LMFDB - Embedded newform 2800.2.a.x.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2800,2,Mod(1,2800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2800, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2800.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2800 = 2^{4} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2800.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:	$22.3581125660$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 350)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2800.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{3} +1.00000 q^{7} -2.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{3} +1.00000 q^{7} -2.00000 q^{9} -3.00000 q^{11} -2.00000 q^{13} -3.00000 q^{17} +7.00000 q^{19} +1.00000 q^{21} -5.00000 q^{27} -6.00000 q^{29} +4.00000 q^{31} -3.00000 q^{33} -8.00000 q^{37} -2.00000 q^{39} -9.00000 q^{41} +8.00000 q^{43} -6.00000 q^{47} +1.00000 q^{49} -3.00000 q^{51} +12.0000 q^{53} +7.00000 q^{57} -12.0000 q^{59} -10.0000 q^{61} -2.00000 q^{63} -7.00000 q^{67} -6.00000 q^{71} -5.00000 q^{73} -3.00000 q^{77} -14.0000 q^{79} +1.00000 q^{81} -9.00000 q^{83} -6.00000 q^{87} -15.0000 q^{89} -2.00000 q^{91} +4.00000 q^{93} +10.0000 q^{97} +6.00000 q^{99} +O(q^{100})$

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
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0	0
$9$	−2.00000	−0.666667
$10$	0	0
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	0	0
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	0	0
$19$	7.00000	1.60591	0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000	1.60591	0.802955	+	0.596040i	$0.203260\pi$
$20$	0	0
$21$	1.00000	0.218218
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−5.00000	−0.962250
$28$	0	0
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	0	0
$33$	−3.00000	−0.522233
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	0	0
$39$	−2.00000	−0.320256
$40$	0	0
$41$	−9.00000	−1.40556	−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000	−1.40556	−0.702782	+	0.711405i	$0.748059\pi$
$42$	0	0
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	−3.00000	−0.420084
$52$	0	0
$53$	12.0000	1.64833	0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000	1.64833	0.824163	+	0.566352i	$0.191646\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	7.00000	0.927173
$58$	0	0
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	0	0
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	0	0
$63$	−2.00000	−0.251976
$64$	0	0
$65$	0	0
$66$	0	0
$67$	−7.00000	−0.855186	−0.427593	−	0.903971i	$-0.640638\pi$
$67$	−7.00000	−0.855186	−0.427593	+	0.903971i	$0.640638\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	0	0
$73$	−5.00000	−0.585206	−0.292603	−	0.956234i	$-0.594521\pi$
$73$	−5.00000	−0.585206	−0.292603	+	0.956234i	$0.594521\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−3.00000	−0.341882
$78$	0	0
$79$	−14.0000	−1.57512	−0.787562	−	0.616236i	$-0.788657\pi$
$79$	−14.0000	−1.57512	−0.787562	+	0.616236i	$0.788657\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	−9.00000	−0.987878	−0.493939	−	0.869496i	$-0.664443\pi$
$83$	−9.00000	−0.987878	−0.493939	+	0.869496i	$0.664443\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−6.00000	−0.643268
$88$	0	0
$89$	−15.0000	−1.59000	−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000	−1.59000	−0.794998	+	0.606612i	$0.792528\pi$
$90$	0	0
$91$	−2.00000	−0.209657
$92$	0	0
$93$	4.00000	0.414781
$94$	0	0
$95$	0	0
$96$	0	0
$97$	10.0000	1.01535	0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000	1.01535	0.507673	+	0.861550i	$0.330506\pi$
$98$	0	0
$99$	6.00000	0.603023
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	20.0000	1.97066	0.985329	−	0.170664i	$-0.0545913\pi$
$103$	20.0000	1.97066	0.985329	+	0.170664i	$0.0545913\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	3.00000	0.290021	0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000	0.290021	0.145010	+	0.989430i	$0.453678\pi$
