LMFDB - Embedded newform 2366.4.a.s.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2366,4,Mod(1,2366)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2366, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2366.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2366.a (trivial)

Newform invariants

comment:select newform

sage:traces = [5,-10,1,20,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$139.598519074$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 95x^{3} + 122x^{2} + 2074x - 2668 $ x^5 - x^4 - 95x^3 + 122x^2 + 2074*x - 2668
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 182)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.28617$ of defining polynomial
Character	$\chi$	$=$	2366.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} +1.28617 q^{3} +4.00000 q^{4} -10.0966 q^{5} -2.57235 q^{6} +7.00000 q^{7} -8.00000 q^{8} -25.3458 q^{9} +20.1932 q^{10} +20.1087 q^{11} +5.14470 q^{12} -14.0000 q^{14} -12.9860 q^{15} +16.0000 q^{16} -63.2530 q^{17} +50.6915 q^{18} -17.1914 q^{19} -40.3864 q^{20} +9.00322 q^{21} -40.2174 q^{22} +199.470 q^{23} -10.2894 q^{24} -23.0588 q^{25} -67.3258 q^{27} +28.0000 q^{28} -3.58751 q^{29} +25.9720 q^{30} +61.0025 q^{31} -32.0000 q^{32} +25.8633 q^{33} +126.506 q^{34} -70.6762 q^{35} -101.383 q^{36} +41.1154 q^{37} +34.3829 q^{38} +80.7728 q^{40} +32.4853 q^{41} -18.0064 q^{42} +234.902 q^{43} +80.4349 q^{44} +255.906 q^{45} -398.941 q^{46} +263.044 q^{47} +20.5788 q^{48} +49.0000 q^{49} +46.1175 q^{50} -81.3544 q^{51} -369.147 q^{53} +134.652 q^{54} -203.030 q^{55} -56.0000 q^{56} -22.1112 q^{57} +7.17503 q^{58} -410.974 q^{59} -51.9439 q^{60} -148.061 q^{61} -122.005 q^{62} -177.420 q^{63} +64.0000 q^{64} -51.7266 q^{66} +45.8863 q^{67} -253.012 q^{68} +256.554 q^{69} +141.352 q^{70} +854.901 q^{71} +202.766 q^{72} +457.581 q^{73} -82.2309 q^{74} -29.6576 q^{75} -68.7657 q^{76} +140.761 q^{77} -1200.31 q^{79} -161.546 q^{80} +597.743 q^{81} -64.9705 q^{82} +271.489 q^{83} +36.0129 q^{84} +638.640 q^{85} -469.804 q^{86} -4.61417 q^{87} -160.870 q^{88} +1182.71 q^{89} -511.812 q^{90} +797.882 q^{92} +78.4598 q^{93} -526.088 q^{94} +173.575 q^{95} -41.1576 q^{96} +832.124 q^{97} -98.0000 q^{98} -509.671 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 10 q^{2} + q^{3} + 20 q^{4} + 6 q^{5} - 2 q^{6} + 35 q^{7} - 40 q^{8} + 56 q^{9} - 12 q^{10} - 9 q^{11} + 4 q^{12} - 70 q^{14} + 137 q^{15} + 80 q^{16} - 89 q^{17} - 112 q^{18} - 49 q^{19} + 24 q^{20}+ \cdots + 81 q^{99}+O(q^{100}) $ 5 * q - 10 * q^2 + q^3 + 20 * q^4 + 6 * q^5 - 2 * q^6 + 35 * q^7 - 40 * q^8 + 56 * q^9 - 12 * q^10 - 9 * q^11 + 4 * q^12 - 70 * q^14 + 137 * q^15 + 80 * q^16 - 89 * q^17 - 112 * q^18 - 49 * q^19 + 24 * q^20 + 7 * q^21 + 18 * q^22 - 60 * q^23 - 8 * q^24 - 59 * q^25 - 134 * q^27 + 140 * q^28 - 196 * q^29 - 274 * q^30 + 154 * q^31 - 160 * q^32 - 433 * q^33 + 178 * q^34 + 42 * q^35 + 224 * q^36 + 61 * q^37 + 98 * q^38 - 48 * q^40 - 237 * q^41 - 14 * q^42 - 459 * q^43 - 36 * q^44 + 384 * q^45 + 120 * q^46 - 314 * q^47 + 16 * q^48 + 245 * q^49 + 118 * q^50 - 1069 * q^51 - 143 * q^53 + 268 * q^54 - 1899 * q^55 - 280 * q^56 + 211 * q^57 + 392 * q^58 + 178 * q^59 + 548 * q^60 - 811 * q^61 - 308 * q^62 + 392 * q^63 + 320 * q^64 + 866 * q^66 - 1078 * q^67 - 356 * q^68 - 654 * q^69 - 84 * q^70 + 1670 * q^71 - 448 * q^72 + 249 * q^73 - 122 * q^74 + 771 * q^75 - 196 * q^76 - 63 * q^77 + 4 * q^79 + 96 * q^80 - 2179 * q^81 + 474 * q^82 + 1986 * q^83 + 28 * q^84 - 2910 * q^85 + 918 * q^86 - 1427 * q^87 + 72 * q^88 + 461 * q^89 - 768 * q^90 - 240 * q^92 - 1055 * q^93 + 628 * q^94 - 543 * q^95 - 32 * q^96 + 2415 * q^97 - 490 * q^98 + 81 * q^99

Coefficient data

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

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

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

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	1.28617	0.247524	0.123762	−	0.992312i	$-0.460504\pi$
$3$	1.28617	0.247524	0.123762	+	0.992312i	$0.460504\pi$
$4$	4.00000	0.500000
$5$	−10.0966	−0.903067	−0.451533	−	0.892254i	$-0.649123\pi$
$5$	−10.0966	−0.903067	−0.451533	+	0.892254i	$0.649123\pi$
$6$	−2.57235	−0.175026
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	−25.3458	−0.938732
$10$	20.1932	0.638565
$11$	20.1087	0.551182	0.275591	−	0.961275i	$-0.411126\pi$
$11$	20.1087	0.551182	0.275591	+	0.961275i	$0.411126\pi$
$12$	5.14470	0.123762
$13$	0	0
$13$	0	0
$14$	−14.0000	−0.267261
$15$	−12.9860	−0.223531
$16$	16.0000	0.250000
$17$	−63.2530	−0.902418	−0.451209	−	0.892418i	$-0.649007\pi$
$17$	−63.2530	−0.902418	−0.451209	+	0.892418i	$0.649007\pi$
$18$	50.6915	0.663784
$19$	−17.1914	−0.207578	−0.103789	−	0.994599i	$-0.533097\pi$
$19$	−17.1914	−0.207578	−0.103789	+	0.994599i	$0.533097\pi$
$20$	−40.3864	−0.451533
$21$	9.00322	0.0935554
$22$	−40.2174	−0.389745
$23$	199.470	1.80837	0.904184	−	0.427143i	$-0.140480\pi$
$23$	199.470	1.80837	0.904184	+	0.427143i	$0.140480\pi$
$24$	−10.2894	−0.0875131
$25$	−23.0588	−0.184470
$26$	0	0
$27$	−67.3258	−0.479883
$28$	28.0000	0.188982
$29$	−3.58751	−0.0229719	−0.0114859	−	0.999934i	$-0.503656\pi$
$29$	−3.58751	−0.0229719	−0.0114859	+	0.999934i	$0.503656\pi$
$30$	25.9720	0.158060
$31$	61.0025	0.353431	0.176716	−	0.984262i	$-0.443453\pi$
$31$	61.0025	0.353431	0.176716	+	0.984262i	$0.443453\pi$
$32$	−32.0000	−0.176777
$33$	25.8633	0.136431
$34$	126.506	0.638106
$35$	−70.6762	−0.341327
$36$	−101.383	−0.469366
$37$	41.1154	0.182685	0.0913424	−	0.995820i	$-0.470884\pi$
$37$	41.1154	0.182685	0.0913424	+	0.995820i	$0.470884\pi$
$38$	34.3829	0.146780
$39$	0	0
$40$	80.7728	0.319282
$41$	32.4853	0.123740	0.0618701	−	0.998084i	$-0.480294\pi$
$41$	32.4853	0.123740	0.0618701	+	0.998084i	$0.480294\pi$
$42$	−18.0064	−0.0661537
$43$	234.902	0.833075	0.416537	−	0.909119i	$-0.363243\pi$
