Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(14.4554679514\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.58579 | −0.560660 | −0.280330 | − | 0.959904i | \(-0.590444\pi\) | ||||
−0.280330 | + | 0.959904i | \(0.590444\pi\) | |||||||
\(3\) | −5.24264 | −1.00895 | −0.504473 | − | 0.863427i | \(-0.668313\pi\) | ||||
−0.504473 | + | 0.863427i | \(0.668313\pi\) | |||||||
\(4\) | −5.48528 | −0.685660 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 8.31371 | 0.565676 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 21.3848 | 0.945083 | ||||||||
\(9\) | 0.485281 | 0.0179734 | ||||||||
\(10\) | −7.92893 | −0.250735 | ||||||||
\(11\) | 28.1421 | 0.771379 | 0.385690 | − | 0.922629i | \(-0.373964\pi\) | ||||
0.385690 | + | 0.922629i | \(0.373964\pi\) | |||||||
\(12\) | 28.7574 | 0.691795 | ||||||||
\(13\) | −3.85786 | −0.0823061 | −0.0411530 | − | 0.999153i | \(-0.513103\pi\) | ||||
−0.0411530 | + | 0.999153i | \(0.513103\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −26.2132 | −0.451215 | ||||||||
\(16\) | 9.97056 | 0.155790 | ||||||||
\(17\) | 38.3675 | 0.547382 | 0.273691 | − | 0.961818i | \(-0.411755\pi\) | ||||
0.273691 | + | 0.961818i | \(0.411755\pi\) | |||||||
\(18\) | −0.769553 | −0.0100770 | ||||||||
\(19\) | 116.770 | 1.40994 | 0.704968 | − | 0.709239i | \(-0.250961\pi\) | ||||
0.704968 | + | 0.709239i | \(0.250961\pi\) | |||||||
\(20\) | −27.4264 | −0.306637 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −44.6274 | −0.432482 | ||||||||
\(23\) | −176.463 | −1.59979 | −0.799893 | − | 0.600143i | \(-0.795110\pi\) | ||||
−0.799893 | + | 0.600143i | \(0.795110\pi\) | |||||||
\(24\) | −112.113 | −0.953538 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 6.11775 | 0.0461457 | ||||||||
\(27\) | 139.007 | 0.990812 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −209.853 | −1.34375 | −0.671874 | − | 0.740666i | \(-0.734510\pi\) | ||||
−0.671874 | + | 0.740666i | \(0.734510\pi\) | |||||||
\(30\) | 41.5685 | 0.252978 | ||||||||
\(31\) | −207.421 | −1.20174 | −0.600871 | − | 0.799346i | \(-0.705179\pi\) | ||||
−0.600871 | + | 0.799346i | \(0.705179\pi\) | |||||||
\(32\) | −186.889 | −1.03243 | ||||||||
\(33\) | −147.539 | −0.778281 | ||||||||
\(34\) | −60.8427 | −0.306895 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.66190 | −0.0123236 | ||||||||
\(37\) | −15.6670 | −0.0696117 | −0.0348058 | − | 0.999394i | \(-0.511081\pi\) | ||||
−0.0348058 | + | 0.999394i | \(0.511081\pi\) | |||||||
\(38\) | −185.172 | −0.790495 | ||||||||
\(39\) | 20.2254 | 0.0830424 | ||||||||
\(40\) | 106.924 | 0.422654 | ||||||||
\(41\) | −10.5736 | −0.0402760 | −0.0201380 | − | 0.999797i | \(-0.506411\pi\) | ||||
−0.0201380 | + | 0.999797i | \(0.506411\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −325.929 | −1.15590 | −0.577950 | − | 0.816072i | \(-0.696147\pi\) | ||||
−0.577950 | + | 0.816072i | \(0.696147\pi\) | |||||||
\(44\) | −154.368 | −0.528904 | ||||||||
\(45\) | 2.42641 | 0.00803794 | ||||||||
\(46\) | 279.833 | 0.896936 | ||||||||
\(47\) | −188.510 | −0.585042 | −0.292521 | − | 0.956259i | \(-0.594494\pi\) | ||||
−0.292521 | + | 0.956259i | \(0.594494\pi\) | |||||||
\(48\) | −52.2721 | −0.157184 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −39.6447 | −0.112132 | ||||||||
\(51\) | −201.147 | −0.552279 | ||||||||
\(52\) | 21.1615 | 0.0564340 | ||||||||
\(53\) | −275.182 | −0.713191 | −0.356595 | − | 0.934259i | \(-0.616063\pi\) | ||||
−0.356595 | + | 0.934259i | \(0.616063\pi\) | |||||||
\(54\) | −220.436 | −0.555509 | ||||||||
\(55\) | 140.711 | 0.344971 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −612.181 | −1.42255 | ||||||||
\(58\) | 332.782 | 0.753386 | ||||||||
\(59\) | 43.8192 | 0.0966911 | 0.0483455 | − | 0.998831i | \(-0.484605\pi\) | ||||
0.0483455 | + | 0.998831i | \(0.484605\pi\) | |||||||
\(60\) | 143.787 | 0.309380 | ||||||||
\(61\) | 855.102 | 1.79483 | 0.897414 | − | 0.441189i | \(-0.145443\pi\) | ||||
0.897414 | + | 0.441189i | \(0.145443\pi\) | |||||||
\(62\) | 328.926 | 0.673768 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 216.602 | 0.423051 | ||||||||
\(65\) | −19.2893 | −0.0368084 | ||||||||
\(66\) | 233.966 | 0.436351 | ||||||||
\(67\) | −545.419 | −0.994531 | −0.497265 | − | 0.867598i | \(-0.665662\pi\) | ||||
−0.497265 | + | 0.867598i | \(0.665662\pi\) | |||||||
\(68\) | −210.457 | −0.375318 | ||||||||
\(69\) | 925.132 | 1.61410 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1026.97 | 1.71661 | 0.858306 | − | 0.513138i | \(-0.171517\pi\) | ||||
0.858306 | + | 0.513138i | \(0.171517\pi\) | |||||||
\(72\) | 10.3776 | 0.0169863 | ||||||||
\(73\) | −252.877 | −0.405439 | −0.202719 | − | 0.979237i | \(-0.564978\pi\) | ||||
−0.202719 | + | 0.979237i | \(0.564978\pi\) | |||||||
\(74\) | 24.8444 | 0.0390285 | ||||||||
\(75\) | −131.066 | −0.201789 | ||||||||
\(76\) | −640.514 | −0.966737 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −32.0732 | −0.0465586 | ||||||||
\(79\) | −922.642 | −1.31399 | −0.656996 | − | 0.753894i | \(-0.728173\pi\) | ||||
−0.656996 | + | 0.753894i | \(0.728173\pi\) | |||||||
\(80\) | 49.8528 | 0.0696714 | ||||||||
\(81\) | −741.867 | −1.01765 | ||||||||
\(82\) | 16.7675 | 0.0225812 | ||||||||
\(83\) | −960.071 | −1.26966 | −0.634828 | − | 0.772653i | \(-0.718929\pi\) | ||||
−0.634828 | + | 0.772653i | \(0.718929\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 191.838 | 0.244797 | ||||||||
\(86\) | 516.854 | 0.648067 | ||||||||
\(87\) | 1100.18 | 1.35577 | ||||||||
\(88\) | 601.813 | 0.729017 | ||||||||
\(89\) | −133.205 | −0.158649 | −0.0793243 | − | 0.996849i | \(-0.525276\pi\) | ||||
−0.0793243 | + | 0.996849i | \(0.525276\pi\) | |||||||
\(90\) | −3.84776 | −0.00450655 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 967.949 | 1.09691 | ||||||||
\(93\) | 1087.44 | 1.21249 | ||||||||
\(94\) | 298.936 | 0.328010 | ||||||||
\(95\) | 583.848 | 0.630542 | ||||||||
\(96\) | 979.794 | 1.04166 | ||||||||
\(97\) | −1021.11 | −1.06884 | −0.534421 | − | 0.845218i | \(-0.679470\pi\) | ||||
−0.534421 | + | 0.845218i | \(0.679470\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.6569 | 0.0138643 | ||||||||
\(100\) | −137.132 | −0.137132 | ||||||||
\(101\) | 963.558 | 0.949284 | 0.474642 | − | 0.880179i | \(-0.342578\pi\) | ||||
0.474642 | + | 0.880179i | \(0.342578\pi\) | |||||||
\(102\) | 318.976 | 0.309641 | ||||||||
\(103\) | −1798.30 | −1.72031 | −0.860155 | − | 0.510034i | \(-0.829633\pi\) | ||||
−0.860155 | + | 0.510034i | \(0.829633\pi\) | |||||||
\(104\) | −82.4996 | −0.0777860 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 436.379 | 0.399858 | ||||||||
\(107\) | 279.003 | 0.252077 | 0.126038 | − | 0.992025i | \(-0.459774\pi\) | ||||
0.126038 | + | 0.992025i | \(0.459774\pi\) | |||||||
\(108\) | −762.493 | −0.679361 | ||||||||
\(109\) | 781.073 | 0.686360 | 0.343180 | − | 0.939270i | \(-0.388496\pi\) | ||||
0.343180 | + | 0.939270i | \(0.388496\pi\) | |||||||
\(110\) | −223.137 | −0.193412 | ||||||||
\(111\) | 82.1362 | 0.0702345 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −587.239 | −0.488874 | −0.244437 | − | 0.969665i | \(-0.578603\pi\) | ||||
−0.244437 | + | 0.969665i | \(0.578603\pi\) | |||||||
