LMFDB - Embedded newform 2268.2.i.n.865.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(865,2268)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2268, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2268.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.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:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 9x^{14} + 31x^{12} - 282x^{10} + 1695x^{8} - 3318x^{6} + 4606x^{4} - 4116x^{2} + 2401 $ x^16 - 9x^14 + 31x^12 - 282x^10 + 1695x^8 - 3318x^6 + 4606x^4 - 4116*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			865.3
Root			$1.04556 - 0.339889i$ of defining polynomial
Character	$\chi$	$=$	2268.865
Dual form			2268.2.i.n.2053.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.515559 + 0.892975i) q^{5} +(-2.63118 + 0.277320i) q^{7} +O(q^{10})$	$q+(-0.515559 + 0.892975i) q^{5} +(-2.63118 + 0.277320i) q^{7} +(0.792879 + 1.37331i) q^{11} +(-2.52415 - 4.37196i) q^{13} +(-2.58242 + 4.47288i) q^{17} +(-0.392975 - 0.680652i) q^{19} +(2.93289 - 5.07991i) q^{23} +(1.96840 + 3.40936i) q^{25} +(4.44511 - 7.69915i) q^{29} -1.15085 q^{31} +(1.10889 - 2.49255i) q^{35} +(4.07991 + 7.06661i) q^{37} +(-3.87206 - 6.70660i) q^{41} +(1.26628 - 2.19326i) q^{43} +8.49189 q^{47} +(6.84619 - 1.45935i) q^{49} +(2.41270 - 4.17892i) q^{53} -1.63510 q^{55} +3.87245 q^{59} -9.64407 q^{61} +5.20540 q^{65} -1.67444 q^{67} +14.2795 q^{71} +(3.04382 - 5.27205i) q^{73} +(-2.46705 - 3.39353i) q^{77} -8.31066 q^{79} +(7.12095 - 12.3339i) q^{83} +(-2.66278 - 4.61207i) q^{85} +(6.69272 + 11.5921i) q^{89} +(7.85392 + 10.8034i) q^{91} +0.810407 q^{95} +(-2.67500 + 4.63323i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{7}+O(q^{10}) $ 16 * q - 6 * q^7	$ 16 q - 6 q^{7} + 10 q^{13} + 8 q^{19} + 16 q^{31} - 4 q^{37} - 10 q^{43} + 10 q^{49} - 32 q^{55} - 56 q^{61} - 36 q^{67} + 40 q^{79} - 38 q^{85} - 2 q^{91} + 42 q^{97}+O(q^{100}) $ 16 * q - 6 * q^7 + 10 * q^13 + 8 * q^19 + 16 * q^31 - 4 * q^37 - 10 * q^43 + 10 * q^49 - 32 * q^55 - 56 * q^61 - 36 * q^67 + 40 * q^79 - 38 * q^85 - 2 * q^91 + 42 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	−0.515559	+	0.892975i	−0.230565	+	0.399350i	−0.957975	−	0.286853i	$-0.907391\pi$
$5$	−0.515559	+	0.892975i	−0.230565	+	0.399350i	0.727409	+	0.686204i	$0.240724\pi$
$6$		0			0
$7$	−2.63118	+	0.277320i	−0.994492	+	0.104817i
$7$	−2.63118	+	0.277320i	−0.994492	+	0.104817i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.792879	+	1.37331i	0.239062	+	0.414067i	0.960445	−	0.278468i	$-0.0898268\pi$
$11$	0.792879	+	1.37331i	0.239062	+	0.414067i	−0.721383	+	0.692536i	$0.756493\pi$
$12$		0			0
$13$	−2.52415	−	4.37196i	−0.700074	−	1.21256i	−0.968440	−	0.249246i	$-0.919817\pi$
$13$	−2.52415	−	4.37196i	−0.700074	−	1.21256i	0.268366	−	0.963317i	$-0.413516\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.58242	+	4.47288i	−0.626329	+	1.08483i	0.361954	+	0.932196i	$0.382110\pi$
$17$	−2.58242	+	4.47288i	−0.626329	+	1.08483i	−0.988282	+	0.152637i	$0.951223\pi$
$18$		0			0
$19$	−0.392975	−	0.680652i	−0.0901546	−	0.156152i	0.817421	−	0.576040i	$-0.195403\pi$
$19$	−0.392975	−	0.680652i	−0.0901546	−	0.156152i	−0.907576	+	0.419888i	$0.862069\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.93289	−	5.07991i	0.611549	−	1.05923i	−0.379431	−	0.925220i	$-0.623880\pi$
$23$	2.93289	−	5.07991i	0.611549	−	1.05923i	0.990980	−	0.134014i	$-0.0427866\pi$
$24$		0			0
$25$	1.96840	+	3.40936i	0.393679	+	0.681873i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.44511	−	7.69915i	0.825435	−	1.42970i	−0.0761506	−	0.997096i	$-0.524263\pi$
$29$	4.44511	−	7.69915i	0.825435	−	1.42970i	0.901586	−	0.432600i	$-0.142404\pi$
$30$		0			0
$31$	−1.15085			−0.206698			−0.103349	−	0.994645i	$-0.532956\pi$
$31$	−1.15085			−0.206698			−0.103349	+	0.994645i	$0.532956\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.10889	−	2.49255i	0.187436	−	0.421318i
$36$		0			0
$37$	4.07991	+	7.06661i	0.670732	+	1.16174i	0.977697	+	0.210022i	$0.0673535\pi$
$37$	4.07991	+	7.06661i	0.670732	+	1.16174i	−0.306964	+	0.951721i	$0.599313\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.87206	−	6.70660i	−0.604714	−	1.04739i	−0.992097	−	0.125476i	$-0.959954\pi$
$41$	−3.87206	−	6.70660i	−0.604714	−	1.04739i	0.387383	−	0.921919i	$-0.373379\pi$
$42$		0			0
$43$	1.26628	−	2.19326i	0.193106	−	0.334470i	−0.753172	−	0.657824i	$-0.771477\pi$
$43$	1.26628	−	2.19326i	0.193106	−	0.334470i	0.946278	+	0.323354i	$0.104811\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	8.49189			1.23867			0.619335	−	0.785127i	$-0.287402\pi$
$47$	8.49189			1.23867			0.619335	+	0.785127i	$0.287402\pi$
$48$		0			0
$49$	6.84619	−	1.45935i	0.978027	−	0.208479i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.41270	−	4.17892i	0.331410	−	0.574019i	−0.651378	−	0.758753i	$-0.725809\pi$
$53$	2.41270	−	4.17892i	0.331410	−	0.574019i	0.982789	+	0.184734i	$0.0591423\pi$
$54$		0			0
$55$	−1.63510			−0.220477
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.87245			0.504150			0.252075	−	0.967708i	$-0.418887\pi$
$59$	3.87245			0.504150			0.252075	+	0.967708i	$0.418887\pi$
$60$		0			0
$61$	−9.64407			−1.23480			−0.617398	−	0.786651i	$-0.711813\pi$
$61$	−9.64407			−1.23480			−0.617398	+	0.786651i	$0.711813\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.20540			0.645650
$66$		0			0
$67$	−1.67444			−0.204565			−0.102283	−	0.994755i	$-0.532615\pi$
$67$	−1.67444			−0.204565			−0.102283	+	0.994755i	$0.532615\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	14.2795			1.69467			0.847333	−	0.531062i	$-0.178207\pi$
$71$	14.2795			1.69467			0.847333	+	0.531062i	$0.178207\pi$
$72$		0			0
$73$	3.04382	−	5.27205i	0.356252	−	0.617047i	−0.631079	−	0.775718i	$-0.717388\pi$
$73$	3.04382	−	5.27205i	0.356252	−	0.617047i	0.987331	+	0.158671i	$0.0507211\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.46705	−	3.39353i	−0.281146	−	0.386729i
