Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,4,Mod(1,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1216.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.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: | \(71.7463225670\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{93}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 23 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 608) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.32183\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.192450 | −0.0962250 | − | 0.995360i | \(-0.530677\pi\) | ||||
−0.0962250 | + | 0.995360i | \(0.530677\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −17.2873 | −1.54622 | −0.773112 | − | 0.634270i | \(-0.781301\pi\) | ||||
−0.773112 | + | 0.634270i | \(0.781301\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −12.3563 | −0.667180 | −0.333590 | − | 0.942718i | \(-0.608260\pi\) | ||||
−0.333590 | + | 0.942718i | \(0.608260\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.0000 | −0.962963 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 39.2873 | 1.07687 | 0.538435 | − | 0.842667i | \(-0.319016\pi\) | ||||
0.538435 | + | 0.842667i | \(0.319016\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −18.9310 | −0.403885 | −0.201942 | − | 0.979397i | \(-0.564725\pi\) | ||||
−0.201942 | + | 0.979397i | \(0.564725\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 17.2873 | 0.297571 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 100.149 | 1.42881 | 0.714404 | − | 0.699733i | \(-0.246698\pi\) | ||||
0.714404 | + | 0.699733i | \(0.246698\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.3563 | 0.128399 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 158.218 | 1.43438 | 0.717191 | − | 0.696877i | \(-0.245428\pi\) | ||||
0.717191 | + | 0.696877i | \(0.245428\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 173.851 | 1.39081 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 53.0000 | 0.377772 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −141.229 | −0.904332 | −0.452166 | − | 0.891934i | \(-0.649349\pi\) | ||||
−0.452166 | + | 0.891934i | \(0.649349\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 215.586 | 1.24904 | 0.624522 | − | 0.781008i | \(-0.285294\pi\) | ||||
0.624522 | + | 0.781008i | \(0.285294\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −39.2873 | −0.207244 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 213.608 | 1.03161 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −209.862 | −0.932462 | −0.466231 | − | 0.884663i | \(-0.654388\pi\) | ||||
−0.466231 | + | 0.884663i | \(0.654388\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 18.9310 | 0.0777277 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 276.873 | 1.05464 | 0.527321 | − | 0.849666i | \(-0.323197\pi\) | ||||
0.527321 | + | 0.849666i | \(0.323197\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −166.713 | −0.591243 | −0.295621 | − | 0.955305i | \(-0.595527\pi\) | ||||
−0.295621 | + | 0.955305i | \(0.595527\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 449.470 | 1.48896 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −60.5524 | −0.187925 | −0.0939625 | − | 0.995576i | \(-0.529953\pi\) | ||||
−0.0939625 | + | 0.995576i | \(0.529953\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −190.321 | −0.554871 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −100.149 | −0.274974 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 76.2405 | 0.197593 | 0.0987966 | − | 0.995108i | \(-0.468501\pi\) | ||||
0.0987966 | + | 0.995108i | \(0.468501\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −679.171 | −1.66508 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −19.0000 | −0.0441511 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −575.575 | −1.27006 | −0.635029 | − | 0.772488i | \(-0.719012\pi\) | ||||
−0.635029 | + | 0.772488i | \(0.719012\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 91.0111 | 0.191029 | 0.0955146 | − | 0.995428i | \(-0.469550\pi\) | ||||
0.0955146 | + | 0.995428i | \(0.469550\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 321.265 | 0.642470 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 327.265 | 0.624496 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 444.978 | 0.811383 | 0.405692 | − | 0.914010i | \(-0.367031\pi\) | ||||
0.405692 | + | 0.914010i | \(0.367031\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −158.218 | −0.276047 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −943.287 | −1.57673 | −0.788363 | − | 0.615210i | \(-0.789071\pi\) | ||||
−0.788363 | + | 0.615210i | \(0.789071\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −569.851 | −0.913644 | −0.456822 | − | 0.889558i | \(-0.651012\pi\) | ||||
−0.456822 | + | 0.889558i | \(0.651012\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −173.851 | −0.267661 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −485.448 | −0.718466 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 336.205 | 0.478810 | 0.239405 | − | 0.970920i | \(-0.423048\pi\) | ||||
0.239405 | + | 0.970920i | \(0.423048\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 649.000 | 0.890261 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −603.929 | −0.798672 | −0.399336 | − | 0.916805i | \(-0.630759\pi\) | ||||
−0.399336 | + | 0.916805i | \(0.630759\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1731.31 | −2.20926 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 141.229 | 0.174039 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1635.63 | 1.94805 | 0.974025 | − | 0.226441i | \(-0.0727089\pi\) | ||||
0.974025 | + | 0.226441i | \(0.0727089\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 233.917 | 0.269464 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −215.586 | −0.240378 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −328.459 | −0.354728 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 319.470 | 0.334405 | 0.167202 | − | 0.985923i | \(-0.446527\pi\) | ||||
0.167202 | + | 0.985923i | \(0.446527\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1021.47 | −1.03699 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1595.19 | −1.57156 | −0.785781 | − | 0.618505i | \(-0.787739\pi\) | ||||
−0.785781 | + | 0.618505i | \(0.787739\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1927.51 | −1.84392 | −0.921959 | − | 0.387287i | \(-0.873412\pi\) | ||||
−0.921959 | + | 0.387287i | \(0.873412\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −213.608 | −0.198533 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 717.089 | 0.647884 | 0.323942 | − | 0.946077i | \(-0.394992\pi\) | ||||
