LMFDB - Embedded newform 6897.2.a.bm.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6897,2,Mod(1,6897)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6897, 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("6897.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6897 = 3 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6897.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:	$55.0728222741$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} - 18 x^{14} + 57 x^{13} + 121 x^{12} - 417 x^{11} - 374 x^{10} + 1494 x^{9} + 490 x^{8} + \cdots - 5 $ x^16 - 3x^15 - 18x^14 + 57x^13 + 121x^12 - 417x^11 - 374x^10 + 1494x^9 + 490x^8 - 2726x^7 - 54x^6 + 2337x^5 - 357x^4 - 700x^3 + 144x^2 + 30*x - 5
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 627)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$2.41640$ of defining polynomial
Character	$\chi$	$=$	6897.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.41640 q^{2} -1.00000 q^{3} +3.83898 q^{4} -2.71140 q^{5} -2.41640 q^{6} +1.98097 q^{7} +4.44371 q^{8} +1.00000 q^{9} -6.55182 q^{10} -3.83898 q^{12} +4.07094 q^{13} +4.78681 q^{14} +2.71140 q^{15} +3.05980 q^{16} -0.380615 q^{17} +2.41640 q^{18} +1.00000 q^{19} -10.4090 q^{20} -1.98097 q^{21} +3.81700 q^{23} -4.44371 q^{24} +2.35169 q^{25} +9.83700 q^{26} -1.00000 q^{27} +7.60490 q^{28} +4.86770 q^{29} +6.55182 q^{30} -6.27840 q^{31} -1.49371 q^{32} -0.919718 q^{34} -5.37120 q^{35} +3.83898 q^{36} -1.36597 q^{37} +2.41640 q^{38} -4.07094 q^{39} -12.0487 q^{40} +3.74262 q^{41} -4.78681 q^{42} +3.45694 q^{43} -2.71140 q^{45} +9.22339 q^{46} +12.8422 q^{47} -3.05980 q^{48} -3.07576 q^{49} +5.68262 q^{50} +0.380615 q^{51} +15.6282 q^{52} -1.40293 q^{53} -2.41640 q^{54} +8.80284 q^{56} -1.00000 q^{57} +11.7623 q^{58} -1.27867 q^{59} +10.4090 q^{60} +1.72418 q^{61} -15.1711 q^{62} +1.98097 q^{63} -9.72900 q^{64} -11.0379 q^{65} -7.59547 q^{67} -1.46117 q^{68} -3.81700 q^{69} -12.9790 q^{70} -9.91341 q^{71} +4.44371 q^{72} +4.03479 q^{73} -3.30072 q^{74} -2.35169 q^{75} +3.83898 q^{76} -9.83700 q^{78} +5.90373 q^{79} -8.29635 q^{80} +1.00000 q^{81} +9.04365 q^{82} +5.04220 q^{83} -7.60490 q^{84} +1.03200 q^{85} +8.35334 q^{86} -4.86770 q^{87} +15.9000 q^{89} -6.55182 q^{90} +8.06440 q^{91} +14.6534 q^{92} +6.27840 q^{93} +31.0319 q^{94} -2.71140 q^{95} +1.49371 q^{96} -1.85278 q^{97} -7.43227 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 16 q^{3} + 13 q^{4} + 8 q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} + 16 q^{9} + 5 q^{10} - 13 q^{12} + 5 q^{13} + 4 q^{14} - 8 q^{15} + 3 q^{16} + 4 q^{17} + 3 q^{18} + 16 q^{19} + 10 q^{20} + 2 q^{21}+ \cdots - 41 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 16 * q^3 + 13 * q^4 + 8 * q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 + 16 * q^9 + 5 * q^10 - 13 * q^12 + 5 * q^13 + 4 * q^14 - 8 * q^15 + 3 * q^16 + 4 * q^17 + 3 * q^18 + 16 * q^19 + 10 * q^20 + 2 * q^21 + 36 * q^23 - 6 * q^24 + 20 * q^25 - 12 * q^26 - 16 * q^27 + 25 * q^28 + 13 * q^29 - 5 * q^30 + 19 * q^31 + 3 * q^34 - 20 * q^35 + 13 * q^36 - 8 * q^37 + 3 * q^38 - 5 * q^39 - 7 * q^41 - 4 * q^42 - 14 * q^43 + 8 * q^45 - 13 * q^46 + 62 * q^47 - 3 * q^48 + 16 * q^49 + 74 * q^50 - 4 * q^51 - 7 * q^52 + 12 * q^53 - 3 * q^54 + 14 * q^56 - 16 * q^57 + q^58 + 7 * q^59 - 10 * q^60 + q^61 - q^62 - 2 * q^63 - 28 * q^64 + 2 * q^65 - 16 * q^68 - 36 * q^69 - 29 * q^70 + 29 * q^71 + 6 * q^72 - 43 * q^73 - 39 * q^74 - 20 * q^75 + 13 * q^76 + 12 * q^78 + 23 * q^79 + 48 * q^80 + 16 * q^81 + 38 * q^82 + 38 * q^83 - 25 * q^84 - 17 * q^85 + 35 * q^86 - 13 * q^87 + 35 * q^89 + 5 * q^90 + 8 * q^91 + 63 * q^92 - 19 * q^93 + 59 * q^94 + 8 * q^95 + 34 * q^97 - 41 * q^98

Coefficient data

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

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

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

$2$	2.41640	1.70865	0.854326	−	0.519738i	$-0.173970\pi$
$2$	2.41640	1.70865	0.854326	+	0.519738i	$0.173970\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.83898	1.91949
$5$	−2.71140	−1.21258	−0.606288	−	0.795246i	$-0.707342\pi$
$5$	−2.71140	−1.21258	−0.606288	+	0.795246i	$0.707342\pi$
$6$	−2.41640	−0.986490
$7$	1.98097	0.748736	0.374368	−	0.927280i	$-0.377860\pi$
$7$	1.98097	0.748736	0.374368	+	0.927280i	$0.377860\pi$
$8$	4.44371	1.57109
$9$	1.00000	0.333333
$10$	−6.55182	−2.07187
$11$	0	0
$11$	0	0
$12$	−3.83898	−1.10822
$13$	4.07094	1.12907	0.564537	−	0.825408i	$-0.309055\pi$
$13$	4.07094	1.12907	0.564537	+	0.825408i	$0.309055\pi$
$14$	4.78681	1.27933
$15$	2.71140	0.700081
$16$	3.05980	0.764951
$17$	−0.380615	−0.0923127	−0.0461564	−	0.998934i	$-0.514697\pi$
$17$	−0.380615	−0.0923127	−0.0461564	+	0.998934i	$0.514697\pi$
$18$	2.41640	0.569550
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−10.4090	−2.32753
$21$	−1.98097	−0.432283
$22$	0	0
$23$	3.81700	0.795899	0.397950	−	0.917407i	$-0.369722\pi$
$23$	3.81700	0.795899	0.397950	+	0.917407i	$0.369722\pi$
$24$	−4.44371	−0.907068
$25$	2.35169	0.470338
$26$	9.83700	1.92919
$27$	−1.00000	−0.192450
$28$	7.60490	1.43719
$29$	4.86770	0.903908	0.451954	−	0.892041i	$-0.350727\pi$
$29$	4.86770	0.903908	0.451954	+	0.892041i	$0.350727\pi$
$30$	6.55182	1.19619
$31$	−6.27840	−1.12763	−0.563817	−	0.825900i	$-0.690668\pi$
$31$	−6.27840	−1.12763	−0.563817	+	0.825900i	$0.690668\pi$
$32$	−1.49371	−0.264053
$33$	0	0
$34$	−0.919718	−0.157730
$35$	−5.37120	−0.907898
$36$	3.83898	0.639830
$37$	−1.36597	−0.224564	−0.112282	−	0.993676i	$-0.535816\pi$
$37$	−1.36597	−0.224564	−0.112282	+	0.993676i	$0.535816\pi$
$38$	2.41640	0.391992
$39$	−4.07094	−0.651871
$40$	−12.0487	−1.90506
$41$	3.74262	0.584499	0.292249	−	0.956342i	$-0.405596\pi$
$41$	3.74262	0.584499	0.292249	+	0.956342i	$0.405596\pi$
