Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 4 x^{18} - 22 x^{17} + 101 x^{16} + 178 x^{15} - 1035 x^{14} - 583 x^{13} + 5572 x^{12} + \cdots + 210 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(-1.91759\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.91759 | 1.35594 | 0.677969 | − | 0.735091i | \(-0.262860\pi\) | ||||
0.677969 | + | 0.735091i | \(0.262860\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.67713 | 0.838567 | ||||||||
\(5\) | −1.63006 | −0.728986 | −0.364493 | − | 0.931206i | \(-0.618758\pi\) | ||||
−0.364493 | + | 0.931206i | \(0.618758\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −0.619124 | −0.218893 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.12578 | −0.988459 | ||||||||
\(11\) | −4.53723 | −1.36803 | −0.684013 | − | 0.729470i | \(-0.739767\pi\) | ||||
−0.684013 | + | 0.729470i | \(0.739767\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.785019 | 0.217725 | 0.108863 | − | 0.994057i | \(-0.465279\pi\) | ||||
0.108863 | + | 0.994057i | \(0.465279\pi\) | |||||||
\(14\) | 1.91759 | 0.512496 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.54149 | −1.13537 | ||||||||
\(17\) | 4.58625 | 1.11233 | 0.556164 | − | 0.831073i | \(-0.312273\pi\) | ||||
0.556164 | + | 0.831073i | \(0.312273\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.32031 | 1.67940 | 0.839698 | − | 0.543054i | \(-0.182732\pi\) | ||||
0.839698 | + | 0.543054i | \(0.182732\pi\) | |||||||
\(20\) | −2.73383 | −0.611303 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.70052 | −1.85496 | ||||||||
\(23\) | −1.77992 | −0.371139 | −0.185569 | − | 0.982631i | \(-0.559413\pi\) | ||||
−0.185569 | + | 0.982631i | \(0.559413\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.34290 | −0.468580 | ||||||||
\(26\) | 1.50534 | 0.295222 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.67713 | 0.316948 | ||||||||
\(29\) | −4.77456 | −0.886614 | −0.443307 | − | 0.896370i | \(-0.646195\pi\) | ||||
−0.443307 | + | 0.896370i | \(0.646195\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.06545 | 0.909781 | 0.454891 | − | 0.890547i | \(-0.349678\pi\) | ||||
0.454891 | + | 0.890547i | \(0.349678\pi\) | |||||||
\(32\) | −7.47045 | −1.32060 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.79452 | 1.50825 | ||||||||
\(35\) | −1.63006 | −0.275531 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.03335 | −0.169881 | −0.0849407 | − | 0.996386i | \(-0.527070\pi\) | ||||
−0.0849407 | + | 0.996386i | \(0.527070\pi\) | |||||||
\(38\) | 14.0373 | 2.27716 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00921 | 0.159570 | ||||||||
\(41\) | 10.6489 | 1.66307 | 0.831536 | − | 0.555471i | \(-0.187462\pi\) | ||||
0.831536 | + | 0.555471i | \(0.187462\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.26855 | 1.26094 | 0.630471 | − | 0.776213i | \(-0.282862\pi\) | ||||
0.630471 | + | 0.776213i | \(0.282862\pi\) | |||||||
\(44\) | −7.60954 | −1.14718 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.41315 | −0.503241 | ||||||||
\(47\) | −7.59560 | −1.10793 | −0.553966 | − | 0.832539i | \(-0.686886\pi\) | ||||
−0.553966 | + | 0.832539i | \(0.686886\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.49271 | −0.635365 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.31658 | 0.182577 | ||||||||
\(53\) | −0.151205 | −0.0207696 | −0.0103848 | − | 0.999946i | \(-0.503306\pi\) | ||||
−0.0103848 | + | 0.999946i | \(0.503306\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.39596 | 0.997272 | ||||||||
\(56\) | −0.619124 | −0.0827339 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.15563 | −1.20219 | ||||||||
\(59\) | −4.69350 | −0.611042 | −0.305521 | − | 0.952185i | \(-0.598831\pi\) | ||||
−0.305521 | + | 0.952185i | \(0.598831\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.1937 | −1.56125 | −0.780623 | − | 0.625002i | \(-0.785098\pi\) | ||||
−0.780623 | + | 0.625002i | \(0.785098\pi\) | |||||||
\(62\) | 9.71343 | 1.23361 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.24224 | −0.655280 | ||||||||
\(65\) | −1.27963 | −0.158718 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.56249 | 0.190889 | 0.0954444 | − | 0.995435i | \(-0.469573\pi\) | ||||
0.0954444 | + | 0.995435i | \(0.469573\pi\) | |||||||
\(68\) | 7.69175 | 0.932761 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.12578 | −0.373602 | ||||||||
\(71\) | 13.2252 | 1.56954 | 0.784768 | − | 0.619789i | \(-0.212782\pi\) | ||||
0.784768 | + | 0.619789i | \(0.212782\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.59318 | 0.654632 | 0.327316 | − | 0.944915i | \(-0.393856\pi\) | ||||
0.327316 | + | 0.944915i | \(0.393856\pi\) | |||||||
\(74\) | −1.98153 | −0.230349 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 12.2771 | 1.40829 | ||||||||
\(77\) | −4.53723 | −0.517065 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.81705 | −0.429451 | −0.214726 | − | 0.976674i | \(-0.568886\pi\) | ||||
−0.214726 | + | 0.976674i | \(0.568886\pi\) | |||||||
\(80\) | 7.40291 | 0.827670 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 20.4201 | 2.25502 | ||||||||
\(83\) | −0.734264 | −0.0805960 | −0.0402980 | − | 0.999188i | \(-0.512831\pi\) | ||||
−0.0402980 | + | 0.999188i | \(0.512831\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.47586 | −0.810871 | ||||||||
\(86\) | 15.8556 | 1.70976 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.80911 | 0.299452 | ||||||||
\(89\) | 5.16974 | 0.547991 | 0.273996 | − | 0.961731i | \(-0.411655\pi\) | ||||
0.273996 | + | 0.961731i | \(0.411655\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.785019 | 0.0822923 | ||||||||
\(92\) | −2.98516 | −0.311225 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −14.5652 | −1.50229 | ||||||||
\(95\) | −11.9326 | −1.22426 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.35014 | −0.543224 | −0.271612 | − | 0.962407i | \(-0.587557\pi\) | ||||
−0.271612 | + | 0.962407i | \(0.587557\pi\) | |||||||
\(98\) | 1.91759 | 0.193705 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.92935 | −0.392935 | ||||||||
\(101\) | 13.8634 | 1.37946 | 0.689731 | − | 0.724065i | \(-0.257729\pi\) | ||||
0.689731 | + | 0.724065i | \(0.257729\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.4513 | 1.71953 | 0.859764 | − | 0.510691i | \(-0.170610\pi\) | ||||
0.859764 | + | 0.510691i | \(0.170610\pi\) | |||||||
\(104\) | −0.486024 | −0.0476586 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.289949 | −0.0281623 | ||||||||
\(107\) | 7.09496 | 0.685896 | 0.342948 | − | 0.939354i | \(-0.388575\pi\) | ||||
0.342948 | + | 0.939354i | \(0.388575\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.4311 | 1.66959 | 0.834796 | − | 0.550559i | \(-0.185586\pi\) | ||||
