LMFDB - Embedded newform 1296.2.i.c.433.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1296,2,Mod(433,1296)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1296, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1296.433");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1296 = 2^{4} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1296.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:	$10.3486121020$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			433.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1296.433
Dual form			1296.2.i.c.865.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{7} +O(q^{10})$	$q+(-1.50000 + 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-1.50000 - 2.59808i) q^{11} +(2.00000 - 3.46410i) q^{13} -2.00000 q^{19} +(-3.00000 + 5.19615i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-3.00000 - 5.19615i) q^{29} +(2.50000 - 4.33013i) q^{31} +3.00000 q^{35} +2.00000 q^{37} +(3.00000 - 5.19615i) q^{41} +(-5.00000 - 8.66025i) q^{43} +(3.00000 + 5.19615i) q^{47} +(3.00000 - 5.19615i) q^{49} +9.00000 q^{53} +9.00000 q^{55} +(6.00000 - 10.3923i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(6.00000 + 10.3923i) q^{65} +(7.00000 - 12.1244i) q^{67} -7.00000 q^{73} +(-1.50000 + 2.59808i) q^{77} +(4.00000 + 6.92820i) q^{79} +(-1.50000 - 2.59808i) q^{83} -18.0000 q^{89} -4.00000 q^{91} +(3.00000 - 5.19615i) q^{95} +(0.500000 + 0.866025i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{5} - q^{7}+O(q^{10}) $ 2 * q - 3 * q^5 - q^7	$ 2 q - 3 q^{5} - q^{7} - 3 q^{11} + 4 q^{13} - 4 q^{19} - 6 q^{23} - 4 q^{25} - 6 q^{29} + 5 q^{31} + 6 q^{35} + 4 q^{37} + 6 q^{41} - 10 q^{43} + 6 q^{47} + 6 q^{49} + 18 q^{53} + 18 q^{55} + 12 q^{59} - 8 q^{61} + 12 q^{65} + 14 q^{67} - 14 q^{73} - 3 q^{77} + 8 q^{79} - 3 q^{83} - 36 q^{89} - 8 q^{91} + 6 q^{95} + q^{97}+O(q^{100}) $ 2 * q - 3 * q^5 - q^7 - 3 * q^11 + 4 * q^13 - 4 * q^19 - 6 * q^23 - 4 * q^25 - 6 * q^29 + 5 * q^31 + 6 * q^35 + 4 * q^37 + 6 * q^41 - 10 * q^43 + 6 * q^47 + 6 * q^49 + 18 * q^53 + 18 * q^55 + 12 * q^59 - 8 * q^61 + 12 * q^65 + 14 * q^67 - 14 * q^73 - 3 * q^77 + 8 * q^79 - 3 * q^83 - 36 * q^89 - 8 * q^91 + 6 * q^95 + q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1217$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	−0.944911	+	0.327327i	$0.893852\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		0			0
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$		0			0
$19$	−2.00000			−0.458831			−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000			−0.458831			−0.229416	+	0.973329i	$0.573682\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$		0			0
$31$	2.50000	−	4.33013i	0.449013	−	0.777714i	−0.549309	−	0.835619i	$-0.685109\pi$
$31$	2.50000	−	4.33013i	0.449013	−	0.777714i	0.998322	+	0.0579057i	$0.0184423\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.00000			0.507093
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	−0.530831	−	0.847477i	$-0.678120\pi$
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	0.999353	+	0.0359748i	$0.0114536\pi$
$42$		0			0
$43$	−5.00000	−	8.66025i	−0.762493	−	1.32068i	−0.941562	−	0.336840i	$-0.890642\pi$
$43$	−5.00000	−	8.66025i	−0.762493	−	1.32068i	0.179069	−	0.983836i	$-0.442691\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$		0			0
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	9.00000			1.23625			0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000			1.23625			0.618123	+	0.786082i	$0.287894\pi$
$54$		0			0
$55$	9.00000			1.21356
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6.00000	+	10.3923i	0.744208	+	1.28901i
$66$		0			0
$67$	7.00000	−	12.1244i	0.855186	−	1.48123i	−0.0212861	−	0.999773i	$-0.506776\pi$
$67$	7.00000	−	12.1244i	0.855186	−	1.48123i	0.876472	−	0.481452i	$-0.159891\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−7.00000			−0.819288			−0.409644	−	0.912245i	$-0.634347\pi$
$73$	−7.00000			−0.819288			−0.409644	+	0.912245i	$0.634347\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.50000	+	2.59808i	−0.170941	+	0.296078i
$78$		0			0
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	0.998388	−	0.0567635i	$-0.0180781\pi$
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	−0.548352	+	0.836247i	$0.684745\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.50000	−	2.59808i	−0.164646	−	0.285176i	0.771883	−	0.635764i	$-0.219315\pi$
$83$	−1.50000	−	2.59808i	−0.164646	−	0.285176i	−0.936530	+	0.350588i	$0.885982\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−18.0000			−1.90800			−0.953998	−	0.299813i	$-0.903076\pi$
$89$	−18.0000			−1.90800			−0.953998	+	0.299813i	$0.903076\pi$
$90$		0			0
$91$	−4.00000			−0.419314
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.00000	−	5.19615i	0.307794	−	0.533114i
$96$		0			0
$97$	0.500000	+	0.866025i	0.0507673	+	0.0879316i	0.890292	−	0.455389i	$-0.150500\pi$
$97$	0.500000	+	0.866025i	0.0507673	+	0.0879316i	−0.839525	+	0.543321i	$0.817167\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$		0			0
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	−0.947576	−	0.319531i	$-0.896475\pi$
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	0.750510	+	0.660859i	$0.229808\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.00000			−0.870063			−0.435031	−	0.900415i	$-0.643263\pi$
