LMFDB - Embedded newform 9800.2.a.cz.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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 18x^{6} + 85x^{4} - 38x^{2} + 4 $ x^8 - 18x^6 + 85x^4 - 38*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.568463$ 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)

$f(q)$	$=$	$q-0.568463 q^{3} -2.67685 q^{9} +O(q^{10})$	$q-0.568463 q^{3} -2.67685 q^{9} +5.17164 q^{11} -3.51826 q^{13} -2.67251 q^{17} -8.14964 q^{19} -3.87292 q^{23} +3.22708 q^{27} +1.49479 q^{29} +0.447097 q^{31} -2.93989 q^{33} +10.4563 q^{37} +2.00000 q^{39} +6.46805 q^{41} -8.45634 q^{43} -6.07930 q^{47} +1.51922 q^{51} -7.36771 q^{53} +4.63277 q^{57} +0.544667 q^{59} -11.8238 q^{61} +6.60786 q^{67} +2.20161 q^{69} +3.10265 q^{71} -1.02547 q^{73} +9.08864 q^{79} +6.19607 q^{81} +7.18253 q^{83} -0.849733 q^{87} +5.60841 q^{89} -0.254158 q^{93} -17.2034 q^{97} -13.8437 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{9}+O(q^{10}) $ 8 * q + 12 * q^9	$ 8 q + 12 q^{9} + 4 q^{11} - 4 q^{23} + 8 q^{29} + 16 q^{39} + 16 q^{43} + 52 q^{51} - 28 q^{53} - 8 q^{57} + 40 q^{67} + 8 q^{71} + 20 q^{79} + 56 q^{81} - 56 q^{93} + 36 q^{99}+O(q^{100}) $ 8 * q + 12 * q^9 + 4 * q^11 - 4 * q^23 + 8 * q^29 + 16 * q^39 + 16 * q^43 + 52 * q^51 - 28 * q^53 - 8 * q^57 + 40 * q^67 + 8 * q^71 + 20 * q^79 + 56 * q^81 - 56 * q^93 + 36 * 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
$3$	−0.568463	−0.328202	−0.164101	−	0.986444i	$-0.552472\pi$
$3$	−0.568463	−0.328202	−0.164101	+	0.986444i	$0.552472\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	−2.67685	−0.892283
$10$	0	0
$11$	5.17164	1.55931	0.779654	−	0.626211i	$-0.215395\pi$
$11$	5.17164	1.55931	0.779654	+	0.626211i	$0.215395\pi$
$12$	0	0
$13$	−3.51826	−0.975789	−0.487894	−	0.872903i	$-0.662235\pi$
$13$	−3.51826	−0.975789	−0.487894	+	0.872903i	$0.662235\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−2.67251	−0.648178	−0.324089	−	0.946027i	$-0.605058\pi$
$17$	−2.67251	−0.648178	−0.324089	+	0.946027i	$0.605058\pi$
$18$	0	0
$19$	−8.14964	−1.86966	−0.934828	−	0.355100i	$-0.884447\pi$
$19$	−8.14964	−1.86966	−0.934828	+	0.355100i	$0.884447\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−3.87292	−0.807560	−0.403780	−	0.914856i	$-0.632304\pi$
$23$	−3.87292	−0.807560	−0.403780	+	0.914856i	$0.632304\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	3.22708	0.621052
$28$	0	0
$29$	1.49479	0.277575	0.138788	−	0.990322i	$-0.455679\pi$
$29$	1.49479	0.277575	0.138788	+	0.990322i	$0.455679\pi$
$30$	0	0
$31$	0.447097	0.0803009	0.0401505	−	0.999194i	$-0.487216\pi$
$31$	0.447097	0.0803009	0.0401505	+	0.999194i	$0.487216\pi$
$32$	0	0
$33$	−2.93989	−0.511769
$34$	0	0
$35$	0	0
$36$	0	0
$37$	10.4563	1.71901	0.859506	−	0.511125i	$-0.170771\pi$
$37$	10.4563	1.71901	0.859506	+	0.511125i	$0.170771\pi$
$38$	0	0
$39$	2.00000	0.320256
$40$	0	0
$41$	6.46805	1.01014	0.505070	−	0.863078i	$-0.331467\pi$
$41$	6.46805	1.01014	0.505070	+	0.863078i	$0.331467\pi$
$42$	0	0
$43$	−8.45634	−1.28958	−0.644790	−	0.764360i	$-0.723055\pi$
$43$	−8.45634	−1.28958	−0.644790	+	0.764360i	$0.723055\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−6.07930	−0.886758	−0.443379	−	0.896334i	$-0.646220\pi$
$47$	−6.07930	−0.886758	−0.443379	+	0.896334i	$0.646220\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	1.51922	0.212734
$52$	0	0
$53$	−7.36771	−1.01203	−0.506016	−	0.862524i	$-0.668882\pi$
$53$	−7.36771	−1.01203	−0.506016	+	0.862524i	$0.668882\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	4.63277	0.613626
$58$	0	0
$59$	0.544667	0.0709096	0.0354548	−	0.999371i	$-0.488712\pi$
$59$	0.544667	0.0709096	0.0354548	+	0.999371i	$0.488712\pi$
$60$	0	0
$61$	−11.8238	−1.51389	−0.756943	−	0.653481i	$-0.773308\pi$
$61$	−11.8238	−1.51389	−0.756943	+	0.653481i	$0.773308\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	6.60786	0.807278	0.403639	−	0.914918i	$-0.367745\pi$
$67$	6.60786	0.807278	0.403639	+	0.914918i	$0.367745\pi$
$68$	0	0
$69$	2.20161	0.265043
$70$	0	0
$71$	3.10265	0.368216	0.184108	−	0.982906i	$-0.441060\pi$
$71$	3.10265	0.368216	0.184108	+	0.982906i	$0.441060\pi$
$72$	0	0
$73$	−1.02547	−0.120022	−0.0600109	−	0.998198i	$-0.519114\pi$
$73$	−1.02547	−0.120022	−0.0600109	+	0.998198i	$0.519114\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	9.08864	1.02255	0.511276	−	0.859417i	$-0.329173\pi$
