LMFDB - Embedded newform 6498.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6498,2,Mod(1,6498)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6498, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6498.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6498 = 2 \cdot 3^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6498.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:	$51.8867912334$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 342)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6498.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} -2.00000 q^{5} +3.00000 q^{7} -1.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{4} -2.00000 q^{5} +3.00000 q^{7} -1.00000 q^{8} +2.00000 q^{10} -2.00000 q^{11} -1.00000 q^{13} -3.00000 q^{14} +1.00000 q^{16} -6.00000 q^{17} -2.00000 q^{20} +2.00000 q^{22} +4.00000 q^{23} -1.00000 q^{25} +1.00000 q^{26} +3.00000 q^{28} +2.00000 q^{29} +7.00000 q^{31} -1.00000 q^{32} +6.00000 q^{34} -6.00000 q^{35} +1.00000 q^{37} +2.00000 q^{40} +8.00000 q^{41} +7.00000 q^{43} -2.00000 q^{44} -4.00000 q^{46} -8.00000 q^{47} +2.00000 q^{49} +1.00000 q^{50} -1.00000 q^{52} -8.00000 q^{53} +4.00000 q^{55} -3.00000 q^{56} -2.00000 q^{58} +12.0000 q^{59} +5.00000 q^{61} -7.00000 q^{62} +1.00000 q^{64} +2.00000 q^{65} -9.00000 q^{67} -6.00000 q^{68} +6.00000 q^{70} -2.00000 q^{71} -15.0000 q^{73} -1.00000 q^{74} -6.00000 q^{77} +11.0000 q^{79} -2.00000 q^{80} -8.00000 q^{82} -6.00000 q^{83} +12.0000 q^{85} -7.00000 q^{86} +2.00000 q^{88} -3.00000 q^{91} +4.00000 q^{92} +8.00000 q^{94} -14.0000 q^{97} -2.00000 q^{98} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	0	0
$7$	3.00000	1.13389	0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000	1.13389	0.566947	+	0.823754i	$0.308125\pi$
$8$	−1.00000	−0.353553
$9$	0	0
$10$	2.00000	0.632456
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	0	0
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	−3.00000	−0.801784
$15$	0	0
$16$	1.00000	0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	0	0
$19$	0	0
$19$	0	0
$20$	−2.00000	−0.447214
$21$	0	0
$22$	2.00000	0.426401
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	0	0
$25$	−1.00000	−0.200000
$26$	1.00000	0.196116
$27$	0	0
$28$	3.00000	0.566947
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	0	0
$31$	7.00000	1.25724	0.628619	−	0.777714i	$-0.283621\pi$
$31$	7.00000	1.25724	0.628619	+	0.777714i	$0.283621\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	6.00000	1.02899
$35$	−6.00000	−1.01419
$36$	0	0
$37$	1.00000	0.164399	0.0821995	−	0.996616i	$-0.473806\pi$
$37$	1.00000	0.164399	0.0821995	+	0.996616i	$0.473806\pi$
$38$	0	0
$39$	0	0
$40$	2.00000	0.316228
$41$	8.00000	1.24939	0.624695	−	0.780869i	$-0.285223\pi$
$41$	8.00000	1.24939	0.624695	+	0.780869i	$0.285223\pi$
$42$	0	0
$43$	7.00000	1.06749	0.533745	−	0.845645i	$-0.320784\pi$
$43$	7.00000	1.06749	0.533745	+	0.845645i	$0.320784\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	−4.00000	−0.589768
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	0	0
$49$	2.00000	0.285714
$50$	1.00000	0.141421
$51$	0	0
$52$	−1.00000	−0.138675
$53$	−8.00000	−1.09888	−0.549442	−	0.835532i	$-0.685160\pi$
$53$	−8.00000	−1.09888	−0.549442	+	0.835532i	$0.685160\pi$
$54$	0	0
$55$	4.00000	0.539360
$56$	−3.00000	−0.400892
$57$	0	0
$58$	−2.00000	−0.262613
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	0	0
$61$	5.00000	0.640184	0.320092	−	0.947386i	$-0.396286\pi$
$61$	5.00000	0.640184	0.320092	+	0.947386i	$0.396286\pi$
$62$	−7.00000	−0.889001
$63$	0	0
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	0	0
$67$	−9.00000	−1.09952	−0.549762	−	0.835321i	$-0.685282\pi$
$67$	−9.00000	−1.09952	−0.549762	+	0.835321i	$0.685282\pi$
$68$	−6.00000	−0.727607
$69$	0	0
$70$	6.00000	0.717137
$71$	−2.00000	−0.237356	−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000	−0.237356	−0.118678	+	0.992933i	$0.537866\pi$
$72$	0	0
$73$	−15.0000	−1.75562	−0.877809	−	0.479012i	$-0.840995\pi$
$73$	−15.0000	−1.75562	−0.877809	+	0.479012i	$0.840995\pi$
$74$	−1.00000	−0.116248
$75$	0	0
$76$	0	0
$77$	−6.00000	−0.683763
$78$	0	0
$79$	11.0000	1.23760	0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000	1.23760	0.618798	+	0.785550i	$0.287620\pi$
$80$	−2.00000	−0.223607
$81$	0	0
$82$	−8.00000	−0.883452
$83$	−6.00000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	0	0
$85$	12.0000	1.30158
$86$	−7.00000	−0.754829
$87$	0	0
