LMFDB - Embedded newform 9800.2.a.db.1.3

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:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 22x^{8} - 16x^{7} + 146x^{6} + 200x^{5} - 206x^{4} - 440x^{3} - 124x^{2} + 72x + 28 $ x^10 - 22x^8 - 16x^7 + 146x^6 + 200x^5 - 206x^4 - 440x^3 - 124x^2 + 72x + 28
Coefficient ring:	$\Z[a_1, \ldots, a_{41}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 1960)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.609577$ 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)

$f(q)$	$=$	$q-1.35056 q^{3} -1.17599 q^{9} +O(q^{10})$	$q-1.35056 q^{3} -1.17599 q^{9} +3.15296 q^{11} +1.17296 q^{13} +2.07395 q^{17} -1.92745 q^{19} +4.51311 q^{23} +5.63992 q^{27} -6.97293 q^{29} -3.07731 q^{31} -4.25827 q^{33} -11.4901 q^{37} -1.58416 q^{39} +2.79587 q^{41} -3.22814 q^{43} -1.89635 q^{47} -2.80099 q^{51} -6.64710 q^{53} +2.60313 q^{57} +7.93376 q^{59} +8.15581 q^{61} -8.63580 q^{67} -6.09523 q^{69} -2.84298 q^{71} +5.35195 q^{73} +15.5300 q^{79} -4.08910 q^{81} -18.0496 q^{83} +9.41736 q^{87} -2.01829 q^{89} +4.15609 q^{93} +7.00968 q^{97} -3.70784 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 14 q^{9}+O(q^{10}) $ 10 * q + 14 * q^9	$ 10 q + 14 q^{9} - 12 q^{11} - 16 q^{23} + 12 q^{29} - 36 q^{37} - 20 q^{39} - 24 q^{43} - 36 q^{51} - 8 q^{53} - 16 q^{57} - 40 q^{67} - 8 q^{71} - 4 q^{79} + 50 q^{81} - 48 q^{93} - 72 q^{99}+O(q^{100}) $ 10 * q + 14 * q^9 - 12 * q^11 - 16 * q^23 + 12 * q^29 - 36 * q^37 - 20 * q^39 - 24 * q^43 - 36 * q^51 - 8 * q^53 - 16 * q^57 - 40 * q^67 - 8 * q^71 - 4 * q^79 + 50 * q^81 - 48 * q^93 - 72 * 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
$3$	−1.35056	−0.779746	−0.389873	−	0.920869i	$-0.627481\pi$
$3$	−1.35056	−0.779746	−0.389873	+	0.920869i	$0.627481\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	−1.17599	−0.391995
$10$	0	0
$11$	3.15296	0.950654	0.475327	−	0.879809i	$-0.342330\pi$
$11$	3.15296	0.950654	0.475327	+	0.879809i	$0.342330\pi$
$12$	0	0
$13$	1.17296	0.325322	0.162661	−	0.986682i	$-0.447992\pi$
$13$	1.17296	0.325322	0.162661	+	0.986682i	$0.447992\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	2.07395	0.503006	0.251503	−	0.967857i	$-0.419075\pi$
$17$	2.07395	0.503006	0.251503	+	0.967857i	$0.419075\pi$
$18$	0	0
$19$	−1.92745	−0.442186	−0.221093	−	0.975253i	$-0.570962\pi$
$19$	−1.92745	−0.442186	−0.221093	+	0.975253i	$0.570962\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	4.51311	0.941049	0.470524	−	0.882387i	$-0.344065\pi$
$23$	4.51311	0.941049	0.470524	+	0.882387i	$0.344065\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	5.63992	1.08540
$28$	0	0
$29$	−6.97293	−1.29484	−0.647420	−	0.762134i	$-0.724152\pi$
$29$	−6.97293	−1.29484	−0.647420	+	0.762134i	$0.724152\pi$
$30$	0	0
$31$	−3.07731	−0.552701	−0.276351	−	0.961057i	$-0.589125\pi$
$31$	−3.07731	−0.552701	−0.276351	+	0.961057i	$0.589125\pi$
$32$	0	0
$33$	−4.25827	−0.741269
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−11.4901	−1.88896	−0.944480	−	0.328570i	$-0.893433\pi$
$37$	−11.4901	−1.88896	−0.944480	+	0.328570i	$0.893433\pi$
$38$	0	0
$39$	−1.58416	−0.253669
$40$	0	0
$41$	2.79587	0.436641	0.218321	−	0.975877i	$-0.429942\pi$
$41$	2.79587	0.436641	0.218321	+	0.975877i	$0.429942\pi$
$42$	0	0
$43$	−3.22814	−0.492286	−0.246143	−	0.969234i	$-0.579163\pi$
$43$	−3.22814	−0.492286	−0.246143	+	0.969234i	$0.579163\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−1.89635	−0.276611	−0.138306	−	0.990390i	$-0.544166\pi$
$47$	−1.89635	−0.276611	−0.138306	+	0.990390i	$0.544166\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	−2.80099	−0.392217
$52$	0	0
$53$	−6.64710	−0.913050	−0.456525	−	0.889711i	$-0.650906\pi$
$53$	−6.64710	−0.913050	−0.456525	+	0.889711i	$0.650906\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	2.60313	0.344793
$58$	0	0
$59$	7.93376	1.03289	0.516444	−	0.856321i	$-0.327255\pi$
$59$	7.93376	1.03289	0.516444	+	0.856321i	$0.327255\pi$
$60$	0	0
$61$	8.15581	1.04424	0.522122	−	0.852871i	$-0.325140\pi$
$61$	8.15581	1.04424	0.522122	+	0.852871i	$0.325140\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	−8.63580	−1.05503	−0.527515	−	0.849545i	$-0.676876\pi$
$67$	−8.63580	−1.05503	−0.527515	+	0.849545i	$0.676876\pi$
$68$	0	0
$69$	−6.09523	−0.733780
$70$	0	0
$71$	−2.84298	−0.337400	−0.168700	−	0.985667i	$-0.553957\pi$
$71$	−2.84298	−0.337400	−0.168700	+	0.985667i	$0.553957\pi$
$72$	0	0
