LMFDB - Embedded newform 1280.2.a.p.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,2,Mod(1,1280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1280, 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("1280.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1280.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:	$10.2208514587$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 320)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	1280.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.73205 q^{3} +1.00000 q^{5} +4.73205 q^{7} +4.46410 q^{9} +O(q^{10})$	$q+2.73205 q^{3} +1.00000 q^{5} +4.73205 q^{7} +4.46410 q^{9} -3.46410 q^{11} +3.46410 q^{13} +2.73205 q^{15} -3.46410 q^{17} -2.00000 q^{19} +12.9282 q^{21} -2.19615 q^{23} +1.00000 q^{25} +4.00000 q^{27} +2.53590 q^{31} -9.46410 q^{33} +4.73205 q^{35} -6.00000 q^{37} +9.46410 q^{39} -9.46410 q^{41} +0.196152 q^{43} +4.46410 q^{45} -2.19615 q^{47} +15.3923 q^{49} -9.46410 q^{51} -10.3923 q^{53} -3.46410 q^{55} -5.46410 q^{57} -6.00000 q^{59} -0.928203 q^{61} +21.1244 q^{63} +3.46410 q^{65} -0.196152 q^{67} -6.00000 q^{69} +16.3923 q^{71} -6.39230 q^{73} +2.73205 q^{75} -16.3923 q^{77} +12.0000 q^{79} -2.46410 q^{81} +1.26795 q^{83} -3.46410 q^{85} +12.9282 q^{89} +16.3923 q^{91} +6.92820 q^{93} -2.00000 q^{95} +14.3923 q^{97} -15.4641 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 2 q^{5} + 6 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^3 + 2 * q^5 + 6 * q^7 + 2 * q^9	$ 2 q + 2 q^{3} + 2 q^{5} + 6 q^{7} + 2 q^{9} + 2 q^{15} - 4 q^{19} + 12 q^{21} + 6 q^{23} + 2 q^{25} + 8 q^{27} + 12 q^{31} - 12 q^{33} + 6 q^{35} - 12 q^{37} + 12 q^{39} - 12 q^{41} - 10 q^{43} + 2 q^{45} + 6 q^{47} + 10 q^{49} - 12 q^{51} - 4 q^{57} - 12 q^{59} + 12 q^{61} + 18 q^{63} + 10 q^{67} - 12 q^{69} + 12 q^{71} + 8 q^{73} + 2 q^{75} - 12 q^{77} + 24 q^{79} + 2 q^{81} + 6 q^{83} + 12 q^{89} + 12 q^{91} - 4 q^{95} + 8 q^{97} - 24 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 + 2 * q^5 + 6 * q^7 + 2 * q^9 + 2 * q^15 - 4 * q^19 + 12 * q^21 + 6 * q^23 + 2 * q^25 + 8 * q^27 + 12 * q^31 - 12 * q^33 + 6 * q^35 - 12 * q^37 + 12 * q^39 - 12 * q^41 - 10 * q^43 + 2 * q^45 + 6 * q^47 + 10 * q^49 - 12 * q^51 - 4 * q^57 - 12 * q^59 + 12 * q^61 + 18 * q^63 + 10 * q^67 - 12 * q^69 + 12 * q^71 + 8 * q^73 + 2 * q^75 - 12 * q^77 + 24 * q^79 + 2 * q^81 + 6 * q^83 + 12 * q^89 + 12 * q^91 - 4 * q^95 + 8 * q^97 - 24 * q^99

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
$3$	2.73205	1.57735	0.788675	−	0.614810i	$-0.210767\pi$
$3$	2.73205	1.57735	0.788675	+	0.614810i	$0.210767\pi$
$4$	0	0
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	4.73205	1.78855	0.894274	−	0.447521i	$-0.147693\pi$
$7$	4.73205	1.78855	0.894274	+	0.447521i	$0.147693\pi$
$8$	0	0
$9$	4.46410	1.48803
$10$	0	0
$11$	−3.46410	−1.04447	−0.522233	−	0.852803i	$-0.674901\pi$
$11$	−3.46410	−1.04447	−0.522233	+	0.852803i	$0.674901\pi$
$12$	0	0
$13$	3.46410	0.960769	0.480384	−	0.877058i	$-0.340497\pi$
$13$	3.46410	0.960769	0.480384	+	0.877058i	$0.340497\pi$
$14$	0	0
$15$	2.73205	0.705412
$16$	0	0
$17$	−3.46410	−0.840168	−0.420084	−	0.907485i	$-0.637999\pi$
$17$	−3.46410	−0.840168	−0.420084	+	0.907485i	$0.637999\pi$
$18$	0	0
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	0	0
$21$	12.9282	2.82117
$22$	0	0
$23$	−2.19615	−0.457929	−0.228965	−	0.973435i	$-0.573534\pi$
$23$	−2.19615	−0.457929	−0.228965	+	0.973435i	$0.573534\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	4.00000	0.769800
$28$	0	0
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	2.53590	0.455461	0.227730	−	0.973724i	$-0.426870\pi$
$31$	2.53590	0.455461	0.227730	+	0.973724i	$0.426870\pi$
$32$	0	0
$33$	−9.46410	−1.64749
$34$	0	0
$35$	4.73205	0.799863
$36$	0	0
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	0	0
$39$	9.46410	1.51547
$40$	0	0
$41$	−9.46410	−1.47804	−0.739022	−	0.673681i	$-0.764712\pi$
$41$	−9.46410	−1.47804	−0.739022	+	0.673681i	$0.764712\pi$
$42$	0	0
$43$	0.196152	0.0299130	0.0149565	−	0.999888i	$-0.495239\pi$
$43$	0.196152	0.0299130	0.0149565	+	0.999888i	$0.495239\pi$
$44$	0	0
$45$	4.46410	0.665469
$46$	0	0
$47$	−2.19615	−0.320342	−0.160171	−	0.987089i	$-0.551205\pi$
$47$	−2.19615	−0.320342	−0.160171	+	0.987089i	$0.551205\pi$
$48$	0	0
$49$	15.3923	2.19890
$50$	0	0
$51$	−9.46410	−1.32524
$52$	0	0
$53$	−10.3923	−1.42749	−0.713746	−	0.700404i	$-0.753003\pi$
$53$	−10.3923	−1.42749	−0.713746	+	0.700404i	$0.753003\pi$
$54$	0	0
$55$	−3.46410	−0.467099
$56$	0	0
$57$	−5.46410	−0.723738
$58$	0	0
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	0	0
$61$	−0.928203	−0.118844	−0.0594221	−	0.998233i	$-0.518926\pi$
$61$	−0.928203	−0.118844	−0.0594221	+	0.998233i	$0.518926\pi$
$62$	0	0
$63$	21.1244	2.66142
$64$	0	0
$65$	3.46410	0.429669
$66$	0	0
$67$	−0.196152	−0.0239638	−0.0119819	−	0.999928i	$-0.503814\pi$
