LMFDB - Embedded newform 1200.2.h.d.1151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1200,2,Mod(1151,1200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1200, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1200.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1200 = 2^{4} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1200.h (of order $2$, degree $1$, 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:	$9.58204824255$
Analytic rank:	$0$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1151.2
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1200.1151
Dual form			1200.2.h.d.1151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.73205i q^{3} -1.73205i q^{7} -3.00000 q^{9} +O(q^{10})$	$q+1.73205i q^{3} -1.73205i q^{7} -3.00000 q^{9} -5.00000 q^{13} -8.66025i q^{19} +3.00000 q^{21} -5.19615i q^{27} -8.66025i q^{31} -10.0000 q^{37} -8.66025i q^{39} +12.1244i q^{43} +4.00000 q^{49} +15.0000 q^{57} -13.0000 q^{61} +5.19615i q^{63} -15.5885i q^{67} +10.0000 q^{73} -17.3205i q^{79} +9.00000 q^{81} +8.66025i q^{91} +15.0000 q^{93} -5.00000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 6 q^{9}+O(q^{10}) $ 2 * q - 6 * q^9	$ 2 q - 6 q^{9} - 10 q^{13} + 6 q^{21} - 20 q^{37} + 8 q^{49} + 30 q^{57} - 26 q^{61} + 20 q^{73} + 18 q^{81} + 30 q^{93} - 10 q^{97}+O(q^{100}) $ 2 * q - 6 * q^9 - 10 * q^13 + 6 * q^21 - 20 * q^37 + 8 * q^49 + 30 * q^57 - 26 * q^61 + 20 * q^73 + 18 * q^81 + 30 * q^93 - 10 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times$.

$n$	$401$	$577$	$751$	$901$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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
$3$	1.73205i	1.00000i
$3$	1.73205i	1.00000i
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	− 1.73205i	− 0.654654i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	− 1.73205i	− 0.654654i	0.944911	−	0.327327i	$-0.106148\pi$
$8$	0	0
$9$	−3.00000	−1.00000
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	0	0
$13$	−5.00000	−1.38675	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000	−1.38675	−0.693375	+	0.720577i	$0.743877\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	− 8.66025i	− 1.98680i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	− 8.66025i	− 1.98680i	0.114708	−	0.993399i	$-0.463407\pi$
$20$	0	0
$21$	3.00000	0.654654
$22$	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
$27$	− 5.19615i	− 1.00000i
$28$	0	0
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	− 8.66025i	− 1.55543i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	− 8.66025i	− 1.55543i	0.628619	−	0.777714i	$-0.283621\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−10.0000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	0	0
$39$	− 8.66025i	− 1.38675i
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	12.1244i	1.84895i	0.381246	+	0.924473i	$0.375495\pi$
$43$	12.1244i	1.84895i	−0.381246	+	0.924473i	$0.624505\pi$
$44$	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
$49$	4.00000	0.571429
$50$	0	0
$51$	0	0
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	15.0000	1.98680
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	−13.0000	−1.66448	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−13.0000	−1.66448	−0.832240	+	0.554416i	$0.812942\pi$
$62$	0	0
$63$	5.19615i	0.654654i
$64$	0	0
$65$	0	0
$66$	0	0
$67$	− 15.5885i	− 1.90443i	−0.305424	−	0.952217i	$-0.598798\pi$
$67$	− 15.5885i	− 1.90443i	0.305424	−	0.952217i	$-0.401202\pi$
$68$	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
$73$	10.0000	1.17041	0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000	1.17041	0.585206	+	0.810885i	$0.301014\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	− 17.3205i	− 1.94871i	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	− 17.3205i	− 1.94871i	0.225018	−	0.974355i	$-0.427756\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	0	0
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	8.66025i	0.907841i
$92$	0	0
$93$	15.0000	1.55543
