LMFDB - Embedded newform 15.8.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,8,Mod(1,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("15.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	15.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:	$4.68577538226$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-13.0000 q^{2} -27.0000 q^{3} +41.0000 q^{4} -125.000 q^{5} +351.000 q^{6} +1380.00 q^{7} +1131.00 q^{8} +729.000 q^{9} +O(q^{10})$

\(q-13.0000 q^{2} -27.0000 q^{3} +41.0000 q^{4} -125.000 q^{5} +351.000 q^{6} +1380.00 q^{7} +1131.00 q^{8} +729.000 q^{9} +1625.00 q^{10} -3304.00 q^{11} -1107.00 q^{12} +8506.00 q^{13} -17940.0 q^{14} +3375.00 q^{15} -19951.0 q^{16} -9994.00 q^{17} -9477.00 q^{18} +41236.0 q^{19} -5125.00 q^{20} -37260.0 q^{21} +42952.0 q^{22} +84120.0 q^{23} -30537.0 q^{24} +15625.0 q^{25} -110578. q^{26} -19683.0 q^{27} +56580.0 q^{28} +132802. q^{29} -43875.0 q^{30} -55800.0 q^{31} +114595. q^{32} +89208.0 q^{33} +129922. q^{34} -172500. q^{35} +29889.0 q^{36} +228170. q^{37} -536068. q^{38} -229662. q^{39} -141375. q^{40} -139670. q^{41} +484380. q^{42} -755492. q^{43} -135464. q^{44} -91125.0 q^{45} -1.09356e6 q^{46} +836984. q^{47} +538677. q^{48} +1.08086e6 q^{49} -203125. q^{50} +269838. q^{51} +348746. q^{52} +1.64165e6 q^{53} +255879. q^{54} +413000. q^{55} +1.56078e6 q^{56} -1.11337e6 q^{57} -1.72643e6 q^{58} -989656. q^{59} +138375. q^{60} -1.65816e6 q^{61} +725400. q^{62} +1.00602e6 q^{63} +1.06399e6 q^{64} -1.06325e6 q^{65} -1.15970e6 q^{66} -4.52384e6 q^{67} -409754. q^{68} -2.27124e6 q^{69} +2.24250e6 q^{70} -389408. q^{71} +824499. q^{72} +5.61733e6 q^{73} -2.96621e6 q^{74} -421875. q^{75} +1.69068e6 q^{76} -4.55952e6 q^{77} +2.98561e6 q^{78} +3.90108e6 q^{79} +2.49388e6 q^{80} +531441. q^{81} +1.81571e6 q^{82} -9.39412e6 q^{83} -1.52766e6 q^{84} +1.24925e6 q^{85} +9.82140e6 q^{86} -3.58565e6 q^{87} -3.73682e6 q^{88} +2.80375e6 q^{89} +1.18462e6 q^{90} +1.17383e7 q^{91} +3.44892e6 q^{92} +1.50660e6 q^{93} -1.08808e7 q^{94} -5.15450e6 q^{95} -3.09406e6 q^{96} +5.09943e6 q^{97} -1.40511e7 q^{98} -2.40862e6 q^{99} +O(q^{100})\)

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 $

$2$	−13.0000	−1.14905	−0.574524	−	0.818488i	$-0.694813\pi$
$2$	−13.0000	−1.14905	−0.574524	+	0.818488i	$0.694813\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	41.0000	0.320312
$5$	−125.000	−0.447214
$5$	−125.000	−0.447214
$6$	351.000	0.663403
$7$	1380.00	1.52067	0.760337	−	0.649529i	$-0.225034\pi$
$7$	1380.00	1.52067	0.760337	+	0.649529i	$0.225034\pi$
$8$	1131.00	0.780994
$9$	729.000	0.333333
$10$	1625.00	0.513870
$11$	−3304.00	−0.748455	−0.374227	−	0.927337i	$-0.622092\pi$
$11$	−3304.00	−0.748455	−0.374227	+	0.927337i	$0.622092\pi$
$12$	−1107.00	−0.184933
$13$	8506.00	1.07380	0.536900	−	0.843646i	$-0.319595\pi$
$13$	8506.00	1.07380	0.536900	+	0.843646i	$0.319595\pi$
$14$	−17940.0	−1.74733
$15$	3375.00	0.258199
$16$	−19951.0	−1.21771
$17$	−9994.00	−0.493365	−0.246682	−	0.969096i	$-0.579340\pi$
$17$	−9994.00	−0.493365	−0.246682	+	0.969096i	$0.579340\pi$
$18$	−9477.00	−0.383016
$19$	41236.0	1.37924	0.689619	−	0.724173i	$-0.257778\pi$
$19$	41236.0	1.37924	0.689619	+	0.724173i	$0.257778\pi$
$20$	−5125.00	−0.143248
$21$	−37260.0	−0.877961
$22$	42952.0	0.860011
$23$	84120.0	1.44162	0.720812	−	0.693131i	$-0.243769\pi$
$23$	84120.0	1.44162	0.720812	+	0.693131i	$0.243769\pi$
$24$	−30537.0	−0.450907
$25$	15625.0	0.200000
$26$	−110578.	−1.23385
$27$	−19683.0	−0.192450
$28$	56580.0	0.487091
$29$	132802.	1.01114	0.505570	−	0.862785i	$-0.331282\pi$
$29$	132802.	1.01114	0.505570	+	0.862785i	$0.331282\pi$
$30$	−43875.0	−0.296683
$31$	−55800.0	−0.336410	−0.168205	−	0.985752i	$-0.553797\pi$
$31$	−55800.0	−0.336410	−0.168205	+	0.985752i	$0.553797\pi$
$32$	114595.	0.618217
$33$	89208.0	0.432121
$34$	129922.	0.566900
$35$	−172500.	−0.680066
$36$	29889.0	0.106771
$37$	228170.	0.740547	0.370273	−	0.928923i	$-0.379264\pi$
$37$	228170.	0.740547	0.370273	+	0.928923i	$0.379264\pi$
$38$	−536068.	−1.58481
$39$	−229662.	−0.619959
$40$	−141375.	−0.349271
$41$	−139670.	−0.316490	−0.158245	−	0.987400i	$-0.550584\pi$
$41$	−139670.	−0.316490	−0.158245	+	0.987400i	$0.550584\pi$
$42$	484380.	1.00882
$43$	−755492.	−1.44907	−0.724537	−	0.689236i	$-0.757946\pi$
$43$	−755492.	−1.44907	−0.724537	+	0.689236i	$0.757946\pi$
$44$	−135464.	−0.239739
$45$	−91125.0	−0.149071
$46$	−1.09356e6	−1.65650
$47$	836984.	1.17591	0.587956	−	0.808893i	$-0.299933\pi$
$47$	836984.	1.17591	0.587956	+	0.808893i	$0.299933\pi$
$48$	538677.	0.703047
$49$	1.08086e6	1.31245
$50$	−203125.	−0.229810
$51$	269838.	0.284844
$52$	348746.	0.343952
$53$	1.64165e6	1.51466	0.757330	−	0.653033i	$-0.226504\pi$
$53$	1.64165e6	1.51466	0.757330	+	0.653033i	$0.226504\pi$
$54$	255879.	0.221134
$55$	413000.	0.334719
$56$	1.56078e6	1.18764
$57$	−1.11337e6	−0.796303
$58$	−1.72643e6	−1.16185
$59$	−989656.	−0.627339	−0.313669	−	0.949532i	$-0.601558\pi$
$59$	−989656.	−0.627339	−0.313669	+	0.949532i	$0.601558\pi$
$60$	138375.	0.0827043
$61$	−1.65816e6	−0.935347	−0.467673	−	0.883901i	$-0.654908\pi$
$61$	−1.65816e6	−0.935347	−0.467673	+	0.883901i	$0.654908\pi$
$62$	725400.	0.386551
$63$	1.00602e6	0.506891
$64$	1.06399e6	0.507351
$65$	−1.06325e6	−0.480218
$66$	−1.15970e6	−0.496528
$67$	−4.52384e6	−1.83758	−0.918789	−	0.394749i	$-0.870832\pi$
$67$	−4.52384e6	−1.83758	−0.918789	+	0.394749i	$0.870832\pi$
$68$	−409754.	−0.158031
$69$	−2.27124e6	−0.832322
$70$	2.24250e6	0.781429
$71$	−389408.	−0.129122	−0.0645611	−	0.997914i	$-0.520565\pi$
$71$	−389408.	−0.129122	−0.0645611	+	0.997914i	$0.520565\pi$
$72$	824499.	0.260331
$73$	5.61733e6	1.69005	0.845026	−	0.534726i	$-0.179585\pi$
