LMFDB - Embedded newform 9800.2.a.cq.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9800,2,Mod(1,9800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9800, 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("9800.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9800.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:	$78.2533939809$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{7}, \sqrt{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 11x^{2} + 4 $ x^4 - 11*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.613616$ of defining polynomial
Character	$\chi$	$=$	9800.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.25937 q^{3} +7.62348 q^{9} +O(q^{10})$	$q-3.25937 q^{3} +7.62348 q^{9} +1.00000 q^{11} -5.29150 q^{13} -2.03214 q^{17} +4.48660 q^{19} -7.62348 q^{23} -15.0696 q^{27} -5.62348 q^{29} +1.22723 q^{31} -3.25937 q^{33} +7.62348 q^{37} +17.2470 q^{39} -9.77810 q^{41} +11.6235 q^{43} -6.51873 q^{47} +6.62348 q^{51} -11.2470 q^{53} -14.6235 q^{57} +5.29150 q^{59} -7.74597 q^{61} +8.24695 q^{67} +24.8477 q^{69} +2.37652 q^{71} +16.2968 q^{73} +5.62348 q^{79} +26.2470 q^{81} +0.804903 q^{83} +18.3290 q^{87} +0.804903 q^{89} -4.00000 q^{93} -14.2647 q^{97} +7.62348 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 10 q^{9}+O(q^{10}) $ 4 * q + 10 * q^9	$ 4 q + 10 q^{9} + 4 q^{11} - 10 q^{23} - 2 q^{29} + 10 q^{37} + 28 q^{39} + 26 q^{43} + 6 q^{51} - 4 q^{53} - 38 q^{57} - 8 q^{67} + 30 q^{71} + 2 q^{79} + 64 q^{81} - 16 q^{93} + 10 q^{99}+O(q^{100}) $ 4 * q + 10 * q^9 + 4 * q^11 - 10 * q^23 - 2 * q^29 + 10 * q^37 + 28 * q^39 + 26 * q^43 + 6 * q^51 - 4 * q^53 - 38 * q^57 - 8 * q^67 + 30 * q^71 + 2 * q^79 + 64 * q^81 - 16 * q^93 + 10 * 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
$3$	−3.25937	−1.88180	−0.940898	−	0.338689i	$-0.890016\pi$
$3$	−3.25937	−1.88180	−0.940898	+	0.338689i	$0.890016\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	7.62348	2.54116
$10$	0	0
$11$	1.00000	0.301511	0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000	0.301511	0.150756	+	0.988571i	$0.451829\pi$
$12$	0	0
$13$	−5.29150	−1.46760	−0.733799	−	0.679366i	$-0.762255\pi$
$13$	−5.29150	−1.46760	−0.733799	+	0.679366i	$0.762255\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−2.03214	−0.492865	−0.246433	−	0.969160i	$-0.579258\pi$
$17$	−2.03214	−0.492865	−0.246433	+	0.969160i	$0.579258\pi$
$18$	0	0
$19$	4.48660	1.02930	0.514648	−	0.857401i	$-0.327923\pi$
$19$	4.48660	1.02930	0.514648	+	0.857401i	$0.327923\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−7.62348	−1.58960	−0.794802	−	0.606869i	$-0.792425\pi$
$23$	−7.62348	−1.58960	−0.794802	+	0.606869i	$0.792425\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−15.0696	−2.90015
$28$	0	0
$29$	−5.62348	−1.04425	−0.522127	−	0.852868i	$-0.674861\pi$
$29$	−5.62348	−1.04425	−0.522127	+	0.852868i	$0.674861\pi$
$30$	0	0
$31$	1.22723	0.220417	0.110209	−	0.993908i	$-0.464848\pi$
$31$	1.22723	0.220417	0.110209	+	0.993908i	$0.464848\pi$
$32$	0	0
$33$	−3.25937	−0.567383
$34$	0	0
$35$	0	0
$36$	0	0
$37$	7.62348	1.25329	0.626646	−	0.779304i	$-0.284427\pi$
$37$	7.62348	1.25329	0.626646	+	0.779304i	$0.284427\pi$
$38$	0	0
$39$	17.2470	2.76172
$40$	0	0
$41$	−9.77810	−1.52708	−0.763541	−	0.645759i	$-0.776541\pi$
$41$	−9.77810	−1.52708	−0.763541	+	0.645759i	$0.776541\pi$
$42$	0	0
$43$	11.6235	1.77256	0.886282	−	0.463147i	$-0.153280\pi$
$43$	11.6235	1.77256	0.886282	+	0.463147i	$0.153280\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−6.51873	−0.950855	−0.475428	−	0.879755i	$-0.657707\pi$
$47$	−6.51873	−0.950855	−0.475428	+	0.879755i	$0.657707\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	6.62348	0.927472
$52$	0	0
$53$	−11.2470	−1.54489	−0.772444	−	0.635083i	$-0.780966\pi$
$53$	−11.2470	−1.54489	−0.772444	+	0.635083i	$0.780966\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−14.6235	−1.93693
$58$	0	0
$59$	5.29150	0.688895	0.344447	−	0.938806i	$-0.388066\pi$
$59$	5.29150	0.688895	0.344447	+	0.938806i	$0.388066\pi$
$60$	0	0
$61$	−7.74597	−0.991769	−0.495885	−	0.868388i	$-0.665156\pi$
$61$	−7.74597	−0.991769	−0.495885	+	0.868388i	$0.665156\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	8.24695	1.00753	0.503763	−	0.863842i	$-0.331949\pi$
$67$	8.24695	1.00753	0.503763	+	0.863842i	$0.331949\pi$
$68$	0	0
$69$	24.8477	2.99131
$70$	0	0
