Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [495,4,Mod(1,495)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(495, 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("495.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 495 = 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 495.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: | \(29.2059454528\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.23612.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 20x + 26 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(4.26150\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 495.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.26150 | 1.86022 | 0.930110 | − | 0.367281i | \(-0.119711\pi\) | ||||
0.930110 | + | 0.367281i | \(0.119711\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 19.6833 | 2.46042 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.3207 | −0.557266 | −0.278633 | − | 0.960398i | \(-0.589881\pi\) | ||||
−0.278633 | + | 0.960398i | \(0.589881\pi\) | |||||||
\(8\) | 61.4719 | 2.71670 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 26.3075 | 0.831916 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 63.9817 | 1.36502 | 0.682512 | − | 0.730874i | \(-0.260887\pi\) | ||||
0.682512 | + | 0.730874i | \(0.260887\pi\) | |||||||
\(14\) | −54.3024 | −1.03664 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 165.967 | 2.59324 | ||||||||
\(17\) | −17.1461 | −0.244620 | −0.122310 | − | 0.992492i | \(-0.539030\pi\) | ||||
−0.122310 | + | 0.992492i | \(0.539030\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 90.2104 | 1.08925 | 0.544623 | − | 0.838681i | \(-0.316673\pi\) | ||||
0.544623 | + | 0.838681i | \(0.316673\pi\) | |||||||
\(20\) | 98.4167 | 1.10033 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −57.8765 | −0.560877 | ||||||||
\(23\) | 212.605 | 1.92744 | 0.963721 | − | 0.266913i | \(-0.0860036\pi\) | ||||
0.963721 | + | 0.266913i | \(0.0860036\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 336.639 | 2.53925 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −203.146 | −1.37111 | ||||||||
\(29\) | −57.5461 | −0.368484 | −0.184242 | − | 0.982881i | \(-0.558983\pi\) | ||||
−0.184242 | + | 0.982881i | \(0.558983\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −141.704 | −0.820991 | −0.410496 | − | 0.911863i | \(-0.634644\pi\) | ||||
−0.410496 | + | 0.911863i | \(0.634644\pi\) | |||||||
\(32\) | 381.462 | 2.10730 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −90.2140 | −0.455046 | ||||||||
\(35\) | −51.6035 | −0.249217 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −257.963 | −1.14619 | −0.573093 | − | 0.819490i | \(-0.694257\pi\) | ||||
−0.573093 | + | 0.819490i | \(0.694257\pi\) | |||||||
\(38\) | 474.642 | 2.02624 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 307.359 | 1.21494 | ||||||||
\(41\) | 225.914 | 0.860533 | 0.430266 | − | 0.902702i | \(-0.358420\pi\) | ||||
0.430266 | + | 0.902702i | \(0.358420\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −347.445 | −1.23221 | −0.616103 | − | 0.787666i | \(-0.711289\pi\) | ||||
−0.616103 | + | 0.787666i | \(0.711289\pi\) | |||||||
\(44\) | −216.517 | −0.741844 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1118.62 | 3.58547 | ||||||||
\(47\) | −404.364 | −1.25495 | −0.627473 | − | 0.778638i | \(-0.715911\pi\) | ||||
−0.627473 | + | 0.778638i | \(0.715911\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −236.483 | −0.689455 | ||||||||
\(50\) | 131.537 | 0.372044 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1259.37 | 3.35853 | ||||||||
\(53\) | −259.568 | −0.672726 | −0.336363 | − | 0.941732i | \(-0.609197\pi\) | ||||
−0.336363 | + | 0.941732i | \(0.609197\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −55.0000 | −0.134840 | ||||||||
\(56\) | −634.433 | −1.51392 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −302.779 | −0.685462 | ||||||||
\(59\) | 853.067 | 1.88237 | 0.941185 | − | 0.337891i | \(-0.109713\pi\) | ||||
0.941185 | + | 0.337891i | \(0.109713\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −203.699 | −0.427558 | −0.213779 | − | 0.976882i | \(-0.568577\pi\) | ||||
−0.213779 | + | 0.976882i | \(0.568577\pi\) | |||||||
\(62\) | −745.573 | −1.52722 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 679.320 | 1.32680 | ||||||||
\(65\) | 319.908 | 0.610458 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 266.890 | 0.486653 | 0.243327 | − | 0.969944i | \(-0.421761\pi\) | ||||
0.243327 | + | 0.969944i | \(0.421761\pi\) | |||||||
\(68\) | −337.492 | −0.601866 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −271.512 | −0.463598 | ||||||||
\(71\) | −92.4460 | −0.154526 | −0.0772629 | − | 0.997011i | \(-0.524618\pi\) | ||||
−0.0772629 | + | 0.997011i | \(0.524618\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −242.026 | −0.388040 | −0.194020 | − | 0.980998i | \(-0.562153\pi\) | ||||
−0.194020 | + | 0.980998i | \(0.562153\pi\) | |||||||
\(74\) | −1357.27 | −2.13216 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1775.64 | 2.68000 | ||||||||
\(77\) | 113.528 | 0.168022 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1021.60 | −1.45492 | −0.727460 | − | 0.686150i | \(-0.759299\pi\) | ||||
−0.727460 | + | 0.686150i | \(0.759299\pi\) | |||||||
\(80\) | 829.837 | 1.15973 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1188.65 | 1.60078 | ||||||||
\(83\) | −706.415 | −0.934206 | −0.467103 | − | 0.884203i | \(-0.654702\pi\) | ||||
−0.467103 | + | 0.884203i | \(0.654702\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −85.7303 | −0.109397 | ||||||||
\(86\) | −1828.08 | −2.29217 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −676.191 | −0.819116 | ||||||||
\(89\) | 440.218 | 0.524304 | 0.262152 | − | 0.965027i | \(-0.415568\pi\) | ||||
0.262152 | + | 0.965027i | \(0.415568\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −660.336 | −0.760682 | ||||||||
\(92\) | 4184.77 | 4.74231 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2127.56 | −2.33448 | ||||||||
\(95\) | 451.052 | 0.487126 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −197.761 | −0.207006 | −0.103503 | − | 0.994629i | \(-0.533005\pi\) | ||||
−0.103503 | + | 0.994629i | \(0.533005\pi\) | |||||||
\(98\) | −1244.25 | −1.28254 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 492.084 | 0.492084 | ||||||||
\(101\) | −1400.62 | −1.37987 | −0.689937 | − | 0.723870i | \(-0.742362\pi\) | ||||
−0.689937 | + | 0.723870i | \(0.742362\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1345.70 | −1.28734 | −0.643669 | − | 0.765304i | \(-0.722589\pi\) | ||||
−0.643669 | + | 0.765304i | \(0.722589\pi\) | |||||||
\(104\) | 3933.07 | 3.70836 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1365.72 | −1.25142 | ||||||||
