LMFDB - Embedded newform 576.8.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,8,Mod(1,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("576.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	576.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:	$179.933774679$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 2)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	576.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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
$5$	−210.000	−0.751319	−0.375659	−	0.926758i	$-0.622584\pi$
$5$	−210.000	−0.751319	−0.375659	+	0.926758i	$0.622584\pi$
$6$	0	0
$7$	−1016.00	−1.11957	−0.559784	−	0.828638i	$-0.689116\pi$
$7$	−1016.00	−1.11957	−0.559784	+	0.828638i	$0.689116\pi$
$8$	0	0
$9$	0	0
$10$	0	0
$11$	−1092.00	−0.247371	−0.123685	−	0.992321i	$-0.539471\pi$
$11$	−1092.00	−0.247371	−0.123685	+	0.992321i	$0.539471\pi$
$12$	0	0
$13$	−1382.00	−0.174464	−0.0872321	−	0.996188i	$-0.527802\pi$
$13$	−1382.00	−0.174464	−0.0872321	+	0.996188i	$0.527802\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−14706.0	−0.725978	−0.362989	−	0.931793i	$-0.618244\pi$
$17$	−14706.0	−0.725978	−0.362989	+	0.931793i	$0.618244\pi$
$18$	0	0
$19$	−39940.0	−1.33589	−0.667945	−	0.744211i	$-0.732826\pi$
$19$	−39940.0	−1.33589	−0.667945	+	0.744211i	$0.732826\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	68712.0	1.17757	0.588783	−	0.808291i	$-0.299607\pi$
$23$	68712.0	1.17757	0.588783	+	0.808291i	$0.299607\pi$
$24$	0	0
$25$	−34025.0	−0.435520
$26$	0	0
$27$	0	0
$28$	0	0
$29$	−102570.	−0.780957	−0.390479	−	0.920612i	$-0.627690\pi$
$29$	−102570.	−0.780957	−0.390479	+	0.920612i	$0.627690\pi$
$30$	0	0
$31$	−227552.	−1.37188	−0.685938	−	0.727660i	$-0.740608\pi$
$31$	−227552.	−1.37188	−0.685938	+	0.727660i	$0.740608\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	213360.	0.841153
$36$	0	0
$37$	−160526.	−0.521002	−0.260501	−	0.965474i	$-0.583888\pi$
$37$	−160526.	−0.521002	−0.260501	+	0.965474i	$0.583888\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−10842.0	−0.0245678	−0.0122839	−	0.999925i	$-0.503910\pi$
$41$	−10842.0	−0.0245678	−0.0122839	+	0.999925i	$0.503910\pi$
$42$	0	0
$43$	−630748.	−1.20981	−0.604904	−	0.796299i	$-0.706788\pi$
$43$	−630748.	−1.20981	−0.604904	+	0.796299i	$0.706788\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	472656.	0.664053	0.332026	−	0.943270i	$-0.392268\pi$
$47$	472656.	0.664053	0.332026	+	0.943270i	$0.392268\pi$
$48$	0	0
$49$	208713.	0.253433
$50$	0	0
$51$	0	0
$52$	0	0
$53$	−1.49402e6	−1.37845	−0.689224	−	0.724548i	$-0.742048\pi$
$53$	−1.49402e6	−1.37845	−0.689224	+	0.724548i	$0.742048\pi$
$54$	0	0
$55$	229320.	0.185854
$56$	0	0
$57$	0	0
$58$	0	0
$59$	−2.64066e6	−1.67390	−0.836952	−	0.547277i	$-0.815665\pi$
$59$	−2.64066e6	−1.67390	−0.836952	+	0.547277i	$0.815665\pi$
$60$	0	0
$61$	−827702.	−0.466895	−0.233448	−	0.972369i	$-0.575001\pi$
$61$	−827702.	−0.466895	−0.233448	+	0.972369i	$0.575001\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	290220.	0.131078
$66$	0	0
$67$	−126004.	−0.0511826	−0.0255913	−	0.999672i	$-0.508147\pi$
$67$	−126004.	−0.0511826	−0.0255913	+	0.999672i	$0.508147\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	−1.41473e6	−0.469104	−0.234552	−	0.972104i	$-0.575362\pi$
$71$	−1.41473e6	−0.469104	−0.234552	+	0.972104i	$0.575362\pi$
$72$	0	0
$73$	980282.	0.294931	0.147466	−	0.989067i	$-0.452888\pi$
$73$	980282.	0.294931	0.147466	+	0.989067i	$0.452888\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	1.10947e6	0.276948
$78$	0	0
$79$	3.56680e6	0.813924	0.406962	−	0.913445i	$-0.366588\pi$
$79$	3.56680e6	0.813924	0.406962	+	0.913445i	$0.366588\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	−5.67289e6	−1.08901	−0.544504	−	0.838758i	$-0.683282\pi$
$83$	−5.67289e6	−1.08901	−0.544504	+	0.838758i	$0.683282\pi$
$84$	0	0
$85$	3.08826e6	0.545441
$86$	0	0
$87$	0	0
$88$	0	0
$89$	1.19512e7	1.79699	0.898496	−	0.438982i	$-0.144661\pi$
$89$	1.19512e7	1.79699	0.898496	+	0.438982i	$0.144661\pi$
$90$	0	0
$91$	1.40411e6	0.195325
$92$	0	0
$93$	0	0
$94$	0	0
$95$	8.38740e6	1.00368
$96$	0	0
$97$	8.68215e6	0.965886	0.482943	−	0.875652i	$-0.339568\pi$
$97$	8.68215e6	0.965886	0.482943	+	0.875652i	$0.339568\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	−1.00795e7	−0.973455	−0.486727	−	0.873554i	$-0.661810\pi$
$101$	−1.00795e7	−0.973455	−0.486727	+	0.873554i	$0.661810\pi$
$102$	0	0
$103$	−3.74799e6	−0.337962	−0.168981	−	0.985619i	$-0.554048\pi$