$78$		0			0
$79$	−8.31066			−0.935022			−0.467511	−	0.883987i	$-0.654849\pi$
$79$	−8.31066			−0.935022			−0.467511	+	0.883987i	$0.654849\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.12095	−	12.3339i	0.781626	−	1.35382i	−0.149368	−	0.988782i	$-0.547724\pi$
$83$	7.12095	−	12.3339i	0.781626	−	1.35382i	0.930994	−	0.365034i	$-0.118943\pi$
$84$		0			0
$85$	−2.66278	−	4.61207i	−0.288819	−	0.500249i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.69272	+	11.5921i	0.709426	+	1.22876i	0.965070	+	0.261992i	$0.0843793\pi$
$89$	6.69272	+	11.5921i	0.709426	+	1.22876i	−0.255644	+	0.966771i	$0.582287\pi$
$90$		0			0
$91$	7.85392	+	10.8034i	0.823315	+	1.13250i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.810407			0.0831460
$96$		0			0
$97$	−2.67500	+	4.63323i	−0.271605	+	0.470433i	−0.969273	−	0.245988i	$-0.920888\pi$
$97$	−2.67500	+	4.63323i	−0.271605	+	0.470433i	0.697668	+	0.716421i	$0.254221\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.59038	+	2.75462i	0.158249	+	0.274095i	0.934237	−	0.356652i	$-0.116082\pi$
$101$	1.59038	+	2.75462i	0.158249	+	0.274095i	−0.775988	+	0.630747i	$0.782749\pi$
$102$		0			0
$103$	5.70660	−	9.88412i	0.562288	−	0.973911i	−0.435008	−	0.900426i	$-0.643255\pi$
$103$	5.70660	−	9.88412i	0.562288	−	0.973911i	0.997296	−	0.0734850i	$-0.0234121\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.311386	−	0.539337i	−0.0301028	−	0.0521396i	0.850582	−	0.525843i	$-0.176250\pi$
$107$	−0.311386	−	0.539337i	−0.0301028	−	0.0521396i	−0.880684	+	0.473704i	$0.842917\pi$
$108$		0			0
$109$	0.971921	−	1.68342i	0.0930932	−	0.161242i	−0.815718	−	0.578450i	$-0.803658\pi$
$109$	0.971921	−	1.68342i	0.0930932	−	0.161242i	0.908811	+	0.417208i	$0.136991\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.79416	−	3.10758i	−0.168781	−	0.292337i	0.769211	−	0.638995i	$-0.220650\pi$
$113$	−1.79416	−	3.10758i	−0.168781	−	0.292337i	−0.937991	+	0.346658i	$0.887316\pi$
$114$		0			0
$115$	3.02415	+	5.23798i	0.282004	+	0.488445i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	5.55438	−	12.4851i	0.509170	−	1.14451i
$120$		0			0
$121$	4.24269	−	7.34855i	0.385699	−	0.668050i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.21489			−0.824205
$126$		0			0
$127$	11.6202			1.03113			0.515563	−	0.856852i	$-0.327583\pi$
$127$	11.6202			1.03113			0.515563	+	0.856852i	$0.327583\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.07898	−	7.06501i	0.356382	−	0.617272i	−0.630971	−	0.775806i	$-0.717343\pi$
$131$	4.07898	−	7.06501i	0.356382	−	0.617272i	0.987354	+	0.158534i	$0.0506767\pi$
$132$		0			0
$133$	1.22274	+	1.68194i	0.106025	+	0.145842i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.28181	+	12.6125i	0.622127	+	1.07756i	0.989089	+	0.147320i	$0.0470647\pi$
$137$	7.28181	+	12.6125i	0.622127	+	1.07756i	−0.366962	+	0.930236i	$0.619602\pi$
$138$		0			0
$139$	5.91713	+	10.2488i	0.501884	+	0.869289i	0.999998	+	0.00217698i	$0.000692954\pi$
$139$	5.91713	+	10.2488i	0.501884	+	0.869289i	−0.498113	+	0.867112i	$0.665974\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.00269	−	6.93287i	0.334722	−	0.579756i
$144$		0			0
$145$	4.58343	+	7.93873i	0.380633	+	0.659276i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.02477	−	12.1673i	0.575492	−	0.996781i	−0.420496	−	0.907294i	$-0.638144\pi$
$149$	7.02477	−	12.1673i	0.575492	−	0.996781i	0.995988	−	0.0894868i	$-0.0285227\pi$
$150$		0			0
$151$	−1.24269	−	2.15240i	−0.101128	−	0.175159i	0.811021	−	0.585016i	$-0.198912\pi$
$151$	−1.24269	−	2.15240i	−0.101128	−	0.175159i	−0.912150	+	0.409857i	$0.865579\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.593329	−	1.02768i	0.0476573	−	0.0825449i
$156$		0			0
$157$	−3.03934			−0.242565			−0.121283	−	0.992618i	$-0.538701\pi$
$157$	−3.03934			−0.242565			−0.121283	+	0.992618i	$0.538701\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−6.30818	+	14.1795i	−0.497154	+	1.11750i
$162$		0			0
$163$	−8.75883	−	15.1707i	−0.686045	−	1.18826i	−0.973107	−	0.230352i	$-0.926012\pi$
$163$	−8.75883	−	15.1707i	−0.686045	−	1.18826i	0.287063	−	0.957912i	$-0.407321\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−12.2738	−	21.2588i	−0.949775	−	1.64506i	−0.745897	−	0.666061i	$-0.767979\pi$
$167$	−12.2738	−	21.2588i	−0.949775	−	1.64506i	−0.203877	−	0.978996i	$-0.565354\pi$
$168$		0			0
$169$	−6.24269	+	10.8126i	−0.480207	+	0.831742i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.0689138			−0.00523942			−0.00261971	−	0.999997i	$-0.500834\pi$
$173$	−0.0689138			−0.00523942			−0.00261971	+	0.999997i	$0.500834\pi$
$174$		0			0
$175$	−6.12469	−	8.42477i	−0.462983	−	0.636853i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.96086	−	6.86041i	0.296049	−	0.512771i	−0.679180	−	0.733972i	$-0.737664\pi$
$179$	3.96086	−	6.86041i	0.296049	−	0.512771i	0.975228	+	0.221201i	$0.0709976\pi$
$180$		0			0
$181$	3.59688			0.267354			0.133677	−	0.991025i	$-0.457322\pi$
$181$	3.59688			0.267354			0.133677	+	0.991025i	$0.457322\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−8.41373			−0.618590
$186$		0			0
$187$	−8.19018			−0.598925
$188$		0			0
$189$		0			0
$190$		0			0
$191$	16.0492			1.16128			0.580638	−	0.814162i	$-0.302803\pi$
$191$	16.0492			1.16128			0.580638	+	0.814162i	$0.302803\pi$
$192$		0			0
$193$	−21.5730			−1.55286			−0.776430	−	0.630204i	$-0.782971\pi$
$193$	−21.5730			−1.55286			−0.776430	+	0.630204i	$0.782971\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−20.4441			−1.45659			−0.728293	−	0.685266i	$-0.759686\pi$
$197$	−20.4441			−1.45659			−0.728293	+	0.685266i	$0.759686\pi$
$198$		0			0
$199$	−6.50056	+	11.2593i	−0.460812	+	0.798150i	−0.999002	−	0.0446737i	$-0.985775\pi$
$199$	−6.50056	+	11.2593i	−0.460812	+	0.798150i	0.538189	+	0.842824i	$0.319109\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−9.56074	+	21.4905i	−0.671032	+	1.50834i
