Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,4,Mod(1,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, 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("1200.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.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: | \(70.8022920069\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.1 |
$q$-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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.2094 | 1.19919 | 0.599597 | − | 0.800302i | \(-0.295328\pi\) | ||||
0.599597 | + | 0.800302i | \(0.295328\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.79063 | 0.0490813 | 0.0245407 | − | 0.999699i | \(-0.492188\pi\) | ||||
0.0245407 | + | 0.999699i | \(0.492188\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −58.2094 | −1.24188 | −0.620938 | − | 0.783860i | \(-0.713248\pi\) | ||||
−0.620938 | + | 0.783860i | \(0.713248\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −18.9844 | −0.270846 | −0.135423 | − | 0.990788i | \(-0.543239\pi\) | ||||
−0.135423 | + | 0.990788i | \(0.543239\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −104.837 | −1.26586 | −0.632931 | − | 0.774208i | \(-0.718148\pi\) | ||||
−0.632931 | + | 0.774208i | \(0.718148\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 66.6281 | 0.692355 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −49.6125 | −0.449779 | −0.224890 | − | 0.974384i | \(-0.572202\pi\) | ||||
−0.224890 | + | 0.974384i | \(0.572202\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −293.466 | −1.87914 | −0.939572 | − | 0.342350i | \(-0.888777\pi\) | ||||
−0.939572 | + | 0.342350i | \(0.888777\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −64.4187 | −0.373224 | −0.186612 | − | 0.982434i | \(-0.559751\pi\) | ||||
−0.186612 | + | 0.982434i | \(0.559751\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.37188 | 0.0283371 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 19.8844 | 0.0883505 | 0.0441752 | − | 0.999024i | \(-0.485934\pi\) | ||||
0.0441752 | + | 0.999024i | \(0.485934\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −174.628 | −0.716997 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −165.581 | −0.630718 | −0.315359 | − | 0.948972i | \(-0.602125\pi\) | ||||
−0.315359 | + | 0.948972i | \(0.602125\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −247.350 | −0.877221 | −0.438611 | − | 0.898677i | \(-0.644529\pi\) | ||||
−0.438611 | + | 0.898677i | \(0.644529\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 384.544 | 1.19344 | 0.596718 | − | 0.802451i | \(-0.296471\pi\) | ||||
0.596718 | + | 0.802451i | \(0.296471\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 150.256 | 0.438065 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −56.9531 | −0.156373 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −463.528 | −1.20133 | −0.600665 | − | 0.799501i | \(-0.705097\pi\) | ||||
−0.600665 | + | 0.799501i | \(0.705097\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −314.512 | −0.730846 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 73.7906 | 0.162826 | 0.0814129 | − | 0.996680i | \(-0.474057\pi\) | ||||
0.0814129 | + | 0.996680i | \(0.474057\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −137.350 | −0.288293 | −0.144146 | − | 0.989556i | \(-0.546044\pi\) | ||||
−0.144146 | + | 0.989556i | \(0.546044\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 199.884 | 0.399731 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 173.906 | 0.317105 | 0.158552 | − | 0.987351i | \(-0.449317\pi\) | ||||
0.158552 | + | 0.987351i | \(0.449317\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −148.837 | −0.259680 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 594.281 | 0.993355 | 0.496677 | − | 0.867935i | \(-0.334553\pi\) | ||||
0.496677 | + | 0.867935i | \(0.334553\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −320.231 | −0.513428 | −0.256714 | − | 0.966487i | \(-0.582640\pi\) | ||||
−0.256714 | + | 0.966487i | \(0.582640\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 39.7687 | 0.0588580 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 770.469 | 1.09727 | 0.548636 | − | 0.836061i | \(-0.315147\pi\) | ||||
0.548636 | + | 0.836061i | \(0.315147\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 173.925 | 0.230009 | 0.115004 | − | 0.993365i | \(-0.463312\pi\) | ||||
0.115004 | + | 0.993365i | \(0.463312\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −880.397 | −1.08492 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1019.02 | 1.21367 | 0.606834 | − | 0.794829i | \(-0.292439\pi\) | ||||
0.606834 | + | 0.794829i | \(0.292439\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1292.79 | −1.48925 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −193.256 | −0.215481 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −384.375 | −0.402344 | −0.201172 | − | 0.979556i | \(-0.564475\pi\) | ||||
−0.201172 | + | 0.979556i | \(0.564475\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.1156 | 0.0163604 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 34.4906 | 0.0339796 | 0.0169898 | − | 0.999856i | \(-0.494592\pi\) | ||||
0.0169898 | + | 0.999856i | \(0.494592\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1756.30 | −1.68013 | −0.840066 | − | 0.542484i | \(-0.817484\pi\) | ||||
−0.840066 | + | 0.542484i | \(0.817484\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1361.74 | −1.23032 | −0.615159 | − | 0.788403i | \(-0.710908\pi\) | ||||
−0.615159 | + | 0.788403i | \(0.710908\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 321.119 | 0.282180 | 0.141090 | − | 0.989997i | \(-0.454939\pi\) | ||||
