Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(47.9741215344\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 | ||||||||
\(3\) | −1.63270 | −0.942640 | −0.471320 | − | 0.881962i | \(-0.656222\pi\) | ||||
−0.471320 | + | 0.881962i | \(0.656222\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.45098 | 1.09611 | 0.548056 | − | 0.836442i | \(-0.315368\pi\) | ||||
0.548056 | + | 0.836442i | \(0.315368\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.216771 | −0.0819319 | −0.0409659 | − | 0.999161i | \(-0.513044\pi\) | ||||
−0.0409659 | + | 0.999161i | \(0.513044\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.334292 | −0.111431 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.722449 | −0.217826 | −0.108913 | − | 0.994051i | \(-0.534737\pi\) | ||||
−0.108913 | + | 0.994051i | \(0.534737\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.74800 | 0.484809 | 0.242405 | − | 0.970175i | \(-0.422064\pi\) | ||||
0.242405 | + | 0.970175i | \(0.422064\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.00172 | −1.03324 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.52699 | −1.58303 | −0.791513 | − | 0.611152i | \(-0.790706\pi\) | ||||
−0.791513 | + | 0.611152i | \(0.790706\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.06353 | 0.702821 | 0.351411 | − | 0.936221i | \(-0.385702\pi\) | ||||
0.351411 | + | 0.936221i | \(0.385702\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.353923 | 0.0772322 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.33600 | 0.487089 | 0.243544 | − | 0.969890i | \(-0.421690\pi\) | ||||
0.243544 | + | 0.969890i | \(0.421690\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00731 | 0.201462 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.44390 | 1.04768 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.05907 | −1.31084 | −0.655418 | − | 0.755266i | \(-0.727508\pi\) | ||||
−0.655418 | + | 0.755266i | \(0.727508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.04386 | 0.726299 | 0.363149 | − | 0.931731i | \(-0.381701\pi\) | ||||
0.363149 | + | 0.931731i | \(0.381701\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.17954 | 0.205332 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.531303 | −0.0898065 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.672407 | 0.110543 | 0.0552715 | − | 0.998471i | \(-0.482398\pi\) | ||||
0.0552715 | + | 0.998471i | \(0.482398\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.85397 | −0.457000 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.91174 | 0.610911 | 0.305456 | − | 0.952206i | \(-0.401191\pi\) | ||||
0.305456 | + | 0.952206i | \(0.401191\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.40292 | 1.28143 | 0.640716 | − | 0.767778i | \(-0.278637\pi\) | ||||
0.640716 | + | 0.767778i | \(0.278637\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.819343 | −0.122140 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.0246 | −1.75397 | −0.876986 | − | 0.480515i | \(-0.840450\pi\) | ||||
−0.876986 | + | 0.480515i | \(0.840450\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.95301 | −0.993287 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.6566 | 1.49222 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.2471 | 1.81962 | 0.909811 | − | 0.415022i | \(-0.136226\pi\) | ||||
0.909811 | + | 0.415022i | \(0.136226\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.77071 | −0.238762 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.00182 | −0.662507 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.35956 | −1.08832 | −0.544161 | − | 0.838981i | \(-0.683152\pi\) | ||||
−0.544161 | + | 0.838981i | \(0.683152\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0828 | −1.54704 | −0.773522 | − | 0.633769i | \(-0.781507\pi\) | ||||
−0.773522 | + | 0.633769i | \(0.781507\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0724649 | 0.00912972 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.28433 | 0.531405 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.88237 | 0.229968 | 0.114984 | − | 0.993367i | \(-0.463318\pi\) | ||||
0.114984 | + | 0.993367i | \(0.463318\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.81398 | −0.459149 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.94202 | 0.823866 | 0.411933 | − | 0.911214i | \(-0.364854\pi\) | ||||
0.411933 | + | 0.911214i | \(0.364854\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.10868 | −0.832008 | −0.416004 | − | 0.909363i | \(-0.636570\pi\) | ||||
−0.416004 | + | 0.909363i | \(0.636570\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.64464 | −0.189906 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.156606 | 0.0178469 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0345 | −1.35398 | −0.676992 | − | 0.735991i | \(-0.736717\pi\) | ||||
−0.676992 | + | 0.735991i | \(0.736717\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.88537 | −0.876153 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.977452 | 0.107289 | 0.0536447 | − | 0.998560i | \(-0.482916\pi\) | ||||
0.0536447 | + | 0.998560i | \(0.482916\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.9975 | −1.73518 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.5253 | 1.23565 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.649985 | 0.0688983 | 0.0344491 | − | 0.999406i | \(-0.489032\pi\) | ||||
0.0344491 | + | 0.999406i | \(0.489032\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.378917 | −0.0397213 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.60241 | −0.684638 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.50865 | 0.770371 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.7156 | −1.29107 | −0.645535 | − | 0.763730i | \(-0.723366\pi\) | ||||
−0.645535 | + | 0.763730i | \(0.723366\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.241509 | 0.0242725 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.99278 | 0.994318 | 0.497159 | − | 0.867659i | \(-0.334376\pi\) | ||||
0.497159 | + | 0.867659i | \(0.334376\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.603426 | 0.0594573 | 0.0297287 | − | 0.999558i | \(-0.490536\pi\) | ||||
0.0297287 | + | 0.999558i | \(0.490536\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.867458 | 0.0846552 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.8596 | 1.33986 | 0.669929 | − | 0.742425i | \(-0.266325\pi\) | ||||