$103$	−3.74799e6	−0.337962	−0.168981	+	0.985619i	$0.554048\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	1.79856e7	1.41932	0.709661	−	0.704543i	$-0.248848\pi$
$107$	1.79856e7	1.41932	0.709661	+	0.704543i	$0.248848\pi$
$108$	0	0
$109$	−1.22570e7	−0.906552	−0.453276	−	0.891370i	$-0.649745\pi$
$109$	−1.22570e7	−0.906552	−0.453276	+	0.891370i	$0.649745\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	−1.65950e7	−1.08194	−0.540968	−	0.841043i	$-0.681942\pi$
$113$	−1.65950e7	−1.08194	−0.540968	+	0.841043i	$0.681942\pi$
$114$	0	0
$115$	−1.44295e7	−0.884727
$116$	0	0
$117$	0	0
$118$	0	0
$119$	1.49413e7	0.812782
$120$	0	0
$121$	−1.82947e7	−0.938808
$122$	0	0
$123$	0	0
$124$	0	0
$125$	2.35515e7	1.07853
$126$	0	0
$127$	−1.16826e6	−0.0506087	−0.0253043	−	0.999680i	$-0.508055\pi$
$127$	−1.16826e6	−0.0506087	−0.0253043	+	0.999680i	$0.508055\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	7.92383e6	0.307954	0.153977	−	0.988074i	$-0.450792\pi$
$131$	7.92383e6	0.307954	0.153977	+	0.988074i	$0.450792\pi$
$132$	0	0
$133$	4.05790e7	1.49562
$134$	0	0
$135$	0	0
$136$	0	0
$137$	315654.	0.0104879	0.00524396	−	0.999986i	$-0.498331\pi$
$137$	315654.	0.0104879	0.00524396	+	0.999986i	$0.498331\pi$
$138$	0	0
$139$	3.92038e7	1.23816	0.619079	−	0.785329i	$-0.287506\pi$
$139$	3.92038e7	1.23816	0.619079	+	0.785329i	$0.287506\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	1.50914e6	0.0431573
$144$	0	0
$145$	2.15397e7	0.586748
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−2.18860e7	−0.542020	−0.271010	−	0.962577i	$-0.587358\pi$
$149$	−2.18860e7	−0.542020	−0.271010	+	0.962577i	$0.587358\pi$
$150$	0	0
$151$	2.94154e7	0.695274	0.347637	−	0.937629i	$-0.386984\pi$
$151$	2.94154e7	0.695274	0.347637	+	0.937629i	$0.386984\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	4.77859e7	1.03072
$156$	0	0
$157$	−6.05550e7	−1.24882	−0.624412	−	0.781095i	$-0.714661\pi$
$157$	−6.05550e7	−1.24882	−0.624412	+	0.781095i	$0.714661\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−6.98114e7	−1.31837
$162$	0	0
$163$	5.70853e7	1.03245	0.516223	−	0.856454i	$-0.327337\pi$
$163$	5.70853e7	1.03245	0.516223	+	0.856454i	$0.327337\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−8.77265e7	−1.45755	−0.728775	−	0.684754i	$-0.759910\pi$
$167$	−8.77265e7	−1.45755	−0.728775	+	0.684754i	$0.759910\pi$
$168$	0	0
$169$	−6.08386e7	−0.969562
$170$	0	0
$171$	0	0
$172$	0	0
$173$	8.56954e6	0.125833	0.0629167	−	0.998019i	$-0.479960\pi$
$173$	8.56954e6	0.125833	0.0629167	+	0.998019i	$0.479960\pi$
$174$	0	0
$175$	3.45694e7	0.487594
$176$	0	0
$177$	0	0
$178$	0	0
$179$	−1.88041e7	−0.245056	−0.122528	−	0.992465i	$-0.539100\pi$
$179$	−1.88041e7	−0.245056	−0.122528	+	0.992465i	$0.539100\pi$
$180$	0	0
$181$	5.99625e7	0.751631	0.375816	−	0.926694i	$-0.377363\pi$
$181$	5.99625e7	0.751631	0.375816	+	0.926694i	$0.377363\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	3.37105e7	0.391439
$186$	0	0
$187$	1.60590e7	0.179586
$188$	0	0
$189$	0	0
$190$	0	0
$191$	9.39861e7	0.975993	0.487997	−	0.872845i	$-0.337728\pi$
$191$	9.39861e7	0.975993	0.487997	+	0.872845i	$0.337728\pi$
$192$	0	0
$193$	−3.51946e7	−0.352391	−0.176196	−	0.984355i	$-0.556379\pi$
$193$	−3.51946e7	−0.352391	−0.176196	+	0.984355i	$0.556379\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	1.02985e8	0.959718	0.479859	−	0.877346i	$-0.340688\pi$
$197$	1.02985e8	0.959718	0.479859	+	0.877346i	$0.340688\pi$
$198$	0	0
$199$	−8.36376e7	−0.752342	−0.376171	−	0.926550i	$-0.622760\pi$
$199$	−8.36376e7	−0.752342	−0.376171	+	0.926550i	$0.622760\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	1.04211e8	0.874335
$204$	0	0
$205$	2.27682e6	0.0184582
$206$	0	0
$207$	0	0
$208$	0	0
$209$	4.36145e7	0.330460
$210$	0	0
$211$	−9.74010e7	−0.713797	−0.356899	−	0.934143i	$-0.616166\pi$
$211$	−9.74010e7	−0.713797	−0.356899	+	0.934143i	$0.616166\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	1.32457e8	0.908951
$216$	0	0
$217$	2.31193e8	1.53591
$218$	0	0
$219$	0	0
$220$	0	0
$221$	2.03237e7	0.126657
$222$	0	0
$223$	1.46457e7	0.0884390	0.0442195	−	0.999022i	$-0.485920\pi$
$223$	1.46457e7	0.0884390	0.0442195	+	0.999022i	$0.485920\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	1.84541e8	1.04713	0.523567	−	0.851985i	$-0.324601\pi$
$227$	1.84541e8	1.04713	0.523567	+	0.851985i	$0.324601\pi$
$228$	0	0
$229$	8.75461e6	0.0481740	0.0240870	−	0.999710i	$-0.492332\pi$
$229$	8.75461e6	0.0481740	0.0240870	+	0.999710i	$0.492332\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	1.19556e8	0.619193	0.309597	−	0.950868i	$-0.399806\pi$