\(107\) | 889.178 | 0.803366 | 0.401683 | − | 0.915779i | \(-0.368425\pi\) | ||||
0.401683 | + | 0.915779i | \(0.368425\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1256.29 | 1.10395 | 0.551974 | − | 0.833861i | \(-0.313875\pi\) | ||||
0.551974 | + | 0.833861i | \(0.313875\pi\) | |||||||
\(110\) | −289.382 | −0.250832 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1712.90 | −1.44512 | ||||||||
\(113\) | 2394.01 | 1.99301 | 0.996504 | − | 0.0835448i | \(-0.0266242\pi\) | ||||
0.996504 | + | 0.0835448i | \(0.0266242\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1063.02 | 0.861978 | ||||||||
\(116\) | −1132.70 | −0.906626 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4488.41 | 3.50162 | ||||||||
\(119\) | 176.960 | 0.136318 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −1071.76 | −0.795352 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2789.20 | −2.01998 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2065.57 | 1.44322 | 0.721612 | − | 0.692298i | \(-0.243402\pi\) | ||||
0.721612 | + | 0.692298i | \(0.243402\pi\) | |||||||
\(128\) | 522.548 | 0.360837 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1683.20 | 1.13559 | ||||||||
\(131\) | −785.526 | −0.523907 | −0.261953 | − | 0.965081i | \(-0.584367\pi\) | ||||
−0.261953 | + | 0.965081i | \(0.584367\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −931.035 | −0.607000 | ||||||||
\(134\) | 1404.24 | 0.905282 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1054.00 | −0.664558 | ||||||||
\(137\) | −1276.24 | −0.795885 | −0.397942 | − | 0.917410i | \(-0.630276\pi\) | ||||
−0.397942 | + | 0.917410i | \(0.630276\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2703.21 | −1.64952 | −0.824760 | − | 0.565482i | \(-0.808690\pi\) | ||||
−0.824760 | + | 0.565482i | \(0.808690\pi\) | |||||||
\(140\) | −1015.73 | −0.613178 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −486.405 | −0.287452 | ||||||||
\(143\) | −703.798 | −0.411570 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −287.731 | −0.164791 | ||||||||
\(146\) | −1273.42 | −0.721840 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5077.58 | −2.82010 | ||||||||
\(149\) | 2400.99 | 1.32011 | 0.660056 | − | 0.751217i | \(-0.270533\pi\) | ||||
0.660056 | + | 0.751217i | \(0.270533\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2517.30 | −1.35665 | −0.678326 | − | 0.734761i | \(-0.737294\pi\) | ||||
−0.678326 | + | 0.734761i | \(0.737294\pi\) | |||||||
\(152\) | 5545.40 | 2.95916 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 597.326 | 0.312558 | ||||||||
\(155\) | −708.518 | −0.367158 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1391.42 | 0.707310 | 0.353655 | − | 0.935376i | \(-0.384939\pi\) | ||||
0.353655 | + | 0.935376i | \(0.384939\pi\) | |||||||
\(158\) | −5375.13 | −2.70647 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1907.31 | 0.942412 | ||||||||
\(161\) | −2194.23 | −1.07410 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2720.53 | −1.30729 | −0.653644 | − | 0.756802i | \(-0.726761\pi\) | ||||
−0.653644 | + | 0.756802i | \(0.726761\pi\) | |||||||
\(164\) | 4446.74 | 2.11727 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3716.80 | −1.73783 | ||||||||
\(167\) | −2950.25 | −1.36705 | −0.683525 | − | 0.729927i | \(-0.739554\pi\) | ||||
−0.683525 | + | 0.729927i | \(0.739554\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1896.65 | 0.863292 | ||||||||
\(170\) | −451.070 | −0.203503 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6838.88 | −3.03174 | ||||||||
\(173\) | −537.049 | −0.236018 | −0.118009 | − | 0.993013i | \(-0.537651\pi\) | ||||
−0.118009 | + | 0.993013i | \(0.537651\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −258.018 | −0.111453 | ||||||||
\(176\) | −1825.64 | −0.781891 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2316.21 | 0.975320 | ||||||||
\(179\) | −2891.25 | −1.20728 | −0.603638 | − | 0.797259i | \(-0.706283\pi\) | ||||
−0.603638 | + | 0.797259i | \(0.706283\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 435.209 | 0.178723 | 0.0893615 | − | 0.995999i | \(-0.471517\pi\) | ||||
0.0893615 | + | 0.995999i | \(0.471517\pi\) | |||||||
\(182\) | −3474.36 | −1.41504 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13069.2 | 5.23628 | ||||||||
\(185\) | −1289.82 | −0.512590 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 188.607 | 0.0737556 | ||||||||
\(188\) | −7959.23 | −3.08769 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2373.21 | 0.906161 | ||||||||
\(191\) | 3779.49 | 1.43180 | 0.715901 | − | 0.698202i | \(-0.246016\pi\) | ||||
0.715901 | + | 0.698202i | \(0.246016\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3751.91 | 1.39932 | 0.699660 | − | 0.714476i | \(-0.253335\pi\) | ||||
0.699660 | + | 0.714476i | \(0.253335\pi\) | |||||||
\(194\) | −1040.52 | −0.385076 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4654.78 | −1.69635 | ||||||||
\(197\) | 3920.73 | 1.41797 | 0.708986 | − | 0.705223i | \(-0.249153\pi\) | ||||
0.708986 | + | 0.705223i | \(0.249153\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −597.084 | −0.212694 | −0.106347 | − | 0.994329i | \(-0.533915\pi\) | ||||
−0.106347 | + | 0.994329i | \(0.533915\pi\) | |||||||
\(200\) | 1536.80 | 0.543340 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7369.37 | −2.56687 | ||||||||
\(203\) | 593.917 | 0.205344 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1129.57 | 0.384842 | ||||||||
\(206\) | −7080.40 | −2.39473 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10618.9 | 3.53984 | ||||||||
\(209\) | −992.314 | −0.328420 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4384.55 | −1.43054 | −0.715272 | − | 0.698846i | \(-0.753697\pi\) | ||||
−0.715272 | + | 0.698846i | \(0.753697\pi\) | |||||||
\(212\) | −5109.17 | −1.65519 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4678.41 | 1.49444 | ||||||||
\(215\) | −1737.22 | −0.551059 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1462.48 | 0.457510 | ||||||||
\(218\) | 6609.95 | 2.05359 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1082.58 | −0.331763 | ||||||||
\(221\) | −1097.03 | −0.333912 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2333.03 | −0.700587 | −0.350294 | − | 0.936640i | \(-0.613918\pi\) | ||||
−0.350294 | + | 0.936640i | \(0.613918\pi\) | |||||||
\(224\) | −3936.95 | −1.17433 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12596.1 | 3.70743 | ||||||||
\(227\) | 2120.00 | 0.619864 | 0.309932 | − | 0.950759i | \(-0.399694\pi\) | ||||
0.309932 | + | 0.950759i | \(0.399694\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2347.12 | 0.677301 | 0.338651 | − | 0.940912i | \(-0.390030\pi\) | ||||
0.338651 | + | 0.940912i | \(0.390030\pi\) | |||||||
\(230\) | 5593.10 | 1.60347 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3537.47 | −1.00106 | ||||||||
