LMFDB - Embedded newform 1225.4.a.s.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1225,4,Mod(1,1225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1225, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1225.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1225 = 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1225.a (trivial)

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:	yes
Analytic conductor:	$72.2773397570$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 245)
Fricke sign:	$+1$
Sato-Tate group:	$N(\mathrm{U}(1))$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	1225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.94427 q^{3} -8.00000 q^{4} +53.0000 q^{9} +72.0000 q^{11} -71.5542 q^{12} +40.2492 q^{13} +64.0000 q^{16} -102.859 q^{17} +232.551 q^{27} +54.0000 q^{29} +643.988 q^{33} -424.000 q^{36} +360.000 q^{39} -576.000 q^{44} +178.885 q^{47} +572.433 q^{48} -920.000 q^{51} -321.994 q^{52} -512.000 q^{64} +822.873 q^{68} +828.000 q^{71} -523.240 q^{73} +236.000 q^{79} +649.000 q^{81} +1511.58 q^{83} +482.991 q^{87} +1650.22 q^{97} +3816.00 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 16 q^{4} + 106 q^{9} + 144 q^{11} + 128 q^{16} + 108 q^{29} - 848 q^{36} + 720 q^{39} - 1152 q^{44} - 1840 q^{51} - 1024 q^{64} + 1656 q^{71} + 472 q^{79} + 1298 q^{81} + 7632 q^{99}+O(q^{100}) $ 2 * q - 16 * q^4 + 106 * q^9 + 144 * q^11 + 128 * q^16 + 108 * q^29 - 848 * q^36 + 720 * q^39 - 1152 * q^44 - 1840 * q^51 - 1024 * q^64 + 1656 * q^71 + 472 * q^79 + 1298 * q^81 + 7632 * q^99

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		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	8.94427	1.72133	0.860663	−	0.509175i	$-0.170049\pi$
$3$	8.94427	1.72133	0.860663	+	0.509175i	$0.170049\pi$
$4$	−8.00000	−1.00000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	53.0000	1.96296
$10$	0	0
$11$	72.0000	1.97353	0.986764	−	0.162160i	$-0.0518462\pi$
$11$	72.0000	1.97353	0.986764	+	0.162160i	$0.0518462\pi$
$12$	−71.5542	−1.72133
$13$	40.2492	0.858702	0.429351	−	0.903138i	$-0.358742\pi$
$13$	40.2492	0.858702	0.429351	+	0.903138i	$0.358742\pi$
$14$	0	0
$15$	0	0
$16$	64.0000	1.00000
$17$	−102.859	−1.46747	−0.733735	−	0.679435i	$-0.762225\pi$
$17$	−102.859	−1.46747	−0.733735	+	0.679435i	$0.762225\pi$
$18$	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		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	232.551	1.65757
$28$	0	0
$29$	54.0000	0.345778	0.172889	−	0.984941i	$-0.444690\pi$
$29$	54.0000	0.345778	0.172889	+	0.984941i	$0.444690\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	0	0
$33$	643.988	3.39709
$34$	0	0
$35$	0	0
$36$	−424.000	−1.96296
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	0	0
$39$	360.000	1.47811
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	−576.000	−1.97353
$45$	0	0
$46$	0	0
$47$	178.885	0.555173	0.277586	−	0.960701i	$-0.410466\pi$
$47$	178.885	0.555173	0.277586	+	0.960701i	$0.410466\pi$
$48$	572.433	1.72133
$49$	0	0
$50$	0	0
$51$	−920.000	−2.52600
$52$	−321.994	−0.858702
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	0	0
$63$	0	0
$64$	−512.000	−1.00000
$65$	0	0
$66$	0	0
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	822.873	1.46747
$69$	0	0
$70$	0	0
$71$	828.000	1.38402	0.692011	−	0.721887i	$-0.256725\pi$
$71$	828.000	1.38402	0.692011	+	0.721887i	$0.256725\pi$