$73$	5.35195	0.626399	0.313199	−	0.949687i	$-0.398599\pi$
$73$	5.35195	0.626399	0.313199	+	0.949687i	$0.398599\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	15.5300	1.74726	0.873631	−	0.486588i	$-0.161759\pi$
$79$	15.5300	1.74726	0.873631	+	0.486588i	$0.161759\pi$
$80$	0	0
$81$	−4.08910	−0.454344
$82$	0	0
$83$	−18.0496	−1.98120	−0.990599	−	0.136795i	$-0.956320\pi$
$83$	−18.0496	−1.98120	−0.990599	+	0.136795i	$0.956320\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	9.41736	1.00965
$88$	0	0
$89$	−2.01829	−0.213938	−0.106969	−	0.994262i	$-0.534115\pi$
$89$	−2.01829	−0.213938	−0.106969	+	0.994262i	$0.534115\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	4.15609	0.430967
$94$	0	0
$95$	0	0
$96$	0	0
$97$	7.00968	0.711725	0.355862	−	0.934538i	$-0.384187\pi$
$97$	7.00968	0.711725	0.355862	+	0.934538i	$0.384187\pi$
$98$	0	0
$99$	−3.70784	−0.372652
$100$	0	0
$101$	15.5026	1.54257	0.771283	−	0.636493i	$-0.219615\pi$
$101$	15.5026	1.54257	0.771283	+	0.636493i	$0.219615\pi$
$102$	0	0
$103$	−16.6990	−1.64540	−0.822702	−	0.568473i	$-0.807534\pi$
$103$	−16.6990	−1.64540	−0.822702	+	0.568473i	$0.807534\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−15.3403	−1.48300	−0.741499	−	0.670954i	$-0.765885\pi$
$107$	−15.3403	−1.48300	−0.741499	+	0.670954i	$0.765885\pi$
$108$	0	0
$109$	15.8272	1.51597	0.757986	−	0.652271i	$-0.226183\pi$
$109$	15.8272	1.51597	0.757986	+	0.652271i	$0.226183\pi$
$110$	0	0
$111$	15.5181	1.47291
$112$	0	0
$113$	−3.41897	−0.321630	−0.160815	−	0.986985i	$-0.551412\pi$
$113$	−3.41897	−0.321630	−0.160815	+	0.986985i	$0.551412\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−1.37939	−0.127525
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−1.05882	−0.0962564
$122$	0	0
$123$	−3.77599	−0.340469
$124$	0	0
$125$	0	0
$126$	0	0
$127$	2.64710	0.234893	0.117446	−	0.993079i	$-0.462529\pi$
$127$	2.64710	0.234893	0.117446	+	0.993079i	$0.462529\pi$
$128$	0	0
$129$	4.35979	0.383858
$130$	0	0
$131$	−13.2514	−1.15778	−0.578891	−	0.815405i	$-0.696514\pi$
$131$	−13.2514	−1.15778	−0.578891	+	0.815405i	$0.696514\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	12.6830	1.08358	0.541790	−	0.840514i	$-0.317747\pi$
$137$	12.6830	1.08358	0.541790	+	0.840514i	$0.317747\pi$
$138$	0	0
$139$	19.7452	1.67477	0.837384	−	0.546614i	$-0.184084\pi$
$139$	19.7452	1.67477	0.837384	+	0.546614i	$0.184084\pi$
$140$	0	0
$141$	2.56114	0.215687
$142$	0	0
$143$	3.69832	0.309269
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	8.78563	0.719747	0.359874	−	0.933001i	$-0.382820\pi$
$149$	8.78563	0.719747	0.359874	+	0.933001i	$0.382820\pi$
$150$	0	0
$151$	11.5874	0.942966	0.471483	−	0.881875i	$-0.343719\pi$
$151$	11.5874	0.942966	0.471483	+	0.881875i	$0.343719\pi$
$152$	0	0
$153$	−2.43893	−0.197176
$154$	0	0
$155$	0	0
$156$	0	0
$157$	15.5528	1.24125	0.620624	−	0.784109i	$-0.286880\pi$
$157$	15.5528	1.24125	0.620624	+	0.784109i	$0.286880\pi$
$158$	0	0
$159$	8.97732	0.711947
$160$	0	0
$161$	0	0
$162$	0	0
$163$	3.68390	0.288545	0.144273	−	0.989538i	$-0.453916\pi$
$163$	3.68390	0.288545	0.144273	+	0.989538i	$0.453916\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−17.8528	−1.38149	−0.690745	−	0.723098i	$-0.742717\pi$
$167$	−17.8528	−1.38149	−0.690745	+	0.723098i	$0.742717\pi$
$168$	0	0
$169$	−11.6242	−0.894166
$170$	0	0
$171$	2.26665	0.173335
$172$	0	0
$173$	17.8551	1.35749	0.678747	−	0.734372i	$-0.262523\pi$
$173$	17.8551	1.35749	0.678747	+	0.734372i	$0.262523\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−10.7150	−0.805390
$178$	0	0
$179$	−18.3059	−1.36825	−0.684125	−	0.729365i	$-0.739816\pi$
$179$	−18.3059	−1.36825	−0.684125	+	0.729365i	$0.739816\pi$
$180$	0	0
$181$	−10.8779	−0.808550	−0.404275	−	0.914637i	$-0.632476\pi$
$181$	−10.8779	−0.808550	−0.404275	+	0.914637i	$0.632476\pi$
$182$	0	0
$183$	−11.0149	−0.814246
$184$	0	0
$185$	0	0
$186$	0	0
$187$	6.53908	0.478185
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−8.74438	−0.632721	−0.316360	−	0.948639i	$-0.602461\pi$
$191$	−8.74438	−0.632721	−0.316360	+	0.948639i	$0.602461\pi$
$192$	0	0
$193$	−1.57691	−0.113508	−0.0567541	−	0.998388i	$-0.518075\pi$
$193$	−1.57691	−0.113508	−0.0567541	+	0.998388i	$0.518075\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−0.873188	−0.0622121	−0.0311060	−	0.999516i	$-0.509903\pi$
$197$	−0.873188	−0.0622121	−0.0311060	+	0.999516i	$0.509903\pi$
$198$	0	0
$199$	−3.33192	−0.236194	−0.118097	−	0.993002i	$-0.537679\pi$
