LMFDB - Embedded newform 9800.2.a.cb.1.2

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:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1400)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.347296$ 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)

$f(q)$	$=$	$q-1.34730 q^{3} -1.18479 q^{9} +O(q^{10})$	$q-1.34730 q^{3} -1.18479 q^{9} +1.41147 q^{11} +6.47565 q^{13} -2.59627 q^{17} -1.16250 q^{19} -1.57398 q^{23} +5.63816 q^{27} +6.22668 q^{29} -4.98545 q^{31} -1.90167 q^{33} -8.47565 q^{37} -8.72462 q^{39} -3.57398 q^{41} -7.24897 q^{43} -10.9436 q^{47} +3.49794 q^{51} +12.7861 q^{53} +1.56624 q^{57} +2.04189 q^{59} +0.615867 q^{61} +6.08378 q^{67} +2.12061 q^{69} -8.27631 q^{71} -3.51754 q^{73} +0.879385 q^{79} -4.04189 q^{81} +3.90167 q^{83} -8.38919 q^{87} -5.96316 q^{89} +6.71688 q^{93} -3.23442 q^{97} -1.67230 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3}+O(q^{10}) $ 3 * q - 3 * q^3	$ 3 q - 3 q^{3} - 6 q^{11} + 6 q^{17} - 6 q^{19} + 3 q^{23} + 12 q^{29} + 3 q^{31} + 6 q^{33} - 6 q^{37} + 6 q^{39} - 3 q^{41} - 9 q^{43} - 18 q^{47} - 15 q^{51} + 6 q^{53} + 21 q^{57} + 3 q^{59} - 9 q^{61} + 12 q^{67} + 12 q^{69} + 9 q^{71} + 12 q^{73} - 3 q^{79} - 9 q^{81} - 21 q^{87} - 6 q^{89} + 12 q^{93} + 21 q^{97} - 9 q^{99}+O(q^{100}) $ 3 * q - 3 * q^3 - 6 * q^11 + 6 * q^17 - 6 * q^19 + 3 * q^23 + 12 * q^29 + 3 * q^31 + 6 * q^33 - 6 * q^37 + 6 * q^39 - 3 * q^41 - 9 * q^43 - 18 * q^47 - 15 * q^51 + 6 * q^53 + 21 * q^57 + 3 * q^59 - 9 * q^61 + 12 * q^67 + 12 * q^69 + 9 * q^71 + 12 * q^73 - 3 * q^79 - 9 * q^81 - 21 * q^87 - 6 * q^89 + 12 * q^93 + 21 * q^97 - 9 * 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
$3$	−1.34730	−0.777862	−0.388931	−	0.921267i	$-0.627156\pi$
$3$	−1.34730	−0.777862	−0.388931	+	0.921267i	$0.627156\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	−1.18479	−0.394931
$10$	0	0
$11$	1.41147	0.425575	0.212788	−	0.977098i	$-0.431746\pi$
$11$	1.41147	0.425575	0.212788	+	0.977098i	$0.431746\pi$
$12$	0	0
$13$	6.47565	1.79602	0.898011	−	0.439972i	$-0.145012\pi$
$13$	6.47565	1.79602	0.898011	+	0.439972i	$0.145012\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−2.59627	−0.629687	−0.314844	−	0.949144i	$-0.601952\pi$
$17$	−2.59627	−0.629687	−0.314844	+	0.949144i	$0.601952\pi$
$18$	0	0
$19$	−1.16250	−0.266697	−0.133348	−	0.991069i	$-0.542573\pi$
$19$	−1.16250	−0.266697	−0.133348	+	0.991069i	$0.542573\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−1.57398	−0.328197	−0.164099	−	0.986444i	$-0.552472\pi$
$23$	−1.57398	−0.328197	−0.164099	+	0.986444i	$0.552472\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	5.63816	1.08506
$28$	0	0
$29$	6.22668	1.15627	0.578133	−	0.815943i	$-0.303782\pi$
$29$	6.22668	1.15627	0.578133	+	0.815943i	$0.303782\pi$
$30$	0	0
$31$	−4.98545	−0.895414	−0.447707	−	0.894180i	$-0.647759\pi$
$31$	−4.98545	−0.895414	−0.447707	+	0.894180i	$0.647759\pi$
$32$	0	0
$33$	−1.90167	−0.331039
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−8.47565	−1.39339	−0.696694	−	0.717368i	$-0.745347\pi$
$37$	−8.47565	−1.39339	−0.696694	+	0.717368i	$0.745347\pi$
$38$	0	0
$39$	−8.72462	−1.39706
$40$	0	0
$41$	−3.57398	−0.558162	−0.279081	−	0.960268i	$-0.590030\pi$
$41$	−3.57398	−0.558162	−0.279081	+	0.960268i	$0.590030\pi$
$42$	0	0
$43$	−7.24897	−1.10546	−0.552729	−	0.833361i	$-0.686413\pi$
$43$	−7.24897	−1.10546	−0.552729	+	0.833361i	$0.686413\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−10.9436	−1.59628	−0.798141	−	0.602470i	$-0.794183\pi$
$47$	−10.9436	−1.59628	−0.798141	+	0.602470i	$0.794183\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	3.49794	0.489810
$52$	0	0
$53$	12.7861	1.75631	0.878154	−	0.478378i	$-0.158775\pi$
$53$	12.7861	1.75631	0.878154	+	0.478378i	$0.158775\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	1.56624	0.207453
$58$	0	0
$59$	2.04189	0.265831	0.132916	−	0.991127i	$-0.457566\pi$
$59$	2.04189	0.265831	0.132916	+	0.991127i	$0.457566\pi$
$60$	0	0
$61$	0.615867	0.0788537	0.0394268	−	0.999222i	$-0.487447\pi$
$61$	0.615867	0.0788537	0.0394268	+	0.999222i	$0.487447\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	6.08378	0.743252	0.371626	−	0.928383i	$-0.378800\pi$
$67$	6.08378	0.743252	0.371626	+	0.928383i	$0.378800\pi$
$68$	0	0
$69$	2.12061	0.255292
$70$	0	0
$71$	−8.27631	−0.982217	−0.491109	−	0.871098i	$-0.663408\pi$
$71$	−8.27631	−0.982217	−0.491109	+	0.871098i	$0.663408\pi$
$72$	0	0
$73$	−3.51754	−0.411697	−0.205849	−	0.978584i	$-0.565995\pi$
