Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2325,2,Mod(1,2325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2325, 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("2325.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2325 = 3 \cdot 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2325.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: | \(18.5652184699\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.136751504.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 9x^{4} + 7x^{3} + 20x^{2} - 8x - 12 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.759793\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2325.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.759793 | −0.537255 | −0.268627 | − | 0.963244i | \(-0.586570\pi\) | ||||
−0.268627 | + | 0.963244i | \(0.586570\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.42271 | −0.711357 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.759793 | 0.310184 | ||||||||
\(7\) | −4.29226 | −1.62232 | −0.811161 | − | 0.584823i | \(-0.801164\pi\) | ||||
−0.811161 | + | 0.584823i | \(0.801164\pi\) | |||||||
\(8\) | 2.60056 | 0.919435 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.35462 | −0.408435 | −0.204217 | − | 0.978926i | \(-0.565465\pi\) | ||||
−0.204217 | + | 0.978926i | \(0.565465\pi\) | |||||||
\(12\) | 1.42271 | 0.410702 | ||||||||
\(13\) | −0.931910 | −0.258465 | −0.129233 | − | 0.991614i | \(-0.541251\pi\) | ||||
−0.129233 | + | 0.991614i | \(0.541251\pi\) | |||||||
\(14\) | 3.26123 | 0.871600 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.869544 | 0.217386 | ||||||||
\(17\) | −3.18251 | −0.771871 | −0.385936 | − | 0.922526i | \(-0.626121\pi\) | ||||
−0.385936 | + | 0.922526i | \(0.626121\pi\) | |||||||
\(18\) | −0.759793 | −0.179085 | ||||||||
\(19\) | −1.13077 | −0.259417 | −0.129709 | − | 0.991552i | \(-0.541404\pi\) | ||||
−0.129709 | + | 0.991552i | \(0.541404\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.29226 | 0.936648 | ||||||||
\(22\) | 1.02923 | 0.219434 | ||||||||
\(23\) | −4.97154 | −1.03664 | −0.518318 | − | 0.855188i | \(-0.673442\pi\) | ||||
−0.518318 | + | 0.855188i | \(0.673442\pi\) | |||||||
\(24\) | −2.60056 | −0.530836 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.708059 | 0.138862 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 6.10666 | 1.15405 | ||||||||
\(29\) | −4.66324 | −0.865942 | −0.432971 | − | 0.901408i | \(-0.642535\pi\) | ||||
−0.432971 | + | 0.901408i | \(0.642535\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −5.86178 | −1.03623 | ||||||||
\(33\) | 1.35462 | 0.235810 | ||||||||
\(34\) | 2.41805 | 0.414692 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.42271 | −0.237119 | ||||||||
\(37\) | −10.9138 | −1.79422 | −0.897112 | − | 0.441804i | \(-0.854339\pi\) | ||||
−0.897112 | + | 0.441804i | \(0.854339\pi\) | |||||||
\(38\) | 0.859154 | 0.139373 | ||||||||
\(39\) | 0.931910 | 0.149225 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.4282 | −1.78478 | −0.892389 | − | 0.451268i | \(-0.850972\pi\) | ||||
−0.892389 | + | 0.451268i | \(0.850972\pi\) | |||||||
\(42\) | −3.26123 | −0.503219 | ||||||||
\(43\) | 5.71497 | 0.871525 | 0.435763 | − | 0.900062i | \(-0.356479\pi\) | ||||
0.435763 | + | 0.900062i | \(0.356479\pi\) | |||||||
\(44\) | 1.92724 | 0.290543 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.77734 | 0.556938 | ||||||||
\(47\) | −0.503231 | −0.0734038 | −0.0367019 | − | 0.999326i | \(-0.511685\pi\) | ||||
−0.0367019 | + | 0.999326i | \(0.511685\pi\) | |||||||
\(48\) | −0.869544 | −0.125508 | ||||||||
\(49\) | 11.4235 | 1.63193 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.18251 | 0.445640 | ||||||||
\(52\) | 1.32584 | 0.183861 | ||||||||
\(53\) | −2.52183 | −0.346400 | −0.173200 | − | 0.984887i | \(-0.555411\pi\) | ||||
−0.173200 | + | 0.984887i | \(0.555411\pi\) | |||||||
\(54\) | 0.759793 | 0.103395 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −11.1623 | −1.49162 | ||||||||
\(57\) | 1.13077 | 0.149775 | ||||||||
\(58\) | 3.54310 | 0.465231 | ||||||||
\(59\) | 10.5500 | 1.37349 | 0.686747 | − | 0.726896i | \(-0.259038\pi\) | ||||
0.686747 | + | 0.726896i | \(0.259038\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.74164 | 0.479068 | 0.239534 | − | 0.970888i | \(-0.423005\pi\) | ||||
0.239534 | + | 0.970888i | \(0.423005\pi\) | |||||||
\(62\) | −0.759793 | −0.0964938 | ||||||||
\(63\) | −4.29226 | −0.540774 | ||||||||
\(64\) | 2.71466 | 0.339332 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.02923 | −0.126690 | ||||||||
\(67\) | −10.7877 | −1.31793 | −0.658965 | − | 0.752173i | \(-0.729006\pi\) | ||||
−0.658965 | + | 0.752173i | \(0.729006\pi\) | |||||||
\(68\) | 4.52780 | 0.549076 | ||||||||
\(69\) | 4.97154 | 0.598503 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.27758 | 0.507656 | 0.253828 | − | 0.967249i | \(-0.418310\pi\) | ||||
0.253828 | + | 0.967249i | \(0.418310\pi\) | |||||||
\(72\) | 2.60056 | 0.306478 | ||||||||
\(73\) | −10.0678 | −1.17835 | −0.589174 | − | 0.808007i | \(-0.700547\pi\) | ||||
−0.589174 | + | 0.808007i | \(0.700547\pi\) | |||||||
\(74\) | 8.29226 | 0.963955 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.60877 | 0.184538 | ||||||||
\(77\) | 5.81440 | 0.662612 | ||||||||
\(78\) | −0.708059 | −0.0801719 | ||||||||
\(79\) | 2.28187 | 0.256730 | 0.128365 | − | 0.991727i | \(-0.459027\pi\) | ||||
0.128365 | + | 0.991727i | \(0.459027\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.68303 | 0.958880 | ||||||||
\(83\) | 8.83536 | 0.969806 | 0.484903 | − | 0.874568i | \(-0.338855\pi\) | ||||
0.484903 | + | 0.874568i | \(0.338855\pi\) | |||||||
\(84\) | −6.10666 | −0.666291 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.34220 | −0.468231 | ||||||||
\(87\) | 4.66324 | 0.499952 | ||||||||
\(88\) | −3.52278 | −0.375529 | ||||||||
\(89\) | 1.21577 | 0.128872 | 0.0644358 | − | 0.997922i | \(-0.479475\pi\) | ||||
0.0644358 | + | 0.997922i | \(0.479475\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 7.07307 | 0.737419 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | 0.382351 | 0.0394365 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.86178 | 0.598266 | ||||||||
\(97\) | −9.32497 | −0.946807 | −0.473404 | − | 0.880846i | \(-0.656975\pi\) | ||||
−0.473404 | + | 0.880846i | \(0.656975\pi\) | |||||||
\(98\) | −8.67949 | −0.876760 | ||||||||
\(99\) | −1.35462 | −0.136145 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.4627 | 1.14058 | 0.570288 | − | 0.821444i | \(-0.306831\pi\) | ||||
0.570288 | + | 0.821444i | \(0.306831\pi\) | |||||||
\(102\) | −2.41805 | −0.239422 | ||||||||
\(103\) | 6.26727 | 0.617533 | 0.308766 | − | 0.951138i | \(-0.400084\pi\) | ||||
0.308766 | + | 0.951138i | \(0.400084\pi\) | |||||||
\(104\) | −2.42348 | −0.237642 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.91607 | 0.186105 | ||||||||
\(107\) | −5.72381 | −0.553342 | −0.276671 | − | 0.960965i | \(-0.589231\pi\) | ||||
