LMFDB - Embedded newform 7935.2.a.c.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7935,2,Mod(1,7935)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7935.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7935, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-2,1,2,1,-2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	7935.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q-2.00000 q^{2} +1.00000 q^{3} +2.00000 q^{4} +1.00000 q^{5} -2.00000 q^{6} +2.00000 q^{7} +1.00000 q^{9} -2.00000 q^{10} +5.00000 q^{11} +2.00000 q^{12} -4.00000 q^{14} +1.00000 q^{15} -4.00000 q^{16} -4.00000 q^{17} -2.00000 q^{18} +1.00000 q^{19} +2.00000 q^{20} +2.00000 q^{21} -10.0000 q^{22} +1.00000 q^{25} +1.00000 q^{27} +4.00000 q^{28} +2.00000 q^{29} -2.00000 q^{30} +7.00000 q^{31} +8.00000 q^{32} +5.00000 q^{33} +8.00000 q^{34} +2.00000 q^{35} +2.00000 q^{36} +10.0000 q^{37} -2.00000 q^{38} -1.00000 q^{41} -4.00000 q^{42} -10.0000 q^{43} +10.0000 q^{44} +1.00000 q^{45} -6.00000 q^{47} -4.00000 q^{48} -3.00000 q^{49} -2.00000 q^{50} -4.00000 q^{51} +6.00000 q^{53} -2.00000 q^{54} +5.00000 q^{55} +1.00000 q^{57} -4.00000 q^{58} +2.00000 q^{60} -9.00000 q^{61} -14.0000 q^{62} +2.00000 q^{63} -8.00000 q^{64} -10.0000 q^{66} -14.0000 q^{67} -8.00000 q^{68} -4.00000 q^{70} +5.00000 q^{71} +10.0000 q^{73} -20.0000 q^{74} +1.00000 q^{75} +2.00000 q^{76} +10.0000 q^{77} +11.0000 q^{79} -4.00000 q^{80} +1.00000 q^{81} +2.00000 q^{82} -6.00000 q^{83} +4.00000 q^{84} -4.00000 q^{85} +20.0000 q^{86} +2.00000 q^{87} +10.0000 q^{89} -2.00000 q^{90} +7.00000 q^{93} +12.0000 q^{94} +1.00000 q^{95} +8.00000 q^{96} -2.00000 q^{97} +6.00000 q^{98} +5.00000 q^{99} +O(q^{100})\)

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 $

$2$	−2.00000	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	−2.00000	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.00000	1.00000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.00000	−0.816497
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	−2.00000	−0.632456
$11$	5.00000	1.50756	0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	2.00000	0.577350
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	−4.00000	−1.06904
$15$	1.00000	0.258199
$16$	−4.00000	−1.00000
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	−2.00000	−0.471405
$19$	1.00000	0.229416	0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000	0.229416	0.114708	+	0.993399i	$0.463407\pi$
$20$	2.00000	0.447214
$21$	2.00000	0.436436
$22$	−10.0000	−2.13201
$23$	0	0
$23$	0	0
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	1.00000	0.192450
$28$	4.00000	0.755929
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	−2.00000	−0.365148
$31$	7.00000	1.25724	0.628619	−	0.777714i	$-0.283621\pi$
$31$	7.00000	1.25724	0.628619	+	0.777714i	$0.283621\pi$
$32$	8.00000	1.41421
$33$	5.00000	0.870388
$34$	8.00000	1.37199
$35$	2.00000	0.338062
$36$	2.00000	0.333333
$37$	10.0000	1.64399	0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000	1.64399	0.821995	+	0.569495i	$0.192861\pi$
$38$	−2.00000	−0.324443
$39$	0	0
$40$	0	0
$41$	−1.00000	−0.156174	−0.0780869	−	0.996947i	$-0.524881\pi$
$41$	−1.00000	−0.156174	−0.0780869	+	0.996947i	$0.524881\pi$
$42$	−4.00000	−0.617213
$43$	−10.0000	−1.52499	−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000	−1.52499	−0.762493	+	0.646997i	$0.776025\pi$
$44$	10.0000	1.50756
$45$	1.00000	0.149071
$46$	0	0
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	−4.00000	−0.577350
$49$	−3.00000	−0.428571
$50$	−2.00000	−0.282843
$51$	−4.00000	−0.560112
$52$	0	0
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	−2.00000	−0.272166
$55$	5.00000	0.674200
$56$	0	0
$57$	1.00000	0.132453
$58$	−4.00000	−0.525226
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	2.00000	0.258199
$61$	−9.00000	−1.15233	−0.576166	−	0.817333i	$-0.695452\pi$
$61$	−9.00000	−1.15233	−0.576166	+	0.817333i	$0.695452\pi$
$62$	−14.0000	−1.77800
$63$	2.00000	0.251976
$64$	−8.00000	−1.00000
$65$	0	0
$66$	−10.0000	−1.23091
$67$	−14.0000	−1.71037	−0.855186	−	0.518321i	$-0.826557\pi$
$67$	−14.0000	−1.71037	−0.855186	+	0.518321i	$0.826557\pi$
$68$	−8.00000	−0.970143
$69$	0	0
$70$	−4.00000	−0.478091
$71$	5.00000	0.593391	0.296695	−	0.954972i	$-0.404115\pi$
$71$	5.00000	0.593391	0.296695	+	0.954972i	$0.404115\pi$
$72$	0	0
$73$	10.0000	1.17041	0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000	1.17041	0.585206	+	0.810885i	$0.301014\pi$
$74$	−20.0000	−2.32495
$75$	1.00000	0.115470
$76$	2.00000	0.229416
$77$	10.0000	1.13961
$78$	0	0
$79$	11.0000	1.23760	0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000	1.23760	0.618798	+	0.785550i	$0.287620\pi$
$80$	−4.00000	−0.447214
$81$	1.00000	0.111111