$88$	2.00000	0.213201
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	−3.00000	−0.314485
$92$	4.00000	0.417029
$93$	0	0
$94$	8.00000	0.825137
$95$	0	0
$96$	0	0
$97$	−14.0000	−1.42148	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000	−1.42148	−0.710742	+	0.703452i	$0.751641\pi$
$98$	−2.00000	−0.202031
$99$	0	0
$100$	−1.00000	−0.100000
$101$	−14.0000	−1.39305	−0.696526	−	0.717532i	$-0.745272\pi$
$101$	−14.0000	−1.39305	−0.696526	+	0.717532i	$0.745272\pi$
$102$	0	0
$103$	3.00000	0.295599	0.147799	−	0.989017i	$-0.452781\pi$
$103$	3.00000	0.295599	0.147799	+	0.989017i	$0.452781\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	8.00000	0.777029
$107$	10.0000	0.966736	0.483368	−	0.875417i	$-0.339413\pi$
$107$	10.0000	0.966736	0.483368	+	0.875417i	$0.339413\pi$
$108$	0	0
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	−4.00000	−0.381385
$111$	0	0
$112$	3.00000	0.283473
$113$	−20.0000	−1.88144	−0.940721	−	0.339182i	$-0.889850\pi$
$113$	−20.0000	−1.88144	−0.940721	+	0.339182i	$0.889850\pi$
$114$	0	0
$115$	−8.00000	−0.746004
$116$	2.00000	0.185695
$117$	0	0
$118$	−12.0000	−1.10469
$119$	−18.0000	−1.65006
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−5.00000	−0.452679
$123$	0	0
$124$	7.00000	0.628619
$125$	12.0000	1.07331
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	−2.00000	−0.175412
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	0	0
$133$	0	0
$134$	9.00000	0.777482
$135$	0	0
$136$	6.00000	0.514496
$137$	14.0000	1.19610	0.598050	−	0.801459i	$-0.295942\pi$
$137$	14.0000	1.19610	0.598050	+	0.801459i	$0.295942\pi$
$138$	0	0
$139$	−3.00000	−0.254457	−0.127228	−	0.991873i	$-0.540608\pi$
$139$	−3.00000	−0.254457	−0.127228	+	0.991873i	$0.540608\pi$
$140$	−6.00000	−0.507093
$141$	0	0
$142$	2.00000	0.167836
$143$	2.00000	0.167248
$144$	0	0
$145$	−4.00000	−0.332182
$146$	15.0000	1.24141
$147$	0	0
$148$	1.00000	0.0821995
$149$	−18.0000	−1.47462	−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000	−1.47462	−0.737309	+	0.675556i	$0.763904\pi$
$150$	0	0
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	0	0
$153$	0	0
$154$	6.00000	0.483494
$155$	−14.0000	−1.12451
$156$	0	0
$157$	13.0000	1.03751	0.518756	−	0.854922i	$-0.326395\pi$
$157$	13.0000	1.03751	0.518756	+	0.854922i	$0.326395\pi$
$158$	−11.0000	−0.875113
$159$	0	0
$160$	2.00000	0.158114
$161$	12.0000	0.945732
$162$	0	0
$163$	−13.0000	−1.01824	−0.509119	−	0.860696i	$-0.670029\pi$
$163$	−13.0000	−1.01824	−0.509119	+	0.860696i	$0.670029\pi$
$164$	8.00000	0.624695
$165$	0	0
$166$	6.00000	0.465690
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	−12.0000	−0.920358
$171$	0	0
$172$	7.00000	0.533745
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	0	0
$175$	−3.00000	−0.226779
$176$	−2.00000	−0.150756
$177$	0	0
$178$	0	0
$179$	24.0000	1.79384	0.896922	−	0.442189i	$-0.145798\pi$
$179$	24.0000	1.79384	0.896922	+	0.442189i	$0.145798\pi$
$180$	0	0
$181$	22.0000	1.63525	0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000	1.63525	0.817624	+	0.575753i	$0.195291\pi$
$182$	3.00000	0.222375
$183$	0	0
$184$	−4.00000	−0.294884
$185$	−2.00000	−0.147043
$186$	0	0
$187$	12.0000	0.877527
$188$	−8.00000	−0.583460
$189$	0	0
$190$	0	0
$191$	−22.0000	−1.59186	−0.795932	−	0.605386i	$-0.793019\pi$
$191$	−22.0000	−1.59186	−0.795932	+	0.605386i	$0.793019\pi$
$192$	0	0
$193$	−9.00000	−0.647834	−0.323917	−	0.946085i	$-0.605000\pi$
$193$	−9.00000	−0.647834	−0.323917	+	0.946085i	$0.605000\pi$
$194$	14.0000	1.00514
$195$	0	0
$196$	2.00000	0.142857
$197$	−8.00000	−0.569976	−0.284988	−	0.958531i	$-0.591990\pi$
$197$	−8.00000	−0.569976	−0.284988	+	0.958531i	$0.591990\pi$
$198$	0	0
$199$	11.0000	0.779769	0.389885	−	0.920864i	$-0.372515\pi$
$199$	11.0000	0.779769	0.389885	+	0.920864i	$0.372515\pi$
$200$	1.00000	0.0707107
$201$	0	0
$202$	14.0000	0.985037
$203$	6.00000	0.421117
$204$	0	0
$205$	−16.0000	−1.11749
$206$	−3.00000	−0.209020
$207$	0	0
$208$	−1.00000	−0.0693375
$209$	0	0
$210$	0	0
$211$	−15.0000	−1.03264	−0.516321	−	0.856395i	$-0.672699\pi$
$211$	−15.0000	−1.03264	−0.516321	+	0.856395i	$0.672699\pi$
$212$	−8.00000	−0.549442
$213$	0	0
$214$	−10.0000	−0.683586
$215$	−14.0000	−0.954792
$216$	0	0
$217$	21.0000	1.42557
$218$	6.00000	0.406371
$219$	0	0
$220$	4.00000	0.269680
$221$	6.00000	0.403604
$222$	0	0
$223$	11.0000	0.736614	0.368307	−	0.929704i	$-0.379937\pi$
$223$	11.0000	0.736614	0.368307	+	0.929704i	$0.379937\pi$
$224$	−3.00000	−0.200446
