LMFDB - Embedded newform 2850.2.a.y.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2850,2,Mod(1,2850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2850, 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("2850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2850.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:	$22.7573645761$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 570)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -6.00000 q^{11} +1.00000 q^{12} -2.00000 q^{14} +1.00000 q^{16} -2.00000 q^{17} +1.00000 q^{18} -1.00000 q^{19} -2.00000 q^{21} -6.00000 q^{22} -4.00000 q^{23} +1.00000 q^{24} +1.00000 q^{27} -2.00000 q^{28} -8.00000 q^{29} -8.00000 q^{31} +1.00000 q^{32} -6.00000 q^{33} -2.00000 q^{34} +1.00000 q^{36} +4.00000 q^{37} -1.00000 q^{38} -4.00000 q^{41} -2.00000 q^{42} +6.00000 q^{43} -6.00000 q^{44} -4.00000 q^{46} +12.0000 q^{47} +1.00000 q^{48} -3.00000 q^{49} -2.00000 q^{51} -6.00000 q^{53} +1.00000 q^{54} -2.00000 q^{56} -1.00000 q^{57} -8.00000 q^{58} -4.00000 q^{59} +2.00000 q^{61} -8.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} -6.00000 q^{66} +8.00000 q^{67} -2.00000 q^{68} -4.00000 q^{69} +1.00000 q^{72} -6.00000 q^{73} +4.00000 q^{74} -1.00000 q^{76} +12.0000 q^{77} +8.00000 q^{79} +1.00000 q^{81} -4.00000 q^{82} -4.00000 q^{83} -2.00000 q^{84} +6.00000 q^{86} -8.00000 q^{87} -6.00000 q^{88} -4.00000 q^{89} -4.00000 q^{92} -8.00000 q^{93} +12.0000 q^{94} +1.00000 q^{96} -12.0000 q^{97} -3.00000 q^{98} -6.00000 q^{99} +O(q^{100})\)

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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−6.00000	−1.80907	−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−6.00000	−1.80907	−0.904534	+	0.426401i	$0.859781\pi$
$12$	1.00000	0.288675
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	−2.00000	−0.534522
$15$	0	0
$16$	1.00000	0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0	0
$21$	−2.00000	−0.436436
$22$	−6.00000	−1.27920
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	0	0
$27$	1.00000	0.192450
$28$	−2.00000	−0.377964
$29$	−8.00000	−1.48556	−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000	−1.48556	−0.742781	+	0.669534i	$0.766494\pi$
$30$	0	0
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	1.00000	0.176777
$33$	−6.00000	−1.04447
$34$	−2.00000	−0.342997
$35$	0	0
$36$	1.00000	0.166667
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	−1.00000	−0.162221
$39$	0	0
$40$	0	0
$41$	−4.00000	−0.624695	−0.312348	−	0.949968i	$-0.601115\pi$
$41$	−4.00000	−0.624695	−0.312348	+	0.949968i	$0.601115\pi$
$42$	−2.00000	−0.308607
$43$	6.00000	0.914991	0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000	0.914991	0.457496	+	0.889212i	$0.348747\pi$
$44$	−6.00000	−0.904534
$45$	0	0
$46$	−4.00000	−0.589768
$47$	12.0000	1.75038	0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000	1.75038	0.875190	+	0.483779i	$0.160736\pi$
$48$	1.00000	0.144338
$49$	−3.00000	−0.428571
$50$	0	0
$51$	−2.00000	−0.280056
$52$	0	0
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−2.00000	−0.267261
$57$	−1.00000	−0.132453
$58$	−8.00000	−1.05045
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−8.00000	−1.01600
$63$	−2.00000	−0.251976
$64$	1.00000	0.125000
$65$	0	0
$66$	−6.00000	−0.738549
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	−2.00000	−0.242536
$69$	−4.00000	−0.481543
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	1.00000	0.117851
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	4.00000	0.464991
$75$	0	0
$76$	−1.00000	−0.114708
$77$	12.0000	1.36753
$78$	0	0
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−4.00000	−0.441726
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	−2.00000	−0.218218
$85$	0	0
$86$	6.00000	0.646997
$87$	−8.00000	−0.857690
$88$	−6.00000	−0.639602
$89$	−4.00000	−0.423999	−0.212000	−	0.977270i	$-0.567998\pi$
$89$	−4.00000	−0.423999	−0.212000	+	0.977270i	$0.567998\pi$
$90$	0	0
$91$	0	0
$92$	−4.00000	−0.417029
$93$	−8.00000	−0.829561
$94$	12.0000	1.23771
$95$	0	0
$96$	1.00000	0.102062
$97$	−12.0000	−1.21842	−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000	−1.21842	−0.609208	+	0.793011i	$0.708512\pi$
$98$	−3.00000	−0.303046
$99$	−6.00000	−0.603023
$100$	0	0
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	−2.00000	−0.198030
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	0	0
