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: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} + 152 x^{17} - 274 x^{16} - 1061 x^{15} + 3125 x^{14} + 2977 x^{13} - 15474 x^{12} + \cdots + 31 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 889) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.70334\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70334 | −1.91155 | −0.955775 | − | 0.294098i | \(-0.904981\pi\) | ||||
−0.955775 | + | 0.294098i | \(0.904981\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.30805 | 2.65402 | ||||||||
\(5\) | 3.37987 | 1.51152 | 0.755761 | − | 0.654848i | \(-0.227267\pi\) | ||||
0.755761 | + | 0.654848i | \(0.227267\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −8.94278 | −3.16175 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −9.13693 | −2.88935 | ||||||||
\(11\) | −5.25067 | −1.58314 | −0.791568 | − | 0.611081i | \(-0.790735\pi\) | ||||
−0.791568 | + | 0.611081i | \(0.790735\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.49005 | 1.24532 | 0.622658 | − | 0.782494i | \(-0.286053\pi\) | ||||
0.622658 | + | 0.782494i | \(0.286053\pi\) | |||||||
\(14\) | −2.70334 | −0.722498 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.5593 | 3.38982 | ||||||||
\(17\) | 2.55842 | 0.620508 | 0.310254 | − | 0.950654i | \(-0.399586\pi\) | ||||
0.310254 | + | 0.950654i | \(0.399586\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.86089 | −1.57400 | −0.786998 | − | 0.616956i | \(-0.788366\pi\) | ||||
−0.786998 | + | 0.616956i | \(0.788366\pi\) | |||||||
\(20\) | 17.9405 | 4.01162 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 14.1943 | 3.02624 | ||||||||
\(23\) | −6.11893 | −1.27588 | −0.637942 | − | 0.770084i | \(-0.720214\pi\) | ||||
−0.637942 | + | 0.770084i | \(0.720214\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.42349 | 1.28470 | ||||||||
\(26\) | −12.1381 | −2.38048 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.30805 | 1.00313 | ||||||||
\(29\) | 9.43242 | 1.75156 | 0.875778 | − | 0.482713i | \(-0.160349\pi\) | ||||
0.875778 | + | 0.482713i | \(0.160349\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.617404 | −0.110889 | −0.0554445 | − | 0.998462i | \(-0.517658\pi\) | ||||
−0.0554445 | + | 0.998462i | \(0.517658\pi\) | |||||||
\(32\) | −18.7698 | −3.31807 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.91628 | −1.18613 | ||||||||
\(35\) | 3.37987 | 0.571302 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.3444 | −1.70061 | −0.850304 | − | 0.526291i | \(-0.823582\pi\) | ||||
−0.850304 | + | 0.526291i | \(0.823582\pi\) | |||||||
\(38\) | 18.5473 | 3.00877 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −30.2254 | −4.77906 | ||||||||
\(41\) | −6.74914 | −1.05404 | −0.527019 | − | 0.849853i | \(-0.676690\pi\) | ||||
−0.527019 | + | 0.849853i | \(0.676690\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.27103 | −1.26132 | −0.630660 | − | 0.776059i | \(-0.717216\pi\) | ||||
−0.630660 | + | 0.776059i | \(0.717216\pi\) | |||||||
\(44\) | −27.8708 | −4.20168 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 16.5415 | 2.43892 | ||||||||
\(47\) | −3.41047 | −0.497469 | −0.248734 | − | 0.968572i | \(-0.580015\pi\) | ||||
−0.248734 | + | 0.968572i | \(0.580015\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −17.3649 | −2.45577 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 23.8334 | 3.30510 | ||||||||
\(53\) | 1.36566 | 0.187588 | 0.0937941 | − | 0.995592i | \(-0.470100\pi\) | ||||
0.0937941 | + | 0.995592i | \(0.470100\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17.7466 | −2.39294 | ||||||||
\(56\) | −8.94278 | −1.19503 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −25.4990 | −3.34819 | ||||||||
\(59\) | −0.337596 | −0.0439512 | −0.0219756 | − | 0.999759i | \(-0.506996\pi\) | ||||
−0.0219756 | + | 0.999759i | \(0.506996\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.71415 | 0.731622 | 0.365811 | − | 0.930689i | \(-0.380792\pi\) | ||||
0.365811 | + | 0.930689i | \(0.380792\pi\) | |||||||
\(62\) | 1.66905 | 0.211970 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 23.6226 | 2.95283 | ||||||||
\(65\) | 15.1758 | 1.88232 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.68440 | 0.816629 | 0.408315 | − | 0.912841i | \(-0.366117\pi\) | ||||
0.408315 | + | 0.912841i | \(0.366117\pi\) | |||||||
\(68\) | 13.5802 | 1.64684 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −9.13693 | −1.09207 | ||||||||
\(71\) | 5.42767 | 0.644146 | 0.322073 | − | 0.946715i | \(-0.395620\pi\) | ||||
0.322073 | + | 0.946715i | \(0.395620\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.39586 | 0.163373 | 0.0816867 | − | 0.996658i | \(-0.473969\pi\) | ||||
0.0816867 | + | 0.996658i | \(0.473969\pi\) | |||||||
\(74\) | 27.9644 | 3.25080 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −36.4179 | −4.17742 | ||||||||
\(77\) | −5.25067 | −0.598369 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.00792 | −0.675944 | −0.337972 | − | 0.941156i | \(-0.609741\pi\) | ||||
−0.337972 | + | 0.941156i | \(0.609741\pi\) | |||||||
\(80\) | 45.8286 | 5.12379 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 18.2452 | 2.01485 | ||||||||
\(83\) | 15.5854 | 1.71072 | 0.855358 | − | 0.518037i | \(-0.173337\pi\) | ||||
0.855358 | + | 0.518037i | \(0.173337\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.64712 | 0.937911 | ||||||||
\(86\) | 22.3594 | 2.41108 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 46.9556 | 5.00548 | ||||||||
\(89\) | 9.64990 | 1.02289 | 0.511444 | − | 0.859317i | \(-0.329111\pi\) | ||||
0.511444 | + | 0.859317i | \(0.329111\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.49005 | 0.470685 | ||||||||
\(92\) | −32.4796 | −3.38623 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.21967 | 0.950937 | ||||||||
\(95\) | −23.1889 | −2.37913 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.82769 | 0.388643 | 0.194322 | − | 0.980938i | \(-0.437749\pi\) | ||||
0.194322 | + | 0.980938i | \(0.437749\pi\) | |||||||
\(98\) | −2.70334 | −0.273079 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 34.0962 | 3.40962 | ||||||||
\(101\) | −6.95323 | −0.691872 | −0.345936 | − | 0.938258i | \(-0.612439\pi\) | ||||
−0.345936 | + | 0.938258i | \(0.612439\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.95576 | −0.882437 | −0.441218 | − | 0.897400i | \(-0.645454\pi\) | ||||
−0.441218 | + | 0.897400i | \(0.645454\pi\) | |||||||
\(104\) | −40.1535 | −3.93738 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.69185 | −0.358584 | ||||||||
\(107\) | −5.94244 | −0.574478 | −0.287239 | − | 0.957859i | \(-0.592737\pi\) | ||||
