LMFDB - Embedded newform 9800.2.a.cu.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:	$0$
Dimension:	$4$
Coefficient field:	4.4.43449.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 7x^{2} + 2x + 1 $ x^4 - x^3 - 7x^2 + 2x + 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			1.3
Root			$-0.265362$ 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)

$f(q)$	$=$	$q+1.26536 q^{3} -1.39886 q^{9} +O(q^{10})$	$q+1.26536 q^{3} -1.39886 q^{9} +6.43265 q^{11} -1.10421 q^{13} -4.50307 q^{17} +5.87265 q^{19} -8.77457 q^{23} -5.56615 q^{27} +3.87265 q^{29} +6.66422 q^{31} +8.13964 q^{33} +1.42651 q^{37} -1.39723 q^{39} +11.8360 q^{41} +6.46645 q^{43} -8.46031 q^{47} -5.69802 q^{51} -0.768433 q^{53} +7.43102 q^{57} +1.79609 q^{59} -3.03994 q^{61} +2.85302 q^{67} -11.1030 q^{69} -9.47542 q^{71} +13.3960 q^{73} -9.30530 q^{79} -2.84662 q^{81} -3.20109 q^{83} +4.90030 q^{87} +2.92344 q^{89} +8.43265 q^{93} +5.96338 q^{97} -8.99837 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{3} + 5 q^{9}+O(q^{10}) $ 4 * q + 3 * q^3 + 5 * q^9	$ 4 q + 3 q^{3} + 5 q^{9} - 4 q^{13} - 7 q^{17} + 10 q^{19} + 12 q^{27} + 2 q^{29} + 14 q^{31} + 2 q^{33} + 2 q^{37} - 10 q^{39} + 4 q^{41} - 15 q^{43} - 15 q^{47} + 5 q^{51} + 10 q^{53} + 19 q^{57} + q^{59} + 25 q^{61} + 4 q^{67} + 16 q^{69} - 20 q^{71} - 2 q^{73} + 2 q^{79} + 24 q^{81} + 26 q^{83} + 13 q^{87} + 19 q^{89} + 8 q^{93} - 6 q^{97} - 51 q^{99}+O(q^{100}) $ 4 * q + 3 * q^3 + 5 * q^9 - 4 * q^13 - 7 * q^17 + 10 * q^19 + 12 * q^27 + 2 * q^29 + 14 * q^31 + 2 * q^33 + 2 * q^37 - 10 * q^39 + 4 * q^41 - 15 * q^43 - 15 * q^47 + 5 * q^51 + 10 * q^53 + 19 * q^57 + q^59 + 25 * q^61 + 4 * q^67 + 16 * q^69 - 20 * q^71 - 2 * q^73 + 2 * q^79 + 24 * q^81 + 26 * q^83 + 13 * q^87 + 19 * q^89 + 8 * q^93 - 6 * q^97 - 51 * 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
$3$	1.26536	0.730557	0.365279	−	0.930898i	$-0.380974\pi$
$3$	1.26536	0.730557	0.365279	+	0.930898i	$0.380974\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	−1.39886	−0.466286
$10$	0	0
$11$	6.43265	1.93952	0.969759	−	0.244065i	$-0.0784809\pi$
$11$	6.43265	1.93952	0.969759	+	0.244065i	$0.0784809\pi$
$12$	0	0
$13$	−1.10421	−0.306253	−0.153127	−	0.988207i	$-0.548934\pi$
$13$	−1.10421	−0.306253	−0.153127	+	0.988207i	$0.548934\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−4.50307	−1.09216	−0.546078	−	0.837735i	$-0.683880\pi$
$17$	−4.50307	−1.09216	−0.546078	+	0.837735i	$0.683880\pi$
$18$	0	0
$19$	5.87265	1.34728	0.673639	−	0.739061i	$-0.264730\pi$
$19$	5.87265	1.34728	0.673639	+	0.739061i	$0.264730\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−8.77457	−1.82963	−0.914813	−	0.403879i	$-0.867662\pi$
$23$	−8.77457	−1.82963	−0.914813	+	0.403879i	$0.867662\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−5.56615	−1.07121
$28$	0	0
$29$	3.87265	0.719132	0.359566	−	0.933120i	$-0.382925\pi$
$29$	3.87265	0.719132	0.359566	+	0.933120i	$0.382925\pi$
$30$	0	0
$31$	6.66422	1.19693	0.598465	−	0.801149i	$-0.295778\pi$
$31$	6.66422	1.19693	0.598465	+	0.801149i	$0.295778\pi$
$32$	0	0
$33$	8.13964	1.41693
$34$	0	0
$35$	0	0
$36$	0	0
$37$	1.42651	0.234517	0.117259	−	0.993101i	$-0.462589\pi$
$37$	1.42651	0.234517	0.117259	+	0.993101i	$0.462589\pi$
$38$	0	0
$39$	−1.39723	−0.223736
$40$	0	0
$41$	11.8360	1.84848	0.924238	−	0.381817i	$-0.124701\pi$
$41$	11.8360	1.84848	0.924238	+	0.381817i	$0.124701\pi$
$42$	0	0
$43$	6.46645	0.986124	0.493062	−	0.869994i	$-0.335878\pi$
$43$	6.46645	0.986124	0.493062	+	0.869994i	$0.335878\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−8.46031	−1.23406	−0.617031	−	0.786939i	$-0.711665\pi$
$47$	−8.46031	−1.23406	−0.617031	+	0.786939i	$0.711665\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	−5.69802	−0.797882
$52$	0	0
$53$	−0.768433	−0.105552	−0.0527762	−	0.998606i	$-0.516807\pi$
$53$	−0.768433	−0.105552	−0.0527762	+	0.998606i	$0.516807\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	7.43102	0.984263
$58$	0	0
$59$	1.79609	0.233831	0.116915	−	0.993142i	$-0.462699\pi$
$59$	1.79609	0.233831	0.116915	+	0.993142i	$0.462699\pi$
$60$	0	0
$61$	−3.03994	−0.389224	−0.194612	−	0.980880i	$-0.562345\pi$
$61$	−3.03994	−0.389224	−0.194612	+	0.980880i	$0.562345\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	2.85302	0.348552	0.174276	−	0.984697i	$-0.444241\pi$
$67$	2.85302	0.348552	0.174276	+	0.984697i	$0.444241\pi$
$68$	0	0
$69$	−11.1030	−1.33665
$70$	0	0
$71$	−9.47542	−1.12453	−0.562263	−	0.826959i	$-0.690069\pi$
