LMFDB - Embedded newform 1944.2.i.k.649.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1944.649");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.5229181529$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			649.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1944.649
Dual form			1944.2.i.k.1297.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 - 2.36603i) q^{5} +(1.73205 - 3.00000i) q^{7} +O(q^{10})$	$q+(-1.36603 - 2.36603i) q^{5} +(1.73205 - 3.00000i) q^{7} +(2.09808 - 3.63397i) q^{11} +(-2.23205 - 3.86603i) q^{13} -2.73205 q^{17} +2.46410 q^{19} +(-2.63397 - 4.56218i) q^{23} +(-1.23205 + 2.13397i) q^{25} +(-4.73205 + 8.19615i) q^{29} +(2.23205 + 3.86603i) q^{31} -9.46410 q^{35} +9.46410 q^{37} +(-1.26795 - 2.19615i) q^{41} +(-3.96410 + 6.86603i) q^{43} +(-3.46410 + 6.00000i) q^{47} +(-2.50000 - 4.33013i) q^{49} +9.66025 q^{53} -11.4641 q^{55} +(-6.09808 - 10.5622i) q^{59} +(4.23205 - 7.33013i) q^{61} +(-6.09808 + 10.5622i) q^{65} +(5.23205 + 9.06218i) q^{67} +4.19615 q^{71} -9.39230 q^{73} +(-7.26795 - 12.5885i) q^{77} +(-0.0358984 + 0.0621778i) q^{79} +(-4.63397 + 8.02628i) q^{83} +(3.73205 + 6.46410i) q^{85} -12.0000 q^{89} -15.4641 q^{91} +(-3.36603 - 5.83013i) q^{95} +(0.964102 - 1.66987i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{5}+O(q^{10}) $ 4 * q - 2 * q^5	$ 4 q - 2 q^{5} - 2 q^{11} - 2 q^{13} - 4 q^{17} - 4 q^{19} - 14 q^{23} + 2 q^{25} - 12 q^{29} + 2 q^{31} - 24 q^{35} + 24 q^{37} - 12 q^{41} - 2 q^{43} - 10 q^{49} + 4 q^{53} - 32 q^{55} - 14 q^{59} + 10 q^{61} - 14 q^{65} + 14 q^{67} - 4 q^{71} + 4 q^{73} - 36 q^{77} - 14 q^{79} - 22 q^{83} + 8 q^{85} - 48 q^{89} - 48 q^{91} - 10 q^{95} - 10 q^{97}+O(q^{100}) $ 4 * q - 2 * q^5 - 2 * q^11 - 2 * q^13 - 4 * q^17 - 4 * q^19 - 14 * q^23 + 2 * q^25 - 12 * q^29 + 2 * q^31 - 24 * q^35 + 24 * q^37 - 12 * q^41 - 2 * q^43 - 10 * q^49 + 4 * q^53 - 32 * q^55 - 14 * q^59 + 10 * q^61 - 14 * q^65 + 14 * q^67 - 4 * q^71 + 4 * q^73 - 36 * q^77 - 14 * q^79 - 22 * q^83 + 8 * q^85 - 48 * q^89 - 48 * q^91 - 10 * q^95 - 10 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.36603	−	2.36603i	−0.610905	−	1.05812i	−0.991088	−	0.133207i	$-0.957472\pi$
$5$	−1.36603	−	2.36603i	−0.610905	−	1.05812i	0.380183	−	0.924911i	$-0.375861\pi$
$6$		0			0
$7$	1.73205	−	3.00000i	0.654654	−	1.13389i	−0.327327	−	0.944911i	$-0.606148\pi$
$7$	1.73205	−	3.00000i	0.654654	−	1.13389i	0.981981	−	0.188982i	$-0.0605189\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.09808	−	3.63397i	0.632594	−	1.09568i	−0.354426	−	0.935084i	$-0.615324\pi$
$11$	2.09808	−	3.63397i	0.632594	−	1.09568i	0.987020	−	0.160600i	$-0.0513430\pi$
$12$		0			0
$13$	−2.23205	−	3.86603i	−0.619060	−	1.07224i	−0.989658	−	0.143449i	$-0.954181\pi$
$13$	−2.23205	−	3.86603i	−0.619060	−	1.07224i	0.370598	−	0.928793i	$-0.379153\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.73205			−0.662620			−0.331310	−	0.943522i	$-0.607491\pi$
$17$	−2.73205			−0.662620			−0.331310	+	0.943522i	$0.607491\pi$
$18$		0			0
$19$	2.46410			0.565304			0.282652	−	0.959223i	$-0.408786\pi$
$19$	2.46410			0.565304			0.282652	+	0.959223i	$0.408786\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.63397	−	4.56218i	−0.549222	−	0.951280i	−0.998328	−	0.0578016i	$-0.981591\pi$
$23$	−2.63397	−	4.56218i	−0.549222	−	0.951280i	0.449106	−	0.893478i	$-0.351742\pi$
$24$		0			0
$25$	−1.23205	+	2.13397i	−0.246410	+	0.426795i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.73205	+	8.19615i	−0.878720	+	1.52199i	−0.0259731	+	0.999663i	$0.508268\pi$
$29$	−4.73205	+	8.19615i	−0.878720	+	1.52199i	−0.852747	+	0.522325i	$0.825065\pi$
$30$		0			0
$31$	2.23205	+	3.86603i	0.400888	+	0.694359i	0.993833	−	0.110884i	$-0.0353683\pi$
$31$	2.23205	+	3.86603i	0.400888	+	0.694359i	−0.592945	+	0.805243i	$0.702035\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−9.46410			−1.59973
$36$		0			0
$37$	9.46410			1.55589			0.777944	−	0.628333i	$-0.216263\pi$
$37$	9.46410			1.55589			0.777944	+	0.628333i	$0.216263\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.26795	−	2.19615i	−0.198020	−	0.342981i	0.749866	−	0.661590i	$-0.230118\pi$
$41$	−1.26795	−	2.19615i	−0.198020	−	0.342981i	−0.947886	+	0.318608i	$0.896785\pi$
$42$		0			0
$43$	−3.96410	+	6.86603i	−0.604520	+	1.04706i	0.387607	+	0.921825i	$0.373302\pi$
$43$	−3.96410	+	6.86603i	−0.604520	+	1.04706i	−0.992127	+	0.125234i	$0.960032\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.46410	+	6.00000i	−0.505291	+	0.875190i	0.494690	+	0.869069i	$0.335282\pi$
$47$	−3.46410	+	6.00000i	−0.505291	+	0.875190i	−0.999981	+	0.00612051i	$0.998052\pi$
$48$		0			0
$49$	−2.50000	−	4.33013i	−0.357143	−	0.618590i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	9.66025			1.32694			0.663469	−	0.748204i	$-0.269083\pi$
$53$	9.66025			1.32694			0.663469	+	0.748204i	$0.269083\pi$
$54$		0			0
$55$	−11.4641			−1.54582
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.09808	−	10.5622i	−0.793902	−	1.37508i	−0.923534	−	0.383516i	$-0.874713\pi$
$59$	−6.09808	−	10.5622i	−0.793902	−	1.37508i	0.129632	−	0.991562i	$-0.458620\pi$
$60$		0			0
$61$	4.23205	−	7.33013i	0.541859	−	0.938527i	−0.456939	−	0.889498i	$-0.651054\pi$
$61$	4.23205	−	7.33013i	0.541859	−	0.938527i	0.998797	−	0.0490285i	$-0.0156125\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.09808	+	10.5622i	−0.756373	+	1.31008i
$66$		0			0
$67$	5.23205	+	9.06218i	0.639197	+	1.10712i	0.985609	+	0.169039i	$0.0540664\pi$
$67$	5.23205	+	9.06218i	0.639197	+	1.10712i	−0.346413	+	0.938082i	$0.612600\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.19615			0.497992			0.248996	−	0.968505i	$-0.419899\pi$
$71$	4.19615			0.497992			0.248996	+	0.968505i	$0.419899\pi$
$72$		0			0
$73$	−9.39230			−1.09929			−0.549643	−	0.835400i	$-0.685236\pi$
