LMFDB - Embedded newform 1944.2.i.o.649.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1944,2,Mod(649,1944)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1944, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1944.649");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1944 = 2^{3} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1944.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:	$15.5229181529$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			649.2
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	1944.649
Dual form			1944.2.i.o.1297.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.300767i) q^{5} +(0.673648 - 1.16679i) q^{7} +O(q^{10})$	$q+(0.173648 + 0.300767i) q^{5} +(0.673648 - 1.16679i) q^{7} +(0.0923963 - 0.160035i) q^{11} +(0.918748 + 1.59132i) q^{13} +0.758770 q^{17} +1.94356 q^{19} +(-2.28699 - 3.96118i) q^{23} +(2.43969 - 4.22567i) q^{25} +(0.233956 - 0.405223i) q^{29} +(2.35844 + 4.08494i) q^{31} +0.467911 q^{35} +2.17024 q^{37} +(4.67752 + 8.10170i) q^{41} +(4.69846 - 8.13798i) q^{43} +(-0.826352 + 1.43128i) q^{47} +(2.59240 + 4.49016i) q^{49} -6.70233 q^{53} +0.0641778 q^{55} +(-3.39053 - 5.87257i) q^{59} +(5.99273 - 10.3797i) q^{61} +(-0.319078 + 0.552659i) q^{65} +(1.35457 + 2.34618i) q^{67} +11.9659 q^{71} +1.55438 q^{73} +(-0.124485 - 0.215615i) q^{77} +(6.27972 - 10.8768i) q^{79} +(5.28359 - 9.15144i) q^{83} +(0.131759 + 0.228213i) q^{85} -7.32770 q^{89} +2.47565 q^{91} +(0.337496 + 0.584561i) q^{95} +(2.88919 - 5.00422i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{7}+O(q^{10}) $ 6 * q + 3 * q^7	$ 6 q + 3 q^{7} - 3 q^{11} + 3 q^{13} - 18 q^{17} - 18 q^{19} - 6 q^{23} + 9 q^{25} + 6 q^{29} + 6 q^{31} + 12 q^{35} - 30 q^{37} + 3 q^{41} - 6 q^{47} + 12 q^{49} + 12 q^{53} - 18 q^{55} - 3 q^{59} + 18 q^{61} + 15 q^{65} + 24 q^{67} + 30 q^{71} - 12 q^{73} + 12 q^{77} + 12 q^{79} - 18 q^{83} + 6 q^{85} - 36 q^{89} - 24 q^{91} - 3 q^{95} + 9 q^{97}+O(q^{100}) $ 6 * q + 3 * q^7 - 3 * q^11 + 3 * q^13 - 18 * q^17 - 18 * q^19 - 6 * q^23 + 9 * q^25 + 6 * q^29 + 6 * q^31 + 12 * q^35 - 30 * q^37 + 3 * q^41 - 6 * q^47 + 12 * q^49 + 12 * q^53 - 18 * q^55 - 3 * q^59 + 18 * q^61 + 15 * q^65 + 24 * q^67 + 30 * q^71 - 12 * q^73 + 12 * q^77 + 12 * q^79 - 18 * q^83 + 6 * q^85 - 36 * q^89 - 24 * q^91 - 3 * q^95 + 9 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1944\mathbb{Z}\right)^\times$.

$n$	$487$	$973$	$1217$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.173648	+	0.300767i	0.0776578	+	0.134507i	0.902239	−	0.431236i	$-0.141922\pi$
$5$	0.173648	+	0.300767i	0.0776578	+	0.134507i	−0.824581	+	0.565744i	$0.808589\pi$
$6$		0			0
$7$	0.673648	−	1.16679i	0.254615	−	0.441006i	−0.710176	−	0.704024i	$-0.751385\pi$
$7$	0.673648	−	1.16679i	0.254615	−	0.441006i	0.964791	+	0.263018i	$0.0847179\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.0923963	−	0.160035i	0.0278585	−	0.0482524i	−0.851760	−	0.523932i	$-0.824465\pi$
$11$	0.0923963	−	0.160035i	0.0278585	−	0.0482524i	0.879619	+	0.475680i	$0.157798\pi$
$12$		0			0
$13$	0.918748	+	1.59132i	0.254815	+	0.441352i	0.964845	−	0.262819i	$-0.0846521\pi$
$13$	0.918748	+	1.59132i	0.254815	+	0.441352i	−0.710030	+	0.704171i	$0.751319\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.758770			0.184029			0.0920144	−	0.995758i	$-0.470669\pi$
$17$	0.758770			0.184029			0.0920144	+	0.995758i	$0.470669\pi$
$18$		0			0
$19$	1.94356			0.445884			0.222942	−	0.974832i	$-0.428434\pi$
$19$	1.94356			0.445884			0.222942	+	0.974832i	$0.428434\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.28699	−	3.96118i	−0.476870	−	0.825963i	0.522779	−	0.852469i	$-0.324895\pi$
$23$	−2.28699	−	3.96118i	−0.476870	−	0.825963i	−0.999649	+	0.0265052i	$0.991562\pi$
$24$		0			0
$25$	2.43969	−	4.22567i	0.487939	−	0.845134i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.233956	−	0.405223i	0.0434445	−	0.0752480i	−0.843486	−	0.537152i	$-0.819500\pi$
$29$	0.233956	−	0.405223i	0.0434445	−	0.0752480i	0.886930	+	0.461904i	$0.152834\pi$
$30$		0			0
$31$	2.35844	+	4.08494i	0.423588	+	0.733677i	0.996287	−	0.0860890i	$-0.0274369\pi$
$31$	2.35844	+	4.08494i	0.423588	+	0.733677i	−0.572699	+	0.819766i	$0.694104\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.467911			0.0790914
$36$		0			0
$37$	2.17024			0.356786			0.178393	−	0.983959i	$-0.442910\pi$
$37$	2.17024			0.356786			0.178393	+	0.983959i	$0.442910\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.67752	+	8.10170i	0.730506	+	1.26527i	0.956667	+	0.291183i	$0.0940489\pi$
$41$	4.67752	+	8.10170i	0.730506	+	1.26527i	−0.226162	+	0.974090i	$0.572618\pi$
$42$		0			0
$43$	4.69846	−	8.13798i	0.716509	−	1.24103i	−0.245866	−	0.969304i	$-0.579072\pi$
$43$	4.69846	−	8.13798i	0.716509	−	1.24103i	0.962375	−	0.271726i	$-0.0875944\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.826352	+	1.43128i	−0.120536	+	0.208774i	−0.919979	−	0.391967i	$-0.871795\pi$
$47$	−0.826352	+	1.43128i	−0.120536	+	0.208774i	0.799443	+	0.600742i	$0.205128\pi$
$48$		0			0
$49$	2.59240	+	4.49016i	0.370342	+	0.641452i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.70233			−0.920636			−0.460318	−	0.887754i	$-0.652265\pi$
$53$	−6.70233			−0.920636			−0.460318	+	0.887754i	$0.652265\pi$
$54$		0			0
$55$	0.0641778			0.00865373
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.39053	−	5.87257i	−0.441409	−	0.764543i	0.556385	−	0.830925i	$-0.312188\pi$
$59$	−3.39053	−	5.87257i	−0.441409	−	0.764543i	−0.997794	+	0.0663812i	$0.978855\pi$
$60$		0			0
$61$	5.99273	−	10.3797i	0.767290	−	1.32899i	−0.171737	−	0.985143i	$-0.554938\pi$
$61$	5.99273	−	10.3797i	0.767290	−	1.32899i	0.939027	−	0.343842i	$-0.111729\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.319078	+	0.552659i	−0.0395767	+	0.0685489i
$66$		0			0
$67$	1.35457	+	2.34618i	0.165487	+	0.286632i	0.936828	−	0.349790i	$-0.113747\pi$
