LMFDB - Embedded newform 9800.2.a.dc.1.10

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:	$10$
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			1.10
Root			$-2.83351$ 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)

$f(q)$	$=$	$q+3.30674 q^{3} +7.93455 q^{9} +O(q^{10})$	$q+3.30674 q^{3} +7.93455 q^{9} -5.53367 q^{11} +1.73908 q^{13} -3.73039 q^{17} +2.64104 q^{19} +4.05679 q^{23} +16.3173 q^{27} -3.81921 q^{29} +9.80694 q^{31} -18.2984 q^{33} +3.34408 q^{37} +5.75069 q^{39} +3.39535 q^{41} +10.5367 q^{43} -1.31544 q^{47} -12.3354 q^{51} -6.60792 q^{53} +8.73323 q^{57} +8.04221 q^{59} +1.03902 q^{61} +4.94145 q^{67} +13.4148 q^{69} -7.95200 q^{71} -4.39609 q^{73} +1.88773 q^{79} +30.1535 q^{81} +5.87327 q^{83} -12.6291 q^{87} +1.12951 q^{89} +32.4290 q^{93} +2.85407 q^{97} -43.9072 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	3.30674	1.90915	0.954575	−	0.297972i	$-0.0963102\pi$
$3$	3.30674	1.90915	0.954575	+	0.297972i	$0.0963102\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	7.93455	2.64485
$10$	0	0
$11$	−5.53367	−1.66847	−0.834233	−	0.551412i	$-0.814089\pi$
$11$	−5.53367	−1.66847	−0.834233	+	0.551412i	$0.814089\pi$
$12$	0	0
$13$	1.73908	0.482334	0.241167	−	0.970484i	$-0.422470\pi$
$13$	1.73908	0.482334	0.241167	+	0.970484i	$0.422470\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−3.73039	−0.904752	−0.452376	−	0.891827i	$-0.649423\pi$
$17$	−3.73039	−0.904752	−0.452376	+	0.891827i	$0.649423\pi$
$18$	0	0
$19$	2.64104	0.605896	0.302948	−	0.953007i	$-0.402029\pi$
$19$	2.64104	0.605896	0.302948	+	0.953007i	$0.402029\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	4.05679	0.845900	0.422950	−	0.906153i	$-0.360995\pi$
$23$	4.05679	0.845900	0.422950	+	0.906153i	$0.360995\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	16.3173	3.14027
$28$	0	0
$29$	−3.81921	−0.709209	−0.354605	−	0.935016i	$-0.615385\pi$
$29$	−3.81921	−0.709209	−0.354605	+	0.935016i	$0.615385\pi$
$30$	0	0
$31$	9.80694	1.76138	0.880689	−	0.473695i	$-0.157080\pi$
$31$	9.80694	1.76138	0.880689	+	0.473695i	$0.157080\pi$
$32$	0	0
$33$	−18.2984	−3.18535
$34$	0	0
$35$	0	0
$36$	0	0
$37$	3.34408	0.549764	0.274882	−	0.961478i	$-0.411361\pi$
$37$	3.34408	0.549764	0.274882	+	0.961478i	$0.411361\pi$
$38$	0	0
$39$	5.75069	0.920847
$40$	0	0
$41$	3.39535	0.530265	0.265133	−	0.964212i	$-0.414584\pi$
$41$	3.39535	0.530265	0.265133	+	0.964212i	$0.414584\pi$
$42$	0	0
$43$	10.5367	1.60684	0.803420	−	0.595413i	$-0.203012\pi$
$43$	10.5367	1.60684	0.803420	+	0.595413i	$0.203012\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−1.31544	−0.191876	−0.0959380	−	0.995387i	$-0.530585\pi$
$47$	−1.31544	−0.191876	−0.0959380	+	0.995387i	$0.530585\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	−12.3354	−1.72731
$52$	0	0
$53$	−6.60792	−0.907668	−0.453834	−	0.891086i	$-0.649944\pi$
$53$	−6.60792	−0.907668	−0.453834	+	0.891086i	$0.649944\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	8.73323	1.15675
$58$	0	0
$59$	8.04221	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$59$	8.04221	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$60$	0	0
$61$	1.03902	0.133033	0.0665166	−	0.997785i	$-0.478811\pi$
$61$	1.03902	0.133033	0.0665166	+	0.997785i	$0.478811\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	4.94145	0.603694	0.301847	−	0.953356i	$-0.402397\pi$
$67$	4.94145	0.603694	0.301847	+	0.953356i	$0.402397\pi$
$68$	0	0
$69$	13.4148	1.61495
$70$	0	0
$71$	−7.95200	−0.943729	−0.471865	−	0.881671i	$-0.656419\pi$
$71$	−7.95200	−0.943729	−0.471865	+	0.881671i	$0.656419\pi$
$72$	0	0
$73$	−4.39609	−0.514524	−0.257262	−	0.966342i	$-0.582820\pi$
$73$	−4.39609	−0.514524	−0.257262	+	0.966342i	$0.582820\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	1.88773	0.212386	0.106193	−	0.994346i	$-0.466134\pi$
$79$	1.88773	0.212386	0.106193	+	0.994346i	$0.466134\pi$
$80$	0	0
$81$	30.1535	3.35039
$82$	0	0
$83$	5.87327	0.644675	0.322338	−	0.946625i	$-0.395531\pi$
$83$	5.87327	0.644675	0.322338	+	0.946625i	$0.395531\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−12.6291	−1.35399
$88$	0	0
$89$	1.12951	0.119728	0.0598638	−	0.998207i	$-0.480933\pi$
$89$	1.12951	0.119728	0.0598638	+	0.998207i	$0.480933\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	32.4290	3.36273