$105$	0	0
$106$	−6.00000	−0.582772
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	1.00000	0.0962250
$109$	−14.0000	−1.34096	−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000	−1.34096	−0.670478	+	0.741929i	$0.733911\pi$
$110$	0	0
$111$	4.00000	0.379663
$112$	−2.00000	−0.188982
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	−1.00000	−0.0936586
$115$	0	0
$116$	−8.00000	−0.742781
$117$	0	0
$118$	−4.00000	−0.368230
$119$	4.00000	0.366679
$120$	0	0
$121$	25.0000	2.27273
$122$	2.00000	0.181071
$123$	−4.00000	−0.360668
$124$	−8.00000	−0.718421
$125$	0	0
$126$	−2.00000	−0.178174
$127$	12.0000	1.06483	0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000	1.06483	0.532414	+	0.846484i	$0.321285\pi$
$128$	1.00000	0.0883883
$129$	6.00000	0.528271
$130$	0	0
$131$	22.0000	1.92215	0.961074	−	0.276289i	$-0.0891049\pi$
$131$	22.0000	1.92215	0.961074	+	0.276289i	$0.0891049\pi$
$132$	−6.00000	−0.522233
$133$	2.00000	0.173422
$134$	8.00000	0.691095
$135$	0	0
$136$	−2.00000	−0.171499
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	−4.00000	−0.340503
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	12.0000	1.01058
$142$	0	0
$143$	0	0
$144$	1.00000	0.0833333
$145$	0	0
$146$	−6.00000	−0.496564
$147$	−3.00000	−0.247436
$148$	4.00000	0.328798
$149$	22.0000	1.80231	0.901155	−	0.433497i	$-0.142720\pi$
$149$	22.0000	1.80231	0.901155	+	0.433497i	$0.142720\pi$
$150$	0	0
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	−1.00000	−0.0811107
$153$	−2.00000	−0.161690
$154$	12.0000	0.966988
$155$	0	0
$156$	0	0
$157$	−6.00000	−0.478852	−0.239426	−	0.970915i	$-0.576959\pi$
$157$	−6.00000	−0.478852	−0.239426	+	0.970915i	$0.576959\pi$
$158$	8.00000	0.636446
$159$	−6.00000	−0.475831
$160$	0	0
$161$	8.00000	0.630488
$162$	1.00000	0.0785674
$163$	−6.00000	−0.469956	−0.234978	−	0.972001i	$-0.575502\pi$
$163$	−6.00000	−0.469956	−0.234978	+	0.972001i	$0.575502\pi$
$164$	−4.00000	−0.312348
$165$	0	0
$166$	−4.00000	−0.310460
$167$	16.0000	1.23812	0.619059	−	0.785345i	$-0.287514\pi$
$167$	16.0000	1.23812	0.619059	+	0.785345i	$0.287514\pi$
$168$	−2.00000	−0.154303
$169$	−13.0000	−1.00000
$170$	0	0
$171$	−1.00000	−0.0764719
$172$	6.00000	0.457496
$173$	−18.0000	−1.36851	−0.684257	−	0.729241i	$-0.739873\pi$
$173$	−18.0000	−1.36851	−0.684257	+	0.729241i	$0.739873\pi$
$174$	−8.00000	−0.606478
$175$	0	0
$176$	−6.00000	−0.452267
$177$	−4.00000	−0.300658
$178$	−4.00000	−0.299813
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	0	0
$183$	2.00000	0.147844
$184$	−4.00000	−0.294884
$185$	0	0
$186$	−8.00000	−0.586588
$187$	12.0000	0.877527
$188$	12.0000	0.875190
$189$	−2.00000	−0.145479
$190$	0	0
$191$	−22.0000	−1.59186	−0.795932	−	0.605386i	$-0.793019\pi$
$191$	−22.0000	−1.59186	−0.795932	+	0.605386i	$0.793019\pi$
$192$	1.00000	0.0721688
$193$	8.00000	0.575853	0.287926	−	0.957653i	$-0.407034\pi$
$193$	8.00000	0.575853	0.287926	+	0.957653i	$0.407034\pi$
$194$	−12.0000	−0.861550
$195$	0	0
$196$	−3.00000	−0.214286
$197$	−14.0000	−0.997459	−0.498729	−	0.866758i	$-0.666200\pi$
$197$	−14.0000	−0.997459	−0.498729	+	0.866758i	$0.666200\pi$
$198$	−6.00000	−0.426401
$199$	20.0000	1.41776	0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000	1.41776	0.708881	+	0.705328i	$0.249200\pi$
$200$	0	0
$201$	8.00000	0.564276
$202$	−10.0000	−0.703598
$203$	16.0000	1.12298
$204$	−2.00000	−0.140028
$205$	0	0
$206$	0	0
$207$	−4.00000	−0.278019
$208$	0	0
$209$	6.00000	0.415029
$210$	0	0
$211$	−28.0000	−1.92760	−0.963800	−	0.266627i	$-0.914091\pi$
$211$	−28.0000	−1.92760	−0.963800	+	0.266627i	$0.914091\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	12.0000	0.820303
$215$	0	0
$216$	1.00000	0.0680414
$217$	16.0000	1.08615
$218$	−14.0000	−0.948200
$219$	−6.00000	−0.405442
$220$	0	0
$221$	0	0
$222$	4.00000	0.268462
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	−2.00000	−0.133631
$225$	0	0
$226$	−14.0000	−0.931266
$227$	28.0000	1.85843	0.929213	−	0.369546i	$-0.120487\pi$
$227$	28.0000	1.85843	0.929213	+	0.369546i	$0.120487\pi$
$228$	−1.00000	−0.0662266
$229$	18.0000	1.18947	0.594737	−	0.803921i	$-0.297256\pi$
$229$	18.0000	1.18947	0.594737	+	0.803921i	$0.297256\pi$
$230$	0	0
$231$	12.0000	0.789542
$232$	−8.00000	−0.525226
$233$	−14.0000	−0.917170	−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000	−0.917170	−0.458585	+	0.888650i	$0.651644\pi$
$234$	0	0
