LMFDB - Embedded newform 9702.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9702,2,Mod(1,9702)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9702, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("9702.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9702.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:	$77.4708600410$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1386)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	9702.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} -3.00000 q^{5} -1.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{4} -3.00000 q^{5} -1.00000 q^{8} +3.00000 q^{10} +1.00000 q^{11} +2.00000 q^{13} +1.00000 q^{16} +3.00000 q^{17} +2.00000 q^{19} -3.00000 q^{20} -1.00000 q^{22} -3.00000 q^{23} +4.00000 q^{25} -2.00000 q^{26} +2.00000 q^{31} -1.00000 q^{32} -3.00000 q^{34} +8.00000 q^{37} -2.00000 q^{38} +3.00000 q^{40} +9.00000 q^{41} -4.00000 q^{43} +1.00000 q^{44} +3.00000 q^{46} -3.00000 q^{47} -4.00000 q^{50} +2.00000 q^{52} -6.00000 q^{53} -3.00000 q^{55} -6.00000 q^{59} +5.00000 q^{61} -2.00000 q^{62} +1.00000 q^{64} -6.00000 q^{65} +11.0000 q^{67} +3.00000 q^{68} +2.00000 q^{73} -8.00000 q^{74} +2.00000 q^{76} -13.0000 q^{79} -3.00000 q^{80} -9.00000 q^{82} -9.00000 q^{83} -9.00000 q^{85} +4.00000 q^{86} -1.00000 q^{88} -12.0000 q^{89} -3.00000 q^{92} +3.00000 q^{94} -6.00000 q^{95} +5.00000 q^{97} +O(q^{100})$

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	−3.00000	−1.34164	−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000	−1.34164	−0.670820	+	0.741620i	$0.734058\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	0	0
$10$	3.00000	0.948683
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0	0
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	3.00000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	0	0
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	−3.00000	−0.670820
$21$	0	0
$22$	−1.00000	−0.213201
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	0	0
$25$	4.00000	0.800000
$26$	−2.00000	−0.392232
$27$	0	0
$28$	0	0
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−3.00000	−0.514496
$35$	0	0
$36$	0	0
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	−2.00000	−0.324443
$39$	0	0
$40$	3.00000	0.474342
$41$	9.00000	1.40556	0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000	1.40556	0.702782	+	0.711405i	$0.251941\pi$
$42$	0	0
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	1.00000	0.150756
$45$	0	0
$46$	3.00000	0.442326
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	0	0
$49$	0	0
$50$	−4.00000	−0.565685
$51$	0	0
$52$	2.00000	0.277350
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	0	0
$55$	−3.00000	−0.404520
$56$	0	0
$57$	0	0
$58$	0	0
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	0	0
$61$	5.00000	0.640184	0.320092	−	0.947386i	$-0.396286\pi$
$61$	5.00000	0.640184	0.320092	+	0.947386i	$0.396286\pi$
$62$	−2.00000	−0.254000
$63$	0	0
$64$	1.00000	0.125000
$65$	−6.00000	−0.744208
$66$	0	0
$67$	11.0000	1.34386	0.671932	−	0.740613i	$-0.265465\pi$
$67$	11.0000	1.34386	0.671932	+	0.740613i	$0.265465\pi$
$68$	3.00000	0.363803
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	−8.00000	−0.929981
$75$	0	0
$76$	2.00000	0.229416
$77$	0	0
$78$	0	0
$79$	−13.0000	−1.46261	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	−13.0000	−1.46261	−0.731307	+	0.682048i	$0.761089\pi$
$80$	−3.00000	−0.335410
$81$	0	0
$82$	−9.00000	−0.993884
$83$	−9.00000	−0.987878	−0.493939	−	0.869496i	$-0.664443\pi$
$83$	−9.00000	−0.987878	−0.493939	+	0.869496i	$0.664443\pi$
$84$	0	0
$85$	−9.00000	−0.976187
$86$	4.00000	0.431331
$87$	0	0
$88$	−1.00000	−0.106600
$89$	−12.0000	−1.27200	−0.635999	−	0.771690i	$-0.719412\pi$
$89$	−12.0000	−1.27200	−0.635999	+	0.771690i	$0.719412\pi$
$90$	0	0
$91$	0	0
$92$	−3.00000	−0.312772
$93$	0	0
$94$	3.00000	0.309426
$95$	−6.00000	−0.615587
$96$	0	0
$97$	5.00000	0.507673	0.253837	−	0.967247i	$-0.418307\pi$
$97$	5.00000	0.507673	0.253837	+	0.967247i	$0.418307\pi$
$98$	0	0
$99$	0	0
$100$	4.00000	0.400000
$101$	12.0000	1.19404	0.597022	−	0.802225i	$-0.296350\pi$
