Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, 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("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.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: | \(72.4642398343\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.381966 | 0.270091 | 0.135045 | − | 0.990839i | \(-0.456882\pi\) | ||||
0.135045 | + | 0.990839i | \(0.456882\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.85410 | −0.927051 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.381966 | 0.155937 | ||||||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | −1.47214 | −0.520479 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.85410 | −0.535233 | ||||||||
\(13\) | 4.23607 | 1.17487 | 0.587437 | − | 0.809270i | \(-0.300137\pi\) | ||||
0.587437 | + | 0.809270i | \(0.300137\pi\) | |||||||
\(14\) | 0.381966 | 0.102085 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.14590 | 0.786475 | ||||||||
\(17\) | 7.85410 | 1.90490 | 0.952450 | − | 0.304696i | \(-0.0985548\pi\) | ||||
0.952450 | + | 0.304696i | \(0.0985548\pi\) | |||||||
\(18\) | 0.381966 | 0.0900303 | ||||||||
\(19\) | −0.854102 | −0.195944 | −0.0979722 | − | 0.995189i | \(-0.531236\pi\) | ||||
−0.0979722 | + | 0.995189i | \(0.531236\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.23607 | 0.883281 | 0.441641 | − | 0.897192i | \(-0.354397\pi\) | ||||
0.441641 | + | 0.897192i | \(0.354397\pi\) | |||||||
\(24\) | −1.47214 | −0.300498 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.61803 | 0.317323 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.85410 | −0.350392 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.09017 | 0.914222 | 0.457111 | − | 0.889410i | \(-0.348884\pi\) | ||||
0.457111 | + | 0.889410i | \(0.348884\pi\) | |||||||
\(32\) | 4.14590 | 0.732898 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.00000 | 0.514496 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.85410 | −0.309017 | ||||||||
\(37\) | 1.76393 | 0.289989 | 0.144994 | − | 0.989432i | \(-0.453684\pi\) | ||||
0.144994 | + | 0.989432i | \(0.453684\pi\) | |||||||
\(38\) | −0.326238 | −0.0529228 | ||||||||
\(39\) | 4.23607 | 0.678314 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.23607 | −0.661563 | −0.330781 | − | 0.943707i | \(-0.607312\pi\) | ||||
−0.330781 | + | 0.943707i | \(0.607312\pi\) | |||||||
\(42\) | 0.381966 | 0.0589386 | ||||||||
\(43\) | −6.70820 | −1.02299 | −0.511496 | − | 0.859286i | \(-0.670908\pi\) | ||||
−0.511496 | + | 0.859286i | \(0.670908\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.61803 | 0.238566 | ||||||||
\(47\) | −1.09017 | −0.159018 | −0.0795088 | − | 0.996834i | \(-0.525335\pi\) | ||||
−0.0795088 | + | 0.996834i | \(0.525335\pi\) | |||||||
\(48\) | 3.14590 | 0.454071 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.85410 | 1.09979 | ||||||||
\(52\) | −7.85410 | −1.08917 | ||||||||
\(53\) | 2.61803 | 0.359615 | 0.179807 | − | 0.983702i | \(-0.442453\pi\) | ||||
0.179807 | + | 0.983702i | \(0.442453\pi\) | |||||||
\(54\) | 0.381966 | 0.0519790 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.47214 | −0.196722 | ||||||||
\(57\) | −0.854102 | −0.113129 | ||||||||
\(58\) | −2.29180 | −0.300928 | ||||||||
\(59\) | 9.61803 | 1.25216 | 0.626081 | − | 0.779758i | \(-0.284658\pi\) | ||||
0.626081 | + | 0.779758i | \(0.284658\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.56231 | 1.09629 | 0.548145 | − | 0.836383i | \(-0.315334\pi\) | ||||
0.548145 | + | 0.836383i | \(0.315334\pi\) | |||||||
\(62\) | 1.94427 | 0.246923 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −4.70820 | −0.588525 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.85410 | 0.593023 | 0.296511 | − | 0.955029i | \(-0.404177\pi\) | ||||
0.296511 | + | 0.955029i | \(0.404177\pi\) | |||||||
\(68\) | −14.5623 | −1.76594 | ||||||||
\(69\) | 4.23607 | 0.509963 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.32624 | −0.632108 | −0.316054 | − | 0.948741i | \(-0.602358\pi\) | ||||
−0.316054 | + | 0.948741i | \(0.602358\pi\) | |||||||
\(72\) | −1.47214 | −0.173493 | ||||||||
\(73\) | −7.70820 | −0.902177 | −0.451089 | − | 0.892479i | \(-0.648964\pi\) | ||||
−0.451089 | + | 0.892479i | \(0.648964\pi\) | |||||||
\(74\) | 0.673762 | 0.0783233 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.58359 | 0.181650 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.61803 | 0.183206 | ||||||||
\(79\) | 11.0000 | 1.23760 | 0.618798 | − | 0.785550i | \(-0.287620\pi\) | ||||
0.618798 | + | 0.785550i | \(0.287620\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.61803 | −0.178682 | ||||||||
\(83\) | 7.47214 | 0.820173 | 0.410087 | − | 0.912047i | \(-0.365498\pi\) | ||||
0.410087 | + | 0.912047i | \(0.365498\pi\) | |||||||
\(84\) | −1.85410 | −0.202299 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.56231 | −0.276301 | ||||||||
\(87\) | −6.00000 | −0.643268 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.76393 | −0.398976 | −0.199488 | − | 0.979900i | \(-0.563928\pi\) | ||||
−0.199488 | + | 0.979900i | \(0.563928\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.23607 | 0.444061 | ||||||||
\(92\) | −7.85410 | −0.818847 | ||||||||
\(93\) | 5.09017 | 0.527826 | ||||||||
\(94\) | −0.416408 | −0.0429492 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 4.14590 | 0.423139 | ||||||||
\(97\) | −1.14590 | −0.116348 | −0.0581742 | − | 0.998306i | \(-0.518528\pi\) | ||||
−0.0581742 | + | 0.998306i | \(0.518528\pi\) | |||||||
\(98\) | −2.29180 | −0.231506 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.76393 | −0.573533 | −0.286766 | − | 0.958001i | \(-0.592580\pi\) | ||||
−0.286766 | + | 0.958001i | \(0.592580\pi\) | |||||||
\(102\) | 3.00000 | 0.297044 | ||||||||
\(103\) | −6.94427 | −0.684239 | −0.342120 | − | 0.939656i | \(-0.611145\pi\) | ||||
−0.342120 | + | 0.939656i | \(0.611145\pi\) | |||||||
\(104\) | −6.23607 | −0.611497 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.00000 | 0.0971286 | ||||||||
\(107\) | 2.52786 | 0.244378 | 0.122189 | − | 0.992507i | \(-0.461009\pi\) | ||||
0.122189 | + | 0.992507i | \(0.461009\pi\) | |||||||
\(108\) | −1.85410 | −0.178411 | ||||||||
\(109\) | −12.0000 | −1.14939 | −0.574696 | − | 0.818367i | \(-0.694880\pi\) | ||||
−0.574696 | + | 0.818367i | \(0.694880\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.76393 | 0.167425 | ||||||||
\(112\) | 3.14590 | 0.297259 | ||||||||
\(113\) | −4.52786 | −0.425946 | −0.212973 | − | 0.977058i | \(-0.568315\pi\) | ||||
−0.212973 | + | 0.977058i | \(0.568315\pi\) | |||||||
