LMFDB - Embedded newform 2592.2.i.s.1729.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2592,2,Mod(865,2592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2592, 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("2592.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2592 = 2^{5} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2592.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:	$20.6972242039$
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 864)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1729.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2592.1729
Dual form			2592.2.i.s.865.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{7} +O(q^{10})$	$q+(1.00000 - 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{11} +(-0.500000 + 0.866025i) q^{13} -6.00000 q^{17} -5.00000 q^{19} +(-3.00000 + 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{25} +(4.00000 + 6.92820i) q^{29} +(-4.00000 + 6.92820i) q^{31} -2.00000 q^{35} -5.00000 q^{37} +(4.00000 - 6.92820i) q^{41} +(2.00000 + 3.46410i) q^{43} +(5.00000 + 8.66025i) q^{47} +(3.00000 - 5.19615i) q^{49} -4.00000 q^{53} +4.00000 q^{55} +(-7.00000 + 12.1244i) q^{59} +(-1.50000 - 2.59808i) q^{61} +(1.00000 + 1.73205i) q^{65} +(6.50000 - 11.2583i) q^{67} -4.00000 q^{71} +9.00000 q^{73} +(1.00000 - 1.73205i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(6.00000 + 10.3923i) q^{83} +(-6.00000 + 10.3923i) q^{85} +2.00000 q^{89} +1.00000 q^{91} +(-5.00000 + 8.66025i) q^{95} +(-0.500000 - 0.866025i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{5} - q^{7}+O(q^{10}) $ 2 * q + 2 * q^5 - q^7	$ 2 q + 2 q^{5} - q^{7} + 2 q^{11} - q^{13} - 12 q^{17} - 10 q^{19} - 6 q^{23} + q^{25} + 8 q^{29} - 8 q^{31} - 4 q^{35} - 10 q^{37} + 8 q^{41} + 4 q^{43} + 10 q^{47} + 6 q^{49} - 8 q^{53} + 8 q^{55} - 14 q^{59} - 3 q^{61} + 2 q^{65} + 13 q^{67} - 8 q^{71} + 18 q^{73} + 2 q^{77} - 11 q^{79} + 12 q^{83} - 12 q^{85} + 4 q^{89} + 2 q^{91} - 10 q^{95} - q^{97}+O(q^{100}) $ 2 * q + 2 * q^5 - q^7 + 2 * q^11 - q^13 - 12 * q^17 - 10 * q^19 - 6 * q^23 + q^25 + 8 * q^29 - 8 * q^31 - 4 * q^35 - 10 * q^37 + 8 * q^41 + 4 * q^43 + 10 * q^47 + 6 * q^49 - 8 * q^53 + 8 * q^55 - 14 * q^59 - 3 * q^61 + 2 * q^65 + 13 * q^67 - 8 * q^71 + 18 * q^73 + 2 * q^77 - 11 * q^79 + 12 * q^83 - 12 * q^85 + 4 * q^89 + 2 * q^91 - 10 * q^95 - q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times$.

$n$	$325$	$1217$	$2431$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	0.998203	+	0.0599153i	$0.0190830\pi$
$6$		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
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	−0.926995	−	0.375073i	$-0.877618\pi$
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	0.788320	+	0.615265i	$0.210951\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$		0			0
$19$	−5.00000			−1.14708			−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000			−1.14708			−0.573539	+	0.819178i	$0.694430\pi$
$20$		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
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.00000	+	6.92820i	0.742781	+	1.28654i	0.951224	+	0.308500i	$0.0998271\pi$
$29$	4.00000	+	6.92820i	0.742781	+	1.28654i	−0.208443	+	0.978035i	$0.566840\pi$
$30$		0			0
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	0.243204	+	0.969975i	$0.421802\pi$
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	−0.961625	+	0.274367i	$0.911532\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.00000			−0.338062
$36$		0			0
$37$	−5.00000			−0.821995			−0.410997	−	0.911636i	$-0.634819\pi$
$37$	−5.00000			−0.821995			−0.410997	+	0.911636i	$0.634819\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.00000	−	6.92820i	0.624695	−	1.08200i	−0.363905	−	0.931436i	$-0.618557\pi$
$41$	4.00000	−	6.92820i	0.624695	−	1.08200i	0.988600	−	0.150567i	$-0.0481100\pi$
$42$		0			0
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	0.977261	−	0.212041i	$-0.0680112\pi$
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	−0.672264	+	0.740312i	$0.734678\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.00000	+	8.66025i	0.729325	+	1.26323i	0.957169	+	0.289530i	$0.0934991\pi$
$47$	5.00000	+	8.66025i	0.729325	+	1.26323i	−0.227844	+	0.973698i	$0.573168\pi$
$48$		0			0
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.00000			−0.549442			−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000			−0.549442			−0.274721	+	0.961524i	$0.588586\pi$
$54$		0			0
$55$	4.00000			0.539360
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−7.00000	+	12.1244i	−0.911322	+	1.57846i	−0.0991242	+	0.995075i	$0.531604\pi$
$59$	−7.00000	+	12.1244i	−0.911322	+	1.57846i	−0.812198	+	0.583382i	$0.801729\pi$
$60$		0			0
$61$	−1.50000	−	2.59808i	−0.192055	−	0.332650i	0.753876	−	0.657017i	$-0.228182\pi$
$61$	−1.50000	−	2.59808i	−0.192055	−	0.332650i	−0.945931	+	0.324367i	$0.894849\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.00000	+	1.73205i	0.124035	+	0.214834i
$66$		0			0
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	−0.129307	−	0.991605i	$-0.541275\pi$
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	0.923408	−	0.383819i	$-0.125391\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−4.00000			−0.474713			−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000			−0.474713			−0.237356	+	0.971423i	$0.576281\pi$
$72$		0			0
$73$	9.00000			1.05337			0.526685	−	0.850060i	$-0.323435\pi$
