LMFDB - Embedded newform 1440.2.x.f.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1440,2,Mod(127,1440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1440, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 0, 1]))

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

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

chi := DirichletCharacter("1440.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1440 = 2^{5} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1440.x (of order $4$, degree $2$, 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:	$11.4984578911$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1440.127
Dual form			1440.2.x.f.703.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 2.00000i) q^{5} +(3.00000 - 3.00000i) q^{7} +O(q^{10})$	$q+(-1.00000 - 2.00000i) q^{5} +(3.00000 - 3.00000i) q^{7} -2.00000i q^{11} +(3.00000 - 3.00000i) q^{13} +(-1.00000 - 1.00000i) q^{17} -4.00000 q^{19} +(-1.00000 - 1.00000i) q^{23} +(-3.00000 + 4.00000i) q^{25} +10.0000i q^{31} +(-9.00000 - 3.00000i) q^{35} +(-1.00000 - 1.00000i) q^{37} +10.0000 q^{41} +(-5.00000 - 5.00000i) q^{43} +(-3.00000 + 3.00000i) q^{47} -11.0000i q^{49} +(5.00000 - 5.00000i) q^{53} +(-4.00000 + 2.00000i) q^{55} -12.0000 q^{59} +2.00000 q^{61} +(-9.00000 - 3.00000i) q^{65} +(1.00000 - 1.00000i) q^{67} -2.00000i q^{71} +(1.00000 - 1.00000i) q^{73} +(-6.00000 - 6.00000i) q^{77} -8.00000 q^{79} +(5.00000 + 5.00000i) q^{83} +(-1.00000 + 3.00000i) q^{85} -16.0000i q^{89} -18.0000i q^{91} +(4.00000 + 8.00000i) q^{95} +(-3.00000 - 3.00000i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{5} + 6 q^{7}+O(q^{10}) $ 2 * q - 2 * q^5 + 6 * q^7	$ 2 q - 2 q^{5} + 6 q^{7} + 6 q^{13} - 2 q^{17} - 8 q^{19} - 2 q^{23} - 6 q^{25} - 18 q^{35} - 2 q^{37} + 20 q^{41} - 10 q^{43} - 6 q^{47} + 10 q^{53} - 8 q^{55} - 24 q^{59} + 4 q^{61} - 18 q^{65} + 2 q^{67} + 2 q^{73} - 12 q^{77} - 16 q^{79} + 10 q^{83} - 2 q^{85} + 8 q^{95} - 6 q^{97}+O(q^{100}) $ 2 * q - 2 * q^5 + 6 * q^7 + 6 * q^13 - 2 * q^17 - 8 * q^19 - 2 * q^23 - 6 * q^25 - 18 * q^35 - 2 * q^37 + 20 * q^41 - 10 * q^43 - 6 * q^47 + 10 * q^53 - 8 * q^55 - 24 * q^59 + 4 * q^61 - 18 * q^65 + 2 * q^67 + 2 * q^73 - 12 * q^77 - 16 * q^79 + 10 * q^83 - 2 * q^85 + 8 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$991$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$-1$

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	−	2.00000i	−0.447214	−	0.894427i
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$6$		0			0
$7$	3.00000	−	3.00000i	1.13389	−	1.13389i	0.144370	−	0.989524i	$-0.453885\pi$
$7$	3.00000	−	3.00000i	1.13389	−	1.13389i	0.989524	−	0.144370i	$-0.0461154\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	2.00000i		−	0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$		0			0
$13$	3.00000	−	3.00000i	0.832050	−	0.832050i	−0.155747	−	0.987797i	$-0.549778\pi$
$13$	3.00000	−	3.00000i	0.832050	−	0.832050i	0.987797	+	0.155747i	$0.0497784\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.00000	−	1.00000i	−0.242536	−	0.242536i	0.575363	−	0.817898i	$-0.304861\pi$
$17$	−1.00000	−	1.00000i	−0.242536	−	0.242536i	−0.817898	+	0.575363i	$0.804861\pi$
$18$		0			0
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.00000	−	1.00000i	−0.208514	−	0.208514i	0.595121	−	0.803636i	$-0.297104\pi$
$23$	−1.00000	−	1.00000i	−0.208514	−	0.208514i	−0.803636	+	0.595121i	$0.797104\pi$
$24$		0			0
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$			10.0000i			1.79605i	0.439941	+	0.898027i	$0.354999\pi$
$31$			10.0000i			1.79605i	−0.439941	+	0.898027i	$0.645001\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−9.00000	−	3.00000i	−1.52128	−	0.507093i
$36$		0			0
$37$	−1.00000	−	1.00000i	−0.164399	−	0.164399i	0.620113	−	0.784512i	$-0.287087\pi$
$37$	−1.00000	−	1.00000i	−0.164399	−	0.164399i	−0.784512	+	0.620113i	$0.787087\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	10.0000			1.56174			0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000			1.56174			0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$	−5.00000	−	5.00000i	−0.762493	−	0.762493i	0.214280	−	0.976772i	$-0.431260\pi$
$43$	−5.00000	−	5.00000i	−0.762493	−	0.762493i	−0.976772	+	0.214280i	$0.931260\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.00000	+	3.00000i	−0.437595	+	0.437595i	−0.891202	−	0.453607i	$-0.850137\pi$
$47$	−3.00000	+	3.00000i	−0.437595	+	0.437595i	0.453607	+	0.891202i	$0.350137\pi$
$48$		0			0
$49$		−	11.0000i		−	1.57143i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	5.00000	−	5.00000i	0.686803	−	0.686803i	−0.274721	−	0.961524i	$-0.588586\pi$
$53$	5.00000	−	5.00000i	0.686803	−	0.686803i	0.961524	+	0.274721i	$0.0885855\pi$
$54$		0			0
$55$	−4.00000	+	2.00000i	−0.539360	+	0.269680i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−12.0000			−1.56227			−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000			−1.56227			−0.781133	+	0.624364i	$0.785358\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−9.00000	−	3.00000i	−1.11631	−	0.372104i
$66$		0			0
$67$	1.00000	−	1.00000i	0.122169	−	0.122169i	−0.643379	−	0.765548i	$-0.722468\pi$
$67$	1.00000	−	1.00000i	0.122169	−	0.122169i	0.765548	+	0.643379i	$0.222468\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	2.00000i		−	0.237356i	−0.992933	−	0.118678i	$-0.962134\pi$
$71$		−	2.00000i		−	0.237356i	0.992933	−	0.118678i	$-0.0378657\pi$
$72$		0			0
$73$	1.00000	−	1.00000i	0.117041	−	0.117041i	−0.646160	−	0.763202i	$-0.723626\pi$
