LMFDB - Embedded newform 9280.2.a.cj.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9280,2,Mod(1,9280)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9280.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9280, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$9280 = 2^{6} \cdot 5 \cdot 29$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	9280.a (trivial)

Newform invariants

comment:select newform

sage:traces = [5,0,1,0,-5,0,-1,0,12,0,4,0,-13,0,-1,0,3,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(21)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$74.1011730757$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.6083172.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{5} - x^{4} - 13x^{3} + 10x^{2} + 40x - 28$ x^5 - x^4 - 13x^3 + 10x^2 + 40*x - 28
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$2$
Twist minimal:	no (minimal twist has level 1160)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$3.11726$ of defining polynomial
Character	$\chi$	$=$	9280.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+3.11726 q^{3} -1.00000 q^{5} -0.964080 q^{7} +6.71730 q^{9} -2.75322 q^{11} +3.87047 q^{13} -3.11726 q^{15} +2.11197 q^{17} +5.82927 q^{19} -3.00529 q^{21} -2.04121 q^{23} +1.00000 q^{25} +11.5878 q^{27} +1.00000 q^{29} +2.96408 q^{31} -8.58248 q^{33} +0.964080 q^{35} -4.75322 q^{37} +12.0653 q^{39} +11.3106 q^{41} +3.27044 q^{43} -6.71730 q^{45} +0.405249 q^{47} -6.07055 q^{49} +6.58356 q^{51} -6.98921 q^{53} +2.75322 q^{55} +18.1713 q^{57} -0.364042 q^{59} -12.1768 q^{61} -6.47601 q^{63} -3.87047 q^{65} -1.48130 q^{67} -6.36297 q^{69} +14.5931 q^{71} -2.16416 q^{73} +3.11726 q^{75} +2.65432 q^{77} +14.1933 q^{79} +15.9702 q^{81} -11.3463 q^{83} -2.11197 q^{85} +3.11726 q^{87} +6.08241 q^{89} -3.73145 q^{91} +9.23980 q^{93} -5.82927 q^{95} -2.31733 q^{97} -18.4942 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$5 q + q^{3} - 5 q^{5} - q^{7} + 12 q^{9} + 4 q^{11} - 13 q^{13} - q^{15} + 3 q^{17} - 8 q^{21} - 7 q^{23} + 5 q^{25} + 4 q^{27} + 5 q^{29} + 11 q^{31} + 4 q^{33} + q^{35} - 6 q^{37} + 21 q^{39} + 16 q^{41}+ \cdots - 10 q^{99}+O(q^{100})$ 5 * q + q^3 - 5 * q^5 - q^7 + 12 * q^9 + 4 * q^11 - 13 * q^13 - q^15 + 3 * q^17 - 8 * q^21 - 7 * q^23 + 5 * q^25 + 4 * q^27 + 5 * q^29 + 11 * q^31 + 4 * q^33 + q^35 - 6 * q^37 + 21 * q^39 + 16 * q^41 - 9 * q^43 - 12 * q^45 + 2 * q^47 + 16 * q^49 - 2 * q^51 - 7 * q^53 - 4 * q^55 + 2 * q^57 - 5 * q^59 - 7 * q^61 - 28 * q^63 + 13 * q^65 + 4 * q^67 - 23 * q^69 + 12 * q^71 + 7 * q^73 + q^75 - 26 * q^77 + 45 * q^79 - 7 * q^81 + 22 * q^83 - 3 * q^85 + q^87 + 24 * q^89 + 20 * q^91 + 10 * q^93 + 17 * q^97 - 10 * q^99

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0	0
$2$	0	0
$3$	3.11726	1.79975	0.899875	−	0.436148i	$-0.143658\pi$
$3$	3.11726	1.79975	0.899875	+	0.436148i	$0.143658\pi$
$4$	0	0
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	−0.964080	−0.364388	−0.182194	−	0.983263i	$-0.558320\pi$
$7$	−0.964080	−0.364388	−0.182194	+	0.983263i	$0.558320\pi$
$8$	0	0
$9$	6.71730	2.23910
$10$	0	0
$11$	−2.75322	−0.830126	−0.415063	−	0.909793i	$-0.636240\pi$
$11$	−2.75322	−0.830126	−0.415063	+	0.909793i	$0.636240\pi$
$12$	0	0
$13$	3.87047	1.07348	0.536738	−	0.843749i	$-0.319656\pi$
$13$	3.87047	1.07348	0.536738	+	0.843749i	$0.319656\pi$
$14$	0	0
$15$	−3.11726	−0.804872
$16$	0	0
$17$	2.11197	0.512228	0.256114	−	0.966647i	$-0.417558\pi$
$17$	2.11197	0.512228	0.256114	+	0.966647i	$0.417558\pi$
$18$	0	0
$19$	5.82927	1.33733	0.668663	−	0.743566i	$-0.266867\pi$
$19$	5.82927	1.33733	0.668663	+	0.743566i	$0.266867\pi$
$20$	0	0
$21$	−3.00529	−0.655807
$22$	0	0
$23$	−2.04121	−0.425621	−0.212811	−	0.977093i	$-0.568262\pi$
$23$	−2.04121	−0.425621	−0.212811	+	0.977093i	$0.568262\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	11.5878	2.23007
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	2.96408	0.532365	0.266182	−	0.963923i	$-0.414238\pi$
$31$	2.96408	0.532365	0.266182	+	0.963923i	$0.414238\pi$
$32$	0	0
$33$	−8.58248	−1.49402
$34$	0	0
$35$	0.964080	0.162959
$36$	0	0
$37$	−4.75322	−0.781424	−0.390712	−	0.920513i	$-0.627771\pi$
$37$	−4.75322	−0.781424	−0.390712	+	0.920513i	$0.627771\pi$
$38$	0	0
$39$	12.0653	1.93199
$40$	0	0
$41$	11.3106	1.76641	0.883207	−	0.468984i	$-0.155380\pi$
$41$	11.3106	1.76641	0.883207	+	0.468984i	$0.155380\pi$
$42$	0	0
$43$	3.27044	0.498737	0.249368	−	0.968409i	$-0.419777\pi$
$43$	3.27044	0.498737	0.249368	+	0.968409i	$0.419777\pi$
$44$	0	0
$45$	−6.71730	−1.00136
$46$	0	0
$47$	0.405249	0.0591117	0.0295558	−	0.999563i	$-0.490591\pi$