$94$	0	0
$95$	0	0
$96$	0	0
$97$	2.85407	0.289787	0.144894	−	0.989447i	$-0.453716\pi$
$97$	2.85407	0.289787	0.144894	+	0.989447i	$0.453716\pi$
$98$	0	0
$99$	−43.9072	−4.41284
$100$	0	0
$101$	−10.1574	−1.01070	−0.505352	−	0.862913i	$-0.668637\pi$
$101$	−10.1574	−1.01070	−0.505352	+	0.862913i	$0.668637\pi$
$102$	0	0
$103$	2.56653	0.252888	0.126444	−	0.991974i	$-0.459644\pi$
$103$	2.56653	0.252888	0.126444	+	0.991974i	$0.459644\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−12.0176	−1.16178	−0.580892	−	0.813980i	$-0.697296\pi$
$107$	−12.0176	−1.16178	−0.580892	+	0.813980i	$0.697296\pi$
$108$	0	0
$109$	8.22184	0.787510	0.393755	−	0.919215i	$-0.371176\pi$
$109$	8.22184	0.787510	0.393755	+	0.919215i	$0.371176\pi$
$110$	0	0
$111$	11.0580	1.04958
$112$	0	0
$113$	−17.1447	−1.61283	−0.806417	−	0.591347i	$-0.798596\pi$
$113$	−17.1447	−1.61283	−0.806417	+	0.591347i	$0.798596\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	13.7988	1.27570
$118$	0	0
$119$	0	0
$120$	0	0
$121$	19.6215	1.78378
$122$	0	0
$123$	11.2276	1.01236
$124$	0	0
$125$	0	0
$126$	0	0
$127$	10.6079	0.941301	0.470650	−	0.882320i	$-0.344019\pi$
$127$	10.6079	0.941301	0.470650	+	0.882320i	$0.344019\pi$
$128$	0	0
$129$	34.8423	3.06770
$130$	0	0
$131$	9.89742	0.864742	0.432371	−	0.901696i	$-0.357677\pi$
$131$	9.89742	0.864742	0.432371	+	0.901696i	$0.357677\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	9.64594	0.824109	0.412054	−	0.911159i	$-0.364811\pi$
$137$	9.64594	0.824109	0.412054	+	0.911159i	$0.364811\pi$
$138$	0	0
$139$	−5.91481	−0.501687	−0.250844	−	0.968028i	$-0.580708\pi$
$139$	−5.91481	−0.501687	−0.250844	+	0.968028i	$0.580708\pi$
$140$	0	0
$141$	−4.34981	−0.366320
$142$	0	0
$143$	−9.62349	−0.804757
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	24.3031	1.99099	0.995495	−	0.0948138i	$-0.0302256\pi$
$149$	24.3031	1.99099	0.995495	+	0.0948138i	$0.0302256\pi$
$150$	0	0
$151$	−12.4634	−1.01426	−0.507128	−	0.861871i	$-0.669293\pi$
$151$	−12.4634	−1.01426	−0.507128	+	0.861871i	$0.669293\pi$
$152$	0	0
$153$	−29.5989	−2.39293
$154$	0	0
$155$	0	0
$156$	0	0
$157$	17.1412	1.36802	0.684009	−	0.729474i	$-0.260235\pi$
$157$	17.1412	1.36802	0.684009	+	0.729474i	$0.260235\pi$
$158$	0	0
$159$	−21.8507	−1.73287
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−12.8311	−1.00501	−0.502504	−	0.864575i	$-0.667588\pi$
$163$	−12.8311	−1.00501	−0.502504	+	0.864575i	$0.667588\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−9.32903	−0.721902	−0.360951	−	0.932585i	$-0.617548\pi$
$167$	−9.32903	−0.721902	−0.360951	+	0.932585i	$0.617548\pi$
$168$	0	0
$169$	−9.97561	−0.767354
$170$	0	0
$171$	20.9555	1.60250
$172$	0	0
$173$	21.1467	1.60775	0.803877	−	0.594796i	$-0.202767\pi$
$173$	21.1467	1.60775	0.803877	+	0.594796i	$0.202767\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	26.5935	1.99889
$178$	0	0
$179$	−0.932652	−0.0697097	−0.0348548	−	0.999392i	$-0.511097\pi$
$179$	−0.932652	−0.0697097	−0.0348548	+	0.999392i	$0.511097\pi$
$180$	0	0
$181$	18.8596	1.40182	0.700910	−	0.713250i	$-0.252777\pi$
$181$	18.8596	1.40182	0.700910	+	0.713250i	$0.252777\pi$
$182$	0	0
$183$	3.43578	0.253980
$184$	0	0
$185$	0	0
$186$	0	0
$187$	20.6427	1.50955
$188$	0	0
$189$	0	0
$190$	0	0
$191$	20.4154	1.47721	0.738603	−	0.674140i	$-0.235486\pi$
$191$	20.4154	1.47721	0.738603	+	0.674140i	$0.235486\pi$
$192$	0	0
$193$	7.38035	0.531249	0.265625	−	0.964077i	$-0.414422\pi$
$193$	7.38035	0.531249	0.265625	+	0.964077i	$0.414422\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−18.7626	−1.33678	−0.668389	−	0.743812i	$-0.733016\pi$
$197$	−18.7626	−1.33678	−0.668389	+	0.743812i	$0.733016\pi$
$198$	0	0
$199$	17.3771	1.23183	0.615913	−	0.787814i	$-0.288787\pi$
$199$	17.3771	1.23183	0.615913	+	0.787814i	$0.288787\pi$
$200$	0	0
$201$	16.3401	1.15254
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	32.1888	2.23728
$208$	0	0
$209$	−14.6146	−1.01092
$210$	0	0
$211$	−5.40571	−0.372144	−0.186072	−	0.982536i	$-0.559576\pi$
$211$	−5.40571	−0.372144	−0.186072	+	0.982536i	$0.559576\pi$
$212$	0	0
$213$	−26.2952	−1.80172
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−14.5367	−0.982302
$220$	0	0
$221$	−6.48744	−0.436392
$222$	0	0
