Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [153,4,Mod(19,153)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(153, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("153.19");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 153 = 3^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 153.l (of order \(8\), degree \(4\), 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: | \(9.02729223088\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 54x^{10} + 1085x^{8} + 9836x^{6} + 38276x^{4} + 49664x^{2} + 16384 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 17) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 100.2 | ||
Root | \(-1.22788i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 153.100 |
Dual form | 153.4.l.a.127.2 |
$q$-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 \(\left(\mathbb{Z}/153\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(137\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.161134 | + | 0.161134i | 0.0569694 | + | 0.0569694i | 0.735018 | − | 0.678048i | \(-0.237174\pi\) |
−0.678048 | + | 0.735018i | \(0.737174\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 7.94807i | − | 0.993509i | ||||||
\(5\) | −2.54200 | + | 1.05293i | −0.227364 | + | 0.0941771i | −0.493457 | − | 0.869770i | \(-0.664267\pi\) |
0.266094 | + | 0.963947i | \(0.414267\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −19.8837 | − | 8.23610i | −1.07362 | − | 0.444707i | −0.225352 | − | 0.974277i | \(-0.572353\pi\) |
−0.848266 | + | 0.529570i | \(0.822353\pi\) | |||||||
\(8\) | 2.56978 | − | 2.56978i | 0.113569 | − | 0.113569i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.579266 | − | 0.239940i | −0.0183180 | − | 0.00758756i | ||||
\(11\) | −20.8709 | + | 50.3869i | −0.572075 | + | 1.38111i | 0.327711 | + | 0.944778i | \(0.393723\pi\) |
−0.899785 | + | 0.436333i | \(0.856277\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 52.4827i | 1.11970i | 0.828594 | + | 0.559850i | \(0.189141\pi\) | ||||
−0.828594 | + | 0.559850i | \(0.810859\pi\) | |||||||
\(14\) | −1.87682 | − | 4.53105i | −0.0358287 | − | 0.0864982i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −62.7564 | −0.980569 | ||||||||
\(17\) | −33.5380 | − | 61.5484i | −0.478479 | − | 0.878099i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13.8808 | + | 13.8808i | 0.167604 | + | 0.167604i | 0.785925 | − | 0.618321i | \(-0.212187\pi\) |
−0.618321 | + | 0.785925i | \(0.712187\pi\) | |||||||
\(20\) | 8.36878 | + | 20.2040i | 0.0935658 | + | 0.225888i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −11.4821 | + | 4.75602i | −0.111272 | + | 0.0460903i | ||||
\(23\) | 5.33276 | − | 12.8744i | 0.0483460 | − | 0.116717i | −0.897862 | − | 0.440278i | \(-0.854880\pi\) |
0.946207 | + | 0.323560i | \(0.104880\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −83.0352 | + | 83.0352i | −0.664282 | + | 0.664282i | ||||
\(26\) | −8.45675 | + | 8.45675i | −0.0637886 | + | 0.0637886i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −65.4611 | + | 158.037i | −0.441821 | + | 1.06665i | ||||
\(29\) | −64.6920 | + | 26.7963i | −0.414241 | + | 0.171584i | −0.580063 | − | 0.814571i | \(-0.696972\pi\) |
0.165822 | + | 0.986156i | \(0.446972\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −63.9131 | − | 154.300i | −0.370295 | − | 0.893971i | −0.993700 | − | 0.112072i | \(-0.964251\pi\) |
0.623405 | − | 0.781899i | \(-0.285749\pi\) | |||||||
\(32\) | −30.6704 | − | 30.6704i | −0.169432 | − | 0.169432i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.51343 | − | 15.3216i | 0.0227661 | − | 0.0772835i | ||||
\(35\) | 59.2165 | 0.285983 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −76.0152 | − | 183.517i | −0.337752 | − | 0.815405i | −0.997931 | − | 0.0642968i | \(-0.979520\pi\) |
0.660179 | − | 0.751108i | \(-0.270480\pi\) | |||||||
\(38\) | 4.47334i | 0.0190966i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.82658 | + | 9.23817i | −0.0151259 | + | 0.0365171i | ||||
\(41\) | −401.250 | − | 166.203i | −1.52841 | − | 0.633087i | −0.549153 | − | 0.835722i | \(-0.685050\pi\) |
−0.979254 | + | 0.202634i | \(0.935050\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 89.9025 | − | 89.9025i | 0.318837 | − | 0.318837i | −0.529483 | − | 0.848320i | \(-0.677614\pi\) |
0.848320 | + | 0.529483i | \(0.177614\pi\) | |||||||
\(44\) | 400.479 | + | 165.884i | 1.37215 | + | 0.568361i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.93379 | − | 1.21522i | 0.00940357 | − | 0.00389509i | ||||
\(47\) | 207.303i | 0.643366i | 0.946847 | + | 0.321683i | \(0.104249\pi\) | ||||
−0.946847 | + | 0.321683i | \(0.895751\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 84.9906 | + | 84.9906i | 0.247786 | + | 0.247786i | ||||
\(50\) | −26.7596 | −0.0756875 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 417.136 | 1.11243 | ||||||||
\(53\) | 220.673 | + | 220.673i | 0.571920 | + | 0.571920i | 0.932665 | − | 0.360745i | \(-0.117477\pi\) |
−0.360745 | + | 0.932665i | \(0.617477\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 150.059i | − | 0.367891i | ||||||
\(56\) | −72.2616 | + | 29.9317i | −0.172435 | + | 0.0714249i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −14.7419 | − | 6.10628i | −0.0333742 | − | 0.0138240i | ||||
\(59\) | 407.819 | − | 407.819i | 0.899890 | − | 0.899890i | −0.0955362 | − | 0.995426i | \(-0.530457\pi\) |
0.995426 | + | 0.0955362i | \(0.0304566\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 72.4205 | + | 29.9976i | 0.152008 | + | 0.0629639i | 0.457390 | − | 0.889266i | \(-0.348784\pi\) |
−0.305382 | + | 0.952230i | \(0.598784\pi\) | |||||||
\(62\) | 14.5644 | − | 35.1615i | 0.0298335 | − | 0.0720245i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 492.167i | 0.961264i | ||||||||
\(65\) | −55.2607 | − | 133.411i | −0.105450 | − | 0.254579i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 359.997 | 0.656428 | 0.328214 | − | 0.944603i | \(-0.393553\pi\) | ||||
0.328214 | + | 0.944603i | \(0.393553\pi\) | |||||||
\(68\) | −489.191 | + | 266.562i | −0.872399 | + | 0.475373i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 9.54178 | + | 9.54178i | 0.0162923 | + | 0.0162923i | ||||
\(71\) | −81.5842 | − | 196.962i | −0.136370 | − | 0.329226i | 0.840911 | − | 0.541173i | \(-0.182020\pi\) |
−0.977281 | + | 0.211947i | \(0.932020\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 26.8357 | − | 11.1157i | 0.0430258 | − | 0.0178219i | −0.361067 | − | 0.932540i | \(-0.617587\pi\) |
0.404093 | + | 0.914718i | \(0.367587\pi\) | |||||||
\(74\) | 17.3222 | − | 41.8194i | 0.0272116 | − | 0.0656947i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 110.326 | − | 110.326i | 0.166516 | − | 0.166516i | ||||
\(77\) | 829.983 | − | 829.983i | 1.22838 | − | 1.22838i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 327.389 | − | 790.386i | 0.466254 | − | 1.12564i | −0.499531 | − | 0.866296i | \(-0.666494\pi\) |
0.965786 | − | 0.259342i | \(-0.0835056\pi\) | |||||||
\(80\) | 159.527 | − | 66.0782i | 0.222946 | − | 0.0923471i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −37.8740 | − | 91.4360i | −0.0510059 | − | 0.123139i | ||||
\(83\) | −9.67821 | − | 9.67821i | −0.0127991 | − | 0.0127991i | 0.700678 | − | 0.713477i | \(-0.252881\pi\) |
−0.713477 | + | 0.700678i | \(0.752881\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 150.060 | + | 121.143i | 0.191486 | + | 0.154586i | ||||
\(86\) | 28.9727 | 0.0363280 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 75.8494 | + | 183.117i | 0.0918815 | + | 0.221822i | ||||
\(89\) | 651.126i | 0.775497i | 0.921765 | + | 0.387748i | \(0.126747\pi\) | ||||
−0.921765 | + | 0.387748i | \(0.873253\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 432.253 | − | 1043.55i | 0.497939 | − | 1.20213i | ||||
\(92\) | −102.327 | − | 42.3851i | −0.115960 | − | 0.0480321i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −33.4035 | + | 33.4035i | −0.0366522 | + | 0.0366522i | ||||
\(95\) | −49.9006 | − | 20.6695i | −0.0538915 | − | 0.0223226i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1107.41 | + | 458.705i | −1.15918 | + | 0.480149i | −0.877602 | − | 0.479389i | \(-0.840858\pi\) |
−0.281579 | + | 0.959538i | \(0.590858\pi\) | |||||||
\(98\) | 27.3897i | 0.0282325i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 659.970 | + | 659.970i | 0.659970 | + | 0.659970i | ||||
\(101\) | −89.2435 | −0.0879214 | −0.0439607 | − | 0.999033i | \(-0.513998\pi\) | ||||
−0.0439607 | + | 0.999033i | \(0.513998\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1242.17 | −1.18830 | −0.594150 | − | 0.804354i | \(-0.702511\pi\) | ||||
−0.594150 | + | 0.804354i | \(0.702511\pi\) | |||||||
\(104\) | 134.869 | + | 134.869i | 0.127163 | + | 0.127163i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 71.1158i | 0.0651639i | ||||||||
