LMFDB - Embedded newform 3564.2.i.t.1189.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3564,2,Mod(1189,3564)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3564, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("3564.1189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3564 = 2^{2} \cdot 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3564.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$28.4586832804$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 18x^{9} + 152x^{8} - 204x^{7} + 162x^{6} - 408x^{5} + 2800x^{4} - 4422x^{3} + 3528x^{2} - 252x + 9 $ x^12 - 18x^9 + 152x^8 - 204x^7 + 162x^6 - 408x^5 + 2800x^4 - 4422x^3 + 3528x^2 - 252*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1189.6
Root			$1.48688 + 1.48688i$ of defining polynomial
Character	$\chi$	$=$	3564.1189
Dual form			3564.2.i.t.2377.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.03112 + 3.51801i) q^{5} +(0.0326133 - 0.0564879i) q^{7} +O(q^{10})$	$q+(2.03112 + 3.51801i) q^{5} +(0.0326133 - 0.0564879i) q^{7} +(0.500000 - 0.866025i) q^{11} +(-0.665097 - 1.15198i) q^{13} +2.03900 q^{17} -0.0245009 q^{19} +(1.08825 + 1.88490i) q^{23} +(-5.75091 + 9.96087i) q^{25} +(-5.00575 + 8.67021i) q^{29} +(-2.22158 - 3.84790i) q^{31} +0.264966 q^{35} +1.48344 q^{37} +(3.77606 + 6.54033i) q^{41} +(-4.82691 + 8.36045i) q^{43} +(6.16360 - 10.6757i) q^{47} +(3.49787 + 6.05849i) q^{49} +3.61780 q^{53} +4.06224 q^{55} +(5.03922 + 8.72819i) q^{59} +(4.07277 - 7.05424i) q^{61} +(2.70178 - 4.67963i) q^{65} +(1.68781 + 2.92338i) q^{67} +0.101239 q^{71} -8.12217 q^{73} +(-0.0326133 - 0.0564879i) q^{77} +(-3.66096 + 6.34096i) q^{79} +(3.94927 - 6.84033i) q^{83} +(4.14145 + 7.17320i) q^{85} -9.48031 q^{89} -0.0867640 q^{91} +(-0.0497642 - 0.0861942i) q^{95} +(-4.31040 + 7.46583i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{7}+O(q^{10}) $ 12 * q + 2 * q^7	$ 12 q + 2 q^{7} + 6 q^{11} + 6 q^{13} - 8 q^{17} + 4 q^{23} - 10 q^{25} - 4 q^{29} - 6 q^{31} - 28 q^{35} - 12 q^{37} + 22 q^{41} + 10 q^{43} + 20 q^{47} - 6 q^{49} - 8 q^{53} + 24 q^{59} + 10 q^{61} + 40 q^{65} + 6 q^{67} - 80 q^{71} - 16 q^{73} - 2 q^{77} + 14 q^{79} + 12 q^{83} - 6 q^{85} - 48 q^{89} + 20 q^{91} + 44 q^{95} - 20 q^{97}+O(q^{100}) $ 12 * q + 2 * q^7 + 6 * q^11 + 6 * q^13 - 8 * q^17 + 4 * q^23 - 10 * q^25 - 4 * q^29 - 6 * q^31 - 28 * q^35 - 12 * q^37 + 22 * q^41 + 10 * q^43 + 20 * q^47 - 6 * q^49 - 8 * q^53 + 24 * q^59 + 10 * q^61 + 40 * q^65 + 6 * q^67 - 80 * q^71 - 16 * q^73 - 2 * q^77 + 14 * q^79 + 12 * q^83 - 6 * q^85 - 48 * q^89 + 20 * q^91 + 44 * q^95 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3564\mathbb{Z}\right)^\times$.

$n$	$1541$	$1783$	$2917$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$5$	2.03112	+	3.51801i	0.908345	+	1.57330i	0.816363	+	0.577540i	$0.195987\pi$
$5$	2.03112	+	3.51801i	0.908345	+	1.57330i	0.0919827	+	0.995761i	$0.470680\pi$
$6$		0			0
$7$	0.0326133	−	0.0564879i	0.0123267	−	0.0213504i	−0.859796	−	0.510637i	$-0.829410\pi$
$7$	0.0326133	−	0.0564879i	0.0123267	−	0.0213504i	0.872123	+	0.489287i	$0.162743\pi$
$8$		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
$13$	−0.665097	−	1.15198i	−0.184465	−	0.319502i	0.758931	−	0.651171i	$-0.225722\pi$
$13$	−0.665097	−	1.15198i	−0.184465	−	0.319502i	−0.943396	+	0.331669i	$0.892388\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.03900			0.494529			0.247265	−	0.968948i	$-0.420468\pi$
$17$	2.03900			0.494529			0.247265	+	0.968948i	$0.420468\pi$
$18$		0			0
$19$	−0.0245009			−0.00562088			−0.00281044	−	0.999996i	$-0.500895\pi$
$19$	−0.0245009			−0.00562088			−0.00281044	+	0.999996i	$0.500895\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.08825	+	1.88490i	0.226915	+	0.393028i	0.956892	−	0.290443i	$-0.0938027\pi$
$23$	1.08825	+	1.88490i	0.226915	+	0.393028i	−0.729977	+	0.683471i	$0.760469\pi$
$24$		0			0
$25$	−5.75091	+	9.96087i	−1.15018	+	1.99217i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.00575	+	8.67021i	−0.929544	+	1.61002i	−0.145458	+	0.989364i	$0.546466\pi$
$29$	−5.00575	+	8.67021i	−0.929544	+	1.61002i	−0.784086	+	0.620653i	$0.786868\pi$
$30$		0			0
$31$	−2.22158	−	3.84790i	−0.399008	−	0.691103i	0.594595	−	0.804025i	$-0.297312\pi$
$31$	−2.22158	−	3.84790i	−0.399008	−	0.691103i	−0.993604	+	0.112922i	$0.963979\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.264966			0.0447875
$36$		0			0
$37$	1.48344			0.243875			0.121938	−	0.992538i	$-0.461089\pi$
$37$	1.48344			0.243875			0.121938	+	0.992538i	$0.461089\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.77606	+	6.54033i	0.589721	+	1.02143i	0.994269	+	0.106910i	$0.0340958\pi$
$41$	3.77606	+	6.54033i	0.589721	+	1.02143i	−0.404547	+	0.914517i	$0.632571\pi$
$42$		0			0
$43$	−4.82691	+	8.36045i	−0.736097	+	1.27496i	0.218144	+	0.975917i	$0.430000\pi$
$43$	−4.82691	+	8.36045i	−0.736097	+	1.27496i	−0.954241	+	0.299040i	$0.903334\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.16360	−	10.6757i	0.899053	−	1.55721i	0.0703457	−	0.997523i	$-0.477590\pi$
$47$	6.16360	−	10.6757i	0.899053	−	1.55721i	0.828707	−	0.559682i	$-0.189077\pi$
$48$		0			0
$49$	3.49787	+	6.05849i	0.499696	+	0.865499i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.61780			0.496943			0.248472	−	0.968639i	$-0.420072\pi$
$53$	3.61780			0.496943			0.248472	+	0.968639i	$0.420072\pi$
$54$		0			0
$55$	4.06224			0.547753
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.03922	+	8.72819i	0.656051	+	1.13631i	0.981629	+	0.190799i	$0.0611078\pi$
$59$	5.03922	+	8.72819i	0.656051	+	1.13631i	−0.325578	+	0.945515i	$0.605559\pi$
$60$		0			0
$61$	4.07277	−	7.05424i	0.521464	−	0.903203i	−0.478224	−	0.878238i	$-0.658719\pi$
$61$	4.07277	−	7.05424i	0.521464	−	0.903203i	0.999688	−	0.0249648i	$-0.00794738\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.70178	−	4.67963i	0.335115	−	0.580436i
$66$		0			0
