LMFDB - Embedded newform 2772.2.s.e.793.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2772,2,Mod(793,2772)] 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("2772.793"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2772, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2772 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2772.s (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,0,-2,0,2,0,0,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$22.1345314403$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1783323.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 $ x^6 - x^5 + 5x^4 - 2x^3 + 19x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 308)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			793.3
Root			$1.09935 - 1.90412i$ of defining polynomial
Character	$\chi$	$=$	2772.793
Dual form			2772.2.s.e.2377.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.599346 - 1.03810i) q^{5} +(-2.43359 + 1.03810i) q^{7} +(0.500000 + 0.866025i) q^{11} +0.834243 q^{13} +(-2.01647 - 3.49262i) q^{17} +(3.38092 - 5.85592i) q^{19} +(-0.0466721 + 0.0808384i) q^{23} +(1.78157 + 3.08577i) q^{25} -3.46980 q^{29} +(-1.29804 - 2.24827i) q^{31} +(-0.380915 + 3.14848i) q^{35} +(-5.19869 + 9.00440i) q^{37} -7.62901 q^{41} +0.894653 q^{43} +(-0.453328 + 0.785187i) q^{47} +(4.84471 - 5.05260i) q^{49} +(-1.58288 - 2.74163i) q^{53} +1.19869 q^{55} +(-6.31450 - 10.9370i) q^{59} +(5.03293 - 8.71730i) q^{61} +(0.500000 - 0.866025i) q^{65} +(-4.23163 - 7.32939i) q^{67} +13.7673 q^{71} +(-6.58561 - 11.4066i) q^{73} +(-2.11581 - 1.58850i) q^{77} +(7.16521 - 12.4105i) q^{79} +4.69596 q^{83} -4.83424 q^{85} +(-7.29804 + 12.6406i) q^{89} +(-2.03020 + 0.866025i) q^{91} +(-4.05267 - 7.01944i) q^{95} -12.9001 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{5} + 2 q^{7} + 3 q^{11} - 6 q^{13} - q^{17} + 9 q^{19} + 5 q^{25} - 10 q^{29} + 9 q^{31} + 9 q^{35} - 20 q^{37} + 10 q^{41} + 16 q^{43} - 3 q^{47} + 12 q^{49} - 15 q^{53} - 4 q^{55} - 10 q^{59}+ \cdots - 22 q^{97}+O(q^{100}) $ 6 * q - 2 * q^5 + 2 * q^7 + 3 * q^11 - 6 * q^13 - q^17 + 9 * q^19 + 5 * q^25 - 10 * q^29 + 9 * q^31 + 9 * q^35 - 20 * q^37 + 10 * q^41 + 16 * q^43 - 3 * q^47 + 12 * q^49 - 15 * q^53 - 4 * q^55 - 10 * q^59 + 8 * q^61 + 3 * q^65 + 8 * q^67 - 6 * q^71 - 12 * q^73 + 4 * q^77 - 7 * q^79 + 50 * q^83 - 18 * q^85 - 27 * q^89 - 23 * q^91 - 19 * q^95 - 22 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2772\mathbb{Z}\right)^\times$.

$n$	$1387$	$1541$	$1585$	$2521$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.599346	−	1.03810i	0.268036	−	0.464251i	−0.700319	−	0.713830i	$-0.746959\pi$
$5$	0.599346	−	1.03810i	0.268036	−	0.464251i	0.968354	+	0.249579i	$0.0802922\pi$
$6$		0			0
$7$	−2.43359	+	1.03810i	−0.919810	+	0.392364i
$7$	−2.43359	+	1.03810i	−0.919810	+	0.392364i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$		0			0
$13$	0.834243			0.231377			0.115689	−	0.993286i	$-0.463092\pi$
$13$	0.834243			0.231377			0.115689	+	0.993286i	$0.463092\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.01647	−	3.49262i	−0.489065	−	0.847086i	0.510856	−	0.859666i	$-0.329329\pi$
$17$	−2.01647	−	3.49262i	−0.489065	−	0.847086i	−0.999921	+	0.0125808i	$0.995995\pi$
$18$		0			0
$19$	3.38092	−	5.85592i	0.775635	−	1.34344i	−0.158802	−	0.987311i	$-0.550763\pi$
$19$	3.38092	−	5.85592i	0.775635	−	1.34344i	0.934437	−	0.356129i	$-0.115904\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.0466721	+	0.0808384i	−0.00973180	+	0.0168560i	−0.870850	−	0.491548i	$-0.836431\pi$
$23$	−0.0466721	+	0.0808384i	−0.00973180	+	0.0168560i	0.861118	+	0.508404i	$0.169764\pi$
$24$		0			0
$25$	1.78157	+	3.08577i	0.356314	+	0.617154i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.46980			−0.644325			−0.322162	−	0.946684i	$-0.604410\pi$
$29$	−3.46980			−0.644325			−0.322162	+	0.946684i	$0.604410\pi$
$30$		0			0
$31$	−1.29804	−	2.24827i	−0.233134	−	0.403800i	0.725595	−	0.688123i	$-0.241565\pi$
$31$	−1.29804	−	2.24827i	−0.233134	−	0.403800i	−0.958729	+	0.284322i	$0.908232\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.380915	+	3.14848i	−0.0643864	+	0.532190i
$36$		0			0
$37$	−5.19869	+	9.00440i	−0.854660	+	1.48031i	0.0223009	+	0.999751i	$0.492901\pi$
$37$	−5.19869	+	9.00440i	−0.854660	+	1.48031i	−0.876960	+	0.480563i	$0.840433\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−7.62901			−1.19145			−0.595725	−	0.803188i	$-0.703135\pi$
$41$	−7.62901			−1.19145			−0.595725	+	0.803188i	$0.703135\pi$
$42$		0			0
$43$	0.894653			0.136433			0.0682166	−	0.997671i	$-0.478269\pi$
$43$	0.894653			0.136433			0.0682166	+	0.997671i	$0.478269\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.453328	+	0.785187i	−0.0661247	+	0.114531i	−0.897192	−	0.441640i	$-0.854397\pi$
$47$	−0.453328	+	0.785187i	−0.0661247	+	0.114531i	0.831068	+	0.556171i	$0.187730\pi$
$48$		0			0
$49$	4.84471	−	5.05260i	0.692101	−	0.721800i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.58288	−	2.74163i	−0.217425	−	0.376591i	0.736595	−	0.676334i	$-0.236432\pi$
$53$	−1.58288	−	2.74163i	−0.217425	−	0.376591i	−0.954020	+	0.299743i	$0.903099\pi$
$54$		0			0
$55$	1.19869			0.161631
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.31450	−	10.9370i	−0.822078	−	1.42388i	−0.904132	−	0.427254i	$-0.859481\pi$
$59$	−6.31450	−	10.9370i	−0.822078	−	1.42388i	0.0820534	−	0.996628i	$-0.473852\pi$
$60$		0			0
$61$	5.03293	−	8.71730i	0.644401	−	1.11614i	−0.340038	−	0.940412i	$-0.610440\pi$
$61$	5.03293	−	8.71730i	0.644401	−	1.11614i	0.984439	−	0.175724i	$-0.0562266\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$		0			0
$67$	−4.23163	−	7.32939i	−0.516975	−	0.895428i	−0.999806	−	0.0197137i	$-0.993725\pi$
$67$	−4.23163	−	7.32939i	−0.516975	−	0.895428i	0.482830	−	0.875714i	$-0.339609\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	13.7673			1.63388			0.816938	−	0.576725i	$-0.195670\pi$