\(233\) | 375.499 | 0.105578 | 0.0527891 | − | 0.998606i | \(-0.483189\pi\) | ||||
0.0527891 | + | 0.998606i | \(0.483189\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2021.82 | −0.561229 | ||||||||
\(236\) | 16791.2 | 4.63142 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 931.072 | 0.253582 | ||||||||
\(239\) | 1428.15 | 0.386524 | 0.193262 | − | 0.981147i | \(-0.438093\pi\) | ||||
0.193262 | + | 0.981147i | \(0.438093\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 190.819 | 0.0510032 | 0.0255016 | − | 0.999675i | \(-0.491882\pi\) | ||||
0.0255016 | + | 0.999675i | \(0.491882\pi\) | |||||||
\(242\) | 636.641 | 0.169111 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4009.49 | −1.05197 | ||||||||
\(245\) | −1182.41 | −0.308334 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5771.81 | 1.48685 | ||||||||
\(248\) | −8710.79 | −2.23039 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 657.687 | 0.166383 | ||||||||
\(251\) | 6294.80 | 1.58297 | 0.791483 | − | 0.611191i | \(-0.209309\pi\) | ||||
0.791483 | + | 0.611191i | \(0.209309\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2338.65 | −0.581145 | ||||||||
\(254\) | 10868.0 | 2.68471 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2685.18 | −0.655561 | ||||||||
\(257\) | −4459.44 | −1.08238 | −0.541191 | − | 0.840900i | \(-0.682026\pi\) | ||||
−0.541191 | + | 0.840900i | \(0.682026\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2662.36 | 0.638731 | ||||||||
\(260\) | 6296.87 | 1.50198 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4133.04 | −0.974581 | ||||||||
\(263\) | 4416.65 | 1.03552 | 0.517761 | − | 0.855525i | \(-0.326766\pi\) | ||||
0.517761 | + | 0.855525i | \(0.326766\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1297.84 | −0.300852 | ||||||||
\(266\) | −4898.64 | −1.12915 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5253.28 | 1.19737 | ||||||||
\(269\) | −1914.86 | −0.434020 | −0.217010 | − | 0.976169i | \(-0.569630\pi\) | ||||
−0.217010 | + | 0.976169i | \(0.569630\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6088.34 | 1.36472 | 0.682362 | − | 0.731014i | \(-0.260953\pi\) | ||||
0.682362 | + | 0.731014i | \(0.260953\pi\) | |||||||
\(272\) | −2845.69 | −0.634357 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6714.91 | −1.48052 | ||||||||
\(275\) | −275.000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −832.321 | −0.180539 | −0.0902696 | − | 0.995917i | \(-0.528773\pi\) | ||||
−0.0902696 | + | 0.995917i | \(0.528773\pi\) | |||||||
\(278\) | −14222.9 | −3.06847 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3172.17 | −0.677047 | ||||||||
\(281\) | 2545.32 | 0.540360 | 0.270180 | − | 0.962810i | \(-0.412917\pi\) | ||||
0.270180 | + | 0.962810i | \(0.412917\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5911.71 | −1.24175 | −0.620874 | − | 0.783911i | \(-0.713222\pi\) | ||||
−0.620874 | + | 0.783911i | \(0.713222\pi\) | |||||||
\(284\) | −1819.65 | −0.380198 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3703.03 | −0.765611 | ||||||||
\(287\) | −2331.59 | −0.479545 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4619.01 | −0.940161 | ||||||||
\(290\) | −1513.89 | −0.306548 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4763.87 | −0.954742 | ||||||||
\(293\) | 6871.03 | 1.37000 | 0.685000 | − | 0.728543i | \(-0.259802\pi\) | ||||
0.685000 | + | 0.728543i | \(0.259802\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4265.34 | 0.841822 | ||||||||
\(296\) | −15857.5 | −3.11384 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12632.8 | 2.45570 | ||||||||
\(299\) | 13602.8 | 2.63100 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3585.88 | 0.686666 | ||||||||
\(302\) | −13244.7 | −2.52367 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14972.0 | 2.82468 | ||||||||
\(305\) | −1018.50 | −0.191210 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 200.179 | 0.0372144 | 0.0186072 | − | 0.999827i | \(-0.494077\pi\) | ||||
0.0186072 | + | 0.999827i | \(0.494077\pi\) | |||||||
\(308\) | 2234.61 | 0.413404 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3727.87 | −0.682995 | ||||||||
\(311\) | −5734.93 | −1.04565 | −0.522827 | − | 0.852439i | \(-0.675122\pi\) | ||||
−0.522827 | + | 0.852439i | \(0.675122\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3077.36 | −0.555727 | −0.277864 | − | 0.960621i | \(-0.589626\pi\) | ||||
−0.277864 | + | 0.960621i | \(0.589626\pi\) | |||||||
\(314\) | 7320.97 | 1.31575 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20108.5 | −3.57971 | ||||||||
\(317\) | −2142.38 | −0.379584 | −0.189792 | − | 0.981824i | \(-0.560781\pi\) | ||||
−0.189792 | + | 0.981824i | \(0.560781\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 633.007 | 0.111102 | ||||||||
\(320\) | 3396.60 | 0.593362 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11544.9 | −1.99806 | ||||||||
\(323\) | −1546.75 | −0.266451 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1599.54 | 0.273005 | ||||||||
\(326\) | −14314.0 | −2.43184 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 13887.4 | 2.33781 | ||||||||
\(329\) | 4173.32 | 0.699339 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1618.23 | −0.268719 | −0.134359 | − | 0.990933i | \(-0.542898\pi\) | ||||
−0.134359 | + | 0.990933i | \(0.542898\pi\) | |||||||
\(332\) | −13904.6 | −2.29854 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −15522.7 | −2.54301 | ||||||||
\(335\) | 1334.45 | 0.217638 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2406.47 | 0.388988 | 0.194494 | − | 0.980904i | \(-0.437694\pi\) | ||||
0.194494 | + | 0.980904i | \(0.437694\pi\) | |||||||
\(338\) | 9979.23 | 1.60591 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1687.46 | −0.269163 | ||||||||
\(341\) | 1558.74 | 0.247538 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5980.67 | 0.941475 | ||||||||
\(344\) | −21358.1 | −3.34753 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2825.68 | −0.439045 | ||||||||
\(347\) | 6612.89 | 1.02305 | 0.511525 | − | 0.859268i | \(-0.329081\pi\) | ||||
0.511525 | + | 0.859268i | \(0.329081\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 349.871 | 0.0536623 | 0.0268311 | − | 0.999640i | \(-0.491458\pi\) | ||||
0.0268311 | + | 0.999640i | \(0.491458\pi\) | |||||||
\(350\) | −1357.56 | −0.207327 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4196.08 | −0.635374 | ||||||||
\(353\) | −1723.29 | −0.259835 | −0.129917 | − | 0.991525i | \(-0.541471\pi\) | ||||
−0.129917 | + | 0.991525i | \(0.541471\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −462.230 | −0.0691060 | ||||||||
\(356\) | 8664.97 | 1.29001 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15212.3 | −2.24580 | ||||||||
\(359\) | −5875.74 | −0.863816 | −0.431908 | − | 0.901918i | \(-0.642159\pi\) | ||||
