LMFDB - Embedded newform 9800.2.a.da.1.8

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			1.8
Root			$3.04118$ of defining polynomial
Character	$\chi$	$=$	9800.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.04118 q^{3} +6.24878 q^{9} +O(q^{10})$	$q+3.04118 q^{3} +6.24878 q^{9} +4.37084 q^{11} +0.657639 q^{13} +5.11303 q^{17} -5.03935 q^{19} +0.0521017 q^{23} +9.88011 q^{27} +9.61961 q^{29} +2.59629 q^{31} +13.2925 q^{33} +9.47970 q^{37} +2.00000 q^{39} -1.72590 q^{41} -11.4797 q^{43} -10.3503 q^{47} +15.5497 q^{51} +11.6717 q^{53} -15.3256 q^{57} +0.682891 q^{59} +2.24447 q^{61} +3.60176 q^{67} +0.158451 q^{69} +1.01786 q^{71} -10.0386 q^{73} -15.1514 q^{79} +11.3009 q^{81} -9.04986 q^{83} +29.2550 q^{87} -15.3048 q^{89} +7.89580 q^{93} -0.404751 q^{97} +27.3124 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	3.04118	1.75583	0.877913	−	0.478820i	$-0.158935\pi$
$3$	3.04118	1.75583	0.877913	+	0.478820i	$0.158935\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	6.24878	2.08293
$10$	0	0
$11$	4.37084	1.31786	0.658928	−	0.752206i	$-0.271010\pi$
$11$	4.37084	1.31786	0.658928	+	0.752206i	$0.271010\pi$
$12$	0	0
$13$	0.657639	0.182396	0.0911982	−	0.995833i	$-0.470930\pi$
$13$	0.657639	0.182396	0.0911982	+	0.995833i	$0.470930\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	5.11303	1.24009	0.620046	−	0.784565i	$-0.287114\pi$
$17$	5.11303	1.24009	0.620046	+	0.784565i	$0.287114\pi$
$18$	0	0
$19$	−5.03935	−1.15611	−0.578053	−	0.815999i	$-0.696187\pi$
$19$	−5.03935	−1.15611	−0.578053	+	0.815999i	$0.696187\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	0.0521017	0.0108639	0.00543197	−	0.999985i	$-0.498271\pi$
$23$	0.0521017	0.0108639	0.00543197	+	0.999985i	$0.498271\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	9.88011	1.90143
$28$	0	0
$29$	9.61961	1.78632	0.893159	−	0.449742i	$-0.148484\pi$
$29$	9.61961	1.78632	0.893159	+	0.449742i	$0.148484\pi$
$30$	0	0
$31$	2.59629	0.466308	0.233154	−	0.972440i	$-0.425095\pi$
$31$	2.59629	0.466308	0.233154	+	0.972440i	$0.425095\pi$
$32$	0	0
$33$	13.2925	2.31393
$34$	0	0
$35$	0	0
$36$	0	0
$37$	9.47970	1.55845	0.779226	−	0.626743i	$-0.215612\pi$
$37$	9.47970	1.55845	0.779226	+	0.626743i	$0.215612\pi$
$38$	0	0
$39$	2.00000	0.320256
$40$	0	0
$41$	−1.72590	−0.269540	−0.134770	−	0.990877i	$-0.543030\pi$
$41$	−1.72590	−0.269540	−0.134770	+	0.990877i	$0.543030\pi$
$42$	0	0
$43$	−11.4797	−1.75064	−0.875319	−	0.483546i	$-0.839348\pi$
$43$	−11.4797	−1.75064	−0.875319	+	0.483546i	$0.839348\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−10.3503	−1.50974	−0.754870	−	0.655875i	$-0.772300\pi$
$47$	−10.3503	−1.50974	−0.754870	+	0.655875i	$0.772300\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	15.5497	2.17739
$52$	0	0
$53$	11.6717	1.60323	0.801617	−	0.597838i	$-0.203974\pi$
$53$	11.6717	1.60323	0.801617	+	0.597838i	$0.203974\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−15.3256	−2.02992
$58$	0	0
$59$	0.682891	0.0889049	0.0444524	−	0.999012i	$-0.485846\pi$
$59$	0.682891	0.0889049	0.0444524	+	0.999012i	$0.485846\pi$
$60$	0	0
$61$	2.24447	0.287375	0.143688	−	0.989623i	$-0.454104\pi$
$61$	2.24447	0.287375	0.143688	+	0.989623i	$0.454104\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	3.60176	0.440025	0.220012	−	0.975497i	$-0.429390\pi$
$67$	3.60176	0.440025	0.220012	+	0.975497i	$0.429390\pi$
$68$	0	0
$69$	0.158451	0.0190752
$70$	0	0
$71$	1.01786	0.120797	0.0603986	−	0.998174i	$-0.480763\pi$
$71$	1.01786	0.120797	0.0603986	+	0.998174i	$0.480763\pi$
$72$	0	0
$73$	−10.0386	−1.17493	−0.587463	−	0.809251i	$-0.699873\pi$
$73$	−10.0386	−1.17493	−0.587463	+	0.809251i	$0.699873\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−15.1514	−1.70467	−0.852333	−	0.522999i	$-0.824813\pi$
$79$	−15.1514	−1.70467	−0.852333	+	0.522999i	$0.824813\pi$
$80$	0	0
$81$	11.3009	1.25565
$82$	0	0
$83$	−9.04986	−0.993351	−0.496675	−	0.867936i	$-0.665446\pi$
$83$	−9.04986	−0.993351	−0.496675	+	0.867936i	$0.665446\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	29.2550	3.13646
$88$	0	0
$89$	−15.3048	−1.62231	−0.811155	−	0.584832i	$-0.801161\pi$
$89$	−15.3048	−1.62231	−0.811155	+	0.584832i	$0.801161\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	7.89580	0.818756