$204$		0			0
$205$	7.98510			0.557703
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.623163	−	1.07935i	0.0431051	−	0.0746602i
$210$		0			0
$211$	−2.11924	−	3.67064i	−0.145895	−	0.252697i	0.783812	−	0.620999i	$-0.213273\pi$
$211$	−2.11924	−	3.67064i	−0.145895	−	0.252697i	−0.929706	+	0.368302i	$0.879939\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.30569	+	2.26151i	0.0890470	+	0.154234i
$216$		0			0
$217$	3.02808	−	0.319152i	0.205559	−	0.0216655i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	26.0737			1.75391
$222$		0			0
$223$	5.83329	−	10.1036i	0.390626	−	0.676584i	−0.601906	−	0.798567i	$-0.705592\pi$
$223$	5.83329	−	10.1036i	0.390626	−	0.676584i	0.992532	+	0.121982i	$0.0389252\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.08989	−	3.61980i	−0.138711	−	0.240255i	0.788298	−	0.615294i	$-0.210963\pi$
$227$	−2.08989	−	3.61980i	−0.138711	−	0.240255i	−0.927009	+	0.375039i	$0.877629\pi$
$228$		0			0
$229$	4.19086	−	7.25878i	0.276940	−	0.479674i	−0.693683	−	0.720280i	$-0.744013\pi$
$229$	4.19086	−	7.25878i	0.276940	−	0.479674i	0.970623	+	0.240607i	$0.0773464\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.499512	+	0.865180i	0.0327241	+	0.0566798i	0.881924	−	0.471392i	$-0.156248\pi$
$233$	0.499512	+	0.865180i	0.0327241	+	0.0566798i	−0.849200	+	0.528072i	$0.822915\pi$
$234$		0			0
$235$	−4.37807	+	7.58305i	−0.285594	+	0.494663i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	6.15412	+	10.6593i	0.398077	+	0.689490i	0.993489	−	0.113931i	$-0.0363443\pi$
$239$	6.15412	+	10.6593i	0.398077	+	0.689490i	−0.595411	+	0.803421i	$0.703011\pi$
$240$		0			0
$241$	−3.23916	−	5.61039i	−0.208653	−	0.361397i	0.742638	−	0.669694i	$-0.233575\pi$
$241$	−3.23916	−	5.61039i	−0.208653	−	0.361397i	−0.951290	+	0.308296i	$0.900241\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.22645	+	6.86586i	−0.142243	+	0.438643i
$246$		0			0
$247$	−1.98386	+	3.43614i	−0.126230	+	0.218636i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	12.2236			0.771544			0.385772	−	0.922594i	$-0.373935\pi$
$251$	12.2236			0.771544			0.385772	+	0.922594i	$0.373935\pi$
$252$		0			0
$253$	9.30169			0.584792
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.96355	+	13.7933i	−0.496753	+	0.860401i	−0.999993	−	0.00374541i	$-0.998808\pi$
$257$	−7.96355	+	13.7933i	−0.496753	+	0.860401i	0.503240	+	0.864147i	$0.332141\pi$
$258$		0			0
$259$	−12.6947	−	17.4621i	−0.788808	−	1.08504i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−11.5305	−	19.9714i	−0.711002	−	1.23149i	−0.964481	−	0.264150i	$-0.914908\pi$
$263$	−11.5305	−	19.9714i	−0.711002	−	1.23149i	0.253480	−	0.967341i	$-0.418425\pi$
$264$		0			0
$265$	2.48778	+	4.30897i	0.152823	+	0.264698i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	5.51107	−	9.54546i	0.336016	−	0.581997i	−0.647663	−	0.761927i	$-0.724254\pi$
$269$	5.51107	−	9.54546i	0.336016	−	0.581997i	0.983679	+	0.179930i	$0.0575871\pi$
$270$		0			0
$271$	2.74213	+	4.74951i	0.166572	+	0.288512i	0.937213	−	0.348759i	$-0.113397\pi$
$271$	2.74213	+	4.74951i	0.166572	+	0.288512i	−0.770640	+	0.637271i	$0.780063\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.12140	+	5.40643i	−0.188228	+	0.326020i
$276$		0			0
$277$	15.0331	+	26.0381i	0.903253	+	1.56448i	0.823246	+	0.567685i	$0.192161\pi$
$277$	15.0331	+	26.0381i	0.903253	+	1.56448i	0.0800068	+	0.996794i	$0.474506\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−5.90908	+	10.2348i	−0.352506	+	0.610559i	−0.986688	−	0.162625i	$-0.948004\pi$
$281$	−5.90908	+	10.2348i	−0.352506	+	0.610559i	0.634182	+	0.773184i	$0.281337\pi$
$282$		0			0
$283$	21.1210			1.25552			0.627758	−	0.778409i	$-0.283973\pi$
$283$	21.1210			1.25552			0.627758	+	0.778409i	$0.283973\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	12.0479	+	16.5725i	0.711167	+	0.978241i
$288$		0			0
$289$	−4.83778	−	8.37928i	−0.284575	−	0.492899i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−6.15098	−	10.6538i	−0.359344	−	0.622402i	0.628507	−	0.777804i	$-0.283666\pi$
$293$	−6.15098	−	10.6538i	−0.359344	−	0.622402i	−0.987851	+	0.155401i	$0.950333\pi$
$294$		0			0
$295$	−1.99648	+	3.45800i	−0.116239	+	0.201332i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−29.6122			−1.71252
$300$		0			0
$301$	−2.72358	+	6.12203i	−0.156984	+	0.352868i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.97209	−	8.61191i	0.284701	−	0.493117i
$306$		0			0
$307$	−33.5033			−1.91213			−0.956067	−	0.293147i	$-0.905297\pi$
$307$	−33.5033			−1.91213			−0.956067	+	0.293147i	$0.905297\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	29.6114			1.67911			0.839555	−	0.543275i	$-0.182816\pi$
$311$	29.6114			1.67911			0.839555	+	0.543275i	$0.182816\pi$
$312$		0			0
$313$	−11.7149			−0.662165			−0.331082	−	0.943602i	$-0.607414\pi$
$313$	−11.7149			−0.662165			−0.331082	+	0.943602i	$0.607414\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.16168			0.121412			0.0607061	−	0.998156i	$-0.480665\pi$
$317$	2.16168			0.121412			0.0607061	+	0.998156i	$0.480665\pi$
$318$		0			0
$319$	14.0977			0.789321
$320$		0			0
$321$		0			0
$322$		0			0
$323$	4.05930			0.225866
$324$		0			0
$325$	9.93707	−	17.2115i	0.551209	−	0.954723i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−22.3437	+	2.35497i	−1.23185	+	0.129834i
$330$		0			0
$331$	31.2003			1.71492			0.857461	−	0.514549i	$-0.172041\pi$
$331$	31.2003			1.71492			0.857461	+	0.514549i	$0.172041\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.863273	−	1.49523i	0.0471656	−	0.0816933i
$336$		0			0
$337$	−1.94425	−	3.36753i	−0.105910	−	0.183441i	0.808200	−	0.588908i	$-0.200442\pi$
$337$	−1.94425	−	3.36753i	−0.105910	−	0.183441i	−0.914110	+	0.405467i	$0.867109\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.912481	−	1.58046i	−0.0494136	−	0.0855869i
$342$		0			0
$343$	−17.6088	+	5.73840i	−0.950787	+	0.309845i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	16.7566			0.899543			0.449771	−	0.893144i	$-0.351505\pi$
