Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,4,Mod(199,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.199");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(48.6765757547\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{97})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 49x^{2} + 576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.2 | ||
Root | \(-4.42443i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.4.c.h.199.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4.42443i | − 1.56427i | −0.623108 | − | 0.782136i | \(-0.714130\pi\) | ||||
0.623108 | − | 0.782136i | \(-0.285870\pi\) | |||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | −11.5756 | −1.44695 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 13.2733 | 0.903133 | ||||||||
\(7\) | 31.6977i | 1.71152i | 0.517377 | + | 0.855758i | \(0.326909\pi\) | ||||
−0.517377 | + | 0.855758i | \(0.673091\pi\) | |||||||
\(8\) | 15.8199i | 0.699146i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | − 34.7267i | − 0.835395i | ||||||||
\(13\) | − 5.15114i | − 0.109898i | −0.998489 | − | 0.0549488i | \(-0.982500\pi\) | ||||
0.998489 | − | 0.0549488i | \(-0.0174996\pi\) | |||||||
\(14\) | 140.244 | 2.67728 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −22.6107 | −0.353293 | ||||||||
\(17\) | 121.942i | 1.73972i | 0.493297 | + | 0.869861i | \(0.335792\pi\) | ||||
−0.493297 | + | 0.869861i | \(0.664208\pi\) | |||||||
\(18\) | 39.8199i | 0.521424i | ||||||||
\(19\) | −34.8489 | −0.420783 | −0.210391 | − | 0.977617i | \(-0.567474\pi\) | ||||
−0.210391 | + | 0.977617i | \(0.567474\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −95.0931 | −0.988144 | ||||||||
\(22\) | 48.6687i | 0.471646i | ||||||||
\(23\) | − 116.244i | − 1.05385i | −0.849911 | − | 0.526926i | \(-0.823344\pi\) | ||||
0.849911 | − | 0.526926i | \(-0.176656\pi\) | |||||||
\(24\) | −47.4596 | −0.403652 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −22.7909 | −0.171910 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | − 366.919i | − 2.47647i | ||||||||
\(29\) | 69.4534 | 0.444730 | 0.222365 | − | 0.974963i | \(-0.428622\pi\) | ||||
0.222365 | + | 0.974963i | \(0.428622\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 140.605 | 0.814623 | 0.407312 | − | 0.913289i | \(-0.366466\pi\) | ||||
0.407312 | + | 0.913289i | \(0.366466\pi\) | |||||||
\(32\) | 226.598i | 1.25179i | ||||||||
\(33\) | − 33.0000i | − 0.174078i | ||||||||
\(34\) | 539.524 | 2.72140 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 104.180 | 0.482315 | ||||||||
\(37\) | − 420.070i | − 1.86646i | −0.359276 | − | 0.933232i | \(-0.616976\pi\) | ||||
0.359276 | − | 0.933232i | \(-0.383024\pi\) | |||||||
\(38\) | 154.186i | 0.658219i | ||||||||
\(39\) | 15.4534 | 0.0634495 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −322.058 | −1.22676 | −0.613378 | − | 0.789789i | \(-0.710190\pi\) | ||||
−0.613378 | + | 0.789789i | \(0.710190\pi\) | |||||||
\(42\) | 420.733i | 1.54573i | ||||||||
\(43\) | − 321.035i | − 1.13854i | −0.822149 | − | 0.569272i | \(-0.807225\pi\) | ||||
0.822149 | − | 0.569272i | \(-0.192775\pi\) | |||||||
\(44\) | 127.331 | 0.436271 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −514.315 | −1.64851 | ||||||||
\(47\) | − 231.408i | − 0.718176i | −0.933304 | − | 0.359088i | \(-0.883088\pi\) | ||||
0.933304 | − | 0.359088i | \(-0.116912\pi\) | |||||||
\(48\) | − 67.8322i | − 0.203974i | ||||||||
\(49\) | −661.745 | −1.92929 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −365.826 | −1.00443 | ||||||||
\(52\) | 59.6274i | 0.159016i | ||||||||
\(53\) | − 4.91916i | − 0.0127490i | −0.999980 | − | 0.00637452i | \(-0.997971\pi\) | ||||
0.999980 | − | 0.00637452i | \(-0.00202909\pi\) | |||||||
\(54\) | −119.460 | −0.301044 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −501.453 | −1.19660 | ||||||||
\(57\) | − 104.547i | − 0.242939i | ||||||||
\(58\) | − 307.292i | − 0.695679i | ||||||||
\(59\) | −406.443 | −0.896854 | −0.448427 | − | 0.893820i | \(-0.648016\pi\) | ||||
−0.448427 | + | 0.893820i | \(0.648016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −556.431 | −1.16793 | −0.583964 | − | 0.811779i | \(-0.698499\pi\) | ||||
−0.583964 | + | 0.811779i | \(0.698499\pi\) | |||||||
\(62\) | − 622.095i | − 1.27429i | ||||||||
\(63\) | − 285.279i | − 0.570505i | ||||||||
\(64\) | 821.683 | 1.60485 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −146.006 | −0.272305 | ||||||||
\(67\) | 84.7452i | 0.154526i | 0.997011 | + | 0.0772632i | \(0.0246182\pi\) | ||||
−0.997011 | + | 0.0772632i | \(0.975382\pi\) | |||||||
\(68\) | − 1411.55i | − 2.51728i | ||||||||
\(69\) | 348.733 | 0.608442 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 49.0808 | 0.0820398 | 0.0410199 | − | 0.999158i | \(-0.486939\pi\) | ||||
0.0410199 | + | 0.999158i | \(0.486939\pi\) | |||||||
\(72\) | − 142.379i | − 0.233049i | ||||||||
\(73\) | − 785.884i | − 1.26001i | −0.776591 | − | 0.630005i | \(-0.783053\pi\) | ||||
0.776591 | − | 0.630005i | \(-0.216947\pi\) | |||||||
\(74\) | −1858.57 | −2.91966 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 403.395 | 0.608850 | ||||||||
\(77\) | − 348.675i | − 0.516041i | ||||||||
\(78\) | − 68.3726i | − 0.0992522i | ||||||||
\(79\) | 383.118 | 0.545622 | 0.272811 | − | 0.962068i | \(-0.412047\pi\) | ||||
0.272811 | + | 0.962068i | \(0.412047\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1424.92i | 1.91898i | ||||||||
\(83\) | 930.211i | 1.23017i | 0.788462 | + | 0.615084i | \(0.210878\pi\) | ||||
−0.788462 | + | 0.615084i | \(0.789122\pi\) | |||||||
\(84\) | 1100.76 | 1.42979 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1420.40 | −1.78099 | ||||||||
\(87\) | 208.360i | 0.256765i | ||||||||
\(88\) | − 174.018i | − 0.210800i | ||||||||
\(89\) | 732.559 | 0.872484 | 0.436242 | − | 0.899829i | \(-0.356309\pi\) | ||||
0.436242 | + | 0.899829i | \(0.356309\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 163.279 | 0.188092 | ||||||||
\(92\) | 1345.59i | 1.52487i | ||||||||
\(93\) | 421.814i | 0.470323i | ||||||||
\(94\) | −1023.85 | −1.12342 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −679.795 | −0.722722 | ||||||||
\(97\) | − 1171.49i | − 1.22626i | −0.789984 | − | 0.613128i | \(-0.789911\pi\) | ||||
0.789984 | − | 0.613128i | \(-0.210089\pi\) | |||||||
\(98\) | 2927.84i | 3.01793i | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1221.27 | −1.20318 | −0.601589 | − | 0.798806i | \(-0.705465\pi\) | ||||
−0.601589 | + | 0.798806i | \(0.705465\pi\) | |||||||
\(102\) | 1618.57i | 1.57120i | ||||||||
\(103\) | − 516.745i | − 0.494334i | −0.968973 | − | 0.247167i | \(-0.920500\pi\) | ||||
0.968973 | − | 0.247167i | \(-0.0794996\pi\) | |||||||
\(104\) | 81.4903 | 0.0768345 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −21.7645 | −0.0199430 | ||||||||
\(107\) | − 152.025i | − 0.137353i | −0.997639 | − | 0.0686765i | \(-0.978122\pi\) | ||||
0.997639 | − | 0.0686765i | \(-0.0218776\pi\) | |||||||
\(108\) | 312.540i | 0.278465i | ||||||||
\(109\) | −2170.32 | −1.90714 | −0.953572 | − | 0.301164i | \(-0.902625\pi\) | ||||
−0.953572 | + | 0.301164i | \(0.902625\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1260.21 | 1.07760 | ||||||||
