Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,4,Mod(1,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, 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("624.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.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: | \(36.8171918436\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{14}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 14 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.74166\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.1 |
$q$-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 | ||||||||
\(5\) | 19.4833 | 1.74264 | 0.871320 | − | 0.490715i | \(-0.163264\pi\) | ||||
0.871320 | + | 0.490715i | \(0.163264\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.48331 | −0.404061 | −0.202031 | − | 0.979379i | \(-0.564754\pi\) | ||||
−0.202031 | + | 0.979379i | \(0.564754\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −22.8999 | −0.627689 | −0.313844 | − | 0.949474i | \(-0.601617\pi\) | ||||
−0.313844 | + | 0.949474i | \(0.601617\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 58.4499 | 1.00611 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 67.0334 | 0.956352 | 0.478176 | − | 0.878264i | \(-0.341298\pi\) | ||||
0.478176 | + | 0.878264i | \(0.341298\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −16.5167 | −0.199431 | −0.0997155 | − | 0.995016i | \(-0.531793\pi\) | ||||
−0.0997155 | + | 0.995016i | \(0.531793\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −22.4499 | −0.233285 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 175.600 | 1.59196 | 0.795979 | − | 0.605324i | \(-0.206956\pi\) | ||||
0.795979 | + | 0.605324i | \(0.206956\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 254.600 | 2.03680 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 291.800 | 1.86848 | 0.934239 | − | 0.356648i | \(-0.116080\pi\) | ||||
0.934239 | + | 0.356648i | \(0.116080\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −117.283 | −0.679505 | −0.339753 | − | 0.940515i | \(-0.610343\pi\) | ||||
−0.339753 | + | 0.940515i | \(0.610343\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −68.6997 | −0.362396 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −145.800 | −0.704133 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −154.766 | −0.687661 | −0.343830 | − | 0.939032i | \(-0.611724\pi\) | ||||
−0.343830 | + | 0.939032i | \(0.611724\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −39.0000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −251.716 | −0.958815 | −0.479407 | − | 0.877592i | \(-0.659148\pi\) | ||||
−0.479407 | + | 0.877592i | \(0.659148\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 502.566 | 1.78234 | 0.891170 | − | 0.453669i | \(-0.149885\pi\) | ||||
0.891170 | + | 0.453669i | \(0.149885\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 175.350 | 0.580880 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 281.733 | 0.874361 | 0.437181 | − | 0.899374i | \(-0.355977\pi\) | ||||
0.437181 | + | 0.899374i | \(0.355977\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −287.000 | −0.836735 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 201.100 | 0.552150 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 366.999 | 0.951154 | 0.475577 | − | 0.879674i | \(-0.342239\pi\) | ||||
0.475577 | + | 0.879674i | \(0.342239\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −446.166 | −1.09384 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −49.5501 | −0.115141 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 79.6663 | 0.175791 | 0.0878955 | − | 0.996130i | \(-0.471986\pi\) | ||||
0.0878955 | + | 0.996130i | \(0.471986\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −194.865 | −0.409016 | −0.204508 | − | 0.978865i | \(-0.565559\pi\) | ||||
−0.204508 | + | 0.978865i | \(0.565559\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −67.3498 | −0.134687 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −253.283 | −0.483322 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −400.082 | −0.729519 | −0.364759 | − | 0.931102i | \(-0.618849\pi\) | ||||
−0.364759 | + | 0.931102i | \(0.618849\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 526.799 | 0.919117 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −528.299 | −0.883065 | −0.441532 | − | 0.897245i | \(-0.645565\pi\) | ||||
−0.441532 | + | 0.897245i | \(0.645565\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −734.366 | −1.17741 | −0.588706 | − | 0.808347i | \(-0.700362\pi\) | ||||
−0.588706 | + | 0.808347i | \(0.700362\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 763.799 | 1.17594 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 171.367 | 0.253625 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −113.266 | −0.161309 | −0.0806545 | − | 0.996742i | \(-0.525701\pi\) | ||||
−0.0806545 | + | 0.996742i | \(0.525701\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 933.466 | 1.23447 | 0.617236 | − | 0.786778i | \(-0.288252\pi\) | ||||
0.617236 | + | 0.786778i | \(0.288252\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1306.03 | 1.66658 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 875.399 | 1.07877 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1190.91 | 1.41839 | 0.709195 | − | 0.705012i | \(-0.249059\pi\) | ||||
0.709195 | + | 0.705012i | \(0.249059\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 97.2831 | 0.112066 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −351.849 | −0.392313 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −321.800 | −0.347536 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 557.165 | 0.583211 | 0.291606 | − | 0.956539i | \(-0.405811\pi\) | ||||
0.291606 | + | 0.956539i | \(0.405811\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −206.099 | −0.209230 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −286.766 | −0.282518 | −0.141259 | − | 0.989973i | \(-0.545115\pi\) | ||||
−0.141259 | + | 0.989973i | \(0.545115\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1911.36 | 1.82847 | 0.914234 | − | 0.405187i | \(-0.132794\pi\) | ||||
0.914234 | + | 0.405187i | \(0.132794\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −437.399 | −0.406531 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −834.334 | −0.753814 | −0.376907 | − | 0.926251i | \(-0.623012\pi\) | ||||
−0.376907 | + | 0.926251i | \(0.623012\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1077.66 | −0.946986 | −0.473493 | − | 0.880798i | \(-0.657007\pi\) | ||||