0.323942 | + | 0.946077i | \(0.394992\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −383.047 | −0.336598 | −0.168299 | − | 0.985736i | \(-0.553827\pi\) | ||||
−0.168299 | + | 0.985736i | \(0.553827\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 209.862 | 0.179452 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 622.917 | 0.518577 | 0.259288 | − | 0.965800i | \(-0.416512\pi\) | ||||
0.259288 | + | 0.965800i | \(0.416512\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2735.17 | −2.21787 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 492.205 | 0.388926 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1237.48 | −0.953273 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 212.492 | 0.159648 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −276.873 | −0.202966 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −844.498 | −0.604274 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −89.3095 | −0.0624011 | −0.0312005 | − | 0.999513i | \(-0.509933\pi\) | ||||
−0.0312005 | + | 0.999513i | \(0.509933\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 166.713 | 0.113785 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 348.690 | 0.232559 | 0.116279 | − | 0.993217i | \(-0.462903\pi\) | ||||
0.116279 | + | 0.993217i | \(0.462903\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −234.771 | −0.153062 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −916.227 | −0.584120 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1356.98 | 0.846237 | 0.423118 | − | 0.906074i | \(-0.360935\pi\) | ||||
0.423118 | + | 0.906074i | \(0.360935\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 629.287 | 0.383996 | 0.191998 | − | 0.981395i | \(-0.438503\pi\) | ||||
0.191998 | + | 0.981395i | \(0.438503\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 60.5524 | 0.0361662 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −743.746 | −0.434931 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2441.47 | 1.39830 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 190.321 | 0.106785 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 872.641 | 0.479796 | 0.239898 | − | 0.970798i | \(-0.422886\pi\) | ||||
0.239898 | + | 0.970798i | \(0.422886\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1892.71 | 1.02004 | 0.510021 | − | 0.860162i | \(-0.329638\pi\) | ||||
0.510021 | + | 0.860162i | \(0.329638\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2603.88 | −1.37589 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3726.90 | −1.93130 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2939.51 | 1.49426 | 0.747129 | − | 0.664679i | \(-0.231432\pi\) | ||||
0.747129 | + | 0.664679i | \(0.231432\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −76.2405 | −0.0380268 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1955.00 | −0.956991 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3301.38 | −1.58640 | −0.793202 | − | 0.608959i | \(-0.791587\pi\) | ||||
−0.793202 | + | 0.608959i | \(0.791587\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 679.171 | 0.320445 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2630.39 | −1.21884 | −0.609418 | − | 0.792849i | \(-0.708597\pi\) | ||||
−0.609418 | + | 0.792849i | \(0.708597\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1838.62 | −0.836877 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −494.000 | −0.220919 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1482.41 | 0.651479 | 0.325740 | − | 0.945460i | \(-0.394387\pi\) | ||||
0.325740 | + | 0.945460i | \(0.394387\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2148.16 | −0.927918 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 575.575 | 0.244423 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1048.00 | −0.437604 | −0.218802 | − | 0.975769i | \(-0.570215\pi\) | ||||
−0.218802 | + | 0.975769i | \(0.570215\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 761.354 | 0.312657 | 0.156329 | − | 0.987705i | \(-0.450034\pi\) | ||||
0.156329 | + | 0.987705i | \(0.450034\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −91.0111 | −0.0367636 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3627.95 | 1.44179 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3934.59 | 1.53864 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −654.887 | −0.252042 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4005.98 | 1.51760 | 0.758802 | − | 0.651322i | \(-0.225785\pi\) | ||||
0.758802 | + | 0.651322i | \(0.225785\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3855.87 | −1.43809 | −0.719046 | − | 0.694962i | \(-0.755421\pi\) | ||||
−0.719046 | + | 0.694962i | \(0.755421\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −327.265 | −0.120184 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2719.72 | 0.983616 | 0.491808 | − | 0.870704i | \(-0.336336\pi\) | ||||
0.491808 | + | 0.870704i | \(0.336336\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4454.56 | −1.58681 | −0.793405 | − | 0.608694i | \(-0.791694\pi\) | ||||
−0.793405 | + | 0.608694i | \(0.791694\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −444.978 | −0.156151 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1745.08 | 0.603353 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4786.39 | −1.63071 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4113.67 | −1.38126 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 746.459 | 0.247051 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3481.06 | 1.13576 | 0.567881 | − | 0.823111i | \(-0.307763\pi\) | ||||
0.567881 | + | 0.823111i | \(0.307763\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 943.287 | 0.303441 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2882.01 | 0.914194 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2663.85 | −0.833337 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 569.851 | 0.175831 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1895.92 | −0.577074 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3193.81 | 0.959074 | 0.479537 | − | 0.877522i | \(-0.340805\pi\) | ||||
0.479537 | + | 0.877522i | \(0.340805\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4520.12 | −1.33930 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5139.70 | −1.50279 | −0.751396 | − | 0.659852i | \(-0.770619\pi\) | ||||
−0.751396 | + | 0.659852i | \(0.770619\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4310.87 | −1.24397 | −0.621987 | − | 0.783027i | \(-0.713674\pi\) | ||||
