LMFDB - Embedded newform 576.7.e.g.449.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,7,Mod(449,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("576.449");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	576.e (of order $2$, degree $1$, 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:	$132.511152165$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-2}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 2 $ x^2 + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			449.2
Root			$1.41421i$ of defining polynomial
Character	$\chi$	$=$	576.449
Dual form			576.7.e.g.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+227.688i q^{5} +O(q^{10})$	$q+227.688i q^{5} +1656.00 q^{13} -7612.71i q^{17} -36217.0 q^{25} +48647.5i q^{29} -55510.0 q^{37} +136827. i q^{41} -117649. q^{49} -188703. i q^{53} -234938. q^{61} +377052. i q^{65} -650016. q^{73} +1.73333e6 q^{85} -1.18291e6i q^{89} -1.07870e6 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q+O(q^{10}) $ 2 * q	$ 2 q + 3312 q^{13} - 72434 q^{25} - 111020 q^{37} - 235298 q^{49} - 469876 q^{61} - 1300032 q^{73} + 3466652 q^{85} - 2157408 q^{97}+O(q^{100}) $ 2 * q + 3312 * q^13 - 72434 * q^25 - 111020 * q^37 - 235298 * q^49 - 469876 * q^61 - 1300032 * q^73 + 3466652 * q^85 - 2157408 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$-1$	$1$	$1$

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
$5$	227.688i	1.82151i	0.412950	+	0.910754i	$0.364498\pi$
$5$	227.688i	1.82151i	−0.412950	+	0.910754i	$0.635502\pi$
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	0	0
$9$	0	0
$10$	0	0
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	0	0
$13$	1656.00	0.753755	0.376878	−	0.926263i	$-0.376998\pi$
$13$	1656.00	0.753755	0.376878	+	0.926263i	$0.376998\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	− 7612.71i	− 1.54950i	−0.632265	−	0.774752i	$-0.717875\pi$
$17$	− 7612.71i	− 1.54950i	0.632265	−	0.774752i	$-0.282125\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	0	0
$25$	−36217.0	−2.31789
$26$	0	0
$27$	0	0
$28$	0	0
$29$	48647.5i	1.99465i	0.0730910	+	0.997325i	$0.476714\pi$
$29$	48647.5i	1.99465i	−0.0730910	+	0.997325i	$0.523286\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−55510.0	−1.09589	−0.547944	−	0.836515i	$-0.684589\pi$
$37$	−55510.0	−1.09589	−0.547944	+	0.836515i	$0.684589\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	136827.i	1.98527i	0.121156	+	0.992633i	$0.461340\pi$
$41$	136827.i	1.98527i	−0.121156	+	0.992633i	$0.538660\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	0	0
$49$	−117649.	−1.00000
$50$	0	0
$51$	0	0
$52$	0	0
$53$	− 188703.i	− 1.26751i	−0.773535	−	0.633754i	$-0.781513\pi$
$53$	− 188703.i	− 1.26751i	0.773535	−	0.633754i	$-0.218487\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	0	0
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	0	0
$61$	−234938.	−1.03506	−0.517528	−	0.855666i	$-0.673148\pi$
$61$	−234938.	−1.03506	−0.517528	+	0.855666i	$0.673148\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	377052.i	1.37297i
$66$	0	0
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	0	0
$73$	−650016.	−1.67092	−0.835460	−	0.549552i	$-0.814798\pi$
$73$	−650016.	−1.67092	−0.835460	+	0.549552i	$0.814798\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0	0
$85$	1.73333e6	2.82243
$86$	0	0
$87$	0	0
$88$	0	0
$89$	− 1.18291e6i	− 1.67795i	−0.544166	−	0.838977i	$-0.683154\pi$
$89$	− 1.18291e6i	− 1.67795i	0.544166	−	0.838977i	$-0.316846\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−1.07870e6	−1.18192	−0.590959	−	0.806702i	$-0.701250\pi$
$97$	−1.07870e6	−1.18192	−0.590959	+	0.806702i	$0.701250\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	− 2.02453e6i	− 1.96499i	−0.186292	−	0.982495i	$-0.559647\pi$