$233$	1.19556e8	0.619193	0.309597	+	0.950868i	$0.399806\pi$
$234$	0	0
$235$	−9.92578e7	−0.498915
$236$	0	0
$237$	0	0
$238$	0	0
$239$	3.96209e8	1.87729	0.938646	−	0.344883i	$-0.112081\pi$
$239$	3.96209e8	1.87729	0.938646	+	0.344883i	$0.112081\pi$
$240$	0	0
$241$	−2.56606e8	−1.18089	−0.590443	−	0.807080i	$-0.701047\pi$
$241$	−2.56606e8	−1.18089	−0.590443	+	0.807080i	$0.701047\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	−4.38297e7	−0.190409
$246$	0	0
$247$	5.51971e7	0.233065
$248$	0	0
$249$	0	0
$250$	0	0
$251$	7.34775e7	0.293290	0.146645	−	0.989189i	$-0.453153\pi$
$251$	7.34775e7	0.293290	0.146645	+	0.989189i	$0.453153\pi$
$252$	0	0
$253$	−7.50335e7	−0.291295
$254$	0	0
$255$	0	0
$256$	0	0
$257$	2.02701e8	0.744886	0.372443	−	0.928055i	$-0.378520\pi$
$257$	2.02701e8	0.744886	0.372443	+	0.928055i	$0.378520\pi$
$258$	0	0
$259$	1.63094e8	0.583297
$260$	0	0
$261$	0	0
$262$	0	0
$263$	1.54254e8	0.522867	0.261434	−	0.965221i	$-0.415805\pi$
$263$	1.54254e8	0.522867	0.261434	+	0.965221i	$0.415805\pi$
$264$	0	0
$265$	3.13744e8	1.03565
$266$	0	0
$267$	0	0
$268$	0	0
$269$	−6.24018e8	−1.95463	−0.977315	−	0.211793i	$-0.932070\pi$
$269$	−6.24018e8	−1.95463	−0.977315	+	0.211793i	$0.932070\pi$
$270$	0	0
$271$	3.87983e8	1.18419	0.592094	−	0.805869i	$-0.298302\pi$
$271$	3.87983e8	1.18419	0.592094	+	0.805869i	$0.298302\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	3.71553e7	0.107735
$276$	0	0
$277$	−4.53952e8	−1.28331	−0.641654	−	0.766994i	$-0.721752\pi$
$277$	−4.53952e8	−1.28331	−0.641654	+	0.766994i	$0.721752\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−3.33770e8	−0.897377	−0.448689	−	0.893688i	$-0.648109\pi$
$281$	−3.33770e8	−0.897377	−0.448689	+	0.893688i	$0.648109\pi$
$282$	0	0
$283$	5.37695e8	1.41021	0.705104	−	0.709104i	$-0.250900\pi$
$283$	5.37695e8	1.41021	0.705104	+	0.709104i	$0.250900\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	1.10155e7	0.0275053
$288$	0	0
$289$	−1.94072e8	−0.472956
$290$	0	0
$291$	0	0
$292$	0	0
$293$	3.35600e8	0.779445	0.389722	−	0.920932i	$-0.372571\pi$
$293$	3.35600e8	0.779445	0.389722	+	0.920932i	$0.372571\pi$
$294$	0	0
$295$	5.54539e8	1.25764
$296$	0	0
$297$	0	0
$298$	0	0
$299$	−9.49600e7	−0.205443
$300$	0	0
$301$	6.40840e8	1.35446
$302$	0	0
$303$	0	0
$304$	0	0
$305$	1.73817e8	0.350787
$306$	0	0
$307$	2.15029e8	0.424143	0.212072	−	0.977254i	$-0.431979\pi$
$307$	2.15029e8	0.424143	0.212072	+	0.977254i	$0.431979\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	7.92062e8	1.49313	0.746565	−	0.665313i	$-0.231702\pi$
$311$	7.92062e8	1.49313	0.746565	+	0.665313i	$0.231702\pi$
$312$	0	0
$313$	−1.18457e8	−0.218352	−0.109176	−	0.994022i	$-0.534821\pi$
$313$	−1.18457e8	−0.218352	−0.109176	+	0.994022i	$0.534821\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−5.07310e7	−0.0894470	−0.0447235	−	0.998999i	$-0.514241\pi$
$317$	−5.07310e7	−0.0894470	−0.0447235	+	0.998999i	$0.514241\pi$
$318$	0	0
$319$	1.12006e8	0.193186
$320$	0	0
$321$	0	0
$322$	0	0
$323$	5.87358e8	0.969826
$324$	0	0
$325$	4.70226e7	0.0759826
$326$	0	0
$327$	0	0
$328$	0	0
$329$	−4.80218e8	−0.743453
$330$	0	0
$331$	2.73757e8	0.414923	0.207461	−	0.978243i	$-0.433480\pi$
$331$	2.73757e8	0.414923	0.207461	+	0.978243i	$0.433480\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	2.64608e7	0.0384545
$336$	0	0
$337$	−9.18512e7	−0.130732	−0.0653658	−	0.997861i	$-0.520821\pi$
$337$	−9.18512e7	−0.130732	−0.0653658	+	0.997861i	$0.520821\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	2.48487e8	0.339362
$342$	0	0
$343$	6.24667e8	0.835833
$344$	0	0
$345$	0	0
$346$	0	0
$347$	1.36700e9	1.75637	0.878187	−	0.478318i	$-0.158753\pi$
$347$	1.36700e9	1.75637	0.878187	+	0.478318i	$0.158753\pi$
$348$	0	0
$349$	−1.13143e9	−1.42475	−0.712377	−	0.701797i	$-0.752381\pi$
$349$	−1.13143e9	−1.42475	−0.712377	+	0.701797i	$0.752381\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	4.48395e7	0.0542562	0.0271281	−	0.999632i	$-0.491364\pi$
$353$	4.48395e7	0.0542562	0.0271281	+	0.999632i	$0.491364\pi$
$354$	0	0
$355$	2.97093e8	0.352446
$356$	0	0
$357$	0	0
$358$	0	0
$359$	3.98281e8	0.454317	0.227158	−	0.973858i	$-0.427057\pi$
$359$	3.98281e8	0.454317	0.227158	+	0.973858i	$0.427057\pi$
$360$	0	0
$361$	7.01332e8	0.784600
$362$	0	0
$363$	0	0
$364$	0	0
$365$	−2.05859e8	−0.221588
$366$	0	0
$367$	−1.63472e9	−1.72628	−0.863140	−	0.504964i	$-0.831506\pi$
$367$	−1.63472e9	−1.72628	−0.863140	+	0.504964i	$0.831506\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	1.51792e9	1.54327