$108$	0	0
$109$	14.0000	1.34096	0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000	1.34096	0.670478	+	0.741929i	$0.266089\pi$
$110$	0	0
$111$	−8.00000	−0.759326
$112$	0	0
$113$	9.00000	0.846649	0.423324	−	0.905978i	$-0.360863\pi$
$113$	9.00000	0.846649	0.423324	+	0.905978i	$0.360863\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	4.00000	0.369800
$118$	0	0
$119$	−3.00000	−0.275010
$120$	0	0
$121$	−2.00000	−0.181818
$122$	0	0
$123$	−9.00000	−0.811503
$124$	0	0
$125$	0	0
$126$	0	0
$127$	2.00000	0.177471	0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000	0.177471	0.0887357	+	0.996055i	$0.471717\pi$
$128$	0	0
$129$	8.00000	0.704361
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	7.00000	0.606977
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−21.0000	−1.79415	−0.897076	−	0.441877i	$-0.854313\pi$
$137$	−21.0000	−1.79415	−0.897076	+	0.441877i	$0.854313\pi$
$138$	0	0
$139$	7.00000	0.593732	0.296866	−	0.954919i	$-0.404058\pi$
$139$	7.00000	0.593732	0.296866	+	0.954919i	$0.404058\pi$
$140$	0	0
$141$	−6.00000	−0.505291
$142$	0	0
$143$	6.00000	0.501745
$144$	0	0
$145$	0	0
$146$	0	0
$147$	1.00000	0.0824786
$148$	0	0
$149$	12.0000	0.983078	0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000	0.983078	0.491539	+	0.870855i	$0.336434\pi$
$150$	0	0
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	0	0
$153$	6.00000	0.485071
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−20.0000	−1.59617	−0.798087	−	0.602542i	$-0.794154\pi$
$157$	−20.0000	−1.59617	−0.798087	+	0.602542i	$0.794154\pi$
$158$	0	0
$159$	12.0000	0.951662
$160$	0	0
$161$	0	0
$162$	0	0
$163$	5.00000	0.391630	0.195815	−	0.980641i	$-0.437265\pi$
$163$	5.00000	0.391630	0.195815	+	0.980641i	$0.437265\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	−14.0000	−1.07061
$172$	0	0
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−12.0000	−0.901975
$178$	0	0
$179$	−3.00000	−0.224231	−0.112115	−	0.993695i	$-0.535763\pi$
$179$	−3.00000	−0.224231	−0.112115	+	0.993695i	$0.535763\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	0	0
$183$	−10.0000	−0.739221
$184$	0	0
$185$	0	0
$186$	0	0
$187$	9.00000	0.658145
$188$	0	0
$189$	−5.00000	−0.363696
$190$	0	0
$191$	6.00000	0.434145	0.217072	−	0.976156i	$-0.430349\pi$
$191$	6.00000	0.434145	0.217072	+	0.976156i	$0.430349\pi$
$192$	0	0
$193$	−5.00000	−0.359908	−0.179954	−	0.983675i	$-0.557595\pi$
$193$	−5.00000	−0.359908	−0.179954	+	0.983675i	$0.557595\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	0	0
$199$	−14.0000	−0.992434	−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−14.0000	−0.992434	−0.496217	+	0.868199i	$0.665278\pi$
$200$	0	0
$201$	−7.00000	−0.493742
$202$	0	0
$203$	−6.00000	−0.421117
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	−21.0000	−1.45260
$210$	0	0
$211$	−17.0000	−1.17033	−0.585164	−	0.810915i	$-0.698970\pi$
$211$	−17.0000	−1.17033	−0.585164	+	0.810915i	$0.698970\pi$
$212$	0	0
$213$	−6.00000	−0.411113
$214$	0	0
$215$	0	0
$216$	0	0
$217$	4.00000	0.271538
$218$	0	0
$219$	−5.00000	−0.337869
$220$	0	0
$221$	6.00000	0.403604
$222$	0	0
$223$	14.0000	0.937509	0.468755	−	0.883328i	$-0.344703\pi$
$223$	14.0000	0.937509	0.468755	+	0.883328i	$0.344703\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	0	0
$229$	26.0000	1.71813	0.859064	−	0.511868i	$-0.171046\pi$
$229$	26.0000	1.71813	0.859064	+	0.511868i	$0.171046\pi$
$230$	0	0
$231$	−3.00000	−0.197386
$232$	0	0
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−14.0000	−0.909398
$238$	0	0
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	0	0
$241$	−25.0000	−1.61039	−0.805196	−	0.593009i	$-0.797940\pi$
$241$	−25.0000	−1.61039	−0.805196	+	0.593009i	$0.797940\pi$
$242$	0	0
$243$	16.0000	1.02640
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−14.0000	−0.890799
$248$	0	0
$249$	−9.00000	−0.570352