\(114\) | −0.326238 | −0.0305550 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 11.1246 | 1.03289 | ||||||||
\(117\) | 4.23607 | 0.391625 | ||||||||
\(118\) | 3.67376 | 0.338197 | ||||||||
\(119\) | 7.85410 | 0.719984 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 3.27051 | 0.296098 | ||||||||
\(123\) | −4.23607 | −0.381953 | ||||||||
\(124\) | −9.43769 | −0.847530 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.381966 | 0.0340282 | ||||||||
\(127\) | 5.70820 | 0.506521 | 0.253261 | − | 0.967398i | \(-0.418497\pi\) | ||||
0.253261 | + | 0.967398i | \(0.418497\pi\) | |||||||
\(128\) | −10.0902 | −0.891853 | ||||||||
\(129\) | −6.70820 | −0.590624 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.7984 | 1.11820 | 0.559100 | − | 0.829101i | \(-0.311147\pi\) | ||||
0.559100 | + | 0.829101i | \(0.311147\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.854102 | −0.0740600 | ||||||||
\(134\) | 1.85410 | 0.160170 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −11.5623 | −0.991460 | ||||||||
\(137\) | −14.2361 | −1.21627 | −0.608135 | − | 0.793834i | \(-0.708082\pi\) | ||||
−0.608135 | + | 0.793834i | \(0.708082\pi\) | |||||||
\(138\) | 1.61803 | 0.137736 | ||||||||
\(139\) | −5.56231 | −0.471789 | −0.235894 | − | 0.971779i | \(-0.575802\pi\) | ||||
−0.235894 | + | 0.971779i | \(0.575802\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.09017 | −0.0918089 | ||||||||
\(142\) | −2.03444 | −0.170727 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.14590 | 0.262158 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.94427 | −0.243670 | ||||||||
\(147\) | −6.00000 | −0.494872 | ||||||||
\(148\) | −3.27051 | −0.268834 | ||||||||
\(149\) | 0.236068 | 0.0193394 | 0.00966972 | − | 0.999953i | \(-0.496922\pi\) | ||||
0.00966972 | + | 0.999953i | \(0.496922\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.9443 | 1.54166 | 0.770831 | − | 0.637039i | \(-0.219841\pi\) | ||||
0.770831 | + | 0.637039i | \(0.219841\pi\) | |||||||
\(152\) | 1.25735 | 0.101985 | ||||||||
\(153\) | 7.85410 | 0.634967 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.85410 | −0.628831 | ||||||||
\(157\) | −2.29180 | −0.182905 | −0.0914526 | − | 0.995809i | \(-0.529151\pi\) | ||||
−0.0914526 | + | 0.995809i | \(0.529151\pi\) | |||||||
\(158\) | 4.20163 | 0.334263 | ||||||||
\(159\) | 2.61803 | 0.207624 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.23607 | 0.333849 | ||||||||
\(162\) | 0.381966 | 0.0300101 | ||||||||
\(163\) | 11.8541 | 0.928485 | 0.464242 | − | 0.885708i | \(-0.346327\pi\) | ||||
0.464242 | + | 0.885708i | \(0.346327\pi\) | |||||||
\(164\) | 7.85410 | 0.613302 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.85410 | 0.221521 | ||||||||
\(167\) | 17.0344 | 1.31816 | 0.659082 | − | 0.752071i | \(-0.270945\pi\) | ||||
0.659082 | + | 0.752071i | \(0.270945\pi\) | |||||||
\(168\) | −1.47214 | −0.113578 | ||||||||
\(169\) | 4.94427 | 0.380329 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.854102 | −0.0653148 | ||||||||
\(172\) | 12.4377 | 0.948365 | ||||||||
\(173\) | −11.0344 | −0.838933 | −0.419467 | − | 0.907771i | \(-0.637783\pi\) | ||||
−0.419467 | + | 0.907771i | \(0.637783\pi\) | |||||||
\(174\) | −2.29180 | −0.173741 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.61803 | 0.722936 | ||||||||
\(178\) | −1.43769 | −0.107760 | ||||||||
\(179\) | −17.4721 | −1.30593 | −0.652964 | − | 0.757389i | \(-0.726475\pi\) | ||||
−0.652964 | + | 0.757389i | \(0.726475\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.4721 | 0.852717 | 0.426359 | − | 0.904554i | \(-0.359796\pi\) | ||||
0.426359 | + | 0.904554i | \(0.359796\pi\) | |||||||
\(182\) | 1.61803 | 0.119937 | ||||||||
\(183\) | 8.56231 | 0.632944 | ||||||||
\(184\) | −6.23607 | −0.459729 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.94427 | 0.142561 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.02129 | 0.147417 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.1803 | −1.67727 | −0.838635 | − | 0.544693i | \(-0.816646\pi\) | ||||
−0.838635 | + | 0.544693i | \(0.816646\pi\) | |||||||
\(192\) | −4.70820 | −0.339785 | ||||||||
\(193\) | 9.85410 | 0.709314 | 0.354657 | − | 0.934997i | \(-0.384598\pi\) | ||||
0.354657 | + | 0.934997i | \(0.384598\pi\) | |||||||
\(194\) | −0.437694 | −0.0314246 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.1246 | 0.794615 | ||||||||
\(197\) | 16.0344 | 1.14241 | 0.571203 | − | 0.820809i | \(-0.306477\pi\) | ||||
0.571203 | + | 0.820809i | \(0.306477\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.70820 | −0.475532 | −0.237766 | − | 0.971322i | \(-0.576415\pi\) | ||||
−0.237766 | + | 0.971322i | \(0.576415\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.85410 | 0.342382 | ||||||||
\(202\) | −2.20163 | −0.154906 | ||||||||
\(203\) | −6.00000 | −0.421117 | ||||||||
\(204\) | −14.5623 | −1.01957 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.65248 | −0.184807 | ||||||||
\(207\) | 4.23607 | 0.294427 | ||||||||
\(208\) | 13.3262 | 0.924008 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.38197 | 0.0951385 | 0.0475692 | − | 0.998868i | \(-0.484853\pi\) | ||||
0.0475692 | + | 0.998868i | \(0.484853\pi\) | |||||||
\(212\) | −4.85410 | −0.333381 | ||||||||
\(213\) | −5.32624 | −0.364948 | ||||||||
\(214\) | 0.965558 | 0.0660042 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.47214 | −0.100166 | ||||||||
\(217\) | 5.09017 | 0.345543 | ||||||||
\(218\) | −4.58359 | −0.310440 | ||||||||
\(219\) | −7.70820 | −0.520872 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 33.2705 | 2.23802 | ||||||||
\(222\) | 0.673762 | 0.0452199 | ||||||||
\(223\) | 15.1803 | 1.01655 | 0.508275 | − | 0.861195i | \(-0.330283\pi\) | ||||
0.508275 | + | 0.861195i | \(0.330283\pi\) | |||||||
\(224\) | 4.14590 | 0.277009 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.72949 | −0.115044 | ||||||||
\(227\) | 9.18034 | 0.609321 | 0.304660 | − | 0.952461i | \(-0.401457\pi\) | ||||
0.304660 | + | 0.952461i | \(0.401457\pi\) | |||||||
\(228\) | 1.58359 | 0.104876 | ||||||||
\(229\) | −8.47214 | −0.559855 | −0.279927 | − | 0.960021i | \(-0.590310\pi\) | ||||
−0.279927 | + | 0.960021i | \(0.590310\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.83282 | 0.579903 | ||||||||
\(233\) | 10.8541 | 0.711076 | 0.355538 | − | 0.934662i | \(-0.384298\pi\) | ||||
0.355538 | + | 0.934662i | \(0.384298\pi\) | |||||||
\(234\) | 1.61803 | 0.105774 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −17.8328 | −1.16082 | ||||||||
\(237\) | 11.0000 | 0.714527 | ||||||||
\(238\) | 3.00000 | 0.194461 | ||||||||
