Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4028,2,Mod(1,4028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4028, 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("4028.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4028 = 2^{2} \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4028.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: | \(32.1637419342\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 4 x^{18} - 30 x^{17} + 132 x^{16} + 332 x^{15} - 1714 x^{14} - 1598 x^{13} + 11179 x^{12} + 2544 x^{11} - 38897 x^{10} + 3416 x^{9} + 71354 x^{8} - 10941 x^{7} + \cdots - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.76613\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4028.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.76613 | −1.01968 | −0.509838 | − | 0.860271i | \(-0.670295\pi\) | ||||
−0.509838 | + | 0.860271i | \(0.670295\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.36988 | −0.612630 | −0.306315 | − | 0.951930i | \(-0.599096\pi\) | ||||
−0.306315 | + | 0.951930i | \(0.599096\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.174249 | 0.0658600 | 0.0329300 | − | 0.999458i | \(-0.489516\pi\) | ||||
0.0329300 | + | 0.999458i | \(0.489516\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.119213 | 0.0397377 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.83583 | 0.553524 | 0.276762 | − | 0.960939i | \(-0.410739\pi\) | ||||
0.276762 | + | 0.960939i | \(0.410739\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.53740 | 0.981098 | 0.490549 | − | 0.871414i | \(-0.336796\pi\) | ||||
0.490549 | + | 0.871414i | \(0.336796\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.41939 | 0.624684 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.42129 | −1.55739 | −0.778696 | − | 0.627401i | \(-0.784119\pi\) | ||||
−0.778696 | + | 0.627401i | \(0.784119\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.307747 | −0.0671558 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.41263 | 0.920096 | 0.460048 | − | 0.887894i | \(-0.347832\pi\) | ||||
0.460048 | + | 0.887894i | \(0.347832\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.12342 | −0.624684 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.08784 | 0.979156 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.386227 | 0.0717206 | 0.0358603 | − | 0.999357i | \(-0.488583\pi\) | ||||
0.0358603 | + | 0.999357i | \(0.488583\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.29764 | −1.13109 | −0.565544 | − | 0.824718i | \(-0.691334\pi\) | ||||
−0.565544 | + | 0.824718i | \(0.691334\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.24231 | −0.564414 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.238701 | −0.0403478 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.89972 | 1.29871 | 0.649353 | − | 0.760487i | \(-0.275040\pi\) | ||||
0.649353 | + | 0.760487i | \(0.275040\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.24751 | −1.00040 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.09598 | −0.171164 | −0.0855818 | − | 0.996331i | \(-0.527275\pi\) | ||||
−0.0855818 | + | 0.996331i | \(0.527275\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.58442 | 0.851616 | 0.425808 | − | 0.904814i | \(-0.359990\pi\) | ||||
0.425808 | + | 0.904814i | \(0.359990\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.163308 | −0.0243445 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.67933 | 1.26601 | 0.633005 | − | 0.774148i | \(-0.281821\pi\) | ||||
0.633005 | + | 0.774148i | \(0.281821\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.96964 | −0.995662 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.3408 | 1.58803 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.51487 | −0.339105 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.76613 | 0.233930 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.0639 | −1.31021 | −0.655103 | − | 0.755539i | \(-0.727375\pi\) | ||||
−0.655103 | + | 0.755539i | \(0.727375\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.1283 | 1.29679 | 0.648395 | − | 0.761304i | \(-0.275440\pi\) | ||||
0.648395 | + | 0.761304i | \(0.275440\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0207728 | 0.00261713 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.84582 | −0.601050 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.8009 | −1.56388 | −0.781940 | − | 0.623354i | \(-0.785770\pi\) | ||||
−0.781940 | + | 0.623354i | \(0.785770\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.79327 | −0.938200 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4879 | 1.36336 | 0.681678 | − | 0.731652i | \(-0.261250\pi\) | ||||
0.681678 | + | 0.731652i | \(0.261250\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.20188 | 0.257711 | 0.128855 | − | 0.991663i | \(-0.458870\pi\) | ||||
0.128855 | + | 0.991663i | \(0.458870\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.51637 | 0.636975 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.319892 | 0.0364551 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.3063 | −1.38457 | −0.692284 | − | 0.721625i | \(-0.743395\pi\) | ||||
−0.692284 | + | 0.721625i | \(0.743395\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.34343 | −1.03816 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.89130 | 1.08571 | 0.542855 | − | 0.839826i | \(-0.317343\pi\) | ||||
0.542855 | + | 0.839826i | \(0.317343\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.79642 | 0.954105 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.682127 | −0.0731317 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.8290 | 1.25387 | 0.626935 | − | 0.779071i | \(-0.284309\pi\) | ||||
0.626935 | + | 0.779071i | \(0.284309\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.616389 | 0.0646151 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.1224 | 1.15334 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.36988 | 0.140547 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.5083 | 1.47310 | 0.736550 | − | 0.676383i | \(-0.236454\pi\) | ||||
0.736550 | + | 0.676383i | \(0.236454\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.218855 | 0.0219958 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.76242 | 0.772389 | 0.386195 | − | 0.922417i | \(-0.373789\pi\) | ||||
0.386195 | + | 0.922417i | \(0.373789\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.46178 | −0.735231 | −0.367615 | − | 0.929978i | \(-0.619826\pi\) | ||||