−0.431908 | + | 0.901918i | \(0.642159\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1278.92 | 0.186458 | ||||||||
\(362\) | 2289.85 | 0.332464 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12997.6 | −1.87159 | ||||||||
\(365\) | −1210.13 | −0.173537 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5368.28 | −0.763548 | −0.381774 | − | 0.924256i | \(-0.624687\pi\) | ||||
−0.381774 | + | 0.924256i | \(0.624687\pi\) | |||||||
\(368\) | 35285.5 | 4.99832 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6786.37 | −0.953531 | ||||||||
\(371\) | 2678.93 | 0.374887 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10393.9 | 1.44282 | 0.721412 | − | 0.692506i | \(-0.243493\pi\) | ||||
0.721412 | + | 0.692506i | \(0.243493\pi\) | |||||||
\(374\) | 992.354 | 0.137202 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24857.0 | −3.40931 | ||||||||
\(377\) | −3681.90 | −0.502990 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10918.9 | 1.47986 | 0.739928 | − | 0.672686i | \(-0.234860\pi\) | ||||
0.739928 | + | 0.672686i | \(0.234860\pi\) | |||||||
\(380\) | 8878.21 | 1.19853 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 19885.8 | 2.66347 | ||||||||
\(383\) | 11663.6 | 1.55609 | 0.778044 | − | 0.628210i | \(-0.216212\pi\) | ||||
0.778044 | + | 0.628210i | \(0.216212\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 567.639 | 0.0751417 | ||||||||
\(386\) | 19740.7 | 2.60304 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3892.59 | −0.509321 | ||||||||
\(389\) | 5827.00 | 0.759487 | 0.379744 | − | 0.925092i | \(-0.376012\pi\) | ||||
0.379744 | + | 0.925092i | \(0.376012\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3645.34 | −0.471490 | ||||||||
\(392\) | −14537.1 | −1.87304 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 20628.9 | 2.63774 | ||||||||
\(395\) | −5107.99 | −0.650660 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7366.99 | 0.931332 | 0.465666 | − | 0.884961i | \(-0.345815\pi\) | ||||
0.465666 | + | 0.884961i | \(0.345815\pi\) | |||||||
\(398\) | −3141.55 | −0.395658 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4149.18 | 0.518648 | ||||||||
\(401\) | −14604.2 | −1.81870 | −0.909349 | − | 0.416035i | \(-0.863419\pi\) | ||||
−0.909349 | + | 0.416035i | \(0.863419\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9066.43 | −1.12067 | ||||||||
\(404\) | −27569.0 | −3.39507 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3124.89 | 0.381985 | ||||||||
\(407\) | 2837.60 | 0.345588 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12581.2 | 1.52103 | 0.760515 | − | 0.649320i | \(-0.224946\pi\) | ||||
0.760515 | + | 0.649320i | \(0.224946\pi\) | |||||||
\(410\) | 5943.23 | 0.715891 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −26487.9 | −3.16739 | ||||||||
\(413\) | −8804.26 | −1.04898 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3532.07 | −0.417790 | ||||||||
\(416\) | 24406.6 | 2.87651 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5221.06 | −0.610934 | ||||||||
\(419\) | 3776.01 | 0.440263 | 0.220131 | − | 0.975470i | \(-0.429351\pi\) | ||||
0.220131 | + | 0.975470i | \(0.429351\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12683.4 | 1.46830 | 0.734148 | − | 0.678989i | \(-0.237582\pi\) | ||||
0.734148 | + | 0.678989i | \(0.237582\pi\) | |||||||
\(422\) | −23069.3 | −2.66113 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −15956.2 | −1.82759 | ||||||||
\(425\) | −428.652 | −0.0489239 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2102.32 | 0.238263 | ||||||||
\(428\) | 17502.0 | 1.97662 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9140.40 | −1.02509 | ||||||||
\(431\) | −14152.6 | −1.58168 | −0.790841 | − | 0.612022i | \(-0.790356\pi\) | ||||
−0.790841 | + | 0.612022i | \(0.790356\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10950.2 | −1.21532 | −0.607661 | − | 0.794197i | \(-0.707892\pi\) | ||||
−0.607661 | + | 0.794197i | \(0.707892\pi\) | |||||||
\(434\) | 7694.84 | 0.851070 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 24727.9 | 2.71618 | ||||||||
\(437\) | 19179.2 | 2.09946 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11221.0 | −1.21993 | −0.609964 | − | 0.792429i | \(-0.708816\pi\) | ||||
−0.609964 | + | 0.792429i | \(0.708816\pi\) | |||||||
\(440\) | −3380.95 | −0.366320 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5772.04 | −0.621149 | ||||||||
\(443\) | −9647.11 | −1.03465 | −0.517323 | − | 0.855790i | \(-0.673071\pi\) | ||||
−0.517323 | + | 0.855790i | \(0.673071\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2201.09 | 0.234476 | ||||||||
\(446\) | −12275.2 | −1.30325 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7011.07 | −0.739379 | ||||||||
\(449\) | −6482.03 | −0.681305 | −0.340652 | − | 0.940189i | \(-0.610648\pi\) | ||||
−0.340652 | + | 0.940189i | \(0.610648\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2485.05 | −0.259460 | ||||||||
\(452\) | 47122.2 | 4.90363 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11154.4 | 1.15308 | ||||||||
\(455\) | −3301.68 | −0.340187 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11319.8 | 1.15868 | 0.579342 | − | 0.815085i | \(-0.303310\pi\) | ||||
0.579342 | + | 0.815085i | \(0.303310\pi\) | |||||||
\(458\) | 12349.4 | 1.25993 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 20923.9 | 2.12083 | ||||||||
\(461\) | 8406.73 | 0.849329 | 0.424664 | − | 0.905351i | \(-0.360392\pi\) | ||||
0.424664 | + | 0.905351i | \(0.360392\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9758.56 | 0.979523 | 0.489761 | − | 0.871857i | \(-0.337084\pi\) | ||||
0.489761 | + | 0.871857i | \(0.337084\pi\) | |||||||
\(464\) | −9550.78 | −0.955568 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1975.68 | 0.196399 | ||||||||
\(467\) | 16388.7 | 1.62394 | 0.811969 | − | 0.583701i | \(-0.198396\pi\) | ||||
0.811969 | + | 0.583701i | \(0.198396\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2754.49 | −0.271195 | ||||||||
\(470\) | −10637.8 | −1.04401 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 52439.6 | 5.11384 | ||||||||
\(473\) | 3821.89 | 0.371524 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2255.26 | 0.217849 | ||||||||
\(476\) | 3483.16 | 0.335400 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7514.20 | 0.719020 | ||||||||
\(479\) | −13829.0 | −1.31913 | −0.659567 | − | 0.751646i | \(-0.729260\pi\) | ||||
−0.659567 | + | 0.751646i | \(0.729260\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16504.9 | −1.56457 | ||||||||
\(482\) | 1004.00 | 0.0948771 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2381.68 | 0.223674 | ||||||||
\(485\) | −988.804 | −0.0925758 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13264.4 | 1.23423 | 0.617113 | − | 0.786875i | \(-0.288302\pi\) | ||||