$43$	234.902	0.833075	0.416537	+	0.909119i	$0.363243\pi$
$44$	80.4349	0.275591
$45$	255.906	0.847738
$46$	−398.941	−1.27871
$47$	263.044	0.816360	0.408180	−	0.912901i	$-0.366163\pi$
$47$	263.044	0.816360	0.408180	+	0.912901i	$0.366163\pi$
$48$	20.5788	0.0618811
$49$	49.0000	0.142857
$50$	46.1175	0.130440
$51$	−81.3544	−0.223370
$52$	0	0
$53$	−369.147	−0.956723	−0.478361	−	0.878163i	$-0.658769\pi$
$53$	−369.147	−0.956723	−0.478361	+	0.878163i	$0.658769\pi$
$54$	134.652	0.339329
$55$	−203.030	−0.497755
$56$	−56.0000	−0.133631
$57$	−22.1112	−0.0513807
$58$	7.17503	0.0162436
$59$	−410.974	−0.906851	−0.453425	−	0.891294i	$-0.649798\pi$
$59$	−410.974	−0.906851	−0.453425	+	0.891294i	$0.649798\pi$
$60$	−51.9439	−0.111766
$61$	−148.061	−0.310775	−0.155388	−	0.987854i	$-0.549663\pi$
$61$	−148.061	−0.310775	−0.155388	+	0.987854i	$0.549663\pi$
$62$	−122.005	−0.249914
$63$	−177.420	−0.354807
$64$	64.0000	0.125000
$65$	0	0
$66$	−51.7266	−0.0964713
$67$	45.8863	0.0836702	0.0418351	−	0.999125i	$-0.486680\pi$
$67$	45.8863	0.0836702	0.0418351	+	0.999125i	$0.486680\pi$
$68$	−253.012	−0.451209
$69$	256.554	0.447615
$70$	141.352	0.241355
$71$	854.901	1.42899	0.714494	−	0.699642i	$-0.246657\pi$
$71$	854.901	1.42899	0.714494	+	0.699642i	$0.246657\pi$
$72$	202.766	0.331892
$73$	457.581	0.733641	0.366821	−	0.930292i	$-0.380446\pi$
$73$	457.581	0.733641	0.366821	+	0.930292i	$0.380446\pi$
$74$	−82.2309	−0.129178
$75$	−29.6576	−0.0456608
$76$	−68.7657	−0.103789
$77$	140.761	0.208327
$78$	0	0
$79$	−1200.31	−1.70943	−0.854716	−	0.519096i	$-0.826269\pi$
$79$	−1200.31	−1.70943	−0.854716	+	0.519096i	$0.826269\pi$
$80$	−161.546	−0.225767
$81$	597.743	0.819949
$82$	−64.9705	−0.0874975
$83$	271.489	0.359033	0.179517	−	0.983755i	$-0.442547\pi$
$83$	271.489	0.359033	0.179517	+	0.983755i	$0.442547\pi$
$84$	36.0129	0.0467777
$85$	638.640	0.814944
$86$	−469.804	−0.589073
$87$	−4.61417	−0.00568610
$88$	−160.870	−0.194872
$89$	1182.71	1.40862	0.704309	−	0.709893i	$-0.251257\pi$
$89$	1182.71	1.40862	0.704309	+	0.709893i	$0.251257\pi$
$90$	−511.812	−0.599441
$91$	0	0
$92$	797.882	0.904184
$93$	78.4598	0.0874828
$94$	−526.088	−0.577254
$95$	173.575	0.187457
$96$	−41.1576	−0.0437565
$97$	832.124	0.871024	0.435512	−	0.900183i	$-0.356567\pi$
$97$	832.124	0.871024	0.435512	+	0.900183i	$0.356567\pi$
$98$	−98.0000	−0.101015
$99$	−509.671	−0.517412
$100$	−92.2350	−0.0922350
$101$	−534.753	−0.526830	−0.263415	−	0.964683i	$-0.584849\pi$
$101$	−534.753	−0.526830	−0.263415	+	0.964683i	$0.584849\pi$
$102$	162.709	0.157947
$103$	−1003.88	−0.960340	−0.480170	−	0.877175i	$-0.659425\pi$
$103$	−1003.88	−0.960340	−0.480170	+	0.877175i	$0.659425\pi$
$104$	0	0
$105$	−90.9019	−0.0844868
$106$	738.295	0.676505
$107$	−223.333	−0.201779	−0.100890	−	0.994898i	$-0.532169\pi$
$107$	−223.333	−0.201779	−0.100890	+	0.994898i	$0.532169\pi$
$108$	−269.303	−0.239942
$109$	627.309	0.551242	0.275621	−	0.961266i	$-0.411117\pi$
$109$	627.309	0.551242	0.275621	+	0.961266i	$0.411117\pi$
$110$	406.059	0.351966
$111$	52.8816	0.0452189
$112$	112.000	0.0944911
$113$	−1465.75	−1.22023	−0.610117	−	0.792311i	$-0.708878\pi$
$113$	−1465.75	−1.22023	−0.610117	+	0.792311i	$0.708878\pi$
$114$	44.2224	0.0363316
$115$	−2013.97	−1.63308
$116$	−14.3501	−0.0114859
$117$	0	0
$118$	821.947	0.641240
$119$	−442.771	−0.341082
$120$	103.888	0.0790302
$121$	−926.639	−0.696198
$122$	296.122	0.219751
$123$	41.7817	0.0306287
$124$	244.010	0.176716
$125$	1494.89	1.06966
$126$	354.841	0.250887
$127$	−1622.68	−1.13378	−0.566890	−	0.823794i	$-0.691853\pi$
$127$	−1622.68	−1.13378	−0.566890	+	0.823794i	$0.691853\pi$
$128$	−128.000	−0.0883883
$129$	302.125	0.206206
$130$	0	0
$131$	1276.93	0.851651	0.425826	−	0.904805i	$-0.359984\pi$
$131$	1276.93	0.851651	0.425826	+	0.904805i	$0.359984\pi$
$132$	103.453	0.0682155
$133$	−120.340	−0.0784572
$134$	−91.7726	−0.0591638
$135$	679.761	0.433367
$136$	506.024	0.319053
$137$	−2071.67	−1.29193	−0.645967	−	0.763366i	$-0.723545\pi$
$137$	−2071.67	−1.29193	−0.645967	+	0.763366i	$0.723545\pi$
$138$	−513.108	−0.316512
$139$	755.679	0.461121	0.230560	−	0.973058i	$-0.425944\pi$
$139$	755.679	0.461121	0.230560	+	0.973058i	$0.425944\pi$
$140$	−282.705	−0.170664
$141$	338.321	0.202069
$142$	−1709.80	−1.01045
$143$	0	0
$144$	−405.532	−0.234683
$145$	36.2217	0.0207451
$146$	−915.162	−0.518763
$147$	63.0225	0.0353606
$148$	164.462	0.0913424
$149$	1076.80	0.592049	0.296024	−	0.955180i	$-0.404339\pi$
$149$	1076.80	0.592049	0.296024	+	0.955180i	$0.404339\pi$
$150$	59.3152	0.0322871
$151$	−311.861	−0.168072	−0.0840361	−	0.996463i	$-0.526781\pi$
$151$	−311.861	−0.168072	−0.0840361	+	0.996463i	$0.526781\pi$
$152$	137.531	0.0733900
$153$	1603.19	0.847128
$154$	−281.522	−0.147310
$155$	−615.917	−0.319172
$156$	0	0
$157$	2442.87	1.24180	0.620898	−	0.783891i	$-0.286768\pi$
$157$	2442.87	1.24180	0.620898	+	0.783891i	$0.286768\pi$
$158$	2400.61	1.20875
$159$	−474.788	−0.236812
$160$	323.091	0.159641
$161$	1396.29	0.683499
$162$	−1195.49	−0.579791
$163$	−1633.00	−0.784702	−0.392351	−	0.919815i	$-0.628338\pi$
$163$	−1633.00	−0.784702	−0.392351	+	0.919815i	$0.628338\pi$
$164$	129.941	0.0618701
$165$	−261.131	−0.123206
$166$	−542.978	−0.253875
$167$	−583.144	−0.270210	−0.135105	−	0.990831i	$-0.543137\pi$
$167$	−583.144	−0.270210	−0.135105	+	0.990831i	$0.543137\pi$
$168$	−72.0258	−0.0330768
$169$	0	0
$170$	−1277.28	−0.576252
$171$	435.730	0.194860
$172$	939.608	0.416537
$173$	−3771.82	−1.65761	−0.828803	−	0.559540i	$-0.810978\pi$
$173$	−3771.82	−1.65761	−0.828803	+	0.559540i	$0.810978\pi$
$174$	9.22834	0.00402068
$175$	−161.411	−0.0697231
$176$	321.740	0.137796
$177$	−528.584	−0.224468
$178$	−2365.42	−0.996044
$179$	3393.20	1.41687	0.708435	−	0.705776i	$-0.249401\pi$
$179$	3393.20	1.41687	0.708435	+	0.705776i	$0.249401\pi$
$180$	1023.62	0.423869