$67$	−0.196152	−0.0239638	−0.0119819	+	0.999928i	$0.503814\pi$
$68$	0	0
$69$	−6.00000	−0.722315
$70$	0	0
$71$	16.3923	1.94541	0.972704	−	0.232048i	$-0.0745426\pi$
$71$	16.3923	1.94541	0.972704	+	0.232048i	$0.0745426\pi$
$72$	0	0
$73$	−6.39230	−0.748163	−0.374081	−	0.927396i	$-0.622042\pi$
$73$	−6.39230	−0.748163	−0.374081	+	0.927396i	$0.622042\pi$
$74$	0	0
$75$	2.73205	0.315470
$76$	0	0
$77$	−16.3923	−1.86808
$78$	0	0
$79$	12.0000	1.35011	0.675053	−	0.737769i	$-0.264121\pi$
$79$	12.0000	1.35011	0.675053	+	0.737769i	$0.264121\pi$
$80$	0	0
$81$	−2.46410	−0.273789
$82$	0	0
$83$	1.26795	0.139176	0.0695878	−	0.997576i	$-0.477832\pi$
$83$	1.26795	0.139176	0.0695878	+	0.997576i	$0.477832\pi$
$84$	0	0
$85$	−3.46410	−0.375735
$86$	0	0
$87$	0	0
$88$	0	0
$89$	12.9282	1.37039	0.685193	−	0.728361i	$-0.259718\pi$
$89$	12.9282	1.37039	0.685193	+	0.728361i	$0.259718\pi$
$90$	0	0
$91$	16.3923	1.71838
$92$	0	0
$93$	6.92820	0.718421
$94$	0	0
$95$	−2.00000	−0.205196
$96$	0	0
$97$	14.3923	1.46132	0.730659	−	0.682743i	$-0.239213\pi$
$97$	14.3923	1.46132	0.730659	+	0.682743i	$0.239213\pi$
$98$	0	0
$99$	−15.4641	−1.55420
$100$	0	0
$101$	−12.0000	−1.19404	−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000	−1.19404	−0.597022	+	0.802225i	$0.703650\pi$
$102$	0	0
$103$	−2.19615	−0.216393	−0.108197	−	0.994130i	$-0.534508\pi$
$103$	−2.19615	−0.216393	−0.108197	+	0.994130i	$0.534508\pi$
$104$	0	0
$105$	12.9282	1.26166
$106$	0	0
$107$	13.2679	1.28266	0.641331	−	0.767265i	$-0.278383\pi$
$107$	13.2679	1.28266	0.641331	+	0.767265i	$0.278383\pi$
$108$	0	0
$109$	−12.9282	−1.23830	−0.619149	−	0.785274i	$-0.712522\pi$
$109$	−12.9282	−1.23830	−0.619149	+	0.785274i	$0.712522\pi$
$110$	0	0
$111$	−16.3923	−1.55589
$112$	0	0
$113$	−12.9282	−1.21618	−0.608092	−	0.793867i	$-0.708065\pi$
$113$	−12.9282	−1.21618	−0.608092	+	0.793867i	$0.708065\pi$
$114$	0	0
$115$	−2.19615	−0.204792
$116$	0	0
$117$	15.4641	1.42966
$118$	0	0
$119$	−16.3923	−1.50268
$120$	0	0
$121$	1.00000	0.0909091
$122$	0	0
$123$	−25.8564	−2.33139
$124$	0	0
$125$	1.00000	0.0894427
$126$	0	0
$127$	14.1962	1.25970	0.629852	−	0.776715i	$-0.283115\pi$
$127$	14.1962	1.25970	0.629852	+	0.776715i	$0.283115\pi$
$128$	0	0
$129$	0.535898	0.0471832
$130$	0	0
$131$	10.3923	0.907980	0.453990	−	0.891007i	$-0.350000\pi$
$131$	10.3923	0.907980	0.453990	+	0.891007i	$0.350000\pi$
$132$	0	0
$133$	−9.46410	−0.820642
$134$	0	0
$135$	4.00000	0.344265
$136$	0	0
$137$	0.928203	0.0793018	0.0396509	−	0.999214i	$-0.487375\pi$
$137$	0.928203	0.0793018	0.0396509	+	0.999214i	$0.487375\pi$
$138$	0	0
$139$	−10.0000	−0.848189	−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000	−0.848189	−0.424094	+	0.905618i	$0.639408\pi$
$140$	0	0
$141$	−6.00000	−0.505291
$142$	0	0
$143$	−12.0000	−1.00349
$144$	0	0
$145$	0	0
$146$	0	0
$147$	42.0526	3.46844
$148$	0	0
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	0	0
$151$	9.46410	0.770178	0.385089	−	0.922880i	$-0.374171\pi$
$151$	9.46410	0.770178	0.385089	+	0.922880i	$0.374171\pi$
$152$	0	0
$153$	−15.4641	−1.25020
$154$	0	0
$155$	2.53590	0.203688
$156$	0	0
$157$	12.9282	1.03178	0.515891	−	0.856654i	$-0.327461\pi$
$157$	12.9282	1.03178	0.515891	+	0.856654i	$0.327461\pi$
$158$	0	0
$159$	−28.3923	−2.25166
$160$	0	0
$161$	−10.3923	−0.819028
$162$	0	0
$163$	−16.1962	−1.26858	−0.634290	−	0.773095i	$-0.718708\pi$
$163$	−16.1962	−1.26858	−0.634290	+	0.773095i	$0.718708\pi$
$164$	0	0
$165$	−9.46410	−0.736779
$166$	0	0
$167$	2.19615	0.169943	0.0849717	−	0.996383i	$-0.472920\pi$
$167$	2.19615	0.169943	0.0849717	+	0.996383i	$0.472920\pi$
$168$	0	0
$169$	−1.00000	−0.0769231
$170$	0	0
$171$	−8.92820	−0.682757
$172$	0	0
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	0	0
$175$	4.73205	0.357709
$176$	0	0
$177$	−16.3923	−1.23212
$178$	0	0
$179$	7.85641	0.587215	0.293608	−	0.955926i	$-0.405144\pi$
$179$	7.85641	0.587215	0.293608	+	0.955926i	$0.405144\pi$
$180$	0	0
$181$	−6.92820	−0.514969	−0.257485	−	0.966282i	$-0.582894\pi$
$181$	−6.92820	−0.514969	−0.257485	+	0.966282i	$0.582894\pi$
$182$	0	0
$183$	−2.53590	−0.187459
$184$	0	0
$185$	−6.00000	−0.441129
$186$	0	0
$187$	12.0000	0.877527
$188$	0	0
$189$	18.9282	1.37682
$190$	0	0
$191$	4.39230	0.317816	0.158908	−	0.987293i	$-0.449203\pi$
$191$	4.39230	0.317816	0.158908	+	0.987293i	$0.449203\pi$
$192$	0	0
$193$	−14.3923	−1.03598	−0.517990	−	0.855386i	$-0.673320\pi$
$193$	−14.3923	−1.03598	−0.517990	+	0.855386i	$0.673320\pi$
$194$	0	0
$195$	9.46410	0.677738
$196$	0	0
$197$	10.3923	0.740421	0.370211	−	0.928948i	$-0.379286\pi$
$197$	10.3923	0.740421	0.370211	+	0.928948i	$0.379286\pi$
$198$	0	0
$199$	6.92820	0.491127	0.245564	−	0.969380i	$-0.421027\pi$
$199$	6.92820	0.491127	0.245564	+	0.969380i	$0.421027\pi$
$200$	0	0
$201$	−0.535898	−0.0377994
$202$	0	0
$203$	0	0
$204$	0	0
$205$	−9.46410	−0.661002
$206$	0	0
$207$	−9.80385	−0.681415
$208$	0	0
