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: | \( x^{19} - 4 x^{18} - 22 x^{17} + 101 x^{16} + 178 x^{15} - 1035 x^{14} - 583 x^{13} + 5572 x^{12} + 21 x^{11} - 17032 x^{10} + 4985 x^{9} + 29792 x^{8} - 13249 x^{7} - 28600 x^{6} + \cdots + 210 \) |
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 | 1.11 | ||
Root | \(-0.249163\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.249163 | 0.176185 | 0.0880923 | − | 0.996112i | \(-0.471923\pi\) | ||||
0.0880923 | + | 0.996112i | \(0.471923\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.93792 | −0.968959 | ||||||||
\(5\) | −0.989651 | −0.442585 | −0.221293 | − | 0.975207i | \(-0.571028\pi\) | ||||
−0.221293 | + | 0.975207i | \(0.571028\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −0.981182 | −0.346900 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.246584 | −0.0779767 | ||||||||
\(11\) | 2.01884 | 0.608704 | 0.304352 | − | 0.952560i | \(-0.401560\pi\) | ||||
0.304352 | + | 0.952560i | \(0.401560\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.18024 | 1.15939 | 0.579695 | − | 0.814833i | \(-0.303172\pi\) | ||||
0.579695 | + | 0.814833i | \(0.303172\pi\) | |||||||
\(14\) | 0.249163 | 0.0665915 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.63136 | 0.907841 | ||||||||
\(17\) | 7.51203 | 1.82193 | 0.910967 | − | 0.412479i | \(-0.135337\pi\) | ||||
0.910967 | + | 0.412479i | \(0.135337\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.64620 | 1.75416 | 0.877080 | − | 0.480345i | \(-0.159488\pi\) | ||||
0.877080 | + | 0.480345i | \(0.159488\pi\) | |||||||
\(20\) | 1.91786 | 0.428847 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.503020 | 0.107244 | ||||||||
\(23\) | 2.82780 | 0.589637 | 0.294819 | − | 0.955553i | \(-0.404741\pi\) | ||||
0.294819 | + | 0.955553i | \(0.404741\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.02059 | −0.804118 | ||||||||
\(26\) | 1.04156 | 0.204267 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.93792 | −0.366232 | ||||||||
\(29\) | −5.08664 | −0.944566 | −0.472283 | − | 0.881447i | \(-0.656570\pi\) | ||||
−0.472283 | + | 0.881447i | \(0.656570\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.14394 | 0.205457 | 0.102729 | − | 0.994709i | \(-0.467243\pi\) | ||||
0.102729 | + | 0.994709i | \(0.467243\pi\) | |||||||
\(32\) | 2.86716 | 0.506848 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.87172 | 0.320997 | ||||||||
\(35\) | −0.989651 | −0.167282 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.6080 | 1.74394 | 0.871970 | − | 0.489559i | \(-0.162842\pi\) | ||||
0.871970 | + | 0.489559i | \(0.162842\pi\) | |||||||
\(38\) | 1.90515 | 0.309056 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.971028 | 0.153533 | ||||||||
\(41\) | −8.51782 | −1.33026 | −0.665130 | − | 0.746728i | \(-0.731624\pi\) | ||||
−0.665130 | + | 0.746728i | \(0.731624\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.46779 | −0.376335 | −0.188167 | − | 0.982137i | \(-0.560255\pi\) | ||||
−0.188167 | + | 0.982137i | \(0.560255\pi\) | |||||||
\(44\) | −3.91235 | −0.589810 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.704583 | 0.103885 | ||||||||
\(47\) | 0.347815 | 0.0507340 | 0.0253670 | − | 0.999678i | \(-0.491925\pi\) | ||||
0.0253670 | + | 0.999678i | \(0.491925\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00178 | −0.141673 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.10096 | −1.12340 | ||||||||
\(53\) | 4.33912 | 0.596024 | 0.298012 | − | 0.954562i | \(-0.403676\pi\) | ||||
0.298012 | + | 0.954562i | \(0.403676\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.99795 | −0.269404 | ||||||||
\(56\) | −0.981182 | −0.131116 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.26740 | −0.166418 | ||||||||
\(59\) | 9.40635 | 1.22460 | 0.612301 | − | 0.790625i | \(-0.290244\pi\) | ||||
0.612301 | + | 0.790625i | \(0.290244\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.40599 | −0.436092 | −0.218046 | − | 0.975938i | \(-0.569968\pi\) | ||||
−0.218046 | + | 0.975938i | \(0.569968\pi\) | |||||||
\(62\) | 0.285027 | 0.0361984 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.54833 | −0.818542 | ||||||||
\(65\) | −4.13698 | −0.513129 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.65641 | 0.691040 | 0.345520 | − | 0.938411i | \(-0.387703\pi\) | ||||
0.345520 | + | 0.938411i | \(0.387703\pi\) | |||||||
\(68\) | −14.5577 | −1.76538 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.246584 | −0.0294724 | ||||||||
\(71\) | −4.93333 | −0.585479 | −0.292740 | − | 0.956192i | \(-0.594567\pi\) | ||||
−0.292740 | + | 0.956192i | \(0.594567\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.89559 | 0.221862 | 0.110931 | − | 0.993828i | \(-0.464617\pi\) | ||||
0.110931 | + | 0.993828i | \(0.464617\pi\) | |||||||
\(74\) | 2.64311 | 0.307255 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.8177 | −1.69971 | ||||||||
\(77\) | 2.01884 | 0.230069 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.24436 | 0.927563 | 0.463782 | − | 0.885950i | \(-0.346492\pi\) | ||||
0.463782 | + | 0.885950i | \(0.346492\pi\) | |||||||
\(80\) | −3.59378 | −0.401797 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.12232 | −0.234371 | ||||||||
\(83\) | −9.21069 | −1.01100 | −0.505502 | − | 0.862825i | \(-0.668693\pi\) | ||||
−0.505502 | + | 0.862825i | \(0.668693\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.43428 | −0.806361 | ||||||||
\(86\) | −0.614881 | −0.0663044 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.98085 | −0.211160 | ||||||||
\(89\) | 1.13183 | 0.119974 | 0.0599869 | − | 0.998199i | \(-0.480894\pi\) | ||||
0.0599869 | + | 0.998199i | \(0.480894\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.18024 | 0.438208 | ||||||||
\(92\) | −5.48005 | −0.571334 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.0866624 | 0.00893855 | ||||||||
\(95\) | −7.56707 | −0.776365 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.6987 | 1.89857 | 0.949285 | − | 0.314418i | \(-0.101809\pi\) | ||||
0.949285 | + | 0.314418i | \(0.101809\pi\) | |||||||
\(98\) | 0.249163 | 0.0251692 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.79158 | 0.779158 | ||||||||
\(101\) | −4.10828 | −0.408790 | −0.204395 | − | 0.978889i | \(-0.565523\pi\) | ||||
−0.204395 | + | 0.978889i | \(0.565523\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.05224 | −0.891944 | −0.445972 | − | 0.895047i | \(-0.647142\pi\) | ||||
−0.445972 | + | 0.895047i | \(0.647142\pi\) | |||||||
\(104\) | −4.10158 | −0.402193 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.08115 | 0.105010 | ||||||||
\(107\) | −13.8515 | −1.33907 | −0.669535 | − | 0.742780i | \(-0.733507\pi\) | ||||