−0.367615 | + | 0.929978i | \(0.619826\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.421577 | 0.0411417 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.2830 | −1.18745 | −0.593723 | − | 0.804670i | \(-0.702342\pi\) | ||||
−0.593723 | + | 0.804670i | \(0.702342\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.0121 | −1.05477 | −0.527383 | − | 0.849628i | \(-0.676827\pi\) | ||||
−0.527383 | + | 0.849628i | \(0.676827\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.9519 | −1.32426 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.45472 | −0.324993 | −0.162496 | − | 0.986709i | \(-0.551955\pi\) | ||||
−0.162496 | + | 0.986709i | \(0.551955\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.04478 | −0.563679 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.421705 | 0.0389866 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.11890 | −0.102570 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.62973 | −0.693612 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.93565 | 0.174531 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1281 | 0.995331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.67880 | −0.415176 | −0.207588 | − | 0.978216i | \(-0.566561\pi\) | ||||
−0.207588 | + | 0.978216i | \(0.566561\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.86281 | −0.868372 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.1421 | −1.32297 | −0.661486 | − | 0.749957i | \(-0.730074\pi\) | ||||
−0.661486 | + | 0.749957i | \(0.730074\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.174249 | −0.0151093 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.96975 | −0.599860 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.5502 | −1.75572 | −0.877860 | − | 0.478918i | \(-0.841029\pi\) | ||||
−0.877860 | + | 0.478918i | \(0.841029\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.75156 | −0.742298 | −0.371149 | − | 0.928573i | \(-0.621036\pi\) | ||||
−0.371149 | + | 0.928573i | \(0.621036\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.3288 | −1.29092 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.49406 | 0.543061 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.529086 | −0.0439382 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.3093 | 1.01525 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.94152 | 0.159055 | 0.0795277 | − | 0.996833i | \(-0.474659\pi\) | ||||
0.0795277 | + | 0.996833i | \(0.474659\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.8236 | 1.04357 | 0.521786 | − | 0.853076i | \(-0.325266\pi\) | ||||
0.521786 | + | 0.853076i | \(0.325266\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.765503 | −0.0618873 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.62702 | 0.692939 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.98964 | −0.637643 | −0.318822 | − | 0.947815i | \(-0.603287\pi\) | ||||
−0.318822 | + | 0.947815i | \(0.603287\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.76613 | −0.140063 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.768896 | 0.0605975 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24.2580 | −1.90003 | −0.950015 | − | 0.312205i | \(-0.898932\pi\) | ||||
−0.950015 | + | 0.312205i | \(0.898932\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.44159 | 0.345777 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.31541 | 0.333937 | 0.166968 | − | 0.985962i | \(-0.446602\pi\) | ||||
0.166968 | + | 0.985962i | \(0.446602\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.486805 | −0.0374465 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.119213 | −0.00911646 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.10440 | −0.236023 | −0.118012 | − | 0.993012i | \(-0.537652\pi\) | ||||
−0.118012 | + | 0.993012i | \(0.537652\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.544254 | −0.0411417 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.7741 | 1.33599 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.88429 | −0.365069 | −0.182535 | − | 0.983199i | \(-0.558430\pi\) | ||||
−0.182535 | + | 0.983199i | \(0.558430\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.38893 | 0.697874 | 0.348937 | − | 0.937146i | \(-0.386543\pi\) | ||||
0.348937 | + | 0.937146i | \(0.386543\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.8878 | −1.32231 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.8217 | −0.795626 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.7884 | −0.862053 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.886552 | 0.0644872 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.77372 | 0.200700 | 0.100350 | − | 0.994952i | \(-0.468004\pi\) | ||||
0.100350 | + | 0.994952i | \(0.468004\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.29614 | −0.309243 | −0.154621 | − | 0.987974i | \(-0.549416\pi\) | ||||
−0.154621 | + | 0.987974i | \(0.549416\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.55835 | 0.612876 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.4574 | −1.24379 | −0.621894 | − | 0.783101i | \(-0.713637\pi\) | ||||
−0.621894 | + | 0.783101i | \(0.713637\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.1602 | −0.720238 | −0.360119 | − | 0.932906i | \(-0.617264\pi\) | ||||
−0.360119 | + | 0.932906i | \(0.617264\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.6081 | 1.59465 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.0672997 | 0.00472352 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.50137 | 0.104860 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.526044 | 0.0365626 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.83583 | −0.126987 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.4394 | −1.82016 | −0.910080 | − | 0.414432i | \(-0.863980\pi\) | ||||
−0.910080 | + | 0.414432i | \(0.863980\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −20.2890 | −1.39018 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.65000 | −0.521726 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.09736 | −0.0744935 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.88881 | −0.262781 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.7147 | −1.52795 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.6328 | −1.91739 | −0.958697 | − | 0.284431i | \(-0.908195\pi\) | ||||
−0.958697 | + | 0.284431i | \(0.908195\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.372353 | −0.0248235 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.5461 | −1.69555 | −0.847777 | − | 0.530353i | \(-0.822059\pi\) | ||||