0.669929 | + | 0.742425i | \(0.266325\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.5180 | −1.29479 | −0.647397 | − | 0.762153i | \(-0.724142\pi\) | ||||
−0.647397 | + | 0.762153i | \(0.724142\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.09784 | −0.104202 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.06976 | −0.476923 | −0.238461 | − | 0.971152i | \(-0.576643\pi\) | ||||
−0.238461 | + | 0.971152i | \(0.576643\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.72548 | 0.533904 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.584344 | −0.0540226 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.41486 | 0.129700 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4781 | −0.952552 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.38670 | −0.575869 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.78601 | −0.875287 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.37240 | 0.299252 | 0.149626 | − | 0.988743i | \(-0.452193\pi\) | ||||
0.149626 | + | 0.988743i | \(0.452193\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.7194 | −1.20793 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7250 | 0.937049 | 0.468524 | − | 0.883451i | \(-0.344786\pi\) | ||||
0.468524 | + | 0.883451i | \(0.344786\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.664085 | −0.0575835 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.3429 | 1.14837 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.64269 | 0.482087 | 0.241044 | − | 0.970514i | \(-0.422510\pi\) | ||||
0.241044 | + | 0.970514i | \(0.422510\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.6517 | −1.07310 | −0.536552 | − | 0.843867i | \(-0.680273\pi\) | ||||
−0.536552 | + | 0.843867i | \(0.680273\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.6326 | 1.65336 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.26284 | −0.105604 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.3016 | −1.43682 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.3522 | 0.936312 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.442952 | 0.0362880 | 0.0181440 | − | 0.999835i | \(-0.494224\pi\) | ||||
0.0181440 | + | 0.999835i | \(0.494224\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.8401 | 1.37043 | 0.685214 | − | 0.728341i | \(-0.259708\pi\) | ||||
0.685214 | + | 0.728341i | \(0.259708\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.18192 | 0.176398 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.91143 | 0.796105 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.746409 | 0.0595699 | 0.0297850 | − | 0.999556i | \(-0.490518\pi\) | ||||
0.0297850 | + | 0.999556i | \(0.490518\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −21.6285 | −1.71525 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.506377 | −0.0399081 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.4720 | −1.05521 | −0.527603 | − | 0.849491i | \(-0.676909\pi\) | ||||
−0.527603 | + | 0.849491i | \(0.676909\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.89104 | 0.225067 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.95905 | −0.383742 | −0.191871 | − | 0.981420i | \(-0.561456\pi\) | ||||
−0.191871 | + | 0.981420i | \(0.561456\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.94448 | −0.764960 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.02411 | −0.0783158 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.6342 | −0.884531 | −0.442265 | − | 0.896884i | \(-0.645825\pi\) | ||||
−0.442265 | + | 0.896884i | \(0.645825\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.218356 | −0.0165062 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.6486 | 1.02590 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.16817 | −0.0873130 | −0.0436565 | − | 0.999047i | \(-0.513901\pi\) | ||||
−0.0436565 | + | 0.999047i | \(0.513901\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.63395 | 0.121450 | 0.0607251 | − | 0.998155i | \(-0.480659\pi\) | ||||
0.0607251 | + | 0.998155i | \(0.480659\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 19.7276 | 1.45831 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.64806 | 0.121168 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.71541 | 0.344825 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.18008 | −0.0858383 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.21157 | −0.377096 | −0.188548 | − | 0.982064i | \(-0.560378\pi\) | ||||
−0.188548 | + | 0.982064i | \(0.560378\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.72307 | −0.196011 | −0.0980054 | − | 0.995186i | \(-0.531246\pi\) | ||||
−0.0980054 | + | 0.995186i | \(0.531246\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.99502 | −0.500924 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.4955 | 0.819021 | 0.409511 | − | 0.912305i | \(-0.365699\pi\) | ||||
0.409511 | + | 0.912305i | \(0.365699\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.79455 | −0.410765 | −0.205382 | − | 0.978682i | \(-0.565844\pi\) | ||||
−0.205382 | + | 0.978682i | \(0.565844\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.07335 | −0.216777 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.53020 | 0.107399 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.58760 | 0.669627 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.780904 | −0.0542766 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.21324 | −0.153093 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.89344 | 0.130350 | 0.0651749 | − | 0.997874i | \(-0.479239\pi\) | ||||
0.0651749 | + | 0.997874i | \(0.479239\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.3342 | −0.776609 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.5954 | 1.40459 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.876593 | −0.0595070 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.6063 | 0.784283 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.4092 | −0.767466 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.110645 | 0.00740936 | 0.00370468 | − | 0.999993i | \(-0.498821\pi\) | ||||
0.00370468 | + | 0.999993i | \(0.498821\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.336736 | −0.0224491 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.36255 | −0.555042 | −0.277521 | − | 0.960720i | \(-0.589513\pi\) | ||||
−0.277521 | + | 0.960720i | \(0.589513\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.1121 | 1.39513 | 0.697563 | − | 0.716523i | \(-0.254268\pi\) | ||||