−0.669535 | + | 0.742780i | \(0.733507\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.27191 | −0.888088 | −0.444044 | − | 0.896005i | \(-0.646457\pi\) | ||||
−0.444044 | + | 0.896005i | \(0.646457\pi\) | |||||||
\(110\) | −0.497815 | −0.0474648 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.63136 | 0.343131 | ||||||||
\(113\) | −2.81376 | −0.264696 | −0.132348 | − | 0.991203i | \(-0.542252\pi\) | ||||
−0.132348 | + | 0.991203i | \(0.542252\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.79854 | −0.260965 | ||||||||
\(116\) | 9.85750 | 0.915246 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.34371 | 0.215756 | ||||||||
\(119\) | 7.51203 | 0.688626 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.92427 | −0.629479 | ||||||||
\(122\) | −0.848645 | −0.0768327 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.21686 | −0.199080 | ||||||||
\(125\) | 8.92724 | 0.798476 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | −7.36593 | −0.651062 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.03078 | −0.0904055 | ||||||||
\(131\) | 0.239985 | 0.0209676 | 0.0104838 | − | 0.999945i | \(-0.496663\pi\) | ||||
0.0104838 | + | 0.999945i | \(0.496663\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.64620 | 0.663010 | ||||||||
\(134\) | 1.40937 | 0.121751 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.37067 | −0.632029 | ||||||||
\(137\) | −15.1732 | −1.29633 | −0.648165 | − | 0.761500i | \(-0.724463\pi\) | ||||
−0.648165 | + | 0.761500i | \(0.724463\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.07164 | 0.0908953 | 0.0454477 | − | 0.998967i | \(-0.485529\pi\) | ||||
0.0454477 | + | 0.998967i | \(0.485529\pi\) | |||||||
\(140\) | 1.91786 | 0.162089 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.22920 | −0.103152 | ||||||||
\(143\) | 8.43925 | 0.705726 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.03400 | 0.418051 | ||||||||
\(146\) | 0.472311 | 0.0390887 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −20.5574 | −1.68981 | ||||||||
\(149\) | −7.00252 | −0.573669 | −0.286834 | − | 0.957980i | \(-0.592603\pi\) | ||||
−0.286834 | + | 0.957980i | \(0.592603\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.72548 | −0.303175 | −0.151587 | − | 0.988444i | \(-0.548439\pi\) | ||||
−0.151587 | + | 0.988444i | \(0.548439\pi\) | |||||||
\(152\) | −7.50232 | −0.608518 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.503020 | 0.0405345 | ||||||||
\(155\) | −1.13210 | −0.0909325 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.6725 | 1.49023 | 0.745113 | − | 0.666938i | \(-0.232396\pi\) | ||||
0.745113 | + | 0.666938i | \(0.232396\pi\) | |||||||
\(158\) | 2.05419 | 0.163422 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.83749 | −0.224323 | ||||||||
\(161\) | 2.82780 | 0.222862 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.99112 | −0.234282 | −0.117141 | − | 0.993115i | \(-0.537373\pi\) | ||||
−0.117141 | + | 0.993115i | \(0.537373\pi\) | |||||||
\(164\) | 16.5068 | 1.28897 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.29496 | −0.178123 | ||||||||
\(167\) | 1.05587 | 0.0817054 | 0.0408527 | − | 0.999165i | \(-0.486993\pi\) | ||||
0.0408527 | + | 0.999165i | \(0.486993\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.47442 | 0.344186 | ||||||||
\(170\) | −1.85235 | −0.142068 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.78238 | 0.364653 | ||||||||
\(173\) | 14.4208 | 1.09639 | 0.548197 | − | 0.836349i | \(-0.315314\pi\) | ||||
0.548197 | + | 0.836349i | \(0.315314\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.02059 | −0.303928 | ||||||||
\(176\) | 7.33115 | 0.552606 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.282010 | 0.0211375 | ||||||||
\(179\) | −22.6413 | −1.69229 | −0.846145 | − | 0.532952i | \(-0.821083\pi\) | ||||
−0.846145 | + | 0.532952i | \(0.821083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.0630 | 1.63993 | 0.819964 | − | 0.572415i | \(-0.193993\pi\) | ||||
0.819964 | + | 0.572415i | \(0.193993\pi\) | |||||||
\(182\) | 1.04156 | 0.0772056 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.77459 | −0.204545 | ||||||||
\(185\) | −10.4982 | −0.771842 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.1656 | 1.10902 | ||||||||
\(188\) | −0.674036 | −0.0491592 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.88543 | −0.136784 | ||||||||
\(191\) | −23.2667 | −1.68352 | −0.841760 | − | 0.539851i | \(-0.818480\pi\) | ||||
−0.841760 | + | 0.539851i | \(0.818480\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.1716 | 1.73991 | 0.869956 | − | 0.493130i | \(-0.164147\pi\) | ||||
0.869956 | + | 0.493130i | \(0.164147\pi\) | |||||||
\(194\) | 4.65903 | 0.334499 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.93792 | −0.138423 | ||||||||
\(197\) | −1.83988 | −0.131086 | −0.0655430 | − | 0.997850i | \(-0.520878\pi\) | ||||
−0.0655430 | + | 0.997850i | \(0.520878\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.75745 | 0.620799 | 0.310400 | − | 0.950606i | \(-0.399537\pi\) | ||||
0.310400 | + | 0.950606i | \(0.399537\pi\) | |||||||
\(200\) | 3.94493 | 0.278949 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.02363 | −0.0720224 | ||||||||
\(203\) | −5.08664 | −0.357012 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.42967 | 0.588753 | ||||||||
\(206\) | −2.25548 | −0.157147 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 15.1800 | 1.05254 | ||||||||
\(209\) | 15.4365 | 1.06776 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.51979 | 0.104626 | 0.0523132 | − | 0.998631i | \(-0.483341\pi\) | ||||
0.0523132 | + | 0.998631i | \(0.483341\pi\) | |||||||
\(212\) | −8.40886 | −0.577523 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.45126 | −0.235924 | ||||||||
\(215\) | 2.44225 | 0.166560 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.14394 | 0.0776556 | ||||||||
\(218\) | −2.31021 | −0.156467 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.87186 | 0.261041 | ||||||||
\(221\) | 31.4021 | 2.11233 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.8448 | 1.12801 | 0.564005 | − | 0.825771i | \(-0.309260\pi\) | ||||
0.564005 | + | 0.825771i | \(0.309260\pi\) | |||||||
\(224\) | 2.86716 | 0.191570 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.701084 | −0.0466354 | ||||||||
\(227\) | 12.6662 | 0.840684 | 0.420342 | − | 0.907366i | \(-0.361910\pi\) | ||||
0.420342 | + | 0.907366i | \(0.361910\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.1710 | −1.13469 | −0.567347 | − | 0.823479i | \(-0.692030\pi\) | ||||
−0.567347 | + | 0.823479i | \(0.692030\pi\) | |||||||
\(230\) | −0.697291 | −0.0459780 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.99092 | 0.327670 | ||||||||
