LMFDB - Embedded newform 9216.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9216,2,Mod(1,9216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9216, 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("9216.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9216 = 2^{10} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9216.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:	$73.5901305028$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 512)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	9216.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{5} +4.00000 q^{7} +O(q^{10})$	$q-1.41421 q^{5} +4.00000 q^{7} +2.82843 q^{11} +4.24264 q^{13} -2.82843 q^{19} -4.00000 q^{23} -3.00000 q^{25} -4.24264 q^{29} -8.00000 q^{31} -5.65685 q^{35} -1.41421 q^{37} -8.00000 q^{41} +2.82843 q^{43} -8.00000 q^{47} +9.00000 q^{49} -1.41421 q^{53} -4.00000 q^{55} -8.48528 q^{59} -4.24264 q^{61} -6.00000 q^{65} +2.82843 q^{67} -12.0000 q^{71} -2.00000 q^{73} +11.3137 q^{77} -14.1421 q^{83} -14.0000 q^{89} +16.9706 q^{91} +4.00000 q^{95} -16.0000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{7}+O(q^{10}) $ 2 * q + 8 * q^7	$ 2 q + 8 q^{7} - 8 q^{23} - 6 q^{25} - 16 q^{31} - 16 q^{41} - 16 q^{47} + 18 q^{49} - 8 q^{55} - 12 q^{65} - 24 q^{71} - 4 q^{73} - 28 q^{89} + 8 q^{95} - 32 q^{97}+O(q^{100}) $ 2 * q + 8 * q^7 - 8 * q^23 - 6 * q^25 - 16 * q^31 - 16 * q^41 - 16 * q^47 + 18 * q^49 - 8 * q^55 - 12 * q^65 - 24 * q^71 - 4 * q^73 - 28 * q^89 + 8 * q^95 - 32 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0	0
$2$	0	0
$3$	0	0
$3$	0	0
$4$	0	0
$5$	−1.41421	−0.632456	−0.316228	−	0.948683i	$-0.602416\pi$
$5$	−1.41421	−0.632456	−0.316228	+	0.948683i	$0.602416\pi$
$6$	0	0
$7$	4.00000	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$8$	0	0
$9$	0	0
$10$	0	0
$11$	2.82843	0.852803	0.426401	−	0.904534i	$-0.359781\pi$
$11$	2.82843	0.852803	0.426401	+	0.904534i	$0.359781\pi$
$12$	0	0
$13$	4.24264	1.17670	0.588348	−	0.808608i	$-0.299778\pi$
$13$	4.24264	1.17670	0.588348	+	0.808608i	$0.299778\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	−2.82843	−0.648886	−0.324443	−	0.945905i	$-0.605177\pi$
$19$	−2.82843	−0.648886	−0.324443	+	0.945905i	$0.605177\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	0	0
$25$	−3.00000	−0.600000
$26$	0	0
$27$	0	0
$28$	0	0
$29$	−4.24264	−0.787839	−0.393919	−	0.919145i	$-0.628881\pi$
$29$	−4.24264	−0.787839	−0.393919	+	0.919145i	$0.628881\pi$
$30$	0	0
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	−5.65685	−0.956183
$36$	0	0
$37$	−1.41421	−0.232495	−0.116248	−	0.993220i	$-0.537087\pi$
$37$	−1.41421	−0.232495	−0.116248	+	0.993220i	$0.537087\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−8.00000	−1.24939	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000	−1.24939	−0.624695	+	0.780869i	$0.714777\pi$
$42$	0	0
$43$	2.82843	0.431331	0.215666	−	0.976467i	$-0.430808\pi$
$43$	2.82843	0.431331	0.215666	+	0.976467i	$0.430808\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	0	0
$49$	9.00000	1.28571
$50$	0	0
$51$	0	0
$52$	0	0
$53$	−1.41421	−0.194257	−0.0971286	−	0.995272i	$-0.530966\pi$
$53$	−1.41421	−0.194257	−0.0971286	+	0.995272i	$0.530966\pi$
$54$	0	0
$55$	−4.00000	−0.539360
$56$	0	0
$57$	0	0
$58$	0	0
$59$	−8.48528	−1.10469	−0.552345	−	0.833616i	$-0.686267\pi$
$59$	−8.48528	−1.10469	−0.552345	+	0.833616i	$0.686267\pi$
$60$	0	0
$61$	−4.24264	−0.543214	−0.271607	−	0.962408i	$-0.587555\pi$
$61$	−4.24264	−0.543214	−0.271607	+	0.962408i	$0.587555\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−6.00000	−0.744208
$66$	0	0
$67$	2.82843	0.345547	0.172774	−	0.984962i	$-0.444727\pi$
$67$	2.82843	0.345547	0.172774	+	0.984962i	$0.444727\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	0	0
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	11.3137	1.28932
$78$	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
$83$	−14.1421	−1.55230	−0.776151	−	0.630548i	$-0.782830\pi$
$83$	−14.1421	−1.55230	−0.776151	+	0.630548i	$0.782830\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	−14.0000	−1.48400	−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000	−1.48400	−0.741999	+	0.670402i	$0.766122\pi$
$90$	0	0
$91$	16.9706	1.77900
$92$	0	0
$93$	0	0
