LMFDB - Embedded newform 1080.2.q.b.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1080,2,Mod(361,1080)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1080, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("1080.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.q (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:	$8.62384341830$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 360)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1080.361
Dual form			1080.2.q.b.721.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{5} +(-0.133975 - 0.232051i) q^{7} +O(q^{10})$	$q+(-0.500000 + 0.866025i) q^{5} +(-0.133975 - 0.232051i) q^{7} +(-0.732051 - 1.26795i) q^{11} +(2.73205 - 4.73205i) q^{13} -0.535898 q^{17} -2.00000 q^{19} +(1.86603 - 3.23205i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(0.767949 + 1.33013i) q^{29} +(1.00000 - 1.73205i) q^{31} +0.267949 q^{35} +10.3923 q^{37} +(4.96410 - 8.59808i) q^{41} +(2.26795 + 3.92820i) q^{43} +(0.133975 + 0.232051i) q^{47} +(3.46410 - 6.00000i) q^{49} -6.00000 q^{53} +1.46410 q^{55} +(7.19615 - 12.4641i) q^{59} +(4.23205 + 7.33013i) q^{61} +(2.73205 + 4.73205i) q^{65} +(-3.13397 + 5.42820i) q^{67} -9.46410 q^{71} +6.92820 q^{73} +(-0.196152 + 0.339746i) q^{77} +(-7.73205 - 13.3923i) q^{79} +(-6.59808 - 11.4282i) q^{83} +(0.267949 - 0.464102i) q^{85} +9.92820 q^{89} -1.46410 q^{91} +(1.00000 - 1.73205i) q^{95} +(4.46410 + 7.73205i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{5} - 4 q^{7}+O(q^{10}) $ 4 * q - 2 * q^5 - 4 * q^7	$ 4 q - 2 q^{5} - 4 q^{7} + 4 q^{11} + 4 q^{13} - 16 q^{17} - 8 q^{19} + 4 q^{23} - 2 q^{25} + 10 q^{29} + 4 q^{31} + 8 q^{35} + 6 q^{41} + 16 q^{43} + 4 q^{47} - 24 q^{53} - 8 q^{55} + 8 q^{59} + 10 q^{61} + 4 q^{65} - 16 q^{67} - 24 q^{71} + 20 q^{77} - 24 q^{79} - 16 q^{83} + 8 q^{85} + 12 q^{89} + 8 q^{91} + 4 q^{95} + 4 q^{97}+O(q^{100}) $ 4 * q - 2 * q^5 - 4 * q^7 + 4 * q^11 + 4 * q^13 - 16 * q^17 - 8 * q^19 + 4 * q^23 - 2 * q^25 + 10 * q^29 + 4 * q^31 + 8 * q^35 + 6 * q^41 + 16 * q^43 + 4 * q^47 - 24 * q^53 - 8 * q^55 + 8 * q^59 + 10 * q^61 + 4 * q^65 - 16 * q^67 - 24 * q^71 + 20 * q^77 - 24 * q^79 - 16 * q^83 + 8 * q^85 + 12 * q^89 + 8 * q^91 + 4 * q^95 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$541$	$1001$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−0.133975	−	0.232051i	−0.0506376	−	0.0877070i	0.839596	−	0.543212i	$-0.182792\pi$
$7$	−0.133975	−	0.232051i	−0.0506376	−	0.0877070i	−0.890233	+	0.455505i	$0.849459\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.732051	−	1.26795i	−0.220722	−	0.382301i	0.734306	−	0.678819i	$-0.237508\pi$
$11$	−0.732051	−	1.26795i	−0.220722	−	0.382301i	−0.955027	+	0.296518i	$0.904175\pi$
$12$		0			0
$13$	2.73205	−	4.73205i	0.757735	−	1.31243i	−0.186269	−	0.982499i	$-0.559640\pi$
$13$	2.73205	−	4.73205i	0.757735	−	1.31243i	0.944003	−	0.329936i	$-0.107027\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.535898			−0.129974			−0.0649872	−	0.997886i	$-0.520701\pi$
$17$	−0.535898			−0.129974			−0.0649872	+	0.997886i	$0.520701\pi$
$18$		0			0
$19$	−2.00000			−0.458831			−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000			−0.458831			−0.229416	+	0.973329i	$0.573682\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.86603	−	3.23205i	0.389093	−	0.673929i	−0.603235	−	0.797564i	$-0.706122\pi$
$23$	1.86603	−	3.23205i	0.389093	−	0.673929i	0.992328	+	0.123635i	$0.0394551\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.767949	+	1.33013i	0.142605	+	0.246998i	0.928477	−	0.371391i	$-0.121119\pi$
$29$	0.767949	+	1.33013i	0.142605	+	0.246998i	−0.785872	+	0.618389i	$0.787786\pi$
$30$		0			0
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.267949			0.0452917
$36$		0			0
$37$	10.3923			1.70848			0.854242	−	0.519875i	$-0.174022\pi$
$37$	10.3923			1.70848			0.854242	+	0.519875i	$0.174022\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.96410	−	8.59808i	0.775262	−	1.34279i	−0.159384	−	0.987217i	$-0.550951\pi$
$41$	4.96410	−	8.59808i	0.775262	−	1.34279i	0.934647	−	0.355577i	$-0.115716\pi$
$42$		0			0
$43$	2.26795	+	3.92820i	0.345859	+	0.599045i	0.985509	−	0.169621i	$-0.0542542\pi$
$43$	2.26795	+	3.92820i	0.345859	+	0.599045i	−0.639650	+	0.768666i	$0.720921\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.133975	+	0.232051i	0.0195422	+	0.0338481i	0.875631	−	0.482980i	$-0.160446\pi$
$47$	0.133975	+	0.232051i	0.0195422	+	0.0338481i	−0.856089	+	0.516829i	$0.827112\pi$
$48$		0			0
$49$	3.46410	−	6.00000i	0.494872	−	0.857143i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	1.46410			0.197419
$56$		0			0
$57$		0			0
$58$		0			0
$59$	7.19615	−	12.4641i	0.936859	−	1.62269i	0.165575	−	0.986197i	$-0.447052\pi$
$59$	7.19615	−	12.4641i	0.936859	−	1.62269i	0.771284	−	0.636491i	$-0.219615\pi$
$60$		0			0
$61$	4.23205	+	7.33013i	0.541859	+	0.938527i	0.998797	+	0.0490285i	$0.0156125\pi$
$61$	4.23205	+	7.33013i	0.541859	+	0.938527i	−0.456939	+	0.889498i	$0.651054\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.73205	+	4.73205i	0.338869	+	0.586939i
$66$		0			0
$67$	−3.13397	+	5.42820i	−0.382876	+	0.663161i	−0.991472	−	0.130320i	$-0.958400\pi$
$67$	−3.13397	+	5.42820i	−0.382876	+	0.663161i	0.608596	+	0.793480i	$0.291733\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−9.46410			−1.12318			−0.561591	−	0.827415i	$-0.689811\pi$
$71$	−9.46410			−1.12318			−0.561591	+	0.827415i	$0.689811\pi$
$72$		0			0
$73$	6.92820			0.810885			0.405442	−	0.914121i	$-0.367117\pi$
$73$	6.92820			0.810885			0.405442	+	0.914121i	$0.367117\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.196152	+	0.339746i	−0.0223536	+	0.0387176i
$78$		0			0
$79$	−7.73205	−	13.3923i	−0.869924	−	1.50675i	−0.862074	−	0.506783i	$-0.830835\pi$