$235$	0	0
$236$	−4.00000	−0.260378
$237$	8.00000	0.519656
$238$	4.00000	0.259281
$239$	−18.0000	−1.16432	−0.582162	−	0.813073i	$-0.697793\pi$
$239$	−18.0000	−1.16432	−0.582162	+	0.813073i	$0.697793\pi$
$240$	0	0
$241$	−22.0000	−1.41714	−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000	−1.41714	−0.708572	+	0.705638i	$0.750660\pi$
$242$	25.0000	1.60706
$243$	1.00000	0.0641500
$244$	2.00000	0.128037
$245$	0	0
$246$	−4.00000	−0.255031
$247$	0	0
$248$	−8.00000	−0.508001
$249$	−4.00000	−0.253490
$250$	0	0
$251$	−14.0000	−0.883672	−0.441836	−	0.897096i	$-0.645673\pi$
$251$	−14.0000	−0.883672	−0.441836	+	0.897096i	$0.645673\pi$
$252$	−2.00000	−0.125988
$253$	24.0000	1.50887
$254$	12.0000	0.752947
$255$	0	0
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	6.00000	0.373544
$259$	−8.00000	−0.497096
$260$	0	0
$261$	−8.00000	−0.495188
$262$	22.0000	1.35916
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	−6.00000	−0.369274
$265$	0	0
$266$	2.00000	0.122628
$267$	−4.00000	−0.244796
$268$	8.00000	0.488678
$269$	8.00000	0.487769	0.243884	−	0.969804i	$-0.421578\pi$
$269$	8.00000	0.487769	0.243884	+	0.969804i	$0.421578\pi$
$270$	0	0
$271$	20.0000	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	−2.00000	−0.121268
$273$	0	0
$274$	−6.00000	−0.362473
$275$	0	0
$276$	−4.00000	−0.240772
$277$	2.00000	0.120168	0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000	0.120168	0.0600842	+	0.998193i	$0.480863\pi$
$278$	0	0
$279$	−8.00000	−0.478947
$280$	0	0
$281$	16.0000	0.954480	0.477240	−	0.878773i	$-0.341637\pi$
$281$	16.0000	0.954480	0.477240	+	0.878773i	$0.341637\pi$
$282$	12.0000	0.714590
$283$	−22.0000	−1.30776	−0.653882	−	0.756596i	$-0.726861\pi$
$283$	−22.0000	−1.30776	−0.653882	+	0.756596i	$0.726861\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	8.00000	0.472225
$288$	1.00000	0.0589256
$289$	−13.0000	−0.764706
$290$	0	0
$291$	−12.0000	−0.703452
$292$	−6.00000	−0.351123
$293$	−10.0000	−0.584206	−0.292103	−	0.956387i	$-0.594355\pi$
$293$	−10.0000	−0.584206	−0.292103	+	0.956387i	$0.594355\pi$
$294$	−3.00000	−0.174964
$295$	0	0
$296$	4.00000	0.232495
$297$	−6.00000	−0.348155
$298$	22.0000	1.27443
$299$	0	0
$300$	0	0
$301$	−12.0000	−0.691669
$302$	0	0
$303$	−10.0000	−0.574485
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	−2.00000	−0.114332
$307$	8.00000	0.456584	0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000	0.456584	0.228292	+	0.973593i	$0.426686\pi$
$308$	12.0000	0.683763
$309$	0	0
$310$	0	0
$311$	−6.00000	−0.340229	−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000	−0.340229	−0.170114	+	0.985424i	$0.554414\pi$
$312$	0	0
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	−6.00000	−0.338600
$315$	0	0
$316$	8.00000	0.450035
$317$	−6.00000	−0.336994	−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000	−0.336994	−0.168497	+	0.985702i	$0.553891\pi$
$318$	−6.00000	−0.336463
$319$	48.0000	2.68748
$320$	0	0
$321$	12.0000	0.669775
$322$	8.00000	0.445823
$323$	2.00000	0.111283
$324$	1.00000	0.0555556
$325$	0	0
$326$	−6.00000	−0.332309
$327$	−14.0000	−0.774202
$328$	−4.00000	−0.220863
$329$	−24.0000	−1.32316
$330$	0	0
$331$	−20.0000	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	−4.00000	−0.219529
$333$	4.00000	0.219199
$334$	16.0000	0.875481
$335$	0	0
$336$	−2.00000	−0.109109
$337$	20.0000	1.08947	0.544735	−	0.838608i	$-0.316630\pi$
$337$	20.0000	1.08947	0.544735	+	0.838608i	$0.316630\pi$
$338$	−13.0000	−0.707107
$339$	−14.0000	−0.760376
$340$	0	0
$341$	48.0000	2.59935
$342$	−1.00000	−0.0540738
$343$	20.0000	1.07990
$344$	6.00000	0.323498
$345$	0	0
$346$	−18.0000	−0.967686
$347$	−36.0000	−1.93258	−0.966291	−	0.257454i	$-0.917117\pi$
$347$	−36.0000	−1.93258	−0.966291	+	0.257454i	$0.917117\pi$
$348$	−8.00000	−0.428845
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	0	0
$351$	0	0
$352$	−6.00000	−0.319801
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	−4.00000	−0.212598
$355$	0	0
$356$	−4.00000	−0.212000
$357$	4.00000	0.211702
$358$	12.0000	0.634220
$359$	−6.00000	−0.316668	−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000	−0.316668	−0.158334	+	0.987386i	$0.550612\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	2.00000	0.105118
$363$	25.0000	1.31216
$364$	0	0
$365$	0	0
$366$	2.00000	0.104542
$367$	10.0000	0.521996	0.260998	−	0.965339i	$-0.415948\pi$
$367$	10.0000	0.521996	0.260998	+	0.965339i	$0.415948\pi$
