Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,4,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(4.42514325043\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.353553 | −0.176777 | − | 0.984251i | \(-0.556567\pi\) | ||||
−0.176777 | + | 0.984251i | \(0.556567\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −7.00000 | −0.875000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.00000 | 0.204124 | ||||||||
\(7\) | 24.0000 | 1.29588 | 0.647939 | − | 0.761692i | \(-0.275631\pi\) | ||||
0.647939 | + | 0.761692i | \(0.275631\pi\) | |||||||
\(8\) | 15.0000 | 0.662913 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 52.0000 | 1.42533 | 0.712663 | − | 0.701506i | \(-0.247489\pi\) | ||||
0.712663 | + | 0.701506i | \(0.247489\pi\) | |||||||
\(12\) | 21.0000 | 0.505181 | ||||||||
\(13\) | −22.0000 | −0.469362 | −0.234681 | − | 0.972072i | \(-0.575405\pi\) | ||||
−0.234681 | + | 0.972072i | \(0.575405\pi\) | |||||||
\(14\) | −24.0000 | −0.458162 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 41.0000 | 0.640625 | ||||||||
\(17\) | 14.0000 | 0.199735 | 0.0998676 | − | 0.995001i | \(-0.468158\pi\) | ||||
0.0998676 | + | 0.995001i | \(0.468158\pi\) | |||||||
\(18\) | −9.00000 | −0.117851 | ||||||||
\(19\) | −20.0000 | −0.241490 | −0.120745 | − | 0.992684i | \(-0.538528\pi\) | ||||
−0.120745 | + | 0.992684i | \(0.538528\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −72.0000 | −0.748176 | ||||||||
\(22\) | −52.0000 | −0.503929 | ||||||||
\(23\) | 168.000 | 1.52306 | 0.761531 | − | 0.648129i | \(-0.224448\pi\) | ||||
0.761531 | + | 0.648129i | \(0.224448\pi\) | |||||||
\(24\) | −45.0000 | −0.382733 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 22.0000 | 0.165944 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −168.000 | −1.13389 | ||||||||
\(29\) | 230.000 | 1.47276 | 0.736378 | − | 0.676570i | \(-0.236535\pi\) | ||||
0.736378 | + | 0.676570i | \(0.236535\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −288.000 | −1.66859 | −0.834296 | − | 0.551317i | \(-0.814125\pi\) | ||||
−0.834296 | + | 0.551317i | \(0.814125\pi\) | |||||||
\(32\) | −161.000 | −0.889408 | ||||||||
\(33\) | −156.000 | −0.822913 | ||||||||
\(34\) | −14.0000 | −0.0706171 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −63.0000 | −0.291667 | ||||||||
\(37\) | 34.0000 | 0.151069 | 0.0755347 | − | 0.997143i | \(-0.475934\pi\) | ||||
0.0755347 | + | 0.997143i | \(0.475934\pi\) | |||||||
\(38\) | 20.0000 | 0.0853797 | ||||||||
\(39\) | 66.0000 | 0.270986 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 122.000 | 0.464712 | 0.232356 | − | 0.972631i | \(-0.425357\pi\) | ||||
0.232356 | + | 0.972631i | \(0.425357\pi\) | |||||||
\(42\) | 72.0000 | 0.264520 | ||||||||
\(43\) | 188.000 | 0.666738 | 0.333369 | − | 0.942796i | \(-0.391815\pi\) | ||||
0.333369 | + | 0.942796i | \(0.391815\pi\) | |||||||
\(44\) | −364.000 | −1.24716 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −168.000 | −0.538484 | ||||||||
\(47\) | −256.000 | −0.794499 | −0.397249 | − | 0.917711i | \(-0.630035\pi\) | ||||
−0.397249 | + | 0.917711i | \(0.630035\pi\) | |||||||
\(48\) | −123.000 | −0.369865 | ||||||||
\(49\) | 233.000 | 0.679300 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −42.0000 | −0.115317 | ||||||||
\(52\) | 154.000 | 0.410691 | ||||||||
\(53\) | 338.000 | 0.875998 | 0.437999 | − | 0.898976i | \(-0.355687\pi\) | ||||
0.437999 | + | 0.898976i | \(0.355687\pi\) | |||||||
\(54\) | 27.0000 | 0.0680414 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 360.000 | 0.859054 | ||||||||
\(57\) | 60.0000 | 0.139424 | ||||||||
\(58\) | −230.000 | −0.520698 | ||||||||
\(59\) | 100.000 | 0.220659 | 0.110330 | − | 0.993895i | \(-0.464809\pi\) | ||||
0.110330 | + | 0.993895i | \(0.464809\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 742.000 | 1.55743 | 0.778716 | − | 0.627376i | \(-0.215871\pi\) | ||||
0.778716 | + | 0.627376i | \(0.215871\pi\) | |||||||
\(62\) | 288.000 | 0.589936 | ||||||||
\(63\) | 216.000 | 0.431959 | ||||||||
\(64\) | −167.000 | −0.326172 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 156.000 | 0.290944 | ||||||||
\(67\) | 84.0000 | 0.153168 | 0.0765838 | − | 0.997063i | \(-0.475599\pi\) | ||||
0.0765838 | + | 0.997063i | \(0.475599\pi\) | |||||||
\(68\) | −98.0000 | −0.174768 | ||||||||
\(69\) | −504.000 | −0.879340 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −328.000 | −0.548260 | −0.274130 | − | 0.961693i | \(-0.588390\pi\) | ||||
−0.274130 | + | 0.961693i | \(0.588390\pi\) | |||||||
\(72\) | 135.000 | 0.220971 | ||||||||
\(73\) | 38.0000 | 0.0609255 | 0.0304628 | − | 0.999536i | \(-0.490302\pi\) | ||||
0.0304628 | + | 0.999536i | \(0.490302\pi\) | |||||||
\(74\) | −34.0000 | −0.0534111 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 140.000 | 0.211304 | ||||||||
\(77\) | 1248.00 | 1.84705 | ||||||||
\(78\) | −66.0000 | −0.0958081 | ||||||||
\(79\) | −240.000 | −0.341799 | −0.170899 | − | 0.985288i | \(-0.554667\pi\) | ||||
−0.170899 | + | 0.985288i | \(0.554667\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −122.000 | −0.164301 | ||||||||
\(83\) | −1212.00 | −1.60282 | −0.801411 | − | 0.598114i | \(-0.795917\pi\) | ||||
−0.801411 | + | 0.598114i | \(0.795917\pi\) | |||||||
\(84\) | 504.000 | 0.654654 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −188.000 | −0.235727 | ||||||||
\(87\) | −690.000 | −0.850296 | ||||||||
\(88\) | 780.000 | 0.944867 | ||||||||
\(89\) | 330.000 | 0.393033 | 0.196516 | − | 0.980501i | \(-0.437037\pi\) | ||||
0.196516 | + | 0.980501i | \(0.437037\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −528.000 | −0.608236 | ||||||||
\(92\) | −1176.00 | −1.33268 | ||||||||
\(93\) | 864.000 | 0.963362 | ||||||||
\(94\) | 256.000 | 0.280898 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 483.000 | 0.513500 | ||||||||
\(97\) | −866.000 | −0.906484 | −0.453242 | − | 0.891387i | \(-0.649733\pi\) | ||||
−0.453242 | + | 0.891387i | \(0.649733\pi\) | |||||||
\(98\) | −233.000 | −0.240169 | ||||||||
\(99\) | 468.000 | 0.475109 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1218.00 | −1.19996 | −0.599978 | − | 0.800017i | \(-0.704824\pi\) | ||||
−0.599978 | + | 0.800017i | \(0.704824\pi\) | |||||||
\(102\) | 42.0000 | 0.0407708 | ||||||||
\(103\) | 88.0000 | 0.0841835 | 0.0420917 | − | 0.999114i | \(-0.486598\pi\) | ||||
0.0420917 | + | 0.999114i | \(0.486598\pi\) | |||||||
\(104\) | −330.000 | −0.311146 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −338.000 | −0.309712 | ||||||||
\(107\) | −36.0000 | −0.0325257 | −0.0162629 | − | 0.999868i | \(-0.505177\pi\) | ||||
−0.0162629 | + | 0.999868i | \(0.505177\pi\) | |||||||
\(108\) | 189.000 | 0.168394 | ||||||||
\(109\) | −970.000 | −0.852378 | −0.426189 | − | 0.904634i | \(-0.640144\pi\) | ||||
−0.426189 | + | 0.904634i | \(0.640144\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −102.000 | −0.0872199 | ||||||||
\(112\) | 984.000 | 0.830172 | ||||||||
\(113\) | −1042.00 | −0.867461 | −0.433731 | − | 0.901043i | \(-0.642803\pi\) | ||||
−0.433731 | + | 0.901043i | \(0.642803\pi\) | |||||||