$79$	−7.73205	−	13.3923i	−0.869924	−	1.50675i	−0.00784992	−	0.999969i	$-0.502499\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−6.59808	−	11.4282i	−0.724233	−	1.25441i	−0.959289	−	0.282426i	$-0.908861\pi$
$83$	−6.59808	−	11.4282i	−0.724233	−	1.25441i	0.235056	−	0.971982i	$-0.424473\pi$
$84$		0			0
$85$	0.267949	−	0.464102i	0.0290632	−	0.0503389i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	9.92820			1.05239			0.526194	−	0.850365i	$-0.323619\pi$
$89$	9.92820			1.05239			0.526194	+	0.850365i	$0.323619\pi$
$90$		0			0
$91$	−1.46410			−0.153480
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.00000	−	1.73205i	0.102598	−	0.177705i
$96$		0			0
$97$	4.46410	+	7.73205i	0.453261	+	0.785071i	0.998586	−	0.0531536i	$-0.0169273\pi$
$97$	4.46410	+	7.73205i	0.453261	+	0.785071i	−0.545326	+	0.838224i	$0.683594\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.464102	+	0.803848i	0.0461798	+	0.0799858i	0.888191	−	0.459474i	$-0.151962\pi$
$101$	0.464102	+	0.803848i	0.0461798	+	0.0799858i	−0.842012	+	0.539459i	$0.818629\pi$
$102$		0			0
$103$	−7.19615	+	12.4641i	−0.709058	+	1.22812i	0.256149	+	0.966637i	$0.417546\pi$
$103$	−7.19615	+	12.4641i	−0.709058	+	1.22812i	−0.965207	+	0.261487i	$0.915787\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.19615			−0.502331			−0.251166	−	0.967944i	$-0.580814\pi$
$107$	−5.19615			−0.502331			−0.251166	+	0.967944i	$0.580814\pi$
$108$		0			0
$109$	−17.3923			−1.66588			−0.832940	−	0.553363i	$-0.813344\pi$
$109$	−17.3923			−1.66588			−0.832940	+	0.553363i	$0.813344\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.92820	−	12.0000i	0.651751	−	1.12887i	−0.330947	−	0.943649i	$-0.607368\pi$
$113$	6.92820	−	12.0000i	0.651751	−	1.12887i	0.982698	−	0.185216i	$-0.0592984\pi$
$114$		0			0
$115$	1.86603	+	3.23205i	0.174008	+	0.301390i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.0717968	+	0.124356i	0.00658160	+	0.0113997i
$120$		0			0
$121$	4.42820	−	7.66987i	0.402564	−	0.697261i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	16.2679			1.44355			0.721774	−	0.692129i	$-0.243327\pi$
$127$	16.2679			1.44355			0.721774	+	0.692129i	$0.243327\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.73205	+	3.00000i	−0.151330	+	0.262111i	−0.931717	−	0.363186i	$-0.881689\pi$
$131$	−1.73205	+	3.00000i	−0.151330	+	0.262111i	0.780387	+	0.625297i	$0.215022\pi$
$132$		0			0
$133$	0.267949	+	0.464102i	0.0232341	+	0.0402427i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	10.9282	+	18.9282i	0.933659	+	1.61715i	0.777007	+	0.629492i	$0.216737\pi$
$137$	10.9282	+	18.9282i	0.933659	+	1.61715i	0.156652	+	0.987654i	$0.449930\pi$
$138$		0			0
$139$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$139$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−8.00000			−0.668994
$144$		0			0
$145$	−1.53590			−0.127549
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.23205	+	2.13397i	−0.100934	+	0.174822i	−0.912070	−	0.410036i	$-0.865516\pi$
$149$	−1.23205	+	2.13397i	−0.100934	+	0.174822i	0.811136	+	0.584858i	$0.198850\pi$
$150$		0			0
$151$	−2.73205	−	4.73205i	−0.222331	−	0.385089i	0.733184	−	0.680030i	$-0.238033\pi$
$151$	−2.73205	−	4.73205i	−0.222331	−	0.385089i	−0.955515	+	0.294941i	$0.904700\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.00000	+	1.73205i	0.0803219	+	0.139122i
$156$		0			0
$157$	−2.46410	+	4.26795i	−0.196657	+	0.340619i	−0.947442	−	0.319926i	$-0.896342\pi$
$157$	−2.46410	+	4.26795i	−0.196657	+	0.340619i	0.750786	+	0.660546i	$0.229675\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.00000			−0.0788110
$162$		0			0
$163$	−13.3205			−1.04334			−0.521671	−	0.853147i	$-0.674691\pi$
$163$	−13.3205			−1.04334			−0.521671	+	0.853147i	$0.674691\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−10.7942	+	18.6962i	−0.835282	+	1.44675i	0.0585177	+	0.998286i	$0.481363\pi$
$167$	−10.7942	+	18.6962i	−0.835282	+	1.44675i	−0.893800	+	0.448465i	$0.851971\pi$
$168$		0			0
$169$	−8.42820	−	14.5981i	−0.648323	−	1.12293i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.53590	+	7.85641i	0.344858	+	0.597312i	0.985328	−	0.170672i	$-0.0545937\pi$
$173$	4.53590	+	7.85641i	0.344858	+	0.597312i	−0.640470	+	0.767983i	$0.721260\pi$
$174$		0			0
$175$	−0.133975	+	0.232051i	−0.0101275	+	0.0175414i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−13.4641			−1.00635			−0.503177	−	0.864183i	$-0.667836\pi$
$179$	−13.4641			−1.00635			−0.503177	+	0.864183i	$0.667836\pi$
$180$		0			0
$181$	−9.53590			−0.708798			−0.354399	−	0.935094i	$-0.615314\pi$
$181$	−9.53590			−0.708798			−0.354399	+	0.935094i	$0.615314\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−5.19615	+	9.00000i	−0.382029	+	0.661693i
$186$		0			0
$187$	0.392305	+	0.679492i	0.0286882	+	0.0496894i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.46410	+	14.6603i	0.612441	+	1.06078i	0.990828	+	0.135131i	$0.0431456\pi$
$191$	8.46410	+	14.6603i	0.612441	+	1.06078i	−0.378387	+	0.925648i	$0.623521\pi$
$192$		0			0
$193$	8.73205	−	15.1244i	0.628547	−	1.08867i	−0.359297	−	0.933223i	$-0.616983\pi$
$193$	8.73205	−	15.1244i	0.628547	−	1.08867i	0.987844	−	0.155452i	$-0.0496833\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−14.9282			−1.06359			−0.531795	−	0.846873i	$-0.678482\pi$
$197$	−14.9282			−1.06359			−0.531795	+	0.846873i	$0.678482\pi$
$198$		0			0
$199$	7.07180			0.501306			0.250653	−	0.968077i	$-0.419355\pi$
$199$	7.07180			0.501306			0.250653	+	0.968077i	$0.419355\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.205771	−	0.356406i	0.0144423	−	0.0250148i
$204$		0			0
$205$	4.96410	+	8.59808i	0.346708	+	0.600516i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.46410	+	2.53590i	0.101274	+	0.175412i
$210$		0			0
$211$	−0.196152	+	0.339746i	−0.0135037	+	0.0233891i	−0.872698	−	0.488260i	$-0.837632\pi$