$107$	−9.00000			−0.870063			−0.435031	+	0.900415i	$0.643263\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	−0.689714	−	0.724082i	$-0.742264\pi$
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	0.971930	+	0.235269i	$0.0755971\pi$
$114$		0			0
$115$	−9.00000	−	15.5885i	−0.839254	−	1.45363i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.00000			−0.268328
$126$		0			0
$127$	7.00000			0.621150			0.310575	−	0.950549i	$-0.399478\pi$
$127$	7.00000			0.621150			0.310575	+	0.950549i	$0.399478\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	0.326546	+	0.945181i	$0.394115\pi$
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	−0.981824	+	0.189794i	$0.939218\pi$
$132$		0			0
$133$	1.00000	+	1.73205i	0.0867110	+	0.150188i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	0.708942	−	0.705266i	$-0.249173\pi$
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$138$		0			0
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	−0.938293	−	0.345843i	$-0.887593\pi$
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	0.768655	+	0.639664i	$0.220926\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−12.0000			−1.00349
$144$		0			0
$145$	18.0000			1.49482
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	−0.920904	−	0.389789i	$-0.872548\pi$
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	0.798019	+	0.602632i	$0.205881\pi$
$150$		0			0
$151$	8.50000	+	14.7224i	0.691720	+	1.19809i	0.971274	+	0.237964i	$0.0764802\pi$
$151$	8.50000	+	14.7224i	0.691720	+	1.19809i	−0.279554	+	0.960130i	$0.590186\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	7.50000	+	12.9904i	0.602414	+	1.04341i
$156$		0			0
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	−0.775113	−	0.631822i	$-0.782307\pi$
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	0.934731	+	0.355357i	$0.115641\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.00000			0.472866
$162$		0			0
$163$	−20.0000			−1.56652			−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000			−1.56652			−0.783260	+	0.621694i	$0.786445\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	−0.958440	−	0.285295i	$-0.907908\pi$
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	0.726293	+	0.687386i	$0.241242\pi$
$168$		0			0
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	−0.996544	−	0.0830722i	$-0.973527\pi$
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	0.426329	−	0.904568i	$-0.359807\pi$
$174$		0			0
$175$	−2.00000	+	3.46410i	−0.151186	+	0.261861i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	9.00000			0.672692			0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000			0.672692			0.336346	+	0.941739i	$0.390809\pi$
$180$		0			0
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$		0			0
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	−0.941865	−	0.335993i	$-0.890928\pi$
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	0.761911	+	0.647682i	$0.224262\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	9.00000			0.641223			0.320612	−	0.947211i	$-0.396112\pi$
$197$	9.00000			0.641223			0.320612	+	0.947211i	$0.396112\pi$
$198$		0			0
$199$	7.00000			0.496217			0.248108	−	0.968732i	$-0.420191\pi$
$199$	7.00000			0.496217			0.248108	+	0.968732i	$0.420191\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.00000	+	5.19615i	−0.210559	+	0.364698i
$204$		0			0
$205$	9.00000	+	15.5885i	0.628587	+	1.08875i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.00000	+	5.19615i	0.207514	+	0.359425i
$210$		0			0
$211$	−11.0000	+	19.0526i	−0.757271	+	1.31163i	0.186966	+	0.982366i	$0.440135\pi$
$211$	−11.0000	+	19.0526i	−0.757271	+	1.31163i	−0.944237	+	0.329266i	$0.893199\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	30.0000			2.04598
$216$		0			0
$217$	−5.00000			−0.339422
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	4.00000	+	6.92820i	0.267860	+	0.463947i	0.968309	−	0.249756i	$-0.0803503\pi$
$223$	4.00000	+	6.92820i	0.267860	+	0.463947i	−0.700449	+	0.713702i	$0.747017\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	0.595274	−	0.803523i	$-0.297043\pi$
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	−0.993508	+	0.113761i	$0.963710\pi$
$228$		0			0
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	−0.999088	−	0.0426906i	$-0.986407\pi$
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	0.536515	+	0.843891i	$0.319740\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$		0			0
$235$	−18.0000			−1.17419
$236$		0			0
$237$		0			0
$238$		0			0
$239$	15.0000	−	25.9808i	0.970269	−	1.68056i	0.275533	−	0.961292i	$-0.411146\pi$
$239$	15.0000	−	25.9808i	0.970269	−	1.68056i	0.694737	−	0.719264i	$-0.255521\pi$
$240$		0			0
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	0.980917	−	0.194429i	$-0.0622852\pi$
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	−0.658838	+	0.752285i	$0.728952\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	9.00000	+	15.5885i	0.574989	+	0.995910i
$246$		0			0
$247$	−4.00000	+	6.92820i	−0.254514	+	0.440831i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	18.0000			1.13165
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	−0.990217	−	0.139533i	$-0.955440\pi$