$223$	11.5368	0.772559	0.386279	−	0.922382i	$-0.373760\pi$
$223$	11.5368	0.772559	0.386279	+	0.922382i	$0.373760\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−14.9952	−0.995268	−0.497634	−	0.867387i	$-0.665798\pi$
$227$	−14.9952	−0.995268	−0.497634	+	0.867387i	$0.665798\pi$
$228$	0	0
$229$	25.6706	1.69636	0.848181	−	0.529707i	$-0.177698\pi$
$229$	25.6706	1.69636	0.848181	+	0.529707i	$0.177698\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−9.36656	−0.613624	−0.306812	−	0.951770i	$-0.599262\pi$
$233$	−9.36656	−0.613624	−0.306812	+	0.951770i	$0.599262\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	6.24224	0.405477
$238$	0	0
$239$	6.83113	0.441869	0.220934	−	0.975289i	$-0.429089\pi$
$239$	6.83113	0.441869	0.220934	+	0.975289i	$0.429089\pi$
$240$	0	0
$241$	0.260025	0.0167497	0.00837485	−	0.999965i	$-0.497334\pi$
$241$	0.260025	0.0167497	0.00837485	+	0.999965i	$0.497334\pi$
$242$	0	0
$243$	50.7579	3.25612
$244$	0	0
$245$	0	0
$246$	0	0
$247$	4.59297	0.292244
$248$	0	0
$249$	19.4214	1.23078
$250$	0	0
$251$	−3.32955	−0.210159	−0.105080	−	0.994464i	$-0.533510\pi$
$251$	−3.32955	−0.210159	−0.105080	+	0.994464i	$0.533510\pi$
$252$	0	0
$253$	−22.4490	−1.41135
$254$	0	0
$255$	0	0
$256$	0	0
$257$	11.6469	0.726512	0.363256	−	0.931689i	$-0.381665\pi$
$257$	11.6469	0.726512	0.363256	+	0.931689i	$0.381665\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−30.3037	−1.87575
$262$	0	0
$263$	−17.4665	−1.07703	−0.538514	−	0.842616i	$-0.681014\pi$
$263$	−17.4665	−1.07703	−0.538514	+	0.842616i	$0.681014\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	3.73499	0.228578
$268$	0	0
$269$	6.41117	0.390896	0.195448	−	0.980714i	$-0.437384\pi$
$269$	6.41117	0.390896	0.195448	+	0.980714i	$0.437384\pi$
$270$	0	0
$271$	−17.6327	−1.07111	−0.535556	−	0.844500i	$-0.679898\pi$
$271$	−17.6327	−1.07111	−0.535556	+	0.844500i	$0.679898\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−10.4421	−0.627406	−0.313703	−	0.949521i	$-0.601570\pi$
$277$	−10.4421	−0.627406	−0.313703	+	0.949521i	$0.601570\pi$
$278$	0	0
$279$	77.8137	4.65858
$280$	0	0
$281$	−9.95332	−0.593765	−0.296883	−	0.954914i	$-0.595947\pi$
$281$	−9.95332	−0.593765	−0.296883	+	0.954914i	$0.595947\pi$
$282$	0	0
$283$	8.58882	0.510552	0.255276	−	0.966868i	$-0.417834\pi$
$283$	8.58882	0.510552	0.255276	+	0.966868i	$0.417834\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−3.08422	−0.181425
$290$	0	0
$291$	9.43768	0.553247
$292$	0	0
$293$	−24.2104	−1.41439	−0.707194	−	0.707020i	$-0.750039\pi$
$293$	−24.2104	−1.41439	−0.707194	+	0.707020i	$0.750039\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−90.2946	−5.23943
$298$	0	0
$299$	7.05508	0.408006
$300$	0	0
$301$	0	0
$302$	0	0
$303$	−33.5881	−1.92958
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−15.7377	−0.898199	−0.449100	−	0.893482i	$-0.648255\pi$
$307$	−15.7377	−0.898199	−0.449100	+	0.893482i	$0.648255\pi$
$308$	0	0
$309$	8.48685	0.482800
$310$	0	0
$311$	−18.9517	−1.07465	−0.537326	−	0.843374i	$-0.680566\pi$
$311$	−18.9517	−1.07465	−0.537326	+	0.843374i	$0.680566\pi$
$312$	0	0
$313$	−11.3005	−0.638742	−0.319371	−	0.947630i	$-0.603472\pi$
$313$	−11.3005	−0.638742	−0.319371	+	0.947630i	$0.603472\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	17.3187	0.972714	0.486357	−	0.873760i	$-0.338325\pi$
$317$	17.3187	0.972714	0.486357	+	0.873760i	$0.338325\pi$
$318$	0	0
$319$	21.1343	1.18329
$320$	0	0
$321$	−39.7391	−2.21802
$322$	0	0
$323$	−9.85209	−0.548185
$324$	0	0
$325$	0	0
$326$	0	0
$327$	27.1875	1.50347
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−12.3936	−0.681211	−0.340606	−	0.940206i	$-0.610632\pi$
$331$	−12.3936	−0.681211	−0.340606	+	0.940206i	$0.610632\pi$
$332$	0	0
$333$	26.5338	1.45404
$334$	0	0
$335$	0	0
$336$	0	0
$337$	26.0499	1.41903	0.709513	−	0.704692i	$-0.248915\pi$
$337$	26.0499	1.41903	0.709513	+	0.704692i	$0.248915\pi$
$338$	0	0
$339$	−56.6930	−3.07914
$340$	0	0
$341$	−54.2684	−2.93880
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	14.3087	0.768132	0.384066	−	0.923306i	$-0.374524\pi$
$347$	14.3087	0.768132	0.384066	+	0.923306i	$0.374524\pi$
$348$	0	0
$349$	−19.0669	−1.02063	−0.510313	−	0.859989i	$-0.670470\pi$
$349$	−19.0669	−1.02063	−0.510313	+	0.859989i	$0.670470\pi$
$350$	0	0