$67$	1.68781	+	2.92338i	0.206199	+	0.357148i	0.950514	−	0.310681i	$-0.100557\pi$
$67$	1.68781	+	2.92338i	0.206199	+	0.357148i	−0.744315	+	0.667829i	$0.767224\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.101239			0.0120149			0.00600745	−	0.999982i	$-0.498088\pi$
$71$	0.101239			0.0120149			0.00600745	+	0.999982i	$0.498088\pi$
$72$		0			0
$73$	−8.12217			−0.950628			−0.475314	−	0.879816i	$-0.657666\pi$
$73$	−8.12217			−0.950628			−0.475314	+	0.879816i	$0.657666\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.0326133	−	0.0564879i	−0.00371663	−	0.00643740i
$78$		0			0
$79$	−3.66096	+	6.34096i	−0.411890	+	0.713414i	−0.995096	−	0.0989099i	$-0.968464\pi$
$79$	−3.66096	+	6.34096i	−0.411890	+	0.713414i	0.583207	+	0.812324i	$0.301798\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.94927	−	6.84033i	0.433488	−	0.750824i	−0.563682	−	0.825992i	$-0.690616\pi$
$83$	3.94927	−	6.84033i	0.433488	−	0.750824i	0.997171	+	0.0751675i	$0.0239492\pi$
$84$		0			0
$85$	4.14145	+	7.17320i	0.449203	+	0.778043i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−9.48031			−1.00491			−0.502455	−	0.864603i	$-0.667570\pi$
$89$	−9.48031			−1.00491			−0.502455	+	0.864603i	$0.667570\pi$
$90$		0			0
$91$	−0.0867640			−0.00909534
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.0497642	−	0.0861942i	−0.00510570	−	0.00884334i
$96$		0			0
$97$	−4.31040	+	7.46583i	−0.437655	+	0.758040i	−0.997508	−	0.0705513i	$-0.977524\pi$
$97$	−4.31040	+	7.46583i	−0.437655	+	0.758040i	0.559853	+	0.828592i	$0.310857\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.11873	+	7.13385i	−0.409829	+	0.709845i	−0.994870	−	0.101159i	$-0.967745\pi$
$101$	−4.11873	+	7.13385i	−0.409829	+	0.709845i	0.585041	+	0.811004i	$0.301078\pi$
$102$		0			0
$103$	6.26052	+	10.8435i	0.616868	+	1.06845i	0.990054	+	0.140690i	$0.0449320\pi$
$103$	6.26052	+	10.8435i	0.616868	+	1.06845i	−0.373186	+	0.927757i	$0.621735\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.79084			−0.849843			−0.424921	−	0.905230i	$-0.639698\pi$
$107$	−8.79084			−0.849843			−0.424921	+	0.905230i	$0.639698\pi$
$108$		0			0
$109$	−9.99172			−0.957033			−0.478517	−	0.878079i	$-0.658825\pi$
$109$	−9.99172			−0.957033			−0.478517	+	0.878079i	$0.658825\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.06725	−	3.58058i	−0.194470	−	0.336832i	0.752256	−	0.658870i	$-0.228965\pi$
$113$	−2.06725	−	3.58058i	−0.194470	−	0.336832i	−0.946727	+	0.322038i	$0.895632\pi$
$114$		0			0
$115$	−4.42072	+	7.65691i	−0.412234	+	0.714011i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.0664984	−	0.115179i	0.00609590	−	0.0105584i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−26.4120			−2.36236
$126$		0			0
$127$	13.9661			1.23929			0.619644	−	0.784883i	$-0.287277\pi$
$127$	13.9661			1.23929			0.619644	+	0.784883i	$0.287277\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−9.75431	−	16.8950i	−0.852238	−	1.47612i	−0.879184	−	0.476483i	$-0.841911\pi$
$131$	−9.75431	−	16.8950i	−0.852238	−	1.47612i	0.0269455	−	0.999637i	$-0.491422\pi$
$132$		0			0
$133$	−0.000799054		0.00138400i	−6.92868e−5		0.000120008i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.39744	−	7.61659i	0.375699	−	0.650729i	−0.614733	−	0.788736i	$-0.710736\pi$
$137$	4.39744	−	7.61659i	0.375699	−	0.650729i	0.990431	+	0.138006i	$0.0440694\pi$
$138$		0			0
$139$	4.71853	+	8.17273i	0.400220	+	0.693202i	0.993752	−	0.111608i	$-0.0356002\pi$
$139$	4.71853	+	8.17273i	0.400220	+	0.693202i	−0.593532	+	0.804810i	$0.702267\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.33019			−0.111236
$144$		0			0
$145$	−40.6691			−3.37739
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.62138	+	6.27242i	0.296675	+	0.513856i	0.975373	−	0.220561i	$-0.0707888\pi$
$149$	3.62138	+	6.27242i	0.296675	+	0.513856i	−0.678698	+	0.734417i	$0.737455\pi$
$150$		0			0
$151$	−5.51708	+	9.55586i	−0.448973	+	0.777645i	−0.998319	−	0.0579502i	$-0.981544\pi$
$151$	−5.51708	+	9.55586i	−0.448973	+	0.777645i	0.549346	+	0.835595i	$0.314877\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	9.02462	−	15.6311i	0.724875	−	1.25552i
$156$		0			0
$157$	1.25444	+	2.17276i	0.100116	+	0.173405i	0.911732	−	0.410785i	$-0.134745\pi$
$157$	1.25444	+	2.17276i	0.100116	+	0.173405i	−0.811617	+	0.584190i	$0.801412\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.141965			0.0111884
$162$		0			0
$163$	−12.6456			−0.990484			−0.495242	−	0.868755i	$-0.664921\pi$
$163$	−12.6456			−0.990484			−0.495242	+	0.868755i	$0.664921\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.55833	−	9.62731i	−0.430117	−	0.744984i	0.566766	−	0.823879i	$-0.308194\pi$
$167$	−5.55833	−	9.62731i	−0.430117	−	0.744984i	−0.996883	+	0.0788947i	$0.974861\pi$
$168$		0			0
$169$	5.61529	−	9.72597i	0.431946	−	0.748152i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.573346	+	0.993065i	−0.0435907	+	0.0755013i	−0.886998	−	0.461774i	$-0.847213\pi$
$173$	−0.573346	+	0.993065i	−0.0435907	+	0.0755013i	0.843407	+	0.537275i	$0.180546\pi$
$174$		0			0
$175$	0.375113	+	0.649714i	0.0283558	+	0.0491138i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.480893			0.0359436			0.0179718	−	0.999838i	$-0.494279\pi$
$179$	0.480893			0.0359436			0.0179718	+	0.999838i	$0.494279\pi$
$180$		0			0
$181$	0.754827			0.0561058			0.0280529	−	0.999606i	$-0.491069\pi$
$181$	0.754827			0.0561058			0.0280529	+	0.999606i	$0.491069\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.01304	+	5.21874i	0.221523	+	0.383689i
$186$		0			0
$187$	1.01950	−	1.76582i	0.0745531	−	0.129130i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.0071	−	19.0649i	0.796449	−	1.37949i	−0.125466	−	0.992098i	$-0.540043\pi$
$191$	11.0071	−	19.0649i	0.796449	−	1.37949i	0.921915	−	0.387392i	$-0.126624\pi$
$192$		0			0
$193$	13.2957	+	23.0288i	0.957043	+	1.65765i	0.729622	+	0.683850i	$0.239696\pi$
$193$	13.2957	+	23.0288i	0.957043	+	1.65765i	0.227420	+	0.973797i	$0.426971\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.25967			−0.0897476			−0.0448738	−	0.998993i	$-0.514289\pi$