$211$	−0.196152	+	0.339746i	−0.0135037	+	0.0233891i	0.859195	+	0.511649i	$0.170965\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4.53590			−0.309346
$216$		0			0
$217$	−0.535898			−0.0363792
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.46410	+	2.53590i	−0.0984861	+	0.170583i
$222$		0			0
$223$	−11.3301	−	19.6244i	−0.758721	−	1.31414i	−0.943503	−	0.331364i	$-0.892491\pi$
$223$	−11.3301	−	19.6244i	−0.758721	−	1.31414i	0.184781	−	0.982780i	$-0.440842\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	12.1244	+	21.0000i	0.804722	+	1.39382i	0.916479	+	0.400083i	$0.131019\pi$
$227$	12.1244	+	21.0000i	0.804722	+	1.39382i	−0.111757	+	0.993736i	$0.535648\pi$
$228$		0			0
$229$	−12.6244	+	21.8660i	−0.834241	+	1.44495i	0.0604061	+	0.998174i	$0.480760\pi$
$229$	−12.6244	+	21.8660i	−0.834241	+	1.44495i	−0.894647	+	0.446774i	$0.852573\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	10.3923			0.680823			0.340411	−	0.940277i	$-0.389434\pi$
$233$	10.3923			0.680823			0.340411	+	0.940277i	$0.389434\pi$
$234$		0			0
$235$	−0.267949			−0.0174791
$236$		0			0
$237$		0			0
$238$		0			0
$239$	10.3923	−	18.0000i	0.672222	−	1.16432i	−0.305050	−	0.952336i	$-0.598673\pi$
$239$	10.3923	−	18.0000i	0.672222	−	1.16432i	0.977273	−	0.211987i	$-0.0679934\pi$
$240$		0			0
$241$	3.03590	+	5.25833i	0.195559	+	0.338719i	0.947084	−	0.320987i	$-0.104014\pi$
$241$	3.03590	+	5.25833i	0.195559	+	0.338719i	−0.751524	+	0.659705i	$0.770681\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.46410	+	6.00000i	0.221313	+	0.383326i
$246$		0			0
$247$	−5.46410	+	9.46410i	−0.347672	+	0.602186i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	7.85641			0.495892			0.247946	−	0.968774i	$-0.420244\pi$
$251$	7.85641			0.495892			0.247946	+	0.968774i	$0.420244\pi$
$252$		0			0
$253$	−5.46410			−0.343525
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.464102	+	0.803848i	−0.0289499	+	0.0501426i	−0.880137	−	0.474719i	$-0.842550\pi$
$257$	−0.464102	+	0.803848i	−0.0289499	+	0.0501426i	0.851187	+	0.524862i	$0.175883\pi$
$258$		0			0
$259$	−1.39230	−	2.41154i	−0.0865136	−	0.149846i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	11.1962	+	19.3923i	0.690384	+	1.19578i	0.971712	+	0.236169i	$0.0758919\pi$
$263$	11.1962	+	19.3923i	0.690384	+	1.19578i	−0.281328	+	0.959612i	$0.590775\pi$
$264$		0			0
$265$	3.00000	−	5.19615i	0.184289	−	0.319197i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−11.3923			−0.694601			−0.347301	−	0.937754i	$-0.612902\pi$
$269$	−11.3923			−0.694601			−0.347301	+	0.937754i	$0.612902\pi$
$270$		0			0
$271$	−19.8564			−1.20619			−0.603095	−	0.797669i	$-0.706066\pi$
$271$	−19.8564			−1.20619			−0.603095	+	0.797669i	$0.706066\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.732051	+	1.26795i	−0.0441443	+	0.0764602i
$276$		0			0
$277$	7.19615	+	12.4641i	0.432375	+	0.748895i	0.997077	−	0.0763993i	$-0.0243424\pi$
$277$	7.19615	+	12.4641i	0.432375	+	0.748895i	−0.564702	+	0.825295i	$0.691009\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−7.42820	−	12.8660i	−0.443129	−	0.767523i	0.554790	−	0.831990i	$-0.312798\pi$
$281$	−7.42820	−	12.8660i	−0.443129	−	0.767523i	−0.997920	+	0.0644675i	$0.979465\pi$
$282$		0			0
$283$	−10.8660	+	18.8205i	−0.645918	+	1.11876i	0.338170	+	0.941085i	$0.390192\pi$
$283$	−10.8660	+	18.8205i	−0.645918	+	1.11876i	−0.984089	+	0.177678i	$0.943141\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.66025			−0.157030
$288$		0			0
$289$	−16.7128			−0.983107
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3.73205	+	6.46410i	−0.218029	+	0.377637i	−0.954205	−	0.299153i	$-0.903296\pi$
$293$	−3.73205	+	6.46410i	−0.218029	+	0.377637i	0.736176	+	0.676790i	$0.236629\pi$
$294$		0			0
$295$	7.19615	+	12.4641i	0.418976	+	0.725688i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−10.1962	−	17.6603i	−0.589659	−	1.02132i
$300$		0			0
$301$	0.607695	−	1.05256i	0.0350270	−	0.0606685i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−8.46410			−0.484653
$306$		0			0
$307$	4.12436			0.235389			0.117695	−	0.993050i	$-0.462450\pi$
$307$	4.12436			0.235389			0.117695	+	0.993050i	$0.462450\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.53590	−	2.66025i	0.0870928	−	0.150849i	−0.819188	−	0.573525i	$-0.805576\pi$
$311$	1.53590	−	2.66025i	0.0870928	−	0.150849i	0.906281	+	0.422676i	$0.138909\pi$
$312$		0			0
$313$	−6.19615	−	10.7321i	−0.350227	−	0.606611i	0.636062	−	0.771638i	$-0.280562\pi$
$313$	−6.19615	−	10.7321i	−0.350227	−	0.606611i	−0.986289	+	0.165027i	$0.947229\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.26795	+	2.19615i	0.0712151	+	0.123348i	0.899434	−	0.437056i	$-0.143979\pi$
$317$	1.26795	+	2.19615i	0.0712151	+	0.123348i	−0.828219	+	0.560405i	$0.810646\pi$
$318$		0			0
$319$	1.12436	−	1.94744i	0.0629518	−	0.109036i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1.07180			0.0596364
$324$		0			0
$325$	−5.46410			−0.303094
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.0358984	−	0.0621778i	0.00197914	−	0.00342797i
$330$		0			0
$331$	1.73205	+	3.00000i	0.0952021	+	0.164895i	0.909693	−	0.415282i	$-0.136317\pi$
$331$	1.73205	+	3.00000i	0.0952021	+	0.164895i	−0.814491	+	0.580176i	$0.802984\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3.13397	−	5.42820i	−0.171227	−	0.296574i
$336$		0			0
$337$	−4.53590	+	7.85641i	−0.247086	+	0.427966i	−0.962716	−	0.270514i	$-0.912806\pi$
$337$	−4.53590	+	7.85641i	−0.247086	+	0.427966i	0.715630	+	0.698480i	$0.246140\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2.92820			−0.158571
$342$		0			0
$343$	−3.73205			−0.201512
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−9.19615	+	15.9282i	−0.493675	+	0.855071i	−0.999973	−	0.00728777i	$-0.997680\pi$
$347$	−9.19615	+	15.9282i	−0.493675	+	0.855071i	0.506298	+	0.862359i	$0.331014\pi$
