LMFDB - Embedded newform 5586.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5586,2,Mod(1,5586)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5586, 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("5586.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5586.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:	$44.6044345691$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 798)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5586.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{10} -4.00000 q^{11} -1.00000 q^{12} +2.00000 q^{13} -2.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} -1.00000 q^{18} +1.00000 q^{19} +2.00000 q^{20} +4.00000 q^{22} -4.00000 q^{23} +1.00000 q^{24} -1.00000 q^{25} -2.00000 q^{26} -1.00000 q^{27} +2.00000 q^{29} +2.00000 q^{30} -4.00000 q^{31} -1.00000 q^{32} +4.00000 q^{33} -2.00000 q^{34} +1.00000 q^{36} -6.00000 q^{37} -1.00000 q^{38} -2.00000 q^{39} -2.00000 q^{40} +10.0000 q^{41} -4.00000 q^{43} -4.00000 q^{44} +2.00000 q^{45} +4.00000 q^{46} +8.00000 q^{47} -1.00000 q^{48} +1.00000 q^{50} -2.00000 q^{51} +2.00000 q^{52} +10.0000 q^{53} +1.00000 q^{54} -8.00000 q^{55} -1.00000 q^{57} -2.00000 q^{58} -12.0000 q^{59} -2.00000 q^{60} +2.00000 q^{61} +4.00000 q^{62} +1.00000 q^{64} +4.00000 q^{65} -4.00000 q^{66} -8.00000 q^{67} +2.00000 q^{68} +4.00000 q^{69} -16.0000 q^{71} -1.00000 q^{72} -10.0000 q^{73} +6.00000 q^{74} +1.00000 q^{75} +1.00000 q^{76} +2.00000 q^{78} -8.00000 q^{79} +2.00000 q^{80} +1.00000 q^{81} -10.0000 q^{82} +4.00000 q^{85} +4.00000 q^{86} -2.00000 q^{87} +4.00000 q^{88} +10.0000 q^{89} -2.00000 q^{90} -4.00000 q^{92} +4.00000 q^{93} -8.00000 q^{94} +2.00000 q^{95} +1.00000 q^{96} +2.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.00000	−0.632456
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	−1.00000	−0.288675
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	0	0
$15$	−2.00000	−0.516398
$16$	1.00000	0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.00000	0.447214
$21$	0	0
$22$	4.00000	0.852803
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	1.00000	0.204124
$25$	−1.00000	−0.200000
$26$	−2.00000	−0.392232
$27$	−1.00000	−0.192450
$28$	0	0
$29$	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
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−1.00000	−0.176777
$33$	4.00000	0.696311
$34$	−2.00000	−0.342997
$35$	0	0
$36$	1.00000	0.166667
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	−1.00000	−0.162221
$39$	−2.00000	−0.320256
$40$	−2.00000	−0.316228
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	0	0
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	−4.00000	−0.603023
$45$	2.00000	0.298142
$46$	4.00000	0.589768
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	1.00000	0.141421
$51$	−2.00000	−0.280056
$52$	2.00000	0.277350
$53$	10.0000	1.37361	0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000	1.37361	0.686803	+	0.726844i	$0.259014\pi$
$54$	1.00000	0.136083
$55$	−8.00000	−1.07872
$56$	0	0
$57$	−1.00000	−0.132453
$58$	−2.00000	−0.262613
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	−2.00000	−0.258199
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	4.00000	0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	−4.00000	−0.492366
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	2.00000	0.242536
$69$	4.00000	0.481543
$70$	0	0
$71$	−16.0000	−1.89885	−0.949425	−	0.313993i	$-0.898333\pi$
$71$	−16.0000	−1.89885	−0.949425	+	0.313993i	$0.898333\pi$
$72$	−1.00000	−0.117851
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	6.00000	0.697486
$75$	1.00000	0.115470
$76$	1.00000	0.114708
$77$	0	0
$78$	2.00000	0.226455
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	2.00000	0.223607
$81$	1.00000	0.111111
$82$	−10.0000	−1.10432
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	4.00000	0.433861
$86$	4.00000	0.431331
$87$	−2.00000	−0.214423
$88$	4.00000	0.426401
$89$	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
$92$	−4.00000	−0.417029
$93$	4.00000	0.414781
$94$	−8.00000	−0.825137
$95$	2.00000	0.205196
$96$	1.00000	0.102062
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	0	0
$99$	−4.00000	−0.402015
$100$	−1.00000	−0.100000
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	2.00000	0.198030
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	−10.0000	−0.971286
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	−1.00000	−0.0962250