−0.276671 | + | 0.960965i | \(0.589231\pi\) | |||||||
\(108\) | 1.42271 | 0.136901 | ||||||||
\(109\) | −3.77840 | −0.361905 | −0.180952 | − | 0.983492i | \(-0.557918\pi\) | ||||
−0.180952 | + | 0.983492i | \(0.557918\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.9138 | 1.03590 | ||||||||
\(112\) | −3.73231 | −0.352670 | ||||||||
\(113\) | 10.2428 | 0.963565 | 0.481783 | − | 0.876291i | \(-0.339990\pi\) | ||||
0.481783 | + | 0.876291i | \(0.339990\pi\) | |||||||
\(114\) | −0.859154 | −0.0804671 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.63446 | 0.615994 | ||||||||
\(117\) | −0.931910 | −0.0861551 | ||||||||
\(118\) | −8.01583 | −0.737917 | ||||||||
\(119\) | 13.6601 | 1.25222 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.16499 | −0.833181 | ||||||||
\(122\) | −2.84287 | −0.257382 | ||||||||
\(123\) | 11.4282 | 1.03044 | ||||||||
\(124\) | −1.42271 | −0.127764 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.26123 | 0.290533 | ||||||||
\(127\) | 20.4646 | 1.81594 | 0.907971 | − | 0.419034i | \(-0.137631\pi\) | ||||
0.907971 | + | 0.419034i | \(0.137631\pi\) | |||||||
\(128\) | 9.66099 | 0.853919 | ||||||||
\(129\) | −5.71497 | −0.503175 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.92205 | −0.517412 | −0.258706 | − | 0.965956i | \(-0.583296\pi\) | ||||
−0.258706 | + | 0.965956i | \(0.583296\pi\) | |||||||
\(132\) | −1.92724 | −0.167745 | ||||||||
\(133\) | 4.85357 | 0.420858 | ||||||||
\(134\) | 8.19644 | 0.708065 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.27629 | −0.709686 | ||||||||
\(137\) | 20.0932 | 1.71668 | 0.858338 | − | 0.513084i | \(-0.171497\pi\) | ||||
0.858338 | + | 0.513084i | \(0.171497\pi\) | |||||||
\(138\) | −3.77734 | −0.321548 | ||||||||
\(139\) | 6.51070 | 0.552231 | 0.276115 | − | 0.961125i | \(-0.410953\pi\) | ||||
0.276115 | + | 0.961125i | \(0.410953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.503231 | 0.0423797 | ||||||||
\(142\) | −3.25008 | −0.272741 | ||||||||
\(143\) | 1.26239 | 0.105566 | ||||||||
\(144\) | 0.869544 | 0.0724620 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.64945 | 0.633073 | ||||||||
\(147\) | −11.4235 | −0.942193 | ||||||||
\(148\) | 15.5273 | 1.27633 | ||||||||
\(149\) | −0.346029 | −0.0283478 | −0.0141739 | − | 0.999900i | \(-0.504512\pi\) | ||||
−0.0141739 | + | 0.999900i | \(0.504512\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.7889 | 1.28488 | 0.642442 | − | 0.766334i | \(-0.277921\pi\) | ||||
0.642442 | + | 0.766334i | \(0.277921\pi\) | |||||||
\(152\) | −2.94064 | −0.238517 | ||||||||
\(153\) | −3.18251 | −0.257290 | ||||||||
\(154\) | −4.41774 | −0.355992 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.32584 | −0.106152 | ||||||||
\(157\) | −19.8274 | −1.58240 | −0.791198 | − | 0.611561i | \(-0.790542\pi\) | ||||
−0.791198 | + | 0.611561i | \(0.790542\pi\) | |||||||
\(158\) | −1.73375 | −0.137930 | ||||||||
\(159\) | 2.52183 | 0.199994 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 21.3391 | 1.68176 | ||||||||
\(162\) | −0.759793 | −0.0596950 | ||||||||
\(163\) | 9.76559 | 0.764900 | 0.382450 | − | 0.923976i | \(-0.375080\pi\) | ||||
0.382450 | + | 0.923976i | \(0.375080\pi\) | |||||||
\(164\) | 16.2590 | 1.26961 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.71304 | −0.521033 | ||||||||
\(167\) | −3.65200 | −0.282600 | −0.141300 | − | 0.989967i | \(-0.545128\pi\) | ||||
−0.141300 | + | 0.989967i | \(0.545128\pi\) | |||||||
\(168\) | 11.1623 | 0.861187 | ||||||||
\(169\) | −12.1315 | −0.933196 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.13077 | −0.0864724 | ||||||||
\(172\) | −8.13077 | −0.619966 | ||||||||
\(173\) | −19.9940 | −1.52011 | −0.760056 | − | 0.649857i | \(-0.774829\pi\) | ||||
−0.760056 | + | 0.649857i | \(0.774829\pi\) | |||||||
\(174\) | −3.54310 | −0.268602 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.17791 | −0.0887880 | ||||||||
\(177\) | −10.5500 | −0.792987 | ||||||||
\(178\) | −0.923736 | −0.0692370 | ||||||||
\(179\) | −2.08420 | −0.155781 | −0.0778904 | − | 0.996962i | \(-0.524818\pi\) | ||||
−0.0778904 | + | 0.996962i | \(0.524818\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.69194 | 0.125761 | 0.0628806 | − | 0.998021i | \(-0.479971\pi\) | ||||
0.0628806 | + | 0.998021i | \(0.479971\pi\) | |||||||
\(182\) | −3.03917 | −0.225278 | ||||||||
\(183\) | −3.74164 | −0.276590 | ||||||||
\(184\) | −12.9288 | −0.953120 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.759793 | 0.0557107 | ||||||||
\(187\) | 4.31110 | 0.315259 | ||||||||
\(188\) | 0.715954 | 0.0522163 | ||||||||
\(189\) | 4.29226 | 0.312216 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.1386 | 1.52954 | 0.764769 | − | 0.644305i | \(-0.222853\pi\) | ||||
0.764769 | + | 0.644305i | \(0.222853\pi\) | |||||||
\(192\) | −2.71466 | −0.195913 | ||||||||
\(193\) | −1.75322 | −0.126200 | −0.0630999 | − | 0.998007i | \(-0.520099\pi\) | ||||
−0.0630999 | + | 0.998007i | \(0.520099\pi\) | |||||||
\(194\) | 7.08505 | 0.508677 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −16.2524 | −1.16088 | ||||||||
\(197\) | 12.8682 | 0.916825 | 0.458412 | − | 0.888740i | \(-0.348418\pi\) | ||||
0.458412 | + | 0.888740i | \(0.348418\pi\) | |||||||
\(198\) | 1.02923 | 0.0731445 | ||||||||
\(199\) | −15.9399 | −1.12995 | −0.564975 | − | 0.825108i | \(-0.691114\pi\) | ||||
−0.564975 | + | 0.825108i | \(0.691114\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.7877 | 0.760908 | ||||||||
\(202\) | −8.70925 | −0.612781 | ||||||||
\(203\) | 20.0158 | 1.40484 | ||||||||
\(204\) | −4.52780 | −0.317009 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.76183 | −0.331772 | ||||||||
\(207\) | −4.97154 | −0.345546 | ||||||||
\(208\) | −0.810337 | −0.0561868 | ||||||||
\(209\) | 1.53177 | 0.105955 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.6144 | 0.799567 | 0.399783 | − | 0.916610i | \(-0.369085\pi\) | ||||
0.399783 | + | 0.916610i | \(0.369085\pi\) | |||||||
\(212\) | 3.58785 | 0.246414 | ||||||||
\(213\) | −4.27758 | −0.293095 | ||||||||
\(214\) | 4.34891 | 0.297285 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.60056 | −0.176945 | ||||||||
\(217\) | −4.29226 | −0.291378 | ||||||||
\(218\) | 2.87080 | 0.194435 | ||||||||
\(219\) | 10.0678 | 0.680319 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.96581 | 0.199502 | ||||||||
\(222\) | −8.29226 | −0.556540 | ||||||||
\(223\) | 10.8903 | 0.729270 | 0.364635 | − | 0.931151i | \(-0.381194\pi\) | ||||
0.364635 | + | 0.931151i | \(0.381194\pi\) | |||||||
\(224\) | 25.1603 | 1.68109 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.78244 | −0.517680 | ||||||||
\(227\) | 20.7528 | 1.37741 | 0.688707 | − | 0.725039i | \(-0.258178\pi\) | ||||
0.688707 | + | 0.725039i | \(0.258178\pi\) | |||||||
\(228\) | −1.60877 | −0.106543 | ||||||||
\(229\) | −15.4796 | −1.02292 | −0.511462 | − | 0.859306i | \(-0.670896\pi\) | ||||
−0.511462 | + | 0.859306i | \(0.670896\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.81440 | −0.382559 | ||||||||
