LMFDB - Embedded newform 8015.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$1$
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	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} +1.00000 q^{3} +2.00000 q^{4} +1.00000 q^{5} +2.00000 q^{6} +1.00000 q^{7} -2.00000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} +1.00000 q^{3} +2.00000 q^{4} +1.00000 q^{5} +2.00000 q^{6} +1.00000 q^{7} -2.00000 q^{9} +2.00000 q^{10} -3.00000 q^{11} +2.00000 q^{12} +3.00000 q^{13} +2.00000 q^{14} +1.00000 q^{15} -4.00000 q^{16} -1.00000 q^{17} -4.00000 q^{18} -6.00000 q^{19} +2.00000 q^{20} +1.00000 q^{21} -6.00000 q^{22} -2.00000 q^{23} +1.00000 q^{25} +6.00000 q^{26} -5.00000 q^{27} +2.00000 q^{28} -3.00000 q^{29} +2.00000 q^{30} -2.00000 q^{31} -8.00000 q^{32} -3.00000 q^{33} -2.00000 q^{34} +1.00000 q^{35} -4.00000 q^{36} -4.00000 q^{37} -12.0000 q^{38} +3.00000 q^{39} -6.00000 q^{41} +2.00000 q^{42} -8.00000 q^{43} -6.00000 q^{44} -2.00000 q^{45} -4.00000 q^{46} +3.00000 q^{47} -4.00000 q^{48} +1.00000 q^{49} +2.00000 q^{50} -1.00000 q^{51} +6.00000 q^{52} +2.00000 q^{53} -10.0000 q^{54} -3.00000 q^{55} -6.00000 q^{57} -6.00000 q^{58} -8.00000 q^{59} +2.00000 q^{60} -10.0000 q^{61} -4.00000 q^{62} -2.00000 q^{63} -8.00000 q^{64} +3.00000 q^{65} -6.00000 q^{66} +8.00000 q^{67} -2.00000 q^{68} -2.00000 q^{69} +2.00000 q^{70} +12.0000 q^{71} -2.00000 q^{73} -8.00000 q^{74} +1.00000 q^{75} -12.0000 q^{76} -3.00000 q^{77} +6.00000 q^{78} +9.00000 q^{79} -4.00000 q^{80} +1.00000 q^{81} -12.0000 q^{82} -4.00000 q^{83} +2.00000 q^{84} -1.00000 q^{85} -16.0000 q^{86} -3.00000 q^{87} +12.0000 q^{89} -4.00000 q^{90} +3.00000 q^{91} -4.00000 q^{92} -2.00000 q^{93} +6.00000 q^{94} -6.00000 q^{95} -8.00000 q^{96} +7.00000 q^{97} +2.00000 q^{98} +6.00000 q^{99} +O(q^{100})\)

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 $

$2$	2.00000	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$2$	2.00000	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	2.00000	1.00000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.00000	0.816497
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0	0
$9$	−2.00000	−0.666667
$10$	2.00000	0.632456
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	2.00000	0.577350
$13$	3.00000	0.832050	0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000	0.832050	0.416025	+	0.909353i	$0.363423\pi$
$14$	2.00000	0.534522
$15$	1.00000	0.258199
$16$	−4.00000	−1.00000
$17$	−1.00000	−0.242536	−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000	−0.242536	−0.121268	+	0.992620i	$0.538696\pi$
$18$	−4.00000	−0.942809
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	2.00000	0.447214
$21$	1.00000	0.218218
$22$	−6.00000	−1.27920
$23$	−2.00000	−0.417029	−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000	−0.417029	−0.208514	+	0.978019i	$0.566863\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	6.00000	1.17670
$27$	−5.00000	−0.962250
$28$	2.00000	0.377964
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	2.00000	0.365148
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	−8.00000	−1.41421
$33$	−3.00000	−0.522233
$34$	−2.00000	−0.342997
$35$	1.00000	0.169031
$36$	−4.00000	−0.666667
$37$	−4.00000	−0.657596	−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000	−0.657596	−0.328798	+	0.944400i	$0.606644\pi$
$38$	−12.0000	−1.94666
$39$	3.00000	0.480384
$40$	0	0
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	2.00000	0.308607
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−6.00000	−0.904534
$45$	−2.00000	−0.298142
$46$	−4.00000	−0.589768
$47$	3.00000	0.437595	0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000	0.437595	0.218797	+	0.975770i	$0.429787\pi$
$48$	−4.00000	−0.577350
$49$	1.00000	0.142857
$50$	2.00000	0.282843
$51$	−1.00000	−0.140028
$52$	6.00000	0.832050
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	−10.0000	−1.36083
$55$	−3.00000	−0.404520
$56$	0	0
$57$	−6.00000	−0.794719
$58$	−6.00000	−0.787839
$59$	−8.00000	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$60$	2.00000	0.258199
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	−4.00000	−0.508001
$63$	−2.00000	−0.251976
$64$	−8.00000	−1.00000
$65$	3.00000	0.372104
$66$	−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
$69$	−2.00000	−0.240772
$70$	2.00000	0.239046
$71$	12.0000	1.42414	0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000	1.42414	0.712069	+	0.702109i	$0.247758\pi$
$72$	0	0
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	−8.00000	−0.929981
$75$	1.00000	0.115470
$76$	−12.0000	−1.37649
$77$	−3.00000	−0.341882
$78$	6.00000	0.679366
$79$	9.00000	1.01258	0.506290	−	0.862364i	$-0.331017\pi$
$79$	9.00000	1.01258	0.506290	+	0.862364i	$0.331017\pi$
$80$	−4.00000	−0.447214
$81$	1.00000	0.111111
$82$	−12.0000	−1.32518
$83$	−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
$85$	−1.00000	−0.108465
$86$	−16.0000	−1.72532
$87$	−3.00000	−0.321634
$88$	0	0