$250$	0	0
$251$	−15.0000	−0.946792	−0.473396	−	0.880850i	$-0.656972\pi$
$251$	−15.0000	−0.946792	−0.473396	+	0.880850i	$0.656972\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	0	0
$257$	30.0000	1.87135	0.935674	−	0.352865i	$-0.114792\pi$
$257$	30.0000	1.87135	0.935674	+	0.352865i	$0.114792\pi$
$258$	0	0
$259$	−8.00000	−0.497096
$260$	0	0
$261$	12.0000	0.742781
$262$	0	0
$263$	6.00000	0.369976	0.184988	−	0.982741i	$-0.440775\pi$
$263$	6.00000	0.369976	0.184988	+	0.982741i	$0.440775\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−15.0000	−0.917985
$268$	0	0
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	0	0
$271$	−2.00000	−0.121491	−0.0607457	−	0.998153i	$-0.519348\pi$
$271$	−2.00000	−0.121491	−0.0607457	+	0.998153i	$0.519348\pi$
$272$	0	0
$273$	−2.00000	−0.121046
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	0	0
$279$	−8.00000	−0.478947
$280$	0	0
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	0	0
$283$	−1.00000	−0.0594438	−0.0297219	−	0.999558i	$-0.509462\pi$
$283$	−1.00000	−0.0594438	−0.0297219	+	0.999558i	$0.509462\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−9.00000	−0.531253
$288$	0	0
$289$	−8.00000	−0.470588
$290$	0	0
$291$	10.0000	0.586210
$292$	0	0
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	15.0000	0.870388
$298$	0	0
$299$	0	0
$300$	0	0
$301$	8.00000	0.461112
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−7.00000	−0.399511	−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000	−0.399511	−0.199756	+	0.979846i	$0.564015\pi$
$308$	0	0
$309$	20.0000	1.13776
$310$	0	0
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	0	0
$313$	10.0000	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	12.0000	0.673987	0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000	0.673987	0.336994	+	0.941507i	$0.390590\pi$
$318$	0	0
$319$	18.0000	1.00781
$320$	0	0
$321$	3.00000	0.167444
$322$	0	0
$323$	−21.0000	−1.16847
$324$	0	0
$325$	0	0
$326$	0	0
$327$	14.0000	0.774202
$328$	0	0
$329$	−6.00000	−0.330791
$330$	0	0
$331$	25.0000	1.37412	0.687062	−	0.726599i	$-0.258900\pi$
$331$	25.0000	1.37412	0.687062	+	0.726599i	$0.258900\pi$
$332$	0	0
$333$	16.0000	0.876795
$334$	0	0
$335$	0	0
$336$	0	0
$337$	13.0000	0.708155	0.354078	−	0.935216i	$-0.384795\pi$
$337$	13.0000	0.708155	0.354078	+	0.935216i	$0.384795\pi$
$338$	0	0
$339$	9.00000	0.488813
$340$	0	0
$341$	−12.0000	−0.649836
$342$	0	0
$343$	1.00000	0.0539949
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−21.0000	−1.12734	−0.563670	−	0.826000i	$-0.690611\pi$
$347$	−21.0000	−1.12734	−0.563670	+	0.826000i	$0.690611\pi$
$348$	0	0
$349$	8.00000	0.428230	0.214115	−	0.976808i	$-0.431313\pi$
$349$	8.00000	0.428230	0.214115	+	0.976808i	$0.431313\pi$
$350$	0	0
$351$	10.0000	0.533761
$352$	0	0
$353$	−30.0000	−1.59674	−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000	−1.59674	−0.798369	+	0.602168i	$0.794304\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−3.00000	−0.158777
$358$	0	0
$359$	6.00000	0.316668	0.158334	−	0.987386i	$-0.449388\pi$
$359$	6.00000	0.316668	0.158334	+	0.987386i	$0.449388\pi$
$360$	0	0
$361$	30.0000	1.57895
$362$	0	0
$363$	−2.00000	−0.104973
$364$	0	0
$365$	0	0
$366$	0	0
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	0	0
$369$	18.0000	0.937043
$370$	0	0
$371$	12.0000	0.623009
$372$	0	0
$373$	4.00000	0.207112	0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000	0.207112	0.103556	+	0.994624i	$0.466978\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	12.0000	0.618031
$378$	0	0
$379$	−17.0000	−0.873231	−0.436616	−	0.899648i	$-0.643823\pi$
$379$	−17.0000	−0.873231	−0.436616	+	0.899648i	$0.643823\pi$
$380$	0	0
$381$	2.00000	0.102463
$382$	0	0
$383$	−30.0000	−1.53293	−0.766464	−	0.642287i	$-0.777986\pi$
$383$	−30.0000	−1.53293	−0.766464	+	0.642287i	$0.777986\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−16.0000	−0.813326
$388$	0	0
