Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,2,Mod(1,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.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: | \(2.89856959337\) |
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 | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61803 | 1.14412 | 0.572061 | − | 0.820211i | \(-0.306144\pi\) | ||||
0.572061 | + | 0.820211i | \(0.306144\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | −0.381966 | −0.170820 | −0.0854102 | − | 0.996346i | \(-0.527220\pi\) | ||||
−0.0854102 | + | 0.996346i | \(0.527220\pi\) | |||||||
\(6\) | 1.61803 | 0.660560 | ||||||||
\(7\) | 3.00000 | 1.13389 | 0.566947 | − | 0.823754i | \(-0.308125\pi\) | ||||
0.566947 | + | 0.823754i | \(0.308125\pi\) | |||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.618034 | −0.195440 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.618034 | 0.178411 | ||||||||
\(13\) | 6.23607 | 1.72957 | 0.864787 | − | 0.502139i | \(-0.167453\pi\) | ||||
0.864787 | + | 0.502139i | \(0.167453\pi\) | |||||||
\(14\) | 4.85410 | 1.29731 | ||||||||
\(15\) | −0.381966 | −0.0986232 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | −0.618034 | −0.149895 | −0.0749476 | − | 0.997187i | \(-0.523879\pi\) | ||||
−0.0749476 | + | 0.997187i | \(0.523879\pi\) | |||||||
\(18\) | 1.61803 | 0.381374 | ||||||||
\(19\) | −0.854102 | −0.195944 | −0.0979722 | − | 0.995189i | \(-0.531236\pi\) | ||||
−0.0979722 | + | 0.995189i | \(0.531236\pi\) | |||||||
\(20\) | −0.236068 | −0.0527864 | ||||||||
\(21\) | 3.00000 | 0.654654 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.47214 | −1.14102 | −0.570510 | − | 0.821291i | \(-0.693254\pi\) | ||||
−0.570510 | + | 0.821291i | \(0.693254\pi\) | |||||||
\(24\) | −2.23607 | −0.456435 | ||||||||
\(25\) | −4.85410 | −0.970820 | ||||||||
\(26\) | 10.0902 | 1.97885 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.85410 | 0.350392 | ||||||||
\(29\) | −4.47214 | −0.830455 | −0.415227 | − | 0.909718i | \(-0.636298\pi\) | ||||
−0.415227 | + | 0.909718i | \(0.636298\pi\) | |||||||
\(30\) | −0.618034 | −0.112837 | ||||||||
\(31\) | −3.85410 | −0.692217 | −0.346109 | − | 0.938194i | \(-0.612497\pi\) | ||||
−0.346109 | + | 0.938194i | \(0.612497\pi\) | |||||||
\(32\) | −3.38197 | −0.597853 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | −1.14590 | −0.193692 | ||||||||
\(36\) | 0.618034 | 0.103006 | ||||||||
\(37\) | −4.23607 | −0.696405 | −0.348203 | − | 0.937419i | \(-0.613208\pi\) | ||||
−0.348203 | + | 0.937419i | \(0.613208\pi\) | |||||||
\(38\) | −1.38197 | −0.224184 | ||||||||
\(39\) | 6.23607 | 0.998570 | ||||||||
\(40\) | 0.854102 | 0.135045 | ||||||||
\(41\) | 5.94427 | 0.928339 | 0.464170 | − | 0.885746i | \(-0.346353\pi\) | ||||
0.464170 | + | 0.885746i | \(0.346353\pi\) | |||||||
\(42\) | 4.85410 | 0.749004 | ||||||||
\(43\) | 1.76393 | 0.268997 | 0.134499 | − | 0.990914i | \(-0.457058\pi\) | ||||
0.134499 | + | 0.990914i | \(0.457058\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.381966 | −0.0569401 | ||||||||
\(46\) | −8.85410 | −1.30547 | ||||||||