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−0.404751	−0.0410962	−0.0205481	−	0.999789i	$-0.506541\pi$
$97$	−0.404751	−0.0410962	−0.0205481	+	0.999789i	$0.506541\pi$
$98$	0	0
$99$	27.3124	2.74500
$100$	0	0
$101$	13.1742	1.31088	0.655440	−	0.755247i	$-0.272483\pi$
$101$	13.1742	1.31088	0.655440	+	0.755247i	$0.272483\pi$
$102$	0	0
$103$	−12.0910	−1.19137	−0.595683	−	0.803220i	$-0.703118\pi$
$103$	−12.0910	−1.19137	−0.595683	+	0.803220i	$0.703118\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−10.8080	−1.04485	−0.522424	−	0.852686i	$-0.674972\pi$
$107$	−10.8080	−1.04485	−0.522424	+	0.852686i	$0.674972\pi$
$108$	0	0
$109$	−6.65386	−0.637324	−0.318662	−	0.947868i	$-0.603233\pi$
$109$	−6.65386	−0.637324	−0.318662	+	0.947868i	$0.603233\pi$
$110$	0	0
$111$	28.8295	2.73637
$112$	0	0
$113$	0.559207	0.0526058	0.0263029	−	0.999654i	$-0.491627\pi$
$113$	0.559207	0.0526058	0.0263029	+	0.999654i	$0.491627\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	4.10944	0.379918
$118$	0	0
$119$	0	0
$120$	0	0
$121$	8.10420	0.736746
$122$	0	0
$123$	−5.24878	−0.473266
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−11.5839	−1.02790	−0.513952	−	0.857819i	$-0.671819\pi$
$127$	−11.5839	−1.02790	−0.513952	+	0.857819i	$0.671819\pi$
$128$	0	0
$129$	−34.9118	−3.07381
$130$	0	0
$131$	14.3950	1.25770	0.628850	−	0.777527i	$-0.283526\pi$
$131$	14.3950	1.25770	0.628850	+	0.777527i	$0.283526\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	16.7806	1.43366	0.716831	−	0.697247i	$-0.245592\pi$
$137$	16.7806	1.43366	0.716831	+	0.697247i	$0.245592\pi$
$138$	0	0
$139$	−2.61567	−0.221859	−0.110929	−	0.993828i	$-0.535383\pi$
$139$	−2.61567	−0.221859	−0.110929	+	0.993828i	$0.535383\pi$
$140$	0	0
$141$	−31.4770	−2.65084
$142$	0	0
$143$	2.87443	0.240372
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	20.3256	1.66514	0.832568	−	0.553923i	$-0.186870\pi$
$149$	20.3256	1.66514	0.832568	+	0.553923i	$0.186870\pi$
$150$	0	0
$151$	15.3398	1.24833	0.624167	−	0.781291i	$-0.285439\pi$
$151$	15.3398	1.24833	0.624167	+	0.781291i	$0.285439\pi$
$152$	0	0
$153$	31.9502	2.58302
$154$	0	0
$155$	0	0
$156$	0	0
$157$	16.8121	1.34175	0.670876	−	0.741569i	$-0.265918\pi$
$157$	16.8121	1.34175	0.670876	+	0.741569i	$0.265918\pi$
$158$	0	0
$159$	35.4958	2.81500
$160$	0	0
$161$	0	0
$162$	0	0
$163$	15.9547	1.24967	0.624836	−	0.780756i	$-0.285166\pi$
$163$	15.9547	1.24967	0.624836	+	0.780756i	$0.285166\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	24.5616	1.90063	0.950316	−	0.311287i	$-0.100760\pi$
$167$	24.5616	1.90063	0.950316	+	0.311287i	$0.100760\pi$
$168$	0	0
$169$	−12.5675	−0.966732
$170$	0	0
$171$	−31.4898	−2.40808
$172$	0	0
$173$	10.4976	0.798119	0.399060	−	0.916925i	$-0.369337\pi$
$173$	10.4976	0.798119	0.399060	+	0.916925i	$0.369337\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	2.07680	0.156101
$178$	0	0
$179$	−6.47970	−0.484315	−0.242158	−	0.970237i	$-0.577855\pi$
$179$	−6.47970	−0.484315	−0.242158	+	0.970237i	$0.577855\pi$
$180$	0	0
$181$	8.95021	0.665264	0.332632	−	0.943057i	$-0.392063\pi$
$181$	8.95021	0.665264	0.332632	+	0.943057i	$0.392063\pi$
$182$	0	0
$183$	6.82584	0.504581
$184$	0	0
$185$	0	0
$186$	0	0
$187$	22.3482	1.63426
$188$	0	0
$189$	0	0
$190$	0	0
$191$	0.468201	0.0338778	0.0169389	−	0.999857i	$-0.494608\pi$
$191$	0.468201	0.0338778	0.0169389	+	0.999857i	$0.494608\pi$
$192$	0	0
$193$	6.31509	0.454570	0.227285	−	0.973828i	$-0.427015\pi$
$193$	6.31509	0.454570	0.227285	+	0.973828i	$0.427015\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−16.9073	−1.20459	−0.602297	−	0.798272i	$-0.705748\pi$
$197$	−16.9073	−1.20459	−0.602297	+	0.798272i	$0.705748\pi$
$198$	0	0
$199$	−15.7750	−1.11826	−0.559129	−	0.829081i	$-0.688864\pi$
$199$	−15.7750	−1.11826	−0.559129	+	0.829081i	$0.688864\pi$
$200$	0	0
$201$	10.9536	0.772607
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0.325572	0.0226288
$208$	0	0
$209$	−22.0262	−1.52358
$210$	0	0
$211$	−20.1871	−1.38974	−0.694869	−	0.719136i	$-0.744538\pi$
$211$	−20.1871	−1.38974	−0.694869	+	0.719136i	$0.744538\pi$
$212$	0	0
$213$	3.09548	0.212099
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−30.5291	−2.06296
$220$	0	0
$221$	3.36253	0.226188
$222$	0	0
