LMFDB - Embedded newform 6400.2.a.bc.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6400,2,Mod(1,6400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6400, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6400.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6400 = 2^{8} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6400.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:	$51.1042572936$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{6}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 6 $ x^2 - 6
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1600)
Fricke sign:	$+1$
Sato-Tate group:	$N(\mathrm{U}(1))$

Embedding invariants

Embedding label			1.1
Root			$-2.44949$ of defining polynomial
Character	$\chi$	$=$	6400.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.44949 q^{3} +8.89898 q^{9} -5.44949 q^{11} -1.89898 q^{17} +6.34847 q^{19} -20.3485 q^{27} +18.7980 q^{33} +6.79796 q^{41} -10.0000 q^{43} -7.00000 q^{49} +6.55051 q^{51} -21.8990 q^{57} +6.00000 q^{59} -0.348469 q^{67} +15.6969 q^{73} +43.4949 q^{81} -6.55051 q^{83} +4.10102 q^{89} +10.0000 q^{97} -48.4949 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + 8 q^{9} - 6 q^{11} + 6 q^{17} - 2 q^{19} - 26 q^{27} + 18 q^{33} - 6 q^{41} - 20 q^{43} - 14 q^{49} + 18 q^{51} - 34 q^{57} + 12 q^{59} + 14 q^{67} + 2 q^{73} + 38 q^{81} - 18 q^{83} + 18 q^{89}+ \cdots - 48 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + 8 * q^9 - 6 * q^11 + 6 * q^17 - 2 * q^19 - 26 * q^27 + 18 * q^33 - 6 * q^41 - 20 * q^43 - 14 * q^49 + 18 * q^51 - 34 * q^57 + 12 * q^59 + 14 * q^67 + 2 * q^73 + 38 * q^81 - 18 * q^83 + 18 * q^89 + 20 * q^97 - 48 * 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
$2$	0	0
$3$	−3.44949	−1.99156	−0.995782	−	0.0917517i	$-0.970753\pi$
$3$	−3.44949	−1.99156	−0.995782	+	0.0917517i	$0.970753\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	0	0
$9$	8.89898	2.96633
$10$	0	0
$11$	−5.44949	−1.64308	−0.821541	−	0.570149i	$-0.806886\pi$
$11$	−5.44949	−1.64308	−0.821541	+	0.570149i	$0.806886\pi$
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−1.89898	−0.460570	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	−1.89898	−0.460570	−0.230285	+	0.973123i	$0.573966\pi$
$18$	0	0
$19$	6.34847	1.45644	0.728219	−	0.685344i	$-0.240348\pi$
$19$	6.34847	1.45644	0.728219	+	0.685344i	$0.240348\pi$
$20$	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
$27$	−20.3485	−3.91606
$28$	0	0
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	0	0
$33$	18.7980	3.27230
$34$	0	0
$35$	0	0
$36$	0	0
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	6.79796	1.06166	0.530831	−	0.847477i	$-0.321880\pi$
$41$	6.79796	1.06166	0.530831	+	0.847477i	$0.321880\pi$
$42$	0	0
$43$	−10.0000	−1.52499	−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000	−1.52499	−0.762493	+	0.646997i	$0.776025\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	0	0
$51$	6.55051	0.917255
$52$	0	0
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−21.8990	−2.90059
$58$	0	0
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	0	0
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	−0.348469	−0.0425723	−0.0212861	−	0.999773i	$-0.506776\pi$
$67$	−0.348469	−0.0425723	−0.0212861	+	0.999773i	$0.506776\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	15.6969	1.83719	0.918594	−	0.395203i	$-0.129326\pi$
$73$	15.6969	1.83719	0.918594	+	0.395203i	$0.129326\pi$
$74$	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
