Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1862,4,Mod(1,1862)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1862, 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("1862.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1862 = 2 \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1862.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: | \(109.861556431\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 38) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1862.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 2.00000 | 0.384900 | 0.192450 | − | 0.981307i | \(-0.438357\pi\) | ||||
0.192450 | + | 0.981307i | \(0.438357\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 9.00000 | 0.804984 | 0.402492 | − | 0.915423i | \(-0.368144\pi\) | ||||
0.402492 | + | 0.915423i | \(0.368144\pi\) | |||||||
\(6\) | −4.00000 | −0.272166 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −23.0000 | −0.851852 | ||||||||
\(10\) | −18.0000 | −0.569210 | ||||||||
\(11\) | 57.0000 | 1.56238 | 0.781188 | − | 0.624295i | \(-0.214614\pi\) | ||||
0.781188 | + | 0.624295i | \(0.214614\pi\) | |||||||
\(12\) | 8.00000 | 0.192450 | ||||||||
\(13\) | 52.0000 | 1.10940 | 0.554700 | − | 0.832050i | \(-0.312833\pi\) | ||||
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 18.0000 | 0.309839 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −69.0000 | −0.984409 | −0.492205 | − | 0.870480i | \(-0.663809\pi\) | ||||
−0.492205 | + | 0.870480i | \(0.663809\pi\) | |||||||
\(18\) | 46.0000 | 0.602350 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | 36.0000 | 0.402492 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −114.000 | −1.10477 | ||||||||
\(23\) | −72.0000 | −0.652741 | −0.326370 | − | 0.945242i | \(-0.605826\pi\) | ||||
−0.326370 | + | 0.945242i | \(0.605826\pi\) | |||||||
\(24\) | −16.0000 | −0.136083 | ||||||||
\(25\) | −44.0000 | −0.352000 | ||||||||
\(26\) | −104.000 | −0.784465 | ||||||||
\(27\) | −100.000 | −0.712778 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −150.000 | −0.960493 | −0.480247 | − | 0.877134i | \(-0.659453\pi\) | ||||
−0.480247 | + | 0.877134i | \(0.659453\pi\) | |||||||
\(30\) | −36.0000 | −0.219089 | ||||||||
\(31\) | −32.0000 | −0.185399 | −0.0926995 | − | 0.995694i | \(-0.529550\pi\) | ||||
−0.0926995 | + | 0.995694i | \(0.529550\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 114.000 | 0.601359 | ||||||||
\(34\) | 138.000 | 0.696082 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −92.0000 | −0.425926 | ||||||||
\(37\) | −226.000 | −1.00417 | −0.502083 | − | 0.864819i | \(-0.667433\pi\) | ||||
−0.502083 | + | 0.864819i | \(0.667433\pi\) | |||||||
\(38\) | 38.0000 | 0.162221 | ||||||||
\(39\) | 104.000 | 0.427008 | ||||||||
\(40\) | −72.0000 | −0.284605 | ||||||||
\(41\) | 258.000 | 0.982752 | 0.491376 | − | 0.870948i | \(-0.336494\pi\) | ||||
0.491376 | + | 0.870948i | \(0.336494\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −67.0000 | −0.237614 | −0.118807 | − | 0.992917i | \(-0.537907\pi\) | ||||
−0.118807 | + | 0.992917i | \(0.537907\pi\) | |||||||
\(44\) | 228.000 | 0.781188 | ||||||||
\(45\) | −207.000 | −0.685728 | ||||||||
\(46\) | 144.000 | 0.461557 | ||||||||
\(47\) | −579.000 | −1.79693 | −0.898466 | − | 0.439043i | \(-0.855318\pi\) | ||||
−0.898466 | + | 0.439043i | \(0.855318\pi\) | |||||||
\(48\) | 32.0000 | 0.0962250 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 88.0000 | 0.248902 | ||||||||
\(51\) | −138.000 | −0.378899 | ||||||||
\(52\) | 208.000 | 0.554700 | ||||||||
\(53\) | −432.000 | −1.11962 | −0.559809 | − | 0.828622i | \(-0.689126\pi\) | ||||
−0.559809 | + | 0.828622i | \(0.689126\pi\) | |||||||
\(54\) | 200.000 | 0.504010 | ||||||||
\(55\) | 513.000 | 1.25769 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −38.0000 | −0.0883022 | ||||||||
\(58\) | 300.000 | 0.679171 | ||||||||
\(59\) | 330.000 | 0.728175 | 0.364088 | − | 0.931365i | \(-0.381381\pi\) | ||||
0.364088 | + | 0.931365i | \(0.381381\pi\) | |||||||
\(60\) | 72.0000 | 0.154919 | ||||||||
\(61\) | 13.0000 | 0.0272865 | 0.0136433 | − | 0.999907i | \(-0.495657\pi\) | ||||
0.0136433 | + | 0.999907i | \(0.495657\pi\) | |||||||
\(62\) | 64.0000 | 0.131097 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 468.000 | 0.893050 | ||||||||
\(66\) | −228.000 | −0.425225 | ||||||||
\(67\) | −856.000 | −1.56085 | −0.780426 | − | 0.625249i | \(-0.784998\pi\) | ||||
−0.780426 | + | 0.625249i | \(0.784998\pi\) | |||||||
\(68\) | −276.000 | −0.492205 | ||||||||
\(69\) | −144.000 | −0.251240 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 642.000 | 1.07312 | 0.536559 | − | 0.843863i | \(-0.319724\pi\) | ||||
0.536559 | + | 0.843863i | \(0.319724\pi\) | |||||||
\(72\) | 184.000 | 0.301175 | ||||||||
\(73\) | 487.000 | 0.780809 | 0.390404 | − | 0.920643i | \(-0.372335\pi\) | ||||
0.390404 | + | 0.920643i | \(0.372335\pi\) | |||||||
\(74\) | 452.000 | 0.710053 | ||||||||
\(75\) | −88.0000 | −0.135485 | ||||||||
\(76\) | −76.0000 | −0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −208.000 | −0.301941 | ||||||||
\(79\) | −700.000 | −0.996913 | −0.498457 | − | 0.866915i | \(-0.666100\pi\) | ||||
−0.498457 | + | 0.866915i | \(0.666100\pi\) | |||||||
\(80\) | 144.000 | 0.201246 | ||||||||
\(81\) | 421.000 | 0.577503 | ||||||||
\(82\) | −516.000 | −0.694911 | ||||||||
\(83\) | 12.0000 | 0.0158695 | 0.00793477 | − | 0.999969i | \(-0.497474\pi\) | ||||
0.00793477 | + | 0.999969i | \(0.497474\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −621.000 | −0.792434 | ||||||||
\(86\) | 134.000 | 0.168019 | ||||||||
\(87\) | −300.000 | −0.369694 | ||||||||
\(88\) | −456.000 | −0.552384 | ||||||||
\(89\) | 600.000 | 0.714605 | 0.357303 | − | 0.933989i | \(-0.383696\pi\) | ||||
0.357303 | + | 0.933989i | \(0.383696\pi\) | |||||||
\(90\) | 414.000 | 0.484883 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −288.000 | −0.326370 | ||||||||
\(93\) | −64.0000 | −0.0713601 | ||||||||
\(94\) | 1158.00 | 1.27062 | ||||||||
\(95\) | −171.000 | −0.184676 | ||||||||
\(96\) | −64.0000 | −0.0680414 | ||||||||
\(97\) | −1424.00 | −1.49057 | −0.745285 | − | 0.666746i | \(-0.767687\pi\) | ||||
−0.745285 | + | 0.666746i | \(0.767687\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1311.00 | −1.33091 | ||||||||
\(100\) | −176.000 | −0.176000 | ||||||||
\(101\) | −1062.00 | −1.04627 | −0.523133 | − | 0.852251i | \(-0.675237\pi\) | ||||
−0.523133 | + | 0.852251i | \(0.675237\pi\) | |||||||
\(102\) | 276.000 | 0.267922 | ||||||||
\(103\) | −1178.00 | −1.12691 | −0.563455 | − | 0.826147i | \(-0.690528\pi\) | ||||
−0.563455 | + | 0.826147i | \(0.690528\pi\) | |||||||
\(104\) | −416.000 | −0.392232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 864.000 | 0.791690 | ||||||||
\(107\) | 114.000 | 0.102998 | 0.0514990 | − | 0.998673i | \(-0.483600\pi\) | ||||
0.0514990 | + | 0.998673i | \(0.483600\pi\) | |||||||
\(108\) | −400.000 | −0.356389 | ||||||||
\(109\) | 1460.00 | 1.28296 | 0.641480 | − | 0.767140i | \(-0.278321\pi\) | ||||
0.641480 | + | 0.767140i | \(0.278321\pi\) | |||||||