$225$	0	0
$226$	20.0000	1.33038
$227$	−22.0000	−1.46019	−0.730096	−	0.683345i	$-0.760525\pi$
$227$	−22.0000	−1.46019	−0.730096	+	0.683345i	$0.760525\pi$
$228$	0	0
$229$	−25.0000	−1.65205	−0.826023	−	0.563636i	$-0.809402\pi$
$229$	−25.0000	−1.65205	−0.826023	+	0.563636i	$0.809402\pi$
$230$	8.00000	0.527504
$231$	0	0
$232$	−2.00000	−0.131306
$233$	−18.0000	−1.17922	−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000	−1.17922	−0.589610	+	0.807688i	$0.700718\pi$
$234$	0	0
$235$	16.0000	1.04372
$236$	12.0000	0.781133
$237$	0	0
$238$	18.0000	1.16677
$239$	18.0000	1.16432	0.582162	−	0.813073i	$-0.302207\pi$
$239$	18.0000	1.16432	0.582162	+	0.813073i	$0.302207\pi$
$240$	0	0
$241$	1.00000	0.0644157	0.0322078	−	0.999481i	$-0.489746\pi$
$241$	1.00000	0.0644157	0.0322078	+	0.999481i	$0.489746\pi$
$242$	7.00000	0.449977
$243$	0	0
$244$	5.00000	0.320092
$245$	−4.00000	−0.255551
$246$	0	0
$247$	0	0
$248$	−7.00000	−0.444500
$249$	0	0
$250$	−12.0000	−0.758947
$251$	16.0000	1.00991	0.504956	−	0.863145i	$-0.331509\pi$
$251$	16.0000	1.00991	0.504956	+	0.863145i	$0.331509\pi$
$252$	0	0
$253$	−8.00000	−0.502956
$254$	0	0
$255$	0	0
$256$	1.00000	0.0625000
$257$	−32.0000	−1.99611	−0.998053	−	0.0623783i	$-0.980131\pi$
$257$	−32.0000	−1.99611	−0.998053	+	0.0623783i	$0.980131\pi$
$258$	0	0
$259$	3.00000	0.186411
$260$	2.00000	0.124035
$261$	0	0
$262$	−6.00000	−0.370681
$263$	18.0000	1.10993	0.554964	−	0.831875i	$-0.312732\pi$
$263$	18.0000	1.10993	0.554964	+	0.831875i	$0.312732\pi$
$264$	0	0
$265$	16.0000	0.982872
$266$	0	0
$267$	0	0
$268$	−9.00000	−0.549762
$269$	−12.0000	−0.731653	−0.365826	−	0.930683i	$-0.619214\pi$
$269$	−12.0000	−0.731653	−0.365826	+	0.930683i	$0.619214\pi$
$270$	0	0
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	−6.00000	−0.363803
$273$	0	0
$274$	−14.0000	−0.845771
$275$	2.00000	0.120605
$276$	0	0
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	3.00000	0.179928
$279$	0	0
$280$	6.00000	0.358569
$281$	−22.0000	−1.31241	−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000	−1.31241	−0.656205	+	0.754583i	$0.727839\pi$
$282$	0	0
$283$	−12.0000	−0.713326	−0.356663	−	0.934233i	$-0.616086\pi$
$283$	−12.0000	−0.713326	−0.356663	+	0.934233i	$0.616086\pi$
$284$	−2.00000	−0.118678
$285$	0	0
$286$	−2.00000	−0.118262
$287$	24.0000	1.41668
$288$	0	0
$289$	19.0000	1.11765
$290$	4.00000	0.234888
$291$	0	0
$292$	−15.0000	−0.877809
$293$	−12.0000	−0.701047	−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000	−0.701047	−0.350524	+	0.936554i	$0.613996\pi$
$294$	0	0
$295$	−24.0000	−1.39733
$296$	−1.00000	−0.0581238
$297$	0	0
$298$	18.0000	1.04271
$299$	−4.00000	−0.231326
$300$	0	0
$301$	21.0000	1.21042
$302$	4.00000	0.230174
$303$	0	0
$304$	0	0
$305$	−10.0000	−0.572598
$306$	0	0
$307$	12.0000	0.684876	0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000	0.684876	0.342438	+	0.939540i	$0.388747\pi$
$308$	−6.00000	−0.341882
$309$	0	0
$310$	14.0000	0.795147
$311$	−16.0000	−0.907277	−0.453638	−	0.891186i	$-0.649874\pi$
$311$	−16.0000	−0.907277	−0.453638	+	0.891186i	$0.649874\pi$
$312$	0	0
$313$	−34.0000	−1.92179	−0.960897	−	0.276907i	$-0.910691\pi$
$313$	−34.0000	−1.92179	−0.960897	+	0.276907i	$0.910691\pi$
$314$	−13.0000	−0.733632
$315$	0	0
$316$	11.0000	0.618798
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	0	0
$319$	−4.00000	−0.223957
$320$	−2.00000	−0.111803
$321$	0	0
$322$	−12.0000	−0.668734
$323$	0	0
$324$	0	0
$325$	1.00000	0.0554700
$326$	13.0000	0.720003
$327$	0	0
$328$	−8.00000	−0.441726
$329$	−24.0000	−1.32316
$330$	0	0
$331$	23.0000	1.26419	0.632097	−	0.774889i	$-0.282194\pi$
$331$	23.0000	1.26419	0.632097	+	0.774889i	$0.282194\pi$
$332$	−6.00000	−0.329293
$333$	0	0
$334$	−12.0000	−0.656611
$335$	18.0000	0.983445
$336$	0	0
$337$	−23.0000	−1.25289	−0.626445	−	0.779466i	$-0.715491\pi$
$337$	−23.0000	−1.25289	−0.626445	+	0.779466i	$0.715491\pi$
$338$	12.0000	0.652714
$339$	0	0
$340$	12.0000	0.650791
$341$	−14.0000	−0.758143
$342$	0	0
$343$	−15.0000	−0.809924
$344$	−7.00000	−0.377415
$345$	0	0
$346$	−18.0000	−0.967686
$347$	2.00000	0.107366	0.0536828	−	0.998558i	$-0.482904\pi$
$347$	2.00000	0.107366	0.0536828	+	0.998558i	$0.482904\pi$
$348$	0	0
$349$	−11.0000	−0.588817	−0.294408	−	0.955680i	$-0.595123\pi$
$349$	−11.0000	−0.588817	−0.294408	+	0.955680i	$0.595123\pi$
$350$	3.00000	0.160357
$351$	0	0
$352$	2.00000	0.106600
$353$	−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
$355$	4.00000	0.212298