−0.473493 | + | 0.880798i | \(0.657007\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −464.299 | −0.397021 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −166.065 | −0.138248 | −0.0691241 | − | 0.997608i | \(-0.522020\pi\) | ||||
−0.0691241 | + | 0.997608i | \(0.522020\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3421.26 | 2.77421 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −117.000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −501.632 | −0.386424 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −806.595 | −0.606007 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −755.147 | −0.553572 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2525.03 | 1.80676 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1296.16 | −0.905637 | −0.452819 | − | 0.891603i | \(-0.649581\pi\) | ||||
−0.452819 | + | 0.891603i | \(0.649581\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1507.70 | 1.02903 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 197.201 | 0.131523 | 0.0657617 | − | 0.997835i | \(-0.479052\pi\) | ||||
0.0657617 | + | 0.997835i | \(0.479052\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 123.600 | 0.0805823 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 526.049 | 0.335371 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −546.915 | −0.341066 | −0.170533 | − | 0.985352i | \(-0.554549\pi\) | ||||
−0.170533 | + | 0.985352i | \(0.554549\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −609.666 | −0.372023 | −0.186012 | − | 0.982548i | \(-0.559556\pi\) | ||||
−0.186012 | + | 0.982548i | \(0.559556\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 845.199 | 0.504813 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 297.699 | 0.174090 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5685.23 | 3.25609 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −861.000 | −0.483089 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2165.08 | −1.19040 | −0.595202 | − | 0.803576i | \(-0.702928\pi\) | ||||
−0.595202 | + | 0.803576i | \(0.702928\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 846.549 | 0.456233 | 0.228116 | − | 0.973634i | \(-0.426743\pi\) | ||||
0.228116 | + | 0.973634i | \(0.426743\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 603.300 | 0.318784 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2285.06 | −1.18413 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1653.60 | 0.840581 | 0.420291 | − | 0.907390i | \(-0.361928\pi\) | ||||
0.420291 | + | 0.907390i | \(0.361928\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1101.00 | 0.549149 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1314.07 | −0.643248 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2866.51 | 1.37744 | 0.688720 | − | 0.725027i | \(-0.258173\pi\) | ||||
0.688720 | + | 0.725027i | \(0.258173\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1338.50 | −0.631526 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −729.066 | −0.337825 | −0.168913 | − | 0.985631i | \(-0.554026\pi\) | ||||
−0.168913 | + | 0.985631i | \(0.554026\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −148.650 | −0.0664770 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3834.83 | −1.68530 | −0.842650 | − | 0.538462i | \(-0.819005\pi\) | ||||
−0.842650 | + | 0.538462i | \(0.819005\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1905.25 | −0.822990 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 238.999 | 0.101493 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 283.862 | 0.118530 | 0.0592649 | − | 0.998242i | \(-0.481124\pi\) | ||||
0.0592649 | + | 0.998242i | \(0.481124\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2363.60 | 0.970634 | 0.485317 | − | 0.874338i | \(-0.338704\pi\) | ||||
0.485317 | + | 0.874338i | \(0.338704\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −584.596 | −0.236145 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3015.36 | −1.19835 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1535.06 | −0.600291 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −202.049 | −0.0777616 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2514.26 | −0.952491 | −0.476246 | − | 0.879312i | \(-0.658003\pi\) | ||||
−0.476246 | + | 0.879312i | \(0.658003\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2420.73 | 0.902839 | 0.451420 | − | 0.892312i | \(-0.350918\pi\) | ||||
0.451420 | + | 0.892312i | \(0.350918\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −759.849 | −0.279046 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4633.65 | −1.67581 | −0.837903 | − | 0.545819i | \(-0.816219\pi\) | ||||
−0.837903 | + | 0.545819i | \(0.816219\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3054.17 | −1.08796 | −0.543980 | − | 0.839098i | \(-0.683083\pi\) | ||||
−0.543980 | + | 0.839098i | \(0.683083\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1200.25 | −0.421188 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2183.63 | −0.754979 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4904.26 | −1.67087 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1580.40 | 0.530653 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 378.230 | 0.125181 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4031.60 | 1.31539 | 0.657694 | − | 0.753285i | \(-0.271532\pi\) | ||||
0.657694 | + | 0.753285i | \(0.271532\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1584.90 | −0.509838 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9791.66 | 3.10598 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 877.666 | 0.274562 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2203.10 | −0.679779 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −871.434 | −0.265244 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3784.95 | −1.13659 | −0.568294 | − | 0.822826i | \(-0.692396\pi\) | ||||
−0.568294 | + | 0.822826i | \(0.692396\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2291.40 | 0.678932 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2013.83 | −0.588821 | −0.294411 | − | 0.955679i | \(-0.595123\pi\) | ||||
−0.294411 | + | 0.955679i | \(0.595123\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3050.73 | −0.880340 | −0.440170 | − | 0.897915i | \(-0.645082\pi\) | ||||
−0.440170 | + | 0.897915i | \(0.645082\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 514.101 | 0.146430 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5587.49 | 1.57103 | 0.785513 | − | 0.618846i | \(-0.212399\pi\) | ||||
0.785513 | + | 0.618846i | \(0.212399\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5489.09 | 1.52370 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −339.798 | −0.0931317 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1335.69 | 0.361501 | 0.180750 | − | 0.983529i | \(-0.442147\pi\) | ||||
