LMFDB - Embedded newform 2366.4.a.r.1.2

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 = [4,8,-7,16,-1] 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:	$4$
Coefficient field:	4.4.8805372.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 33x^{2} - 12x + 162 $ x^4 - x^3 - 33x^2 - 12x + 162
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-3.20283$ 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)

$f(q)$	$=$	\(q+2.00000 q^{2} -5.20283 q^{3} +4.00000 q^{4} +17.5606 q^{5} -10.4057 q^{6} -7.00000 q^{7} +8.00000 q^{8} +0.0694513 q^{9} +35.1211 q^{10} -35.5540 q^{11} -20.8113 q^{12} -14.0000 q^{14} -91.3647 q^{15} +16.0000 q^{16} -19.4372 q^{17} +0.138903 q^{18} +72.6851 q^{19} +70.2423 q^{20} +36.4198 q^{21} -71.1081 q^{22} -55.3616 q^{23} -41.6226 q^{24} +183.374 q^{25} +140.115 q^{27} -28.0000 q^{28} -125.036 q^{29} -182.729 q^{30} +71.0166 q^{31} +32.0000 q^{32} +184.982 q^{33} -38.8743 q^{34} -122.924 q^{35} +0.277805 q^{36} +352.358 q^{37} +145.370 q^{38} +140.485 q^{40} -240.523 q^{41} +72.8396 q^{42} -244.932 q^{43} -142.216 q^{44} +1.21960 q^{45} -110.723 q^{46} -237.059 q^{47} -83.2453 q^{48} +49.0000 q^{49} +366.747 q^{50} +101.128 q^{51} -152.742 q^{53} +280.230 q^{54} -624.349 q^{55} -56.0000 q^{56} -378.168 q^{57} -250.071 q^{58} +24.5960 q^{59} -365.459 q^{60} +714.671 q^{61} +142.033 q^{62} -0.486159 q^{63} +64.0000 q^{64} +369.963 q^{66} -960.665 q^{67} -77.7486 q^{68} +288.037 q^{69} -245.848 q^{70} -458.376 q^{71} +0.555610 q^{72} -100.872 q^{73} +704.716 q^{74} -954.062 q^{75} +290.740 q^{76} +248.878 q^{77} -1145.74 q^{79} +280.969 q^{80} -730.870 q^{81} -481.047 q^{82} -861.573 q^{83} +145.679 q^{84} -341.328 q^{85} -489.863 q^{86} +650.539 q^{87} -284.432 q^{88} +1057.18 q^{89} +2.43921 q^{90} -221.446 q^{92} -369.487 q^{93} -474.119 q^{94} +1276.39 q^{95} -166.491 q^{96} -903.577 q^{97} +98.0000 q^{98} -2.46927 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} - 7 q^{3} + 16 q^{4} - q^{5} - 14 q^{6} - 28 q^{7} + 32 q^{8} - 29 q^{9} - 2 q^{10} - 15 q^{11} - 28 q^{12} - 56 q^{14} + 67 q^{15} + 64 q^{16} - 24 q^{17} - 58 q^{18} + 21 q^{19} - 4 q^{20}+ \cdots - 129 q^{99}+O(q^{100}) $ 4 * q + 8 * q^2 - 7 * q^3 + 16 * q^4 - q^5 - 14 * q^6 - 28 * q^7 + 32 * q^8 - 29 * q^9 - 2 * q^10 - 15 * q^11 - 28 * q^12 - 56 * q^14 + 67 * q^15 + 64 * q^16 - 24 * q^17 - 58 * q^18 + 21 * q^19 - 4 * q^20 + 49 * q^21 - 30 * q^22 - 182 * q^23 - 56 * q^24 + 365 * q^25 + 92 * q^27 - 112 * q^28 + 133 * q^29 + 134 * q^30 - 282 * q^31 + 128 * q^32 + 95 * q^33 - 48 * q^34 + 7 * q^35 - 116 * q^36 + 730 * q^37 + 42 * q^38 - 8 * q^40 - 182 * q^41 + 98 * q^42 + 83 * q^43 - 60 * q^44 - 73 * q^45 - 364 * q^46 - 560 * q^47 - 112 * q^48 + 196 * q^49 + 730 * q^50 + 209 * q^51 - 106 * q^53 + 184 * q^54 - 997 * q^55 - 224 * q^56 - 341 * q^57 + 266 * q^58 - 782 * q^59 + 268 * q^60 - 708 * q^61 - 564 * q^62 + 203 * q^63 + 256 * q^64 + 190 * q^66 - 528 * q^67 - 96 * q^68 + 1198 * q^69 + 14 * q^70 - 82 * q^71 - 232 * q^72 + 560 * q^73 + 1460 * q^74 - 2873 * q^75 + 84 * q^76 + 105 * q^77 - 1998 * q^79 - 16 * q^80 - 1220 * q^81 - 364 * q^82 - 358 * q^83 + 196 * q^84 - 547 * q^85 + 166 * q^86 - 245 * q^87 - 120 * q^88 + 2385 * q^89 - 146 * q^90 - 728 * q^92 - 1963 * q^93 - 1120 * q^94 + 1117 * q^95 - 224 * q^96 - 1155 * q^97 + 392 * q^98 - 129 * 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
$3$	−5.20283	−1.00129	−0.500643	−	0.865654i	$-0.666903\pi$
$3$	−5.20283	−1.00129	−0.500643	+	0.865654i	$0.666903\pi$
$4$	4.00000	0.500000
$5$	17.5606	1.57067	0.785333	−	0.619074i	$-0.212492\pi$
$5$	17.5606	1.57067	0.785333	+	0.619074i	$0.212492\pi$
$6$	−10.4057	−0.708016
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.00000	0.353553
$9$	0.0694513	0.00257227
$10$	35.1211	1.11063
$11$	−35.5540	−0.974540	−0.487270	−	0.873251i	$-0.662007\pi$
$11$	−35.5540	−0.974540	−0.487270	+	0.873251i	$0.662007\pi$
$12$	−20.8113	−0.500643
$13$	0	0
$13$	0	0
$14$	−14.0000	−0.267261
$15$	−91.3647	−1.57268
$16$	16.0000	0.250000
$17$	−19.4372	−0.277306	−0.138653	−	0.990341i	$-0.544277\pi$
$17$	−19.4372	−0.277306	−0.138653	+	0.990341i	$0.544277\pi$
$18$	0.138903	0.00181887
$19$	72.6851	0.877637	0.438818	−	0.898576i	$-0.355397\pi$
$19$	72.6851	0.877637	0.438818	+	0.898576i	$0.355397\pi$
$20$	70.2423	0.785333
$21$	36.4198	0.378450
$22$	−71.1081	−0.689104
$23$	−55.3616	−0.501900	−0.250950	−	0.968000i	$-0.580743\pi$
$23$	−55.3616	−0.501900	−0.250950	+	0.968000i	$0.580743\pi$
$24$	−41.6226	−0.354008
$25$	183.374	1.46699
$26$	0	0
$27$	140.115	0.998710
$28$	−28.0000	−0.188982
$29$	−125.036	−0.800639	−0.400319	−	0.916376i	$-0.631101\pi$
$29$	−125.036	−0.800639	−0.400319	+	0.916376i	$0.631101\pi$
$30$	−182.729	−1.11206
$31$	71.0166	0.411450	0.205725	−	0.978610i	$-0.434045\pi$
$31$	71.0166	0.411450	0.205725	+	0.978610i	$0.434045\pi$
$32$	32.0000	0.176777
$33$	184.982	0.975793
$34$	−38.8743	−0.196085
$35$	−122.924	−0.593656
$36$	0.277805	0.00128614
$37$	352.358	1.56560	0.782801	−	0.622272i	$-0.213790\pi$
$37$	352.358	1.56560	0.782801	+	0.622272i	$0.213790\pi$
$38$	145.370	0.620583
$39$	0	0
$40$	140.485	0.555314
$41$	−240.523	−0.916181	−0.458091	−	0.888906i	$-0.651466\pi$
$41$	−240.523	−0.916181	−0.458091	+	0.888906i	$0.651466\pi$
$42$	72.8396	0.267605
$43$	−244.932	−0.868645	−0.434322	−	0.900757i	$-0.643012\pi$
$43$	−244.932	−0.868645	−0.434322	+	0.900757i	$0.643012\pi$
$44$	−142.216	−0.487270
$45$	1.21960	0.00404018
$46$	−110.723	−0.354897
$47$	−237.059	−0.735716	−0.367858	−	0.929882i	$-0.619909\pi$
$47$	−237.059	−0.735716	−0.367858	+	0.929882i	$0.619909\pi$
$48$	−83.2453	−0.250321
$49$	49.0000	0.142857
$50$	366.747	1.03732
$51$	101.128	0.277662
$52$	0	0
$53$	−152.742	−0.395863	−0.197932	−	0.980216i	$-0.563422\pi$