0.141090 | + | 0.989997i | \(0.454939\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 59.6531 | 0.0510092 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1582.25 | 1.31721 | 0.658607 | − | 0.752487i | \(-0.271146\pi\) | ||||
0.658607 | + | 0.752487i | \(0.271146\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −523.884 | −0.413958 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −421.631 | −0.324797 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1327.79 | −0.997591 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −496.744 | −0.364145 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1197.14 | −0.836449 | −0.418225 | − | 0.908344i | \(-0.637348\pi\) | ||||
−0.418225 | + | 0.908344i | \(0.637348\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −742.050 | −0.506464 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 321.647 | 0.214522 | 0.107261 | − | 0.994231i | \(-0.465792\pi\) | ||||
0.107261 | + | 0.994231i | \(0.465792\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2328.37 | −1.51801 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −354.291 | −0.220942 | −0.110471 | − | 0.993879i | \(-0.535236\pi\) | ||||
−0.110471 | + | 0.993879i | \(0.535236\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −77.2562 | −0.0471424 | −0.0235712 | − | 0.999722i | \(-0.507504\pi\) | ||||
−0.0235712 | + | 0.999722i | \(0.507504\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1153.63 | 0.689030 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −104.231 | −0.0609529 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 450.769 | 0.252917 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1705.38 | −0.937651 | −0.468826 | − | 0.883291i | \(-0.655323\pi\) | ||||
−0.468826 | + | 0.883291i | \(0.655323\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −758.281 | −0.408663 | −0.204331 | − | 0.978902i | \(-0.565502\pi\) | ||||
−0.204331 | + | 0.978902i | \(0.565502\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −170.859 | −0.0902821 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1769.05 | 0.899273 | 0.449636 | − | 0.893212i | \(-0.351554\pi\) | ||||
0.449636 | + | 0.893212i | \(0.351554\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1390.58 | −0.693588 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1101.86 | −0.539372 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −881.719 | −0.423690 | −0.211845 | − | 0.977303i | \(-0.567947\pi\) | ||||
−0.211845 | + | 0.977303i | \(0.567947\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −216.900 | −0.100504 | −0.0502522 | − | 0.998737i | \(-0.516003\pi\) | ||||
−0.0502522 | + | 0.998737i | \(0.516003\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1191.33 | 0.542254 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −943.537 | −0.421954 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4125.91 | −1.81322 | −0.906610 | − | 0.421970i | \(-0.861339\pi\) | ||||
−0.906610 | + | 0.421970i | \(0.861339\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 221.372 | 0.0940075 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3213.14 | 1.34168 | 0.670842 | − | 0.741600i | \(-0.265933\pi\) | ||||
0.670842 | + | 0.741600i | \(0.265933\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3394.42 | 1.39395 | 0.696976 | − | 0.717095i | \(-0.254529\pi\) | ||||
0.696976 | + | 0.717095i | \(0.254529\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −412.050 | −0.166446 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −33.9939 | −0.0132935 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 599.653 | 0.230785 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3467.49 | 1.31361 | 0.656804 | − | 0.754062i | \(-0.271908\pi\) | ||||
0.656804 | + | 0.754062i | \(0.271908\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1792.14 | −0.668401 | −0.334200 | − | 0.942502i | \(-0.608466\pi\) | ||||
−0.334200 | + | 0.942502i | \(0.608466\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1678.19 | −0.606935 | −0.303467 | − | 0.952842i | \(-0.598144\pi\) | ||||
−0.303467 | + | 0.952842i | \(0.598144\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3108.23 | −1.10722 | −0.553610 | − | 0.832776i | \(-0.686750\pi\) | ||||
−0.553610 | + | 0.832776i | \(0.686750\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 521.719 | 0.183081 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6517.69 | −2.25346 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −446.512 | −0.149926 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −187.725 | −0.0621301 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4473.27 | 1.45949 | 0.729745 | − | 0.683719i | \(-0.239639\pi\) | ||||
0.729745 | + | 0.683719i | \(0.239639\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1782.84 | 0.573514 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1430.70 | −0.447568 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −960.694 | −0.296428 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1105.07 | 0.336357 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1753.42 | −0.526535 | −0.263268 | − | 0.964723i | \(-0.584800\pi\) | ||||
−0.263268 | + | 0.964723i | \(0.584800\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −936.900 | −0.273939 | −0.136970 | − | 0.990575i | \(-0.543736\pi\) | ||||
−0.136970 | + | 0.990575i | \(0.543736\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2582.06 | −0.745096 | −0.372548 | − | 0.928013i | \(-0.621516\pi\) | ||||
−0.372548 | + | 0.928013i | \(0.621516\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 119.306 | 0.0339817 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2295.01 | −0.645284 | −0.322642 | − | 0.946521i | \(-0.604571\pi\) | ||||
−0.322642 | + | 0.946521i | \(0.604571\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2311.41 | 0.633510 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2294.01 | 0.620866 | 0.310433 | − | 0.950595i | \(-0.399526\pi\) | ||||