$72$	0	0
$73$	−523.240	−0.838912	−0.419456	−	0.907776i	$-0.637779\pi$
$73$	−523.240	−0.838912	−0.419456	+	0.907776i	$0.637779\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	236.000	0.336102	0.168051	−	0.985778i	$-0.446253\pi$
$79$	236.000	0.336102	0.168051	+	0.985778i	$0.446253\pi$
$80$	0	0
$81$	649.000	0.890261
$82$	0	0
$83$	1511.58	1.99901	0.999504	−	0.0314901i	$-0.0100253\pi$
$83$	1511.58	1.99901	0.999504	+	0.0314901i	$0.0100253\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	482.991	0.595196
$88$	0	0
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	1650.22	1.72736	0.863682	−	0.504037i	$-0.168153\pi$
$97$	1650.22	1.72736	0.863682	+	0.504037i	$0.168153\pi$
$98$	0	0
$99$	3816.00	3.87396
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	−1931.96	−1.84817	−0.924087	−	0.382182i	$-0.875173\pi$
$103$	−1931.96	−1.84817	−0.924087	+	0.382182i	$0.875173\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	−1860.41	−1.65757
$109$	2266.00	1.99122	0.995612	−	0.0935765i	$-0.0298300\pi$
$109$	2266.00	1.99122	0.995612	+	0.0935765i	$0.0298300\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	0	0
$115$	0	0
$116$	−432.000	−0.345778
$117$	2133.21	1.68560
$118$	0	0
$119$	0	0
$120$	0	0
$121$	3853.00	2.89482
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	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		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	−5151.90	−3.39709
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	1600.00	0.955633
$142$	0	0
$143$	2897.94	1.69467
$144$	3392.00	1.96296
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−2466.00	−1.35586	−0.677928	−	0.735128i	$-0.737122\pi$
$149$	−2466.00	−1.35586	−0.677928	+	0.735128i	$0.737122\pi$
$150$	0	0
$151$	2788.00	1.50254	0.751272	−	0.659992i	$-0.229441\pi$
$151$	2788.00	1.50254	0.751272	+	0.659992i	$0.229441\pi$
$152$	0	0
$153$	−5451.53	−2.88059
$154$	0	0
$155$	0	0
$156$	−2880.00	−1.47811
$157$	3904.17	1.98463	0.992315	−	0.123734i	$-0.0394868\pi$
$157$	3904.17	1.98463	0.992315	+	0.123734i	$0.0394868\pi$
$158$	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
$167$	2558.06	1.18532	0.592661	−	0.805452i	$-0.298077\pi$
$167$	2558.06	1.18532	0.592661	+	0.805452i	$0.298077\pi$
$168$	0	0
$169$	−577.000	−0.262631
$170$	0	0
$171$	0	0
$172$	0	0
$173$	−4405.05	−1.93590	−0.967948	−	0.251150i	$-0.919191\pi$
$173$	−4405.05	−1.93590	−0.967948	+	0.251150i	$0.919191\pi$
$174$	0	0
$175$	0	0
$176$	4608.00	1.97353
$177$	0	0
$178$	0	0
$179$	936.000	0.390838	0.195419	−	0.980720i	$-0.437393\pi$
$179$	936.000	0.390838	0.195419	+	0.980720i	$0.437393\pi$
$180$	0	0
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−7405.86	−2.89610
$188$	−1431.08	−0.555173
$189$	0	0
$190$	0	0
$191$	−4212.00	−1.59565	−0.797826	−	0.602887i	$-0.794017\pi$
$191$	−4212.00	−1.59565	−0.797826	+	0.602887i	$0.794017\pi$
$192$	−4579.47	−1.72133
$193$	0	0		−	1.00000i	$-0.5\pi$
$193$	0	0			1.00000i	$0.5\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	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
$204$	7360.00	2.52600
$205$	0	0
$206$	0	0
$207$	0	0
$208$	2575.95	0.858702
$209$	0	0
$210$	0	0
$211$	−2392.00	−0.780436	−0.390218	−	0.920722i	$-0.627600\pi$
$211$	−2392.00	−0.780436	−0.390218	+	0.920722i	$0.627600\pi$
$212$	0	0
$213$	7405.86	2.38235