$73$	9.00000			1.05337			0.526685	+	0.850060i	$0.323435\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.00000	−	1.73205i	0.113961	−	0.197386i
$78$		0			0
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	−0.989705	−	0.143120i	$-0.954286\pi$
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	0.370907	−	0.928670i	$-0.379047\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	0.980982	+	0.194099i	$0.0621783\pi$
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	−0.322396	+	0.946605i	$0.604488\pi$
$84$		0			0
$85$	−6.00000	+	10.3923i	−0.650791	+	1.12720i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.00000			0.212000			0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000			0.212000			0.106000	+	0.994366i	$0.466196\pi$
$90$		0			0
$91$	1.00000			0.104828
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−5.00000	+	8.66025i	−0.512989	+	0.888523i
$96$		0			0
$97$	−0.500000	−	0.866025i	−0.0507673	−	0.0879316i	0.839525	−	0.543321i	$-0.182833\pi$
$97$	−0.500000	−	0.866025i	−0.0507673	−	0.0879316i	−0.890292	+	0.455389i	$0.849500\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	1.50000	−	2.59808i	0.147799	−	0.255996i	−0.782614	−	0.622507i	$-0.786114\pi$
$103$	1.50000	−	2.59808i	0.147799	−	0.255996i	0.930414	+	0.366511i	$0.119448\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.00000			0.193347			0.0966736	−	0.995316i	$-0.469180\pi$
$107$	2.00000			0.193347			0.0966736	+	0.995316i	$0.469180\pi$
$108$		0			0
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.00000	+	8.66025i	−0.470360	+	0.814688i	−0.999425	−	0.0338931i	$-0.989209\pi$
$113$	−5.00000	+	8.66025i	−0.470360	+	0.814688i	0.529065	+	0.848581i	$0.322543\pi$
$114$		0			0
$115$	6.00000	+	10.3923i	0.559503	+	0.969087i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.00000	+	5.19615i	0.275010	+	0.476331i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	12.0000			1.07331
$126$		0			0
$127$	20.0000			1.77471			0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000			1.77471			0.887357	+	0.461084i	$0.152539\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8.00000	+	13.8564i	−0.698963	+	1.21064i	0.269863	+	0.962899i	$0.413022\pi$
$131$	−8.00000	+	13.8564i	−0.698963	+	1.21064i	−0.968826	+	0.247741i	$0.920312\pi$
$132$		0			0
$133$	2.50000	+	4.33013i	0.216777	+	0.375470i
$134$		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
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	−0.952355	−	0.304991i	$-0.901346\pi$
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	0.740308	+	0.672268i	$0.234680\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.00000			−0.167248
$144$		0			0
$145$	16.0000			1.32873
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.00000	+	10.3923i	−0.491539	+	0.851371i	−0.999953	−	0.00974235i	$-0.996899\pi$
$149$	−6.00000	+	10.3923i	−0.491539	+	0.851371i	0.508413	+	0.861113i	$0.330232\pi$
$150$		0			0
$151$	4.50000	+	7.79423i	0.366205	+	0.634285i	0.988969	−	0.148124i	$-0.0473236\pi$
$151$	4.50000	+	7.79423i	0.366205	+	0.634285i	−0.622764	+	0.782410i	$0.713990\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	8.00000	+	13.8564i	0.642575	+	1.11297i
$156$		0			0
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	−0.903167	−	0.429289i	$-0.858764\pi$
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	0.823359	+	0.567521i	$0.192098\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.00000			0.472866
$162$		0			0
$163$	−11.0000			−0.861586			−0.430793	−	0.902451i	$-0.641766\pi$
$163$	−11.0000			−0.861586			−0.430793	+	0.902451i	$0.641766\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.00000	+	12.1244i	−0.541676	+	0.938211i	0.457132	+	0.889399i	$0.348877\pi$
$167$	−7.00000	+	12.1244i	−0.541676	+	0.938211i	−0.998808	+	0.0488118i	$0.984457\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−12.0000	−	20.7846i	−0.912343	−	1.58022i	−0.810745	−	0.585399i	$-0.800938\pi$
$173$	−12.0000	−	20.7846i	−0.912343	−	1.58022i	−0.101598	−	0.994826i	$-0.532395\pi$
$174$		0			0
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	−19.0000			−1.41226			−0.706129	−	0.708083i	$-0.749560\pi$
$181$	−19.0000			−1.41226			−0.706129	+	0.708083i	$0.749560\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−5.00000	+	8.66025i	−0.367607	+	0.636715i
$186$		0			0
$187$	−6.00000	−	10.3923i	−0.438763	−	0.759961i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$		0			0
$193$	10.5000	−	18.1865i	0.755807	−	1.30910i	−0.189166	−	0.981945i	$-0.560578\pi$
$193$	10.5000	−	18.1865i	0.755807	−	1.30910i	0.944972	−	0.327150i	$-0.106088\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	−19.0000			−1.34687			−0.673437	−	0.739244i	$-0.735183\pi$
$199$	−19.0000			−1.34687			−0.673437	+	0.739244i	$0.735183\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.00000	−	6.92820i	0.280745	−	0.486265i
$204$		0			0
$205$	−8.00000	−	13.8564i	−0.558744	−	0.967773i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−5.00000	−	8.66025i	−0.345857	−	0.599042i
$210$		0			0
$211$	−0.500000	+	0.866025i	−0.0344214	+	0.0596196i	−0.882723	−	0.469894i	$-0.844292\pi$
$211$	−0.500000	+	0.866025i	−0.0344214	+	0.0596196i	0.848301	+	0.529514i	$0.177626\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	8.00000			0.545595
$216$		0			0
$217$	8.00000			0.543075
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.00000	−	5.19615i	0.201802	−	0.349531i
$222$		0			0