$82$	2.00000	0.220863
$83$	−6.00000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	4.00000	0.436436
$85$	−4.00000	−0.433861
$86$	20.0000	2.15666
$87$	2.00000	0.214423
$88$	0	0
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	−2.00000	−0.210819
$91$	0	0
$92$	0	0
$93$	7.00000	0.725866
$94$	12.0000	1.23771
$95$	1.00000	0.102598
$96$	8.00000	0.816497
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	6.00000	0.606092
$99$	5.00000	0.502519
$100$	2.00000	0.200000
$101$	17.0000	1.69156	0.845782	−	0.533529i	$-0.179135\pi$
$101$	17.0000	1.69156	0.845782	+	0.533529i	$0.179135\pi$
$102$	8.00000	0.792118
$103$	12.0000	1.18240	0.591198	−	0.806527i	$-0.298655\pi$
$103$	12.0000	1.18240	0.591198	+	0.806527i	$0.298655\pi$
$104$	0	0
$105$	2.00000	0.195180
$106$	−12.0000	−1.16554
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	2.00000	0.192450
$109$	1.00000	0.0957826	0.0478913	−	0.998853i	$-0.484750\pi$
$109$	1.00000	0.0957826	0.0478913	+	0.998853i	$0.484750\pi$
$110$	−10.0000	−0.953463
$111$	10.0000	0.949158
$112$	−8.00000	−0.755929
$113$	8.00000	0.752577	0.376288	−	0.926503i	$-0.377200\pi$
$113$	8.00000	0.752577	0.376288	+	0.926503i	$0.377200\pi$
$114$	−2.00000	−0.187317
$115$	0	0
$116$	4.00000	0.371391
$117$	0	0
$118$	0	0
$119$	−8.00000	−0.733359
$120$	0	0
$121$	14.0000	1.27273
$122$	18.0000	1.62964
$123$	−1.00000	−0.0901670
$124$	14.0000	1.25724
$125$	1.00000	0.0894427
$126$	−4.00000	−0.356348
$127$	12.0000	1.06483	0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000	1.06483	0.532414	+	0.846484i	$0.321285\pi$
$128$	0	0
$129$	−10.0000	−0.880451
$130$	0	0
$131$	−7.00000	−0.611593	−0.305796	−	0.952097i	$-0.598923\pi$
$131$	−7.00000	−0.611593	−0.305796	+	0.952097i	$0.598923\pi$
$132$	10.0000	0.870388
$133$	2.00000	0.173422
$134$	28.0000	2.41883
$135$	1.00000	0.0860663
$136$	0	0
$137$	16.0000	1.36697	0.683486	−	0.729964i	$-0.260463\pi$
$137$	16.0000	1.36697	0.683486	+	0.729964i	$0.260463\pi$
$138$	0	0
$139$	−5.00000	−0.424094	−0.212047	−	0.977259i	$-0.568013\pi$
$139$	−5.00000	−0.424094	−0.212047	+	0.977259i	$0.568013\pi$
$140$	4.00000	0.338062
$141$	−6.00000	−0.505291
$142$	−10.0000	−0.839181
$143$	0	0
$144$	−4.00000	−0.333333
$145$	2.00000	0.166091
$146$	−20.0000	−1.65521
$147$	−3.00000	−0.247436
$148$	20.0000	1.64399
$149$	15.0000	1.22885	0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000	1.22885	0.614424	+	0.788976i	$0.289388\pi$
$150$	−2.00000	−0.163299
$151$	17.0000	1.38344	0.691720	−	0.722166i	$-0.256853\pi$
$151$	17.0000	1.38344	0.691720	+	0.722166i	$0.256853\pi$
$152$	0	0
$153$	−4.00000	−0.323381
$154$	−20.0000	−1.61165
$155$	7.00000	0.562254
$156$	0	0
$157$	−22.0000	−1.75579	−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000	−1.75579	−0.877896	+	0.478852i	$0.841053\pi$
$158$	−22.0000	−1.75023
$159$	6.00000	0.475831
$160$	8.00000	0.632456
$161$	0	0
$162$	−2.00000	−0.157135
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	−2.00000	−0.156174
$165$	5.00000	0.389249
$166$	12.0000	0.931381
$167$	14.0000	1.08335	0.541676	−	0.840587i	$-0.317790\pi$
$167$	14.0000	1.08335	0.541676	+	0.840587i	$0.317790\pi$
$168$	0	0
$169$	−13.0000	−1.00000
$170$	8.00000	0.613572
$171$	1.00000	0.0764719
$172$	−20.0000	−1.52499
$173$	14.0000	1.06440	0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000	1.06440	0.532200	+	0.846619i	$0.321365\pi$
$174$	−4.00000	−0.303239
$175$	2.00000	0.151186
$176$	−20.0000	−1.50756
$177$	0	0
$178$	−20.0000	−1.49906
$179$	−15.0000	−1.12115	−0.560576	−	0.828103i	$-0.689420\pi$
$179$	−15.0000	−1.12115	−0.560576	+	0.828103i	$0.689420\pi$
$180$	2.00000	0.149071
$181$	−7.00000	−0.520306	−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000	−0.520306	−0.260153	+	0.965567i	$0.583773\pi$
$182$	0	0
$183$	−9.00000	−0.665299
$184$	0	0
$185$	10.0000	0.735215
$186$	−14.0000	−1.02653
$187$	−20.0000	−1.46254
$188$	−12.0000	−0.875190
$189$	2.00000	0.145479
$190$	−2.00000	−0.145095
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	−8.00000	−0.577350
$193$	12.0000	0.863779	0.431889	−	0.901927i	$-0.357847\pi$
$193$	12.0000	0.863779	0.431889	+	0.901927i	$0.357847\pi$
$194$	4.00000	0.287183
$195$	0	0
$196$	−6.00000	−0.428571
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	−10.0000	−0.710669
$199$	21.0000	1.48865	0.744325	−	0.667817i	$-0.232771\pi$
$199$	21.0000	1.48865	0.744325	+	0.667817i	$0.232771\pi$
$200$	0	0
$201$	−14.0000	−0.987484
$202$	−34.0000	−2.39223
$203$	4.00000	0.280745
$204$	−8.00000	−0.560112
$205$	−1.00000	−0.0698430
$206$	−24.0000	−1.67216
$207$	0	0
$208$	0	0
$209$	5.00000	0.345857
$210$	−4.00000	−0.276026
$211$	−7.00000	−0.481900	−0.240950	−	0.970538i	$-0.577459\pi$
$211$	−7.00000	−0.481900	−0.240950	+	0.970538i	$0.577459\pi$
$212$	12.0000	0.824163