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−4680.00	−1.44404
$220$	0	0
$221$	−4140.00	−1.26012
$222$	0	0
$223$	−4185.92	−1.25700	−0.628498	−	0.777812i	$-0.716330\pi$
$223$	−4185.92	−1.25700	−0.628498	+	0.777812i	$0.716330\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−4767.30	−1.39391	−0.696953	−	0.717117i	$-0.745461\pi$
$227$	−4767.30	−1.39391	−0.696953	+	0.717117i	$0.745461\pi$
$228$	0	0
$229$	0	0		−	1.00000i	$-0.5\pi$
$229$	0	0			1.00000i	$0.5\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0		−	1.00000i	$-0.5\pi$
$233$	0	0			1.00000i	$0.5\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	2110.85	0.578541
$238$	0	0
$239$	5724.00	1.54918	0.774592	−	0.632462i	$-0.217955\pi$
$239$	5724.00	1.54918	0.774592	+	0.632462i	$0.217955\pi$
$240$	0	0
$241$	0	0		−	1.00000i	$-0.5\pi$
$241$	0	0			1.00000i	$0.5\pi$
$242$	0	0
$243$	−474.046	−0.125144
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	13520.0	3.44094
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	4096.00	1.00000
$257$	−3358.57	−0.815183	−0.407592	−	0.913164i	$-0.633631\pi$
$257$	−3358.57	−0.815183	−0.407592	+	0.913164i	$0.633631\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	2862.00	0.678748
$262$	0	0
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	−6582.98	−1.46747
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	0	0		−	1.00000i	$-0.5\pi$
$277$	0	0			1.00000i	$0.5\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−8118.00	−1.72341	−0.861707	−	0.507406i	$-0.830604\pi$
$281$	−8118.00	−1.72341	−0.861707	+	0.507406i	$0.830604\pi$
$282$	0	0
$283$	−9257.32	−1.94449	−0.972245	−	0.233965i	$-0.924830\pi$
$283$	−9257.32	−1.94449	−0.972245	+	0.233965i	$0.924830\pi$
$284$	−6624.00	−1.38402
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	5667.00	1.15347
$290$	0	0
$291$	14760.0	2.97336
$292$	4185.92	0.838912
$293$	6739.51	1.34378	0.671888	−	0.740653i	$-0.265484\pi$
$293$	6739.51	1.34378	0.671888	+	0.740653i	$0.265484\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	16743.7	3.27127
$298$	0	0
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	5876.39	1.09245	0.546227	−	0.837637i	$-0.316064\pi$
$307$	5876.39	1.09245	0.546227	+	0.837637i	$0.316064\pi$
$308$	0	0
$309$	−17280.0	−3.18131
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	10746.5	1.94067	0.970336	−	0.241759i	$-0.0777244\pi$
$313$	10746.5	1.94067	0.970336	+	0.241759i	$0.0777244\pi$
$314$	0	0
$315$	0	0
$316$	−1888.00	−0.336102
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	0	0
$319$	3888.00	0.682402
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	−5192.00	−0.890261
$325$	0	0
$326$	0	0
$327$	20267.7	3.42755
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−7432.00	−1.23414	−0.617069	−	0.786909i	$-0.711680\pi$
$331$	−7432.00	−1.23414	−0.617069	+	0.786909i	$0.711680\pi$
$332$	−12092.7	−1.99901
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	0	0		−	1.00000i	$-0.5\pi$
$337$	0	0			1.00000i	$0.5\pi$
$338$	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		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	−3863.93	−0.595196
$349$	0	0		−	1.00000i	$-0.5\pi$
$349$	0	0			1.00000i	$0.5\pi$
$350$	0	0
$351$	9360.00	1.42336
$352$	0	0
$353$	−6220.74	−0.937951	−0.468975	−	0.883211i	$-0.655377\pi$
$353$	−6220.74	−0.937951	−0.468975	+	0.883211i	$0.655377\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−7884.00	−1.15906	−0.579529	−	0.814952i	$-0.696763\pi$