\(110\) | −1026.00 | −0.889321 | ||||||||
\(111\) | −452.000 | −0.386504 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −822.000 | −0.684312 | −0.342156 | − | 0.939643i | \(-0.611157\pi\) | ||||
−0.342156 | + | 0.939643i | \(0.611157\pi\) | |||||||
\(114\) | 76.0000 | 0.0624391 | ||||||||
\(115\) | −648.000 | −0.525446 | ||||||||
\(116\) | −600.000 | −0.480247 | ||||||||
\(117\) | −1196.00 | −0.945045 | ||||||||
\(118\) | −660.000 | −0.514898 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −144.000 | −0.109545 | ||||||||
\(121\) | 1918.00 | 1.44102 | ||||||||
\(122\) | −26.0000 | −0.0192945 | ||||||||
\(123\) | 516.000 | 0.378261 | ||||||||
\(124\) | −128.000 | −0.0926995 | ||||||||
\(125\) | −1521.00 | −1.08834 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2086.00 | −1.45750 | −0.728750 | − | 0.684780i | \(-0.759898\pi\) | ||||
−0.728750 | + | 0.684780i | \(0.759898\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −134.000 | −0.0914577 | ||||||||
\(130\) | −936.000 | −0.631482 | ||||||||
\(131\) | 93.0000 | 0.0620263 | 0.0310132 | − | 0.999519i | \(-0.490127\pi\) | ||||
0.0310132 | + | 0.999519i | \(0.490127\pi\) | |||||||
\(132\) | 456.000 | 0.300680 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1712.00 | 1.10369 | ||||||||
\(135\) | −900.000 | −0.573775 | ||||||||
\(136\) | 552.000 | 0.348041 | ||||||||
\(137\) | 1269.00 | 0.791372 | 0.395686 | − | 0.918386i | \(-0.370507\pi\) | ||||
0.395686 | + | 0.918386i | \(0.370507\pi\) | |||||||
\(138\) | 288.000 | 0.177654 | ||||||||
\(139\) | 1975.00 | 1.20516 | 0.602580 | − | 0.798058i | \(-0.294139\pi\) | ||||
0.602580 | + | 0.798058i | \(0.294139\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1158.00 | −0.691640 | ||||||||
\(142\) | −1284.00 | −0.758809 | ||||||||
\(143\) | 2964.00 | 1.73330 | ||||||||
\(144\) | −368.000 | −0.212963 | ||||||||
\(145\) | −1350.00 | −0.773182 | ||||||||
\(146\) | −974.000 | −0.552115 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −904.000 | −0.502083 | ||||||||
\(149\) | −1695.00 | −0.931945 | −0.465973 | − | 0.884799i | \(-0.654295\pi\) | ||||
−0.465973 | + | 0.884799i | \(0.654295\pi\) | |||||||
\(150\) | 176.000 | 0.0958023 | ||||||||
\(151\) | 1802.00 | 0.971157 | 0.485578 | − | 0.874193i | \(-0.338609\pi\) | ||||
0.485578 | + | 0.874193i | \(0.338609\pi\) | |||||||
\(152\) | 152.000 | 0.0811107 | ||||||||
\(153\) | 1587.00 | 0.838571 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −288.000 | −0.149243 | ||||||||
\(156\) | 416.000 | 0.213504 | ||||||||
\(157\) | 3226.00 | 1.63989 | 0.819945 | − | 0.572442i | \(-0.194004\pi\) | ||||
0.819945 | + | 0.572442i | \(0.194004\pi\) | |||||||
\(158\) | 1400.00 | 0.704924 | ||||||||
\(159\) | −864.000 | −0.430941 | ||||||||
\(160\) | −288.000 | −0.142302 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −842.000 | −0.408357 | ||||||||
\(163\) | 1268.00 | 0.609309 | 0.304655 | − | 0.952463i | \(-0.401459\pi\) | ||||
0.304655 | + | 0.952463i | \(0.401459\pi\) | |||||||
\(164\) | 1032.00 | 0.491376 | ||||||||
\(165\) | 1026.00 | 0.484085 | ||||||||
\(166\) | −24.0000 | −0.0112215 | ||||||||
\(167\) | −654.000 | −0.303042 | −0.151521 | − | 0.988454i | \(-0.548417\pi\) | ||||
−0.151521 | + | 0.988454i | \(0.548417\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 507.000 | 0.230769 | ||||||||
\(170\) | 1242.00 | 0.560336 | ||||||||
\(171\) | 437.000 | 0.195428 | ||||||||
\(172\) | −268.000 | −0.118807 | ||||||||
\(173\) | 1362.00 | 0.598560 | 0.299280 | − | 0.954165i | \(-0.403253\pi\) | ||||
0.299280 | + | 0.954165i | \(0.403253\pi\) | |||||||
\(174\) | 600.000 | 0.261413 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 912.000 | 0.390594 | ||||||||
\(177\) | 660.000 | 0.280275 | ||||||||
\(178\) | −1200.00 | −0.505302 | ||||||||
\(179\) | −210.000 | −0.0876879 | −0.0438440 | − | 0.999038i | \(-0.513960\pi\) | ||||
−0.0438440 | + | 0.999038i | \(0.513960\pi\) | |||||||
\(180\) | −828.000 | −0.342864 | ||||||||
\(181\) | −2.00000 | −0.000821319 0 | −0.000410660 | − | 1.00000i | \(-0.500131\pi\) | ||||
−0.000410660 | 1.00000i | \(0.500131\pi\) | ||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 26.0000 | 0.0105026 | ||||||||
\(184\) | 576.000 | 0.230779 | ||||||||
\(185\) | −2034.00 | −0.808339 | ||||||||
\(186\) | 128.000 | 0.0504592 | ||||||||
\(187\) | −3933.00 | −1.53802 | ||||||||
\(188\) | −2316.00 | −0.898466 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 342.000 | 0.130586 | ||||||||
\(191\) | −2643.00 | −1.00126 | −0.500630 | − | 0.865661i | \(-0.666898\pi\) | ||||
−0.500630 | + | 0.865661i | \(0.666898\pi\) | |||||||
\(192\) | 128.000 | 0.0481125 | ||||||||
\(193\) | 3248.00 | 1.21138 | 0.605690 | − | 0.795701i | \(-0.292897\pi\) | ||||
0.605690 | + | 0.795701i | \(0.292897\pi\) | |||||||
\(194\) | 2848.00 | 1.05399 | ||||||||
\(195\) | 936.000 | 0.343735 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3126.00 | −1.13055 | −0.565275 | − | 0.824903i | \(-0.691230\pi\) | ||||
−0.565275 | + | 0.824903i | \(0.691230\pi\) | |||||||
\(198\) | 2622.00 | 0.941098 | ||||||||
\(199\) | 2995.00 | 1.06688 | 0.533442 | − | 0.845837i | \(-0.320898\pi\) | ||||
0.533442 | + | 0.845837i | \(0.320898\pi\) | |||||||
\(200\) | 352.000 | 0.124451 | ||||||||
\(201\) | −1712.00 | −0.600772 | ||||||||
\(202\) | 2124.00 | 0.739822 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −552.000 | −0.189450 | ||||||||
\(205\) | 2322.00 | 0.791100 | ||||||||
\(206\) | 2356.00 | 0.796846 | ||||||||
\(207\) | 1656.00 | 0.556038 | ||||||||
\(208\) | 832.000 | 0.277350 | ||||||||
\(209\) | −1083.00 | −0.358434 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4318.00 | −1.40883 | −0.704416 | − | 0.709788i | \(-0.748791\pi\) | ||||
−0.704416 | + | 0.709788i | \(0.748791\pi\) | |||||||
\(212\) | −1728.00 | −0.559809 | ||||||||
\(213\) | 1284.00 | 0.413043 | ||||||||
\(214\) | −228.000 | −0.0728307 | ||||||||
\(215\) | −603.000 | −0.191276 | ||||||||
\(216\) | 800.000 | 0.252005 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2920.00 | −0.907190 | ||||||||
\(219\) | 974.000 | 0.300533 | ||||||||
\(220\) | 2052.00 | 0.628845 | ||||||||
\(221\) | −3588.00 | −1.09210 | ||||||||
\(222\) | 904.000 | 0.273300 | ||||||||
\(223\) | −518.000 | −0.155551 | −0.0777754 | − | 0.996971i | \(-0.524782\pi\) | ||||
−0.0777754 | + | 0.996971i | \(0.524782\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1012.00 | 0.299852 | ||||||||
\(226\) | 1644.00 | 0.483882 | ||||||||
\(227\) | −2844.00 | −0.831555 | −0.415777 | − | 0.909466i | \(-0.636490\pi\) | ||||
−0.415777 | + | 0.909466i | \(0.636490\pi\) | |||||||
\(228\) | −152.000 | −0.0441511 | ||||||||
\(229\) | −1745.00 | −0.503550 | −0.251775 | − | 0.967786i | \(-0.581014\pi\) | ||||
−0.251775 | + | 0.967786i | \(0.581014\pi\) | |||||||
\(230\) | 1296.00 | 0.371547 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1200.00 | 0.339586 | ||||||||
\(233\) | 5283.00 | 1.48541 | 0.742706 | − | 0.669618i | \(-0.233542\pi\) | ||||
0.742706 | + | 0.669618i | \(0.233542\pi\) | |||||||
\(234\) | 2392.00 | 0.668248 | ||||||||
\(235\) | −5211.00 | −1.44650 | ||||||||