−0.847777 | + | 0.530353i | \(0.822059\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.3725 | 0.949761 | 0.474881 | − | 0.880050i | \(-0.342491\pi\) | ||||
0.474881 | + | 0.880050i | \(0.342491\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.564970 | −0.0371723 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.6238 | 1.22008 | 0.610042 | − | 0.792369i | \(-0.291153\pi\) | ||||
0.610042 | + | 0.792369i | \(0.291153\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.8897 | −0.775596 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 21.7345 | 1.41181 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.72660 | −0.629161 | −0.314581 | − | 0.949231i | \(-0.601864\pi\) | ||||
−0.314581 | + | 0.949231i | \(0.601864\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.2510 | −0.982401 | −0.491201 | − | 0.871046i | \(-0.663442\pi\) | ||||
−0.491201 | + | 0.871046i | \(0.663442\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.23818 | 0.0794290 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.54758 | 0.609973 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.53740 | −0.225079 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.4693 | −1.10707 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.62526 | 0.355063 | 0.177532 | − | 0.984115i | \(-0.443189\pi\) | ||||
0.177532 | + | 0.984115i | \(0.443189\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.10083 | 0.509295 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −15.5356 | −0.972878 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.39109 | 0.149152 | 0.0745759 | − | 0.997215i | \(-0.476240\pi\) | ||||
0.0745759 | + | 0.997215i | \(0.476240\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.37652 | 0.0855327 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0460434 | 0.00285001 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.97017 | 0.614787 | 0.307393 | − | 0.951583i | \(-0.400543\pi\) | ||||
0.307393 | + | 0.951583i | \(0.400543\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.36988 | −0.0841512 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −20.8915 | −1.27854 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.03028 | 0.428644 | 0.214322 | − | 0.976763i | \(-0.431246\pi\) | ||||
0.214322 | + | 0.976763i | \(0.431246\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.46965 | 0.575240 | 0.287620 | − | 0.957745i | \(-0.407136\pi\) | ||||
0.287620 | + | 0.957745i | \(0.407136\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.08862 | −0.0658864 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.73407 | −0.345777 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.0357 | −1.32399 | −0.661997 | − | 0.749506i | \(-0.730291\pi\) | ||||
−0.661997 | + | 0.749506i | \(0.730291\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.750762 | −0.0449469 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.64111 | 0.336520 | 0.168260 | − | 0.985743i | \(-0.446185\pi\) | ||||
0.168260 | + | 0.985743i | \(0.446185\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.0684 | 0.657947 | 0.328973 | − | 0.944339i | \(-0.393297\pi\) | ||||
0.328973 | + | 0.944339i | \(0.393297\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.41939 | −0.143312 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.190974 | −0.0112728 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.2330 | 1.42547 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −25.6236 | −1.50208 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.58229 | 0.326121 | 0.163060 | − | 0.986616i | \(-0.447863\pi\) | ||||
0.163060 | + | 0.986616i | \(0.447863\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.7863 | 0.802672 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.34041 | 0.541986 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.6092 | 0.902705 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.973080 | 0.0560874 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.7094 | −0.787586 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.8745 | −0.794453 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.68897 | −0.324687 | −0.162343 | − | 0.986734i | \(-0.551905\pi\) | ||||
−0.162343 | + | 0.986734i | \(0.551905\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.1785 | 0.749697 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.40086 | 0.192845 | 0.0964225 | − | 0.995340i | \(-0.469260\pi\) | ||||
0.0964225 | + | 0.995340i | \(0.469260\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.8936 | −1.35055 | −0.675273 | − | 0.737568i | \(-0.735974\pi\) | ||||
−0.675273 | + | 0.737568i | \(0.735974\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0284563 | −0.00160333 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.318310 | −0.0178781 | −0.00893904 | − | 0.999960i | \(-0.502845\pi\) | ||||
−0.00893904 | + | 0.999960i | \(0.502845\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.709047 | 0.0396990 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.6934 | 1.21081 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.42129 | 0.357290 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.0488 | −0.612877 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.4487 | 1.07552 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.51237 | 0.0833794 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.36958 | −0.405069 | −0.202534 | − | 0.979275i | \(-0.564918\pi\) | ||||
−0.202534 | + | 0.979275i | \(0.564918\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.941751 | 0.0516076 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.5357 | 0.958080 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.30089 | 0.179811 | 0.0899055 | − | 0.995950i | \(-0.471344\pi\) | ||||
0.0899055 | + | 0.995950i | \(0.471344\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.10148 | 0.331387 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.5614 | −0.626084 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.43420 | −0.131434 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.6759 | 0.574769 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.6717 | −1.27076 | −0.635381 | − | 0.772199i | \(-0.719157\pi\) | ||||
−0.635381 | + | 0.772199i | \(0.719157\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.312831 | −0.0167455 | −0.00837274 | − | 0.999965i | \(-0.502665\pi\) | ||||
−0.00837274 | + | 0.999965i | \(0.502665\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.9977 | 0.960648 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.51566 | 0.346793 | 0.173397 | − | 0.984852i | \(-0.444526\pi\) | ||||