\(114\) | 970.788 | 0.797567 | ||||||||
\(115\) | −882.315 | −0.715446 | ||||||||
\(116\) | 1151.10 | 0.921354 | ||||||||
\(117\) | −1.87215 | −0.00147932 | ||||||||
\(118\) | −69.4879 | −0.0542108 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −560.563 | −0.426435 | ||||||||
\(121\) | −539.020 | −0.404974 | ||||||||
\(122\) | −1356.01 | −1.00629 | ||||||||
\(123\) | 55.4335 | 0.0406364 | ||||||||
\(124\) | 1137.76 | 0.823986 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1559.62 | 1.08972 | 0.544860 | − | 0.838527i | \(-0.316583\pi\) | ||||
0.544860 | + | 0.838527i | \(0.316583\pi\) | |||||||
\(128\) | 1151.63 | 0.795240 | ||||||||
\(129\) | 1708.73 | 1.16624 | ||||||||
\(130\) | 30.5887 | 0.0206370 | ||||||||
\(131\) | −1653.65 | −1.10290 | −0.551449 | − | 0.834209i | \(-0.685925\pi\) | ||||
−0.551449 | + | 0.834209i | \(0.685925\pi\) | |||||||
\(132\) | 809.294 | 0.533636 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 864.918 | 0.557594 | ||||||||
\(135\) | 695.036 | 0.443105 | ||||||||
\(136\) | 820.481 | 0.517321 | ||||||||
\(137\) | −296.658 | −0.185001 | −0.0925007 | − | 0.995713i | \(-0.529486\pi\) | ||||
−0.0925007 | + | 0.995713i | \(0.529486\pi\) | |||||||
\(138\) | −1467.06 | −0.904961 | ||||||||
\(139\) | 237.868 | 0.145149 | 0.0725745 | − | 0.997363i | \(-0.476879\pi\) | ||||
0.0725745 | + | 0.997363i | \(0.476879\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 988.288 | 0.590276 | ||||||||
\(142\) | −1628.56 | −0.962436 | ||||||||
\(143\) | −108.569 | −0.0634892 | ||||||||
\(144\) | 4.83853 | 0.00280007 | ||||||||
\(145\) | −1049.26 | −0.600942 | ||||||||
\(146\) | 401.009 | 0.227313 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 85.9377 | 0.0477299 | ||||||||
\(149\) | 2737.11 | 1.50492 | 0.752459 | − | 0.658639i | \(-0.228868\pi\) | ||||
0.752459 | + | 0.658639i | \(0.228868\pi\) | |||||||
\(150\) | 207.843 | 0.113135 | ||||||||
\(151\) | −3563.65 | −1.92057 | −0.960283 | − | 0.279030i | \(-0.909987\pi\) | ||||
−0.960283 | + | 0.279030i | \(0.909987\pi\) | |||||||
\(152\) | 2497.09 | 1.33251 | ||||||||
\(153\) | 18.6190 | 0.00983831 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1037.11 | −0.537435 | ||||||||
\(156\) | −110.942 | −0.0569389 | ||||||||
\(157\) | 1249.08 | 0.634951 | 0.317475 | − | 0.948266i | \(-0.397165\pi\) | ||||
0.317475 | + | 0.948266i | \(0.397165\pi\) | |||||||
\(158\) | 1463.11 | 0.736703 | ||||||||
\(159\) | 1442.68 | 0.719571 | ||||||||
\(160\) | −934.447 | −0.461716 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1176.44 | 0.570556 | ||||||||
\(163\) | −1964.64 | −0.944062 | −0.472031 | − | 0.881582i | \(-0.656479\pi\) | ||||
−0.472031 | + | 0.881582i | \(0.656479\pi\) | |||||||
\(164\) | 57.9991 | 0.0276157 | ||||||||
\(165\) | −737.696 | −0.348058 | ||||||||
\(166\) | 1522.47 | 0.711846 | ||||||||
\(167\) | −939.402 | −0.435288 | −0.217644 | − | 0.976028i | \(-0.569837\pi\) | ||||
−0.217644 | + | 0.976028i | \(0.569837\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2182.12 | −0.993226 | ||||||||
\(170\) | −304.214 | −0.137248 | ||||||||
\(171\) | 56.6661 | 0.0253413 | ||||||||
\(172\) | 1787.81 | 0.792555 | ||||||||
\(173\) | −2702.43 | −1.18764 | −0.593821 | − | 0.804597i | \(-0.702381\pi\) | ||||
−0.593821 | + | 0.804597i | \(0.702381\pi\) | |||||||
\(174\) | −1744.66 | −0.760126 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 280.593 | 0.120173 | ||||||||
\(177\) | −229.728 | −0.0975561 | ||||||||
\(178\) | 211.235 | 0.0889479 | ||||||||
\(179\) | −1434.05 | −0.598804 | −0.299402 | − | 0.954127i | \(-0.596787\pi\) | ||||
−0.299402 | + | 0.954127i | \(0.596787\pi\) | |||||||
\(180\) | −13.3095 | −0.00551130 | ||||||||
\(181\) | 2711.21 | 1.11339 | 0.556693 | − | 0.830718i | \(-0.312070\pi\) | ||||
0.556693 | + | 0.830718i | \(0.312070\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4482.99 | −1.81089 | ||||||||
\(184\) | −3773.62 | −1.51193 | ||||||||
\(185\) | −78.3348 | −0.0311313 | ||||||||
\(186\) | −1724.44 | −0.679796 | ||||||||
\(187\) | 1079.74 | 0.422239 | ||||||||
\(188\) | 1034.03 | 0.401140 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −925.858 | −0.353520 | ||||||||
\(191\) | −3494.60 | −1.32388 | −0.661938 | − | 0.749559i | \(-0.730266\pi\) | ||||
−0.661938 | + | 0.749559i | \(0.730266\pi\) | |||||||
\(192\) | −1135.57 | −0.426836 | ||||||||
\(193\) | −1629.76 | −0.607838 | −0.303919 | − | 0.952698i | \(-0.598295\pi\) | ||||
−0.303919 | + | 0.952698i | \(0.598295\pi\) | |||||||
\(194\) | 1619.26 | 0.599257 | ||||||||
\(195\) | 101.127 | 0.0371377 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 693.696 | 0.250882 | 0.125441 | − | 0.992101i | \(-0.459965\pi\) | ||||
0.125441 | + | 0.992101i | \(0.459965\pi\) | |||||||
\(198\) | −21.6569 | −0.00777316 | ||||||||
\(199\) | −3805.61 | −1.35564 | −0.677821 | − | 0.735227i | \(-0.737076\pi\) | ||||
−0.677821 | + | 0.735227i | \(0.737076\pi\) | |||||||
\(200\) | 534.619 | 0.189017 | ||||||||
\(201\) | 2859.44 | 1.00343 | ||||||||
\(202\) | −1528.00 | −0.532226 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1103.35 | 0.378676 | ||||||||
\(205\) | −52.8680 | −0.0180120 | ||||||||
\(206\) | 2851.72 | 0.964509 | ||||||||
\(207\) | −85.6342 | −0.0287536 | ||||||||
\(208\) | −38.4651 | −0.0128225 | ||||||||
\(209\) | 3286.14 | 1.08760 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −627.239 | −0.204649 | −0.102324 | − | 0.994751i | \(-0.532628\pi\) | ||||
−0.102324 | + | 0.994751i | \(0.532628\pi\) | |||||||
\(212\) | 1509.45 | 0.489006 | ||||||||
\(213\) | −5384.06 | −1.73197 | ||||||||
\(214\) | −442.439 | −0.141330 | ||||||||
\(215\) | −1629.64 | −0.516934 | ||||||||
\(216\) | 2972.64 | 0.936400 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1238.62 | −0.384815 | ||||||||
\(219\) | 1325.74 | 0.409066 | ||||||||
\(220\) | −771.838 | −0.236533 | ||||||||
\(221\) | −148.017 | −0.0450529 | ||||||||
\(222\) | −130.251 | −0.0393777 | ||||||||
\(223\) | −2000.99 | −0.600878 | −0.300439 | − | 0.953801i | \(-0.597133\pi\) | ||||
−0.300439 | + | 0.953801i | \(0.597133\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.1320 | 0.00359468 | ||||||||
\(226\) | 931.235 | 0.274092 | ||||||||
\(227\) | −1592.24 | −0.465554 | −0.232777 | − | 0.972530i | \(-0.574781\pi\) | ||||
−0.232777 | + | 0.972530i | \(0.574781\pi\) | |||||||
\(228\) | 3357.98 | 0.975386 | ||||||||
\(229\) | −3925.16 | −1.13267 | −0.566336 | − | 0.824174i | \(-0.691640\pi\) | ||||
−0.566336 | + | 0.824174i | \(0.691640\pi\) | |||||||
\(230\) | 1399.16 | 0.401122 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4487.66 | −1.26995 | ||||||||
\(233\) | 2169.75 | 0.610065 | 0.305032 | − | 0.952342i | \(-0.401333\pi\) | ||||
0.305032 | + | 0.952342i | \(0.401333\pi\) | |||||||
\(234\) | 2.96883 | 0.000829395 0 | ||||||||
\(235\) | −942.548 | −0.261639 | ||||||||
\(236\) | −240.361 | −0.0662972 | ||||||||
\(237\) | 4837.08 | 1.32575 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1057.70 | 0.286262 | 0.143131 | − | 0.989704i | \(-0.454283\pi\) | ||||
0.143131 | + | 0.989704i | \(0.454283\pi\) | |||||||
\(240\) | −261.360 | −0.0702948 | ||||||||
\(241\) | 2399.24 | 0.641281 | 0.320640 | − | 0.947201i | \(-0.396102\pi\) | ||||