$368$	−4.00000	−0.208514
$369$	−4.00000	−0.208232
$370$	0	0
$371$	12.0000	0.623009
$372$	−8.00000	−0.414781
$373$	24.0000	1.24267	0.621336	−	0.783544i	$-0.286590\pi$
$373$	24.0000	1.24267	0.621336	+	0.783544i	$0.286590\pi$
$374$	12.0000	0.620505
$375$	0	0
$376$	12.0000	0.618853
$377$	0	0
$378$	−2.00000	−0.102869
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	0	0
$381$	12.0000	0.614779
$382$	−22.0000	−1.12562
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	8.00000	0.407189
$387$	6.00000	0.304997
$388$	−12.0000	−0.609208
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	0	0
$391$	8.00000	0.404577
$392$	−3.00000	−0.151523
$393$	22.0000	1.10975
$394$	−14.0000	−0.705310
$395$	0	0
$396$	−6.00000	−0.301511
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	20.0000	1.00251
$399$	2.00000	0.100125
$400$	0	0
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	8.00000	0.399004
$403$	0	0
$404$	−10.0000	−0.497519
$405$	0	0
$406$	16.0000	0.794067
$407$	−24.0000	−1.18964
$408$	−2.00000	−0.0990148
$409$	14.0000	0.692255	0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000	0.692255	0.346128	+	0.938187i	$0.387496\pi$
$410$	0	0
$411$	−6.00000	−0.295958
$412$	0	0
$413$	8.00000	0.393654
$414$	−4.00000	−0.196589
$415$	0	0
$416$	0	0
$417$	0	0
$418$	6.00000	0.293470
$419$	−14.0000	−0.683945	−0.341972	−	0.939710i	$-0.611095\pi$
$419$	−14.0000	−0.683945	−0.341972	+	0.939710i	$0.611095\pi$
$420$	0	0
$421$	−2.00000	−0.0974740	−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000	−0.0974740	−0.0487370	+	0.998812i	$0.515520\pi$
$422$	−28.0000	−1.36302
$423$	12.0000	0.583460
$424$	−6.00000	−0.291386
$425$	0	0
$426$	0	0
$427$	−4.00000	−0.193574
$428$	12.0000	0.580042
$429$	0	0
$430$	0	0
$431$	36.0000	1.73406	0.867029	−	0.498257i	$-0.166026\pi$
$431$	36.0000	1.73406	0.867029	+	0.498257i	$0.166026\pi$
$432$	1.00000	0.0481125
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	16.0000	0.768025
$435$	0	0
$436$	−14.0000	−0.670478
$437$	4.00000	0.191346
$438$	−6.00000	−0.286691
$439$	−8.00000	−0.381819	−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000	−0.381819	−0.190910	+	0.981608i	$0.561144\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	0	0
$443$	24.0000	1.14027	0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000	1.14027	0.570137	+	0.821549i	$0.306890\pi$
$444$	4.00000	0.189832
$445$	0	0
$446$	16.0000	0.757622
$447$	22.0000	1.04056
$448$	−2.00000	−0.0944911
$449$	−4.00000	−0.188772	−0.0943858	−	0.995536i	$-0.530089\pi$
$449$	−4.00000	−0.188772	−0.0943858	+	0.995536i	$0.530089\pi$
$450$	0	0
$451$	24.0000	1.13012
$452$	−14.0000	−0.658505
$453$	0	0
$454$	28.0000	1.31411
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	14.0000	0.654892	0.327446	−	0.944870i	$-0.393812\pi$
$457$	14.0000	0.654892	0.327446	+	0.944870i	$0.393812\pi$
$458$	18.0000	0.841085
$459$	−2.00000	−0.0933520
$460$	0	0
$461$	−34.0000	−1.58354	−0.791769	−	0.610821i	$-0.790840\pi$
$461$	−34.0000	−1.58354	−0.791769	+	0.610821i	$0.790840\pi$
$462$	12.0000	0.558291
$463$	26.0000	1.20832	0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000	1.20832	0.604161	+	0.796862i	$0.293508\pi$
$464$	−8.00000	−0.371391
$465$	0	0
$466$	−14.0000	−0.648537
$467$	8.00000	0.370196	0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000	0.370196	0.185098	+	0.982720i	$0.440740\pi$
$468$	0	0
$469$	−16.0000	−0.738811
$470$	0	0
$471$	−6.00000	−0.276465
$472$	−4.00000	−0.184115
$473$	−36.0000	−1.65528
$474$	8.00000	0.367452
$475$	0	0
$476$	4.00000	0.183340
$477$	−6.00000	−0.274721
$478$	−18.0000	−0.823301
$479$	18.0000	0.822441	0.411220	−	0.911536i	$-0.365103\pi$
$479$	18.0000	0.822441	0.411220	+	0.911536i	$0.365103\pi$
$480$	0	0
$481$	0	0
$482$	−22.0000	−1.00207
$483$	8.00000	0.364013
$484$	25.0000	1.13636
$485$	0	0
$486$	1.00000	0.0453609
$487$	−16.0000	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$488$	2.00000	0.0905357
$489$	−6.00000	−0.271329
$490$	0	0
$491$	−34.0000	−1.53440	−0.767199	−	0.641409i	$-0.778350\pi$
$491$	−34.0000	−1.53440	−0.767199	+	0.641409i	$0.778350\pi$
$492$	−4.00000	−0.180334
$493$	16.0000	0.720604
$494$	0	0
$495$	0	0
$496$	−8.00000	−0.359211
$497$	0	0
$498$	−4.00000	−0.179244
$499$	24.0000	1.07439	0.537194	−	0.843459i	$-0.319484\pi$
$499$	24.0000	1.07439	0.537194	+	0.843459i	$0.319484\pi$
$500$	0	0
$501$	16.0000	0.714827
$502$	−14.0000	−0.624851