$71$	2.37652	0.282042	0.141021	−	0.990007i	$-0.454962\pi$
$71$	2.37652	0.282042	0.141021	+	0.990007i	$0.454962\pi$
$72$	0	0
$73$	16.2968	1.90740	0.953700	−	0.300759i	$-0.0972399\pi$
$73$	16.2968	1.90740	0.953700	+	0.300759i	$0.0972399\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	5.62348	0.632690	0.316345	−	0.948644i	$-0.397544\pi$
$79$	5.62348	0.632690	0.316345	+	0.948644i	$0.397544\pi$
$80$	0	0
$81$	26.2470	2.91633
$82$	0	0
$83$	0.804903	0.0883496	0.0441748	−	0.999024i	$-0.485934\pi$
$83$	0.804903	0.0883496	0.0441748	+	0.999024i	$0.485934\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	18.3290	1.96507
$88$	0	0
$89$	0.804903	0.0853196	0.0426598	−	0.999090i	$-0.486417\pi$
$89$	0.804903	0.0853196	0.0426598	+	0.999090i	$0.486417\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	−4.00000	−0.414781
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−14.2647	−1.44836	−0.724180	−	0.689610i	$-0.757782\pi$
$97$	−14.2647	−1.44836	−0.724180	+	0.689610i	$0.757782\pi$
$98$	0	0
$99$	7.62348	0.766188
$100$	0	0
$101$	−1.22723	−0.122114	−0.0610571	−	0.998134i	$-0.519447\pi$
$101$	−1.22723	−0.122114	−0.0610571	+	0.998134i	$0.519447\pi$
$102$	0	0
$103$	−13.0375	−1.28462	−0.642310	−	0.766445i	$-0.722024\pi$
$103$	−13.0375	−1.28462	−0.642310	+	0.766445i	$0.722024\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	14.6235	1.41370	0.706852	−	0.707361i	$-0.250115\pi$
$107$	14.6235	1.41370	0.706852	+	0.707361i	$0.250115\pi$
$108$	0	0
$109$	−5.62348	−0.538631	−0.269316	−	0.963052i	$-0.586797\pi$
$109$	−5.62348	−0.538631	−0.269316	+	0.963052i	$0.586797\pi$
$110$	0	0
$111$	−24.8477	−2.35844
$112$	0	0
$113$	−10.2470	−0.963952	−0.481976	−	0.876184i	$-0.660081\pi$
$113$	−10.2470	−0.963952	−0.481976	+	0.876184i	$0.660081\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−40.3396	−3.72940
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−10.0000	−0.909091
$122$	0	0
$123$	31.8704	2.87366
$124$	0	0
$125$	0	0
$126$	0	0
$127$	9.62348	0.853945	0.426973	−	0.904265i	$-0.359580\pi$
$127$	9.62348	0.853945	0.426973	+	0.904265i	$0.359580\pi$
$128$	0	0
$129$	−37.8852	−3.33560
$130$	0	0
$131$	−17.1017	−1.49419	−0.747093	−	0.664720i	$-0.768551\pi$
$131$	−17.1017	−1.49419	−0.747093	+	0.664720i	$0.768551\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−12.6235	−1.07850	−0.539248	−	0.842147i	$-0.681292\pi$
$137$	−12.6235	−1.07850	−0.539248	+	0.842147i	$0.681292\pi$
$138$	0	0
$139$	−0.804903	−0.0682710	−0.0341355	−	0.999417i	$-0.510868\pi$
$139$	−0.804903	−0.0682710	−0.0341355	+	0.999417i	$0.510868\pi$
$140$	0	0
$141$	21.2470	1.78932
$142$	0	0
$143$	−5.29150	−0.442498
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−7.62348	−0.624539	−0.312270	−	0.949993i	$-0.601089\pi$
$149$	−7.62348	−0.624539	−0.312270	+	0.949993i	$0.601089\pi$
$150$	0	0
$151$	−6.87043	−0.559107	−0.279554	−	0.960130i	$-0.590186\pi$
$151$	−6.87043	−0.559107	−0.279554	+	0.960130i	$0.590186\pi$
$152$	0	0
$153$	−15.4919	−1.25245
$154$	0	0
$155$	0	0
$156$	0	0
$157$	9.35577	0.746672	0.373336	−	0.927696i	$-0.378214\pi$
$157$	9.35577	0.746672	0.373336	+	0.927696i	$0.378214\pi$
$158$	0	0
$159$	36.6579	2.90716
$160$	0	0
$161$	0	0
$162$	0	0
$163$	2.62348	0.205486	0.102743	−	0.994708i	$-0.467238\pi$
$163$	2.62348	0.205486	0.102743	+	0.994708i	$0.467238\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−16.7192	−1.29377	−0.646884	−	0.762588i	$-0.723928\pi$
$167$	−16.7192	−1.29377	−0.646884	+	0.762588i	$0.723928\pi$
$168$	0	0
$169$	15.0000	1.15385
$170$	0	0
$171$	34.2035	2.61561
$172$	0	0
$173$	19.5562	1.48683	0.743415	−	0.668830i	$-0.233205\pi$
$173$	19.5562	1.48683	0.743415	+	0.668830i	$0.233205\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−17.2470	−1.29636
$178$	0	0
$179$	−7.87043	−0.588263	−0.294132	−	0.955765i	$-0.595030\pi$
$179$	−7.87043	−0.588263	−0.294132	+	0.955765i	$0.595030\pi$
$180$	0	0
$181$	18.3290	1.36238	0.681191	−	0.732106i	$-0.261462\pi$
$181$	18.3290	1.36238	0.681191	+	0.732106i	$0.261462\pi$
$182$	0	0
$183$	25.2470	1.86631
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−2.03214	−0.148604
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−21.2470	−1.53738	−0.768688	−	0.639624i	$-0.779090\pi$
$191$	−21.2470	−1.53738	−0.768688	+	0.639624i	$0.779090\pi$
$192$	0	0
$193$	15.0000	1.07972	0.539862	−	0.841754i	$-0.318476\pi$