$181$	464.782	0.190867	0.0954337	−	0.995436i	$-0.469576\pi$
$181$	464.782	0.190867	0.0954337	+	0.995436i	$0.469576\pi$
$182$	0	0
$183$	−190.432	−0.0769245
$184$	−1595.76	−0.639355
$185$	−415.126	−0.164977
$186$	−156.920	−0.0618597
$187$	−1271.94	−0.497397
$188$	1052.18	0.408180
$189$	−471.280	−0.181379
$190$	−347.150	−0.132552
$191$	−3094.71	−1.17238	−0.586191	−	0.810173i	$-0.699373\pi$
$191$	−3094.71	−1.17238	−0.586191	+	0.810173i	$0.699373\pi$
$192$	82.3152	0.0309405
$193$	1560.11	0.581862	0.290931	−	0.956744i	$-0.406035\pi$
$193$	1560.11	0.581862	0.290931	+	0.956744i	$0.406035\pi$
$194$	−1664.25	−0.615907
$195$	0	0
$196$	196.000	0.0714286
$197$	−4795.28	−1.73426	−0.867131	−	0.498080i	$-0.834039\pi$
$197$	−4795.28	−1.73426	−0.867131	+	0.498080i	$0.834039\pi$
$198$	1019.34	0.365866
$199$	2554.82	0.910084	0.455042	−	0.890470i	$-0.349624\pi$
$199$	2554.82	0.910084	0.455042	+	0.890470i	$0.349624\pi$
$200$	184.470	0.0652200
$201$	59.0178	0.0207104
$202$	1069.51	0.372525
$203$	−25.1126	−0.00868256
$204$	−325.417	−0.111685
$205$	−327.991	−0.111746
$206$	2007.76	0.679063
$207$	−5055.73	−1.69757
$208$	0	0
$209$	−345.698	−0.114413
$210$	181.804	0.0597412
$211$	−4309.86	−1.40618	−0.703088	−	0.711103i	$-0.748196\pi$
$211$	−4309.86	−1.40618	−0.703088	+	0.711103i	$0.748196\pi$
$212$	−1476.59	−0.478361
$213$	1099.55	0.353709
$214$	446.666	0.142680
$215$	−2371.71	−0.752322
$216$	538.606	0.169664
$217$	427.017	0.133584
$218$	−1254.62	−0.389787
$219$	588.529	0.181594
$220$	−812.118	−0.248877
$221$	0	0
$222$	−105.763	−0.0319746
$223$	−6022.44	−1.80849	−0.904243	−	0.427018i	$-0.859564\pi$
$223$	−6022.44	−1.80849	−0.904243	+	0.427018i	$0.859564\pi$
$224$	−224.000	−0.0668153
$225$	584.442	0.173168
$226$	2931.51	0.862836
$227$	5027.42	1.46996	0.734982	−	0.678087i	$-0.237191\pi$
$227$	5027.42	1.46996	0.734982	+	0.678087i	$0.237191\pi$
$228$	−88.4447	−0.0256903
$229$	−1251.97	−0.361279	−0.180639	−	0.983549i	$-0.557817\pi$
$229$	−1251.97	−0.361279	−0.180639	+	0.983549i	$0.557817\pi$
$230$	4027.95	1.15476
$231$	181.043	0.0515661
$232$	28.7001	0.00812179
$233$	−2527.42	−0.710629	−0.355315	−	0.934747i	$-0.615626\pi$
$233$	−2527.42	−0.710629	−0.355315	+	0.934747i	$0.615626\pi$
$234$	0	0
$235$	−2655.85	−0.737228
$236$	−1643.89	−0.453425
$237$	−1543.80	−0.423126
$238$	885.542	0.241181
$239$	2340.32	0.633401	0.316700	−	0.948526i	$-0.397425\pi$
$239$	2340.32	0.633401	0.316700	+	0.948526i	$0.397425\pi$
$240$	−207.776	−0.0558828
$241$	−2052.01	−0.548471	−0.274236	−	0.961663i	$-0.588425\pi$
$241$	−2052.01	−0.548471	−0.274236	+	0.961663i	$0.588425\pi$
$242$	1853.28	0.492286
$243$	2586.60	0.682841
$244$	−592.245	−0.155388
$245$	−494.733	−0.129010
$246$	−83.5634	−0.0216578
$247$	0	0
$248$	−488.020	−0.124957
$249$	349.182	0.0888695
$250$	−2989.78	−0.756361
$251$	−2598.68	−0.653496	−0.326748	−	0.945112i	$-0.605953\pi$
$251$	−2598.68	−0.653496	−0.326748	+	0.945112i	$0.605953\pi$
$252$	−709.681	−0.177404
$253$	4011.10	0.996741
$254$	3245.37	0.801703
$255$	821.402	0.201718
$256$	256.000	0.0625000
$257$	5577.60	1.35378	0.676890	−	0.736084i	$-0.263327\pi$
$257$	5577.60	1.35378	0.676890	+	0.736084i	$0.263327\pi$
$258$	−604.250	−0.145810
$259$	287.808	0.0690484
$260$	0	0
$261$	90.9283	0.0215644
$262$	−2553.87	−0.602208
$263$	3792.97	0.889295	0.444647	−	0.895706i	$-0.353329\pi$
$263$	3792.97	0.889295	0.444647	+	0.895706i	$0.353329\pi$
$264$	−206.907	−0.0482357
$265$	3727.13	0.863984
$266$	240.680	0.0554776
$267$	1521.17	0.348668
$268$	183.545	0.0418351
$269$	8045.89	1.82367	0.911834	−	0.410559i	$-0.134666\pi$
$269$	8045.89	1.82367	0.911834	+	0.410559i	$0.134666\pi$
$270$	−1359.52	−0.306437
$271$	−7606.20	−1.70496	−0.852479	−	0.522761i	$-0.824902\pi$
$271$	−7606.20	−1.70496	−0.852479	+	0.522761i	$0.824902\pi$
$272$	−1012.05	−0.225604
$273$	0	0
$274$	4143.34	0.913535
$275$	−463.682	−0.101677
$276$	1026.22	0.223808
$277$	2593.54	0.562566	0.281283	−	0.959625i	$-0.409240\pi$
$277$	2593.54	0.562566	0.281283	+	0.959625i	$0.409240\pi$
$278$	−1511.36	−0.326062
$279$	−1546.15	−0.331777
$280$	565.409	0.120677
$281$	−4886.24	−1.03733	−0.518663	−	0.854979i	$-0.673570\pi$
$281$	−4886.24	−1.03733	−0.518663	+	0.854979i	$0.673570\pi$
$282$	−676.641	−0.142884
$283$	−6749.94	−1.41782	−0.708908	−	0.705300i	$-0.750812\pi$
$283$	−6749.94	−1.41782	−0.708908	+	0.705300i	$0.750812\pi$
$284$	3419.60	0.714494
$285$	223.248	0.0464002
$286$	0	0
$287$	227.397	0.0467694
$288$	811.064	0.165946
$289$	−912.060	−0.185642
$290$	−72.4434	−0.0146690
$291$	1070.26	0.215600
$292$	1830.32	0.366821
$293$	−6844.98	−1.36481	−0.682403	−	0.730976i	$-0.739065\pi$
$293$	−6844.98	−1.36481	−0.682403	+	0.730976i	$0.739065\pi$
$294$	−126.045	−0.0250037
$295$	4149.43	0.818947
$296$	−328.924	−0.0645888
$297$	−1353.83	−0.264503
$298$	−2153.61	−0.418642
$299$	0	0
$300$	−118.630	−0.0228304
$301$	1644.31	0.314873
$302$	623.722	0.118845
$303$	−687.785	−0.130403
$304$	−275.063	−0.0518946
$305$	1494.91	0.280651
$306$	−3206.39	−0.599010
$307$	1739.96	0.323468	0.161734	−	0.986834i	$-0.448291\pi$
$307$	1739.96	0.323468	0.161734	+	0.986834i	$0.448291\pi$
$308$	563.044	0.104164
$309$	−1291.16	−0.237708
$310$	1231.83	0.225689
$311$	−9225.55	−1.68210	−0.841050	−	0.540958i	$-0.818062\pi$
$311$	−9225.55	−1.68210	−0.841050	+	0.540958i	$0.818062\pi$
$312$	0	0
$313$	−3367.68	−0.608155	−0.304078	−	0.952647i	$-0.598348\pi$
$313$	−3367.68	−0.608155	−0.304078	+	0.952647i	$0.598348\pi$
$314$	−4885.73	−0.878082
$315$	1791.34	0.320415
$316$	−4801.23	−0.854716
$317$	8919.62	1.58036	0.790182	−	0.612872i	$-0.209986\pi$
$317$	8919.62	1.58036	0.790182	+	0.612872i	$0.209986\pi$
$318$	949.576	0.167451
$319$	−72.1403	−0.0126617
$320$	−646.182	−0.112883
$321$	−287.245	−0.0499453
$322$	−2792.59	−0.483307
$323$	1087.41	0.187322
$324$	2390.97	0.409974
$325$	0	0
$326$	3266.00	0.554868