$47$	0.405249	0.0591117	0.0295558	+	0.999563i	$0.490591\pi$
$48$	0	0
$49$	−6.07055	−0.867221
$50$	0	0
$51$	6.58356	0.921882
$52$	0	0
$53$	−6.98921	−0.960042	−0.480021	−	0.877257i	$-0.659371\pi$
$53$	−6.98921	−0.960042	−0.480021	+	0.877257i	$0.659371\pi$
$54$	0	0
$55$	2.75322	0.371243
$56$	0	0
$57$	18.1713	2.40685
$58$	0	0
$59$	−0.364042	−0.0473943	−0.0236971	−	0.999719i	$-0.507544\pi$
$59$	−0.364042	−0.0473943	−0.0236971	+	0.999719i	$0.507544\pi$
$60$	0	0
$61$	−12.1768	−1.55908	−0.779542	−	0.626351i	$-0.784548\pi$
$61$	−12.1768	−1.55908	−0.779542	+	0.626351i	$0.784548\pi$
$62$	0	0
$63$	−6.47601	−0.815901
$64$	0	0
$65$	−3.87047	−0.480073
$66$	0	0
$67$	−1.48130	−0.180970	−0.0904848	−	0.995898i	$-0.528842\pi$
$67$	−1.48130	−0.180970	−0.0904848	+	0.995898i	$0.528842\pi$
$68$	0	0
$69$	−6.36297	−0.766011
$70$	0	0
$71$	14.5931	1.73188	0.865939	−	0.500150i	$-0.166722\pi$
$71$	14.5931	1.73188	0.865939	+	0.500150i	$0.166722\pi$
$72$	0	0
$73$	−2.16416	−0.253295	−0.126648	−	0.991948i	$-0.540422\pi$
$73$	−2.16416	−0.253295	−0.126648	+	0.991948i	$0.540422\pi$
$74$	0	0
$75$	3.11726	0.359950
$76$	0	0
$77$	2.65432	0.302488
$78$	0	0
$79$	14.1933	1.59687	0.798436	−	0.602080i	$-0.205661\pi$
$79$	14.1933	1.59687	0.798436	+	0.602080i	$0.205661\pi$
$80$	0	0
$81$	15.9702	1.77446
$82$	0	0
$83$	−11.3463	−1.24542	−0.622708	−	0.782455i	$-0.713967\pi$
$83$	−11.3463	−1.24542	−0.622708	+	0.782455i	$0.713967\pi$
$84$	0	0
$85$	−2.11197	−0.229075
$86$	0	0
$87$	3.11726	0.334205
$88$	0	0
$89$	6.08241	0.644735	0.322367	−	0.946615i	$-0.395521\pi$
$89$	6.08241	0.644735	0.322367	+	0.946615i	$0.395521\pi$
$90$	0	0
$91$	−3.73145	−0.391162
$92$	0	0
$93$	9.23980	0.958123
$94$	0	0
$95$	−5.82927	−0.598070
$96$	0	0
$97$	−2.31733	−0.235290	−0.117645	−	0.993056i	$-0.537534\pi$
$97$	−2.31733	−0.235290	−0.117645	+	0.993056i	$0.537534\pi$
$98$	0	0
$99$	−18.4942	−1.85873
$100$	0	0
$101$	10.3009	1.02497	0.512487	−	0.858695i	$-0.328724\pi$
$101$	10.3009	1.02497	0.512487	+	0.858695i	$0.328724\pi$
$102$	0	0
$103$	−2.51870	−0.248175	−0.124087	−	0.992271i	$-0.539600\pi$
$103$	−2.51870	−0.248175	−0.124087	+	0.992271i	$0.539600\pi$
$104$	0	0
$105$	3.00529	0.293286
$106$	0	0
$107$	−8.13562	−0.786500	−0.393250	−	0.919432i	$-0.628649\pi$
$107$	−8.13562	−0.786500	−0.393250	+	0.919432i	$0.628649\pi$
$108$	0	0
$109$	3.31057	0.317095	0.158547	−	0.987351i	$-0.449319\pi$
$109$	3.31057	0.317095	0.158547	+	0.987351i	$0.449319\pi$
$110$	0	0
$111$	−14.8170	−1.40637
$112$	0	0
$113$	−0.810903	−0.0762833	−0.0381417	−	0.999272i	$-0.512144\pi$
$113$	−0.810903	−0.0762833	−0.0381417	+	0.999272i	$0.512144\pi$
$114$	0	0
$115$	2.04121	0.190344
$116$	0	0
$117$	25.9991	2.40362
$118$	0	0
$119$	−2.03611	−0.186650
$120$	0	0
$121$	−3.41981	−0.310891
$122$	0	0
$123$	35.2580	3.17910
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	19.9201	1.76762	0.883812	−	0.467843i	$-0.154969\pi$
$127$	19.9201	1.76762	0.883812	+	0.467843i	$0.154969\pi$
$128$	0	0
$129$	10.1948	0.897601
$130$	0	0
$131$	20.6182	1.80142	0.900710	−	0.434422i	$-0.143047\pi$
$131$	20.6182	1.80142	0.900710	+	0.434422i	$0.143047\pi$
$132$	0	0
$133$	−5.61988	−0.487306
$134$	0	0
$135$	−11.5878	−0.997316
$136$	0	0
$137$	9.16944	0.783398	0.391699	−	0.920093i	$-0.371887\pi$
$137$	9.16944	0.783398	0.391699	+	0.920093i	$0.371887\pi$
$138$	0	0
$139$	−14.3822	−1.21988	−0.609941	−	0.792447i	$-0.708807\pi$
$139$	−14.3822	−1.21988	−0.609941	+	0.792447i	$0.708807\pi$
$140$	0	0
$141$	1.26327	0.106386
$142$	0	0
$143$	−10.6562	−0.891120
$144$	0	0
$145$	−1.00000	−0.0830455
$146$	0	0
$147$	−18.9235	−1.56078
$148$	0	0
$149$	−2.97613	−0.243814	−0.121907	−	0.992541i	$-0.538901\pi$
$149$	−2.97613	−0.243814	−0.121907	+	0.992541i	$0.538901\pi$
$150$	0	0
$151$	1.14789	0.0934140	0.0467070	−	0.998909i	$-0.485127\pi$
$151$	1.14789	0.0934140	0.0467070	+	0.998909i	$0.485127\pi$
$152$	0	0
$153$	14.1867	1.14693
$154$	0	0
$155$	−2.96408	−0.238081
$156$	0	0
$157$	−1.59475	−0.127275	−0.0636375	−	0.997973i	$-0.520270\pi$
$157$	−1.59475	−0.127275	−0.0636375	+	0.997973i	$0.520270\pi$
$158$	0	0
$159$	−21.7872	−1.72784
$160$	0	0
$161$	1.96789	0.155091
$162$	0	0
$163$	−20.7809	−1.62768	−0.813841	−	0.581087i	$-0.802628\pi$
$163$	−20.7809	−1.62768	−0.813841	+	0.581087i	$0.802628\pi$
$164$	0	0
$165$	8.58248	0.668145
$166$	0	0
$167$	21.2875	1.64728	0.823638	−	0.567115i	$-0.191941\pi$
$167$	21.2875	1.64728	0.823638	+	0.567115i	$0.191941\pi$
$168$	0	0
$169$	1.98056	0.152351
$170$	0	0
$171$	39.1569	2.99440
$172$	0	0
$173$	19.6114	1.49103	0.745514	−	0.666490i	$-0.232204\pi$