$73$	1.00000	−	1.00000i	0.117041	−	0.117041i	0.763202	+	0.646160i	$0.223626\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−6.00000	−	6.00000i	−0.683763	−	0.683763i
$78$		0			0
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.00000	+	5.00000i	0.548821	+	0.548821i	0.926100	−	0.377279i	$-0.123140\pi$
$83$	5.00000	+	5.00000i	0.548821	+	0.548821i	−0.377279	+	0.926100i	$0.623140\pi$
$84$		0			0
$85$	−1.00000	+	3.00000i	−0.108465	+	0.325396i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	16.0000i		−	1.69600i	−0.529999	−	0.847998i	$-0.677808\pi$
$89$		−	16.0000i		−	1.69600i	0.529999	−	0.847998i	$-0.322192\pi$
$90$		0			0
$91$		−	18.0000i		−	1.88691i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.00000	+	8.00000i	0.410391	+	0.820783i
$96$		0			0
$97$	−3.00000	−	3.00000i	−0.304604	−	0.304604i	0.538208	−	0.842812i	$-0.319101\pi$
$97$	−3.00000	−	3.00000i	−0.304604	−	0.304604i	−0.842812	+	0.538208i	$0.819101\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$		0			0
$103$	9.00000	+	9.00000i	0.886796	+	0.886796i	0.994214	−	0.107418i	$-0.0342582\pi$
$103$	9.00000	+	9.00000i	0.886796	+	0.886796i	−0.107418	+	0.994214i	$0.534258\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.00000	−	3.00000i	0.290021	−	0.290021i	−0.547068	−	0.837088i	$-0.684256\pi$
$107$	3.00000	−	3.00000i	0.290021	−	0.290021i	0.837088	+	0.547068i	$0.184256\pi$
$108$		0			0
$109$		−	4.00000i		−	0.383131i	−0.981480	−	0.191565i	$-0.938644\pi$
$109$		−	4.00000i		−	0.383131i	0.981480	−	0.191565i	$-0.0613564\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.00000	−	3.00000i	0.282216	−	0.282216i	−0.551776	−	0.833992i	$-0.686050\pi$
$113$	3.00000	−	3.00000i	0.282216	−	0.282216i	0.833992	+	0.551776i	$0.186050\pi$
$114$		0			0
$115$	−1.00000	+	3.00000i	−0.0932505	+	0.279751i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−6.00000			−0.550019
$120$		0			0
$121$	7.00000			0.636364
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$		0			0
$127$	7.00000	−	7.00000i	0.621150	−	0.621150i	−0.324676	−	0.945825i	$-0.605255\pi$
$127$	7.00000	−	7.00000i	0.621150	−	0.621150i	0.945825	+	0.324676i	$0.105255\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		−	10.0000i		−	0.873704i	−0.899533	−	0.436852i	$-0.856093\pi$
$131$		−	10.0000i		−	0.873704i	0.899533	−	0.436852i	$-0.143907\pi$
$132$		0			0
$133$	−12.0000	+	12.0000i	−1.04053	+	1.04053i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	11.0000	+	11.0000i	0.939793	+	0.939793i	0.998288	−	0.0584943i	$-0.0186300\pi$
$137$	11.0000	+	11.0000i	0.939793	+	0.939793i	−0.0584943	+	0.998288i	$0.518630\pi$
$138$		0			0
$139$	−12.0000			−1.01783			−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000			−1.01783			−0.508913	+	0.860818i	$0.669953\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−6.00000	−	6.00000i	−0.501745	−	0.501745i
$144$		0			0
$145$		0			0
$146$		0			0
$147$		0			0
$148$		0			0
$149$			4.00000i			0.327693i	0.986486	+	0.163846i	$0.0523901\pi$
$149$			4.00000i			0.327693i	−0.986486	+	0.163846i	$0.947610\pi$
$150$		0			0
$151$		−	6.00000i		−	0.488273i	−0.969741	−	0.244137i	$-0.921495\pi$
$151$		−	6.00000i		−	0.488273i	0.969741	−	0.244137i	$-0.0785045\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	20.0000	−	10.0000i	1.60644	−	0.803219i
$156$		0			0
$157$	−1.00000	−	1.00000i	−0.0798087	−	0.0798087i	0.666076	−	0.745884i	$-0.267973\pi$
$157$	−1.00000	−	1.00000i	−0.0798087	−	0.0798087i	−0.745884	+	0.666076i	$0.767973\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−6.00000			−0.472866
$162$		0			0
$163$	−1.00000	−	1.00000i	−0.0783260	−	0.0783260i	0.666858	−	0.745184i	$-0.267639\pi$
$163$	−1.00000	−	1.00000i	−0.0783260	−	0.0783260i	−0.745184	+	0.666858i	$0.767639\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.00000	−	1.00000i	0.0773823	−	0.0773823i	−0.667356	−	0.744739i	$-0.732574\pi$
$167$	1.00000	−	1.00000i	0.0773823	−	0.0773823i	0.744739	+	0.667356i	$0.232574\pi$
$168$		0			0
$169$		−	5.00000i		−	0.384615i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.00000	−	5.00000i	0.380143	−	0.380143i	−0.491011	−	0.871154i	$-0.663372\pi$
$173$	5.00000	−	5.00000i	0.380143	−	0.380143i	0.871154	+	0.491011i	$0.163372\pi$
$174$		0			0
$175$	3.00000	+	21.0000i	0.226779	+	1.58745i
$176$		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
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.00000	+	3.00000i	−0.0735215	+	0.220564i
$186$		0			0
$187$	−2.00000	+	2.00000i	−0.146254	+	0.146254i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			14.0000i			1.01300i	0.862239	+	0.506502i	$0.169062\pi$
$191$			14.0000i			1.01300i	−0.862239	+	0.506502i	$0.830938\pi$
$192$		0			0
$193$	−15.0000	+	15.0000i	−1.07972	+	1.07972i	−0.0831899	+	0.996534i	$0.526511\pi$
$193$	−15.0000	+	15.0000i	−1.07972	+	1.07972i	−0.996534	+	0.0831899i	$0.973489\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	13.0000	+	13.0000i	0.926212	+	0.926212i	0.997459	−	0.0712470i	$-0.0226979\pi$
$197$	13.0000	+	13.0000i	0.926212	+	0.926212i	−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	16.0000			1.13421			0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000			1.13421			0.567105	+	0.823646i	$0.308063\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−10.0000	−	20.0000i	−0.698430	−	1.39686i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			8.00000i			0.553372i
$210$		0			0
$211$		−	14.0000i		−	0.963800i	−0.876226	−	0.481900i	$-0.839947\pi$
$211$		−	14.0000i		−	0.963800i	0.876226	−	0.481900i	$-0.160053\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−5.00000	+	15.0000i	−0.340997	+	1.02299i
$216$		0			0