$223$	16.2392	1.08746	0.543730	−	0.839260i	$-0.317012\pi$
$223$	16.2392	1.08746	0.543730	+	0.839260i	$0.317012\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	6.32866	0.420048	0.210024	−	0.977696i	$-0.432646\pi$
$227$	6.32866	0.420048	0.210024	+	0.977696i	$0.432646\pi$
$228$	0	0
$229$	13.1787	0.870872	0.435436	−	0.900220i	$-0.356594\pi$
$229$	13.1787	0.870872	0.435436	+	0.900220i	$0.356594\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	3.45035	0.226040	0.113020	−	0.993593i	$-0.463948\pi$
$233$	3.45035	0.226040	0.113020	+	0.993593i	$0.463948\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−46.0782	−2.99310
$238$	0	0
$239$	−6.58172	−0.425736	−0.212868	−	0.977081i	$-0.568280\pi$
$239$	−6.58172	−0.425736	−0.212868	+	0.977081i	$0.568280\pi$
$240$	0	0
$241$	−23.9233	−1.54104	−0.770518	−	0.637418i	$-0.780002\pi$
$241$	−23.9233	−1.54104	−0.770518	+	0.637418i	$0.780002\pi$
$242$	0	0
$243$	4.72766	0.303280
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−3.31408	−0.210870
$248$	0	0
$249$	−27.5222	−1.74415
$250$	0	0
$251$	24.1696	1.52557	0.762786	−	0.646651i	$-0.223831\pi$
$251$	24.1696	1.52557	0.762786	+	0.646651i	$0.223831\pi$
$252$	0	0
$253$	0.227728	0.0143171
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−2.76891	−0.172720	−0.0863600	−	0.996264i	$-0.527524\pi$
$257$	−2.76891	−0.172720	−0.0863600	+	0.996264i	$0.527524\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	60.1108	3.72077
$262$	0	0
$263$	−1.61961	−0.0998696	−0.0499348	−	0.998752i	$-0.515901\pi$
$263$	−1.61961	−0.0998696	−0.0499348	+	0.998752i	$0.515901\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−46.5448	−2.84849
$268$	0	0
$269$	−13.2866	−0.810100	−0.405050	−	0.914295i	$-0.632746\pi$
$269$	−13.2866	−0.810100	−0.405050	+	0.914295i	$0.632746\pi$
$270$	0	0
$271$	1.00287	0.0609203	0.0304601	−	0.999536i	$-0.490303\pi$
$271$	1.00287	0.0609203	0.0304601	+	0.999536i	$0.490303\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−4.35764	−0.261825	−0.130913	−	0.991394i	$-0.541791\pi$
$277$	−4.35764	−0.261825	−0.130913	+	0.991394i	$0.541791\pi$
$278$	0	0
$279$	16.2237	0.971285
$280$	0	0
$281$	24.3256	1.45114	0.725571	−	0.688147i	$-0.241576\pi$
$281$	24.3256	1.45114	0.725571	+	0.688147i	$0.241576\pi$
$282$	0	0
$283$	−8.23826	−0.489714	−0.244857	−	0.969559i	$-0.578741\pi$
$283$	−8.23826	−0.489714	−0.244857	+	0.969559i	$0.578741\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	9.14311	0.537830
$290$	0	0
$291$	−1.23092	−0.0721579
$292$	0	0
$293$	0.459770	0.0268601	0.0134300	−	0.999910i	$-0.495725\pi$
$293$	0.459770	0.0268601	0.0134300	+	0.999910i	$0.495725\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	43.1844	2.50581
$298$	0	0
$299$	0.0342641	0.00198154
$300$	0	0
$301$	0	0
$302$	0	0
$303$	40.0651	2.30168
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−12.5612	−0.716904	−0.358452	−	0.933548i	$-0.616695\pi$
$307$	−12.5612	−0.716904	−0.358452	+	0.933548i	$0.616695\pi$
$308$	0	0
$309$	−36.7710	−2.09183
$310$	0	0
$311$	3.95758	0.224414	0.112207	−	0.993685i	$-0.464208\pi$
$311$	3.95758	0.224414	0.112207	+	0.993685i	$0.464208\pi$
$312$	0	0
$313$	−22.9657	−1.29810	−0.649050	−	0.760746i	$-0.724833\pi$
$313$	−22.9657	−1.29810	−0.649050	+	0.760746i	$0.724833\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	7.29133	0.409522	0.204761	−	0.978812i	$-0.434358\pi$
$317$	7.29133	0.409522	0.204761	+	0.978812i	$0.434358\pi$
$318$	0	0
$319$	42.0457	2.35411
$320$	0	0
$321$	−32.8690	−1.83457
$322$	0	0
$323$	−25.7664	−1.43368
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−20.2356	−1.11903
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−26.5695	−1.46039	−0.730195	−	0.683239i	$-0.760571\pi$
$331$	−26.5695	−1.46039	−0.730195	+	0.683239i	$0.760571\pi$
$332$	0	0
$333$	59.2365	3.24614
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−7.32557	−0.399049	−0.199525	−	0.979893i	$-0.563940\pi$
$337$	−7.32557	−0.399049	−0.199525	+	0.979893i	$0.563940\pi$
$338$	0	0
$339$	1.70065	0.0923666
$340$	0	0
$341$	11.3480	0.614527
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−28.3708	−1.52303	−0.761513	−	0.648149i	$-0.775543\pi$
$347$	−28.3708	−1.52303	−0.761513	+	0.648149i	$0.775543\pi$
$348$	0	0