$347$	16.7566			0.899543			0.449771	+	0.893144i	$0.351505\pi$
$348$		0			0
$349$	15.9097	−	27.5564i	0.851625	−	1.47506i	−0.0281152	−	0.999605i	$-0.508951\pi$
$349$	15.9097	−	27.5564i	0.851625	−	1.47506i	0.879741	−	0.475454i	$-0.157716\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.66867	−	6.35431i	−0.195263	−	0.338206i	0.751723	−	0.659478i	$-0.229223\pi$
$353$	−3.66867	−	6.35431i	−0.195263	−	0.338206i	−0.946987	+	0.321272i	$0.895889\pi$
$354$		0			0
$355$	−7.36193	+	12.7512i	−0.390731	+	0.676765i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−7.16644	−	12.4126i	−0.378230	−	0.655114i	0.612574	−	0.790413i	$-0.290134\pi$
$359$	−7.16644	−	12.4126i	−0.378230	−	0.655114i	−0.990805	+	0.135299i	$0.956801\pi$
$360$		0			0
$361$	9.19114	−	15.9195i	0.483744	−	0.837870i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	3.13854	+	5.43611i	0.164279	+	0.284539i
$366$		0			0
$367$	−12.7865	−	22.1469i	−0.667450	−	1.15606i	−0.978615	−	0.205702i	$-0.934052\pi$
$367$	−12.7865	−	22.1469i	−0.667450	−	1.15606i	0.311165	−	0.950356i	$-0.399281\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−5.18935	+	11.6646i	−0.269418	+	0.605595i
$372$		0			0
$373$	−15.5734	+	26.9739i	−0.806361	+	1.39666i	0.109008	+	0.994041i	$0.465233\pi$
$373$	−15.5734	+	26.9739i	−0.806361	+	1.39666i	−0.915368	+	0.402617i	$0.868101\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−44.8805			−2.31146
$378$		0			0
$379$	−6.72979			−0.345686			−0.172843	−	0.984949i	$-0.555295\pi$
$379$	−6.72979			−0.345686			−0.172843	+	0.984949i	$0.555295\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−18.7673	+	32.5060i	−0.958967	+	1.66098i	−0.233949	+	0.972249i	$0.575165\pi$
$383$	−18.7673	+	32.5060i	−0.958967	+	1.66098i	−0.725018	+	0.688730i	$0.758168\pi$
$384$		0			0
$385$	4.30225	−	0.453446i	0.219263	−	0.0231098i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	15.3213	+	26.5372i	0.776819	+	1.34549i	0.933766	+	0.357883i	$0.116501\pi$
$389$	15.3213	+	26.5372i	0.776819	+	1.34549i	−0.156947	+	0.987607i	$0.550165\pi$
$390$		0			0
$391$	15.1479	+	26.2369i	0.766061	+	1.32686i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	4.28464	−	7.42121i	0.215583	−	0.373401i
$396$		0			0
$397$	−2.65885	−	4.60527i	−0.133444	−	0.231132i	0.791558	−	0.611094i	$-0.209270\pi$
$397$	−2.65885	−	4.60527i	−0.133444	−	0.231132i	−0.925002	+	0.379962i	$0.875937\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−0.328399	+	0.568803i	−0.0163994	+	0.0284047i	−0.874109	−	0.485730i	$-0.838554\pi$
$401$	−0.328399	+	0.568803i	−0.0163994	+	0.0284047i	0.857709	+	0.514135i	$0.171887\pi$
$402$		0			0
$403$	2.90491	+	5.03145i	0.144704	+	0.250634i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.46974	+	11.2059i	−0.320693	+	0.555457i
$408$		0			0
$409$	−31.5988			−1.56246			−0.781230	−	0.624243i	$-0.785407\pi$
$409$	−31.5988			−1.56246			−0.781230	+	0.624243i	$0.785407\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−10.1891	+	1.07391i	−0.501373	+	0.0528435i
$414$		0			0
$415$	7.34254	+	12.7177i	0.360431	+	0.624285i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.4424	−	18.0868i	−0.510146	−	0.883598i	−0.999931	−	0.0117550i	$-0.996258\pi$
$419$	−10.4424	−	18.0868i	−0.510146	−	0.883598i	0.489785	−	0.871843i	$-0.337075\pi$
$420$		0			0
$421$	−6.79788	+	11.7743i	−0.331309	+	0.573843i	−0.982769	−	0.184840i	$-0.940823\pi$
$421$	−6.79788	+	11.7743i	−0.331309	+	0.573843i	0.651460	+	0.758683i	$0.274157\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−20.3329			−0.986291
$426$		0			0
$427$	25.3753	−	2.67449i	1.22799	−	0.129428i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	13.9416	−	24.1475i	0.671541	−	1.16314i	−0.305926	−	0.952055i	$-0.598966\pi$
$431$	13.9416	−	24.1475i	0.671541	−	1.16314i	0.977467	−	0.211088i	$-0.0677006\pi$
$432$		0			0
$433$	−22.7059			−1.09118			−0.545589	−	0.838053i	$-0.683694\pi$
$433$	−22.7059			−1.09118			−0.545589	+	0.838053i	$0.683694\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.61020			−0.220536
$438$		0			0
$439$	31.9016			1.52258			0.761290	−	0.648411i	$-0.224566\pi$
$439$	31.9016			1.52258			0.761290	+	0.648411i	$0.224566\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−35.1257			−1.66887			−0.834436	−	0.551104i	$-0.814207\pi$
$443$	−35.1257			−1.66887			−0.834436	+	0.551104i	$0.814207\pi$
$444$		0			0
$445$	−13.8020			−0.654276
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.0966532			−0.00456135			−0.00228067	−	0.999997i	$-0.500726\pi$
$449$	−0.0966532			−0.00456135			−0.00228067	+	0.999997i	$0.500726\pi$
$450$		0			0
$451$	6.14014	−	10.6350i	0.289128	−	0.500785i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−13.6963	+	1.44356i	−0.642094	+	0.0676751i
$456$		0			0
$457$	−17.0185			−0.796092			−0.398046	−	0.917365i	$-0.630312\pi$
$457$	−17.0185			−0.796092			−0.398046	+	0.917365i	$0.630312\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−8.08817	+	14.0091i	−0.376704	+	0.652470i	−0.990580	−	0.136932i	$-0.956276\pi$
$461$	−8.08817	+	14.0091i	−0.376704	+	0.652470i	0.613877	+	0.789402i	$0.289609\pi$
$462$		0			0
$463$	6.24297	+	10.8131i	0.290135	+	0.502529i	0.973842	−	0.227228i	$-0.0729663\pi$
$463$	6.24297	+	10.8131i	0.290135	+	0.502529i	−0.683706	+	0.729757i	$0.739633\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.72717	+	11.6518i	0.311296	+	0.539181i	0.978643	−	0.205566i	$-0.0659035\pi$
$467$	6.72717	+	11.6518i	0.311296	+	0.539181i	−0.667347	+	0.744747i	$0.732570\pi$
$468$		0			0
$469$	4.40575	−	0.464355i	0.203439	−	0.0214419i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.01603			0.184657
$474$		0			0
$475$	1.54706	−	2.67959i	0.0709840	−	0.122948i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	6.98107	+	12.0916i	0.318973	+	0.552478i	0.980274	−	0.197643i	$-0.0633287\pi$