$348$		0			0
$349$	−0.232051	−	0.401924i	−0.0124214	−	0.0215145i	0.859748	−	0.510719i	$-0.170621\pi$
$349$	−0.232051	−	0.401924i	−0.0124214	−	0.0215145i	−0.872169	+	0.489204i	$0.837287\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−10.9282	−	18.9282i	−0.581650	−	1.00745i	−0.995284	−	0.0970036i	$-0.969074\pi$
$353$	−10.9282	−	18.9282i	−0.581650	−	1.00745i	0.413634	−	0.910443i	$-0.364259\pi$
$354$		0			0
$355$	4.73205	−	8.19615i	0.251151	−	0.435007i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	12.9282			0.682324			0.341162	−	0.940004i	$-0.389179\pi$
$359$	12.9282			0.682324			0.341162	+	0.940004i	$0.389179\pi$
$360$		0			0
$361$	−15.0000			−0.789474
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.46410	+	6.00000i	−0.181319	+	0.314054i
$366$		0			0
$367$	7.19615	+	12.4641i	0.375636	+	0.650621i	0.990422	−	0.138073i	$-0.0440909\pi$
$367$	7.19615	+	12.4641i	0.375636	+	0.650621i	−0.614786	+	0.788694i	$0.710758\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.803848	+	1.39230i	0.0417337	+	0.0722849i
$372$		0			0
$373$	4.46410	−	7.73205i	0.231142	−	0.400350i	−0.727002	−	0.686635i	$-0.759087\pi$
$373$	4.46410	−	7.73205i	0.231142	−	0.400350i	0.958145	+	0.286285i	$0.0924203\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	8.39230			0.432226
$378$		0			0
$379$	35.1769			1.80692			0.903458	−	0.428676i	$-0.141020\pi$
$379$	35.1769			1.80692			0.903458	+	0.428676i	$0.141020\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.73205	−	3.00000i	0.0885037	−	0.153293i	−0.818375	−	0.574684i	$-0.805125\pi$
$383$	1.73205	−	3.00000i	0.0885037	−	0.153293i	0.906879	+	0.421392i	$0.138458\pi$
$384$		0			0
$385$	−0.196152	−	0.339746i	−0.00999685	−	0.0173151i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−11.7679	−	20.3827i	−0.596659	−	1.03344i	−0.993310	−	0.115474i	$-0.963161\pi$
$389$	−11.7679	−	20.3827i	−0.596659	−	1.03344i	0.396652	−	0.917969i	$-0.370172\pi$
$390$		0			0
$391$	−1.00000	+	1.73205i	−0.0505722	+	0.0875936i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	15.4641			0.778083
$396$		0			0
$397$	10.0000			0.501886			0.250943	−	0.968002i	$-0.419259\pi$
$397$	10.0000			0.501886			0.250943	+	0.968002i	$0.419259\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.39230	−	12.8038i	0.369154	−	0.639394i	−0.620279	−	0.784381i	$-0.712981\pi$
$401$	7.39230	−	12.8038i	0.369154	−	0.639394i	0.989434	+	0.144987i	$0.0463141\pi$
$402$		0			0
$403$	−5.46410	−	9.46410i	−0.272186	−	0.471440i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.60770	−	13.1769i	−0.377099	−	0.653155i
$408$		0			0
$409$	−2.46410	+	4.26795i	−0.121842	+	0.211037i	−0.920494	−	0.390757i	$-0.872213\pi$
$409$	−2.46410	+	4.26795i	−0.121842	+	0.211037i	0.798652	+	0.601793i	$0.205547\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−3.85641			−0.189761
$414$		0			0
$415$	13.1962			0.647774
$416$		0			0
$417$		0			0
$418$		0			0
$419$	15.1244	−	26.1962i	0.738873	−	1.27977i	−0.214130	−	0.976805i	$-0.568692\pi$
$419$	15.1244	−	26.1962i	0.738873	−	1.27977i	0.953003	−	0.302961i	$-0.0979751\pi$
$420$		0			0
$421$	18.4641	+	31.9808i	0.899885	+	1.55865i	0.827639	+	0.561260i	$0.189683\pi$
$421$	18.4641	+	31.9808i	0.899885	+	1.55865i	0.0722458	+	0.997387i	$0.476983\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.267949	+	0.464102i	0.0129974	+	0.0225122i
$426$		0			0
$427$	1.13397	−	1.96410i	0.0548769	−	0.0950495i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	4.53590			0.218487			0.109243	−	0.994015i	$-0.465157\pi$
$431$	4.53590			0.218487			0.109243	+	0.994015i	$0.465157\pi$
$432$		0			0
$433$	−12.5359			−0.602437			−0.301218	−	0.953555i	$-0.597393\pi$
$433$	−12.5359			−0.602437			−0.301218	+	0.953555i	$0.597393\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.73205	+	6.46410i	−0.178528	+	0.309220i
$438$		0			0
$439$	−10.5359	−	18.2487i	−0.502851	−	0.870963i	−0.999995	−	0.00329518i	$-0.998951\pi$
$439$	−10.5359	−	18.2487i	−0.502851	−	0.870963i	0.497144	−	0.867668i	$-0.334382\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	17.2583	+	29.8923i	0.819968	+	1.42023i	0.905705	+	0.423908i	$0.139342\pi$
$443$	17.2583	+	29.8923i	0.819968	+	1.42023i	−0.0857370	+	0.996318i	$0.527324\pi$
$444$		0			0
$445$	−4.96410	+	8.59808i	−0.235321	+	0.407588i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−4.14359			−0.195548			−0.0977741	−	0.995209i	$-0.531172\pi$
$449$	−4.14359			−0.195548			−0.0977741	+	0.995209i	$0.531172\pi$
$450$		0			0
$451$	−14.5359			−0.684469
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.732051	−	1.26795i	0.0343191	−	0.0594424i
$456$		0			0
$457$	−2.80385	−	4.85641i	−0.131158	−	0.227173i	0.792965	−	0.609267i	$-0.208536\pi$
$457$	−2.80385	−	4.85641i	−0.131158	−	0.227173i	−0.924123	+	0.382094i	$0.875203\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.30385	+	3.99038i	0.107301	+	0.185851i	0.914676	−	0.404188i	$-0.132446\pi$
$461$	2.30385	+	3.99038i	0.107301	+	0.185851i	−0.807375	+	0.590039i	$0.799113\pi$
$462$		0			0
$463$	1.73205	−	3.00000i	0.0804952	−	0.139422i	−0.822968	−	0.568088i	$-0.807683\pi$
$463$	1.73205	−	3.00000i	0.0804952	−	0.139422i	0.903463	+	0.428667i	$0.141016\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	30.3923			1.40639			0.703194	−	0.710998i	$-0.251757\pi$
$467$	30.3923			1.40639			0.703194	+	0.710998i	$0.251757\pi$
$468$		0			0
$469$	1.67949			0.0775517
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3.32051	−	5.75129i	0.152677	−	0.264445i
$474$		0			0
$475$	1.00000	+	1.73205i	0.0458831	+	0.0794719i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7.19615	−	12.4641i	−0.328801	−	0.569499i	0.653474	−	0.756949i	$-0.273311\pi$
$479$	−7.19615	−	12.4641i	−0.328801	−	0.569499i	−0.982274	+	0.187450i	$0.939978\pi$
$480$		0			0