$94$	0	0
$95$	4.00000	0.410391
$96$	0	0
$97$	−16.0000	−1.62455	−0.812277	−	0.583272i	$-0.801772\pi$
$97$	−16.0000	−1.62455	−0.812277	+	0.583272i	$0.801772\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	1.41421	0.140720	0.0703598	−	0.997522i	$-0.477585\pi$
$101$	1.41421	0.140720	0.0703598	+	0.997522i	$0.477585\pi$
$102$	0	0
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	2.82843	0.273434	0.136717	−	0.990610i	$-0.456345\pi$
$107$	2.82843	0.273434	0.136717	+	0.990610i	$0.456345\pi$
$108$	0	0
$109$	18.3848	1.76094	0.880471	−	0.474100i	$-0.157226\pi$
$109$	18.3848	1.76094	0.880471	+	0.474100i	$0.157226\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	0	0
$115$	5.65685	0.527504
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−3.00000	−0.272727
$122$	0	0
$123$	0	0
$124$	0	0
$125$	11.3137	1.01193
$126$	0	0
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	−14.1421	−1.23560	−0.617802	−	0.786334i	$-0.711977\pi$
$131$	−14.1421	−1.23560	−0.617802	+	0.786334i	$0.711977\pi$
$132$	0	0
$133$	−11.3137	−0.981023
$134$	0	0
$135$	0	0
$136$	0	0
$137$	8.00000	0.683486	0.341743	−	0.939793i	$-0.388983\pi$
$137$	8.00000	0.683486	0.341743	+	0.939793i	$0.388983\pi$
$138$	0	0
$139$	−8.48528	−0.719712	−0.359856	−	0.933008i	$-0.617174\pi$
$139$	−8.48528	−0.719712	−0.359856	+	0.933008i	$0.617174\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	12.0000	1.00349
$144$	0	0
$145$	6.00000	0.498273
$146$	0	0
$147$	0	0
$148$	0	0
$149$	1.41421	0.115857	0.0579284	−	0.998321i	$-0.481550\pi$
$149$	1.41421	0.115857	0.0579284	+	0.998321i	$0.481550\pi$
$150$	0	0
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	11.3137	0.908739
$156$	0	0
$157$	−4.24264	−0.338600	−0.169300	−	0.985565i	$-0.554151\pi$
$157$	−4.24264	−0.338600	−0.169300	+	0.985565i	$0.554151\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−16.0000	−1.26098
$162$	0	0
$163$	8.48528	0.664619	0.332309	−	0.943170i	$-0.392172\pi$
$163$	8.48528	0.664619	0.332309	+	0.943170i	$0.392172\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−4.00000	−0.309529	−0.154765	−	0.987951i	$-0.549462\pi$
$167$	−4.00000	−0.309529	−0.154765	+	0.987951i	$0.549462\pi$
$168$	0	0
$169$	5.00000	0.384615
$170$	0	0
$171$	0	0
$172$	0	0
$173$	18.3848	1.39777	0.698884	−	0.715235i	$-0.253680\pi$
$173$	18.3848	1.39777	0.698884	+	0.715235i	$0.253680\pi$
$174$	0	0
$175$	−12.0000	−0.907115
$176$	0	0
$177$	0	0
$178$	0	0
$179$	19.7990	1.47985	0.739923	−	0.672692i	$-0.234862\pi$
$179$	19.7990	1.47985	0.739923	+	0.672692i	$0.234862\pi$
$180$	0	0
$181$	21.2132	1.57676	0.788382	−	0.615185i	$-0.210919\pi$
$181$	21.2132	1.57676	0.788382	+	0.615185i	$0.210919\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	2.00000	0.147043
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	24.0000	1.73658	0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000	1.73658	0.868290	+	0.496058i	$0.165220\pi$
$192$	0	0
$193$	−16.0000	−1.15171	−0.575853	−	0.817554i	$-0.695330\pi$
$193$	−16.0000	−1.15171	−0.575853	+	0.817554i	$0.695330\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−24.0416	−1.71290	−0.856448	−	0.516234i	$-0.827334\pi$
$197$	−24.0416	−1.71290	−0.856448	+	0.516234i	$0.827334\pi$
$198$	0	0
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	−16.9706	−1.19110
$204$	0	0
$205$	11.3137	0.790184
$206$	0	0
$207$	0	0
$208$	0	0
$209$	−8.00000	−0.553372
$210$	0	0
$211$	14.1421	0.973585	0.486792	−	0.873518i	$-0.338167\pi$
$211$	14.1421	0.973585	0.486792	+	0.873518i	$0.338167\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	−4.00000	−0.272798
$216$	0	0
$217$	−32.0000	−2.17230
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	24.0000	1.60716	0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000	1.60716	0.803579	+	0.595198i	$0.202926\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	25.4558	1.68956	0.844782	−	0.535111i	$-0.179730\pi$
$227$	25.4558	1.68956	0.844782	+	0.535111i	$0.179730\pi$
$228$	0	0
$229$	1.41421	0.0934539	0.0467269	−	0.998908i	$-0.485121\pi$
$229$	1.41421	0.0934539	0.0467269	+	0.998908i	$0.485121\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	2.00000	0.131024	0.0655122	−	0.997852i	$-0.479132\pi$
$233$	2.00000	0.131024	0.0655122	+	0.997852i	$0.479132\pi$
$234$	0	0