$42$	−4.78681	−0.738621
$43$	3.45694	0.527178	0.263589	−	0.964635i	$-0.415094\pi$
$43$	3.45694	0.527178	0.263589	+	0.964635i	$0.415094\pi$
$44$	0	0
$45$	−2.71140	−0.404192
$46$	9.22339	1.35991
$47$	12.8422	1.87323	0.936615	−	0.350361i	$-0.113941\pi$
$47$	12.8422	1.87323	0.936615	+	0.350361i	$0.113941\pi$
$48$	−3.05980	−0.441645
$49$	−3.07576	−0.439395
$50$	5.68262	0.803644
$51$	0.380615	0.0532968
$52$	15.6282	2.16725
$53$	−1.40293	−0.192707	−0.0963533	−	0.995347i	$-0.530718\pi$
$53$	−1.40293	−0.192707	−0.0963533	+	0.995347i	$0.530718\pi$
$54$	−2.41640	−0.328830
$55$	0	0
$56$	8.80284	1.17633
$57$	−1.00000	−0.132453
$58$	11.7623	1.54446
$59$	−1.27867	−0.166469	−0.0832346	−	0.996530i	$-0.526525\pi$
$59$	−1.27867	−0.166469	−0.0832346	+	0.996530i	$0.526525\pi$
$60$	10.4090	1.34380
$61$	1.72418	0.220759	0.110379	−	0.993890i	$-0.464793\pi$
$61$	1.72418	0.220759	0.110379	+	0.993890i	$0.464793\pi$
$62$	−15.1711	−1.92673
$63$	1.98097	0.249579
$64$	−9.72900	−1.21613
$65$	−11.0379	−1.36909
$66$	0	0
$67$	−7.59547	−0.927935	−0.463967	−	0.885852i	$-0.653575\pi$
$67$	−7.59547	−0.927935	−0.463967	+	0.885852i	$0.653575\pi$
$68$	−1.46117	−0.177193
$69$	−3.81700	−0.459513
$70$	−12.9790	−1.55128
$71$	−9.91341	−1.17651	−0.588253	−	0.808677i	$-0.700184\pi$
$71$	−9.91341	−1.17651	−0.588253	+	0.808677i	$0.700184\pi$
$72$	4.44371	0.523696
$73$	4.03479	0.472237	0.236118	−	0.971724i	$-0.424125\pi$
$73$	4.03479	0.472237	0.236118	+	0.971724i	$0.424125\pi$
$74$	−3.30072	−0.383701
$75$	−2.35169	−0.271550
$76$	3.83898	0.440361
$77$	0	0
$78$	−9.83700	−1.11382
$79$	5.90373	0.664221	0.332111	−	0.943240i	$-0.392239\pi$
$79$	5.90373	0.664221	0.332111	+	0.943240i	$0.392239\pi$
$80$	−8.29635	−0.927560
$81$	1.00000	0.111111
$82$	9.04365	0.998704
$83$	5.04220	0.553454	0.276727	−	0.960949i	$-0.410750\pi$
$83$	5.04220	0.553454	0.276727	+	0.960949i	$0.410750\pi$
$84$	−7.60490	−0.829762
$85$	1.03200	0.111936
$86$	8.35334	0.900764
$87$	−4.86770	−0.521872
$88$	0	0
$89$	15.9000	1.68540	0.842700	−	0.538384i	$-0.180965\pi$
$89$	15.9000	1.68540	0.842700	+	0.538384i	$0.180965\pi$
$90$	−6.55182	−0.690623
$91$	8.06440	0.845379
$92$	14.6534	1.52772
$93$	6.27840	0.651040
$94$	31.0319	3.20070
$95$	−2.71140	−0.278184
$96$	1.49371	0.152451
$97$	−1.85278	−0.188121	−0.0940607	−	0.995566i	$-0.529985\pi$
$97$	−1.85278	−0.188121	−0.0940607	+	0.995566i	$0.529985\pi$
$98$	−7.43227	−0.750772
$99$	0	0
$100$	9.02809	0.902809
$101$	14.9641	1.48898	0.744490	−	0.667634i	$-0.232693\pi$
$101$	14.9641	1.48898	0.744490	+	0.667634i	$0.232693\pi$
$102$	0.919718	0.0910656
$103$	9.51262	0.937306	0.468653	−	0.883382i	$-0.344739\pi$
$103$	9.51262	0.937306	0.468653	+	0.883382i	$0.344739\pi$
$104$	18.0900	1.77387
$105$	5.37120	0.524175
$106$	−3.39003	−0.329268
$107$	16.2310	1.56911	0.784553	−	0.620062i	$-0.212893\pi$
$107$	16.2310	1.56911	0.784553	+	0.620062i	$0.212893\pi$
$108$	−3.83898	−0.369406
$109$	12.0781	1.15687	0.578436	−	0.815728i	$-0.303663\pi$
$109$	12.0781	1.15687	0.578436	+	0.815728i	$0.303663\pi$
$110$	0	0
$111$	1.36597	0.129652
$112$	6.06137	0.572746
$113$	−3.96097	−0.372617	−0.186308	−	0.982491i	$-0.559652\pi$
$113$	−3.96097	−0.372617	−0.186308	+	0.982491i	$0.559652\pi$
$114$	−2.41640	−0.226316
$115$	−10.3494	−0.965088
$116$	18.6870	1.73504
$117$	4.07094	0.376358
$118$	−3.08979	−0.284438
$119$	−0.753987	−0.0691179
$120$	12.0487	1.09989
$121$	0	0
$122$	4.16631	0.377200
$123$	−3.74262	−0.337460
$124$	−24.1027	−2.16448
$125$	7.18062	0.642255
$126$	4.78681	0.426443
$127$	−0.924370	−0.0820246	−0.0410123	−	0.999159i	$-0.513058\pi$
$127$	−0.924370	−0.0820246	−0.0410123	+	0.999159i	$0.513058\pi$
$128$	−20.5217	−1.81388
$129$	−3.45694	−0.304366
$130$	−26.6720	−2.33929
$131$	17.2255	1.50500	0.752499	−	0.658594i	$-0.228848\pi$
$131$	17.2255	1.50500	0.752499	+	0.658594i	$0.228848\pi$
$132$	0	0
$133$	1.98097	0.171772
$134$	−18.3537	−1.58552
$135$	2.71140	0.233360
$136$	−1.69134	−0.145031
$137$	16.9171	1.44532	0.722661	−	0.691202i	$-0.242919\pi$
$137$	16.9171	1.44532	0.722661	+	0.691202i	$0.242919\pi$
$138$	−9.22339	−0.785147
$139$	15.4247	1.30830	0.654151	−	0.756364i	$-0.273026\pi$
$139$	15.4247	1.30830	0.654151	+	0.756364i	$0.273026\pi$
$140$	−20.6199	−1.74270
$141$	−12.8422	−1.08151
$142$	−23.9547	−2.01024
$143$	0	0
$144$	3.05980	0.254984
$145$	−13.1983	−1.09606
$146$	9.74966	0.806888
$147$	3.07576	0.253685
$148$	−5.24392	−0.431047
$149$	−13.4087	−1.09848	−0.549240	−	0.835665i	$-0.685083\pi$
$149$	−13.4087	−1.09848	−0.549240	+	0.835665i	$0.685083\pi$
$150$	−5.68262	−0.463984
$151$	9.94201	0.809069	0.404535	−	0.914523i	$-0.367434\pi$
$151$	9.94201	0.809069	0.404535	+	0.914523i	$0.367434\pi$
$152$	4.44371	0.360432
$153$	−0.380615	−0.0307709
$154$	0	0
$155$	17.0233	1.36734
$156$	−15.6282	−1.25126
$157$	−24.4982	−1.95517	−0.977585	−	0.210541i	$-0.932478\pi$
$157$	−24.4982	−1.95517	−0.977585	+	0.210541i	$0.932478\pi$
$158$	14.2658	1.13492
$159$	1.40293	0.111259
$160$	4.05004	0.320184
$161$	7.56136	0.595918
$162$	2.41640	0.189850
$163$	−5.21612	−0.408558	−0.204279	−	0.978913i	$-0.565485\pi$
$163$	−5.21612	−0.408558	−0.204279	+	0.978913i	$0.565485\pi$
$164$	14.3678	1.12194
$165$	0	0
$166$	12.1840	0.945659
$167$	22.8758	1.77018	0.885090	−	0.465420i	$-0.154097\pi$
$167$	22.8758	1.77018	0.885090	+	0.465420i	$0.154097\pi$
$168$	−8.80284	−0.679154
$169$	3.57252	0.274809
$170$	2.49372	0.191260
$171$	1.00000	0.0764719
$172$	13.2711	1.01191
$173$	−16.2794	−1.23770	−0.618849	−	0.785510i	$-0.712401\pi$
$173$	−16.2794	−1.23770	−0.618849	+	0.785510i	$0.712401\pi$
$174$	−11.7623	−0.891697
$175$	4.65863	0.352159
$176$	0	0
$177$	1.27867	0.0961111
$178$	38.4208	2.87976
$179$	−20.9532	−1.56611	−0.783057	−	0.621949i	$-0.786341\pi$