$359$	−7884.00	−1.15906	−0.579529	+	0.814952i	$0.696763\pi$
$360$	0	0
$361$	−6859.00	−1.00000
$362$	0	0
$363$	34462.3	4.98292
$364$	0	0
$365$	0	0
$366$	0	0
$367$	804.984	0.114495	0.0572477	−	0.998360i	$-0.481768\pi$
$367$	804.984	0.114495	0.0572477	+	0.998360i	$0.481768\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	0	0		−	1.00000i	$-0.5\pi$
$373$	0	0			1.00000i	$0.5\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	2173.46	0.296920
$378$	0	0
$379$	14096.0	1.91046	0.955228	−	0.295870i	$-0.0956097\pi$
$379$	14096.0	1.91046	0.955228	+	0.295870i	$0.0956097\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	−4686.80	−0.625285	−0.312643	−	0.949871i	$-0.601214\pi$
$383$	−4686.80	−0.625285	−0.312643	+	0.949871i	$0.601214\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	0	0
$388$	−13201.7	−1.72736
$389$	−13806.0	−1.79947	−0.899733	−	0.436442i	$-0.856239\pi$
$389$	−13806.0	−1.79947	−0.899733	+	0.436442i	$0.856239\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	−30528.0	−3.87396
$397$	−15817.9	−1.99970	−0.999849	−	0.0173927i	$-0.994463\pi$
$397$	−15817.9	−1.99970	−0.999849	+	0.0173927i	$0.994463\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	12798.0	1.59377	0.796885	−	0.604131i	$-0.206480\pi$
$401$	12798.0	1.59377	0.796885	+	0.604131i	$0.206480\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0		−	1.00000i	$-0.5\pi$
$409$	0	0			1.00000i	$0.5\pi$
$410$	0	0
$411$	0	0
$412$	15455.7	1.84817
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	3922.00	0.454030	0.227015	−	0.973891i	$-0.427103\pi$
$421$	3922.00	0.454030	0.227015	+	0.973891i	$0.427103\pi$
$422$	0	0
$423$	9480.93	1.08978
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	25920.0	2.91708
$430$	0	0
$431$	3852.00	0.430497	0.215249	−	0.976559i	$-0.430944\pi$
$431$	3852.00	0.430497	0.215249	+	0.976559i	$0.430944\pi$
$432$	14883.3	1.65757
$433$	−12920.0	−1.43394	−0.716970	−	0.697105i	$-0.754471\pi$
$433$	−12920.0	−1.43394	−0.716970	+	0.697105i	$0.754471\pi$
$434$	0	0
$435$	0	0
$436$	−18128.0	−1.99122
$437$	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		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−22056.6	−2.33387
$448$	0	0
$449$	11394.0	1.19759	0.598793	−	0.800904i	$-0.295647\pi$
$449$	11394.0	1.19759	0.598793	+	0.800904i	$0.295647\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	24936.6	2.58637
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0	0		−	1.00000i	$-0.5\pi$
$457$	0	0			1.00000i	$0.5\pi$
$458$	0	0
$459$	−23920.0	−2.43244
$460$	0	0
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	0	0
$463$	0	0		−	1.00000i	$-0.5\pi$
$463$	0	0			1.00000i	$0.5\pi$
$464$	3456.00	0.345778
$465$	0	0
$466$	0	0
$467$	−17164.1	−1.70077	−0.850383	−	0.526164i	$-0.823630\pi$
$467$	−17164.1	−1.70077	−0.850383	+	0.526164i	$0.823630\pi$
$468$	−17065.7	−1.68560
$469$	0	0
$470$	0	0
$471$	34920.0	3.41620
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	0	0
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	−30824.0	−2.89482
$485$	0	0
$486$	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
$491$	12672.0	1.16472	0.582362	−	0.812930i	$-0.302129\pi$
$491$	12672.0	1.16472	0.582362	+	0.812930i	$0.302129\pi$
$492$	0	0
$493$	−5554.39	−0.507418