$73$	−9.39230			−1.09929			−0.549643	+	0.835400i	$0.685236\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.26795	−	12.5885i	−0.828260	−	1.43459i
$78$		0			0
$79$	−0.0358984	+	0.0621778i	−0.00403888	+	0.00699555i	−0.868038	−	0.496498i	$-0.834619\pi$
$79$	−0.0358984	+	0.0621778i	−0.00403888	+	0.00699555i	0.863999	+	0.503494i	$0.167952\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.63397	+	8.02628i	−0.508645	+	0.880999i	0.491305	+	0.870988i	$0.336520\pi$
$83$	−4.63397	+	8.02628i	−0.508645	+	0.880999i	−0.999950	+	0.0100111i	$0.996813\pi$
$84$		0			0
$85$	3.73205	+	6.46410i	0.404798	+	0.701130i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−12.0000			−1.27200			−0.635999	−	0.771690i	$-0.719412\pi$
$89$	−12.0000			−1.27200			−0.635999	+	0.771690i	$0.719412\pi$
$90$		0			0
$91$	−15.4641			−1.62108
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.36603	−	5.83013i	−0.345347	−	0.598158i
$96$		0			0
$97$	0.964102	−	1.66987i	0.0978897	−	0.169550i	−0.812921	−	0.582374i	$-0.802124\pi$
$97$	0.964102	−	1.66987i	0.0978897	−	0.169550i	0.910811	+	0.412824i	$0.135457\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	8.19615	−	14.1962i	0.815548	−	1.41257i	−0.0933864	−	0.995630i	$-0.529769\pi$
$101$	8.19615	−	14.1962i	0.815548	−	1.41257i	0.908934	−	0.416940i	$-0.136897\pi$
$102$		0			0
$103$	−4.42820	−	7.66987i	−0.436324	−	0.755735i	0.561079	−	0.827762i	$-0.310386\pi$
$103$	−4.42820	−	7.66987i	−0.436324	−	0.755735i	−0.997403	+	0.0720273i	$0.977053\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.53590			0.245155			0.122577	−	0.992459i	$-0.460884\pi$
$107$	2.53590			0.245155			0.122577	+	0.992459i	$0.460884\pi$
$108$		0			0
$109$	9.53590			0.913373			0.456687	−	0.889628i	$-0.349036\pi$
$109$	9.53590			0.913373			0.456687	+	0.889628i	$0.349036\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.46410	+	6.00000i	0.325875	+	0.564433i	0.981689	−	0.190490i	$-0.0610077\pi$
$113$	3.46410	+	6.00000i	0.325875	+	0.564433i	−0.655814	+	0.754923i	$0.727674\pi$
$114$		0			0
$115$	−7.19615	+	12.4641i	−0.671045	+	1.16228i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−4.73205	+	8.19615i	−0.433786	+	0.751340i
$120$		0			0
$121$	−3.30385	−	5.72243i	−0.300350	−	0.520221i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−6.92820			−0.619677
$126$		0			0
$127$	−11.9282			−1.05846			−0.529228	−	0.848479i	$-0.677519\pi$
$127$	−11.9282			−1.05846			−0.529228	+	0.848479i	$0.677519\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−9.36603	−	16.2224i	−0.818313	−	1.41736i	−0.906924	−	0.421294i	$-0.861576\pi$
$131$	−9.36603	−	16.2224i	−0.818313	−	1.41736i	0.0886106	−	0.996066i	$-0.471757\pi$
$132$		0			0
$133$	4.26795	−	7.39230i	0.370078	−	0.640994i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.53590	+	4.39230i	−0.216656	+	0.375260i	−0.953784	−	0.300494i	$-0.902848\pi$
$137$	−2.53590	+	4.39230i	−0.216656	+	0.375260i	0.737127	+	0.675754i	$0.236182\pi$
$138$		0			0
$139$	−1.73205	−	3.00000i	−0.146911	−	0.254457i	0.783174	−	0.621803i	$-0.213600\pi$
$139$	−1.73205	−	3.00000i	−0.146911	−	0.254457i	−0.930084	+	0.367347i	$0.880266\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−18.7321			−1.56645
$144$		0			0
$145$	25.8564			2.14726
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.02628	−	15.6340i	−0.739462	−	1.28079i	−0.952738	−	0.303793i	$-0.901747\pi$
$149$	−9.02628	−	15.6340i	−0.739462	−	1.28079i	0.213276	−	0.976992i	$-0.431587\pi$
$150$		0			0
$151$	5.23205	−	9.06218i	0.425778	−	0.737470i	−0.570715	−	0.821149i	$-0.693334\pi$
$151$	5.23205	−	9.06218i	0.425778	−	0.737470i	0.996493	+	0.0836790i	$0.0266670\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	6.09808	−	10.5622i	0.489809	−	0.848375i
$156$		0			0
$157$	7.69615	+	13.3301i	0.614220	+	1.06386i	0.990521	+	0.137362i	$0.0438625\pi$
$157$	7.69615	+	13.3301i	0.614220	+	1.06386i	−0.376301	+	0.926497i	$0.622804\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−18.2487			−1.43820
$162$		0			0
$163$	−1.60770			−0.125924			−0.0629622	−	0.998016i	$-0.520055\pi$
$163$	−1.60770			−0.125924			−0.0629622	+	0.998016i	$0.520055\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.19615	+	14.1962i	0.634237	+	1.09853i	0.986676	+	0.162696i	$0.0520191\pi$
$167$	8.19615	+	14.1962i	0.634237	+	1.09853i	−0.352439	+	0.935835i	$0.614648\pi$
$168$		0			0
$169$	−3.46410	+	6.00000i	−0.266469	+	0.461538i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.46410	−	6.00000i	0.263371	−	0.456172i	−0.703765	−	0.710433i	$-0.748499\pi$
$173$	3.46410	−	6.00000i	0.263371	−	0.456172i	0.967135	+	0.254262i	$0.0818324\pi$
$174$		0			0
$175$	4.26795	+	7.39230i	0.322627	+	0.558806i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	9.46410			0.707380			0.353690	−	0.935363i	$-0.384927\pi$
$179$	9.46410			0.707380			0.353690	+	0.935363i	$0.384927\pi$
$180$		0			0
$181$	23.3205			1.73340			0.866700	−	0.498830i	$-0.166237\pi$
$181$	23.3205			1.73340			0.866700	+	0.498830i	$0.166237\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−12.9282	−	22.3923i	−0.950500	−	1.64631i
$186$		0			0
$187$	−5.73205	+	9.92820i	−0.419169	+	0.726022i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.53590	+	4.39230i	−0.183491	+	0.317816i	−0.943067	−	0.332603i	$-0.892073\pi$
$191$	−2.53590	+	4.39230i	−0.183491	+	0.317816i	0.759576	+	0.650419i	$0.225407\pi$
$192$		0			0
$193$	−12.4282	−	21.5263i	−0.894602	−	1.54950i	−0.834297	−	0.551315i	$-0.814126\pi$
$193$	−12.4282	−	21.5263i	−0.894602	−	1.54950i	−0.0603048	−	0.998180i	$-0.519207\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	11.3205			0.806553			0.403276	−	0.915078i	$-0.367871\pi$
$197$	11.3205			0.806553			0.403276	+	0.915078i	$0.367871\pi$
$198$		0			0
$199$	−11.0000			−0.779769			−0.389885	−	0.920864i	$-0.627485\pi$
$199$	−11.0000			−0.779769			−0.389885	+	0.920864i	$0.627485\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	16.3923	+	28.3923i	1.15051	+	1.99275i