$356$	0	0
$357$	0	0
$358$	−24.0000	−1.26844
$359$	−36.0000	−1.90001	−0.950004	−	0.312239i	$-0.898921\pi$
$359$	−36.0000	−1.90001	−0.950004	+	0.312239i	$0.898921\pi$
$360$	0	0
$361$	0	0
$362$	−22.0000	−1.15629
$363$	0	0
$364$	−3.00000	−0.157243
$365$	30.0000	1.57027
$366$	0	0
$367$	−11.0000	−0.574195	−0.287098	−	0.957901i	$-0.592690\pi$
$367$	−11.0000	−0.574195	−0.287098	+	0.957901i	$0.592690\pi$
$368$	4.00000	0.208514
$369$	0	0
$370$	2.00000	0.103975
$371$	−24.0000	−1.24602
$372$	0	0
$373$	−22.0000	−1.13912	−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000	−1.13912	−0.569558	+	0.821951i	$0.692886\pi$
$374$	−12.0000	−0.620505
$375$	0	0
$376$	8.00000	0.412568
$377$	−2.00000	−0.103005
$378$	0	0
$379$	3.00000	0.154100	0.0770498	−	0.997027i	$-0.475450\pi$
$379$	3.00000	0.154100	0.0770498	+	0.997027i	$0.475450\pi$
$380$	0	0
$381$	0	0
$382$	22.0000	1.12562
$383$	14.0000	0.715367	0.357683	−	0.933843i	$-0.383567\pi$
$383$	14.0000	0.715367	0.357683	+	0.933843i	$0.383567\pi$
$384$	0	0
$385$	12.0000	0.611577
$386$	9.00000	0.458088
$387$	0	0
$388$	−14.0000	−0.710742
$389$	−12.0000	−0.608424	−0.304212	−	0.952604i	$-0.598393\pi$
$389$	−12.0000	−0.608424	−0.304212	+	0.952604i	$0.598393\pi$
$390$	0	0
$391$	−24.0000	−1.21373
$392$	−2.00000	−0.101015
$393$	0	0
$394$	8.00000	0.403034
$395$	−22.0000	−1.10694
$396$	0	0
$397$	−7.00000	−0.351320	−0.175660	−	0.984451i	$-0.556206\pi$
$397$	−7.00000	−0.351320	−0.175660	+	0.984451i	$0.556206\pi$
$398$	−11.0000	−0.551380
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	−4.00000	−0.199750	−0.0998752	−	0.995000i	$-0.531844\pi$
$401$	−4.00000	−0.199750	−0.0998752	+	0.995000i	$0.531844\pi$
$402$	0	0
$403$	−7.00000	−0.348695
$404$	−14.0000	−0.696526
$405$	0	0
$406$	−6.00000	−0.297775
$407$	−2.00000	−0.0991363
$408$	0	0
$409$	−14.0000	−0.692255	−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000	−0.692255	−0.346128	+	0.938187i	$0.612504\pi$
$410$	16.0000	0.790184
$411$	0	0
$412$	3.00000	0.147799
$413$	36.0000	1.77144
$414$	0	0
$415$	12.0000	0.589057
$416$	1.00000	0.0490290
$417$	0	0
$418$	0	0
$419$	−6.00000	−0.293119	−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000	−0.293119	−0.146560	+	0.989202i	$0.546820\pi$
$420$	0	0
$421$	26.0000	1.26716	0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000	1.26716	0.633581	+	0.773676i	$0.281584\pi$
$422$	15.0000	0.730189
$423$	0	0
$424$	8.00000	0.388514
$425$	6.00000	0.291043
$426$	0	0
$427$	15.0000	0.725901
$428$	10.0000	0.483368
$429$	0	0
$430$	14.0000	0.675140
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	0	0
$433$	−13.0000	−0.624740	−0.312370	−	0.949960i	$-0.601123\pi$
$433$	−13.0000	−0.624740	−0.312370	+	0.949960i	$0.601123\pi$
$434$	−21.0000	−1.00803
$435$	0	0
$436$	−6.00000	−0.287348
$437$	0	0
$438$	0	0
$439$	−19.0000	−0.906821	−0.453410	−	0.891302i	$-0.649793\pi$
$439$	−19.0000	−0.906821	−0.453410	+	0.891302i	$0.649793\pi$
$440$	−4.00000	−0.190693
$441$	0	0
$442$	−6.00000	−0.285391
$443$	26.0000	1.23530	0.617649	−	0.786454i	$-0.288085\pi$
$443$	26.0000	1.23530	0.617649	+	0.786454i	$0.288085\pi$
$444$	0	0
$445$	0	0
$446$	−11.0000	−0.520865
$447$	0	0
$448$	3.00000	0.141737
$449$	14.0000	0.660701	0.330350	−	0.943858i	$-0.392833\pi$
$449$	14.0000	0.660701	0.330350	+	0.943858i	$0.392833\pi$
$450$	0	0
$451$	−16.0000	−0.753411
$452$	−20.0000	−0.940721
$453$	0	0
$454$	22.0000	1.03251
$455$	6.00000	0.281284
$456$	0	0
$457$	17.0000	0.795226	0.397613	−	0.917553i	$-0.369839\pi$
$457$	17.0000	0.795226	0.397613	+	0.917553i	$0.369839\pi$
$458$	25.0000	1.16817
$459$	0	0
$460$	−8.00000	−0.373002
$461$	−32.0000	−1.49039	−0.745194	−	0.666847i	$-0.767643\pi$
$461$	−32.0000	−1.49039	−0.745194	+	0.666847i	$0.767643\pi$
$462$	0	0
$463$	25.0000	1.16185	0.580924	−	0.813958i	$-0.302691\pi$
$463$	25.0000	1.16185	0.580924	+	0.813958i	$0.302691\pi$
$464$	2.00000	0.0928477
$465$	0	0
$466$	18.0000	0.833834
$467$	−16.0000	−0.740392	−0.370196	−	0.928954i	$-0.620709\pi$
$467$	−16.0000	−0.740392	−0.370196	+	0.928954i	$0.620709\pi$
$468$	0	0
$469$	−27.0000	−1.24674
$470$	−16.0000	−0.738025
$471$	0	0
$472$	−12.0000	−0.552345
$473$	−14.0000	−0.643721
$474$	0	0
$475$	0	0
$476$	−18.0000	−0.825029
$477$	0	0
$478$	−18.0000	−0.823301
$479$	2.00000	0.0913823	0.0456912	−	0.998956i	$-0.485451\pi$
$479$	2.00000	0.0913823	0.0456912	+	0.998956i	$0.485451\pi$
$480$	0	0
$481$	−1.00000	−0.0455961
$482$	−1.00000	−0.0455488
$483$	0	0
$484$	−7.00000	−0.318182