$197$	−1.25967			−0.0897476			−0.0448738	+	0.998993i	$0.514289\pi$
$198$		0			0
$199$	0.0762801			0.00540735			0.00270368	−	0.999996i	$-0.499139\pi$
$199$	0.0762801			0.00540735			0.00270368	+	0.999996i	$0.499139\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.326508	+	0.565528i	0.0229164	+	0.0396923i
$204$		0			0
$205$	−15.3393	+	26.5684i	−1.07134	+	1.85562i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.0122504	+	0.0212184i	−0.000847380	+	0.00146771i
$210$		0			0
$211$	4.52933	+	7.84503i	0.311812	+	0.540074i	0.978755	−	0.205035i	$-0.0657308\pi$
$211$	4.52933	+	7.84503i	0.311812	+	0.540074i	−0.666943	+	0.745109i	$0.732397\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−39.2162			−2.67452
$216$		0			0
$217$	−0.289813			−0.0196738
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.35613	−	2.34888i	−0.0912231	−	0.158003i
$222$		0			0
$223$	10.3912	−	17.9980i	0.695844	−	1.20524i	−0.274051	−	0.961715i	$-0.588364\pi$
$223$	10.3912	−	17.9980i	0.695844	−	1.20524i	0.969895	−	0.243522i	$-0.0783028\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.63856	−	16.6945i	0.639734	−	1.10805i	−0.345757	−	0.938324i	$-0.612378\pi$
$227$	9.63856	−	16.6945i	0.639734	−	1.10805i	0.985491	−	0.169728i	$-0.0542888\pi$
$228$		0			0
$229$	−2.92345	−	5.06357i	−0.193187	−	0.334610i	0.753118	−	0.657886i	$-0.228549\pi$
$229$	−2.92345	−	5.06357i	−0.193187	−	0.334610i	−0.946305	+	0.323276i	$0.895216\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.58641			0.431490			0.215745	−	0.976450i	$-0.430782\pi$
$233$	6.58641			0.431490			0.215745	+	0.976450i	$0.430782\pi$
$234$		0			0
$235$	50.0761			3.26660
$236$		0			0
$237$		0			0
$238$		0			0
$239$	3.33037	+	5.76836i	0.215423	+	0.373124i	0.953403	−	0.301698i	$-0.0975535\pi$
$239$	3.33037	+	5.76836i	0.215423	+	0.373124i	−0.737980	+	0.674823i	$0.764220\pi$
$240$		0			0
$241$	−2.27308	+	3.93708i	−0.146422	+	0.253610i	−0.929902	−	0.367806i	$-0.880109\pi$
$241$	−2.27308	+	3.93708i	−0.146422	+	0.253610i	0.783481	+	0.621416i	$0.213442\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−14.2092	+	24.6111i	−0.907793	+	1.57234i
$246$		0			0
$247$	0.0162954	+	0.0282245i	0.00103685	+	0.00179588i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	10.6963			0.675144			0.337572	−	0.941300i	$-0.390394\pi$
$251$	10.6963			0.675144			0.337572	+	0.941300i	$0.390394\pi$
$252$		0			0
$253$	2.17649			0.136835
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.04104	+	10.4634i	0.376829	+	0.652688i	0.990599	−	0.136797i	$-0.0436810\pi$
$257$	6.04104	+	10.4634i	0.376829	+	0.652688i	−0.613770	+	0.789485i	$0.710348\pi$
$258$		0			0
$259$	0.0483798	−	0.0837962i	0.00300617	−	0.00520684i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−10.0327	+	17.3772i	−0.618643	+	1.07152i	0.371090	+	0.928597i	$0.378984\pi$
$263$	−10.0327	+	17.3772i	−0.618643	+	1.07152i	−0.989734	+	0.142925i	$0.954349\pi$
$264$		0			0
$265$	7.34820	+	12.7275i	0.451396	+	0.781841i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.65060			0.100639			0.0503194	−	0.998733i	$-0.483976\pi$
$269$	1.65060			0.100639			0.0503194	+	0.998733i	$0.483976\pi$
$270$		0			0
$271$	−21.5070			−1.30646			−0.653229	−	0.757160i	$-0.726586\pi$
$271$	−21.5070			−1.30646			−0.653229	+	0.757160i	$0.726586\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.75091	+	9.96087i	0.346793	+	0.600663i
$276$		0			0
$277$	−15.1750	+	26.2839i	−0.911779	+	1.57925i	−0.100230	+	0.994964i	$0.531958\pi$
$277$	−15.1750	+	26.2839i	−0.911779	+	1.57925i	−0.811549	+	0.584284i	$0.801376\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	10.5791	−	18.3235i	0.631096	−	1.09309i	−0.356232	−	0.934398i	$-0.615939\pi$
$281$	10.5791	−	18.3235i	0.631096	−	1.09309i	0.987328	−	0.158693i	$-0.0507281\pi$
$282$		0			0
$283$	−14.6096	−	25.3046i	−0.868453	−	1.50420i	−0.863578	−	0.504216i	$-0.831782\pi$
$283$	−14.6096	−	25.3046i	−0.868453	−	1.50420i	−0.00487508	−	0.999988i	$-0.501552\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.492599			0.0290772
$288$		0			0
$289$	−12.8425			−0.755441
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5.00172	−	8.66323i	−0.292204	−	0.506112i	0.682127	−	0.731234i	$-0.261055\pi$
$293$	−5.00172	−	8.66323i	−0.292204	−	0.506112i	−0.974331	+	0.225122i	$0.927722\pi$
$294$		0			0
$295$	−20.4706	+	35.4560i	−1.19184	+	2.06433i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.44758	−	2.50728i	0.0837155	−	0.145000i
$300$		0			0
$301$	0.314843	+	0.545324i	0.0181472	+	0.0314319i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	33.0891			1.89468
$306$		0			0
$307$	−28.8466			−1.64636			−0.823182	−	0.567777i	$-0.807804\pi$
$307$	−28.8466			−1.64636			−0.823182	+	0.567777i	$0.807804\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	14.5377	+	25.1801i	0.824360	+	1.42783i	0.902408	+	0.430883i	$0.141798\pi$
$311$	14.5377	+	25.1801i	0.824360	+	1.42783i	−0.0780481	+	0.996950i	$0.524869\pi$
$312$		0			0
$313$	4.82932	−	8.36462i	0.272969	−	0.472797i	−0.696652	−	0.717410i	$-0.745328\pi$
$313$	4.82932	−	8.36462i	0.272969	−	0.472797i	0.969621	+	0.244613i	$0.0786610\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.77307	+	16.9274i	−0.548910	+	0.950740i	0.449439	+	0.893311i	$0.351624\pi$
$317$	−9.77307	+	16.9274i	−0.548910	+	0.950740i	−0.998350	+	0.0574294i	$0.981710\pi$
$318$		0			0
$319$	5.00575	+	8.67021i	0.280268	+	0.485438i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.0499571			−0.00277969
$324$		0			0
$325$	15.2996			0.848672
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.402031	−	0.696337i	−0.0221647	−	0.0383903i
$330$		0			0
$331$	10.3490	−	17.9250i	0.568832	−	0.985247i	−0.427849	−	0.903850i	$-0.640729\pi$
$331$	10.3490	−	17.9250i	0.568832	−	0.985247i	0.996682	−	0.0813966i	$-0.0259380\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−6.85631	+	11.8755i	−0.374600	+	0.648827i