\(232\) | −12.1270 | −0.796177 | ||||||||
\(233\) | 2.20143 | 0.144220 | 0.0721102 | − | 0.997397i | \(-0.477027\pi\) | ||||
0.0721102 | + | 0.997397i | \(0.477027\pi\) | |||||||
\(234\) | 0.708059 | 0.0462873 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −15.0097 | −0.977045 | ||||||||
\(237\) | −2.28187 | −0.148223 | ||||||||
\(238\) | −10.3789 | −0.672763 | ||||||||
\(239\) | 14.8091 | 0.957924 | 0.478962 | − | 0.877836i | \(-0.341013\pi\) | ||||
0.478962 | + | 0.877836i | \(0.341013\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.0442 | 1.54882 | 0.774411 | − | 0.632683i | \(-0.218046\pi\) | ||||
0.774411 | + | 0.632683i | \(0.218046\pi\) | |||||||
\(242\) | 6.96350 | 0.447631 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −5.32329 | −0.340789 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.68303 | −0.553610 | ||||||||
\(247\) | 1.05378 | 0.0670504 | ||||||||
\(248\) | 2.60056 | 0.165135 | ||||||||
\(249\) | −8.83536 | −0.559918 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.23395 | −0.267245 | −0.133622 | − | 0.991032i | \(-0.542661\pi\) | ||||
−0.133622 | + | 0.991032i | \(0.542661\pi\) | |||||||
\(252\) | 6.10666 | 0.384683 | ||||||||
\(253\) | 6.73456 | 0.423398 | ||||||||
\(254\) | −15.5489 | −0.975623 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.7697 | −0.798104 | ||||||||
\(257\) | 24.3613 | 1.51962 | 0.759808 | − | 0.650147i | \(-0.225293\pi\) | ||||
0.759808 | + | 0.650147i | \(0.225293\pi\) | |||||||
\(258\) | 4.34220 | 0.270333 | ||||||||
\(259\) | 46.8450 | 2.91081 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.66324 | −0.288647 | ||||||||
\(262\) | 4.49953 | 0.277982 | ||||||||
\(263\) | −8.58093 | −0.529123 | −0.264561 | − | 0.964369i | \(-0.585227\pi\) | ||||
−0.264561 | + | 0.964369i | \(0.585227\pi\) | |||||||
\(264\) | 3.52278 | 0.216812 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.68771 | −0.226108 | ||||||||
\(267\) | −1.21577 | −0.0744041 | ||||||||
\(268\) | 15.3479 | 0.937520 | ||||||||
\(269\) | −13.9684 | −0.851671 | −0.425835 | − | 0.904801i | \(-0.640020\pi\) | ||||
−0.425835 | + | 0.904801i | \(0.640020\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.8507 | −1.08435 | −0.542176 | − | 0.840265i | \(-0.682400\pi\) | ||||
−0.542176 | + | 0.840265i | \(0.682400\pi\) | |||||||
\(272\) | −2.76733 | −0.167794 | ||||||||
\(273\) | −4.00000 | −0.242091 | ||||||||
\(274\) | −15.2667 | −0.922293 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.07307 | −0.425749 | ||||||||
\(277\) | −21.2156 | −1.27472 | −0.637360 | − | 0.770566i | \(-0.719974\pi\) | ||||
−0.637360 | + | 0.770566i | \(0.719974\pi\) | |||||||
\(278\) | −4.94679 | −0.296689 | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.3013 | −0.733834 | −0.366917 | − | 0.930254i | \(-0.619587\pi\) | ||||
−0.366917 | + | 0.930254i | \(0.619587\pi\) | |||||||
\(282\) | −0.382351 | −0.0227687 | ||||||||
\(283\) | −7.30671 | −0.434339 | −0.217169 | − | 0.976134i | \(-0.569682\pi\) | ||||
−0.217169 | + | 0.976134i | \(0.569682\pi\) | |||||||
\(284\) | −6.08578 | −0.361125 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.959154 | −0.0567160 | ||||||||
\(287\) | 49.0526 | 2.89548 | ||||||||
\(288\) | −5.86178 | −0.345409 | ||||||||
\(289\) | −6.87165 | −0.404214 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.32497 | 0.546639 | ||||||||
\(292\) | 14.3236 | 0.838226 | ||||||||
\(293\) | −2.40359 | −0.140419 | −0.0702097 | − | 0.997532i | \(-0.522367\pi\) | ||||
−0.0702097 | + | 0.997532i | \(0.522367\pi\) | |||||||
\(294\) | 8.67949 | 0.506198 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −28.3820 | −1.64967 | ||||||||
\(297\) | 1.35462 | 0.0786033 | ||||||||
\(298\) | 0.262911 | 0.0152300 | ||||||||
\(299\) | 4.63302 | 0.267935 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.5301 | −1.41389 | ||||||||
\(302\) | −11.9963 | −0.690310 | ||||||||
\(303\) | −11.4627 | −0.658512 | ||||||||
\(304\) | −0.983258 | −0.0563937 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.41805 | 0.138231 | ||||||||
\(307\) | 27.1451 | 1.54925 | 0.774626 | − | 0.632419i | \(-0.217938\pi\) | ||||
0.774626 | + | 0.632419i | \(0.217938\pi\) | |||||||
\(308\) | −8.27223 | −0.471354 | ||||||||
\(309\) | −6.26727 | −0.356533 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.3041 | −1.60498 | −0.802489 | − | 0.596667i | \(-0.796491\pi\) | ||||
−0.802489 | + | 0.596667i | \(0.796491\pi\) | |||||||
\(312\) | 2.42348 | 0.137203 | ||||||||
\(313\) | 18.1802 | 1.02761 | 0.513803 | − | 0.857908i | \(-0.328236\pi\) | ||||
0.513803 | + | 0.857908i | \(0.328236\pi\) | |||||||
\(314\) | 15.0647 | 0.850150 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.24645 | −0.182627 | ||||||||
\(317\) | 9.28110 | 0.521278 | 0.260639 | − | 0.965436i | \(-0.416067\pi\) | ||||
0.260639 | + | 0.965436i | \(0.416067\pi\) | |||||||
\(318\) | −1.91607 | −0.107448 | ||||||||
\(319\) | 6.31694 | 0.353681 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.72381 | 0.319472 | ||||||||
\(322\) | −16.2133 | −0.903533 | ||||||||
\(323\) | 3.59869 | 0.200237 | ||||||||
\(324\) | −1.42271 | −0.0790397 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7.41983 | −0.410946 | ||||||||
\(327\) | 3.77840 | 0.208946 | ||||||||
\(328\) | −29.7195 | −1.64099 | ||||||||
\(329\) | 2.16000 | 0.119084 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.54506 | −0.359749 | −0.179874 | − | 0.983690i | \(-0.557569\pi\) | ||||
−0.179874 | + | 0.983690i | \(0.557569\pi\) | |||||||
\(332\) | −12.5702 | −0.689879 | ||||||||
\(333\) | −10.9138 | −0.598075 | ||||||||
\(334\) | 2.77477 | 0.151828 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.73231 | 0.203614 | ||||||||
\(337\) | 1.68787 | 0.0919442 | 0.0459721 | − | 0.998943i | \(-0.485361\pi\) | ||||
0.0459721 | + | 0.998943i | \(0.485361\pi\) | |||||||
\(338\) | 9.21746 | 0.501364 | ||||||||
\(339\) | −10.2428 | −0.556315 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.35462 | −0.0733570 | ||||||||
\(342\) | 0.859154 | 0.0464577 | ||||||||
\(343\) | −18.9867 | −1.02519 | ||||||||
\(344\) | 14.8621 | 0.801311 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.1913 | 0.816688 | ||||||||
\(347\) | 8.71061 | 0.467610 | 0.233805 | − | 0.972283i | \(-0.424882\pi\) | ||||
0.233805 | + | 0.972283i | \(0.424882\pi\) | |||||||
\(348\) | −6.63446 | −0.355644 | ||||||||
\(349\) | 18.8459 | 1.00880 | 0.504399 | − | 0.863471i | \(-0.331714\pi\) | ||||
0.504399 | + | 0.863471i | \(0.331714\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.931910 | 0.0497417 | ||||||||
\(352\) | 7.94052 | 0.423231 | ||||||||
\(353\) | 27.5743 | 1.46763 | 0.733815 | − | 0.679349i | \(-0.237738\pi\) | ||||
0.733815 | + | 0.679349i | \(0.237738\pi\) | |||||||
\(354\) | 8.01583 | 0.426036 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.72970 | −0.0916738 | ||||||||
\(357\) | −13.6601 | −0.722972 | ||||||||
\(358\) | 1.58356 | 0.0836940 | ||||||||