$67$	1.35457	+	2.34618i	0.165487	+	0.286632i	−0.771341	+	0.636422i	$0.780414\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	11.9659			1.42009			0.710043	−	0.704159i	$-0.248676\pi$
$71$	11.9659			1.42009			0.710043	+	0.704159i	$0.248676\pi$
$72$		0			0
$73$	1.55438			0.181926			0.0909631	−	0.995854i	$-0.471005\pi$
$73$	1.55438			0.181926			0.0909631	+	0.995854i	$0.471005\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.124485	−	0.215615i	−0.0141864	−	0.0245716i
$78$		0			0
$79$	6.27972	−	10.8768i	0.706523	−	1.22373i	−0.259616	−	0.965712i	$-0.583596\pi$
$79$	6.27972	−	10.8768i	0.706523	−	1.22373i	0.966139	−	0.258022i	$-0.0830707\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.28359	−	9.15144i	0.579949	−	1.00450i	−0.415536	−	0.909577i	$-0.636406\pi$
$83$	5.28359	−	9.15144i	0.579949	−	1.00450i	0.995485	−	0.0949240i	$-0.0302608\pi$
$84$		0			0
$85$	0.131759	+	0.228213i	0.0142913	+	0.0247532i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−7.32770			−0.776734			−0.388367	−	0.921505i	$-0.626961\pi$
$89$	−7.32770			−0.776734			−0.388367	+	0.921505i	$0.626961\pi$
$90$		0			0
$91$	2.47565			0.259519
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.337496	+	0.584561i	0.0346264	+	0.0599746i
$96$		0			0
$97$	2.88919	−	5.00422i	0.293352	−	0.508101i	−0.681248	−	0.732053i	$-0.738562\pi$
$97$	2.88919	−	5.00422i	0.293352	−	0.508101i	0.974600	+	0.223952i	$0.0718958\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−8.60014	+	14.8959i	−0.855746	+	1.48219i	0.0202059	+	0.999796i	$0.493568\pi$
$101$	−8.60014	+	14.8959i	−0.855746	+	1.48219i	−0.875952	+	0.482399i	$0.839766\pi$
$102$		0			0
$103$	0.990200	+	1.71508i	0.0975673	+	0.168991i	0.910677	−	0.413119i	$-0.135561\pi$
$103$	0.990200	+	1.71508i	0.0975673	+	0.168991i	−0.813110	+	0.582110i	$0.802227\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.28817			−0.317879			−0.158940	−	0.987288i	$-0.550808\pi$
$107$	−3.28817			−0.317879			−0.158940	+	0.987288i	$0.550808\pi$
$108$		0			0
$109$	7.29860			0.699079			0.349540	−	0.936922i	$-0.386338\pi$
$109$	7.29860			0.699079			0.349540	+	0.936922i	$0.386338\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.36824	+	11.0301i	0.599074	+	1.03763i	0.992958	+	0.118466i	$0.0377977\pi$
$113$	6.36824	+	11.0301i	0.599074	+	1.03763i	−0.393884	+	0.919160i	$0.628869\pi$
$114$		0			0
$115$	0.794263	−	1.37570i	0.0740654	−	0.128285i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.511144	−	0.885328i	0.0468565	−	0.0811579i
$120$		0			0
$121$	5.48293	+	9.49671i	0.498448	+	0.863337i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.43107			0.306885
$126$		0			0
$127$	9.43882			0.837559			0.418780	−	0.908088i	$-0.362458\pi$
$127$	9.43882			0.837559			0.418780	+	0.908088i	$0.362458\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8.50640	−	14.7335i	−0.743207	−	1.28727i	−0.951028	−	0.309106i	$-0.899970\pi$
$131$	−8.50640	−	14.7335i	−0.743207	−	1.28727i	0.207820	−	0.978167i	$-0.433363\pi$
$132$		0			0
$133$	1.30928	−	2.26774i	0.113529	−	0.196638i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.77972	−	11.7428i	0.579230	−	1.00326i	−0.416338	−	0.909210i	$-0.636687\pi$
$137$	6.77972	−	11.7428i	0.579230	−	1.00326i	0.995568	−	0.0940460i	$-0.0299801\pi$
$138$		0			0
$139$	6.74170	+	11.6770i	0.571823	+	0.990427i	0.996379	+	0.0850250i	$0.0270970\pi$
$139$	6.74170	+	11.6770i	0.571823	+	0.990427i	−0.424556	+	0.905402i	$0.639570\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.339556			0.0283951
$144$		0			0
$145$	0.162504			0.0134952
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.30453	+	12.6518i	0.598410	+	1.03648i	0.993056	+	0.117644i	$0.0375341\pi$
$149$	7.30453	+	12.6518i	0.598410	+	1.03648i	−0.394645	+	0.918833i	$0.629133\pi$
$150$		0			0
$151$	2.01842	−	3.49600i	0.164257	−	0.284501i	−0.772134	−	0.635459i	$-0.780811\pi$
$151$	2.01842	−	3.49600i	0.164257	−	0.284501i	0.936391	+	0.350958i	$0.114144\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.819078	+	1.41868i	−0.0657899	+	0.113951i
$156$		0			0
$157$	2.24763	+	3.89300i	0.179380	+	0.310695i	0.941668	−	0.336542i	$-0.109257\pi$
$157$	2.24763	+	3.89300i	0.179380	+	0.310695i	−0.762288	+	0.647238i	$0.775924\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−6.16250			−0.485673
$162$		0			0
$163$	−0.411474			−0.0322291			−0.0161146	−	0.999870i	$-0.505130\pi$
$163$	−0.411474			−0.0322291			−0.0161146	+	0.999870i	$0.505130\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.38666	−	11.0620i	−0.494215	−	0.856005i	0.505763	−	0.862672i	$-0.331211\pi$
$167$	−6.38666	−	11.0620i	−0.494215	−	0.856005i	−0.999978	+	0.00666766i	$0.997878\pi$
$168$		0			0
$169$	4.81180	−	8.33429i	0.370139	−	0.641099i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.57650	+	14.8549i	−0.652060	+	1.12940i	0.330563	+	0.943784i	$0.392761\pi$
$173$	−8.57650	+	14.8549i	−0.652060	+	1.12940i	−0.982622	+	0.185616i	$0.940572\pi$
$174$		0			0
$175$	−3.28699	−	5.69323i	−0.248473	−	0.430368i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	18.4047			1.37563			0.687815	−	0.725886i	$-0.258570\pi$
$179$	18.4047			1.37563			0.687815	+	0.725886i	$0.258570\pi$
$180$		0			0
$181$	−8.31315			−0.617911			−0.308956	−	0.951076i	$-0.599979\pi$
$181$	−8.31315			−0.617911			−0.308956	+	0.951076i	$0.599979\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.376859	+	0.652739i	0.0277072	+	0.0479903i
$186$		0			0
$187$	0.0701076	−	0.121430i	0.00512677	−	0.00887983i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	10.1532	−	17.5858i	0.734658	−	1.27246i	−0.220216	−	0.975451i	$-0.570676\pi$
$191$	10.1532	−	17.5858i	0.734658	−	1.27246i	0.954873	−	0.297013i	$-0.0959905\pi$
$192$		0			0
$193$	−7.40807	−	12.8312i	−0.533245	−	0.923607i	−0.999246	−	0.0388228i	$-0.987639\pi$
$193$	−7.40807	−	12.8312i	−0.533245	−	0.923607i	0.466002	−	0.884784i	$-0.345694\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−17.2371			−1.22809			−0.614047	−	0.789270i	$-0.710459\pi$