$327$	806.829	0.136446
$328$	−259.882	−0.0437488
$329$	1841.31	0.308555
$330$	522.263	0.0871201
$331$	−1857.79	−0.308499	−0.154250	−	0.988032i	$-0.549296\pi$
$331$	−1857.79	−0.308499	−0.154250	+	0.988032i	$0.549296\pi$
$332$	1085.96	0.179517
$333$	−1042.10	−0.171492
$334$	1166.29	0.191067
$335$	−463.295	−0.0755598
$336$	144.052	0.0233889
$337$	894.541	0.144596	0.0722978	−	0.997383i	$-0.476967\pi$
$337$	894.541	0.144596	0.0722978	+	0.997383i	$0.476967\pi$
$338$	0	0
$339$	−1885.21	−0.302038
$340$	2554.56	0.407472
$341$	1226.68	0.194805
$342$	−871.460	−0.137787
$343$	343.000	0.0539949
$344$	−1879.22	−0.294536
$345$	−2590.32	−0.404226
$346$	7543.63	1.17210
$347$	3743.70	0.579172	0.289586	−	0.957152i	$-0.406482\pi$
$347$	3743.70	0.579172	0.289586	+	0.957152i	$0.406482\pi$
$348$	−18.4567	−0.00284305
$349$	7542.34	1.15683	0.578413	−	0.815744i	$-0.303672\pi$
$349$	7542.34	1.15683	0.578413	+	0.815744i	$0.303672\pi$
$350$	322.823	0.0493017
$351$	0	0
$352$	−643.479	−0.0974362
$353$	10820.7	1.63152	0.815761	−	0.578389i	$-0.196318\pi$
$353$	10820.7	1.63152	0.815761	+	0.578389i	$0.196318\pi$
$354$	1057.17	0.158723
$355$	−8631.59	−1.29047
$356$	4730.84	0.704309
$357$	−569.481	−0.0844261
$358$	−6786.40	−1.00188
$359$	−4757.76	−0.699457	−0.349729	−	0.936851i	$-0.613726\pi$
$359$	−4757.76	−0.699457	−0.349729	+	0.936851i	$0.613726\pi$
$360$	−2047.25	−0.299720
$361$	−6563.45	−0.956911
$362$	−929.564	−0.134964
$363$	−1191.82	−0.172326
$364$	0	0
$365$	−4620.01	−0.662527
$366$	380.865	0.0543938
$367$	1350.57	0.192096	0.0960481	−	0.995377i	$-0.469380\pi$
$367$	1350.57	0.192096	0.0960481	+	0.995377i	$0.469380\pi$
$368$	3191.53	0.452092
$369$	−823.364	−0.116159
$370$	830.252	0.116656
$371$	−2584.03	−0.361607
$372$	313.839	0.0437414
$373$	−9024.75	−1.25277	−0.626386	−	0.779513i	$-0.715466\pi$
$373$	−9024.75	−1.25277	−0.626386	+	0.779513i	$0.715466\pi$
$374$	2543.87	0.351713
$375$	1922.69	0.264766
$376$	−2104.35	−0.288627
$377$	0	0
$378$	942.561	0.128254
$379$	−4574.02	−0.619925	−0.309963	−	0.950749i	$-0.600317\pi$
$379$	−4574.02	−0.619925	−0.309963	+	0.950749i	$0.600317\pi$
$380$	694.300	0.0937285
$381$	−2087.05	−0.280638
$382$	6189.41	0.829000
$383$	−5952.75	−0.794181	−0.397091	−	0.917779i	$-0.629980\pi$
$383$	−5952.75	−0.794181	−0.397091	+	0.917779i	$0.629980\pi$
$384$	−164.630	−0.0218783
$385$	−1421.21	−0.188134
$386$	−3120.22	−0.411438
$387$	−5953.77	−0.782034
$388$	3328.49	0.435512
$389$	3307.15	0.431051	0.215526	−	0.976498i	$-0.430853\pi$
$389$	3307.15	0.431051	0.215526	+	0.976498i	$0.430853\pi$
$390$	0	0
$391$	−12617.1	−1.63190
$392$	−392.000	−0.0505076
$393$	1642.36	0.210804
$394$	9590.56	1.22631
$395$	12119.0	1.54373
$396$	−2038.68	−0.258706
$397$	−13605.7	−1.72003	−0.860013	−	0.510271i	$-0.829545\pi$
$397$	−13605.7	−1.72003	−0.860013	+	0.510271i	$0.829545\pi$
$398$	−5109.65	−0.643527
$399$	−154.778	−0.0194201
$400$	−368.940	−0.0461175
$401$	267.509	0.0333136	0.0166568	−	0.999861i	$-0.494698\pi$
$401$	267.509	0.0333136	0.0166568	+	0.999861i	$0.494698\pi$
$402$	−118.036	−0.0146445
$403$	0	0
$404$	−2139.01	−0.263415
$405$	−6035.17	−0.740469
$406$	50.2252	0.00613949
$407$	826.779	0.100693
$408$	650.835	0.0789734
$409$	−51.9055	−0.00627522	−0.00313761	−	0.999995i	$-0.500999\pi$
$409$	−51.9055	−0.00627522	−0.00313761	+	0.999995i	$0.500999\pi$
$410$	655.981	0.0790161
$411$	−2664.53	−0.319785
$412$	−4015.51	−0.480170
$413$	−2876.81	−0.342757
$414$	10111.5	1.20036
$415$	−2741.11	−0.324231
$416$	0	0
$417$	971.934	0.114139
$418$	691.396	0.0809025
$419$	−2053.19	−0.239391	−0.119695	−	0.992811i	$-0.538192\pi$
$419$	−2053.19	−0.239391	−0.119695	+	0.992811i	$0.538192\pi$
$420$	−363.607	−0.0422434
$421$	−5807.91	−0.672352	−0.336176	−	0.941799i	$-0.609134\pi$
$421$	−5807.91	−0.672352	−0.336176	+	0.941799i	$0.609134\pi$
$422$	8619.72	0.994316
$423$	−6667.05	−0.766343
$424$	2953.18	0.338252
$425$	1458.54	0.166469
$426$	−2199.10	−0.250110
$427$	−1036.43	−0.117462
$428$	−893.331	−0.100890
$429$	0	0
$430$	4743.42	0.531972
$431$	−1341.49	−0.149924	−0.0749620	−	0.997186i	$-0.523884\pi$
$431$	−1341.49	−0.149924	−0.0749620	+	0.997186i	$0.523884\pi$
$432$	−1077.21	−0.119971
$433$	−8216.08	−0.911869	−0.455935	−	0.890013i	$-0.650695\pi$
$433$	−8216.08	−0.911869	−0.455935	+	0.890013i	$0.650695\pi$
$434$	−854.035	−0.0944585
$435$	46.5874	0.00513493
$436$	2509.24	0.275621
$437$	−3429.18	−0.375378
$438$	−1177.06	−0.128406
$439$	−16733.8	−1.81928	−0.909638	−	0.415402i	$-0.863641\pi$
$439$	−16733.8	−1.81928	−0.909638	+	0.415402i	$0.863641\pi$
$440$	1624.24	0.175983
$441$	−1241.94	−0.134105
$442$	0	0
$443$	−9550.55	−1.02429	−0.512145	−	0.858899i	$-0.671149\pi$
$443$	−9550.55	−1.02429	−0.512145	+	0.858899i	$0.671149\pi$
$444$	211.526	0.0226095
$445$	−11941.4	−1.27208
$446$	12044.9	1.27879
$447$	1384.96	0.146546
$448$	448.000	0.0472456
$449$	−4799.99	−0.504511	−0.252255	−	0.967661i	$-0.581172\pi$
$449$	−4799.99	−0.504511	−0.252255	+	0.967661i	$0.581172\pi$
$450$	−1168.88	−0.122448
$451$	653.237	0.0682034
$452$	−5863.02	−0.610117
$453$	−401.108	−0.0416020
$454$	−10054.8	−1.03942
$455$	0	0
$456$	176.889	0.0181658
$457$	−10085.4	−1.03233	−0.516167	−	0.856488i	$-0.672642\pi$
$457$	−10085.4	−1.03233	−0.516167	+	0.856488i	$0.672642\pi$
$458$	2503.95	0.255463
$459$	4258.56	0.433055
$460$	−8055.89	−0.816539
$461$	1186.34	0.119855	0.0599277	−	0.998203i	$-0.480913\pi$
$461$	1186.34	0.119855	0.0599277	+	0.998203i	$0.480913\pi$
$462$	−362.086	−0.0364627
$463$	8088.41	0.811880	0.405940	−	0.913900i	$-0.366944\pi$
$463$	8088.41	0.811880	0.405940	+	0.913900i	$0.366944\pi$
$464$	−57.4002	−0.00574297
$465$	−792.177	−0.0790028
$466$	5054.84	0.502491
$467$	6613.77	0.655351	0.327676	−	0.944790i	$-0.393735\pi$
$467$	6613.77	0.655351	0.327676	+	0.944790i	$0.393735\pi$
$468$	0	0
$469$	321.204	0.0316244
$470$	5311.70	0.521299