$53$	−152.742	−0.395863	−0.197932	+	0.980216i	$0.563422\pi$
$54$	280.230	0.706194
$55$	−624.349	−1.53068
$56$	−56.0000	−0.133631
$57$	−378.168	−0.878765
$58$	−250.071	−0.566137
$59$	24.5960	0.0542733	0.0271367	−	0.999632i	$-0.491361\pi$
$59$	24.5960	0.0542733	0.0271367	+	0.999632i	$0.491361\pi$
$60$	−365.459	−0.786342
$61$	714.671	1.50007	0.750035	−	0.661398i	$-0.230037\pi$
$61$	714.671	1.50007	0.750035	+	0.661398i	$0.230037\pi$
$62$	142.033	0.290939
$63$	−0.486159	−0.000972227 0
$64$	64.0000	0.125000
$65$	0	0
$66$	369.963	0.689990
$67$	−960.665	−1.75170	−0.875850	−	0.482583i	$-0.839699\pi$
$67$	−960.665	−1.75170	−0.875850	+	0.482583i	$0.839699\pi$
$68$	−77.7486	−0.138653
$69$	288.037	0.502545
$70$	−245.848	−0.419778
$71$	−458.376	−0.766185	−0.383093	−	0.923710i	$-0.625141\pi$
$71$	−458.376	−0.766185	−0.383093	+	0.923710i	$0.625141\pi$
$72$	0.555610	0.000909435 0
$73$	−100.872	−0.161729	−0.0808645	−	0.996725i	$-0.525768\pi$
$73$	−100.872	−0.161729	−0.0808645	+	0.996725i	$0.525768\pi$
$74$	704.716	1.10705
$75$	−954.062	−1.46888
$76$	290.740	0.438818
$77$	248.878	0.368342
$78$	0	0
$79$	−1145.74	−1.63172	−0.815862	−	0.578246i	$-0.803737\pi$
$79$	−1145.74	−1.63172	−0.815862	+	0.578246i	$0.803737\pi$
$80$	280.969	0.392666
$81$	−730.870	−1.00257
$82$	−481.047	−0.647838
$83$	−861.573	−1.13940	−0.569698	−	0.821854i	$-0.692940\pi$
$83$	−861.573	−1.13940	−0.569698	+	0.821854i	$0.692940\pi$
$84$	145.679	0.189225
$85$	−341.328	−0.435555
$86$	−489.863	−0.614225
$87$	650.539	0.801668
$88$	−284.432	−0.344552
$89$	1057.18	1.25912	0.629558	−	0.776953i	$-0.283236\pi$
$89$	1057.18	1.25912	0.629558	+	0.776953i	$0.283236\pi$
$90$	2.43921	0.00285684
$91$	0	0
$92$	−221.446	−0.250950
$93$	−369.487	−0.411979
$94$	−474.119	−0.520230
$95$	1276.39	1.37847
$96$	−166.491	−0.177004
$97$	−903.577	−0.945818	−0.472909	−	0.881111i	$-0.656796\pi$
$97$	−903.577	−0.945818	−0.472909	+	0.881111i	$0.656796\pi$
$98$	98.0000	0.101015
$99$	−2.46927	−0.00250678
$100$	733.495	0.733495
$101$	928.839	0.915079	0.457539	−	0.889189i	$-0.348731\pi$
$101$	928.839	0.915079	0.457539	+	0.889189i	$0.348731\pi$
$102$	202.256	0.196337
$103$	−386.662	−0.369893	−0.184946	−	0.982749i	$-0.559211\pi$
$103$	−386.662	−0.369893	−0.184946	+	0.982749i	$0.559211\pi$
$104$	0	0
$105$	639.553	0.594419
$106$	−305.484	−0.279917
$107$	1017.09	0.918930	0.459465	−	0.888196i	$-0.348041\pi$
$107$	1017.09	0.918930	0.459465	+	0.888196i	$0.348041\pi$
$108$	560.460	0.499355
$109$	−1889.22	−1.66013	−0.830066	−	0.557665i	$-0.811697\pi$
$109$	−1889.22	−1.66013	−0.830066	+	0.557665i	$0.811697\pi$
$110$	−1248.70	−1.08235
$111$	−1833.26	−1.56761
$112$	−112.000	−0.0944911
$113$	57.6390	0.0479842	0.0239921	−	0.999712i	$-0.492362\pi$
$113$	57.6390	0.0479842	0.0239921	+	0.999712i	$0.492362\pi$
$114$	−756.336	−0.621381
$115$	−972.181	−0.788316
$116$	−500.142	−0.400319
$117$	0	0
$118$	49.1920	0.0383771
$119$	136.060	0.104812
$120$	−730.918	−0.556028
$121$	−66.9105	−0.0502709
$122$	1429.34	1.06071
$123$	1251.40	0.917359
$124$	284.066	0.205725
$125$	1025.08	0.733485
$126$	−0.972318	−0.000687468 0
$127$	956.570	0.668361	0.334181	−	0.942509i	$-0.391540\pi$
$127$	956.570	0.668361	0.334181	+	0.942509i	$0.391540\pi$
$128$	128.000	0.0883883
$129$	1274.34	0.869761
$130$	0	0
$131$	2119.14	1.41336	0.706678	−	0.707535i	$-0.250193\pi$
$131$	2119.14	1.41336	0.706678	+	0.707535i	$0.250193\pi$
$132$	739.927	0.487897
$133$	−508.796	−0.331716
$134$	−1921.33	−1.23864
$135$	2460.50	1.56864
$136$	−155.497	−0.0980425
$137$	−2457.73	−1.53269	−0.766344	−	0.642431i	$-0.777926\pi$
$137$	−2457.73	−1.53269	−0.766344	+	0.642431i	$0.777926\pi$
$138$	576.074	0.355353
$139$	−2209.74	−1.34840	−0.674200	−	0.738549i	$-0.735511\pi$
$139$	−2209.74	−1.34840	−0.674200	+	0.738549i	$0.735511\pi$
$140$	−491.696	−0.296828
$141$	1233.38	0.736662
$142$	−916.751	−0.541775
$143$	0	0
$144$	1.11122	0.000643068 0
$145$	−2195.70	−1.25754
$146$	−201.745	−0.114360
$147$	−254.939	−0.143041
$148$	1409.43	0.782801
$149$	−708.063	−0.389307	−0.194654	−	0.980872i	$-0.562358\pi$
$149$	−708.063	−0.389307	−0.194654	+	0.980872i	$0.562358\pi$
$150$	−1908.12	−1.03865
$151$	−1080.25	−0.582181	−0.291091	−	0.956695i	$-0.594018\pi$
$151$	−1080.25	−0.582181	−0.291091	+	0.956695i	$0.594018\pi$
$152$	581.481	0.310291
$153$	−1.34994	−0.000713306 0
$154$	497.757	0.260457
$155$	1247.09	0.646250
$156$	0	0
$157$	−1253.02	−0.636954	−0.318477	−	0.947931i	$-0.603171\pi$
$157$	−1253.02	−0.636954	−0.318477	+	0.947931i	$0.603171\pi$
$158$	−2291.49	−1.15380
$159$	794.691	0.396372
$160$	561.938	0.277657
$161$	387.531	0.189700
$162$	−1461.74	−0.708921
$163$	3441.78	1.65387	0.826936	−	0.562296i	$-0.190082\pi$
$163$	3441.78	1.65387	0.826936	+	0.562296i	$0.190082\pi$
$164$	−962.093	−0.458091
$165$	3248.38	1.53264
$166$	−1723.15	−0.805675
$167$	2348.77	1.08834	0.544171	−	0.838974i	$-0.316844\pi$
$167$	2348.77	1.08834	0.544171	+	0.838974i	$0.316844\pi$
$168$	291.359	0.133802
$169$	0	0
$170$	−682.655	−0.307984
$171$	5.04807	0.00225752
$172$	−979.727	−0.434322
$173$	4349.62	1.91154	0.955768	−	0.294122i	$-0.0950272\pi$
$173$	4349.62	1.91154	0.955768	+	0.294122i	$0.0950272\pi$
$174$	1301.08	0.566865
$175$	−1283.62	−0.554470
$176$	−568.865	−0.243635
$177$	−127.969	−0.0543431
$178$	2114.37	0.890330
$179$	−3486.82	−1.45596	−0.727981	−	0.685597i	$-0.759541\pi$
$179$	−3486.82	−1.45596	−0.727981	+	0.685597i	$0.759541\pi$
$180$	4.87842	0.00202009
$181$	238.968	0.0981344	0.0490672	−	0.998795i	$-0.484375\pi$
$181$	238.968	0.0981344	0.0490672	+	0.998795i	$0.484375\pi$
$182$	0	0
$183$	−3718.31	−1.50200
$184$	−442.893	−0.177448
$185$	6187.61	2.45904
$186$	−738.974	−0.291313
$187$	691.069	0.270246
$188$	−948.238	−0.367858
$189$	−980.806	−0.377477
$190$	2552.78	0.974728