$73$	5.61733e6	1.69005	0.845026	+	0.534726i	$0.179585\pi$
$74$	−2.96621e6	−0.850924
$75$	−421875.	−0.115470
$76$	1.69068e6	0.441787
$77$	−4.55952e6	−1.13816
$78$	2.98561e6	0.712363
$79$	3.90108e6	0.890205	0.445103	−	0.895480i	$-0.353167\pi$
$79$	3.90108e6	0.890205	0.445103	+	0.895480i	$0.353167\pi$
$80$	2.49388e6	0.544578
$81$	531441.	0.111111
$82$	1.81571e6	0.363662
$83$	−9.39412e6	−1.80336	−0.901680	−	0.432403i	$-0.857666\pi$
$83$	−9.39412e6	−1.80336	−0.901680	+	0.432403i	$0.857666\pi$
$84$	−1.52766e6	−0.281222
$85$	1.24925e6	0.220639
$86$	9.82140e6	1.66506
$87$	−3.58565e6	−0.583782
$88$	−3.73682e6	−0.584539
$89$	2.80375e6	0.421574	0.210787	−	0.977532i	$-0.432397\pi$
$89$	2.80375e6	0.421574	0.210787	+	0.977532i	$0.432397\pi$
$90$	1.18462e6	0.171290
$91$	1.17383e7	1.63290
$92$	3.44892e6	0.461770
$93$	1.50660e6	0.194226
$94$	−1.08808e7	−1.35118
$95$	−5.15450e6	−0.616814
$96$	−3.09406e6	−0.356928
$97$	5.09943e6	0.567310	0.283655	−	0.958926i	$-0.408453\pi$
$97$	5.09943e6	0.567310	0.283655	+	0.958926i	$0.408453\pi$
$98$	−1.40511e7	−1.50807
$99$	−2.40862e6	−0.249485
$100$	640625.	0.0640625
$101$	1.51723e7	1.46530	0.732648	−	0.680607i	$-0.238284\pi$
$101$	1.51723e7	1.46530	0.732648	+	0.680607i	$0.238284\pi$
$102$	−3.50789e6	−0.327300
$103$	4.70527e6	0.424281	0.212141	−	0.977239i	$-0.431956\pi$
$103$	4.70527e6	0.424281	0.212141	+	0.977239i	$0.431956\pi$
$104$	9.62029e6	0.838632
$105$	4.65750e6	0.392636
$106$	−2.13414e7	−1.74042
$107$	2.63120e6	0.207640	0.103820	−	0.994596i	$-0.466893\pi$
$107$	2.63120e6	0.207640	0.103820	+	0.994596i	$0.466893\pi$
$108$	−807003.	−0.0616442
$109$	−4.30059e6	−0.318080	−0.159040	−	0.987272i	$-0.550840\pi$
$109$	−4.30059e6	−0.318080	−0.159040	+	0.987272i	$0.550840\pi$
$110$	−5.36900e6	−0.384609
$111$	−6.16059e6	−0.427555
$112$	−2.75324e7	−1.85174
$113$	3.98233e6	0.259635	0.129817	−	0.991538i	$-0.458561\pi$
$113$	3.98233e6	0.259635	0.129817	+	0.991538i	$0.458561\pi$
$114$	1.44738e7	0.914991
$115$	−1.05150e7	−0.644714
$116$	5.44488e6	0.323881
$117$	6.20087e6	0.357934
$118$	1.28655e7	0.720843
$119$	−1.37917e7	−0.750247
$120$	3.81712e6	0.201652
$121$	−8.57076e6	−0.439815
$122$	2.15561e7	1.07476
$123$	3.77109e6	0.182725
$124$	−2.28780e6	−0.107756
$125$	−1.95312e6	−0.0894427
$126$	−1.30783e7	−0.582443
$127$	2.80177e7	1.21372	0.606861	−	0.794808i	$-0.292429\pi$
$127$	2.80177e7	1.21372	0.606861	+	0.794808i	$0.292429\pi$
$128$	−2.85001e7	−1.20119
$129$	2.03983e7	0.836623
$130$	1.38222e7	0.551794
$131$	−8.19919e6	−0.318656	−0.159328	−	0.987226i	$-0.550933\pi$
$131$	−8.19919e6	−0.318656	−0.159328	+	0.987226i	$0.550933\pi$
$132$	3.65753e6	0.138414
$133$	5.69057e7	2.09737
$134$	5.88100e7	2.11147
$135$	2.46038e6	0.0860663
$136$	−1.13032e7	−0.385315
$137$	−1.66646e6	−0.0553697	−0.0276849	−	0.999617i	$-0.508813\pi$
$137$	−1.66646e6	−0.0553697	−0.0276849	+	0.999617i	$0.508813\pi$
$138$	2.95261e7	0.956378
$139$	−5.87456e7	−1.85534	−0.927670	−	0.373401i	$-0.878192\pi$
$139$	−5.87456e7	−1.85534	−0.927670	+	0.373401i	$0.878192\pi$
$140$	−7.07250e6	−0.217834
$141$	−2.25986e7	−0.678913
$142$	5.06230e6	0.148368
$143$	−2.81038e7	−0.803691
$144$	−1.45443e7	−0.405904
$145$	−1.66002e7	−0.452196
$146$	−7.30253e7	−1.94195
$147$	−2.91831e7	−0.757742
$148$	9.35497e6	0.237206
$149$	−1.93697e7	−0.479702	−0.239851	−	0.970810i	$-0.577099\pi$
$149$	−1.93697e7	−0.479702	−0.239851	+	0.970810i	$0.577099\pi$
$150$	5.48438e6	0.132681
$151$	−5.33952e7	−1.26207	−0.631034	−	0.775755i	$-0.717369\pi$
$151$	−5.33952e7	−1.26207	−0.631034	+	0.775755i	$0.717369\pi$
$152$	4.66379e7	1.07718
$153$	−7.28563e6	−0.164455
$154$	5.92738e7	1.30780
$155$	6.97500e6	0.150447
$156$	−9.41614e6	−0.198581
$157$	2.04529e7	0.421800	0.210900	−	0.977508i	$-0.432361\pi$
$157$	2.04529e7	0.421800	0.210900	+	0.977508i	$0.432361\pi$
$158$	−5.07140e7	−1.02289
$159$	−4.43246e7	−0.874489
$160$	−1.43244e7	−0.276475
$161$	1.16086e8	2.19224
$162$	−6.90873e6	−0.127672
$163$	−733588.	−0.0132677	−0.00663385	−	0.999978i	$-0.502112\pi$
$163$	−733588.	−0.0132677	−0.00663385	+	0.999978i	$0.502112\pi$
$164$	−5.72647e6	−0.101376
$165$	−1.11510e7	−0.193250
$166$	1.22124e8	2.07215
$167$	1.68925e7	0.280664	0.140332	−	0.990105i	$-0.455183\pi$
$167$	1.68925e7	0.280664	0.140332	+	0.990105i	$0.455183\pi$
$168$	−4.21411e7	−0.685682
$169$	9.60352e6	0.153048
$170$	−1.62402e7	−0.253525
$171$	3.00610e7	0.459746
$172$	−3.09752e7	−0.464156
$173$	1.18186e7	0.173541	0.0867707	−	0.996228i	$-0.472345\pi$
$173$	1.18186e7	0.173541	0.0867707	+	0.996228i	$0.472345\pi$
$174$	4.66135e7	0.670794
$175$	2.15625e7	0.304135
$176$	6.59181e7	0.911403
$177$	2.67207e7	0.362194
$178$	−3.64487e7	−0.484409
$179$	−3.13746e7	−0.408877	−0.204439	−	0.978879i	$-0.565537\pi$
$179$	−3.13746e7	−0.408877	−0.204439	+	0.978879i	$0.565537\pi$
$180$	−3.73612e6	−0.0477494
$181$	−5.83555e7	−0.731488	−0.365744	−	0.930716i	$-0.619185\pi$
$181$	−5.83555e7	−0.731488	−0.365744	+	0.930716i	$0.619185\pi$
$182$	−1.52598e8	−1.87628
$183$	4.47704e7	0.540023
$184$	9.51397e7	1.12590
$185$	−2.85213e7	−0.331183
$186$	−1.95858e7	−0.223175
$187$	3.30202e7	0.369261
$188$	3.43163e7	0.376659
$189$	−2.71625e7	−0.292654
$190$	6.70085e7	0.708749
$191$	4.06166e6	0.0421780	0.0210890	−	0.999778i	$-0.493287\pi$
$191$	4.06166e6	0.0421780	0.0210890	+	0.999778i	$0.493287\pi$
$192$	−2.87278e7	−0.292919
$193$	−1.33221e8	−1.33389	−0.666946	−	0.745106i	$-0.732399\pi$
$193$	−1.33221e8	−1.33389	−0.666946	+	0.745106i	$0.732399\pi$
$194$	−6.62925e7	−0.651866
$195$	2.87078e7	0.277254
$196$	4.43151e7	0.420393
$197$	1.30771e7	0.121866	0.0609328	−	0.998142i	$-0.480592\pi$
$197$	1.30771e7	0.121866	0.0609328	+	0.998142i	$0.480592\pi$
$198$	3.13120e7	0.286670
$199$	−6.98502e7	−0.628322	−0.314161	−	0.949370i	$-0.601723\pi$