\(233\) | 10.5646 | 0.692110 | 0.346055 | − | 0.938214i | \(-0.387521\pi\) | ||||
0.346055 | + | 0.938214i | \(0.387521\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.344215 | −0.0224541 | ||||||||
\(236\) | −18.2287 | −1.18659 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.87172 | 0.121325 | ||||||||
\(239\) | 26.4159 | 1.70870 | 0.854352 | − | 0.519695i | \(-0.173955\pi\) | ||||
0.854352 | + | 0.519695i | \(0.173955\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.0042 | −0.773261 | −0.386631 | − | 0.922235i | \(-0.626361\pi\) | ||||
−0.386631 | + | 0.922235i | \(0.626361\pi\) | |||||||
\(242\) | −1.72527 | −0.110905 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.60052 | 0.422555 | ||||||||
\(245\) | −0.989651 | −0.0632265 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 31.9630 | 2.03376 | ||||||||
\(248\) | −1.12241 | −0.0712732 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.22433 | 0.140679 | ||||||||
\(251\) | 26.9138 | 1.69878 | 0.849391 | − | 0.527764i | \(-0.176970\pi\) | ||||
0.849391 | + | 0.527764i | \(0.176970\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.70889 | 0.358915 | ||||||||
\(254\) | 0.249163 | 0.0156339 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.2614 | 0.703835 | ||||||||
\(257\) | 15.2607 | 0.951934 | 0.475967 | − | 0.879463i | \(-0.342098\pi\) | ||||
0.475967 | + | 0.879463i | \(0.342098\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.6080 | 0.659147 | ||||||||
\(260\) | 8.01713 | 0.497201 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.0597953 | 0.00369416 | ||||||||
\(263\) | −8.60088 | −0.530353 | −0.265176 | − | 0.964200i | \(-0.585430\pi\) | ||||
−0.265176 | + | 0.964200i | \(0.585430\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.29422 | −0.263792 | ||||||||
\(266\) | 1.90515 | 0.116812 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.9617 | −0.669590 | ||||||||
\(269\) | 11.7574 | 0.716862 | 0.358431 | − | 0.933556i | \(-0.383312\pi\) | ||||
0.358431 | + | 0.933556i | \(0.383312\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.0495 | −0.914191 | −0.457095 | − | 0.889418i | \(-0.651110\pi\) | ||||
−0.457095 | + | 0.889418i | \(0.651110\pi\) | |||||||
\(272\) | 27.2789 | 1.65403 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.78059 | −0.228393 | ||||||||
\(275\) | −8.11694 | −0.489470 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.7389 | −1.30616 | −0.653082 | − | 0.757287i | \(-0.726524\pi\) | ||||
−0.653082 | + | 0.757287i | \(0.726524\pi\) | |||||||
\(278\) | 0.267013 | 0.0160144 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.971028 | 0.0580300 | ||||||||
\(281\) | −7.64133 | −0.455844 | −0.227922 | − | 0.973679i | \(-0.573193\pi\) | ||||
−0.227922 | + | 0.973679i | \(0.573193\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.9456 | 1.06675 | 0.533377 | − | 0.845878i | \(-0.320923\pi\) | ||||
0.533377 | + | 0.845878i | \(0.320923\pi\) | |||||||
\(284\) | 9.56040 | 0.567305 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.10275 | 0.124338 | ||||||||
\(287\) | −8.51782 | −0.502791 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 39.4305 | 2.31944 | ||||||||
\(290\) | 1.25429 | 0.0736542 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.67350 | −0.214976 | ||||||||
\(293\) | 13.9233 | 0.813407 | 0.406704 | − | 0.913560i | \(-0.366678\pi\) | ||||
0.406704 | + | 0.913560i | \(0.366678\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.30901 | −0.541991 | ||||||||
\(296\) | −10.4084 | −0.604973 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.74477 | −0.101072 | ||||||||
\(299\) | 11.8209 | 0.683620 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.46779 | −0.142241 | ||||||||
\(302\) | −0.928250 | −0.0534148 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 27.7661 | 1.59250 | ||||||||
\(305\) | 3.37074 | 0.193008 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.1985 | 0.582057 | 0.291029 | − | 0.956714i | \(-0.406003\pi\) | ||||
0.291029 | + | 0.956714i | \(0.406003\pi\) | |||||||
\(308\) | −3.91235 | −0.222927 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.282077 | −0.0160209 | ||||||||
\(311\) | −17.8032 | −1.00953 | −0.504765 | − | 0.863257i | \(-0.668421\pi\) | ||||
−0.504765 | + | 0.863257i | \(0.668421\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.9298 | −1.40912 | −0.704559 | − | 0.709646i | \(-0.748855\pi\) | ||||
−0.704559 | + | 0.709646i | \(0.748855\pi\) | |||||||
\(314\) | 4.65248 | 0.262555 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.9769 | −0.898771 | ||||||||
\(317\) | 11.8136 | 0.663518 | 0.331759 | − | 0.943364i | \(-0.392358\pi\) | ||||
0.331759 | + | 0.943364i | \(0.392358\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.2691 | −0.574961 | ||||||||
\(320\) | 6.48057 | 0.362275 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.704583 | 0.0392648 | ||||||||
\(323\) | 57.4385 | 3.19596 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.8070 | −0.932287 | ||||||||
\(326\) | −0.745275 | −0.0412770 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.35753 | 0.461467 | ||||||||
\(329\) | 0.347815 | 0.0191756 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.4087 | −0.901905 | −0.450952 | − | 0.892548i | \(-0.648916\pi\) | ||||
−0.450952 | + | 0.892548i | \(0.648916\pi\) | |||||||
\(332\) | 17.8496 | 0.979622 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.263083 | 0.0143952 | ||||||||
\(335\) | −5.59787 | −0.305844 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.8302 | 1.84285 | 0.921424 | − | 0.388559i | \(-0.127027\pi\) | ||||
0.921424 | + | 0.388559i | \(0.127027\pi\) | |||||||
\(338\) | 1.11486 | 0.0606403 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 14.4070 | 0.781331 | ||||||||
\(341\) | 2.30943 | 0.125063 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 2.42135 | 0.130551 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.59313 | 0.193168 | ||||||||
\(347\) | 0.903135 | 0.0484828 | 0.0242414 | − | 0.999706i | \(-0.492283\pi\) | ||||
0.0242414 | + | 0.999706i | \(0.492283\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.6244 | −0.836356 | −0.418178 | − | 0.908365i | \(-0.637331\pi\) | ||||
−0.418178 | + | 0.908365i | \(0.637331\pi\) | |||||||
\(350\) | −1.00178 | −0.0535474 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.78836 | 0.308520 | ||||||||
\(353\) | −2.70320 | −0.143877 | −0.0719384 | − | 0.997409i | \(-0.522919\pi\) | ||||
−0.0719384 | + | 0.997409i | \(0.522919\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.88228 | 0.259124 | ||||||||
\(356\) | −2.19339 | −0.116250 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.64137 | −0.298156 | ||||||||