$71$	−9.47542	−1.12453	−0.562263	+	0.826959i	$0.690069\pi$
$72$	0	0
$73$	13.3960	1.56789	0.783943	−	0.620832i	$-0.213205\pi$
$73$	13.3960	1.56789	0.783943	+	0.620832i	$0.213205\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−9.30530	−1.04693	−0.523464	−	0.852048i	$-0.675361\pi$
$79$	−9.30530	−1.04693	−0.523464	+	0.852048i	$0.675361\pi$
$80$	0	0
$81$	−2.84662	−0.316291
$82$	0	0
$83$	−3.20109	−0.351365	−0.175682	−	0.984447i	$-0.556213\pi$
$83$	−3.20109	−0.351365	−0.175682	+	0.984447i	$0.556213\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	4.90030	0.525367
$88$	0	0
$89$	2.92344	0.309884	0.154942	−	0.987924i	$-0.450481\pi$
$89$	2.92344	0.309884	0.154942	+	0.987924i	$0.450481\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	8.43265	0.874425
$94$	0	0
$95$	0	0
$96$	0	0
$97$	5.96338	0.605489	0.302745	−	0.953072i	$-0.402097\pi$
$97$	5.96338	0.605489	0.302745	+	0.953072i	$0.402097\pi$
$98$	0	0
$99$	−8.99837	−0.904370
$100$	0	0
$101$	10.5092	1.04571	0.522853	−	0.852423i	$-0.324868\pi$
$101$	10.5092	1.04571	0.522853	+	0.852423i	$0.324868\pi$
$102$	0	0
$103$	9.11035	0.897670	0.448835	−	0.893615i	$-0.351839\pi$
$103$	9.11035	0.897670	0.448835	+	0.893615i	$0.351839\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−8.39886	−0.811948	−0.405974	−	0.913885i	$-0.633068\pi$
$107$	−8.39886	−0.811948	−0.405974	+	0.913885i	$0.633068\pi$
$108$	0	0
$109$	4.84048	0.463634	0.231817	−	0.972759i	$-0.425533\pi$
$109$	4.84048	0.463634	0.231817	+	0.972759i	$0.425533\pi$
$110$	0	0
$111$	1.80505	0.171328
$112$	0	0
$113$	3.87879	0.364886	0.182443	−	0.983216i	$-0.441600\pi$
$113$	3.87879	0.364886	0.182443	+	0.983216i	$0.441600\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	1.54464	0.142802
$118$	0	0
$119$	0	0
$120$	0	0
$121$	30.3790	2.76173
$122$	0	0
$123$	14.9769	1.35042
$124$	0	0
$125$	0	0
$126$	0	0
$127$	11.8681	1.05313	0.526563	−	0.850136i	$-0.323480\pi$
$127$	11.8681	1.05313	0.526563	+	0.850136i	$0.323480\pi$
$128$	0	0
$129$	8.18240	0.720420
$130$	0	0
$131$	13.9785	1.22131	0.610653	−	0.791898i	$-0.290907\pi$
$131$	13.9785	1.22131	0.610653	+	0.791898i	$0.290907\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	5.03831	0.430452	0.215226	−	0.976564i	$-0.430951\pi$
$137$	5.03831	0.430452	0.215226	+	0.976564i	$0.430951\pi$
$138$	0	0
$139$	−6.69639	−0.567980	−0.283990	−	0.958827i	$-0.591658\pi$
$139$	−6.69639	−0.567980	−0.283990	+	0.958827i	$0.591658\pi$
$140$	0	0
$141$	−10.7054	−0.901553
$142$	0	0
$143$	−7.10302	−0.593984
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	7.52339	0.616340	0.308170	−	0.951331i	$-0.400283\pi$
$149$	7.52339	0.616340	0.308170	+	0.951331i	$0.400283\pi$
$150$	0	0
$151$	16.4034	1.33489	0.667444	−	0.744660i	$-0.267389\pi$
$151$	16.4034	1.33489	0.667444	+	0.744660i	$0.267389\pi$
$152$	0	0
$153$	6.29916	0.509257
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−3.19777	−0.255210	−0.127605	−	0.991825i	$-0.540729\pi$
$157$	−3.19777	−0.255210	−0.127605	+	0.991825i	$0.540729\pi$
$158$	0	0
$159$	−0.972346	−0.0771121
$160$	0	0
$161$	0	0
$162$	0	0
$163$	13.5076	1.05800	0.528998	−	0.848623i	$-0.322568\pi$
$163$	13.5076	1.05800	0.528998	+	0.848623i	$0.322568\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	9.55267	0.739208	0.369604	−	0.929189i	$-0.379493\pi$
$167$	9.55267	0.739208	0.369604	+	0.929189i	$0.379493\pi$
$168$	0	0
$169$	−11.7807	−0.906209
$170$	0	0
$171$	−8.21500	−0.628217
$172$	0	0
$173$	−18.1137	−1.37716	−0.688578	−	0.725162i	$-0.741765\pi$
$173$	−18.1137	−1.37716	−0.688578	+	0.725162i	$0.741765\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	2.27270	0.170827
$178$	0	0
$179$	−18.1937	−1.35986	−0.679932	−	0.733275i	$-0.737991\pi$
$179$	−18.1937	−1.35986	−0.679932	+	0.733275i	$0.737991\pi$
$180$	0	0
$181$	−15.3542	−1.14127	−0.570634	−	0.821204i	$-0.693303\pi$
$181$	−15.3542	−1.14127	−0.570634	+	0.821204i	$0.693303\pi$
$182$	0	0
$183$	−3.84662	−0.284350
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−28.9667	−2.11825
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−1.41685	−0.102520	−0.0512598	−	0.998685i	$-0.516324\pi$
$191$	−1.41685	−0.102520	−0.0512598	+	0.998685i	$0.516324\pi$
$192$	0	0
$193$	−0.915408	−0.0658925	−0.0329463	−	0.999457i	$-0.510489\pi$
$193$	−0.915408	−0.0658925	−0.0329463	+	0.999457i	$0.510489\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	14.7167	1.04852	0.524261	−	0.851558i	$-0.324342\pi$
$197$	14.7167	1.04852	0.524261	+	0.851558i	$0.324342\pi$
$198$	0	0
$199$	−9.41114	−0.667138	−0.333569	−	0.942726i	$-0.608253\pi$