$191$	−2955.27	−1.11956	−0.559779	−	0.828642i	$-0.689114\pi$
$191$	−2955.27	−1.11956	−0.559779	+	0.828642i	$0.689114\pi$
$192$	−332.981	−0.125161
$193$	2721.69	1.01509	0.507543	−	0.861627i	$-0.330554\pi$
$193$	2721.69	1.01509	0.507543	+	0.861627i	$0.330554\pi$
$194$	−1807.15	−0.668795
$195$	0	0
$196$	196.000	0.0714286
$197$	−595.085	−0.215218	−0.107609	−	0.994193i	$-0.534320\pi$
$197$	−595.085	−0.215218	−0.107609	+	0.994193i	$0.534320\pi$
$198$	−4.93855	−0.00177256
$199$	−167.295	−0.0595943	−0.0297971	−	0.999556i	$-0.509486\pi$
$199$	−167.295	−0.0595943	−0.0297971	+	0.999556i	$0.509486\pi$
$200$	1466.99	0.518659
$201$	4998.18	1.75395
$202$	1857.68	0.647058
$203$	875.249	0.302613
$204$	404.513	0.138831
$205$	−4223.73	−1.43901
$206$	−773.324	−0.261554
$207$	−3.84493	−0.00129102
$208$	0	0
$209$	−2584.25	−0.855293
$210$	1279.11	0.420318
$211$	−2201.74	−0.718361	−0.359181	−	0.933268i	$-0.616944\pi$
$211$	−2201.74	−0.718361	−0.359181	+	0.933268i	$0.616944\pi$
$212$	−610.968	−0.197932
$213$	2384.85	0.767170
$214$	2034.17	0.649781
$215$	−4301.14	−1.36435
$216$	1120.92	0.353097
$217$	−497.116	−0.155513
$218$	−3778.44	−1.17389
$219$	524.822	0.161937
$220$	−2497.40	−0.765338
$221$	0	0
$222$	−3666.52	−1.10847
$223$	−5914.92	−1.77620	−0.888099	−	0.459651i	$-0.847974\pi$
$223$	−5914.92	−1.77620	−0.888099	+	0.459651i	$0.847974\pi$
$224$	−224.000	−0.0668153
$225$	12.7355	0.00377349
$226$	115.278	0.0339300
$227$	−5571.04	−1.62891	−0.814456	−	0.580225i	$-0.802965\pi$
$227$	−5571.04	−1.62891	−0.814456	+	0.580225i	$0.802965\pi$
$228$	−1512.67	−0.439382
$229$	−3027.24	−0.873562	−0.436781	−	0.899568i	$-0.643882\pi$
$229$	−3027.24	−0.873562	−0.436781	+	0.899568i	$0.643882\pi$
$230$	−1944.36	−0.557424
$231$	−1294.87	−0.368815
$232$	−1000.28	−0.283069
$233$	−3763.80	−1.05826	−0.529131	−	0.848540i	$-0.677482\pi$
$233$	−3763.80	−1.05826	−0.529131	+	0.848540i	$0.677482\pi$
$234$	0	0
$235$	−4162.90	−1.15556
$236$	98.3840	0.0271367
$237$	5961.11	1.63382
$238$	272.120	0.0741132
$239$	836.766	0.226468	0.113234	−	0.993568i	$-0.463879\pi$
$239$	836.766	0.226468	0.113234	+	0.993568i	$0.463879\pi$
$240$	−1461.84	−0.393171
$241$	−4974.34	−1.32957	−0.664784	−	0.747036i	$-0.731476\pi$
$241$	−4974.34	−1.32957	−0.664784	+	0.747036i	$0.731476\pi$
$242$	−133.821	−0.0355469
$243$	19.4874	0.00514453
$244$	2858.68	0.750035
$245$	860.468	0.224381
$246$	2502.80	0.648671
$247$	0	0
$248$	568.133	0.145470
$249$	4482.62	1.14086
$250$	2050.15	0.518652
$251$	2140.33	0.538232	0.269116	−	0.963108i	$-0.413268\pi$
$251$	2140.33	0.538232	0.269116	+	0.963108i	$0.413268\pi$
$252$	−1.94464	−0.000486113 0
$253$	1968.33	0.489121
$254$	1913.14	0.472603
$255$	1775.87	0.436115
$256$	256.000	0.0625000
$257$	−5068.22	−1.23014	−0.615071	−	0.788471i	$-0.710873\pi$
$257$	−5068.22	−1.23014	−0.615071	+	0.788471i	$0.710873\pi$
$258$	2548.68	0.615014
$259$	−2466.51	−0.591742
$260$	0	0
$261$	−8.68388	−0.00205946
$262$	4238.27	0.999394
$263$	3299.09	0.773501	0.386751	−	0.922184i	$-0.373597\pi$
$263$	3299.09	0.773501	0.386751	+	0.922184i	$0.373597\pi$
$264$	1479.85	0.344995
$265$	−2682.24	−0.621768
$266$	−1017.59	−0.234558
$267$	−5500.35	−1.26073
$268$	−3842.66	−0.875850
$269$	4751.92	1.07706	0.538531	−	0.842606i	$-0.318980\pi$
$269$	4751.92	1.07706	0.538531	+	0.842606i	$0.318980\pi$
$270$	4921.00	1.10920
$271$	−1373.64	−0.307906	−0.153953	−	0.988078i	$-0.549200\pi$
$271$	−1373.64	−0.307906	−0.153953	+	0.988078i	$0.549200\pi$
$272$	−310.994	−0.0693265
$273$	0	0
$274$	−4915.46	−1.08377
$275$	−6519.68	−1.42964
$276$	1152.15	0.251272
$277$	3579.60	0.776452	0.388226	−	0.921564i	$-0.373088\pi$
$277$	3579.60	0.776452	0.388226	+	0.921564i	$0.373088\pi$
$278$	−4419.47	−0.953462
$279$	4.93219	0.00105836
$280$	−983.392	−0.209889
$281$	−7576.39	−1.60843	−0.804216	−	0.594337i	$-0.797415\pi$
$281$	−7576.39	−1.60843	−0.804216	+	0.594337i	$0.797415\pi$
$282$	2466.76	0.520899
$283$	−6258.61	−1.31461	−0.657307	−	0.753623i	$-0.728304\pi$
$283$	−6258.61	−1.31461	−0.657307	+	0.753623i	$0.728304\pi$
$284$	−1833.50	−0.383093
$285$	−6640.85	−1.38025
$286$	0	0
$287$	1683.66	0.346284
$288$	2.22244	0.000454717 0
$289$	−4535.20	−0.923101
$290$	−4391.39	−0.889212
$291$	4701.16	0.947034
$292$	−403.489	−0.0808645
$293$	−1933.08	−0.385433	−0.192717	−	0.981254i	$-0.561730\pi$
$293$	−1933.08	−0.385433	−0.192717	+	0.981254i	$0.561730\pi$
$294$	−509.877	−0.101145
$295$	431.920	0.0852453
$296$	2818.86	0.553524
$297$	−4981.66	−0.973283
$298$	−1416.13	−0.275282
$299$	0	0
$300$	−3816.25	−0.734438
$301$	1714.52	0.328317
$302$	−2160.50	−0.411664
$303$	−4832.59	−0.916255
$304$	1162.96	0.219409
$305$	12550.0	2.35611
$306$	−2.69987	−0.000504384 0
$307$	4886.39	0.908408	0.454204	−	0.890898i	$-0.349924\pi$
$307$	4886.39	0.908408	0.454204	+	0.890898i	$0.349924\pi$
$308$	995.513	0.184171
$309$	2011.74	0.370368
$310$	2494.18	0.456968
$311$	−8145.44	−1.48516	−0.742581	−	0.669756i	$-0.766399\pi$
$311$	−8145.44	−1.48516	−0.742581	+	0.669756i	$0.766399\pi$
$312$	0	0
$313$	10759.6	1.94304	0.971518	−	0.236966i	$-0.0761531\pi$
$313$	10759.6	1.94304	0.971518	+	0.236966i	$0.0761531\pi$
$314$	−2506.04	−0.450395
$315$	−8.53723	−0.00152704
$316$	−4582.97	−0.815862
$317$	5799.15	1.02748	0.513742	−	0.857945i	$-0.328259\pi$
$317$	5799.15	1.02748	0.513742	+	0.857945i	$0.328259\pi$
$318$	1589.38	0.280277
$319$	4445.52	0.780255
$320$	1123.88	0.196333
$321$	−5291.73	−0.920111
$322$	775.062	0.134138
$323$	−1412.79	−0.243374
$324$	−2923.48	−0.501283
$325$	0	0
$326$	6883.56	1.16946
$327$	9829.29	1.66227
$328$	−1924.19	−0.323919
$329$	1659.42	0.278075
$330$	6496.77	1.08374
$331$	6499.20	1.07924	0.539620	−	0.841909i	$-0.318568\pi$
$331$	6499.20	1.07924	0.539620	+	0.841909i	$0.318568\pi$
$332$	−3446.29	−0.569698
$333$	24.4717	0.00402715