$209$	6.92820	0.479234
$210$	0	0
$211$	−14.3923	−0.990807	−0.495404	−	0.868663i	$-0.664980\pi$
$211$	−14.3923	−0.990807	−0.495404	+	0.868663i	$0.664980\pi$
$212$	0	0
$213$	44.7846	3.06859
$214$	0	0
$215$	0.196152	0.0133775
$216$	0	0
$217$	12.0000	0.814613
$218$	0	0
$219$	−17.4641	−1.18011
$220$	0	0
$221$	−12.0000	−0.807207
$222$	0	0
$223$	−9.12436	−0.611012	−0.305506	−	0.952190i	$-0.598826\pi$
$223$	−9.12436	−0.611012	−0.305506	+	0.952190i	$0.598826\pi$
$224$	0	0
$225$	4.46410	0.297607
$226$	0	0
$227$	−12.5885	−0.835525	−0.417763	−	0.908556i	$-0.637186\pi$
$227$	−12.5885	−0.835525	−0.417763	+	0.908556i	$0.637186\pi$
$228$	0	0
$229$	−5.07180	−0.335154	−0.167577	−	0.985859i	$-0.553594\pi$
$229$	−5.07180	−0.335154	−0.167577	+	0.985859i	$0.553594\pi$
$230$	0	0
$231$	−44.7846	−2.94661
$232$	0	0
$233$	22.3923	1.46697	0.733484	−	0.679706i	$-0.237893\pi$
$233$	22.3923	1.46697	0.733484	+	0.679706i	$0.237893\pi$
$234$	0	0
$235$	−2.19615	−0.143261
$236$	0	0
$237$	32.7846	2.12959
$238$	0	0
$239$	20.7846	1.34444	0.672222	−	0.740349i	$-0.265340\pi$
$239$	20.7846	1.34444	0.672222	+	0.740349i	$0.265340\pi$
$240$	0	0
$241$	0.392305	0.0252706	0.0126353	−	0.999920i	$-0.495978\pi$
$241$	0.392305	0.0252706	0.0126353	+	0.999920i	$0.495978\pi$
$242$	0	0
$243$	−18.7321	−1.20166
$244$	0	0
$245$	15.3923	0.983378
$246$	0	0
$247$	−6.92820	−0.440831
$248$	0	0
$249$	3.46410	0.219529
$250$	0	0
$251$	−8.53590	−0.538781	−0.269391	−	0.963031i	$-0.586822\pi$
$251$	−8.53590	−0.538781	−0.269391	+	0.963031i	$0.586822\pi$
$252$	0	0
$253$	7.60770	0.478292
$254$	0	0
$255$	−9.46410	−0.592665
$256$	0	0
$257$	6.00000	0.374270	0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000	0.374270	0.187135	+	0.982334i	$0.440080\pi$
$258$	0	0
$259$	−28.3923	−1.76421
$260$	0	0
$261$	0	0
$262$	0	0
$263$	−9.80385	−0.604531	−0.302266	−	0.953224i	$-0.597743\pi$
$263$	−9.80385	−0.604531	−0.302266	+	0.953224i	$0.597743\pi$
$264$	0	0
$265$	−10.3923	−0.638394
$266$	0	0
$267$	35.3205	2.16158
$268$	0	0
$269$	26.7846	1.63309	0.816543	−	0.577284i	$-0.195888\pi$
$269$	26.7846	1.63309	0.816543	+	0.577284i	$0.195888\pi$
$270$	0	0
$271$	16.3923	0.995762	0.497881	−	0.867245i	$-0.334112\pi$
$271$	16.3923	0.995762	0.497881	+	0.867245i	$0.334112\pi$
$272$	0	0
$273$	44.7846	2.71049
$274$	0	0
$275$	−3.46410	−0.208893
$276$	0	0
$277$	−7.85641	−0.472046	−0.236023	−	0.971748i	$-0.575844\pi$
$277$	−7.85641	−0.472046	−0.236023	+	0.971748i	$0.575844\pi$
$278$	0	0
$279$	11.3205	0.677741
$280$	0	0
$281$	7.60770	0.453837	0.226919	−	0.973914i	$-0.427135\pi$
$281$	7.60770	0.453837	0.226919	+	0.973914i	$0.427135\pi$
$282$	0	0
$283$	20.5885	1.22386	0.611928	−	0.790913i	$-0.290394\pi$
$283$	20.5885	1.22386	0.611928	+	0.790913i	$0.290394\pi$
$284$	0	0
$285$	−5.46410	−0.323665
$286$	0	0
$287$	−44.7846	−2.64355
$288$	0	0
$289$	−5.00000	−0.294118
$290$	0	0
$291$	39.3205	2.30501
$292$	0	0
$293$	−30.0000	−1.75262	−0.876309	−	0.481749i	$-0.840002\pi$
$293$	−30.0000	−1.75262	−0.876309	+	0.481749i	$0.840002\pi$
$294$	0	0
$295$	−6.00000	−0.349334
$296$	0	0
$297$	−13.8564	−0.804030
$298$	0	0
$299$	−7.60770	−0.439964
$300$	0	0
$301$	0.928203	0.0535007
$302$	0	0
$303$	−32.7846	−1.88343
$304$	0	0
$305$	−0.928203	−0.0531488
$306$	0	0
$307$	23.8038	1.35856	0.679279	−	0.733880i	$-0.262293\pi$
$307$	23.8038	1.35856	0.679279	+	0.733880i	$0.262293\pi$
$308$	0	0
$309$	−6.00000	−0.341328
$310$	0	0
$311$	−28.3923	−1.60998	−0.804990	−	0.593288i	$-0.797829\pi$
$311$	−28.3923	−1.60998	−0.804990	+	0.593288i	$0.797829\pi$
$312$	0	0
$313$	−22.0000	−1.24351	−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000	−1.24351	−0.621757	+	0.783210i	$0.713581\pi$
$314$	0	0
$315$	21.1244	1.19022
$316$	0	0
$317$	1.60770	0.0902972	0.0451486	−	0.998980i	$-0.485624\pi$
$317$	1.60770	0.0902972	0.0451486	+	0.998980i	$0.485624\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	36.2487	2.02321
$322$	0	0
$323$	6.92820	0.385496
$324$	0	0
$325$	3.46410	0.192154
$326$	0	0
$327$	−35.3205	−1.95323
$328$	0	0
$329$	−10.3923	−0.572946
$330$	0	0
$331$	−26.3923	−1.45065	−0.725326	−	0.688405i	$-0.758311\pi$
$331$	−26.3923	−1.45065	−0.725326	+	0.688405i	$0.758311\pi$
$332$	0	0
$333$	−26.7846	−1.46779
$334$	0	0
$335$	−0.196152	−0.0107170
$336$	0	0
$337$	−14.0000	−0.762629	−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000	−0.762629	−0.381314	+	0.924445i	$0.624528\pi$
$338$	0	0
$339$	−35.3205	−1.91835
$340$	0	0
$341$	−8.78461	−0.475713
$342$	0	0
$343$	39.7128	2.14429
$344$	0	0
$345$	−6.00000	−0.323029
$346$	0	0
$347$	−10.0526	−0.539650	−0.269825	−	0.962909i	$-0.586966\pi$
$347$	−10.0526	−0.539650	−0.269825	+	0.962909i	$0.586966\pi$
$348$	0	0
$349$	−32.7846	−1.75492	−0.877460	−	0.479650i	$-0.840764\pi$
$349$	−32.7846	−1.75492	−0.877460	+	0.479650i	$0.840764\pi$
$350$	0	0
$351$	13.8564	0.739600
$352$	0	0
$353$	26.7846	1.42560	0.712800	−	0.701367i	$-0.247427\pi$