$101$	12.0000	1.19404	0.597022	+	0.802225i	$0.296350\pi$
$102$	0	0
$103$	20.0000	1.97066	0.985329	−	0.170664i	$-0.0545913\pi$
$103$	20.0000	1.97066	0.985329	+	0.170664i	$0.0545913\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	6.00000	0.582772
$107$	−3.00000	−0.290021	−0.145010	−	0.989430i	$-0.546322\pi$
$107$	−3.00000	−0.290021	−0.145010	+	0.989430i	$0.546322\pi$
$108$	0	0
$109$	−1.00000	−0.0957826	−0.0478913	−	0.998853i	$-0.515250\pi$
$109$	−1.00000	−0.0957826	−0.0478913	+	0.998853i	$0.515250\pi$
$110$	3.00000	0.286039
$111$	0	0
$112$	0	0
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	0	0
$115$	9.00000	0.839254
$116$	0	0
$117$	0	0
$118$	6.00000	0.552345
$119$	0	0
$120$	0	0
$121$	1.00000	0.0909091
$122$	−5.00000	−0.452679
$123$	0	0
$124$	2.00000	0.179605
$125$	3.00000	0.268328
$126$	0	0
$127$	−19.0000	−1.68598	−0.842989	−	0.537931i	$-0.819206\pi$
$127$	−19.0000	−1.68598	−0.842989	+	0.537931i	$0.819206\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	6.00000	0.526235
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	0	0
$133$	0	0
$134$	−11.0000	−0.950255
$135$	0	0
$136$	−3.00000	−0.257248
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	0	0
$139$	2.00000	0.169638	0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000	0.169638	0.0848189	+	0.996396i	$0.472969\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	2.00000	0.167248
$144$	0	0
$145$	0	0
$146$	−2.00000	−0.165521
$147$	0	0
$148$	8.00000	0.657596
$149$	−12.0000	−0.983078	−0.491539	−	0.870855i	$-0.663566\pi$
$149$	−12.0000	−0.983078	−0.491539	+	0.870855i	$0.663566\pi$
$150$	0	0
$151$	5.00000	0.406894	0.203447	−	0.979086i	$-0.434786\pi$
$151$	5.00000	0.406894	0.203447	+	0.979086i	$0.434786\pi$
$152$	−2.00000	−0.162221
$153$	0	0
$154$	0	0
$155$	−6.00000	−0.481932
$156$	0	0
$157$	−4.00000	−0.319235	−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000	−0.319235	−0.159617	+	0.987179i	$0.551026\pi$
$158$	13.0000	1.03422
$159$	0	0
$160$	3.00000	0.237171
$161$	0	0
$162$	0	0
$163$	−19.0000	−1.48819	−0.744097	−	0.668071i	$-0.767120\pi$
$163$	−19.0000	−1.48819	−0.744097	+	0.668071i	$0.767120\pi$
$164$	9.00000	0.702782
$165$	0	0
$166$	9.00000	0.698535
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	9.00000	0.690268
$171$	0	0
$172$	−4.00000	−0.304997
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	0	0
$175$	0	0
$176$	1.00000	0.0753778
$177$	0	0
$178$	12.0000	0.899438
$179$	−6.00000	−0.448461	−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000	−0.448461	−0.224231	+	0.974536i	$0.571987\pi$
$180$	0	0
$181$	20.0000	1.48659	0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000	1.48659	0.743294	+	0.668965i	$0.233262\pi$
$182$	0	0
$183$	0	0
$184$	3.00000	0.221163
$185$	−24.0000	−1.76452
$186$	0	0
$187$	3.00000	0.219382
$188$	−3.00000	−0.218797
$189$	0	0
$190$	6.00000	0.435286
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	0	0
$193$	−16.0000	−1.15171	−0.575853	−	0.817554i	$-0.695330\pi$
$193$	−16.0000	−1.15171	−0.575853	+	0.817554i	$0.695330\pi$
$194$	−5.00000	−0.358979
$195$	0	0
$196$	0	0
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	−10.0000	−0.708881	−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000	−0.708881	−0.354441	+	0.935079i	$0.615329\pi$
$200$	−4.00000	−0.282843
$201$	0	0
$202$	−12.0000	−0.844317
$203$	0	0
$204$	0	0
$205$	−27.0000	−1.88576
$206$	−20.0000	−1.39347
$207$	0	0
$208$	2.00000	0.138675
$209$	2.00000	0.138343
$210$	0	0
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	3.00000	0.205076
$215$	12.0000	0.818393
$216$	0	0
$217$	0	0
$218$	1.00000	0.0677285
$219$	0	0
$220$	−3.00000	−0.202260
$221$	6.00000	0.403604
$222$	0	0
$223$	26.0000	1.74109	0.870544	−	0.492090i	$-0.163767\pi$
$223$	26.0000	1.74109	0.870544	+	0.492090i	$0.163767\pi$
$224$	0	0
$225$	0	0
$226$	−18.0000	−1.19734
$227$	−15.0000	−0.995585	−0.497792	−	0.867296i	$-0.665856\pi$
$227$	−15.0000	−0.995585	−0.497792	+	0.867296i	$0.665856\pi$
$228$	0	0
$229$	20.0000	1.32164	0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000	1.32164	0.660819	+	0.750546i	$0.270209\pi$
$230$	−9.00000	−0.593442
$231$	0	0
$232$	0	0