\(359\) | −16.4160 | −0.866401 | −0.433200 | − | 0.901298i | \(-0.642616\pi\) | ||||
−0.433200 | + | 0.901298i | \(0.642616\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7214 | −0.932703 | ||||||||
\(362\) | −1.28553 | −0.0675659 | ||||||||
\(363\) | 9.16499 | 0.481037 | ||||||||
\(364\) | −5.69086 | −0.298282 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.84287 | 0.148599 | ||||||||
\(367\) | −11.3882 | −0.594461 | −0.297231 | − | 0.954806i | \(-0.596063\pi\) | ||||
−0.297231 | + | 0.954806i | \(0.596063\pi\) | |||||||
\(368\) | −4.32297 | −0.225350 | ||||||||
\(369\) | −11.4282 | −0.594926 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.8244 | 0.561973 | ||||||||
\(372\) | 1.42271 | 0.0737643 | ||||||||
\(373\) | −27.6598 | −1.43217 | −0.716086 | − | 0.698012i | \(-0.754068\pi\) | ||||
−0.716086 | + | 0.698012i | \(0.754068\pi\) | |||||||
\(374\) | −3.27555 | −0.169374 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.30868 | −0.0674900 | ||||||||
\(377\) | 4.34572 | 0.223816 | ||||||||
\(378\) | −3.26123 | −0.167740 | ||||||||
\(379\) | −21.5637 | −1.10765 | −0.553827 | − | 0.832632i | \(-0.686833\pi\) | ||||
−0.553827 | + | 0.832632i | \(0.686833\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20.4646 | −1.04843 | ||||||||
\(382\) | −16.0610 | −0.821752 | ||||||||
\(383\) | 35.2566 | 1.80153 | 0.900764 | − | 0.434309i | \(-0.143007\pi\) | ||||
0.900764 | + | 0.434309i | \(0.143007\pi\) | |||||||
\(384\) | −9.66099 | −0.493010 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.33209 | 0.0678015 | ||||||||
\(387\) | 5.71497 | 0.290508 | ||||||||
\(388\) | 13.2668 | 0.673518 | ||||||||
\(389\) | −12.3703 | −0.627200 | −0.313600 | − | 0.949555i | \(-0.601535\pi\) | ||||
−0.313600 | + | 0.949555i | \(0.601535\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.8219 | 0.800150 | ||||||||
\(392\) | 29.7074 | 1.50045 | ||||||||
\(393\) | 5.92205 | 0.298728 | ||||||||
\(394\) | −9.77721 | −0.492569 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.92724 | 0.0968476 | ||||||||
\(397\) | 25.8597 | 1.29786 | 0.648931 | − | 0.760847i | \(-0.275216\pi\) | ||||
0.648931 | + | 0.760847i | \(0.275216\pi\) | |||||||
\(398\) | 12.1110 | 0.607071 | ||||||||
\(399\) | −4.85357 | −0.242983 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.7209 | 1.28444 | 0.642220 | − | 0.766520i | \(-0.278013\pi\) | ||||
0.642220 | + | 0.766520i | \(0.278013\pi\) | |||||||
\(402\) | −8.19644 | −0.408801 | ||||||||
\(403\) | −0.931910 | −0.0464218 | ||||||||
\(404\) | −16.3081 | −0.811358 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.2079 | −0.754755 | ||||||||
\(407\) | 14.7842 | 0.732823 | ||||||||
\(408\) | 8.27629 | 0.409737 | ||||||||
\(409\) | −18.1825 | −0.899069 | −0.449534 | − | 0.893263i | \(-0.648410\pi\) | ||||
−0.449534 | + | 0.893263i | \(0.648410\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.0932 | −0.991124 | ||||||||
\(412\) | −8.91654 | −0.439286 | ||||||||
\(413\) | −45.2834 | −2.22825 | ||||||||
\(414\) | 3.77734 | 0.185646 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.46266 | 0.267829 | ||||||||
\(417\) | −6.51070 | −0.318831 | ||||||||
\(418\) | −1.16383 | −0.0569248 | ||||||||
\(419\) | −14.3499 | −0.701038 | −0.350519 | − | 0.936556i | \(-0.613995\pi\) | ||||
−0.350519 | + | 0.936556i | \(0.613995\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.9088 | 1.16525 | 0.582623 | − | 0.812743i | \(-0.302026\pi\) | ||||
0.582623 | + | 0.812743i | \(0.302026\pi\) | |||||||
\(422\) | −8.82452 | −0.429571 | ||||||||
\(423\) | −0.503231 | −0.0244679 | ||||||||
\(424\) | −6.55817 | −0.318493 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.25008 | 0.157467 | ||||||||
\(427\) | −16.0601 | −0.777203 | ||||||||
\(428\) | 8.14335 | 0.393623 | ||||||||
\(429\) | −1.26239 | −0.0609487 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.8546 | −1.24537 | −0.622686 | − | 0.782472i | \(-0.713959\pi\) | ||||
−0.622686 | + | 0.782472i | \(0.713959\pi\) | |||||||
\(432\) | −0.869544 | −0.0418360 | ||||||||
\(433\) | −17.4970 | −0.840853 | −0.420427 | − | 0.907327i | \(-0.638120\pi\) | ||||
−0.420427 | + | 0.907327i | \(0.638120\pi\) | |||||||
\(434\) | 3.26123 | 0.156544 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.37558 | 0.257443 | ||||||||
\(437\) | 5.62168 | 0.268921 | ||||||||
\(438\) | −7.64945 | −0.365505 | ||||||||
\(439\) | −11.3551 | −0.541948 | −0.270974 | − | 0.962587i | \(-0.587346\pi\) | ||||
−0.270974 | + | 0.962587i | \(0.587346\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.4235 | 0.543975 | ||||||||
\(442\) | −2.25340 | −0.107183 | ||||||||
\(443\) | −17.0042 | −0.807892 | −0.403946 | − | 0.914783i | \(-0.632362\pi\) | ||||
−0.403946 | + | 0.914783i | \(0.632362\pi\) | |||||||
\(444\) | −15.5273 | −0.736892 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.27440 | −0.391804 | ||||||||
\(447\) | 0.346029 | 0.0163666 | ||||||||
\(448\) | −11.6520 | −0.550505 | ||||||||
\(449\) | −29.0151 | −1.36931 | −0.684654 | − | 0.728868i | \(-0.740047\pi\) | ||||
−0.684654 | + | 0.728868i | \(0.740047\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.4809 | 0.728965 | ||||||||
\(452\) | −14.5726 | −0.685439 | ||||||||
\(453\) | −15.7889 | −0.741828 | ||||||||
\(454\) | −15.7679 | −0.740023 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.94064 | 0.137708 | ||||||||
\(457\) | 7.88481 | 0.368836 | 0.184418 | − | 0.982848i | \(-0.440960\pi\) | ||||
0.184418 | + | 0.982848i | \(0.440960\pi\) | |||||||
\(458\) | 11.7613 | 0.549571 | ||||||||
\(459\) | 3.18251 | 0.148547 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.8317 | 0.970231 | 0.485116 | − | 0.874450i | \(-0.338778\pi\) | ||||
0.485116 | + | 0.874450i | \(0.338778\pi\) | |||||||
\(462\) | 4.41774 | 0.205532 | ||||||||
\(463\) | −33.0145 | −1.53431 | −0.767157 | − | 0.641460i | \(-0.778329\pi\) | ||||
−0.767157 | + | 0.641460i | \(0.778329\pi\) | |||||||
\(464\) | −4.05489 | −0.188244 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.67263 | −0.0774831 | ||||||||
\(467\) | 9.98212 | 0.461917 | 0.230959 | − | 0.972964i | \(-0.425814\pi\) | ||||
0.230959 | + | 0.972964i | \(0.425814\pi\) | |||||||
\(468\) | 1.32584 | 0.0612871 | ||||||||
\(469\) | 46.3037 | 2.13811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.8274 | 0.913596 | ||||||||
\(472\) | 27.4359 | 1.26284 | ||||||||
\(473\) | −7.74164 | −0.355961 | ||||||||
\(474\) | 1.73375 | 0.0796337 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −19.4345 | −0.890778 | ||||||||
\(477\) | −2.52183 | −0.115467 | ||||||||
\(478\) | −11.2519 | −0.514649 | ||||||||
\(479\) | −16.5755 | −0.757355 | −0.378678 | − | 0.925529i | \(-0.623621\pi\) | ||||
−0.378678 | + | 0.925529i | \(0.623621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.1707 | 0.463745 | ||||||||
\(482\) | −18.2686 | −0.832112 | ||||||||
\(483\) | −21.3391 | −0.970963 | ||||||||
\(484\) | 13.0392 | 0.592689 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.759793 | 0.0344649 | ||||||||