$213$	5.00000	0.342594
$214$	0	0
$215$	−10.0000	−0.681994
$216$	0	0
$217$	14.0000	0.950382
$218$	−2.00000	−0.135457
$219$	10.0000	0.675737
$220$	10.0000	0.674200
$221$	0	0
$222$	−20.0000	−1.34231
$223$	−24.0000	−1.60716	−0.803579	−	0.595198i	$-0.797074\pi$
$223$	−24.0000	−1.60716	−0.803579	+	0.595198i	$0.797074\pi$
$224$	16.0000	1.06904
$225$	1.00000	0.0666667
$226$	−16.0000	−1.06430
$227$	24.0000	1.59294	0.796468	−	0.604681i	$-0.206699\pi$
$227$	24.0000	1.59294	0.796468	+	0.604681i	$0.206699\pi$
$228$	2.00000	0.132453
$229$	−21.0000	−1.38772	−0.693860	−	0.720110i	$-0.744091\pi$
$229$	−21.0000	−1.38772	−0.693860	+	0.720110i	$0.744091\pi$
$230$	0	0
$231$	10.0000	0.657952
$232$	0	0
$233$	−26.0000	−1.70332	−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000	−1.70332	−0.851658	+	0.524097i	$0.824403\pi$
$234$	0	0
$235$	−6.00000	−0.391397
$236$	0	0
$237$	11.0000	0.714527
$238$	16.0000	1.03713
$239$	11.0000	0.711531	0.355765	−	0.934575i	$-0.384220\pi$
$239$	11.0000	0.711531	0.355765	+	0.934575i	$0.384220\pi$
$240$	−4.00000	−0.258199
$241$	−25.0000	−1.61039	−0.805196	−	0.593009i	$-0.797940\pi$
$241$	−25.0000	−1.61039	−0.805196	+	0.593009i	$0.797940\pi$
$242$	−28.0000	−1.79991
$243$	1.00000	0.0641500
$244$	−18.0000	−1.15233
$245$	−3.00000	−0.191663
$246$	2.00000	0.127515
$247$	0	0
$248$	0	0
$249$	−6.00000	−0.380235
$250$	−2.00000	−0.126491
$251$	3.00000	0.189358	0.0946792	−	0.995508i	$-0.469817\pi$
$251$	3.00000	0.189358	0.0946792	+	0.995508i	$0.469817\pi$
$252$	4.00000	0.251976
$253$	0	0
$254$	−24.0000	−1.50589
$255$	−4.00000	−0.250490
$256$	16.0000	1.00000
$257$	6.00000	0.374270	0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000	0.374270	0.187135	+	0.982334i	$0.440080\pi$
$258$	20.0000	1.24515
$259$	20.0000	1.24274
$260$	0	0
$261$	2.00000	0.123797
$262$	14.0000	0.864923
$263$	12.0000	0.739952	0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000	0.739952	0.369976	+	0.929041i	$0.379366\pi$
$264$	0	0
$265$	6.00000	0.368577
$266$	−4.00000	−0.245256
$267$	10.0000	0.611990
$268$	−28.0000	−1.71037
$269$	1.00000	0.0609711	0.0304855	−	0.999535i	$-0.490295\pi$
$269$	1.00000	0.0609711	0.0304855	+	0.999535i	$0.490295\pi$
$270$	−2.00000	−0.121716
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	16.0000	0.970143
$273$	0	0
$274$	−32.0000	−1.93319
$275$	5.00000	0.301511
$276$	0	0
$277$	−22.0000	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$278$	10.0000	0.599760
$279$	7.00000	0.419079
$280$	0	0
$281$	21.0000	1.25275	0.626377	−	0.779520i	$-0.284537\pi$
$281$	21.0000	1.25275	0.626377	+	0.779520i	$0.284537\pi$
$282$	12.0000	0.714590
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	10.0000	0.593391
$285$	1.00000	0.0592349
$286$	0	0
$287$	−2.00000	−0.118056
$288$	8.00000	0.471405
$289$	−1.00000	−0.0588235
$290$	−4.00000	−0.234888
$291$	−2.00000	−0.117242
$292$	20.0000	1.17041
$293$	16.0000	0.934730	0.467365	−	0.884064i	$-0.345203\pi$
$293$	16.0000	0.934730	0.467365	+	0.884064i	$0.345203\pi$
$294$	6.00000	0.349927
$295$	0	0
$296$	0	0
$297$	5.00000	0.290129
$298$	−30.0000	−1.73785
$299$	0	0
$300$	2.00000	0.115470
$301$	−20.0000	−1.15278
$302$	−34.0000	−1.95648
$303$	17.0000	0.976624
$304$	−4.00000	−0.229416
$305$	−9.00000	−0.515339
$306$	8.00000	0.457330
$307$	−10.0000	−0.570730	−0.285365	−	0.958419i	$-0.592115\pi$
$307$	−10.0000	−0.570730	−0.285365	+	0.958419i	$0.592115\pi$
$308$	20.0000	1.13961
$309$	12.0000	0.682656
$310$	−14.0000	−0.795147
$311$	24.0000	1.36092	0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000	1.36092	0.680458	+	0.732787i	$0.261781\pi$
$312$	0	0
$313$	16.0000	0.904373	0.452187	−	0.891923i	$-0.350644\pi$
$313$	16.0000	0.904373	0.452187	+	0.891923i	$0.350644\pi$
$314$	44.0000	2.48306
$315$	2.00000	0.112687
$316$	22.0000	1.23760
$317$	−30.0000	−1.68497	−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000	−1.68497	−0.842484	+	0.538721i	$0.818908\pi$
$318$	−12.0000	−0.672927
$319$	10.0000	0.559893
$320$	−8.00000	−0.447214
$321$	0	0
$322$	0	0
$323$	−4.00000	−0.222566
$324$	2.00000	0.111111
$325$	0	0
$326$	8.00000	0.443079
$327$	1.00000	0.0553001
$328$	0	0
$329$	−12.0000	−0.661581
$330$	−10.0000	−0.550482
$331$	−9.00000	−0.494685	−0.247342	−	0.968928i	$-0.579557\pi$
$331$	−9.00000	−0.494685	−0.247342	+	0.968928i	$0.579557\pi$
$332$	−12.0000	−0.658586
$333$	10.0000	0.547997
$334$	−28.0000	−1.53209
$335$	−14.0000	−0.764902
$336$	−8.00000	−0.436436
$337$	−16.0000	−0.871576	−0.435788	−	0.900049i	$-0.643530\pi$
$337$	−16.0000	−0.871576	−0.435788	+	0.900049i	$0.643530\pi$
$338$	26.0000	1.41421
$339$	8.00000	0.434500
$340$	−8.00000	−0.433861
$341$	35.0000	1.89536
$342$	−2.00000	−0.108148
$343$	−20.0000	−1.07990
$344$	0	0
$345$	0	0
$346$	−28.0000	−1.50529