$233$	−21.0000	−1.37576	−0.687878	−	0.725826i	$-0.741458\pi$
$233$	−21.0000	−1.37576	−0.687878	+	0.725826i	$0.741458\pi$
$234$	0	0
$235$	9.00000	0.587095
$236$	−6.00000	−0.390567
$237$	0	0
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	−4.00000	−0.257663	−0.128831	−	0.991667i	$-0.541123\pi$
$241$	−4.00000	−0.257663	−0.128831	+	0.991667i	$0.541123\pi$
$242$	−1.00000	−0.0642824
$243$	0	0
$244$	5.00000	0.320092
$245$	0	0
$246$	0	0
$247$	4.00000	0.254514
$248$	−2.00000	−0.127000
$249$	0	0
$250$	−3.00000	−0.189737
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	−3.00000	−0.188608
$254$	19.0000	1.19217
$255$	0	0
$256$	1.00000	0.0625000
$257$	24.0000	1.49708	0.748539	−	0.663090i	$-0.230755\pi$
$257$	24.0000	1.49708	0.748539	+	0.663090i	$0.230755\pi$
$258$	0	0
$259$	0	0
$260$	−6.00000	−0.372104
$261$	0	0
$262$	12.0000	0.741362
$263$	30.0000	1.84988	0.924940	−	0.380114i	$-0.124115\pi$
$263$	30.0000	1.84988	0.924940	+	0.380114i	$0.124115\pi$
$264$	0	0
$265$	18.0000	1.10573
$266$	0	0
$267$	0	0
$268$	11.0000	0.671932
$269$	−15.0000	−0.914566	−0.457283	−	0.889321i	$-0.651177\pi$
$269$	−15.0000	−0.914566	−0.457283	+	0.889321i	$0.651177\pi$
$270$	0	0
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	3.00000	0.181902
$273$	0	0
$274$	6.00000	0.362473
$275$	4.00000	0.241209
$276$	0	0
$277$	14.0000	0.841178	0.420589	−	0.907251i	$-0.361823\pi$
$277$	14.0000	0.841178	0.420589	+	0.907251i	$0.361823\pi$
$278$	−2.00000	−0.119952
$279$	0	0
$280$	0	0
$281$	27.0000	1.61068	0.805342	−	0.592810i	$-0.201981\pi$
$281$	27.0000	1.61068	0.805342	+	0.592810i	$0.201981\pi$
$282$	0	0
$283$	−16.0000	−0.951101	−0.475551	−	0.879688i	$-0.657751\pi$
$283$	−16.0000	−0.951101	−0.475551	+	0.879688i	$0.657751\pi$
$284$	0	0
$285$	0	0
$286$	−2.00000	−0.118262
$287$	0	0
$288$	0	0
$289$	−8.00000	−0.470588
$290$	0	0
$291$	0	0
$292$	2.00000	0.117041
$293$	18.0000	1.05157	0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000	1.05157	0.525786	+	0.850617i	$0.323771\pi$
$294$	0	0
$295$	18.0000	1.04800
$296$	−8.00000	−0.464991
$297$	0	0
$298$	12.0000	0.695141
$299$	−6.00000	−0.346989
$300$	0	0
$301$	0	0
$302$	−5.00000	−0.287718
$303$	0	0
$304$	2.00000	0.114708
$305$	−15.0000	−0.858898
$306$	0	0
$307$	8.00000	0.456584	0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000	0.456584	0.228292	+	0.973593i	$0.426686\pi$
$308$	0	0
$309$	0	0
$310$	6.00000	0.340777
$311$	3.00000	0.170114	0.0850572	−	0.996376i	$-0.472893\pi$
$311$	3.00000	0.170114	0.0850572	+	0.996376i	$0.472893\pi$
$312$	0	0
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	4.00000	0.225733
$315$	0	0
$316$	−13.0000	−0.731307
$317$	15.0000	0.842484	0.421242	−	0.906948i	$-0.361594\pi$
$317$	15.0000	0.842484	0.421242	+	0.906948i	$0.361594\pi$
$318$	0	0
$319$	0	0
$320$	−3.00000	−0.167705
$321$	0	0
$322$	0	0
$323$	6.00000	0.333849
$324$	0	0
$325$	8.00000	0.443760
$326$	19.0000	1.05231
$327$	0	0
$328$	−9.00000	−0.496942
$329$	0	0
$330$	0	0
$331$	−19.0000	−1.04433	−0.522167	−	0.852843i	$-0.674876\pi$
$331$	−19.0000	−1.04433	−0.522167	+	0.852843i	$0.674876\pi$
$332$	−9.00000	−0.493939
$333$	0	0
$334$	0	0
$335$	−33.0000	−1.80298
$336$	0	0
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	9.00000	0.489535
$339$	0	0
$340$	−9.00000	−0.488094
$341$	2.00000	0.108306
$342$	0	0
$343$	0	0
$344$	4.00000	0.215666
$345$	0	0
$346$	−6.00000	−0.322562
$347$	21.0000	1.12734	0.563670	−	0.826000i	$-0.309389\pi$
$347$	21.0000	1.12734	0.563670	+	0.826000i	$0.309389\pi$
$348$	0	0
$349$	23.0000	1.23116	0.615581	−	0.788074i	$-0.288921\pi$
$349$	23.0000	1.23116	0.615581	+	0.788074i	$0.288921\pi$
$350$	0	0
$351$	0	0
$352$	−1.00000	−0.0533002
$353$	30.0000	1.59674	0.798369	−	0.602168i	$-0.205696\pi$
$353$	30.0000	1.59674	0.798369	+	0.602168i	$0.205696\pi$
$354$	0	0
$355$	0	0
$356$	−12.0000	−0.635999
$357$	0	0
$358$	6.00000	0.317110
$359$	−12.0000	−0.633336	−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000	−0.633336	−0.316668	+	0.948536i	$0.602564\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	−20.0000	−1.05118
$363$	0	0
$364$	0	0
$365$	−6.00000	−0.314054
$366$	0	0
$367$	−10.0000	−0.521996	−0.260998	−	0.965339i	$-0.584052\pi$