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	8.00000	0.762770
$111$	6.00000	0.569495
$112$	0	0
$113$	−10.0000	−0.940721	−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000	−0.940721	−0.470360	+	0.882474i	$0.655876\pi$
$114$	1.00000	0.0936586
$115$	−8.00000	−0.746004
$116$	2.00000	0.185695
$117$	2.00000	0.184900
$118$	12.0000	1.10469
$119$	0	0
$120$	2.00000	0.182574
$121$	5.00000	0.454545
$122$	−2.00000	−0.181071
$123$	−10.0000	−0.901670
$124$	−4.00000	−0.359211
$125$	−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
$129$	4.00000	0.352180
$130$	−4.00000	−0.350823
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	4.00000	0.348155
$133$	0	0
$134$	8.00000	0.691095
$135$	−2.00000	−0.172133
$136$	−2.00000	−0.171499
$137$	−14.0000	−1.19610	−0.598050	−	0.801459i	$-0.704058\pi$
$137$	−14.0000	−1.19610	−0.598050	+	0.801459i	$0.704058\pi$
$138$	−4.00000	−0.340503
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	0	0
$141$	−8.00000	−0.673722
$142$	16.0000	1.34269
$143$	−8.00000	−0.668994
$144$	1.00000	0.0833333
$145$	4.00000	0.332182
$146$	10.0000	0.827606
$147$	0	0
$148$	−6.00000	−0.493197
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	−1.00000	−0.0816497
$151$	16.0000	1.30206	0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000	1.30206	0.651031	+	0.759051i	$0.274337\pi$
$152$	−1.00000	−0.0811107
$153$	2.00000	0.161690
$154$	0	0
$155$	−8.00000	−0.642575
$156$	−2.00000	−0.160128
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	8.00000	0.636446
$159$	−10.0000	−0.793052
$160$	−2.00000	−0.158114
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	10.0000	0.780869
$165$	8.00000	0.622799
$166$	0	0
$167$	−24.0000	−1.85718	−0.928588	−	0.371113i	$-0.878976\pi$
$167$	−24.0000	−1.85718	−0.928588	+	0.371113i	$0.878976\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	−4.00000	−0.306786
$171$	1.00000	0.0764719
$172$	−4.00000	−0.304997
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	2.00000	0.151620
$175$	0	0
$176$	−4.00000	−0.301511
$177$	12.0000	0.901975
$178$	−10.0000	−0.749532
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	2.00000	0.149071
$181$	−22.0000	−1.63525	−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000	−1.63525	−0.817624	+	0.575753i	$0.804709\pi$
$182$	0	0
$183$	−2.00000	−0.147844
$184$	4.00000	0.294884
$185$	−12.0000	−0.882258
$186$	−4.00000	−0.293294
$187$	−8.00000	−0.585018
$188$	8.00000	0.583460
$189$	0	0
$190$	−2.00000	−0.145095
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	−1.00000	−0.0721688
$193$	−22.0000	−1.58359	−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000	−1.58359	−0.791797	+	0.610784i	$0.790854\pi$
$194$	−2.00000	−0.143592
$195$	−4.00000	−0.286446
$196$	0	0
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	4.00000	0.284268
$199$	−8.00000	−0.567105	−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000	−0.567105	−0.283552	+	0.958957i	$0.591513\pi$
$200$	1.00000	0.0707107
$201$	8.00000	0.564276
$202$	6.00000	0.422159
$203$	0	0
$204$	−2.00000	−0.140028
$205$	20.0000	1.39686
$206$	−4.00000	−0.278693
$207$	−4.00000	−0.278019
$208$	2.00000	0.138675
$209$	−4.00000	−0.276686
$210$	0	0
$211$	16.0000	1.10149	0.550743	−	0.834675i	$-0.314345\pi$
$211$	16.0000	1.10149	0.550743	+	0.834675i	$0.314345\pi$
$212$	10.0000	0.686803
$213$	16.0000	1.09630
$214$	−12.0000	−0.820303
$215$	−8.00000	−0.545595
$216$	1.00000	0.0680414
$217$	0	0
$218$	−2.00000	−0.135457
$219$	10.0000	0.675737
$220$	−8.00000	−0.539360
$221$	4.00000	0.269069
$222$	−6.00000	−0.402694
$223$	12.0000	0.803579	0.401790	−	0.915732i	$-0.368388\pi$
$223$	12.0000	0.803579	0.401790	+	0.915732i	$0.368388\pi$
$224$	0	0
$225$	−1.00000	−0.0666667
$226$	10.0000	0.665190
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	−1.00000	−0.0662266
$229$	−6.00000	−0.396491	−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000	−0.396491	−0.198246	+	0.980152i	$0.563524\pi$
$230$	8.00000	0.527504
$231$	0	0
$232$	−2.00000	−0.131306
$233$	2.00000	0.131024	0.0655122	−	0.997852i	$-0.479132\pi$
$233$	2.00000	0.131024	0.0655122	+	0.997852i	$0.479132\pi$
$234$	−2.00000	−0.130744
$235$	16.0000	1.04372
$236$	−12.0000	−0.781133
$237$	8.00000	0.519656
$238$	0	0
$239$	20.0000	1.29369	0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000	1.29369	0.646846	+	0.762620i	$0.276088\pi$
$240$	−2.00000	−0.129099
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	−5.00000	−0.321412
$243$	−1.00000	−0.0641500