\(112\) | − 716.708i | − 0.604666i | ||||||||
\(113\) | 646.397i | 0.538123i | 0.963123 | + | 0.269062i | \(0.0867135\pi\) | ||||
−0.963123 | + | 0.269062i | \(0.913286\pi\) | |||||||
\(114\) | −462.559 | −0.380023 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −803.963 | −0.643501 | ||||||||
\(117\) | 46.3603i | 0.0366326i | ||||||||
\(118\) | 1798.28i | 1.40292i | ||||||||
\(119\) | −3865.28 | −2.97756 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 2461.89i | 1.82696i | ||||||||
\(123\) | − 966.174i | − 0.708268i | ||||||||
\(124\) | −1627.58 | −1.17872 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1262.20 | −0.892425 | ||||||||
\(127\) | − 993.304i | − 0.694027i | −0.937860 | − | 0.347014i | \(-0.887196\pi\) | ||||
0.937860 | − | 0.347014i | \(-0.112804\pi\) | |||||||
\(128\) | − 1822.69i | − 1.25863i | ||||||||
\(129\) | 963.105 | 0.657339 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 385.814 | 0.257318 | 0.128659 | − | 0.991689i | \(-0.458933\pi\) | ||||
0.128659 | + | 0.991689i | \(0.458933\pi\) | |||||||
\(132\) | 381.994i | 0.251881i | ||||||||
\(133\) | − 1104.63i | − 0.720177i | ||||||||
\(134\) | 374.949 | 0.241721 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1929.11 | −1.21632 | ||||||||
\(137\) | 884.840i | 0.551803i | 0.961186 | + | 0.275901i | \(0.0889763\pi\) | ||||
−0.961186 | + | 0.275901i | \(0.911024\pi\) | |||||||
\(138\) | − 1542.94i | − 0.951769i | ||||||||
\(139\) | 1091.94 | 0.666312 | 0.333156 | − | 0.942872i | \(-0.391886\pi\) | ||||
0.333156 | + | 0.942872i | \(0.391886\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 694.223 | 0.414639 | ||||||||
\(142\) | − 217.155i | − 0.128333i | ||||||||
\(143\) | 56.6626i | 0.0331354i | ||||||||
\(144\) | 203.497 | 0.117764 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3477.09 | −1.97100 | ||||||||
\(147\) | − 1985.24i | − 1.11387i | ||||||||
\(148\) | 4862.55i | 2.70067i | ||||||||
\(149\) | −297.014 | −0.163304 | −0.0816522 | − | 0.996661i | \(-0.526020\pi\) | ||||
−0.0816522 | + | 0.996661i | \(0.526020\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1887.86 | −1.01743 | −0.508716 | − | 0.860935i | \(-0.669880\pi\) | ||||
−0.508716 | + | 0.860935i | \(0.669880\pi\) | |||||||
\(152\) | − 551.304i | − 0.294189i | ||||||||
\(153\) | − 1097.48i | − 0.579907i | ||||||||
\(154\) | −1542.69 | −0.807229 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −178.882 | −0.0918080 | ||||||||
\(157\) | − 56.5343i | − 0.0287384i | −0.999897 | − | 0.0143692i | \(-0.995426\pi\) | ||||
0.999897 | − | 0.0143692i | \(-0.00457401\pi\) | |||||||
\(158\) | − 1695.08i | − 0.853501i | ||||||||
\(159\) | 14.7575 | 0.00736066 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3684.68 | 1.80369 | ||||||||
\(162\) | − 358.379i | − 0.173808i | ||||||||
\(163\) | 49.2338i | 0.0236582i | 0.999930 | + | 0.0118291i | \(0.00376541\pi\) | ||||
−0.999930 | + | 0.0118291i | \(0.996235\pi\) | |||||||
\(164\) | 3728.01 | 1.77505 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4115.65 | 1.92432 | ||||||||
\(167\) | 2068.75i | 0.958589i | 0.877654 | + | 0.479294i | \(0.159107\pi\) | ||||
−0.877654 | + | 0.479294i | \(0.840893\pi\) | |||||||
\(168\) | − 1504.36i | − 0.690857i | ||||||||
\(169\) | 2170.47 | 0.987923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 313.640 | 0.140261 | ||||||||
\(172\) | 3716.17i | 1.64741i | ||||||||
\(173\) | 604.012i | 0.265446i | 0.991153 | + | 0.132723i | \(0.0423721\pi\) | ||||
−0.991153 | + | 0.132723i | \(0.957628\pi\) | |||||||
\(174\) | 921.875 | 0.401650 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 248.718 | 0.106522 | ||||||||
\(177\) | − 1219.33i | − 0.517799i | ||||||||
\(178\) | − 3241.15i | − 1.36480i | ||||||||
\(179\) | 2132.02 | 0.890251 | 0.445126 | − | 0.895468i | \(-0.353159\pi\) | ||||
0.445126 | + | 0.895468i | \(0.353159\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −589.371 | −0.242031 | −0.121015 | − | 0.992651i | \(-0.538615\pi\) | ||||
−0.121015 | + | 0.992651i | \(0.538615\pi\) | |||||||
\(182\) | − 722.418i | − 0.294226i | ||||||||
\(183\) | − 1669.29i | − 0.674304i | ||||||||
\(184\) | 1838.97 | 0.736796 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1866.28 | 0.735713 | ||||||||
\(187\) | − 1341.36i | − 0.524546i | ||||||||
\(188\) | 2678.68i | 1.03916i | ||||||||
\(189\) | 855.838 | 0.329381 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2160.90 | −0.818624 | −0.409312 | − | 0.912395i | \(-0.634231\pi\) | ||||
−0.409312 | + | 0.912395i | \(0.634231\pi\) | |||||||
\(192\) | 2465.05i | 0.926560i | ||||||||
\(193\) | 1490.91i | 0.556052i | 0.960574 | + | 0.278026i | \(0.0896802\pi\) | ||||
−0.960574 | + | 0.278026i | \(0.910320\pi\) | |||||||
\(194\) | −5183.18 | −1.91820 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7660.08 | 2.79157 | ||||||||
\(197\) | − 230.529i | − 0.0833732i | −0.999131 | − | 0.0416866i | \(-0.986727\pi\) | ||||
0.999131 | − | 0.0416866i | \(-0.0132731\pi\) | |||||||
\(198\) | − 438.018i | − 0.157215i | ||||||||
\(199\) | −22.4007 | −0.00797963 | −0.00398982 | − | 0.999992i | \(-0.501270\pi\) | ||||
−0.00398982 | + | 0.999992i | \(0.501270\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −254.236 | −0.0892159 | ||||||||
\(202\) | 5403.43i | 1.88210i | ||||||||
\(203\) | 2201.51i | 0.761163i | ||||||||
\(204\) | 4234.65 | 1.45336 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2286.30 | −0.773273 | ||||||||
\(207\) | 1046.20i | 0.351284i | ||||||||
\(208\) | 116.471i | 0.0388260i | ||||||||
\(209\) | 383.337 | 0.126871 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1051.64 | −0.343117 | −0.171558 | − | 0.985174i | \(-0.554880\pi\) | ||||
−0.171558 | + | 0.985174i | \(0.554880\pi\) | |||||||
\(212\) | 56.9421i | 0.0184472i | ||||||||
\(213\) | 147.243i | 0.0473657i | ||||||||
\(214\) | −672.622 | −0.214857 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 427.136 | 0.134551 | ||||||||
\(217\) | 4456.84i | 1.39424i | ||||||||
\(218\) | 9602.42i | 2.98329i | ||||||||
\(219\) | 2357.65 | 0.727467 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 628.141 | 0.191191 | ||||||||
\(222\) | − 5575.71i | − 1.68566i | ||||||||
\(223\) | − 3861.80i | − 1.15966i | −0.814736 | − | 0.579832i | \(-0.803118\pi\) | ||||
0.814736 | − | 0.579832i | \(-0.196882\pi\) | |||||||
\(224\) | −7182.65 | −2.14246 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2859.94 | 0.841771 | ||||||||
\(227\) | − 872.721i | − 0.255174i | −0.991827 | − | 0.127587i | \(-0.959277\pi\) | ||||
0.991827 | − | 0.127587i | \(-0.0407232\pi\) | |||||||
\(228\) | 1210.19i | 0.351520i | ||||||||
\(229\) | −1841.72 | −0.531459 | −0.265730 | − | 0.964048i | \(-0.585613\pi\) | ||||
−0.265730 | + | 0.964048i | \(0.585613\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1046.02 | 0.297937 | ||||||||
\(232\) | 1098.74i | 0.310931i | ||||||||
\(233\) | − 3932.14i | − 1.10559i | −0.833317 | − | 0.552796i | \(-0.813561\pi\) | ||||
0.833317 | − | 0.552796i | \(-0.186439\pi\) | |||||||
\(234\) | 205.118 | 0.0573033 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4704.81 | 1.29770 | ||||||||
\(237\) | 1149.35i | 0.315015i | ||||||||