$79$	9.08864	1.02255	0.511276	+	0.859417i	$0.329173\pi$
$80$	0	0
$81$	6.19607	0.688452
$82$	0	0
$83$	7.18253	0.788385	0.394192	−	0.919028i	$-0.371024\pi$
$83$	7.18253	0.788385	0.394192	+	0.919028i	$0.371024\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−0.849733	−0.0911009
$88$	0	0
$89$	5.60841	0.594490	0.297245	−	0.954801i	$-0.403932\pi$
$89$	5.60841	0.594490	0.297245	+	0.954801i	$0.403932\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	−0.254158	−0.0263550
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−17.2034	−1.74674	−0.873370	−	0.487058i	$-0.838070\pi$
$97$	−17.2034	−1.74674	−0.873370	+	0.487058i	$0.838070\pi$
$98$	0	0
$99$	−13.8437	−1.39134
$100$	0	0
$101$	18.0630	1.79734	0.898669	−	0.438627i	$-0.144535\pi$
$101$	18.0630	1.79734	0.898669	+	0.438627i	$0.144535\pi$
$102$	0	0
$103$	7.75099	0.763728	0.381864	−	0.924219i	$-0.375282\pi$
$103$	7.75099	0.763728	0.381864	+	0.924219i	$0.375282\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−4.82405	−0.466359	−0.233179	−	0.972434i	$-0.574913\pi$
$107$	−4.82405	−0.466359	−0.233179	+	0.972434i	$0.574913\pi$
$108$	0	0
$109$	−0.265064	−0.0253885	−0.0126943	−	0.999919i	$-0.504041\pi$
$109$	−0.265064	−0.0253885	−0.0126943	+	0.999919i	$0.504041\pi$
$110$	0	0
$111$	−5.94405	−0.564184
$112$	0	0
$113$	6.14720	0.578280	0.289140	−	0.957287i	$-0.406631\pi$
$113$	6.14720	0.578280	0.289140	+	0.957287i	$0.406631\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	9.41784	0.870680
$118$	0	0
$119$	0	0
$120$	0	0
$121$	15.7458	1.43144
$122$	0	0
$123$	−3.67685	−0.331530
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−0.710503	−0.0630469	−0.0315235	−	0.999503i	$-0.510036\pi$
$127$	−0.710503	−0.0630469	−0.0315235	+	0.999503i	$0.510036\pi$
$128$	0	0
$129$	4.80712	0.423243
$130$	0	0
$131$	6.57951	0.574854	0.287427	−	0.957802i	$-0.407200\pi$
$131$	6.57951	0.574854	0.287427	+	0.957802i	$0.407200\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	8.26027	0.705723	0.352861	−	0.935676i	$-0.385209\pi$
$137$	8.26027	0.705723	0.352861	+	0.935676i	$0.385209\pi$
$138$	0	0
$139$	6.22532	0.528025	0.264012	−	0.964519i	$-0.414954\pi$
$139$	6.22532	0.528025	0.264012	+	0.964519i	$0.414954\pi$
$140$	0	0
$141$	3.45586	0.291036
$142$	0	0
$143$	−18.1952	−1.52156
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	9.63277	0.789148	0.394574	−	0.918864i	$-0.370892\pi$
$149$	9.63277	0.789148	0.394574	+	0.918864i	$0.370892\pi$
$150$	0	0
$151$	−16.4075	−1.33522	−0.667611	−	0.744510i	$-0.732683\pi$
$151$	−16.4075	−1.33522	−0.667611	+	0.744510i	$0.732683\pi$
$152$	0	0
$153$	7.15390	0.578358
$154$	0	0
$155$	0	0
$156$	0	0
$157$	19.1722	1.53011	0.765053	−	0.643967i	$-0.222713\pi$
$157$	19.1722	1.53011	0.765053	+	0.643967i	$0.222713\pi$
$158$	0	0
$159$	4.18827	0.332152
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−4.46114	−0.349423	−0.174712	−	0.984620i	$-0.555899\pi$
$163$	−4.46114	−0.349423	−0.174712	+	0.984620i	$0.555899\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−1.27218	−0.0984444	−0.0492222	−	0.998788i	$-0.515674\pi$
$167$	−1.27218	−0.0984444	−0.0492222	+	0.998788i	$0.515674\pi$
$168$	0	0
$169$	−0.621868	−0.0478360
$170$	0	0
$171$	21.8154	1.66826
$172$	0	0
$173$	17.0336	1.29504	0.647520	−	0.762049i	$-0.275806\pi$
$173$	17.0336	1.29504	0.647520	+	0.762049i	$0.275806\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−0.309623	−0.0232727
$178$	0	0
$179$	13.4563	1.00577	0.502887	−	0.864352i	$-0.332271\pi$
$179$	13.4563	1.00577	0.502887	+	0.864352i	$0.332271\pi$
$180$	0	0
$181$	−20.7946	−1.54565	−0.772824	−	0.634620i	$-0.781156\pi$
$181$	−20.7946	−1.54565	−0.772824	+	0.634620i	$0.781156\pi$
$182$	0	0
$183$	6.72141	0.496861
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−13.8212	−1.01071
$188$	0	0
$189$	0	0
$190$	0	0
$191$	16.5834	1.19993	0.599967	−	0.800025i	$-0.295180\pi$
$191$	16.5834	1.19993	0.599967	+	0.800025i	$0.295180\pi$
$192$	0	0
$193$	19.8442	1.42842	0.714208	−	0.699934i	$-0.246787\pi$
$193$	19.8442	1.42842	0.714208	+	0.699934i	$0.246787\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−26.7856	−1.90840	−0.954198	−	0.299176i	$-0.903288\pi$
$197$	−26.7856	−1.90840	−0.954198	+	0.299176i	$0.903288\pi$
$198$	0	0
$199$	8.46063	0.599758	0.299879	−	0.953977i	$-0.403054\pi$
$199$	8.46063	0.599758	0.299879	+	0.953977i	$0.403054\pi$