$351$	28.3771	1.51466
$352$	0	0
$353$	0.885373	0.0471236	0.0235618	−	0.999722i	$-0.492499\pi$
$353$	0.885373	0.0471236	0.0235618	+	0.999722i	$0.492499\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	25.7417	1.35860	0.679298	−	0.733862i	$-0.262284\pi$
$359$	25.7417	1.35860	0.679298	+	0.733862i	$0.262284\pi$
$360$	0	0
$361$	−12.0249	−0.632890
$362$	0	0
$363$	64.8834	3.40550
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−3.30447	−0.172492	−0.0862459	−	0.996274i	$-0.527487\pi$
$367$	−3.30447	−0.172492	−0.0862459	+	0.996274i	$0.527487\pi$
$368$	0	0
$369$	26.9406	1.40247
$370$	0	0
$371$	0	0
$372$	0	0
$373$	13.8446	0.716844	0.358422	−	0.933560i	$-0.383315\pi$
$373$	13.8446	0.716844	0.358422	+	0.933560i	$0.383315\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−6.64190	−0.342075
$378$	0	0
$379$	−10.0931	−0.518446	−0.259223	−	0.965818i	$-0.583466\pi$
$379$	−10.0931	−0.518446	−0.259223	+	0.965818i	$0.583466\pi$
$380$	0	0
$381$	35.0777	1.79708
$382$	0	0
$383$	17.8137	0.910238	0.455119	−	0.890431i	$-0.349597\pi$
$383$	17.8137	0.910238	0.455119	+	0.890431i	$0.349597\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	83.6044	4.24985
$388$	0	0
$389$	−1.25429	−0.0635949	−0.0317975	−	0.999494i	$-0.510123\pi$
$389$	−1.25429	−0.0635949	−0.0317975	+	0.999494i	$0.510123\pi$
$390$	0	0
$391$	−15.1334	−0.765329
$392$	0	0
$393$	32.7282	1.65092
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−13.7953	−0.692365	−0.346183	−	0.938167i	$-0.612522\pi$
$397$	−13.7953	−0.692365	−0.346183	+	0.938167i	$0.612522\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−9.16524	−0.457690	−0.228845	−	0.973463i	$-0.573495\pi$
$401$	−9.16524	−0.457690	−0.228845	+	0.973463i	$0.573495\pi$
$402$	0	0
$403$	17.0550	0.849572
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−18.5051	−0.917263
$408$	0	0
$409$	−10.5839	−0.523338	−0.261669	−	0.965158i	$-0.584273\pi$
$409$	−10.5839	−0.523338	−0.261669	+	0.965158i	$0.584273\pi$
$410$	0	0
$411$	31.8967	1.57335
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−19.5588	−0.957796
$418$	0	0
$419$	−16.5234	−0.807219	−0.403609	−	0.914931i	$-0.632244\pi$
$419$	−16.5234	−0.807219	−0.403609	+	0.914931i	$0.632244\pi$
$420$	0	0
$421$	−29.6540	−1.44525	−0.722624	−	0.691242i	$-0.757064\pi$
$421$	−29.6540	−1.44525	−0.722624	+	0.691242i	$0.757064\pi$
$422$	0	0
$423$	−10.4374	−0.507483
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−31.8224	−1.53640
$430$	0	0
$431$	8.60044	0.414269	0.207134	−	0.978313i	$-0.433586\pi$
$431$	8.60044	0.414269	0.207134	+	0.978313i	$0.433586\pi$
$432$	0	0
$433$	−6.01904	−0.289257	−0.144628	−	0.989486i	$-0.546199\pi$
$433$	−6.01904	−0.289257	−0.144628	+	0.989486i	$0.546199\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	10.7141	0.512527
$438$	0	0
$439$	−35.2239	−1.68115	−0.840573	−	0.541698i	$-0.817782\pi$
$439$	−35.2239	−1.68115	−0.840573	+	0.541698i	$0.817782\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−16.5887	−0.788151	−0.394076	−	0.919078i	$-0.628935\pi$
$443$	−16.5887	−0.788151	−0.394076	+	0.919078i	$0.628935\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	80.3642	3.80110
$448$	0	0
$449$	16.4930	0.778353	0.389176	−	0.921163i	$-0.372760\pi$
$449$	16.4930	0.778353	0.389176	+	0.921163i	$0.372760\pi$
$450$	0	0
$451$	−18.7888	−0.884729
$452$	0	0
$453$	−41.2133	−1.93637
$454$	0	0
$455$	0	0
$456$	0	0
$457$	27.6547	1.29363	0.646817	−	0.762645i	$-0.276100\pi$
$457$	27.6547	1.29363	0.646817	+	0.762645i	$0.276100\pi$
$458$	0	0
$459$	−60.8698	−2.84116
$460$	0	0
$461$	−26.7136	−1.24417	−0.622087	−	0.782948i	$-0.713715\pi$
$461$	−26.7136	−1.24417	−0.622087	+	0.782948i	$0.713715\pi$
$462$	0	0
$463$	32.0176	1.48798	0.743992	−	0.668189i	$-0.232930\pi$
$463$	32.0176	1.48798	0.743992	+	0.668189i	$0.232930\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−37.0586	−1.71487	−0.857434	−	0.514594i	$-0.827943\pi$
$467$	−37.0586	−1.71487	−0.857434	+	0.514594i	$0.827943\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	56.6816	2.61175
$472$	0	0
$473$	−58.3069	−2.68096
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−52.4309	−2.40065
$478$	0	0
$479$	2.89899	0.132458	0.0662291	−	0.997804i	$-0.478903\pi$
$479$	2.89899	0.132458	0.0662291	+	0.997804i	$0.478903\pi$
$480$	0	0