\(114\) | −60.0000 | −0.0492940 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1610.00 | −1.28866 | ||||||||
\(117\) | −198.000 | −0.156454 | ||||||||
\(118\) | −100.000 | −0.0780148 | ||||||||
\(119\) | 336.000 | 0.258833 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1373.00 | 1.03156 | ||||||||
\(122\) | −742.000 | −0.550635 | ||||||||
\(123\) | −366.000 | −0.268302 | ||||||||
\(124\) | 2016.00 | 1.46002 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −216.000 | −0.152721 | ||||||||
\(127\) | −1936.00 | −1.35269 | −0.676347 | − | 0.736583i | \(-0.736438\pi\) | ||||
−0.676347 | + | 0.736583i | \(0.736438\pi\) | |||||||
\(128\) | 1455.00 | 1.00473 | ||||||||
\(129\) | −564.000 | −0.384941 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 732.000 | 0.488207 | 0.244104 | − | 0.969749i | \(-0.421506\pi\) | ||||
0.244104 | + | 0.969749i | \(0.421506\pi\) | |||||||
\(132\) | 1092.00 | 0.720048 | ||||||||
\(133\) | −480.000 | −0.312942 | ||||||||
\(134\) | −84.0000 | −0.0541529 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 210.000 | 0.132407 | ||||||||
\(137\) | 2214.00 | 1.38069 | 0.690346 | − | 0.723479i | \(-0.257458\pi\) | ||||
0.690346 | + | 0.723479i | \(0.257458\pi\) | |||||||
\(138\) | 504.000 | 0.310894 | ||||||||
\(139\) | 20.0000 | 0.0122042 | 0.00610208 | − | 0.999981i | \(-0.498058\pi\) | ||||
0.00610208 | + | 0.999981i | \(0.498058\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 768.000 | 0.458704 | ||||||||
\(142\) | 328.000 | 0.193839 | ||||||||
\(143\) | −1144.00 | −0.668994 | ||||||||
\(144\) | 369.000 | 0.213542 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −38.0000 | −0.0215404 | ||||||||
\(147\) | −699.000 | −0.392194 | ||||||||
\(148\) | −238.000 | −0.132186 | ||||||||
\(149\) | −1330.00 | −0.731261 | −0.365630 | − | 0.930760i | \(-0.619147\pi\) | ||||
−0.365630 | + | 0.930760i | \(0.619147\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1208.00 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | −300.000 | −0.160087 | ||||||||
\(153\) | 126.000 | 0.0665784 | ||||||||
\(154\) | −1248.00 | −0.653031 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −462.000 | −0.237113 | ||||||||
\(157\) | 3514.00 | 1.78629 | 0.893146 | − | 0.449768i | \(-0.148493\pi\) | ||||
0.893146 | + | 0.449768i | \(0.148493\pi\) | |||||||
\(158\) | 240.000 | 0.120844 | ||||||||
\(159\) | −1014.00 | −0.505757 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4032.00 | 1.97370 | ||||||||
\(162\) | −81.0000 | −0.0392837 | ||||||||
\(163\) | 2068.00 | 0.993732 | 0.496866 | − | 0.867827i | \(-0.334484\pi\) | ||||
0.496866 | + | 0.867827i | \(0.334484\pi\) | |||||||
\(164\) | −854.000 | −0.406623 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1212.00 | 0.566683 | ||||||||
\(167\) | 24.0000 | 0.0111208 | 0.00556041 | − | 0.999985i | \(-0.498230\pi\) | ||||
0.00556041 | + | 0.999985i | \(0.498230\pi\) | |||||||
\(168\) | −1080.00 | −0.495975 | ||||||||
\(169\) | −1713.00 | −0.779700 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −180.000 | −0.0804967 | ||||||||
\(172\) | −1316.00 | −0.583396 | ||||||||
\(173\) | 618.000 | 0.271593 | 0.135797 | − | 0.990737i | \(-0.456641\pi\) | ||||
0.135797 | + | 0.990737i | \(0.456641\pi\) | |||||||
\(174\) | 690.000 | 0.300625 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2132.00 | 0.913100 | ||||||||
\(177\) | −300.000 | −0.127398 | ||||||||
\(178\) | −330.000 | −0.138958 | ||||||||
\(179\) | 3340.00 | 1.39466 | 0.697328 | − | 0.716752i | \(-0.254372\pi\) | ||||
0.697328 | + | 0.716752i | \(0.254372\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −178.000 | −0.0730974 | −0.0365487 | − | 0.999332i | \(-0.511636\pi\) | ||||
−0.0365487 | + | 0.999332i | \(0.511636\pi\) | |||||||
\(182\) | 528.000 | 0.215044 | ||||||||
\(183\) | −2226.00 | −0.899184 | ||||||||
\(184\) | 2520.00 | 1.00966 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −864.000 | −0.340600 | ||||||||
\(187\) | 728.000 | 0.284688 | ||||||||
\(188\) | 1792.00 | 0.695186 | ||||||||
\(189\) | −648.000 | −0.249392 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1888.00 | −0.715240 | −0.357620 | − | 0.933867i | \(-0.616412\pi\) | ||||
−0.357620 | + | 0.933867i | \(0.616412\pi\) | |||||||
\(192\) | 501.000 | 0.188315 | ||||||||
\(193\) | −1922.00 | −0.716832 | −0.358416 | − | 0.933562i | \(-0.616683\pi\) | ||||
−0.358416 | + | 0.933562i | \(0.616683\pi\) | |||||||
\(194\) | 866.000 | 0.320491 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1631.00 | −0.594388 | ||||||||
\(197\) | −2526.00 | −0.913554 | −0.456777 | − | 0.889581i | \(-0.650996\pi\) | ||||
−0.456777 | + | 0.889581i | \(0.650996\pi\) | |||||||
\(198\) | −468.000 | −0.167976 | ||||||||
\(199\) | −1160.00 | −0.413217 | −0.206609 | − | 0.978424i | \(-0.566243\pi\) | ||||
−0.206609 | + | 0.978424i | \(0.566243\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −252.000 | −0.0884314 | ||||||||
\(202\) | 1218.00 | 0.424248 | ||||||||
\(203\) | 5520.00 | 1.90851 | ||||||||
\(204\) | 294.000 | 0.100903 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −88.0000 | −0.0297634 | ||||||||
\(207\) | 1512.00 | 0.507687 | ||||||||
\(208\) | −902.000 | −0.300685 | ||||||||
\(209\) | −1040.00 | −0.344202 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4468.00 | −1.45777 | −0.728886 | − | 0.684635i | \(-0.759961\pi\) | ||||
−0.728886 | + | 0.684635i | \(0.759961\pi\) | |||||||
\(212\) | −2366.00 | −0.766498 | ||||||||
\(213\) | 984.000 | 0.316538 | ||||||||
\(214\) | 36.0000 | 0.0114996 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −405.000 | −0.127578 | ||||||||
\(217\) | −6912.00 | −2.16229 | ||||||||
\(218\) | 970.000 | 0.301361 | ||||||||
\(219\) | −114.000 | −0.0351754 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −308.000 | −0.0937481 | ||||||||
\(222\) | 102.000 | 0.0308369 | ||||||||
\(223\) | −6032.00 | −1.81136 | −0.905678 | − | 0.423965i | \(-0.860638\pi\) | ||||
−0.905678 | + | 0.423965i | \(0.860638\pi\) | |||||||
\(224\) | −3864.00 | −1.15256 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1042.00 | 0.306694 | ||||||||
\(227\) | −2636.00 | −0.770738 | −0.385369 | − | 0.922763i | \(-0.625926\pi\) | ||||
−0.385369 | + | 0.922763i | \(0.625926\pi\) | |||||||
\(228\) | −420.000 | −0.121996 | ||||||||
\(229\) | 4830.00 | 1.39378 | 0.696889 | − | 0.717179i | \(-0.254567\pi\) | ||||
0.696889 | + | 0.717179i | \(0.254567\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3744.00 | −1.06639 | ||||||||
\(232\) | 3450.00 | 0.976309 | ||||||||
\(233\) | −2682.00 | −0.754093 | −0.377046 | − | 0.926194i | \(-0.623060\pi\) | ||||
−0.377046 | + | 0.926194i | \(0.623060\pi\) | |||||||
\(234\) | 198.000 | 0.0553148 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −700.000 | −0.193077 | ||||||||
\(237\) | 720.000 | 0.197338 | ||||||||
\(238\) | −336.000 | −0.0915111 | ||||||||
\(239\) | 2320.00 | 0.627901 | 0.313950 | − | 0.949439i | \(-0.398347\pi\) | ||||
0.313950 | + | 0.949439i | \(0.398347\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2002.00 | 0.535104 | 0.267552 | − | 0.963543i | \(-0.413785\pi\) | ||||
0.267552 | + | 0.963543i | \(0.413785\pi\) | |||||||