$200$	0	0
$201$	−3.75632	−0.264951
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	10.3672	0.720572
$208$	0	0
$209$	−42.1470	−2.91537
$210$	0	0
$211$	−0.116657	−0.00803097	−0.00401548	−	0.999992i	$-0.501278\pi$
$211$	−0.116657	−0.00803097	−0.00401548	+	0.999992i	$0.501278\pi$
$212$	0	0
$213$	−1.76374	−0.120849
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0.582940	0.0393915
$220$	0	0
$221$	9.40257	0.632485
$222$	0	0
$223$	15.0117	1.00526	0.502628	−	0.864503i	$-0.332366\pi$
$223$	15.0117	1.00526	0.502628	+	0.864503i	$0.332366\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	18.2681	1.21249	0.606247	−	0.795276i	$-0.292674\pi$
$227$	18.2681	1.21249	0.606247	+	0.795276i	$0.292674\pi$
$228$	0	0
$229$	−8.90773	−0.588639	−0.294320	−	0.955707i	$-0.595093\pi$
$229$	−8.90773	−0.588639	−0.294320	+	0.955707i	$0.595093\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−17.4808	−1.14520	−0.572602	−	0.819834i	$-0.694066\pi$
$233$	−17.4808	−1.14520	−0.572602	+	0.819834i	$0.694066\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−5.16656	−0.335604
$238$	0	0
$239$	26.4184	1.70886	0.854432	−	0.519564i	$-0.173906\pi$
$239$	26.4184	1.70886	0.854432	+	0.519564i	$0.173906\pi$
$240$	0	0
$241$	8.91849	0.574490	0.287245	−	0.957857i	$-0.407261\pi$
$241$	8.91849	0.574490	0.287245	+	0.957857i	$0.407261\pi$
$242$	0	0
$243$	−13.2035	−0.847004
$244$	0	0
$245$	0	0
$246$	0	0
$247$	28.6725	1.82439
$248$	0	0
$249$	−4.08300	−0.258750
$250$	0	0
$251$	−28.3235	−1.78776	−0.893881	−	0.448303i	$-0.852028\pi$
$251$	−28.3235	−1.78776	−0.893881	+	0.448303i	$0.852028\pi$
$252$	0	0
$253$	−20.0293	−1.25923
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−13.4808	−0.840907	−0.420454	−	0.907314i	$-0.638129\pi$
$257$	−13.4808	−0.840907	−0.420454	+	0.907314i	$0.638129\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−4.00132	−0.247676
$262$	0	0
$263$	−6.50521	−0.401129	−0.200564	−	0.979681i	$-0.564278\pi$
$263$	−6.50521	−0.401129	−0.200564	+	0.979681i	$0.564278\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−3.18818	−0.195113
$268$	0	0
$269$	0.758938	0.0462732	0.0231366	−	0.999732i	$-0.492635\pi$
$269$	0.758938	0.0462732	0.0231366	+	0.999732i	$0.492635\pi$
$270$	0	0
$271$	−24.3375	−1.47840	−0.739198	−	0.673488i	$-0.764795\pi$
$271$	−24.3375	−1.47840	−0.739198	+	0.673488i	$0.764795\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−25.3048	−1.52042	−0.760210	−	0.649677i	$-0.774904\pi$
$277$	−25.3048	−1.52042	−0.760210	+	0.649677i	$0.774904\pi$
$278$	0	0
$279$	−1.19681	−0.0716512
$280$	0	0
$281$	13.6328	0.813263	0.406632	−	0.913592i	$-0.366703\pi$
$281$	13.6328	0.813263	0.406632	+	0.913592i	$0.366703\pi$
$282$	0	0
$283$	−25.5081	−1.51630	−0.758150	−	0.652081i	$-0.773896\pi$
$283$	−25.5081	−1.51630	−0.758150	+	0.652081i	$0.773896\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−9.85771	−0.579865
$290$	0	0
$291$	9.77950	0.573284
$292$	0	0
$293$	−20.4197	−1.19293	−0.596466	−	0.802638i	$-0.703429\pi$
$293$	−20.4197	−1.19293	−0.596466	+	0.802638i	$0.703429\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	16.6893	0.968411
$298$	0	0
$299$	13.6259	0.788008
$300$	0	0
$301$	0	0
$302$	0	0
$303$	−10.2682	−0.589891
$304$	0	0
$305$	0	0
$306$	0	0
$307$	4.89877	0.279587	0.139794	−	0.990181i	$-0.455356\pi$
$307$	4.89877	0.279587	0.139794	+	0.990181i	$0.455356\pi$
$308$	0	0
$309$	−4.40615	−0.250657
$310$	0	0
$311$	28.5072	1.61649	0.808247	−	0.588843i	$-0.200416\pi$
$311$	28.5072	1.61649	0.808247	+	0.588843i	$0.200416\pi$
$312$	0	0
$313$	0.0147396	0.000833133 0	0.000416567	−	1.00000i	$-0.499867\pi$
$313$	0.0147396	0.000833133 0	0.000416567		1.00000i	$0.499867\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	5.13750	0.288551	0.144275	−	0.989538i	$-0.453915\pi$
$317$	5.13750	0.288551	0.144275	+	0.989538i	$0.453915\pi$
$318$	0	0
$319$	7.73051	0.432825
$320$	0	0
$321$	2.74230	0.153060
$322$	0	0
$323$	21.7800	1.21187
$324$	0	0
$325$	0	0
$326$	0	0
$327$	0.150679	0.00833257
$328$	0	0
$329$	0	0
$330$	0	0
$331$	28.7515	1.58032	0.790162	−	0.612898i	$-0.209996\pi$
$331$	28.7515	1.58032	0.790162	+	0.612898i	$0.209996\pi$
$332$	0	0
$333$	−27.9901	−1.53385
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−3.36723	−0.183425	−0.0917123	−	0.995786i	$-0.529234\pi$
$337$	−3.36723	−0.183425	−0.0917123	+	0.995786i	$0.529234\pi$
$338$	0	0
