Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,4,Mod(1,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("1232.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.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: | \(72.6903531271\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{3} - 43x^{2} - 11x + 222 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 308) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.21425\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.21425 | −0.233683 | −0.116842 | − | 0.993151i | \(-0.537277\pi\) | ||||
−0.116842 | + | 0.993151i | \(0.537277\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −20.5256 | −1.83586 | −0.917932 | − | 0.396737i | \(-0.870142\pi\) | ||||
−0.917932 | + | 0.396737i | \(0.870142\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −25.5256 | −0.945392 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 66.7086 | 1.42320 | 0.711601 | − | 0.702584i | \(-0.247970\pi\) | ||||
0.711601 | + | 0.702584i | \(0.247970\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 24.9233 | 0.429011 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −59.7289 | −0.852141 | −0.426070 | − | 0.904690i | \(-0.640102\pi\) | ||||
−0.426070 | + | 0.904690i | \(0.640102\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −131.071 | −1.58262 | −0.791310 | − | 0.611416i | \(-0.790600\pi\) | ||||
−0.791310 | + | 0.611416i | \(0.790600\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.49978 | −0.0883240 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −163.117 | −1.47879 | −0.739395 | − | 0.673272i | \(-0.764888\pi\) | ||||
−0.739395 | + | 0.673272i | \(0.764888\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 296.300 | 2.37040 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 63.7794 | 0.454605 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −77.2961 | −0.494949 | −0.247474 | − | 0.968894i | \(-0.579601\pi\) | ||||
−0.247474 | + | 0.968894i | \(0.579601\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −206.358 | −1.19558 | −0.597791 | − | 0.801652i | \(-0.703955\pi\) | ||||
−0.597791 | + | 0.801652i | \(0.703955\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 13.3568 | 0.0704581 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −143.679 | −0.693892 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −215.238 | −0.956348 | −0.478174 | − | 0.878265i | \(-0.658701\pi\) | ||||
−0.478174 | + | 0.878265i | \(0.658701\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −81.0011 | −0.332578 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −403.218 | −1.53590 | −0.767952 | − | 0.640508i | \(-0.778724\pi\) | ||||
−0.767952 | + | 0.640508i | \(0.778724\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −43.5690 | −0.154517 | −0.0772583 | − | 0.997011i | \(-0.524617\pi\) | ||||
−0.0772583 | + | 0.997011i | \(0.524617\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 523.928 | 1.73561 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −69.1706 | −0.214672 | −0.107336 | − | 0.994223i | \(-0.534232\pi\) | ||||
−0.107336 | + | 0.994223i | \(0.534232\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 72.5261 | 0.199131 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 334.969 | 0.868143 | 0.434071 | − | 0.900878i | \(-0.357077\pi\) | ||||
0.434071 | + | 0.900878i | \(0.357077\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 225.781 | 0.553534 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 159.154 | 0.369832 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −681.283 | −1.50331 | −0.751656 | − | 0.659555i | \(-0.770745\pi\) | ||||
−0.751656 | + | 0.659555i | \(0.770745\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −24.4899 | −0.0514034 | −0.0257017 | − | 0.999670i | \(-0.508182\pi\) | ||||
−0.0257017 | + | 0.999670i | \(0.508182\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −178.679 | −0.357325 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1369.23 | −2.61281 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 285.338 | 0.520292 | 0.260146 | − | 0.965569i | \(-0.416229\pi\) | ||||
0.260146 | + | 0.965569i | \(0.416229\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 198.065 | 0.345568 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 522.204 | 0.872876 | 0.436438 | − | 0.899734i | \(-0.356240\pi\) | ||||
0.436438 | + | 0.899734i | \(0.356240\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 592.444 | 0.949867 | 0.474934 | − | 0.880022i | \(-0.342472\pi\) | ||||
0.474934 | + | 0.880022i | \(0.342472\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −359.783 | −0.553922 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −77.0000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 92.7989 | 0.132161 | 0.0660803 | − | 0.997814i | \(-0.478951\pi\) | ||||
0.0660803 | + | 0.997814i | \(0.478951\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 611.747 | 0.839158 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −480.928 | −0.636008 | −0.318004 | − | 0.948089i | \(-0.603013\pi\) | ||||
−0.318004 | + | 0.948089i | \(0.603013\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1225.97 | 1.56441 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 93.8570 | 0.115661 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1197.02 | 1.42566 | 0.712831 | − | 0.701336i | \(-0.247413\pi\) | ||||
0.712831 | + | 0.701336i | \(0.247413\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 466.960 | 0.537920 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 250.571 | 0.279388 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2690.31 | 2.90547 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 308.934 | 0.323377 | 0.161688 | − | 0.986842i | \(-0.448306\pi\) | ||||
0.161688 | + | 0.986842i | \(0.448306\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 280.781 | 0.285046 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1742.73 | 1.71691 | 0.858454 | − | 0.512891i | \(-0.171425\pi\) | ||||
0.858454 | + | 0.512891i | \(0.171425\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1043.91 | −0.998635 | −0.499318 | − | 0.866419i | \(-0.666416\pi\) | ||||
−0.499318 | + | 0.866419i | \(0.666416\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 174.463 | 0.162151 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −204.369 | −0.184646 | −0.0923230 | − | 0.995729i | \(-0.529429\pi\) | ||||
−0.0923230 | + | 0.995729i | \(0.529429\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 944.275 | 0.829772 | 0.414886 | − | 0.909873i | \(-0.363821\pi\) | ||||