$481$	5.81563	0.265170
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	1.52912	0.0692912	0.0346456	−	0.999400i	$-0.488970\pi$
$487$	1.52912	0.0692912	0.0346456	+	0.999400i	$0.488970\pi$
$488$	0	0
$489$	−42.4291	−1.91871
$490$	0	0
$491$	−25.4371	−1.14796	−0.573980	−	0.818869i	$-0.694601\pi$
$491$	−25.4371	−1.14796	−0.573980	+	0.818869i	$0.694601\pi$
$492$	0	0
$493$	14.2471	0.641658
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	1.52459	0.0682502	0.0341251	−	0.999418i	$-0.489136\pi$
$499$	1.52459	0.0682502	0.0341251	+	0.999418i	$0.489136\pi$
$500$	0	0
$501$	−30.8487	−1.37822
$502$	0	0
$503$	26.0371	1.16094	0.580468	−	0.814283i	$-0.302870\pi$
$503$	26.0371	1.16094	0.580468	+	0.814283i	$0.302870\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−32.9868	−1.46499
$508$	0	0
$509$	4.52693	0.200653	0.100326	−	0.994955i	$-0.468011\pi$
$509$	4.52693	0.200653	0.100326	+	0.994955i	$0.468011\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	43.0946	1.90267
$514$	0	0
$515$	0	0
$516$	0	0
$517$	7.27919	0.320139
$518$	0	0
$519$	69.9267	3.06944
$520$	0	0
$521$	13.1936	0.578022	0.289011	−	0.957326i	$-0.406674\pi$
$521$	13.1936	0.578022	0.289011	+	0.957326i	$0.406674\pi$
$522$	0	0
$523$	−40.9246	−1.78951	−0.894754	−	0.446560i	$-0.852649\pi$
$523$	−40.9246	−1.78951	−0.894754	+	0.446560i	$0.852649\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−36.5837	−1.59361
$528$	0	0
$529$	−6.54243	−0.284453
$530$	0	0
$531$	63.8114	2.76918
$532$	0	0
$533$	5.90479	0.255765
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−3.08404	−0.133086
$538$	0	0
$539$	0	0
$540$	0	0
$541$	23.8163	1.02394	0.511971	−	0.859003i	$-0.328916\pi$
$541$	23.8163	1.02394	0.511971	+	0.859003i	$0.328916\pi$
$542$	0	0
$543$	62.3637	2.67628
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−4.41965	−0.188971	−0.0944853	−	0.995526i	$-0.530121\pi$
$547$	−4.41965	−0.188971	−0.0944853	+	0.995526i	$0.530121\pi$
$548$	0	0
$549$	8.24418	0.351853
$550$	0	0
$551$	−10.0867	−0.429707
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	36.7365	1.55657	0.778287	−	0.627909i	$-0.216089\pi$
$557$	36.7365	1.55657	0.778287	+	0.627909i	$0.216089\pi$
$558$	0	0
$559$	18.3242	0.775033
$560$	0	0
$561$	68.2603	2.88195
$562$	0	0
$563$	−6.23643	−0.262834	−0.131417	−	0.991327i	$-0.541953\pi$
$563$	−6.23643	−0.262834	−0.131417	+	0.991327i	$0.541953\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−42.4926	−1.78138	−0.890690	−	0.454611i	$-0.849778\pi$
$569$	−42.4926	−1.78138	−0.890690	+	0.454611i	$0.849778\pi$
$570$	0	0
$571$	−32.6127	−1.36480	−0.682400	−	0.730979i	$-0.739064\pi$
$571$	−32.6127	−1.36480	−0.682400	+	0.730979i	$0.739064\pi$
$572$	0	0
$573$	67.5085	2.82021
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−1.77745	−0.0739962	−0.0369981	−	0.999315i	$-0.511780\pi$
$577$	−1.77745	−0.0739962	−0.0369981	+	0.999315i	$0.511780\pi$
$578$	0	0
$579$	24.4049	1.01423
$580$	0	0
$581$	0	0
$582$	0	0
$583$	36.5661	1.51441
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−20.5603	−0.848616	−0.424308	−	0.905518i	$-0.639483\pi$
$587$	−20.5603	−0.848616	−0.424308	+	0.905518i	$0.639483\pi$
$588$	0	0
$589$	25.9005	1.06721
$590$	0	0
$591$	−62.0430	−2.55211
$592$	0	0
$593$	33.8144	1.38859	0.694296	−	0.719689i	$-0.255716\pi$
$593$	33.8144	1.38859	0.694296	+	0.719689i	$0.255716\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	57.4615	2.35174
$598$	0	0
$599$	−24.7209	−1.01007	−0.505034	−	0.863100i	$-0.668520\pi$
$599$	−24.7209	−1.01007	−0.505034	+	0.863100i	$0.668520\pi$
$600$	0	0
$601$	−11.7712	−0.480158	−0.240079	−	0.970753i	$-0.577173\pi$
$601$	−11.7712	−0.480158	−0.240079	+	0.970753i	$0.577173\pi$
$602$	0	0
$603$	39.2082	1.59668
$604$	0	0
$605$	0	0
$606$	0	0
$607$	1.10836	0.0449869	0.0224935	−	0.999747i	$-0.492840\pi$
$607$	1.10836	0.0449869	0.0224935	+	0.999747i	$0.492840\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−2.28765	−0.0925483
$612$	0	0
$613$	23.8979	0.965225	0.482613	−	0.875834i	$-0.339688\pi$
$613$	23.8979	0.965225	0.482613	+	0.875834i	$0.339688\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	43.0274	1.73222	0.866108	−	0.499857i	$-0.166614\pi$
$617$	43.0274	1.73222	0.866108	+	0.499857i	$0.166614\pi$
$618$	0	0