$199$	−3.33192	−0.236194	−0.118097	+	0.993002i	$0.537679\pi$
$200$	0	0
$201$	11.6632	0.822657
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−5.30736	−0.368887
$208$	0	0
$209$	−6.07716	−0.420366
$210$	0	0
$211$	−11.2354	−0.773476	−0.386738	−	0.922190i	$-0.626398\pi$
$211$	−11.2354	−0.773476	−0.386738	+	0.922190i	$0.626398\pi$
$212$	0	0
$213$	3.83962	0.263087
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−7.22814	−0.488432
$220$	0	0
$221$	2.43267	0.163639
$222$	0	0
$223$	2.21315	0.148204	0.0741018	−	0.997251i	$-0.476391\pi$
$223$	2.21315	0.148204	0.0741018	+	0.997251i	$0.476391\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	22.1760	1.47187	0.735937	−	0.677050i	$-0.236742\pi$
$227$	22.1760	1.47187	0.735937	+	0.677050i	$0.236742\pi$
$228$	0	0
$229$	−1.55568	−0.102802	−0.0514012	−	0.998678i	$-0.516369\pi$
$229$	−1.55568	−0.102802	−0.0514012	+	0.998678i	$0.516369\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−22.0467	−1.44433	−0.722163	−	0.691723i	$-0.756852\pi$
$233$	−22.0467	−1.44433	−0.722163	+	0.691723i	$0.756852\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−20.9742	−1.36242
$238$	0	0
$239$	−20.7710	−1.34357	−0.671783	−	0.740748i	$-0.734471\pi$
$239$	−20.7710	−1.34357	−0.671783	+	0.740748i	$0.734471\pi$
$240$	0	0
$241$	−2.25118	−0.145011	−0.0725057	−	0.997368i	$-0.523100\pi$
$241$	−2.25118	−0.145011	−0.0725057	+	0.997368i	$0.523100\pi$
$242$	0	0
$243$	−11.3972	−0.731130
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−2.26083	−0.143853
$248$	0	0
$249$	24.3770	1.54483
$250$	0	0
$251$	−18.6537	−1.17741	−0.588704	−	0.808349i	$-0.700362\pi$
$251$	−18.6537	−1.17741	−0.588704	+	0.808349i	$0.700362\pi$
$252$	0	0
$253$	14.2297	0.894612
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−22.2112	−1.38550	−0.692748	−	0.721180i	$-0.743600\pi$
$257$	−22.2112	−1.38550	−0.692748	+	0.721180i	$0.743600\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	8.20007	0.507571
$262$	0	0
$263$	−5.20626	−0.321032	−0.160516	−	0.987033i	$-0.551316\pi$
$263$	−5.20626	−0.321032	−0.160516	+	0.987033i	$0.551316\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	2.72582	0.166817
$268$	0	0
$269$	10.3802	0.632890	0.316445	−	0.948611i	$-0.397511\pi$
$269$	10.3802	0.632890	0.316445	+	0.948611i	$0.397511\pi$
$270$	0	0
$271$	7.53627	0.457796	0.228898	−	0.973450i	$-0.426488\pi$
$271$	7.53627	0.457796	0.228898	+	0.973450i	$0.426488\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−29.0370	−1.74467	−0.872333	−	0.488913i	$-0.837394\pi$
$277$	−29.0370	−1.74467	−0.872333	+	0.488913i	$0.837394\pi$
$278$	0	0
$279$	3.61887	0.216656
$280$	0	0
$281$	−1.34677	−0.0803416	−0.0401708	−	0.999193i	$-0.512790\pi$
$281$	−1.34677	−0.0803416	−0.0401708	+	0.999193i	$0.512790\pi$
$282$	0	0
$283$	2.50433	0.148867	0.0744335	−	0.997226i	$-0.476285\pi$
$283$	2.50433	0.148867	0.0744335	+	0.997226i	$0.476285\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−12.6987	−0.746985
$290$	0	0
$291$	−9.46699	−0.554965
$292$	0	0
$293$	3.13770	0.183306	0.0916531	−	0.995791i	$-0.470785\pi$
$293$	3.13770	0.183306	0.0916531	+	0.995791i	$0.470785\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	17.7825	1.03184
$298$	0	0
$299$	5.29372	0.306144
$300$	0	0
$301$	0	0
$302$	0	0
$303$	−20.9372	−1.20281
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−14.3702	−0.820150	−0.410075	−	0.912052i	$-0.634497\pi$
$307$	−14.3702	−0.820150	−0.410075	+	0.912052i	$0.634497\pi$
$308$	0	0
$309$	22.5530	1.28300
$310$	0	0
$311$	−18.3522	−1.04066	−0.520329	−	0.853966i	$-0.674191\pi$
$311$	−18.3522	−1.04066	−0.520329	+	0.853966i	$0.674191\pi$
$312$	0	0
$313$	1.81933	0.102835	0.0514174	−	0.998677i	$-0.483626\pi$
$313$	1.81933	0.102835	0.0514174	+	0.998677i	$0.483626\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−32.2865	−1.81339	−0.906696	−	0.421785i	$-0.861404\pi$
$317$	−32.2865	−1.81339	−0.906696	+	0.421785i	$0.861404\pi$
$318$	0	0
$319$	−21.9854	−1.23094
$320$	0	0
$321$	20.7179	1.15636
$322$	0	0
$323$	−3.99742	−0.222422
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−21.3756	−1.18207
$328$	0	0
$329$	0	0
$330$	0	0
$331$	18.6482	1.02500	0.512500	−	0.858687i	$-0.328720\pi$
$331$	18.6482	1.02500	0.512500	+	0.858687i	$0.328720\pi$
$332$	0	0
$333$	13.5122	0.740463
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−23.1300	−1.25997	−0.629986	−	0.776606i	$-0.716939\pi$