$485$	28.0000	1.27141
$486$	0	0
$487$	−32.0000	−1.45006	−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000	−1.45006	−0.725029	+	0.688718i	$0.758174\pi$
$488$	−5.00000	−0.226339
$489$	0	0
$490$	4.00000	0.180702
$491$	−38.0000	−1.71492	−0.857458	−	0.514554i	$-0.827958\pi$
$491$	−38.0000	−1.71492	−0.857458	+	0.514554i	$0.827958\pi$
$492$	0	0
$493$	−12.0000	−0.540453
$494$	0	0
$495$	0	0
$496$	7.00000	0.314309
$497$	−6.00000	−0.269137
$498$	0	0
$499$	−23.0000	−1.02962	−0.514811	−	0.857304i	$-0.672138\pi$
$499$	−23.0000	−1.02962	−0.514811	+	0.857304i	$0.672138\pi$
$500$	12.0000	0.536656
$501$	0	0
$502$	−16.0000	−0.714115
$503$	18.0000	0.802580	0.401290	−	0.915951i	$-0.368562\pi$
$503$	18.0000	0.802580	0.401290	+	0.915951i	$0.368562\pi$
$504$	0	0
$505$	28.0000	1.24598
$506$	8.00000	0.355643
$507$	0	0
$508$	0	0
$509$	12.0000	0.531891	0.265945	−	0.963988i	$-0.414316\pi$
$509$	12.0000	0.531891	0.265945	+	0.963988i	$0.414316\pi$
$510$	0	0
$511$	−45.0000	−1.99068
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	32.0000	1.41146
$515$	−6.00000	−0.264392
$516$	0	0
$517$	16.0000	0.703679
$518$	−3.00000	−0.131812
$519$	0	0
$520$	−2.00000	−0.0877058
$521$	−26.0000	−1.13908	−0.569540	−	0.821963i	$-0.692879\pi$
$521$	−26.0000	−1.13908	−0.569540	+	0.821963i	$0.692879\pi$
$522$	0	0
$523$	−31.0000	−1.35554	−0.677768	−	0.735276i	$-0.737052\pi$
$523$	−31.0000	−1.35554	−0.677768	+	0.735276i	$0.737052\pi$
$524$	6.00000	0.262111
$525$	0	0
$526$	−18.0000	−0.784837
$527$	−42.0000	−1.82955
$528$	0	0
$529$	−7.00000	−0.304348
$530$	−16.0000	−0.694996
$531$	0	0
$532$	0	0
$533$	−8.00000	−0.346518
$534$	0	0
$535$	−20.0000	−0.864675
$536$	9.00000	0.388741
$537$	0	0
$538$	12.0000	0.517357
$539$	−4.00000	−0.172292
$540$	0	0
$541$	−1.00000	−0.0429934	−0.0214967	−	0.999769i	$-0.506843\pi$
$541$	−1.00000	−0.0429934	−0.0214967	+	0.999769i	$0.506843\pi$
$542$	8.00000	0.343629
$543$	0	0
$544$	6.00000	0.257248
$545$	12.0000	0.514024
$546$	0	0
$547$	43.0000	1.83855	0.919274	−	0.393619i	$-0.128777\pi$
$547$	43.0000	1.83855	0.919274	+	0.393619i	$0.128777\pi$
$548$	14.0000	0.598050
$549$	0	0
$550$	−2.00000	−0.0852803
$551$	0	0
$552$	0	0
$553$	33.0000	1.40330
$554$	−10.0000	−0.424859
$555$	0	0
$556$	−3.00000	−0.127228
$557$	−10.0000	−0.423714	−0.211857	−	0.977301i	$-0.567951\pi$
$557$	−10.0000	−0.423714	−0.211857	+	0.977301i	$0.567951\pi$
$558$	0	0
$559$	−7.00000	−0.296068
$560$	−6.00000	−0.253546
$561$	0	0
$562$	22.0000	0.928014
$563$	18.0000	0.758610	0.379305	−	0.925272i	$-0.376163\pi$
$563$	18.0000	0.758610	0.379305	+	0.925272i	$0.376163\pi$
$564$	0	0
$565$	40.0000	1.68281
$566$	12.0000	0.504398
$567$	0	0
$568$	2.00000	0.0839181
$569$	−4.00000	−0.167689	−0.0838444	−	0.996479i	$-0.526720\pi$
$569$	−4.00000	−0.167689	−0.0838444	+	0.996479i	$0.526720\pi$
$570$	0	0
$571$	29.0000	1.21361	0.606806	−	0.794850i	$-0.292450\pi$
$571$	29.0000	1.21361	0.606806	+	0.794850i	$0.292450\pi$
$572$	2.00000	0.0836242
$573$	0	0
$574$	−24.0000	−1.00174
$575$	−4.00000	−0.166812
$576$	0	0
$577$	14.0000	0.582828	0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000	0.582828	0.291414	+	0.956597i	$0.405874\pi$
$578$	−19.0000	−0.790296
$579$	0	0
$580$	−4.00000	−0.166091
$581$	−18.0000	−0.746766
$582$	0	0
$583$	16.0000	0.662652
$584$	15.0000	0.620704
$585$	0	0
$586$	12.0000	0.495715
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	0	0
$589$	0	0
$590$	24.0000	0.988064
$591$	0	0
$592$	1.00000	0.0410997
$593$	−16.0000	−0.657041	−0.328521	−	0.944497i	$-0.606550\pi$
$593$	−16.0000	−0.657041	−0.328521	+	0.944497i	$0.606550\pi$
$594$	0	0
$595$	36.0000	1.47586
$596$	−18.0000	−0.737309
$597$	0	0
$598$	4.00000	0.163572
$599$	−30.0000	−1.22577	−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000	−1.22577	−0.612883	+	0.790173i	$0.709990\pi$
$600$	0	0
$601$	−41.0000	−1.67242	−0.836212	−	0.548406i	$-0.815235\pi$
$601$	−41.0000	−1.67242	−0.836212	+	0.548406i	$0.815235\pi$
$602$	−21.0000	−0.855896
$603$	0	0
$604$	−4.00000	−0.162758
$605$	14.0000	0.569181
$606$	0	0
$607$	−13.0000	−0.527654	−0.263827	−	0.964570i	$-0.584985\pi$
$607$	−13.0000	−0.527654	−0.263827	+	0.964570i	$0.584985\pi$
$608$	0	0
$609$	0	0
$610$	10.0000	0.404888
$611$	8.00000	0.323645
$612$	0	0
$613$	46.0000	1.85792	0.928961	−	0.370177i	$-0.120703\pi$
$613$	46.0000	1.85792	0.928961	+	0.370177i	$0.120703\pi$
$614$	−12.0000	−0.484281
$615$	0	0
$616$	6.00000	0.241747
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	0	0