$173$	19.6114	1.49103	0.745514	+	0.666490i	$0.232204\pi$
$174$	0	0
$175$	−0.964080	−0.0728776
$176$	0	0
$177$	−1.13481	−0.0852978
$178$	0	0
$179$	14.4881	1.08289	0.541444	−	0.840736i	$-0.317878\pi$
$179$	14.4881	1.08289	0.541444	+	0.840736i	$0.317878\pi$
$180$	0	0
$181$	21.4627	1.59531	0.797654	−	0.603116i	$-0.206074\pi$
$181$	21.4627	1.59531	0.797654	+	0.603116i	$0.206074\pi$
$182$	0	0
$183$	−37.9583	−2.80596
$184$	0	0
$185$	4.75322	0.349463
$186$	0	0
$187$	−5.81471	−0.425214
$188$	0	0
$189$	−11.1715	−0.812610
$190$	0	0
$191$	12.5227	0.906111	0.453055	−	0.891482i	$-0.350334\pi$
$191$	12.5227	0.906111	0.453055	+	0.891482i	$0.350334\pi$
$192$	0	0
$193$	24.0999	1.73475	0.867374	−	0.497657i	$-0.165806\pi$
$193$	24.0999	1.73475	0.867374	+	0.497657i	$0.165806\pi$
$194$	0	0
$195$	−12.0653	−0.864011
$196$	0	0
$197$	10.9370	0.779231	0.389615	−	0.920978i	$-0.372608\pi$
$197$	10.9370	0.779231	0.389615	+	0.920978i	$0.372608\pi$
$198$	0	0
$199$	9.45424	0.670194	0.335097	−	0.942184i	$-0.391231\pi$
$199$	9.45424	0.670194	0.335097	+	0.942184i	$0.391231\pi$
$200$	0	0
$201$	−4.61759	−0.325700
$202$	0	0
$203$	−0.964080	−0.0676652
$204$	0	0
$205$	−11.3106	−0.789964
$206$	0	0
$207$	−13.7114	−0.953007
$208$	0	0
$209$	−16.0492	−1.11015
$210$	0	0
$211$	−14.4117	−0.992146	−0.496073	−	0.868281i	$-0.665225\pi$
$211$	−14.4117	−0.992146	−0.496073	+	0.868281i	$0.665225\pi$
$212$	0	0
$213$	45.4903	3.11695
$214$	0	0
$215$	−3.27044	−0.223042
$216$	0	0
$217$	−2.85761	−0.193987
$218$	0	0
$219$	−6.74623	−0.455868
$220$	0	0
$221$	8.17433	0.549865
$222$	0	0
$223$	−20.9104	−1.40026	−0.700132	−	0.714014i	$-0.746875\pi$
$223$	−20.9104	−1.40026	−0.700132	+	0.714014i	$0.746875\pi$
$224$	0	0
$225$	6.71730	0.447820
$226$	0	0
$227$	8.97716	0.595835	0.297917	−	0.954592i	$-0.403708\pi$
$227$	8.97716	0.595835	0.297917	+	0.954592i	$0.403708\pi$
$228$	0	0
$229$	−20.1371	−1.33070	−0.665349	−	0.746533i	$-0.731717\pi$
$229$	−20.1371	−1.33070	−0.665349	+	0.746533i	$0.731717\pi$
$230$	0	0
$231$	8.27420	0.544403
$232$	0	0
$233$	−16.8692	−1.10514	−0.552568	−	0.833468i	$-0.686352\pi$
$233$	−16.8692	−1.10514	−0.552568	+	0.833468i	$0.686352\pi$
$234$	0	0
$235$	−0.405249	−0.0264355
$236$	0	0
$237$	44.2442	2.87397
$238$	0	0
$239$	−3.88655	−0.251400	−0.125700	−	0.992068i	$-0.540118\pi$
$239$	−3.88655	−0.251400	−0.125700	+	0.992068i	$0.540118\pi$
$240$	0	0
$241$	2.80285	0.180547	0.0902736	−	0.995917i	$-0.471226\pi$
$241$	2.80285	0.180547	0.0902736	+	0.995917i	$0.471226\pi$
$242$	0	0
$243$	15.0198	0.963523
$244$	0	0
$245$	6.07055	0.387833
$246$	0	0
$247$	22.5620	1.43559
$248$	0	0
$249$	−35.3693	−2.24144
$250$	0	0
$251$	15.8701	1.00171	0.500855	−	0.865531i	$-0.333019\pi$
$251$	15.8701	1.00171	0.500855	+	0.865531i	$0.333019\pi$
$252$	0	0
$253$	5.61988	0.353319
$254$	0	0
$255$	−6.58356	−0.412278
$256$	0	0
$257$	−16.3691	−1.02108	−0.510539	−	0.859855i	$-0.670554\pi$
$257$	−16.3691	−1.02108	−0.510539	+	0.859855i	$0.670554\pi$
$258$	0	0
$259$	4.58248	0.284742
$260$	0	0
$261$	6.71730	0.415790
$262$	0	0
$263$	3.17006	0.195474	0.0977372	−	0.995212i	$-0.468840\pi$
$263$	3.17006	0.195474	0.0977372	+	0.995212i	$0.468840\pi$
$264$	0	0
$265$	6.98921	0.429344
$266$	0	0
$267$	18.9604	1.16036
$268$	0	0
$269$	−14.0342	−0.855682	−0.427841	−	0.903854i	$-0.640726\pi$
$269$	−14.0342	−0.855682	−0.427841	+	0.903854i	$0.640726\pi$
$270$	0	0
$271$	−15.4462	−0.938289	−0.469145	−	0.883121i	$-0.655438\pi$
$271$	−15.4462	−0.938289	−0.469145	+	0.883121i	$0.655438\pi$
$272$	0	0
$273$	−11.6319	−0.703994
$274$	0	0
$275$	−2.75322	−0.166025
$276$	0	0
$277$	6.27613	0.377096	0.188548	−	0.982064i	$-0.439622\pi$
$277$	6.27613	0.377096	0.188548	+	0.982064i	$0.439622\pi$
$278$	0	0
$279$	19.9106	1.19202
$280$	0	0
$281$	23.6209	1.40911	0.704553	−	0.709651i	$-0.251148\pi$
$281$	23.6209	1.40911	0.704553	+	0.709651i	$0.251148\pi$
$282$	0	0
$283$	23.5180	1.39800	0.699001	−	0.715121i	$-0.253628\pi$
$283$	23.5180	1.39800	0.699001	+	0.715121i	$0.253628\pi$
$284$	0	0
$285$	−18.1713	−1.07638
$286$	0	0
$287$	−10.9043	−0.643660
$288$	0	0
$289$	−12.5396	−0.737622
$290$	0	0
$291$	−7.22373	−0.423462
$292$	0	0
$293$	−15.3463	−0.896539	−0.448269	−	0.893899i	$-0.647959\pi$
$293$	−15.3463	−0.896539	−0.448269	+	0.893899i	$0.647959\pi$
$294$	0	0
$295$	0.364042	0.0211954
$296$	0	0
$297$	−31.9036	−1.85124
$298$	0	0
$299$	−7.90044	−0.456894
$300$	0	0
$301$	−3.15296	−0.181734
$302$	0	0
$303$	32.1104	1.84469
$304$	0	0
$305$	12.1768	0.697243
$306$	0	0
$307$	−23.9201	−1.36519	−0.682596	−	0.730796i	$-0.739149\pi$
$307$	−23.9201	−1.36519	−0.682596	+	0.730796i	$0.739149\pi$