\(47\) | −0.618034 | −0.0901495 | −0.0450748 | − | 0.998984i | \(-0.514353\pi\) | ||||
−0.0450748 | + | 0.998984i | \(0.514353\pi\) | |||||||
\(48\) | −4.85410 | −0.700629 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | −7.85410 | −1.11074 | ||||||||
\(51\) | −0.618034 | −0.0865421 | ||||||||
\(52\) | 3.85410 | 0.534468 | ||||||||
\(53\) | −7.38197 | −1.01399 | −0.506996 | − | 0.861949i | \(-0.669244\pi\) | ||||
−0.506996 | + | 0.861949i | \(0.669244\pi\) | |||||||
\(54\) | 1.61803 | 0.220187 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.70820 | −0.896421 | ||||||||
\(57\) | −0.854102 | −0.113129 | ||||||||
\(58\) | −7.23607 | −0.950142 | ||||||||
\(59\) | −5.32624 | −0.693417 | −0.346709 | − | 0.937973i | \(-0.612701\pi\) | ||||
−0.346709 | + | 0.937973i | \(0.612701\pi\) | |||||||
\(60\) | −0.236068 | −0.0304762 | ||||||||
\(61\) | 1.14590 | 0.146717 | 0.0733586 | − | 0.997306i | \(-0.476628\pi\) | ||||
0.0733586 | + | 0.997306i | \(0.476628\pi\) | |||||||
\(62\) | −6.23607 | −0.791981 | ||||||||
\(63\) | 3.00000 | 0.377964 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | −2.38197 | −0.295447 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.5623 | 1.29039 | 0.645196 | − | 0.764017i | \(-0.276776\pi\) | ||||
0.645196 | + | 0.764017i | \(0.276776\pi\) | |||||||
\(68\) | −0.381966 | −0.0463202 | ||||||||
\(69\) | −5.47214 | −0.658768 | ||||||||
\(70\) | −1.85410 | −0.221608 | ||||||||
\(71\) | 14.5623 | 1.72823 | 0.864114 | − | 0.503296i | \(-0.167880\pi\) | ||||
0.864114 | + | 0.503296i | \(0.167880\pi\) | |||||||
\(72\) | −2.23607 | −0.263523 | ||||||||
\(73\) | 1.23607 | 0.144671 | 0.0723354 | − | 0.997380i | \(-0.476955\pi\) | ||||
0.0723354 | + | 0.997380i | \(0.476955\pi\) | |||||||
\(74\) | −6.85410 | −0.796773 | ||||||||
\(75\) | −4.85410 | −0.560503 | ||||||||
\(76\) | −0.527864 | −0.0605502 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 10.0902 | 1.14249 | ||||||||
\(79\) | 0.527864 | 0.0593893 | 0.0296947 | − | 0.999559i | \(-0.490547\pi\) | ||||
0.0296947 | + | 0.999559i | \(0.490547\pi\) | |||||||
\(80\) | 1.85410 | 0.207295 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.61803 | 1.06213 | ||||||||
\(83\) | −12.7082 | −1.39491 | −0.697453 | − | 0.716630i | \(-0.745684\pi\) | ||||
−0.697453 | + | 0.716630i | \(0.745684\pi\) | |||||||
\(84\) | 1.85410 | 0.202299 | ||||||||
\(85\) | 0.236068 | 0.0256052 | ||||||||
\(86\) | 2.85410 | 0.307766 | ||||||||
\(87\) | −4.47214 | −0.479463 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.47214 | 1.00404 | 0.502022 | − | 0.864855i | \(-0.332590\pi\) | ||||
0.502022 | + | 0.864855i | \(0.332590\pi\) | |||||||
\(90\) | −0.618034 | −0.0651465 | ||||||||
\(91\) | 18.7082 | 1.96115 | ||||||||
\(92\) | −3.38197 | −0.352594 | ||||||||
\(93\) | −3.85410 | −0.399652 | ||||||||
\(94\) | −1.00000 | −0.103142 | ||||||||
\(95\) | 0.326238 | 0.0334713 | ||||||||
\(96\) | −3.38197 | −0.345170 | ||||||||
\(97\) | 15.0344 | 1.52652 | 0.763258 | − | 0.646094i | \(-0.223598\pi\) | ||||
0.763258 | + | 0.646094i | \(0.223598\pi\) | |||||||
\(98\) | 3.23607 | 0.326892 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | −0.300000 | ||||||||