$349$	−32.4746	−1.73833	−0.869164	−	0.494524i	$-0.835342\pi$
$349$	−32.4746	−1.73833	−0.869164	+	0.494524i	$0.835342\pi$
$350$	0	0
$351$	6.49755	0.346814
$352$	0	0
$353$	−4.42943	−0.235755	−0.117877	−	0.993028i	$-0.537609\pi$
$353$	−4.42943	−0.235755	−0.117877	+	0.993028i	$0.537609\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	13.1221	0.692556	0.346278	−	0.938132i	$-0.387445\pi$
$359$	13.1221	0.692556	0.346278	+	0.938132i	$0.387445\pi$
$360$	0	0
$361$	6.39505	0.336582
$362$	0	0
$363$	24.6463	1.29360
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−12.4020	−0.647380	−0.323690	−	0.946163i	$-0.604923\pi$
$367$	−12.4020	−0.647380	−0.323690	+	0.946163i	$0.604923\pi$
$368$	0	0
$369$	−10.7848	−0.561433
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−3.51541	−0.182021	−0.0910105	−	0.995850i	$-0.529010\pi$
$373$	−3.51541	−0.182021	−0.0910105	+	0.995850i	$0.529010\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	6.32624	0.325818
$378$	0	0
$379$	27.9383	1.43510	0.717548	−	0.696509i	$-0.245264\pi$
$379$	27.9383	1.43510	0.717548	+	0.696509i	$0.245264\pi$
$380$	0	0
$381$	−35.2287	−1.80482
$382$	0	0
$383$	10.8539	0.554610	0.277305	−	0.960782i	$-0.410559\pi$
$383$	10.8539	0.554610	0.277305	+	0.960782i	$0.410559\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−71.7341	−3.64645
$388$	0	0
$389$	−2.13627	−0.108313	−0.0541566	−	0.998532i	$-0.517247\pi$
$389$	−2.13627	−0.108313	−0.0541566	+	0.998532i	$0.517247\pi$
$390$	0	0
$391$	0.266398	0.0134723
$392$	0	0
$393$	43.7779	2.20830
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−26.3923	−1.32459	−0.662295	−	0.749243i	$-0.730418\pi$
$397$	−26.3923	−1.32459	−0.662295	+	0.749243i	$0.730418\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	5.60812	0.280056	0.140028	−	0.990148i	$-0.455281\pi$
$401$	5.60812	0.280056	0.140028	+	0.990148i	$0.455281\pi$
$402$	0	0
$403$	1.70743	0.0850529
$404$	0	0
$405$	0	0
$406$	0	0
$407$	41.4342	2.05382
$408$	0	0
$409$	6.80539	0.336505	0.168252	−	0.985744i	$-0.446188\pi$
$409$	6.80539	0.336505	0.168252	+	0.985744i	$0.446188\pi$
$410$	0	0
$411$	51.0328	2.51726
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−7.95474	−0.389545
$418$	0	0
$419$	31.9167	1.55923	0.779615	−	0.626259i	$-0.215415\pi$
$419$	31.9167	1.55923	0.779615	+	0.626259i	$0.215415\pi$
$420$	0	0
$421$	15.0179	0.731926	0.365963	−	0.930629i	$-0.380740\pi$
$421$	15.0179	0.731926	0.365963	+	0.930629i	$0.380740\pi$
$422$	0	0
$423$	−64.6764	−3.14467
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	8.74167	0.422052
$430$	0	0
$431$	10.5176	0.506614	0.253307	−	0.967386i	$-0.418482\pi$
$431$	10.5176	0.506614	0.253307	+	0.967386i	$0.418482\pi$
$432$	0	0
$433$	−30.6356	−1.47225	−0.736127	−	0.676843i	$-0.763348\pi$
$433$	−30.6356	−1.47225	−0.736127	+	0.676843i	$0.763348\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−0.262559	−0.0125599
$438$	0	0
$439$	21.0800	1.00609	0.503047	−	0.864259i	$-0.332212\pi$
$439$	21.0800	1.00609	0.503047	+	0.864259i	$0.332212\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	6.33978	0.301212	0.150606	−	0.988594i	$-0.451877\pi$
$443$	6.33978	0.301212	0.150606	+	0.988594i	$0.451877\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	61.8137	2.92369
$448$	0	0
$449$	12.3234	0.581577	0.290788	−	0.956787i	$-0.406082\pi$
$449$	12.3234	0.581577	0.290788	+	0.956787i	$0.406082\pi$
$450$	0	0
$451$	−7.54363	−0.355216
$452$	0	0
$453$	46.6510	2.19186
$454$	0	0
$455$	0	0
$456$	0	0
$457$	7.90263	0.369670	0.184835	−	0.982770i	$-0.440825\pi$
$457$	7.90263	0.369670	0.184835	+	0.982770i	$0.440825\pi$
$458$	0	0
$459$	50.5174	2.35795
$460$	0	0
$461$	28.9834	1.34989	0.674946	−	0.737867i	$-0.264167\pi$
$461$	28.9834	1.34989	0.674946	+	0.737867i	$0.264167\pi$
$462$	0	0
$463$	−1.75588	−0.0816028	−0.0408014	−	0.999167i	$-0.512991\pi$
$463$	−1.75588	−0.0816028	−0.0408014	+	0.999167i	$0.512991\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	12.3439	0.571209	0.285604	−	0.958348i	$-0.407806\pi$
$467$	12.3439	0.571209	0.285604	+	0.958348i	$0.407806\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	51.1287	2.35588
$472$	0	0
$473$	−50.1759	−2.30709
$474$	0	0
$475$	0	0
$476$	0	0
$477$	72.9339	3.33942
$478$	0	0
$479$	9.72754	0.444462	0.222231	−	0.974994i	$-0.428666\pi$