$101$	− 2.02453e6i	− 1.96499i	0.186292	−	0.982495i	$-0.440353\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	0	0
$109$	2.54916e6	1.96842	0.984210	−	0.177007i	$-0.0566415\pi$
$109$	2.54916e6	1.96842	0.984210	+	0.177007i	$0.0566415\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	1.08643e6i	0.752951i	0.926426	+	0.376476i	$0.122864\pi$
$113$	1.08643e6i	0.752951i	−0.926426	+	0.376476i	$0.877136\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	1.77156e6	1.00000
$122$	0	0
$123$	0	0
$124$	0	0
$125$	− 4.68856e6i	− 2.40054i
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	1.33982e6i	0.521055i	0.965466	+	0.260527i	$0.0838964\pi$
$137$	1.33982e6i	0.521055i	−0.965466	+	0.260527i	$0.916104\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	−1.10765e7	−3.63327
$146$	0	0
$147$	0	0
$148$	0	0
$149$	− 6.38903e6i	− 1.93142i	−0.259626	−	0.965709i	$-0.583599\pi$
$149$	− 6.38903e6i	− 1.93142i	0.259626	−	0.965709i	$-0.416401\pi$
$150$	0	0
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−7.65799e6	−1.97886	−0.989432	−	0.144999i	$-0.953682\pi$
$157$	−7.65799e6	−1.97886	−0.989432	+	0.144999i	$0.953682\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	0	0		−	1.00000i	$-0.5\pi$
$163$	0	0			1.00000i	$0.5\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	−2.08447e6	−0.431853
$170$	0	0
$171$	0	0
$172$	0	0
$173$	1.02674e7i	1.98299i	0.130128	+	0.991497i	$0.458461\pi$
$173$	1.02674e7i	1.98299i	−0.130128	+	0.991497i	$0.541539\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0	0
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	1.12741e7	1.90128	0.950642	−	0.310290i	$-0.100426\pi$
$181$	1.12741e7	1.90128	0.950642	+	0.310290i	$0.100426\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	− 1.26390e7i	− 1.99617i
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	0	0
$193$	−1.43729e7	−1.99928	−0.999639	−	0.0268508i	$-0.991452\pi$
$193$	−1.43729e7	−1.99928	−0.999639	+	0.0268508i	$0.991452\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	− 5.35151e6i	− 0.699967i	−0.936756	−	0.349983i	$-0.886187\pi$
$197$	− 5.35151e6i	− 0.699967i	0.936756	−	0.349983i	$-0.113813\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	−3.11538e7	−3.61618
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	− 1.26067e7i	− 1.16795i
$222$	0	0
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	−1.71508e7	−1.42816	−0.714080	−	0.700064i	$-0.753155\pi$
$229$	−1.71508e7	−1.42816	−0.714080	+	0.700064i	$0.753155\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	− 2.06332e7i	− 1.63117i	−0.578641	−	0.815583i	$-0.696417\pi$
$233$	− 2.06332e7i	− 1.63117i	0.578641	−	0.815583i	$-0.303583\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	2.79943e7	1.99995	0.999974	−	0.00718191i	$-0.00228609\pi$
$241$	2.79943e7	1.99995	0.999974	+	0.00718191i	$0.00228609\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	− 2.67873e7i	− 1.82151i
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	0	0
$257$	− 3.11235e7i	− 1.83354i	−0.399421	−	0.916768i	$-0.630789\pi$
$257$	− 3.11235e7i	− 1.83354i	0.399421	−	0.916768i	$-0.369211\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	4.29654e7	2.30877
$266$	0	0
$267$	0	0
$268$	0	0
$269$	279631.i	0.0143658i	0.999974	+	0.00718288i	$0.00228640\pi$
$269$	279631.i	0.0143658i	−0.999974	+	0.00718288i	$0.997714\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−1.20098e7	−0.565063	−0.282532	−	0.959258i	$-0.591174\pi$
$277$	−1.20098e7	−0.565063	−0.282532	+	0.959258i	$0.591174\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	− 3.80872e7i	− 1.71656i	−0.513180	−	0.858281i	$-0.671533\pi$