0.173397 | + | 0.984852i | \(0.444526\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.7370 | −0.835234 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.97613 | 0.104588 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.5474 | 1.19000 | 0.595002 | − | 0.803724i | \(-0.297151\pi\) | ||||
0.595002 | + | 0.803724i | \(0.297151\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.4751 | 0.707259 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.01632 | −0.157881 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.73263 | −0.247041 | −0.123521 | − | 0.992342i | \(-0.539418\pi\) | ||||
−0.123521 | + | 0.992342i | \(0.539418\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.130656 | −0.00680165 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.174249 | 0.00904656 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.0542 | −0.986588 | −0.493294 | − | 0.869863i | \(-0.664207\pi\) | ||||
−0.493294 | + | 0.869863i | \(0.664207\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −19.6537 | −1.01491 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.36624 | 0.0703649 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.7120 | 1.11527 | 0.557634 | − | 0.830087i | \(-0.311709\pi\) | ||||
0.557634 | + | 0.830087i | \(0.311709\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.26336 | 0.423345 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.51509 | 0.332906 | 0.166453 | − | 0.986049i | \(-0.446769\pi\) | ||||
0.166453 | + | 0.986049i | \(0.446769\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.438214 | −0.0223335 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.665737 | 0.0338413 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.0965 | −0.714723 | −0.357361 | − | 0.933966i | \(-0.616324\pi\) | ||||
−0.357361 | + | 0.933966i | \(0.616324\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.3348 | −1.43295 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 26.7429 | 1.34900 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.8582 | 0.848228 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.0017 | 1.35518 | 0.677588 | − | 0.735442i | \(-0.263025\pi\) | ||||
0.677588 | + | 0.735442i | \(0.263025\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.307747 | 0.0154066 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.1494 | −1.25590 | −0.627950 | − | 0.778253i | \(-0.716106\pi\) | ||||
−0.627950 | + | 0.778253i | \(0.716106\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.2773 | −1.10971 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.7994 | 0.636007 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.5025 | 0.718864 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.0864 | 1.04265 | 0.521327 | − | 0.853357i | \(-0.325437\pi\) | ||||
0.521327 | + | 0.853357i | \(0.325437\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 36.2943 | 1.79026 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.75362 | −0.0862902 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.5499 | −0.665139 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.4564 | 0.756903 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.2247 | −0.939187 | −0.469593 | − | 0.882883i | \(-0.655599\pi\) | ||||
−0.469593 | + | 0.882883i | \(0.655599\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.78295 | −0.233107 | −0.116553 | − | 0.993184i | \(-0.537185\pi\) | ||||
−0.116553 | + | 0.993184i | \(0.537185\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.03469 | 0.0503084 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.0564 | 0.972878 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.76484 | 0.0854066 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.4694 | −0.553746 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.20085 | 0.298685 | 0.149342 | − | 0.988786i | \(-0.452284\pi\) | ||||
0.149342 | + | 0.988786i | \(0.452284\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.5071 | −0.889396 | −0.444698 | − | 0.895681i | \(-0.646689\pi\) | ||||
−0.444698 | + | 0.895681i | \(0.646689\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.934434 | 0.0448027 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.41263 | −0.211085 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.5302 | −0.932124 | −0.466062 | − | 0.884752i | \(-0.654328\pi\) | ||||
−0.466062 | + | 0.884752i | \(0.654328\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.830873 | −0.0395654 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −36.6212 | −1.73992 | −0.869962 | − | 0.493118i | \(-0.835857\pi\) | ||||
−0.869962 | + | 0.493118i | \(0.835857\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.2043 | −0.768159 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.42897 | −0.162185 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.77823 | −0.367077 | −0.183539 | − | 0.983012i | \(-0.558755\pi\) | ||||
−0.183539 | + | 0.983012i | \(0.558755\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.01204 | −0.0947431 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.6482 | −1.06410 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.844380 | −0.0395852 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.00559014 | −0.000261496 0 | −0.000130748 | − | 1.00000i | \(-0.500042\pi\) | ||||
−0.000130748 | 1.00000i | \(0.500042\pi\) | ||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −32.6705 | −1.52493 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.52873 | −0.210924 | −0.105462 | − | 0.994423i | \(-0.533632\pi\) | ||||
−0.105462 | + | 0.994423i | \(0.533632\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.0424 | −0.513182 | −0.256591 | − | 0.966520i | \(-0.582599\pi\) | ||||
−0.256591 | + | 0.966520i | \(0.582599\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −15.2364 | −0.706573 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.0357 | −0.649494 | −0.324747 | − | 0.945801i | \(-0.605279\pi\) | ||||
−0.324747 | + | 0.945801i | \(0.605279\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.23055 | −0.102997 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.1107 | 0.650189 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.2520 | 0.471390 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.12342 | 0.143312 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.119213 | 0.00545840 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 41.7101 | 1.90578 | 0.952892 | − | 0.303311i | \(-0.0980920\pi\) | ||||