0.320640 | + | 0.947201i | \(0.396102\pi\) | |||||||
\(242\) | 854.771 | 0.227053 | ||||||||
\(243\) | 136.150 | 0.0359424 | ||||||||
\(244\) | −4690.47 | −1.23064 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −87.9058 | −0.0227832 | ||||||||
\(247\) | −450.481 | −0.116046 | ||||||||
\(248\) | −4435.66 | −1.13574 | ||||||||
\(249\) | 5033.31 | 1.28102 | ||||||||
\(250\) | −198.223 | −0.0501470 | ||||||||
\(251\) | −3812.95 | −0.958848 | −0.479424 | − | 0.877583i | \(-0.659154\pi\) | ||||
−0.479424 | + | 0.877583i | \(0.659154\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4966.05 | −1.23404 | ||||||||
\(254\) | −2473.23 | −0.610962 | ||||||||
\(255\) | −1005.74 | −0.246987 | ||||||||
\(256\) | −3559.06 | −0.868910 | ||||||||
\(257\) | 3490.16 | 0.847122 | 0.423561 | − | 0.905868i | \(-0.360780\pi\) | ||||
0.423561 | + | 0.905868i | \(0.360780\pi\) | |||||||
\(258\) | −2709.68 | −0.653865 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 105.807 | 0.0252381 | ||||||||
\(261\) | −101.838 | −0.0241517 | ||||||||
\(262\) | 2622.33 | 0.618351 | ||||||||
\(263\) | 7124.56 | 1.67041 | 0.835207 | − | 0.549936i | \(-0.185348\pi\) | ||||
0.835207 | + | 0.549936i | \(0.185348\pi\) | |||||||
\(264\) | −3155.09 | −0.735539 | ||||||||
\(265\) | −1375.91 | −0.318949 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 698.347 | 0.160068 | ||||||||
\(268\) | 2991.78 | 0.681910 | ||||||||
\(269\) | −427.943 | −0.0969968 | −0.0484984 | − | 0.998823i | \(-0.515444\pi\) | ||||
−0.0484984 | + | 0.998823i | \(0.515444\pi\) | |||||||
\(270\) | −1102.18 | −0.248431 | ||||||||
\(271\) | 8188.58 | 1.83550 | 0.917751 | − | 0.397157i | \(-0.130003\pi\) | ||||
0.917751 | + | 0.397157i | \(0.130003\pi\) | |||||||
\(272\) | 382.546 | 0.0852767 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 470.436 | 0.103723 | ||||||||
\(275\) | 703.553 | 0.154276 | ||||||||
\(276\) | −5074.61 | −1.10672 | ||||||||
\(277\) | −4169.96 | −0.904507 | −0.452254 | − | 0.891889i | \(-0.649380\pi\) | ||||
−0.452254 | + | 0.891889i | \(0.649380\pi\) | |||||||
\(278\) | −377.208 | −0.0813792 | ||||||||
\(279\) | −100.658 | −0.0215994 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1284.60 | 0.272714 | 0.136357 | − | 0.990660i | \(-0.456461\pi\) | ||||
0.136357 | + | 0.990660i | \(0.456461\pi\) | |||||||
\(282\) | −1567.21 | −0.330944 | ||||||||
\(283\) | 4789.35 | 1.00600 | 0.502998 | − | 0.864287i | \(-0.332230\pi\) | ||||
0.502998 | + | 0.864287i | \(0.332230\pi\) | |||||||
\(284\) | −5633.25 | −1.17701 | ||||||||
\(285\) | −3060.90 | −0.636184 | ||||||||
\(286\) | 172.167 | 0.0355959 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −90.6939 | −0.0185562 | ||||||||
\(289\) | −3440.93 | −0.700373 | ||||||||
\(290\) | 1663.91 | 0.336924 | ||||||||
\(291\) | 5353.30 | 1.07840 | ||||||||
\(292\) | 1387.10 | 0.277993 | ||||||||
\(293\) | 6983.27 | 1.39238 | 0.696189 | − | 0.717858i | \(-0.254877\pi\) | ||||
0.696189 | + | 0.717858i | \(0.254877\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 219.096 | 0.0432416 | ||||||||
\(296\) | −335.034 | −0.0657888 | ||||||||
\(297\) | 3911.96 | 0.764292 | ||||||||
\(298\) | −4340.47 | −0.843748 | ||||||||
\(299\) | 680.770 | 0.131672 | ||||||||
\(300\) | 718.934 | 0.138359 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5651.18 | 1.07678 | ||||||||
\(303\) | −5051.59 | −0.957777 | ||||||||
\(304\) | 1164.26 | 0.219654 | ||||||||
\(305\) | 4275.51 | 0.802672 | ||||||||
\(306\) | −29.5258 | −0.00551595 | ||||||||
\(307\) | −2069.43 | −0.384719 | −0.192359 | − | 0.981325i | \(-0.561614\pi\) | ||||
−0.192359 | + | 0.981325i | \(0.561614\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9427.84 | 1.73570 | ||||||||
\(310\) | 1644.63 | 0.301318 | ||||||||
\(311\) | 2121.96 | 0.386898 | 0.193449 | − | 0.981110i | \(-0.438033\pi\) | ||||
0.193449 | + | 0.981110i | \(0.438033\pi\) | |||||||
\(312\) | 432.516 | 0.0784820 | ||||||||
\(313\) | 1528.80 | 0.276079 | 0.138039 | − | 0.990427i | \(-0.455920\pi\) | ||||
0.138039 | + | 0.990427i | \(0.455920\pi\) | |||||||
\(314\) | −1980.77 | −0.355992 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5060.95 | 0.900951 | ||||||||
\(317\) | 5142.44 | 0.911131 | 0.455565 | − | 0.890202i | \(-0.349437\pi\) | ||||
0.455565 | + | 0.890202i | \(0.349437\pi\) | |||||||
\(318\) | −2287.78 | −0.403435 | ||||||||
\(319\) | −5905.71 | −1.03654 | ||||||||
\(320\) | 1083.01 | 0.189194 | ||||||||
\(321\) | −1462.71 | −0.254332 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4480.16 | 0.771773 | ||||||||
\(324\) | 4069.35 | 0.697762 | ||||||||
\(325\) | −96.4466 | −0.0164612 | ||||||||
\(326\) | 3115.49 | 0.529298 | ||||||||
\(327\) | −4094.89 | −0.692501 | ||||||||
\(328\) | −226.114 | −0.0380642 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1169.83 | 0.195142 | ||||||||
\(331\) | −5774.04 | −0.958822 | −0.479411 | − | 0.877591i | \(-0.659150\pi\) | ||||
−0.479411 | + | 0.877591i | \(0.659150\pi\) | |||||||
\(332\) | 5266.26 | 0.870553 | ||||||||
\(333\) | −7.60288 | −0.00125116 | ||||||||
\(334\) | 1489.69 | 0.244049 | ||||||||
\(335\) | −2727.10 | −0.444768 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −484.761 | −0.0783579 | −0.0391790 | − | 0.999232i | \(-0.512474\pi\) | ||||
−0.0391790 | + | 0.999232i | \(0.512474\pi\) | |||||||
\(338\) | 3460.37 | 0.556862 | ||||||||
\(339\) | 3078.68 | 0.493248 | ||||||||
\(340\) | −1052.28 | −0.167847 | ||||||||
\(341\) | −5837.28 | −0.926998 | ||||||||
\(342\) | −89.8603 | −0.0142079 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6969.92 | −1.09242 | ||||||||
\(345\) | 4625.66 | 0.721847 | ||||||||
\(346\) | 4285.48 | 0.665864 | ||||||||
\(347\) | −7798.21 | −1.20643 | −0.603213 | − | 0.797580i | \(-0.706113\pi\) | ||||
−0.603213 | + | 0.797580i | \(0.706113\pi\) | |||||||
\(348\) | −6034.81 | −0.929597 | ||||||||
\(349\) | −662.157 | −0.101560 | −0.0507800 | − | 0.998710i | \(-0.516171\pi\) | ||||
−0.0507800 | + | 0.998710i | \(0.516171\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −536.271 | −0.0815499 | ||||||||
\(352\) | −5259.47 | −0.796394 | ||||||||
\(353\) | 6626.14 | 0.999076 | 0.499538 | − | 0.866292i | \(-0.333503\pi\) | ||||
0.499538 | + | 0.866292i | \(0.333503\pi\) | |||||||
\(354\) | 364.300 | 0.0546958 | ||||||||
\(355\) | 5134.87 | 0.767692 | ||||||||
\(356\) | 730.668 | 0.108779 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2274.10 | 0.335725 | ||||||||
\(359\) | 10398.1 | 1.52866 | 0.764329 | − | 0.644827i | \(-0.223070\pi\) | ||||
0.764329 | + | 0.644827i | \(0.223070\pi\) | |||||||
\(360\) | 51.8882 | 0.00759652 | ||||||||
\(361\) | 6776.13 | 0.987918 | ||||||||
\(362\) | −4299.41 | −0.624231 | ||||||||
\(363\) | 2825.89 | 0.408597 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1264.39 | −0.181318 | ||||||||
\(366\) | 7109.07 | 1.01529 | ||||||||
\(367\) | 2246.31 | 0.319499 | 0.159750 | − | 0.987158i | \(-0.448931\pi\) | ||||
0.159750 | + | 0.987158i | \(0.448931\pi\) | |||||||
\(368\) | −1759.44 | −0.249231 | ||||||||
\(369\) | −5.13117 | −0.000723897 0 | ||||||||
\(370\) | 124.222 | 0.0174541 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −5964.89 | −0.831358 | ||||||||