0.414886 | + | 0.909873i | \(0.363821\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 261.353 | 0.223483 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1905.29 | −1.58615 | −0.793073 | − | 0.609127i | \(-0.791520\pi\) | ||||
−0.793073 | + | 0.609127i | \(0.791520\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3348.06 | 2.71486 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1702.78 | −1.34548 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −418.102 | −0.322079 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 489.609 | 0.358915 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3516.03 | −2.51587 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −547.690 | −0.382674 | −0.191337 | − | 0.981524i | \(-0.561282\pi\) | ||||
−0.191337 | + | 0.981524i | \(0.561282\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 52.9038 | 0.0361079 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1926.59 | 1.28494 | 0.642468 | − | 0.766312i | \(-0.277910\pi\) | ||||
0.642468 | + | 0.766312i | \(0.277910\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −917.498 | −0.598174 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1309.11 | −0.834594 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1440.77 | −0.898491 | −0.449245 | − | 0.893408i | \(-0.648307\pi\) | ||||
−0.449245 | + | 0.893408i | \(0.648307\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2430.80 | 1.48330 | 0.741648 | − | 0.670790i | \(-0.234045\pi\) | ||||
0.741648 | + | 0.670790i | \(0.234045\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 83.9906 | 0.0501652 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −733.794 | −0.429112 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1586.55 | 0.908659 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −59.4984 | −0.0333833 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 686.765 | 0.377597 | 0.188798 | − | 0.982016i | \(-0.439541\pi\) | ||||
0.188798 | + | 0.982016i | \(0.439541\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1759.45 | −0.948225 | −0.474113 | − | 0.880464i | \(-0.657231\pi\) | ||||
−0.474113 | + | 0.880464i | \(0.657231\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1524.62 | 0.805607 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4235.63 | 2.19493 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1833.85 | 0.932211 | 0.466105 | − | 0.884729i | \(-0.345657\pi\) | ||||
0.466105 | + | 0.884729i | \(0.345657\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −406.738 | −0.202870 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1141.82 | −0.558930 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2306.20 | 1.10820 | 0.554098 | − | 0.832452i | \(-0.313063\pi\) | ||||
0.554098 | + | 0.832452i | \(0.313063\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −274.156 | −0.129352 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2243.47 | −1.03955 | −0.519774 | − | 0.854304i | \(-0.673984\pi\) | ||||
−0.519774 | + | 0.854304i | \(0.673984\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2253.03 | 1.02550 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3345.67 | 1.49620 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2499.07 | −1.09827 | −0.549136 | − | 0.835733i | \(-0.685043\pi\) | ||||
−0.549136 | + | 0.835733i | \(0.685043\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2074.10 | 0.895926 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 827.250 | 0.351299 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −270.765 | −0.113061 | −0.0565304 | − | 0.998401i | \(-0.518004\pi\) | ||||
−0.0565304 | + | 0.998401i | \(0.518004\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1480.59 | 0.608018 | 0.304009 | − | 0.952669i | \(-0.401675\pi\) | ||||
0.304009 | + | 0.952669i | \(0.401675\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 29.7369 | 0.0120121 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4417.88 | 1.75573 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 657.018 | 0.256930 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 446.456 | 0.171825 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2461.01 | −0.932317 | −0.466158 | − | 0.884701i | \(-0.654362\pi\) | ||||
−0.466158 | + | 0.884701i | \(0.654362\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1419.76 | −0.529518 | −0.264759 | − | 0.964315i | \(-0.585292\pi\) | ||||
−0.264759 | + | 0.964315i | \(0.585292\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1662.60 | 0.610569 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2918.28 | 1.05542 | 0.527712 | − | 0.849423i | \(-0.323050\pi\) | ||||
0.527712 | + | 0.849423i | \(0.323050\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3767.60 | −1.34210 | −0.671050 | − | 0.741412i | \(-0.734156\pi\) | ||||
−0.671050 | + | 0.741412i | \(0.734156\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −346.472 | −0.121583 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −541.072 | −0.187073 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8276.28 | 2.81971 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4163.65 | 1.39804 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1441.78 | 0.477178 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3565.15 | 1.16320 | 0.581600 | − | 0.813475i | \(-0.302427\pi\) | ||||
0.581600 | + | 0.813475i | \(0.302427\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −634.088 | −0.203976 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 894.280 | 0.283672 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1444.51 | −0.451888 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −719.377 | −0.221968 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3984.43 | −1.21277 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2531.28 | −0.760122 | −0.380061 | − | 0.924962i | \(-0.624097\pi\) | ||||
−0.380061 | + | 0.924962i | \(0.624097\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7563.23 | −2.24096 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1207.47 | −0.353050 | −0.176525 | − | 0.984296i | \(-0.556486\pi\) | ||||
−0.176525 | + | 0.984296i | \(0.556486\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3998.70 | −1.15389 | −0.576946 | − | 0.816782i | \(-0.695756\pi\) | ||||
−0.576946 | + | 0.816782i | \(0.695756\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 93.4975 | 0.0266307 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1429.63 | 0.401966 | 0.200983 | − | 0.979595i | \(-0.435586\pi\) | ||||