\(242\) | −1373.00 | −0.364710 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −5194.00 | −1.36275 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 366.000 | 0.0948590 | ||||||||
\(247\) | 440.000 | 0.113346 | ||||||||
\(248\) | −4320.00 | −1.10613 | ||||||||
\(249\) | 3636.00 | 0.925390 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 132.000 | 0.0331943 | 0.0165971 | − | 0.999862i | \(-0.494717\pi\) | ||||
0.0165971 | + | 0.999862i | \(0.494717\pi\) | |||||||
\(252\) | −1512.00 | −0.377964 | ||||||||
\(253\) | 8736.00 | 2.17086 | ||||||||
\(254\) | 1936.00 | 0.478250 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −119.000 | −0.0290527 | ||||||||
\(257\) | 7614.00 | 1.84805 | 0.924024 | − | 0.382335i | \(-0.124880\pi\) | ||||
0.924024 | + | 0.382335i | \(0.124880\pi\) | |||||||
\(258\) | 564.000 | 0.136097 | ||||||||
\(259\) | 816.000 | 0.195767 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2070.00 | 0.490919 | ||||||||
\(262\) | −732.000 | −0.172607 | ||||||||
\(263\) | 4888.00 | 1.14603 | 0.573017 | − | 0.819543i | \(-0.305773\pi\) | ||||
0.573017 | + | 0.819543i | \(0.305773\pi\) | |||||||
\(264\) | −2340.00 | −0.545519 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 480.000 | 0.110642 | ||||||||
\(267\) | −990.000 | −0.226918 | ||||||||
\(268\) | −588.000 | −0.134022 | ||||||||
\(269\) | 1270.00 | 0.287856 | 0.143928 | − | 0.989588i | \(-0.454027\pi\) | ||||
0.143928 | + | 0.989588i | \(0.454027\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1072.00 | 0.240293 | 0.120146 | − | 0.992756i | \(-0.461664\pi\) | ||||
0.120146 | + | 0.992756i | \(0.461664\pi\) | |||||||
\(272\) | 574.000 | 0.127955 | ||||||||
\(273\) | 1584.00 | 0.351165 | ||||||||
\(274\) | −2214.00 | −0.488148 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3528.00 | 0.769423 | ||||||||
\(277\) | 5394.00 | 1.17001 | 0.585007 | − | 0.811028i | \(-0.301092\pi\) | ||||
0.585007 | + | 0.811028i | \(0.301092\pi\) | |||||||
\(278\) | −20.0000 | −0.00431482 | ||||||||
\(279\) | −2592.00 | −0.556197 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2442.00 | 0.518425 | 0.259213 | − | 0.965820i | \(-0.416537\pi\) | ||||
0.259213 | + | 0.965820i | \(0.416537\pi\) | |||||||
\(282\) | −768.000 | −0.162176 | ||||||||
\(283\) | −2772.00 | −0.582255 | −0.291128 | − | 0.956684i | \(-0.594030\pi\) | ||||
−0.291128 | + | 0.956684i | \(0.594030\pi\) | |||||||
\(284\) | 2296.00 | 0.479727 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1144.00 | 0.236525 | ||||||||
\(287\) | 2928.00 | 0.602210 | ||||||||
\(288\) | −1449.00 | −0.296469 | ||||||||
\(289\) | −4717.00 | −0.960106 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2598.00 | 0.523359 | ||||||||
\(292\) | −266.000 | −0.0533098 | ||||||||
\(293\) | −4542.00 | −0.905619 | −0.452810 | − | 0.891607i | \(-0.649578\pi\) | ||||
−0.452810 | + | 0.891607i | \(0.649578\pi\) | |||||||
\(294\) | 699.000 | 0.138662 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 510.000 | 0.100146 | ||||||||
\(297\) | −1404.00 | −0.274304 | ||||||||
\(298\) | 1330.00 | 0.258540 | ||||||||
\(299\) | −3696.00 | −0.714867 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4512.00 | 0.864011 | ||||||||
\(302\) | 1208.00 | 0.230174 | ||||||||
\(303\) | 3654.00 | 0.692795 | ||||||||
\(304\) | −820.000 | −0.154705 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −126.000 | −0.0235390 | ||||||||
\(307\) | −5116.00 | −0.951093 | −0.475546 | − | 0.879691i | \(-0.657750\pi\) | ||||
−0.475546 | + | 0.879691i | \(0.657750\pi\) | |||||||
\(308\) | −8736.00 | −1.61617 | ||||||||
\(309\) | −264.000 | −0.0486034 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2808.00 | −0.511984 | −0.255992 | − | 0.966679i | \(-0.582402\pi\) | ||||
−0.255992 | + | 0.966679i | \(0.582402\pi\) | |||||||
\(312\) | 990.000 | 0.179640 | ||||||||
\(313\) | 7318.00 | 1.32153 | 0.660763 | − | 0.750594i | \(-0.270233\pi\) | ||||
0.660763 | + | 0.750594i | \(0.270233\pi\) | |||||||
\(314\) | −3514.00 | −0.631549 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1680.00 | 0.299074 | ||||||||
\(317\) | −2246.00 | −0.397943 | −0.198971 | − | 0.980005i | \(-0.563760\pi\) | ||||
−0.198971 | + | 0.980005i | \(0.563760\pi\) | |||||||
\(318\) | 1014.00 | 0.178812 | ||||||||
\(319\) | 11960.0 | 2.09916 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 108.000 | 0.0187787 | ||||||||
\(322\) | −4032.00 | −0.697809 | ||||||||
\(323\) | −280.000 | −0.0482341 | ||||||||
\(324\) | −567.000 | −0.0972222 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2068.00 | −0.351337 | ||||||||
\(327\) | 2910.00 | 0.492120 | ||||||||
\(328\) | 1830.00 | 0.308064 | ||||||||
\(329\) | −6144.00 | −1.02957 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1332.00 | 0.221188 | 0.110594 | − | 0.993866i | \(-0.464725\pi\) | ||||
0.110594 | + | 0.993866i | \(0.464725\pi\) | |||||||
\(332\) | 8484.00 | 1.40247 | ||||||||
\(333\) | 306.000 | 0.0503564 | ||||||||
\(334\) | −24.0000 | −0.00393180 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2952.00 | −0.479300 | ||||||||
\(337\) | 11534.0 | 1.86438 | 0.932191 | − | 0.361966i | \(-0.117894\pi\) | ||||
0.932191 | + | 0.361966i | \(0.117894\pi\) | |||||||
\(338\) | 1713.00 | 0.275665 | ||||||||
\(339\) | 3126.00 | 0.500829 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14976.0 | −2.37829 | ||||||||
\(342\) | 180.000 | 0.0284599 | ||||||||
\(343\) | −2640.00 | −0.415588 | ||||||||
\(344\) | 2820.00 | 0.441989 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −618.000 | −0.0960228 | ||||||||
\(347\) | −11956.0 | −1.84966 | −0.924830 | − | 0.380382i | \(-0.875793\pi\) | ||||
−0.924830 | + | 0.380382i | \(0.875793\pi\) | |||||||
\(348\) | 4830.00 | 0.744009 | ||||||||
\(349\) | 4870.00 | 0.746949 | 0.373474 | − | 0.927640i | \(-0.378166\pi\) | ||||
0.373474 | + | 0.927640i | \(0.378166\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 594.000 | 0.0903287 | ||||||||
\(352\) | −8372.00 | −1.26770 | ||||||||
\(353\) | −10722.0 | −1.61664 | −0.808321 | − | 0.588742i | \(-0.799623\pi\) | ||||
−0.808321 | + | 0.588742i | \(0.799623\pi\) | |||||||
\(354\) | 300.000 | 0.0450419 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2310.00 | −0.343904 | ||||||||
\(357\) | −1008.00 | −0.149437 | ||||||||
\(358\) | −3340.00 | −0.493085 | ||||||||
\(359\) | 120.000 | 0.0176417 | 0.00882083 | − | 0.999961i | \(-0.497192\pi\) | ||||
0.00882083 | + | 0.999961i | \(0.497192\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6459.00 | −0.941682 | ||||||||
\(362\) | 178.000 | 0.0258438 | ||||||||
\(363\) | −4119.00 | −0.595569 | ||||||||
\(364\) | 3696.00 | 0.532206 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2226.00 | 0.317910 | ||||||||
\(367\) | −3936.00 | −0.559830 | −0.279915 | − | 0.960025i | \(-0.590306\pi\) | ||||
−0.279915 | + | 0.960025i | \(0.590306\pi\) | |||||||
\(368\) | 6888.00 | 0.975711 | ||||||||
\(369\) | 1098.00 | 0.154904 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8112.00 | 1.13519 | ||||||||
\(372\) | −6048.00 | −0.842941 | ||||||||
\(373\) | −3022.00 | −0.419499 | −0.209750 | − | 0.977755i | \(-0.567265\pi\) | ||||