$334$	4697.53	0.769574
$335$	−16869.8	−2.75134
$336$	582.717	0.0946126
$337$	−3846.02	−0.621680	−0.310840	−	0.950462i	$-0.600610\pi$
$337$	−3846.02	−0.621680	−0.310840	+	0.950462i	$0.600610\pi$
$338$	0	0
$339$	−299.886	−0.0480459
$340$	−1365.31	−0.217778
$341$	−2524.93	−0.400975
$342$	10.0961	0.00159631
$343$	−343.000	−0.0539949
$344$	−1959.45	−0.307112
$345$	5058.09	0.789329
$346$	8699.25	1.35166
$347$	6447.65	0.997487	0.498744	−	0.866750i	$-0.333795\pi$
$347$	6447.65	0.997487	0.498744	+	0.866750i	$0.333795\pi$
$348$	2602.16	0.400834
$349$	−2636.70	−0.404411	−0.202205	−	0.979343i	$-0.564811\pi$
$349$	−2636.70	−0.404411	−0.202205	+	0.979343i	$0.564811\pi$
$350$	−2567.23	−0.392069
$351$	0	0
$352$	−1137.73	−0.172276
$353$	4096.10	0.617602	0.308801	−	0.951127i	$-0.400072\pi$
$353$	4096.10	0.617602	0.308801	+	0.951127i	$0.400072\pi$
$354$	−255.938	−0.0384264
$355$	−8049.34	−1.20342
$356$	4228.74	0.629558
$357$	−707.898	−0.104947
$358$	−6973.65	−1.02952
$359$	−4036.48	−0.593418	−0.296709	−	0.954968i	$-0.595889\pi$
$359$	−4036.48	−0.593418	−0.296709	+	0.954968i	$0.595889\pi$
$360$	9.75684	0.00142842
$361$	−1575.88	−0.229754
$362$	477.935	0.0693915
$363$	348.124	0.0503355
$364$	0	0
$365$	−1771.38	−0.254022
$366$	−7436.63	−1.06207
$367$	−13364.6	−1.90089	−0.950446	−	0.310889i	$-0.899373\pi$
$367$	−13364.6	−1.90089	−0.950446	+	0.310889i	$0.899373\pi$
$368$	−885.785	−0.125475
$369$	−16.7047	−0.00235667
$370$	12375.2	1.73880
$371$	1069.19	0.149622
$372$	−1477.95	−0.205989
$373$	−6873.84	−0.954193	−0.477097	−	0.878851i	$-0.658311\pi$
$373$	−6873.84	−0.954193	−0.477097	+	0.878851i	$0.658311\pi$
$374$	1382.14	0.191093
$375$	−5333.30	−0.734427
$376$	−1896.48	−0.260115
$377$	0	0
$378$	−1961.61	−0.266916
$379$	9844.51	1.33424	0.667122	−	0.744949i	$-0.267526\pi$
$379$	9844.51	1.33424	0.667122	+	0.744949i	$0.267526\pi$
$380$	5105.57	0.689237
$381$	−4976.87	−0.669220
$382$	−5910.53	−0.791647
$383$	−9164.87	−1.22272	−0.611361	−	0.791352i	$-0.709378\pi$
$383$	−9164.87	−1.22272	−0.611361	+	0.791352i	$0.709378\pi$
$384$	−665.962	−0.0885020
$385$	4370.44	0.578542
$386$	5443.38	0.717774
$387$	−17.0108	−0.00223439
$388$	−3614.31	−0.472909
$389$	5545.20	0.722758	0.361379	−	0.932419i	$-0.382306\pi$
$389$	5545.20	0.722758	0.361379	+	0.932419i	$0.382306\pi$
$390$	0	0
$391$	1076.07	0.139180
$392$	392.000	0.0505076
$393$	−11025.5	−1.41517
$394$	−1190.17	−0.152182
$395$	−20119.9	−2.56289
$396$	−9.87710	−0.00125339
$397$	−12183.0	−1.54018	−0.770088	−	0.637938i	$-0.779788\pi$
$397$	−12183.0	−1.54018	−0.770088	+	0.637938i	$0.779788\pi$
$398$	−334.591	−0.0421395
$399$	2647.18	0.332142
$400$	2933.98	0.366747
$401$	11242.3	1.40004	0.700018	−	0.714126i	$-0.253175\pi$
$401$	11242.3	1.40004	0.700018	+	0.714126i	$0.253175\pi$
$402$	9996.36	1.24023
$403$	0	0
$404$	3715.36	0.457539
$405$	−12834.5	−1.57470
$406$	1750.50	0.213980
$407$	−12527.7	−1.52574
$408$	809.026	0.0981685
$409$	12124.4	1.46580	0.732902	−	0.680334i	$-0.238165\pi$
$409$	12124.4	1.46580	0.732902	+	0.680334i	$0.238165\pi$
$410$	−8447.45	−1.01754
$411$	12787.2	1.53466
$412$	−1546.65	−0.184946
$413$	−172.172	−0.0205134
$414$	−7.68987	−0.000912890 0
$415$	−15129.7	−1.78961
$416$	0	0
$417$	11496.9	1.35013
$418$	−5168.50	−0.604783
$419$	−7332.86	−0.854973	−0.427487	−	0.904022i	$-0.640601\pi$
$419$	−7332.86	−0.854973	−0.427487	+	0.904022i	$0.640601\pi$
$420$	2558.21	0.297209
$421$	8750.98	1.01306	0.506528	−	0.862223i	$-0.330929\pi$
$421$	8750.98	1.01306	0.506528	+	0.862223i	$0.330929\pi$
$422$	−4403.48	−0.507958
$423$	−16.4641	−0.00189246
$424$	−1221.94	−0.139959
$425$	−3564.26	−0.406805
$426$	4769.70	0.542471
$427$	−5002.70	−0.566973
$428$	4068.35	0.459465
$429$	0	0
$430$	−8602.28	−0.964742
$431$	−2444.15	−0.273157	−0.136578	−	0.990629i	$-0.543611\pi$
$431$	−2444.15	−0.273157	−0.136578	+	0.990629i	$0.543611\pi$
$432$	2241.84	0.249677
$433$	−10018.1	−1.11186	−0.555932	−	0.831228i	$-0.687638\pi$
$433$	−10018.1	−1.11186	−0.555932	+	0.831228i	$0.687638\pi$
$434$	−994.232	−0.109965
$435$	11423.8	1.25915
$436$	−7556.88	−0.830066
$437$	−4023.96	−0.440485
$438$	1049.64	0.114507
$439$	−1642.32	−0.178550	−0.0892750	−	0.996007i	$-0.528455\pi$
$439$	−1642.32	−0.178550	−0.0892750	+	0.996007i	$0.528455\pi$
$440$	−4994.79	−0.541176
$441$	3.40311	0.000367467 0
$442$	0	0
$443$	−2864.36	−0.307201	−0.153600	−	0.988133i	$-0.549087\pi$
$443$	−2864.36	−0.307201	−0.153600	+	0.988133i	$0.549087\pi$
$444$	−7333.03	−0.783807
$445$	18564.8	1.97765
$446$	−11829.8	−1.25596
$447$	3683.93	0.389807
$448$	−448.000	−0.0472456
$449$	14230.7	1.49574	0.747870	−	0.663846i	$-0.231077\pi$
$449$	14230.7	1.49574	0.747870	+	0.663846i	$0.231077\pi$
$450$	25.4711	0.00266826
$451$	8551.57	0.892856
$452$	230.556	0.0239921
$453$	5620.35	0.582930
$454$	−11142.1	−1.15181
$455$	0	0
$456$	−3025.35	−0.310690
$457$	−17058.6	−1.74610	−0.873052	−	0.487627i	$-0.837863\pi$
$457$	−17058.6	−1.74610	−0.873052	+	0.487627i	$0.837863\pi$
$458$	−6054.48	−0.617702
$459$	−2723.44	−0.276948
$460$	−3888.72	−0.394158
$461$	−11124.1	−1.12386	−0.561930	−	0.827185i	$-0.689941\pi$
$461$	−11124.1	−1.12386	−0.561930	+	0.827185i	$0.689941\pi$
$462$	−2589.74	−0.260792
$463$	−4793.11	−0.481112	−0.240556	−	0.970635i	$-0.577330\pi$
$463$	−4793.11	−0.481112	−0.240556	+	0.970635i	$0.577330\pi$
$464$	−2000.57	−0.200160
$465$	−6488.41	−0.647081
$466$	−7527.61	−0.748304
$467$	1176.28	0.116557	0.0582783	−	0.998300i	$-0.481439\pi$
$467$	1176.28	0.116557	0.0582783	+	0.998300i	$0.481439\pi$
$468$	0	0
$469$	6724.66	0.662081
$470$	−8325.80	−0.817107
$471$	6519.25	0.637773
$472$	196.768	0.0191885
$473$	8708.31	0.846530
$474$	11922.2	1.15529
$475$	13328.5	1.28748
$476$	544.240	0.0524059
$477$	−10.6081	−0.00101827
$478$	1673.53	0.160137