$89$	12.0000	1.27200	0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000	1.27200	0.635999	+	0.771690i	$0.280588\pi$
$90$	−4.00000	−0.421637
$91$	3.00000	0.314485
$92$	−4.00000	−0.417029
$93$	−2.00000	−0.207390
$94$	6.00000	0.618853
$95$	−6.00000	−0.615587
$96$	−8.00000	−0.816497
$97$	7.00000	0.710742	0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000	0.710742	0.355371	+	0.934725i	$0.384354\pi$
$98$	2.00000	0.202031
$99$	6.00000	0.603023
$100$	2.00000	0.200000
$101$	8.00000	0.796030	0.398015	−	0.917379i	$-0.369699\pi$
$101$	8.00000	0.796030	0.398015	+	0.917379i	$0.369699\pi$
$102$	−2.00000	−0.198030
$103$	9.00000	0.886796	0.443398	−	0.896325i	$-0.353773\pi$
$103$	9.00000	0.886796	0.443398	+	0.896325i	$0.353773\pi$
$104$	0	0
$105$	1.00000	0.0975900
$106$	4.00000	0.388514
$107$	14.0000	1.35343	0.676716	−	0.736245i	$-0.263403\pi$
$107$	14.0000	1.35343	0.676716	+	0.736245i	$0.263403\pi$
$108$	−10.0000	−0.962250
$109$	−1.00000	−0.0957826	−0.0478913	−	0.998853i	$-0.515250\pi$
$109$	−1.00000	−0.0957826	−0.0478913	+	0.998853i	$0.515250\pi$
$110$	−6.00000	−0.572078
$111$	−4.00000	−0.379663
$112$	−4.00000	−0.377964
$113$	8.00000	0.752577	0.376288	−	0.926503i	$-0.377200\pi$
$113$	8.00000	0.752577	0.376288	+	0.926503i	$0.377200\pi$
$114$	−12.0000	−1.12390
$115$	−2.00000	−0.186501
$116$	−6.00000	−0.557086
$117$	−6.00000	−0.554700
$118$	−16.0000	−1.47292
$119$	−1.00000	−0.0916698
$120$	0	0
$121$	−2.00000	−0.181818
$122$	−20.0000	−1.81071
$123$	−6.00000	−0.541002
$124$	−4.00000	−0.359211
$125$	1.00000	0.0894427
$126$	−4.00000	−0.356348
$127$	−6.00000	−0.532414	−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000	−0.532414	−0.266207	+	0.963916i	$0.585770\pi$
$128$	0	0
$129$	−8.00000	−0.704361
$130$	6.00000	0.526235
$131$	−18.0000	−1.57267	−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000	−1.57267	−0.786334	+	0.617802i	$0.788023\pi$
$132$	−6.00000	−0.522233
$133$	−6.00000	−0.520266
$134$	16.0000	1.38219
$135$	−5.00000	−0.430331
$136$	0	0
$137$	−8.00000	−0.683486	−0.341743	−	0.939793i	$-0.611017\pi$
$137$	−8.00000	−0.683486	−0.341743	+	0.939793i	$0.611017\pi$
$138$	−4.00000	−0.340503
$139$	−2.00000	−0.169638	−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000	−0.169638	−0.0848189	+	0.996396i	$0.527031\pi$
$140$	2.00000	0.169031
$141$	3.00000	0.252646
$142$	24.0000	2.01404
$143$	−9.00000	−0.752618
$144$	8.00000	0.666667
$145$	−3.00000	−0.249136
$146$	−4.00000	−0.331042
$147$	1.00000	0.0824786
$148$	−8.00000	−0.657596
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	2.00000	0.163299
$151$	15.0000	1.22068	0.610341	−	0.792139i	$-0.291032\pi$
$151$	15.0000	1.22068	0.610341	+	0.792139i	$0.291032\pi$
$152$	0	0
$153$	2.00000	0.161690
$154$	−6.00000	−0.483494
$155$	−2.00000	−0.160644
$156$	6.00000	0.480384
$157$	2.00000	0.159617	0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000	0.159617	0.0798087	+	0.996810i	$0.474569\pi$
$158$	18.0000	1.43200
$159$	2.00000	0.158610
$160$	−8.00000	−0.632456
$161$	−2.00000	−0.157622
$162$	2.00000	0.157135
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	−12.0000	−0.937043
$165$	−3.00000	−0.233550
$166$	−8.00000	−0.620920
$167$	−15.0000	−1.16073	−0.580367	−	0.814355i	$-0.697091\pi$
$167$	−15.0000	−1.16073	−0.580367	+	0.814355i	$0.697091\pi$
$168$	0	0
$169$	−4.00000	−0.307692
$170$	−2.00000	−0.153393
$171$	12.0000	0.917663
$172$	−16.0000	−1.21999
$173$	−9.00000	−0.684257	−0.342129	−	0.939653i	$-0.611148\pi$
$173$	−9.00000	−0.684257	−0.342129	+	0.939653i	$0.611148\pi$
$174$	−6.00000	−0.454859
$175$	1.00000	0.0755929
$176$	12.0000	0.904534
$177$	−8.00000	−0.601317
$178$	24.0000	1.79888
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	−4.00000	−0.298142
$181$	−6.00000	−0.445976	−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000	−0.445976	−0.222988	+	0.974821i	$0.571581\pi$
$182$	6.00000	0.444750
$183$	−10.0000	−0.739221
$184$	0	0
$185$	−4.00000	−0.294086
$186$	−4.00000	−0.293294
$187$	3.00000	0.219382
$188$	6.00000	0.437595
$189$	−5.00000	−0.363696
$190$	−12.0000	−0.870572
$191$	−13.0000	−0.940647	−0.470323	−	0.882494i	$-0.655863\pi$
$191$	−13.0000	−0.940647	−0.470323	+	0.882494i	$0.655863\pi$
$192$	−8.00000	−0.577350
$193$	4.00000	0.287926	0.143963	−	0.989583i	$-0.454015\pi$
$193$	4.00000	0.287926	0.143963	+	0.989583i	$0.454015\pi$
$194$	14.0000	1.00514
$195$	3.00000	0.214834
$196$	2.00000	0.142857
$197$	10.0000	0.712470	0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000	0.712470	0.356235	+	0.934396i	$0.384060\pi$
$198$	12.0000	0.852803
$199$	−20.0000	−1.41776	−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000	−1.41776	−0.708881	+	0.705328i	$0.750800\pi$
$200$	0	0
$201$	8.00000	0.564276
$202$	16.0000	1.12576
$203$	−3.00000	−0.210559
$204$	−2.00000	−0.140028
$205$	−6.00000	−0.419058
$206$	18.0000	1.25412
$207$	4.00000	0.278019
$208$	−12.0000	−0.832050
$209$	18.0000	1.24509
$210$	2.00000	0.138013
$211$	−23.0000	−1.58339	−0.791693	−	0.610920i	$-0.790800\pi$
$211$	−23.0000	−1.58339	−0.791693	+	0.610920i	$0.790800\pi$