−0.209750 | + | 0.977755i | \(0.567265\pi\) | |||||||
\(374\) | −728.000 | −0.100652 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3840.00 | −0.526683 | ||||||||
\(377\) | −5060.00 | −0.691255 | ||||||||
\(378\) | 648.000 | 0.0881733 | ||||||||
\(379\) | −13340.0 | −1.80799 | −0.903997 | − | 0.427539i | \(-0.859381\pi\) | ||||
−0.903997 | + | 0.427539i | \(0.859381\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5808.00 | 0.780979 | ||||||||
\(382\) | 1888.00 | 0.252876 | ||||||||
\(383\) | 1008.00 | 0.134481 | 0.0672407 | − | 0.997737i | \(-0.478580\pi\) | ||||
0.0672407 | + | 0.997737i | \(0.478580\pi\) | |||||||
\(384\) | −4365.00 | −0.580079 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1922.00 | 0.253438 | ||||||||
\(387\) | 1692.00 | 0.222246 | ||||||||
\(388\) | 6062.00 | 0.793174 | ||||||||
\(389\) | 9630.00 | 1.25517 | 0.627584 | − | 0.778549i | \(-0.284044\pi\) | ||||
0.627584 | + | 0.778549i | \(0.284044\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2352.00 | 0.304209 | ||||||||
\(392\) | 3495.00 | 0.450317 | ||||||||
\(393\) | −2196.00 | −0.281867 | ||||||||
\(394\) | 2526.00 | 0.322990 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3276.00 | −0.415720 | ||||||||
\(397\) | −7126.00 | −0.900866 | −0.450433 | − | 0.892810i | \(-0.648730\pi\) | ||||
−0.450433 | + | 0.892810i | \(0.648730\pi\) | |||||||
\(398\) | 1160.00 | 0.146094 | ||||||||
\(399\) | 1440.00 | 0.180677 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8718.00 | −1.08568 | −0.542838 | − | 0.839837i | \(-0.682650\pi\) | ||||
−0.542838 | + | 0.839837i | \(0.682650\pi\) | |||||||
\(402\) | 252.000 | 0.0312652 | ||||||||
\(403\) | 6336.00 | 0.783173 | ||||||||
\(404\) | 8526.00 | 1.04996 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5520.00 | −0.674761 | ||||||||
\(407\) | 1768.00 | 0.215323 | ||||||||
\(408\) | −630.000 | −0.0764452 | ||||||||
\(409\) | −10870.0 | −1.31415 | −0.657074 | − | 0.753826i | \(-0.728206\pi\) | ||||
−0.657074 | + | 0.753826i | \(0.728206\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6642.00 | −0.797143 | ||||||||
\(412\) | −616.000 | −0.0736605 | ||||||||
\(413\) | 2400.00 | 0.285947 | ||||||||
\(414\) | −1512.00 | −0.179495 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3542.00 | 0.417454 | ||||||||
\(417\) | −60.0000 | −0.00704607 | ||||||||
\(418\) | 1040.00 | 0.121694 | ||||||||
\(419\) | −9700.00 | −1.13097 | −0.565484 | − | 0.824759i | \(-0.691311\pi\) | ||||
−0.565484 | + | 0.824759i | \(0.691311\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 862.000 | 0.0997893 | 0.0498947 | − | 0.998754i | \(-0.484111\pi\) | ||||
0.0498947 | + | 0.998754i | \(0.484111\pi\) | |||||||
\(422\) | 4468.00 | 0.515400 | ||||||||
\(423\) | −2304.00 | −0.264833 | ||||||||
\(424\) | 5070.00 | 0.580710 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −984.000 | −0.111913 | ||||||||
\(427\) | 17808.0 | 2.01824 | ||||||||
\(428\) | 252.000 | 0.0284600 | ||||||||
\(429\) | 3432.00 | 0.386244 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15792.0 | 1.76490 | 0.882452 | − | 0.470402i | \(-0.155891\pi\) | ||||
0.882452 | + | 0.470402i | \(0.155891\pi\) | |||||||
\(432\) | −1107.00 | −0.123288 | ||||||||
\(433\) | −11602.0 | −1.28766 | −0.643830 | − | 0.765169i | \(-0.722655\pi\) | ||||
−0.643830 | + | 0.765169i | \(0.722655\pi\) | |||||||
\(434\) | 6912.00 | 0.764485 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6790.00 | 0.745830 | ||||||||
\(437\) | −3360.00 | −0.367805 | ||||||||
\(438\) | 114.000 | 0.0124364 | ||||||||
\(439\) | −440.000 | −0.0478361 | −0.0239181 | − | 0.999714i | \(-0.507614\pi\) | ||||
−0.0239181 | + | 0.999714i | \(0.507614\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2097.00 | 0.226433 | ||||||||
\(442\) | 308.000 | 0.0331449 | ||||||||
\(443\) | 10188.0 | 1.09266 | 0.546328 | − | 0.837571i | \(-0.316025\pi\) | ||||
0.546328 | + | 0.837571i | \(0.316025\pi\) | |||||||
\(444\) | 714.000 | 0.0763174 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6032.00 | 0.640411 | ||||||||
\(447\) | 3990.00 | 0.422194 | ||||||||
\(448\) | −4008.00 | −0.422679 | ||||||||
\(449\) | −13310.0 | −1.39897 | −0.699485 | − | 0.714647i | \(-0.746587\pi\) | ||||
−0.699485 | + | 0.714647i | \(0.746587\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6344.00 | 0.662367 | ||||||||
\(452\) | 7294.00 | 0.759029 | ||||||||
\(453\) | 3624.00 | 0.375873 | ||||||||
\(454\) | 2636.00 | 0.272497 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 900.000 | 0.0924262 | ||||||||
\(457\) | −3226.00 | −0.330210 | −0.165105 | − | 0.986276i | \(-0.552796\pi\) | ||||
−0.165105 | + | 0.986276i | \(0.552796\pi\) | |||||||
\(458\) | −4830.00 | −0.492775 | ||||||||
\(459\) | −378.000 | −0.0384391 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6582.00 | 0.664977 | 0.332488 | − | 0.943107i | \(-0.392112\pi\) | ||||
0.332488 | + | 0.943107i | \(0.392112\pi\) | |||||||
\(462\) | 3744.00 | 0.377027 | ||||||||
\(463\) | −15072.0 | −1.51286 | −0.756431 | − | 0.654073i | \(-0.773059\pi\) | ||||
−0.756431 | + | 0.654073i | \(0.773059\pi\) | |||||||
\(464\) | 9430.00 | 0.943484 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2682.00 | 0.266612 | ||||||||
\(467\) | −476.000 | −0.0471663 | −0.0235831 | − | 0.999722i | \(-0.507507\pi\) | ||||
−0.0235831 | + | 0.999722i | \(0.507507\pi\) | |||||||
\(468\) | 1386.00 | 0.136897 | ||||||||
\(469\) | 2016.00 | 0.198487 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10542.0 | −1.03132 | ||||||||
\(472\) | 1500.00 | 0.146278 | ||||||||
\(473\) | 9776.00 | 0.950319 | ||||||||
\(474\) | −720.000 | −0.0697694 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2352.00 | −0.226478 | ||||||||
\(477\) | 3042.00 | 0.291999 | ||||||||
\(478\) | −2320.00 | −0.221997 | ||||||||
\(479\) | −19680.0 | −1.87725 | −0.938624 | − | 0.344941i | \(-0.887899\pi\) | ||||
−0.938624 | + | 0.344941i | \(0.887899\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −748.000 | −0.0709062 | ||||||||
\(482\) | −2002.00 | −0.189188 | ||||||||
\(483\) | −12096.0 | −1.13952 | ||||||||
\(484\) | −9611.00 | −0.902611 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 243.000 | 0.0226805 | ||||||||
\(487\) | 5944.00 | 0.553077 | 0.276538 | − | 0.961003i | \(-0.410813\pi\) | ||||
0.276538 | + | 0.961003i | \(0.410813\pi\) | |||||||
\(488\) | 11130.0 | 1.03244 | ||||||||
\(489\) | −6204.00 | −0.573731 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10772.0 | 0.990089 | 0.495044 | − | 0.868868i | \(-0.335152\pi\) | ||||
0.495044 | + | 0.868868i | \(0.335152\pi\) | |||||||
\(492\) | 2562.00 | 0.234764 | ||||||||
\(493\) | 3220.00 | 0.294161 | ||||||||
\(494\) | −440.000 | −0.0400740 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11808.0 | −1.06894 | ||||||||
\(497\) | −7872.00 | −0.710478 | ||||||||
\(498\) | −3636.00 | −0.327175 | ||||||||
\(499\) | 8140.00 | 0.730253 | 0.365127 | − | 0.930958i | \(-0.381026\pi\) | ||||
0.365127 | + | 0.930958i | \(0.381026\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −72.0000 | −0.00642060 | ||||||||