0.834796 | + | 0.550559i | \(0.185586\pi\) | |||||||
\(110\) | 14.1824 | 1.35224 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.54149 | −0.429130 | ||||||||
\(113\) | 7.36358 | 0.692707 | 0.346353 | − | 0.938104i | \(-0.387420\pi\) | ||||
0.346353 | + | 0.938104i | \(0.387420\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.90138 | 0.270555 | ||||||||
\(116\) | −8.00758 | −0.743485 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.00019 | −0.828534 | ||||||||
\(119\) | 4.58625 | 0.420420 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.58645 | 0.871495 | ||||||||
\(122\) | −23.3825 | −2.11695 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.49543 | 0.762912 | ||||||||
\(125\) | 11.9694 | 1.07057 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 4.88845 | 0.432082 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.45380 | −0.215212 | ||||||||
\(131\) | −3.42397 | −0.299153 | −0.149577 | − | 0.988750i | \(-0.547791\pi\) | ||||
−0.149577 | + | 0.988750i | \(0.547791\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.32031 | 0.634752 | ||||||||
\(134\) | 2.99621 | 0.258833 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.83945 | −0.243481 | ||||||||
\(137\) | 8.60770 | 0.735405 | 0.367703 | − | 0.929943i | \(-0.380144\pi\) | ||||
0.367703 | + | 0.929943i | \(0.380144\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.1427 | 0.945108 | 0.472554 | − | 0.881302i | \(-0.343332\pi\) | ||||
0.472554 | + | 0.881302i | \(0.343332\pi\) | |||||||
\(140\) | −2.73383 | −0.231051 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 25.3604 | 2.12819 | ||||||||
\(143\) | −3.56181 | −0.297854 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.78283 | 0.646329 | ||||||||
\(146\) | 10.7254 | 0.887640 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.73306 | −0.142457 | ||||||||
\(149\) | 20.6563 | 1.69223 | 0.846117 | − | 0.532997i | \(-0.178934\pi\) | ||||
0.846117 | + | 0.532997i | \(0.178934\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.83421 | 0.149266 | 0.0746330 | − | 0.997211i | \(-0.476221\pi\) | ||||
0.0746330 | + | 0.997211i | \(0.476221\pi\) | |||||||
\(152\) | −4.53218 | −0.367608 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.70052 | −0.701108 | ||||||||
\(155\) | −8.25699 | −0.663218 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.98994 | 0.797284 | 0.398642 | − | 0.917107i | \(-0.369482\pi\) | ||||
0.398642 | + | 0.917107i | \(0.369482\pi\) | |||||||
\(158\) | −7.31952 | −0.582309 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.1773 | 0.962699 | ||||||||
\(161\) | −1.77992 | −0.140277 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.49104 | 0.430092 | 0.215046 | − | 0.976604i | \(-0.431010\pi\) | ||||
0.215046 | + | 0.976604i | \(0.431010\pi\) | |||||||
\(164\) | 17.8596 | 1.39460 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.40801 | −0.109283 | ||||||||
\(167\) | −1.35423 | −0.104794 | −0.0523969 | − | 0.998626i | \(-0.516686\pi\) | ||||
−0.0523969 | + | 0.998626i | \(0.516686\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3837 | −0.952596 | ||||||||
\(170\) | −14.3356 | −1.09949 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.8675 | 1.05738 | ||||||||
\(173\) | 5.51469 | 0.419274 | 0.209637 | − | 0.977779i | \(-0.432772\pi\) | ||||
0.209637 | + | 0.977779i | \(0.432772\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.34290 | −0.177106 | ||||||||
\(176\) | 20.6058 | 1.55322 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.91342 | 0.743042 | ||||||||
\(179\) | 9.88587 | 0.738904 | 0.369452 | − | 0.929250i | \(-0.379545\pi\) | ||||
0.369452 | + | 0.929250i | \(0.379545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.10026 | 0.230441 | 0.115220 | − | 0.993340i | \(-0.463243\pi\) | ||||
0.115220 | + | 0.993340i | \(0.463243\pi\) | |||||||
\(182\) | 1.50534 | 0.111583 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.10199 | 0.0812398 | ||||||||
\(185\) | 1.68442 | 0.123841 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.8088 | −1.52169 | ||||||||
\(188\) | −12.7388 | −0.929075 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −22.8817 | −1.66001 | ||||||||
\(191\) | −5.18368 | −0.375078 | −0.187539 | − | 0.982257i | \(-0.560051\pi\) | ||||
−0.187539 | + | 0.982257i | \(0.560051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.06423 | 0.508494 | 0.254247 | − | 0.967139i | \(-0.418172\pi\) | ||||
0.254247 | + | 0.967139i | \(0.418172\pi\) | |||||||
\(194\) | −10.2594 | −0.736578 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.67713 | 0.119795 | ||||||||
\(197\) | 4.38545 | 0.312450 | 0.156225 | − | 0.987721i | \(-0.450067\pi\) | ||||
0.156225 | + | 0.987721i | \(0.450067\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.65748 | 0.117496 | 0.0587479 | − | 0.998273i | \(-0.481289\pi\) | ||||
0.0587479 | + | 0.998273i | \(0.481289\pi\) | |||||||
\(200\) | 1.45054 | 0.102569 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 26.5843 | 1.87047 | ||||||||
\(203\) | −4.77456 | −0.335109 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.3583 | −1.21236 | ||||||||
\(206\) | 33.4644 | 2.33157 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.56516 | −0.247199 | ||||||||
\(209\) | −33.2139 | −2.29746 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.9651 | −1.64983 | −0.824913 | − | 0.565259i | \(-0.808776\pi\) | ||||
−0.824913 | + | 0.565259i | \(0.808776\pi\) | |||||||
\(212\) | −0.253591 | −0.0174167 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.6052 | 0.930032 | ||||||||
\(215\) | −13.4782 | −0.919209 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.06545 | 0.343865 | ||||||||
\(218\) | 33.4255 | 2.26386 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 12.4040 | 0.836279 | ||||||||
\(221\) | 3.60029 | 0.242182 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.48293 | −0.434129 | −0.217065 | − | 0.976157i | \(-0.569648\pi\) | ||||
−0.217065 | + | 0.976157i | \(0.569648\pi\) | |||||||
\(224\) | −7.47045 | −0.499140 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.1203 | 0.939267 | ||||||||
\(227\) | −10.4264 | −0.692024 | −0.346012 | − | 0.938230i | \(-0.612464\pi\) | ||||
−0.346012 | + | 0.938230i | \(0.612464\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.8797 | −1.44585 | −0.722925 | − | 0.690926i | \(-0.757203\pi\) | ||||
−0.722925 | + | 0.690926i | \(0.757203\pi\) | |||||||
\(230\) | 5.56364 | 0.366855 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.95605 | 0.194074 | ||||||||
\(233\) | −19.7154 | −1.29160 | −0.645799 | − | 0.763508i | \(-0.723476\pi\) | ||||