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	0.615948	+	0.787787i	$0.288773\pi$
$258$		0			0
$259$	−1.00000	−	1.73205i	−0.0621370	−	0.107624i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−15.0000	−	25.9808i	−0.924940	−	1.60204i	−0.791658	−	0.610964i	$-0.790782\pi$
$263$	−15.0000	−	25.9808i	−0.924940	−	1.60204i	−0.133281	−	0.991078i	$-0.542551\pi$
$264$		0			0
$265$	−13.5000	+	23.3827i	−0.829298	+	1.43639i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−18.0000			−1.09748			−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000			−1.09748			−0.548740	+	0.835993i	$0.684892\pi$
$270$		0			0
$271$	25.0000			1.51864			0.759321	−	0.650716i	$-0.225531\pi$
$271$	25.0000			1.51864			0.759321	+	0.650716i	$0.225531\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−6.00000	+	10.3923i	−0.361814	+	0.626680i
$276$		0			0
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	0.720473	−	0.693482i	$-0.243925\pi$
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	−0.960810	+	0.277207i	$0.910591\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−12.0000	−	20.7846i	−0.715860	−	1.23991i	−0.962627	−	0.270831i	$-0.912702\pi$
$281$	−12.0000	−	20.7846i	−0.715860	−	1.23991i	0.246767	−	0.969075i	$-0.420632\pi$
$282$		0			0
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	−0.579437	−	0.815017i	$-0.696728\pi$
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	0.995544	+	0.0942988i	$0.0300609\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.00000			−0.354169
$288$		0			0
$289$	−17.0000			−1.00000
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3.00000	−	5.19615i	0.175262	−	0.303562i	−0.764990	−	0.644042i	$-0.777256\pi$
$293$	3.00000	−	5.19615i	0.175262	−	0.303562i	0.940252	+	0.340480i	$0.110589\pi$
$294$		0			0
$295$	18.0000	+	31.1769i	1.04800	+	1.81519i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	12.0000	+	20.7846i	0.693978	+	1.20201i
$300$		0			0
$301$	−5.00000	+	8.66025i	−0.288195	+	0.499169i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	24.0000			1.37424
$306$		0			0
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.00000	+	5.19615i	−0.170114	+	0.294647i	−0.938460	−	0.345389i	$-0.887747\pi$
$311$	−3.00000	+	5.19615i	−0.170114	+	0.294647i	0.768345	+	0.640036i	$0.221080\pi$
$312$		0			0
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	0.999065	+	0.0432311i	$0.0137652\pi$
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	−0.462093	+	0.886831i	$0.652902\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.50000	+	2.59808i	0.0842484	+	0.145922i	0.905071	−	0.425261i	$-0.139818\pi$
$317$	1.50000	+	2.59808i	0.0842484	+	0.145922i	−0.820822	+	0.571184i	$0.806484\pi$
$318$		0			0
$319$	−9.00000	+	15.5885i	−0.503903	+	0.872786i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−16.0000			−0.887520
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3.00000	−	5.19615i	0.165395	−	0.286473i
$330$		0			0
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	0.695266	−	0.718752i	$-0.255287\pi$
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	−0.970091	+	0.242742i	$0.921953\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	21.0000	+	36.3731i	1.14735	+	1.98727i
$336$		0			0
$337$	11.0000	−	19.0526i	0.599208	−	1.03786i	−0.393730	−	0.919226i	$-0.628816\pi$
$337$	11.0000	−	19.0526i	0.599208	−	1.03786i	0.992938	−	0.118633i	$-0.0378512\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−15.0000			−0.812296
$342$		0			0
$343$	−13.0000			−0.701934
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.50000	−	2.59808i	0.0805242	−	0.139472i	−0.822951	−	0.568112i	$-0.807674\pi$
$347$	1.50000	−	2.59808i	0.0805242	−	0.139472i	0.903475	+	0.428640i	$0.141007\pi$
$348$		0			0
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	0.968253	−	0.249973i	$-0.0804216\pi$
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	−0.700609	+	0.713545i	$0.747088\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	0.775077	−	0.631867i	$-0.217711\pi$
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	−0.934751	+	0.355303i	$0.884378\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−18.0000			−0.950004			−0.475002	−	0.879985i	$-0.657553\pi$
$359$	−18.0000			−0.950004			−0.475002	+	0.879985i	$0.657553\pi$
$360$		0			0
$361$	−15.0000			−0.789474
$362$		0			0
$363$		0			0
$364$		0			0
$365$	10.5000	−	18.1865i	0.549595	−	0.951927i
$366$		0			0
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	0.997960	−	0.0638362i	$-0.0203335\pi$
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	−0.554264	+	0.832341i	$0.687000\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.50000	−	7.79423i	−0.233628	−	0.404656i
$372$		0			0
$373$	−16.0000	+	27.7128i	−0.828449	+	1.43492i	0.0708063	+	0.997490i	$0.477443\pi$
$373$	−16.0000	+	27.7128i	−0.828449	+	1.43492i	−0.899255	+	0.437425i	$0.855891\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−24.0000			−1.23606
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	0.377531	+	0.925997i	$0.376773\pi$
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	−0.990702	+	0.136047i	$0.956560\pi$
$384$		0			0
$385$	−4.50000	−	7.79423i	−0.229341	−	0.397231i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	10.5000	+	18.1865i	0.532371	+	0.922094i	0.999286	+	0.0377914i	$0.0120322\pi$