\(107\) | −1420.54 | + | 588.407i | −1.28345 | + | 0.531621i | −0.917025 | − | 0.398829i | \(-0.869417\pi\) |
−0.366420 | + | 0.930449i | \(0.619417\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 95.9730 | + | 39.7533i | 0.0843353 | + | 0.0349328i | 0.424452 | − | 0.905450i | \(-0.360467\pi\) |
−0.340117 | + | 0.940383i | \(0.610467\pi\) | |||||||
\(110\) | 24.1796 | − | 24.1796i | 0.0209585 | − | 0.0209585i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1247.83 | + | 516.868i | 1.05276 | + | 0.436066i | ||||
\(113\) | 140.908 | − | 340.183i | 0.117306 | − | 0.283201i | −0.854311 | − | 0.519762i | \(-0.826020\pi\) |
0.971617 | + | 0.236562i | \(0.0760205\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 38.3418i | 0.0310904i | ||||||||
\(116\) | 212.979 | + | 514.176i | 0.170471 | + | 0.411552i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 131.427 | 0.102532 | ||||||||
\(119\) | 159.940 | + | 1500.03i | 0.123207 | + | 1.15553i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1162.08 | − | 1162.08i | −0.873091 | − | 0.873091i | ||||
\(122\) | 6.83578 | + | 16.5030i | 0.00507281 | + | 0.0122468i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1226.39 | + | 507.986i | −0.888168 | + | 0.367891i | ||||
\(125\) | 255.262 | − | 616.256i | 0.182650 | − | 0.440957i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −886.309 | + | 886.309i | −0.619269 | + | 0.619269i | −0.945344 | − | 0.326075i | \(-0.894274\pi\) |
0.326075 | + | 0.945344i | \(0.394274\pi\) | |||||||
\(128\) | −324.668 | + | 324.668i | −0.224194 | + | 0.224194i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.5927 | − | 30.4014i | 0.00849578 | − | 0.0205106i | ||||
\(131\) | 1806.01 | − | 748.072i | 1.20452 | − | 0.498927i | 0.312060 | − | 0.950062i | \(-0.398981\pi\) |
0.892455 | + | 0.451136i | \(0.148981\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −161.678 | − | 390.326i | −0.105408 | − | 0.254478i | ||||
\(134\) | 58.0078 | + | 58.0078i | 0.0373963 | + | 0.0373963i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −244.351 | − | 71.9806i | −0.154065 | − | 0.0453844i | ||||
\(137\) | −1749.91 | −1.09127 | −0.545637 | − | 0.838022i | \(-0.683712\pi\) | ||||
−0.545637 | + | 0.838022i | \(0.683712\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 78.9509 | + | 190.604i | 0.0481765 | + | 0.116308i | 0.946136 | − | 0.323770i | \(-0.104951\pi\) |
−0.897959 | + | 0.440079i | \(0.854951\pi\) | |||||||
\(140\) | − | 470.657i | − | 0.284127i | ||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 18.5912 | − | 44.8832i | 0.0109869 | − | 0.0265248i | ||||
\(143\) | −2644.44 | − | 1095.36i | −1.54643 | − | 0.640552i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 136.232 | − | 136.232i | 0.0780241 | − | 0.0780241i | ||||
\(146\) | 6.11526 | + | 2.53303i | 0.00346646 | + | 0.00143585i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1458.61 | + | 604.174i | −0.810112 | + | 0.335559i | ||||
\(149\) | − | 2013.39i | − | 1.10700i | −0.832849 | − | 0.553501i | \(-0.813292\pi\) | ||
0.832849 | − | 0.553501i | \(-0.186708\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 53.4946 | + | 53.4946i | 0.0288300 | + | 0.0288300i | 0.721375 | − | 0.692545i | \(-0.243511\pi\) |
−0.692545 | + | 0.721375i | \(0.743511\pi\) | |||||||
\(152\) | 71.3412 | 0.0380693 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 267.477 | 0.139960 | ||||||||
\(155\) | 324.935 | + | 324.935i | 0.168383 | + | 0.168383i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2301.81i | 1.17009i | 0.811000 | + | 0.585046i | \(0.198924\pi\) | ||||
−0.811000 | + | 0.585046i | \(0.801076\pi\) | |||||||
\(158\) | 180.111 | − | 74.6046i | 0.0906892 | − | 0.0375647i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 110.258 | + | 45.6704i | 0.0544791 | + | 0.0225660i | ||||
\(161\) | −212.070 | + | 212.070i | −0.103810 | + | 0.103810i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1748.91 | − | 724.420i | −0.840398 | − | 0.348104i | −0.0793874 | − | 0.996844i | \(-0.525296\pi\) |
−0.761010 | + | 0.648740i | \(0.775296\pi\) | |||||||
\(164\) | −1320.99 | + | 3189.16i | −0.628978 | + | 1.51849i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 3.11898i | − | 0.00145831i | ||||||
\(167\) | −41.5126 | − | 100.220i | −0.0192356 | − | 0.0464388i | 0.913970 | − | 0.405782i | \(-0.133001\pi\) |
−0.933205 | + | 0.359343i | \(0.883001\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −557.436 | −0.253726 | ||||||||
\(170\) | 4.65948 | + | 43.7000i | 0.00210215 | + | 0.0197155i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −714.551 | − | 714.551i | −0.316768 | − | 0.316768i | ||||
\(173\) | 1054.59 | + | 2546.01i | 0.463463 | + | 1.11890i | 0.966966 | + | 0.254905i | \(0.0820441\pi\) |
−0.503504 | + | 0.863993i | \(0.667956\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2334.93 | − | 967.161i | 1.00860 | − | 0.417774i | ||||
\(176\) | 1309.78 | − | 3162.10i | 0.560959 | − | 1.35427i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −104.918 | + | 104.918i | −0.0441796 | + | 0.0441796i | ||||
\(179\) | 1418.56 | − | 1418.56i | 0.592337 | − | 0.592337i | −0.345925 | − | 0.938262i | \(-0.612435\pi\) |
0.938262 | + | 0.345925i | \(0.112435\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −927.705 | + | 2239.68i | −0.380971 | + | 0.919745i | 0.610808 | + | 0.791779i | \(0.290845\pi\) |
−0.991779 | + | 0.127966i | \(0.959155\pi\) | |||||||
\(182\) | 237.802 | − | 98.5008i | 0.0968520 | − | 0.0401174i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −19.3804 | − | 46.7883i | −0.00776489 | − | 0.0187461i | ||||
\(185\) | 386.461 | + | 386.461i | 0.153585 | + | 0.153585i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3801.20 | − | 405.300i | 1.48648 | − | 0.158495i | ||||
\(188\) | 1647.66 | 0.639190 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.71012 | − | 11.3712i | −0.00179846 | − | 0.00434188i | ||||
\(191\) | 4153.64i | 1.57354i | 0.617243 | + | 0.786772i | \(0.288249\pi\) | ||||
−0.617243 | + | 0.786772i | \(0.711751\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 794.611 | − | 1918.36i | 0.296360 | − | 0.715475i | −0.703628 | − | 0.710568i | \(-0.748438\pi\) |
0.999988 | − | 0.00490706i | \(-0.00156197\pi\) | |||||||
\(194\) | −252.355 | − | 104.529i | −0.0933917 | − | 0.0386841i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 675.511 | − | 675.511i | 0.246178 | − | 0.246178i | ||||
\(197\) | −3513.98 | − | 1455.54i | −1.27087 | − | 0.526410i | −0.357638 | − | 0.933860i | \(-0.616418\pi\) |
−0.913227 | + | 0.407450i | \(0.866418\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3346.19 | − | 1386.04i | 1.19199 | − | 0.493736i | 0.303584 | − | 0.952805i | \(-0.401817\pi\) |
0.888401 | + | 0.459068i | \(0.151817\pi\) | |||||||
\(200\) | 426.764i | 0.150884i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14.3802 | − | 14.3802i | −0.00500883 | − | 0.00500883i | ||||
\(203\) | 1507.01 | 0.521042 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1194.98 | 0.407127 | ||||||||
\(206\) | −200.156 | − | 200.156i | −0.0676968 | − | 0.0676968i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 3293.63i | − | 1.09794i | ||||||
\(209\) | −989.117 | + | 409.706i | −0.327362 | + | 0.135598i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −584.358 | − | 242.049i | −0.190658 | − | 0.0789732i | 0.285312 | − | 0.958435i | \(-0.407903\pi\) |
−0.475970 | + | 0.879462i | \(0.657903\pi\) | |||||||
\(212\) | 1753.92 | − | 1753.92i | 0.568207 | − | 0.568207i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −323.709 | − | 134.085i | −0.103403 | − | 0.0428311i | ||||
\(215\) | −133.871 | + | 323.193i | −0.0424648 | + | 0.102519i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3594.45i | 1.12446i | ||||||||
\(218\) | 9.05890 | + | 21.8701i | 0.00281443 | + | 0.00679464i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1192.68 | −0.365503 | ||||||||
\(221\) | 3230.23 | − | 1760.16i | 0.983206 | − | 0.535753i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 377.462 | + | 377.462i | 0.113348 | + | 0.113348i | 0.761506 | − | 0.648158i | \(-0.224460\pi\) |
−0.648158 | + | 0.761506i | \(0.724460\pi\) | |||||||
\(224\) | 357.237 | + | 862.445i | 0.106557 | + | 0.257252i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 77.5201 | − | 32.1099i | 0.0228166 | − | 0.00945096i | ||||
\(227\) | −225.340 | + | 544.019i | −0.0658870 | + | 0.159065i | −0.953393 | − | 0.301730i | \(-0.902436\pi\) |
0.887506 | + | 0.460795i | \(0.152436\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1867.57 | − | 1867.57i | 0.538920 | − | 0.538920i | −0.384292 | − | 0.923212i | \(-0.625554\pi\) |
0.923212 | + | 0.384292i | \(0.125554\pi\) | |||||||