$197$	−17.2371			−1.22809			−0.614047	+	0.789270i	$0.710459\pi$
$198$		0			0
$199$	3.65539			0.259124			0.129562	−	0.991571i	$-0.458643\pi$
$199$	3.65539			0.259124			0.129562	+	0.991571i	$0.458643\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.315207	−	0.545955i	−0.0221232	−	0.0383186i
$204$		0			0
$205$	−1.62449	+	2.81369i	−0.113459	+	0.196517i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.179578	−	0.311038i	0.0124217	−	0.0215150i
$210$		0			0
$211$	−1.59492	−	2.76249i	−0.109799	−	0.190177i	0.805890	−	0.592066i	$-0.201687\pi$
$211$	−1.59492	−	2.76249i	−0.109799	−	0.190177i	−0.915689	+	0.401888i	$0.868354\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3.26352			0.222570
$216$		0			0
$217$	6.35504			0.431408
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.697119	+	1.20745i	0.0468933	+	0.0812216i
$222$		0			0
$223$	−6.85844	+	11.8792i	−0.459275	+	0.795488i	−0.998923	−	0.0464031i	$-0.985224\pi$
$223$	−6.85844	+	11.8792i	−0.459275	+	0.795488i	0.539648	+	0.841891i	$0.318557\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.72281	+	4.71605i	−0.180719	+	0.313015i	−0.942126	−	0.335260i	$-0.891176\pi$
$227$	−2.72281	+	4.71605i	−0.180719	+	0.313015i	0.761406	+	0.648275i	$0.224509\pi$
$228$		0			0
$229$	1.10607	+	1.91576i	0.0730910	+	0.126597i	0.900255	−	0.435364i	$-0.143380\pi$
$229$	1.10607	+	1.91576i	0.0730910	+	0.126597i	−0.827164	+	0.561961i	$0.810047\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	16.7597			1.09796			0.548982	−	0.835834i	$-0.315015\pi$
$233$	16.7597			1.09796			0.548982	+	0.835834i	$0.315015\pi$
$234$		0			0
$235$	−0.573978			−0.0374422
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−8.80840	−	15.2566i	−0.569768	−	0.986867i	−0.996589	−	0.0825308i	$-0.973700\pi$
$239$	−8.80840	−	15.2566i	−0.569768	−	0.986867i	0.426820	−	0.904336i	$-0.359634\pi$
$240$		0			0
$241$	−8.29473	+	14.3669i	−0.534311	+	0.925453i	0.464886	+	0.885371i	$0.346095\pi$
$241$	−8.29473	+	14.3669i	−0.534311	+	0.925453i	−0.999196	+	0.0400823i	$0.987238\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.900330	+	1.55942i	−0.0575200	+	0.0996275i
$246$		0			0
$247$	1.78564	+	3.09283i	0.113618	+	0.196792i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−10.4115			−0.657166			−0.328583	−	0.944475i	$-0.606571\pi$
$251$	−10.4115			−0.657166			−0.328583	+	0.944475i	$0.606571\pi$
$252$		0			0
$253$	−0.845237			−0.0531396
$254$		0			0
$255$		0			0
$256$		0			0
$257$	14.4547	+	25.0363i	0.901660	+	1.56172i	0.825339	+	0.564637i	$0.190984\pi$
$257$	14.4547	+	25.0363i	0.901660	+	1.56172i	0.0763208	+	0.997083i	$0.475683\pi$
$258$		0			0
$259$	1.46198	−	2.53223i	0.0908431	−	0.157345i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−7.75624	+	13.4342i	−0.478271	+	0.828389i	−0.999690	−	0.0249119i	$-0.992069\pi$
$263$	−7.75624	+	13.4342i	−0.478271	+	0.828389i	0.521419	+	0.853301i	$0.325403\pi$
$264$		0			0
$265$	−1.16385	−	2.01584i	−0.0714946	−	0.123832i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−18.8503			−1.14932			−0.574661	−	0.818391i	$-0.694866\pi$
$269$	−18.8503			−1.14932			−0.574661	+	0.818391i	$0.694866\pi$
$270$		0			0
$271$	−27.8607			−1.69242			−0.846209	−	0.532851i	$-0.821121\pi$
$271$	−27.8607			−1.69242			−0.846209	+	0.532851i	$0.821121\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.450837	−	0.780873i	−0.0271865	−	0.0470884i
$276$		0			0
$277$	1.16772	−	2.02255i	0.0701614	−	0.121523i	−0.828811	−	0.559529i	$-0.810982\pi$
$277$	1.16772	−	2.02255i	0.0701614	−	0.121523i	0.898972	+	0.438006i	$0.144315\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	7.69459	−	13.3274i	0.459021	−	0.795048i	−0.539889	−	0.841737i	$-0.681534\pi$
$281$	7.69459	−	13.3274i	0.459021	−	0.795048i	0.998909	+	0.0466890i	$0.0148670\pi$
$282$		0			0
$283$	−11.8204	−	20.4736i	−0.702651	−	1.21703i	−0.967533	−	0.252746i	$-0.918666\pi$
$283$	−11.8204	−	20.4736i	−0.702651	−	1.21703i	0.264881	−	0.964281i	$-0.414667\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	12.6040			0.743991
$288$		0			0
$289$	−16.4243			−0.966133
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5.65657	−	9.79747i	−0.330461	−	0.572375i	0.652142	−	0.758097i	$-0.273871\pi$
$293$	−5.65657	−	9.79747i	−0.330461	−	0.572375i	−0.982602	+	0.185723i	$0.940537\pi$
$294$		0			0
$295$	1.17752	−	2.03952i	0.0685578	−	0.118746i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	4.20233	−	7.27866i	0.243027	−	0.420935i
$300$		0			0
$301$	−6.33022	−	10.9643i	−0.364868	−	0.631970i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.16250			0.238344
$306$		0			0
$307$	−4.68273			−0.267258			−0.133629	−	0.991031i	$-0.542663\pi$
$307$	−4.68273			−0.267258			−0.133629	+	0.991031i	$0.542663\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	2.63816	+	4.56942i	0.149596	+	0.259108i	0.931078	−	0.364820i	$-0.118869\pi$
$311$	2.63816	+	4.56942i	0.149596	+	0.259108i	−0.781482	+	0.623928i	$0.785536\pi$
$312$		0			0
$313$	−8.36097	+	14.4816i	−0.472590	+	0.818550i	−0.999508	−	0.0313665i	$-0.990014\pi$
$313$	−8.36097	+	14.4816i	−0.472590	+	0.818550i	0.526918	+	0.849916i	$0.323347\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.89693	+	15.4099i	−0.499701	+	0.865508i	−1.00000		0.000345037i	$-0.999890\pi$
$317$	−8.89693	+	15.4099i	−0.499701	+	0.865508i	0.500299	+	0.865853i	$0.333224\pi$
$318$		0			0
$319$	−0.0432332	−	0.0748822i	−0.00242060	−	0.00419260i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1.47472			0.0820555
$324$		0			0
$325$	8.96585			0.497336
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.11334	+	1.92836i	0.0613805	+	0.106314i
$330$		0			0
$331$	−14.3503	+	24.8554i	−0.788763	+	1.36618i	0.137962	+	0.990438i	$0.455945\pi$
$331$	−14.3503	+	24.8554i	−0.788763	+	1.36618i	−0.926725	+	0.375740i	$0.877388\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.470437	+	0.814821i	−0.0257027	+	0.0445184i
$336$		0			0