$179$	−20.9532	−1.56611	−0.783057	+	0.621949i	$0.786341\pi$
$180$	−10.4090	−0.775842
$181$	17.5122	1.30167	0.650835	−	0.759219i	$-0.274419\pi$
$181$	17.5122	1.30167	0.650835	+	0.759219i	$0.274419\pi$
$182$	19.4868	1.44446
$183$	−1.72418	−0.127455
$184$	16.9616	1.25043
$185$	3.70368	0.272300
$186$	15.1711	1.11240
$187$	0	0
$188$	49.3010	3.59565
$189$	−1.98097	−0.144094
$190$	−6.55182	−0.475319
$191$	−24.8822	−1.80041	−0.900207	−	0.435463i	$-0.856585\pi$
$191$	−24.8822	−1.80041	−0.900207	+	0.435463i	$0.856585\pi$
$192$	9.72900	0.702130
$193$	1.39448	0.100377	0.0501885	−	0.998740i	$-0.484018\pi$
$193$	1.39448	0.100377	0.0501885	+	0.998740i	$0.484018\pi$
$194$	−4.47706	−0.321434
$195$	11.0379	0.790443
$196$	−11.8078	−0.843414
$197$	−3.64041	−0.259368	−0.129684	−	0.991555i	$-0.541396\pi$
$197$	−3.64041	−0.259368	−0.129684	+	0.991555i	$0.541396\pi$
$198$	0	0
$199$	−10.2786	−0.728629	−0.364315	−	0.931276i	$-0.618697\pi$
$199$	−10.2786	−0.728629	−0.364315	+	0.931276i	$0.618697\pi$
$200$	10.4502	0.738942
$201$	7.59547	0.535743
$202$	36.1591	2.54415
$203$	9.64275	0.676789
$204$	1.46117	0.102303
$205$	−10.1477	−0.708748
$206$	22.9863	1.60153
$207$	3.81700	0.265300
$208$	12.4563	0.863687
$209$	0	0
$210$	12.9790	0.895633
$211$	−0.613934	−0.0422650	−0.0211325	−	0.999777i	$-0.506727\pi$
$211$	−0.613934	−0.0422650	−0.0211325	+	0.999777i	$0.506727\pi$
$212$	−5.38580	−0.369898
$213$	9.91341	0.679256
$214$	39.2204	2.68105
$215$	−9.37314	−0.639243
$216$	−4.44371	−0.302356
$217$	−12.4373	−0.844300
$218$	29.1855	1.97669
$219$	−4.03479	−0.272646
$220$	0	0
$221$	−1.54946	−0.104228
$222$	3.30072	0.221530
$223$	19.2106	1.28644	0.643219	−	0.765682i	$-0.277598\pi$
$223$	19.2106	1.28644	0.643219	+	0.765682i	$0.277598\pi$
$224$	−2.95899	−0.197706
$225$	2.35169	0.156779
$226$	−9.57128	−0.636672
$227$	14.3541	0.952712	0.476356	−	0.879252i	$-0.341957\pi$
$227$	14.3541	0.952712	0.476356	+	0.879252i	$0.341957\pi$
$228$	−3.83898	−0.254243
$229$	−17.7597	−1.17359	−0.586797	−	0.809734i	$-0.699611\pi$
$229$	−17.7597	−1.17359	−0.586797	+	0.809734i	$0.699611\pi$
$230$	−25.0083	−1.64900
$231$	0	0
$232$	21.6306	1.42012
$233$	12.5203	0.820233	0.410116	−	0.912033i	$-0.365488\pi$
$233$	12.5203	0.820233	0.410116	+	0.912033i	$0.365488\pi$
$234$	9.83700	0.643065
$235$	−34.8204	−2.27143
$236$	−4.90881	−0.319536
$237$	−5.90373	−0.383488
$238$	−1.82193	−0.118098
$239$	−4.23480	−0.273926	−0.136963	−	0.990576i	$-0.543734\pi$
$239$	−4.23480	−0.273926	−0.136963	+	0.990576i	$0.543734\pi$
$240$	8.29635	0.535527
$241$	−6.89447	−0.444112	−0.222056	−	0.975034i	$-0.571277\pi$
$241$	−6.89447	−0.444112	−0.222056	+	0.975034i	$0.571277\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	6.61910	0.423744
$245$	8.33962	0.532799
$246$	−9.04365	−0.576602
$247$	4.07094	0.259027
$248$	−27.8994	−1.77161
$249$	−5.04220	−0.319537
$250$	17.3512	1.09739
$251$	10.2944	0.649775	0.324888	−	0.945753i	$-0.394674\pi$
$251$	10.2944	0.649775	0.324888	+	0.945753i	$0.394674\pi$
$252$	7.60490	0.479064
$253$	0	0
$254$	−2.23365	−0.140151
$255$	−1.03200	−0.0646264
$256$	−30.1306	−1.88317
$257$	−30.7898	−1.92062	−0.960308	−	0.278944i	$-0.910016\pi$
$257$	−30.7898	−1.92062	−0.960308	+	0.278944i	$0.910016\pi$
$258$	−8.35334	−0.520056
$259$	−2.70594	−0.168139
$260$	−42.3744	−2.62795
$261$	4.86770	0.301303
$262$	41.6236	2.57152
$263$	−27.9296	−1.72221	−0.861105	−	0.508427i	$-0.830227\pi$
$263$	−27.9296	−1.72221	−0.861105	+	0.508427i	$0.830227\pi$
$264$	0	0
$265$	3.80389	0.233671
$266$	4.78681	0.293498
$267$	−15.9000	−0.973066
$268$	−29.1589	−1.78116
$269$	18.9856	1.15758	0.578788	−	0.815478i	$-0.303526\pi$
$269$	18.9856	1.15758	0.578788	+	0.815478i	$0.303526\pi$
$270$	6.55182	0.398731
$271$	14.9195	0.906292	0.453146	−	0.891436i	$-0.350302\pi$
$271$	14.9195	0.906292	0.453146	+	0.891436i	$0.350302\pi$
$272$	−1.16461	−0.0706147
$273$	−8.06440	−0.488080
$274$	40.8784	2.46955
$275$	0	0
$276$	−14.6534	−0.882030
$277$	9.04573	0.543505	0.271753	−	0.962367i	$-0.412397\pi$
$277$	9.04573	0.543505	0.271753	+	0.962367i	$0.412397\pi$
$278$	37.2721	2.23543
$279$	−6.27840	−0.375878
$280$	−23.8680	−1.42639
$281$	26.1087	1.55752	0.778758	−	0.627325i	$-0.215850\pi$
$281$	26.1087	1.55752	0.778758	+	0.627325i	$0.215850\pi$
$282$	−31.0319	−1.84792
$283$	−24.7141	−1.46910	−0.734550	−	0.678555i	$-0.762607\pi$
$283$	−24.7141	−1.46910	−0.734550	+	0.678555i	$0.762607\pi$
$284$	−38.0574	−2.25829
$285$	2.71140	0.160609
$286$	0	0
$287$	7.41401	0.437635
$288$	−1.49371	−0.0880177
$289$	−16.8551	−0.991478
$290$	−31.8923	−1.87278
$291$	1.85278	0.108612
$292$	15.4895	0.906453
$293$	21.6622	1.26552	0.632759	−	0.774349i	$-0.281922\pi$
$293$	21.6622	1.26552	0.632759	+	0.774349i	$0.281922\pi$
$294$	7.43227	0.433459
$295$	3.46700	0.201856
$296$	−6.06996	−0.352809
$297$	0	0
$298$	−32.4006	−1.87692
$299$	15.5388	0.898630
$300$	−9.02809	−0.521237
$301$	6.84809	0.394717
$302$	24.0238	1.38242
$303$	−14.9641	−0.859663
$304$	3.05980	0.175492
$305$	−4.67495	−0.267687
$306$	−0.919718	−0.0525768
$307$	−8.39607	−0.479189	−0.239595	−	0.970873i	$-0.577015\pi$
$307$	−8.39607	−0.479189	−0.239595	+	0.970873i	$0.577015\pi$
$308$	0	0
$309$	−9.51262	−0.541154
$310$	41.1350	2.33631
$311$	19.9824	1.13310	0.566549	−	0.824028i	$-0.308278\pi$
$311$	19.9824	1.13310	0.566549	+	0.824028i	$0.308278\pi$
$312$	−18.0900	−1.02415
$313$	−7.35515	−0.415737	−0.207869	−	0.978157i	$-0.566653\pi$
$313$	−7.35515	−0.415737	−0.207869	+	0.978157i	$0.566653\pi$
$314$	−59.1974	−3.34070
$315$	−5.37120	−0.302633
$316$	22.6643	1.27497
$317$	4.09062	0.229752	0.114876	−	0.993380i	$-0.463353\pi$
$317$	4.09062	0.229752	0.114876	+	0.993380i	$0.463353\pi$
$318$	3.39003	0.190103
$319$	0	0
$320$	26.3792	1.47464
$321$	−16.2310	−0.905923
$322$	18.2712	1.01822
$323$	−0.380615	−0.0211780