$479$	6794.88	0.648154	0.324077	−	0.946031i	$-0.394946\pi$
$479$	6794.88	0.648154	0.324077	+	0.946031i	$0.394946\pi$
$480$	−2923.67	−0.278014
$481$	0	0
$482$	−9948.69	−0.940146
$483$	−2016.26	−0.189944
$484$	−267.642	−0.0251354
$485$	−15867.3	−1.48556
$486$	38.9749	0.00363773
$487$	−15075.0	−1.40270	−0.701348	−	0.712819i	$-0.747418\pi$
$487$	−15075.0	−1.40270	−0.701348	+	0.712819i	$0.747418\pi$
$488$	5717.37	0.530355
$489$	−17907.0	−1.65600
$490$	1720.94	0.158661
$491$	−700.777	−0.0644107	−0.0322053	−	0.999481i	$-0.510253\pi$
$491$	−700.777	−0.0644107	−0.0322053	+	0.999481i	$0.510253\pi$
$492$	5005.61	0.458679
$493$	2430.34	0.222022
$494$	0	0
$495$	−43.3619	−0.00393731
$496$	1136.27	0.102863
$497$	3208.63	0.289591
$498$	8965.24	0.806711
$499$	−1528.64	−0.137137	−0.0685683	−	0.997646i	$-0.521843\pi$
$499$	−1528.64	−0.137137	−0.0685683	+	0.997646i	$0.521843\pi$
$500$	4100.30	0.366742
$501$	−12220.2	−1.08974
$502$	4280.66	0.380588
$503$	−4013.82	−0.355800	−0.177900	−	0.984049i	$-0.556930\pi$
$503$	−4013.82	−0.355800	−0.177900	+	0.984049i	$0.556930\pi$
$504$	−3.88927	−0.000343734 0
$505$	16310.9	1.43728
$506$	3936.66	0.345861
$507$	0	0
$508$	3826.28	0.334181
$509$	−894.419	−0.0778869	−0.0389434	−	0.999241i	$-0.512399\pi$
$509$	−894.419	−0.0778869	−0.0389434	+	0.999241i	$0.512399\pi$
$510$	3551.74	0.308380
$511$	706.106	0.0611278
$512$	512.000	0.0441942
$513$	10184.3	0.876504
$514$	−10136.4	−0.869842
$515$	−6790.01	−0.580978
$516$	5097.35	0.434881
$517$	8428.42	0.716986
$518$	−4933.01	−0.418425
$519$	−22630.4	−1.91399
$520$	0	0
$521$	−586.692	−0.0493349	−0.0246674	−	0.999696i	$-0.507853\pi$
$521$	−586.692	−0.0493349	−0.0246674	+	0.999696i	$0.507853\pi$
$522$	−17.3678	−0.00145626
$523$	−13018.5	−1.08845	−0.544224	−	0.838940i	$-0.683176\pi$
$523$	−13018.5	−1.08845	−0.544224	+	0.838940i	$0.683176\pi$
$524$	8476.54	0.706678
$525$	6678.44	0.555183
$526$	6598.19	0.546948
$527$	−1380.36	−0.114098
$528$	2959.71	0.243948
$529$	−9102.09	−0.748097
$530$	−5364.48	−0.439657
$531$	1.70822	0.000139606 0
$532$	−2035.18	−0.165858
$533$	0	0
$534$	−11000.7	−0.891474
$535$	17860.6	1.44333
$536$	−7685.32	−0.619320
$537$	18141.3	1.45783
$538$	9503.83	0.761597
$539$	−1742.15	−0.139220
$540$	9842.01	0.784319
$541$	−4069.61	−0.323413	−0.161706	−	0.986839i	$-0.551700\pi$
$541$	−4069.61	−0.323413	−0.161706	+	0.986839i	$0.551700\pi$
$542$	−2747.27	−0.217722
$543$	−1243.31	−0.0982605
$544$	−621.989	−0.0490212
$545$	−33175.8	−2.60751
$546$	0	0
$547$	−13272.7	−1.03748	−0.518740	−	0.854932i	$-0.673599\pi$
$547$	−13272.7	−1.03748	−0.518740	+	0.854932i	$0.673599\pi$
$548$	−9830.93	−0.766344
$549$	49.6348	0.00385859
$550$	−13039.4	−1.01091
$551$	−9088.22	−0.702670
$552$	2304.30	0.177676
$553$	8020.20	0.616734
$554$	7159.19	0.549034
$555$	−32193.1	−2.46220
$556$	−8838.95	−0.674200
$557$	12239.3	0.931053	0.465527	−	0.885034i	$-0.345865\pi$
$557$	12239.3	0.931053	0.465527	+	0.885034i	$0.345865\pi$
$558$	9.86438	0.000748374 0
$559$	0	0
$560$	−1966.78	−0.148414
$561$	−3595.52	−0.270593
$562$	−15152.8	−1.13733
$563$	19627.0	1.46923	0.734616	−	0.678483i	$-0.237362\pi$
$563$	19627.0	1.46923	0.734616	+	0.678483i	$0.237362\pi$
$564$	4933.52	0.368331
$565$	1012.17	0.0753672
$566$	−12517.2	−0.929572
$567$	5116.09	0.378934
$568$	−3667.00	−0.270887
$569$	16866.9	1.24270	0.621349	−	0.783534i	$-0.286585\pi$
$569$	16866.9	1.24270	0.621349	+	0.783534i	$0.286585\pi$
$570$	−13281.7	−0.975981
$571$	3470.38	0.254345	0.127173	−	0.991881i	$-0.459410\pi$
$571$	3470.38	0.254345	0.127173	+	0.991881i	$0.459410\pi$
$572$	0	0
$573$	15375.7	1.12100
$574$	3367.33	0.244860
$575$	−10151.9	−0.736281
$576$	4.44488	0.000321534 0
$577$	7642.02	0.551372	0.275686	−	0.961248i	$-0.411095\pi$
$577$	7642.02	0.551372	0.275686	+	0.961248i	$0.411095\pi$
$578$	−9070.39	−0.652731
$579$	−14160.5	−1.01639
$580$	−8782.79	−0.628768
$581$	6031.01	0.430652
$582$	9402.32	0.669654
$583$	5430.60	0.385785
$584$	−806.979	−0.0571798
$585$	0	0
$586$	−3866.17	−0.272543
$587$	−4255.99	−0.299256	−0.149628	−	0.988742i	$-0.547808\pi$
$587$	−4255.99	−0.299256	−0.149628	+	0.988742i	$0.547808\pi$
$588$	−1019.75	−0.0715204
$589$	5161.84	0.361104
$590$	863.840	0.0602775
$591$	3096.13	0.215495
$592$	5637.73	0.391401
$593$	25016.9	1.73242	0.866208	−	0.499684i	$-0.166551\pi$
$593$	25016.9	1.73242	0.866208	+	0.499684i	$0.166551\pi$
$594$	−9963.31	−0.688215
$595$	2389.29	0.164624
$596$	−2832.25	−0.194654
$597$	870.410	0.0596709
$598$	0	0
$599$	7004.91	0.477818	0.238909	−	0.971042i	$-0.423210\pi$
$599$	7004.91	0.477818	0.238909	+	0.971042i	$0.423210\pi$
$600$	−7632.50	−0.519326
$601$	−17899.3	−1.21485	−0.607427	−	0.794376i	$-0.707798\pi$
$601$	−17899.3	−1.21485	−0.607427	+	0.794376i	$0.707798\pi$
$602$	3429.04	0.232155
$603$	−66.7194	−0.00450585
$604$	−4321.00	−0.291091
$605$	−1174.99	−0.0789587
$606$	−9665.19	−0.647890
$607$	315.379	0.0210887	0.0105444	−	0.999944i	$-0.496644\pi$
$607$	315.379	0.0210887	0.0105444	+	0.999944i	$0.496644\pi$
$608$	2325.92	0.155146
$609$	−4553.77	−0.303002
$610$	25100.1	1.66602
$611$	0	0
$612$	−5.39974	−0.000356653 0
$613$	28048.6	1.84808	0.924041	−	0.382294i	$-0.124866\pi$
$613$	28048.6	1.84808	0.924041	+	0.382294i	$0.124866\pi$
$614$	9772.79	0.642341
$615$	21975.3	1.44086
$616$	1991.03	0.130228
$617$	26956.3	1.75886	0.879432	−	0.476025i	$-0.157923\pi$
$617$	26956.3	1.75886	0.879432	+	0.476025i	$0.157923\pi$
$618$	4023.48	0.261890
$619$	9116.91	0.591986	0.295993	−	0.955190i	$-0.404349\pi$
$619$	9116.91	0.591986	0.295993	+	0.955190i	$0.404349\pi$
$620$	4988.37	0.323125
$621$	−7756.99	−0.501252
$622$	−16290.9	−1.05017
$623$	−7400.29	−0.475901
$624$	0	0
$625$	−4920.80	−0.314931
$626$	21519.3	1.37393
$627$	13445.4	0.856392
$628$	−5012.08	−0.318477
$629$	−6848.84	−0.434151
