Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6005,2,Mod(1,6005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6005, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6005 = 5 \cdot 1201 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6005.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: | \(47.9501664138\) |
Analytic rank: | \(1\) |
Dimension: | \(88\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6005.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.21323 | −1.56499 | −0.782496 | − | 0.622655i | \(-0.786054\pi\) | ||||
−0.782496 | + | 0.622655i | \(0.786054\pi\) | |||||||
\(3\) | −3.30657 | −1.90905 | −0.954524 | − | 0.298133i | \(-0.903636\pi\) | ||||
−0.954524 | + | 0.298133i | \(0.903636\pi\) | |||||||
\(4\) | 2.89841 | 1.44920 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 7.31821 | 2.98765 | ||||||||
\(7\) | −1.75850 | −0.664650 | −0.332325 | − | 0.943165i | \(-0.607833\pi\) | ||||
−0.332325 | + | 0.943165i | \(0.607833\pi\) | |||||||
\(8\) | −1.98838 | −0.702999 | ||||||||
\(9\) | 7.93340 | 2.64447 | ||||||||
\(10\) | −2.21323 | −0.699886 | ||||||||
\(11\) | −1.41426 | −0.426415 | −0.213207 | − | 0.977007i | \(-0.568391\pi\) | ||||
−0.213207 | + | 0.977007i | \(0.568391\pi\) | |||||||
\(12\) | −9.58378 | −2.76660 | ||||||||
\(13\) | 6.37747 | 1.76879 | 0.884395 | − | 0.466739i | \(-0.154571\pi\) | ||||
0.884395 | + | 0.466739i | \(0.154571\pi\) | |||||||
\(14\) | 3.89197 | 1.04017 | ||||||||
\(15\) | −3.30657 | −0.853753 | ||||||||
\(16\) | −1.39606 | −0.349014 | ||||||||
\(17\) | 5.66946 | 1.37505 | 0.687523 | − | 0.726163i | \(-0.258698\pi\) | ||||
0.687523 | + | 0.726163i | \(0.258698\pi\) | |||||||
\(18\) | −17.5585 | −4.13857 | ||||||||
\(19\) | 3.56162 | 0.817092 | 0.408546 | − | 0.912738i | \(-0.366036\pi\) | ||||
0.408546 | + | 0.912738i | \(0.366036\pi\) | |||||||
\(20\) | 2.89841 | 0.648103 | ||||||||
\(21\) | 5.81460 | 1.26885 | ||||||||
\(22\) | 3.13008 | 0.667336 | ||||||||
\(23\) | −4.98391 | −1.03922 | −0.519608 | − | 0.854405i | \(-0.673922\pi\) | ||||
−0.519608 | + | 0.854405i | \(0.673922\pi\) | |||||||
\(24\) | 6.57472 | 1.34206 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −14.1148 | −2.76814 | ||||||||
\(27\) | −16.3126 | −3.13937 | ||||||||
\(28\) | −5.09684 | −0.963213 | ||||||||
\(29\) | 4.39018 | 0.815236 | 0.407618 | − | 0.913153i | \(-0.366360\pi\) | ||||
0.407618 | + | 0.913153i | \(0.366360\pi\) | |||||||
\(30\) | 7.31821 | 1.33612 | ||||||||
\(31\) | 8.18670 | 1.47038 | 0.735188 | − | 0.677864i | \(-0.237094\pi\) | ||||
0.735188 | + | 0.677864i | \(0.237094\pi\) | |||||||
\(32\) | 7.06656 | 1.24920 | ||||||||
\(33\) | 4.67634 | 0.814047 | ||||||||
\(34\) | −12.5478 | −2.15194 | ||||||||
\(35\) | −1.75850 | −0.297241 | ||||||||
\(36\) | 22.9942 | 3.83237 | ||||||||
\(37\) | −5.92369 | −0.973848 | −0.486924 | − | 0.873444i | \(-0.661881\pi\) | ||||
−0.486924 | + | 0.873444i | \(0.661881\pi\) | |||||||
\(38\) | −7.88270 | −1.27874 | ||||||||
\(39\) | −21.0875 | −3.37671 | ||||||||
\(40\) | −1.98838 | −0.314391 | ||||||||
\(41\) | 4.90053 | 0.765335 | 0.382667 | − | 0.923886i | \(-0.375006\pi\) | ||||
0.382667 | + | 0.923886i | \(0.375006\pi\) | |||||||
\(42\) | −12.8691 | −1.98574 | ||||||||
\(43\) | −9.26427 | −1.41279 | −0.706394 | − | 0.707819i | \(-0.749679\pi\) | ||||
−0.706394 | + | 0.707819i | \(0.749679\pi\) | |||||||
\(44\) | −4.09909 | −0.617962 | ||||||||
\(45\) | 7.93340 | 1.18264 | ||||||||
\(46\) | 11.0306 | 1.62637 | ||||||||
\(47\) | −0.752947 | −0.109829 | −0.0549143 | − | 0.998491i | \(-0.517489\pi\) | ||||
−0.0549143 | + | 0.998491i | \(0.517489\pi\) | |||||||
\(48\) | 4.61616 | 0.666285 | ||||||||
\(49\) | −3.90768 | −0.558240 | ||||||||
\(50\) | −2.21323 | −0.312999 | ||||||||
\(51\) | −18.7465 | −2.62503 | ||||||||
\(52\) | 18.4845 | 2.56334 | ||||||||
\(53\) | −5.63464 | −0.773977 | −0.386988 | − | 0.922085i | \(-0.626485\pi\) | ||||
−0.386988 | + | 0.922085i | \(0.626485\pi\) | |||||||
\(54\) | 36.1037 | 4.91309 | ||||||||
\(55\) | −1.41426 | −0.190698 | ||||||||
\(56\) | 3.49657 | 0.467249 | ||||||||
\(57\) | −11.7768 | −1.55987 | ||||||||
\(58\) | −9.71649 | −1.27584 | ||||||||
\(59\) | 3.28232 | 0.427322 | 0.213661 | − | 0.976908i | \(-0.431461\pi\) | ||||
0.213661 | + | 0.976908i | \(0.431461\pi\) | |||||||
\(60\) | −9.58378 | −1.23726 | ||||||||
\(61\) | −11.0519 | −1.41505 | −0.707527 | − | 0.706686i | \(-0.750189\pi\) | ||||
−0.707527 | + | 0.706686i | \(0.750189\pi\) | |||||||
\(62\) | −18.1191 | −2.30113 | ||||||||
\(63\) | −13.9509 | −1.75765 | ||||||||
\(64\) | −12.8478 | −1.60598 | ||||||||
\(65\) | 6.37747 | 0.791027 | ||||||||
\(66\) | −10.3498 | −1.27398 | ||||||||
\(67\) | −4.25209 | −0.519475 | −0.259738 | − | 0.965679i | \(-0.583636\pi\) | ||||
−0.259738 | + | 0.965679i | \(0.583636\pi\) | |||||||
\(68\) | 16.4324 | 1.99272 | ||||||||
\(69\) | 16.4796 | 1.98391 | ||||||||
\(70\) | 3.89197 | 0.465180 | ||||||||
\(71\) | 7.64807 | 0.907659 | 0.453829 | − | 0.891089i | \(-0.350058\pi\) | ||||
0.453829 | + | 0.891089i | \(0.350058\pi\) | |||||||
\(72\) | −15.7746 | −1.85906 | ||||||||
\(73\) | 3.27383 | 0.383173 | 0.191587 | − | 0.981476i | \(-0.438637\pi\) | ||||
0.191587 | + | 0.981476i | \(0.438637\pi\) | |||||||
\(74\) | 13.1105 | 1.52407 | ||||||||
\(75\) | −3.30657 | −0.381810 | ||||||||
\(76\) | 10.3230 | 1.18413 | ||||||||
\(77\) | 2.48697 | 0.283417 | ||||||||
\(78\) | 46.6716 | 5.28452 | ||||||||
\(79\) | 15.0568 | 1.69403 | 0.847014 | − | 0.531571i | \(-0.178398\pi\) | ||||
0.847014 | + | 0.531571i | \(0.178398\pi\) | |||||||
\(80\) | −1.39606 | −0.156084 | ||||||||
\(81\) | 30.1386 | 3.34874 | ||||||||
\(82\) | −10.8460 | −1.19774 | ||||||||
\(83\) | −17.3867 | −1.90844 | −0.954222 | − | 0.299100i | \(-0.903314\pi\) | ||||
−0.954222 | + | 0.299100i | \(0.903314\pi\) | |||||||
\(84\) | 16.8531 | 1.83882 | ||||||||
\(85\) | 5.66946 | 0.614939 | ||||||||
\(86\) | 20.5040 | 2.21100 | ||||||||
\(87\) | −14.5164 | −1.55632 | ||||||||
\(88\) | 2.81208 | 0.299769 | ||||||||
\(89\) | −8.34891 | −0.884982 | −0.442491 | − | 0.896773i | \(-0.645905\pi\) | ||||
−0.442491 | + | 0.896773i | \(0.645905\pi\) | |||||||
\(90\) | −17.5585 | −1.85083 | ||||||||
\(91\) | −11.2148 | −1.17563 | ||||||||
\(92\) | −14.4454 | −1.50604 | ||||||||
\(93\) | −27.0699 | −2.80702 | ||||||||
\(94\) | 1.66645 | 0.171881 | ||||||||
\(95\) | 3.56162 | 0.365415 | ||||||||
\(96\) | −23.3661 | −2.38479 | ||||||||
\(97\) | −19.2057 | −1.95005 | −0.975024 | − | 0.222100i | \(-0.928709\pi\) | ||||
−0.975024 | + | 0.222100i | \(0.928709\pi\) | |||||||
\(98\) | 8.64861 | 0.873642 | ||||||||
\(99\) | −11.2199 | −1.12764 | ||||||||
\(100\) | 2.89841 | 0.289841 | ||||||||
\(101\) | −12.4981 | −1.24361 | −0.621804 | − | 0.783173i | \(-0.713600\pi\) | ||||
−0.621804 | + | 0.783173i | \(0.713600\pi\) | |||||||
\(102\) | 41.4903 | 4.10815 | ||||||||
\(103\) | −14.6960 | −1.44804 | −0.724020 | − | 0.689779i | \(-0.757707\pi\) | ||||
−0.724020 | + | 0.689779i | \(0.757707\pi\) | |||||||
\(104\) | −12.6808 | −1.24346 | ||||||||
\(105\) | 5.81460 | 0.567447 | ||||||||
\(106\) | 12.4708 | 1.21127 | ||||||||