\(239\) | 2.61803 | 0.169347 | 0.0846733 | − | 0.996409i | \(-0.473015\pi\) | ||||
0.0846733 | + | 0.996409i | \(0.473015\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.7082 | 1.39835 | 0.699174 | − | 0.714951i | \(-0.253551\pi\) | ||||
0.699174 | + | 0.714951i | \(0.253551\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −15.8754 | −1.01632 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.61803 | −0.103162 | ||||||||
\(247\) | −3.61803 | −0.230210 | ||||||||
\(248\) | −7.49342 | −0.475833 | ||||||||
\(249\) | 7.47214 | 0.473527 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.9787 | 1.57664 | 0.788321 | − | 0.615264i | \(-0.210951\pi\) | ||||
0.788321 | + | 0.615264i | \(0.210951\pi\) | |||||||
\(252\) | −1.85410 | −0.116797 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 2.18034 | 0.136807 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.56231 | 0.347644 | ||||||||
\(257\) | 12.7426 | 0.794864 | 0.397432 | − | 0.917632i | \(-0.369901\pi\) | ||||
0.397432 | + | 0.917632i | \(0.369901\pi\) | |||||||
\(258\) | −2.56231 | −0.159522 | ||||||||
\(259\) | 1.76393 | 0.109605 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | −0.371391 | ||||||||
\(262\) | 4.88854 | 0.302015 | ||||||||
\(263\) | −18.2705 | −1.12661 | −0.563304 | − | 0.826250i | \(-0.690470\pi\) | ||||
−0.563304 | + | 0.826250i | \(0.690470\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.326238 | −0.0200029 | ||||||||
\(267\) | −3.76393 | −0.230349 | ||||||||
\(268\) | −9.00000 | −0.549762 | ||||||||
\(269\) | 1.41641 | 0.0863599 | 0.0431800 | − | 0.999067i | \(-0.486251\pi\) | ||||
0.0431800 | + | 0.999067i | \(0.486251\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.3820 | 0.995134 | 0.497567 | − | 0.867426i | \(-0.334227\pi\) | ||||
0.497567 | + | 0.867426i | \(0.334227\pi\) | |||||||
\(272\) | 24.7082 | 1.49815 | ||||||||
\(273\) | 4.23607 | 0.256378 | ||||||||
\(274\) | −5.43769 | −0.328503 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.85410 | −0.472761 | ||||||||
\(277\) | −22.2148 | −1.33476 | −0.667378 | − | 0.744719i | \(-0.732584\pi\) | ||||
−0.667378 | + | 0.744719i | \(0.732584\pi\) | |||||||
\(278\) | −2.12461 | −0.127426 | ||||||||
\(279\) | 5.09017 | 0.304741 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.2361 | 1.74408 | 0.872039 | − | 0.489437i | \(-0.162798\pi\) | ||||
0.872039 | + | 0.489437i | \(0.162798\pi\) | |||||||
\(282\) | −0.416408 | −0.0247967 | ||||||||
\(283\) | −7.70820 | −0.458205 | −0.229103 | − | 0.973402i | \(-0.573579\pi\) | ||||
−0.229103 | + | 0.973402i | \(0.573579\pi\) | |||||||
\(284\) | 9.87539 | 0.585996 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.23607 | −0.250047 | ||||||||
\(288\) | 4.14590 | 0.244299 | ||||||||
\(289\) | 44.6869 | 2.62864 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.14590 | −0.0671737 | ||||||||
\(292\) | 14.2918 | 0.836364 | ||||||||
\(293\) | −9.65248 | −0.563904 | −0.281952 | − | 0.959429i | \(-0.590982\pi\) | ||||
−0.281952 | + | 0.959429i | \(0.590982\pi\) | |||||||
\(294\) | −2.29180 | −0.133660 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.59675 | −0.150933 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.0901699 | 0.00522340 | ||||||||
\(299\) | 17.9443 | 1.03774 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.70820 | −0.386654 | ||||||||
\(302\) | 7.23607 | 0.416389 | ||||||||
\(303\) | −5.76393 | −0.331129 | ||||||||
\(304\) | −2.68692 | −0.154105 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.00000 | 0.171499 | ||||||||
\(307\) | 18.9787 | 1.08317 | 0.541586 | − | 0.840645i | \(-0.317824\pi\) | ||||
0.541586 | + | 0.840645i | \(0.317824\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.94427 | −0.395046 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.6525 | −1.11439 | −0.557195 | − | 0.830382i | \(-0.688122\pi\) | ||||
−0.557195 | + | 0.830382i | \(0.688122\pi\) | |||||||
\(312\) | −6.23607 | −0.353048 | ||||||||
\(313\) | 11.4721 | 0.648443 | 0.324222 | − | 0.945981i | \(-0.394898\pi\) | ||||
0.324222 | + | 0.945981i | \(0.394898\pi\) | |||||||
\(314\) | −0.875388 | −0.0494010 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.3951 | −1.14732 | ||||||||
\(317\) | 29.1803 | 1.63893 | 0.819466 | − | 0.573128i | \(-0.194270\pi\) | ||||
0.819466 | + | 0.573128i | \(0.194270\pi\) | |||||||
\(318\) | 1.00000 | 0.0560772 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.52786 | 0.141092 | ||||||||
\(322\) | 1.61803 | 0.0901695 | ||||||||
\(323\) | −6.70820 | −0.373254 | ||||||||
\(324\) | −1.85410 | −0.103006 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.52786 | 0.250775 | ||||||||
\(327\) | −12.0000 | −0.663602 | ||||||||
\(328\) | 6.23607 | 0.344329 | ||||||||
\(329\) | −1.09017 | −0.0601030 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.29180 | 0.180933 | 0.0904667 | − | 0.995899i | \(-0.471164\pi\) | ||||
0.0904667 | + | 0.995899i | \(0.471164\pi\) | |||||||
\(332\) | −13.8541 | −0.760343 | ||||||||
\(333\) | 1.76393 | 0.0966629 | ||||||||
\(334\) | 6.50658 | 0.356024 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.14590 | 0.171623 | ||||||||
\(337\) | −4.18034 | −0.227718 | −0.113859 | − | 0.993497i | \(-0.536321\pi\) | ||||
−0.113859 | + | 0.993497i | \(0.536321\pi\) | |||||||
\(338\) | 1.88854 | 0.102723 | ||||||||
\(339\) | −4.52786 | −0.245920 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.326238 | −0.0176409 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | 9.87539 | 0.532445 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.21478 | −0.226588 | ||||||||
\(347\) | 10.4721 | 0.562174 | 0.281087 | − | 0.959682i | \(-0.409305\pi\) | ||||
0.281087 | + | 0.959682i | \(0.409305\pi\) | |||||||
\(348\) | 11.1246 | 0.596342 | ||||||||
\(349\) | −0.708204 | −0.0379093 | −0.0189546 | − | 0.999820i | \(-0.506034\pi\) | ||||
−0.0189546 | + | 0.999820i | \(0.506034\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.23607 | 0.226105 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0000 | 0.638696 | 0.319348 | − | 0.947638i | \(-0.396536\pi\) | ||||
0.319348 | + | 0.947638i | \(0.396536\pi\) | |||||||
\(354\) | 3.67376 | 0.195258 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.97871 | 0.369871 | ||||||||
\(357\) | 7.85410 | 0.415683 | ||||||||
\(358\) | −6.67376 | −0.352719 | ||||||||
\(359\) | 3.70820 | 0.195712 | 0.0978558 | − | 0.995201i | \(-0.468802\pi\) | ||||
0.0978558 | + | 0.995201i | \(0.468802\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.2705 | −0.961606 | ||||||||