$73$	−3.51754	−0.411697	−0.205849	+	0.978584i	$0.565995\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0.879385	0.0989386	0.0494693	−	0.998776i	$-0.484247\pi$
$79$	0.879385	0.0989386	0.0494693	+	0.998776i	$0.484247\pi$
$80$	0	0
$81$	−4.04189	−0.449099
$82$	0	0
$83$	3.90167	0.428264	0.214132	−	0.976805i	$-0.431308\pi$
$83$	3.90167	0.428264	0.214132	+	0.976805i	$0.431308\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−8.38919	−0.899415
$88$	0	0
$89$	−5.96316	−0.632094	−0.316047	−	0.948744i	$-0.602356\pi$
$89$	−5.96316	−0.632094	−0.316047	+	0.948744i	$0.602356\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	6.71688	0.696508
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−3.23442	−0.328406	−0.164203	−	0.986427i	$-0.552505\pi$
$97$	−3.23442	−0.328406	−0.164203	+	0.986427i	$0.552505\pi$
$98$	0	0
$99$	−1.67230	−0.168073
$100$	0	0
$101$	−14.5321	−1.44600	−0.722998	−	0.690850i	$-0.757237\pi$
$101$	−14.5321	−1.44600	−0.722998	+	0.690850i	$0.757237\pi$
$102$	0	0
$103$	15.9736	1.57392	0.786962	−	0.617001i	$-0.211653\pi$
$103$	15.9736	1.57392	0.786962	+	0.617001i	$0.211653\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	17.8307	1.72376	0.861879	−	0.507114i	$-0.169288\pi$
$107$	17.8307	1.72376	0.861879	+	0.507114i	$0.169288\pi$
$108$	0	0
$109$	12.2344	1.17185	0.585923	−	0.810367i	$-0.300732\pi$
$109$	12.2344	1.17185	0.585923	+	0.810367i	$0.300732\pi$
$110$	0	0
$111$	11.4192	1.08386
$112$	0	0
$113$	−4.29086	−0.403650	−0.201825	−	0.979422i	$-0.564687\pi$
$113$	−4.29086	−0.403650	−0.201825	+	0.979422i	$0.564687\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−7.67230	−0.709305
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−9.00774	−0.818886
$122$	0	0
$123$	4.81521	0.434173
$124$	0	0
$125$	0	0
$126$	0	0
$127$	9.89899	0.878393	0.439196	−	0.898391i	$-0.355263\pi$
$127$	9.89899	0.878393	0.439196	+	0.898391i	$0.355263\pi$
$128$	0	0
$129$	9.76651	0.859893
$130$	0	0
$131$	−15.9659	−1.39494	−0.697471	−	0.716613i	$-0.745692\pi$
$131$	−15.9659	−1.39494	−0.697471	+	0.716613i	$0.745692\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	12.7219	1.08691	0.543454	−	0.839439i	$-0.317116\pi$
$137$	12.7219	1.08691	0.543454	+	0.839439i	$0.317116\pi$
$138$	0	0
$139$	−7.65270	−0.649094	−0.324547	−	0.945870i	$-0.605212\pi$
$139$	−7.65270	−0.649094	−0.324547	+	0.945870i	$0.605212\pi$
$140$	0	0
$141$	14.7442	1.24169
$142$	0	0
$143$	9.14022	0.764343
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	3.29086	0.269598	0.134799	−	0.990873i	$-0.456961\pi$
$149$	3.29086	0.269598	0.134799	+	0.990873i	$0.456961\pi$
$150$	0	0
$151$	−18.7246	−1.52379	−0.761894	−	0.647702i	$-0.775730\pi$
$151$	−18.7246	−1.52379	−0.761894	+	0.647702i	$0.775730\pi$
$152$	0	0
$153$	3.07604	0.248683
$154$	0	0
$155$	0	0
$156$	0	0
$157$	18.7074	1.49301	0.746506	−	0.665379i	$-0.231730\pi$
$157$	18.7074	1.49301	0.746506	+	0.665379i	$0.231730\pi$
$158$	0	0
$159$	−17.2267	−1.36616
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−1.87939	−0.147205	−0.0736024	−	0.997288i	$-0.523450\pi$
$163$	−1.87939	−0.147205	−0.0736024	+	0.997288i	$0.523450\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	1.25402	0.0970392	0.0485196	−	0.998822i	$-0.484550\pi$
$167$	1.25402	0.0970392	0.0485196	+	0.998822i	$0.484550\pi$
$168$	0	0
$169$	28.9341	2.22570
$170$	0	0
$171$	1.37733	0.105327
$172$	0	0
$173$	−1.35504	−0.103022	−0.0515108	−	0.998672i	$-0.516404\pi$
$173$	−1.35504	−0.103022	−0.0515108	+	0.998672i	$0.516404\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−2.75103	−0.206780
$178$	0	0
$179$	11.4047	0.852425	0.426212	−	0.904623i	$-0.359848\pi$
$179$	11.4047	0.852425	0.426212	+	0.904623i	$0.359848\pi$
$180$	0	0
$181$	−9.40373	−0.698974	−0.349487	−	0.936941i	$-0.613644\pi$
$181$	−9.40373	−0.698974	−0.349487	+	0.936941i	$0.613644\pi$
$182$	0	0
$183$	−0.829755	−0.0613373
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−3.66456	−0.267979
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−24.7743	−1.79260	−0.896301	−	0.443446i	$-0.853756\pi$
$191$	−24.7743	−1.79260	−0.896301	+	0.443446i	$0.853756\pi$
$192$	0	0
$193$	−10.9786	−0.790260	−0.395130	−	0.918625i	$-0.629300\pi$
$193$	−10.9786	−0.790260	−0.395130	+	0.918625i	$0.629300\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	24.1019	1.71719	0.858596	−	0.512652i	$-0.171337\pi$
$197$	24.1019	1.71719	0.858596	+	0.512652i	$0.171337\pi$
$198$	0	0
$199$	−9.79561	−0.694392	−0.347196	−	0.937793i	$-0.612866\pi$
$199$	−9.79561	−0.694392	−0.347196	+	0.937793i	$0.612866\pi$
$200$	0	0