$199$	−6.98502e7	−0.628322	−0.314161	+	0.949370i	$0.601723\pi$
$200$	1.76719e7	0.156199
$201$	1.22144e8	1.06093
$202$	−1.97239e8	−1.68370
$203$	1.83267e8	1.53761
$204$	1.10634e7	0.0912392
$205$	1.74588e7	0.141539
$206$	−6.11685e7	−0.487520
$207$	6.13235e7	0.480541
$208$	−1.69703e8	−1.30758
$209$	−1.36244e8	−1.03230
$210$	−6.05475e7	−0.451158
$211$	3.28535e7	0.240765	0.120382	−	0.992728i	$-0.461588\pi$
$211$	3.28535e7	0.240765	0.120382	+	0.992728i	$0.461588\pi$
$212$	6.73076e7	0.485164
$213$	1.05140e7	0.0745487
$214$	−3.42057e7	−0.238589
$215$	9.44365e7	0.648045
$216$	−2.22615e7	−0.150302
$217$	−7.70040e7	−0.511569
$218$	5.59077e7	0.365489
$219$	−1.51668e8	−0.975752
$220$	1.69330e7	0.107215
$221$	−8.50090e7	−0.529775
$222$	8.00877e7	0.491281
$223$	6.95194e7	0.419796	0.209898	−	0.977723i	$-0.432687\pi$
$223$	6.95194e7	0.419796	0.209898	+	0.977723i	$0.432687\pi$
$224$	1.58141e8	0.940106
$225$	1.13906e7	0.0666667
$226$	−5.17703e7	−0.298333
$227$	−2.30779e8	−1.30950	−0.654750	−	0.755845i	$-0.727226\pi$
$227$	−2.30779e8	−1.30950	−0.654750	+	0.755845i	$0.727226\pi$
$228$	−4.56483e7	−0.255066
$229$	1.46157e8	0.804258	0.402129	−	0.915583i	$-0.368270\pi$
$229$	1.46157e8	0.804258	0.402129	+	0.915583i	$0.368270\pi$
$230$	1.36695e8	0.740807
$231$	1.23107e8	0.657114
$232$	1.50199e8	0.789695
$233$	3.11907e8	1.61540	0.807700	−	0.589594i	$-0.200712\pi$
$233$	3.11907e8	1.61540	0.807700	+	0.589594i	$0.200712\pi$
$234$	−8.06114e7	−0.411283
$235$	−1.04623e8	−0.525884
$236$	−4.05759e7	−0.200944
$237$	−1.05329e8	−0.513960
$238$	1.79292e8	0.862070
$239$	2.27310e8	1.07703	0.538513	−	0.842617i	$-0.318986\pi$
$239$	2.27310e8	1.07703	0.538513	+	0.842617i	$0.318986\pi$
$240$	−6.73346e7	−0.314412
$241$	−1.98483e8	−0.913404	−0.456702	−	0.889620i	$-0.650969\pi$
$241$	−1.98483e8	−0.913404	−0.456702	+	0.889620i	$0.650969\pi$
$242$	1.11420e8	0.505369
$243$	−1.43489e7	−0.0641500
$244$	−6.79846e7	−0.299603
$245$	−1.35107e8	−0.586944
$246$	−4.90242e7	−0.209960
$247$	3.50753e8	1.48103
$248$	−6.31098e7	−0.262734
$249$	2.53641e8	1.04117
$250$	2.53906e7	0.102774
$251$	−1.32536e8	−0.529024	−0.264512	−	0.964382i	$-0.585211\pi$
$251$	−1.32536e8	−0.529024	−0.264512	+	0.964382i	$0.585211\pi$
$252$	4.12468e7	0.162364
$253$	−2.77932e8	−1.07899
$254$	−3.64230e8	−1.39463
$255$	−3.37298e7	−0.127386
$256$	2.34310e8	0.872872
$257$	−3.58642e7	−0.131794	−0.0658970	−	0.997826i	$-0.520991\pi$
$257$	−3.58642e7	−0.131794	−0.0658970	+	0.997826i	$0.520991\pi$
$258$	−2.65178e8	−0.961320
$259$	3.14875e8	1.12613
$260$	−4.35932e7	−0.153820
$261$	9.68127e7	0.337047
$262$	1.06589e8	0.366151
$263$	−4.79640e8	−1.62581	−0.812907	−	0.582394i	$-0.802116\pi$
$263$	−4.79640e8	−1.62581	−0.812907	+	0.582394i	$0.802116\pi$
$264$	1.00894e8	0.337484
$265$	−2.05206e8	−0.677376
$266$	−7.39774e8	−2.40998
$267$	−7.57011e7	−0.243396
$268$	−1.85478e8	−0.588599
$269$	−7.08764e7	−0.222008	−0.111004	−	0.993820i	$-0.535407\pi$
$269$	−7.08764e7	−0.222008	−0.111004	+	0.993820i	$0.535407\pi$
$270$	−3.19849e7	−0.0988944
$271$	4.07490e8	1.24373	0.621863	−	0.783126i	$-0.286376\pi$
$271$	4.07490e8	1.24373	0.621863	+	0.783126i	$0.286376\pi$
$272$	1.99390e8	0.600776
$273$	−3.16934e8	−0.942755
$274$	2.16640e7	0.0636225
$275$	−5.16250e7	−0.149691
$276$	−9.31208e7	−0.266603
$277$	−7.93477e7	−0.224313	−0.112157	−	0.993691i	$-0.535776\pi$
$277$	−7.93477e7	−0.224313	−0.112157	+	0.993691i	$0.535776\pi$
$278$	7.63693e8	2.13188
$279$	−4.06782e7	−0.112137
$280$	−1.95098e8	−0.531127
$281$	−8.70068e7	−0.233928	−0.116964	−	0.993136i	$-0.537316\pi$
$281$	−8.70068e7	−0.233928	−0.116964	+	0.993136i	$0.537316\pi$
$282$	2.93781e8	0.780104
$283$	2.77612e8	0.728091	0.364045	−	0.931381i	$-0.381395\pi$
$283$	2.77612e8	0.728091	0.364045	+	0.931381i	$0.381395\pi$
$284$	−1.59657e7	−0.0413594
$285$	1.39172e8	0.356117
$286$	3.65350e8	0.923480
$287$	−1.92745e8	−0.481278
$288$	8.35398e7	0.206072
$289$	−3.10459e8	−0.756591
$290$	2.15803e8	0.519595
$291$	−1.37685e8	−0.327536
$292$	2.30311e8	0.541345
$293$	2.46490e8	0.572484	0.286242	−	0.958157i	$-0.407594\pi$
$293$	2.46490e8	0.572484	0.286242	+	0.958157i	$0.407594\pi$
$294$	3.79381e8	0.870682
$295$	1.23707e8	0.280554
$296$	2.58060e8	0.578363
$297$	6.50326e7	0.144040
$298$	2.51807e8	0.551201
$299$	7.15525e8	1.54802
$300$	−1.72969e7	−0.0369865
$301$	−1.04258e9	−2.20357
$302$	6.94138e8	1.45018
$303$	−4.09651e8	−0.845990
$304$	−8.22699e8	−1.67951
$305$	2.07270e8	0.418300
$306$	9.47131e7	0.188967
$307$	3.84965e8	0.759340	0.379670	−	0.925122i	$-0.376037\pi$
$307$	3.84965e8	0.759340	0.379670	+	0.925122i	$0.376037\pi$
$308$	−1.86940e8	−0.364565
$309$	−1.27042e8	−0.244959
$310$	−9.06750e7	−0.172871
$311$	4.64435e7	0.0875514	0.0437757	−	0.999041i	$-0.486061\pi$
$311$	4.64435e7	0.0875514	0.0437757	+	0.999041i	$0.486061\pi$
$312$	−2.59748e8	−0.484184
$313$	2.10558e8	0.388120	0.194060	−	0.980990i	$-0.437834\pi$
$313$	2.10558e8	0.388120	0.194060	+	0.980990i	$0.437834\pi$
$314$	−2.65888e8	−0.484669
$315$	−1.25752e8	−0.226689
$316$	1.59944e8	0.285144
$317$	−9.60971e8	−1.69435	−0.847175	−	0.531314i	$-0.821698\pi$
$317$	−9.60971e8	−1.69435	−0.847175	+	0.531314i	$0.821698\pi$
$318$	5.76219e8	1.00483
$319$	−4.38778e8	−0.756793
$320$	−1.32999e8	−0.226894
$321$	−7.10425e7	−0.119881
$322$	−1.50911e9	−2.51899
$323$	−4.12113e8	−0.680467
$324$	2.17891e7	0.0355903
$325$	1.32906e8	0.214760
$326$	9.53664e6	0.0152452
$327$	1.16116e8	0.183643
$328$	−1.57967e8	−0.247177
$329$	1.15504e9	1.78818
$330$	1.44963e8	0.222054
$331$	3.99923e8	0.606147	0.303074	−	0.952967i	$-0.401987\pi$
$331$	3.99923e8	0.606147	0.303074	+	0.952967i	$0.401987\pi$
$332$	−3.85159e8	−0.577639
$333$	1.66336e8	0.246849
$334$	−2.19603e8	−0.322497