\(362\) | 4.38197 | 0.230311 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.85410 | −0.411667 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.27051 | 0.170952 | ||||||||
\(367\) | −28.8541 | −1.50617 | −0.753086 | − | 0.657922i | \(-0.771436\pi\) | ||||
−0.753086 | + | 0.657922i | \(0.771436\pi\) | |||||||
\(368\) | 13.3262 | 0.694678 | ||||||||
\(369\) | −4.23607 | −0.220521 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.61803 | 0.135922 | ||||||||
\(372\) | −9.43769 | −0.489322 | ||||||||
\(373\) | 34.8885 | 1.80646 | 0.903230 | − | 0.429156i | \(-0.141189\pi\) | ||||
0.903230 | + | 0.429156i | \(0.141189\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.60488 | 0.0827653 | ||||||||
\(377\) | −25.4164 | −1.30901 | ||||||||
\(378\) | 0.381966 | 0.0196462 | ||||||||
\(379\) | 10.8885 | 0.559307 | 0.279653 | − | 0.960101i | \(-0.409780\pi\) | ||||
0.279653 | + | 0.960101i | \(0.409780\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.70820 | 0.292440 | ||||||||
\(382\) | −8.85410 | −0.453015 | ||||||||
\(383\) | −0.708204 | −0.0361875 | −0.0180938 | − | 0.999836i | \(-0.505760\pi\) | ||||
−0.0180938 | + | 0.999836i | \(0.505760\pi\) | |||||||
\(384\) | −10.0902 | −0.514912 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.76393 | 0.191579 | ||||||||
\(387\) | −6.70820 | −0.340997 | ||||||||
\(388\) | 2.12461 | 0.107861 | ||||||||
\(389\) | 5.74265 | 0.291164 | 0.145582 | − | 0.989346i | \(-0.453495\pi\) | ||||
0.145582 | + | 0.989346i | \(0.453495\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.2705 | 1.68256 | ||||||||
\(392\) | 8.83282 | 0.446125 | ||||||||
\(393\) | 12.7984 | 0.645593 | ||||||||
\(394\) | 6.12461 | 0.308553 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.29180 | 0.265588 | 0.132794 | − | 0.991144i | \(-0.457605\pi\) | ||||
0.132794 | + | 0.991144i | \(0.457605\pi\) | |||||||
\(398\) | −2.56231 | −0.128437 | ||||||||
\(399\) | −0.854102 | −0.0427586 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.6869 | 1.43256 | 0.716278 | − | 0.697815i | \(-0.245844\pi\) | ||||
0.716278 | + | 0.697815i | \(0.245844\pi\) | |||||||
\(402\) | 1.85410 | 0.0924742 | ||||||||
\(403\) | 21.5623 | 1.07409 | ||||||||
\(404\) | 10.6869 | 0.531694 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.29180 | −0.113740 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −11.5623 | −0.572419 | ||||||||
\(409\) | 2.47214 | 0.122239 | 0.0611196 | − | 0.998130i | \(-0.480533\pi\) | ||||
0.0611196 | + | 0.998130i | \(0.480533\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.2361 | −0.702213 | ||||||||
\(412\) | 12.8754 | 0.634325 | ||||||||
\(413\) | 9.61803 | 0.473273 | ||||||||
\(414\) | 1.61803 | 0.0795220 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 17.5623 | 0.861063 | ||||||||
\(417\) | −5.56231 | −0.272387 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.4508 | −1.19450 | −0.597251 | − | 0.802054i | \(-0.703740\pi\) | ||||
−0.597251 | + | 0.802054i | \(0.703740\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.5066 | −1.34059 | −0.670294 | − | 0.742095i | \(-0.733832\pi\) | ||||
−0.670294 | + | 0.742095i | \(0.733832\pi\) | |||||||
\(422\) | 0.527864 | 0.0256960 | ||||||||
\(423\) | −1.09017 | −0.0530059 | ||||||||
\(424\) | −3.85410 | −0.187172 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.03444 | −0.0985690 | ||||||||
\(427\) | 8.56231 | 0.414359 | ||||||||
\(428\) | −4.68692 | −0.226551 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.0902 | −0.823205 | −0.411602 | − | 0.911364i | \(-0.635031\pi\) | ||||
−0.411602 | + | 0.911364i | \(0.635031\pi\) | |||||||
\(432\) | 3.14590 | 0.151357 | ||||||||
\(433\) | 27.3050 | 1.31219 | 0.656096 | − | 0.754677i | \(-0.272207\pi\) | ||||
0.656096 | + | 0.754677i | \(0.272207\pi\) | |||||||
\(434\) | 1.94427 | 0.0933280 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 22.2492 | 1.06554 | ||||||||
\(437\) | −3.61803 | −0.173074 | ||||||||
\(438\) | −2.94427 | −0.140683 | ||||||||
\(439\) | 36.7082 | 1.75199 | 0.875993 | − | 0.482323i | \(-0.160207\pi\) | ||||
0.875993 | + | 0.482323i | \(0.160207\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.00000 | −0.285714 | ||||||||
\(442\) | 12.7082 | 0.604468 | ||||||||
\(443\) | −17.5967 | −0.836047 | −0.418023 | − | 0.908436i | \(-0.637277\pi\) | ||||
−0.418023 | + | 0.908436i | \(0.637277\pi\) | |||||||
\(444\) | −3.27051 | −0.155212 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.79837 | 0.274561 | ||||||||
\(447\) | 0.236068 | 0.0111656 | ||||||||
\(448\) | −4.70820 | −0.222442 | ||||||||
\(449\) | −26.9443 | −1.27158 | −0.635789 | − | 0.771863i | \(-0.719325\pi\) | ||||
−0.635789 | + | 0.771863i | \(0.719325\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 8.39512 | 0.394873 | ||||||||
\(453\) | 18.9443 | 0.890080 | ||||||||
\(454\) | 3.50658 | 0.164572 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.25735 | 0.0588810 | ||||||||
\(457\) | 22.9787 | 1.07490 | 0.537449 | − | 0.843296i | \(-0.319388\pi\) | ||||
0.537449 | + | 0.843296i | \(0.319388\pi\) | |||||||
\(458\) | −3.23607 | −0.151212 | ||||||||
\(459\) | 7.85410 | 0.366598 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.2705 | −1.13039 | −0.565195 | − | 0.824957i | \(-0.691199\pi\) | ||||
−0.565195 | + | 0.824957i | \(0.691199\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.2705 | −1.63916 | −0.819580 | − | 0.572965i | \(-0.805793\pi\) | ||||
−0.819580 | + | 0.572965i | \(0.805793\pi\) | |||||||
\(464\) | −18.8754 | −0.876268 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.14590 | 0.192055 | ||||||||
\(467\) | 14.8885 | 0.688960 | 0.344480 | − | 0.938794i | \(-0.388055\pi\) | ||||
0.344480 | + | 0.938794i | \(0.388055\pi\) | |||||||
\(468\) | −7.85410 | −0.363056 | ||||||||
\(469\) | 4.85410 | 0.224142 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.29180 | −0.105600 | ||||||||
\(472\) | −14.1591 | −0.651723 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 4.20163 | 0.192987 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −14.5623 | −0.667462 | ||||||||
\(477\) | 2.61803 | 0.119872 | ||||||||
\(478\) | 1.00000 | 0.0457389 | ||||||||
\(479\) | −30.6180 | −1.39897 | −0.699487 | − | 0.714645i | \(-0.746588\pi\) | ||||
−0.699487 | + | 0.714645i | \(0.746588\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.47214 | 0.340700 | ||||||||
\(482\) | 8.29180 | 0.377681 | ||||||||
\(483\) | 4.23607 | 0.192748 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.381966 | 0.0173263 | ||||||||
\(487\) | −0.708204 | −0.0320918 | −0.0160459 | − | 0.999871i | \(-0.505108\pi\) | ||||