$201$	−8.19665	−0.578147
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	1.86484	0.129615
$208$	0	0
$209$	−1.64084	−0.113500
$210$	0	0
$211$	6.68954	0.460527	0.230263	−	0.973128i	$-0.426041\pi$
$211$	6.68954	0.460527	0.230263	+	0.973128i	$0.426041\pi$
$212$	0	0
$213$	11.1506	0.764030
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	4.73917	0.320243
$220$	0	0
$221$	−16.8125	−1.13093
$222$	0	0
$223$	−25.4911	−1.70701	−0.853506	−	0.521083i	$-0.825528\pi$
$223$	−25.4911	−1.70701	−0.853506	+	0.521083i	$0.825528\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−11.3396	−0.752633	−0.376316	−	0.926491i	$-0.622809\pi$
$227$	−11.3396	−0.752633	−0.376316	+	0.926491i	$0.622809\pi$
$228$	0	0
$229$	5.64321	0.372914	0.186457	−	0.982463i	$-0.440300\pi$
$229$	5.64321	0.372914	0.186457	+	0.982463i	$0.440300\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	10.3601	0.678712	0.339356	−	0.940658i	$-0.389791\pi$
$233$	10.3601	0.678712	0.339356	+	0.940658i	$0.389791\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−1.18479	−0.0769605
$238$	0	0
$239$	−12.2422	−0.791880	−0.395940	−	0.918276i	$-0.629581\pi$
$239$	−12.2422	−0.791880	−0.395940	+	0.918276i	$0.629581\pi$
$240$	0	0
$241$	−17.8598	−1.15045	−0.575225	−	0.817995i	$-0.695085\pi$
$241$	−17.8598	−1.15045	−0.575225	+	0.817995i	$0.695085\pi$
$242$	0	0
$243$	−11.4688	−0.735727
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−7.52797	−0.478993
$248$	0	0
$249$	−5.25671	−0.333131
$250$	0	0
$251$	−16.7888	−1.05970	−0.529850	−	0.848091i	$-0.677752\pi$
$251$	−16.7888	−1.05970	−0.529850	+	0.848091i	$0.677752\pi$
$252$	0	0
$253$	−2.22163	−0.139673
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−18.3250	−1.14308	−0.571541	−	0.820573i	$-0.693654\pi$
$257$	−18.3250	−1.14308	−0.571541	+	0.820573i	$0.693654\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−7.37733	−0.456645
$262$	0	0
$263$	13.5202	0.833693	0.416847	−	0.908977i	$-0.363135\pi$
$263$	13.5202	0.833693	0.416847	+	0.908977i	$0.363135\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	8.03415	0.491682
$268$	0	0
$269$	−27.7648	−1.69285	−0.846424	−	0.532510i	$-0.821249\pi$
$269$	−27.7648	−1.69285	−0.846424	+	0.532510i	$0.821249\pi$
$270$	0	0
$271$	−15.8794	−0.964604	−0.482302	−	0.876005i	$-0.660199\pi$
$271$	−15.8794	−0.964604	−0.482302	+	0.876005i	$0.660199\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−16.7074	−1.00385	−0.501925	−	0.864911i	$-0.667375\pi$
$277$	−16.7074	−1.00385	−0.501925	+	0.864911i	$0.667375\pi$
$278$	0	0
$279$	5.90673	0.353626
$280$	0	0
$281$	32.0155	1.90988	0.954942	−	0.296793i	$-0.0959172\pi$
$281$	32.0155	1.90988	0.954942	+	0.296793i	$0.0959172\pi$
$282$	0	0
$283$	10.7074	0.636488	0.318244	−	0.948009i	$-0.396907\pi$
$283$	10.7074	0.636488	0.318244	+	0.948009i	$0.396907\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−10.2594	−0.603494
$290$	0	0
$291$	4.35773	0.255454
$292$	0	0
$293$	8.20439	0.479306	0.239653	−	0.970859i	$-0.422966\pi$
$293$	8.20439	0.479306	0.239653	+	0.970859i	$0.422966\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	7.95811	0.461776
$298$	0	0
$299$	−10.1925	−0.589449
$300$	0	0
$301$	0	0
$302$	0	0
$303$	19.5790	1.12479
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−26.3678	−1.50489	−0.752446	−	0.658654i	$-0.771126\pi$
$307$	−26.3678	−1.50489	−0.752446	+	0.658654i	$0.771126\pi$
$308$	0	0
$309$	−21.5212	−1.22430
$310$	0	0
$311$	14.6655	0.831604	0.415802	−	0.909455i	$-0.363501\pi$
$311$	14.6655	0.831604	0.415802	+	0.909455i	$0.363501\pi$
$312$	0	0
$313$	30.5202	1.72511	0.862553	−	0.505967i	$-0.168864\pi$
$313$	30.5202	1.72511	0.862553	+	0.505967i	$0.168864\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−16.8716	−0.947606	−0.473803	−	0.880631i	$-0.657119\pi$
$317$	−16.8716	−0.947606	−0.473803	+	0.880631i	$0.657119\pi$
$318$	0	0
$319$	8.78880	0.492078
$320$	0	0
$321$	−24.0232	−1.34085
$322$	0	0
$323$	3.01817	0.167935
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−16.4834	−0.911534
$328$	0	0
$329$	0	0
$330$	0	0
$331$	14.3756	0.790153	0.395076	−	0.918648i	$-0.370718\pi$
$331$	14.3756	0.790153	0.395076	+	0.918648i	$0.370718\pi$
$332$	0	0
$333$	10.0419	0.550292
$334$	0	0
$335$	0	0
$336$	0	0
$337$	18.2909	0.996367	0.498183	−	0.867072i	$-0.334001\pi$
$337$	18.2909	0.996367	0.498183	+	0.867072i	$0.334001\pi$
$338$	0	0
$339$	5.78106	0.313984
$340$	0	0
$341$	−7.03684	−0.381066
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−31.0378	−1.66619	−0.833097	−	0.553126i	$-0.813435\pi$