$308$	0	0
$309$	−7.85144	−0.446653
$310$	0	0
$311$	2.64527	0.149999	0.0749997	−	0.997184i	$-0.476104\pi$
$311$	2.64527	0.149999	0.0749997	+	0.997184i	$0.476104\pi$
$312$	0	0
$313$	21.7078	1.22700	0.613498	−	0.789697i	$-0.289762\pi$
$313$	21.7078	1.22700	0.613498	+	0.789697i	$0.289762\pi$
$314$	0	0
$315$	6.47601	0.364882
$316$	0	0
$317$	8.24907	0.463314	0.231657	−	0.972798i	$-0.425585\pi$
$317$	8.24907	0.463314	0.231657	+	0.972798i	$0.425585\pi$
$318$	0	0
$319$	−2.75322	−0.154150
$320$	0	0
$321$	−25.3608	−1.41550
$322$	0	0
$323$	12.3112	0.685016
$324$	0	0
$325$	3.87047	0.214695
$326$	0	0
$327$	10.3199	0.570691
$328$	0	0
$329$	−0.390693	−0.0215396
$330$	0	0
$331$	13.2026	0.725680	0.362840	−	0.931851i	$-0.381807\pi$
$331$	13.2026	0.725680	0.362840	+	0.931851i	$0.381807\pi$
$332$	0	0
$333$	−31.9288	−1.74968
$334$	0	0
$335$	1.48130	0.0809321
$336$	0	0
$337$	−21.2573	−1.15796	−0.578979	−	0.815343i	$-0.696549\pi$
$337$	−21.2573	−1.15796	−0.578979	+	0.815343i	$0.696549\pi$
$338$	0	0
$339$	−2.52779	−0.137291
$340$	0	0
$341$	−8.16075	−0.441929
$342$	0	0
$343$	12.6011	0.680393
$344$	0	0
$345$	6.36297	0.342571
$346$	0	0
$347$	21.6421	1.16181	0.580903	−	0.813973i	$-0.302700\pi$
$347$	21.6421	1.16181	0.580903	+	0.813973i	$0.302700\pi$
$348$	0	0
$349$	21.1755	1.13350	0.566750	−	0.823890i	$-0.308200\pi$
$349$	21.1755	1.13350	0.566750	+	0.823890i	$0.308200\pi$
$350$	0	0
$351$	44.8501	2.39392
$352$	0	0
$353$	16.7557	0.891818	0.445909	−	0.895078i	$-0.352881\pi$
$353$	16.7557	0.891818	0.445909	+	0.895078i	$0.352881\pi$
$354$	0	0
$355$	−14.5931	−0.774519
$356$	0	0
$357$	−6.34708	−0.335923
$358$	0	0
$359$	36.0794	1.90420	0.952100	−	0.305788i	$-0.0989198\pi$
$359$	36.0794	1.90420	0.952100	+	0.305788i	$0.0989198\pi$
$360$	0	0
$361$	14.9803	0.788439
$362$	0	0
$363$	−10.6604	−0.559527
$364$	0	0
$365$	2.16416	0.113277
$366$	0	0
$367$	−10.6398	−0.555391	−0.277696	−	0.960669i	$-0.589571\pi$
$367$	−10.6398	−0.555391	−0.277696	+	0.960669i	$0.589571\pi$
$368$	0	0
$369$	75.9764	3.95517
$370$	0	0
$371$	6.73816	0.349828
$372$	0	0
$373$	−34.5533	−1.78910	−0.894551	−	0.446966i	$-0.852504\pi$
$373$	−34.5533	−1.78910	−0.894551	+	0.446966i	$0.852504\pi$
$374$	0	0
$375$	−3.11726	−0.160974
$376$	0	0
$377$	3.87047	0.199340
$378$	0	0
$379$	−16.7616	−0.860988	−0.430494	−	0.902594i	$-0.641661\pi$
$379$	−16.7616	−0.860988	−0.430494	+	0.902594i	$0.641661\pi$
$380$	0	0
$381$	62.0961	3.18128
$382$	0	0
$383$	−12.1536	−0.621019	−0.310510	−	0.950570i	$-0.600500\pi$
$383$	−12.1536	−0.621019	−0.310510	+	0.950570i	$0.600500\pi$
$384$	0	0
$385$	−2.65432	−0.135277
$386$	0	0
$387$	21.9685	1.11672
$388$	0	0
$389$	−27.2142	−1.37981	−0.689907	−	0.723898i	$-0.742349\pi$
$389$	−27.2142	−1.37981	−0.689907	+	0.723898i	$0.742349\pi$
$390$	0	0
$391$	−4.31097	−0.218015
$392$	0	0
$393$	64.2722	3.24210
$394$	0	0
$395$	−14.1933	−0.714143
$396$	0	0
$397$	−31.2624	−1.56901	−0.784507	−	0.620120i	$-0.787084\pi$
$397$	−31.2624	−1.56901	−0.784507	+	0.620120i	$0.787084\pi$
$398$	0	0
$399$	−17.5186	−0.877028
$400$	0	0
$401$	21.7876	1.08802	0.544011	−	0.839078i	$-0.316905\pi$
$401$	21.7876	1.08802	0.544011	+	0.839078i	$0.316905\pi$
$402$	0	0
$403$	11.4724	0.571481
$404$	0	0
$405$	−15.9702	−0.793564
$406$	0	0
$407$	13.0866	0.648680
$408$	0	0
$409$	−26.0141	−1.28632	−0.643158	−	0.765734i	$-0.722376\pi$
$409$	−26.0141	−1.28632	−0.643158	+	0.765734i	$0.722376\pi$
$410$	0	0
$411$	28.5835	1.40992
$412$	0	0
$413$	0.350966	0.0172699
$414$	0	0
$415$	11.3463	0.556967
$416$	0	0
$417$	−44.8330	−2.19548
$418$	0	0
$419$	40.8104	1.99372	0.996860	−	0.0791875i	$-0.0252326\pi$
$419$	40.8104	1.99372	0.996860	+	0.0791875i	$0.0252326\pi$
$420$	0	0
$421$	−30.5685	−1.48982	−0.744909	−	0.667166i	$-0.767507\pi$
$421$	−30.5685	−1.48982	−0.744909	+	0.667166i	$0.767507\pi$
$422$	0	0
$423$	2.72218	0.132357
$424$	0	0
$425$	2.11197	0.102446
$426$	0	0
$427$	11.7394	0.568111
$428$	0	0
$429$	−33.2183	−1.60379
$430$	0	0
$431$	−3.59727	−0.173274	−0.0866371	−	0.996240i	$-0.527612\pi$
$431$	−3.59727	−0.173274	−0.0866371	+	0.996240i	$0.527612\pi$
$432$	0	0
$433$	−20.8837	−1.00361	−0.501804	−	0.864981i	$-0.667330\pi$
$433$	−20.8837	−1.00361	−0.501804	+	0.864981i	$0.667330\pi$
$434$	0	0
$435$	−3.11726	−0.149461
$436$	0	0
$437$	−11.8987	−0.569194
$438$	0	0
$439$	27.2409	1.30014	0.650068	−	0.759876i	$-0.274740\pi$
$439$	27.2409	1.30014	0.650068	+	0.759876i	$0.274740\pi$
$440$	0	0
$441$	−40.7777	−1.94179
$442$	0	0
$443$	26.7145	1.26925	0.634623	−	0.772822i	$-0.281156\pi$
$443$	26.7145	1.26925	0.634623	+	0.772822i	$0.281156\pi$
$444$	0	0