\(236\) | 1320.00 | 0.364088 | ||||||||
\(237\) | −1400.00 | −0.383712 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 465.000 | 0.125851 | 0.0629254 | − | 0.998018i | \(-0.479957\pi\) | ||||
0.0629254 | + | 0.998018i | \(0.479957\pi\) | |||||||
\(240\) | 288.000 | 0.0774597 | ||||||||
\(241\) | 7078.00 | 1.89184 | 0.945921 | − | 0.324396i | \(-0.105161\pi\) | ||||
0.945921 | + | 0.324396i | \(0.105161\pi\) | |||||||
\(242\) | −3836.00 | −1.01896 | ||||||||
\(243\) | 3542.00 | 0.935059 | ||||||||
\(244\) | 52.0000 | 0.0136433 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1032.00 | −0.267471 | ||||||||
\(247\) | −988.000 | −0.254514 | ||||||||
\(248\) | 256.000 | 0.0655485 | ||||||||
\(249\) | 24.0000 | 0.00610819 | ||||||||
\(250\) | 3042.00 | 0.769572 | ||||||||
\(251\) | −3567.00 | −0.897000 | −0.448500 | − | 0.893783i | \(-0.648042\pi\) | ||||
−0.448500 | + | 0.893783i | \(0.648042\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4104.00 | −1.01983 | ||||||||
\(254\) | 4172.00 | 1.03061 | ||||||||
\(255\) | −1242.00 | −0.305008 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 1896.00 | 0.460192 | 0.230096 | − | 0.973168i | \(-0.426096\pi\) | ||||
0.230096 | + | 0.973168i | \(0.426096\pi\) | |||||||
\(258\) | 268.000 | 0.0646704 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1872.00 | 0.446525 | ||||||||
\(261\) | 3450.00 | 0.818198 | ||||||||
\(262\) | −186.000 | −0.0438592 | ||||||||
\(263\) | −57.0000 | −0.0133641 | −0.00668207 | − | 0.999978i | \(-0.502127\pi\) | ||||
−0.00668207 | + | 0.999978i | \(0.502127\pi\) | |||||||
\(264\) | −912.000 | −0.212613 | ||||||||
\(265\) | −3888.00 | −0.901275 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1200.00 | 0.275052 | ||||||||
\(268\) | −3424.00 | −0.780426 | ||||||||
\(269\) | −2700.00 | −0.611977 | −0.305989 | − | 0.952035i | \(-0.598987\pi\) | ||||
−0.305989 | + | 0.952035i | \(0.598987\pi\) | |||||||
\(270\) | 1800.00 | 0.405720 | ||||||||
\(271\) | −3872.00 | −0.867923 | −0.433962 | − | 0.900931i | \(-0.642885\pi\) | ||||
−0.433962 | + | 0.900931i | \(0.642885\pi\) | |||||||
\(272\) | −1104.00 | −0.246102 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2538.00 | −0.559585 | ||||||||
\(275\) | −2508.00 | −0.549957 | ||||||||
\(276\) | −576.000 | −0.125620 | ||||||||
\(277\) | −7711.00 | −1.67260 | −0.836298 | − | 0.548275i | \(-0.815285\pi\) | ||||
−0.836298 | + | 0.548275i | \(0.815285\pi\) | |||||||
\(278\) | −3950.00 | −0.852177 | ||||||||
\(279\) | 736.000 | 0.157932 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6858.00 | −1.45592 | −0.727961 | − | 0.685619i | \(-0.759532\pi\) | ||||
−0.727961 | + | 0.685619i | \(0.759532\pi\) | |||||||
\(282\) | 2316.00 | 0.489063 | ||||||||
\(283\) | 1807.00 | 0.379558 | 0.189779 | − | 0.981827i | \(-0.439223\pi\) | ||||
0.189779 | + | 0.981827i | \(0.439223\pi\) | |||||||
\(284\) | 2568.00 | 0.536559 | ||||||||
\(285\) | −342.000 | −0.0710819 | ||||||||
\(286\) | −5928.00 | −1.22563 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 736.000 | 0.150588 | ||||||||
\(289\) | −152.000 | −0.0309383 | ||||||||
\(290\) | 2700.00 | 0.546722 | ||||||||
\(291\) | −2848.00 | −0.573721 | ||||||||
\(292\) | 1948.00 | 0.390404 | ||||||||
\(293\) | 3012.00 | 0.600556 | 0.300278 | − | 0.953852i | \(-0.402921\pi\) | ||||
0.300278 | + | 0.953852i | \(0.402921\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2970.00 | 0.586170 | ||||||||
\(296\) | 1808.00 | 0.355027 | ||||||||
\(297\) | −5700.00 | −1.11363 | ||||||||
\(298\) | 3390.00 | 0.658985 | ||||||||
\(299\) | −3744.00 | −0.724151 | ||||||||
\(300\) | −352.000 | −0.0677424 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3604.00 | −0.686712 | ||||||||
\(303\) | −2124.00 | −0.402708 | ||||||||
\(304\) | −304.000 | −0.0573539 | ||||||||
\(305\) | 117.000 | 0.0219652 | ||||||||
\(306\) | −3174.00 | −0.592959 | ||||||||
\(307\) | 1096.00 | 0.203753 | 0.101876 | − | 0.994797i | \(-0.467515\pi\) | ||||
0.101876 | + | 0.994797i | \(0.467515\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2356.00 | −0.433748 | ||||||||
\(310\) | 576.000 | 0.105531 | ||||||||
\(311\) | −1947.00 | −0.354998 | −0.177499 | − | 0.984121i | \(-0.556801\pi\) | ||||
−0.177499 | + | 0.984121i | \(0.556801\pi\) | |||||||
\(312\) | −832.000 | −0.150970 | ||||||||
\(313\) | −7598.00 | −1.37209 | −0.686045 | − | 0.727559i | \(-0.740655\pi\) | ||||
−0.686045 | + | 0.727559i | \(0.740655\pi\) | |||||||
\(314\) | −6452.00 | −1.15958 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2800.00 | −0.498457 | ||||||||
\(317\) | 8334.00 | 1.47661 | 0.738303 | − | 0.674469i | \(-0.235627\pi\) | ||||
0.738303 | + | 0.674469i | \(0.235627\pi\) | |||||||
\(318\) | 1728.00 | 0.304721 | ||||||||
\(319\) | −8550.00 | −1.50065 | ||||||||
\(320\) | 576.000 | 0.100623 | ||||||||
\(321\) | 228.000 | 0.0396440 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1311.00 | 0.225839 | ||||||||
\(324\) | 1684.00 | 0.288752 | ||||||||
\(325\) | −2288.00 | −0.390509 | ||||||||
\(326\) | −2536.00 | −0.430847 | ||||||||
\(327\) | 2920.00 | 0.493812 | ||||||||
\(328\) | −2064.00 | −0.347455 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2052.00 | −0.342300 | ||||||||
\(331\) | −8368.00 | −1.38957 | −0.694784 | − | 0.719219i | \(-0.744500\pi\) | ||||
−0.694784 | + | 0.719219i | \(0.744500\pi\) | |||||||
\(332\) | 48.0000 | 0.00793477 | ||||||||
\(333\) | 5198.00 | 0.855401 | ||||||||
\(334\) | 1308.00 | 0.214283 | ||||||||
\(335\) | −7704.00 | −1.25646 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10336.0 | −1.67074 | −0.835368 | − | 0.549692i | \(-0.814745\pi\) | ||||
−0.835368 | + | 0.549692i | \(0.814745\pi\) | |||||||
\(338\) | −1014.00 | −0.163178 | ||||||||
\(339\) | −1644.00 | −0.263392 | ||||||||
\(340\) | −2484.00 | −0.396217 | ||||||||
\(341\) | −1824.00 | −0.289663 | ||||||||
\(342\) | −874.000 | −0.138189 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 536.000 | 0.0840093 | ||||||||
\(345\) | −1296.00 | −0.202244 | ||||||||
\(346\) | −2724.00 | −0.423246 | ||||||||
\(347\) | 6879.00 | 1.06422 | 0.532110 | − | 0.846675i | \(-0.321399\pi\) | ||||
0.532110 | + | 0.846675i | \(0.321399\pi\) | |||||||
\(348\) | −1200.00 | −0.184847 | ||||||||
\(349\) | 6355.00 | 0.974714 | 0.487357 | − | 0.873203i | \(-0.337961\pi\) | ||||
0.487357 | + | 0.873203i | \(0.337961\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5200.00 | −0.790756 | ||||||||
\(352\) | −1824.00 | −0.276192 | ||||||||
\(353\) | −7218.00 | −1.08832 | −0.544158 | − | 0.838983i | \(-0.683151\pi\) | ||||
−0.544158 | + | 0.838983i | \(0.683151\pi\) | |||||||
\(354\) | −1320.00 | −0.198184 | ||||||||
\(355\) | 5778.00 | 0.863843 | ||||||||
\(356\) | 2400.00 | 0.357303 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 420.000 | 0.0620047 | ||||||||
\(359\) | 1665.00 | 0.244778 | 0.122389 | − | 0.992482i | \(-0.460944\pi\) | ||||
0.122389 | + | 0.992482i | \(0.460944\pi\) | |||||||
\(360\) | 1656.00 | 0.242441 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 4.00000 | 0.000580761 0 | ||||||||