$619$	−23.0000	−0.924448	−0.462224	−	0.886763i	$-0.652948\pi$
$619$	−23.0000	−0.924448	−0.462224	+	0.886763i	$0.652948\pi$
$620$	−14.0000	−0.562254
$621$	0	0
$622$	16.0000	0.641542
$623$	0	0
$624$	0	0
$625$	−19.0000	−0.760000
$626$	34.0000	1.35891
$627$	0	0
$628$	13.0000	0.518756
$629$	−6.00000	−0.239236
$630$	0	0
$631$	47.0000	1.87104	0.935520	−	0.353273i	$-0.114931\pi$
$631$	47.0000	1.87104	0.935520	+	0.353273i	$0.114931\pi$
$632$	−11.0000	−0.437557
$633$	0	0
$634$	−6.00000	−0.238290
$635$	0	0
$636$	0	0
$637$	−2.00000	−0.0792429
$638$	4.00000	0.158362
$639$	0	0
$640$	2.00000	0.0790569
$641$	0	0		−	1.00000i	$-0.5\pi$
$641$	0	0			1.00000i	$0.5\pi$
$642$	0	0
$643$	13.0000	0.512670	0.256335	−	0.966588i	$-0.417485\pi$
$643$	13.0000	0.512670	0.256335	+	0.966588i	$0.417485\pi$
$644$	12.0000	0.472866
$645$	0	0
$646$	0	0
$647$	10.0000	0.393141	0.196570	−	0.980490i	$-0.437020\pi$
$647$	10.0000	0.393141	0.196570	+	0.980490i	$0.437020\pi$
$648$	0	0
$649$	−24.0000	−0.942082
$650$	−1.00000	−0.0392232
$651$	0	0
$652$	−13.0000	−0.509119
$653$	18.0000	0.704394	0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000	0.704394	0.352197	+	0.935926i	$0.385435\pi$
$654$	0	0
$655$	−12.0000	−0.468879
$656$	8.00000	0.312348
$657$	0	0
$658$	24.0000	0.935617
$659$	22.0000	0.856998	0.428499	−	0.903542i	$-0.359042\pi$
$659$	22.0000	0.856998	0.428499	+	0.903542i	$0.359042\pi$
$660$	0	0
$661$	−2.00000	−0.0777910	−0.0388955	−	0.999243i	$-0.512384\pi$
$661$	−2.00000	−0.0777910	−0.0388955	+	0.999243i	$0.512384\pi$
$662$	−23.0000	−0.893920
$663$	0	0
$664$	6.00000	0.232845
$665$	0	0
$666$	0	0
$667$	8.00000	0.309761
$668$	12.0000	0.464294
$669$	0	0
$670$	−18.0000	−0.695401
$671$	−10.0000	−0.386046
$672$	0	0
$673$	−1.00000	−0.0385472	−0.0192736	−	0.999814i	$-0.506135\pi$
$673$	−1.00000	−0.0385472	−0.0192736	+	0.999814i	$0.506135\pi$
$674$	23.0000	0.885927
$675$	0	0
$676$	−12.0000	−0.461538
$677$	8.00000	0.307465	0.153732	−	0.988113i	$-0.450871\pi$
$677$	8.00000	0.307465	0.153732	+	0.988113i	$0.450871\pi$
$678$	0	0
$679$	−42.0000	−1.61181
$680$	−12.0000	−0.460179
$681$	0	0
$682$	14.0000	0.536088
$683$	−46.0000	−1.76014	−0.880071	−	0.474843i	$-0.842505\pi$
$683$	−46.0000	−1.76014	−0.880071	+	0.474843i	$0.842505\pi$
$684$	0	0
$685$	−28.0000	−1.06983
$686$	15.0000	0.572703
$687$	0	0
$688$	7.00000	0.266872
$689$	8.00000	0.304776
$690$	0	0
$691$	−12.0000	−0.456502	−0.228251	−	0.973602i	$-0.573301\pi$
$691$	−12.0000	−0.456502	−0.228251	+	0.973602i	$0.573301\pi$
$692$	18.0000	0.684257
$693$	0	0
$694$	−2.00000	−0.0759190
$695$	6.00000	0.227593
$696$	0	0
$697$	−48.0000	−1.81813
$698$	11.0000	0.416356
$699$	0	0
$700$	−3.00000	−0.113389
$701$	34.0000	1.28416	0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000	1.28416	0.642081	+	0.766637i	$0.278071\pi$
$702$	0	0
$703$	0	0
$704$	−2.00000	−0.0753778
$705$	0	0
$706$	6.00000	0.225813
$707$	−42.0000	−1.57957
$708$	0	0
$709$	−9.00000	−0.338002	−0.169001	−	0.985616i	$-0.554054\pi$
$709$	−9.00000	−0.338002	−0.169001	+	0.985616i	$0.554054\pi$
$710$	−4.00000	−0.150117
$711$	0	0
$712$	0	0
$713$	28.0000	1.04861
$714$	0	0
$715$	−4.00000	−0.149592
$716$	24.0000	0.896922
$717$	0	0
$718$	36.0000	1.34351
$719$	44.0000	1.64092	0.820462	−	0.571702i	$-0.193717\pi$
$719$	44.0000	1.64092	0.820462	+	0.571702i	$0.193717\pi$
$720$	0	0
$721$	9.00000	0.335178
$722$	0	0
$723$	0	0
$724$	22.0000	0.817624
$725$	−2.00000	−0.0742781
$726$	0	0
$727$	7.00000	0.259616	0.129808	−	0.991539i	$-0.458564\pi$
$727$	7.00000	0.259616	0.129808	+	0.991539i	$0.458564\pi$
$728$	3.00000	0.111187
$729$	0	0
$730$	−30.0000	−1.11035
$731$	−42.0000	−1.55343
$732$	0	0
$733$	−6.00000	−0.221615	−0.110808	−	0.993842i	$-0.535344\pi$
$733$	−6.00000	−0.221615	−0.110808	+	0.993842i	$0.535344\pi$
$734$	11.0000	0.406017
$735$	0	0
$736$	−4.00000	−0.147442
$737$	18.0000	0.663039
$738$	0	0
$739$	−1.00000	−0.0367856	−0.0183928	−	0.999831i	$-0.505855\pi$
$739$	−1.00000	−0.0367856	−0.0183928	+	0.999831i	$0.505855\pi$
$740$	−2.00000	−0.0735215
$741$	0	0
$742$	24.0000	0.881068
$743$	10.0000	0.366864	0.183432	−	0.983032i	$-0.441279\pi$
$743$	10.0000	0.366864	0.183432	+	0.983032i	$0.441279\pi$
$744$	0	0
$745$	36.0000	1.31894
$746$	22.0000	0.805477
$747$	0	0
$748$	12.0000	0.438763
$749$	30.0000	1.09618
$750$	0	0
$751$	−37.0000	−1.35015	−0.675075	−	0.737749i	$-0.735889\pi$
$751$	−37.0000	−1.35015	−0.675075	+	0.737749i	$0.735889\pi$
$752$	−8.00000	−0.291730
$753$	0	0