$204$		0			0
$205$	−3.46410	+	6.00000i	−0.241943	+	0.419058i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	5.16987	−	8.95448i	0.357608	−	0.619395i
$210$		0			0
$211$	6.42820	+	11.1340i	0.442536	+	0.766494i	0.997877	−	0.0651282i	$-0.0207456\pi$
$211$	6.42820	+	11.1340i	0.442536	+	0.766494i	−0.555341	+	0.831623i	$0.687412\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	21.6603			1.47722
$216$		0			0
$217$	15.4641			1.04977
$218$		0			0
$219$		0			0
$220$		0			0
$221$	6.09808	+	10.5622i	0.410201	+	0.710489i
$222$		0			0
$223$	−0.0358984	+	0.0621778i	−0.00240393	+	0.00416374i	−0.867225	−	0.497917i	$-0.834099\pi$
$223$	−0.0358984	+	0.0621778i	−0.00240393	+	0.00416374i	0.864821	+	0.502080i	$0.167432\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.3923	+	18.0000i	−0.689761	+	1.19470i	0.282153	+	0.959369i	$0.408951\pi$
$227$	−10.3923	+	18.0000i	−0.689761	+	1.19470i	−0.971915	+	0.235333i	$0.924382\pi$
$228$		0			0
$229$	−9.16025	−	15.8660i	−0.605327	−	1.04846i	−0.992000	−	0.126240i	$-0.959709\pi$
$229$	−9.16025	−	15.8660i	−0.605327	−	1.04846i	0.386673	−	0.922217i	$-0.373624\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.12436			0.466732			0.233366	−	0.972389i	$-0.425026\pi$
$233$	7.12436			0.466732			0.233366	+	0.972389i	$0.425026\pi$
$234$		0			0
$235$	18.9282			1.23474
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−11.5622	−	20.0263i	−0.747895	−	1.29539i	−0.948830	−	0.315788i	$-0.897731\pi$
$239$	−11.5622	−	20.0263i	−0.747895	−	1.29539i	0.200935	−	0.979605i	$-0.435602\pi$
$240$		0			0
$241$	11.6603	−	20.1962i	0.751103	−	1.30095i	−0.196186	−	0.980567i	$-0.562855\pi$
$241$	11.6603	−	20.1962i	0.751103	−	1.30095i	0.947289	−	0.320382i	$-0.103811\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−6.83013	+	11.8301i	−0.436361	+	0.755799i
$246$		0			0
$247$	−5.50000	−	9.52628i	−0.349957	−	0.606143i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	8.58846			0.542099			0.271049	−	0.962565i	$-0.412629\pi$
$251$	8.58846			0.542099			0.271049	+	0.962565i	$0.412629\pi$
$252$		0			0
$253$	−22.1051			−1.38974
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.8301	+	18.7583i	0.675565	+	1.17011i	0.976303	+	0.216406i	$0.0694335\pi$
$257$	10.8301	+	18.7583i	0.675565	+	1.17011i	−0.300739	+	0.953707i	$0.597233\pi$
$258$		0			0
$259$	16.3923	−	28.3923i	1.01857	−	1.76421i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	8.09808	−	14.0263i	0.499349	−	0.864897i	−0.500651	−	0.865649i	$-0.666906\pi$
$263$	8.09808	−	14.0263i	0.499349	−	0.864897i	1.00000		0.000751811i	$0.000239309\pi$
$264$		0			0
$265$	−13.1962	−	22.8564i	−0.810633	−	1.40406i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	18.7321			1.14211			0.571057	−	0.820911i	$-0.306534\pi$
$269$	18.7321			1.14211			0.571057	+	0.820911i	$0.306534\pi$
$270$		0			0
$271$	−3.53590			−0.214791			−0.107395	−	0.994216i	$-0.534251\pi$
$271$	−3.53590			−0.214791			−0.107395	+	0.994216i	$0.534251\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.16987	+	8.95448i	0.311755	+	0.539976i
$276$		0			0
$277$	10.6962	−	18.5263i	0.642670	−	1.11314i	−0.342165	−	0.939640i	$-0.611160\pi$
$277$	10.6962	−	18.5263i	0.642670	−	1.11314i	0.984835	−	0.173496i	$-0.0555065\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2.63397	−	4.56218i	0.157130	−	0.272157i	−0.776703	−	0.629867i	$-0.783109\pi$
$281$	2.63397	−	4.56218i	0.157130	−	0.272157i	0.933832	+	0.357711i	$0.116443\pi$
$282$		0			0
$283$	7.76795	+	13.4545i	0.461757	+	0.799786i	0.999049	−	0.0436103i	$-0.0138860\pi$
$283$	7.76795	+	13.4545i	0.461757	+	0.799786i	−0.537292	+	0.843396i	$0.680553\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−8.78461			−0.518539
$288$		0			0
$289$	−9.53590			−0.560935
$290$		0			0
$291$		0			0
$292$		0			0
$293$	11.6603	+	20.1962i	0.681199	+	1.17987i	0.974615	+	0.223887i	$0.0718746\pi$
$293$	11.6603	+	20.1962i	0.681199	+	1.17987i	−0.293416	+	0.955985i	$0.594792\pi$
$294$		0			0
$295$	−16.6603	+	28.8564i	−0.969997	+	1.68008i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−11.7583	+	20.3660i	−0.680002	+	1.17780i
$300$		0			0
$301$	13.7321	+	23.7846i	0.791502	+	1.37092i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−23.1244			−1.32410
$306$		0			0
$307$	−27.4641			−1.56746			−0.783730	−	0.621102i	$-0.786685\pi$
$307$	−27.4641			−1.56746			−0.783730	+	0.621102i	$0.786685\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.80385	+	6.58846i	0.215696	+	0.373597i	0.953488	−	0.301432i	$-0.0974645\pi$
$311$	3.80385	+	6.58846i	0.215696	+	0.373597i	−0.737791	+	0.675029i	$0.764131\pi$
$312$		0			0
$313$	−14.1962	+	24.5885i	−0.802414	+	1.38982i	0.115609	+	0.993295i	$0.463118\pi$
$313$	−14.1962	+	24.5885i	−0.802414	+	1.38982i	−0.918023	+	0.396527i	$0.870215\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.53590	−	4.39230i	0.142430	−	0.246696i	−0.785981	−	0.618251i	$-0.787842\pi$
$317$	2.53590	−	4.39230i	0.142430	−	0.246696i	0.928411	+	0.371554i	$0.121175\pi$
$318$		0			0
$319$	19.8564	+	34.3923i	1.11175	+	1.92560i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−6.73205			−0.374581
$324$		0			0
$325$	11.0000			0.610170
$326$		0			0
$327$		0			0
$328$		0			0
$329$	12.0000	+	20.7846i	0.661581	+	1.14589i
$330$		0			0
$331$	−6.76795	+	11.7224i	−0.372000	+	0.644323i	−0.989873	−	0.141955i	$-0.954661\pi$
$331$	−6.76795	+	11.7224i	−0.372000	+	0.644323i	0.617873	+	0.786278i	$0.287995\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	14.2942	−	24.7583i	0.780977	−	1.35269i
$336$		0			0
$337$	−13.2679	−	22.9808i	−0.722751	−	1.25184i	−0.959893	−	0.280367i	$-0.909544\pi$
$337$	−13.2679	−	22.9808i	−0.722751	−	1.25184i	0.237142	−	0.971475i	$-0.423789\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	18.7321			1.01440
$342$		0			0
$343$	6.92820			0.374088