−0.287239 | + | 0.957859i | \(0.592737\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.18703 | −0.879958 | −0.439979 | − | 0.898008i | \(-0.645014\pi\) | ||||
−0.439979 | + | 0.898008i | \(0.645014\pi\) | |||||||
\(110\) | 47.9750 | 4.57423 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 13.5593 | 1.28123 | ||||||||
\(113\) | −19.6841 | −1.85173 | −0.925863 | − | 0.377859i | \(-0.876660\pi\) | ||||
−0.925863 | + | 0.377859i | \(0.876660\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20.6812 | −1.92853 | ||||||||
\(116\) | 50.0678 | 4.64868 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.912636 | 0.0840149 | ||||||||
\(119\) | 2.55842 | 0.234530 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.5695 | 1.50632 | ||||||||
\(122\) | −15.4473 | −1.39853 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.27721 | −0.294302 | ||||||||
\(125\) | 4.81121 | 0.430327 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −26.3203 | −2.32641 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −41.0252 | −3.59815 | ||||||||
\(131\) | −3.12882 | −0.273367 | −0.136683 | − | 0.990615i | \(-0.543644\pi\) | ||||
−0.136683 | + | 0.990615i | \(0.543644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.86089 | −0.594914 | ||||||||
\(134\) | −18.0702 | −1.56103 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −22.8794 | −1.96189 | ||||||||
\(137\) | 1.05209 | 0.0898865 | 0.0449433 | − | 0.998990i | \(-0.485689\pi\) | ||||
0.0449433 | + | 0.998990i | \(0.485689\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.33299 | 0.197882 | 0.0989410 | − | 0.995093i | \(-0.468454\pi\) | ||||
0.0989410 | + | 0.995093i | \(0.468454\pi\) | |||||||
\(140\) | 17.9405 | 1.51625 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.6728 | −1.23132 | ||||||||
\(143\) | −23.5758 | −1.97150 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 31.8803 | 2.64752 | ||||||||
\(146\) | −3.77349 | −0.312297 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −54.9086 | −4.51346 | ||||||||
\(149\) | −15.2050 | −1.24564 | −0.622821 | − | 0.782365i | \(-0.714013\pi\) | ||||
−0.622821 | + | 0.782365i | \(0.714013\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.99981 | 0.406879 | 0.203439 | − | 0.979088i | \(-0.434788\pi\) | ||||
0.203439 | + | 0.979088i | \(0.434788\pi\) | |||||||
\(152\) | 61.3554 | 4.97658 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.1943 | 1.14381 | ||||||||
\(155\) | −2.08674 | −0.167611 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.3318 | 1.46304 | 0.731520 | − | 0.681820i | \(-0.238811\pi\) | ||||
0.731520 | + | 0.681820i | \(0.238811\pi\) | |||||||
\(158\) | 16.2415 | 1.29210 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −63.4394 | −5.01533 | ||||||||
\(161\) | −6.11893 | −0.482239 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.16547 | −0.247939 | −0.123970 | − | 0.992286i | \(-0.539563\pi\) | ||||
−0.123970 | + | 0.992286i | \(0.539563\pi\) | |||||||
\(164\) | −35.8248 | −2.79744 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −42.1326 | −3.27012 | ||||||||
\(167\) | −7.87265 | −0.609204 | −0.304602 | − | 0.952480i | \(-0.598523\pi\) | ||||
−0.304602 | + | 0.952480i | \(0.598523\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.16053 | 0.550810 | ||||||||
\(170\) | −23.3761 | −1.79286 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −43.9030 | −3.34757 | ||||||||
\(173\) | −18.3086 | −1.39198 | −0.695990 | − | 0.718052i | \(-0.745034\pi\) | ||||
−0.695990 | + | 0.718052i | \(0.745034\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.42349 | 0.485570 | ||||||||
\(176\) | −71.1954 | −5.36655 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −26.0870 | −1.95530 | ||||||||
\(179\) | 15.1624 | 1.13329 | 0.566645 | − | 0.823962i | \(-0.308241\pi\) | ||||
0.566645 | + | 0.823962i | \(0.308241\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.7500 | −0.947697 | −0.473849 | − | 0.880606i | \(-0.657136\pi\) | ||||
−0.473849 | + | 0.880606i | \(0.657136\pi\) | |||||||
\(182\) | −12.1381 | −0.899738 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 54.7203 | 4.03403 | ||||||||
\(185\) | −34.9627 | −2.57051 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.4334 | −0.982349 | ||||||||
\(188\) | −18.1030 | −1.32029 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 62.6874 | 4.54782 | ||||||||
\(191\) | −17.0688 | −1.23506 | −0.617528 | − | 0.786549i | \(-0.711866\pi\) | ||||
−0.617528 | + | 0.786549i | \(0.711866\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.72396 | 0.699946 | 0.349973 | − | 0.936760i | \(-0.386191\pi\) | ||||
0.349973 | + | 0.936760i | \(0.386191\pi\) | |||||||
\(194\) | −10.3476 | −0.742911 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.30805 | 0.379146 | ||||||||
\(197\) | −14.9898 | −1.06798 | −0.533989 | − | 0.845491i | \(-0.679308\pi\) | ||||
−0.533989 | + | 0.845491i | \(0.679308\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.3640 | −0.734684 | −0.367342 | − | 0.930086i | \(-0.619732\pi\) | ||||
−0.367342 | + | 0.930086i | \(0.619732\pi\) | |||||||
\(200\) | −57.4439 | −4.06190 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 18.7969 | 1.32255 | ||||||||
\(203\) | 9.43242 | 0.662026 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.8112 | −1.59320 | ||||||||
\(206\) | 24.2105 | 1.68682 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 60.8819 | 4.22140 | ||||||||
\(209\) | 36.0243 | 2.49185 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.4342 | −0.718323 | −0.359162 | − | 0.933275i | \(-0.616937\pi\) | ||||
−0.359162 | + | 0.933275i | \(0.616937\pi\) | |||||||
\(212\) | 7.24900 | 0.497864 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 16.0644 | 1.09814 | ||||||||
\(215\) | −27.9550 | −1.90651 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.617404 | −0.0419121 | ||||||||
\(218\) | 24.8357 | 1.68208 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −94.1996 | −6.35094 | ||||||||
\(221\) | 11.4874 | 0.772728 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.78334 | 0.521211 | 0.260605 | − | 0.965445i | \(-0.416078\pi\) | ||||
0.260605 | + | 0.965445i | \(0.416078\pi\) | |||||||
\(224\) | −18.7698 | −1.25411 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 53.2129 | 3.53967 | ||||||||
\(227\) | −15.3057 | −1.01588 | −0.507938 | − | 0.861394i | \(-0.669592\pi\) | ||||
−0.507938 | + | 0.861394i | \(0.669592\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.3312 | 0.880950 | 0.440475 | − | 0.897765i | \(-0.354810\pi\) | ||||
0.440475 | + | 0.897765i | \(0.354810\pi\) | |||||||
\(230\) | 55.9082 | 3.68648 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −84.3521 | −5.53799 | ||||||||
\(233\) | 0.980505 | 0.0642351 | 0.0321175 | − | 0.999484i | \(-0.489775\pi\) | ||||