$199$	−9.41114	−0.667138	−0.333569	+	0.942726i	$0.608253\pi$
$200$	0	0
$201$	3.61011	0.254638
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	12.2744	0.853129
$208$	0	0
$209$	37.7767	2.61307
$210$	0	0
$211$	−3.08622	−0.212464	−0.106232	−	0.994341i	$-0.533879\pi$
$211$	−3.08622	−0.212464	−0.106232	+	0.994341i	$0.533879\pi$
$212$	0	0
$213$	−11.9898	−0.821530
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	16.9508	1.14543
$220$	0	0
$221$	4.97235	0.334476
$222$	0	0
$223$	3.96338	0.265407	0.132704	−	0.991156i	$-0.457634\pi$
$223$	3.96338	0.265407	0.132704	+	0.991156i	$0.457634\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	17.8930	1.18760	0.593799	−	0.804614i	$-0.297628\pi$
$227$	17.8930	1.18760	0.593799	+	0.804614i	$0.297628\pi$
$228$	0	0
$229$	26.3391	1.74054	0.870268	−	0.492578i	$-0.163945\pi$
$229$	26.3391	1.74054	0.870268	+	0.492578i	$0.163945\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−6.22874	−0.408058	−0.204029	−	0.978965i	$-0.565404\pi$
$233$	−6.22874	−0.408058	−0.204029	+	0.978965i	$0.565404\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−11.7746	−0.764841
$238$	0	0
$239$	−7.94213	−0.513734	−0.256867	−	0.966447i	$-0.582690\pi$
$239$	−7.94213	−0.513734	−0.256867	+	0.966447i	$0.582690\pi$
$240$	0	0
$241$	−4.78875	−0.308470	−0.154235	−	0.988034i	$-0.549291\pi$
$241$	−4.78875	−0.308470	−0.154235	+	0.988034i	$0.549291\pi$
$242$	0	0
$243$	13.0964	0.840137
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−6.48465	−0.412608
$248$	0	0
$249$	−4.05053	−0.256692
$250$	0	0
$251$	−0.242220	−0.0152888	−0.00764439	−	0.999971i	$-0.502433\pi$
$251$	−0.242220	−0.0152888	−0.00764439	+	0.999971i	$0.502433\pi$
$252$	0	0
$253$	−56.4438	−3.54859
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−15.9447	−0.994603	−0.497301	−	0.867578i	$-0.665676\pi$
$257$	−15.9447	−0.994603	−0.497301	+	0.867578i	$0.665676\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−5.41728	−0.335321
$262$	0	0
$263$	9.82254	0.605684	0.302842	−	0.953041i	$-0.402065\pi$
$263$	9.82254	0.605684	0.302842	+	0.953041i	$0.402065\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	3.69921	0.226388
$268$	0	0
$269$	−14.5048	−0.884371	−0.442185	−	0.896924i	$-0.645797\pi$
$269$	−14.5048	−0.884371	−0.442185	+	0.896924i	$0.645797\pi$
$270$	0	0
$271$	25.6659	1.55909	0.779545	−	0.626347i	$-0.215451\pi$
$271$	25.6659	1.55909	0.779545	+	0.626347i	$0.215451\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−6.35703	−0.381957	−0.190978	−	0.981594i	$-0.561166\pi$
$277$	−6.35703	−0.381957	−0.190978	+	0.981594i	$0.561166\pi$
$278$	0	0
$279$	−9.32230	−0.558112
$280$	0	0
$281$	−11.8360	−0.706075	−0.353037	−	0.935609i	$-0.614851\pi$
$281$	−11.8360	−0.706075	−0.353037	+	0.935609i	$0.614851\pi$
$282$	0	0
$283$	14.6793	0.872596	0.436298	−	0.899802i	$-0.356289\pi$
$283$	14.6793	0.872596	0.436298	+	0.899802i	$0.356289\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	3.27764	0.192803
$290$	0	0
$291$	7.54583	0.442345
$292$	0	0
$293$	−13.6800	−0.799196	−0.399598	−	0.916691i	$-0.630850\pi$
$293$	−13.6800	−0.799196	−0.399598	+	0.916691i	$0.630850\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−35.8051	−2.07762
$298$	0	0
$299$	9.68899	0.560329
$300$	0	0
$301$	0	0
$302$	0	0
$303$	13.2980	0.763948
$304$	0	0
$305$	0	0
$306$	0	0
$307$	21.4140	1.22216	0.611081	−	0.791568i	$-0.290735\pi$
$307$	21.4140	1.22216	0.611081	+	0.791568i	$0.290735\pi$
$308$	0	0
$309$	11.5279	0.655799
$310$	0	0
$311$	25.0203	1.41877	0.709386	−	0.704820i	$-0.248972\pi$
$311$	25.0203	1.41877	0.709386	+	0.704820i	$0.248972\pi$
$312$	0	0
$313$	7.20391	0.407189	0.203595	−	0.979055i	$-0.434738\pi$
$313$	7.20391	0.407189	0.203595	+	0.979055i	$0.434738\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	8.48345	0.476478	0.238239	−	0.971207i	$-0.423430\pi$
$317$	8.48345	0.476478	0.238239	+	0.971207i	$0.423430\pi$
$318$	0	0
$319$	24.9114	1.39477
$320$	0	0
$321$	−10.6276	−0.593175
$322$	0	0
$323$	−26.4449	−1.47144
$324$	0	0
$325$	0	0
$326$	0	0
$327$	6.12496	0.338711
$328$	0	0
$329$	0	0
$330$	0	0
$331$	1.10872	0.0609410	0.0304705	−	0.999536i	$-0.490299\pi$
$331$	1.10872	0.0609410	0.0304705	+	0.999536i	$0.490299\pi$
$332$	0	0
$333$	−1.99549	−0.109352
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−4.00168	−0.217986	−0.108993	−	0.994043i	$-0.534763\pi$
$337$	−4.00168	−0.217986	−0.108993	+	0.994043i	$0.534763\pi$
$338$	0	0
$339$	4.90807	0.266570
$340$	0	0
$341$	42.8686	2.32147