$347$	−30.0000	−1.61048	−0.805242	−	0.592946i	$-0.797965\pi$
$347$	−30.0000	−1.61048	−0.805242	+	0.592946i	$0.797965\pi$
$348$	4.00000	0.214423
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	−4.00000	−0.213809
$351$	0	0
$352$	40.0000	2.13201
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	0	0
$355$	5.00000	0.265372
$356$	20.0000	1.06000
$357$	−8.00000	−0.423405
$358$	30.0000	1.58555
$359$	−8.00000	−0.422224	−0.211112	−	0.977462i	$-0.567708\pi$
$359$	−8.00000	−0.422224	−0.211112	+	0.977462i	$0.567708\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	14.0000	0.735824
$363$	14.0000	0.734809
$364$	0	0
$365$	10.0000	0.523424
$366$	18.0000	0.940875
$367$	−28.0000	−1.46159	−0.730794	−	0.682598i	$-0.760850\pi$
$367$	−28.0000	−1.46159	−0.730794	+	0.682598i	$0.760850\pi$
$368$	0	0
$369$	−1.00000	−0.0520579
$370$	−20.0000	−1.03975
$371$	12.0000	0.623009
$372$	14.0000	0.725866
$373$	32.0000	1.65690	0.828449	−	0.560065i	$-0.189224\pi$
$373$	32.0000	1.65690	0.828449	+	0.560065i	$0.189224\pi$
$374$	40.0000	2.06835
$375$	1.00000	0.0516398
$376$	0	0
$377$	0	0
$378$	−4.00000	−0.205738
$379$	−4.00000	−0.205466	−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000	−0.205466	−0.102733	+	0.994709i	$0.532759\pi$
$380$	2.00000	0.102598
$381$	12.0000	0.614779
$382$	0	0
$383$	34.0000	1.73732	0.868659	−	0.495410i	$-0.164982\pi$
$383$	34.0000	1.73732	0.868659	+	0.495410i	$0.164982\pi$
$384$	0	0
$385$	10.0000	0.509647
$386$	−24.0000	−1.22157
$387$	−10.0000	−0.508329
$388$	−4.00000	−0.203069
$389$	−25.0000	−1.26755	−0.633775	−	0.773517i	$-0.718496\pi$
$389$	−25.0000	−1.26755	−0.633775	+	0.773517i	$0.718496\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	−7.00000	−0.353103
$394$	36.0000	1.81365
$395$	11.0000	0.553470
$396$	10.0000	0.502519
$397$	−12.0000	−0.602263	−0.301131	−	0.953583i	$-0.597364\pi$
$397$	−12.0000	−0.602263	−0.301131	+	0.953583i	$0.597364\pi$
$398$	−42.0000	−2.10527
$399$	2.00000	0.100125
$400$	−4.00000	−0.200000
$401$	−5.00000	−0.249688	−0.124844	−	0.992176i	$-0.539843\pi$
$401$	−5.00000	−0.249688	−0.124844	+	0.992176i	$0.539843\pi$
$402$	28.0000	1.39651
$403$	0	0
$404$	34.0000	1.69156
$405$	1.00000	0.0496904
$406$	−8.00000	−0.397033
$407$	50.0000	2.47841
$408$	0	0
$409$	−5.00000	−0.247234	−0.123617	−	0.992330i	$-0.539449\pi$
$409$	−5.00000	−0.247234	−0.123617	+	0.992330i	$0.539449\pi$
$410$	2.00000	0.0987730
$411$	16.0000	0.789222
$412$	24.0000	1.18240
$413$	0	0
$414$	0	0
$415$	−6.00000	−0.294528
$416$	0	0
$417$	−5.00000	−0.244851
$418$	−10.0000	−0.489116
$419$	−11.0000	−0.537385	−0.268693	−	0.963226i	$-0.586592\pi$
$419$	−11.0000	−0.537385	−0.268693	+	0.963226i	$0.586592\pi$
$420$	4.00000	0.195180
$421$	−17.0000	−0.828529	−0.414265	−	0.910156i	$-0.635961\pi$
$421$	−17.0000	−0.828529	−0.414265	+	0.910156i	$0.635961\pi$
$422$	14.0000	0.681509
$423$	−6.00000	−0.291730
$424$	0	0
$425$	−4.00000	−0.194029
$426$	−10.0000	−0.484502
$427$	−18.0000	−0.871081
$428$	0	0
$429$	0	0
$430$	20.0000	0.964486
$431$	21.0000	1.01153	0.505767	−	0.862670i	$-0.331209\pi$
$431$	21.0000	1.01153	0.505767	+	0.862670i	$0.331209\pi$
$432$	−4.00000	−0.192450
$433$	−8.00000	−0.384455	−0.192228	−	0.981350i	$-0.561571\pi$
$433$	−8.00000	−0.384455	−0.192228	+	0.981350i	$0.561571\pi$
$434$	−28.0000	−1.34404
$435$	2.00000	0.0958927
$436$	2.00000	0.0957826
$437$	0	0
$438$	−20.0000	−0.955637
$439$	32.0000	1.52728	0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000	1.52728	0.763638	+	0.645644i	$0.223411\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	0	0
$443$	36.0000	1.71041	0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000	1.71041	0.855206	+	0.518289i	$0.173431\pi$
$444$	20.0000	0.949158
$445$	10.0000	0.474045
$446$	48.0000	2.27287
$447$	15.0000	0.709476
$448$	−16.0000	−0.755929
$449$	−2.00000	−0.0943858	−0.0471929	−	0.998886i	$-0.515028\pi$
$449$	−2.00000	−0.0943858	−0.0471929	+	0.998886i	$0.515028\pi$
$450$	−2.00000	−0.0942809
$451$	−5.00000	−0.235441
$452$	16.0000	0.752577
$453$	17.0000	0.798730
$454$	−48.0000	−2.25275
$455$	0	0
$456$	0	0
$457$	12.0000	0.561336	0.280668	−	0.959805i	$-0.409444\pi$
$457$	12.0000	0.561336	0.280668	+	0.959805i	$0.409444\pi$
$458$	42.0000	1.96253
$459$	−4.00000	−0.186704
$460$	0	0
$461$	−7.00000	−0.326023	−0.163011	−	0.986624i	$-0.552121\pi$
$461$	−7.00000	−0.326023	−0.163011	+	0.986624i	$0.552121\pi$
$462$	−20.0000	−0.930484
$463$	−14.0000	−0.650635	−0.325318	−	0.945605i	$-0.605471\pi$
$463$	−14.0000	−0.650635	−0.325318	+	0.945605i	$0.605471\pi$
$464$	−8.00000	−0.371391
$465$	7.00000	0.324617
$466$	52.0000	2.40885
$467$	10.0000	0.462745	0.231372	−	0.972865i	$-0.425678\pi$
$467$	10.0000	0.462745	0.231372	+	0.972865i	$0.425678\pi$
$468$	0	0
$469$	−28.0000	−1.29292
$470$	12.0000	0.553519