0.200983 | + | 0.979595i | \(0.435586\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1419.77 | 0.394108 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −112.681 | −0.0308837 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3223.01 | −0.872297 | −0.436148 | − | 0.899875i | \(-0.643658\pi\) | ||||
−0.436148 | + | 0.899875i | \(0.643658\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 580.569 | 0.155177 | 0.0775887 | − | 0.996985i | \(-0.475278\pi\) | ||||
0.0775887 | + | 0.996985i | \(0.475278\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2464.86 | −0.650703 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1005.75 | −0.262266 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8743.56 | −2.25239 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 583.968 | 0.148624 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1277.24 | −0.321190 | −0.160595 | − | 0.987020i | \(-0.551341\pi\) | ||||
−0.160595 | + | 0.987020i | \(0.551341\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1794.28 | 0.445872 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1488.64 | −0.365577 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2517.10 | 0.610943 | 0.305471 | − | 0.952201i | \(-0.401186\pi\) | ||||
0.305471 | + | 0.952201i | \(0.401186\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1506.67 | −0.361466 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1973.03 | 0.467921 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5684.42 | 1.33276 | 0.666381 | − | 0.745611i | \(-0.267842\pi\) | ||||
0.666381 | + | 0.745611i | \(0.267842\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6875.44 | −1.59379 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1453.49 | −0.333153 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 870.076 | 0.197210 | 0.0986049 | − | 0.995127i | \(-0.468562\pi\) | ||||
0.0986049 | + | 0.995127i | \(0.468562\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −190.969 | −0.0428065 | −0.0214033 | − | 0.999771i | \(-0.506813\pi\) | ||||
−0.0214033 | + | 0.999771i | \(0.506813\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −567.008 | −0.125703 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3259.30 | −0.714702 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5601.27 | 1.21497 | 0.607487 | − | 0.794330i | \(-0.292178\pi\) | ||||
0.607487 | + | 0.794330i | \(0.292178\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5267.42 | 1.13029 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6878.31 | 1.46023 | 0.730117 | − | 0.683322i | \(-0.239466\pi\) | ||||
0.730117 | + | 0.683322i | \(0.239466\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5722.15 | −1.20193 | −0.600965 | − | 0.799275i | \(-0.705217\pi\) | ||||
−0.600965 | + | 0.799275i | \(0.705217\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3266.72 | −0.678961 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2822.53 | −0.580517 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1345.46 | −0.273856 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −375.125 | −0.0755677 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8278.49 | 1.65063 | 0.825315 | − | 0.564673i | \(-0.190998\pi\) | ||||
0.825315 | + | 0.564673i | \(0.190998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13983.7 | 2.75988 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −701.573 | −0.137069 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10881.3 | −2.10462 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −304.983 | −0.0584018 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2116.11 | −0.401213 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 502.669 | 0.0943696 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 645.184 | 0.119943 | 0.0599717 | − | 0.998200i | \(-0.480899\pi\) | ||||
0.0599717 | + | 0.998200i | \(0.480899\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1267.57 | 0.233364 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7930.96 | −1.44606 | −0.723028 | − | 0.690819i | \(-0.757250\pi\) | ||||
−0.723028 | + | 0.690819i | \(0.757250\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6600.26 | 1.19191 | 0.595956 | − | 0.803017i | \(-0.296773\pi\) | ||||
0.595956 | + | 0.803017i | \(0.296773\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3667.49 | 0.656000 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10260.0 | −1.81785 | −0.908923 | − | 0.416963i | \(-0.863094\pi\) | ||||
−0.908923 | + | 0.416963i | \(0.863094\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 850.257 | 0.149233 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 248.156 | 0.0431487 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7828.73 | 1.34861 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19765.7 | 3.37356 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1146.59 | −0.193904 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −484.194 | −0.0811383 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9625.35 | 1.59836 | 0.799180 | − | 0.601092i | \(-0.205268\pi\) | ||||
0.799180 | + | 0.601092i | \(0.205268\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5494.07 | 0.904124 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5856.72 | −0.955185 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5877.46 | 0.950046 | 0.475023 | − | 0.879973i | \(-0.342440\pi\) | ||||
0.475023 | + | 0.879973i | \(0.342440\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2313.50 | 0.370656 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2269.94 | 0.360482 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4065.40 | −0.634416 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10051.4 | 1.55501 | 0.777506 | − | 0.628875i | \(-0.216484\pi\) | ||||
0.777506 | + | 0.628875i | \(0.216484\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12242.2 | −1.87768 | −0.938839 | − | 0.344356i | \(-0.888097\pi\) | ||||
−0.938839 | + | 0.344356i | \(0.888097\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4254.63 | 0.646996 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11468.0 | −1.72912 | −0.864559 | − | 0.502532i | \(-0.832402\pi\) | ||||
−0.864559 | + | 0.502532i | \(0.832402\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10718.5 | −1.60248 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 507.682 | 0.0752644 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8566.44 | 1.25939 | 0.629693 | − | 0.776844i | \(-0.283181\pi\) | ||||