0.697563 | + | 0.716523i | \(0.254268\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.255691 | −0.0168232 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.0549 | −1.57589 | −0.787946 | − | 0.615745i | \(-0.788855\pi\) | ||||
−0.787946 | + | 0.615745i | \(0.788855\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −29.4721 | −1.92255 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.6487 | 1.27632 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.8969 | 0.704862 | 0.352431 | − | 0.935838i | \(-0.385355\pi\) | ||||
0.352431 | + | 0.935838i | \(0.385355\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.52561 | 0.484767 | 0.242384 | − | 0.970180i | \(-0.422071\pi\) | ||||
0.242384 | + | 0.970180i | \(0.422071\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.45725 | −0.221782 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.0417 | −1.08875 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.35506 | 0.340734 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.59589 | −0.101135 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.08174 | −0.446996 | −0.223498 | − | 0.974704i | \(-0.571748\pi\) | ||||
−0.223498 | + | 0.974704i | \(0.571748\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.68764 | −0.106101 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 26.1192 | 1.63564 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.9031 | −0.742496 | −0.371248 | − | 0.928534i | \(-0.621070\pi\) | ||||
−0.371248 | + | 0.928534i | \(0.621070\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.145759 | −0.00905700 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.35979 | 0.146067 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.2708 | −0.633326 | −0.316663 | − | 0.948538i | \(-0.602562\pi\) | ||||
−0.316663 | + | 0.948538i | \(0.602562\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 32.4683 | 1.99451 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.06123 | −0.0649463 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.6077 | 1.01259 | 0.506295 | − | 0.862360i | \(-0.331015\pi\) | ||||
0.506295 | + | 0.862360i | \(0.331015\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.09259 | −0.187862 | −0.0939308 | − | 0.995579i | \(-0.529943\pi\) | ||||
−0.0939308 | + | 0.995579i | \(0.529943\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.618658 | 0.0374429 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.727731 | −0.0438838 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.74912 | −0.225263 | −0.112632 | − | 0.993637i | \(-0.535928\pi\) | ||||
−0.112632 | + | 0.993637i | \(0.535928\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.35183 | −0.0809319 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.14713 | 0.0684322 | 0.0342161 | − | 0.999414i | \(-0.489107\pi\) | ||||
0.0342161 | + | 0.999414i | \(0.489107\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.29719 | −0.552660 | −0.276330 | − | 0.961063i | \(-0.589118\pi\) | ||||
−0.276330 | + | 0.961063i | \(0.589118\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −12.2594 | −0.726182 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.847953 | −0.0500531 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.6015 | 1.50597 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20.7607 | 1.21701 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.6804 | −1.61711 | −0.808553 | − | 0.588424i | \(-0.799749\pi\) | ||||
−0.808553 | + | 0.588424i | \(0.799749\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.4891 | −1.19292 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.93294 | −0.228212 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.08333 | 0.236145 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.82151 | −0.104990 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.3152 | −0.937284 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −29.6147 | −1.69574 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −31.0143 | −1.77008 | −0.885039 | − | 0.465517i | \(-0.845868\pi\) | ||||
−0.885039 | + | 0.465517i | \(0.845868\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.985214 | −0.0560468 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.46185 | −0.196303 | −0.0981516 | − | 0.995171i | \(-0.531293\pi\) | ||||
−0.0981516 | + | 0.995171i | \(0.531293\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.4342 | −1.49415 | −0.747074 | − | 0.664741i | \(-0.768542\pi\) | ||||
−0.747074 | + | 0.664741i | \(0.768542\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.177610 | 0.0100072 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.931881 | −0.0523396 | −0.0261698 | − | 0.999658i | \(-0.508331\pi\) | ||||
−0.0261698 | + | 0.999658i | \(0.508331\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.09981 | 0.285535 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −22.6286 | −1.26300 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.9956 | −1.11258 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.76079 | 0.0976708 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 22.0709 | 1.22052 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.60660 | 0.143706 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.82835 | 0.430285 | 0.215142 | − | 0.976583i | \(-0.430978\pi\) | ||||
0.215142 | + | 0.976583i | \(0.430978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.224780 | −0.0123179 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.61366 | 0.252071 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.23331 | −0.339550 | −0.169775 | − | 0.985483i | \(-0.554304\pi\) | ||||
−0.169775 | + | 0.985483i | \(0.554304\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.27740 | 0.449566 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.92148 | −0.158207 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.02461 | 0.163314 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.34799 | −0.503279 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −33.0875 | −1.77623 | −0.888115 | − | 0.459622i | \(-0.847985\pi\) | ||||
−0.888115 | + | 0.459622i | \(0.847985\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.2394 | 0.708690 | 0.354345 | − | 0.935115i | \(-0.384704\pi\) | ||||
0.354345 | + | 0.935115i | \(0.384704\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.51595 | 0.507924 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.7848 | 1.31916 | 0.659582 | − | 0.751633i | \(-0.270733\pi\) | ||||