$337$	4.70233	+	8.14468i	0.256152	+	0.443669i	0.965208	−	0.261484i	$-0.0842118\pi$
$337$	4.70233	+	8.14468i	0.256152	+	0.443669i	−0.709055	+	0.705153i	$0.750878\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.871644			0.0472022
$342$		0			0
$343$	16.4165			0.886409
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.55303	−	13.0822i	−0.405468	−	0.702291i	0.588908	−	0.808200i	$-0.299558\pi$
$347$	−7.55303	−	13.0822i	−0.405468	−	0.702291i	−0.994376	+	0.105909i	$0.966225\pi$
$348$		0			0
$349$	−11.2763	+	19.5311i	−0.603607	+	1.04548i	0.388663	+	0.921380i	$0.372937\pi$
$349$	−11.2763	+	19.5311i	−0.603607	+	1.04548i	−0.992270	+	0.124098i	$0.960396\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	15.6937	−	27.1823i	0.835292	−	1.44677i	−0.0585001	−	0.998287i	$-0.518632\pi$
$353$	15.6937	−	27.1823i	0.835292	−	1.44677i	0.893792	−	0.448481i	$-0.148035\pi$
$354$		0			0
$355$	2.07785	+	3.59894i	0.110281	+	0.191012i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.59627			−0.0842477			−0.0421239	−	0.999112i	$-0.513412\pi$
$359$	−1.59627			−0.0842477			−0.0421239	+	0.999112i	$0.513412\pi$
$360$		0			0
$361$	−15.2226			−0.801188
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.269915	+	0.467506i	0.0141280	+	0.0244704i
$366$		0			0
$367$	−12.4251	+	21.5210i	−0.648587	+	1.12339i	0.334873	+	0.942263i	$0.391307\pi$
$367$	−12.4251	+	21.5210i	−0.648587	+	1.12339i	−0.983460	+	0.181123i	$0.942027\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.51501	+	7.82023i	−0.234408	+	0.406006i
$372$		0			0
$373$	−7.79813	−	13.5068i	−0.403772	−	0.699354i	0.590406	−	0.807107i	$-0.298968\pi$
$373$	−7.79813	−	13.5068i	−0.403772	−	0.699354i	−0.994178	+	0.107753i	$0.965634\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.859785			0.0442812
$378$		0			0
$379$	−5.37733			−0.276215			−0.138107	−	0.990417i	$-0.544102\pi$
$379$	−5.37733			−0.276215			−0.138107	+	0.990417i	$0.544102\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.0846555	+	0.146628i	0.00432569	+	0.00749232i	0.868180	−	0.496249i	$-0.165290\pi$
$383$	0.0846555	+	0.146628i	0.00432569	+	0.00749232i	−0.863854	+	0.503741i	$0.831956\pi$
$384$		0			0
$385$	0.0432332	−	0.0748822i	0.00220337	−	0.00381635i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−11.2836	+	19.5437i	−0.572100	+	0.990907i	0.424250	+	0.905545i	$0.360538\pi$
$389$	−11.2836	+	19.5437i	−0.572100	+	0.990907i	−0.996350	+	0.0853618i	$0.972795\pi$
$390$		0			0
$391$	−1.73530	−	3.00563i	−0.0877579	−	0.152001i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	4.36184			0.219468
$396$		0			0
$397$	−17.9641			−0.901592			−0.450796	−	0.892627i	$-0.648860\pi$
$397$	−17.9641			−0.901592			−0.450796	+	0.892627i	$0.648860\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.14290	+	10.6398i	0.306762	+	0.531327i	0.977652	−	0.210229i	$-0.0674211\pi$
$401$	6.14290	+	10.6398i	0.306762	+	0.531327i	−0.670890	+	0.741557i	$0.734088\pi$
$402$		0			0
$403$	−4.33363	+	7.50606i	−0.215873	+	0.373903i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.200522	−	0.347315i	0.00993953	−	0.0172158i
$408$		0			0
$409$	−8.76604	−	15.1832i	−0.433453	−	0.750763i	0.563715	−	0.825969i	$-0.309372\pi$
$409$	−8.76604	−	15.1832i	−0.433453	−	0.750763i	−0.997168	+	0.0752068i	$0.976038\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−9.13610			−0.449558
$414$		0			0
$415$	3.66994			0.180150
$416$		0			0
$417$		0			0
$418$		0			0
$419$	12.9094	+	22.3598i	0.630666	+	1.09235i	0.987416	+	0.158146i	$0.0505516\pi$
$419$	12.9094	+	22.3598i	0.630666	+	1.09235i	−0.356750	+	0.934200i	$0.616115\pi$
$420$		0			0
$421$	−13.4945	+	23.3732i	−0.657683	+	1.13914i	0.323530	+	0.946218i	$0.395130\pi$
$421$	−13.4945	+	23.3732i	−0.657683	+	1.13914i	−0.981214	+	0.192923i	$0.938203\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.85117	−	3.20631i	0.0897948	−	0.155529i
$426$		0			0
$427$	−8.07398	−	13.9845i	−0.390727	−	0.676759i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−32.8280			−1.58127			−0.790635	−	0.612288i	$-0.790249\pi$
$431$	−32.8280			−1.58127			−0.790635	+	0.612288i	$0.790249\pi$
$432$		0			0
$433$	28.4115			1.36537			0.682684	−	0.730714i	$-0.260812\pi$
$433$	28.4115			1.36537			0.682684	+	0.730714i	$0.260812\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.44491	−	7.69881i	−0.212629	−	0.368284i
$438$		0			0
$439$	−9.60401	+	16.6346i	−0.458374	+	0.793928i	−0.998875	−	0.0474159i	$-0.984901\pi$
$439$	−9.60401	+	16.6346i	−0.458374	+	0.793928i	0.540501	+	0.841343i	$0.318235\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.72028	−	9.90782i	0.271779	−	0.470735i	−0.697538	−	0.716547i	$-0.745721\pi$
$443$	5.72028	−	9.90782i	0.271779	−	0.470735i	0.969317	+	0.245812i	$0.0790547\pi$
$444$		0			0
$445$	−1.27244	−	2.20393i	−0.0603195	−	0.104476i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	12.6117			0.595185			0.297593	−	0.954693i	$-0.403816\pi$
$449$	12.6117			0.595185			0.297593	+	0.954693i	$0.403816\pi$
$450$		0			0
$451$	1.72874			0.0814032
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.429892	+	0.744596i	0.0201537	+	0.0349072i
$456$		0			0
$457$	−11.3883	+	19.7251i	−0.532723	+	0.922703i	0.466547	+	0.884496i	$0.345498\pi$
$457$	−11.3883	+	19.7251i	−0.532723	+	0.922703i	−0.999270	+	0.0382063i	$0.987836\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−12.0885	+	20.9379i	−0.563019	+	0.975177i	0.434212	+	0.900811i	$0.357027\pi$
$461$	−12.0885	+	20.9379i	−0.563019	+	0.975177i	−0.997231	+	0.0743665i	$0.976307\pi$
$462$		0			0
$463$	−8.20961	−	14.2195i	−0.381533	−	0.660834i	0.609749	−	0.792595i	$-0.291270\pi$
$463$	−8.20961	−	14.2195i	−0.381533	−	0.660834i	−0.991282	+	0.131761i	$0.957937\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	21.2814			0.984784			0.492392	−	0.870374i	$-0.336123\pi$
$467$	21.2814			0.984784			0.492392	+	0.870374i	$0.336123\pi$
$468$		0			0
$469$	3.65002			0.168542
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.868241	−	1.50384i	−0.0399218	−	0.0691465i