$336$		0			0
$337$	−10.8104	−	18.7242i	−0.588880	−	1.01997i	−0.994379	−	0.105875i	$-0.966236\pi$
$337$	−10.8104	−	18.7242i	−0.588880	−	1.01997i	0.405499	−	0.914095i	$-0.367098\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−4.44317			−0.240611
$342$		0			0
$343$	0.912895			0.0492917
$344$		0			0
$345$		0			0
$346$		0			0
$347$	12.9751	+	22.4735i	0.696540	+	1.20644i	0.969659	+	0.244462i	$0.0786113\pi$
$347$	12.9751	+	22.4735i	0.696540	+	1.20644i	−0.273119	+	0.961980i	$0.588055\pi$
$348$		0			0
$349$	−8.81880	+	15.2746i	−0.472059	+	0.817631i	−0.999489	−	0.0319680i	$-0.989823\pi$
$349$	−8.81880	+	15.2746i	−0.472059	+	0.817631i	0.527430	+	0.849599i	$0.323156\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.728839	−	1.26239i	0.0387922	−	0.0671900i	−0.845977	−	0.533219i	$-0.820982\pi$
$353$	0.728839	−	1.26239i	0.0387922	−	0.0671900i	0.884770	+	0.466029i	$0.154316\pi$
$354$		0			0
$355$	0.205630	+	0.356161i	0.0109137	+	0.0189031i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	27.4306			1.44773			0.723867	−	0.689940i	$-0.242363\pi$
$359$	27.4306			1.44773			0.723867	+	0.689940i	$0.242363\pi$
$360$		0			0
$361$	−18.9994			−0.999968
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−16.4971	−	28.5739i	−0.863499	−	1.49562i
$366$		0			0
$367$	14.7642	−	25.5724i	0.770685	−	1.33487i	−0.166503	−	0.986041i	$-0.553247\pi$
$367$	14.7642	−	25.5724i	0.770685	−	1.33487i	0.937188	−	0.348825i	$-0.113419\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.117989	−	0.204362i	0.00612566	−	0.0106100i
$372$		0			0
$373$	5.60267	+	9.70410i	0.290095	+	0.502459i	0.973832	−	0.227269i	$-0.0729797\pi$
$373$	5.60267	+	9.70410i	0.290095	+	0.502459i	−0.683737	+	0.729729i	$0.739646\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	13.3172			0.685872
$378$		0			0
$379$	30.5553			1.56952			0.784760	−	0.619799i	$-0.212786\pi$
$379$	30.5553			1.56952			0.784760	+	0.619799i	$0.212786\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	14.4138	+	24.9655i	0.736512	+	1.27568i	0.954057	+	0.299626i	$0.0968618\pi$
$383$	14.4138	+	24.9655i	0.736512	+	1.27568i	−0.217545	+	0.976050i	$0.569805\pi$
$384$		0			0
$385$	0.132483	−	0.229468i	0.00675197	−	0.0116948i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	15.4694	−	26.7938i	0.784329	−	1.35850i	−0.145070	−	0.989421i	$-0.546341\pi$
$389$	15.4694	−	26.7938i	0.784329	−	1.35850i	0.929399	−	0.369076i	$-0.120326\pi$
$390$		0			0
$391$	2.21893	+	3.84330i	0.112216	+	0.194364i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−29.7434			−1.49655
$396$		0			0
$397$	21.7282			1.09050			0.545252	−	0.838272i	$-0.316434\pi$
$397$	21.7282			1.09050			0.545252	+	0.838272i	$0.316434\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	13.5328	+	23.4396i	0.675798	+	1.17052i	0.976235	+	0.216714i	$0.0695340\pi$
$401$	13.5328	+	23.4396i	0.675798	+	1.17052i	−0.300438	+	0.953801i	$0.597133\pi$
$402$		0			0
$403$	−2.95514	+	5.11845i	−0.147206	+	0.254968i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.741718	−	1.28469i	0.0367656	−	0.0636799i
$408$		0			0
$409$	−18.8406	−	32.6329i	−0.931610	−	1.61360i	−0.780570	−	0.625068i	$-0.785071\pi$
$409$	−18.8406	−	32.6329i	−0.931610	−	1.61360i	−0.151039	−	0.988528i	$-0.548262\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.657383			0.0323477
$414$		0			0
$415$	32.0858			1.57503
$416$		0			0
$417$		0			0
$418$		0			0
$419$	8.14703	+	14.1111i	0.398009	+	0.689371i	0.993480	−	0.114005i	$-0.0363681\pi$
$419$	8.14703	+	14.1111i	0.398009	+	0.689371i	−0.595471	+	0.803376i	$0.703035\pi$
$420$		0			0
$421$	−12.8369	+	22.2342i	−0.625633	+	1.08363i	0.362785	+	0.931873i	$0.381826\pi$
$421$	−12.8369	+	22.2342i	−0.625633	+	1.08363i	−0.988418	+	0.151756i	$0.951507\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−11.7261	+	20.3102i	−0.568799	+	0.985188i
$426$		0			0
$427$	−0.265653	−	0.460124i	−0.0128558	−	0.0222670i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	10.2321			0.492861			0.246431	−	0.969160i	$-0.420742\pi$
$431$	10.2321			0.492861			0.246431	+	0.969160i	$0.420742\pi$
$432$		0			0
$433$	19.6352			0.943606			0.471803	−	0.881704i	$-0.343603\pi$
$433$	19.6352			0.943606			0.471803	+	0.881704i	$0.343603\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.0266630	−	0.0461816i	−0.00127546	−	0.00220917i
$438$		0			0
$439$	8.42212	−	14.5875i	0.401966	−	0.696226i	−0.591997	−	0.805940i	$-0.701660\pi$
$439$	8.42212	−	14.5875i	0.401966	−	0.696226i	0.993963	+	0.109715i	$0.0349937\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.88022	+	10.1848i	−0.279378	+	0.483897i	−0.971230	−	0.238142i	$-0.923462\pi$
$443$	−5.88022	+	10.1848i	−0.279378	+	0.483897i	0.691852	+	0.722039i	$0.256795\pi$
$444$		0			0
$445$	−19.2557	−	33.3518i	−0.912806	−	1.58103i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	29.4906			1.39175			0.695873	−	0.718165i	$-0.255018\pi$
$449$	29.4906			1.39175			0.695873	+	0.718165i	$0.255018\pi$
$450$		0			0
$451$	7.55212			0.355615
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.176228	−	0.305236i	−0.00826171	−	0.0143097i
$456$		0			0
$457$	10.5520	−	18.2766i	0.493602	−	0.854944i	−0.506371	−	0.862316i	$-0.669013\pi$
$457$	10.5520	−	18.2766i	0.493602	−	0.854944i	0.999973	+	0.00737216i	$0.00234665\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−4.94710	+	8.56863i	−0.230409	+	0.399081i	−0.957929	−	0.287007i	$-0.907340\pi$
$461$	−4.94710	+	8.56863i	−0.230409	+	0.399081i	0.727519	+	0.686087i	$0.240673\pi$
$462$		0			0
$463$	10.6411	+	18.4308i	0.494532	+	0.856554i	0.999980	−	0.00630289i	$-0.00200629\pi$
$463$	10.6411	+	18.4308i	0.494532	+	0.856554i	−0.505449	+	0.862857i	$0.668673\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.29453			0.291276			0.145638	−	0.989338i	$-0.453477\pi$
$467$	6.29453			0.291276			0.145638	+	0.989338i	$0.453477\pi$
$468$		0			0
$469$	0.220181			0.0101670