$223$	−8.00000	−	13.8564i	−0.535720	−	0.927894i	−0.999128	−	0.0417488i	$-0.986707\pi$
$223$	−8.00000	−	13.8564i	−0.535720	−	0.927894i	0.463409	−	0.886145i	$-0.346626\pi$
$224$		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
$229$	−13.0000	+	22.5167i	−0.859064	+	1.48794i	0.0137585	+	0.999905i	$0.495620\pi$
$229$	−13.0000	+	22.5167i	−0.859064	+	1.48794i	−0.872823	+	0.488037i	$0.837713\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	24.0000			1.57229			0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000			1.57229			0.786146	+	0.618041i	$0.212073\pi$
$234$		0			0
$235$	20.0000			1.30466
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.00000	+	10.3923i	−0.388108	+	0.672222i	−0.992195	−	0.124696i	$-0.960204\pi$
$239$	−6.00000	+	10.3923i	−0.388108	+	0.672222i	0.604087	+	0.796918i	$0.293538\pi$
$240$		0			0
$241$	−6.50000	−	11.2583i	−0.418702	−	0.725213i	0.577107	−	0.816668i	$-0.304181\pi$
$241$	−6.50000	−	11.2583i	−0.418702	−	0.725213i	−0.995809	+	0.0914555i	$0.970848\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−6.00000	−	10.3923i	−0.383326	−	0.663940i
$246$		0			0
$247$	2.50000	−	4.33013i	0.159071	−	0.275519i
$248$		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
$253$	−12.0000			−0.754434
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2.00000	+	3.46410i	−0.124757	+	0.216085i	−0.921638	−	0.388051i	$-0.873148\pi$
$257$	−2.00000	+	3.46410i	−0.124757	+	0.216085i	0.796881	+	0.604136i	$0.206482\pi$
$258$		0			0
$259$	2.50000	+	4.33013i	0.155342	+	0.269061i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	0.989561	−	0.144112i	$-0.0460326\pi$
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	−0.619586	+	0.784929i	$0.712699\pi$
$264$		0			0
$265$	−4.00000	+	6.92820i	−0.245718	+	0.425596i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−6.00000			−0.365826			−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000			−0.365826			−0.182913	+	0.983129i	$0.558553\pi$
$270$		0			0
$271$	−21.0000			−1.27566			−0.637830	−	0.770178i	$-0.720168\pi$
$271$	−21.0000			−1.27566			−0.637830	+	0.770178i	$0.720168\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.00000	+	1.73205i	−0.0603023	+	0.104447i
$276$		0			0
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	0.894503	−	0.447062i	$-0.147530\pi$
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	−0.834419	+	0.551131i	$0.814196\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	12.0000	+	20.7846i	0.715860	+	1.23991i	0.962627	+	0.270831i	$0.0872985\pi$
$281$	12.0000	+	20.7846i	0.715860	+	1.23991i	−0.246767	+	0.969075i	$0.579368\pi$
$282$		0			0
$283$	−10.0000	+	17.3205i	−0.594438	+	1.02960i	0.399188	+	0.916869i	$0.369292\pi$
$283$	−10.0000	+	17.3205i	−0.594438	+	1.02960i	−0.993626	+	0.112728i	$0.964041\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−8.00000			−0.472225
$288$		0			0
$289$	19.0000			1.11765
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	0.473763	+	0.880652i	$0.342895\pi$
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	−0.999549	+	0.0300351i	$0.990438\pi$
$294$		0			0
$295$	14.0000	+	24.2487i	0.815112	+	1.41181i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.00000	−	5.19615i	−0.173494	−	0.300501i
$300$		0			0
$301$	2.00000	−	3.46410i	0.115278	−	0.199667i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−6.00000			−0.343559
$306$		0			0
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	15.0000	−	25.9808i	0.850572	−	1.47323i	−0.0301210	−	0.999546i	$-0.509589\pi$
$311$	15.0000	−	25.9808i	0.850572	−	1.47323i	0.880693	−	0.473688i	$-0.157077\pi$
$312$		0			0
$313$	8.50000	+	14.7224i	0.480448	+	0.832161i	0.999748	−	0.0224310i	$-0.00714060\pi$
$313$	8.50000	+	14.7224i	0.480448	+	0.832161i	−0.519300	+	0.854592i	$0.673807\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	0.983866	−	0.178908i	$-0.0572566\pi$
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	−0.646872	+	0.762598i	$0.723923\pi$
$318$		0			0
$319$	−8.00000	+	13.8564i	−0.447914	+	0.775810i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	30.0000			1.66924
$324$		0			0
$325$	−1.00000			−0.0554700
$326$		0			0
$327$		0			0
$328$		0			0
$329$	5.00000	−	8.66025i	0.275659	−	0.477455i
$330$		0			0
$331$	−14.5000	−	25.1147i	−0.796992	−	1.38043i	−0.921567	−	0.388221i	$-0.873090\pi$
$331$	−14.5000	−	25.1147i	−0.796992	−	1.38043i	0.124574	−	0.992210i	$-0.460243\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−13.0000	−	22.5167i	−0.710266	−	1.23022i
$336$		0			0
$337$	15.5000	−	26.8468i	0.844339	−	1.46244i	−0.0418554	−	0.999124i	$-0.513327\pi$
$337$	15.5000	−	26.8468i	0.844339	−	1.46244i	0.886194	−	0.463314i	$-0.153340\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−16.0000			−0.866449
$342$		0			0
$343$	−13.0000			−0.701934
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.00000	−	3.46410i	0.107366	−	0.185963i	−0.807337	−	0.590091i	$-0.799092\pi$
$347$	2.00000	−	3.46410i	0.107366	−	0.185963i	0.914702	+	0.404128i	$0.132425\pi$
$348$		0			0
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	0.925147	−	0.379610i	$-0.123942\pi$
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	−0.791325	+	0.611396i	$0.790608\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2.00000	+	3.46410i	0.106449	+	0.184376i	0.914329	−	0.404971i	$-0.132718\pi$
$353$	2.00000	+	3.46410i	0.106449	+	0.184376i	−0.807880	+	0.589347i	$0.799385\pi$
$354$		0			0