$474$		0			0
$475$	4.74170	−	8.21286i	0.217564	−	0.376832i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	5.64543	−	9.77817i	0.257946	−	0.446776i	−0.707745	−	0.706468i	$-0.750288\pi$
$479$	5.64543	−	9.77817i	0.257946	−	0.446776i	0.965692	+	0.259692i	$0.0836209\pi$
$480$		0			0
$481$	1.99391	+	3.45355i	0.0909144	+	0.157468i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.00681			0.0911244
$486$		0			0
$487$	−39.4894			−1.78943			−0.894717	−	0.446633i	$-0.852623\pi$
$487$	−39.4894			−1.78943			−0.894717	+	0.446633i	$0.852623\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−5.31315	−	9.20264i	−0.239779	−	0.415309i	0.720872	−	0.693068i	$-0.243742\pi$
$491$	−5.31315	−	9.20264i	−0.239779	−	0.415309i	−0.960651	+	0.277759i	$0.910408\pi$
$492$		0			0
$493$	0.177519	−	0.307471i	0.00799503	−	0.0138478i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	8.06077	−	13.9617i	0.361575	−	0.626267i
$498$		0			0
$499$	−6.56939	−	11.3785i	−0.294086	−	0.509373i	0.680686	−	0.732576i	$-0.261682\pi$
$499$	−6.56939	−	11.3785i	−0.294086	−	0.509373i	−0.974772	+	0.223203i	$0.928349\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−1.69635			−0.0756364			−0.0378182	−	0.999285i	$-0.512041\pi$
$503$	−1.69635			−0.0756364			−0.0378182	+	0.999285i	$0.512041\pi$
$504$		0			0
$505$	−5.97359			−0.265821
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−19.3059	−	33.4388i	−0.855718	−	1.48215i	−0.875977	−	0.482352i	$-0.839783\pi$
$509$	−19.3059	−	33.4388i	−0.855718	−	1.48215i	0.0202597	−	0.999795i	$-0.493551\pi$
$510$		0			0
$511$	1.04710	−	1.81364i	0.0463211	−	0.0802306i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.343893	+	0.595640i	−0.0151537	+	0.0262470i
$516$		0			0
$517$	0.152704	+	0.264490i	0.00671590	+	0.0116323i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	13.1070			0.574228			0.287114	−	0.957896i	$-0.407304\pi$
$521$	13.1070			0.574228			0.287114	+	0.957896i	$0.407304\pi$
$522$		0			0
$523$	−8.50030			−0.371692			−0.185846	−	0.982579i	$-0.559503\pi$
$523$	−8.50030			−0.371692			−0.185846	+	0.982579i	$0.559503\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.78952	+	3.09953i	0.0779525	+	0.135018i
$528$		0			0
$529$	1.03936	−	1.80023i	0.0451897	−	0.0782708i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−8.59492	+	14.8868i	−0.372287	+	0.644821i
$534$		0			0
$535$	−0.570985	−	0.988975i	−0.0246858	−	0.0427571i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.958111			0.0412688
$540$		0			0
$541$	−4.32770			−0.186062			−0.0930311	−	0.995663i	$-0.529656\pi$
$541$	−4.32770			−0.186062			−0.0930311	+	0.995663i	$0.529656\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.26739	+	2.19518i	0.0542890	+	0.0940312i
$546$		0			0
$547$	−15.0424	+	26.0541i	−0.643165	+	1.11399i	0.341557	+	0.939861i	$0.389046\pi$
$547$	−15.0424	+	26.0541i	−0.643165	+	1.11399i	−0.984722	+	0.174133i	$0.944288\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.454707	−	0.787576i	0.0193712	−	0.0335519i
$552$		0			0
$553$	−8.46064	−	14.6543i	−0.359783	−	0.623162i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.31221			0.182714			0.0913572	−	0.995818i	$-0.470879\pi$
$557$	4.31221			0.182714			0.0913572	+	0.995818i	$0.470879\pi$
$558$		0			0
$559$	17.2668			0.730309
$560$		0			0
$561$		0			0
$562$		0			0
$563$	13.9636	+	24.1857i	0.588497	+	1.01931i	0.994430	+	0.105403i	$0.0336134\pi$
$563$	13.9636	+	24.1857i	0.588497	+	1.01931i	−0.405933	+	0.913903i	$0.633053\pi$
$564$		0			0
$565$	−2.21167	+	3.83072i	−0.0930455	+	0.161160i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	11.9697	−	20.7322i	0.501797	−	0.869138i	−0.498201	−	0.867062i	$-0.666006\pi$
$569$	11.9697	−	20.7322i	0.501797	−	0.869138i	0.999998	−	0.00207607i	$-0.000660835\pi$
$570$		0			0
$571$	20.9846	+	36.3463i	0.878177	+	1.52105i	0.853339	+	0.521356i	$0.174574\pi$
$571$	20.9846	+	36.3463i	0.878177	+	1.52105i	0.0248378	+	0.999691i	$0.492093\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−22.3182			−0.930733
$576$		0			0
$577$	−13.4851			−0.561394			−0.280697	−	0.959796i	$-0.590566\pi$
$577$	−13.4851			−0.561394			−0.280697	+	0.959796i	$0.590566\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−7.11856	−	12.3297i	−0.295327	−	0.511522i
$582$		0			0
$583$	−0.619271	+	1.07261i	−0.0256476	+	0.0444229i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4.54189	+	7.86678i	−0.187464	+	0.324697i	−0.944404	−	0.328787i	$-0.893360\pi$
$587$	−4.54189	+	7.86678i	−0.187464	+	0.324697i	0.756940	+	0.653484i	$0.226693\pi$
$588$		0			0
$589$	4.58378	+	7.93934i	0.188871	+	0.327135i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−3.22844			−0.132576			−0.0662880	−	0.997801i	$-0.521116\pi$
$593$	−3.22844			−0.132576			−0.0662880	+	0.997801i	$0.521116\pi$
$594$		0			0
$595$	0.355037			0.0145551
$596$		0			0
$597$		0			0
$598$		0			0
$599$	15.8293	+	27.4172i	0.646769	+	1.12024i	0.983890	+	0.178776i	$0.0572138\pi$
$599$	15.8293	+	27.4172i	0.646769	+	1.12024i	−0.337120	+	0.941462i	$0.609453\pi$
$600$		0			0
$601$	0.666374	−	1.15419i	0.0271820	−	0.0470806i	−0.852114	−	0.523356i	$-0.824680\pi$
$601$	0.666374	−	1.15419i	0.0271820	−	0.0470806i	0.879296	+	0.476275i	$0.158013\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.90420	+	3.29817i	−0.0774167	+	0.134090i
$606$		0			0
$607$	−3.90673	−	6.76665i	−0.158569	−	0.274650i	0.775784	−	0.630999i	$-0.217355\pi$
$607$	−3.90673	−	6.76665i	−0.158569	−	0.274650i	−0.934353	+	0.356349i	$0.884021\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3.03684			−0.122857
$612$		0			0
$613$	−21.6901			−0.876057			−0.438028	−	0.898961i	$-0.644323\pi$
$613$	−21.6901			−0.876057			−0.438028	+	0.898961i	$0.644323\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.01589	+	1.75958i	0.0408983	+	0.0708379i	0.885750	−	0.464163i	$-0.153645\pi$
$617$	1.01589	+	1.75958i	0.0408983	+	0.0708379i	−0.844852	+	0.535001i	$0.820311\pi$