$339$	−3.49446	−0.189793
$340$	0	0
$341$	2.31222	0.125214
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	29.1716	1.56602	0.783008	−	0.622012i	$-0.213684\pi$
$347$	29.1716	1.56602	0.783008	+	0.622012i	$0.213684\pi$
$348$	0	0
$349$	8.81084	0.471634	0.235817	−	0.971798i	$-0.424223\pi$
$349$	8.81084	0.471634	0.235817	+	0.971798i	$0.424223\pi$
$350$	0	0
$351$	−11.3537	−0.606016
$352$	0	0
$353$	−34.3000	−1.82560	−0.912802	−	0.408402i	$-0.866086\pi$
$353$	−34.3000	−1.82560	−0.912802	+	0.408402i	$0.866086\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	22.8485	1.20590	0.602949	−	0.797780i	$-0.293992\pi$
$359$	22.8485	1.20590	0.602949	+	0.797780i	$0.293992\pi$
$360$	0	0
$361$	47.4167	2.49562
$362$	0	0
$363$	−8.95093	−0.469802
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−33.7307	−1.76073	−0.880363	−	0.474300i	$-0.842701\pi$
$367$	−33.7307	−1.76073	−0.880363	+	0.474300i	$0.842701\pi$
$368$	0	0
$369$	−17.3140	−0.901331
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−12.2511	−0.634335	−0.317168	−	0.948369i	$-0.602732\pi$
$373$	−12.2511	−0.634335	−0.317168	+	0.948369i	$0.602732\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−5.25905	−0.270855
$378$	0	0
$379$	16.7935	0.862624	0.431312	−	0.902203i	$-0.358051\pi$
$379$	16.7935	0.862624	0.431312	+	0.902203i	$0.358051\pi$
$380$	0	0
$381$	0.403895	0.0206922
$382$	0	0
$383$	31.7334	1.62150	0.810751	−	0.585391i	$-0.199059\pi$
$383$	31.7334	1.62150	0.810751	+	0.585391i	$0.199059\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	22.6364	1.15067
$388$	0	0
$389$	9.19176	0.466041	0.233020	−	0.972472i	$-0.425139\pi$
$389$	9.19176	0.466041	0.233020	+	0.972472i	$0.425139\pi$
$390$	0	0
$391$	10.3504	0.523443
$392$	0	0
$393$	−3.74021	−0.188669
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−9.94777	−0.499264	−0.249632	−	0.968341i	$-0.580310\pi$
$397$	−9.94777	−0.499264	−0.249632	+	0.968341i	$0.580310\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	33.5346	1.67464	0.837318	−	0.546716i	$-0.184122\pi$
$401$	33.5346	1.67464	0.837318	+	0.546716i	$0.184122\pi$
$402$	0	0
$403$	−1.57300	−0.0783568
$404$	0	0
$405$	0	0
$406$	0	0
$407$	54.0764	2.68047
$408$	0	0
$409$	19.0063	0.939803	0.469902	−	0.882719i	$-0.344289\pi$
$409$	19.0063	0.939803	0.469902	+	0.882719i	$0.344289\pi$
$410$	0	0
$411$	−4.69566	−0.231620
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−3.53886	−0.173299
$418$	0	0
$419$	15.6480	0.764455	0.382227	−	0.924068i	$-0.375157\pi$
$419$	15.6480	0.764455	0.382227	+	0.924068i	$0.375157\pi$
$420$	0	0
$421$	17.1026	0.833532	0.416766	−	0.909014i	$-0.363163\pi$
$421$	17.1026	0.833532	0.416766	+	0.909014i	$0.363163\pi$
$422$	0	0
$423$	16.2734	0.791239
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	10.3433	0.499378
$430$	0	0
$431$	15.4568	0.744529	0.372265	−	0.928127i	$-0.378581\pi$
$431$	15.4568	0.744529	0.372265	+	0.928127i	$0.378581\pi$
$432$	0	0
$433$	22.2374	1.06866	0.534331	−	0.845275i	$-0.320564\pi$
$433$	22.2374	1.06866	0.534331	+	0.845275i	$0.320564\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	31.5629	1.50986
$438$	0	0
$439$	−26.3884	−1.25945	−0.629725	−	0.776818i	$-0.716832\pi$
$439$	−26.3884	−1.25945	−0.629725	+	0.776818i	$0.716832\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	25.4075	1.20715	0.603573	−	0.797308i	$-0.293743\pi$
$443$	25.4075	1.20715	0.603573	+	0.797308i	$0.293743\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−5.47588	−0.259000
$448$	0	0
$449$	−19.0751	−0.900210	−0.450105	−	0.892976i	$-0.648613\pi$
$449$	−19.0751	−0.900210	−0.450105	+	0.892976i	$0.648613\pi$
$450$	0	0
$451$	33.4504	1.57512
$452$	0	0
$453$	9.32705	0.438223
$454$	0	0
$455$	0	0
$456$	0	0
$457$	7.41179	0.346709	0.173354	−	0.984860i	$-0.444539\pi$
$457$	7.41179	0.346709	0.173354	+	0.984860i	$0.444539\pi$
$458$	0	0
$459$	−8.62439	−0.402552
$460$	0	0
$461$	23.2283	1.08185	0.540925	−	0.841071i	$-0.318074\pi$
$461$	23.2283	1.08185	0.540925	+	0.841071i	$0.318074\pi$
$462$	0	0
$463$	−17.6970	−0.822448	−0.411224	−	0.911534i	$-0.634899\pi$
$463$	−17.6970	−0.822448	−0.411224	+	0.911534i	$0.634899\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−28.4726	−1.31756	−0.658778	−	0.752337i	$-0.728926\pi$
$467$	−28.4726	−1.31756	−0.658778	+	0.752337i	$0.728926\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−10.8987	−0.502185
$472$	0	0