\(230\) | −6.17817 | + | 6.17817i | −0.00177120 | + | 0.00177120i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −97.3834 | + | 235.104i | −0.0275583 | + | 0.0665317i | ||||
\(233\) | −354.195 | + | 146.712i | −0.0995882 | + | 0.0412508i | −0.431921 | − | 0.901911i | \(-0.642164\pi\) |
0.332333 | + | 0.943162i | \(0.392164\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −218.276 | − | 526.964i | −0.0605904 | − | 0.146278i | ||||
\(236\) | −3241.37 | − | 3241.37i | −0.894049 | − | 0.894049i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −215.934 | + | 267.478i | −0.0588107 | + | 0.0728488i | ||||
\(239\) | 4344.62 | 1.17586 | 0.587929 | − | 0.808913i | \(-0.299944\pi\) | ||||
0.587929 | + | 0.808913i | \(0.299944\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −785.906 | − | 1897.34i | −0.210061 | − | 0.507131i | 0.783371 | − | 0.621554i | \(-0.213498\pi\) |
−0.993432 | + | 0.114422i | \(0.963498\pi\) | |||||||
\(242\) | − | 374.502i | − | 0.0994790i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 238.423 | − | 575.604i | 0.0625552 | − | 0.151022i | ||||
\(245\) | −305.535 | − | 126.557i | −0.0796732 | − | 0.0330017i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −728.503 | + | 728.503i | −0.187666 | + | 0.187666i | ||||
\(248\) | −560.759 | − | 232.274i | −0.143581 | − | 0.0594734i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 140.431 | − | 58.1685i | 0.0355266 | − | 0.0147156i | ||||
\(251\) | 907.953i | 0.228325i | 0.993462 | + | 0.114162i | \(0.0364184\pi\) | ||||
−0.993462 | + | 0.114162i | \(0.963582\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 537.402 | + | 537.402i | 0.133542 | + | 0.133542i | ||||
\(254\) | −285.629 | −0.0705589 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3832.71 | 0.935720 | ||||||||
\(257\) | −5296.81 | − | 5296.81i | −1.28563 | − | 1.28563i | −0.937417 | − | 0.348209i | \(-0.886790\pi\) |
−0.348209 | − | 0.937417i | \(-0.613210\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4275.06i | 1.02564i | ||||||||
\(260\) | −1060.36 | + | 439.216i | −0.252926 | + | 0.104765i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 411.549 | + | 170.469i | 0.0970441 | + | 0.0401970i | ||||
\(263\) | 5558.34 | − | 5558.34i | 1.30320 | − | 1.30320i | 0.376982 | − | 0.926221i | \(-0.376962\pi\) |
0.926221 | − | 0.376982i | \(-0.123038\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −793.304 | − | 328.597i | −0.183895 | − | 0.0761720i | ||||
\(266\) | 36.8429 | − | 88.9466i | 0.00849241 | − | 0.0205025i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 2861.29i | − | 0.652167i | ||||||
\(269\) | 2890.74 | + | 6978.86i | 0.655210 | + | 1.58182i | 0.805117 | + | 0.593116i | \(0.202102\pi\) |
−0.149908 | + | 0.988700i | \(0.547898\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6394.46 | 1.43334 | 0.716672 | − | 0.697411i | \(-0.245665\pi\) | ||||
0.716672 | + | 0.697411i | \(0.245665\pi\) | |||||||
\(272\) | 2104.72 | + | 3862.56i | 0.469182 | + | 0.861037i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −281.969 | − | 281.969i | −0.0621693 | − | 0.0621693i | ||||
\(275\) | −2450.86 | − | 5916.91i | −0.537428 | − | 1.29747i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6247.84 | + | 2587.94i | −1.35522 | + | 0.561351i | −0.937741 | − | 0.347335i | \(-0.887087\pi\) |
−0.417480 | + | 0.908686i | \(0.637087\pi\) | |||||||
\(278\) | −17.9912 | + | 43.4345i | −0.00388143 | + | 0.00937061i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 152.173 | − | 152.173i | 0.0324788 | − | 0.0324788i | ||||
\(281\) | −4453.39 | + | 4453.39i | −0.945433 | + | 0.945433i | −0.998586 | − | 0.0531529i | \(-0.983073\pi\) |
0.0531529 | + | 0.998586i | \(0.483073\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1022.77 | + | 2469.18i | −0.214831 | + | 0.518648i | −0.994154 | − | 0.107975i | \(-0.965563\pi\) |
0.779323 | + | 0.626623i | \(0.215563\pi\) | |||||||
\(284\) | −1565.47 | + | 648.437i | −0.327089 | + | 0.135485i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −249.609 | − | 602.609i | −0.0516073 | − | 0.124591i | ||||
\(287\) | 6609.47 | + | 6609.47i | 1.35939 | + | 1.35939i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2663.41 | + | 4128.41i | −0.542115 | + | 0.840304i | ||||
\(290\) | 43.9033 | 0.00888998 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −88.3485 | − | 213.292i | −0.0177062 | − | 0.0427465i | ||||
\(293\) | 2183.30i | 0.435323i | 0.976024 | + | 0.217661i | \(0.0698428\pi\) | ||||
−0.976024 | + | 0.217661i | \(0.930157\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −607.271 | + | 1466.08i | −0.119853 | + | 0.289351i | ||||
\(296\) | −666.939 | − | 276.255i | −0.130963 | − | 0.0542467i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 324.425 | − | 324.425i | 0.0630653 | − | 0.0630653i | ||||
\(299\) | 675.684 | + | 279.878i | 0.130688 | + | 0.0541329i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2528.04 | + | 1047.15i | −0.484099 | + | 0.200520i | ||||
\(302\) | 17.2396i | 0.00328485i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −871.110 | − | 871.110i | −0.164347 | − | 0.164347i | ||||
\(305\) | −215.679 | −0.0404909 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3905.30 | −0.726018 | −0.363009 | − | 0.931786i | \(-0.618250\pi\) | ||||
−0.363009 | + | 0.931786i | \(0.618250\pi\) | |||||||
\(308\) | −6596.76 | − | 6596.76i | −1.22041 | − | 1.22041i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 104.716i | 0.0191854i | ||||||||
\(311\) | −6806.60 | + | 2819.39i | −1.24105 | + | 0.514060i | −0.904043 | − | 0.427441i | \(-0.859415\pi\) |
−0.337008 | + | 0.941502i | \(0.609415\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2149.71 | − | 890.438i | −0.388207 | − | 0.160800i | 0.180039 | − | 0.983659i | \(-0.442378\pi\) |
−0.568246 | + | 0.822859i | \(0.692378\pi\) | |||||||
\(314\) | −370.900 | + | 370.900i | −0.0666595 | + | 0.0666595i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6282.05 | − | 2602.11i | −1.11833 | − | 0.463228i | ||||
\(317\) | −2858.75 | + | 6901.62i | −0.506508 | + | 1.22282i | 0.439372 | + | 0.898305i | \(0.355201\pi\) |
−0.945881 | + | 0.324514i | \(0.894799\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3818.89i | − | 0.670272i | ||||||
\(320\) | −518.218 | − | 1251.09i | −0.0905290 | − | 0.218556i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −68.3433 | −0.0118280 | ||||||||
\(323\) | 388.808 | − | 1319.88i | 0.0669779 | − | 0.227368i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4357.92 | − | 4357.92i | −0.743796 | − | 0.743796i | ||||
\(326\) | −165.079 | − | 398.537i | −0.0280457 | − | 0.0677083i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1458.23 | + | 604.017i | −0.245479 | + | 0.101681i | ||||
\(329\) | 1707.37 | − | 4121.95i | 0.286110 | − | 0.690730i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6613.70 | − | 6613.70i | 1.09825 | − | 1.09825i | 0.103637 | − | 0.994615i | \(-0.466952\pi\) |
0.994615 | − | 0.103637i | \(-0.0330482\pi\) | |||||||
\(332\) | −76.9231 | + | 76.9231i | −0.0127160 | + | 0.0127160i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.45981 | − | 22.8380i | 0.00154975 | − | 0.00374143i | ||||
\(335\) | −915.114 | + | 379.053i | −0.149248 | + | 0.0618205i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2657.39 | + | 6415.50i | 0.429546 | + | 1.03702i | 0.979432 | + | 0.201776i | \(0.0646714\pi\) |
−0.549885 | + | 0.835240i | \(0.685329\pi\) | |||||||
\(338\) | −89.8218 | − | 89.8218i | −0.0144546 | − | 0.0144546i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 962.853 | − | 1192.69i | 0.153582 | − | 0.190243i | ||||
\(341\) | 9108.62 | 1.44651 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1835.05 | + | 4430.19i | 0.288872 | + | 0.697399i | ||||
\(344\) | − | 462.058i | − | 0.0724201i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −240.318 | + | 580.178i | −0.0373398 | + | 0.0901462i | ||||
\(347\) | −2226.53 | − | 922.261i | −0.344457 | − | 0.142679i | 0.203747 | − | 0.979024i | \(-0.434688\pi\) |
−0.548204 | + | 0.836345i | \(0.684688\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7781.94 | + | 7781.94i | −1.19357 | + | 1.19357i | −0.217518 | + | 0.976056i | \(0.569796\pi\) |
−0.976056 | + | 0.217518i | \(0.930204\pi\) | |||||||
\(350\) | 532.080 | + | 220.395i | 0.0812596 | + | 0.0336588i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2185.51 | − | 905.266i | 0.330931 | − | 0.137076i | ||||
\(353\) | 7713.23i | 1.16299i | 0.813552 | + | 0.581493i | \(0.197531\pi\) | ||||
−0.813552 | + | 0.581493i | \(0.802469\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 414.775 | + | 414.775i | 0.0620111 | + | 0.0620111i | ||||
\(356\) | 5175.20 | 0.770463 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 457.157 | 0.0674902 | ||||||||