\(107\) | 2.99789 | 0.289817 | 0.144909 | − | 0.989445i | \(-0.453711\pi\) | ||||
0.144909 | + | 0.989445i | \(0.453711\pi\) | |||||||
\(108\) | −47.2806 | −4.54958 | ||||||||
\(109\) | −18.0284 | −1.72681 | −0.863403 | − | 0.504514i | \(-0.831672\pi\) | ||||
−0.863403 | + | 0.504514i | \(0.831672\pi\) | |||||||
\(110\) | 3.13008 | 0.298442 | ||||||||
\(111\) | 19.5871 | 1.85912 | ||||||||
\(112\) | 2.45496 | 0.231972 | ||||||||
\(113\) | −8.87769 | −0.835142 | −0.417571 | − | 0.908644i | \(-0.637119\pi\) | ||||
−0.417571 | + | 0.908644i | \(0.637119\pi\) | |||||||
\(114\) | 26.0647 | 2.44118 | ||||||||
\(115\) | −4.98391 | −0.464752 | ||||||||
\(116\) | 12.7245 | 1.18144 | ||||||||
\(117\) | 50.5950 | 4.67751 | ||||||||
\(118\) | −7.26455 | −0.668756 | ||||||||
\(119\) | −9.96974 | −0.913925 | ||||||||
\(120\) | 6.57472 | 0.600187 | ||||||||
\(121\) | −8.99987 | −0.818170 | ||||||||
\(122\) | 24.4605 | 2.21455 | ||||||||
\(123\) | −16.2040 | −1.46106 | ||||||||
\(124\) | 23.7284 | 2.13087 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 30.8766 | 2.75070 | ||||||||
\(127\) | 6.59658 | 0.585352 | 0.292676 | − | 0.956212i | \(-0.405454\pi\) | ||||
0.292676 | + | 0.956212i | \(0.405454\pi\) | |||||||
\(128\) | 14.3022 | 1.26414 | ||||||||
\(129\) | 30.6329 | 2.69708 | ||||||||
\(130\) | −14.1148 | −1.23795 | ||||||||
\(131\) | −5.76425 | −0.503625 | −0.251813 | − | 0.967776i | \(-0.581027\pi\) | ||||
−0.251813 | + | 0.967776i | \(0.581027\pi\) | |||||||
\(132\) | 13.5539 | 1.17972 | ||||||||
\(133\) | −6.26311 | −0.543081 | ||||||||
\(134\) | 9.41086 | 0.812975 | ||||||||
\(135\) | −16.3126 | −1.40397 | ||||||||
\(136\) | −11.2731 | −0.966656 | ||||||||
\(137\) | 15.9338 | 1.36131 | 0.680657 | − | 0.732602i | \(-0.261694\pi\) | ||||
0.680657 | + | 0.732602i | \(0.261694\pi\) | |||||||
\(138\) | −36.4733 | −3.10481 | ||||||||
\(139\) | −7.86966 | −0.667496 | −0.333748 | − | 0.942662i | \(-0.608313\pi\) | ||||
−0.333748 | + | 0.942662i | \(0.608313\pi\) | |||||||
\(140\) | −5.09684 | −0.430762 | ||||||||
\(141\) | 2.48967 | 0.209668 | ||||||||
\(142\) | −16.9270 | −1.42048 | ||||||||
\(143\) | −9.01938 | −0.754239 | ||||||||
\(144\) | −11.0755 | −0.922956 | ||||||||
\(145\) | 4.39018 | 0.364584 | ||||||||
\(146\) | −7.24576 | −0.599663 | ||||||||
\(147\) | 12.9210 | 1.06571 | ||||||||
\(148\) | −17.1693 | −1.41130 | ||||||||
\(149\) | −0.985931 | −0.0807706 | −0.0403853 | − | 0.999184i | \(-0.512859\pi\) | ||||
−0.0403853 | + | 0.999184i | \(0.512859\pi\) | |||||||
\(150\) | 7.31821 | 0.597530 | ||||||||
\(151\) | −1.66557 | −0.135542 | −0.0677712 | − | 0.997701i | \(-0.521589\pi\) | ||||
−0.0677712 | + | 0.997701i | \(0.521589\pi\) | |||||||
\(152\) | −7.08186 | −0.574415 | ||||||||
\(153\) | 44.9781 | 3.63626 | ||||||||
\(154\) | −5.50425 | −0.443545 | ||||||||
\(155\) | 8.18670 | 0.657572 | ||||||||
\(156\) | −61.1202 | −4.89353 | ||||||||
\(157\) | 4.38148 | 0.349681 | 0.174840 | − | 0.984597i | \(-0.444059\pi\) | ||||
0.174840 | + | 0.984597i | \(0.444059\pi\) | |||||||
\(158\) | −33.3243 | −2.65114 | ||||||||
\(159\) | 18.6313 | 1.47756 | ||||||||
\(160\) | 7.06656 | 0.558661 | ||||||||
\(161\) | 8.76420 | 0.690716 | ||||||||
\(162\) | −66.7039 | −5.24075 | ||||||||
\(163\) | 15.2070 | 1.19111 | 0.595553 | − | 0.803316i | \(-0.296933\pi\) | ||||
0.595553 | + | 0.803316i | \(0.296933\pi\) | |||||||
\(164\) | 14.2037 | 1.10913 | ||||||||
\(165\) | 4.67634 | 0.364053 | ||||||||
\(166\) | 38.4809 | 2.98670 | ||||||||
\(167\) | −12.1629 | −0.941192 | −0.470596 | − | 0.882349i | \(-0.655961\pi\) | ||||
−0.470596 | + | 0.882349i | \(0.655961\pi\) | |||||||
\(168\) | −11.5616 | −0.892000 | ||||||||
\(169\) | 27.6721 | 2.12862 | ||||||||
\(170\) | −12.5478 | −0.962376 | ||||||||
\(171\) | 28.2558 | 2.16077 | ||||||||
\(172\) | −26.8516 | −2.04742 | ||||||||
\(173\) | 13.3700 | 1.01651 | 0.508253 | − | 0.861208i | \(-0.330292\pi\) | ||||
0.508253 | + | 0.861208i | \(0.330292\pi\) | |||||||
\(174\) | 32.1283 | 2.43564 | ||||||||
\(175\) | −1.75850 | −0.132930 | ||||||||
\(176\) | 1.97438 | 0.148825 | ||||||||
\(177\) | −10.8532 | −0.815778 | ||||||||
\(178\) | 18.4781 | 1.38499 | ||||||||
\(179\) | −14.3501 | −1.07258 | −0.536290 | − | 0.844034i | \(-0.680175\pi\) | ||||
−0.536290 | + | 0.844034i | \(0.680175\pi\) | |||||||
\(180\) | 22.9942 | 1.71389 | ||||||||
\(181\) | 6.35877 | 0.472644 | 0.236322 | − | 0.971675i | \(-0.424058\pi\) | ||||
0.236322 | + | 0.971675i | \(0.424058\pi\) | |||||||
\(182\) | 24.8209 | 1.83985 | ||||||||
\(183\) | 36.5440 | 2.70141 | ||||||||
\(184\) | 9.90991 | 0.730568 | ||||||||
\(185\) | −5.92369 | −0.435518 | ||||||||
\(186\) | 59.9120 | 4.39296 | ||||||||
\(187\) | −8.01808 | −0.586340 | ||||||||
\(188\) | −2.18235 | −0.159164 | ||||||||
\(189\) | 28.6858 | 2.08658 | ||||||||
\(190\) | −7.88270 | −0.571871 | ||||||||
\(191\) | 13.1222 | 0.949488 | 0.474744 | − | 0.880124i | \(-0.342541\pi\) | ||||
0.474744 | + | 0.880124i | \(0.342541\pi\) | |||||||
\(192\) | 42.4823 | 3.06590 | ||||||||
\(193\) | 17.6345 | 1.26936 | 0.634678 | − | 0.772777i | \(-0.281133\pi\) | ||||
0.634678 | + | 0.772777i | \(0.281133\pi\) | |||||||
\(194\) | 42.5068 | 3.05181 | ||||||||
\(195\) | −21.0875 | −1.51011 | ||||||||
\(196\) | −11.3260 | −0.809003 | ||||||||
\(197\) | 7.05391 | 0.502570 | 0.251285 | − | 0.967913i | \(-0.419147\pi\) | ||||
0.251285 | + | 0.967913i | \(0.419147\pi\) | |||||||
\(198\) | 24.8322 | 1.76475 | ||||||||
\(199\) | −2.85062 | −0.202075 | −0.101037 | − | 0.994883i | \(-0.532216\pi\) | ||||
−0.101037 | + | 0.994883i | \(0.532216\pi\) | |||||||
\(200\) | −1.98838 | −0.140600 | ||||||||
\(201\) | 14.0598 | 0.991703 | ||||||||
\(202\) | 27.6612 | 1.94624 | ||||||||
\(203\) | −7.72013 | −0.541847 | ||||||||
\(204\) | −54.3349 | −3.80420 | ||||||||
\(205\) | 4.90053 | 0.342268 | ||||||||
\(206\) | 32.5257 | 2.26617 | ||||||||
\(207\) | −39.5393 | −2.74817 | ||||||||
\(208\) | −8.90330 | −0.617333 | ||||||||
\(209\) | −5.03705 | −0.348420 | ||||||||
\(210\) | −12.8691 | −0.888050 | ||||||||
\(211\) | −11.0620 | −0.761537 | −0.380769 | − | 0.924670i | \(-0.624341\pi\) | ||||
−0.380769 | + | 0.924670i | \(0.624341\pi\) | |||||||
\(212\) | −16.3315 | −1.12165 | ||||||||
\(213\) | −25.2889 | −1.73276 | ||||||||
\(214\) | −6.63504 | −0.453562 | ||||||||
\(215\) | −9.26427 | −0.631818 | ||||||||
\(216\) | 32.4357 | 2.20697 | ||||||||
\(217\) | −14.3963 | −0.977286 | ||||||||
\(218\) | 39.9011 | 2.70244 | ||||||||
\(219\) | −10.8252 | −0.731496 | ||||||||
\(220\) | −4.09909 | −0.276361 | ||||||||
\(221\) | 36.1568 | 2.43217 | ||||||||
\(222\) | −43.3508 | −2.90952 | ||||||||
\(223\) | −7.19544 | −0.481842 | −0.240921 | − | 0.970545i | \(-0.577450\pi\) | ||||
−0.240921 | + | 0.970545i | \(0.577450\pi\) | |||||||
\(224\) | −12.4265 | −0.830284 | ||||||||
\(225\) | 7.93340 | 0.528893 | ||||||||
\(226\) | 19.6484 | 1.30699 | ||||||||
\(227\) | 2.11977 | 0.140694 | 0.0703471 | − | 0.997523i | \(-0.477589\pi\) | ||||
0.0703471 | + | 0.997523i | \(0.477589\pi\) | |||||||
\(228\) | −34.1338 | −2.26057 | ||||||||
\(229\) | 3.58754 | 0.237071 | 0.118536 | − | 0.992950i | \(-0.462180\pi\) | ||||