$473$	−43.7332	−2.01085
$474$	0	0
$475$	0	0
$476$	0	0
$477$	19.7222	0.903020
$478$	0	0
$479$	−1.72987	−0.0790398	−0.0395199	−	0.999219i	$-0.512583\pi$
$479$	−1.72987	−0.0790398	−0.0395199	+	0.999219i	$0.512583\pi$
$480$	0	0
$481$	−36.7881	−1.67739
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	33.7079	1.52745	0.763725	−	0.645542i	$-0.223368\pi$
$487$	33.7079	1.52745	0.763725	+	0.645542i	$0.223368\pi$
$488$	0	0
$489$	2.53599	0.114682
$490$	0	0
$491$	−2.11307	−0.0953614	−0.0476807	−	0.998863i	$-0.515183\pi$
$491$	−2.11307	−0.0953614	−0.0476807	+	0.998863i	$0.515183\pi$
$492$	0	0
$493$	−3.99483	−0.179918
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	17.7250	0.793480	0.396740	−	0.917931i	$-0.370141\pi$
$499$	17.7250	0.793480	0.396740	+	0.917931i	$0.370141\pi$
$500$	0	0
$501$	0.723189	0.0323097
$502$	0	0
$503$	19.0925	0.851292	0.425646	−	0.904890i	$-0.360047\pi$
$503$	19.0925	0.851292	0.425646	+	0.904890i	$0.360047\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0.353509	0.0156999
$508$	0	0
$509$	4.98684	0.221038	0.110519	−	0.993874i	$-0.464749\pi$
$509$	4.98684	0.221038	0.110519	+	0.993874i	$0.464749\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−26.2996	−1.16115
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−31.4400	−1.38273
$518$	0	0
$519$	−9.68296	−0.425035
$520$	0	0
$521$	−4.91181	−0.215190	−0.107595	−	0.994195i	$-0.534315\pi$
$521$	−4.91181	−0.215190	−0.107595	+	0.994195i	$0.534315\pi$
$522$	0	0
$523$	−1.82761	−0.0799157	−0.0399578	−	0.999201i	$-0.512722\pi$
$523$	−1.82761	−0.0799157	−0.0399578	+	0.999201i	$0.512722\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−1.19487	−0.0520493
$528$	0	0
$529$	−8.00048	−0.347847
$530$	0	0
$531$	−1.45799	−0.0632714
$532$	0	0
$533$	−22.7563	−0.985683
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−7.64944	−0.330098
$538$	0	0
$539$	0	0
$540$	0	0
$541$	36.7996	1.58214	0.791070	−	0.611726i	$-0.209525\pi$
$541$	36.7996	1.58214	0.791070	+	0.611726i	$0.209525\pi$
$542$	0	0
$543$	11.8209	0.507285
$544$	0	0
$545$	0	0
$546$	0	0
$547$	15.6171	0.667738	0.333869	−	0.942619i	$-0.391646\pi$
$547$	15.6171	0.667738	0.333869	+	0.942619i	$0.391646\pi$
$548$	0	0
$549$	31.6506	1.35081
$550$	0	0
$551$	−12.1820	−0.518970
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−12.3184	−0.521946	−0.260973	−	0.965346i	$-0.584043\pi$
$557$	−12.3184	−0.521946	−0.260973	+	0.965346i	$0.584043\pi$
$558$	0	0
$559$	29.7516	1.25836
$560$	0	0
$561$	7.85687	0.331717
$562$	0	0
$563$	41.6317	1.75457	0.877283	−	0.479974i	$-0.159354\pi$
$563$	41.6317	1.75457	0.877283	+	0.479974i	$0.159354\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	19.6866	0.825303	0.412652	−	0.910889i	$-0.364603\pi$
$569$	19.6866	0.825303	0.412652	+	0.910889i	$0.364603\pi$
$570$	0	0
$571$	24.2022	1.01283	0.506415	−	0.862290i	$-0.330970\pi$
$571$	24.2022	1.01283	0.506415	+	0.862290i	$0.330970\pi$
$572$	0	0
$573$	−9.42707	−0.393821
$574$	0	0
$575$	0	0
$576$	0	0
$577$	26.0144	1.08299	0.541497	−	0.840703i	$-0.317858\pi$
$577$	26.0144	1.08299	0.541497	+	0.840703i	$0.317858\pi$
$578$	0	0
$579$	−11.2807	−0.468809
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−38.1031	−1.57807
$584$	0	0
$585$	0	0
$586$	0	0
$587$	35.4124	1.46163	0.730814	−	0.682577i	$-0.239141\pi$
$587$	35.4124	1.46163	0.730814	+	0.682577i	$0.239141\pi$
$588$	0	0
$589$	−3.64368	−0.150135
$590$	0	0
$591$	15.2266	0.626340
$592$	0	0
$593$	−2.31307	−0.0949865	−0.0474933	−	0.998872i	$-0.515123\pi$
$593$	−2.31307	−0.0949865	−0.0474933	+	0.998872i	$0.515123\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−4.80956	−0.196842
$598$	0	0
$599$	15.6861	0.640915	0.320458	−	0.947263i	$-0.396163\pi$
$599$	15.6861	0.640915	0.320458	+	0.947263i	$0.396163\pi$
$600$	0	0
$601$	9.58367	0.390926	0.195463	−	0.980711i	$-0.437379\pi$
$601$	9.58367	0.390926	0.195463	+	0.980711i	$0.437379\pi$
$602$	0	0
$603$	−17.6882	−0.720321
$604$	0	0
$605$	0	0
$606$	0	0
$607$	23.4711	0.952661	0.476330	−	0.879266i	$-0.341967\pi$
$607$	23.4711	0.952661	0.476330	+	0.879266i	$0.341967\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	21.3886	0.865288
$612$	0	0
$613$	−23.5419	−0.950847	−0.475424	−	0.879757i	$-0.657705\pi$
$613$	−23.5419	−0.950847	−0.475424	+	0.879757i	$0.657705\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−35.9132	−1.44581	−0.722905	−	0.690947i	$-0.757194\pi$