0.659582 | + | 0.751633i | \(0.270733\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.0148 | 0.903050 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.31005 | −0.122261 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.80295 | −0.0951560 | −0.0475780 | − | 0.998868i | \(-0.515150\pi\) | ||||
−0.0475780 | + | 0.998868i | \(0.515150\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.61481 | −0.506042 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.1075 | 0.897913 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.4232 | −0.911974 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.8016 | 0.981434 | 0.490717 | − | 0.871319i | \(-0.336735\pi\) | ||||
0.490717 | + | 0.871319i | \(0.336735\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.30766 | −0.0680742 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.87158 | −0.149085 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.1253 | 1.04205 | 0.521024 | − | 0.853542i | \(-0.325550\pi\) | ||||
0.521024 | + | 0.853542i | \(0.325550\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.9776 | 0.825080 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.3393 | −0.635505 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.7595 | −1.16908 | −0.584539 | − | 0.811365i | \(-0.698725\pi\) | ||||
−0.584539 | + | 0.811365i | \(0.698725\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.50611 | −0.282087 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.4688 | −0.739319 | −0.369659 | − | 0.929167i | \(-0.620526\pi\) | ||||
−0.369659 | + | 0.929167i | \(0.620526\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.383839 | 0.0195622 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.80903 | −0.142791 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.8828 | −1.56582 | −0.782910 | − | 0.622136i | \(-0.786265\pi\) | ||||
−0.782910 | + | 0.622136i | \(0.786265\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.2470 | −0.771074 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.5107 | −0.883299 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −29.4963 | −1.48412 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.3597 | −1.02183 | −0.510913 | − | 0.859632i | \(-0.670693\pi\) | ||||
−0.510913 | + | 0.859632i | \(0.670693\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.08425 | 0.0542804 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.89366 | −0.444128 | −0.222064 | − | 0.975032i | \(-0.571279\pi\) | ||||
−0.222064 | + | 0.975032i | \(0.571279\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.06868 | 0.352116 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −19.3269 | −0.960362 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.485780 | −0.0240792 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.2994 | 0.707062 | 0.353531 | − | 0.935423i | \(-0.384981\pi\) | ||||
0.353531 | + | 0.935423i | \(0.384981\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.21281 | −0.454434 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.81211 | 0.0891682 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.39572 | 0.117601 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.6564 | 1.01155 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.36618 | −0.262155 | −0.131078 | − | 0.991372i | \(-0.541844\pi\) | ||||
−0.131078 | + | 0.991372i | \(0.541844\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.40879 | 0.263608 | 0.131804 | − | 0.991276i | \(-0.457923\pi\) | ||||
0.131804 | + | 0.991276i | \(0.457923\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.01974 | 0.195446 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.57471 | −0.318920 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.61921 | 0.126752 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.06184 | 0.0995468 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.8058 | −0.713171 | −0.356586 | − | 0.934263i | \(-0.616059\pi\) | ||||
−0.356586 | + | 0.934263i | \(0.616059\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.4306 | −0.789602 | −0.394801 | − | 0.918767i | \(-0.629187\pi\) | ||||
−0.394801 | + | 0.918767i | \(0.629187\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 28.2484 | 1.35441 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.15638 | 0.342336 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.2426 | −0.918401 | −0.459201 | − | 0.888333i | \(-0.651864\pi\) | ||||
−0.459201 | + | 0.888333i | \(0.651864\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.32433 | 0.110683 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.9368 | 1.61238 | 0.806192 | − | 0.591654i | \(-0.201525\pi\) | ||||
0.806192 | + | 0.591654i | \(0.201525\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.59310 | 0.0755203 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.723208 | −0.0342065 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.7481 | −1.26232 | −0.631161 | − | 0.775652i | \(-0.717421\pi\) | ||||
−0.631161 | + | 0.775652i | \(0.717421\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.82603 | −0.133073 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −27.4948 | −1.29182 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.928719 | −0.0435390 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.0791 | −1.68771 | −0.843855 | − | 0.536571i | \(-0.819719\pi\) | ||||
−0.843855 | + | 0.536571i | \(0.819719\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −35.5322 | −1.65850 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.3001 | 0.898893 | 0.449447 | − | 0.893307i | \(-0.351621\pi\) | ||||
0.449447 | + | 0.893307i | \(0.351621\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.9353 | −1.01942 | −0.509710 | − | 0.860346i | \(-0.670247\pi\) | ||||
−0.509710 | + | 0.860346i | \(0.670247\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −16.1824 | −0.750440 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.1837 | −0.563792 | −0.281896 | − | 0.959445i | \(-0.590963\pi\) | ||||
−0.281896 | + | 0.959445i | \(0.590963\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.408044 | −0.0188417 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.21866 | −0.0561530 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.07068 | −0.279130 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.08593 | 0.141592 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.42838 | −0.202762 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.5541 | 0.619304 | 0.309652 | − | 0.950850i | \(-0.399787\pi\) | ||||