0.952892 | + | 0.303311i | \(0.0980920\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.9445 | 1.27416 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.35797 | −0.0617898 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.8747 | −0.902465 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.43394 | −0.382178 | −0.191089 | − | 0.981573i | \(-0.561202\pi\) | ||||
−0.191089 | + | 0.981573i | \(0.561202\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 42.8427 | 1.93741 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.2449 | 0.642862 | 0.321431 | − | 0.946933i | \(-0.395836\pi\) | ||||
0.321431 | + | 0.946933i | \(0.395836\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.48008 | −0.111697 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.299806 | −0.0134753 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.00175 | 0.0897907 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.8944 | −1.60685 | −0.803426 | − | 0.595404i | \(-0.796992\pi\) | ||||
−0.803426 | + | 0.595404i | \(0.796992\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.62157 | −0.340507 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.3858 | −1.80071 | −0.900357 | − | 0.435152i | \(-0.856694\pi\) | ||||
−0.900357 | + | 0.435152i | \(0.856694\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.6336 | −0.473189 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.859760 | 0.0381833 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 41.8060 | 1.85302 | 0.926508 | − | 0.376274i | \(-0.122795\pi\) | ||||
0.926508 | + | 0.376274i | \(0.122795\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.383676 | 0.0169728 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.08784 | −0.224634 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.2218 | 0.450425 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.9338 | 0.700766 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.48278 | 0.240667 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.78143 | 0.384721 | 0.192361 | − | 0.981324i | \(-0.438386\pi\) | ||||
0.192361 | + | 0.981324i | \(0.438386\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 39.4697 | 1.72589 | 0.862946 | − | 0.505297i | \(-0.168617\pi\) | ||||
0.862946 | + | 0.505297i | \(0.168617\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.961222 | 0.0419512 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 40.4390 | 1.76155 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.52872 | −0.153423 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.19975 | −0.0520646 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.87692 | −0.167928 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.8263 | 0.727465 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.62630 | 0.372252 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.7951 | −0.551123 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.8505 | −1.79929 | −0.899646 | − | 0.436620i | \(-0.856175\pi\) | ||||
−0.899646 | + | 0.436620i | \(0.856175\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.5821 | −0.711605 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.0852 | 0.646181 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.1956 | 1.33383 | 0.666915 | − | 0.745134i | \(-0.267615\pi\) | ||||
0.666915 | + | 0.745134i | \(0.267615\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.20742 | 0.0515315 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.386227 | −0.0164538 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.14436 | −0.0911876 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19.1125 | 0.811280 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −41.2850 | −1.74930 | −0.874650 | − | 0.484754i | \(-0.838909\pi\) | ||||
−0.874650 | + | 0.484754i | \(0.838909\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.7543 | 0.835519 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.8198 | 0.879014 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.5099 | −1.37013 | −0.685064 | − | 0.728483i | \(-0.740226\pi\) | ||||
−0.685064 | + | 0.728483i | \(0.740226\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.73256 | 0.199100 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.62808 | −0.0683731 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.62215 | −0.193771 | −0.0968854 | − | 0.995296i | \(-0.530888\pi\) | ||||
−0.0968854 | + | 0.995296i | \(0.530888\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.9927 | −1.79919 | −0.899593 | − | 0.436728i | \(-0.856137\pi\) | ||||
−0.899593 | + | 0.436728i | \(0.856137\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.89876 | −0.204648 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.7825 | −0.574770 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.9759 | 1.24791 | 0.623957 | − | 0.781459i | \(-0.285524\pi\) | ||||
0.623957 | + | 0.781459i | \(0.285524\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.58754 | 0.315327 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.72355 | 0.0715049 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.83583 | 0.0760323 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.577686 | −0.0238844 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.8181 | −1.56092 | −0.780460 | − | 0.625206i | \(-0.785015\pi\) | ||||
−0.780460 | + | 0.625206i | \(0.785015\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.29764 | 0.259490 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30.8320 | 1.26826 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.5076 | −0.924278 | −0.462139 | − | 0.886807i | \(-0.652918\pi\) | ||||
−0.462139 | + | 0.886807i | \(0.652918\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.53277 | 0.0628374 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.9442 | 0.734408 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.4783 | 1.49046 | 0.745232 | − | 0.666806i | \(-0.232339\pi\) | ||||
0.745232 | + | 0.666806i | \(0.232339\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.84200 | −0.115928 | −0.0579638 | − | 0.998319i | \(-0.518461\pi\) | ||||
−0.0579638 | + | 0.998319i | \(0.518461\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.52604 | −0.0621451 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.4518 | 0.424927 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.8080 | −0.966335 | −0.483168 | − | 0.875528i | \(-0.660514\pi\) | ||||