0.629693 | + | 0.776844i | \(0.283181\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10320.6 | 1.50468 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −146.925 | −0.0212439 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12160.3 | −1.74383 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6925.30 | −0.985008 | −0.492504 | − | 0.870310i | \(-0.663918\pi\) | ||||
−0.492504 | + | 0.870310i | \(0.663918\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10292.4 | 1.45203 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2344.78 | 0.328127 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5752.39 | 0.798518 | 0.399259 | − | 0.916838i | \(-0.369267\pi\) | ||||
0.399259 | + | 0.916838i | \(0.369267\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4269.35 | 0.587915 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5156.31 | −0.704412 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10010.2 | 1.35670 | 0.678348 | − | 0.734740i | \(-0.262696\pi\) | ||||
0.678348 | + | 0.734740i | \(0.262696\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 665.034 | 0.0894245 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4686.10 | −0.625192 | −0.312596 | − | 0.949886i | \(-0.601199\pi\) | ||||
−0.312596 | + | 0.949886i | \(0.601199\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1580.47 | 0.209216 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1112.13 | 0.146079 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11018.9 | −1.43619 | −0.718095 | − | 0.695945i | \(-0.754986\pi\) | ||||
−0.718095 | + | 0.695945i | \(0.754986\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9742.77 | 1.26014 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2339.37 | −0.300268 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1904.75 | −0.242629 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9780.07 | −1.23639 | −0.618196 | − | 0.786024i | \(-0.712136\pi\) | ||||
−0.618196 | + | 0.786024i | \(0.712136\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1114.07 | 0.139783 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5288.90 | 0.658641 | 0.329320 | − | 0.944218i | \(-0.393180\pi\) | ||||
0.329320 | + | 0.944218i | \(0.393180\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13765.9 | −1.70156 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12556.5 | −1.54058 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2367.62 | 0.288350 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7276.22 | 0.879672 | 0.439836 | − | 0.898078i | \(-0.355037\pi\) | ||||
0.439836 | + | 0.898078i | \(0.355037\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1749.46 | 0.209962 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4768.98 | −0.568199 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9871.32 | 1.16762 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2951.61 | −0.346621 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11032.7 | 1.28636 | 0.643178 | − | 0.765717i | \(-0.277616\pi\) | ||||
0.643178 | + | 0.765717i | \(0.277616\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16046.8 | 1.85765 | 0.928826 | − | 0.370517i | \(-0.120820\pi\) | ||||
0.928826 | + | 0.370517i | \(0.120820\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1765.62 | 0.202949 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17697.7 | −2.01991 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −171.429 | −0.0194286 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 891.012 | 0.100276 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6726.13 | 0.751709 | 0.375854 | − | 0.926679i | \(-0.377349\pi\) | ||||
0.375854 | + | 0.926679i | \(0.377349\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4622.57 | 0.513041 | 0.256520 | − | 0.966539i | \(-0.417424\pi\) | ||||
0.256520 | + | 0.966539i | \(0.417424\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1926.47 | −0.212338 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21379.9 | 2.34036 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11917.6 | −1.29566 | −0.647830 | − | 0.761785i | \(-0.724323\pi\) | ||||
−0.647830 | + | 0.761785i | \(0.724323\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1250.75 | −0.135056 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5606.28 | −0.601270 | −0.300635 | − | 0.953739i | \(-0.597199\pi\) | ||||
−0.300635 | + | 0.953739i | \(0.597199\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24569.6 | −2.61732 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −833.906 | −0.0882381 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2144.37 | −0.225388 | −0.112694 | − | 0.993630i | \(-0.535948\pi\) | ||||
−0.112694 | + | 0.993630i | \(0.535948\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4435.40 | 0.463092 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2136.42 | 0.221584 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9584.63 | −0.987548 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8524.38 | 0.872546 | 0.436273 | − | 0.899814i | \(-0.356298\pi\) | ||||
0.436273 | + | 0.899814i | \(0.356298\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3809.47 | −0.387388 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11768.7 | −1.18899 | −0.594494 | − | 0.804100i | \(-0.702647\pi\) | ||||
−0.594494 | + | 0.804100i | \(0.702647\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −393.751 | −0.0395230 | −0.0197615 | − | 0.999805i | \(-0.506291\pi\) | ||||
−0.0197615 | + | 0.999805i | \(0.506291\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5143.13 | −0.512918 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3258.65 | 0.322896 | 0.161448 | − | 0.986881i | \(-0.448384\pi\) | ||||
0.161448 | + | 0.986881i | \(0.448384\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1997.36 | 0.196652 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2226.76 | −0.217842 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 479.259 | 0.0465885 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −38836.3 | −3.75144 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8550.29 | −0.820735 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7913.65 | −0.754873 | −0.377436 | − | 0.926036i | \(-0.623194\pi\) | ||||
−0.377436 | + | 0.926036i | \(0.623194\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14358.2 | −1.36108 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1386.45 | 0.130612 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6341.06 | −0.593676 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5667.52 | −0.527351 | −0.263676 | − | 0.964611i | \(-0.584935\pi\) | ||||