$71$	13.7673			1.63388			0.816938	+	0.576725i	$0.195670\pi$
$72$		0			0
$73$	−6.58561	−	11.4066i	−0.770787	−	1.33504i	−0.937132	−	0.348975i	$-0.886530\pi$
$73$	−6.58561	−	11.4066i	−0.770787	−	1.33504i	0.166345	−	0.986068i	$-0.446803\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.11581	−	1.58850i	−0.241119	−	0.181027i
$78$		0			0
$79$	7.16521	−	12.4105i	0.806150	−	1.39629i	−0.109363	−	0.994002i	$-0.534881\pi$
$79$	7.16521	−	12.4105i	0.806150	−	1.39629i	0.915512	−	0.402290i	$-0.131786\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.69596			0.515449			0.257724	−	0.966218i	$-0.417027\pi$
$83$	4.69596			0.515449			0.257724	+	0.966218i	$0.417027\pi$
$84$		0			0
$85$	−4.83424			−0.524347
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−7.29804	+	12.6406i	−0.773590	+	1.33990i	0.161993	+	0.986792i	$0.448208\pi$
$89$	−7.29804	+	12.6406i	−0.773590	+	1.33990i	−0.935583	+	0.353106i	$0.885126\pi$
$90$		0			0
$91$	−2.03020	+	0.866025i	−0.212823	+	0.0907841i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.05267	−	7.01944i	−0.415796	−	0.720179i
$96$		0			0
$97$	−12.9001			−1.30981			−0.654904	−	0.755712i	$-0.727291\pi$
$97$	−12.9001			−1.30981			−0.654904	+	0.755712i	$0.727291\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.11908	+	3.67036i	0.210857	+	0.365215i	0.951983	−	0.306151i	$-0.0990413\pi$
$101$	2.11908	+	3.67036i	0.210857	+	0.365215i	−0.741126	+	0.671366i	$0.765708\pi$
$102$		0			0
$103$	5.51647	−	9.55480i	0.543554	−	0.941463i	−0.455143	−	0.890418i	$-0.650412\pi$
$103$	5.51647	−	9.55480i	0.543554	−	0.941463i	0.998696	−	0.0510441i	$-0.0162549\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.328242	−	0.568531i	0.0317323	−	0.0549620i	−0.849723	−	0.527229i	$-0.823231\pi$
$107$	0.328242	−	0.568531i	0.0317323	−	0.0549620i	0.881455	+	0.472267i	$0.156564\pi$
$108$		0			0
$109$	−1.16248	−	2.01348i	−0.111346	−	0.192857i	0.804967	−	0.593319i	$-0.202183\pi$
$109$	−1.16248	−	2.01348i	−0.111346	−	0.192857i	−0.916313	+	0.400463i	$0.868849\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−19.7673			−1.85955			−0.929775	−	0.368128i	$-0.879999\pi$
$113$	−19.7673			−1.85955			−0.929775	+	0.368128i	$0.879999\pi$
$114$		0			0
$115$	0.0559454	+	0.0969003i	0.00521694	+	0.00903600i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	8.53293	+	6.40632i	0.782213	+	0.587266i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.2646			0.918090
$126$		0			0
$127$	−14.7738			−1.31097			−0.655483	−	0.755210i	$-0.727535\pi$
$127$	−14.7738			−1.31097			−0.655483	+	0.755210i	$0.727535\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.60208	−	7.97103i	0.402085	−	0.696432i	−0.591892	−	0.806017i	$-0.701619\pi$
$131$	4.60208	−	7.97103i	0.402085	−	0.696432i	0.993977	+	0.109585i	$0.0349522\pi$
$132$		0			0
$133$	−2.14875	+	17.7606i	−0.186320	+	1.54004i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.1487	−	17.5781i	−0.867066	−	1.50180i	−0.864981	−	0.501805i	$-0.832670\pi$
$137$	−10.1487	−	17.5781i	−0.867066	−	1.50180i	−0.00208495	−	0.999998i	$-0.500664\pi$
$138$		0			0
$139$	−6.27110			−0.531908			−0.265954	−	0.963986i	$-0.585687\pi$
$139$	−6.27110			−0.531908			−0.265954	+	0.963986i	$0.585687\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.417122	+	0.722476i	0.0348815	+	0.0604165i
$144$		0			0
$145$	−2.07961	+	3.60198i	−0.172702	+	0.299129i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.60535	+	6.24464i	−0.295362	+	0.511581i	−0.975069	−	0.221902i	$-0.928773\pi$
$149$	−3.60535	+	6.24464i	−0.295362	+	0.511581i	0.679707	+	0.733483i	$0.262107\pi$
$150$		0			0
$151$	2.01974	+	3.49829i	0.164364	+	0.284687i	0.936429	−	0.350856i	$-0.114109\pi$
$151$	2.01974	+	3.49829i	0.164364	+	0.284687i	−0.772065	+	0.635543i	$0.780776\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.11189			−0.249953
$156$		0			0
$157$	2.79204	+	4.83595i	0.222829	+	0.385951i	0.955666	−	0.294454i	$-0.0951376\pi$
$157$	2.79204	+	4.83595i	0.222829	+	0.385951i	−0.732837	+	0.680404i	$0.761804\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.0296625	−	0.245178i	0.00233774	−	0.0193227i
$162$		0			0
$163$	4.50000	−	7.79423i	0.352467	−	0.610491i	−0.634214	−	0.773158i	$-0.718676\pi$
$163$	4.50000	−	7.79423i	0.352467	−	0.610491i	0.986681	+	0.162667i	$0.0520095\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−15.6015			−1.20728			−0.603641	−	0.797256i	$-0.706284\pi$
$167$	−15.6015			−1.20728			−0.603641	+	0.797256i	$0.706284\pi$
$168$		0			0
$169$	−12.3040			−0.946464
$170$		0			0
$171$		0			0
$172$		0			0
$173$	11.3776	−	19.7067i	0.865026	−	1.49827i	−0.00199494	−	0.999998i	$-0.500635\pi$
$173$	11.3776	−	19.7067i	0.865026	−	1.49827i	0.867021	−	0.498271i	$-0.166032\pi$
$174$		0			0
$175$	−7.53894	−	5.66005i	−0.569890	−	0.427860i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.58561	−	2.74635i	−0.118514	−	0.205272i	0.800665	−	0.599112i	$-0.204480\pi$
$179$	−1.58561	−	2.74635i	−0.118514	−	0.205272i	−0.919179	+	0.393840i	$0.871146\pi$
$180$		0			0
$181$	−5.56860			−0.413911			−0.206955	−	0.978350i	$-0.566355\pi$
$181$	−5.56860			−0.413911			−0.206955	+	0.978350i	$0.566355\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	6.23163	+	10.7935i	0.458158	+	0.793553i
$186$		0			0
$187$	2.01647	−	3.49262i	0.147459	−	0.255406i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.26183	+	9.11376i	−0.380733	+	0.659448i	−0.991167	−	0.132618i	$-0.957662\pi$
$191$	−5.26183	+	9.11376i	−0.380733	+	0.659448i	0.610434	+	0.792067i	$0.290995\pi$
$192$		0			0
$193$	−0.510466	−	0.884153i	−0.0367441	−	0.0636427i	0.847069	−	0.531484i	$-0.178365\pi$
$193$	−0.510466	−	0.884153i	−0.0367441	−	0.0636427i	−0.883813	+	0.467841i	$0.845032\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	22.2910			1.58816			0.794082	−	0.607810i	$-0.207952\pi$
$197$	22.2910			1.58816			0.794082	+	0.607810i	$0.207952\pi$
$198$		0			0
$199$	−6.63501	−	11.4922i	−0.470343	−	0.814659i	0.529081	−	0.848571i	$-0.322537\pi$