0.0321175 | + | 0.999484i | \(0.489775\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.5269 | −0.751935 | ||||||||
\(236\) | −1.79197 | −0.116648 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.91628 | −0.448316 | ||||||||
\(239\) | −15.3472 | −0.992726 | −0.496363 | − | 0.868115i | \(-0.665332\pi\) | ||||
−0.496363 | + | 0.868115i | \(0.665332\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.8878 | −0.959008 | −0.479504 | − | 0.877540i | \(-0.659183\pi\) | ||||
−0.479504 | + | 0.877540i | \(0.659183\pi\) | |||||||
\(242\) | −44.7931 | −2.87941 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 30.3310 | 1.94174 | ||||||||
\(245\) | 3.37987 | 0.215932 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.8057 | −1.96012 | ||||||||
\(248\) | 5.52131 | 0.350603 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −13.0063 | −0.822592 | ||||||||
\(251\) | 7.46391 | 0.471118 | 0.235559 | − | 0.971860i | \(-0.424308\pi\) | ||||
0.235559 | + | 0.971860i | \(0.424308\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 32.1285 | 2.01990 | ||||||||
\(254\) | 2.70334 | 0.169623 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 23.9076 | 1.49422 | ||||||||
\(257\) | 14.5952 | 0.910424 | 0.455212 | − | 0.890383i | \(-0.349564\pi\) | ||||
0.455212 | + | 0.890383i | \(0.349564\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.3444 | −0.642770 | ||||||||
\(260\) | 80.5537 | 4.99573 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.45827 | 0.522554 | ||||||||
\(263\) | −3.51267 | −0.216600 | −0.108300 | − | 0.994118i | \(-0.534541\pi\) | ||||
−0.108300 | + | 0.994118i | \(0.534541\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.61575 | 0.283544 | ||||||||
\(266\) | 18.5473 | 1.13721 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 35.4811 | 2.16735 | ||||||||
\(269\) | −28.4308 | −1.73346 | −0.866730 | − | 0.498778i | \(-0.833782\pi\) | ||||
−0.866730 | + | 0.498778i | \(0.833782\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.5540 | −0.884091 | −0.442046 | − | 0.896993i | \(-0.645747\pi\) | ||||
−0.442046 | + | 0.896993i | \(0.645747\pi\) | |||||||
\(272\) | 34.6904 | 2.10341 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.84417 | −0.171823 | ||||||||
\(275\) | −33.7276 | −2.03385 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.94513 | −0.297124 | −0.148562 | − | 0.988903i | \(-0.547464\pi\) | ||||
−0.148562 | + | 0.988903i | \(0.547464\pi\) | |||||||
\(278\) | −6.30688 | −0.378261 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −30.2254 | −1.80631 | ||||||||
\(281\) | 6.32037 | 0.377041 | 0.188521 | − | 0.982069i | \(-0.439631\pi\) | ||||
0.188521 | + | 0.982069i | \(0.439631\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.0334489 | −0.00198833 | −0.000994166 | − | 1.00000i | \(-0.500316\pi\) | ||||
−0.000994166 | 1.00000i | \(0.500316\pi\) | ||||||||
\(284\) | 28.8104 | 1.70958 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 63.7333 | 3.76863 | ||||||||
\(287\) | −6.74914 | −0.398389 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.4545 | −0.614970 | ||||||||
\(290\) | −86.1834 | −5.06086 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.40931 | 0.433597 | ||||||||
\(293\) | −2.54882 | −0.148904 | −0.0744518 | − | 0.997225i | \(-0.523721\pi\) | ||||
−0.0744518 | + | 0.997225i | \(0.523721\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.14103 | −0.0664332 | ||||||||
\(296\) | 92.5077 | 5.37690 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 41.1043 | 2.38111 | ||||||||
\(299\) | −27.4743 | −1.58888 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.27103 | −0.476734 | ||||||||
\(302\) | −13.5162 | −0.777769 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −93.0288 | −5.33557 | ||||||||
\(305\) | 19.3131 | 1.10586 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.5638 | 0.659978 | 0.329989 | − | 0.943985i | \(-0.392955\pi\) | ||||
0.329989 | + | 0.943985i | \(0.392955\pi\) | |||||||
\(308\) | −27.8708 | −1.58809 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.64117 | 0.320397 | ||||||||
\(311\) | 4.48029 | 0.254054 | 0.127027 | − | 0.991899i | \(-0.459457\pi\) | ||||
0.127027 | + | 0.991899i | \(0.459457\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.70683 | 0.266046 | 0.133023 | − | 0.991113i | \(-0.457532\pi\) | ||||
0.133023 | + | 0.991113i | \(0.457532\pi\) | |||||||
\(314\) | −49.5572 | −2.79668 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −31.8903 | −1.79397 | ||||||||
\(317\) | 17.3945 | 0.976973 | 0.488487 | − | 0.872571i | \(-0.337549\pi\) | ||||
0.488487 | + | 0.872571i | \(0.337549\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −49.5265 | −2.77295 | ||||||||
\(320\) | 79.8412 | 4.46326 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 16.5415 | 0.921824 | ||||||||
\(323\) | −17.5530 | −0.976677 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.8418 | 1.59985 | ||||||||
\(326\) | 8.55735 | 0.473948 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 60.3561 | 3.33261 | ||||||||
\(329\) | −3.41047 | −0.188026 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.3051 | −1.66572 | −0.832858 | − | 0.553486i | \(-0.813297\pi\) | ||||
−0.832858 | + | 0.553486i | \(0.813297\pi\) | |||||||
\(332\) | 82.7279 | 4.54028 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 21.2824 | 1.16452 | ||||||||
\(335\) | 22.5924 | 1.23435 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.7859 | −0.914387 | −0.457193 | − | 0.889367i | \(-0.651145\pi\) | ||||
−0.457193 | + | 0.889367i | \(0.651145\pi\) | |||||||
\(338\) | −19.3574 | −1.05290 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 45.8993 | 2.48924 | ||||||||
\(341\) | 3.24178 | 0.175552 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 73.9660 | 3.98798 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 49.4945 | 2.66084 | ||||||||
\(347\) | −10.5664 | −0.567237 | −0.283618 | − | 0.958937i | \(-0.591535\pi\) | ||||
−0.283618 | + | 0.958937i | \(0.591535\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.9202 | −1.28042 | −0.640210 | − | 0.768200i | \(-0.721153\pi\) | ||||
−0.640210 | + | 0.768200i | \(0.721153\pi\) | |||||||
\(350\) | −17.3649 | −0.928192 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 98.5541 | 5.25295 | ||||||||
\(353\) | −16.7448 | −0.891234 | −0.445617 | − | 0.895224i | \(-0.647016\pi\) | ||||
−0.445617 | + | 0.895224i | \(0.647016\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.3448 | 0.973641 | ||||||||
\(356\) | 51.2222 | 2.71477 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −40.9891 | −2.16634 | ||||||||
\(359\) | −20.7481 | −1.09504 | −0.547521 | − | 0.836792i | \(-0.684428\pi\) | ||||