\(359\) | −7226.67 | − | 7226.67i | −1.06242 | − | 1.06242i | −0.997917 | − | 0.0645037i | \(-0.979454\pi\) |
−0.0645037 | − | 0.997917i | \(-0.520546\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 6473.65i | − | 0.943818i | ||||||
\(362\) | −510.373 | + | 211.403i | −0.0741011 | + | 0.0306937i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8294.22 | − | 3435.58i | −1.19433 | − | 0.494706i | ||||
\(365\) | −56.5124 | + | 56.5124i | −0.00810409 | + | 0.00810409i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9536.68 | + | 3950.22i | 1.35643 | + | 0.561853i | 0.938076 | − | 0.346430i | \(-0.112606\pi\) |
0.418356 | + | 0.908283i | \(0.362606\pi\) | |||||||
\(368\) | −334.665 | + | 807.952i | −0.0474065 | + | 0.114450i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 124.544i | 0.0174993i | ||||||||
\(371\) | −2570.31 | − | 6205.27i | −0.359687 | − | 0.868361i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2744.09 | −0.380921 | −0.190461 | − | 0.981695i | \(-0.560998\pi\) | ||||
−0.190461 | + | 0.981695i | \(0.560998\pi\) | |||||||
\(374\) | 677.810 | + | 547.195i | 0.0937132 | + | 0.0756545i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 532.722 | + | 532.722i | 0.0730666 | + | 0.0730666i | ||||
\(377\) | −1406.34 | − | 3395.21i | −0.192123 | − | 0.463826i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5917.45 | + | 2451.09i | −0.802003 | + | 0.332200i | −0.745758 | − | 0.666217i | \(-0.767913\pi\) |
−0.0562446 | + | 0.998417i | \(0.517913\pi\) | |||||||
\(380\) | −164.283 | + | 396.614i | −0.0221777 | + | 0.0535417i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −669.293 | + | 669.293i | −0.0896440 | + | 0.0896440i | ||||
\(383\) | 2611.23 | − | 2611.23i | 0.348375 | − | 0.348375i | −0.511129 | − | 0.859504i | \(-0.670773\pi\) |
0.859504 | + | 0.511129i | \(0.170773\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1235.90 | + | 2983.73i | −0.163604 | + | 0.394974i | ||||
\(386\) | 437.152 | − | 181.074i | 0.0576437 | − | 0.0238768i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3645.82 | + | 8801.79i | 0.477032 | + | 1.15166i | ||||
\(389\) | 1508.22 | + | 1508.22i | 0.196581 | + | 0.196581i | 0.798532 | − | 0.601952i | \(-0.205610\pi\) |
−0.601952 | + | 0.798532i | \(0.705610\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −971.250 | + | 103.559i | −0.125622 | + | 0.0133944i | ||||
\(392\) | 436.813 | 0.0562816 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −331.685 | − | 800.758i | −0.0424112 | − | 0.102390i | ||||
\(395\) | 2353.88i | 0.299840i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −904.995 | + | 2184.85i | −0.114409 | + | 0.276208i | −0.970704 | − | 0.240280i | \(-0.922761\pi\) |
0.856295 | + | 0.516488i | \(0.172761\pi\) | |||||||
\(398\) | 762.522 | + | 315.847i | 0.0960346 | + | 0.0397788i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5210.99 | − | 5210.99i | 0.651374 | − | 0.651374i | ||||
\(401\) | −1906.65 | − | 789.759i | −0.237440 | − | 0.0983509i | 0.260791 | − | 0.965395i | \(-0.416017\pi\) |
−0.498231 | + | 0.867044i | \(0.666017\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8098.08 | − | 3354.33i | 1.00098 | − | 0.414619i | ||||
\(404\) | 709.314i | 0.0873507i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 242.831 | + | 242.831i | 0.0296835 | + | 0.0296835i | ||||
\(407\) | 10833.4 | 1.31938 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9245.03 | 1.11769 | 0.558847 | − | 0.829271i | \(-0.311244\pi\) | ||||
0.558847 | + | 0.829271i | \(0.311244\pi\) | |||||||
\(410\) | 192.552 | + | 192.552i | 0.0231938 | + | 0.0231938i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9872.87i | 1.18059i | ||||||||
\(413\) | −11467.8 | + | 4750.11i | −1.36633 | + | 0.565951i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 34.7925 | + | 14.4115i | 0.00411542 | + | 0.00170466i | ||||
\(416\) | 1609.67 | − | 1609.67i | 0.189712 | − | 0.189712i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −225.398 | − | 93.3628i | −0.0263746 | − | 0.0109247i | ||||
\(419\) | −1590.19 | + | 3839.06i | −0.185408 | + | 0.447614i | −0.989065 | − | 0.147478i | \(-0.952884\pi\) |
0.803657 | + | 0.595092i | \(0.202884\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 4609.26i | − | 0.533591i | −0.963753 | − | 0.266795i | \(-0.914035\pi\) | ||
0.963753 | − | 0.266795i | \(-0.0859648\pi\) | |||||||
\(422\) | −55.1576 | − | 133.162i | −0.00636263 | − | 0.0153608i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1134.16 | 0.129905 | ||||||||
\(425\) | 7895.52 | + | 2325.85i | 0.901150 | + | 0.265460i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1192.93 | − | 1192.93i | −0.135198 | − | 0.135198i | ||||
\(428\) | 4676.70 | + | 11290.5i | 0.528170 | + | 1.27511i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −73.6486 | + | 30.5063i | −0.00825965 | + | 0.00342126i | ||||
\(431\) | 6632.04 | − | 16011.2i | 0.741193 | − | 1.78940i | 0.140235 | − | 0.990118i | \(-0.455214\pi\) |
0.600958 | − | 0.799281i | \(-0.294786\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8028.41 | − | 8028.41i | 0.891041 | − | 0.891041i | −0.103580 | − | 0.994621i | \(-0.533030\pi\) |
0.994621 | + | 0.103580i | \(0.0330297\pi\) | |||||||
\(434\) | −579.188 | + | 579.188i | −0.0640597 | + | 0.0640597i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 315.962 | − | 762.801i | 0.0347061 | − | 0.0837879i | ||||
\(437\) | 252.730 | − | 104.684i | 0.0276653 | − | 0.0114593i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1962.43 | − | 4737.72i | −0.213352 | − | 0.515078i | 0.780582 | − | 0.625053i | \(-0.214923\pi\) |
−0.993934 | + | 0.109975i | \(0.964923\pi\) | |||||||
\(440\) | −385.619 | − | 385.619i | −0.0417810 | − | 0.0417810i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 804.121 | + | 236.877i | 0.0865343 | + | 0.0254912i | ||||
\(443\) | 3133.00 | 0.336012 | 0.168006 | − | 0.985786i | \(-0.446267\pi\) | ||||
0.168006 | + | 0.985786i | \(0.446267\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −685.591 | − | 1655.16i | −0.0730340 | − | 0.176320i | ||||
\(446\) | 121.644i | 0.0129148i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4053.54 | − | 9786.11i | 0.427481 | − | 1.03203i | ||||
\(449\) | −10855.2 | − | 4496.37i | −1.14095 | − | 0.472599i | −0.269464 | − | 0.963010i | \(-0.586846\pi\) |
−0.871491 | + | 0.490411i | \(0.836846\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16748.9 | − | 16748.9i | 1.74873 | − | 1.74873i | ||||
\(452\) | −2703.80 | − | 1119.95i | −0.281363 | − | 0.116544i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −123.970 | + | 51.3500i | −0.0128154 | + | 0.00530831i | ||||
\(455\) | 3107.84i | 0.320215i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8774.30 | − | 8774.30i | −0.898128 | − | 0.898128i | 0.0971425 | − | 0.995270i | \(-0.469030\pi\) |
−0.995270 | + | 0.0971425i | \(0.969030\pi\) | |||||||
\(458\) | 601.859 | 0.0614039 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 304.744 | 0.0308886 | ||||||||
\(461\) | −5211.73 | − | 5211.73i | −0.526539 | − | 0.526539i | 0.393000 | − | 0.919539i | \(-0.371437\pi\) |
−0.919539 | + | 0.393000i | \(0.871437\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11446.9i | 1.14899i | 0.818508 | + | 0.574495i | \(0.194802\pi\) | ||||
−0.818508 | + | 0.574495i | \(0.805198\pi\) | |||||||
\(464\) | 4059.84 | − | 1681.64i | 0.406192 | − | 0.168250i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −80.7131 | − | 33.4325i | −0.00802352 | − | 0.00332345i | ||||
\(467\) | −3124.20 | + | 3124.20i | −0.309573 | + | 0.309573i | −0.844744 | − | 0.535171i | \(-0.820247\pi\) |
0.535171 | + | 0.844744i | \(0.320247\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7158.08 | − | 2964.97i | −0.704754 | − | 0.291919i | ||||
\(470\) | 49.7402 | − | 120.083i | 0.00488158 | − | 0.0117852i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 2096.01i | − | 0.204399i | ||||||
\(473\) | 2653.56 | + | 6406.25i | 0.257951 | + | 0.622748i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2305.19 | −0.222673 | ||||||||
\(476\) | 11922.4 | − | 1271.21i | 1.14803 | − | 0.122407i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 700.065 | + | 700.065i | 0.0669879 | + | 0.0669879i | ||||
\(479\) | 108.152 | + | 261.102i | 0.0103165 | + | 0.0249062i | 0.928954 | − | 0.370196i | \(-0.120709\pi\) |
−0.918637 | + | 0.395102i | \(0.870709\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9631.46 | − | 3989.48i | 0.913008 | − | 0.378180i | ||||
\(482\) | 179.090 | − | 432.363i | 0.0169240 | − | 0.0408580i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9236.32 | + | 9236.32i | −0.867423 | + | 0.867423i | ||||
\(485\) | 2332.06 | − | 2332.06i | 0.218337 | − | 0.218337i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2909.21 | + | 7023.45i | −0.270696 | + | 0.653518i | −0.999513 | − | 0.0311903i | \(-0.990070\pi\) |