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.73205	+	8.19615i	0.254030	+	0.439993i	0.964632	−	0.263602i	$-0.0849105\pi$
$347$	4.73205	+	8.19615i	0.254030	+	0.439993i	−0.710602	+	0.703594i	$0.751577\pi$
$348$		0			0
$349$	3.80385	−	6.58846i	0.203615	−	0.352672i	−0.746075	−	0.665862i	$-0.768064\pi$
$349$	3.80385	−	6.58846i	0.203615	−	0.352672i	0.949691	+	0.313189i	$0.101397\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.16987	+	2.02628i	−0.0622661	+	0.107848i	−0.895478	−	0.445106i	$-0.853166\pi$
$353$	−1.16987	+	2.02628i	−0.0622661	+	0.107848i	0.833212	+	0.552954i	$0.186499\pi$
$354$		0			0
$355$	−5.73205	−	9.92820i	−0.304226	−	0.526934i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−20.7846			−1.09697			−0.548485	−	0.836160i	$-0.684795\pi$
$359$	−20.7846			−1.09697			−0.548485	+	0.836160i	$0.684795\pi$
$360$		0			0
$361$	−12.9282			−0.680432
$362$		0			0
$363$		0			0
$364$		0			0
$365$	12.8301	+	22.2224i	0.671560	+	1.16318i
$366$		0			0
$367$	1.57180	−	2.72243i	0.0820471	−	0.142110i	−0.822082	−	0.569369i	$-0.807188\pi$
$367$	1.57180	−	2.72243i	0.0820471	−	0.142110i	0.904129	+	0.427259i	$0.140521\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	16.7321	−	28.9808i	0.868685	−	1.50461i
$372$		0			0
$373$	12.5000	+	21.6506i	0.647225	+	1.12103i	0.983783	+	0.179364i	$0.0574041\pi$
$373$	12.5000	+	21.6506i	0.647225	+	1.12103i	−0.336557	+	0.941663i	$0.609263\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	42.2487			2.17592
$378$		0			0
$379$	−24.7846			−1.27310			−0.636550	−	0.771235i	$-0.719639\pi$
$379$	−24.7846			−1.27310			−0.636550	+	0.771235i	$0.719639\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	3.80385	+	6.58846i	0.194368	+	0.336654i	0.946693	−	0.322137i	$-0.104401\pi$
$383$	3.80385	+	6.58846i	0.194368	+	0.336654i	−0.752325	+	0.658792i	$0.771068\pi$
$384$		0			0
$385$	−19.8564	+	34.3923i	−1.01198	+	1.75279i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	0.830127	−	1.43782i	0.0420891	−	0.0729005i	−0.844213	−	0.536007i	$-0.819932\pi$
$389$	0.830127	−	1.43782i	0.0420891	−	0.0729005i	0.886303	+	0.463107i	$0.153265\pi$
$390$		0			0
$391$	7.19615	+	12.4641i	0.363925	+	0.630337i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.196152			0.00986950
$396$		0			0
$397$	−13.0000			−0.652451			−0.326226	−	0.945292i	$-0.605777\pi$
$397$	−13.0000			−0.652451			−0.326226	+	0.945292i	$0.605777\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	2.19615	+	3.80385i	0.109671	+	0.189955i	0.915637	−	0.402006i	$-0.131687\pi$
$401$	2.19615	+	3.80385i	0.109671	+	0.189955i	−0.805966	+	0.591962i	$0.798354\pi$
$402$		0			0
$403$	9.96410	−	17.2583i	0.496347	−	0.859699i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	19.8564	−	34.3923i	0.984246	−	1.70476i
$408$		0			0
$409$	5.66025	+	9.80385i	0.279882	+	0.484769i	0.971355	−	0.237633i	$-0.0763715\pi$
$409$	5.66025	+	9.80385i	0.279882	+	0.484769i	−0.691474	+	0.722402i	$0.743038\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−42.2487			−2.07892
$414$		0			0
$415$	25.3205			1.24293
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−9.12436	−	15.8038i	−0.445754	−	0.772068i	0.552350	−	0.833612i	$-0.313731\pi$
$419$	−9.12436	−	15.8038i	−0.445754	−	0.772068i	−0.998104	+	0.0615435i	$0.980398\pi$
$420$		0			0
$421$	−1.00000	+	1.73205i	−0.0487370	+	0.0844150i	−0.889365	−	0.457198i	$-0.848853\pi$
$421$	−1.00000	+	1.73205i	−0.0487370	+	0.0844150i	0.840628	+	0.541613i	$0.182186\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.36603	−	5.83013i	0.163276	−	0.282803i
$426$		0			0
$427$	−14.6603	−	25.3923i	−0.709459	−	1.22882i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	37.6603			1.81403			0.907015	−	0.421098i	$-0.138355\pi$
$431$	37.6603			1.81403			0.907015	+	0.421098i	$0.138355\pi$
$432$		0			0
$433$	5.39230			0.259138			0.129569	−	0.991570i	$-0.458641\pi$
$433$	5.39230			0.259138			0.129569	+	0.991570i	$0.458641\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.49038	−	11.2417i	−0.310477	−	0.537762i
$438$		0			0
$439$	0.803848	−	1.39230i	0.0383656	−	0.0664511i	−0.846205	−	0.532857i	$-0.821118\pi$
$439$	0.803848	−	1.39230i	0.0383656	−	0.0664511i	0.884571	+	0.466406i	$0.154452\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	15.2224	−	26.3660i	0.723240	−	1.25269i	−0.236455	−	0.971642i	$-0.575986\pi$
$443$	15.2224	−	26.3660i	0.723240	−	1.25269i	0.959695	−	0.281045i	$-0.0906811\pi$
$444$		0			0
$445$	16.3923	+	28.3923i	0.777070	+	1.34592i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	24.1962			1.14189			0.570944	−	0.820989i	$-0.306578\pi$
$449$	24.1962			1.14189			0.570944	+	0.820989i	$0.306578\pi$
$450$		0			0
$451$	−10.6410			−0.501066
$452$		0			0
$453$		0			0
$454$		0			0
$455$	21.1244	+	36.5885i	0.990325	+	1.71529i
$456$		0			0
$457$	4.42820	−	7.66987i	0.207143	−	0.358782i	−0.743671	−	0.668546i	$-0.766917\pi$
$457$	4.42820	−	7.66987i	0.207143	−	0.358782i	0.950813	+	0.309765i	$0.100250\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	5.90192	−	10.2224i	0.274880	−	0.476106i	−0.695225	−	0.718792i	$-0.744695\pi$
$461$	5.90192	−	10.2224i	0.274880	−	0.476106i	0.970105	+	0.242686i	$0.0780285\pi$
$462$		0			0
$463$	−13.6962	−	23.7224i	−0.636514	−	1.10247i	−0.986192	−	0.165605i	$-0.947042\pi$
$463$	−13.6962	−	23.7224i	−0.636514	−	1.10247i	0.349678	−	0.936870i	$-0.386291\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.53590			0.117347			0.0586737	−	0.998277i	$-0.481313\pi$
$467$	2.53590			0.117347			0.0586737	+	0.998277i	$0.481313\pi$
$468$		0			0
$469$	36.2487			1.67381
$470$		0			0
$471$		0			0
$472$		0			0
$473$	16.6340	+	28.8109i	0.764831	+	1.32473i
$474$		0			0
$475$	−3.03590	+	5.25833i	−0.139297	+	0.241269i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−0.830127	+	1.43782i	−0.0379295	+	0.0656958i	−0.884367	−	0.466792i	$-0.845410\pi$