$281$	− 3.80872e7i	− 1.71656i	0.513180	−	0.858281i	$-0.328467\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−3.38158e7	−1.40096
$290$	0	0
$291$	0	0
$292$	0	0
$293$	− 4.15798e6i	− 0.165303i	−0.996579	−	0.0826513i	$-0.973661\pi$
$293$	− 4.15798e6i	− 0.165303i	0.996579	−	0.0826513i	$-0.0263388\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	− 5.34927e7i	− 1.88536i
$306$	0	0
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	0	0
$313$	−1.45704e7	−0.475157	−0.237578	−	0.971368i	$-0.576354\pi$
$313$	−1.45704e7	−0.475157	−0.237578	+	0.971368i	$0.576354\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	6.35592e7i	1.99527i	0.0687703	+	0.997633i	$0.478092\pi$
$317$	6.35592e7i	1.99527i	−0.0687703	+	0.997633i	$0.521908\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	−5.99754e7	−1.74712
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−5.14426e6	−0.134410	−0.0672052	−	0.997739i	$-0.521408\pi$
$337$	−5.14426e6	−0.134410	−0.0672052	+	0.997739i	$0.521408\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	−4.66380e6	−0.109714	−0.0548572	−	0.998494i	$-0.517470\pi$
$349$	−4.66380e6	−0.109714	−0.0548572	+	0.998494i	$0.517470\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	8.44779e7i	1.92052i	0.279104	+	0.960261i	$0.409963\pi$
$353$	8.44779e7i	1.92052i	−0.279104	+	0.960261i	$0.590037\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	0	0
$361$	−4.70459e7	−1.00000
$362$	0	0
$363$	0	0
$364$	0	0
$365$	− 1.48001e8i	− 3.04359i
$366$	0	0
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−6.31878e7	−1.21761	−0.608803	−	0.793321i	$-0.708350\pi$
$373$	−6.31878e7	−1.21761	−0.608803	+	0.793321i	$0.708350\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	8.05603e7i	1.50348i
$378$	0	0
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	0	0
$388$	0	0
$389$	8.72040e7i	1.48145i	0.671808	+	0.740726i	$0.265518\pi$
$389$	8.72040e7i	1.48145i	−0.671808	+	0.740726i	$0.734482\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	3.27126e7	0.522809	0.261404	−	0.965229i	$-0.415814\pi$
$397$	3.27126e7	0.522809	0.261404	+	0.965229i	$0.415814\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	− 6.01972e7i	− 0.933563i	−0.884373	−	0.466781i	$-0.845414\pi$
$401$	− 6.01972e7i	− 0.933563i	0.884373	−	0.466781i	$-0.154586\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−1.06618e8	−1.55834	−0.779169	−	0.626813i	$-0.784359\pi$
$409$	−1.06618e8	−1.55834	−0.779169	+	0.626813i	$0.784359\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	1.46057e8	1.95738	0.978690	−	0.205343i	$-0.0658311\pi$
$421$	1.46057e8	1.95738	0.978690	+	0.205343i	$0.0658311\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	2.75710e8i	3.59158i
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	0	0
$433$	1.38726e8	1.70882	0.854408	−	0.519602i	$-0.173920\pi$
$433$	1.38726e8	1.70882	0.854408	+	0.519602i	$0.173920\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0	0
$445$	2.69334e8	3.05641
$446$	0	0
$447$	0	0
$448$	0	0
$449$	− 1.70906e8i	− 1.88807i	−0.329851	−	0.944033i	$-0.606998\pi$
$449$	− 1.70906e8i	− 1.88807i	0.329851	−	0.944033i	$-0.393002\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−1.72587e8	−1.80825	−0.904126	−	0.427267i	$-0.859477\pi$
$457$	−1.72587e8	−1.80825	−0.904126	+	0.427267i	$0.859477\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	1.66978e8i	1.70435i	0.523261	+	0.852173i	$0.324715\pi$
$461$	1.66978e8i	1.70435i	−0.523261	+	0.852173i	$0.675285\pi$
$462$	0	0
$463$	0	0		−	1.00000i	$-0.5\pi$
$463$	0	0			1.00000i	$0.5\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	0	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	−9.19246e7	−0.826031