$244$	2.00000	0.128037
$245$	0	0
$246$	10.0000	0.637577
$247$	2.00000	0.127257
$248$	4.00000	0.254000
$249$	0	0
$250$	12.0000	0.758947
$251$	−16.0000	−1.00991	−0.504956	−	0.863145i	$-0.668491\pi$
$251$	−16.0000	−1.00991	−0.504956	+	0.863145i	$0.668491\pi$
$252$	0	0
$253$	16.0000	1.00591
$254$	0	0
$255$	−4.00000	−0.250490
$256$	1.00000	0.0625000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	−4.00000	−0.249029
$259$	0	0
$260$	4.00000	0.248069
$261$	2.00000	0.123797
$262$	0	0
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	−4.00000	−0.246183
$265$	20.0000	1.22859
$266$	0	0
$267$	−10.0000	−0.611990
$268$	−8.00000	−0.488678
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	2.00000	0.121716
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	2.00000	0.121268
$273$	0	0
$274$	14.0000	0.845771
$275$	4.00000	0.241209
$276$	4.00000	0.240772
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	−4.00000	−0.239904
$279$	−4.00000	−0.239474
$280$	0	0
$281$	6.00000	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$282$	8.00000	0.476393
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	−16.0000	−0.949425
$285$	−2.00000	−0.118470
$286$	8.00000	0.473050
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−13.0000	−0.764706
$290$	−4.00000	−0.234888
$291$	−2.00000	−0.117242
$292$	−10.0000	−0.585206
$293$	30.0000	1.75262	0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000	1.75262	0.876309	+	0.481749i	$0.159998\pi$
$294$	0	0
$295$	−24.0000	−1.39733
$296$	6.00000	0.348743
$297$	4.00000	0.232104
$298$	6.00000	0.347571
$299$	−8.00000	−0.462652
$300$	1.00000	0.0577350
$301$	0	0
$302$	−16.0000	−0.920697
$303$	6.00000	0.344691
$304$	1.00000	0.0573539
$305$	4.00000	0.229039
$306$	−2.00000	−0.114332
$307$	28.0000	1.59804	0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000	1.59804	0.799022	+	0.601302i	$0.205351\pi$
$308$	0	0
$309$	−4.00000	−0.227552
$310$	8.00000	0.454369
$311$	−24.0000	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$312$	2.00000	0.113228
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	14.0000	0.790066
$315$	0	0
$316$	−8.00000	−0.450035
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	10.0000	0.560772
$319$	−8.00000	−0.447914
$320$	2.00000	0.111803
$321$	−12.0000	−0.669775
$322$	0	0
$323$	2.00000	0.111283
$324$	1.00000	0.0555556
$325$	−2.00000	−0.110940
$326$	−4.00000	−0.221540
$327$	−2.00000	−0.110600
$328$	−10.0000	−0.552158
$329$	0	0
$330$	−8.00000	−0.440386
$331$	−16.0000	−0.879440	−0.439720	−	0.898135i	$-0.644922\pi$
$331$	−16.0000	−0.879440	−0.439720	+	0.898135i	$0.644922\pi$
$332$	0	0
$333$	−6.00000	−0.328798
$334$	24.0000	1.31322
$335$	−16.0000	−0.874173
$336$	0	0
$337$	−30.0000	−1.63420	−0.817102	−	0.576493i	$-0.804421\pi$
$337$	−30.0000	−1.63420	−0.817102	+	0.576493i	$0.804421\pi$
$338$	9.00000	0.489535
$339$	10.0000	0.543125
$340$	4.00000	0.216930
$341$	16.0000	0.866449
$342$	−1.00000	−0.0540738
$343$	0	0
$344$	4.00000	0.215666
$345$	8.00000	0.430706
$346$	−6.00000	−0.322562
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	−2.00000	−0.107211
$349$	−14.0000	−0.749403	−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000	−0.749403	−0.374701	+	0.927146i	$0.622255\pi$
$350$	0	0
$351$	−2.00000	−0.106752
$352$	4.00000	0.213201
$353$	26.0000	1.38384	0.691920	−	0.721974i	$-0.256765\pi$
$353$	26.0000	1.38384	0.691920	+	0.721974i	$0.256765\pi$
$354$	−12.0000	−0.637793
$355$	−32.0000	−1.69838
$356$	10.0000	0.529999
$357$	0	0
$358$	−12.0000	−0.634220
$359$	−4.00000	−0.211112	−0.105556	−	0.994413i	$-0.533662\pi$
$359$	−4.00000	−0.211112	−0.105556	+	0.994413i	$0.533662\pi$
$360$	−2.00000	−0.105409
$361$	1.00000	0.0526316
$362$	22.0000	1.15629
$363$	−5.00000	−0.262432
$364$	0	0
$365$	−20.0000	−1.04685
$366$	2.00000	0.104542
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	−4.00000	−0.208514
$369$	10.0000	0.520579
$370$	12.0000	0.623850
$371$	0	0
$372$	4.00000	0.207390
$373$	−30.0000	−1.55334	−0.776671	−	0.629907i	$-0.783093\pi$
$373$	−30.0000	−1.55334	−0.776671	+	0.629907i	$0.783093\pi$
$374$	8.00000	0.413670
$375$	12.0000	0.619677
$376$	−8.00000	−0.412568
$377$	4.00000	0.206010
$378$	0	0
$379$	−32.0000	−1.64373	−0.821865	−	0.569683i	$-0.807066\pi$
$379$	−32.0000	−1.64373	−0.821865	+	0.569683i	$0.807066\pi$
$380$	2.00000	0.102598
$381$	0	0
$382$	−12.0000	−0.613973
$383$	8.00000	0.408781	0.204390	−	0.978889i	$-0.434479\pi$