0.118536 | + | 0.992950i | \(0.462180\pi\) | |||||||
\(230\) | 11.0306 | 0.727333 | ||||||||
\(231\) | −8.22334 | −0.541056 | ||||||||
\(232\) | −8.72935 | −0.573110 | ||||||||
\(233\) | −14.2110 | −0.930996 | −0.465498 | − | 0.885049i | \(-0.654125\pi\) | ||||
−0.465498 | + | 0.885049i | \(0.654125\pi\) | |||||||
\(234\) | −111.979 | −7.32027 | ||||||||
\(235\) | −0.752947 | −0.0491169 | ||||||||
\(236\) | 9.51350 | 0.619276 | ||||||||
\(237\) | −49.7865 | −3.23398 | ||||||||
\(238\) | 22.0654 | 1.43029 | ||||||||
\(239\) | −9.65240 | −0.624362 | −0.312181 | − | 0.950023i | \(-0.601060\pi\) | ||||
−0.312181 | + | 0.950023i | \(0.601060\pi\) | |||||||
\(240\) | 4.61616 | 0.297972 | ||||||||
\(241\) | −17.1502 | −1.10474 | −0.552369 | − | 0.833600i | \(-0.686276\pi\) | ||||
−0.552369 | + | 0.833600i | \(0.686276\pi\) | |||||||
\(242\) | 19.9188 | 1.28043 | ||||||||
\(243\) | −50.7176 | −3.25354 | ||||||||
\(244\) | −32.0330 | −2.05070 | ||||||||
\(245\) | −3.90768 | −0.249652 | ||||||||
\(246\) | 35.8631 | 2.28655 | ||||||||
\(247\) | 22.7141 | 1.44526 | ||||||||
\(248\) | −16.2783 | −1.03367 | ||||||||
\(249\) | 57.4905 | 3.64331 | ||||||||
\(250\) | −2.21323 | −0.139977 | ||||||||
\(251\) | 3.37939 | 0.213305 | 0.106653 | − | 0.994296i | \(-0.465987\pi\) | ||||
0.106653 | + | 0.994296i | \(0.465987\pi\) | |||||||
\(252\) | −40.4353 | −2.54719 | ||||||||
\(253\) | 7.04853 | 0.443137 | ||||||||
\(254\) | −14.5998 | −0.916071 | ||||||||
\(255\) | −18.7465 | −1.17395 | ||||||||
\(256\) | −5.95835 | −0.372397 | ||||||||
\(257\) | 19.4592 | 1.21383 | 0.606916 | − | 0.794766i | \(-0.292406\pi\) | ||||
0.606916 | + | 0.794766i | \(0.292406\pi\) | |||||||
\(258\) | −67.7979 | −4.22091 | ||||||||
\(259\) | 10.4168 | 0.647269 | ||||||||
\(260\) | 18.4845 | 1.14636 | ||||||||
\(261\) | 34.8290 | 2.15586 | ||||||||
\(262\) | 12.7576 | 0.788170 | ||||||||
\(263\) | −11.8290 | −0.729407 | −0.364704 | − | 0.931124i | \(-0.618830\pi\) | ||||
−0.364704 | + | 0.931124i | \(0.618830\pi\) | |||||||
\(264\) | −9.29835 | −0.572274 | ||||||||
\(265\) | −5.63464 | −0.346133 | ||||||||
\(266\) | 13.8617 | 0.849917 | ||||||||
\(267\) | 27.6062 | 1.68947 | ||||||||
\(268\) | −12.3243 | −0.752825 | ||||||||
\(269\) | 3.58178 | 0.218385 | 0.109193 | − | 0.994021i | \(-0.465173\pi\) | ||||
0.109193 | + | 0.994021i | \(0.465173\pi\) | |||||||
\(270\) | 36.1037 | 2.19720 | ||||||||
\(271\) | −30.8656 | −1.87495 | −0.937475 | − | 0.348053i | \(-0.886843\pi\) | ||||
−0.937475 | + | 0.348053i | \(0.886843\pi\) | |||||||
\(272\) | −7.91489 | −0.479911 | ||||||||
\(273\) | 37.0824 | 2.24433 | ||||||||
\(274\) | −35.2652 | −2.13045 | ||||||||
\(275\) | −1.41426 | −0.0852830 | ||||||||
\(276\) | 47.7647 | 2.87510 | ||||||||
\(277\) | 10.4875 | 0.630132 | 0.315066 | − | 0.949070i | \(-0.397973\pi\) | ||||
0.315066 | + | 0.949070i | \(0.397973\pi\) | |||||||
\(278\) | 17.4174 | 1.04463 | ||||||||
\(279\) | 64.9484 | 3.88836 | ||||||||
\(280\) | 3.49657 | 0.208960 | ||||||||
\(281\) | 28.6662 | 1.71008 | 0.855042 | − | 0.518559i | \(-0.173531\pi\) | ||||
0.855042 | + | 0.518559i | \(0.173531\pi\) | |||||||
\(282\) | −5.51023 | −0.328129 | ||||||||
\(283\) | −7.62727 | −0.453394 | −0.226697 | − | 0.973965i | \(-0.572793\pi\) | ||||
−0.226697 | + | 0.973965i | \(0.572793\pi\) | |||||||
\(284\) | 22.1672 | 1.31538 | ||||||||
\(285\) | −11.7768 | −0.697594 | ||||||||
\(286\) | 19.9620 | 1.18038 | ||||||||
\(287\) | −8.61759 | −0.508680 | ||||||||
\(288\) | 56.0619 | 3.30348 | ||||||||
\(289\) | 15.1428 | 0.890752 | ||||||||
\(290\) | −9.71649 | −0.570572 | ||||||||
\(291\) | 63.5051 | 3.72274 | ||||||||
\(292\) | 9.48890 | 0.555296 | ||||||||
\(293\) | 18.3935 | 1.07456 | 0.537279 | − | 0.843405i | \(-0.319452\pi\) | ||||
0.537279 | + | 0.843405i | \(0.319452\pi\) | |||||||
\(294\) | −28.5972 | −1.66782 | ||||||||
\(295\) | 3.28232 | 0.191104 | ||||||||
\(296\) | 11.7786 | 0.684615 | ||||||||
\(297\) | 23.0703 | 1.33867 | ||||||||
\(298\) | 2.18210 | 0.126405 | ||||||||
\(299\) | −31.7847 | −1.83816 | ||||||||
\(300\) | −9.58378 | −0.553320 | ||||||||
\(301\) | 16.2912 | 0.939010 | ||||||||
\(302\) | 3.68630 | 0.212123 | ||||||||
\(303\) | 41.3259 | 2.37411 | ||||||||
\(304\) | −4.97223 | −0.285177 | ||||||||
\(305\) | −11.0519 | −0.632832 | ||||||||
\(306\) | −99.5471 | −5.69073 | ||||||||
\(307\) | −28.3885 | −1.62022 | −0.810108 | − | 0.586281i | \(-0.800591\pi\) | ||||
−0.810108 | + | 0.586281i | \(0.800591\pi\) | |||||||
\(308\) | 7.20825 | 0.410728 | ||||||||
\(309\) | 48.5933 | 2.76438 | ||||||||
\(310\) | −18.1191 | −1.02910 | ||||||||
\(311\) | −23.5820 | −1.33721 | −0.668606 | − | 0.743616i | \(-0.733109\pi\) | ||||
−0.668606 | + | 0.743616i | \(0.733109\pi\) | |||||||
\(312\) | 41.9301 | 2.37382 | ||||||||
\(313\) | 15.1001 | 0.853508 | 0.426754 | − | 0.904368i | \(-0.359657\pi\) | ||||
0.426754 | + | 0.904368i | \(0.359657\pi\) | |||||||
\(314\) | −9.69725 | −0.547248 | ||||||||
\(315\) | −13.9509 | −0.786043 | ||||||||
\(316\) | 43.6408 | 2.45499 | ||||||||
\(317\) | −13.1733 | −0.739887 | −0.369944 | − | 0.929054i | \(-0.620623\pi\) | ||||
−0.369944 | + | 0.929054i | \(0.620623\pi\) | |||||||
\(318\) | −41.2355 | −2.31237 | ||||||||
\(319\) | −6.20884 | −0.347629 | ||||||||
\(320\) | −12.8478 | −0.718216 | ||||||||
\(321\) | −9.91274 | −0.553275 | ||||||||
\(322\) | −19.3972 | −1.08097 | ||||||||
\(323\) | 20.1925 | 1.12354 | ||||||||
\(324\) | 87.3540 | 4.85300 | ||||||||
\(325\) | 6.37747 | 0.353758 | ||||||||
\(326\) | −33.6567 | −1.86407 | ||||||||
\(327\) | 59.6121 | 3.29656 | ||||||||
\(328\) | −9.74413 | −0.538030 | ||||||||
\(329\) | 1.32406 | 0.0729977 | ||||||||
\(330\) | −10.3498 | −0.569740 | ||||||||
\(331\) | 17.8972 | 0.983719 | 0.491859 | − | 0.870675i | \(-0.336317\pi\) | ||||
0.491859 | + | 0.870675i | \(0.336317\pi\) | |||||||
\(332\) | −50.3939 | −2.76572 | ||||||||
\(333\) | −46.9950 | −2.57531 | ||||||||
\(334\) | 26.9193 | 1.47296 | ||||||||
\(335\) | −4.25209 | −0.232316 | ||||||||
\(336\) | −8.11751 | −0.442847 | ||||||||
\(337\) | −24.8081 | −1.35138 | −0.675691 | − | 0.737185i | \(-0.736154\pi\) | ||||
−0.675691 | + | 0.737185i | \(0.736154\pi\) | |||||||
\(338\) | −61.2448 | −3.33128 | ||||||||
\(339\) | 29.3547 | 1.59433 | ||||||||
\(340\) | 16.4324 | 0.891172 | ||||||||
\(341\) | −11.5781 | −0.626990 | ||||||||
\(342\) | −62.5366 | −3.38159 | ||||||||
\(343\) | 19.1811 | 1.03568 | ||||||||
\(344\) | 18.4209 | 0.993188 | ||||||||
\(345\) | 16.4796 | 0.887234 | ||||||||
\(346\) | −29.5910 | −1.59082 | ||||||||
\(347\) | 19.6964 | 1.05736 | 0.528679 | − | 0.848822i | \(-0.322688\pi\) | ||||
0.528679 | + | 0.848822i | \(0.322688\pi\) | |||||||
\(348\) | −42.0745 | −2.25543 | ||||||||
\(349\) | −12.4834 | −0.668222 | −0.334111 | − | 0.942534i | \(-0.608436\pi\) | ||||
−0.334111 | + | 0.942534i | \(0.608436\pi\) | |||||||
\(350\) | 3.89197 | 0.208035 | ||||||||
\(351\) | −104.033 | −5.55288 | ||||||||
\(352\) | −9.99394 | −0.532679 | ||||||||
\(353\) | 22.4562 | 1.19522 | 0.597612 | − | 0.801786i | \(-0.296116\pi\) | ||||
0.597612 | + | 0.801786i | \(0.296116\pi\) | |||||||
\(354\) | 24.0207 | 1.27669 | ||||||||