$481$	28.3923	−	49.1769i	1.29458	−	2.24227i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−8.92820			−0.405409
$486$		0			0
$487$	40.2487			1.82384			0.911922	−	0.410364i	$-0.134599\pi$
$487$	40.2487			1.82384			0.911922	+	0.410364i	$0.134599\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−12.9282	+	22.3923i	−0.583442	+	1.01055i	0.411626	+	0.911353i	$0.364961\pi$
$491$	−12.9282	+	22.3923i	−0.583442	+	1.01055i	−0.995068	+	0.0991978i	$0.968372\pi$
$492$		0			0
$493$	−0.411543	−	0.712813i	−0.0185350	−	0.0321035i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.26795	+	2.19615i	0.0568753	+	0.0985109i
$498$		0			0
$499$	8.92820	−	15.4641i	0.399681	−	0.692268i	−0.594005	−	0.804461i	$-0.702454\pi$
$499$	8.92820	−	15.4641i	0.399681	−	0.692268i	0.993686	+	0.112193i	$0.0357875\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	18.1244			0.808125			0.404063	−	0.914731i	$-0.367598\pi$
$503$	18.1244			0.808125			0.404063	+	0.914731i	$0.367598\pi$
$504$		0			0
$505$	−0.928203			−0.0413045
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−10.3038	+	17.8468i	−0.456710	+	0.791045i	−0.998785	−	0.0492853i	$-0.984306\pi$
$509$	−10.3038	+	17.8468i	−0.456710	+	0.791045i	0.542075	+	0.840330i	$0.317639\pi$
$510$		0			0
$511$	−0.928203	−	1.60770i	−0.0410613	−	0.0711202i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−7.19615	−	12.4641i	−0.317100	−	0.549234i
$516$		0			0
$517$	0.196152	−	0.339746i	0.00862677	−	0.0149420i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	13.0000			0.569540			0.284770	−	0.958596i	$-0.408083\pi$
$521$	13.0000			0.569540			0.284770	+	0.958596i	$0.408083\pi$
$522$		0			0
$523$	10.8038			0.472419			0.236210	−	0.971702i	$-0.424095\pi$
$523$	10.8038			0.472419			0.236210	+	0.971702i	$0.424095\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.535898	+	0.928203i	−0.0233441	+	0.0404332i
$528$		0			0
$529$	4.53590	+	7.85641i	0.197213	+	0.341583i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−27.1244	−	46.9808i	−1.17489	−	2.03496i
$534$		0			0
$535$	2.59808	−	4.50000i	0.112325	−	0.194552i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−10.1436			−0.436916
$540$		0			0
$541$	−18.6077			−0.800007			−0.400004	−	0.916514i	$-0.630991\pi$
$541$	−18.6077			−0.800007			−0.400004	+	0.916514i	$0.630991\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	8.69615	−	15.0622i	0.372502	−	0.645193i
$546$		0			0
$547$	−22.9904	−	39.8205i	−0.982998	−	1.70260i	−0.650517	−	0.759492i	$-0.725448\pi$
$547$	−22.9904	−	39.8205i	−0.982998	−	1.70260i	−0.332481	−	0.943110i	$-0.607886\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.53590	−	2.66025i	−0.0654315	−	0.113331i
$552$		0			0
$553$	−2.07180	+	3.58846i	−0.0881018	+	0.152597i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−32.6410			−1.38304			−0.691522	−	0.722355i	$-0.743060\pi$
$557$	−32.6410			−1.38304			−0.691522	+	0.722355i	$0.743060\pi$
$558$		0			0
$559$	24.7846			1.04828
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−6.20577	+	10.7487i	−0.261542	+	0.453004i	−0.966652	−	0.256094i	$-0.917564\pi$
$563$	−6.20577	+	10.7487i	−0.261542	+	0.453004i	0.705110	+	0.709098i	$0.250898\pi$
$564$		0			0
$565$	6.92820	+	12.0000i	0.291472	+	0.504844i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.00000	+	8.66025i	0.209611	+	0.363057i	0.951592	−	0.307364i	$-0.0994469\pi$
$569$	5.00000	+	8.66025i	0.209611	+	0.363057i	−0.741981	+	0.670421i	$0.766114\pi$
$570$		0			0
$571$	20.3923	−	35.3205i	0.853391	−	1.47812i	−0.0247380	−	0.999694i	$-0.507875\pi$
$571$	20.3923	−	35.3205i	0.853391	−	1.47812i	0.878129	−	0.478423i	$-0.158792\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.73205			−0.155637
$576$		0			0
$577$	32.9282			1.37082			0.685410	−	0.728158i	$-0.259623\pi$
$577$	32.9282			1.37082			0.685410	+	0.728158i	$0.259623\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.76795	+	3.06218i	−0.0733469	+	0.127041i
$582$		0			0
$583$	4.39230	+	7.60770i	0.181911	+	0.315079i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.20577	+	7.28461i	0.173591	+	0.300668i	0.939673	−	0.342075i	$-0.111130\pi$
$587$	4.20577	+	7.28461i	0.173591	+	0.300668i	−0.766082	+	0.642743i	$0.777796\pi$
$588$		0			0
$589$	−2.00000	+	3.46410i	−0.0824086	+	0.142736i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	39.4641			1.62060			0.810298	−	0.586018i	$-0.199305\pi$
$593$	39.4641			1.62060			0.810298	+	0.586018i	$0.199305\pi$
$594$		0			0
$595$	−0.143594			−0.00588676
$596$		0			0
$597$		0			0
$598$		0			0
$599$	0.803848	−	1.39230i	0.0328443	−	0.0568880i	−0.849136	−	0.528174i	$-0.822877\pi$
$599$	0.803848	−	1.39230i	0.0328443	−	0.0568880i	0.881980	+	0.471286i	$0.156210\pi$
$600$		0			0
$601$	−15.3923	−	26.6603i	−0.627865	−	1.08749i	−0.987979	−	0.154586i	$-0.950596\pi$
$601$	−15.3923	−	26.6603i	−0.627865	−	1.08749i	0.360114	−	0.932908i	$-0.382738\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	4.42820	+	7.66987i	0.180032	+	0.311825i
$606$		0			0
$607$	−20.1340	+	34.8731i	−0.817213	+	1.41545i	0.0905152	+	0.995895i	$0.471149\pi$
$607$	−20.1340	+	34.8731i	−0.817213	+	1.41545i	−0.907728	+	0.419559i	$0.862185\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.46410			0.0592312
$612$		0			0
$613$	22.3923			0.904417			0.452208	−	0.891912i	$-0.350636\pi$
$613$	22.3923			0.904417			0.452208	+	0.891912i	$0.350636\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	15.4641	−	26.7846i	0.622561	−	1.07831i	−0.366446	−	0.930439i	$-0.619425\pi$
$617$	15.4641	−	26.7846i	0.622561	−	1.07831i	0.989007	−	0.147868i	$-0.0472412\pi$
$618$		0			0
$619$	18.8564	+	32.6603i	0.757903	+	1.31273i	0.943918	+	0.330180i	$0.107109\pi$
$619$	18.8564	+	32.6603i	0.757903	+	1.31273i	−0.186015	+	0.982547i	$0.559557\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.33013	−	2.30385i	−0.0532904	−	0.0923017i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−5.56922			−0.222059