$618$		0			0
$619$	−0.763985	+	1.32326i	−0.0307072	+	0.0531863i	−0.880971	−	0.473171i	$-0.843109\pi$
$619$	−0.763985	+	1.32326i	−0.0307072	+	0.0531863i	0.850263	+	0.526357i	$0.176443\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−4.93629	+	8.54990i	−0.197768	+	0.342545i
$624$		0			0
$625$	−11.6027	−	20.0964i	−0.464107	−	0.803856i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.64672			0.0656589
$630$		0			0
$631$	6.32594			0.251832			0.125916	−	0.992041i	$-0.459813\pi$
$631$	6.32594			0.251832			0.125916	+	0.992041i	$0.459813\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.63903	+	2.83889i	0.0650430	+	0.112658i
$636$		0			0
$637$	−4.76352	+	8.25066i	−0.188737	+	0.326903i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	18.1800	−	31.4888i	0.718069	−	1.24373i	−0.243695	−	0.969852i	$-0.578360\pi$
$641$	18.1800	−	31.4888i	0.718069	−	1.24373i	0.961764	−	0.273879i	$-0.0883069\pi$
$642$		0			0
$643$	−14.6792	−	25.4251i	−0.578890	−	1.00267i	−0.995607	−	0.0936304i	$-0.970153\pi$
$643$	−14.6792	−	25.4251i	−0.578890	−	1.00267i	0.416717	−	0.909036i	$-0.363181\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	22.0966			0.868706			0.434353	−	0.900743i	$-0.356977\pi$
$647$	22.0966			0.868706			0.434353	+	0.900743i	$0.356977\pi$
$648$		0			0
$649$	−1.25309			−0.0491880
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−21.6552	−	37.5080i	−0.847435	−	1.46780i	−0.883490	−	0.468450i	$-0.844813\pi$
$653$	−21.6552	−	37.5080i	−0.847435	−	1.46780i	0.0360554	−	0.999350i	$-0.488521\pi$
$654$		0			0
$655$	2.95424	−	5.11689i	0.115432	−	0.199934i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−15.9030	+	27.5448i	−0.619494	+	1.07299i	0.370085	+	0.928998i	$0.379329\pi$
$659$	−15.9030	+	27.5448i	−0.619494	+	1.07299i	−0.989578	+	0.143996i	$0.954005\pi$
$660$		0			0
$661$	15.5594	+	26.9497i	0.605192	+	1.04822i	0.992021	+	0.126071i	$0.0402369\pi$
$661$	15.5594	+	26.9497i	0.605192	+	1.04822i	−0.386829	+	0.922151i	$0.626430\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.909415			0.0352656
$666$		0			0
$667$	−2.14022			−0.0828695
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.10741	−	1.91809i	−0.0427511	−	0.0740471i
$672$		0			0
$673$	6.65317	−	11.5236i	0.256461	−	0.444203i	−0.708830	−	0.705379i	$-0.750777\pi$
$673$	6.65317	−	11.5236i	0.256461	−	0.444203i	0.965291	+	0.261176i	$0.0841102\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.12701	+	12.3443i	−0.273913	+	0.474432i	−0.969860	−	0.243661i	$-0.921651\pi$
$677$	−7.12701	+	12.3443i	−0.273913	+	0.474432i	0.695947	+	0.718093i	$0.254985\pi$
$678$		0			0
$679$	−3.89259	−	6.74216i	−0.149384	−	0.258740i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−23.4679			−0.897975			−0.448987	−	0.893538i	$-0.648215\pi$
$683$	−23.4679			−0.897975			−0.448987	+	0.893538i	$0.648215\pi$
$684$		0			0
$685$	4.70914			0.179927
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−6.15776	−	10.6655i	−0.234592	−	0.406325i
$690$		0			0
$691$	7.25150	−	12.5600i	0.275860	−	0.477803i	−0.694492	−	0.719501i	$-0.744371\pi$
$691$	7.25150	−	12.5600i	0.275860	−	0.477803i	0.970352	+	0.241697i	$0.0777041\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.34137	+	4.05537i	−0.0888131	+	0.153829i
$696$		0			0
$697$	3.54916	+	6.14733i	0.134434	+	0.232847i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	24.0196			0.907208			0.453604	−	0.891203i	$-0.350138\pi$
$701$	24.0196			0.907208			0.453604	+	0.891203i	$0.350138\pi$
$702$		0			0
$703$	4.21801			0.159085
$704$		0			0
$705$		0			0
$706$		0			0
$707$	11.5869	+	20.0692i	0.435771	+	0.754778i
$708$		0			0
$709$	16.9349	−	29.3322i	0.636005	−	1.10159i	−0.350296	−	0.936639i	$-0.613919\pi$
$709$	16.9349	−	29.3322i	0.636005	−	1.10159i	0.986301	−	0.164954i	$-0.0527477\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	10.7875	−	18.6844i	0.403993	−	0.699737i
$714$		0			0
$715$	0.0589632	+	0.102127i	0.00220510	+	0.00381934i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−21.5134			−0.802315			−0.401158	−	0.916009i	$-0.631392\pi$
$719$	−21.5134			−0.802315			−0.401158	+	0.916009i	$0.631392\pi$
$720$		0			0
$721$	2.66819			0.0993684
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.14156	−	1.97724i	−0.0423964	−	0.0734328i
$726$		0			0
$727$	12.2686	−	21.2498i	0.455016	−	0.788111i	−0.543673	−	0.839297i	$-0.682967\pi$
$727$	12.2686	−	21.2498i	0.455016	−	0.788111i	0.998689	+	0.0511861i	$0.0163002\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	3.56506	−	6.17486i	0.131858	−	0.228385i
$732$		0			0
$733$	−16.3084	−	28.2470i	−0.602365	−	1.04333i	−0.992462	−	0.122552i	$-0.960892\pi$
$733$	−16.3084	−	28.2470i	−0.602365	−	1.04333i	0.390098	−	0.920774i	$-0.372441\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.500629			0.0184409
$738$		0			0
$739$	−13.5280			−0.497634			−0.248817	−	0.968550i	$-0.580042\pi$
$739$	−13.5280			−0.497634			−0.248817	+	0.968550i	$0.580042\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	4.47771	+	7.75562i	0.164271	+	0.284526i	0.936396	−	0.350944i	$-0.114139\pi$
$743$	4.47771	+	7.75562i	0.164271	+	0.284526i	−0.772125	+	0.635471i	$0.780806\pi$
$744$		0			0
$745$	−2.53684	+	4.39393i	−0.0929425	+	0.160981i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2.21507	+	3.83661i	−0.0809369	+	0.140187i
$750$		0			0
$751$	15.3833	+	26.6446i	0.561343	+	0.972275i	0.997380	+	0.0723456i	$0.0230485\pi$
$751$	15.3833	+	26.6446i	0.561343	+	0.972275i	−0.436037	+	0.899929i	$0.643618\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.40198			0.0510232
$756$		0			0
$757$	17.7169			0.643931			0.321966	−	0.946751i	$-0.395656\pi$
$757$	17.7169			0.643931			0.321966	+	0.946751i	$0.395656\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	6.60488	+	11.4400i	0.239427	+	0.414700i	0.960550	−	0.278107i	$-0.0897071\pi$
$761$	6.60488	+	11.4400i	0.239427	+	0.414700i	−0.721123	+	0.692807i	$0.756374\pi$
$762$		0			0