0.310433 | + | 0.950595i | \(0.399526\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 382.287 | 0.102180 | 0.0510898 | − | 0.998694i | \(-0.483731\pi\) | ||||
0.0510898 | + | 0.998694i | \(0.483731\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6102.52 | 1.57204 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 521.775 | 0.132796 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2259.98 | 0.568322 | 0.284161 | − | 0.958777i | \(-0.408285\pi\) | ||||
0.284161 | + | 0.958777i | \(0.408285\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −88.8375 | −0.0220758 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 92.7843 | 0.0225203 | 0.0112602 | − | 0.999937i | \(-0.496416\pi\) | ||||
0.0112602 | + | 0.999937i | \(0.496416\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 441.619 | 0.105949 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2641.19 | −0.626382 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −568.312 | −0.133246 | −0.0666229 | − | 0.997778i | \(-0.521222\pi\) | ||||
−0.0666229 | + | 0.997778i | \(0.521222\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3057.07 | 0.700711 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7582.41 | 1.71862 | 0.859309 | − | 0.511458i | \(-0.170894\pi\) | ||||
0.859309 | + | 0.511458i | \(0.170894\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7943.69 | −1.78061 | −0.890304 | − | 0.455366i | \(-0.849508\pi\) | ||||
−0.890304 | + | 0.455366i | \(0.849508\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3878.38 | −0.859818 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6823.00 | −1.47998 | −0.739990 | − | 0.672618i | \(-0.765170\pi\) | ||||
−0.739990 | + | 0.672618i | \(0.765170\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −579.769 | −0.124408 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3315.86 | 0.703942 | 0.351971 | − | 0.936011i | \(-0.385512\pi\) | ||||
0.351971 | + | 0.936011i | \(0.385512\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6602.76 | 1.38690 | 0.693451 | − | 0.720504i | \(-0.256090\pi\) | ||||
0.693451 | + | 0.720504i | \(0.256090\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3677.46 | −0.756353 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4552.59 | −0.926642 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1153.12 | −0.232293 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5814.14 | −1.15927 | −0.579634 | − | 0.814877i | \(-0.696805\pi\) | ||||
−0.579634 | + | 0.814877i | \(0.696805\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 48.3469 | 0.00944570 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2887.91 | 0.558570 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5493.49 | −1.05196 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 103.472 | 0.0196181 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8124.86 | −1.51046 | −0.755229 | − | 0.655462i | \(-0.772474\pi\) | ||||
−0.755229 | + | 0.655462i | \(0.772474\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5268.91 | −0.970025 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7336.26 | −1.33762 | −0.668812 | − | 0.743432i | \(-0.733197\pi\) | ||||
−0.668812 | + | 0.743432i | \(0.733197\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2202.66 | 0.397768 | 0.198884 | − | 0.980023i | \(-0.436268\pi\) | ||||
0.198884 | + | 0.980023i | \(0.436268\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10008.9 | −1.77336 | −0.886679 | − | 0.462386i | \(-0.846993\pi\) | ||||
−0.886679 | + | 0.462386i | \(0.846993\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −525.488 | −0.0922309 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4085.21 | −0.710325 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1990.27 | 0.342854 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 963.356 | 0.162917 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8540.47 | 1.43116 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8695.94 | 1.44402 | 0.722012 | − | 0.691881i | \(-0.243218\pi\) | ||||
0.722012 | + | 0.691881i | \(0.243218\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 178.959 | 0.0294502 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7400.61 | 1.19625 | 0.598126 | − | 0.801402i | \(-0.295912\pi\) | ||||
0.598126 | + | 0.801402i | \(0.295912\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4746.74 | 0.760494 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −115.350 | −0.0183183 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4280.72 | −0.673869 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7841.44 | 1.21311 | 0.606557 | − | 0.795040i | \(-0.292550\pi\) | ||||
0.606557 | + | 0.795040i | \(0.292550\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4961.26 | −0.760946 | −0.380473 | − | 0.924792i | \(-0.624239\pi\) | ||||
−0.380473 | + | 0.924792i | \(0.624239\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1571.65 | −0.238999 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12163.0 | 1.83392 | 0.916959 | − | 0.398981i | \(-0.130636\pi\) | ||||
0.916959 | + | 0.398981i | \(0.130636\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1264.89 | −0.187522 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5193.79 | −0.763559 | −0.381779 | − | 0.924253i | \(-0.624689\pi\) | ||||
−0.381779 | + | 0.924253i | \(0.624689\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4131.90 | 0.602406 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3983.38 | −0.575959 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6086.09 | −0.865644 | −0.432822 | − | 0.901479i | \(-0.642482\pi\) | ||||