$754$	2.00000	0.0728357
$755$	8.00000	0.291150
$756$	0	0
$757$	−41.0000	−1.49017	−0.745085	−	0.666969i	$-0.767591\pi$
$757$	−41.0000	−1.49017	−0.745085	+	0.666969i	$0.767591\pi$
$758$	−3.00000	−0.108965
$759$	0	0
$760$	0	0
$761$	12.0000	0.435000	0.217500	−	0.976060i	$-0.430210\pi$
$761$	12.0000	0.435000	0.217500	+	0.976060i	$0.430210\pi$
$762$	0	0
$763$	−18.0000	−0.651644
$764$	−22.0000	−0.795932
$765$	0	0
$766$	−14.0000	−0.505841
$767$	−12.0000	−0.433295
$768$	0	0
$769$	−29.0000	−1.04577	−0.522883	−	0.852404i	$-0.675144\pi$
$769$	−29.0000	−1.04577	−0.522883	+	0.852404i	$0.675144\pi$
$770$	−12.0000	−0.432450
$771$	0	0
$772$	−9.00000	−0.323917
$773$	−48.0000	−1.72644	−0.863220	−	0.504828i	$-0.831556\pi$
$773$	−48.0000	−1.72644	−0.863220	+	0.504828i	$0.831556\pi$
$774$	0	0
$775$	−7.00000	−0.251447
$776$	14.0000	0.502571
$777$	0	0
$778$	12.0000	0.430221
$779$	0	0
$780$	0	0
$781$	4.00000	0.143131
$782$	24.0000	0.858238
$783$	0	0
$784$	2.00000	0.0714286
$785$	−26.0000	−0.927980
$786$	0	0
$787$	−35.0000	−1.24762	−0.623808	−	0.781578i	$-0.714415\pi$
$787$	−35.0000	−1.24762	−0.623808	+	0.781578i	$0.714415\pi$
$788$	−8.00000	−0.284988
$789$	0	0
$790$	22.0000	0.782725
$791$	−60.0000	−2.13335
$792$	0	0
$793$	−5.00000	−0.177555
$794$	7.00000	0.248421
$795$	0	0
$796$	11.0000	0.389885
$797$	18.0000	0.637593	0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000	0.637593	0.318796	+	0.947823i	$0.396721\pi$
$798$	0	0
$799$	48.0000	1.69812
$800$	1.00000	0.0353553
$801$	0	0
$802$	4.00000	0.141245
$803$	30.0000	1.05868
$804$	0	0
$805$	−24.0000	−0.845889
$806$	7.00000	0.246564
$807$	0	0
$808$	14.0000	0.492518
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	0	0
$811$	12.0000	0.421377	0.210688	−	0.977553i	$-0.432429\pi$
$811$	12.0000	0.421377	0.210688	+	0.977553i	$0.432429\pi$
$812$	6.00000	0.210559
$813$	0	0
$814$	2.00000	0.0701000
$815$	26.0000	0.910740
$816$	0	0
$817$	0	0
$818$	14.0000	0.489499
$819$	0	0
$820$	−16.0000	−0.558744
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	0	0
$823$	−16.0000	−0.557725	−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000	−0.557725	−0.278862	+	0.960331i	$0.589957\pi$
$824$	−3.00000	−0.104510
$825$	0	0
$826$	−36.0000	−1.25260
$827$	22.0000	0.765015	0.382507	−	0.923952i	$-0.375061\pi$
$827$	22.0000	0.765015	0.382507	+	0.923952i	$0.375061\pi$
$828$	0	0
$829$	−9.00000	−0.312583	−0.156291	−	0.987711i	$-0.549954\pi$
$829$	−9.00000	−0.312583	−0.156291	+	0.987711i	$0.549954\pi$
$830$	−12.0000	−0.416526
$831$	0	0
$832$	−1.00000	−0.0346688
$833$	−12.0000	−0.415775
$834$	0	0
$835$	−24.0000	−0.830554
$836$	0	0
$837$	0	0
$838$	6.00000	0.207267
$839$	−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
$841$	−25.0000	−0.862069
$842$	−26.0000	−0.896019
$843$	0	0
$844$	−15.0000	−0.516321
$845$	24.0000	0.825625
$846$	0	0
$847$	−21.0000	−0.721569
$848$	−8.00000	−0.274721
$849$	0	0
$850$	−6.00000	−0.205798
$851$	4.00000	0.137118
$852$	0	0
$853$	9.00000	0.308154	0.154077	−	0.988059i	$-0.450760\pi$
$853$	9.00000	0.308154	0.154077	+	0.988059i	$0.450760\pi$
$854$	−15.0000	−0.513289
$855$	0	0
$856$	−10.0000	−0.341793
$857$	−24.0000	−0.819824	−0.409912	−	0.912125i	$-0.634441\pi$
$857$	−24.0000	−0.819824	−0.409912	+	0.912125i	$0.634441\pi$
$858$	0	0
$859$	−5.00000	−0.170598	−0.0852989	−	0.996355i	$-0.527185\pi$
$859$	−5.00000	−0.170598	−0.0852989	+	0.996355i	$0.527185\pi$
$860$	−14.0000	−0.477396
$861$	0	0
$862$	−12.0000	−0.408722
$863$	12.0000	0.408485	0.204242	−	0.978920i	$-0.434527\pi$
$863$	12.0000	0.408485	0.204242	+	0.978920i	$0.434527\pi$
$864$	0	0
$865$	−36.0000	−1.22404
$866$	13.0000	0.441758
$867$	0	0
$868$	21.0000	0.712786
$869$	−22.0000	−0.746299
$870$	0	0
$871$	9.00000	0.304953
$872$	6.00000	0.203186
$873$	0	0
$874$	0	0
$875$	36.0000	1.21702
$876$	0	0
$877$	25.0000	0.844190	0.422095	−	0.906552i	$-0.361295\pi$
$877$	25.0000	0.844190	0.422095	+	0.906552i	$0.361295\pi$
$878$	19.0000	0.641219
$879$	0	0
$880$	4.00000	0.134840
$881$	30.0000	1.01073	0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000	1.01073	0.505363	+	0.862907i	$0.331359\pi$
$882$	0	0
$883$	−29.0000	−0.975928	−0.487964	−	0.872864i	$-0.662260\pi$
$883$	−29.0000	−0.975928	−0.487964	+	0.872864i	$0.662260\pi$
$884$	6.00000	0.201802
$885$	0	0
$886$	−26.0000	−0.873487
$887$	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
$889$	0	0
$890$	0	0
$891$	0	0
$892$	11.0000	0.368307
$893$	0	0
$894$	0	0
$895$	−48.0000	−1.60446