$347$	−31.0378	−1.66619	−0.833097	+	0.553126i	$0.813435\pi$
$348$	0	0
$349$	21.3286	1.14170	0.570848	−	0.821056i	$-0.306615\pi$
$349$	21.3286	1.14170	0.570848	+	0.821056i	$0.306615\pi$
$350$	0	0
$351$	36.5107	1.94880
$352$	0	0
$353$	34.6313	1.84324	0.921620	−	0.388093i	$-0.126866\pi$
$353$	34.6313	1.84324	0.921620	+	0.388093i	$0.126866\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−22.7151	−1.19886	−0.599429	−	0.800428i	$-0.704606\pi$
$359$	−22.7151	−1.19886	−0.599429	+	0.800428i	$0.704606\pi$
$360$	0	0
$361$	−17.6486	−0.928873
$362$	0	0
$363$	12.1361	0.636980
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−30.7050	−1.60279	−0.801395	−	0.598136i	$-0.795908\pi$
$367$	−30.7050	−1.60279	−0.801395	+	0.598136i	$0.795908\pi$
$368$	0	0
$369$	4.23442	0.220435
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−17.3705	−0.899411	−0.449706	−	0.893177i	$-0.648471\pi$
$373$	−17.3705	−0.899411	−0.449706	+	0.893177i	$0.648471\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	40.3218	2.07668
$378$	0	0
$379$	2.78880	0.143251	0.0716255	−	0.997432i	$-0.477181\pi$
$379$	2.78880	0.143251	0.0716255	+	0.997432i	$0.477181\pi$
$380$	0	0
$381$	−13.3369	−0.683268
$382$	0	0
$383$	5.07098	0.259115	0.129558	−	0.991572i	$-0.458644\pi$
$383$	5.07098	0.259115	0.129558	+	0.991572i	$0.458644\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	8.58853	0.436579
$388$	0	0
$389$	−8.59896	−0.435984	−0.217992	−	0.975951i	$-0.569951\pi$
$389$	−8.59896	−0.435984	−0.217992	+	0.975951i	$0.569951\pi$
$390$	0	0
$391$	4.08647	0.206661
$392$	0	0
$393$	21.5107	1.08507
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−2.57398	−0.129184	−0.0645921	−	0.997912i	$-0.520575\pi$
$397$	−2.57398	−0.129184	−0.0645921	+	0.997912i	$0.520575\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	29.4620	1.47126	0.735632	−	0.677381i	$-0.236885\pi$
$401$	29.4620	1.47126	0.735632	+	0.677381i	$0.236885\pi$
$402$	0	0
$403$	−32.2841	−1.60818
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−11.9632	−0.592992
$408$	0	0
$409$	−5.85204	−0.289365	−0.144682	−	0.989478i	$-0.546216\pi$
$409$	−5.85204	−0.289365	−0.144682	+	0.989478i	$0.546216\pi$
$410$	0	0
$411$	−17.1402	−0.845464
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	10.3105	0.504905
$418$	0	0
$419$	1.03952	0.0507841	0.0253921	−	0.999678i	$-0.491917\pi$
$419$	1.03952	0.0507841	0.0253921	+	0.999678i	$0.491917\pi$
$420$	0	0
$421$	−32.1566	−1.56722	−0.783609	−	0.621254i	$-0.786623\pi$
$421$	−32.1566	−1.56722	−0.783609	+	0.621254i	$0.786623\pi$
$422$	0	0
$423$	12.9659	0.630421
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−12.3146	−0.594553
$430$	0	0
$431$	0.460170	0.0221656	0.0110828	−	0.999939i	$-0.496472\pi$
$431$	0.460170	0.0221656	0.0110828	+	0.999939i	$0.496472\pi$
$432$	0	0
$433$	−24.6509	−1.18465	−0.592325	−	0.805699i	$-0.701790\pi$
$433$	−24.6509	−1.18465	−0.592325	+	0.805699i	$0.701790\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	1.82976	0.0875291
$438$	0	0
$439$	−29.9145	−1.42774	−0.713870	−	0.700278i	$-0.753059\pi$
$439$	−29.9145	−1.42774	−0.713870	+	0.700278i	$0.753059\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−12.5868	−0.598016	−0.299008	−	0.954251i	$-0.596656\pi$
$443$	−12.5868	−0.598016	−0.299008	+	0.954251i	$0.596656\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−4.43376	−0.209710
$448$	0	0
$449$	24.4783	1.15520	0.577602	−	0.816318i	$-0.303989\pi$
$449$	24.4783	1.15520	0.577602	+	0.816318i	$0.303989\pi$
$450$	0	0
$451$	−5.04458	−0.237540
$452$	0	0
$453$	25.2276	1.18530
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−40.4611	−1.89269	−0.946345	−	0.323157i	$-0.895256\pi$
$457$	−40.4611	−1.89269	−0.946345	+	0.323157i	$0.895256\pi$
$458$	0	0
$459$	−14.6382	−0.683251
$460$	0	0
$461$	5.22668	0.243431	0.121715	−	0.992565i	$-0.461160\pi$
$461$	5.22668	0.243431	0.121715	+	0.992565i	$0.461160\pi$
$462$	0	0
$463$	−40.0547	−1.86150	−0.930749	−	0.365658i	$-0.880844\pi$
$463$	−40.0547	−1.86150	−0.930749	+	0.365658i	$0.880844\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−20.5767	−0.952175	−0.476087	−	0.879398i	$-0.657945\pi$
$467$	−20.5767	−0.952175	−0.476087	+	0.879398i	$0.657945\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−25.2044	−1.16136
$472$	0	0
$473$	−10.2317	−0.470456
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−15.1489	−0.693620
$478$	0	0
$479$	−22.6040	−1.03280	−0.516402	−	0.856346i	$-0.672729\pi$
$479$	−22.6040	−1.03280	−0.516402	+	0.856346i	$0.672729\pi$
$480$	0	0
$481$	−54.8854	−2.50256