$235$	11.3137	0.738025
$236$	0	0
$237$	0	0
$238$	0	0
$239$	16.0000	1.03495	0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000	1.03495	0.517477	+	0.855697i	$0.326871\pi$
$240$	0	0
$241$	0	0		−	1.00000i	$-0.5\pi$
$241$	0	0			1.00000i	$0.5\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	−12.7279	−0.813157
$246$	0	0
$247$	−12.0000	−0.763542
$248$	0	0
$249$	0	0
$250$	0	0
$251$	−19.7990	−1.24970	−0.624851	−	0.780744i	$-0.714840\pi$
$251$	−19.7990	−1.24970	−0.624851	+	0.780744i	$0.714840\pi$
$252$	0	0
$253$	−11.3137	−0.711287
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	0	0
$259$	−5.65685	−0.351500
$260$	0	0
$261$	0	0
$262$	0	0
$263$	20.0000	1.23325	0.616626	−	0.787256i	$-0.288499\pi$
$263$	20.0000	1.23325	0.616626	+	0.787256i	$0.288499\pi$
$264$	0	0
$265$	2.00000	0.122859
$266$	0	0
$267$	0	0
$268$	0	0
$269$	4.24264	0.258678	0.129339	−	0.991600i	$-0.458714\pi$
$269$	4.24264	0.258678	0.129339	+	0.991600i	$0.458714\pi$
$270$	0	0
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−8.48528	−0.511682
$276$	0	0
$277$	−21.2132	−1.27458	−0.637289	−	0.770625i	$-0.719944\pi$
$277$	−21.2132	−1.27458	−0.637289	+	0.770625i	$0.719944\pi$
$278$	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
$283$	−19.7990	−1.17693	−0.588464	−	0.808523i	$-0.700267\pi$
$283$	−19.7990	−1.17693	−0.588464	+	0.808523i	$0.700267\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−32.0000	−1.88890
$288$	0	0
$289$	−17.0000	−1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	−24.0416	−1.40453	−0.702264	−	0.711917i	$-0.747827\pi$
$293$	−24.0416	−1.40453	−0.702264	+	0.711917i	$0.747827\pi$
$294$	0	0
$295$	12.0000	0.698667
$296$	0	0
$297$	0	0
$298$	0	0
$299$	−16.9706	−0.981433
$300$	0	0
$301$	11.3137	0.652111
$302$	0	0
$303$	0	0
$304$	0	0
$305$	6.00000	0.343559
$306$	0	0
$307$	8.48528	0.484281	0.242140	−	0.970241i	$-0.422151\pi$
$307$	8.48528	0.484281	0.242140	+	0.970241i	$0.422151\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	4.00000	0.226819	0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000	0.226819	0.113410	+	0.993548i	$0.463823\pi$
$312$	0	0
$313$	8.00000	0.452187	0.226093	−	0.974106i	$-0.427405\pi$
$313$	8.00000	0.452187	0.226093	+	0.974106i	$0.427405\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	18.3848	1.03259	0.516296	−	0.856410i	$-0.327310\pi$
$317$	18.3848	1.03259	0.516296	+	0.856410i	$0.327310\pi$
$318$	0	0
$319$	−12.0000	−0.671871
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	−12.7279	−0.706018
$326$	0	0
$327$	0	0
$328$	0	0
$329$	−32.0000	−1.76422
$330$	0	0
$331$	31.1127	1.71011	0.855054	−	0.518538i	$-0.173524\pi$
$331$	31.1127	1.71011	0.855054	+	0.518538i	$0.173524\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	−4.00000	−0.218543
$336$	0	0
$337$	18.0000	0.980522	0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000	0.980522	0.490261	+	0.871576i	$0.336901\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	−22.6274	−1.22534
$342$	0	0
$343$	8.00000	0.431959
$344$	0	0
$345$	0	0
$346$	0	0
$347$	2.82843	0.151838	0.0759190	−	0.997114i	$-0.475811\pi$
$347$	2.82843	0.151838	0.0759190	+	0.997114i	$0.475811\pi$
$348$	0	0
$349$	−18.3848	−0.984115	−0.492057	−	0.870563i	$-0.663755\pi$
$349$	−18.3848	−0.984115	−0.492057	+	0.870563i	$0.663755\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	−14.0000	−0.745145	−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000	−0.745145	−0.372572	+	0.928003i	$0.621524\pi$
$354$	0	0
$355$	16.9706	0.900704
$356$	0	0
$357$	0	0
$358$	0	0
$359$	20.0000	1.05556	0.527780	−	0.849381i	$-0.323025\pi$
$359$	20.0000	1.05556	0.527780	+	0.849381i	$0.323025\pi$
$360$	0	0
$361$	−11.0000	−0.578947
$362$	0	0
$363$	0	0
$364$	0	0
$365$	2.82843	0.148047
$366$	0	0
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	−5.65685	−0.293689
$372$	0	0
$373$	−21.2132	−1.09838	−0.549189	−	0.835698i	$-0.685063\pi$
$373$	−21.2132	−1.09838	−0.549189	+	0.835698i	$0.685063\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−18.0000	−0.927047
$378$	0	0
$379$	−25.4558	−1.30758	−0.653789	−	0.756677i	$-0.726822\pi$
$379$	−25.4558	−1.30758	−0.653789	+	0.756677i	$0.726822\pi$
$380$	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
$385$	−16.0000	−0.815436
$386$	0	0