$471$	−22.0000	−1.01371
$472$	0	0
$473$	−50.0000	−2.29900
$474$	−22.0000	−1.01049
$475$	1.00000	0.0458831
$476$	−16.0000	−0.733359
$477$	6.00000	0.274721
$478$	−22.0000	−1.00626
$479$	−25.0000	−1.14228	−0.571140	−	0.820853i	$-0.693499\pi$
$479$	−25.0000	−1.14228	−0.571140	+	0.820853i	$0.693499\pi$
$480$	8.00000	0.365148
$481$	0	0
$482$	50.0000	2.27744
$483$	0	0
$484$	28.0000	1.27273
$485$	−2.00000	−0.0908153
$486$	−2.00000	−0.0907218
$487$	−12.0000	−0.543772	−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000	−0.543772	−0.271886	+	0.962329i	$0.587647\pi$
$488$	0	0
$489$	−4.00000	−0.180886
$490$	6.00000	0.271052
$491$	28.0000	1.26362	0.631811	−	0.775122i	$-0.282312\pi$
$491$	28.0000	1.26362	0.631811	+	0.775122i	$0.282312\pi$
$492$	−2.00000	−0.0901670
$493$	−8.00000	−0.360302
$494$	0	0
$495$	5.00000	0.224733
$496$	−28.0000	−1.25724
$497$	10.0000	0.448561
$498$	12.0000	0.537733
$499$	−29.0000	−1.29822	−0.649109	−	0.760695i	$-0.724858\pi$
$499$	−29.0000	−1.29822	−0.649109	+	0.760695i	$0.724858\pi$
$500$	2.00000	0.0894427
$501$	14.0000	0.625474
$502$	−6.00000	−0.267793
$503$	14.0000	0.624229	0.312115	−	0.950044i	$-0.398963\pi$
$503$	14.0000	0.624229	0.312115	+	0.950044i	$0.398963\pi$
$504$	0	0
$505$	17.0000	0.756490
$506$	0	0
$507$	−13.0000	−0.577350
$508$	24.0000	1.06483
$509$	34.0000	1.50702	0.753512	−	0.657434i	$-0.228358\pi$
$509$	34.0000	1.50702	0.753512	+	0.657434i	$0.228358\pi$
$510$	8.00000	0.354246
$511$	20.0000	0.884748
$512$	−32.0000	−1.41421
$513$	1.00000	0.0441511
$514$	−12.0000	−0.529297
$515$	12.0000	0.528783
$516$	−20.0000	−0.880451
$517$	−30.0000	−1.31940
$518$	−40.0000	−1.75750
$519$	14.0000	0.614532
$520$	0	0
$521$	27.0000	1.18289	0.591446	−	0.806345i	$-0.298557\pi$
$521$	27.0000	1.18289	0.591446	+	0.806345i	$0.298557\pi$
$522$	−4.00000	−0.175075
$523$	−8.00000	−0.349816	−0.174908	−	0.984585i	$-0.555963\pi$
$523$	−8.00000	−0.349816	−0.174908	+	0.984585i	$0.555963\pi$
$524$	−14.0000	−0.611593
$525$	2.00000	0.0872872
$526$	−24.0000	−1.04645
$527$	−28.0000	−1.21970
$528$	−20.0000	−0.870388
$529$	0	0
$530$	−12.0000	−0.521247
$531$	0	0
$532$	4.00000	0.173422
$533$	0	0
$534$	−20.0000	−0.865485
$535$	0	0
$536$	0	0
$537$	−15.0000	−0.647298
$538$	−2.00000	−0.0862261
$539$	−15.0000	−0.646096
$540$	2.00000	0.0860663
$541$	11.0000	0.472927	0.236463	−	0.971640i	$-0.424012\pi$
$541$	11.0000	0.472927	0.236463	+	0.971640i	$0.424012\pi$
$542$	−32.0000	−1.37452
$543$	−7.00000	−0.300399
$544$	−32.0000	−1.37199
$545$	1.00000	0.0428353
$546$	0	0
$547$	−22.0000	−0.940652	−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000	−0.940652	−0.470326	+	0.882493i	$0.655864\pi$
$548$	32.0000	1.36697
$549$	−9.00000	−0.384111
$550$	−10.0000	−0.426401
$551$	2.00000	0.0852029
$552$	0	0
$553$	22.0000	0.935535
$554$	44.0000	1.86938
$555$	10.0000	0.424476
$556$	−10.0000	−0.424094
$557$	28.0000	1.18640	0.593199	−	0.805056i	$-0.297865\pi$
$557$	28.0000	1.18640	0.593199	+	0.805056i	$0.297865\pi$
$558$	−14.0000	−0.592667
$559$	0	0
$560$	−8.00000	−0.338062
$561$	−20.0000	−0.844401
$562$	−42.0000	−1.77166
$563$	−12.0000	−0.505740	−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000	−0.505740	−0.252870	+	0.967500i	$0.581374\pi$
$564$	−12.0000	−0.505291
$565$	8.00000	0.336563
$566$	0	0
$567$	2.00000	0.0839921
$568$	0	0
$569$	−33.0000	−1.38343	−0.691716	−	0.722170i	$-0.743145\pi$
$569$	−33.0000	−1.38343	−0.691716	+	0.722170i	$0.743145\pi$
$570$	−2.00000	−0.0837708
$571$	31.0000	1.29731	0.648655	−	0.761083i	$-0.275332\pi$
$571$	31.0000	1.29731	0.648655	+	0.761083i	$0.275332\pi$
$572$	0	0
$573$	0	0
$574$	4.00000	0.166957
$575$	0	0
$576$	−8.00000	−0.333333
$577$	−38.0000	−1.58196	−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000	−1.58196	−0.790980	+	0.611842i	$0.790429\pi$
$578$	2.00000	0.0831890
$579$	12.0000	0.498703
$580$	4.00000	0.166091
$581$	−12.0000	−0.497844
$582$	4.00000	0.165805
$583$	30.0000	1.24247
$584$	0	0
$585$	0	0
$586$	−32.0000	−1.32191
$587$	−30.0000	−1.23823	−0.619116	−	0.785299i	$-0.712509\pi$
$587$	−30.0000	−1.23823	−0.619116	+	0.785299i	$0.712509\pi$
$588$	−6.00000	−0.247436
$589$	7.00000	0.288430
$590$	0	0
$591$	−18.0000	−0.740421
$592$	−40.0000	−1.64399
$593$	−38.0000	−1.56047	−0.780236	−	0.625485i	$-0.784901\pi$
$593$	−38.0000	−1.56047	−0.780236	+	0.625485i	$0.784901\pi$
$594$	−10.0000	−0.410305
$595$	−8.00000	−0.327968
$596$	30.0000	1.22885
$597$	21.0000	0.859473
$598$	0	0
$599$	19.0000	0.776319	0.388159	−	0.921592i	$-0.373111\pi$
$599$	19.0000	0.776319	0.388159	+	0.921592i	$0.373111\pi$
$600$	0	0
$601$	37.0000	1.50926	0.754631	−	0.656150i	$-0.227816\pi$
$601$	37.0000	1.50926	0.754631	+	0.656150i	$0.227816\pi$
$602$	40.0000	1.63028
$603$	−14.0000	−0.570124
$604$	34.0000	1.38344
$605$	14.0000	0.569181