$896$	−3.00000	−0.100223
$897$	0	0
$898$	−14.0000	−0.467186
$899$	14.0000	0.466926
$900$	0	0
$901$	48.0000	1.59911
$902$	16.0000	0.532742
$903$	0	0
$904$	20.0000	0.665190
$905$	−44.0000	−1.46261
$906$	0	0
$907$	−28.0000	−0.929725	−0.464862	−	0.885383i	$-0.653896\pi$
$907$	−28.0000	−0.929725	−0.464862	+	0.885383i	$0.653896\pi$
$908$	−22.0000	−0.730096
$909$	0	0
$910$	−6.00000	−0.198898
$911$	48.0000	1.59031	0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000	1.59031	0.795155	+	0.606406i	$0.207389\pi$
$912$	0	0
$913$	12.0000	0.397142
$914$	−17.0000	−0.562310
$915$	0	0
$916$	−25.0000	−0.826023
$917$	18.0000	0.594412
$918$	0	0
$919$	17.0000	0.560778	0.280389	−	0.959886i	$-0.409536\pi$
$919$	17.0000	0.560778	0.280389	+	0.959886i	$0.409536\pi$
$920$	8.00000	0.263752
$921$	0	0
$922$	32.0000	1.05386
$923$	2.00000	0.0658308
$924$	0	0
$925$	−1.00000	−0.0328798
$926$	−25.0000	−0.821551
$927$	0	0
$928$	−2.00000	−0.0656532
$929$	34.0000	1.11550	0.557752	−	0.830008i	$-0.311664\pi$
$929$	34.0000	1.11550	0.557752	+	0.830008i	$0.311664\pi$
$930$	0	0
$931$	0	0
$932$	−18.0000	−0.589610
$933$	0	0
$934$	16.0000	0.523536
$935$	−24.0000	−0.784884
$936$	0	0
$937$	47.0000	1.53542	0.767712	−	0.640796i	$-0.221395\pi$
$937$	47.0000	1.53542	0.767712	+	0.640796i	$0.221395\pi$
$938$	27.0000	0.881581
$939$	0	0
$940$	16.0000	0.521862
$941$	−40.0000	−1.30396	−0.651981	−	0.758235i	$-0.726062\pi$
$941$	−40.0000	−1.30396	−0.651981	+	0.758235i	$0.726062\pi$
$942$	0	0
$943$	32.0000	1.04206
$944$	12.0000	0.390567
$945$	0	0
$946$	14.0000	0.455179
$947$	−6.00000	−0.194974	−0.0974869	−	0.995237i	$-0.531080\pi$
$947$	−6.00000	−0.194974	−0.0974869	+	0.995237i	$0.531080\pi$
$948$	0	0
$949$	15.0000	0.486921
$950$	0	0
$951$	0	0
$952$	18.0000	0.583383
$953$	−26.0000	−0.842223	−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000	−0.842223	−0.421111	+	0.907009i	$0.638360\pi$
$954$	0	0
$955$	44.0000	1.42381
$956$	18.0000	0.582162
$957$	0	0
$958$	−2.00000	−0.0646171
$959$	42.0000	1.35625
$960$	0	0
$961$	18.0000	0.580645
$962$	1.00000	0.0322413
$963$	0	0
$964$	1.00000	0.0322078
$965$	18.0000	0.579441
$966$	0	0
$967$	9.00000	0.289420	0.144710	−	0.989474i	$-0.453775\pi$
$967$	9.00000	0.289420	0.144710	+	0.989474i	$0.453775\pi$
$968$	7.00000	0.224989
$969$	0	0
$970$	−28.0000	−0.899026
$971$	−20.0000	−0.641831	−0.320915	−	0.947108i	$-0.603990\pi$
$971$	−20.0000	−0.641831	−0.320915	+	0.947108i	$0.603990\pi$
$972$	0	0
$973$	−9.00000	−0.288527
$974$	32.0000	1.02535
$975$	0	0
$976$	5.00000	0.160046
$977$	4.00000	0.127971	0.0639857	−	0.997951i	$-0.479619\pi$
$977$	4.00000	0.127971	0.0639857	+	0.997951i	$0.479619\pi$
$978$	0	0
$979$	0	0
$980$	−4.00000	−0.127775
$981$	0	0
$982$	38.0000	1.21263
$983$	−6.00000	−0.191370	−0.0956851	−	0.995412i	$-0.530504\pi$
$983$	−6.00000	−0.191370	−0.0956851	+	0.995412i	$0.530504\pi$
$984$	0	0
$985$	16.0000	0.509802
$986$	12.0000	0.382158
$987$	0	0
$988$	0	0
$989$	28.0000	0.890348
$990$	0	0
$991$	−11.0000	−0.349427	−0.174713	−	0.984619i	$-0.555900\pi$
$991$	−11.0000	−0.349427	−0.174713	+	0.984619i	$0.555900\pi$
$992$	−7.00000	−0.222250
$993$	0	0
$994$	6.00000	0.190308
$995$	−22.0000	−0.697447
$996$	0	0
$997$	1.00000	0.0316703	0.0158352	−	0.999875i	$-0.494959\pi$
$997$	1.00000	0.0316703	0.0158352	+	0.999875i	$0.494959\pi$
$998$	23.0000	0.728052
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6498.2.a.c.1.1		1
3.2	odd	2		6498.2.a.w.1.1		1
19.7	even	3		342.2.g.e.163.1	yes	2
19.11	even	3		342.2.g.e.235.1	yes	2
19.18	odd	2		6498.2.a.q.1.1		1
57.11	odd	6		342.2.g.a.235.1	yes	2
57.26	odd	6		342.2.g.a.163.1	✓	2
57.56	even	2		6498.2.a.k.1.1		1
76.7	odd	6		2736.2.s.o.1873.1		2
76.11	odd	6		2736.2.s.o.577.1		2
228.11	even	6		2736.2.s.d.577.1		2
228.83	even	6		2736.2.s.d.1873.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.g.a.163.1	✓	2	57.26	odd	6
342.2.g.a.235.1	yes	2	57.11	odd	6
342.2.g.e.163.1	yes	2	19.7	even	3
342.2.g.e.235.1	yes	2	19.11	even	3
2736.2.s.d.577.1		2	228.11	even	6
2736.2.s.d.1873.1		2	228.83	even	6
2736.2.s.o.577.1		2	76.11	odd	6
2736.2.s.o.1873.1		2	76.7	odd	6
6498.2.a.c.1.1		1	1.1	even	1	trivial
6498.2.a.k.1.1		1	57.56	even	2
6498.2.a.q.1.1		1	19.18	odd	2
6498.2.a.w.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:	\( N \)	\(=\)	\( 6498 = 2 \cdot 3^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6498.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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