\(359\) | 26.8365 | 1.41638 | 0.708188 | − | 0.706024i | \(-0.249513\pi\) | ||||
0.708188 | + | 0.706024i | \(0.249513\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.4644 | 2.07708 | ||||||||
\(362\) | 5.49727 | 0.288930 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.10096 | −0.424606 | ||||||||
\(365\) | −1.87598 | −0.0981931 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.8366 | −1.55746 | −0.778729 | − | 0.627361i | \(-0.784135\pi\) | ||||
−0.778729 | + | 0.627361i | \(0.784135\pi\) | |||||||
\(368\) | 10.2688 | 0.535297 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.61576 | −0.135987 | ||||||||
\(371\) | 4.33912 | 0.225276 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.76444 | −0.194915 | −0.0974577 | − | 0.995240i | \(-0.531071\pi\) | ||||
−0.0974577 | + | 0.995240i | \(0.531071\pi\) | |||||||
\(374\) | 3.77870 | 0.195392 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.341270 | −0.0175996 | ||||||||
\(377\) | −21.2634 | −1.09512 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.4272 | −1.15201 | −0.576004 | − | 0.817447i | \(-0.695389\pi\) | ||||
−0.576004 | + | 0.817447i | \(0.695389\pi\) | |||||||
\(380\) | 14.6644 | 0.752266 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.79720 | −0.296610 | ||||||||
\(383\) | 7.38438 | 0.377324 | 0.188662 | − | 0.982042i | \(-0.439585\pi\) | ||||
0.188662 | + | 0.982042i | \(0.439585\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.99795 | −0.101825 | ||||||||
\(386\) | 6.02267 | 0.306546 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −36.2366 | −1.83964 | ||||||||
\(389\) | −31.3727 | −1.59066 | −0.795328 | − | 0.606179i | \(-0.792702\pi\) | ||||
−0.795328 | + | 0.606179i | \(0.792702\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.2425 | 1.07428 | ||||||||
\(392\) | −0.981182 | −0.0495572 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.458429 | −0.0230953 | ||||||||
\(395\) | −8.15904 | −0.410526 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.82272 | −0.242045 | −0.121023 | − | 0.992650i | \(-0.538617\pi\) | ||||
−0.121023 | + | 0.992650i | \(0.538617\pi\) | |||||||
\(398\) | 2.18203 | 0.109375 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14.6002 | −0.730011 | ||||||||
\(401\) | −9.35881 | −0.467357 | −0.233678 | − | 0.972314i | \(-0.575076\pi\) | ||||
−0.233678 | + | 0.972314i | \(0.575076\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.78194 | 0.238205 | ||||||||
\(404\) | 7.96152 | 0.396100 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.26740 | −0.0629001 | ||||||||
\(407\) | 21.4158 | 1.06154 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.09685 | −0.350917 | −0.175458 | − | 0.984487i | \(-0.556141\pi\) | ||||
−0.175458 | + | 0.984487i | \(0.556141\pi\) | |||||||
\(410\) | 2.10036 | 0.103729 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 17.5425 | 0.864257 | ||||||||
\(413\) | 9.40635 | 0.462856 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.11537 | 0.447456 | ||||||||
\(416\) | 11.9854 | 0.587634 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.84620 | 0.188124 | ||||||||
\(419\) | −17.5160 | −0.855715 | −0.427857 | − | 0.903846i | \(-0.640731\pi\) | ||||
−0.427857 | + | 0.903846i | \(0.640731\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.4704 | 0.656507 | 0.328254 | − | 0.944590i | \(-0.393540\pi\) | ||||
0.328254 | + | 0.944590i | \(0.393540\pi\) | |||||||
\(422\) | 0.378674 | 0.0184336 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.25747 | −0.206761 | ||||||||
\(425\) | −30.2028 | −1.46505 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.40599 | −0.164827 | ||||||||
\(428\) | 26.8430 | 1.29750 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.608518 | 0.0293453 | ||||||||
\(431\) | −10.2490 | −0.493677 | −0.246839 | − | 0.969057i | \(-0.579392\pi\) | ||||
−0.246839 | + | 0.969057i | \(0.579392\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.8600 | 0.666071 | 0.333035 | − | 0.942914i | \(-0.391927\pi\) | ||||
0.333035 | + | 0.942914i | \(0.391927\pi\) | |||||||
\(434\) | 0.285027 | 0.0136817 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.9682 | 0.860521 | ||||||||
\(437\) | 21.6219 | 1.03432 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.2215 | −1.39467 | −0.697333 | − | 0.716748i | \(-0.745630\pi\) | ||||
−0.697333 | + | 0.716748i | \(0.745630\pi\) | |||||||
\(440\) | 1.96035 | 0.0934562 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.82423 | 0.372160 | ||||||||
\(443\) | 32.0230 | 1.52146 | 0.760729 | − | 0.649070i | \(-0.224842\pi\) | ||||
0.760729 | + | 0.649070i | \(0.224842\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.12012 | −0.0530986 | ||||||||
\(446\) | 4.19709 | 0.198738 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.54833 | −0.309380 | ||||||||
\(449\) | −27.7086 | −1.30765 | −0.653824 | − | 0.756647i | \(-0.726836\pi\) | ||||
−0.653824 | + | 0.756647i | \(0.726836\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.1961 | −0.809735 | ||||||||
\(452\) | 5.45284 | 0.256480 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.15594 | 0.148116 | ||||||||
\(455\) | −4.13698 | −0.193945 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.9872 | −0.888184 | −0.444092 | − | 0.895981i | \(-0.646474\pi\) | ||||
−0.444092 | + | 0.895981i | \(0.646474\pi\) | |||||||
\(458\) | −4.27838 | −0.199916 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.42333 | 0.252864 | ||||||||
\(461\) | −20.9874 | −0.977481 | −0.488740 | − | 0.872429i | \(-0.662544\pi\) | ||||
−0.488740 | + | 0.872429i | \(0.662544\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.5933 | −1.00353 | −0.501763 | − | 0.865005i | \(-0.667315\pi\) | ||||
−0.501763 | + | 0.865005i | \(0.667315\pi\) | |||||||
\(464\) | −18.4714 | −0.857515 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.63231 | 0.121939 | ||||||||
\(467\) | −24.6377 | −1.14010 | −0.570048 | − | 0.821611i | \(-0.693075\pi\) | ||||
−0.570048 | + | 0.821611i | \(0.693075\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.65641 | 0.261189 | ||||||||
\(470\) | −0.0857656 | −0.00395607 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.22934 | −0.424815 | ||||||||
\(473\) | −4.98209 | −0.229077 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −30.7423 | −1.41055 | ||||||||
\(476\) | −14.5577 | −0.667251 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.58186 | 0.301047 | ||||||||
\(479\) | 20.7967 | 0.950226 | 0.475113 | − | 0.879925i | \(-0.342407\pi\) | ||||
0.475113 | + | 0.879925i | \(0.342407\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 44.3439 | 2.02191 | ||||||||
\(482\) | −2.99101 | −0.136237 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13.4187 | 0.609939 | ||||||||