$619$	−0.154550	−0.00621190	−0.00310595	−	0.999995i	$-0.500989\pi$
$619$	−0.154550	−0.00621190	−0.00310595	+	0.999995i	$0.500989\pi$
$620$	0	0
$621$	66.1959	2.65635
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−48.3269	−1.92999
$628$	0	0
$629$	−12.4747	−0.497400
$630$	0	0
$631$	−10.4189	−0.414770	−0.207385	−	0.978259i	$-0.566495\pi$
$631$	−10.4189	−0.414770	−0.207385	+	0.978259i	$0.566495\pi$
$632$	0	0
$633$	−17.8753	−0.710479
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−63.0956	−2.49602
$640$	0	0
$641$	23.0284	0.909568	0.454784	−	0.890602i	$-0.349716\pi$
$641$	23.0284	0.909568	0.454784	+	0.890602i	$0.349716\pi$
$642$	0	0
$643$	−31.3769	−1.23738	−0.618692	−	0.785634i	$-0.712337\pi$
$643$	−31.3769	−1.23738	−0.618692	+	0.785634i	$0.712337\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−36.0837	−1.41860	−0.709299	−	0.704908i	$-0.750988\pi$
$647$	−36.0837	−1.41860	−0.709299	+	0.704908i	$0.750988\pi$
$648$	0	0
$649$	−44.5030	−1.74690
$650$	0	0
$651$	0	0
$652$	0	0
$653$	16.8331	0.658732	0.329366	−	0.944202i	$-0.393165\pi$
$653$	16.8331	0.658732	0.329366	+	0.944202i	$0.393165\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−34.8810	−1.36084
$658$	0	0
$659$	−5.46123	−0.212739	−0.106370	−	0.994327i	$-0.533923\pi$
$659$	−5.46123	−0.212739	−0.106370	+	0.994327i	$0.533923\pi$
$660$	0	0
$661$	−14.3347	−0.557555	−0.278778	−	0.960356i	$-0.589929\pi$
$661$	−14.3347	−0.557555	−0.278778	+	0.960356i	$0.589929\pi$
$662$	0	0
$663$	−21.4523	−0.833138
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−15.4937	−0.599920
$668$	0	0
$669$	38.1491	1.47493
$670$	0	0
$671$	−5.74961	−0.221961
$672$	0	0
$673$	13.3392	0.514189	0.257094	−	0.966386i	$-0.417235\pi$
$673$	13.3392	0.514189	0.257094	+	0.966386i	$0.417235\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−17.2764	−0.663984	−0.331992	−	0.943282i	$-0.607721\pi$
$677$	−17.2764	−0.663984	−0.331992	+	0.943282i	$0.607721\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−49.5854	−1.90012
$682$	0	0
$683$	16.3327	0.624955	0.312477	−	0.949925i	$-0.398841\pi$
$683$	16.3327	0.624955	0.312477	+	0.949925i	$0.398841\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	84.8861	3.23861
$688$	0	0
$689$	−11.4917	−0.437799
$690$	0	0
$691$	−35.1470	−1.33705	−0.668527	−	0.743688i	$-0.733075\pi$
$691$	−35.1470	−1.33705	−0.668527	+	0.743688i	$0.733075\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−12.6660	−0.479758
$698$	0	0
$699$	−30.9728	−1.17150
$700$	0	0
$701$	20.0848	0.758592	0.379296	−	0.925275i	$-0.376166\pi$
$701$	20.0848	0.758592	0.379296	+	0.925275i	$0.376166\pi$
$702$	0	0
$703$	8.83186	0.333100
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−10.4839	−0.393732	−0.196866	−	0.980430i	$-0.563076\pi$
$709$	−10.4839	−0.393732	−0.196866	+	0.980430i	$0.563076\pi$
$710$	0	0
$711$	14.9783	0.561730
$712$	0	0
$713$	39.7847	1.48995
$714$	0	0
$715$	0	0
$716$	0	0
$717$	22.5888	0.843594
$718$	0	0
$719$	0.743549	0.0277297	0.0138648	−	0.999904i	$-0.495587\pi$
$719$	0.743549	0.0277297	0.0138648	+	0.999904i	$0.495587\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	0.859836	0.0319777
$724$	0	0
$725$	0	0
$726$	0	0
$727$	6.96793	0.258426	0.129213	−	0.991617i	$-0.458755\pi$
$727$	6.96793	0.258426	0.129213	+	0.991617i	$0.458755\pi$
$728$	0	0
$729$	77.3829	2.86603
$730$	0	0
$731$	−39.3061	−1.45379
$732$	0	0
$733$	−4.65157	−0.171810	−0.0859048	−	0.996303i	$-0.527378\pi$
$733$	−4.65157	−0.171810	−0.0859048	+	0.996303i	$0.527378\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−27.3444	−1.00724
$738$	0	0
$739$	−17.9266	−0.659442	−0.329721	−	0.944078i	$-0.606955\pi$
$739$	−17.9266	−0.659442	−0.329721	+	0.944078i	$0.606955\pi$
$740$	0	0
$741$	15.1878	0.557937
$742$	0	0
$743$	15.7786	0.578860	0.289430	−	0.957199i	$-0.406534\pi$
$743$	15.7786	0.578860	0.289430	+	0.957199i	$0.406534\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	46.6018	1.70507
$748$	0	0
$749$	0	0
$750$	0	0
$751$	11.1654	0.407430	0.203715	−	0.979030i	$-0.434698\pi$
$751$	11.1654	0.407430	0.203715	+	0.979030i	$0.434698\pi$
$752$	0	0
$753$	−11.0100	−0.401226
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−9.56588	−0.347678	−0.173839	−	0.984774i	$-0.555617\pi$
$757$	−9.56588	−0.347678	−0.173839	+	0.984774i	$0.555617\pi$
$758$	0	0