$479$	9.72754	0.444462	0.222231	+	0.974994i	$0.428666\pi$
$480$	0	0
$481$	6.23422	0.284256
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−13.0022	−0.589185	−0.294592	−	0.955623i	$-0.595184\pi$
$487$	−13.0022	−0.589185	−0.294592	+	0.955623i	$0.595184\pi$
$488$	0	0
$489$	48.5212	2.19421
$490$	0	0
$491$	16.2214	0.732060	0.366030	−	0.930603i	$-0.380717\pi$
$491$	16.2214	0.732060	0.366030	+	0.930603i	$0.380717\pi$
$492$	0	0
$493$	49.1854	2.21520
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	42.5827	1.90626	0.953131	−	0.302559i	$-0.0978409\pi$
$499$	42.5827	1.90626	0.953131	+	0.302559i	$0.0978409\pi$
$500$	0	0
$501$	74.6962	3.33718
$502$	0	0
$503$	−36.8460	−1.64288	−0.821441	−	0.570294i	$-0.806829\pi$
$503$	−36.8460	−1.64288	−0.821441	+	0.570294i	$0.806829\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−38.2201	−1.69741
$508$	0	0
$509$	−40.4950	−1.79491	−0.897455	−	0.441107i	$-0.854586\pi$
$509$	−40.4950	−1.79491	−0.897455	+	0.441107i	$0.854586\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−49.7894	−2.19825
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−45.2393	−1.98962
$518$	0	0
$519$	31.9251	1.40136
$520$	0	0
$521$	−25.6641	−1.12436	−0.562182	−	0.827013i	$-0.690038\pi$
$521$	−25.6641	−1.12436	−0.562182	+	0.827013i	$0.690038\pi$
$522$	0	0
$523$	14.4998	0.634033	0.317017	−	0.948420i	$-0.397319\pi$
$523$	14.4998	0.634033	0.317017	+	0.948420i	$0.397319\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	13.2749	0.578265
$528$	0	0
$529$	−22.9973	−0.999882
$530$	0	0
$531$	4.26723	0.185182
$532$	0	0
$533$	−1.13502	−0.0491632
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−19.7059	−0.850373
$538$	0	0
$539$	0	0
$540$	0	0
$541$	15.2620	0.656164	0.328082	−	0.944649i	$-0.393598\pi$
$541$	15.2620	0.656164	0.328082	+	0.944649i	$0.393598\pi$
$542$	0	0
$543$	27.2192	1.16809
$544$	0	0
$545$	0	0
$546$	0	0
$547$	3.86692	0.165338	0.0826688	−	0.996577i	$-0.473656\pi$
$547$	3.86692	0.165338	0.0826688	+	0.996577i	$0.473656\pi$
$548$	0	0
$549$	14.0252	0.598581
$550$	0	0
$551$	−48.4766	−2.06517
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−10.1857	−0.431580	−0.215790	−	0.976440i	$-0.569233\pi$
$557$	−10.1857	−0.431580	−0.215790	+	0.976440i	$0.569233\pi$
$558$	0	0
$559$	−7.54950	−0.319310
$560$	0	0
$561$	67.9650	2.86948
$562$	0	0
$563$	−41.1340	−1.73359	−0.866795	−	0.498664i	$-0.833824\pi$
$563$	−41.1340	−1.73359	−0.866795	+	0.498664i	$0.833824\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	16.4833	0.691018	0.345509	−	0.938416i	$-0.387706\pi$
$569$	16.4833	0.691018	0.345509	+	0.938416i	$0.387706\pi$
$570$	0	0
$571$	−3.37549	−0.141260	−0.0706300	−	0.997503i	$-0.522501\pi$
$571$	−3.37549	−0.141260	−0.0706300	+	0.997503i	$0.522501\pi$
$572$	0	0
$573$	1.42388	0.0594836
$574$	0	0
$575$	0	0
$576$	0	0
$577$	6.73863	0.280533	0.140266	−	0.990114i	$-0.455204\pi$
$577$	6.73863	0.280533	0.140266	+	0.990114i	$0.455204\pi$
$578$	0	0
$579$	19.2053	0.798146
$580$	0	0
$581$	0	0
$582$	0	0
$583$	51.0151	2.11283
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−20.5040	−0.846291	−0.423146	−	0.906062i	$-0.639074\pi$
$587$	−20.5040	−0.846291	−0.423146	+	0.906062i	$0.639074\pi$
$588$	0	0
$589$	−13.0836	−0.539102
$590$	0	0
$591$	−51.4181	−2.11506
$592$	0	0
$593$	16.2794	0.668514	0.334257	−	0.942482i	$-0.391515\pi$
$593$	16.2794	0.668514	0.334257	+	0.942482i	$0.391515\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−47.9745	−1.96347
$598$	0	0
$599$	−2.51394	−0.102717	−0.0513585	−	0.998680i	$-0.516355\pi$
$599$	−2.51394	−0.102717	−0.0513585	+	0.998680i	$0.516355\pi$
$600$	0	0
$601$	−27.7269	−1.13101	−0.565503	−	0.824746i	$-0.691318\pi$
$601$	−27.7269	−1.13101	−0.565503	+	0.824746i	$0.691318\pi$
$602$	0	0
$603$	22.5066	0.916538
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−29.8732	−1.21252	−0.606258	−	0.795268i	$-0.707330\pi$
$607$	−29.8732	−1.21252	−0.606258	+	0.795268i	$0.707330\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−6.80673	−0.275371
$612$	0	0
$613$	−44.0423	−1.77885	−0.889426	−	0.457079i	$-0.848896\pi$
$613$	−44.0423	−1.77885	−0.889426	+	0.457079i	$0.848896\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	11.0379	0.444369	0.222184	−	0.975005i	$-0.428681\pi$