$387$	0	0
$388$	0	0
$389$	1.41421	0.0717035	0.0358517	−	0.999357i	$-0.488586\pi$
$389$	1.41421	0.0717035	0.0358517	+	0.999357i	$0.488586\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−4.24264	−0.212932	−0.106466	−	0.994316i	$-0.533954\pi$
$397$	−4.24264	−0.212932	−0.106466	+	0.994316i	$0.533954\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	0	0
$403$	−33.9411	−1.69073
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−4.00000	−0.198273
$408$	0	0
$409$	8.00000	0.395575	0.197787	−	0.980245i	$-0.436624\pi$
$409$	8.00000	0.395575	0.197787	+	0.980245i	$0.436624\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	−33.9411	−1.67013
$414$	0	0
$415$	20.0000	0.981761
$416$	0	0
$417$	0	0
$418$	0	0
$419$	8.48528	0.414533	0.207267	−	0.978285i	$-0.433543\pi$
$419$	8.48528	0.414533	0.207267	+	0.978285i	$0.433543\pi$
$420$	0	0
$421$	−21.2132	−1.03387	−0.516934	−	0.856025i	$-0.672927\pi$
$421$	−21.2132	−1.03387	−0.516934	+	0.856025i	$0.672927\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−16.9706	−0.821263
$428$	0	0
$429$	0	0
$430$	0	0
$431$	16.0000	0.770693	0.385346	−	0.922772i	$-0.374082\pi$
$431$	16.0000	0.770693	0.385346	+	0.922772i	$0.374082\pi$
$432$	0	0
$433$	−32.0000	−1.53782	−0.768911	−	0.639356i	$-0.779201\pi$
$433$	−32.0000	−1.53782	−0.768911	+	0.639356i	$0.779201\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	11.3137	0.541208
$438$	0	0
$439$	−4.00000	−0.190910	−0.0954548	−	0.995434i	$-0.530431\pi$
$439$	−4.00000	−0.190910	−0.0954548	+	0.995434i	$0.530431\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	8.48528	0.403148	0.201574	−	0.979473i	$-0.435394\pi$
$443$	8.48528	0.403148	0.201574	+	0.979473i	$0.435394\pi$
$444$	0	0
$445$	19.7990	0.938562
$446$	0	0
$447$	0	0
$448$	0	0
$449$	16.0000	0.755087	0.377543	−	0.925992i	$-0.376769\pi$
$449$	16.0000	0.755087	0.377543	+	0.925992i	$0.376769\pi$
$450$	0	0
$451$	−22.6274	−1.06548
$452$	0	0
$453$	0	0
$454$	0	0
$455$	−24.0000	−1.12514
$456$	0	0
$457$	8.00000	0.374224	0.187112	−	0.982339i	$-0.440087\pi$
$457$	8.00000	0.374224	0.187112	+	0.982339i	$0.440087\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	26.8701	1.25146	0.625732	−	0.780038i	$-0.284800\pi$
$461$	26.8701	1.25146	0.625732	+	0.780038i	$0.284800\pi$
$462$	0	0
$463$	−32.0000	−1.48717	−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000	−1.48717	−0.743583	+	0.668644i	$0.766875\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	2.82843	0.130884	0.0654420	−	0.997856i	$-0.479154\pi$
$467$	2.82843	0.130884	0.0654420	+	0.997856i	$0.479154\pi$
$468$	0	0
$469$	11.3137	0.522419
$470$	0	0
$471$	0	0
$472$	0	0
$473$	8.00000	0.367840
$474$	0	0
$475$	8.48528	0.389331
$476$	0	0
$477$	0	0
$478$	0	0
$479$	−8.00000	−0.365529	−0.182765	−	0.983157i	$-0.558505\pi$
$479$	−8.00000	−0.365529	−0.182765	+	0.983157i	$0.558505\pi$
$480$	0	0
$481$	−6.00000	−0.273576
$482$	0	0
$483$	0	0
$484$	0	0
$485$	22.6274	1.02746
$486$	0	0
$487$	−12.0000	−0.543772	−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000	−0.543772	−0.271886	+	0.962329i	$0.587647\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	19.7990	0.893516	0.446758	−	0.894655i	$-0.352579\pi$
$491$	19.7990	0.893516	0.446758	+	0.894655i	$0.352579\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−48.0000	−2.15309
$498$	0	0
$499$	2.82843	0.126618	0.0633089	−	0.997994i	$-0.479835\pi$
$499$	2.82843	0.126618	0.0633089	+	0.997994i	$0.479835\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	28.0000	1.24846	0.624229	−	0.781241i	$-0.285413\pi$
$503$	28.0000	1.24846	0.624229	+	0.781241i	$0.285413\pi$
$504$	0	0
$505$	−2.00000	−0.0889988
$506$	0	0
$507$	0	0
$508$	0	0
$509$	26.8701	1.19099	0.595497	−	0.803357i	$-0.296955\pi$
$509$	26.8701	1.19099	0.595497	+	0.803357i	$0.296955\pi$
$510$	0	0
$511$	−8.00000	−0.353899
$512$	0	0
$513$	0	0
$514$	0	0
$515$	5.65685	0.249271
$516$	0	0
$517$	−22.6274	−0.995153
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−24.0000	−1.05146	−0.525730	−	0.850652i	$-0.676208\pi$
$521$	−24.0000	−1.05146	−0.525730	+	0.850652i	$0.676208\pi$
$522$	0	0
$523$	−25.4558	−1.11311	−0.556553	−	0.830812i	$-0.687876\pi$
$523$	−25.4558	−1.11311	−0.556553	+	0.830812i	$0.687876\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−7.00000	−0.304348