$372$	0	0
$373$	1.54633e9	1.54284	0.771421	−	0.636325i	$-0.219546\pi$
$373$	1.54633e9	1.54284	0.771421	+	0.636325i	$0.219546\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	1.41752e8	0.136249
$378$	0	0
$379$	−1.05688e9	−0.997216	−0.498608	−	0.866828i	$-0.666155\pi$
$379$	−1.05688e9	−0.997216	−0.498608	+	0.866828i	$0.666155\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	2.24910e8	0.204556	0.102278	−	0.994756i	$-0.467387\pi$
$383$	2.24910e8	0.204556	0.102278	+	0.994756i	$0.467387\pi$
$384$	0	0
$385$	−2.32989e8	−0.208077
$386$	0	0
$387$	0	0
$388$	0	0
$389$	1.01788e9	0.876746	0.438373	−	0.898793i	$-0.355555\pi$
$389$	1.01788e9	0.876746	0.438373	+	0.898793i	$0.355555\pi$
$390$	0	0
$391$	−1.01048e9	−0.854887
$392$	0	0
$393$	0	0
$394$	0	0
$395$	−7.49028e8	−0.611517
$396$	0	0
$397$	1.47565e9	1.18363	0.591817	−	0.806072i	$-0.298411\pi$
$397$	1.47565e9	1.18363	0.591817	+	0.806072i	$0.298411\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−2.74912e8	−0.212906	−0.106453	−	0.994318i	$-0.533949\pi$
$401$	−2.74912e8	−0.212906	−0.106453	+	0.994318i	$0.533949\pi$
$402$	0	0
$403$	3.14477e8	0.239343
$404$	0	0
$405$	0	0
$406$	0	0
$407$	1.75294e8	0.128881
$408$	0	0
$409$	−1.63427e9	−1.18112	−0.590558	−	0.806995i	$-0.701092\pi$
$409$	−1.63427e9	−1.18112	−0.590558	+	0.806995i	$0.701092\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	2.68291e9	1.87405
$414$	0	0
$415$	1.19131e9	0.818192
$416$	0	0
$417$	0	0
$418$	0	0
$419$	1.11280e9	0.739039	0.369519	−	0.929223i	$-0.379522\pi$
$419$	1.11280e9	0.739039	0.369519	+	0.929223i	$0.379522\pi$
$420$	0	0
$421$	−9.22528e8	−0.602549	−0.301274	−	0.953537i	$-0.597412\pi$
$421$	−9.22528e8	−0.602549	−0.301274	+	0.953537i	$0.597412\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	5.00372e8	0.316178
$426$	0	0
$427$	8.40945e8	0.522721
$428$	0	0
$429$	0	0
$430$	0	0
$431$	−9.81508e8	−0.590505	−0.295252	−	0.955419i	$-0.595404\pi$
$431$	−9.81508e8	−0.590505	−0.295252	+	0.955419i	$0.595404\pi$
$432$	0	0
$433$	2.84998e9	1.68707	0.843537	−	0.537071i	$-0.180469\pi$
$433$	2.84998e9	1.68707	0.843537	+	0.537071i	$0.180469\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−2.74436e9	−1.57310
$438$	0	0
$439$	1.05622e9	0.595838	0.297919	−	0.954591i	$-0.403708\pi$
$439$	1.05622e9	0.595838	0.297919	+	0.954591i	$0.403708\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−1.82325e9	−0.996401	−0.498201	−	0.867062i	$-0.666006\pi$
$443$	−1.82325e9	−0.996401	−0.498201	+	0.867062i	$0.666006\pi$
$444$	0	0
$445$	−2.50975e9	−1.35011
$446$	0	0
$447$	0	0
$448$	0	0
$449$	−1.84846e9	−0.963713	−0.481856	−	0.876250i	$-0.660037\pi$
$449$	−1.84846e9	−0.963713	−0.481856	+	0.876250i	$0.660037\pi$
$450$	0	0
$451$	1.18395e7	0.00607735
$452$	0	0
$453$	0	0
$454$	0	0
$455$	−2.94864e8	−0.146751
$456$	0	0
$457$	−2.98066e9	−1.46085	−0.730425	−	0.682993i	$-0.760678\pi$
$457$	−2.98066e9	−1.46085	−0.730425	+	0.682993i	$0.760678\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	−2.52781e9	−1.20169	−0.600843	−	0.799367i	$-0.705168\pi$
$461$	−2.52781e9	−1.20169	−0.600843	+	0.799367i	$0.705168\pi$
$462$	0	0
$463$	8.90291e8	0.416868	0.208434	−	0.978036i	$-0.433163\pi$
$463$	8.90291e8	0.416868	0.208434	+	0.978036i	$0.433163\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−2.65667e9	−1.20706	−0.603529	−	0.797341i	$-0.706239\pi$
$467$	−2.65667e9	−1.20706	−0.603529	+	0.797341i	$0.706239\pi$
$468$	0	0
$469$	1.28020e8	0.0573024
$470$	0	0
$471$	0	0
$472$	0	0
$473$	6.88777e8	0.299271
$474$	0	0
$475$	1.35896e9	0.581806
$476$	0	0
$477$	0	0
$478$	0	0
$479$	1.30093e9	0.540855	0.270428	−	0.962740i	$-0.412835\pi$
$479$	1.30093e9	0.540855	0.270428	+	0.962740i	$0.412835\pi$
$480$	0	0
$481$	2.21847e8	0.0908962
$482$	0	0
$483$	0	0
$484$	0	0
$485$	−1.82325e9	−0.725689
$486$	0	0
$487$	1.07447e9	0.421542	0.210771	−	0.977535i	$-0.432402\pi$
$487$	1.07447e9	0.421542	0.210771	+	0.977535i	$0.432402\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	7.83344e8	0.298653	0.149327	−	0.988788i	$-0.452289\pi$
$491$	7.83344e8	0.298653	0.149327	+	0.988788i	$0.452289\pi$
$492$	0	0
$493$	1.50839e9	0.566958
$494$	0	0
$495$	0	0
$496$	0	0
$497$	1.43736e9	0.525193
$498$	0	0
$499$	−6.23188e8	−0.224526	−0.112263	−	0.993679i	$-0.535810\pi$
$499$	−6.23188e8	−0.224526	−0.112263	+	0.993679i	$0.535810\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	−2.70927e9	−0.949215	−0.474607	−	0.880198i	$-0.657410\pi$
$503$	−2.70927e9	−0.949215	−0.474607	+	0.880198i	$0.657410\pi$
