LMFDB - Embedded newform 1296.2.i.d.865.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1296.433");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.3486121020$
Analytic rank:	$1$
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 324)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			865.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1296.865
Dual form			1296.2.i.d.433.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 2.59808i) q^{5} +(1.00000 - 1.73205i) q^{7} +O(q^{10})$	$q+(-1.50000 - 2.59808i) q^{5} +(1.00000 - 1.73205i) q^{7} +(-3.00000 + 5.19615i) q^{11} +(-2.50000 - 4.33013i) q^{13} -3.00000 q^{17} -2.00000 q^{19} +(3.00000 + 5.19615i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(-1.50000 + 2.59808i) q^{29} +(-2.00000 - 3.46410i) q^{31} -6.00000 q^{35} +5.00000 q^{37} +(3.00000 + 5.19615i) q^{41} +(-5.00000 + 8.66025i) q^{43} +(1.50000 + 2.59808i) q^{49} -6.00000 q^{53} +18.0000 q^{55} +(-6.00000 - 10.3923i) q^{59} +(-2.50000 + 4.33013i) q^{61} +(-7.50000 + 12.9904i) q^{65} +(1.00000 + 1.73205i) q^{67} -6.00000 q^{71} -1.00000 q^{73} +(6.00000 + 10.3923i) q^{77} +(-5.00000 + 8.66025i) q^{79} +(4.50000 + 7.79423i) q^{85} -3.00000 q^{89} -10.0000 q^{91} +(3.00000 + 5.19615i) q^{95} +(5.00000 - 8.66025i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{5} + 2 q^{7}+O(q^{10}) $ 2 * q - 3 * q^5 + 2 * q^7	$ 2 q - 3 q^{5} + 2 q^{7} - 6 q^{11} - 5 q^{13} - 6 q^{17} - 4 q^{19} + 6 q^{23} - 4 q^{25} - 3 q^{29} - 4 q^{31} - 12 q^{35} + 10 q^{37} + 6 q^{41} - 10 q^{43} + 3 q^{49} - 12 q^{53} + 36 q^{55} - 12 q^{59} - 5 q^{61} - 15 q^{65} + 2 q^{67} - 12 q^{71} - 2 q^{73} + 12 q^{77} - 10 q^{79} + 9 q^{85} - 6 q^{89} - 20 q^{91} + 6 q^{95} + 10 q^{97}+O(q^{100}) $ 2 * q - 3 * q^5 + 2 * q^7 - 6 * q^11 - 5 * q^13 - 6 * q^17 - 4 * q^19 + 6 * q^23 - 4 * q^25 - 3 * q^29 - 4 * q^31 - 12 * q^35 + 10 * q^37 + 6 * q^41 - 10 * q^43 + 3 * q^49 - 12 * q^53 + 36 * q^55 - 12 * q^59 - 5 * q^61 - 15 * q^65 + 2 * q^67 - 12 * q^71 - 2 * q^73 + 12 * q^77 - 10 * q^79 + 9 * q^85 - 6 * q^89 - 20 * q^91 + 6 * q^95 + 10 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$1135$	$1217$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	−0.977672	−	0.210138i	$-0.932609\pi$
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	0.306851	−	0.951757i	$-0.400725\pi$
$6$		0			0
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	−0.612801	−	0.790237i	$-0.709957\pi$
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	0.990766	+	0.135583i	$0.0432908\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.0829925	+	0.996550i	$0.526448\pi$
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.821541	+	0.570149i	$0.806886\pi$
$12$		0			0
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	0.277350	−	0.960769i	$-0.410544\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$		0			0
$19$	−2.00000			−0.458831			−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000			−0.458831			−0.229416	+	0.973329i	$0.573682\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.00000			−1.01419
$36$		0			0
$37$	5.00000			0.821995			0.410997	−	0.911636i	$-0.365181\pi$
$37$	5.00000			0.821995			0.410997	+	0.911636i	$0.365181\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	0.999353	−	0.0359748i	$-0.0114536\pi$
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	−0.530831	+	0.847477i	$0.678120\pi$
$42$		0			0
$43$	−5.00000	+	8.66025i	−0.762493	+	1.32068i	0.179069	+	0.983836i	$0.442691\pi$
$43$	−5.00000	+	8.66025i	−0.762493	+	1.32068i	−0.941562	+	0.336840i	$0.890642\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	18.0000			2.42712
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	−0.931282	−	0.364299i	$-0.881308\pi$
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	0.150148	−	0.988663i	$-0.452025\pi$
$60$		0			0
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	−0.980507	−	0.196485i	$-0.937047\pi$
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	0.660415	+	0.750901i	$0.270381\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−7.50000	+	12.9904i	−0.930261	+	1.61126i
$66$		0			0
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	−1.00000			−0.117041			−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000			−0.117041			−0.0585206	+	0.998286i	$0.518638\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.00000	+	10.3923i	0.683763	+	1.18431i
$78$		0			0
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	0.434730	+	0.900561i	$0.356844\pi$
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	−0.997274	+	0.0737937i	$0.976489\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$83$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$84$		0			0
$85$	4.50000	+	7.79423i	0.488094	+	0.845403i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$		0			0
$91$	−10.0000			−1.04828
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.00000	+	5.19615i	0.307794	+	0.533114i
$96$		0			0
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	−0.492287	−	0.870433i	$-0.663839\pi$
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	0.999961	−	0.00888289i	$-0.00282755\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$		0			0
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	−0.927030	−	0.374987i	$-0.877647\pi$