$630$		0			0
$631$	31.7128			1.26247			0.631234	−	0.775593i	$-0.282549\pi$
$631$	31.7128			1.26247			0.631234	+	0.775593i	$0.282549\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−8.13397	+	14.0885i	−0.322787	+	0.559083i
$636$		0			0
$637$	−18.9282	−	32.7846i	−0.749963	−	1.29897i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−17.4282	−	30.1865i	−0.688373	−	1.19230i	−0.972364	−	0.233470i	$-0.924992\pi$
$641$	−17.4282	−	30.1865i	−0.688373	−	1.19230i	0.283991	−	0.958827i	$-0.408341\pi$
$642$		0			0
$643$	17.1340	−	29.6769i	0.675698	−	1.17034i	−0.300566	−	0.953761i	$-0.597176\pi$
$643$	17.1340	−	29.6769i	0.675698	−	1.17034i	0.976264	−	0.216582i	$-0.0694910\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	16.5167			0.649337			0.324668	−	0.945828i	$-0.394747\pi$
$647$	16.5167			0.649337			0.324668	+	0.945828i	$0.394747\pi$
$648$		0			0
$649$	−21.0718			−0.827140
$650$		0			0
$651$		0			0
$652$		0			0
$653$	15.7321	−	27.2487i	0.615643	−	1.06632i	−0.374629	−	0.927175i	$-0.622230\pi$
$653$	15.7321	−	27.2487i	0.615643	−	1.06632i	0.990271	−	0.139150i	$-0.0444369\pi$
$654$		0			0
$655$	−1.73205	−	3.00000i	−0.0676768	−	0.117220i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−10.3923	−	18.0000i	−0.404827	−	0.701180i	0.589475	−	0.807787i	$-0.299335\pi$
$659$	−10.3923	−	18.0000i	−0.404827	−	0.701180i	−0.994301	+	0.106606i	$0.966001\pi$
$660$		0			0
$661$	−10.8564	+	18.8038i	−0.422265	+	0.731385i	−0.996161	−	0.0875437i	$-0.972098\pi$
$661$	−10.8564	+	18.8038i	−0.422265	+	0.731385i	0.573895	+	0.818929i	$0.305432\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.535898			−0.0207812
$666$		0			0
$667$	5.73205			0.221946
$668$		0			0
$669$		0			0
$670$		0			0
$671$	6.19615	−	10.7321i	0.239200	−	0.414306i
$672$		0			0
$673$	6.33975	+	10.9808i	0.244379	+	0.423277i	0.961957	−	0.273201i	$-0.0880825\pi$
$673$	6.33975	+	10.9808i	0.244379	+	0.423277i	−0.717578	+	0.696479i	$0.754749\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−8.58846	−	14.8756i	−0.330081	−	0.571717i	0.652446	−	0.757835i	$-0.273743\pi$
$677$	−8.58846	−	14.8756i	−0.330081	−	0.571717i	−0.982527	+	0.186118i	$0.940409\pi$
$678$		0			0
$679$	1.19615	−	2.07180i	0.0459041	−	0.0795083i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−22.3923			−0.856818			−0.428409	−	0.903585i	$-0.640926\pi$
$683$	−22.3923			−0.856818			−0.428409	+	0.903585i	$0.640926\pi$
$684$		0			0
$685$	−21.8564			−0.835090
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−16.3923	+	28.3923i	−0.624497	+	1.08166i
$690$		0			0
$691$	25.1962	+	43.6410i	0.958507	+	1.66018i	0.726131	+	0.687556i	$0.241317\pi$
$691$	25.1962	+	43.6410i	0.958507	+	1.66018i	0.232376	+	0.972626i	$0.425350\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−2.66025	+	4.60770i	−0.100764	+	0.174529i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	24.1769			0.913149			0.456575	−	0.889685i	$-0.349076\pi$
$701$	24.1769			0.913149			0.456575	+	0.889685i	$0.349076\pi$
$702$		0			0
$703$	−20.7846			−0.783906
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.124356	−	0.215390i	0.00467688	−	0.00810059i
$708$		0			0
$709$	−7.69615	−	13.3301i	−0.289035	−	0.500623i	0.684545	−	0.728971i	$-0.260001\pi$
$709$	−7.69615	−	13.3301i	−0.289035	−	0.500623i	−0.973580	+	0.228348i	$0.926668\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.73205	−	6.46410i	−0.139766	−	0.242083i
$714$		0			0
$715$	4.00000	−	6.92820i	0.149592	−	0.259100i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	33.3205			1.24265			0.621323	−	0.783555i	$-0.286596\pi$
$719$	33.3205			1.24265			0.621323	+	0.783555i	$0.286596\pi$
$720$		0			0
$721$	3.85641			0.143620
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.767949	−	1.33013i	0.0285209	−	0.0493997i
$726$		0			0
$727$	−7.99038	−	13.8397i	−0.296347	−	0.513288i	0.678950	−	0.734184i	$-0.262435\pi$
$727$	−7.99038	−	13.8397i	−0.296347	−	0.513288i	−0.975297	+	0.220896i	$0.929102\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.21539	−	2.10512i	−0.0449528	−	0.0778606i
$732$		0			0
$733$	−8.07180	+	13.9808i	−0.298139	+	0.516391i	−0.975710	−	0.219066i	$-0.929699\pi$
$733$	−8.07180	+	13.9808i	−0.298139	+	0.516391i	0.677571	+	0.735457i	$0.263032\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	9.17691			0.338036
$738$		0			0
$739$	−0.248711			−0.00914899			−0.00457450	−	0.999990i	$-0.501456\pi$
$739$	−0.248711			−0.00914899			−0.00457450	+	0.999990i	$0.501456\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−16.9186	+	29.3038i	−0.620683	+	1.07505i	0.368676	+	0.929558i	$0.379811\pi$
$743$	−16.9186	+	29.3038i	−0.620683	+	1.07505i	−0.989359	+	0.145496i	$0.953522\pi$
$744$		0			0
$745$	−1.23205	−	2.13397i	−0.0451388	−	0.0781828i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.696152	+	1.20577i	0.0254369	+	0.0440579i
$750$		0			0
$751$	−8.19615	+	14.1962i	−0.299082	+	0.518025i	−0.975926	−	0.218101i	$-0.930014\pi$
$751$	−8.19615	+	14.1962i	−0.299082	+	0.518025i	0.676844	+	0.736126i	$0.263347\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	5.46410			0.198859
$756$		0			0
$757$	−20.3923			−0.741171			−0.370585	−	0.928798i	$-0.620843\pi$
$757$	−20.3923			−0.741171			−0.370585	+	0.928798i	$0.620843\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−10.5000	+	18.1865i	−0.380625	+	0.659261i	−0.991152	−	0.132734i	$-0.957624\pi$
$761$	−10.5000	+	18.1865i	−0.380625	+	0.659261i	0.610527	+	0.791995i	$0.290958\pi$
$762$		0			0
$763$	2.33013	+	4.03590i	0.0843563	+	0.146109i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−39.3205	−	68.1051i	−1.41978	−	2.45913i
$768$		0			0
$769$	−16.8923	+	29.2583i	−0.609152	+	1.05508i	0.382228	+	0.924068i	$0.375157\pi$