−0.645799 | + | 0.763508i | \(0.723476\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.3813 | 0.807667 | ||||||||
\(236\) | −7.87163 | −0.512399 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.79452 | 0.570064 | ||||||||
\(239\) | 18.5429 | 1.19944 | 0.599721 | − | 0.800209i | \(-0.295278\pi\) | ||||
0.599721 | + | 0.800209i | \(0.295278\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.9917 | 1.86752 | 0.933761 | − | 0.357897i | \(-0.116506\pi\) | ||||
0.933761 | + | 0.357897i | \(0.116506\pi\) | |||||||
\(242\) | 18.3828 | 1.18169 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −20.4505 | −1.30921 | ||||||||
\(245\) | −1.63006 | −0.104141 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.74658 | 0.365646 | ||||||||
\(248\) | −3.13614 | −0.199145 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 22.9523 | 1.45163 | ||||||||
\(251\) | −28.0776 | −1.77225 | −0.886123 | − | 0.463451i | \(-0.846611\pi\) | ||||
−0.886123 | + | 0.463451i | \(0.846611\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.07590 | 0.507727 | ||||||||
\(254\) | 1.91759 | 0.120320 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.8585 | 1.24116 | ||||||||
\(257\) | −3.12939 | −0.195206 | −0.0976029 | − | 0.995225i | \(-0.531118\pi\) | ||||
−0.0976029 | + | 0.995225i | \(0.531118\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.03335 | −0.0642092 | ||||||||
\(260\) | −2.14611 | −0.133096 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.56575 | −0.405633 | ||||||||
\(263\) | −23.7229 | −1.46281 | −0.731407 | − | 0.681941i | \(-0.761136\pi\) | ||||
−0.731407 | + | 0.681941i | \(0.761136\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.246474 | 0.0151408 | ||||||||
\(266\) | 14.0373 | 0.860684 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.62051 | 0.160073 | ||||||||
\(269\) | −4.27831 | −0.260853 | −0.130427 | − | 0.991458i | \(-0.541635\pi\) | ||||
−0.130427 | + | 0.991458i | \(0.541635\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.9618 | 0.787375 | 0.393687 | − | 0.919244i | \(-0.371199\pi\) | ||||
0.393687 | + | 0.919244i | \(0.371199\pi\) | |||||||
\(272\) | −20.8284 | −1.26291 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.5060 | 0.997163 | ||||||||
\(275\) | 10.6303 | 0.641029 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.8719 | 1.61457 | 0.807287 | − | 0.590160i | \(-0.200935\pi\) | ||||
0.807287 | + | 0.590160i | \(0.200935\pi\) | |||||||
\(278\) | 21.3670 | 1.28151 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.00921 | 0.0603118 | ||||||||
\(281\) | −7.21075 | −0.430157 | −0.215079 | − | 0.976597i | \(-0.569001\pi\) | ||||
−0.215079 | + | 0.976597i | \(0.569001\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.06754 | 0.420121 | 0.210061 | − | 0.977688i | \(-0.432634\pi\) | ||||
0.210061 | + | 0.977688i | \(0.432634\pi\) | |||||||
\(284\) | 22.1803 | 1.31616 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.83008 | −0.403871 | ||||||||
\(287\) | 10.6489 | 0.628582 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.03365 | 0.237273 | ||||||||
\(290\) | 14.9242 | 0.876382 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.38050 | 0.548952 | ||||||||
\(293\) | −6.10993 | −0.356946 | −0.178473 | − | 0.983945i | \(-0.557116\pi\) | ||||
−0.178473 | + | 0.983945i | \(0.557116\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.65070 | 0.445441 | ||||||||
\(296\) | 0.639771 | 0.0371859 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 39.6103 | 2.29456 | ||||||||
\(299\) | −1.39727 | −0.0808062 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.26855 | 0.476591 | ||||||||
\(302\) | 3.51726 | 0.202395 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −33.2451 | −1.90674 | ||||||||
\(305\) | 19.8765 | 1.13813 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.8475 | −0.847389 | −0.423695 | − | 0.905805i | \(-0.639267\pi\) | ||||
−0.423695 | + | 0.905805i | \(0.639267\pi\) | |||||||
\(308\) | −7.60954 | −0.433594 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.8335 | −0.899282 | ||||||||
\(311\) | 12.1323 | 0.687961 | 0.343981 | − | 0.938977i | \(-0.388225\pi\) | ||||
0.343981 | + | 0.938977i | \(0.388225\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.476080 | 0.0269097 | 0.0134548 | − | 0.999909i | \(-0.495717\pi\) | ||||
0.0134548 | + | 0.999909i | \(0.495717\pi\) | |||||||
\(314\) | 19.1566 | 1.08107 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.40170 | −0.360124 | ||||||||
\(317\) | 1.09825 | 0.0616840 | 0.0308420 | − | 0.999524i | \(-0.490181\pi\) | ||||
0.0308420 | + | 0.999524i | \(0.490181\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.6633 | 1.21291 | ||||||||
\(320\) | 8.54518 | 0.477690 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.41315 | −0.190207 | ||||||||
\(323\) | 33.5728 | 1.86804 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.83922 | −0.102022 | ||||||||
\(326\) | 10.5295 | 0.583177 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.59296 | −0.364035 | ||||||||
\(329\) | −7.59560 | −0.418759 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.4769 | 1.18048 | 0.590239 | − | 0.807228i | \(-0.299033\pi\) | ||||
0.590239 | + | 0.807228i | \(0.299033\pi\) | |||||||
\(332\) | −1.23146 | −0.0675851 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.59686 | −0.142094 | ||||||||
\(335\) | −2.54696 | −0.139155 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.56002 | −0.139453 | −0.0697267 | − | 0.997566i | \(-0.522213\pi\) | ||||
−0.0697267 | + | 0.997566i | \(0.522213\pi\) | |||||||
\(338\) | −23.7469 | −1.29166 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12.5380 | −0.679970 | ||||||||
\(341\) | −22.9831 | −1.24460 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −5.11926 | −0.276012 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.5749 | 0.568509 | ||||||||
\(347\) | −17.8141 | −0.956312 | −0.478156 | − | 0.878275i | \(-0.658695\pi\) | ||||
−0.478156 | + | 0.878275i | \(0.658695\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.98746 | −0.534616 | −0.267308 | − | 0.963611i | \(-0.586134\pi\) | ||||
−0.267308 | + | 0.963611i | \(0.586134\pi\) | |||||||
\(350\) | −4.49271 | −0.240145 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 33.8951 | 1.80662 | ||||||||
\(353\) | 1.59328 | 0.0848018 | 0.0424009 | − | 0.999101i | \(-0.486499\pi\) | ||||
0.0424009 | + | 0.999101i | \(0.486499\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.5578 | −1.14417 | ||||||||
\(356\) | 8.67035 | 0.459527 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.9570 | 1.00191 | ||||||||
\(359\) | 15.8997 | 0.839153 | 0.419576 | − | 0.907720i | \(-0.362179\pi\) | ||||