0.728818 | + | 0.684708i | \(0.240070\pi\) | |||||||
\(488\) | 263.192 | − | 109.018i | 0.0244142 | − | 0.0101127i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −28.8395 | − | 69.6247i | −0.00265885 | − | 0.00641903i | ||||
\(491\) | 9075.67 | + | 9075.67i | 0.834174 | + | 0.834174i | 0.988085 | − | 0.153911i | \(-0.0491870\pi\) |
−0.153911 | + | 0.988085i | \(0.549187\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3818.91 | + | 3082.99i | 0.348874 | + | 0.281645i | ||||
\(494\) | −234.773 | −0.0213825 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4010.96 | + | 9683.31i | 0.363100 | + | 0.876600i | ||||
\(497\) | 4588.27i | 0.414108i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1039.84 | − | 2510.39i | 0.0932855 | − | 0.225211i | −0.870349 | − | 0.492436i | \(-0.836107\pi\) |
0.963634 | + | 0.267225i | \(0.0861066\pi\) | |||||||
\(500\) | −4898.05 | − | 2028.84i | −0.438095 | − | 0.181465i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −146.302 | + | 146.302i | −0.0130075 | + | 0.0130075i | ||||
\(503\) | −7589.15 | − | 3143.53i | −0.672731 | − | 0.278654i | 0.0200537 | − | 0.999799i | \(-0.493616\pi\) |
−0.692784 | + | 0.721145i | \(0.743616\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 226.857 | − | 93.9673i | 0.0199901 | − | 0.00828018i | ||||
\(506\) | 173.187i | 0.0152157i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7044.45 | + | 7044.45i | 0.615250 | + | 0.615250i | ||||
\(509\) | −8243.18 | −0.717824 | −0.358912 | − | 0.933371i | \(-0.616852\pi\) | ||||
−0.358912 | + | 0.933371i | \(0.616852\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −625.144 | −0.0541188 | ||||||||
\(512\) | 3214.92 | + | 3214.92i | 0.277502 | + | 0.277502i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 1706.99i | − | 0.146483i | ||||||
\(515\) | 3157.60 | − | 1307.92i | 0.270176 | − | 0.111911i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10445.3 | − | 4326.60i | −0.888560 | − | 0.368054i | ||||
\(518\) | −688.858 | + | 688.858i | −0.0584299 | + | 0.0584299i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −484.844 | − | 200.829i | −0.0408881 | − | 0.0169364i | ||||
\(521\) | 3426.22 | − | 8271.63i | 0.288110 | − | 0.695559i | −0.711867 | − | 0.702314i | \(-0.752150\pi\) |
0.999977 | + | 0.00675482i | \(0.00215014\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15665.1i | 1.30973i | 0.755747 | + | 0.654864i | \(0.227274\pi\) | ||||
−0.755747 | + | 0.654864i | \(0.772726\pi\) | |||||||
\(524\) | −5945.73 | − | 14354.3i | −0.495688 | − | 1.19670i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1791.28 | 0.148485 | ||||||||
\(527\) | −7353.40 | + | 9108.65i | −0.607816 | + | 0.752902i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8466.06 | + | 8466.06i | 0.695821 | + | 0.695821i | ||||
\(530\) | −74.8800 | − | 180.776i | −0.00613694 | − | 0.0148159i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3102.34 | + | 1285.03i | −0.252826 | + | 0.104724i | ||||
\(533\) | 8722.79 | − | 21058.7i | 0.708867 | − | 1.71136i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2991.46 | − | 2991.46i | 0.241742 | − | 0.241742i | ||||
\(536\) | 925.113 | − | 925.113i | 0.0745500 | − | 0.0745500i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −658.735 | + | 1590.33i | −0.0527882 | + | 0.127442i | ||||
\(539\) | −6056.24 | + | 2508.58i | −0.483972 | + | 0.200468i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3547.46 | − | 8564.31i | −0.281917 | − | 0.680607i | 0.717963 | − | 0.696081i | \(-0.245074\pi\) |
−0.999880 | + | 0.0154734i | \(0.995074\pi\) | |||||||
\(542\) | 1030.37 | + | 1030.37i | 0.0816568 | + | 0.0816568i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −859.092 | + | 2916.34i | −0.0677082 | + | 0.229847i | ||||
\(545\) | −285.821 | −0.0224647 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6005.27 | − | 14498.0i | −0.469409 | − | 1.13325i | −0.964422 | − | 0.264368i | \(-0.914837\pi\) |
0.495013 | − | 0.868886i | \(-0.335163\pi\) | |||||||
\(548\) | 13908.4i | 1.08419i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 558.498 | − | 1348.33i | 0.0432989 | − | 0.104533i | ||||
\(551\) | −1269.93 | − | 526.023i | −0.0981868 | − | 0.0406703i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13019.4 | + | 13019.4i | −1.00116 | + | 1.00116i | ||||
\(554\) | −1423.74 | − | 589.734i | −0.109186 | − | 0.0452263i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1514.94 | − | 627.508i | 0.115553 | − | 0.0478638i | ||||
\(557\) | 3540.22i | 0.269307i | 0.990893 | + | 0.134654i | \(0.0429922\pi\) | ||||
−0.990893 | + | 0.134654i | \(0.957008\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4718.33 | + | 4718.33i | 0.357002 | + | 0.357002i | ||||
\(560\) | −3716.21 | −0.280426 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1435.18 | −0.107722 | ||||||||
\(563\) | 222.747 | + | 222.747i | 0.0166744 | + | 0.0166744i | 0.715395 | − | 0.698720i | \(-0.246247\pi\) |
−0.698720 | + | 0.715395i | \(0.746247\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1013.11i | 0.0754371i | ||||||||
\(566\) | −562.671 | + | 233.066i | −0.0417859 | + | 0.0173083i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −715.801 | − | 296.494i | −0.0528773 | − | 0.0219025i | ||||
\(569\) | 6032.76 | − | 6032.76i | 0.444475 | − | 0.444475i | −0.449038 | − | 0.893513i | \(-0.648233\pi\) |
0.893513 | + | 0.449038i | \(0.148233\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8156.50 | − | 3378.53i | −0.597791 | − | 0.247613i | 0.0632073 | − | 0.998000i | \(-0.479867\pi\) |
−0.660999 | + | 0.750387i | \(0.729867\pi\) | |||||||
\(572\) | −8706.03 | + | 21018.2i | −0.636394 | + | 1.53639i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2130.02i | 0.154887i | ||||||||
\(575\) | 626.223 | + | 1511.84i | 0.0454180 | + | 0.109649i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21726.1 | −1.56754 | −0.783769 | − | 0.621052i | \(-0.786705\pi\) | ||||
−0.783769 | + | 0.621052i | \(0.786705\pi\) | |||||||
\(578\) | −1094.39 | + | 236.062i | −0.0787557 | + | 0.0169877i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1082.79 | − | 1082.79i | −0.0775176 | − | 0.0775176i | ||||
\(581\) | 112.728 | + | 272.149i | 0.00804947 | + | 0.0194331i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15724.7 | + | 6513.37i | −1.11707 | + | 0.462704i | ||||
\(584\) | 40.3969 | − | 97.5267i | 0.00286239 | − | 0.00691042i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −351.803 | + | 351.803i | −0.0248001 | + | 0.0248001i | ||||
\(587\) | 17447.6 | − | 17447.6i | 1.22682 | − | 1.22682i | 0.261653 | − | 0.965162i | \(-0.415732\pi\) |
0.965162 | − | 0.261653i | \(-0.0842678\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1254.64 | − | 3028.98i | 0.0877702 | − | 0.211896i | ||||
\(590\) | −334.087 | + | 138.384i | −0.0233121 | + | 0.00965621i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4770.44 | + | 11516.9i | 0.331189 | + | 0.799561i | ||||
\(593\) | −6673.49 | − | 6673.49i | −0.462137 | − | 0.462137i | 0.437218 | − | 0.899356i | \(-0.355964\pi\) |
−0.899356 | + | 0.437218i | \(0.855964\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1986.00 | − | 3644.68i | −0.136837 | − | 0.251121i | ||||
\(596\) | −16002.6 | −1.09982 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 63.7779 | + | 153.973i | 0.00436132 | + | 0.0105292i | ||||
\(599\) | 28257.9i | 1.92753i | 0.266759 | + | 0.963763i | \(0.414047\pi\) | ||||
−0.266759 | + | 0.963763i | \(0.585953\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6674.25 | − | 16113.1i | 0.452993 | − | 1.09362i | −0.518186 | − | 0.855268i | \(-0.673393\pi\) |
0.971179 | − | 0.238353i | \(-0.0766075\pi\) | |||||||
\(602\) | −576.084 | − | 238.622i | −0.0390024 | − | 0.0161553i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 425.179 | − | 425.179i | 0.0286428 | − | 0.0286428i | ||||
\(605\) | 4177.61 | + | 1730.42i | 0.280734 | + | 0.116284i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 418.146 | − | 173.202i | 0.0279605 | − | 0.0115816i | −0.368659 | − | 0.929565i | \(-0.620183\pi\) |
0.396620 | + | 0.917983i | \(0.370183\pi\) | |||||||
\(608\) | − | 851.460i | − | 0.0567948i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −34.7531 | − | 34.7531i | −0.00230674 | − | 0.00230674i | ||||
\(611\) | −10879.8 | −0.720377 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10731.9 | −0.707106 | −0.353553 | − | 0.935415i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935415i | \(0.615027\pi\) | |||||||
\(614\) | −629.277 | − | 629.277i | −0.0413608 | − | 0.0413608i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 4265.74i | − | 0.279012i | ||||||
\(617\) | −18626.4 | + | 7715.29i | −1.21535 | + | 0.503413i | −0.895928 | − | 0.444200i | \(-0.853488\pi\) |