\(101\) | −3.00000 | −0.298511 | −0.149256 | − | 0.988799i | \(-0.547688\pi\) | ||||
−0.149256 | + | 0.988799i | \(0.547688\pi\) | |||||||
\(102\) | −1.00000 | −0.0990148 | ||||||||
\(103\) | −6.00000 | −0.591198 | −0.295599 | − | 0.955312i | \(-0.595519\pi\) | ||||
−0.295599 | + | 0.955312i | \(0.595519\pi\) | |||||||
\(104\) | −13.9443 | −1.36735 | ||||||||
\(105\) | −1.14590 | −0.111828 | ||||||||
\(106\) | −11.9443 | −1.16013 | ||||||||
\(107\) | 0.236068 | 0.0228216 | 0.0114108 | − | 0.999935i | \(-0.496368\pi\) | ||||
0.0114108 | + | 0.999935i | \(0.496368\pi\) | |||||||
\(108\) | 0.618034 | 0.0594703 | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.23607 | −0.402070 | ||||||||
\(112\) | −14.5623 | −1.37601 | ||||||||
\(113\) | −12.7082 | −1.19549 | −0.597744 | − | 0.801687i | \(-0.703936\pi\) | ||||
−0.597744 | + | 0.801687i | \(0.703936\pi\) | |||||||
\(114\) | −1.38197 | −0.129433 | ||||||||
\(115\) | 2.09017 | 0.194909 | ||||||||
\(116\) | −2.76393 | −0.256625 | ||||||||
\(117\) | 6.23607 | 0.576525 | ||||||||
\(118\) | −8.61803 | −0.793354 | ||||||||
\(119\) | −1.85410 | −0.169965 | ||||||||
\(120\) | 0.854102 | 0.0779685 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 1.85410 | 0.167863 | ||||||||
\(123\) | 5.94427 | 0.535977 | ||||||||
\(124\) | −2.38197 | −0.213907 | ||||||||
\(125\) | 3.76393 | 0.336656 | ||||||||
\(126\) | 4.85410 | 0.432438 | ||||||||
\(127\) | 9.70820 | 0.861464 | 0.430732 | − | 0.902480i | \(-0.358255\pi\) | ||||
0.430732 | + | 0.902480i | \(0.358255\pi\) | |||||||
\(128\) | 13.6180 | 1.20368 | ||||||||
\(129\) | 1.76393 | 0.155306 | ||||||||
\(130\) | −3.85410 | −0.338027 | ||||||||
\(131\) | −13.8541 | −1.21044 | −0.605219 | − | 0.796059i | \(-0.706915\pi\) | ||||
−0.605219 | + | 0.796059i | \(0.706915\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.56231 | −0.222180 | ||||||||
\(134\) | 17.0902 | 1.47637 | ||||||||
\(135\) | −0.381966 | −0.0328744 | ||||||||
\(136\) | 1.38197 | 0.118503 | ||||||||
\(137\) | −1.47214 | −0.125773 | −0.0628865 | − | 0.998021i | \(-0.520031\pi\) | ||||
−0.0628865 | + | 0.998021i | \(0.520031\pi\) | |||||||
\(138\) | −8.85410 | −0.753711 | ||||||||
\(139\) | 5.85410 | 0.496538 | 0.248269 | − | 0.968691i | \(-0.420138\pi\) | ||||
0.248269 | + | 0.968691i | \(0.420138\pi\) | |||||||
\(140\) | −0.708204 | −0.0598542 | ||||||||
\(141\) | −0.618034 | −0.0520479 | ||||||||
\(142\) | 23.5623 | 1.97730 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.85410 | −0.404508 | ||||||||
\(145\) | 1.70820 | 0.141859 | ||||||||
\(146\) | 2.00000 | 0.165521 | ||||||||
\(147\) | 2.00000 | 0.164957 | ||||||||
\(148\) | −2.61803 | −0.215201 | ||||||||
\(149\) | 15.0000 | 1.22885 | 0.614424 | − | 0.788976i | \(-0.289388\pi\) | ||||
0.614424 | + | 0.788976i | \(0.289388\pi\) | |||||||
\(150\) | −7.85410 | −0.641285 | ||||||||
\(151\) | 2.00000 | 0.162758 | 0.0813788 | − | 0.996683i | \(-0.474068\pi\) | ||||
0.0813788 | + | 0.996683i | \(0.474068\pi\) | |||||||
\(152\) | 1.90983 | 0.154908 | ||||||||
\(153\) | −0.618034 | −0.0499651 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.47214 | 0.118245 | ||||||||