−0.483168 | + | 0.875528i | \(0.660514\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.118860 | −0.00481645 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.7022 | 1.24208 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.6638 | 0.955770 | 0.477885 | − | 0.878422i | \(-0.341403\pi\) | ||||
0.477885 | + | 0.878422i | \(0.341403\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.65161 | −0.106923 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.7357 | 0.593236 | 0.296618 | − | 0.954996i | \(-0.404141\pi\) | ||||
0.296618 | + | 0.954996i | \(0.404141\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.03783 | 0.242681 | 0.121340 | − | 0.992611i | \(-0.461281\pi\) | ||||
0.121340 | + | 0.992611i | \(0.461281\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.4508 | 0.900918 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.06119 | 0.0825799 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.372871 | 0.0149148 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.24231 | 0.129486 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −50.7264 | −2.02259 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.9794 | 0.437084 | 0.218542 | − | 0.975828i | \(-0.429870\pi\) | ||||
0.218542 | + | 0.975828i | \(0.429870\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 46.6953 | 1.85597 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.40941 | 0.254350 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.6544 | −0.976843 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.36950 | 0.0541767 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 45.6726 | 1.80396 | 0.901979 | − | 0.431780i | \(-0.142114\pi\) | ||||
0.901979 | + | 0.431780i | \(0.142114\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.3798 | −0.409339 | −0.204669 | − | 0.978831i | \(-0.565612\pi\) | ||||
−0.204669 | + | 0.978831i | \(0.565612\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.5109 | 0.531991 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.92658 | 0.350940 | 0.175470 | − | 0.984485i | \(-0.443856\pi\) | ||||
0.175470 | + | 0.984485i | \(0.443856\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.4756 | −0.725230 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.93808 | 0.0759592 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.4895 | −0.449617 | −0.224809 | − | 0.974403i | \(-0.572176\pi\) | ||||
−0.224809 | + | 0.974403i | \(0.572176\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.7429 | 0.810493 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.262493 | 0.0102408 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.576352 | −0.0224515 | −0.0112257 | − | 0.999937i | \(-0.503573\pi\) | ||||
−0.0112257 | + | 0.999937i | \(0.503573\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.1219 | 1.13271 | 0.566356 | − | 0.824161i | \(-0.308353\pi\) | ||||
0.566356 | + | 0.824161i | \(0.308353\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 40.1171 | 1.55802 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.238701 | 0.00925642 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.70428 | 0.0659898 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 50.5692 | 1.95512 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.5938 | 0.717804 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.5808 | 0.947521 | 0.473761 | − | 0.880654i | \(-0.342896\pi\) | ||||
0.473761 | + | 0.880654i | \(0.342896\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15.8915 | −0.611663 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.6663 | 1.21704 | 0.608518 | − | 0.793540i | \(-0.291764\pi\) | ||||
0.608518 | + | 0.793540i | \(0.291764\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.52807 | 0.0970183 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 45.1177 | 1.72891 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.46482 | 0.247370 | 0.123685 | − | 0.992322i | \(-0.460529\pi\) | ||||
0.123685 | + | 0.992322i | \(0.460529\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.1513 | 1.07561 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.3837 | −0.968448 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.53740 | 0.134764 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.5987 | 0.707527 | 0.353763 | − | 0.935335i | \(-0.384902\pi\) | ||||
0.353763 | + | 0.935335i | \(0.384902\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.0381353 | 0.00144864 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.9886 | 0.454754 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.03762 | 0.266569 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −32.8920 | −1.24409 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.7131 | 1.65102 | 0.825511 | − | 0.564387i | \(-0.190887\pi\) | ||||
0.825511 | + | 0.564387i | \(0.190887\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.89972 | −0.297943 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 20.9987 | 0.790856 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.35259 | 0.0508695 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.2792 | −0.461156 | −0.230578 | − | 0.973054i | \(-0.574062\pi\) | ||||
−0.230578 | + | 0.973054i | \(0.574062\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.46707 | −0.0550196 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.7891 | −1.04071 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.89611 | −0.332695 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.1784 | 0.641540 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.04974 | −0.188323 | −0.0941617 | − | 0.995557i | \(-0.530017\pi\) | ||||
−0.0941617 | + | 0.995557i | \(0.530017\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.30021 | −0.0484223 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26.9352 | 1.00173 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.20635 | −0.0448027 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −51.1591 | −1.89739 | −0.948694 | − | 0.316196i | \(-0.897594\pi\) | ||||
−0.948694 | + | 0.316196i | \(0.897594\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.8435 | 0.957167 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −35.8592 | −1.32630 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.8535 | 1.69364 | 0.846819 | − | 0.531882i | \(-0.178515\pi\) | ||||
0.846819 | + | 0.531882i | \(0.178515\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.8623 | −0.621974 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23.5003 | −0.865644 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.43358 | 0.310234 | 0.155117 | − | 0.987896i | \(-0.450425\pi\) | ||||