$193$	15.0000	1.07972	0.539862	+	0.841754i	$0.318476\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−14.3765	−1.02428	−0.512142	−	0.858901i	$-0.671148\pi$
$197$	−14.3765	−1.02428	−0.512142	+	0.858901i	$0.671148\pi$
$198$	0	0
$199$	10.2004	0.723089	0.361545	−	0.932355i	$-0.382249\pi$
$199$	10.2004	0.723089	0.361545	+	0.932355i	$0.382249\pi$
$200$	0	0
$201$	−26.8798	−1.89596
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−58.1174	−4.03944
$208$	0	0
$209$	4.48660	0.310345
$210$	0	0
$211$	13.3765	0.920878	0.460439	−	0.887691i	$-0.347692\pi$
$211$	13.3765	0.920878	0.460439	+	0.887691i	$0.347692\pi$
$212$	0	0
$213$	−7.74597	−0.530745
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−53.1174	−3.58934
$220$	0	0
$221$	10.7530	0.723328
$222$	0	0
$223$	−13.4200	−0.898673	−0.449336	−	0.893363i	$-0.648339\pi$
$223$	−13.4200	−0.898673	−0.449336	+	0.893363i	$0.648339\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	22.0107	1.46090	0.730450	−	0.682967i	$-0.239311\pi$
$227$	22.0107	1.46090	0.730450	+	0.682967i	$0.239311\pi$
$228$	0	0
$229$	−14.6473	−0.967919	−0.483960	−	0.875090i	$-0.660802\pi$
$229$	−14.6473	−0.967919	−0.483960	+	0.875090i	$0.660802\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	12.8704	0.843170	0.421585	−	0.906789i	$-0.361474\pi$
$233$	12.8704	0.843170	0.421585	+	0.906789i	$0.361474\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−18.3290	−1.19059
$238$	0	0
$239$	−8.00000	−0.517477	−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000	−0.517477	−0.258738	+	0.965947i	$0.583307\pi$
$240$	0	0
$241$	6.94106	0.447113	0.223557	−	0.974691i	$-0.428233\pi$
$241$	6.94106	0.447113	0.223557	+	0.974691i	$0.428233\pi$
$242$	0	0
$243$	−40.3396	−2.58779
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−23.7409	−1.51059
$248$	0	0
$249$	−2.62348	−0.166256
$250$	0	0
$251$	−6.94106	−0.438116	−0.219058	−	0.975712i	$-0.570298\pi$
$251$	−6.94106	−0.438116	−0.219058	+	0.975712i	$0.570298\pi$
$252$	0	0
$253$	−7.62348	−0.479284
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−9.35577	−0.583597	−0.291799	−	0.956480i	$-0.594254\pi$
$257$	−9.35577	−0.583597	−0.291799	+	0.956480i	$0.594254\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−42.8704	−2.65361
$262$	0	0
$263$	−1.62348	−0.100108	−0.0500539	−	0.998747i	$-0.515939\pi$
$263$	−1.62348	−0.100108	−0.0500539	+	0.998747i	$0.515939\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−2.62348	−0.160554
$268$	0	0
$269$	−7.74597	−0.472280	−0.236140	−	0.971719i	$-0.575882\pi$
$269$	−7.74597	−0.472280	−0.236140	+	0.971719i	$0.575882\pi$
$270$	0	0
$271$	26.4575	1.60718	0.803590	−	0.595184i	$-0.202921\pi$
$271$	26.4575	1.60718	0.803590	+	0.595184i	$0.202921\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	0	0
$279$	9.35577	0.560115
$280$	0	0
$281$	−1.62348	−0.0968484	−0.0484242	−	0.998827i	$-0.515420\pi$
$281$	−1.62348	−0.0968484	−0.0484242	+	0.998827i	$0.515420\pi$
$282$	0	0
$283$	12.6151	0.749892	0.374946	−	0.927047i	$-0.377661\pi$
$283$	12.6151	0.749892	0.374946	+	0.927047i	$0.377661\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−12.8704	−0.757084
$290$	0	0
$291$	46.4939	2.72552
$292$	0	0
$293$	5.29150	0.309133	0.154566	−	0.987982i	$-0.450602\pi$
$293$	5.29150	0.309133	0.154566	+	0.987982i	$0.450602\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−15.0696	−0.874427
$298$	0	0
$299$	40.3396	2.33290
$300$	0	0
$301$	0	0
$302$	0	0
$303$	4.00000	0.229794
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−19.1339	−1.09203	−0.546014	−	0.837776i	$-0.683855\pi$
$307$	−19.1339	−1.09203	−0.546014	+	0.837776i	$0.683855\pi$
$308$	0	0
$309$	42.4939	2.41739
$310$	0	0
$311$	−27.6847	−1.56986	−0.784929	−	0.619586i	$-0.787301\pi$
$311$	−27.6847	−1.56986	−0.784929	+	0.619586i	$0.787301\pi$
$312$	0	0
$313$	2.45446	0.138735	0.0693673	−	0.997591i	$-0.477902\pi$
$313$	2.45446	0.138735	0.0693673	+	0.997591i	$0.477902\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−19.6235	−1.10216	−0.551082	−	0.834451i	$-0.685785\pi$
$317$	−19.6235	−1.10216	−0.551082	+	0.834451i	$0.685785\pi$
$318$	0	0
$319$	−5.62348	−0.314854
$320$	0	0
$321$	−47.6633	−2.66030
$322$	0	0
$323$	−9.11738	−0.507304
$324$	0	0
$325$	0	0
$326$	0	0
$327$	18.3290	1.01359
$328$	0	0
$329$	0	0
$330$	0	0
$331$	20.2470	1.11287	0.556437	−	0.830890i	$-0.312168\pi$
$331$	20.2470	1.11287	0.556437	+	0.830890i	$0.312168\pi$
$332$	0	0