$503$	−40.0000	−1.78351	−0.891756	−	0.452517i	$-0.850526\pi$
$503$	−40.0000	−1.78351	−0.891756	+	0.452517i	$0.850526\pi$
$504$	−2.00000	−0.0890871
$505$	0	0
$506$	24.0000	1.06693
$507$	−13.0000	−0.577350
$508$	12.0000	0.532414
$509$	36.0000	1.59567	0.797836	−	0.602875i	$-0.205978\pi$
$509$	36.0000	1.59567	0.797836	+	0.602875i	$0.205978\pi$
$510$	0	0
$511$	12.0000	0.530849
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	−6.00000	−0.264649
$515$	0	0
$516$	6.00000	0.264135
$517$	−72.0000	−3.16656
$518$	−8.00000	−0.351500
$519$	−18.0000	−0.790112
$520$	0	0
$521$	24.0000	1.05146	0.525730	−	0.850652i	$-0.323792\pi$
$521$	24.0000	1.05146	0.525730	+	0.850652i	$0.323792\pi$
$522$	−8.00000	−0.350150
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	22.0000	0.961074
$525$	0	0
$526$	−16.0000	−0.697633
$527$	16.0000	0.696971
$528$	−6.00000	−0.261116
$529$	−7.00000	−0.304348
$530$	0	0
$531$	−4.00000	−0.173585
$532$	2.00000	0.0867110
$533$	0	0
$534$	−4.00000	−0.173097
$535$	0	0
$536$	8.00000	0.345547
$537$	12.0000	0.517838
$538$	8.00000	0.344904
$539$	18.0000	0.775315
$540$	0	0
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	20.0000	0.859074
$543$	2.00000	0.0858282
$544$	−2.00000	−0.0857493
$545$	0	0
$546$	0	0
$547$	−40.0000	−1.71028	−0.855138	−	0.518400i	$-0.826528\pi$
$547$	−40.0000	−1.71028	−0.855138	+	0.518400i	$0.826528\pi$
$548$	−6.00000	−0.256307
$549$	2.00000	0.0853579
$550$	0	0
$551$	8.00000	0.340811
$552$	−4.00000	−0.170251
$553$	−16.0000	−0.680389
$554$	2.00000	0.0849719
$555$	0	0
$556$	0	0
$557$	22.0000	0.932170	0.466085	−	0.884740i	$-0.345664\pi$
$557$	22.0000	0.932170	0.466085	+	0.884740i	$0.345664\pi$
$558$	−8.00000	−0.338667
$559$	0	0
$560$	0	0
$561$	12.0000	0.506640
$562$	16.0000	0.674919
$563$	−4.00000	−0.168580	−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000	−0.168580	−0.0842900	+	0.996441i	$0.526862\pi$
$564$	12.0000	0.505291
$565$	0	0
$566$	−22.0000	−0.924729
$567$	−2.00000	−0.0839921
$568$	0	0
$569$	−20.0000	−0.838444	−0.419222	−	0.907884i	$-0.637697\pi$
$569$	−20.0000	−0.838444	−0.419222	+	0.907884i	$0.637697\pi$
$570$	0	0
$571$	16.0000	0.669579	0.334790	−	0.942293i	$-0.391335\pi$
$571$	16.0000	0.669579	0.334790	+	0.942293i	$0.391335\pi$
$572$	0	0
$573$	−22.0000	−0.919063
$574$	8.00000	0.333914
$575$	0	0
$576$	1.00000	0.0416667
$577$	38.0000	1.58196	0.790980	−	0.611842i	$-0.209571\pi$
$577$	38.0000	1.58196	0.790980	+	0.611842i	$0.209571\pi$
$578$	−13.0000	−0.540729
$579$	8.00000	0.332469
$580$	0	0
$581$	8.00000	0.331896
$582$	−12.0000	−0.497416
$583$	36.0000	1.49097
$584$	−6.00000	−0.248282
$585$	0	0
$586$	−10.0000	−0.413096
$587$	−24.0000	−0.990586	−0.495293	−	0.868726i	$-0.664939\pi$
$587$	−24.0000	−0.990586	−0.495293	+	0.868726i	$0.664939\pi$
$588$	−3.00000	−0.123718
$589$	8.00000	0.329634
$590$	0	0
$591$	−14.0000	−0.575883
$592$	4.00000	0.164399
$593$	−14.0000	−0.574911	−0.287456	−	0.957794i	$-0.592809\pi$
$593$	−14.0000	−0.574911	−0.287456	+	0.957794i	$0.592809\pi$
$594$	−6.00000	−0.246183
$595$	0	0
$596$	22.0000	0.901155
$597$	20.0000	0.818546
$598$	0	0
$599$	−36.0000	−1.47092	−0.735460	−	0.677568i	$-0.763034\pi$
$599$	−36.0000	−1.47092	−0.735460	+	0.677568i	$0.763034\pi$
$600$	0	0
$601$	−10.0000	−0.407909	−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000	−0.407909	−0.203954	+	0.978980i	$0.565379\pi$
$602$	−12.0000	−0.489083
$603$	8.00000	0.325785
$604$	0	0
$605$	0	0
$606$	−10.0000	−0.406222
$607$	−40.0000	−1.62355	−0.811775	−	0.583970i	$-0.801498\pi$
$607$	−40.0000	−1.62355	−0.811775	+	0.583970i	$0.801498\pi$
$608$	−1.00000	−0.0405554
$609$	16.0000	0.648353
$610$	0	0
$611$	0	0
$612$	−2.00000	−0.0808452
$613$	10.0000	0.403896	0.201948	−	0.979396i	$-0.435273\pi$
$613$	10.0000	0.403896	0.201948	+	0.979396i	$0.435273\pi$
$614$	8.00000	0.322854
$615$	0	0
$616$	12.0000	0.483494
$617$	38.0000	1.52982	0.764911	−	0.644136i	$-0.222783\pi$
$617$	38.0000	1.52982	0.764911	+	0.644136i	$0.222783\pi$
$618$	0	0
$619$	−8.00000	−0.321547	−0.160774	−	0.986991i	$-0.551399\pi$
$619$	−8.00000	−0.321547	−0.160774	+	0.986991i	$0.551399\pi$
$620$	0	0
$621$	−4.00000	−0.160514
$622$	−6.00000	−0.240578
$623$	8.00000	0.320513
$624$	0	0
$625$	0	0
$626$	14.0000	0.559553
$627$	6.00000	0.239617
$628$	−6.00000	−0.239426
$629$	−8.00000	−0.318981
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	8.00000	0.318223