$504$	0	0
$505$	2.11670e9	0.731375
$506$	0	0
$507$	0	0
$508$	0	0
$509$	3.49943e9	1.17621	0.588106	−	0.808784i	$-0.299874\pi$
$509$	3.49943e9	1.17621	0.588106	+	0.808784i	$0.299874\pi$
$510$	0	0
$511$	−9.95967e8	−0.330196
$512$	0	0
$513$	0	0
$514$	0	0
$515$	7.87078e8	0.253918
$516$	0	0
$517$	−5.16140e8	−0.164267
$518$	0	0
$519$	0	0
$520$	0	0
$521$	1.37683e9	0.426530	0.213265	−	0.976994i	$-0.431590\pi$
$521$	1.37683e9	0.426530	0.213265	+	0.976994i	$0.431590\pi$
$522$	0	0
$523$	−2.86154e9	−0.874669	−0.437334	−	0.899299i	$-0.644077\pi$
$523$	−2.86154e9	−0.874669	−0.437334	+	0.899299i	$0.644077\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	3.34638e9	0.995951
$528$	0	0
$529$	1.31651e9	0.386661
$530$	0	0
$531$	0	0
$532$	0	0
$533$	1.49836e7	0.00428620
$534$	0	0
$535$	−3.77697e9	−1.06636
$536$	0	0
$537$	0	0
$538$	0	0
$539$	−2.27915e8	−0.0626919
$540$	0	0
$541$	−5.34467e9	−1.45121	−0.725605	−	0.688111i	$-0.758440\pi$
$541$	−5.34467e9	−1.45121	−0.725605	+	0.688111i	$0.758440\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	2.57398e9	0.681109
$546$	0	0
$547$	−3.37135e9	−0.880740	−0.440370	−	0.897816i	$-0.645153\pi$
$547$	−3.37135e9	−0.880740	−0.440370	+	0.897816i	$0.645153\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	4.09665e9	1.04327
$552$	0	0
$553$	−3.62387e9	−0.911244
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−5.61106e9	−1.37579	−0.687894	−	0.725811i	$-0.741465\pi$
$557$	−5.61106e9	−1.37579	−0.687894	+	0.725811i	$0.741465\pi$
$558$	0	0
$559$	8.71694e8	0.211068
$560$	0	0
$561$	0	0
$562$	0	0
$563$	−6.69690e9	−1.58159	−0.790795	−	0.612081i	$-0.790333\pi$
$563$	−6.69690e9	−1.58159	−0.790795	+	0.612081i	$0.790333\pi$
$564$	0	0
$565$	3.48494e9	0.812879
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−1.96850e9	−0.447964	−0.223982	−	0.974593i	$-0.571906\pi$
$569$	−1.96850e9	−0.447964	−0.223982	+	0.974593i	$0.571906\pi$
$570$	0	0
$571$	1.02926e9	0.231365	0.115682	−	0.993286i	$-0.463094\pi$
$571$	1.02926e9	0.231365	0.115682	+	0.993286i	$0.463094\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	−2.33793e9	−0.512853
$576$	0	0
$577$	3.31179e9	0.717708	0.358854	−	0.933394i	$-0.383168\pi$
$577$	3.31179e9	0.717708	0.358854	+	0.933394i	$0.383168\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	5.76366e9	1.21922
$582$	0	0
$583$	1.63147e9	0.340988
$584$	0	0
$585$	0	0
$586$	0	0
$587$	5.59411e8	0.114156	0.0570778	−	0.998370i	$-0.481822\pi$
$587$	5.59411e8	0.114156	0.0570778	+	0.998370i	$0.481822\pi$
$588$	0	0
$589$	9.08843e9	1.83267
$590$	0	0
$591$	0	0
$592$	0	0
$593$	3.02459e9	0.595628	0.297814	−	0.954624i	$-0.403742\pi$
$593$	3.02459e9	0.595628	0.297814	+	0.954624i	$0.403742\pi$
$594$	0	0
$595$	−3.13767e9	−0.610658
$596$	0	0
$597$	0	0
$598$	0	0
$599$	−5.63246e9	−1.07079	−0.535395	−	0.844602i	$-0.679837\pi$
$599$	−5.63246e9	−1.07079	−0.535395	+	0.844602i	$0.679837\pi$
$600$	0	0
$601$	3.40792e8	0.0640366	0.0320183	−	0.999487i	$-0.489807\pi$
$601$	3.40792e8	0.0640366	0.0320183	+	0.999487i	$0.489807\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	3.84189e9	0.705344
$606$	0	0
$607$	−3.85420e9	−0.699477	−0.349739	−	0.936847i	$-0.613730\pi$
$607$	−3.85420e9	−0.699477	−0.349739	+	0.936847i	$0.613730\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−6.53211e8	−0.115853
$612$	0	0
$613$	−9.22245e9	−1.61709	−0.808545	−	0.588434i	$-0.799745\pi$
$613$	−9.22245e9	−1.61709	−0.808545	+	0.588434i	$0.799745\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−6.53611e9	−1.12027	−0.560133	−	0.828402i	$-0.689250\pi$
$617$	−6.53611e9	−1.12027	−0.560133	+	0.828402i	$0.689250\pi$
$618$	0	0
$619$	1.36559e9	0.231420	0.115710	−	0.993283i	$-0.463086\pi$
$619$	1.36559e9	0.231420	0.115710	+	0.993283i	$0.463086\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	−1.21424e10	−2.01186
$624$	0	0
$625$	−2.28761e9	−0.374802
$626$	0	0
$627$	0	0
$628$	0	0
$629$	2.36070e9	0.378236
$630$	0	0
$631$	−1.54079e9	−0.244141	−0.122070	−	0.992521i	$-0.538953\pi$
$631$	−1.54079e9	−0.244141	−0.122070	+	0.992521i	$0.538953\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	2.45334e8	0.0380233
$636$	0	0
$637$	−2.88441e8	−0.0442150
$638$	0	0
$639$	0	0
$640$	0	0
$641$	4.54018e9	0.680879	0.340440	−	0.940266i	$-0.389424\pi$
$641$	4.54018e9	0.680879	0.340440	+	0.940266i	$0.389424\pi$
$642$	0	0
$643$	1.14054e10	1.69189	0.845944	−	0.533272i	$-0.179038\pi$
$643$	1.14054e10	1.69189	0.845944	+	0.533272i	$0.179038\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−1.26393e10	−1.83468	−0.917338	−	0.398109i	$-0.869666\pi$