$471$	3141.95	0.307375
$472$	3287.79	0.320620
$473$	4723.58	0.459176
$474$	3087.61	0.299195
$475$	396.413	0.0382920
$476$	−1771.08	−0.170541
$477$	9356.32	0.898106
$478$	−4680.64	−0.447882
$479$	70.4349	0.00671869	0.00335934	−	0.999994i	$-0.498931\pi$
$479$	70.4349	0.00671869	0.00335934	+	0.999994i	$0.498931\pi$
$480$	415.551	0.0395151
$481$	0	0
$482$	4104.02	0.387828
$483$	1795.88	0.169183
$484$	−3706.56	−0.348099
$485$	−8401.62	−0.786593
$486$	−5173.19	−0.482841
$487$	−9403.87	−0.875011	−0.437505	−	0.899216i	$-0.644138\pi$
$487$	−9403.87	−0.875011	−0.437505	+	0.899216i	$0.644138\pi$
$488$	1184.49	0.109876
$489$	−2100.32	−0.194233
$490$	989.466	0.0912235
$491$	−9385.96	−0.862694	−0.431347	−	0.902186i	$-0.641961\pi$
$491$	−9385.96	−0.862694	−0.431347	+	0.902186i	$0.641961\pi$
$492$	167.127	0.0153144
$493$	226.921	0.0207302
$494$	0	0
$495$	5145.94	0.467258
$496$	976.039	0.0883578
$497$	5984.31	0.540106
$498$	−698.364	−0.0628402
$499$	757.562	0.0679622	0.0339811	−	0.999422i	$-0.489181\pi$
$499$	757.562	0.0679622	0.0339811	+	0.999422i	$0.489181\pi$
$500$	5979.56	0.534828
$501$	−750.024	−0.0668835
$502$	5197.37	0.462091
$503$	−8692.50	−0.770535	−0.385268	−	0.922805i	$-0.625891\pi$
$503$	−8692.50	−0.770535	−0.385268	+	0.922805i	$0.625891\pi$
$504$	1419.36	0.125443
$505$	5399.18	0.475763
$506$	−8022.19	−0.704802
$507$	0	0
$508$	−6490.74	−0.566890
$509$	−17169.2	−1.49511	−0.747557	−	0.664197i	$-0.768773\pi$
$509$	−17169.2	−1.49511	−0.747557	+	0.664197i	$0.768773\pi$
$510$	−1642.80	−0.142636
$511$	3203.07	0.277290
$512$	−512.000	−0.0441942
$513$	1157.43	0.0996133
$514$	−11155.2	−0.957267
$515$	10135.7	0.867251
$516$	1208.50	0.103103
$517$	5289.48	0.449964
$518$	−575.616	−0.0488246
$519$	−4851.21	−0.410298
$520$	0	0
$521$	−2635.94	−0.221656	−0.110828	−	0.993840i	$-0.535350\pi$
$521$	−2635.94	−0.221656	−0.110828	+	0.993840i	$0.535350\pi$
$522$	−181.857	−0.0152484
$523$	−4967.76	−0.415344	−0.207672	−	0.978199i	$-0.566589\pi$
$523$	−4967.76	−0.415344	−0.207672	+	0.978199i	$0.566589\pi$
$524$	5107.74	0.425826
$525$	−207.603	−0.0172582
$526$	−7585.94	−0.628826
$527$	−3858.59	−0.318943
$528$	413.813	0.0341078
$529$	27621.5	2.27020
$530$	−7454.26	−0.610929
$531$	10416.4	0.851290
$532$	−481.360	−0.0392286
$533$	0	0
$534$	−3042.34	−0.246545
$535$	2254.90	0.182220
$536$	−367.090	−0.0295819
$537$	4364.25	0.350710
$538$	−16091.8	−1.28953
$539$	985.327	0.0787404
$540$	2719.04	0.216683
$541$	−22793.4	−1.81140	−0.905698	−	0.423924i	$-0.860652\pi$
$541$	−22793.4	−1.81140	−0.905698	+	0.423924i	$0.860652\pi$
$542$	15212.4	1.20559
$543$	597.791	0.0472443
$544$	2024.10	0.159526
$545$	−6333.69	−0.497808
$546$	0	0
$547$	−18297.3	−1.43023	−0.715115	−	0.699006i	$-0.753626\pi$
$547$	−18297.3	−1.43023	−0.715115	+	0.699006i	$0.753626\pi$
$548$	−8286.69	−0.645967
$549$	3752.72	0.291735
$550$	927.364	0.0718963
$551$	61.6745	0.00476846
$552$	−2052.43	−0.158256
$553$	−8402.15	−0.646104
$554$	−5187.08	−0.397794
$555$	−533.924	−0.0408357
$556$	3022.71	0.230560
$557$	−20224.0	−1.53845	−0.769225	−	0.638978i	$-0.779358\pi$
$557$	−20224.0	−1.53845	−0.769225	+	0.638978i	$0.779358\pi$
$558$	3092.31	0.234602
$559$	0	0
$560$	−1130.82	−0.0853318
$561$	−1635.93	−0.123118
$562$	9772.48	0.733500
$563$	−11421.3	−0.854975	−0.427488	−	0.904021i	$-0.640601\pi$
$563$	−11421.3	−0.854975	−0.427488	+	0.904021i	$0.640601\pi$
$564$	1353.28	0.101035
$565$	14799.1	1.10195
$566$	13499.9	1.00255
$567$	4184.20	0.309912
$568$	−6839.21	−0.505223
$569$	8897.20	0.655518	0.327759	−	0.944761i	$-0.393707\pi$
$569$	8897.20	0.655518	0.327759	+	0.944761i	$0.393707\pi$
$570$	−446.495	−0.0328099
$571$	4705.87	0.344894	0.172447	−	0.985019i	$-0.444833\pi$
$571$	4705.87	0.344894	0.172447	+	0.985019i	$0.444833\pi$
$572$	0	0
$573$	−3980.33	−0.290193
$574$	−454.794	−0.0330710
$575$	−4599.54	−0.333590
$576$	−1622.13	−0.117341
$577$	2764.45	0.199455	0.0997275	−	0.995015i	$-0.468203\pi$
$577$	2764.45	0.199455	0.0997275	+	0.995015i	$0.468203\pi$
$578$	1824.12	0.131269
$579$	2006.58	0.144025
$580$	144.887	0.0103726
$581$	1900.42	0.135702
$582$	−2140.51	−0.152452
$583$	−7423.08	−0.527329
$584$	−3660.65	−0.259381
$585$	0	0
$586$	13690.0	0.965063
$587$	6635.35	0.466559	0.233280	−	0.972410i	$-0.425054\pi$
$587$	6635.35	0.466559	0.233280	+	0.972410i	$0.425054\pi$
$588$	252.090	0.0176803
$589$	−1048.72	−0.0733646
$590$	−8298.87	−0.579083
$591$	−6167.57	−0.429272
$592$	657.847	0.0456712
$593$	25268.7	1.74985	0.874925	−	0.484258i	$-0.160910\pi$
$593$	25268.7	1.74985	0.874925	+	0.484258i	$0.160910\pi$
$594$	2707.67	0.187032
$595$	4470.48	0.308020
$596$	4307.22	0.296024
$597$	3285.95	0.225268
$598$	0	0
$599$	−2579.57	−0.175957	−0.0879787	−	0.996122i	$-0.528041\pi$
$599$	−2579.57	−0.175957	−0.0879787	+	0.996122i	$0.528041\pi$
$600$	237.261	0.0161435
$601$	16399.7	1.11307	0.556537	−	0.830823i	$-0.312130\pi$
$601$	16399.7	1.11307	0.556537	+	0.830823i	$0.312130\pi$
$602$	−3288.63	−0.222649
$603$	−1163.02	−0.0785439
$604$	−1247.44	−0.0840361
$605$	9355.90	0.628713
$606$	1375.57	0.0922091
$607$	−19956.6	−1.33445	−0.667227	−	0.744855i	$-0.732519\pi$
$607$	−19956.6	−1.33445	−0.667227	+	0.744855i	$0.732519\pi$
$608$	550.126	0.0366950
$609$	−32.2992	−0.00214914
$610$	−2989.83	−0.198450
$611$	0	0
$612$	6412.78	0.423564
$613$	−20630.8	−1.35933	−0.679665	−	0.733522i	$-0.737875\pi$
$613$	−20630.8	−1.35933	−0.679665	+	0.733522i	$0.737875\pi$
$614$	−3479.92	−0.228727
$615$	−421.853	−0.0276598
$616$	−1126.09	−0.0736549
$617$	17517.8	1.14301	0.571507	−	0.820597i	$-0.306359\pi$
$617$	17517.8	1.14301	0.571507	+	0.820597i	$0.306359\pi$
$618$	2582.32	0.168085
$619$	−5315.91	−0.345177	−0.172589	−	0.984994i	$-0.555213\pi$
$619$	−5315.91	−0.345177	−0.172589	+	0.984994i	$0.555213\pi$
$620$	−2463.67	−0.159586
$621$	−13429.5	−0.867806
$622$	18451.1	1.18942
$623$	8278.98	0.532408