\(502\) | −132.000 | −0.0117360 | ||||||||
\(503\) | 13768.0 | 1.22045 | 0.610223 | − | 0.792229i | \(-0.291080\pi\) | ||||
0.610223 | + | 0.792229i | \(0.291080\pi\) | |||||||
\(504\) | 3240.00 | 0.286351 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8736.00 | −0.767515 | ||||||||
\(507\) | 5139.00 | 0.450160 | ||||||||
\(508\) | 13552.0 | 1.18361 | ||||||||
\(509\) | 22150.0 | 1.92884 | 0.964422 | − | 0.264368i | \(-0.0851633\pi\) | ||||
0.964422 | + | 0.264368i | \(0.0851633\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 912.000 | 0.0789521 | ||||||||
\(512\) | −11521.0 | −0.994455 | ||||||||
\(513\) | 540.000 | 0.0464748 | ||||||||
\(514\) | −7614.00 | −0.653384 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3948.00 | 0.336824 | ||||||||
\(517\) | −13312.0 | −1.13242 | ||||||||
\(518\) | −816.000 | −0.0692143 | ||||||||
\(519\) | −1854.00 | −0.156805 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1562.00 | 0.131348 | 0.0656741 | − | 0.997841i | \(-0.479080\pi\) | ||||
0.0656741 | + | 0.997841i | \(0.479080\pi\) | |||||||
\(522\) | −2070.00 | −0.173566 | ||||||||
\(523\) | 668.000 | 0.0558501 | 0.0279250 | − | 0.999610i | \(-0.491110\pi\) | ||||
0.0279250 | + | 0.999610i | \(0.491110\pi\) | |||||||
\(524\) | −5124.00 | −0.427181 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4888.00 | −0.405184 | ||||||||
\(527\) | −4032.00 | −0.333276 | ||||||||
\(528\) | −6396.00 | −0.527178 | ||||||||
\(529\) | 16057.0 | 1.31972 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 900.000 | 0.0735531 | ||||||||
\(532\) | 3360.00 | 0.273824 | ||||||||
\(533\) | −2684.00 | −0.218118 | ||||||||
\(534\) | 990.000 | 0.0802275 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1260.00 | 0.101537 | ||||||||
\(537\) | −10020.0 | −0.805205 | ||||||||
\(538\) | −1270.00 | −0.101772 | ||||||||
\(539\) | 12116.0 | 0.968225 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6138.00 | −0.487788 | −0.243894 | − | 0.969802i | \(-0.578425\pi\) | ||||
−0.243894 | + | 0.969802i | \(0.578425\pi\) | |||||||
\(542\) | −1072.00 | −0.0849564 | ||||||||
\(543\) | 534.000 | 0.0422028 | ||||||||
\(544\) | −2254.00 | −0.177646 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1584.00 | −0.124156 | ||||||||
\(547\) | 10484.0 | 0.819494 | 0.409747 | − | 0.912199i | \(-0.365617\pi\) | ||||
0.409747 | + | 0.912199i | \(0.365617\pi\) | |||||||
\(548\) | −15498.0 | −1.20811 | ||||||||
\(549\) | 6678.00 | 0.519144 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4600.00 | −0.355656 | ||||||||
\(552\) | −7560.00 | −0.582926 | ||||||||
\(553\) | −5760.00 | −0.442930 | ||||||||
\(554\) | −5394.00 | −0.413663 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −140.000 | −0.0106786 | ||||||||
\(557\) | −3606.00 | −0.274311 | −0.137155 | − | 0.990550i | \(-0.543796\pi\) | ||||
−0.137155 | + | 0.990550i | \(0.543796\pi\) | |||||||
\(558\) | 2592.00 | 0.196645 | ||||||||
\(559\) | −4136.00 | −0.312941 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2184.00 | −0.164365 | ||||||||
\(562\) | −2442.00 | −0.183291 | ||||||||
\(563\) | −12252.0 | −0.917159 | −0.458579 | − | 0.888654i | \(-0.651641\pi\) | ||||
−0.458579 | + | 0.888654i | \(0.651641\pi\) | |||||||
\(564\) | −5376.00 | −0.401366 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2772.00 | 0.205858 | ||||||||
\(567\) | 1944.00 | 0.143986 | ||||||||
\(568\) | −4920.00 | −0.363448 | ||||||||
\(569\) | −14550.0 | −1.07200 | −0.536000 | − | 0.844218i | \(-0.680065\pi\) | ||||
−0.536000 | + | 0.844218i | \(0.680065\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25468.0 | −1.86655 | −0.933277 | − | 0.359157i | \(-0.883064\pi\) | ||||
−0.933277 | + | 0.359157i | \(0.883064\pi\) | |||||||
\(572\) | 8008.00 | 0.585369 | ||||||||
\(573\) | 5664.00 | 0.412944 | ||||||||
\(574\) | −2928.00 | −0.212914 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1503.00 | −0.108724 | ||||||||
\(577\) | −12866.0 | −0.928282 | −0.464141 | − | 0.885761i | \(-0.653637\pi\) | ||||
−0.464141 | + | 0.885761i | \(0.653637\pi\) | |||||||
\(578\) | 4717.00 | 0.339449 | ||||||||
\(579\) | 5766.00 | 0.413863 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29088.0 | −2.07706 | ||||||||
\(582\) | −2598.00 | −0.185035 | ||||||||
\(583\) | 17576.0 | 1.24858 | ||||||||
\(584\) | 570.000 | 0.0403883 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4542.00 | 0.320185 | ||||||||
\(587\) | 14844.0 | 1.04374 | 0.521872 | − | 0.853024i | \(-0.325234\pi\) | ||||
0.521872 | + | 0.853024i | \(0.325234\pi\) | |||||||
\(588\) | 4893.00 | 0.343170 | ||||||||
\(589\) | 5760.00 | 0.402948 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7578.00 | 0.527440 | ||||||||
\(592\) | 1394.00 | 0.0967788 | ||||||||
\(593\) | −20402.0 | −1.41283 | −0.706416 | − | 0.707797i | \(-0.749689\pi\) | ||||
−0.706416 | + | 0.707797i | \(0.749689\pi\) | |||||||
\(594\) | 1404.00 | 0.0969812 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9310.00 | 0.639853 | ||||||||
\(597\) | 3480.00 | 0.238571 | ||||||||
\(598\) | 3696.00 | 0.252744 | ||||||||
\(599\) | 10760.0 | 0.733959 | 0.366980 | − | 0.930229i | \(-0.380392\pi\) | ||||
0.366980 | + | 0.930229i | \(0.380392\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14282.0 | 0.969343 | 0.484671 | − | 0.874696i | \(-0.338939\pi\) | ||||
0.484671 | + | 0.874696i | \(0.338939\pi\) | |||||||
\(602\) | −4512.00 | −0.305474 | ||||||||
\(603\) | 756.000 | 0.0510559 | ||||||||
\(604\) | 8456.00 | 0.569652 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3654.00 | −0.244940 | ||||||||
\(607\) | −11056.0 | −0.739290 | −0.369645 | − | 0.929173i | \(-0.620521\pi\) | ||||
−0.369645 | + | 0.929173i | \(0.620521\pi\) | |||||||
\(608\) | 3220.00 | 0.214783 | ||||||||
\(609\) | −16560.0 | −1.10188 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5632.00 | 0.372907 | ||||||||
\(612\) | −882.000 | −0.0582561 | ||||||||
\(613\) | 16418.0 | 1.08176 | 0.540878 | − | 0.841101i | \(-0.318092\pi\) | ||||
0.540878 | + | 0.841101i | \(0.318092\pi\) | |||||||
\(614\) | 5116.00 | 0.336262 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 18720.0 | 1.22443 | ||||||||
\(617\) | 10374.0 | 0.676891 | 0.338445 | − | 0.940986i | \(-0.390099\pi\) | ||||
0.338445 | + | 0.940986i | \(0.390099\pi\) | |||||||
\(618\) | 264.000 | 0.0171839 | ||||||||
\(619\) | −5260.00 | −0.341546 | −0.170773 | − | 0.985310i | \(-0.554627\pi\) | ||||
−0.170773 | + | 0.985310i | \(0.554627\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4536.00 | −0.293113 | ||||||||
\(622\) | 2808.00 | 0.181014 | ||||||||
\(623\) | 7920.00 | 0.509323 | ||||||||
\(624\) | 2706.00 | 0.173600 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7318.00 | −0.467230 | ||||||||
\(627\) | 3120.00 | 0.198725 | ||||||||
\(628\) | −24598.0 | −1.56300 | ||||||||
\(629\) | 476.000 | 0.0301739 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21352.0 | 1.34708 | 0.673542 | − | 0.739149i | \(-0.264772\pi\) | ||||
0.673542 | + | 0.739149i | \(0.264772\pi\) | |||||||
\(632\) | −3600.00 | −0.226583 | ||||||||
\(633\) | 13404.0 | 0.841645 | ||||||||