$479$	−0.830127	+	1.43782i	−0.0379295	+	0.0656958i	0.846437	+	0.532488i	$0.178743\pi$
$480$		0			0
$481$	−21.1244	−	36.5885i	−0.963188	−	1.66829i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−5.26795			−0.239205
$486$		0			0
$487$	−17.9282			−0.812404			−0.406202	−	0.913783i	$-0.633147\pi$
$487$	−17.9282			−0.812404			−0.406202	+	0.913783i	$0.633147\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	12.9282	+	22.3923i	0.583442	+	1.01055i	0.995068	+	0.0991978i	$0.0316276\pi$
$491$	12.9282	+	22.3923i	0.583442	+	1.01055i	−0.411626	+	0.911353i	$0.635039\pi$
$492$		0			0
$493$	12.9282	−	22.3923i	0.582257	−	1.00850i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.26795	−	12.5885i	0.326012	−	0.564669i
$498$		0			0
$499$	−2.66025	−	4.60770i	−0.119089	−	0.206269i	0.800318	−	0.599576i	$-0.204664\pi$
$499$	−2.66025	−	4.60770i	−0.119089	−	0.206269i	−0.919407	+	0.393307i	$0.871331\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−14.5359			−0.648124			−0.324062	−	0.946036i	$-0.605049\pi$
$503$	−14.5359			−0.648124			−0.324062	+	0.946036i	$0.605049\pi$
$504$		0			0
$505$	−44.7846			−1.99289
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−4.39230	−	7.60770i	−0.194685	−	0.337205i	0.752112	−	0.659035i	$-0.229035\pi$
$509$	−4.39230	−	7.60770i	−0.194685	−	0.337205i	−0.946797	+	0.321830i	$0.895702\pi$
$510$		0			0
$511$	−16.2679	+	28.1769i	−0.719652	+	1.24647i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−12.0981	+	20.9545i	−0.533105	+	0.923365i
$516$		0			0
$517$	14.5359	+	25.1769i	0.639288	+	1.10728i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	28.1962			1.23530			0.617648	−	0.786455i	$-0.288086\pi$
$521$	28.1962			1.23530			0.617648	+	0.786455i	$0.288086\pi$
$522$		0			0
$523$	14.8564			0.649625			0.324813	−	0.945778i	$-0.394699\pi$
$523$	14.8564			0.649625			0.324813	+	0.945778i	$0.394699\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.09808	−	10.5622i	−0.265636	−	0.460096i
$528$		0			0
$529$	−2.37564	+	4.11474i	−0.103289	+	0.178902i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−5.66025	+	9.80385i	−0.245173	+	0.424652i
$534$		0			0
$535$	−3.46410	−	6.00000i	−0.149766	−	0.259403i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−20.9808			−0.903705
$540$		0			0
$541$	16.3923			0.704760			0.352380	−	0.935857i	$-0.385372\pi$
$541$	16.3923			0.704760			0.352380	+	0.935857i	$0.385372\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−13.0263	−	22.5622i	−0.557985	−	0.966458i
$546$		0			0
$547$	21.1603	−	36.6506i	0.904747	−	1.56707i	0.0834908	−	0.996509i	$-0.473393\pi$
$547$	21.1603	−	36.6506i	0.904747	−	1.56707i	0.821256	−	0.570559i	$-0.193274\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−11.6603	+	20.1962i	−0.496744	+	0.860385i
$552$		0			0
$553$	0.124356	+	0.215390i	0.00528814	+	0.00915933i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.19615			−0.177797			−0.0888983	−	0.996041i	$-0.528335\pi$
$557$	−4.19615			−0.177797			−0.0888983	+	0.996041i	$0.528335\pi$
$558$		0			0
$559$	35.3923			1.49693
$560$		0			0
$561$		0			0
$562$		0			0
$563$	5.56218	+	9.63397i	0.234418	+	0.406024i	0.959103	−	0.283056i	$-0.0913483\pi$
$563$	5.56218	+	9.63397i	0.234418	+	0.406024i	−0.724685	+	0.689080i	$0.758015\pi$
$564$		0			0
$565$	9.46410	−	16.3923i	0.398158	−	0.689629i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.29423	+	3.97372i	−0.0961791	+	0.166587i	−0.910100	−	0.414389i	$-0.863995\pi$
$569$	−2.29423	+	3.97372i	−0.0961791	+	0.166587i	0.813921	+	0.580976i	$0.197329\pi$
$570$		0			0
$571$	−1.73205	−	3.00000i	−0.0724841	−	0.125546i	0.827505	−	0.561458i	$-0.189759\pi$
$571$	−1.73205	−	3.00000i	−0.0724841	−	0.125546i	−0.899989	+	0.435912i	$0.856426\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	12.9808			0.541335
$576$		0			0
$577$	12.8564			0.535219			0.267610	−	0.963527i	$-0.413766\pi$
$577$	12.8564			0.535219			0.267610	+	0.963527i	$0.413766\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	16.0526	+	27.8038i	0.665972	+	1.15350i
$582$		0			0
$583$	20.2679	−	35.1051i	0.839413	−	1.45391i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	8.09808	−	14.0263i	0.334243	−	0.578927i	−0.649096	−	0.760707i	$-0.724853\pi$
$587$	8.09808	−	14.0263i	0.334243	−	0.578927i	0.983339	+	0.181780i	$0.0581859\pi$
$588$		0			0
$589$	5.50000	+	9.52628i	0.226624	+	0.392524i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	4.58846			0.188425			0.0942127	−	0.995552i	$-0.469967\pi$
$593$	4.58846			0.188425			0.0942127	+	0.995552i	$0.469967\pi$
$594$		0			0
$595$	25.8564			1.06001
$596$		0			0
$597$		0			0
$598$		0			0
$599$	19.8564	+	34.3923i	0.811311	+	1.40523i	0.911947	+	0.410308i	$0.134579\pi$
$599$	19.8564	+	34.3923i	0.811311	+	1.40523i	−0.100636	+	0.994923i	$0.532088\pi$
$600$		0			0
$601$	11.1603	−	19.3301i	0.455236	−	0.788492i	−0.543465	−	0.839432i	$-0.682888\pi$
$601$	11.1603	−	19.3301i	0.455236	−	0.788492i	0.998702	+	0.0509392i	$0.0162215\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−9.02628	+	15.6340i	−0.366970	+	0.635611i
$606$		0			0
$607$	−14.3923	−	24.9282i	−0.584166	−	1.01180i	−0.994979	−	0.100085i	$-0.968089\pi$
$607$	−14.3923	−	24.9282i	−0.584166	−	1.01180i	0.410813	−	0.911720i	$-0.365245\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	30.9282			1.25122
$612$		0			0
$613$	−6.07180			−0.245238			−0.122619	−	0.992454i	$-0.539129\pi$
$613$	−6.07180			−0.245238			−0.122619	+	0.992454i	$0.539129\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.26795	+	2.19615i	0.0510457	+	0.0884138i	0.890419	−	0.455141i	$-0.150411\pi$
$617$	1.26795	+	2.19615i	0.0510457	+	0.0884138i	−0.839374	+	0.543555i	$0.817078\pi$
$618$		0			0
$619$	−0.500000	+	0.866025i	−0.0200967	+	0.0348085i	−0.875899	−	0.482495i	$-0.839731\pi$
$619$	−0.500000	+	0.866025i	−0.0200967	+	0.0348085i	0.855802	+	0.517303i	$0.173064\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−20.7846	+	36.0000i	−0.832718	+	1.44231i