$367$	−10.0000	−0.521996	−0.260998	+	0.965339i	$0.584052\pi$
$368$	−3.00000	−0.156386
$369$	0	0
$370$	24.0000	1.24770
$371$	0	0
$372$	0	0
$373$	23.0000	1.19089	0.595447	−	0.803394i	$-0.296975\pi$
$373$	23.0000	1.19089	0.595447	+	0.803394i	$0.296975\pi$
$374$	−3.00000	−0.155126
$375$	0	0
$376$	3.00000	0.154713
$377$	0	0
$378$	0	0
$379$	−1.00000	−0.0513665	−0.0256833	−	0.999670i	$-0.508176\pi$
$379$	−1.00000	−0.0513665	−0.0256833	+	0.999670i	$0.508176\pi$
$380$	−6.00000	−0.307794
$381$	0	0
$382$	12.0000	0.613973
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	0	0
$385$	0	0
$386$	16.0000	0.814379
$387$	0	0
$388$	5.00000	0.253837
$389$	21.0000	1.06474	0.532371	−	0.846511i	$-0.321301\pi$
$389$	21.0000	1.06474	0.532371	+	0.846511i	$0.321301\pi$
$390$	0	0
$391$	−9.00000	−0.455150
$392$	0	0
$393$	0	0
$394$	0	0
$395$	39.0000	1.96230
$396$	0	0
$397$	−28.0000	−1.40528	−0.702640	−	0.711546i	$-0.747995\pi$
$397$	−28.0000	−1.40528	−0.702640	+	0.711546i	$0.747995\pi$
$398$	10.0000	0.501255
$399$	0	0
$400$	4.00000	0.200000
$401$	−12.0000	−0.599251	−0.299626	−	0.954057i	$-0.596862\pi$
$401$	−12.0000	−0.599251	−0.299626	+	0.954057i	$0.596862\pi$
$402$	0	0
$403$	4.00000	0.199254
$404$	12.0000	0.597022
$405$	0	0
$406$	0	0
$407$	8.00000	0.396545
$408$	0	0
$409$	2.00000	0.0988936	0.0494468	−	0.998777i	$-0.484254\pi$
$409$	2.00000	0.0988936	0.0494468	+	0.998777i	$0.484254\pi$
$410$	27.0000	1.33343
$411$	0	0
$412$	20.0000	0.985329
$413$	0	0
$414$	0	0
$415$	27.0000	1.32538
$416$	−2.00000	−0.0980581
$417$	0	0
$418$	−2.00000	−0.0978232
$419$	−18.0000	−0.879358	−0.439679	−	0.898155i	$-0.644908\pi$
$419$	−18.0000	−0.879358	−0.439679	+	0.898155i	$0.644908\pi$
$420$	0	0
$421$	8.00000	0.389896	0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000	0.389896	0.194948	+	0.980814i	$0.437546\pi$
$422$	−20.0000	−0.973585
$423$	0	0
$424$	6.00000	0.291386
$425$	12.0000	0.582086
$426$	0	0
$427$	0	0
$428$	−3.00000	−0.145010
$429$	0	0
$430$	−12.0000	−0.578691
$431$	30.0000	1.44505	0.722525	−	0.691345i	$-0.242982\pi$
$431$	30.0000	1.44505	0.722525	+	0.691345i	$0.242982\pi$
$432$	0	0
$433$	35.0000	1.68199	0.840996	−	0.541041i	$-0.181970\pi$
$433$	35.0000	1.68199	0.840996	+	0.541041i	$0.181970\pi$
$434$	0	0
$435$	0	0
$436$	−1.00000	−0.0478913
$437$	−6.00000	−0.287019
$438$	0	0
$439$	35.0000	1.67046	0.835229	−	0.549902i	$-0.185335\pi$
$439$	35.0000	1.67046	0.835229	+	0.549902i	$0.185335\pi$
$440$	3.00000	0.143019
$441$	0	0
$442$	−6.00000	−0.285391
$443$	24.0000	1.14027	0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000	1.14027	0.570137	+	0.821549i	$0.306890\pi$
$444$	0	0
$445$	36.0000	1.70656
$446$	−26.0000	−1.23114
$447$	0	0
$448$	0	0
$449$	36.0000	1.69895	0.849473	−	0.527633i	$-0.176920\pi$
$449$	36.0000	1.69895	0.849473	+	0.527633i	$0.176920\pi$
$450$	0	0
$451$	9.00000	0.423793
$452$	18.0000	0.846649
$453$	0	0
$454$	15.0000	0.703985
$455$	0	0
$456$	0	0
$457$	−40.0000	−1.87112	−0.935561	−	0.353166i	$-0.885105\pi$
$457$	−40.0000	−1.87112	−0.935561	+	0.353166i	$0.885105\pi$
$458$	−20.0000	−0.934539
$459$	0	0
$460$	9.00000	0.419627
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	0	0
$463$	−4.00000	−0.185896	−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000	−0.185896	−0.0929479	+	0.995671i	$0.529629\pi$
$464$	0	0
$465$	0	0
$466$	21.0000	0.972806
$467$	42.0000	1.94353	0.971764	−	0.235954i	$-0.0758216\pi$
$467$	42.0000	1.94353	0.971764	+	0.235954i	$0.0758216\pi$
$468$	0	0
$469$	0	0
$470$	−9.00000	−0.415139
$471$	0	0
$472$	6.00000	0.276172
$473$	−4.00000	−0.183920
$474$	0	0
$475$	8.00000	0.367065
$476$	0	0
$477$	0	0
$478$	0	0
$479$	12.0000	0.548294	0.274147	−	0.961688i	$-0.411605\pi$
$479$	12.0000	0.548294	0.274147	+	0.961688i	$0.411605\pi$
$480$	0	0
$481$	16.0000	0.729537
$482$	4.00000	0.182195
$483$	0	0
$484$	1.00000	0.0454545
$485$	−15.0000	−0.681115
$486$	0	0
$487$	38.0000	1.72194	0.860972	−	0.508652i	$-0.169856\pi$
$487$	38.0000	1.72194	0.860972	+	0.508652i	$0.169856\pi$
$488$	−5.00000	−0.226339
$489$	0	0
$490$	0	0
$491$	−9.00000	−0.406164	−0.203082	−	0.979162i	$-0.565096\pi$
$491$	−9.00000	−0.406164	−0.203082	+	0.979162i	$0.565096\pi$