$333$	58.1174	3.18481
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−2.12957	−0.116005	−0.0580026	−	0.998316i	$-0.518473\pi$
$337$	−2.12957	−0.116005	−0.0580026	+	0.998316i	$0.518473\pi$
$338$	0	0
$339$	33.3986	1.81396
$340$	0	0
$341$	1.22723	0.0664583
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	15.4939	0.831756	0.415878	−	0.909420i	$-0.363474\pi$
$347$	15.4939	0.831756	0.415878	+	0.909420i	$0.363474\pi$
$348$	0	0
$349$	2.45446	0.131384	0.0656922	−	0.997840i	$-0.479074\pi$
$349$	2.45446	0.131384	0.0656922	+	0.997840i	$0.479074\pi$
$350$	0	0
$351$	79.7409	4.25625
$352$	0	0
$353$	27.3022	1.45315	0.726574	−	0.687088i	$-0.241111\pi$
$353$	27.3022	1.45315	0.726574	+	0.687088i	$0.241111\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	12.8704	0.679275	0.339638	−	0.940556i	$-0.389696\pi$
$359$	12.8704	0.679275	0.339638	+	0.940556i	$0.389696\pi$
$360$	0	0
$361$	1.12957	0.0594513
$362$	0	0
$363$	32.5937	1.71072
$364$	0	0
$365$	0	0
$366$	0	0
$367$	1.22723	0.0640610	0.0320305	−	0.999487i	$-0.489803\pi$
$367$	1.22723	0.0640610	0.0320305	+	0.999487i	$0.489803\pi$
$368$	0	0
$369$	−74.5431	−3.88056
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−27.6235	−1.43029	−0.715145	−	0.698976i	$-0.753639\pi$
$373$	−27.6235	−1.43029	−0.715145	+	0.698976i	$0.753639\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	29.7566	1.53254
$378$	0	0
$379$	11.0000	0.565032	0.282516	−	0.959263i	$-0.408831\pi$
$379$	11.0000	0.565032	0.282516	+	0.959263i	$0.408831\pi$
$380$	0	0
$381$	−31.3664	−1.60695
$382$	0	0
$383$	7.74597	0.395800	0.197900	−	0.980222i	$-0.436588\pi$
$383$	7.74597	0.395800	0.197900	+	0.980222i	$0.436588\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	88.6113	4.50436
$388$	0	0
$389$	15.6235	0.792142	0.396071	−	0.918220i	$-0.370373\pi$
$389$	15.6235	0.792142	0.396071	+	0.918220i	$0.370373\pi$
$390$	0	0
$391$	15.4919	0.783461
$392$	0	0
$393$	55.7409	2.81175
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−8.97320	−0.450352	−0.225176	−	0.974318i	$-0.572296\pi$
$397$	−8.97320	−0.450352	−0.225176	+	0.974318i	$0.572296\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	11.4939	0.573978	0.286989	−	0.957934i	$-0.407346\pi$
$401$	11.4939	0.573978	0.286989	+	0.957934i	$0.407346\pi$
$402$	0	0
$403$	−6.49390	−0.323484
$404$	0	0
$405$	0	0
$406$	0	0
$407$	7.62348	0.377882
$408$	0	0
$409$	23.1981	1.14707	0.573537	−	0.819179i	$-0.305571\pi$
$409$	23.1981	1.14707	0.573537	+	0.819179i	$0.305571\pi$
$410$	0	0
$411$	41.1445	2.02951
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	2.62348	0.128472
$418$	0	0
$419$	4.86917	0.237875	0.118937	−	0.992902i	$-0.462051\pi$
$419$	4.86917	0.237875	0.118937	+	0.992902i	$0.462051\pi$
$420$	0	0
$421$	−22.1174	−1.07793	−0.538967	−	0.842327i	$-0.681185\pi$
$421$	−22.1174	−1.07793	−0.538967	+	0.842327i	$0.681185\pi$
$422$	0	0
$423$	−49.6954	−2.41627
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	17.2470	0.832691
$430$	0	0
$431$	24.0000	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$432$	0	0
$433$	−32.1713	−1.54606	−0.773028	−	0.634372i	$-0.781259\pi$
$433$	−32.1713	−1.54606	−0.773028	+	0.634372i	$0.781259\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−34.2035	−1.63617
$438$	0	0
$439$	9.35577	0.446527	0.223263	−	0.974758i	$-0.428329\pi$
$439$	9.35577	0.446527	0.223263	+	0.974758i	$0.428329\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	23.8704	1.13412	0.567059	−	0.823677i	$-0.308081\pi$
$443$	23.8704	1.13412	0.567059	+	0.823677i	$0.308081\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	24.8477	1.17526
$448$	0	0
$449$	1.75305	0.0827315	0.0413658	−	0.999144i	$-0.486829\pi$
$449$	1.75305	0.0827315	0.0413658	+	0.999144i	$0.486829\pi$
$450$	0	0
$451$	−9.77810	−0.460433
$452$	0	0
$453$	22.3932	1.05213
$454$	0	0
$455$	0	0
$456$	0	0
$457$	17.4939	0.818330	0.409165	−	0.912460i	$-0.365820\pi$
$457$	17.4939	0.818330	0.409165	+	0.912460i	$0.365820\pi$
$458$	0	0
$459$	30.6235	1.42938
$460$	0	0
$461$	38.7298	1.80383	0.901914	−	0.431915i	$-0.142162\pi$
$461$	38.7298	1.80383	0.901914	+	0.431915i	$0.142162\pi$
$462$	0	0
$463$	−30.4939	−1.41717	−0.708586	−	0.705625i	$-0.750667\pi$
$463$	−30.4939	−1.41717	−0.708586	+	0.705625i	$0.750667\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	40.7222	1.88440	0.942200	−	0.335052i	$-0.108754\pi$