\(634\) | 2246.00 | 0.140694 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7098.00 | 0.442538 | ||||||||
\(637\) | −5126.00 | −0.318838 | ||||||||
\(638\) | −11960.0 | −0.742164 | ||||||||
\(639\) | −2952.00 | −0.182753 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29118.0 | −1.79422 | −0.897108 | − | 0.441812i | \(-0.854336\pi\) | ||||
−0.897108 | + | 0.441812i | \(0.854336\pi\) | |||||||
\(642\) | −108.000 | −0.00663928 | ||||||||
\(643\) | −5772.00 | −0.354005 | −0.177003 | − | 0.984210i | \(-0.556640\pi\) | ||||
−0.177003 | + | 0.984210i | \(0.556640\pi\) | |||||||
\(644\) | −28224.0 | −1.72699 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 280.000 | 0.0170533 | ||||||||
\(647\) | 14264.0 | 0.866732 | 0.433366 | − | 0.901218i | \(-0.357326\pi\) | ||||
0.433366 | + | 0.901218i | \(0.357326\pi\) | |||||||
\(648\) | 1215.00 | 0.0736570 | ||||||||
\(649\) | 5200.00 | 0.314511 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20736.0 | 1.24840 | ||||||||
\(652\) | −14476.0 | −0.869515 | ||||||||
\(653\) | −6902.00 | −0.413623 | −0.206812 | − | 0.978381i | \(-0.566309\pi\) | ||||
−0.206812 | + | 0.978381i | \(0.566309\pi\) | |||||||
\(654\) | −2910.00 | −0.173991 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5002.00 | 0.297706 | ||||||||
\(657\) | 342.000 | 0.0203085 | ||||||||
\(658\) | 6144.00 | 0.364009 | ||||||||
\(659\) | 20140.0 | 1.19051 | 0.595253 | − | 0.803539i | \(-0.297052\pi\) | ||||
0.595253 | + | 0.803539i | \(0.297052\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3218.00 | −0.189358 | −0.0946790 | − | 0.995508i | \(-0.530182\pi\) | ||||
−0.0946790 | + | 0.995508i | \(0.530182\pi\) | |||||||
\(662\) | −1332.00 | −0.0782019 | ||||||||
\(663\) | 924.000 | 0.0541255 | ||||||||
\(664\) | −18180.0 | −1.06253 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −306.000 | −0.0178037 | ||||||||
\(667\) | 38640.0 | 2.24310 | ||||||||
\(668\) | −168.000 | −0.00973071 | ||||||||
\(669\) | 18096.0 | 1.04579 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38584.0 | 2.21985 | ||||||||
\(672\) | 11592.0 | 0.665433 | ||||||||
\(673\) | 7518.00 | 0.430606 | 0.215303 | − | 0.976547i | \(-0.430926\pi\) | ||||
0.215303 | + | 0.976547i | \(0.430926\pi\) | |||||||
\(674\) | −11534.0 | −0.659159 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11991.0 | 0.682237 | ||||||||
\(677\) | 18114.0 | 1.02833 | 0.514164 | − | 0.857692i | \(-0.328102\pi\) | ||||
0.514164 | + | 0.857692i | \(0.328102\pi\) | |||||||
\(678\) | −3126.00 | −0.177070 | ||||||||
\(679\) | −20784.0 | −1.17469 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7908.00 | 0.444986 | ||||||||
\(682\) | 14976.0 | 0.840851 | ||||||||
\(683\) | 23868.0 | 1.33716 | 0.668582 | − | 0.743638i | \(-0.266901\pi\) | ||||
0.668582 | + | 0.743638i | \(0.266901\pi\) | |||||||
\(684\) | 1260.00 | 0.0704347 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2640.00 | 0.146932 | ||||||||
\(687\) | −14490.0 | −0.804699 | ||||||||
\(688\) | 7708.00 | 0.427129 | ||||||||
\(689\) | −7436.00 | −0.411160 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 172.000 | 0.00946916 | 0.00473458 | − | 0.999989i | \(-0.498493\pi\) | ||||
0.00473458 | + | 0.999989i | \(0.498493\pi\) | |||||||
\(692\) | −4326.00 | −0.237644 | ||||||||
\(693\) | 11232.0 | 0.615683 | ||||||||
\(694\) | 11956.0 | 0.653953 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −10350.0 | −0.563672 | ||||||||
\(697\) | 1708.00 | 0.0928194 | ||||||||
\(698\) | −4870.00 | −0.264086 | ||||||||
\(699\) | 8046.00 | 0.435376 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22138.0 | −1.19278 | −0.596391 | − | 0.802694i | \(-0.703399\pi\) | ||||
−0.596391 | + | 0.802694i | \(0.703399\pi\) | |||||||
\(702\) | −594.000 | −0.0319360 | ||||||||
\(703\) | −680.000 | −0.0364818 | ||||||||
\(704\) | −8684.00 | −0.464901 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10722.0 | 0.571569 | ||||||||
\(707\) | −29232.0 | −1.55500 | ||||||||
\(708\) | 2100.00 | 0.111473 | ||||||||
\(709\) | 3070.00 | 0.162618 | 0.0813091 | − | 0.996689i | \(-0.474090\pi\) | ||||
0.0813091 | + | 0.996689i | \(0.474090\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2160.00 | −0.113933 | ||||||||
\(712\) | 4950.00 | 0.260546 | ||||||||
\(713\) | −48384.0 | −2.54137 | ||||||||
\(714\) | 1008.00 | 0.0528340 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −23380.0 | −1.22032 | ||||||||
\(717\) | −6960.00 | −0.362519 | ||||||||
\(718\) | −120.000 | −0.00623727 | ||||||||
\(719\) | 15600.0 | 0.809154 | 0.404577 | − | 0.914504i | \(-0.367419\pi\) | ||||
0.404577 | + | 0.914504i | \(0.367419\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2112.00 | 0.109092 | ||||||||
\(722\) | 6459.00 | 0.332935 | ||||||||
\(723\) | −6006.00 | −0.308943 | ||||||||
\(724\) | 1246.00 | 0.0639603 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4119.00 | 0.210565 | ||||||||
\(727\) | −20696.0 | −1.05581 | −0.527904 | − | 0.849304i | \(-0.677022\pi\) | ||||
−0.527904 | + | 0.849304i | \(0.677022\pi\) | |||||||
\(728\) | −7920.00 | −0.403207 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2632.00 | 0.133171 | ||||||||
\(732\) | 15582.0 | 0.786786 | ||||||||
\(733\) | 30778.0 | 1.55090 | 0.775451 | − | 0.631408i | \(-0.217522\pi\) | ||||
0.775451 | + | 0.631408i | \(0.217522\pi\) | |||||||
\(734\) | 3936.00 | 0.197930 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −27048.0 | −1.35462 | ||||||||
\(737\) | 4368.00 | 0.218314 | ||||||||
\(738\) | −1098.00 | −0.0547669 | ||||||||
\(739\) | 11740.0 | 0.584388 | 0.292194 | − | 0.956359i | \(-0.405615\pi\) | ||||
0.292194 | + | 0.956359i | \(0.405615\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1320.00 | −0.0654405 | ||||||||
\(742\) | −8112.00 | −0.401349 | ||||||||
\(743\) | −2632.00 | −0.129958 | −0.0649789 | − | 0.997887i | \(-0.520698\pi\) | ||||
−0.0649789 | + | 0.997887i | \(0.520698\pi\) | |||||||
\(744\) | 12960.0 | 0.638625 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3022.00 | 0.148315 | ||||||||
\(747\) | −10908.0 | −0.534274 | ||||||||
\(748\) | −5096.00 | −0.249102 | ||||||||
\(749\) | −864.000 | −0.0421494 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20528.0 | −0.997440 | −0.498720 | − | 0.866763i | \(-0.666196\pi\) | ||||
−0.498720 | + | 0.866763i | \(0.666196\pi\) | |||||||
\(752\) | −10496.0 | −0.508976 | ||||||||
\(753\) | −396.000 | −0.0191647 | ||||||||
\(754\) | 5060.00 | 0.244396 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4536.00 | 0.218218 | ||||||||
\(757\) | −21646.0 | −1.03928 | −0.519642 | − | 0.854384i | \(-0.673934\pi\) | ||||
−0.519642 | + | 0.854384i | \(0.673934\pi\) | |||||||
\(758\) | 13340.0 | 0.639222 | ||||||||
\(759\) | −26208.0 | −1.25335 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18282.0 | 0.870857 | 0.435428 | − | 0.900223i | \(-0.356597\pi\) | ||||
0.435428 | + | 0.900223i | \(0.356597\pi\) | |||||||
\(762\) | −5808.00 | −0.276118 | ||||||||
\(763\) | −23280.0 | −1.10458 | ||||||||
\(764\) | 13216.0 | 0.625835 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1008.00 | −0.0475464 | ||||||||
\(767\) | −2200.00 | −0.103569 | ||||||||