$383$	8.00000	0.408781	0.204390	+	0.978889i	$0.434479\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	22.0000	1.11977
$387$	−4.00000	−0.203331
$388$	2.00000	0.101535
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	4.00000	0.202548
$391$	−8.00000	−0.404577
$392$	0	0
$393$	0	0
$394$	−18.0000	−0.906827
$395$	−16.0000	−0.805047
$396$	−4.00000	−0.201008
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	8.00000	0.401004
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	−10.0000	−0.499376	−0.249688	−	0.968326i	$-0.580328\pi$
$401$	−10.0000	−0.499376	−0.249688	+	0.968326i	$0.580328\pi$
$402$	−8.00000	−0.399004
$403$	−8.00000	−0.398508
$404$	−6.00000	−0.298511
$405$	2.00000	0.0993808
$406$	0	0
$407$	24.0000	1.18964
$408$	2.00000	0.0990148
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	−20.0000	−0.987730
$411$	14.0000	0.690569
$412$	4.00000	0.197066
$413$	0	0
$414$	4.00000	0.196589
$415$	0	0
$416$	−2.00000	−0.0980581
$417$	−4.00000	−0.195881
$418$	4.00000	0.195646
$419$	−24.0000	−1.17248	−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000	−1.17248	−0.586238	+	0.810139i	$0.699392\pi$
$420$	0	0
$421$	−22.0000	−1.07221	−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000	−1.07221	−0.536107	+	0.844150i	$0.680106\pi$
$422$	−16.0000	−0.778868
$423$	8.00000	0.388973
$424$	−10.0000	−0.485643
$425$	−2.00000	−0.0970143
$426$	−16.0000	−0.775203
$427$	0	0
$428$	12.0000	0.580042
$429$	8.00000	0.386244
$430$	8.00000	0.385794
$431$	16.0000	0.770693	0.385346	−	0.922772i	$-0.374082\pi$
$431$	16.0000	0.770693	0.385346	+	0.922772i	$0.374082\pi$
$432$	−1.00000	−0.0481125
$433$	26.0000	1.24948	0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000	1.24948	0.624740	+	0.780833i	$0.285205\pi$
$434$	0	0
$435$	−4.00000	−0.191785
$436$	2.00000	0.0957826
$437$	−4.00000	−0.191346
$438$	−10.0000	−0.477818
$439$	−20.0000	−0.954548	−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000	−0.954548	−0.477274	+	0.878755i	$0.658375\pi$
$440$	8.00000	0.381385
$441$	0	0
$442$	−4.00000	−0.190261
$443$	12.0000	0.570137	0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000	0.570137	0.285069	+	0.958507i	$0.407984\pi$
$444$	6.00000	0.284747
$445$	20.0000	0.948091
$446$	−12.0000	−0.568216
$447$	6.00000	0.283790
$448$	0	0
$449$	14.0000	0.660701	0.330350	−	0.943858i	$-0.392833\pi$
$449$	14.0000	0.660701	0.330350	+	0.943858i	$0.392833\pi$
$450$	1.00000	0.0471405
$451$	−40.0000	−1.88353
$452$	−10.0000	−0.470360
$453$	−16.0000	−0.751746
$454$	12.0000	0.563188
$455$	0	0
$456$	1.00000	0.0468293
$457$	−6.00000	−0.280668	−0.140334	−	0.990104i	$-0.544818\pi$
$457$	−6.00000	−0.280668	−0.140334	+	0.990104i	$0.544818\pi$
$458$	6.00000	0.280362
$459$	−2.00000	−0.0933520
$460$	−8.00000	−0.373002
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	0	0
$463$	−40.0000	−1.85896	−0.929479	−	0.368875i	$-0.879743\pi$
$463$	−40.0000	−1.85896	−0.929479	+	0.368875i	$0.879743\pi$
$464$	2.00000	0.0928477
$465$	8.00000	0.370991
$466$	−2.00000	−0.0926482
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	2.00000	0.0924500
$469$	0	0
$470$	−16.0000	−0.738025
$471$	14.0000	0.645086
$472$	12.0000	0.552345
$473$	16.0000	0.735681
$474$	−8.00000	−0.367452
$475$	−1.00000	−0.0458831
$476$	0	0
$477$	10.0000	0.457869
$478$	−20.0000	−0.914779
$479$	−16.0000	−0.731059	−0.365529	−	0.930800i	$-0.619112\pi$
$479$	−16.0000	−0.731059	−0.365529	+	0.930800i	$0.619112\pi$
$480$	2.00000	0.0912871
$481$	−12.0000	−0.547153
$482$	−10.0000	−0.455488
$483$	0	0
$484$	5.00000	0.227273
$485$	4.00000	0.181631
$486$	1.00000	0.0453609
$487$	−16.0000	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$488$	−2.00000	−0.0905357
$489$	−4.00000	−0.180886
$490$	0	0
$491$	−20.0000	−0.902587	−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000	−0.902587	−0.451294	+	0.892375i	$0.649037\pi$
$492$	−10.0000	−0.450835
$493$	4.00000	0.180151
$494$	−2.00000	−0.0899843
$495$	−8.00000	−0.359573
$496$	−4.00000	−0.179605
$497$	0	0
$498$	0	0
$499$	−20.0000	−0.895323	−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000	−0.895323	−0.447661	+	0.894203i	$0.647743\pi$
$500$	−12.0000	−0.536656
$501$	24.0000	1.07224
$502$	16.0000	0.714115
$503$	−16.0000	−0.713405	−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000	−0.713405	−0.356702	+	0.934218i	$0.616099\pi$
$504$	0	0
$505$	−12.0000	−0.533993
$506$	−16.0000	−0.711287
$507$	9.00000	0.399704
$508$	0	0
$509$	−10.0000	−0.443242	−0.221621	−	0.975133i	$-0.571135\pi$
$509$	−10.0000	−0.443242	−0.221621	+	0.975133i	$0.571135\pi$