\(485\) | −18.5052 | −0.840279 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.7043 | 0.711628 | 0.355814 | − | 0.934557i | \(-0.384204\pi\) | ||||
0.355814 | + | 0.934557i | \(0.384204\pi\) | |||||||
\(488\) | 3.34189 | 0.151280 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.246584 | −0.0111395 | ||||||||
\(491\) | 36.7734 | 1.65956 | 0.829781 | − | 0.558089i | \(-0.188465\pi\) | ||||
0.829781 | + | 0.558089i | \(0.188465\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −38.2110 | −1.72094 | ||||||||
\(494\) | 7.96398 | 0.358316 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.15406 | 0.186523 | ||||||||
\(497\) | −4.93333 | −0.221290 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.7782 | −0.616796 | −0.308398 | − | 0.951257i | \(-0.599793\pi\) | ||||
−0.308398 | + | 0.951257i | \(0.599793\pi\) | |||||||
\(500\) | −17.3003 | −0.773691 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.70590 | 0.299299 | ||||||||
\(503\) | −4.77246 | −0.212793 | −0.106397 | − | 0.994324i | \(-0.533931\pi\) | ||||
−0.106397 | + | 0.994324i | \(0.533931\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.06577 | 0.180924 | ||||||||
\(506\) | 1.42244 | 0.0632353 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.93792 | −0.0859812 | ||||||||
\(509\) | 40.0552 | 1.77541 | 0.887707 | − | 0.460409i | \(-0.152297\pi\) | ||||
0.887707 | + | 0.460409i | \(0.152297\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.89559 | 0.0838561 | ||||||||
\(512\) | 17.5378 | 0.775067 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.80239 | 0.167716 | ||||||||
\(515\) | 8.95856 | 0.394761 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.702184 | 0.0308820 | ||||||||
\(518\) | 2.64311 | 0.116132 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.05913 | 0.178005 | ||||||||
\(521\) | −30.7739 | −1.34823 | −0.674114 | − | 0.738627i | \(-0.735474\pi\) | ||||
−0.674114 | + | 0.738627i | \(0.735474\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.3386 | 1.23916 | 0.619580 | − | 0.784933i | \(-0.287303\pi\) | ||||
0.619580 | + | 0.784933i | \(0.287303\pi\) | |||||||
\(524\) | −0.465071 | −0.0203167 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.14302 | −0.0934400 | ||||||||
\(527\) | 8.59330 | 0.374330 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0035 | −0.652328 | ||||||||
\(530\) | −1.06996 | −0.0464760 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.8177 | −0.642429 | ||||||||
\(533\) | −35.6065 | −1.54229 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.7081 | 0.592653 | ||||||||
\(536\) | −5.54997 | −0.239722 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.92951 | 0.126300 | ||||||||
\(539\) | 2.01884 | 0.0869578 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.3417 | −0.702585 | −0.351292 | − | 0.936266i | \(-0.614258\pi\) | ||||
−0.351292 | + | 0.936266i | \(0.614258\pi\) | |||||||
\(542\) | −3.74977 | −0.161066 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 21.5382 | 0.923443 | ||||||||
\(545\) | 9.17596 | 0.393055 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.5444 | −0.963930 | −0.481965 | − | 0.876191i | \(-0.660077\pi\) | ||||
−0.481965 | + | 0.876191i | \(0.660077\pi\) | |||||||
\(548\) | 29.4043 | 1.25609 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.02244 | −0.0862371 | ||||||||
\(551\) | −38.8935 | −1.65692 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.24436 | 0.350586 | ||||||||
\(554\) | −5.41652 | −0.230126 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.07675 | −0.0880738 | ||||||||
\(557\) | 18.6953 | 0.792147 | 0.396074 | − | 0.918219i | \(-0.370372\pi\) | ||||
0.396074 | + | 0.918219i | \(0.370372\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.3160 | −0.436319 | ||||||||
\(560\) | −3.59378 | −0.151865 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.90393 | −0.0803126 | ||||||||
\(563\) | 19.7540 | 0.832530 | 0.416265 | − | 0.909243i | \(-0.363339\pi\) | ||||
0.416265 | + | 0.909243i | \(0.363339\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.78464 | 0.117151 | ||||||||
\(566\) | 4.47137 | 0.187946 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.84050 | 0.203103 | ||||||||
\(569\) | −26.0936 | −1.09390 | −0.546950 | − | 0.837165i | \(-0.684211\pi\) | ||||
−0.546950 | + | 0.837165i | \(0.684211\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.6941 | −1.53560 | −0.767801 | − | 0.640688i | \(-0.778649\pi\) | ||||
−0.767801 | + | 0.640688i | \(0.778649\pi\) | |||||||
\(572\) | −16.3546 | −0.683819 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.12232 | −0.0885840 | ||||||||
\(575\) | −11.3694 | −0.474138 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.8155 | −1.65754 | −0.828771 | − | 0.559589i | \(-0.810959\pi\) | ||||
−0.828771 | + | 0.559589i | \(0.810959\pi\) | |||||||
\(578\) | 9.82462 | 0.408650 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.75548 | −0.405074 | ||||||||
\(581\) | −9.21069 | −0.382124 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.76001 | 0.362803 | ||||||||
\(584\) | −1.85992 | −0.0769641 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.46916 | 0.143310 | ||||||||
\(587\) | 34.3425 | 1.41747 | 0.708734 | − | 0.705476i | \(-0.249267\pi\) | ||||
0.708734 | + | 0.705476i | \(0.249267\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.74679 | 0.360405 | ||||||||
\(590\) | −2.31946 | −0.0954905 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 38.5214 | 1.58322 | ||||||||
\(593\) | 12.0324 | 0.494111 | 0.247055 | − | 0.969001i | \(-0.420537\pi\) | ||||
0.247055 | + | 0.969001i | \(0.420537\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.43428 | −0.304776 | ||||||||
\(596\) | 13.5703 | 0.555861 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.94533 | 0.120443 | ||||||||
\(599\) | 41.4773 | 1.69472 | 0.847358 | − | 0.531021i | \(-0.178192\pi\) | ||||
0.847358 | + | 0.531021i | \(0.178192\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.46716 | 0.386174 | 0.193087 | − | 0.981182i | \(-0.438150\pi\) | ||||
0.193087 | + | 0.981182i | \(0.438150\pi\) | |||||||
\(602\) | −0.614881 | −0.0250607 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.21967 | 0.293764 | ||||||||
\(605\) | 6.85261 | 0.278598 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.9801 | −0.648613 | −0.324306 | − | 0.945952i | \(-0.605131\pi\) | ||||
−0.324306 | + | 0.945952i | \(0.605131\pi\) | |||||||
\(608\) | 21.9229 | 0.889092 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.839862 | 0.0340050 | ||||||||
\(611\) | 1.45395 | 0.0588205 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.360332 | 0.0145537 | 0.00727683 | − | 0.999974i | \(-0.497684\pi\) | ||||