$217$	30.0000	+	30.0000i	2.03653	+	2.03653i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−6.00000			−0.403604
$222$		0			0
$223$	1.00000	+	1.00000i	0.0669650	+	0.0669650i	0.739796	−	0.672831i	$-0.234922\pi$
$223$	1.00000	+	1.00000i	0.0669650	+	0.0669650i	−0.672831	+	0.739796i	$0.734922\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.00000	+	5.00000i	−0.331862	+	0.331862i	−0.853293	−	0.521431i	$-0.825398\pi$
$227$	−5.00000	+	5.00000i	−0.331862	+	0.331862i	0.521431	+	0.853293i	$0.325398\pi$
$228$		0			0
$229$		−	8.00000i		−	0.528655i	−0.964433	−	0.264327i	$-0.914850\pi$
$229$		−	8.00000i		−	0.528655i	0.964433	−	0.264327i	$-0.0851500\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−21.0000	+	21.0000i	−1.37576	+	1.37576i	−0.524097	+	0.851658i	$0.675597\pi$
$233$	−21.0000	+	21.0000i	−1.37576	+	1.37576i	−0.851658	+	0.524097i	$0.824403\pi$
$234$		0			0
$235$	9.00000	+	3.00000i	0.587095	+	0.195698i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$	−2.00000			−0.128831			−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000			−0.128831			−0.0644157	+	0.997923i	$0.520518\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−22.0000	+	11.0000i	−1.40553	+	0.702764i
$246$		0			0
$247$	−12.0000	+	12.0000i	−0.763542	+	0.763542i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			6.00000i			0.378717i	0.981908	+	0.189358i	$0.0606408\pi$
$251$			6.00000i			0.378717i	−0.981908	+	0.189358i	$0.939359\pi$
$252$		0			0
$253$	−2.00000	+	2.00000i	−0.125739	+	0.125739i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.00000	−	5.00000i	−0.311891	−	0.311891i	0.533751	−	0.845642i	$-0.320782\pi$
$257$	−5.00000	−	5.00000i	−0.311891	−	0.311891i	−0.845642	+	0.533751i	$0.820782\pi$
$258$		0			0
$259$	−6.00000			−0.372822
$260$		0			0
$261$		0			0
$262$		0			0
$263$	11.0000	+	11.0000i	0.678289	+	0.678289i	0.959613	−	0.281324i	$-0.0907735\pi$
$263$	11.0000	+	11.0000i	0.678289	+	0.678289i	−0.281324	+	0.959613i	$0.590774\pi$
$264$		0			0
$265$	−15.0000	−	5.00000i	−0.921443	−	0.307148i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	20.0000i		−	1.21942i	−0.792624	−	0.609711i	$-0.791286\pi$
$269$		−	20.0000i		−	1.21942i	0.792624	−	0.609711i	$-0.208714\pi$
$270$		0			0
$271$		−	14.0000i		−	0.850439i	−0.905090	−	0.425220i	$-0.860197\pi$
$271$		−	14.0000i		−	0.850439i	0.905090	−	0.425220i	$-0.139803\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.00000	+	6.00000i	0.482418	+	0.361814i
$276$		0			0
$277$	11.0000	+	11.0000i	0.660926	+	0.660926i	0.955598	−	0.294672i	$-0.0952105\pi$
$277$	11.0000	+	11.0000i	0.660926	+	0.660926i	−0.294672	+	0.955598i	$0.595211\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	7.00000	+	7.00000i	0.416107	+	0.416107i	0.883859	−	0.467753i	$-0.154936\pi$
$283$	7.00000	+	7.00000i	0.416107	+	0.416107i	−0.467753	+	0.883859i	$0.654936\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	30.0000	−	30.0000i	1.77084	−	1.77084i
$288$		0			0
$289$		−	15.0000i		−	0.882353i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−11.0000	+	11.0000i	−0.642627	+	0.642627i	−0.951200	−	0.308574i	$-0.900148\pi$
$293$	−11.0000	+	11.0000i	−0.642627	+	0.642627i	0.308574	+	0.951200i	$0.400148\pi$
$294$		0			0
$295$	12.0000	+	24.0000i	0.698667	+	1.39733i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−6.00000			−0.346989
$300$		0			0
$301$	−30.0000			−1.72917
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.00000	−	4.00000i	−0.114520	−	0.229039i
$306$		0			0
$307$	17.0000	−	17.0000i	0.970241	−	0.970241i	−0.0293286	−	0.999570i	$-0.509337\pi$
$307$	17.0000	−	17.0000i	0.970241	−	0.970241i	0.999570	+	0.0293286i	$0.00933691\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		−	18.0000i		−	1.02069i	−0.859971	−	0.510343i	$-0.829518\pi$
$311$		−	18.0000i		−	1.02069i	0.859971	−	0.510343i	$-0.170482\pi$
$312$		0			0
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	−0.405420	−	0.914130i	$-0.632875\pi$
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	0.914130	+	0.405420i	$0.132875\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	13.0000	+	13.0000i	0.730153	+	0.730153i	0.970650	−	0.240497i	$-0.0773105\pi$
$317$	13.0000	+	13.0000i	0.730153	+	0.730153i	−0.240497	+	0.970650i	$0.577310\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$	4.00000	+	4.00000i	0.222566	+	0.222566i
$324$		0			0
$325$	3.00000	+	21.0000i	0.166410	+	1.16487i
$326$		0			0
$327$		0			0
$328$		0			0
$329$			18.0000i			0.992372i
$330$		0			0
$331$			26.0000i			1.42909i	0.699590	+	0.714545i	$0.253366\pi$
$331$			26.0000i			1.42909i	−0.699590	+	0.714545i	$0.746634\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3.00000	−	1.00000i	−0.163908	−	0.0546358i
$336$		0			0
$337$	−15.0000	−	15.0000i	−0.817102	−	0.817102i	0.168585	−	0.985687i	$-0.446080\pi$
$337$	−15.0000	−	15.0000i	−0.817102	−	0.817102i	−0.985687	+	0.168585i	$0.946080\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	20.0000			1.08306
$342$		0			0
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−9.00000	+	9.00000i	−0.483145	+	0.483145i	−0.906135	−	0.422989i	$-0.860981\pi$
$347$	−9.00000	+	9.00000i	−0.483145	+	0.483145i	0.422989	+	0.906135i	$0.360981\pi$
$348$		0			0
$349$		−	8.00000i		−	0.428230i	−0.976808	−	0.214115i	$-0.931313\pi$
$349$		−	8.00000i		−	0.428230i	0.976808	−	0.214115i	$-0.0686868\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	15.0000	−	15.0000i	0.798369	−	0.798369i	−0.184469	−	0.982838i	$-0.559057\pi$
$353$	15.0000	−	15.0000i	0.798369	−	0.798369i	0.982838	+	0.184469i	$0.0590565\pi$
$354$		0			0