$624$	0	0
$625$	−12210.9	−0.781501
$626$	6735.36	0.430031
$627$	−444.628	−0.0283201
$628$	9771.47	0.620898
$629$	−2600.67	−0.164858
$630$	−3582.68	−0.226567
$631$	−17829.3	−1.12484	−0.562420	−	0.826852i	$-0.690130\pi$
$631$	−17829.3	−1.12484	−0.562420	+	0.826852i	$0.690130\pi$
$632$	9602.45	0.604375
$633$	−5543.23	−0.348063
$634$	−17839.2	−1.11749
$635$	16383.6	1.02388
$636$	−1899.15	−0.118406
$637$	0	0
$638$	144.281	0.00895317
$639$	−21668.1	−1.34144
$640$	1292.36	0.0798206
$641$	−25756.8	−1.58710	−0.793550	−	0.608505i	$-0.791770\pi$
$641$	−25756.8	−1.58710	−0.793550	+	0.608505i	$0.791770\pi$
$642$	574.490	0.0353167
$643$	−22080.1	−1.35421	−0.677104	−	0.735888i	$-0.736765\pi$
$643$	−22080.1	−1.35421	−0.677104	+	0.735888i	$0.736765\pi$
$644$	5585.17	0.341749
$645$	−3050.43	−0.186218
$646$	−2174.82	−0.132457
$647$	18439.2	1.12043	0.560216	−	0.828347i	$-0.310718\pi$
$647$	18439.2	1.12043	0.560216	+	0.828347i	$0.310718\pi$
$648$	−4781.94	−0.289896
$649$	−8264.15	−0.499840
$650$	0	0
$651$	549.219	0.0330654
$652$	−6532.00	−0.392351
$653$	−16124.1	−0.966284	−0.483142	−	0.875542i	$-0.660505\pi$
$653$	−16124.1	−0.966284	−0.483142	+	0.875542i	$0.660505\pi$
$654$	−1613.66	−0.0964817
$655$	−12892.7	−0.769098
$656$	519.764	0.0309350
$657$	−11597.7	−0.688692
$658$	−3682.62	−0.218182
$659$	−3810.64	−0.225252	−0.112626	−	0.993637i	$-0.535926\pi$
$659$	−3810.64	−0.225252	−0.112626	+	0.993637i	$0.535926\pi$
$660$	−1044.53	−0.0616032
$661$	−16914.1	−0.995285	−0.497642	−	0.867382i	$-0.665801\pi$
$661$	−16914.1	−0.995285	−0.497642	+	0.867382i	$0.665801\pi$
$662$	3715.58	0.218142
$663$	0	0
$664$	−2171.91	−0.126937
$665$	1215.02	0.0708521
$666$	2084.20	0.121263
$667$	−715.603	−0.0415416
$668$	−2332.57	−0.135105
$669$	−7745.91	−0.447644
$670$	926.591	0.0534288
$671$	−2977.32	−0.171294
$672$	−288.103	−0.0165384
$673$	13683.4	0.783736	0.391868	−	0.920021i	$-0.371829\pi$
$673$	13683.4	0.783736	0.391868	+	0.920021i	$0.371829\pi$
$674$	−1789.08	−0.102245
$675$	1552.45	0.0885241
$676$	0	0
$677$	13672.6	0.776187	0.388094	−	0.921620i	$-0.373134\pi$
$677$	13672.6	0.776187	0.388094	+	0.921620i	$0.373134\pi$
$678$	3770.43	0.213573
$679$	5824.87	0.329216
$680$	−5109.12	−0.288126
$681$	6466.14	0.363852
$682$	−2453.36	−0.137748
$683$	−22577.7	−1.26488	−0.632439	−	0.774611i	$-0.717946\pi$
$683$	−22577.7	−1.26488	−0.632439	+	0.774611i	$0.717946\pi$
$684$	1742.92	0.0974301
$685$	20916.8	1.16670
$686$	−686.000	−0.0381802
$687$	−1610.26	−0.0894253
$688$	3758.43	0.208269
$689$	0	0
$690$	5180.64	0.285831
$691$	24591.0	1.35382	0.676908	−	0.736067i	$-0.263319\pi$
$691$	24591.0	1.35382	0.676908	+	0.736067i	$0.263319\pi$
$692$	−15087.3	−0.828803
$693$	−3567.69	−0.195564
$694$	−7487.41	−0.409536
$695$	−7629.78	−0.416423
$696$	36.9133	0.00201034
$697$	−2054.79	−0.111665
$698$	−15084.7	−0.817999
$699$	−3250.70	−0.175898
$700$	−645.645	−0.0348616
$701$	31427.9	1.69332	0.846658	−	0.532137i	$-0.178611\pi$
$701$	31427.9	1.69332	0.846658	+	0.532137i	$0.178611\pi$
$702$	0	0
$703$	−706.833	−0.0379214
$704$	1286.96	0.0688978
$705$	−3415.89	−0.182482
$706$	−21641.4	−1.15366
$707$	−3743.27	−0.199123
$708$	−2114.33	−0.112234
$709$	28442.3	1.50659	0.753295	−	0.657683i	$-0.228463\pi$
$709$	28442.3	1.50659	0.753295	+	0.657683i	$0.228463\pi$
$710$	17263.2	0.912501
$711$	30422.7	1.60470
$712$	−9461.69	−0.498022
$713$	12168.2	0.639134
$714$	1138.96	0.0596982
$715$	0	0
$716$	13572.8	0.708435
$717$	3010.06	0.156782
$718$	9515.53	0.494591
$719$	−4213.94	−0.218572	−0.109286	−	0.994010i	$-0.534856\pi$
$719$	−4213.94	−0.218572	−0.109286	+	0.994010i	$0.534856\pi$
$720$	4094.49	0.211934
$721$	−7027.15	−0.362974
$722$	13126.9	0.676638
$723$	−2639.24	−0.135760
$724$	1859.13	0.0954337
$725$	82.7236	0.00423763
$726$	2383.64	0.121853
$727$	−9573.02	−0.488368	−0.244184	−	0.969729i	$-0.578520\pi$
$727$	−9573.02	−0.488368	−0.244184	+	0.969729i	$0.578520\pi$
$728$	0	0
$729$	−12812.2	−0.650929
$730$	9240.02	0.468478
$731$	−14858.3	−0.751782
$732$	−761.730	−0.0384622
$733$	−28072.8	−1.41459	−0.707293	−	0.706920i	$-0.750084\pi$
$733$	−28072.8	−1.41459	−0.707293	+	0.706920i	$0.750084\pi$
$734$	−2701.14	−0.135832
$735$	−636.313	−0.0319330
$736$	−6383.05	−0.319677
$737$	922.715	0.0461175
$738$	1646.73	0.0821367
$739$	−28350.3	−1.41121	−0.705604	−	0.708607i	$-0.749324\pi$
$739$	−28350.3	−1.41121	−0.705604	+	0.708607i	$0.749324\pi$
$740$	−1660.50	−0.0824883
$741$	0	0
$742$	5168.06	0.255695
$743$	12951.7	0.639503	0.319752	−	0.947501i	$-0.396401\pi$
$743$	12951.7	0.639503	0.319752	+	0.947501i	$0.396401\pi$
$744$	−627.678	−0.0309298
$745$	−10872.1	−0.534660
$746$	18049.5	0.885843
$747$	−6881.09	−0.337036
$748$	−5087.75	−0.248698
$749$	−1563.33	−0.0762655
$750$	−3845.38	−0.187218
$751$	32145.1	1.56191	0.780953	−	0.624589i	$-0.214734\pi$
$751$	32145.1	1.56191	0.780953	+	0.624589i	$0.214734\pi$
$752$	4208.71	0.204090
$753$	−3342.36	−0.161756
$754$	0	0
$755$	3148.74	0.151780
$756$	−1885.12	−0.0906894
$757$	19847.0	0.952906	0.476453	−	0.879200i	$-0.341922\pi$
$757$	19847.0	0.952906	0.476453	+	0.879200i	$0.341922\pi$
$758$	9148.04	0.438353
$759$	5158.97	0.246718
$760$	−1388.60	−0.0662761
$761$	−10596.0	−0.504739	−0.252369	−	0.967631i	$-0.581210\pi$
$761$	−10596.0	−0.504739	−0.252369	+	0.967631i	$0.581210\pi$
$762$	4174.11	0.198441
$763$	4391.16	0.208350
$764$	−12378.8	−0.586191
$765$	−16186.8	−0.765013
$766$	11905.5	0.561571
$767$	0	0
$768$	329.261	0.0154703
$769$	17945.5	0.841521	0.420761	−	0.907172i	$-0.361763\pi$
$769$	17945.5	0.841521	0.420761	+	0.907172i	$0.361763\pi$
$770$	2842.41	0.133031
$771$	7173.77	0.335093
$772$	6240.45	0.290931
$773$	4840.84	0.225243	0.112622	−	0.993638i	$-0.464075\pi$
$773$	4840.84	0.225243	0.112622	+	0.993638i	$0.464075\pi$
$774$	11907.5	0.552981
$775$	−1406.64	−0.0651975
$776$	−6656.99	−0.307954
$777$	370.171	0.0170911