$324$	3.83898	0.213277
$325$	9.57359	0.531047
$326$	−12.6042	−0.698083
$327$	−12.0781	−0.667920
$328$	16.6311	0.918298
$329$	25.4400	1.40255
$330$	0	0
$331$	−17.3165	−0.951803	−0.475901	−	0.879499i	$-0.657878\pi$
$331$	−17.3165	−0.951803	−0.475901	+	0.879499i	$0.657878\pi$
$332$	19.3569	1.06235
$333$	−1.36597	−0.0748545
$334$	55.2769	3.02462
$335$	20.5944	1.12519
$336$	−6.06137	−0.330675
$337$	−3.06979	−0.167222	−0.0836111	−	0.996498i	$-0.526645\pi$
$337$	−3.06979	−0.167222	−0.0836111	+	0.996498i	$0.526645\pi$
$338$	8.63263	0.469553
$339$	3.96097	0.215130
$340$	3.96183	0.214860
$341$	0	0
$342$	2.41640	0.130664
$343$	−19.9598	−1.07773
$344$	15.3616	0.828243
$345$	10.3494	0.557194
$346$	−39.3375	−2.11479
$347$	−4.71298	−0.253006	−0.126503	−	0.991966i	$-0.540375\pi$
$347$	−4.71298	−0.253006	−0.126503	+	0.991966i	$0.540375\pi$
$348$	−18.6870	−1.00173
$349$	1.85108	0.0990858	0.0495429	−	0.998772i	$-0.484224\pi$
$349$	1.85108	0.0990858	0.0495429	+	0.998772i	$0.484224\pi$
$350$	11.2571	0.601717
$351$	−4.07094	−0.217290
$352$	0	0
$353$	−7.20110	−0.383276	−0.191638	−	0.981466i	$-0.561380\pi$
$353$	−7.20110	−0.383276	−0.191638	+	0.981466i	$0.561380\pi$
$354$	3.08979	0.164220
$355$	26.8792	1.42660
$356$	61.0399	3.23511
$357$	0.753987	0.0399052
$358$	−50.6312	−2.67594
$359$	23.6552	1.24848	0.624238	−	0.781234i	$-0.285410\pi$
$359$	23.6552	1.24848	0.624238	+	0.781234i	$0.285410\pi$
$360$	−12.0487	−0.635020
$361$	1.00000	0.0526316
$362$	42.3164	2.22410
$363$	0	0
$364$	30.9591	1.62270
$365$	−10.9399	−0.572622
$366$	−4.16631	−0.217776
$367$	18.7627	0.979407	0.489704	−	0.871889i	$-0.337105\pi$
$367$	18.7627	0.979407	0.489704	+	0.871889i	$0.337105\pi$
$368$	11.6793	0.608824
$369$	3.74262	0.194833
$370$	8.94957	0.465266
$371$	−2.77915	−0.144286
$372$	24.1027	1.24966
$373$	17.7552	0.919332	0.459666	−	0.888092i	$-0.347969\pi$
$373$	17.7552	0.919332	0.459666	+	0.888092i	$0.347969\pi$
$374$	0	0
$375$	−7.18062	−0.370806
$376$	57.0670	2.94301
$377$	19.8161	1.02058
$378$	−4.78681	−0.246207
$379$	−35.0648	−1.80116	−0.900578	−	0.434694i	$-0.856857\pi$
$379$	−35.0648	−1.80116	−0.900578	+	0.434694i	$0.856857\pi$
$380$	−10.4090	−0.533971
$381$	0.924370	0.0473569
$382$	−60.1253	−3.07628
$383$	−31.7282	−1.62124	−0.810618	−	0.585576i	$-0.800868\pi$
$383$	−31.7282	−1.62124	−0.810618	+	0.585576i	$0.800868\pi$
$384$	20.5217	1.04724
$385$	0	0
$386$	3.36962	0.171509
$387$	3.45694	0.175726
$388$	−7.11279	−0.361097
$389$	2.07556	0.105235	0.0526174	−	0.998615i	$-0.483244\pi$
$389$	2.07556	0.105235	0.0526174	+	0.998615i	$0.483244\pi$
$390$	26.6720	1.35059
$391$	−1.45281	−0.0734717
$392$	−13.6678	−0.690327
$393$	−17.2255	−0.868911
$394$	−8.79668	−0.443170
$395$	−16.0074	−0.805418
$396$	0	0
$397$	−35.6381	−1.78863	−0.894313	−	0.447443i	$-0.852335\pi$
$397$	−35.6381	−1.78863	−0.894313	+	0.447443i	$0.852335\pi$
$398$	−24.8371	−1.24497
$399$	−1.98097	−0.0991725
$400$	7.19571	0.359786
$401$	23.3571	1.16640	0.583200	−	0.812329i	$-0.301800\pi$
$401$	23.3571	1.16640	0.583200	+	0.812329i	$0.301800\pi$
$402$	18.3537	0.915399
$403$	−25.5590	−1.27318
$404$	57.4467	2.85808
$405$	−2.71140	−0.134731
$406$	23.3007	1.15640
$407$	0	0
$408$	1.69134	0.0837339
$409$	20.1272	0.995225	0.497612	−	0.867399i	$-0.334210\pi$
$409$	20.1272	0.995225	0.497612	+	0.867399i	$0.334210\pi$
$410$	−24.5210	−1.21100
$411$	−16.9171	−0.834457
$412$	36.5187	1.79915
$413$	−2.53301	−0.124642
$414$	9.22339	0.453305
$415$	−13.6714	−0.671104
$416$	−6.08079	−0.298135
$417$	−15.4247	−0.755349
$418$	0	0
$419$	−12.7433	−0.622552	−0.311276	−	0.950320i	$-0.600756\pi$
$419$	−12.7433	−0.622552	−0.311276	+	0.950320i	$0.600756\pi$
$420$	20.6199	1.00615
$421$	5.03792	0.245533	0.122767	−	0.992436i	$-0.460823\pi$
$421$	5.03792	0.245533	0.122767	+	0.992436i	$0.460823\pi$
$422$	−1.48351	−0.0722161
$423$	12.8422	0.624410
$424$	−6.23419	−0.302759
$425$	−0.895089	−0.0434182
$426$	23.9547	1.16061
$427$	3.41555	0.165290
$428$	62.3103	3.01188
$429$	0	0
$430$	−22.6492	−1.09224
$431$	−27.5373	−1.32642	−0.663212	−	0.748432i	$-0.730807\pi$
$431$	−27.5373	−1.32642	−0.663212	+	0.748432i	$0.730807\pi$
$432$	−3.05980	−0.147215
$433$	−16.1772	−0.777427	−0.388714	−	0.921359i	$-0.627080\pi$
$433$	−16.1772	−0.777427	−0.388714	+	0.921359i	$0.627080\pi$
$434$	−30.0535	−1.44262
$435$	13.1983	0.632809
$436$	46.3676	2.22060
$437$	3.81700	0.182592
$438$	−9.74966	−0.465857
$439$	−15.2525	−0.727963	−0.363981	−	0.931406i	$-0.618583\pi$
$439$	−15.2525	−0.727963	−0.363981	+	0.931406i	$0.618583\pi$
$440$	0	0
$441$	−3.07576	−0.146465
$442$	−3.74411	−0.178089
$443$	−6.99485	−0.332335	−0.166168	−	0.986098i	$-0.553139\pi$
$443$	−6.99485	−0.332335	−0.166168	+	0.986098i	$0.553139\pi$
$444$	5.24392	0.248865
$445$	−43.1113	−2.04367
$446$	46.4205	2.19807
$447$	13.4087	0.634208
$448$	−19.2728	−0.910557
$449$	24.8068	1.17070	0.585352	−	0.810779i	$-0.300956\pi$
$449$	24.8068	1.17070	0.585352	+	0.810779i	$0.300956\pi$
$450$	5.68262	0.267881
$451$	0	0
$452$	−15.2061	−0.715234
$453$	−9.94201	−0.467116
$454$	34.6851	1.62785
$455$	−21.8658	−1.02508
$456$	−4.44371	−0.208096
$457$	−22.3656	−1.04622	−0.523110	−	0.852265i	$-0.675228\pi$
$457$	−22.3656	−1.04622	−0.523110	+	0.852265i	$0.675228\pi$
$458$	−42.9145	−2.00526
$459$	0.380615	0.0177656
$460$	−39.7312	−1.85248
$461$	−18.8329	−0.877137	−0.438568	−	0.898698i	$-0.644514\pi$
$461$	−18.8329	−0.877137	−0.438568	+	0.898698i	$0.644514\pi$
$462$	0	0
$463$	−9.61412	−0.446806	−0.223403	−	0.974726i	$-0.571717\pi$
$463$	−9.61412	−0.446806	−0.223403	+	0.974726i	$0.571717\pi$
$464$	14.8942	0.691446
$465$	−17.0233	−0.789435
$466$	30.2540	1.40149
$467$	35.2153	1.62957	0.814784	−	0.579764i	$-0.196855\pi$
$467$	35.2153	1.62957	0.814784	+	0.579764i	$0.196855\pi$
$468$	15.6282	0.722416