−0.547521 | + | 0.836792i | \(0.684428\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 28.0718 | 1.47746 | ||||||||
\(362\) | 34.4675 | 1.81157 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 23.8334 | 1.24921 | ||||||||
\(365\) | 4.71783 | 0.246942 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.6774 | 0.870552 | 0.435276 | − | 0.900297i | \(-0.356651\pi\) | ||||
0.435276 | + | 0.900297i | \(0.356651\pi\) | |||||||
\(368\) | −82.9683 | −4.32502 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 94.5160 | 4.91365 | ||||||||
\(371\) | 1.36566 | 0.0709017 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.9735 | −0.930630 | −0.465315 | − | 0.885145i | \(-0.654059\pi\) | ||||
−0.465315 | + | 0.885145i | \(0.654059\pi\) | |||||||
\(374\) | 36.3151 | 1.87781 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 30.4991 | 1.57287 | ||||||||
\(377\) | 42.3520 | 2.18124 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.7475 | 1.27119 | 0.635596 | − | 0.772022i | \(-0.280754\pi\) | ||||
0.635596 | + | 0.772022i | \(0.280754\pi\) | |||||||
\(380\) | −123.088 | −6.31427 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 46.1428 | 2.36087 | ||||||||
\(383\) | −12.0933 | −0.617937 | −0.308969 | − | 0.951072i | \(-0.599984\pi\) | ||||
−0.308969 | + | 0.951072i | \(0.599984\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.7466 | −0.904448 | ||||||||
\(386\) | −26.2872 | −1.33798 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 20.3176 | 1.03147 | ||||||||
\(389\) | 17.9749 | 0.911366 | 0.455683 | − | 0.890142i | \(-0.349395\pi\) | ||||
0.455683 | + | 0.890142i | \(0.349395\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.6548 | −0.791697 | ||||||||
\(392\) | −8.94278 | −0.451679 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 40.5225 | 2.04149 | ||||||||
\(395\) | −20.3060 | −1.02170 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.0933 | −1.00845 | −0.504227 | − | 0.863571i | \(-0.668223\pi\) | ||||
−0.504227 | + | 0.863571i | \(0.668223\pi\) | |||||||
\(398\) | 28.0174 | 1.40438 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 87.0980 | 4.35490 | ||||||||
\(401\) | 12.8155 | 0.639977 | 0.319988 | − | 0.947421i | \(-0.396321\pi\) | ||||
0.319988 | + | 0.947421i | \(0.396321\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.77217 | −0.138092 | ||||||||
\(404\) | −36.9081 | −1.83625 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −25.4990 | −1.26550 | ||||||||
\(407\) | 54.3150 | 2.69230 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −36.7896 | −1.81913 | −0.909565 | − | 0.415561i | \(-0.863585\pi\) | ||||
−0.909565 | + | 0.415561i | \(0.863585\pi\) | |||||||
\(410\) | 61.6664 | 3.04548 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −47.5376 | −2.34201 | ||||||||
\(413\) | −0.337596 | −0.0166120 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 52.6764 | 2.58578 | ||||||||
\(416\) | −84.2774 | −4.13204 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −97.3858 | −4.76330 | ||||||||
\(419\) | −6.79609 | −0.332011 | −0.166005 | − | 0.986125i | \(-0.553087\pi\) | ||||
−0.166005 | + | 0.986125i | \(0.553087\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.22713 | −0.157281 | −0.0786403 | − | 0.996903i | \(-0.525058\pi\) | ||||
−0.0786403 | + | 0.996903i | \(0.525058\pi\) | |||||||
\(422\) | 28.2073 | 1.37311 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.2128 | −0.593107 | ||||||||
\(425\) | 16.4340 | 0.797165 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.71415 | 0.276527 | ||||||||
\(428\) | −31.5428 | −1.52468 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 75.5718 | 3.64439 | ||||||||
\(431\) | −0.898205 | −0.0432650 | −0.0216325 | − | 0.999766i | \(-0.506886\pi\) | ||||
−0.0216325 | + | 0.999766i | \(0.506886\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.28781 | −0.446344 | −0.223172 | − | 0.974779i | \(-0.571641\pi\) | ||||
−0.223172 | + | 0.974779i | \(0.571641\pi\) | |||||||
\(434\) | 1.66905 | 0.0801171 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −48.7652 | −2.33543 | ||||||||
\(437\) | 41.9813 | 2.00824 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.8478 | 1.52001 | 0.760007 | − | 0.649915i | \(-0.225195\pi\) | ||||
0.760007 | + | 0.649915i | \(0.225195\pi\) | |||||||
\(440\) | 158.704 | 7.56590 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −31.0544 | −1.47711 | ||||||||
\(443\) | 30.0862 | 1.42944 | 0.714719 | − | 0.699412i | \(-0.246555\pi\) | ||||
0.714719 | + | 0.699412i | \(0.246555\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 32.6154 | 1.54612 | ||||||||
\(446\) | −21.0410 | −0.996321 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 23.6226 | 1.11606 | ||||||||
\(449\) | 4.23952 | 0.200075 | 0.100038 | − | 0.994984i | \(-0.468104\pi\) | ||||
0.100038 | + | 0.994984i | \(0.468104\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 35.4375 | 1.66869 | ||||||||
\(452\) | −104.484 | −4.91453 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 41.3765 | 1.94190 | ||||||||
\(455\) | 15.1758 | 0.711451 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.7568 | 1.57907 | 0.789537 | − | 0.613702i | \(-0.210321\pi\) | ||||
0.789537 | + | 0.613702i | \(0.210321\pi\) | |||||||
\(458\) | −36.0388 | −1.68398 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −109.777 | −5.11836 | ||||||||
\(461\) | −26.6862 | −1.24290 | −0.621450 | − | 0.783454i | \(-0.713456\pi\) | ||||
−0.621450 | + | 0.783454i | \(0.713456\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.67632 | 0.356749 | 0.178374 | − | 0.983963i | \(-0.442916\pi\) | ||||
0.178374 | + | 0.983963i | \(0.442916\pi\) | |||||||
\(464\) | 127.897 | 5.93747 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.65064 | −0.122789 | ||||||||
\(467\) | 19.7939 | 0.915951 | 0.457976 | − | 0.888965i | \(-0.348575\pi\) | ||||
0.457976 | + | 0.888965i | \(0.348575\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.68440 | 0.308657 | ||||||||
\(470\) | 31.1613 | 1.43736 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.01904 | 0.138963 | ||||||||
\(473\) | 43.4284 | 1.99684 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −44.0708 | −2.02211 | ||||||||
\(476\) | 13.5802 | 0.622448 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 41.4886 | 1.89765 | ||||||||
\(479\) | −17.6105 | −0.804645 | −0.402323 | − | 0.915498i | \(-0.631797\pi\) | ||||
−0.402323 | + | 0.915498i | \(0.631797\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −46.4468 | −2.11779 | ||||||||
\(482\) | 40.2468 | 1.83319 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 87.9519 | 3.99781 | ||||||||