\(487\) | −31.3786 | −1.42190 | −0.710951 | − | 0.703242i | \(-0.751735\pi\) | ||||
−0.710951 | + | 0.703242i | \(0.751735\pi\) | |||||||
\(488\) | 9.73035 | 0.440472 | ||||||||
\(489\) | −9.76559 | −0.441615 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.07019 | 0.273944 | 0.136972 | − | 0.990575i | \(-0.456263\pi\) | ||||
0.136972 | + | 0.990575i | \(0.456263\pi\) | |||||||
\(492\) | −16.2590 | −0.733012 | ||||||||
\(493\) | 14.8408 | 0.668396 | ||||||||
\(494\) | −0.800654 | −0.0360231 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.869544 | 0.0390437 | ||||||||
\(497\) | −18.3605 | −0.823581 | ||||||||
\(498\) | 6.71304 | 0.300819 | ||||||||
\(499\) | −2.36790 | −0.106002 | −0.0530008 | − | 0.998594i | \(-0.516879\pi\) | ||||
−0.0530008 | + | 0.998594i | \(0.516879\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.65200 | 0.163159 | ||||||||
\(502\) | 3.21693 | 0.143579 | ||||||||
\(503\) | 30.2479 | 1.34869 | 0.674343 | − | 0.738418i | \(-0.264427\pi\) | ||||
0.674343 | + | 0.738418i | \(0.264427\pi\) | |||||||
\(504\) | −11.1623 | −0.497206 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.11688 | −0.227473 | ||||||||
\(507\) | 12.1315 | 0.538781 | ||||||||
\(508\) | −29.1153 | −1.29178 | ||||||||
\(509\) | 14.4792 | 0.641780 | 0.320890 | − | 0.947116i | \(-0.396018\pi\) | ||||
0.320890 | + | 0.947116i | \(0.396018\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 43.2136 | 1.91166 | ||||||||
\(512\) | −9.61968 | −0.425134 | ||||||||
\(513\) | 1.13077 | 0.0499249 | ||||||||
\(514\) | −18.5096 | −0.816421 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.13077 | 0.357937 | ||||||||
\(517\) | 0.681689 | 0.0299806 | ||||||||
\(518\) | −35.5925 | −1.56385 | ||||||||
\(519\) | 19.9940 | 0.877637 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.3640 | −1.37408 | −0.687041 | − | 0.726619i | \(-0.741091\pi\) | ||||
−0.687041 | + | 0.726619i | \(0.741091\pi\) | |||||||
\(522\) | 3.54310 | 0.155077 | ||||||||
\(523\) | −30.1333 | −1.31764 | −0.658819 | − | 0.752302i | \(-0.728944\pi\) | ||||
−0.658819 | + | 0.752302i | \(0.728944\pi\) | |||||||
\(524\) | 8.42538 | 0.368065 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.51973 | 0.284274 | ||||||||
\(527\) | −3.18251 | −0.138632 | ||||||||
\(528\) | 1.17791 | 0.0512618 | ||||||||
\(529\) | 1.71616 | 0.0746158 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.5500 | 0.457831 | ||||||||
\(532\) | −6.90525 | −0.299380 | ||||||||
\(533\) | 10.6500 | 0.461303 | ||||||||
\(534\) | 0.923736 | 0.0399740 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −28.0541 | −1.21175 | ||||||||
\(537\) | 2.08420 | 0.0899400 | ||||||||
\(538\) | 10.6131 | 0.457564 | ||||||||
\(539\) | −15.4745 | −0.666535 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.4347 | 1.22250 | 0.611251 | − | 0.791437i | \(-0.290667\pi\) | ||||
0.611251 | + | 0.791437i | \(0.290667\pi\) | |||||||
\(542\) | 13.5628 | 0.582574 | ||||||||
\(543\) | −1.69194 | −0.0726083 | ||||||||
\(544\) | 18.6552 | 0.799834 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.03917 | 0.130065 | ||||||||
\(547\) | 30.0885 | 1.28649 | 0.643247 | − | 0.765659i | \(-0.277587\pi\) | ||||
0.643247 | + | 0.765659i | \(0.277587\pi\) | |||||||
\(548\) | −28.5869 | −1.22117 | ||||||||
\(549\) | 3.74164 | 0.159689 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.27307 | 0.224640 | ||||||||
\(552\) | 12.9288 | 0.550284 | ||||||||
\(553\) | −9.79437 | −0.416499 | ||||||||
\(554\) | 16.1194 | 0.684850 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.26287 | −0.392833 | ||||||||
\(557\) | 2.97797 | 0.126181 | 0.0630903 | − | 0.998008i | \(-0.479904\pi\) | ||||
0.0630903 | + | 0.998008i | \(0.479904\pi\) | |||||||
\(558\) | −0.759793 | −0.0321646 | ||||||||
\(559\) | −5.32584 | −0.225259 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.31110 | −0.182015 | ||||||||
\(562\) | 9.34645 | 0.394256 | ||||||||
\(563\) | 13.5587 | 0.571430 | 0.285715 | − | 0.958315i | \(-0.407769\pi\) | ||||
0.285715 | + | 0.958315i | \(0.407769\pi\) | |||||||
\(564\) | −0.715954 | −0.0301471 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5.55159 | 0.233351 | ||||||||
\(567\) | −4.29226 | −0.180258 | ||||||||
\(568\) | 11.1241 | 0.466757 | ||||||||
\(569\) | 0.614510 | 0.0257616 | 0.0128808 | − | 0.999917i | \(-0.495900\pi\) | ||||
0.0128808 | + | 0.999917i | \(0.495900\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.23557 | 0.0517068 | 0.0258534 | − | 0.999666i | \(-0.491770\pi\) | ||||
0.0258534 | + | 0.999666i | \(0.491770\pi\) | |||||||
\(572\) | −1.79602 | −0.0750953 | ||||||||
\(573\) | −21.1386 | −0.883079 | ||||||||
\(574\) | −37.2698 | −1.55561 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.71466 | 0.113111 | ||||||||
\(577\) | −4.04626 | −0.168448 | −0.0842240 | − | 0.996447i | \(-0.526841\pi\) | ||||
−0.0842240 | + | 0.996447i | \(0.526841\pi\) | |||||||
\(578\) | 5.22103 | 0.217166 | ||||||||
\(579\) | 1.75322 | 0.0728615 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −37.9236 | −1.57334 | ||||||||
\(582\) | −7.08505 | −0.293685 | ||||||||
\(583\) | 3.41614 | 0.141482 | ||||||||
\(584\) | −26.1819 | −1.08341 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.82623 | 0.0754411 | ||||||||
\(587\) | −19.5517 | −0.806985 | −0.403493 | − | 0.914983i | \(-0.632204\pi\) | ||||
−0.403493 | + | 0.914983i | \(0.632204\pi\) | |||||||
\(588\) | 16.2524 | 0.670236 | ||||||||
\(589\) | −1.13077 | −0.0465927 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.8682 | −0.529329 | ||||||||
\(592\) | −9.49006 | −0.390039 | ||||||||
\(593\) | −4.97964 | −0.204489 | −0.102245 | − | 0.994759i | \(-0.532602\pi\) | ||||
−0.102245 | + | 0.994759i | \(0.532602\pi\) | |||||||
\(594\) | −1.02923 | −0.0422300 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.492301 | 0.0201654 | ||||||||
\(597\) | 15.9399 | 0.652377 | ||||||||
\(598\) | −3.52014 | −0.143949 | ||||||||
\(599\) | −45.0854 | −1.84214 | −0.921069 | − | 0.389399i | \(-0.872683\pi\) | ||||
−0.921069 | + | 0.389399i | \(0.872683\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.4753 | −1.44707 | −0.723534 | − | 0.690289i | \(-0.757483\pi\) | ||||
−0.723534 | + | 0.690289i | \(0.757483\pi\) | |||||||
\(602\) | 18.6378 | 0.759621 | ||||||||
\(603\) | −10.7877 | −0.439310 | ||||||||
\(604\) | −22.4631 | −0.914011 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 8.70925 | 0.353789 | ||||||||
\(607\) | −29.1844 | −1.18456 | −0.592280 | − | 0.805732i | \(-0.701772\pi\) | ||||
−0.592280 | + | 0.805732i | \(0.701772\pi\) | |||||||
\(608\) | 6.62835 | 0.268815 | ||||||||
\(609\) | −20.0158 | −0.811082 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.468966 | 0.0189723 | ||||||||
\(612\) | 4.52780 | 0.183025 | ||||||||
\(613\) | 27.6353 | 1.11618 | 0.558089 | − | 0.829781i | \(-0.311535\pi\) | ||||
0.558089 | + | 0.829781i | \(0.311535\pi\) | |||||||
\(614\) | −20.6247 | −0.832344 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15.1207 | 0.609229 | ||||||||