\(363\) | 3836.00 | 0.554650 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4383.00 | 0.628539 | ||||||||
\(366\) | −52.0000 | −0.00742646 | ||||||||
\(367\) | −13064.0 | −1.85813 | −0.929067 | − | 0.369911i | \(-0.879388\pi\) | ||||
−0.929067 | + | 0.369911i | \(0.879388\pi\) | |||||||
\(368\) | −1152.00 | −0.163185 | ||||||||
\(369\) | −5934.00 | −0.837159 | ||||||||
\(370\) | 4068.00 | 0.571582 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −256.000 | −0.0356801 | ||||||||
\(373\) | −10492.0 | −1.45645 | −0.728224 | − | 0.685339i | \(-0.759654\pi\) | ||||
−0.728224 | + | 0.685339i | \(0.759654\pi\) | |||||||
\(374\) | 7866.00 | 1.08754 | ||||||||
\(375\) | −3042.00 | −0.418902 | ||||||||
\(376\) | 4632.00 | 0.635312 | ||||||||
\(377\) | −7800.00 | −1.06557 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7610.00 | 1.03140 | 0.515698 | − | 0.856770i | \(-0.327532\pi\) | ||||
0.515698 | + | 0.856770i | \(0.327532\pi\) | |||||||
\(380\) | −684.000 | −0.0923381 | ||||||||
\(381\) | −4172.00 | −0.560992 | ||||||||
\(382\) | 5286.00 | 0.707998 | ||||||||
\(383\) | −4008.00 | −0.534724 | −0.267362 | − | 0.963596i | \(-0.586152\pi\) | ||||
−0.267362 | + | 0.963596i | \(0.586152\pi\) | |||||||
\(384\) | −256.000 | −0.0340207 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6496.00 | −0.856574 | ||||||||
\(387\) | 1541.00 | 0.202412 | ||||||||
\(388\) | −5696.00 | −0.745285 | ||||||||
\(389\) | −3525.00 | −0.459446 | −0.229723 | − | 0.973256i | \(-0.573782\pi\) | ||||
−0.229723 | + | 0.973256i | \(0.573782\pi\) | |||||||
\(390\) | −1872.00 | −0.243057 | ||||||||
\(391\) | 4968.00 | 0.642564 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 186.000 | 0.0238739 | ||||||||
\(394\) | 6252.00 | 0.799419 | ||||||||
\(395\) | −6300.00 | −0.802500 | ||||||||
\(396\) | −5244.00 | −0.665457 | ||||||||
\(397\) | −6629.00 | −0.838035 | −0.419018 | − | 0.907978i | \(-0.637625\pi\) | ||||
−0.419018 | + | 0.907978i | \(0.637625\pi\) | |||||||
\(398\) | −5990.00 | −0.754401 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −704.000 | −0.0880000 | ||||||||
\(401\) | −10848.0 | −1.35093 | −0.675465 | − | 0.737392i | \(-0.736057\pi\) | ||||
−0.675465 | + | 0.737392i | \(0.736057\pi\) | |||||||
\(402\) | 3424.00 | 0.424810 | ||||||||
\(403\) | −1664.00 | −0.205682 | ||||||||
\(404\) | −4248.00 | −0.523133 | ||||||||
\(405\) | 3789.00 | 0.464881 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12882.0 | −1.56889 | ||||||||
\(408\) | 1104.00 | 0.133961 | ||||||||
\(409\) | 3040.00 | 0.367526 | 0.183763 | − | 0.982971i | \(-0.441172\pi\) | ||||
0.183763 | + | 0.982971i | \(0.441172\pi\) | |||||||
\(410\) | −4644.00 | −0.559392 | ||||||||
\(411\) | 2538.00 | 0.304599 | ||||||||
\(412\) | −4712.00 | −0.563455 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3312.00 | −0.393179 | ||||||||
\(415\) | 108.000 | 0.0127747 | ||||||||
\(416\) | −1664.00 | −0.196116 | ||||||||
\(417\) | 3950.00 | 0.463867 | ||||||||
\(418\) | 2166.00 | 0.253451 | ||||||||
\(419\) | 3900.00 | 0.454719 | 0.227360 | − | 0.973811i | \(-0.426991\pi\) | ||||
0.227360 | + | 0.973811i | \(0.426991\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4412.00 | 0.510755 | 0.255377 | − | 0.966841i | \(-0.417800\pi\) | ||||
0.255377 | + | 0.966841i | \(0.417800\pi\) | |||||||
\(422\) | 8636.00 | 0.996194 | ||||||||
\(423\) | 13317.0 | 1.53072 | ||||||||
\(424\) | 3456.00 | 0.395845 | ||||||||
\(425\) | 3036.00 | 0.346512 | ||||||||
\(426\) | −2568.00 | −0.292066 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 456.000 | 0.0514990 | ||||||||
\(429\) | 5928.00 | 0.667148 | ||||||||
\(430\) | 1206.00 | 0.135252 | ||||||||
\(431\) | 432.000 | 0.0482801 | 0.0241400 | − | 0.999709i | \(-0.492315\pi\) | ||||
0.0241400 | + | 0.999709i | \(0.492315\pi\) | |||||||
\(432\) | −1600.00 | −0.178195 | ||||||||
\(433\) | 2002.00 | 0.222194 | 0.111097 | − | 0.993810i | \(-0.464564\pi\) | ||||
0.111097 | + | 0.993810i | \(0.464564\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2700.00 | −0.297598 | ||||||||
\(436\) | 5840.00 | 0.641480 | ||||||||
\(437\) | 1368.00 | 0.149749 | ||||||||
\(438\) | −1948.00 | −0.212509 | ||||||||
\(439\) | 1690.00 | 0.183734 | 0.0918671 | − | 0.995771i | \(-0.470717\pi\) | ||||
0.0918671 | + | 0.995771i | \(0.470717\pi\) | |||||||
\(440\) | −4104.00 | −0.444660 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7176.00 | 0.772234 | ||||||||
\(443\) | −1977.00 | −0.212032 | −0.106016 | − | 0.994364i | \(-0.533809\pi\) | ||||
−0.106016 | + | 0.994364i | \(0.533809\pi\) | |||||||
\(444\) | −1808.00 | −0.193252 | ||||||||
\(445\) | 5400.00 | 0.575246 | ||||||||
\(446\) | 1036.00 | 0.109991 | ||||||||
\(447\) | −3390.00 | −0.358706 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2760.00 | −0.290095 | −0.145047 | − | 0.989425i | \(-0.546333\pi\) | ||||
−0.145047 | + | 0.989425i | \(0.546333\pi\) | |||||||
\(450\) | −2024.00 | −0.212027 | ||||||||
\(451\) | 14706.0 | 1.53543 | ||||||||
\(452\) | −3288.00 | −0.342156 | ||||||||
\(453\) | 3604.00 | 0.373798 | ||||||||
\(454\) | 5688.00 | 0.587998 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 304.000 | 0.0312195 | ||||||||
\(457\) | 4499.00 | 0.460513 | 0.230256 | − | 0.973130i | \(-0.426044\pi\) | ||||
0.230256 | + | 0.973130i | \(0.426044\pi\) | |||||||
\(458\) | 3490.00 | 0.356063 | ||||||||
\(459\) | 6900.00 | 0.701665 | ||||||||
\(460\) | −2592.00 | −0.262723 | ||||||||
\(461\) | 11643.0 | 1.17629 | 0.588144 | − | 0.808756i | \(-0.299859\pi\) | ||||
0.588144 | + | 0.808756i | \(0.299859\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1537.00 | −0.154277 | −0.0771387 | − | 0.997020i | \(-0.524578\pi\) | ||||
−0.0771387 | + | 0.997020i | \(0.524578\pi\) | |||||||
\(464\) | −2400.00 | −0.240123 | ||||||||
\(465\) | −576.000 | −0.0574438 | ||||||||
\(466\) | −10566.0 | −1.05034 | ||||||||
\(467\) | 7641.00 | 0.757138 | 0.378569 | − | 0.925573i | \(-0.376416\pi\) | ||||
0.378569 | + | 0.925573i | \(0.376416\pi\) | |||||||
\(468\) | −4784.00 | −0.472522 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 10422.0 | 1.02283 | ||||||||
\(471\) | 6452.00 | 0.631194 | ||||||||
\(472\) | −2640.00 | −0.257449 | ||||||||
\(473\) | −3819.00 | −0.371243 | ||||||||
\(474\) | 2800.00 | 0.271325 | ||||||||
\(475\) | 836.000 | 0.0807543 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9936.00 | 0.953749 | ||||||||
\(478\) | −930.000 | −0.0889900 | ||||||||
\(479\) | 8580.00 | 0.818435 | 0.409217 | − | 0.912437i | \(-0.365802\pi\) | ||||
0.409217 | + | 0.912437i | \(0.365802\pi\) | |||||||
\(480\) | −576.000 | −0.0547723 | ||||||||
\(481\) | −11752.0 | −1.11402 | ||||||||
\(482\) | −14156.0 | −1.33773 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7672.00 | 0.720511 | ||||||||
\(485\) | −12816.0 | −1.19989 | ||||||||
\(486\) | −7084.00 | −0.661187 | ||||||||
\(487\) | 12134.0 | 1.12904 | 0.564522 | − | 0.825418i | \(-0.309061\pi\) | ||||
0.564522 | + | 0.825418i | \(0.309061\pi\) | |||||||
\(488\) | −104.000 | −0.00964725 | ||||||||