$467$	40.7222	1.88440	0.942200	+	0.335052i	$0.108754\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−30.4939	−1.40508
$472$	0	0
$473$	11.6235	0.534448
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−85.7409	−3.92580
$478$	0	0
$479$	−7.74597	−0.353922	−0.176961	−	0.984218i	$-0.556627\pi$
$479$	−7.74597	−0.353922	−0.176961	+	0.984218i	$0.556627\pi$
$480$	0	0
$481$	−40.3396	−1.83933
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−37.6235	−1.70488	−0.852441	−	0.522823i	$-0.824879\pi$
$487$	−37.6235	−1.70488	−0.852441	+	0.522823i	$0.824879\pi$
$488$	0	0
$489$	−8.55087	−0.386684
$490$	0	0
$491$	1.12957	0.0509770	0.0254885	−	0.999675i	$-0.491886\pi$
$491$	1.12957	0.0509770	0.0254885	+	0.999675i	$0.491886\pi$
$492$	0	0
$493$	11.4277	0.514676
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	18.4939	0.827901	0.413950	−	0.910299i	$-0.364149\pi$
$499$	18.4939	0.827901	0.413950	+	0.910299i	$0.364149\pi$
$500$	0	0
$501$	54.4939	2.43461
$502$	0	0
$503$	−11.4277	−0.509534	−0.254767	−	0.967002i	$-0.581999\pi$
$503$	−11.4277	−0.509534	−0.254767	+	0.967002i	$0.581999\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−48.8905	−2.17130
$508$	0	0
$509$	10.9656	0.486041	0.243020	−	0.970021i	$-0.421862\pi$
$509$	10.9656	0.486041	0.243020	+	0.970021i	$0.421862\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−67.6113	−2.98511
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−6.51873	−0.286694
$518$	0	0
$519$	−63.7409	−2.79791
$520$	0	0
$521$	20.7437	0.908797	0.454399	−	0.890798i	$-0.349854\pi$
$521$	20.7437	0.908797	0.454399	+	0.890798i	$0.349854\pi$
$522$	0	0
$523$	33.0160	1.44369	0.721844	−	0.692055i	$-0.243295\pi$
$523$	33.0160	1.44369	0.721844	+	0.692055i	$0.243295\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−2.49390	−0.108636
$528$	0	0
$529$	35.1174	1.52684
$530$	0	0
$531$	40.3396	1.75059
$532$	0	0
$533$	51.7409	2.24115
$534$	0	0
$535$	0	0
$536$	0	0
$537$	25.6526	1.10699
$538$	0	0
$539$	0	0
$540$	0	0
$541$	24.1174	1.03689	0.518444	−	0.855112i	$-0.326512\pi$
$541$	24.1174	1.03689	0.518444	+	0.855112i	$0.326512\pi$
$542$	0	0
$543$	−59.7409	−2.56373
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−20.7409	−0.886815	−0.443407	−	0.896320i	$-0.646230\pi$
$547$	−20.7409	−0.886815	−0.443407	+	0.896320i	$0.646230\pi$
$548$	0	0
$549$	−59.0512	−2.52024
$550$	0	0
$551$	−25.2303	−1.07485
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	22.8704	0.969051	0.484526	−	0.874777i	$-0.338992\pi$
$557$	22.8704	0.969051	0.484526	+	0.874777i	$0.338992\pi$
$558$	0	0
$559$	−61.5057	−2.60141
$560$	0	0
$561$	6.62348	0.279643
$562$	0	0
$563$	−17.1017	−0.720752	−0.360376	−	0.932807i	$-0.617352\pi$
$563$	−17.1017	−0.720752	−0.360376	+	0.932807i	$0.617352\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	35.4939	1.48798	0.743991	−	0.668190i	$-0.232931\pi$
$569$	35.4939	1.48798	0.743991	+	0.668190i	$0.232931\pi$
$570$	0	0
$571$	22.8704	0.957098	0.478549	−	0.878061i	$-0.341163\pi$
$571$	22.8704	0.957098	0.478549	+	0.878061i	$0.341163\pi$
$572$	0	0
$573$	69.2516	2.89303
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−13.4598	−0.560339	−0.280169	−	0.959951i	$-0.590391\pi$
$577$	−13.4598	−0.560339	−0.280169	+	0.959951i	$0.590391\pi$
$578$	0	0
$579$	−48.8905	−2.03182
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−11.2470	−0.465801
$584$	0	0
$585$	0	0
$586$	0	0
$587$	33.3986	1.37851	0.689253	−	0.724520i	$-0.257939\pi$
$587$	33.3986	1.37851	0.689253	+	0.724520i	$0.257939\pi$
$588$	0	0
$589$	5.50610	0.226875
$590$	0	0
$591$	46.8584	1.92750
$592$	0	0
$593$	23.1981	0.952634	0.476317	−	0.879274i	$-0.341972\pi$
$593$	23.1981	0.952634	0.476317	+	0.879274i	$0.341972\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−33.2470	−1.36071
$598$	0	0
$599$	34.8704	1.42477	0.712383	−	0.701790i	$-0.247616\pi$
$599$	34.8704	1.42477	0.712383	+	0.701790i	$0.247616\pi$
$600$	0	0
$601$	16.6794	0.680367	0.340184	−	0.940359i	$-0.389511\pi$
$601$	16.6794	0.680367	0.340184	+	0.940359i	$0.389511\pi$
$602$	0	0
$603$	62.8704	2.56028
$604$	0	0
$605$	0	0
$606$	0	0
$607$	29.7566	1.20778	0.603892	−	0.797066i	$-0.293616\pi$
$607$	29.7566	1.20778	0.603892	+	0.797066i	$0.293616\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	34.4939	1.39547
$612$	0	0
$613$	18.3765	0.742221	0.371110	−	0.928589i	$-0.378977\pi$