$479$	6.98107	+	12.0916i	0.318973	+	0.552478i	−0.661301	+	0.750121i	$0.729995\pi$
$480$		0			0
$481$	20.5966	−	35.6744i	0.939124	−	1.62661i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.75824	−	4.77741i	−0.125245	−	0.216931i
$486$		0			0
$487$	14.4858	−	25.0901i	0.656413	−	1.13694i	−0.325124	−	0.945671i	$-0.605406\pi$
$487$	14.4858	−	25.0901i	0.656413	−	1.13694i	0.981538	−	0.191270i	$-0.0612605\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	20.8775	+	36.1609i	0.942189	+	1.63192i	0.761283	+	0.648419i	$0.224570\pi$
$491$	20.8775	+	36.1609i	0.942189	+	1.63192i	0.180906	+	0.983500i	$0.442097\pi$
$492$		0			0
$493$	22.9583	+	39.7649i	1.03399	+	1.79092i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−37.5719	+	3.95999i	−1.68533	+	0.177630i
$498$		0			0
$499$	−10.7230	+	18.5728i	−0.480028	+	0.831433i	−0.999738	−	0.0229099i	$-0.992707\pi$
$499$	−10.7230	+	18.5728i	−0.480028	+	0.831433i	0.519709	+	0.854343i	$0.326040\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−28.3098			−1.26227			−0.631135	−	0.775673i	$-0.717411\pi$
$503$	−28.3098			−1.26227			−0.631135	+	0.775673i	$0.717411\pi$
$504$		0			0
$505$	−3.27974			−0.145947
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−15.8142	+	27.3910i	−0.700951	+	1.21408i	0.267182	+	0.963646i	$0.413908\pi$
$509$	−15.8142	+	27.3910i	−0.700951	+	1.21408i	−0.968133	+	0.250437i	$0.919426\pi$
$510$		0			0
$511$	−6.54679	+	14.7158i	−0.289613	+	0.650989i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	5.88418	+	10.1917i	0.259288	+	0.449100i
$516$		0			0
$517$	6.73304	+	11.6620i	0.296119	+	0.512893i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−15.0364	+	26.0439i	−0.658759	+	1.14100i	0.322179	+	0.946679i	$0.395585\pi$
$521$	−15.0364	+	26.0439i	−0.658759	+	1.14100i	−0.980937	+	0.194325i	$0.937749\pi$
$522$		0			0
$523$	7.73793	+	13.4025i	0.338356	+	0.586050i	0.984124	−	0.177484i	$-0.0567959\pi$
$523$	7.73793	+	13.4025i	0.338356	+	0.586050i	−0.645768	+	0.763534i	$0.723463\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.97197	−	5.14760i	0.129461	−	0.224233i
$528$		0			0
$529$	−5.70363	−	9.87898i	−0.247984	−	0.429521i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−19.5473	+	33.8570i	−0.846689	+	1.46651i
$534$		0			0
$535$	0.642152			0.0277626
$536$		0			0
$537$		0			0
$538$		0			0
$539$	7.43234	+	8.24482i	0.320133	+	0.355130i
$540$		0			0
$541$	−8.11884	−	14.0622i	−0.349056	−	0.604583i	0.637026	−	0.770842i	$-0.280164\pi$
$541$	−8.11884	−	14.0622i	−0.349056	−	0.604583i	−0.986082	+	0.166259i	$0.946831\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.00217	+	1.73580i	0.0429281	+	0.0743536i
$546$		0			0
$547$	19.4541	−	33.6954i	0.831795	−	1.44071i	−0.0648180	−	0.997897i	$-0.520647\pi$
$547$	19.4541	−	33.6954i	0.831795	−	1.44071i	0.896613	−	0.442815i	$-0.146020\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−6.98726			−0.297667
$552$		0			0
$553$	21.8668	−	2.30471i	0.929872	−	0.0980062i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.86210	+	4.95730i	−0.121271	+	0.210048i	−0.920269	−	0.391286i	$-0.872030\pi$
$557$	−2.86210	+	4.95730i	−0.121271	+	0.210048i	0.798998	+	0.601334i	$0.205364\pi$
$558$		0			0
$559$	−12.7851			−0.540754
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.94667			−0.208477			−0.104239	−	0.994552i	$-0.533241\pi$
$563$	−4.94667			−0.208477			−0.104239	+	0.994552i	$0.533241\pi$
$564$		0			0
$565$	3.69999			0.155660
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−16.2194			−0.679954			−0.339977	−	0.940434i	$-0.610419\pi$
$569$	−16.2194			−0.679954			−0.339977	+	0.940434i	$0.610419\pi$
$570$		0			0
$571$	−36.6058			−1.53191			−0.765954	−	0.642896i	$-0.777733\pi$
$571$	−36.6058			−1.53191			−0.765954	+	0.642896i	$0.777733\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	23.0923			0.963017
$576$		0			0
$577$	−18.2684	+	31.6417i	−0.760522	+	1.31726i	0.182060	+	0.983287i	$0.441723\pi$
$577$	−18.2684	+	31.6417i	−0.760522	+	1.31726i	−0.942582	+	0.333975i	$0.891610\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−15.3161	+	34.4273i	−0.635418	+	1.42829i
$582$		0			0
$583$	7.65192			0.316910
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.9237	−	20.6525i	0.492144	−	0.852419i	−0.507815	−	0.861466i	$-0.669547\pi$
$587$	11.9237	−	20.6525i	0.492144	−	0.852419i	0.999959	+	0.00904721i	$0.00287986\pi$
$588$		0			0
$589$	0.452253	+	0.783325i	0.0186348	+	0.0322764i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	6.54751	+	11.3406i	0.268874	+	0.465704i	0.968571	−	0.248736i	$-0.0800151\pi$
$593$	6.54751	+	11.3406i	0.268874	+	0.465704i	−0.699697	+	0.714439i	$0.746682\pi$
$594$		0			0
$595$	8.28526	+	11.3967i	0.339663	+	0.467220i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	37.1539			1.51807			0.759034	−	0.651051i	$-0.225672\pi$
$599$	37.1539			1.51807			0.759034	+	0.651051i	$0.225672\pi$
$600$		0			0
$601$	8.53133	−	14.7767i	0.348000	−	0.602754i	−0.637894	−	0.770124i	$-0.720194\pi$
$601$	8.53133	−	14.7767i	0.348000	−	0.602754i	0.985894	+	0.167370i	$0.0535275\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	4.37471	+	7.57722i	0.177857	+	0.308058i
$606$		0			0
$607$	−11.5973	+	20.0871i	−0.470719	+	0.815310i	−0.999439	−	0.0334867i	$-0.989339\pi$
$607$	−11.5973	+	20.0871i	−0.470719	+	0.815310i	0.528720	+	0.848796i	$0.322672\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−21.4348	−	37.1262i	−0.867160	−	1.50197i
$612$		0			0
$613$	22.2875	−	38.6030i	0.900182	−	1.55916i	0.0729255	−	0.997337i	$-0.476766\pi$
$613$	22.2875	−	38.6030i	0.900182	−	1.55916i	0.827257	−	0.561824i	$-0.189900\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.12703	+	5.41618i	0.125890	+	0.218047i	0.922080	−	0.386999i	$-0.126488\pi$
$617$	3.12703	+	5.41618i	0.125890	+	0.218047i	−0.796191	+	0.605046i	$0.793155\pi$
$618$		0			0
$619$	0.770208	+	1.33404i	0.0309573	+	0.0536196i	0.881089	−	0.472951i	$-0.156811\pi$