\(238\) | 17101.7i | 4.65772i | ||||||||
\(239\) | −4772.10 | −1.29155 | −0.645777 | − | 0.763526i | \(-0.723466\pi\) | ||||
−0.645777 | + | 0.763526i | \(0.723466\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3988.84 | 1.06616 | 0.533078 | − | 0.846066i | \(-0.321035\pi\) | ||||
0.533078 | + | 0.846066i | \(0.321035\pi\) | |||||||
\(242\) | − 535.356i | − 0.142207i | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 6441.00 | 1.68993 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4274.77 | −1.10792 | ||||||||
\(247\) | 179.511i | 0.0462431i | ||||||||
\(248\) | 2224.34i | 0.569540i | ||||||||
\(249\) | −2790.63 | −0.710238 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5474.22 | −1.37661 | −0.688306 | − | 0.725421i | \(-0.741645\pi\) | ||||
−0.688306 | + | 0.725421i | \(0.741645\pi\) | |||||||
\(252\) | 3302.27i | 0.825491i | ||||||||
\(253\) | 1278.69i | 0.317749i | ||||||||
\(254\) | −4394.80 | −1.08565 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1490.90 | −0.363989 | ||||||||
\(257\) | − 6434.01i | − 1.56164i | −0.624754 | − | 0.780822i | \(-0.714801\pi\) | ||||
0.624754 | − | 0.780822i | \(-0.285199\pi\) | |||||||
\(258\) | − 4261.19i | − 1.02826i | ||||||||
\(259\) | 13315.3 | 3.19448 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −625.081 | −0.148243 | ||||||||
\(262\) | − 1707.01i | − 0.402516i | ||||||||
\(263\) | − 7589.00i | − 1.77931i | −0.456636 | − | 0.889654i | \(-0.650946\pi\) | ||||
0.456636 | − | 0.889654i | \(-0.349054\pi\) | |||||||
\(264\) | 522.055 | 0.121706 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4887.35 | −1.12655 | ||||||||
\(267\) | 2197.68i | 0.503729i | ||||||||
\(268\) | − 980.974i | − 0.223591i | ||||||||
\(269\) | −478.178 | −0.108383 | −0.0541914 | − | 0.998531i | \(-0.517258\pi\) | ||||
−0.0541914 | + | 0.998531i | \(0.517258\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −122.323 | −0.0274192 | −0.0137096 | − | 0.999906i | \(-0.504364\pi\) | ||||
−0.0137096 | + | 0.999906i | \(0.504364\pi\) | |||||||
\(272\) | − 2757.20i | − 0.614631i | ||||||||
\(273\) | 489.838i | 0.108595i | ||||||||
\(274\) | 3914.91 | 0.863170 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4036.78 | −0.880383 | ||||||||
\(277\) | 8199.41i | 1.77854i | 0.457385 | + | 0.889269i | \(0.348786\pi\) | ||||
−0.457385 | + | 0.889269i | \(0.651214\pi\) | |||||||
\(278\) | − 4831.22i | − 1.04229i | ||||||||
\(279\) | −1265.44 | −0.271541 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6943.79 | 1.47413 | 0.737067 | − | 0.675820i | \(-0.236210\pi\) | ||||
0.737067 | + | 0.675820i | \(0.236210\pi\) | |||||||
\(282\) | − 3071.54i | − 0.648609i | ||||||||
\(283\) | − 1035.14i | − 0.217429i | −0.994073 | − | 0.108715i | \(-0.965327\pi\) | ||||
0.994073 | − | 0.108715i | \(-0.0346735\pi\) | |||||||
\(284\) | −568.139 | −0.118707 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 250.699 | 0.0518328 | ||||||||
\(287\) | − 10208.5i | − 2.09961i | ||||||||
\(288\) | − 2039.39i | − 0.417264i | ||||||||
\(289\) | −9956.85 | −2.02663 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3514.47 | 0.707979 | ||||||||
\(292\) | 9097.06i | 1.82317i | ||||||||
\(293\) | 6144.81i | 1.22520i | 0.790393 | + | 0.612600i | \(0.209876\pi\) | ||||
−0.790393 | + | 0.612600i | \(0.790124\pi\) | |||||||
\(294\) | −8783.53 | −1.74240 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6645.45 | 1.30493 | ||||||||
\(297\) | 297.000i | 0.0580259i | ||||||||
\(298\) | 1314.12i | 0.255452i | ||||||||
\(299\) | −598.791 | −0.115816 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10176.1 | 1.94864 | ||||||||
\(302\) | 8352.72i | 1.59154i | ||||||||
\(303\) | − 3663.81i | − 0.694655i | ||||||||
\(304\) | 787.958 | 0.148659 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4855.71 | −0.907133 | ||||||||
\(307\) | − 2186.09i | − 0.406406i | −0.979137 | − | 0.203203i | \(-0.934865\pi\) | ||||
0.979137 | − | 0.203203i | \(-0.0651351\pi\) | |||||||
\(308\) | 4036.11i | 0.746684i | ||||||||
\(309\) | 1550.24 | 0.285404 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7484.83 | −1.36471 | −0.682357 | − | 0.731019i | \(-0.739045\pi\) | ||||
−0.682357 | + | 0.731019i | \(0.739045\pi\) | |||||||
\(312\) | 244.471i | 0.0443604i | ||||||||
\(313\) | 6833.33i | 1.23400i | 0.786962 | + | 0.617001i | \(0.211653\pi\) | ||||
−0.786962 | + | 0.617001i | \(0.788347\pi\) | |||||||
\(314\) | −250.132 | −0.0449546 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4434.81 | −0.789485 | ||||||||
\(317\) | 924.265i | 0.163760i | 0.996642 | + | 0.0818800i | \(0.0260924\pi\) | ||||
−0.996642 | + | 0.0818800i | \(0.973908\pi\) | |||||||
\(318\) | − 65.2934i | − 0.0115141i | ||||||||
\(319\) | −763.988 | −0.134091 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 456.074 | 0.0793008 | ||||||||
\(322\) | − 16302.6i | − 2.82145i | ||||||||
\(323\) | − 4249.54i | − 0.732046i | ||||||||
\(324\) | −937.621 | −0.160772 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 217.831 | 0.0370078 | ||||||||
\(327\) | − 6510.95i | − 1.10109i | ||||||||
\(328\) | − 5094.91i | − 0.857681i | ||||||||
\(329\) | 7335.10 | 1.22917 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9820.46 | −1.63076 | −0.815380 | − | 0.578927i | \(-0.803472\pi\) | ||||
−0.815380 | + | 0.578927i | \(0.803472\pi\) | |||||||
\(332\) | − 10767.7i | − 1.77999i | ||||||||
\(333\) | 3780.63i | 0.622154i | ||||||||
\(334\) | 9153.02 | 1.49949 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2150.12 | 0.349104 | ||||||||
\(337\) | 600.808i | 0.0971161i | 0.998820 | + | 0.0485580i | \(0.0154626\pi\) | ||||
−0.998820 | + | 0.0485580i | \(0.984537\pi\) | |||||||
\(338\) | − 9603.07i | − 1.54538i | ||||||||
\(339\) | −1939.19 | −0.310686 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1546.65 | −0.245618 | ||||||||
\(342\) | − 1387.68i | − 0.219406i | ||||||||
\(343\) | − 10103.5i | − 1.59049i | ||||||||
\(344\) | 5078.73 | 0.796008 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2672.41 | 0.415230 | ||||||||
\(347\) | − 3143.41i | − 0.486303i | −0.969988 | − | 0.243152i | \(-0.921819\pi\) | ||||
0.969988 | − | 0.243152i | \(-0.0781813\pi\) | |||||||
\(348\) | − 2411.89i | − 0.371525i | ||||||||
\(349\) | −720.663 | −0.110533 | −0.0552667 | − | 0.998472i | \(-0.517601\pi\) | ||||
−0.0552667 | + | 0.998472i | \(0.517601\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −139.081 | −0.0211498 | ||||||||
\(352\) | − 2492.58i | − 0.377429i | ||||||||
\(353\) | − 1207.12i | − 0.182007i | −0.995851 | − | 0.0910034i | \(-0.970993\pi\) | ||||
0.995851 | − | 0.0910034i | \(-0.0290074\pi\) | |||||||
\(354\) | −5394.83 | −0.809978 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8479.79 | −1.26244 | ||||||||
\(357\) | − 11595.8i | − 1.71910i | ||||||||
\(358\) | − 9432.99i | − 1.39260i | ||||||||
\(359\) | −8748.31 | −1.28612 | −0.643062 | − | 0.765814i | \(-0.722336\pi\) | ||||
−0.643062 | + | 0.765814i | \(0.722336\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5644.56 | −0.822942 | ||||||||
\(362\) | 2607.63i | 0.378602i | ||||||||
\(363\) | 363.000i | 0.0524864i | ||||||||
\(364\) | −1890.05 | −0.272158 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7385.66 | −1.05479 | ||||||||