\(617\) | 31.6280 | 1.27330 | 0.636648 | − | 0.771154i | \(-0.280320\pi\) | ||||
0.636648 | + | 0.771154i | \(0.280320\pi\) | |||||||
\(618\) | 4.76183 | 0.191549 | ||||||||
\(619\) | 12.1802 | 0.489562 | 0.244781 | − | 0.969578i | \(-0.421284\pi\) | ||||
0.244781 | + | 0.969578i | \(0.421284\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.97154 | 0.199501 | ||||||||
\(622\) | 21.5052 | 0.862282 | ||||||||
\(623\) | −5.21841 | −0.209071 | ||||||||
\(624\) | 0.810337 | 0.0324395 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −13.8132 | −0.552086 | ||||||||
\(627\) | −1.53177 | −0.0611731 | ||||||||
\(628\) | 28.2087 | 1.12565 | ||||||||
\(629\) | 34.7334 | 1.38491 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.68350 | 0.146638 | 0.0733190 | − | 0.997309i | \(-0.476641\pi\) | ||||
0.0733190 | + | 0.997309i | \(0.476641\pi\) | |||||||
\(632\) | 5.93412 | 0.236047 | ||||||||
\(633\) | −11.6144 | −0.461630 | ||||||||
\(634\) | −7.05172 | −0.280059 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.58785 | −0.142267 | ||||||||
\(637\) | −10.6457 | −0.421797 | ||||||||
\(638\) | −4.79957 | −0.190017 | ||||||||
\(639\) | 4.27758 | 0.169219 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.4209 | 1.43854 | 0.719269 | − | 0.694731i | \(-0.244477\pi\) | ||||
0.719269 | + | 0.694731i | \(0.244477\pi\) | |||||||
\(642\) | −4.34891 | −0.171638 | ||||||||
\(643\) | −11.2298 | −0.442858 | −0.221429 | − | 0.975176i | \(-0.571072\pi\) | ||||
−0.221429 | + | 0.975176i | \(0.571072\pi\) | |||||||
\(644\) | −30.3595 | −1.19633 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.73426 | −0.107578 | ||||||||
\(647\) | −32.2242 | −1.26686 | −0.633432 | − | 0.773798i | \(-0.718355\pi\) | ||||
−0.633432 | + | 0.773798i | \(0.718355\pi\) | |||||||
\(648\) | 2.60056 | 0.102159 | ||||||||
\(649\) | −14.2913 | −0.560983 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.29226 | 0.168227 | ||||||||
\(652\) | −13.8936 | −0.544117 | ||||||||
\(653\) | −39.4220 | −1.54270 | −0.771351 | − | 0.636410i | \(-0.780419\pi\) | ||||
−0.771351 | + | 0.636410i | \(0.780419\pi\) | |||||||
\(654\) | −2.87080 | −0.112257 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.93728 | −0.387986 | ||||||||
\(657\) | −10.0678 | −0.392782 | ||||||||
\(658\) | −1.64115 | −0.0639787 | ||||||||
\(659\) | 36.0597 | 1.40469 | 0.702343 | − | 0.711839i | \(-0.252137\pi\) | ||||
0.702343 | + | 0.711839i | \(0.252137\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.8543 | −0.499974 | −0.249987 | − | 0.968249i | \(-0.580426\pi\) | ||||
−0.249987 | + | 0.968249i | \(0.580426\pi\) | |||||||
\(662\) | 4.97289 | 0.193277 | ||||||||
\(663\) | −2.96581 | −0.115183 | ||||||||
\(664\) | 22.9768 | 0.891674 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.29226 | 0.321318 | ||||||||
\(667\) | 23.1835 | 0.897667 | ||||||||
\(668\) | 5.19576 | 0.201030 | ||||||||
\(669\) | −10.8903 | −0.421044 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.06852 | −0.195668 | ||||||||
\(672\) | −25.1603 | −0.970579 | ||||||||
\(673\) | −36.1228 | −1.39243 | −0.696216 | − | 0.717832i | \(-0.745134\pi\) | ||||
−0.696216 | + | 0.717832i | \(0.745134\pi\) | |||||||
\(674\) | −1.28243 | −0.0493975 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.2597 | 0.663835 | ||||||||
\(677\) | 10.6701 | 0.410086 | 0.205043 | − | 0.978753i | \(-0.434267\pi\) | ||||
0.205043 | + | 0.978753i | \(0.434267\pi\) | |||||||
\(678\) | 7.78244 | 0.298883 | ||||||||
\(679\) | 40.0252 | 1.53603 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.7528 | −0.795251 | ||||||||
\(682\) | 1.02923 | 0.0394114 | ||||||||
\(683\) | 35.2542 | 1.34897 | 0.674483 | − | 0.738290i | \(-0.264367\pi\) | ||||
0.674483 | + | 0.738290i | \(0.264367\pi\) | |||||||
\(684\) | 1.60877 | 0.0615128 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 14.4260 | 0.550787 | ||||||||
\(687\) | 15.4796 | 0.590585 | ||||||||
\(688\) | 4.96942 | 0.189457 | ||||||||
\(689\) | 2.35012 | 0.0895325 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.34244 | −0.355403 | −0.177702 | − | 0.984084i | \(-0.556866\pi\) | ||||
−0.177702 | + | 0.984084i | \(0.556866\pi\) | |||||||
\(692\) | 28.4457 | 1.08134 | ||||||||
\(693\) | 5.81440 | 0.220871 | ||||||||
\(694\) | −6.61826 | −0.251226 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 12.1270 | 0.459673 | ||||||||
\(697\) | 36.3702 | 1.37762 | ||||||||
\(698\) | −14.3190 | −0.541982 | ||||||||
\(699\) | −2.20143 | −0.0832657 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.2061 | 0.385479 | 0.192739 | − | 0.981250i | \(-0.438263\pi\) | ||||
0.192739 | + | 0.981250i | \(0.438263\pi\) | |||||||
\(702\) | −0.708059 | −0.0267240 | ||||||||
\(703\) | 12.3411 | 0.465452 | ||||||||
\(704\) | −3.67734 | −0.138595 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.9507 | −0.788491 | ||||||||
\(707\) | −49.2007 | −1.85038 | ||||||||
\(708\) | 15.0097 | 0.564097 | ||||||||
\(709\) | −25.1752 | −0.945473 | −0.472737 | − | 0.881204i | \(-0.656734\pi\) | ||||
−0.472737 | + | 0.881204i | \(0.656734\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.28187 | 0.0855767 | ||||||||
\(712\) | 3.16169 | 0.118489 | ||||||||
\(713\) | −4.97154 | −0.186185 | ||||||||
\(714\) | 10.3789 | 0.388420 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.96523 | 0.110816 | ||||||||
\(717\) | −14.8091 | −0.553057 | ||||||||
\(718\) | 12.4727 | 0.465478 | ||||||||
\(719\) | −0.997764 | −0.0372103 | −0.0186052 | − | 0.999827i | \(-0.505923\pi\) | ||||
−0.0186052 | + | 0.999827i | \(0.505923\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.9007 | −1.00184 | ||||||||
\(722\) | 13.4646 | 0.501099 | ||||||||
\(723\) | −24.0442 | −0.894213 | ||||||||
\(724\) | −2.40715 | −0.0894612 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −6.96350 | −0.258440 | ||||||||
\(727\) | 17.8993 | 0.663847 | 0.331923 | − | 0.943306i | \(-0.392302\pi\) | ||||
0.331923 | + | 0.943306i | \(0.392302\pi\) | |||||||
\(728\) | 10.4022 | 0.385532 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.1879 | −0.672705 | ||||||||
\(732\) | 5.32329 | 0.196754 | ||||||||
\(733\) | −36.4270 | −1.34546 | −0.672731 | − | 0.739887i | \(-0.734879\pi\) | ||||
−0.672731 | + | 0.739887i | \(0.734879\pi\) | |||||||
\(734\) | 8.65271 | 0.319377 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 29.1421 | 1.07419 | ||||||||
\(737\) | 14.6133 | 0.538289 | ||||||||
\(738\) | 8.68303 | 0.319627 | ||||||||
\(739\) | −13.7225 | −0.504789 | −0.252394 | − | 0.967624i | \(-0.581218\pi\) | ||||
−0.252394 | + | 0.967624i | \(0.581218\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.05378 | −0.0387116 | ||||||||
\(742\) | −8.22428 | −0.301923 | ||||||||
\(743\) | 20.5884 | 0.755317 | 0.377658 | − | 0.925945i | \(-0.376729\pi\) | ||||
0.377658 | + | 0.925945i | \(0.376729\pi\) | |||||||
\(744\) | −2.60056 | −0.0953410 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 21.0157 | 0.769441 | ||||||||