$199$	−6.63501	−	11.4922i	−0.470343	−	0.814659i	−0.999425	+	0.0339125i	$0.989203\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	8.44405	−	3.60198i	0.592656	−	0.252810i
$204$		0			0
$205$	−4.57241	+	7.91965i	−0.319351	+	0.553132i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.76183			0.467726
$210$		0			0
$211$	−9.12628			−0.628279			−0.314139	−	0.949377i	$-0.601716\pi$
$211$	−9.12628			−0.628279			−0.314139	+	0.949377i	$0.601716\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.536206	−	0.928737i	0.0365690	−	0.0633393i
$216$		0			0
$217$	5.49281	+	4.12387i	0.372876	+	0.279946i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.68222	−	2.91370i	−0.113159	−	0.195997i
$222$		0			0
$223$	−0.139366			−0.00933265			−0.00466632	−	0.999989i	$-0.501485\pi$
$223$	−0.139366			−0.00933265			−0.00466632	+	0.999989i	$0.501485\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	12.5993	+	21.8227i	0.836248	+	1.44842i	0.893010	+	0.450036i	$0.148589\pi$
$227$	12.5993	+	21.8227i	0.836248	+	1.44842i	−0.0567624	+	0.998388i	$0.518078\pi$
$228$		0			0
$229$	−0.605347	+	1.04849i	−0.0400025	+	0.0692863i	−0.885333	−	0.464957i	$-0.846070\pi$
$229$	−0.605347	+	1.04849i	−0.0400025	+	0.0692863i	0.845331	+	0.534243i	$0.179403\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.66576	−	9.81338i	0.371176	−	0.642896i	−0.618571	−	0.785729i	$-0.712288\pi$
$233$	5.66576	−	9.81338i	0.371176	−	0.642896i	0.989747	+	0.142833i	$0.0456213\pi$
$234$		0			0
$235$	0.543400	+	0.941197i	0.0354475	+	0.0613969i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	11.6805			0.755548			0.377774	−	0.925898i	$-0.376690\pi$
$239$	11.6805			0.755548			0.377774	+	0.925898i	$0.376690\pi$
$240$		0			0
$241$	4.15529	+	7.19718i	0.267666	+	0.463611i	0.968259	−	0.249950i	$-0.0804144\pi$
$241$	4.15529	+	7.19718i	0.267666	+	0.463611i	−0.700593	+	0.713561i	$0.747081\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.34144	−	8.05753i	−0.149589	−	0.514777i
$246$		0			0
$247$	2.82051	−	4.88526i	0.179464	−	0.310842i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2.03293			−0.128318			−0.0641588	−	0.997940i	$-0.520436\pi$
$251$	−2.03293			−0.128318			−0.0641588	+	0.997940i	$0.520436\pi$
$252$		0			0
$253$	−0.0933442			−0.00586850
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−11.8337	+	20.4966i	−0.738166	+	1.27854i	0.215154	+	0.976580i	$0.430975\pi$
$257$	−11.8337	+	20.4966i	−0.738166	+	1.27854i	−0.953320	+	0.301961i	$0.902359\pi$
$258$		0			0
$259$	3.30404	−	27.3097i	0.205303	−	1.69695i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−7.11254	−	12.3193i	−0.438578	−	0.759639i	0.559002	−	0.829166i	$-0.311184\pi$
$263$	−7.11254	−	12.3193i	−0.438578	−	0.759639i	−0.997580	+	0.0695268i	$0.977851\pi$
$264$		0			0
$265$	−3.79476			−0.233111
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−5.96652	−	10.3343i	−0.363785	−	0.630095i	0.624795	−	0.780789i	$-0.285182\pi$
$269$	−5.96652	−	10.3343i	−0.363785	−	0.630095i	−0.988580	+	0.150694i	$0.951849\pi$
$270$		0			0
$271$	13.0357	−	22.5784i	0.791860	−	1.37154i	−0.132954	−	0.991122i	$-0.542446\pi$
$271$	13.0357	−	22.5784i	0.791860	−	1.37154i	0.924814	−	0.380420i	$-0.124221\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.78157	+	3.08577i	−0.107433	+	0.186079i
$276$		0			0
$277$	4.87764	+	8.44833i	0.293069	+	0.507611i	0.974534	−	0.224240i	$-0.0719900\pi$
$277$	4.87764	+	8.44833i	0.293069	+	0.507611i	−0.681465	+	0.731851i	$0.738657\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	25.1437			1.49995			0.749975	−	0.661466i	$-0.230066\pi$
$281$	25.1437			1.49995			0.749975	+	0.661466i	$0.230066\pi$
$282$		0			0
$283$	9.07961	+	15.7263i	0.539727	+	0.934834i	0.998918	+	0.0464967i	$0.0148057\pi$
$283$	9.07961	+	15.7263i	0.539727	+	0.934834i	−0.459192	+	0.888337i	$0.651861\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	18.5659	−	7.91965i	1.09591	−	0.467482i
$288$		0			0
$289$	0.367720	−	0.636910i	0.0216306	−	0.0374653i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−12.0604			−0.704577			−0.352288	−	0.935892i	$-0.614596\pi$
$293$	−12.0604			−0.704577			−0.352288	+	0.935892i	$0.614596\pi$
$294$		0			0
$295$	−15.1383			−0.881385
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.0389359	+	0.0674389i	−0.00225172	+	0.00390009i
$300$		0			0
$301$	−2.17722	+	0.928737i	−0.125493	+	0.0535315i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−6.03293	−	10.4493i	−0.345445	−	0.598328i
$306$		0			0
$307$	8.20415			0.468236			0.234118	−	0.972208i	$-0.424780\pi$
$307$	8.20415			0.468236			0.234118	+	0.972208i	$0.424780\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.93086	−	8.54050i	−0.279603	−	0.484287i	0.691683	−	0.722201i	$-0.256870\pi$
$311$	−4.93086	−	8.54050i	−0.279603	−	0.484287i	−0.971286	+	0.237914i	$0.923536\pi$
$312$		0			0
$313$	0.619085	−	1.07229i	0.0349927	−	0.0606092i	−0.847999	−	0.529998i	$-0.822193\pi$
$313$	0.619085	−	1.07229i	0.0349927	−	0.0606092i	0.882991	+	0.469389i	$0.155526\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−15.1422	+	26.2271i	−0.850471	+	1.47306i	0.0303131	+	0.999540i	$0.490350\pi$
$317$	−15.1422	+	26.2271i	−0.850471	+	1.47306i	−0.880784	+	0.473518i	$0.842984\pi$
$318$		0			0
$319$	−1.73490	−	3.00493i	−0.0971356	−	0.168244i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−27.2700			−1.51734
$324$		0			0
$325$	1.48626	+	2.57428i	0.0824430	+	0.142795i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.288113	−	2.38142i	0.0158842	−	0.131292i
$330$		0			0
$331$	−12.6712	+	21.9472i	−0.696473	+	1.20633i	0.273209	+	0.961955i	$0.411915\pi$
$331$	−12.6712	+	21.9472i	−0.696473	+	1.20633i	−0.969682	+	0.244372i	$0.921418\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−10.1448			−0.554271
$336$		0			0
$337$	−5.35899			−0.291923			−0.145961	−	0.989290i	$-0.546628\pi$
$337$	−5.35899			−0.291923			−0.145961	+	0.989290i	$0.546628\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.29804	−	2.24827i	0.0702926	−	0.121750i