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	0.138767	−	0.990325i	$-0.455686\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$		0			0
$109$	−7.00000			−0.670478			−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000			−0.670478			−0.335239	+	0.942133i	$0.608817\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.50000	−	7.79423i	−0.423324	−	0.733219i	0.572938	−	0.819599i	$-0.305804\pi$
$113$	−4.50000	−	7.79423i	−0.423324	−	0.733219i	−0.996262	+	0.0863794i	$0.972470\pi$
$114$		0			0
$115$	9.00000	−	15.5885i	0.839254	−	1.45363i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.00000	+	5.19615i	−0.275010	+	0.476331i
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.00000			−0.268328
$126$		0			0
$127$	−2.00000			−0.177471			−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000			−0.177471			−0.0887357	+	0.996055i	$0.528283\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	0.704692	−	0.709514i	$-0.251085\pi$
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	−0.966803	+	0.255524i	$0.917752\pi$
$132$		0			0
$133$	−2.00000	+	3.46410i	−0.173422	+	0.300376i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.50000	−	12.9904i	0.640768	−	1.10984i	−0.344493	−	0.938789i	$-0.611949\pi$
$137$	7.50000	−	12.9904i	0.640768	−	1.10984i	0.985262	−	0.171054i	$-0.0547174\pi$
$138$		0			0
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	0.984297	−	0.176522i	$-0.0564848\pi$
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	−0.645021	+	0.764165i	$0.723151\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	30.0000			2.50873
$144$		0			0
$145$	9.00000			0.747409
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.50000	−	12.9904i	−0.614424	−	1.06421i	−0.990485	−	0.137619i	$-0.956055\pi$
$149$	−7.50000	−	12.9904i	−0.614424	−	1.06421i	0.376061	−	0.926595i	$-0.377278\pi$
$150$		0			0
$151$	−2.00000	+	3.46410i	−0.162758	+	0.281905i	−0.935857	−	0.352381i	$-0.885372\pi$
$151$	−2.00000	+	3.46410i	−0.162758	+	0.281905i	0.773099	+	0.634285i	$0.218706\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.00000	+	10.3923i	−0.481932	+	0.834730i
$156$		0			0
$157$	−2.50000	−	4.33013i	−0.199522	−	0.345582i	0.748852	−	0.662738i	$-0.230606\pi$
$157$	−2.50000	−	4.33013i	−0.199522	−	0.345582i	−0.948373	+	0.317156i	$0.897272\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	12.0000			0.945732
$162$		0			0
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	0.969693	+	0.244328i	$0.0785675\pi$
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	−0.273252	+	0.961943i	$0.588099\pi$
$168$		0			0
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.50000	−	7.79423i	0.342129	−	0.592584i	−0.642699	−	0.766119i	$-0.722185\pi$
$173$	4.50000	−	7.79423i	0.342129	−	0.592584i	0.984828	+	0.173534i	$0.0555188\pi$
$174$		0			0
$175$	4.00000	+	6.92820i	0.302372	+	0.523723i
$176$		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
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−7.50000	−	12.9904i	−0.551411	−	0.955072i
$186$		0			0
$187$	9.00000	−	15.5885i	0.658145	−	1.13994i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	−0.736839	−	0.676068i	$-0.763683\pi$
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	0.953912	+	0.300088i	$0.0970159\pi$
$192$		0			0
$193$	12.5000	+	21.6506i	0.899770	+	1.55845i	0.827788	+	0.561041i	$0.189599\pi$
$193$	12.5000	+	21.6506i	0.899770	+	1.55845i	0.0719816	+	0.997406i	$0.477068\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	15.0000			1.06871			0.534353	−	0.845262i	$-0.320555\pi$
$197$	15.0000			1.06871			0.534353	+	0.845262i	$0.320555\pi$
$198$		0			0
$199$	−20.0000			−1.41776			−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000			−1.41776			−0.708881	+	0.705328i	$0.750800\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.00000	+	5.19615i	0.210559	+	0.364698i
$204$		0			0
$205$	9.00000	−	15.5885i	0.628587	−	1.08875i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.00000	−	10.3923i	0.415029	−	0.718851i
$210$		0			0
$211$	7.00000	+	12.1244i	0.481900	+	0.834675i	0.999784	−	0.0207756i	$-0.00661356\pi$
$211$	7.00000	+	12.1244i	0.481900	+	0.834675i	−0.517884	+	0.855451i	$0.673280\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	30.0000			2.04598
$216$		0			0
$217$	−8.00000			−0.543075
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.50000	+	12.9904i	0.504505	+	0.873828i
$222$		0			0
$223$	−5.00000	+	8.66025i	−0.334825	+	0.579934i	−0.983451	−	0.181173i	$-0.942010\pi$
$223$	−5.00000	+	8.66025i	−0.334825	+	0.579934i	0.648626	+	0.761107i	$0.275344\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	−0.395860	−	0.918311i	$-0.629553\pi$
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	0.993210	−	0.116331i	$-0.0371134\pi$
$228$		0			0
$229$	−2.50000	−	4.33013i	−0.165205	−	0.286143i	0.771523	−	0.636201i	$-0.219495\pi$
$229$	−2.50000	−	4.33013i	−0.165205	−	0.286143i	−0.936728	+	0.350058i	$0.886162\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−15.0000			−0.982683			−0.491341	−	0.870967i	$-0.663493\pi$
$233$	−15.0000			−0.982683			−0.491341	+	0.870967i	$0.663493\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$239$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$240$		0			0