\(355\) | 7.64807 | 0.405917 | ||||||||
\(356\) | −24.1985 | −1.28252 | ||||||||
\(357\) | 32.9656 | 1.74473 | ||||||||
\(358\) | 31.7602 | 1.67858 | ||||||||
\(359\) | −30.1873 | −1.59323 | −0.796614 | − | 0.604489i | \(-0.793377\pi\) | ||||
−0.796614 | + | 0.604489i | \(0.793377\pi\) | |||||||
\(360\) | −15.7746 | −0.831396 | ||||||||
\(361\) | −6.31485 | −0.332360 | ||||||||
\(362\) | −14.0734 | −0.739684 | ||||||||
\(363\) | 29.7587 | 1.56193 | ||||||||
\(364\) | −32.5050 | −1.70372 | ||||||||
\(365\) | 3.27383 | 0.171360 | ||||||||
\(366\) | −80.8804 | −4.22768 | ||||||||
\(367\) | −6.67536 | −0.348451 | −0.174226 | − | 0.984706i | \(-0.555742\pi\) | ||||
−0.174226 | + | 0.984706i | \(0.555742\pi\) | |||||||
\(368\) | 6.95782 | 0.362701 | ||||||||
\(369\) | 38.8779 | 2.02390 | ||||||||
\(370\) | 13.1105 | 0.681583 | ||||||||
\(371\) | 9.90850 | 0.514424 | ||||||||
\(372\) | −78.4596 | −4.06794 | ||||||||
\(373\) | 13.7500 | 0.711948 | 0.355974 | − | 0.934496i | \(-0.384149\pi\) | ||||
0.355974 | + | 0.934496i | \(0.384149\pi\) | |||||||
\(374\) | 17.7459 | 0.917618 | ||||||||
\(375\) | −3.30657 | −0.170751 | ||||||||
\(376\) | 1.49715 | 0.0772095 | ||||||||
\(377\) | 27.9982 | 1.44198 | ||||||||
\(378\) | −63.4883 | −3.26549 | ||||||||
\(379\) | −25.9804 | −1.33452 | −0.667262 | − | 0.744824i | \(-0.732534\pi\) | ||||
−0.667262 | + | 0.744824i | \(0.732534\pi\) | |||||||
\(380\) | 10.3230 | 0.529560 | ||||||||
\(381\) | −21.8120 | −1.11746 | ||||||||
\(382\) | −29.0425 | −1.48594 | ||||||||
\(383\) | −16.7450 | −0.855631 | −0.427815 | − | 0.903866i | \(-0.640717\pi\) | ||||
−0.427815 | + | 0.903866i | \(0.640717\pi\) | |||||||
\(384\) | −47.2911 | −2.41331 | ||||||||
\(385\) | 2.48697 | 0.126748 | ||||||||
\(386\) | −39.0292 | −1.98653 | ||||||||
\(387\) | −73.4971 | −3.73607 | ||||||||
\(388\) | −55.6660 | −2.82601 | ||||||||
\(389\) | 9.99885 | 0.506962 | 0.253481 | − | 0.967340i | \(-0.418425\pi\) | ||||
0.253481 | + | 0.967340i | \(0.418425\pi\) | |||||||
\(390\) | 46.6716 | 2.36331 | ||||||||
\(391\) | −28.2561 | −1.42897 | ||||||||
\(392\) | 7.76996 | 0.392442 | ||||||||
\(393\) | 19.0599 | 0.961445 | ||||||||
\(394\) | −15.6119 | −0.786518 | ||||||||
\(395\) | 15.0568 | 0.757592 | ||||||||
\(396\) | −32.5197 | −1.63418 | ||||||||
\(397\) | −27.5823 | −1.38432 | −0.692159 | − | 0.721746i | \(-0.743340\pi\) | ||||
−0.692159 | + | 0.721746i | \(0.743340\pi\) | |||||||
\(398\) | 6.30908 | 0.316246 | ||||||||
\(399\) | 20.7094 | 1.03677 | ||||||||
\(400\) | −1.39606 | −0.0698028 | ||||||||
\(401\) | −17.0172 | −0.849798 | −0.424899 | − | 0.905241i | \(-0.639690\pi\) | ||||
−0.424899 | + | 0.905241i | \(0.639690\pi\) | |||||||
\(402\) | −31.1177 | −1.55201 | ||||||||
\(403\) | 52.2104 | 2.60079 | ||||||||
\(404\) | −36.2246 | −1.80224 | ||||||||
\(405\) | 30.1386 | 1.49760 | ||||||||
\(406\) | 17.0864 | 0.847986 | ||||||||
\(407\) | 8.37762 | 0.415263 | ||||||||
\(408\) | 37.2751 | 1.84539 | ||||||||
\(409\) | 0.672432 | 0.0332496 | 0.0166248 | − | 0.999862i | \(-0.494708\pi\) | ||||
0.0166248 | + | 0.999862i | \(0.494708\pi\) | |||||||
\(410\) | −10.8460 | −0.535647 | ||||||||
\(411\) | −52.6862 | −2.59882 | ||||||||
\(412\) | −42.5949 | −2.09850 | ||||||||
\(413\) | −5.77196 | −0.284020 | ||||||||
\(414\) | 87.5098 | 4.30087 | ||||||||
\(415\) | −17.3867 | −0.853482 | ||||||||
\(416\) | 45.0668 | 2.20958 | ||||||||
\(417\) | 26.0216 | 1.27428 | ||||||||
\(418\) | 11.1482 | 0.545275 | ||||||||
\(419\) | 13.5291 | 0.660941 | 0.330470 | − | 0.943816i | \(-0.392793\pi\) | ||||
0.330470 | + | 0.943816i | \(0.392793\pi\) | |||||||
\(420\) | 16.8531 | 0.822346 | ||||||||
\(421\) | −37.4882 | −1.82706 | −0.913532 | − | 0.406766i | \(-0.866656\pi\) | ||||
−0.913532 | + | 0.406766i | \(0.866656\pi\) | |||||||
\(422\) | 24.4827 | 1.19180 | ||||||||
\(423\) | −5.97343 | −0.290438 | ||||||||
\(424\) | 11.2038 | 0.544105 | ||||||||
\(425\) | 5.66946 | 0.275009 | ||||||||
\(426\) | 55.9702 | 2.71176 | ||||||||
\(427\) | 19.4348 | 0.940516 | ||||||||
\(428\) | 8.68911 | 0.420004 | ||||||||
\(429\) | 29.8232 | 1.43988 | ||||||||
\(430\) | 20.5040 | 0.988790 | ||||||||
\(431\) | −14.4354 | −0.695330 | −0.347665 | − | 0.937619i | \(-0.613025\pi\) | ||||
−0.347665 | + | 0.937619i | \(0.613025\pi\) | |||||||
\(432\) | 22.7734 | 1.09568 | ||||||||
\(433\) | −16.0558 | −0.771593 | −0.385796 | − | 0.922584i | \(-0.626073\pi\) | ||||
−0.385796 | + | 0.922584i | \(0.626073\pi\) | |||||||
\(434\) | 31.8624 | 1.52944 | ||||||||
\(435\) | −14.5164 | −0.696009 | ||||||||
\(436\) | −52.2536 | −2.50249 | ||||||||
\(437\) | −17.7508 | −0.849136 | ||||||||
\(438\) | 23.9586 | 1.14479 | ||||||||
\(439\) | 32.1758 | 1.53567 | 0.767833 | − | 0.640650i | \(-0.221335\pi\) | ||||
0.767833 | + | 0.640650i | \(0.221335\pi\) | |||||||
\(440\) | 2.81208 | 0.134061 | ||||||||
\(441\) | −31.0012 | −1.47625 | ||||||||
\(442\) | −80.0234 | −3.80633 | ||||||||
\(443\) | −1.60687 | −0.0763446 | −0.0381723 | − | 0.999271i | \(-0.512154\pi\) | ||||
−0.0381723 | + | 0.999271i | \(0.512154\pi\) | |||||||
\(444\) | 56.7713 | 2.69425 | ||||||||
\(445\) | −8.34891 | −0.395776 | ||||||||
\(446\) | 15.9252 | 0.754080 | ||||||||
\(447\) | 3.26005 | 0.154195 | ||||||||
\(448\) | 22.5929 | 1.06742 | ||||||||
\(449\) | −6.64889 | −0.313781 | −0.156890 | − | 0.987616i | \(-0.550147\pi\) | ||||
−0.156890 | + | 0.987616i | \(0.550147\pi\) | |||||||
\(450\) | −17.5585 | −0.827714 | ||||||||
\(451\) | −6.93062 | −0.326350 | ||||||||
\(452\) | −25.7311 | −1.21029 | ||||||||
\(453\) | 5.50733 | 0.258757 | ||||||||
\(454\) | −4.69155 | −0.220185 | ||||||||
\(455\) | −11.2148 | −0.525757 | ||||||||
\(456\) | 23.4167 | 1.09659 | ||||||||
\(457\) | −13.5646 | −0.634524 | −0.317262 | − | 0.948338i | \(-0.602763\pi\) | ||||
−0.317262 | + | 0.948338i | \(0.602763\pi\) | |||||||
\(458\) | −7.94007 | −0.371015 | ||||||||
\(459\) | −92.4838 | −4.31677 | ||||||||
\(460\) | −14.4454 | −0.673520 | ||||||||
\(461\) | 5.14324 | 0.239544 | 0.119772 | − | 0.992801i | \(-0.461784\pi\) | ||||
0.119772 | + | 0.992801i | \(0.461784\pi\) | |||||||
\(462\) | 18.2002 | 0.846749 | ||||||||
\(463\) | −7.06479 | −0.328329 | −0.164164 | − | 0.986433i | \(-0.552493\pi\) | ||||
−0.164164 | + | 0.986433i | \(0.552493\pi\) | |||||||
\(464\) | −6.12894 | −0.284529 | ||||||||
\(465\) | −27.0699 | −1.25534 | ||||||||
\(466\) | 31.4523 | 1.45700 | ||||||||
\(467\) | −20.3291 | −0.940716 | −0.470358 | − | 0.882476i | \(-0.655875\pi\) | ||||
−0.470358 | + | 0.882476i | \(0.655875\pi\) | |||||||
\(468\) | 146.645 | 6.77866 | ||||||||
\(469\) | 7.47729 | 0.345269 | ||||||||
\(470\) | 1.66645 | 0.0768676 | ||||||||
\(471\) | −14.4877 | −0.667557 | ||||||||
\(472\) | −6.52651 | −0.300407 | ||||||||
\(473\) | 13.1021 | 0.602433 | ||||||||
\(474\) | 110.189 | 5.06116 | ||||||||
\(475\) | 3.56162 | 0.163418 | ||||||||
\(476\) | −28.8964 | −1.32446 | ||||||||
\(477\) | −44.7018 | −2.04676 | ||||||||
\(478\) | 21.3630 | 0.977122 | ||||||||
\(479\) | 25.0546 | 1.14477 | 0.572387 | − | 0.819984i | \(-0.306018\pi\) | ||||
0.572387 | + | 0.819984i | \(0.306018\pi\) | |||||||
\(480\) | −23.3661 | −1.06651 | ||||||||