−0.319420 | + | 0.947613i | \(0.603488\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2395.44 | + | 992.223i | 0.155543 | + | 0.0644278i | 0.459096 | − | 0.888386i | \(-0.348173\pi\) |
−0.303554 | + | 0.952814i | \(0.598173\pi\) | |||||||
\(620\) | 2582.60 | − | 2582.60i | 0.167290 | − | 0.167290i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1551.07 | − | 642.476i | −0.0999877 | − | 0.0414163i | ||||
\(623\) | 5362.74 | − | 12946.8i | 0.344869 | − | 0.832588i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 12843.4i | − | 0.821977i | ||||||
\(626\) | −202.911 | − | 489.871i | −0.0129552 | − | 0.0312766i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18295.0 | 1.16250 | ||||||||
\(629\) | −8745.78 | + | 10833.4i | −0.554399 | + | 0.686734i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14799.4 | − | 14799.4i | −0.933685 | − | 0.933685i | 0.0642487 | − | 0.997934i | \(-0.479535\pi\) |
−0.997934 | + | 0.0642487i | \(0.979535\pi\) | |||||||
\(632\) | −1189.80 | − | 2872.43i | −0.0748856 | − | 0.180790i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1572.73 | + | 651.445i | −0.0985188 | + | 0.0408078i | ||||
\(635\) | 1319.78 | − | 3186.22i | 0.0824783 | − | 0.199120i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4460.54 | + | 4460.54i | −0.277446 | + | 0.277446i | ||||
\(638\) | 615.353 | − | 615.353i | 0.0381850 | − | 0.0381850i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 483.453 | − | 1167.16i | 0.0298596 | − | 0.0720876i | ||||
\(641\) | 8975.50 | − | 3717.77i | 0.553059 | − | 0.229085i | −0.0886097 | − | 0.996066i | \(-0.528242\pi\) |
0.641669 | + | 0.766982i | \(0.278242\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9268.20 | − | 22375.4i | −0.568433 | − | 1.37232i | −0.902876 | − | 0.429902i | \(-0.858548\pi\) |
0.334443 | − | 0.942416i | \(-0.391452\pi\) | |||||||
\(644\) | 1685.55 | + | 1685.55i | 0.103136 | + | 0.103136i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 275.327 | − | 150.027i | 0.0167687 | − | 0.00913734i | ||||
\(647\) | −5143.07 | −0.312511 | −0.156256 | − | 0.987717i | \(-0.549942\pi\) | ||||
−0.156256 | + | 0.987717i | \(0.549942\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12037.2 | + | 29060.3i | 0.728043 | + | 1.75765i | ||||
\(650\) | − | 1404.42i | − | 0.0847473i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5757.74 | + | 13900.4i | −0.345845 | + | 0.834943i | ||||
\(653\) | 2700.35 | + | 1118.52i | 0.161827 | + | 0.0670308i | 0.462126 | − | 0.886814i | \(-0.347087\pi\) |
−0.300300 | + | 0.953845i | \(0.597087\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3803.20 | + | 3803.20i | −0.226875 | + | 0.226875i | ||||
\(656\) | 25181.0 | + | 10430.3i | 1.49871 | + | 0.620786i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 939.300 | − | 389.071i | 0.0556500 | − | 0.0230510i | ||||
\(659\) | − | 17368.4i | − | 1.02667i | −0.858188 | − | 0.513336i | \(-0.828409\pi\) | ||
0.858188 | − | 0.513336i | \(-0.171591\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5685.94 | + | 5685.94i | 0.334580 | + | 0.334580i | 0.854323 | − | 0.519743i | \(-0.173972\pi\) |
−0.519743 | + | 0.854323i | \(0.673972\pi\) | |||||||
\(662\) | 2131.38 | 0.125134 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −49.7417 | −0.00290715 | ||||||||
\(665\) | 821.973 | + | 821.973i | 0.0479319 | + | 0.0479319i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 975.769i | 0.0566446i | ||||||||
\(668\) | −796.558 | + | 329.945i | −0.0461374 | + | 0.0191107i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −208.534 | − | 86.3777i | −0.0120244 | − | 0.00498069i | ||||
\(671\) | −3022.97 | + | 3022.97i | −0.173920 | + | 0.173920i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8385.45 | + | 3473.37i | 0.480290 | + | 0.198943i | 0.609675 | − | 0.792652i | \(-0.291300\pi\) |
−0.129384 | + | 0.991595i | \(0.541300\pi\) | |||||||
\(674\) | −605.559 | + | 1461.95i | −0.0346072 | + | 0.0835493i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4430.54i | 0.252079i | ||||||||
\(677\) | 9550.85 | + | 23057.8i | 0.542199 | + | 1.30899i | 0.923168 | + | 0.384397i | \(0.125591\pi\) |
−0.380969 | + | 0.924588i | \(0.624409\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25797.4 | 1.45805 | ||||||||
\(680\) | 696.930 | − | 74.3097i | 0.0393030 | − | 0.00419066i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1467.71 | + | 1467.71i | 0.0824068 | + | 0.0824068i | ||||
\(683\) | 2322.36 | + | 5606.67i | 0.130106 | + | 0.314105i | 0.975486 | − | 0.220061i | \(-0.0706258\pi\) |
−0.845380 | + | 0.534166i | \(0.820626\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4448.26 | − | 1842.53i | 0.248116 | − | 0.102773i | ||||
\(686\) | −418.166 | + | 1009.54i | −0.0232735 | + | 0.0561873i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5641.96 | + | 5641.96i | −0.312642 | + | 0.312642i | ||||
\(689\) | −11581.5 | + | 11581.5i | −0.640378 | + | 0.640378i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6641.71 | − | 16034.5i | 0.365648 | − | 0.882752i | −0.628804 | − | 0.777564i | \(-0.716455\pi\) |
0.994452 | − | 0.105189i | \(-0.0335446\pi\) | |||||||
\(692\) | 20235.8 | − | 8381.96i | 1.11163 | − | 0.460454i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −210.163 | − | 507.378i | −0.0114952 | − | 0.0277519i | ||||
\(695\) | −401.387 | − | 401.387i | −0.0219072 | − | 0.0219072i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3227.56 | + | 30270.4i | 0.175398 | + | 1.64501i | ||||
\(698\) | −2507.87 | −0.135995 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7687.07 | − | 18558.2i | −0.415063 | − | 1.00205i | ||||
\(701\) | − | 34827.5i | − | 1.87649i | −0.345976 | − | 0.938243i | \(-0.612452\pi\) | ||
0.345976 | − | 0.938243i | \(-0.387548\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1492.21 | − | 3602.52i | 0.0800566 | − | 0.193274i | ||||
\(704\) | −24798.8 | − | 10272.0i | −1.32761 | − | 0.549915i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1242.86 | + | 1242.86i | −0.0662546 | + | 0.0662546i | ||||
\(707\) | 1774.49 | + | 735.018i | 0.0943941 | + | 0.0390993i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23731.7 | + | 9830.00i | −1.25707 | + | 0.520696i | −0.909009 | − | 0.416775i | \(-0.863160\pi\) |
−0.348062 | + | 0.937472i | \(0.613160\pi\) | |||||||
\(710\) | 133.669i | 0.00706548i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1673.25 | + | 1673.25i | 0.0880725 | + | 0.0880725i | ||||
\(713\) | −2327.35 | −0.122244 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7875.52 | 0.411927 | ||||||||
\(716\) | −11274.8 | − | 11274.8i | −0.588492 | − | 0.588492i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 2328.92i | − | 0.121051i | ||||||
\(719\) | 16792.7 | − | 6955.77i | 0.871018 | − | 0.360788i | 0.0980115 | − | 0.995185i | \(-0.468752\pi\) |
0.773007 | + | 0.634398i | \(0.218752\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24699.0 | + | 10230.7i | 1.27578 | + | 0.528446i | ||||
\(722\) | 1043.12 | − | 1043.12i | 0.0537688 | − | 0.0537688i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 17801.1 | + | 7373.46i | 0.913775 | + | 0.378498i | ||||
\(725\) | 3146.68 | − | 7596.75i | 0.161193 | − | 0.389153i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8657.73i | 0.441674i | 0.975311 | + | 0.220837i | \(0.0708789\pi\) | ||||
−0.975311 | + | 0.220837i | \(0.929121\pi\) | |||||||
\(728\) | −1570.90 | − | 3792.48i | −0.0799744 | − | 0.193075i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −18.2121 | −0.000923371 | ||||||||
\(731\) | −8548.50 | − | 2518.21i | −0.432528 | − | 0.127414i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7989.74 | − | 7989.74i | −0.402603 | − | 0.402603i | 0.476546 | − | 0.879149i | \(-0.341888\pi\) |
−0.879149 | + | 0.476546i | \(0.841888\pi\) | |||||||
\(734\) | 900.168 | + | 2173.20i | 0.0452668 | + | 0.109284i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −558.421 | + | 231.306i | −0.0279670 | + | 0.0115843i | ||||
\(737\) | −7513.48 | + | 18139.1i | −0.375526 | + | 0.906600i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8885.48 | − | 8885.48i | 0.442297 | − | 0.442297i | −0.450486 | − | 0.892783i | \(-0.648749\pi\) |
0.892783 | + | 0.450486i | \(0.148749\pi\) | |||||||
\(740\) | 3071.62 | − | 3071.62i | 0.152588 | − | 0.152588i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 585.716 | − | 1414.04i | 0.0289789 | − | 0.0699612i | ||||
\(743\) | −12980.0 | + | 5376.49i | −0.640902 | + | 0.265470i | −0.679377 | − | 0.733789i | \(-0.737750\pi\) |
0.0384753 | + | 0.999260i | \(0.487750\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2119.96 | + | 5118.04i | 0.104254 | + | 0.251692i | ||||
\(746\) | −442.166 | − | 442.166i | −0.0217009 | − | 0.0217009i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3221.36 | − | 30212.2i | −0.157466 | − | 1.47683i | ||||