$212$	4.00000	0.274721
$213$	12.0000	0.822226
$214$	28.0000	1.91404
$215$	−8.00000	−0.545595
$216$	0	0
$217$	−2.00000	−0.135769
$218$	−2.00000	−0.135457
$219$	−2.00000	−0.135147
$220$	−6.00000	−0.404520
$221$	−3.00000	−0.201802
$222$	−8.00000	−0.536925
$223$	−13.0000	−0.870544	−0.435272	−	0.900299i	$-0.643348\pi$
$223$	−13.0000	−0.870544	−0.435272	+	0.900299i	$0.643348\pi$
$224$	−8.00000	−0.534522
$225$	−2.00000	−0.133333
$226$	16.0000	1.06430
$227$	7.00000	0.464606	0.232303	−	0.972643i	$-0.425374\pi$
$227$	7.00000	0.464606	0.232303	+	0.972643i	$0.425374\pi$
$228$	−12.0000	−0.794719
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−4.00000	−0.263752
$231$	−3.00000	−0.197386
$232$	0	0
$233$	−20.0000	−1.31024	−0.655122	−	0.755523i	$-0.727383\pi$
$233$	−20.0000	−1.31024	−0.655122	+	0.755523i	$0.727383\pi$
$234$	−12.0000	−0.784465
$235$	3.00000	0.195698
$236$	−16.0000	−1.04151
$237$	9.00000	0.584613
$238$	−2.00000	−0.129641
$239$	25.0000	1.61712	0.808558	−	0.588417i	$-0.200249\pi$
$239$	25.0000	1.61712	0.808558	+	0.588417i	$0.200249\pi$
$240$	−4.00000	−0.258199
$241$	26.0000	1.67481	0.837404	−	0.546585i	$-0.184072\pi$
$241$	26.0000	1.67481	0.837404	+	0.546585i	$0.184072\pi$
$242$	−4.00000	−0.257130
$243$	16.0000	1.02640
$244$	−20.0000	−1.28037
$245$	1.00000	0.0638877
$246$	−12.0000	−0.765092
$247$	−18.0000	−1.14531
$248$	0	0
$249$	−4.00000	−0.253490
$250$	2.00000	0.126491
$251$	30.0000	1.89358	0.946792	−	0.321847i	$-0.104304\pi$
$251$	30.0000	1.89358	0.946792	+	0.321847i	$0.104304\pi$
$252$	−4.00000	−0.251976
$253$	6.00000	0.377217
$254$	−12.0000	−0.752947
$255$	−1.00000	−0.0626224
$256$	16.0000	1.00000
$257$	−30.0000	−1.87135	−0.935674	−	0.352865i	$-0.885208\pi$
$257$	−30.0000	−1.87135	−0.935674	+	0.352865i	$0.885208\pi$
$258$	−16.0000	−0.996116
$259$	−4.00000	−0.248548
$260$	6.00000	0.372104
$261$	6.00000	0.371391
$262$	−36.0000	−2.22409
$263$	−18.0000	−1.10993	−0.554964	−	0.831875i	$-0.687268\pi$
$263$	−18.0000	−1.10993	−0.554964	+	0.831875i	$0.687268\pi$
$264$	0	0
$265$	2.00000	0.122859
$266$	−12.0000	−0.735767
$267$	12.0000	0.734388
$268$	16.0000	0.977356
$269$	24.0000	1.46331	0.731653	−	0.681677i	$-0.238749\pi$
$269$	24.0000	1.46331	0.731653	+	0.681677i	$0.238749\pi$
$270$	−10.0000	−0.608581
$271$	22.0000	1.33640	0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000	1.33640	0.668202	+	0.743980i	$0.267064\pi$
$272$	4.00000	0.242536
$273$	3.00000	0.181568
$274$	−16.0000	−0.966595
$275$	−3.00000	−0.180907
$276$	−4.00000	−0.240772
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	−4.00000	−0.239904
$279$	4.00000	0.239474
$280$	0	0
$281$	−23.0000	−1.37206	−0.686032	−	0.727571i	$-0.740649\pi$
$281$	−23.0000	−1.37206	−0.686032	+	0.727571i	$0.740649\pi$
$282$	6.00000	0.357295
$283$	−3.00000	−0.178331	−0.0891657	−	0.996017i	$-0.528420\pi$
$283$	−3.00000	−0.178331	−0.0891657	+	0.996017i	$0.528420\pi$
$284$	24.0000	1.42414
$285$	−6.00000	−0.355409
$286$	−18.0000	−1.06436
$287$	−6.00000	−0.354169
$288$	16.0000	0.942809
$289$	−16.0000	−0.941176
$290$	−6.00000	−0.352332
$291$	7.00000	0.410347
$292$	−4.00000	−0.234082
$293$	−9.00000	−0.525786	−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000	−0.525786	−0.262893	+	0.964825i	$0.584677\pi$
$294$	2.00000	0.116642
$295$	−8.00000	−0.465778
$296$	0	0
$297$	15.0000	0.870388
$298$	−12.0000	−0.695141
$299$	−6.00000	−0.346989
$300$	2.00000	0.115470
$301$	−8.00000	−0.461112
$302$	30.0000	1.72631
$303$	8.00000	0.459588
$304$	24.0000	1.37649
$305$	−10.0000	−0.572598
$306$	4.00000	0.228665
$307$	31.0000	1.76926	0.884632	−	0.466290i	$-0.154410\pi$
$307$	31.0000	1.76926	0.884632	+	0.466290i	$0.154410\pi$
$308$	−6.00000	−0.341882
$309$	9.00000	0.511992
$310$	−4.00000	−0.227185
$311$	20.0000	1.13410	0.567048	−	0.823685i	$-0.308085\pi$
$311$	20.0000	1.13410	0.567048	+	0.823685i	$0.308085\pi$
$312$	0	0
$313$	−17.0000	−0.960897	−0.480448	−	0.877023i	$-0.659526\pi$
$313$	−17.0000	−0.960897	−0.480448	+	0.877023i	$0.659526\pi$
$314$	4.00000	0.225733
$315$	−2.00000	−0.112687
$316$	18.0000	1.01258
$317$	2.00000	0.112331	0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000	0.112331	0.0561656	+	0.998421i	$0.482113\pi$
$318$	4.00000	0.224309
$319$	9.00000	0.503903
$320$	−8.00000	−0.447214
$321$	14.0000	0.781404
$322$	−4.00000	−0.222911
$323$	6.00000	0.333849
$324$	2.00000	0.111111
$325$	3.00000	0.166410
$326$	8.00000	0.443079
$327$	−1.00000	−0.0553001
$328$	0	0
$329$	3.00000	0.165395
$330$	−6.00000	−0.330289
$331$	24.0000	1.31916	0.659580	−	0.751635i	$-0.270734\pi$
$331$	24.0000	1.31916	0.659580	+	0.751635i	$0.270734\pi$
$332$	−8.00000	−0.439057
$333$	8.00000	0.438397
$334$	−30.0000	−1.64153
$335$	8.00000	0.437087
$336$	−4.00000	−0.218218
$337$	−28.0000	−1.52526	−0.762629	−	0.646837i	$-0.776092\pi$
$337$	−28.0000	−1.52526	−0.762629	+	0.646837i	$0.776092\pi$
$338$	−8.00000	−0.435143
$339$	8.00000	0.434500
$340$	−2.00000	−0.108465
$341$	6.00000	0.324918
$342$	24.0000	1.29777