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−25.9118	−1.17417	−0.587087	−	0.809524i	$-0.699726\pi$
$487$	−25.9118	−1.17417	−0.587087	+	0.809524i	$0.699726\pi$
$488$	0	0
$489$	2.53209	0.114505
$490$	0	0
$491$	39.7297	1.79298	0.896488	−	0.443069i	$-0.146110\pi$
$491$	39.7297	1.79298	0.896488	+	0.443069i	$0.146110\pi$
$492$	0	0
$493$	−16.1661	−0.728086
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	20.1925	0.903942	0.451971	−	0.892033i	$-0.350721\pi$
$499$	20.1925	0.903942	0.451971	+	0.892033i	$0.350721\pi$
$500$	0	0
$501$	−1.68954	−0.0754831
$502$	0	0
$503$	7.29086	0.325083	0.162542	−	0.986702i	$-0.448031\pi$
$503$	7.29086	0.325083	0.162542	+	0.986702i	$0.448031\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−38.9828	−1.73129
$508$	0	0
$509$	−6.54252	−0.289992	−0.144996	−	0.989432i	$-0.546317\pi$
$509$	−6.54252	−0.289992	−0.144996	+	0.989432i	$0.546317\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−6.55438	−0.289383
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−15.4466	−0.679339
$518$	0	0
$519$	1.82564	0.0801366
$520$	0	0
$521$	−11.7588	−0.515161	−0.257581	−	0.966257i	$-0.582925\pi$
$521$	−11.7588	−0.515161	−0.257581	+	0.966257i	$0.582925\pi$
$522$	0	0
$523$	−0.984518	−0.0430500	−0.0215250	−	0.999768i	$-0.506852\pi$
$523$	−0.984518	−0.0430500	−0.0215250	+	0.999768i	$0.506852\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	12.9436	0.563830
$528$	0	0
$529$	−20.5226	−0.892287
$530$	0	0
$531$	−2.41921	−0.104985
$532$	0	0
$533$	−23.1438	−1.00247
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−15.3655	−0.663069
$538$	0	0
$539$	0	0
$540$	0	0
$541$	16.2098	0.696912	0.348456	−	0.937325i	$-0.386706\pi$
$541$	16.2098	0.696912	0.348456	+	0.937325i	$0.386706\pi$
$542$	0	0
$543$	12.6696	0.543705
$544$	0	0
$545$	0	0
$546$	0	0
$547$	29.3337	1.25422	0.627109	−	0.778932i	$-0.284238\pi$
$547$	29.3337	1.25422	0.627109	+	0.778932i	$0.284238\pi$
$548$	0	0
$549$	−0.729675	−0.0311418
$550$	0	0
$551$	−7.23854	−0.308372
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−13.0469	−0.552817	−0.276408	−	0.961040i	$-0.589144\pi$
$557$	−13.0469	−0.552817	−0.276408	+	0.961040i	$0.589144\pi$
$558$	0	0
$559$	−46.9418	−1.98543
$560$	0	0
$561$	4.93725	0.208451
$562$	0	0
$563$	−26.9418	−1.13546	−0.567731	−	0.823214i	$-0.692179\pi$
$563$	−26.9418	−1.13546	−0.567731	+	0.823214i	$0.692179\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	13.2327	0.554742	0.277371	−	0.960763i	$-0.410537\pi$
$569$	13.2327	0.554742	0.277371	+	0.960763i	$0.410537\pi$
$570$	0	0
$571$	−6.32770	−0.264806	−0.132403	−	0.991196i	$-0.542269\pi$
$571$	−6.32770	−0.264806	−0.132403	+	0.991196i	$0.542269\pi$
$572$	0	0
$573$	33.3783	1.39440
$574$	0	0
$575$	0	0
$576$	0	0
$577$	6.19160	0.257760	0.128880	−	0.991660i	$-0.458862\pi$
$577$	6.19160	0.257760	0.128880	+	0.991660i	$0.458862\pi$
$578$	0	0
$579$	14.7915	0.614713
$580$	0	0
$581$	0	0
$582$	0	0
$583$	18.0473	0.747441
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−26.6186	−1.09867	−0.549333	−	0.835604i	$-0.685118\pi$
$587$	−26.6186	−1.09867	−0.549333	+	0.835604i	$0.685118\pi$
$588$	0	0
$589$	5.79561	0.238804
$590$	0	0
$591$	−32.4725	−1.33574
$592$	0	0
$593$	13.5466	0.556294	0.278147	−	0.960539i	$-0.410280\pi$
$593$	13.5466	0.556294	0.278147	+	0.960539i	$0.410280\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	13.1976	0.540141
$598$	0	0
$599$	−29.6013	−1.20948	−0.604739	−	0.796424i	$-0.706722\pi$
$599$	−29.6013	−1.20948	−0.604739	+	0.796424i	$0.706722\pi$
$600$	0	0
$601$	20.9050	0.852732	0.426366	−	0.904551i	$-0.359794\pi$
$601$	20.9050	0.852732	0.426366	+	0.904551i	$0.359794\pi$
$602$	0	0
$603$	−7.20801	−0.293533
$604$	0	0
$605$	0	0
$606$	0	0
$607$	37.2036	1.51005	0.755023	−	0.655698i	$-0.227626\pi$
$607$	37.2036	1.51005	0.755023	+	0.655698i	$0.227626\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−70.8667	−2.86696
$612$	0	0
$613$	26.1138	1.05473	0.527363	−	0.849640i	$-0.323181\pi$
$613$	26.1138	1.05473	0.527363	+	0.849640i	$0.323181\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−25.4698	−1.02537	−0.512687	−	0.858575i	$-0.671350\pi$
$617$	−25.4698	−1.02537	−0.512687	+	0.858575i	$0.671350\pi$
$618$	0	0
$619$	−15.0291	−0.604070	−0.302035	−	0.953297i	$-0.597666\pi$
$619$	−15.0291	−0.604070	−0.302035	+	0.953297i	$0.597666\pi$
$620$	0	0
$621$	−8.87433	−0.356115
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	2.21070	0.0882870
$628$	0	0
$629$	22.0051	0.877399
$630$	0	0
$631$	0.605762	0.0241150	0.0120575	−	0.999927i	$-0.496162\pi$