$353$	26.7846	1.42560	0.712800	+	0.701367i	$0.247427\pi$
$354$	0	0
$355$	16.3923	0.870013
$356$	0	0
$357$	−44.7846	−2.37025
$358$	0	0
$359$	−32.7846	−1.73031	−0.865153	−	0.501508i	$-0.832779\pi$
$359$	−32.7846	−1.73031	−0.865153	+	0.501508i	$0.832779\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	0	0
$363$	2.73205	0.143395
$364$	0	0
$365$	−6.39230	−0.334589
$366$	0	0
$367$	28.0526	1.46433	0.732166	−	0.681126i	$-0.238510\pi$
$367$	28.0526	1.46433	0.732166	+	0.681126i	$0.238510\pi$
$368$	0	0
$369$	−42.2487	−2.19938
$370$	0	0
$371$	−49.1769	−2.55314
$372$	0	0
$373$	19.8564	1.02813	0.514063	−	0.857753i	$-0.328140\pi$
$373$	19.8564	1.02813	0.514063	+	0.857753i	$0.328140\pi$
$374$	0	0
$375$	2.73205	0.141082
$376$	0	0
$377$	0	0
$378$	0	0
$379$	−2.00000	−0.102733	−0.0513665	−	0.998680i	$-0.516358\pi$
$379$	−2.00000	−0.102733	−0.0513665	+	0.998680i	$0.516358\pi$
$380$	0	0
$381$	38.7846	1.98700
$382$	0	0
$383$	−14.1962	−0.725390	−0.362695	−	0.931908i	$-0.618143\pi$
$383$	−14.1962	−0.725390	−0.362695	+	0.931908i	$0.618143\pi$
$384$	0	0
$385$	−16.3923	−0.835429
$386$	0	0
$387$	0.875644	0.0445115
$388$	0	0
$389$	−14.7846	−0.749609	−0.374805	−	0.927104i	$-0.622290\pi$
$389$	−14.7846	−0.749609	−0.374805	+	0.927104i	$0.622290\pi$
$390$	0	0
$391$	7.60770	0.384738
$392$	0	0
$393$	28.3923	1.43220
$394$	0	0
$395$	12.0000	0.603786
$396$	0	0
$397$	−20.5359	−1.03067	−0.515334	−	0.856990i	$-0.672332\pi$
$397$	−20.5359	−1.03067	−0.515334	+	0.856990i	$0.672332\pi$
$398$	0	0
$399$	−25.8564	−1.29444
$400$	0	0
$401$	−31.8564	−1.59083	−0.795417	−	0.606063i	$-0.792748\pi$
$401$	−31.8564	−1.59083	−0.795417	+	0.606063i	$0.792748\pi$
$402$	0	0
$403$	8.78461	0.437593
$404$	0	0
$405$	−2.46410	−0.122442
$406$	0	0
$407$	20.7846	1.03025
$408$	0	0
$409$	−24.3923	−1.20612	−0.603061	−	0.797695i	$-0.706052\pi$
$409$	−24.3923	−1.20612	−0.603061	+	0.797695i	$0.706052\pi$
$410$	0	0
$411$	2.53590	0.125087
$412$	0	0
$413$	−28.3923	−1.39709
$414$	0	0
$415$	1.26795	0.0622412
$416$	0	0
$417$	−27.3205	−1.33789
$418$	0	0
$419$	12.9282	0.631584	0.315792	−	0.948828i	$-0.397730\pi$
$419$	12.9282	0.631584	0.315792	+	0.948828i	$0.397730\pi$
$420$	0	0
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	0	0
$423$	−9.80385	−0.476679
$424$	0	0
$425$	−3.46410	−0.168034
$426$	0	0
$427$	−4.39230	−0.212559
$428$	0	0
$429$	−32.7846	−1.58286
$430$	0	0
$431$	−7.60770	−0.366450	−0.183225	−	0.983071i	$-0.558654\pi$
$431$	−7.60770	−0.366450	−0.183225	+	0.983071i	$0.558654\pi$
$432$	0	0
$433$	5.60770	0.269489	0.134744	−	0.990880i	$-0.456979\pi$
$433$	5.60770	0.269489	0.134744	+	0.990880i	$0.456979\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	4.39230	0.210112
$438$	0	0
$439$	5.07180	0.242064	0.121032	−	0.992649i	$-0.461380\pi$
$439$	5.07180	0.242064	0.121032	+	0.992649i	$0.461380\pi$
$440$	0	0
$441$	68.7128	3.27204
$442$	0	0
$443$	17.6603	0.839064	0.419532	−	0.907741i	$-0.362194\pi$
$443$	17.6603	0.839064	0.419532	+	0.907741i	$0.362194\pi$
$444$	0	0
$445$	12.9282	0.612856
$446$	0	0
$447$	49.1769	2.32599
$448$	0	0
$449$	−9.46410	−0.446639	−0.223319	−	0.974745i	$-0.571689\pi$
$449$	−9.46410	−0.446639	−0.223319	+	0.974745i	$0.571689\pi$
$450$	0	0
$451$	32.7846	1.54377
$452$	0	0
$453$	25.8564	1.21484
$454$	0	0
$455$	16.3923	0.768483
$456$	0	0
$457$	18.7846	0.878707	0.439353	−	0.898314i	$-0.355208\pi$
$457$	18.7846	0.878707	0.439353	+	0.898314i	$0.355208\pi$
$458$	0	0
$459$	−13.8564	−0.646762
$460$	0	0
$461$	12.0000	0.558896	0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000	0.558896	0.279448	+	0.960161i	$0.409849\pi$
$462$	0	0
$463$	26.1962	1.21744	0.608719	−	0.793386i	$-0.291684\pi$
$463$	26.1962	1.21744	0.608719	+	0.793386i	$0.291684\pi$
$464$	0	0
$465$	6.92820	0.321288
$466$	0	0
$467$	28.9808	1.34107	0.670535	−	0.741878i	$-0.266065\pi$
$467$	28.9808	1.34107	0.670535	+	0.741878i	$0.266065\pi$
$468$	0	0
$469$	−0.928203	−0.0428604
$470$	0	0
$471$	35.3205	1.62748
$472$	0	0
$473$	−0.679492	−0.0312431
$474$	0	0
$475$	−2.00000	−0.0917663
$476$	0	0
$477$	−46.3923	−2.12416
$478$	0	0
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	−20.7846	−0.947697
$482$	0	0
$483$	−28.3923	−1.29189
$484$	0	0
$485$	14.3923	0.653521
$486$	0	0
$487$	14.8756	0.674080	0.337040	−	0.941490i	$-0.390574\pi$
$487$	14.8756	0.674080	0.337040	+	0.941490i	$0.390574\pi$
$488$	0	0
$489$	−44.2487	−2.00100
$490$	0	0
$491$	−1.60770	−0.0725543	−0.0362771	−	0.999342i	$-0.511550\pi$
$491$	−1.60770	−0.0725543	−0.0362771	+	0.999342i	$0.511550\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	−15.4641	−0.695060
$496$	0	0
$497$	77.5692	3.47946
$498$	0	0
$499$	43.5692	1.95043	0.975213	−	0.221268i	$-0.0710195\pi$
$499$	43.5692	1.95043	0.975213	+	0.221268i	$0.0710195\pi$
$500$	0	0
$501$	6.00000	0.268060
$502$	0	0
$503$	−2.19615	−0.0979216	−0.0489608	−	0.998801i	$-0.515591\pi$