−0.432822 | + | 0.901479i | \(0.642482\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1490.23 | −0.210239 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10294.7 | −1.44063 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10581.9 | 1.46893 | 0.734466 | − | 0.678646i | \(-0.237433\pi\) | ||||
0.734466 | + | 0.678646i | \(0.237433\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17082.4 | 2.33366 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11655.2 | −1.57964 | −0.789822 | − | 0.613336i | \(-0.789827\pi\) | ||||
−0.789822 | + | 0.613336i | \(0.789827\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3591.42 | −0.482924 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6364.97 | 0.849177 | 0.424588 | − | 0.905387i | \(-0.360419\pi\) | ||||
0.424588 | + | 0.905387i | \(0.360419\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2226.15 | −0.292407 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6134.33 | 0.799545 | 0.399773 | − | 0.916614i | \(-0.369089\pi\) | ||||
0.399773 | + | 0.916614i | \(0.369089\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 941.862 | 0.121821 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 964.941 | 0.123855 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9746.46 | −1.23214 | −0.616072 | − | 0.787690i | \(-0.711277\pi\) | ||||
−0.616072 | + | 0.787690i | \(0.711277\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6985.12 | −0.876425 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1306.44 | −0.162695 | −0.0813474 | − | 0.996686i | \(-0.525922\pi\) | ||||
−0.0813474 | + | 0.996686i | \(0.525922\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3749.77 | 0.463498 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 35.6055 | 0.00433636 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3876.93 | −0.468709 | −0.234354 | − | 0.972151i | \(-0.575298\pi\) | ||||
−0.234354 | + | 0.972151i | \(0.575298\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1062.87 | −0.127561 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1638.84 | 0.195260 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −231.769 | −0.0272177 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16022.5 | 1.86814 | 0.934071 | − | 0.357088i | \(-0.116230\pi\) | ||||
0.934071 | + | 0.357088i | \(0.116230\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8119.73 | −0.939980 | −0.469990 | − | 0.882672i | \(-0.655742\pi\) | ||||
−0.469990 | + | 0.882672i | \(0.655742\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3460.89 | 0.397812 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3050.46 | −0.345719 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −312.694 | −0.0351911 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5713.99 | 0.638592 | 0.319296 | − | 0.947655i | \(-0.396554\pi\) | ||||
0.319296 | + | 0.947655i | \(0.396554\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6251.34 | −0.693811 | −0.346906 | − | 0.937900i | \(-0.612768\pi\) | ||||
−0.346906 | + | 0.937900i | \(0.612768\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5201.25 | 0.569358 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4230.97 | 0.459984 | 0.229992 | − | 0.973192i | \(-0.426130\pi\) | ||||
0.229992 | + | 0.973192i | \(0.426130\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1352.31 | 0.146022 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6314.29 | 0.677203 | 0.338601 | − | 0.940930i | \(-0.390046\pi\) | ||||
0.338601 | + | 0.940930i | \(0.390046\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5116.13 | −0.541353 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9349.71 | −0.982717 | −0.491358 | − | 0.870957i | \(-0.663499\pi\) | ||||
−0.491358 | + | 0.870957i | \(0.663499\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −296.494 | −0.0309565 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2274.84 | −0.235941 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9547.46 | 0.977268 | 0.488634 | − | 0.872489i | \(-0.337495\pi\) | ||||
0.488634 | + | 0.872489i | \(0.337495\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −512.578 | −0.0521244 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6237.23 | 0.630145 | 0.315073 | − | 0.949068i | \(-0.397971\pi\) | ||||
0.315073 | + | 0.949068i | \(0.397971\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6469.98 | 0.649428 | 0.324714 | − | 0.945812i | \(-0.394732\pi\) | ||||
0.324714 | + | 0.945812i | \(0.394732\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7206.64 | 0.714097 | 0.357049 | − | 0.934086i | \(-0.383783\pi\) | ||||
0.357049 | + | 0.934086i | \(0.383783\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3862.35 | 0.380270 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5307.16 | 0.519195 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −442.912 | −0.0430552 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4171.75 | −0.400443 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10851.8 | 1.03514 | 0.517571 | − | 0.855640i | \(-0.326836\pi\) | ||||
0.517571 | + | 0.855640i | \(0.326836\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1157.46 | −0.109720 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3305.59 | −0.311407 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12757.1 | 1.18702 | 0.593510 | − | 0.804827i | \(-0.297742\pi\) | ||||
0.593510 | + | 0.804827i | \(0.297742\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2645.16 | −0.244618 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7016.52 | 0.644911 | 0.322455 | − | 0.946585i | \(-0.395492\pi\) | ||||
0.322455 | + | 0.946585i | \(0.395492\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5571.26 | 0.508960 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13198.6 | 1.19122 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11372.3 | −1.02023 | −0.510113 | − | 0.860107i | \(-0.670396\pi\) | ||||