\(367\) | − 6730.45i | − 0.957293i | −0.878008 | − | 0.478647i | \(-0.841128\pi\) | ||||
0.878008 | − | 0.478647i | \(-0.158872\pi\) | |||||||
\(368\) | 2628.37i | 0.372318i | ||||||||
\(369\) | 2898.52 | 0.408919 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 155.926 | 0.0218202 | ||||||||
\(372\) | − 4882.73i | − 0.680532i | ||||||||
\(373\) | 227.394i | 0.0315657i | 0.999875 | + | 0.0157828i | \(0.00502404\pi\) | ||||
−0.999875 | + | 0.0157828i | \(0.994976\pi\) | |||||||
\(374\) | −5934.76 | −0.820533 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3660.84 | 0.502110 | ||||||||
\(377\) | − 357.764i | − 0.0488748i | ||||||||
\(378\) | − 3786.60i | − 0.515242i | ||||||||
\(379\) | −11356.2 | −1.53913 | −0.769565 | − | 0.638568i | \(-0.779527\pi\) | ||||
−0.769565 | + | 0.638568i | \(0.779527\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2979.91 | 0.400697 | ||||||||
\(382\) | 9560.74i | 1.28055i | ||||||||
\(383\) | − 10753.6i | − 1.43468i | −0.696725 | − | 0.717338i | \(-0.745360\pi\) | ||||
0.696725 | − | 0.717338i | \(-0.254640\pi\) | |||||||
\(384\) | 5468.07 | 0.726670 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6596.43 | 0.869817 | ||||||||
\(387\) | 2889.32i | 0.379515i | ||||||||
\(388\) | 13560.7i | 1.77433i | ||||||||
\(389\) | 11727.1 | 1.52850 | 0.764252 | − | 0.644918i | \(-0.223109\pi\) | ||||
0.764252 | + | 0.644918i | \(0.223109\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14175.1 | 1.83341 | ||||||||
\(392\) | − 10468.7i | − 1.34885i | ||||||||
\(393\) | 1157.44i | 0.148563i | ||||||||
\(394\) | −1019.96 | −0.130418 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1145.98 | −0.145424 | ||||||||
\(397\) | − 359.905i | − 0.0454990i | −0.999741 | − | 0.0227495i | \(-0.992758\pi\) | ||||
0.999741 | − | 0.0227495i | \(-0.00724202\pi\) | |||||||
\(398\) | 99.1105i | 0.0124823i | ||||||||
\(399\) | 3313.89 | 0.415794 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4066.71 | −0.506438 | −0.253219 | − | 0.967409i | \(-0.581489\pi\) | ||||
−0.253219 | + | 0.967409i | \(0.581489\pi\) | |||||||
\(402\) | 1124.85i | 0.139558i | ||||||||
\(403\) | − 724.274i | − 0.0895252i | ||||||||
\(404\) | 14136.9 | 1.74093 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9740.45 | 1.19067 | ||||||||
\(407\) | 4620.77i | 0.562760i | ||||||||
\(408\) | − 5787.32i | − 0.702242i | ||||||||
\(409\) | 13488.8 | 1.63076 | 0.815379 | − | 0.578927i | \(-0.196528\pi\) | ||||
0.815379 | + | 0.578927i | \(0.196528\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2654.52 | −0.318584 | ||||||||
\(412\) | 5981.62i | 0.715275i | ||||||||
\(413\) | − 12883.3i | − 1.53498i | ||||||||
\(414\) | 4628.83 | 0.549504 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1167.24 | 0.137569 | ||||||||
\(417\) | 3275.83i | 0.384695i | ||||||||
\(418\) | − 1696.05i | − 0.198460i | ||||||||
\(419\) | 7040.12 | 0.820841 | 0.410420 | − | 0.911896i | \(-0.365382\pi\) | ||||
0.410420 | + | 0.911896i | \(0.365382\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9171.74 | 1.06177 | 0.530883 | − | 0.847445i | \(-0.321860\pi\) | ||||
0.530883 | + | 0.847445i | \(0.321860\pi\) | |||||||
\(422\) | 4652.89i | 0.536728i | ||||||||
\(423\) | 2082.67i | 0.239392i | ||||||||
\(424\) | 77.8204 | 0.00891343 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 651.464 | 0.0740928 | ||||||||
\(427\) | − 17637.6i | − 1.99893i | ||||||||
\(428\) | 1759.77i | 0.198742i | ||||||||
\(429\) | −169.988 | −0.0191307 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 992.995 | 0.110976 | 0.0554882 | − | 0.998459i | \(-0.482328\pi\) | ||||
0.0554882 | + | 0.998459i | \(0.482328\pi\) | |||||||
\(432\) | 610.490i | 0.0679912i | ||||||||
\(433\) | − 3790.21i | − 0.420660i | −0.977630 | − | 0.210330i | \(-0.932546\pi\) | ||||
0.977630 | − | 0.210330i | \(-0.0674538\pi\) | |||||||
\(434\) | 19719.0 | 2.18097 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 25122.7 | 2.75954 | ||||||||
\(437\) | 4050.98i | 0.443443i | ||||||||
\(438\) | − 10431.3i | − 1.13796i | ||||||||
\(439\) | 5136.97 | 0.558483 | 0.279242 | − | 0.960221i | \(-0.409917\pi\) | ||||
0.279242 | + | 0.960221i | \(0.409917\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5955.71 | 0.643095 | ||||||||
\(442\) | − 2779.16i | − 0.299075i | ||||||||
\(443\) | − 10676.8i | − 1.14508i | −0.819876 | − | 0.572541i | \(-0.805958\pi\) | ||||
0.819876 | − | 0.572541i | \(-0.194042\pi\) | |||||||
\(444\) | −14587.7 | −1.55923 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −17086.2 | −1.81403 | ||||||||
\(447\) | − 891.042i | − 0.0942838i | ||||||||
\(448\) | 26045.5i | 2.74672i | ||||||||
\(449\) | −10529.9 | −1.10676 | −0.553379 | − | 0.832929i | \(-0.686662\pi\) | ||||
−0.553379 | + | 0.832929i | \(0.686662\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3542.64 | 0.369881 | ||||||||
\(452\) | − 7482.42i | − 0.778636i | ||||||||
\(453\) | − 5663.59i | − 0.587414i | ||||||||
\(454\) | −3861.29 | −0.399162 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1653.91 | 0.169850 | ||||||||
\(457\) | − 14072.5i | − 1.44045i | −0.693741 | − | 0.720225i | \(-0.744039\pi\) | ||||
0.693741 | − | 0.720225i | \(-0.255961\pi\) | |||||||
\(458\) | 8148.55i | 0.831347i | ||||||||
\(459\) | 3292.43 | 0.334810 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.8173 | −0.00311346 | −0.00155673 | − | 0.999999i | \(-0.500496\pi\) | ||||
−0.00155673 | + | 0.999999i | \(0.500496\pi\) | |||||||
\(462\) | − 4628.06i | − 0.466054i | ||||||||
\(463\) | − 17591.3i | − 1.76573i | −0.469622 | − | 0.882867i | \(-0.655610\pi\) | ||||
0.469622 | − | 0.882867i | \(-0.344390\pi\) | |||||||
\(464\) | −1570.39 | −0.157120 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17397.5 | −1.72945 | ||||||||
\(467\) | 13273.1i | 1.31522i | 0.753360 | + | 0.657609i | \(0.228432\pi\) | ||||
−0.753360 | + | 0.657609i | \(0.771568\pi\) | |||||||
\(468\) | − 536.647i | − 0.0530053i | ||||||||
\(469\) | −2686.23 | −0.264474 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 169.603 | 0.0165921 | ||||||||
\(472\) | − 6429.87i | − 0.627031i | ||||||||
\(473\) | 3531.39i | 0.343284i | ||||||||
\(474\) | 5085.23 | 0.492769 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 44742.9 | 4.30837 | ||||||||
\(477\) | 44.2724i | 0.00424968i | ||||||||
\(478\) | 21113.8i | 2.02034i | ||||||||
\(479\) | −2496.68 | −0.238155 | −0.119077 | − | 0.992885i | \(-0.537994\pi\) | ||||
−0.119077 | + | 0.992885i | \(0.537994\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2163.84 | −0.205120 | ||||||||
\(482\) | − 17648.3i | − 1.66776i | ||||||||
\(483\) | 11054.0i | 1.04136i | ||||||||
\(484\) | −1400.64 | −0.131541 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1075.14 | 0.100348 | ||||||||
\(487\) | − 3464.42i | − 0.322357i | −0.986925 | − | 0.161178i | \(-0.948471\pi\) | ||||
0.986925 | − | 0.161178i | \(-0.0515295\pi\) | |||||||
\(488\) | − 8802.65i | − 0.816552i | ||||||||
\(489\) | −147.701 | −0.0136591 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16224.6 | −1.49125 | −0.745625 | − | 0.666366i | \(-0.767849\pi\) | ||||
−0.745625 | + | 0.666366i | \(0.767849\pi\) | |||||||