$530$	0	0
$531$	0	0
$532$	0	0
$533$	−33.9411	−1.47015
$534$	0	0
$535$	−4.00000	−0.172935
$536$	0	0
$537$	0	0
$538$	0	0
$539$	25.4558	1.09646
$540$	0	0
$541$	−4.24264	−0.182405	−0.0912027	−	0.995832i	$-0.529071\pi$
$541$	−4.24264	−0.182405	−0.0912027	+	0.995832i	$0.529071\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	−26.0000	−1.11372
$546$	0	0
$547$	−42.4264	−1.81402	−0.907011	−	0.421107i	$-0.861642\pi$
$547$	−42.4264	−1.81402	−0.907011	+	0.421107i	$0.861642\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	12.0000	0.511217
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	18.3848	0.778988	0.389494	−	0.921029i	$-0.372650\pi$
$557$	18.3848	0.778988	0.389494	+	0.921029i	$0.372650\pi$
$558$	0	0
$559$	12.0000	0.507546
$560$	0	0
$561$	0	0
$562$	0	0
$563$	2.82843	0.119204	0.0596020	−	0.998222i	$-0.481017\pi$
$563$	2.82843	0.119204	0.0596020	+	0.998222i	$0.481017\pi$
$564$	0	0
$565$	−2.82843	−0.118993
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−24.0000	−1.00613	−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000	−1.00613	−0.503066	+	0.864248i	$0.667795\pi$
$570$	0	0
$571$	−8.48528	−0.355098	−0.177549	−	0.984112i	$-0.556817\pi$
$571$	−8.48528	−0.355098	−0.177549	+	0.984112i	$0.556817\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	12.0000	0.500435
$576$	0	0
$577$	30.0000	1.24892	0.624458	−	0.781058i	$-0.285320\pi$
$577$	30.0000	1.24892	0.624458	+	0.781058i	$0.285320\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	−56.5685	−2.34686
$582$	0	0
$583$	−4.00000	−0.165663
$584$	0	0
$585$	0	0
$586$	0	0
$587$	14.1421	0.583708	0.291854	−	0.956463i	$-0.405728\pi$
$587$	14.1421	0.583708	0.291854	+	0.956463i	$0.405728\pi$
$588$	0	0
$589$	22.6274	0.932346
$590$	0	0
$591$	0	0
$592$	0	0
$593$	−14.0000	−0.574911	−0.287456	−	0.957794i	$-0.592809\pi$
$593$	−14.0000	−0.574911	−0.287456	+	0.957794i	$0.592809\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	−28.0000	−1.14405	−0.572024	−	0.820237i	$-0.693842\pi$
$599$	−28.0000	−1.14405	−0.572024	+	0.820237i	$0.693842\pi$
$600$	0	0
$601$	14.0000	0.571072	0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000	0.571072	0.285536	+	0.958368i	$0.407828\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	4.24264	0.172488
$606$	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
$611$	−33.9411	−1.37311
$612$	0	0
$613$	24.0416	0.971032	0.485516	−	0.874228i	$-0.338632\pi$
$613$	24.0416	0.971032	0.485516	+	0.874228i	$0.338632\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−2.00000	−0.0805170	−0.0402585	−	0.999189i	$-0.512818\pi$
$617$	−2.00000	−0.0805170	−0.0402585	+	0.999189i	$0.512818\pi$
$618$	0	0
$619$	−25.4558	−1.02316	−0.511578	−	0.859237i	$-0.670939\pi$
$619$	−25.4558	−1.02316	−0.511578	+	0.859237i	$0.670939\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	−56.0000	−2.24359
$624$	0	0
$625$	−1.00000	−0.0400000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	4.00000	0.159237	0.0796187	−	0.996825i	$-0.474630\pi$
$631$	4.00000	0.159237	0.0796187	+	0.996825i	$0.474630\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	11.3137	0.448971
$636$	0	0
$637$	38.1838	1.51290
$638$	0	0
$639$	0	0
$640$	0	0
$641$	−16.0000	−0.631962	−0.315981	−	0.948766i	$-0.602334\pi$
$641$	−16.0000	−0.631962	−0.315981	+	0.948766i	$0.602334\pi$
$642$	0	0
$643$	25.4558	1.00388	0.501940	−	0.864902i	$-0.332620\pi$
$643$	25.4558	1.00388	0.501940	+	0.864902i	$0.332620\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−12.0000	−0.471769	−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000	−0.471769	−0.235884	+	0.971781i	$0.575799\pi$
$648$	0	0
$649$	−24.0000	−0.942082
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−41.0122	−1.60493	−0.802466	−	0.596698i	$-0.796479\pi$
$653$	−41.0122	−1.60493	−0.802466	+	0.596698i	$0.796479\pi$
$654$	0	0
$655$	20.0000	0.781465
$656$	0	0
$657$	0	0
$658$	0	0
$659$	31.1127	1.21198	0.605989	−	0.795473i	$-0.292777\pi$
$659$	31.1127	1.21198	0.605989	+	0.795473i	$0.292777\pi$
$660$	0	0
$661$	−24.0416	−0.935111	−0.467556	−	0.883964i	$-0.654865\pi$
$661$	−24.0416	−0.935111	−0.467556	+	0.883964i	$0.654865\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	16.0000	0.620453
$666$	0	0
$667$	16.9706	0.657103