$337$	−23.1300	−1.25997	−0.629986	+	0.776606i	$0.716939\pi$
$338$	0	0
$339$	4.61752	0.250790
$340$	0	0
$341$	−9.70264	−0.525428
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−15.0936	−0.810269	−0.405134	−	0.914257i	$-0.632775\pi$
$347$	−15.0936	−0.810269	−0.405134	+	0.914257i	$0.632775\pi$
$348$	0	0
$349$	−13.8618	−0.742005	−0.371003	−	0.928632i	$-0.620986\pi$
$349$	−13.8618	−0.742005	−0.371003	+	0.928632i	$0.620986\pi$
$350$	0	0
$351$	6.61543	0.353106
$352$	0	0
$353$	27.7238	1.47559	0.737795	−	0.675025i	$-0.235867\pi$
$353$	27.7238	1.47559	0.737795	+	0.675025i	$0.235867\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−0.949322	−0.0501033	−0.0250516	−	0.999686i	$-0.507975\pi$
$359$	−0.949322	−0.0501033	−0.0250516	+	0.999686i	$0.507975\pi$
$360$	0	0
$361$	−15.2850	−0.804471
$362$	0	0
$363$	1.43000	0.0750556
$364$	0	0
$365$	0	0
$366$	0	0
$367$	22.5483	1.17701	0.588506	−	0.808493i	$-0.299716\pi$
$367$	22.5483	1.17701	0.588506	+	0.808493i	$0.299716\pi$
$368$	0	0
$369$	−3.28790	−0.171161
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−28.6314	−1.48248	−0.741239	−	0.671241i	$-0.765761\pi$
$373$	−28.6314	−1.48248	−0.741239	+	0.671241i	$0.765761\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−8.17900	−0.421240
$378$	0	0
$379$	12.4263	0.638296	0.319148	−	0.947705i	$-0.396603\pi$
$379$	12.4263	0.638296	0.319148	+	0.947705i	$0.396603\pi$
$380$	0	0
$381$	−3.57507	−0.183157
$382$	0	0
$383$	27.8845	1.42483	0.712415	−	0.701758i	$-0.247601\pi$
$383$	27.8845	1.42483	0.712415	+	0.701758i	$0.247601\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	3.79624	0.192974
$388$	0	0
$389$	16.5167	0.837428	0.418714	−	0.908118i	$-0.362481\pi$
$389$	16.5167	0.837428	0.418714	+	0.908118i	$0.362481\pi$
$390$	0	0
$391$	9.35995	0.473353
$392$	0	0
$393$	17.8968	0.902776
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−26.4055	−1.32525	−0.662626	−	0.748951i	$-0.730558\pi$
$397$	−26.4055	−1.32525	−0.662626	+	0.748951i	$0.730558\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	24.4738	1.22216	0.611082	−	0.791567i	$-0.290735\pi$
$401$	24.4738	1.22216	0.611082	+	0.791567i	$0.290735\pi$
$402$	0	0
$403$	−3.60958	−0.179806
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−36.2278	−1.79575
$408$	0	0
$409$	15.8212	0.782309	0.391154	−	0.920325i	$-0.372076\pi$
$409$	15.8212	0.782309	0.391154	+	0.920325i	$0.372076\pi$
$410$	0	0
$411$	−17.1291	−0.844917
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−26.6671	−1.30590
$418$	0	0
$419$	29.8828	1.45987	0.729934	−	0.683517i	$-0.239551\pi$
$419$	29.8828	1.45987	0.729934	+	0.683517i	$0.239551\pi$
$420$	0	0
$421$	16.4027	0.799418	0.399709	−	0.916642i	$-0.369111\pi$
$421$	16.4027	0.799418	0.399709	+	0.916642i	$0.369111\pi$
$422$	0	0
$423$	2.23008	0.108430
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−4.99480	−0.241151
$430$	0	0
$431$	5.52681	0.266217	0.133109	−	0.991101i	$-0.457504\pi$
$431$	5.52681	0.266217	0.133109	+	0.991101i	$0.457504\pi$
$432$	0	0
$433$	24.1912	1.16255	0.581277	−	0.813706i	$-0.302553\pi$
$433$	24.1912	1.16255	0.581277	+	0.813706i	$0.302553\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−8.69878	−0.416119
$438$	0	0
$439$	−22.7223	−1.08447	−0.542237	−	0.840225i	$-0.682423\pi$
$439$	−22.7223	−1.08447	−0.542237	+	0.840225i	$0.682423\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	12.9115	0.613445	0.306722	−	0.951799i	$-0.400768\pi$
$443$	12.9115	0.613445	0.306722	+	0.951799i	$0.400768\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−11.8655	−0.561220
$448$	0	0
$449$	33.3152	1.57224	0.786121	−	0.618072i	$-0.212086\pi$
$449$	33.3152	1.57224	0.786121	+	0.618072i	$0.212086\pi$
$450$	0	0
$451$	8.81527	0.415095
$452$	0	0
$453$	−15.6494	−0.735274
$454$	0	0
$455$	0	0
$456$	0	0
$457$	8.35310	0.390742	0.195371	−	0.980729i	$-0.437409\pi$
$457$	8.35310	0.390742	0.195371	+	0.980729i	$0.437409\pi$
$458$	0	0
$459$	11.6969	0.545964
$460$	0	0
$461$	−24.8066	−1.15536	−0.577680	−	0.816263i	$-0.696042\pi$
$461$	−24.8066	−1.15536	−0.577680	+	0.816263i	$0.696042\pi$
$462$	0	0
$463$	−4.65975	−0.216557	−0.108278	−	0.994121i	$-0.534534\pi$
$463$	−4.65975	−0.216557	−0.108278	+	0.994121i	$0.534534\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−36.9637	−1.71048	−0.855239	−	0.518234i	$-0.826590\pi$
$467$	−36.9637	−1.71048	−0.855239	+	0.518234i	$0.826590\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−21.0050	−0.967858
$472$	0	0
$473$	−10.1782	−0.467994