\(485\) | 12.9371 | 0.587442 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.7475 | 1.07610 | 0.538051 | − | 0.842912i | \(-0.319161\pi\) | ||||
0.538051 | + | 0.842912i | \(0.319161\pi\) | |||||||
\(488\) | −51.1004 | −2.31321 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9.13693 | −0.412764 | ||||||||
\(491\) | 19.9562 | 0.900610 | 0.450305 | − | 0.892875i | \(-0.351315\pi\) | ||||
0.450305 | + | 0.892875i | \(0.351315\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.1321 | 1.08686 | ||||||||
\(494\) | 83.2783 | 3.74687 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.37156 | −0.375894 | ||||||||
\(497\) | 5.42767 | 0.243464 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.66691 | 0.387984 | 0.193992 | − | 0.981003i | \(-0.437856\pi\) | ||||
0.193992 | + | 0.981003i | \(0.437856\pi\) | |||||||
\(500\) | 25.5381 | 1.14210 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −20.1775 | −0.900566 | ||||||||
\(503\) | 4.93173 | 0.219895 | 0.109948 | − | 0.993937i | \(-0.464932\pi\) | ||||
0.109948 | + | 0.993937i | \(0.464932\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.5010 | −1.04578 | ||||||||
\(506\) | −86.8542 | −3.86114 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.30805 | −0.235507 | ||||||||
\(509\) | −31.0693 | −1.37712 | −0.688561 | − | 0.725178i | \(-0.741757\pi\) | ||||
−0.688561 | + | 0.725178i | \(0.741757\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.39586 | 0.0617494 | ||||||||
\(512\) | −11.9897 | −0.529875 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −39.4558 | −1.74032 | ||||||||
\(515\) | −30.2693 | −1.33382 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.9073 | 0.787561 | ||||||||
\(518\) | 27.9644 | 1.22869 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −135.714 | −5.95143 | ||||||||
\(521\) | 19.9687 | 0.874845 | 0.437423 | − | 0.899256i | \(-0.355891\pi\) | ||||
0.437423 | + | 0.899256i | \(0.355891\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.4320 | −1.54933 | −0.774666 | − | 0.632370i | \(-0.782082\pi\) | ||||
−0.774666 | + | 0.632370i | \(0.782082\pi\) | |||||||
\(524\) | −16.6079 | −0.725522 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.49594 | 0.414043 | ||||||||
\(527\) | −1.57958 | −0.0688075 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.4413 | 0.627882 | ||||||||
\(530\) | −12.4780 | −0.542008 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −36.4179 | −1.57892 | ||||||||
\(533\) | −30.3040 | −1.31261 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.0847 | −0.868335 | ||||||||
\(536\) | −59.7771 | −2.58198 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 76.8583 | 3.31359 | ||||||||
\(539\) | −5.25067 | −0.226162 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.7052 | 1.36311 | 0.681557 | − | 0.731765i | \(-0.261303\pi\) | ||||
0.681557 | + | 0.731765i | \(0.261303\pi\) | |||||||
\(542\) | 39.3444 | 1.68999 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −48.0211 | −2.05889 | ||||||||
\(545\) | −31.0509 | −1.33008 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.49178 | 0.192055 | 0.0960274 | − | 0.995379i | \(-0.469386\pi\) | ||||
0.0960274 | + | 0.995379i | \(0.469386\pi\) | |||||||
\(548\) | 5.58457 | 0.238561 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 91.1772 | 3.88781 | ||||||||
\(551\) | −64.7148 | −2.75694 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.00792 | −0.255483 | ||||||||
\(554\) | 13.3684 | 0.567968 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.3837 | 0.525184 | ||||||||
\(557\) | 40.0124 | 1.69538 | 0.847691 | − | 0.530491i | \(-0.177992\pi\) | ||||
0.847691 | + | 0.530491i | \(0.177992\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −37.1373 | −1.57074 | ||||||||
\(560\) | 45.8286 | 1.93661 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.0861 | −0.720734 | ||||||||
\(563\) | 3.72850 | 0.157138 | 0.0785689 | − | 0.996909i | \(-0.474965\pi\) | ||||
0.0785689 | + | 0.996909i | \(0.474965\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −66.5297 | −2.79892 | ||||||||
\(566\) | 0.0904239 | 0.00380080 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −48.5385 | −2.03663 | ||||||||
\(569\) | 16.1147 | 0.675565 | 0.337782 | − | 0.941224i | \(-0.390323\pi\) | ||||
0.337782 | + | 0.941224i | \(0.390323\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.1134 | 0.674323 | 0.337162 | − | 0.941447i | \(-0.390533\pi\) | ||||
0.337162 | + | 0.941447i | \(0.390533\pi\) | |||||||
\(572\) | −125.141 | −5.23242 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 18.2452 | 0.761541 | ||||||||
\(575\) | −39.3049 | −1.63913 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.0898 | −0.628195 | −0.314097 | − | 0.949391i | \(-0.601702\pi\) | ||||
−0.314097 | + | 0.949391i | \(0.601702\pi\) | |||||||
\(578\) | 28.2620 | 1.17555 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 169.222 | 7.02657 | ||||||||
\(581\) | 15.5854 | 0.646590 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.17064 | −0.296978 | ||||||||
\(584\) | −12.4829 | −0.516546 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.89033 | 0.284637 | ||||||||
\(587\) | −33.6856 | −1.39035 | −0.695176 | − | 0.718839i | \(-0.744674\pi\) | ||||
−0.695176 | + | 0.718839i | \(0.744674\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.23594 | 0.174539 | ||||||||
\(590\) | 3.08459 | 0.126990 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −140.263 | −5.76476 | ||||||||
\(593\) | 32.7387 | 1.34442 | 0.672208 | − | 0.740363i | \(-0.265346\pi\) | ||||
0.672208 | + | 0.740363i | \(0.265346\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.64712 | 0.354497 | ||||||||
\(596\) | −80.7088 | −3.30596 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 74.2724 | 3.03722 | ||||||||
\(599\) | 9.12458 | 0.372820 | 0.186410 | − | 0.982472i | \(-0.440315\pi\) | ||||
0.186410 | + | 0.982472i | \(0.440315\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.9337 | 1.75130 | 0.875651 | − | 0.482944i | \(-0.160433\pi\) | ||||
0.875651 | + | 0.482944i | \(0.160433\pi\) | |||||||
\(602\) | 22.3594 | 0.911301 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 26.5392 | 1.07987 | ||||||||
\(605\) | 56.0028 | 2.27684 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.8019 | 1.45315 | 0.726576 | − | 0.687086i | \(-0.241110\pi\) | ||||
0.726576 | + | 0.687086i | \(0.241110\pi\) | |||||||
\(608\) | 128.778 | 5.22262 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −52.2097 | −2.11391 | ||||||||
\(611\) | −15.3132 | −0.619506 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.5183 | 0.586390 | 0.293195 | − | 0.956053i | \(-0.405281\pi\) | ||||
0.293195 | + | 0.956053i | \(0.405281\pi\) | |||||||