$631$	0.605762	0.0241150	0.0120575	+	0.999927i	$0.496162\pi$
$632$	0	0
$633$	−9.01279	−0.358226
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	9.80571	0.387908
$640$	0	0
$641$	22.7543	0.898742	0.449371	−	0.893345i	$-0.351648\pi$
$641$	22.7543	0.898742	0.449371	+	0.893345i	$0.351648\pi$
$642$	0	0
$643$	−1.85204	−0.0730375	−0.0365187	−	0.999333i	$-0.511627\pi$
$643$	−1.85204	−0.0730375	−0.0365187	+	0.999333i	$0.511627\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−6.68685	−0.262887	−0.131444	−	0.991324i	$-0.541961\pi$
$647$	−6.68685	−0.262887	−0.131444	+	0.991324i	$0.541961\pi$
$648$	0	0
$649$	2.88207	0.113131
$650$	0	0
$651$	0	0
$652$	0	0
$653$	11.0327	0.431744	0.215872	−	0.976422i	$-0.430741\pi$
$653$	11.0327	0.431744	0.215872	+	0.976422i	$0.430741\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	4.16756	0.162592
$658$	0	0
$659$	−13.5202	−0.526673	−0.263337	−	0.964704i	$-0.584823\pi$
$659$	−13.5202	−0.526673	−0.263337	+	0.964704i	$0.584823\pi$
$660$	0	0
$661$	−42.1385	−1.63900	−0.819498	−	0.573082i	$-0.805748\pi$
$661$	−42.1385	−1.63900	−0.819498	+	0.573082i	$0.805748\pi$
$662$	0	0
$663$	22.6514	0.879709
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−9.80066	−0.379483
$668$	0	0
$669$	34.3441	1.32782
$670$	0	0
$671$	0.869280	0.0335582
$672$	0	0
$673$	−18.8494	−0.726589	−0.363295	−	0.931674i	$-0.618348\pi$
$673$	−18.8494	−0.726589	−0.363295	+	0.931674i	$0.618348\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	24.9760	0.959904	0.479952	−	0.877295i	$-0.340654\pi$
$677$	24.9760	0.959904	0.479952	+	0.877295i	$0.340654\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	15.2777	0.585444
$682$	0	0
$683$	17.1266	0.655331	0.327666	−	0.944794i	$-0.393738\pi$
$683$	17.1266	0.655331	0.327666	+	0.944794i	$0.393738\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−7.60307	−0.290075
$688$	0	0
$689$	82.7984	3.15437
$690$	0	0
$691$	13.6100	0.517749	0.258874	−	0.965911i	$-0.416648\pi$
$691$	13.6100	0.517749	0.258874	+	0.965911i	$0.416648\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	9.27900	0.351467
$698$	0	0
$699$	−13.9581	−0.527944
$700$	0	0
$701$	3.86247	0.145884	0.0729418	−	0.997336i	$-0.476761\pi$
$701$	3.86247	0.145884	0.0729418	+	0.997336i	$0.476761\pi$
$702$	0	0
$703$	9.85298	0.371612
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−21.7870	−0.818230	−0.409115	−	0.912483i	$-0.634162\pi$
$709$	−21.7870	−0.818230	−0.409115	+	0.912483i	$0.634162\pi$
$710$	0	0
$711$	−1.04189	−0.0390739
$712$	0	0
$713$	7.84699	0.293872
$714$	0	0
$715$	0	0
$716$	0	0
$717$	16.4938	0.615973
$718$	0	0
$719$	50.7853	1.89397	0.946986	−	0.321275i	$-0.104111\pi$
$719$	50.7853	1.89397	0.946986	+	0.321275i	$0.104111\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	24.0624	0.894891
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−38.1607	−1.41530	−0.707652	−	0.706561i	$-0.750245\pi$
$727$	−38.1607	−1.41530	−0.707652	+	0.706561i	$0.750245\pi$
$728$	0	0
$729$	27.5776	1.02139
$730$	0	0
$731$	18.8203	0.696092
$732$	0	0
$733$	15.3942	0.568599	0.284300	−	0.958735i	$-0.408239\pi$
$733$	15.3942	0.568599	0.284300	+	0.958735i	$0.408239\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	8.58710	0.316310
$738$	0	0
$739$	−44.1498	−1.62408	−0.812039	−	0.583604i	$-0.801642\pi$
$739$	−44.1498	−1.62408	−0.812039	+	0.583604i	$0.801642\pi$
$740$	0	0
$741$	10.1424	0.372591
$742$	0	0
$743$	−53.0378	−1.94577	−0.972884	−	0.231296i	$-0.925704\pi$
$743$	−53.0378	−1.94577	−0.972884	+	0.231296i	$0.925704\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−4.62267	−0.169135
$748$	0	0
$749$	0	0
$750$	0	0
$751$	9.71688	0.354574	0.177287	−	0.984159i	$-0.443268\pi$
$751$	9.71688	0.354574	0.177287	+	0.984159i	$0.443268\pi$
$752$	0	0
$753$	22.6195	0.824300
$754$	0	0
$755$	0	0
$756$	0	0
$757$	22.2030	0.806980	0.403490	−	0.914984i	$-0.367797\pi$
$757$	22.2030	0.806980	0.403490	+	0.914984i	$0.367797\pi$
$758$	0	0
$759$	2.99319	0.108646
$760$	0	0
$761$	−37.0547	−1.34323	−0.671616	−	0.740900i	$-0.734399\pi$
$761$	−37.0547	−1.34323	−0.671616	+	0.740900i	$0.734399\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	13.2226	0.477439
$768$	0	0
$769$	−41.7948	−1.50716	−0.753579	−	0.657357i	$-0.771674\pi$
$769$	−41.7948	−1.50716	−0.753579	+	0.657357i	$0.771674\pi$
$770$	0	0
$771$	24.6892	0.889160
$772$	0	0
$773$	31.3381	1.12715	0.563577	−	0.826064i	$-0.309425\pi$
$773$	31.3381	1.12715	0.563577	+	0.826064i	$0.309425\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	4.15476	0.148860