0.180750 | + | 0.983529i | \(0.442147\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −571.558 | −0.152769 | −0.0763845 | − | 0.997078i | \(-0.524338\pi\) | ||||
−0.0763845 | + | 0.997078i | \(0.524338\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5591.71 | −1.45813 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 214.717 | 0.0553122 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2800.40 | 0.712723 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4088.60 | −1.02817 | −0.514084 | − | 0.857740i | \(-0.671868\pi\) | ||||
−0.514084 | + | 0.857740i | \(0.671868\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4021.21 | −0.999254 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3918.10 | 0.962199 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3050.23 | 0.740342 | 0.370171 | − | 0.928964i | \(-0.379299\pi\) | ||||
0.370171 | + | 0.928964i | \(0.379299\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1158.17 | 0.277857 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2626.20 | 0.622826 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5770.99 | −1.35306 | −0.676530 | − | 0.736415i | \(-0.736517\pi\) | ||||
−0.676530 | + | 0.736415i | \(0.736517\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7150.35 | 1.65752 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3572.74 | 0.818908 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2079.40 | −0.471314 | −0.235657 | − | 0.971836i | \(-0.575724\pi\) | ||||
−0.235657 | + | 0.971836i | \(0.575724\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6012.00 | −1.34761 | −0.673807 | − | 0.738908i | \(-0.735342\pi\) | ||||
−0.673807 | + | 0.738908i | \(0.735342\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 291.849 | 0.0647015 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5830.30 | −1.27847 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −735.201 | −0.159473 | −0.0797364 | − | 0.996816i | \(-0.525408\pi\) | ||||
−0.0797364 | + | 0.996816i | \(0.525408\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1055.55 | −0.226502 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1902.92 | −0.403981 | −0.201990 | − | 0.979387i | \(-0.564741\pi\) | ||||
−0.201990 | + | 0.979387i | \(0.564741\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2125.71 | −0.446502 | −0.223251 | − | 0.974761i | \(-0.571667\pi\) | ||||
−0.223251 | + | 0.974761i | \(0.571667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −965.399 | −0.200650 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1883.67 | 0.387420 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −419.527 | −0.0853913 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1671.49 | 0.336717 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1641.03 | −0.327200 | −0.163600 | − | 0.986527i | \(-0.552311\pi\) | ||||
−0.163600 | + | 0.986527i | \(0.552311\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1552.16 | 0.306341 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −618.297 | −0.120799 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2282.79 | −0.441530 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3760.86 | −0.720174 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −860.299 | −0.163112 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3796.62 | −0.712767 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3373.27 | 0.627111 | 0.313555 | − | 0.949570i | \(-0.398480\pi\) | ||||
0.313555 | + | 0.949570i | \(0.398480\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5734.09 | 1.05567 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 868.525 | 0.158359 | 0.0791793 | − | 0.996860i | \(-0.474770\pi\) | ||||
0.0791793 | + | 0.996860i | \(0.474770\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4343.19 | −0.784319 | −0.392159 | − | 0.919897i | \(-0.628272\pi\) | ||||
−0.392159 | + | 0.919897i | \(0.628272\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1312.20 | −0.234711 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3277.65 | −0.580730 | −0.290365 | − | 0.956916i | \(-0.593777\pi\) | ||||
−0.290365 | + | 0.956916i | \(0.593777\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6682.18 | −1.17282 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2503.00 | −0.435215 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1107.17 | −0.190726 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3309.79 | −0.564906 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3232.99 | −0.546743 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2108.30 | −0.353295 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5589.62 | −0.928197 | −0.464099 | − | 0.885784i | \(-0.653622\pi\) | ||||
−0.464099 | + | 0.885784i | \(0.653622\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1392.90 | −0.229220 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7794.92 | −1.27129 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 901.544 | 0.145728 | 0.0728638 | − | 0.997342i | \(-0.476786\pi\) | ||||
0.0728638 | + | 0.997342i | \(0.476786\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −498.194 | −0.0798176 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2685.77 | 0.426518 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4714.49 | 0.742153 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10263.8 | 1.60169 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 812.318 | 0.125670 | 0.0628350 | − | 0.998024i | \(-0.479986\pi\) | ||||
0.0628350 | + | 0.998024i | \(0.479986\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4437.96 | 0.680683 | 0.340342 | − | 0.940302i | \(-0.389457\pi\) | ||||
0.340342 | + | 0.940302i | \(0.389457\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −351.000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7115.35 | 1.07284 | 0.536419 | − | 0.843952i | \(-0.319777\pi\) | ||||
0.536419 | + | 0.843952i | \(0.319777\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10293.0 | −1.53886 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1504.90 | −0.223102 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4693.98 | −0.690081 | −0.345040 | − | 0.938588i | \(-0.612135\pi\) | ||||
−0.345040 | + | 0.938588i | \(0.612135\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6586.20 | −0.960227 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2419.79 | −0.349878 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14307.9 | −2.05181 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9243.98 | −1.31480 | −0.657400 | − | 0.753542i | \(-0.728344\pi\) | ||||