−0.510113 | + | 0.860107i | \(0.670396\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −650.700 | −0.0580262 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5587.37 | −0.495285 | −0.247643 | − | 0.968851i | \(-0.579656\pi\) | ||||
−0.247643 | + | 0.968851i | \(0.579656\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3573.99 | 0.313070 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16256.7 | 1.41565 | 0.707825 | − | 0.706388i | \(-0.249676\pi\) | ||||
0.707825 | + | 0.706388i | \(0.249676\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7112.14 | −0.615699 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2830.61 | −0.243615 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 688.574 | 0.0585754 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12377.7 | −1.04686 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19748.4 | 1.66064 | 0.830320 | − | 0.557286i | \(-0.188157\pi\) | ||||
0.830320 | + | 0.557286i | \(0.188157\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7843.44 | −0.655774 | −0.327887 | − | 0.944717i | \(-0.606337\pi\) | ||||
−0.327887 | + | 0.944717i | \(0.606337\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1222.95 | 0.101086 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9705.60 | −0.797699 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 664.116 | 0.0542753 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9638.38 | 0.783273 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9639.42 | 0.774622 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 269.053 | 0.0215008 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7383.29 | 0.586751 | 0.293376 | − | 0.955997i | \(-0.405221\pi\) | ||||
0.293376 | + | 0.955997i | \(0.405221\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10183.3 | 0.804798 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3354.90 | −0.262240 | −0.131120 | − | 0.991367i | \(-0.541857\pi\) | ||||
−0.131120 | + | 0.991367i | \(0.541857\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1236.15 | −0.0960976 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30766.2 | 2.37874 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17111.6 | 1.31584 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20771.8 | −1.58012 | −0.790061 | − | 0.613028i | \(-0.789951\pi\) | ||||
−0.790061 | + | 0.613028i | \(0.789951\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14398.1 | 1.08940 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −101.982 | −0.00767500 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7194.86 | 0.538592 | 0.269296 | − | 0.963057i | \(-0.413209\pi\) | ||||
0.269296 | + | 0.963057i | \(0.413209\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1798.96 | 0.133244 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11549.5 | 0.850931 | 0.425466 | − | 0.904975i | \(-0.360110\pi\) | ||||
0.425466 | + | 0.904975i | \(0.360110\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1482.54 | −0.108655 | −0.0543277 | − | 0.998523i | \(-0.517302\pi\) | ||||
−0.0543277 | + | 0.998523i | \(0.517302\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10402.5 | 0.758412 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15264.0 | 1.10130 | 0.550649 | − | 0.834737i | \(-0.314380\pi\) | ||||
0.550649 | + | 0.834737i | \(0.314380\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5376.43 | −0.385901 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3862.76 | 0.275825 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −830.006 | −0.0589628 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1736.89 | 0.122128 | 0.0610639 | − | 0.998134i | \(-0.480551\pi\) | ||||
0.0610639 | + | 0.998134i | \(0.480551\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6753.50 | 0.472450 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5034.57 | −0.350414 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11764.8 | 0.814707 | 0.407353 | − | 0.913271i | \(-0.366452\pi\) | ||||
0.407353 | + | 0.913271i | \(0.366452\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9324.69 | −0.639253 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9451.99 | 0.644737 | 0.322369 | − | 0.946614i | \(-0.395521\pi\) | ||||
0.322369 | + | 0.946614i | \(0.395521\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3131.93 | −0.212569 | −0.106285 | − | 0.994336i | \(-0.533895\pi\) | ||||
−0.106285 | + | 0.994336i | \(0.533895\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1565.16 | 0.105702 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22700.8 | 1.51795 | 0.758975 | − | 0.651120i | \(-0.225700\pi\) | ||||
0.758975 | + | 0.651120i | \(0.225700\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −19553.1 | −1.30103 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22384.0 | −1.48210 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28911.6 | −1.90494 | −0.952471 | − | 0.304629i | \(-0.901468\pi\) | ||||
−0.952471 | + | 0.304629i | \(0.901468\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5566.87 | 0.363231 | 0.181616 | − | 0.983370i | \(-0.441867\pi\) | ||||
0.181616 | + | 0.983370i | \(0.441867\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4150.32 | −0.269492 | −0.134746 | − | 0.990880i | \(-0.543022\pi\) | ||||
−0.134746 | + | 0.990880i | \(0.543022\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1339.54 | −0.0865600 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22631.9 | 1.45542 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −563.175 | −0.0358709 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −377.492 | −0.0239294 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4090.09 | 0.258041 | 0.129021 | − | 0.991642i | \(-0.458817\pi\) | ||||