$606$	−34.0000	−1.38116
$607$	−20.0000	−0.811775	−0.405887	−	0.913923i	$-0.633038\pi$
$607$	−20.0000	−0.811775	−0.405887	+	0.913923i	$0.633038\pi$
$608$	8.00000	0.324443
$609$	4.00000	0.162088
$610$	18.0000	0.728799
$611$	0	0
$612$	−8.00000	−0.323381
$613$	36.0000	1.45403	0.727013	−	0.686624i	$-0.240908\pi$
$613$	36.0000	1.45403	0.727013	+	0.686624i	$0.240908\pi$
$614$	20.0000	0.807134
$615$	−1.00000	−0.0403239
$616$	0	0
$617$	−18.0000	−0.724653	−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000	−0.724653	−0.362326	+	0.932051i	$0.618017\pi$
$618$	−24.0000	−0.965422
$619$	25.0000	1.00483	0.502417	−	0.864625i	$-0.332444\pi$
$619$	25.0000	1.00483	0.502417	+	0.864625i	$0.332444\pi$
$620$	14.0000	0.562254
$621$	0	0
$622$	−48.0000	−1.92462
$623$	20.0000	0.801283
$624$	0	0
$625$	1.00000	0.0400000
$626$	−32.0000	−1.27898
$627$	5.00000	0.199681
$628$	−44.0000	−1.75579
$629$	−40.0000	−1.59490
$630$	−4.00000	−0.159364
$631$	43.0000	1.71180	0.855901	−	0.517139i	$-0.173003\pi$
$631$	43.0000	1.71180	0.855901	+	0.517139i	$0.173003\pi$
$632$	0	0
$633$	−7.00000	−0.278225
$634$	60.0000	2.38290
$635$	12.0000	0.476205
$636$	12.0000	0.475831
$637$	0	0
$638$	−20.0000	−0.791808
$639$	5.00000	0.197797
$640$	0	0
$641$	29.0000	1.14543	0.572716	−	0.819754i	$-0.305890\pi$
$641$	29.0000	1.14543	0.572716	+	0.819754i	$0.305890\pi$
$642$	0	0
$643$	−16.0000	−0.630978	−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000	−0.630978	−0.315489	+	0.948929i	$0.602169\pi$
$644$	0	0
$645$	−10.0000	−0.393750
$646$	8.00000	0.314756
$647$	26.0000	1.02217	0.511083	−	0.859532i	$-0.329245\pi$
$647$	26.0000	1.02217	0.511083	+	0.859532i	$0.329245\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	14.0000	0.548703
$652$	−8.00000	−0.313304
$653$	−24.0000	−0.939193	−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000	−0.939193	−0.469596	+	0.882881i	$0.655601\pi$
$654$	−2.00000	−0.0782062
$655$	−7.00000	−0.273513
$656$	4.00000	0.156174
$657$	10.0000	0.390137
$658$	24.0000	0.935617
$659$	47.0000	1.83086	0.915430	−	0.402477i	$-0.131851\pi$
$659$	47.0000	1.83086	0.915430	+	0.402477i	$0.131851\pi$
$660$	10.0000	0.389249
$661$	−5.00000	−0.194477	−0.0972387	−	0.995261i	$-0.531001\pi$
$661$	−5.00000	−0.194477	−0.0972387	+	0.995261i	$0.531001\pi$
$662$	18.0000	0.699590
$663$	0	0
$664$	0	0
$665$	2.00000	0.0775567
$666$	−20.0000	−0.774984
$667$	0	0
$668$	28.0000	1.08335
$669$	−24.0000	−0.927894
$670$	28.0000	1.08173
$671$	−45.0000	−1.73721
$672$	16.0000	0.617213
$673$	26.0000	1.00223	0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000	1.00223	0.501113	+	0.865382i	$0.332924\pi$
$674$	32.0000	1.23259
$675$	1.00000	0.0384900
$676$	−26.0000	−1.00000
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	−16.0000	−0.614476
$679$	−4.00000	−0.153506
$680$	0	0
$681$	24.0000	0.919682
$682$	−70.0000	−2.68044
$683$	−4.00000	−0.153056	−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000	−0.153056	−0.0765279	+	0.997067i	$0.524383\pi$
$684$	2.00000	0.0764719
$685$	16.0000	0.611329
$686$	40.0000	1.52721
$687$	−21.0000	−0.801200
$688$	40.0000	1.52499
$689$	0	0
$690$	0	0
$691$	43.0000	1.63580	0.817899	−	0.575362i	$-0.195139\pi$
$691$	43.0000	1.63580	0.817899	+	0.575362i	$0.195139\pi$
$692$	28.0000	1.06440
$693$	10.0000	0.379869
$694$	60.0000	2.27757
$695$	−5.00000	−0.189661
$696$	0	0
$697$	4.00000	0.151511
$698$	−4.00000	−0.151402
$699$	−26.0000	−0.983410
$700$	4.00000	0.151186
$701$	2.00000	0.0755390	0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000	0.0755390	0.0377695	+	0.999286i	$0.487975\pi$
$702$	0	0
$703$	10.0000	0.377157
$704$	−40.0000	−1.50756
$705$	−6.00000	−0.225973
$706$	12.0000	0.451626
$707$	34.0000	1.27870
$708$	0	0
$709$	6.00000	0.225335	0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000	0.225335	0.112667	+	0.993633i	$0.464061\pi$
$710$	−10.0000	−0.375293
$711$	11.0000	0.412532
$712$	0	0
$713$	0	0
$714$	16.0000	0.598785
$715$	0	0
$716$	−30.0000	−1.12115
$717$	11.0000	0.410803
$718$	16.0000	0.597115
$719$	24.0000	0.895049	0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000	0.895049	0.447524	+	0.894272i	$0.352306\pi$
$720$	−4.00000	−0.149071
$721$	24.0000	0.893807
$722$	36.0000	1.33978
$723$	−25.0000	−0.929760
$724$	−14.0000	−0.520306
$725$	2.00000	0.0742781
$726$	−28.0000	−1.03918
$727$	12.0000	0.445055	0.222528	−	0.974926i	$-0.428569\pi$
$727$	12.0000	0.445055	0.222528	+	0.974926i	$0.428569\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−20.0000	−0.740233
$731$	40.0000	1.47945
$732$	−18.0000	−0.665299
$733$	0	0		−	1.00000i	$-0.5\pi$
$733$	0	0			1.00000i	$0.5\pi$
$734$	56.0000	2.06700
$735$	−3.00000	−0.110657
$736$	0	0
$737$	−70.0000	−2.57848
$738$	2.00000	0.0736210
$739$	15.0000	0.551784	0.275892	−	0.961189i	$-0.411027\pi$