\(156\) | 3.85410 | 0.308575 | ||||||||
\(157\) | 9.70820 | 0.774799 | 0.387400 | − | 0.921912i | \(-0.373373\pi\) | ||||
0.387400 | + | 0.921912i | \(0.373373\pi\) | |||||||
\(158\) | 0.854102 | 0.0679487 | ||||||||
\(159\) | −7.38197 | −0.585428 | ||||||||
\(160\) | 1.29180 | 0.102125 | ||||||||
\(161\) | −16.4164 | −1.29379 | ||||||||
\(162\) | 1.61803 | 0.127125 | ||||||||
\(163\) | −15.2705 | −1.19608 | −0.598039 | − | 0.801467i | \(-0.704053\pi\) | ||||
−0.598039 | + | 0.801467i | \(0.704053\pi\) | |||||||
\(164\) | 3.67376 | 0.286873 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −20.5623 | −1.59594 | ||||||||
\(167\) | −19.0344 | −1.47293 | −0.736465 | − | 0.676476i | \(-0.763506\pi\) | ||||
−0.736465 | + | 0.676476i | \(0.763506\pi\) | |||||||
\(168\) | −6.70820 | −0.517549 | ||||||||
\(169\) | 25.8885 | 1.99143 | ||||||||
\(170\) | 0.381966 | 0.0292955 | ||||||||
\(171\) | −0.854102 | −0.0653148 | ||||||||
\(172\) | 1.09017 | 0.0831247 | ||||||||
\(173\) | 17.6180 | 1.33947 | 0.669737 | − | 0.742598i | \(-0.266407\pi\) | ||||
0.669737 | + | 0.742598i | \(0.266407\pi\) | |||||||
\(174\) | −7.23607 | −0.548565 | ||||||||
\(175\) | −14.5623 | −1.10081 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.32624 | −0.400345 | ||||||||
\(178\) | 15.3262 | 1.14875 | ||||||||
\(179\) | 2.23607 | 0.167132 | 0.0835658 | − | 0.996502i | \(-0.473369\pi\) | ||||
0.0835658 | + | 0.996502i | \(0.473369\pi\) | |||||||
\(180\) | −0.236068 | −0.0175955 | ||||||||
\(181\) | −8.52786 | −0.633871 | −0.316936 | − | 0.948447i | \(-0.602654\pi\) | ||||
−0.316936 | + | 0.948447i | \(0.602654\pi\) | |||||||
\(182\) | 30.2705 | 2.24380 | ||||||||
\(183\) | 1.14590 | 0.0847072 | ||||||||
\(184\) | 12.2361 | 0.902055 | ||||||||
\(185\) | 1.61803 | 0.118960 | ||||||||
\(186\) | −6.23607 | −0.457251 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.381966 | −0.0278577 | ||||||||
\(189\) | 3.00000 | 0.218218 | ||||||||
\(190\) | 0.527864 | 0.0382953 | ||||||||
\(191\) | 1.47214 | 0.106520 | 0.0532600 | − | 0.998581i | \(-0.483039\pi\) | ||||
0.0532600 | + | 0.998581i | \(0.483039\pi\) | |||||||
\(192\) | 4.23607 | 0.305712 | ||||||||
\(193\) | 1.56231 | 0.112457 | 0.0562286 | − | 0.998418i | \(-0.482092\pi\) | ||||
0.0562286 | + | 0.998418i | \(0.482092\pi\) | |||||||
\(194\) | 24.3262 | 1.74652 | ||||||||
\(195\) | −2.38197 | −0.170576 | ||||||||
\(196\) | 1.23607 | 0.0882906 | ||||||||
\(197\) | 26.6180 | 1.89646 | 0.948228 | − | 0.317590i | \(-0.102873\pi\) | ||||
0.948228 | + | 0.317590i | \(0.102873\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.29180 | −0.233349 | −0.116675 | − | 0.993170i | \(-0.537223\pi\) | ||||
−0.116675 | + | 0.993170i | \(0.537223\pi\) | |||||||
\(200\) | 10.8541 | 0.767501 | ||||||||
\(201\) | 10.5623 | 0.745008 | ||||||||
\(202\) | −4.85410 | −0.341533 | ||||||||
\(203\) | −13.4164 | −0.941647 | ||||||||
\(204\) | −0.381966 | −0.0267430 | ||||||||
\(205\) | −2.27051 | −0.158579 | ||||||||
\(206\) | −9.70820 | −0.676403 | ||||||||
\(207\) | −5.47214 | −0.380340 | ||||||||