$335$	5.65480e8	0.821790
$336$	7.43374e8	1.06910
$337$	2.69185e8	0.383129	0.191565	−	0.981480i	$-0.438644\pi$
$337$	2.69185e8	0.383129	0.191565	+	0.981480i	$0.438644\pi$
$338$	−1.24846e8	−0.175859
$339$	−1.07523e8	−0.149900
$340$	5.12192e7	0.0706736
$341$	1.84363e8	0.251787
$342$	−3.90794e8	−0.528270
$343$	3.55093e8	0.475131
$344$	−8.54461e8	−1.13172
$345$	2.83905e8	0.372226
$346$	−1.53641e8	−0.199407
$347$	−8.21868e8	−1.05596	−0.527982	−	0.849256i	$-0.677051\pi$
$347$	−8.21868e8	−1.05596	−0.527982	+	0.849256i	$0.677051\pi$
$348$	−1.47012e8	−0.186993
$349$	6.48354e8	0.816438	0.408219	−	0.912884i	$-0.366150\pi$
$349$	6.48354e8	0.816438	0.408219	+	0.912884i	$0.366150\pi$
$350$	−2.80312e8	−0.349466
$351$	−1.67424e8	−0.206653
$352$	−3.78622e8	−0.462707
$353$	6.52666e8	0.789732	0.394866	−	0.918739i	$-0.370791\pi$
$353$	6.52666e8	0.789732	0.394866	+	0.918739i	$0.370791\pi$
$354$	−3.47369e8	−0.416179
$355$	4.86760e7	0.0577452
$356$	1.14954e8	0.135035
$357$	3.72376e8	0.433155
$358$	4.07870e8	0.469820
$359$	−8.77431e8	−1.00088	−0.500440	−	0.865771i	$-0.666829\pi$
$359$	−8.77431e8	−1.00088	−0.500440	+	0.865771i	$0.666829\pi$
$360$	−1.03062e8	−0.116424
$361$	8.06536e8	0.902295
$362$	7.58622e8	0.840515
$363$	2.31410e8	0.253927
$364$	4.81269e8	0.523038
$365$	−7.02166e8	−0.755814
$366$	−5.82015e8	−0.620512
$367$	2.86989e8	0.303064	0.151532	−	0.988452i	$-0.451579\pi$
$367$	2.86989e8	0.303064	0.151532	+	0.988452i	$0.451579\pi$
$368$	−1.67828e9	−1.75548
$369$	−1.01819e8	−0.105497
$370$	3.70776e8	0.380545
$371$	2.26548e9	2.30330
$372$	6.17706e7	0.0622131
$373$	−1.77013e9	−1.76614	−0.883069	−	0.469242i	$-0.844527\pi$
$373$	−1.77013e9	−1.76614	−0.883069	+	0.469242i	$0.844527\pi$
$374$	−4.29262e8	−0.424299
$375$	5.27344e7	0.0516398
$376$	9.46629e8	0.918380
$377$	1.12961e9	1.08576
$378$	3.53113e8	0.336273
$379$	1.46311e9	1.38051	0.690257	−	0.723565i	$-0.257498\pi$
$379$	1.46311e9	1.38051	0.690257	+	0.723565i	$0.257498\pi$
$380$	−2.11335e8	−0.197573
$381$	−7.56477e8	−0.700742
$382$	−5.28015e7	−0.0484646
$383$	−9.90456e8	−0.900823	−0.450412	−	0.892821i	$-0.648723\pi$
$383$	−9.90456e8	−0.900823	−0.450412	+	0.892821i	$0.648723\pi$
$384$	7.69502e8	0.693506
$385$	5.69940e8	0.508999
$386$	1.73187e9	1.53271
$387$	−5.50754e8	−0.483024
$388$	2.09076e8	0.181716
$389$	−7.96901e8	−0.686406	−0.343203	−	0.939261i	$-0.611512\pi$
$389$	−7.96901e8	−0.686406	−0.343203	+	0.939261i	$0.611512\pi$
$390$	−3.73201e8	−0.318578
$391$	−8.40695e8	−0.711246
$392$	1.22245e9	1.02501
$393$	2.21378e8	0.183976
$394$	−1.70003e8	−0.140029
$395$	−4.87635e8	−0.398112
$396$	−9.87533e7	−0.0799132
$397$	7.95584e8	0.638145	0.319073	−	0.947730i	$-0.396629\pi$
$397$	7.95584e8	0.638145	0.319073	+	0.947730i	$0.396629\pi$
$398$	9.08053e8	0.721972
$399$	−1.53645e9	−1.21092
$400$	−3.11734e8	−0.243542
$401$	−2.01632e9	−1.56154	−0.780771	−	0.624817i	$-0.785174\pi$
$401$	−2.01632e9	−1.56154	−0.780771	+	0.624817i	$0.785174\pi$
$402$	−1.58787e9	−1.21906
$403$	−4.74635e8	−0.361237
$404$	6.22063e8	0.469353
$405$	−6.64301e7	−0.0496904
$406$	−2.38247e9	−1.76679
$407$	−7.53874e8	−0.554266
$408$	3.05187e8	0.222462
$409$	−5.48030e7	−0.0396070	−0.0198035	−	0.999804i	$-0.506304\pi$
$409$	−5.48030e7	−0.0396070	−0.0198035	+	0.999804i	$0.506304\pi$
$410$	−2.26964e8	−0.162635
$411$	4.49944e7	0.0319677
$412$	1.92916e8	0.135903
$413$	−1.36573e9	−0.953978
$414$	−7.97205e8	−0.552165
$415$	1.17426e9	0.806487
$416$	9.74745e8	0.663841
$417$	1.58613e9	1.07118
$418$	1.77117e9	1.18616
$419$	1.10925e8	0.0736679	0.0368340	−	0.999321i	$-0.488273\pi$
$419$	1.10925e8	0.0736679	0.0368340	+	0.999321i	$0.488273\pi$
$420$	1.90958e8	0.125766
$421$	−2.12064e9	−1.38509	−0.692547	−	0.721373i	$-0.743511\pi$
$421$	−2.12064e9	−1.38509	−0.692547	+	0.721373i	$0.743511\pi$
$422$	−4.27096e8	−0.276650
$423$	6.10161e8	0.391971
$424$	1.85671e9	1.18294
$425$	−1.56156e8	−0.0986730
$426$	−1.36682e8	−0.0856601
$427$	−2.28826e9	−1.42236
$428$	1.07879e8	0.0665097
$429$	7.58803e8	0.464011
$430$	−1.22767e9	−0.744635
$431$	−2.48533e9	−1.49525	−0.747624	−	0.664123i	$-0.768805\pi$
$431$	−2.48533e9	−1.49525	−0.747624	+	0.664123i	$0.768805\pi$
$432$	3.92696e8	0.234349
$433$	2.99956e7	0.0177562	0.00887811	−	0.999961i	$-0.497174\pi$
$433$	2.99956e7	0.0177562	0.00887811	+	0.999961i	$0.497174\pi$
$434$	1.00105e9	0.587818
$435$	4.48207e8	0.261075
$436$	−1.76324e8	−0.101885
$437$	3.46877e9	1.98834
$438$	1.97168e9	1.12119
$439$	−1.04873e9	−0.591616	−0.295808	−	0.955247i	$-0.595589\pi$
$439$	−1.04873e9	−0.591616	−0.295808	+	0.955247i	$0.595589\pi$
$440$	4.67103e8	0.261414
$441$	7.87945e8	0.437483
$442$	1.10512e9	0.608738
$443$	2.04679e8	0.111856	0.0559282	−	0.998435i	$-0.482188\pi$
$443$	2.04679e8	0.111856	0.0559282	+	0.998435i	$0.482188\pi$
$444$	−2.52584e8	−0.136951
$445$	−3.50468e8	−0.188534
$446$	−9.03752e8	−0.482366
$447$	5.22983e8	0.276956
$448$	1.46831e9	0.771516
$449$	2.63962e9	1.37619	0.688097	−	0.725619i	$-0.258446\pi$
$449$	2.63962e9	1.37619	0.688097	+	0.725619i	$0.258446\pi$
$450$	−1.48078e8	−0.0766032
$451$	4.61470e8	0.236878
$452$	1.63276e8	0.0831643
$453$	1.44167e9	0.728656
$454$	3.00013e9	1.50468
$455$	−1.46728e9	−0.730255
$456$	−1.25922e9	−0.621908
$457$	1.83738e9	0.900519	0.450260	−	0.892898i	$-0.351331\pi$
$457$	1.83738e9	0.900519	0.450260	+	0.892898i	$0.351331\pi$
$458$	−1.90004e9	−0.924132
$459$	1.96712e8	0.0949481
$460$	−4.31115e8	−0.206510
$461$	3.57678e9	1.70035	0.850176	−	0.526499i	$-0.176495\pi$
$461$	3.57678e9	1.70035	0.850176	+	0.526499i	$0.176495\pi$
$462$	−1.60039e9	−0.755056
$463$	1.28068e9	0.599662	0.299831	−	0.953992i	$-0.403070\pi$
$463$	1.28068e9	0.599662	0.299831	+	0.953992i	$0.403070\pi$
$464$	−2.64953e9	−1.23128