$510$	4.00000	0.177123
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	−18.0000	−0.793946
$515$	8.00000	0.352522
$516$	4.00000	0.176090
$517$	−32.0000	−1.40736
$518$	0	0
$519$	−6.00000	−0.263371
$520$	−4.00000	−0.175412
$521$	−22.0000	−0.963837	−0.481919	−	0.876216i	$-0.660060\pi$
$521$	−22.0000	−0.963837	−0.481919	+	0.876216i	$0.660060\pi$
$522$	−2.00000	−0.0875376
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	0	0
$525$	0	0
$526$	12.0000	0.523225
$527$	−8.00000	−0.348485
$528$	4.00000	0.174078
$529$	−7.00000	−0.304348
$530$	−20.0000	−0.868744
$531$	−12.0000	−0.520756
$532$	0	0
$533$	20.0000	0.866296
$534$	10.0000	0.432742
$535$	24.0000	1.03761
$536$	8.00000	0.345547
$537$	−12.0000	−0.517838
$538$	−6.00000	−0.258678
$539$	0	0
$540$	−2.00000	−0.0860663
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	8.00000	0.343629
$543$	22.0000	0.944110
$544$	−2.00000	−0.0857493
$545$	4.00000	0.171341
$546$	0	0
$547$	−32.0000	−1.36822	−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000	−1.36822	−0.684111	+	0.729378i	$0.739809\pi$
$548$	−14.0000	−0.598050
$549$	2.00000	0.0853579
$550$	−4.00000	−0.170561
$551$	2.00000	0.0852029
$552$	−4.00000	−0.170251
$553$	0	0
$554$	10.0000	0.424859
$555$	12.0000	0.509372
$556$	4.00000	0.169638
$557$	2.00000	0.0847427	0.0423714	−	0.999102i	$-0.486509\pi$
$557$	2.00000	0.0847427	0.0423714	+	0.999102i	$0.486509\pi$
$558$	4.00000	0.169334
$559$	−8.00000	−0.338364
$560$	0	0
$561$	8.00000	0.337760
$562$	−6.00000	−0.253095
$563$	36.0000	1.51722	0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000	1.51722	0.758610	+	0.651546i	$0.225879\pi$
$564$	−8.00000	−0.336861
$565$	−20.0000	−0.841406
$566$	4.00000	0.168133
$567$	0	0
$568$	16.0000	0.671345
$569$	−42.0000	−1.76073	−0.880366	−	0.474295i	$-0.842703\pi$
$569$	−42.0000	−1.76073	−0.880366	+	0.474295i	$0.842703\pi$
$570$	2.00000	0.0837708
$571$	4.00000	0.167395	0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000	0.167395	0.0836974	+	0.996491i	$0.473327\pi$
$572$	−8.00000	−0.334497
$573$	−12.0000	−0.501307
$574$	0	0
$575$	4.00000	0.166812
$576$	1.00000	0.0416667
$577$	−34.0000	−1.41544	−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000	−1.41544	−0.707719	+	0.706494i	$0.750276\pi$
$578$	13.0000	0.540729
$579$	22.0000	0.914289
$580$	4.00000	0.166091
$581$	0	0
$582$	2.00000	0.0829027
$583$	−40.0000	−1.65663
$584$	10.0000	0.413803
$585$	4.00000	0.165380
$586$	−30.0000	−1.23929
$587$	16.0000	0.660391	0.330195	−	0.943913i	$-0.392885\pi$
$587$	16.0000	0.660391	0.330195	+	0.943913i	$0.392885\pi$
$588$	0	0
$589$	−4.00000	−0.164817
$590$	24.0000	0.988064
$591$	−18.0000	−0.740421
$592$	−6.00000	−0.246598
$593$	−6.00000	−0.246390	−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000	−0.246390	−0.123195	+	0.992382i	$0.539314\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	−6.00000	−0.245770
$597$	8.00000	0.327418
$598$	8.00000	0.327144
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	−1.00000	−0.0408248
$601$	−22.0000	−0.897399	−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000	−0.897399	−0.448699	+	0.893683i	$0.648113\pi$
$602$	0	0
$603$	−8.00000	−0.325785
$604$	16.0000	0.651031
$605$	10.0000	0.406558
$606$	−6.00000	−0.243733
$607$	−4.00000	−0.162355	−0.0811775	−	0.996700i	$-0.525868\pi$
$607$	−4.00000	−0.162355	−0.0811775	+	0.996700i	$0.525868\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	−4.00000	−0.161955
$611$	16.0000	0.647291
$612$	2.00000	0.0808452
$613$	14.0000	0.565455	0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000	0.565455	0.282727	+	0.959200i	$0.408761\pi$
$614$	−28.0000	−1.12999
$615$	−20.0000	−0.806478
$616$	0	0
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	4.00000	0.160904
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	−8.00000	−0.321288
$621$	4.00000	0.160514
$622$	24.0000	0.962312
$623$	0	0
$624$	−2.00000	−0.0800641
$625$	−19.0000	−0.760000
$626$	10.0000	0.399680
$627$	4.00000	0.159745
$628$	−14.0000	−0.558661
$629$	−12.0000	−0.478471
$630$	0	0
$631$	40.0000	1.59237	0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000	1.59237	0.796187	+	0.605050i	$0.206847\pi$
$632$	8.00000	0.318223
$633$	−16.0000	−0.635943
$634$	−18.0000	−0.714871
$635$	0	0
$636$	−10.0000	−0.396526
$637$	0	0
$638$	8.00000	0.316723
$639$	−16.0000	−0.632950
$640$	−2.00000	−0.0790569
$641$	−42.0000	−1.65890	−0.829450	−	0.558581i	$-0.811346\pi$
$641$	−42.0000	−1.65890	−0.829450	+	0.558581i	$0.811346\pi$