$343$	1.00000	0.0539949
$344$	0	0
$345$	−2.00000	−0.107676
$346$	−18.0000	−0.967686
$347$	30.0000	1.61048	0.805242	−	0.592946i	$-0.202035\pi$
$347$	30.0000	1.61048	0.805242	+	0.592946i	$0.202035\pi$
$348$	−6.00000	−0.321634
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	2.00000	0.106904
$351$	−15.0000	−0.800641
$352$	24.0000	1.27920
$353$	−15.0000	−0.798369	−0.399185	−	0.916871i	$-0.630707\pi$
$353$	−15.0000	−0.798369	−0.399185	+	0.916871i	$0.630707\pi$
$354$	−16.0000	−0.850390
$355$	12.0000	0.636894
$356$	24.0000	1.27200
$357$	−1.00000	−0.0529256
$358$	−24.0000	−1.26844
$359$	32.0000	1.68890	0.844448	−	0.535638i	$-0.179929\pi$
$359$	32.0000	1.68890	0.844448	+	0.535638i	$0.179929\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	−12.0000	−0.630706
$363$	−2.00000	−0.104973
$364$	6.00000	0.314485
$365$	−2.00000	−0.104685
$366$	−20.0000	−1.04542
$367$	−27.0000	−1.40939	−0.704694	−	0.709511i	$-0.748916\pi$
$367$	−27.0000	−1.40939	−0.704694	+	0.709511i	$0.748916\pi$
$368$	8.00000	0.417029
$369$	12.0000	0.624695
$370$	−8.00000	−0.415900
$371$	2.00000	0.103835
$372$	−4.00000	−0.207390
$373$	−24.0000	−1.24267	−0.621336	−	0.783544i	$-0.713410\pi$
$373$	−24.0000	−1.24267	−0.621336	+	0.783544i	$0.713410\pi$
$374$	6.00000	0.310253
$375$	1.00000	0.0516398
$376$	0	0
$377$	−9.00000	−0.463524
$378$	−10.0000	−0.514344
$379$	12.0000	0.616399	0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000	0.616399	0.308199	+	0.951322i	$0.400274\pi$
$380$	−12.0000	−0.615587
$381$	−6.00000	−0.307389
$382$	−26.0000	−1.33028
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	0	0
$385$	−3.00000	−0.152894
$386$	8.00000	0.407189
$387$	16.0000	0.813326
$388$	14.0000	0.710742
$389$	−33.0000	−1.67317	−0.836583	−	0.547840i	$-0.815450\pi$
$389$	−33.0000	−1.67317	−0.836583	+	0.547840i	$0.815450\pi$
$390$	6.00000	0.303822
$391$	2.00000	0.101144
$392$	0	0
$393$	−18.0000	−0.907980
$394$	20.0000	1.00759
$395$	9.00000	0.452839
$396$	12.0000	0.603023
$397$	11.0000	0.552074	0.276037	−	0.961147i	$-0.410979\pi$
$397$	11.0000	0.552074	0.276037	+	0.961147i	$0.410979\pi$
$398$	−40.0000	−2.00502
$399$	−6.00000	−0.300376
$400$	−4.00000	−0.200000
$401$	−39.0000	−1.94757	−0.973784	−	0.227477i	$-0.926952\pi$
$401$	−39.0000	−1.94757	−0.973784	+	0.227477i	$0.926952\pi$
$402$	16.0000	0.798007
$403$	−6.00000	−0.298881
$404$	16.0000	0.796030
$405$	1.00000	0.0496904
$406$	−6.00000	−0.297775
$407$	12.0000	0.594818
$408$	0	0
$409$	−24.0000	−1.18672	−0.593362	−	0.804936i	$-0.702200\pi$
$409$	−24.0000	−1.18672	−0.593362	+	0.804936i	$0.702200\pi$
$410$	−12.0000	−0.592638
$411$	−8.00000	−0.394611
$412$	18.0000	0.886796
$413$	−8.00000	−0.393654
$414$	8.00000	0.393179
$415$	−4.00000	−0.196352
$416$	−24.0000	−1.17670
$417$	−2.00000	−0.0979404
$418$	36.0000	1.76082
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	2.00000	0.0975900
$421$	29.0000	1.41337	0.706687	−	0.707527i	$-0.250189\pi$
$421$	29.0000	1.41337	0.706687	+	0.707527i	$0.250189\pi$
$422$	−46.0000	−2.23924
$423$	−6.00000	−0.291730
$424$	0	0
$425$	−1.00000	−0.0485071
$426$	24.0000	1.16280
$427$	−10.0000	−0.483934
$428$	28.0000	1.35343
$429$	−9.00000	−0.434524
$430$	−16.0000	−0.771589
$431$	5.00000	0.240842	0.120421	−	0.992723i	$-0.461576\pi$
$431$	5.00000	0.240842	0.120421	+	0.992723i	$0.461576\pi$
$432$	20.0000	0.962250
$433$	−38.0000	−1.82616	−0.913082	−	0.407777i	$-0.866304\pi$
$433$	−38.0000	−1.82616	−0.913082	+	0.407777i	$0.866304\pi$
$434$	−4.00000	−0.192006
$435$	−3.00000	−0.143839
$436$	−2.00000	−0.0957826
$437$	12.0000	0.574038
$438$	−4.00000	−0.191127
$439$	−14.0000	−0.668184	−0.334092	−	0.942541i	$-0.608430\pi$
$439$	−14.0000	−0.668184	−0.334092	+	0.942541i	$0.608430\pi$
$440$	0	0
$441$	−2.00000	−0.0952381
$442$	−6.00000	−0.285391
$443$	−6.00000	−0.285069	−0.142534	−	0.989790i	$-0.545525\pi$
$443$	−6.00000	−0.285069	−0.142534	+	0.989790i	$0.545525\pi$
$444$	−8.00000	−0.379663
$445$	12.0000	0.568855
$446$	−26.0000	−1.23114
$447$	−6.00000	−0.283790
$448$	−8.00000	−0.377964
$449$	−1.00000	−0.0471929	−0.0235965	−	0.999722i	$-0.507512\pi$
$449$	−1.00000	−0.0471929	−0.0235965	+	0.999722i	$0.507512\pi$
$450$	−4.00000	−0.188562
$451$	18.0000	0.847587
$452$	16.0000	0.752577
$453$	15.0000	0.704761
$454$	14.0000	0.657053
$455$	3.00000	0.140642
$456$	0	0
$457$	26.0000	1.21623	0.608114	−	0.793849i	$-0.291926\pi$
$457$	26.0000	1.21623	0.608114	+	0.793849i	$0.291926\pi$
$458$	−2.00000	−0.0934539
$459$	5.00000	0.233380
$460$	−4.00000	−0.186501
$461$	14.0000	0.652045	0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000	0.652045	0.326023	+	0.945362i	$0.394291\pi$
$462$	−6.00000	−0.279145
$463$	−10.0000	−0.464739	−0.232370	−	0.972628i	$-0.574648\pi$
$463$	−10.0000	−0.464739	−0.232370	+	0.972628i	$0.574648\pi$
$464$	12.0000	0.557086
$465$	−2.00000	−0.0927478
$466$	−40.0000	−1.85296
$467$	−1.00000	−0.0462745	−0.0231372	−	0.999732i	$-0.507365\pi$
$467$	−1.00000	−0.0462745	−0.0231372	+	0.999732i	$0.507365\pi$
$468$	−12.0000	−0.554700