0.155117 | + | 0.987896i | \(0.450425\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.24751 | 0.229508 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −41.8989 | −1.53712 | −0.768560 | − | 0.639777i | \(-0.779027\pi\) | ||||
−0.768560 | + | 0.639777i | \(0.779027\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.65965 | −0.0974421 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.17917 | 0.0431437 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.14031 | −0.0782051 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.8017 | 0.868536 | 0.434268 | − | 0.900784i | \(-0.357007\pi\) | ||||
0.434268 | + | 0.900784i | \(0.357007\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.93494 | −0.362049 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.5669 | −0.639324 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.3321 | −1.21147 | −0.605737 | − | 0.795665i | \(-0.707122\pi\) | ||||
−0.605737 | + | 0.795665i | \(0.707122\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −14.3071 | −0.519316 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.0974 | 0.692282 | 0.346141 | − | 0.938183i | \(-0.387492\pi\) | ||||
0.346141 | + | 0.938183i | \(0.387492\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.91884 | −0.0694668 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.04865 | 0.0379140 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35.6000 | −1.28544 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.8020 | −0.389532 | −0.194766 | − | 0.980850i | \(-0.562395\pi\) | ||||
−0.194766 | + | 0.980850i | \(0.562395\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.22297 | −0.152086 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.7904 | 1.14342 | 0.571711 | − | 0.820455i | \(-0.306280\pi\) | ||||
0.571711 | + | 0.820455i | \(0.306280\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.6702 | 0.706573 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.43111 | −0.0872156 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.09598 | 0.0392676 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.0897 | 0.754650 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.96506 | 0.0702256 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.9449 | 0.390639 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.3732 | 0.583640 | 0.291820 | − | 0.956473i | \(-0.405739\pi\) | ||||
0.291820 | + | 0.956473i | \(0.405739\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −17.6086 | −0.626883 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.601982 | −0.0214040 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.8277 | 1.27228 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.41939 | 0.0858069 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.9402 | −0.741741 | −0.370871 | − | 0.928685i | \(-0.620941\pi\) | ||||
−0.370871 | + | 0.928685i | \(0.620941\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −55.7325 | −1.97167 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.41017 | 0.0498260 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.04228 | 0.142649 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.05330 | −0.0371239 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.4164 | −0.437077 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.0817 | 0.811510 | 0.405755 | − | 0.913982i | \(-0.367009\pi\) | ||||
0.405755 | + | 0.913982i | \(0.367009\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.1158 | 1.61935 | 0.809673 | − | 0.586882i | \(-0.199645\pi\) | ||||
0.809673 | + | 0.586882i | \(0.199645\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.7246 | −0.586558 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 33.2305 | 1.16402 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.58442 | −0.195374 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.0734817 | 0.00256766 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.36631 | −0.117485 | −0.0587426 | − | 0.998273i | \(-0.518709\pi\) | ||||
−0.0587426 | + | 0.998273i | \(0.518709\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.0847 | 0.351532 | 0.175766 | − | 0.984432i | \(-0.443760\pi\) | ||||
0.175766 | + | 0.984432i | \(0.443760\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.1271 | 0.352581 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.3024 | −0.601663 | −0.300832 | − | 0.953677i | \(-0.597264\pi\) | ||||
−0.300832 | + | 0.953677i | \(0.597264\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.2250 | 0.945564 | 0.472782 | − | 0.881180i | \(-0.343250\pi\) | ||||
0.472782 | + | 0.881180i | \(0.343250\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 38.9178 | 1.35004 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 44.7541 | 1.55064 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.91161 | −0.204580 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −32.0414 | −1.10751 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 53.2889 | 1.83974 | 0.919869 | − | 0.392226i | \(-0.128295\pi\) | ||||
0.919869 | + | 0.392226i | \(0.128295\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8508 | −0.994856 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.96293 | −0.343142 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.666865 | 0.0229409 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.32947 | −0.0456813 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.5482 | −0.670892 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34.8585 | 1.19493 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −53.9727 | −1.84799 | −0.923996 | − | 0.382403i | \(-0.875097\pi\) | ||||
−0.923996 | + | 0.382403i | \(0.875097\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.163308 | 0.00558502 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45.3914 | 1.55054 | 0.775270 | − | 0.631630i | \(-0.217614\pi\) | ||||
0.775270 | + | 0.631630i | \(0.217614\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.3659 | 1.44551 | 0.722753 | − | 0.691106i | \(-0.242876\pi\) | ||||
0.722753 | + | 0.691106i | \(0.242876\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.337284 | 0.0114946 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.56657 | 0.121407 | 0.0607037 | − | 0.998156i | \(-0.480666\pi\) | ||||