$668$	0	0
$669$	0	0
$670$	0	0
$671$	−12.0000	−0.463255
$672$	0	0
$673$	16.0000	0.616755	0.308377	−	0.951264i	$-0.400214\pi$
$673$	16.0000	0.616755	0.308377	+	0.951264i	$0.400214\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	46.6690	1.79364	0.896819	−	0.442398i	$-0.145872\pi$
$677$	46.6690	1.79364	0.896819	+	0.442398i	$0.145872\pi$
$678$	0	0
$679$	−64.0000	−2.45609
$680$	0	0
$681$	0	0
$682$	0	0
$683$	8.48528	0.324680	0.162340	−	0.986735i	$-0.448096\pi$
$683$	8.48528	0.324680	0.162340	+	0.986735i	$0.448096\pi$
$684$	0	0
$685$	−11.3137	−0.432275
$686$	0	0
$687$	0	0
$688$	0	0
$689$	−6.00000	−0.228582
$690$	0	0
$691$	−8.48528	−0.322795	−0.161398	−	0.986889i	$-0.551600\pi$
$691$	−8.48528	−0.322795	−0.161398	+	0.986889i	$0.551600\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	12.0000	0.455186
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	26.8701	1.01487	0.507434	−	0.861691i	$-0.330594\pi$
$701$	26.8701	1.01487	0.507434	+	0.861691i	$0.330594\pi$
$702$	0	0
$703$	4.00000	0.150863
$704$	0	0
$705$	0	0
$706$	0	0
$707$	5.65685	0.212748
$708$	0	0
$709$	21.2132	0.796679	0.398339	−	0.917238i	$-0.369587\pi$
$709$	21.2132	0.796679	0.398339	+	0.917238i	$0.369587\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	32.0000	1.19841
$714$	0	0
$715$	−16.9706	−0.634663
$716$	0	0
$717$	0	0
$718$	0	0
$719$	−48.0000	−1.79010	−0.895049	−	0.445968i	$-0.852860\pi$
$719$	−48.0000	−1.79010	−0.895049	+	0.445968i	$0.852860\pi$
$720$	0	0
$721$	−16.0000	−0.595871
$722$	0	0
$723$	0	0
$724$	0	0
$725$	12.7279	0.472703
$726$	0	0
$727$	−20.0000	−0.741759	−0.370879	−	0.928681i	$-0.620944\pi$
$727$	−20.0000	−0.741759	−0.370879	+	0.928681i	$0.620944\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	26.8701	0.992468	0.496234	−	0.868189i	$-0.334716\pi$
$733$	26.8701	0.992468	0.496234	+	0.868189i	$0.334716\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	8.00000	0.294684
$738$	0	0
$739$	8.48528	0.312136	0.156068	−	0.987746i	$-0.450118\pi$
$739$	8.48528	0.312136	0.156068	+	0.987746i	$0.450118\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	12.0000	0.440237	0.220119	−	0.975473i	$-0.429356\pi$
$743$	12.0000	0.440237	0.220119	+	0.975473i	$0.429356\pi$
$744$	0	0
$745$	−2.00000	−0.0732743
$746$	0	0
$747$	0	0
$748$	0	0
$749$	11.3137	0.413394
$750$	0	0
$751$	32.0000	1.16770	0.583848	−	0.811863i	$-0.301546\pi$
$751$	32.0000	1.16770	0.583848	+	0.811863i	$0.301546\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	−28.2843	−1.02937
$756$	0	0
$757$	−1.41421	−0.0514005	−0.0257002	−	0.999670i	$-0.508182\pi$
$757$	−1.41421	−0.0514005	−0.0257002	+	0.999670i	$0.508182\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	24.0000	0.869999	0.435000	−	0.900431i	$-0.356748\pi$
$761$	24.0000	0.869999	0.435000	+	0.900431i	$0.356748\pi$
$762$	0	0
$763$	73.5391	2.66229
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−36.0000	−1.29988
$768$	0	0
$769$	16.0000	0.576975	0.288487	−	0.957484i	$-0.406848\pi$
$769$	16.0000	0.576975	0.288487	+	0.957484i	$0.406848\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	−21.2132	−0.762986	−0.381493	−	0.924372i	$-0.624590\pi$
$773$	−21.2132	−0.762986	−0.381493	+	0.924372i	$0.624590\pi$
$774$	0	0
$775$	24.0000	0.862105
$776$	0	0
$777$	0	0
$778$	0	0
$779$	22.6274	0.810711
$780$	0	0
$781$	−33.9411	−1.21451
$782$	0	0
$783$	0	0
$784$	0	0
$785$	6.00000	0.214149
$786$	0	0
$787$	25.4558	0.907403	0.453701	−	0.891154i	$-0.350103\pi$
$787$	25.4558	0.907403	0.453701	+	0.891154i	$0.350103\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	8.00000	0.284447
$792$	0	0
$793$	−18.0000	−0.639199
$794$	0	0
$795$	0	0
$796$	0	0
$797$	26.8701	0.951786	0.475893	−	0.879503i	$-0.342125\pi$
$797$	26.8701	0.951786	0.475893	+	0.879503i	$0.342125\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	0	0
$803$	−5.65685	−0.199626
$804$	0	0
$805$	22.6274	0.797512
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−40.0000	−1.40633	−0.703163	−	0.711029i	$-0.748229\pi$
$809$	−40.0000	−1.40633	−0.703163	+	0.711029i	$0.748229\pi$
$810$	0	0
$811$	31.1127	1.09251	0.546257	−	0.837617i	$-0.316052\pi$
$811$	31.1127	1.09251	0.546257	+	0.837617i	$0.316052\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	−12.0000	−0.420342