$241$	−5.50000	+	9.52628i	−0.354286	+	0.613642i	−0.986996	−	0.160748i	$-0.948609\pi$
$241$	−5.50000	+	9.52628i	−0.354286	+	0.613642i	0.632709	+	0.774389i	$0.281943\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	4.50000	−	7.79423i	0.287494	−	0.497955i
$246$		0			0
$247$	5.00000	+	8.66025i	0.318142	+	0.551039i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−30.0000			−1.89358			−0.946792	−	0.321847i	$-0.895696\pi$
$251$	−30.0000			−1.89358			−0.946792	+	0.321847i	$0.895696\pi$
$252$		0			0
$253$	−36.0000			−2.26330
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.5000	+	23.3827i	0.842107	+	1.45857i	0.888110	+	0.459631i	$0.152018\pi$
$257$	13.5000	+	23.3827i	0.842107	+	1.45857i	−0.0460033	+	0.998941i	$0.514648\pi$
$258$		0			0
$259$	5.00000	−	8.66025i	0.310685	−	0.538122i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	−0.212565	−	0.977147i	$-0.568182\pi$
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	0.952517	−	0.304487i	$-0.0984850\pi$
$264$		0			0
$265$	9.00000	+	15.5885i	0.552866	+	0.957591i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.00000			0.182913			0.0914566	−	0.995809i	$-0.470848\pi$
$269$	3.00000			0.182913			0.0914566	+	0.995809i	$0.470848\pi$
$270$		0			0
$271$	10.0000			0.607457			0.303728	−	0.952759i	$-0.401768\pi$
$271$	10.0000			0.607457			0.303728	+	0.952759i	$0.401768\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−12.0000	−	20.7846i	−0.723627	−	1.25336i
$276$		0			0
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	−0.675810	−	0.737075i	$-0.736206\pi$
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	0.976231	+	0.216731i	$0.0695395\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	7.50000	−	12.9904i	0.447412	−	0.774941i	−0.550804	−	0.834634i	$-0.685679\pi$
$281$	7.50000	−	12.9904i	0.447412	−	0.774941i	0.998217	+	0.0596933i	$0.0190123\pi$
$282$		0			0
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	12.0000			0.708338
$288$		0			0
$289$	−8.00000			−0.470588
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−7.50000	−	12.9904i	−0.438155	−	0.758906i	0.559393	−	0.828903i	$-0.311034\pi$
$293$	−7.50000	−	12.9904i	−0.438155	−	0.758906i	−0.997547	+	0.0699967i	$0.977701\pi$
$294$		0			0
$295$	−18.0000	+	31.1769i	−1.04800	+	1.81519i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	15.0000	−	25.9808i	0.867472	−	1.50251i
$300$		0			0
$301$	10.0000	+	17.3205i	0.576390	+	0.998337i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	15.0000			0.858898
$306$		0			0
$307$	−20.0000			−1.14146			−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000			−1.14146			−0.570730	+	0.821138i	$0.693340\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$		0			0
$313$	12.5000	−	21.6506i	0.706542	−	1.22377i	−0.259590	−	0.965719i	$-0.583588\pi$
$313$	12.5000	−	21.6506i	0.706542	−	1.22377i	0.966132	−	0.258047i	$-0.0830791\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.50000	+	12.9904i	−0.421242	+	0.729612i	−0.996061	−	0.0886679i	$-0.971739\pi$
$317$	−7.50000	+	12.9904i	−0.421242	+	0.729612i	0.574819	+	0.818280i	$0.305072\pi$
$318$		0			0
$319$	−9.00000	−	15.5885i	−0.503903	−	0.872786i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	6.00000			0.333849
$324$		0			0
$325$	20.0000			1.10940
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	13.0000	−	22.5167i	0.714545	−	1.23763i	−0.248590	−	0.968609i	$-0.579967\pi$
$331$	13.0000	−	22.5167i	0.714545	−	1.23763i	0.963135	−	0.269019i	$-0.0866994\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	3.00000	−	5.19615i	0.163908	−	0.283896i
$336$		0			0
$337$	5.00000	+	8.66025i	0.272367	+	0.471754i	0.969468	−	0.245220i	$-0.0788601\pi$
$337$	5.00000	+	8.66025i	0.272367	+	0.471754i	−0.697100	+	0.716974i	$0.745527\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	24.0000			1.29967
$342$		0			0
$343$	20.0000			1.07990
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−9.00000	−	15.5885i	−0.483145	−	0.836832i	0.516667	−	0.856186i	$-0.327172\pi$
$347$	−9.00000	−	15.5885i	−0.483145	−	0.836832i	−0.999813	+	0.0193540i	$0.993839\pi$
$348$		0			0
$349$	−1.00000	+	1.73205i	−0.0535288	+	0.0927146i	−0.891548	−	0.452926i	$-0.850380\pi$
$349$	−1.00000	+	1.73205i	−0.0535288	+	0.0927146i	0.838019	+	0.545640i	$0.183714\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−15.0000	+	25.9808i	−0.798369	+	1.38282i	0.122308	+	0.992492i	$0.460970\pi$
$353$	−15.0000	+	25.9808i	−0.798369	+	1.38282i	−0.920677	+	0.390324i	$0.872363\pi$
$354$		0			0
$355$	9.00000	+	15.5885i	0.477670	+	0.827349i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	18.0000			0.950004			0.475002	−	0.879985i	$-0.342447\pi$
$359$	18.0000			0.950004			0.475002	+	0.879985i	$0.342447\pi$
$360$		0			0
$361$	−15.0000			−0.789474
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.50000	+	2.59808i	0.0785136	+	0.135990i
$366$		0			0
$367$	16.0000	−	27.7128i	0.835193	−	1.44660i	−0.0586798	−	0.998277i	$-0.518689\pi$
$367$	16.0000	−	27.7128i	0.835193	−	1.44660i	0.893873	−	0.448320i	$-0.147978\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.00000	+	10.3923i	−0.311504	+	0.539542i
$372$		0			0
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	0.625917	−	0.779890i	$-0.284725\pi$