0.0607037 | + | 0.998156i | \(0.480666\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.25267 | 0.144595 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −42.7986 | −1.45352 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.5923 | −0.766391 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −45.2819 | −1.53432 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.72959 | 0.0585377 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.93907 | 0.0655525 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.6030 | 0.932087 | 0.466043 | − | 0.884762i | \(-0.345679\pi\) | ||||
0.466043 | + | 0.884762i | \(0.345679\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.85904 | −0.332537 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.6725 | 0.898621 | 0.449310 | − | 0.893376i | \(-0.351670\pi\) | ||||
0.449310 | + | 0.893376i | \(0.351670\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.22789 | −0.243238 | −0.121619 | − | 0.992577i | \(-0.538809\pi\) | ||||
−0.121619 | + | 0.992577i | \(0.538809\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24.3485 | −0.818465 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −55.9296 | −1.87793 | −0.938966 | − | 0.344009i | \(-0.888215\pi\) | ||||
−0.938966 | + | 0.344009i | \(0.888215\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.815277 | −0.0273435 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.1529 | −0.574645 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.67933 | −0.290443 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.69091 | 0.223652 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −27.5679 | −0.920466 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.43232 | −0.0811223 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.42129 | −0.213924 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.71859 | −0.0571910 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.8617 | −0.427539 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.4857 | −1.24469 | −0.622346 | − | 0.782742i | \(-0.713820\pi\) | ||||
−0.622346 | + | 0.782742i | \(0.713820\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.925383 | 0.0306930 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.8543 | −0.392749 | −0.196375 | − | 0.980529i | \(-0.562917\pi\) | ||||
−0.196375 | + | 0.980529i | \(0.562917\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.1587 | 0.600967 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 24.5042 | 0.810084 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.63850 | −0.0871309 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.5585 | −1.00803 | −0.504015 | − | 0.863695i | \(-0.668145\pi\) | ||||
−0.504015 | + | 0.863695i | \(0.668145\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0475 | 0.331075 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 40.6371 | 1.33759 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.6741 | −0.811281 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.889543 | −0.0292164 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.7104 | −0.679486 | −0.339743 | − | 0.940518i | \(-0.610340\pi\) | ||||
−0.339743 | + | 0.940518i | \(0.610340\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.96964 | 0.228421 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.00636 | −0.196639 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.1487 | 0.528120 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.7638 | −0.580317 | −0.290158 | − | 0.956979i | \(-0.593708\pi\) | ||||
−0.290158 | + | 0.956979i | \(0.593708\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 42.1992 | 1.37712 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.8581 | 1.29934 | 0.649668 | − | 0.760218i | \(-0.274908\pi\) | ||||
0.649668 | + | 0.760218i | \(0.274908\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.83616 | −0.157487 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.21447 | −0.0395068 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.1937 | 0.818684 | 0.409342 | − | 0.912381i | \(-0.365758\pi\) | ||||
0.409342 | + | 0.912381i | \(0.365758\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.78893 | 0.252839 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.562177 | 0.0182298 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.8841 | 0.417357 | 0.208678 | − | 0.977984i | \(-0.433084\pi\) | ||||
0.208678 | + | 0.977984i | \(0.433084\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.79968 | −0.122955 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.25227 | −0.0404801 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.58085 | −0.115632 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.66022 | 0.279362 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.46430 | −0.0471864 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.88521 | 0.189451 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.5160 | −0.498961 | −0.249481 | − | 0.968380i | \(-0.580260\pi\) | ||||
−0.249481 | + | 0.968380i | \(0.580260\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.3408 | −0.364320 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.0964 | 0.773289 | 0.386644 | − | 0.922229i | \(-0.373634\pi\) | ||||
0.386644 | + | 0.922229i | \(0.373634\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.52495 | −0.0488877 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19.5136 | 0.624935 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.2529 | −0.871897 | −0.435949 | − | 0.899972i | \(-0.643587\pi\) | ||||
−0.435949 | + | 0.899972i | \(0.643587\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.7160 | 0.694047 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.31278 | −0.0419140 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.30774 | −0.201186 | −0.100593 | − | 0.994928i | \(-0.532074\pi\) | ||||
−0.100593 | + | 0.994928i | \(0.532074\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.9146 | 0.761982 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.67103 | −0.0850199 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.6420 | 0.783569 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.43876 | 0.204534 | 0.102267 | − | 0.994757i | \(-0.467390\pi\) | ||||
0.102267 | + | 0.994757i | \(0.467390\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.0156 | 0.413038 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.9183 | 0.441239 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.86331 | 0.280704 | 0.140352 | − | 0.990102i | \(-0.455177\pi\) | ||||
0.140352 | + | 0.990102i | \(0.455177\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 40.1925 | 1.27163 |
(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 | 4028.2.a.d.1.7 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4028.2.a.d.1.7 | ✓ | 19 | 1.1 | even | 1 | trivial |