$624$		0			0
$625$	15.6244	+	27.0622i	0.624974	+	1.08249i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−25.8564			−1.03096
$630$		0			0
$631$	28.0000			1.11466			0.557331	−	0.830290i	$-0.311825\pi$
$631$	28.0000			1.11466			0.557331	+	0.830290i	$0.311825\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	16.2942	+	28.2224i	0.646617	+	1.11997i
$636$		0			0
$637$	−11.1603	+	19.3301i	−0.442185	+	0.765888i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.90192	+	17.1506i	−0.391102	+	0.677409i	−0.992595	−	0.121469i	$-0.961240\pi$
$641$	−9.90192	+	17.1506i	−0.391102	+	0.677409i	0.601493	+	0.798878i	$0.294573\pi$
$642$		0			0
$643$	−23.1962	−	40.1769i	−0.914767	−	1.58442i	−0.807242	−	0.590220i	$-0.799041\pi$
$643$	−23.1962	−	40.1769i	−0.914767	−	1.58442i	−0.107525	−	0.994202i	$-0.534293\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.875644			−0.0344251			−0.0172126	−	0.999852i	$-0.505479\pi$
$647$	−0.875644			−0.0344251			−0.0172126	+	0.999852i	$0.505479\pi$
$648$		0			0
$649$	−51.1769			−2.00887
$650$		0			0
$651$		0			0
$652$		0			0
$653$	16.3923	+	28.3923i	0.641480	+	1.11108i	0.985102	+	0.171969i	$0.0550128\pi$
$653$	16.3923	+	28.3923i	0.641480	+	1.11108i	−0.343622	+	0.939108i	$0.611654\pi$
$654$		0			0
$655$	−25.5885	+	44.3205i	−0.999824	+	1.73175i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	−0.725175	−	0.688565i	$-0.758241\pi$
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	0.958902	+	0.283738i	$0.0915745\pi$
$660$		0			0
$661$	−13.3564	−	23.1340i	−0.519504	−	0.899807i	−0.999743	−	0.0226697i	$-0.992783\pi$
$661$	−13.3564	−	23.1340i	−0.519504	−	0.899807i	0.480239	−	0.877138i	$-0.340550\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−23.3205			−0.904331
$666$		0			0
$667$	49.8564			1.93045
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−17.7583	−	30.7583i	−0.685553	−	1.18741i
$672$		0			0
$673$	−15.6244	+	27.0622i	−0.602275	+	1.04317i	0.390201	+	0.920730i	$0.372405\pi$
$673$	−15.6244	+	27.0622i	−0.602275	+	1.04317i	−0.992476	+	0.122441i	$0.960928\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	9.95448	−	17.2417i	0.382582	−	0.662651i	−0.608849	−	0.793286i	$-0.708368\pi$
$677$	9.95448	−	17.2417i	0.382582	−	0.662651i	0.991431	+	0.130635i	$0.0417017\pi$
$678$		0			0
$679$	−3.33975	−	5.78461i	−0.128168	−	0.221993i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	38.0526			1.45604			0.728020	−	0.685556i	$-0.240441\pi$
$683$	38.0526			1.45604			0.728020	+	0.685556i	$0.240441\pi$
$684$		0			0
$685$	13.8564			0.529426
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−21.5622	−	37.3468i	−0.821454	−	1.42280i
$690$		0			0
$691$	−15.0885	+	26.1340i	−0.573992	+	0.994183i	0.422158	+	0.906522i	$0.361273\pi$
$691$	−15.0885	+	26.1340i	−0.573992	+	0.994183i	−0.996150	+	0.0876612i	$0.972061\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.73205	+	8.19615i	−0.179497	+	0.310898i
$696$		0			0
$697$	3.46410	+	6.00000i	0.131212	+	0.227266i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−11.3205			−0.427570			−0.213785	−	0.976881i	$-0.568579\pi$
$701$	−11.3205			−0.427570			−0.213785	+	0.976881i	$0.568579\pi$
$702$		0			0
$703$	23.3205			0.879550
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−28.3923	−	49.1769i	−1.06780	−	1.84949i
$708$		0			0
$709$	6.96410	−	12.0622i	0.261542	−	0.453005i	−0.705110	−	0.709098i	$-0.749102\pi$
$709$	6.96410	−	12.0622i	0.261542	−	0.453005i	0.966652	+	0.256094i	$0.0824356\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	11.7583	−	20.3660i	0.440353	−	0.762714i
$714$		0			0
$715$	25.5885	+	44.3205i	0.956954	+	1.65749i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−9.26795			−0.345636			−0.172818	−	0.984954i	$-0.555287\pi$
$719$	−9.26795			−0.345636			−0.172818	+	0.984954i	$0.555287\pi$
$720$		0			0
$721$	−30.6795			−1.14256
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−11.6603	−	20.1962i	−0.433051	−	0.750066i
$726$		0			0
$727$	0.803848	−	1.39230i	0.0298131	−	0.0516377i	−0.850734	−	0.525597i	$-0.823842\pi$
$727$	0.803848	−	1.39230i	0.0298131	−	0.0516377i	0.880547	+	0.473959i	$0.157175\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	10.8301	−	18.7583i	0.400567	−	0.693802i
$732$		0			0
$733$	12.0359	+	20.8468i	0.444556	+	0.769994i	0.998021	−	0.0628787i	$-0.0200281\pi$
$733$	12.0359	+	20.8468i	0.444556	+	0.769994i	−0.553465	+	0.832872i	$0.686695\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	43.9090			1.61741
$738$		0			0
$739$	−35.3923			−1.30193			−0.650963	−	0.759109i	$-0.725635\pi$
$739$	−35.3923			−1.30193			−0.650963	+	0.759109i	$0.725635\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−13.0263	−	22.5622i	−0.477888	−	0.827726i	0.521791	−	0.853073i	$-0.325264\pi$
$743$	−13.0263	−	22.5622i	−0.477888	−	0.827726i	−0.999679	+	0.0253474i	$0.991931\pi$
$744$		0			0
$745$	−24.6603	+	42.7128i	−0.903482	+	1.56488i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	4.39230	−	7.60770i	0.160491	−	0.277979i
$750$		0			0
$751$	13.7321	+	23.7846i	0.501090	+	0.867913i	0.999999	+	0.00125868i	$0.000400650\pi$
$751$	13.7321	+	23.7846i	0.501090	+	0.867913i	−0.498910	+	0.866654i	$0.666266\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−28.5885			−1.04044
$756$		0			0
$757$	−13.9282			−0.506229			−0.253115	−	0.967436i	$-0.581455\pi$
$757$	−13.9282			−0.506229			−0.253115	+	0.967436i	$0.581455\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−11.9019	−	20.6147i	−0.431444	−	0.747284i	0.565554	−	0.824712i	$-0.308663\pi$
$761$	−11.9019	−	20.6147i	−0.431444	−	0.747284i	−0.996998	+	0.0774280i	$0.975329\pi$
$762$		0			0
$763$	16.5167	−	28.6077i	0.597943	−	1.03567i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−27.2224	+	47.1506i	−0.982945	+	1.70251i
$768$		0			0