$469$	8.00000	0.369406
$470$	6.00000	0.276759
$471$	2.00000	0.0921551
$472$	0	0
$473$	24.0000	1.10352
$474$	18.0000	0.826767
$475$	−6.00000	−0.275299
$476$	−2.00000	−0.0916698
$477$	−4.00000	−0.183147
$478$	50.0000	2.28695
$479$	16.0000	0.731059	0.365529	−	0.930800i	$-0.380888\pi$
$479$	16.0000	0.731059	0.365529	+	0.930800i	$0.380888\pi$
$480$	−8.00000	−0.365148
$481$	−12.0000	−0.547153
$482$	52.0000	2.36854
$483$	−2.00000	−0.0910032
$484$	−4.00000	−0.181818
$485$	7.00000	0.317854
$486$	32.0000	1.45155
$487$	−4.00000	−0.181257	−0.0906287	−	0.995885i	$-0.528888\pi$
$487$	−4.00000	−0.181257	−0.0906287	+	0.995885i	$0.528888\pi$
$488$	0	0
$489$	4.00000	0.180886
$490$	2.00000	0.0903508
$491$	19.0000	0.857458	0.428729	−	0.903433i	$-0.358962\pi$
$491$	19.0000	0.857458	0.428729	+	0.903433i	$0.358962\pi$
$492$	−12.0000	−0.541002
$493$	3.00000	0.135113
$494$	−36.0000	−1.61972
$495$	6.00000	0.269680
$496$	8.00000	0.359211
$497$	12.0000	0.538274
$498$	−8.00000	−0.358489
$499$	−13.0000	−0.581960	−0.290980	−	0.956729i	$-0.593981\pi$
$499$	−13.0000	−0.581960	−0.290980	+	0.956729i	$0.593981\pi$
$500$	2.00000	0.0894427
$501$	−15.0000	−0.670151
$502$	60.0000	2.67793
$503$	−33.0000	−1.47140	−0.735699	−	0.677309i	$-0.763146\pi$
$503$	−33.0000	−1.47140	−0.735699	+	0.677309i	$0.763146\pi$
$504$	0	0
$505$	8.00000	0.355995
$506$	12.0000	0.533465
$507$	−4.00000	−0.177646
$508$	−12.0000	−0.532414
$509$	−26.0000	−1.15243	−0.576215	−	0.817298i	$-0.695471\pi$
$509$	−26.0000	−1.15243	−0.576215	+	0.817298i	$0.695471\pi$
$510$	−2.00000	−0.0885615
$511$	−2.00000	−0.0884748
$512$	32.0000	1.41421
$513$	30.0000	1.32453
$514$	−60.0000	−2.64649
$515$	9.00000	0.396587
$516$	−16.0000	−0.704361
$517$	−9.00000	−0.395820
$518$	−8.00000	−0.351500
$519$	−9.00000	−0.395056
$520$	0	0
$521$	30.0000	1.31432	0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000	1.31432	0.657162	+	0.753749i	$0.271757\pi$
$522$	12.0000	0.525226
$523$	8.00000	0.349816	0.174908	−	0.984585i	$-0.444037\pi$
$523$	8.00000	0.349816	0.174908	+	0.984585i	$0.444037\pi$
$524$	−36.0000	−1.57267
$525$	1.00000	0.0436436
$526$	−36.0000	−1.56967
$527$	2.00000	0.0871214
$528$	12.0000	0.522233
$529$	−19.0000	−0.826087
$530$	4.00000	0.173749
$531$	16.0000	0.694341
$532$	−12.0000	−0.520266
$533$	−18.0000	−0.779667
$534$	24.0000	1.03858
$535$	14.0000	0.605273
$536$	0	0
$537$	−12.0000	−0.517838
$538$	48.0000	2.06943
$539$	−3.00000	−0.129219
$540$	−10.0000	−0.430331
$541$	−29.0000	−1.24681	−0.623404	−	0.781900i	$-0.714251\pi$
$541$	−29.0000	−1.24681	−0.623404	+	0.781900i	$0.714251\pi$
$542$	44.0000	1.88996
$543$	−6.00000	−0.257485
$544$	8.00000	0.342997
$545$	−1.00000	−0.0428353
$546$	6.00000	0.256776
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	−16.0000	−0.683486
$549$	20.0000	0.853579
$550$	−6.00000	−0.255841
$551$	18.0000	0.766826
$552$	0	0
$553$	9.00000	0.382719
$554$	−4.00000	−0.169944
$555$	−4.00000	−0.169791
$556$	−4.00000	−0.169638
$557$	−34.0000	−1.44063	−0.720313	−	0.693649i	$-0.756002\pi$
$557$	−34.0000	−1.44063	−0.720313	+	0.693649i	$0.756002\pi$
$558$	8.00000	0.338667
$559$	−24.0000	−1.01509
$560$	−4.00000	−0.169031
$561$	3.00000	0.126660
$562$	−46.0000	−1.94039
$563$	−12.0000	−0.505740	−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000	−0.505740	−0.252870	+	0.967500i	$0.581374\pi$
$564$	6.00000	0.252646
$565$	8.00000	0.336563
$566$	−6.00000	−0.252199
$567$	1.00000	0.0419961
$568$	0	0
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	−12.0000	−0.502625
$571$	−20.0000	−0.836974	−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000	−0.836974	−0.418487	+	0.908223i	$0.637439\pi$
$572$	−18.0000	−0.752618
$573$	−13.0000	−0.543083
$574$	−12.0000	−0.500870
$575$	−2.00000	−0.0834058
$576$	16.0000	0.666667
$577$	11.0000	0.457936	0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000	0.457936	0.228968	+	0.973434i	$0.426465\pi$
$578$	−32.0000	−1.33102
$579$	4.00000	0.166234
$580$	−6.00000	−0.249136
$581$	−4.00000	−0.165948
$582$	14.0000	0.580319
$583$	−6.00000	−0.248495
$584$	0	0
$585$	−6.00000	−0.248069
$586$	−18.0000	−0.743573
$587$	36.0000	1.48588	0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000	1.48588	0.742940	+	0.669359i	$0.233431\pi$
$588$	2.00000	0.0824786
$589$	12.0000	0.494451
$590$	−16.0000	−0.658710
$591$	10.0000	0.411345
$592$	16.0000	0.657596
$593$	33.0000	1.35515	0.677574	−	0.735455i	$-0.263031\pi$
$593$	33.0000	1.35515	0.677574	+	0.735455i	$0.263031\pi$
$594$	30.0000	1.23091
$595$	−1.00000	−0.0409960
$596$	−12.0000	−0.491539
$597$	−20.0000	−0.818546
$598$	−12.0000	−0.490716
$599$	−33.0000	−1.34834	−0.674172	−	0.738575i	$-0.735499\pi$
$599$	−33.0000	−1.34834	−0.674172	+	0.738575i	$0.735499\pi$
$600$	0	0
$601$	8.00000	0.326327	0.163163	−	0.986599i	$-0.447830\pi$
$601$	8.00000	0.326327	0.163163	+	0.986599i	$0.447830\pi$
$602$	−16.0000	−0.652111
$603$	−16.0000	−0.651570
$604$	30.0000	1.22068
$605$	−2.00000	−0.0813116
$606$	16.0000	0.649956
$607$	−1.00000	−0.0405887	−0.0202944	−	0.999794i	$-0.506460\pi$