0.309652 | + | 0.950850i | \(0.399787\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.17537 | 0.0535923 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.826762 | 0.0376190 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −31.1656 | −1.41516 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.7308 | 0.758144 | 0.379072 | − | 0.925367i | \(-0.376243\pi\) | ||||
0.379072 | + | 0.925367i | \(0.376243\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.9957 | 0.994678 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.8942 | 1.93579 | 0.967894 | − | 0.251358i | \(-0.0808773\pi\) | ||||
0.967894 | + | 0.251358i | \(0.0808773\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 46.0744 | 2.07509 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.591934 | 0.0266054 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.50483 | −0.0675009 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.2406 | −1.21946 | −0.609729 | − | 0.792610i | \(-0.708722\pi\) | ||||
−0.609729 | + | 0.792610i | \(0.708722\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.09663 | 0.361731 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.8683 | −0.529182 | −0.264591 | − | 0.964361i | \(-0.585237\pi\) | ||||
−0.264591 | + | 0.964361i | \(0.585237\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.4921 | 1.08988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.2364 | 0.721082 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.2059 | −0.541017 | −0.270509 | − | 0.962718i | \(-0.587192\pi\) | ||||
−0.270509 | + | 0.962718i | \(0.587192\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.54096 | 0.0681679 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.6775 | 0.736331 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.47899 | 0.0651719 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.68718 | 0.382062 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.9951 | 0.833794 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.8313 | 1.04407 | 0.522034 | − | 0.852925i | \(-0.325174\pi\) | ||||
0.522034 | + | 0.852925i | \(0.325174\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.2004 | 1.27685 | 0.638423 | − | 0.769686i | \(-0.279587\pi\) | ||||
0.638423 | + | 0.769686i | \(0.279587\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.356510 | 0.0155594 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.3942 | −1.14975 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.5431 | −0.762745 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.79453 | 0.121272 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.83774 | 0.296175 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.9696 | 1.46863 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.90727 | 0.0823047 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.02319 | 0.216364 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.1650 | −1.76982 | −0.884910 | − | 0.465761i | \(-0.845781\pi\) | ||||
−0.884910 | + | 0.465761i | \(0.845781\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.66774 | −0.114484 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −33.1325 | −1.41924 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −45.2808 | −1.93607 | −0.968034 | − | 0.250819i | \(-0.919300\pi\) | ||||
−0.968034 | + | 0.250819i | \(0.919300\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.03918 | 0.172388 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.6256 | −0.921283 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.60873 | 0.110934 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.69078 | −0.114217 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.07523 | −0.299787 | −0.149893 | − | 0.988702i | \(-0.547893\pi\) | ||||
−0.149893 | + | 0.988702i | \(0.547893\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.6883 | 0.621250 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.69885 | −0.325046 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.6808 | 1.29304 | 0.646521 | − | 0.762896i | \(-0.276223\pi\) | ||||
0.646521 | + | 0.762896i | \(0.276223\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.4259 | −0.522761 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.70932 | 0.0717848 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.2766 | 1.26926 | 0.634632 | − | 0.772815i | \(-0.281152\pi\) | ||||
0.634632 | + | 0.772815i | \(0.281152\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.63372 | 0.110218 | 0.0551088 | − | 0.998480i | \(-0.482449\pi\) | ||||
0.0551088 | + | 0.998480i | \(0.482449\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.50893 | 0.355465 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.35308 | 0.0981301 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.3538 | 0.805710 | 0.402855 | − | 0.915264i | \(-0.368018\pi\) | ||||
0.402855 | + | 0.915264i | \(0.368018\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.44596 | 0.184768 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.211884 | −0.00879042 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.57032 | −0.396362 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.43222 | −0.0592148 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.0409 | −1.11610 | −0.558049 | − | 0.829808i | \(-0.688450\pi\) | ||||
−0.558049 | + | 0.829808i | \(0.688450\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.3885 | 0.510458 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.7687 | −0.772042 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −43.3177 | −1.77885 | −0.889423 | − | 0.457084i | \(-0.848894\pi\) | ||||
−0.889423 | + | 0.457084i | \(0.848894\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.46781 | 0.142166 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.46076 | 0.387203 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.61337 | 0.392792 | 0.196396 | − | 0.980525i | \(-0.437076\pi\) | ||||
0.196396 | + | 0.980525i | \(0.437076\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.7859 | 0.725503 | 0.362752 | − | 0.931886i | \(-0.381837\pi\) | ||||
0.362752 | + | 0.931886i | \(0.381837\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.629261 | −0.0256255 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −25.6816 | −1.04410 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.73656 | 0.232840 | 0.116420 | − | 0.993200i | \(-0.462858\pi\) | ||||