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−5.00000	−0.507673	−0.253837	−	0.967247i	$-0.581693\pi$
$97$	−5.00000	−0.507673	−0.253837	+	0.967247i	$0.581693\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	− 3.46410i	− 0.341328i	−0.985329	−	0.170664i	$-0.945409\pi$
$103$	− 3.46410i	− 0.341328i	0.985329	−	0.170664i	$-0.0545913\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	0	0
$109$	19.0000	1.81987	0.909935	−	0.414751i	$-0.136131\pi$
$109$	19.0000	1.81987	0.909935	+	0.414751i	$0.136131\pi$
$110$	0	0
$111$	− 17.3205i	− 1.64399i
$112$	0	0
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	15.0000	1.38675
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−11.0000	−1.00000
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	10.3923i	0.922168i	0.887357	+	0.461084i	$0.152539\pi$
$127$	10.3923i	0.922168i	−0.887357	+	0.461084i	$0.847461\pi$
$128$	0	0
$129$	−21.0000	−1.84895
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	−15.0000	−1.30066
$134$	0	0
$135$	0	0
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	17.3205i	1.46911i	0.678551	+	0.734553i	$0.262608\pi$
$139$	17.3205i	1.46911i	−0.678551	+	0.734553i	$0.737392\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	6.92820i	0.571429i
$148$	0	0
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0	0
$151$	− 8.66025i	− 0.704761i	−0.935857	−	0.352381i	$-0.885372\pi$
$151$	− 8.66025i	− 0.704761i	0.935857	−	0.352381i	$-0.114628\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−25.0000	−1.99522	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−25.0000	−1.99522	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	5.19615i	0.406994i	0.979076	+	0.203497i	$0.0652307\pi$
$163$	5.19615i	0.406994i	−0.979076	+	0.203497i	$0.934769\pi$
$164$	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
$169$	12.0000	0.923077
$170$	0	0
$171$	25.9808i	1.98680i
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0	0
$178$	0	0
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	7.00000	0.520306	0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000	0.520306	0.260153	+	0.965567i	$0.416227\pi$
$182$	0	0
$183$	− 22.5167i	− 1.66448i
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	−9.00000	−0.654654
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	0	0
$193$	−25.0000	−1.79954	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−25.0000	−1.79954	−0.899770	+	0.436365i	$0.856266\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	25.9808i	1.84173i	0.389885	+	0.920864i	$0.372515\pi$
$199$	25.9808i	1.84173i	−0.389885	+	0.920864i	$0.627485\pi$
$200$	0	0
$201$	27.0000	1.90443
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	25.9808i	1.78859i	0.447478	+	0.894295i	$0.352322\pi$
$211$	25.9808i	1.78859i	−0.447478	+	0.894295i	$0.647678\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−15.0000	−1.01827
$218$	0	0
$219$	17.3205i	1.17041i
$220$	0	0
$221$	0	0
$222$	0	0
$223$	− 29.4449i	− 1.97177i	−0.167412	−	0.985887i	$-0.553541\pi$
$223$	− 29.4449i	− 1.97177i	0.167412	−	0.985887i	$-0.446459\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	0	0
$229$	−29.0000	−1.91637	−0.958187	−	0.286143i	$-0.907627\pi$
$229$	−29.0000	−1.91637	−0.958187	+	0.286143i	$0.907627\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	30.0000	1.94871
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	−17.0000	−1.09507	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	−17.0000	−1.09507	−0.547533	+	0.836784i	$0.684433\pi$
$242$	0	0
$243$	15.5885i	1.00000i
$244$	0	0
$245$	0	0
$246$	0	0
$247$	43.3013i	2.75519i
$248$	0	0
$249$	0	0
$250$	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
$256$	0	0
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	17.3205i	1.07624i
$260$	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
$267$	0	0
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	− 17.3205i	− 1.05215i	−0.850439	−	0.526073i	$-0.823664\pi$
$271$	− 17.3205i	− 1.05215i	0.850439	−	0.526073i	$-0.176336\pi$
$272$	0	0
$273$	−15.0000	−0.907841