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	7544.00	0.676785	0.338393	−	0.941005i	$-0.390117\pi$
$499$	7544.00	0.676785	0.338393	+	0.941005i	$0.390117\pi$
$500$	0	0
$501$	22880.0	2.04033
$502$	0	0
$503$	−2432.84	−0.215656	−0.107828	−	0.994170i	$-0.534390\pi$
$503$	−2432.84	−0.215656	−0.107828	+	0.994170i	$0.534390\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−5160.84	−0.452073
$508$	0	0
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	12879.8	1.09565
$518$	0	0
$519$	−39400.0	−3.33231
$520$	0	0
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	0	0
$523$	−22781.1	−1.90468	−0.952339	−	0.305043i	$-0.901329\pi$
$523$	−22781.1	−1.90468	−0.952339	+	0.305043i	$0.901329\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	41215.2	3.39709
$529$	−12167.0	−1.00000
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	8371.84	0.672759
$538$	0	0
$539$	0	0
$540$	0	0
$541$	9718.00	0.772291	0.386146	−	0.922438i	$-0.373806\pi$
$541$	9718.00	0.772291	0.386146	+	0.922438i	$0.373806\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	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
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	−66240.0	−4.98512
$562$	0	0
$563$	13908.3	1.04115	0.520574	−	0.853816i	$-0.325718\pi$
$563$	13908.3	1.04115	0.520574	+	0.853816i	$0.325718\pi$
$564$	−12800.0	−0.955633
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−10026.0	−0.738685	−0.369343	−	0.929293i	$-0.620417\pi$
$569$	−10026.0	−0.738685	−0.369343	+	0.929293i	$0.620417\pi$
$570$	0	0
$571$	−22048.0	−1.61590	−0.807951	−	0.589250i	$-0.799423\pi$
$571$	−22048.0	−1.61590	−0.807951	+	0.589250i	$0.799423\pi$
$572$	−23183.6	−1.69467
$573$	−37673.3	−2.74664
$574$	0	0
$575$	0	0
$576$	−27136.0	−1.96296
$577$	−20325.9	−1.46651	−0.733255	−	0.679954i	$-0.762000\pi$
$577$	−20325.9	−1.46651	−0.733255	+	0.679954i	$0.762000\pi$
$578$	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
$587$	−15035.3	−1.05720	−0.528598	−	0.848872i	$-0.677282\pi$
$587$	−15035.3	−1.05720	−0.528598	+	0.848872i	$0.677282\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	1104.62	0.0764944	0.0382472	−	0.999268i	$-0.487823\pi$
$593$	1104.62	0.0764944	0.0382472	+	0.999268i	$0.487823\pi$
$594$	0	0
$595$	0	0
$596$	19728.0	1.35586
$597$	0	0
$598$	0	0
$599$	10764.0	0.734232	0.367116	−	0.930175i	$-0.380345\pi$
$599$	10764.0	0.734232	0.367116	+	0.930175i	$0.380345\pi$
$600$	0	0
$601$	0	0		−	1.00000i	$-0.5\pi$
$601$	0	0			1.00000i	$0.5\pi$
$602$	0	0
$603$	0	0
$604$	−22304.0	−1.50254
$605$	0	0
$606$	0	0
$607$	−28496.5	−1.90549	−0.952747	−	0.303764i	$-0.901757\pi$
$607$	−28496.5	−1.90549	−0.952747	+	0.303764i	$0.901757\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	7200.00	0.476728
$612$	43612.3	2.88059
$613$	0	0		−	1.00000i	$-0.5\pi$
$613$	0	0			1.00000i	$0.5\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	0	0		−	1.00000i	$-0.5\pi$
$617$	0	0			1.00000i	$0.5\pi$
$618$	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
$624$	23040.0	1.47811
$625$	0	0
$626$	0	0
$627$	0	0
$628$	−31233.4	−1.98463
$629$	0	0
$630$	0	0
$631$	−14852.0	−0.937003	−0.468501	−	0.883463i	$-0.655206\pi$
$631$	−14852.0	−0.937003	−0.468501	+	0.883463i	$0.655206\pi$
$632$	0	0
$633$	−21394.7	−1.34339
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	43884.0	2.71678
$640$	0	0
$641$	−28782.0	−1.77351	−0.886756	−	0.462239i	$-0.847046\pi$