$482$	0	0
$483$	0	0
$484$	0	0
$485$	− 2.45608e8i	− 2.15287i
$486$	0	0
$487$	0	0		−	1.00000i	$-0.5\pi$
$487$	0	0			1.00000i	$0.5\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	3.70340e8	3.09072
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	0	0		−	1.00000i	$-0.5\pi$
$499$	0	0			1.00000i	$0.5\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	4.60962e8	3.57924
$506$	0	0
$507$	0	0
$508$	0	0
$509$	− 1.39082e8i	− 1.05467i	−0.849657	−	0.527335i	$-0.823191\pi$
$509$	− 1.39082e8i	− 1.05467i	0.849657	−	0.527335i	$-0.176809\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	1.73608e8i	1.22760i	0.789462	+	0.613800i	$0.210360\pi$
$521$	1.73608e8i	1.22760i	−0.789462	+	0.613800i	$0.789640\pi$
$522$	0	0
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	1.48036e8	1.00000
$530$	0	0
$531$	0	0
$532$	0	0
$533$	2.26585e8i	1.49641i
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−1.44852e8	−0.914815	−0.457407	−	0.889257i	$-0.651222\pi$
$541$	−1.44852e8	−0.914815	−0.457407	+	0.889257i	$0.651222\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	5.80414e8i	3.58549i
$546$	0	0
$547$	0	0		−	1.00000i	$-0.5\pi$
$547$	0	0			1.00000i	$0.5\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	3.43261e8i	1.98637i	0.116565	+	0.993183i	$0.462812\pi$
$557$	3.43261e8i	1.98637i	−0.116565	+	0.993183i	$0.537188\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	−2.47368e8	−1.37151
$566$	0	0
$567$	0	0
$568$	0	0
$569$	1.66447e8i	0.903524i	0.892138	+	0.451762i	$0.149204\pi$
$569$	1.66447e8i	0.903524i	−0.892138	+	0.451762i	$0.850796\pi$
$570$	0	0
$571$	0	0		−	1.00000i	$-0.5\pi$
$571$	0	0			1.00000i	$0.5\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−3.72270e8	−1.93790	−0.968948	−	0.247264i	$-0.920469\pi$
$577$	−3.72270e8	−1.93790	−0.968948	+	0.247264i	$0.920469\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	− 3.92088e8i	− 1.88027i	−0.340805	−	0.940134i	$-0.610700\pi$
$593$	− 3.92088e8i	− 1.88027i	0.340805	−	0.940134i	$-0.389300\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	0	0
$601$	1.44143e8	0.664002	0.332001	−	0.943279i	$-0.392276\pi$
$601$	1.44143e8	0.664002	0.332001	+	0.943279i	$0.392276\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	4.03364e8i	1.82151i
$606$	0	0
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	−7.85685e7	−0.341088	−0.170544	−	0.985350i	$-0.554553\pi$
$613$	−7.85685e7	−0.341088	−0.170544	+	0.985350i	$0.554553\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	− 1.26374e8i	− 0.538023i	−0.963137	−	0.269011i	$-0.913303\pi$
$617$	− 1.26374e8i	− 0.538023i	0.963137	−	0.269011i	$-0.0866969\pi$
$618$	0	0
$619$	0	0		−	1.00000i	$-0.5\pi$
$619$	0	0			1.00000i	$0.5\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	5.01640e8	2.05472
$626$	0	0
$627$	0	0
$628$	0	0
$629$	4.22582e8i	1.69808i
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−1.94827e8	−0.753755
$638$	0	0
$639$	0	0
$640$	0	0
$641$	− 8.73165e7i	− 0.331529i	−0.986165	−	0.165765i	$-0.946991\pi$
$641$	− 8.73165e7i	− 0.331529i	0.986165	−	0.165765i	$-0.0530092\pi$
$642$	0	0
$643$	0	0		−	1.00000i	$-0.5\pi$
$643$	0	0			1.00000i	$0.5\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	4.16927e8i	1.49734i	0.662942	+	0.748671i	$0.269308\pi$
$653$	4.16927e8i	1.49734i	−0.662942	+	0.748671i	$0.730692\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	9.06129e7	0.313752	0.156876	−	0.987618i	$-0.449858\pi$
$661$	9.06129e7	0.313752	0.156876	+	0.987618i	$0.449858\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−5.89733e8	−1.93468	−0.967342	−	0.253473i	$-0.918427\pi$