$474$	0	0
$475$	0	0
$476$	0	0
$477$	7.81690	0.357911
$478$	0	0
$479$	−27.3295	−1.24872	−0.624359	−	0.781137i	$-0.714640\pi$
$479$	−27.3295	−1.24872	−0.624359	+	0.781137i	$0.714640\pi$
$480$	0	0
$481$	−13.4775	−0.614520
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−35.7613	−1.62050	−0.810249	−	0.586086i	$-0.800668\pi$
$487$	−35.7613	−1.62050	−0.810249	+	0.586086i	$0.800668\pi$
$488$	0	0
$489$	−4.97533	−0.224992
$490$	0	0
$491$	−29.5187	−1.33216	−0.666080	−	0.745880i	$-0.732029\pi$
$491$	−29.5187	−1.33216	−0.666080	+	0.745880i	$0.732029\pi$
$492$	0	0
$493$	−14.4615	−0.651312
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−42.6555	−1.90952	−0.954761	−	0.297375i	$-0.903889\pi$
$499$	−42.6555	−1.90952	−0.954761	+	0.297375i	$0.903889\pi$
$500$	0	0
$501$	24.1113	1.07721
$502$	0	0
$503$	5.52860	0.246508	0.123254	−	0.992375i	$-0.460667\pi$
$503$	5.52860	0.246508	0.123254	+	0.992375i	$0.460667\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	15.6991	0.697222
$508$	0	0
$509$	23.9285	1.06061	0.530306	−	0.847806i	$-0.322077\pi$
$509$	23.9285	1.06061	0.530306	+	0.847806i	$0.322077\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−10.8706	−0.479950
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−5.97913	−0.262962
$518$	0	0
$519$	−24.1143	−1.05850
$520$	0	0
$521$	−4.18778	−0.183470	−0.0917350	−	0.995783i	$-0.529241\pi$
$521$	−4.18778	−0.183470	−0.0917350	+	0.995783i	$0.529241\pi$
$522$	0	0
$523$	−30.6134	−1.33863	−0.669316	−	0.742978i	$-0.733413\pi$
$523$	−30.6134	−1.33863	−0.669316	+	0.742978i	$0.733413\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−6.38218	−0.278012
$528$	0	0
$529$	−2.63182	−0.114427
$530$	0	0
$531$	−9.33000	−0.404887
$532$	0	0
$533$	3.27945	0.142049
$534$	0	0
$535$	0	0
$536$	0	0
$537$	24.7233	1.06689
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−5.76740	−0.247960	−0.123980	−	0.992285i	$-0.539566\pi$
$541$	−5.76740	−0.247960	−0.123980	+	0.992285i	$0.539566\pi$
$542$	0	0
$543$	14.6913	0.630464
$544$	0	0
$545$	0	0
$546$	0	0
$547$	4.49973	0.192395	0.0961974	−	0.995362i	$-0.469332\pi$
$547$	4.49973	0.192395	0.0961974	+	0.995362i	$0.469332\pi$
$548$	0	0
$549$	−9.59113	−0.409339
$550$	0	0
$551$	13.4399	0.572560
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	4.58126	0.194114	0.0970571	−	0.995279i	$-0.469057\pi$
$557$	4.58126	0.194114	0.0970571	+	0.995279i	$0.469057\pi$
$558$	0	0
$559$	−3.78649	−0.160151
$560$	0	0
$561$	−8.83142	−0.372863
$562$	0	0
$563$	14.3871	0.606345	0.303172	−	0.952936i	$-0.401954\pi$
$563$	14.3871	0.606345	0.303172	+	0.952936i	$0.401954\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	22.8927	0.959712	0.479856	−	0.877347i	$-0.340689\pi$
$569$	22.8927	0.959712	0.479856	+	0.877347i	$0.340689\pi$
$570$	0	0
$571$	−44.0662	−1.84411	−0.922057	−	0.387054i	$-0.873493\pi$
$571$	−44.0662	−1.84411	−0.922057	+	0.387054i	$0.873493\pi$
$572$	0	0
$573$	11.8098	0.493362
$574$	0	0
$575$	0	0
$576$	0	0
$577$	40.8358	1.70002	0.850009	−	0.526768i	$-0.176596\pi$
$577$	40.8358	1.70002	0.850009	+	0.526768i	$0.176596\pi$
$578$	0	0
$579$	2.12971	0.0885077
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−20.9581	−0.867995
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−10.9756	−0.453012	−0.226506	−	0.974010i	$-0.572730\pi$
$587$	−10.9756	−0.453012	−0.226506	+	0.974010i	$0.572730\pi$
$588$	0	0
$589$	5.93135	0.244397
$590$	0	0
$591$	1.17929	0.0485097
$592$	0	0
$593$	17.4526	0.716690	0.358345	−	0.933589i	$-0.383341\pi$
$593$	17.4526	0.716690	0.358345	+	0.933589i	$0.383341\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	4.49996	0.184171
$598$	0	0
$599$	−35.7673	−1.46141	−0.730706	−	0.682693i	$-0.760809\pi$
$599$	−35.7673	−1.46141	−0.730706	+	0.682693i	$0.760809\pi$
$600$	0	0
$601$	−41.7828	−1.70436	−0.852179	−	0.523251i	$-0.824719\pi$
$601$	−41.7828	−1.70436	−0.852179	+	0.523251i	$0.824719\pi$
$602$	0	0
$603$	10.1556	0.413567
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−20.0829	−0.815139	−0.407569	−	0.913174i	$-0.633624\pi$
$607$	−20.0829	−0.815139	−0.407569	+	0.913174i	$0.633624\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−2.22435	−0.0899877
$612$	0	0
$613$	−10.9238	−0.441207	−0.220603	−	0.975364i	$-0.570803\pi$
$613$	−10.9238	−0.441207	−0.220603	+	0.975364i	$0.570803\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−15.2723	−0.614838	−0.307419	−	0.951574i	$-0.599465\pi$