−0.657400 | + | 0.753542i | \(0.728344\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2265.44 | −0.319605 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2746.37 | −0.384324 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4311.99 | −0.598569 | −0.299285 | − | 0.954164i | \(-0.596748\pi\) | ||||
−0.299285 | + | 0.954164i | \(0.596748\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7575.09 | 1.04314 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3793.40 | −0.518223 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2382.73 | 0.322936 | 0.161468 | − | 0.986878i | \(-0.448377\pi\) | ||||
0.161468 | + | 0.986878i | \(0.448377\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3888.49 | −0.522870 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4845.81 | −0.646499 | −0.323250 | − | 0.946314i | \(-0.604775\pi\) | ||||
−0.323250 | + | 0.946314i | \(0.604775\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3338.80 | 0.441976 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4523.10 | 0.594113 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9561.50 | 1.24624 | 0.623120 | − | 0.782127i | \(-0.285865\pi\) | ||||
0.623120 | + | 0.782127i | \(0.285865\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11771.0 | 1.52247 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 591.604 | 0.0759350 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2206.79 | −0.281103 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7440.11 | −0.940575 | −0.470287 | − | 0.882513i | \(-0.655850\pi\) | ||||
−0.470287 | + | 0.882513i | \(0.655850\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 370.799 | 0.0465242 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8687.80 | −1.08192 | −0.540958 | − | 0.841050i | \(-0.681938\pi\) | ||||
−0.540958 | + | 0.841050i | \(0.681938\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1524.68 | 0.188461 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1578.15 | 0.193627 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3544.13 | 0.431637 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2556.10 | 0.309024 | 0.154512 | − | 0.987991i | \(-0.450619\pi\) | ||||
0.154512 | + | 0.987991i | \(0.450619\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1640.74 | −0.196915 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −596.168 | −0.0710303 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18187.0 | 2.15124 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1829.00 | −0.214788 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3347.46 | 0.390296 | 0.195148 | − | 0.980774i | \(-0.437481\pi\) | ||||
0.195148 | + | 0.980774i | \(0.437481\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1854.48 | −0.214684 | −0.107342 | − | 0.994222i | \(-0.534234\pi\) | ||||
−0.107342 | + | 0.994222i | \(0.534234\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2535.60 | 0.291454 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17066.7 | 1.94789 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1458.24 | 0.165267 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 893.096 | 0.100511 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14043.1 | 1.56945 | 0.784725 | − | 0.619844i | \(-0.212804\pi\) | ||||
0.784725 | + | 0.619844i | \(0.212804\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3086.47 | 0.342555 | 0.171278 | − | 0.985223i | \(-0.445210\pi\) | ||||
0.171278 | + | 0.985223i | \(0.445210\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17055.7 | 1.87990 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2900.32 | −0.317486 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2837.68 | −0.308508 | −0.154254 | − | 0.988031i | \(-0.549297\pi\) | ||||
−0.154254 | + | 0.988031i | \(0.549297\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2583.00 | −0.278912 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18309.4 | −1.96367 | −0.981834 | − | 0.189744i | \(-0.939234\pi\) | ||||
−0.981834 | + | 0.189744i | \(0.939234\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23203.0 | 2.47174 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6495.24 | −0.687281 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13861.2 | 1.45690 | 0.728451 | − | 0.685098i | \(-0.240241\pi\) | ||||
0.728451 | + | 0.685098i | \(0.240241\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5764.26 | 0.601837 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2539.65 | 0.263406 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1895.40 | 0.195291 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8990.36 | −0.920243 | −0.460122 | − | 0.887856i | \(-0.652194\pi\) | ||||
−0.460122 | + | 0.887856i | \(0.652194\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1809.90 | 0.184050 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3406.90 | −0.344198 | −0.172099 | − | 0.985080i | \(-0.555055\pi\) | ||||
−0.172099 | + | 0.985080i | \(0.555055\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7498.45 | 0.752662 | 0.376331 | − | 0.926485i | \(-0.377186\pi\) | ||||
0.376331 | + | 0.926485i | \(0.377186\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6855.19 | −0.683660 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7711.38 | −0.764112 | −0.382056 | − | 0.924139i | \(-0.624784\pi\) | ||||
−0.382056 | + | 0.924139i | \(0.624784\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2993.94 | 0.294770 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4960.79 | 0.485310 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11508.7 | −1.11875 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4205.14 | −0.406200 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3302.99 | 0.317051 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9439.82 | 0.900451 | 0.450226 | − | 0.892915i | \(-0.351344\pi\) | ||||
0.450226 | + | 0.892915i | \(0.351344\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2011.96 | 0.190723 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3942.20 | −0.371380 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10855.4 | 1.01633 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6156.20 | 0.572821 | 0.286411 | − | 0.958107i | \(-0.407538\pi\) | ||||
0.286411 | + | 0.958107i | \(0.407538\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8599.54 | 0.795265 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3842.74 | −0.353198 | −0.176599 | − | 0.984283i | \(-0.556510\pi\) | ||||