\(614\) | −31.2608 | −1.26158 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 46.9556 | 1.89190 | ||||||||
\(617\) | −20.4296 | −0.822465 | −0.411233 | − | 0.911530i | \(-0.634902\pi\) | ||||
−0.411233 | + | 0.911530i | \(0.634902\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.9525 | −0.882344 | −0.441172 | − | 0.897423i | \(-0.645437\pi\) | ||||
−0.441172 | + | 0.897423i | \(0.645437\pi\) | |||||||
\(620\) | −11.0765 | −0.444844 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.1117 | −0.485637 | ||||||||
\(623\) | 9.64990 | 0.386615 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.8562 | −0.634249 | ||||||||
\(626\) | −12.7242 | −0.508560 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 97.3064 | 3.88295 | ||||||||
\(629\) | −26.4653 | −1.05524 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.2276 | −0.964484 | −0.482242 | − | 0.876038i | \(-0.660177\pi\) | ||||
−0.482242 | + | 0.876038i | \(0.660177\pi\) | |||||||
\(632\) | 53.7275 | 2.13717 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −47.0233 | −1.86753 | ||||||||
\(635\) | −3.37987 | −0.134126 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.49005 | 0.177902 | ||||||||
\(638\) | 133.887 | 5.30064 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −88.9592 | −3.51642 | ||||||||
\(641\) | −12.2334 | −0.483190 | −0.241595 | − | 0.970377i | \(-0.577670\pi\) | ||||
−0.241595 | + | 0.970377i | \(0.577670\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.0429 | −0.474927 | −0.237463 | − | 0.971396i | \(-0.576316\pi\) | ||||
−0.237463 | + | 0.971396i | \(0.576316\pi\) | |||||||
\(644\) | −32.4796 | −1.27987 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 47.4518 | 1.86697 | ||||||||
\(647\) | 1.39209 | 0.0547288 | 0.0273644 | − | 0.999626i | \(-0.491289\pi\) | ||||
0.0273644 | + | 0.999626i | \(0.491289\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.77260 | 0.0695807 | ||||||||
\(650\) | −77.9692 | −3.05820 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.8025 | −0.658036 | ||||||||
\(653\) | −2.45928 | −0.0962392 | −0.0481196 | − | 0.998842i | \(-0.515323\pi\) | ||||
−0.0481196 | + | 0.998842i | \(0.515323\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.5750 | −0.413200 | ||||||||
\(656\) | −91.5135 | −3.57300 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.21967 | 0.359420 | ||||||||
\(659\) | −20.6958 | −0.806193 | −0.403097 | − | 0.915157i | \(-0.632066\pi\) | ||||
−0.403097 | + | 0.915157i | \(0.632066\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.6274 | 0.724520 | 0.362260 | − | 0.932077i | \(-0.382005\pi\) | ||||
0.362260 | + | 0.932077i | \(0.382005\pi\) | |||||||
\(662\) | 81.9249 | 3.18410 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −139.377 | −5.40886 | ||||||||
\(665\) | −23.1889 | −0.899226 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −57.7163 | −2.23479 | ||||||||
\(668\) | −41.7884 | −1.61684 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −61.0749 | −2.35953 | ||||||||
\(671\) | −30.0031 | −1.15826 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.42948 | −0.286385 | −0.143193 | − | 0.989695i | \(-0.545737\pi\) | ||||
−0.143193 | + | 0.989695i | \(0.545737\pi\) | |||||||
\(674\) | 45.3780 | 1.74790 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 38.0085 | 1.46186 | ||||||||
\(677\) | −26.4077 | −1.01493 | −0.507465 | − | 0.861672i | \(-0.669417\pi\) | ||||
−0.507465 | + | 0.861672i | \(0.669417\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.82769 | 0.146893 | ||||||||
\(680\) | −77.3293 | −2.96544 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.76364 | −0.335577 | ||||||||
\(683\) | 29.6157 | 1.13321 | 0.566607 | − | 0.823988i | \(-0.308256\pi\) | ||||
0.566607 | + | 0.823988i | \(0.308256\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.55594 | 0.135865 | ||||||||
\(686\) | −2.70334 | −0.103214 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −112.149 | −4.27565 | ||||||||
\(689\) | 6.13189 | 0.233606 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.9659 | −1.48233 | −0.741166 | − | 0.671322i | \(-0.765727\pi\) | ||||
−0.741166 | + | 0.671322i | \(0.765727\pi\) | |||||||
\(692\) | −97.1831 | −3.69435 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.5647 | 1.08430 | ||||||||
\(695\) | 7.88521 | 0.299103 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.2671 | −0.654039 | ||||||||
\(698\) | 64.6645 | 2.44759 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 34.0962 | 1.28872 | ||||||||
\(701\) | −0.751645 | −0.0283893 | −0.0141946 | − | 0.999899i | \(-0.504518\pi\) | ||||
−0.0141946 | + | 0.999899i | \(0.504518\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 70.9718 | 2.67675 | ||||||||
\(704\) | −124.034 | −4.67473 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 45.2668 | 1.70364 | ||||||||
\(707\) | −6.95323 | −0.261503 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.20397 | −0.308106 | −0.154053 | − | 0.988063i | \(-0.549233\pi\) | ||||
−0.154053 | + | 0.988063i | \(0.549233\pi\) | |||||||
\(710\) | −49.5922 | −1.86116 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −86.2970 | −3.23412 | ||||||||
\(713\) | 3.77785 | 0.141482 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −79.6829 | −2.97997 | ||||||||
\(716\) | 80.4826 | 3.00778 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 56.0891 | 2.09323 | ||||||||
\(719\) | −47.3025 | −1.76409 | −0.882043 | − | 0.471169i | \(-0.843832\pi\) | ||||
−0.882043 | + | 0.471169i | \(0.843832\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.95576 | −0.333530 | ||||||||
\(722\) | −75.8876 | −2.82424 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −67.6774 | −2.51521 | ||||||||
\(725\) | 60.5891 | 2.25022 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.4466 | −0.609972 | −0.304986 | − | 0.952357i | \(-0.598652\pi\) | ||||
−0.304986 | + | 0.952357i | \(0.598652\pi\) | |||||||
\(728\) | −40.1535 | −1.48819 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12.7539 | −0.472043 | ||||||||
\(731\) | −21.1608 | −0.782659 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.21251 | 0.0817209 | 0.0408604 | − | 0.999165i | \(-0.486990\pi\) | ||||
0.0408604 | + | 0.999165i | \(0.486990\pi\) | |||||||
\(734\) | −45.0846 | −1.66410 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 114.851 | 4.23347 | ||||||||
\(737\) | −35.0976 | −1.29284 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.2766 | −1.37124 | −0.685622 | − | 0.727958i | \(-0.740470\pi\) | ||||
−0.685622 | + | 0.727958i | \(0.740470\pi\) | |||||||
\(740\) | −185.584 | −6.82219 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.69185 | −0.135532 | ||||||||
\(743\) | −19.2950 | −0.707865 | −0.353933 | − | 0.935271i | \(-0.615156\pi\) | ||||