$389$	10.5000	+	18.1865i	0.532371	+	0.922094i	−0.466915	+	0.884302i	$0.654634\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−24.0000			−1.20757
$396$		0			0
$397$	20.0000			1.00377			0.501886	−	0.864934i	$-0.332640\pi$
$397$	20.0000			1.00377			0.501886	+	0.864934i	$0.332640\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−6.00000	+	10.3923i	−0.299626	+	0.518967i	−0.976050	−	0.217545i	$-0.930195\pi$
$401$	−6.00000	+	10.3923i	−0.299626	+	0.518967i	0.676425	+	0.736512i	$0.263528\pi$
$402$		0			0
$403$	−10.0000	−	17.3205i	−0.498135	−	0.862796i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.00000	−	5.19615i	−0.148704	−	0.257564i
$408$		0			0
$409$	−11.5000	+	19.9186i	−0.568638	+	0.984911i	0.428063	+	0.903749i	$0.359196\pi$
$409$	−11.5000	+	19.9186i	−0.568638	+	0.984911i	−0.996701	+	0.0811615i	$0.974137\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−12.0000			−0.590481
$414$		0			0
$415$	9.00000			0.441793
$416$		0			0
$417$		0			0
$418$		0			0
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	−0.681426	−	0.731887i	$-0.738640\pi$
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	0.974546	+	0.224189i	$0.0719734\pi$
$420$		0			0
$421$	−4.00000	−	6.92820i	−0.194948	−	0.337660i	0.751935	−	0.659237i	$-0.229121\pi$
$421$	−4.00000	−	6.92820i	−0.194948	−	0.337660i	−0.946883	+	0.321577i	$0.895787\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−4.00000	+	6.92820i	−0.193574	+	0.335279i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−18.0000			−0.867029			−0.433515	−	0.901146i	$-0.642727\pi$
$431$	−18.0000			−0.867029			−0.433515	+	0.901146i	$0.642727\pi$
$432$		0			0
$433$	29.0000			1.39365			0.696826	−	0.717241i	$-0.254595\pi$
$433$	29.0000			1.39365			0.696826	+	0.717241i	$0.254595\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.00000	−	10.3923i	0.287019	−	0.497131i
$438$		0			0
$439$	−9.50000	−	16.4545i	−0.453410	−	0.785330i	0.545185	−	0.838316i	$-0.316459\pi$
$439$	−9.50000	−	16.4545i	−0.453410	−	0.785330i	−0.998595	+	0.0529862i	$0.983126\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	0.687557	−	0.726130i	$-0.258683\pi$
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	−0.972626	+	0.232377i	$0.925350\pi$
$444$		0			0
$445$	27.0000	−	46.7654i	1.27992	−	2.21689i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$	−18.0000			−0.847587
$452$		0			0
$453$		0			0
$454$		0			0
$455$	6.00000	−	10.3923i	0.281284	−	0.487199i
$456$		0			0
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	0.877483	−	0.479608i	$-0.159221\pi$
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	−0.854094	+	0.520119i	$0.825888\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	10.5000	+	18.1865i	0.489034	+	0.847031i	0.999920	−	0.0126168i	$-0.00401615\pi$
$461$	10.5000	+	18.1865i	0.489034	+	0.847031i	−0.510887	+	0.859648i	$0.670683\pi$
$462$		0			0
$463$	−6.50000	+	11.2583i	−0.302081	+	0.523219i	−0.976607	−	0.215032i	$-0.931015\pi$
$463$	−6.50000	+	11.2583i	−0.302081	+	0.523219i	0.674526	+	0.738251i	$0.264348\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	27.0000			1.24941			0.624705	−	0.780860i	$-0.285219\pi$
$467$	27.0000			1.24941			0.624705	+	0.780860i	$0.285219\pi$
$468$		0			0
$469$	−14.0000			−0.646460
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−15.0000	+	25.9808i	−0.689701	+	1.19460i
$474$		0			0
$475$	4.00000	+	6.92820i	0.183533	+	0.317888i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.00000	+	5.19615i	0.137073	+	0.237418i	0.926388	−	0.376571i	$-0.122897\pi$
$479$	3.00000	+	5.19615i	0.137073	+	0.237418i	−0.789314	+	0.613990i	$0.789564\pi$
$480$		0			0
$481$	4.00000	−	6.92820i	0.182384	−	0.315899i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.00000			−0.136223
$486$		0			0
$487$	16.0000			0.725029			0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000			0.725029			0.362515	+	0.931978i	$0.381918\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	19.5000	−	33.7750i	0.880023	−	1.52424i	0.0287085	−	0.999588i	$-0.490861\pi$
$491$	19.5000	−	33.7750i	0.880023	−	1.52424i	0.851314	−	0.524656i	$-0.175806\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	7.00000	−	12.1244i	0.313363	−	0.542761i	−0.665725	−	0.746197i	$-0.731878\pi$
$499$	7.00000	−	12.1244i	0.313363	−	0.542761i	0.979088	+	0.203436i	$0.0652110\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	18.0000			0.802580			0.401290	−	0.915951i	$-0.368562\pi$
$503$	18.0000			0.802580			0.401290	+	0.915951i	$0.368562\pi$
$504$		0			0
$505$	−9.00000			−0.400495
$506$		0			0
$507$		0			0
$508$		0			0
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	−0.650556	−	0.759458i	$-0.725464\pi$
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	0.982988	+	0.183669i	$0.0587976\pi$
$510$		0			0
$511$	3.50000	+	6.06218i	0.154831	+	0.268175i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−6.00000	−	10.3923i	−0.264392	−	0.457940i
$516$		0			0
$517$	9.00000	−	15.5885i	0.395820	−	0.685580i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	36.0000			1.57719			0.788594	−	0.614914i	$-0.210809\pi$
$521$	36.0000			1.57719			0.788594	+	0.614914i	$0.210809\pi$
$522$		0			0