\(768\) | 357.000 | 0.0167736 | ||||||||
\(769\) | −24190.0 | −1.13435 | −0.567174 | − | 0.823598i | \(-0.691963\pi\) | ||||
−0.567174 | + | 0.823598i | \(0.691963\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22842.0 | −1.06697 | ||||||||
\(772\) | 13454.0 | 0.627228 | ||||||||
\(773\) | 25698.0 | 1.19572 | 0.597861 | − | 0.801600i | \(-0.296018\pi\) | ||||
0.597861 | + | 0.801600i | \(0.296018\pi\) | |||||||
\(774\) | −1692.00 | −0.0785758 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12990.0 | −0.600920 | ||||||||
\(777\) | −2448.00 | −0.113026 | ||||||||
\(778\) | −9630.00 | −0.443769 | ||||||||
\(779\) | −2440.00 | −0.112223 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17056.0 | −0.781449 | ||||||||
\(782\) | −2352.00 | −0.107554 | ||||||||
\(783\) | −6210.00 | −0.283432 | ||||||||
\(784\) | 9553.00 | 0.435177 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2196.00 | 0.0996549 | ||||||||
\(787\) | −33436.0 | −1.51444 | −0.757220 | − | 0.653160i | \(-0.773443\pi\) | ||||
−0.757220 | + | 0.653160i | \(0.773443\pi\) | |||||||
\(788\) | 17682.0 | 0.799359 | ||||||||
\(789\) | −14664.0 | −0.661663 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25008.0 | −1.12412 | ||||||||
\(792\) | 7020.00 | 0.314956 | ||||||||
\(793\) | −16324.0 | −0.730999 | ||||||||
\(794\) | 7126.00 | 0.318504 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8120.00 | 0.361565 | ||||||||
\(797\) | 37594.0 | 1.67083 | 0.835413 | − | 0.549623i | \(-0.185229\pi\) | ||||
0.835413 | + | 0.549623i | \(0.185229\pi\) | |||||||
\(798\) | −1440.00 | −0.0638790 | ||||||||
\(799\) | −3584.00 | −0.158689 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2970.00 | 0.131011 | ||||||||
\(802\) | 8718.00 | 0.383844 | ||||||||
\(803\) | 1976.00 | 0.0868388 | ||||||||
\(804\) | 1764.00 | 0.0773775 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6336.00 | −0.276893 | ||||||||
\(807\) | −3810.00 | −0.166194 | ||||||||
\(808\) | −18270.0 | −0.795466 | ||||||||
\(809\) | 4730.00 | 0.205560 | 0.102780 | − | 0.994704i | \(-0.467226\pi\) | ||||
0.102780 | + | 0.994704i | \(0.467226\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8748.00 | −0.378772 | −0.189386 | − | 0.981903i | \(-0.560650\pi\) | ||||
−0.189386 | + | 0.981903i | \(0.560650\pi\) | |||||||
\(812\) | −38640.0 | −1.66995 | ||||||||
\(813\) | −3216.00 | −0.138733 | ||||||||
\(814\) | −1768.00 | −0.0761282 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1722.00 | −0.0738751 | ||||||||
\(817\) | −3760.00 | −0.161011 | ||||||||
\(818\) | 10870.0 | 0.464622 | ||||||||
\(819\) | −4752.00 | −0.202745 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44142.0 | 1.87645 | 0.938226 | − | 0.346024i | \(-0.112468\pi\) | ||||
0.938226 | + | 0.346024i | \(0.112468\pi\) | |||||||
\(822\) | 6642.00 | 0.281833 | ||||||||
\(823\) | −3992.00 | −0.169079 | −0.0845397 | − | 0.996420i | \(-0.526942\pi\) | ||||
−0.0845397 | + | 0.996420i | \(0.526942\pi\) | |||||||
\(824\) | 1320.00 | 0.0558063 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2400.00 | −0.101098 | ||||||||
\(827\) | 14444.0 | 0.607336 | 0.303668 | − | 0.952778i | \(-0.401789\pi\) | ||||
0.303668 | + | 0.952778i | \(0.401789\pi\) | |||||||
\(828\) | −10584.0 | −0.444226 | ||||||||
\(829\) | 42150.0 | 1.76590 | 0.882949 | − | 0.469468i | \(-0.155554\pi\) | ||||
0.882949 | + | 0.469468i | \(0.155554\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16182.0 | −0.675508 | ||||||||
\(832\) | 3674.00 | 0.153093 | ||||||||
\(833\) | 3262.00 | 0.135680 | ||||||||
\(834\) | 60.0000 | 0.00249116 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7280.00 | 0.301177 | ||||||||
\(837\) | 7776.00 | 0.321121 | ||||||||
\(838\) | 9700.00 | 0.399858 | ||||||||
\(839\) | 13400.0 | 0.551394 | 0.275697 | − | 0.961245i | \(-0.411091\pi\) | ||||
0.275697 | + | 0.961245i | \(0.411091\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28511.0 | 1.16901 | ||||||||
\(842\) | −862.000 | −0.0352809 | ||||||||
\(843\) | −7326.00 | −0.299313 | ||||||||
\(844\) | 31276.0 | 1.27555 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2304.00 | 0.0936326 | ||||||||
\(847\) | 32952.0 | 1.33677 | ||||||||
\(848\) | 13858.0 | 0.561186 | ||||||||
\(849\) | 8316.00 | 0.336165 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5712.00 | 0.230088 | ||||||||
\(852\) | −6888.00 | −0.276971 | ||||||||
\(853\) | 8658.00 | 0.347531 | 0.173766 | − | 0.984787i | \(-0.444406\pi\) | ||||
0.173766 | + | 0.984787i | \(0.444406\pi\) | |||||||
\(854\) | −17808.0 | −0.713556 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −540.000 | −0.0215617 | ||||||||
\(857\) | −42826.0 | −1.70701 | −0.853505 | − | 0.521084i | \(-0.825528\pi\) | ||||
−0.853505 | + | 0.521084i | \(0.825528\pi\) | |||||||
\(858\) | −3432.00 | −0.136558 | ||||||||
\(859\) | −35900.0 | −1.42595 | −0.712976 | − | 0.701189i | \(-0.752653\pi\) | ||||
−0.712976 | + | 0.701189i | \(0.752653\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8784.00 | −0.347686 | ||||||||
\(862\) | −15792.0 | −0.623988 | ||||||||
\(863\) | 3088.00 | 0.121804 | 0.0609019 | − | 0.998144i | \(-0.480602\pi\) | ||||
0.0609019 | + | 0.998144i | \(0.480602\pi\) | |||||||
\(864\) | 4347.00 | 0.171167 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11602.0 | 0.455256 | ||||||||
\(867\) | 14151.0 | 0.554317 | ||||||||
\(868\) | 48384.0 | 1.89200 | ||||||||
\(869\) | −12480.0 | −0.487175 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1848.00 | −0.0718910 | ||||||||
\(872\) | −14550.0 | −0.565052 | ||||||||
\(873\) | −7794.00 | −0.302161 | ||||||||
\(874\) | 3360.00 | 0.130039 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 798.000 | 0.0307784 | ||||||||
\(877\) | 35274.0 | 1.35817 | 0.679087 | − | 0.734058i | \(-0.262376\pi\) | ||||
0.679087 | + | 0.734058i | \(0.262376\pi\) | |||||||
\(878\) | 440.000 | 0.0169126 | ||||||||
\(879\) | 13626.0 | 0.522860 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25042.0 | 0.957646 | 0.478823 | − | 0.877911i | \(-0.341064\pi\) | ||||
0.478823 | + | 0.877911i | \(0.341064\pi\) | |||||||
\(882\) | −2097.00 | −0.0800563 | ||||||||
\(883\) | −12572.0 | −0.479141 | −0.239570 | − | 0.970879i | \(-0.577007\pi\) | ||||
−0.239570 | + | 0.970879i | \(0.577007\pi\) | |||||||
\(884\) | 2156.00 | 0.0820296 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10188.0 | −0.386312 | ||||||||
\(887\) | 21864.0 | 0.827645 | 0.413823 | − | 0.910358i | \(-0.364193\pi\) | ||||
0.413823 | + | 0.910358i | \(0.364193\pi\) | |||||||
\(888\) | −1530.00 | −0.0578192 | ||||||||
\(889\) | −46464.0 | −1.75293 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4212.00 | 0.158370 | ||||||||
\(892\) | 42224.0 | 1.58494 | ||||||||
\(893\) | 5120.00 | 0.191864 | ||||||||
\(894\) | −3990.00 | −0.149268 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 34920.0 | 1.30200 | ||||||||
\(897\) | 11088.0 | 0.412729 | ||||||||
\(898\) | 13310.0 | 0.494611 | ||||||||
\(899\) | −66240.0 | −2.45743 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4732.00 | 0.174968 | ||||||||
\(902\) | −6344.00 | −0.234182 | ||||||||
\(903\) | −13536.0 | −0.498837 | ||||||||