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−5.00000	−0.300421	−0.150210	−	0.988654i	$-0.547995\pi$
$277$	−5.00000	−0.300421	−0.150210	+	0.988654i	$0.547995\pi$
$278$	0	0
$279$	25.9808i	1.55543i
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	0	0
$283$	− 22.5167i	− 1.33848i	−0.743048	−	0.669238i	$-0.766621\pi$
$283$	− 22.5167i	− 1.33848i	0.743048	−	0.669238i	$-0.233379\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	17.0000	1.00000
$290$	0	0
$291$	− 8.66025i	− 0.507673i
$292$	0	0
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	21.0000	1.21042
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	− 1.73205i	− 0.0988534i	−0.998778	−	0.0494267i	$-0.984261\pi$
$307$	− 1.73205i	− 0.0988534i	0.998778	−	0.0494267i	$-0.0157394\pi$
$308$	0	0
$309$	6.00000	0.341328
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	35.0000	1.97832	0.989158	−	0.146852i	$-0.0469141\pi$
$313$	35.0000	1.97832	0.989158	+	0.146852i	$0.0469141\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	0	0
$326$	0	0
$327$	32.9090i	1.81987i
$328$	0	0
$329$	0	0
$330$	0	0
$331$	17.3205i	0.952021i	0.879440	+	0.476011i	$0.157918\pi$
$331$	17.3205i	0.952021i	−0.879440	+	0.476011i	$0.842082\pi$
$332$	0	0
$333$	30.0000	1.64399
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−5.00000	−0.272367	−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000	−0.272367	−0.136184	+	0.990684i	$0.543484\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	− 19.0526i	− 1.02874i
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	0	0
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	0	0
$351$	25.9808i	1.38675i
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	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
$361$	−56.0000	−2.94737
$362$	0	0
$363$	− 19.0526i	− 1.00000i
$364$	0	0
$365$	0	0
$366$	0	0
$367$	− 15.5885i	− 0.813711i	−0.913493	−	0.406855i	$-0.866625\pi$
$367$	− 15.5885i	− 0.813711i	0.913493	−	0.406855i	$-0.133375\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−25.0000	−1.29445	−0.647225	−	0.762299i	$-0.724071\pi$
$373$	−25.0000	−1.29445	−0.647225	+	0.762299i	$0.724071\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	25.9808i	1.33454i	0.744815	+	0.667271i	$0.232538\pi$
$379$	25.9808i	1.33454i	−0.744815	+	0.667271i	$0.767462\pi$
$380$	0	0
$381$	−18.0000	−0.922168
$382$	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
$387$	− 36.3731i	− 1.84895i
$388$	0	0
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	35.0000	1.75660	0.878300	−	0.478110i	$-0.158678\pi$
$397$	35.0000	1.75660	0.878300	+	0.478110i	$0.158678\pi$
$398$	0	0
$399$	− 25.9808i	− 1.30066i
$400$	0	0
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	43.3013i	2.15699i
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	31.0000	1.53285	0.766426	−	0.642333i	$-0.222033\pi$
$409$	31.0000	1.53285	0.766426	+	0.642333i	$0.222033\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−30.0000	−1.46911
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	22.5167i	1.08966i
$428$	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
$433$	35.0000	1.68199	0.840996	−	0.541041i	$-0.181970\pi$
$433$	35.0000	1.68199	0.840996	+	0.541041i	$0.181970\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	− 8.66025i	− 0.413331i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	− 8.66025i	− 0.413331i	0.978412	−	0.206666i	$-0.0662612\pi$
$440$	0	0
$441$	−12.0000	−0.571429
$442$	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
$447$	0	0
$448$	0	0
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	15.0000	0.704761
$454$	0	0
$455$	0	0
$456$	0	0
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	38.1051i	1.77090i	0.464739	+	0.885448i	$0.346148\pi$
$463$	38.1051i	1.77090i	−0.464739	+	0.885448i	$0.653852\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	0	0
$469$	−27.0000	−1.24674
$470$	0	0
$471$	− 43.3013i	− 1.99522i
$472$	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
$481$	50.0000	2.27980
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	− 36.3731i	− 1.64822i	−0.566429	−	0.824110i	$-0.691675\pi$