\(489\) | 2536.00 | 0.234523 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5508.00 | −0.506258 | −0.253129 | − | 0.967433i | \(-0.581460\pi\) | ||||
−0.253129 | + | 0.967433i | \(0.581460\pi\) | |||||||
\(492\) | 2064.00 | 0.189131 | ||||||||
\(493\) | 10350.0 | 0.945518 | ||||||||
\(494\) | 1976.00 | 0.179969 | ||||||||
\(495\) | −11799.0 | −1.07136 | ||||||||
\(496\) | −512.000 | −0.0463498 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −48.0000 | −0.00431914 | ||||||||
\(499\) | −11905.0 | −1.06802 | −0.534009 | − | 0.845479i | \(-0.679315\pi\) | ||||
−0.534009 | + | 0.845479i | \(0.679315\pi\) | |||||||
\(500\) | −6084.00 | −0.544170 | ||||||||
\(501\) | −1308.00 | −0.116641 | ||||||||
\(502\) | 7134.00 | 0.634275 | ||||||||
\(503\) | −9108.00 | −0.807367 | −0.403684 | − | 0.914899i | \(-0.632270\pi\) | ||||
−0.403684 | + | 0.914899i | \(0.632270\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9558.00 | −0.842229 | ||||||||
\(506\) | 8208.00 | 0.721127 | ||||||||
\(507\) | 1014.00 | 0.0888231 | ||||||||
\(508\) | −8344.00 | −0.728750 | ||||||||
\(509\) | 2520.00 | 0.219444 | 0.109722 | − | 0.993962i | \(-0.465004\pi\) | ||||
0.109722 | + | 0.993962i | \(0.465004\pi\) | |||||||
\(510\) | 2484.00 | 0.215673 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 1900.00 | 0.163523 | ||||||||
\(514\) | −3792.00 | −0.325405 | ||||||||
\(515\) | −10602.0 | −0.907146 | ||||||||
\(516\) | −536.000 | −0.0457288 | ||||||||
\(517\) | −33003.0 | −2.80749 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2724.00 | 0.230386 | ||||||||
\(520\) | −3744.00 | −0.315741 | ||||||||
\(521\) | −21612.0 | −1.81735 | −0.908675 | − | 0.417505i | \(-0.862905\pi\) | ||||
−0.908675 | + | 0.417505i | \(0.862905\pi\) | |||||||
\(522\) | −6900.00 | −0.578553 | ||||||||
\(523\) | 9022.00 | 0.754311 | 0.377155 | − | 0.926150i | \(-0.376902\pi\) | ||||
0.377155 | + | 0.926150i | \(0.376902\pi\) | |||||||
\(524\) | 372.000 | 0.0310132 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 114.000 | 0.00944988 | ||||||||
\(527\) | 2208.00 | 0.182509 | ||||||||
\(528\) | 1824.00 | 0.150340 | ||||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | 7776.00 | 0.637298 | ||||||||
\(531\) | −7590.00 | −0.620297 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13416.0 | 1.09027 | ||||||||
\(534\) | −2400.00 | −0.194491 | ||||||||
\(535\) | 1026.00 | 0.0829119 | ||||||||
\(536\) | 6848.00 | 0.551844 | ||||||||
\(537\) | −420.000 | −0.0337511 | ||||||||
\(538\) | 5400.00 | 0.432733 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3600.00 | −0.286888 | ||||||||
\(541\) | −9253.00 | −0.735337 | −0.367669 | − | 0.929957i | \(-0.619844\pi\) | ||||
−0.367669 | + | 0.929957i | \(0.619844\pi\) | |||||||
\(542\) | 7744.00 | 0.613715 | ||||||||
\(543\) | −4.00000 | −0.000316126 0 | ||||||||
\(544\) | 2208.00 | 0.174021 | ||||||||
\(545\) | 13140.0 | 1.03276 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13244.0 | 1.03523 | 0.517617 | − | 0.855613i | \(-0.326819\pi\) | ||||
0.517617 | + | 0.855613i | \(0.326819\pi\) | |||||||
\(548\) | 5076.00 | 0.395686 | ||||||||
\(549\) | −299.000 | −0.0232441 | ||||||||
\(550\) | 5016.00 | 0.388878 | ||||||||
\(551\) | 2850.00 | 0.220352 | ||||||||
\(552\) | 1152.00 | 0.0888268 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 15422.0 | 1.18270 | ||||||||
\(555\) | −4068.00 | −0.311130 | ||||||||
\(556\) | 7900.00 | 0.602580 | ||||||||
\(557\) | 1569.00 | 0.119355 | 0.0596774 | − | 0.998218i | \(-0.480993\pi\) | ||||
0.0596774 | + | 0.998218i | \(0.480993\pi\) | |||||||
\(558\) | −1472.00 | −0.111675 | ||||||||
\(559\) | −3484.00 | −0.263609 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7866.00 | −0.591984 | ||||||||
\(562\) | 13716.0 | 1.02949 | ||||||||
\(563\) | 15762.0 | 1.17991 | 0.589955 | − | 0.807436i | \(-0.299146\pi\) | ||||
0.589955 | + | 0.807436i | \(0.299146\pi\) | |||||||
\(564\) | −4632.00 | −0.345820 | ||||||||
\(565\) | −7398.00 | −0.550861 | ||||||||
\(566\) | −3614.00 | −0.268388 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5136.00 | −0.379405 | ||||||||
\(569\) | −13800.0 | −1.01674 | −0.508371 | − | 0.861138i | \(-0.669752\pi\) | ||||
−0.508371 | + | 0.861138i | \(0.669752\pi\) | |||||||
\(570\) | 684.000 | 0.0502625 | ||||||||
\(571\) | −4348.00 | −0.318666 | −0.159333 | − | 0.987225i | \(-0.550934\pi\) | ||||
−0.159333 | + | 0.987225i | \(0.550934\pi\) | |||||||
\(572\) | 11856.0 | 0.866651 | ||||||||
\(573\) | −5286.00 | −0.385385 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3168.00 | 0.229765 | ||||||||
\(576\) | −1472.00 | −0.106481 | ||||||||
\(577\) | −3539.00 | −0.255339 | −0.127669 | − | 0.991817i | \(-0.540750\pi\) | ||||
−0.127669 | + | 0.991817i | \(0.540750\pi\) | |||||||
\(578\) | 304.000 | 0.0218767 | ||||||||
\(579\) | 6496.00 | 0.466260 | ||||||||
\(580\) | −5400.00 | −0.386591 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5696.00 | 0.405682 | ||||||||
\(583\) | −24624.0 | −1.74927 | ||||||||
\(584\) | −3896.00 | −0.276058 | ||||||||
\(585\) | −10764.0 | −0.760746 | ||||||||
\(586\) | −6024.00 | −0.424657 | ||||||||
\(587\) | 6321.00 | 0.444456 | 0.222228 | − | 0.974995i | \(-0.428667\pi\) | ||||
0.222228 | + | 0.974995i | \(0.428667\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 608.000 | 0.0425335 | ||||||||
\(590\) | −5940.00 | −0.414485 | ||||||||
\(591\) | −6252.00 | −0.435149 | ||||||||
\(592\) | −3616.00 | −0.251042 | ||||||||
\(593\) | −13278.0 | −0.919498 | −0.459749 | − | 0.888049i | \(-0.652061\pi\) | ||||
−0.459749 | + | 0.888049i | \(0.652061\pi\) | |||||||
\(594\) | 11400.0 | 0.787454 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6780.00 | −0.465973 | ||||||||
\(597\) | 5990.00 | 0.410644 | ||||||||
\(598\) | 7488.00 | 0.512052 | ||||||||
\(599\) | 20400.0 | 1.39152 | 0.695761 | − | 0.718274i | \(-0.255067\pi\) | ||||
0.695761 | + | 0.718274i | \(0.255067\pi\) | |||||||
\(600\) | 704.000 | 0.0479011 | ||||||||
\(601\) | 22198.0 | 1.50661 | 0.753307 | − | 0.657669i | \(-0.228457\pi\) | ||||
0.753307 | + | 0.657669i | \(0.228457\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19688.0 | 1.32961 | ||||||||
\(604\) | 7208.00 | 0.485578 | ||||||||
\(605\) | 17262.0 | 1.16000 | ||||||||
\(606\) | 4248.00 | 0.284758 | ||||||||
\(607\) | −9824.00 | −0.656909 | −0.328455 | − | 0.944520i | \(-0.606528\pi\) | ||||
−0.328455 | + | 0.944520i | \(0.606528\pi\) | |||||||
\(608\) | 608.000 | 0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −234.000 | −0.0155318 | ||||||||
\(611\) | −30108.0 | −1.99352 | ||||||||
\(612\) | 6348.00 | 0.419285 | ||||||||
\(613\) | −4327.00 | −0.285099 | −0.142550 | − | 0.989788i | \(-0.545530\pi\) | ||||
−0.142550 | + | 0.989788i | \(0.545530\pi\) | |||||||
\(614\) | −2192.00 | −0.144075 | ||||||||
\(615\) | 4644.00 | 0.304495 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14151.0 | −0.923335 | −0.461668 | − | 0.887053i | \(-0.652749\pi\) | ||||
−0.461668 | + | 0.887053i | \(0.652749\pi\) | |||||||
\(618\) | 4712.00 | 0.306706 | ||||||||
\(619\) | −22460.0 | −1.45839 | −0.729195 | − | 0.684306i | \(-0.760105\pi\) | ||||
−0.729195 | + | 0.684306i | \(0.760105\pi\) | |||||||