$613$	18.3765	0.742221	0.371110	+	0.928589i	$0.378977\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−7.12957	−0.287026	−0.143513	−	0.989648i	$-0.545840\pi$
$617$	−7.12957	−0.287026	−0.143513	+	0.989648i	$0.545840\pi$
$618$	0	0
$619$	7.74597	0.311337	0.155668	−	0.987809i	$-0.450247\pi$
$619$	7.74597	0.311337	0.155668	+	0.987809i	$0.450247\pi$
$620$	0	0
$621$	114.883	4.61009
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−14.6235	−0.584005
$628$	0	0
$629$	−15.4919	−0.617704
$630$	0	0
$631$	36.3765	1.44813	0.724063	−	0.689734i	$-0.242272\pi$
$631$	36.3765	1.44813	0.724063	+	0.689734i	$0.242272\pi$
$632$	0	0
$633$	−43.5990	−1.73290
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	18.1174	0.716712
$640$	0	0
$641$	−8.11738	−0.320617	−0.160309	−	0.987067i	$-0.551249\pi$
$641$	−8.11738	−0.320617	−0.160309	+	0.987067i	$0.551249\pi$
$642$	0	0
$643$	−11.4277	−0.450663	−0.225332	−	0.974282i	$-0.572347\pi$
$643$	−11.4277	−0.450663	−0.225332	+	0.974282i	$0.572347\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	31.7490	1.24818	0.624091	−	0.781351i	$-0.285469\pi$
$647$	31.7490	1.24818	0.624091	+	0.781351i	$0.285469\pi$
$648$	0	0
$649$	5.29150	0.207710
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−31.2470	−1.22279	−0.611394	−	0.791326i	$-0.709391\pi$
$653$	−31.2470	−1.22279	−0.611394	+	0.791326i	$0.709391\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	124.239	4.84701
$658$	0	0
$659$	−9.37652	−0.365258	−0.182629	−	0.983182i	$-0.558461\pi$
$659$	−9.37652	−0.365258	−0.182629	+	0.983182i	$0.558461\pi$
$660$	0	0
$661$	−48.0856	−1.87031	−0.935157	−	0.354234i	$-0.884742\pi$
$661$	−48.0856	−1.87031	−0.935157	+	0.354234i	$0.884742\pi$
$662$	0	0
$663$	−35.0481	−1.36116
$664$	0	0
$665$	0	0
$666$	0	0
$667$	42.8704	1.65995
$668$	0	0
$669$	43.7409	1.69112
$670$	0	0
$671$	−7.74597	−0.299030
$672$	0	0
$673$	−40.4939	−1.56093	−0.780463	−	0.625202i	$-0.785016\pi$
$673$	−40.4939	−1.56093	−0.780463	+	0.625202i	$0.785016\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	20.4009	0.784069	0.392034	−	0.919951i	$-0.371771\pi$
$677$	20.4009	0.784069	0.392034	+	0.919951i	$0.371771\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−71.7409	−2.74912
$682$	0	0
$683$	19.7530	0.755829	0.377915	−	0.925840i	$-0.376641\pi$
$683$	19.7530	0.755829	0.377915	+	0.925840i	$0.376641\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	47.7409	1.82143
$688$	0	0
$689$	59.5133	2.26727
$690$	0	0
$691$	−17.9066	−0.681201	−0.340600	−	0.940208i	$-0.610630\pi$
$691$	−17.9066	−0.681201	−0.340600	+	0.940208i	$0.610630\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	19.8704	0.752646
$698$	0	0
$699$	−41.9494	−1.58667
$700$	0	0
$701$	−0.753049	−0.0284423	−0.0142211	−	0.999899i	$-0.504527\pi$
$701$	−0.753049	−0.0284423	−0.0142211	+	0.999899i	$0.504527\pi$
$702$	0	0
$703$	34.2035	1.29001
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	43.2470	1.62417	0.812087	−	0.583537i	$-0.198332\pi$
$709$	43.2470	1.62417	0.812087	+	0.583537i	$0.198332\pi$
$710$	0	0
$711$	42.8704	1.60777
$712$	0	0
$713$	−9.35577	−0.350376
$714$	0	0
$715$	0	0
$716$	0	0
$717$	26.0749	0.973786
$718$	0	0
$719$	−28.0673	−1.04673	−0.523367	−	0.852107i	$-0.675324\pi$
$719$	−28.0673	−1.04673	−0.523367	+	0.852107i	$0.675324\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	−22.6235	−0.841376
$724$	0	0
$725$	0	0
$726$	0	0
$727$	48.0856	1.78340	0.891698	−	0.452630i	$-0.149514\pi$
$727$	48.0856	1.78340	0.891698	+	0.452630i	$0.149514\pi$
$728$	0	0
$729$	52.7409	1.95336
$730$	0	0
$731$	−23.6205	−0.873635
$732$	0	0
$733$	17.9464	0.662865	0.331433	−	0.943479i	$-0.392468\pi$
$733$	17.9464	0.662865	0.331433	+	0.943479i	$0.392468\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	8.24695	0.303780
$738$	0	0
$739$	−14.8704	−0.547017	−0.273509	−	0.961870i	$-0.588184\pi$
$739$	−14.8704	−0.547017	−0.273509	+	0.961870i	$0.588184\pi$
$740$	0	0
$741$	77.3802	2.84263
$742$	0	0
$743$	26.4939	0.971967	0.485983	−	0.873968i	$-0.338462\pi$
$743$	26.4939	0.971967	0.485983	+	0.873968i	$0.338462\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	6.13616	0.224510
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−9.24695	−0.337426	−0.168713	−	0.985665i	$-0.553961\pi$
$751$	−9.24695	−0.337426	−0.168713	+	0.985665i	$0.553961\pi$
$752$	0	0
$753$	22.6235	0.824445
$754$	0	0
$755$	0	0
$756$	0	0
$757$	43.3643	1.57610	0.788052	−	0.615609i	$-0.211090\pi$