$355$	−4.00000	+	2.00000i	−0.212298	+	0.106149i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	32.0000			1.68890			0.844448	−	0.535638i	$-0.179929\pi$
$359$	32.0000			1.68890			0.844448	+	0.535638i	$0.179929\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.00000	−	1.00000i	−0.157027	−	0.0523424i
$366$		0			0
$367$	15.0000	−	15.0000i	0.782994	−	0.782994i	−0.197341	−	0.980335i	$-0.563231\pi$
$367$	15.0000	−	15.0000i	0.782994	−	0.782994i	0.980335	+	0.197341i	$0.0632307\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		−	30.0000i		−	1.55752i
$372$		0			0
$373$	−9.00000	+	9.00000i	−0.466002	+	0.466002i	−0.900617	−	0.434614i	$-0.856885\pi$
$373$	−9.00000	+	9.00000i	−0.466002	+	0.466002i	0.434614	+	0.900617i	$0.356885\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.00000	−	1.00000i	−0.0510976	−	0.0510976i	0.681096	−	0.732194i	$-0.261504\pi$
$383$	−1.00000	−	1.00000i	−0.0510976	−	0.0510976i	−0.732194	+	0.681096i	$0.761504\pi$
$384$		0			0
$385$	−6.00000	+	18.0000i	−0.305788	+	0.917365i
$386$		0			0
$387$		0			0
$388$		0			0
$389$			4.00000i			0.202808i	0.994845	+	0.101404i	$0.0323335\pi$
$389$			4.00000i			0.202808i	−0.994845	+	0.101404i	$0.967667\pi$
$390$		0			0
$391$			2.00000i			0.101144i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	8.00000	+	16.0000i	0.402524	+	0.805047i
$396$		0			0
$397$	15.0000	+	15.0000i	0.752828	+	0.752828i	0.975006	−	0.222178i	$-0.0713165\pi$
$397$	15.0000	+	15.0000i	0.752828	+	0.752828i	−0.222178	+	0.975006i	$0.571317\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	22.0000			1.09863			0.549314	−	0.835616i	$-0.314889\pi$
$401$	22.0000			1.09863			0.549314	+	0.835616i	$0.314889\pi$
$402$		0			0
$403$	30.0000	+	30.0000i	1.49441	+	1.49441i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.00000	+	2.00000i	−0.0991363	+	0.0991363i
$408$		0			0
$409$			20.0000i			0.988936i	0.869196	+	0.494468i	$0.164637\pi$
$409$			20.0000i			0.988936i	−0.869196	+	0.494468i	$0.835363\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−36.0000	+	36.0000i	−1.77144	+	1.77144i
$414$		0			0
$415$	5.00000	−	15.0000i	0.245440	−	0.736321i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	28.0000			1.36789			0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000			1.36789			0.683945	+	0.729534i	$0.260263\pi$
$420$		0			0
$421$	34.0000			1.65706			0.828529	−	0.559946i	$-0.189178\pi$
$421$	34.0000			1.65706			0.828529	+	0.559946i	$0.189178\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	7.00000	−	1.00000i	0.339550	−	0.0485071i
$426$		0			0
$427$	6.00000	−	6.00000i	0.290360	−	0.290360i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			30.0000i			1.44505i	0.691345	+	0.722525i	$0.257018\pi$
$431$			30.0000i			1.44505i	−0.691345	+	0.722525i	$0.742982\pi$
$432$		0			0
$433$	21.0000	−	21.0000i	1.00920	−	1.00920i	0.00923827	−	0.999957i	$-0.497059\pi$
$433$	21.0000	−	21.0000i	1.00920	−	1.00920i	0.999957	−	0.00923827i	$-0.00294067\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.00000	+	4.00000i	0.191346	+	0.191346i
$438$		0			0
$439$	−16.0000			−0.763638			−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000			−0.763638			−0.381819	+	0.924237i	$0.624702\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	25.0000	+	25.0000i	1.18779	+	1.18779i	0.977678	+	0.210108i	$0.0673814\pi$
$443$	25.0000	+	25.0000i	1.18779	+	1.18779i	0.210108	+	0.977678i	$0.432619\pi$
$444$		0			0
$445$	−32.0000	+	16.0000i	−1.51695	+	0.758473i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			12.0000i			0.566315i	0.959073	+	0.283158i	$0.0913819\pi$
$449$			12.0000i			0.566315i	−0.959073	+	0.283158i	$0.908618\pi$
$450$		0			0
$451$		−	20.0000i		−	0.941763i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−36.0000	+	18.0000i	−1.68771	+	0.843853i
$456$		0			0
$457$	9.00000	+	9.00000i	0.421002	+	0.421002i	0.885549	−	0.464546i	$-0.153783\pi$
$457$	9.00000	+	9.00000i	0.421002	+	0.421002i	−0.464546	+	0.885549i	$0.653783\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.00000			0.0931493			0.0465746	−	0.998915i	$-0.485169\pi$
$461$	2.00000			0.0931493			0.0465746	+	0.998915i	$0.485169\pi$
$462$		0			0
$463$	−11.0000	−	11.0000i	−0.511213	−	0.511213i	0.403685	−	0.914898i	$-0.367729\pi$
$463$	−11.0000	−	11.0000i	−0.511213	−	0.511213i	−0.914898	+	0.403685i	$0.867729\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−13.0000	+	13.0000i	−0.601568	+	0.601568i	−0.940729	−	0.339160i	$-0.889857\pi$
$467$	−13.0000	+	13.0000i	−0.601568	+	0.601568i	0.339160	+	0.940729i	$0.389857\pi$
$468$		0			0
$469$		−	6.00000i		−	0.277054i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10.0000	+	10.0000i	−0.459800	+	0.459800i
$474$		0			0
$475$	12.0000	−	16.0000i	0.550598	−	0.734130i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−40.0000			−1.82765			−0.913823	−	0.406112i	$-0.866884\pi$
$479$	−40.0000			−1.82765			−0.913823	+	0.406112i	$0.866884\pi$
$480$		0			0
$481$	−6.00000			−0.273576
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.00000	+	9.00000i	−0.136223	+	0.408669i
$486$		0			0
$487$	19.0000	−	19.0000i	0.860972	−	0.860972i	−0.130479	−	0.991451i	$-0.541651\pi$
$487$	19.0000	−	19.0000i	0.860972	−	0.860972i	0.991451	+	0.130479i	$0.0416515\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	10.0000i		−	0.451294i	−0.974209	−	0.225647i	$-0.927550\pi$
$491$		−	10.0000i		−	0.451294i	0.974209	−	0.225647i	$-0.0724495\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.00000	−	6.00000i	−0.269137	−	0.269137i
$498$		0			0
$499$	−28.0000			−1.25345			−0.626726	−	0.779240i	$-0.715605\pi$