−0.353933 | + | 0.935271i | \(0.615156\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −51.3908 | −1.88281 | ||||||||
\(746\) | 48.5884 | 1.77895 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −71.3052 | −2.60718 | ||||||||
\(749\) | −5.94244 | −0.217132 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.882173 | −0.0321909 | −0.0160955 | − | 0.999870i | \(-0.505124\pi\) | ||||
−0.0160955 | + | 0.999870i | \(0.505124\pi\) | |||||||
\(752\) | −46.2436 | −1.68633 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −114.492 | −4.16955 | ||||||||
\(755\) | 16.8987 | 0.615006 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.911581 | 0.0331320 | 0.0165660 | − | 0.999863i | \(-0.494727\pi\) | ||||
0.0165660 | + | 0.999863i | \(0.494727\pi\) | |||||||
\(758\) | −66.9009 | −2.42995 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 207.373 | 7.52221 | ||||||||
\(761\) | −17.7994 | −0.645228 | −0.322614 | − | 0.946531i | \(-0.604561\pi\) | ||||
−0.322614 | + | 0.946531i | \(0.604561\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.18703 | −0.332593 | ||||||||
\(764\) | −90.6022 | −3.27787 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.6922 | 1.18122 | ||||||||
\(767\) | −1.51582 | −0.0547331 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.9737 | −0.576028 | −0.288014 | − | 0.957626i | \(-0.592995\pi\) | ||||
−0.288014 | + | 0.957626i | \(0.592995\pi\) | |||||||
\(770\) | 47.9750 | 1.72890 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 51.6153 | 1.85767 | ||||||||
\(773\) | 42.1447 | 1.51584 | 0.757919 | − | 0.652349i | \(-0.226216\pi\) | ||||
0.757919 | + | 0.652349i | \(0.226216\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.96589 | −0.142459 | ||||||||
\(776\) | −34.2302 | −1.22879 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −48.5924 | −1.74212 | ||||||||
\(779\) | 46.3051 | 1.65905 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.4989 | −1.01977 | ||||||||
\(782\) | 42.3202 | 1.51337 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 13.5593 | 0.484260 | ||||||||
\(785\) | 61.9592 | 2.21142 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.5620 | −0.946833 | −0.473417 | − | 0.880839i | \(-0.656979\pi\) | ||||
−0.473417 | + | 0.880839i | \(0.656979\pi\) | |||||||
\(788\) | −79.5665 | −2.83444 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 54.8939 | 1.95304 | ||||||||
\(791\) | −19.6841 | −0.699887 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.6568 | 0.911100 | ||||||||
\(794\) | 54.3191 | 1.92771 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −55.0126 | −1.94987 | ||||||||
\(797\) | −26.1504 | −0.926295 | −0.463148 | − | 0.886281i | \(-0.653280\pi\) | ||||
−0.463148 | + | 0.886281i | \(0.653280\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.72543 | −0.308683 | ||||||||
\(800\) | −120.568 | −4.26271 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −34.6447 | −1.22335 | ||||||||
\(803\) | −7.32922 | −0.258642 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.6812 | −0.728915 | ||||||||
\(806\) | 7.49413 | 0.263969 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 62.1812 | 2.18753 | ||||||||
\(809\) | −14.9716 | −0.526372 | −0.263186 | − | 0.964745i | \(-0.584773\pi\) | ||||
−0.263186 | + | 0.964745i | \(0.584773\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.8044 | −0.625198 | −0.312599 | − | 0.949885i | \(-0.601200\pi\) | ||||
−0.312599 | + | 0.949885i | \(0.601200\pi\) | |||||||
\(812\) | 50.0678 | 1.75703 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −146.832 | −5.14646 | ||||||||
\(815\) | −10.6989 | −0.374765 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 56.7466 | 1.98531 | ||||||||
\(818\) | 99.4549 | 3.47736 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −121.083 | −4.22840 | ||||||||
\(821\) | 21.6246 | 0.754704 | 0.377352 | − | 0.926070i | \(-0.376835\pi\) | ||||
0.377352 | + | 0.926070i | \(0.376835\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.7893 | 1.17782 | 0.588911 | − | 0.808198i | \(-0.299557\pi\) | ||||
0.588911 | + | 0.808198i | \(0.299557\pi\) | |||||||
\(824\) | 80.0894 | 2.79005 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.912636 | 0.0317547 | ||||||||
\(827\) | 20.3700 | 0.708335 | 0.354167 | − | 0.935182i | \(-0.384764\pi\) | ||||
0.354167 | + | 0.935182i | \(0.384764\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.1516 | 0.665163 | 0.332581 | − | 0.943075i | \(-0.392080\pi\) | ||||
0.332581 | + | 0.943075i | \(0.392080\pi\) | |||||||
\(830\) | −142.402 | −4.94286 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 106.067 | 3.67720 | ||||||||
\(833\) | 2.55842 | 0.0886440 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.6085 | −0.920825 | ||||||||
\(836\) | 191.219 | 6.61343 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18.3722 | 0.634656 | ||||||||
\(839\) | 19.0227 | 0.656737 | 0.328368 | − | 0.944550i | \(-0.393501\pi\) | ||||
0.328368 | + | 0.944550i | \(0.393501\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.9706 | 2.06795 | ||||||||
\(842\) | 8.72402 | 0.300650 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −55.3855 | −1.90645 | ||||||||
\(845\) | 24.2016 | 0.832562 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.5695 | 0.569336 | ||||||||
\(848\) | 18.5174 | 0.635891 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −44.4267 | −1.52382 | ||||||||
\(851\) | 63.2966 | 2.16978 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.4911 | −0.975517 | −0.487758 | − | 0.872979i | \(-0.662185\pi\) | ||||
−0.487758 | + | 0.872979i | \(0.662185\pi\) | |||||||
\(854\) | −15.4473 | −0.528595 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 53.1420 | 1.81636 | ||||||||
\(857\) | −11.1578 | −0.381143 | −0.190571 | − | 0.981673i | \(-0.561034\pi\) | ||||
−0.190571 | + | 0.981673i | \(0.561034\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.6130 | −0.600948 | −0.300474 | − | 0.953790i | \(-0.597145\pi\) | ||||
−0.300474 | + | 0.953790i | \(0.597145\pi\) | |||||||
\(860\) | −148.386 | −5.05993 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.42815 | 0.0827033 | ||||||||
\(863\) | −28.3944 | −0.966555 | −0.483278 | − | 0.875467i | \(-0.660554\pi\) | ||||
−0.483278 | + | 0.875467i | \(0.660554\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −61.8807 | −2.10401 | ||||||||
\(866\) | 25.1081 | 0.853208 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.27721 | −0.111236 | ||||||||
\(869\) | 31.5456 | 1.07011 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.0133 | 1.01696 | ||||||||
\(872\) | 82.1576 | 2.78221 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −113.490 | −3.83885 | ||||||||