$619$	0.770208	+	1.33404i	0.0309573	+	0.0536196i	−0.850132	+	0.526570i	$0.823478\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−20.8244	−	28.6449i	−0.834314	−	1.14763i
$624$		0			0
$625$	−5.09116	+	8.81816i	−0.203647	+	0.352726i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−42.1441			−1.68040
$630$		0			0
$631$	−44.5148			−1.77210			−0.886052	−	0.463585i	$-0.846563\pi$
$631$	−44.5148			−1.77210			−0.886052	+	0.463585i	$0.846563\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−5.99090	+	10.3765i	−0.237742	+	0.411781i
$636$		0			0
$637$	−23.6611	−	26.2476i	−0.937485	−	1.03997i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.87520	+	3.24794i	0.0740660	+	0.128286i	0.900680	−	0.434484i	$-0.143069\pi$
$641$	1.87520	+	3.24794i	0.0740660	+	0.128286i	−0.826614	+	0.562770i	$0.809736\pi$
$642$		0			0
$643$	−0.818392	−	1.41750i	−0.0322742	−	0.0559006i	0.849437	−	0.527690i	$-0.176942\pi$
$643$	−0.818392	−	1.41750i	−0.0322742	−	0.0559006i	−0.881711	+	0.471789i	$0.843608\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	10.0748	−	17.4501i	0.396082	−	0.686034i	−0.597157	−	0.802125i	$-0.703703\pi$
$647$	10.0748	−	17.4501i	0.396082	−	0.686034i	0.993239	+	0.116091i	$0.0370363\pi$
$648$		0			0
$649$	3.07038	+	5.31806i	0.120523	+	0.208752i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	21.4570	−	37.1646i	0.839677	−	1.45436i	−0.0504888	−	0.998725i	$-0.516078\pi$
$653$	21.4570	−	37.1646i	0.839677	−	1.45436i	0.890165	−	0.455638i	$-0.150589\pi$
$654$		0			0
$655$	4.20591	+	7.28486i	0.164339	+	0.284643i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	10.8526	−	18.7973i	0.422758	−	0.732238i	−0.573450	−	0.819240i	$-0.694395\pi$
$659$	10.8526	−	18.7973i	0.422758	−	0.732238i	0.996208	+	0.0870025i	$0.0277288\pi$
$660$		0			0
$661$	−25.3815			−0.987225			−0.493613	−	0.869682i	$-0.664324\pi$
$661$	−25.3815			−0.987225			−0.493613	+	0.869682i	$0.664324\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−2.13232	+	0.224742i	−0.0826880	+	0.00871511i
$666$		0			0
$667$	−26.0740	−	45.1614i	−1.00959	−	1.74866i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−7.64658	−	13.2443i	−0.295193	−	0.511289i
$672$		0			0
$673$	7.88676	−	13.6603i	0.304012	−	0.526565i	−0.673029	−	0.739616i	$-0.735007\pi$
$673$	7.88676	−	13.6603i	0.304012	−	0.526565i	0.977041	+	0.213052i	$0.0683403\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	10.6506			0.409336			0.204668	−	0.978831i	$-0.434388\pi$
$677$	10.6506			0.409336			0.204668	+	0.978831i	$0.434388\pi$
$678$		0			0
$679$	5.75351	−	12.9327i	0.220799	−	0.496311i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	14.3656	−	24.8819i	0.549683	−	0.952078i	−0.448613	−	0.893726i	$-0.648082\pi$
$683$	14.3656	−	24.8819i	0.549683	−	0.952078i	0.998296	−	0.0583524i	$-0.0185847\pi$
$684$		0			0
$685$	−15.0168			−0.573763
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−24.3601			−0.928046
$690$		0			0
$691$	−39.2272			−1.49227			−0.746136	−	0.665794i	$-0.768093\pi$
$691$	−39.2272			−1.49227			−0.746136	+	0.665794i	$0.768093\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−12.2025			−0.462868
$696$		0			0
$697$	39.9971			1.51500
$698$		0			0
$699$		0			0
$700$		0			0
$701$	34.1643			1.29037			0.645184	−	0.764028i	$-0.276781\pi$
$701$	34.1643			1.29037			0.645184	+	0.764028i	$0.276781\pi$
$702$		0			0
$703$	3.20660	−	5.55399i	0.120939	−	0.209473i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.94848	−	6.80685i	−0.186107	−	0.255998i
$708$		0			0
$709$	19.7070			0.740113			0.370057	−	0.929009i	$-0.379338\pi$
$709$	19.7070			0.740113			0.370057	+	0.929009i	$0.379338\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.37530	+	5.84619i	−0.126406	+	0.218941i
$714$		0			0
$715$	4.12725	+	7.14861i	0.154350	+	0.267343i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	5.87829	+	10.1815i	0.219223	+	0.379705i	0.954571	−	0.297985i	$-0.0963144\pi$
$719$	5.87829	+	10.1815i	0.219223	+	0.379705i	−0.735348	+	0.677690i	$0.762981\pi$
$720$		0			0
$721$	−12.2740	+	27.5894i	−0.457108	+	1.02748i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	34.9989			1.29983
$726$		0			0
$727$	22.8161	−	39.5186i	0.846202	−	1.46567i	−0.0383705	−	0.999264i	$-0.512217\pi$
$727$	22.8161	−	39.5186i	0.846202	−	1.46567i	0.884573	−	0.466402i	$-0.154450\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	6.54014	+	11.3279i	0.241896	+	0.418976i
$732$		0			0
$733$	−19.4901	+	33.7579i	−0.719885	+	1.24688i	0.241160	+	0.970485i	$0.422472\pi$
$733$	−19.4901	+	33.7579i	−0.719885	+	1.24688i	−0.961045	+	0.276392i	$0.910861\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.32763	−	2.29952i	−0.0489038	−	0.0847039i
$738$		0			0
$739$	−11.7719	+	20.3895i	−0.433036	+	0.750040i	−0.997133	−	0.0756686i	$-0.975891\pi$
$739$	−11.7719	+	20.3895i	−0.433036	+	0.750040i	0.564097	+	0.825708i	$0.309224\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	4.09612	+	7.09469i	0.150272	+	0.260279i	0.931327	−	0.364183i	$-0.118652\pi$
$743$	4.09612	+	7.09469i	0.150272	+	0.260279i	−0.781055	+	0.624462i	$0.785318\pi$
$744$		0			0
$745$	7.24337	+	12.5459i	0.265377	+	0.459646i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.968881	+	1.33274i	0.0354021	+	0.0486971i
$750$		0			0
$751$	14.0936	−	24.4109i	0.514284	−	0.890766i	−0.485578	−	0.874193i	$-0.661391\pi$
$751$	14.0936	−	24.4109i	0.514284	−	0.890766i	0.999863	−	0.0165733i	$-0.00527570\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2.56271			0.0932667
$756$		0			0
$757$	7.42352			0.269812			0.134906	−	0.990858i	$-0.456927\pi$
$757$	7.42352			0.269812			0.134906	+	0.990858i	$0.456927\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−15.3534	+	26.5928i	−0.556559	+	0.963988i	0.441222	+	0.897398i	$0.354545\pi$
$761$	−15.3534	+	26.5928i	−0.556559	+	0.963988i	−0.997780	+	0.0665900i	$0.978788\pi$
$762$		0			0