$492$	0	0
$493$	0	0
$494$	−4.00000	−0.179969
$495$	0	0
$496$	2.00000	0.0898027
$497$	0	0
$498$	0	0
$499$	20.0000	0.895323	0.447661	−	0.894203i	$-0.352257\pi$
$499$	20.0000	0.895323	0.447661	+	0.894203i	$0.352257\pi$
$500$	3.00000	0.134164
$501$	0	0
$502$	0	0
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	−36.0000	−1.60198
$506$	3.00000	0.133366
$507$	0	0
$508$	−19.0000	−0.842989
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−24.0000	−1.05859
$515$	−60.0000	−2.64392
$516$	0	0
$517$	−3.00000	−0.131940
$518$	0	0
$519$	0	0
$520$	6.00000	0.263117
$521$	−42.0000	−1.84005	−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000	−1.84005	−0.920027	+	0.391856i	$0.871833\pi$
$522$	0	0
$523$	−10.0000	−0.437269	−0.218635	−	0.975807i	$-0.570160\pi$
$523$	−10.0000	−0.437269	−0.218635	+	0.975807i	$0.570160\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	−30.0000	−1.30806
$527$	6.00000	0.261364
$528$	0	0
$529$	−14.0000	−0.608696
$530$	−18.0000	−0.781870
$531$	0	0
$532$	0	0
$533$	18.0000	0.779667
$534$	0	0
$535$	9.00000	0.389104
$536$	−11.0000	−0.475128
$537$	0	0
$538$	15.0000	0.646696
$539$	0	0
$540$	0	0
$541$	11.0000	0.472927	0.236463	−	0.971640i	$-0.424012\pi$
$541$	11.0000	0.472927	0.236463	+	0.971640i	$0.424012\pi$
$542$	−8.00000	−0.343629
$543$	0	0
$544$	−3.00000	−0.128624
$545$	3.00000	0.128506
$546$	0	0
$547$	14.0000	0.598597	0.299298	−	0.954160i	$-0.403247\pi$
$547$	14.0000	0.598597	0.299298	+	0.954160i	$0.403247\pi$
$548$	−6.00000	−0.256307
$549$	0	0
$550$	−4.00000	−0.170561
$551$	0	0
$552$	0	0
$553$	0	0
$554$	−14.0000	−0.594803
$555$	0	0
$556$	2.00000	0.0848189
$557$	−24.0000	−1.01691	−0.508456	−	0.861088i	$-0.669784\pi$
$557$	−24.0000	−1.01691	−0.508456	+	0.861088i	$0.669784\pi$
$558$	0	0
$559$	−8.00000	−0.338364
$560$	0	0
$561$	0	0
$562$	−27.0000	−1.13893
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	0	0
$565$	−54.0000	−2.27180
$566$	16.0000	0.672530
$567$	0	0
$568$	0	0
$569$	42.0000	1.76073	0.880366	−	0.474295i	$-0.157297\pi$
$569$	42.0000	1.76073	0.880366	+	0.474295i	$0.157297\pi$
$570$	0	0
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	2.00000	0.0836242
$573$	0	0
$574$	0	0
$575$	−12.0000	−0.500435
$576$	0	0
$577$	17.0000	0.707719	0.353860	−	0.935299i	$-0.384869\pi$
$577$	17.0000	0.707719	0.353860	+	0.935299i	$0.384869\pi$
$578$	8.00000	0.332756
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−6.00000	−0.248495
$584$	−2.00000	−0.0827606
$585$	0	0
$586$	−18.0000	−0.743573
$587$	−18.0000	−0.742940	−0.371470	−	0.928445i	$-0.621146\pi$
$587$	−18.0000	−0.742940	−0.371470	+	0.928445i	$0.621146\pi$
$588$	0	0
$589$	4.00000	0.164817
$590$	−18.0000	−0.741048
$591$	0	0
$592$	8.00000	0.328798
$593$	6.00000	0.246390	0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000	0.246390	0.123195	+	0.992382i	$0.460686\pi$
$594$	0	0
$595$	0	0
$596$	−12.0000	−0.491539
$597$	0	0
$598$	6.00000	0.245358
$599$	−15.0000	−0.612883	−0.306442	−	0.951889i	$-0.599138\pi$
$599$	−15.0000	−0.612883	−0.306442	+	0.951889i	$0.599138\pi$
$600$	0	0
$601$	−40.0000	−1.63163	−0.815817	−	0.578310i	$-0.803712\pi$
$601$	−40.0000	−1.63163	−0.815817	+	0.578310i	$0.803712\pi$
$602$	0	0
$603$	0	0
$604$	5.00000	0.203447
$605$	−3.00000	−0.121967
$606$	0	0
$607$	41.0000	1.66414	0.832069	−	0.554672i	$-0.187156\pi$
$607$	41.0000	1.66414	0.832069	+	0.554672i	$0.187156\pi$
$608$	−2.00000	−0.0811107
$609$	0	0
$610$	15.0000	0.607332
$611$	−6.00000	−0.242734
$612$	0	0
$613$	17.0000	0.686624	0.343312	−	0.939222i	$-0.388451\pi$
$613$	17.0000	0.686624	0.343312	+	0.939222i	$0.388451\pi$
$614$	−8.00000	−0.322854
$615$	0	0
$616$	0	0
$617$	0	0		−	1.00000i	$-0.5\pi$
$617$	0	0			1.00000i	$0.5\pi$
$618$	0	0
$619$	−31.0000	−1.24600	−0.622998	−	0.782224i	$-0.714085\pi$
$619$	−31.0000	−1.24600	−0.622998	+	0.782224i	$0.714085\pi$
$620$	−6.00000	−0.240966
$621$	0	0
$622$	−3.00000	−0.120289
$623$	0	0
$624$	0	0
$625$	−29.0000	−1.16000
$626$	10.0000	0.399680
$627$	0	0
$628$	−4.00000	−0.159617
$629$	24.0000	0.956943
$630$	0	0
$631$	−10.0000	−0.398094	−0.199047	−	0.979990i	$-0.563785\pi$
$631$	−10.0000	−0.398094	−0.199047	+	0.979990i	$0.563785\pi$