0.116420 | + | 0.993200i | \(0.462858\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.49836 | −0.101239 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.0191 | −0.850342 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.95489 | 0.280905 | 0.140453 | − | 0.990087i | \(-0.455144\pi\) | ||||
0.140453 | + | 0.990087i | \(0.455144\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.6537 | −0.631217 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.5321 | 0.585041 | 0.292521 | − | 0.956259i | \(-0.405506\pi\) | ||||
0.292521 | + | 0.956259i | \(0.405506\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.2203 | −1.41562 | −0.707812 | − | 0.706400i | \(-0.750318\pi\) | ||||
−0.707812 | + | 0.706400i | \(0.750318\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.7169 | 0.510312 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.140898 | −0.00564497 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0219 | −1.16088 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.61356 | 0.144312 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.38879 | −0.174993 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.384100 | 0.0152908 | 0.00764540 | − | 0.999971i | \(-0.497566\pi\) | ||||
0.00764540 | + | 0.999971i | \(0.497566\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.09142 | −0.122873 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.26568 | 0.328014 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.1539 | −0.481555 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.32066 | −0.0918039 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.6923 | 0.659307 | 0.329654 | − | 0.944102i | \(-0.393068\pi\) | ||||
0.329654 | + | 0.944102i | \(0.393068\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.2636 | −0.996301 | −0.498150 | − | 0.867091i | \(-0.665987\pi\) | ||||
−0.498150 | + | 0.867091i | \(0.665987\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −33.6261 | −1.32403 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.2406 | 1.07094 | 0.535470 | − | 0.844554i | \(-0.320135\pi\) | ||||
0.535470 | + | 0.844554i | \(0.320135\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.03935 | 0.237065 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.43121 | 0.0560937 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.11824 | −0.200292 | −0.100146 | − | 0.994973i | \(-0.531931\pi\) | ||||
−0.100146 | + | 0.994973i | \(0.531931\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.2868 | 1.02711 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.37637 | 0.0927111 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.2093 | 0.826195 | 0.413098 | − | 0.910687i | \(-0.364447\pi\) | ||||
0.413098 | + | 0.910687i | \(0.364447\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.6518 | 1.19222 | 0.596109 | − | 0.802903i | \(-0.296712\pi\) | ||||
0.596109 | + | 0.802903i | \(0.296712\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.6278 | 0.723444 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.62766 | −0.0631179 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.4900 | −0.638494 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.180651 | −0.00698436 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.72921 | 0.336987 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.6681 | 0.411226 | 0.205613 | − | 0.978633i | \(-0.434081\pi\) | ||||
0.205613 | + | 0.978633i | \(0.434081\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.48370 | 0.211068 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.32641 | −0.320010 | −0.160005 | − | 0.987116i | \(-0.551151\pi\) | ||||
−0.160005 | + | 0.987116i | \(0.551151\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.75637 | 0.105780 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.6535 | 0.523205 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.91915 | 0.341282 | 0.170641 | − | 0.985333i | \(-0.445416\pi\) | ||||
0.170641 | + | 0.985333i | \(0.445416\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.8301 | 0.528422 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −34.4697 | −1.31510 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 23.1559 | 0.882170 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.8769 | −1.51699 | −0.758495 | − | 0.651679i | \(-0.774065\pi\) | ||||
−0.758495 | + | 0.651679i | \(0.774065\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.0523522 | −0.00198869 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31.0091 | −1.17624 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.5319 | −0.967089 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 39.2745 | 1.48550 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.2094 | 0.612220 | 0.306110 | − | 0.951996i | \(-0.400972\pi\) | ||||
0.306110 | + | 0.951996i | \(0.400972\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.05994 | 0.0776920 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 48.1192 | 1.81227 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.16615 | −0.0814664 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.9447 | −0.824149 | −0.412074 | − | 0.911150i | \(-0.635196\pi\) | ||||
−0.412074 | + | 0.911150i | \(0.635196\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.02302 | 0.150875 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.44644 | 0.353772 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.09521 | −0.115754 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.7914 | −0.664430 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.3711 | 0.535952 | 0.267976 | − | 0.963426i | \(-0.413645\pi\) | ||||
0.267976 | + | 0.963426i | \(0.413645\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.130805 | −0.00487145 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.2871 | −0.456961 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.11068 | −0.264084 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −47.9070 | −1.77677 | −0.888387 | − | 0.459095i | \(-0.848174\pi\) | ||||
−0.888387 | + | 0.459095i | \(0.848174\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.3008 | 1.08521 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −54.8457 | −2.02854 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −51.9621 | −1.91926 | −0.959631 | − | 0.281261i | \(-0.909247\pi\) | ||||
−0.959631 | + | 0.281261i | \(0.909247\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 27.8240 | 1.02630 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.35992 | −0.0500932 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.5752 | −1.45580 | −0.727898 | − | 0.685685i | \(-0.759503\pi\) | ||||