\(481\) | −37.7781 | −1.72253 | ||||||||
\(482\) | 37.9573 | 1.72891 | ||||||||
\(483\) | −28.9794 | −1.31861 | ||||||||
\(484\) | −26.0853 | −1.18569 | ||||||||
\(485\) | −19.2057 | −0.872088 | ||||||||
\(486\) | 112.250 | 5.09176 | ||||||||
\(487\) | 11.8732 | 0.538024 | 0.269012 | − | 0.963137i | \(-0.413303\pi\) | ||||
0.269012 | + | 0.963137i | \(0.413303\pi\) | |||||||
\(488\) | 21.9755 | 0.994782 | ||||||||
\(489\) | −50.2831 | −2.27388 | ||||||||
\(490\) | 8.64861 | 0.390704 | ||||||||
\(491\) | −0.788457 | −0.0355826 | −0.0177913 | − | 0.999842i | \(-0.505663\pi\) | ||||
−0.0177913 | + | 0.999842i | \(0.505663\pi\) | |||||||
\(492\) | −46.9656 | −2.11737 | ||||||||
\(493\) | 24.8899 | 1.12099 | ||||||||
\(494\) | −50.2717 | −2.26183 | ||||||||
\(495\) | −11.2199 | −0.504296 | ||||||||
\(496\) | −11.4291 | −0.513182 | ||||||||
\(497\) | −13.4491 | −0.603276 | ||||||||
\(498\) | −127.240 | −5.70176 | ||||||||
\(499\) | 30.7816 | 1.37797 | 0.688986 | − | 0.724775i | \(-0.258056\pi\) | ||||
0.688986 | + | 0.724775i | \(0.258056\pi\) | |||||||
\(500\) | 2.89841 | 0.129621 | ||||||||
\(501\) | 40.2174 | 1.79678 | ||||||||
\(502\) | −7.47939 | −0.333821 | ||||||||
\(503\) | 12.6963 | 0.566098 | 0.283049 | − | 0.959105i | \(-0.408654\pi\) | ||||
0.283049 | + | 0.959105i | \(0.408654\pi\) | |||||||
\(504\) | 27.7397 | 1.23562 | ||||||||
\(505\) | −12.4981 | −0.556158 | ||||||||
\(506\) | −15.6000 | −0.693507 | ||||||||
\(507\) | −91.4996 | −4.06364 | ||||||||
\(508\) | 19.1196 | 0.848293 | ||||||||
\(509\) | −27.6214 | −1.22430 | −0.612148 | − | 0.790743i | \(-0.709694\pi\) | ||||
−0.612148 | + | 0.790743i | \(0.709694\pi\) | |||||||
\(510\) | 41.4903 | 1.83722 | ||||||||
\(511\) | −5.75703 | −0.254676 | ||||||||
\(512\) | −15.4171 | −0.681346 | ||||||||
\(513\) | −58.0994 | −2.56515 | ||||||||
\(514\) | −43.0678 | −1.89964 | ||||||||
\(515\) | −14.6960 | −0.647583 | ||||||||
\(516\) | 88.7867 | 3.90862 | ||||||||
\(517\) | 1.06486 | 0.0468326 | ||||||||
\(518\) | −23.0548 | −1.01297 | ||||||||
\(519\) | −44.2090 | −1.94056 | ||||||||
\(520\) | −12.6808 | −0.556091 | ||||||||
\(521\) | 30.1040 | 1.31888 | 0.659441 | − | 0.751756i | \(-0.270793\pi\) | ||||
0.659441 | + | 0.751756i | \(0.270793\pi\) | |||||||
\(522\) | −77.0848 | −3.37391 | ||||||||
\(523\) | 1.20578 | 0.0527250 | 0.0263625 | − | 0.999652i | \(-0.491608\pi\) | ||||
0.0263625 | + | 0.999652i | \(0.491608\pi\) | |||||||
\(524\) | −16.7071 | −0.729855 | ||||||||
\(525\) | 5.81460 | 0.253770 | ||||||||
\(526\) | 26.1803 | 1.14152 | ||||||||
\(527\) | 46.4142 | 2.02183 | ||||||||
\(528\) | −6.52844 | −0.284114 | ||||||||
\(529\) | 1.83933 | 0.0799710 | ||||||||
\(530\) | 12.4708 | 0.541696 | ||||||||
\(531\) | 26.0400 | 1.13004 | ||||||||
\(532\) | −18.1530 | −0.787034 | ||||||||
\(533\) | 31.2530 | 1.35372 | ||||||||
\(534\) | −61.0991 | −2.64402 | ||||||||
\(535\) | 2.99789 | 0.129610 | ||||||||
\(536\) | 8.45477 | 0.365190 | ||||||||
\(537\) | 47.4497 | 2.04761 | ||||||||
\(538\) | −7.92732 | −0.341771 | ||||||||
\(539\) | 5.52647 | 0.238042 | ||||||||
\(540\) | −47.2806 | −2.03463 | ||||||||
\(541\) | −31.1045 | −1.33728 | −0.668642 | − | 0.743584i | \(-0.733124\pi\) | ||||
−0.668642 | + | 0.743584i | \(0.733124\pi\) | |||||||
\(542\) | 68.3127 | 2.93428 | ||||||||
\(543\) | −21.0257 | −0.902300 | ||||||||
\(544\) | 40.0636 | 1.71771 | ||||||||
\(545\) | −18.0284 | −0.772251 | ||||||||
\(546\) | −82.0721 | −3.51236 | ||||||||
\(547\) | −16.8140 | −0.718915 | −0.359458 | − | 0.933161i | \(-0.617038\pi\) | ||||
−0.359458 | + | 0.933161i | \(0.617038\pi\) | |||||||
\(548\) | 46.1826 | 1.97282 | ||||||||
\(549\) | −87.6794 | −3.74206 | ||||||||
\(550\) | 3.13008 | 0.133467 | ||||||||
\(551\) | 15.6362 | 0.666123 | ||||||||
\(552\) | −32.7678 | −1.39469 | ||||||||
\(553\) | −26.4774 | −1.12594 | ||||||||
\(554\) | −23.2113 | −0.986152 | ||||||||
\(555\) | 19.5871 | 0.831426 | ||||||||
\(556\) | −22.8095 | −0.967337 | ||||||||
\(557\) | 6.61948 | 0.280476 | 0.140238 | − | 0.990118i | \(-0.455213\pi\) | ||||
0.140238 | + | 0.990118i | \(0.455213\pi\) | |||||||
\(558\) | −143.746 | −6.08525 | ||||||||
\(559\) | −59.0825 | −2.49893 | ||||||||
\(560\) | 2.45496 | 0.103741 | ||||||||
\(561\) | 26.5123 | 1.11935 | ||||||||
\(562\) | −63.4451 | −2.67627 | ||||||||
\(563\) | 24.4468 | 1.03031 | 0.515155 | − | 0.857097i | \(-0.327734\pi\) | ||||
0.515155 | + | 0.857097i | \(0.327734\pi\) | |||||||
\(564\) | 7.21608 | 0.303852 | ||||||||
\(565\) | −8.87769 | −0.373487 | ||||||||
\(566\) | 16.8809 | 0.709559 | ||||||||
\(567\) | −52.9988 | −2.22574 | ||||||||
\(568\) | −15.2073 | −0.638083 | ||||||||
\(569\) | −21.7949 | −0.913691 | −0.456846 | − | 0.889546i | \(-0.651021\pi\) | ||||
−0.456846 | + | 0.889546i | \(0.651021\pi\) | |||||||
\(570\) | 26.0647 | 1.09173 | ||||||||
\(571\) | 25.6516 | 1.07349 | 0.536743 | − | 0.843746i | \(-0.319655\pi\) | ||||
0.536743 | + | 0.843746i | \(0.319655\pi\) | |||||||
\(572\) | −26.1418 | −1.09304 | ||||||||
\(573\) | −43.3894 | −1.81262 | ||||||||
\(574\) | 19.0727 | 0.796081 | ||||||||
\(575\) | −4.98391 | −0.207843 | ||||||||
\(576\) | −101.927 | −4.24696 | ||||||||
\(577\) | −41.8920 | −1.74399 | −0.871994 | − | 0.489517i | \(-0.837173\pi\) | ||||
−0.871994 | + | 0.489517i | \(0.837173\pi\) | |||||||
\(578\) | −33.5145 | −1.39402 | ||||||||
\(579\) | −58.3096 | −2.42326 | ||||||||
\(580\) | 12.7245 | 0.528357 | ||||||||
\(581\) | 30.5746 | 1.26845 | ||||||||
\(582\) | −140.552 | −5.82605 | ||||||||
\(583\) | 7.96883 | 0.330035 | ||||||||
\(584\) | −6.50963 | −0.269370 | ||||||||
\(585\) | 50.5950 | 2.09185 | ||||||||
\(586\) | −40.7091 | −1.68168 | ||||||||
\(587\) | 18.8402 | 0.777619 | 0.388810 | − | 0.921318i | \(-0.372886\pi\) | ||||
0.388810 | + | 0.921318i | \(0.372886\pi\) | |||||||
\(588\) | 37.4503 | 1.54443 | ||||||||
\(589\) | 29.1579 | 1.20143 | ||||||||
\(590\) | −7.26455 | −0.299077 | ||||||||
\(591\) | −23.3242 | −0.959431 | ||||||||
\(592\) | 8.26980 | 0.339887 | ||||||||
\(593\) | −14.0499 | −0.576961 | −0.288480 | − | 0.957486i | \(-0.593150\pi\) | ||||
−0.288480 | + | 0.957486i | \(0.593150\pi\) | |||||||
\(594\) | −51.0599 | −2.09501 | ||||||||
\(595\) | −9.96974 | −0.408720 | ||||||||
\(596\) | −2.85763 | −0.117053 | ||||||||
\(597\) | 9.42576 | 0.385771 | ||||||||
\(598\) | 70.3470 | 2.87670 | ||||||||
\(599\) | 38.7788 | 1.58446 | 0.792229 | − | 0.610224i | \(-0.208921\pi\) | ||||
0.792229 | + | 0.610224i | \(0.208921\pi\) | |||||||
\(600\) | 6.57472 | 0.268412 | ||||||||
\(601\) | 12.9244 | 0.527198 | 0.263599 | − | 0.964632i | \(-0.415090\pi\) | ||||
0.263599 | + | 0.964632i | \(0.415090\pi\) | |||||||
\(602\) | −36.0563 | −1.46954 | ||||||||
\(603\) | −33.7335 | −1.37373 | ||||||||
\(604\) | −4.82751 | −0.196428 | ||||||||
\(605\) | −8.99987 | −0.365897 | ||||||||
\(606\) | −91.4638 | −3.71546 | ||||||||
\(607\) | −27.1158 | −1.10060 | −0.550298 | − | 0.834969i | \(-0.685486\pi\) | ||||
−0.550298 | + | 0.834969i | \(0.685486\pi\) | |||||||
\(608\) | 25.1684 | 1.02071 | ||||||||
\(609\) | 25.5271 | 1.03441 | ||||||||
\(610\) | 24.4605 | 0.990377 | ||||||||
\(611\) | −4.80190 | −0.194264 | ||||||||