$81$	43.4949	4.83277
$82$	0	0
$83$	−6.55051	−0.719012	−0.359506	−	0.933143i	$-0.617055\pi$
$83$	−6.55051	−0.719012	−0.359506	+	0.933143i	$0.617055\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	4.10102	0.434707	0.217354	−	0.976093i	$-0.430258\pi$
$89$	4.10102	0.434707	0.217354	+	0.976093i	$0.430258\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	10.0000	1.01535	0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000	1.01535	0.507673	+	0.861550i	$0.330506\pi$
$98$	0	0
$99$	−48.4949	−4.87392
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	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
$107$	14.1464	1.36759	0.683793	−	0.729676i	$-0.260329\pi$
$107$	14.1464	1.36759	0.683793	+	0.729676i	$0.260329\pi$
$108$	0	0
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	−18.7980	−1.76836	−0.884182	−	0.467143i	$-0.845283\pi$
$113$	−18.7980	−1.76836	−0.884182	+	0.467143i	$0.845283\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	18.6969	1.69972
$122$	0	0
$123$	−23.4495	−2.11437
$124$	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
$129$	34.4949	3.03711
$130$	0	0
$131$	18.0000	1.57267	0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000	1.57267	0.786334	+	0.617802i	$0.211977\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−22.5959	−1.93050	−0.965250	−	0.261329i	$-0.915839\pi$
$137$	−22.5959	−1.93050	−0.965250	+	0.261329i	$0.915839\pi$
$138$	0	0
$139$	−3.65153	−0.309719	−0.154859	−	0.987937i	$-0.549492\pi$
$139$	−3.65153	−0.309719	−0.154859	+	0.987937i	$0.549492\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	24.1464	1.99156
$148$	0	0
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	0	0
$153$	−16.8990	−1.36620
$154$	0	0
$155$	0	0
$156$	0	0
$157$	0	0		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	21.0454	1.64840	0.824202	−	0.566296i	$-0.191624\pi$
$163$	21.0454	1.64840	0.824202	+	0.566296i	$0.191624\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	−13.0000	−1.00000
$170$	0	0
$171$	56.4949	4.32027
$172$	0	0
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−20.6969	−1.55568
$178$	0	0
$179$	8.14643	0.608893	0.304446	−	0.952529i	$-0.401529\pi$
$179$	8.14643	0.608893	0.304446	+	0.952529i	$0.401529\pi$
$180$	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
$187$	10.3485	0.756755
$188$	0	0
$189$	0	0
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	0	0
$193$	25.6969	1.84971	0.924853	−	0.380325i	$-0.124188\pi$
$193$	25.6969	1.84971	0.924853	+	0.380325i	$0.124188\pi$
$194$	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
$201$	1.20204	0.0847854
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	−34.5959	−2.39305
$210$	0	0
$211$	29.0454	1.99957	0.999784	−	0.0207756i	$-0.00661356\pi$
$211$	29.0454	1.99957	0.999784	+	0.0207756i	$0.00661356\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−54.1464	−3.65888
$220$	0	0
$221$	0	0
$222$	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
$227$	−30.0000	−1.99117	−0.995585	−	0.0938647i	$-0.970078\pi$
$227$	−30.0000	−1.99117	−0.995585	+	0.0938647i	$0.970078\pi$
$228$	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
$233$	30.0000	1.96537	0.982683	−	0.185296i	$-0.0593245\pi$
$233$	30.0000	1.96537	0.982683	+	0.185296i	$0.0593245\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	−27.6969	−1.78412	−0.892058	−	0.451920i	$-0.850739\pi$
$241$	−27.6969	−1.78412	−0.892058	+	0.451920i	$0.850739\pi$
$242$	0	0
$243$	−88.9898	−5.70870