$342$		0			0
$343$	−6.54494	+	17.3252i	−0.353393	+	0.935475i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.73490	+	11.6652i	0.361548	+	0.626220i	0.988216	−	0.153067i	$-0.0489149\pi$
$347$	6.73490	+	11.6652i	0.361548	+	0.626220i	−0.626668	+	0.779287i	$0.715582\pi$
$348$		0			0
$349$	26.5477			1.42106			0.710532	−	0.703665i	$-0.248454\pi$
$349$	26.5477			1.42106			0.710532	+	0.703665i	$0.248454\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	9.72116	+	16.8375i	0.517405	+	0.896172i	0.999796	+	0.0202157i	$0.00643530\pi$
$353$	9.72116	+	16.8375i	0.517405	+	0.896172i	−0.482391	+	0.875956i	$0.660231\pi$
$354$		0			0
$355$	8.25136	−	14.2918i	0.437937	−	0.758529i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	16.6482	−	28.8355i	0.878659	−	1.52188i	0.0258451	−	0.999666i	$-0.491772\pi$
$359$	16.6482	−	28.8355i	0.878659	−	1.52188i	0.852814	−	0.522215i	$-0.174894\pi$
$360$		0			0
$361$	−13.3612	−	23.1422i	−0.703220	−	1.21801i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−15.7882			−0.826393
$366$		0			0
$367$	3.16521	+	5.48231i	0.165223	+	0.286174i	0.936734	−	0.350041i	$-0.113832\pi$
$367$	3.16521	+	5.48231i	0.165223	+	0.286174i	−0.771512	+	0.636215i	$0.780499\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	6.69815	+	5.02881i	0.347751	+	0.261083i
$372$		0			0
$373$	−2.96325	+	5.13250i	−0.153431	+	0.265751i	−0.932487	−	0.361204i	$-0.882366\pi$
$373$	−2.96325	+	5.13250i	−0.153431	+	0.265751i	0.779055	+	0.626955i	$0.215699\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.89465			−0.149082
$378$		0			0
$379$	−6.11189			−0.313947			−0.156973	−	0.987603i	$-0.550174\pi$
$379$	−6.11189			−0.313947			−0.156973	+	0.987603i	$0.550174\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−10.1515	+	17.5829i	−0.518716	+	0.898443i	0.481047	+	0.876695i	$0.340257\pi$
$383$	−10.1515	+	17.5829i	−0.518716	+	0.898443i	−0.999763	+	0.0217482i	$0.993077\pi$
$384$		0			0
$385$	−2.91712	+	1.24436i	−0.148670	+	0.0634183i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.56914	−	14.8422i	−0.434473	−	0.752529i	0.562780	−	0.826607i	$-0.309732\pi$
$389$	−8.56914	−	14.8422i	−0.434473	−	0.752529i	−0.997252	+	0.0740781i	$0.976399\pi$
$390$		0			0
$391$	0.376451			0.0190379
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−8.58888	−	14.8764i	−0.432153	−	0.748512i
$396$		0			0
$397$	8.13828	−	14.0959i	0.408449	−	0.707454i	−0.586267	−	0.810118i	$-0.699403\pi$
$397$	8.13828	−	14.0959i	0.408449	−	0.707454i	0.994716	+	0.102664i	$0.0327366\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.58561	−	6.21046i	0.179057	−	0.310135i	−0.762501	−	0.646987i	$-0.776029\pi$
$401$	3.58561	−	6.21046i	0.179057	−	0.310135i	0.941558	+	0.336852i	$0.109362\pi$
$402$		0			0
$403$	−1.08288	−	1.87560i	−0.0539420	−	0.0934303i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−10.3974			−0.515379
$408$		0			0
$409$	3.11135	+	5.38901i	0.153846	+	0.266470i	0.932638	−	0.360813i	$-0.117501\pi$
$409$	3.11135	+	5.38901i	0.153846	+	0.266470i	−0.778792	+	0.627282i	$0.784167\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	26.7206	+	20.0612i	1.31484	+	0.987147i
$414$		0			0
$415$	2.81450	−	4.87486i	0.138159	−	0.239298i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−16.0473			−0.783963			−0.391981	−	0.919973i	$-0.628210\pi$
$419$	−16.0473			−0.783963			−0.391981	+	0.919973i	$0.628210\pi$
$420$		0			0
$421$	−9.49619			−0.462816			−0.231408	−	0.972857i	$-0.574333\pi$
$421$	−9.49619			−0.462816			−0.231408	+	0.972857i	$0.574333\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	7.18495	−	12.4447i	0.348521	−	0.603657i
$426$		0			0
$427$	−3.19869	+	26.4390i	−0.154796	+	1.27947i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	17.4540	+	30.2312i	0.840729	+	1.45618i	0.889280	+	0.457364i	$0.151206\pi$
$431$	17.4540	+	30.2312i	0.840729	+	1.45618i	−0.0485511	+	0.998821i	$0.515460\pi$
$432$		0			0
$433$	14.8737			0.714785			0.357393	−	0.933954i	$-0.383666\pi$
$433$	14.8737			0.714785			0.357393	+	0.933954i	$0.383666\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.315589	+	0.546616i	0.0150967	+	0.0261482i
$438$		0			0
$439$	12.2574	−	21.2304i	0.585012	−	1.01327i	−0.409862	−	0.912148i	$-0.634423\pi$
$439$	12.2574	−	21.2304i	0.585012	−	1.01327i	0.994874	−	0.101123i	$-0.0322436\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.33370	−	2.31004i	0.0633660	−	0.109753i	−0.832602	−	0.553872i	$-0.813150\pi$
$443$	1.33370	−	2.31004i	0.0633660	−	0.109753i	0.895968	+	0.444119i	$0.146483\pi$
$444$		0			0
$445$	8.74809	+	15.1521i	0.414699	+	0.718280i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	9.60808			0.453433			0.226717	−	0.973961i	$-0.427201\pi$
$449$	9.60808			0.453433			0.226717	+	0.973961i	$0.427201\pi$
$450$		0			0
$451$	−3.81450	−	6.60691i	−0.179618	−	0.311107i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.317776	+	2.62660i	−0.0148976	+	0.123137i
$456$		0			0
$457$	11.0823	−	19.1952i	0.518410	−	0.897912i	−0.481361	−	0.876522i	$-0.659858\pi$
$457$	11.0823	−	19.1952i	0.518410	−	0.897912i	0.999771	−	0.0213899i	$-0.00680914\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−14.9725			−0.697340			−0.348670	−	0.937246i	$-0.613367\pi$
$461$	−14.9725			−0.697340			−0.348670	+	0.937246i	$0.613367\pi$
$462$		0			0
$463$	31.8122			1.47844			0.739220	−	0.673464i	$-0.235194\pi$
$463$	31.8122			1.47844			0.739220	+	0.673464i	$0.235194\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	14.0521	−	24.3390i	0.650255	−	1.12627i	−0.332806	−	0.942995i	$-0.607995\pi$
$467$	14.0521	−	24.3390i	0.650255	−	1.12627i	0.983061	−	0.183279i	$-0.0586713\pi$
$468$		0			0
$469$	17.9067	+	13.4439i	0.826853	+	0.620781i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.447326	+	0.774792i	0.0205681	+	0.0356250i
$474$		0			0
$475$	24.0933			1.10548
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−5.64155	−	9.77146i	−0.257769	−	0.446469i	0.707875	−	0.706338i	$-0.249654\pi$