0.00727683 | + | 0.999974i | \(0.497684\pi\) | |||||||
\(614\) | 2.54108 | 0.102550 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.98085 | −0.0798109 | ||||||||
\(617\) | 5.97404 | 0.240506 | 0.120253 | − | 0.992743i | \(-0.461629\pi\) | ||||
0.120253 | + | 0.992743i | \(0.461629\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.06486 | −0.123187 | −0.0615935 | − | 0.998101i | \(-0.519618\pi\) | ||||
−0.0615935 | + | 0.998101i | \(0.519618\pi\) | |||||||
\(620\) | 2.19392 | 0.0881098 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.43590 | −0.177863 | ||||||||
\(623\) | 1.13183 | 0.0453458 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.2681 | 0.450724 | ||||||||
\(626\) | −6.21158 | −0.248265 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −36.1857 | −1.44397 | ||||||||
\(629\) | 79.6874 | 3.17734 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.2128 | 0.725041 | 0.362521 | − | 0.931976i | \(-0.381916\pi\) | ||||
0.362521 | + | 0.931976i | \(0.381916\pi\) | |||||||
\(632\) | −8.08922 | −0.321772 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.94351 | 0.116902 | ||||||||
\(635\) | −0.989651 | −0.0392731 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.18024 | 0.165627 | ||||||||
\(638\) | −2.55869 | −0.101299 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7.28970 | 0.288151 | ||||||||
\(641\) | 12.4263 | 0.490808 | 0.245404 | − | 0.969421i | \(-0.421079\pi\) | ||||
0.245404 | + | 0.969421i | \(0.421079\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.7289 | 1.21183 | 0.605914 | − | 0.795530i | \(-0.292807\pi\) | ||||
0.605914 | + | 0.795530i | \(0.292807\pi\) | |||||||
\(644\) | −5.48005 | −0.215944 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14.3115 | 0.563079 | ||||||||
\(647\) | −29.0224 | −1.14099 | −0.570493 | − | 0.821302i | \(-0.693248\pi\) | ||||
−0.570493 | + | 0.821302i | \(0.693248\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.9900 | 0.745421 | ||||||||
\(650\) | −4.18769 | −0.164255 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.79654 | 0.227010 | ||||||||
\(653\) | 37.0748 | 1.45085 | 0.725424 | − | 0.688302i | \(-0.241644\pi\) | ||||
0.725424 | + | 0.688302i | \(0.241644\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.237501 | −0.00927994 | ||||||||
\(656\) | −30.9313 | −1.20766 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.0866624 | 0.00337845 | ||||||||
\(659\) | 22.7194 | 0.885021 | 0.442511 | − | 0.896763i | \(-0.354088\pi\) | ||||
0.442511 | + | 0.896763i | \(0.354088\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.5855 | 0.489519 | 0.244759 | − | 0.969584i | \(-0.421291\pi\) | ||||
0.244759 | + | 0.969584i | \(0.421291\pi\) | |||||||
\(662\) | −4.08844 | −0.158902 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.03737 | 0.350718 | ||||||||
\(665\) | −7.56707 | −0.293439 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.3840 | −0.556951 | ||||||||
\(668\) | −2.04618 | −0.0791692 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.39478 | −0.0538851 | ||||||||
\(671\) | −6.87616 | −0.265451 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.2339 | 1.62800 | 0.813999 | − | 0.580866i | \(-0.197286\pi\) | ||||
0.813999 | + | 0.580866i | \(0.197286\pi\) | |||||||
\(674\) | 8.42922 | 0.324681 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.67105 | −0.333502 | ||||||||
\(677\) | −8.92244 | −0.342917 | −0.171459 | − | 0.985191i | \(-0.554848\pi\) | ||||
−0.171459 | + | 0.985191i | \(0.554848\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.6987 | 0.717592 | ||||||||
\(680\) | 7.29439 | 0.279727 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.575425 | 0.0220341 | ||||||||
\(683\) | 29.9500 | 1.14600 | 0.573002 | − | 0.819554i | \(-0.305779\pi\) | ||||
0.573002 | + | 0.819554i | \(0.305779\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.0161 | 0.573737 | ||||||||
\(686\) | 0.249163 | 0.00951307 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.96144 | −0.341652 | ||||||||
\(689\) | 18.1386 | 0.691025 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.8529 | −0.450905 | −0.225453 | − | 0.974254i | \(-0.572386\pi\) | ||||
−0.225453 | + | 0.974254i | \(0.572386\pi\) | |||||||
\(692\) | −27.9463 | −1.06236 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.225027 | 0.00854192 | ||||||||
\(695\) | −1.06055 | −0.0402289 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −63.9861 | −2.42364 | ||||||||
\(698\) | −3.89302 | −0.147353 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.79158 | 0.294494 | ||||||||
\(701\) | 35.9250 | 1.35687 | 0.678434 | − | 0.734662i | \(-0.262659\pi\) | ||||
0.678434 | + | 0.734662i | \(0.262659\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 81.1107 | 3.05915 | ||||||||
\(704\) | −13.2201 | −0.498250 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.673537 | −0.0253489 | ||||||||
\(707\) | −4.10828 | −0.154508 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.74062 | 0.178038 | 0.0890189 | − | 0.996030i | \(-0.471627\pi\) | ||||
0.0890189 | + | 0.996030i | \(0.471627\pi\) | |||||||
\(710\) | 1.21648 | 0.0456537 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.11053 | −0.0416189 | ||||||||
\(713\) | 3.23483 | 0.121145 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.35192 | −0.312344 | ||||||||
\(716\) | 43.8770 | 1.63976 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.68665 | 0.249544 | ||||||||
\(719\) | −24.3352 | −0.907551 | −0.453776 | − | 0.891116i | \(-0.649923\pi\) | ||||
−0.453776 | + | 0.891116i | \(0.649923\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.05224 | −0.337123 | ||||||||
\(722\) | 9.83306 | 0.365949 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −42.7563 | −1.58902 | ||||||||
\(725\) | 20.4513 | 0.759543 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.13742 | −0.116360 | −0.0581802 | − | 0.998306i | \(-0.518530\pi\) | ||||
−0.0581802 | + | 0.998306i | \(0.518530\pi\) | |||||||
\(728\) | −4.10158 | −0.152015 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.467423 | −0.0173001 | ||||||||
\(731\) | −18.5381 | −0.685657 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.0961 | 1.14856 | 0.574280 | − | 0.818659i | \(-0.305282\pi\) | ||||
0.574280 | + | 0.818659i | \(0.305282\pi\) | |||||||
\(734\) | −7.43416 | −0.274400 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.10777 | 0.298856 | ||||||||
\(737\) | 11.4194 | 0.420639 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.3763 | 1.11741 | 0.558705 | − | 0.829367i | \(-0.311299\pi\) | ||||
0.558705 | + | 0.829367i | \(0.311299\pi\) | |||||||
\(740\) | 20.3446 | 0.747884 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.08115 | 0.0396902 | ||||||||