−0.727898 | + | 0.685685i | \(0.759503\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.74320 | −0.321189 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.9308 | 0.694504 | 0.347252 | − | 0.937772i | \(-0.387115\pi\) | ||||
0.347252 | + | 0.937772i | \(0.387115\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.08567 | 0.0397758 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.326754 | −0.0119553 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.00436 | −0.109777 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | 0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.5624 | 0.421356 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 41.2748 | 1.50214 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.40445 | 0.160082 | 0.0800412 | − | 0.996792i | \(-0.474495\pi\) | ||||
0.0800412 | + | 0.996792i | \(0.474495\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.75540 | 0.100015 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.9490 | −1.04940 | −0.524701 | − | 0.851287i | \(-0.675823\pi\) | ||||
−0.524701 | + | 0.851287i | \(0.675823\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.93032 | 0.106085 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.34784 | 0.193352 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.6125 | −0.527628 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.11891 | 0.292776 | 0.146388 | − | 0.989227i | \(-0.453235\pi\) | ||||
0.146388 | + | 0.989227i | \(0.453235\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.4342 | 0.699906 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.6159 | 0.741502 | 0.370751 | − | 0.928732i | \(-0.379100\pi\) | ||||
0.370751 | + | 0.928732i | \(0.379100\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.07343 | 0.146322 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.237980 | 0.00853748 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.9837 | 0.429361 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.01525 | −0.179460 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −38.4288 | −1.37333 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.82944 | 0.0652953 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 52.0811 | 1.85649 | 0.928245 | − | 0.371970i | \(-0.121318\pi\) | ||||
0.928245 | + | 0.371970i | \(0.121318\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.7692 | 0.596998 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.09898 | 0.0390752 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.1208 | −0.750021 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −53.0110 | −1.88010 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.5260 | −1.25839 | −0.629197 | − | 0.777246i | \(-0.716616\pi\) | ||||
−0.629197 | + | 0.777246i | \(0.716616\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 78.4846 | 2.77659 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.217285 | −0.00767738 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.13565 | 0.181233 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.24112 | −0.0437438 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.1154 | −0.954507 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.7961 | 0.625677 | 0.312838 | − | 0.949806i | \(-0.398720\pi\) | ||||
0.312838 | + | 0.949806i | \(0.398720\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.9819 | 1.12304 | 0.561519 | − | 0.827464i | \(-0.310217\pi\) | ||||
0.561519 | + | 0.827464i | \(0.310217\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.04928 | 0.177086 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −33.0195 | −1.15662 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.7426 | 0.900618 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.126669 | 0.00442617 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.6748 | −1.24506 | −0.622529 | − | 0.782597i | \(-0.713895\pi\) | ||||
−0.622529 | + | 0.782597i | \(0.713895\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.0246 | 0.349437 | 0.174718 | − | 0.984618i | \(-0.444099\pi\) | ||||
0.174718 | + | 0.984618i | \(0.444099\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.18817 | 0.0413666 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.9793 | −1.66840 | −0.834201 | − | 0.551460i | \(-0.814071\pi\) | ||||
−0.834201 | + | 0.551460i | \(0.814071\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.1850 | −0.527396 | −0.263698 | − | 0.964605i | \(-0.584942\pi\) | ||||
−0.263698 | + | 0.964605i | \(0.584942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.12119 | 0.212342 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 45.3822 | 1.57240 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.1545 | −0.420625 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.0144 | 0.760928 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.6370 | 1.02318 | 0.511591 | − | 0.859229i | \(-0.329056\pi\) | ||||
0.511591 | + | 0.859229i | \(0.329056\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.8304 | 0.718291 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.87292 | −0.0645069 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.3737 | −0.838482 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.27135 | 0.0780443 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.1795 | 0.520960 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.57074 | 0.0538443 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.3001 | −1.34561 | −0.672805 | − | 0.739820i | \(-0.734911\pi\) | ||||
−0.672805 | + | 0.739820i | \(0.734911\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.51008 | −0.0858429 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.6417 | 0.363514 | 0.181757 | − | 0.983343i | \(-0.441822\pi\) | ||||
0.181757 | + | 0.983343i | \(0.441822\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.7384 | 0.536989 | 0.268494 | − | 0.963281i | \(-0.413474\pi\) | ||||
0.268494 | + | 0.963281i | \(0.413474\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.38445 | 0.0471820 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.3684 | −0.795470 | −0.397735 | − | 0.917500i | \(-0.630204\pi\) | ||||
−0.397735 | + | 0.917500i | \(0.630204\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.5152 | −0.969545 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −41.7996 | −1.41959 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.69429 | 0.294933 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.29039 | 0.111491 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.25071 | 0.143865 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.12133 | 0.0717139 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.8808 | 1.07654 | 0.538270 | − | 0.842773i | \(-0.319078\pi\) | ||||