$389$	−24.0000	−1.21685	−0.608424	−	0.793612i	$-0.708198\pi$
$389$	−24.0000	−1.21685	−0.608424	+	0.793612i	$0.708198\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	0	0
$399$	7.00000	0.350438
$400$	0	0
$401$	−27.0000	−1.34832	−0.674158	−	0.738587i	$-0.735493\pi$
$401$	−27.0000	−1.34832	−0.674158	+	0.738587i	$0.735493\pi$
$402$	0	0
$403$	−8.00000	−0.398508
$404$	0	0
$405$	0	0
$406$	0	0
$407$	24.0000	1.18964
$408$	0	0
$409$	−25.0000	−1.23617	−0.618085	−	0.786111i	$-0.712091\pi$
$409$	−25.0000	−1.23617	−0.618085	+	0.786111i	$0.712091\pi$
$410$	0	0
$411$	−21.0000	−1.03585
$412$	0	0
$413$	−12.0000	−0.590481
$414$	0	0
$415$	0	0
$416$	0	0
$417$	7.00000	0.342791
$418$	0	0
$419$	3.00000	0.146560	0.0732798	−	0.997311i	$-0.476653\pi$
$419$	3.00000	0.146560	0.0732798	+	0.997311i	$0.476653\pi$
$420$	0	0
$421$	20.0000	0.974740	0.487370	−	0.873195i	$-0.337956\pi$
$421$	20.0000	0.974740	0.487370	+	0.873195i	$0.337956\pi$
$422$	0	0
$423$	12.0000	0.583460
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−10.0000	−0.483934
$428$	0	0
$429$	6.00000	0.289683
$430$	0	0
$431$	36.0000	1.73406	0.867029	−	0.498257i	$-0.166026\pi$
$431$	36.0000	1.73406	0.867029	+	0.498257i	$0.166026\pi$
$432$	0	0
$433$	−11.0000	−0.528626	−0.264313	−	0.964437i	$-0.585145\pi$
$433$	−11.0000	−0.528626	−0.264313	+	0.964437i	$0.585145\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	4.00000	0.190910	0.0954548	−	0.995434i	$-0.469569\pi$
$439$	4.00000	0.190910	0.0954548	+	0.995434i	$0.469569\pi$
$440$	0	0
$441$	−2.00000	−0.0952381
$442$	0	0
$443$	21.0000	0.997740	0.498870	−	0.866677i	$-0.333748\pi$
$443$	21.0000	0.997740	0.498870	+	0.866677i	$0.333748\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	12.0000	0.567581
$448$	0	0
$449$	−15.0000	−0.707894	−0.353947	−	0.935266i	$-0.615161\pi$
$449$	−15.0000	−0.707894	−0.353947	+	0.935266i	$0.615161\pi$
$450$	0	0
$451$	27.0000	1.27138
$452$	0	0
$453$	−8.00000	−0.375873
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−17.0000	−0.795226	−0.397613	−	0.917553i	$-0.630161\pi$
$457$	−17.0000	−0.795226	−0.397613	+	0.917553i	$0.630161\pi$
$458$	0	0
$459$	15.0000	0.700140
$460$	0	0
$461$	18.0000	0.838344	0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000	0.838344	0.419172	+	0.907907i	$0.362320\pi$
$462$	0	0
$463$	8.00000	0.371792	0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000	0.371792	0.185896	+	0.982569i	$0.440481\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	36.0000	1.66588	0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000	1.66588	0.832941	+	0.553362i	$0.186655\pi$
$468$	0	0
$469$	−7.00000	−0.323230
$470$	0	0
$471$	−20.0000	−0.921551
$472$	0	0
$473$	−24.0000	−1.10352
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−24.0000	−1.09888
$478$	0	0
$479$	−18.0000	−0.822441	−0.411220	−	0.911536i	$-0.634897\pi$
$479$	−18.0000	−0.822441	−0.411220	+	0.911536i	$0.634897\pi$
$480$	0	0
$481$	16.0000	0.729537
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−34.0000	−1.54069	−0.770344	−	0.637629i	$-0.779915\pi$
$487$	−34.0000	−1.54069	−0.770344	+	0.637629i	$0.779915\pi$
$488$	0	0
$489$	5.00000	0.226108
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	0	0
$493$	18.0000	0.810679
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−6.00000	−0.269137
$498$	0	0
$499$	28.0000	1.25345	0.626726	−	0.779240i	$-0.284395\pi$
$499$	28.0000	1.25345	0.626726	+	0.779240i	$0.284395\pi$
$500$	0	0
$501$	12.0000	0.536120
$502$	0	0
$503$	−6.00000	−0.267527	−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000	−0.267527	−0.133763	+	0.991013i	$0.542706\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−9.00000	−0.399704
$508$	0	0
$509$	42.0000	1.86162	0.930809	−	0.365507i	$-0.119104\pi$
$509$	42.0000	1.86162	0.930809	+	0.365507i	$0.119104\pi$
$510$	0	0
$511$	−5.00000	−0.221187
$512$	0	0
$513$	−35.0000	−1.54529
$514$	0	0
$515$	0	0
$516$	0	0
$517$	18.0000	0.791639
$518$	0	0