$355$	−4.00000	+	6.92820i	−0.212298	+	0.367711i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−14.0000			−0.738892			−0.369446	−	0.929252i	$-0.620452\pi$
$359$	−14.0000			−0.738892			−0.369446	+	0.929252i	$0.620452\pi$
$360$		0			0
$361$	6.00000			0.315789
$362$		0			0
$363$		0			0
$364$		0			0
$365$	9.00000	−	15.5885i	0.471082	−	0.815937i
$366$		0			0
$367$	7.50000	+	12.9904i	0.391497	+	0.678092i	0.992647	−	0.121044i	$-0.0386241\pi$
$367$	7.50000	+	12.9904i	0.391497	+	0.678092i	−0.601150	+	0.799136i	$0.705291\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2.00000	+	3.46410i	0.103835	+	0.179847i
$372$		0			0
$373$	−5.50000	+	9.52628i	−0.284779	+	0.493252i	−0.972556	−	0.232671i	$-0.925254\pi$
$373$	−5.50000	+	9.52628i	−0.284779	+	0.493252i	0.687776	+	0.725923i	$0.258587\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−8.00000			−0.412021
$378$		0			0
$379$	19.0000			0.975964			0.487982	−	0.872854i	$-0.337733\pi$
$379$	19.0000			0.975964			0.487982	+	0.872854i	$0.337733\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	8.00000	−	13.8564i	0.408781	−	0.708029i	−0.585973	−	0.810331i	$-0.699287\pi$
$383$	8.00000	−	13.8564i	0.408781	−	0.708029i	0.994753	+	0.102302i	$0.0326207\pi$
$384$		0			0
$385$	−2.00000	−	3.46410i	−0.101929	−	0.176547i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	0.998763	−	0.0497253i	$-0.0158346\pi$
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	−0.542445	+	0.840091i	$0.682501\pi$
$390$		0			0
$391$	18.0000	−	31.1769i	0.910299	−	1.57668i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−22.0000			−1.10694
$396$		0			0
$397$	−14.0000			−0.702640			−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000			−0.702640			−0.351320	+	0.936255i	$0.614267\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	14.0000	−	24.2487i	0.699127	−	1.21092i	−0.269643	−	0.962960i	$-0.586906\pi$
$401$	14.0000	−	24.2487i	0.699127	−	1.21092i	0.968770	−	0.247962i	$-0.0797610\pi$
$402$		0			0
$403$	−4.00000	−	6.92820i	−0.199254	−	0.345118i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.00000	−	8.66025i	−0.247841	−	0.429273i
$408$		0			0
$409$	−6.50000	+	11.2583i	−0.321404	+	0.556689i	−0.980778	−	0.195127i	$-0.937488\pi$
$409$	−6.50000	+	11.2583i	−0.321404	+	0.556689i	0.659374	+	0.751815i	$0.270822\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	14.0000			0.688895
$414$		0			0
$415$	24.0000			1.17811
$416$		0			0
$417$		0			0
$418$		0			0
$419$	13.0000	−	22.5167i	0.635092	−	1.10001i	−0.351404	−	0.936224i	$-0.614296\pi$
$419$	13.0000	−	22.5167i	0.635092	−	1.10001i	0.986496	−	0.163787i	$-0.0523710\pi$
$420$		0			0
$421$	9.50000	+	16.4545i	0.463002	+	0.801942i	0.999109	−	0.0422075i	$-0.0134391\pi$
$421$	9.50000	+	16.4545i	0.463002	+	0.801942i	−0.536107	+	0.844150i	$0.680106\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.00000	−	5.19615i	−0.145521	−	0.252050i
$426$		0			0
$427$	−1.50000	+	2.59808i	−0.0725901	+	0.125730i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	30.0000			1.44505			0.722525	−	0.691345i	$-0.242982\pi$
$431$	30.0000			1.44505			0.722525	+	0.691345i	$0.242982\pi$
$432$		0			0
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	15.0000	−	25.9808i	0.717547	−	1.24283i
$438$		0			0
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	−0.876454	−	0.481486i	$-0.840097\pi$
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	0.0212481	−	0.999774i	$-0.493236\pi$
$444$		0			0
$445$	2.00000	−	3.46410i	0.0948091	−	0.164214i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−34.0000			−1.60456			−0.802280	−	0.596948i	$-0.796380\pi$
$449$	−34.0000			−1.60456			−0.802280	+	0.596948i	$0.796380\pi$
$450$		0			0
$451$	16.0000			0.753411
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.00000	−	1.73205i	0.0468807	−	0.0811998i
$456$		0			0
$457$	−1.00000	−	1.73205i	−0.0467780	−	0.0810219i	0.841688	−	0.539964i	$-0.181562\pi$
$457$	−1.00000	−	1.73205i	−0.0467780	−	0.0810219i	−0.888466	+	0.458942i	$0.848229\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	0.968945	+	0.247276i	$0.0795353\pi$
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	−0.270326	+	0.962769i	$0.587131\pi$
$462$		0			0
$463$	9.50000	−	16.4545i	0.441502	−	0.764705i	−0.556299	−	0.830982i	$-0.687779\pi$
$463$	9.50000	−	16.4545i	0.441502	−	0.764705i	0.997801	+	0.0662777i	$0.0211123\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.00000			−0.0925490			−0.0462745	−	0.998929i	$-0.514735\pi$
$467$	−2.00000			−0.0925490			−0.0462745	+	0.998929i	$0.514735\pi$
$468$		0			0
$469$	−13.0000			−0.600284
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.00000	+	6.92820i	−0.183920	+	0.318559i
$474$		0			0
$475$	−2.50000	−	4.33013i	−0.114708	−	0.198680i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	0.695773	−	0.718262i	$-0.255062\pi$
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	−0.969920	+	0.243426i	$0.921729\pi$
$480$		0			0
$481$	2.50000	−	4.33013i	0.113990	−	0.197437i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.00000			−0.0908153
$486$		0			0
$487$	−11.0000			−0.498458			−0.249229	−	0.968445i	$-0.580177\pi$
$487$	−11.0000			−0.498458			−0.249229	+	0.968445i	$0.580177\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	7.00000	−	12.1244i	0.315906	−	0.547165i	−0.663724	−	0.747978i	$-0.731025\pi$
$491$	7.00000	−	12.1244i	0.315906	−	0.547165i	0.979630	+	0.200813i	$0.0643584\pi$
$492$		0			0
$493$	−24.0000	−	41.5692i	−1.08091	−	1.87218i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.00000	+	3.46410i	0.0897123	+	0.155386i