0.538270 | + | 0.842773i | \(0.319078\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 45.1938 | 1.52435 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.3238 | 1.02163 | 0.510817 | − | 0.859689i | \(-0.329343\pi\) | ||||
0.510817 | + | 0.859689i | \(0.329343\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.01819 | −0.135223 | −0.0676114 | − | 0.997712i | \(-0.521538\pi\) | ||||
−0.0676114 | + | 0.997712i | \(0.521538\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 33.4526 | 1.12450 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.36563 | 0.280890 | 0.140445 | − | 0.990088i | \(-0.455147\pi\) | ||||
0.140445 | + | 0.990088i | \(0.455147\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.731039 | −0.0245183 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.69678 | 0.190849 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −36.8378 | −1.23273 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.86316 | −0.0957049 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.66685 | −0.222600 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.5459 | −0.952059 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −86.4633 | −2.88051 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.97398 | 0.0989679 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.00477 | 0.133123 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.1342 | 0.369706 | 0.184853 | − | 0.982766i | \(-0.440819\pi\) | ||||
0.184853 | + | 0.982766i | \(0.440819\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.34050 | −0.110798 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.36090 | −0.310141 | −0.155070 | − | 0.987903i | \(-0.549560\pi\) | ||||
−0.155070 | + | 0.987903i | \(0.549560\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.706159 | −0.0233705 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 48.3520 | 1.59847 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.32488 | −0.0767742 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.0683 | 0.859915 | 0.429958 | − | 0.902849i | \(-0.358528\pi\) | ||||
0.429958 | + | 0.902849i | \(0.358528\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 50.6370 | 1.66855 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.1347 | 0.399418 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.677323 | 0.0222703 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.201720 | −0.00662537 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.6291 | 1.30019 | 0.650095 | − | 0.759853i | \(-0.274729\pi\) | ||||
0.650095 | + | 0.759853i | \(0.274729\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.3007 | −0.698103 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.65215 | 0.185043 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.5574 | 0.377967 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.64247 | 0.151663 | 0.0758315 | − | 0.997121i | \(-0.475839\pi\) | ||||
0.0758315 | + | 0.997121i | \(0.475839\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 43.1591 | 1.40844 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.4373 | 0.405444 | 0.202722 | − | 0.979236i | \(-0.435021\pi\) | ||||
0.202722 | + | 0.979236i | \(0.435021\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.13781 | 0.297568 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.89236 | −0.0940884 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.6020 | −1.38438 | −0.692190 | − | 0.721716i | \(-0.743354\pi\) | ||||
−0.692190 | + | 0.721716i | \(0.743354\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.4260 | −0.403365 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.52148 | 0.0493374 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.7829 | 0.640832 | 0.320416 | − | 0.947277i | \(-0.396177\pi\) | ||||
0.320416 | + | 0.947277i | \(0.396177\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.7735 | −0.413339 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.32647 | −0.269156 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.22317 | −0.0394983 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.6472 | −0.472490 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.63315 | −0.149301 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.67420 | −0.214850 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 55.8191 | 1.79502 | 0.897510 | − | 0.440993i | \(-0.145374\pi\) | ||||
0.897510 | + | 0.440993i | \(0.145374\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 32.6468 | 1.04877 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.5676 | −1.20560 | −0.602801 | − | 0.797892i | \(-0.705949\pi\) | ||||
−0.602801 | + | 0.797892i | \(0.705949\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.74253 | 0.0879214 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.87483 | −0.0920684 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.4503 | 1.29412 | 0.647060 | − | 0.762439i | \(-0.275998\pi\) | ||||
0.647060 | + | 0.762439i | \(0.275998\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.469581 | −0.0150079 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.51897 | 0.144280 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.9552 | 1.37006 | 0.685029 | − | 0.728516i | \(-0.259790\pi\) | ||||
0.685029 | + | 0.728516i | \(0.259790\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.1753 | 0.897739 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.25579 | −0.135463 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.6292 | 0.624172 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.4814 | 1.69889 | 0.849447 | − | 0.527674i | \(-0.176936\pi\) | ||||
0.849447 | + | 0.527674i | \(0.176936\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.7813 | −0.405603 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.2023 | −0.450244 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.16721 | 0.258658 | 0.129329 | − | 0.991602i | \(-0.458718\pi\) | ||||
0.129329 | + | 0.991602i | \(0.458718\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.66051 | 0.115814 |
(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 | 6008.2.a.c.1.13 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.c.1.13 | ✓ | 44 | 1.1 | even | 1 | trivial |