$617$	−35.9132	−1.44581	−0.722905	+	0.690947i	$0.757194\pi$
$618$	0	0
$619$	−12.2178	−0.491075	−0.245538	−	0.969387i	$-0.578964\pi$
$619$	−12.2178	−0.491075	−0.245538	+	0.969387i	$0.578964\pi$
$620$	0	0
$621$	−12.4982	−0.501537
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	23.9590	0.956831
$628$	0	0
$629$	−27.9447	−1.11423
$630$	0	0
$631$	−12.6965	−0.505439	−0.252720	−	0.967540i	$-0.581325\pi$
$631$	−12.6965	−0.505439	−0.252720	+	0.967540i	$0.581325\pi$
$632$	0	0
$633$	0.0663150	0.00263578
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−8.30532	−0.328553
$640$	0	0
$641$	2.79423	0.110365	0.0551826	−	0.998476i	$-0.482426\pi$
$641$	2.79423	0.110365	0.0551826	+	0.998476i	$0.482426\pi$
$642$	0	0
$643$	28.6325	1.12916	0.564579	−	0.825379i	$-0.309039\pi$
$643$	28.6325	1.12916	0.564579	+	0.825379i	$0.309039\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	32.1744	1.26491	0.632454	−	0.774598i	$-0.282048\pi$
$647$	32.1744	1.26491	0.632454	+	0.774598i	$0.282048\pi$
$648$	0	0
$649$	2.81682	0.110570
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−30.8245	−1.20626	−0.603129	−	0.797644i	$-0.706079\pi$
$653$	−30.8245	−1.20626	−0.603129	+	0.797644i	$0.706079\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	2.74502	0.107093
$658$	0	0
$659$	−0.839268	−0.0326932	−0.0163466	−	0.999866i	$-0.505204\pi$
$659$	−0.839268	−0.0326932	−0.0163466	+	0.999866i	$0.505204\pi$
$660$	0	0
$661$	19.5779	0.761494	0.380747	−	0.924679i	$-0.375667\pi$
$661$	19.5779	0.761494	0.380747	+	0.924679i	$0.375667\pi$
$662$	0	0
$663$	−5.34501	−0.207583
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−5.78920	−0.224159
$668$	0	0
$669$	−8.53359	−0.329928
$670$	0	0
$671$	−61.1485	−2.36061
$672$	0	0
$673$	32.5346	1.25412	0.627058	−	0.778973i	$-0.284259\pi$
$673$	32.5346	1.25412	0.627058	+	0.778973i	$0.284259\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	22.6491	0.870476	0.435238	−	0.900315i	$-0.356664\pi$
$677$	22.6491	0.870476	0.435238	+	0.900315i	$0.356664\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−10.3847	−0.397944
$682$	0	0
$683$	23.0891	0.883481	0.441740	−	0.897143i	$-0.354361\pi$
$683$	23.0891	0.883481	0.441740	+	0.897143i	$0.354361\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	5.06372	0.193193
$688$	0	0
$689$	25.9215	0.987530
$690$	0	0
$691$	4.53450	0.172501	0.0862503	−	0.996274i	$-0.472512\pi$
$691$	4.53450	0.172501	0.0862503	+	0.996274i	$0.472512\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−17.2859	−0.654750
$698$	0	0
$699$	9.93718	0.375859
$700$	0	0
$701$	3.97198	0.150020	0.0750098	−	0.997183i	$-0.476101\pi$
$701$	3.97198	0.150020	0.0750098	+	0.997183i	$0.476101\pi$
$702$	0	0
$703$	−85.2155	−3.21396
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−50.7661	−1.90656	−0.953280	−	0.302087i	$-0.902317\pi$
$709$	−50.7661	−1.90656	−0.953280	+	0.302087i	$0.902317\pi$
$710$	0	0
$711$	−24.3289	−0.912405
$712$	0	0
$713$	−1.73157	−0.0648478
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−15.0179	−0.560853
$718$	0	0
$719$	−11.3661	−0.423885	−0.211943	−	0.977282i	$-0.567979\pi$
$719$	−11.3661	−0.423885	−0.211943	+	0.977282i	$0.567979\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	−5.06983	−0.188549
$724$	0	0
$725$	0	0
$726$	0	0
$727$	24.5894	0.911971	0.455986	−	0.889987i	$-0.349287\pi$
$727$	24.5894	0.911971	0.455986	+	0.889987i	$0.349287\pi$
$728$	0	0
$729$	−11.0825	−0.410464
$730$	0	0
$731$	22.5996	0.835878
$732$	0	0
$733$	−5.85199	−0.216148	−0.108074	−	0.994143i	$-0.534468\pi$
$733$	−5.85199	−0.216148	−0.108074	+	0.994143i	$0.534468\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	34.1734	1.25880
$738$	0	0
$739$	43.5699	1.60274	0.801372	−	0.598166i	$-0.204104\pi$
$739$	43.5699	1.60274	0.801372	+	0.598166i	$0.204104\pi$
$740$	0	0
$741$	−16.2993	−0.598769
$742$	0	0
$743$	14.5161	0.532545	0.266272	−	0.963898i	$-0.414208\pi$
$743$	14.5161	0.532545	0.266272	+	0.963898i	$0.414208\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−19.2265	−0.703462
$748$	0	0
$749$	0	0
$750$	0	0
$751$	1.02886	0.0375437	0.0187719	−	0.999824i	$-0.494024\pi$
$751$	1.02886	0.0375437	0.0187719	+	0.999824i	$0.494024\pi$
$752$	0	0
$753$	16.1009	0.586748
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−3.69565	−0.134321	−0.0671604	−	0.997742i	$-0.521394\pi$
$757$	−3.69565	−0.134321	−0.0671604	+	0.997742i	$0.521394\pi$