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.82691	+	8.36045i	0.221941	+	0.384414i
$474$		0			0
$475$	0.140902	−	0.244050i	0.00646504	−	0.0111978i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	12.0492	−	20.8699i	0.550544	−	0.953570i	−0.447692	−	0.894188i	$-0.647754\pi$
$479$	12.0492	−	20.8699i	0.550544	−	0.953570i	0.998235	−	0.0593816i	$-0.0189129\pi$
$480$		0			0
$481$	−0.986628	−	1.70889i	−0.0449864	−	0.0779187i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−35.0198			−1.59017
$486$		0			0
$487$	−10.0710			−0.456359			−0.228180	−	0.973619i	$-0.573277\pi$
$487$	−10.0710			−0.456359			−0.228180	+	0.973619i	$0.573277\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−10.0667	−	17.4361i	−0.454305	−	0.786879i	0.544343	−	0.838863i	$-0.316779\pi$
$491$	−10.0667	−	17.4361i	−0.454305	−	0.786879i	−0.998648	+	0.0519833i	$0.983446\pi$
$492$		0			0
$493$	−10.2067	+	17.6785i	−0.459686	+	0.796200i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.00330175	−	0.00571880i	0.000148104	−	0.000256523i
$498$		0			0
$499$	7.65567	+	13.2600i	0.342715	+	0.593600i	0.984936	−	0.172920i	$-0.0553201\pi$
$499$	7.65567	+	13.2600i	0.342715	+	0.593600i	−0.642221	+	0.766520i	$0.721987\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−1.52374			−0.0679401			−0.0339701	−	0.999423i	$-0.510815\pi$
$503$	−1.52374			−0.0679401			−0.0339701	+	0.999423i	$0.510815\pi$
$504$		0			0
$505$	−33.4626			−1.48907
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−16.1477	−	27.9687i	−0.715736	−	1.23969i	−0.962675	−	0.270660i	$-0.912758\pi$
$509$	−16.1477	−	27.9687i	−0.715736	−	1.23969i	0.246939	−	0.969031i	$-0.420575\pi$
$510$		0			0
$511$	−0.264891	+	0.458805i	−0.0117181	+	0.0202963i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−25.4318	+	44.0491i	−1.12066	+	1.94104i
$516$		0			0
$517$	−6.16360	−	10.6757i	−0.271075	−	0.469515i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	9.21862			0.403875			0.201937	−	0.979398i	$-0.435276\pi$
$521$	9.21862			0.403875			0.201937	+	0.979398i	$0.435276\pi$
$522$		0			0
$523$	24.5934			1.07539			0.537697	−	0.843138i	$-0.319295\pi$
$523$	24.5934			1.07539			0.537697	+	0.843138i	$0.319295\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.52980	−	7.84585i	−0.197321	−	0.341770i
$528$		0			0
$529$	9.13144	−	15.8161i	0.397019	−	0.687657i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	5.02289	−	8.69990i	0.217565	−	0.376834i
$534$		0			0
$535$	−17.8553	−	30.9262i	−0.771951	−	1.33706i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	6.99575			0.301328
$540$		0			0
$541$	−29.7563			−1.27933			−0.639663	−	0.768656i	$-0.720926\pi$
$541$	−29.7563			−1.27933			−0.639663	+	0.768656i	$0.720926\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−20.2944	−	35.1509i	−0.869317	−	1.50570i
$546$		0			0
$547$	14.8796	−	25.7722i	0.636206	−	1.10194i	−0.350053	−	0.936730i	$-0.613836\pi$
$547$	14.8796	−	25.7722i	0.636206	−	1.10194i	0.986258	−	0.165211i	$-0.0528304\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.122645	−	0.212428i	0.00522486	−	0.00904972i
$552$		0			0
$553$	0.238792	+	0.413600i	0.0101545	+	0.0175880i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.85395			0.120926			0.0604628	−	0.998170i	$-0.480742\pi$
$557$	2.85395			0.120926			0.0604628	+	0.998170i	$0.480742\pi$
$558$		0			0
$559$	12.8414			0.543135
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−20.4188	−	35.3664i	−0.860551	−	1.49052i	−0.871398	−	0.490576i	$-0.836786\pi$
$563$	−20.4188	−	35.3664i	−0.860551	−	1.49052i	0.0108475	−	0.999941i	$-0.496547\pi$
$564$		0			0
$565$	8.39766	−	14.5452i	0.353292	−	0.611920i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.02267	+	10.4316i	−0.252483	+	0.437314i	−0.964209	−	0.265144i	$-0.914581\pi$
$569$	−6.02267	+	10.4316i	−0.252483	+	0.437314i	0.711726	+	0.702458i	$0.247914\pi$
$570$		0			0
$571$	7.28430	+	12.6168i	0.304839	+	0.527996i	0.977225	−	0.212204i	$-0.0680642\pi$
$571$	7.28430	+	12.6168i	0.304839	+	0.527996i	−0.672387	+	0.740200i	$0.734731\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−25.0336			−1.04397
$576$		0			0
$577$	−38.5694			−1.60567			−0.802834	−	0.596203i	$-0.796675\pi$
$577$	−38.5694			−1.60567			−0.802834	+	0.596203i	$0.796675\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.257597	−	0.446172i	−0.0106869	−	0.0185103i
$582$		0			0
$583$	1.80890	−	3.13311i	0.0749170	−	0.129760i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.47077	+	16.4039i	−0.390900	+	0.677060i	−0.992569	−	0.121687i	$-0.961170\pi$
$587$	−9.47077	+	16.4039i	−0.390900	+	0.677060i	0.601668	+	0.798746i	$0.294503\pi$
$588$		0			0
$589$	0.0544307	+	0.0942768i	0.00224278	+	0.00388461i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	29.4929			1.21113			0.605564	−	0.795797i	$-0.292948\pi$
$593$	29.4929			1.21113			0.605564	+	0.795797i	$0.292948\pi$
$594$		0			0
$595$	0.540265			0.0221487
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−6.95571	−	12.0476i	−0.284202	−	0.492253i	0.688213	−	0.725509i	$-0.258395\pi$
$599$	−6.95571	−	12.0476i	−0.284202	−	0.492253i	−0.972415	+	0.233256i	$0.925062\pi$
$600$		0			0
$601$	8.57465	−	14.8517i	0.349767	−	0.605815i	−0.636441	−	0.771326i	$-0.719594\pi$
$601$	8.57465	−	14.8517i	0.349767	−	0.605815i	0.986208	+	0.165511i	$0.0529274\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.03112	−	3.51801i	0.0825768	−	0.143027i
$606$		0			0
$607$	18.0161	+	31.2047i	0.731249	+	1.26656i	0.956350	+	0.292225i	$0.0943956\pi$
$607$	18.0161	+	31.2047i	0.731249	+	1.26656i	−0.225101	+	0.974336i	$0.572271\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−16.3975			−0.663374
$612$		0			0
$613$	5.24646			0.211903			0.105951	−	0.994371i	$-0.466211\pi$
$613$	5.24646			0.211903			0.105951	+	0.994371i	$0.466211\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−21.9328	−	37.9886i	−0.882979	−	1.52937i	−0.848012	−	0.529977i	$-0.822201\pi$