$759$	−74.2330	−2.69449
$760$	0	0
$761$	−37.7208	−1.36738	−0.683689	−	0.729774i	$-0.739625\pi$
$761$	−37.7208	−1.36738	−0.683689	+	0.729774i	$0.739625\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	13.9860	0.505007
$768$	0	0
$769$	−22.8409	−0.823665	−0.411833	−	0.911259i	$-0.635111\pi$
$769$	−22.8409	−0.823665	−0.411833	+	0.911259i	$0.635111\pi$
$770$	0	0
$771$	38.5132	1.38702
$772$	0	0
$773$	4.12485	0.148361	0.0741803	−	0.997245i	$-0.476366\pi$
$773$	4.12485	0.148361	0.0741803	+	0.997245i	$0.476366\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	8.96726	0.321285
$780$	0	0
$781$	44.0038	1.57458
$782$	0	0
$783$	−62.3192	−2.22711
$784$	0	0
$785$	0	0
$786$	0	0
$787$	24.4002	0.869774	0.434887	−	0.900485i	$-0.356788\pi$
$787$	24.4002	0.869774	0.434887	+	0.900485i	$0.356788\pi$
$788$	0	0
$789$	−57.7571	−2.05621
$790$	0	0
$791$	0	0
$792$	0	0
$793$	1.80694	0.0641664
$794$	0	0
$795$	0	0
$796$	0	0
$797$	49.6787	1.75971	0.879855	−	0.475242i	$-0.157640\pi$
$797$	49.6787	1.75971	0.879855	+	0.475242i	$0.157640\pi$
$798$	0	0
$799$	4.90708	0.173600
$800$	0	0
$801$	8.96214	0.316662
$802$	0	0
$803$	24.3265	0.858465
$804$	0	0
$805$	0	0
$806$	0	0
$807$	21.2001	0.746279
$808$	0	0
$809$	−17.3809	−0.611079	−0.305540	−	0.952179i	$-0.598837\pi$
$809$	−17.3809	−0.611079	−0.305540	+	0.952179i	$0.598837\pi$
$810$	0	0
$811$	−49.9096	−1.75256	−0.876281	−	0.481801i	$-0.839983\pi$
$811$	−49.9096	−1.75256	−0.876281	+	0.481801i	$0.839983\pi$
$812$	0	0
$813$	−58.3069	−2.04491
$814$	0	0
$815$	0	0
$816$	0	0
$817$	27.8280	0.973577
$818$	0	0
$819$	0	0
$820$	0	0
$821$	26.1264	0.911819	0.455909	−	0.890026i	$-0.349314\pi$
$821$	26.1264	0.911819	0.455909	+	0.890026i	$0.349314\pi$
$822$	0	0
$823$	−7.89785	−0.275302	−0.137651	−	0.990481i	$-0.543955\pi$
$823$	−7.89785	−0.275302	−0.137651	+	0.990481i	$0.543955\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−33.5985	−1.16833	−0.584167	−	0.811633i	$-0.698579\pi$
$827$	−33.5985	−1.16833	−0.584167	+	0.811633i	$0.698579\pi$
$828$	0	0
$829$	−54.9673	−1.90909	−0.954547	−	0.298059i	$-0.903661\pi$
$829$	−54.9673	−1.90909	−0.954547	+	0.298059i	$0.903661\pi$
$830$	0	0
$831$	−34.5294	−1.19781
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	160.023	5.53120
$838$	0	0
$839$	−2.58145	−0.0891214	−0.0445607	−	0.999007i	$-0.514189\pi$
$839$	−2.58145	−0.0891214	−0.0445607	+	0.999007i	$0.514189\pi$
$840$	0	0
$841$	−14.4136	−0.497022
$842$	0	0
$843$	−32.9131	−1.13359
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	28.4010	0.974721
$850$	0	0
$851$	13.5663	0.465045
$852$	0	0
$853$	−49.3984	−1.69137	−0.845685	−	0.533683i	$-0.820808\pi$
$853$	−49.3984	−1.69137	−0.845685	+	0.533683i	$0.820808\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−10.1139	−0.345485	−0.172743	−	0.984967i	$-0.555263\pi$
$857$	−10.1139	−0.345485	−0.172743	+	0.984967i	$0.555263\pi$
$858$	0	0
$859$	−17.7564	−0.605840	−0.302920	−	0.953016i	$-0.597962\pi$
$859$	−17.7564	−0.605840	−0.302920	+	0.953016i	$0.597962\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	22.2709	0.758109	0.379055	−	0.925374i	$-0.376249\pi$
$863$	22.2709	0.758109	0.379055	+	0.925374i	$0.376249\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−10.1987	−0.346367
$868$	0	0
$869$	−10.4461	−0.354359
$870$	0	0
$871$	8.59357	0.291182
$872$	0	0
$873$	22.6458	0.766444
$874$	0	0
$875$	0	0
$876$	0	0
$877$	14.3066	0.483101	0.241551	−	0.970388i	$-0.422344\pi$
$877$	14.3066	0.483101	0.241551	+	0.970388i	$0.422344\pi$
$878$	0	0
$879$	−80.0576	−2.70028
$880$	0	0
$881$	−48.7950	−1.64395	−0.821973	−	0.569527i	$-0.807126\pi$
$881$	−48.7950	−1.64395	−0.821973	+	0.569527i	$0.807126\pi$
$882$	0	0
$883$	−2.68231	−0.0902669	−0.0451334	−	0.998981i	$-0.514371\pi$
$883$	−2.68231	−0.0902669	−0.0451334	+	0.998981i	$0.514371\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	35.1648	1.18072	0.590360	−	0.807140i	$-0.298986\pi$
$887$	35.1648	1.18072	0.590360	+	0.807140i	$0.298986\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−166.859	−5.59000
$892$	0	0
$893$	−3.47412	−0.116257
$894$	0	0
$895$	0	0
$896$	0	0
$897$	23.3293	0.778944
$898$	0	0
$899$	−37.4547	−1.24919
$900$	0	0
$901$	24.6501	0.821214
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	42.0161	1.39512	0.697561	−	0.716525i	$-0.254269\pi$