$519$	6.00000	0.263371
$520$	0	0
$521$	39.0000	1.70862	0.854311	−	0.519763i	$-0.173980\pi$
$521$	39.0000	1.70862	0.854311	+	0.519763i	$0.173980\pi$
$522$	0	0
$523$	−7.00000	−0.306089	−0.153044	−	0.988219i	$-0.548908\pi$
$523$	−7.00000	−0.306089	−0.153044	+	0.988219i	$0.548908\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−12.0000	−0.522728
$528$	0	0
$529$	−23.0000	−1.00000
$530$	0	0
$531$	24.0000	1.04151
$532$	0	0
$533$	18.0000	0.779667
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−3.00000	−0.129460
$538$	0	0
$539$	−3.00000	−0.129219
$540$	0	0
$541$	38.0000	1.63375	0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000	1.63375	0.816874	+	0.576816i	$0.195705\pi$
$542$	0	0
$543$	2.00000	0.0858282
$544$	0	0
$545$	0	0
$546$	0	0
$547$	35.0000	1.49649	0.748246	−	0.663421i	$-0.230896\pi$
$547$	35.0000	1.49649	0.748246	+	0.663421i	$0.230896\pi$
$548$	0	0
$549$	20.0000	0.853579
$550$	0	0
$551$	−42.0000	−1.78926
$552$	0	0
$553$	−14.0000	−0.595341
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−36.0000	−1.52537	−0.762684	−	0.646771i	$-0.776119\pi$
$557$	−36.0000	−1.52537	−0.762684	+	0.646771i	$0.776119\pi$
$558$	0	0
$559$	−16.0000	−0.676728
$560$	0	0
$561$	9.00000	0.379980
$562$	0	0
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	1.00000	0.0419961
$568$	0	0
$569$	−27.0000	−1.13190	−0.565949	−	0.824440i	$-0.691490\pi$
$569$	−27.0000	−1.13190	−0.565949	+	0.824440i	$0.691490\pi$
$570$	0	0
$571$	4.00000	0.167395	0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000	0.167395	0.0836974	+	0.996491i	$0.473327\pi$
$572$	0	0
$573$	6.00000	0.250654
$574$	0	0
$575$	0	0
$576$	0	0
$577$	7.00000	0.291414	0.145707	−	0.989328i	$-0.453454\pi$
$577$	7.00000	0.291414	0.145707	+	0.989328i	$0.453454\pi$
$578$	0	0
$579$	−5.00000	−0.207793
$580$	0	0
$581$	−9.00000	−0.373383
$582$	0	0
$583$	−36.0000	−1.49097
$584$	0	0
$585$	0	0
$586$	0	0
$587$	39.0000	1.60970	0.804851	−	0.593477i	$-0.202245\pi$
$587$	39.0000	1.60970	0.804851	+	0.593477i	$0.202245\pi$
$588$	0	0
$589$	28.0000	1.15372
$590$	0	0
$591$	6.00000	0.246807
$592$	0	0
$593$	27.0000	1.10876	0.554379	−	0.832265i	$-0.312956\pi$
$593$	27.0000	1.10876	0.554379	+	0.832265i	$0.312956\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−14.0000	−0.572982
$598$	0	0
$599$	−24.0000	−0.980613	−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000	−0.980613	−0.490307	+	0.871550i	$0.663115\pi$
$600$	0	0
$601$	−7.00000	−0.285536	−0.142768	−	0.989756i	$-0.545600\pi$
$601$	−7.00000	−0.285536	−0.142768	+	0.989756i	$0.545600\pi$
$602$	0	0
$603$	14.0000	0.570124
$604$	0	0
$605$	0	0
$606$	0	0
$607$	44.0000	1.78590	0.892952	−	0.450151i	$-0.148630\pi$
$607$	44.0000	1.78590	0.892952	+	0.450151i	$0.148630\pi$
$608$	0	0
$609$	−6.00000	−0.243132
$610$	0	0
$611$	12.0000	0.485468
$612$	0	0
$613$	−2.00000	−0.0807792	−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000	−0.0807792	−0.0403896	+	0.999184i	$0.512860\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	18.0000	0.724653	0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000	0.724653	0.362326	+	0.932051i	$0.381983\pi$
$618$	0	0
$619$	28.0000	1.12542	0.562708	−	0.826656i	$-0.309760\pi$
$619$	28.0000	1.12542	0.562708	+	0.826656i	$0.309760\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	−15.0000	−0.600962
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−21.0000	−0.838659
$628$	0	0
$629$	24.0000	0.956943
$630$	0	0
$631$	−32.0000	−1.27390	−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000	−1.27390	−0.636950	+	0.770905i	$0.719804\pi$
$632$	0	0
$633$	−17.0000	−0.675689
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−2.00000	−0.0792429
$638$	0	0
$639$	12.0000	0.474713
$640$	0	0
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	0	0
$643$	−40.0000	−1.57745	−0.788723	−	0.614749i	$-0.789257\pi$