\(492\) | 11184.0i | 1.02483i | ||||||||
\(493\) | 8469.29i | 0.773707i | ||||||||
\(494\) | 794.236 | 0.0723367 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3179.17 | −0.287800 | ||||||||
\(497\) | 1555.75i | 0.140412i | ||||||||
\(498\) | 12347.0i | 1.11100i | ||||||||
\(499\) | −9993.81 | −0.896562 | −0.448281 | − | 0.893893i | \(-0.647964\pi\) | ||||
−0.448281 | + | 0.893893i | \(0.647964\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6206.24 | −0.553441 | ||||||||
\(502\) | 24220.3i | 2.15340i | ||||||||
\(503\) | 15334.8i | 1.35933i | 0.733520 | + | 0.679667i | \(0.237876\pi\) | ||||
−0.733520 | + | 0.679667i | \(0.762124\pi\) | |||||||
\(504\) | 4513.08 | 0.398866 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5657.46 | 0.497045 | ||||||||
\(507\) | 6511.40i | 0.570377i | ||||||||
\(508\) | 11498.1i | 1.00422i | ||||||||
\(509\) | 7291.23 | 0.634927 | 0.317464 | − | 0.948270i | \(-0.397169\pi\) | ||||
0.317464 | + | 0.948270i | \(0.397169\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24910.7 | 2.15653 | ||||||||
\(512\) | − 7985.14i | − 0.689251i | ||||||||
\(513\) | 940.919i | 0.0809797i | ||||||||
\(514\) | −28466.8 | −2.44283 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −11148.5 | −0.951134 | ||||||||
\(517\) | 2545.49i | 0.216538i | ||||||||
\(518\) | − 58912.5i | − 4.99704i | ||||||||
\(519\) | −1812.04 | −0.153255 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16794.3 | 1.41223 | 0.706114 | − | 0.708098i | \(-0.250447\pi\) | ||||
0.706114 | + | 0.708098i | \(0.250447\pi\) | |||||||
\(522\) | 2765.63i | 0.231893i | ||||||||
\(523\) | 21009.4i | 1.75655i | 0.478157 | + | 0.878275i | \(0.341305\pi\) | ||||
−0.478157 | + | 0.878275i | \(0.658695\pi\) | |||||||
\(524\) | −4466.01 | −0.372326 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −33577.0 | −2.78332 | ||||||||
\(527\) | 17145.6i | 1.41722i | ||||||||
\(528\) | 746.154i | 0.0615003i | ||||||||
\(529\) | −1345.73 | −0.110605 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3657.99 | 0.298951 | ||||||||
\(532\) | 12786.7i | 1.04206i | ||||||||
\(533\) | 1658.97i | 0.134818i | ||||||||
\(534\) | 9723.46 | 0.787969 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1340.66 | −0.108036 | ||||||||
\(537\) | 6396.07i | 0.513987i | ||||||||
\(538\) | 2115.66i | 0.169540i | ||||||||
\(539\) | 7279.20 | 0.581702 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16802.8 | −1.33532 | −0.667662 | − | 0.744464i | \(-0.732705\pi\) | ||||
−0.667662 | + | 0.744464i | \(0.732705\pi\) | |||||||
\(542\) | 541.211i | 0.0428911i | ||||||||
\(543\) | − 1768.11i | − 0.139737i | ||||||||
\(544\) | −27631.9 | −2.17777 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2167.25 | 0.169872 | ||||||||
\(547\) | 16784.5i | 1.31198i | 0.754770 | + | 0.655990i | \(0.227749\pi\) | ||||
−0.754770 | + | 0.655990i | \(0.772251\pi\) | |||||||
\(548\) | − 10242.5i | − 0.798429i | ||||||||
\(549\) | 5007.88 | 0.389309 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2420.37 | −0.187135 | ||||||||
\(552\) | 5516.91i | 0.425390i | ||||||||
\(553\) | 12144.0i | 0.933840i | ||||||||
\(554\) | 36277.7 | 2.78212 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12639.9 | −0.964117 | ||||||||
\(557\) | 18127.0i | 1.37893i | 0.724317 | + | 0.689467i | \(0.242155\pi\) | ||||
−0.724317 | + | 0.689467i | \(0.757845\pi\) | |||||||
\(558\) | 5598.85i | 0.424764i | ||||||||
\(559\) | −1653.70 | −0.125123 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4024.09 | 0.302847 | ||||||||
\(562\) | − 30722.3i | − 2.30595i | ||||||||
\(563\) | − 2090.88i | − 0.156518i | −0.996933 | − | 0.0782592i | \(-0.975064\pi\) | ||||
0.996933 | − | 0.0782592i | \(-0.0249362\pi\) | |||||||
\(564\) | −8036.03 | −0.599961 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4579.89 | −0.340119 | ||||||||
\(567\) | 2567.51i | 0.190168i | ||||||||
\(568\) | 776.452i | 0.0573578i | ||||||||
\(569\) | −6249.23 | −0.460424 | −0.230212 | − | 0.973140i | \(-0.573942\pi\) | ||||
−0.230212 | + | 0.973140i | \(0.573942\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6048.79 | 0.443317 | 0.221659 | − | 0.975124i | \(-0.428853\pi\) | ||||
0.221659 | + | 0.975124i | \(0.428853\pi\) | |||||||
\(572\) | − 655.902i | − 0.0479451i | ||||||||
\(573\) | − 6482.69i | − 0.472633i | ||||||||
\(574\) | −45166.8 | −3.28437 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7395.15 | −0.534950 | ||||||||
\(577\) | − 15729.1i | − 1.13486i | −0.823423 | − | 0.567429i | \(-0.807938\pi\) | ||||
0.823423 | − | 0.567429i | \(-0.192062\pi\) | |||||||
\(578\) | 44053.4i | 3.17021i | ||||||||
\(579\) | −4472.73 | −0.321037 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29485.6 | −2.10545 | ||||||||
\(582\) | − 15549.5i | − 1.10747i | ||||||||
\(583\) | 54.1108i | 0.00384398i | ||||||||
\(584\) | 12432.6 | 0.880931 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27187.3 | 1.91655 | ||||||||
\(587\) | 15620.5i | 1.09835i | 0.835709 | + | 0.549173i | \(0.185057\pi\) | ||||
−0.835709 | + | 0.549173i | \(0.814943\pi\) | |||||||
\(588\) | 22980.2i | 1.61172i | ||||||||
\(589\) | −4899.91 | −0.342780 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 691.587 | 0.0481355 | ||||||||
\(592\) | 9498.09i | 0.659407i | ||||||||
\(593\) | 493.541i | 0.0341776i | 0.999854 | + | 0.0170888i | \(0.00543980\pi\) | ||||
−0.999854 | + | 0.0170888i | \(0.994560\pi\) | |||||||
\(594\) | 1314.06 | 0.0907683 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3438.11 | 0.236293 | ||||||||
\(597\) | − 67.2022i | − 0.00460704i | ||||||||
\(598\) | 2649.31i | 0.181168i | ||||||||
\(599\) | 12455.1 | 0.849585 | 0.424793 | − | 0.905291i | \(-0.360347\pi\) | ||||
0.424793 | + | 0.905291i | \(0.360347\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12454.8 | 0.845329 | 0.422664 | − | 0.906286i | \(-0.361095\pi\) | ||||
0.422664 | + | 0.906286i | \(0.361095\pi\) | |||||||
\(602\) | − 45023.3i | − 3.04820i | ||||||||
\(603\) | − 762.707i | − 0.0515088i | ||||||||
\(604\) | 21853.1 | 1.47217 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −16210.3 | −1.08663 | ||||||||
\(607\) | − 4243.19i | − 0.283733i | −0.989886 | − | 0.141867i | \(-0.954690\pi\) | ||||
0.989886 | − | 0.141867i | \(-0.0453104\pi\) | |||||||
\(608\) | − 7896.70i | − 0.526732i | ||||||||
\(609\) | −6604.54 | −0.439458 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1192.01 | −0.0789259 | ||||||||
\(612\) | 12703.9i | 0.839095i | ||||||||
\(613\) | − 5733.14i | − 0.377748i | −0.982001 | − | 0.188874i | \(-0.939516\pi\) | ||||
0.982001 | − | 0.188874i | \(-0.0604838\pi\) | |||||||
\(614\) | −9672.18 | −0.635729 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5515.99 | 0.360788 | ||||||||
\(617\) | 15642.1i | 1.02063i | 0.859988 | + | 0.510314i | \(0.170471\pi\) | ||||
−0.859988 | + | 0.510314i | \(0.829529\pi\) | |||||||
\(618\) | − 6858.91i | − 0.446449i | ||||||||
\(619\) | 7467.40 | 0.484879 | 0.242440 | − | 0.970167i | \(-0.422052\pi\) | ||||
0.242440 | + | 0.970167i | \(0.422052\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3138.60 | −0.202814 | ||||||||
\(622\) | 33116.1i | 2.13478i | ||||||||