$469$	−15.0464	−0.694778
$470$	−84.1399	−3.88109
$471$	24.4982	1.12882
$472$	−5.68205	−0.261538
$473$	0	0
$474$	−14.2658	−0.655248
$475$	2.35169	0.107903
$476$	−2.89454	−0.132671
$477$	−1.40293	−0.0642355
$478$	−10.2330	−0.468045
$479$	−11.9368	−0.545405	−0.272702	−	0.962098i	$-0.587917\pi$
$479$	−11.9368	−0.545405	−0.272702	+	0.962098i	$0.587917\pi$
$480$	−4.05004	−0.184858
$481$	−5.56076	−0.253549
$482$	−16.6598	−0.758833
$483$	−7.56136	−0.344054
$484$	0	0
$485$	5.02363	0.228111
$486$	−2.41640	−0.109610
$487$	−1.61768	−0.0733040	−0.0366520	−	0.999328i	$-0.511669\pi$
$487$	−1.61768	−0.0733040	−0.0366520	+	0.999328i	$0.511669\pi$
$488$	7.66175	0.346831
$489$	5.21612	0.235881
$490$	20.1519	0.910368
$491$	23.3799	1.05512	0.527560	−	0.849518i	$-0.323107\pi$
$491$	23.3799	1.05512	0.527560	+	0.849518i	$0.323107\pi$
$492$	−14.3678	−0.647752
$493$	−1.85272	−0.0834423
$494$	9.83700	0.442588
$495$	0	0
$496$	−19.2107	−0.862585
$497$	−19.6382	−0.880892
$498$	−12.1840	−0.545977
$499$	−10.7934	−0.483177	−0.241589	−	0.970379i	$-0.577668\pi$
$499$	−10.7934	−0.483177	−0.241589	+	0.970379i	$0.577668\pi$
$500$	27.5663	1.23280
$501$	−22.8758	−1.02201
$502$	24.8753	1.11024
$503$	−7.98371	−0.355976	−0.177988	−	0.984033i	$-0.556959\pi$
$503$	−7.98371	−0.355976	−0.177988	+	0.984033i	$0.556959\pi$
$504$	8.80284	0.392110
$505$	−40.5736	−1.80550
$506$	0	0
$507$	−3.57252	−0.158661
$508$	−3.54864	−0.157445
$509$	−40.4404	−1.79249	−0.896244	−	0.443562i	$-0.853715\pi$
$509$	−40.4404	−1.79249	−0.896244	+	0.443562i	$0.853715\pi$
$510$	−2.49372	−0.110424
$511$	7.99279	0.353580
$512$	−31.7642	−1.40379
$513$	−1.00000	−0.0441511
$514$	−74.4004	−3.28166
$515$	−25.7925	−1.13655
$516$	−13.2711	−0.584228
$517$	0	0
$518$	−6.53862	−0.287291
$519$	16.2794	0.714585
$520$	−49.0493	−2.15096
$521$	10.7620	0.471491	0.235745	−	0.971815i	$-0.424247\pi$
$521$	10.7620	0.471491	0.235745	+	0.971815i	$0.424247\pi$
$522$	11.7623	0.514821
$523$	−20.6043	−0.900962	−0.450481	−	0.892786i	$-0.648748\pi$
$523$	−20.6043	−0.900962	−0.450481	+	0.892786i	$0.648748\pi$
$524$	66.1283	2.88883
$525$	−4.65863	−0.203319
$526$	−67.4889	−2.94266
$527$	2.38966	0.104095
$528$	0	0
$529$	−8.43051	−0.366544
$530$	9.19172	0.399263
$531$	−1.27867	−0.0554898
$532$	7.60490	0.329714
$533$	15.2360	0.659942
$534$	−38.4208	−1.66263
$535$	−44.0086	−1.90266
$536$	−33.7521	−1.45787
$537$	20.9532	0.904197
$538$	45.8769	1.97789
$539$	0	0
$540$	10.4090	0.447932
$541$	−11.0958	−0.477046	−0.238523	−	0.971137i	$-0.576663\pi$
$541$	−11.0958	−0.477046	−0.238523	+	0.971137i	$0.576663\pi$
$542$	36.0513	1.54854
$543$	−17.5122	−0.751520
$544$	0.568528	0.0243755
$545$	−32.7486	−1.40279
$546$	−19.4868	−0.833958
$547$	14.1474	0.604898	0.302449	−	0.953166i	$-0.402196\pi$
$547$	14.1474	0.604898	0.302449	+	0.953166i	$0.402196\pi$
$548$	64.9443	2.77428
$549$	1.72418	0.0735863
$550$	0	0
$551$	4.86770	0.207371
$552$	−16.9616	−0.721935
$553$	11.6951	0.497326
$554$	21.8581	0.928661
$555$	−3.70368	−0.157213
$556$	59.2149	2.51127
$557$	7.84237	0.332292	0.166146	−	0.986101i	$-0.446868\pi$
$557$	7.84237	0.332292	0.166146	+	0.986101i	$0.446868\pi$
$558$	−15.1711	−0.642245
$559$	14.0730	0.595224
$560$	−16.4348	−0.694498
$561$	0	0
$562$	63.0891	2.66125
$563$	−4.36007	−0.183755	−0.0918776	−	0.995770i	$-0.529287\pi$
$563$	−4.36007	−0.183755	−0.0918776	+	0.995770i	$0.529287\pi$
$564$	−49.3010	−2.07595
$565$	10.7398	0.451826
$566$	−59.7191	−2.51018
$567$	1.98097	0.0831929
$568$	−44.0523	−1.84839
$569$	25.6121	1.07372	0.536858	−	0.843673i	$-0.319611\pi$
$569$	25.6121	1.07372	0.536858	+	0.843673i	$0.319611\pi$
$570$	6.55182	0.274426
$571$	−12.3483	−0.516759	−0.258380	−	0.966043i	$-0.583189\pi$
$571$	−12.3483	−0.516759	−0.258380	+	0.966043i	$0.583189\pi$
$572$	0	0
$573$	24.8822	1.03947
$574$	17.9152	0.747766
$575$	8.97640	0.374342
$576$	−9.72900	−0.405375
$577$	−15.9053	−0.662147	−0.331073	−	0.943605i	$-0.607411\pi$
$577$	−15.9053	−0.662147	−0.331073	+	0.943605i	$0.607411\pi$
$578$	−40.7287	−1.69409
$579$	−1.39448	−0.0579527
$580$	−50.6679	−2.10387
$581$	9.98844	0.414390
$582$	4.47706	0.185580
$583$	0	0
$584$	17.9294	0.741925
$585$	−11.0379	−0.456363
$586$	52.3445	2.16233
$587$	−38.5275	−1.59020	−0.795100	−	0.606478i	$-0.792582\pi$
$587$	−38.5275	−1.59020	−0.795100	+	0.606478i	$0.792582\pi$
$588$	11.8078	0.486945
$589$	−6.27840	−0.258697
$590$	8.37765	0.344902
$591$	3.64041	0.149746
$592$	−4.17959	−0.171780
$593$	24.9717	1.02547	0.512733	−	0.858548i	$-0.328633\pi$
$593$	24.9717	1.02547	0.512733	+	0.858548i	$0.328633\pi$
$594$	0	0
$595$	2.04436	0.0838106
$596$	−51.4755	−2.10852
$597$	10.2786	0.420674
$598$	37.5478	1.53545
$599$	−5.89740	−0.240961	−0.120481	−	0.992716i	$-0.538444\pi$
$599$	−5.89740	−0.240961	−0.120481	+	0.992716i	$0.538444\pi$
$600$	−10.4502	−0.426629
$601$	34.0666	1.38960	0.694802	−	0.719201i	$-0.255492\pi$
$601$	34.0666	1.38960	0.694802	+	0.719201i	$0.255492\pi$
$602$	16.5477	0.674434
$603$	−7.59547	−0.309312
$604$	38.1672	1.55300
$605$	0	0
$606$	−36.1591	−1.46886
$607$	−31.2272	−1.26747	−0.633737	−	0.773549i	$-0.718480\pi$
$607$	−31.2272	−1.26747	−0.633737	+	0.773549i	$0.718480\pi$
$608$	−1.49371	−0.0605779
$609$	−9.64275	−0.390744
$610$	−11.2965	−0.457383
$611$	52.2798	2.11502
$612$	−1.46117	−0.0590644
$613$	−36.7807	−1.48556	−0.742779	−	0.669537i	$-0.766493\pi$
$613$	−36.7807	−1.48556	−0.742779	+	0.669537i	$0.766493\pi$
$614$	−20.2883	−0.818767
$615$	10.1477	0.409196
$616$	0	0
$617$	34.0252	1.36980	0.684902	−	0.728636i	$-0.259845\pi$
$617$	34.0252	1.36980	0.684902	+	0.728636i	$0.259845\pi$
$618$	−22.9863	−0.924643
$619$	31.8467	1.28003	0.640013	−	0.768364i	$-0.278929\pi$
$619$	31.8467	1.28003	0.640013	+	0.768364i	$0.278929\pi$
$620$	65.3520	2.62460
$621$	−3.81700	−0.153171