\(373\) | 192.025 | 0.0266560 | 0.0133280 | − | 0.999911i | \(-0.495757\pi\) | ||||
0.0133280 | + | 0.999911i | \(0.495757\pi\) | |||||||
\(374\) | −1712.24 | −0.236733 | ||||||||
\(375\) | −655.330 | −0.0902429 | ||||||||
\(376\) | −4031.24 | −0.552913 | ||||||||
\(377\) | 809.584 | 0.110599 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4565.76 | −0.618805 | −0.309403 | − | 0.950931i | \(-0.600129\pi\) | ||||
−0.309403 | + | 0.950931i | \(0.600129\pi\) | |||||||
\(380\) | −3202.57 | −0.432338 | ||||||||
\(381\) | −8176.55 | −1.09947 | ||||||||
\(382\) | 5541.69 | 0.742245 | ||||||||
\(383\) | 1387.07 | 0.185055 | 0.0925273 | − | 0.995710i | \(-0.470505\pi\) | ||||
0.0925273 | + | 0.995710i | \(0.470505\pi\) | |||||||
\(384\) | −6037.58 | −0.802355 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2584.45 | 0.340791 | ||||||||
\(387\) | −158.167 | −0.0207754 | ||||||||
\(388\) | 5601.06 | 0.732862 | ||||||||
\(389\) | 4583.01 | 0.597346 | 0.298673 | − | 0.954355i | \(-0.403456\pi\) | ||||
0.298673 | + | 0.954355i | \(0.403456\pi\) | |||||||
\(390\) | −160.366 | −0.0208216 | ||||||||
\(391\) | −6770.45 | −0.875694 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8669.47 | 1.11277 | ||||||||
\(394\) | −1100.05 | −0.140660 | ||||||||
\(395\) | −4613.21 | −0.587635 | ||||||||
\(396\) | −74.9117 | −0.00950620 | ||||||||
\(397\) | −8961.06 | −1.13285 | −0.566426 | − | 0.824112i | \(-0.691674\pi\) | ||||
−0.566426 | + | 0.824112i | \(0.691674\pi\) | |||||||
\(398\) | 6034.89 | 0.760054 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 249.264 | 0.0311580 | ||||||||
\(401\) | 11629.3 | 1.44823 | 0.724113 | − | 0.689682i | \(-0.242250\pi\) | ||||
0.724113 | + | 0.689682i | \(0.242250\pi\) | |||||||
\(402\) | −4534.46 | −0.562582 | ||||||||
\(403\) | 800.203 | 0.0989106 | ||||||||
\(404\) | −5285.39 | −0.650886 | ||||||||
\(405\) | −3709.34 | −0.455107 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −440.902 | −0.0536970 | ||||||||
\(408\) | −4301.49 | −0.521949 | ||||||||
\(409\) | 4320.13 | 0.522290 | 0.261145 | − | 0.965300i | \(-0.415900\pi\) | ||||
0.261145 | + | 0.965300i | \(0.415900\pi\) | |||||||
\(410\) | 83.8373 | 0.0100986 | ||||||||
\(411\) | 1555.27 | 0.186656 | ||||||||
\(412\) | 9864.19 | 1.17955 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 135.798 | 0.0161210 | ||||||||
\(415\) | −4800.36 | −0.567808 | ||||||||
\(416\) | 720.994 | 0.0849751 | ||||||||
\(417\) | −1247.06 | −0.146448 | ||||||||
\(418\) | −5211.12 | −0.609771 | ||||||||
\(419\) | 7824.02 | 0.912240 | 0.456120 | − | 0.889918i | \(-0.349239\pi\) | ||||
0.456120 | + | 0.889918i | \(0.349239\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6944.28 | 0.803904 | 0.401952 | − | 0.915661i | \(-0.368332\pi\) | ||||
0.401952 | + | 0.915661i | \(0.368332\pi\) | |||||||
\(422\) | 994.667 | 0.114738 | ||||||||
\(423\) | −91.4802 | −0.0105152 | ||||||||
\(424\) | −5884.70 | −0.674024 | ||||||||
\(425\) | 959.188 | 0.109476 | ||||||||
\(426\) | 8537.97 | 0.971047 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1530.41 | −0.172839 | ||||||||
\(429\) | 569.186 | 0.0640572 | ||||||||
\(430\) | 2584.27 | 0.289824 | ||||||||
\(431\) | 3257.36 | 0.364041 | 0.182020 | − | 0.983295i | \(-0.441736\pi\) | ||||
0.182020 | + | 0.983295i | \(0.441736\pi\) | |||||||
\(432\) | 1385.98 | 0.154359 | ||||||||
\(433\) | −16857.1 | −1.87090 | −0.935449 | − | 0.353461i | \(-0.885005\pi\) | ||||
−0.935449 | + | 0.353461i | \(0.885005\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5500.91 | 0.606319 | ||||||||
\(436\) | −4284.41 | −0.470610 | ||||||||
\(437\) | −20605.5 | −2.25559 | ||||||||
\(438\) | −2102.35 | −0.229347 | ||||||||
\(439\) | 7953.02 | 0.864640 | 0.432320 | − | 0.901720i | \(-0.357695\pi\) | ||||
0.432320 | + | 0.901720i | \(0.357695\pi\) | |||||||
\(440\) | 3009.07 | 0.326026 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 234.723 | 0.0252593 | ||||||||
\(443\) | −9709.76 | −1.04137 | −0.520683 | − | 0.853750i | \(-0.674323\pi\) | ||||
−0.520683 | + | 0.853750i | \(0.674323\pi\) | |||||||
\(444\) | −450.540 | −0.0481570 | ||||||||
\(445\) | −666.026 | −0.0709498 | ||||||||
\(446\) | 3173.14 | 0.336889 | ||||||||
\(447\) | −14349.7 | −1.51838 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11758.3 | −1.23588 | −0.617938 | − | 0.786227i | \(-0.712032\pi\) | ||||
−0.617938 | + | 0.786227i | \(0.712032\pi\) | |||||||
\(450\) | −19.2388 | −0.00201539 | ||||||||
\(451\) | −297.563 | −0.0310681 | ||||||||
\(452\) | 3221.17 | 0.335202 | ||||||||
\(453\) | 18682.9 | 1.93775 | ||||||||
\(454\) | 2524.96 | 0.261018 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13091.3 | −1.34443 | ||||||||
\(457\) | 2750.18 | 0.281505 | 0.140753 | − | 0.990045i | \(-0.455048\pi\) | ||||
0.140753 | + | 0.990045i | \(0.455048\pi\) | |||||||
\(458\) | 6224.47 | 0.635044 | ||||||||
\(459\) | 5333.36 | 0.542353 | ||||||||
\(460\) | 4839.75 | 0.490553 | ||||||||
\(461\) | −3041.43 | −0.307275 | −0.153637 | − | 0.988127i | \(-0.549099\pi\) | ||||
−0.153637 | + | 0.988127i | \(0.549099\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5422.89 | 0.544327 | 0.272163 | − | 0.962251i | \(-0.412261\pi\) | ||||
0.272163 | + | 0.962251i | \(0.412261\pi\) | |||||||
\(464\) | −2092.35 | −0.209343 | ||||||||
\(465\) | 5437.18 | 0.542243 | ||||||||
\(466\) | −3440.76 | −0.342039 | ||||||||
\(467\) | −5547.60 | −0.549705 | −0.274853 | − | 0.961486i | \(-0.588629\pi\) | ||||
−0.274853 | + | 0.961486i | \(0.588629\pi\) | |||||||
\(468\) | 10.2693 | 0.00101431 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1494.68 | 0.146690 | ||||||||
\(471\) | −6548.47 | −0.640632 | ||||||||
\(472\) | 937.064 | 0.0913810 | ||||||||
\(473\) | −9172.34 | −0.891637 | ||||||||
\(474\) | −7670.57 | −0.743294 | ||||||||
\(475\) | 2919.24 | 0.281987 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −133.541 | −0.0128185 | ||||||||
\(478\) | −1677.28 | −0.160496 | ||||||||
\(479\) | 1128.55 | 0.107651 | 0.0538254 | − | 0.998550i | \(-0.482859\pi\) | ||||
0.0538254 | + | 0.998550i | \(0.482859\pi\) | |||||||
\(480\) | 4898.97 | 0.465847 | ||||||||
\(481\) | 60.4410 | 0.00572946 | ||||||||
\(482\) | −3804.68 | −0.359540 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2956.68 | 0.277674 | ||||||||
\(485\) | −5105.53 | −0.478001 | ||||||||
\(486\) | −215.904 | −0.0201515 | ||||||||
\(487\) | 4806.18 | 0.447205 | 0.223602 | − | 0.974680i | \(-0.428218\pi\) | ||||
0.223602 | + | 0.974680i | \(0.428218\pi\) | |||||||
\(488\) | 18286.2 | 1.69626 | ||||||||
\(489\) | 10299.9 | 0.952508 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12452.1 | −1.14451 | −0.572255 | − | 0.820076i | \(-0.693931\pi\) | ||||
−0.572255 | + | 0.820076i | \(0.693931\pi\) | |||||||
\(492\) | −304.069 | −0.0278627 | ||||||||
\(493\) | −8051.53 | −0.735543 | ||||||||
\(494\) | 714.367 | 0.0650625 | ||||||||
\(495\) | 68.2843 | 0.00620030 | ||||||||
\(496\) | −2068.11 | −0.187219 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7981.75 | −0.718214 | ||||||||
\(499\) | −11797.4 | −1.05836 | −0.529180 | − | 0.848509i | \(-0.677501\pi\) | ||||
−0.529180 | + | 0.848509i | \(0.677501\pi\) | |||||||