$617$	−15.2723	−0.614838	−0.307419	+	0.951574i	$0.599465\pi$
$618$	0	0
$619$	−46.4570	−1.86727	−0.933633	−	0.358232i	$-0.883380\pi$
$619$	−46.4570	−1.86727	−0.933633	+	0.358232i	$0.883380\pi$
$620$	0	0
$621$	25.4536	1.02142
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	8.20758	0.327779
$628$	0	0
$629$	−23.8298	−0.950158
$630$	0	0
$631$	8.98975	0.357876	0.178938	−	0.983860i	$-0.442734\pi$
$631$	8.98975	0.357876	0.178938	+	0.983860i	$0.442734\pi$
$632$	0	0
$633$	15.1741	0.603115
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	3.34331	0.132259
$640$	0	0
$641$	36.0396	1.42348	0.711739	−	0.702444i	$-0.247908\pi$
$641$	36.0396	1.42348	0.711739	+	0.702444i	$0.247908\pi$
$642$	0	0
$643$	−3.95563	−0.155995	−0.0779974	−	0.996954i	$-0.524853\pi$
$643$	−3.95563	−0.155995	−0.0779974	+	0.996954i	$0.524853\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−21.2626	−0.835920	−0.417960	−	0.908465i	$-0.637255\pi$
$647$	−21.2626	−0.835920	−0.417960	+	0.908465i	$0.637255\pi$
$648$	0	0
$649$	25.0149	0.981919
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−14.2373	−0.557148	−0.278574	−	0.960415i	$-0.589862\pi$
$653$	−14.2373	−0.557148	−0.278574	+	0.960415i	$0.589862\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−6.29382	−0.245545
$658$	0	0
$659$	12.2364	0.476663	0.238332	−	0.971184i	$-0.423399\pi$
$659$	12.2364	0.476663	0.238332	+	0.971184i	$0.423399\pi$
$660$	0	0
$661$	11.6555	0.453347	0.226673	−	0.973971i	$-0.427215\pi$
$661$	11.6555	0.453347	0.226673	+	0.973971i	$0.427215\pi$
$662$	0	0
$663$	−3.28546	−0.127597
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−31.4696	−1.21851
$668$	0	0
$669$	−2.98899	−0.115561
$670$	0	0
$671$	25.7150	0.992716
$672$	0	0
$673$	−33.6866	−1.29852	−0.649261	−	0.760565i	$-0.724922\pi$
$673$	−33.6866	−1.29852	−0.649261	+	0.760565i	$0.724922\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−19.4835	−0.748812	−0.374406	−	0.927265i	$-0.622153\pi$
$677$	−19.4835	−0.748812	−0.374406	+	0.927265i	$0.622153\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−29.9500	−1.14769
$682$	0	0
$683$	−41.6882	−1.59516	−0.797578	−	0.603216i	$-0.793886\pi$
$683$	−41.6882	−1.59516	−0.797578	+	0.603216i	$0.793886\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	2.10104	0.0801597
$688$	0	0
$689$	−7.79682	−0.297035
$690$	0	0
$691$	−27.7762	−1.05665	−0.528327	−	0.849041i	$-0.677181\pi$
$691$	−27.7762	−1.05665	−0.528327	+	0.849041i	$0.677181\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	5.79848	0.219633
$698$	0	0
$699$	29.7754	1.12621
$700$	0	0
$701$	6.71304	0.253548	0.126774	−	0.991932i	$-0.459538\pi$
$701$	6.71304	0.253548	0.126774	+	0.991932i	$0.459538\pi$
$702$	0	0
$703$	22.1465	0.835272
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	8.18729	0.307480	0.153740	−	0.988111i	$-0.450868\pi$
$709$	8.18729	0.307480	0.153740	+	0.988111i	$0.450868\pi$
$710$	0	0
$711$	−18.2631	−0.684919
$712$	0	0
$713$	−13.8882	−0.520119
$714$	0	0
$715$	0	0
$716$	0	0
$717$	28.0525	1.04764
$718$	0	0
$719$	−22.3339	−0.832915	−0.416458	−	0.909155i	$-0.636729\pi$
$719$	−22.3339	−0.832915	−0.416458	+	0.909155i	$0.636729\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	3.04036	0.113072
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−8.48235	−0.314593	−0.157296	−	0.987551i	$-0.550278\pi$
$727$	−8.48235	−0.314593	−0.157296	+	0.987551i	$0.550278\pi$
$728$	0	0
$729$	27.6599	1.02444
$730$	0	0
$731$	−6.69498	−0.247623
$732$	0	0
$733$	−33.6227	−1.24188	−0.620942	−	0.783857i	$-0.713250\pi$
$733$	−33.6227	−1.24188	−0.620942	+	0.783857i	$0.713250\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−27.2284	−1.00297
$738$	0	0
$739$	−1.18450	−0.0435727	−0.0217863	−	0.999763i	$-0.506935\pi$
$739$	−1.18450	−0.0435727	−0.0217863	+	0.999763i	$0.506935\pi$
$740$	0	0
$741$	3.05338	0.112169
$742$	0	0
$743$	47.8482	1.75538	0.877690	−	0.479228i	$-0.159083\pi$
$743$	47.8482	1.75538	0.877690	+	0.479228i	$0.159083\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	21.2261	0.776621
$748$	0	0
$749$	0	0
$750$	0	0
$751$	29.0164	1.05882	0.529412	−	0.848365i	$-0.322413\pi$
$751$	29.0164	1.05882	0.529412	+	0.848365i	$0.322413\pi$
$752$	0	0
$753$	25.1929	0.918080
$754$	0	0
$755$	0	0
$756$	0	0
$757$	43.7722	1.59093	0.795464	−	0.606001i	$-0.207227\pi$
$757$	43.7722	1.59093	0.795464	+	0.606001i	$0.207227\pi$
$758$	0	0
$759$	−19.2180	−0.697571
$760$	0	0
$761$	−17.6484	−0.639753	−0.319877	−	0.947459i	$-0.603642\pi$