$523$	16.0000			0.699631			0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000			0.699631			0.349816	+	0.936819i	$0.386244\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−12.0000	−	20.7846i	−0.519778	−	0.900281i
$534$		0			0
$535$	13.5000	−	23.3827i	0.583656	−	1.01092i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−18.0000			−0.775315
$540$		0			0
$541$	20.0000			0.859867			0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000			0.859867			0.429934	+	0.902861i	$0.358537\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.00000	+	5.19615i	−0.128506	+	0.222579i
$546$		0			0
$547$	4.00000	+	6.92820i	0.171028	+	0.296229i	0.938779	−	0.344519i	$-0.111958\pi$
$547$	4.00000	+	6.92820i	0.171028	+	0.296229i	−0.767752	+	0.640747i	$0.778625\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	6.00000	+	10.3923i	0.255609	+	0.442727i
$552$		0			0
$553$	4.00000	−	6.92820i	0.170097	−	0.294617i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	27.0000			1.14403			0.572013	−	0.820244i	$-0.306163\pi$
$557$	27.0000			1.14403			0.572013	+	0.820244i	$0.306163\pi$
$558$		0			0
$559$	−40.0000			−1.69182
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.50000	−	2.59808i	0.0632175	−	0.109496i	−0.832684	−	0.553748i	$-0.813197\pi$
$563$	1.50000	−	2.59808i	0.0632175	−	0.109496i	0.895902	+	0.444252i	$0.146530\pi$
$564$		0			0
$565$	9.00000	+	15.5885i	0.378633	+	0.655811i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	6.00000	+	10.3923i	0.251533	+	0.435668i	0.963948	−	0.266090i	$-0.0857319\pi$
$569$	6.00000	+	10.3923i	0.251533	+	0.435668i	−0.712415	+	0.701758i	$0.752399\pi$
$570$		0			0
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	−0.904835	−	0.425762i	$-0.860006\pi$
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	0.821138	+	0.570730i	$0.193340\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	24.0000			1.00087
$576$		0			0
$577$	38.0000			1.58196			0.790980	−	0.611842i	$-0.209571\pi$
$577$	38.0000			1.58196			0.790980	+	0.611842i	$0.209571\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.50000	+	2.59808i	−0.0622305	+	0.107786i
$582$		0			0
$583$	−13.5000	−	23.3827i	−0.559113	−	0.968412i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	0.833408	−	0.552658i	$-0.186386\pi$
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	−0.895320	+	0.445424i	$0.853053\pi$
$588$		0			0
$589$	−5.00000	+	8.66025i	−0.206021	+	0.356840i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	18.0000			0.739171			0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000			0.739171			0.369586	+	0.929197i	$0.379500\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−21.0000	+	36.3731i	−0.858037	+	1.48616i	0.0157622	+	0.999876i	$0.494983\pi$
$599$	−21.0000	+	36.3731i	−0.858037	+	1.48616i	−0.873799	+	0.486287i	$0.838351\pi$
$600$		0			0
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	−0.963405	−	0.268049i	$-0.913621\pi$
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	0.249565	−	0.968358i	$-0.419712\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	3.00000	+	5.19615i	0.121967	+	0.211254i
$606$		0			0
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	−0.333842	−	0.942629i	$-0.608345\pi$
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	0.983262	−	0.182199i	$-0.0583216\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	24.0000			0.970936
$612$		0			0
$613$	−34.0000			−1.37325			−0.686624	−	0.727013i	$-0.740908\pi$
$613$	−34.0000			−1.37325			−0.686624	+	0.727013i	$0.740908\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	21.0000	−	36.3731i	0.845428	−	1.46432i	−0.0398207	−	0.999207i	$-0.512679\pi$
$617$	21.0000	−	36.3731i	0.845428	−	1.46432i	0.885249	−	0.465118i	$-0.153988\pi$
$618$		0			0
$619$	−14.0000	−	24.2487i	−0.562708	−	0.974638i	−0.997259	−	0.0739910i	$-0.976426\pi$
$619$	−14.0000	−	24.2487i	−0.562708	−	0.974638i	0.434551	−	0.900647i	$-0.356907\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	9.00000	+	15.5885i	0.360577	+	0.624538i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	25.0000			0.995234			0.497617	−	0.867397i	$-0.334208\pi$
$631$	25.0000			0.995234			0.497617	+	0.867397i	$0.334208\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−10.5000	+	18.1865i	−0.416680	+	0.721711i
$636$		0			0
$637$	−12.0000	−	20.7846i	−0.475457	−	0.823516i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−21.0000	−	36.3731i	−0.829450	−	1.43665i	−0.898470	−	0.439034i	$-0.855321\pi$
$641$	−21.0000	−	36.3731i	−0.829450	−	1.43665i	0.0690201	−	0.997615i	$-0.478013\pi$
$642$		0			0
$643$	−2.00000	+	3.46410i	−0.0788723	+	0.136611i	−0.902764	−	0.430137i	$-0.858465\pi$
$643$	−2.00000	+	3.46410i	−0.0788723	+	0.136611i	0.823891	+	0.566748i	$0.191799\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$		0			0
$649$	−36.0000			−1.41312
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−19.5000	+	33.7750i	−0.763094	+	1.32172i	0.178154	+	0.984003i	$0.442987\pi$
$653$	−19.5000	+	33.7750i	−0.763094	+	1.32172i	−0.941248	+	0.337715i	$0.890346\pi$
$654$		0			0
$655$	−22.5000	−	38.9711i	−0.879148	−	1.52273i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−10.5000	−	18.1865i	−0.409022	−	0.708447i	0.585758	−	0.810486i	$-0.300797\pi$