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	−0.988363	+	0.152115i	$0.951392\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	15.0000			0.772539
$378$		0			0
$379$	4.00000			0.205466			0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000			0.205466			0.102733	+	0.994709i	$0.467241\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	15.0000	+	25.9808i	0.766464	+	1.32755i	0.939469	+	0.342634i	$0.111319\pi$
$383$	15.0000	+	25.9808i	0.766464	+	1.32755i	−0.173005	+	0.984921i	$0.555348\pi$
$384$		0			0
$385$	18.0000	−	31.1769i	0.917365	−	1.58892i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	−0.182047	−	0.983290i	$-0.558272\pi$
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	0.942578	−	0.333987i	$-0.108394\pi$
$390$		0			0
$391$	−9.00000	−	15.5885i	−0.455150	−	0.788342i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	30.0000			1.50946
$396$		0			0
$397$	−7.00000			−0.351320			−0.175660	−	0.984451i	$-0.556206\pi$
$397$	−7.00000			−0.351320			−0.175660	+	0.984451i	$0.556206\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	0.990257	−	0.139253i	$-0.0444700\pi$
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	−0.615725	+	0.787961i	$0.711137\pi$
$402$		0			0
$403$	−10.0000	+	17.3205i	−0.498135	+	0.862796i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−15.0000	+	25.9808i	−0.743522	+	1.28782i
$408$		0			0
$409$	−17.5000	−	30.3109i	−0.865319	−	1.49878i	−0.866730	−	0.498778i	$-0.833782\pi$
$409$	−17.5000	−	30.3109i	−0.865319	−	1.49878i	0.00141047	−	0.999999i	$-0.499551\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−24.0000			−1.18096
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$419$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$420$		0			0
$421$	−14.5000	+	25.1147i	−0.706687	+	1.22402i	0.259393	+	0.965772i	$0.416478\pi$
$421$	−14.5000	+	25.1147i	−0.706687	+	1.22402i	−0.966079	+	0.258245i	$0.916856\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$	5.00000	+	8.66025i	0.241967	+	0.419099i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−24.0000			−1.15604			−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000			−1.15604			−0.578020	+	0.816023i	$0.696174\pi$
$432$		0			0
$433$	11.0000			0.528626			0.264313	−	0.964437i	$-0.414855\pi$
$433$	11.0000			0.528626			0.264313	+	0.964437i	$0.414855\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.00000	−	10.3923i	−0.287019	−	0.497131i
$438$		0			0
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	−0.754642	−	0.656136i	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$443$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$444$		0			0
$445$	4.50000	+	7.79423i	0.213320	+	0.369482i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		0			0
$451$	−36.0000			−1.69517
$452$		0			0
$453$		0			0
$454$		0			0
$455$	15.0000	+	25.9808i	0.703211	+	1.21800i
$456$		0			0
$457$	−17.5000	+	30.3109i	−0.818615	+	1.41788i	0.0880870	+	0.996113i	$0.471925\pi$
$457$	−17.5000	+	30.3109i	−0.818615	+	1.41788i	−0.906702	+	0.421771i	$0.861409\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.00000	−	5.19615i	0.139724	−	0.242009i	−0.787668	−	0.616100i	$-0.788712\pi$
$461$	3.00000	−	5.19615i	0.139724	−	0.242009i	0.927392	+	0.374091i	$0.122045\pi$
$462$		0			0
$463$	−2.00000	−	3.46410i	−0.0929479	−	0.160990i	0.815802	−	0.578331i	$-0.196296\pi$
$463$	−2.00000	−	3.46410i	−0.0929479	−	0.160990i	−0.908750	+	0.417340i	$0.862962\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$		0			0
$469$	4.00000			0.184703
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−30.0000	−	51.9615i	−1.37940	−	2.38919i
$474$		0			0
$475$	4.00000	−	6.92820i	0.183533	−	0.317888i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	−0.583803	−	0.811895i	$-0.698436\pi$
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	0.995023	+	0.0996406i	$0.0317693\pi$
$480$		0			0
$481$	−12.5000	−	21.6506i	−0.569951	−	0.987184i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−30.0000			−1.36223
$486$		0			0
$487$	−20.0000			−0.906287			−0.453143	−	0.891438i	$-0.649697\pi$
$487$	−20.0000			−0.906287			−0.453143	+	0.891438i	$0.649697\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	3.00000	+	5.19615i	0.135388	+	0.234499i	0.925746	−	0.378147i	$-0.123439\pi$
$491$	3.00000	+	5.19615i	0.135388	+	0.234499i	−0.790358	+	0.612646i	$0.790105\pi$
$492$		0			0
$493$	4.50000	−	7.79423i	0.202670	−	0.351034i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.00000	+	10.3923i	−0.269137	+	0.466159i
$498$		0			0
$499$	−11.0000	−	19.0526i	−0.492428	−	0.852910i	0.507534	−	0.861632i	$-0.330557\pi$
$499$	−11.0000	−	19.0526i	−0.492428	−	0.852910i	−0.999962	+	0.00872186i	$0.997224\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$		0			0
$511$	−1.00000	+	1.73205i	−0.0442374	+	0.0766214i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−24.0000	+	41.5692i	−1.05757	+	1.83176i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−30.0000			−1.31432			−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000			−1.31432			−0.657162	+	0.753749i	$0.728243\pi$
$522$		0			0
$523$	10.0000			0.437269			0.218635	−	0.975807i	$-0.429840\pi$
$523$	10.0000			0.437269			0.218635	+	0.975807i	$0.429840\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	15.0000	−	25.9808i	0.649722	−	1.12535i