$647$	−1.26393e10	−1.83468	−0.917338	+	0.398109i	$0.869666\pi$
$648$	0	0
$649$	2.88360e9	0.414075
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−1.05004e10	−1.47575	−0.737873	−	0.674940i	$-0.764170\pi$
$653$	−1.05004e10	−1.47575	−0.737873	+	0.674940i	$0.764170\pi$
$654$	0	0
$655$	−1.66400e9	−0.231371
$656$	0	0
$657$	0	0
$658$	0	0
$659$	−9.64818e9	−1.31325	−0.656624	−	0.754219i	$-0.728016\pi$
$659$	−9.64818e9	−1.31325	−0.656624	+	0.754219i	$0.728016\pi$
$660$	0	0
$661$	6.58299e9	0.886580	0.443290	−	0.896378i	$-0.353811\pi$
$661$	6.58299e9	0.886580	0.443290	+	0.896378i	$0.353811\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	−8.52160e9	−1.12369
$666$	0	0
$667$	−7.04779e9	−0.919629
$668$	0	0
$669$	0	0
$670$	0	0
$671$	9.03851e8	0.115496
$672$	0	0
$673$	−8.54649e9	−1.08077	−0.540387	−	0.841416i	$-0.681722\pi$
$673$	−8.54649e9	−1.08077	−0.540387	+	0.841416i	$0.681722\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	8.71305e9	1.07922	0.539610	−	0.841915i	$-0.318572\pi$
$677$	8.71305e9	1.07922	0.539610	+	0.841915i	$0.318572\pi$
$678$	0	0
$679$	−8.82106e9	−1.08138
$680$	0	0
$681$	0	0
$682$	0	0
$683$	−1.46109e10	−1.75470	−0.877351	−	0.479849i	$-0.840692\pi$
$683$	−1.46109e10	−1.75470	−0.877351	+	0.479849i	$0.840692\pi$
$684$	0	0
$685$	−6.62873e7	−0.00787977
$686$	0	0
$687$	0	0
$688$	0	0
$689$	2.06473e9	0.240490
$690$	0	0
$691$	−1.47348e10	−1.69891	−0.849454	−	0.527662i	$-0.823069\pi$
$691$	−1.47348e10	−1.69891	−0.849454	+	0.527662i	$0.823069\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−8.23279e9	−0.930252
$696$	0	0
$697$	1.59442e8	0.0178357
$698$	0	0
$699$	0	0
$700$	0	0
$701$	1.31502e9	0.144185	0.0720923	−	0.997398i	$-0.477032\pi$
$701$	1.31502e9	0.144185	0.0720923	+	0.997398i	$0.477032\pi$
$702$	0	0
$703$	6.41141e9	0.696001
$704$	0	0
$705$	0	0
$706$	0	0
$707$	1.02408e10	1.08985
$708$	0	0
$709$	−6.64028e8	−0.0699721	−0.0349860	−	0.999388i	$-0.511139\pi$
$709$	−6.64028e8	−0.0699721	−0.0349860	+	0.999388i	$0.511139\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	−1.56356e10	−1.61547
$714$	0	0
$715$	−3.16920e8	−0.0324249
$716$	0	0
$717$	0	0
$718$	0	0
$719$	4.95034e9	0.496689	0.248344	−	0.968672i	$-0.420114\pi$
$719$	4.95034e9	0.496689	0.248344	+	0.968672i	$0.420114\pi$
$720$	0	0
$721$	3.80796e9	0.378372
$722$	0	0
$723$	0	0
$724$	0	0
$725$	3.48994e9	0.340123
$726$	0	0
$727$	−8.81101e9	−0.850463	−0.425231	−	0.905085i	$-0.639807\pi$
$727$	−8.81101e9	−0.850463	−0.425231	+	0.905085i	$0.639807\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	9.27578e9	0.878293
$732$	0	0
$733$	1.49414e8	0.0140129	0.00700643	−	0.999975i	$-0.497770\pi$
$733$	1.49414e8	0.0140129	0.00700643	+	0.999975i	$0.497770\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	1.37596e8	0.0126611
$738$	0	0
$739$	−4.70806e9	−0.429127	−0.214564	−	0.976710i	$-0.568833\pi$
$739$	−4.70806e9	−0.429127	−0.214564	+	0.976710i	$0.568833\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	1.69676e9	0.151761	0.0758805	−	0.997117i	$-0.475823\pi$
$743$	1.69676e9	0.151761	0.0758805	+	0.997117i	$0.475823\pi$
$744$	0	0
$745$	4.59607e9	0.407230
$746$	0	0
$747$	0	0
$748$	0	0
$749$	−1.82733e10	−1.58903
$750$	0	0
$751$	−1.06650e10	−0.918800	−0.459400	−	0.888229i	$-0.651936\pi$
$751$	−1.06650e10	−0.918800	−0.459400	+	0.888229i	$0.651936\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	−6.17724e9	−0.522373
$756$	0	0
$757$	−6.22876e9	−0.521874	−0.260937	−	0.965356i	$-0.584032\pi$
$757$	−6.22876e9	−0.521874	−0.260937	+	0.965356i	$0.584032\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	8.38334e9	0.689558	0.344779	−	0.938684i	$-0.387954\pi$
$761$	8.38334e9	0.689558	0.344779	+	0.938684i	$0.387954\pi$
$762$	0	0
$763$	1.24531e10	1.01495
$764$	0	0
$765$	0	0
$766$	0	0
$767$	3.64939e9	0.292036
$768$	0	0
$769$	−1.18649e10	−0.940852	−0.470426	−	0.882439i	$-0.655900\pi$
$769$	−1.18649e10	−0.940852	−0.470426	+	0.882439i	$0.655900\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	5.56680e9	0.433488	0.216744	−	0.976228i	$-0.430456\pi$
$773$	5.56680e9	0.433488	0.216744	+	0.976228i	$0.430456\pi$
$774$	0	0
$775$	7.74246e9	0.597479
$776$	0	0
$777$	0	0
$778$	0	0
$779$	4.33029e8	0.0328198
$780$	0	0
$781$	1.54488e9	0.116042
$782$	0	0
$783$	0	0
$784$	0	0
$785$	1.27165e10	0.938264
$786$	0	0
$787$	1.34611e8	0.00984395	0.00492198	−	0.999988i	$-0.498433\pi$
$787$	1.34611e8	0.00984395	0.00492198	+	0.999988i	$0.498433\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	1.68605e10	1.21130
