3		8820.2.a.bn.1.2		3
7.4	even	3	inner	1260.2.s.h.361.2	yes	6
7.5	odd	6		8820.2.a.bp.1.2		3
21.2	odd	6		8820.2.a.bq.1.2		3
21.5	even	6		8820.2.a.bo.1.2		3
21.11	odd	6		1260.2.s.g.361.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.s.g.361.2	✓	6	21.11	odd	6
1260.2.s.g.541.2	yes	6	3.2	odd	2
1260.2.s.h.361.2	yes	6	7.4	even	3	inner
1260.2.s.h.541.2	yes	6	1.1	even	1	trivial
8820.2.a.bn.1.2		3	7.2	even	3
8820.2.a.bo.1.2		3	21.5	even	6
8820.2.a.bp.1.2		3	7.5	odd	6
8820.2.a.bq.1.2		3	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{5} +(-1.16166 - 2.37709i) q^{7} +(-0.661657 - 1.14602i) q^{11} +0.323314 q^{13} +(-3.13945 - 5.43768i) q^{17} +(-1.97779 + 3.42563i) q^{19} +(-1.81613 + 3.14564i) q^{23} +(-0.500000 - 0.866025i) q^{25} -5.23448 q^{29} +(0.500000 + 0.866025i) q^{31} +(-2.63945 - 0.182520i) q^{35} +(2.31613 - 4.01166i) q^{37} -8.58785 q^{41} +5.27890 q^{43} +(-1.95558 + 3.38717i) q^{47} +(-4.30111 + 5.52273i) q^{49} +(-6.27890 - 10.8754i) q^{53} -1.32331 q^{55} +(-3.66166 - 6.34218i) q^{59} +(1.47779 - 2.55961i) q^{61} +(0.161657 - 0.279998i) q^{65} +(-0.161657 - 0.279998i) q^{67} +4.67669 q^{71} +(1.68387 + 2.91654i) q^{73} +(-1.95558 + 2.90410i) q^{77} +(-5.25669 + 9.10485i) q^{79} -8.92552 q^{83} -6.27890 q^{85} +(6.94055 - 12.0214i) q^{89} +(-0.375580 - 0.768547i) q^{91} +(1.97779 + 3.42563i) q^{95} +3.60221 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} - q^{7} + 2 q^{11} - 10 q^{13} - 2 q^{17} - q^{19} - 6 q^{23} - 3 q^{25} + 24 q^{29} + 3 q^{31} + q^{35} + 9 q^{37} - 20 q^{41} - 2 q^{43} + 10 q^{47} - 3 q^{49} - 4 q^{53} + 4 q^{55} - 16 q^{59}+ \cdots - 24 q^{97}+O(q^{100}) \) 6 * q + 3 * q^5 - q^7 + 2 * q^11 - 10 * q^13 - 2 * q^17 - q^19 - 6 * q^23 - 3 * q^25 + 24 * q^29 + 3 * q^31 + q^35 + 9 * q^37 - 20 * q^41 - 2 * q^43 + 10 * q^47 - 3 * q^49 - 4 * q^53 + 4 * q^55 - 16 * q^59 - 2 * q^61 - 5 * q^65 + 5 * q^67 + 40 * q^71 + 15 * q^73 + 10 * q^77 + 13 * q^79 + 4 * q^83 - 4 * q^85 + 2 * q^89 - 37 * q^91 + q^95 - 24 * q^97

Introduction

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