$659$	−10.5000	−	18.1865i	−0.409022	−	0.708447i	−0.994780	+	0.102039i	$0.967463\pi$
$660$		0			0
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−6.00000			−0.232670
$666$		0			0
$667$	36.0000			1.39393
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−12.0000	+	20.7846i	−0.463255	+	0.802381i
$672$		0			0
$673$	9.50000	+	16.4545i	0.366198	+	0.634274i	0.988968	−	0.148132i	$-0.0473259\pi$
$673$	9.50000	+	16.4545i	0.366198	+	0.634274i	−0.622770	+	0.782405i	$0.713993\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.0000	−	36.3731i	−0.807096	−	1.39793i	−0.914867	−	0.403755i	$-0.867705\pi$
$677$	−21.0000	−	36.3731i	−0.807096	−	1.39793i	0.107772	−	0.994176i	$-0.465628\pi$
$678$		0			0
$679$	0.500000	−	0.866025i	0.0191882	−	0.0332350i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$		0			0
$685$	18.0000			0.687745
$686$		0			0
$687$		0			0
$688$		0			0
$689$	18.0000	−	31.1769i	0.685745	−	1.18775i
$690$		0			0
$691$	22.0000	+	38.1051i	0.836919	+	1.44959i	0.892458	+	0.451130i	$0.148979\pi$
$691$	22.0000	+	38.1051i	0.836919	+	1.44959i	−0.0555386	+	0.998457i	$0.517688\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−6.00000	−	10.3923i	−0.227593	−	0.394203i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$	9.00000			0.339925			0.169963	−	0.985451i	$-0.445635\pi$
$701$	9.00000			0.339925			0.169963	+	0.985451i	$0.445635\pi$
$702$		0			0
$703$	−4.00000			−0.150863
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.50000	−	2.59808i	0.0564133	−	0.0977107i
$708$		0			0
$709$	−22.0000	−	38.1051i	−0.826227	−	1.43107i	−0.900978	−	0.433865i	$-0.857149\pi$
$709$	−22.0000	−	38.1051i	−0.826227	−	1.43107i	0.0747503	−	0.997202i	$-0.476184\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	15.0000	+	25.9808i	0.561754	+	0.972987i
$714$		0			0
$715$	18.0000	−	31.1769i	0.673162	−	1.16595i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−36.0000			−1.34257			−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000			−1.34257			−0.671287	+	0.741198i	$0.734258\pi$
$720$		0			0
$721$	4.00000			0.148968
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−12.0000	+	20.7846i	−0.445669	+	0.771921i
$726$		0			0
$727$	−0.500000	−	0.866025i	−0.0185440	−	0.0321191i	0.856605	−	0.515974i	$-0.172570\pi$
$727$	−0.500000	−	0.866025i	−0.0185440	−	0.0321191i	−0.875148	+	0.483854i	$0.839236\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−42.0000			−1.54709
$738$		0			0
$739$	16.0000			0.588570			0.294285	−	0.955718i	$-0.404919\pi$
$739$	16.0000			0.588570			0.294285	+	0.955718i	$0.404919\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	6.00000	−	10.3923i	0.220119	−	0.381257i	−0.734725	−	0.678365i	$-0.762689\pi$
$743$	6.00000	−	10.3923i	0.220119	−	0.381257i	0.954844	+	0.297108i	$0.0960222\pi$
$744$		0			0
$745$	−4.50000	−	7.79423i	−0.164867	−	0.285558i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	4.50000	+	7.79423i	0.164426	+	0.284795i
$750$		0			0
$751$	20.5000	−	35.5070i	0.748056	−	1.29567i	−0.200698	−	0.979653i	$-0.564321\pi$
$751$	20.5000	−	35.5070i	0.748056	−	1.29567i	0.948753	−	0.316017i	$-0.102346\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−51.0000			−1.85608
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−24.0000	+	41.5692i	−0.869999	+	1.50688i	−0.00800331	+	0.999968i	$0.502548\pi$
$761$	−24.0000	+	41.5692i	−0.869999	+	1.50688i	−0.861996	+	0.506915i	$0.830786\pi$
$762$		0			0
$763$	−1.00000	−	1.73205i	−0.0362024	−	0.0627044i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−24.0000	−	41.5692i	−0.866590	−	1.50098i
$768$		0			0
$769$	15.5000	−	26.8468i	0.558944	−	0.968120i	−0.438641	−	0.898663i	$-0.644540\pi$
$769$	15.5000	−	26.8468i	0.558944	−	0.968120i	0.997585	−	0.0694574i	$-0.0221268\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−18.0000			−0.647415			−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000			−0.647415			−0.323708	+	0.946157i	$0.604929\pi$
$774$		0			0
$775$	−20.0000			−0.718421
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−6.00000	+	10.3923i	−0.214972	+	0.372343i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6.00000	+	10.3923i	0.214149	+	0.370917i
$786$		0			0
$787$	16.0000	−	27.7128i	0.570338	−	0.987855i	−0.426193	−	0.904632i	$-0.640145\pi$
$787$	16.0000	−	27.7128i	0.570338	−	0.987855i	0.996531	−	0.0832226i	$-0.0265213\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−6.00000			−0.213335
$792$		0			0
$793$	−32.0000			−1.13635
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−19.5000	+	33.7750i	−0.690725	+	1.19637i	0.280875	+	0.959744i	$0.409375\pi$
$797$	−19.5000	+	33.7750i	−0.690725	+	1.19637i	−0.971601	+	0.236627i	$0.923958\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	10.5000	+	18.1865i	0.370537	+	0.641789i
$804$		0			0
$805$	−9.00000	+	15.5885i	−0.317208	+	0.549421i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	18.0000			0.632846			0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000			0.632846			0.316423	+	0.948618i	$0.397518\pi$
$810$		0			0
$811$	−2.00000			−0.0702295			−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000			−0.0702295			−0.0351147	+	0.999383i	$0.511180\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	30.0000	−	51.9615i	1.05085	−	1.82013i
$816$		0			0