\(747\) | 8.83536 | 0.323269 | ||||||||
\(748\) | −6.13347 | −0.224262 | ||||||||
\(749\) | 24.5681 | 0.897698 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.23331 | −0.154476 | −0.0772379 | − | 0.997013i | \(-0.524610\pi\) | ||||
−0.0772379 | + | 0.997013i | \(0.524610\pi\) | |||||||
\(752\) | −0.437582 | −0.0159570 | ||||||||
\(753\) | 4.23395 | 0.154294 | ||||||||
\(754\) | −3.30185 | −0.120246 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −6.10666 | −0.222097 | ||||||||
\(757\) | 43.2109 | 1.57053 | 0.785263 | − | 0.619162i | \(-0.212528\pi\) | ||||
0.785263 | + | 0.619162i | \(0.212528\pi\) | |||||||
\(758\) | 16.3840 | 0.595093 | ||||||||
\(759\) | −6.73456 | −0.244449 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 52.1836 | 1.89165 | 0.945827 | − | 0.324670i | \(-0.105253\pi\) | ||||
0.945827 | + | 0.324670i | \(0.105253\pi\) | |||||||
\(762\) | 15.5489 | 0.563276 | ||||||||
\(763\) | 16.2179 | 0.587126 | ||||||||
\(764\) | −30.0742 | −1.08805 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.7877 | −0.967880 | ||||||||
\(767\) | −9.83166 | −0.355001 | ||||||||
\(768\) | 12.7697 | 0.460786 | ||||||||
\(769\) | −12.6632 | −0.456645 | −0.228323 | − | 0.973586i | \(-0.573324\pi\) | ||||
−0.228323 | + | 0.973586i | \(0.573324\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.3613 | −0.877351 | ||||||||
\(772\) | 2.49434 | 0.0897732 | ||||||||
\(773\) | −29.7529 | −1.07014 | −0.535069 | − | 0.844809i | \(-0.679714\pi\) | ||||
−0.535069 | + | 0.844809i | \(0.679714\pi\) | |||||||
\(774\) | −4.34220 | −0.156077 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −24.2501 | −0.870528 | ||||||||
\(777\) | −46.8450 | −1.68056 | ||||||||
\(778\) | 9.39888 | 0.336966 | ||||||||
\(779\) | 12.9226 | 0.463002 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.79452 | −0.207344 | ||||||||
\(782\) | −12.0214 | −0.429885 | ||||||||
\(783\) | 4.66324 | 0.166651 | ||||||||
\(784\) | 9.93323 | 0.354758 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.49953 | −0.160493 | ||||||||
\(787\) | 8.35273 | 0.297743 | 0.148871 | − | 0.988857i | \(-0.452436\pi\) | ||||
0.148871 | + | 0.988857i | \(0.452436\pi\) | |||||||
\(788\) | −18.3078 | −0.652190 | ||||||||
\(789\) | 8.58093 | 0.305489 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −43.9649 | −1.56321 | ||||||||
\(792\) | −3.52278 | −0.125176 | ||||||||
\(793\) | −3.48688 | −0.123823 | ||||||||
\(794\) | −19.6480 | −0.697283 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.6779 | 0.803798 | ||||||||
\(797\) | 35.2382 | 1.24820 | 0.624101 | − | 0.781344i | \(-0.285466\pi\) | ||||
0.624101 | + | 0.781344i | \(0.285466\pi\) | |||||||
\(798\) | 3.68771 | 0.130544 | ||||||||
\(799\) | 1.60154 | 0.0566583 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.21577 | 0.0429572 | ||||||||
\(802\) | −19.5426 | −0.690072 | ||||||||
\(803\) | 13.6381 | 0.481278 | ||||||||
\(804\) | −15.3479 | −0.541277 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.708059 | 0.0249403 | ||||||||
\(807\) | 13.9684 | 0.491712 | ||||||||
\(808\) | 29.8093 | 1.04869 | ||||||||
\(809\) | 29.4886 | 1.03676 | 0.518382 | − | 0.855149i | \(-0.326535\pi\) | ||||
0.518382 | + | 0.855149i | \(0.326535\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.4610 | 1.59635 | 0.798176 | − | 0.602425i | \(-0.205799\pi\) | ||||
0.798176 | + | 0.602425i | \(0.205799\pi\) | |||||||
\(812\) | −28.4768 | −0.999340 | ||||||||
\(813\) | 17.8507 | 0.626051 | ||||||||
\(814\) | −11.2329 | −0.393713 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.76733 | 0.0968760 | ||||||||
\(817\) | −6.46234 | −0.226089 | ||||||||
\(818\) | 13.8150 | 0.483029 | ||||||||
\(819\) | 4.00000 | 0.139771 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.3261 | −1.40739 | −0.703695 | − | 0.710503i | \(-0.748468\pi\) | ||||
−0.703695 | + | 0.710503i | \(0.748468\pi\) | |||||||
\(822\) | 15.2667 | 0.532486 | ||||||||
\(823\) | 39.9929 | 1.39406 | 0.697032 | − | 0.717040i | \(-0.254503\pi\) | ||||
0.697032 | + | 0.717040i | \(0.254503\pi\) | |||||||
\(824\) | 16.2984 | 0.567781 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 34.4060 | 1.19714 | ||||||||
\(827\) | −5.43802 | −0.189098 | −0.0945492 | − | 0.995520i | \(-0.530141\pi\) | ||||
−0.0945492 | + | 0.995520i | \(0.530141\pi\) | |||||||
\(828\) | 7.07307 | 0.245806 | ||||||||
\(829\) | −2.77873 | −0.0965094 | −0.0482547 | − | 0.998835i | \(-0.515366\pi\) | ||||
−0.0482547 | + | 0.998835i | \(0.515366\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.2156 | 0.735960 | ||||||||
\(832\) | −2.52982 | −0.0877056 | ||||||||
\(833\) | −36.3553 | −1.25964 | ||||||||
\(834\) | 4.94679 | 0.171293 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.17928 | −0.0753718 | ||||||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | 10.9029 | 0.376636 | ||||||||
\(839\) | 49.1509 | 1.69688 | 0.848439 | − | 0.529293i | \(-0.177543\pi\) | ||||
0.848439 | + | 0.529293i | \(0.177543\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.25420 | −0.250145 | ||||||||
\(842\) | −18.1658 | −0.626034 | ||||||||
\(843\) | 12.3013 | 0.423679 | ||||||||
\(844\) | −16.5239 | −0.568777 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.382351 | 0.0131455 | ||||||||
\(847\) | 39.3385 | 1.35169 | ||||||||
\(848\) | −2.19285 | −0.0753026 | ||||||||
\(849\) | 7.30671 | 0.250766 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 54.2585 | 1.85996 | ||||||||
\(852\) | 6.08578 | 0.208495 | ||||||||
\(853\) | −20.7849 | −0.711660 | −0.355830 | − | 0.934551i | \(-0.615802\pi\) | ||||
−0.355830 | + | 0.934551i | \(0.615802\pi\) | |||||||
\(854\) | 12.2024 | 0.417556 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.8851 | −0.508762 | ||||||||
\(857\) | 23.3327 | 0.797031 | 0.398516 | − | 0.917162i | \(-0.369525\pi\) | ||||
0.398516 | + | 0.917162i | \(0.369525\pi\) | |||||||
\(858\) | 0.959154 | 0.0327450 | ||||||||
\(859\) | 29.8998 | 1.02017 | 0.510084 | − | 0.860124i | \(-0.329614\pi\) | ||||
0.510084 | + | 0.860124i | \(0.329614\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −49.0526 | −1.67171 | ||||||||
\(862\) | 19.6441 | 0.669082 | ||||||||
\(863\) | 51.4297 | 1.75069 | 0.875344 | − | 0.483501i | \(-0.160635\pi\) | ||||
0.875344 | + | 0.483501i | \(0.160635\pi\) | |||||||
\(864\) | 5.86178 | 0.199422 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 13.2941 | 0.451752 | ||||||||
\(867\) | 6.87165 | 0.233373 | ||||||||
\(868\) | 6.10666 | 0.207273 | ||||||||
\(869\) | −3.09107 | −0.104858 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.0532 | 0.340640 | ||||||||
\(872\) | −9.82593 | −0.332748 | ||||||||
\(873\) | −9.32497 | −0.315602 | ||||||||
\(874\) | −4.27131 | −0.144479 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −14.3236 | −0.483950 | ||||||||
\(877\) | −30.3170 | −1.02373 | −0.511866 | − | 0.859065i | \(-0.671046\pi\) | ||||
−0.511866 | + | 0.859065i | \(0.671046\pi\) | |||||||
\(878\) | 8.62751 | 0.291164 | ||||||||