\(612\) | 130.365 | 5.26968 | ||||||||
\(613\) | −14.4932 | −0.585376 | −0.292688 | − | 0.956208i | \(-0.594550\pi\) | ||||
−0.292688 | + | 0.956208i | \(0.594550\pi\) | |||||||
\(614\) | 62.8303 | 2.53563 | ||||||||
\(615\) | −16.2040 | −0.653406 | ||||||||
\(616\) | −4.94505 | −0.199242 | ||||||||
\(617\) | −48.9862 | −1.97211 | −0.986056 | − | 0.166413i | \(-0.946781\pi\) | ||||
−0.986056 | + | 0.166413i | \(0.946781\pi\) | |||||||
\(618\) | −107.548 | −4.32623 | ||||||||
\(619\) | −17.0116 | −0.683755 | −0.341877 | − | 0.939745i | \(-0.611063\pi\) | ||||
−0.341877 | + | 0.939745i | \(0.611063\pi\) | |||||||
\(620\) | 23.7284 | 0.952955 | ||||||||
\(621\) | 81.3006 | 3.26248 | ||||||||
\(622\) | 52.1925 | 2.09273 | ||||||||
\(623\) | 14.6815 | 0.588204 | ||||||||
\(624\) | 29.4394 | 1.17852 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −33.4200 | −1.33573 | ||||||||
\(627\) | 16.6554 | 0.665151 | ||||||||
\(628\) | 12.6993 | 0.506758 | ||||||||
\(629\) | −33.5841 | −1.33909 | ||||||||
\(630\) | 30.8766 | 1.23015 | ||||||||
\(631\) | −17.3368 | −0.690167 | −0.345084 | − | 0.938572i | \(-0.612149\pi\) | ||||
−0.345084 | + | 0.938572i | \(0.612149\pi\) | |||||||
\(632\) | −29.9387 | −1.19090 | ||||||||
\(633\) | 36.5772 | 1.45381 | ||||||||
\(634\) | 29.1556 | 1.15792 | ||||||||
\(635\) | 6.59658 | 0.261777 | ||||||||
\(636\) | 54.0011 | 2.14128 | ||||||||
\(637\) | −24.9211 | −0.987410 | ||||||||
\(638\) | 13.7416 | 0.544036 | ||||||||
\(639\) | 60.6752 | 2.40027 | ||||||||
\(640\) | 14.3022 | 0.565343 | ||||||||
\(641\) | −27.1103 | −1.07079 | −0.535396 | − | 0.844601i | \(-0.679837\pi\) | ||||
−0.535396 | + | 0.844601i | \(0.679837\pi\) | |||||||
\(642\) | 21.9392 | 0.865872 | ||||||||
\(643\) | 11.6770 | 0.460498 | 0.230249 | − | 0.973132i | \(-0.426046\pi\) | ||||
0.230249 | + | 0.973132i | \(0.426046\pi\) | |||||||
\(644\) | 25.4022 | 1.00099 | ||||||||
\(645\) | 30.6329 | 1.20617 | ||||||||
\(646\) | −44.6907 | −1.75833 | ||||||||
\(647\) | 11.4300 | 0.449360 | 0.224680 | − | 0.974433i | \(-0.427866\pi\) | ||||
0.224680 | + | 0.974433i | \(0.427866\pi\) | |||||||
\(648\) | −59.9271 | −2.35416 | ||||||||
\(649\) | −4.64205 | −0.182216 | ||||||||
\(650\) | −14.1148 | −0.553629 | ||||||||
\(651\) | 47.6024 | 1.86569 | ||||||||
\(652\) | 44.0762 | 1.72616 | ||||||||
\(653\) | 25.9529 | 1.01562 | 0.507808 | − | 0.861470i | \(-0.330456\pi\) | ||||
0.507808 | + | 0.861470i | \(0.330456\pi\) | |||||||
\(654\) | −131.936 | −5.15909 | ||||||||
\(655\) | −5.76425 | −0.225228 | ||||||||
\(656\) | −6.84142 | −0.267113 | ||||||||
\(657\) | 25.9726 | 1.01329 | ||||||||
\(658\) | −2.93045 | −0.114241 | ||||||||
\(659\) | −34.3043 | −1.33630 | −0.668152 | − | 0.744024i | \(-0.732915\pi\) | ||||
−0.668152 | + | 0.744024i | \(0.732915\pi\) | |||||||
\(660\) | 13.5539 | 0.527586 | ||||||||
\(661\) | −8.07834 | −0.314211 | −0.157105 | − | 0.987582i | \(-0.550216\pi\) | ||||
−0.157105 | + | 0.987582i | \(0.550216\pi\) | |||||||
\(662\) | −39.6107 | −1.53951 | ||||||||
\(663\) | −119.555 | −4.64313 | ||||||||
\(664\) | 34.5715 | 1.34163 | ||||||||
\(665\) | −6.26311 | −0.242873 | ||||||||
\(666\) | 104.011 | 4.03034 | ||||||||
\(667\) | −21.8802 | −0.847206 | ||||||||
\(668\) | −35.2530 | −1.36398 | ||||||||
\(669\) | 23.7922 | 0.919861 | ||||||||
\(670\) | 9.41086 | 0.363573 | ||||||||
\(671\) | 15.6303 | 0.603400 | ||||||||
\(672\) | 41.0892 | 1.58505 | ||||||||
\(673\) | 22.8377 | 0.880327 | 0.440163 | − | 0.897918i | \(-0.354920\pi\) | ||||
0.440163 | + | 0.897918i | \(0.354920\pi\) | |||||||
\(674\) | 54.9060 | 2.11490 | ||||||||
\(675\) | −16.3126 | −0.627873 | ||||||||
\(676\) | 80.2049 | 3.08480 | ||||||||
\(677\) | −4.77156 | −0.183386 | −0.0916931 | − | 0.995787i | \(-0.529228\pi\) | ||||
−0.0916931 | + | 0.995787i | \(0.529228\pi\) | |||||||
\(678\) | −64.9688 | −2.49511 | ||||||||
\(679\) | 33.7733 | 1.29610 | ||||||||
\(680\) | −11.2731 | −0.432302 | ||||||||
\(681\) | −7.00917 | −0.268592 | ||||||||
\(682\) | 25.6251 | 0.981235 | ||||||||
\(683\) | 13.4433 | 0.514393 | 0.257197 | − | 0.966359i | \(-0.417201\pi\) | ||||
0.257197 | + | 0.966359i | \(0.417201\pi\) | |||||||
\(684\) | 81.8967 | 3.13140 | ||||||||
\(685\) | 15.9338 | 0.608799 | ||||||||
\(686\) | −42.4524 | −1.62084 | ||||||||
\(687\) | −11.8625 | −0.452581 | ||||||||
\(688\) | 12.9334 | 0.493083 | ||||||||
\(689\) | −35.9347 | −1.36900 | ||||||||
\(690\) | −36.4733 | −1.38851 | ||||||||
\(691\) | 44.1211 | 1.67845 | 0.839224 | − | 0.543786i | \(-0.183010\pi\) | ||||
0.839224 | + | 0.543786i | \(0.183010\pi\) | |||||||
\(692\) | 38.7518 | 1.47312 | ||||||||
\(693\) | 19.7301 | 0.749486 | ||||||||
\(694\) | −43.5927 | −1.65476 | ||||||||
\(695\) | −7.86966 | −0.298513 | ||||||||
\(696\) | 28.8642 | 1.09409 | ||||||||
\(697\) | 27.7834 | 1.05237 | ||||||||
\(698\) | 27.6287 | 1.04576 | ||||||||
\(699\) | 46.9898 | 1.77732 | ||||||||
\(700\) | −5.09684 | −0.192643 | ||||||||
\(701\) | −8.77431 | −0.331401 | −0.165701 | − | 0.986176i | \(-0.552989\pi\) | ||||
−0.165701 | + | 0.986176i | \(0.552989\pi\) | |||||||
\(702\) | 230.250 | 8.69022 | ||||||||
\(703\) | −21.0979 | −0.795724 | ||||||||
\(704\) | 18.1702 | 0.684814 | ||||||||
\(705\) | 2.48967 | 0.0937665 | ||||||||
\(706\) | −49.7008 | −1.87052 | ||||||||
\(707\) | 21.9779 | 0.826565 | ||||||||
\(708\) | −31.4570 | −1.18223 | ||||||||
\(709\) | −46.4474 | −1.74437 | −0.872184 | − | 0.489179i | \(-0.837297\pi\) | ||||
−0.872184 | + | 0.489179i | \(0.837297\pi\) | |||||||
\(710\) | −16.9270 | −0.635258 | ||||||||
\(711\) | 119.452 | 4.47980 | ||||||||
\(712\) | 16.6008 | 0.622142 | ||||||||
\(713\) | −40.8018 | −1.52804 | ||||||||
\(714\) | −72.9607 | −2.73049 | ||||||||
\(715\) | −9.01938 | −0.337306 | ||||||||
\(716\) | −41.5925 | −1.55439 | ||||||||
\(717\) | 31.9163 | 1.19194 | ||||||||
\(718\) | 66.8117 | 2.49339 | ||||||||
\(719\) | −17.0092 | −0.634334 | −0.317167 | − | 0.948370i | \(-0.602732\pi\) | ||||
−0.317167 | + | 0.948370i | \(0.602732\pi\) | |||||||
\(720\) | −11.0755 | −0.412759 | ||||||||
\(721\) | 25.8429 | 0.962440 | ||||||||
\(722\) | 13.9762 | 0.520142 | ||||||||
\(723\) | 56.7082 | 2.10900 | ||||||||
\(724\) | 18.4303 | 0.684956 | ||||||||
\(725\) | 4.39018 | 0.163047 | ||||||||
\(726\) | −65.8630 | −2.44440 | ||||||||
\(727\) | −2.35940 | −0.0875054 | −0.0437527 | − | 0.999042i | \(-0.513931\pi\) | ||||
−0.0437527 | + | 0.999042i | \(0.513931\pi\) | |||||||
\(728\) | 22.2992 | 0.826465 | ||||||||
\(729\) | 77.2854 | 2.86242 | ||||||||
\(730\) | −7.24576 | −0.268178 | ||||||||
\(731\) | −52.5234 | −1.94265 | ||||||||
\(732\) | 105.919 | 3.91489 | ||||||||
\(733\) | −2.67642 | −0.0988560 | −0.0494280 | − | 0.998778i | \(-0.515740\pi\) | ||||
−0.0494280 | + | 0.998778i | \(0.515740\pi\) | |||||||
\(734\) | 14.7741 | 0.545323 | ||||||||
\(735\) | 12.9210 | 0.476599 | ||||||||
\(736\) | −35.2191 | −1.29819 | ||||||||
\(737\) | 6.01355 | 0.221512 | ||||||||
\(738\) | −86.0459 | −3.16739 | ||||||||
\(739\) | −39.0062 | −1.43487 | −0.717433 | − | 0.696627i | \(-0.754683\pi\) | ||||
−0.717433 | + | 0.696627i | \(0.754683\pi\) | |||||||