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−23.4005	−1.25621	−0.628103	−	0.778130i	$-0.716169\pi$
$347$	−23.4005	−1.25621	−0.628103	+	0.778130i	$0.716169\pi$
$348$	0	0
$349$	−6.05059	−0.323881	−0.161940	−	0.986801i	$-0.551775\pi$
$349$	−6.05059	−0.323881	−0.161940	+	0.986801i	$0.551775\pi$
$350$	0	0
$351$	6.14621	0.328060
$352$	0	0
$353$	25.1217	1.33709	0.668547	−	0.743670i	$-0.266917\pi$
$353$	25.1217	1.33709	0.668547	+	0.743670i	$0.266917\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	18.9846	1.00197	0.500985	−	0.865456i	$-0.332971\pi$
$359$	18.9846	1.00197	0.500985	+	0.865456i	$0.332971\pi$
$360$	0	0
$361$	15.4880	0.815156
$362$	0	0
$363$	38.4405	2.01760
$364$	0	0
$365$	0	0
$366$	0	0
$367$	12.9723	0.677151	0.338575	−	0.940939i	$-0.390055\pi$
$367$	12.9723	0.677151	0.338575	+	0.940939i	$0.390055\pi$
$368$	0	0
$369$	−16.5569	−0.861919
$370$	0	0
$371$	0	0
$372$	0	0
$373$	33.7946	1.74982	0.874910	−	0.484286i	$-0.160921\pi$
$373$	33.7946	1.74982	0.874910	+	0.484286i	$0.160921\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−4.27622	−0.220237
$378$	0	0
$379$	−35.9052	−1.84433	−0.922164	−	0.386799i	$-0.873581\pi$
$379$	−35.9052	−1.84433	−0.922164	+	0.386799i	$0.873581\pi$
$380$	0	0
$381$	15.0175	0.769369
$382$	0	0
$383$	7.17695	0.366725	0.183363	−	0.983045i	$-0.441302\pi$
$383$	7.17695	0.366725	0.183363	+	0.983045i	$0.441302\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−9.04565	−0.459816
$388$	0	0
$389$	−17.8625	−0.905664	−0.452832	−	0.891596i	$-0.649586\pi$
$389$	−17.8625	−0.905664	−0.452832	+	0.891596i	$0.649586\pi$
$390$	0	0
$391$	39.5125	1.99823
$392$	0	0
$393$	17.6879	0.892234
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−35.8275	−1.79813	−0.899065	−	0.437815i	$-0.855752\pi$
$397$	−35.8275	−1.79813	−0.899065	+	0.437815i	$0.855752\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	1.98321	0.0990366	0.0495183	−	0.998773i	$-0.484231\pi$
$401$	1.98321	0.0990366	0.0495183	+	0.998773i	$0.484231\pi$
$402$	0	0
$403$	−7.35871	−0.366564
$404$	0	0
$405$	0	0
$406$	0	0
$407$	9.17626	0.454850
$408$	0	0
$409$	31.7977	1.57230	0.786148	−	0.618038i	$-0.212072\pi$
$409$	31.7977	1.57230	0.786148	+	0.618038i	$0.212072\pi$
$410$	0	0
$411$	6.37528	0.314470
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−8.47335	−0.414942
$418$	0	0
$419$	4.05411	0.198056	0.0990281	−	0.995085i	$-0.468427\pi$
$419$	4.05411	0.198056	0.0990281	+	0.995085i	$0.468427\pi$
$420$	0	0
$421$	−6.19163	−0.301762	−0.150881	−	0.988552i	$-0.548211\pi$
$421$	−6.19163	−0.301762	−0.150881	+	0.988552i	$0.548211\pi$
$422$	0	0
$423$	11.8348	0.575426
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−8.98789	−0.433939
$430$	0	0
$431$	−17.4190	−0.839042	−0.419521	−	0.907746i	$-0.637802\pi$
$431$	−17.4190	−0.839042	−0.419521	+	0.907746i	$0.637802\pi$
$432$	0	0
$433$	14.6292	0.703036	0.351518	−	0.936181i	$-0.385666\pi$
$433$	14.6292	0.703036	0.351518	+	0.936181i	$0.385666\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−51.5300	−2.46501
$438$	0	0
$439$	−23.4868	−1.12096	−0.560481	−	0.828167i	$-0.689384\pi$
$439$	−23.4868	−1.12096	−0.560481	+	0.828167i	$0.689384\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−7.09524	−0.337105	−0.168553	−	0.985693i	$-0.553909\pi$
$443$	−7.09524	−0.337105	−0.168553	+	0.985693i	$0.553909\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	9.51981	0.450272
$448$	0	0
$449$	1.96690	0.0928237	0.0464119	−	0.998922i	$-0.485221\pi$
$449$	1.96690	0.0928237	0.0464119	+	0.998922i	$0.485221\pi$
$450$	0	0
$451$	76.1370	3.58515
$452$	0	0
$453$	20.7562	0.975212
$454$	0	0
$455$	0	0
$456$	0	0
$457$	27.1829	1.27156	0.635781	−	0.771870i	$-0.280678\pi$
$457$	27.1829	1.27156	0.635781	+	0.771870i	$0.280678\pi$
$458$	0	0
$459$	25.0648	1.16992
$460$	0	0
$461$	13.9232	0.648467	0.324234	−	0.945977i	$-0.394894\pi$
$461$	13.9232	0.648467	0.324234	+	0.945977i	$0.394894\pi$
$462$	0	0
$463$	27.9834	1.30050	0.650250	−	0.759720i	$-0.274664\pi$
$463$	27.9834	1.30050	0.650250	+	0.759720i	$0.274664\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	41.5773	1.92397	0.961984	−	0.273107i	$-0.0880512\pi$
$467$	41.5773	1.92397	0.961984	+	0.273107i	$0.0880512\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−4.04634	−0.186446
$472$	0	0
$473$	41.5964	1.91261
$474$	0	0
$475$	0	0
$476$	0	0
$477$	1.07493	0.0492176
$478$	0	0
$479$	32.0173	1.46291	0.731453	−	0.681891i	$-0.238842\pi$
$479$	32.0173	1.46291	0.731453	+	0.681891i	$0.238842\pi$
$480$	0	0
$481$	−1.57517	−0.0718217