$445$	−6.08241	−0.288334
$446$	0	0
$447$	−9.27738	−0.438805
$448$	0	0
$449$	−35.6862	−1.68413	−0.842067	−	0.539372i	$-0.818662\pi$
$449$	−35.6862	−1.68413	−0.842067	+	0.539372i	$0.818662\pi$
$450$	0	0
$451$	−31.1404	−1.46635
$452$	0	0
$453$	3.57827	0.168122
$454$	0	0
$455$	3.73145	0.174933
$456$	0	0
$457$	6.27613	0.293585	0.146792	−	0.989167i	$-0.453105\pi$
$457$	6.27613	0.293585	0.146792	+	0.989167i	$0.453105\pi$
$458$	0	0
$459$	24.4730	1.14230
$460$	0	0
$461$	−8.47857	−0.394886	−0.197443	−	0.980314i	$-0.563264\pi$
$461$	−8.47857	−0.394886	−0.197443	+	0.980314i	$0.563264\pi$
$462$	0	0
$463$	−9.89622	−0.459916	−0.229958	−	0.973201i	$-0.573859\pi$
$463$	−9.89622	−0.459916	−0.229958	+	0.973201i	$0.573859\pi$
$464$	0	0
$465$	−9.23980	−0.428486
$466$	0	0
$467$	−22.2592	−1.03003	−0.515016	−	0.857180i	$-0.672214\pi$
$467$	−22.2592	−1.03003	−0.515016	+	0.857180i	$0.672214\pi$
$468$	0	0
$469$	1.42809	0.0659432
$470$	0	0
$471$	−4.97125	−0.229063
$472$	0	0
$473$	−9.00421	−0.414014
$474$	0	0
$475$	5.82927	0.267465
$476$	0	0
$477$	−46.9486	−2.14963
$478$	0	0
$479$	0.00340484	0.000155571 0	7.77855e−5	−	1.00000i	$-0.499975\pi$
$479$	0.00340484	0.000155571 0	7.77855e−5		1.00000i	$0.499975\pi$
$480$	0	0
$481$	−18.3972	−0.838840
$482$	0	0
$483$	6.13441	0.279125
$484$	0	0
$485$	2.31733	0.105225
$486$	0	0
$487$	3.25036	0.147288	0.0736440	−	0.997285i	$-0.476537\pi$
$487$	3.25036	0.147288	0.0736440	+	0.997285i	$0.476537\pi$
$488$	0	0
$489$	−64.7793	−2.92942
$490$	0	0
$491$	25.5200	1.15170	0.575850	−	0.817556i	$-0.304671\pi$
$491$	25.5200	1.15170	0.575850	+	0.817556i	$0.304671\pi$
$492$	0	0
$493$	2.11197	0.0951184
$494$	0	0
$495$	18.4942	0.831251
$496$	0	0
$497$	−14.0689	−0.631075
$498$	0	0
$499$	−5.12020	−0.229212	−0.114606	−	0.993411i	$-0.536561\pi$
$499$	−5.12020	−0.229212	−0.114606	+	0.993411i	$0.536561\pi$
$500$	0	0
$501$	66.3586	2.96469
$502$	0	0
$503$	−1.66363	−0.0741776	−0.0370888	−	0.999312i	$-0.511808\pi$
$503$	−1.66363	−0.0741776	−0.0370888	+	0.999312i	$0.511808\pi$
$504$	0	0
$505$	−10.3009	−0.458382
$506$	0	0
$507$	6.17392	0.274193
$508$	0	0
$509$	7.70229	0.341398	0.170699	−	0.985323i	$-0.445397\pi$
$509$	7.70229	0.341398	0.170699	+	0.985323i	$0.445397\pi$
$510$	0	0
$511$	2.08642	0.0922978
$512$	0	0
$513$	67.5482	2.98233
$514$	0	0
$515$	2.51870	0.110987
$516$	0	0
$517$	−1.11574	−0.0490701
$518$	0	0
$519$	61.1338	2.68348
$520$	0	0
$521$	−22.1948	−0.972370	−0.486185	−	0.873856i	$-0.661612\pi$
$521$	−22.1948	−0.972370	−0.486185	+	0.873856i	$0.661612\pi$
$522$	0	0
$523$	−44.0373	−1.92562	−0.962809	−	0.270184i	$-0.912916\pi$
$523$	−44.0373	−1.92562	−0.962809	+	0.270184i	$0.912916\pi$
$524$	0	0
$525$	−3.00529	−0.131161
$526$	0	0
$527$	6.26005	0.272692
$528$	0	0
$529$	−18.8335	−0.818847
$530$	0	0
$531$	−2.44538	−0.106120
$532$	0	0
$533$	43.7772	1.89620
$534$	0	0
$535$	8.13562	0.351734
$536$	0	0
$537$	45.1630	1.94893
$538$	0	0
$539$	16.7135	0.719903
$540$	0	0
$541$	32.3822	1.39222	0.696110	−	0.717936i	$-0.254913\pi$
$541$	32.3822	1.39222	0.696110	+	0.717936i	$0.254913\pi$
$542$	0	0
$543$	66.9047	2.87115
$544$	0	0
$545$	−3.31057	−0.141809
$546$	0	0
$547$	−9.51449	−0.406810	−0.203405	−	0.979095i	$-0.565201\pi$
$547$	−9.51449	−0.406810	−0.203405	+	0.979095i	$0.565201\pi$
$548$	0	0
$549$	−81.7954	−3.49094
$550$	0	0
$551$	5.82927	0.248335
$552$	0	0
$553$	−13.6835	−0.581881
$554$	0	0
$555$	14.8170	0.628947
$556$	0	0
$557$	15.7329	0.666625	0.333312	−	0.942816i	$-0.391834\pi$
$557$	15.7329	0.666625	0.333312	+	0.942816i	$0.391834\pi$
$558$	0	0
$559$	12.6581	0.535382
$560$	0	0
$561$	−18.1259	−0.765278
$562$	0	0
$563$	−14.9626	−0.630597	−0.315299	−	0.948992i	$-0.602105\pi$
$563$	−14.9626	−0.630597	−0.315299	+	0.948992i	$0.602105\pi$
$564$	0	0
$565$	0.810903	0.0341149
$566$	0	0
$567$	−15.3965	−0.646594
$568$	0	0
$569$	−12.8491	−0.538664	−0.269332	−	0.963047i	$-0.586803\pi$
$569$	−12.8491	−0.538664	−0.269332	+	0.963047i	$0.586803\pi$
$570$	0	0
$571$	−37.2419	−1.55852	−0.779262	−	0.626698i	$-0.784406\pi$
$571$	−37.2419	−1.55852	−0.779262	+	0.626698i	$0.784406\pi$
$572$	0	0
$573$	39.0365	1.63077
$574$	0	0
$575$	−2.04121	−0.0851242
$576$	0	0
$577$	44.3355	1.84571	0.922855	−	0.385147i	$-0.125849\pi$
$577$	44.3355	1.84571	0.922855	+	0.385147i	$0.125849\pi$
$578$	0	0
$579$	75.1256	3.12211
$580$	0	0
$581$	10.9387	0.453814
$582$	0	0
$583$	19.2428	0.796955
$584$	0	0
$585$	−25.9991	−1.07493
$586$	0	0
$587$	22.8812	0.944409	0.472204	−	0.881489i	$-0.343458\pi$
$587$	22.8812	0.944409	0.472204	+	0.881489i	$0.343458\pi$
$588$	0	0
$589$	17.2784	0.711945
$590$	0	0