$622$	48.2855	1.93607
$623$	31.4974	1.26192
$624$	−12.4563	−0.498650
$625$	−31.2280	−1.24912
$626$	−17.7730	−0.710350
$627$	0	0
$628$	−94.0481	−3.75293
$629$	0.519908	0.0207301
$630$	−12.9790	−0.517094
$631$	14.7162	0.585844	0.292922	−	0.956136i	$-0.405372\pi$
$631$	14.7162	0.585844	0.292922	+	0.956136i	$0.405372\pi$
$632$	26.2344	1.04355
$633$	0.613934	0.0244017
$634$	9.88457	0.392566
$635$	2.50634	0.0994610
$636$	5.38580	0.213561
$637$	−12.5212	−0.496109
$638$	0	0
$639$	−9.91341	−0.392168
$640$	55.6426	2.19947
$641$	21.0416	0.831094	0.415547	−	0.909572i	$-0.363590\pi$
$641$	21.0416	0.831094	0.415547	+	0.909572i	$0.363590\pi$
$642$	−39.2204	−1.54791
$643$	33.8532	1.33504	0.667520	−	0.744592i	$-0.267356\pi$
$643$	33.8532	1.33504	0.667520	+	0.744592i	$0.267356\pi$
$644$	29.0279	1.14386
$645$	9.37314	0.369067
$646$	−0.919718	−0.0361858
$647$	47.1764	1.85469	0.927347	−	0.374203i	$-0.122084\pi$
$647$	47.1764	1.85469	0.927347	+	0.374203i	$0.122084\pi$
$648$	4.44371	0.174565
$649$	0	0
$650$	23.1336	0.907374
$651$	12.4373	0.487457
$652$	−20.0246	−0.784223
$653$	1.94079	0.0759488	0.0379744	−	0.999279i	$-0.487909\pi$
$653$	1.94079	0.0759488	0.0379744	+	0.999279i	$0.487909\pi$
$654$	−29.1855	−1.14124
$655$	−46.7052	−1.82492
$656$	11.4517	0.447113
$657$	4.03479	0.157412
$658$	61.4732	2.39648
$659$	−7.79796	−0.303766	−0.151883	−	0.988399i	$-0.548534\pi$
$659$	−7.79796	−0.303766	−0.151883	+	0.988399i	$0.548534\pi$
$660$	0	0
$661$	−41.6336	−1.61936	−0.809679	−	0.586872i	$-0.800359\pi$
$661$	−41.6336	−1.61936	−0.809679	+	0.586872i	$0.800359\pi$
$662$	−41.8436	−1.62630
$663$	1.54946	0.0601760
$664$	22.4061	0.869524
$665$	−5.37120	−0.208286
$666$	−3.30072	−0.127900
$667$	18.5800	0.719420
$668$	87.8196	3.39784
$669$	−19.2106	−0.742725
$670$	49.7642	1.92256
$671$	0	0
$672$	2.95899	0.114146
$673$	20.1469	0.776606	0.388303	−	0.921532i	$-0.373061\pi$
$673$	20.1469	0.776606	0.388303	+	0.921532i	$0.373061\pi$
$674$	−7.41784	−0.285724
$675$	−2.35169	−0.0905166
$676$	13.7148	0.527494
$677$	−17.4703	−0.671437	−0.335718	−	0.941962i	$-0.608979\pi$
$677$	−17.4703	−0.671437	−0.335718	+	0.941962i	$0.608979\pi$
$678$	9.57128	0.367583
$679$	−3.67030	−0.140853
$680$	4.58590	0.175861
$681$	−14.3541	−0.550049
$682$	0	0
$683$	−9.67208	−0.370092	−0.185046	−	0.982730i	$-0.559243\pi$
$683$	−9.67208	−0.370092	−0.185046	+	0.982730i	$0.559243\pi$
$684$	3.83898	0.146787
$685$	−45.8689	−1.75256
$686$	−48.2308	−1.84146
$687$	17.7597	0.677575
$688$	10.5776	0.403265
$689$	−5.71122	−0.217580
$690$	25.0083	0.952050
$691$	22.9560	0.873286	0.436643	−	0.899635i	$-0.356167\pi$
$691$	22.9560	0.873286	0.436643	+	0.899635i	$0.356167\pi$
$692$	−62.4962	−2.37575
$693$	0	0
$694$	−11.3884	−0.432299
$695$	−41.8224	−1.58641
$696$	−21.6306	−0.819906
$697$	−1.42450	−0.0539567
$698$	4.47294	0.169303
$699$	−12.5203	−0.473562
$700$	17.8844	0.675966
$701$	−29.2883	−1.10620	−0.553101	−	0.833114i	$-0.686556\pi$
$701$	−29.2883	−1.10620	−0.553101	+	0.833114i	$0.686556\pi$
$702$	−9.83700	−0.371274
$703$	−1.36597	−0.0515184
$704$	0	0
$705$	34.8204	1.31141
$706$	−17.4007	−0.654884
$707$	29.6433	1.11485
$708$	4.90881	0.184484
$709$	26.5445	0.996899	0.498450	−	0.866919i	$-0.333903\pi$
$709$	26.5445	0.996899	0.498450	+	0.866919i	$0.333903\pi$
$710$	64.9509	2.43756
$711$	5.90373	0.221407
$712$	70.6550	2.64791
$713$	−23.9647	−0.897484
$714$	1.82193	0.0681841
$715$	0	0
$716$	−80.4389	−3.00614
$717$	4.23480	0.158152
$718$	57.1605	2.13321
$719$	−16.3628	−0.610229	−0.305115	−	0.952316i	$-0.598695\pi$
$719$	−16.3628	−0.610229	−0.305115	+	0.952316i	$0.598695\pi$
$720$	−8.29635	−0.309187
$721$	18.8442	0.701795
$722$	2.41640	0.0899290
$723$	6.89447	0.256408
$724$	67.2289	2.49854
$725$	11.4473	0.425143
$726$	0	0
$727$	25.2731	0.937328	0.468664	−	0.883376i	$-0.344735\pi$
$727$	25.2731	0.937328	0.468664	+	0.883376i	$0.344735\pi$
$728$	35.8358	1.32816
$729$	1.00000	0.0370370
$730$	−26.4352	−0.978412
$731$	−1.31576	−0.0486653
$732$	−6.61910	−0.244649
$733$	−39.9922	−1.47715	−0.738573	−	0.674173i	$-0.764500\pi$
$733$	−39.9922	−1.47715	−0.738573	+	0.674173i	$0.764500\pi$
$734$	45.3383	1.67347
$735$	−8.33962	−0.307612
$736$	−5.70149	−0.210160
$737$	0	0
$738$	9.04365	0.332901
$739$	−42.1816	−1.55168	−0.775838	−	0.630932i	$-0.782673\pi$
$739$	−42.1816	−1.55168	−0.775838	+	0.630932i	$0.782673\pi$
$740$	14.2184	0.522677
$741$	−4.07094	−0.149550
$742$	−6.71553	−0.246535
$743$	−2.42319	−0.0888983	−0.0444491	−	0.999012i	$-0.514153\pi$
$743$	−2.42319	−0.0888983	−0.0444491	+	0.999012i	$0.514153\pi$
$744$	27.8994	1.02284
$745$	36.3562	1.33199
$746$	42.9037	1.57082
$747$	5.04220	0.184485
$748$	0	0
$749$	32.1530	1.17485
$750$	−17.3512	−0.633578
$751$	−14.3133	−0.522300	−0.261150	−	0.965298i	$-0.584102\pi$
$751$	−14.3133	−0.522300	−0.261150	+	0.965298i	$0.584102\pi$
$752$	39.2947	1.43293
$753$	−10.2944	−0.375148
$754$	47.8835	1.74382
$755$	−26.9568	−0.981057
$756$	−7.60490	−0.276587
$757$	4.62612	0.168139	0.0840697	−	0.996460i	$-0.473208\pi$
$757$	4.62612	0.168139	0.0840697	+	0.996460i	$0.473208\pi$
$758$	−84.7305	−3.07755
$759$	0	0
$760$	−12.0487	−0.437051
$761$	−32.2344	−1.16850	−0.584249	−	0.811575i	$-0.698611\pi$
$761$	−32.2344	−1.16850	−0.584249	+	0.811575i	$0.698611\pi$
$762$	2.23365	0.0809165
$763$	23.9263	0.866191
$764$	−95.5223	−3.45588
$765$	1.03200	0.0373120
$766$	−76.6680	−2.77013
$767$	−5.20540	−0.187956
$768$	30.1306	1.08725
$769$	−40.2599	−1.45181	−0.725905	−	0.687795i	$-0.758579\pi$
$769$	−40.2599	−1.45181	−0.725905	+	0.687795i	$0.758579\pi$
$770$	0	0
$771$	30.7898	1.10887
$772$	5.35338	0.192672
$773$	−9.91335	−0.356558	−0.178279	−	0.983980i	$-0.557053\pi$
$773$	−9.91335	−0.356558	−0.178279	+	0.983980i	$0.557053\pi$
$774$	8.35334	0.300255
$775$	−14.7649	−0.530370