−0.176599 | + | 0.984283i | \(0.556510\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19560.3 | 1.78692 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4015.49 | −0.364612 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3953.43 | 0.356812 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12842.4 | 1.15211 | 0.576056 | − | 0.817410i | \(-0.304591\pi\) | ||||
0.576056 | + | 0.817410i | \(0.304591\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2187.20 | −0.195043 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8580.11 | −0.760573 | −0.380287 | − | 0.924869i | \(-0.624175\pi\) | ||||
−0.380287 | + | 0.924869i | \(0.624175\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5587.16 | −0.492327 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 507.000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −43.5957 | −0.00379635 | −0.00189818 | − | 0.999998i | \(-0.500604\pi\) | ||||
−0.00189818 | + | 0.999998i | \(0.500604\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5495.49 | 0.475746 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −445.951 | −0.0383805 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 37239.7 | 3.18636 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6451.66 | −0.548827 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11504.5 | −0.973008 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11368.1 | 0.955939 | 0.477969 | − | 0.878377i | \(-0.341373\pi\) | ||||
0.477969 | + | 0.878377i | \(0.341373\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5229.53 | 0.437230 | 0.218615 | − | 0.975811i | \(-0.429846\pi\) | ||||
0.218615 | + | 0.975811i | \(0.429846\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5715.75 | −0.475154 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7861.88 | −0.649846 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18668.2 | 1.53433 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 716.997 | 0.0585970 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3272.31 | 0.265927 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16255.6 | −1.31363 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 851.586 | 0.0684333 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6572.27 | 0.525209 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6567.99 | −0.521959 | −0.260980 | − | 0.965344i | \(-0.584046\pi\) | ||||
−0.260980 | + | 0.965344i | \(0.584046\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7090.79 | 0.560396 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20996.5 | −1.65026 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13675.7 | 1.06897 | 0.534487 | − | 0.845177i | \(-0.320505\pi\) | ||||
0.534487 | + | 0.845177i | \(0.320505\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1753.79 | −0.136339 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4819.57 | −0.372632 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 847.604 | 0.0651786 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9046.09 | −0.691865 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4527.96 | 0.344445 | 0.172222 | − | 0.985058i | \(-0.444905\pi\) | ||||
0.172222 | + | 0.985058i | \(0.444905\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6533.36 | −0.494332 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4605.17 | −0.346578 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18441.8 | −1.38051 | −0.690256 | − | 0.723566i | \(-0.742502\pi\) | ||||
−0.690256 | + | 0.723566i | \(0.742502\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3235.49 | −0.240917 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −606.148 | −0.0448957 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13553.5 | −0.998578 | −0.499289 | − | 0.866436i | \(-0.666405\pi\) | ||||
−0.499289 | + | 0.866436i | \(0.666405\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14815.5 | −1.08583 | −0.542915 | − | 0.839788i | \(-0.682679\pi\) | ||||
−0.542915 | + | 0.839788i | \(0.682679\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7542.79 | −0.549921 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 44707.6 | 3.24249 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21596.2 | 1.55816 | 0.779081 | − | 0.626923i | \(-0.215686\pi\) | ||||
0.779081 | + | 0.626923i | \(0.215686\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7262.19 | 0.521254 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6985.42 | −0.498802 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8404.23 | −0.597029 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2279.55 | −0.161107 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 918.801 | 0.0646047 | 0.0323024 | − | 0.999478i | \(-0.489716\pi\) | ||||
0.0323024 | + | 0.999478i | \(0.489716\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1937.13 | 0.135514 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13900.9 | −0.967527 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19816.0 | 1.37226 | 0.686128 | − | 0.727481i | \(-0.259309\pi\) | ||||
0.686128 | + | 0.727481i | \(0.259309\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9773.45 | −0.673399 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9162.50 | −0.628134 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5141.86 | 0.350736 | 0.175368 | − | 0.984503i | \(-0.443889\pi\) | ||||
0.175368 | + | 0.984503i | \(0.443889\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12380.9 | 0.840312 | 0.420156 | − | 0.907452i | \(-0.361975\pi\) | ||||
0.420156 | + | 0.907452i | \(0.361975\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3600.74 | −0.243173 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15715.1 | −1.05605 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23717.0 | 1.58590 | 0.792951 | − | 0.609286i | \(-0.208544\pi\) | ||||
0.792951 | + | 0.609286i | \(0.208544\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6550.89 | −0.435887 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3662.53 | −0.242504 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26157.1 | −1.72345 | −0.861726 | − | 0.507373i | \(-0.830617\pi\) | ||||
−0.861726 | + | 0.507373i | \(0.830617\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14712.8 | −0.964677 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23613.9 | 1.54077 | 0.770387 | − | 0.637576i | \(-0.220063\pi\) | ||||
0.770387 | + | 0.637576i | \(0.220063\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23345.4 | −1.51588 | −0.757940 | − | 0.652324i | \(-0.773794\pi\) | ||||