$498$		0			0
$499$	12.0000	−	20.7846i	0.537194	−	0.930447i	−0.461860	−	0.886953i	$-0.652818\pi$
$499$	12.0000	−	20.7846i	0.537194	−	0.930447i	0.999054	−	0.0434940i	$-0.0138489\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	−0.924821	−	0.380402i	$-0.875786\pi$
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	0.791849	+	0.610718i	$0.209119\pi$
$510$		0			0
$511$	−4.50000	−	7.79423i	−0.199068	−	0.344796i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−3.00000	−	5.19615i	−0.132196	−	0.228970i
$516$		0			0
$517$	−10.0000	+	17.3205i	−0.439799	+	0.761755i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−42.0000			−1.84005			−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000			−1.84005			−0.920027	+	0.391856i	$0.871833\pi$
$522$		0			0
$523$	15.0000			0.655904			0.327952	−	0.944694i	$-0.393642\pi$
$523$	15.0000			0.655904			0.327952	+	0.944694i	$0.393642\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	24.0000	−	41.5692i	1.04546	−	1.81078i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	4.00000	+	6.92820i	0.173259	+	0.300094i
$534$		0			0
$535$	2.00000	−	3.46410i	0.0864675	−	0.149766i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	12.0000			0.516877
$540$		0			0
$541$	37.0000			1.59075			0.795377	−	0.606115i	$-0.207273\pi$
$541$	37.0000			1.59075			0.795377	+	0.606115i	$0.207273\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−10.0000	+	17.3205i	−0.428353	+	0.741929i
$546$		0			0
$547$	7.50000	+	12.9904i	0.320677	+	0.555429i	0.980628	−	0.195880i	$-0.0627563\pi$
$547$	7.50000	+	12.9904i	0.320677	+	0.555429i	−0.659951	+	0.751309i	$0.729423\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−20.0000	−	34.6410i	−0.852029	−	1.47576i
$552$		0			0
$553$	−5.50000	+	9.52628i	−0.233884	+	0.405099i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−14.0000			−0.593199			−0.296600	−	0.955002i	$-0.595853\pi$
$557$	−14.0000			−0.593199			−0.296600	+	0.955002i	$0.595853\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$		0			0
$561$		0			0
$562$		0			0
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	−0.494238	−	0.869326i	$-0.664553\pi$
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	0.999978	−	0.00664037i	$-0.00211371\pi$
$564$		0			0
$565$	10.0000	+	17.3205i	0.420703	+	0.728679i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.00000	−	8.66025i	−0.209611	−	0.363057i	0.741981	−	0.670421i	$-0.233886\pi$
$569$	−5.00000	−	8.66025i	−0.209611	−	0.363057i	−0.951592	+	0.307364i	$0.900553\pi$
$570$		0			0
$571$	−9.50000	+	16.4545i	−0.397563	+	0.688599i	−0.993425	−	0.114488i	$-0.963477\pi$
$571$	−9.50000	+	16.4545i	−0.397563	+	0.688599i	0.595862	+	0.803087i	$0.296811\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−6.00000			−0.250217
$576$		0			0
$577$	3.00000			0.124892			0.0624458	−	0.998048i	$-0.480110\pi$
$577$	3.00000			0.124892			0.0624458	+	0.998048i	$0.480110\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$		0			0
$583$	−4.00000	−	6.92820i	−0.165663	−	0.286937i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.00000	+	5.19615i	0.123823	+	0.214468i	0.921272	−	0.388918i	$-0.127151\pi$
$587$	3.00000	+	5.19615i	0.123823	+	0.214468i	−0.797449	+	0.603386i	$0.793818\pi$
$588$		0			0
$589$	20.0000	−	34.6410i	0.824086	−	1.42736i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	36.0000			1.47834			0.739171	−	0.673517i	$-0.235217\pi$
$593$	36.0000			1.47834			0.739171	+	0.673517i	$0.235217\pi$
$594$		0			0
$595$	12.0000			0.491952
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−4.00000	+	6.92820i	−0.163436	+	0.283079i	−0.936099	−	0.351738i	$-0.885591\pi$
$599$	−4.00000	+	6.92820i	−0.163436	+	0.283079i	0.772663	+	0.634816i	$0.218924\pi$
$600$		0			0
$601$	13.0000	+	22.5167i	0.530281	+	0.918474i	0.999376	+	0.0353259i	$0.0112469\pi$
$601$	13.0000	+	22.5167i	0.530281	+	0.918474i	−0.469095	+	0.883148i	$0.655420\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−7.00000	−	12.1244i	−0.284590	−	0.492925i
$606$		0			0
$607$	−20.5000	+	35.5070i	−0.832069	+	1.44119i	0.0643251	+	0.997929i	$0.479511\pi$
$607$	−20.5000	+	35.5070i	−0.832069	+	1.44119i	−0.896394	+	0.443257i	$0.853823\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−10.0000			−0.404557
$612$		0			0
$613$	−9.00000			−0.363507			−0.181753	−	0.983344i	$-0.558177\pi$
$613$	−9.00000			−0.363507			−0.181753	+	0.983344i	$0.558177\pi$
$614$		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
$619$	4.50000	+	7.79423i	0.180870	+	0.313276i	0.942177	−	0.335115i	$-0.108775\pi$
$619$	4.50000	+	7.79423i	0.180870	+	0.313276i	−0.761307	+	0.648392i	$0.775442\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.00000	−	1.73205i	−0.0400642	−	0.0693932i
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	30.0000			1.19618
$630$		0			0
$631$	−1.00000			−0.0398094			−0.0199047	−	0.999802i	$-0.506336\pi$
$631$	−1.00000			−0.0398094			−0.0199047	+	0.999802i	$0.506336\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	20.0000	−	34.6410i	0.793676	−	1.37469i
$636$		0			0
$637$	3.00000	+	5.19615i	0.118864	+	0.205879i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	2.00000	+	3.46410i	0.0789953	+	0.136824i	0.902817	−	0.430026i	$-0.141495\pi$
$641$	2.00000	+	3.46410i	0.0789953	+	0.136824i	−0.823821	+	0.566849i	$0.808162\pi$
$642$		0			0
$643$	6.00000	−	10.3923i	0.236617	−	0.409832i	−0.723124	−	0.690718i	$-0.757295\pi$