$780$	0	0
$781$	−11.6818	−0.418008
$782$	0	0
$783$	35.1070	1.25462
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−24.7719	−0.883022	−0.441511	−	0.897256i	$-0.645557\pi$
$787$	−24.7719	−0.883022	−0.441511	+	0.897256i	$0.645557\pi$
$788$	0	0
$789$	−18.2158	−0.648498
$790$	0	0
$791$	0	0
$792$	0	0
$793$	3.98814	0.141623
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−5.07697	−0.179836	−0.0899178	−	0.995949i	$-0.528660\pi$
$797$	−5.07697	−0.179836	−0.0899178	+	0.995949i	$0.528660\pi$
$798$	0	0
$799$	28.4124	1.00516
$800$	0	0
$801$	7.06511	0.249633
$802$	0	0
$803$	−4.96492	−0.175208
$804$	0	0
$805$	0	0
$806$	0	0
$807$	37.4074	1.31680
$808$	0	0
$809$	2.95037	0.103729	0.0518647	−	0.998654i	$-0.483484\pi$
$809$	2.95037	0.103729	0.0518647	+	0.998654i	$0.483484\pi$
$810$	0	0
$811$	13.1753	0.462647	0.231324	−	0.972877i	$-0.425694\pi$
$811$	13.1753	0.462647	0.231324	+	0.972877i	$0.425694\pi$
$812$	0	0
$813$	21.3942	0.750329
$814$	0	0
$815$	0	0
$816$	0	0
$817$	8.42696	0.294822
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−23.6064	−0.823868	−0.411934	−	0.911214i	$-0.635147\pi$
$821$	−23.6064	−0.823868	−0.411934	+	0.911214i	$0.635147\pi$
$822$	0	0
$823$	5.64084	0.196627	0.0983137	−	0.995155i	$-0.468655\pi$
$823$	5.64084	0.196627	0.0983137	+	0.995155i	$0.468655\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−19.2368	−0.668929	−0.334464	−	0.942408i	$-0.608555\pi$
$827$	−19.2368	−0.668929	−0.334464	+	0.942408i	$0.608555\pi$
$828$	0	0
$829$	−27.3523	−0.949986	−0.474993	−	0.879989i	$-0.657549\pi$
$829$	−27.3523	−0.949986	−0.474993	+	0.879989i	$0.657549\pi$
$830$	0	0
$831$	22.5098	0.780856
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−28.1088	−0.971581
$838$	0	0
$839$	−16.5425	−0.571111	−0.285556	−	0.958362i	$-0.592178\pi$
$839$	−16.5425	−0.571111	−0.285556	+	0.958362i	$0.592178\pi$
$840$	0	0
$841$	9.77156	0.336950
$842$	0	0
$843$	−43.1343	−1.48563
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−14.4260	−0.495100
$850$	0	0
$851$	13.3405	0.457306
$852$	0	0
$853$	0.633103	0.0216770	0.0108385	−	0.999941i	$-0.496550\pi$
$853$	0.633103	0.0216770	0.0108385	+	0.999941i	$0.496550\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−6.15570	−0.210275	−0.105137	−	0.994458i	$-0.533528\pi$
$857$	−6.15570	−0.210275	−0.105137	+	0.994458i	$0.533528\pi$
$858$	0	0
$859$	25.5107	0.870415	0.435208	−	0.900330i	$-0.356675\pi$
$859$	25.5107	0.870415	0.435208	+	0.900330i	$0.356675\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	12.7469	0.433910	0.216955	−	0.976182i	$-0.430388\pi$
$863$	12.7469	0.433910	0.216955	+	0.976182i	$0.430388\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	13.8225	0.469435
$868$	0	0
$869$	1.24123	0.0421058
$870$	0	0
$871$	39.3964	1.33490
$872$	0	0
$873$	3.83212	0.129698
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−42.5817	−1.43788	−0.718941	−	0.695071i	$-0.755373\pi$
$877$	−42.5817	−1.43788	−0.718941	+	0.695071i	$0.755373\pi$
$878$	0	0
$879$	−11.0537	−0.372834
$880$	0	0
$881$	23.0033	0.775001	0.387500	−	0.921870i	$-0.373339\pi$
$881$	23.0033	0.775001	0.387500	+	0.921870i	$0.373339\pi$
$882$	0	0
$883$	1.92303	0.0647151	0.0323575	−	0.999476i	$-0.489698\pi$
$883$	1.92303	0.0647151	0.0323575	+	0.999476i	$0.489698\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−20.7529	−0.696814	−0.348407	−	0.937343i	$-0.613277\pi$
$887$	−20.7529	−0.696814	−0.348407	+	0.937343i	$0.613277\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−5.70502	−0.191125
$892$	0	0
$893$	12.7219	0.425723
$894$	0	0
$895$	0	0
$896$	0	0
$897$	13.7324	0.458510
$898$	0	0
$899$	−31.0428	−1.03534
$900$	0	0
$901$	−33.1962	−1.10592
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−3.76289	−0.124945	−0.0624723	−	0.998047i	$-0.519899\pi$
$907$	−3.76289	−0.124945	−0.0624723	+	0.998047i	$0.519899\pi$
$908$	0	0
$909$	17.2175	0.571069
$910$	0	0
$911$	−19.0618	−0.631546	−0.315773	−	0.948835i	$-0.602264\pi$
$911$	−19.0618	−0.631546	−0.315773	+	0.948835i	$0.602264\pi$
$912$	0	0
$913$	5.50711	0.182259
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	19.2267	0.634230	0.317115	−	0.948387i	$-0.397286\pi$
$919$	19.2267	0.634230	0.317115	+	0.948387i	$0.397286\pi$
$920$	0	0
$921$	35.5253	1.17060
$922$	0	0
$923$	−53.5945	−1.76408
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−18.9254	−0.621591
$928$	0	0
$929$	−52.3242	−1.71670	−0.858350	−	0.513064i	$-0.828510\pi$
$929$	−52.3242	−1.71670	−0.858350	+	0.513064i	$0.828510\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−19.7588	−0.646873