0.419576 | + | 0.907720i | \(0.362179\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 34.5870 | 1.82037 | ||||||||
\(362\) | 5.94501 | 0.312463 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.31658 | 0.0690076 | ||||||||
\(365\) | −9.11722 | −0.477217 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.3461 | 1.58405 | 0.792027 | − | 0.610486i | \(-0.209026\pi\) | ||||
0.792027 | + | 0.610486i | \(0.209026\pi\) | |||||||
\(368\) | 8.08348 | 0.421381 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.23002 | 0.167921 | ||||||||
\(371\) | −0.151205 | −0.00785017 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.699026 | −0.0361942 | −0.0180971 | − | 0.999836i | \(-0.505761\pi\) | ||||
−0.0180971 | + | 0.999836i | \(0.505761\pi\) | |||||||
\(374\) | −39.9027 | −2.06332 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.70262 | 0.242519 | ||||||||
\(377\) | −3.74812 | −0.193038 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.08955 | 0.107333 | 0.0536665 | − | 0.998559i | \(-0.482909\pi\) | ||||
0.0536665 | + | 0.998559i | \(0.482909\pi\) | |||||||
\(380\) | −20.0125 | −1.02662 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.94015 | −0.508583 | ||||||||
\(383\) | −7.36514 | −0.376341 | −0.188170 | − | 0.982136i | \(-0.560256\pi\) | ||||
−0.188170 | + | 0.982136i | \(0.560256\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.39596 | 0.376933 | ||||||||
\(386\) | 13.5463 | 0.689486 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.97290 | −0.455530 | ||||||||
\(389\) | −25.3382 | −1.28470 | −0.642348 | − | 0.766413i | \(-0.722040\pi\) | ||||
−0.642348 | + | 0.766413i | \(0.722040\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.16314 | −0.412828 | ||||||||
\(392\) | −0.619124 | −0.0312705 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.40948 | 0.423663 | ||||||||
\(395\) | 6.22202 | 0.313064 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.4952 | −1.12900 | −0.564500 | − | 0.825433i | \(-0.690931\pi\) | ||||
−0.564500 | + | 0.825433i | \(0.690931\pi\) | |||||||
\(398\) | 3.17836 | 0.159317 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.6402 | 0.532012 | ||||||||
\(401\) | −16.0902 | −0.803508 | −0.401754 | − | 0.915748i | \(-0.631599\pi\) | ||||
−0.401754 | + | 0.915748i | \(0.631599\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.97647 | 0.198082 | ||||||||
\(404\) | 23.2508 | 1.15677 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.15563 | −0.454386 | ||||||||
\(407\) | 4.68854 | 0.232402 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.5315 | −1.31190 | −0.655949 | − | 0.754805i | \(-0.727731\pi\) | ||||
−0.655949 | + | 0.754805i | \(0.727731\pi\) | |||||||
\(410\) | −33.2860 | −1.64388 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 29.2682 | 1.44194 | ||||||||
\(413\) | −4.69350 | −0.230952 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.19690 | 0.0587533 | ||||||||
\(416\) | −5.86444 | −0.287528 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −63.6906 | −3.11521 | ||||||||
\(419\) | 13.0559 | 0.637821 | 0.318911 | − | 0.947785i | \(-0.396683\pi\) | ||||
0.318911 | + | 0.947785i | \(0.396683\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.503178 | −0.0245234 | −0.0122617 | − | 0.999925i | \(-0.503903\pi\) | ||||
−0.0122617 | + | 0.999925i | \(0.503903\pi\) | |||||||
\(422\) | −45.9551 | −2.23706 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.0936146 | 0.00454633 | ||||||||
\(425\) | −10.7451 | −0.521214 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.1937 | −0.590095 | ||||||||
\(428\) | 11.8992 | 0.575170 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −25.8457 | −1.24639 | ||||||||
\(431\) | −19.3583 | −0.932457 | −0.466228 | − | 0.884664i | \(-0.654388\pi\) | ||||
−0.466228 | + | 0.884664i | \(0.654388\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.9626 | −1.58408 | −0.792041 | − | 0.610468i | \(-0.790982\pi\) | ||||
−0.792041 | + | 0.610468i | \(0.790982\pi\) | |||||||
\(434\) | 9.71343 | 0.466260 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 29.2342 | 1.40006 | ||||||||
\(437\) | −13.0296 | −0.623289 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.0599 | 1.53013 | 0.765067 | − | 0.643951i | \(-0.222706\pi\) | ||||
0.765067 | + | 0.643951i | \(0.222706\pi\) | |||||||
\(440\) | −4.57902 | −0.218296 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.90386 | 0.328383 | ||||||||
\(443\) | 19.0080 | 0.903096 | 0.451548 | − | 0.892247i | \(-0.350872\pi\) | ||||
0.451548 | + | 0.892247i | \(0.350872\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.42700 | −0.399478 | ||||||||
\(446\) | −12.4316 | −0.588652 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.24224 | −0.247673 | ||||||||
\(449\) | −16.2304 | −0.765960 | −0.382980 | − | 0.923757i | \(-0.625102\pi\) | ||||
−0.382980 | + | 0.923757i | \(0.625102\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −48.3163 | −2.27513 | ||||||||
\(452\) | 12.3497 | 0.580881 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −19.9935 | −0.938341 | ||||||||
\(455\) | −1.27963 | −0.0599899 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.6324 | 0.731254 | 0.365627 | − | 0.930761i | \(-0.380855\pi\) | ||||
0.365627 | + | 0.930761i | \(0.380855\pi\) | |||||||
\(458\) | −41.9562 | −1.96048 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.86600 | 0.226878 | ||||||||
\(461\) | 21.3891 | 0.996191 | 0.498096 | − | 0.867122i | \(-0.334033\pi\) | ||||
0.498096 | + | 0.867122i | \(0.334033\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.8588 | −0.876445 | −0.438222 | − | 0.898867i | \(-0.644392\pi\) | ||||
−0.438222 | + | 0.898867i | \(0.644392\pi\) | |||||||
\(464\) | 21.6836 | 1.00664 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −37.8059 | −1.75133 | ||||||||
\(467\) | −21.0632 | −0.974689 | −0.487344 | − | 0.873210i | \(-0.662034\pi\) | ||||
−0.487344 | + | 0.873210i | \(0.662034\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.56249 | 0.0721492 | ||||||||
\(470\) | 23.7422 | 1.09515 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.90586 | 0.133753 | ||||||||
\(473\) | −37.5163 | −1.72500 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.1508 | −0.786930 | ||||||||
\(476\) | 7.69175 | 0.352551 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 35.5577 | 1.62637 | ||||||||
\(479\) | −23.6039 | −1.07849 | −0.539245 | − | 0.842149i | \(-0.681290\pi\) | ||||
−0.539245 | + | 0.842149i | \(0.681290\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.811198 | −0.0369875 | ||||||||
\(482\) | 55.5941 | 2.53224 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.0778 | 0.730807 | ||||||||