$769$	−26.2846	−	45.5263i	−0.947847	−	1.64172i	−0.749947	−	0.661497i	$-0.769921\pi$
$769$	−26.2846	−	45.5263i	−0.947847	−	1.64172i	−0.197900	−	0.980222i	$-0.563412\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−26.5359			−0.954430			−0.477215	−	0.878787i	$-0.658354\pi$
$773$	−26.5359			−0.954430			−0.477215	+	0.878787i	$0.658354\pi$
$774$		0			0
$775$	−11.0000			−0.395132
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.12436	−	5.41154i	−0.111942	−	0.193889i
$780$		0			0
$781$	8.80385	−	15.2487i	0.315026	−	0.545642i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	21.0263	−	36.4186i	0.750460	−	1.29984i
$786$		0			0
$787$	10.8205	+	18.7417i	0.385709	+	0.668068i	0.991867	−	0.127276i	$-0.0406234\pi$
$787$	10.8205	+	18.7417i	0.385709	+	0.668068i	−0.606158	+	0.795344i	$0.707290\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	24.0000			0.853342
$792$		0			0
$793$	−37.7846			−1.34177
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−2.63397	−	4.56218i	−0.0933002	−	0.161601i	0.815598	−	0.578619i	$-0.196408\pi$
$797$	−2.63397	−	4.56218i	−0.0933002	−	0.161601i	−0.908898	+	0.417019i	$0.863075\pi$
$798$		0			0
$799$	9.46410	−	16.3923i	0.334816	−	0.579918i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−19.7058	+	34.1314i	−0.695402	+	1.20447i
$804$		0			0
$805$	24.9282	+	43.1769i	0.878604	+	1.52179i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−21.6603			−0.761534			−0.380767	−	0.924671i	$-0.624340\pi$
$809$	−21.6603			−0.761534			−0.380767	+	0.924671i	$0.624340\pi$
$810$		0			0
$811$	4.21539			0.148022			0.0740112	−	0.997257i	$-0.476420\pi$
$811$	4.21539			0.148022			0.0740112	+	0.997257i	$0.476420\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	2.19615	+	3.80385i	0.0769279	+	0.133243i
$816$		0			0
$817$	−9.76795	+	16.9186i	−0.341737	+	0.591906i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.928203	+	1.60770i	−0.0323945	+	0.0561089i	−0.881768	−	0.471683i	$-0.843647\pi$
$821$	−0.928203	+	1.60770i	−0.0323945	+	0.0561089i	0.849374	+	0.527792i	$0.176980\pi$
$822$		0			0
$823$	10.0885	+	17.4737i	0.351662	+	0.609096i	0.986541	−	0.163516i	$-0.0522835\pi$
$823$	10.0885	+	17.4737i	0.351662	+	0.609096i	−0.634879	+	0.772611i	$0.718950\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−23.5167			−0.817754			−0.408877	−	0.912589i	$-0.634080\pi$
$827$	−23.5167			−0.817754			−0.408877	+	0.912589i	$0.634080\pi$
$828$		0			0
$829$	−35.2487			−1.22424			−0.612119	−	0.790766i	$-0.709683\pi$
$829$	−35.2487			−1.22424			−0.612119	+	0.790766i	$0.709683\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	6.83013	+	11.8301i	0.236650	+	0.409890i
$834$		0			0
$835$	22.3923	−	38.7846i	0.774918	−	1.34220i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	11.6603	−	20.1962i	0.402557	−	0.697249i	−0.591477	−	0.806322i	$-0.701455\pi$
$839$	11.6603	−	20.1962i	0.402557	−	0.697249i	0.994034	+	0.109073i	$0.0347883\pi$
$840$		0			0
$841$	−30.2846	−	52.4545i	−1.04430	−	1.80878i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	18.9282			0.651150
$846$		0			0
$847$	−22.8897			−0.786500
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−24.9282	−	43.1769i	−0.854528	−	1.48009i
$852$		0			0
$853$	4.89230	−	8.47372i	0.167509	−	0.290135i	−0.770034	−	0.638003i	$-0.779761\pi$
$853$	4.89230	−	8.47372i	0.167509	−	0.290135i	0.937544	+	0.347868i	$0.113094\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	24.5885	−	42.5885i	0.839926	−	1.45479i	−0.0500304	−	0.998748i	$-0.515932\pi$
$857$	24.5885	−	42.5885i	0.839926	−	1.45479i	0.889956	−	0.456046i	$-0.150735\pi$
$858$		0			0
$859$	−19.7321	−	34.1769i	−0.673249	−	1.16610i	−0.976977	−	0.213343i	$-0.931565\pi$
$859$	−19.7321	−	34.1769i	−0.673249	−	1.16610i	0.303729	−	0.952759i	$-0.401768\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−54.0526			−1.83997			−0.919985	−	0.391953i	$-0.871800\pi$
$863$	−54.0526			−1.83997			−0.919985	+	0.391953i	$0.871800\pi$
$864$		0			0
$865$	−18.9282			−0.643578
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.150635	+	0.260908i	0.00510995	+	0.00885069i
$870$		0			0
$871$	23.3564	−	40.4545i	0.791402	−	1.37075i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−12.0000	+	20.7846i	−0.405674	+	0.702648i
$876$		0			0
$877$	19.2679	+	33.3731i	0.650632	+	1.12693i	0.982970	+	0.183768i	$0.0588294\pi$
$877$	19.2679	+	33.3731i	0.650632	+	1.12693i	−0.332337	+	0.943161i	$0.607837\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.66025			0.0559354			0.0279677	−	0.999609i	$-0.491096\pi$
$881$	1.66025			0.0559354			0.0279677	+	0.999609i	$0.491096\pi$
$882$		0			0
$883$	46.3205			1.55881			0.779405	−	0.626521i	$-0.215522\pi$
$883$	46.3205			1.55881			0.779405	+	0.626521i	$0.215522\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.43782	−	4.22243i	−0.0818541	−	0.141775i	0.822192	−	0.569210i	$-0.192751\pi$
$887$	−2.43782	−	4.22243i	−0.0818541	−	0.141775i	−0.904046	+	0.427434i	$0.859417\pi$
$888$		0			0
$889$	−20.6603	+	35.7846i	−0.692923	+	1.20018i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−8.53590	+	14.7846i	−0.285643	+	0.494748i
$894$		0			0
$895$	−12.9282	−	22.3923i	−0.432142	−	0.748492i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−42.2487			−1.40907
$900$		0			0
$901$	−26.3923			−0.879255
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−31.8564	−	55.1769i	−1.05894	−	1.83414i
$906$		0			0
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	−0.918265	−	0.395966i	$-0.870410\pi$
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	0.802049	+	0.597258i	$0.203743\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−12.0981	+	20.9545i	−0.400827	+	0.694253i	−0.993826	−	0.110950i	$-0.964611\pi$
$911$	−12.0981	+	20.9545i	−0.400827	+	0.694253i	0.592999	+	0.805203i	$0.297944\pi$
$912$		0			0
$913$	19.4449	+	33.6795i	0.643531	+	1.11463i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−64.8897			−2.14285