−0.757940 | + | 0.652324i | \(0.773794\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4741.19 | 0.306372 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8911.99 | −0.573116 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17371.0 | 1.11174 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1134.69 | 0.0722730 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10374.5 | −0.657645 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15245.7 | −0.961841 | −0.480921 | − | 0.876764i | \(-0.659698\pi\) | ||||
−0.480921 | + | 0.876764i | \(0.659698\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12094.8 | 0.759439 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −25253.6 | −1.57820 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3731.00 | 0.232068 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4754.69 | −0.294355 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10192.7 | 0.628063 | 0.314032 | − | 0.949413i | \(-0.398320\pi\) | ||||
0.314032 | + | 0.949413i | \(0.398320\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5506.31 | 0.337710 | 0.168855 | − | 0.985641i | \(-0.445993\pi\) | ||||
0.168855 | + | 0.985641i | \(0.445993\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 29375.0 | 1.79324 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13297.5 | 0.808005 | 0.404003 | − | 0.914758i | \(-0.367619\pi\) | ||||
0.404003 | + | 0.914758i | \(0.367619\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1824.35 | −0.110342 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2633.00 | 0.158518 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12440.2 | −0.745519 | −0.372760 | − | 0.927928i | \(-0.621588\pi\) | ||||
−0.372760 | + | 0.927928i | \(0.621588\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3842.14 | 0.229198 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6609.29 | −0.392470 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9562.87 | 0.565276 | 0.282638 | − | 0.959227i | \(-0.408791\pi\) | ||||
0.282638 | + | 0.959227i | \(0.408791\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2409.69 | 0.141795 | 0.0708973 | − | 0.997484i | \(-0.477414\pi\) | ||||
0.0708973 | + | 0.997484i | \(0.477414\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2614.30 | −0.153139 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2408.13 | 0.140426 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 51239.9 | 2.97454 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11354.9 | −0.656209 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4462.40 | 0.256735 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7929.02 | 0.454147 | 0.227074 | − | 0.973878i | \(-0.427084\pi\) | ||||
0.227074 | + | 0.973878i | \(0.427084\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6874.19 | 0.391982 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2628.26 | −0.149206 | −0.0746030 | − | 0.997213i | \(-0.523769\pi\) | ||||
−0.0746030 | + | 0.997213i | \(0.523769\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4169.44 | −0.235653 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6041.48 | −0.339956 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10021.5 | −0.561437 | −0.280719 | − | 0.959790i | \(-0.590573\pi\) | ||||
−0.280719 | + | 0.959790i | \(0.590573\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10655.7 | −0.594356 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9152.18 | −0.508264 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4770.99 | −0.263803 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23987.2 | −1.32057 | −0.660286 | − | 0.751014i | \(-0.729565\pi\) | ||||
−0.660286 | + | 0.751014i | \(0.729565\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1542.30 | 0.0845415 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11878.3 | −0.648303 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16873.4 | −0.916964 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16762.5 | 0.907032 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3763.71 | −0.202787 | −0.101393 | − | 0.994846i | \(-0.532330\pi\) | ||||
−0.101393 | + | 0.994846i | \(0.532330\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2556.23 | 0.137141 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16467.3 | 0.879707 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2145.96 | 0.114155 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36047.8 | −1.90946 | −0.954728 | − | 0.297479i | \(-0.903854\pi\) | ||||
−0.954728 | + | 0.297479i | \(0.903854\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1019.39 | −0.0537696 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20594.9 | −1.08174 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5800.15 | 0.303376 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4007.08 | 0.208713 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3944.18 | 0.204580 | 0.102290 | − | 0.994755i | \(-0.467383\pi\) | ||||
0.102290 | + | 0.994755i | \(0.467383\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14303.3 | −0.738812 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1714.68 | −0.0882012 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 74292.1 | 3.80571 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20447.8 | 1.04315 | 0.521573 | − | 0.853206i | \(-0.325345\pi\) | ||||
0.521573 | + | 0.853206i | \(0.325345\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 33688.7 | 1.70454 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13536.2 | −0.682089 | −0.341045 | − | 0.940047i | \(-0.610781\pi\) | ||||
−0.341045 | + | 0.940047i | \(0.610781\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16775.1 | −0.841851 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9161.83 | 0.457911 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15839.1 | −0.788433 | −0.394217 | − | 0.919018i | \(-0.628984\pi\) | ||||
−0.394217 | + | 0.919018i | \(0.628984\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 644.151 | 0.0319345 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1664.92 | 0.0822075 | 0.0411037 | − | 0.999155i | \(-0.486913\pi\) | ||||
0.0411037 | + | 0.999155i | \(0.486913\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −42182.9 | −2.07445 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8401.19 | 0.411491 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6243.58 | 0.304587 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22399.1 | −1.08835 | −0.544177 | − | 0.838970i | \(-0.683158\pi\) | ||||
−0.544177 | + | 0.838970i | \(0.683158\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12265.8 | −0.593613 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16493.6 | 0.795050 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23798.9 | 1.14265 | 0.571326 | − | 0.820723i | \(-0.306429\pi\) | ||||