−0.0160459 | + | 0.999871i | \(0.505108\pi\) | |||||||
\(488\) | −12.6049 | −0.570596 | ||||||||
\(489\) | 11.8541 | 0.536061 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.0902 | −1.31282 | −0.656410 | − | 0.754404i | \(-0.727926\pi\) | ||||
−0.656410 | + | 0.754404i | \(0.727926\pi\) | |||||||
\(492\) | 7.85410 | 0.354090 | ||||||||
\(493\) | −47.1246 | −2.12239 | ||||||||
\(494\) | −1.38197 | −0.0621776 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.0132 | 0.719012 | ||||||||
\(497\) | −5.32624 | −0.238914 | ||||||||
\(498\) | 2.85410 | 0.127895 | ||||||||
\(499\) | −24.8541 | −1.11262 | −0.556311 | − | 0.830974i | \(-0.687784\pi\) | ||||
−0.556311 | + | 0.830974i | \(0.687784\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.0344 | 0.761043 | ||||||||
\(502\) | 9.54102 | 0.425837 | ||||||||
\(503\) | 22.6525 | 1.01002 | 0.505012 | − | 0.863112i | \(-0.331488\pi\) | ||||
0.505012 | + | 0.863112i | \(0.331488\pi\) | |||||||
\(504\) | −1.47214 | −0.0655741 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.94427 | 0.219583 | ||||||||
\(508\) | −10.5836 | −0.469571 | ||||||||
\(509\) | −3.74265 | −0.165890 | −0.0829449 | − | 0.996554i | \(-0.526433\pi\) | ||||
−0.0829449 | + | 0.996554i | \(0.526433\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.70820 | −0.340991 | ||||||||
\(512\) | 22.3050 | 0.985749 | ||||||||
\(513\) | −0.854102 | −0.0377095 | ||||||||
\(514\) | 4.86726 | 0.214686 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 12.4377 | 0.547539 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.673762 | 0.0296034 | ||||||||
\(519\) | −11.0344 | −0.484358 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.94427 | −0.391856 | −0.195928 | − | 0.980618i | \(-0.562772\pi\) | ||||
−0.195928 | + | 0.980618i | \(0.562772\pi\) | |||||||
\(522\) | −2.29180 | −0.100309 | ||||||||
\(523\) | 15.2705 | 0.667733 | 0.333866 | − | 0.942620i | \(-0.391647\pi\) | ||||
0.333866 | + | 0.942620i | \(0.391647\pi\) | |||||||
\(524\) | −23.7295 | −1.03663 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.97871 | −0.304286 | ||||||||
\(527\) | 39.9787 | 1.74150 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.05573 | −0.219814 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.61803 | 0.417387 | ||||||||
\(532\) | 1.58359 | 0.0686574 | ||||||||
\(533\) | −17.9443 | −0.777253 | ||||||||
\(534\) | −1.43769 | −0.0622151 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.14590 | −0.308656 | ||||||||
\(537\) | −17.4721 | −0.753978 | ||||||||
\(538\) | 0.541020 | 0.0233250 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −45.5066 | −1.95648 | −0.978240 | − | 0.207475i | \(-0.933475\pi\) | ||||
−0.978240 | + | 0.207475i | \(0.933475\pi\) | |||||||
\(542\) | 6.25735 | 0.268776 | ||||||||
\(543\) | 11.4721 | 0.492316 | ||||||||
\(544\) | 32.5623 | 1.39610 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.61803 | 0.0692455 | ||||||||
\(547\) | −11.7426 | −0.502079 | −0.251040 | − | 0.967977i | \(-0.580772\pi\) | ||||
−0.251040 | + | 0.967977i | \(0.580772\pi\) | |||||||
\(548\) | 26.3951 | 1.12754 | ||||||||
\(549\) | 8.56231 | 0.365430 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.12461 | 0.218316 | ||||||||
\(552\) | −6.23607 | −0.265425 | ||||||||
\(553\) | 11.0000 | 0.467768 | ||||||||
\(554\) | −8.48529 | −0.360505 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.3131 | 0.437372 | ||||||||
\(557\) | 40.6312 | 1.72160 | 0.860799 | − | 0.508944i | \(-0.169964\pi\) | ||||
0.860799 | + | 0.508944i | \(0.169964\pi\) | |||||||
\(558\) | 1.94427 | 0.0823076 | ||||||||
\(559\) | −28.4164 | −1.20189 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.1672 | 0.471059 | ||||||||
\(563\) | 8.59675 | 0.362310 | 0.181155 | − | 0.983455i | \(-0.442016\pi\) | ||||
0.181155 | + | 0.983455i | \(0.442016\pi\) | |||||||
\(564\) | 2.02129 | 0.0851115 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.94427 | −0.123757 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 7.84095 | 0.328999 | ||||||||
\(569\) | 11.8197 | 0.495506 | 0.247753 | − | 0.968823i | \(-0.420308\pi\) | ||||
0.247753 | + | 0.968823i | \(0.420308\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.09017 | 0.0874709 | 0.0437354 | − | 0.999043i | \(-0.486074\pi\) | ||||
0.0437354 | + | 0.999043i | \(0.486074\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23.1803 | −0.968373 | ||||||||
\(574\) | −1.61803 | −0.0675354 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.70820 | −0.196175 | ||||||||
\(577\) | −18.2918 | −0.761497 | −0.380749 | − | 0.924679i | \(-0.624334\pi\) | ||||
−0.380749 | + | 0.924679i | \(0.624334\pi\) | |||||||
\(578\) | 17.0689 | 0.709972 | ||||||||
\(579\) | 9.85410 | 0.409523 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.47214 | 0.309996 | ||||||||
\(582\) | −0.437694 | −0.0181430 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 11.3475 | 0.469564 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.68692 | −0.152305 | ||||||||
\(587\) | −38.1246 | −1.57357 | −0.786786 | − | 0.617226i | \(-0.788256\pi\) | ||||
−0.786786 | + | 0.617226i | \(0.788256\pi\) | |||||||
\(588\) | 11.1246 | 0.458771 | ||||||||
\(589\) | −4.34752 | −0.179137 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.0344 | 0.659569 | ||||||||
\(592\) | 5.54915 | 0.228069 | ||||||||
\(593\) | −15.0344 | −0.617391 | −0.308695 | − | 0.951161i | \(-0.599892\pi\) | ||||
−0.308695 | + | 0.951161i | \(0.599892\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.437694 | −0.0179286 | ||||||||
\(597\) | −6.70820 | −0.274549 | ||||||||
\(598\) | 6.85410 | 0.280285 | ||||||||
\(599\) | −18.6525 | −0.762120 | −0.381060 | − | 0.924550i | \(-0.624441\pi\) | ||||
−0.381060 | + | 0.924550i | \(0.624441\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.8885 | 1.17839 | 0.589194 | − | 0.807992i | \(-0.299445\pi\) | ||||
0.589194 | + | 0.807992i | \(0.299445\pi\) | |||||||
\(602\) | −2.56231 | −0.104432 | ||||||||
\(603\) | 4.85410 | 0.197674 | ||||||||
\(604\) | −35.1246 | −1.42920 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.20163 | −0.0894349 | ||||||||
\(607\) | −3.56231 | −0.144590 | −0.0722948 | − | 0.997383i | \(-0.523032\pi\) | ||||
−0.0722948 | + | 0.997383i | \(0.523032\pi\) | |||||||
\(608\) | −3.54102 | −0.143607 | ||||||||
\(609\) | −6.00000 | −0.243132 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.61803 | −0.186826 | ||||||||
\(612\) | −14.5623 | −0.588646 | ||||||||
\(613\) | 27.7082 | 1.11912 | 0.559562 | − | 0.828789i | \(-0.310969\pi\) | ||||
0.559562 | + | 0.828789i | \(0.310969\pi\) | |||||||