$479$	−5.64155	−	9.77146i	−0.257769	−	0.446469i	−0.965644	+	0.259869i	$0.916321\pi$
$480$		0			0
$481$	−4.33697	+	7.51186i	−0.197749	+	0.342511i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−7.73163	+	13.3916i	−0.351075	+	0.608080i
$486$		0			0
$487$	13.9764	+	24.2079i	0.633333	+	1.09697i	0.986866	+	0.161543i	$0.0516471\pi$
$487$	13.9764	+	24.2079i	0.633333	+	1.09697i	−0.353532	+	0.935422i	$0.615020\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	9.77076			0.440948			0.220474	−	0.975393i	$-0.429240\pi$
$491$	9.77076			0.440948			0.220474	+	0.975393i	$0.429240\pi$
$492$		0			0
$493$	6.99673	+	12.1187i	0.315117	+	0.545798i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−33.5039	+	14.2918i	−1.50286	+	0.641074i
$498$		0			0
$499$	−15.6559	+	27.1169i	−0.700856	+	1.21392i	0.267310	+	0.963611i	$0.413865\pi$
$499$	−15.6559	+	27.1169i	−0.700856	+	1.21392i	−0.968166	+	0.250308i	$0.919468\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	0.779293			0.0347469			0.0173735	−	0.999849i	$-0.494470\pi$
$503$	0.779293			0.0347469			0.0173735	+	0.999849i	$0.494470\pi$
$504$		0			0
$505$	5.08026			0.226068
$506$		0			0
$507$		0			0
$508$		0			0
$509$	15.2059	−	26.3374i	0.673989	−	1.16738i	−0.302774	−	0.953062i	$-0.597913\pi$
$509$	15.2059	−	26.3374i	0.673989	−	1.16738i	0.976763	−	0.214321i	$-0.0687538\pi$
$510$		0			0
$511$	27.8678	+	20.9225i	1.23280	+	0.925557i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−6.61254	−	11.4533i	−0.291383	−	0.504691i
$516$		0			0
$517$	−0.906656			−0.0398747
$518$		0			0
$519$		0			0
$520$		0			0
$521$	18.6273	+	32.2634i	0.816076	+	1.41348i	0.908553	+	0.417770i	$0.137188\pi$
$521$	18.6273	+	32.2634i	0.816076	+	1.41348i	−0.0924773	+	0.995715i	$0.529479\pi$
$522$		0			0
$523$	−7.18768	+	12.4494i	−0.314295	+	0.544376i	−0.979287	−	0.202475i	$-0.935102\pi$
$523$	−7.18768	+	12.4494i	−0.314295	+	0.544376i	0.664992	+	0.746850i	$0.268435\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.23490	+	9.06711i	−0.228036	+	0.394969i
$528$		0			0
$529$	11.4956	+	19.9110i	0.499811	+	0.865697i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−6.36445			−0.275675
$534$		0			0
$535$	−0.393460	−	0.681494i	−0.0170108	−	0.0294635i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	6.79804	+	1.66934i	0.292812	+	0.0719035i
$540$		0			0
$541$	−15.1981	+	26.3240i	−0.653419	+	1.13176i	0.328868	+	0.944376i	$0.393333\pi$
$541$	−15.1981	+	26.3240i	−0.653419	+	1.13176i	−0.982288	+	0.187380i	$0.940000\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.78692			−0.119379
$546$		0			0
$547$	−6.74744			−0.288500			−0.144250	−	0.989541i	$-0.546077\pi$
$547$	−6.74744			−0.288500			−0.144250	+	0.989541i	$0.546077\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−11.7311	+	20.3188i	−0.499761	+	0.865611i
$552$		0			0
$553$	−4.55387	+	37.6403i	−0.193650	+	1.60063i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	11.2613	+	19.5051i	0.477156	+	0.826459i	0.999657	−	0.0261800i	$-0.00833430\pi$
$557$	11.2613	+	19.5051i	0.477156	+	0.826459i	−0.522501	+	0.852639i	$0.675001\pi$
$558$		0			0
$559$	0.746358			0.0315676
$560$		0			0
$561$		0			0
$562$		0			0
$563$	8.17449	+	14.1586i	0.344514	+	0.596715i	0.985265	−	0.171033i	$-0.0547105\pi$
$563$	8.17449	+	14.1586i	0.344514	+	0.596715i	−0.640752	+	0.767748i	$0.721377\pi$
$564$		0			0
$565$	−11.8474	+	20.5204i	−0.498425	+	0.863298i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−20.5549	+	35.6021i	−0.861705	+	1.49252i	0.00857791	+	0.999963i	$0.497270\pi$
$569$	−20.5549	+	35.6021i	−0.861705	+	1.49252i	−0.870282	+	0.492553i	$0.836064\pi$
$570$		0			0
$571$	−20.8112	−	36.0461i	−0.870923	−	1.50848i	−0.861043	−	0.508532i	$-0.830188\pi$
$571$	−20.8112	−	36.0461i	−0.870923	−	1.50848i	−0.00987965	−	0.999951i	$-0.503145\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.332598			−0.0138703
$576$		0			0
$577$	3.71789	+	6.43957i	0.154778	+	0.268083i	0.932978	−	0.359933i	$-0.117201\pi$
$577$	3.71789	+	6.43957i	0.154778	+	0.268083i	−0.778200	+	0.628016i	$0.783867\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−11.4280	+	4.87486i	−0.474115	+	0.202243i
$582$		0			0
$583$	1.58288	−	2.74163i	0.0655561	−	0.113547i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−14.5631			−0.601085			−0.300543	−	0.953768i	$-0.597168\pi$
$587$	−14.5631			−0.601085			−0.300543	+	0.953768i	$0.597168\pi$
$588$		0			0
$589$	−17.5542			−0.723309
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−9.89411	+	17.1371i	−0.406302	+	0.703736i	−0.994472	−	0.105001i	$-0.966515\pi$
$593$	−9.89411	+	17.1371i	−0.406302	+	0.703736i	0.588170	+	0.808738i	$0.299849\pi$
$594$		0			0
$595$	11.7646	−	5.01841i	0.482300	−	0.205735i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−14.5461	−	25.1946i	−0.594339	−	1.02942i	−0.993640	−	0.112605i	$-0.964081\pi$
$599$	−14.5461	−	25.1946i	−0.594339	−	1.02942i	0.399301	−	0.916820i	$-0.369253\pi$
$600$		0			0
$601$	−0.680489			−0.0277577			−0.0138789	−	0.999904i	$-0.504418\pi$
$601$	−0.680489			−0.0277577			−0.0138789	+	0.999904i	$0.504418\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.599346	+	1.03810i	0.0243669	+	0.0422046i
$606$		0			0
$607$	20.5763	−	35.6393i	0.835168	−	1.44655i	−0.0587262	−	0.998274i	$-0.518704\pi$
$607$	20.5763	−	35.6393i	0.835168	−	1.44655i	0.893894	−	0.448279i	$-0.147963\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.378186	+	0.655037i	−0.0152998	+	0.0265000i
$612$		0			0
$613$	5.97252	+	10.3447i	0.241228	+	0.417819i	0.961064	−	0.276325i	$-0.0891165\pi$
$613$	5.97252	+	10.3447i	0.241228	+	0.417819i	−0.719836	+	0.694144i	$0.755783\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−20.3952			−0.821080			−0.410540	−	0.911843i	$-0.634660\pi$
$617$	−20.3952			−0.821080			−0.410540	+	0.911843i	$0.634660\pi$
$618$		0			0
$619$	12.7684	+	22.1155i	0.513204	+	0.888896i	0.999883	+	0.0153147i	$0.00487502\pi$