$633$	−28.0000	−1.11290
$634$	−6.00000	−0.238290
$635$	0	0
$636$	−6.00000	−0.237915
$637$	0	0
$638$	48.0000	1.90034
$639$	0	0
$640$	0	0
$641$	−12.0000	−0.473972	−0.236986	−	0.971513i	$-0.576159\pi$
$641$	−12.0000	−0.473972	−0.236986	+	0.971513i	$0.576159\pi$
$642$	12.0000	0.473602
$643$	26.0000	1.02534	0.512670	−	0.858586i	$-0.328656\pi$
$643$	26.0000	1.02534	0.512670	+	0.858586i	$0.328656\pi$
$644$	8.00000	0.315244
$645$	0	0
$646$	2.00000	0.0786889
$647$	24.0000	0.943537	0.471769	−	0.881722i	$-0.343616\pi$
$647$	24.0000	0.943537	0.471769	+	0.881722i	$0.343616\pi$
$648$	1.00000	0.0392837
$649$	24.0000	0.942082
$650$	0	0
$651$	16.0000	0.627089
$652$	−6.00000	−0.234978
$653$	18.0000	0.704394	0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000	0.704394	0.352197	+	0.935926i	$0.385435\pi$
$654$	−14.0000	−0.547443
$655$	0	0
$656$	−4.00000	−0.156174
$657$	−6.00000	−0.234082
$658$	−24.0000	−0.935617
$659$	−48.0000	−1.86981	−0.934907	−	0.354892i	$-0.884518\pi$
$659$	−48.0000	−1.86981	−0.934907	+	0.354892i	$0.884518\pi$
$660$	0	0
$661$	26.0000	1.01128	0.505641	−	0.862744i	$-0.331256\pi$
$661$	26.0000	1.01128	0.505641	+	0.862744i	$0.331256\pi$
$662$	−20.0000	−0.777322
$663$	0	0
$664$	−4.00000	−0.155230
$665$	0	0
$666$	4.00000	0.154997
$667$	32.0000	1.23904
$668$	16.0000	0.619059
$669$	16.0000	0.618596
$670$	0	0
$671$	−12.0000	−0.463255
$672$	−2.00000	−0.0771517
$673$	28.0000	1.07932	0.539660	−	0.841883i	$-0.318553\pi$
$673$	28.0000	1.07932	0.539660	+	0.841883i	$0.318553\pi$
$674$	20.0000	0.770371
$675$	0	0
$676$	−13.0000	−0.500000
$677$	−22.0000	−0.845529	−0.422764	−	0.906240i	$-0.638940\pi$
$677$	−22.0000	−0.845529	−0.422764	+	0.906240i	$0.638940\pi$
$678$	−14.0000	−0.537667
$679$	24.0000	0.921035
$680$	0	0
$681$	28.0000	1.07296
$682$	48.0000	1.83801
$683$	36.0000	1.37750	0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000	1.37750	0.688751	+	0.724998i	$0.258159\pi$
$684$	−1.00000	−0.0382360
$685$	0	0
$686$	20.0000	0.763604
$687$	18.0000	0.686743
$688$	6.00000	0.228748
$689$	0	0
$690$	0	0
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	−18.0000	−0.684257
$693$	12.0000	0.455842
$694$	−36.0000	−1.36654
$695$	0	0
$696$	−8.00000	−0.303239
$697$	8.00000	0.303022
$698$	−2.00000	−0.0757011
$699$	−14.0000	−0.529529
$700$	0	0
$701$	6.00000	0.226617	0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000	0.226617	0.113308	+	0.993560i	$0.463855\pi$
$702$	0	0
$703$	−4.00000	−0.150863
$704$	−6.00000	−0.226134
$705$	0	0
$706$	18.0000	0.677439
$707$	20.0000	0.752177
$708$	−4.00000	−0.150329
$709$	50.0000	1.87779	0.938895	−	0.344204i	$-0.111851\pi$
$709$	50.0000	1.87779	0.938895	+	0.344204i	$0.111851\pi$
$710$	0	0
$711$	8.00000	0.300023
$712$	−4.00000	−0.149906
$713$	32.0000	1.19841
$714$	4.00000	0.149696
$715$	0	0
$716$	12.0000	0.448461
$717$	−18.0000	−0.672222
$718$	−6.00000	−0.223918
$719$	14.0000	0.522112	0.261056	−	0.965324i	$-0.415929\pi$
$719$	14.0000	0.522112	0.261056	+	0.965324i	$0.415929\pi$
$720$	0	0
$721$	0	0
$722$	1.00000	0.0372161
$723$	−22.0000	−0.818189
$724$	2.00000	0.0743294
$725$	0	0
$726$	25.0000	0.927837
$727$	−14.0000	−0.519231	−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000	−0.519231	−0.259616	+	0.965712i	$0.583596\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	−12.0000	−0.443836
$732$	2.00000	0.0739221
$733$	−18.0000	−0.664845	−0.332423	−	0.943131i	$-0.607866\pi$
$733$	−18.0000	−0.664845	−0.332423	+	0.943131i	$0.607866\pi$
$734$	10.0000	0.369107
$735$	0	0
$736$	−4.00000	−0.147442
$737$	−48.0000	−1.76810
$738$	−4.00000	−0.147242
$739$	−28.0000	−1.03000	−0.514998	−	0.857191i	$-0.672207\pi$
$739$	−28.0000	−1.03000	−0.514998	+	0.857191i	$0.672207\pi$
$740$	0	0
$741$	0	0
$742$	12.0000	0.440534
$743$	8.00000	0.293492	0.146746	−	0.989174i	$-0.453120\pi$
$743$	8.00000	0.293492	0.146746	+	0.989174i	$0.453120\pi$
$744$	−8.00000	−0.293294
$745$	0	0
$746$	24.0000	0.878702
$747$	−4.00000	−0.146352
$748$	12.0000	0.438763
$749$	−24.0000	−0.876941
$750$	0	0
$751$	40.0000	1.45962	0.729810	−	0.683650i	$-0.239608\pi$
$751$	40.0000	1.45962	0.729810	+	0.683650i	$0.239608\pi$
$752$	12.0000	0.437595
$753$	−14.0000	−0.510188
$754$	0	0
$755$	0	0
$756$	−2.00000	−0.0727393
$757$	38.0000	1.38113	0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000	1.38113	0.690567	+	0.723269i	$0.257361\pi$
$758$	20.0000	0.726433
$759$	24.0000	0.871145
$760$	0	0