$778$	−6614.29	−0.304799
$779$	−558.469	−0.0256858
$780$	0	0
$781$	17191.0	0.787633
$782$	25234.2	1.15393
$783$	241.532	0.0110238
$784$	784.000	0.0357143
$785$	−24664.6	−1.12142
$786$	−3284.72	−0.149061
$787$	2308.39	0.104556	0.0522778	−	0.998633i	$-0.483352\pi$
$787$	2308.39	0.104556	0.0522778	+	0.998633i	$0.483352\pi$
$788$	−19181.1	−0.867131
$789$	4878.42	0.220122
$790$	−24238.0	−1.09158
$791$	−10260.3	−0.461205
$792$	4077.37	0.182933
$793$	0	0
$794$	27211.4	1.21624
$795$	4793.74	0.213857
$796$	10219.3	0.455042
$797$	12168.7	0.540826	0.270413	−	0.962744i	$-0.412840\pi$
$797$	12168.7	0.540826	0.270413	+	0.962744i	$0.412840\pi$
$798$	309.557	0.0137321
$799$	−16638.3	−0.736698
$800$	737.880	0.0326100
$801$	−29976.7	−1.32232
$802$	−535.017	−0.0235563
$803$	9201.37	0.404370
$804$	236.071	0.0103552
$805$	−14097.8	−0.617245
$806$	0	0
$807$	10348.4	0.451402
$808$	4278.02	0.186263
$809$	−4400.44	−0.191237	−0.0956187	−	0.995418i	$-0.530483\pi$
$809$	−4400.44	−0.191237	−0.0956187	+	0.995418i	$0.530483\pi$
$810$	12070.3	0.523590
$811$	4690.58	0.203093	0.101547	−	0.994831i	$-0.467621\pi$
$811$	4690.58	0.203093	0.101547	+	0.994831i	$0.467621\pi$
$812$	−100.450	−0.00434128
$813$	−9782.90	−0.422019
$814$	−1653.56	−0.0712004
$815$	16487.7	0.708639
$816$	−1301.67	−0.0558426
$817$	−4038.30	−0.172928
$818$	103.811	0.00443725
$819$	0	0
$820$	−1311.96	−0.0558728
$821$	−15023.4	−0.638638	−0.319319	−	0.947647i	$-0.603454\pi$
$821$	−15023.4	−0.638638	−0.319319	+	0.947647i	$0.603454\pi$
$822$	5329.06	0.226122
$823$	−10720.4	−0.454057	−0.227028	−	0.973888i	$-0.572901\pi$
$823$	−10720.4	−0.454057	−0.227028	+	0.973888i	$0.572901\pi$
$824$	8031.02	0.339532
$825$	−596.376	−0.0251675
$826$	5753.63	0.242366
$827$	−29565.5	−1.24316	−0.621579	−	0.783352i	$-0.713508\pi$
$827$	−29565.5	−1.24316	−0.621579	+	0.783352i	$0.713508\pi$
$828$	−20222.9	−0.848786
$829$	31645.4	1.32580	0.662901	−	0.748707i	$-0.269325\pi$
$829$	31645.4	1.32580	0.662901	+	0.748707i	$0.269325\pi$
$830$	5482.23	0.229266
$831$	3335.75	0.139249
$832$	0	0
$833$	−3099.40	−0.128917
$834$	−1943.87	−0.0807082
$835$	5887.76	0.244017
$836$	−1382.79	−0.0572067
$837$	−4107.04	−0.169606
$838$	4106.37	0.169275
$839$	15062.8	0.619817	0.309909	−	0.950766i	$-0.399702\pi$
$839$	15062.8	0.619817	0.309909	+	0.950766i	$0.399702\pi$
$840$	727.215	0.0298706
$841$	−24376.1	−0.999472
$842$	11615.8	0.475424
$843$	−6284.56	−0.256763
$844$	−17239.4	−0.703088
$845$	0	0
$846$	13334.1	0.541887
$847$	−6486.48	−0.263138
$848$	−5906.36	−0.239181
$849$	−8681.60	−0.350944
$850$	−2917.07	−0.117711
$851$	8201.32	0.330361
$852$	4398.21	0.176855
$853$	28710.1	1.15242	0.576210	−	0.817302i	$-0.304531\pi$
$853$	28710.1	1.15242	0.576210	+	0.817302i	$0.304531\pi$
$854$	2072.86	0.0830582
$855$	−4399.39	−0.175972
$856$	1786.66	0.0713398
$857$	−4657.93	−0.185661	−0.0928307	−	0.995682i	$-0.529592\pi$
$857$	−4657.93	−0.185661	−0.0928307	+	0.995682i	$0.529592\pi$
$858$	0	0
$859$	−46811.9	−1.85937	−0.929687	−	0.368351i	$-0.879922\pi$
$859$	−46811.9	−1.85937	−0.929687	+	0.368351i	$0.879922\pi$
$860$	−9486.84	−0.376161
$861$	292.472	0.0115766
$862$	2682.98	0.106012
$863$	27491.0	1.08436	0.542181	−	0.840262i	$-0.317599\pi$
$863$	27491.0	1.08436	0.542181	+	0.840262i	$0.317599\pi$
$864$	2154.42	0.0848322
$865$	38082.5	1.49693
$866$	16432.2	0.644789
$867$	−1173.07	−0.0459509
$868$	1708.07	0.0667922
$869$	−24136.6	−0.942209
$870$	−93.1748	−0.00363094
$871$	0	0
$872$	−5018.47	−0.194893
$873$	−21090.8	−0.817658
$874$	6858.37	0.265432
$875$	10464.2	0.404292
$876$	2354.12	0.0907971
$877$	−7751.91	−0.298476	−0.149238	−	0.988801i	$-0.547682\pi$
$877$	−7751.91	−0.298476	−0.149238	+	0.988801i	$0.547682\pi$
$878$	33467.7	1.28642
$879$	−8803.84	−0.337823
$880$	−3248.47	−0.124439
$881$	12398.8	0.474150	0.237075	−	0.971491i	$-0.423811\pi$
$881$	12398.8	0.474150	0.237075	+	0.971491i	$0.423811\pi$
$882$	2483.88	0.0948262
$883$	42621.6	1.62438	0.812192	−	0.583390i	$-0.198274\pi$
$883$	42621.6	1.62438	0.812192	+	0.583390i	$0.198274\pi$
$884$	0	0
$885$	5336.89	0.202709
$886$	19101.1	0.724282
$887$	−19752.4	−0.747713	−0.373856	−	0.927487i	$-0.621965\pi$
$887$	−19752.4	−0.747713	−0.373856	+	0.927487i	$0.621965\pi$
$888$	−423.053	−0.0159873
$889$	−11358.8	−0.428528
$890$	23882.7	0.899494
$891$	12019.8	0.451941
$892$	−24089.8	−0.904243
$893$	−4522.11	−0.169459
$894$	−2769.92	−0.103624
$895$	−34259.8	−1.27953
$896$	−896.000	−0.0334077
$897$	0	0
$898$	9599.97	0.356743
$899$	−218.847	−0.00811898
$900$	2337.77	0.0865840
$901$	23349.7	0.863363
$902$	−1306.47	−0.0482271
$903$	2114.87	0.0779387
$904$	11726.0	0.431418
$905$	−4692.72	−0.172366
$906$	802.216	0.0294170
$907$	43586.8	1.59567	0.797837	−	0.602873i	$-0.205977\pi$
$907$	43586.8	1.59567	0.797837	+	0.602873i	$0.205977\pi$
$908$	20109.7	0.734982
$909$	13553.7	0.494552
$910$	0	0
$911$	−40214.4	−1.46253	−0.731263	−	0.682095i	$-0.761069\pi$
$911$	−40214.4	−1.46253	−0.731263	+	0.682095i	$0.761069\pi$
$912$	−353.779	−0.0128452
$913$	5459.29	0.197893
$914$	20170.9	0.729971
$915$	1922.72	0.0694679
$916$	−5007.90	−0.180639
$917$	8938.54	0.321894
$918$	−8517.11	−0.306216
$919$	1088.55	0.0390727	0.0195364	−	0.999809i	$-0.493781\pi$
$919$	1088.55	0.0390727	0.0195364	+	0.999809i	$0.493781\pi$
$920$	16111.8	0.577380
$921$	2237.89	0.0800662
$922$	−2372.68	−0.0847506
$923$	0	0
$924$	724.173	0.0257831
$925$	−948.071	−0.0336999
$926$	−16176.8	−0.574086
$927$	25444.0	0.901502
$928$	114.800	0.00406089
$929$	42990.0	1.51825	0.759126	−	0.650944i	$-0.225627\pi$
$929$	42990.0	1.51825	0.759126	+	0.650944i	$0.225627\pi$
$930$	1584.35	0.0558634
$931$	−842.380	−0.0296540
$932$	−10109.7	−0.355315
$933$	−11865.7	−0.416361
$934$	−13227.5	−0.463403
$935$	12842.2	0.449183
$936$	0	0
$937$	−1310.49	−0.0456903	−0.0228451	−	0.999739i	$-0.507272\pi$