$534$		0			0
$535$	18.0000	+	31.1769i	0.778208	+	1.34790i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−18.0000			−0.775315
$540$		0			0
$541$	41.0000			1.76273			0.881364	−	0.472438i	$-0.156626\pi$
$541$	41.0000			1.76273			0.881364	+	0.472438i	$0.156626\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	10.5000	+	18.1865i	0.449771	+	0.779026i
$546$		0			0
$547$	−20.0000	+	34.6410i	−0.855138	+	1.48114i	0.0213785	+	0.999771i	$0.493195\pi$
$547$	−20.0000	+	34.6410i	−0.855138	+	1.48114i	−0.876517	+	0.481371i	$0.840139\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.00000	−	5.19615i	0.127804	−	0.221364i
$552$		0			0
$553$	10.0000	+	17.3205i	0.425243	+	0.736543i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	15.0000			0.635570			0.317785	−	0.948163i	$-0.397061\pi$
$557$	15.0000			0.635570			0.317785	+	0.948163i	$0.397061\pi$
$558$		0			0
$559$	50.0000			2.11477
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$563$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$564$		0			0
$565$	−13.5000	+	23.3827i	−0.567949	+	0.983717i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.50000	−	2.59808i	0.0628833	−	0.108917i	−0.832870	−	0.553469i	$-0.813304\pi$
$569$	1.50000	−	2.59808i	0.0628833	−	0.108917i	0.895753	+	0.444552i	$0.146637\pi$
$570$		0			0
$571$	22.0000	+	38.1051i	0.920671	+	1.59465i	0.798379	+	0.602155i	$0.205691\pi$
$571$	22.0000	+	38.1051i	0.920671	+	1.59465i	0.122292	+	0.992494i	$0.460975\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−24.0000			−1.00087
$576$		0			0
$577$	−37.0000			−1.54033			−0.770165	−	0.637845i	$-0.779826\pi$
$577$	−37.0000			−1.54033			−0.770165	+	0.637845i	$0.779826\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	18.0000	−	31.1769i	0.745484	−	1.29122i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−15.0000	+	25.9808i	−0.619116	+	1.07234i	0.370531	+	0.928820i	$0.379176\pi$
$587$	−15.0000	+	25.9808i	−0.619116	+	1.07234i	−0.989647	+	0.143521i	$0.954158\pi$
$588$		0			0
$589$	4.00000	+	6.92820i	0.164817	+	0.285472i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−39.0000			−1.60154			−0.800769	−	0.598973i	$-0.795576\pi$
$593$	−39.0000			−1.60154			−0.800769	+	0.598973i	$0.795576\pi$
$594$		0			0
$595$	18.0000			0.737928
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−6.00000	−	10.3923i	−0.245153	−	0.424618i	0.717021	−	0.697051i	$-0.245505\pi$
$599$	−6.00000	−	10.3923i	−0.245153	−	0.424618i	−0.962175	+	0.272433i	$0.912172\pi$
$600$		0			0
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	−0.855648	−	0.517559i	$-0.826841\pi$
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	0.876043	+	0.482233i	$0.160174\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−37.5000	+	64.9519i	−1.52459	+	2.64067i
$606$		0			0
$607$	−5.00000	−	8.66025i	−0.202944	−	0.351509i	0.746532	−	0.665350i	$-0.231718\pi$
$607$	−5.00000	−	8.66025i	−0.202944	−	0.351509i	−0.949476	+	0.313841i	$0.898384\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−10.0000			−0.403896			−0.201948	−	0.979396i	$-0.564727\pi$
$613$	−10.0000			−0.403896			−0.201948	+	0.979396i	$0.564727\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	7.50000	+	12.9904i	0.301939	+	0.522973i	0.976575	−	0.215177i	$-0.0690329\pi$
$617$	7.50000	+	12.9904i	0.301939	+	0.522973i	−0.674636	+	0.738150i	$0.735700\pi$
$618$		0			0
$619$	−20.0000	+	34.6410i	−0.803868	+	1.39234i	0.113185	+	0.993574i	$0.463895\pi$
$619$	−20.0000	+	34.6410i	−0.803868	+	1.39234i	−0.917053	+	0.398766i	$0.869439\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.00000	+	5.19615i	−0.120192	+	0.208179i
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−15.0000			−0.598089
$630$		0			0
$631$	4.00000			0.159237			0.0796187	−	0.996825i	$-0.474630\pi$
$631$	4.00000			0.159237			0.0796187	+	0.996825i	$0.474630\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	3.00000	+	5.19615i	0.119051	+	0.206203i
$636$		0			0
$637$	7.50000	−	12.9904i	0.297161	−	0.514698i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−10.5000	+	18.1865i	−0.414725	+	0.718325i	−0.995400	−	0.0958109i	$-0.969456\pi$
$641$	−10.5000	+	18.1865i	−0.414725	+	0.718325i	0.580674	+	0.814136i	$0.302789\pi$
$642$		0			0
$643$	−20.0000	−	34.6410i	−0.788723	−	1.36611i	−0.926750	−	0.375680i	$-0.877409\pi$
$643$	−20.0000	−	34.6410i	−0.788723	−	1.36611i	0.138027	−	0.990429i	$-0.455924\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.0000			−0.707653			−0.353827	−	0.935311i	$-0.615120\pi$
$647$	−18.0000			−0.707653			−0.353827	+	0.935311i	$0.615120\pi$
$648$		0			0
$649$	72.0000			2.82625
$650$		0			0
$651$		0			0
$652$		0			0
$653$	15.0000	+	25.9808i	0.586995	+	1.01671i	0.994623	+	0.103558i	$0.0330227\pi$
$653$	15.0000	+	25.9808i	0.586995	+	1.01671i	−0.407628	+	0.913148i	$0.633644\pi$
$654$		0			0
$655$	−9.00000	+	15.5885i	−0.351659	+	0.609091i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	3.00000	−	5.19615i	0.116863	−	0.202413i	−0.801660	−	0.597781i	$-0.796049\pi$
$659$	3.00000	−	5.19615i	0.116863	−	0.202413i	0.918523	+	0.395367i	$0.129383\pi$
$660$		0			0
$661$	−14.5000	−	25.1147i	−0.563985	−	0.976850i	−0.997143	−	0.0755324i	$-0.975934\pi$