$769$	−16.8923	+	29.2583i	−0.609152	+	1.05508i	−0.991380	+	0.131014i	$0.958177\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	8.78461			0.315960			0.157980	−	0.987442i	$-0.449502\pi$
$773$	8.78461			0.315960			0.157980	+	0.987442i	$0.449502\pi$
$774$		0			0
$775$	−2.00000			−0.0718421
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−9.92820	+	17.1962i	−0.355715	+	0.616116i
$780$		0			0
$781$	6.92820	+	12.0000i	0.247911	+	0.429394i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.46410	−	4.26795i	−0.0879476	−	0.152330i
$786$		0			0
$787$	−0.660254	+	1.14359i	−0.0235355	+	0.0407647i	−0.877553	−	0.479479i	$-0.840826\pi$
$787$	−0.660254	+	1.14359i	−0.0235355	+	0.0407647i	0.854018	+	0.520244i	$0.174159\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−3.71281			−0.132012
$792$		0			0
$793$	46.2487			1.64234
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−3.80385	+	6.58846i	−0.134739	+	0.233375i	−0.925498	−	0.378753i	$-0.876353\pi$
$797$	−3.80385	+	6.58846i	−0.134739	+	0.233375i	0.790759	+	0.612128i	$0.209686\pi$
$798$		0			0
$799$	−0.0717968	−	0.124356i	−0.00253999	−	0.00439939i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.07180	−	8.78461i	−0.178980	−	0.310002i
$804$		0			0
$805$	0.500000	−	0.866025i	0.0176227	−	0.0305234i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	48.9282			1.72022			0.860112	−	0.510105i	$-0.170394\pi$
$809$	48.9282			1.72022			0.860112	+	0.510105i	$0.170394\pi$
$810$		0			0
$811$	−50.3923			−1.76951			−0.884757	−	0.466053i	$-0.845675\pi$
$811$	−50.3923			−1.76951			−0.884757	+	0.466053i	$0.845675\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.66025	−	11.5359i	0.233299	−	0.404085i
$816$		0			0
$817$	−4.53590	−	7.85641i	−0.158691	−	0.274861i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	11.6244	+	20.1340i	0.405693	+	0.702681i	0.994402	−	0.105664i	$-0.0336969\pi$
$821$	11.6244	+	20.1340i	0.405693	+	0.702681i	−0.588709	+	0.808345i	$0.700364\pi$
$822$		0			0
$823$	−11.8660	+	20.5526i	−0.413624	+	0.716417i	−0.995283	−	0.0970154i	$-0.969070\pi$
$823$	−11.8660	+	20.5526i	−0.413624	+	0.716417i	0.581659	+	0.813433i	$0.302404\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	16.9474			0.589320			0.294660	−	0.955602i	$-0.404794\pi$
$827$	16.9474			0.589320			0.294660	+	0.955602i	$0.404794\pi$
$828$		0			0
$829$	11.3923			0.395671			0.197836	−	0.980235i	$-0.436609\pi$
$829$	11.3923			0.395671			0.197836	+	0.980235i	$0.436609\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.85641	+	3.21539i	−0.0643207	+	0.111407i
$834$		0			0
$835$	−10.7942	−	18.6962i	−0.373550	−	0.647007i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	17.9282	+	31.0526i	0.618950	+	1.07205i	0.989678	+	0.143312i	$0.0457751\pi$
$839$	17.9282	+	31.0526i	0.618950	+	1.07205i	−0.370727	+	0.928742i	$0.620892\pi$
$840$		0			0
$841$	13.3205	−	23.0718i	0.459328	−	0.795579i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	16.8564			0.579878
$846$		0			0
$847$	−2.37307			−0.0815395
$848$		0			0
$849$		0			0
$850$		0			0
$851$	19.3923	−	33.5885i	0.664760	−	1.15140i
$852$		0			0
$853$	24.7321	+	42.8372i	0.846809	+	1.46672i	0.884041	+	0.467410i	$0.154813\pi$
$853$	24.7321	+	42.8372i	0.846809	+	1.46672i	−0.0372313	+	0.999307i	$0.511854\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	9.12436	+	15.8038i	0.311682	+	0.539849i	0.978727	−	0.205169i	$-0.0657743\pi$
$857$	9.12436	+	15.8038i	0.311682	+	0.539849i	−0.667045	+	0.745018i	$0.732441\pi$
$858$		0			0
$859$	10.1962	−	17.6603i	0.347888	−	0.602560i	−0.637986	−	0.770048i	$-0.720232\pi$
$859$	10.1962	−	17.6603i	0.347888	−	0.602560i	0.985874	+	0.167488i	$0.0535655\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−26.6603			−0.907526			−0.453763	−	0.891123i	$-0.649919\pi$
$863$	−26.6603			−0.907526			−0.453763	+	0.891123i	$0.649919\pi$
$864$		0			0
$865$	−9.07180			−0.308450
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−11.3205	+	19.6077i	−0.384022	+	0.665146i
$870$		0			0
$871$	17.1244	+	29.6603i	0.580237	+	1.00500i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.133975	−	0.232051i	−0.00452917	−	0.00784475i
$876$		0			0
$877$	−5.80385	+	10.0526i	−0.195982	+	0.339451i	−0.947222	−	0.320578i	$-0.896123\pi$
$877$	−5.80385	+	10.0526i	−0.195982	+	0.339451i	0.751240	+	0.660029i	$0.229456\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−37.6410			−1.26816			−0.634079	−	0.773268i	$-0.718621\pi$
$881$	−37.6410			−1.26816			−0.634079	+	0.773268i	$0.718621\pi$
$882$		0			0
$883$	−9.19615			−0.309475			−0.154738	−	0.987956i	$-0.549453\pi$
$883$	−9.19615			−0.309475			−0.154738	+	0.987956i	$0.549453\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−4.66025	+	8.07180i	−0.156476	+	0.271024i	−0.933596	−	0.358329i	$-0.883347\pi$
$887$	−4.66025	+	8.07180i	−0.156476	+	0.271024i	0.777119	+	0.629353i	$0.216680\pi$
$888$		0			0
$889$	−2.17949	−	3.77499i	−0.0730978	−	0.126609i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.267949	−	0.464102i	−0.00896658	−	0.0155306i
$894$		0			0
$895$	6.73205	−	11.6603i	0.225028	−	0.389759i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.07180			0.102450
$900$		0			0
$901$	3.21539			0.107120
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4.76795	−	8.25833i	0.158492	−	0.274516i
$906$		0			0
$907$	6.86603	+	11.8923i	0.227983	+	0.394878i	0.957210	−	0.289394i	$-0.0934537\pi$
$907$	6.86603	+	11.8923i	0.227983	+	0.394878i	−0.729227	+	0.684271i	$0.760120\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−6.26795	−	10.8564i	−0.207666	−	0.359689i	0.743313	−	0.668944i	$-0.233254\pi$
$911$	−6.26795	−	10.8564i	−0.207666	−	0.359689i	−0.950979	+	0.309255i	$0.899920\pi$
$912$		0			0
$913$	−9.66025	+	16.7321i	−0.319708	+	0.553750i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.928203			0.0306520