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−30.4974	−1.38197	−0.690985	−	0.722869i	$-0.742823\pi$
$487$	−30.4974	−1.38197	−0.690985	+	0.722869i	$0.742823\pi$
$488$	0	0
$489$	17.0920	0.772926
$490$	0	0
$491$	−14.6253	−0.660029	−0.330015	−	0.943976i	$-0.607054\pi$
$491$	−14.6253	−0.660029	−0.330015	+	0.943976i	$0.607054\pi$
$492$	0	0
$493$	−17.4388	−0.785404
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−35.3148	−1.58091	−0.790453	−	0.612523i	$-0.790155\pi$
$499$	−35.3148	−1.58091	−0.790453	+	0.612523i	$0.790155\pi$
$500$	0	0
$501$	12.0876	0.540034
$502$	0	0
$503$	18.4066	0.820711	0.410356	−	0.911926i	$-0.365405\pi$
$503$	18.4066	0.820711	0.410356	+	0.911926i	$0.365405\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−14.9069	−0.662037
$508$	0	0
$509$	24.8190	1.10008	0.550042	−	0.835137i	$-0.314612\pi$
$509$	24.8190	1.10008	0.550042	+	0.835137i	$0.314612\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−32.6880	−1.44321
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−54.4222	−2.39349
$518$	0	0
$519$	−22.9204	−1.00609
$520$	0	0
$521$	−25.8663	−1.13322	−0.566612	−	0.823985i	$-0.691746\pi$
$521$	−25.8663	−1.13322	−0.566612	+	0.823985i	$0.691746\pi$
$522$	0	0
$523$	2.82369	0.123471	0.0617356	−	0.998093i	$-0.480336\pi$
$523$	2.82369	0.123471	0.0617356	+	0.998093i	$0.480336\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−30.0095	−1.30723
$528$	0	0
$529$	53.9931	2.34753
$530$	0	0
$531$	−2.51247	−0.109032
$532$	0	0
$533$	−13.0695	−0.566102
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−23.0217	−0.993459
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−17.9651	−0.772378	−0.386189	−	0.922420i	$-0.626209\pi$
$541$	−17.9651	−0.772378	−0.386189	+	0.922420i	$0.626209\pi$
$542$	0	0
$543$	−19.4286	−0.833762
$544$	0	0
$545$	0	0
$546$	0	0
$547$	2.40331	0.102758	0.0513792	−	0.998679i	$-0.483638\pi$
$547$	2.40331	0.102758	0.0513792	+	0.998679i	$0.483638\pi$
$548$	0	0
$549$	4.25244	0.181490
$550$	0	0
$551$	22.7427	0.968870
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−3.09877	−0.131299	−0.0656495	−	0.997843i	$-0.520912\pi$
$557$	−3.09877	−0.131299	−0.0656495	+	0.997843i	$0.520912\pi$
$558$	0	0
$559$	−7.14033	−0.302004
$560$	0	0
$561$	−36.6534	−1.54751
$562$	0	0
$563$	38.4957	1.62240	0.811201	−	0.584768i	$-0.198814\pi$
$563$	38.4957	1.62240	0.811201	+	0.584768i	$0.198814\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	7.59474	0.318388	0.159194	−	0.987247i	$-0.449110\pi$
$569$	7.59474	0.318388	0.159194	+	0.987247i	$0.449110\pi$
$570$	0	0
$571$	−0.679330	−0.0284291	−0.0142145	−	0.999899i	$-0.504525\pi$
$571$	−0.679330	−0.0284291	−0.0142145	+	0.999899i	$0.504525\pi$
$572$	0	0
$573$	−1.79283	−0.0748964
$574$	0	0
$575$	0	0
$576$	0	0
$577$	17.6808	0.736059	0.368030	−	0.929814i	$-0.380032\pi$
$577$	17.6808	0.736059	0.368030	+	0.929814i	$0.380032\pi$
$578$	0	0
$579$	−1.15832	−0.0481383
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−4.94306	−0.204721
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−14.0359	−0.579324	−0.289662	−	0.957129i	$-0.593543\pi$
$587$	−14.0359	−0.579324	−0.289662	+	0.957129i	$0.593543\pi$
$588$	0	0
$589$	39.1366	1.61260
$590$	0	0
$591$	18.6220	0.766005
$592$	0	0
$593$	12.1512	0.498991	0.249495	−	0.968376i	$-0.419735\pi$
$593$	12.1512	0.498991	0.249495	+	0.968376i	$0.419735\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−11.9085	−0.487383
$598$	0	0
$599$	−34.8724	−1.42485	−0.712425	−	0.701749i	$-0.752403\pi$
$599$	−34.8724	−1.42485	−0.712425	+	0.701749i	$0.752403\pi$
$600$	0	0
$601$	−11.8128	−0.481855	−0.240928	−	0.970543i	$-0.577452\pi$
$601$	−11.8128	−0.481855	−0.240928	+	0.970543i	$0.577452\pi$
$602$	0	0
$603$	−3.99098	−0.162525
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−32.3192	−1.31180	−0.655898	−	0.754849i	$-0.727710\pi$
$607$	−32.3192	−1.31180	−0.655898	+	0.754849i	$0.727710\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	9.34198	0.377936
$612$	0	0
$613$	−17.8424	−0.720649	−0.360324	−	0.932827i	$-0.617334\pi$
$613$	−17.8424	−0.720649	−0.360324	+	0.932827i	$0.617334\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−40.8670	−1.64524	−0.822622	−	0.568589i	$-0.807489\pi$
$617$	−40.8670	−1.64524	−0.822622	+	0.568589i	$0.807489\pi$
$618$	0	0
$619$	−8.86956	−0.356498	−0.178249	−	0.983985i	$-0.557043\pi$
$619$	−8.86956	−0.356498	−0.178249	+	0.983985i	$0.557043\pi$
$620$	0	0
$621$	48.8406	1.95991
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	47.8012	1.90900
$628$	0	0
$629$	−6.42369	−0.256129
$630$	0	0