$619$	12.7684	+	22.1155i	0.513204	+	0.888896i	−0.486678	+	0.873581i	$0.661792\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	4.63828	−	38.3380i	0.185829	−	1.53598i
$624$		0			0
$625$	−2.75583	+	4.77324i	−0.110233	+	0.190929i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	41.9320			1.67194
$630$		0			0
$631$	11.0504			0.439909			0.219955	−	0.975510i	$-0.429409\pi$
$631$	11.0504			0.439909			0.219955	+	0.975510i	$0.429409\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−8.85463	+	15.3367i	−0.351385	+	0.608617i
$636$		0			0
$637$	4.04167	−	4.21510i	0.160137	−	0.167008i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	11.3639	+	19.6829i	0.448847	+	0.777426i	0.998311	−	0.0580911i	$-0.0185014\pi$
$641$	11.3639	+	19.6829i	0.448847	+	0.777426i	−0.549464	+	0.835517i	$0.685168\pi$
$642$		0			0
$643$	4.31843			0.170302			0.0851510	−	0.996368i	$-0.472863\pi$
$643$	4.31843			0.170302			0.0851510	+	0.996368i	$0.472863\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	24.5621	+	42.5427i	0.965634	+	1.67253i	0.707902	+	0.706311i	$0.249642\pi$
$647$	24.5621	+	42.5427i	0.965634	+	1.67253i	0.257732	+	0.966216i	$0.417025\pi$
$648$		0			0
$649$	6.31450	−	10.9370i	0.247866	−	0.429316i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.40512	−	7.62989i	0.172386	−	0.298581i	−0.766868	−	0.641805i	$-0.778186\pi$
$653$	4.40512	−	7.62989i	0.172386	−	0.298581i	0.939253	+	0.343224i	$0.111519\pi$
$654$		0			0
$655$	−5.51647	−	9.55480i	−0.215546	−	0.373337i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	19.5621			0.762029			0.381015	−	0.924569i	$-0.375575\pi$
$659$	19.5621			0.762029			0.381015	+	0.924569i	$0.375575\pi$
$660$		0			0
$661$	2.43359	+	4.21510i	0.0946556	+	0.163948i	0.909465	−	0.415781i	$-0.136492\pi$
$661$	2.43359	+	4.21510i	0.0946556	+	0.163948i	−0.814809	+	0.579729i	$0.803158\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	17.1494	+	12.8754i	0.665025	+	0.499285i
$666$		0			0
$667$	0.161943	−	0.280493i	0.00627044	−	0.0108607i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	10.0659			0.388589
$672$		0			0
$673$	−45.9080			−1.76962			−0.884811	−	0.465950i	$-0.845713\pi$
$673$	−45.9080			−1.76962			−0.884811	+	0.465950i	$0.845713\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.02301	−	10.4322i	0.231483	−	0.400941i	−0.726762	−	0.686890i	$-0.758976\pi$
$677$	6.02301	−	10.4322i	0.231483	−	0.400941i	0.958245	+	0.285949i	$0.0923089\pi$
$678$		0			0
$679$	31.3936	−	13.3916i	1.20477	−	0.513921i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	3.89892	+	6.75313i	0.149188	+	0.258401i	0.930928	−	0.365204i	$-0.119001\pi$
$683$	3.89892	+	6.75313i	0.149188	+	0.258401i	−0.781740	+	0.623605i	$0.785667\pi$
$684$		0			0
$685$	−24.3304			−0.929618
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.32051	−	2.28718i	−0.0503073	−	0.0871347i
$690$		0			0
$691$	2.47634	−	4.28914i	0.0942044	−	0.163167i	−0.815072	−	0.579360i	$-0.803303\pi$
$691$	2.47634	−	4.28914i	0.0942044	−	0.163167i	0.909276	+	0.416193i	$0.136636\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.75856	+	6.51001i	−0.142570	+	0.246939i
$696$		0			0
$697$	15.3836	+	26.6453i	0.582697	+	1.00926i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−11.0275			−0.416502			−0.208251	−	0.978075i	$-0.566777\pi$
$701$	−11.0275			−0.416502			−0.208251	+	0.978075i	$0.566777\pi$
$702$		0			0
$703$	35.1527	+	60.8862i	1.32581	+	2.29637i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−8.96717	−	6.73234i	−0.337245	−	0.253196i
$708$		0			0
$709$	19.6799	−	34.0867i	0.739096	−	1.28015i	−0.213807	−	0.976876i	$-0.568586\pi$
$709$	19.6799	−	34.0867i	0.739096	−	1.28015i	0.952903	−	0.303276i	$-0.0980803\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.242328			0.00907527
$714$		0			0
$715$	1.00000			0.0373979
$716$		0			0
$717$		0			0
$718$		0			0
$719$	18.9363	−	32.7987i	0.706206	−	1.22318i	−0.260049	−	0.965595i	$-0.583739\pi$
$719$	18.9363	−	32.7987i	0.706206	−	1.22318i	0.966255	−	0.257588i	$-0.0829279\pi$
$720$		0			0
$721$	−3.50600	+	28.9791i	−0.130570	+	1.07924i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−6.18168	−	10.7070i	−0.229582	−	0.397648i
$726$		0			0
$727$	−21.3250			−0.790899			−0.395450	−	0.918488i	$-0.629411\pi$
$727$	−21.3250			−0.790899			−0.395450	+	0.918488i	$0.629411\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.80404	−	3.12469i	−0.0667248	−	0.115571i
$732$		0			0
$733$	13.2810	−	23.0034i	0.490546	−	0.849650i	−0.509395	−	0.860533i	$-0.670131\pi$
$733$	13.2810	−	23.0034i	0.490546	−	0.849650i	0.999941	+	0.0108824i	$0.00346405\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.23163	−	7.32939i	0.155874	−	0.269982i
$738$		0			0
$739$	−7.94351	−	13.7586i	−0.292207	−	0.506117i	0.682124	−	0.731236i	$-0.261056\pi$
$739$	−7.94351	−	13.7586i	−0.292207	−	0.506117i	−0.974331	+	0.225119i	$0.927723\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−34.9385			−1.28177			−0.640885	−	0.767637i	$-0.721432\pi$
$743$	−34.9385			−1.28177			−0.640885	+	0.767637i	$0.721432\pi$
$744$		0			0
$745$	4.32170	+	7.48540i	0.158335	+	0.274244i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.208615	+	1.72432i	−0.00762261	+	0.0630052i
$750$		0			0
$751$	6.49400	−	11.2479i	0.236969	−	0.410443i	−0.722874	−	0.690980i	$-0.757179\pi$
$751$	6.49400	−	11.2479i	0.236969	−	0.410443i	0.959843	+	0.280537i	$0.0905126\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	4.84209			0.176222
$756$		0			0
$757$	−27.0408			−0.982814			−0.491407	−	0.870930i	$-0.663517\pi$
$757$	−27.0408			−0.982814			−0.491407	+	0.870930i	$0.663517\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.588880	−	1.01997i	0.0213469	−	0.0369739i	−0.855155	−	0.518373i	$-0.826538\pi$
$761$	0.588880	−	1.01997i	0.0213469	−	0.0369739i	0.876502	+	0.481399i	$0.159871\pi$
$762$		0			0
$763$	4.91920	+	3.69322i	0.178087	+	0.133703i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.26783	−	9.12415i	−0.190210	−	0.329454i