$643$	6.00000	−	10.3923i	0.236617	−	0.409832i	0.959741	+	0.280885i	$0.0906280\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	24.0000			0.943537			0.471769	−	0.881722i	$-0.343616\pi$
$647$	24.0000			0.943537			0.471769	+	0.881722i	$0.343616\pi$
$648$		0			0
$649$	−28.0000			−1.09910
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−22.0000	+	38.1051i	−0.860927	+	1.49117i	0.0101092	+	0.999949i	$0.496782\pi$
$653$	−22.0000	+	38.1051i	−0.860927	+	1.49117i	−0.871036	+	0.491220i	$0.836551\pi$
$654$		0			0
$655$	16.0000	+	27.7128i	0.625172	+	1.08283i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	−0.968052	−	0.250748i	$-0.919323\pi$
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	0.266872	−	0.963732i	$-0.414010\pi$
$660$		0			0
$661$	−11.5000	+	19.9186i	−0.447298	+	0.774743i	−0.998209	−	0.0598209i	$-0.980947\pi$
$661$	−11.5000	+	19.9186i	−0.447298	+	0.774743i	0.550911	+	0.834564i	$0.314280\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	10.0000			0.387783
$666$		0			0
$667$	−48.0000			−1.85857
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3.00000	−	5.19615i	0.115814	−	0.200595i
$672$		0			0
$673$	−11.5000	−	19.9186i	−0.443292	−	0.767805i	0.554639	−	0.832091i	$-0.312856\pi$
$673$	−11.5000	−	19.9186i	−0.443292	−	0.767805i	−0.997932	+	0.0642860i	$0.979523\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.00000	−	12.1244i	−0.269032	−	0.465977i	0.699580	−	0.714554i	$-0.253370\pi$
$677$	−7.00000	−	12.1244i	−0.269032	−	0.465977i	−0.968612	+	0.248577i	$0.920037\pi$
$678$		0			0
$679$	−0.500000	+	0.866025i	−0.0191882	+	0.0332350i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	24.0000			0.918334			0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000			0.918334			0.459167	+	0.888350i	$0.348148\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.00000	−	3.46410i	0.0761939	−	0.131972i
$690$		0			0
$691$	−2.00000	−	3.46410i	−0.0760836	−	0.131781i	0.825473	−	0.564441i	$-0.190908\pi$
$691$	−2.00000	−	3.46410i	−0.0760836	−	0.131781i	−0.901557	+	0.432660i	$0.857575\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	5.00000	+	8.66025i	0.189661	+	0.328502i
$696$		0			0
$697$	−24.0000	+	41.5692i	−0.909065	+	1.57455i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	25.0000			0.942893
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	11.5000	+	19.9186i	0.431892	+	0.748058i	0.997036	−	0.0769337i	$-0.0245130\pi$
$709$	11.5000	+	19.9186i	0.431892	+	0.748058i	−0.565145	+	0.824992i	$0.691180\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−24.0000	−	41.5692i	−0.898807	−	1.55678i
$714$		0			0
$715$	−2.00000	+	3.46410i	−0.0747958	+	0.129550i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−52.0000			−1.93927			−0.969636	−	0.244551i	$-0.921359\pi$
$719$	−52.0000			−1.93927			−0.969636	+	0.244551i	$0.921359\pi$
$720$		0			0
$721$	−3.00000			−0.111726
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−4.00000	+	6.92820i	−0.148556	+	0.257307i
$726$		0			0
$727$	−24.0000	−	41.5692i	−0.890111	−	1.54172i	−0.839742	−	0.542986i	$-0.817294\pi$
$727$	−24.0000	−	41.5692i	−0.890111	−	1.54172i	−0.0503692	−	0.998731i	$-0.516040\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−12.0000	−	20.7846i	−0.443836	−	0.768747i
$732$		0			0
$733$	17.0000	−	29.4449i	0.627909	−	1.08757i	−0.360061	−	0.932929i	$-0.617244\pi$
$733$	17.0000	−	29.4449i	0.627909	−	1.08757i	0.987971	−	0.154642i	$-0.0494225\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	26.0000			0.957722
$738$		0			0
$739$	−20.0000			−0.735712			−0.367856	−	0.929883i	$-0.619908\pi$
$739$	−20.0000			−0.735712			−0.367856	+	0.929883i	$0.619908\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	21.0000	−	36.3731i	0.770415	−	1.33440i	−0.166920	−	0.985970i	$-0.553382\pi$
$743$	21.0000	−	36.3731i	0.770415	−	1.33440i	0.937336	−	0.348428i	$-0.113284\pi$
$744$		0			0
$745$	12.0000	+	20.7846i	0.439646	+	0.761489i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.00000	−	1.73205i	−0.0365392	−	0.0632878i
$750$		0			0
$751$	12.5000	−	21.6506i	0.456131	−	0.790043i	−0.542621	−	0.839978i	$-0.682568\pi$
$751$	12.5000	−	21.6506i	0.456131	−	0.790043i	0.998752	+	0.0499348i	$0.0159013\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	18.0000			0.655087
$756$		0			0
$757$	33.0000			1.19941			0.599703	−	0.800223i	$-0.295286\pi$
$757$	33.0000			1.19941			0.599703	+	0.800223i	$0.295286\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	0.180957	+	0.983491i	$0.442080\pi$
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	−0.942207	+	0.335032i	$0.891253\pi$
$762$		0			0
$763$	5.00000	+	8.66025i	0.181012	+	0.313522i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−7.00000	−	12.1244i	−0.252755	−	0.437785i
$768$		0			0
$769$	8.50000	−	14.7224i	0.306518	−	0.530904i	−0.671080	−	0.741385i	$-0.734169\pi$
$769$	8.50000	−	14.7224i	0.306518	−	0.530904i	0.977598	+	0.210480i	$0.0675028\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	36.0000			1.29483			0.647415	−	0.762138i	$-0.275850\pi$
$773$	36.0000			1.29483			0.647415	+	0.762138i	$0.275850\pi$
$774$		0			0
$775$	−8.00000			−0.287368
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−20.0000	+	34.6410i	−0.716574	+	1.24114i
$780$		0			0
$781$	−4.00000	−	6.92820i	−0.143131	−	0.247911i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	2.00000	+	3.46410i	0.0713831	+	0.123639i
$786$		0			0