$937$	−1310.49	−0.0456903	−0.0228451	+	0.999739i	$0.507272\pi$
$938$	−642.408	−0.0223618
$939$	−4331.43	−0.150533
$940$	−10623.4	−0.368614
$941$	34271.0	1.18725	0.593626	−	0.804741i	$-0.297696\pi$
$941$	34271.0	1.18725	0.593626	+	0.804741i	$0.297696\pi$
$942$	−6283.90	−0.217347
$943$	6479.85	0.223768
$944$	−6575.58	−0.226713
$945$	4758.33	0.163797
$946$	−9447.16	−0.324687
$947$	3275.78	0.112406	0.0562030	−	0.998419i	$-0.482101\pi$
$947$	3275.78	0.112406	0.0562030	+	0.998419i	$0.482101\pi$
$948$	−6175.22	−0.211563
$949$	0	0
$950$	−792.826	−0.0270765
$951$	11472.2	0.391179
$952$	3542.17	0.120591
$953$	12804.0	0.435217	0.217608	−	0.976036i	$-0.430174\pi$
$953$	12804.0	0.435217	0.217608	+	0.976036i	$0.430174\pi$
$954$	−18712.6	−0.635057
$955$	31246.0	1.05874
$956$	9361.29	0.316700
$957$	−92.7850	−0.00313408
$958$	−140.870	−0.00475083
$959$	−14501.7	−0.488305
$960$	−831.103	−0.0279414
$961$	−26069.7	−0.875086
$962$	0	0
$963$	5660.54	0.189417
$964$	−8208.04	−0.274236
$965$	−15751.8	−0.525460
$966$	−3591.75	−0.119630
$967$	33358.1	1.10933	0.554667	−	0.832073i	$-0.312846\pi$
$967$	33358.1	1.10933	0.554667	+	0.832073i	$0.312846\pi$
$968$	7413.12	0.246143
$969$	1398.60	0.0463668
$970$	16803.2	0.556205
$971$	−29682.0	−0.980988	−0.490494	−	0.871445i	$-0.663184\pi$
$971$	−29682.0	−0.980988	−0.490494	+	0.871445i	$0.663184\pi$
$972$	10346.4	0.341420
$973$	5289.75	0.174287
$974$	18807.7	0.618726
$975$	0	0
$976$	−2368.98	−0.0776938
$977$	15783.2	0.516836	0.258418	−	0.966033i	$-0.416799\pi$
$977$	15783.2	0.516836	0.258418	+	0.966033i	$0.416799\pi$
$978$	4200.65	0.137343
$979$	23782.8	0.776406
$980$	−1978.93	−0.0645048
$981$	−15899.6	−0.517468
$982$	18771.9	0.610016
$983$	48753.0	1.58187	0.790935	−	0.611901i	$-0.209595\pi$
$983$	48753.0	1.58187	0.790935	+	0.611901i	$0.209595\pi$
$984$	−334.254	−0.0108289
$985$	48416.0	1.56616
$986$	−453.842	−0.0146585
$987$	2368.24	0.0763749
$988$	0	0
$989$	46856.0	1.50651
$990$	−10291.9	−0.330401
$991$	54660.8	1.75213	0.876063	−	0.482196i	$-0.160161\pi$
$991$	54660.8	1.75213	0.876063	+	0.482196i	$0.160161\pi$
$992$	−1952.08	−0.0624784
$993$	−2389.44	−0.0763611
$994$	−11968.6	−0.381913
$995$	−25795.0	−0.821867
$996$	1396.73	0.0444348
$997$	−52523.4	−1.66844	−0.834220	−	0.551432i	$-0.814082\pi$
$997$	−52523.4	−1.66844	−0.834220	+	0.551432i	$0.814082\pi$
$998$	−1515.12	−0.0480565
$999$	−2768.13	−0.0876674

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.4.a.s.1.3		5
13.3	even	3		182.4.g.b.113.3	yes	10
13.9	even	3		182.4.g.b.29.3	✓	10
13.12	even	2		2366.4.a.t.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.4.g.b.29.3	✓	10	13.9	even	3
182.4.g.b.113.3	yes	10	13.3	even	3
2366.4.a.s.1.3		5	1.1	even	1	trivial
2366.4.a.t.1.3		5	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2366.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +1.28617 q^{3} +4.00000 q^{4} -10.0966 q^{5} -2.57235 q^{6} +7.00000 q^{7} -8.00000 q^{8} -25.3458 q^{9} +20.1932 q^{10} +20.1087 q^{11} +5.14470 q^{12} -14.0000 q^{14} -12.9860 q^{15} +16.0000 q^{16} -63.2530 q^{17} +50.6915 q^{18} -17.1914 q^{19} -40.3864 q^{20} +9.00322 q^{21} -40.2174 q^{22} +199.470 q^{23} -10.2894 q^{24} -23.0588 q^{25} -67.3258 q^{27} +28.0000 q^{28} -3.58751 q^{29} +25.9720 q^{30} +61.0025 q^{31} -32.0000 q^{32} +25.8633 q^{33} +126.506 q^{34} -70.6762 q^{35} -101.383 q^{36} +41.1154 q^{37} +34.3829 q^{38} +80.7728 q^{40} +32.4853 q^{41} -18.0064 q^{42} +234.902 q^{43} +80.4349 q^{44} +255.906 q^{45} -398.941 q^{46} +263.044 q^{47} +20.5788 q^{48} +49.0000 q^{49} +46.1175 q^{50} -81.3544 q^{51} -369.147 q^{53} +134.652 q^{54} -203.030 q^{55} -56.0000 q^{56} -22.1112 q^{57} +7.17503 q^{58} -410.974 q^{59} -51.9439 q^{60} -148.061 q^{61} -122.005 q^{62} -177.420 q^{63} +64.0000 q^{64} -51.7266 q^{66} +45.8863 q^{67} -253.012 q^{68} +256.554 q^{69} +141.352 q^{70} +854.901 q^{71} +202.766 q^{72} +457.581 q^{73} -82.2309 q^{74} -29.6576 q^{75} -68.7657 q^{76} +140.761 q^{77} -1200.31 q^{79} -161.546 q^{80} +597.743 q^{81} -64.9705 q^{82} +271.489 q^{83} +36.0129 q^{84} +638.640 q^{85} -469.804 q^{86} -4.61417 q^{87} -160.870 q^{88} +1182.71 q^{89} -511.812 q^{90} +797.882 q^{92} +78.4598 q^{93} -526.088 q^{94} +173.575 q^{95} -41.1576 q^{96} +832.124 q^{97} -98.0000 q^{98} -509.671 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 10 q^{2} + q^{3} + 20 q^{4} + 6 q^{5} - 2 q^{6} + 35 q^{7} - 40 q^{8} + 56 q^{9} - 12 q^{10} - 9 q^{11} + 4 q^{12} - 70 q^{14} + 137 q^{15} + 80 q^{16} - 89 q^{17} - 112 q^{18} - 49 q^{19} + 24 q^{20}+ \cdots + 81 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 + q^3 + 20 * q^4 + 6 * q^5 - 2 * q^6 + 35 * q^7 - 40 * q^8 + 56 * q^9 - 12 * q^10 - 9 * q^11 + 4 * q^12 - 70 * q^14 + 137 * q^15 + 80 * q^16 - 89 * q^17 - 112 * q^18 - 49 * q^19 + 24 * q^20 + 7 * q^21 + 18 * q^22 - 60 * q^23 - 8 * q^24 - 59 * q^25 - 134 * q^27 + 140 * q^28 - 196 * q^29 - 274 * q^30 + 154 * q^31 - 160 * q^32 - 433 * q^33 + 178 * q^34 + 42 * q^35 + 224 * q^36 + 61 * q^37 + 98 * q^38 - 48 * q^40 - 237 * q^41 - 14 * q^42 - 459 * q^43 - 36 * q^44 + 384 * q^45 + 120 * q^46 - 314 * q^47 + 16 * q^48 + 245 * q^49 + 118 * q^50 - 1069 * q^51 - 143 * q^53 + 268 * q^54 - 1899 * q^55 - 280 * q^56 + 211 * q^57 + 392 * q^58 + 178 * q^59 + 548 * q^60 - 811 * q^61 - 308 * q^62 + 392 * q^63 + 320 * q^64 + 866 * q^66 - 1078 * q^67 - 356 * q^68 - 654 * q^69 - 84 * q^70 + 1670 * q^71 - 448 * q^72 + 249 * q^73 - 122 * q^74 + 771 * q^75 - 196 * q^76 - 63 * q^77 + 4 * q^79 + 96 * q^80 - 2179 * q^81 + 474 * q^82 + 1986 * q^83 + 28 * q^84 - 2910 * q^85 + 918 * q^86 - 1427 * q^87 + 72 * q^88 + 461 * q^89 - 768 * q^90 - 240 * q^92 - 1055 * q^93 + 628 * q^94 - 543 * q^95 - 32 * q^96 + 2415 * q^97 - 490 * q^98 + 81 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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