$617$	−21.9328	−	37.9886i	−0.882979	−	1.52937i	−0.0349672	−	0.999388i	$-0.511133\pi$
$618$		0			0
$619$	1.75213	−	3.03477i	0.0704240	−	0.121978i	−0.828663	−	0.559748i	$-0.810898\pi$
$619$	1.75213	−	3.03477i	0.0704240	−	0.121978i	0.899087	+	0.437770i	$0.144231\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−0.309184	+	0.535523i	−0.0123872	+	0.0214553i
$624$		0			0
$625$	−24.8914	−	43.1132i	−0.995657	−	1.72453i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	3.02472			0.120603
$630$		0			0
$631$	1.01155			0.0402690			0.0201345	−	0.999797i	$-0.493591\pi$
$631$	1.01155			0.0402690			0.0201345	+	0.999797i	$0.493591\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	28.3668	+	49.1327i	1.12570	+	1.94977i
$636$		0			0
$637$	4.65285	−	8.05897i	0.184352	−	0.319308i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	22.0619	−	38.2124i	0.871394	−	1.50930i	0.0108390	−	0.999941i	$-0.496550\pi$
$641$	22.0619	−	38.2124i	0.871394	−	1.50930i	0.860555	−	0.509357i	$-0.170117\pi$
$642$		0			0
$643$	21.4009	+	37.0674i	0.843969	+	1.46180i	0.886514	+	0.462702i	$0.153120\pi$
$643$	21.4009	+	37.0674i	0.843969	+	1.46180i	−0.0425451	+	0.999095i	$0.513547\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	37.3725			1.46926			0.734632	−	0.678466i	$-0.237355\pi$
$647$	37.3725			1.46926			0.734632	+	0.678466i	$0.237355\pi$
$648$		0			0
$649$	10.0784			0.395614
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.997227	+	1.72725i	0.0390245	+	0.0675924i	0.884878	−	0.465823i	$-0.154242\pi$
$653$	0.997227	+	1.72725i	0.0390245	+	0.0675924i	−0.845853	+	0.533415i	$0.820908\pi$
$654$		0			0
$655$	39.6244	−	68.6315i	1.54825	−	2.68165i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	21.8763	−	37.8909i	0.852180	−	1.47602i	−0.0270565	−	0.999634i	$-0.508613\pi$
$659$	21.8763	−	37.8909i	0.852180	−	1.47602i	0.879237	−	0.476385i	$-0.158053\pi$
$660$		0			0
$661$	−4.94013	−	8.55656i	−0.192149	−	0.332811i	0.753813	−	0.657089i	$-0.228212\pi$
$661$	−4.94013	−	8.55656i	−0.192149	−	0.332811i	−0.945962	+	0.324277i	$0.894879\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.00649191			−0.000251745
$666$		0			0
$667$	−21.7899			−0.843709
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.07277	−	7.05424i	−0.157227	−	0.272326i
$672$		0			0
$673$	19.9386	−	34.5347i	0.768578	−	1.33122i	−0.169757	−	0.985486i	$-0.554298\pi$
$673$	19.9386	−	34.5347i	0.768578	−	1.33122i	0.938334	−	0.345730i	$-0.112369\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−14.6321	+	25.3436i	−0.562358	+	0.974033i	0.434932	+	0.900463i	$0.356772\pi$
$677$	−14.6321	+	25.3436i	−0.562358	+	0.974033i	−0.997290	+	0.0735697i	$0.976561\pi$
$678$		0			0
$679$	0.281153	+	0.486971i	0.0107897	+	0.0186882i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−15.8274			−0.605618			−0.302809	−	0.953051i	$-0.597924\pi$
$683$	−15.8274			−0.605618			−0.302809	+	0.953051i	$0.597924\pi$
$684$		0			0
$685$	35.7269			1.36506
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2.40619	−	4.16764i	−0.0916685	−	0.158774i
$690$		0			0
$691$	19.5082	−	33.7891i	0.742126	−	1.28540i	−0.209400	−	0.977830i	$-0.567151\pi$
$691$	19.5082	−	33.7891i	0.742126	−	1.28540i	0.951526	−	0.307569i	$-0.0995157\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−19.1678	+	33.1996i	−0.727077	+	1.25933i
$696$		0			0
$697$	7.69937	+	13.3357i	0.291634	+	0.505125i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	10.8646			0.410350			0.205175	−	0.978725i	$-0.434224\pi$
$701$	10.8646			0.410350			0.205175	+	0.978725i	$0.434224\pi$
$702$		0			0
$703$	−0.0363455			−0.00137079
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.268651	+	0.465317i	0.0101037	+	0.0175001i
$708$		0			0
$709$	−12.3842	+	21.4501i	−0.465099	+	0.805575i	−0.999206	−	0.0398420i	$-0.987315\pi$
$709$	−12.3842	+	21.4501i	−0.465099	+	0.805575i	0.534107	+	0.845417i	$0.320648\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4.83526	−	8.37492i	0.181082	−	0.313643i
$714$		0			0
$715$	−2.70178	−	4.67963i	−0.101041	−	0.175008i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−45.2606			−1.68794			−0.843968	−	0.536393i	$-0.819787\pi$
$719$	−45.2606			−1.68794			−0.843968	+	0.536393i	$0.819787\pi$
$720$		0			0
$721$	0.816706			0.0304157
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−57.5752	−	99.7232i	−2.13829	−	3.70363i
$726$		0			0
$727$	12.2434	−	21.2062i	0.454082	−	0.786493i	−0.544553	−	0.838727i	$-0.683301\pi$
$727$	12.2434	−	21.2062i	0.454082	−	0.786493i	0.998635	+	0.0522333i	$0.0166339\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−9.84204	+	17.0469i	−0.364021	+	0.630503i
$732$		0			0
$733$	17.1709	+	29.7409i	0.634221	+	1.09850i	0.986680	+	0.162676i	$0.0520126\pi$
$733$	17.1709	+	29.7409i	0.634221	+	1.09850i	−0.352458	+	0.935828i	$0.614654\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.37563			0.124343
$738$		0			0
$739$	−25.6418			−0.943250			−0.471625	−	0.881799i	$-0.656332\pi$
$739$	−25.6418			−0.943250			−0.471625	+	0.881799i	$0.656332\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−12.6008	−	21.8252i	−0.462277	−	0.800688i	0.536797	−	0.843712i	$-0.319634\pi$
$743$	−12.6008	−	21.8252i	−0.462277	−	0.800688i	−0.999074	+	0.0430239i	$0.986301\pi$
$744$		0			0
$745$	−14.7109	+	25.4801i	−0.538967	+	0.933518i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.286698	+	0.496576i	−0.0104757	+	0.0181445i
$750$		0			0
$751$	−21.4245	−	37.1084i	−0.781792	−	1.35410i	−0.930897	−	0.365282i	$-0.880973\pi$
$751$	−21.4245	−	37.1084i	−0.781792	−	1.35410i	0.149105	−	0.988821i	$-0.452361\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−44.8234			−1.63129
$756$		0			0
$757$	32.4265			1.17856			0.589280	−	0.807929i	$-0.299412\pi$
$757$	32.4265			1.17856			0.589280	+	0.807929i	$0.299412\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.121551	+	0.210533i	0.00440623	+	0.00763182i	0.868220	−	0.496179i	$-0.165264\pi$