$499$	−28.0000			−1.25345			−0.626726	+	0.779240i	$0.715605\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−17.0000	−	17.0000i	−0.757993	−	0.757993i	0.217964	−	0.975957i	$-0.430058\pi$
$503$	−17.0000	−	17.0000i	−0.757993	−	0.757993i	−0.975957	+	0.217964i	$0.930058\pi$
$504$		0			0
$505$	6.00000	+	12.0000i	0.266996	+	0.533993i
$506$		0			0
$507$		0			0
$508$		0			0
$509$		−	24.0000i		−	1.06378i	−0.846813	−	0.531891i	$-0.821482\pi$
$509$		−	24.0000i		−	1.06378i	0.846813	−	0.531891i	$-0.178518\pi$
$510$		0			0
$511$		−	6.00000i		−	0.265424i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	9.00000	−	27.0000i	0.396587	−	1.18976i
$516$		0			0
$517$	6.00000	+	6.00000i	0.263880	+	0.263880i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	14.0000			0.613351			0.306676	−	0.951814i	$-0.400783\pi$
$521$	14.0000			0.613351			0.306676	+	0.951814i	$0.400783\pi$
$522$		0			0
$523$	15.0000	+	15.0000i	0.655904	+	0.655904i	0.954408	−	0.298504i	$-0.0964877\pi$
$523$	15.0000	+	15.0000i	0.655904	+	0.655904i	−0.298504	+	0.954408i	$0.596488\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	10.0000	−	10.0000i	0.435607	−	0.435607i
$528$		0			0
$529$		−	21.0000i		−	0.913043i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	30.0000	−	30.0000i	1.29944	−	1.29944i
$534$		0			0
$535$	−9.00000	−	3.00000i	−0.389104	−	0.129701i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−22.0000			−0.947607
$540$		0			0
$541$	30.0000			1.28980			0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000			1.28980			0.644900	+	0.764267i	$0.276899\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−8.00000	+	4.00000i	−0.342682	+	0.171341i
$546$		0			0
$547$	−11.0000	+	11.0000i	−0.470326	+	0.470326i	−0.902020	−	0.431694i	$-0.857916\pi$
$547$	−11.0000	+	11.0000i	−0.470326	+	0.470326i	0.431694	+	0.902020i	$0.357916\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−24.0000	+	24.0000i	−1.02058	+	1.02058i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−27.0000	−	27.0000i	−1.14403	−	1.14403i	−0.987706	−	0.156320i	$-0.950037\pi$
$557$	−27.0000	−	27.0000i	−1.14403	−	1.14403i	−0.156320	−	0.987706i	$-0.549963\pi$
$558$		0			0
$559$	−30.0000			−1.26886
$560$		0			0
$561$		0			0
$562$		0			0
$563$	33.0000	+	33.0000i	1.39078	+	1.39078i	0.823571	+	0.567213i	$0.191978\pi$
$563$	33.0000	+	33.0000i	1.39078	+	1.39078i	0.567213	+	0.823571i	$0.308022\pi$
$564$		0			0
$565$	−9.00000	−	3.00000i	−0.378633	−	0.126211i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	12.0000i		−	0.503066i	−0.967849	−	0.251533i	$-0.919065\pi$
$569$		−	12.0000i		−	0.503066i	0.967849	−	0.251533i	$-0.0809347\pi$
$570$		0			0
$571$			34.0000i			1.42286i	0.702759	+	0.711428i	$0.251951\pi$
$571$			34.0000i			1.42286i	−0.702759	+	0.711428i	$0.748049\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	7.00000	−	1.00000i	0.291920	−	0.0417029i
$576$		0			0
$577$	−19.0000	−	19.0000i	−0.790980	−	0.790980i	0.190673	−	0.981654i	$-0.438933\pi$
$577$	−19.0000	−	19.0000i	−0.790980	−	0.790980i	−0.981654	+	0.190673i	$0.938933\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	30.0000			1.24461
$582$		0			0
$583$	−10.0000	−	10.0000i	−0.414158	−	0.414158i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	23.0000	−	23.0000i	0.949312	−	0.949312i	−0.0494643	−	0.998776i	$-0.515751\pi$
$587$	23.0000	−	23.0000i	0.949312	−	0.949312i	0.998776	+	0.0494643i	$0.0157514\pi$
$588$		0			0
$589$		−	40.0000i		−	1.64817i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	7.00000	−	7.00000i	0.287456	−	0.287456i	−0.548618	−	0.836073i	$-0.684846\pi$
$593$	7.00000	−	7.00000i	0.287456	−	0.287456i	0.836073	+	0.548618i	$0.184846\pi$
$594$		0			0
$595$	6.00000	+	12.0000i	0.245976	+	0.491952i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−7.00000	−	14.0000i	−0.284590	−	0.569181i
$606$		0			0
$607$	−5.00000	+	5.00000i	−0.202944	+	0.202944i	−0.801260	−	0.598316i	$-0.795837\pi$
$607$	−5.00000	+	5.00000i	−0.202944	+	0.202944i	0.598316	+	0.801260i	$0.295837\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			18.0000i			0.728202i
$612$		0			0
$613$	15.0000	−	15.0000i	0.605844	−	0.605844i	−0.336013	−	0.941857i	$-0.609079\pi$
$613$	15.0000	−	15.0000i	0.605844	−	0.605844i	0.941857	+	0.336013i	$0.109079\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13.0000	−	13.0000i	−0.523360	−	0.523360i	0.395224	−	0.918585i	$-0.370667\pi$
$617$	−13.0000	−	13.0000i	−0.523360	−	0.523360i	−0.918585	+	0.395224i	$0.870667\pi$
$618$		0			0
$619$	12.0000			0.482321			0.241160	−	0.970485i	$-0.422472\pi$
$619$	12.0000			0.482321			0.241160	+	0.970485i	$0.422472\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−48.0000	−	48.0000i	−1.92308	−	1.92308i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			2.00000i			0.0797452i
$630$		0			0
$631$		−	14.0000i		−	0.557331i	−0.960388	−	0.278666i	$-0.910108\pi$
$631$		−	14.0000i		−	0.557331i	0.960388	−	0.278666i	$-0.0898921\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−21.0000	−	7.00000i	−0.833360	−	0.277787i
$636$		0			0
$637$	−33.0000	−	33.0000i	−1.30751	−	1.30751i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−30.0000			−1.18493			−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000			−1.18493			−0.592464	+	0.805597i	$0.701845\pi$
$642$		0			0
$643$	27.0000	+	27.0000i	1.06478	+	1.06478i	0.997751	+	0.0670247i	$0.0213506\pi$
$643$	27.0000	+	27.0000i	1.06478	+	1.06478i	0.0670247	+	0.997751i	$0.478649\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	29.0000	−	29.0000i	1.14011	−	1.14011i	0.151678	−	0.988430i	$-0.451532\pi$
$647$	29.0000	−	29.0000i	1.14011	−	1.14011i	0.988430	−	0.151678i	$-0.0484676\pi$