$758$	0	0
$759$	11.3859	0.413284
$760$	0	0
$761$	−17.4192	−0.631445	−0.315723	−	0.948852i	$-0.602247\pi$
$761$	−17.4192	−0.631445	−0.315723	+	0.948852i	$0.602247\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−1.91628	−0.0691928
$768$	0	0
$769$	−8.23731	−0.297045	−0.148522	−	0.988909i	$-0.547452\pi$
$769$	−8.23731	−0.297045	−0.148522	+	0.988909i	$0.547452\pi$
$770$	0	0
$771$	7.66332	0.275988
$772$	0	0
$773$	2.62576	0.0944422	0.0472211	−	0.998884i	$-0.484963\pi$
$773$	2.62576	0.0944422	0.0472211	+	0.998884i	$0.484963\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	−52.7123	−1.88861
$780$	0	0
$781$	16.0458	0.574162
$782$	0	0
$783$	4.82380	0.172389
$784$	0	0
$785$	0	0
$786$	0	0
$787$	47.7752	1.70300	0.851502	−	0.524352i	$-0.175692\pi$
$787$	47.7752	1.70300	0.851502	+	0.524352i	$0.175692\pi$
$788$	0	0
$789$	3.69797	0.131651
$790$	0	0
$791$	0	0
$792$	0	0
$793$	41.5992	1.47723
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−52.8553	−1.87223	−0.936115	−	0.351695i	$-0.885605\pi$
$797$	−52.8553	−1.87223	−0.936115	+	0.351695i	$0.885605\pi$
$798$	0	0
$799$	16.2470	0.574777
$800$	0	0
$801$	−15.0129	−0.530454
$802$	0	0
$803$	−5.30335	−0.187151
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−0.431428	−0.0151870
$808$	0	0
$809$	−27.8381	−0.978734	−0.489367	−	0.872078i	$-0.662772\pi$
$809$	−27.8381	−0.978734	−0.489367	+	0.872078i	$0.662772\pi$
$810$	0	0
$811$	−47.8629	−1.68069	−0.840347	−	0.542049i	$-0.817649\pi$
$811$	−47.8629	−1.68069	−0.840347	+	0.542049i	$0.817649\pi$
$812$	0	0
$813$	13.8350	0.485213
$814$	0	0
$815$	0	0
$816$	0	0
$817$	68.9162	2.41107
$818$	0	0
$819$	0	0
$820$	0	0
$821$	8.50211	0.296726	0.148363	−	0.988933i	$-0.452600\pi$
$821$	8.50211	0.296726	0.148363	+	0.988933i	$0.452600\pi$
$822$	0	0
$823$	−18.7183	−0.652479	−0.326240	−	0.945287i	$-0.605782\pi$
$823$	−18.7183	−0.652479	−0.326240	+	0.945287i	$0.605782\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	1.33788	0.0465227	0.0232613	−	0.999729i	$-0.492595\pi$
$827$	1.33788	0.0465227	0.0232613	+	0.999729i	$0.492595\pi$
$828$	0	0
$829$	11.0296	0.383075	0.191538	−	0.981485i	$-0.438653\pi$
$829$	11.0296	0.383075	0.191538	+	0.981485i	$0.438653\pi$
$830$	0	0
$831$	14.3849	0.499006
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	1.44282	0.0498711
$838$	0	0
$839$	−38.0158	−1.31245	−0.656226	−	0.754564i	$-0.727848\pi$
$839$	−38.0158	−1.31245	−0.656226	+	0.754564i	$0.727848\pi$
$840$	0	0
$841$	−26.7656	−0.922952
$842$	0	0
$843$	−7.74973	−0.266915
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	14.5004	0.497653
$850$	0	0
$851$	−40.4966	−1.38821
$852$	0	0
$853$	−8.34877	−0.285856	−0.142928	−	0.989733i	$-0.545652\pi$
$853$	−8.34877	−0.285856	−0.142928	+	0.989733i	$0.545652\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	10.1431	0.346481	0.173240	−	0.984880i	$-0.444576\pi$
$857$	10.1431	0.346481	0.173240	+	0.984880i	$0.444576\pi$
$858$	0	0
$859$	−19.1015	−0.651736	−0.325868	−	0.945415i	$-0.605656\pi$
$859$	−19.1015	−0.651736	−0.325868	+	0.945415i	$0.605656\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	3.39706	0.115637	0.0578186	−	0.998327i	$-0.481586\pi$
$863$	3.39706	0.115637	0.0578186	+	0.998327i	$0.481586\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	5.60375	0.190313
$868$	0	0
$869$	47.0031	1.59447
$870$	0	0
$871$	−23.2481	−0.787733
$872$	0	0
$873$	46.0509	1.55859
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−20.5065	−0.692457	−0.346228	−	0.938150i	$-0.612538\pi$
$877$	−20.5065	−0.692457	−0.346228	+	0.938150i	$0.612538\pi$
$878$	0	0
$879$	11.6079	0.391523
$880$	0	0
$881$	−8.11424	−0.273376	−0.136688	−	0.990614i	$-0.543646\pi$
$881$	−8.11424	−0.273376	−0.136688	+	0.990614i	$0.543646\pi$
$882$	0	0
$883$	21.8454	0.735156	0.367578	−	0.929993i	$-0.380187\pi$
$883$	21.8454	0.735156	0.367578	+	0.929993i	$0.380187\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−49.5445	−1.66354	−0.831771	−	0.555119i	$-0.812673\pi$
$887$	−49.5445	−1.66354	−0.831771	+	0.555119i	$0.812673\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	32.0438	1.07351
$892$	0	0
$893$	49.5442	1.65793
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−7.74584	−0.258626
$898$	0	0
$899$	0.668315	0.0222896
$900$	0	0
$901$	19.6903	0.655977
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−5.19487	−0.172493	−0.0862464	−	0.996274i	$-0.527487\pi$