$487$	− 36.3731i	− 1.64822i	0.566429	−	0.824110i	$-0.308325\pi$
$488$	0	0
$489$	−9.00000	−0.406994
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	− 43.3013i	− 1.93843i	−0.246214	−	0.969216i	$-0.579187\pi$
$499$	− 43.3013i	− 1.93843i	0.246214	−	0.969216i	$-0.420813\pi$
$500$	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
$507$	20.7846i	0.923077i
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	− 17.3205i	− 0.766214i
$512$	0	0
$513$	−45.0000	−1.98680
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	− 29.4449i	− 1.28753i	−0.765222	−	0.643767i	$-0.777371\pi$
$523$	− 29.4449i	− 1.28753i	0.765222	−	0.643767i	$-0.222629\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−23.0000	−1.00000
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−17.0000	−0.730887	−0.365444	−	0.930834i	$-0.619083\pi$
$541$	−17.0000	−0.730887	−0.365444	+	0.930834i	$0.619083\pi$
$542$	0	0
$543$	12.1244i	0.520306i
$544$	0	0
$545$	0	0
$546$	0	0
$547$	− 24.2487i	− 1.03680i	−0.855138	−	0.518400i	$-0.826528\pi$
$547$	− 24.2487i	− 1.03680i	0.855138	−	0.518400i	$-0.173472\pi$
$548$	0	0
$549$	39.0000	1.66448
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−30.0000	−1.27573
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	− 60.6218i	− 2.56403i
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	− 15.5885i	− 0.654654i
$568$	0	0
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	0	0
$571$	− 8.66025i	− 0.362420i	−0.983444	−	0.181210i	$-0.941999\pi$
$571$	− 8.66025i	− 0.362420i	0.983444	−	0.181210i	$-0.0580014\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	35.0000	1.45707	0.728535	−	0.685009i	$-0.240202\pi$
$577$	35.0000	1.45707	0.728535	+	0.685009i	$0.240202\pi$
$578$	0	0
$579$	− 43.3013i	− 1.79954i
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	0	0
$589$	−75.0000	−3.09032
$590$	0	0
$591$	0	0
$592$	0	0
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−45.0000	−1.84173
$598$	0	0
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	23.0000	0.938190	0.469095	−	0.883148i	$-0.344580\pi$
$601$	23.0000	0.938190	0.469095	+	0.883148i	$0.344580\pi$
$602$	0	0
$603$	46.7654i	1.90443i
$604$	0	0
$605$	0	0
$606$	0	0
$607$	− 45.0333i	− 1.82785i	−0.405887	−	0.913923i	$-0.633038\pi$
$607$	− 45.0333i	− 1.82785i	0.405887	−	0.913923i	$-0.366962\pi$
$608$	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
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	− 8.66025i	− 0.348085i	−0.984738	−	0.174042i	$-0.944317\pi$
$619$	− 8.66025i	− 0.348085i	0.984738	−	0.174042i	$-0.0556830\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	25.9808i	1.03428i	0.855901	+	0.517139i	$0.173003\pi$
$631$	25.9808i	1.03428i	−0.855901	+	0.517139i	$0.826997\pi$
$632$	0	0
$633$	−45.0000	−1.78859
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−20.0000	−0.792429
$638$	0	0
$639$	0	0
$640$	0	0
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	0	0
$643$	31.1769i	1.22950i	0.788723	+	0.614749i	$0.210743\pi$
$643$	31.1769i	1.22950i	−0.788723	+	0.614749i	$0.789257\pi$
$644$	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
$649$	0	0
$650$	0	0
$651$	− 25.9808i	− 1.01827i
$652$	0	0
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−30.0000	−1.17041
$658$	0	0
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	38.0000	1.47803	0.739014	−	0.673690i	$-0.235292\pi$
$661$	38.0000	1.47803	0.739014	+	0.673690i	$0.235292\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	51.0000	1.97177
$670$	0	0
$671$	0	0
$672$	0	0
$673$	50.0000	1.92736	0.963679	−	0.267063i	$-0.0860531\pi$
$673$	50.0000	1.92736	0.963679	+	0.267063i	$0.0860531\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	8.66025i	0.332350i
$680$	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
$685$	0	0
$686$	0	0
$687$	− 50.2295i	− 1.91637i
$688$	0	0
$689$	0	0
$690$	0	0
$691$	− 51.9615i	− 1.97671i	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	− 51.9615i	− 1.97671i	0.152167	−	0.988355i	$-0.451375\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	86.6025i	3.26628i