$503$	−2.19615	−0.0979216	−0.0489608	+	0.998801i	$0.515591\pi$
$504$	0	0
$505$	−12.0000	−0.533993
$506$	0	0
$507$	−2.73205	−0.121335
$508$	0	0
$509$	32.7846	1.45315	0.726576	−	0.687086i	$-0.241110\pi$
$509$	32.7846	1.45315	0.726576	+	0.687086i	$0.241110\pi$
$510$	0	0
$511$	−30.2487	−1.33812
$512$	0	0
$513$	−8.00000	−0.353209
$514$	0	0
$515$	−2.19615	−0.0967740
$516$	0	0
$517$	7.60770	0.334586
$518$	0	0
$519$	−16.3923	−0.719542
$520$	0	0
$521$	−4.14359	−0.181534	−0.0907671	−	0.995872i	$-0.528932\pi$
$521$	−4.14359	−0.181534	−0.0907671	+	0.995872i	$0.528932\pi$
$522$	0	0
$523$	−36.9808	−1.61706	−0.808528	−	0.588458i	$-0.799735\pi$
$523$	−36.9808	−1.61706	−0.808528	+	0.588458i	$0.799735\pi$
$524$	0	0
$525$	12.9282	0.564233
$526$	0	0
$527$	−8.78461	−0.382664
$528$	0	0
$529$	−18.1769	−0.790301
$530$	0	0
$531$	−26.7846	−1.16235
$532$	0	0
$533$	−32.7846	−1.42006
$534$	0	0
$535$	13.2679	0.573623
$536$	0	0
$537$	21.4641	0.926244
$538$	0	0
$539$	−53.3205	−2.29668
$540$	0	0
$541$	39.7128	1.70739	0.853694	−	0.520776i	$-0.174357\pi$
$541$	39.7128	1.70739	0.853694	+	0.520776i	$0.174357\pi$
$542$	0	0
$543$	−18.9282	−0.812287
$544$	0	0
$545$	−12.9282	−0.553783
$546$	0	0
$547$	12.1962	0.521470	0.260735	−	0.965410i	$-0.416035\pi$
$547$	12.1962	0.521470	0.260735	+	0.965410i	$0.416035\pi$
$548$	0	0
$549$	−4.14359	−0.176844
$550$	0	0
$551$	0	0
$552$	0	0
$553$	56.7846	2.41473
$554$	0	0
$555$	−16.3923	−0.695815
$556$	0	0
$557$	−26.7846	−1.13490	−0.567450	−	0.823408i	$-0.692070\pi$
$557$	−26.7846	−1.13490	−0.567450	+	0.823408i	$0.692070\pi$
$558$	0	0
$559$	0.679492	0.0287394
$560$	0	0
$561$	32.7846	1.38417
$562$	0	0
$563$	15.8038	0.666053	0.333026	−	0.942918i	$-0.391930\pi$
$563$	15.8038	0.666053	0.333026	+	0.942918i	$0.391930\pi$
$564$	0	0
$565$	−12.9282	−0.543894
$566$	0	0
$567$	−11.6603	−0.489685
$568$	0	0
$569$	−6.24871	−0.261960	−0.130980	−	0.991385i	$-0.541812\pi$
$569$	−6.24871	−0.261960	−0.130980	+	0.991385i	$0.541812\pi$
$570$	0	0
$571$	9.60770	0.402070	0.201035	−	0.979584i	$-0.435570\pi$
$571$	9.60770	0.402070	0.201035	+	0.979584i	$0.435570\pi$
$572$	0	0
$573$	12.0000	0.501307
$574$	0	0
$575$	−2.19615	−0.0915859
$576$	0	0
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	0	0
$579$	−39.3205	−1.63410
$580$	0	0
$581$	6.00000	0.248922
$582$	0	0
$583$	36.0000	1.49097
$584$	0	0
$585$	15.4641	0.639362
$586$	0	0
$587$	31.5167	1.30083	0.650416	−	0.759578i	$-0.274595\pi$
$587$	31.5167	1.30083	0.650416	+	0.759578i	$0.274595\pi$
$588$	0	0
$589$	−5.07180	−0.208980
$590$	0	0
$591$	28.3923	1.16790
$592$	0	0
$593$	12.9282	0.530898	0.265449	−	0.964125i	$-0.414480\pi$
$593$	12.9282	0.530898	0.265449	+	0.964125i	$0.414480\pi$
$594$	0	0
$595$	−16.3923	−0.672019
$596$	0	0
$597$	18.9282	0.774680
$598$	0	0
$599$	12.0000	0.490307	0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000	0.490307	0.245153	+	0.969484i	$0.421162\pi$
$600$	0	0
$601$	−0.392305	−0.0160024	−0.00800122	−	0.999968i	$-0.502547\pi$
$601$	−0.392305	−0.0160024	−0.00800122	+	0.999968i	$0.502547\pi$
$602$	0	0
$603$	−0.875644	−0.0356590
$604$	0	0
$605$	1.00000	0.0406558
$606$	0	0
$607$	−2.19615	−0.0891391	−0.0445695	−	0.999006i	$-0.514192\pi$
$607$	−2.19615	−0.0891391	−0.0445695	+	0.999006i	$0.514192\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−7.60770	−0.307774
$612$	0	0
$613$	34.3923	1.38909	0.694546	−	0.719448i	$-0.255605\pi$
$613$	34.3923	1.38909	0.694546	+	0.719448i	$0.255605\pi$
$614$	0	0
$615$	−25.8564	−1.04263
$616$	0	0
$617$	−34.3923	−1.38458	−0.692291	−	0.721618i	$-0.743399\pi$
$617$	−34.3923	−1.38458	−0.692291	+	0.721618i	$0.743399\pi$
$618$	0	0
$619$	34.7846	1.39811	0.699056	−	0.715067i	$-0.253604\pi$
$619$	34.7846	1.39811	0.699056	+	0.715067i	$0.253604\pi$
$620$	0	0
$621$	−8.78461	−0.352514
$622$	0	0
$623$	61.1769	2.45100
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	18.9282	0.755920
$628$	0	0
$629$	20.7846	0.828737
$630$	0	0
$631$	14.5359	0.578665	0.289332	−	0.957229i	$-0.406567\pi$
$631$	14.5359	0.578665	0.289332	+	0.957229i	$0.406567\pi$
$632$	0	0
$633$	−39.3205	−1.56285
$634$	0	0
$635$	14.1962	0.563357
$636$	0	0
$637$	53.3205	2.11264
$638$	0	0
$639$	73.1769	2.89483
$640$	0	0
$641$	16.3923	0.647457	0.323729	−	0.946150i	$-0.395064\pi$
$641$	16.3923	0.647457	0.323729	+	0.946150i	$0.395064\pi$
$642$	0	0
$643$	−20.5885	−0.811929	−0.405965	−	0.913889i	$-0.633064\pi$
$643$	−20.5885	−0.811929	−0.405965	+	0.913889i	$0.633064\pi$
$644$	0	0
$645$	0.535898	0.0211010
$646$	0	0
$647$	−5.41154	−0.212750	−0.106375	−	0.994326i	$-0.533924\pi$
$647$	−5.41154	−0.212750	−0.106375	+	0.994326i	$0.533924\pi$
$648$	0	0
$649$	20.7846	0.815867
$650$	0	0
$651$	32.7846	1.28493
$652$	0	0
$653$	43.1769	1.68964	0.844822	−	0.535048i	$-0.179707\pi$
$653$	43.1769	1.68964	0.844822	+	0.535048i	$0.179707\pi$
$654$	0	0
$655$	10.3923	0.406061
$656$	0	0
$657$	−28.5359	−1.11329
$658$	0	0
$659$	−28.6410	−1.11570	−0.557848	−	0.829943i	$-0.688373\pi$