$761$	−17.6484	−0.639753	−0.319877	+	0.947459i	$0.603642\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	9.30602	0.336021
$768$	0	0
$769$	−44.3759	−1.60024	−0.800118	−	0.599842i	$-0.795230\pi$
$769$	−44.3759	−1.60024	−0.800118	+	0.599842i	$0.795230\pi$
$770$	0	0
$771$	29.9976	1.08034
$772$	0	0
$773$	15.1494	0.544886	0.272443	−	0.962172i	$-0.412168\pi$
$773$	15.1494	0.544886	0.272443	+	0.962172i	$0.412168\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	−5.38888	−0.193077
$780$	0	0
$781$	−8.96383	−0.320751
$782$	0	0
$783$	−39.3268	−1.40542
$784$	0	0
$785$	0	0
$786$	0	0
$787$	2.99429	0.106735	0.0533674	−	0.998575i	$-0.483005\pi$
$787$	2.99429	0.106735	0.0533674	+	0.998575i	$0.483005\pi$
$788$	0	0
$789$	7.03137	0.250323
$790$	0	0
$791$	0	0
$792$	0	0
$793$	9.56648	0.339716
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−9.26106	−0.328044	−0.164022	−	0.986457i	$-0.552447\pi$
$797$	−9.26106	−0.328044	−0.164022	+	0.986457i	$0.552447\pi$
$798$	0	0
$799$	−3.93293	−0.139137
$800$	0	0
$801$	2.37348	0.0838627
$802$	0	0
$803$	16.8745	0.595489
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−14.0190	−0.493494
$808$	0	0
$809$	−16.4860	−0.579617	−0.289809	−	0.957085i	$-0.593592\pi$
$809$	−16.4860	−0.579617	−0.289809	+	0.957085i	$0.593592\pi$
$810$	0	0
$811$	17.6119	0.618437	0.309218	−	0.950991i	$-0.399933\pi$
$811$	17.6119	0.618437	0.309218	+	0.950991i	$0.399933\pi$
$812$	0	0
$813$	−10.1782	−0.356965
$814$	0	0
$815$	0	0
$816$	0	0
$817$	6.22205	0.217682
$818$	0	0
$819$	0	0
$820$	0	0
$821$	0.527484	0.0184093	0.00920465	−	0.999958i	$-0.497070\pi$
$821$	0.527484	0.0184093	0.00920465	+	0.999958i	$0.497070\pi$
$822$	0	0
$823$	4.36367	0.152108	0.0760540	−	0.997104i	$-0.475768\pi$
$823$	4.36367	0.152108	0.0760540	+	0.997104i	$0.475768\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−7.38579	−0.256829	−0.128415	−	0.991721i	$-0.540989\pi$
$827$	−7.38579	−0.256829	−0.128415	+	0.991721i	$0.540989\pi$
$828$	0	0
$829$	38.2988	1.33017	0.665087	−	0.746766i	$-0.268395\pi$
$829$	38.2988	1.33017	0.665087	+	0.746766i	$0.268395\pi$
$830$	0	0
$831$	39.2163	1.36040
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−17.3558	−0.599904
$838$	0	0
$839$	−10.9391	−0.377660	−0.188830	−	0.982010i	$-0.560470\pi$
$839$	−10.9391	−0.377660	−0.188830	+	0.982010i	$0.560470\pi$
$840$	0	0
$841$	19.6217	0.676610
$842$	0	0
$843$	1.81890	0.0626461
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−3.38225	−0.116078
$850$	0	0
$851$	−51.8561	−1.77760
$852$	0	0
$853$	−24.9925	−0.855726	−0.427863	−	0.903844i	$-0.640733\pi$
$853$	−24.9925	−0.855726	−0.427863	+	0.903844i	$0.640733\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	35.5504	1.21438	0.607189	−	0.794557i	$-0.292297\pi$
$857$	35.5504	1.21438	0.607189	+	0.794557i	$0.292297\pi$
$858$	0	0
$859$	−36.2283	−1.23609	−0.618047	−	0.786141i	$-0.712076\pi$
$859$	−36.2283	−1.23609	−0.618047	+	0.786141i	$0.712076\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	17.6846	0.601992	0.300996	−	0.953625i	$-0.402681\pi$
$863$	17.6846	0.601992	0.300996	+	0.953625i	$0.402681\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	17.1504	0.582459
$868$	0	0
$869$	48.9656	1.66104
$870$	0	0
$871$	−10.1295	−0.343225
$872$	0	0
$873$	−8.24329	−0.278993
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−8.54026	−0.288384	−0.144192	−	0.989550i	$-0.546058\pi$
$877$	−8.54026	−0.288384	−0.144192	+	0.989550i	$0.546058\pi$
$878$	0	0
$879$	−4.23765	−0.142932
$880$	0	0
$881$	9.40485	0.316857	0.158429	−	0.987370i	$-0.449357\pi$
$881$	9.40485	0.316857	0.158429	+	0.987370i	$0.449357\pi$
$882$	0	0
$883$	−46.5005	−1.56487	−0.782433	−	0.622735i	$-0.786021\pi$
$883$	−46.5005	−1.56487	−0.782433	+	0.622735i	$0.786021\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	6.76370	0.227103	0.113551	−	0.993532i	$-0.463777\pi$
$887$	6.76370	0.227103	0.113551	+	0.993532i	$0.463777\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−12.8928	−0.431924
$892$	0	0
$893$	3.65511	0.122314
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−7.14949	−0.238715
$898$	0	0
$899$	21.4579	0.715659
$900$	0	0
$901$	−13.7857	−0.459270
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	14.8793	0.494060	0.247030	−	0.969008i	$-0.420545\pi$
$907$	14.8793	0.494060	0.247030	+	0.969008i	$0.420545\pi$
$908$	0	0
$909$	−18.2308	−0.604679
$910$	0	0
$911$	30.6643	1.01595	0.507977	−	0.861371i	$-0.330394\pi$