−0.621987 | + | 0.783027i | \(0.713674\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 485.448 | 0.138269 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 175.879 | 0.0494517 | 0.0247258 | − | 0.999694i | \(-0.492129\pi\) | ||||
0.0247258 | + | 0.999694i | \(0.492129\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1046.79 | 0.290574 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −336.205 | −0.0921470 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3811.82 | 1.03166 | 0.515829 | − | 0.856692i | \(-0.327484\pi\) | ||||
0.515829 | + | 0.856692i | \(0.327484\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1356.97 | −0.362698 | −0.181349 | − | 0.983419i | \(-0.558046\pi\) | ||||
−0.181349 | + | 0.983419i | \(0.558046\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2080.00 | −0.549103 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3290.13 | 0.857954 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −359.688 | −0.0926575 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 603.929 | 0.153704 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5465.11 | −1.37432 | −0.687160 | − | 0.726506i | \(-0.741143\pi\) | ||||
−0.687160 | + | 0.726506i | \(0.741143\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6215.97 | 1.54464 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1731.31 | 0.425172 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1249.60 | 0.303299 | 0.151649 | − | 0.988434i | \(-0.451542\pi\) | ||||
0.151649 | + | 0.988434i | \(0.451542\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2593.13 | 0.622120 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3671.96 | 0.870838 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8043.06 | −1.88577 | −0.942883 | − | 0.333124i | \(-0.891897\pi\) | ||||
−0.942883 | + | 0.333124i | \(0.891897\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1317.99 | −0.305523 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1635.63 | −0.374902 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3051.13 | −0.691565 | −0.345782 | − | 0.938315i | \(-0.612386\pi\) | ||||
−0.345782 | + | 0.938315i | \(0.612386\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1967.96 | 0.441127 | 0.220563 | − | 0.975373i | \(-0.429210\pi\) | ||||
0.220563 | + | 0.975373i | \(0.429210\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −233.917 | −0.0518583 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6830.13 | 1.49772 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4077.51 | 0.884454 | 0.442227 | − | 0.896903i | \(-0.354189\pi\) | ||||
0.442227 | + | 0.896903i | \(0.354189\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5605.23 | −1.20278 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7982.51 | −1.69465 | −0.847325 | − | 0.531075i | \(-0.821788\pi\) | ||||
−0.847325 | + | 0.531075i | \(0.821788\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4137.36 | −0.869049 | −0.434524 | − | 0.900660i | \(-0.643083\pi\) | ||||
−0.434524 | + | 0.900660i | \(0.643083\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 328.459 | 0.0682674 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3421.14 | −0.703636 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5116.86 | 1.04149 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −319.470 | −0.0643562 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6807.50 | −1.35733 | −0.678666 | − | 0.734447i | \(-0.737442\pi\) | ||||
−0.678666 | + | 0.734447i | \(0.737442\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9950.13 | 1.96379 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2082.23 | 0.406812 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2995.22 | −0.579325 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2059.96 | 0.394466 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1595.19 | 0.302447 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1573.34 | −0.295374 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2822.75 | −0.524765 | −0.262383 | − | 0.964964i | \(-0.584508\pi\) | ||||
−0.262383 | + | 0.964964i | \(0.584508\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1927.51 | 0.354862 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8221.36 | −1.49901 | −0.749503 | − | 0.662001i | \(-0.769707\pi\) | ||||
−0.749503 | + | 0.662001i | \(0.769707\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1896.42 | −0.342466 | −0.171233 | − | 0.985231i | \(-0.554775\pi\) | ||||
−0.171233 | + | 0.985231i | \(0.554775\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5553.81 | −0.993402 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2875.66 | 0.509505 | 0.254753 | − | 0.967006i | \(-0.418006\pi\) | ||||
0.254753 | + | 0.967006i | \(0.418006\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5548.52 | −0.973848 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −717.089 | −0.124685 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1902.83 | 0.327791 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3291.16 | −0.561725 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 383.047 | 0.0647784 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 748.206 | 0.125380 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9263.48 | 1.53827 | 0.769134 | − | 0.639088i | \(-0.220688\pi\) | ||||
0.769134 | + | 0.639088i | \(0.220688\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5456.41 | 0.897926 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7692.47 | −1.25458 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2071.30 | −0.334810 | −0.167405 | − | 0.985888i | \(-0.553539\pi\) | ||||
−0.167405 | + | 0.985888i | \(0.553539\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −622.917 | −0.0998001 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8469.78 | 1.34506 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6589.90 | 1.03738 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2735.17 | 0.426830 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8255.77 | −1.27721 | −0.638607 | − | 0.769533i | \(-0.720489\pi\) | ||||
−0.638607 | + | 0.769533i | \(0.720489\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6600.97 | 1.01244 | 0.506220 | − | 0.862404i | \(-0.331042\pi\) | ||||
0.506220 | + | 0.862404i | \(0.331042\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1003.34 | −0.152577 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6136.89 | −0.925308 | −0.462654 | − | 0.886539i | \(-0.653103\pi\) | ||||