\(743\) | 33.5807 | 1.23196 | 0.615979 | − | 0.787763i | \(-0.288761\pi\) | ||||
0.615979 | + | 0.787763i | \(0.288761\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.93005 | 0.253897 | ||||||||
\(746\) | −0.937959 | −0.0343411 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −29.3897 | −1.07459 | ||||||||
\(749\) | −13.8515 | −0.506121 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.1545 | −0.735447 | −0.367723 | − | 0.929935i | \(-0.619863\pi\) | ||||
−0.367723 | + | 0.929935i | \(0.619863\pi\) | |||||||
\(752\) | 1.26304 | 0.0460584 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.29804 | −0.192943 | ||||||||
\(755\) | 3.68692 | 0.134181 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.0444 | −0.692182 | −0.346091 | − | 0.938201i | \(-0.612491\pi\) | ||||
−0.346091 | + | 0.938201i | \(0.612491\pi\) | |||||||
\(758\) | −5.58802 | −0.202966 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.42468 | 0.269321 | ||||||||
\(761\) | −28.3840 | −1.02892 | −0.514459 | − | 0.857515i | \(-0.672007\pi\) | ||||
−0.514459 | + | 0.857515i | \(0.672007\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.27191 | −0.335666 | ||||||||
\(764\) | 45.0890 | 1.63126 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.83991 | 0.0664787 | ||||||||
\(767\) | 39.3208 | 1.41979 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.5905 | −1.75222 | −0.876110 | − | 0.482112i | \(-0.839870\pi\) | ||||
−0.876110 | + | 0.482112i | \(0.839870\pi\) | |||||||
\(770\) | −0.497815 | −0.0179400 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −46.8426 | −1.68590 | ||||||||
\(773\) | −28.9932 | −1.04281 | −0.521407 | − | 0.853308i | \(-0.674592\pi\) | ||||
−0.521407 | + | 0.853308i | \(0.674592\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.59931 | −0.165212 | ||||||||
\(776\) | −18.3469 | −0.658614 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.81689 | −0.280249 | ||||||||
\(779\) | −65.1290 | −2.33349 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.95963 | −0.356384 | ||||||||
\(782\) | 5.29284 | 0.189272 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.63136 | 0.129692 | ||||||||
\(785\) | −18.4792 | −0.659552 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.2829 | −0.829946 | −0.414973 | − | 0.909834i | \(-0.636209\pi\) | ||||
−0.414973 | + | 0.909834i | \(0.636209\pi\) | |||||||
\(788\) | 3.56554 | 0.127017 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.03293 | −0.0723283 | ||||||||
\(791\) | −2.81376 | −0.100046 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.2378 | −0.505601 | ||||||||
\(794\) | −1.20164 | −0.0426446 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.9712 | −0.601529 | ||||||||
\(797\) | 38.6556 | 1.36925 | 0.684625 | − | 0.728895i | \(-0.259966\pi\) | ||||
0.684625 | + | 0.728895i | \(0.259966\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.61279 | 0.0924340 | ||||||||
\(800\) | −11.5277 | −0.407565 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.33187 | −0.0823411 | ||||||||
\(803\) | 3.82691 | 0.135049 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.79854 | −0.0986355 | ||||||||
\(806\) | 1.19148 | 0.0419681 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.03098 | 0.141809 | ||||||||
\(809\) | 34.9165 | 1.22760 | 0.613799 | − | 0.789463i | \(-0.289641\pi\) | ||||
0.613799 | + | 0.789463i | \(0.289641\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.9951 | −0.772354 | −0.386177 | − | 0.922425i | \(-0.626205\pi\) | ||||
−0.386177 | + | 0.922425i | \(0.626205\pi\) | |||||||
\(812\) | 9.85750 | 0.345930 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.33603 | 0.187028 | ||||||||
\(815\) | 2.96016 | 0.103690 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.8692 | −0.660151 | ||||||||
\(818\) | −1.76827 | −0.0618261 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −16.3360 | −0.570478 | ||||||||
\(821\) | −22.7829 | −0.795128 | −0.397564 | − | 0.917574i | \(-0.630144\pi\) | ||||
−0.397564 | + | 0.917574i | \(0.630144\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.4790 | 0.748711 | 0.374355 | − | 0.927285i | \(-0.377864\pi\) | ||||
0.374355 | + | 0.927285i | \(0.377864\pi\) | |||||||
\(824\) | 8.88190 | 0.309416 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.34371 | 0.0815481 | ||||||||
\(827\) | −46.5756 | −1.61959 | −0.809795 | − | 0.586712i | \(-0.800422\pi\) | ||||
−0.809795 | + | 0.586712i | \(0.800422\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.19813 | 0.284733 | 0.142366 | − | 0.989814i | \(-0.454529\pi\) | ||||
0.142366 | + | 0.989814i | \(0.454529\pi\) | |||||||
\(830\) | 2.27121 | 0.0788348 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −27.3736 | −0.949009 | ||||||||
\(833\) | 7.51203 | 0.260276 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.04494 | −0.0361616 | ||||||||
\(836\) | −29.9147 | −1.03462 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.36434 | −0.150764 | ||||||||
\(839\) | 9.68783 | 0.334461 | 0.167230 | − | 0.985918i | \(-0.446518\pi\) | ||||
0.167230 | + | 0.985918i | \(0.446518\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.12607 | −0.107795 | ||||||||
\(842\) | 3.35632 | 0.115666 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.94522 | −0.101379 | ||||||||
\(845\) | −4.42811 | −0.152332 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.92427 | −0.237921 | ||||||||
\(848\) | 15.7569 | 0.541095 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.52541 | −0.258119 | ||||||||
\(851\) | 29.9972 | 1.02829 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.08607 | −0.208383 | −0.104192 | − | 0.994557i | \(-0.533225\pi\) | ||||
−0.104192 | + | 0.994557i | \(0.533225\pi\) | |||||||
\(854\) | −0.848645 | −0.0290400 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.5908 | 0.464524 | ||||||||
\(857\) | 7.84241 | 0.267892 | 0.133946 | − | 0.990989i | \(-0.457235\pi\) | ||||
0.133946 | + | 0.990989i | \(0.457235\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.86004 | −0.268181 | −0.134091 | − | 0.990969i | \(-0.542811\pi\) | ||||
−0.134091 | + | 0.990969i | \(0.542811\pi\) | |||||||
\(860\) | −4.73288 | −0.161390 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.55367 | −0.0869784 | ||||||||
\(863\) | −0.941391 | −0.0320453 | −0.0160227 | − | 0.999872i | \(-0.505100\pi\) | ||||
−0.0160227 | + | 0.999872i | \(0.505100\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.2716 | −0.485248 | ||||||||
\(866\) | 3.45340 | 0.117351 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.21686 | −0.0752451 | ||||||||
\(869\) | 16.6441 | 0.564612 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.6452 | 0.801185 | ||||||||