\(485\) | 8.72106 | 0.396003 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.2006 | −0.734119 | −0.367060 | − | 0.930197i | \(-0.619636\pi\) | ||||
−0.367060 | + | 0.930197i | \(0.619636\pi\) | |||||||
\(488\) | 7.54942 | 0.341746 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.12578 | −0.141208 | ||||||||
\(491\) | 20.8074 | 0.939025 | 0.469512 | − | 0.882926i | \(-0.344430\pi\) | ||||
0.469512 | + | 0.882926i | \(0.344430\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.8973 | −0.986206 | ||||||||
\(494\) | 11.0196 | 0.495794 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −23.0047 | −1.03294 | ||||||||
\(497\) | 13.2252 | 0.593229 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.17234 | −0.276312 | −0.138156 | − | 0.990410i | \(-0.544118\pi\) | ||||
−0.138156 | + | 0.990410i | \(0.544118\pi\) | |||||||
\(500\) | 20.0742 | 0.897748 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −53.8413 | −2.40305 | ||||||||
\(503\) | 28.7432 | 1.28159 | 0.640797 | − | 0.767710i | \(-0.278604\pi\) | ||||
0.640797 | + | 0.767710i | \(0.278604\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.5982 | −1.00561 | ||||||||
\(506\) | 15.4862 | 0.688447 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.67713 | 0.0744108 | ||||||||
\(509\) | −13.2246 | −0.586169 | −0.293084 | − | 0.956087i | \(-0.594682\pi\) | ||||
−0.293084 | + | 0.956087i | \(0.594682\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.59318 | 0.247428 | ||||||||
\(512\) | 28.3035 | 1.25085 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.00087 | −0.264687 | ||||||||
\(515\) | −28.4467 | −1.25351 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.4630 | 1.51568 | ||||||||
\(518\) | −1.98153 | −0.0870636 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.792249 | 0.0347424 | ||||||||
\(521\) | 32.9614 | 1.44407 | 0.722033 | − | 0.691858i | \(-0.243208\pi\) | ||||
0.722033 | + | 0.691858i | \(0.243208\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.22512 | −0.141025 | −0.0705123 | − | 0.997511i | \(-0.522463\pi\) | ||||
−0.0705123 | + | 0.997511i | \(0.522463\pi\) | |||||||
\(524\) | −5.74245 | −0.250860 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −45.4906 | −1.98349 | ||||||||
\(527\) | 23.2314 | 1.01198 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.8319 | −0.862256 | ||||||||
\(530\) | 0.472634 | 0.0205299 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.2771 | 0.532282 | ||||||||
\(533\) | 8.35955 | 0.362092 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.5652 | −0.500009 | ||||||||
\(536\) | −0.967376 | −0.0417843 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.20403 | −0.353701 | ||||||||
\(539\) | −4.53723 | −0.195432 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.01886 | −0.172784 | −0.0863922 | − | 0.996261i | \(-0.527534\pi\) | ||||
−0.0863922 | + | 0.996261i | \(0.527534\pi\) | |||||||
\(542\) | 24.8554 | 1.06763 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −34.2613 | −1.46894 | ||||||||
\(545\) | −28.4137 | −1.21711 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.36285 | −0.143785 | −0.0718926 | − | 0.997412i | \(-0.522904\pi\) | ||||
−0.0718926 | + | 0.997412i | \(0.522904\pi\) | |||||||
\(548\) | 14.4363 | 0.616686 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 20.3844 | 0.869196 | ||||||||
\(551\) | −34.9513 | −1.48898 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.81705 | −0.162317 | ||||||||
\(554\) | 51.5291 | 2.18926 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.6877 | 0.792536 | ||||||||
\(557\) | 36.3729 | 1.54117 | 0.770584 | − | 0.637339i | \(-0.219965\pi\) | ||||
0.770584 | + | 0.637339i | \(0.219965\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.49097 | 0.274539 | ||||||||
\(560\) | 7.40291 | 0.312830 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.8272 | −0.583266 | ||||||||
\(563\) | 21.8814 | 0.922190 | 0.461095 | − | 0.887351i | \(-0.347457\pi\) | ||||
0.461095 | + | 0.887351i | \(0.347457\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.0031 | −0.504974 | ||||||||
\(566\) | 13.5526 | 0.569658 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.18801 | −0.343561 | ||||||||
\(569\) | 1.52443 | 0.0639073 | 0.0319536 | − | 0.999489i | \(-0.489827\pi\) | ||||
0.0319536 | + | 0.999489i | \(0.489827\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.407383 | −0.0170485 | −0.00852423 | − | 0.999964i | \(-0.502713\pi\) | ||||
−0.00852423 | + | 0.999964i | \(0.502713\pi\) | |||||||
\(572\) | −5.97363 | −0.249770 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 20.4201 | 0.852318 | ||||||||
\(575\) | 4.17017 | 0.173908 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.40086 | −0.391363 | −0.195681 | − | 0.980668i | \(-0.562692\pi\) | ||||
−0.195681 | + | 0.980668i | \(0.562692\pi\) | |||||||
\(578\) | 7.73486 | 0.321728 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.0529 | 0.541990 | ||||||||
\(581\) | −0.734264 | −0.0304624 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.686052 | 0.0284134 | ||||||||
\(584\) | −3.46287 | −0.143295 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.7163 | −0.483996 | ||||||||
\(587\) | −7.47968 | −0.308719 | −0.154360 | − | 0.988015i | \(-0.549331\pi\) | ||||
−0.154360 | + | 0.988015i | \(0.549331\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 37.0807 | 1.52788 | ||||||||
\(590\) | 14.6709 | 0.603990 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.69294 | 0.192879 | ||||||||
\(593\) | −26.7023 | −1.09653 | −0.548266 | − | 0.836304i | \(-0.684712\pi\) | ||||
−0.548266 | + | 0.836304i | \(0.684712\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.47586 | −0.306481 | ||||||||
\(596\) | 34.6434 | 1.41905 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.67938 | −0.109568 | ||||||||
\(599\) | 9.66950 | 0.395085 | 0.197543 | − | 0.980294i | \(-0.436704\pi\) | ||||
0.197543 | + | 0.980294i | \(0.436704\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.1650 | 0.863340 | 0.431670 | − | 0.902032i | \(-0.357925\pi\) | ||||
0.431670 | + | 0.902032i | \(0.357925\pi\) | |||||||
\(602\) | 15.8556 | 0.646228 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.07622 | 0.125170 | ||||||||
\(605\) | −15.6265 | −0.635308 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.3837 | 0.664993 | 0.332496 | − | 0.943105i | \(-0.392109\pi\) | ||||
0.332496 | + | 0.943105i | \(0.392109\pi\) | |||||||
\(608\) | −54.6860 | −2.21781 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 38.1149 | 1.54323 | ||||||||
\(611\) | −5.96269 | −0.241225 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.7506 | −1.48434 | −0.742171 | − | 0.670210i | \(-0.766204\pi\) | ||||
−0.742171 | + | 0.670210i | \(0.766204\pi\) | |||||||