−0.462654 | + | 0.886539i | \(0.653103\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16306.9 | 2.43797 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1237.48 | 0.183457 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4314.86 | −0.634344 | −0.317172 | − | 0.948368i | \(-0.602733\pi\) | ||||
−0.317172 | + | 0.948368i | \(0.602733\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −212.492 | −0.0307244 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9851.18 | 1.41270 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2643.59 | 0.376006 | 0.188003 | − | 0.982168i | \(-0.439798\pi\) | ||||
0.188003 | + | 0.982168i | \(0.439798\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7198.70 | −1.01558 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −942.054 | −0.131830 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3643.51 | −0.505774 | −0.252887 | − | 0.967496i | \(-0.581380\pi\) | ||||
−0.252887 | + | 0.967496i | \(0.581380\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 844.498 | 0.116293 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2673.61 | 0.365246 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9731.09 | −1.31887 | −0.659436 | − | 0.751761i | \(-0.729205\pi\) | ||||
−0.659436 | + | 0.751761i | \(0.729205\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 89.3095 | 0.0120091 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4167.84 | −0.556049 | −0.278025 | − | 0.960574i | \(-0.589680\pi\) | ||||
−0.278025 | + | 0.960574i | \(0.589680\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8392.08 | 1.11091 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4334.53 | 0.569345 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4267.52 | 0.556226 | 0.278113 | − | 0.960548i | \(-0.410291\pi\) | ||||
0.278113 | + | 0.960548i | \(0.410291\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15845.4 | 2.04946 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −348.690 | −0.0447560 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5812.07 | −0.740347 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7610.34 | −0.962096 | −0.481048 | − | 0.876694i | \(-0.659744\pi\) | ||||
−0.481048 | + | 0.876694i | \(0.659744\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 234.771 | 0.0294567 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15827.1 | −1.97099 | −0.985495 | − | 0.169704i | \(-0.945719\pi\) | ||||
−0.985495 | + | 0.169704i | \(0.945719\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4081.24 | −0.504469 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11219.5 | −1.37654 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8244.91 | −1.00414 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5134.26 | 0.620716 | 0.310358 | − | 0.950620i | \(-0.399551\pi\) | ||||
0.310358 | + | 0.950620i | \(0.399551\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1356.98 | −0.162858 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7112.00 | 0.847358 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10440.3 | 1.23493 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −629.287 | −0.0739001 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5437.64 | −0.634001 | −0.317000 | − | 0.948425i | \(-0.602676\pi\) | ||||
−0.317000 | + | 0.948425i | \(0.602676\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1552.15 | 0.179685 | 0.0898423 | − | 0.995956i | \(-0.471364\pi\) | ||||
0.0898423 | + | 0.995956i | \(0.471364\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1574.36 | 0.180965 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17411.0 | 1.98720 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1124.57 | −0.127451 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 743.746 | 0.0837026 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5106.26 | −0.570673 | −0.285336 | − | 0.958427i | \(-0.592105\pi\) | ||||
−0.285336 | + | 0.958427i | \(0.592105\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17422.7 | 1.93367 | 0.966835 | − | 0.255401i | \(-0.0822076\pi\) | ||||
0.966835 | + | 0.255401i | \(0.0822076\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2441.47 | −0.269103 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3006.15 | 0.329070 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2682.09 | 0.291592 | 0.145796 | − | 0.989315i | \(-0.453426\pi\) | ||||
0.145796 | + | 0.989315i | \(0.453426\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4948.34 | 0.534320 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7407.64 | −0.794464 | −0.397232 | − | 0.917718i | \(-0.630029\pi\) | ||||
−0.397232 | + | 0.917718i | \(0.630029\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28275.6 | −3.01212 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −872.641 | −0.0923367 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15930.7 | −1.67442 | −0.837212 | − | 0.546878i | \(-0.815816\pi\) | ||||
−0.837212 | + | 0.546878i | \(0.815816\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10877.6 | 1.13571 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1892.71 | −0.196307 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4043.80 | −0.416651 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6952.91 | −0.711693 | −0.355846 | − | 0.934544i | \(-0.615807\pi\) | ||||
−0.355846 | + | 0.934544i | \(0.615807\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5307.91 | 0.539765 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13281.0 | −1.34177 | −0.670886 | − | 0.741561i | \(-0.734086\pi\) | ||||
−0.670886 | + | 0.741561i | \(0.734086\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6220.21 | −0.624358 | −0.312179 | − | 0.950023i | \(-0.601059\pi\) | ||||
−0.312179 | + | 0.950023i | \(0.601059\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3726.90 | 0.371679 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9875.06 | 0.978508 | 0.489254 | − | 0.872141i | \(-0.337269\pi\) | ||||
0.489254 | + | 0.872141i | \(0.337269\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5498.30 | −0.541339 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2939.51 | −0.287570 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6549.69 | −0.636692 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3303.17 | 0.319073 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1982.25 | −0.190275 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19014.0 | 1.81372 | 0.906861 | − | 0.421429i | \(-0.138471\pi\) | ||||
0.906861 | + | 0.421429i | \(0.138471\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3972.89 | 0.376607 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1955.00 | 0.184173 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5522.77 | −0.517064 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8907.07 | 0.828784 | 0.414392 | − | 0.910099i | \(-0.363994\pi\) | ||||