$607$	−1.00000	−0.0405887	−0.0202944	+	0.999794i	$0.506460\pi$
$608$	48.0000	1.94666
$609$	−3.00000	−0.121566
$610$	−20.0000	−0.809776
$611$	9.00000	0.364101
$612$	4.00000	0.161690
$613$	38.0000	1.53481	0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000	1.53481	0.767403	+	0.641165i	$0.221549\pi$
$614$	62.0000	2.50212
$615$	−6.00000	−0.241943
$616$	0	0
$617$	−24.0000	−0.966204	−0.483102	−	0.875564i	$-0.660490\pi$
$617$	−24.0000	−0.966204	−0.483102	+	0.875564i	$0.660490\pi$
$618$	18.0000	0.724066
$619$	44.0000	1.76851	0.884255	−	0.467005i	$-0.154667\pi$
$619$	44.0000	1.76851	0.884255	+	0.467005i	$0.154667\pi$
$620$	−4.00000	−0.160644
$621$	10.0000	0.401286
$622$	40.0000	1.60385
$623$	12.0000	0.480770
$624$	−12.0000	−0.480384
$625$	1.00000	0.0400000
$626$	−34.0000	−1.35891
$627$	18.0000	0.718851
$628$	4.00000	0.159617
$629$	4.00000	0.159490
$630$	−4.00000	−0.159364
$631$	−7.00000	−0.278666	−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000	−0.278666	−0.139333	+	0.990246i	$0.544496\pi$
$632$	0	0
$633$	−23.0000	−0.914168
$634$	4.00000	0.158860
$635$	−6.00000	−0.238103
$636$	4.00000	0.158610
$637$	3.00000	0.118864
$638$	18.0000	0.712627
$639$	−24.0000	−0.949425
$640$	0	0
$641$	30.0000	1.18493	0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000	1.18493	0.592464	+	0.805597i	$0.298155\pi$
$642$	28.0000	1.10507
$643$	−11.0000	−0.433798	−0.216899	−	0.976194i	$-0.569594\pi$
$643$	−11.0000	−0.433798	−0.216899	+	0.976194i	$0.569594\pi$
$644$	−4.00000	−0.157622
$645$	−8.00000	−0.315000
$646$	12.0000	0.472134
$647$	32.0000	1.25805	0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000	1.25805	0.629025	+	0.777385i	$0.283454\pi$
$648$	0	0
$649$	24.0000	0.942082
$650$	6.00000	0.235339
$651$	−2.00000	−0.0783862
$652$	8.00000	0.313304
$653$	30.0000	1.17399	0.586995	−	0.809590i	$-0.300311\pi$
$653$	30.0000	1.17399	0.586995	+	0.809590i	$0.300311\pi$
$654$	−2.00000	−0.0782062
$655$	−18.0000	−0.703318
$656$	24.0000	0.937043
$657$	4.00000	0.156055
$658$	6.00000	0.233904
$659$	−1.00000	−0.0389545	−0.0194772	−	0.999810i	$-0.506200\pi$
$659$	−1.00000	−0.0389545	−0.0194772	+	0.999810i	$0.506200\pi$
$660$	−6.00000	−0.233550
$661$	32.0000	1.24466	0.622328	−	0.782757i	$-0.286187\pi$
$661$	32.0000	1.24466	0.622328	+	0.782757i	$0.286187\pi$
$662$	48.0000	1.86557
$663$	−3.00000	−0.116510
$664$	0	0
$665$	−6.00000	−0.232670
$666$	16.0000	0.619987
$667$	6.00000	0.232321
$668$	−30.0000	−1.16073
$669$	−13.0000	−0.502609
$670$	16.0000	0.618134
$671$	30.0000	1.15814
$672$	−8.00000	−0.308607
$673$	−12.0000	−0.462566	−0.231283	−	0.972887i	$-0.574292\pi$
$673$	−12.0000	−0.462566	−0.231283	+	0.972887i	$0.574292\pi$
$674$	−56.0000	−2.15704
$675$	−5.00000	−0.192450
$676$	−8.00000	−0.307692
$677$	−5.00000	−0.192166	−0.0960828	−	0.995373i	$-0.530631\pi$
$677$	−5.00000	−0.192166	−0.0960828	+	0.995373i	$0.530631\pi$
$678$	16.0000	0.614476
$679$	7.00000	0.268635
$680$	0	0
$681$	7.00000	0.268241
$682$	12.0000	0.459504
$683$	36.0000	1.37750	0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000	1.37750	0.688751	+	0.724998i	$0.258159\pi$
$684$	24.0000	0.917663
$685$	−8.00000	−0.305664
$686$	2.00000	0.0763604
$687$	−1.00000	−0.0381524
$688$	32.0000	1.21999
$689$	6.00000	0.228582
$690$	−4.00000	−0.152277
$691$	−26.0000	−0.989087	−0.494543	−	0.869153i	$-0.664665\pi$
$691$	−26.0000	−0.989087	−0.494543	+	0.869153i	$0.664665\pi$
$692$	−18.0000	−0.684257
$693$	6.00000	0.227921
$694$	60.0000	2.27757
$695$	−2.00000	−0.0758643
$696$	0	0
$697$	6.00000	0.227266
$698$	4.00000	0.151402
$699$	−20.0000	−0.756469
$700$	2.00000	0.0755929
$701$	−17.0000	−0.642081	−0.321041	−	0.947065i	$-0.604033\pi$
$701$	−17.0000	−0.642081	−0.321041	+	0.947065i	$0.604033\pi$
$702$	−30.0000	−1.13228
$703$	24.0000	0.905177
$704$	24.0000	0.904534
$705$	3.00000	0.112987
$706$	−30.0000	−1.12906
$707$	8.00000	0.300871
$708$	−16.0000	−0.601317
$709$	13.0000	0.488225	0.244113	−	0.969747i	$-0.421503\pi$
$709$	13.0000	0.488225	0.244113	+	0.969747i	$0.421503\pi$
$710$	24.0000	0.900704
$711$	−18.0000	−0.675053
$712$	0	0
$713$	4.00000	0.149801
$714$	−2.00000	−0.0748481
$715$	−9.00000	−0.336581
$716$	−24.0000	−0.896922
$717$	25.0000	0.933642
$718$	64.0000	2.38846
$719$	6.00000	0.223762	0.111881	−	0.993722i	$-0.464312\pi$
$719$	6.00000	0.223762	0.111881	+	0.993722i	$0.464312\pi$
$720$	8.00000	0.298142
$721$	9.00000	0.335178
$722$	34.0000	1.26535
$723$	26.0000	0.966950
$724$	−12.0000	−0.445976
$725$	−3.00000	−0.111417
$726$	−4.00000	−0.148454
$727$	−40.0000	−1.48352	−0.741759	−	0.670667i	$-0.766008\pi$
$727$	−40.0000	−1.48352	−0.741759	+	0.670667i	$0.766008\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	−4.00000	−0.148047
$731$	8.00000	0.295891
$732$	−20.0000	−0.739221
$733$	−15.0000	−0.554038	−0.277019	−	0.960864i	$-0.589346\pi$
$733$	−15.0000	−0.554038	−0.277019	+	0.960864i	$0.589346\pi$
$734$	−54.0000	−1.99318
$735$	1.00000	0.0368856
$736$	16.0000	0.589768
$737$	−24.0000	−0.884051