\(749\) | 33091.7 | 1.61435 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3111.79 | − | 7512.52i | −0.151199 | − | 0.365027i | 0.830073 | − | 0.557655i | \(-0.188299\pi\) |
−0.981272 | + | 0.192628i | \(0.938299\pi\) | |||||||
\(752\) | − | 13009.6i | − | 0.630865i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 320.474 | − | 773.693i | 0.0154788 | − | 0.0373690i | ||||
\(755\) | −192.309 | − | 79.6572i | −0.00927001 | − | 0.00383976i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16245.0 | − | 16245.0i | 0.779964 | − | 0.779964i | −0.199860 | − | 0.979824i | \(-0.564049\pi\) |
0.979824 | + | 0.199860i | \(0.0640488\pi\) | |||||||
\(758\) | −1348.46 | − | 558.549i | −0.0646149 | − | 0.0267644i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −181.349 | + | 75.1174i | −0.00865557 | + | 0.00358525i | ||||
\(761\) | 15071.9i | 0.717946i | 0.933348 | + | 0.358973i | \(0.116873\pi\) | ||||
−0.933348 | + | 0.358973i | \(0.883127\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1580.89 | − | 1580.89i | −0.0750091 | − | 0.0750091i | ||||
\(764\) | 33013.4 | 1.56333 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 841.515 | 0.0396934 | ||||||||
\(767\) | 21403.4 | + | 21403.4i | 1.00761 | + | 1.00761i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 10392.1i | − | 0.487321i | −0.969861 | − | 0.243660i | \(-0.921652\pi\) | ||
0.969861 | − | 0.243660i | \(-0.0783482\pi\) | |||||||
\(770\) | −679.926 | + | 281.635i | −0.0318219 | + | 0.0131811i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15247.3 | − | 6315.63i | −0.710831 | − | 0.294436i | ||||
\(773\) | 24316.4 | − | 24316.4i | 1.13144 | − | 1.13144i | 0.141499 | − | 0.989938i | \(-0.454808\pi\) |
0.989938 | − | 0.141499i | \(-0.0451921\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18119.4 | + | 7505.29i | 0.839829 | + | 0.347868i | ||||
\(776\) | −1667.03 | + | 4024.57i | −0.0771172 | + | 0.186177i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 486.052i | 0.0223982i | ||||||||
\(779\) | −3262.64 | − | 7876.71i | −0.150059 | − | 0.362275i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11627.0 | 0.532712 | ||||||||
\(782\) | −173.188 | − | 139.814i | −0.00791968 | − | 0.00639355i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5333.70 | − | 5333.70i | −0.242971 | − | 0.242971i | ||||
\(785\) | −2423.65 | − | 5851.21i | −0.110196 | − | 0.266036i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23671.4 | − | 9805.02i | 1.07217 | − | 0.444106i | 0.224411 | − | 0.974494i | \(-0.427954\pi\) |
0.847754 | + | 0.530389i | \(0.177954\pi\) | |||||||
\(788\) | −11568.7 | + | 27929.3i | −0.522993 | + | 1.26262i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −379.290 | + | 379.290i | −0.0170817 | + | 0.0170817i | ||||
\(791\) | −5603.56 | + | 5603.56i | −0.251883 | + | 0.251883i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1574.35 | + | 3800.83i | −0.0705006 | + | 0.170203i | ||||
\(794\) | −497.879 | + | 206.228i | −0.0222532 | + | 0.00921759i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11016.3 | − | 26595.7i | −0.490532 | − | 1.18425i | ||||
\(797\) | −20108.4 | − | 20108.4i | −0.893698 | − | 0.893698i | 0.101171 | − | 0.994869i | \(-0.467741\pi\) |
−0.994869 | + | 0.101171i | \(0.967741\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12759.2 | − | 6952.51i | 0.564939 | − | 0.307838i | ||||
\(800\) | 5093.45 | 0.225101 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −179.969 | − | 434.483i | −0.00792383 | − | 0.0191298i | ||||
\(803\) | 1584.16i | 0.0696188i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 315.787 | − | 762.377i | 0.0138261 | − | 0.0333792i | ||||
\(806\) | 1845.37 | + | 764.378i | 0.0806458 | + | 0.0334046i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −229.336 | + | 229.336i | −0.00998515 | + | 0.00998515i | ||||
\(809\) | −20652.5 | − | 8554.55i | −0.897532 | − | 0.371770i | −0.114261 | − | 0.993451i | \(-0.536450\pi\) |
−0.783271 | + | 0.621681i | \(0.786450\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5572.70 | + | 2308.29i | −0.241287 | + | 0.0999444i | −0.500050 | − | 0.865996i | \(-0.666685\pi\) |
0.258763 | + | 0.965941i | \(0.416685\pi\) | |||||||
\(812\) | − | 11977.8i | − | 0.517660i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1745.62 | + | 1745.62i | 0.0751646 | + | 0.0751646i | ||||
\(815\) | 5208.49 | 0.223859 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2495.84 | 0.106877 | ||||||||
\(818\) | 1489.69 | + | 1489.69i | 0.0636744 | + | 0.0636744i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 9497.78i | − | 0.404484i | ||||||
\(821\) | −11698.6 | + | 4845.73i | −0.497302 | + | 0.205989i | −0.617214 | − | 0.786795i | \(-0.711739\pi\) |
0.119912 | + | 0.992785i | \(0.461739\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10190.3 | + | 4220.95i | 0.431605 | + | 0.178777i | 0.587900 | − | 0.808934i | \(-0.299955\pi\) |
−0.156295 | + | 0.987710i | \(0.549955\pi\) | |||||||
\(824\) | −3192.10 | + | 3192.10i | −0.134954 | + | 0.134954i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2613.25 | − | 1082.44i | −0.110081 | − | 0.0455969i | ||||
\(827\) | −10962.5 | + | 26465.9i | −0.460948 | + | 1.11283i | 0.507060 | + | 0.861911i | \(0.330732\pi\) |
−0.968009 | + | 0.250917i | \(0.919268\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15663.7i | 0.656239i | 0.944636 | + | 0.328120i | \(0.106415\pi\) | ||||
−0.944636 | + | 0.328120i | \(0.893585\pi\) | |||||||
\(830\) | 3.28407 | + | 7.92844i | 0.000137339 | + | 0.000331567i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −25830.3 | −1.07633 | ||||||||
\(833\) | 2380.62 | − | 8081.44i | 0.0990201 | − | 0.336141i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 211.050 | + | 211.050i | 0.00874694 | + | 0.00874694i | ||||
\(836\) | 3256.37 | + | 7861.57i | 0.134718 | + | 0.325237i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −874.837 | + | 362.369i | −0.0360629 | + | 0.0149378i | ||||
\(839\) | −8669.06 | + | 20929.0i | −0.356721 | + | 0.861201i | 0.639036 | + | 0.769177i | \(0.279334\pi\) |
−0.995757 | + | 0.0920240i | \(0.970666\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13778.6 | + | 13778.6i | −0.564952 | + | 0.564952i | ||||
\(842\) | 742.709 | − | 742.709i | 0.0303984 | − | 0.0303984i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1923.82 | + | 4644.52i | −0.0784606 | + | 0.189421i | ||||
\(845\) | 1417.00 | − | 586.942i | 0.0576880 | − | 0.0238952i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13535.5 | + | 32677.6i | 0.549097 | + | 1.32564i | ||||
\(848\) | −13848.6 | − | 13848.6i | −0.560807 | − | 0.560807i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 897.462 | + | 1647.01i | 0.0362149 | + | 0.0664611i | ||||
\(851\) | −2768.04 | −0.111501 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1702.92 | − | 4111.21i | −0.0683551 | − | 0.165024i | 0.886010 | − | 0.463666i | \(-0.153466\pi\) |
−0.954365 | + | 0.298642i | \(0.903466\pi\) | |||||||
\(854\) | − | 384.442i | − | 0.0154044i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2138.39 | + | 5162.54i | −0.0853841 | + | 0.206135i | ||||
\(857\) | 20994.3 | + | 8696.11i | 0.836815 | + | 0.346620i | 0.759597 | − | 0.650394i | \(-0.225396\pi\) |
0.0772178 | + | 0.997014i | \(0.475396\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29733.4 | + | 29733.4i | −1.18102 | + | 1.18102i | −0.201533 | + | 0.979482i | \(0.564592\pi\) |
−0.979482 | + | 0.201533i | \(0.935408\pi\) | |||||||
\(860\) | 2568.76 | + | 1064.02i | 0.101854 | + | 0.0421892i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3648.59 | − | 1511.30i | 0.144166 | − | 0.0597157i | ||||
\(863\) | − | 7875.51i | − | 0.310644i | −0.987864 | − | 0.155322i | \(-0.950359\pi\) | ||
0.987864 | − | 0.155322i | \(-0.0496414\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5361.54 | − | 5361.54i | −0.210749 | − | 0.210749i | ||||
\(866\) | 2587.30 | 0.101524 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 28568.9 | 1.11716 | ||||||||
\(869\) | 32992.2 | + | 32992.2i | 1.28790 | + | 1.28790i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18893.6i | 0.735002i | ||||||||
\(872\) | 348.786 | − | 144.472i | 0.0135452 | − | 0.00561060i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 57.5917 | + | 23.8552i | 0.00222891 | + | 0.000923244i | ||||
\(875\) | −10151.1 | + | 10151.1i | −0.392194 | + | 0.392194i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24138.0 | − | 9998.27i | −0.929397 | − | 0.384969i | −0.133947 | − | 0.990988i | \(-0.542765\pi\) |
−0.795450 | + | 0.606020i | \(0.792765\pi\) | |||||||
\(878\) | 447.194 | − | 1079.62i | 0.0171891 | − | 0.0414983i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9417.18i | 0.360742i | ||||||||