$907$	−5.19487	−0.172493	−0.0862464	+	0.996274i	$0.527487\pi$
$908$	0	0
$909$	−48.3520	−1.60373
$910$	0	0
$911$	−17.0398	−0.564553	−0.282276	−	0.959333i	$-0.591090\pi$
$911$	−17.0398	−0.564553	−0.282276	+	0.959333i	$0.591090\pi$
$912$	0	0
$913$	37.1454	1.22933
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	47.0267	1.55127	0.775634	−	0.631183i	$-0.217430\pi$
$919$	47.0267	1.55127	0.775634	+	0.631183i	$0.217430\pi$
$920$	0	0
$921$	−2.78477	−0.0917613
$922$	0	0
$923$	−10.9159	−0.359301
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−20.7482	−0.681461
$928$	0	0
$929$	46.6480	1.53047	0.765235	−	0.643751i	$-0.222623\pi$
$929$	46.6480	1.53047	0.765235	+	0.643751i	$0.222623\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−16.2053	−0.530537
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−50.8072	−1.65980	−0.829899	−	0.557914i	$-0.811602\pi$
$937$	−50.8072	−1.65980	−0.829899	+	0.557914i	$0.811602\pi$
$938$	0	0
$939$	−0.00837894	−0.000273436 0
$940$	0	0
$941$	30.0221	0.978693	0.489346	−	0.872090i	$-0.337235\pi$
$941$	30.0221	0.978693	0.489346	+	0.872090i	$0.337235\pi$
$942$	0	0
$943$	−25.0502	−0.815748
$944$	0	0
$945$	0	0
$946$	0	0
$947$	37.7154	1.22559	0.612793	−	0.790243i	$-0.290046\pi$
$947$	37.7154	1.22559	0.612793	+	0.790243i	$0.290046\pi$
$948$	0	0
$949$	3.60786	0.117116
$950$	0	0
$951$	−2.92048	−0.0947031
$952$	0	0
$953$	−32.3188	−1.04691	−0.523455	−	0.852053i	$-0.675357\pi$
$953$	−32.3188	−1.04691	−0.523455	+	0.852053i	$0.675357\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−4.39451	−0.142054
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−30.8001	−0.993552
$962$	0	0
$963$	12.9133	0.416124
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−20.0403	−0.644451	−0.322226	−	0.946663i	$-0.604431\pi$
$967$	−20.0403	−0.644451	−0.322226	+	0.946663i	$0.604431\pi$
$968$	0	0
$969$	−12.3811	−0.397739
$970$	0	0
$971$	−16.5658	−0.531622	−0.265811	−	0.964025i	$-0.585640\pi$
$971$	−16.5658	−0.531622	−0.265811	+	0.964025i	$0.585640\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−42.5796	−1.36224	−0.681121	−	0.732171i	$-0.738507\pi$
$977$	−42.5796	−1.36224	−0.681121	+	0.732171i	$0.738507\pi$
$978$	0	0
$979$	29.0047	0.926993
$980$	0	0
$981$	0.709536	0.0226537
$982$	0	0
$983$	−39.0421	−1.24525	−0.622626	−	0.782520i	$-0.713934\pi$
$983$	−39.0421	−1.24525	−0.622626	+	0.782520i	$0.713934\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	32.7508	1.04141
$990$	0	0
$991$	−17.5549	−0.557650	−0.278825	−	0.960342i	$-0.589945\pi$
$991$	−17.5549	−0.557650	−0.278825	+	0.960342i	$0.589945\pi$
$992$	0	0
$993$	−16.3442	−0.518666
$994$	0	0
$995$	0	0
$996$	0	0
$997$	53.1398	1.68296	0.841478	−	0.540292i	$-0.181686\pi$
$997$	53.1398	1.68296	0.841478	+	0.540292i	$0.181686\pi$
$998$	0	0
$999$	33.7435	1.06760

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9800.2.a.cz.1.3	✓	8
5.4	even	2		9800.2.a.da.1.6	yes	8
7.6	odd	2	inner	9800.2.a.cz.1.6	yes	8
35.34	odd	2		9800.2.a.da.1.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9800.2.a.cz.1.3	✓	8	1.1	even	1	trivial
9800.2.a.cz.1.6	yes	8	7.6	odd	2	inner
9800.2.a.da.1.3	yes	8	35.34	odd	2
9800.2.a.da.1.6	yes	8	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.568463 q^{3} -2.67685 q^{9} +O(q^{10})\)	\(q-0.568463 q^{3} -2.67685 q^{9} +5.17164 q^{11} -3.51826 q^{13} -2.67251 q^{17} -8.14964 q^{19} -3.87292 q^{23} +3.22708 q^{27} +1.49479 q^{29} +0.447097 q^{31} -2.93989 q^{33} +10.4563 q^{37} +2.00000 q^{39} +6.46805 q^{41} -8.45634 q^{43} -6.07930 q^{47} +1.51922 q^{51} -7.36771 q^{53} +4.63277 q^{57} +0.544667 q^{59} -11.8238 q^{61} +6.60786 q^{67} +2.20161 q^{69} +3.10265 q^{71} -1.02547 q^{73} +9.08864 q^{79} +6.19607 q^{81} +7.18253 q^{83} -0.849733 q^{87} +5.60841 q^{89} -0.254158 q^{93} -17.2034 q^{97} -13.8437 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{9}+O(q^{10}) \) 8 * q + 12 * q^9	\( 8 q + 12 q^{9} + 4 q^{11} - 4 q^{23} + 8 q^{29} + 16 q^{39} + 16 q^{43} + 52 q^{51} - 28 q^{53} - 8 q^{57} + 40 q^{67} + 8 q^{71} + 20 q^{79} + 56 q^{81} - 56 q^{93} + 36 q^{99}+O(q^{100}) \) 8 * q + 12 * q^9 + 4 * q^11 - 4 * q^23 + 8 * q^29 + 16 * q^39 + 16 * q^43 + 52 * q^51 - 28 * q^53 - 8 * q^57 + 40 * q^67 + 8 * q^71 + 20 * q^79 + 56 * q^81 - 56 * q^93 + 36 * q^99

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