$768$		0			0
$769$	32.8530			1.18471			0.592355	−	0.805677i	$-0.298198\pi$
$769$	32.8530			1.18471			0.592355	+	0.805677i	$0.298198\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−5.08342	−	8.80474i	−0.182838	−	0.316685i	0.760008	−	0.649914i	$-0.225195\pi$
$773$	−5.08342	−	8.80474i	−0.182838	−	0.316685i	−0.942846	+	0.333229i	$0.891862\pi$
$774$		0			0
$775$	4.62509	−	8.01088i	0.166138	−	0.287759i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−25.7930	+	44.6748i	−0.924131	+	1.60064i
$780$		0			0
$781$	6.88364	+	11.9228i	0.246316	+	0.426632i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6.69358			0.238904
$786$		0			0
$787$	−4.31723	−	7.47767i	−0.153893	−	0.266550i	0.778763	−	0.627319i	$-0.215848\pi$
$787$	−4.31723	−	7.47767i	−0.153893	−	0.266550i	−0.932655	+	0.360769i	$0.882514\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	48.1055	−	20.5204i	1.71043	−	0.729620i
$792$		0			0
$793$	4.19869	−	7.27235i	0.149100	−	0.258249i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	20.9671			0.742692			0.371346	−	0.928495i	$-0.378896\pi$
$797$	20.9671			0.742692			0.371346	+	0.928495i	$0.378896\pi$
$798$		0			0
$799$	3.65648			0.129357
$800$		0			0
$801$		0			0
$802$		0			0
$803$	6.58561	−	11.4066i	0.232401	−	0.402530i
$804$		0			0
$805$	−0.236740	−	0.177739i	−0.00834399	−	0.00626447i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	7.48145	+	12.9583i	0.263034	+	0.455588i	0.967047	−	0.254599i	$-0.0819436\pi$
$809$	7.48145	+	12.9583i	0.263034	+	0.455588i	−0.704013	+	0.710187i	$0.748610\pi$
$810$		0			0
$811$	−53.1965			−1.86798			−0.933991	−	0.357296i	$-0.883699\pi$
$811$	−53.1965			−1.86798			−0.933991	+	0.357296i	$0.883699\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5.39411	−	9.34287i	−0.188947	−	0.327267i
$816$		0			0
$817$	3.02475	−	5.23901i	0.105822	−	0.183290i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	17.9363	−	31.0666i	0.625982	−	1.08423i	−0.362368	−	0.932035i	$-0.618032\pi$
$821$	17.9363	−	31.0666i	0.625982	−	1.08423i	0.988350	−	0.152197i	$-0.0486349\pi$
$822$		0			0
$823$	6.34297	+	10.9864i	0.221102	+	0.382960i	0.955143	−	0.296145i	$-0.0957012\pi$
$823$	6.34297	+	10.9864i	0.221102	+	0.382960i	−0.734041	+	0.679105i	$0.762368\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	2.92412			0.101682			0.0508408	−	0.998707i	$-0.483810\pi$
$827$	2.92412			0.101682			0.0508408	+	0.998707i	$0.483810\pi$
$828$		0			0
$829$	5.88965	+	10.2012i	0.204556	+	0.354301i	0.949991	−	0.312277i	$-0.101092\pi$
$829$	5.88965	+	10.2012i	0.204556	+	0.354301i	−0.745435	+	0.666578i	$0.767758\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−27.4160	−	6.73234i	−0.949909	−	0.233262i
$834$		0			0
$835$	−9.35071	+	16.1959i	−0.323595	+	0.560482i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	18.5117			0.639093			0.319547	−	0.947571i	$-0.396469\pi$
$839$	18.5117			0.639093			0.319547	+	0.947571i	$0.396469\pi$
$840$		0			0
$841$	−16.9605			−0.584846
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−7.37437	+	12.7728i	−0.253686	+	0.439397i
$846$		0			0
$847$	0.317776	−	2.62660i	0.0109189	−	0.0902510i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−0.485268	−	0.840508i	−0.0166348	−	0.0288122i
$852$		0			0
$853$	−37.0342			−1.26803			−0.634014	−	0.773322i	$-0.718594\pi$
$853$	−37.0342			−1.26803			−0.634014	+	0.773322i	$0.718594\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−2.11908	−	3.67036i	−0.0723866	−	0.125377i	0.827560	−	0.561377i	$-0.189728\pi$
$857$	−2.11908	−	3.67036i	−0.0723866	−	0.125377i	−0.899947	+	0.436000i	$0.856395\pi$
$858$		0			0
$859$	1.70916	−	2.96035i	0.0583157	−	0.101006i	−0.835394	−	0.549652i	$-0.814760\pi$
$859$	1.70916	−	2.96035i	0.0583157	−	0.101006i	0.893709	+	0.448646i	$0.148094\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	19.3601	−	33.5327i	0.659025	−	1.14147i	−0.321843	−	0.946793i	$-0.604302\pi$
$863$	19.3601	−	33.5327i	0.659025	−	1.14147i	0.980868	−	0.194672i	$-0.0623643\pi$
$864$		0			0
$865$	−13.6383	−	23.6222i	−0.463715	−	0.803179i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	14.3304			0.486127
$870$		0			0
$871$	−3.53020	−	6.11449i	−0.119616	−	0.207182i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−24.9797	+	10.6556i	−0.844469	+	0.360225i
$876$		0			0
$877$	−23.3804	+	40.4960i	−0.789499	+	1.36745i	0.136775	+	0.990602i	$0.456326\pi$
$877$	−23.3804	+	40.4960i	−0.789499	+	1.36745i	−0.926274	+	0.376850i	$0.877007\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	19.6050			0.660509			0.330255	−	0.943892i	$-0.392865\pi$
$881$	19.6050			0.660509			0.330255	+	0.943892i	$0.392865\pi$
$882$		0			0
$883$	10.0395			0.337855			0.168928	−	0.985628i	$-0.445970\pi$
$883$	10.0395			0.337855			0.168928	+	0.985628i	$0.445970\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	23.0967	−	40.0047i	0.775512	−	1.34323i	−0.158994	−	0.987280i	$-0.550825\pi$
$887$	23.0967	−	40.0047i	0.775512	−	1.34323i	0.934506	−	0.355947i	$-0.115842\pi$
$888$		0			0
$889$	35.9534	−	15.3367i	1.20584	−	0.514376i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3.06533	+	5.30930i	0.102577	+	0.177669i
$894$		0			0
$895$	−3.80131			−0.127064
$896$		0			0
$897$		0			0
$898$		0			0
$899$	4.50392	+	7.80102i	0.150214	+	0.260179i
$900$		0			0
$901$	−6.38364	+	11.0568i	−0.212670	+	0.368355i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−3.33752	+	5.78075i	−0.110943	+	0.192158i
$906$		0			0
$907$	−12.1290	−	21.0081i	−0.402737	−	0.697561i	0.591318	−	0.806438i	$-0.298608\pi$
$907$	−12.1290	−	21.0081i	−0.402737	−	0.697561i	−0.994055	+	0.108877i	$0.965274\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−22.7991			−0.755369			−0.377685	−	0.925934i	$-0.623280\pi$
$911$	−22.7991			−0.755369			−0.377685	+	0.925934i	$0.623280\pi$
$912$		0			0
$913$	2.34798	+	4.06682i	0.0777068	+	0.134592i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−2.92486	+	24.1756i	−0.0965873	+	0.798349i