$816$	0	0
$817$	−8.00000	−0.279885
$818$	0	0
$819$	0	0
$820$	0	0
$821$	21.2132	0.740346	0.370173	−	0.928963i	$-0.379298\pi$
$821$	21.2132	0.740346	0.370173	+	0.928963i	$0.379298\pi$
$822$	0	0
$823$	−52.0000	−1.81261	−0.906303	−	0.422628i	$-0.861108\pi$
$823$	−52.0000	−1.81261	−0.906303	+	0.422628i	$0.861108\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	19.7990	0.688478	0.344239	−	0.938882i	$-0.388137\pi$
$827$	19.7990	0.688478	0.344239	+	0.938882i	$0.388137\pi$
$828$	0	0
$829$	18.3848	0.638530	0.319265	−	0.947666i	$-0.396564\pi$
$829$	18.3848	0.638530	0.319265	+	0.947666i	$0.396564\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	5.65685	0.195764
$836$	0	0
$837$	0	0
$838$	0	0
$839$	−36.0000	−1.24286	−0.621429	−	0.783470i	$-0.713448\pi$
$839$	−36.0000	−1.24286	−0.621429	+	0.783470i	$0.713448\pi$
$840$	0	0
$841$	−11.0000	−0.379310
$842$	0	0
$843$	0	0
$844$	0	0
$845$	−7.07107	−0.243252
$846$	0	0
$847$	−12.0000	−0.412325
$848$	0	0
$849$	0	0
$850$	0	0
$851$	5.65685	0.193914
$852$	0	0
$853$	1.41421	0.0484218	0.0242109	−	0.999707i	$-0.492293\pi$
$853$	1.41421	0.0484218	0.0242109	+	0.999707i	$0.492293\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−24.0000	−0.819824	−0.409912	−	0.912125i	$-0.634441\pi$
$857$	−24.0000	−0.819824	−0.409912	+	0.912125i	$0.634441\pi$
$858$	0	0
$859$	−25.4558	−0.868542	−0.434271	−	0.900782i	$-0.642994\pi$
$859$	−25.4558	−0.868542	−0.434271	+	0.900782i	$0.642994\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	24.0000	0.816970	0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000	0.816970	0.408485	+	0.912765i	$0.366057\pi$
$864$	0	0
$865$	−26.0000	−0.884027
$866$	0	0
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	12.0000	0.406604
$872$	0	0
$873$	0	0
$874$	0	0
$875$	45.2548	1.52989
$876$	0	0
$877$	−26.8701	−0.907337	−0.453669	−	0.891170i	$-0.649885\pi$
$877$	−26.8701	−0.907337	−0.453669	+	0.891170i	$0.649885\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	0	0
$883$	−48.0833	−1.61813	−0.809065	−	0.587719i	$-0.800026\pi$
$883$	−48.0833	−1.61813	−0.809065	+	0.587719i	$0.800026\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	36.0000	1.20876	0.604381	−	0.796696i	$-0.293421\pi$
$887$	36.0000	1.20876	0.604381	+	0.796696i	$0.293421\pi$
$888$	0	0
$889$	−32.0000	−1.07325
$890$	0	0
$891$	0	0
$892$	0	0
$893$	22.6274	0.757198
$894$	0	0
$895$	−28.0000	−0.935937
$896$	0	0
$897$	0	0
$898$	0	0
$899$	33.9411	1.13200
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−30.0000	−0.997234
$906$	0	0
$907$	14.1421	0.469582	0.234791	−	0.972046i	$-0.424559\pi$
$907$	14.1421	0.469582	0.234791	+	0.972046i	$0.424559\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	56.0000	1.85536	0.927681	−	0.373373i	$-0.121799\pi$
$911$	56.0000	1.85536	0.927681	+	0.373373i	$0.121799\pi$
$912$	0	0
$913$	−40.0000	−1.32381
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−56.5685	−1.86806
$918$	0	0
$919$	4.00000	0.131948	0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000	0.131948	0.0659739	+	0.997821i	$0.478985\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	−50.9117	−1.67578
$924$	0	0
$925$	4.24264	0.139497
$926$	0	0
$927$	0	0
$928$	0	0
$929$	48.0000	1.57483	0.787414	−	0.616424i	$-0.211419\pi$
$929$	48.0000	1.57483	0.787414	+	0.616424i	$0.211419\pi$
$930$	0	0
$931$	−25.4558	−0.834282
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−2.00000	−0.0653372	−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000	−0.0653372	−0.0326686	+	0.999466i	$0.510401\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	−18.3848	−0.599327	−0.299663	−	0.954045i	$-0.596874\pi$
$941$	−18.3848	−0.599327	−0.299663	+	0.954045i	$0.596874\pi$
$942$	0	0
$943$	32.0000	1.04206
$944$	0	0
$945$	0	0
$946$	0	0
$947$	14.1421	0.459558	0.229779	−	0.973243i	$-0.426200\pi$
$947$	14.1421	0.459558	0.229779	+	0.973243i	$0.426200\pi$
$948$	0	0
$949$	−8.48528	−0.275444
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−24.0000	−0.777436	−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000	−0.777436	−0.388718	+	0.921357i	$0.627082\pi$
$954$	0	0
$955$	−33.9411	−1.09831
$956$	0	0
$957$	0	0
$958$	0	0
$959$	32.0000	1.03333
$960$	0	0
$961$	33.0000	1.06452
$962$	0	0
$963$	0	0
$964$	0	0
$965$	22.6274	0.728402