$761$	−18.0000	−0.652499	−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000	−0.652499	−0.326250	+	0.945284i	$0.605785\pi$
$762$	12.0000	0.434714
$763$	28.0000	1.01367
$764$	−22.0000	−0.795932
$765$	0	0
$766$	−24.0000	−0.867155
$767$	0	0
$768$	1.00000	0.0360844
$769$	−14.0000	−0.504853	−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000	−0.504853	−0.252426	+	0.967616i	$0.581229\pi$
$770$	0	0
$771$	−6.00000	−0.216085
$772$	8.00000	0.287926
$773$	−6.00000	−0.215805	−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000	−0.215805	−0.107903	+	0.994161i	$0.534413\pi$
$774$	6.00000	0.215666
$775$	0	0
$776$	−12.0000	−0.430775
$777$	−8.00000	−0.286998
$778$	−30.0000	−1.07555
$779$	4.00000	0.143315
$780$	0	0
$781$	0	0
$782$	8.00000	0.286079
$783$	−8.00000	−0.285897
$784$	−3.00000	−0.107143
$785$	0	0
$786$	22.0000	0.784714
$787$	−44.0000	−1.56843	−0.784215	−	0.620489i	$-0.786934\pi$
$787$	−44.0000	−1.56843	−0.784215	+	0.620489i	$0.786934\pi$
$788$	−14.0000	−0.498729
$789$	−16.0000	−0.569615
$790$	0	0
$791$	28.0000	0.995565
$792$	−6.00000	−0.213201
$793$	0	0
$794$	−22.0000	−0.780751
$795$	0	0
$796$	20.0000	0.708881
$797$	−2.00000	−0.0708436	−0.0354218	−	0.999372i	$-0.511277\pi$
$797$	−2.00000	−0.0708436	−0.0354218	+	0.999372i	$0.511277\pi$
$798$	2.00000	0.0707992
$799$	−24.0000	−0.849059
$800$	0	0
$801$	−4.00000	−0.141333
$802$	0	0
$803$	36.0000	1.27041
$804$	8.00000	0.282138
$805$	0	0
$806$	0	0
$807$	8.00000	0.281613
$808$	−10.0000	−0.351799
$809$	−30.0000	−1.05474	−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000	−1.05474	−0.527372	+	0.849635i	$0.676823\pi$
$810$	0	0
$811$	−28.0000	−0.983213	−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000	−0.983213	−0.491606	+	0.870817i	$0.663590\pi$
$812$	16.0000	0.561490
$813$	20.0000	0.701431
$814$	−24.0000	−0.841200
$815$	0	0
$816$	−2.00000	−0.0700140
$817$	−6.00000	−0.209913
$818$	14.0000	0.489499
$819$	0	0
$820$	0	0
$821$	−50.0000	−1.74501	−0.872506	−	0.488603i	$-0.837507\pi$
$821$	−50.0000	−1.74501	−0.872506	+	0.488603i	$0.837507\pi$
$822$	−6.00000	−0.209274
$823$	−14.0000	−0.488009	−0.244005	−	0.969774i	$-0.578461\pi$
$823$	−14.0000	−0.488009	−0.244005	+	0.969774i	$0.578461\pi$
$824$	0	0
$825$	0	0
$826$	8.00000	0.278356
$827$	36.0000	1.25184	0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000	1.25184	0.625921	+	0.779886i	$0.284723\pi$
$828$	−4.00000	−0.139010
$829$	−30.0000	−1.04194	−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000	−1.04194	−0.520972	+	0.853574i	$0.674430\pi$
$830$	0	0
$831$	2.00000	0.0693792
$832$	0	0
$833$	6.00000	0.207888
$834$	0	0
$835$	0	0
$836$	6.00000	0.207514
$837$	−8.00000	−0.276520
$838$	−14.0000	−0.483622
$839$	24.0000	0.828572	0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000	0.828572	0.414286	+	0.910147i	$0.364031\pi$
$840$	0	0
$841$	35.0000	1.20690
$842$	−2.00000	−0.0689246
$843$	16.0000	0.551069
$844$	−28.0000	−0.963800
$845$	0	0
$846$	12.0000	0.412568
$847$	−50.0000	−1.71802
$848$	−6.00000	−0.206041
$849$	−22.0000	−0.755038
$850$	0	0
$851$	−16.0000	−0.548473
$852$	0	0
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	−4.00000	−0.136877
$855$	0	0
$856$	12.0000	0.410152
$857$	−18.0000	−0.614868	−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000	−0.614868	−0.307434	+	0.951569i	$0.599470\pi$
$858$	0	0
$859$	20.0000	0.682391	0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000	0.682391	0.341196	+	0.939992i	$0.389168\pi$
$860$	0	0
$861$	8.00000	0.272639
$862$	36.0000	1.22616
$863$	−24.0000	−0.816970	−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000	−0.816970	−0.408485	+	0.912765i	$0.633943\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	0	0
$867$	−13.0000	−0.441503
$868$	16.0000	0.543075
$869$	−48.0000	−1.62829
$870$	0	0
$871$	0	0
$872$	−14.0000	−0.474100
$873$	−12.0000	−0.406138
$874$	4.00000	0.135302
$875$	0	0
$876$	−6.00000	−0.202721
$877$	32.0000	1.08056	0.540282	−	0.841484i	$-0.318318\pi$
$877$	32.0000	1.08056	0.540282	+	0.841484i	$0.318318\pi$
$878$	−8.00000	−0.269987
$879$	−10.0000	−0.337292
$880$	0	0
$881$	14.0000	0.471672	0.235836	−	0.971793i	$-0.424217\pi$
$881$	14.0000	0.471672	0.235836	+	0.971793i	$0.424217\pi$
$882$	−3.00000	−0.101015
$883$	−14.0000	−0.471138	−0.235569	−	0.971858i	$-0.575695\pi$
$883$	−14.0000	−0.471138	−0.235569	+	0.971858i	$0.575695\pi$
$884$	0	0
$885$	0	0
$886$	24.0000	0.806296