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	22.5959	1.43196
$250$	0	0
$251$	−29.9444	−1.89007	−0.945036	−	0.326965i	$-0.893974\pi$
$251$	−29.9444	−1.89007	−0.945036	+	0.326965i	$0.893974\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−30.0000	−1.87135	−0.935674	−	0.352865i	$-0.885208\pi$
$257$	−30.0000	−1.87135	−0.935674	+	0.352865i	$0.885208\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	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
$267$	−14.1464	−0.865747
$268$	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	$0.5\pi$
$272$	0	0
$273$	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
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	0	0
$283$	11.0454	0.656581	0.328291	−	0.944577i	$-0.393527\pi$
$283$	11.0454	0.656581	0.328291	+	0.944577i	$0.393527\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−13.3939	−0.787875
$290$	0	0
$291$	−34.4949	−2.02213
$292$	0	0
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	110.889	6.43442
$298$	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
$307$	−9.65153	−0.550842	−0.275421	−	0.961324i	$-0.588817\pi$
$307$	−9.65153	−0.550842	−0.275421	+	0.961324i	$0.588817\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	−48.7980	−2.72364
$322$	0	0
$323$	−12.0556	−0.670792
$324$	0	0
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−9.04541	−0.497181	−0.248590	−	0.968609i	$-0.579967\pi$
$331$	−9.04541	−0.497181	−0.248590	+	0.968609i	$0.579967\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	36.3939	1.98250	0.991250	−	0.131995i	$-0.0421382\pi$
$337$	36.3939	1.98250	0.991250	+	0.131995i	$0.0421382\pi$
$338$	0	0
$339$	64.8434	3.52181
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−34.8434	−1.87049	−0.935245	−	0.354001i	$-0.884821\pi$
$347$	−34.8434	−1.87049	−0.935245	+	0.354001i	$0.884821\pi$
$348$	0	0
$349$	0	0		−	1.00000i	$-0.5\pi$
$349$	0	0			1.00000i	$0.5\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	−30.0000	−1.59674	−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000	−1.59674	−0.798369	+	0.602168i	$0.794304\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	21.3031	1.12121
$362$	0	0
$363$	−64.4949	−3.38510
$364$	0	0
$365$	0	0
$366$	0	0
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	0	0
$369$	60.4949	3.14924
$370$	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
$377$	0	0
$378$	0	0
$379$	−26.3485	−1.35343	−0.676715	−	0.736245i	$-0.736597\pi$
$379$	−26.3485	−1.35343	−0.676715	+	0.736245i	$0.736597\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−88.9898	−4.52361
$388$	0	0
$389$	0	0		−	1.00000i	$-0.5\pi$
$389$	0	0			1.00000i	$0.5\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	−62.0908	−3.13207
$394$	0	0
$395$	0	0
$396$	0	0
$397$	0	0		−	1.00000i	$-0.5\pi$
$397$	0	0			1.00000i	$0.5\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−31.2929	−1.56269	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	−31.2929	−1.56269	−0.781345	+	0.624099i	$0.785466\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−40.3939	−1.99735	−0.998674	−	0.0514740i	$-0.983608\pi$
$409$	−40.3939	−1.99735	−0.998674	+	0.0514740i	$0.983608\pi$
$410$	0	0
$411$	77.9444	3.84471
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	12.5959	0.616825
$418$	0	0
$419$	−40.8434	−1.99533	−0.997665	−	0.0683046i	$-0.978241\pi$
$419$	−40.8434	−1.99533	−0.997665	+	0.0683046i	$0.978241\pi$
$420$	0	0
$421$	0	0		−	1.00000i	$-0.5\pi$