\(500\) | −685.660 | −0.0613273 | ||||||||
\(501\) | 4924.94 | 0.439182 | ||||||||
\(502\) | 6046.52 | 0.537588 | ||||||||
\(503\) | 2900.55 | 0.257116 | 0.128558 | − | 0.991702i | \(-0.458965\pi\) | ||||
0.128558 | + | 0.991702i | \(0.458965\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4817.79 | 0.424533 | ||||||||
\(506\) | 7875.09 | 0.691878 | ||||||||
\(507\) | 11440.1 | 1.00211 | ||||||||
\(508\) | −8554.98 | −0.747177 | ||||||||
\(509\) | 9486.85 | 0.826124 | 0.413062 | − | 0.910703i | \(-0.364459\pi\) | ||||
0.413062 | + | 0.910703i | \(0.364459\pi\) | |||||||
\(510\) | 1594.88 | 0.138476 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −3569.14 | −0.308076 | ||||||||
\(513\) | 16231.8 | 1.39698 | ||||||||
\(514\) | −5534.65 | −0.474947 | ||||||||
\(515\) | −8991.50 | −0.769346 | ||||||||
\(516\) | −9372.86 | −0.799645 | ||||||||
\(517\) | −5305.06 | −0.451289 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14167.9 | 1.19827 | ||||||||
\(520\) | −412.498 | −0.0347870 | ||||||||
\(521\) | −20353.0 | −1.71148 | −0.855740 | − | 0.517406i | \(-0.826898\pi\) | ||||
−0.855740 | + | 0.517406i | \(0.826898\pi\) | |||||||
\(522\) | 161.493 | 0.0135409 | ||||||||
\(523\) | 9228.89 | 0.771608 | 0.385804 | − | 0.922581i | \(-0.373924\pi\) | ||||
0.385804 | + | 0.922581i | \(0.373924\pi\) | |||||||
\(524\) | 9070.71 | 0.756213 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11298.0 | −0.936535 | ||||||||
\(527\) | −7958.25 | −0.657811 | ||||||||
\(528\) | −1471.05 | −0.121248 | ||||||||
\(529\) | 18972.2 | 1.55932 | ||||||||
\(530\) | 2181.90 | 0.178822 | ||||||||
\(531\) | 21.2646 | 0.00173787 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.7915 | 0.00331496 | ||||||||
\(534\) | −1107.43 | −0.0897437 | ||||||||
\(535\) | 1395.01 | 0.112732 | ||||||||
\(536\) | −11663.7 | −0.939914 | ||||||||
\(537\) | 7518.20 | 0.604161 | ||||||||
\(538\) | 678.626 | 0.0543822 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3812.47 | −0.303819 | ||||||||
\(541\) | −697.274 | −0.0554125 | −0.0277062 | − | 0.999616i | \(-0.508820\pi\) | ||||
−0.0277062 | + | 0.999616i | \(0.508820\pi\) | |||||||
\(542\) | −12985.3 | −1.02909 | ||||||||
\(543\) | −14213.9 | −1.12335 | ||||||||
\(544\) | −7170.48 | −0.565132 | ||||||||
\(545\) | 3905.37 | 0.306950 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8032.62 | −0.627879 | −0.313940 | − | 0.949443i | \(-0.601649\pi\) | ||||
−0.313940 | + | 0.949443i | \(0.601649\pi\) | |||||||
\(548\) | 1627.25 | 0.126848 | ||||||||
\(549\) | 414.965 | 0.0322591 | ||||||||
\(550\) | −1115.69 | −0.0864963 | ||||||||
\(551\) | −24504.4 | −1.89460 | ||||||||
\(552\) | 19783.7 | 1.52546 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6612.66 | 0.507121 | ||||||||
\(555\) | 410.681 | 0.0314098 | ||||||||
\(556\) | −1304.77 | −0.0995228 | ||||||||
\(557\) | 13586.7 | 1.03355 | 0.516776 | − | 0.856120i | \(-0.327132\pi\) | ||||
0.516776 | + | 0.856120i | \(0.327132\pi\) | |||||||
\(558\) | 159.622 | 0.0121099 | ||||||||
\(559\) | 1257.39 | 0.0951376 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5660.71 | −0.426017 | ||||||||
\(562\) | −2037.10 | −0.152900 | ||||||||
\(563\) | 17215.8 | 1.28874 | 0.644369 | − | 0.764715i | \(-0.277120\pi\) | ||||
0.644369 | + | 0.764715i | \(0.277120\pi\) | |||||||
\(564\) | −5421.04 | −0.404729 | ||||||||
\(565\) | −2936.19 | −0.218631 | ||||||||
\(566\) | −7594.88 | −0.564022 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 21961.6 | 1.62234 | ||||||||
\(569\) | −18441.5 | −1.35871 | −0.679357 | − | 0.733808i | \(-0.737741\pi\) | ||||
−0.679357 | + | 0.733808i | \(0.737741\pi\) | |||||||
\(570\) | 4853.94 | 0.356683 | ||||||||
\(571\) | −10780.3 | −0.790093 | −0.395046 | − | 0.918661i | \(-0.629271\pi\) | ||||
−0.395046 | + | 0.918661i | \(0.629271\pi\) | |||||||
\(572\) | 595.529 | 0.0435320 | ||||||||
\(573\) | 18320.9 | 1.33572 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4411.57 | −0.319957 | ||||||||
\(576\) | 105.113 | 0.00760366 | ||||||||
\(577\) | −12963.0 | −0.935279 | −0.467640 | − | 0.883919i | \(-0.654895\pi\) | ||||
−0.467640 | + | 0.883919i | \(0.654895\pi\) | |||||||
\(578\) | 5456.58 | 0.392671 | ||||||||
\(579\) | 8544.25 | 0.613276 | ||||||||
\(580\) | 5755.51 | 0.412042 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −8489.18 | −0.604619 | ||||||||
\(583\) | −7744.20 | −0.550141 | ||||||||
\(584\) | −5407.72 | −0.383173 | ||||||||
\(585\) | −9.36075 | −0.000661571 0 | ||||||||
\(586\) | −11074.0 | −0.780651 | ||||||||
\(587\) | −16181.8 | −1.13781 | −0.568905 | − | 0.822403i | \(-0.692633\pi\) | ||||
−0.568905 | + | 0.822403i | \(0.692633\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24220.5 | −1.69438 | ||||||||
\(590\) | −347.439 | −0.0242438 | ||||||||
\(591\) | −3636.80 | −0.253127 | ||||||||
\(592\) | −156.208 | −0.0108448 | ||||||||
\(593\) | 747.630 | 0.0517732 | 0.0258866 | − | 0.999665i | \(-0.491759\pi\) | ||||
0.0258866 | + | 0.999665i | \(0.491759\pi\) | |||||||
\(594\) | −6203.53 | −0.428508 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15013.8 | −1.03186 | ||||||||
\(597\) | 19951.5 | 1.36777 | ||||||||
\(598\) | −1079.56 | −0.0738233 | ||||||||
\(599\) | 3849.86 | 0.262606 | 0.131303 | − | 0.991342i | \(-0.458084\pi\) | ||||
0.131303 | + | 0.991342i | \(0.458084\pi\) | |||||||
\(600\) | −2802.82 | −0.190708 | ||||||||
\(601\) | 1808.82 | 0.122768 | 0.0613838 | − | 0.998114i | \(-0.480449\pi\) | ||||
0.0613838 | + | 0.998114i | \(0.480449\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −264.682 | −0.0178751 | ||||||||
\(604\) | 19547.6 | 1.31685 | ||||||||
\(605\) | −2695.10 | −0.181110 | ||||||||
\(606\) | 8010.74 | 0.536987 | ||||||||
\(607\) | 536.092 | 0.0358473 | 0.0179237 | − | 0.999839i | \(-0.494294\pi\) | ||||
0.0179237 | + | 0.999839i | \(0.494294\pi\) | |||||||
\(608\) | −21823.0 | −1.45566 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6780.04 | −0.450026 | ||||||||
\(611\) | 727.245 | 0.0481525 | ||||||||
\(612\) | −102.131 | −0.00674573 | ||||||||
\(613\) | 14736.0 | 0.970931 | 0.485465 | − | 0.874256i | \(-0.338650\pi\) | ||||
0.485465 | + | 0.874256i | \(0.338650\pi\) | |||||||
\(614\) | 3281.68 | 0.215697 | ||||||||
\(615\) | 277.168 | 0.0181731 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9604.91 | 0.626709 | 0.313354 | − | 0.949636i | \(-0.398547\pi\) | ||||
0.313354 | + | 0.949636i | \(0.398547\pi\) | |||||||
\(618\) | −14950.5 | −0.973138 | ||||||||
\(619\) | −8594.22 | −0.558047 | −0.279023 | − | 0.960284i | \(-0.590011\pi\) | ||||
−0.279023 | + | 0.960284i | \(0.590011\pi\) | |||||||
\(620\) | 5688.82 | 0.368498 | ||||||||
\(621\) | −24529.6 | −1.58509 | ||||||||
\(622\) | −3364.98 | −0.216918 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 201.659 | 0.0129372 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −2424.34 | −0.154786 | ||||||||
\(627\) | −17228.1 | −1.09733 | ||||||||
\(628\) | −6851.55 | −0.435361 | ||||||||
\(629\) | −601.102 | −0.0381042 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14803.3 | −0.933933 | −0.466966 | − | 0.884275i | \(-0.654653\pi\) | ||||
−0.466966 | + | 0.884275i | \(0.654653\pi\) | |||||||