$661$	−14.5000	−	25.1147i	−0.563985	−	0.976850i	0.433159	−	0.901318i	$-0.357399\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	12.0000			0.465340
$666$		0			0
$667$	−18.0000			−0.696963
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−15.0000	−	25.9808i	−0.579069	−	1.00298i
$672$		0			0
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	−0.856228	−	0.516599i	$-0.827198\pi$
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	0.875501	+	0.483216i	$0.160531\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	0.107772	+	0.994176i	$0.465628\pi$
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	−0.914867	+	0.403755i	$0.867705\pi$
$678$		0			0
$679$	−10.0000	−	17.3205i	−0.383765	−	0.664700i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0			−	1.00000i	$-0.5\pi$
$683$		0			0				1.00000i	$0.5\pi$
$684$		0			0
$685$	−45.0000			−1.71936
$686$		0			0
$687$		0			0
$688$		0			0
$689$	15.0000	+	25.9808i	0.571454	+	0.989788i
$690$		0			0
$691$	−5.00000	+	8.66025i	−0.190209	+	0.329452i	−0.945319	−	0.326146i	$-0.894250\pi$
$691$	−5.00000	+	8.66025i	−0.190209	+	0.329452i	0.755110	+	0.655598i	$0.227583\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	12.0000	−	20.7846i	0.455186	−	0.788405i
$696$		0			0
$697$	−9.00000	−	15.5885i	−0.340899	−	0.590455i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	39.0000			1.47301			0.736505	−	0.676432i	$-0.236475\pi$
$701$	39.0000			1.47301			0.736505	+	0.676432i	$0.236475\pi$
$702$		0			0
$703$	−10.0000			−0.377157
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.00000	+	10.3923i	0.225653	+	0.390843i
$708$		0			0
$709$	9.50000	−	16.4545i	0.356780	−	0.617961i	−0.630641	−	0.776075i	$-0.717208\pi$
$709$	9.50000	−	16.4545i	0.356780	−	0.617961i	0.987421	+	0.158114i	$0.0505412\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	12.0000	−	20.7846i	0.449404	−	0.778390i
$714$		0			0
$715$	−45.0000	−	77.9423i	−1.68290	−	2.91488i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−18.0000			−0.671287			−0.335643	−	0.941989i	$-0.608954\pi$
$719$	−18.0000			−0.671287			−0.335643	+	0.941989i	$0.608954\pi$
$720$		0			0
$721$	−32.0000			−1.19174
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−6.00000	−	10.3923i	−0.222834	−	0.385961i
$726$		0			0
$727$	−5.00000	+	8.66025i	−0.185440	+	0.321191i	−0.943725	−	0.330732i	$-0.892704\pi$
$727$	−5.00000	+	8.66025i	−0.185440	+	0.321191i	0.758285	+	0.651923i	$0.226038\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	15.0000	−	25.9808i	0.554795	−	0.960933i
$732$		0			0
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	0.707303	−	0.706910i	$-0.249912\pi$
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	−0.965854	+	0.259087i	$0.916578\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.0000			−0.442026
$738$		0			0
$739$	52.0000			1.91285			0.956425	−	0.291977i	$-0.0943129\pi$
$739$	52.0000			1.91285			0.956425	+	0.291977i	$0.0943129\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	−0.980522	−	0.196409i	$-0.937072\pi$
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	0.320166	−	0.947361i	$-0.396261\pi$
$744$		0			0
$745$	−22.5000	+	38.9711i	−0.824336	+	1.42779i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−12.0000	+	20.7846i	−0.438470	+	0.759453i
$750$		0			0
$751$	−5.00000	−	8.66025i	−0.182453	−	0.316017i	0.760263	−	0.649616i	$-0.225070\pi$
$751$	−5.00000	−	8.66025i	−0.182453	−	0.316017i	−0.942715	+	0.333599i	$0.891737\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	12.0000			0.436725
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−4.50000	−	7.79423i	−0.163125	−	0.282541i	0.772863	−	0.634573i	$-0.218824\pi$
$761$	−4.50000	−	7.79423i	−0.163125	−	0.282541i	−0.935988	+	0.352032i	$0.885491\pi$
$762$		0			0
$763$	−7.00000	+	12.1244i	−0.253417	+	0.438931i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−30.0000	+	51.9615i	−1.08324	+	1.87622i
$768$		0			0
$769$	−11.5000	−	19.9186i	−0.414701	−	0.718283i	0.580696	−	0.814120i	$-0.302780\pi$
$769$	−11.5000	−	19.9186i	−0.414701	−	0.718283i	−0.995397	+	0.0958377i	$0.969447\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−45.0000			−1.61854			−0.809269	−	0.587439i	$-0.800136\pi$
$773$	−45.0000			−1.61854			−0.809269	+	0.587439i	$0.800136\pi$
$774$		0			0
$775$	16.0000			0.574737
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−6.00000	−	10.3923i	−0.214972	−	0.372343i
$780$		0			0
$781$	18.0000	−	31.1769i	0.644091	−	1.11560i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−7.50000	+	12.9904i	−0.267686	+	0.463647i
$786$		0			0
$787$	19.0000	+	32.9090i	0.677277	+	1.17308i	0.975798	+	0.218675i	$0.0701734\pi$
$787$	19.0000	+	32.9090i	0.677277	+	1.17308i	−0.298521	+	0.954403i	$0.596493\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−18.0000			−0.640006
$792$		0			0
$793$	25.0000			0.887776
$794$		0			0
$795$		0			0
$796$		0			0
$797$	22.5000	+	38.9711i	0.796991	+	1.38043i	0.921567	+	0.388219i	$0.126909\pi$
$797$	22.5000	+	38.9711i	0.796991	+	1.38043i	−0.124576	+	0.992210i	$0.539757\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3.00000	−	5.19615i	0.105868	−	0.183368i
$804$		0			0
$805$	−18.0000	−	31.1769i	−0.634417	−	1.09884i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−3.00000			−0.105474			−0.0527372	−	0.998608i	$-0.516795\pi$
$809$	−3.00000			−0.105474			−0.0527372	+	0.998608i	$0.516795\pi$