\(208\) | −30.2705 | −2.09888 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.85410 | −0.127945 | ||||||||
\(211\) | 11.2705 | 0.775894 | 0.387947 | − | 0.921682i | \(-0.373184\pi\) | ||||
0.387947 | + | 0.921682i | \(0.373184\pi\) | |||||||
\(212\) | −4.56231 | −0.313340 | ||||||||
\(213\) | 14.5623 | 0.997793 | ||||||||
\(214\) | 0.381966 | 0.0261107 | ||||||||
\(215\) | −0.673762 | −0.0459502 | ||||||||
\(216\) | −2.23607 | −0.152145 | ||||||||
\(217\) | −11.5623 | −0.784900 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.23607 | 0.0835257 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.85410 | −0.259255 | ||||||||
\(222\) | −6.85410 | −0.460017 | ||||||||
\(223\) | −12.7082 | −0.851004 | −0.425502 | − | 0.904957i | \(-0.639903\pi\) | ||||
−0.425502 | + | 0.904957i | \(0.639903\pi\) | |||||||
\(224\) | −10.1459 | −0.677901 | ||||||||
\(225\) | −4.85410 | −0.323607 | ||||||||
\(226\) | −20.5623 | −1.36778 | ||||||||
\(227\) | 10.8885 | 0.722698 | 0.361349 | − | 0.932431i | \(-0.382316\pi\) | ||||
0.361349 | + | 0.932431i | \(0.382316\pi\) | |||||||
\(228\) | −0.527864 | −0.0349587 | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 3.38197 | 0.223000 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.0000 | 0.656532 | ||||||||
\(233\) | 8.67376 | 0.568237 | 0.284119 | − | 0.958789i | \(-0.408299\pi\) | ||||
0.284119 | + | 0.958789i | \(0.408299\pi\) | |||||||
\(234\) | 10.0902 | 0.659615 | ||||||||
\(235\) | 0.236068 | 0.0153994 | ||||||||
\(236\) | −3.29180 | −0.214278 | ||||||||
\(237\) | 0.527864 | 0.0342885 | ||||||||
\(238\) | −3.00000 | −0.194461 | ||||||||
\(239\) | −17.5623 | −1.13601 | −0.568006 | − | 0.823025i | \(-0.692285\pi\) | ||||
−0.568006 | + | 0.823025i | \(0.692285\pi\) | |||||||
\(240\) | 1.85410 | 0.119682 | ||||||||
\(241\) | 17.1246 | 1.10309 | 0.551547 | − | 0.834144i | \(-0.314038\pi\) | ||||
0.551547 | + | 0.834144i | \(0.314038\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.708204 | 0.0453381 | ||||||||
\(245\) | −0.763932 | −0.0488058 | ||||||||
\(246\) | 9.61803 | 0.613223 | ||||||||
\(247\) | −5.32624 | −0.338900 | ||||||||
\(248\) | 8.61803 | 0.547246 | ||||||||
\(249\) | −12.7082 | −0.805350 | ||||||||
\(250\) | 6.09017 | 0.385176 | ||||||||
\(251\) | 16.7984 | 1.06030 | 0.530152 | − | 0.847903i | \(-0.322135\pi\) | ||||
0.530152 | + | 0.847903i | \(0.322135\pi\) | |||||||
\(252\) | 1.85410 | 0.116797 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 15.7082 | 0.985620 | ||||||||
\(255\) | 0.236068 | 0.0147832 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | −27.3262 | −1.70456 | −0.852282 | − | 0.523083i | \(-0.824782\pi\) | ||||
−0.852282 | + | 0.523083i | \(0.824782\pi\) | |||||||
\(258\) | 2.85410 | 0.177689 | ||||||||
\(259\) | −12.7082 | −0.789649 | ||||||||
\(260\) | −1.47214 | −0.0912980 | ||||||||
\(261\) | −4.47214 | −0.276818 | ||||||||
\(262\) | −22.4164 | −1.38489 | ||||||||
\(263\) | −0.673762 | −0.0415459 | −0.0207730 | − | 0.999784i | \(-0.506613\pi\) | ||||
−0.0207730 | + | 0.999784i | \(0.506613\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.81966 | 0.173210 | ||||||||