$907$	42.0161	1.39512	0.697561	+	0.716525i	$0.254269\pi$
$908$	0	0
$909$	−80.5948	−2.67316
$910$	0	0
$911$	−38.3619	−1.27099	−0.635493	−	0.772107i	$-0.719203\pi$
$911$	−38.3619	−1.27099	−0.635493	+	0.772107i	$0.719203\pi$
$912$	0	0
$913$	−32.5008	−1.07562
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	20.9551	0.691244	0.345622	−	0.938374i	$-0.387668\pi$
$919$	20.9551	0.691244	0.345622	+	0.938374i	$0.387668\pi$
$920$	0	0
$921$	−52.0406	−1.71480
$922$	0	0
$923$	−13.8292	−0.455192
$924$	0	0
$925$	0	0
$926$	0	0
$927$	20.3643	0.668850
$928$	0	0
$929$	28.5054	0.935233	0.467617	−	0.883931i	$-0.345113\pi$
$929$	28.5054	0.935233	0.467617	+	0.883931i	$0.345113\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−62.6684	−2.05167
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−47.9615	−1.56683	−0.783417	−	0.621496i	$-0.786525\pi$
$937$	−47.9615	−1.56683	−0.783417	+	0.621496i	$0.786525\pi$
$938$	0	0
$939$	−37.3679	−1.21945
$940$	0	0
$941$	−3.02985	−0.0987704	−0.0493852	−	0.998780i	$-0.515726\pi$
$941$	−3.02985	−0.0987704	−0.0493852	+	0.998780i	$0.515726\pi$
$942$	0	0
$943$	13.7743	0.448551
$944$	0	0
$945$	0	0
$946$	0	0
$947$	21.5228	0.699396	0.349698	−	0.936863i	$-0.386284\pi$
$947$	21.5228	0.699396	0.349698	+	0.936863i	$0.386284\pi$
$948$	0	0
$949$	−7.64515	−0.248172
$950$	0	0
$951$	57.2684	1.85706
$952$	0	0
$953$	0.731872	0.0237077	0.0118538	−	0.999930i	$-0.496227\pi$
$953$	0.731872	0.0237077	0.0118538	+	0.999930i	$0.496227\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	69.8856	2.25908
$958$	0	0
$959$	0	0
$960$	0	0
$961$	65.1760	2.10245
$962$	0	0
$963$	−95.3542	−3.07275
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−57.8798	−1.86129	−0.930644	−	0.365926i	$-0.880752\pi$
$967$	−57.8798	−1.86129	−0.930644	+	0.365926i	$0.880752\pi$
$968$	0	0
$969$	−32.5783	−1.04657
$970$	0	0
$971$	−12.4955	−0.401000	−0.200500	−	0.979694i	$-0.564257\pi$
$971$	−12.4955	−0.401000	−0.200500	+	0.979694i	$0.564257\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−42.5509	−1.36132	−0.680662	−	0.732597i	$-0.738308\pi$
$977$	−42.5509	−1.36132	−0.680662	+	0.732597i	$0.738308\pi$
$978$	0	0
$979$	−6.25033	−0.199761
$980$	0	0
$981$	65.2367	2.08285
$982$	0	0
$983$	48.1540	1.53587	0.767937	−	0.640526i	$-0.221284\pi$
$983$	48.1540	1.53587	0.767937	+	0.640526i	$0.221284\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	42.7454	1.35923
$990$	0	0
$991$	−29.8798	−0.949165	−0.474582	−	0.880211i	$-0.657401\pi$
$991$	−29.8798	−0.949165	−0.474582	+	0.880211i	$0.657401\pi$
$992$	0	0
$993$	−40.9823	−1.30053
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−35.2693	−1.11699	−0.558495	−	0.829508i	$-0.688621\pi$
$997$	−35.2693	−1.11699	−0.558495	+	0.829508i	$0.688621\pi$
$998$	0	0
$999$	54.5664	1.72641

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9800.2.a.dc.1.10		10
5.2	odd	4		1960.2.g.g.1569.1	✓	20
5.3	odd	4		1960.2.g.g.1569.19	yes	20
5.4	even	2		9800.2.a.db.1.1		10
7.6	odd	2	inner	9800.2.a.dc.1.1		10
35.13	even	4		1960.2.g.g.1569.2	yes	20
35.27	even	4		1960.2.g.g.1569.20	yes	20
35.34	odd	2		9800.2.a.db.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1960.2.g.g.1569.1	✓	20	5.2	odd	4
1960.2.g.g.1569.2	yes	20	35.13	even	4
1960.2.g.g.1569.19	yes	20	5.3	odd	4
1960.2.g.g.1569.20	yes	20	35.27	even	4
9800.2.a.db.1.1		10	5.4	even	2
9800.2.a.db.1.10		10	35.34	odd	2
9800.2.a.dc.1.1		10	7.6	odd	2	inner
9800.2.a.dc.1.10		10	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+3.30674 q^{3} +7.93455 q^{9} +O(q^{10})\)	\(q+3.30674 q^{3} +7.93455 q^{9} -5.53367 q^{11} +1.73908 q^{13} -3.73039 q^{17} +2.64104 q^{19} +4.05679 q^{23} +16.3173 q^{27} -3.81921 q^{29} +9.80694 q^{31} -18.2984 q^{33} +3.34408 q^{37} +5.75069 q^{39} +3.39535 q^{41} +10.5367 q^{43} -1.31544 q^{47} -12.3354 q^{51} -6.60792 q^{53} +8.73323 q^{57} +8.04221 q^{59} +1.03902 q^{61} +4.94145 q^{67} +13.4148 q^{69} -7.95200 q^{71} -4.39609 q^{73} +1.88773 q^{79} +30.1535 q^{81} +5.87327 q^{83} -12.6291 q^{87} +1.12951 q^{89} +32.4290 q^{93} +2.85407 q^{97} -43.9072 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 14 q^{9}+O(q^{10}) \) 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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