$787$	−1.50000	+	2.59808i	−0.0534692	+	0.0926114i	−0.891521	−	0.452979i	$-0.850361\pi$
$787$	−1.50000	+	2.59808i	−0.0534692	+	0.0926114i	0.838052	+	0.545590i	$0.183695\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	10.0000			0.355559
$792$		0			0
$793$	3.00000			0.106533
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−12.0000	+	20.7846i	−0.425062	+	0.736229i	−0.996426	−	0.0844678i	$-0.973081\pi$
$797$	−12.0000	+	20.7846i	−0.425062	+	0.736229i	0.571364	+	0.820696i	$0.306414\pi$
$798$		0			0
$799$	−30.0000	−	51.9615i	−1.06132	−	1.83827i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	9.00000	+	15.5885i	0.317603	+	0.550105i
$804$		0			0
$805$	6.00000	−	10.3923i	0.211472	−	0.366281i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	20.0000			0.703163			0.351581	−	0.936157i	$-0.385644\pi$
$809$	20.0000			0.703163			0.351581	+	0.936157i	$0.385644\pi$
$810$		0			0
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−11.0000	+	19.0526i	−0.385313	+	0.667382i
$816$		0			0
$817$	−10.0000	−	17.3205i	−0.349856	−	0.605968i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.00000	+	1.73205i	0.0349002	+	0.0604490i	0.882948	−	0.469471i	$-0.155555\pi$
$821$	1.00000	+	1.73205i	0.0349002	+	0.0604490i	−0.848048	+	0.529920i	$0.822222\pi$
$822$		0			0
$823$	−21.5000	+	37.2391i	−0.749443	+	1.29807i	0.198647	+	0.980071i	$0.436345\pi$
$823$	−21.5000	+	37.2391i	−0.749443	+	1.29807i	−0.948090	+	0.318002i	$0.896988\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−2.00000			−0.0695468			−0.0347734	−	0.999395i	$-0.511071\pi$
$827$	−2.00000			−0.0695468			−0.0347734	+	0.999395i	$0.511071\pi$
$828$		0			0
$829$	41.0000			1.42399			0.711994	−	0.702185i	$-0.247792\pi$
$829$	41.0000			1.42399			0.711994	+	0.702185i	$0.247792\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−18.0000	+	31.1769i	−0.623663	+	1.08022i
$834$		0			0
$835$	14.0000	+	24.2487i	0.484490	+	0.839161i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	2.00000	+	3.46410i	0.0690477	+	0.119594i	0.898482	−	0.439010i	$-0.144671\pi$
$839$	2.00000	+	3.46410i	0.0690477	+	0.119594i	−0.829435	+	0.558604i	$0.811337\pi$
$840$		0			0
$841$	−17.5000	+	30.3109i	−0.603448	+	1.04520i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	24.0000			0.825625
$846$		0			0
$847$	−7.00000			−0.240523
$848$		0			0
$849$		0			0
$850$		0			0
$851$	15.0000	−	25.9808i	0.514193	−	0.890609i
$852$		0			0
$853$	−7.50000	−	12.9904i	−0.256795	−	0.444782i	0.708586	−	0.705624i	$-0.249333\pi$
$853$	−7.50000	−	12.9904i	−0.256795	−	0.444782i	−0.965382	+	0.260842i	$0.916000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	14.0000	+	24.2487i	0.478231	+	0.828320i	0.999689	−	0.0249570i	$-0.00794488\pi$
$857$	14.0000	+	24.2487i	0.478231	+	0.828320i	−0.521458	+	0.853277i	$0.674612\pi$
$858$		0			0
$859$	9.50000	−	16.4545i	0.324136	−	0.561420i	−0.657201	−	0.753715i	$-0.728260\pi$
$859$	9.50000	−	16.4545i	0.324136	−	0.561420i	0.981337	+	0.192295i	$0.0615932\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	38.0000			1.29354			0.646768	−	0.762687i	$-0.276120\pi$
$863$	38.0000			1.29354			0.646768	+	0.762687i	$0.276120\pi$
$864$		0			0
$865$	−48.0000			−1.63205
$866$		0			0
$867$		0			0
$868$		0			0
$869$	11.0000	−	19.0526i	0.373149	−	0.646314i
$870$		0			0
$871$	6.50000	+	11.2583i	0.220244	+	0.381474i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−6.00000	−	10.3923i	−0.202837	−	0.351324i
$876$		0			0
$877$	8.50000	−	14.7224i	0.287025	−	0.497141i	−0.686074	−	0.727532i	$-0.740667\pi$
$877$	8.50000	−	14.7224i	0.287025	−	0.497141i	0.973098	+	0.230391i	$0.0740005\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	6.00000			0.202145			0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000			0.202145			0.101073	+	0.994879i	$0.467773\pi$
$882$		0			0
$883$	−31.0000			−1.04323			−0.521617	−	0.853180i	$-0.674671\pi$
$883$	−31.0000			−1.04323			−0.521617	+	0.853180i	$0.674671\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−6.00000	+	10.3923i	−0.201460	+	0.348939i	−0.948999	−	0.315279i	$-0.897902\pi$
$887$	−6.00000	+	10.3923i	−0.201460	+	0.348939i	0.747539	+	0.664218i	$0.231235\pi$
$888$		0			0
$889$	−10.0000	−	17.3205i	−0.335389	−	0.580911i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−25.0000	−	43.3013i	−0.836593	−	1.44902i
$894$		0			0
$895$	−12.0000	+	20.7846i	−0.401116	+	0.694753i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−64.0000			−2.13452
$900$		0			0
$901$	24.0000			0.799556
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−19.0000	+	32.9090i	−0.631581	+	1.09393i
$906$		0			0
$907$	8.50000	+	14.7224i	0.282238	+	0.488850i	0.971936	−	0.235247i	$-0.0755899\pi$
$907$	8.50000	+	14.7224i	0.282238	+	0.488850i	−0.689698	+	0.724097i	$0.742257\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	24.0000	+	41.5692i	0.795155	+	1.37725i	0.922740	+	0.385422i	$0.125944\pi$
$911$	24.0000	+	41.5692i	0.795155	+	1.37725i	−0.127585	+	0.991828i	$0.540723\pi$
$912$		0			0
$913$	−12.0000	+	20.7846i	−0.397142	+	0.687870i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	16.0000			0.528367
$918$		0			0
$919$	48.0000			1.58337			0.791687	−	0.610927i	$-0.209203\pi$
$919$	48.0000			1.58337			0.791687	+	0.610927i	$0.209203\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	2.00000	−	3.46410i	0.0658308	−	0.114022i
$924$		0			0
$925$	−2.50000	−	4.33013i	−0.0821995	−	0.142374i
$926$		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