$421$	0	0			1.00000i	$0.5\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	4.30306	0.206792	0.103396	−	0.994640i	$-0.467029\pi$
$433$	4.30306	0.206792	0.103396	+	0.994640i	$0.467029\pi$
$434$	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
$441$	−62.2929	−2.96633
$442$	0	0
$443$	23.4495	1.11412	0.557059	−	0.830473i	$-0.311930\pi$
$443$	23.4495	1.11412	0.557059	+	0.830473i	$0.311930\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	−25.8990	−1.22225	−0.611124	−	0.791535i	$-0.709282\pi$
$449$	−25.8990	−1.22225	−0.611124	+	0.791535i	$0.709282\pi$
$450$	0	0
$451$	−37.0454	−1.74440
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−16.3939	−0.766873	−0.383437	−	0.923567i	$-0.625260\pi$
$457$	−16.3939	−0.766873	−0.383437	+	0.923567i	$0.625260\pi$
$458$	0	0
$459$	38.6413	1.80362
$460$	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	$0.5\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−30.0000	−1.38823	−0.694117	−	0.719862i	$-0.744205\pi$
$467$	−30.0000	−1.38823	−0.694117	+	0.719862i	$0.744205\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	54.4949	2.50568
$474$	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
$484$	0	0
$485$	0	0
$486$	0	0
$487$	0	0		−	1.00000i	$-0.5\pi$
$487$	0	0			1.00000i	$0.5\pi$
$488$	0	0
$489$	−72.5959	−3.28290
$490$	0	0
$491$	−42.0000	−1.89543	−0.947717	−	0.319113i	$-0.896615\pi$
$491$	−42.0000	−1.89543	−0.947717	+	0.319113i	$0.896615\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−14.0000	−0.626726	−0.313363	−	0.949633i	$-0.601456\pi$
$499$	−14.0000	−0.626726	−0.313363	+	0.949633i	$0.601456\pi$
$500$	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
$505$	0	0
$506$	0	0
$507$	44.8434	1.99156
$508$	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
$513$	−129.182	−5.70351
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−42.1918	−1.84846	−0.924229	−	0.381839i	$-0.875291\pi$
$521$	−42.1918	−1.84846	−0.924229	+	0.381839i	$0.875291\pi$
$522$	0	0
$523$	−41.0454	−1.79479	−0.897395	−	0.441228i	$-0.854543\pi$
$523$	−41.0454	−1.79479	−0.897395	+	0.441228i	$0.854543\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−23.0000	−1.00000
$530$	0	0
$531$	53.3939	2.31710
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−28.1010	−1.21265
$538$	0	0
$539$	38.1464	1.64308
$540$	0	0
$541$	0	0		−	1.00000i	$-0.5\pi$
$541$	0	0			1.00000i	$0.5\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	30.3485	1.29761	0.648803	−	0.760956i	$-0.275270\pi$
$547$	30.3485	1.29761	0.648803	+	0.760956i	$0.275270\pi$
$548$	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
$561$	−35.6969	−1.50713
$562$	0	0
$563$	−30.0000	−1.26435	−0.632175	−	0.774826i	$-0.717837\pi$
$563$	−30.0000	−1.26435	−0.632175	+	0.774826i	$0.717837\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	1.40408	0.0588622	0.0294311	−	0.999567i	$-0.490630\pi$
$569$	1.40408	0.0588622	0.0294311	+	0.999567i	$0.490630\pi$
$570$	0	0
$571$	22.0000	0.920671	0.460336	−	0.887745i	$-0.347729\pi$
$571$	22.0000	0.920671	0.460336	+	0.887745i	$0.347729\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−46.3939	−1.93140	−0.965701	−	0.259656i	$-0.916391\pi$
$577$	−46.3939	−1.93140	−0.965701	+	0.259656i	$0.916391\pi$
$578$	0	0
$579$	−88.6413	−3.68381
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	38.6413	1.59490	0.797449	−	0.603386i	$-0.206182\pi$
$587$	38.6413	1.59490	0.797449	+	0.603386i	$0.206182\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	30.1918	1.23983	0.619915	−	0.784669i	$-0.287167\pi$