\(614\) | −28.4713 | −1.14901 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.80911 | 0.113182 | ||||||||
\(617\) | −27.8500 | −1.12120 | −0.560600 | − | 0.828087i | \(-0.689429\pi\) | ||||
−0.560600 | + | 0.828087i | \(0.689429\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.3590 | −1.05946 | −0.529730 | − | 0.848167i | \(-0.677707\pi\) | ||||
−0.529730 | + | 0.848167i | \(0.677707\pi\) | |||||||
\(620\) | −13.8481 | −0.556152 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 23.2648 | 0.932832 | ||||||||
\(623\) | 5.16974 | 0.207121 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.79634 | −0.311853 | ||||||||
\(626\) | 0.912925 | 0.0364878 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.7545 | 0.668576 | ||||||||
\(629\) | −4.73919 | −0.188964 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.1225 | 0.960303 | 0.480151 | − | 0.877186i | \(-0.340582\pi\) | ||||
0.480151 | + | 0.877186i | \(0.340582\pi\) | |||||||
\(632\) | 2.36323 | 0.0940041 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.10599 | 0.0836397 | ||||||||
\(635\) | −1.63006 | −0.0646870 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.785019 | 0.0311036 | ||||||||
\(638\) | 41.5412 | 1.64463 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7.96848 | −0.314982 | ||||||||
\(641\) | 31.6483 | 1.25003 | 0.625017 | − | 0.780611i | \(-0.285092\pi\) | ||||
0.625017 | + | 0.780611i | \(0.285092\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.3625 | −1.43400 | −0.716998 | − | 0.697075i | \(-0.754484\pi\) | ||||
−0.716998 | + | 0.697075i | \(0.754484\pi\) | |||||||
\(644\) | −2.98516 | −0.117632 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 64.3786 | 2.53294 | ||||||||
\(647\) | 30.6486 | 1.20492 | 0.602460 | − | 0.798149i | \(-0.294187\pi\) | ||||
0.602460 | + | 0.798149i | \(0.294187\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.2955 | 0.835921 | ||||||||
\(650\) | −3.52686 | −0.138335 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.20921 | 0.360660 | ||||||||
\(653\) | 5.09863 | 0.199525 | 0.0997625 | − | 0.995011i | \(-0.468192\pi\) | ||||
0.0997625 | + | 0.995011i | \(0.468192\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.58128 | 0.218078 | ||||||||
\(656\) | −48.3617 | −1.88821 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14.5652 | −0.567811 | ||||||||
\(659\) | −25.9346 | −1.01027 | −0.505135 | − | 0.863041i | \(-0.668557\pi\) | ||||
−0.505135 | + | 0.863041i | \(0.668557\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.2692 | −1.06065 | −0.530324 | − | 0.847795i | \(-0.677930\pi\) | ||||
−0.530324 | + | 0.847795i | \(0.677930\pi\) | |||||||
\(662\) | 41.1838 | 1.60065 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.454601 | 0.0176419 | ||||||||
\(665\) | −11.9326 | −0.462725 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.49833 | 0.329057 | ||||||||
\(668\) | −2.27123 | −0.0878766 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.88401 | −0.188686 | ||||||||
\(671\) | 55.3257 | 2.13582 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.5849 | −1.10187 | −0.550933 | − | 0.834549i | \(-0.685728\pi\) | ||||
−0.550933 | + | 0.834549i | \(0.685728\pi\) | |||||||
\(674\) | −4.90906 | −0.189090 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.7692 | −0.798815 | ||||||||
\(677\) | −28.2536 | −1.08588 | −0.542938 | − | 0.839773i | \(-0.682688\pi\) | ||||
−0.542938 | + | 0.839773i | \(0.682688\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.35014 | −0.205320 | ||||||||
\(680\) | 4.62849 | 0.177494 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −44.0721 | −1.68761 | ||||||||
\(683\) | 10.4079 | 0.398248 | 0.199124 | − | 0.979974i | \(-0.436190\pi\) | ||||
0.199124 | + | 0.979974i | \(0.436190\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.0311 | −0.536100 | ||||||||
\(686\) | 1.91759 | 0.0732137 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −37.5515 | −1.43164 | ||||||||
\(689\) | −0.118699 | −0.00452206 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.1483 | −1.37515 | −0.687574 | − | 0.726115i | \(-0.741324\pi\) | ||||
−0.687574 | + | 0.726115i | \(0.741324\pi\) | |||||||
\(692\) | 9.24887 | 0.351589 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −34.1601 | −1.29670 | ||||||||
\(695\) | −18.1632 | −0.688970 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 48.8383 | 1.84988 | ||||||||
\(698\) | −19.1518 | −0.724906 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.92935 | −0.148516 | ||||||||
\(701\) | 9.20252 | 0.347574 | 0.173787 | − | 0.984783i | \(-0.444399\pi\) | ||||
0.173787 | + | 0.984783i | \(0.444399\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.56444 | −0.285298 | ||||||||
\(704\) | 23.7852 | 0.896440 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.05525 | 0.114986 | ||||||||
\(707\) | 13.8634 | 0.521388 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.72738 | 0.290208 | 0.145104 | − | 0.989416i | \(-0.453648\pi\) | ||||
0.145104 | + | 0.989416i | \(0.453648\pi\) | |||||||
\(710\) | −41.3389 | −1.55142 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.20071 | −0.119952 | ||||||||
\(713\) | −9.01609 | −0.337655 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.80597 | 0.217131 | ||||||||
\(716\) | 16.5799 | 0.619621 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 30.4890 | 1.13784 | ||||||||
\(719\) | 43.6917 | 1.62942 | 0.814712 | − | 0.579865i | \(-0.196895\pi\) | ||||
0.814712 | + | 0.579865i | \(0.196895\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.4513 | 0.649921 | ||||||||
\(722\) | 66.3235 | 2.46831 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.19955 | 0.193240 | ||||||||
\(725\) | 11.1863 | 0.415449 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.4150 | 0.460447 | 0.230224 | − | 0.973138i | \(-0.426054\pi\) | ||||
0.230224 | + | 0.973138i | \(0.426054\pi\) | |||||||
\(728\) | −0.486024 | −0.0180132 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −17.4831 | −0.647077 | ||||||||
\(731\) | 37.9216 | 1.40258 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.8586 | −0.585752 | −0.292876 | − | 0.956150i | \(-0.594612\pi\) | ||||
−0.292876 | + | 0.956150i | \(0.594612\pi\) | |||||||
\(734\) | 58.1913 | 2.14788 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.2968 | 0.490126 | ||||||||
\(737\) | −7.08939 | −0.261141 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −50.8373 | −1.87008 | −0.935040 | − | 0.354542i | \(-0.884637\pi\) | ||||
−0.935040 | + | 0.354542i | \(0.884637\pi\) | |||||||
\(740\) | 2.82500 | 0.103849 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.289949 | −0.0106443 | ||||||||