$631$	−42.3216	−1.68480	−0.842398	−	0.538856i	$-0.818857\pi$
$631$	−42.3216	−1.68480	−0.842398	+	0.538856i	$0.818857\pi$
$632$	0	0
$633$	−3.90519	−0.155217
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	13.2548	0.524350
$640$	0	0
$641$	30.3608	1.19918	0.599590	−	0.800307i	$-0.295330\pi$
$641$	30.3608	1.19918	0.599590	+	0.800307i	$0.295330\pi$
$642$	0	0
$643$	−40.4617	−1.59565	−0.797827	−	0.602886i	$-0.794017\pi$
$643$	−40.4617	−1.59565	−0.797827	+	0.602886i	$0.794017\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−0.319975	−0.0125795	−0.00628976	−	0.999980i	$-0.502002\pi$
$647$	−0.319975	−0.0125795	−0.00628976	+	0.999980i	$0.502002\pi$
$648$	0	0
$649$	11.5536	0.453519
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−2.50144	−0.0978889	−0.0489445	−	0.998802i	$-0.515586\pi$
$653$	−2.50144	−0.0978889	−0.0489445	+	0.998802i	$0.515586\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−18.7391	−0.731084
$658$	0	0
$659$	12.0291	0.468586	0.234293	−	0.972166i	$-0.424722\pi$
$659$	12.0291	0.468586	0.234293	+	0.972166i	$0.424722\pi$
$660$	0	0
$661$	−26.5251	−1.03171	−0.515853	−	0.856677i	$-0.672525\pi$
$661$	−26.5251	−1.03171	−0.515853	+	0.856677i	$0.672525\pi$
$662$	0	0
$663$	6.29182	0.244354
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−33.9808	−1.31574
$668$	0	0
$669$	5.01511	0.193895
$670$	0	0
$671$	−19.5549	−0.754907
$672$	0	0
$673$	1.97566	0.0761561	0.0380781	−	0.999275i	$-0.487876\pi$
$673$	1.97566	0.0761561	0.0380781	+	0.999275i	$0.487876\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	9.60326	0.369083	0.184542	−	0.982825i	$-0.440920\pi$
$677$	9.60326	0.369083	0.184542	+	0.982825i	$0.440920\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	22.6411	0.867608
$682$	0	0
$683$	25.0600	0.958894	0.479447	−	0.877571i	$-0.340837\pi$
$683$	25.0600	0.958894	0.479447	+	0.877571i	$0.340837\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	33.3285	1.27156
$688$	0	0
$689$	0.848513	0.0323258
$690$	0	0
$691$	−15.6042	−0.593611	−0.296806	−	0.954938i	$-0.595921\pi$
$691$	−15.6042	−0.593611	−0.296806	+	0.954938i	$0.595921\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−53.2984	−2.01882
$698$	0	0
$699$	−7.88161	−0.298110
$700$	0	0
$701$	−10.1004	−0.381487	−0.190743	−	0.981640i	$-0.561090\pi$
$701$	−10.1004	−0.381487	−0.190743	+	0.981640i	$0.561090\pi$
$702$	0	0
$703$	8.37740	0.315960
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−45.5659	−1.71126	−0.855632	−	0.517584i	$-0.826832\pi$
$709$	−45.5659	−1.71126	−0.855632	+	0.517584i	$0.826832\pi$
$710$	0	0
$711$	13.0168	0.488168
$712$	0	0
$713$	−58.4757	−2.18993
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−10.0497	−0.375312
$718$	0	0
$719$	8.41277	0.313743	0.156872	−	0.987619i	$-0.449859\pi$
$719$	8.41277	0.313743	0.156872	+	0.987619i	$0.449859\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	−6.05950	−0.225355
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−3.22522	−0.119617	−0.0598084	−	0.998210i	$-0.519049\pi$
$727$	−3.22522	−0.119617	−0.0598084	+	0.998210i	$0.519049\pi$
$728$	0	0
$729$	25.1116	0.930059
$730$	0	0
$731$	−29.1189	−1.07700
$732$	0	0
$733$	49.8320	1.84059	0.920293	−	0.391229i	$-0.127950\pi$
$733$	49.8320	1.84059	0.920293	+	0.391229i	$0.127950\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	18.3525	0.676024
$738$	0	0
$739$	−14.1825	−0.521710	−0.260855	−	0.965378i	$-0.584004\pi$
$739$	−14.1825	−0.521710	−0.260855	+	0.965378i	$0.584004\pi$
$740$	0	0
$741$	−8.20543	−0.301434
$742$	0	0
$743$	−22.5740	−0.828159	−0.414079	−	0.910241i	$-0.635896\pi$
$743$	−22.5740	−0.828159	−0.414079	+	0.910241i	$0.635896\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	4.47787	0.163837
$748$	0	0
$749$	0	0
$750$	0	0
$751$	26.3334	0.960921	0.480460	−	0.877016i	$-0.340470\pi$
$751$	26.3334	0.960921	0.480460	+	0.877016i	$0.340470\pi$
$752$	0	0
$753$	−0.306496	−0.0111693
$754$	0	0
$755$	0	0
$756$	0	0
$757$	19.0442	0.692173	0.346086	−	0.938203i	$-0.387510\pi$
$757$	19.0442	0.692173	0.346086	+	0.938203i	$0.387510\pi$
$758$	0	0
$759$	−71.4218	−2.59245
$760$	0	0
$761$	4.85917	0.176145	0.0880723	−	0.996114i	$-0.471929\pi$
$761$	4.85917	0.176145	0.0880723	+	0.996114i	$0.471929\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−1.98326	−0.0716114
$768$	0	0
$769$	10.8462	0.391124	0.195562	−	0.980691i	$-0.437347\pi$
$769$	10.8462	0.391124	0.195562	+	0.980691i	$0.437347\pi$
$770$	0	0
$771$	−20.1758	−0.726614
$772$	0	0
$773$	−18.4664	−0.664192	−0.332096	−	0.943246i	$-0.607756\pi$