$593$	30.1918	1.23983	0.619915	+	0.784669i	$0.287167\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	−37.6969	−1.53769	−0.768845	−	0.639435i	$-0.779168\pi$
$601$	−37.6969	−1.53769	−0.768845	+	0.639435i	$0.779168\pi$
$602$	0	0
$603$	−3.10102	−0.126283
$604$	0	0
$605$	0	0
$606$	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
$613$	0	0		−	1.00000i	$-0.5\pi$
$613$	0	0			1.00000i	$0.5\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	30.0000	1.20775	0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000	1.20775	0.603877	+	0.797077i	$0.293622\pi$
$618$	0	0
$619$	−26.0000	−1.04503	−0.522514	−	0.852631i	$-0.675006\pi$
$619$	−26.0000	−1.04503	−0.522514	+	0.852631i	$0.675006\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	119.338	4.76591
$628$	0	0
$629$	0	0
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	0	0
$633$	−100.192	−3.98227
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	42.0000	1.65890	0.829450	−	0.558581i	$-0.188654\pi$
$641$	42.0000	1.65890	0.829450	+	0.558581i	$0.188654\pi$
$642$	0	0
$643$	50.0000	1.97181	0.985904	−	0.167313i	$-0.0535092\pi$
$643$	50.0000	1.97181	0.985904	+	0.167313i	$0.0535092\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	0	0
$649$	−32.6969	−1.28347
$650$	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
$657$	139.687	5.44970
$658$	0	0
$659$	32.6413	1.27153	0.635763	−	0.771885i	$-0.280686\pi$
$659$	32.6413	1.27153	0.635763	+	0.771885i	$0.280686\pi$
$660$	0	0
$661$	0	0		−	1.00000i	$-0.5\pi$
$661$	0	0			1.00000i	$0.5\pi$
$662$	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
$673$	10.0000	0.385472	0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000	0.385472	0.192736	+	0.981251i	$0.438264\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	103.485	3.96554
$682$	0	0
$683$	47.9444	1.83454	0.917270	−	0.398265i	$-0.130387\pi$
$683$	47.9444	1.83454	0.917270	+	0.398265i	$0.130387\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	0.954592	0.0363144	0.0181572	−	0.999835i	$-0.494220\pi$
$691$	0.954592	0.0363144	0.0181572	+	0.999835i	$0.494220\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−12.9092	−0.488970
$698$	0	0
$699$	−103.485	−3.91415
$700$	0	0
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	0	0		−	1.00000i	$-0.5\pi$
$709$	0	0			1.00000i	$0.5\pi$
$710$	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		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	95.5403	3.55318
$724$	0	0
$725$	0	0
$726$	0	0
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	176.485	6.53647
$730$	0	0
$731$	18.9898	0.702363
$732$	0	0
$733$	0	0		−	1.00000i	$-0.5\pi$
$733$	0	0			1.00000i	$0.5\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	1.89898	0.0699498
$738$	0	0
$739$	34.0000	1.25071	0.625355	−	0.780340i	$-0.284954\pi$
$739$	34.0000	1.25071	0.625355	+	0.780340i	$0.284954\pi$
$740$	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
$747$	−58.2929	−2.13282
$748$	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
$753$	103.293	3.76420
$754$	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
$761$	−36.7980	−1.33392	−0.666962	−	0.745091i	$-0.732406\pi$
$761$	−36.7980	−1.33392	−0.666962	+	0.745091i	$0.732406\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−33.0908	−1.19329	−0.596643	−	0.802507i	$-0.703499\pi$
$769$	−33.0908	−1.19329	−0.596643	+	0.802507i	$0.703499\pi$
$770$	0	0
$771$	103.485	3.72691
$772$	0	0
$773$	0	0		−	1.00000i	$-0.5\pi$
$773$	0	0			1.00000i	$0.5\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	43.1566	1.54625