0.571326 | + | 0.820723i | \(0.306429\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12063.6 | −0.576920 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13693.5 | 0.652285 | 0.326142 | − | 0.945321i | \(-0.394251\pi\) | ||||
0.326142 | + | 0.945321i | \(0.394251\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8064.50 | 0.382640 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11754.3 | 0.555526 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1035.66 | −0.0487556 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16299.9 | 0.764358 | 0.382179 | − | 0.924088i | \(-0.375174\pi\) | ||||
0.382179 | + | 0.924088i | \(0.375174\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9150.68 | 0.427437 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33532.2 | 1.56024 | 0.780122 | − | 0.625628i | \(-0.215157\pi\) | ||||
0.780122 | + | 0.625628i | \(0.215157\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29860.2 | −1.38401 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3474.50 | 0.160421 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4157.51 | 0.191217 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12098.0 | 0.554290 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7878.59 | 0.359589 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32217.5 | 1.46483 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16163.3 | −0.732097 | −0.366049 | − | 0.930596i | \(-0.619290\pi\) | ||||
−0.366049 | + | 0.930596i | \(0.619290\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −17313.0 | −0.781189 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1242.71 | 0.0558607 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2533.25 | 0.113441 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 21451.1 | 0.956970 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39636.4 | −1.76160 | −0.880798 | − | 0.473492i | \(-0.842993\pi\) | ||||
−0.880798 | + | 0.473492i | \(0.842993\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18885.5 | 0.836197 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10718.2 | 0.472797 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16816.9 | 0.739048 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25602.4 | −1.12095 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6238.21 | −0.272113 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23811.2 | −1.03481 | −0.517403 | − | 0.855742i | \(-0.673101\pi\) | ||||
−0.517403 | + | 0.855742i | \(0.673101\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27218.6 | −1.17851 | −0.589256 | − | 0.807946i | \(-0.700579\pi\) | ||||
−0.589256 | + | 0.807946i | \(0.700579\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18036.0 | −0.778045 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 55849.2 | 2.40038 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8300.73 | −0.355454 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 875.548 | 0.0373555 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43094.8 | −1.83193 | −0.915967 | − | 0.401253i | \(-0.868575\pi\) | ||||
−0.915967 | + | 0.401253i | \(0.868575\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26541.1 | −1.12414 | −0.562068 | − | 0.827091i | \(-0.689994\pi\) | ||||
−0.562068 | + | 0.827091i | \(0.689994\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −17490.9 | −0.738127 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44898.7 | 1.88788 | 0.943942 | − | 0.330112i | \(-0.107087\pi\) | ||||
0.943942 | + | 0.330112i | \(0.107087\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7137.48 | −0.299029 | −0.149514 | − | 0.988760i | \(-0.547771\pi\) | ||||
−0.149514 | + | 0.988760i | \(0.547771\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2205.60 | −0.0920717 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19238.6 | −0.800213 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14204.6 | −0.588708 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3166.64 | −0.130771 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4387.17 | 0.180527 | 0.0902634 | − | 0.995918i | \(-0.471229\pi\) | ||||
0.0902634 | + | 0.995918i | \(0.471229\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 60758.1 | 2.49121 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5708.76 | −0.233239 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3292.68 | 0.134049 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6036.01 | 0.244864 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6377.12 | −0.257788 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27176.9 | −1.09473 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9328.85 | −0.374459 | −0.187230 | − | 0.982316i | \(-0.559951\pi\) | ||||
−0.187230 | + | 0.982316i | \(0.559951\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2896.20 | −0.115845 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5010.39 | −0.199710 | −0.0998552 | − | 0.995002i | \(-0.531838\pi\) | ||||
−0.0998552 | + | 0.995002i | \(0.531838\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30233.4 | −1.20088 | −0.600438 | − | 0.799672i | \(-0.705007\pi\) | ||||
−0.600438 | + | 0.799672i | \(0.705007\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5651.01 | 0.223677 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4334.93 | −0.170988 | −0.0854940 | − | 0.996339i | \(-0.527247\pi\) | ||||
−0.0854940 | + | 0.996339i | \(0.527247\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −74715.2 | −2.93687 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1258.58 | −0.0493007 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2593.78 | 0.101252 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5201.06 | 0.202332 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5014.48 | 0.194404 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18895.6 | −0.730043 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34683.3 | 1.33543 | 0.667716 | − | 0.744416i | \(-0.267272\pi\) | ||||
0.667716 | + | 0.744416i | \(0.267272\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4923.08 | −0.188909 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18269.2 | −0.698642 | −0.349321 | − | 0.937003i | \(-0.613588\pi\) | ||||
−0.349321 | + | 0.937003i | \(0.613588\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14592.0 | 0.556128 | 0.278064 | − | 0.960563i | \(-0.410307\pi\) | ||||
0.278064 | + | 0.960563i | \(0.410307\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4656.49 | 0.176866 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30459.3 | −1.15301 | −0.576507 | − | 0.817092i | \(-0.695585\pi\) | ||||