\(875\) | 4.81121 | 0.162648 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.9532 | −0.538703 | −0.269351 | − | 0.963042i | \(-0.586809\pi\) | ||||
−0.269351 | + | 0.963042i | \(0.586809\pi\) | |||||||
\(878\) | −86.0955 | −2.90558 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −240.631 | −8.11166 | ||||||||
\(881\) | 10.2652 | 0.345842 | 0.172921 | − | 0.984936i | \(-0.444680\pi\) | ||||
0.172921 | + | 0.984936i | \(0.444680\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.8873 | 0.972134 | 0.486067 | − | 0.873921i | \(-0.338431\pi\) | ||||
0.486067 | + | 0.873921i | \(0.338431\pi\) | |||||||
\(884\) | 60.9758 | 2.05084 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −81.3332 | −2.73244 | ||||||||
\(887\) | 18.2617 | 0.613168 | 0.306584 | − | 0.951844i | \(-0.400814\pi\) | ||||
0.306584 | + | 0.951844i | \(0.400814\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | −88.1705 | −2.95548 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 41.3143 | 1.38331 | ||||||||
\(893\) | 23.3989 | 0.783014 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 51.2468 | 1.71299 | ||||||||
\(896\) | −26.3203 | −0.879300 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.4609 | −0.382454 | ||||||||
\(899\) | −5.82361 | −0.194228 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.49394 | 0.116400 | ||||||||
\(902\) | −95.7996 | −3.18978 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 176.031 | 5.85470 | ||||||||
\(905\) | −43.0932 | −1.43247 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 44.4961 | 1.47747 | 0.738735 | − | 0.673996i | \(-0.235424\pi\) | ||||
0.738735 | + | 0.673996i | \(0.235424\pi\) | |||||||
\(908\) | −81.2434 | −2.69616 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −41.0252 | −1.35997 | ||||||||
\(911\) | 10.0562 | 0.333176 | 0.166588 | − | 0.986027i | \(-0.446725\pi\) | ||||
0.166588 | + | 0.986027i | \(0.446725\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −81.8336 | −2.70830 | ||||||||
\(914\) | −91.2560 | −3.01848 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 70.7627 | 2.33806 | ||||||||
\(917\) | −3.12882 | −0.103323 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.74615 | 0.123574 | 0.0617870 | − | 0.998089i | \(-0.480320\pi\) | ||||
0.0617870 | + | 0.998089i | \(0.480320\pi\) | |||||||
\(920\) | 184.947 | 6.09753 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 72.1419 | 2.37587 | ||||||||
\(923\) | 24.3705 | 0.802165 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −66.4471 | −2.18477 | ||||||||
\(926\) | −20.7517 | −0.681944 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −177.045 | −5.81178 | ||||||||
\(929\) | 0.579663 | 0.0190181 | 0.00950906 | − | 0.999955i | \(-0.496973\pi\) | ||||
0.00950906 | + | 0.999955i | \(0.496973\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.86089 | −0.224857 | ||||||||
\(932\) | 5.20457 | 0.170481 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −53.5096 | −1.75089 | ||||||||
\(935\) | −45.4031 | −1.48484 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.3440 | 1.05663 | 0.528315 | − | 0.849048i | \(-0.322824\pi\) | ||||
0.528315 | + | 0.849048i | \(0.322824\pi\) | |||||||
\(938\) | −18.0702 | −0.590013 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −61.1856 | −1.99565 | ||||||||
\(941\) | −41.9432 | −1.36731 | −0.683654 | − | 0.729806i | \(-0.739610\pi\) | ||||
−0.683654 | + | 0.729806i | \(0.739610\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 41.2975 | 1.34483 | ||||||||
\(944\) | −4.57756 | −0.148987 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −117.402 | −3.81706 | ||||||||
\(947\) | 8.39075 | 0.272663 | 0.136331 | − | 0.990663i | \(-0.456469\pi\) | ||||
0.136331 | + | 0.990663i | \(0.456469\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.26749 | 0.203451 | ||||||||
\(950\) | 119.139 | 3.86536 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −22.8794 | −0.741526 | ||||||||
\(953\) | 54.9918 | 1.78136 | 0.890680 | − | 0.454631i | \(-0.150229\pi\) | ||||
0.890680 | + | 0.454631i | \(0.150229\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −57.6903 | −1.86682 | ||||||||
\(956\) | −81.4636 | −2.63472 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 47.6072 | 1.53812 | ||||||||
\(959\) | 1.05209 | 0.0339739 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6188 | −0.987704 | ||||||||
\(962\) | 125.562 | 4.04827 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −79.0252 | −2.54523 | ||||||||
\(965\) | 32.8657 | 1.05798 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.4952 | −1.46303 | −0.731514 | − | 0.681826i | \(-0.761186\pi\) | ||||
−0.731514 | + | 0.681826i | \(0.761186\pi\) | |||||||
\(968\) | −148.178 | −4.76261 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −34.9733 | −1.12293 | ||||||||
\(971\) | 6.90693 | 0.221654 | 0.110827 | − | 0.993840i | \(-0.464650\pi\) | ||||
0.110827 | + | 0.993840i | \(0.464650\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.33299 | 0.0747924 | ||||||||
\(974\) | −64.1976 | −2.05702 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 77.4798 | 2.48007 | ||||||||
\(977\) | −0.719851 | −0.0230301 | −0.0115150 | − | 0.999934i | \(-0.503665\pi\) | ||||
−0.0115150 | + | 0.999934i | \(0.503665\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −50.6684 | −1.61937 | ||||||||
\(980\) | 17.9405 | 0.573088 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −53.9484 | −1.72156 | ||||||||
\(983\) | 27.5040 | 0.877243 | 0.438621 | − | 0.898672i | \(-0.355467\pi\) | ||||
0.438621 | + | 0.898672i | \(0.355467\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −50.6635 | −1.61427 | ||||||||
\(986\) | −65.2373 | −2.07758 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −163.518 | −5.20221 | ||||||||
\(989\) | 50.6098 | 1.60930 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.91961 | 0.251575 | 0.125787 | − | 0.992057i | \(-0.459854\pi\) | ||||
0.125787 | + | 0.992057i | \(0.459854\pi\) | |||||||
\(992\) | 11.5886 | 0.367937 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −14.6728 | −0.465394 | ||||||||
\(995\) | −35.0289 | −1.11049 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.9260 | −0.789414 | −0.394707 | − | 0.918807i | \(-0.629154\pi\) | ||||
−0.394707 | + | 0.918807i | \(0.629154\pi\) | |||||||
\(998\) | −23.4296 | −0.741652 | ||||||||
\(999\) | 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.w.1.2 | 20 | ||
3.2 | odd | 2 | 889.2.a.d.1.19 | ✓ | 20 | ||
21.20 | even | 2 | 6223.2.a.l.1.19 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
889.2.a.d.1.19 | ✓ | 20 | 3.2 | odd | 2 | ||
6223.2.a.l.1.19 | 20 | 21.20 | even | 2 | |||
8001.2.a.w.1.2 | 20 | 1.1 | even | 1 | trivial |