$641$	−28782.0	−1.77351	−0.886756	+	0.462239i	$0.847046\pi$
$642$	0	0
$643$	−12638.3	−0.775123	−0.387562	−	0.921844i	$-0.626683\pi$
$643$	−12638.3	−0.775123	−0.387562	+	0.921844i	$0.626683\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−28997.3	−1.76198	−0.880991	−	0.473133i	$-0.843123\pi$
$647$	−28997.3	−1.76198	−0.880991	+	0.473133i	$0.843123\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	0	0		−	1.00000i	$-0.5\pi$
$653$	0	0			1.00000i	$0.5\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−27731.7	−1.64675
$658$	0	0
$659$	−31824.0	−1.88116	−0.940582	−	0.339567i	$-0.889720\pi$
$659$	−31824.0	−1.88116	−0.940582	+	0.339567i	$0.889720\pi$
$660$	0	0
$661$	0	0		−	1.00000i	$-0.5\pi$
$661$	0	0			1.00000i	$0.5\pi$
$662$	0	0
$663$	−37029.3	−2.16908
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	−20464.5	−1.18532
$669$	−37440.0	−2.16370
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0		−	1.00000i	$-0.5\pi$
$673$	0	0			1.00000i	$0.5\pi$
$674$	0	0
$675$	0	0
$676$	4616.00	0.262631
$677$	31577.8	1.79266	0.896331	−	0.443386i	$-0.146223\pi$
$677$	31577.8	1.79266	0.896331	+	0.443386i	$0.146223\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−42640.0	−2.39937
$682$	0	0
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	0	0		−	1.00000i	$-0.5\pi$
$691$	0	0			1.00000i	$0.5\pi$
$692$	35240.4	1.93590
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	33462.0	1.80291	0.901457	−	0.432869i	$-0.142499\pi$
$701$	33462.0	1.80291	0.901457	+	0.432869i	$0.142499\pi$
$702$	0	0
$703$	0	0
$704$	−36864.0	−1.97353
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	2126.00	0.112614	0.0563072	−	0.998413i	$-0.482067\pi$
$709$	2126.00	0.112614	0.0563072	+	0.998413i	$0.482067\pi$
$710$	0	0
$711$	12508.0	0.659756
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	−7488.00	−0.390838
$717$	51197.0	2.66665
$718$	0	0
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−37512.3	−1.91369	−0.956845	−	0.290597i	$-0.906146\pi$
$727$	−37512.3	−1.91369	−0.956845	+	0.290597i	$0.906146\pi$
$728$	0	0
$729$	−21763.0	−1.10567
$730$	0	0
$731$	0	0
$732$	0	0
$733$	36103.6	1.81926	0.909628	−	0.415423i	$-0.136366\pi$
$733$	36103.6	1.81926	0.909628	+	0.415423i	$0.136366\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	23056.0	1.14767	0.573835	−	0.818971i	$-0.305455\pi$
$739$	23056.0	1.14767	0.573835	+	0.818971i	$0.305455\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	0	0		−	1.00000i	$-0.5\pi$
$743$	0	0			1.00000i	$0.5\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	80113.8	3.92398
$748$	59246.9	2.89610
$749$	0	0
$750$	0	0
$751$	27092.0	1.31638	0.658190	−	0.752852i	$-0.271322\pi$
$751$	27092.0	1.31638	0.658190	+	0.752852i	$0.271322\pi$
$752$	11448.7	0.555173
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	0	0		−	1.00000i	$-0.5\pi$
$757$	0	0			1.00000i	$0.5\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	0	0		−	1.00000i	$-0.5\pi$
$761$	0	0			1.00000i	$0.5\pi$
$762$	0	0
$763$	0	0
$764$	33696.0	1.59565
$765$	0	0
$766$	0	0
$767$	0	0
$768$	36635.7	1.72133
$769$	0	0		−	1.00000i	$-0.5\pi$
$769$	0	0			1.00000i	$0.5\pi$
$770$	0	0
$771$	−30040.0	−1.40320
$772$	0	0
$773$	5174.26	0.240757	0.120379	−	0.992728i	$-0.461589\pi$
$773$	5174.26	0.240757	0.120379	+	0.992728i	$0.461589\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	59616.0	2.73141
$782$	0	0