$630$	−17.0745	−0.00107978
$631$	18502.8	1.16733	0.583664	−	0.811995i	$-0.301619\pi$
$631$	18502.8	1.16733	0.583664	+	0.811995i	$0.301619\pi$
$632$	−9165.95	−0.576902
$633$	11455.3	0.719284
$634$	11598.3	0.726541
$635$	16797.9	1.04977
$636$	3178.77	0.198186
$637$	0	0
$638$	8891.04	0.551724
$639$	−31.8348	−0.00197084
$640$	2247.75	0.138829
$641$	12083.0	0.744539	0.372269	−	0.928125i	$-0.378580\pi$
$641$	12083.0	0.744539	0.372269	+	0.928125i	$0.378580\pi$
$642$	−10583.5	−0.650617
$643$	−9565.30	−0.586654	−0.293327	−	0.956012i	$-0.594762\pi$
$643$	−9565.30	−0.586654	−0.293327	+	0.956012i	$0.594762\pi$
$644$	1550.12	0.0948501
$645$	22378.1	1.36610
$646$	−2825.58	−0.172091
$647$	−32164.0	−1.95440	−0.977199	−	0.212325i	$-0.931896\pi$
$647$	−32164.0	−1.95440	−0.977199	+	0.212325i	$0.931896\pi$
$648$	−5846.96	−0.354460
$649$	−874.487	−0.0528916
$650$	0	0
$651$	2586.41	0.155713
$652$	13767.1	0.826936
$653$	4503.88	0.269909	0.134954	−	0.990852i	$-0.456911\pi$
$653$	4503.88	0.269909	0.134954	+	0.990852i	$0.456911\pi$
$654$	19658.6	1.17540
$655$	37213.2	2.21991
$656$	−3848.37	−0.229045
$657$	−7.00571	−0.000416011 0
$658$	3318.83	0.196629
$659$	15596.3	0.921921	0.460960	−	0.887421i	$-0.347505\pi$
$659$	15596.3	0.921921	0.460960	+	0.887421i	$0.347505\pi$
$660$	12993.5	0.766322
$661$	12427.9	0.731299	0.365649	−	0.930753i	$-0.380847\pi$
$661$	12427.9	0.731299	0.365649	+	0.930753i	$0.380847\pi$
$662$	12998.4	0.763137
$663$	0	0
$664$	−6892.59	−0.402838
$665$	−8934.74	−0.521014
$666$	48.9434	0.00284763
$667$	6922.17	0.401840
$668$	9395.07	0.544171
$669$	30774.3	1.77848
$670$	−33739.7	−1.94549
$671$	−25409.4	−1.46188
$672$	1165.43	0.0669012
$673$	13124.9	0.751752	0.375876	−	0.926670i	$-0.377342\pi$
$673$	13124.9	0.751752	0.375876	+	0.926670i	$0.377342\pi$
$674$	−7692.05	−0.439594
$675$	25693.4	1.46510
$676$	0	0
$677$	15546.9	0.882595	0.441297	−	0.897361i	$-0.354518\pi$
$677$	15546.9	0.882595	0.441297	+	0.897361i	$0.354518\pi$
$678$	−599.772	−0.0339736
$679$	6325.04	0.357486
$680$	−2730.62	−0.153992
$681$	28985.2	1.63101
$682$	−5049.85	−0.283532
$683$	−24550.1	−1.37538	−0.687688	−	0.726006i	$-0.741374\pi$
$683$	−24550.1	−1.37538	−0.687688	+	0.726006i	$0.741374\pi$
$684$	20.1923	0.00112876
$685$	−43159.2	−2.40734
$686$	−686.000	−0.0381802
$687$	15750.2	0.874685
$688$	−3918.91	−0.217161
$689$	0	0
$690$	10116.2	0.558140
$691$	−10327.2	−0.568548	−0.284274	−	0.958743i	$-0.591752\pi$
$691$	−10327.2	−0.568548	−0.284274	+	0.958743i	$0.591752\pi$
$692$	17398.5	0.955768
$693$	17.2849	0.000947474 0
$694$	12895.3	0.705330
$695$	−38804.3	−2.11788
$696$	5204.31	0.283432
$697$	4675.09	0.254063
$698$	−5273.40	−0.285962
$699$	19582.4	1.05962
$700$	−5134.46	−0.277235
$701$	19970.4	1.07599	0.537996	−	0.842947i	$-0.319181\pi$
$701$	19970.4	1.07599	0.537996	+	0.842947i	$0.319181\pi$
$702$	0	0
$703$	25611.2	1.37403
$704$	−2275.46	−0.121818
$705$	21658.9	1.15705
$706$	8192.20	0.436710
$707$	−6501.87	−0.345867
$708$	−511.875	−0.0271716
$709$	14075.4	0.745574	0.372787	−	0.927917i	$-0.378402\pi$
$709$	14075.4	0.745574	0.372787	+	0.927917i	$0.378402\pi$
$710$	−16098.7	−0.850947
$711$	−79.5734	−0.00419724
$712$	8457.48	0.445165
$713$	−3931.59	−0.206507
$714$	−1415.80	−0.0742084
$715$	0	0
$716$	−13947.3	−0.727981
$717$	−4353.55	−0.226759
$718$	−8072.95	−0.419610
$719$	26600.4	1.37973	0.689867	−	0.723937i	$-0.257669\pi$
$719$	26600.4	1.37973	0.689867	+	0.723937i	$0.257669\pi$
$720$	19.5137	0.00101004
$721$	2706.64	0.139806
$722$	−3151.76	−0.162460
$723$	25880.7	1.33128
$724$	955.870	0.0490672
$725$	−22928.2	−1.17453
$726$	696.248	0.0355926
$727$	25153.0	1.28318	0.641591	−	0.767047i	$-0.278275\pi$
$727$	25153.0	1.28318	0.641591	+	0.767047i	$0.278275\pi$
$728$	0	0
$729$	19632.1	0.997415
$730$	−3542.75	−0.179621
$731$	4760.78	0.240881
$732$	−14873.3	−0.750999
$733$	18255.3	0.919886	0.459943	−	0.887948i	$-0.347870\pi$
$733$	18255.3	0.919886	0.459943	+	0.887948i	$0.347870\pi$
$734$	−26729.2	−1.34413
$735$	−4476.87	−0.224669
$736$	−1771.57	−0.0887241
$737$	34155.5	1.70710
$738$	−33.4093	−0.00166641
$739$	21855.0	1.08789	0.543943	−	0.839122i	$-0.316931\pi$
$739$	21855.0	1.08789	0.543943	+	0.839122i	$0.316931\pi$
$740$	24750.4	1.22952
$741$	0	0
$742$	2138.39	0.105799
$743$	12216.6	0.603207	0.301604	−	0.953433i	$-0.402478\pi$
$743$	12216.6	0.603207	0.301604	+	0.953433i	$0.402478\pi$
$744$	−2955.90	−0.145657
$745$	−12434.0	−0.611471
$746$	−13747.7	−0.674716
$747$	−59.8374	−0.00293084
$748$	2764.28	0.135123
$749$	−7119.61	−0.347323
$750$	−10666.6	−0.519319
$751$	−17533.1	−0.851918	−0.425959	−	0.904742i	$-0.640063\pi$
$751$	−17533.1	−0.851918	−0.425959	+	0.904742i	$0.640063\pi$
$752$	−3792.95	−0.183929
$753$	−11135.8	−0.538924
$754$	0	0
$755$	−18969.8	−0.914412
$756$	−3923.22	−0.188738
$757$	−33216.3	−1.59481	−0.797403	−	0.603447i	$-0.793794\pi$
$757$	−33216.3	−1.59481	−0.797403	+	0.603447i	$0.793794\pi$
$758$	19689.0	0.943453
$759$	−10240.9	−0.489750
$760$	10211.1	0.487364
$761$	−12598.4	−0.600121	−0.300061	−	0.953920i	$-0.597007\pi$
$761$	−12598.4	−0.600121	−0.300061	+	0.953920i	$0.597007\pi$
$762$	−9953.75	−0.473210
$763$	13224.5	0.627471
$764$	−11821.1	−0.559779
$765$	−23.7056	−0.00112037
$766$	−18329.7	−0.864596
$767$	0	0
$768$	−1331.92	−0.0625803
$769$	8651.03	0.405675	0.202838	−	0.979212i	$-0.434984\pi$
$769$	8651.03	0.405675	0.202838	+	0.979212i	$0.434984\pi$
$770$	8740.89	0.409091
$771$	26369.1	1.23172
$772$	10886.8	0.507543
$773$	−16967.8	−0.789506	−0.394753	−	0.918787i	$-0.629170\pi$
$773$	−16967.8	−0.789506	−0.394753	+	0.918787i	$0.629170\pi$
$774$	−34.0216	−0.00157995
$775$	13022.6	0.603593
$776$	−7228.62	−0.334397
$777$	12832.8	0.592503
$778$	11090.4	0.511067
$779$	−17482.5	−0.804074
$780$	0	0
$781$	16297.1	0.746679