$817$	10.0000	+	17.3205i	0.349856	+	0.605968i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3.00000	−	5.19615i	−0.104701	−	0.181347i	0.808915	−	0.587925i	$-0.200055\pi$
$821$	−3.00000	−	5.19615i	−0.104701	−	0.181347i	−0.913616	+	0.406578i	$0.866722\pi$
$822$		0			0
$823$	−15.5000	+	26.8468i	−0.540296	+	0.935820i	0.458591	+	0.888648i	$0.348354\pi$
$823$	−15.5000	+	26.8468i	−0.540296	+	0.935820i	−0.998887	+	0.0471726i	$0.984979\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$		0			0
$829$	2.00000			0.0694629			0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000			0.0694629			0.0347314	+	0.999397i	$0.488942\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−9.00000	−	15.5885i	−0.311458	−	0.539461i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	12.0000	+	20.7846i	0.414286	+	0.717564i	0.995353	−	0.0962912i	$-0.0306980\pi$
$839$	12.0000	+	20.7846i	0.414286	+	0.717564i	−0.581067	+	0.813856i	$0.697365\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	9.00000			0.309609
$846$		0			0
$847$	−2.00000			−0.0687208
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−6.00000	+	10.3923i	−0.205677	+	0.356244i
$852$		0			0
$853$	5.00000	+	8.66025i	0.171197	+	0.296521i	0.938839	−	0.344358i	$-0.111903\pi$
$853$	5.00000	+	8.66025i	0.171197	+	0.296521i	−0.767642	+	0.640879i	$0.778570\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	24.0000	+	41.5692i	0.819824	+	1.41998i	0.905811	+	0.423681i	$0.139262\pi$
$857$	24.0000	+	41.5692i	0.819824	+	1.41998i	−0.0859870	+	0.996296i	$0.527404\pi$
$858$		0			0
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	0.291858	+	0.956462i	$0.405727\pi$
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	−0.974249	+	0.225475i	$0.927607\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	36.0000			1.22545			0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000			1.22545			0.612727	+	0.790295i	$0.290072\pi$
$864$		0			0
$865$	45.0000			1.53005
$866$		0			0
$867$		0			0
$868$		0			0
$869$	12.0000	−	20.7846i	0.407072	−	0.705070i
$870$		0			0
$871$	−28.0000	−	48.4974i	−0.948744	−	1.64327i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.50000	+	2.59808i	0.0507093	+	0.0878310i
$876$		0			0
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−36.0000			−1.21287			−0.606435	−	0.795133i	$-0.707401\pi$
$881$	−36.0000			−1.21287			−0.606435	+	0.795133i	$0.707401\pi$
$882$		0			0
$883$	−2.00000			−0.0673054			−0.0336527	−	0.999434i	$-0.510714\pi$
$883$	−2.00000			−0.0673054			−0.0336527	+	0.999434i	$0.510714\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	6.00000	−	10.3923i	0.201460	−	0.348939i	−0.747539	−	0.664218i	$-0.768765\pi$
$887$	6.00000	−	10.3923i	0.201460	−	0.348939i	0.948999	+	0.315279i	$0.102098\pi$
$888$		0			0
$889$	−3.50000	−	6.06218i	−0.117386	−	0.203319i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−6.00000	−	10.3923i	−0.200782	−	0.347765i
$894$		0			0
$895$	−13.5000	+	23.3827i	−0.451255	+	0.781597i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−30.0000			−1.00056
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	24.0000	−	41.5692i	0.797787	−	1.38181i
$906$		0			0
$907$	13.0000	+	22.5167i	0.431658	+	0.747653i	0.997016	−	0.0771920i	$-0.0245954\pi$
$907$	13.0000	+	22.5167i	0.431658	+	0.747653i	−0.565358	+	0.824845i	$0.691262\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	3.00000	+	5.19615i	0.0993944	+	0.172156i	0.911434	−	0.411446i	$-0.134976\pi$
$911$	3.00000	+	5.19615i	0.0993944	+	0.172156i	−0.812040	+	0.583602i	$0.801643\pi$
$912$		0			0
$913$	−4.50000	+	7.79423i	−0.148928	+	0.257951i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	15.0000			0.495344
$918$		0			0
$919$	−29.0000			−0.956622			−0.478311	−	0.878191i	$-0.658751\pi$
$919$	−29.0000			−0.956622			−0.478311	+	0.878191i	$0.658751\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−4.00000	−	6.92820i	−0.131519	−	0.227798i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	6.00000	+	10.3923i	0.196854	+	0.340960i	0.947507	−	0.319736i	$-0.103594\pi$
$929$	6.00000	+	10.3923i	0.196854	+	0.340960i	−0.750653	+	0.660697i	$0.770261\pi$
$930$		0			0
$931$	−6.00000	+	10.3923i	−0.196642	+	0.340594i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	11.0000			0.359354			0.179677	−	0.983726i	$-0.442495\pi$
$937$	11.0000			0.359354			0.179677	+	0.983726i	$0.442495\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	16.5000	−	28.5788i	0.537885	−	0.931644i	−0.461133	−	0.887331i	$-0.652557\pi$
$941$	16.5000	−	28.5788i	0.537885	−	0.931644i	0.999018	−	0.0443125i	$-0.0141097\pi$
$942$		0			0
$943$	18.0000	+	31.1769i	0.586161	+	1.01526i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	25.5000	+	44.1673i	0.828639	+	1.43524i	0.899106	+	0.437730i	$0.144217\pi$
$947$	25.5000	+	44.1673i	0.828639	+	1.43524i	−0.0704677	+	0.997514i	$0.522449\pi$
$948$		0			0
$949$	−14.0000	+	24.2487i	−0.454459	+	0.787146i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−36.0000			−1.16615			−0.583077	−	0.812417i	$-0.698151\pi$
$953$	−36.0000			−1.16615			−0.583077	+	0.812417i	$0.698151\pi$
$954$		0			0
$955$	36.0000			1.16493
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−3.00000	+	5.19615i	−0.0968751	+	0.167793i
$960$		0			0