\(740\) | −17.1693 | −0.631154 | ||||||||
\(741\) | −75.1058 | −2.75908 | ||||||||
\(742\) | −21.9298 | −0.805070 | ||||||||
\(743\) | −7.91776 | −0.290474 | −0.145237 | − | 0.989397i | \(-0.546395\pi\) | ||||
−0.145237 | + | 0.989397i | \(0.546395\pi\) | |||||||
\(744\) | 53.8253 | 1.97333 | ||||||||
\(745\) | −0.985931 | −0.0361217 | ||||||||
\(746\) | −30.4320 | −1.11419 | ||||||||
\(747\) | −137.936 | −5.04682 | ||||||||
\(748\) | −23.2396 | −0.849726 | ||||||||
\(749\) | −5.27179 | −0.192627 | ||||||||
\(750\) | 7.31821 | 0.267223 | ||||||||
\(751\) | −24.6760 | −0.900441 | −0.450220 | − | 0.892918i | \(-0.648655\pi\) | ||||
−0.450220 | + | 0.892918i | \(0.648655\pi\) | |||||||
\(752\) | 1.05116 | 0.0383318 | ||||||||
\(753\) | −11.1742 | −0.407210 | ||||||||
\(754\) | −61.9666 | −2.25669 | ||||||||
\(755\) | −1.66557 | −0.0606164 | ||||||||
\(756\) | 83.1429 | 3.02388 | ||||||||
\(757\) | −31.7681 | −1.15463 | −0.577315 | − | 0.816521i | \(-0.695900\pi\) | ||||
−0.577315 | + | 0.816521i | \(0.695900\pi\) | |||||||
\(758\) | 57.5007 | 2.08852 | ||||||||
\(759\) | −23.3065 | −0.845971 | ||||||||
\(760\) | −7.08186 | −0.256886 | ||||||||
\(761\) | −19.6610 | −0.712711 | −0.356356 | − | 0.934350i | \(-0.615981\pi\) | ||||
−0.356356 | + | 0.934350i | \(0.615981\pi\) | |||||||
\(762\) | 48.2752 | 1.74882 | ||||||||
\(763\) | 31.7029 | 1.14772 | ||||||||
\(764\) | 38.0334 | 1.37600 | ||||||||
\(765\) | 44.9781 | 1.62619 | ||||||||
\(766\) | 37.0607 | 1.33906 | ||||||||
\(767\) | 20.9329 | 0.755843 | ||||||||
\(768\) | 19.7017 | 0.710924 | ||||||||
\(769\) | −16.6797 | −0.601484 | −0.300742 | − | 0.953706i | \(-0.597234\pi\) | ||||
−0.300742 | + | 0.953706i | \(0.597234\pi\) | |||||||
\(770\) | −5.50425 | −0.198359 | ||||||||
\(771\) | −64.3432 | −2.31726 | ||||||||
\(772\) | 51.1118 | 1.83955 | ||||||||
\(773\) | 37.5716 | 1.35135 | 0.675677 | − | 0.737197i | \(-0.263851\pi\) | ||||
0.675677 | + | 0.737197i | \(0.263851\pi\) | |||||||
\(774\) | 162.666 | 5.84692 | ||||||||
\(775\) | 8.18670 | 0.294075 | ||||||||
\(776\) | 38.1883 | 1.37088 | ||||||||
\(777\) | −34.4439 | −1.23567 | ||||||||
\(778\) | −22.1298 | −0.793391 | ||||||||
\(779\) | 17.4538 | 0.625349 | ||||||||
\(780\) | −61.1202 | −2.18845 | ||||||||
\(781\) | −10.8163 | −0.387039 | ||||||||
\(782\) | 62.5373 | 2.23633 | ||||||||
\(783\) | −71.6153 | −2.55932 | ||||||||
\(784\) | 5.45534 | 0.194834 | ||||||||
\(785\) | 4.38148 | 0.156382 | ||||||||
\(786\) | −42.1840 | −1.50465 | ||||||||
\(787\) | 26.2070 | 0.934179 | 0.467090 | − | 0.884210i | \(-0.345303\pi\) | ||||
0.467090 | + | 0.884210i | \(0.345303\pi\) | |||||||
\(788\) | 20.4451 | 0.728326 | ||||||||
\(789\) | 39.1134 | 1.39247 | ||||||||
\(790\) | −33.3243 | −1.18563 | ||||||||
\(791\) | 15.6114 | 0.555078 | ||||||||
\(792\) | 22.3094 | 0.792730 | ||||||||
\(793\) | −70.4833 | −2.50294 | ||||||||
\(794\) | 61.0461 | 2.16645 | ||||||||
\(795\) | 18.6313 | 0.660785 | ||||||||
\(796\) | −8.26224 | −0.292847 | ||||||||
\(797\) | −13.5027 | −0.478290 | −0.239145 | − | 0.970984i | \(-0.576867\pi\) | ||||
−0.239145 | + | 0.970984i | \(0.576867\pi\) | |||||||
\(798\) | −45.8348 | −1.62253 | ||||||||
\(799\) | −4.26881 | −0.151019 | ||||||||
\(800\) | 7.06656 | 0.249841 | ||||||||
\(801\) | −66.2352 | −2.34031 | ||||||||
\(802\) | 37.6630 | 1.32993 | ||||||||
\(803\) | −4.63004 | −0.163391 | ||||||||
\(804\) | 40.7511 | 1.43718 | ||||||||
\(805\) | 8.76420 | 0.308897 | ||||||||
\(806\) | −115.554 | −4.07021 | ||||||||
\(807\) | −11.8434 | −0.416908 | ||||||||
\(808\) | 24.8510 | 0.874255 | ||||||||
\(809\) | 51.5901 | 1.81381 | 0.906905 | − | 0.421334i | \(-0.138438\pi\) | ||||
0.906905 | + | 0.421334i | \(0.138438\pi\) | |||||||
\(810\) | −66.7039 | −2.34374 | ||||||||
\(811\) | 0.458462 | 0.0160988 | 0.00804939 | − | 0.999968i | \(-0.497438\pi\) | ||||
0.00804939 | + | 0.999968i | \(0.497438\pi\) | |||||||
\(812\) | −22.3761 | −0.785246 | ||||||||
\(813\) | 102.059 | 3.57937 | ||||||||
\(814\) | −18.5416 | −0.649884 | ||||||||
\(815\) | 15.2070 | 0.532679 | ||||||||
\(816\) | 26.1711 | 0.916173 | ||||||||
\(817\) | −32.9958 | −1.15438 | ||||||||
\(818\) | −1.48825 | −0.0520354 | ||||||||
\(819\) | −88.9713 | −3.10891 | ||||||||
\(820\) | 14.2037 | 0.496016 | ||||||||
\(821\) | 5.44952 | 0.190189 | 0.0950947 | − | 0.995468i | \(-0.469685\pi\) | ||||
0.0950947 | + | 0.995468i | \(0.469685\pi\) | |||||||
\(822\) | 116.607 | 4.06713 | ||||||||
\(823\) | 45.6465 | 1.59114 | 0.795568 | − | 0.605865i | \(-0.207173\pi\) | ||||
0.795568 | + | 0.605865i | \(0.207173\pi\) | |||||||
\(824\) | 29.2212 | 1.01797 | ||||||||
\(825\) | 4.67634 | 0.162809 | ||||||||
\(826\) | 12.7747 | 0.444489 | ||||||||
\(827\) | −40.1101 | −1.39477 | −0.697383 | − | 0.716698i | \(-0.745652\pi\) | ||||
−0.697383 | + | 0.716698i | \(0.745652\pi\) | |||||||
\(828\) | −114.601 | −3.98266 | ||||||||
\(829\) | −21.4879 | −0.746307 | −0.373153 | − | 0.927770i | \(-0.621724\pi\) | ||||
−0.373153 | + | 0.927770i | \(0.621724\pi\) | |||||||
\(830\) | 38.4809 | 1.33569 | ||||||||
\(831\) | −34.6776 | −1.20295 | ||||||||
\(832\) | −81.9367 | −2.84064 | ||||||||
\(833\) | −22.1544 | −0.767606 | ||||||||
\(834\) | −57.5919 | −1.99424 | ||||||||
\(835\) | −12.1629 | −0.420914 | ||||||||
\(836\) | −14.5994 | −0.504931 | ||||||||
\(837\) | −133.547 | −4.61605 | ||||||||
\(838\) | −29.9431 | −1.03437 | ||||||||
\(839\) | 51.9675 | 1.79412 | 0.897059 | − | 0.441912i | \(-0.145700\pi\) | ||||
0.897059 | + | 0.441912i | \(0.145700\pi\) | |||||||
\(840\) | −11.5616 | −0.398915 | ||||||||
\(841\) | −9.72634 | −0.335391 | ||||||||
\(842\) | 82.9702 | 2.85934 | ||||||||
\(843\) | −94.7868 | −3.26463 | ||||||||
\(844\) | −32.0621 | −1.10362 | ||||||||
\(845\) | 27.6721 | 0.951948 | ||||||||
\(846\) | 13.2206 | 0.454534 | ||||||||
\(847\) | 15.8263 | 0.543797 | ||||||||
\(848\) | 7.86627 | 0.270129 | ||||||||
\(849\) | 25.2201 | 0.865552 | ||||||||
\(850\) | −12.5478 | −0.430387 | ||||||||
\(851\) | 29.5231 | 1.01204 | ||||||||
\(852\) | −73.2974 | −2.51113 | ||||||||
\(853\) | −25.4040 | −0.869816 | −0.434908 | − | 0.900475i | \(-0.643219\pi\) | ||||
−0.434908 | + | 0.900475i | \(0.643219\pi\) | |||||||
\(854\) | −43.0138 | −1.47190 | ||||||||
\(855\) | 28.2558 | 0.966327 | ||||||||
\(856\) | −5.96096 | −0.203741 | ||||||||
\(857\) | 17.2590 | 0.589557 | 0.294778 | − | 0.955566i | \(-0.404754\pi\) | ||||
0.294778 | + | 0.955566i | \(0.404754\pi\) | |||||||
\(858\) | −66.0057 | −2.25340 | ||||||||
\(859\) | −14.4909 | −0.494424 | −0.247212 | − | 0.968961i | \(-0.579514\pi\) | ||||
−0.247212 | + | 0.968961i | \(0.579514\pi\) | |||||||
\(860\) | −26.8516 | −0.915632 | ||||||||
\(861\) | 28.4946 | 0.971095 | ||||||||
\(862\) | 31.9490 | 1.08819 | ||||||||
\(863\) | 47.1849 | 1.60619 | 0.803097 | − | 0.595848i | \(-0.203184\pi\) | ||||
0.803097 | + | 0.595848i | \(0.203184\pi\) | |||||||
\(864\) | −115.274 | −3.92171 | ||||||||
\(865\) | 13.3700 | 0.454595 | ||||||||
\(866\) | 35.5353 | 1.20754 | ||||||||
\(867\) | −50.0707 | −1.70049 | ||||||||
\(868\) | −41.7264 | −1.41628 | ||||||||
\(869\) | −21.2943 | −0.722358 | ||||||||
\(870\) | 32.1283 | 1.08925 | ||||||||