$783$	12557.8	0.573152
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−41456.7	−1.87773	−0.938864	−	0.344289i	$-0.888120\pi$
$787$	−41456.7	−1.87773	−0.938864	+	0.344289i	$0.888120\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	41031.8	1.82362	0.911808	−	0.410616i	$-0.134686\pi$
$797$	41031.8	1.82362	0.911808	+	0.410616i	$0.134686\pi$
$798$	0	0
$799$	−18400.0	−0.814700
$800$	0	0
$801$	0	0
$802$	0	0
$803$	−37673.3	−1.65562
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	35334.0	1.53557	0.767786	−	0.640707i	$-0.221359\pi$
$809$	35334.0	1.53557	0.767786	+	0.640707i	$0.221359\pi$
$810$	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
$816$	−58880.0	−2.52600
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	44802.0	1.90451	0.952254	−	0.305308i	$-0.0987594\pi$
$821$	44802.0	1.90451	0.952254	+	0.305308i	$0.0987594\pi$
$822$	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		−	1.00000i	$-0.5\pi$
$827$	0	0			1.00000i	$0.5\pi$
$828$	0	0
$829$	0	0		−	1.00000i	$-0.5\pi$
$829$	0	0			1.00000i	$0.5\pi$
$830$	0	0
$831$	0	0
$832$	−20607.6	−0.858702
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	−21473.0	−0.880438
$842$	0	0
$843$	−72609.6	−2.96656
$844$	19136.0	0.780436
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−82800.0	−3.34710
$850$	0	0
$851$	0	0
$852$	−59246.9	−2.38235
$853$	37794.0	1.51705	0.758524	−	0.651645i	$-0.225921\pi$
$853$	37794.0	1.51705	0.758524	+	0.651645i	$0.225921\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−7428.22	−0.296083	−0.148041	−	0.988981i	$-0.547297\pi$
$857$	−7428.22	−0.296083	−0.148041	+	0.988981i	$0.547297\pi$
$858$	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		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	50687.2	1.98550
$868$	0	0
$869$	16992.0	0.663307
$870$	0	0
$871$	0	0
$872$	0	0
$873$	87461.6	3.39075
$874$	0	0
$875$	0	0
$876$	37440.0	1.44404
$877$	0	0		−	1.00000i	$-0.5\pi$
$877$	0	0			1.00000i	$0.5\pi$
$878$	0	0
$879$	60280.0	2.31308
$880$	0	0
$881$	0	0		−	1.00000i	$-0.5\pi$
$881$	0	0			1.00000i	$0.5\pi$
$882$	0	0
$883$	0	0		−	1.00000i	$-0.5\pi$
$883$	0	0			1.00000i	$0.5\pi$
$884$	33120.0	1.26012
$885$	0	0
$886$	0	0
$887$	−49408.2	−1.87031	−0.935154	−	0.354241i	$-0.884739\pi$
$887$	−49408.2	−1.87031	−0.935154	+	0.354241i	$0.884739\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	46728.0	1.75695
$892$	33487.4	1.25700
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	0	0		−	1.00000i	$-0.5\pi$
$907$	0	0			1.00000i	$0.5\pi$
$908$	38138.4	1.39391
$909$	0	0
$910$	0	0
$911$	31068.0	1.12989	0.564944	−	0.825129i	$-0.308898\pi$
$911$	31068.0	1.12989	0.564944	+	0.825129i	$0.308898\pi$
$912$	0	0
$913$	108834.	3.94510
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	55564.0	1.99444	0.997218	−	0.0745363i	$-0.0237477\pi$
$919$	55564.0	1.99444	0.997218	+	0.0745363i	$0.0237477\pi$
$920$	0	0
$921$	52560.0	1.88047
$922$	0	0
$923$	33326.4	1.18846
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−102394.	−3.62790
$928$	0	0
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	18554.9	0.646918	0.323459	−	0.946242i	$-0.395154\pi$
$937$	18554.9	0.646918	0.323459	+	0.946242i	$0.395154\pi$
$938$	0	0
$939$	96120.0	3.34053
$940$	0	0
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	−16886.8	−0.578541
$949$	−21060.0	−0.720376