$810$		0			0
$811$	16.0000			0.561836			0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000			0.561836			0.280918	+	0.959732i	$0.409361\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−6.00000	−	10.3923i	−0.210171	−	0.364027i
$816$		0			0
$817$	10.0000	−	17.3205i	0.349856	−	0.605968i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	10.5000	−	18.1865i	0.366453	−	0.634714i	−0.622556	−	0.782576i	$-0.713906\pi$
$821$	10.5000	−	18.1865i	0.366453	−	0.634714i	0.989008	+	0.147861i	$0.0472389\pi$
$822$		0			0
$823$	−2.00000	−	3.46410i	−0.0697156	−	0.120751i	0.829060	−	0.559159i	$-0.188876\pi$
$823$	−2.00000	−	3.46410i	−0.0697156	−	0.120751i	−0.898776	+	0.438408i	$0.855543\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	30.0000			1.04320			0.521601	−	0.853189i	$-0.325335\pi$
$827$	30.0000			1.04320			0.521601	+	0.853189i	$0.325335\pi$
$828$		0			0
$829$	38.0000			1.31979			0.659897	−	0.751356i	$-0.270600\pi$
$829$	38.0000			1.31979			0.659897	+	0.751356i	$0.270600\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.50000	−	7.79423i	−0.155916	−	0.270054i
$834$		0			0
$835$	27.0000	−	46.7654i	0.934374	−	1.61838i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−9.00000	+	15.5885i	−0.310715	+	0.538173i	−0.978517	−	0.206165i	$-0.933902\pi$
$839$	−9.00000	+	15.5885i	−0.310715	+	0.538173i	0.667803	+	0.744338i	$0.267235\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	36.0000			1.23844
$846$		0			0
$847$	−50.0000			−1.71802
$848$		0			0
$849$		0			0
$850$		0			0
$851$	15.0000	+	25.9808i	0.514193	+	0.890609i
$852$		0			0
$853$	−7.00000	+	12.1244i	−0.239675	+	0.415130i	−0.960621	−	0.277862i	$-0.910374\pi$
$853$	−7.00000	+	12.1244i	−0.239675	+	0.415130i	0.720946	+	0.692992i	$0.243708\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−22.5000	+	38.9711i	−0.768585	+	1.33123i	0.169745	+	0.985488i	$0.445706\pi$
$857$	−22.5000	+	38.9711i	−0.768585	+	1.33123i	−0.938330	+	0.345741i	$0.887628\pi$
$858$		0			0
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	0.926161	−	0.377128i	$-0.123088\pi$
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	−0.789683	+	0.613515i	$0.789755\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−6.00000			−0.204242			−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000			−0.204242			−0.102121	+	0.994772i	$0.532563\pi$
$864$		0			0
$865$	−27.0000			−0.918028
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−30.0000	−	51.9615i	−1.01768	−	1.76267i
$870$		0			0
$871$	5.00000	−	8.66025i	0.169419	−	0.293442i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−3.00000	+	5.19615i	−0.101419	+	0.175662i
$876$		0			0
$877$	27.5000	+	47.6314i	0.928609	+	1.60840i	0.785652	+	0.618669i	$0.212328\pi$
$877$	27.5000	+	47.6314i	0.928609	+	1.60840i	0.142957	+	0.989729i	$0.454339\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$		0			0
$883$	16.0000			0.538443			0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000			0.538443			0.269221	+	0.963078i	$0.413234\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	15.0000	+	25.9808i	0.503651	+	0.872349i	0.999991	+	0.00422062i	$0.00134347\pi$
$887$	15.0000	+	25.9808i	0.503651	+	0.872349i	−0.496340	+	0.868128i	$0.665323\pi$
$888$		0			0
$889$	−2.00000	+	3.46410i	−0.0670778	+	0.116182i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	18.0000	+	31.1769i	0.601674	+	1.04213i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	12.0000			0.400222
$900$		0			0
$901$	18.0000			0.599667
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−21.0000	−	36.3731i	−0.698064	−	1.20908i
$906$		0			0
$907$	4.00000	−	6.92820i	0.132818	−	0.230047i	−0.791944	−	0.610594i	$-0.790931\pi$
$907$	4.00000	−	6.92820i	0.132818	−	0.230047i	0.924762	+	0.380547i	$0.124264\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−27.0000	+	46.7654i	−0.894550	+	1.54941i	−0.0601892	+	0.998187i	$0.519170\pi$
$911$	−27.0000	+	46.7654i	−0.894550	+	1.54941i	−0.834361	+	0.551219i	$0.814163\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−12.0000			−0.396275
$918$		0			0
$919$	−38.0000			−1.25350			−0.626752	−	0.779219i	$-0.715616\pi$
$919$	−38.0000			−1.25350			−0.626752	+	0.779219i	$0.715616\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	15.0000	+	25.9808i	0.493731	+	0.855167i
$924$		0			0
$925$	−10.0000	+	17.3205i	−0.328798	+	0.569495i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	13.5000	−	23.3827i	0.442921	−	0.767161i	−0.554984	−	0.831861i	$-0.687276\pi$
$929$	13.5000	−	23.3827i	0.442921	−	0.767161i	0.997905	+	0.0646999i	$0.0206090\pi$
$930$		0			0
$931$	−3.00000	−	5.19615i	−0.0983210	−	0.170297i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−54.0000			−1.76599
$936$		0			0
$937$	23.0000			0.751377			0.375689	−	0.926746i	$-0.377406\pi$
$937$	23.0000			0.751377			0.375689	+	0.926746i	$0.377406\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−7.50000	−	12.9904i	−0.244493	−	0.423474i	0.717496	−	0.696563i	$-0.245288\pi$
$941$	−7.50000	−	12.9904i	−0.244493	−	0.423474i	−0.961989	+	0.273088i	$0.911955\pi$
$942$		0			0
$943$	−18.0000	+	31.1769i	−0.586161	+	1.01526i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.00000	−	15.5885i	0.292461	−	0.506557i	−0.681930	−	0.731417i	$-0.738859\pi$