$738$	24.0000	0.883452
$739$	−29.0000	−1.06678	−0.533391	−	0.845869i	$-0.679083\pi$
$739$	−29.0000	−1.06678	−0.533391	+	0.845869i	$0.679083\pi$
$740$	−8.00000	−0.294086
$741$	−18.0000	−0.661247
$742$	4.00000	0.146845
$743$	16.0000	0.586983	0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000	0.586983	0.293492	+	0.955962i	$0.405183\pi$
$744$	0	0
$745$	−6.00000	−0.219823
$746$	−48.0000	−1.75740
$747$	8.00000	0.292705
$748$	6.00000	0.219382
$749$	14.0000	0.511549
$750$	2.00000	0.0730297
$751$	7.00000	0.255434	0.127717	−	0.991811i	$-0.459235\pi$
$751$	7.00000	0.255434	0.127717	+	0.991811i	$0.459235\pi$
$752$	−12.0000	−0.437595
$753$	30.0000	1.09326
$754$	−18.0000	−0.655521
$755$	15.0000	0.545906
$756$	−10.0000	−0.363696
$757$	−42.0000	−1.52652	−0.763258	−	0.646094i	$-0.776401\pi$
$757$	−42.0000	−1.52652	−0.763258	+	0.646094i	$0.776401\pi$
$758$	24.0000	0.871719
$759$	6.00000	0.217786
$760$	0	0
$761$	22.0000	0.797499	0.398750	−	0.917060i	$-0.369444\pi$
$761$	22.0000	0.797499	0.398750	+	0.917060i	$0.369444\pi$
$762$	−12.0000	−0.434714
$763$	−1.00000	−0.0362024
$764$	−26.0000	−0.940647
$765$	2.00000	0.0723102
$766$	−48.0000	−1.73431
$767$	−24.0000	−0.866590
$768$	16.0000	0.577350
$769$	14.0000	0.504853	0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000	0.504853	0.252426	+	0.967616i	$0.418771\pi$
$770$	−6.00000	−0.216225
$771$	−30.0000	−1.08042
$772$	8.00000	0.287926
$773$	−37.0000	−1.33080	−0.665399	−	0.746488i	$-0.731738\pi$
$773$	−37.0000	−1.33080	−0.665399	+	0.746488i	$0.731738\pi$
$774$	32.0000	1.15022
$775$	−2.00000	−0.0718421
$776$	0	0
$777$	−4.00000	−0.143499
$778$	−66.0000	−2.36621
$779$	36.0000	1.28983
$780$	6.00000	0.214834
$781$	−36.0000	−1.28818
$782$	4.00000	0.143040
$783$	15.0000	0.536056
$784$	−4.00000	−0.142857
$785$	2.00000	0.0713831
$786$	−36.0000	−1.28408
$787$	37.0000	1.31891	0.659454	−	0.751745i	$-0.270788\pi$
$787$	37.0000	1.31891	0.659454	+	0.751745i	$0.270788\pi$
$788$	20.0000	0.712470
$789$	−18.0000	−0.640817
$790$	18.0000	0.640411
$791$	8.00000	0.284447
$792$	0	0
$793$	−30.0000	−1.06533
$794$	22.0000	0.780751
$795$	2.00000	0.0709327
$796$	−40.0000	−1.41776
$797$	13.0000	0.460484	0.230242	−	0.973133i	$-0.426048\pi$
$797$	13.0000	0.460484	0.230242	+	0.973133i	$0.426048\pi$
$798$	−12.0000	−0.424795
$799$	−3.00000	−0.106132
$800$	−8.00000	−0.282843
$801$	−24.0000	−0.847998
$802$	−78.0000	−2.75428
$803$	6.00000	0.211735
$804$	16.0000	0.564276
$805$	−2.00000	−0.0704907
$806$	−12.0000	−0.422682
$807$	24.0000	0.844840
$808$	0	0
$809$	27.0000	0.949269	0.474635	−	0.880183i	$-0.342580\pi$
$809$	27.0000	0.949269	0.474635	+	0.880183i	$0.342580\pi$
$810$	2.00000	0.0702728
$811$	6.00000	0.210688	0.105344	−	0.994436i	$-0.466406\pi$
$811$	6.00000	0.210688	0.105344	+	0.994436i	$0.466406\pi$
$812$	−6.00000	−0.210559
$813$	22.0000	0.771574
$814$	24.0000	0.841200
$815$	4.00000	0.140114
$816$	4.00000	0.140028
$817$	48.0000	1.67931
$818$	−48.0000	−1.67828
$819$	−6.00000	−0.209657
$820$	−12.0000	−0.419058
$821$	−3.00000	−0.104701	−0.0523504	−	0.998629i	$-0.516671\pi$
$821$	−3.00000	−0.104701	−0.0523504	+	0.998629i	$0.516671\pi$
$822$	−16.0000	−0.558064
$823$	4.00000	0.139431	0.0697156	−	0.997567i	$-0.477791\pi$
$823$	4.00000	0.139431	0.0697156	+	0.997567i	$0.477791\pi$
$824$	0	0
$825$	−3.00000	−0.104447
$826$	−16.0000	−0.556711
$827$	10.0000	0.347734	0.173867	−	0.984769i	$-0.444374\pi$
$827$	10.0000	0.347734	0.173867	+	0.984769i	$0.444374\pi$
$828$	8.00000	0.278019
$829$	−52.0000	−1.80603	−0.903017	−	0.429604i	$-0.858653\pi$
$829$	−52.0000	−1.80603	−0.903017	+	0.429604i	$0.858653\pi$
$830$	−8.00000	−0.277684
$831$	−2.00000	−0.0693792
$832$	−24.0000	−0.832050
$833$	−1.00000	−0.0346479
$834$	−4.00000	−0.138509
$835$	−15.0000	−0.519096
$836$	36.0000	1.24509
$837$	10.0000	0.345651
$838$	0	0
$839$	−14.0000	−0.483334	−0.241667	−	0.970359i	$-0.577694\pi$
$839$	−14.0000	−0.483334	−0.241667	+	0.970359i	$0.577694\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	58.0000	1.99881
$843$	−23.0000	−0.792162
$844$	−46.0000	−1.58339
$845$	−4.00000	−0.137604
$846$	−12.0000	−0.412568
$847$	−2.00000	−0.0687208
$848$	−8.00000	−0.274721
$849$	−3.00000	−0.102960
$850$	−2.00000	−0.0685994
$851$	8.00000	0.274236
$852$	24.0000	0.822226
$853$	−50.0000	−1.71197	−0.855984	−	0.517003i	$-0.827048\pi$
$853$	−50.0000	−1.71197	−0.855984	+	0.517003i	$0.827048\pi$
$854$	−20.0000	−0.684386
$855$	12.0000	0.410391
$856$	0	0
$857$	26.0000	0.888143	0.444072	−	0.895991i	$-0.353534\pi$
$857$	26.0000	0.888143	0.444072	+	0.895991i	$0.353534\pi$
$858$	−18.0000	−0.614510
$859$	−8.00000	−0.272956	−0.136478	−	0.990643i	$-0.543578\pi$
$859$	−8.00000	−0.272956	−0.136478	+	0.990643i	$0.543578\pi$
$860$	−16.0000	−0.545595
$861$	−6.00000	−0.204479
$862$	10.0000	0.340601
$863$	−48.0000	−1.63394	−0.816970	−	0.576681i	$-0.804348\pi$
$863$	−48.0000	−1.63394	−0.816970	+	0.576681i	$0.804348\pi$
$864$	40.0000	1.36083
$865$	−9.00000	−0.306009
$866$	−76.0000	−2.58259
$867$	−16.0000	−0.543388