0.617113 | + | 0.786875i | \(0.288302\pi\) | |||||||
\(488\) | −12521.8 | −1.16155 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6221.27 | −0.573568 | ||||||||
\(491\) | 7468.22 | 0.686428 | 0.343214 | − | 0.939257i | \(-0.388484\pi\) | ||||
0.343214 | + | 0.939257i | \(0.388484\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 986.690 | 0.0901385 | ||||||||
\(494\) | 30368.4 | 2.76586 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −23518.2 | −2.12903 | ||||||||
\(497\) | 954.109 | 0.0861119 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5276.64 | −0.473377 | −0.236688 | − | 0.971586i | \(-0.576062\pi\) | ||||
−0.236688 | + | 0.971586i | \(0.576062\pi\) | |||||||
\(500\) | 2460.42 | 0.220067 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 33120.1 | 2.94466 | ||||||||
\(503\) | 10956.8 | 0.971253 | 0.485626 | − | 0.874166i | \(-0.338592\pi\) | ||||
0.485626 | + | 0.874166i | \(0.338592\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7003.12 | −0.617098 | ||||||||
\(506\) | −12304.8 | −1.08106 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 40657.3 | 3.55093 | ||||||||
\(509\) | −12734.4 | −1.10892 | −0.554462 | − | 0.832209i | \(-0.687076\pi\) | ||||
−0.554462 | + | 0.832209i | \(0.687076\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2497.87 | 0.216242 | ||||||||
\(512\) | −18308.4 | −1.58032 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −23463.3 | −2.01347 | ||||||||
\(515\) | −6728.51 | −0.575715 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4448.00 | 0.378381 | ||||||||
\(518\) | 14008.0 | 1.18818 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 19665.4 | 1.65843 | ||||||||
\(521\) | 5650.70 | 0.475166 | 0.237583 | − | 0.971367i | \(-0.423645\pi\) | ||||
0.237583 | + | 0.971367i | \(0.423645\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14103.2 | 1.17914 | 0.589572 | − | 0.807716i | \(-0.299297\pi\) | ||||
0.589572 | + | 0.807716i | \(0.299297\pi\) | |||||||
\(524\) | −15461.8 | −1.28903 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23238.2 | 1.92630 | ||||||||
\(527\) | 2429.66 | 0.200830 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 33033.8 | 2.71503 | ||||||||
\(530\) | −6828.59 | −0.559651 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −18325.9 | −1.49347 | ||||||||
\(533\) | 14454.4 | 1.17465 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4445.89 | 0.359276 | ||||||||
\(536\) | 16406.2 | 1.32209 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10075.0 | −0.807372 | ||||||||
\(539\) | 2601.31 | 0.207878 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6391.90 | −0.507965 | −0.253983 | − | 0.967209i | \(-0.581741\pi\) | ||||
−0.253983 | + | 0.967209i | \(0.581741\pi\) | |||||||
\(542\) | 32033.8 | 2.53869 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6540.57 | −0.515486 | ||||||||
\(545\) | 6281.43 | 0.493701 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20786.7 | 1.62482 | 0.812409 | − | 0.583088i | \(-0.198156\pi\) | ||||
0.812409 | + | 0.583088i | \(0.198156\pi\) | |||||||
\(548\) | −25120.6 | −1.95821 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1446.91 | −0.112175 | ||||||||
\(551\) | −5191.26 | −0.401370 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10543.6 | 0.810777 | ||||||||
\(554\) | −4379.26 | −0.335843 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −53208.2 | −4.05851 | ||||||||
\(557\) | 15125.9 | 1.15064 | 0.575320 | − | 0.817928i | \(-0.304877\pi\) | ||||
0.575320 | + | 0.817928i | \(0.304877\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22230.1 | −1.68199 | ||||||||
\(560\) | −8564.50 | −0.646279 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13392.2 | 1.00519 | ||||||||
\(563\) | −8706.42 | −0.651744 | −0.325872 | − | 0.945414i | \(-0.605658\pi\) | ||||
−0.325872 | + | 0.945414i | \(0.605658\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11970.1 | 0.891300 | ||||||||
\(566\) | −31104.4 | −2.30992 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5682.83 | −0.419800 | ||||||||
\(569\) | −7067.76 | −0.520731 | −0.260366 | − | 0.965510i | \(-0.583843\pi\) | ||||
−0.260366 | + | 0.965510i | \(0.583843\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3326.42 | −0.243794 | −0.121897 | − | 0.992543i | \(-0.538898\pi\) | ||||
−0.121897 | + | 0.992543i | \(0.538898\pi\) | |||||||
\(572\) | −13853.1 | −1.01264 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12267.7 | −0.892060 | ||||||||
\(575\) | 5315.12 | 0.385488 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3308.06 | −0.238676 | −0.119338 | − | 0.992854i | \(-0.538077\pi\) | ||||
−0.119338 | + | 0.992854i | \(0.538077\pi\) | |||||||
\(578\) | −24302.9 | −1.74891 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5663.50 | −0.405455 | ||||||||
\(581\) | 7290.70 | 0.520601 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2855.25 | 0.202834 | ||||||||
\(584\) | −14877.8 | −1.05419 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 36151.9 | 2.54850 | ||||||||
\(587\) | 5694.88 | 0.400431 | 0.200215 | − | 0.979752i | \(-0.435836\pi\) | ||||
0.200215 | + | 0.979752i | \(0.435836\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12783.1 | −0.894262 | ||||||||
\(590\) | 22442.0 | 1.56597 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −42813.5 | −2.97234 | ||||||||
\(593\) | 3907.69 | 0.270606 | 0.135303 | − | 0.990804i | \(-0.456799\pi\) | ||||
0.135303 | + | 0.990804i | \(0.456799\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 884.798 | 0.0609633 | ||||||||
\(596\) | 47259.5 | 3.24803 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 71571.1 | 4.89425 | ||||||||
\(599\) | −10727.2 | −0.731720 | −0.365860 | − | 0.930670i | \(-0.619225\pi\) | ||||
−0.365860 | + | 0.930670i | \(0.619225\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3348.98 | 0.227301 | 0.113650 | − | 0.993521i | \(-0.463746\pi\) | ||||
0.113650 | + | 0.993521i | \(0.463746\pi\) | |||||||
\(602\) | 18867.1 | 1.27735 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −49548.8 | −3.33793 | ||||||||
\(605\) | 605.000 | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21539.9 | −1.44032 | −0.720162 | − | 0.693806i | \(-0.755932\pi\) | ||||
−0.720162 | + | 0.693806i | \(0.755932\pi\) | |||||||
\(608\) | 34411.8 | 2.29537 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5358.82 | −0.355692 | ||||||||
\(611\) | −25871.9 | −1.71303 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9284.33 | −0.611730 | −0.305865 | − | 0.952075i | \(-0.598946\pi\) | ||||
−0.305865 | + | 0.952075i | \(0.598946\pi\) | |||||||
\(614\) | 1053.24 | 0.0692270 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6978.77 | 0.456465 | ||||||||
\(617\) | 20711.3 | 1.35139 | 0.675695 | − | 0.737181i | \(-0.263844\pi\) | ||||