$632$	13.0000	0.517112
$633$	0	0
$634$	−15.0000	−0.595726
$635$	57.0000	2.26198
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	3.00000	0.118585
$641$	12.0000	0.473972	0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000	0.473972	0.236986	+	0.971513i	$0.423841\pi$
$642$	0	0
$643$	20.0000	0.788723	0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000	0.788723	0.394362	+	0.918955i	$0.370966\pi$
$644$	0	0
$645$	0	0
$646$	−6.00000	−0.236067
$647$	−15.0000	−0.589711	−0.294855	−	0.955542i	$-0.595271\pi$
$647$	−15.0000	−0.589711	−0.294855	+	0.955542i	$0.595271\pi$
$648$	0	0
$649$	−6.00000	−0.235521
$650$	−8.00000	−0.313786
$651$	0	0
$652$	−19.0000	−0.744097
$653$	15.0000	0.586995	0.293498	−	0.955960i	$-0.405181\pi$
$653$	15.0000	0.586995	0.293498	+	0.955960i	$0.405181\pi$
$654$	0	0
$655$	36.0000	1.40664
$656$	9.00000	0.351391
$657$	0	0
$658$	0	0
$659$	45.0000	1.75295	0.876476	−	0.481446i	$-0.159888\pi$
$659$	45.0000	1.75295	0.876476	+	0.481446i	$0.159888\pi$
$660$	0	0
$661$	14.0000	0.544537	0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000	0.544537	0.272268	+	0.962221i	$0.412226\pi$
$662$	19.0000	0.738456
$663$	0	0
$664$	9.00000	0.349268
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	33.0000	1.27490
$671$	5.00000	0.193023
$672$	0	0
$673$	−10.0000	−0.385472	−0.192736	−	0.981251i	$-0.561736\pi$
$673$	−10.0000	−0.385472	−0.192736	+	0.981251i	$0.561736\pi$
$674$	22.0000	0.847408
$675$	0	0
$676$	−9.00000	−0.346154
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	0	0
$679$	0	0
$680$	9.00000	0.345134
$681$	0	0
$682$	−2.00000	−0.0765840
$683$	−24.0000	−0.918334	−0.459167	−	0.888350i	$-0.651852\pi$
$683$	−24.0000	−0.918334	−0.459167	+	0.888350i	$0.651852\pi$
$684$	0	0
$685$	18.0000	0.687745
$686$	0	0
$687$	0	0
$688$	−4.00000	−0.152499
$689$	−12.0000	−0.457164
$690$	0	0
$691$	23.0000	0.874961	0.437481	−	0.899228i	$-0.355871\pi$
$691$	23.0000	0.874961	0.437481	+	0.899228i	$0.355871\pi$
$692$	6.00000	0.228086
$693$	0	0
$694$	−21.0000	−0.797149
$695$	−6.00000	−0.227593
$696$	0	0
$697$	27.0000	1.02270
$698$	−23.0000	−0.870563
$699$	0	0
$700$	0	0
$701$	−18.0000	−0.679851	−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000	−0.679851	−0.339925	+	0.940452i	$0.610402\pi$
$702$	0	0
$703$	16.0000	0.603451
$704$	1.00000	0.0376889
$705$	0	0
$706$	−30.0000	−1.12906
$707$	0	0
$708$	0	0
$709$	14.0000	0.525781	0.262891	−	0.964826i	$-0.415324\pi$
$709$	14.0000	0.525781	0.262891	+	0.964826i	$0.415324\pi$
$710$	0	0
$711$	0	0
$712$	12.0000	0.449719
$713$	−6.00000	−0.224702
$714$	0	0
$715$	−6.00000	−0.224387
$716$	−6.00000	−0.224231
$717$	0	0
$718$	12.0000	0.447836
$719$	−39.0000	−1.45445	−0.727227	−	0.686397i	$-0.759191\pi$
$719$	−39.0000	−1.45445	−0.727227	+	0.686397i	$0.759191\pi$
$720$	0	0
$721$	0	0
$722$	15.0000	0.558242
$723$	0	0
$724$	20.0000	0.743294
$725$	0	0
$726$	0	0
$727$	−4.00000	−0.148352	−0.0741759	−	0.997245i	$-0.523633\pi$
$727$	−4.00000	−0.148352	−0.0741759	+	0.997245i	$0.523633\pi$
$728$	0	0
$729$	0	0
$730$	6.00000	0.222070
$731$	−12.0000	−0.443836
$732$	0	0
$733$	47.0000	1.73598	0.867992	−	0.496578i	$-0.165410\pi$
$733$	47.0000	1.73598	0.867992	+	0.496578i	$0.165410\pi$
$734$	10.0000	0.369107
$735$	0	0
$736$	3.00000	0.110581
$737$	11.0000	0.405190
$738$	0	0
$739$	−10.0000	−0.367856	−0.183928	−	0.982940i	$-0.558881\pi$
$739$	−10.0000	−0.367856	−0.183928	+	0.982940i	$0.558881\pi$
$740$	−24.0000	−0.882258
$741$	0	0
$742$	0	0
$743$	−36.0000	−1.32071	−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000	−1.32071	−0.660356	+	0.750953i	$0.729595\pi$
$744$	0	0
$745$	36.0000	1.31894
$746$	−23.0000	−0.842090
$747$	0	0
$748$	3.00000	0.109691
$749$	0	0
$750$	0	0
$751$	50.0000	1.82453	0.912263	−	0.409605i	$-0.134333\pi$
$751$	50.0000	1.82453	0.912263	+	0.409605i	$0.134333\pi$
$752$	−3.00000	−0.109399
$753$	0	0
$754$	0	0
$755$	−15.0000	−0.545906
$756$	0	0
$757$	−10.0000	−0.363456	−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000	−0.363456	−0.181728	+	0.983349i	$0.558169\pi$
$758$	1.00000	0.0363216
$759$	0	0
$760$	6.00000	0.217643
$761$	15.0000	0.543750	0.271875	−	0.962333i	$-0.412356\pi$