$739$	15.0000	0.551784	0.275892	+	0.961189i	$0.411027\pi$
$740$	20.0000	0.735215
$741$	0	0
$742$	−24.0000	−0.881068
$743$	−34.0000	−1.24734	−0.623670	−	0.781688i	$-0.714359\pi$
$743$	−34.0000	−1.24734	−0.623670	+	0.781688i	$0.714359\pi$
$744$	0	0
$745$	15.0000	0.549557
$746$	−64.0000	−2.34321
$747$	−6.00000	−0.219529
$748$	−40.0000	−1.46254
$749$	0	0
$750$	−2.00000	−0.0730297
$751$	−24.0000	−0.875772	−0.437886	−	0.899030i	$-0.644273\pi$
$751$	−24.0000	−0.875772	−0.437886	+	0.899030i	$0.644273\pi$
$752$	24.0000	0.875190
$753$	3.00000	0.109326
$754$	0	0
$755$	17.0000	0.618693
$756$	4.00000	0.145479
$757$	−10.0000	−0.363456	−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000	−0.363456	−0.181728	+	0.983349i	$0.558169\pi$
$758$	8.00000	0.290573
$759$	0	0
$760$	0	0
$761$	−27.0000	−0.978749	−0.489375	−	0.872074i	$-0.662775\pi$
$761$	−27.0000	−0.978749	−0.489375	+	0.872074i	$0.662775\pi$
$762$	−24.0000	−0.869428
$763$	2.00000	0.0724049
$764$	0	0
$765$	−4.00000	−0.144620
$766$	−68.0000	−2.45694
$767$	0	0
$768$	16.0000	0.577350
$769$	51.0000	1.83911	0.919554	−	0.392965i	$-0.128551\pi$
$769$	51.0000	1.83911	0.919554	+	0.392965i	$0.128551\pi$
$770$	−20.0000	−0.720750
$771$	6.00000	0.216085
$772$	24.0000	0.863779
$773$	38.0000	1.36677	0.683383	−	0.730061i	$-0.260508\pi$
$773$	38.0000	1.36677	0.683383	+	0.730061i	$0.260508\pi$
$774$	20.0000	0.718885
$775$	7.00000	0.251447
$776$	0	0
$777$	20.0000	0.717496
$778$	50.0000	1.79259
$779$	−1.00000	−0.0358287
$780$	0	0
$781$	25.0000	0.894570
$782$	0	0
$783$	2.00000	0.0714742
$784$	12.0000	0.428571
$785$	−22.0000	−0.785214
$786$	14.0000	0.499363
$787$	−14.0000	−0.499046	−0.249523	−	0.968369i	$-0.580274\pi$
$787$	−14.0000	−0.499046	−0.249523	+	0.968369i	$0.580274\pi$
$788$	−36.0000	−1.28245
$789$	12.0000	0.427211
$790$	−22.0000	−0.782725
$791$	16.0000	0.568895
$792$	0	0
$793$	0	0
$794$	24.0000	0.851728
$795$	6.00000	0.212798
$796$	42.0000	1.48865
$797$	22.0000	0.779280	0.389640	−	0.920967i	$-0.372599\pi$
$797$	22.0000	0.779280	0.389640	+	0.920967i	$0.372599\pi$
$798$	−4.00000	−0.141598
$799$	24.0000	0.849059
$800$	8.00000	0.282843
$801$	10.0000	0.353333
$802$	10.0000	0.353112
$803$	50.0000	1.76446
$804$	−28.0000	−0.987484
$805$	0	0
$806$	0	0
$807$	1.00000	0.0352017
$808$	0	0
$809$	−41.0000	−1.44148	−0.720742	−	0.693204i	$-0.756199\pi$
$809$	−41.0000	−1.44148	−0.720742	+	0.693204i	$0.756199\pi$
$810$	−2.00000	−0.0702728
$811$	−37.0000	−1.29925	−0.649623	−	0.760257i	$-0.725073\pi$
$811$	−37.0000	−1.29925	−0.649623	+	0.760257i	$0.725073\pi$
$812$	8.00000	0.280745
$813$	16.0000	0.561144
$814$	−100.000	−3.50500
$815$	−4.00000	−0.140114
$816$	16.0000	0.560112
$817$	−10.0000	−0.349856
$818$	10.0000	0.349642
$819$	0	0
$820$	−2.00000	−0.0698430
$821$	7.00000	0.244302	0.122151	−	0.992512i	$-0.461021\pi$
$821$	7.00000	0.244302	0.122151	+	0.992512i	$0.461021\pi$
$822$	−32.0000	−1.11613
$823$	40.0000	1.39431	0.697156	−	0.716919i	$-0.254448\pi$
$823$	40.0000	1.39431	0.697156	+	0.716919i	$0.254448\pi$
$824$	0	0
$825$	5.00000	0.174078
$826$	0	0
$827$	4.00000	0.139094	0.0695468	−	0.997579i	$-0.477845\pi$
$827$	4.00000	0.139094	0.0695468	+	0.997579i	$0.477845\pi$
$828$	0	0
$829$	19.0000	0.659897	0.329949	−	0.943999i	$-0.392969\pi$
$829$	19.0000	0.659897	0.329949	+	0.943999i	$0.392969\pi$
$830$	12.0000	0.416526
$831$	−22.0000	−0.763172
$832$	0	0
$833$	12.0000	0.415775
$834$	10.0000	0.346272
$835$	14.0000	0.484490
$836$	10.0000	0.345857
$837$	7.00000	0.241955
$838$	22.0000	0.759977
$839$	21.0000	0.725001	0.362500	−	0.931984i	$-0.381923\pi$
$839$	21.0000	0.725001	0.362500	+	0.931984i	$0.381923\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	34.0000	1.17172
$843$	21.0000	0.723278
$844$	−14.0000	−0.481900
$845$	−13.0000	−0.447214
$846$	12.0000	0.412568
$847$	28.0000	0.962091
$848$	−24.0000	−0.824163
$849$	0	0
$850$	8.00000	0.274398
$851$	0	0
$852$	10.0000	0.342594
$853$	−44.0000	−1.50653	−0.753266	−	0.657716i	$-0.771523\pi$
$853$	−44.0000	−1.50653	−0.753266	+	0.657716i	$0.771523\pi$
$854$	36.0000	1.23189
$855$	1.00000	0.0341993
$856$	0	0
$857$	−28.0000	−0.956462	−0.478231	−	0.878234i	$-0.658722\pi$
$857$	−28.0000	−0.956462	−0.478231	+	0.878234i	$0.658722\pi$
$858$	0	0
$859$	56.0000	1.91070	0.955348	−	0.295484i	$-0.0954809\pi$
$859$	56.0000	1.91070	0.955348	+	0.295484i	$0.0954809\pi$
$860$	−20.0000	−0.681994
$861$	−2.00000	−0.0681598
$862$	−42.0000	−1.43053
$863$	−14.0000	−0.476566	−0.238283	−	0.971196i	$-0.576585\pi$
$863$	−14.0000	−0.476566	−0.238283	+	0.971196i	$0.576585\pi$
$864$	8.00000	0.272166
$865$	14.0000	0.476014
$866$	16.0000	0.543702
$867$	−1.00000	−0.0339618
$868$	28.0000	0.950382
$869$	55.0000	1.86575
$870$	−4.00000	−0.135613
$871$	0	0
$872$	0	0