$782$	2152.14	0.0984150
$783$	−17519.4	−0.799606
$784$	784.000	0.0357143
$785$	−22003.7	−1.00044
$786$	−22051.0	−1.00068
$787$	28155.5	1.27527	0.637633	−	0.770340i	$-0.279914\pi$
$787$	28155.5	1.27527	0.637633	+	0.770340i	$0.279914\pi$
$788$	−2380.34	−0.107609
$789$	−17164.6	−0.774495
$790$	−40239.8	−1.81224
$791$	−403.473	−0.0181363
$792$	−19.7542	−0.000886281 0
$793$	0	0
$794$	−24366.1	−1.08907
$795$	13955.2	0.622568
$796$	−669.182	−0.0297971
$797$	−15628.0	−0.694568	−0.347284	−	0.937760i	$-0.612896\pi$
$797$	−15628.0	−0.694568	−0.347284	+	0.937760i	$0.612896\pi$
$798$	5294.35	0.234860
$799$	4607.76	0.204019
$800$	5867.96	0.259330
$801$	73.4228	0.00323879
$802$	22484.6	0.989974
$803$	3586.42	0.157611
$804$	19992.7	0.876976
$805$	6805.27	0.297956
$806$	0	0
$807$	−24723.4	−1.07845
$808$	7430.71	0.323529
$809$	6228.55	0.270685	0.135343	−	0.990799i	$-0.456787\pi$
$809$	6228.55	0.270685	0.135343	+	0.990799i	$0.456787\pi$
$810$	−25669.0	−1.11348
$811$	−20273.2	−0.877790	−0.438895	−	0.898538i	$-0.644630\pi$
$811$	−20273.2	−0.877790	−0.438895	+	0.898538i	$0.644630\pi$
$812$	3501.00	0.151307
$813$	7146.80	0.308301
$814$	−25055.5	−1.07886
$815$	60439.6	2.59768
$816$	1618.05	0.0694156
$817$	−17802.9	−0.762355
$818$	24248.8	1.03648
$819$	0	0
$820$	−16894.9	−0.719507
$821$	−21540.3	−0.915666	−0.457833	−	0.889038i	$-0.651374\pi$
$821$	−21540.3	−0.915666	−0.457833	+	0.889038i	$0.651374\pi$
$822$	25574.3	1.08517
$823$	5784.95	0.245019	0.122510	−	0.992467i	$-0.460906\pi$
$823$	5784.95	0.245019	0.122510	+	0.992467i	$0.460906\pi$
$824$	−3093.30	−0.130777
$825$	33920.8	1.43148
$826$	−344.344	−0.0145052
$827$	−5065.76	−0.213003	−0.106502	−	0.994313i	$-0.533965\pi$
$827$	−5065.76	−0.213003	−0.106502	+	0.994313i	$0.533965\pi$
$828$	−15.3797	−0.000645511 0
$829$	26111.1	1.09394	0.546971	−	0.837152i	$-0.315781\pi$
$829$	26111.1	1.09394	0.546971	+	0.837152i	$0.315781\pi$
$830$	−30259.4	−1.26545
$831$	−18624.0	−0.777450
$832$	0	0
$833$	−952.421	−0.0396151
$834$	22993.8	0.954688
$835$	41245.7	1.70942
$836$	−10337.0	−0.427646
$837$	9950.49	0.410919
$838$	−14665.7	−0.604557
$839$	36836.2	1.51576	0.757882	−	0.652392i	$-0.226234\pi$
$839$	36836.2	1.51576	0.757882	+	0.652392i	$0.226234\pi$
$840$	5116.42	0.210159
$841$	−8755.10	−0.358977
$842$	17502.0	0.716339
$843$	39418.7	1.61050
$844$	−8806.97	−0.359181
$845$	0	0
$846$	−32.9282	−0.00133817
$847$	468.374	0.0190006
$848$	−2443.87	−0.0989658
$849$	32562.5	1.31630
$850$	−7128.53	−0.287655
$851$	−19507.1	−0.785775
$852$	9539.40	0.383585
$853$	37518.2	1.50598	0.752989	−	0.658033i	$-0.228611\pi$
$853$	37518.2	1.50598	0.752989	+	0.658033i	$0.228611\pi$
$854$	−10005.4	−0.400911
$855$	88.6470	0.00354581
$856$	8136.69	0.324891
$857$	28899.8	1.15192	0.575962	−	0.817477i	$-0.304628\pi$
$857$	28899.8	1.15192	0.575962	+	0.817477i	$0.304628\pi$
$858$	0	0
$859$	−23027.2	−0.914643	−0.457322	−	0.889301i	$-0.651191\pi$
$859$	−23027.2	−0.914643	−0.457322	+	0.889301i	$0.651191\pi$
$860$	−17204.6	−0.682175
$861$	−8759.81	−0.346729
$862$	−4888.30	−0.193151
$863$	−13042.4	−0.514450	−0.257225	−	0.966352i	$-0.582808\pi$
$863$	−13042.4	−0.514450	−0.257225	+	0.966352i	$0.582808\pi$
$864$	4483.68	0.176549
$865$	76381.9	3.00238
$866$	−20036.1	−0.786206
$867$	23595.9	0.924288
$868$	−1988.46	−0.0777567
$869$	40735.8	1.59018
$870$	22847.7	0.890355
$871$	0	0
$872$	−15113.8	−0.586945
$873$	−62.7546	−0.00243290
$874$	−8047.92	−0.311470
$875$	−7175.53	−0.277231
$876$	2099.29	0.0809684
$877$	−6860.30	−0.264146	−0.132073	−	0.991240i	$-0.542163\pi$
$877$	−6860.30	−0.264146	−0.132073	+	0.991240i	$0.542163\pi$
$878$	−3284.63	−0.126254
$879$	10057.5	0.385929
$880$	−9989.59	−0.382669
$881$	−5787.24	−0.221313	−0.110657	−	0.993859i	$-0.535295\pi$
$881$	−5787.24	−0.221313	−0.110657	+	0.993859i	$0.535295\pi$
$882$	6.80623	0.000259839 0
$883$	35206.6	1.34178	0.670892	−	0.741555i	$-0.265911\pi$
$883$	35206.6	1.34178	0.670892	+	0.741555i	$0.265911\pi$
$884$	0	0
$885$	−2247.21	−0.0853548
$886$	−5728.72	−0.217224
$887$	3252.02	0.123103	0.0615513	−	0.998104i	$-0.480395\pi$
$887$	3252.02	0.123103	0.0615513	+	0.998104i	$0.480395\pi$
$888$	−14666.1	−0.554235
$889$	−6695.99	−0.252617
$890$	37129.5	1.39841
$891$	25985.4	0.977041
$892$	−23659.7	−0.888099
$893$	−17230.7	−0.645692
$894$	7367.86	0.275635
$895$	−61230.6	−2.28683
$896$	−896.000	−0.0334077
$897$	0	0
$898$	28461.3	1.05765
$899$	−8879.60	−0.329423
$900$	50.9422	0.00188675
$901$	2968.87	0.109775
$902$	17103.1	0.631344
$903$	−8920.37	−0.328739
$904$	461.112	0.0169650
$905$	4196.41	0.154136
$906$	11240.7	0.412194
$907$	51382.9	1.88108	0.940541	−	0.339679i	$-0.110318\pi$
$907$	51382.9	1.88108	0.940541	+	0.339679i	$0.110318\pi$
$908$	−22284.2	−0.814456
$909$	64.5091	0.00235383
$910$	0	0
$911$	2406.21	0.0875096	0.0437548	−	0.999042i	$-0.486068\pi$
$911$	2406.21	0.0875096	0.0437548	+	0.999042i	$0.486068\pi$
$912$	−6050.69	−0.219691
$913$	30632.4	1.11039
$914$	−34117.3	−1.23468
$915$	−65295.7	−2.35914
$916$	−12109.0	−0.436781
$917$	−14833.9	−0.534199
$918$	−5446.88	−0.195832
$919$	−3168.94	−0.113747	−0.0568736	−	0.998381i	$-0.518113\pi$
$919$	−3168.94	−0.113747	−0.0568736	+	0.998381i	$0.518113\pi$
$920$	−7777.45	−0.278712
$921$	−25423.1	−0.909576
$922$	−22248.1	−0.794688
$923$	0	0
$924$	−5179.49	−0.184408
$925$	64613.2	2.29672
$926$	−9586.23	−0.340198
$927$	−26.8542	−0.000951464 0
$928$	−4001.14	−0.141534
$929$	−27980.8	−0.988180	−0.494090	−	0.869411i	$-0.664499\pi$
$929$	−27980.8	−0.988180	−0.494090	+	0.869411i	$0.664499\pi$
$930$	−12976.8	−0.457555
$931$	3561.57	0.125377
$932$	−15055.2	−0.529131
$933$	42379.3	1.48707
$934$	2352.57	0.0824179
$935$	12135.6	0.424466
$936$	0	0
$937$	39522.4	1.37795	0.688975	−	0.724785i	$-0.258061\pi$
$937$	39522.4	1.37795	0.688975	+	0.724785i	$0.258061\pi$