$761$	15.0000	0.543750	0.271875	+	0.962333i	$0.412356\pi$
$762$	0	0
$763$	0	0
$764$	−12.0000	−0.434145
$765$	0	0
$766$	−24.0000	−0.867155
$767$	−12.0000	−0.433295
$768$	0	0
$769$	−22.0000	−0.793340	−0.396670	−	0.917961i	$-0.629834\pi$
$769$	−22.0000	−0.793340	−0.396670	+	0.917961i	$0.629834\pi$
$770$	0	0
$771$	0	0
$772$	−16.0000	−0.575853
$773$	21.0000	0.755318	0.377659	−	0.925945i	$-0.376729\pi$
$773$	21.0000	0.755318	0.377659	+	0.925945i	$0.376729\pi$
$774$	0	0
$775$	8.00000	0.287368
$776$	−5.00000	−0.179490
$777$	0	0
$778$	−21.0000	−0.752886
$779$	18.0000	0.644917
$780$	0	0
$781$	0	0
$782$	9.00000	0.321839
$783$	0	0
$784$	0	0
$785$	12.0000	0.428298
$786$	0	0
$787$	38.0000	1.35455	0.677277	−	0.735728i	$-0.263160\pi$
$787$	38.0000	1.35455	0.677277	+	0.735728i	$0.263160\pi$
$788$	0	0
$789$	0	0
$790$	−39.0000	−1.38756
$791$	0	0
$792$	0	0
$793$	10.0000	0.355110
$794$	28.0000	0.993683
$795$	0	0
$796$	−10.0000	−0.354441
$797$	45.0000	1.59398	0.796991	−	0.603991i	$-0.206424\pi$
$797$	45.0000	1.59398	0.796991	+	0.603991i	$0.206424\pi$
$798$	0	0
$799$	−9.00000	−0.318397
$800$	−4.00000	−0.141421
$801$	0	0
$802$	12.0000	0.423735
$803$	2.00000	0.0705785
$804$	0	0
$805$	0	0
$806$	−4.00000	−0.140894
$807$	0	0
$808$	−12.0000	−0.422159
$809$	39.0000	1.37117	0.685583	−	0.727994i	$-0.259547\pi$
$809$	39.0000	1.37117	0.685583	+	0.727994i	$0.259547\pi$
$810$	0	0
$811$	2.00000	0.0702295	0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000	0.0702295	0.0351147	+	0.999383i	$0.488820\pi$
$812$	0	0
$813$	0	0
$814$	−8.00000	−0.280400
$815$	57.0000	1.99662
$816$	0	0
$817$	−8.00000	−0.279885
$818$	−2.00000	−0.0699284
$819$	0	0
$820$	−27.0000	−0.942881
$821$	−30.0000	−1.04701	−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000	−1.04701	−0.523504	+	0.852023i	$0.675375\pi$
$822$	0	0
$823$	−34.0000	−1.18517	−0.592583	−	0.805510i	$-0.701892\pi$
$823$	−34.0000	−1.18517	−0.592583	+	0.805510i	$0.701892\pi$
$824$	−20.0000	−0.696733
$825$	0	0
$826$	0	0
$827$	−45.0000	−1.56480	−0.782402	−	0.622774i	$-0.786006\pi$
$827$	−45.0000	−1.56480	−0.782402	+	0.622774i	$0.786006\pi$
$828$	0	0
$829$	−52.0000	−1.80603	−0.903017	−	0.429604i	$-0.858653\pi$
$829$	−52.0000	−1.80603	−0.903017	+	0.429604i	$0.858653\pi$
$830$	−27.0000	−0.937184
$831$	0	0
$832$	2.00000	0.0693375
$833$	0	0
$834$	0	0
$835$	0	0
$836$	2.00000	0.0691714
$837$	0	0
$838$	18.0000	0.621800
$839$	−9.00000	−0.310715	−0.155357	−	0.987858i	$-0.549653\pi$
$839$	−9.00000	−0.310715	−0.155357	+	0.987858i	$0.549653\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	−8.00000	−0.275698
$843$	0	0
$844$	20.0000	0.688428
$845$	27.0000	0.928828
$846$	0	0
$847$	0	0
$848$	−6.00000	−0.206041
$849$	0	0
$850$	−12.0000	−0.411597
$851$	−24.0000	−0.822709
$852$	0	0
$853$	−19.0000	−0.650548	−0.325274	−	0.945620i	$-0.605456\pi$
$853$	−19.0000	−0.650548	−0.325274	+	0.945620i	$0.605456\pi$
$854$	0	0
$855$	0	0
$856$	3.00000	0.102538
$857$	39.0000	1.33221	0.666107	−	0.745856i	$-0.267959\pi$
$857$	39.0000	1.33221	0.666107	+	0.745856i	$0.267959\pi$
$858$	0	0
$859$	−7.00000	−0.238837	−0.119418	−	0.992844i	$-0.538103\pi$
$859$	−7.00000	−0.238837	−0.119418	+	0.992844i	$0.538103\pi$
$860$	12.0000	0.409197
$861$	0	0
$862$	−30.0000	−1.02180
$863$	33.0000	1.12333	0.561667	−	0.827364i	$-0.310160\pi$
$863$	33.0000	1.12333	0.561667	+	0.827364i	$0.310160\pi$
$864$	0	0
$865$	−18.0000	−0.612018
$866$	−35.0000	−1.18935
$867$	0	0
$868$	0	0
$869$	−13.0000	−0.440995
$870$	0	0
$871$	22.0000	0.745442
$872$	1.00000	0.0338643
$873$	0	0
$874$	6.00000	0.202953
$875$	0	0
$876$	0	0
$877$	11.0000	0.371444	0.185722	−	0.982602i	$-0.440538\pi$
$877$	11.0000	0.371444	0.185722	+	0.982602i	$0.440538\pi$
$878$	−35.0000	−1.18119
$879$	0	0
$880$	−3.00000	−0.101130
$881$	54.0000	1.81931	0.909653	−	0.415369i	$-0.136347\pi$
$881$	54.0000	1.81931	0.909653	+	0.415369i	$0.136347\pi$
$882$	0	0
$883$	−7.00000	−0.235569	−0.117784	−	0.993039i	$-0.537579\pi$
$883$	−7.00000	−0.235569	−0.117784	+	0.993039i	$0.537579\pi$
$884$	6.00000	0.201802
$885$	0	0
$886$	−24.0000	−0.806296
$887$	−30.0000	−1.00730	−0.503651	−	0.863907i	$-0.668010\pi$