$918$		0			0
$919$	−8.84352	+	15.3174i	−0.291721	+	0.505275i	−0.974217	−	0.225614i	$-0.927561\pi$
$919$	−8.84352	+	15.3174i	−0.291721	+	0.505275i	0.682496	+	0.730889i	$0.260894\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	11.4853			0.378042
$924$		0			0
$925$	−37.0473			−1.21811
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−4.42813	+	7.66975i	−0.145282	+	0.251636i	−0.929478	−	0.368877i	$-0.879742\pi$
$929$	−4.42813	+	7.66975i	−0.145282	+	0.251636i	0.784196	+	0.620513i	$0.213076\pi$
$930$		0			0
$931$	−13.2081	−	45.4526i	−0.432877	−	1.48965i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−2.41712	−	4.18658i	−0.0790483	−	0.136916i
$936$		0			0
$937$	13.9880			0.456968			0.228484	−	0.973548i	$-0.426623\pi$
$937$	13.9880			0.456968			0.228484	+	0.973548i	$0.426623\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	16.8776	+	29.2329i	0.550195	+	0.952966i	0.998260	+	0.0589653i	$0.0187801\pi$
$941$	16.8776	+	29.2329i	0.550195	+	0.952966i	−0.448065	+	0.894001i	$0.647887\pi$
$942$		0			0
$943$	0.356062	−	0.616717i	0.0115950	−	0.0200831i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	20.4545	−	35.4283i	0.664683	−	1.15126i	−0.314689	−	0.949195i	$-0.601900\pi$
$947$	20.4545	−	35.4283i	0.664683	−	1.15126i	0.979371	−	0.202069i	$-0.0647666\pi$
$948$		0			0
$949$	−5.49400	−	9.51588i	−0.178343	−	0.308899i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	16.5147			0.534965			0.267482	−	0.963563i	$-0.413808\pi$
$953$	16.5147			0.534965			0.267482	+	0.963563i	$0.413808\pi$
$954$		0			0
$955$	6.30731	+	10.9246i	0.204100	+	0.353511i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	42.9457	+	32.2426i	1.38679	+	1.04117i
$960$		0			0
$961$	12.1302	−	21.0101i	0.391297	−	0.677746i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.22378			−0.0393949
$966$		0			0
$967$	−15.0024			−0.482444			−0.241222	−	0.970470i	$-0.577548\pi$
$967$	−15.0024			−0.482444			−0.241222	+	0.970470i	$0.577548\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	6.09161	−	10.5510i	0.195489	−	0.338597i	−0.751572	−	0.659651i	$-0.770704\pi$
$971$	6.09161	−	10.5510i	0.195489	−	0.338597i	0.947061	+	0.321054i	$0.104037\pi$
$972$		0			0
$973$	15.2613	−	6.51001i	0.489254	−	0.208701i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	19.7865	+	34.2712i	0.633026	+	1.09643i	0.986930	+	0.161151i	$0.0515206\pi$
$977$	19.7865	+	34.2712i	0.633026	+	1.09643i	−0.353904	+	0.935282i	$0.615146\pi$
$978$		0			0
$979$	−14.5961			−0.466493
$980$		0			0
$981$		0			0
$982$		0			0
$983$	11.3420	+	19.6449i	0.361753	+	0.626575i	0.988249	−	0.152850i	$-0.0488451\pi$
$983$	11.3420	+	19.6449i	0.361753	+	0.626575i	−0.626496	+	0.779424i	$0.715512\pi$
$984$		0			0
$985$	13.3600	−	23.1402i	0.425684	−	0.737307i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.0417553	+	0.0723223i	−0.00132774	+	0.00229972i
$990$		0			0
$991$	9.43478	+	16.3415i	0.299706	+	0.519106i	0.976069	−	0.217463i	$-0.0697782\pi$
$991$	9.43478	+	16.3415i	0.299706	+	0.519106i	−0.676363	+	0.736569i	$0.736445\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−15.9067			−0.504275
$996$		0			0
$997$	−13.4710	−	23.3324i	−0.426630	−	0.738946i	0.569941	−	0.821686i	$-0.306966\pi$
$997$	−13.4710	−	23.3324i	−0.426630	−	0.738946i	−0.996571	+	0.0827402i	$0.973633\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2772.2.s.e.793.3		6
3.2	odd	2		308.2.i.b.177.3	✓	6
7.4	even	3	inner	2772.2.s.e.2377.3		6
12.11	even	2		1232.2.q.j.177.1		6
21.2	odd	6		2156.2.a.g.1.1		3
21.5	even	6		2156.2.a.k.1.3		3
21.11	odd	6		308.2.i.b.221.3	yes	6
21.17	even	6		2156.2.i.j.1145.1		6
21.20	even	2		2156.2.i.j.177.1		6
84.11	even	6		1232.2.q.j.529.1		6
84.23	even	6		8624.2.a.cp.1.3		3
84.47	odd	6		8624.2.a.cg.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.i.b.177.3	✓	6	3.2	odd	2
308.2.i.b.221.3	yes	6	21.11	odd	6
1232.2.q.j.177.1		6	12.11	even	2
1232.2.q.j.529.1		6	84.11	even	6
2156.2.a.g.1.1		3	21.2	odd	6
2156.2.a.k.1.3		3	21.5	even	6
2156.2.i.j.177.1		6	21.20	even	2
2156.2.i.j.1145.1		6	21.17	even	6
2772.2.s.e.793.3		6	1.1	even	1	trivial
2772.2.s.e.2377.3		6	7.4	even	3	inner
8624.2.a.cg.1.1		3	84.47	odd	6
8624.2.a.cp.1.3		3	84.23	even	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:	\( N \)	\(=\)	\( 2772 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2772.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.599346 - 1.03810i) q^{5} +(-2.43359 + 1.03810i) q^{7} +(0.500000 + 0.866025i) q^{11} +0.834243 q^{13} +(-2.01647 - 3.49262i) q^{17} +(3.38092 - 5.85592i) q^{19} +(-0.0466721 + 0.0808384i) q^{23} +(1.78157 + 3.08577i) q^{25} -3.46980 q^{29} +(-1.29804 - 2.24827i) q^{31} +(-0.380915 + 3.14848i) q^{35} +(-5.19869 + 9.00440i) q^{37} -7.62901 q^{41} +0.894653 q^{43} +(-0.453328 + 0.785187i) q^{47} +(4.84471 - 5.05260i) q^{49} +(-1.58288 - 2.74163i) q^{53} +1.19869 q^{55} +(-6.31450 - 10.9370i) q^{59} +(5.03293 - 8.71730i) q^{61} +(0.500000 - 0.866025i) q^{65} +(-4.23163 - 7.32939i) q^{67} +13.7673 q^{71} +(-6.58561 - 11.4066i) q^{73} +(-2.11581 - 1.58850i) q^{77} +(7.16521 - 12.4105i) q^{79} +4.69596 q^{83} -4.83424 q^{85} +(-7.29804 + 12.6406i) q^{89} +(-2.03020 + 0.866025i) q^{91} +(-4.05267 - 7.01944i) q^{95} -12.9001 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{5} + 2 q^{7} + 3 q^{11} - 6 q^{13} - q^{17} + 9 q^{19} + 5 q^{25} - 10 q^{29} + 9 q^{31} + 9 q^{35} - 20 q^{37} + 10 q^{41} + 16 q^{43} - 3 q^{47} + 12 q^{49} - 15 q^{53} - 4 q^{55} - 10 q^{59}+ \cdots - 22 q^{97}+O(q^{100}) \) 6 * q - 2 * q^5 + 2 * q^7 + 3 * q^11 - 6 * q^13 - q^17 + 9 * q^19 + 5 * q^25 - 10 * q^29 + 9 * q^31 + 9 * q^35 - 20 * q^37 + 10 * q^41 + 16 * q^43 - 3 * q^47 + 12 * q^49 - 15 * q^53 - 4 * q^55 - 10 * q^59 + 8 * q^61 + 3 * q^65 + 8 * q^67 - 6 * q^71 - 12 * q^73 + 4 * q^77 - 7 * q^79 + 50 * q^83 - 18 * q^85 - 27 * q^89 - 23 * q^91 - 19 * q^95 - 22 * q^97

Introduction

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