$643$	−40.0000	−1.57745	−0.788723	+	0.614749i	$0.789257\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−24.0000	−0.943537	−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000	−0.943537	−0.471769	+	0.881722i	$0.656384\pi$
$648$	0	0
$649$	36.0000	1.41312
$650$	0	0
$651$	4.00000	0.156772
$652$	0	0
$653$	−36.0000	−1.40879	−0.704394	−	0.709809i	$-0.748781\pi$
$653$	−36.0000	−1.40879	−0.704394	+	0.709809i	$0.748781\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	10.0000	0.390137
$658$	0	0
$659$	−9.00000	−0.350590	−0.175295	−	0.984516i	$-0.556088\pi$
$659$	−9.00000	−0.350590	−0.175295	+	0.984516i	$0.556088\pi$
$660$	0	0
$661$	−10.0000	−0.388955	−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000	−0.388955	−0.194477	+	0.980907i	$0.562301\pi$
$662$	0	0
$663$	6.00000	0.233021
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	14.0000	0.541271
$670$	0	0
$671$	30.0000	1.15814
$672$	0	0
$673$	−2.00000	−0.0770943	−0.0385472	−	0.999257i	$-0.512273\pi$
$673$	−2.00000	−0.0770943	−0.0385472	+	0.999257i	$0.512273\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	10.0000	0.383765
$680$	0	0
$681$	12.0000	0.459841
$682$	0	0
$683$	3.00000	0.114792	0.0573959	−	0.998351i	$-0.481720\pi$
$683$	3.00000	0.114792	0.0573959	+	0.998351i	$0.481720\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	26.0000	0.991962
$688$	0	0
$689$	−24.0000	−0.914327
$690$	0	0
$691$	19.0000	0.722794	0.361397	−	0.932412i	$-0.382300\pi$
$691$	19.0000	0.722794	0.361397	+	0.932412i	$0.382300\pi$
$692$	0	0
$693$	6.00000	0.227921
$694$	0	0
$695$	0	0
$696$	0	0
$697$	27.0000	1.02270
$698$	0	0
$699$	−6.00000	−0.226941
$700$	0	0
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	0	0
$703$	−56.0000	−2.11208
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−28.0000	−1.05156	−0.525781	−	0.850620i	$-0.676227\pi$
$709$	−28.0000	−1.05156	−0.525781	+	0.850620i	$0.676227\pi$
$710$	0	0
$711$	28.0000	1.05008
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	12.0000	0.448148
$718$	0	0
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	20.0000	0.744839
$722$	0	0
$723$	−25.0000	−0.929760
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−34.0000	−1.26099	−0.630495	−	0.776193i	$-0.717148\pi$
$727$	−34.0000	−1.26099	−0.630495	+	0.776193i	$0.717148\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	−24.0000	−0.887672
$732$	0	0
$733$	40.0000	1.47743	0.738717	−	0.674016i	$-0.235432\pi$
$733$	40.0000	1.47743	0.738717	+	0.674016i	$0.235432\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	21.0000	0.773545
$738$	0	0
$739$	−20.0000	−0.735712	−0.367856	−	0.929883i	$-0.619908\pi$
$739$	−20.0000	−0.735712	−0.367856	+	0.929883i	$0.619908\pi$
$740$	0	0
$741$	−14.0000	−0.514303
$742$	0	0
$743$	−24.0000	−0.880475	−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000	−0.880475	−0.440237	+	0.897881i	$0.645106\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	18.0000	0.658586
$748$	0	0
$749$	3.00000	0.109618
$750$	0	0
$751$	46.0000	1.67856	0.839282	−	0.543696i	$-0.182976\pi$
$751$	46.0000	1.67856	0.839282	+	0.543696i	$0.182976\pi$
$752$	0	0
$753$	−15.0000	−0.546630
$754$	0	0
$755$	0	0
$756$	0	0
$757$	34.0000	1.23575	0.617876	−	0.786276i	$-0.287994\pi$
$757$	34.0000	1.23575	0.617876	+	0.786276i	$0.287994\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−9.00000	−0.326250	−0.163125	−	0.986605i	$-0.552157\pi$
$761$	−9.00000	−0.326250	−0.163125	+	0.986605i	$0.552157\pi$
$762$	0	0
$763$	14.0000	0.506834
$764$	0	0
$765$	0	0
$766$	0	0
$767$	24.0000	0.866590
$768$	0	0
$769$	23.0000	0.829401	0.414701	−	0.909958i	$-0.363886\pi$
$769$	23.0000	0.829401	0.414701	+	0.909958i	$0.363886\pi$
$770$	0	0
$771$	30.0000	1.08042
$772$	0	0
$773$	12.0000	0.431610	0.215805	−	0.976436i	$-0.430762\pi$
$773$	12.0000	0.431610	0.215805	+	0.976436i	$0.430762\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−8.00000	−0.286998
$778$	0	0
$779$	−63.0000	−2.25721
$780$	0	0
$781$	18.0000	0.644091
$782$	0	0
$783$	30.0000	1.07211