$465$	−1.88325e8	−0.0868606
$466$	−4.05480e9	−1.85617
$467$	−4.19984e9	−1.90820	−0.954100	−	0.299490i	$-0.903184\pi$
$467$	−4.19984e9	−1.90820	−0.954100	+	0.299490i	$0.903184\pi$
$468$	2.54236e8	0.114651
$469$	−6.24290e9	−2.79436
$470$	1.36010e9	0.604266
$471$	−5.52229e8	−0.243526
$472$	−1.11930e9	−0.489948
$473$	2.49615e9	1.08457
$474$	1.36928e9	0.590565
$475$	6.44312e8	0.275847
$476$	−5.65461e8	−0.240313
$477$	1.19676e9	0.504887
$478$	−2.95503e9	−1.23756
$479$	2.48202e9	1.03188	0.515942	−	0.856623i	$-0.327442\pi$
$479$	2.48202e9	1.03188	0.515942	+	0.856623i	$0.327442\pi$
$480$	3.86758e8	0.159623
$481$	1.94081e9	0.795200
$482$	2.58027e9	1.04955
$483$	−3.13431e9	−1.26569
$484$	−3.51401e8	−0.140878
$485$	−6.37428e8	−0.253709
$486$	1.86536e8	0.0737115
$487$	−1.08065e9	−0.423970	−0.211985	−	0.977273i	$-0.567993\pi$
$487$	−1.08065e9	−0.423970	−0.211985	+	0.977273i	$0.567993\pi$
$488$	−1.87538e9	−0.730500
$489$	1.98069e7	0.00766011
$490$	1.75639e9	0.674428
$491$	−9.47787e8	−0.361348	−0.180674	−	0.983543i	$-0.557828\pi$
$491$	−9.47787e8	−0.361348	−0.180674	+	0.983543i	$0.557828\pi$
$492$	1.54615e8	0.0585292
$493$	−1.32722e9	−0.498861
$494$	−4.55979e9	−1.70177
$495$	3.01077e8	0.111573
$496$	1.11327e9	0.409650
$497$	−5.37383e8	−0.196353
$498$	−3.29733e9	−1.19636
$499$	−2.07692e9	−0.748286	−0.374143	−	0.927371i	$-0.622063\pi$
$499$	−2.07692e9	−0.748286	−0.374143	+	0.927371i	$0.622063\pi$
$500$	−8.00781e7	−0.0286496
$501$	−4.56098e8	−0.162041
$502$	1.72297e9	0.607875
$503$	2.73265e9	0.957408	0.478704	−	0.877976i	$-0.341107\pi$
$503$	2.73265e9	0.957408	0.478704	+	0.877976i	$0.341107\pi$
$504$	1.13781e9	0.395879
$505$	−1.89653e9	−0.655301
$506$	3.61312e9	1.23981
$507$	−2.59295e8	−0.0883622
$508$	1.14872e9	0.388770
$509$	4.52470e9	1.52082	0.760409	−	0.649444i	$-0.224998\pi$
$509$	4.52470e9	1.52082	0.760409	+	0.649444i	$0.224998\pi$
$510$	4.38487e8	0.146373
$511$	7.75192e9	2.57002
$512$	6.01982e8	0.198216
$513$	−8.11648e8	−0.265434
$514$	4.66235e8	0.151438
$515$	−5.88158e8	−0.189744
$516$	8.36330e8	0.267981
$517$	−2.76540e9	−0.880117
$518$	−4.09337e9	−1.29398
$519$	−3.19101e8	−0.100194
$520$	−1.20254e9	−0.375048
$521$	−2.79533e8	−0.0865965	−0.0432983	−	0.999062i	$-0.513787\pi$
$521$	−2.79533e8	−0.0865965	−0.0432983	+	0.999062i	$0.513787\pi$
$522$	−1.25856e9	−0.387283
$523$	1.46376e9	0.447419	0.223710	−	0.974656i	$-0.428183\pi$
$523$	1.46376e9	0.447419	0.223710	+	0.974656i	$0.428183\pi$
$524$	−3.36167e8	−0.102069
$525$	−5.82188e8	−0.175592
$526$	6.23533e9	1.86814
$527$	5.57665e8	0.165973
$528$	−1.77979e9	−0.526199
$529$	3.67135e9	1.07828
$530$	2.66768e9	0.778338
$531$	−7.21459e8	−0.209113
$532$	2.33313e9	0.671814
$533$	−1.18803e9	−0.339847
$534$	9.84115e8	0.279674
$535$	−3.28900e8	−0.0928595
$536$	−5.11647e9	−1.43514
$537$	8.47115e8	0.236065
$538$	9.21393e8	0.255098
$539$	−3.57115e9	−0.982308
$540$	1.00875e8	0.0275681
$541$	−2.72194e9	−0.739073	−0.369537	−	0.929216i	$-0.620484\pi$
$541$	−2.72194e9	−0.739073	−0.369537	+	0.929216i	$0.620484\pi$
$542$	−5.29737e9	−1.42910
$543$	1.57560e9	0.422325
$544$	−1.14526e9	−0.305006
$545$	5.37574e8	0.142249
$546$	4.12014e9	1.08327
$547$	−6.73048e8	−0.175829	−0.0879145	−	0.996128i	$-0.528020\pi$
$547$	−6.73048e8	−0.175829	−0.0879145	+	0.996128i	$0.528020\pi$
$548$	−6.83248e7	−0.0177356
$549$	−1.20880e9	−0.311782
$550$	6.71125e8	0.172002
$551$	5.47622e9	1.39460
$552$	−2.56877e9	−0.650038
$553$	5.38349e9	1.35371
$554$	1.03152e9	0.257747
$555$	7.70074e8	0.191208
$556$	−2.40857e9	−0.594289
$557$	−7.19994e9	−1.76537	−0.882685	−	0.469964i	$-0.844267\pi$
$557$	−7.19994e9	−1.76537	−0.882685	+	0.469964i	$0.844267\pi$
$558$	5.28817e8	0.128850
$559$	−6.42621e9	−1.55602
$560$	3.44155e9	0.828125
$561$	−8.91545e8	−0.213193
$562$	1.13109e9	0.268794
$563$	5.80114e9	1.37004	0.685021	−	0.728524i	$-0.259793\pi$
$563$	5.80114e9	1.37004	0.685021	+	0.728524i	$0.259793\pi$
$564$	−9.26541e8	−0.217464
$565$	−4.97792e8	−0.116112
$566$	−3.60895e9	−0.836612
$567$	7.33389e8	0.168964
$568$	−4.40420e8	−0.100844
$569$	−1.67069e9	−0.380192	−0.190096	−	0.981766i	$-0.560880\pi$
$569$	−1.67069e9	−0.380192	−0.190096	+	0.981766i	$0.560880\pi$
$570$	−1.80923e9	−0.409196
$571$	5.70139e9	1.28160	0.640802	−	0.767706i	$-0.278602\pi$
$571$	5.70139e9	1.28160	0.640802	+	0.767706i	$0.278602\pi$
$572$	−1.15226e9	−0.257432
$573$	−1.09665e8	−0.0243515
$574$	2.50568e9	0.553011
$575$	1.31438e9	0.288325
$576$	7.75651e8	0.169117
$577$	2.43063e9	0.526750	0.263375	−	0.964694i	$-0.415164\pi$
$577$	2.43063e9	0.526750	0.263375	+	0.964694i	$0.415164\pi$
$578$	4.03596e9	0.869360
$579$	3.59696e9	0.770123
$580$	−6.80610e8	−0.144844
$581$	−1.29639e10	−2.74232
$582$	1.78990e9	0.376355
$583$	−5.42401e9	−1.13365
$584$	6.35320e9	1.31992
$585$	−7.75109e8	−0.160073
$586$	−3.20438e9	−0.657812
$587$	−3.33378e9	−0.680305	−0.340153	−	0.940370i	$-0.610479\pi$
$587$	−3.33378e9	−0.680305	−0.340153	+	0.940370i	$0.610479\pi$
$588$	−1.19651e9	−0.242714
$589$	−2.30097e9	−0.463988
$590$	−1.60819e9	−0.322371
$591$	−3.53083e8	−0.0703591
$592$	−4.55222e9	−0.901773
$593$	3.42280e9	0.674048	0.337024	−	0.941496i	$-0.390580\pi$
$593$	3.42280e9	0.674048	0.337024	+	0.941496i	$0.390580\pi$
$594$	−8.45424e8	−0.165509
$595$	1.72396e9	0.335521
$596$	−7.94159e8	−0.153655
$597$	1.88596e9	0.362762
$598$	−9.30182e9	−1.77875
$599$	−9.28661e8	−0.176548	−0.0882741	−	0.996096i	$-0.528135\pi$
$599$	−9.28661e8	−0.176548	−0.0882741	+	0.996096i	$0.528135\pi$
$600$	−4.77141e8	−0.0901814
$601$	−6.56974e9	−1.23449	−0.617245	−	0.786771i	$-0.711751\pi$
$601$	−6.56974e9	−1.23449	−0.617245	+	0.786771i	$0.711751\pi$
$602$	1.35535e10	2.53201
$603$	−3.29788e9	−0.612526
$604$	−2.18920e9	−0.404256
$605$	1.07134e9	0.196691