$918$		0			0
$919$	−17.6077			−0.580824			−0.290412	−	0.956902i	$-0.593792\pi$
$919$	−17.6077			−0.580824			−0.290412	+	0.956902i	$0.593792\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−25.8564	+	44.7846i	−0.851074	+	1.47410i
$924$		0			0
$925$	−5.19615	−	9.00000i	−0.170848	−	0.295918i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	12.3205	+	21.3397i	0.404223	+	0.700134i	0.994231	−	0.107263i	$-0.0342087\pi$
$929$	12.3205	+	21.3397i	0.404223	+	0.700134i	−0.590008	+	0.807397i	$0.700875\pi$
$930$		0			0
$931$	−6.92820	+	12.0000i	−0.227063	+	0.393284i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.784610			−0.0256595
$936$		0			0
$937$	−11.7128			−0.382641			−0.191320	−	0.981528i	$-0.561277\pi$
$937$	−11.7128			−0.382641			−0.191320	+	0.981528i	$0.561277\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−11.6962	+	20.2583i	−0.381284	+	0.660403i	−0.991246	−	0.132028i	$-0.957851\pi$
$941$	−11.6962	+	20.2583i	−0.381284	+	0.660403i	0.609962	+	0.792430i	$0.291185\pi$
$942$		0			0
$943$	−18.5263	−	32.0885i	−0.603299	−	1.04494i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.25833	−	12.5718i	−0.235864	−	0.408529i	0.723659	−	0.690157i	$-0.242459\pi$
$947$	−7.25833	−	12.5718i	−0.235864	−	0.408529i	−0.959523	+	0.281629i	$0.909125\pi$
$948$		0			0
$949$	18.9282	−	32.7846i	0.614435	−	1.06423i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−40.3923			−1.30844			−0.654218	−	0.756306i	$-0.727002\pi$
$953$	−40.3923			−1.30844			−0.654218	+	0.756306i	$0.727002\pi$
$954$		0			0
$955$	−16.9282			−0.547784
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.92820	−	5.07180i	0.0945566	−	0.163777i
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	8.73205	+	15.1244i	0.281095	+	0.486870i
$966$		0			0
$967$	−10.6699	+	18.4808i	−0.343120	+	0.594301i	−0.985010	−	0.172495i	$-0.944817\pi$
$967$	−10.6699	+	18.4808i	−0.343120	+	0.594301i	0.641890	+	0.766796i	$0.278150\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−25.7128			−0.825163			−0.412582	−	0.910921i	$-0.635373\pi$
$971$	−25.7128			−0.825163			−0.412582	+	0.910921i	$0.635373\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.58846	−	14.8756i	0.274769	−	0.475914i	−0.695308	−	0.718712i	$-0.744732\pi$
$977$	8.58846	−	14.8756i	0.274769	−	0.475914i	0.970077	+	0.242798i	$0.0780653\pi$
$978$		0			0
$979$	−7.26795	−	12.5885i	−0.232285	−	0.402329i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	20.2583	+	35.0885i	0.646140	+	1.11915i	0.984037	+	0.177965i	$0.0569513\pi$
$983$	20.2583	+	35.0885i	0.646140	+	1.11915i	−0.337896	+	0.941183i	$0.609715\pi$
$984$		0			0
$985$	7.46410	−	12.9282i	0.237826	−	0.411927i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	16.9282			0.538286
$990$		0			0
$991$	−37.0333			−1.17640			−0.588201	−	0.808715i	$-0.700164\pi$
$991$	−37.0333			−1.17640			−0.588201	+	0.808715i	$0.700164\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−3.53590	+	6.12436i	−0.112096	+	0.194155i
$996$		0			0
$997$	−23.7846	−	41.1962i	−0.753266	−	1.30470i	−0.946232	−	0.323490i	$-0.895144\pi$
$997$	−23.7846	−	41.1962i	−0.753266	−	1.30470i	0.192966	−	0.981206i	$-0.438189\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.q.b.361.2		4
3.2	odd	2		360.2.q.b.121.2	✓	4
4.3	odd	2		2160.2.q.h.1441.1		4
9.2	odd	6		360.2.q.b.241.2	yes	4
9.4	even	3		3240.2.a.p.1.1		2
9.5	odd	6		3240.2.a.k.1.1		2
9.7	even	3	inner	1080.2.q.b.721.2		4
12.11	even	2		720.2.q.h.481.1		4
36.7	odd	6		2160.2.q.h.721.1		4
36.11	even	6		720.2.q.h.241.1		4
36.23	even	6		6480.2.a.ba.1.2		2
36.31	odd	6		6480.2.a.bk.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.q.b.121.2	✓	4	3.2	odd	2
360.2.q.b.241.2	yes	4	9.2	odd	6
720.2.q.h.241.1		4	36.11	even	6
720.2.q.h.481.1		4	12.11	even	2
1080.2.q.b.361.2		4	1.1	even	1	trivial
1080.2.q.b.721.2		4	9.7	even	3	inner
2160.2.q.h.721.1		4	36.7	odd	6
2160.2.q.h.1441.1		4	4.3	odd	2
3240.2.a.k.1.1		2	9.5	odd	6
3240.2.a.p.1.1		2	9.4	even	3
6480.2.a.ba.1.2		2	36.23	even	6
6480.2.a.bk.1.2		2	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{5} +(-0.133975 - 0.232051i) q^{7} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{5} +(-0.133975 - 0.232051i) q^{7} +(-0.732051 - 1.26795i) q^{11} +(2.73205 - 4.73205i) q^{13} -0.535898 q^{17} -2.00000 q^{19} +(1.86603 - 3.23205i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(0.767949 + 1.33013i) q^{29} +(1.00000 - 1.73205i) q^{31} +0.267949 q^{35} +10.3923 q^{37} +(4.96410 - 8.59808i) q^{41} +(2.26795 + 3.92820i) q^{43} +(0.133975 + 0.232051i) q^{47} +(3.46410 - 6.00000i) q^{49} -6.00000 q^{53} +1.46410 q^{55} +(7.19615 - 12.4641i) q^{59} +(4.23205 + 7.33013i) q^{61} +(2.73205 + 4.73205i) q^{65} +(-3.13397 + 5.42820i) q^{67} -9.46410 q^{71} +6.92820 q^{73} +(-0.196152 + 0.339746i) q^{77} +(-7.73205 - 13.3923i) q^{79} +(-6.59808 - 11.4282i) q^{83} +(0.267949 - 0.464102i) q^{85} +9.92820 q^{89} -1.46410 q^{91} +(1.00000 - 1.73205i) q^{95} +(4.46410 + 7.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{5} - 4 q^{7}+O(q^{10}) \) 4 * q - 2 * q^5 - 4 * q^7	\( 4 q - 2 q^{5} - 4 q^{7} + 4 q^{11} + 4 q^{13} - 16 q^{17} - 8 q^{19} + 4 q^{23} - 2 q^{25} + 10 q^{29} + 4 q^{31} + 8 q^{35} + 6 q^{41} + 16 q^{43} + 4 q^{47} - 24 q^{53} - 8 q^{55} + 8 q^{59} + 10 q^{61} + 4 q^{65} - 16 q^{67} - 24 q^{71} + 20 q^{77} - 24 q^{79} - 16 q^{83} + 8 q^{85} + 12 q^{89} + 8 q^{91} + 4 q^{95} + 4 q^{97}+O(q^{100}) \) 4 * q - 2 * q^5 - 4 * q^7 + 4 * q^11 + 4 * q^13 - 16 * q^17 - 8 * q^19 + 4 * q^23 - 2 * q^25 + 10 * q^29 + 4 * q^31 + 8 * q^35 + 6 * q^41 + 16 * q^43 + 4 * q^47 - 24 * q^53 - 8 * q^55 + 8 * q^59 + 10 * q^61 + 4 * q^65 - 16 * q^67 - 24 * q^71 + 20 * q^77 - 24 * q^79 - 16 * q^83 + 8 * q^85 + 12 * q^89 + 8 * q^91 + 4 * q^95 + 4 * q^97

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