\(614\) | 7.24922 | 0.292555 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.1803 | 0.450104 | 0.225052 | − | 0.974347i | \(-0.427745\pi\) | ||||
0.225052 | + | 0.974347i | \(0.427745\pi\) | |||||||
\(618\) | −2.65248 | −0.106698 | ||||||||
\(619\) | −16.1246 | −0.648103 | −0.324051 | − | 0.946039i | \(-0.605045\pi\) | ||||
−0.324051 | + | 0.946039i | \(0.605045\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.23607 | 0.169988 | ||||||||
\(622\) | −7.50658 | −0.300986 | ||||||||
\(623\) | −3.76393 | −0.150799 | ||||||||
\(624\) | 13.3262 | 0.533476 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.38197 | 0.175139 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.24922 | 0.169562 | ||||||||
\(629\) | 13.8541 | 0.552399 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.2148 | −1.28245 | −0.641225 | − | 0.767353i | \(-0.721574\pi\) | ||||
−0.641225 | + | 0.767353i | \(0.721574\pi\) | |||||||
\(632\) | −16.1935 | −0.644143 | ||||||||
\(633\) | 1.38197 | 0.0549282 | ||||||||
\(634\) | 11.1459 | 0.442660 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.85410 | −0.192478 | ||||||||
\(637\) | −25.4164 | −1.00703 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.32624 | −0.210703 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.9098 | −0.549405 | −0.274703 | − | 0.961529i | \(-0.588579\pi\) | ||||
−0.274703 | + | 0.961529i | \(0.588579\pi\) | |||||||
\(642\) | 0.965558 | 0.0381075 | ||||||||
\(643\) | −14.1459 | −0.557860 | −0.278930 | − | 0.960311i | \(-0.589980\pi\) | ||||
−0.278930 | + | 0.960311i | \(0.589980\pi\) | |||||||
\(644\) | −7.85410 | −0.309495 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.56231 | −0.100813 | ||||||||
\(647\) | −15.9656 | −0.627671 | −0.313835 | − | 0.949477i | \(-0.601614\pi\) | ||||
−0.313835 | + | 0.949477i | \(0.601614\pi\) | |||||||
\(648\) | −1.47214 | −0.0578310 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.09017 | 0.199499 | ||||||||
\(652\) | −21.9787 | −0.860753 | ||||||||
\(653\) | 3.38197 | 0.132347 | 0.0661733 | − | 0.997808i | \(-0.478921\pi\) | ||||
0.0661733 | + | 0.997808i | \(0.478921\pi\) | |||||||
\(654\) | −4.58359 | −0.179233 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −13.3262 | −0.520302 | ||||||||
\(657\) | −7.70820 | −0.300726 | ||||||||
\(658\) | −0.416408 | −0.0162333 | ||||||||
\(659\) | −0.875388 | −0.0341003 | −0.0170501 | − | 0.999855i | \(-0.505427\pi\) | ||||
−0.0170501 | + | 0.999855i | \(0.505427\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.4377 | 0.639352 | 0.319676 | − | 0.947527i | \(-0.396426\pi\) | ||||
0.319676 | + | 0.947527i | \(0.396426\pi\) | |||||||
\(662\) | 1.25735 | 0.0488685 | ||||||||
\(663\) | 33.2705 | 1.29212 | ||||||||
\(664\) | −11.0000 | −0.426883 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.673762 | 0.0261078 | ||||||||
\(667\) | −25.4164 | −0.984127 | ||||||||
\(668\) | −31.5836 | −1.22201 | ||||||||
\(669\) | 15.1803 | 0.586906 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 4.14590 | 0.159931 | ||||||||
\(673\) | 17.8328 | 0.687405 | 0.343702 | − | 0.939079i | \(-0.388319\pi\) | ||||
0.343702 | + | 0.939079i | \(0.388319\pi\) | |||||||
\(674\) | −1.59675 | −0.0615044 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.16718 | −0.352584 | ||||||||
\(677\) | −22.4721 | −0.863674 | −0.431837 | − | 0.901952i | \(-0.642134\pi\) | ||||
−0.431837 | + | 0.901952i | \(0.642134\pi\) | |||||||
\(678\) | −1.72949 | −0.0664207 | ||||||||
\(679\) | −1.14590 | −0.0439755 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.18034 | 0.351791 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 49.0689 | 1.87757 | 0.938784 | − | 0.344505i | \(-0.111953\pi\) | ||||
0.938784 | + | 0.344505i | \(0.111953\pi\) | |||||||
\(684\) | 1.58359 | 0.0605502 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.96556 | −0.189586 | ||||||||
\(687\) | −8.47214 | −0.323232 | ||||||||
\(688\) | −21.1033 | −0.804557 | ||||||||
\(689\) | 11.0902 | 0.422502 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.6525 | 1.24216 | 0.621079 | − | 0.783748i | \(-0.286694\pi\) | ||||
0.621079 | + | 0.783748i | \(0.286694\pi\) | |||||||
\(692\) | 20.4590 | 0.777734 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.00000 | 0.151838 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.83282 | 0.334807 | ||||||||
\(697\) | −33.2705 | −1.26021 | ||||||||
\(698\) | −0.270510 | −0.0102389 | ||||||||
\(699\) | 10.8541 | 0.410540 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.2016 | −0.385310 | −0.192655 | − | 0.981267i | \(-0.561710\pi\) | ||||
−0.192655 | + | 0.981267i | \(0.561710\pi\) | |||||||
\(702\) | 1.61803 | 0.0610688 | ||||||||
\(703\) | −1.50658 | −0.0568217 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.58359 | 0.172506 | ||||||||
\(707\) | −5.76393 | −0.216775 | ||||||||
\(708\) | −17.8328 | −0.670198 | ||||||||
\(709\) | −40.2148 | −1.51030 | −0.755149 | − | 0.655553i | \(-0.772435\pi\) | ||||
−0.755149 | + | 0.655553i | \(0.772435\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.0000 | 0.412532 | ||||||||
\(712\) | 5.54102 | 0.207658 | ||||||||
\(713\) | 21.5623 | 0.807515 | ||||||||
\(714\) | 3.00000 | 0.112272 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 32.3951 | 1.21066 | ||||||||
\(717\) | 2.61803 | 0.0977723 | ||||||||
\(718\) | 1.41641 | 0.0528599 | ||||||||
\(719\) | 46.4853 | 1.73361 | 0.866804 | − | 0.498648i | \(-0.166170\pi\) | ||||
0.866804 | + | 0.498648i | \(0.166170\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.94427 | −0.258618 | ||||||||
\(722\) | −6.97871 | −0.259721 | ||||||||
\(723\) | 21.7082 | 0.807337 | ||||||||
\(724\) | −21.2705 | −0.790512 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.8541 | 0.587996 | 0.293998 | − | 0.955806i | \(-0.405014\pi\) | ||||
0.293998 | + | 0.955806i | \(0.405014\pi\) | |||||||
\(728\) | −6.23607 | −0.231124 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −52.6869 | −1.94870 | ||||||||
\(732\) | −15.8754 | −0.586771 | ||||||||
\(733\) | 49.5967 | 1.83190 | 0.915949 | − | 0.401295i | \(-0.131440\pi\) | ||||
0.915949 | + | 0.401295i | \(0.131440\pi\) | |||||||
\(734\) | −11.0213 | −0.406803 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17.5623 | 0.647355 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −1.61803 | −0.0595607 | ||||||||
\(739\) | 3.00000 | 0.110357 | 0.0551784 | − | 0.998477i | \(-0.482427\pi\) | ||||
0.0551784 | + | 0.998477i | \(0.482427\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.61803 | −0.132912 | ||||||||
\(742\) | 1.00000 | 0.0367112 | ||||||||