−0.263676 | + | 0.964611i | \(0.584935\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2800.32 | −0.258967 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 389.830 | 0.0358305 | 0.0179152 | − | 0.999840i | \(-0.494297\pi\) | ||||
0.0179152 | + | 0.999840i | \(0.494297\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4616.81 | 0.421766 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5763.20 | −0.523307 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3655.43 | 0.329916 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13968.3 | −1.25312 | −0.626558 | − | 0.779375i | \(-0.715537\pi\) | ||||
−0.626558 | + | 0.779375i | \(0.715537\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2724.14 | 0.242925 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15152.6 | −1.34318 | −0.671591 | − | 0.740922i | \(-0.734389\pi\) | ||||
−0.671591 | + | 0.740922i | \(0.734389\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −35770.5 | −3.15201 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2735.75 | −0.239643 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11774.4 | −1.02532 | −0.512662 | − | 0.858591i | \(-0.671341\pi\) | ||||
−0.512662 | + | 0.858591i | \(0.671341\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4147.11 | 0.359016 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8359.63 | −0.719467 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 21426.9 | 1.83336 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 760.877 | 0.0647259 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3034.51 | 0.256648 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7972.13 | −0.670375 | −0.335188 | − | 0.942151i | \(-0.608800\pi\) | ||||
−0.335188 | + | 0.942151i | \(0.608800\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20833.0 | 1.74181 | 0.870904 | − | 0.491454i | \(-0.163534\pi\) | ||||
0.870904 | + | 0.491454i | \(0.163534\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2518.48 | −0.209363 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12325.6 | 1.01880 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14440.0 | 1.18682 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17390.1 | 1.42122 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26898.1 | −2.18590 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4194.80 | 0.338985 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 328.777 | 0.0264204 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −539.000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9288.86 | 0.738187 | 0.369093 | − | 0.929392i | \(-0.379668\pi\) | ||||
0.369093 | + | 0.929392i | \(0.379668\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1797.81 | −0.142084 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19381.8 | −1.52335 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22942.9 | −1.79336 | −0.896681 | − | 0.442678i | \(-0.854028\pi\) | ||||
−0.896681 | + | 0.442678i | \(0.854028\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 625.118 | 0.0485963 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10131.3 | 0.783316 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 649.592 | 0.0499520 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5364.43 | −0.410284 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4841.26 | −0.368278 | −0.184139 | − | 0.982900i | \(-0.558950\pi\) | ||||
−0.184139 | + | 0.982900i | \(0.558950\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2906.43 | −0.219908 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −797.787 | −0.0600402 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2784.32 | 0.208428 | 0.104214 | − | 0.994555i | \(-0.466767\pi\) | ||||
0.104214 | + | 0.994555i | \(0.466767\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 39107.2 | 2.91195 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4282.23 | 0.317172 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2229.27 | −0.164246 | −0.0821228 | − | 0.996622i | \(-0.526170\pi\) | ||||
−0.0821228 | + | 0.996622i | \(0.526170\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6752.10 | 0.494863 | 0.247431 | − | 0.968905i | \(-0.420414\pi\) | ||||
0.247431 | + | 0.968905i | \(0.420414\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2988.29 | 0.217867 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −48331.4 | −3.50532 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18454.6 | −1.33150 | −0.665749 | − | 0.746175i | \(-0.731888\pi\) | ||||
−0.665749 | + | 0.746175i | \(0.731888\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1723.95 | 0.123739 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3366.49 | −0.240388 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3684.66 | −0.261755 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 34950.5 | 2.47013 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11807.7 | −0.830250 | −0.415125 | − | 0.909764i | \(-0.636262\pi\) | ||||
−0.415125 | + | 0.909764i | \(0.636262\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27047.6 | 1.89215 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3543.53 | −0.246635 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2300.54 | −0.159311 | −0.0796557 | − | 0.996822i | \(-0.525382\pi\) | ||||
−0.0796557 | + | 0.996822i | \(0.525382\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8581.80 | 0.591293 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4574.82 | 0.313626 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6654.41 | 0.453909 | 0.226955 | − | 0.973905i | \(-0.427123\pi\) | ||||
0.226955 | + | 0.973905i | \(0.427123\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10631.7 | −0.721588 | −0.360794 | − | 0.932646i | \(-0.617494\pi\) | ||||
−0.360794 | + | 0.932646i | \(0.617494\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7283.41 | −0.491880 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2483.60 | −0.166897 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14834.8 | −0.991971 | −0.495985 | − | 0.868331i | \(-0.665193\pi\) | ||||
−0.495985 | + | 0.868331i | \(0.665193\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 656.999 | 0.0437158 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4614.27 | −0.305521 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21769.1 | −1.43433 | −0.717167 | − | 0.696902i | \(-0.754561\pi\) | ||||