\(871\) | −27.1175 | −0.918843 | ||||||||
\(872\) | 35.8473 | 1.21394 | ||||||||
\(873\) | −152.367 | −5.15684 | ||||||||
\(874\) | 39.2867 | 1.32889 | ||||||||
\(875\) | −1.75850 | −0.0594481 | ||||||||
\(876\) | −31.3757 | −1.06009 | ||||||||
\(877\) | −7.23788 | −0.244406 | −0.122203 | − | 0.992505i | \(-0.538996\pi\) | ||||
−0.122203 | + | 0.992505i | \(0.538996\pi\) | |||||||
\(878\) | −71.2126 | −2.40331 | ||||||||
\(879\) | −60.8193 | −2.05138 | ||||||||
\(880\) | 1.97438 | 0.0665565 | ||||||||
\(881\) | 22.3412 | 0.752694 | 0.376347 | − | 0.926479i | \(-0.377180\pi\) | ||||
0.376347 | + | 0.926479i | \(0.377180\pi\) | |||||||
\(882\) | 68.6129 | 2.31032 | ||||||||
\(883\) | 50.8611 | 1.71161 | 0.855807 | − | 0.517296i | \(-0.173061\pi\) | ||||
0.855807 | + | 0.517296i | \(0.173061\pi\) | |||||||
\(884\) | 104.797 | 3.52471 | ||||||||
\(885\) | −10.8532 | −0.364827 | ||||||||
\(886\) | 3.55638 | 0.119479 | ||||||||
\(887\) | −2.96240 | −0.0994678 | −0.0497339 | − | 0.998763i | \(-0.515837\pi\) | ||||
−0.0497339 | + | 0.998763i | \(0.515837\pi\) | |||||||
\(888\) | −38.9466 | −1.30696 | ||||||||
\(889\) | −11.6001 | −0.389054 | ||||||||
\(890\) | 18.4781 | 0.619387 | ||||||||
\(891\) | −42.6238 | −1.42795 | ||||||||
\(892\) | −20.8553 | −0.698287 | ||||||||
\(893\) | −2.68171 | −0.0897401 | ||||||||
\(894\) | −7.21525 | −0.241314 | ||||||||
\(895\) | −14.3501 | −0.479672 | ||||||||
\(896\) | −25.1504 | −0.840214 | ||||||||
\(897\) | 105.098 | 3.50913 | ||||||||
\(898\) | 14.7156 | 0.491065 | ||||||||
\(899\) | 35.9411 | 1.19870 | ||||||||
\(900\) | 22.9942 | 0.766474 | ||||||||
\(901\) | −31.9453 | −1.06425 | ||||||||
\(902\) | 15.3391 | 0.510736 | ||||||||
\(903\) | −53.8680 | −1.79262 | ||||||||
\(904\) | 17.6522 | 0.587104 | ||||||||
\(905\) | 6.35877 | 0.211373 | ||||||||
\(906\) | −12.1890 | −0.404953 | ||||||||
\(907\) | 10.5716 | 0.351023 | 0.175512 | − | 0.984477i | \(-0.443842\pi\) | ||||
0.175512 | + | 0.984477i | \(0.443842\pi\) | |||||||
\(908\) | 6.14396 | 0.203894 | ||||||||
\(909\) | −99.1525 | −3.28868 | ||||||||
\(910\) | 24.8209 | 0.822805 | ||||||||
\(911\) | 24.0762 | 0.797679 | 0.398840 | − | 0.917021i | \(-0.369413\pi\) | ||||
0.398840 | + | 0.917021i | \(0.369413\pi\) | |||||||
\(912\) | 16.4410 | 0.544416 | ||||||||
\(913\) | 24.5893 | 0.813789 | ||||||||
\(914\) | 30.0216 | 0.993025 | ||||||||
\(915\) | 36.5440 | 1.20811 | ||||||||
\(916\) | 10.3982 | 0.343565 | ||||||||
\(917\) | 10.1364 | 0.334735 | ||||||||
\(918\) | 204.688 | 6.75572 | ||||||||
\(919\) | −41.6721 | −1.37463 | −0.687317 | − | 0.726357i | \(-0.741212\pi\) | ||||
−0.687317 | + | 0.726357i | \(0.741212\pi\) | |||||||
\(920\) | 9.90991 | 0.326720 | ||||||||
\(921\) | 93.8684 | 3.09307 | ||||||||
\(922\) | −11.3832 | −0.374885 | ||||||||
\(923\) | 48.7753 | 1.60546 | ||||||||
\(924\) | −23.8346 | −0.784100 | ||||||||
\(925\) | −5.92369 | −0.194770 | ||||||||
\(926\) | 15.6360 | 0.513832 | ||||||||
\(927\) | −116.589 | −3.82929 | ||||||||
\(928\) | 31.0235 | 1.01840 | ||||||||
\(929\) | 19.7462 | 0.647851 | 0.323926 | − | 0.946083i | \(-0.394997\pi\) | ||||
0.323926 | + | 0.946083i | \(0.394997\pi\) | |||||||
\(930\) | 59.9120 | 1.96459 | ||||||||
\(931\) | −13.9177 | −0.456133 | ||||||||
\(932\) | −41.1893 | −1.34920 | ||||||||
\(933\) | 77.9755 | 2.55280 | ||||||||
\(934\) | 44.9930 | 1.47221 | ||||||||
\(935\) | −8.01808 | −0.262219 | ||||||||
\(936\) | −100.602 | −3.28828 | ||||||||
\(937\) | 50.8359 | 1.66074 | 0.830368 | − | 0.557216i | \(-0.188130\pi\) | ||||
0.830368 | + | 0.557216i | \(0.188130\pi\) | |||||||
\(938\) | −16.5490 | −0.540344 | ||||||||
\(939\) | −49.9295 | −1.62939 | ||||||||
\(940\) | −2.18235 | −0.0711803 | ||||||||
\(941\) | 9.53341 | 0.310780 | 0.155390 | − | 0.987853i | \(-0.450337\pi\) | ||||
0.155390 | + | 0.987853i | \(0.450337\pi\) | |||||||
\(942\) | 32.0646 | 1.04472 | ||||||||
\(943\) | −24.4238 | −0.795348 | ||||||||
\(944\) | −4.58231 | −0.149141 | ||||||||
\(945\) | 28.6858 | 0.933148 | ||||||||
\(946\) | −28.9979 | −0.942804 | ||||||||
\(947\) | 51.4667 | 1.67244 | 0.836222 | − | 0.548391i | \(-0.184759\pi\) | ||||
0.836222 | + | 0.548391i | \(0.184759\pi\) | |||||||
\(948\) | −144.301 | −4.68669 | ||||||||
\(949\) | 20.8788 | 0.677753 | ||||||||
\(950\) | −7.88270 | −0.255749 | ||||||||
\(951\) | 43.5585 | 1.41248 | ||||||||
\(952\) | 19.8237 | 0.642488 | ||||||||
\(953\) | 17.8156 | 0.577105 | 0.288553 | − | 0.957464i | \(-0.406826\pi\) | ||||
0.288553 | + | 0.957464i | \(0.406826\pi\) | |||||||
\(954\) | 98.9356 | 3.20316 | ||||||||
\(955\) | 13.1222 | 0.424624 | ||||||||
\(956\) | −27.9766 | −0.904827 | ||||||||
\(957\) | 20.5300 | 0.663640 | ||||||||
\(958\) | −55.4517 | −1.79156 | ||||||||
\(959\) | −28.0195 | −0.904798 | ||||||||
\(960\) | 42.4823 | 1.37111 | ||||||||
\(961\) | 36.0221 | 1.16200 | ||||||||
\(962\) | 83.6118 | 2.69575 | ||||||||
\(963\) | 23.7835 | 0.766412 | ||||||||
\(964\) | −49.7081 | −1.60099 | ||||||||
\(965\) | 17.6345 | 0.567673 | ||||||||
\(966\) | 64.1383 | 2.06361 | ||||||||
\(967\) | 7.35619 | 0.236559 | 0.118280 | − | 0.992980i | \(-0.462262\pi\) | ||||
0.118280 | + | 0.992980i | \(0.462262\pi\) | |||||||
\(968\) | 17.8952 | 0.575173 | ||||||||
\(969\) | −66.7678 | −2.14489 | ||||||||
\(970\) | 42.5068 | 1.36481 | ||||||||
\(971\) | 15.7621 | 0.505829 | 0.252915 | − | 0.967489i | \(-0.418611\pi\) | ||||
0.252915 | + | 0.967489i | \(0.418611\pi\) | |||||||
\(972\) | −147.000 | −4.71503 | ||||||||
\(973\) | 13.8388 | 0.443651 | ||||||||
\(974\) | −26.2781 | −0.842004 | ||||||||
\(975\) | −21.0875 | −0.675341 | ||||||||
\(976\) | 15.4291 | 0.493874 | ||||||||
\(977\) | −1.55023 | −0.0495964 | −0.0247982 | − | 0.999692i | \(-0.507894\pi\) | ||||
−0.0247982 | + | 0.999692i | \(0.507894\pi\) | |||||||
\(978\) | 111.288 | 3.55861 | ||||||||
\(979\) | 11.8075 | 0.377370 | ||||||||
\(980\) | −11.3260 | −0.361797 | ||||||||
\(981\) | −143.026 | −4.56648 | ||||||||
\(982\) | 1.74504 | 0.0556865 | ||||||||
\(983\) | −26.6716 | −0.850693 | −0.425346 | − | 0.905031i | \(-0.639848\pi\) | ||||
−0.425346 | + | 0.905031i | \(0.639848\pi\) | |||||||
\(984\) | 32.2196 | 1.02712 | ||||||||
\(985\) | 7.05391 | 0.224756 | ||||||||
\(986\) | −55.0873 | −1.75434 | ||||||||
\(987\) | −4.37809 | −0.139356 | ||||||||
\(988\) | 65.8347 | 2.09448 | ||||||||
\(989\) | 46.1722 | 1.46819 | ||||||||
\(990\) | 24.8322 | 0.789219 | ||||||||
\(991\) | 29.8067 | 0.946842 | 0.473421 | − | 0.880836i | \(-0.343019\pi\) | ||||
0.473421 | + | 0.880836i | \(0.343019\pi\) | |||||||
\(992\) | 57.8519 | 1.83680 | ||||||||
\(993\) | −59.1783 | −1.87797 | ||||||||
\(994\) | 29.7661 | 0.944122 | ||||||||
\(995\) | −2.85062 | −0.0903706 | ||||||||
\(996\) | 166.631 | 5.27990 | ||||||||
\(997\) | −36.1045 | −1.14344 | −0.571720 | − | 0.820449i | \(-0.693724\pi\) | ||||
−0.571720 | + | 0.820449i | \(0.693724\pi\) | |||||||
\(998\) | −68.1268 | −2.15652 | ||||||||
\(999\) | 96.6310 | 3.05727 |
(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 | 6005.2.a.e.1.13 | ✓ | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6005.2.a.e.1.13 | ✓ | 88 | 1.1 | even | 1 | trivial |