\(879\) | 2.40359 | 0.0810712 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.6125 | 1.67149 | 0.835743 | − | 0.549120i | \(-0.185037\pi\) | ||||
0.835743 | + | 0.549120i | \(0.185037\pi\) | |||||||
\(882\) | −8.67949 | −0.292253 | ||||||||
\(883\) | −48.6385 | −1.63682 | −0.818408 | − | 0.574638i | \(-0.805143\pi\) | ||||
−0.818408 | + | 0.574638i | \(0.805143\pi\) | |||||||
\(884\) | −4.21950 | −0.141917 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.9197 | 0.434044 | ||||||||
\(887\) | −10.9891 | −0.368978 | −0.184489 | − | 0.982835i | \(-0.559063\pi\) | ||||
−0.184489 | + | 0.982835i | \(0.559063\pi\) | |||||||
\(888\) | 28.3820 | 0.952439 | ||||||||
\(889\) | −87.8394 | −2.94604 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.35462 | −0.0453816 | ||||||||
\(892\) | −15.4938 | −0.518771 | ||||||||
\(893\) | 0.569040 | 0.0190422 | ||||||||
\(894\) | −0.262911 | −0.00879305 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −41.4675 | −1.38533 | ||||||||
\(897\) | −4.63302 | −0.154692 | ||||||||
\(898\) | 22.0455 | 0.735668 | ||||||||
\(899\) | −4.66324 | −0.155528 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.02575 | 0.267377 | ||||||||
\(902\) | −11.7622 | −0.391640 | ||||||||
\(903\) | 24.5301 | 0.816312 | ||||||||
\(904\) | 26.6371 | 0.885935 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 11.9963 | 0.398551 | ||||||||
\(907\) | −22.6235 | −0.751201 | −0.375600 | − | 0.926782i | \(-0.622563\pi\) | ||||
−0.375600 | + | 0.926782i | \(0.622563\pi\) | |||||||
\(908\) | −29.5254 | −0.979834 | ||||||||
\(909\) | 11.4627 | 0.380192 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.5226 | 0.414894 | 0.207447 | − | 0.978246i | \(-0.433485\pi\) | ||||
0.207447 | + | 0.978246i | \(0.433485\pi\) | |||||||
\(912\) | 0.983258 | 0.0325589 | ||||||||
\(913\) | −11.9686 | −0.396103 | ||||||||
\(914\) | −5.99082 | −0.198159 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 22.0231 | 0.727664 | ||||||||
\(917\) | 25.4190 | 0.839408 | ||||||||
\(918\) | −2.41805 | −0.0798075 | ||||||||
\(919\) | 4.33540 | 0.143012 | 0.0715059 | − | 0.997440i | \(-0.477220\pi\) | ||||
0.0715059 | + | 0.997440i | \(0.477220\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.1451 | −0.894462 | ||||||||
\(922\) | −15.8278 | −0.521261 | ||||||||
\(923\) | −3.98633 | −0.131211 | ||||||||
\(924\) | 8.27223 | 0.272136 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 25.0842 | 0.824317 | ||||||||
\(927\) | 6.26727 | 0.205844 | ||||||||
\(928\) | 27.3349 | 0.897312 | ||||||||
\(929\) | 13.4205 | 0.440312 | 0.220156 | − | 0.975465i | \(-0.429343\pi\) | ||||
0.220156 | + | 0.975465i | \(0.429343\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.9174 | −0.423350 | ||||||||
\(932\) | −3.13200 | −0.102592 | ||||||||
\(933\) | 28.3041 | 0.926634 | ||||||||
\(934\) | −7.58434 | −0.248167 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.42348 | −0.0792141 | ||||||||
\(937\) | 29.3362 | 0.958372 | 0.479186 | − | 0.877713i | \(-0.340932\pi\) | ||||
0.479186 | + | 0.877713i | \(0.340932\pi\) | |||||||
\(938\) | −35.1813 | −1.14871 | ||||||||
\(939\) | −18.1802 | −0.593288 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.99467 | −0.325817 | −0.162908 | − | 0.986641i | \(-0.552088\pi\) | ||||
−0.162908 | + | 0.986641i | \(0.552088\pi\) | |||||||
\(942\) | −15.0647 | −0.490834 | ||||||||
\(943\) | 56.8155 | 1.85017 | ||||||||
\(944\) | 9.17370 | 0.298579 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.88205 | 0.191242 | ||||||||
\(947\) | −58.8338 | −1.91184 | −0.955921 | − | 0.293624i | \(-0.905139\pi\) | ||||
−0.955921 | + | 0.293624i | \(0.905139\pi\) | |||||||
\(948\) | 3.24645 | 0.105440 | ||||||||
\(949\) | 9.38229 | 0.304562 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.28110 | −0.300960 | ||||||||
\(952\) | 35.5240 | 1.15134 | ||||||||
\(953\) | 53.4153 | 1.73029 | 0.865146 | − | 0.501520i | \(-0.167226\pi\) | ||||
0.865146 | + | 0.501520i | \(0.167226\pi\) | |||||||
\(954\) | 1.91607 | 0.0620351 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −21.0692 | −0.681426 | ||||||||
\(957\) | −6.31694 | −0.204198 | ||||||||
\(958\) | 12.5940 | 0.406893 | ||||||||
\(959\) | −86.2451 | −2.78500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −7.72764 | −0.249149 | ||||||||
\(963\) | −5.72381 | −0.184447 | ||||||||
\(964\) | −34.2080 | −1.10177 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 16.2133 | 0.521655 | ||||||||
\(967\) | −42.0597 | −1.35255 | −0.676275 | − | 0.736649i | \(-0.736407\pi\) | ||||
−0.676275 | + | 0.736649i | \(0.736407\pi\) | |||||||
\(968\) | −23.8341 | −0.766056 | ||||||||
\(969\) | −3.59869 | −0.115607 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.2778 | −0.907479 | −0.453740 | − | 0.891134i | \(-0.649910\pi\) | ||||
−0.453740 | + | 0.891134i | \(0.649910\pi\) | |||||||
\(972\) | 1.42271 | 0.0456336 | ||||||||
\(973\) | −27.9456 | −0.895896 | ||||||||
\(974\) | 23.8413 | 0.763923 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.25352 | 0.104143 | ||||||||
\(977\) | −28.3622 | −0.907386 | −0.453693 | − | 0.891158i | \(-0.649894\pi\) | ||||
−0.453693 | + | 0.891158i | \(0.649894\pi\) | |||||||
\(978\) | 7.41983 | 0.237260 | ||||||||
\(979\) | −1.64692 | −0.0526357 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.77840 | −0.120635 | ||||||||
\(982\) | −4.61209 | −0.147178 | ||||||||
\(983\) | −38.4019 | −1.22483 | −0.612416 | − | 0.790536i | \(-0.709802\pi\) | ||||
−0.612416 | + | 0.790536i | \(0.709802\pi\) | |||||||
\(984\) | 29.7195 | 0.947424 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −11.2759 | −0.359099 | ||||||||
\(987\) | −2.16000 | −0.0687535 | ||||||||
\(988\) | −1.49923 | −0.0476968 | ||||||||
\(989\) | −28.4122 | −0.903455 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.5490 | −0.938655 | −0.469327 | − | 0.883024i | \(-0.655504\pi\) | ||||
−0.469327 | + | 0.883024i | \(0.655504\pi\) | |||||||
\(992\) | −5.86178 | −0.186112 | ||||||||
\(993\) | 6.54506 | 0.207701 | ||||||||
\(994\) | 13.9502 | 0.442473 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 12.5702 | 0.398302 | ||||||||
\(997\) | 31.7648 | 1.00600 | 0.503001 | − | 0.864286i | \(-0.332229\pi\) | ||||
0.503001 | + | 0.864286i | \(0.332229\pi\) | |||||||
\(998\) | 1.79911 | 0.0569499 | ||||||||
\(999\) | 10.9138 | 0.345298 |
(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 | 2325.2.a.ba.1.3 | yes | 6 | |
3.2 | odd | 2 | 6975.2.a.bz.1.4 | 6 | |||
5.2 | odd | 4 | 2325.2.c.q.1024.6 | 12 | |||
5.3 | odd | 4 | 2325.2.c.q.1024.7 | 12 | |||
5.4 | even | 2 | 2325.2.a.z.1.4 | ✓ | 6 | ||
15.14 | odd | 2 | 6975.2.a.cd.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2325.2.a.z.1.4 | ✓ | 6 | 5.4 | even | 2 | ||
2325.2.a.ba.1.3 | yes | 6 | 1.1 | even | 1 | trivial | |
2325.2.c.q.1024.6 | 12 | 5.2 | odd | 4 | |||
2325.2.c.q.1024.7 | 12 | 5.3 | odd | 4 | |||
6975.2.a.bz.1.4 | 6 | 3.2 | odd | 2 | |||
6975.2.a.cd.1.3 | 6 | 15.14 | odd | 2 |