$659$	−28.6410	−1.11570	−0.557848	+	0.829943i	$0.688373\pi$
$660$	0	0
$661$	47.5692	1.85023	0.925114	−	0.379689i	$-0.123969\pi$
$661$	47.5692	1.85023	0.925114	+	0.379689i	$0.123969\pi$
$662$	0	0
$663$	−32.7846	−1.27325
$664$	0	0
$665$	−9.46410	−0.367002
$666$	0	0
$667$	0	0
$668$	0	0
$669$	−24.9282	−0.963780
$670$	0	0
$671$	3.21539	0.124129
$672$	0	0
$673$	23.1769	0.893404	0.446702	−	0.894683i	$-0.352598\pi$
$673$	23.1769	0.893404	0.446702	+	0.894683i	$0.352598\pi$
$674$	0	0
$675$	4.00000	0.153960
$676$	0	0
$677$	19.1769	0.737029	0.368514	−	0.929622i	$-0.379867\pi$
$677$	19.1769	0.737029	0.368514	+	0.929622i	$0.379867\pi$
$678$	0	0
$679$	68.1051	2.61363
$680$	0	0
$681$	−34.3923	−1.31792
$682$	0	0
$683$	−5.66025	−0.216584	−0.108292	−	0.994119i	$-0.534538\pi$
$683$	−5.66025	−0.216584	−0.108292	+	0.994119i	$0.534538\pi$
$684$	0	0
$685$	0.928203	0.0354648
$686$	0	0
$687$	−13.8564	−0.528655
$688$	0	0
$689$	−36.0000	−1.37149
$690$	0	0
$691$	26.3923	1.00401	0.502005	−	0.864865i	$-0.332596\pi$
$691$	26.3923	1.00401	0.502005	+	0.864865i	$0.332596\pi$
$692$	0	0
$693$	−73.1769	−2.77976
$694$	0	0
$695$	−10.0000	−0.379322
$696$	0	0
$697$	32.7846	1.24181
$698$	0	0
$699$	61.1769	2.31392
$700$	0	0
$701$	−26.7846	−1.01164	−0.505820	−	0.862639i	$-0.668810\pi$
$701$	−26.7846	−1.01164	−0.505820	+	0.862639i	$0.668810\pi$
$702$	0	0
$703$	12.0000	0.452589
$704$	0	0
$705$	−6.00000	−0.225973
$706$	0	0
$707$	−56.7846	−2.13561
$708$	0	0
$709$	37.8564	1.42173	0.710864	−	0.703330i	$-0.248304\pi$
$709$	37.8564	1.42173	0.710864	+	0.703330i	$0.248304\pi$
$710$	0	0
$711$	53.5692	2.00900
$712$	0	0
$713$	−5.56922	−0.208569
$714$	0	0
$715$	−12.0000	−0.448775
$716$	0	0
$717$	56.7846	2.12066
$718$	0	0
$719$	−3.21539	−0.119914	−0.0599569	−	0.998201i	$-0.519096\pi$
$719$	−3.21539	−0.119914	−0.0599569	+	0.998201i	$0.519096\pi$
$720$	0	0
$721$	−10.3923	−0.387030
$722$	0	0
$723$	1.07180	0.0398606
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−4.05256	−0.150301	−0.0751505	−	0.997172i	$-0.523944\pi$
$727$	−4.05256	−0.150301	−0.0751505	+	0.997172i	$0.523944\pi$
$728$	0	0
$729$	−43.7846	−1.62165
$730$	0	0
$731$	−0.679492	−0.0251319
$732$	0	0
$733$	2.78461	0.102852	0.0514260	−	0.998677i	$-0.483623\pi$
$733$	2.78461	0.102852	0.0514260	+	0.998677i	$0.483623\pi$
$734$	0	0
$735$	42.0526	1.55113
$736$	0	0
$737$	0.679492	0.0250294
$738$	0	0
$739$	2.00000	0.0735712	0.0367856	−	0.999323i	$-0.488288\pi$
$739$	2.00000	0.0735712	0.0367856	+	0.999323i	$0.488288\pi$
$740$	0	0
$741$	−18.9282	−0.695345
$742$	0	0
$743$	5.41154	0.198530	0.0992651	−	0.995061i	$-0.468351\pi$
$743$	5.41154	0.198530	0.0992651	+	0.995061i	$0.468351\pi$
$744$	0	0
$745$	18.0000	0.659469
$746$	0	0
$747$	5.66025	0.207098
$748$	0	0
$749$	62.7846	2.29410
$750$	0	0
$751$	19.6077	0.715495	0.357747	−	0.933818i	$-0.383545\pi$
$751$	19.6077	0.715495	0.357747	+	0.933818i	$0.383545\pi$
$752$	0	0
$753$	−23.3205	−0.849847
$754$	0	0
$755$	9.46410	0.344434
$756$	0	0
$757$	−36.9282	−1.34218	−0.671089	−	0.741377i	$-0.734173\pi$
$757$	−36.9282	−1.34218	−0.671089	+	0.741377i	$0.734173\pi$
$758$	0	0
$759$	20.7846	0.754434
$760$	0	0
$761$	−33.7128	−1.22209	−0.611044	−	0.791596i	$-0.709250\pi$
$761$	−33.7128	−1.22209	−0.611044	+	0.791596i	$0.709250\pi$
$762$	0	0
$763$	−61.1769	−2.21475
$764$	0	0
$765$	−15.4641	−0.559106
$766$	0	0
$767$	−20.7846	−0.750489
$768$	0	0
$769$	34.7846	1.25437	0.627183	−	0.778872i	$-0.284208\pi$
$769$	34.7846	1.25437	0.627183	+	0.778872i	$0.284208\pi$
$770$	0	0
$771$	16.3923	0.590354
$772$	0	0
$773$	25.6077	0.921045	0.460522	−	0.887648i	$-0.347662\pi$
$773$	25.6077	0.921045	0.460522	+	0.887648i	$0.347662\pi$
$774$	0	0
$775$	2.53590	0.0910922
$776$	0	0
$777$	−77.5692	−2.78278
$778$	0	0
$779$	18.9282	0.678173
$780$	0	0
$781$	−56.7846	−2.03191
$782$	0	0
$783$	0	0
$784$	0	0
$785$	12.9282	0.461427
$786$	0	0
$787$	−16.1962	−0.577330	−0.288665	−	0.957430i	$-0.593211\pi$
$787$	−16.1962	−0.577330	−0.288665	+	0.957430i	$0.593211\pi$
$788$	0	0
$789$	−26.7846	−0.953557
$790$	0	0
$791$	−61.1769	−2.17520
$792$	0	0
$793$	−3.21539	−0.114182
$794$	0	0
$795$	−28.3923	−1.00697
$796$	0	0
$797$	−22.3923	−0.793176	−0.396588	−	0.917997i	$-0.629806\pi$
$797$	−22.3923	−0.793176	−0.396588	+	0.917997i	$0.629806\pi$
$798$	0	0
$799$	7.60770	0.269141
$800$	0	0
$801$	57.7128	2.03918
$802$	0	0
$803$	22.1436	0.781430
$804$	0	0
$805$	−10.3923	−0.366281
$806$	0	0
$807$	73.1769	2.57595
$808$	0	0
$809$	47.5692	1.67244	0.836222	−	0.548391i	$-0.184759\pi$
$809$	47.5692	1.67244	0.836222	+	0.548391i	$0.184759\pi$
$810$	0	0
$811$	17.6077	0.618290	0.309145	−	0.951015i	$-0.399957\pi$
$811$	17.6077	0.618290	0.309145	+	0.951015i	$0.399957\pi$
$812$	0	0
$813$	44.7846	1.57066
$814$	0	0
$815$	−16.1962	−0.567326
$816$	0	0
$817$	−0.392305	−0.0137250
$818$	0	0
$819$	73.1769	2.55701
$820$	0	0