$873$	−2.00000	−0.0676897
$874$	0	0
$875$	2.00000	0.0676123
$876$	20.0000	0.675737
$877$	−36.0000	−1.21563	−0.607817	−	0.794077i	$-0.707955\pi$
$877$	−36.0000	−1.21563	−0.607817	+	0.794077i	$0.707955\pi$
$878$	−64.0000	−2.15990
$879$	16.0000	0.539667
$880$	−20.0000	−0.674200
$881$	18.0000	0.606435	0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000	0.606435	0.303218	+	0.952921i	$0.401939\pi$
$882$	6.00000	0.202031
$883$	16.0000	0.538443	0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000	0.538443	0.269221	+	0.963078i	$0.413234\pi$
$884$	0	0
$885$	0	0
$886$	−72.0000	−2.41889
$887$	−6.00000	−0.201460	−0.100730	−	0.994914i	$-0.532118\pi$
$887$	−6.00000	−0.201460	−0.100730	+	0.994914i	$0.532118\pi$
$888$	0	0
$889$	24.0000	0.804934
$890$	−20.0000	−0.670402
$891$	5.00000	0.167506
$892$	−48.0000	−1.60716
$893$	−6.00000	−0.200782
$894$	−30.0000	−1.00335
$895$	−15.0000	−0.501395
$896$	0	0
$897$	0	0
$898$	4.00000	0.133482
$899$	14.0000	0.466926
$900$	2.00000	0.0666667
$901$	−24.0000	−0.799556
$902$	10.0000	0.332964
$903$	−20.0000	−0.665558
$904$	0	0
$905$	−7.00000	−0.232688
$906$	−34.0000	−1.12957
$907$	−38.0000	−1.26177	−0.630885	−	0.775877i	$-0.717308\pi$
$907$	−38.0000	−1.26177	−0.630885	+	0.775877i	$0.717308\pi$
$908$	48.0000	1.59294
$909$	17.0000	0.563854
$910$	0	0
$911$	−13.0000	−0.430709	−0.215355	−	0.976536i	$-0.569091\pi$
$911$	−13.0000	−0.430709	−0.215355	+	0.976536i	$0.569091\pi$
$912$	−4.00000	−0.132453
$913$	−30.0000	−0.992855
$914$	−24.0000	−0.793849
$915$	−9.00000	−0.297531
$916$	−42.0000	−1.38772
$917$	−14.0000	−0.462321
$918$	8.00000	0.264039
$919$	−37.0000	−1.22052	−0.610259	−	0.792202i	$-0.708935\pi$
$919$	−37.0000	−1.22052	−0.610259	+	0.792202i	$0.708935\pi$
$920$	0	0
$921$	−10.0000	−0.329511
$922$	14.0000	0.461065
$923$	0	0
$924$	20.0000	0.657952
$925$	10.0000	0.328798
$926$	28.0000	0.920137
$927$	12.0000	0.394132
$928$	16.0000	0.525226
$929$	−51.0000	−1.67326	−0.836628	−	0.547772i	$-0.815476\pi$
$929$	−51.0000	−1.67326	−0.836628	+	0.547772i	$0.815476\pi$
$930$	−14.0000	−0.459078
$931$	−3.00000	−0.0983210
$932$	−52.0000	−1.70332
$933$	24.0000	0.785725
$934$	−20.0000	−0.654420
$935$	−20.0000	−0.654070
$936$	0	0
$937$	−10.0000	−0.326686	−0.163343	−	0.986569i	$-0.552228\pi$
$937$	−10.0000	−0.326686	−0.163343	+	0.986569i	$0.552228\pi$
$938$	56.0000	1.82846
$939$	16.0000	0.522140
$940$	−12.0000	−0.391397
$941$	−13.0000	−0.423788	−0.211894	−	0.977293i	$-0.567963\pi$
$941$	−13.0000	−0.423788	−0.211894	+	0.977293i	$0.567963\pi$
$942$	44.0000	1.43360
$943$	0	0
$944$	0	0
$945$	2.00000	0.0650600
$946$	100.000	3.25128
$947$	−44.0000	−1.42981	−0.714904	−	0.699223i	$-0.753530\pi$
$947$	−44.0000	−1.42981	−0.714904	+	0.699223i	$0.753530\pi$
$948$	22.0000	0.714527
$949$	0	0
$950$	−2.00000	−0.0648886
$951$	−30.0000	−0.972817
$952$	0	0
$953$	30.0000	0.971795	0.485898	−	0.874016i	$-0.338493\pi$
$953$	30.0000	0.971795	0.485898	+	0.874016i	$0.338493\pi$
$954$	−12.0000	−0.388514
$955$	0	0
$956$	22.0000	0.711531
$957$	10.0000	0.323254
$958$	50.0000	1.61543
$959$	32.0000	1.03333
$960$	−8.00000	−0.258199
$961$	18.0000	0.580645
$962$	0	0
$963$	0	0
$964$	−50.0000	−1.61039
$965$	12.0000	0.386294
$966$	0	0
$967$	−32.0000	−1.02905	−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000	−1.02905	−0.514525	+	0.857475i	$0.672032\pi$
$968$	0	0
$969$	−4.00000	−0.128499
$970$	4.00000	0.128432
$971$	20.0000	0.641831	0.320915	−	0.947108i	$-0.396010\pi$
$971$	20.0000	0.641831	0.320915	+	0.947108i	$0.396010\pi$
$972$	2.00000	0.0641500
$973$	−10.0000	−0.320585
$974$	24.0000	0.769010
$975$	0	0
$976$	36.0000	1.15233
$977$	−16.0000	−0.511885	−0.255943	−	0.966692i	$-0.582386\pi$
$977$	−16.0000	−0.511885	−0.255943	+	0.966692i	$0.582386\pi$
$978$	8.00000	0.255812
$979$	50.0000	1.59801
$980$	−6.00000	−0.191663
$981$	1.00000	0.0319275
$982$	−56.0000	−1.78703
$983$	−20.0000	−0.637901	−0.318950	−	0.947771i	$-0.603330\pi$
$983$	−20.0000	−0.637901	−0.318950	+	0.947771i	$0.603330\pi$
$984$	0	0
$985$	−18.0000	−0.573528
$986$	16.0000	0.509544
$987$	−12.0000	−0.381964
$988$	0	0
$989$	0	0
$990$	−10.0000	−0.317821
$991$	−28.0000	−0.889449	−0.444725	−	0.895667i	$-0.646698\pi$
$991$	−28.0000	−0.889449	−0.444725	+	0.895667i	$0.646698\pi$
$992$	56.0000	1.77800
$993$	−9.00000	−0.285606
$994$	−20.0000	−0.634361
$995$	21.0000	0.665745
$996$	−12.0000	−0.380235
$997$	−8.00000	−0.253363	−0.126681	−	0.991943i	$-0.540433\pi$
$997$	−8.00000	−0.253363	−0.126681	+	0.991943i	$0.540433\pi$
$998$	58.0000	1.83596
$999$	10.0000	0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.c.1.1	yes	1
23.22	odd	2		7935.2.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.a.1.1	✓	1	23.22	odd	2
7935.2.a.c.1.1	yes	1	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more