$763$	−2.09045	+	4.69890i	−0.0756795	+	0.170112i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−9.77465	−	16.9302i	−0.352942	−	0.611314i
$768$		0			0
$769$	20.0973	+	34.8095i	0.724727	+	1.25526i	0.959086	+	0.283113i	$0.0913673\pi$
$769$	20.0973	+	34.8095i	0.724727	+	1.25526i	−0.234360	+	0.972150i	$0.575299\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−1.69611	+	2.93775i	−0.0610050	+	0.105664i	−0.894915	−	0.446237i	$-0.852764\pi$
$773$	−1.69611	+	2.93775i	−0.0610050	+	0.105664i	0.833910	+	0.551901i	$0.186097\pi$
$774$		0			0
$775$	−2.26532	−	3.92365i	−0.0813727	−	0.140942i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.04324	+	5.27105i	−0.109035	+	0.188855i
$780$		0			0
$781$	11.3219	+	19.6101i	0.405130	+	0.701706i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.56696	−	2.71405i	0.0559271	−	0.0968686i
$786$		0			0
$787$	10.8331			0.386160			0.193080	−	0.981183i	$-0.438152\pi$
$787$	10.8331			0.386160			0.193080	+	0.981183i	$0.438152\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	5.58256	+	7.67904i	0.198493	+	0.273035i
$792$		0			0
$793$	24.3431	+	42.1635i	0.864449	+	1.49727i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−23.4982	−	40.7001i	−0.832350	−	1.44167i	−0.896170	−	0.443712i	$-0.853661\pi$
$797$	−23.4982	−	40.7001i	−0.832350	−	1.44167i	0.0638193	−	0.997961i	$-0.479672\pi$
$798$		0			0
$799$	−21.9296	+	37.9832i	−0.775814	+	1.34375i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	9.65352			0.340665
$804$		0			0
$805$	−9.40968	−	12.9434i	−0.331648	−	0.456195i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−14.5052	+	25.1238i	−0.509977	+	0.883306i	0.489957	+	0.871747i	$0.337013\pi$
$809$	−14.5052	+	25.1238i	−0.509977	+	0.883306i	−0.999933	+	0.0115587i	$0.996321\pi$
$810$		0			0
$811$	34.6805			1.21780			0.608899	−	0.793248i	$-0.291612\pi$
$811$	34.6805			1.21780			0.608899	+	0.793248i	$0.291612\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	18.0628			0.632712
$816$		0			0
$817$	−1.99047			−0.0696376
$818$		0			0
$819$		0			0
$820$		0			0
$821$	39.3213			1.37232			0.686161	−	0.727450i	$-0.259295\pi$
$821$	39.3213			1.37232			0.686161	+	0.727450i	$0.259295\pi$
$822$		0			0
$823$	−42.6864			−1.48796			−0.743978	−	0.668204i	$-0.767063\pi$
$823$	−42.6864			−1.48796			−0.743978	+	0.668204i	$0.767063\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	14.5672			0.506551			0.253276	−	0.967394i	$-0.418492\pi$
$827$	14.5672			0.506551			0.253276	+	0.967394i	$0.418492\pi$
$828$		0			0
$829$	16.6920	−	28.9113i	0.579736	−	1.00413i	−0.415773	−	0.909468i	$-0.636489\pi$
$829$	16.6920	−	28.9113i	0.579736	−	1.00413i	0.995509	−	0.0946641i	$-0.0301777\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−11.1522	+	34.3908i	−0.386401	+	1.19157i
$834$		0			0
$835$	25.3115			0.875939
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−0.987290	+	1.71004i	−0.0340850	+	0.0590370i	−0.882565	−	0.470191i	$-0.844185\pi$
$839$	−0.987290	+	1.71004i	−0.0340850	+	0.0590370i	0.848480	+	0.529228i	$0.177518\pi$
$840$		0			0
$841$	−25.0179	−	43.3323i	−0.862687	−	1.49422i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−6.43695	−	11.1491i	−0.221438	−	0.383541i
$846$		0			0
$847$	−9.12536	+	20.5119i	−0.313551	+	0.704798i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	47.8636			1.64074
$852$		0			0
$853$	6.68637	−	11.5811i	0.228937	−	0.396531i	−0.728556	−	0.684986i	$-0.759808\pi$
$853$	6.68637	−	11.5811i	0.228937	−	0.396531i	0.957493	+	0.288455i	$0.0931417\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−13.4324	−	23.2656i	−0.458842	−	0.794738i	0.540058	−	0.841628i	$-0.318402\pi$
$857$	−13.4324	−	23.2656i	−0.458842	−	0.794738i	−0.998900	+	0.0468899i	$0.985069\pi$
$858$		0			0
$859$	22.9212	−	39.7007i	0.782062	−	1.35457i	−0.148677	−	0.988886i	$-0.547502\pi$
$859$	22.9212	−	39.7007i	0.782062	−	1.35457i	0.930739	−	0.365685i	$-0.119165\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	5.90612	+	10.2297i	0.201047	+	0.348223i	0.948866	−	0.315679i	$-0.102232\pi$
$863$	5.90612	+	10.2297i	0.201047	+	0.348223i	−0.747819	+	0.663902i	$0.768899\pi$
$864$		0			0
$865$	0.0355291	−	0.0615383i	0.00120803	−	0.00209236i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−6.58935	−	11.4131i	−0.223528	−	0.387162i
$870$		0			0
$871$	4.22654	+	7.32059i	0.143211	+	0.248049i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	24.2460	−	2.55547i	0.819665	−	0.0863907i
$876$		0			0
$877$	12.6046	−	21.8318i	0.425628	−	0.737209i	−0.570851	−	0.821054i	$-0.693387\pi$
$877$	12.6046	−	21.8318i	0.425628	−	0.737209i	0.996479	+	0.0838449i	$0.0267200\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.268589			−0.00904898			−0.00452449	−	0.999990i	$-0.501440\pi$
$881$	−0.268589			−0.00904898			−0.00452449	+	0.999990i	$0.501440\pi$
$882$		0			0
$883$	25.8915			0.871319			0.435660	−	0.900112i	$-0.356515\pi$
$883$	25.8915			0.871319			0.435660	+	0.900112i	$0.356515\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−21.8396	+	37.8274i	−0.733303	+	1.27012i	0.222160	+	0.975010i	$0.428689\pi$
$887$	−21.8396	+	37.8274i	−0.733303	+	1.27012i	−0.955464	+	0.295109i	$0.904644\pi$
$888$		0			0
$889$	−30.5748	+	3.22251i	−1.02545	+	0.108080i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−3.33710	−	5.78003i	−0.111672	−	0.193421i
$894$		0			0
$895$	4.08412	+	7.07390i	0.136517	+	0.236454i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−5.11563	+	8.86053i	−0.170616	+	0.295515i
$900$		0			0
$901$	12.4612	+	21.5835i	0.415143	+	0.719050i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.85441	+	3.21192i	−0.0616425	+	0.106768i
$906$		0			0
$907$	0.0146274	+	0.0253355i	0.000485696	+	0.000841251i	0.866268	−	0.499579i	$-0.166512\pi$
$907$	0.0146274	+	0.0253355i	0.000485696	+	0.000841251i	−0.865782	+	0.500421i	$0.833179\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−14.0048	+	24.2569i	−0.463998	+	0.803668i	−0.999156	−	0.0410839i	$-0.986919\pi$