\(632\) | −19730.5 | −1.24183 | ||||||||
\(633\) | 3288.39 | 0.206480 | ||||||||
\(634\) | −8154.82 | −0.510835 | ||||||||
\(635\) | 7798.12 | 0.487337 | ||||||||
\(636\) | −7913.50 | −0.493381 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9365.19 | 0.581146 | ||||||||
\(639\) | 498.372 | 0.0308533 | ||||||||
\(640\) | 5758.15 | 0.355642 | ||||||||
\(641\) | −9290.31 | −0.572458 | −0.286229 | − | 0.958161i | \(-0.592402\pi\) | ||||
−0.286229 | + | 0.958161i | \(0.592402\pi\) | |||||||
\(642\) | 2319.55 | 0.142594 | ||||||||
\(643\) | −1861.78 | −0.114186 | −0.0570928 | − | 0.998369i | \(-0.518183\pi\) | ||||
−0.0570928 | + | 0.998369i | \(0.518183\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8543.64 | 0.521559 | ||||||||
\(646\) | −7104.58 | −0.432703 | ||||||||
\(647\) | 29527.4 | 1.79419 | 0.897095 | − | 0.441837i | \(-0.145673\pi\) | ||||
0.897095 | + | 0.441837i | \(0.145673\pi\) | |||||||
\(648\) | −15864.7 | −0.961764 | ||||||||
\(649\) | 1233.17 | 0.0745855 | ||||||||
\(650\) | 152.944 | 0.00922915 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10776.6 | 0.647306 | ||||||||
\(653\) | 5192.55 | 0.311180 | 0.155590 | − | 0.987822i | \(-0.450272\pi\) | ||||
0.155590 | + | 0.987822i | \(0.450272\pi\) | |||||||
\(654\) | 6493.61 | 0.388258 | ||||||||
\(655\) | −8268.23 | −0.493231 | ||||||||
\(656\) | −105.425 | −0.00627461 | ||||||||
\(657\) | −122.717 | −0.00728711 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11740.1 | −0.693976 | −0.346988 | − | 0.937870i | \(-0.612795\pi\) | ||||
−0.346988 | + | 0.937870i | \(0.612795\pi\) | |||||||
\(660\) | 4046.47 | 0.238649 | ||||||||
\(661\) | 8792.50 | 0.517381 | 0.258690 | − | 0.965960i | \(-0.416709\pi\) | ||||
0.258690 | + | 0.965960i | \(0.416709\pi\) | |||||||
\(662\) | 9156.39 | 0.537573 | ||||||||
\(663\) | 775.999 | 0.0454559 | ||||||||
\(664\) | −20530.9 | −1.19993 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.0565 | 0.000701474 0 | ||||||||
\(667\) | 37031.3 | 2.14971 | ||||||||
\(668\) | 5152.88 | 0.298460 | ||||||||
\(669\) | 10490.4 | 0.606254 | ||||||||
\(670\) | 4324.59 | 0.249364 | ||||||||
\(671\) | 24064.4 | 1.38449 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30366.5 | 1.73929 | 0.869646 | − | 0.493676i | \(-0.164347\pi\) | ||||
0.869646 | + | 0.493676i | \(0.164347\pi\) | |||||||
\(674\) | 768.728 | 0.0439322 | ||||||||
\(675\) | 3475.18 | 0.198162 | ||||||||
\(676\) | 11969.5 | 0.681015 | ||||||||
\(677\) | −17416.9 | −0.988754 | −0.494377 | − | 0.869248i | \(-0.664604\pi\) | ||||
−0.494377 | + | 0.869248i | \(0.664604\pi\) | |||||||
\(678\) | −4882.13 | −0.276544 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4102.41 | 0.231353 | ||||||||
\(681\) | 8347.55 | 0.469719 | ||||||||
\(682\) | 9256.68 | 0.519731 | ||||||||
\(683\) | 8828.32 | 0.494592 | 0.247296 | − | 0.968940i | \(-0.420458\pi\) | ||||
0.247296 | + | 0.968940i | \(0.420458\pi\) | |||||||
\(684\) | −310.829 | −0.0173755 | ||||||||
\(685\) | −1483.29 | −0.0827351 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20578.2 | 1.14281 | ||||||||
\(688\) | −3249.69 | −0.180078 | ||||||||
\(689\) | 1061.61 | 0.0586999 | ||||||||
\(690\) | −7335.31 | −0.404711 | ||||||||
\(691\) | 10631.0 | 0.585273 | 0.292636 | − | 0.956224i | \(-0.405467\pi\) | ||||
0.292636 | + | 0.956224i | \(0.405467\pi\) | |||||||
\(692\) | 14823.6 | 0.814319 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12366.3 | 0.676395 | ||||||||
\(695\) | 1189.34 | 0.0649126 | ||||||||
\(696\) | 23527.2 | 1.28131 | ||||||||
\(697\) | −405.683 | −0.0220464 | ||||||||
\(698\) | 1050.04 | 0.0569407 | ||||||||
\(699\) | −11375.2 | −0.615523 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30120.7 | 1.62289 | 0.811443 | − | 0.584431i | \(-0.198682\pi\) | ||||
0.811443 | + | 0.584431i | \(0.198682\pi\) | |||||||
\(702\) | 850.411 | 0.0457218 | ||||||||
\(703\) | −1829.42 | −0.0981480 | ||||||||
\(704\) | 6095.65 | 0.326333 | ||||||||
\(705\) | 4941.44 | 0.263979 | ||||||||
\(706\) | −10507.6 | −0.560142 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1260.12 | 0.0668904 | ||||||||
\(709\) | 4414.94 | 0.233860 | 0.116930 | − | 0.993140i | \(-0.462695\pi\) | ||||
0.116930 | + | 0.993140i | \(0.462695\pi\) | |||||||
\(710\) | −8142.81 | −0.430415 | ||||||||
\(711\) | −447.741 | −0.0236169 | ||||||||
\(712\) | −2848.56 | −0.149936 | ||||||||
\(713\) | 36602.2 | 1.92253 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −542.843 | −0.0283932 | ||||||||
\(716\) | 7866.16 | 0.410576 | ||||||||
\(717\) | −5545.12 | −0.288823 | ||||||||
\(718\) | −16489.1 | −0.857058 | ||||||||
\(719\) | 17136.0 | 0.888822 | 0.444411 | − | 0.895823i | \(-0.353413\pi\) | ||||
0.444411 | + | 0.895823i | \(0.353413\pi\) | |||||||
\(720\) | 24.1926 | 0.00125223 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −10745.5 | −0.553886 | ||||||||
\(723\) | −12578.4 | −0.647018 | ||||||||
\(724\) | −14871.8 | −0.763405 | ||||||||
\(725\) | −5246.32 | −0.268750 | ||||||||
\(726\) | −4481.26 | −0.229084 | ||||||||
\(727\) | −3271.77 | −0.166909 | −0.0834546 | − | 0.996512i | \(-0.526595\pi\) | ||||
−0.0834546 | + | 0.996512i | \(0.526595\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19316.6 | 0.981386 | ||||||||
\(730\) | 2005.05 | 0.101658 | ||||||||
\(731\) | −12505.1 | −0.632719 | ||||||||
\(732\) | 24590.5 | 1.24165 | ||||||||
\(733\) | 4469.84 | 0.225235 | 0.112618 | − | 0.993638i | \(-0.464077\pi\) | ||||
0.112618 | + | 0.993638i | \(0.464077\pi\) | |||||||
\(734\) | −3562.16 | −0.179130 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 32979.1 | 1.65166 | ||||||||
\(737\) | −15349.3 | −0.767161 | ||||||||
\(738\) | 8.13694 | 0.000405860 0 | ||||||||
\(739\) | −2475.20 | −0.123209 | −0.0616046 | − | 0.998101i | \(-0.519622\pi\) | ||||
−0.0616046 | + | 0.998101i | \(0.519622\pi\) | |||||||
\(740\) | 429.688 | 0.0213455 | ||||||||
\(741\) | 2361.71 | 0.117084 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9240.48 | 0.456259 | 0.228129 | − | 0.973631i | \(-0.426739\pi\) | ||||
0.228129 | + | 0.973631i | \(0.426739\pi\) | |||||||
\(744\) | 23254.6 | 1.14591 | ||||||||
\(745\) | 13685.6 | 0.673020 | ||||||||
\(746\) | −304.511 | −0.0149450 | ||||||||
\(747\) | −465.905 | −0.0228200 | ||||||||
\(748\) | −5922.70 | −0.289513 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1039.21 | 0.0505956 | ||||||||
\(751\) | 5052.47 | 0.245496 | 0.122748 | − | 0.992438i | \(-0.460829\pi\) | ||||
0.122748 | + | 0.992438i | \(0.460829\pi\) | |||||||
\(752\) | −1879.55 | −0.0911437 | ||||||||
\(753\) | 19989.9 | 0.967427 | ||||||||
\(754\) | −1283.83 | −0.0620082 | ||||||||
\(755\) | −17818.2 | −0.858903 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37779.2 | −1.81388 | −0.906942 | − | 0.421256i | \(-0.861589\pi\) | ||||
−0.906942 | + | 0.421256i | \(0.861589\pi\) | |||||||
\(758\) | 7240.32 | 0.346939 | ||||||||
\(759\) | 26035.2 | 1.24508 | ||||||||
\(760\) | 12485.5 | 0.595914 | ||||||||
\(761\) | 7502.70 | 0.357388 | 0.178694 | − | 0.983905i | \(-0.442813\pi\) | ||||
0.178694 | + | 0.983905i | \(0.442813\pi\) | |||||||
\(762\) | 12966.3 | 0.616428 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 19168.9 | 0.907729 | ||||||||