$947$	9.00000	−	15.5885i	0.292461	−	0.506557i	0.974391	+	0.224860i	$0.0721926\pi$
$948$		0			0
$949$	2.50000	+	4.33013i	0.0811534	+	0.140562i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	45.0000			1.45769			0.728846	−	0.684677i	$-0.240057\pi$
$953$	45.0000			1.45769			0.728846	+	0.684677i	$0.240057\pi$
$954$		0			0
$955$	−18.0000			−0.582466
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−15.0000	−	25.9808i	−0.484375	−	0.838963i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	37.5000	−	64.9519i	1.20717	−	2.09088i
$966$		0			0
$967$	19.0000	+	32.9090i	0.610999	+	1.05828i	0.991072	+	0.133325i	$0.0425653\pi$
$967$	19.0000	+	32.9090i	0.610999	+	1.05828i	−0.380074	+	0.924956i	$0.624101\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	54.0000			1.73294			0.866471	−	0.499227i	$-0.166383\pi$
$971$	54.0000			1.73294			0.866471	+	0.499227i	$0.166383\pi$
$972$		0			0
$973$	16.0000			0.512936
$974$		0			0
$975$		0			0
$976$		0			0
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	0.999734	−	0.0230645i	$-0.00734232\pi$
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	−0.519841	+	0.854263i	$0.674009\pi$
$978$		0			0
$979$	9.00000	−	15.5885i	0.287641	−	0.498209i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	12.0000	−	20.7846i	0.382741	−	0.662926i	−0.608712	−	0.793391i	$-0.708314\pi$
$983$	12.0000	−	20.7846i	0.382741	−	0.662926i	0.991453	+	0.130465i	$0.0416470\pi$
$984$		0			0
$985$	−22.5000	−	38.9711i	−0.716910	−	1.24172i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−60.0000			−1.90789
$990$		0			0
$991$	−26.0000			−0.825917			−0.412959	−	0.910750i	$-0.635505\pi$
$991$	−26.0000			−0.825917			−0.412959	+	0.910750i	$0.635505\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	30.0000	+	51.9615i	0.951064	+	1.64729i
$996$		0			0
$997$	−26.5000	+	45.8993i	−0.839263	+	1.45365i	0.0512480	+	0.998686i	$0.483680\pi$
$997$	−26.5000	+	45.8993i	−0.839263	+	1.45365i	−0.890511	+	0.454961i	$0.849653\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1296.2.i.d.865.1		2
3.2	odd	2		1296.2.i.p.865.1		2
4.3	odd	2		324.2.e.a.217.1		2
9.2	odd	6		1296.2.a.a.1.1		1
9.4	even	3	inner	1296.2.i.d.433.1		2
9.5	odd	6		1296.2.i.p.433.1		2
9.7	even	3		1296.2.a.j.1.1		1
12.11	even	2		324.2.e.d.217.1		2
36.7	odd	6		324.2.a.d.1.1	yes	1
36.11	even	6		324.2.a.b.1.1	✓	1
36.23	even	6		324.2.e.d.109.1		2
36.31	odd	6		324.2.e.a.109.1		2
72.11	even	6		5184.2.a.bc.1.1		1
72.29	odd	6		5184.2.a.z.1.1		1
72.43	odd	6		5184.2.a.g.1.1		1
72.61	even	6		5184.2.a.d.1.1		1
180.7	even	12		8100.2.d.a.649.2		2
180.43	even	12		8100.2.d.a.649.1		2
180.47	odd	12		8100.2.d.j.649.2		2
180.79	odd	6		8100.2.a.a.1.1		1
180.83	odd	12		8100.2.d.j.649.1		2
180.119	even	6		8100.2.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.a.b.1.1	✓	1	36.11	even	6
324.2.a.d.1.1	yes	1	36.7	odd	6
324.2.e.a.109.1		2	36.31	odd	6
324.2.e.a.217.1		2	4.3	odd	2
324.2.e.d.109.1		2	36.23	even	6
324.2.e.d.217.1		2	12.11	even	2
1296.2.a.a.1.1		1	9.2	odd	6
1296.2.a.j.1.1		1	9.7	even	3
1296.2.i.d.433.1		2	9.4	even	3	inner
1296.2.i.d.865.1		2	1.1	even	1	trivial
1296.2.i.p.433.1		2	9.5	odd	6
1296.2.i.p.865.1		2	3.2	odd	2
5184.2.a.d.1.1		1	72.61	even	6
5184.2.a.g.1.1		1	72.43	odd	6
5184.2.a.z.1.1		1	72.29	odd	6
5184.2.a.bc.1.1		1	72.11	even	6
8100.2.a.a.1.1		1	180.79	odd	6
8100.2.a.f.1.1		1	180.119	even	6
8100.2.d.a.649.1		2	180.43	even	12
8100.2.d.a.649.2		2	180.7	even	12
8100.2.d.j.649.1		2	180.83	odd	12
8100.2.d.j.649.2		2	180.47	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.50000 - 2.59808i) q^{5} +(1.00000 - 1.73205i) q^{7} +O(q^{10})\)	\(q+(-1.50000 - 2.59808i) q^{5} +(1.00000 - 1.73205i) q^{7} +(-3.00000 + 5.19615i) q^{11} +(-2.50000 - 4.33013i) q^{13} -3.00000 q^{17} -2.00000 q^{19} +(3.00000 + 5.19615i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(-1.50000 + 2.59808i) q^{29} +(-2.00000 - 3.46410i) q^{31} -6.00000 q^{35} +5.00000 q^{37} +(3.00000 + 5.19615i) q^{41} +(-5.00000 + 8.66025i) q^{43} +(1.50000 + 2.59808i) q^{49} -6.00000 q^{53} +18.0000 q^{55} +(-6.00000 - 10.3923i) q^{59} +(-2.50000 + 4.33013i) q^{61} +(-7.50000 + 12.9904i) q^{65} +(1.00000 + 1.73205i) q^{67} -6.00000 q^{71} -1.00000 q^{73} +(6.00000 + 10.3923i) q^{77} +(-5.00000 + 8.66025i) q^{79} +(4.50000 + 7.79423i) q^{85} -3.00000 q^{89} -10.0000 q^{91} +(3.00000 + 5.19615i) q^{95} +(5.00000 - 8.66025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{5} + 2 q^{7}+O(q^{10}) \) 2 * q - 3 * q^5 + 2 * q^7	\( 2 q - 3 q^{5} + 2 q^{7} - 6 q^{11} - 5 q^{13} - 6 q^{17} - 4 q^{19} + 6 q^{23} - 4 q^{25} - 3 q^{29} - 4 q^{31} - 12 q^{35} + 10 q^{37} + 6 q^{41} - 10 q^{43} + 3 q^{49} - 12 q^{53} + 36 q^{55} - 12 q^{59} - 5 q^{61} - 15 q^{65} + 2 q^{67} - 12 q^{71} - 2 q^{73} + 12 q^{77} - 10 q^{79} + 9 q^{85} - 6 q^{89} - 20 q^{91} + 6 q^{95} + 10 q^{97}+O(q^{100}) \) 2 * q - 3 * q^5 + 2 * q^7 - 6 * q^11 - 5 * q^13 - 6 * q^17 - 4 * q^19 + 6 * q^23 - 4 * q^25 - 3 * q^29 - 4 * q^31 - 12 * q^35 + 10 * q^37 + 6 * q^41 - 10 * q^43 + 3 * q^49 - 12 * q^53 + 36 * q^55 - 12 * q^59 - 5 * q^61 - 15 * q^65 + 2 * q^67 - 12 * q^71 - 2 * q^73 + 12 * q^77 - 10 * q^79 + 9 * q^85 - 6 * q^89 - 20 * q^91 + 6 * q^95 + 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more