0.414392 | + | 0.910099i | \(0.363994\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3301.38 | 0.305303 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18451.8 | 1.69596 | 0.847981 | − | 0.530027i | \(-0.177818\pi\) | ||||
0.847981 | + | 0.530027i | \(0.177818\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14144.0 | −1.29212 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17658.5 | 1.60341 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11655.6 | 1.05196 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14771.6 | 1.32519 | 0.662594 | − | 0.748979i | \(-0.269456\pi\) | ||||
0.662594 | + | 0.748979i | \(0.269456\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2630.39 | 0.234565 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18175.4 | 1.61114 | 0.805570 | − | 0.592501i | \(-0.201859\pi\) | ||||
0.805570 | + | 0.592501i | \(0.201859\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27576.6 | 2.42998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1838.62 | 0.161057 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5172.14 | 0.450395 | 0.225198 | − | 0.974313i | \(-0.427697\pi\) | ||||
0.225198 | + | 0.974313i | \(0.427697\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7041.28 | 0.609565 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1007.00 | 0.0866669 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 33321.5 | 2.85111 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2378.94 | −0.202371 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1482.41 | −0.125377 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12920.1 | −1.08645 | −0.543225 | − | 0.839587i | \(-0.682797\pi\) | ||||
−0.543225 | + | 0.839587i | \(0.682797\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2486.41 | −0.207884 | −0.103942 | − | 0.994583i | \(-0.533146\pi\) | ||||
−0.103942 | + | 0.994583i | \(0.533146\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2148.16 | 0.178578 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21590.7 | 1.78464 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12866.0 | 1.05745 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14964.9 | 1.22302 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5241.47 | −0.425954 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12396.5 | −1.00177 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1048.00 | 0.0842170 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7477.18 | −0.597523 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4553.45 | −0.361863 | −0.180932 | − | 0.983496i | \(-0.557911\pi\) | ||||
−0.180932 | + | 0.983496i | \(0.557911\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −761.354 | −0.0601710 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6621.85 | 0.520456 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18289.1 | 1.42959 | 0.714796 | − | 0.699333i | \(-0.246520\pi\) | ||||
0.714796 | + | 0.699333i | \(0.246520\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2366.29 | −0.183954 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2683.36 | −0.207468 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4154.26 | −0.319453 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3627.95 | −0.277473 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21732.8 | 1.65323 | 0.826613 | − | 0.562771i | \(-0.190265\pi\) | ||||
0.826613 | + | 0.562771i | \(0.190265\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3156.03 | 0.238794 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3934.59 | −0.296112 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6231.21 | −0.466455 | −0.233227 | − | 0.972422i | \(-0.574929\pi\) | ||||
−0.233227 | + | 0.972422i | \(0.574929\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10768.6 | −0.801835 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8019.27 | −0.593964 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24670.7 | −1.81766 | −0.908829 | − | 0.417168i | \(-0.863023\pi\) | ||||
−0.908829 | + | 0.417168i | \(0.863023\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20912.5 | −1.53268 | −0.766342 | − | 0.642433i | \(-0.777925\pi\) | ||||
−0.766342 | + | 0.642433i | \(0.777925\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4005.98 | −0.292063 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27506.4 | 1.99495 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20604.1 | 1.48659 | 0.743294 | − | 0.668965i | \(-0.233262\pi\) | ||||
0.743294 | + | 0.668965i | \(0.233262\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3855.87 | 0.276761 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7462.35 | 0.532858 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2995.28 | 0.212782 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8508.89 | −0.601366 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5511.88 | −0.387563 | −0.193781 | − | 0.981045i | \(-0.562075\pi\) | ||||
−0.193781 | + | 0.981045i | \(0.562075\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4096.13 | 0.286550 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2719.72 | −0.189297 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11836.1 | 0.819648 | 0.409824 | − | 0.912165i | \(-0.365590\pi\) | ||||
0.409824 | + | 0.912165i | \(0.365590\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21392.7 | 1.47397 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4454.56 | 0.305382 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8407.13 | −0.573466 | −0.286733 | − | 0.958011i | \(-0.592569\pi\) | ||||
−0.286733 | + | 0.958011i | \(0.592569\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11313.6 | 0.767872 | 0.383936 | − | 0.923360i | \(-0.374568\pi\) | ||||
0.383936 | + | 0.923360i | \(0.374568\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11569.4 | −0.781332 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3673.41 | −0.246852 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1581.43 | 0.105747 | 0.0528733 | − | 0.998601i | \(-0.483162\pi\) | ||||
0.0528733 | + | 0.998601i | \(0.483162\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1745.08 | −0.116115 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1146.31 | 0.0759000 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2299.35 | 0.151500 | 0.0757502 | − | 0.997127i | \(-0.475865\pi\) | ||||