$617$	11.0379	0.444369	0.222184	+	0.975005i	$0.428681\pi$
$618$	0	0
$619$	21.7972	0.876102	0.438051	−	0.898950i	$-0.355669\pi$
$619$	21.7972	0.876102	0.438051	+	0.898950i	$0.355669\pi$
$620$	0	0
$621$	0.514770	0.0206570
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−66.9856	−2.67515
$628$	0	0
$629$	48.4700	1.93263
$630$	0	0
$631$	21.7532	0.865980	0.432990	−	0.901399i	$-0.357459\pi$
$631$	21.7532	0.865980	0.432990	+	0.901399i	$0.357459\pi$
$632$	0	0
$633$	−61.3927	−2.44014
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	6.36035	0.251612
$640$	0	0
$641$	−8.03300	−0.317284	−0.158642	−	0.987336i	$-0.550712\pi$
$641$	−8.03300	−0.317284	−0.158642	+	0.987336i	$0.550712\pi$
$642$	0	0
$643$	−38.1128	−1.50302	−0.751512	−	0.659720i	$-0.770675\pi$
$643$	−38.1128	−1.50302	−0.751512	+	0.659720i	$0.770675\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−14.9880	−0.589239	−0.294619	−	0.955615i	$-0.595193\pi$
$647$	−14.9880	−0.589239	−0.294619	+	0.955615i	$0.595193\pi$
$648$	0	0
$649$	2.98481	0.117164
$650$	0	0
$651$	0	0
$652$	0	0
$653$	30.1893	1.18140	0.590699	−	0.806892i	$-0.298852\pi$
$653$	30.1893	1.18140	0.590699	+	0.806892i	$0.298852\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−62.7287	−2.44728
$658$	0	0
$659$	−0.387226	−0.0150842	−0.00754209	−	0.999972i	$-0.502401\pi$
$659$	−0.387226	−0.0150842	−0.00754209	+	0.999972i	$0.502401\pi$
$660$	0	0
$661$	38.6255	1.50236	0.751180	−	0.660098i	$-0.229485\pi$
$661$	38.6255	1.50236	0.751180	+	0.660098i	$0.229485\pi$
$662$	0	0
$663$	10.2261	0.397148
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0.501198	0.0194065
$668$	0	0
$669$	49.3865	1.90939
$670$	0	0
$671$	9.81021	0.378719
$672$	0	0
$673$	−4.60812	−0.177630	−0.0888149	−	0.996048i	$-0.528308\pi$
$673$	−4.60812	−0.177630	−0.0888149	+	0.996048i	$0.528308\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−36.6869	−1.40999	−0.704996	−	0.709212i	$-0.749051\pi$
$677$	−36.6869	−1.40999	−0.704996	+	0.709212i	$0.749051\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	19.2466	0.737531
$682$	0	0
$683$	−13.8459	−0.529798	−0.264899	−	0.964276i	$-0.585339\pi$
$683$	−13.8459	−0.529798	−0.264899	+	0.964276i	$0.585339\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	40.0787	1.52910
$688$	0	0
$689$	7.67578	0.292424
$690$	0	0
$691$	−14.9143	−0.567365	−0.283682	−	0.958918i	$-0.591556\pi$
$691$	−14.9143	−0.567365	−0.283682	+	0.958918i	$0.591556\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−8.82459	−0.334255
$698$	0	0
$699$	10.4931	0.396886
$700$	0	0
$701$	−40.3385	−1.52357	−0.761783	−	0.647833i	$-0.775676\pi$
$701$	−40.3385	−1.52357	−0.761783	+	0.647833i	$0.775676\pi$
$702$	0	0
$703$	−47.7715	−1.80174
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	24.5397	0.921606	0.460803	−	0.887502i	$-0.347561\pi$
$709$	24.5397	0.921606	0.460803	+	0.887502i	$0.347561\pi$
$710$	0	0
$711$	−94.6778	−3.55069
$712$	0	0
$713$	0.135271	0.00506595
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−20.0162	−0.747519
$718$	0	0
$719$	−32.0446	−1.19506	−0.597532	−	0.801845i	$-0.703852\pi$
$719$	−32.0446	−1.19506	−0.597532	+	0.801845i	$0.703852\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	−72.7551	−2.70579
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−5.42022	−0.201025	−0.100512	−	0.994936i	$-0.532048\pi$
$727$	−5.42022	−0.201025	−0.100512	+	0.994936i	$0.532048\pi$
$728$	0	0
$729$	−19.5250	−0.723147
$730$	0	0
$731$	−58.6961	−2.17095
$732$	0	0
$733$	−9.48366	−0.350287	−0.175143	−	0.984543i	$-0.556039\pi$
$733$	−9.48366	−0.350287	−0.175143	+	0.984543i	$0.556039\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	15.7427	0.579889
$738$	0	0
$739$	20.2962	0.746609	0.373304	−	0.927709i	$-0.378225\pi$
$739$	20.2962	0.746609	0.373304	+	0.927709i	$0.378225\pi$
$740$	0	0
$741$	−10.0787	−0.370250
$742$	0	0
$743$	−5.13845	−0.188511	−0.0942557	−	0.995548i	$-0.530047\pi$
$743$	−5.13845	−0.188511	−0.0942557	+	0.995548i	$0.530047\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−56.5505	−2.06908
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−33.7696	−1.23227	−0.616134	−	0.787641i	$-0.711302\pi$
$751$	−33.7696	−1.23227	−0.616134	+	0.787641i	$0.711302\pi$
$752$	0	0
$753$	73.5042	2.67864
$754$	0	0