\(620\) | −1152.00 | −0.0746217 | ||||||||
\(621\) | 7200.00 | 0.465259 | ||||||||
\(622\) | 3894.00 | 0.251021 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1664.00 | 0.106752 | ||||||||
\(625\) | −8189.00 | −0.524096 | ||||||||
\(626\) | 15196.0 | 0.970215 | ||||||||
\(627\) | −2166.00 | −0.137961 | ||||||||
\(628\) | 12904.0 | 0.819945 | ||||||||
\(629\) | 15594.0 | 0.988511 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16363.0 | −1.03233 | −0.516165 | − | 0.856489i | \(-0.672641\pi\) | ||||
−0.516165 | + | 0.856489i | \(0.672641\pi\) | |||||||
\(632\) | 5600.00 | 0.352462 | ||||||||
\(633\) | −8636.00 | −0.542259 | ||||||||
\(634\) | −16668.0 | −1.04412 | ||||||||
\(635\) | −18774.0 | −1.17327 | ||||||||
\(636\) | −3456.00 | −0.215471 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 17100.0 | 1.06112 | ||||||||
\(639\) | −14766.0 | −0.914138 | ||||||||
\(640\) | −1152.00 | −0.0711512 | ||||||||
\(641\) | 5592.00 | 0.344572 | 0.172286 | − | 0.985047i | \(-0.444885\pi\) | ||||
0.172286 | + | 0.985047i | \(0.444885\pi\) | |||||||
\(642\) | −456.000 | −0.0280325 | ||||||||
\(643\) | −16553.0 | −1.01522 | −0.507610 | − | 0.861587i | \(-0.669471\pi\) | ||||
−0.507610 | + | 0.861587i | \(0.669471\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1206.00 | −0.0736220 | ||||||||
\(646\) | −2622.00 | −0.159692 | ||||||||
\(647\) | 4611.00 | 0.280181 | 0.140091 | − | 0.990139i | \(-0.455261\pi\) | ||||
0.140091 | + | 0.990139i | \(0.455261\pi\) | |||||||
\(648\) | −3368.00 | −0.204178 | ||||||||
\(649\) | 18810.0 | 1.13768 | ||||||||
\(650\) | 4576.00 | 0.276132 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5072.00 | 0.304655 | ||||||||
\(653\) | 16413.0 | 0.983599 | 0.491800 | − | 0.870708i | \(-0.336339\pi\) | ||||
0.491800 | + | 0.870708i | \(0.336339\pi\) | |||||||
\(654\) | −5840.00 | −0.349177 | ||||||||
\(655\) | 837.000 | 0.0499302 | ||||||||
\(656\) | 4128.00 | 0.245688 | ||||||||
\(657\) | −11201.0 | −0.665133 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27390.0 | 1.61906 | 0.809532 | − | 0.587076i | \(-0.199721\pi\) | ||||
0.809532 | + | 0.587076i | \(0.199721\pi\) | |||||||
\(660\) | 4104.00 | 0.242042 | ||||||||
\(661\) | −26912.0 | −1.58359 | −0.791797 | − | 0.610784i | \(-0.790854\pi\) | ||||
−0.791797 | + | 0.610784i | \(0.790854\pi\) | |||||||
\(662\) | 16736.0 | 0.982573 | ||||||||
\(663\) | −7176.00 | −0.420351 | ||||||||
\(664\) | −96.0000 | −0.00561073 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10396.0 | −0.604860 | ||||||||
\(667\) | 10800.0 | 0.626953 | ||||||||
\(668\) | −2616.00 | −0.151521 | ||||||||
\(669\) | −1036.00 | −0.0598716 | ||||||||
\(670\) | 15408.0 | 0.888452 | ||||||||
\(671\) | 741.000 | 0.0426319 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21562.0 | −1.23500 | −0.617499 | − | 0.786571i | \(-0.711854\pi\) | ||||
−0.617499 | + | 0.786571i | \(0.711854\pi\) | |||||||
\(674\) | 20672.0 | 1.18139 | ||||||||
\(675\) | 4400.00 | 0.250898 | ||||||||
\(676\) | 2028.00 | 0.115385 | ||||||||
\(677\) | 21966.0 | 1.24700 | 0.623502 | − | 0.781822i | \(-0.285709\pi\) | ||||
0.623502 | + | 0.781822i | \(0.285709\pi\) | |||||||
\(678\) | 3288.00 | 0.186246 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4968.00 | 0.280168 | ||||||||
\(681\) | −5688.00 | −0.320066 | ||||||||
\(682\) | 3648.00 | 0.204823 | ||||||||
\(683\) | 15348.0 | 0.859846 | 0.429923 | − | 0.902866i | \(-0.358541\pi\) | ||||
0.429923 | + | 0.902866i | \(0.358541\pi\) | |||||||
\(684\) | 1748.00 | 0.0977141 | ||||||||
\(685\) | 11421.0 | 0.637042 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3490.00 | −0.193816 | ||||||||
\(688\) | −1072.00 | −0.0594035 | ||||||||
\(689\) | −22464.0 | −1.24210 | ||||||||
\(690\) | 2592.00 | 0.143008 | ||||||||
\(691\) | −8147.00 | −0.448519 | −0.224259 | − | 0.974529i | \(-0.571996\pi\) | ||||
−0.224259 | + | 0.974529i | \(0.571996\pi\) | |||||||
\(692\) | 5448.00 | 0.299280 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13758.0 | −0.752517 | ||||||||
\(695\) | 17775.0 | 0.970136 | ||||||||
\(696\) | 2400.00 | 0.130707 | ||||||||
\(697\) | −17802.0 | −0.967430 | ||||||||
\(698\) | −12710.0 | −0.689227 | ||||||||
\(699\) | 10566.0 | 0.571735 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14982.0 | 0.807222 | 0.403611 | − | 0.914931i | \(-0.367755\pi\) | ||||
0.403611 | + | 0.914931i | \(0.367755\pi\) | |||||||
\(702\) | 10400.0 | 0.559149 | ||||||||
\(703\) | 4294.00 | 0.230372 | ||||||||
\(704\) | 3648.00 | 0.195297 | ||||||||
\(705\) | −10422.0 | −0.556759 | ||||||||
\(706\) | 14436.0 | 0.769555 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2640.00 | 0.140137 | ||||||||
\(709\) | 21890.0 | 1.15952 | 0.579758 | − | 0.814789i | \(-0.303147\pi\) | ||||
0.579758 | + | 0.814789i | \(0.303147\pi\) | |||||||
\(710\) | −11556.0 | −0.610830 | ||||||||
\(711\) | 16100.0 | 0.849222 | ||||||||
\(712\) | −4800.00 | −0.252651 | ||||||||
\(713\) | 2304.00 | 0.121018 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 26676.0 | 1.39528 | ||||||||
\(716\) | −840.000 | −0.0438440 | ||||||||
\(717\) | 930.000 | 0.0484400 | ||||||||
\(718\) | −3330.00 | −0.173084 | ||||||||
\(719\) | 27015.0 | 1.40124 | 0.700619 | − | 0.713536i | \(-0.252907\pi\) | ||||
0.700619 | + | 0.713536i | \(0.252907\pi\) | |||||||
\(720\) | −3312.00 | −0.171432 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −722.000 | −0.0372161 | ||||||||
\(723\) | 14156.0 | 0.728171 | ||||||||
\(724\) | −8.00000 | −0.000410660 0 | ||||||||
\(725\) | 6600.00 | 0.338094 | ||||||||
\(726\) | −7672.00 | −0.392196 | ||||||||
\(727\) | 13021.0 | 0.664267 | 0.332134 | − | 0.943232i | \(-0.392232\pi\) | ||||
0.332134 | + | 0.943232i | \(0.392232\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4283.00 | −0.217599 | ||||||||
\(730\) | −8766.00 | −0.444444 | ||||||||
\(731\) | 4623.00 | 0.233909 | ||||||||
\(732\) | 104.000 | 0.00525130 | ||||||||
\(733\) | 6262.00 | 0.315542 | 0.157771 | − | 0.987476i | \(-0.449569\pi\) | ||||
0.157771 | + | 0.987476i | \(0.449569\pi\) | |||||||
\(734\) | 26128.0 | 1.31390 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2304.00 | 0.115389 | ||||||||
\(737\) | −48792.0 | −2.43864 | ||||||||
\(738\) | 11868.0 | 0.591961 | ||||||||
\(739\) | −10855.0 | −0.540335 | −0.270168 | − | 0.962813i | \(-0.587079\pi\) | ||||
−0.270168 | + | 0.962813i | \(0.587079\pi\) | |||||||
\(740\) | −8136.00 | −0.404169 | ||||||||
\(741\) | −1976.00 | −0.0979624 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14892.0 | −0.735309 | −0.367654 | − | 0.929962i | \(-0.619839\pi\) | ||||
−0.367654 | + | 0.929962i | \(0.619839\pi\) | |||||||
\(744\) | 512.000 | 0.0252296 | ||||||||
\(745\) | −15255.0 | −0.750201 | ||||||||
\(746\) | 20984.0 | 1.02986 | ||||||||
\(747\) | −276.000 | −0.0135185 | ||||||||
\(748\) | −15732.0 | −0.769009 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 6084.00 | 0.296208 | ||||||||
\(751\) | 28952.0 | 1.40676 | 0.703378 | − | 0.710816i | \(-0.251674\pi\) | ||||
0.703378 | + | 0.710816i | \(0.251674\pi\) | |||||||