$606$	5.32547e9	0.972083
$607$	−3.50790e9	−0.636629	−0.318315	−	0.947985i	$-0.603117\pi$
$607$	−3.50790e9	−0.636629	−0.318315	+	0.947985i	$0.603117\pi$
$608$	4.72544e9	0.852667
$609$	−4.94820e9	−0.887742
$610$	−2.69451e9	−0.480647
$611$	7.11939e9	1.26269
$612$	−2.98711e8	−0.0526770
$613$	3.63970e9	0.638196	0.319098	−	0.947722i	$-0.396620\pi$
$613$	3.63970e9	0.638196	0.319098	+	0.947722i	$0.396620\pi$
$614$	−5.00454e9	−0.872519
$615$	−4.71386e8	−0.0817173
$616$	−5.15682e9	−0.888892
$617$	7.82559e9	1.34128	0.670639	−	0.741784i	$-0.266020\pi$
$617$	7.82559e9	1.34128	0.670639	+	0.741784i	$0.266020\pi$
$618$	1.65155e9	0.281470
$619$	8.35173e9	1.41533	0.707667	−	0.706546i	$-0.249748\pi$
$619$	8.35173e9	1.41533	0.707667	+	0.706546i	$0.249748\pi$
$620$	2.85975e8	0.0481900
$621$	−1.65573e9	−0.277441
$622$	−6.03765e8	−0.100601
$623$	3.86917e9	0.641076
$624$	4.58199e9	0.754932
$625$	2.44141e8	0.0400000
$626$	−2.73725e9	−0.445969
$627$	3.67858e9	0.595997
$628$	8.38570e8	0.135108
$629$	−2.28033e9	−0.365360
$630$	1.63478e9	0.260476
$631$	−2.16820e7	−0.00343555	−0.00171777	−	0.999999i	$-0.500547\pi$
$631$	−2.16820e7	−0.00343555	−0.00171777	+	0.999999i	$0.500547\pi$
$632$	4.41212e9	0.695245
$633$	−8.87044e8	−0.139006
$634$	1.24926e10	1.94689
$635$	−3.50221e9	−0.542793
$636$	−1.81731e9	−0.280110
$637$	9.19377e9	1.40931
$638$	5.70411e9	0.869592
$639$	−2.83878e8	−0.0430407
$640$	3.56251e9	0.537188
$641$	−7.85361e9	−1.17779	−0.588893	−	0.808211i	$-0.700436\pi$
$641$	−7.85361e9	−1.17779	−0.588893	+	0.808211i	$0.700436\pi$
$642$	9.23553e8	0.137749
$643$	−8.81820e9	−1.30810	−0.654051	−	0.756451i	$-0.726932\pi$
$643$	−8.81820e9	−1.30810	−0.654051	+	0.756451i	$0.726932\pi$
$644$	4.75951e9	0.702201
$645$	−2.54979e9	−0.374149
$646$	5.35746e9	0.781890
$647$	−8.71997e9	−1.26576	−0.632878	−	0.774252i	$-0.718127\pi$
$647$	−8.71997e9	−1.26576	−0.632878	+	0.774252i	$0.718127\pi$
$648$	6.01060e8	0.0867771
$649$	3.26982e9	0.469535
$650$	−1.72778e9	−0.246770
$651$	2.07911e9	0.295354
$652$	−3.00771e7	−0.00424981
$653$	−6.65755e8	−0.0935661	−0.0467830	−	0.998905i	$-0.514897\pi$
$653$	−6.65755e8	−0.0935661	−0.0467830	+	0.998905i	$0.514897\pi$
$654$	−1.50951e9	−0.211015
$655$	1.02490e9	0.142507
$656$	2.78656e9	0.385393
$657$	4.09503e9	0.563350
$658$	−1.50155e10	−2.05470
$659$	−9.99513e9	−1.36047	−0.680236	−	0.732994i	$-0.738123\pi$
$659$	−9.99513e9	−1.36047	−0.680236	+	0.732994i	$0.738123\pi$
$660$	−4.57191e8	−0.0619005
$661$	−2.89160e9	−0.389434	−0.194717	−	0.980859i	$-0.562379\pi$
$661$	−2.89160e9	−0.389434	−0.194717	+	0.980859i	$0.562379\pi$
$662$	−5.19900e9	−0.696493
$663$	2.29524e9	0.305866
$664$	−1.06247e10	−1.40841
$665$	−7.11321e9	−0.937972
$666$	−2.16237e9	−0.283641
$667$	1.11713e10	1.45768
$668$	6.92593e8	0.0899002
$669$	−1.87702e9	−0.242370
$670$	−7.35125e9	−0.944276
$671$	5.47857e9	0.700065
$672$	−4.26981e9	−0.542770
$673$	−5.83236e9	−0.737550	−0.368775	−	0.929519i	$-0.620223\pi$
$673$	−5.83236e9	−0.737550	−0.368775	+	0.929519i	$0.620223\pi$
$674$	−3.49940e9	−0.440234
$675$	−3.07547e8	−0.0384900
$676$	3.93744e8	0.0490231
$677$	−1.22524e10	−1.51762	−0.758808	−	0.651315i	$-0.774218\pi$
$677$	−1.22524e10	−1.51762	−0.758808	+	0.651315i	$0.774218\pi$
$678$	1.39780e9	0.172243
$679$	7.03721e9	0.862693
$680$	1.41290e9	0.172318
$681$	6.23103e9	0.756040
$682$	−2.39672e9	−0.289316
$683$	−9.69293e9	−1.16408	−0.582040	−	0.813160i	$-0.697745\pi$
$683$	−9.69293e9	−1.16408	−0.582040	+	0.813160i	$0.697745\pi$
$684$	1.23250e9	0.147262
$685$	2.08307e8	0.0247621
$686$	−4.61621e9	−0.545948
$687$	−3.94624e9	−0.464339
$688$	1.50728e10	1.76455
$689$	1.39639e10	1.62644
$690$	−3.69076e9	−0.427705
$691$	3.33285e9	0.384276	0.192138	−	0.981368i	$-0.438458\pi$
$691$	3.33285e9	0.384276	0.192138	+	0.981368i	$0.438458\pi$
$692$	4.84561e8	0.0555875
$693$	−3.32389e9	−0.379385
$694$	1.06843e10	1.21335
$695$	7.34320e9	0.829733
$696$	−4.05537e9	−0.455931
$697$	1.39586e9	0.156145
$698$	−8.42860e9	−0.938127
$699$	−8.42150e9	−0.932651
$700$	8.84062e8	0.0974181
$701$	−2.73199e9	−0.299548	−0.149774	−	0.988720i	$-0.547855\pi$
$701$	−2.73199e9	−0.299548	−0.149774	+	0.988720i	$0.547855\pi$
$702$	2.17651e9	0.237454
$703$	9.40882e9	1.02139
$704$	−3.51543e9	−0.379730
$705$	2.82482e9	0.303619
$706$	−8.48466e9	−0.907440
$707$	2.09377e10	2.22824
$708$	1.09555e9	0.116015
$709$	3.44620e8	0.0363144	0.0181572	−	0.999835i	$-0.494220\pi$
$709$	3.44620e8	0.0363144	0.0181572	+	0.999835i	$0.494220\pi$
$710$	−6.32788e8	−0.0663520
$711$	2.84389e9	0.296735
$712$	3.17104e9	0.329247
$713$	−4.69390e9	−0.484976
$714$	−4.84089e9	−0.497716
$715$	3.51298e9	0.359422
$716$	−1.28636e9	−0.130969
$717$	−6.13738e9	−0.621822
$718$	1.14066e10	1.15006
$719$	3.35749e9	0.336871	0.168436	−	0.985713i	$-0.446128\pi$
$719$	3.35749e9	0.336871	0.168436	+	0.985713i	$0.446128\pi$
$720$	1.81803e9	0.181526
$721$	6.49327e9	0.645194
$722$	−1.04850e10	−1.03678
$723$	5.35903e9	0.527354
$724$	−2.39258e9	−0.234305
$725$	2.07503e9	0.202228
$726$	−3.00834e9	−0.291775
$727$	−1.32017e10	−1.27426	−0.637132	−	0.770755i	$-0.719879\pi$
$727$	−1.32017e10	−1.27426	−0.637132	+	0.770755i	$0.719879\pi$
$728$	1.32760e10	1.27528
$729$	3.87420e8	0.0370370
$730$	9.12816e9	0.868467
$731$	7.55039e9	0.714922
$732$	1.83559e9	0.172976
$733$	4.30179e9	0.403446	0.201723	−	0.979443i	$-0.435346\pi$
$733$	4.30179e9	0.403446	0.201723	+	0.979443i	$0.435346\pi$
$734$	−3.73086e9	−0.348235
$735$	3.64789e9	0.338873
$736$	9.63973e9	0.891236
$737$	1.49468e10	1.37534
$738$	1.32365e9	0.121221
$739$	−1.82414e10	−1.66266	−0.831330	−	0.555780i	$-0.812420\pi$
$739$	−1.82414e10	−1.66266	−0.831330	+	0.555780i	$0.812420\pi$
$740$	−1.16937e9	−0.106082
$741$	−9.47034e9	−0.855071
$742$	−2.94512e10	−2.64661