$642$	12.0000	0.473602
$643$	44.0000	1.73519	0.867595	−	0.497271i	$-0.165665\pi$
$643$	44.0000	1.73519	0.867595	+	0.497271i	$0.165665\pi$
$644$	0	0
$645$	8.00000	0.315000
$646$	−2.00000	−0.0786889
$647$	−48.0000	−1.88707	−0.943537	−	0.331266i	$-0.892524\pi$
$647$	−48.0000	−1.88707	−0.943537	+	0.331266i	$0.892524\pi$
$648$	−1.00000	−0.0392837
$649$	48.0000	1.88416
$650$	2.00000	0.0784465
$651$	0	0
$652$	4.00000	0.156652
$653$	−6.00000	−0.234798	−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000	−0.234798	−0.117399	+	0.993085i	$0.537456\pi$
$654$	2.00000	0.0782062
$655$	0	0
$656$	10.0000	0.390434
$657$	−10.0000	−0.390137
$658$	0	0
$659$	−12.0000	−0.467454	−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000	−0.467454	−0.233727	+	0.972302i	$0.575092\pi$
$660$	8.00000	0.311400
$661$	26.0000	1.01128	0.505641	−	0.862744i	$-0.331256\pi$
$661$	26.0000	1.01128	0.505641	+	0.862744i	$0.331256\pi$
$662$	16.0000	0.621858
$663$	−4.00000	−0.155347
$664$	0	0
$665$	0	0
$666$	6.00000	0.232495
$667$	−8.00000	−0.309761
$668$	−24.0000	−0.928588
$669$	−12.0000	−0.463947
$670$	16.0000	0.618134
$671$	−8.00000	−0.308837
$672$	0	0
$673$	34.0000	1.31060	0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000	1.31060	0.655302	+	0.755367i	$0.272541\pi$
$674$	30.0000	1.15556
$675$	1.00000	0.0384900
$676$	−9.00000	−0.346154
$677$	22.0000	0.845529	0.422764	−	0.906240i	$-0.361060\pi$
$677$	22.0000	0.845529	0.422764	+	0.906240i	$0.361060\pi$
$678$	−10.0000	−0.384048
$679$	0	0
$680$	−4.00000	−0.153393
$681$	12.0000	0.459841
$682$	−16.0000	−0.612672
$683$	−4.00000	−0.153056	−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000	−0.153056	−0.0765279	+	0.997067i	$0.524383\pi$
$684$	1.00000	0.0382360
$685$	−28.0000	−1.06983
$686$	0	0
$687$	6.00000	0.228914
$688$	−4.00000	−0.152499
$689$	20.0000	0.761939
$690$	−8.00000	−0.304555
$691$	−52.0000	−1.97817	−0.989087	−	0.147335i	$-0.952930\pi$
$691$	−52.0000	−1.97817	−0.989087	+	0.147335i	$0.952930\pi$
$692$	6.00000	0.228086
$693$	0	0
$694$	12.0000	0.455514
$695$	8.00000	0.303457
$696$	2.00000	0.0758098
$697$	20.0000	0.757554
$698$	14.0000	0.529908
$699$	−2.00000	−0.0756469
$700$	0	0
$701$	18.0000	0.679851	0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000	0.679851	0.339925	+	0.940452i	$0.389598\pi$
$702$	2.00000	0.0754851
$703$	−6.00000	−0.226294
$704$	−4.00000	−0.150756
$705$	−16.0000	−0.602595
$706$	−26.0000	−0.978523
$707$	0	0
$708$	12.0000	0.450988
$709$	−26.0000	−0.976450	−0.488225	−	0.872718i	$-0.662356\pi$
$709$	−26.0000	−0.976450	−0.488225	+	0.872718i	$0.662356\pi$
$710$	32.0000	1.20094
$711$	−8.00000	−0.300023
$712$	−10.0000	−0.374766
$713$	16.0000	0.599205
$714$	0	0
$715$	−16.0000	−0.598366
$716$	12.0000	0.448461
$717$	−20.0000	−0.746914
$718$	4.00000	0.149279
$719$	16.0000	0.596699	0.298350	−	0.954457i	$-0.403564\pi$
$719$	16.0000	0.596699	0.298350	+	0.954457i	$0.403564\pi$
$720$	2.00000	0.0745356
$721$	0	0
$722$	−1.00000	−0.0372161
$723$	−10.0000	−0.371904
$724$	−22.0000	−0.817624
$725$	−2.00000	−0.0742781
$726$	5.00000	0.185567
$727$	24.0000	0.890111	0.445055	−	0.895503i	$-0.353184\pi$
$727$	24.0000	0.890111	0.445055	+	0.895503i	$0.353184\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	20.0000	0.740233
$731$	−8.00000	−0.295891
$732$	−2.00000	−0.0739221
$733$	18.0000	0.664845	0.332423	−	0.943131i	$-0.392134\pi$
$733$	18.0000	0.664845	0.332423	+	0.943131i	$0.392134\pi$
$734$	8.00000	0.295285
$735$	0	0
$736$	4.00000	0.147442
$737$	32.0000	1.17874
$738$	−10.0000	−0.368105
$739$	44.0000	1.61857	0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000	1.61857	0.809283	+	0.587419i	$0.199856\pi$
$740$	−12.0000	−0.441129
$741$	−2.00000	−0.0734718
$742$	0	0
$743$	0	0		−	1.00000i	$-0.5\pi$
$743$	0	0			1.00000i	$0.5\pi$
$744$	−4.00000	−0.146647
$745$	−12.0000	−0.439646
$746$	30.0000	1.09838
$747$	0	0
$748$	−8.00000	−0.292509
$749$	0	0
$750$	−12.0000	−0.438178
$751$	32.0000	1.16770	0.583848	−	0.811863i	$-0.301546\pi$
$751$	32.0000	1.16770	0.583848	+	0.811863i	$0.301546\pi$
$752$	8.00000	0.291730
$753$	16.0000	0.583072
$754$	−4.00000	−0.145671
$755$	32.0000	1.16460
$756$	0	0
$757$	−2.00000	−0.0726912	−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000	−0.0726912	−0.0363456	+	0.999339i	$0.511572\pi$
$758$	32.0000	1.16229
$759$	−16.0000	−0.580763
$760$	−2.00000	−0.0725476
$761$	−30.0000	−1.08750	−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000	−1.08750	−0.543750	+	0.839248i	$0.682996\pi$