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	31.0000	1.16423	0.582115	−	0.813107i	$-0.302225\pi$
$709$	31.0000	1.16423	0.582115	+	0.813107i	$0.302225\pi$
$710$	0	0
$711$	51.9615i	1.94871i
$712$	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
$721$	−6.00000	−0.223452
$722$	0	0
$723$	− 29.4449i	− 1.09507i
$724$	0	0
$725$	0	0
$726$	0	0
$727$	53.6936i	1.99138i	0.0927199	+	0.995692i	$0.470444\pi$
$727$	53.6936i	1.99138i	−0.0927199	+	0.995692i	$0.529556\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−50.0000	−1.84679	−0.923396	−	0.383849i	$-0.874598\pi$
$733$	−50.0000	−1.84679	−0.923396	+	0.383849i	$0.874598\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	− 51.9615i	− 1.91144i	−0.294285	−	0.955718i	$-0.595081\pi$
$739$	− 51.9615i	− 1.91144i	0.294285	−	0.955718i	$-0.404919\pi$
$740$	0	0
$741$	−75.0000	−2.75519
$742$	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
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	− 17.3205i	− 0.632034i	−0.948753	−	0.316017i	$-0.897654\pi$
$751$	− 17.3205i	− 0.632034i	0.948753	−	0.316017i	$-0.102346\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	55.0000	1.99901	0.999505	−	0.0314762i	$-0.0100208\pi$
$757$	55.0000	1.99901	0.999505	+	0.0314762i	$0.0100208\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	− 32.9090i	− 1.19138i
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−49.0000	−1.76699	−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−49.0000	−1.76699	−0.883493	+	0.468445i	$0.844814\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−30.0000	−1.07624
$778$	0	0
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	0	0
$786$	0	0
$787$	− 50.2295i	− 1.79049i	−0.445577	−	0.895244i	$-0.647001\pi$
$787$	− 50.2295i	− 1.79049i	0.445577	−	0.895244i	$-0.352999\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	65.0000	2.30822
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	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
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0	0
$811$	− 43.3013i	− 1.52051i	−0.649623	−	0.760257i	$-0.725073\pi$
$811$	− 43.3013i	− 1.52051i	0.649623	−	0.760257i	$-0.274927\pi$
$812$	0	0
$813$	30.0000	1.05215
$814$	0	0
$815$	0	0
$816$	0	0
$817$	105.000	3.67348
$818$	0	0
$819$	− 25.9808i	− 0.907841i
$820$	0	0
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	0	0
$823$	− 57.1577i	− 1.99239i	−0.0871445	−	0.996196i	$-0.527774\pi$
$823$	− 57.1577i	− 1.99239i	0.0871445	−	0.996196i	$-0.472226\pi$
$824$	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
$829$	46.0000	1.59765	0.798823	−	0.601566i	$-0.205456\pi$
$829$	46.0000	1.59765	0.798823	+	0.601566i	$0.205456\pi$
$830$	0	0
$831$	− 8.66025i	− 0.300421i
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−45.0000	−1.55543
$838$	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
$843$	0	0
$844$	0	0
$845$	0	0
$846$	0	0
$847$	19.0526i	0.654654i
$848$	0	0
$849$	39.0000	1.33848
$850$	0	0
$851$	0	0
$852$	0	0
$853$	35.0000	1.19838	0.599189	−	0.800608i	$-0.295490\pi$
$853$	35.0000	1.19838	0.599189	+	0.800608i	$0.295490\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	17.3205i	0.590968i	0.955348	+	0.295484i	$0.0954809\pi$
$859$	17.3205i	0.590968i	−0.955348	+	0.295484i	$0.904519\pi$
$860$	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
$867$	29.4449i	1.00000i
$868$	0	0
$869$	0	0
$870$	0	0
$871$	77.9423i	2.64097i
$872$	0	0
$873$	15.0000	0.507673
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−25.0000	−0.844190	−0.422095	−	0.906552i	$-0.638705\pi$
$877$	−25.0000	−0.844190	−0.422095	+	0.906552i	$0.638705\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	0	0
$883$	− 22.5167i	− 0.757746i	−0.925449	−	0.378873i	$-0.876312\pi$
$883$	− 22.5167i	− 0.757746i	0.925449	−	0.378873i	$-0.123688\pi$
$884$	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
$889$	18.0000	0.603701
$890$	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
$901$	0	0
$902$	0	0
$903$	36.3731i	1.21042i
$904$	0	0
$905$	0	0
$906$	0	0