$911$	−14.0048	+	24.2569i	−0.463998	+	0.803668i	0.535158	+	0.844752i	$0.320252\pi$
$912$		0			0
$913$	22.5842			0.747428
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−8.77326	+	19.7205i	−0.289719	+	0.651227i
$918$		0			0
$919$	−6.11476	−	10.5911i	−0.201707	−	0.349367i	0.747371	−	0.664407i	$-0.231316\pi$
$919$	−6.11476	−	10.5911i	−0.201707	−	0.349367i	−0.949079	+	0.315039i	$0.897982\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−36.0436	−	62.4294i	−1.18639	−	2.05489i
$924$		0			0
$925$	−16.0618	+	27.8198i	−0.528107	+	0.914709i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−7.96405			−0.261292			−0.130646	−	0.991429i	$-0.541705\pi$
$929$	−7.96405			−0.261292			−0.130646	+	0.991429i	$0.541705\pi$
$930$		0			0
$931$	−3.68369	−	4.08638i	−0.120728	−	0.133926i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	4.22252	−	7.31363i	0.138091	−	0.239181i
$936$		0			0
$937$	−15.0407			−0.491358			−0.245679	−	0.969351i	$-0.579011\pi$
$937$	−15.0407			−0.491358			−0.245679	+	0.969351i	$0.579011\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	57.9119			1.88787			0.943936	−	0.330128i	$-0.107092\pi$
$941$	57.9119			1.88787			0.943936	+	0.330128i	$0.107092\pi$
$942$		0			0
$943$	−45.4252			−1.47925
$944$		0			0
$945$		0			0
$946$		0			0
$947$	23.6883			0.769767			0.384883	−	0.922965i	$-0.374242\pi$
$947$	23.6883			0.769767			0.384883	+	0.922965i	$0.374242\pi$
$948$		0			0
$949$	−30.7323			−0.997611
$950$		0			0
$951$		0			0
$952$		0			0
$953$	14.2226			0.460716			0.230358	−	0.973106i	$-0.426010\pi$
$953$	14.2226			0.460716			0.230358	+	0.973106i	$0.426010\pi$
$954$		0			0
$955$	−8.27429	+	14.3315i	−0.267750	+	0.463756i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−22.6574	−	31.1663i	−0.731646	−	1.00641i
$960$		0			0
$961$	−29.6756			−0.957276
$962$		0			0
$963$		0			0
$964$		0			0
$965$	11.1222	−	19.2642i	0.358035	−	0.620135i
$966$		0			0
$967$	10.3665	+	17.9554i	0.333365	+	0.577405i	0.983169	−	0.182696i	$-0.0584825\pi$
$967$	10.3665	+	17.9554i	0.333365	+	0.577405i	−0.649804	+	0.760102i	$0.725149\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	8.39847	+	14.5466i	0.269520	+	0.466822i	0.968738	−	0.248087i	$-0.0798018\pi$
$971$	8.39847	+	14.5466i	0.269520	+	0.466822i	−0.699218	+	0.714908i	$0.746468\pi$
$972$		0			0
$973$	−18.4112	−	25.3254i	−0.590236	−	0.811894i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−37.4327			−1.19758			−0.598788	−	0.800907i	$-0.704351\pi$
$977$	−37.4327			−1.19758			−0.598788	+	0.800907i	$0.704351\pi$
$978$		0			0
$979$	−10.6130	+	18.3823i	−0.339194	+	0.587501i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	25.8389	+	44.7543i	0.824132	+	1.42744i	0.902581	+	0.430521i	$0.141670\pi$
$983$	25.8389	+	44.7543i	0.824132	+	1.42744i	−0.0784482	+	0.996918i	$0.524997\pi$
$984$		0			0
$985$	10.5402	−	18.2561i	0.335838	−	0.581688i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−7.42771	−	12.8652i	−0.236188	−	0.409089i
$990$		0			0
$991$	28.5452	−	49.4418i	0.906769	−	1.57057i	0.0882435	−	0.996099i	$-0.471875\pi$
$991$	28.5452	−	49.4418i	0.906769	−	1.57057i	0.818525	−	0.574471i	$-0.194792\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−6.70284	−	11.6097i	−0.212494	−	0.368051i
$996$		0			0
$997$	1.00745	+	1.74496i	0.0319063	+	0.0552633i	0.881538	−	0.472114i	$-0.156509\pi$
$997$	1.00745	+	1.74496i	0.0319063	+	0.0552633i	−0.849631	+	0.527377i	$0.823176\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.i.n.865.3		16
3.2	odd	2	inner	2268.2.i.n.865.6		16
7.2	even	3		2268.2.l.n.541.6		16
9.2	odd	6		2268.2.k.g.1621.6	yes	16
9.4	even	3		2268.2.l.n.109.6		16
9.5	odd	6		2268.2.l.n.109.3		16
9.7	even	3		2268.2.k.g.1621.3	yes	16
21.2	odd	6		2268.2.l.n.541.3		16
63.2	odd	6		2268.2.k.g.1297.6	yes	16
63.16	even	3		2268.2.k.g.1297.3	✓	16
63.23	odd	6	inner	2268.2.i.n.2053.6		16
63.58	even	3	inner	2268.2.i.n.2053.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2268.2.i.n.865.3		16	1.1	even	1	trivial
2268.2.i.n.865.6		16	3.2	odd	2	inner
2268.2.i.n.2053.3		16	63.58	even	3	inner
2268.2.i.n.2053.6		16	63.23	odd	6	inner
2268.2.k.g.1297.3	✓	16	63.16	even	3
2268.2.k.g.1297.6	yes	16	63.2	odd	6
2268.2.k.g.1621.3	yes	16	9.7	even	3
2268.2.k.g.1621.6	yes	16	9.2	odd	6
2268.2.l.n.109.3		16	9.5	odd	6
2268.2.l.n.109.6		16	9.4	even	3
2268.2.l.n.541.3		16	21.2	odd	6
2268.2.l.n.541.6		16	7.2	even	3

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:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.515559 + 0.892975i) q^{5} +(-2.63118 + 0.277320i) q^{7} +O(q^{10})\)	\(q+(-0.515559 + 0.892975i) q^{5} +(-2.63118 + 0.277320i) q^{7} +(0.792879 + 1.37331i) q^{11} +(-2.52415 - 4.37196i) q^{13} +(-2.58242 + 4.47288i) q^{17} +(-0.392975 - 0.680652i) q^{19} +(2.93289 - 5.07991i) q^{23} +(1.96840 + 3.40936i) q^{25} +(4.44511 - 7.69915i) q^{29} -1.15085 q^{31} +(1.10889 - 2.49255i) q^{35} +(4.07991 + 7.06661i) q^{37} +(-3.87206 - 6.70660i) q^{41} +(1.26628 - 2.19326i) q^{43} +8.49189 q^{47} +(6.84619 - 1.45935i) q^{49} +(2.41270 - 4.17892i) q^{53} -1.63510 q^{55} +3.87245 q^{59} -9.64407 q^{61} +5.20540 q^{65} -1.67444 q^{67} +14.2795 q^{71} +(3.04382 - 5.27205i) q^{73} +(-2.46705 - 3.39353i) q^{77} -8.31066 q^{79} +(7.12095 - 12.3339i) q^{83} +(-2.66278 - 4.61207i) q^{85} +(6.69272 + 11.5921i) q^{89} +(7.85392 + 10.8034i) q^{91} +0.810407 q^{95} +(-2.67500 + 4.63323i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{7}+O(q^{10}) \) 16 * q - 6 * q^7	\( 16 q - 6 q^{7} + 10 q^{13} + 8 q^{19} + 16 q^{31} - 4 q^{37} - 10 q^{43} + 10 q^{49} - 32 q^{55} - 56 q^{61} - 36 q^{67} + 40 q^{79} - 38 q^{85} - 2 q^{91} + 42 q^{97}+O(q^{100}) \) 16 * q - 6 * q^7 + 10 * q^13 + 8 * q^19 + 16 * q^31 - 4 * q^37 - 10 * q^43 + 10 * q^49 - 32 * q^55 - 56 * q^61 - 36 * q^67 + 40 * q^79 - 38 * q^85 - 2 * q^91 + 42 * q^97

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