\(765\) | 93.0952 | 0.00439982 | ||||||||
\(766\) | −2199.60 | −0.103753 | ||||||||
\(767\) | −169.049 | −0.00795826 | ||||||||
\(768\) | 18658.9 | 0.876684 | ||||||||
\(769\) | 24209.4 | 1.13526 | 0.567628 | − | 0.823285i | \(-0.307861\pi\) | ||||
0.567628 | + | 0.823285i | \(0.307861\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18297.7 | −0.854701 | ||||||||
\(772\) | 8939.70 | 0.416770 | ||||||||
\(773\) | 7520.99 | 0.349950 | 0.174975 | − | 0.984573i | \(-0.444016\pi\) | ||||
0.174975 | + | 0.984573i | \(0.444016\pi\) | |||||||
\(774\) | 250.819 | 0.0116480 | ||||||||
\(775\) | −5185.53 | −0.240348 | ||||||||
\(776\) | −21836.1 | −1.01014 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7267.67 | −0.334908 | ||||||||
\(779\) | −1234.67 | −0.0567866 | ||||||||
\(780\) | −554.710 | −0.0254638 | ||||||||
\(781\) | 28901.3 | 1.32416 | ||||||||
\(782\) | 10736.5 | 0.490967 | ||||||||
\(783\) | −29171.0 | −1.33140 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6245.39 | 0.283959 | ||||||||
\(786\) | −13747.9 | −0.623883 | ||||||||
\(787\) | −16121.4 | −0.730196 | −0.365098 | − | 0.930969i | \(-0.618965\pi\) | ||||
−0.365098 | + | 0.930969i | \(0.618965\pi\) | |||||||
\(788\) | −3805.12 | −0.172020 | ||||||||
\(789\) | −37351.5 | −1.68536 | ||||||||
\(790\) | 7315.56 | 0.329463 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 292.049 | 0.0131029 | ||||||||
\(793\) | −3298.87 | −0.147725 | ||||||||
\(794\) | 14210.3 | 0.635146 | ||||||||
\(795\) | 7213.39 | 0.321802 | ||||||||
\(796\) | 20874.9 | 0.929510 | ||||||||
\(797\) | −32223.0 | −1.43212 | −0.716058 | − | 0.698041i | \(-0.754056\pi\) | ||||
−0.716058 | + | 0.698041i | \(0.754056\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7232.65 | −0.320241 | ||||||||
\(800\) | −4672.23 | −0.206486 | ||||||||
\(801\) | −64.6420 | −0.00285145 | ||||||||
\(802\) | −18441.5 | −0.811962 | ||||||||
\(803\) | −7116.50 | −0.312747 | ||||||||
\(804\) | −15684.8 | −0.688011 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1268.95 | −0.0554552 | ||||||||
\(807\) | 2243.55 | 0.0978646 | ||||||||
\(808\) | 20605.5 | 0.897151 | ||||||||
\(809\) | −24544.4 | −1.06667 | −0.533334 | − | 0.845905i | \(-0.679061\pi\) | ||||
−0.533334 | + | 0.845905i | \(0.679061\pi\) | |||||||
\(810\) | 5882.21 | 0.255160 | ||||||||
\(811\) | 18783.9 | 0.813308 | 0.406654 | − | 0.913582i | \(-0.366695\pi\) | ||||
0.406654 | + | 0.913582i | \(0.366695\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −42929.8 | −1.85192 | ||||||||
\(814\) | 699.176 | 0.0301058 | ||||||||
\(815\) | −9823.18 | −0.422197 | ||||||||
\(816\) | −2005.55 | −0.0860396 | ||||||||
\(817\) | −38058.6 | −1.62974 | ||||||||
\(818\) | −6850.80 | −0.292827 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 289.996 | 0.0123501 | ||||||||
\(821\) | 18085.1 | 0.768786 | 0.384393 | − | 0.923170i | \(-0.374411\pi\) | ||||
0.384393 | + | 0.923170i | \(0.374411\pi\) | |||||||
\(822\) | −2466.33 | −0.104651 | ||||||||
\(823\) | 7435.18 | 0.314914 | 0.157457 | − | 0.987526i | \(-0.449670\pi\) | ||||
0.157457 | + | 0.987526i | \(0.449670\pi\) | |||||||
\(824\) | −38456.3 | −1.62583 | ||||||||
\(825\) | −3688.48 | −0.155656 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26487.2 | 1.11373 | 0.556863 | − | 0.830604i | \(-0.312005\pi\) | ||||
0.556863 | + | 0.830604i | \(0.312005\pi\) | |||||||
\(828\) | 469.728 | 0.0197152 | ||||||||
\(829\) | −19377.1 | −0.811813 | −0.405906 | − | 0.913915i | \(-0.633044\pi\) | ||||
−0.405906 | + | 0.913915i | \(0.633044\pi\) | |||||||
\(830\) | 7612.34 | 0.318347 | ||||||||
\(831\) | 21861.6 | 0.912600 | ||||||||
\(832\) | −835.622 | −0.0348197 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1977.56 | 0.0821073 | ||||||||
\(835\) | −4697.01 | −0.194667 | ||||||||
\(836\) | −18025.4 | −0.745721 | ||||||||
\(837\) | −28833.1 | −1.19070 | ||||||||
\(838\) | −12407.2 | −0.511456 | ||||||||
\(839\) | −4645.97 | −0.191176 | −0.0955880 | − | 0.995421i | \(-0.530473\pi\) | ||||
−0.0955880 | + | 0.995421i | \(0.530473\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19649.2 | 0.805658 | ||||||||
\(842\) | −11012.1 | −0.450717 | ||||||||
\(843\) | −6734.69 | −0.275154 | ||||||||
\(844\) | 3440.58 | 0.140320 | ||||||||
\(845\) | −10910.6 | −0.444184 | ||||||||
\(846\) | 145.068 | 0.00589544 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2743.72 | −0.111108 | ||||||||
\(849\) | −25108.8 | −1.01500 | ||||||||
\(850\) | −1521.07 | −0.0613791 | ||||||||
\(851\) | 2764.64 | 0.111364 | ||||||||
\(852\) | 29533.1 | 1.18754 | ||||||||
\(853\) | 32566.5 | 1.30722 | 0.653609 | − | 0.756833i | \(-0.273254\pi\) | ||||
0.653609 | + | 0.756833i | \(0.273254\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 283.330 | 0.0113330 | ||||||||
\(856\) | 5966.42 | 0.238234 | ||||||||
\(857\) | 134.941 | 0.00537865 | 0.00268932 | − | 0.999996i | \(-0.499144\pi\) | ||||
0.00268932 | + | 0.999996i | \(0.499144\pi\) | |||||||
\(858\) | −902.607 | −0.0359143 | ||||||||
\(859\) | −10380.9 | −0.412331 | −0.206165 | − | 0.978517i | \(-0.566098\pi\) | ||||
−0.206165 | + | 0.978517i | \(0.566098\pi\) | |||||||
\(860\) | 8939.06 | 0.354441 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5165.48 | −0.204103 | ||||||||
\(863\) | 25349.3 | 0.999883 | 0.499941 | − | 0.866059i | \(-0.333355\pi\) | ||||
0.499941 | + | 0.866059i | \(0.333355\pi\) | |||||||
\(864\) | −25979.0 | −1.02294 | ||||||||
\(865\) | −13512.2 | −0.531130 | ||||||||
\(866\) | 26731.7 | 1.04894 | ||||||||
\(867\) | 18039.6 | 0.706639 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25965.1 | −1.01359 | ||||||||
\(870\) | −8723.28 | −0.339939 | ||||||||
\(871\) | 2104.15 | 0.0818559 | ||||||||
\(872\) | 16703.1 | 0.648667 | ||||||||
\(873\) | −495.524 | −0.0192107 | ||||||||
\(874\) | 32675.9 | 1.26462 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7272.08 | −0.280480 | ||||||||
\(877\) | −22519.4 | −0.867075 | −0.433537 | − | 0.901136i | \(-0.642735\pi\) | ||||
−0.433537 | + | 0.901136i | \(0.642735\pi\) | |||||||
\(878\) | −12611.8 | −0.484769 | ||||||||
\(879\) | −36610.8 | −1.40484 | ||||||||
\(880\) | 1402.96 | 0.0537431 | ||||||||
\(881\) | −12419.9 | −0.474958 | −0.237479 | − | 0.971393i | \(-0.576321\pi\) | ||||
−0.237479 | + | 0.971393i | \(0.576321\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46011.8 | −1.75359 | −0.876794 | − | 0.480866i | \(-0.840322\pi\) | ||||
−0.876794 | + | 0.480866i | \(0.840322\pi\) | |||||||
\(884\) | 811.913 | 0.0308910 | ||||||||
\(885\) | −1148.64 | −0.0436284 | ||||||||
\(886\) | 15397.6 | 0.583852 | ||||||||
\(887\) | −28086.7 | −1.06320 | −0.531600 | − | 0.846995i | \(-0.678409\pi\) | ||||
−0.531600 | + | 0.846995i | \(0.678409\pi\) | |||||||
\(888\) | 1756.46 | 0.0663774 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1056.17 | 0.0397787 | ||||||||
\(891\) | −20877.7 | −0.784994 | ||||||||
\(892\) | 10976.0 | 0.411998 | ||||||||
\(893\) | −22012.2 | −0.824871 | ||||||||
\(894\) | 22755.5 | 0.851296 | ||||||||
\(895\) | −7170.24 | −0.267793 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3569.03 | −0.132850 | ||||||||
\(898\) | 18646.2 | 0.692907 | ||||||||