$591$	34.0935	1.40242
$592$	0	0
$593$	31.3127	1.28586	0.642930	−	0.765925i	$-0.277719\pi$
$593$	31.3127	1.28586	0.642930	+	0.765925i	$0.277719\pi$
$594$	0	0
$595$	2.03611	0.0834724
$596$	0	0
$597$	29.4713	1.20618
$598$	0	0
$599$	−28.4022	−1.16048	−0.580241	−	0.814445i	$-0.697042\pi$
$599$	−28.4022	−1.16048	−0.580241	+	0.814445i	$0.697042\pi$
$600$	0	0
$601$	−15.7817	−0.643751	−0.321875	−	0.946782i	$-0.604313\pi$
$601$	−15.7817	−0.643751	−0.321875	+	0.946782i	$0.604313\pi$
$602$	0	0
$603$	−9.95033	−0.405209
$604$	0	0
$605$	3.41981	0.139035
$606$	0	0
$607$	−1.66363	−0.0675247	−0.0337623	−	0.999430i	$-0.510749\pi$
$607$	−1.66363	−0.0675247	−0.0337623	+	0.999430i	$0.510749\pi$
$608$	0	0
$609$	−3.00529	−0.121780
$610$	0	0
$611$	1.56851	0.0634549
$612$	0	0
$613$	13.6727	0.552236	0.276118	−	0.961124i	$-0.410952\pi$
$613$	13.6727	0.552236	0.276118	+	0.961124i	$0.410952\pi$
$614$	0	0
$615$	−35.2580	−1.42174
$616$	0	0
$617$	−32.4350	−1.30578	−0.652891	−	0.757452i	$-0.726444\pi$
$617$	−32.4350	−1.30578	−0.652891	+	0.757452i	$0.726444\pi$
$618$	0	0
$619$	−8.62307	−0.346590	−0.173295	−	0.984870i	$-0.555441\pi$
$619$	−8.62307	−0.346590	−0.173295	+	0.984870i	$0.555441\pi$
$620$	0	0
$621$	−23.6530	−0.949163
$622$	0	0
$623$	−5.86394	−0.234934
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	−50.0296	−1.99799
$628$	0	0
$629$	−10.0387	−0.400267
$630$	0	0
$631$	−26.8341	−1.06825	−0.534124	−	0.845406i	$-0.679358\pi$
$631$	−26.8341	−1.06825	−0.534124	+	0.845406i	$0.679358\pi$
$632$	0	0
$633$	−44.9251	−1.78561
$634$	0	0
$635$	−19.9201	−0.790505
$636$	0	0
$637$	−23.4959	−0.930941
$638$	0	0
$639$	98.0259	3.87784
$640$	0	0
$641$	−28.4967	−1.12555	−0.562776	−	0.826610i	$-0.690266\pi$
$641$	−28.4967	−1.12555	−0.562776	+	0.826610i	$0.690266\pi$
$642$	0	0
$643$	7.82438	0.308563	0.154282	−	0.988027i	$-0.450694\pi$
$643$	7.82438	0.308563	0.154282	+	0.988027i	$0.450694\pi$
$644$	0	0
$645$	−10.1948	−0.401419
$646$	0	0
$647$	−8.78640	−0.345429	−0.172715	−	0.984972i	$-0.555254\pi$
$647$	−8.78640	−0.345429	−0.172715	+	0.984972i	$0.555254\pi$
$648$	0	0
$649$	1.00229	0.0393432
$650$	0	0
$651$	−8.90791	−0.349129
$652$	0	0
$653$	−44.2983	−1.73353	−0.866763	−	0.498720i	$-0.833804\pi$
$653$	−44.2983	−1.73353	−0.866763	+	0.498720i	$0.833804\pi$
$654$	0	0
$655$	−20.6182	−0.805619
$656$	0	0
$657$	−14.5373	−0.567153
$658$	0	0
$659$	−25.9590	−1.01122	−0.505609	−	0.862763i	$-0.668732\pi$
$659$	−25.9590	−1.01122	−0.505609	+	0.862763i	$0.668732\pi$
$660$	0	0
$661$	19.7424	0.767892	0.383946	−	0.923356i	$-0.374565\pi$
$661$	19.7424	0.767892	0.383946	+	0.923356i	$0.374565\pi$
$662$	0	0
$663$	25.4815	0.989619
$664$	0	0
$665$	5.61988	0.217930
$666$	0	0
$667$	−2.04121	−0.0790358
$668$	0	0
$669$	−65.1831	−2.52012
$670$	0	0
$671$	33.5254	1.29423
$672$	0	0
$673$	4.15506	0.160166	0.0800829	−	0.996788i	$-0.474481\pi$
$673$	4.15506	0.160166	0.0800829	+	0.996788i	$0.474481\pi$
$674$	0	0
$675$	11.5878	0.446013
$676$	0	0
$677$	−26.0828	−1.00244	−0.501221	−	0.865319i	$-0.667116\pi$
$677$	−26.0828	−1.00244	−0.501221	+	0.865319i	$0.667116\pi$
$678$	0	0
$679$	2.23410	0.0857367
$680$	0	0
$681$	27.9841	1.07235
$682$	0	0
$683$	28.8969	1.10571	0.552854	−	0.833278i	$-0.313539\pi$
$683$	28.8969	1.10571	0.552854	+	0.833278i	$0.313539\pi$
$684$	0	0
$685$	−9.16944	−0.350346
$686$	0	0
$687$	−62.7725	−2.39492
$688$	0	0
$689$	−27.0516	−1.03058
$690$	0	0
$691$	0.458915	0.0174579	0.00872897	−	0.999962i	$-0.497221\pi$
$691$	0.458915	0.0174579	0.00872897	+	0.999962i	$0.497221\pi$
$692$	0	0
$693$	17.8299	0.677300
$694$	0	0
$695$	14.3822	0.545548
$696$	0	0
$697$	23.8876	0.904807
$698$	0	0
$699$	−52.5856	−1.98897
$700$	0	0
$701$	−46.5073	−1.75655	−0.878277	−	0.478152i	$-0.841307\pi$
$701$	−46.5073	−1.75655	−0.878277	+	0.478152i	$0.841307\pi$
$702$	0	0
$703$	−27.7078	−1.04502
$704$	0	0
$705$	−1.26327	−0.0475773
$706$	0	0
$707$	−9.93085	−0.373488
$708$	0	0
$709$	32.2735	1.21206	0.606029	−	0.795442i	$-0.292761\pi$
$709$	32.2735	1.21206	0.606029	+	0.795442i	$0.292761\pi$
$710$	0	0
$711$	95.3407	3.57555
$712$	0	0
$713$	−6.05030	−0.226586
$714$	0	0
$715$	10.6562	0.398521
$716$	0	0
$717$	−12.1154	−0.452457
$718$	0	0
$719$	−26.5821	−0.991343	−0.495672	−	0.868510i	$-0.665078\pi$
$719$	−26.5821	−0.991343	−0.495672	+	0.868510i	$0.665078\pi$
$720$	0	0
$721$	2.42823	0.0904320
$722$	0	0
$723$	8.73719	0.324940
$724$	0	0
$725$	1.00000	0.0371391
$726$	0	0
$727$	−12.9998	−0.482135	−0.241067	−	0.970508i	$-0.577497\pi$
$727$	−12.9998	−0.482135	−0.241067	+	0.970508i	$0.577497\pi$
$728$	0	0
$729$	−1.08980	−0.0403630
$730$	0	0