$673$	−5.89733e8	−1.93468	−0.967342	+	0.253473i	$0.918427\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	− 3.26873e8i	− 1.05345i	−0.850036	−	0.526725i	$-0.823420\pi$
$677$	− 3.26873e8i	− 1.05345i	0.850036	−	0.526725i	$-0.176580\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	−3.05061e8	−0.949105
$686$	0	0
$687$	0	0
$688$	0	0
$689$	− 3.12492e8i	− 0.955390i
$690$	0	0
$691$	0	0		−	1.00000i	$-0.5\pi$
$691$	0	0			1.00000i	$0.5\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	1.04162e9	3.07618
$698$	0	0
$699$	0	0
$700$	0	0
$701$	6.46098e8i	1.87562i	0.347151	+	0.937809i	$0.387149\pi$
$701$	6.46098e8i	1.87562i	−0.347151	+	0.937809i	$0.612851\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−3.09351e8	−0.867987	−0.433993	−	0.900916i	$-0.642896\pi$
$709$	−3.09351e8	−0.867987	−0.433993	+	0.900916i	$0.642896\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	0	0
$724$	0	0
$725$	− 1.76187e9i	− 4.62338i
$726$	0	0
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−3.38086e8	−0.858449	−0.429225	−	0.903198i	$-0.641213\pi$
$733$	−3.38086e8	−0.858449	−0.429225	+	0.903198i	$0.641213\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0		−	1.00000i	$-0.5\pi$
$739$	0	0			1.00000i	$0.5\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	1.45471e9	3.51809
$746$	0	0
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	0	0		−	1.00000i	$-0.5\pi$
$751$	0	0			1.00000i	$0.5\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	7.89096e8	1.81904	0.909520	−	0.415661i	$-0.136450\pi$
$757$	7.89096e8	1.81904	0.909520	+	0.415661i	$0.136450\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	5.20414e8i	1.18085i	0.807092	+	0.590425i	$0.201040\pi$
$761$	5.20414e8i	1.18085i	−0.807092	+	0.590425i	$0.798960\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−8.16391e8	−1.79523	−0.897613	−	0.440785i	$-0.854700\pi$
$769$	−8.16391e8	−1.79523	−0.897613	+	0.440785i	$0.854700\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	1.87891e7i	0.0406788i	0.999793	+	0.0203394i	$0.00647468\pi$
$773$	1.87891e7i	0.0406788i	−0.999793	+	0.0203394i	$0.993525\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	− 1.74364e9i	− 3.60451i
$786$	0	0
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−3.89057e8	−0.780179
$794$	0	0
$795$	0	0
$796$	0	0
$797$	4.58005e7i	0.0904680i	0.998976	+	0.0452340i	$0.0144033\pi$
$797$	4.58005e7i	0.0904680i	−0.998976	+	0.0452340i	$0.985597\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	− 2.87407e8i	− 0.542815i	−0.962465	−	0.271407i	$-0.912511\pi$
$809$	− 2.87407e8i	− 0.542815i	0.962465	−	0.271407i	$-0.0874891\pi$
$810$	0	0
$811$	0	0		−	1.00000i	$-0.5\pi$
$811$	0	0			1.00000i	$0.5\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	− 7.18690e8i	− 1.29871i	−0.760486	−	0.649355i	$-0.775039\pi$
$821$	− 7.18690e8i	− 1.29871i	0.760486	−	0.649355i	$-0.224961\pi$
$822$	0	0
$823$	0	0		−	1.00000i	$-0.5\pi$
$823$	0	0			1.00000i	$0.5\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	9.66949e8	1.69723	0.848613	−	0.529013i	$-0.177438\pi$
$829$	9.66949e8	1.69723	0.848613	+	0.529013i	$0.177438\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	8.95628e8i	1.54950i
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	−1.77176e9	−2.97863
$842$	0	0
$843$	0	0
$844$	0	0
$845$	− 4.74610e8i	− 0.786624i
$846$	0	0
$847$	0	0
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	−8.26038e8	−1.33092	−0.665462	−	0.746432i	$-0.731765\pi$
$853$	−8.26038e8	−1.33092	−0.665462	+	0.746432i	$0.731765\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	− 1.25798e9i	− 1.99863i	−0.0369904	−	0.999316i	$-0.511777\pi$
$857$	− 1.25798e9i	− 1.99863i	0.0369904	−	0.999316i	$-0.488223\pi$
$858$	0	0
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	−2.33776e9	−3.61204