\(904\) | −15630.0 | −0.575051 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3624.00 | −0.132891 | ||||||||
\(907\) | −31236.0 | −1.14352 | −0.571761 | − | 0.820420i | \(-0.693740\pi\) | ||||
−0.571761 | + | 0.820420i | \(0.693740\pi\) | |||||||
\(908\) | 18452.0 | 0.674396 | ||||||||
\(909\) | −10962.0 | −0.399985 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8272.00 | 0.300838 | 0.150419 | − | 0.988622i | \(-0.451938\pi\) | ||||
0.150419 | + | 0.988622i | \(0.451938\pi\) | |||||||
\(912\) | 2460.00 | 0.0893188 | ||||||||
\(913\) | −63024.0 | −2.28455 | ||||||||
\(914\) | 3226.00 | 0.116747 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −33810.0 | −1.21956 | ||||||||
\(917\) | 17568.0 | 0.632657 | ||||||||
\(918\) | 378.000 | 0.0135903 | ||||||||
\(919\) | 20200.0 | 0.725067 | 0.362533 | − | 0.931971i | \(-0.381912\pi\) | ||||
0.362533 | + | 0.931971i | \(0.381912\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15348.0 | 0.549114 | ||||||||
\(922\) | −6582.00 | −0.235105 | ||||||||
\(923\) | 7216.00 | 0.257332 | ||||||||
\(924\) | 26208.0 | 0.933095 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15072.0 | 0.534878 | ||||||||
\(927\) | 792.000 | 0.0280612 | ||||||||
\(928\) | −37030.0 | −1.30988 | ||||||||
\(929\) | 31010.0 | 1.09516 | 0.547581 | − | 0.836753i | \(-0.315549\pi\) | ||||
0.547581 | + | 0.836753i | \(0.315549\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4660.00 | −0.164044 | ||||||||
\(932\) | 18774.0 | 0.659831 | ||||||||
\(933\) | 8424.00 | 0.295594 | ||||||||
\(934\) | 476.000 | 0.0166758 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2970.00 | −0.103715 | ||||||||
\(937\) | 39174.0 | 1.36580 | 0.682902 | − | 0.730510i | \(-0.260717\pi\) | ||||
0.682902 | + | 0.730510i | \(0.260717\pi\) | |||||||
\(938\) | −2016.00 | −0.0701756 | ||||||||
\(939\) | −21954.0 | −0.762984 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4138.00 | −0.143353 | −0.0716764 | − | 0.997428i | \(-0.522835\pi\) | ||||
−0.0716764 | + | 0.997428i | \(0.522835\pi\) | |||||||
\(942\) | 10542.0 | 0.364625 | ||||||||
\(943\) | 20496.0 | 0.707785 | ||||||||
\(944\) | 4100.00 | 0.141360 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9776.00 | −0.335989 | ||||||||
\(947\) | −23676.0 | −0.812425 | −0.406213 | − | 0.913779i | \(-0.633151\pi\) | ||||
−0.406213 | + | 0.913779i | \(0.633151\pi\) | |||||||
\(948\) | −5040.00 | −0.172670 | ||||||||
\(949\) | −836.000 | −0.0285961 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6738.00 | 0.229752 | ||||||||
\(952\) | 5040.00 | 0.171583 | ||||||||
\(953\) | −18922.0 | −0.643173 | −0.321586 | − | 0.946880i | \(-0.604216\pi\) | ||||
−0.321586 | + | 0.946880i | \(0.604216\pi\) | |||||||
\(954\) | −3042.00 | −0.103237 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −16240.0 | −0.549413 | ||||||||
\(957\) | −35880.0 | −1.21195 | ||||||||
\(958\) | 19680.0 | 0.663708 | ||||||||
\(959\) | 53136.0 | 1.78921 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53153.0 | 1.78420 | ||||||||
\(962\) | 748.000 | 0.0250691 | ||||||||
\(963\) | −324.000 | −0.0108419 | ||||||||
\(964\) | −14014.0 | −0.468216 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 12096.0 | 0.402880 | ||||||||
\(967\) | −39656.0 | −1.31877 | −0.659385 | − | 0.751805i | \(-0.729183\pi\) | ||||
−0.659385 | + | 0.751805i | \(0.729183\pi\) | |||||||
\(968\) | 20595.0 | 0.683831 | ||||||||
\(969\) | 840.000 | 0.0278480 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33228.0 | −1.09818 | −0.549092 | − | 0.835762i | \(-0.685026\pi\) | ||||
−0.549092 | + | 0.835762i | \(0.685026\pi\) | |||||||
\(972\) | 1701.00 | 0.0561313 | ||||||||
\(973\) | 480.000 | 0.0158151 | ||||||||
\(974\) | −5944.00 | −0.195542 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30422.0 | 0.997730 | ||||||||
\(977\) | 974.000 | 0.0318946 | 0.0159473 | − | 0.999873i | \(-0.494924\pi\) | ||||
0.0159473 | + | 0.999873i | \(0.494924\pi\) | |||||||
\(978\) | 6204.00 | 0.202845 | ||||||||
\(979\) | 17160.0 | 0.560200 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8730.00 | −0.284126 | ||||||||
\(982\) | −10772.0 | −0.350049 | ||||||||
\(983\) | 13608.0 | 0.441534 | 0.220767 | − | 0.975327i | \(-0.429144\pi\) | ||||
0.220767 | + | 0.975327i | \(0.429144\pi\) | |||||||
\(984\) | −5490.00 | −0.177861 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3220.00 | −0.104002 | ||||||||
\(987\) | 18432.0 | 0.594425 | ||||||||
\(988\) | −3080.00 | −0.0991780 | ||||||||
\(989\) | 31584.0 | 1.01548 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13472.0 | 0.431839 | 0.215919 | − | 0.976411i | \(-0.430725\pi\) | ||||
0.215919 | + | 0.976411i | \(0.430725\pi\) | |||||||
\(992\) | 46368.0 | 1.48406 | ||||||||
\(993\) | −3996.00 | −0.127703 | ||||||||
\(994\) | 7872.00 | 0.251192 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −25452.0 | −0.809716 | ||||||||
\(997\) | 3234.00 | 0.102730 | 0.0513650 | − | 0.998680i | \(-0.483643\pi\) | ||||
0.0513650 | + | 0.998680i | \(0.483643\pi\) | |||||||
\(998\) | −8140.00 | −0.258184 | ||||||||
\(999\) | −918.000 | −0.0290733 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 75.4.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 225.4.a.f.1.1 | 1 | |||
4.3 | odd | 2 | 1200.4.a.t.1.1 | 1 | |||
5.2 | odd | 4 | 75.4.b.b.49.1 | 2 | |||
5.3 | odd | 4 | 75.4.b.b.49.2 | 2 | |||
5.4 | even | 2 | 15.4.a.a.1.1 | ✓ | 1 | ||
15.2 | even | 4 | 225.4.b.e.199.2 | 2 | |||
15.8 | even | 4 | 225.4.b.e.199.1 | 2 | |||
15.14 | odd | 2 | 45.4.a.c.1.1 | 1 | |||
20.3 | even | 4 | 1200.4.f.b.49.2 | 2 | |||
20.7 | even | 4 | 1200.4.f.b.49.1 | 2 | |||
20.19 | odd | 2 | 240.4.a.e.1.1 | 1 | |||
35.34 | odd | 2 | 735.4.a.e.1.1 | 1 | |||
40.19 | odd | 2 | 960.4.a.ba.1.1 | 1 | |||
40.29 | even | 2 | 960.4.a.b.1.1 | 1 | |||
45.4 | even | 6 | 405.4.e.g.136.1 | 2 | |||
45.14 | odd | 6 | 405.4.e.i.136.1 | 2 | |||
45.29 | odd | 6 | 405.4.e.i.271.1 | 2 | |||
45.34 | even | 6 | 405.4.e.g.271.1 | 2 | |||
55.54 | odd | 2 | 1815.4.a.e.1.1 | 1 | |||
60.59 | even | 2 | 720.4.a.n.1.1 | 1 | |||
105.104 | even | 2 | 2205.4.a.l.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.4.a.a.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
45.4.a.c.1.1 | 1 | 15.14 | odd | 2 | |||
75.4.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
75.4.b.b.49.1 | 2 | 5.2 | odd | 4 | |||
75.4.b.b.49.2 | 2 | 5.3 | odd | 4 | |||
225.4.a.f.1.1 | 1 | 3.2 | odd | 2 | |||
225.4.b.e.199.1 | 2 | 15.8 | even | 4 | |||
225.4.b.e.199.2 | 2 | 15.2 | even | 4 | |||
240.4.a.e.1.1 | 1 | 20.19 | odd | 2 | |||
405.4.e.g.136.1 | 2 | 45.4 | even | 6 | |||
405.4.e.g.271.1 | 2 | 45.34 | even | 6 | |||
405.4.e.i.136.1 | 2 | 45.14 | odd | 6 | |||
405.4.e.i.271.1 | 2 | 45.29 | odd | 6 | |||
720.4.a.n.1.1 | 1 | 60.59 | even | 2 | |||
735.4.a.e.1.1 | 1 | 35.34 | odd | 2 | |||
960.4.a.b.1.1 | 1 | 40.29 | even | 2 | |||
960.4.a.ba.1.1 | 1 | 40.19 | odd | 2 | |||
1200.4.a.t.1.1 | 1 | 4.3 | odd | 2 | |||
1200.4.f.b.49.1 | 2 | 20.7 | even | 4 | |||
1200.4.f.b.49.2 | 2 | 20.3 | even | 4 | |||
1815.4.a.e.1.1 | 1 | 55.54 | odd | 2 | |||
2205.4.a.l.1.1 | 1 | 105.104 | even | 2 |