$773$	−18.4664	−0.664192	−0.332096	+	0.943246i	$0.607756\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	69.5088	2.49041
$780$	0	0
$781$	−60.9521	−2.18104
$782$	0	0
$783$	−21.5557	−0.770339
$784$	0	0
$785$	0	0
$786$	0	0
$787$	24.5397	0.874746	0.437373	−	0.899280i	$-0.355909\pi$
$787$	24.5397	0.874746	0.437373	+	0.899280i	$0.355909\pi$
$788$	0	0
$789$	12.4291	0.442487
$790$	0	0
$791$	0	0
$792$	0	0
$793$	3.35674	0.119201
$794$	0	0
$795$	0	0
$796$	0	0
$797$	16.3424	0.578876	0.289438	−	0.957197i	$-0.406532\pi$
$797$	16.3424	0.578876	0.289438	+	0.957197i	$0.406532\pi$
$798$	0	0
$799$	38.0974	1.34779
$800$	0	0
$801$	−4.08948	−0.144495
$802$	0	0
$803$	86.1720	3.04094
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−18.3538	−0.646083
$808$	0	0
$809$	41.6799	1.46539	0.732693	−	0.680559i	$-0.238263\pi$
$809$	41.6799	1.46539	0.732693	+	0.680559i	$0.238263\pi$
$810$	0	0
$811$	21.9750	0.771645	0.385823	−	0.922573i	$-0.373918\pi$
$811$	21.9750	0.771645	0.385823	+	0.922573i	$0.373918\pi$
$812$	0	0
$813$	32.4766	1.13900
$814$	0	0
$815$	0	0
$816$	0	0
$817$	37.9752	1.32858
$818$	0	0
$819$	0	0
$820$	0	0
$821$	52.9383	1.84756	0.923780	−	0.382923i	$-0.125082\pi$
$821$	52.9383	1.84756	0.923780	+	0.382923i	$0.125082\pi$
$822$	0	0
$823$	−20.7583	−0.723588	−0.361794	−	0.932258i	$-0.617836\pi$
$823$	−20.7583	−0.723588	−0.361794	+	0.932258i	$0.617836\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	35.0645	1.21931	0.609656	−	0.792666i	$-0.291308\pi$
$827$	35.0645	1.21931	0.609656	+	0.792666i	$0.291308\pi$
$828$	0	0
$829$	45.6035	1.58388	0.791938	−	0.610602i	$-0.209072\pi$
$829$	45.6035	1.58388	0.791938	+	0.610602i	$0.209072\pi$
$830$	0	0
$831$	−8.04395	−0.279041
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−37.0940	−1.28216
$838$	0	0
$839$	−33.7589	−1.16549	−0.582744	−	0.812656i	$-0.698021\pi$
$839$	−33.7589	−1.16549	−0.582744	+	0.812656i	$0.698021\pi$
$840$	0	0
$841$	−14.0026	−0.482849
$842$	0	0
$843$	−14.9768	−0.515828
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	18.5747	0.637481
$850$	0	0
$851$	−12.5170	−0.429079
$852$	0	0
$853$	3.05793	0.104701	0.0523507	−	0.998629i	$-0.483329\pi$
$853$	3.05793	0.104701	0.0523507	+	0.998629i	$0.483329\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−21.1290	−0.721752	−0.360876	−	0.932614i	$-0.617522\pi$
$857$	−21.1290	−0.721752	−0.360876	+	0.932614i	$0.617522\pi$
$858$	0	0
$859$	19.5617	0.667436	0.333718	−	0.942673i	$-0.391697\pi$
$859$	19.5617	0.667436	0.333718	+	0.942673i	$0.391697\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−2.23960	−0.0762369	−0.0381184	−	0.999273i	$-0.512136\pi$
$863$	−2.23960	−0.0762369	−0.0381184	+	0.999273i	$0.512136\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	4.14741	0.140853
$868$	0	0
$869$	−59.8578	−2.03054
$870$	0	0
$871$	−3.15034	−0.106745
$872$	0	0
$873$	−8.34192	−0.282331
$874$	0	0
$875$	0	0
$876$	0	0
$877$	37.5582	1.26825	0.634125	−	0.773231i	$-0.281361\pi$
$877$	37.5582	1.26825	0.634125	+	0.773231i	$0.281361\pi$
$878$	0	0
$879$	−17.3102	−0.583858
$880$	0	0
$881$	13.2210	0.445426	0.222713	−	0.974884i	$-0.428509\pi$
$881$	13.2210	0.445426	0.222713	+	0.974884i	$0.428509\pi$
$882$	0	0
$883$	−30.9332	−1.04098	−0.520492	−	0.853867i	$-0.674251\pi$
$883$	−30.9332	−1.04098	−0.520492	+	0.853867i	$0.674251\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	29.3034	0.983912	0.491956	−	0.870620i	$-0.336282\pi$
$887$	29.3034	0.983912	0.491956	+	0.870620i	$0.336282\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−18.3113	−0.613452
$892$	0	0
$893$	−49.6844	−1.66262
$894$	0	0
$895$	0	0
$896$	0	0
$897$	12.2601	0.409352
$898$	0	0
$899$	25.8082	0.860750
$900$	0	0
$901$	3.46031	0.115280
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	18.4249	0.611788	0.305894	−	0.952066i	$-0.401045\pi$
$907$	18.4249	0.611788	0.305894	+	0.952066i	$0.401045\pi$
$908$	0	0
$909$	−14.7009	−0.487598
$910$	0	0
$911$	20.5402	0.680527	0.340263	−	0.940330i	$-0.389484\pi$
$911$	20.5402	0.680527	0.340263	+	0.940330i	$0.389484\pi$
$912$	0	0
$913$	−20.5915	−0.681478
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−22.4469	−0.740454	−0.370227	−	0.928941i	$-0.620720\pi$
$919$	−22.4469	−0.740454	−0.370227	+	0.928941i	$0.620720\pi$
$920$	0	0
$921$	27.0965	0.892860
$922$	0	0
$923$	10.4629	0.344390
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−12.7441	−0.418571
$928$	0	0
$929$	−31.0782	−1.01964	−0.509822	−	0.860280i	$-0.670289\pi$
$929$	−31.0782	−1.01964	−0.509822	+	0.860280i	$0.670289\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	31.6598	1.03649