$907$	45.0333i	1.49531i	0.664089	+	0.747653i	$0.268820\pi$
$907$	45.0333i	1.49531i	−0.664089	+	0.747653i	$0.731180\pi$
$908$	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
$913$	0	0
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	60.6218i	1.99973i	0.0164935	+	0.999864i	$0.494750\pi$
$919$	60.6218i	1.99973i	−0.0164935	+	0.999864i	$0.505250\pi$
$920$	0	0
$921$	3.00000	0.0988534
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	10.3923i	0.341328i
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	− 34.6410i	− 1.13531i
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	35.0000	1.14340	0.571700	−	0.820463i	$-0.306284\pi$
$937$	35.0000	1.14340	0.571700	+	0.820463i	$0.306284\pi$
$938$	0	0
$939$	60.6218i	1.97832i
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	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	$0.5\pi$
$948$	0	0
$949$	−50.0000	−1.62307
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−44.0000	−1.41935
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	− 58.8897i	− 1.89377i	−0.321578	−	0.946883i	$-0.604213\pi$
$967$	− 58.8897i	− 1.89377i	0.321578	−	0.946883i	$-0.395787\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	0	0
$973$	30.0000	0.961756
$974$	0	0
$975$	0	0
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−57.0000	−1.81987
$982$	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
$991$	60.6218i	1.92571i	0.270011	+	0.962857i	$0.412973\pi$
$991$	60.6218i	1.92571i	−0.270011	+	0.962857i	$0.587027\pi$
$992$	0	0
$993$	−30.0000	−0.952021
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−10.0000	−0.316703	−0.158352	−	0.987383i	$-0.550618\pi$
$997$	−10.0000	−0.316703	−0.158352	+	0.987383i	$0.550618\pi$
$998$	0	0
$999$	51.9615i	1.64399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1200.2.h.d.1151.2	yes	2
3.2	odd	2	CM	1200.2.h.d.1151.2	yes	2
4.3	odd	2	inner	1200.2.h.d.1151.1	✓	2
5.2	odd	4		1200.2.o.h.1199.4		4
5.3	odd	4		1200.2.o.h.1199.1		4
5.4	even	2		1200.2.h.f.1151.1	yes	2
12.11	even	2	inner	1200.2.h.d.1151.1	✓	2
15.2	even	4		1200.2.o.h.1199.4		4
15.8	even	4		1200.2.o.h.1199.1		4
15.14	odd	2		1200.2.h.f.1151.1	yes	2
20.3	even	4		1200.2.o.h.1199.3		4
20.7	even	4		1200.2.o.h.1199.2		4
20.19	odd	2		1200.2.h.f.1151.2	yes	2
60.23	odd	4		1200.2.o.h.1199.3		4
60.47	odd	4		1200.2.o.h.1199.2		4
60.59	even	2		1200.2.h.f.1151.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1200.2.h.d.1151.1	✓	2	4.3	odd	2	inner
1200.2.h.d.1151.1	✓	2	12.11	even	2	inner
1200.2.h.d.1151.2	yes	2	1.1	even	1	trivial
1200.2.h.d.1151.2	yes	2	3.2	odd	2	CM
1200.2.h.f.1151.1	yes	2	5.4	even	2
1200.2.h.f.1151.1	yes	2	15.14	odd	2
1200.2.h.f.1151.2	yes	2	20.19	odd	2
1200.2.h.f.1151.2	yes	2	60.59	even	2
1200.2.o.h.1199.1		4	5.3	odd	4
1200.2.o.h.1199.1		4	15.8	even	4
1200.2.o.h.1199.2		4	20.7	even	4
1200.2.o.h.1199.2		4	60.47	odd	4
1200.2.o.h.1199.3		4	20.3	even	4
1200.2.o.h.1199.3		4	60.23	odd	4
1200.2.o.h.1199.4		4	5.2	odd	4
1200.2.o.h.1199.4		4	15.2	even	4

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:	\( N \)	\(=\)	\( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1200.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.73205i q^{3} -1.73205i q^{7} -3.00000 q^{9} +O(q^{10})\)	\(q+1.73205i q^{3} -1.73205i q^{7} -3.00000 q^{9} -5.00000 q^{13} -8.66025i q^{19} +3.00000 q^{21} -5.19615i q^{27} -8.66025i q^{31} -10.0000 q^{37} -8.66025i q^{39} +12.1244i q^{43} +4.00000 q^{49} +15.0000 q^{57} -13.0000 q^{61} +5.19615i q^{63} -15.5885i q^{67} +10.0000 q^{73} -17.3205i q^{79} +9.00000 q^{81} +8.66025i q^{91} +15.0000 q^{93} -5.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 6 q^{9}+O(q^{10}) \) 2 * q - 6 * q^9	\( 2 q - 6 q^{9} - 10 q^{13} + 6 q^{21} - 20 q^{37} + 8 q^{49} + 30 q^{57} - 26 q^{61} + 20 q^{73} + 18 q^{81} + 30 q^{93} - 10 q^{97}+O(q^{100}) \) 2 * q - 6 * q^9 - 10 * q^13 + 6 * q^21 - 20 * q^37 + 8 * q^49 + 30 * q^57 - 26 * q^61 + 20 * q^73 + 18 * q^81 + 30 * q^93 - 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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