$887$	8.00000	0.268614	0.134307	−	0.990940i	$-0.457119\pi$
$887$	8.00000	0.268614	0.134307	+	0.990940i	$0.457119\pi$
$888$	4.00000	0.134231
$889$	−24.0000	−0.804934
$890$	0	0
$891$	−6.00000	−0.201008
$892$	16.0000	0.535720
$893$	−12.0000	−0.401565
$894$	22.0000	0.735790
$895$	0	0
$896$	−2.00000	−0.0668153
$897$	0	0
$898$	−4.00000	−0.133482
$899$	64.0000	2.13452
$900$	0	0
$901$	12.0000	0.399778
$902$	24.0000	0.799113
$903$	−12.0000	−0.399335
$904$	−14.0000	−0.465633
$905$	0	0
$906$	0	0
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	28.0000	0.929213
$909$	−10.0000	−0.331679
$910$	0	0
$911$	16.0000	0.530104	0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000	0.530104	0.265052	+	0.964234i	$0.414611\pi$
$912$	−1.00000	−0.0331133
$913$	24.0000	0.794284
$914$	14.0000	0.463079
$915$	0	0
$916$	18.0000	0.594737
$917$	−44.0000	−1.45301
$918$	−2.00000	−0.0660098
$919$	32.0000	1.05558	0.527791	−	0.849374i	$-0.323020\pi$
$919$	32.0000	1.05558	0.527791	+	0.849374i	$0.323020\pi$
$920$	0	0
$921$	8.00000	0.263609
$922$	−34.0000	−1.11973
$923$	0	0
$924$	12.0000	0.394771
$925$	0	0
$926$	26.0000	0.854413
$927$	0	0
$928$	−8.00000	−0.262613
$929$	−6.00000	−0.196854	−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000	−0.196854	−0.0984268	+	0.995144i	$0.531381\pi$
$930$	0	0
$931$	3.00000	0.0983210
$932$	−14.0000	−0.458585
$933$	−6.00000	−0.196431
$934$	8.00000	0.261768
$935$	0	0
$936$	0	0
$937$	34.0000	1.11073	0.555366	−	0.831606i	$-0.312578\pi$
$937$	34.0000	1.11073	0.555366	+	0.831606i	$0.312578\pi$
$938$	−16.0000	−0.522419
$939$	14.0000	0.456873
$940$	0	0
$941$	−40.0000	−1.30396	−0.651981	−	0.758235i	$-0.726062\pi$
$941$	−40.0000	−1.30396	−0.651981	+	0.758235i	$0.726062\pi$
$942$	−6.00000	−0.195491
$943$	16.0000	0.521032
$944$	−4.00000	−0.130189
$945$	0	0
$946$	−36.0000	−1.17046
$947$	−44.0000	−1.42981	−0.714904	−	0.699223i	$-0.753530\pi$
$947$	−44.0000	−1.42981	−0.714904	+	0.699223i	$0.753530\pi$
$948$	8.00000	0.259828
$949$	0	0
$950$	0	0
$951$	−6.00000	−0.194563
$952$	4.00000	0.129641
$953$	34.0000	1.10137	0.550684	−	0.834714i	$-0.314367\pi$
$953$	34.0000	1.10137	0.550684	+	0.834714i	$0.314367\pi$
$954$	−6.00000	−0.194257
$955$	0	0
$956$	−18.0000	−0.582162
$957$	48.0000	1.55162
$958$	18.0000	0.581554
$959$	12.0000	0.387500
$960$	0	0
$961$	33.0000	1.06452
$962$	0	0
$963$	12.0000	0.386695
$964$	−22.0000	−0.708572
$965$	0	0
$966$	8.00000	0.257396
$967$	18.0000	0.578841	0.289420	−	0.957202i	$-0.406537\pi$
$967$	18.0000	0.578841	0.289420	+	0.957202i	$0.406537\pi$
$968$	25.0000	0.803530
$969$	2.00000	0.0642493
$970$	0	0
$971$	−24.0000	−0.770197	−0.385098	−	0.922876i	$-0.625832\pi$
$971$	−24.0000	−0.770197	−0.385098	+	0.922876i	$0.625832\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−16.0000	−0.512673
$975$	0	0
$976$	2.00000	0.0640184
$977$	−42.0000	−1.34370	−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000	−1.34370	−0.671850	+	0.740688i	$0.734500\pi$
$978$	−6.00000	−0.191859
$979$	24.0000	0.767043
$980$	0	0
$981$	−14.0000	−0.446986
$982$	−34.0000	−1.08498
$983$	−24.0000	−0.765481	−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000	−0.765481	−0.382741	+	0.923856i	$0.625020\pi$
$984$	−4.00000	−0.127515
$985$	0	0
$986$	16.0000	0.509544
$987$	−24.0000	−0.763928
$988$	0	0
$989$	−24.0000	−0.763156
$990$	0	0
$991$	8.00000	0.254128	0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000	0.254128	0.127064	+	0.991894i	$0.459445\pi$
$992$	−8.00000	−0.254000
$993$	−20.0000	−0.634681
$994$	0	0
$995$	0	0
$996$	−4.00000	−0.126745
$997$	58.0000	1.83688	0.918439	−	0.395562i	$-0.129450\pi$
$997$	58.0000	1.83688	0.918439	+	0.395562i	$0.129450\pi$
$998$	24.0000	0.759707
$999$	4.00000	0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2850.2.a.y.1.1		1
3.2	odd	2		8550.2.a.g.1.1		1
5.2	odd	4		2850.2.d.j.799.2		2
5.3	odd	4		2850.2.d.j.799.1		2
5.4	even	2		570.2.a.b.1.1	✓	1
15.14	odd	2		1710.2.a.s.1.1		1
20.19	odd	2		4560.2.a.r.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.a.b.1.1	✓	1	5.4	even	2
1710.2.a.s.1.1		1	15.14	odd	2
2850.2.a.y.1.1		1	1.1	even	1	trivial
2850.2.d.j.799.1		2	5.3	odd	4
2850.2.d.j.799.2		2	5.2	odd	4
4560.2.a.r.1.1		1	20.19	odd	2
8550.2.a.g.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:	\( N \)	\(=\)	\( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2850.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more