0.129021 | + | 0.991642i | \(0.458817\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13419.8 | 0.842637 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8746.32 | −0.544022 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5348.53 | 0.331118 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3909.35 | 0.240890 | 0.120445 | − | 0.992720i | \(-0.461568\pi\) | ||||
0.120445 | + | 0.992720i | \(0.461568\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30539.5 | 1.87303 | 0.936516 | − | 0.350624i | \(-0.114031\pi\) | ||||
0.936516 | + | 0.350624i | \(0.114031\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12707.7 | −0.772167 | −0.386083 | − | 0.922464i | \(-0.626172\pi\) | ||||
−0.386083 | + | 0.922464i | \(0.626172\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 132.132 | 0.00799170 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4292.10 | −0.258403 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12777.6 | −0.765737 | −0.382869 | − | 0.923803i | \(-0.625064\pi\) | ||||
−0.382869 | + | 0.923803i | \(0.625064\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2882.08 | −0.171143 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23563.5 | −1.39287 | −0.696435 | − | 0.717620i | \(-0.745232\pi\) | ||||
−0.696435 | + | 0.717620i | \(0.745232\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4361.31 | −0.256634 | −0.128317 | − | 0.991733i | \(-0.540958\pi\) | ||||
−0.128317 | + | 0.991733i | \(0.540958\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3315.21 | 0.194196 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14559.6 | 0.845200 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5260.25 | −0.303995 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −245.943 | −0.0141498 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8203.52 | 0.469870 | 0.234935 | − | 0.972011i | \(-0.424512\pi\) | ||||
0.234935 | + | 0.972011i | \(0.424512\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28057.1 | −1.59279 | −0.796397 | − | 0.604774i | \(-0.793263\pi\) | ||||
−0.796397 | + | 0.604774i | \(0.793263\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8536.73 | −0.482488 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2810.70 | −0.158159 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3344.62 | −0.187377 | −0.0936885 | − | 0.995602i | \(-0.529866\pi\) | ||||
−0.0936885 | + | 0.995602i | \(0.529866\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7746.17 | −0.430182 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 26981.7 | 1.49190 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12964.8 | −0.713757 | −0.356879 | − | 0.934151i | \(-0.616159\pi\) | ||||
−0.356879 | + | 0.934151i | \(0.616159\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 357.918 | 0.0196193 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3143.46 | 0.170828 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6885.03 | −0.372555 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16162.1 | −0.870806 | −0.435403 | − | 0.900236i | \(-0.643394\pi\) | ||||
−0.435403 | + | 0.900236i | \(0.643394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2084.63 | −0.111839 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 766.014 | 0.0407481 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14244.4 | −0.754529 | −0.377265 | − | 0.926105i | \(-0.623135\pi\) | ||||
−0.377265 | + | 0.926105i | \(0.623135\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6934.22 | 0.365757 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3195.97 | 0.167868 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6882.02 | 0.358457 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27638.5 | 1.43358 | 0.716790 | − | 0.697289i | \(-0.245611\pi\) | ||||
0.716790 | + | 0.697289i | \(0.245611\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −39006.4 | −2.01480 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1146.86 | 0.0589934 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2525.52 | −0.128840 | −0.0644199 | − | 0.997923i | \(-0.520520\pi\) | ||||
−0.0644199 | + | 0.997923i | \(0.520520\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4695.79 | 0.237592 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8400.27 | 0.423289 | 0.211645 | − | 0.977347i | \(-0.432118\pi\) | ||||
0.211645 | + | 0.977347i | \(0.432118\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 311.401 | 0.0155639 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19689.1 | 0.980074 | 0.490037 | − | 0.871702i | \(-0.336983\pi\) | ||||
0.490037 | + | 0.871702i | \(0.336983\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18307.6 | 0.907619 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22526.6 | −1.11227 | −0.556137 | − | 0.831091i | \(-0.687717\pi\) | ||||
−0.556137 | + | 0.831091i | \(0.687717\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1565.32 | 0.0766696 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −30243.3 | −1.47539 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34691.1 | −1.68562 | −0.842808 | − | 0.538215i | \(-0.819099\pi\) | ||||
−0.842808 | + | 0.538215i | \(0.819099\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6779.95 | 0.328121 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6619.98 | −0.317843 | −0.158922 | − | 0.987291i | \(-0.550802\pi\) | ||||
−0.158922 | + | 0.987291i | \(0.550802\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −266.512 | −0.0127454 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29368.7 | −1.39897 | −0.699483 | − | 0.714649i | \(-0.746586\pi\) | ||||