\(743\) | 7.11146 | 0.260894 | 0.130447 | − | 0.991455i | \(-0.458359\pi\) | ||||
0.130447 | + | 0.991455i | \(0.458359\pi\) | |||||||
\(744\) | −7.49342 | −0.274722 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 13.3262 | 0.487908 | ||||||||
\(747\) | 7.47214 | 0.273391 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.52786 | 0.0923661 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.8541 | 0.833958 | 0.416979 | − | 0.908916i | \(-0.363089\pi\) | ||||
0.416979 | + | 0.908916i | \(0.363089\pi\) | |||||||
\(752\) | −3.42956 | −0.125063 | ||||||||
\(753\) | 24.9787 | 0.910275 | ||||||||
\(754\) | −9.70820 | −0.353552 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.85410 | −0.0674330 | ||||||||
\(757\) | −5.00000 | −0.181728 | −0.0908640 | − | 0.995863i | \(-0.528963\pi\) | ||||
−0.0908640 | + | 0.995863i | \(0.528963\pi\) | |||||||
\(758\) | 4.15905 | 0.151064 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.7082 | 1.54817 | 0.774086 | − | 0.633081i | \(-0.218210\pi\) | ||||
0.774086 | + | 0.633081i | \(0.218210\pi\) | |||||||
\(762\) | 2.18034 | 0.0789854 | ||||||||
\(763\) | −12.0000 | −0.434429 | ||||||||
\(764\) | 42.9787 | 1.55492 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.270510 | −0.00977392 | ||||||||
\(767\) | 40.7426 | 1.47113 | ||||||||
\(768\) | 5.56231 | 0.200712 | ||||||||
\(769\) | 3.50658 | 0.126450 | 0.0632252 | − | 0.997999i | \(-0.479861\pi\) | ||||
0.0632252 | + | 0.997999i | \(0.479861\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.7426 | 0.458915 | ||||||||
\(772\) | −18.2705 | −0.657570 | ||||||||
\(773\) | −4.81966 | −0.173351 | −0.0866756 | − | 0.996237i | \(-0.527624\pi\) | ||||
−0.0866756 | + | 0.996237i | \(0.527624\pi\) | |||||||
\(774\) | −2.56231 | −0.0921002 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.68692 | 0.0605568 | ||||||||
\(777\) | 1.76393 | 0.0632807 | ||||||||
\(778\) | 2.19350 | 0.0786406 | ||||||||
\(779\) | 3.61803 | 0.129630 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 12.7082 | 0.454444 | ||||||||
\(783\) | −6.00000 | −0.214423 | ||||||||
\(784\) | −18.8754 | −0.674121 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.88854 | 0.174369 | ||||||||
\(787\) | −3.70820 | −0.132183 | −0.0660916 | − | 0.997814i | \(-0.521053\pi\) | ||||
−0.0660916 | + | 0.997814i | \(0.521053\pi\) | |||||||
\(788\) | −29.7295 | −1.05907 | ||||||||
\(789\) | −18.2705 | −0.650447 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.52786 | −0.160992 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.2705 | 1.28800 | ||||||||
\(794\) | 2.02129 | 0.0717328 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.4377 | 0.440842 | ||||||||
\(797\) | 48.5410 | 1.71941 | 0.859706 | − | 0.510790i | \(-0.170647\pi\) | ||||
0.859706 | + | 0.510790i | \(0.170647\pi\) | |||||||
\(798\) | −0.326238 | −0.0115487 | ||||||||
\(799\) | −8.56231 | −0.302913 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.76393 | −0.132992 | ||||||||
\(802\) | 10.9574 | 0.386920 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −9.00000 | −0.317406 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.23607 | 0.290103 | ||||||||
\(807\) | 1.41641 | 0.0498599 | ||||||||
\(808\) | 8.48529 | 0.298512 | ||||||||
\(809\) | 15.9098 | 0.559360 | 0.279680 | − | 0.960093i | \(-0.409772\pi\) | ||||
0.279680 | + | 0.960093i | \(0.409772\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.4377 | 0.577206 | 0.288603 | − | 0.957449i | \(-0.406809\pi\) | ||||
0.288603 | + | 0.957449i | \(0.406809\pi\) | |||||||
\(812\) | 11.1246 | 0.390397 | ||||||||
\(813\) | 16.3820 | 0.574541 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 24.7082 | 0.864960 | ||||||||
\(817\) | 5.72949 | 0.200449 | ||||||||
\(818\) | 0.944272 | 0.0330157 | ||||||||
\(819\) | 4.23607 | 0.148020 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.59675 | −0.300029 | −0.150014 | − | 0.988684i | \(-0.547932\pi\) | ||||
−0.150014 | + | 0.988684i | \(0.547932\pi\) | |||||||
\(822\) | −5.43769 | −0.189661 | ||||||||
\(823\) | −25.8328 | −0.900475 | −0.450238 | − | 0.892909i | \(-0.648661\pi\) | ||||
−0.450238 | + | 0.892909i | \(0.648661\pi\) | |||||||
\(824\) | 10.2229 | 0.356132 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.67376 | 0.127827 | ||||||||
\(827\) | −20.6525 | −0.718157 | −0.359078 | − | 0.933307i | \(-0.616909\pi\) | ||||
−0.359078 | + | 0.933307i | \(0.616909\pi\) | |||||||
\(828\) | −7.85410 | −0.272949 | ||||||||
\(829\) | 42.3951 | 1.47244 | 0.736222 | − | 0.676740i | \(-0.236608\pi\) | ||||
0.736222 | + | 0.676740i | \(0.236608\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.2148 | −0.770622 | ||||||||
\(832\) | −19.9443 | −0.691443 | ||||||||
\(833\) | −47.1246 | −1.63277 | ||||||||
\(834\) | −2.12461 | −0.0735693 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.09017 | 0.175942 | ||||||||
\(838\) | −9.33939 | −0.322624 | ||||||||
\(839\) | 35.8328 | 1.23709 | 0.618543 | − | 0.785751i | \(-0.287723\pi\) | ||||
0.618543 | + | 0.785751i | \(0.287723\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | −10.5066 | −0.362081 | ||||||||
\(843\) | 29.2361 | 1.00694 | ||||||||
\(844\) | −2.56231 | −0.0881982 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.416408 | −0.0143164 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.23607 | 0.282828 | ||||||||
\(849\) | −7.70820 | −0.264545 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.47214 | 0.256142 | ||||||||
\(852\) | 9.87539 | 0.338325 | ||||||||
\(853\) | 2.16718 | 0.0742030 | 0.0371015 | − | 0.999312i | \(-0.488188\pi\) | ||||
0.0371015 | + | 0.999312i | \(0.488188\pi\) | |||||||
\(854\) | 3.27051 | 0.111915 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.72136 | −0.127193 | ||||||||
\(857\) | −32.2361 | −1.10116 | −0.550582 | − | 0.834781i | \(-0.685594\pi\) | ||||
−0.550582 | + | 0.834781i | \(0.685594\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.58359 | −0.258749 | −0.129374 | − | 0.991596i | \(-0.541297\pi\) | ||||
−0.129374 | + | 0.991596i | \(0.541297\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.23607 | −0.144365 | ||||||||
\(862\) | −6.52786 | −0.222340 | ||||||||
\(863\) | −35.8885 | −1.22166 | −0.610830 | − | 0.791762i | \(-0.709164\pi\) | ||||
−0.610830 | + | 0.791762i | \(0.709164\pi\) | |||||||
\(864\) | 4.14590 | 0.141046 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.4296 | 0.354411 | ||||||||
\(867\) | 44.6869 | 1.51765 | ||||||||
\(868\) | −9.43769 | −0.320336 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.5623 | 0.696727 | ||||||||
\(872\) | 17.6656 | 0.598234 | ||||||||