$762$	0	0
$763$	0	0
$764$	12.0000	0.434145
$765$	4.00000	0.144620
$766$	−8.00000	−0.289052
$767$	−24.0000	−0.866590
$768$	−1.00000	−0.0360844
$769$	−34.0000	−1.22607	−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000	−1.22607	−0.613036	+	0.790055i	$0.710052\pi$
$770$	0	0
$771$	−18.0000	−0.648254
$772$	−22.0000	−0.791797
$773$	30.0000	1.07903	0.539513	−	0.841978i	$-0.318609\pi$
$773$	30.0000	1.07903	0.539513	+	0.841978i	$0.318609\pi$
$774$	4.00000	0.143777
$775$	4.00000	0.143684
$776$	−2.00000	−0.0717958
$777$	0	0
$778$	30.0000	1.07555
$779$	10.0000	0.358287
$780$	−4.00000	−0.143223
$781$	64.0000	2.29010
$782$	8.00000	0.286079
$783$	−2.00000	−0.0714742
$784$	0	0
$785$	−28.0000	−0.999363
$786$	0	0
$787$	−4.00000	−0.142585	−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000	−0.142585	−0.0712923	+	0.997455i	$0.522712\pi$
$788$	18.0000	0.641223
$789$	12.0000	0.427211
$790$	16.0000	0.569254
$791$	0	0
$792$	4.00000	0.142134
$793$	4.00000	0.142044
$794$	−2.00000	−0.0709773
$795$	−20.0000	−0.709327
$796$	−8.00000	−0.283552
$797$	−10.0000	−0.354218	−0.177109	−	0.984191i	$-0.556675\pi$
$797$	−10.0000	−0.354218	−0.177109	+	0.984191i	$0.556675\pi$
$798$	0	0
$799$	16.0000	0.566039
$800$	1.00000	0.0353553
$801$	10.0000	0.353333
$802$	10.0000	0.353112
$803$	40.0000	1.41157
$804$	8.00000	0.282138
$805$	0	0
$806$	8.00000	0.281788
$807$	−6.00000	−0.211210
$808$	6.00000	0.211079
$809$	2.00000	0.0703163	0.0351581	−	0.999382i	$-0.488807\pi$
$809$	2.00000	0.0703163	0.0351581	+	0.999382i	$0.488807\pi$
$810$	−2.00000	−0.0702728
$811$	20.0000	0.702295	0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000	0.702295	0.351147	+	0.936320i	$0.385792\pi$
$812$	0	0
$813$	8.00000	0.280572
$814$	−24.0000	−0.841200
$815$	8.00000	0.280228
$816$	−2.00000	−0.0700140
$817$	−4.00000	−0.139942
$818$	−10.0000	−0.349642
$819$	0	0
$820$	20.0000	0.698430
$821$	−46.0000	−1.60541	−0.802706	−	0.596376i	$-0.796607\pi$
$821$	−46.0000	−1.60541	−0.802706	+	0.596376i	$0.796607\pi$
$822$	−14.0000	−0.488306
$823$	−32.0000	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−32.0000	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$824$	−4.00000	−0.139347
$825$	−4.00000	−0.139262
$826$	0	0
$827$	36.0000	1.25184	0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000	1.25184	0.625921	+	0.779886i	$0.284723\pi$
$828$	−4.00000	−0.139010
$829$	26.0000	0.903017	0.451509	−	0.892267i	$-0.350886\pi$
$829$	26.0000	0.903017	0.451509	+	0.892267i	$0.350886\pi$
$830$	0	0
$831$	10.0000	0.346896
$832$	2.00000	0.0693375
$833$	0	0
$834$	4.00000	0.138509
$835$	−48.0000	−1.66111
$836$	−4.00000	−0.138343
$837$	4.00000	0.138260
$838$	24.0000	0.829066
$839$	48.0000	1.65714	0.828572	−	0.559883i	$-0.189154\pi$
$839$	48.0000	1.65714	0.828572	+	0.559883i	$0.189154\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	22.0000	0.758170
$843$	−6.00000	−0.206651
$844$	16.0000	0.550743
$845$	−18.0000	−0.619219
$846$	−8.00000	−0.275046
$847$	0	0
$848$	10.0000	0.343401
$849$	4.00000	0.137280
$850$	2.00000	0.0685994
$851$	24.0000	0.822709
$852$	16.0000	0.548151
$853$	−22.0000	−0.753266	−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000	−0.753266	−0.376633	+	0.926363i	$0.622918\pi$
$854$	0	0
$855$	2.00000	0.0683986
$856$	−12.0000	−0.410152
$857$	26.0000	0.888143	0.444072	−	0.895991i	$-0.353534\pi$
$857$	26.0000	0.888143	0.444072	+	0.895991i	$0.353534\pi$
$858$	−8.00000	−0.273115
$859$	−44.0000	−1.50126	−0.750630	−	0.660722i	$-0.770250\pi$
$859$	−44.0000	−1.50126	−0.750630	+	0.660722i	$0.770250\pi$
$860$	−8.00000	−0.272798
$861$	0	0
$862$	−16.0000	−0.544962
$863$	−40.0000	−1.36162	−0.680808	−	0.732462i	$-0.738371\pi$
$863$	−40.0000	−1.36162	−0.680808	+	0.732462i	$0.738371\pi$
$864$	1.00000	0.0340207
$865$	12.0000	0.408012
$866$	−26.0000	−0.883516
$867$	13.0000	0.441503
$868$	0	0
$869$	32.0000	1.08553
$870$	4.00000	0.135613
$871$	−16.0000	−0.542139
$872$	−2.00000	−0.0677285
$873$	2.00000	0.0676897
$874$	4.00000	0.135302
$875$	0	0
$876$	10.0000	0.337869
$877$	−46.0000	−1.55331	−0.776655	−	0.629926i	$-0.783085\pi$
$877$	−46.0000	−1.55331	−0.776655	+	0.629926i	$0.783085\pi$
$878$	20.0000	0.674967
$879$	−30.0000	−1.01187
$880$	−8.00000	−0.269680
$881$	10.0000	0.336909	0.168454	−	0.985709i	$-0.446122\pi$
$881$	10.0000	0.336909	0.168454	+	0.985709i	$0.446122\pi$
$882$	0	0
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	4.00000	0.134535
$885$	24.0000	0.806751