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	0	0
$786$	0	0
$787$	50.0000	1.78231	0.891154	−	0.453701i	$-0.149897\pi$
$787$	50.0000	1.78231	0.891154	+	0.453701i	$0.149897\pi$
$788$	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
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	36.4949	1.28948
$802$	0	0
$803$	−85.5403	−3.01865
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	0	0
$811$	38.0000	1.33436	0.667180	−	0.744896i	$-0.267501\pi$
$811$	38.0000	1.33436	0.667180	+	0.744896i	$0.267501\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−63.4847	−2.22105
$818$	0	0
$819$	0	0
$820$	0	0
$821$	0	0		−	1.00000i	$-0.5\pi$
$821$	0	0			1.00000i	$0.5\pi$
$822$	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
$827$	−44.1464	−1.53512	−0.767561	−	0.640976i	$-0.778530\pi$
$827$	−44.1464	−1.53512	−0.767561	+	0.640976i	$0.778530\pi$
$828$	0	0
$829$	0	0		−	1.00000i	$-0.5\pi$
$829$	0	0			1.00000i	$0.5\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	13.2929	0.460570
$834$	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
$841$	−29.0000	−1.00000
$842$	0	0
$843$	62.0908	2.13852
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−38.1010	−1.30762
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−7.40408	−0.252919	−0.126459	−	0.991972i	$-0.540361\pi$
$857$	−7.40408	−0.252919	−0.126459	+	0.991972i	$0.540361\pi$
$858$	0	0
$859$	36.3485	1.24019	0.620097	−	0.784525i	$-0.287093\pi$
$859$	36.3485	1.24019	0.620097	+	0.784525i	$0.287093\pi$
$860$	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
$867$	46.2020	1.56910
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	88.9898	3.01185
$874$	0	0
$875$	0	0
$876$	0	0
$877$	0	0		−	1.00000i	$-0.5\pi$
$877$	0	0			1.00000i	$0.5\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	18.0000	0.606435	0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000	0.606435	0.303218	+	0.952921i	$0.401939\pi$
$882$	0	0
$883$	−52.4393	−1.76472	−0.882361	−	0.470573i	$-0.844047\pi$
$883$	−52.4393	−1.76472	−0.882361	+	0.470573i	$0.844047\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−237.025	−7.94064
$892$	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
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−10.0000	−0.332045	−0.166022	−	0.986122i	$-0.553092\pi$
$907$	−10.0000	−0.332045	−0.166022	+	0.986122i	$0.553092\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	0	0
$913$	35.6969	1.18140
$914$	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
$921$	33.2929	1.09704
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0	0
$928$	0	0
$929$	−54.0000	−1.77168	−0.885841	−	0.463988i	$-0.846418\pi$
$929$	−54.0000	−1.77168	−0.885841	+	0.463988i	$0.846418\pi$
$930$	0	0
$931$	−44.4393	−1.45644
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−27.0908	−0.885018	−0.442509	−	0.896764i	$-0.645912\pi$
$937$	−27.0908	−0.885018	−0.442509	+	0.896764i	$0.645912\pi$
$938$	0	0
$939$	34.4949	1.12570
$940$	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
$947$	−30.0000	−0.974869	−0.487435	−	0.873160i	$-0.662067\pi$
$947$	−30.0000	−0.974869	−0.487435	+	0.873160i	$0.662067\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	60.1918	1.94980	0.974902	−	0.222633i	$-0.0714650\pi$
$953$	60.1918	1.94980	0.974902	+	0.222633i	$0.0714650\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−31.0000	−1.00000
$962$	0	0
$963$	125.889	4.05671
$964$	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