−0.717167 | + | 0.696902i | \(0.754561\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10049.5 | −0.658919 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11615.5 | 0.757899 | 0.378949 | − | 0.925417i | \(-0.376285\pi\) | ||||
0.378949 | + | 0.925417i | \(0.376285\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25928.4 | −1.68360 | −0.841800 | − | 0.539789i | \(-0.818504\pi\) | ||||
−0.841800 | + | 0.539789i | \(0.818504\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10403.5 | −0.672266 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8379.15 | 0.538850 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 35131.1 | 2.24839 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1750.69 | −0.111508 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12855.9 | 0.814943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1291.82 | 0.0815003 | 0.0407502 | − | 0.999169i | \(-0.487025\pi\) | ||||
0.0407502 | + | 0.999169i | \(0.487025\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4329.00 | −0.271820 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11241.7 | 0.702538 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3268.72 | 0.203315 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13329.6 | −0.825210 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5836.16 | −0.359617 | −0.179808 | − | 0.983702i | \(-0.557548\pi\) | ||||
−0.179808 | + | 0.983702i | \(0.557548\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1068.38 | 0.0655254 | 0.0327627 | − | 0.999463i | \(-0.489569\pi\) | ||||
0.0327627 | + | 0.999463i | \(0.489569\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1085.88 | −0.0662893 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14064.4 | 0.854607 | 0.427303 | − | 0.904108i | \(-0.359464\pi\) | ||||
0.427303 | + | 0.904108i | \(0.359464\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7494.11 | 0.453266 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1754.00 | 0.105599 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23428.7 | 1.40404 | 0.702018 | − | 0.712160i | \(-0.252283\pi\) | ||||
0.702018 | + | 0.712160i | \(0.252283\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −39544.3 | −2.35897 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15122.5 | −0.897997 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23122.9 | −1.36683 | −0.683414 | − | 0.730031i | \(-0.739506\pi\) | ||||
−0.683414 | + | 0.730031i | \(0.739506\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30074.8 | −1.76970 | −0.884851 | − | 0.465873i | \(-0.845740\pi\) | ||||
−0.884851 | + | 0.465873i | \(0.845740\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4838.11 | 0.283404 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 18832.2 | 1.09817 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12608.3 | 0.731925 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3073.62 | 0.177628 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 269.388 | 0.0154987 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27970.6 | −1.60206 | −0.801032 | − | 0.598621i | \(-0.795715\pi\) | ||||
−0.801032 | + | 0.598621i | \(0.795715\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18897.8 | 1.07760 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3911.49 | −0.222054 | −0.111027 | − | 0.993817i | \(-0.535414\pi\) | ||||
−0.111027 | + | 0.993817i | \(0.535414\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2162.54 | 0.122225 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1466.17 | 0.0825019 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14125.7 | 0.791367 | 0.395683 | − | 0.918387i | \(-0.370508\pi\) | ||||
0.395683 | + | 0.918387i | \(0.370508\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29572.6 | 1.64951 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4855.43 | 0.269645 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22345.3 | 1.23554 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20549.5 | −1.13132 | −0.565658 | − | 0.824640i | \(-0.691378\pi\) | ||||
−0.565658 | + | 0.824640i | \(0.691378\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1965.47 | 0.107737 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −49893.7 | −2.72313 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24083.8 | 1.30881 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1735.93 | −0.0939328 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24071.4 | 1.29695 | 0.648475 | − | 0.761236i | \(-0.275407\pi\) | ||||
0.648475 | + | 0.761236i | \(0.275407\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28211.5 | 1.51354 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1723.96 | −0.0920964 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12199.1 | 0.648930 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29125.6 | −1.54278 | −0.771392 | − | 0.636360i | \(-0.780439\pi\) | ||||
−0.771392 | + | 0.636360i | \(0.780439\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2368.75 | −0.124944 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 33660.5 | 1.76801 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15061.6 | 0.787791 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3913.55 | 0.203841 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34567.0 | 1.79295 | 0.896475 | − | 0.443094i | \(-0.146119\pi\) | ||||
0.896475 | + | 0.443094i | \(0.146119\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7307.36 | −0.377449 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −704.958 | −0.0362623 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22902.8 | −1.17323 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16450.2 | 0.839206 | 0.419603 | − | 0.907708i | \(-0.362169\pi\) | ||||
0.419603 | + | 0.907708i | \(0.362169\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13524.2 | −0.687100 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2602.33 | 0.131670 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21032.1 | −1.05981 | −0.529904 | − | 0.848058i | \(-0.677772\pi\) | ||||
−0.529904 | + | 0.848058i | \(0.677772\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1221.24 | 0.0612872 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3138.71 | −0.156874 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33830.2 | 1.68398 | 0.841991 | − | 0.539491i | \(-0.181383\pi\) | ||||
0.841991 | + | 0.539491i | \(0.181383\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10616.9 | 0.526345 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30148.6 | −1.48862 | −0.744311 | − | 0.667833i | \(-0.767222\pi\) | ||||