0.675695 | + | 0.737181i | \(0.263844\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13282.9 | −0.862496 | −0.431248 | − | 0.902233i | \(-0.641927\pi\) | ||||
−0.431248 | + | 0.902233i | \(0.641927\pi\) | |||||||
\(620\) | −13946.0 | −0.903363 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −30174.3 | −1.94515 | ||||||||
\(623\) | −4543.36 | −0.292177 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −16191.5 | −1.03378 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 27387.9 | 1.74028 | ||||||||
\(629\) | 4423.06 | 0.280380 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14789.9 | −0.933086 | −0.466543 | − | 0.884498i | \(-0.654501\pi\) | ||||
−0.466543 | + | 0.884498i | \(0.654501\pi\) | |||||||
\(632\) | −62799.5 | −3.95258 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11272.1 | −0.706109 | ||||||||
\(635\) | 10327.8 | 0.645429 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15130.6 | −0.941123 | ||||||||
\(638\) | 3330.57 | 0.206675 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2612.74 | 0.161371 | ||||||||
\(641\) | 5808.52 | 0.357914 | 0.178957 | − | 0.983857i | \(-0.442728\pi\) | ||||
0.178957 | + | 0.983857i | \(0.442728\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18891.2 | −1.15862 | −0.579311 | − | 0.815106i | \(-0.696678\pi\) | ||||
−0.579311 | + | 0.815106i | \(0.696678\pi\) | |||||||
\(644\) | −43189.8 | −2.64273 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8138.24 | −0.495657 | ||||||||
\(647\) | 243.046 | 0.0147684 | 0.00738418 | − | 0.999973i | \(-0.497650\pi\) | ||||
0.00738418 | + | 0.999973i | \(0.497650\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9383.74 | −0.567556 | ||||||||
\(650\) | 8415.98 | 0.507849 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −53549.0 | −3.21648 | ||||||||
\(653\) | 15920.4 | 0.954081 | 0.477041 | − | 0.878881i | \(-0.341709\pi\) | ||||
0.477041 | + | 0.878881i | \(0.341709\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3927.63 | −0.234298 | ||||||||
\(656\) | 37494.4 | 2.23157 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 21957.9 | 1.30092 | ||||||||
\(659\) | 7476.38 | 0.441940 | 0.220970 | − | 0.975281i | \(-0.429078\pi\) | ||||
0.220970 | + | 0.975281i | \(0.429078\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14920.1 | −0.877948 | −0.438974 | − | 0.898500i | \(-0.644658\pi\) | ||||
−0.438974 | + | 0.898500i | \(0.644658\pi\) | |||||||
\(662\) | −8514.30 | −0.499876 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −43424.7 | −2.53796 | ||||||||
\(665\) | −4655.18 | −0.271459 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12234.6 | −0.710232 | ||||||||
\(668\) | −58070.8 | −3.36351 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7021.20 | 0.404854 | ||||||||
\(671\) | 2240.69 | 0.128914 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 563.692 | 0.0322864 | 0.0161432 | − | 0.999870i | \(-0.494861\pi\) | ||||
0.0161432 | + | 0.999870i | \(0.494861\pi\) | |||||||
\(674\) | 12661.6 | 0.723602 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 37332.5 | 2.12406 | ||||||||
\(677\) | −13280.2 | −0.753914 | −0.376957 | − | 0.926231i | \(-0.623030\pi\) | ||||
−0.376957 | + | 0.926231i | \(0.623030\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2041.03 | 0.115357 | ||||||||
\(680\) | −5270.01 | −0.297199 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8201.30 | 0.460475 | ||||||||
\(683\) | −6856.80 | −0.384141 | −0.192070 | − | 0.981381i | \(-0.561520\pi\) | ||||
−0.192070 | + | 0.981381i | \(0.561520\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6381.18 | −0.355930 | ||||||||
\(686\) | 31467.3 | 1.75135 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −57664.5 | −3.19541 | ||||||||
\(689\) | −16607.6 | −0.918287 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28374.6 | −1.56211 | −0.781057 | − | 0.624460i | \(-0.785319\pi\) | ||||
−0.781057 | + | 0.624460i | \(0.785319\pi\) | |||||||
\(692\) | −10570.9 | −0.580702 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 34793.7 | 1.90310 | ||||||||
\(695\) | −13516.1 | −0.737688 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3873.54 | −0.210503 | ||||||||
\(698\) | 1840.84 | 0.0998237 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5078.65 | −0.274221 | ||||||||
\(701\) | −667.753 | −0.0359781 | −0.0179891 | − | 0.999838i | \(-0.505726\pi\) | ||||
−0.0179891 | + | 0.999838i | \(0.505726\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23271.0 | −1.24848 | ||||||||
\(704\) | −7472.52 | −0.400044 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9067.10 | −0.483349 | ||||||||
\(707\) | 14455.4 | 0.768956 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23667.8 | 1.25368 | 0.626842 | − | 0.779147i | \(-0.284347\pi\) | ||||
0.626842 | + | 0.779147i | \(0.284347\pi\) | |||||||
\(710\) | −2432.02 | −0.128552 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 27061.0 | 1.42438 | ||||||||
\(713\) | −30126.9 | −1.58241 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3518.99 | −0.184060 | ||||||||
\(716\) | −56909.5 | −2.97040 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −30915.2 | −1.60689 | ||||||||
\(719\) | −11835.5 | −0.613896 | −0.306948 | − | 0.951726i | \(-0.599308\pi\) | ||||
−0.306948 | + | 0.951726i | \(0.599308\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13888.6 | 0.717390 | ||||||||
\(722\) | 6729.01 | 0.346853 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8566.38 | 0.439733 | ||||||||
\(725\) | −1438.65 | −0.0736969 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15633.2 | 0.797530 | 0.398765 | − | 0.917053i | \(-0.369439\pi\) | ||||
0.398765 | + | 0.917053i | \(0.369439\pi\) | |||||||
\(728\) | −40592.1 | −2.06654 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6367.08 | −0.322817 | ||||||||
\(731\) | 5957.31 | 0.301422 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14870.7 | −0.749335 | −0.374668 | − | 0.927159i | \(-0.622243\pi\) | ||||
−0.374668 | + | 0.927159i | \(0.622243\pi\) | |||||||
\(734\) | −28245.2 | −1.42037 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 81100.6 | 4.06169 | ||||||||
\(737\) | −2935.79 | −0.146731 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20850.3 | 1.03788 | 0.518939 | − | 0.854812i | \(-0.326327\pi\) | ||||
0.518939 | + | 0.854812i | \(0.326327\pi\) | |||||||
\(740\) | −25387.9 | −1.26119 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14095.2 | 0.697372 | ||||||||
\(743\) | 29254.7 | 1.44448 | 0.722242 | − | 0.691641i | \(-0.243112\pi\) | ||||
0.722242 | + | 0.691641i | \(0.243112\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12004.9 | 0.590372 | ||||||||
\(746\) | 54687.2 | 2.68397 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3712.41 | 0.181470 | ||||||||