$911$	30.6643	1.01595	0.507977	+	0.861371i	$0.330394\pi$
$912$	0	0
$913$	−56.9097	−1.88343
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	17.2241	0.568170	0.284085	−	0.958799i	$-0.408310\pi$
$919$	17.2241	0.568170	0.284085	+	0.958799i	$0.408310\pi$
$920$	0	0
$921$	19.4078	0.639509
$922$	0	0
$923$	−3.33472	−0.109764
$924$	0	0
$925$	0	0
$926$	0	0
$927$	19.6378	0.644991
$928$	0	0
$929$	26.3768	0.865395	0.432698	−	0.901539i	$-0.357562\pi$
$929$	26.3768	0.865395	0.432698	+	0.901539i	$0.357562\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	24.7858	0.811450
$934$	0	0
$935$	0	0
$936$	0	0
$937$	23.8347	0.778647	0.389323	−	0.921101i	$-0.372709\pi$
$937$	23.8347	0.778647	0.389323	+	0.921101i	$0.372709\pi$
$938$	0	0
$939$	−2.45712	−0.0801851
$940$	0	0
$941$	−53.7553	−1.75237	−0.876186	−	0.481974i	$-0.839920\pi$
$941$	−53.7553	−1.75237	−0.876186	+	0.481974i	$0.839920\pi$
$942$	0	0
$943$	12.6181	0.410901
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−38.4187	−1.24844	−0.624220	−	0.781249i	$-0.714583\pi$
$947$	−38.4187	−1.24844	−0.624220	+	0.781249i	$0.714583\pi$
$948$	0	0
$949$	6.27765	0.203781
$950$	0	0
$951$	43.6049	1.41399
$952$	0	0
$953$	−11.3480	−0.367598	−0.183799	−	0.982964i	$-0.558839\pi$
$953$	−11.3480	−0.367598	−0.183799	+	0.982964i	$0.558839\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	29.6926	0.959825
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−21.5302	−0.694521
$962$	0	0
$963$	18.0399	0.581329
$964$	0	0
$965$	0	0
$966$	0	0
$967$	17.9509	0.577262	0.288631	−	0.957440i	$-0.406800\pi$
$967$	17.9509	0.577262	0.288631	+	0.957440i	$0.406800\pi$
$968$	0	0
$969$	5.39876	0.173433
$970$	0	0
$971$	1.44215	0.0462807	0.0231404	−	0.999732i	$-0.492634\pi$
$971$	1.44215	0.0462807	0.0231404	+	0.999732i	$0.492634\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	23.2856	0.744973	0.372487	−	0.928038i	$-0.378505\pi$
$977$	23.2856	0.744973	0.372487	+	0.928038i	$0.378505\pi$
$978$	0	0
$979$	−6.36359	−0.203381
$980$	0	0
$981$	−18.6126	−0.594254
$982$	0	0
$983$	6.99917	0.223239	0.111619	−	0.993751i	$-0.464396\pi$
$983$	6.99917	0.223239	0.111619	+	0.993751i	$0.464396\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−14.5689	−0.463265
$990$	0	0
$991$	46.9589	1.49170	0.745850	−	0.666114i	$-0.232044\pi$
$991$	46.9589	1.49170	0.745850	+	0.666114i	$0.232044\pi$
$992$	0	0
$993$	−25.1856	−0.799240
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−39.9501	−1.26523	−0.632616	−	0.774465i	$-0.718019\pi$
$997$	−39.9501	−1.26523	−0.632616	+	0.774465i	$0.718019\pi$
$998$	0	0
$999$	−64.8032	−2.05028

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9800.2.a.db.1.3		10
5.2	odd	4		1960.2.g.g.1569.16	yes	20
5.3	odd	4		1960.2.g.g.1569.6	yes	20
5.4	even	2		9800.2.a.dc.1.8		10
7.6	odd	2	inner	9800.2.a.db.1.8		10
35.13	even	4		1960.2.g.g.1569.15	yes	20
35.27	even	4		1960.2.g.g.1569.5	✓	20
35.34	odd	2		9800.2.a.dc.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1960.2.g.g.1569.5	✓	20	35.27	even	4
1960.2.g.g.1569.6	yes	20	5.3	odd	4
1960.2.g.g.1569.15	yes	20	35.13	even	4
1960.2.g.g.1569.16	yes	20	5.2	odd	4
9800.2.a.db.1.3		10	1.1	even	1	trivial
9800.2.a.db.1.8		10	7.6	odd	2	inner
9800.2.a.dc.1.3		10	35.34	odd	2
9800.2.a.dc.1.8		10	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)

\(f(q)\)	\(=\)	\(q-1.35056 q^{3} -1.17599 q^{9} +O(q^{10})\)	\(q-1.35056 q^{3} -1.17599 q^{9} +3.15296 q^{11} +1.17296 q^{13} +2.07395 q^{17} -1.92745 q^{19} +4.51311 q^{23} +5.63992 q^{27} -6.97293 q^{29} -3.07731 q^{31} -4.25827 q^{33} -11.4901 q^{37} -1.58416 q^{39} +2.79587 q^{41} -3.22814 q^{43} -1.89635 q^{47} -2.80099 q^{51} -6.64710 q^{53} +2.60313 q^{57} +7.93376 q^{59} +8.15581 q^{61} -8.63580 q^{67} -6.09523 q^{69} -2.84298 q^{71} +5.35195 q^{73} +15.5300 q^{79} -4.08910 q^{81} -18.0496 q^{83} +9.41736 q^{87} -2.01829 q^{89} +4.15609 q^{93} +7.00968 q^{97} -3.70784 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 14 q^{9}+O(q^{10}) \) 10 * q + 14 * q^9	\( 10 q + 14 q^{9} - 12 q^{11} - 16 q^{23} + 12 q^{29} - 36 q^{37} - 20 q^{39} - 24 q^{43} - 36 q^{51} - 8 q^{53} - 16 q^{57} - 40 q^{67} - 8 q^{71} - 4 q^{79} + 50 q^{81} - 48 q^{93} - 72 q^{99}+O(q^{100}) \) 10 * q + 14 * q^9 - 12 * q^11 - 16 * q^23 + 12 * q^29 - 36 * q^37 - 20 * q^39 - 24 * q^43 - 36 * q^51 - 8 * q^53 - 16 * q^57 - 40 * q^67 - 8 * q^71 - 4 * q^79 + 50 * q^81 - 48 * q^93 - 72 * q^99

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