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0		−	1.00000i	$-0.5\pi$
$953$	0	0			1.00000i	$0.5\pi$
$954$	0	0
$955$	0	0
$956$	−45792.0	−1.54918
$957$	34775.3	1.17464
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−29791.0	−1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	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		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	3792.37	0.125144
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	0	0		−	1.00000i	$-0.5\pi$
$977$	0	0			1.00000i	$0.5\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	120098.	3.90870
$982$	0	0
$983$	−61160.9	−1.98447	−0.992233	−	0.124390i	$-0.960302\pi$
$983$	−61160.9	−1.98447	−0.992233	+	0.124390i	$0.960302\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	13988.0	0.448379	0.224189	−	0.974546i	$-0.428027\pi$
$991$	13988.0	0.448379	0.224189	+	0.974546i	$0.428027\pi$
$992$	0	0
$993$	−66473.8	−2.12435
$994$	0	0
$995$	0	0
$996$	−108160.	−3.44094
$997$	−39484.5	−1.25425	−0.627125	−	0.778919i	$-0.715768\pi$
$997$	−39484.5	−1.25425	−0.627125	+	0.778919i	$0.715768\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1225.4.a.s.1.2		2
5.2	odd	4		245.4.b.a.99.1	✓	2
5.3	odd	4		245.4.b.a.99.2	yes	2
5.4	even	2	inner	1225.4.a.s.1.1		2
7.6	odd	2	inner	1225.4.a.s.1.1		2
35.2	odd	12		245.4.j.a.214.2		4
35.3	even	12		245.4.j.a.79.1		4
35.12	even	12		245.4.j.a.214.1		4
35.13	even	4		245.4.b.a.99.1	✓	2
35.17	even	12		245.4.j.a.79.2		4
35.18	odd	12		245.4.j.a.79.2		4
35.23	odd	12		245.4.j.a.214.1		4
35.27	even	4		245.4.b.a.99.2	yes	2
35.32	odd	12		245.4.j.a.79.1		4
35.33	even	12		245.4.j.a.214.2		4
35.34	odd	2	CM	1225.4.a.s.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.4.b.a.99.1	✓	2	5.2	odd	4
245.4.b.a.99.1	✓	2	35.13	even	4
245.4.b.a.99.2	yes	2	5.3	odd	4
245.4.b.a.99.2	yes	2	35.27	even	4
245.4.j.a.79.1		4	35.3	even	12
245.4.j.a.79.1		4	35.32	odd	12
245.4.j.a.79.2		4	35.17	even	12
245.4.j.a.79.2		4	35.18	odd	12
245.4.j.a.214.1		4	35.12	even	12
245.4.j.a.214.1		4	35.23	odd	12
245.4.j.a.214.2		4	35.2	odd	12
245.4.j.a.214.2		4	35.33	even	12
1225.4.a.s.1.1		2	5.4	even	2	inner
1225.4.a.s.1.1		2	7.6	odd	2	inner
1225.4.a.s.1.2		2	1.1	even	1	trivial
1225.4.a.s.1.2		2	35.34	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:	\( N \)	\(=\)	\( 1225 = 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1225.a (trivial)

\(f(q)\)	\(=\)	\(q+8.94427 q^{3} -8.00000 q^{4} +53.0000 q^{9} +72.0000 q^{11} -71.5542 q^{12} +40.2492 q^{13} +64.0000 q^{16} -102.859 q^{17} +232.551 q^{27} +54.0000 q^{29} +643.988 q^{33} -424.000 q^{36} +360.000 q^{39} -576.000 q^{44} +178.885 q^{47} +572.433 q^{48} -920.000 q^{51} -321.994 q^{52} -512.000 q^{64} +822.873 q^{68} +828.000 q^{71} -523.240 q^{73} +236.000 q^{79} +649.000 q^{81} +1511.58 q^{83} +482.991 q^{87} +1650.22 q^{97} +3816.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 16 q^{4} + 106 q^{9} + 144 q^{11} + 128 q^{16} + 108 q^{29} - 848 q^{36} + 720 q^{39} - 1152 q^{44} - 1840 q^{51} - 1024 q^{64} + 1656 q^{71} + 472 q^{79} + 1298 q^{81} + 7632 q^{99}+O(q^{100}) \) 2 * q - 16 * q^4 + 106 * q^9 + 144 * q^11 + 128 * q^16 + 108 * q^29 - 848 * q^36 + 720 * q^39 - 1152 * q^44 - 1840 * q^51 - 1024 * q^64 + 1656 * q^71 + 472 * q^79 + 1298 * q^81 + 7632 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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