\(743\) | −19.4170 | −0.712341 | −0.356170 | − | 0.934421i | \(-0.615918\pi\) | ||||
−0.356170 | + | 0.934421i | \(0.615918\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33.6711 | −1.23361 | ||||||||
\(746\) | −1.34044 | −0.0490771 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −34.8992 | −1.27604 | ||||||||
\(749\) | 7.09496 | 0.259244 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.2814 | 1.10498 | 0.552491 | − | 0.833519i | \(-0.313677\pi\) | ||||
0.552491 | + | 0.833519i | \(0.313677\pi\) | |||||||
\(752\) | 34.4953 | 1.25792 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.18734 | −0.261748 | ||||||||
\(755\) | −2.98988 | −0.108813 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.73773 | −0.281233 | −0.140616 | − | 0.990064i | \(-0.544908\pi\) | ||||
−0.140616 | + | 0.990064i | \(0.544908\pi\) | |||||||
\(758\) | 4.00689 | 0.145537 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.38774 | 0.267981 | ||||||||
\(761\) | 42.4083 | 1.53730 | 0.768650 | − | 0.639669i | \(-0.220929\pi\) | ||||
0.768650 | + | 0.639669i | \(0.220929\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.4311 | 0.631047 | ||||||||
\(764\) | −8.69373 | −0.314528 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.1233 | −0.510295 | ||||||||
\(767\) | −3.68449 | −0.133039 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.9692 | 1.47739 | 0.738694 | − | 0.674041i | \(-0.235443\pi\) | ||||
0.738694 | + | 0.674041i | \(0.235443\pi\) | |||||||
\(770\) | 14.1824 | 0.511098 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.8477 | 0.426406 | ||||||||
\(773\) | −24.7232 | −0.889232 | −0.444616 | − | 0.895721i | \(-0.646660\pi\) | ||||
−0.444616 | + | 0.895721i | \(0.646660\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.8678 | −0.426305 | ||||||||
\(776\) | 3.31240 | 0.118908 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −48.5881 | −1.74197 | ||||||||
\(779\) | 77.9530 | 2.79295 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −60.0055 | −2.14717 | ||||||||
\(782\) | −15.6535 | −0.559769 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.54149 | −0.162196 | ||||||||
\(785\) | −16.2842 | −0.581209 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.2059 | 1.36189 | 0.680946 | − | 0.732334i | \(-0.261569\pi\) | ||||
0.680946 | + | 0.732334i | \(0.261569\pi\) | |||||||
\(788\) | 7.35499 | 0.262011 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.9313 | 0.424495 | ||||||||
\(791\) | 7.36358 | 0.261819 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.57230 | −0.339922 | ||||||||
\(794\) | −43.1364 | −1.53085 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.77982 | 0.0985280 | ||||||||
\(797\) | 39.8094 | 1.41012 | 0.705061 | − | 0.709147i | \(-0.250920\pi\) | ||||
0.705061 | + | 0.709147i | \(0.250920\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.8353 | −1.23238 | ||||||||
\(800\) | 17.5025 | 0.618807 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −30.8544 | −1.08951 | ||||||||
\(803\) | −25.3775 | −0.895553 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.90138 | 0.102260 | ||||||||
\(806\) | 7.62523 | 0.268587 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.58318 | −0.301955 | ||||||||
\(809\) | 19.8034 | 0.696250 | 0.348125 | − | 0.937448i | \(-0.386818\pi\) | ||||
0.348125 | + | 0.937448i | \(0.386818\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.6032 | −1.70669 | −0.853344 | − | 0.521348i | \(-0.825430\pi\) | ||||
−0.853344 | + | 0.521348i | \(0.825430\pi\) | |||||||
\(812\) | −8.00758 | −0.281011 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.99068 | 0.315123 | ||||||||
\(815\) | −8.95074 | −0.313531 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 60.5284 | 2.11762 | ||||||||
\(818\) | −50.8764 | −1.77885 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −29.1122 | −1.01664 | ||||||||
\(821\) | 27.5660 | 0.962060 | 0.481030 | − | 0.876704i | \(-0.340263\pi\) | ||||
0.481030 | + | 0.876704i | \(0.340263\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.5300 | 1.76136 | 0.880682 | − | 0.473708i | \(-0.157085\pi\) | ||||
0.880682 | + | 0.473708i | \(0.157085\pi\) | |||||||
\(824\) | −10.8045 | −0.376393 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.00019 | −0.313157 | ||||||||
\(827\) | 34.5514 | 1.20147 | 0.600735 | − | 0.799448i | \(-0.294875\pi\) | ||||
0.600735 | + | 0.799448i | \(0.294875\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.2920 | 1.57305 | 0.786527 | − | 0.617555i | \(-0.211877\pi\) | ||||
0.786527 | + | 0.617555i | \(0.211877\pi\) | |||||||
\(830\) | 2.29515 | 0.0796658 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.11526 | −0.142671 | ||||||||
\(833\) | 4.58625 | 0.158904 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.20749 | 0.0763932 | ||||||||
\(836\) | −55.7042 | −1.92657 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.0358 | 0.864846 | ||||||||
\(839\) | 45.4572 | 1.56936 | 0.784679 | − | 0.619902i | \(-0.212828\pi\) | ||||
0.784679 | + | 0.619902i | \(0.212828\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.20354 | −0.213915 | ||||||||
\(842\) | −0.964886 | −0.0332522 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −40.1927 | −1.38349 | ||||||||
\(845\) | 20.1863 | 0.694429 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.58645 | 0.329394 | ||||||||
\(848\) | 0.686696 | 0.0235812 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −20.6047 | −0.706734 | ||||||||
\(851\) | 1.83928 | 0.0630496 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.10046 | 0.243115 | 0.121558 | − | 0.992584i | \(-0.461211\pi\) | ||||
0.121558 | + | 0.992584i | \(0.461211\pi\) | |||||||
\(854\) | −23.3825 | −0.800132 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.39266 | −0.150138 | ||||||||
\(857\) | −38.1705 | −1.30388 | −0.651940 | − | 0.758270i | \(-0.726045\pi\) | ||||
−0.651940 | + | 0.758270i | \(0.726045\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.939629 | −0.0320597 | −0.0160299 | − | 0.999872i | \(-0.505103\pi\) | ||||
−0.0160299 | + | 0.999872i | \(0.505103\pi\) | |||||||
\(860\) | −22.6048 | −0.770818 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −37.1212 | −1.26435 | ||||||||
\(863\) | −37.0524 | −1.26128 | −0.630639 | − | 0.776077i | \(-0.717207\pi\) | ||||
−0.630639 | + | 0.776077i | \(0.717207\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.98928 | −0.305645 | ||||||||
\(866\) | −63.2086 | −2.14792 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.49543 | 0.288354 | ||||||||
\(869\) | 17.3188 | 0.587501 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.22659 | 0.0415613 | ||||||||