\(749\) | −9176.95 | −0.447688 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10936.8 | 0.531411 | 0.265705 | − | 0.964054i | \(-0.414395\pi\) | ||||
0.265705 | + | 0.964054i | \(0.414395\pi\) | |||||||
\(752\) | −67111.2 | −3.25438 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −19372.3 | −0.935672 | ||||||||
\(755\) | −12586.5 | −0.606714 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8476.34 | −0.406972 | −0.203486 | − | 0.979078i | \(-0.565227\pi\) | ||||
−0.203486 | + | 0.979078i | \(0.565227\pi\) | |||||||
\(758\) | 57449.6 | 2.75286 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 27727.0 | 1.32337 | ||||||||
\(761\) | −913.964 | −0.0435364 | −0.0217682 | − | 0.999763i | \(-0.506930\pi\) | ||||
−0.0217682 | + | 0.999763i | \(0.506930\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12965.8 | −0.615193 | ||||||||
\(764\) | 74393.0 | 3.52283 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 61367.9 | 2.89466 | ||||||||
\(767\) | 54580.6 | 2.56948 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32215.2 | 1.51067 | 0.755337 | − | 0.655337i | \(-0.227473\pi\) | ||||
0.755337 | + | 0.655337i | \(0.227473\pi\) | |||||||
\(770\) | 2986.63 | 0.139780 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 73850.2 | 3.44291 | ||||||||
\(773\) | −72.6900 | −0.00338225 | −0.00169112 | − | 0.999999i | \(-0.500538\pi\) | ||||
−0.00169112 | + | 0.999999i | \(0.500538\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3542.59 | −0.164198 | ||||||||
\(776\) | −12156.7 | −0.562373 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 30658.7 | 1.41281 | ||||||||
\(779\) | 20379.8 | 0.937332 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1016.91 | 0.0465913 | ||||||||
\(782\) | −19179.9 | −0.877075 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −39248.5 | −1.78792 | ||||||||
\(785\) | 6957.11 | 0.316319 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 487.318 | 0.0220724 | 0.0110362 | − | 0.999939i | \(-0.496487\pi\) | ||||
0.0110362 | + | 0.999939i | \(0.496487\pi\) | |||||||
\(788\) | 77173.1 | 3.48880 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −26875.7 | −1.21037 | ||||||||
\(791\) | −24707.9 | −1.11064 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13033.0 | −0.583627 | ||||||||
\(794\) | 38761.4 | 1.73248 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11752.6 | −0.523317 | ||||||||
\(797\) | −31379.9 | −1.39465 | −0.697324 | − | 0.716756i | \(-0.745626\pi\) | ||||
−0.697324 | + | 0.716756i | \(0.745626\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6933.25 | 0.306985 | ||||||||
\(800\) | 9536.54 | 0.421460 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −76839.8 | −3.38318 | ||||||||
\(803\) | 2662.28 | 0.116999 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10971.2 | −0.480351 | ||||||||
\(806\) | −47703.0 | −2.08470 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −86099.0 | −3.74870 | ||||||||
\(809\) | −1824.26 | −0.0792802 | −0.0396401 | − | 0.999214i | \(-0.512621\pi\) | ||||
−0.0396401 | + | 0.999214i | \(0.512621\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4364.52 | −0.188976 | −0.0944878 | − | 0.995526i | \(-0.530121\pi\) | ||||
−0.0944878 | + | 0.995526i | \(0.530121\pi\) | |||||||
\(812\) | 11690.3 | 0.505232 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14930.0 | 0.642870 | ||||||||
\(815\) | −13602.6 | −0.584637 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31343.1 | −1.34218 | ||||||||
\(818\) | 66196.1 | 2.82945 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 22233.7 | 0.946872 | ||||||||
\(821\) | −3306.16 | −0.140543 | −0.0702714 | − | 0.997528i | \(-0.522387\pi\) | ||||
−0.0702714 | + | 0.997528i | \(0.522387\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19183.7 | −0.812519 | −0.406259 | − | 0.913758i | \(-0.633167\pi\) | ||||
−0.406259 | + | 0.913758i | \(0.633167\pi\) | |||||||
\(824\) | −82722.8 | −3.49731 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −46323.6 | −1.95134 | ||||||||
\(827\) | −20646.4 | −0.868131 | −0.434066 | − | 0.900881i | \(-0.642921\pi\) | ||||
−0.434066 | + | 0.900881i | \(0.642921\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5345.44 | 0.223950 | 0.111975 | − | 0.993711i | \(-0.464282\pi\) | ||||
0.111975 | + | 0.993711i | \(0.464282\pi\) | |||||||
\(830\) | −18584.0 | −0.777181 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 43464.0 | 1.81111 | ||||||||
\(833\) | 4054.75 | 0.168654 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14751.3 | −0.611363 | ||||||||
\(836\) | −19532.1 | −0.808051 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 19867.5 | 0.818985 | ||||||||
\(839\) | −29284.9 | −1.20504 | −0.602519 | − | 0.798105i | \(-0.705836\pi\) | ||||
−0.602519 | + | 0.798105i | \(0.705836\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21077.4 | −0.864219 | ||||||||
\(842\) | 66733.8 | 2.73135 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −86302.6 | −3.51974 | ||||||||
\(845\) | 9483.26 | 0.386076 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1248.81 | −0.0506605 | ||||||||
\(848\) | −43079.9 | −1.74454 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2255.35 | −0.0910092 | ||||||||
\(851\) | −54844.2 | −2.20921 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8070.62 | −0.323954 | −0.161977 | − | 0.986795i | \(-0.551787\pi\) | ||||
−0.161977 | + | 0.986795i | \(0.551787\pi\) | |||||||
\(854\) | 11061.4 | 0.443222 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 54659.5 | 2.18250 | ||||||||
\(857\) | 11344.2 | 0.452169 | 0.226085 | − | 0.974108i | \(-0.427407\pi\) | ||||
0.226085 | + | 0.974108i | \(0.427407\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25470.6 | 1.01170 | 0.505848 | − | 0.862623i | \(-0.331180\pi\) | ||||
0.505848 | + | 0.862623i | \(0.331180\pi\) | |||||||
\(860\) | −34194.4 | −1.35584 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −74463.6 | −2.94228 | ||||||||
\(863\) | 14558.4 | 0.574243 | 0.287122 | − | 0.957894i | \(-0.407302\pi\) | ||||
0.287122 | + | 0.957894i | \(0.407302\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2685.24 | −0.105550 | ||||||||
\(866\) | −57614.6 | −2.26077 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 28786.5 | 1.12567 | ||||||||
\(869\) | 11237.6 | 0.438675 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17076.0 | 0.664294 | ||||||||
\(872\) | 77226.3 | 2.99910 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 100911. | 3.90546 | ||||||||
\(875\) | −1290.09 | −0.0498434 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 185.528 | 0.00714350 | 0.00357175 | − | 0.999994i | \(-0.498863\pi\) | ||||
0.00357175 | + | 0.999994i | \(0.498863\pi\) | |||||||
\(878\) | −59039.1 | −2.26933 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9128.21 | −0.349672 | ||||||||