$755$	0	0
$756$	0	0
$757$	48.3549	1.75749	0.878745	−	0.477292i	$-0.158382\pi$
$757$	48.3549	1.75749	0.878745	+	0.477292i	$0.158382\pi$
$758$	0	0
$759$	0.692561	0.0251384
$760$	0	0
$761$	30.6522	1.11114	0.555571	−	0.831469i	$-0.312500\pi$
$761$	30.6522	1.11114	0.555571	+	0.831469i	$0.312500\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0.449096	0.0162159
$768$	0	0
$769$	−18.8020	−0.678017	−0.339008	−	0.940783i	$-0.610092\pi$
$769$	−18.8020	−0.678017	−0.339008	+	0.940783i	$0.610092\pi$
$770$	0	0
$771$	−8.42076	−0.303266
$772$	0	0
$773$	−5.32786	−0.191630	−0.0958149	−	0.995399i	$-0.530546\pi$
$773$	−5.32786	−0.191630	−0.0958149	+	0.995399i	$0.530546\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	8.69742	0.311617
$780$	0	0
$781$	4.44888	0.159193
$782$	0	0
$783$	95.0429	3.39656
$784$	0	0
$785$	0	0
$786$	0	0
$787$	24.6307	0.877991	0.438996	−	0.898489i	$-0.355334\pi$
$787$	24.6307	0.877991	0.438996	+	0.898489i	$0.355334\pi$
$788$	0	0
$789$	−4.92553	−0.175354
$790$	0	0
$791$	0	0
$792$	0	0
$793$	1.47605	0.0524162
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−33.9307	−1.20189	−0.600944	−	0.799292i	$-0.705208\pi$
$797$	−33.9307	−1.20189	−0.600944	+	0.799292i	$0.705208\pi$
$798$	0	0
$799$	−52.9212	−1.87222
$800$	0	0
$801$	−95.6365	−3.37915
$802$	0	0
$803$	−43.8769	−1.54838
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−40.4070	−1.42239
$808$	0	0
$809$	−34.3613	−1.20808	−0.604039	−	0.796955i	$-0.706443\pi$
$809$	−34.3613	−1.20808	−0.604039	+	0.796955i	$0.706443\pi$
$810$	0	0
$811$	10.8681	0.381631	0.190815	−	0.981626i	$-0.438887\pi$
$811$	10.8681	0.381631	0.190815	+	0.981626i	$0.438887\pi$
$812$	0	0
$813$	3.04992	0.106965
$814$	0	0
$815$	0	0
$816$	0	0
$817$	57.8502	2.02392
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−23.0308	−0.803781	−0.401891	−	0.915688i	$-0.631647\pi$
$821$	−23.0308	−0.803781	−0.401891	+	0.915688i	$0.631647\pi$
$822$	0	0
$823$	−18.2370	−0.635703	−0.317852	−	0.948140i	$-0.602961\pi$
$823$	−18.2370	−0.635703	−0.317852	+	0.948140i	$0.602961\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−10.4467	−0.363267	−0.181634	−	0.983366i	$-0.558139\pi$
$827$	−10.4467	−0.363267	−0.181634	+	0.983366i	$0.558139\pi$
$828$	0	0
$829$	40.6379	1.41141	0.705706	−	0.708505i	$-0.250630\pi$
$829$	40.6379	1.41141	0.705706	+	0.708505i	$0.250630\pi$
$830$	0	0
$831$	−13.2524	−0.459719
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	25.6517	0.886652
$838$	0	0
$839$	−42.3897	−1.46346	−0.731728	−	0.681597i	$-0.761286\pi$
$839$	−42.3897	−1.46346	−0.731728	+	0.681597i	$0.761286\pi$
$840$	0	0
$841$	63.5369	2.19093
$842$	0	0
$843$	73.9784	2.54795
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−25.0540	−0.859853
$850$	0	0
$851$	0.493908	0.0169310
$852$	0	0
$853$	34.9229	1.19574	0.597869	−	0.801594i	$-0.296014\pi$
$853$	34.9229	1.19574	0.597869	+	0.801594i	$0.296014\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	4.07832	0.139313	0.0696564	−	0.997571i	$-0.477810\pi$
$857$	4.07832	0.139313	0.0696564	+	0.997571i	$0.477810\pi$
$858$	0	0
$859$	−16.2385	−0.554052	−0.277026	−	0.960862i	$-0.589349\pi$
$859$	−16.2385	−0.554052	−0.277026	+	0.960862i	$0.589349\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	12.1006	0.411908	0.205954	−	0.978562i	$-0.433970\pi$
$863$	12.1006	0.411908	0.205954	+	0.978562i	$0.433970\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	27.8058	0.944336
$868$	0	0
$869$	−66.2243	−2.24651
$870$	0	0
$871$	2.36866	0.0802589
$872$	0	0
$873$	−2.52920	−0.0856004
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−51.7304	−1.74681	−0.873406	−	0.486993i	$-0.838094\pi$
$877$	−51.7304	−1.74681	−0.873406	+	0.486993i	$0.838094\pi$
$878$	0	0
$879$	1.39824	0.0471616
$880$	0	0
$881$	−8.49429	−0.286180	−0.143090	−	0.989710i	$-0.545704\pi$
$881$	−8.49429	−0.286180	−0.143090	+	0.989710i	$0.545704\pi$
$882$	0	0
$883$	11.2891	0.379910	0.189955	−	0.981793i	$-0.439166\pi$
$883$	11.2891	0.379910	0.189955	+	0.981793i	$0.439166\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−4.10285	−0.137760	−0.0688802	−	0.997625i	$-0.521943\pi$
$887$	−4.10285	−0.137760	−0.0688802	+	0.997625i	$0.521943\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	49.3943	1.65477
$892$	0	0