$757$	43.3643	1.57610	0.788052	+	0.615609i	$0.211090\pi$
$758$	0	0
$759$	24.8477	0.901915
$760$	0	0
$761$	−5.33126	−0.193258	−0.0966290	−	0.995320i	$-0.530806\pi$
$761$	−5.33126	−0.193258	−0.0966290	+	0.995320i	$0.530806\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−28.0000	−1.01102
$768$	0	0
$769$	−10.6228	−0.383067	−0.191533	−	0.981486i	$-0.561346\pi$
$769$	−10.6228	−0.383067	−0.191533	+	0.981486i	$0.561346\pi$
$770$	0	0
$771$	30.4939	1.09821
$772$	0	0
$773$	41.1048	1.47844	0.739218	−	0.673466i	$-0.235195\pi$
$773$	41.1048	1.47844	0.739218	+	0.673466i	$0.235195\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	−43.8704	−1.57182
$780$	0	0
$781$	2.37652	0.0850387
$782$	0	0
$783$	84.7436	3.02849
$784$	0	0
$785$	0	0
$786$	0	0
$787$	31.3664	1.11809	0.559046	−	0.829136i	$-0.311167\pi$
$787$	31.3664	1.11809	0.559046	+	0.829136i	$0.311167\pi$
$788$	0	0
$789$	5.29150	0.188382
$790$	0	0
$791$	0	0
$792$	0	0
$793$	40.9878	1.45552
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−24.4651	−0.866599	−0.433300	−	0.901250i	$-0.642651\pi$
$797$	−24.4651	−0.866599	−0.433300	+	0.901250i	$0.642651\pi$
$798$	0	0
$799$	13.2470	0.468643
$800$	0	0
$801$	6.13616	0.216811
$802$	0	0
$803$	16.2968	0.575103
$804$	0	0
$805$	0	0
$806$	0	0
$807$	25.2470	0.888735
$808$	0	0
$809$	−24.8704	−0.874398	−0.437199	−	0.899365i	$-0.644029\pi$
$809$	−24.8704	−0.874398	−0.437199	+	0.899365i	$0.644029\pi$
$810$	0	0
$811$	−32.5937	−1.14452	−0.572259	−	0.820073i	$-0.693933\pi$
$811$	−32.5937	−1.14452	−0.572259	+	0.820073i	$0.693933\pi$
$812$	0	0
$813$	−86.2348	−3.02438
$814$	0	0
$815$	0	0
$816$	0	0
$817$	52.1499	1.82449
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−0.753049	−0.0262816	−0.0131408	−	0.999914i	$-0.504183\pi$
$821$	−0.753049	−0.0262816	−0.0131408	+	0.999914i	$0.504183\pi$
$822$	0	0
$823$	4.11738	0.143523	0.0717614	−	0.997422i	$-0.477138\pi$
$823$	4.11738	0.143523	0.0717614	+	0.997422i	$0.477138\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−5.49390	−0.191042	−0.0955208	−	0.995427i	$-0.530452\pi$
$827$	−5.49390	−0.191042	−0.0955208	+	0.995427i	$0.530452\pi$
$828$	0	0
$829$	−2.45446	−0.0852471	−0.0426235	−	0.999091i	$-0.513572\pi$
$829$	−2.45446	−0.0852471	−0.0426235	+	0.999091i	$0.513572\pi$
$830$	0	0
$831$	32.5937	1.13066
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−18.4939	−0.639243
$838$	0	0
$839$	−10.9656	−0.378574	−0.189287	−	0.981922i	$-0.560618\pi$
$839$	−10.9656	−0.378574	−0.189287	+	0.981922i	$0.560618\pi$
$840$	0	0
$841$	2.62348	0.0904647
$842$	0	0
$843$	5.29150	0.182249
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−41.1174	−1.41114
$850$	0	0
$851$	−58.1174	−1.99224
$852$	0	0
$853$	32.5937	1.11599	0.557993	−	0.829846i	$-0.311572\pi$
$853$	32.5937	1.11599	0.557993	+	0.829846i	$0.311572\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−14.6870	−0.501699	−0.250850	−	0.968026i	$-0.580710\pi$
$857$	−14.6870	−0.501699	−0.250850	+	0.968026i	$0.580710\pi$
$858$	0	0
$859$	8.55087	0.291752	0.145876	−	0.989303i	$-0.453400\pi$
$859$	8.55087	0.291752	0.145876	+	0.989303i	$0.453400\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	13.1296	0.446936	0.223468	−	0.974711i	$-0.428262\pi$
$863$	13.1296	0.446936	0.223468	+	0.974711i	$0.428262\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	41.9494	1.42468
$868$	0	0
$869$	5.62348	0.190763
$870$	0	0
$871$	−43.6388	−1.47864
$872$	0	0
$873$	−108.747	−3.68051
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−7.24695	−0.244712	−0.122356	−	0.992486i	$-0.539045\pi$
$877$	−7.24695	−0.244712	−0.122356	+	0.992486i	$0.539045\pi$
$878$	0	0
$879$	−17.2470	−0.581725
$880$	0	0
$881$	−9.35577	−0.315204	−0.157602	−	0.987503i	$-0.550376\pi$
$881$	−9.35577	−0.315204	−0.157602	+	0.987503i	$0.550376\pi$
$882$	0	0
$883$	15.0000	0.504790	0.252395	−	0.967624i	$-0.418782\pi$
$883$	15.0000	0.504790	0.252395	+	0.967624i	$0.418782\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−7.74597	−0.260084	−0.130042	−	0.991508i	$-0.541511\pi$
$887$	−7.74597	−0.260084	−0.130042	+	0.991508i	$0.541511\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	26.2470	0.879306
$892$	0	0
$893$	−29.2470	−0.978712
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−131.482	−4.39005
$898$	0	0
$899$	−6.90131	−0.230172
$900$	0	0
$901$	22.8553	0.761421
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−20.0000	−0.664089	−0.332045	−	0.943264i	$-0.607738\pi$