\(752\) | −9264.00 | −0.449233 | ||||||||
\(753\) | −7134.00 | −0.345256 | ||||||||
\(754\) | 15600.0 | 0.753473 | ||||||||
\(755\) | 16218.0 | 0.781766 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3541.00 | −0.170013 | −0.0850065 | − | 0.996380i | \(-0.527091\pi\) | ||||
−0.0850065 | + | 0.996380i | \(0.527091\pi\) | |||||||
\(758\) | −15220.0 | −0.729308 | ||||||||
\(759\) | −8208.00 | −0.392532 | ||||||||
\(760\) | 1368.00 | 0.0652929 | ||||||||
\(761\) | −22617.0 | −1.07735 | −0.538676 | − | 0.842513i | \(-0.681075\pi\) | ||||
−0.538676 | + | 0.842513i | \(0.681075\pi\) | |||||||
\(762\) | 8344.00 | 0.396681 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10572.0 | −0.500630 | ||||||||
\(765\) | 14283.0 | 0.675037 | ||||||||
\(766\) | 8016.00 | 0.378107 | ||||||||
\(767\) | 17160.0 | 0.807838 | ||||||||
\(768\) | 512.000 | 0.0240563 | ||||||||
\(769\) | −11495.0 | −0.539038 | −0.269519 | − | 0.962995i | \(-0.586865\pi\) | ||||
−0.269519 | + | 0.962995i | \(0.586865\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3792.00 | 0.177128 | ||||||||
\(772\) | 12992.0 | 0.605690 | ||||||||
\(773\) | 14622.0 | 0.680358 | 0.340179 | − | 0.940361i | \(-0.389512\pi\) | ||||
0.340179 | + | 0.940361i | \(0.389512\pi\) | |||||||
\(774\) | −3082.00 | −0.143127 | ||||||||
\(775\) | 1408.00 | 0.0652605 | ||||||||
\(776\) | 11392.0 | 0.526996 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7050.00 | 0.324878 | ||||||||
\(779\) | −4902.00 | −0.225459 | ||||||||
\(780\) | 3744.00 | 0.171868 | ||||||||
\(781\) | 36594.0 | 1.67661 | ||||||||
\(782\) | −9936.00 | −0.454361 | ||||||||
\(783\) | 15000.0 | 0.684618 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 29034.0 | 1.32009 | ||||||||
\(786\) | −372.000 | −0.0168814 | ||||||||
\(787\) | −7124.00 | −0.322672 | −0.161336 | − | 0.986900i | \(-0.551580\pi\) | ||||
−0.161336 | + | 0.986900i | \(0.551580\pi\) | |||||||
\(788\) | −12504.0 | −0.565275 | ||||||||
\(789\) | −114.000 | −0.00514386 | ||||||||
\(790\) | 12600.0 | 0.567453 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 10488.0 | 0.470549 | ||||||||
\(793\) | 676.000 | 0.0302717 | ||||||||
\(794\) | 13258.0 | 0.592580 | ||||||||
\(795\) | −7776.00 | −0.346901 | ||||||||
\(796\) | 11980.0 | 0.533442 | ||||||||
\(797\) | 3576.00 | 0.158932 | 0.0794658 | − | 0.996838i | \(-0.474679\pi\) | ||||
0.0794658 | + | 0.996838i | \(0.474679\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39951.0 | 1.76892 | ||||||||
\(800\) | 1408.00 | 0.0622254 | ||||||||
\(801\) | −13800.0 | −0.608738 | ||||||||
\(802\) | 21696.0 | 0.955252 | ||||||||
\(803\) | 27759.0 | 1.21992 | ||||||||
\(804\) | −6848.00 | −0.300386 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3328.00 | 0.145439 | ||||||||
\(807\) | −5400.00 | −0.235550 | ||||||||
\(808\) | 8496.00 | 0.369911 | ||||||||
\(809\) | 42855.0 | 1.86242 | 0.931212 | − | 0.364477i | \(-0.118752\pi\) | ||||
0.931212 | + | 0.364477i | \(0.118752\pi\) | |||||||
\(810\) | −7578.00 | −0.328721 | ||||||||
\(811\) | 15568.0 | 0.674065 | 0.337032 | − | 0.941493i | \(-0.390577\pi\) | ||||
0.337032 | + | 0.941493i | \(0.390577\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7744.00 | −0.334064 | ||||||||
\(814\) | 25764.0 | 1.10937 | ||||||||
\(815\) | 11412.0 | 0.490485 | ||||||||
\(816\) | −2208.00 | −0.0947248 | ||||||||
\(817\) | 1273.00 | 0.0545124 | ||||||||
\(818\) | −6080.00 | −0.259880 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9288.00 | 0.395550 | ||||||||
\(821\) | 2517.00 | 0.106996 | 0.0534981 | − | 0.998568i | \(-0.482963\pi\) | ||||
0.0534981 | + | 0.998568i | \(0.482963\pi\) | |||||||
\(822\) | −5076.00 | −0.215384 | ||||||||
\(823\) | −9727.00 | −0.411983 | −0.205991 | − | 0.978554i | \(-0.566042\pi\) | ||||
−0.205991 | + | 0.978554i | \(0.566042\pi\) | |||||||
\(824\) | 9424.00 | 0.398423 | ||||||||
\(825\) | −5016.00 | −0.211678 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28224.0 | 1.18675 | 0.593376 | − | 0.804925i | \(-0.297795\pi\) | ||||
0.593376 | + | 0.804925i | \(0.297795\pi\) | |||||||
\(828\) | 6624.00 | 0.278019 | ||||||||
\(829\) | −3080.00 | −0.129038 | −0.0645192 | − | 0.997916i | \(-0.520551\pi\) | ||||
−0.0645192 | + | 0.997916i | \(0.520551\pi\) | |||||||
\(830\) | −216.000 | −0.00903310 | ||||||||
\(831\) | −15422.0 | −0.643782 | ||||||||
\(832\) | 3328.00 | 0.138675 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −7900.00 | −0.328003 | ||||||||
\(835\) | −5886.00 | −0.243944 | ||||||||
\(836\) | −4332.00 | −0.179217 | ||||||||
\(837\) | 3200.00 | 0.132148 | ||||||||
\(838\) | −7800.00 | −0.321535 | ||||||||
\(839\) | −26790.0 | −1.10238 | −0.551188 | − | 0.834381i | \(-0.685825\pi\) | ||||
−0.551188 | + | 0.834381i | \(0.685825\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1889.00 | −0.0774530 | ||||||||
\(842\) | −8824.00 | −0.361158 | ||||||||
\(843\) | −13716.0 | −0.560385 | ||||||||
\(844\) | −17272.0 | −0.704416 | ||||||||
\(845\) | 4563.00 | 0.185766 | ||||||||
\(846\) | −26634.0 | −1.08238 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6912.00 | −0.279905 | ||||||||
\(849\) | 3614.00 | 0.146092 | ||||||||
\(850\) | −6072.00 | −0.245021 | ||||||||
\(851\) | 16272.0 | 0.655461 | ||||||||
\(852\) | 5136.00 | 0.206522 | ||||||||
\(853\) | −19178.0 | −0.769803 | −0.384902 | − | 0.922958i | \(-0.625765\pi\) | ||||
−0.384902 | + | 0.922958i | \(0.625765\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3933.00 | 0.157317 | ||||||||
\(856\) | −912.000 | −0.0364153 | ||||||||
\(857\) | 2406.00 | 0.0959013 | 0.0479506 | − | 0.998850i | \(-0.484731\pi\) | ||||
0.0479506 | + | 0.998850i | \(0.484731\pi\) | |||||||
\(858\) | −11856.0 | −0.471745 | ||||||||
\(859\) | −9125.00 | −0.362446 | −0.181223 | − | 0.983442i | \(-0.558006\pi\) | ||||
−0.181223 | + | 0.983442i | \(0.558006\pi\) | |||||||
\(860\) | −2412.00 | −0.0956378 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −864.000 | −0.0341392 | ||||||||
\(863\) | 8898.00 | 0.350975 | 0.175488 | − | 0.984482i | \(-0.443850\pi\) | ||||
0.175488 | + | 0.984482i | \(0.443850\pi\) | |||||||
\(864\) | 3200.00 | 0.126003 | ||||||||
\(865\) | 12258.0 | 0.481832 | ||||||||
\(866\) | −4004.00 | −0.157115 | ||||||||
\(867\) | −304.000 | −0.0119082 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −39900.0 | −1.55755 | ||||||||
\(870\) | 5400.00 | 0.210434 | ||||||||
\(871\) | −44512.0 | −1.73161 | ||||||||
\(872\) | −11680.0 | −0.453595 | ||||||||
\(873\) | 32752.0 | 1.26974 | ||||||||
\(874\) | −2736.00 | −0.105889 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3896.00 | 0.150267 | ||||||||
\(877\) | −15886.0 | −0.611667 | −0.305834 | − | 0.952085i | \(-0.598935\pi\) | ||||
−0.305834 | + | 0.952085i | \(0.598935\pi\) | |||||||
\(878\) | −3380.00 | −0.129920 | ||||||||
\(879\) | 6024.00 | 0.231154 | ||||||||
\(880\) | 8208.00 | 0.314422 | ||||||||
\(881\) | 25683.0 | 0.982159 | 0.491080 | − | 0.871115i | \(-0.336602\pi\) | ||||
0.491080 | + | 0.871115i | \(0.336602\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28267.0 | −1.07730 | −0.538652 | − | 0.842528i | \(-0.681066\pi\) | ||||