$648$		0			0
$649$			24.0000i			0.942082i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.00000	−	1.00000i	0.0391330	−	0.0391330i	−0.687270	−	0.726403i	$-0.741191\pi$
$653$	1.00000	−	1.00000i	0.0391330	−	0.0391330i	0.726403	+	0.687270i	$0.241191\pi$
$654$		0			0
$655$	−20.0000	+	10.0000i	−0.781465	+	0.390732i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$	−30.0000			−1.16686			−0.583432	−	0.812162i	$-0.698291\pi$
$661$	−30.0000			−1.16686			−0.583432	+	0.812162i	$0.698291\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	36.0000	+	12.0000i	1.39602	+	0.465340i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	4.00000i		−	0.154418i
$672$		0			0
$673$	−3.00000	+	3.00000i	−0.115642	+	0.115642i	−0.762560	−	0.646918i	$-0.776058\pi$
$673$	−3.00000	+	3.00000i	−0.115642	+	0.115642i	0.646918	+	0.762560i	$0.276058\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.00000	−	3.00000i	−0.115299	−	0.115299i	0.647103	−	0.762402i	$-0.275980\pi$
$677$	−3.00000	−	3.00000i	−0.115299	−	0.115299i	−0.762402	+	0.647103i	$0.775980\pi$
$678$		0			0
$679$	−18.0000			−0.690777
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−11.0000	−	11.0000i	−0.420903	−	0.420903i	0.464611	−	0.885515i	$-0.346194\pi$
$683$	−11.0000	−	11.0000i	−0.420903	−	0.420903i	−0.885515	+	0.464611i	$0.846194\pi$
$684$		0			0
$685$	11.0000	−	33.0000i	0.420288	−	1.26087i
$686$		0			0
$687$		0			0
$688$		0			0
$689$		−	30.0000i		−	1.14291i
$690$		0			0
$691$		−	14.0000i		−	0.532585i	−0.963892	−	0.266293i	$-0.914201\pi$
$691$		−	14.0000i		−	0.532585i	0.963892	−	0.266293i	$-0.0857987\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	12.0000	+	24.0000i	0.455186	+	0.910372i
$696$		0			0
$697$	−10.0000	−	10.0000i	−0.378777	−	0.378777i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−34.0000			−1.28416			−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000			−1.28416			−0.642081	+	0.766637i	$0.721929\pi$
$702$		0			0
$703$	4.00000	+	4.00000i	0.150863	+	0.150863i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−18.0000	+	18.0000i	−0.676960	+	0.676960i
$708$		0			0
$709$			48.0000i			1.80268i	0.433114	+	0.901339i	$0.357415\pi$
$709$			48.0000i			1.80268i	−0.433114	+	0.901339i	$0.642585\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	10.0000	−	10.0000i	0.374503	−	0.374503i
$714$		0			0
$715$	−6.00000	+	18.0000i	−0.224387	+	0.673162i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	16.0000			0.596699			0.298350	−	0.954457i	$-0.403564\pi$
$719$	16.0000			0.596699			0.298350	+	0.954457i	$0.403564\pi$
$720$		0			0
$721$	54.0000			2.01107
$722$		0			0
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	3.00000	−	3.00000i	0.111264	−	0.111264i	−0.649283	−	0.760547i	$-0.724931\pi$
$727$	3.00000	−	3.00000i	0.111264	−	0.111264i	0.760547	+	0.649283i	$0.224931\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$			10.0000i			0.369863i
$732$		0			0
$733$	27.0000	−	27.0000i	0.997268	−	0.997268i	−0.00272852	−	0.999996i	$-0.500869\pi$
$733$	27.0000	−	27.0000i	0.997268	−	0.997268i	0.999996	+	0.00272852i	$0.000868517\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.00000	−	2.00000i	−0.0736709	−	0.0736709i
$738$		0			0
$739$	28.0000			1.03000			0.514998	−	0.857191i	$-0.327793\pi$
$739$	28.0000			1.03000			0.514998	+	0.857191i	$0.327793\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−21.0000	−	21.0000i	−0.770415	−	0.770415i	0.207764	−	0.978179i	$-0.433381\pi$
$743$	−21.0000	−	21.0000i	−0.770415	−	0.770415i	−0.978179	+	0.207764i	$0.933381\pi$
$744$		0			0
$745$	8.00000	−	4.00000i	0.293097	−	0.146549i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	18.0000i		−	0.657706i
$750$		0			0
$751$			2.00000i			0.0729810i	0.999334	+	0.0364905i	$0.0116179\pi$
$751$			2.00000i			0.0729810i	−0.999334	+	0.0364905i	$0.988382\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−12.0000	+	6.00000i	−0.436725	+	0.218362i
$756$		0			0
$757$	19.0000	+	19.0000i	0.690567	+	0.690567i	0.962357	−	0.271790i	$-0.0876156\pi$
$757$	19.0000	+	19.0000i	0.690567	+	0.690567i	−0.271790	+	0.962357i	$0.587616\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−18.0000			−0.652499			−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000			−0.652499			−0.326250	+	0.945284i	$0.605785\pi$
$762$		0			0
$763$	−12.0000	−	12.0000i	−0.434429	−	0.434429i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−36.0000	+	36.0000i	−1.29988	+	1.29988i
$768$		0			0
$769$		−	8.00000i		−	0.288487i	−0.989542	−	0.144244i	$-0.953925\pi$
$769$		−	8.00000i		−	0.288487i	0.989542	−	0.144244i	$-0.0460749\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	17.0000	−	17.0000i	0.611448	−	0.611448i	−0.331876	−	0.943323i	$-0.607681\pi$
$773$	17.0000	−	17.0000i	0.611448	−	0.611448i	0.943323	+	0.331876i	$0.107681\pi$
$774$		0			0
$775$	−40.0000	−	30.0000i	−1.43684	−	1.07763i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−40.0000			−1.43315
$780$		0			0
$781$	−4.00000			−0.143131
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.00000	+	3.00000i	−0.0356915	+	0.107075i
$786$		0			0
$787$	−31.0000	+	31.0000i	−1.10503	+	1.10503i	−0.111237	+	0.993794i	$0.535481\pi$
$787$	−31.0000	+	31.0000i	−1.10503	+	1.10503i	−0.993794	+	0.111237i	$0.964519\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	18.0000i		−	0.640006i
$792$		0			0
$793$	6.00000	−	6.00000i	0.213066	−	0.213066i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	37.0000	+	37.0000i	1.31061	+	1.31061i	0.920967	+	0.389640i	$0.127401\pi$
$797$	37.0000	+	37.0000i	1.31061	+	1.31061i	0.389640	+	0.920967i	$0.372599\pi$