$731$	6.90706	0.255467
$732$	0	0
$733$	−9.44834	−0.348982	−0.174491	−	0.984659i	$-0.555828\pi$
$733$	−9.44834	−0.348982	−0.174491	+	0.984659i	$0.555828\pi$
$734$	0	0
$735$	18.9235	0.698003
$736$	0	0
$737$	4.07834	0.150228
$738$	0	0
$739$	14.2700	0.524930	0.262465	−	0.964941i	$-0.415465\pi$
$739$	14.2700	0.524930	0.262465	+	0.964941i	$0.415465\pi$
$740$	0	0
$741$	70.3316	2.58370
$742$	0	0
$743$	−44.4064	−1.62911	−0.814557	−	0.580084i	$-0.803020\pi$
$743$	−44.4064	−1.62911	−0.814557	+	0.580084i	$0.803020\pi$
$744$	0	0
$745$	2.97613	0.109037
$746$	0	0
$747$	−76.2163	−2.78861
$748$	0	0
$749$	7.84339	0.286591
$750$	0	0
$751$	−17.6534	−0.644183	−0.322092	−	0.946709i	$-0.604386\pi$
$751$	−17.6534	−0.644183	−0.322092	+	0.946709i	$0.604386\pi$
$752$	0	0
$753$	49.4711	1.80283
$754$	0	0
$755$	−1.14789	−0.0417760
$756$	0	0
$757$	−7.76504	−0.282225	−0.141113	−	0.989994i	$-0.545068\pi$
$757$	−7.76504	−0.282225	−0.141113	+	0.989994i	$0.545068\pi$
$758$	0	0
$759$	17.5186	0.635886
$760$	0	0
$761$	−32.6141	−1.18226	−0.591131	−	0.806576i	$-0.701318\pi$
$761$	−32.6141	−1.18226	−0.591131	+	0.806576i	$0.701318\pi$
$762$	0	0
$763$	−3.19165	−0.115546
$764$	0	0
$765$	−14.1867	−0.512922
$766$	0	0
$767$	−1.40902	−0.0508766
$768$	0	0
$769$	−6.53030	−0.235488	−0.117744	−	0.993044i	$-0.537566\pi$
$769$	−6.53030	−0.235488	−0.117744	+	0.993044i	$0.537566\pi$
$770$	0	0
$771$	−51.0267	−1.83768
$772$	0	0
$773$	10.8419	0.389956	0.194978	−	0.980808i	$-0.437536\pi$
$773$	10.8419	0.389956	0.194978	+	0.980808i	$0.437536\pi$
$774$	0	0
$775$	2.96408	0.106473
$776$	0	0
$777$	14.2848	0.512463
$778$	0	0
$779$	65.9323	2.36227
$780$	0	0
$781$	−40.1778	−1.43768
$782$	0	0
$783$	11.5878	0.414113
$784$	0	0
$785$	1.59475	0.0569191
$786$	0	0
$787$	18.1943	0.648557	0.324278	−	0.945962i	$-0.394879\pi$
$787$	18.1943	0.648557	0.324278	+	0.945962i	$0.394879\pi$
$788$	0	0
$789$	9.88190	0.351805
$790$	0	0
$791$	0.781776	0.0277967
$792$	0	0
$793$	−47.1301	−1.67364
$794$	0	0
$795$	21.7872	0.772711
$796$	0	0
$797$	−0.272145	−0.00963986	−0.00481993	−	0.999988i	$-0.501534\pi$
$797$	−0.272145	−0.00963986	−0.00481993	+	0.999988i	$0.501534\pi$
$798$	0	0
$799$	0.855874	0.0302787
$800$	0	0
$801$	40.8574	1.44362
$802$	0	0
$803$	5.95839	0.210267
$804$	0	0
$805$	−1.96789	−0.0693589
$806$	0	0
$807$	−43.7483	−1.54001
$808$	0	0
$809$	−56.6806	−1.99278	−0.996392	−	0.0848672i	$-0.972953\pi$
$809$	−56.6806	−1.99278	−0.996392	+	0.0848672i	$0.972953\pi$
$810$	0	0
$811$	11.5299	0.404868	0.202434	−	0.979296i	$-0.435115\pi$
$811$	11.5299	0.404868	0.202434	+	0.979296i	$0.435115\pi$
$812$	0	0
$813$	−48.1497	−1.68869
$814$	0	0
$815$	20.7809	0.727922
$816$	0	0
$817$	19.0642	0.666973
$818$	0	0
$819$	−25.0652	−0.875850
$820$	0	0
$821$	−20.7538	−0.724313	−0.362156	−	0.932117i	$-0.617959\pi$
$821$	−20.7538	−0.724313	−0.362156	+	0.932117i	$0.617959\pi$
$822$	0	0
$823$	24.0287	0.837587	0.418793	−	0.908082i	$-0.362453\pi$
$823$	24.0287	0.837587	0.418793	+	0.908082i	$0.362453\pi$
$824$	0	0
$825$	−8.58248	−0.298804
$826$	0	0
$827$	−53.3130	−1.85387	−0.926937	−	0.375216i	$-0.877569\pi$
$827$	−53.3130	−1.85387	−0.926937	+	0.375216i	$0.877569\pi$
$828$	0	0
$829$	51.8419	1.80054	0.900272	−	0.435328i	$-0.143368\pi$
$829$	51.8419	1.80054	0.900272	+	0.435328i	$0.143368\pi$
$830$	0	0
$831$	19.5643	0.678678
$832$	0	0
$833$	−12.8208	−0.444215
$834$	0	0
$835$	−21.2875	−0.736685
$836$	0	0
$837$	34.3471	1.18721
$838$	0	0
$839$	5.77493	0.199373	0.0996864	−	0.995019i	$-0.468216\pi$
$839$	5.77493	0.199373	0.0996864	+	0.995019i	$0.468216\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	0	0
$843$	73.6325	2.53604
$844$	0	0
$845$	−1.98056	−0.0681334
$846$	0	0
$847$	3.29697	0.113285
$848$	0	0
$849$	73.3118	2.51605
$850$	0	0
$851$	9.70229	0.332590
$852$	0	0
$853$	13.3659	0.457641	0.228820	−	0.973469i	$-0.426513\pi$
$853$	13.3659	0.457641	0.228820	+	0.973469i	$0.426513\pi$
$854$	0	0
$855$	−39.1569	−1.33914
$856$	0	0
$857$	16.7528	0.572264	0.286132	−	0.958190i	$-0.407630\pi$
$857$	16.7528	0.572264	0.286132	+	0.958190i	$0.407630\pi$
$858$	0	0
$859$	−10.8927	−0.371654	−0.185827	−	0.982582i	$-0.559496\pi$
$859$	−10.8927	−0.371654	−0.185827	+	0.982582i	$0.559496\pi$
$860$	0	0
$861$	−33.9915	−1.15843
$862$	0	0
$863$	−12.8210	−0.436434	−0.218217	−	0.975900i	$-0.570024\pi$
$863$	−12.8210	−0.436434	−0.218217	+	0.975900i	$0.570024\pi$
$864$	0	0
$865$	−19.6114	−0.666808
$866$	0	0
$867$	−39.0891	−1.32754
$868$	0	0
$869$	−39.0772	−1.32560
$870$	0	0
$871$	−5.73333	−0.194267
$872$	0	0
$873$	−15.5662	−0.526837
$874$	0	0
$875$	0.964080	0.0325919
$876$	0	0