0.0757502 | + | 0.997127i | \(0.475865\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4786.39 | 0.313831 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16144.5 | −1.05341 | −0.526703 | − | 0.850049i | \(-0.676572\pi\) | ||||
−0.526703 | + | 0.850049i | \(0.676572\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2734.58 | 0.177564 | 0.0887819 | − | 0.996051i | \(-0.471703\pi\) | ||||
0.0887819 | + | 0.996051i | \(0.471703\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8385.57 | 0.541870 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −20210.4 | −1.29970 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7132.25 | −0.456464 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −746.459 | −0.0475450 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21017.5 | −1.33231 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15419.2 | −0.972787 | −0.486393 | − | 0.873740i | \(-0.661688\pi\) | ||||
−0.486393 | + | 0.873740i | \(0.661688\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3481.06 | −0.218578 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1543.92 | 0.0964860 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3602.95 | 0.224104 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24525.5 | 1.51833 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11905.5 | −0.733600 | −0.366800 | − | 0.930300i | \(-0.619547\pi\) | ||||
−0.366800 | + | 0.930300i | \(0.619547\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3525.47 | −0.216223 | −0.108111 | − | 0.994139i | \(-0.534480\pi\) | ||||
−0.108111 | + | 0.994139i | \(0.534480\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2882.01 | −0.175937 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7502.61 | −0.455886 | −0.227943 | − | 0.973675i | \(-0.573200\pi\) | ||||
−0.227943 | + | 0.973675i | \(0.573200\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22612.8 | −1.36769 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2663.85 | 0.160376 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6539.35 | 0.391891 | 0.195945 | − | 0.980615i | \(-0.437222\pi\) | ||||
0.195945 | + | 0.980615i | \(0.437222\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6027.92 | −0.359588 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14816.1 | 0.879805 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22229.4 | −1.31401 | −0.657007 | − | 0.753884i | \(-0.728178\pi\) | ||||
−0.657007 | + | 0.753884i | \(0.728178\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19497.3 | 1.14729 | 0.573643 | − | 0.819105i | \(-0.305530\pi\) | ||||
0.573643 | + | 0.819105i | \(0.305530\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1895.92 | 0.111058 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4058.55 | 0.236667 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22345.1 | −1.29716 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3193.81 | −0.184574 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3575.58 | 0.205714 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6952.91 | −0.398239 | −0.199120 | − | 0.979975i | \(-0.563808\pi\) | ||||
−0.199120 | + | 0.979975i | \(0.563808\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9214.09 | 0.525408 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2010.38 | −0.114129 | −0.0570643 | − | 0.998371i | \(-0.518174\pi\) | ||||
−0.0570643 | + | 0.998371i | \(0.518174\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3947.48 | −0.223108 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5139.70 | 0.289212 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16401.7 | 0.918877 | 0.459439 | − | 0.888209i | \(-0.348051\pi\) | ||||
0.459439 | + | 0.888209i | \(0.348051\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23458.5 | −1.30847 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4310.87 | 0.239403 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1443.30 | −0.0798048 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15967.5 | −0.879064 | −0.439532 | − | 0.898227i | \(-0.644856\pi\) | ||||
−0.439532 | + | 0.898227i | \(0.644856\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12621.6 | 0.691856 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10878.7 | −0.593744 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27728.6 | 1.50688 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −175.879 | −0.00951698 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22503.7 | −1.21248 | −0.606242 | − | 0.795280i | \(-0.707324\pi\) | ||||
−0.606242 | + | 0.795280i | \(0.707324\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3987.38 | −0.213921 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1046.79 | −0.0559210 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19710.8 | 1.04851 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14922.1 | −0.790426 | −0.395213 | − | 0.918590i | \(-0.629329\pi\) | ||||
−0.395213 | + | 0.918590i | \(0.629329\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8741.32 | −0.461076 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 34109.6 | 1.79161 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12857.4 | 0.672501 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3811.82 | −0.198543 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3483.14 | 0.180667 | 0.0903333 | − | 0.995912i | \(-0.471207\pi\) | ||||
0.0903333 | + | 0.995912i | \(0.471207\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23817.0 | 1.23023 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1356.97 | 0.0698013 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24552.8 | −1.25775 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6572.23 | −0.335283 | −0.167641 | − | 0.985848i | \(-0.553615\pi\) | ||||
−0.167641 | + | 0.985848i | \(0.553615\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15443.0 | −0.784586 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16696.1 | −0.844773 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27149.4 | 1.36806 | 0.684030 | − | 0.729454i | \(-0.260226\pi\) | ||||
0.684030 | + | 0.729454i | \(0.260226\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3290.13 | −0.165113 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17482.0 | 0.873754 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26251.0 | −1.30671 | −0.653355 | − | 0.757051i | \(-0.726639\pi\) | ||||
−0.653355 | + | 0.757051i | \(0.726639\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 359.688 | 0.0178319 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10583.0 | −0.522545 | −0.261273 | − | 0.965265i | \(-0.584142\pi\) | ||||