\(623\) | 23220.4i | 1.49327i | ||||||||
\(624\) | −349.413 | −0.0224162 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 30233.6 | 1.93031 | ||||||||
\(627\) | 1150.01i | 0.0732489i | ||||||||
\(628\) | 654.416i | 0.0415829i | ||||||||
\(629\) | 51224.2 | 3.24713 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1486.38 | −0.0937745 | −0.0468872 | − | 0.998900i | \(-0.514930\pi\) | ||||
−0.0468872 | + | 0.998900i | \(0.514930\pi\) | |||||||
\(632\) | 6060.87i | 0.381469i | ||||||||
\(633\) | − 3154.91i | − 0.198099i | ||||||||
\(634\) | 4089.35 | 0.256165 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −170.826 | −0.0106505 | ||||||||
\(637\) | 3408.74i | 0.212024i | ||||||||
\(638\) | 3380.21i | 0.209755i | ||||||||
\(639\) | −441.728 | −0.0273466 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12386.0 | 0.763211 | 0.381606 | − | 0.924325i | \(-0.375371\pi\) | ||||
0.381606 | + | 0.924325i | \(0.375371\pi\) | |||||||
\(642\) | − 2017.87i | − 0.124048i | ||||||||
\(643\) | 14458.1i | 0.886737i | 0.896339 | + | 0.443369i | \(0.146217\pi\) | ||||
−0.896339 | + | 0.443369i | \(0.853783\pi\) | |||||||
\(644\) | −42652.3 | −2.60984 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18801.8 | −1.14512 | ||||||||
\(647\) | 15792.8i | 0.959625i | 0.877371 | + | 0.479813i | \(0.159295\pi\) | ||||
−0.877371 | + | 0.479813i | \(0.840705\pi\) | |||||||
\(648\) | 1281.41i | 0.0776828i | ||||||||
\(649\) | 4470.87 | 0.270412 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13370.5 | −0.804965 | ||||||||
\(652\) | − 569.909i | − 0.0342321i | ||||||||
\(653\) | 3179.93i | 0.190567i | 0.995450 | + | 0.0952837i | \(0.0303758\pi\) | ||||
−0.995450 | + | 0.0952837i | \(0.969624\pi\) | |||||||
\(654\) | −28807.3 | −1.72240 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7281.96 | 0.433404 | ||||||||
\(657\) | 7072.96i | 0.420003i | ||||||||
\(658\) | − 32453.6i | − 1.92276i | ||||||||
\(659\) | −11593.5 | −0.685308 | −0.342654 | − | 0.939462i | \(-0.611326\pi\) | ||||
−0.342654 | + | 0.939462i | \(0.611326\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3233.88 | 0.190293 | 0.0951464 | − | 0.995463i | \(-0.469668\pi\) | ||||
0.0951464 | + | 0.995463i | \(0.469668\pi\) | |||||||
\(662\) | 43449.9i | 2.55095i | ||||||||
\(663\) | 1884.42i | 0.110384i | ||||||||
\(664\) | −14715.8 | −0.860066 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16727.1 | 0.973219 | ||||||||
\(667\) | − 8073.56i | − 0.468680i | ||||||||
\(668\) | − 23946.9i | − 1.38703i | ||||||||
\(669\) | 11585.4 | 0.669532 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6120.74 | 0.352144 | ||||||||
\(672\) | − 21548.0i | − 1.23695i | ||||||||
\(673\) | 5495.72i | 0.314776i | 0.987537 | + | 0.157388i | \(0.0503074\pi\) | ||||
−0.987537 | + | 0.157388i | \(0.949693\pi\) | |||||||
\(674\) | 2658.23 | 0.151916 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −25124.4 | −1.42947 | ||||||||
\(677\) | 33836.7i | 1.92090i | 0.278448 | + | 0.960451i | \(0.410180\pi\) | ||||
−0.278448 | + | 0.960451i | \(0.589820\pi\) | |||||||
\(678\) | 8579.82i | 0.485997i | ||||||||
\(679\) | 37133.6 | 2.09876 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2618.16 | 0.147325 | ||||||||
\(682\) | 6843.04i | 0.384214i | ||||||||
\(683\) | 21080.3i | 1.18099i | 0.807043 | + | 0.590493i | \(0.201067\pi\) | ||||
−0.807043 | + | 0.590493i | \(0.798933\pi\) | |||||||
\(684\) | −3630.56 | −0.202950 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −44702.2 | −2.48796 | ||||||||
\(687\) | − 5525.16i | − 0.306838i | ||||||||
\(688\) | 7258.84i | 0.402239i | ||||||||
\(689\) | −25.3393 | −0.00140109 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11811.3 | 0.650253 | 0.325127 | − | 0.945671i | \(-0.394593\pi\) | ||||
0.325127 | + | 0.945671i | \(0.394593\pi\) | |||||||
\(692\) | − 6991.79i | − 0.384087i | ||||||||
\(693\) | 3138.07i | 0.172014i | ||||||||
\(694\) | −13907.8 | −0.760711 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3296.23 | −0.179516 | ||||||||
\(697\) | − 39272.4i | − 2.13422i | ||||||||
\(698\) | 3188.52i | 0.172904i | ||||||||
\(699\) | 11796.4 | 0.638313 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4244.99 | 0.228718 | 0.114359 | − | 0.993440i | \(-0.463519\pi\) | ||||
0.114359 | + | 0.993440i | \(0.463519\pi\) | |||||||
\(702\) | 615.353i | 0.0330841i | ||||||||
\(703\) | 14639.0i | 0.785376i | ||||||||
\(704\) | −9038.51 | −0.483880 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5340.81 | −0.284708 | ||||||||
\(707\) | − 38711.5i | − 2.05926i | ||||||||
\(708\) | 14114.4i | 0.749227i | ||||||||
\(709\) | 898.822 | 0.0476107 | 0.0238053 | − | 0.999717i | \(-0.492422\pi\) | ||||
0.0238053 | + | 0.999717i | \(0.492422\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3448.06 | −0.181874 | ||||||||
\(712\) | 11589.0i | 0.609993i | ||||||||
\(713\) | − 16344.5i | − 0.858493i | ||||||||
\(714\) | −51305.0 | −2.68913 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24679.4 | −1.28815 | ||||||||
\(717\) | − 14316.3i | − 0.745679i | ||||||||
\(718\) | 38706.3i | 2.01185i | ||||||||
\(719\) | −10741.8 | −0.557165 | −0.278582 | − | 0.960412i | \(-0.589865\pi\) | ||||
−0.278582 | + | 0.960412i | \(0.589865\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16379.6 | 0.846061 | ||||||||
\(722\) | 24973.9i | 1.28730i | ||||||||
\(723\) | 11966.5i | 0.615546i | ||||||||
\(724\) | 6822.30 | 0.350206 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1606.07 | 0.0821030 | ||||||||
\(727\) | 16794.2i | 0.856758i | 0.903599 | + | 0.428379i | \(0.140915\pi\) | ||||
−0.903599 | + | 0.428379i | \(0.859085\pi\) | |||||||
\(728\) | 2583.06i | 0.131503i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39147.7 | 1.98075 | ||||||||
\(732\) | 19323.0i | 0.975681i | ||||||||
\(733\) | − 8659.40i | − 0.436347i | −0.975910 | − | 0.218173i | \(-0.929990\pi\) | ||||
0.975910 | − | 0.218173i | \(-0.0700098\pi\) | |||||||
\(734\) | −29778.4 | −1.49747 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26340.8 | 1.31920 | ||||||||
\(737\) | − 932.197i | − 0.0465915i | ||||||||
\(738\) | − 12824.3i | − 0.639660i | ||||||||
\(739\) | −16705.7 | −0.831567 | −0.415783 | − | 0.909464i | \(-0.636493\pi\) | ||||
−0.415783 | + | 0.909464i | \(0.636493\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −538.534 | −0.0266984 | ||||||||
\(742\) | − 689.884i | − 0.0341327i | ||||||||
\(743\) | − 1292.12i | − 0.0637996i | −0.999491 | − | 0.0318998i | \(-0.989844\pi\) | ||||
0.999491 | − | 0.0318998i | \(-0.0101558\pi\) | |||||||
\(744\) | −6673.03 | −0.328824 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1006.09 | 0.0493773 | ||||||||
\(747\) | − 8371.90i | − 0.410056i | ||||||||
\(748\) | 15527.0i | 0.758990i | ||||||||
\(749\) | 4818.83 | 0.235082 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14980.4 | −0.727886 | −0.363943 | − | 0.931421i | \(-0.618570\pi\) | ||||
−0.363943 | + | 0.931421i | \(0.618570\pi\) | |||||||
\(752\) | 5232.30i | 0.253726i | ||||||||
\(753\) | − 16422.7i | − 0.794787i | ||||||||
\(754\) | −1582.90 | −0.0764535 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −9906.82 | −0.476597 | ||||||||