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−4.00000	−0.142585	−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000	−0.142585	−0.0712923	+	0.997455i	$0.522712\pi$
$788$	0	0
$789$	6.00000	0.213606
$790$	0	0
$791$	9.00000	0.320003
$792$	0	0
$793$	20.0000	0.710221
$794$	0	0
$795$	0	0
$796$	0	0
$797$	30.0000	1.06265	0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000	1.06265	0.531327	+	0.847167i	$0.321693\pi$
$798$	0	0
$799$	18.0000	0.636794
$800$	0	0
$801$	30.0000	1.06000
$802$	0	0
$803$	15.0000	0.529339
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−6.00000	−0.211210
$808$	0	0
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	0	0
$811$	−44.0000	−1.54505	−0.772524	−	0.634985i	$-0.781006\pi$
$811$	−44.0000	−1.54505	−0.772524	+	0.634985i	$0.781006\pi$
$812$	0	0
$813$	−2.00000	−0.0701431
$814$	0	0
$815$	0	0
$816$	0	0
$817$	56.0000	1.95919
$818$	0	0
$819$	4.00000	0.139771
$820$	0	0
$821$	24.0000	0.837606	0.418803	−	0.908077i	$-0.362450\pi$
$821$	24.0000	0.837606	0.418803	+	0.908077i	$0.362450\pi$
$822$	0	0
$823$	26.0000	0.906303	0.453152	−	0.891434i	$-0.350300\pi$
$823$	26.0000	0.906303	0.453152	+	0.891434i	$0.350300\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	9.00000	0.312961	0.156480	−	0.987681i	$-0.449985\pi$
$827$	9.00000	0.312961	0.156480	+	0.987681i	$0.449985\pi$
$828$	0	0
$829$	−4.00000	−0.138926	−0.0694629	−	0.997585i	$-0.522129\pi$
$829$	−4.00000	−0.138926	−0.0694629	+	0.997585i	$0.522129\pi$
$830$	0	0
$831$	−2.00000	−0.0693792
$832$	0	0
$833$	−3.00000	−0.103944
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−20.0000	−0.691301
$838$	0	0
$839$	6.00000	0.207143	0.103572	−	0.994622i	$-0.466973\pi$
$839$	6.00000	0.207143	0.103572	+	0.994622i	$0.466973\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	0	0
$843$	−18.0000	−0.619953
$844$	0	0
$845$	0	0
$846$	0	0
$847$	−2.00000	−0.0687208
$848$	0	0
$849$	−1.00000	−0.0343199
$850$	0	0
$851$	0	0
$852$	0	0
$853$	10.0000	0.342393	0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000	0.342393	0.171197	+	0.985237i	$0.445237\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−15.0000	−0.512390	−0.256195	−	0.966625i	$-0.582469\pi$
$857$	−15.0000	−0.512390	−0.256195	+	0.966625i	$0.582469\pi$
$858$	0	0
$859$	31.0000	1.05771	0.528853	−	0.848713i	$-0.322622\pi$
$859$	31.0000	1.05771	0.528853	+	0.848713i	$0.322622\pi$
$860$	0	0
$861$	−9.00000	−0.306719
$862$	0	0
$863$	−12.0000	−0.408485	−0.204242	−	0.978920i	$-0.565473\pi$
$863$	−12.0000	−0.408485	−0.204242	+	0.978920i	$0.565473\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−8.00000	−0.271694
$868$	0	0
$869$	42.0000	1.42475
$870$	0	0
$871$	14.0000	0.474372
$872$	0	0
$873$	−20.0000	−0.676897
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−32.0000	−1.08056	−0.540282	−	0.841484i	$-0.681682\pi$
$877$	−32.0000	−1.08056	−0.540282	+	0.841484i	$0.681682\pi$
$878$	0	0
$879$	6.00000	0.202375
$880$	0	0
$881$	−6.00000	−0.202145	−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000	−0.202145	−0.101073	+	0.994879i	$0.532227\pi$
$882$	0	0
$883$	47.0000	1.58168	0.790838	−	0.612026i	$-0.209645\pi$
$883$	47.0000	1.58168	0.790838	+	0.612026i	$0.209645\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	6.00000	0.201460	0.100730	−	0.994914i	$-0.467882\pi$
$887$	6.00000	0.201460	0.100730	+	0.994914i	$0.467882\pi$
$888$	0	0
$889$	2.00000	0.0670778
$890$	0	0
$891$	−3.00000	−0.100504
$892$	0	0
$893$	−42.0000	−1.40548
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	−24.0000	−0.800445
$900$	0	0
$901$	−36.0000	−1.19933
$902$	0	0
$903$	8.00000	0.266223
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−4.00000	−0.132818	−0.0664089	−	0.997792i	$-0.521154\pi$
$907$	−4.00000	−0.132818	−0.0664089	+	0.997792i	$0.521154\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	−36.0000	−1.19273	−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000	−1.19273	−0.596367	+	0.802712i	$0.703390\pi$