$934$	0	0
$935$	0	0
$936$	0	0
$937$	36.0145	1.17654	0.588272	−	0.808663i	$-0.299808\pi$
$937$	36.0145	1.17654	0.588272	+	0.808663i	$0.299808\pi$
$938$	0	0
$939$	−41.1198	−1.34189
$940$	0	0
$941$	−30.8215	−1.00475	−0.502376	−	0.864649i	$-0.667541\pi$
$941$	−30.8215	−1.00475	−0.502376	+	0.864649i	$0.667541\pi$
$942$	0	0
$943$	5.62536	0.183187
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−6.96679	−0.226390	−0.113195	−	0.993573i	$-0.536108\pi$
$947$	−6.96679	−0.226390	−0.113195	+	0.993573i	$0.536108\pi$
$948$	0	0
$949$	−22.7784	−0.739417
$950$	0	0
$951$	22.7311	0.737107
$952$	0	0
$953$	−6.84491	−0.221728	−0.110864	−	0.993836i	$-0.535362\pi$
$953$	−6.84491	−0.221728	−0.110864	+	0.993836i	$0.535362\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−11.8411	−0.382769
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−6.14527	−0.198234
$962$	0	0
$963$	−21.1257	−0.680765
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−19.2909	−0.620352	−0.310176	−	0.950679i	$-0.600388\pi$
$967$	−19.2909	−0.620352	−0.310176	+	0.950679i	$0.600388\pi$
$968$	0	0
$969$	−4.06637	−0.130631
$970$	0	0
$971$	−42.7452	−1.37176	−0.685879	−	0.727716i	$-0.740582\pi$
$971$	−42.7452	−1.37176	−0.685879	+	0.727716i	$0.740582\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	12.5149	0.400386	0.200193	−	0.979757i	$-0.435843\pi$
$977$	12.5149	0.400386	0.200193	+	0.979757i	$0.435843\pi$
$978$	0	0
$979$	−8.41685	−0.269004
$980$	0	0
$981$	−14.4953	−0.462798
$982$	0	0
$983$	−29.1370	−0.929327	−0.464663	−	0.885487i	$-0.653825\pi$
$983$	−29.1370	−0.929327	−0.464663	+	0.885487i	$0.653825\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	11.4097	0.362808
$990$	0	0
$991$	60.0215	1.90664	0.953322	−	0.301954i	$-0.0976390\pi$
$991$	60.0215	1.90664	0.953322	+	0.301954i	$0.0976390\pi$
$992$	0	0
$993$	−19.3682	−0.614630
$994$	0	0
$995$	0	0
$996$	0	0
$997$	35.5990	1.12743	0.563715	−	0.825969i	$-0.309372\pi$
$997$	35.5990	1.12743	0.563715	+	0.825969i	$0.309372\pi$
$998$	0	0
$999$	−47.7870	−1.51192

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9800.2.a.cb.1.2		3
5.4	even	2		9800.2.a.ch.1.2		3
7.3	odd	6		1400.2.q.i.401.2	✓	6
7.5	odd	6		1400.2.q.i.1201.2	yes	6
7.6	odd	2		9800.2.a.ci.1.2		3
35.3	even	12		1400.2.bh.h.849.5		12
35.12	even	12		1400.2.bh.h.249.5		12
35.17	even	12		1400.2.bh.h.849.2		12
35.19	odd	6		1400.2.q.k.1201.2	yes	6
35.24	odd	6		1400.2.q.k.401.2	yes	6
35.33	even	12		1400.2.bh.h.249.2		12
35.34	odd	2		9800.2.a.cc.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1400.2.q.i.401.2	✓	6	7.3	odd	6
1400.2.q.i.1201.2	yes	6	7.5	odd	6
1400.2.q.k.401.2	yes	6	35.24	odd	6
1400.2.q.k.1201.2	yes	6	35.19	odd	6
1400.2.bh.h.249.2		12	35.33	even	12
1400.2.bh.h.249.5		12	35.12	even	12
1400.2.bh.h.849.2		12	35.17	even	12
1400.2.bh.h.849.5		12	35.3	even	12
9800.2.a.cb.1.2		3	1.1	even	1	trivial
9800.2.a.cc.1.2		3	35.34	odd	2
9800.2.a.ch.1.2		3	5.4	even	2
9800.2.a.ci.1.2		3	7.6	odd	2

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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)

\(f(q)\)	\(=\)	\(q-1.34730 q^{3} -1.18479 q^{9} +O(q^{10})\)	\(q-1.34730 q^{3} -1.18479 q^{9} +1.41147 q^{11} +6.47565 q^{13} -2.59627 q^{17} -1.16250 q^{19} -1.57398 q^{23} +5.63816 q^{27} +6.22668 q^{29} -4.98545 q^{31} -1.90167 q^{33} -8.47565 q^{37} -8.72462 q^{39} -3.57398 q^{41} -7.24897 q^{43} -10.9436 q^{47} +3.49794 q^{51} +12.7861 q^{53} +1.56624 q^{57} +2.04189 q^{59} +0.615867 q^{61} +6.08378 q^{67} +2.12061 q^{69} -8.27631 q^{71} -3.51754 q^{73} +0.879385 q^{79} -4.04189 q^{81} +3.90167 q^{83} -8.38919 q^{87} -5.96316 q^{89} +6.71688 q^{93} -3.23442 q^{97} -1.67230 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3}+O(q^{10}) \) 3 * q - 3 * q^3	\( 3 q - 3 q^{3} - 6 q^{11} + 6 q^{17} - 6 q^{19} + 3 q^{23} + 12 q^{29} + 3 q^{31} + 6 q^{33} - 6 q^{37} + 6 q^{39} - 3 q^{41} - 9 q^{43} - 18 q^{47} - 15 q^{51} + 6 q^{53} + 21 q^{57} + 3 q^{59} - 9 q^{61} + 12 q^{67} + 12 q^{69} + 9 q^{71} + 12 q^{73} - 3 q^{79} - 9 q^{81} - 21 q^{87} - 6 q^{89} + 12 q^{93} + 21 q^{97} - 9 q^{99}+O(q^{100}) \) 3 * q - 3 * q^3 - 6 * q^11 + 6 * q^17 - 6 * q^19 + 3 * q^23 + 12 * q^29 + 3 * q^31 + 6 * q^33 - 6 * q^37 + 6 * q^39 - 3 * q^41 - 9 * q^43 - 18 * q^47 - 15 * q^51 + 6 * q^53 + 21 * q^57 + 3 * q^59 - 9 * q^61 + 12 * q^67 + 12 * q^69 + 9 * q^71 + 12 * q^73 - 3 * q^79 - 9 * q^81 - 21 * q^87 - 6 * q^89 + 12 * q^93 + 21 * q^97 - 9 * q^99

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