$934$	0	0
$935$	0	0
$936$	0	0
$937$	29.7564	0.972098	0.486049	−	0.873931i	$-0.338438\pi$
$937$	29.7564	0.972098	0.486049	+	0.873931i	$0.338438\pi$
$938$	0	0
$939$	9.11556	0.297475
$940$	0	0
$941$	−48.9577	−1.59598	−0.797988	−	0.602673i	$-0.794102\pi$
$941$	−48.9577	−1.59598	−0.797988	+	0.602673i	$0.794102\pi$
$942$	0	0
$943$	−103.856	−3.38202
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−26.7245	−0.868429	−0.434214	−	0.900810i	$-0.642974\pi$
$947$	−26.7245	−0.868429	−0.434214	+	0.900810i	$0.642974\pi$
$948$	0	0
$949$	−14.7921	−0.480171
$950$	0	0
$951$	10.7346	0.348094
$952$	0	0
$953$	−26.5373	−0.859627	−0.429814	−	0.902918i	$-0.641421\pi$
$953$	−26.5373	−0.859627	−0.429814	+	0.902918i	$0.641421\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	31.5219	1.01896
$958$	0	0
$959$	0	0
$960$	0	0
$961$	13.4118	0.432640
$962$	0	0
$963$	11.7488	0.378600
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−29.3042	−0.942358	−0.471179	−	0.882038i	$-0.656171\pi$
$967$	−29.3042	−0.942358	−0.471179	+	0.882038i	$0.656171\pi$
$968$	0	0
$969$	−33.4624	−1.07497
$970$	0	0
$971$	−27.7835	−0.891616	−0.445808	−	0.895129i	$-0.647084\pi$
$971$	−27.7835	−0.891616	−0.445808	+	0.895129i	$0.647084\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−29.3268	−0.938248	−0.469124	−	0.883132i	$-0.655430\pi$
$977$	−29.3268	−0.938248	−0.469124	+	0.883132i	$0.655430\pi$
$978$	0	0
$979$	18.8055	0.601026
$980$	0	0
$981$	−6.77114	−0.216186
$982$	0	0
$983$	5.85139	0.186631	0.0933153	−	0.995637i	$-0.470254\pi$
$983$	5.85139	0.186631	0.0933153	+	0.995637i	$0.470254\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−56.7403	−1.80424
$990$	0	0
$991$	12.3870	0.393486	0.196743	−	0.980455i	$-0.436963\pi$
$991$	12.3870	0.393486	0.196743	+	0.980455i	$0.436963\pi$
$992$	0	0
$993$	1.40294	0.0445209
$994$	0	0
$995$	0	0
$996$	0	0
$997$	21.2259	0.672231	0.336116	−	0.941821i	$-0.390887\pi$
$997$	21.2259	0.672231	0.336116	+	0.941821i	$0.390887\pi$
$998$	0	0
$999$	−7.94018	−0.251216

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9800.2.a.cu.1.3		4
5.4	even	2		9800.2.a.ck.1.2		4
7.3	odd	6		1400.2.q.m.401.3	yes	8
7.5	odd	6		1400.2.q.m.1201.3	yes	8
7.6	odd	2		9800.2.a.cj.1.2		4
35.3	even	12		1400.2.bh.j.849.3		16
35.12	even	12		1400.2.bh.j.249.3		16
35.17	even	12		1400.2.bh.j.849.6		16
35.19	odd	6		1400.2.q.l.1201.2	yes	8
35.24	odd	6		1400.2.q.l.401.2	✓	8
35.33	even	12		1400.2.bh.j.249.6		16
35.34	odd	2		9800.2.a.ct.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1400.2.q.l.401.2	✓	8	35.24	odd	6
1400.2.q.l.1201.2	yes	8	35.19	odd	6
1400.2.q.m.401.3	yes	8	7.3	odd	6
1400.2.q.m.1201.3	yes	8	7.5	odd	6
1400.2.bh.j.249.3		16	35.12	even	12
1400.2.bh.j.249.6		16	35.33	even	12
1400.2.bh.j.849.3		16	35.3	even	12
1400.2.bh.j.849.6		16	35.17	even	12
9800.2.a.cj.1.2		4	7.6	odd	2
9800.2.a.ck.1.2		4	5.4	even	2
9800.2.a.ct.1.3		4	35.34	odd	2
9800.2.a.cu.1.3		4	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)

\(f(q)\)	\(=\)	\(q+1.26536 q^{3} -1.39886 q^{9} +O(q^{10})\)	\(q+1.26536 q^{3} -1.39886 q^{9} +6.43265 q^{11} -1.10421 q^{13} -4.50307 q^{17} +5.87265 q^{19} -8.77457 q^{23} -5.56615 q^{27} +3.87265 q^{29} +6.66422 q^{31} +8.13964 q^{33} +1.42651 q^{37} -1.39723 q^{39} +11.8360 q^{41} +6.46645 q^{43} -8.46031 q^{47} -5.69802 q^{51} -0.768433 q^{53} +7.43102 q^{57} +1.79609 q^{59} -3.03994 q^{61} +2.85302 q^{67} -11.1030 q^{69} -9.47542 q^{71} +13.3960 q^{73} -9.30530 q^{79} -2.84662 q^{81} -3.20109 q^{83} +4.90030 q^{87} +2.92344 q^{89} +8.43265 q^{93} +5.96338 q^{97} -8.99837 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{3} + 5 q^{9}+O(q^{10}) \) 4 * q + 3 * q^3 + 5 * q^9	\( 4 q + 3 q^{3} + 5 q^{9} - 4 q^{13} - 7 q^{17} + 10 q^{19} + 12 q^{27} + 2 q^{29} + 14 q^{31} + 2 q^{33} + 2 q^{37} - 10 q^{39} + 4 q^{41} - 15 q^{43} - 15 q^{47} + 5 q^{51} + 10 q^{53} + 19 q^{57} + q^{59} + 25 q^{61} + 4 q^{67} + 16 q^{69} - 20 q^{71} - 2 q^{73} + 2 q^{79} + 24 q^{81} + 26 q^{83} + 13 q^{87} + 19 q^{89} + 8 q^{93} - 6 q^{97} - 51 q^{99}+O(q^{100}) \) 4 * q + 3 * q^3 + 5 * q^9 - 4 * q^13 - 7 * q^17 + 10 * q^19 + 12 * q^27 + 2 * q^29 + 14 * q^31 + 2 * q^33 + 2 * q^37 - 10 * q^39 + 4 * q^41 - 15 * q^43 - 15 * q^47 + 5 * q^51 + 10 * q^53 + 19 * q^57 + q^59 + 25 * q^61 + 4 * q^67 + 16 * q^69 - 20 * q^71 - 2 * q^73 + 2 * q^79 + 24 * q^81 + 26 * q^83 + 13 * q^87 + 19 * q^89 + 8 * q^93 - 6 * q^97 - 51 * q^99

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