$761$	0.121551	+	0.210533i	0.00440623	+	0.00763182i	−0.863814	+	0.503811i	$0.831931\pi$
$762$		0			0
$763$	−0.325863	+	0.564411i	−0.0117970	+	0.0204331i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	6.70314	−	11.6102i	0.242036	−	0.419219i
$768$		0			0
$769$	−7.99151	−	13.8417i	−0.288181	−	0.499145i	0.685194	−	0.728360i	$-0.259717\pi$
$769$	−7.99151	−	13.8417i	−0.288181	−	0.499145i	−0.973376	+	0.229216i	$0.926384\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	27.0172			0.971740			0.485870	−	0.874031i	$-0.338503\pi$
$773$	27.0172			0.971740			0.485870	+	0.874031i	$0.338503\pi$
$774$		0			0
$775$	51.1046			1.83573
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.0925167	−	0.160244i	−0.00331475	−	0.00574132i
$780$		0			0
$781$	0.0506197	−	0.0876759i	0.00181132	−	0.00313729i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−5.09586	+	8.82628i	−0.181879	+	0.315024i
$786$		0			0
$787$	−3.58984	−	6.21779i	−0.127964	−	0.221640i	0.794924	−	0.606710i	$-0.207511\pi$
$787$	−3.58984	−	6.21779i	−0.127964	−	0.221640i	−0.922888	+	0.385069i	$0.874178\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−0.269679			−0.00958868
$792$		0			0
$793$	−10.8351			−0.384767
$794$		0			0
$795$		0			0
$796$		0			0
$797$	17.9938	+	31.1662i	0.637374	+	1.10396i	0.986007	+	0.166705i	$0.0533129\pi$
$797$	17.9938	+	31.1662i	0.637374	+	1.10396i	−0.348632	+	0.937260i	$0.613354\pi$
$798$		0			0
$799$	12.5675	−	21.7676i	0.444608	−	0.770083i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−4.06109	+	7.03401i	−0.143313	+	0.248225i
$804$		0			0
$805$	0.288349	+	0.499434i	0.0101630	+	0.0176028i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	8.20307			0.288405			0.144202	−	0.989548i	$-0.453938\pi$
$809$	8.20307			0.288405			0.144202	+	0.989548i	$0.453938\pi$
$810$		0			0
$811$	−24.6156			−0.864371			−0.432185	−	0.901785i	$-0.642257\pi$
$811$	−24.6156			−0.864371			−0.432185	+	0.901785i	$0.642257\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−25.6849	−	44.4875i	−0.899701	−	1.55833i
$816$		0			0
$817$	0.118263	−	0.204838i	0.00413751	−	0.00716638i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−15.8497	+	27.4524i	−0.553157	+	0.958096i	0.444887	+	0.895586i	$0.353244\pi$
$821$	−15.8497	+	27.4524i	−0.553157	+	0.958096i	−0.998044	+	0.0625094i	$0.980090\pi$
$822$		0			0
$823$	−14.1219	−	24.4598i	−0.492257	−	0.852615i	0.507703	−	0.861532i	$-0.330495\pi$
$823$	−14.1219	−	24.4598i	−0.492257	−	0.852615i	−0.999960	+	0.00891743i	$0.997161\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−9.57682			−0.333019			−0.166509	−	0.986040i	$-0.553250\pi$
$827$	−9.57682			−0.333019			−0.166509	+	0.986040i	$0.553250\pi$
$828$		0			0
$829$	−23.0188			−0.799478			−0.399739	−	0.916629i	$-0.630899\pi$
$829$	−23.0188			−0.799478			−0.399739	+	0.916629i	$0.630899\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	7.13215	+	12.3532i	0.247114	+	0.428014i
$834$		0			0
$835$	22.5793	−	39.1085i	0.781389	−	1.35341i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−12.9156	+	22.3704i	−0.445895	+	0.772313i	−0.998114	−	0.0613862i	$-0.980448\pi$
$839$	−12.9156	+	22.3704i	−0.445895	+	0.772313i	0.552219	+	0.833699i	$0.313781\pi$
$840$		0			0
$841$	−35.6150	−	61.6870i	−1.22810	−	2.12714i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	45.6214			1.56942
$846$		0			0
$847$	−0.0652266			−0.00224121
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.61434	+	2.79612i	0.0553390	+	0.0958499i
$852$		0			0
$853$	−5.47755	+	9.48739i	−0.187548	+	0.324842i	−0.944432	−	0.328707i	$-0.893387\pi$
$853$	−5.47755	+	9.48739i	−0.187548	+	0.324842i	0.756884	+	0.653549i	$0.226721\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	21.8972	−	37.9271i	0.747994	−	1.29556i	−0.200789	−	0.979635i	$-0.564350\pi$
$857$	21.8972	−	37.9271i	0.747994	−	1.29556i	0.948783	−	0.315929i	$-0.102316\pi$
$858$		0			0
$859$	−12.5803	−	21.7897i	−0.429233	−	0.743454i	0.567572	−	0.823324i	$-0.307883\pi$
$859$	−12.5803	−	21.7897i	−0.429233	−	0.743454i	−0.996805	+	0.0798697i	$0.974550\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	10.9731			0.373528			0.186764	−	0.982405i	$-0.440200\pi$
$863$	10.9731			0.373528			0.186764	+	0.982405i	$0.440200\pi$
$864$		0			0
$865$	−4.65814			−0.158382
$866$		0			0
$867$		0			0
$868$		0			0
$869$	3.66096	+	6.34096i	0.124189	+	0.215102i
$870$		0			0
$871$	2.24512	−	3.88866i	0.0760729	−	0.131762i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.861383	+	1.49196i	−0.0291201	+	0.0504374i
$876$		0			0
$877$	10.9602	+	18.9836i	0.370099	+	0.641031i	0.989580	−	0.143981i	$-0.0459903\pi$
$877$	10.9602	+	18.9836i	0.370099	+	0.641031i	−0.619481	+	0.785011i	$0.712657\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	19.9225			0.671205			0.335602	−	0.942004i	$-0.391060\pi$
$881$	19.9225			0.671205			0.335602	+	0.942004i	$0.391060\pi$
$882$		0			0
$883$	4.61989			0.155472			0.0777359	−	0.996974i	$-0.475231\pi$
$883$	4.61989			0.155472			0.0777359	+	0.996974i	$0.475231\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	26.3789	+	45.6896i	0.885717	+	1.53411i	0.844890	+	0.534940i	$0.179666\pi$
$887$	26.3789	+	45.6896i	0.885717	+	1.53411i	0.0408269	+	0.999166i	$0.487001\pi$
$888$		0			0
$889$	0.455480	−	0.788914i	0.0152763	−	0.0264593i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.151013	+	0.261563i	−0.00505347	+	0.00875287i
$894$		0			0
$895$	0.976752	+	1.69178i	0.0326492	+	0.0565501i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	44.4828			1.48358
$900$		0			0
$901$	7.37668			0.245753
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.53314	+	2.65548i	0.0509635	+	0.0882713i
$906$		0			0
$907$	11.1686	−	19.3446i	0.370848	−	0.642328i	−0.618848	−	0.785511i	$-0.712400\pi$
$907$	11.1686	−	19.3446i	0.370848	−	0.642328i	0.989696	+	0.143183i	$0.0457337\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	15.2343	−	26.3865i	0.504733	−	0.874224i	−0.495252	−	0.868750i	$-0.664924\pi$