$961$	3.00000	+	5.19615i	0.0967742	+	0.167618i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−7.50000	−	12.9904i	−0.241434	−	0.418175i
$966$		0			0
$967$	11.5000	−	19.9186i	0.369815	−	0.640538i	−0.619721	−	0.784822i	$-0.712754\pi$
$967$	11.5000	−	19.9186i	0.369815	−	0.640538i	0.989536	+	0.144283i	$0.0460877\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	27.0000			0.866471			0.433236	−	0.901281i	$-0.357372\pi$
$971$	27.0000			0.866471			0.433236	+	0.901281i	$0.357372\pi$
$972$		0			0
$973$	4.00000			0.128234
$974$		0			0
$975$		0			0
$976$		0			0
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	−0.305530	−	0.952183i	$-0.598833\pi$
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	0.977379	−	0.211495i	$-0.0678332\pi$
$978$		0			0
$979$	27.0000	+	46.7654i	0.862924	+	1.49463i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	3.00000	+	5.19615i	0.0956851	+	0.165732i	0.909894	−	0.414840i	$-0.136162\pi$
$983$	3.00000	+	5.19615i	0.0956851	+	0.165732i	−0.814209	+	0.580572i	$0.802829\pi$
$984$		0			0
$985$	−13.5000	+	23.3827i	−0.430146	+	0.745034i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	60.0000			1.90789
$990$		0			0
$991$	−47.0000			−1.49300			−0.746502	−	0.665383i	$-0.768268\pi$
$991$	−47.0000			−1.49300			−0.746502	+	0.665383i	$0.768268\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−10.5000	+	18.1865i	−0.332872	+	0.576552i
$996$		0			0
$997$	14.0000	+	24.2487i	0.443384	+	0.767964i	0.997938	−	0.0641836i	$-0.0204443\pi$
$997$	14.0000	+	24.2487i	0.443384	+	0.767964i	−0.554554	+	0.832148i	$0.687111\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1296.2.i.c.433.1		2
3.2	odd	2		1296.2.i.o.433.1		2
4.3	odd	2		162.2.c.c.109.1		2
9.2	odd	6		1296.2.i.o.865.1		2
9.4	even	3		432.2.a.g.1.1		1
9.5	odd	6		432.2.a.b.1.1		1
9.7	even	3	inner	1296.2.i.c.865.1		2
12.11	even	2		162.2.c.b.109.1		2
36.7	odd	6		162.2.c.c.55.1		2
36.11	even	6		162.2.c.b.55.1		2
36.23	even	6		54.2.a.b.1.1	yes	1
36.31	odd	6		54.2.a.a.1.1	✓	1
72.5	odd	6		1728.2.a.z.1.1		1
72.13	even	6		1728.2.a.d.1.1		1
72.59	even	6		1728.2.a.y.1.1		1
72.67	odd	6		1728.2.a.c.1.1		1
180.23	odd	12		1350.2.c.k.649.1		2
180.59	even	6		1350.2.a.h.1.1		1
180.67	even	12		1350.2.c.b.649.1		2
180.103	even	12		1350.2.c.b.649.2		2
180.139	odd	6		1350.2.a.r.1.1		1
180.167	odd	12		1350.2.c.k.649.2		2
252.139	even	6		2646.2.a.a.1.1		1
252.167	odd	6		2646.2.a.bd.1.1		1
396.131	odd	6		6534.2.a.b.1.1		1
396.175	even	6		6534.2.a.bc.1.1		1
468.103	odd	6		9126.2.a.u.1.1		1
468.311	even	6		9126.2.a.r.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.a.a.1.1	✓	1	36.31	odd	6
54.2.a.b.1.1	yes	1	36.23	even	6
162.2.c.b.55.1		2	36.11	even	6
162.2.c.b.109.1		2	12.11	even	2
162.2.c.c.55.1		2	36.7	odd	6
162.2.c.c.109.1		2	4.3	odd	2
432.2.a.b.1.1		1	9.5	odd	6
432.2.a.g.1.1		1	9.4	even	3
1296.2.i.c.433.1		2	1.1	even	1	trivial
1296.2.i.c.865.1		2	9.7	even	3	inner
1296.2.i.o.433.1		2	3.2	odd	2
1296.2.i.o.865.1		2	9.2	odd	6
1350.2.a.h.1.1		1	180.59	even	6
1350.2.a.r.1.1		1	180.139	odd	6
1350.2.c.b.649.1		2	180.67	even	12
1350.2.c.b.649.2		2	180.103	even	12
1350.2.c.k.649.1		2	180.23	odd	12
1350.2.c.k.649.2		2	180.167	odd	12
1728.2.a.c.1.1		1	72.67	odd	6
1728.2.a.d.1.1		1	72.13	even	6
1728.2.a.y.1.1		1	72.59	even	6
1728.2.a.z.1.1		1	72.5	odd	6
2646.2.a.a.1.1		1	252.139	even	6
2646.2.a.bd.1.1		1	252.167	odd	6
6534.2.a.b.1.1		1	396.131	odd	6
6534.2.a.bc.1.1		1	396.175	even	6
9126.2.a.r.1.1		1	468.311	even	6
9126.2.a.u.1.1		1	468.103	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1296 = 2^{4} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1296.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{7} +O(q^{10})\)	\(q+(-1.50000 + 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-1.50000 - 2.59808i) q^{11} +(2.00000 - 3.46410i) q^{13} -2.00000 q^{19} +(-3.00000 + 5.19615i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-3.00000 - 5.19615i) q^{29} +(2.50000 - 4.33013i) q^{31} +3.00000 q^{35} +2.00000 q^{37} +(3.00000 - 5.19615i) q^{41} +(-5.00000 - 8.66025i) q^{43} +(3.00000 + 5.19615i) q^{47} +(3.00000 - 5.19615i) q^{49} +9.00000 q^{53} +9.00000 q^{55} +(6.00000 - 10.3923i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(6.00000 + 10.3923i) q^{65} +(7.00000 - 12.1244i) q^{67} -7.00000 q^{73} +(-1.50000 + 2.59808i) q^{77} +(4.00000 + 6.92820i) q^{79} +(-1.50000 - 2.59808i) q^{83} -18.0000 q^{89} -4.00000 q^{91} +(3.00000 - 5.19615i) q^{95} +(0.500000 + 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{5} - q^{7}+O(q^{10}) \) 2 * q - 3 * q^5 - q^7	\( 2 q - 3 q^{5} - q^{7} - 3 q^{11} + 4 q^{13} - 4 q^{19} - 6 q^{23} - 4 q^{25} - 6 q^{29} + 5 q^{31} + 6 q^{35} + 4 q^{37} + 6 q^{41} - 10 q^{43} + 6 q^{47} + 6 q^{49} + 18 q^{53} + 18 q^{55} + 12 q^{59} - 8 q^{61} + 12 q^{65} + 14 q^{67} - 14 q^{73} - 3 q^{77} + 8 q^{79} - 3 q^{83} - 36 q^{89} - 8 q^{91} + 6 q^{95} + q^{97}+O(q^{100}) \) 2 * q - 3 * q^5 - q^7 - 3 * q^11 + 4 * q^13 - 4 * q^19 - 6 * q^23 - 4 * q^25 - 6 * q^29 + 5 * q^31 + 6 * q^35 + 4 * q^37 + 6 * q^41 - 10 * q^43 + 6 * q^47 + 6 * q^49 + 18 * q^53 + 18 * q^55 + 12 * q^59 - 8 * q^61 + 12 * q^65 + 14 * q^67 - 14 * q^73 - 3 * q^77 + 8 * q^79 - 3 * q^83 - 36 * q^89 - 8 * q^91 + 6 * q^95 + q^97

Introduction

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