$907$	−20.0000	−0.664089	−0.332045	+	0.943264i	$0.607738\pi$
$908$	0	0
$909$	−9.35577	−0.310311
$910$	0	0
$911$	−18.1174	−0.600255	−0.300128	−	0.953899i	$-0.597029\pi$
$911$	−18.1174	−0.600255	−0.300128	+	0.953899i	$0.597029\pi$
$912$	0	0
$913$	0.804903	0.0266384
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−35.3643	−1.16656	−0.583281	−	0.812271i	$-0.698231\pi$
$919$	−35.3643	−1.16656	−0.583281	+	0.812271i	$0.698231\pi$
$920$	0	0
$921$	62.3643	2.05497
$922$	0	0
$923$	−12.5754	−0.413924
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−99.3908	−3.26442
$928$	0	0
$929$	19.1736	0.629066	0.314533	−	0.949246i	$-0.398152\pi$
$929$	19.1736	0.629066	0.314533	+	0.949246i	$0.398152\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	90.2348	2.95415
$934$	0	0
$935$	0	0
$936$	0	0
$937$	25.2700	0.825536	0.412768	−	0.910836i	$-0.364562\pi$
$937$	25.2700	0.825536	0.412768	+	0.910836i	$0.364562\pi$
$938$	0	0
$939$	−8.00000	−0.261070
$940$	0	0
$941$	21.6281	0.705056	0.352528	−	0.935801i	$-0.385322\pi$
$941$	21.6281	0.705056	0.352528	+	0.935801i	$0.385322\pi$
$942$	0	0
$943$	74.5431	2.42746
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−48.9878	−1.59189	−0.795945	−	0.605369i	$-0.793026\pi$
$947$	−48.9878	−1.59189	−0.795945	+	0.605369i	$0.793026\pi$
$948$	0	0
$949$	−86.2348	−2.79930
$950$	0	0
$951$	63.9601	2.07405
$952$	0	0
$953$	16.2470	0.526290	0.263145	−	0.964756i	$-0.415240\pi$
$953$	16.2470	0.526290	0.263145	+	0.964756i	$0.415240\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	18.3290	0.592492
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−29.4939	−0.951416
$962$	0	0
$963$	111.482	3.59245
$964$	0	0
$965$	0	0
$966$	0	0
$967$	26.7530	0.860320	0.430160	−	0.902753i	$-0.358457\pi$
$967$	26.7530	0.860320	0.430160	+	0.902753i	$0.358457\pi$
$968$	0	0
$969$	29.7169	0.954644
$970$	0	0
$971$	18.2892	0.586929	0.293464	−	0.955970i	$-0.405192\pi$
$971$	18.2892	0.586929	0.293464	+	0.955970i	$0.405192\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	7.75305	0.248042	0.124021	−	0.992280i	$-0.460421\pi$
$977$	7.75305	0.248042	0.124021	+	0.992280i	$0.460421\pi$
$978$	0	0
$979$	0.804903	0.0257248
$980$	0	0
$981$	−42.8704	−1.36875
$982$	0	0
$983$	19.1736	0.611544	0.305772	−	0.952105i	$-0.401086\pi$
$983$	19.1736	0.611544	0.305772	+	0.952105i	$0.401086\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−88.6113	−2.81767
$990$	0	0
$991$	−30.1174	−0.956710	−0.478355	−	0.878167i	$-0.658767\pi$
$991$	−30.1174	−0.956710	−0.478355	+	0.878167i	$0.658767\pi$
$992$	0	0
$993$	−65.9922	−2.09420
$994$	0	0
$995$	0	0
$996$	0	0
$997$	3.29912	0.104484	0.0522421	−	0.998634i	$-0.483363\pi$
$997$	3.29912	0.104484	0.0522421	+	0.998634i	$0.483363\pi$
$998$	0	0
$999$	−114.883	−3.63473

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9800.2.a.cq.1.1	✓	4
5.4	even	2		9800.2.a.cr.1.4	yes	4
7.6	odd	2	inner	9800.2.a.cq.1.4	yes	4
35.34	odd	2		9800.2.a.cr.1.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9800.2.a.cq.1.1	✓	4	1.1	even	1	trivial
9800.2.a.cq.1.4	yes	4	7.6	odd	2	inner
9800.2.a.cr.1.1	yes	4	35.34	odd	2
9800.2.a.cr.1.4	yes	4	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9800.a (trivial)

\(f(q)\)	\(=\)	\(q-3.25937 q^{3} +7.62348 q^{9} +O(q^{10})\)	\(q-3.25937 q^{3} +7.62348 q^{9} +1.00000 q^{11} -5.29150 q^{13} -2.03214 q^{17} +4.48660 q^{19} -7.62348 q^{23} -15.0696 q^{27} -5.62348 q^{29} +1.22723 q^{31} -3.25937 q^{33} +7.62348 q^{37} +17.2470 q^{39} -9.77810 q^{41} +11.6235 q^{43} -6.51873 q^{47} +6.62348 q^{51} -11.2470 q^{53} -14.6235 q^{57} +5.29150 q^{59} -7.74597 q^{61} +8.24695 q^{67} +24.8477 q^{69} +2.37652 q^{71} +16.2968 q^{73} +5.62348 q^{79} +26.2470 q^{81} +0.804903 q^{83} +18.3290 q^{87} +0.804903 q^{89} -4.00000 q^{93} -14.2647 q^{97} +7.62348 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 10 q^{9}+O(q^{10}) \) 4 * q + 10 * q^9	\( 4 q + 10 q^{9} + 4 q^{11} - 10 q^{23} - 2 q^{29} + 10 q^{37} + 28 q^{39} + 26 q^{43} + 6 q^{51} - 4 q^{53} - 38 q^{57} - 8 q^{67} + 30 q^{71} + 2 q^{79} + 64 q^{81} - 16 q^{93} + 10 q^{99}+O(q^{100}) \) 4 * q + 10 * q^9 + 4 * q^11 - 10 * q^23 - 2 * q^29 + 10 * q^37 + 28 * q^39 + 26 * q^43 + 6 * q^51 - 4 * q^53 - 38 * q^57 - 8 * q^67 + 30 * q^71 + 2 * q^79 + 64 * q^81 - 16 * q^93 + 10 * q^99

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