$776$	−8.23322	−0.295555
$777$	2.70594	0.0970750
$778$	5.01537	0.179810
$779$	3.74262	0.134093
$780$	42.3744	1.51725
$781$	0	0
$782$	−3.51056	−0.125537
$783$	−4.86770	−0.173957
$784$	−9.41123	−0.336115
$785$	66.4245	2.37079
$786$	−41.6236	−1.48467
$787$	−44.6044	−1.58998	−0.794988	−	0.606625i	$-0.792523\pi$
$787$	−44.6044	−1.58998	−0.794988	+	0.606625i	$0.792523\pi$
$788$	−13.9755	−0.497855
$789$	27.9296	0.994319
$790$	−38.6802	−1.37618
$791$	−7.84656	−0.278991
$792$	0	0
$793$	7.01903	0.249253
$794$	−86.1158	−3.05614
$795$	−3.80389	−0.134910
$796$	−39.4593	−1.39860
$797$	−19.5372	−0.692042	−0.346021	−	0.938227i	$-0.612467\pi$
$797$	−19.5372	−0.692042	−0.346021	+	0.938227i	$0.612467\pi$
$798$	−4.78681	−0.169451
$799$	−4.88794	−0.172923
$800$	−3.51274	−0.124194
$801$	15.9000	0.561800
$802$	56.4401	1.99297
$803$	0	0
$804$	29.1589	1.02835
$805$	−20.5019	−0.722596
$806$	−61.7607	−2.17543
$807$	−18.9856	−0.668326
$808$	66.4959	2.33932
$809$	−4.28885	−0.150788	−0.0753939	−	0.997154i	$-0.524021\pi$
$809$	−4.28885	−0.150788	−0.0753939	+	0.997154i	$0.524021\pi$
$810$	−6.55182	−0.230208
$811$	40.2476	1.41329	0.706643	−	0.707570i	$-0.250209\pi$
$811$	40.2476	1.41329	0.706643	+	0.707570i	$0.250209\pi$
$812$	37.0183	1.29909
$813$	−14.9195	−0.523248
$814$	0	0
$815$	14.1430	0.495407
$816$	1.16461	0.0407694
$817$	3.45694	0.120943
$818$	48.6353	1.70049
$819$	8.06440	0.281793
$820$	−38.9569	−1.36044
$821$	−28.3890	−0.990782	−0.495391	−	0.868670i	$-0.664975\pi$
$821$	−28.3890	−0.990782	−0.495391	+	0.868670i	$0.664975\pi$
$822$	−40.8784	−1.42580
$823$	19.4943	0.679527	0.339764	−	0.940511i	$-0.389653\pi$
$823$	19.4943	0.679527	0.339764	+	0.940511i	$0.389653\pi$
$824$	42.2713	1.47259
$825$	0	0
$826$	−6.12077	−0.212969
$827$	−37.5772	−1.30669	−0.653344	−	0.757061i	$-0.726634\pi$
$827$	−37.5772	−1.30669	−0.653344	+	0.757061i	$0.726634\pi$
$828$	14.6534	0.509240
$829$	41.2628	1.43311	0.716557	−	0.697528i	$-0.245717\pi$
$829$	41.2628	1.43311	0.716557	+	0.697528i	$0.245717\pi$
$830$	−33.0356	−1.14668
$831$	−9.04573	−0.313793
$832$	−39.6061	−1.37310
$833$	1.17068	0.0405617
$834$	−37.2721	−1.29063
$835$	−62.0253	−2.14648
$836$	0	0
$837$	6.27840	0.217013
$838$	−30.7929	−1.06372
$839$	26.6255	0.919215	0.459608	−	0.888122i	$-0.347990\pi$
$839$	26.6255	0.919215	0.459608	+	0.888122i	$0.347990\pi$
$840$	23.8680	0.823525
$841$	−5.30554	−0.182949
$842$	12.1736	0.419531
$843$	−26.1087	−0.899232
$844$	−2.35688	−0.0811271
$845$	−9.68654	−0.333227
$846$	31.0319	1.06690
$847$	0	0
$848$	−4.29268	−0.147411
$849$	24.7141	0.848185
$850$	−2.16289	−0.0741866
$851$	−5.21390	−0.178730
$852$	38.0574	1.30382
$853$	7.38894	0.252993	0.126496	−	0.991967i	$-0.459627\pi$
$853$	7.38894	0.252993	0.126496	+	0.991967i	$0.459627\pi$
$854$	8.25333	0.282423
$855$	−2.71140	−0.0927279
$856$	72.1256	2.46520
$857$	−21.9094	−0.748410	−0.374205	−	0.927346i	$-0.622084\pi$
$857$	−21.9094	−0.748410	−0.374205	+	0.927346i	$0.622084\pi$
$858$	0	0
$859$	10.6865	0.364617	0.182309	−	0.983241i	$-0.441643\pi$
$859$	10.6865	0.364617	0.182309	+	0.983241i	$0.441643\pi$
$860$	−35.9833	−1.22702
$861$	−7.41401	−0.252669
$862$	−66.5410	−2.26639
$863$	−10.8540	−0.369476	−0.184738	−	0.982788i	$-0.559144\pi$
$863$	−10.8540	−0.369476	−0.184738	+	0.982788i	$0.559144\pi$
$864$	1.49371	0.0508170
$865$	44.1399	1.50080
$866$	−39.0906	−1.32835
$867$	16.8551	0.572430
$868$	−47.7466	−1.62063
$869$	0	0
$870$	31.8923	1.08125
$871$	−30.9207	−1.04771
$872$	53.6715	1.81755
$873$	−1.85278	−0.0627072
$874$	9.22339	0.311986
$875$	14.2246	0.480879
$876$	−15.4895	−0.523341
$877$	−46.2754	−1.56261	−0.781305	−	0.624149i	$-0.785446\pi$
$877$	−46.2754	−1.56261	−0.781305	+	0.624149i	$0.785446\pi$
$878$	−36.8561	−1.24383
$879$	−21.6622	−0.730647
$880$	0	0
$881$	−8.75040	−0.294808	−0.147404	−	0.989076i	$-0.547092\pi$
$881$	−8.75040	−0.294808	−0.147404	+	0.989076i	$0.547092\pi$
$882$	−7.43227	−0.250257
$883$	32.5946	1.09690	0.548448	−	0.836185i	$-0.315219\pi$
$883$	32.5946	1.09690	0.548448	+	0.836185i	$0.315219\pi$
$884$	−5.94835	−0.200065
$885$	−3.46700	−0.116542
$886$	−16.9023	−0.567845
$887$	−39.7710	−1.33538	−0.667690	−	0.744439i	$-0.732717\pi$
$887$	−39.7710	−1.33538	−0.667690	+	0.744439i	$0.732717\pi$
$888$	6.06996	0.203694
$889$	−1.83115	−0.0614148
$890$	−104.174	−3.49192
$891$	0	0
$892$	73.7492	2.46930
$893$	12.8422	0.429748
$894$	32.4006	1.08364
$895$	56.8125	1.89903
$896$	−40.6529	−1.35812
$897$	−15.5388	−0.518824
$898$	59.9431	2.00033
$899$	−30.5614	−1.01928
$900$	9.02809	0.300936
$901$	0.533975	0.0177893
$902$	0	0
$903$	−6.84809	−0.227890
$904$	−17.6014	−0.585413
$905$	−47.4826	−1.57837
$906$	−24.0238	−0.798139
$907$	−18.5189	−0.614911	−0.307456	−	0.951562i	$-0.599478\pi$
$907$	−18.5189	−0.614911	−0.307456	+	0.951562i	$0.599478\pi$
$908$	55.1049	1.82872
$909$	14.9641	0.496327
$910$	−52.8365	−1.75151
$911$	−17.3452	−0.574672	−0.287336	−	0.957830i	$-0.592770\pi$
$911$	−17.3452	−0.574672	−0.287336	+	0.957830i	$0.592770\pi$
$912$	−3.05980	−0.101320
$913$	0	0
$914$	−54.0443	−1.78763
$915$	4.67495	0.154549
$916$	−68.1791	−2.25270
$917$	34.1231	1.12685
$918$	0.919718	0.0303552
$919$	−15.9679	−0.526731	−0.263366	−	0.964696i	$-0.584833\pi$
$919$	−15.9679	−0.526731	−0.263366	+	0.964696i	$0.584833\pi$
$920$	−45.9897	−1.51624
$921$	8.39607	0.276660
$922$	−45.5078	−1.49872
$923$	−40.3569	−1.32836
$924$	0	0
$925$	−3.21233	−0.105621
$926$	−23.2315	−0.763436
$927$	9.51262	0.312435
$928$	−7.27092	−0.238680
$929$	41.0151	1.34566	0.672831	−	0.739796i	$-0.265078\pi$
$929$	41.0151	1.34566	0.672831	+	0.739796i	$0.265078\pi$
$930$	−41.1350	−1.34887
$931$	−3.07576	−0.100804
$932$	48.0652	1.57443
$933$	−19.9824	−0.654195
$934$	85.0941	2.78436
$935$	0	0
$936$	18.0900	0.591292