$792$	0	0
$793$	1.14388e9	0.0814565
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−7.41548e9	−0.518842	−0.259421	−	0.965764i	$-0.583532\pi$
$797$	−7.41548e9	−0.518842	−0.259421	+	0.965764i	$0.583532\pi$
$798$	0	0
$799$	−6.95088e9	−0.482088
$800$	0	0
$801$	0	0
$802$	0	0
$803$	−1.07047e9	−0.0729574
$804$	0	0
$805$	1.46604e10	0.990513
$806$	0	0
$807$	0	0
$808$	0	0
$809$	1.41542e10	0.939863	0.469932	−	0.882703i	$-0.344279\pi$
$809$	1.41542e10	0.939863	0.469932	+	0.882703i	$0.344279\pi$
$810$	0	0
$811$	−2.63708e10	−1.73600	−0.868001	−	0.496563i	$-0.834595\pi$
$811$	−2.63708e10	−1.73600	−0.868001	+	0.496563i	$0.834595\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	−1.19879e10	−0.775697
$816$	0	0
$817$	2.51921e10	1.61617
$818$	0	0
$819$	0	0
$820$	0	0
$821$	8.06264e9	0.508483	0.254241	−	0.967141i	$-0.418174\pi$
$821$	8.06264e9	0.508483	0.254241	+	0.967141i	$0.418174\pi$
$822$	0	0
$823$	2.34202e10	1.46451	0.732253	−	0.681033i	$-0.238469\pi$
$823$	2.34202e10	1.46451	0.732253	+	0.681033i	$0.238469\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−5.55722e9	−0.341655	−0.170828	−	0.985301i	$-0.554644\pi$
$827$	−5.55722e9	−0.341655	−0.170828	+	0.985301i	$0.554644\pi$
$828$	0	0
$829$	−2.84256e10	−1.73288	−0.866440	−	0.499281i	$-0.833597\pi$
$829$	−2.84256e10	−1.73288	−0.866440	+	0.499281i	$0.833597\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	−3.06933e9	−0.183987
$834$	0	0
$835$	1.84226e10	1.09508
$836$	0	0
$837$	0	0
$838$	0	0
$839$	1.04036e10	0.608156	0.304078	−	0.952647i	$-0.401652\pi$
$839$	1.04036e10	0.608156	0.304078	+	0.952647i	$0.401652\pi$
$840$	0	0
$841$	−6.72927e9	−0.390105
$842$	0	0
$843$	0	0
$844$	0	0
$845$	1.27761e10	0.728450
$846$	0	0
$847$	1.85874e10	1.05106
$848$	0	0
$849$	0	0
$850$	0	0
$851$	−1.10301e10	−0.613514
$852$	0	0
$853$	1.80580e10	0.996205	0.498102	−	0.867118i	$-0.334030\pi$
$853$	1.80580e10	0.996205	0.498102	+	0.867118i	$0.334030\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	6.34034e9	0.344096	0.172048	−	0.985089i	$-0.444962\pi$
$857$	6.34034e9	0.344096	0.172048	+	0.985089i	$0.444962\pi$
$858$	0	0
$859$	1.21489e10	0.653973	0.326987	−	0.945029i	$-0.393967\pi$
$859$	1.21489e10	0.653973	0.326987	+	0.945029i	$0.393967\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−2.87111e10	−1.52059	−0.760295	−	0.649578i	$-0.774946\pi$
$863$	−2.87111e10	−1.52059	−0.760295	+	0.649578i	$0.774946\pi$
$864$	0	0
$865$	−1.79960e9	−0.0945411
$866$	0	0
$867$	0	0
$868$	0	0
$869$	−3.89495e9	−0.201341
$870$	0	0
$871$	1.74138e8	0.00892953
$872$	0	0
$873$	0	0
$874$	0	0
$875$	−2.39283e10	−1.20749
$876$	0	0
$877$	−2.46021e10	−1.23161	−0.615806	−	0.787898i	$-0.711169\pi$
$877$	−2.46021e10	−1.23161	−0.615806	+	0.787898i	$0.711169\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	1.25378e10	0.617738	0.308869	−	0.951105i	$-0.400049\pi$
$881$	1.25378e10	0.617738	0.308869	+	0.951105i	$0.400049\pi$
$882$	0	0
$883$	1.93097e10	0.943873	0.471937	−	0.881633i	$-0.343555\pi$
$883$	1.93097e10	0.943873	0.471937	+	0.881633i	$0.343555\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	3.20268e10	1.54092	0.770462	−	0.637486i	$-0.220026\pi$
$887$	3.20268e10	1.54092	0.770462	+	0.637486i	$0.220026\pi$
$888$	0	0
$889$	1.18695e9	0.0566599
$890$	0	0
$891$	0	0
$892$	0	0
$893$	−1.88779e10	−0.887101
$894$	0	0
$895$	3.94885e9	0.184115
$896$	0	0
$897$	0	0
$898$	0	0
$899$	2.33400e10	1.07138
$900$	0	0
$901$	2.19710e10	1.00072
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−1.25921e10	−0.564715
$906$	0	0
$907$	2.33703e9	0.104002	0.0520008	−	0.998647i	$-0.483440\pi$
$907$	2.33703e9	0.104002	0.0520008	+	0.998647i	$0.483440\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	2.20343e10	0.965573	0.482786	−	0.875738i	$-0.339625\pi$
$911$	2.20343e10	0.965573	0.482786	+	0.875738i	$0.339625\pi$
$912$	0	0
$913$	6.19480e9	0.269389
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−8.05061e9	−0.344775
$918$	0	0
$919$	1.43277e10	0.608938	0.304469	−	0.952522i	$-0.401521\pi$
$919$	1.43277e10	0.608938	0.304469	+	0.952522i	$0.401521\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	1.95515e9	0.0818418
$924$	0	0
$925$	5.46190e9	0.226907
$926$	0	0
$927$	0	0
$928$	0	0
$929$	−1.31280e10	−0.537208	−0.268604	−	0.963251i	$-0.586562\pi$
$929$	−1.31280e10	−0.537208	−0.268604	+	0.963251i	$0.586562\pi$
$930$	0	0
$931$	−8.33600e9	−0.338558
$932$	0	0
$933$	0	0
$934$	0	0
$935$	−3.37238e9	−0.134926
$936$	0	0