$743$	−2.36847e8	−0.0211840	−0.0105920	−	0.999944i	$-0.503372\pi$
$743$	−2.36847e8	−0.0211840	−0.0105920	+	0.999944i	$0.503372\pi$
$744$	1.70396e9	0.151689
$745$	2.42122e9	0.214529
$746$	2.30117e10	2.02938
$747$	−6.84831e9	−0.601120
$748$	1.35383e9	0.118279
$749$	3.63106e9	0.315753
$750$	−6.85547e8	−0.0593366
$751$	−1.44326e10	−1.24338	−0.621690	−	0.783264i	$-0.713553\pi$
$751$	−1.44326e10	−1.24338	−0.621690	+	0.783264i	$0.713553\pi$
$752$	−1.66987e10	−1.43192
$753$	3.57847e9	0.305432
$754$	−1.46850e10	−1.24760
$755$	6.67440e9	0.564414
$756$	−1.11366e9	−0.0937406
$757$	1.64934e10	1.38189	0.690945	−	0.722907i	$-0.257195\pi$
$757$	1.64934e10	1.38189	0.690945	+	0.722907i	$0.257195\pi$
$758$	−1.90205e10	−1.58628
$759$	7.50418e9	0.622955
$760$	−5.82974e9	−0.481728
$761$	−2.96845e9	−0.244165	−0.122083	−	0.992520i	$-0.538957\pi$
$761$	−2.96845e9	−0.244165	−0.122083	+	0.992520i	$0.538957\pi$
$762$	9.83420e9	0.805187
$763$	−5.93482e9	−0.483695
$764$	1.66528e8	0.0135102
$765$	9.10703e8	0.0735465
$766$	1.28759e10	1.03509
$767$	−8.41801e9	−0.673637
$768$	−6.32636e9	−0.503953
$769$	8.15400e9	0.646590	0.323295	−	0.946298i	$-0.395209\pi$
$769$	8.15400e9	0.646590	0.323295	+	0.946298i	$0.395209\pi$
$770$	−7.40922e9	−0.584864
$771$	9.68334e8	0.0760913
$772$	−5.46204e9	−0.427262
$773$	−2.78059e9	−0.216525	−0.108263	−	0.994122i	$-0.534529\pi$
$773$	−2.78059e9	−0.216525	−0.108263	+	0.994122i	$0.534529\pi$
$774$	7.15980e9	0.555018
$775$	−8.71875e8	−0.0672819
$776$	5.76745e9	0.443065
$777$	−8.50161e9	−0.650171
$778$	1.03597e10	0.788713
$779$	−5.75943e9	−0.436514
$780$	1.17702e9	0.0888080
$781$	1.28660e9	0.0966421
$782$	1.09290e10	0.817256
$783$	−2.61394e9	−0.194594
$784$	−2.15642e10	−1.59818
$785$	−2.55662e9	−0.188635
$786$	−2.87792e9	−0.211397
$787$	−8.20982e9	−0.600374	−0.300187	−	0.953880i	$-0.597049\pi$
$787$	−8.20982e9	−0.600374	−0.300187	+	0.953880i	$0.597049\pi$
$788$	5.36163e8	0.0390351
$789$	1.29503e10	0.938664
$790$	6.33926e9	0.457450
$791$	5.49562e9	0.394820
$792$	−2.72414e9	−0.194846
$793$	−1.41043e10	−1.00438
$794$	−1.03426e10	−0.733260
$795$	5.54057e9	0.391083
$796$	−2.86386e9	−0.201259
$797$	−5.47916e7	−0.00383363	−0.00191681	−	0.999998i	$-0.500610\pi$
$797$	−5.47916e7	−0.00383363	−0.00191681	+	0.999998i	$0.500610\pi$
$798$	1.99739e10	1.39140
$799$	−8.36482e9	−0.580153
$800$	1.79055e9	0.123643
$801$	2.04393e9	0.140525
$802$	2.62121e10	1.79429
$803$	−1.85597e10	−1.26493
$804$	5.00790e9	0.339828
$805$	−1.45107e10	−0.980399
$806$	6.17025e9	0.415079
$807$	1.91366e9	0.128176
$808$	1.71598e10	1.14439
$809$	2.04973e9	0.136106	0.0680529	−	0.997682i	$-0.478321\pi$
$809$	2.04973e9	0.136106	0.0680529	+	0.997682i	$0.478321\pi$
$810$	8.63592e8	0.0570967
$811$	−1.59471e10	−1.04981	−0.524903	−	0.851162i	$-0.675899\pi$
$811$	−1.59471e10	−1.04981	−0.524903	+	0.851162i	$0.675899\pi$
$812$	7.51394e9	0.492517
$813$	−1.10022e10	−0.718066
$814$	9.80036e9	0.636878
$815$	9.16985e7	0.00593350
$816$	−5.38354e9	−0.346858
$817$	−3.11535e10	−1.99862
$818$	7.12439e8	0.0455104
$819$	8.55721e9	0.544300
$820$	7.15809e8	0.0453366
$821$	9.65923e9	0.609174	0.304587	−	0.952484i	$-0.401482\pi$
$821$	9.65923e9	0.609174	0.304587	+	0.952484i	$0.401482\pi$
$822$	−5.84927e8	−0.0367325
$823$	3.90398e9	0.244123	0.122061	−	0.992523i	$-0.461050\pi$
$823$	3.90398e9	0.244123	0.122061	+	0.992523i	$0.461050\pi$
$824$	5.32166e9	0.331361
$825$	1.39388e9	0.0864241
$826$	1.77544e10	1.09617
$827$	−1.32224e10	−0.812910	−0.406455	−	0.913671i	$-0.633235\pi$
$827$	−1.32224e10	−0.812910	−0.406455	+	0.913671i	$0.633235\pi$
$828$	2.51426e9	0.153923
$829$	1.20482e10	0.734484	0.367242	−	0.930125i	$-0.380302\pi$
$829$	1.20482e10	0.734484	0.367242	+	0.930125i	$0.380302\pi$
$830$	−1.52654e10	−0.926693
$831$	2.14239e9	0.129507
$832$	9.05032e9	0.544794
$833$	−1.08021e10	−0.647515
$834$	−2.06197e10	−1.23084
$835$	−2.11156e9	−0.125517
$836$	−5.58599e9	−0.330658
$837$	1.09831e9	0.0647420
$838$	−1.44202e9	−0.0846480
$839$	3.10603e10	1.81568	0.907839	−	0.419319i	$-0.137731\pi$
$839$	3.10603e10	1.81568	0.907839	+	0.419319i	$0.137731\pi$
$840$	5.26763e9	0.306646
$841$	3.86495e8	0.0224057
$842$	2.75683e10	1.59154
$843$	2.34918e9	0.135058
$844$	1.34699e9	0.0771200
$845$	−1.20044e9	−0.0684450
$846$	−7.93210e9	−0.450393
$847$	−1.18276e10	−0.668815
$848$	−3.27526e10	−1.84442
$849$	−7.49552e9	−0.420363
$850$	2.03003e9	0.113380
$851$	1.91937e10	1.06759
$852$	4.31075e8	0.0238789
$853$	2.52157e10	1.39107	0.695536	−	0.718491i	$-0.255167\pi$
$853$	2.52157e10	1.39107	0.695536	+	0.718491i	$0.255167\pi$
$854$	2.97474e10	1.63436
$855$	−3.75763e9	−0.205605
$856$	2.97589e9	0.162166
$857$	2.25314e10	1.22280	0.611401	−	0.791321i	$-0.290606\pi$
$857$	2.25314e10	1.22280	0.611401	+	0.791321i	$0.290606\pi$
$858$	−9.86444e9	−0.533172
$859$	4.07863e9	0.219552	0.109776	−	0.993956i	$-0.464987\pi$
$859$	4.07863e9	0.219552	0.109776	+	0.993956i	$0.464987\pi$
$860$	3.87190e9	0.207577
$861$	5.20410e9	0.277866
$862$	3.23092e10	1.71811
$863$	−1.10643e10	−0.585986	−0.292993	−	0.956115i	$-0.594651\pi$
$863$	−1.10643e10	−0.585986	−0.292993	+	0.956115i	$0.594651\pi$
$864$	−2.25557e9	−0.118976
$865$	−1.47732e9	−0.0776101
$866$	−3.89943e8	−0.0204028
$867$	8.38238e9	0.436818
$868$	−3.15716e9	−0.163862
$869$	−1.28892e10	−0.666278
$870$	−5.82669e9	−0.299988
$871$	−3.84798e10	−1.97319
$872$	−4.86397e9	−0.248418
$873$	3.71748e9	0.189103
$874$	−4.50940e10	−2.28470
$875$	−2.69531e9	−0.136013
$876$	−6.21838e9	−0.312545
$877$	3.60595e10	1.80518	0.902590	−	0.430501i	$-0.141663\pi$
$877$	3.60595e10	1.80518	0.902590	+	0.430501i	$0.141663\pi$
$878$	1.36336e10	0.679795
$879$	−6.65524e9	−0.330524
$880$	−8.23976e9	−0.407592
$881$	−2.62954e10	−1.29558	−0.647789	−	0.761820i	$-0.724306\pi$