$821$	−9.21539	−0.321619	−0.160810	−	0.986985i	$-0.551411\pi$
$821$	−9.21539	−0.321619	−0.160810	+	0.986985i	$0.551411\pi$
$822$	0	0
$823$	−48.8372	−1.70236	−0.851178	−	0.524877i	$-0.824111\pi$
$823$	−48.8372	−1.70236	−0.851178	+	0.524877i	$0.824111\pi$
$824$	0	0
$825$	−9.46410	−0.329498
$826$	0	0
$827$	−1.26795	−0.0440909	−0.0220455	−	0.999757i	$-0.507018\pi$
$827$	−1.26795	−0.0440909	−0.0220455	+	0.999757i	$0.507018\pi$
$828$	0	0
$829$	9.21539	0.320064	0.160032	−	0.987112i	$-0.448840\pi$
$829$	9.21539	0.320064	0.160032	+	0.987112i	$0.448840\pi$
$830$	0	0
$831$	−21.4641	−0.744581
$832$	0	0
$833$	−53.3205	−1.84745
$834$	0	0
$835$	2.19615	0.0760010
$836$	0	0
$837$	10.1436	0.350614
$838$	0	0
$839$	−32.7846	−1.13185	−0.565925	−	0.824457i	$-0.691481\pi$
$839$	−32.7846	−1.13185	−0.565925	+	0.824457i	$0.691481\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	0	0
$843$	20.7846	0.715860
$844$	0	0
$845$	−1.00000	−0.0344010
$846$	0	0
$847$	4.73205	0.162595
$848$	0	0
$849$	56.2487	1.93045
$850$	0	0
$851$	13.1769	0.451699
$852$	0	0
$853$	−3.46410	−0.118609	−0.0593043	−	0.998240i	$-0.518888\pi$
$853$	−3.46410	−0.118609	−0.0593043	+	0.998240i	$0.518888\pi$
$854$	0	0
$855$	−8.92820	−0.305338
$856$	0	0
$857$	43.8564	1.49811	0.749053	−	0.662510i	$-0.230509\pi$
$857$	43.8564	1.49811	0.749053	+	0.662510i	$0.230509\pi$
$858$	0	0
$859$	−31.5692	−1.07713	−0.538564	−	0.842585i	$-0.681033\pi$
$859$	−31.5692	−1.07713	−0.538564	+	0.842585i	$0.681033\pi$
$860$	0	0
$861$	−122.354	−4.16981
$862$	0	0
$863$	10.9808	0.373789	0.186895	−	0.982380i	$-0.440158\pi$
$863$	10.9808	0.373789	0.186895	+	0.982380i	$0.440158\pi$
$864$	0	0
$865$	−6.00000	−0.204006
$866$	0	0
$867$	−13.6603	−0.463927
$868$	0	0
$869$	−41.5692	−1.41014
$870$	0	0
$871$	−0.679492	−0.0230237
$872$	0	0
$873$	64.2487	2.17449
$874$	0	0
$875$	4.73205	0.159973
$876$	0	0
$877$	−19.8564	−0.670503	−0.335252	−	0.942129i	$-0.608821\pi$
$877$	−19.8564	−0.670503	−0.335252	+	0.942129i	$0.608821\pi$
$878$	0	0
$879$	−81.9615	−2.76449
$880$	0	0
$881$	−28.3923	−0.956561	−0.478281	−	0.878207i	$-0.658740\pi$
$881$	−28.3923	−0.956561	−0.478281	+	0.878207i	$0.658740\pi$
$882$	0	0
$883$	−16.1962	−0.545044	−0.272522	−	0.962150i	$-0.587858\pi$
$883$	−16.1962	−0.545044	−0.272522	+	0.962150i	$0.587858\pi$
$884$	0	0
$885$	−16.3923	−0.551021
$886$	0	0
$887$	51.3731	1.72494	0.862469	−	0.506109i	$-0.168917\pi$
$887$	51.3731	1.72494	0.862469	+	0.506109i	$0.168917\pi$
$888$	0	0
$889$	67.1769	2.25304
$890$	0	0
$891$	8.53590	0.285963
$892$	0	0
$893$	4.39230	0.146983
$894$	0	0
$895$	7.85641	0.262611
$896$	0	0
$897$	−20.7846	−0.693978
$898$	0	0
$899$	0	0
$900$	0	0
$901$	36.0000	1.19933
$902$	0	0
$903$	2.53590	0.0843894
$904$	0	0
$905$	−6.92820	−0.230301
$906$	0	0
$907$	−32.5885	−1.08208	−0.541041	−	0.840996i	$-0.681970\pi$
$907$	−32.5885	−1.08208	−0.541041	+	0.840996i	$0.681970\pi$
$908$	0	0
$909$	−53.5692	−1.77678
$910$	0	0
$911$	−25.1769	−0.834148	−0.417074	−	0.908872i	$-0.636944\pi$
$911$	−25.1769	−0.834148	−0.417074	+	0.908872i	$0.636944\pi$
$912$	0	0
$913$	−4.39230	−0.145364
$914$	0	0
$915$	−2.53590	−0.0838342
$916$	0	0
$917$	49.1769	1.62396
$918$	0	0
$919$	−15.7128	−0.518318	−0.259159	−	0.965835i	$-0.583445\pi$
$919$	−15.7128	−0.518318	−0.259159	+	0.965835i	$0.583445\pi$
$920$	0	0
$921$	65.0333	2.14292
$922$	0	0
$923$	56.7846	1.86909
$924$	0	0
$925$	−6.00000	−0.197279
$926$	0	0
$927$	−9.80385	−0.322001
$928$	0	0
$929$	28.3923	0.931521	0.465761	−	0.884911i	$-0.345781\pi$
$929$	28.3923	0.931521	0.465761	+	0.884911i	$0.345781\pi$
$930$	0	0
$931$	−30.7846	−1.00892
$932$	0	0
$933$	−77.5692	−2.53950
$934$	0	0
$935$	12.0000	0.392442
$936$	0	0
$937$	30.3923	0.992873	0.496437	−	0.868073i	$-0.334641\pi$
$937$	30.3923	0.992873	0.496437	+	0.868073i	$0.334641\pi$
$938$	0	0
$939$	−60.1051	−1.96146
$940$	0	0
$941$	20.7846	0.677559	0.338779	−	0.940866i	$-0.389986\pi$
$941$	20.7846	0.677559	0.338779	+	0.940866i	$0.389986\pi$
$942$	0	0
$943$	20.7846	0.676840
$944$	0	0
$945$	18.9282	0.615734
$946$	0	0
$947$	−56.1962	−1.82613	−0.913065	−	0.407815i	$-0.866291\pi$
$947$	−56.1962	−1.82613	−0.913065	+	0.407815i	$0.866291\pi$
$948$	0	0
$949$	−22.1436	−0.718811
$950$	0	0
$951$	4.39230	0.142430
$952$	0	0
$953$	−11.0718	−0.358651	−0.179325	−	0.983790i	$-0.557391\pi$
$953$	−11.0718	−0.358651	−0.179325	+	0.983790i	$0.557391\pi$
$954$	0	0
$955$	4.39230	0.142132
$956$	0	0
$957$	0	0
$958$	0	0
$959$	4.39230	0.141835
$960$	0	0
$961$	−24.5692	−0.792555
$962$	0	0
$963$	59.2295	1.90864
$964$	0	0
$965$	−14.3923	−0.463305
$966$	0	0
$967$	2.19615	0.0706235	0.0353118	−	0.999376i	$-0.488758\pi$
$967$	2.19615	0.0706235	0.0353118	+	0.999376i	$0.488758\pi$
$968$	0	0
$969$	18.9282	0.608061
$970$	0	0
$971$	−57.0333	−1.83029	−0.915143	−	0.403129i	$-0.867923\pi$
$971$	−57.0333	−1.83029	−0.915143	+	0.403129i	$0.867923\pi$
$972$	0	0
$973$	−47.3205	−1.51703
$974$	0	0
$975$	9.46410	0.303094