\(872\) | 9.09743 | 0.308078 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.38738 | 0.182231 | ||||||||
\(875\) | 8.92724 | 0.301796 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.9307 | 0.639245 | 0.319622 | − | 0.947545i | \(-0.396444\pi\) | ||||
0.319622 | + | 0.947545i | \(0.396444\pi\) | |||||||
\(878\) | −7.28090 | −0.245719 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7.25528 | −0.244576 | ||||||||
\(881\) | 11.4488 | 0.385720 | 0.192860 | − | 0.981226i | \(-0.438224\pi\) | ||||
0.192860 | + | 0.981226i | \(0.438224\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.2769 | −0.413150 | −0.206575 | − | 0.978431i | \(-0.566232\pi\) | ||||
−0.206575 | + | 0.978431i | \(0.566232\pi\) | |||||||
\(884\) | −60.8547 | −2.04676 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.97893 | 0.268057 | ||||||||
\(887\) | −46.7593 | −1.57002 | −0.785012 | − | 0.619481i | \(-0.787343\pi\) | ||||
−0.785012 | + | 0.619481i | \(0.787343\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −0.279091 | −0.00935516 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −32.6438 | −1.09300 | ||||||||
\(893\) | 2.65946 | 0.0889955 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.4070 | 0.748983 | ||||||||
\(896\) | −7.36593 | −0.246078 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.90394 | −0.230387 | ||||||||
\(899\) | −5.81881 | −0.194068 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.5956 | 1.08592 | ||||||||
\(902\) | −4.28464 | −0.142663 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.76081 | 0.0918232 | ||||||||
\(905\) | −21.8347 | −0.725808 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.9186 | −1.09305 | −0.546523 | − | 0.837444i | \(-0.684049\pi\) | ||||
−0.546523 | + | 0.837444i | \(0.684049\pi\) | |||||||
\(908\) | −24.5460 | −0.814588 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.03078 | −0.0341701 | ||||||||
\(911\) | 35.2054 | 1.16641 | 0.583204 | − | 0.812326i | \(-0.301799\pi\) | ||||
0.583204 | + | 0.812326i | \(0.301799\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.5949 | −0.615403 | ||||||||
\(914\) | −4.73090 | −0.156484 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 33.2761 | 1.09947 | ||||||||
\(917\) | 0.239985 | 0.00792500 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.74081 | −0.222359 | −0.111179 | − | 0.993800i | \(-0.535463\pi\) | ||||
−0.111179 | + | 0.993800i | \(0.535463\pi\) | |||||||
\(920\) | 2.74587 | 0.0905288 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.22928 | −0.172217 | ||||||||
\(923\) | −20.6225 | −0.678799 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −42.6503 | −1.40233 | ||||||||
\(926\) | −5.38024 | −0.176806 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −14.5842 | −0.478751 | ||||||||
\(929\) | −2.08267 | −0.0683303 | −0.0341652 | − | 0.999416i | \(-0.510877\pi\) | ||||
−0.0341652 | + | 0.999416i | \(0.510877\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.64620 | 0.250594 | ||||||||
\(932\) | −20.4733 | −0.670627 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.13879 | −0.200867 | ||||||||
\(935\) | −15.0087 | −0.490836 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.5135 | 0.637479 | 0.318739 | − | 0.947842i | \(-0.396741\pi\) | ||||
0.318739 | + | 0.947842i | \(0.396741\pi\) | |||||||
\(938\) | 1.40937 | 0.0460174 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.667061 | 0.0217571 | ||||||||
\(941\) | −29.9195 | −0.975347 | −0.487673 | − | 0.873026i | \(-0.662154\pi\) | ||||
−0.487673 | + | 0.873026i | \(0.662154\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.0867 | −0.784371 | ||||||||
\(944\) | 34.1579 | 1.11174 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.24135 | −0.0403598 | ||||||||
\(947\) | −2.17516 | −0.0706831 | −0.0353415 | − | 0.999375i | \(-0.511252\pi\) | ||||
−0.0353415 | + | 0.999375i | \(0.511252\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.92404 | 0.257225 | ||||||||
\(950\) | −7.65982 | −0.248517 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.37067 | −0.238885 | ||||||||
\(953\) | −36.1891 | −1.17228 | −0.586140 | − | 0.810210i | \(-0.699353\pi\) | ||||
−0.586140 | + | 0.810210i | \(0.699353\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.0259 | 0.745102 | ||||||||
\(956\) | −51.1919 | −1.65566 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.18177 | 0.167415 | ||||||||
\(959\) | −15.1732 | −0.489967 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6914 | −0.957787 | ||||||||
\(962\) | 11.0488 | 0.356229 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 23.2632 | 0.749259 | ||||||||
\(965\) | −23.9215 | −0.770060 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.8359 | −1.44183 | −0.720913 | − | 0.693026i | \(-0.756277\pi\) | ||||
−0.720913 | + | 0.693026i | \(0.756277\pi\) | |||||||
\(968\) | 6.79397 | 0.218366 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.61081 | −0.148044 | ||||||||
\(971\) | −43.3703 | −1.39182 | −0.695910 | − | 0.718129i | \(-0.744999\pi\) | ||||
−0.695910 | + | 0.718129i | \(0.744999\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.07164 | 0.0343552 | ||||||||
\(974\) | 3.91291 | 0.125378 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.3684 | −0.395902 | ||||||||
\(977\) | 27.9074 | 0.892837 | 0.446419 | − | 0.894824i | \(-0.352699\pi\) | ||||
0.446419 | + | 0.894824i | \(0.352699\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.28499 | 0.0730285 | ||||||||
\(980\) | 1.91786 | 0.0612639 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.16257 | 0.292389 | ||||||||
\(983\) | −44.0231 | −1.40412 | −0.702059 | − | 0.712118i | \(-0.747736\pi\) | ||||
−0.702059 | + | 0.712118i | \(0.747736\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.82084 | 0.0580168 | ||||||||
\(986\) | −9.52075 | −0.303203 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −61.9416 | −1.97063 | ||||||||
\(989\) | −6.97842 | −0.221901 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.6198 | 1.19503 | 0.597516 | − | 0.801857i | \(-0.296154\pi\) | ||||
0.597516 | + | 0.801857i | \(0.296154\pi\) | |||||||
\(992\) | 3.27986 | 0.104136 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.22920 | −0.0389879 | ||||||||
\(995\) | −8.66682 | −0.274757 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52.6691 | 1.66805 | 0.834023 | − | 0.551729i | \(-0.186032\pi\) | ||||
0.834023 | + | 0.551729i | \(0.186032\pi\) | |||||||
\(998\) | −3.43301 | −0.108670 | ||||||||
\(999\) | 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.1.11 | 19 | ||
3.2 | odd | 2 | 2667.2.a.q.1.9 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.q.1.9 | ✓ | 19 | 3.2 | odd | 2 | ||
8001.2.a.v.1.11 | 19 | 1.1 | even | 1 | trivial |