−0.699483 | + | 0.714649i | \(0.746586\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7131.84 | 0.338388 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4295.31 | −0.202209 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32677.4 | 1.53235 | 0.766174 | − | 0.642633i | \(-0.222158\pi\) | ||||
0.766174 | + | 0.642633i | \(0.222158\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 278.353 | 0.0130021 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28047.5 | 1.30504 | 0.652522 | − | 0.757770i | \(-0.273711\pi\) | ||||
0.652522 | + | 0.757770i | \(0.273711\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1324.86 | 0.0611699 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17359.1 | 0.798402 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1064.14 | 0.0487552 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7923.57 | −0.361642 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22172.1 | −1.00426 | −0.502128 | − | 0.864793i | \(-0.667449\pi\) | ||||
−0.502128 | + | 0.864793i | \(0.667449\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1704.94 | −0.0769295 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35140.7 | 1.57960 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7995.06 | 0.358024 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24170.3 | 1.07422 | 0.537112 | − | 0.843511i | \(-0.319515\pi\) | ||||
0.537112 | + | 0.843511i | \(0.319515\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7300.32 | −0.323238 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9171.22 | 0.404556 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −573.415 | −0.0251997 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22747.2 | 0.992244 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15304.2 | 0.665102 | 0.332551 | − | 0.943085i | \(-0.392091\pi\) | ||||
0.332551 | + | 0.943085i | \(0.392091\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27002.2 | 1.16914 | 0.584572 | − | 0.811342i | \(-0.301262\pi\) | ||||
0.584572 | + | 0.811342i | \(0.301262\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23831.1 | −1.02803 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25931.5 | 1.11044 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11635.1 | −0.496416 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25061.4 | 1.06535 | 0.532673 | − | 0.846321i | \(-0.321188\pi\) | ||||
0.532673 | + | 0.846321i | \(0.321188\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24896.4 | −1.05448 | −0.527238 | − | 0.849718i | \(-0.676772\pi\) | ||||
−0.527238 | + | 0.849718i | \(0.676772\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20063.2 | −0.843612 | −0.421806 | − | 0.906686i | \(-0.638604\pi\) | ||||
−0.421806 | + | 0.906686i | \(0.638604\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13884.2 | −0.581687 | −0.290844 | − | 0.956771i | \(-0.593936\pi\) | ||||
−0.290844 | + | 0.956771i | \(0.593936\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20469.0 | −0.854467 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2852.52 | −0.118648 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1739.31 | −0.0718270 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13678.1 | 0.562838 | 0.281419 | − | 0.959585i | \(-0.409195\pi\) | ||||
0.281419 | + | 0.959585i | \(0.409195\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 61733.1 | 2.53118 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9947.59 | 0.406421 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29489.5 | −1.19630 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19808.3 | 0.800728 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −986.512 | −0.0397382 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29802.9 | −1.19629 | −0.598143 | − | 0.801390i | \(-0.704094\pi\) | ||||
−0.598143 | + | 0.801390i | \(0.704094\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22045.2 | −0.878706 | −0.439353 | − | 0.898314i | \(-0.644792\pi\) | ||||
−0.439353 | + | 0.898314i | \(0.644792\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33609.5 | −1.33497 | −0.667487 | − | 0.744622i | \(-0.732630\pi\) | ||||
−0.667487 | + | 0.744622i | \(0.732630\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11032.4 | −0.436681 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33775.6 | 1.33226 | 0.666128 | − | 0.745838i | \(-0.267951\pi\) | ||||
0.666128 | + | 0.745838i | \(0.267951\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13657.8 | −0.534997 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1379.62 | 0.0538556 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10123.0 | −0.393805 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3459.37 | −0.134115 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12637.0 | −0.486570 | −0.243285 | − | 0.969955i | \(-0.578225\pi\) | ||||
−0.243285 | + | 0.969955i | \(0.578225\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17442.4 | −0.669304 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6579.45 | −0.251609 | −0.125804 | − | 0.992055i | \(-0.540151\pi\) | ||||
−0.125804 | + | 0.992055i | \(0.540151\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −50442.1 | −1.92244 | −0.961219 | − | 0.275786i | \(-0.911062\pi\) | ||||
−0.961219 | + | 0.275786i | \(0.911062\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 984.823 | 0.0372797 | 0.0186399 | − | 0.999826i | \(-0.494066\pi\) | ||||
0.0186399 | + | 0.999826i | \(0.494066\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26587.7 | −1.00306 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 145.041 | 0.00545348 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −40314.6 | −1.51072 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8663.74 | 0.322490 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18904.7 | 0.701342 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8799.79 | 0.325376 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16480.5 | −0.607348 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43679.9 | 1.59908 | 0.799541 | − | 0.600612i | \(-0.205076\pi\) | ||||