$966$	0	0
$967$	20.0000	0.643157	0.321578	−	0.946883i	$-0.395787\pi$
$967$	20.0000	0.643157	0.321578	+	0.946883i	$0.395787\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	19.7990	0.635380	0.317690	−	0.948195i	$-0.397093\pi$
$971$	19.7990	0.635380	0.317690	+	0.948195i	$0.397093\pi$
$972$	0	0
$973$	−33.9411	−1.08810
$974$	0	0
$975$	0	0
$976$	0	0
$977$	32.0000	1.02377	0.511885	−	0.859054i	$-0.328947\pi$
$977$	32.0000	1.02377	0.511885	+	0.859054i	$0.328947\pi$
$978$	0	0
$979$	−39.5980	−1.26556
$980$	0	0
$981$	0	0
$982$	0	0
$983$	−28.0000	−0.893061	−0.446531	−	0.894768i	$-0.647341\pi$
$983$	−28.0000	−0.893061	−0.446531	+	0.894768i	$0.647341\pi$
$984$	0	0
$985$	34.0000	1.08333
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−11.3137	−0.359755
$990$	0	0
$991$	16.0000	0.508257	0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000	0.508257	0.254128	+	0.967170i	$0.418211\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	−5.65685	−0.179334
$996$	0	0
$997$	21.2132	0.671829	0.335914	−	0.941893i	$-0.390955\pi$
$997$	21.2132	0.671829	0.335914	+	0.941893i	$0.390955\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9216.2.a.u.1.1		2
3.2	odd	2		1024.2.a.f.1.1		2
4.3	odd	2		9216.2.a.b.1.1		2
8.3	odd	2		9216.2.a.b.1.2		2
8.5	even	2	inner	9216.2.a.u.1.2		2
12.11	even	2		1024.2.a.a.1.2		2
24.5	odd	2		1024.2.a.f.1.2		2
24.11	even	2		1024.2.a.a.1.1		2
32.3	odd	8		4608.2.k.o.1153.1		2
32.5	even	8		4608.2.k.f.3457.1		2
32.11	odd	8		4608.2.k.o.3457.1		2
32.13	even	8		4608.2.k.f.1153.1		2
32.19	odd	8		4608.2.k.j.1153.1		2
32.21	even	8		4608.2.k.s.3457.1		2
32.27	odd	8		4608.2.k.j.3457.1		2
32.29	even	8		4608.2.k.s.1153.1		2
48.5	odd	4		1024.2.b.a.513.2		2
48.11	even	4		1024.2.b.f.513.1		2
48.29	odd	4		1024.2.b.a.513.1		2
48.35	even	4		1024.2.b.f.513.2		2
96.5	odd	8		512.2.e.h.385.1	yes	2
96.11	even	8		512.2.e.g.385.1	yes	2
96.29	odd	8		512.2.e.a.129.1	✓	2
96.35	even	8		512.2.e.g.129.1	yes	2
96.53	odd	8		512.2.e.a.385.1	yes	2
96.59	even	8		512.2.e.b.385.1	yes	2
96.77	odd	8		512.2.e.h.129.1	yes	2
96.83	even	8		512.2.e.b.129.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.e.a.129.1	✓	2	96.29	odd	8
512.2.e.a.385.1	yes	2	96.53	odd	8
512.2.e.b.129.1	yes	2	96.83	even	8
512.2.e.b.385.1	yes	2	96.59	even	8
512.2.e.g.129.1	yes	2	96.35	even	8
512.2.e.g.385.1	yes	2	96.11	even	8
512.2.e.h.129.1	yes	2	96.77	odd	8
512.2.e.h.385.1	yes	2	96.5	odd	8
1024.2.a.a.1.1		2	24.11	even	2
1024.2.a.a.1.2		2	12.11	even	2
1024.2.a.f.1.1		2	3.2	odd	2
1024.2.a.f.1.2		2	24.5	odd	2
1024.2.b.a.513.1		2	48.29	odd	4
1024.2.b.a.513.2		2	48.5	odd	4
1024.2.b.f.513.1		2	48.11	even	4
1024.2.b.f.513.2		2	48.35	even	4
4608.2.k.f.1153.1		2	32.13	even	8
4608.2.k.f.3457.1		2	32.5	even	8
4608.2.k.j.1153.1		2	32.19	odd	8
4608.2.k.j.3457.1		2	32.27	odd	8
4608.2.k.o.1153.1		2	32.3	odd	8
4608.2.k.o.3457.1		2	32.11	odd	8
4608.2.k.s.1153.1		2	32.29	even	8
4608.2.k.s.3457.1		2	32.21	even	8
9216.2.a.b.1.1		2	4.3	odd	2
9216.2.a.b.1.2		2	8.3	odd	2
9216.2.a.u.1.1		2	1.1	even	1	trivial
9216.2.a.u.1.2		2	8.5	even	2	inner

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:	\( N \)	\(=\)	\( 9216 = 2^{10} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9216.a (trivial)

\(f(q)\)	\(=\)	\(q-1.41421 q^{5} +4.00000 q^{7} +O(q^{10})\)	\(q-1.41421 q^{5} +4.00000 q^{7} +2.82843 q^{11} +4.24264 q^{13} -2.82843 q^{19} -4.00000 q^{23} -3.00000 q^{25} -4.24264 q^{29} -8.00000 q^{31} -5.65685 q^{35} -1.41421 q^{37} -8.00000 q^{41} +2.82843 q^{43} -8.00000 q^{47} +9.00000 q^{49} -1.41421 q^{53} -4.00000 q^{55} -8.48528 q^{59} -4.24264 q^{61} -6.00000 q^{65} +2.82843 q^{67} -12.0000 q^{71} -2.00000 q^{73} +11.3137 q^{77} -14.1421 q^{83} -14.0000 q^{89} +16.9706 q^{91} +4.00000 q^{95} -16.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{7}+O(q^{10}) \) 2 * q + 8 * q^7	\( 2 q + 8 q^{7} - 8 q^{23} - 6 q^{25} - 16 q^{31} - 16 q^{41} - 16 q^{47} + 18 q^{49} - 8 q^{55} - 12 q^{65} - 24 q^{71} - 4 q^{73} - 28 q^{89} + 8 q^{95} - 32 q^{97}+O(q^{100}) \) 2 * q + 8 * q^7 - 8 * q^23 - 6 * q^25 - 16 * q^31 - 16 * q^41 - 16 * q^47 + 18 * q^49 - 8 * q^55 - 12 * q^65 - 24 * q^71 - 4 * q^73 - 28 * q^89 + 8 * q^95 - 32 * q^97

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