−0.261273 | + | 0.965265i | \(0.584142\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15085.6 | −0.741871 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15702.1 | 0.769092 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8860.60 | −0.432255 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9812.03 | −0.476759 | −0.238380 | − | 0.971172i | \(-0.576616\pi\) | ||||
−0.238380 | + | 0.971172i | \(0.576616\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5465.11 | 0.264488 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −32719.8 | −1.57721 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10954.1 | −0.525938 | −0.262969 | − | 0.964804i | \(-0.584702\pi\) | ||||
−0.262969 | + | 0.964804i | \(0.584702\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6215.97 | −0.297267 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19350.2 | −0.921739 | −0.460869 | − | 0.887468i | \(-0.652462\pi\) | ||||
−0.460869 | + | 0.887468i | \(0.652462\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4733.06 | 0.224572 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 45014.0 | 2.12743 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10896.2 | 0.512957 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17844.5 | 0.836786 | 0.418393 | − | 0.908266i | \(-0.362593\pi\) | ||||
0.418393 | + | 0.908266i | \(0.362593\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1249.60 | −0.0583699 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38019.3 | 1.76903 | 0.884514 | − | 0.466513i | \(-0.154490\pi\) | ||||
0.884514 | + | 0.466513i | \(0.154490\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37479.7 | 1.73718 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2593.13 | −0.119727 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5260.59 | 0.241951 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37059.2 | −1.69793 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7485.16 | −0.341632 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −50816.2 | −2.31046 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32884.2 | 1.48945 | 0.744724 | − | 0.667373i | \(-0.232581\pi\) | ||||
0.744724 | + | 0.667373i | \(0.232581\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8043.06 | 0.362916 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7696.99 | −0.345984 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1722.93 | −0.0771538 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1317.99 | 0.0587979 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4141.59 | −0.184069 | −0.0920344 | − | 0.995756i | \(-0.529337\pi\) | ||||
−0.0920344 | + | 0.995756i | \(0.529337\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6064.27 | −0.268509 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −42526.4 | −1.87590 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22387.9 | −0.983875 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 33796.7 | 1.47972 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3051.13 | 0.133092 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17007.2 | 0.739111 | 0.369555 | − | 0.929209i | \(-0.379510\pi\) | ||||
0.369555 | + | 0.929209i | \(0.379510\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18814.0 | −0.814611 | −0.407306 | − | 0.913292i | \(-0.633532\pi\) | ||||
−0.407306 | + | 0.913292i | \(0.633532\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1967.96 | −0.0848949 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 57071.9 | 2.45293 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3167.54 | −0.135640 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6081.85 | −0.259484 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30735.2 | 1.30653 | 0.653267 | − | 0.757128i | \(-0.273398\pi\) | ||||
0.653267 | + | 0.757128i | \(0.273398\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11638.0 | −0.492923 | −0.246461 | − | 0.969153i | \(-0.579268\pi\) | ||||
−0.246461 | + | 0.969153i | \(0.579268\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6830.13 | −0.288236 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4691.30 | 0.197258 | 0.0986291 | − | 0.995124i | \(-0.468554\pi\) | ||||
0.0986291 | + | 0.995124i | \(0.468554\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12990.2 | 0.544232 | 0.272116 | − | 0.962264i | \(-0.412276\pi\) | ||||
0.272116 | + | 0.962264i | \(0.412276\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4077.51 | −0.170213 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19060.5 | −0.792804 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 45472.3 | 1.88459 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11426.0 | 0.471854 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22152.7 | −0.911558 | −0.455779 | − | 0.890093i | \(-0.650639\pi\) | ||||
−0.455779 | + | 0.890093i | \(0.650639\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4443.27 | −0.182183 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7982.51 | 0.326136 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 31784.8 | 1.29400 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2625.63 | −0.106514 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4137.36 | 0.167248 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33204.0 | −1.33751 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27556.6 | −1.10612 | −0.553060 | − | 0.833141i | \(-0.686540\pi\) | ||||
−0.553060 | + | 0.833141i | \(0.686540\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8539.93 | 0.341590 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2728.49 | −0.108755 | −0.0543777 | − | 0.998520i | \(-0.517318\pi\) | ||||
−0.0543777 | + | 0.998520i | \(0.517318\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24012.7 | 0.953786 | 0.476893 | − | 0.878961i | \(-0.341763\pi\) | ||||
0.476893 | + | 0.878961i | \(0.341763\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3421.14 | 0.135415 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23821.0 | −0.939603 | −0.469802 | − | 0.882772i | \(-0.655675\pi\) | ||||
−0.469802 | + | 0.882772i | \(0.655675\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25626.9 | −1.00733 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5116.86 | −0.200436 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13208.6 | 0.515616 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8423.85 | −0.327705 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8306.22 | −0.322019 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10434.9 | 0.403160 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.8882 | −0.000765765 0 | −0.000382882 | − | 1.00000i | \(-0.500122\pi\) | ||||