$969$	41.5857	1.33593
$970$	0	0
$971$	−0.0556128	−0.00178470	−0.000892350	−	1.00000i	$-0.500284\pi$
$971$	−0.0556128	−0.00178470	−0.000892350		1.00000i	$0.500284\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−50.8888	−1.62808	−0.814038	−	0.580812i	$-0.802735\pi$
$977$	−50.8888	−1.62808	−0.814038	+	0.580812i	$0.802735\pi$
$978$	0	0
$979$	−22.3485	−0.714260
$980$	0	0
$981$	0	0
$982$	0	0
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	0	0
$985$	0	0
$986$	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
$993$	31.2020	0.990167
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0		−	1.00000i	$-0.5\pi$
$997$	0	0			1.00000i	$0.5\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6400.2.a.bc.1.1		2
4.3	odd	2		6400.2.a.ci.1.2		2
5.4	even	2		6400.2.a.ch.1.2		2
8.3	odd	2	CM	6400.2.a.bc.1.1		2
8.5	even	2		6400.2.a.ci.1.2		2
16.3	odd	4		1600.2.d.d.801.4	yes	4
16.5	even	4		1600.2.d.d.801.4	yes	4
16.11	odd	4		1600.2.d.d.801.1	yes	4
16.13	even	4		1600.2.d.d.801.1	yes	4
20.19	odd	2		6400.2.a.bd.1.1		2
40.19	odd	2		6400.2.a.ch.1.2		2
40.29	even	2		6400.2.a.bd.1.1		2
80.3	even	4		1600.2.f.f.1249.1		4
80.13	odd	4		1600.2.f.j.1249.4		4
80.19	odd	4		1600.2.d.c.801.1	✓	4
80.27	even	4		1600.2.f.f.1249.2		4
80.29	even	4		1600.2.d.c.801.4	yes	4
80.37	odd	4		1600.2.f.j.1249.3		4
80.43	even	4		1600.2.f.j.1249.4		4
80.53	odd	4		1600.2.f.f.1249.1		4
80.59	odd	4		1600.2.d.c.801.4	yes	4
80.67	even	4		1600.2.f.j.1249.3		4
80.69	even	4		1600.2.d.c.801.1	✓	4
80.77	odd	4		1600.2.f.f.1249.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1600.2.d.c.801.1	✓	4	80.19	odd	4
1600.2.d.c.801.1	✓	4	80.69	even	4
1600.2.d.c.801.4	yes	4	80.29	even	4
1600.2.d.c.801.4	yes	4	80.59	odd	4
1600.2.d.d.801.1	yes	4	16.11	odd	4
1600.2.d.d.801.1	yes	4	16.13	even	4
1600.2.d.d.801.4	yes	4	16.3	odd	4
1600.2.d.d.801.4	yes	4	16.5	even	4
1600.2.f.f.1249.1		4	80.3	even	4
1600.2.f.f.1249.1		4	80.53	odd	4
1600.2.f.f.1249.2		4	80.27	even	4
1600.2.f.f.1249.2		4	80.77	odd	4
1600.2.f.j.1249.3		4	80.37	odd	4
1600.2.f.j.1249.3		4	80.67	even	4
1600.2.f.j.1249.4		4	80.13	odd	4
1600.2.f.j.1249.4		4	80.43	even	4
6400.2.a.bc.1.1		2	1.1	even	1	trivial
6400.2.a.bc.1.1		2	8.3	odd	2	CM
6400.2.a.bd.1.1		2	20.19	odd	2
6400.2.a.bd.1.1		2	40.29	even	2
6400.2.a.ch.1.2		2	5.4	even	2
6400.2.a.ch.1.2		2	40.19	odd	2
6400.2.a.ci.1.2		2	4.3	odd	2
6400.2.a.ci.1.2		2	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6400 = 2^{8} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6400.a (trivial)

\(f(q)\)	\(=\)	\(q-3.44949 q^{3} +8.89898 q^{9} -5.44949 q^{11} -1.89898 q^{17} +6.34847 q^{19} -20.3485 q^{27} +18.7980 q^{33} +6.79796 q^{41} -10.0000 q^{43} -7.00000 q^{49} +6.55051 q^{51} -21.8990 q^{57} +6.00000 q^{59} -0.348469 q^{67} +15.6969 q^{73} +43.4949 q^{81} -6.55051 q^{83} +4.10102 q^{89} +10.0000 q^{97} -48.4949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 8 q^{9} - 6 q^{11} + 6 q^{17} - 2 q^{19} - 26 q^{27} + 18 q^{33} - 6 q^{41} - 20 q^{43} - 14 q^{49} + 18 q^{51} - 34 q^{57} + 12 q^{59} + 14 q^{67} + 2 q^{73} + 38 q^{81} - 18 q^{83} + 18 q^{89}+ \cdots - 48 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + 8 * q^9 - 6 * q^11 + 6 * q^17 - 2 * q^19 - 26 * q^27 + 18 * q^33 - 6 * q^41 - 20 * q^43 - 14 * q^49 + 18 * q^51 - 34 * q^57 + 12 * q^59 + 14 * q^67 + 2 * q^73 + 38 * q^81 - 18 * q^83 + 18 * q^89 + 20 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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