$912$	0	0
$913$	27.0000	0.893570
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	34.0000	1.12156	0.560778	−	0.827966i	$-0.310502\pi$
$919$	34.0000	1.12156	0.560778	+	0.827966i	$0.310502\pi$
$920$	0	0
$921$	−7.00000	−0.230658
$922$	0	0
$923$	12.0000	0.394985
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−40.0000	−1.31377
$928$	0	0
$929$	−18.0000	−0.590561	−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000	−0.590561	−0.295280	+	0.955411i	$0.595413\pi$
$930$	0	0
$931$	7.00000	0.229416
$932$	0	0
$933$	18.0000	0.589294
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−29.0000	−0.947389	−0.473694	−	0.880689i	$-0.657080\pi$
$937$	−29.0000	−0.947389	−0.473694	+	0.880689i	$0.657080\pi$
$938$	0	0
$939$	10.0000	0.326338
$940$	0	0
$941$	24.0000	0.782378	0.391189	−	0.920310i	$-0.372064\pi$
$941$	24.0000	0.782378	0.391189	+	0.920310i	$0.372064\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	12.0000	0.389948	0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000	0.389948	0.194974	+	0.980808i	$0.437538\pi$
$948$	0	0
$949$	10.0000	0.324614
$950$	0	0
$951$	12.0000	0.389127
$952$	0	0
$953$	−57.0000	−1.84641	−0.923206	−	0.384307i	$-0.874441\pi$
$953$	−57.0000	−1.84641	−0.923206	+	0.384307i	$0.874441\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	18.0000	0.581857
$958$	0	0
$959$	−21.0000	−0.678125
$960$	0	0
$961$	−15.0000	−0.483871
$962$	0	0
$963$	−6.00000	−0.193347
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−34.0000	−1.09337	−0.546683	−	0.837340i	$-0.684110\pi$
$967$	−34.0000	−1.09337	−0.546683	+	0.837340i	$0.684110\pi$
$968$	0	0
$969$	−21.0000	−0.674617
$970$	0	0
$971$	−9.00000	−0.288824	−0.144412	−	0.989518i	$-0.546129\pi$
$971$	−9.00000	−0.288824	−0.144412	+	0.989518i	$0.546129\pi$
$972$	0	0
$973$	7.00000	0.224410
$974$	0	0
$975$	0	0
$976$	0	0
$977$	3.00000	0.0959785	0.0479893	−	0.998848i	$-0.484719\pi$
$977$	3.00000	0.0959785	0.0479893	+	0.998848i	$0.484719\pi$
$978$	0	0
$979$	45.0000	1.43821
$980$	0	0
$981$	−28.0000	−0.893971
$982$	0	0
$983$	12.0000	0.382741	0.191370	−	0.981518i	$-0.438707\pi$
$983$	12.0000	0.382741	0.191370	+	0.981518i	$0.438707\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	−6.00000	−0.190982
$988$	0	0
$989$	0	0
$990$	0	0
$991$	−20.0000	−0.635321	−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000	−0.635321	−0.317660	+	0.948205i	$0.602897\pi$
$992$	0	0
$993$	25.0000	0.793351
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−62.0000	−1.96356	−0.981780	−	0.190022i	$-0.939144\pi$
$997$	−62.0000	−1.96356	−0.981780	+	0.190022i	$0.939144\pi$
$998$	0	0
$999$	40.0000	1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2800.2.a.x.1.1		1
4.3	odd	2		350.2.a.a.1.1	✓	1
5.2	odd	4		2800.2.g.i.449.1		2
5.3	odd	4		2800.2.g.i.449.2		2
5.4	even	2		2800.2.a.h.1.1		1
12.11	even	2		3150.2.a.x.1.1		1
20.3	even	4		350.2.c.c.99.2		2
20.7	even	4		350.2.c.c.99.1		2
20.19	odd	2		350.2.a.e.1.1	yes	1
28.27	even	2		2450.2.a.m.1.1		1
60.23	odd	4		3150.2.g.f.2899.1		2
60.47	odd	4		3150.2.g.f.2899.2		2
60.59	even	2		3150.2.a.m.1.1		1
140.27	odd	4		2450.2.c.h.99.1		2
140.83	odd	4		2450.2.c.h.99.2		2
140.139	even	2		2450.2.a.x.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.a.a.1.1	✓	1	4.3	odd	2
350.2.a.e.1.1	yes	1	20.19	odd	2
350.2.c.c.99.1		2	20.7	even	4
350.2.c.c.99.2		2	20.3	even	4
2450.2.a.m.1.1		1	28.27	even	2
2450.2.a.x.1.1		1	140.139	even	2
2450.2.c.h.99.1		2	140.27	odd	4
2450.2.c.h.99.2		2	140.83	odd	4
2800.2.a.h.1.1		1	5.4	even	2
2800.2.a.x.1.1		1	1.1	even	1	trivial
2800.2.g.i.449.1		2	5.2	odd	4
2800.2.g.i.449.2		2	5.3	odd	4
3150.2.a.m.1.1		1	60.59	even	2
3150.2.a.x.1.1		1	12.11	even	2
3150.2.g.f.2899.1		2	60.23	odd	4
3150.2.g.f.2899.2		2	60.47	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2800.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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