$798$		0			0
$799$	6.00000			0.212265
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.00000	−	2.00000i	−0.0705785	−	0.0705785i
$804$		0			0
$805$	6.00000	+	12.0000i	0.211472	+	0.422944i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	16.0000i		−	0.562530i	−0.959630	−	0.281265i	$-0.909246\pi$
$809$		−	16.0000i		−	0.562530i	0.959630	−	0.281265i	$-0.0907540\pi$
$810$		0			0
$811$		−	54.0000i		−	1.89620i	−0.317978	−	0.948098i	$-0.603004\pi$
$811$		−	54.0000i		−	1.89620i	0.317978	−	0.948098i	$-0.396996\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1.00000	+	3.00000i	−0.0350285	+	0.105085i
$816$		0			0
$817$	20.0000	+	20.0000i	0.699711	+	0.699711i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−10.0000			−0.349002			−0.174501	−	0.984657i	$-0.555831\pi$
$821$	−10.0000			−0.349002			−0.174501	+	0.984657i	$0.555831\pi$
$822$		0			0
$823$	−7.00000	−	7.00000i	−0.244005	−	0.244005i	0.574500	−	0.818505i	$-0.305197\pi$
$823$	−7.00000	−	7.00000i	−0.244005	−	0.244005i	−0.818505	+	0.574500i	$0.805197\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−25.0000	+	25.0000i	−0.869335	+	0.869335i	−0.992399	−	0.123064i	$-0.960728\pi$
$827$	−25.0000	+	25.0000i	−0.869335	+	0.869335i	0.123064	+	0.992399i	$0.460728\pi$
$828$		0			0
$829$			20.0000i			0.694629i	0.937749	+	0.347314i	$0.112906\pi$
$829$			20.0000i			0.694629i	−0.937749	+	0.347314i	$0.887094\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−11.0000	+	11.0000i	−0.381127	+	0.381127i
$834$		0			0
$835$	−3.00000	−	1.00000i	−0.103819	−	0.0346064i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−10.0000	+	5.00000i	−0.344010	+	0.172005i
$846$		0			0
$847$	21.0000	−	21.0000i	0.721569	−	0.721569i
$848$		0			0
$849$		0			0
$850$		0			0
$851$			2.00000i			0.0685591i
$852$		0			0
$853$	−9.00000	+	9.00000i	−0.308154	+	0.308154i	−0.844193	−	0.536039i	$-0.819920\pi$
$853$	−9.00000	+	9.00000i	−0.308154	+	0.308154i	0.536039	+	0.844193i	$0.319920\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	35.0000	+	35.0000i	1.19558	+	1.19558i	0.975477	+	0.220100i	$0.0706383\pi$
$857$	35.0000	+	35.0000i	1.19558	+	1.19558i	0.220100	+	0.975477i	$0.429362\pi$
$858$		0			0
$859$	28.0000			0.955348			0.477674	−	0.878537i	$-0.341480\pi$
$859$	28.0000			0.955348			0.477674	+	0.878537i	$0.341480\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−13.0000	−	13.0000i	−0.442525	−	0.442525i	0.450335	−	0.892860i	$-0.351305\pi$
$863$	−13.0000	−	13.0000i	−0.442525	−	0.442525i	−0.892860	+	0.450335i	$0.851305\pi$
$864$		0			0
$865$	−15.0000	−	5.00000i	−0.510015	−	0.170005i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			16.0000i			0.542763i
$870$		0			0
$871$		−	6.00000i		−	0.203302i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	39.0000	−	27.0000i	1.31844	−	0.912767i
$876$		0			0
$877$	7.00000	+	7.00000i	0.236373	+	0.236373i	0.815347	−	0.578973i	$-0.196546\pi$
$877$	7.00000	+	7.00000i	0.236373	+	0.236373i	−0.578973	+	0.815347i	$0.696546\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$		0			0
$883$	−33.0000	−	33.0000i	−1.11054	−	1.11054i	−0.993078	−	0.117461i	$-0.962525\pi$
$883$	−33.0000	−	33.0000i	−1.11054	−	1.11054i	−0.117461	−	0.993078i	$-0.537475\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.00000	−	5.00000i	0.167884	−	0.167884i	−0.618165	−	0.786048i	$-0.712124\pi$
$887$	5.00000	−	5.00000i	0.167884	−	0.167884i	0.786048	+	0.618165i	$0.212124\pi$
$888$		0			0
$889$		−	42.0000i		−	1.40863i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	12.0000	−	12.0000i	0.401565	−	0.401565i
$894$		0			0
$895$	12.0000	+	24.0000i	0.401116	+	0.802232i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−10.0000			−0.333148
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−22.0000	−	44.0000i	−0.731305	−	1.46261i
$906$		0			0
$907$	−27.0000	+	27.0000i	−0.896520	+	0.896520i	−0.995127	−	0.0986062i	$-0.968562\pi$
$907$	−27.0000	+	27.0000i	−0.896520	+	0.896520i	0.0986062	+	0.995127i	$0.468562\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			6.00000i			0.198789i	0.995048	+	0.0993944i	$0.0316906\pi$
$911$			6.00000i			0.198789i	−0.995048	+	0.0993944i	$0.968309\pi$
$912$		0			0
$913$	10.0000	−	10.0000i	0.330952	−	0.330952i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−30.0000	−	30.0000i	−0.990687	−	0.990687i
$918$		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
$923$	−6.00000	−	6.00000i	−0.197492	−	0.197492i
$924$		0			0
$925$	7.00000	−	1.00000i	0.230159	−	0.0328798i
$926$		0			0
$927$		0			0
$928$		0			0
$929$		−	28.0000i		−	0.918650i	−0.888268	−	0.459325i	$-0.848091\pi$
$929$		−	28.0000i		−	0.918650i	0.888268	−	0.459325i	$-0.151909\pi$
$930$		0			0
$931$			44.0000i			1.44204i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	6.00000	+	2.00000i	0.196221	+	0.0654070i
$936$		0			0
$937$	21.0000	+	21.0000i	0.686040	+	0.686040i	0.961354	−	0.275314i	$-0.0887819\pi$
$937$	21.0000	+	21.0000i	0.686040	+	0.686040i	−0.275314	+	0.961354i	$0.588782\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	34.0000			1.10837			0.554184	−	0.832394i	$-0.313030\pi$
$941$	34.0000			1.10837			0.554184	+	0.832394i	$0.313030\pi$
$942$		0			0
$943$	−10.0000	−	10.0000i	−0.325645	−	0.325645i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	31.0000	−	31.0000i	1.00736	−	1.00736i	0.00739197	−	0.999973i	$-0.497647\pi$
$947$	31.0000	−	31.0000i	1.00736	−	1.00736i	0.999973	−	0.00739197i	$-0.00235296\pi$
$948$		0			0
$949$		−	6.00000i		−	0.194768i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	31.0000	−	31.0000i	1.00419	−	1.00419i	0.00419731	−	0.999991i	$-0.498664\pi$