0.799541 | + | 0.600612i | \(0.205076\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 310.415 | 0.0113265 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10364.3 | 0.376930 | 0.188465 | − | 0.982080i | \(-0.439649\pi\) | ||||
0.188465 | + | 0.982080i | \(0.439649\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 311.435 | 0.0112891 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7143.58 | 0.257254 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11451.9 | −0.411059 | −0.205530 | − | 0.978651i | \(-0.565892\pi\) | ||||
−0.205530 | + | 0.978651i | \(0.565892\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24374.6 | −0.872063 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −34592.7 | −1.23362 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15806.7 | −0.560044 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27701.8 | −0.978326 | −0.489163 | − | 0.872192i | \(-0.662698\pi\) | ||||
−0.489163 | + | 0.872192i | \(0.662698\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15752.5 | −0.554529 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22008.8 | −0.772277 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5878.01 | 0.204937 | 0.102469 | − | 0.994736i | \(-0.467326\pi\) | ||||
0.102469 | + | 0.994736i | \(0.467326\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6607.97 | 0.229652 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28786.0 | −0.997234 | −0.498617 | − | 0.866823i | \(-0.666159\pi\) | ||||
−0.498617 | + | 0.866823i | \(0.666159\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8214.90 | 0.283684 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1695.04 | −0.0581641 | −0.0290821 | − | 0.999577i | \(-0.509258\pi\) | ||||
−0.0290821 | + | 0.999577i | \(0.509258\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18640.5 | 0.637613 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30026.6 | −1.02385 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31929.4 | −1.08530 | −0.542651 | − | 0.839958i | \(-0.682580\pi\) | ||||
−0.542651 | + | 0.839958i | \(0.682580\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1576.46 | −0.0532495 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7868.57 | −0.264952 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25641.2 | −0.860704 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12255.6 | −0.410106 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10897.1 | −0.362385 | −0.181193 | − | 0.983448i | \(-0.557996\pi\) | ||||
−0.181193 | + | 0.983448i | \(0.557996\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5970.82 | 0.197947 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7041.97 | −0.232737 | −0.116368 | − | 0.993206i | \(-0.537125\pi\) | ||||
−0.116368 | + | 0.993206i | \(0.537125\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1715.81 | −0.0565328 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37607.6 | 1.23150 | 0.615749 | − | 0.787943i | \(-0.288854\pi\) | ||||
0.615749 | + | 0.787943i | \(0.288854\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1824.69 | 0.0595684 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2890.07 | 0.0940599 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25297.7 | −0.820826 | −0.410413 | − | 0.911900i | \(-0.634615\pi\) | ||||
−0.410413 | + | 0.911900i | \(0.634615\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 25621.4 | 0.826281 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12271.6 | 0.394556 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41686.5 | 1.33624 | 0.668120 | − | 0.744053i | \(-0.267099\pi\) | ||||
0.668120 | + | 0.744053i | \(0.267099\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26087.8 | 0.833708 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25465.9 | −0.808939 | −0.404470 | − | 0.914551i | \(-0.632544\pi\) | ||||
−0.404470 | + | 0.914551i | \(0.632544\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 536.878 | 0.0170031 |
(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 | 1200.4.a.bt.1.2 | 2 | ||
4.3 | odd | 2 | 75.4.a.c.1.2 | 2 | |||
5.2 | odd | 4 | 240.4.f.f.49.1 | 4 | |||
5.3 | odd | 4 | 240.4.f.f.49.3 | 4 | |||
5.4 | even | 2 | 1200.4.a.bn.1.1 | 2 | |||
12.11 | even | 2 | 225.4.a.o.1.1 | 2 | |||
15.2 | even | 4 | 720.4.f.j.289.4 | 4 | |||
15.8 | even | 4 | 720.4.f.j.289.3 | 4 | |||
20.3 | even | 4 | 15.4.b.a.4.2 | ✓ | 4 | ||
20.7 | even | 4 | 15.4.b.a.4.3 | yes | 4 | ||
20.19 | odd | 2 | 75.4.a.f.1.1 | 2 | |||
40.3 | even | 4 | 960.4.f.q.769.4 | 4 | |||
40.13 | odd | 4 | 960.4.f.p.769.2 | 4 | |||
40.27 | even | 4 | 960.4.f.q.769.2 | 4 | |||
40.37 | odd | 4 | 960.4.f.p.769.4 | 4 | |||
60.23 | odd | 4 | 45.4.b.b.19.3 | 4 | |||
60.47 | odd | 4 | 45.4.b.b.19.2 | 4 | |||
60.59 | even | 2 | 225.4.a.i.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.4.b.a.4.2 | ✓ | 4 | 20.3 | even | 4 | ||
15.4.b.a.4.3 | yes | 4 | 20.7 | even | 4 | ||
45.4.b.b.19.2 | 4 | 60.47 | odd | 4 | |||
45.4.b.b.19.3 | 4 | 60.23 | odd | 4 | |||
75.4.a.c.1.2 | 2 | 4.3 | odd | 2 | |||
75.4.a.f.1.1 | 2 | 20.19 | odd | 2 | |||
225.4.a.i.1.2 | 2 | 60.59 | even | 2 | |||
225.4.a.o.1.1 | 2 | 12.11 | even | 2 | |||
240.4.f.f.49.1 | 4 | 5.2 | odd | 4 | |||
240.4.f.f.49.3 | 4 | 5.3 | odd | 4 | |||
720.4.f.j.289.3 | 4 | 15.8 | even | 4 | |||
720.4.f.j.289.4 | 4 | 15.2 | even | 4 | |||
960.4.f.p.769.2 | 4 | 40.13 | odd | 4 | |||
960.4.f.p.769.4 | 4 | 40.37 | odd | 4 | |||
960.4.f.q.769.2 | 4 | 40.27 | even | 4 | |||
960.4.f.q.769.4 | 4 | 40.3 | even | 4 | |||
1200.4.a.bn.1.1 | 2 | 5.4 | even | 2 | |||
1200.4.a.bt.1.2 | 2 | 1.1 | even | 1 | trivial |