$937$	−3.87626e10	−1.53930	−0.769652	−	0.638463i	$-0.779571\pi$
$937$	−3.87626e10	−1.53930	−0.769652	+	0.638463i	$0.779571\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	2.06279e10	0.807035	0.403517	−	0.914972i	$-0.367788\pi$
$941$	2.06279e10	0.807035	0.403517	+	0.914972i	$0.367788\pi$
$942$	0	0
$943$	−7.44976e8	−0.0289302
$944$	0	0
$945$	0	0
$946$	0	0
$947$	2.11705e10	0.810040	0.405020	−	0.914308i	$-0.367264\pi$
$947$	2.11705e10	0.810040	0.405020	+	0.914308i	$0.367264\pi$
$948$	0	0
$949$	−1.35475e9	−0.0514550
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−2.14876e10	−0.804196	−0.402098	−	0.915597i	$-0.631719\pi$
$953$	−2.14876e10	−0.804196	−0.402098	+	0.915597i	$0.631719\pi$
$954$	0	0
$955$	−1.97371e10	−0.733282
$956$	0	0
$957$	0	0
$958$	0	0
$959$	−3.20704e8	−0.0117419
$960$	0	0
$961$	2.42673e10	0.882043
$962$	0	0
$963$	0	0
$964$	0	0
$965$	7.39086e9	0.264758
$966$	0	0
$967$	−3.92625e10	−1.39632	−0.698161	−	0.715941i	$-0.745998\pi$
$967$	−3.92625e10	−1.39632	−0.698161	+	0.715941i	$0.745998\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	5.62647e10	1.97228	0.986140	−	0.165917i	$-0.0530585\pi$
$971$	5.62647e10	1.97228	0.986140	+	0.165917i	$0.0530585\pi$
$972$	0	0
$973$	−3.98310e10	−1.38620
$974$	0	0
$975$	0	0
$976$	0	0
$977$	8.43437e9	0.289349	0.144674	−	0.989479i	$-0.453787\pi$
$977$	8.43437e9	0.289349	0.144674	+	0.989479i	$0.453787\pi$
$978$	0	0
$979$	−1.30507e10	−0.444523
$980$	0	0
$981$	0	0
$982$	0	0
$983$	−2.24230e10	−0.752932	−0.376466	−	0.926430i	$-0.622861\pi$
$983$	−2.24230e10	−0.752932	−0.376466	+	0.926430i	$0.622861\pi$
$984$	0	0
$985$	−2.16269e10	−0.721054
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−4.33400e10	−1.42463
$990$	0	0
$991$	−3.46728e10	−1.13170	−0.565849	−	0.824509i	$-0.691452\pi$
$991$	−3.46728e10	−1.13170	−0.565849	+	0.824509i	$0.691452\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	1.75639e10	0.565249
$996$	0	0
$997$	2.96474e10	0.947444	0.473722	−	0.880674i	$-0.342910\pi$
$997$	2.96474e10	0.947444	0.473722	+	0.880674i	$0.342910\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.8.a.f.1.1		1
3.2	odd	2		64.8.a.e.1.1		1
4.3	odd	2		576.8.a.g.1.1		1
8.3	odd	2		18.8.a.b.1.1		1
8.5	even	2		144.8.a.i.1.1		1
12.11	even	2		64.8.a.c.1.1		1
24.5	odd	2		16.8.a.b.1.1		1
24.11	even	2		2.8.a.a.1.1	✓	1
40.3	even	4		450.8.c.g.199.1		2
40.19	odd	2		450.8.a.c.1.1		1
40.27	even	4		450.8.c.g.199.2		2
48.5	odd	4		256.8.b.f.129.1		2
48.11	even	4		256.8.b.b.129.2		2
48.29	odd	4		256.8.b.f.129.2		2
48.35	even	4		256.8.b.b.129.1		2
72.11	even	6		162.8.c.l.109.1		2
72.43	odd	6		162.8.c.a.109.1		2
72.59	even	6		162.8.c.l.55.1		2
72.67	odd	6		162.8.c.a.55.1		2
120.29	odd	2		400.8.a.l.1.1		1
120.53	even	4		400.8.c.j.49.1		2
120.59	even	2		50.8.a.g.1.1		1
120.77	even	4		400.8.c.j.49.2		2
120.83	odd	4		50.8.b.c.49.2		2
120.107	odd	4		50.8.b.c.49.1		2
168.11	even	6		98.8.c.d.79.1		2
168.59	odd	6		98.8.c.e.79.1		2
168.83	odd	2		98.8.a.a.1.1		1
168.107	even	6		98.8.c.d.67.1		2
168.131	odd	6		98.8.c.e.67.1		2
264.131	odd	2		242.8.a.e.1.1		1
312.83	odd	4		338.8.b.d.337.2		2
312.155	even	2		338.8.a.d.1.1		1
312.203	odd	4		338.8.b.d.337.1		2
408.203	even	2		578.8.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.8.a.a.1.1	✓	1	24.11	even	2
16.8.a.b.1.1		1	24.5	odd	2
18.8.a.b.1.1		1	8.3	odd	2
50.8.a.g.1.1		1	120.59	even	2
50.8.b.c.49.1		2	120.107	odd	4
50.8.b.c.49.2		2	120.83	odd	4
64.8.a.c.1.1		1	12.11	even	2
64.8.a.e.1.1		1	3.2	odd	2
98.8.a.a.1.1		1	168.83	odd	2
98.8.c.d.67.1		2	168.107	even	6
98.8.c.d.79.1		2	168.11	even	6
98.8.c.e.67.1		2	168.131	odd	6
98.8.c.e.79.1		2	168.59	odd	6
144.8.a.i.1.1		1	8.5	even	2
162.8.c.a.55.1		2	72.67	odd	6
162.8.c.a.109.1		2	72.43	odd	6
162.8.c.l.55.1		2	72.59	even	6
162.8.c.l.109.1		2	72.11	even	6
242.8.a.e.1.1		1	264.131	odd	2
256.8.b.b.129.1		2	48.35	even	4
256.8.b.b.129.2		2	48.11	even	4
256.8.b.f.129.1		2	48.5	odd	4
256.8.b.f.129.2		2	48.29	odd	4
338.8.a.d.1.1		1	312.155	even	2
338.8.b.d.337.1		2	312.203	odd	4
338.8.b.d.337.2		2	312.83	odd	4
400.8.a.l.1.1		1	120.29	odd	2
400.8.c.j.49.1		2	120.53	even	4
400.8.c.j.49.2		2	120.77	even	4
450.8.a.c.1.1		1	40.19	odd	2
450.8.c.g.199.1		2	40.3	even	4
450.8.c.g.199.2		2	40.27	even	4
576.8.a.f.1.1		1	1.1	even	1	trivial
576.8.a.g.1.1		1	4.3	odd	2
578.8.a.b.1.1		1	408.203	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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	576.a (trivial)

Introduction

L-functions

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