$937$	−14.3060	−0.467356	−0.233678	−	0.972314i	$-0.575076\pi$
$937$	−14.3060	−0.467356	−0.233678	+	0.972314i	$0.575076\pi$
$938$	−36.3581	−1.18713
$939$	7.35515	0.240026
$940$	−133.675	−4.35999
$941$	−13.9424	−0.454509	−0.227254	−	0.973835i	$-0.572975\pi$
$941$	−13.9424	−0.454509	−0.227254	+	0.973835i	$0.572975\pi$
$942$	59.1974	1.92876
$943$	14.2856	0.465202
$944$	−3.91249	−0.127341
$945$	5.37120	0.174725
$946$	0	0
$947$	−20.4080	−0.663172	−0.331586	−	0.943425i	$-0.607584\pi$
$947$	−20.4080	−0.663172	−0.331586	+	0.943425i	$0.607584\pi$
$948$	−22.6643	−0.736102
$949$	16.4254	0.533190
$950$	5.68262	0.184369
$951$	−4.09062	−0.132648
$952$	−3.35050	−0.108590
$953$	−33.9482	−1.09969	−0.549845	−	0.835266i	$-0.685313\pi$
$953$	−33.9482	−1.09969	−0.549845	+	0.835266i	$0.685313\pi$
$954$	−3.39003	−0.109756
$955$	67.4656	2.18314
$956$	−16.2573	−0.525799
$957$	0	0
$958$	−28.8440	−0.931907
$959$	33.5122	1.08216
$960$	−26.3792	−0.851386
$961$	8.41836	0.271560
$962$	−13.4370	−0.433227
$963$	16.2310	0.523035
$964$	−26.4677	−0.852469
$965$	−3.78100	−0.121715
$966$	−18.2712	−0.587868
$967$	14.7792	0.475268	0.237634	−	0.971355i	$-0.423628\pi$
$967$	14.7792	0.475268	0.237634	+	0.971355i	$0.423628\pi$
$968$	0	0
$969$	0.380615	0.0122271
$970$	12.1391	0.389763
$971$	−46.5274	−1.49314	−0.746568	−	0.665310i	$-0.768300\pi$
$971$	−46.5274	−1.49314	−0.746568	+	0.665310i	$0.768300\pi$
$972$	−3.83898	−0.123135
$973$	30.5558	0.979573
$974$	−3.90895	−0.125251
$975$	−9.57359	−0.306600
$976$	5.27566	0.168870
$977$	−36.7798	−1.17669	−0.588345	−	0.808610i	$-0.700220\pi$
$977$	−36.7798	−1.17669	−0.588345	+	0.808610i	$0.700220\pi$
$978$	12.6042	0.403038
$979$	0	0
$980$	32.0156	1.02270
$981$	12.0781	0.385624
$982$	56.4951	1.80283
$983$	47.4862	1.51457	0.757287	−	0.653082i	$-0.226524\pi$
$983$	47.4862	1.51457	0.757287	+	0.653082i	$0.226524\pi$
$984$	−16.6311	−0.530180
$985$	9.87061	0.314504
$986$	−4.47691	−0.142574
$987$	−25.4400	−0.809765
$988$	15.6282	0.497201
$989$	13.1951	0.419581
$990$	0	0
$991$	−8.43710	−0.268013	−0.134007	−	0.990980i	$-0.542784\pi$
$991$	−8.43710	−0.268013	−0.134007	+	0.990980i	$0.542784\pi$
$992$	9.37811	0.297755
$993$	17.3165	0.549523
$994$	−47.4536	−1.50514
$995$	27.8693	0.883518
$996$	−19.3569	−0.613347
$997$	26.7930	0.848543	0.424271	−	0.905535i	$-0.360530\pi$
$997$	26.7930	0.848543	0.424271	+	0.905535i	$0.360530\pi$
$998$	−26.0811	−0.825582
$999$	1.36597	0.0432173

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6897.2.a.bm.1.15		16
11.5	even	5		627.2.j.b.58.1	✓	32
11.9	even	5		627.2.j.b.400.1	yes	32
11.10	odd	2		6897.2.a.bl.1.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.j.b.58.1	✓	32	11.5	even	5
627.2.j.b.400.1	yes	32	11.9	even	5
6897.2.a.bl.1.2		16	11.10	odd	2
6897.2.a.bm.1.15		16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6897 = 3 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6897.a (trivial)

\(f(q)\)	\(=\)	\(q+2.41640 q^{2} -1.00000 q^{3} +3.83898 q^{4} -2.71140 q^{5} -2.41640 q^{6} +1.98097 q^{7} +4.44371 q^{8} +1.00000 q^{9} -6.55182 q^{10} -3.83898 q^{12} +4.07094 q^{13} +4.78681 q^{14} +2.71140 q^{15} +3.05980 q^{16} -0.380615 q^{17} +2.41640 q^{18} +1.00000 q^{19} -10.4090 q^{20} -1.98097 q^{21} +3.81700 q^{23} -4.44371 q^{24} +2.35169 q^{25} +9.83700 q^{26} -1.00000 q^{27} +7.60490 q^{28} +4.86770 q^{29} +6.55182 q^{30} -6.27840 q^{31} -1.49371 q^{32} -0.919718 q^{34} -5.37120 q^{35} +3.83898 q^{36} -1.36597 q^{37} +2.41640 q^{38} -4.07094 q^{39} -12.0487 q^{40} +3.74262 q^{41} -4.78681 q^{42} +3.45694 q^{43} -2.71140 q^{45} +9.22339 q^{46} +12.8422 q^{47} -3.05980 q^{48} -3.07576 q^{49} +5.68262 q^{50} +0.380615 q^{51} +15.6282 q^{52} -1.40293 q^{53} -2.41640 q^{54} +8.80284 q^{56} -1.00000 q^{57} +11.7623 q^{58} -1.27867 q^{59} +10.4090 q^{60} +1.72418 q^{61} -15.1711 q^{62} +1.98097 q^{63} -9.72900 q^{64} -11.0379 q^{65} -7.59547 q^{67} -1.46117 q^{68} -3.81700 q^{69} -12.9790 q^{70} -9.91341 q^{71} +4.44371 q^{72} +4.03479 q^{73} -3.30072 q^{74} -2.35169 q^{75} +3.83898 q^{76} -9.83700 q^{78} +5.90373 q^{79} -8.29635 q^{80} +1.00000 q^{81} +9.04365 q^{82} +5.04220 q^{83} -7.60490 q^{84} +1.03200 q^{85} +8.35334 q^{86} -4.86770 q^{87} +15.9000 q^{89} -6.55182 q^{90} +8.06440 q^{91} +14.6534 q^{92} +6.27840 q^{93} +31.0319 q^{94} -2.71140 q^{95} +1.49371 q^{96} -1.85278 q^{97} -7.43227 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 16 q^{3} + 13 q^{4} + 8 q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} + 16 q^{9} + 5 q^{10} - 13 q^{12} + 5 q^{13} + 4 q^{14} - 8 q^{15} + 3 q^{16} + 4 q^{17} + 3 q^{18} + 16 q^{19} + 10 q^{20} + 2 q^{21}+ \cdots - 41 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 16 * q^3 + 13 * q^4 + 8 * q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 + 16 * q^9 + 5 * q^10 - 13 * q^12 + 5 * q^13 + 4 * q^14 - 8 * q^15 + 3 * q^16 + 4 * q^17 + 3 * q^18 + 16 * q^19 + 10 * q^20 + 2 * q^21 + 36 * q^23 - 6 * q^24 + 20 * q^25 - 12 * q^26 - 16 * q^27 + 25 * q^28 + 13 * q^29 - 5 * q^30 + 19 * q^31 + 3 * q^34 - 20 * q^35 + 13 * q^36 - 8 * q^37 + 3 * q^38 - 5 * q^39 - 7 * q^41 - 4 * q^42 - 14 * q^43 + 8 * q^45 - 13 * q^46 + 62 * q^47 - 3 * q^48 + 16 * q^49 + 74 * q^50 - 4 * q^51 - 7 * q^52 + 12 * q^53 - 3 * q^54 + 14 * q^56 - 16 * q^57 + q^58 + 7 * q^59 - 10 * q^60 + q^61 - q^62 - 2 * q^63 - 28 * q^64 + 2 * q^65 - 16 * q^68 - 36 * q^69 - 29 * q^70 + 29 * q^71 + 6 * q^72 - 43 * q^73 - 39 * q^74 - 20 * q^75 + 13 * q^76 + 12 * q^78 + 23 * q^79 + 48 * q^80 + 16 * q^81 + 38 * q^82 + 38 * q^83 - 25 * q^84 - 17 * q^85 + 35 * q^86 - 13 * q^87 + 35 * q^89 + 5 * q^90 + 8 * q^91 + 63 * q^92 - 19 * q^93 + 59 * q^94 + 8 * q^95 + 34 * q^97 - 41 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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