$881$	−2.62954e10	−1.29558	−0.647789	+	0.761820i	$0.724306\pi$
$882$	−1.02433e10	−0.502689
$883$	2.78873e9	0.136315	0.0681575	−	0.997675i	$-0.478288\pi$
$883$	2.78873e9	0.136315	0.0681575	+	0.997675i	$0.478288\pi$
$884$	−3.48537e9	−0.169694
$885$	−3.34009e9	−0.161978
$886$	−2.66083e9	−0.128528
$887$	−1.82970e10	−0.880332	−0.440166	−	0.897916i	$-0.645080\pi$
$887$	−1.82970e10	−0.880332	−0.440166	+	0.897916i	$0.645080\pi$
$888$	−6.96763e9	−0.333918
$889$	3.86644e10	1.84567
$890$	4.55609e9	0.216634
$891$	−1.75588e9	−0.0831617
$892$	2.85029e9	0.134466
$893$	3.45139e10	1.62186
$894$	−6.79878e9	−0.318236
$895$	3.92183e9	0.182856
$896$	−3.93301e10	−1.82661
$897$	−1.93192e10	−0.893748
$898$	−3.43151e10	−1.58131
$899$	−7.41035e9	−0.340157
$900$	4.67016e8	0.0213542
$901$	−1.64067e10	−0.747280
$902$	−5.99911e9	−0.272185
$903$	2.81496e10	1.27223
$904$	4.50402e9	0.202773
$905$	7.29444e9	0.327131
$906$	−1.87417e10	−0.837261
$907$	−1.21245e9	−0.0539559	−0.0269780	−	0.999636i	$-0.508588\pi$
$907$	−1.21245e9	−0.0539559	−0.0269780	+	0.999636i	$0.508588\pi$
$908$	−9.46193e9	−0.419449
$909$	1.10606e10	0.488432
$910$	1.90747e10	0.839099
$911$	−2.09181e10	−0.916659	−0.458329	−	0.888782i	$-0.651552\pi$
$911$	−2.09181e10	−0.916659	−0.458329	+	0.888782i	$0.651552\pi$
$912$	2.22129e10	0.969668
$913$	3.10382e10	1.34973
$914$	−2.38860e10	−1.03474
$915$	−5.59630e9	−0.241505
$916$	5.99244e9	0.257614
$917$	−1.13149e10	−0.484571
$918$	−2.55725e9	−0.109100
$919$	−1.81545e10	−0.771577	−0.385789	−	0.922587i	$-0.626071\pi$
$919$	−1.81545e10	−0.771577	−0.385789	+	0.922587i	$0.626071\pi$
$920$	−1.18925e10	−0.503517
$921$	−1.03940e10	−0.438405
$922$	−4.64981e10	−1.95379
$923$	−3.31230e9	−0.138651
$924$	5.04739e9	0.210482
$925$	3.56516e9	0.148109
$926$	−1.66488e10	−0.689040
$927$	3.43014e9	0.141427
$928$	1.52184e10	0.625104
$929$	−3.39225e10	−1.38814	−0.694069	−	0.719908i	$-0.744184\pi$
$929$	−3.39225e10	−1.38814	−0.694069	+	0.719908i	$0.744184\pi$
$930$	2.44822e9	0.0998070
$931$	4.45702e10	1.81018
$932$	1.27882e10	0.517433
$933$	−1.25397e9	−0.0505478
$934$	5.45979e10	2.19261
$935$	−4.12752e9	−0.165139
$936$	7.01319e9	0.279544
$937$	3.64023e10	1.44557	0.722786	−	0.691072i	$-0.242861\pi$
$937$	3.64023e10	1.44557	0.722786	+	0.691072i	$0.242861\pi$
$938$	8.11578e10	3.21085
$939$	−5.68507e9	−0.224081
$940$	−4.28954e9	−0.168447
$941$	5.07117e10	1.98401	0.992007	−	0.126181i	$-0.0402719\pi$
$941$	5.07117e10	1.98401	0.992007	+	0.126181i	$0.0402719\pi$
$942$	7.17898e9	0.279824
$943$	−1.17490e10	−0.456259
$944$	1.97446e10	0.763918
$945$	3.39532e9	0.130879
$946$	−3.24499e10	−1.24622
$947$	2.30994e10	0.883845	0.441922	−	0.897053i	$-0.354297\pi$
$947$	2.30994e10	0.883845	0.441922	+	0.897053i	$0.354297\pi$
$948$	−4.31850e9	−0.164628
$949$	4.77810e10	1.81478
$950$	−8.37606e9	−0.316962
$951$	2.59462e10	0.978233
$952$	−1.55984e10	−0.585938
$953$	−4.16368e9	−0.155830	−0.0779151	−	0.996960i	$-0.524826\pi$
$953$	−4.16368e9	−0.155830	−0.0779151	+	0.996960i	$0.524826\pi$
$954$	−1.55579e10	−0.580139
$955$	−5.07707e8	−0.0188626
$956$	9.31972e9	0.344985
$957$	1.18470e10	0.436935
$958$	−3.22663e10	−1.18569
$959$	−2.29971e9	−0.0841993
$960$	3.59098e9	0.130998
$961$	−2.43990e10	−0.886829
$962$	−2.52306e10	−0.913723
$963$	1.91815e9	0.0692134
$964$	−8.13779e9	−0.292575
$965$	1.66526e10	0.596535
$966$	4.07460e10	1.45434
$967$	−5.20468e10	−1.85098	−0.925489	−	0.378775i	$-0.876345\pi$
$967$	−5.20468e10	−1.85098	−0.925489	+	0.378775i	$0.876345\pi$
$968$	−9.69352e9	−0.343493
$969$	1.11270e10	0.392868
$970$	8.28657e9	0.291524
$971$	−3.64573e8	−0.0127796	−0.00638979	−	0.999980i	$-0.502034\pi$
$971$	−3.64573e8	−0.0127796	−0.00638979	+	0.999980i	$0.502034\pi$
$972$	−5.88305e8	−0.0205481
$973$	−8.10689e10	−2.82137
$974$	1.40485e10	0.487162
$975$	−3.58847e9	−0.123992
$976$	3.30820e10	1.13898
$977$	−1.81785e10	−0.623631	−0.311816	−	0.950143i	$-0.600937\pi$
$977$	−1.81785e10	−0.623631	−0.311816	+	0.950143i	$0.600937\pi$
$978$	−2.57489e8	−0.00880184
$979$	−9.26358e9	−0.315529
$980$	−5.53939e9	−0.188006
$981$	−3.13513e9	−0.106027
$982$	1.23212e10	0.415206
$983$	−1.85778e10	−0.623816	−0.311908	−	0.950112i	$-0.600968\pi$
$983$	−1.85778e10	−0.623816	−0.311908	+	0.950112i	$0.600968\pi$
$984$	4.26510e9	0.142707
$985$	−1.63464e9	−0.0544999
$986$	1.72539e10	0.573216
$987$	−3.11860e10	−1.03240
$988$	1.43809e10	0.474391
$989$	−6.35520e10	−2.08902
$990$	−3.91400e9	−0.128203
$991$	1.82520e10	0.595735	0.297867	−	0.954607i	$-0.403725\pi$
$991$	1.82520e10	0.595735	0.297867	+	0.954607i	$0.403725\pi$
$992$	−6.39440e9	−0.207974
$993$	−1.07979e10	−0.349959
$994$	6.98598e9	0.225619
$995$	8.73128e9	0.280994
$996$	1.03993e10	0.333500
$997$	−1.24534e9	−0.0397975	−0.0198987	−	0.999802i	$-0.506334\pi$
$997$	−1.24534e9	−0.0397975	−0.0198987	+	0.999802i	$0.506334\pi$
$998$	2.70000e10	0.859817
$999$	−4.49107e9	−0.142518

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.8.a.b.1.1	✓	1
3.2	odd	2		45.8.a.e.1.1		1
4.3	odd	2		240.8.a.h.1.1		1
5.2	odd	4		75.8.b.b.49.1		2
5.3	odd	4		75.8.b.b.49.2		2
5.4	even	2		75.8.a.b.1.1		1
15.2	even	4		225.8.b.c.199.2		2
15.8	even	4		225.8.b.c.199.1		2
15.14	odd	2		225.8.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.8.a.b.1.1	✓	1	1.1	even	1	trivial
45.8.a.e.1.1		1	3.2	odd	2
75.8.a.b.1.1		1	5.4	even	2
75.8.b.b.49.1		2	5.2	odd	4
75.8.b.b.49.2		2	5.3	odd	4
225.8.a.c.1.1		1	15.14	odd	2
225.8.b.c.199.1		2	15.8	even	4
225.8.b.c.199.2		2	15.2	even	4
240.8.a.h.1.1		1	4.3	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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	15.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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