−0.576507 | + | 0.817092i | \(0.695585\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9699.60 | 0.365933 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1854.89 | −0.0697432 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4653.30 | −0.174375 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5530.57 | 0.206555 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6848.38 | −0.254917 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34223.2 | −1.26964 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24601.2 | 0.909638 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11282.6 | −0.415793 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 46050.7 | 1.69147 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9364.89 | 0.342840 | 0.171420 | − | 0.985198i | \(-0.445164\pi\) | ||||
0.171420 | + | 0.985198i | \(0.445164\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2580.90 | −0.0941727 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32479.8 | −1.18123 | −0.590616 | − | 0.806952i | \(-0.701115\pi\) | ||||
−0.590616 | + | 0.806952i | \(0.701115\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21376.3 | −0.774864 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11389.9 | −0.411516 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1475.72 | −0.0531435 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −295.958 | −0.0106232 | −0.00531161 | − | 0.999986i | \(-0.501691\pi\) | ||||
−0.00531161 | + | 0.999986i | \(0.501691\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10119.8 | 0.362062 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6867.89 | 0.244918 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −39403.5 | −1.40062 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17202.3 | 0.609489 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5620.38 | −0.198492 | −0.0992458 | − | 0.995063i | \(-0.531643\pi\) | ||||
−0.0992458 | + | 0.995063i | \(0.531643\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4740.29 | 0.166871 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2605.58 | 0.0914284 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −29908.0 | −1.04609 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32583.1 | −1.13601 | −0.568006 | − | 0.823024i | \(-0.692285\pi\) | ||||
−0.568006 | + | 0.823024i | \(0.692285\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13029.6 | −0.452827 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8812.99 | 0.305308 | 0.152654 | − | 0.988280i | \(-0.451218\pi\) | ||||
0.152654 | + | 0.988280i | \(0.451218\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −44201.2 | −1.52639 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3936.59 | −0.135510 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13426.8 | −0.460732 | −0.230366 | − | 0.973104i | \(-0.573992\pi\) | ||||
−0.230366 | + | 0.973104i | \(0.573992\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9546.76 | 0.326555 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9832.96 | −0.335285 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13394.6 | −0.455293 | −0.227647 | − | 0.973744i | \(-0.573103\pi\) | ||||
−0.227647 | + | 0.973744i | \(0.573103\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −48986.2 | −1.65985 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20046.5 | −0.677129 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4092.74 | 0.137812 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16035.7 | −0.538273 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7509.00 | −0.251271 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 47163.8 | 1.57332 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45590.8 | −1.51613 | −0.758066 | − | 0.652178i | \(-0.773856\pi\) | ||||
−0.758066 | + | 0.652178i | \(0.773856\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3321.51 | −0.110116 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −264.763 | −0.00875041 | −0.00437521 | − | 0.999990i | \(-0.501393\pi\) | ||||
−0.00437521 | + | 0.999990i | \(0.501393\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4562.32 | 0.150320 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9929.38 | −0.326148 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 610.521 | 0.0199921 | 0.00999606 | − | 0.999950i | \(-0.496818\pi\) | ||||
0.00999606 | + | 0.999950i | \(0.496818\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27271.8 | −0.890308 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9698.98 | −0.315662 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 57829.7 | 1.87638 | 0.938190 | − | 0.346121i | \(-0.112501\pi\) | ||||
0.938190 | + | 0.346121i | \(0.112501\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −90278.8 | −2.92033 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6324.89 | −0.203975 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 88250.4 | 2.83741 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 56780.7 | 1.82008 | 0.910039 | − | 0.414522i | \(-0.136051\pi\) | ||||
0.910039 | + | 0.414522i | \(0.136051\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16768.9 | −0.535895 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −59505.3 | −1.89592 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18616.6 | 0.591369 | 0.295684 | − | 0.955286i | \(-0.404452\pi\) | ||||
0.295684 | + | 0.955286i | \(0.404452\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4178.69 | −0.132340 |
(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 | 624.4.a.r.1.2 | 2 | ||
3.2 | odd | 2 | 1872.4.a.t.1.1 | 2 | |||
4.3 | odd | 2 | 39.4.a.b.1.1 | ✓ | 2 | ||
8.3 | odd | 2 | 2496.4.a.bc.1.1 | 2 | |||
8.5 | even | 2 | 2496.4.a.s.1.1 | 2 | |||
12.11 | even | 2 | 117.4.a.c.1.2 | 2 | |||
20.19 | odd | 2 | 975.4.a.j.1.2 | 2 | |||
28.27 | even | 2 | 1911.4.a.h.1.1 | 2 | |||
52.31 | even | 4 | 507.4.b.f.337.3 | 4 | |||
52.47 | even | 4 | 507.4.b.f.337.2 | 4 | |||
52.51 | odd | 2 | 507.4.a.f.1.2 | 2 | |||
156.155 | even | 2 | 1521.4.a.s.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.a.b.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
117.4.a.c.1.2 | 2 | 12.11 | even | 2 | |||
507.4.a.f.1.2 | 2 | 52.51 | odd | 2 | |||
507.4.b.f.337.2 | 4 | 52.47 | even | 4 | |||
507.4.b.f.337.3 | 4 | 52.31 | even | 4 | |||
624.4.a.r.1.2 | 2 | 1.1 | even | 1 | trivial | ||
975.4.a.j.1.2 | 2 | 20.19 | odd | 2 | |||
1521.4.a.s.1.1 | 2 | 156.155 | even | 2 | |||
1872.4.a.t.1.1 | 2 | 3.2 | odd | 2 | |||
1911.4.a.h.1.1 | 2 | 28.27 | even | 2 | |||
2496.4.a.s.1.1 | 2 | 8.5 | even | 2 | |||
2496.4.a.bc.1.1 | 2 | 8.3 | odd | 2 |