$893$	52.1585	1.74542
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0.104203	0.00347925
$898$	0	0
$899$	24.9753	0.832974
$900$	0	0
$901$	59.6779	1.98816
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	17.2749	0.573605	0.286802	−	0.957990i	$-0.407408\pi$
$907$	17.2749	0.573605	0.286802	+	0.957990i	$0.407408\pi$
$908$	0	0
$909$	82.3225	2.73047
$910$	0	0
$911$	19.0115	0.629879	0.314939	−	0.949112i	$-0.398016\pi$
$911$	19.0115	0.629879	0.314939	+	0.949112i	$0.398016\pi$
$912$	0	0
$913$	−39.5554	−1.30909
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	18.8138	0.620610	0.310305	−	0.950637i	$-0.399569\pi$
$919$	18.8138	0.620610	0.310305	+	0.950637i	$0.399569\pi$
$920$	0	0
$921$	−38.2008	−1.25876
$922$	0	0
$923$	0.669382	0.0220330
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−75.5542	−2.48153
$928$	0	0
$929$	46.5704	1.52793	0.763963	−	0.645260i	$-0.223251\pi$
$929$	46.5704	1.52793	0.763963	+	0.645260i	$0.223251\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	12.0357	0.394032
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−30.6841	−1.00240	−0.501202	−	0.865330i	$-0.667109\pi$
$937$	−30.6841	−1.00240	−0.501202	+	0.865330i	$0.667109\pi$
$938$	0	0
$939$	−69.8429	−2.27924
$940$	0	0
$941$	29.4089	0.958704	0.479352	−	0.877623i	$-0.340872\pi$
$941$	29.4089	0.958704	0.479352	+	0.877623i	$0.340872\pi$
$942$	0	0
$943$	−0.0899223	−0.00292827
$944$	0	0
$945$	0	0
$946$	0	0
$947$	0.286215	0.00930075	0.00465038	−	0.999989i	$-0.498520\pi$
$947$	0.286215	0.00930075	0.00465038	+	0.999989i	$0.498520\pi$
$948$	0	0
$949$	−6.60176	−0.214302
$950$	0	0
$951$	22.1742	0.719049
$952$	0	0
$953$	24.8116	0.803727	0.401864	−	0.915699i	$-0.368363\pi$
$953$	24.8116	0.803727	0.401864	+	0.915699i	$0.368363\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	127.869	4.13341
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−24.2593	−0.782557
$962$	0	0
$963$	−67.5367	−2.17634
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−1.01421	−0.0326148	−0.0163074	−	0.999867i	$-0.505191\pi$
$967$	−1.01421	−0.0326148	−0.0163074	+	0.999867i	$0.505191\pi$
$968$	0	0
$969$	−78.3602	−2.51729
$970$	0	0
$971$	−13.3268	−0.427676	−0.213838	−	0.976869i	$-0.568596\pi$
$971$	−13.3268	−0.427676	−0.213838	+	0.976869i	$0.568596\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	25.0283	0.800727	0.400364	−	0.916356i	$-0.368884\pi$
$977$	25.0283	0.800727	0.400364	+	0.916356i	$0.368884\pi$
$978$	0	0
$979$	−66.8949	−2.13797
$980$	0	0
$981$	−41.5785	−1.32750
$982$	0	0
$983$	37.2826	1.18913	0.594565	−	0.804048i	$-0.297324\pi$
$983$	37.2826	1.18913	0.594565	+	0.804048i	$0.297324\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−0.598111	−0.0190188
$990$	0	0
$991$	57.8676	1.83823	0.919113	−	0.393995i	$-0.128907\pi$
$991$	57.8676	1.83823	0.919113	+	0.393995i	$0.128907\pi$
$992$	0	0
$993$	−80.8025	−2.56419
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−47.2028	−1.49493	−0.747464	−	0.664302i	$-0.768729\pi$
$997$	−47.2028	−1.49493	−0.747464	+	0.664302i	$0.768729\pi$
$998$	0	0
$999$	93.6605	2.96329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9800.2.a.da.1.8	yes	8
5.4	even	2		9800.2.a.cz.1.1	✓	8
7.6	odd	2	inner	9800.2.a.da.1.1	yes	8
35.34	odd	2		9800.2.a.cz.1.8	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9800.2.a.cz.1.1	✓	8	5.4	even	2
9800.2.a.cz.1.8	yes	8	35.34	odd	2
9800.2.a.da.1.1	yes	8	7.6	odd	2	inner
9800.2.a.da.1.8	yes	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+3.04118 q^{3} +6.24878 q^{9} +O(q^{10})\)	\(q+3.04118 q^{3} +6.24878 q^{9} +4.37084 q^{11} +0.657639 q^{13} +5.11303 q^{17} -5.03935 q^{19} +0.0521017 q^{23} +9.88011 q^{27} +9.61961 q^{29} +2.59629 q^{31} +13.2925 q^{33} +9.47970 q^{37} +2.00000 q^{39} -1.72590 q^{41} -11.4797 q^{43} -10.3503 q^{47} +15.5497 q^{51} +11.6717 q^{53} -15.3256 q^{57} +0.682891 q^{59} +2.24447 q^{61} +3.60176 q^{67} +0.158451 q^{69} +1.01786 q^{71} -10.0386 q^{73} -15.1514 q^{79} +11.3009 q^{81} -9.04986 q^{83} +29.2550 q^{87} -15.3048 q^{89} +7.89580 q^{93} -0.404751 q^{97} +27.3124 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{9}+O(q^{10}) \) 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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