$868$	−4.00000	−0.135769
$869$	−27.0000	−0.915912
$870$	−6.00000	−0.203419
$871$	24.0000	0.813209
$872$	0	0
$873$	−14.0000	−0.473828
$874$	24.0000	0.811812
$875$	1.00000	0.0338062
$876$	−4.00000	−0.135147
$877$	22.0000	0.742887	0.371444	−	0.928456i	$-0.378863\pi$
$877$	22.0000	0.742887	0.371444	+	0.928456i	$0.378863\pi$
$878$	−28.0000	−0.944954
$879$	−9.00000	−0.303562
$880$	12.0000	0.404520
$881$	2.00000	0.0673817	0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000	0.0673817	0.0336909	+	0.999432i	$0.489274\pi$
$882$	−4.00000	−0.134687
$883$	14.0000	0.471138	0.235569	−	0.971858i	$-0.424305\pi$
$883$	14.0000	0.471138	0.235569	+	0.971858i	$0.424305\pi$
$884$	−6.00000	−0.201802
$885$	−8.00000	−0.268917
$886$	−12.0000	−0.403148
$887$	8.00000	0.268614	0.134307	−	0.990940i	$-0.457119\pi$
$887$	8.00000	0.268614	0.134307	+	0.990940i	$0.457119\pi$
$888$	0	0
$889$	−6.00000	−0.201234
$890$	24.0000	0.804482
$891$	−3.00000	−0.100504
$892$	−26.0000	−0.870544
$893$	−18.0000	−0.602347
$894$	−12.0000	−0.401340
$895$	−12.0000	−0.401116
$896$	0	0
$897$	−6.00000	−0.200334
$898$	−2.00000	−0.0667409
$899$	6.00000	0.200111
$900$	−4.00000	−0.133333
$901$	−2.00000	−0.0666297
$902$	36.0000	1.19867
$903$	−8.00000	−0.266223
$904$	0	0
$905$	−6.00000	−0.199447
$906$	30.0000	0.996683
$907$	−24.0000	−0.796907	−0.398453	−	0.917189i	$-0.630453\pi$
$907$	−24.0000	−0.796907	−0.398453	+	0.917189i	$0.630453\pi$
$908$	14.0000	0.464606
$909$	−16.0000	−0.530687
$910$	6.00000	0.198898
$911$	−36.0000	−1.19273	−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000	−1.19273	−0.596367	+	0.802712i	$0.703390\pi$
$912$	24.0000	0.794719
$913$	12.0000	0.397142
$914$	52.0000	1.72001
$915$	−10.0000	−0.330590
$916$	−2.00000	−0.0660819
$917$	−18.0000	−0.594412
$918$	10.0000	0.330049
$919$	−9.00000	−0.296883	−0.148441	−	0.988921i	$-0.547426\pi$
$919$	−9.00000	−0.296883	−0.148441	+	0.988921i	$0.547426\pi$
$920$	0	0
$921$	31.0000	1.02148
$922$	28.0000	0.922131
$923$	36.0000	1.18495
$924$	−6.00000	−0.197386
$925$	−4.00000	−0.131519
$926$	−20.0000	−0.657241
$927$	−18.0000	−0.591198
$928$	24.0000	0.787839
$929$	16.0000	0.524943	0.262471	−	0.964940i	$-0.415462\pi$
$929$	16.0000	0.524943	0.262471	+	0.964940i	$0.415462\pi$
$930$	−4.00000	−0.131165
$931$	−6.00000	−0.196642
$932$	−40.0000	−1.31024
$933$	20.0000	0.654771
$934$	−2.00000	−0.0654420
$935$	3.00000	0.0981105
$936$	0	0
$937$	−35.0000	−1.14340	−0.571700	−	0.820463i	$-0.693716\pi$
$937$	−35.0000	−1.14340	−0.571700	+	0.820463i	$0.693716\pi$
$938$	16.0000	0.522419
$939$	−17.0000	−0.554774
$940$	6.00000	0.195698
$941$	28.0000	0.912774	0.456387	−	0.889781i	$-0.349143\pi$
$941$	28.0000	0.912774	0.456387	+	0.889781i	$0.349143\pi$
$942$	4.00000	0.130327
$943$	12.0000	0.390774
$944$	32.0000	1.04151
$945$	−5.00000	−0.162650
$946$	48.0000	1.56061
$947$	48.0000	1.55979	0.779895	−	0.625910i	$-0.215272\pi$
$947$	48.0000	1.55979	0.779895	+	0.625910i	$0.215272\pi$
$948$	18.0000	0.584613
$949$	−6.00000	−0.194768
$950$	−12.0000	−0.389331
$951$	2.00000	0.0648544
$952$	0	0
$953$	14.0000	0.453504	0.226752	−	0.973952i	$-0.427189\pi$
$953$	14.0000	0.453504	0.226752	+	0.973952i	$0.427189\pi$
$954$	−8.00000	−0.259010
$955$	−13.0000	−0.420670
$956$	50.0000	1.61712
$957$	9.00000	0.290929
$958$	32.0000	1.03387
$959$	−8.00000	−0.258333
$960$	−8.00000	−0.258199
$961$	−27.0000	−0.870968
$962$	−24.0000	−0.773791
$963$	−28.0000	−0.902287
$964$	52.0000	1.67481
$965$	4.00000	0.128765
$966$	−4.00000	−0.128698
$967$	−34.0000	−1.09337	−0.546683	−	0.837340i	$-0.684110\pi$
$967$	−34.0000	−1.09337	−0.546683	+	0.837340i	$0.684110\pi$
$968$	0	0
$969$	6.00000	0.192748
$970$	14.0000	0.449513
$971$	−14.0000	−0.449281	−0.224641	−	0.974442i	$-0.572121\pi$
$971$	−14.0000	−0.449281	−0.224641	+	0.974442i	$0.572121\pi$
$972$	32.0000	1.02640
$973$	−2.00000	−0.0641171
$974$	−8.00000	−0.256337
$975$	3.00000	0.0960769
$976$	40.0000	1.28037
$977$	−12.0000	−0.383914	−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000	−0.383914	−0.191957	+	0.981403i	$0.561483\pi$
$978$	8.00000	0.255812
$979$	−36.0000	−1.15056
$980$	2.00000	0.0638877
$981$	2.00000	0.0638551
$982$	38.0000	1.21263
$983$	−39.0000	−1.24391	−0.621953	−	0.783054i	$-0.713661\pi$
$983$	−39.0000	−1.24391	−0.621953	+	0.783054i	$0.713661\pi$
$984$	0	0
$985$	10.0000	0.318626
$986$	6.00000	0.191079
$987$	3.00000	0.0954911
$988$	−36.0000	−1.14531
$989$	16.0000	0.508770
$990$	12.0000	0.381385
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	16.0000	0.508001
$993$	24.0000	0.761617
$994$	24.0000	0.761234
$995$	−20.0000	−0.634043
$996$	−8.00000	−0.253490
$997$	−33.0000	−1.04512	−0.522560	−	0.852602i	$-0.675023\pi$
$997$	−33.0000	−1.04512	−0.522560	+	0.852602i	$0.675023\pi$
$998$	−26.0000	−0.823016
$999$	20.0000	0.632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.f.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.f.1.1	✓	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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