−0.538652 | + | 0.842528i | \(0.681066\pi\) | |||||||
\(884\) | −14352.0 | −0.546052 | ||||||||
\(885\) | 5940.00 | 0.225617 | ||||||||
\(886\) | 3954.00 | 0.149929 | ||||||||
\(887\) | 2466.00 | 0.0933486 | 0.0466743 | − | 0.998910i | \(-0.485138\pi\) | ||||
0.0466743 | + | 0.998910i | \(0.485138\pi\) | |||||||
\(888\) | 3616.00 | 0.136650 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −10800.0 | −0.406760 | ||||||||
\(891\) | 23997.0 | 0.902278 | ||||||||
\(892\) | −2072.00 | −0.0777754 | ||||||||
\(893\) | 11001.0 | 0.412245 | ||||||||
\(894\) | 6780.00 | 0.253643 | ||||||||
\(895\) | −1890.00 | −0.0705874 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7488.00 | −0.278726 | ||||||||
\(898\) | 5520.00 | 0.205128 | ||||||||
\(899\) | 4800.00 | 0.178074 | ||||||||
\(900\) | 4048.00 | 0.149926 | ||||||||
\(901\) | 29808.0 | 1.10216 | ||||||||
\(902\) | −29412.0 | −1.08571 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6576.00 | 0.241941 | ||||||||
\(905\) | −18.0000 | −0.000661149 0 | ||||||||
\(906\) | −7208.00 | −0.264315 | ||||||||
\(907\) | 29324.0 | 1.07353 | 0.536763 | − | 0.843733i | \(-0.319647\pi\) | ||||
0.536763 | + | 0.843733i | \(0.319647\pi\) | |||||||
\(908\) | −11376.0 | −0.415777 | ||||||||
\(909\) | 24426.0 | 0.891264 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47142.0 | 1.71447 | 0.857236 | − | 0.514924i | \(-0.172180\pi\) | ||||
0.857236 | + | 0.514924i | \(0.172180\pi\) | |||||||
\(912\) | −608.000 | −0.0220755 | ||||||||
\(913\) | 684.000 | 0.0247942 | ||||||||
\(914\) | −8998.00 | −0.325632 | ||||||||
\(915\) | 234.000 | 0.00845443 | ||||||||
\(916\) | −6980.00 | −0.251775 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −13800.0 | −0.496152 | ||||||||
\(919\) | −39940.0 | −1.43362 | −0.716811 | − | 0.697267i | \(-0.754399\pi\) | ||||
−0.716811 | + | 0.697267i | \(0.754399\pi\) | |||||||
\(920\) | 5184.00 | 0.185773 | ||||||||
\(921\) | 2192.00 | 0.0784244 | ||||||||
\(922\) | −23286.0 | −0.831761 | ||||||||
\(923\) | 33384.0 | 1.19052 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9944.00 | 0.353467 | ||||||||
\(926\) | 3074.00 | 0.109091 | ||||||||
\(927\) | 27094.0 | 0.959961 | ||||||||
\(928\) | 4800.00 | 0.169793 | ||||||||
\(929\) | 4410.00 | 0.155745 | 0.0778727 | − | 0.996963i | \(-0.475187\pi\) | ||||
0.0778727 | + | 0.996963i | \(0.475187\pi\) | |||||||
\(930\) | 1152.00 | 0.0406189 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 21132.0 | 0.742706 | ||||||||
\(933\) | −3894.00 | −0.136639 | ||||||||
\(934\) | −15282.0 | −0.535377 | ||||||||
\(935\) | −35397.0 | −1.23808 | ||||||||
\(936\) | 9568.00 | 0.334124 | ||||||||
\(937\) | 41671.0 | 1.45286 | 0.726431 | − | 0.687239i | \(-0.241178\pi\) | ||||
0.726431 | + | 0.687239i | \(0.241178\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15196.0 | −0.528118 | ||||||||
\(940\) | −20844.0 | −0.723251 | ||||||||
\(941\) | −4062.00 | −0.140720 | −0.0703599 | − | 0.997522i | \(-0.522415\pi\) | ||||
−0.0703599 | + | 0.997522i | \(0.522415\pi\) | |||||||
\(942\) | −12904.0 | −0.446322 | ||||||||
\(943\) | −18576.0 | −0.641482 | ||||||||
\(944\) | 5280.00 | 0.182044 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7638.00 | 0.262508 | ||||||||
\(947\) | −45036.0 | −1.54538 | −0.772689 | − | 0.634785i | \(-0.781089\pi\) | ||||
−0.772689 | + | 0.634785i | \(0.781089\pi\) | |||||||
\(948\) | −5600.00 | −0.191856 | ||||||||
\(949\) | 25324.0 | 0.866230 | ||||||||
\(950\) | −1672.00 | −0.0571019 | ||||||||
\(951\) | 16668.0 | 0.568346 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26508.0 | 0.901027 | 0.450513 | − | 0.892770i | \(-0.351241\pi\) | ||||
0.450513 | + | 0.892770i | \(0.351241\pi\) | |||||||
\(954\) | −19872.0 | −0.674402 | ||||||||
\(955\) | −23787.0 | −0.805999 | ||||||||
\(956\) | 1860.00 | 0.0629254 | ||||||||
\(957\) | −17100.0 | −0.577601 | ||||||||
\(958\) | −17160.0 | −0.578721 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1152.00 | 0.0387298 | ||||||||
\(961\) | −28767.0 | −0.965627 | ||||||||
\(962\) | 23504.0 | 0.787733 | ||||||||
\(963\) | −2622.00 | −0.0877391 | ||||||||
\(964\) | 28312.0 | 0.945921 | ||||||||
\(965\) | 29232.0 | 0.975141 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15976.0 | −0.531286 | −0.265643 | − | 0.964071i | \(-0.585584\pi\) | ||||
−0.265643 | + | 0.964071i | \(0.585584\pi\) | |||||||
\(968\) | −15344.0 | −0.509478 | ||||||||
\(969\) | 2622.00 | 0.0869255 | ||||||||
\(970\) | 25632.0 | 0.848447 | ||||||||
\(971\) | 39468.0 | 1.30442 | 0.652208 | − | 0.758040i | \(-0.273843\pi\) | ||||
0.652208 | + | 0.758040i | \(0.273843\pi\) | |||||||
\(972\) | 14168.0 | 0.467530 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −24268.0 | −0.798354 | ||||||||
\(975\) | −4576.00 | −0.150307 | ||||||||
\(976\) | 208.000 | 0.00682164 | ||||||||
\(977\) | 21804.0 | 0.713994 | 0.356997 | − | 0.934106i | \(-0.383801\pi\) | ||||
0.356997 | + | 0.934106i | \(0.383801\pi\) | |||||||
\(978\) | −5072.00 | −0.165833 | ||||||||
\(979\) | 34200.0 | 1.11648 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −33580.0 | −1.09289 | ||||||||
\(982\) | 11016.0 | 0.357978 | ||||||||
\(983\) | −11268.0 | −0.365609 | −0.182804 | − | 0.983149i | \(-0.558517\pi\) | ||||
−0.182804 | + | 0.983149i | \(0.558517\pi\) | |||||||
\(984\) | −4128.00 | −0.133736 | ||||||||
\(985\) | −28134.0 | −0.910075 | ||||||||
\(986\) | −20700.0 | −0.668582 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3952.00 | −0.127257 | ||||||||
\(989\) | 4824.00 | 0.155100 | ||||||||
\(990\) | 23598.0 | 0.757569 | ||||||||
\(991\) | −778.000 | −0.0249384 | −0.0124692 | − | 0.999922i | \(-0.503969\pi\) | ||||
−0.0124692 | + | 0.999922i | \(0.503969\pi\) | |||||||
\(992\) | 1024.00 | 0.0327742 | ||||||||
\(993\) | −16736.0 | −0.534845 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26955.0 | 0.858825 | ||||||||
\(996\) | 96.0000 | 0.00305409 | ||||||||
\(997\) | −389.000 | −0.0123568 | −0.00617841 | − | 0.999981i | \(-0.501967\pi\) | ||||
−0.00617841 | + | 0.999981i | \(0.501967\pi\) | |||||||
\(998\) | 23810.0 | 0.755203 | ||||||||
\(999\) | 22600.0 | 0.715748 |
(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 | 1862.4.a.a.1.1 | 1 | ||
7.6 | odd | 2 | 38.4.a.a.1.1 | ✓ | 1 | ||
21.20 | even | 2 | 342.4.a.d.1.1 | 1 | |||
28.27 | even | 2 | 304.4.a.a.1.1 | 1 | |||
35.13 | even | 4 | 950.4.b.d.799.2 | 2 | |||
35.27 | even | 4 | 950.4.b.d.799.1 | 2 | |||
35.34 | odd | 2 | 950.4.a.d.1.1 | 1 | |||
56.13 | odd | 2 | 1216.4.a.e.1.1 | 1 | |||
56.27 | even | 2 | 1216.4.a.b.1.1 | 1 | |||
133.132 | even | 2 | 722.4.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.4.a.a.1.1 | ✓ | 1 | 7.6 | odd | 2 | ||
304.4.a.a.1.1 | 1 | 28.27 | even | 2 | |||
342.4.a.d.1.1 | 1 | 21.20 | even | 2 | |||
722.4.a.d.1.1 | 1 | 133.132 | even | 2 | |||
950.4.a.d.1.1 | 1 | 35.34 | odd | 2 | |||
950.4.b.d.799.1 | 2 | 35.27 | even | 4 | |||
950.4.b.d.799.2 | 2 | 35.13 | even | 4 | |||
1216.4.a.b.1.1 | 1 | 56.27 | even | 2 | |||
1216.4.a.e.1.1 | 1 | 56.13 | odd | 2 | |||
1862.4.a.a.1.1 | 1 | 1.1 | even | 1 | trivial |