\(899\) | 43528.0 | 1.61484 | ||||||||
\(900\) | −66.5476 | −0.00246473 | ||||||||
\(901\) | −10558.0 | −0.390388 | ||||||||
\(902\) | 471.872 | 0.0174187 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12558.0 | −0.462026 | ||||||||
\(905\) | 13556.1 | 0.497921 | ||||||||
\(906\) | −29627.1 | −1.08642 | ||||||||
\(907\) | −30458.8 | −1.11507 | −0.557534 | − | 0.830154i | \(-0.688252\pi\) | ||||
−0.557534 | + | 0.830154i | \(0.688252\pi\) | |||||||
\(908\) | 8733.90 | 0.319212 | ||||||||
\(909\) | 467.597 | 0.0170618 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26850.4 | −0.976502 | −0.488251 | − | 0.872703i | \(-0.662365\pi\) | ||||
−0.488251 | + | 0.872703i | \(0.662365\pi\) | |||||||
\(912\) | −6103.79 | −0.221619 | ||||||||
\(913\) | −27018.5 | −0.979387 | ||||||||
\(914\) | −4361.20 | −0.157829 | ||||||||
\(915\) | −22415.0 | −0.809853 | ||||||||
\(916\) | 21530.6 | 0.776628 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −8457.57 | −0.304076 | ||||||||
\(919\) | −38095.8 | −1.36743 | −0.683714 | − | 0.729750i | \(-0.739636\pi\) | ||||
−0.683714 | + | 0.729750i | \(0.739636\pi\) | |||||||
\(920\) | −18868.1 | −0.676156 | ||||||||
\(921\) | 10849.3 | 0.388161 | ||||||||
\(922\) | 4823.06 | 0.172277 | ||||||||
\(923\) | −3961.93 | −0.141288 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −391.674 | −0.0139223 | ||||||||
\(926\) | −8599.55 | −0.305182 | ||||||||
\(927\) | −872.682 | −0.0309198 | ||||||||
\(928\) | 39219.3 | 1.38732 | ||||||||
\(929\) | 36355.0 | 1.28393 | 0.641964 | − | 0.766735i | \(-0.278120\pi\) | ||||
0.641964 | + | 0.766735i | \(0.278120\pi\) | |||||||
\(930\) | −8622.20 | −0.304014 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −11901.7 | −0.418297 | ||||||||
\(933\) | −11124.7 | −0.390360 | ||||||||
\(934\) | 8797.31 | 0.308198 | ||||||||
\(935\) | 5398.72 | 0.188831 | ||||||||
\(936\) | −40.0355 | −0.00139808 | ||||||||
\(937\) | 37878.5 | 1.32064 | 0.660318 | − | 0.750986i | \(-0.270421\pi\) | ||||
0.660318 | + | 0.750986i | \(0.270421\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8014.93 | −0.278549 | ||||||||
\(940\) | 5170.14 | 0.179395 | ||||||||
\(941\) | 54125.6 | 1.87507 | 0.937536 | − | 0.347887i | \(-0.113101\pi\) | ||||
0.937536 | + | 0.347887i | \(0.113101\pi\) | |||||||
\(942\) | 10384.5 | 0.359177 | ||||||||
\(943\) | 1865.85 | 0.0644330 | ||||||||
\(944\) | 436.902 | 0.0150635 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14545.4 | 0.499906 | ||||||||
\(947\) | −38345.9 | −1.31581 | −0.657906 | − | 0.753100i | \(-0.728557\pi\) | ||||
−0.657906 | + | 0.753100i | \(0.728557\pi\) | |||||||
\(948\) | −26532.7 | −0.909012 | ||||||||
\(949\) | 975.566 | 0.0333701 | ||||||||
\(950\) | −4629.29 | −0.158099 | ||||||||
\(951\) | −26960.0 | −0.919282 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15096.4 | −0.513137 | −0.256569 | − | 0.966526i | \(-0.582592\pi\) | ||||
−0.256569 | + | 0.966526i | \(0.582592\pi\) | |||||||
\(954\) | 211.767 | 0.00718680 | ||||||||
\(955\) | −17473.0 | −0.592055 | ||||||||
\(956\) | −5801.76 | −0.196279 | ||||||||
\(957\) | 30961.5 | 1.04581 | ||||||||
\(958\) | −1789.64 | −0.0603556 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −5677.84 | −0.190887 | ||||||||
\(961\) | 13232.6 | 0.444182 | ||||||||
\(962\) | −95.8465 | −0.00321228 | ||||||||
\(963\) | 135.395 | 0.00453068 | ||||||||
\(964\) | −13160.5 | −0.439701 | ||||||||
\(965\) | −8148.81 | −0.271833 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6917.06 | 0.230029 | 0.115014 | − | 0.993364i | \(-0.463309\pi\) | ||||
0.115014 | + | 0.993364i | \(0.463309\pi\) | |||||||
\(968\) | −11526.8 | −0.382734 | ||||||||
\(969\) | −23487.9 | −0.778678 | ||||||||
\(970\) | 8096.29 | 0.267996 | ||||||||
\(971\) | 39517.7 | 1.30606 | 0.653029 | − | 0.757333i | \(-0.273498\pi\) | ||||
0.653029 | + | 0.757333i | \(0.273498\pi\) | |||||||
\(972\) | −746.820 | −0.0246443 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −7621.57 | −0.250730 | ||||||||
\(975\) | 505.635 | 0.0166085 | ||||||||
\(976\) | 8525.85 | 0.279616 | ||||||||
\(977\) | −38858.4 | −1.27246 | −0.636229 | − | 0.771500i | \(-0.719507\pi\) | ||||
−0.636229 | + | 0.771500i | \(0.719507\pi\) | |||||||
\(978\) | −16333.4 | −0.534034 | ||||||||
\(979\) | −3748.68 | −0.122378 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 379.040 | 0.0123362 | ||||||||
\(982\) | 19746.3 | 0.641681 | ||||||||
\(983\) | −510.230 | −0.0165552 | −0.00827762 | − | 0.999966i | \(-0.502635\pi\) | ||||
−0.00827762 | + | 0.999966i | \(0.502635\pi\) | |||||||
\(984\) | 1185.43 | 0.0384047 | ||||||||
\(985\) | 3468.48 | 0.112198 | ||||||||
\(986\) | 12768.0 | 0.412390 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2471.02 | 0.0795683 | ||||||||
\(989\) | 57514.4 | 1.84919 | ||||||||
\(990\) | −108.284 | −0.00347626 | ||||||||
\(991\) | −36222.8 | −1.16111 | −0.580553 | − | 0.814223i | \(-0.697164\pi\) | ||||
−0.580553 | + | 0.814223i | \(0.697164\pi\) | |||||||
\(992\) | 38764.9 | 1.24071 | ||||||||
\(993\) | 30271.2 | 0.967400 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19028.1 | −0.606262 | ||||||||
\(996\) | −27609.1 | −0.878341 | ||||||||
\(997\) | −20856.1 | −0.662505 | −0.331253 | − | 0.943542i | \(-0.607471\pi\) | ||||
−0.331253 | + | 0.943542i | \(0.607471\pi\) | |||||||
\(998\) | 18708.1 | 0.593381 | ||||||||
\(999\) | −2177.82 | −0.0689721 |
(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 | 245.4.a.g.1.2 | 2 | ||
3.2 | odd | 2 | 2205.4.a.bf.1.1 | 2 | |||
5.4 | even | 2 | 1225.4.a.x.1.1 | 2 | |||
7.2 | even | 3 | 35.4.e.b.11.1 | ✓ | 4 | ||
7.3 | odd | 6 | 245.4.e.l.226.1 | 4 | |||
7.4 | even | 3 | 35.4.e.b.16.1 | yes | 4 | ||
7.5 | odd | 6 | 245.4.e.l.116.1 | 4 | |||
7.6 | odd | 2 | 245.4.a.h.1.2 | 2 | |||
21.2 | odd | 6 | 315.4.j.c.46.2 | 4 | |||
21.11 | odd | 6 | 315.4.j.c.226.2 | 4 | |||
21.20 | even | 2 | 2205.4.a.bg.1.1 | 2 | |||
28.11 | odd | 6 | 560.4.q.i.401.1 | 4 | |||
28.23 | odd | 6 | 560.4.q.i.81.1 | 4 | |||
35.2 | odd | 12 | 175.4.k.c.74.2 | 8 | |||
35.4 | even | 6 | 175.4.e.c.51.2 | 4 | |||
35.9 | even | 6 | 175.4.e.c.151.2 | 4 | |||
35.18 | odd | 12 | 175.4.k.c.149.2 | 8 | |||
35.23 | odd | 12 | 175.4.k.c.74.3 | 8 | |||
35.32 | odd | 12 | 175.4.k.c.149.3 | 8 | |||
35.34 | odd | 2 | 1225.4.a.v.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.e.b.11.1 | ✓ | 4 | 7.2 | even | 3 | ||
35.4.e.b.16.1 | yes | 4 | 7.4 | even | 3 | ||
175.4.e.c.51.2 | 4 | 35.4 | even | 6 | |||
175.4.e.c.151.2 | 4 | 35.9 | even | 6 | |||
175.4.k.c.74.2 | 8 | 35.2 | odd | 12 | |||
175.4.k.c.74.3 | 8 | 35.23 | odd | 12 | |||
175.4.k.c.149.2 | 8 | 35.18 | odd | 12 | |||
175.4.k.c.149.3 | 8 | 35.32 | odd | 12 | |||
245.4.a.g.1.2 | 2 | 1.1 | even | 1 | trivial | ||
245.4.a.h.1.2 | 2 | 7.6 | odd | 2 | |||
245.4.e.l.116.1 | 4 | 7.5 | odd | 6 | |||
245.4.e.l.226.1 | 4 | 7.3 | odd | 6 | |||
315.4.j.c.46.2 | 4 | 21.2 | odd | 6 | |||
315.4.j.c.226.2 | 4 | 21.11 | odd | 6 | |||
560.4.q.i.81.1 | 4 | 28.23 | odd | 6 | |||
560.4.q.i.401.1 | 4 | 28.11 | odd | 6 | |||
1225.4.a.v.1.1 | 2 | 35.34 | odd | 2 | |||
1225.4.a.x.1.1 | 2 | 5.4 | even | 2 | |||
2205.4.a.bf.1.1 | 2 | 3.2 | odd | 2 | |||
2205.4.a.bg.1.1 | 2 | 21.20 | even | 2 |