$763$	4.91669	−	8.51595i	0.177996	−	0.308298i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	6.23009	−	10.7908i	0.224955	−	0.389634i
$768$		0			0
$769$	14.5660	+	25.2290i	0.525263	+	0.909782i	0.999567	+	0.0294211i	$0.00936638\pi$
$769$	14.5660	+	25.2290i	0.525263	+	0.909782i	−0.474304	+	0.880361i	$0.657300\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−5.99556			−0.215645			−0.107823	−	0.994170i	$-0.534388\pi$
$773$	−5.99556			−0.215645			−0.107823	+	0.994170i	$0.534388\pi$
$774$		0			0
$775$	23.0155			0.826741
$776$		0			0
$777$		0			0
$778$		0			0
$779$	9.09105	+	15.7462i	0.325721	+	0.564165i
$780$		0			0
$781$	1.10560	−	1.91496i	0.0395615	−	0.0685225i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.780592	+	1.35203i	−0.0278605	+	0.0482559i
$786$		0			0
$787$	24.4873	+	42.4132i	0.872877	+	1.51187i	0.859008	+	0.511963i	$0.171081\pi$
$787$	24.4873	+	42.4132i	0.872877	+	1.51187i	0.0138691	+	0.999904i	$0.495585\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	17.1598			0.610133
$792$		0			0
$793$	22.0232			0.782068
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−23.6721	−	41.0012i	−0.838507	−	1.45234i	−0.891143	−	0.453723i	$-0.850095\pi$
$797$	−23.6721	−	41.0012i	−0.838507	−	1.45234i	0.0526354	−	0.998614i	$-0.483238\pi$
$798$		0			0
$799$	−0.627011	+	1.08602i	−0.0221821	+	0.0384205i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.143619	−	0.248755i	0.00506819	−	0.00877837i
$804$		0			0
$805$	−1.07011	−	1.85348i	−0.0377163	−	0.0653266i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	32.7009			1.14970			0.574851	−	0.818258i	$-0.305060\pi$
$809$	32.7009			1.14970			0.574851	+	0.818258i	$0.305060\pi$
$810$		0			0
$811$	30.0137			1.05392			0.526962	−	0.849889i	$-0.323331\pi$
$811$	30.0137			1.05392			0.526962	+	0.849889i	$0.323331\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.0714517	−	0.123758i	−0.00250285	−	0.00433505i
$816$		0			0
$817$	9.13176	−	15.8167i	0.319480	−	0.553355i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−14.7032	+	25.4667i	−0.513146	+	0.888794i	0.486738	+	0.873548i	$0.338187\pi$
$821$	−14.7032	+	25.4667i	−0.513146	+	0.888794i	−0.999884	+	0.0152463i	$0.995147\pi$
$822$		0			0
$823$	−11.7848	−	20.4118i	−0.410791	−	0.711511i	0.584185	−	0.811620i	$-0.301414\pi$
$823$	−11.7848	−	20.4118i	−0.410791	−	0.711511i	−0.994976	+	0.100109i	$0.968081\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−49.7333			−1.72940			−0.864698	−	0.502292i	$-0.832490\pi$
$827$	−49.7333			−1.72940			−0.864698	+	0.502292i	$0.832490\pi$
$828$		0			0
$829$	18.7939			0.652737			0.326369	−	0.945243i	$-0.394175\pi$
$829$	18.7939			0.652737			0.326369	+	0.945243i	$0.394175\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.96703	+	3.40700i	0.0681537	+	0.118046i
$834$		0			0
$835$	2.21806	−	3.84180i	0.0767593	−	0.132951i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−11.2947	+	19.5630i	−0.389937	+	0.675391i	−0.992441	−	0.122725i	$-0.960837\pi$
$839$	−11.2947	+	19.5630i	−0.389937	+	0.675391i	0.602503	+	0.798116i	$0.294170\pi$
$840$		0			0
$841$	14.3905	+	24.9251i	0.496225	+	0.859487i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	3.34224			0.114977
$846$		0			0
$847$	14.7743			0.507649
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−4.96333	−	8.59673i	−0.170141	−	0.294692i
$852$		0			0
$853$	10.1086	−	17.5086i	0.346112	−	0.599483i	−0.639443	−	0.768838i	$-0.720835\pi$
$853$	10.1086	−	17.5086i	0.346112	−	0.599483i	0.985555	+	0.169355i	$0.0541685\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	20.1917	−	34.9730i	0.689734	−	1.19465i	−0.282190	−	0.959359i	$-0.591061\pi$
$857$	20.1917	−	34.9730i	0.689734	−	1.19465i	0.971924	−	0.235296i	$-0.0756058\pi$
$858$		0			0
$859$	−4.51279	−	7.81639i	−0.153975	−	0.266692i	0.778711	−	0.627383i	$-0.215874\pi$
$859$	−4.51279	−	7.81639i	−0.153975	−	0.266692i	−0.932685	+	0.360692i	$0.882541\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−10.9932			−0.374213			−0.187106	−	0.982340i	$-0.559911\pi$
$863$	−10.9932			−0.374213			−0.187106	+	0.982340i	$0.559911\pi$
$864$		0			0
$865$	−5.95718			−0.202550
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.16044	−	2.00995i	−0.0393654	−	0.0681828i
$870$		0			0
$871$	−2.48902	+	4.31111i	−0.0843371	+	0.146076i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.31134	−	4.00335i	0.0781375	−	0.135338i
$876$		0			0
$877$	9.20755	+	15.9479i	0.310917	+	0.538524i	0.978561	−	0.205957i	$-0.0660306\pi$
$877$	9.20755	+	15.9479i	0.310917	+	0.538524i	−0.667644	+	0.744480i	$0.732697\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	20.7433			0.698859			0.349430	−	0.936963i	$-0.386375\pi$
$881$	20.7433			0.698859			0.349430	+	0.936963i	$0.386375\pi$
$882$		0			0
$883$	8.36547			0.281520			0.140760	−	0.990044i	$-0.455045\pi$
$883$	8.36547			0.281520			0.140760	+	0.990044i	$0.455045\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	29.0180	+	50.2607i	0.974329	+	1.68759i	0.682131	+	0.731230i	$0.261054\pi$
$887$	29.0180	+	50.2607i	0.974329	+	1.68759i	0.292199	+	0.956358i	$0.405613\pi$
$888$		0			0
$889$	6.35844	−	11.0131i	0.213255	−	0.369369i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.60607	+	2.78179i	−0.0537450	+	0.0930890i
$894$		0			0
$895$	3.19594	+	5.53553i	0.106828	+	0.185032i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.20708			0.0736103
$900$		0			0
$901$	−5.08553			−0.169424
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.44356	−	2.50032i	−0.0479857	−	0.0831136i
$906$		0			0
$907$	27.5621	−	47.7390i	0.915185	−	1.58515i	0.108555	−	0.994090i	$-0.465378\pi$
$907$	27.5621	−	47.7390i	0.915185	−	1.58515i	0.806630	−	0.591057i	$-0.201289\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−2.05422	+	3.55801i	−0.0680592	+	0.117882i	−0.898047	−	0.439900i	$-0.855014\pi$
$911$	−2.05422	+	3.55801i	−0.0680592	+	0.117882i	0.829988	+	0.557782i	$0.188347\pi$
$912$		0			0