$877$	−57.1419	−1.92954	−0.964772	−	0.263089i	$-0.915259\pi$
$877$	−57.1419	−1.92954	−0.964772	+	0.263089i	$0.915259\pi$
$878$	0	0
$879$	−47.8383	−1.61355
$880$	0	0
$881$	−7.16689	−0.241459	−0.120729	−	0.992685i	$-0.538523\pi$
$881$	−7.16689	−0.241459	−0.120729	+	0.992685i	$0.538523\pi$
$882$	0	0
$883$	−34.8070	−1.17135	−0.585675	−	0.810546i	$-0.699170\pi$
$883$	−34.8070	−1.17135	−0.585675	+	0.810546i	$0.699170\pi$
$884$	0	0
$885$	1.13481	0.0381464
$886$	0	0
$887$	−30.0452	−1.00882	−0.504409	−	0.863465i	$-0.668290\pi$
$887$	−30.0452	−1.00882	−0.504409	+	0.863465i	$0.668290\pi$
$888$	0	0
$889$	−19.2046	−0.644101
$890$	0	0
$891$	−43.9693	−1.47303
$892$	0	0
$893$	2.36230	0.0790515
$894$	0	0
$895$	−14.4881	−0.484283
$896$	0	0
$897$	−24.6277	−0.822295
$898$	0	0
$899$	2.96408	0.0988576
$900$	0	0
$901$	−14.7610	−0.491760
$902$	0	0
$903$	−9.82860	−0.327075
$904$	0	0
$905$	−21.4627	−0.713443
$906$	0	0
$907$	−9.09718	−0.302067	−0.151034	−	0.988529i	$-0.548260\pi$
$907$	−9.09718	−0.302067	−0.151034	+	0.988529i	$0.548260\pi$
$908$	0	0
$909$	69.1939	2.29502
$910$	0	0
$911$	−2.71749	−0.0900343	−0.0450172	−	0.998986i	$-0.514334\pi$
$911$	−2.71749	−0.0900343	−0.0450172	+	0.998986i	$0.514334\pi$
$912$	0	0
$913$	31.2387	1.03385
$914$	0	0
$915$	37.9583	1.25486
$916$	0	0
$917$	−19.8776	−0.656416
$918$	0	0
$919$	47.5311	1.56791	0.783953	−	0.620820i	$-0.213200\pi$
$919$	47.5311	1.56791	0.783953	+	0.620820i	$0.213200\pi$
$920$	0	0
$921$	−74.5651	−2.45700
$922$	0	0
$923$	56.4820	1.85913
$924$	0	0
$925$	−4.75322	−0.156285
$926$	0	0
$927$	−16.9189	−0.555688
$928$	0	0
$929$	25.8413	0.847826	0.423913	−	0.905703i	$-0.360656\pi$
$929$	25.8413	0.847826	0.423913	+	0.905703i	$0.360656\pi$
$930$	0	0
$931$	−35.3868	−1.15976
$932$	0	0
$933$	8.24598	0.269961
$934$	0	0
$935$	5.81471	0.190161
$936$	0	0
$937$	−15.7023	−0.512972	−0.256486	−	0.966548i	$-0.582565\pi$
$937$	−15.7023	−0.512972	−0.256486	+	0.966548i	$0.582565\pi$
$938$	0	0
$939$	67.6687	2.20828
$940$	0	0
$941$	−5.36829	−0.175001	−0.0875007	−	0.996164i	$-0.527888\pi$
$941$	−5.36829	−0.175001	−0.0875007	+	0.996164i	$0.527888\pi$
$942$	0	0
$943$	−23.0872	−0.751823
$944$	0	0
$945$	11.1715	0.363410
$946$	0	0
$947$	26.0799	0.847482	0.423741	−	0.905784i	$-0.360717\pi$
$947$	26.0799	0.847482	0.423741	+	0.905784i	$0.360717\pi$
$948$	0	0
$949$	−8.37631	−0.271906
$950$	0	0
$951$	25.7145	0.833849
$952$	0	0
$953$	44.1512	1.43020	0.715100	−	0.699023i	$-0.246381\pi$
$953$	44.1512	1.43020	0.715100	+	0.699023i	$0.246381\pi$
$954$	0	0
$955$	−12.5227	−0.405225
$956$	0	0
$957$	−8.58248	−0.277432
$958$	0	0
$959$	−8.84008	−0.285461
$960$	0	0
$961$	−22.2142	−0.716588
$962$	0	0
$963$	−54.6494	−1.76105
$964$	0	0
$965$	−24.0999	−0.775803
$966$	0	0
$967$	0.237462	0.00763627	0.00381813	−	0.999993i	$-0.498785\pi$
$967$	0.237462	0.00763627	0.00381813	+	0.999993i	$0.498785\pi$
$968$	0	0
$969$	38.3773	1.23286
$970$	0	0
$971$	−58.7571	−1.88561	−0.942803	−	0.333350i	$-0.891821\pi$
$971$	−58.7571	−1.88561	−0.942803	+	0.333350i	$0.891821\pi$
$972$	0	0
$973$	13.8656	0.444510
$974$	0	0
$975$	12.0653	0.386398
$976$	0	0
$977$	19.4403	0.621950	0.310975	−	0.950418i	$-0.399345\pi$
$977$	19.4403	0.621950	0.310975	+	0.950418i	$0.399345\pi$
$978$	0	0
$979$	−16.7462	−0.535211
$980$	0	0
$981$	22.2381	0.710006
$982$	0	0
$983$	5.20340	0.165963	0.0829814	−	0.996551i	$-0.473556\pi$
$983$	5.20340	0.165963	0.0829814	+	0.996551i	$0.473556\pi$
$984$	0	0
$985$	−10.9370	−0.348483
$986$	0	0
$987$	−1.21789	−0.0387659
$988$	0	0
$989$	−6.67563	−0.212273
$990$	0	0
$991$	−16.8757	−0.536074	−0.268037	−	0.963409i	$-0.586375\pi$
$991$	−16.8757	−0.536074	−0.268037	+	0.963409i	$0.586375\pi$
$992$	0	0
$993$	41.1559	1.30604
$994$	0	0
$995$	−9.45424	−0.299720
$996$	0	0
$997$	27.1836	0.860913	0.430457	−	0.902611i	$-0.358353\pi$
$997$	27.1836	0.860913	0.430457	+	0.902611i	$0.358353\pi$
$998$	0	0
$999$	−55.0792	−1.74263

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9280.2.a.cj.1.5		5
4.3	odd	2		9280.2.a.ch.1.1		5
8.3	odd	2		2320.2.a.w.1.5		5
8.5	even	2		1160.2.a.i.1.1	✓	5
40.29	even	2		5800.2.a.v.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1160.2.a.i.1.1	✓	5	8.5	even	2
2320.2.a.w.1.5		5	8.3	odd	2
5800.2.a.v.1.5		5	40.29	even	2
9280.2.a.ch.1.1		5	4.3	odd	2
9280.2.a.cj.1.5		5	1.1	even	1	trivial

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Hilbert	Bianchi

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	9280.2.a.cj.1.5

Level	$9280$
Weight	$2$
Character	9280.1
Self dual	yes
Analytic conductor	$74.101$
Analytic rank	$0$
Dimension	$5$
CM	no
Inner twists	$1$