\(757\) | 3003.41i | 0.144202i | 0.997397 | + | 0.0721010i | \(0.0229704\pi\) | ||||
−0.997397 | + | 0.0721010i | \(0.977030\pi\) | |||||||
\(758\) | 50244.8i | 2.40762i | ||||||||
\(759\) | −3836.06 | −0.183452 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20375.0 | −0.970555 | −0.485277 | − | 0.874360i | \(-0.661281\pi\) | ||||
−0.485277 | + | 0.874360i | \(0.661281\pi\) | |||||||
\(762\) | − 13184.4i | − 0.626799i | ||||||||
\(763\) | − 68794.1i | − 3.26411i | ||||||||
\(764\) | 25013.6 | 1.18450 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −47578.4 | −2.24422 | ||||||||
\(767\) | 2093.65i | 0.0985621i | ||||||||
\(768\) | − 4472.70i | − 0.210149i | ||||||||
\(769\) | 12372.4 | 0.580184 | 0.290092 | − | 0.956999i | \(-0.406314\pi\) | ||||
0.290092 | + | 0.956999i | \(0.406314\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19302.0 | 0.901615 | ||||||||
\(772\) | − 17258.1i | − 0.804578i | ||||||||
\(773\) | − 21023.6i | − 0.978225i | −0.872221 | − | 0.489113i | \(-0.837321\pi\) | ||||
0.872221 | − | 0.489113i | \(-0.162679\pi\) | |||||||
\(774\) | 12783.6 | 0.593664 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 18532.8 | 0.857331 | ||||||||
\(777\) | 39945.8i | 1.84433i | ||||||||
\(778\) | − 51885.7i | − 2.39099i | ||||||||
\(779\) | 11223.4 | 0.516198 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −539.889 | −0.0247359 | ||||||||
\(782\) | − 62716.6i | − 2.86795i | ||||||||
\(783\) | − 1875.24i | − 0.0855884i | ||||||||
\(784\) | 14962.5 | 0.681602 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5121.02 | 0.232393 | ||||||||
\(787\) | 30286.2i | 1.37177i | 0.727709 | + | 0.685886i | \(0.240585\pi\) | ||||
−0.727709 | + | 0.685886i | \(0.759415\pi\) | |||||||
\(788\) | 2668.51i | 0.120637i | ||||||||
\(789\) | 22767.0 | 1.02728 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20489.3 | −0.921007 | ||||||||
\(792\) | 1566.17i | 0.0702668i | ||||||||
\(793\) | 2866.25i | 0.128353i | ||||||||
\(794\) | −1592.37 | −0.0711729 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 259.301 | 0.0115461 | ||||||||
\(797\) | 32337.8i | 1.43722i | 0.695413 | + | 0.718610i | \(0.255221\pi\) | ||||
−0.695413 | + | 0.718610i | \(0.744779\pi\) | |||||||
\(798\) | − 14662.1i | − 0.650415i | ||||||||
\(799\) | 28218.3 | 1.24943 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6593.03 | −0.290828 | ||||||||
\(802\) | 17992.9i | 0.792207i | ||||||||
\(803\) | 8644.72i | 0.379907i | ||||||||
\(804\) | 2942.92 | 0.129091 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3204.50 | −0.140042 | ||||||||
\(807\) | − 1434.53i | − 0.0625749i | ||||||||
\(808\) | − 19320.3i | − 0.841197i | ||||||||
\(809\) | 891.707 | 0.0387525 | 0.0193762 | − | 0.999812i | \(-0.493832\pi\) | ||||
0.0193762 | + | 0.999812i | \(0.493832\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10114.9 | −0.437957 | −0.218978 | − | 0.975730i | \(-0.570272\pi\) | ||||
−0.218978 | + | 0.975730i | \(0.570272\pi\) | |||||||
\(812\) | − 25483.8i | − 1.10136i | ||||||||
\(813\) | − 366.970i | − 0.0158305i | ||||||||
\(814\) | 20444.3 | 0.880309 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8271.59 | 0.354857 | ||||||||
\(817\) | 11187.7i | 0.479080i | ||||||||
\(818\) | − 59680.4i | − 2.55095i | ||||||||
\(819\) | −1469.51 | −0.0626972 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10833.5 | 0.460525 | 0.230262 | − | 0.973129i | \(-0.426042\pi\) | ||||
0.230262 | + | 0.973129i | \(0.426042\pi\) | |||||||
\(822\) | 11744.7i | 0.498351i | ||||||||
\(823\) | − 31958.5i | − 1.35359i | −0.736173 | − | 0.676794i | \(-0.763369\pi\) | ||||
0.736173 | − | 0.676794i | \(-0.236631\pi\) | |||||||
\(824\) | 8174.84 | 0.345612 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −57001.3 | −2.40112 | ||||||||
\(827\) | 34847.3i | 1.46525i | 0.680634 | + | 0.732624i | \(0.261704\pi\) | ||||
−0.680634 | + | 0.732624i | \(0.738296\pi\) | |||||||
\(828\) | − 12110.3i | − 0.508289i | ||||||||
\(829\) | −6537.91 | −0.273910 | −0.136955 | − | 0.990577i | \(-0.543732\pi\) | ||||
−0.136955 | + | 0.990577i | \(0.543732\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24598.2 | −1.02684 | ||||||||
\(832\) | − 4232.60i | − 0.176369i | ||||||||
\(833\) | − 80694.5i | − 3.35642i | ||||||||
\(834\) | 14493.7 | 0.601768 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4437.35 | −0.183575 | ||||||||
\(837\) | − 3796.32i | − 0.156774i | ||||||||
\(838\) | − 31148.5i | − 1.28402i | ||||||||
\(839\) | −2710.34 | −0.111527 | −0.0557635 | − | 0.998444i | \(-0.517759\pi\) | ||||
−0.0557635 | + | 0.998444i | \(0.517759\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19565.2 | −0.802215 | ||||||||
\(842\) | − 40579.7i | − 1.66089i | ||||||||
\(843\) | 20831.4i | 0.851092i | ||||||||
\(844\) | 12173.3 | 0.496471 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9214.62 | 0.374474 | ||||||||
\(847\) | 3835.42i | 0.155592i | ||||||||
\(848\) | 111.226i | 0.00450414i | ||||||||
\(849\) | 3105.41 | 0.125533 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −48830.8 | −1.96698 | ||||||||
\(852\) | − 1704.42i | − 0.0685356i | ||||||||
\(853\) | − 9759.32i | − 0.391738i | −0.980630 | − | 0.195869i | \(-0.937247\pi\) | ||||
0.980630 | − | 0.195869i | \(-0.0627528\pi\) | |||||||
\(854\) | −78036.2 | −3.12687 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2405.01 | 0.0960298 | ||||||||
\(857\) | − 13649.8i | − 0.544072i | −0.962287 | − | 0.272036i | \(-0.912303\pi\) | ||||
0.962287 | − | 0.272036i | \(-0.0876970\pi\) | |||||||
\(858\) | 752.098i | 0.0299257i | ||||||||
\(859\) | −7796.42 | −0.309674 | −0.154837 | − | 0.987940i | \(-0.549485\pi\) | ||||
−0.154837 | + | 0.987940i | \(0.549485\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 30625.5 | 1.21221 | ||||||||
\(862\) | − 4393.43i | − 0.173597i | ||||||||
\(863\) | − 7183.57i | − 0.283350i | −0.989913 | − | 0.141675i | \(-0.954751\pi\) | ||||
0.989913 | − | 0.141675i | \(-0.0452489\pi\) | |||||||
\(864\) | 6118.16 | 0.240907 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16769.5 | −0.658026 | ||||||||
\(867\) | − 29870.6i | − 1.17008i | ||||||||
\(868\) | − 51590.5i | − 2.01739i | ||||||||
\(869\) | −4214.30 | −0.164511 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 436.534 | 0.0169821 | ||||||||
\(872\) | − 34334.1i | − 1.33337i | ||||||||
\(873\) | 10543.4i | 0.408752i | ||||||||
\(874\) | 17923.3 | 0.693666 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −27291.2 | −1.05261 | ||||||||
\(877\) | 17063.1i | 0.656991i | 0.944506 | + | 0.328495i | \(0.106542\pi\) | ||||
−0.944506 | + | 0.328495i | \(0.893458\pi\) | |||||||
\(878\) | − 22728.2i | − 0.873620i | ||||||||
\(879\) | −18434.4 | −0.707369 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32174.9 | −1.23042 | −0.615210 | − | 0.788363i | \(-0.710929\pi\) | ||||
−0.615210 | + | 0.788363i | \(0.710929\pi\) | |||||||
\(882\) | − 26350.6i | − 1.00598i | ||||||||
\(883\) | − 2843.68i | − 0.108378i | −0.998531 | − | 0.0541889i | \(-0.982743\pi\) | ||||
0.998531 | − | 0.0541889i | \(-0.0172573\pi\) | |||||||
\(884\) | −7271.09 | −0.276644 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −47238.9 | −1.79122 | ||||||||