\(881\) | −18950.1 | −0.724681 | −0.362340 | − | 0.932046i | \(-0.618022\pi\) | ||||
−0.362340 | + | 0.932046i | \(0.618022\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21258.3 | 0.810189 | 0.405095 | − | 0.914275i | \(-0.367239\pi\) | ||||
0.405095 | + | 0.914275i | \(0.367239\pi\) | |||||||
\(884\) | −21593.3 | −0.821563 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −50758.2 | −1.92467 | ||||||||
\(887\) | −35707.4 | −1.35168 | −0.675839 | − | 0.737049i | \(-0.736219\pi\) | ||||
−0.675839 | + | 0.737049i | \(0.736219\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21318.1 | −0.804259 | ||||||||
\(890\) | 11581.0 | 0.436177 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −45921.8 | −1.72374 | ||||||||
\(893\) | −36477.8 | −1.36695 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14456.3 | −0.539910 | ||||||||
\(896\) | −5393.06 | −0.201082 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −34105.2 | −1.26738 | ||||||||
\(899\) | 8154.49 | 0.302522 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4450.58 | 0.164562 | ||||||||
\(902\) | −13075.1 | −0.482653 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 147165. | 5.41440 | ||||||||
\(905\) | 2176.05 | 0.0799274 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6542.52 | −0.239516 | −0.119758 | − | 0.992803i | \(-0.538212\pi\) | ||||
−0.119758 | + | 0.992803i | \(0.538212\pi\) | |||||||
\(908\) | 41728.6 | 1.52512 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −17371.8 | −0.632823 | ||||||||
\(911\) | −31171.2 | −1.13364 | −0.566821 | − | 0.823841i | \(-0.691827\pi\) | ||||
−0.566821 | + | 0.823841i | \(0.691827\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7770.56 | 0.281674 | ||||||||
\(914\) | 59559.2 | 2.15541 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 46199.2 | 1.66644 | ||||||||
\(917\) | 8107.19 | 0.291955 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12031.9 | 0.431877 | 0.215938 | − | 0.976407i | \(-0.430719\pi\) | ||||
0.215938 | + | 0.976407i | \(0.430719\pi\) | |||||||
\(920\) | 65346.1 | 2.34174 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 44232.0 | 1.57994 | ||||||||
\(923\) | −5914.85 | −0.210931 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6449.08 | −0.229237 | ||||||||
\(926\) | 51344.7 | 1.82213 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −21951.6 | −0.776506 | ||||||||
\(929\) | 12546.2 | 0.443085 | 0.221542 | − | 0.975151i | \(-0.428891\pi\) | ||||
0.221542 | + | 0.975151i | \(0.428891\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21333.2 | −0.750986 | ||||||||
\(932\) | 7391.07 | 0.259767 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 86229.1 | 3.02088 | ||||||||
\(935\) | 943.034 | 0.0329845 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17909.8 | 0.624427 | 0.312214 | − | 0.950012i | \(-0.398930\pi\) | ||||
0.312214 | + | 0.950012i | \(0.398930\pi\) | |||||||
\(938\) | −14492.7 | −0.504483 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −39796.2 | −1.38086 | ||||||||
\(941\) | −829.893 | −0.0287500 | −0.0143750 | − | 0.999897i | \(-0.504576\pi\) | ||||
−0.0143750 | + | 0.999897i | \(0.504576\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 48030.4 | 1.65863 | ||||||||
\(944\) | 141581. | 4.88144 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20108.9 | 0.691116 | ||||||||
\(947\) | 17654.9 | 0.605814 | 0.302907 | − | 0.953020i | \(-0.402043\pi\) | ||||
0.302907 | + | 0.953020i | \(0.402043\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15485.2 | −0.529685 | ||||||||
\(950\) | 11866.0 | 0.405248 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10878.0 | 0.370335 | ||||||||
\(953\) | −30736.6 | −1.04476 | −0.522380 | − | 0.852713i | \(-0.674956\pi\) | ||||
−0.522380 | + | 0.852713i | \(0.674956\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18897.4 | 0.640321 | ||||||||
\(956\) | 28110.8 | 0.951012 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −72761.5 | −2.45388 | ||||||||
\(959\) | 13171.7 | 0.443519 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9711.08 | −0.325974 | ||||||||
\(962\) | −86840.6 | −2.91045 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3755.97 | 0.125489 | ||||||||
\(965\) | 18759.6 | 0.625794 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23645.2 | 0.786327 | 0.393163 | − | 0.919469i | \(-0.371381\pi\) | ||||
0.393163 | + | 0.919469i | \(0.371381\pi\) | |||||||
\(968\) | 7438.10 | 0.246973 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5202.59 | −0.172211 | ||||||||
\(971\) | −27402.0 | −0.905635 | −0.452818 | − | 0.891603i | \(-0.649581\pi\) | ||||
−0.452818 | + | 0.891603i | \(0.649581\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 27899.1 | 0.919222 | ||||||||
\(974\) | 69790.6 | 2.29593 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −33807.5 | −1.10876 | ||||||||
\(977\) | 49118.7 | 1.60844 | 0.804220 | − | 0.594332i | \(-0.202584\pi\) | ||||
0.804220 | + | 0.594332i | \(0.202584\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4842.40 | −0.158084 | ||||||||
\(980\) | −23273.9 | −0.758630 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 39294.0 | 1.27691 | ||||||||
\(983\) | −52630.5 | −1.70768 | −0.853842 | − | 0.520533i | \(-0.825733\pi\) | ||||
−0.853842 | + | 0.520533i | \(0.825733\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19603.7 | 0.634136 | ||||||||
\(986\) | 5191.47 | 0.167677 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 113609. | 3.65827 | ||||||||
\(989\) | −73868.4 | −2.37500 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45472.7 | 1.45761 | 0.728803 | − | 0.684724i | \(-0.240077\pi\) | ||||
0.728803 | + | 0.684724i | \(0.240077\pi\) | |||||||
\(992\) | −54054.5 | −1.73007 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5020.04 | 0.160187 | ||||||||
\(995\) | −2985.42 | −0.0951197 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 55068.1 | 1.74927 | 0.874637 | − | 0.484779i | \(-0.161100\pi\) | ||||
0.874637 | + | 0.484779i | \(0.161100\pi\) | |||||||
\(998\) | −27763.0 | −0.880585 | ||||||||
\(999\) | 0 | 0 |
(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 | 495.4.a.l.1.3 | 3 | ||
3.2 | odd | 2 | 165.4.a.d.1.1 | ✓ | 3 | ||
5.4 | even | 2 | 2475.4.a.s.1.1 | 3 | |||
15.2 | even | 4 | 825.4.c.l.199.1 | 6 | |||
15.8 | even | 4 | 825.4.c.l.199.6 | 6 | |||
15.14 | odd | 2 | 825.4.a.s.1.3 | 3 | |||
33.32 | even | 2 | 1815.4.a.s.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.4.a.d.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
495.4.a.l.1.3 | 3 | 1.1 | even | 1 | trivial | ||
825.4.a.s.1.3 | 3 | 15.14 | odd | 2 | |||
825.4.c.l.199.1 | 6 | 15.2 | even | 4 | |||
825.4.c.l.199.6 | 6 | 15.8 | even | 4 | |||
1815.4.a.s.1.3 | 3 | 33.32 | even | 2 | |||
2475.4.a.s.1.1 | 3 | 5.4 | even | 2 |