$887$	−30.0000	−1.00730	−0.503651	+	0.863907i	$0.668010\pi$
$888$	0	0
$889$	0	0
$890$	−36.0000	−1.20672
$891$	0	0
$892$	26.0000	0.870544
$893$	−6.00000	−0.200782
$894$	0	0
$895$	18.0000	0.601674
$896$	0	0
$897$	0	0
$898$	−36.0000	−1.20134
$899$	0	0
$900$	0	0
$901$	−18.0000	−0.599667
$902$	−9.00000	−0.299667
$903$	0	0
$904$	−18.0000	−0.598671
$905$	−60.0000	−1.99447
$906$	0	0
$907$	41.0000	1.36138	0.680691	−	0.732570i	$-0.261680\pi$
$907$	41.0000	1.36138	0.680691	+	0.732570i	$0.261680\pi$
$908$	−15.0000	−0.497792
$909$	0	0
$910$	0	0
$911$	27.0000	0.894550	0.447275	−	0.894397i	$-0.352395\pi$
$911$	27.0000	0.894550	0.447275	+	0.894397i	$0.352395\pi$
$912$	0	0
$913$	−9.00000	−0.297857
$914$	40.0000	1.32308
$915$	0	0
$916$	20.0000	0.660819
$917$	0	0
$918$	0	0
$919$	−37.0000	−1.22052	−0.610259	−	0.792202i	$-0.708935\pi$
$919$	−37.0000	−1.22052	−0.610259	+	0.792202i	$0.708935\pi$
$920$	−9.00000	−0.296721
$921$	0	0
$922$	18.0000	0.592798
$923$	0	0
$924$	0	0
$925$	32.0000	1.05215
$926$	4.00000	0.131448
$927$	0	0
$928$	0	0
$929$	6.00000	0.196854	0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000	0.196854	0.0984268	+	0.995144i	$0.468619\pi$
$930$	0	0
$931$	0	0
$932$	−21.0000	−0.687878
$933$	0	0
$934$	−42.0000	−1.37428
$935$	−9.00000	−0.294331
$936$	0	0
$937$	26.0000	0.849383	0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000	0.849383	0.424691	+	0.905338i	$0.360383\pi$
$938$	0	0
$939$	0	0
$940$	9.00000	0.293548
$941$	30.0000	0.977972	0.488986	−	0.872292i	$-0.337367\pi$
$941$	30.0000	0.977972	0.488986	+	0.872292i	$0.337367\pi$
$942$	0	0
$943$	−27.0000	−0.879241
$944$	−6.00000	−0.195283
$945$	0	0
$946$	4.00000	0.130051
$947$	42.0000	1.36482	0.682408	−	0.730971i	$-0.260933\pi$
$947$	42.0000	1.36482	0.682408	+	0.730971i	$0.260933\pi$
$948$	0	0
$949$	4.00000	0.129845
$950$	−8.00000	−0.259554
$951$	0	0
$952$	0	0
$953$	−45.0000	−1.45769	−0.728846	−	0.684677i	$-0.759943\pi$
$953$	−45.0000	−1.45769	−0.728846	+	0.684677i	$0.759943\pi$
$954$	0	0
$955$	36.0000	1.16493
$956$	0	0
$957$	0	0
$958$	−12.0000	−0.387702
$959$	0	0
$960$	0	0
$961$	−27.0000	−0.870968
$962$	−16.0000	−0.515861
$963$	0	0
$964$	−4.00000	−0.128831
$965$	48.0000	1.54517
$966$	0	0
$967$	47.0000	1.51142	0.755709	−	0.654907i	$-0.227292\pi$
$967$	47.0000	1.51142	0.755709	+	0.654907i	$0.227292\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	15.0000	0.481621
$971$	6.00000	0.192549	0.0962746	−	0.995355i	$-0.469307\pi$
$971$	6.00000	0.192549	0.0962746	+	0.995355i	$0.469307\pi$
$972$	0	0
$973$	0	0
$974$	−38.0000	−1.21760
$975$	0	0
$976$	5.00000	0.160046
$977$	−6.00000	−0.191957	−0.0959785	−	0.995383i	$-0.530598\pi$
$977$	−6.00000	−0.191957	−0.0959785	+	0.995383i	$0.530598\pi$
$978$	0	0
$979$	−12.0000	−0.383522
$980$	0	0
$981$	0	0
$982$	9.00000	0.287202
$983$	21.0000	0.669796	0.334898	−	0.942254i	$-0.391298\pi$
$983$	21.0000	0.669796	0.334898	+	0.942254i	$0.391298\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	4.00000	0.127257
$989$	12.0000	0.381578
$990$	0	0
$991$	8.00000	0.254128	0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000	0.254128	0.127064	+	0.991894i	$0.459445\pi$
$992$	−2.00000	−0.0635001
$993$	0	0
$994$	0	0
$995$	30.0000	0.951064
$996$	0	0
$997$	50.0000	1.58352	0.791758	−	0.610835i	$-0.209166\pi$
$997$	50.0000	1.58352	0.791758	+	0.610835i	$0.209166\pi$
$998$	−20.0000	−0.633089
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9702.2.a.c.1.1		1
3.2	odd	2		9702.2.a.cd.1.1		1
7.2	even	3		1386.2.k.p.991.1	yes	2
7.4	even	3		1386.2.k.p.793.1	yes	2
7.6	odd	2		9702.2.a.z.1.1		1
21.2	odd	6		1386.2.k.b.991.1	yes	2
21.11	odd	6		1386.2.k.b.793.1	✓	2
21.20	even	2		9702.2.a.bc.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.k.b.793.1	✓	2	21.11	odd	6
1386.2.k.b.991.1	yes	2	21.2	odd	6
1386.2.k.p.793.1	yes	2	7.4	even	3
1386.2.k.p.991.1	yes	2	7.2	even	3
9702.2.a.c.1.1		1	1.1	even	1	trivial
9702.2.a.z.1.1		1	7.6	odd	2
9702.2.a.bc.1.1		1	21.20	even	2
9702.2.a.cd.1.1		1	3.2	odd	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:	\( N \)	\(=\)	\( 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9702.a (trivial)

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