$938$	13449.3	0.468162
$939$	−55980.5	−1.94553
$940$	−16651.6	−0.577782
$941$	4246.22	0.147102	0.0735509	−	0.997291i	$-0.476567\pi$
$941$	4246.22	0.147102	0.0735509	+	0.997291i	$0.476567\pi$
$942$	13038.5	0.450974
$943$	13315.8	0.459831
$944$	393.536	0.0135683
$945$	−17223.5	−0.592890
$946$	17416.6	0.598587
$947$	−24063.5	−0.825722	−0.412861	−	0.910794i	$-0.635471\pi$
$947$	−24063.5	−0.825722	−0.412861	+	0.910794i	$0.635471\pi$
$948$	23844.4	0.816911
$949$	0	0
$950$	26657.1	0.910389
$951$	−30172.0	−1.02881
$952$	1088.48	0.0370566
$953$	−47821.8	−1.62550	−0.812750	−	0.582613i	$-0.802030\pi$
$953$	−47821.8	−1.62550	−0.812750	+	0.582613i	$0.802030\pi$
$954$	−21.2163	−0.000720023 0
$955$	−51896.2	−1.75845
$956$	3347.06	0.113234
$957$	−23129.3	−0.781258
$958$	13589.8	0.458314
$959$	17204.1	0.579302
$960$	−5847.34	−0.196586
$961$	−24747.6	−0.830709
$962$	0	0
$963$	70.6380	0.00236374
$964$	−19897.4	−0.664784
$965$	47794.4	1.59436
$966$	−4032.52	−0.134311
$967$	−45369.7	−1.50878	−0.754391	−	0.656425i	$-0.772068\pi$
$967$	−45369.7	−1.50878	−0.754391	+	0.656425i	$0.772068\pi$
$968$	−535.284	−0.0177734
$969$	7350.51	0.243687
$970$	−31734.7	−1.05045
$971$	−12542.2	−0.414520	−0.207260	−	0.978286i	$-0.566455\pi$
$971$	−12542.2	−0.414520	−0.207260	+	0.978286i	$0.566455\pi$
$972$	77.9498	0.00257226
$973$	15468.2	0.509647
$974$	−30150.0	−0.991855
$975$	0	0
$976$	11434.7	0.375018
$977$	18512.7	0.606218	0.303109	−	0.952956i	$-0.401975\pi$
$977$	18512.7	0.606218	0.303109	+	0.952956i	$0.401975\pi$
$978$	−35814.0	−1.17097
$979$	−37587.2	−1.22706
$980$	3441.87	0.112190
$981$	−131.209	−0.00427031
$982$	−1401.55	−0.0455452
$983$	−28145.6	−0.913231	−0.456615	−	0.889664i	$-0.650938\pi$
$983$	−28145.6	−0.913231	−0.456615	+	0.889664i	$0.650938\pi$
$984$	10011.2	0.324335
$985$	−10450.0	−0.338036
$986$	4860.67	0.156993
$987$	−8633.66	−0.278432
$988$	0	0
$989$	13559.8	0.435972
$990$	−86.7237	−0.00278410
$991$	−24434.7	−0.783243	−0.391621	−	0.920126i	$-0.628086\pi$
$991$	−24434.7	−0.783243	−0.391621	+	0.920126i	$0.628086\pi$
$992$	2272.53	0.0727348
$993$	−33814.2	−1.08063
$994$	6417.26	0.204772
$995$	−2937.80	−0.0936027
$996$	17930.5	0.570431
$997$	6620.14	0.210293	0.105146	−	0.994457i	$-0.466469\pi$
$997$	6620.14	0.210293	0.105146	+	0.994457i	$0.466469\pi$
$998$	−3057.27	−0.0969703
$999$	49370.7	1.56358

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.4.a.r.1.2		4
13.3	even	3		182.4.g.a.113.3	yes	8
13.9	even	3		182.4.g.a.29.3	✓	8
13.12	even	2		2366.4.a.q.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.4.g.a.29.3	✓	8	13.9	even	3
182.4.g.a.113.3	yes	8	13.3	even	3
2366.4.a.q.1.2		4	13.12	even	2
2366.4.a.r.1.2		4	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -5.20283 q^{3} +4.00000 q^{4} +17.5606 q^{5} -10.4057 q^{6} -7.00000 q^{7} +8.00000 q^{8} +0.0694513 q^{9} +35.1211 q^{10} -35.5540 q^{11} -20.8113 q^{12} -14.0000 q^{14} -91.3647 q^{15} +16.0000 q^{16} -19.4372 q^{17} +0.138903 q^{18} +72.6851 q^{19} +70.2423 q^{20} +36.4198 q^{21} -71.1081 q^{22} -55.3616 q^{23} -41.6226 q^{24} +183.374 q^{25} +140.115 q^{27} -28.0000 q^{28} -125.036 q^{29} -182.729 q^{30} +71.0166 q^{31} +32.0000 q^{32} +184.982 q^{33} -38.8743 q^{34} -122.924 q^{35} +0.277805 q^{36} +352.358 q^{37} +145.370 q^{38} +140.485 q^{40} -240.523 q^{41} +72.8396 q^{42} -244.932 q^{43} -142.216 q^{44} +1.21960 q^{45} -110.723 q^{46} -237.059 q^{47} -83.2453 q^{48} +49.0000 q^{49} +366.747 q^{50} +101.128 q^{51} -152.742 q^{53} +280.230 q^{54} -624.349 q^{55} -56.0000 q^{56} -378.168 q^{57} -250.071 q^{58} +24.5960 q^{59} -365.459 q^{60} +714.671 q^{61} +142.033 q^{62} -0.486159 q^{63} +64.0000 q^{64} +369.963 q^{66} -960.665 q^{67} -77.7486 q^{68} +288.037 q^{69} -245.848 q^{70} -458.376 q^{71} +0.555610 q^{72} -100.872 q^{73} +704.716 q^{74} -954.062 q^{75} +290.740 q^{76} +248.878 q^{77} -1145.74 q^{79} +280.969 q^{80} -730.870 q^{81} -481.047 q^{82} -861.573 q^{83} +145.679 q^{84} -341.328 q^{85} -489.863 q^{86} +650.539 q^{87} -284.432 q^{88} +1057.18 q^{89} +2.43921 q^{90} -221.446 q^{92} -369.487 q^{93} -474.119 q^{94} +1276.39 q^{95} -166.491 q^{96} -903.577 q^{97} +98.0000 q^{98} -2.46927 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} - 7 q^{3} + 16 q^{4} - q^{5} - 14 q^{6} - 28 q^{7} + 32 q^{8} - 29 q^{9} - 2 q^{10} - 15 q^{11} - 28 q^{12} - 56 q^{14} + 67 q^{15} + 64 q^{16} - 24 q^{17} - 58 q^{18} + 21 q^{19} - 4 q^{20}+ \cdots - 129 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 - 7 * q^3 + 16 * q^4 - q^5 - 14 * q^6 - 28 * q^7 + 32 * q^8 - 29 * q^9 - 2 * q^10 - 15 * q^11 - 28 * q^12 - 56 * q^14 + 67 * q^15 + 64 * q^16 - 24 * q^17 - 58 * q^18 + 21 * q^19 - 4 * q^20 + 49 * q^21 - 30 * q^22 - 182 * q^23 - 56 * q^24 + 365 * q^25 + 92 * q^27 - 112 * q^28 + 133 * q^29 + 134 * q^30 - 282 * q^31 + 128 * q^32 + 95 * q^33 - 48 * q^34 + 7 * q^35 - 116 * q^36 + 730 * q^37 + 42 * q^38 - 8 * q^40 - 182 * q^41 + 98 * q^42 + 83 * q^43 - 60 * q^44 - 73 * q^45 - 364 * q^46 - 560 * q^47 - 112 * q^48 + 196 * q^49 + 730 * q^50 + 209 * q^51 - 106 * q^53 + 184 * q^54 - 997 * q^55 - 224 * q^56 - 341 * q^57 + 266 * q^58 - 782 * q^59 + 268 * q^60 - 708 * q^61 - 564 * q^62 + 203 * q^63 + 256 * q^64 + 190 * q^66 - 528 * q^67 - 96 * q^68 + 1198 * q^69 + 14 * q^70 - 82 * q^71 - 232 * q^72 + 560 * q^73 + 1460 * q^74 - 2873 * q^75 + 84 * q^76 + 105 * q^77 - 1998 * q^79 - 16 * q^80 - 1220 * q^81 - 364 * q^82 - 358 * q^83 + 196 * q^84 - 547 * q^85 + 166 * q^86 - 245 * q^87 - 120 * q^88 + 2385 * q^89 - 146 * q^90 - 728 * q^92 - 1963 * q^93 - 1120 * q^94 + 1117 * q^95 - 224 * q^96 - 1155 * q^97 + 392 * q^98 - 129 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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