$953$	31.0000	−	31.0000i	1.00419	−	1.00419i	0.999991	−	0.00419731i	$-0.00133605\pi$
$954$		0			0
$955$	28.0000	−	14.0000i	0.906059	−	0.453029i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	66.0000			2.13125
$960$		0			0
$961$	−69.0000			−2.22581
$962$		0			0
$963$		0			0
$964$		0			0
$965$	45.0000	+	15.0000i	1.44860	+	0.482867i
$966$		0			0
$967$	−1.00000	+	1.00000i	−0.0321578	+	0.0321578i	−0.723003	−	0.690845i	$-0.757239\pi$
$967$	−1.00000	+	1.00000i	−0.0321578	+	0.0321578i	0.690845	+	0.723003i	$0.257239\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	2.00000i		−	0.0641831i	−0.999485	−	0.0320915i	$-0.989783\pi$
$971$		−	2.00000i		−	0.0641831i	0.999485	−	0.0320915i	$-0.0102168\pi$
$972$		0			0
$973$	−36.0000	+	36.0000i	−1.15411	+	1.15411i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−21.0000	−	21.0000i	−0.671850	−	0.671850i	0.286293	−	0.958142i	$-0.407577\pi$
$977$	−21.0000	−	21.0000i	−0.671850	−	0.671850i	−0.958142	+	0.286293i	$0.907577\pi$
$978$		0			0
$979$	−32.0000			−1.02272
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−5.00000	−	5.00000i	−0.159475	−	0.159475i	0.622859	−	0.782334i	$-0.285971\pi$
$983$	−5.00000	−	5.00000i	−0.159475	−	0.159475i	−0.782334	+	0.622859i	$0.785971\pi$
$984$		0			0
$985$	13.0000	−	39.0000i	0.414214	−	1.24264i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			10.0000i			0.317982i
$990$		0			0
$991$			10.0000i			0.317660i	0.987306	+	0.158830i	$0.0507723\pi$
$991$			10.0000i			0.317660i	−0.987306	+	0.158830i	$0.949228\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−16.0000	−	32.0000i	−0.507234	−	1.01447i
$996$		0			0
$997$	−17.0000	−	17.0000i	−0.538395	−	0.538395i	0.384662	−	0.923057i	$-0.374318\pi$
$997$	−17.0000	−	17.0000i	−0.538395	−	0.538395i	−0.923057	+	0.384662i	$0.874318\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1440.2.x.f.127.1		2
3.2	odd	2		160.2.n.c.127.1	yes	2
4.3	odd	2		1440.2.x.a.127.1		2
5.3	odd	4		1440.2.x.a.703.1		2
12.11	even	2		160.2.n.d.127.1	yes	2
15.2	even	4		800.2.n.e.543.1		2
15.8	even	4		160.2.n.d.63.1	yes	2
15.14	odd	2		800.2.n.f.607.1		2
20.3	even	4	inner	1440.2.x.f.703.1		2
24.5	odd	2		320.2.n.g.127.1		2
24.11	even	2		320.2.n.b.127.1		2
48.5	odd	4		1280.2.o.c.127.1		2
48.11	even	4		1280.2.o.l.127.1		2
48.29	odd	4		1280.2.o.m.127.1		2
48.35	even	4		1280.2.o.f.127.1		2
60.23	odd	4		160.2.n.c.63.1	✓	2
60.47	odd	4		800.2.n.f.543.1		2
60.59	even	2		800.2.n.e.607.1		2
120.29	odd	2		1600.2.n.c.1407.1		2
120.53	even	4		320.2.n.b.63.1		2
120.59	even	2		1600.2.n.m.1407.1		2
120.77	even	4		1600.2.n.m.1343.1		2
120.83	odd	4		320.2.n.g.63.1		2
120.107	odd	4		1600.2.n.c.1343.1		2
240.53	even	4		1280.2.o.f.383.1		2
240.83	odd	4		1280.2.o.c.383.1		2
240.173	even	4		1280.2.o.l.383.1		2
240.203	odd	4		1280.2.o.m.383.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.n.c.63.1	✓	2	60.23	odd	4
160.2.n.c.127.1	yes	2	3.2	odd	2
160.2.n.d.63.1	yes	2	15.8	even	4
160.2.n.d.127.1	yes	2	12.11	even	2
320.2.n.b.63.1		2	120.53	even	4
320.2.n.b.127.1		2	24.11	even	2
320.2.n.g.63.1		2	120.83	odd	4
320.2.n.g.127.1		2	24.5	odd	2
800.2.n.e.543.1		2	15.2	even	4
800.2.n.e.607.1		2	60.59	even	2
800.2.n.f.543.1		2	60.47	odd	4
800.2.n.f.607.1		2	15.14	odd	2
1280.2.o.c.127.1		2	48.5	odd	4
1280.2.o.c.383.1		2	240.83	odd	4
1280.2.o.f.127.1		2	48.35	even	4
1280.2.o.f.383.1		2	240.53	even	4
1280.2.o.l.127.1		2	48.11	even	4
1280.2.o.l.383.1		2	240.173	even	4
1280.2.o.m.127.1		2	48.29	odd	4
1280.2.o.m.383.1		2	240.203	odd	4
1440.2.x.a.127.1		2	4.3	odd	2
1440.2.x.a.703.1		2	5.3	odd	4
1440.2.x.f.127.1		2	1.1	even	1	trivial
1440.2.x.f.703.1		2	20.3	even	4	inner
1600.2.n.c.1343.1		2	120.107	odd	4
1600.2.n.c.1407.1		2	120.29	odd	2
1600.2.n.m.1343.1		2	120.77	even	4
1600.2.n.m.1407.1		2	120.59	even	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:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 2.00000i) q^{5} +(3.00000 - 3.00000i) q^{7} +O(q^{10})\)	\(q+(-1.00000 - 2.00000i) q^{5} +(3.00000 - 3.00000i) q^{7} -2.00000i q^{11} +(3.00000 - 3.00000i) q^{13} +(-1.00000 - 1.00000i) q^{17} -4.00000 q^{19} +(-1.00000 - 1.00000i) q^{23} +(-3.00000 + 4.00000i) q^{25} +10.0000i q^{31} +(-9.00000 - 3.00000i) q^{35} +(-1.00000 - 1.00000i) q^{37} +10.0000 q^{41} +(-5.00000 - 5.00000i) q^{43} +(-3.00000 + 3.00000i) q^{47} -11.0000i q^{49} +(5.00000 - 5.00000i) q^{53} +(-4.00000 + 2.00000i) q^{55} -12.0000 q^{59} +2.00000 q^{61} +(-9.00000 - 3.00000i) q^{65} +(1.00000 - 1.00000i) q^{67} -2.00000i q^{71} +(1.00000 - 1.00000i) q^{73} +(-6.00000 - 6.00000i) q^{77} -8.00000 q^{79} +(5.00000 + 5.00000i) q^{83} +(-1.00000 + 3.00000i) q^{85} -16.0000i q^{89} -18.0000i q^{91} +(4.00000 + 8.00000i) q^{95} +(-3.00000 - 3.00000i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{5} + 6 q^{7}+O(q^{10}) \) 2 * q - 2 * q^5 + 6 * q^7	\( 2 q - 2 q^{5} + 6 q^{7} + 6 q^{13} - 2 q^{17} - 8 q^{19} - 2 q^{23} - 6 q^{25} - 18 q^{35} - 2 q^{37} + 20 q^{41} - 10 q^{43} - 6 q^{47} + 10 q^{53} - 8 q^{55} - 24 q^{59} + 4 q^{61} - 18 q^{65} + 2 q^{67} + 2 q^{73} - 12 q^{77} - 16 q^{79} + 10 q^{83} - 2 q^{85} + 8 q^{95} - 6 q^{97}+O(q^{100}) \) 2 * q - 2 * q^5 + 6 * q^7 + 6 * q^13 - 2 * q^17 - 8 * q^19 - 2 * q^23 - 6 * q^25 - 18 * q^35 - 2 * q^37 + 20 * q^41 - 10 * q^43 - 6 * q^47 + 10 * q^53 - 8 * q^55 - 24 * q^59 + 4 * q^61 - 18 * q^65 + 2 * q^67 + 2 * q^73 - 12 * q^77 - 16 * q^79 + 10 * q^83 - 2 * q^85 + 8 * q^95 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

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