$931$	−15.0000	+	25.9808i	−0.491605	+	0.851485i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−24.0000			−0.784884
$936$		0			0
$937$	−25.0000			−0.816714			−0.408357	−	0.912822i	$-0.633898\pi$
$937$	−25.0000			−0.816714			−0.408357	+	0.912822i	$0.633898\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	11.0000	−	19.0526i	0.358590	−	0.621096i	−0.629136	−	0.777295i	$-0.716591\pi$
$941$	11.0000	−	19.0526i	0.358590	−	0.621096i	0.987725	+	0.156200i	$0.0499244\pi$
$942$		0			0
$943$	24.0000	+	41.5692i	0.781548	+	1.35368i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.00000	+	5.19615i	0.0974869	+	0.168852i	0.910644	−	0.413192i	$-0.135586\pi$
$947$	3.00000	+	5.19615i	0.0974869	+	0.168852i	−0.813157	+	0.582045i	$0.802253\pi$
$948$		0			0
$949$	−4.50000	+	7.79423i	−0.146076	+	0.253011i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		0			0
$955$	12.0000			0.388311
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−3.00000	+	5.19615i	−0.0968751	+	0.167793i
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−21.0000	−	36.3731i	−0.676014	−	1.17089i
$966$		0			0
$967$	−13.5000	+	23.3827i	−0.434131	+	0.751936i	−0.997224	−	0.0744567i	$-0.976278\pi$
$967$	−13.5000	+	23.3827i	−0.434131	+	0.751936i	0.563094	+	0.826393i	$0.309611\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	34.0000			1.09111			0.545556	−	0.838074i	$-0.316319\pi$
$971$	34.0000			1.09111			0.545556	+	0.838074i	$0.316319\pi$
$972$		0			0
$973$	5.00000			0.160293
$974$		0			0
$975$		0			0
$976$		0			0
$977$	22.0000	−	38.1051i	0.703842	−	1.21909i	−0.263265	−	0.964723i	$-0.584799\pi$
$977$	22.0000	−	38.1051i	0.703842	−	1.21909i	0.967108	−	0.254367i	$-0.0818672\pi$
$978$		0			0
$979$	2.00000	+	3.46410i	0.0639203	+	0.110713i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−21.0000	−	36.3731i	−0.669796	−	1.16012i	−0.977961	−	0.208788i	$-0.933048\pi$
$983$	−21.0000	−	36.3731i	−0.669796	−	1.16012i	0.308165	−	0.951333i	$-0.400285\pi$
$984$		0			0
$985$	−2.00000	+	3.46410i	−0.0637253	+	0.110375i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−24.0000			−0.763156
$990$		0			0
$991$	−7.00000			−0.222362			−0.111181	−	0.993800i	$-0.535463\pi$
$991$	−7.00000			−0.222362			−0.111181	+	0.993800i	$0.535463\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−19.0000	+	32.9090i	−0.602340	+	1.04328i
$996$		0			0
$997$	27.0000	+	46.7654i	0.855099	+	1.48107i	0.876554	+	0.481304i	$0.159837\pi$
$997$	27.0000	+	46.7654i	0.855099	+	1.48107i	−0.0214550	+	0.999770i	$0.506830\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2592.2.i.s.1729.1		2
3.2	odd	2		2592.2.i.d.1729.1		2
4.3	odd	2		2592.2.i.u.1729.1		2
9.2	odd	6		2592.2.i.d.865.1		2
9.4	even	3		864.2.a.c.1.1	yes	1
9.5	odd	6		864.2.a.k.1.1	yes	1
9.7	even	3	inner	2592.2.i.s.865.1		2
12.11	even	2		2592.2.i.f.1729.1		2
36.7	odd	6		2592.2.i.u.865.1		2
36.11	even	6		2592.2.i.f.865.1		2
36.23	even	6		864.2.a.j.1.1	yes	1
36.31	odd	6		864.2.a.b.1.1	✓	1
72.5	odd	6		1728.2.a.g.1.1		1
72.13	even	6		1728.2.a.w.1.1		1
72.59	even	6		1728.2.a.f.1.1		1
72.67	odd	6		1728.2.a.v.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.a.b.1.1	✓	1	36.31	odd	6
864.2.a.c.1.1	yes	1	9.4	even	3
864.2.a.j.1.1	yes	1	36.23	even	6
864.2.a.k.1.1	yes	1	9.5	odd	6
1728.2.a.f.1.1		1	72.59	even	6
1728.2.a.g.1.1		1	72.5	odd	6
1728.2.a.v.1.1		1	72.67	odd	6
1728.2.a.w.1.1		1	72.13	even	6
2592.2.i.d.865.1		2	9.2	odd	6
2592.2.i.d.1729.1		2	3.2	odd	2
2592.2.i.f.865.1		2	36.11	even	6
2592.2.i.f.1729.1		2	12.11	even	2
2592.2.i.s.865.1		2	9.7	even	3	inner
2592.2.i.s.1729.1		2	1.1	even	1	trivial
2592.2.i.u.865.1		2	36.7	odd	6
2592.2.i.u.1729.1		2	4.3	odd	2

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:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{7} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{11} +(-0.500000 + 0.866025i) q^{13} -6.00000 q^{17} -5.00000 q^{19} +(-3.00000 + 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{25} +(4.00000 + 6.92820i) q^{29} +(-4.00000 + 6.92820i) q^{31} -2.00000 q^{35} -5.00000 q^{37} +(4.00000 - 6.92820i) q^{41} +(2.00000 + 3.46410i) q^{43} +(5.00000 + 8.66025i) q^{47} +(3.00000 - 5.19615i) q^{49} -4.00000 q^{53} +4.00000 q^{55} +(-7.00000 + 12.1244i) q^{59} +(-1.50000 - 2.59808i) q^{61} +(1.00000 + 1.73205i) q^{65} +(6.50000 - 11.2583i) q^{67} -4.00000 q^{71} +9.00000 q^{73} +(1.00000 - 1.73205i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(6.00000 + 10.3923i) q^{83} +(-6.00000 + 10.3923i) q^{85} +2.00000 q^{89} +1.00000 q^{91} +(-5.00000 + 8.66025i) q^{95} +(-0.500000 - 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{5} - q^{7}+O(q^{10}) \) 2 * q + 2 * q^5 - q^7	\( 2 q + 2 q^{5} - q^{7} + 2 q^{11} - q^{13} - 12 q^{17} - 10 q^{19} - 6 q^{23} + q^{25} + 8 q^{29} - 8 q^{31} - 4 q^{35} - 10 q^{37} + 8 q^{41} + 4 q^{43} + 10 q^{47} + 6 q^{49} - 8 q^{53} + 8 q^{55} - 14 q^{59} - 3 q^{61} + 2 q^{65} + 13 q^{67} - 8 q^{71} + 18 q^{73} + 2 q^{77} - 11 q^{79} + 12 q^{83} - 12 q^{85} + 4 q^{89} + 2 q^{91} - 10 q^{95} - q^{97}+O(q^{100}) \) 2 * q + 2 * q^5 - q^7 + 2 * q^11 - q^13 - 12 * q^17 - 10 * q^19 - 6 * q^23 + q^25 + 8 * q^29 - 8 * q^31 - 4 * q^35 - 10 * q^37 + 8 * q^41 + 4 * q^43 + 10 * q^47 + 6 * q^49 - 8 * q^53 + 8 * q^55 - 14 * q^59 - 3 * q^61 + 2 * q^65 + 13 * q^67 - 8 * q^71 + 18 * q^73 + 2 * q^77 - 11 * q^79 + 12 * q^83 - 12 * q^85 + 4 * q^89 + 2 * q^91 - 10 * q^95 - q^97

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