−0.000382882 | 1.00000i | \(0.500122\pi\) | ||||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6807.50 | 0.261219 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −846.013 | −0.0323529 | −0.0161764 | − | 0.999869i | \(-0.505149\pi\) | ||||
−0.0161764 | + | 0.999869i | \(0.505149\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14028.9 | 0.534666 | 0.267333 | − | 0.963604i | \(-0.413858\pi\) | ||||
0.267333 | + | 0.963604i | \(0.413858\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9950.13 | −0.377932 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6993.33 | 0.264727 | 0.132364 | − | 0.991201i | \(-0.457743\pi\) | ||||
0.132364 | + | 0.991201i | \(0.457743\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1103.54 | 0.0416328 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 25497.5 | 0.958695 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1150.50 | −0.0431129 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18117.1 | 0.676634 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2995.22 | 0.111491 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30447.0 | −1.12955 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7635.42 | 0.282323 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2059.96 | −0.0759149 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13161.8 | −0.483438 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26569.7 | −0.972693 | −0.486347 | − | 0.873766i | \(-0.661671\pi\) | ||||
−0.486347 | + | 0.873766i | \(0.661671\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 41475.0 | 1.51336 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3037.05 | −0.110452 | −0.0552260 | − | 0.998474i | \(-0.517588\pi\) | ||||
−0.0552260 | + | 0.998474i | \(0.517588\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23726.7 | −0.860066 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1573.34 | 0.0568447 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4308.54 | −0.155159 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30480.3 | −1.09407 | −0.547036 | − | 0.837109i | \(-0.684244\pi\) | ||||
−0.547036 | + | 0.837109i | \(0.684244\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2822.75 | 0.100991 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17857.3 | 0.636816 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36484.7 | −1.29687 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 50115.4 | 1.77563 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12218.1 | −0.431498 | −0.215749 | − | 0.976449i | \(-0.569219\pi\) | ||||
−0.215749 | + | 0.976449i | \(0.569219\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3616.09 | −0.127296 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8221.36 | 0.288484 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −68018.5 | −2.37908 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29036.4 | 1.01236 | 0.506178 | − | 0.862429i | \(-0.331058\pi\) | ||||
0.506178 | + | 0.862429i | \(0.331058\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1896.42 | 0.0659076 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15188.6 | 0.526179 | 0.263090 | − | 0.964771i | \(-0.415259\pi\) | ||||
0.263090 | + | 0.964771i | \(0.415259\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43806.4 | 1.51276 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11321.2 | 0.389714 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38267.7 | −1.31313 | −0.656565 | − | 0.754270i | \(-0.727991\pi\) | ||||
−0.656565 | + | 0.754270i | \(0.727991\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10787.8 | 0.369007 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2875.66 | −0.0980544 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30092.6 | −1.02287 | −0.511434 | − | 0.859322i | \(-0.670886\pi\) | ||||
−0.511434 | + | 0.859322i | \(0.670886\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −69252.5 | −2.34655 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5548.52 | 0.187417 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16767.3 | −0.564592 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16686.2 | 0.560109 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18644.3 | −0.623888 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 66657.7 | 2.22361 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22521.1 | 0.748943 | 0.374472 | − | 0.927238i | \(-0.377824\pi\) | ||||
0.374472 | + | 0.927238i | \(0.377824\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1902.83 | −0.0630835 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16791.8 | −0.554969 | −0.277485 | − | 0.960730i | \(-0.589501\pi\) | ||||
−0.277485 | + | 0.960730i | \(0.589501\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7775.69 | −0.256195 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3291.16 | 0.108104 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28654.3 | −0.938312 | −0.469156 | − | 0.883115i | \(-0.655442\pi\) | ||||
−0.469156 | + | 0.883115i | \(0.655442\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 64259.5 | 2.09780 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9959.22 | 0.324132 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −43981.3 | −1.42704 | −0.713522 | − | 0.700633i | \(-0.752901\pi\) | ||||
−0.713522 | + | 0.700633i | \(0.752901\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −47016.7 | −1.52089 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −748.206 | −0.0241294 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26377.0 | −0.848068 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10308.7 | −0.330442 | −0.165221 | − | 0.986257i | \(-0.552834\pi\) | ||||
−0.165221 | + | 0.986257i | \(0.552834\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9263.48 | −0.296040 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 77007.3 | 2.45356 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −56141.7 | −1.78337 | −0.891687 | − | 0.452652i | \(-0.850478\pi\) | ||||
−0.891687 | + | 0.452652i | \(0.850478\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11122.7 | −0.352258 |
(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 | 1216.4.a.i.1.1 | 2 | ||
4.3 | odd | 2 | 1216.4.a.n.1.1 | 2 | |||
8.3 | odd | 2 | 608.4.a.c.1.2 | ✓ | 2 | ||
8.5 | even | 2 | 608.4.a.d.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.4.a.c.1.2 | ✓ | 2 | 8.3 | odd | 2 | ||
608.4.a.d.1.2 | yes | 2 | 8.5 | even | 2 | ||
1216.4.a.i.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1216.4.a.n.1.1 | 2 | 4.3 | odd | 2 |