$913$	−0.976367	−	1.69112i	−0.0323130	−	0.0559678i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−22.9213			−0.756927
$918$		0			0
$919$	−38.7297			−1.27757			−0.638787	−	0.769384i	$-0.720564\pi$
$919$	−38.7297			−1.27757			−0.638787	+	0.769384i	$0.720564\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	10.9936	+	19.0415i	0.361859	+	0.626758i
$924$		0			0
$925$	5.29473	−	9.17074i	0.174090	−	0.301532i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	18.5658	−	32.1570i	0.609125	−	1.05504i	−0.382260	−	0.924055i	$-0.624854\pi$
$929$	18.5658	−	32.1570i	0.609125	−	1.05504i	0.991385	−	0.130981i	$-0.0418126\pi$
$930$		0			0
$931$	5.03849	+	8.72691i	0.165130	+	0.286013i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.0486962			0.00159254
$936$		0			0
$937$	−4.42097			−0.144427			−0.0722134	−	0.997389i	$-0.523006\pi$
$937$	−4.42097			−0.144427			−0.0722134	+	0.997389i	$0.523006\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	6.74809	+	11.6880i	0.219982	+	0.381019i	0.954802	−	0.297242i	$-0.0960670\pi$
$941$	6.74809	+	11.6880i	0.219982	+	0.381019i	−0.734821	+	0.678262i	$0.762734\pi$
$942$		0			0
$943$	21.3949	−	37.0570i	0.696713	−	1.20674i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−26.3846	+	45.6995i	−0.857384	+	1.48503i	0.0170310	+	0.999855i	$0.494579\pi$
$947$	−26.3846	+	45.6995i	−0.857384	+	1.48503i	−0.874415	+	0.485178i	$0.838755\pi$
$948$		0			0
$949$	1.42808	+	2.47351i	0.0463575	+	0.0802935i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	44.2235			1.43254			0.716270	−	0.697823i	$-0.245848\pi$
$953$	44.2235			1.43254			0.716270	+	0.697823i	$0.245848\pi$
$954$		0			0
$955$	7.05232			0.228208
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−9.13429	−	15.8210i	−0.294961	−	0.510888i
$960$		0			0
$961$	4.37551	−	7.57861i	0.141146	−	0.244471i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2.57280	−	4.45621i	0.0828212	−	0.143451i
$966$		0			0
$967$	27.0219	+	46.8033i	0.868965	+	1.50509i	0.863056	+	0.505109i	$0.168548\pi$
$967$	27.0219	+	46.8033i	0.868965	+	1.50509i	0.00590948	+	0.999983i	$0.498119\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−24.5348			−0.787358			−0.393679	−	0.919248i	$-0.628798\pi$
$971$	−24.5348			−0.787358			−0.393679	+	0.919248i	$0.628798\pi$
$972$		0			0
$973$	18.1661			0.582379
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−13.0016	−	22.5195i	−0.415960	−	0.720463i	0.579569	−	0.814923i	$-0.303221\pi$
$977$	−13.0016	−	22.5195i	−0.415960	−	0.720463i	−0.995529	+	0.0944600i	$0.969888\pi$
$978$		0			0
$979$	−0.677052	+	1.17269i	−0.0216387	+	0.0374793i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−13.5202	+	23.4177i	−0.431228	+	0.746909i	−0.996979	−	0.0776667i	$-0.975253\pi$
$983$	−13.5202	+	23.4177i	−0.431228	+	0.746909i	0.565751	+	0.824576i	$0.308586\pi$
$984$		0			0
$985$	−2.99319	−	5.18436i	−0.0953711	−	0.165188i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−42.9813			−1.36673
$990$		0			0
$991$	−23.7041			−0.752985			−0.376493	−	0.926420i	$-0.622870\pi$
$991$	−23.7041			−0.752985			−0.376493	+	0.926420i	$0.622870\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.634752	+	1.09942i	0.0201230	+	0.0348541i
$996$		0			0
$997$	6.02094	−	10.4286i	0.190685	−	0.330277i	−0.754792	−	0.655964i	$-0.772262\pi$
$997$	6.02094	−	10.4286i	0.190685	−	0.330277i	0.945478	+	0.325687i	$0.105596\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1944.2.i.o.649.2		6
3.2	odd	2		1944.2.i.p.649.2		6
9.2	odd	6		1944.2.a.o.1.2	✓	3
9.4	even	3	inner	1944.2.i.o.1297.2		6
9.5	odd	6		1944.2.i.p.1297.2		6
9.7	even	3		1944.2.a.p.1.2	yes	3
36.7	odd	6		3888.2.a.bh.1.2		3
36.11	even	6		3888.2.a.bi.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1944.2.a.o.1.2	✓	3	9.2	odd	6
1944.2.a.p.1.2	yes	3	9.7	even	3
1944.2.i.o.649.2		6	1.1	even	1	trivial
1944.2.i.o.1297.2		6	9.4	even	3	inner
1944.2.i.p.649.2		6	3.2	odd	2
1944.2.i.p.1297.2		6	9.5	odd	6
3888.2.a.bh.1.2		3	36.7	odd	6
3888.2.a.bi.1.2		3	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1944 = 2^{3} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1944.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.300767i) q^{5} +(0.673648 - 1.16679i) q^{7} +O(q^{10})\)	\(q+(0.173648 + 0.300767i) q^{5} +(0.673648 - 1.16679i) q^{7} +(0.0923963 - 0.160035i) q^{11} +(0.918748 + 1.59132i) q^{13} +0.758770 q^{17} +1.94356 q^{19} +(-2.28699 - 3.96118i) q^{23} +(2.43969 - 4.22567i) q^{25} +(0.233956 - 0.405223i) q^{29} +(2.35844 + 4.08494i) q^{31} +0.467911 q^{35} +2.17024 q^{37} +(4.67752 + 8.10170i) q^{41} +(4.69846 - 8.13798i) q^{43} +(-0.826352 + 1.43128i) q^{47} +(2.59240 + 4.49016i) q^{49} -6.70233 q^{53} +0.0641778 q^{55} +(-3.39053 - 5.87257i) q^{59} +(5.99273 - 10.3797i) q^{61} +(-0.319078 + 0.552659i) q^{65} +(1.35457 + 2.34618i) q^{67} +11.9659 q^{71} +1.55438 q^{73} +(-0.124485 - 0.215615i) q^{77} +(6.27972 - 10.8768i) q^{79} +(5.28359 - 9.15144i) q^{83} +(0.131759 + 0.228213i) q^{85} -7.32770 q^{89} +2.47565 q^{91} +(0.337496 + 0.584561i) q^{95} +(2.88919 - 5.00422i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{7}+O(q^{10}) \) 6 * q + 3 * q^7	\( 6 q + 3 q^{7} - 3 q^{11} + 3 q^{13} - 18 q^{17} - 18 q^{19} - 6 q^{23} + 9 q^{25} + 6 q^{29} + 6 q^{31} + 12 q^{35} - 30 q^{37} + 3 q^{41} - 6 q^{47} + 12 q^{49} + 12 q^{53} - 18 q^{55} - 3 q^{59} + 18 q^{61} + 15 q^{65} + 24 q^{67} + 30 q^{71} - 12 q^{73} + 12 q^{77} + 12 q^{79} - 18 q^{83} + 6 q^{85} - 36 q^{89} - 24 q^{91} - 3 q^{95} + 9 q^{97}+O(q^{100}) \) 6 * q + 3 * q^7 - 3 * q^11 + 3 * q^13 - 18 * q^17 - 18 * q^19 - 6 * q^23 + 9 * q^25 + 6 * q^29 + 6 * q^31 + 12 * q^35 - 30 * q^37 + 3 * q^41 - 6 * q^47 + 12 * q^49 + 12 * q^53 - 18 * q^55 - 3 * q^59 + 18 * q^61 + 15 * q^65 + 24 * q^67 + 30 * q^71 - 12 * q^73 + 12 * q^77 + 12 * q^79 - 18 * q^83 + 6 * q^85 - 36 * q^89 - 24 * q^91 - 3 * q^95 + 9 * q^97

Introduction

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