\(887\) | − 31417.8i | − 1.18930i | −0.803985 | − | 0.594649i | \(-0.797291\pi\) | ||||
0.803985 | − | 0.594649i | \(-0.202709\pi\) | |||||||
\(888\) | 19936.4i | 0.753401i | ||||||||
\(889\) | 31485.5 | 1.18784 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −891.000 | −0.0335013 | ||||||||
\(892\) | 44702.5i | 1.67797i | ||||||||
\(893\) | 8064.30i | 0.302196i | ||||||||
\(894\) | −3942.35 | −0.147485 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 57775.1 | 2.15416 | ||||||||
\(897\) | − 1796.37i | − 0.0668664i | ||||||||
\(898\) | 46588.6i | 1.73127i | ||||||||
\(899\) | 9765.47 | 0.362288 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 599.852 | 0.0221798 | ||||||||
\(902\) | − 15674.1i | − 0.578594i | ||||||||
\(903\) | 30528.2i | 1.12505i | ||||||||
\(904\) | −10225.9 | −0.376227 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −25058.1 | −0.918875 | ||||||||
\(907\) | 12253.1i | 0.448573i | 0.974523 | + | 0.224287i | \(0.0720052\pi\) | ||||
−0.974523 | + | 0.224287i | \(0.927995\pi\) | |||||||
\(908\) | 10102.2i | 0.369223i | ||||||||
\(909\) | 10991.4 | 0.401059 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48422.4 | −1.76104 | −0.880518 | − | 0.474012i | \(-0.842805\pi\) | ||||
−0.880518 | + | 0.474012i | \(0.842805\pi\) | |||||||
\(912\) | 2363.87i | 0.0858286i | ||||||||
\(913\) | − 10232.3i | − 0.370909i | ||||||||
\(914\) | −62262.9 | −2.25326 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21318.9 | 0.768993 | ||||||||
\(917\) | 12229.4i | 0.440404i | ||||||||
\(918\) | − 14567.1i | − 0.523733i | ||||||||
\(919\) | −5546.18 | −0.199077 | −0.0995385 | − | 0.995034i | \(-0.531737\pi\) | ||||
−0.0995385 | + | 0.995034i | \(0.531737\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6558.26 | 0.234638 | ||||||||
\(922\) | 136.349i | 0.00487030i | ||||||||
\(923\) | − 252.822i | − 0.00901598i | ||||||||
\(924\) | −12108.3 | −0.431098 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −77831.3 | −2.76209 | ||||||||
\(927\) | 4650.71i | 0.164778i | ||||||||
\(928\) | 15738.0i | 0.556709i | ||||||||
\(929\) | 35684.5 | 1.26025 | 0.630125 | − | 0.776494i | \(-0.283004\pi\) | ||||
0.630125 | + | 0.776494i | \(0.283004\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23061.1 | 0.811811 | ||||||||
\(932\) | 45516.7i | 1.59973i | ||||||||
\(933\) | − 22454.5i | − 0.787918i | ||||||||
\(934\) | 58726.0 | 2.05736 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −733.413 | −0.0256115 | ||||||||
\(937\) | − 48903.6i | − 1.70503i | −0.522705 | − | 0.852514i | \(-0.675077\pi\) | ||||
0.522705 | − | 0.852514i | \(-0.324923\pi\) | |||||||
\(938\) | 11885.0i | 0.413710i | ||||||||
\(939\) | −20500.0 | −0.712451 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23741.9 | −0.822490 | −0.411245 | − | 0.911525i | \(-0.634906\pi\) | ||||
−0.411245 | + | 0.911525i | \(0.634906\pi\) | |||||||
\(942\) | − 750.396i | − 0.0259546i | ||||||||
\(943\) | 37437.4i | 1.29282i | ||||||||
\(944\) | 9189.97 | 0.316852 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15624.4 | 0.536989 | ||||||||
\(947\) | 37612.4i | 1.29064i | 0.763911 | + | 0.645321i | \(0.223276\pi\) | ||||
−0.763911 | + | 0.645321i | \(0.776724\pi\) | |||||||
\(948\) | − 13304.4i | − 0.455810i | ||||||||
\(949\) | −4048.20 | −0.138472 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2772.80 | −0.0945469 | ||||||||
\(952\) | − 61148.2i | − 2.08175i | ||||||||
\(953\) | 48294.3i | 1.64156i | 0.571246 | + | 0.820779i | \(0.306460\pi\) | ||||
−0.571246 | + | 0.820779i | \(0.693540\pi\) | |||||||
\(954\) | 195.880 | 0.00664765 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 55239.8 | 1.86881 | ||||||||
\(957\) | − 2291.96i | − 0.0774176i | ||||||||
\(958\) | 11046.4i | 0.372539i | ||||||||
\(959\) | −28047.4 | −0.944419 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10021.4 | −0.336389 | ||||||||
\(962\) | 9573.76i | 0.320863i | ||||||||
\(963\) | 1368.22i | 0.0457843i | ||||||||
\(964\) | −46173.1 | −1.54267 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 48907.8 | 1.62897 | ||||||||
\(967\) | 1840.92i | 0.0612204i | 0.999531 | + | 0.0306102i | \(0.00974505\pi\) | ||||
−0.999531 | + | 0.0306102i | \(0.990255\pi\) | |||||||
\(968\) | 1914.20i | 0.0635587i | ||||||||
\(969\) | 12748.6 | 0.422647 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31461.8 | 1.03981 | 0.519906 | − | 0.854223i | \(-0.325967\pi\) | ||||
0.519906 | + | 0.854223i | \(0.325967\pi\) | |||||||
\(972\) | − 2812.86i | − 0.0928217i | ||||||||
\(973\) | 34612.1i | 1.14040i | ||||||||
\(974\) | −15328.1 | −0.504254 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12581.3 | 0.412620 | ||||||||
\(977\) | − 7040.11i | − 0.230535i | −0.993334 | − | 0.115268i | \(-0.963227\pi\) | ||||
0.993334 | − | 0.115268i | \(-0.0367726\pi\) | |||||||
\(978\) | 653.494i | 0.0213665i | ||||||||
\(979\) | −8058.15 | −0.263064 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19532.9 | 0.635715 | ||||||||
\(982\) | 71784.4i | 2.33272i | ||||||||
\(983\) | 24610.9i | 0.798541i | 0.916833 | + | 0.399270i | \(0.130737\pi\) | ||||
−0.916833 | + | 0.399270i | \(0.869263\pi\) | |||||||
\(984\) | 15284.7 | 0.495183 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 37471.8 | 1.21029 | ||||||||
\(987\) | 22005.3i | 0.709662i | ||||||||
\(988\) | − 2077.95i | − 0.0669112i | ||||||||
\(989\) | −37318.5 | −1.19986 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40003.3 | −1.28229 | −0.641144 | − | 0.767421i | \(-0.721540\pi\) | ||||
−0.641144 | + | 0.767421i | \(0.721540\pi\) | |||||||
\(992\) | 31860.8i | 1.01974i | ||||||||
\(993\) | − 29461.4i | − 0.941519i | ||||||||
\(994\) | 6883.31 | 0.219643 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 32303.2 | 1.02768 | ||||||||
\(997\) | − 7342.61i | − 0.233242i | −0.993176 | − | 0.116621i | \(-0.962794\pi\) | ||||
0.993176 | − | 0.116621i | \(-0.0372063\pi\) | |||||||
\(998\) | 44216.9i | 1.40247i | ||||||||
\(999\) | −11341.9 | −0.359201 |
(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 | 825.4.c.h.199.2 | 4 | ||
5.2 | odd | 4 | 825.4.a.l.1.2 | 2 | |||
5.3 | odd | 4 | 33.4.a.c.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 825.4.c.h.199.3 | 4 | ||
15.2 | even | 4 | 2475.4.a.p.1.1 | 2 | |||
15.8 | even | 4 | 99.4.a.f.1.2 | 2 | |||
20.3 | even | 4 | 528.4.a.p.1.2 | 2 | |||
35.13 | even | 4 | 1617.4.a.k.1.1 | 2 | |||
40.3 | even | 4 | 2112.4.a.bg.1.1 | 2 | |||
40.13 | odd | 4 | 2112.4.a.bn.1.1 | 2 | |||
55.43 | even | 4 | 363.4.a.i.1.2 | 2 | |||
60.23 | odd | 4 | 1584.4.a.bj.1.1 | 2 | |||
165.98 | odd | 4 | 1089.4.a.u.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.4.a.c.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
99.4.a.f.1.2 | 2 | 15.8 | even | 4 | |||
363.4.a.i.1.2 | 2 | 55.43 | even | 4 | |||
528.4.a.p.1.2 | 2 | 20.3 | even | 4 | |||
825.4.a.l.1.2 | 2 | 5.2 | odd | 4 | |||
825.4.c.h.199.2 | 4 | 1.1 | even | 1 | trivial | ||
825.4.c.h.199.3 | 4 | 5.4 | even | 2 | inner | ||
1089.4.a.u.1.1 | 2 | 165.98 | odd | 4 | |||
1584.4.a.bj.1.1 | 2 | 60.23 | odd | 4 | |||
1617.4.a.k.1.1 | 2 | 35.13 | even | 4 | |||
2112.4.a.bg.1.1 | 2 | 40.3 | even | 4 | |||
2112.4.a.bn.1.1 | 2 | 40.13 | odd | 4 | |||
2475.4.a.p.1.1 | 2 | 15.2 | even | 4 |