\(873\) | −1.14590 | −0.0387828 | ||||||||
\(874\) | −1.38197 | −0.0467457 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.2918 | 0.482875 | ||||||||
\(877\) | 40.0557 | 1.35259 | 0.676293 | − | 0.736633i | \(-0.263585\pi\) | ||||
0.676293 | + | 0.736633i | \(0.263585\pi\) | |||||||
\(878\) | 14.0213 | 0.473195 | ||||||||
\(879\) | −9.65248 | −0.325570 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.7984 | 1.03762 | 0.518812 | − | 0.854888i | \(-0.326375\pi\) | ||||
0.518812 | + | 0.854888i | \(0.326375\pi\) | |||||||
\(882\) | −2.29180 | −0.0771688 | ||||||||
\(883\) | −18.9443 | −0.637526 | −0.318763 | − | 0.947835i | \(-0.603267\pi\) | ||||
−0.318763 | + | 0.947835i | \(0.603267\pi\) | |||||||
\(884\) | −61.6869 | −2.07476 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.72136 | −0.225808 | ||||||||
\(887\) | −30.4853 | −1.02360 | −0.511798 | − | 0.859106i | \(-0.671020\pi\) | ||||
−0.511798 | + | 0.859106i | \(0.671020\pi\) | |||||||
\(888\) | −2.59675 | −0.0871411 | ||||||||
\(889\) | 5.70820 | 0.191447 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −28.1459 | −0.942394 | ||||||||
\(893\) | 0.931116 | 0.0311586 | ||||||||
\(894\) | 0.0901699 | 0.00301573 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −10.0902 | −0.337089 | ||||||||
\(897\) | 17.9443 | 0.599142 | ||||||||
\(898\) | −10.2918 | −0.343442 | ||||||||
\(899\) | −30.5410 | −1.01860 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.5623 | 0.685030 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.70820 | −0.223235 | ||||||||
\(904\) | 6.66563 | 0.221696 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.23607 | 0.240402 | ||||||||
\(907\) | −31.3951 | −1.04246 | −0.521229 | − | 0.853417i | \(-0.674526\pi\) | ||||
−0.521229 | + | 0.853417i | \(0.674526\pi\) | |||||||
\(908\) | −17.0213 | −0.564871 | ||||||||
\(909\) | −5.76393 | −0.191178 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.5967 | −0.351086 | −0.175543 | − | 0.984472i | \(-0.556168\pi\) | ||||
−0.175543 | + | 0.984472i | \(0.556168\pi\) | |||||||
\(912\) | −2.68692 | −0.0889727 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 8.77709 | 0.290320 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.7082 | 0.519014 | ||||||||
\(917\) | 12.7984 | 0.422640 | ||||||||
\(918\) | 3.00000 | 0.0990148 | ||||||||
\(919\) | −5.65248 | −0.186458 | −0.0932290 | − | 0.995645i | \(-0.529719\pi\) | ||||
−0.0932290 | + | 0.995645i | \(0.529719\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.9787 | 0.625370 | ||||||||
\(922\) | −9.27051 | −0.305308 | ||||||||
\(923\) | −22.5623 | −0.742647 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −13.4721 | −0.442722 | ||||||||
\(927\) | −6.94427 | −0.228080 | ||||||||
\(928\) | −24.8754 | −0.816575 | ||||||||
\(929\) | 0.708204 | 0.0232354 | 0.0116177 | − | 0.999933i | \(-0.496302\pi\) | ||||
0.0116177 | + | 0.999933i | \(0.496302\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.12461 | 0.167952 | ||||||||
\(932\) | −20.1246 | −0.659204 | ||||||||
\(933\) | −19.6525 | −0.643393 | ||||||||
\(934\) | 5.68692 | 0.186082 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.23607 | −0.203832 | ||||||||
\(937\) | −10.3475 | −0.338039 | −0.169019 | − | 0.985613i | \(-0.554060\pi\) | ||||
−0.169019 | + | 0.985613i | \(0.554060\pi\) | |||||||
\(938\) | 1.85410 | 0.0605386 | ||||||||
\(939\) | 11.4721 | 0.374379 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.4508 | 1.35126 | 0.675630 | − | 0.737241i | \(-0.263872\pi\) | ||||
0.675630 | + | 0.737241i | \(0.263872\pi\) | |||||||
\(942\) | −0.875388 | −0.0285217 | ||||||||
\(943\) | −17.9443 | −0.584346 | ||||||||
\(944\) | 30.2574 | 0.984793 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.3951 | −1.34516 | −0.672580 | − | 0.740024i | \(-0.734814\pi\) | ||||
−0.672580 | + | 0.740024i | \(0.734814\pi\) | |||||||
\(948\) | −20.3951 | −0.662403 | ||||||||
\(949\) | −32.6525 | −1.05994 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.1803 | 0.946237 | ||||||||
\(952\) | −11.5623 | −0.374736 | ||||||||
\(953\) | −42.6525 | −1.38165 | −0.690825 | − | 0.723022i | \(-0.742752\pi\) | ||||
−0.690825 | + | 0.723022i | \(0.742752\pi\) | |||||||
\(954\) | 1.00000 | 0.0323762 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.85410 | −0.156993 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11.6950 | −0.377850 | ||||||||
\(959\) | −14.2361 | −0.459707 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.09017 | −0.164199 | ||||||||
\(962\) | 2.85410 | 0.0920199 | ||||||||
\(963\) | 2.52786 | 0.0814593 | ||||||||
\(964\) | −40.2492 | −1.29634 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.61803 | 0.0520594 | ||||||||
\(967\) | 20.9230 | 0.672838 | 0.336419 | − | 0.941712i | \(-0.390784\pi\) | ||||
0.336419 | + | 0.941712i | \(0.390784\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.70820 | −0.215499 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.0000 | −1.34784 | −0.673922 | − | 0.738802i | \(-0.735392\pi\) | ||||
−0.673922 | + | 0.738802i | \(0.735392\pi\) | |||||||
\(972\) | −1.85410 | −0.0594703 | ||||||||
\(973\) | −5.56231 | −0.178319 | ||||||||
\(974\) | −0.270510 | −0.00866769 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 26.9361 | 0.862205 | ||||||||
\(977\) | −48.5967 | −1.55475 | −0.777374 | − | 0.629039i | \(-0.783449\pi\) | ||||
−0.777374 | + | 0.629039i | \(0.783449\pi\) | |||||||
\(978\) | 4.52786 | 0.144785 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.0000 | −0.383131 | ||||||||
\(982\) | −11.1115 | −0.354581 | ||||||||
\(983\) | 43.8885 | 1.39983 | 0.699914 | − | 0.714228i | \(-0.253222\pi\) | ||||
0.699914 | + | 0.714228i | \(0.253222\pi\) | |||||||
\(984\) | 6.23607 | 0.198799 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −18.0000 | −0.573237 | ||||||||
\(987\) | −1.09017 | −0.0347005 | ||||||||
\(988\) | 6.70820 | 0.213416 | ||||||||
\(989\) | −28.4164 | −0.903589 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.7426 | −1.23070 | −0.615350 | − | 0.788254i | \(-0.710985\pi\) | ||||
−0.615350 | + | 0.788254i | \(0.710985\pi\) | |||||||
\(992\) | 21.1033 | 0.670031 | ||||||||
\(993\) | 3.29180 | 0.104462 | ||||||||
\(994\) | −2.03444 | −0.0645286 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −13.8541 | −0.438984 | ||||||||
\(997\) | 45.7984 | 1.45045 | 0.725225 | − | 0.688512i | \(-0.241736\pi\) | ||||
0.725225 | + | 0.688512i | \(0.241736\pi\) | |||||||
\(998\) | −9.49342 | −0.300509 | ||||||||
\(999\) | 1.76393 | 0.0558083 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))