$866$	0	0
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−4.58388e8	−0.679570	−0.339785	−	0.940503i	$-0.610354\pi$
$877$	−4.58388e8	−0.679570	−0.339785	+	0.940503i	$0.610354\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	− 6.68956e8i	− 0.978294i	−0.872201	−	0.489147i	$-0.837308\pi$
$881$	− 6.68956e8i	− 0.978294i	0.872201	−	0.489147i	$-0.162692\pi$
$882$	0	0
$883$	0	0		−	1.00000i	$-0.5\pi$
$883$	0	0			1.00000i	$0.5\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	0	0
$901$	−1.43654e9	−1.96401
$902$	0	0
$903$	0	0
$904$	0	0
$905$	2.56699e9i	3.46320i
$906$	0	0
$907$	0	0		−	1.00000i	$-0.5\pi$
$907$	0	0			1.00000i	$0.5\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	2.01041e9	2.54014
$926$	0	0
$927$	0	0
$928$	0	0
$929$	5.76078e8i	0.718512i	0.933239	+	0.359256i	$0.116970\pi$
$929$	5.76078e8i	0.718512i	−0.933239	+	0.359256i	$0.883030\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−1.05307e9	−1.28009	−0.640044	−	0.768338i	$-0.721084\pi$
$937$	−1.05307e9	−1.28009	−0.640044	+	0.768338i	$0.721084\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	− 5.93037e8i	− 0.711727i	−0.934538	−	0.355863i	$-0.884187\pi$
$941$	− 5.93037e8i	− 0.711727i	0.934538	−	0.355863i	$-0.115813\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	−1.07643e9	−1.25946
$950$	0	0
$951$	0	0
$952$	0	0
$953$	4.31331e8i	0.498347i	0.968459	+	0.249174i	$0.0801590\pi$
$953$	4.31331e8i	0.498347i	−0.968459	+	0.249174i	$0.919841\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−8.87504e8	−1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	− 3.27255e9i	− 3.64170i
$966$	0	0
$967$	0	0		−	1.00000i	$-0.5\pi$
$967$	0	0			1.00000i	$0.5\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	− 2.88318e7i	− 0.0309164i	−0.999881	−	0.0154582i	$-0.995079\pi$
$977$	− 2.88318e7i	− 0.0309164i	0.999881	−	0.0154582i	$-0.00492069\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	0	0
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	0	0
$985$	1.21848e9	1.27499
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−8.14875e8	−0.822253	−0.411127	−	0.911578i	$-0.634865\pi$
$997$	−8.14875e8	−0.822253	−0.411127	+	0.911578i	$0.634865\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.7.e.g.449.2		2
3.2	odd	2	inner	576.7.e.g.449.1		2
4.3	odd	2	CM	576.7.e.g.449.2		2
8.3	odd	2		288.7.e.b.161.1	✓	2
8.5	even	2		288.7.e.b.161.1	✓	2
12.11	even	2	inner	576.7.e.g.449.1		2
24.5	odd	2		288.7.e.b.161.2	yes	2
24.11	even	2		288.7.e.b.161.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.7.e.b.161.1	✓	2	8.3	odd	2
288.7.e.b.161.1	✓	2	8.5	even	2
288.7.e.b.161.2	yes	2	24.5	odd	2
288.7.e.b.161.2	yes	2	24.11	even	2
576.7.e.g.449.1		2	3.2	odd	2	inner
576.7.e.g.449.1		2	12.11	even	2	inner
576.7.e.g.449.2		2	1.1	even	1	trivial
576.7.e.g.449.2		2	4.3	odd	2	CM

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	576.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+227.688i q^{5} +O(q^{10})\)	\(q+227.688i q^{5} +1656.00 q^{13} -7612.71i q^{17} -36217.0 q^{25} +48647.5i q^{29} -55510.0 q^{37} +136827. i q^{41} -117649. q^{49} -188703. i q^{53} -234938. q^{61} +377052. i q^{65} -650016. q^{73} +1.73333e6 q^{85} -1.18291e6i q^{89} -1.07870e6 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q+O(q^{10}) \) 2 * q	\( 2 q + 3312 q^{13} - 72434 q^{25} - 111020 q^{37} - 235298 q^{49} - 469876 q^{61} - 1300032 q^{73} + 3466652 q^{85} - 2157408 q^{97}+O(q^{100}) \) 2 * q + 3312 * q^13 - 72434 * q^25 - 111020 * q^37 - 235298 * q^49 - 469876 * q^61 - 1300032 * q^73 + 3466652 * q^85 - 2157408 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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