$918$		0			0
$919$	4.00000			0.131948			0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000			0.131948			0.0659739	+	0.997821i	$0.478985\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−9.36603	−	16.2224i	−0.308286	−	0.533968i
$924$		0			0
$925$	−11.6603	+	20.1962i	−0.383387	+	0.664045i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−9.70577	+	16.8109i	−0.318436	+	0.551547i	−0.980162	−	0.198198i	$-0.936491\pi$
$929$	−9.70577	+	16.8109i	−0.318436	+	0.551547i	0.661726	+	0.749746i	$0.269824\pi$
$930$		0			0
$931$	−6.16025	−	10.6699i	−0.201894	−	0.349691i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	31.3205			1.02429
$936$		0			0
$937$	4.39230			0.143490			0.0717452	−	0.997423i	$-0.477143\pi$
$937$	4.39230			0.143490			0.0717452	+	0.997423i	$0.477143\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−3.46410	−	6.00000i	−0.112926	−	0.195594i	0.804022	−	0.594599i	$-0.202689\pi$
$941$	−3.46410	−	6.00000i	−0.112926	−	0.195594i	−0.916949	+	0.399004i	$0.869356\pi$
$942$		0			0
$943$	−6.67949	+	11.5692i	−0.217514	+	0.376746i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	15.1244	−	26.1962i	0.491476	−	0.851261i	−0.508476	−	0.861076i	$-0.669791\pi$
$947$	15.1244	−	26.1962i	0.491476	−	0.851261i	0.999952	+	0.00981541i	$0.00312439\pi$
$948$		0			0
$949$	20.9641	+	36.3109i	0.680524	+	1.17870i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−44.7846			−1.45072			−0.725358	−	0.688372i	$-0.758326\pi$
$953$	−44.7846			−1.45072			−0.725358	+	0.688372i	$0.758326\pi$
$954$		0			0
$955$	13.8564			0.448383
$956$		0			0
$957$		0			0
$958$		0			0
$959$	8.78461	+	15.2154i	0.283670	+	0.491331i
$960$		0			0
$961$	5.53590	−	9.58846i	0.178577	−	0.309305i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−33.9545	+	58.8109i	−1.09303	+	1.89319i
$966$		0			0
$967$	−2.62436	−	4.54552i	−0.0843936	−	0.146174i	0.820739	−	0.571303i	$-0.193562\pi$
$967$	−2.62436	−	4.54552i	−0.0843936	−	0.146174i	−0.905133	+	0.425129i	$0.860229\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	22.6410			0.726585			0.363292	−	0.931675i	$-0.381653\pi$
$971$	22.6410			0.726585			0.363292	+	0.931675i	$0.381653\pi$
$972$		0			0
$973$	−12.0000			−0.384702
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−11.6603	−	20.1962i	−0.373045	−	0.646132i	0.616988	−	0.786973i	$-0.288353\pi$
$977$	−11.6603	−	20.1962i	−0.373045	−	0.646132i	−0.990032	+	0.140841i	$0.955019\pi$
$978$		0			0
$979$	−25.1769	+	43.6077i	−0.804658	+	1.39371i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	9.80385	−	16.9808i	0.312694	−	0.541602i	−0.666250	−	0.745728i	$-0.732102\pi$
$983$	9.80385	−	16.9808i	0.312694	−	0.541602i	0.978945	+	0.204126i	$0.0654352\pi$
$984$		0			0
$985$	−15.4641	−	26.7846i	−0.492727	−	0.853429i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	41.7654			1.32806
$990$		0			0
$991$	0.0717968			0.00228070			0.00114035	−	0.999999i	$-0.499637\pi$
$991$	0.0717968			0.00228070			0.00114035	+	0.999999i	$0.499637\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	15.0263	+	26.0263i	0.476365	+	0.825089i
$996$		0			0
$997$	−5.00000	+	8.66025i	−0.158352	+	0.274273i	−0.934274	−	0.356555i	$-0.883951\pi$
$997$	−5.00000	+	8.66025i	−0.158352	+	0.274273i	0.775923	+	0.630828i	$0.217285\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1944.2.i.k.649.1		4
3.2	odd	2		1944.2.i.n.649.2		4
9.2	odd	6		1944.2.a.k.1.1	✓	2
9.4	even	3	inner	1944.2.i.k.1297.1		4
9.5	odd	6		1944.2.i.n.1297.2		4
9.7	even	3		1944.2.a.n.1.2	yes	2
36.7	odd	6		3888.2.a.bc.1.2		2
36.11	even	6		3888.2.a.w.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1944.2.a.k.1.1	✓	2	9.2	odd	6
1944.2.a.n.1.2	yes	2	9.7	even	3
1944.2.i.k.649.1		4	1.1	even	1	trivial
1944.2.i.k.1297.1		4	9.4	even	3	inner
1944.2.i.n.649.2		4	3.2	odd	2
1944.2.i.n.1297.2		4	9.5	odd	6
3888.2.a.w.1.1		2	36.11	even	6
3888.2.a.bc.1.2		2	36.7	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:	\( N \)	\(=\)	\( 1944 = 2^{3} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1944.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 2.36603i) q^{5} +(1.73205 - 3.00000i) q^{7} +O(q^{10})\)	\(q+(-1.36603 - 2.36603i) q^{5} +(1.73205 - 3.00000i) q^{7} +(2.09808 - 3.63397i) q^{11} +(-2.23205 - 3.86603i) q^{13} -2.73205 q^{17} +2.46410 q^{19} +(-2.63397 - 4.56218i) q^{23} +(-1.23205 + 2.13397i) q^{25} +(-4.73205 + 8.19615i) q^{29} +(2.23205 + 3.86603i) q^{31} -9.46410 q^{35} +9.46410 q^{37} +(-1.26795 - 2.19615i) q^{41} +(-3.96410 + 6.86603i) q^{43} +(-3.46410 + 6.00000i) q^{47} +(-2.50000 - 4.33013i) q^{49} +9.66025 q^{53} -11.4641 q^{55} +(-6.09808 - 10.5622i) q^{59} +(4.23205 - 7.33013i) q^{61} +(-6.09808 + 10.5622i) q^{65} +(5.23205 + 9.06218i) q^{67} +4.19615 q^{71} -9.39230 q^{73} +(-7.26795 - 12.5885i) q^{77} +(-0.0358984 + 0.0621778i) q^{79} +(-4.63397 + 8.02628i) q^{83} +(3.73205 + 6.46410i) q^{85} -12.0000 q^{89} -15.4641 q^{91} +(-3.36603 - 5.83013i) q^{95} +(0.964102 - 1.66987i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{5}+O(q^{10}) \) 4 * q - 2 * q^5	\( 4 q - 2 q^{5} - 2 q^{11} - 2 q^{13} - 4 q^{17} - 4 q^{19} - 14 q^{23} + 2 q^{25} - 12 q^{29} + 2 q^{31} - 24 q^{35} + 24 q^{37} - 12 q^{41} - 2 q^{43} - 10 q^{49} + 4 q^{53} - 32 q^{55} - 14 q^{59} + 10 q^{61} - 14 q^{65} + 14 q^{67} - 4 q^{71} + 4 q^{73} - 36 q^{77} - 14 q^{79} - 22 q^{83} + 8 q^{85} - 48 q^{89} - 48 q^{91} - 10 q^{95} - 10 q^{97}+O(q^{100}) \) 4 * q - 2 * q^5 - 2 * q^11 - 2 * q^13 - 4 * q^17 - 4 * q^19 - 14 * q^23 + 2 * q^25 - 12 * q^29 + 2 * q^31 - 24 * q^35 + 24 * q^37 - 12 * q^41 - 2 * q^43 - 10 * q^49 + 4 * q^53 - 32 * q^55 - 14 * q^59 + 10 * q^61 - 14 * q^65 + 14 * q^67 - 4 * q^71 + 4 * q^73 - 36 * q^77 - 14 * q^79 - 22 * q^83 + 8 * q^85 - 48 * q^89 - 48 * q^91 - 10 * q^95 - 10 * q^97

Introduction

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