$911$	15.2343	−	26.3865i	0.504733	−	0.874224i	0.999985	−	0.00547419i	$-0.00174250\pi$
$912$		0			0
$913$	−3.94927	−	6.84033i	−0.130702	−	0.226382i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.27248			−0.0420210
$918$		0			0
$919$	−37.9543			−1.25200			−0.625998	−	0.779824i	$-0.715308\pi$
$919$	−37.9543			−1.25200			−0.625998	+	0.779824i	$0.715308\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.0673340	−	0.116626i	−0.00221633	−	0.00383879i
$924$		0			0
$925$	−8.53111	+	14.7763i	−0.280501	+	0.485842i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−2.36910	+	4.10341i	−0.0777278	+	0.134628i	−0.902269	−	0.431173i	$-0.858100\pi$
$929$	−2.36910	+	4.10341i	−0.0777278	+	0.134628i	0.824541	+	0.565802i	$0.191433\pi$
$930$		0			0
$931$	−0.0857009	−	0.148438i	−0.00280873	−	0.00486487i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	8.28290			0.270880
$936$		0			0
$937$	−25.7283			−0.840507			−0.420254	−	0.907407i	$-0.638059\pi$
$937$	−25.7283			−0.840507			−0.420254	+	0.907407i	$0.638059\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−20.0752	−	34.7712i	−0.654432	−	1.13351i	−0.982036	−	0.188695i	$-0.939574\pi$
$941$	−20.0752	−	34.7712i	−0.654432	−	1.13351i	0.327603	−	0.944815i	$-0.393759\pi$
$942$		0			0
$943$	−8.21856	+	14.2350i	−0.267633	+	0.463554i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.05784	−	1.83224i	0.0343753	−	0.0595397i	−0.848326	−	0.529474i	$-0.822389\pi$
$947$	1.05784	−	1.83224i	0.0343753	−	0.0595397i	0.882701	+	0.469935i	$0.155723\pi$
$948$		0			0
$949$	5.40203	+	9.35659i	0.175357	+	0.303728i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	60.0206			1.94426			0.972129	−	0.234448i	$-0.0753282\pi$
$953$	60.0206			1.94426			0.972129	+	0.234448i	$0.0753282\pi$
$954$		0			0
$955$	89.4274			2.89380
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.286830	−	0.496804i	−0.00926223	−	0.0160427i
$960$		0			0
$961$	5.62913	−	9.74993i	0.181585	−	0.314514i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−54.0102	+	93.5485i	−1.73865	+	3.01143i
$966$		0			0
$967$	−3.12794	−	5.41776i	−0.100588	−	0.174223i	0.811339	−	0.584576i	$-0.198739\pi$
$967$	−3.12794	−	5.41776i	−0.100588	−	0.174223i	−0.911927	+	0.410352i	$0.865406\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	23.5467			0.755649			0.377825	−	0.925877i	$-0.376672\pi$
$971$	23.5467			0.755649			0.377825	+	0.925877i	$0.376672\pi$
$972$		0			0
$973$	0.615547			0.0197335
$974$		0			0
$975$		0			0
$976$		0			0
$977$	23.6751	+	41.0065i	0.757434	+	1.31191i	0.944155	+	0.329501i	$0.106881\pi$
$977$	23.6751	+	41.0065i	0.757434	+	1.31191i	−0.186721	+	0.982413i	$0.559786\pi$
$978$		0			0
$979$	−4.74015	+	8.21019i	−0.151496	+	0.262399i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	5.35029	−	9.26698i	0.170648	−	0.295571i	−0.767999	−	0.640451i	$-0.778747\pi$
$983$	5.35029	−	9.26698i	0.170648	−	0.295571i	0.938647	+	0.344881i	$0.112081\pi$
$984$		0			0
$985$	−2.55854	−	4.43152i	−0.0815218	−	0.141200i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−21.0114			−0.668125
$990$		0			0
$991$	−8.54573			−0.271464			−0.135732	−	0.990746i	$-0.543339\pi$
$991$	−8.54573			−0.271464			−0.135732	+	0.990746i	$0.543339\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.154934	+	0.268354i	0.00491174	+	0.00850739i
$996$		0			0
$997$	12.3913	−	21.4623i	0.392436	−	0.679719i	−0.600334	−	0.799749i	$-0.704966\pi$
$997$	12.3913	−	21.4623i	0.392436	−	0.679719i	0.992770	+	0.120030i	$0.0382992\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3564.2.i.t.1189.6		12
3.2	odd	2		3564.2.i.s.1189.1		12
9.2	odd	6		3564.2.a.p.1.6	yes	6
9.4	even	3	inner	3564.2.i.t.2377.6		12
9.5	odd	6		3564.2.i.s.2377.1		12
9.7	even	3		3564.2.a.o.1.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3564.2.a.o.1.1	✓	6	9.7	even	3
3564.2.a.p.1.6	yes	6	9.2	odd	6
3564.2.i.s.1189.1		12	3.2	odd	2
3564.2.i.s.2377.1		12	9.5	odd	6
3564.2.i.t.1189.6		12	1.1	even	1	trivial
3564.2.i.t.2377.6		12	9.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3564 = 2^{2} \cdot 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3564.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.03112 + 3.51801i) q^{5} +(0.0326133 - 0.0564879i) q^{7} +O(q^{10})\)	\(q+(2.03112 + 3.51801i) q^{5} +(0.0326133 - 0.0564879i) q^{7} +(0.500000 - 0.866025i) q^{11} +(-0.665097 - 1.15198i) q^{13} +2.03900 q^{17} -0.0245009 q^{19} +(1.08825 + 1.88490i) q^{23} +(-5.75091 + 9.96087i) q^{25} +(-5.00575 + 8.67021i) q^{29} +(-2.22158 - 3.84790i) q^{31} +0.264966 q^{35} +1.48344 q^{37} +(3.77606 + 6.54033i) q^{41} +(-4.82691 + 8.36045i) q^{43} +(6.16360 - 10.6757i) q^{47} +(3.49787 + 6.05849i) q^{49} +3.61780 q^{53} +4.06224 q^{55} +(5.03922 + 8.72819i) q^{59} +(4.07277 - 7.05424i) q^{61} +(2.70178 - 4.67963i) q^{65} +(1.68781 + 2.92338i) q^{67} +0.101239 q^{71} -8.12217 q^{73} +(-0.0326133 - 0.0564879i) q^{77} +(-3.66096 + 6.34096i) q^{79} +(3.94927 - 6.84033i) q^{83} +(4.14145 + 7.17320i) q^{85} -9.48031 q^{89} -0.0867640 q^{91} +(-0.0497642 - 0.0861942i) q^{95} +(-4.31040 + 7.46583i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{7}+O(q^{10}) \) 12 * q + 2 * q^7	\( 12 q + 2 q^{7} + 6 q^{11} + 6 q^{13} - 8 q^{17} + 4 q^{23} - 10 q^{25} - 4 q^{29} - 6 q^{31} - 28 q^{35} - 12 q^{37} + 22 q^{41} + 10 q^{43} + 20 q^{47} - 6 q^{49} - 8 q^{53} + 24 q^{59} + 10 q^{61} + 40 q^{65} + 6 q^{67} - 80 q^{71} - 16 q^{73} - 2 q^{77} + 14 q^{79} + 12 q^{83} - 6 q^{85} - 48 q^{89} + 20 q^{91} + 44 q^{95} - 20 q^{97}+O(q^{100}) \) 12 * q + 2 * q^7 + 6 * q^11 + 6 * q^13 - 8 * q^17 + 4 * q^23 - 10 * q^25 - 4 * q^29 - 6 * q^31 - 28 * q^35 - 12 * q^37 + 22 * q^41 + 10 * q^43 + 20 * q^47 - 6 * q^49 - 8 * q^53 + 24 * q^59 + 10 * q^61 + 40 * q^65 + 6 * q^67 - 80 * q^71 - 16 * q^73 - 2 * q^77 + 14 * q^79 + 12 * q^83 - 6 * q^85 - 48 * q^89 + 20 * q^91 + 44 * q^95 - 20 * q^97

Introduction

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