$886$	−12.0000	−0.403148
$887$	−32.0000	−1.07445	−0.537227	−	0.843437i	$-0.680528\pi$
$887$	−32.0000	−1.07445	−0.537227	+	0.843437i	$0.680528\pi$
$888$	−6.00000	−0.201347
$889$	0	0
$890$	−20.0000	−0.670402
$891$	−4.00000	−0.134005
$892$	12.0000	0.401790
$893$	8.00000	0.267710
$894$	−6.00000	−0.200670
$895$	24.0000	0.802232
$896$	0	0
$897$	8.00000	0.267112
$898$	−14.0000	−0.467186
$899$	−8.00000	−0.266815
$900$	−1.00000	−0.0333333
$901$	20.0000	0.666297
$902$	40.0000	1.33185
$903$	0	0
$904$	10.0000	0.332595
$905$	−44.0000	−1.46261
$906$	16.0000	0.531564
$907$	8.00000	0.265636	0.132818	−	0.991140i	$-0.457597\pi$
$907$	8.00000	0.265636	0.132818	+	0.991140i	$0.457597\pi$
$908$	−12.0000	−0.398234
$909$	−6.00000	−0.199007
$910$	0	0
$911$	8.00000	0.265052	0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000	0.265052	0.132526	+	0.991180i	$0.457691\pi$
$912$	−1.00000	−0.0331133
$913$	0	0
$914$	6.00000	0.198462
$915$	−4.00000	−0.132236
$916$	−6.00000	−0.198246
$917$	0	0
$918$	2.00000	0.0660098
$919$	32.0000	1.05558	0.527791	−	0.849374i	$-0.323020\pi$
$919$	32.0000	1.05558	0.527791	+	0.849374i	$0.323020\pi$
$920$	8.00000	0.263752
$921$	−28.0000	−0.922631
$922$	6.00000	0.197599
$923$	−32.0000	−1.05329
$924$	0	0
$925$	6.00000	0.197279
$926$	40.0000	1.31448
$927$	4.00000	0.131377
$928$	−2.00000	−0.0656532
$929$	58.0000	1.90292	0.951459	−	0.307775i	$-0.0995844\pi$
$929$	58.0000	1.90292	0.951459	+	0.307775i	$0.0995844\pi$
$930$	−8.00000	−0.262330
$931$	0	0
$932$	2.00000	0.0655122
$933$	24.0000	0.785725
$934$	0	0
$935$	−16.0000	−0.523256
$936$	−2.00000	−0.0653720
$937$	30.0000	0.980057	0.490029	−	0.871706i	$-0.336986\pi$
$937$	30.0000	0.980057	0.490029	+	0.871706i	$0.336986\pi$
$938$	0	0
$939$	10.0000	0.326338
$940$	16.0000	0.521862
$941$	6.00000	0.195594	0.0977972	−	0.995206i	$-0.468820\pi$
$941$	6.00000	0.195594	0.0977972	+	0.995206i	$0.468820\pi$
$942$	−14.0000	−0.456145
$943$	−40.0000	−1.30258
$944$	−12.0000	−0.390567
$945$	0	0
$946$	−16.0000	−0.520205
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	8.00000	0.259828
$949$	−20.0000	−0.649227
$950$	1.00000	0.0324443
$951$	−18.0000	−0.583690
$952$	0	0
$953$	54.0000	1.74923	0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000	1.74923	0.874616	+	0.484817i	$0.161114\pi$
$954$	−10.0000	−0.323762
$955$	24.0000	0.776622
$956$	20.0000	0.646846
$957$	8.00000	0.258603
$958$	16.0000	0.516937
$959$	0	0
$960$	−2.00000	−0.0645497
$961$	−15.0000	−0.483871
$962$	12.0000	0.386896
$963$	12.0000	0.386695
$964$	10.0000	0.322078
$965$	−44.0000	−1.41641
$966$	0	0
$967$	32.0000	1.02905	0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000	1.02905	0.514525	+	0.857475i	$0.327968\pi$
$968$	−5.00000	−0.160706
$969$	−2.00000	−0.0642493
$970$	−4.00000	−0.128432
$971$	12.0000	0.385098	0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000	0.385098	0.192549	+	0.981287i	$0.438325\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	16.0000	0.512673
$975$	2.00000	0.0640513
$976$	2.00000	0.0640184
$977$	6.00000	0.191957	0.0959785	−	0.995383i	$-0.469402\pi$
$977$	6.00000	0.191957	0.0959785	+	0.995383i	$0.469402\pi$
$978$	4.00000	0.127906
$979$	−40.0000	−1.27841
$980$	0	0
$981$	2.00000	0.0638551
$982$	20.0000	0.638226
$983$	48.0000	1.53096	0.765481	−	0.643458i	$-0.222501\pi$
$983$	48.0000	1.53096	0.765481	+	0.643458i	$0.222501\pi$
$984$	10.0000	0.318788
$985$	36.0000	1.14706
$986$	−4.00000	−0.127386
$987$	0	0
$988$	2.00000	0.0636285
$989$	16.0000	0.508770
$990$	8.00000	0.254257
$991$	40.0000	1.27064	0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000	1.27064	0.635321	+	0.772248i	$0.280868\pi$
$992$	4.00000	0.127000
$993$	16.0000	0.507745
$994$	0	0
$995$	−16.0000	−0.507234
$996$	0	0
$997$	−6.00000	−0.190022	−0.0950110	−	0.995476i	$-0.530289\pi$
$997$	−6.00000	−0.190022	−0.0950110	+	0.995476i	$0.530289\pi$
$998$	20.0000	0.633089
$999$	6.00000	0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.i.1.1		1
7.6	odd	2		798.2.a.c.1.1	✓	1
21.20	even	2		2394.2.a.n.1.1		1
28.27	even	2		6384.2.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.a.c.1.1	✓	1	7.6	odd	2
2394.2.a.n.1.1		1	21.20	even	2
5586.2.a.i.1.1		1	1.1	even	1	trivial
6384.2.a.e.1.1		1	28.27	even	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:	\( N \)	\(=\)	\( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5586.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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