\(872\) | −10.7920 | −0.365463 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −24.9853 | −0.845140 | ||||||||
\(875\) | 11.9694 | 0.404639 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.41666 | 0.284210 | 0.142105 | − | 0.989852i | \(-0.454613\pi\) | ||||
0.142105 | + | 0.989852i | \(0.454613\pi\) | |||||||
\(878\) | 61.4775 | 2.07477 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −33.5887 | −1.13227 | ||||||||
\(881\) | 16.1308 | 0.543462 | 0.271731 | − | 0.962373i | \(-0.412404\pi\) | ||||
0.271731 | + | 0.962373i | \(0.412404\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −54.9590 | −1.84952 | −0.924759 | − | 0.380553i | \(-0.875734\pi\) | ||||
−0.924759 | + | 0.380553i | \(0.875734\pi\) | |||||||
\(884\) | 6.03817 | 0.203086 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36.4494 | 1.22454 | ||||||||
\(887\) | 6.72375 | 0.225761 | 0.112881 | − | 0.993609i | \(-0.463992\pi\) | ||||
0.112881 | + | 0.993609i | \(0.463992\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −16.1595 | −0.541667 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10.8727 | −0.364046 | ||||||||
\(893\) | −55.6022 | −1.86066 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.1146 | −0.538651 | ||||||||
\(896\) | 4.88845 | 0.163312 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −31.1232 | −1.03859 | ||||||||
\(899\) | −24.1853 | −0.806625 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.693463 | −0.0231026 | ||||||||
\(902\) | −92.6506 | −3.08493 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.55897 | −0.151629 | ||||||||
\(905\) | −5.05362 | −0.167988 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.3476 | −1.47254 | −0.736269 | − | 0.676689i | \(-0.763414\pi\) | ||||
−0.736269 | + | 0.676689i | \(0.763414\pi\) | |||||||
\(908\) | −17.4865 | −0.580308 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.45380 | −0.0813426 | ||||||||
\(911\) | 26.5885 | 0.880916 | 0.440458 | − | 0.897773i | \(-0.354816\pi\) | ||||
0.440458 | + | 0.897773i | \(0.354816\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.33153 | 0.110257 | ||||||||
\(914\) | 29.9765 | 0.991535 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −36.6952 | −1.21244 | ||||||||
\(917\) | −3.42397 | −0.113069 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.91175 | −0.227998 | −0.113999 | − | 0.993481i | \(-0.536366\pi\) | ||||
−0.113999 | + | 0.993481i | \(0.536366\pi\) | |||||||
\(920\) | −1.79631 | −0.0592227 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 41.0155 | 1.35077 | ||||||||
\(923\) | 10.3820 | 0.341727 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.42103 | 0.0796030 | ||||||||
\(926\) | −36.1634 | −1.18840 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 35.6681 | 1.17086 | ||||||||
\(929\) | −50.6624 | −1.66218 | −0.831090 | − | 0.556138i | \(-0.812283\pi\) | ||||
−0.831090 | + | 0.556138i | \(0.812283\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.32031 | 0.239914 | ||||||||
\(932\) | −33.0653 | −1.08309 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −40.3905 | −1.32162 | ||||||||
\(935\) | 33.9197 | 1.10929 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.0802 | 0.884671 | 0.442335 | − | 0.896850i | \(-0.354150\pi\) | ||||
0.442335 | + | 0.896850i | \(0.354150\pi\) | |||||||
\(938\) | 2.99621 | 0.0978298 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 20.7651 | 0.677283 | ||||||||
\(941\) | 53.5291 | 1.74500 | 0.872500 | − | 0.488614i | \(-0.162497\pi\) | ||||
0.872500 | + | 0.488614i | \(0.162497\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.9541 | −0.617230 | ||||||||
\(944\) | 21.3155 | 0.693760 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −71.9407 | −2.33899 | ||||||||
\(947\) | −45.4863 | −1.47811 | −0.739053 | − | 0.673647i | \(-0.764727\pi\) | ||||
−0.739053 | + | 0.673647i | \(0.764727\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.39075 | 0.142530 | ||||||||
\(950\) | −32.8880 | −1.06703 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.83945 | −0.0920272 | ||||||||
\(953\) | 32.2357 | 1.04422 | 0.522108 | − | 0.852880i | \(-0.325146\pi\) | ||||
0.522108 | + | 0.852880i | \(0.325146\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.44972 | 0.273427 | ||||||||
\(956\) | 31.0990 | 1.00581 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −45.2625 | −1.46237 | ||||||||
\(959\) | 8.60770 | 0.277957 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.34123 | −0.172298 | ||||||||
\(962\) | −1.55554 | −0.0501527 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 48.6230 | 1.56604 | ||||||||
\(965\) | −11.5151 | −0.370685 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.3030 | 0.813690 | 0.406845 | − | 0.913497i | \(-0.366629\pi\) | ||||
0.406845 | + | 0.913497i | \(0.366629\pi\) | |||||||
\(968\) | −5.93520 | −0.190765 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 16.7234 | 0.536955 | ||||||||
\(971\) | −20.9204 | −0.671367 | −0.335683 | − | 0.941975i | \(-0.608967\pi\) | ||||
−0.335683 | + | 0.941975i | \(0.608967\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.1427 | 0.357217 | ||||||||
\(974\) | −31.0660 | −0.995420 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 55.3776 | 1.77260 | ||||||||
\(977\) | 31.9865 | 1.02334 | 0.511669 | − | 0.859183i | \(-0.329027\pi\) | ||||
0.511669 | + | 0.859183i | \(0.329027\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.4563 | −0.749667 | ||||||||
\(980\) | −2.73383 | −0.0873290 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 39.9000 | 1.27326 | ||||||||
\(983\) | 21.4363 | 0.683712 | 0.341856 | − | 0.939752i | \(-0.388944\pi\) | ||||
0.341856 | + | 0.939752i | \(0.388944\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.14856 | −0.227772 | ||||||||
\(986\) | −41.9900 | −1.33723 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.63779 | 0.306619 | ||||||||
\(989\) | −14.7173 | −0.467984 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.1601 | −1.49809 | −0.749044 | − | 0.662520i | \(-0.769487\pi\) | ||||
−0.749044 | + | 0.662520i | \(0.769487\pi\) | |||||||
\(992\) | −37.8412 | −1.20146 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 25.3604 | 0.804382 | ||||||||
\(995\) | −2.70180 | −0.0856527 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.2481 | 1.59137 | 0.795687 | − | 0.605708i | \(-0.207110\pi\) | ||||
0.795687 | + | 0.605708i | \(0.207110\pi\) | |||||||
\(998\) | −11.8360 | −0.374662 | ||||||||
\(999\) | 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 | 8001.2.a.v.1.16 | 19 | ||
3.2 | odd | 2 | 2667.2.a.q.1.4 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.q.1.4 | ✓ | 19 | 3.2 | odd | 2 | ||
8001.2.a.v.1.16 | 19 | 1.1 | even | 1 | trivial |