−0.744311 | + | 0.667833i | \(0.767222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14096.2 | −0.693217 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12276.0 | 0.601277 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1430.58 | −0.0697896 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25821.0 | 1.25462 | 0.627311 | − | 0.778769i | \(-0.284156\pi\) | ||||
0.627311 | + | 0.778769i | \(0.284156\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1550.90 | 0.0750568 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 36113.8 | 1.74081 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8504.19 | 0.408309 | 0.204155 | − | 0.978939i | \(-0.434555\pi\) | ||||
0.204155 | + | 0.978939i | \(0.434555\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2178.71 | −0.104193 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4597.99 | 0.219024 | 0.109512 | − | 0.993985i | \(-0.465071\pi\) | ||||
0.109512 | + | 0.993985i | \(0.465071\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6609.93 | 0.313624 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −31293.6 | −1.47899 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −45447.4 | −2.13952 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38871.6 | 1.82282 | 0.911408 | − | 0.411505i | \(-0.134997\pi\) | ||||
0.911408 | + | 0.411505i | \(0.134997\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3056.39 | −0.142767 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21974.1 | 1.02245 | 0.511224 | − | 0.859447i | \(-0.329192\pi\) | ||||
0.511224 | + | 0.859447i | \(0.329192\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −61144.0 | −2.83401 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1829.47 | 0.0844685 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 52850.2 | 2.43075 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5744.24 | −0.263182 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4929.90 | −0.225007 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −37640.8 | −1.71141 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14241.7 | 0.645061 | 0.322531 | − | 0.946559i | \(-0.395466\pi\) | ||||
0.322531 | + | 0.946559i | \(0.395466\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6902.33 | −0.311444 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13337.0 | −0.599507 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1633.68 | −0.0731574 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8348.53 | 0.372443 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39470.7 | 1.75424 | 0.877118 | − | 0.480276i | \(-0.159463\pi\) | ||||
0.877118 | + | 0.480276i | \(0.159463\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4131.48 | 0.182930 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −30554.7 | −1.34781 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6516.88 | −0.286396 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 23436.4 | 1.02612 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1056.49 | −0.0460846 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11073.5 | 0.481238 | 0.240619 | − | 0.970620i | \(-0.422650\pi\) | ||||
0.240619 | + | 0.970620i | \(0.422650\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38855.7 | 1.68238 | 0.841189 | − | 0.540741i | \(-0.181856\pi\) | ||||
0.841189 | + | 0.540741i | \(0.181856\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 231.885 | 0.0100032 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −47336.2 | −2.03450 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5710.64 | 0.244541 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11919.4 | −0.508545 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9523.67 | −0.404846 | −0.202423 | − | 0.979298i | \(-0.564882\pi\) | ||||
−0.202423 | + | 0.979298i | \(0.564882\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2542.13 | 0.107671 | 0.0538355 | − | 0.998550i | \(-0.482855\pi\) | ||||
0.0538355 | + | 0.998550i | \(0.482855\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3957.61 | 0.167014 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8794.30 | −0.369779 | −0.184890 | − | 0.982759i | \(-0.559193\pi\) | ||||
−0.184890 | + | 0.982759i | \(0.559193\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18268.3 | −0.765362 | −0.382681 | − | 0.923881i | \(-0.624999\pi\) | ||||
−0.382681 | + | 0.923881i | \(0.624999\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6801.36 | −0.283919 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2926.72 | −0.121734 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 46048.5 | 1.90847 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13161.4 | −0.543519 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6216.04 | −0.255783 | −0.127891 | − | 0.991788i | \(-0.540821\pi\) | ||||
−0.127891 | + | 0.991788i | \(0.540821\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18414.3 | −0.755026 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8352.02 | −0.341232 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −46244.8 | −1.88269 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 847.000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6948.14 | 0.280871 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35108.9 | 1.41424 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3081.20 | 0.123679 | 0.0618396 | − | 0.998086i | \(-0.480303\pi\) | ||||
0.0618396 | + | 0.998086i | \(0.480303\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −68671.8 | −2.74681 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2992.90 | 0.119295 | 0.0596473 | − | 0.998220i | \(-0.481002\pi\) | ||||
0.0596473 | + | 0.998220i | \(0.481002\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1740.43 | −0.0691300 | −0.0345650 | − | 0.999402i | \(-0.511005\pi\) | ||||
−0.0345650 | + | 0.999402i | \(0.511005\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3427.26 | 0.135657 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35296.5 | 1.39225 | 0.696123 | − | 0.717923i | \(-0.254907\pi\) | ||||
0.696123 | + | 0.717923i | \(0.254907\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 51294.9 | 2.01628 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1633.73 | 0.0639956 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1020.79 | −0.0398479 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19034.5 | 0.740480 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7885.73 | −0.305718 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24612.2 | −0.950908 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1103.09 | 0.0424727 | 0.0212364 | − | 0.999774i | \(-0.493240\pi\) | ||||