$976$	0	0
$977$	−29.3205	−0.938046	−0.469023	−	0.883186i	$-0.655394\pi$
$977$	−29.3205	−0.938046	−0.469023	+	0.883186i	$0.655394\pi$
$978$	0	0
$979$	−44.7846	−1.43132
$980$	0	0
$981$	−57.7128	−1.84263
$982$	0	0
$983$	−42.5885	−1.35836	−0.679180	−	0.733971i	$-0.737665\pi$
$983$	−42.5885	−1.35836	−0.679180	+	0.733971i	$0.737665\pi$
$984$	0	0
$985$	10.3923	0.331126
$986$	0	0
$987$	−28.3923	−0.903737
$988$	0	0
$989$	−0.430781	−0.0136980
$990$	0	0
$991$	32.1051	1.01985	0.509926	−	0.860218i	$-0.329673\pi$
$991$	32.1051	1.01985	0.509926	+	0.860218i	$0.329673\pi$
$992$	0	0
$993$	−72.1051	−2.28819
$994$	0	0
$995$	6.92820	0.219639
$996$	0	0
$997$	46.3923	1.46926	0.734630	−	0.678468i	$-0.237356\pi$
$997$	46.3923	1.46926	0.734630	+	0.678468i	$0.237356\pi$
$998$	0	0
$999$	−24.0000	−0.759326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.a.p.1.2		2
4.3	odd	2		1280.2.a.c.1.1		2
5.4	even	2		6400.2.a.y.1.1		2
8.3	odd	2		1280.2.a.m.1.2		2
8.5	even	2		1280.2.a.b.1.1		2
16.3	odd	4		320.2.d.b.161.1	yes	4
16.5	even	4		320.2.d.a.161.1	✓	4
16.11	odd	4		320.2.d.b.161.4	yes	4
16.13	even	4		320.2.d.a.161.4	yes	4
20.19	odd	2		6400.2.a.ck.1.2		2
40.19	odd	2		6400.2.a.bf.1.1		2
40.29	even	2		6400.2.a.cd.1.2		2
48.5	odd	4		2880.2.k.e.1441.1		4
48.11	even	4		2880.2.k.l.1441.2		4
48.29	odd	4		2880.2.k.e.1441.3		4
48.35	even	4		2880.2.k.l.1441.4		4
80.3	even	4		1600.2.f.h.1249.3		4
80.13	odd	4		1600.2.f.e.1249.2		4
80.19	odd	4		1600.2.d.b.801.4		4
80.27	even	4		1600.2.f.h.1249.4		4
80.29	even	4		1600.2.d.h.801.1		4
80.37	odd	4		1600.2.f.e.1249.1		4
80.43	even	4		1600.2.f.d.1249.1		4
80.53	odd	4		1600.2.f.i.1249.4		4
80.59	odd	4		1600.2.d.b.801.1		4
80.67	even	4		1600.2.f.d.1249.2		4
80.69	even	4		1600.2.d.h.801.4		4
80.77	odd	4		1600.2.f.i.1249.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
320.2.d.a.161.1	✓	4	16.5	even	4
320.2.d.a.161.4	yes	4	16.13	even	4
320.2.d.b.161.1	yes	4	16.3	odd	4
320.2.d.b.161.4	yes	4	16.11	odd	4
1280.2.a.b.1.1		2	8.5	even	2
1280.2.a.c.1.1		2	4.3	odd	2
1280.2.a.m.1.2		2	8.3	odd	2
1280.2.a.p.1.2		2	1.1	even	1	trivial
1600.2.d.b.801.1		4	80.59	odd	4
1600.2.d.b.801.4		4	80.19	odd	4
1600.2.d.h.801.1		4	80.29	even	4
1600.2.d.h.801.4		4	80.69	even	4
1600.2.f.d.1249.1		4	80.43	even	4
1600.2.f.d.1249.2		4	80.67	even	4
1600.2.f.e.1249.1		4	80.37	odd	4
1600.2.f.e.1249.2		4	80.13	odd	4
1600.2.f.h.1249.3		4	80.3	even	4
1600.2.f.h.1249.4		4	80.27	even	4
1600.2.f.i.1249.3		4	80.77	odd	4
1600.2.f.i.1249.4		4	80.53	odd	4
2880.2.k.e.1441.1		4	48.5	odd	4
2880.2.k.e.1441.3		4	48.29	odd	4
2880.2.k.l.1441.2		4	48.11	even	4
2880.2.k.l.1441.4		4	48.35	even	4
6400.2.a.y.1.1		2	5.4	even	2
6400.2.a.bf.1.1		2	40.19	odd	2
6400.2.a.cd.1.2		2	40.29	even	2
6400.2.a.ck.1.2		2	20.19	odd	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:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.a (trivial)

\(f(q)\)	\(=\)	\(q+2.73205 q^{3} +1.00000 q^{5} +4.73205 q^{7} +4.46410 q^{9} +O(q^{10})\)	\(q+2.73205 q^{3} +1.00000 q^{5} +4.73205 q^{7} +4.46410 q^{9} -3.46410 q^{11} +3.46410 q^{13} +2.73205 q^{15} -3.46410 q^{17} -2.00000 q^{19} +12.9282 q^{21} -2.19615 q^{23} +1.00000 q^{25} +4.00000 q^{27} +2.53590 q^{31} -9.46410 q^{33} +4.73205 q^{35} -6.00000 q^{37} +9.46410 q^{39} -9.46410 q^{41} +0.196152 q^{43} +4.46410 q^{45} -2.19615 q^{47} +15.3923 q^{49} -9.46410 q^{51} -10.3923 q^{53} -3.46410 q^{55} -5.46410 q^{57} -6.00000 q^{59} -0.928203 q^{61} +21.1244 q^{63} +3.46410 q^{65} -0.196152 q^{67} -6.00000 q^{69} +16.3923 q^{71} -6.39230 q^{73} +2.73205 q^{75} -16.3923 q^{77} +12.0000 q^{79} -2.46410 q^{81} +1.26795 q^{83} -3.46410 q^{85} +12.9282 q^{89} +16.3923 q^{91} +6.92820 q^{93} -2.00000 q^{95} +14.3923 q^{97} -15.4641 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 2 q^{5} + 6 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 + 2 * q^5 + 6 * q^7 + 2 * q^9	\( 2 q + 2 q^{3} + 2 q^{5} + 6 q^{7} + 2 q^{9} + 2 q^{15} - 4 q^{19} + 12 q^{21} + 6 q^{23} + 2 q^{25} + 8 q^{27} + 12 q^{31} - 12 q^{33} + 6 q^{35} - 12 q^{37} + 12 q^{39} - 12 q^{41} - 10 q^{43} + 2 q^{45} + 6 q^{47} + 10 q^{49} - 12 q^{51} - 4 q^{57} - 12 q^{59} + 12 q^{61} + 18 q^{63} + 10 q^{67} - 12 q^{69} + 12 q^{71} + 8 q^{73} + 2 q^{75} - 12 q^{77} + 24 q^{79} + 2 q^{81} + 6 q^{83} + 12 q^{89} + 12 q^{91} - 4 q^{95} + 8 q^{97} - 24 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 + 2 * q^5 + 6 * q^7 + 2 * q^9 + 2 * q^15 - 4 * q^19 + 12 * q^21 + 6 * q^23 + 2 * q^25 + 8 * q^27 + 12 * q^31 - 12 * q^33 + 6 * q^35 - 12 * q^37 + 12 * q^39 - 12 * q^41 - 10 * q^43 + 2 * q^45 + 6 * q^47 + 10 * q^49 - 12 * q^51 - 4 * q^57 - 12 * q^59 + 12 * q^61 + 18 * q^63 + 10 * q^67 - 12 * q^69 + 12 * q^71 + 8 * q^73 + 2 * q^75 - 12 * q^77 + 24 * q^79 + 2 * q^81 + 6 * q^83 + 12 * q^89 + 12 * q^91 - 4 * q^95 + 8 * q^97 - 24 * q^99

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