\(881\) | −2449.18 | − | 5912.84i | −0.0936604 | − | 0.226116i | 0.870106 | − | 0.492865i | \(-0.164051\pi\) |
−0.963766 | + | 0.266749i | \(0.914051\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43393.3 | −1.65379 | −0.826897 | − | 0.562354i | \(-0.809896\pi\) | ||||
−0.826897 | + | 0.562354i | \(0.809896\pi\) | |||||||
\(884\) | −13989.9 | − | 25674.1i | −0.532275 | − | 0.976824i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 504.832 | + | 504.832i | 0.0191424 | + | 0.0191424i | ||||
\(887\) | −7831.78 | − | 18907.6i | −0.296466 | − | 0.715733i | −0.999987 | − | 0.00505836i | \(-0.998390\pi\) |
0.703521 | − | 0.710675i | \(-0.251610\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24922.8 | − | 10323.4i | 0.940253 | − | 0.389466i | ||||
\(890\) | 156.231 | − | 377.175i | 0.00588413 | − | 0.0142055i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3000.09 | − | 3000.09i | 0.112613 | − | 0.112613i | ||||
\(893\) | −2877.53 | + | 2877.53i | −0.107831 | + | 0.107831i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2112.34 | + | 5099.64i | −0.0788913 | + | 0.190460i | ||||
\(896\) | 9129.60 | − | 3781.60i | 0.340400 | − | 0.140998i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1024.62 | − | 2473.66i | −0.0380759 | − | 0.0919233i | ||||
\(899\) | 8269.33 | + | 8269.33i | 0.306783 | + | 0.306783i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6181.15 | − | 20983.0i | 0.228550 | − | 0.775854i | ||||
\(902\) | 5397.64 | 0.199248 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −512.091 | − | 1236.30i | −0.0188406 | − | 0.0454852i | ||||
\(905\) | − | 6670.07i | − | 0.244995i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11555.0 | + | 27896.3i | −0.423019 | + | 1.02126i | 0.558433 | + | 0.829550i | \(0.311403\pi\) |
−0.981452 | + | 0.191709i | \(0.938597\pi\) | |||||||
\(908\) | 4323.90 | + | 1791.02i | 0.158033 | + | 0.0654593i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −500.779 | + | 500.779i | −0.0182425 | + | 0.0182425i | ||||
\(911\) | −21246.6 | − | 8800.64i | −0.772703 | − | 0.320064i | −0.0387363 | − | 0.999249i | \(-0.512333\pi\) |
−0.733967 | + | 0.679185i | \(0.762333\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 689.648 | − | 285.662i | 0.0249989 | − | 0.0103549i | ||||
\(914\) | − | 2827.68i | − | 0.102332i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14843.6 | − | 14843.6i | −0.535422 | − | 0.535422i | ||||
\(917\) | −42071.3 | −1.51507 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40432.8 | −1.45131 | −0.725656 | − | 0.688057i | \(-0.758464\pi\) | ||||
−0.725656 | + | 0.688057i | \(0.758464\pi\) | |||||||
\(920\) | 98.5299 | + | 98.5299i | 0.00353091 | + | 0.00353091i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 1679.57i | − | 0.0599932i | ||||||
\(923\) | 10337.1 | − | 4281.76i | 0.368634 | − | 0.152693i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21550.3 | + | 8926.43i | 0.766021 | + | 0.317296i | ||||
\(926\) | −1844.48 | + | 1844.48i | −0.0654574 | + | 0.0654574i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2805.98 | + | 1162.28i | 0.0992574 | + | 0.0411137i | ||||
\(929\) | 13044.2 | − | 31491.4i | 0.460673 | − | 1.11216i | −0.507448 | − | 0.861682i | \(-0.669411\pi\) |
0.968121 | − | 0.250482i | \(-0.0805890\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2359.48i | 0.0830599i | ||||||||
\(932\) | 1166.08 | + | 2815.16i | 0.0409830 | + | 0.0989418i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1006.83 | −0.0352724 | ||||||||
\(935\) | −9235.91 | + | 5032.68i | −0.323044 | + | 0.176028i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −539.977 | − | 539.977i | −0.0188263 | − | 0.0188263i | 0.697631 | − | 0.716457i | \(-0.254238\pi\) |
−0.716457 | + | 0.697631i | \(0.754238\pi\) | |||||||
\(938\) | −675.652 | − | 1631.17i | −0.0235190 | − | 0.0567799i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4188.35 | + | 1734.87i | −0.145329 | + | 0.0601971i | ||||
\(941\) | 170.281 | − | 411.094i | 0.00589904 | − | 0.0142415i | −0.920903 | − | 0.389793i | \(-0.872547\pi\) |
0.926802 | + | 0.375551i | \(0.122547\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4279.54 | + | 4279.54i | −0.147785 | + | 0.147785i | ||||
\(944\) | −25593.3 | + | 25593.3i | −0.882404 | + | 0.882404i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −604.687 | + | 1459.84i | −0.0207823 | + | 0.0501729i | ||||
\(947\) | 10304.9 | − | 4268.42i | 0.353604 | − | 0.146468i | −0.198808 | − | 0.980038i | \(-0.563707\pi\) |
0.552413 | + | 0.833571i | \(0.313707\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 583.383 | + | 1408.41i | 0.0199551 | + | 0.0481759i | ||||
\(950\) | −371.445 | − | 371.445i | −0.0126855 | − | 0.0126855i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4265.75 | + | 3443.74i | 0.145225 | + | 0.117240i | ||||
\(953\) | −48344.2 | −1.64325 | −0.821627 | − | 0.570026i | \(-0.806933\pi\) | ||||
−0.821627 | + | 0.570026i | \(0.806933\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4373.50 | − | 10558.6i | −0.148192 | − | 0.357767i | ||||
\(956\) | − | 34531.3i | − | 1.16822i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.6455 | + | 59.4994i | −0.000831168 | + | 0.00200662i | ||||
\(959\) | 34794.6 | + | 14412.4i | 1.17161 | + | 0.485298i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1341.84 | − | 1341.84i | 0.0450417 | − | 0.0450417i | ||||
\(962\) | 2194.80 | + | 909.115i | 0.0735583 | + | 0.0304688i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15080.2 | + | 6246.43i | −0.503840 | + | 0.208697i | ||||
\(965\) | 5713.15i | 0.190583i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −618.214 | − | 618.214i | −0.0205589 | − | 0.0205589i | 0.696753 | − | 0.717311i | \(-0.254628\pi\) |
−0.717311 | + | 0.696753i | \(0.754628\pi\) | |||||||
\(968\) | −5972.59 | −0.198312 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 751.547 | 0.0248770 | ||||||||
\(971\) | −20420.3 | − | 20420.3i | −0.674892 | − | 0.674892i | 0.283948 | − | 0.958840i | \(-0.408356\pi\) |
−0.958840 | + | 0.283948i | \(0.908356\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 4440.17i | − | 0.146295i | ||||||
\(974\) | −1600.49 | + | 662.944i | −0.0526519 | + | 0.0218091i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4544.85 | − | 1882.54i | −0.149055 | − | 0.0617404i | ||||
\(977\) | 3143.83 | − | 3143.83i | 0.102948 | − | 0.102948i | −0.653757 | − | 0.756705i | \(-0.726808\pi\) |
0.756705 | + | 0.653757i | \(0.226808\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32808.2 | − | 13589.6i | −1.07105 | − | 0.443642i | ||||
\(980\) | −1005.88 | + | 2428.42i | −0.0327875 | + | 0.0791561i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2924.80i | 0.0950448i | ||||||||
\(983\) | 15780.7 | + | 38098.1i | 0.512032 | + | 1.23615i | 0.942699 | + | 0.333644i | \(0.108278\pi\) |
−0.430667 | + | 0.902511i | \(0.641722\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10465.1 | 0.338524 | ||||||||
\(986\) | 118.580 | + | 1112.13i | 0.00382998 | + | 0.0359203i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5790.19 | + | 5790.19i | 0.186448 | + | 0.186448i | ||||
\(989\) | −678.014 | − | 1636.87i | −0.0217994 | − | 0.0526284i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30566.7 | + | 12661.1i | −0.979801 | + | 0.405847i | −0.814352 | − | 0.580372i | \(-0.802907\pi\) |
−0.165449 | + | 0.986218i | \(0.552907\pi\) | |||||||
\(992\) | −2772.20 | + | 6692.68i | −0.0887272 | + | 0.214206i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −739.325 | + | 739.325i | −0.0235915 | + | 0.0235915i | ||||
\(995\) | −7046.62 | + | 7046.62i | −0.224515 | + | 0.224515i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4318.18 | + | 10425.0i | −0.137170 | + | 0.331157i | −0.977506 | − | 0.210909i | \(-0.932358\pi\) |
0.840336 | + | 0.542066i | \(0.182358\pi\) | |||||||
\(998\) | 572.061 | − | 236.956i | 0.0181446 | − | 0.00751573i | ||||
\(999\) | 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 | 153.4.l.a.100.2 | 12 | ||
3.2 | odd | 2 | 17.4.d.a.15.2 | yes | 12 | ||
17.8 | even | 8 | inner | 153.4.l.a.127.2 | 12 | ||
51.5 | even | 16 | 289.4.a.g.1.7 | 12 | |||
51.8 | odd | 8 | 17.4.d.a.8.2 | ✓ | 12 | ||
51.14 | even | 16 | 289.4.b.e.288.5 | 12 | |||
51.20 | even | 16 | 289.4.b.e.288.6 | 12 | |||
51.29 | even | 16 | 289.4.a.g.1.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.d.a.8.2 | ✓ | 12 | 51.8 | odd | 8 | ||
17.4.d.a.15.2 | yes | 12 | 3.2 | odd | 2 | ||
153.4.l.a.100.2 | 12 | 1.1 | even | 1 | trivial | ||
153.4.l.a.127.2 | 12 | 17.8 | even | 8 | inner | ||
289.4.a.g.1.7 | 12 | 51.5 | even | 16 | |||
289.4.a.g.1.8 | 12 | 51.29 | even | 16 | |||
289.4.b.e.288.5 | 12 | 51.14 | even | 16 | |||
289.4.b.e.288.6 | 12 | 51.20 | even | 16 |