0.0212364 | + | 0.999774i | \(0.493240\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10052.2 | −0.385725 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37691.0 | −1.44136 | −0.720682 | − | 0.693266i | \(-0.756171\pi\) | ||||
−0.720682 | + | 0.693266i | \(0.756171\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23031.4 | −0.877769 | −0.438884 | − | 0.898544i | \(-0.644626\pi\) | ||||
−0.438884 | + | 0.898544i | \(0.644626\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16979.8 | −0.644937 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −47839.7 | −1.81094 | −0.905468 | − | 0.424414i | \(-0.860480\pi\) | ||||
−0.905468 | + | 0.424414i | \(0.860480\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3833.83 | −0.144637 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6729.21 | −0.253016 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9066.26 | 0.339744 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5557.60 | 0.207564 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13212.6 | 0.491813 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15950.7 | 0.591752 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20007.4 | −0.739780 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 370.327 | 0.0136475 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30389.9 | −1.11624 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35960.6 | −1.31649 | −0.658243 | − | 0.752805i | \(-0.728700\pi\) | ||||
−0.658243 | + | 0.752805i | \(0.728700\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −44484.1 | −1.62315 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25190.4 | 0.916132 | 0.458066 | − | 0.888918i | \(-0.348542\pi\) | ||||
0.458066 | + | 0.888918i | \(0.348542\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5290.20 | 0.191764 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −610.367 | −0.0220526 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13486.1 | 0.485660 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42686.9 | 1.53222 | 0.766111 | − | 0.642709i | \(-0.222189\pi\) | ||||
0.766111 | + | 0.642709i | \(0.222189\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −783.417 | −0.0280287 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 34835.5 | 1.24228 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −63774.9 | −2.26693 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26646.4 | 0.944102 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29206.6 | 1.03147 | 0.515736 | − | 0.856748i | \(-0.327519\pi\) | ||||
0.515736 | + | 0.856748i | \(0.327519\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6422.48 | −0.226088 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9630.19 | 0.337919 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13485.7 | −0.471689 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27326.2 | −0.952730 | −0.476365 | − | 0.879248i | \(-0.658046\pi\) | ||||
−0.476365 | + | 0.879248i | \(0.658046\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8014.39 | −0.278530 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6802.35 | 0.235654 | 0.117827 | − | 0.993034i | \(-0.462407\pi\) | ||||
0.117827 | + | 0.993034i | \(0.462407\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 65771.5 | 2.27128 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9163.77 | −0.315447 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1090.60 | −0.0374231 | −0.0187116 | − | 0.999825i | \(-0.505956\pi\) | ||||
−0.0187116 | + | 0.999825i | \(0.505956\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39521.1 | 1.35185 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12458.2 | 0.424800 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48392.3 | 1.64489 | 0.822446 | − | 0.568843i | \(-0.192609\pi\) | ||||
0.822446 | + | 0.568843i | \(0.192609\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 50513.7 | 1.71161 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1032.43 | −0.0348732 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10085.4 | −0.339598 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12792.8 | 0.429418 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5216.65 | 0.174563 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29141.5 | 0.972123 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27678.0 | −0.920438 | −0.460219 | − | 0.887805i | \(-0.652229\pi\) | ||||
−0.460219 | + | 0.887805i | \(0.652229\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9506.07 | −0.315149 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17642.8 | 0.583096 | 0.291548 | − | 0.956556i | \(-0.405830\pi\) | ||||
0.291548 | + | 0.956556i | \(0.405830\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17015.6 | 0.560633 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −24000.6 | −0.788343 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4539.48 | −0.148650 | −0.0743249 | − | 0.997234i | \(-0.523680\pi\) | ||||
−0.0743249 | + | 0.997234i | \(0.523680\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13167.2 | −0.429853 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24103.2 | −0.784460 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7250.49 | −0.235254 | −0.117627 | − | 0.993058i | \(-0.537529\pi\) | ||||
−0.117627 | + | 0.993058i | \(0.537529\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −59899.4 | −1.93762 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 587.935 | 0.0189607 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7106.83 | 0.228497 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −851.834 | −0.0273052 | −0.0136526 | − | 0.999907i | \(-0.504346\pi\) | ||||
−0.0136526 | + | 0.999907i | \(0.504346\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11687.6 | −0.373510 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 77332.1 | 2.46391 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52462.3 | 1.66650 | 0.833249 | − | 0.552897i | \(-0.186478\pi\) | ||||
0.833249 | + | 0.552897i | \(0.186478\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13727.7 | −0.434761 |
(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 | 1232.4.a.v.1.2 | 4 | ||
4.3 | odd | 2 | 308.4.a.d.1.3 | ✓ | 4 | ||
28.27 | even | 2 | 2156.4.a.f.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
308.4.a.d.1.3 | ✓ | 4 | 4.3 | odd | 2 | ||
1232.4.a.v.1.2 | 4 | 1.1 | even | 1 | trivial | ||
2156.4.a.f.1.2 | 4 | 28.27 | even | 2 |