\(266\) | −4.14590 | −0.254201 | ||||||||
\(267\) | 9.47214 | 0.579685 | ||||||||
\(268\) | 6.52786 | 0.398753 | ||||||||
\(269\) | 24.4721 | 1.49209 | 0.746046 | − | 0.665894i | \(-0.231950\pi\) | ||||
0.746046 | + | 0.665894i | \(0.231950\pi\) | |||||||
\(270\) | −0.618034 | −0.0376124 | ||||||||
\(271\) | 6.27051 | 0.380906 | 0.190453 | − | 0.981696i | \(-0.439004\pi\) | ||||
0.190453 | + | 0.981696i | \(0.439004\pi\) | |||||||
\(272\) | 3.00000 | 0.181902 | ||||||||
\(273\) | 18.7082 | 1.13227 | ||||||||
\(274\) | −2.38197 | −0.143900 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.38197 | −0.203570 | ||||||||
\(277\) | 10.4377 | 0.627140 | 0.313570 | − | 0.949565i | \(-0.398475\pi\) | ||||
0.313570 | + | 0.949565i | \(0.398475\pi\) | |||||||
\(278\) | 9.47214 | 0.568101 | ||||||||
\(279\) | −3.85410 | −0.230739 | ||||||||
\(280\) | 2.56231 | 0.153127 | ||||||||
\(281\) | −5.23607 | −0.312358 | −0.156179 | − | 0.987729i | \(-0.549918\pi\) | ||||
−0.156179 | + | 0.987729i | \(0.549918\pi\) | |||||||
\(282\) | −1.00000 | −0.0595491 | ||||||||
\(283\) | −22.1803 | −1.31848 | −0.659242 | − | 0.751931i | \(-0.729123\pi\) | ||||
−0.659242 | + | 0.751931i | \(0.729123\pi\) | |||||||
\(284\) | 9.00000 | 0.534052 | ||||||||
\(285\) | 0.326238 | 0.0193247 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.8328 | 1.05264 | ||||||||
\(288\) | −3.38197 | −0.199284 | ||||||||
\(289\) | −16.6180 | −0.977531 | ||||||||
\(290\) | 2.76393 | 0.162304 | ||||||||
\(291\) | 15.0344 | 0.881335 | ||||||||
\(292\) | 0.763932 | 0.0447057 | ||||||||
\(293\) | 17.9443 | 1.04832 | 0.524158 | − | 0.851621i | \(-0.324380\pi\) | ||||
0.524158 | + | 0.851621i | \(0.324380\pi\) | |||||||
\(294\) | 3.23607 | 0.188731 | ||||||||
\(295\) | 2.03444 | 0.118450 | ||||||||
\(296\) | 9.47214 | 0.550557 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 24.2705 | 1.40595 | ||||||||
\(299\) | −34.1246 | −1.97348 | ||||||||
\(300\) | −3.00000 | −0.173205 | ||||||||
\(301\) | 5.29180 | 0.305014 | ||||||||
\(302\) | 3.23607 | 0.186215 | ||||||||
\(303\) | −3.00000 | −0.172345 | ||||||||
\(304\) | 4.14590 | 0.237784 | ||||||||
\(305\) | −0.437694 | −0.0250623 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | −19.5623 | −1.11648 | −0.558240 | − | 0.829680i | \(-0.688523\pi\) | ||||
−0.558240 | + | 0.829680i | \(0.688523\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.00000 | −0.341328 | ||||||||
\(310\) | 2.38197 | 0.135287 | ||||||||
\(311\) | 11.4721 | 0.650525 | 0.325263 | − | 0.945624i | \(-0.394547\pi\) | ||||
0.325263 | + | 0.945624i | \(0.394547\pi\) | |||||||
\(312\) | −13.9443 | −0.789439 | ||||||||
\(313\) | −27.8328 | −1.57320 | −0.786602 | − | 0.617461i | \(-0.788162\pi\) | ||||
−0.786602 | + | 0.617461i | \(0.788162\pi\) | |||||||
\(314\) | 15.7082 | 0.886465 | ||||||||
\(315\) | −1.14590 | −0.0645640 | ||||||||
\(316\) | 0.326238 | 0.0183523 | ||||||||
\(317\) | 25.3607 | 1.42440 | 0.712199 | − | 0.701978i | \(-0.247699\pi\) | ||||
0.712199 | + | 0.701978i | \(0.247699\pi\) | |||||||
\(318\) | −11.9443 | −0.669802 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.61803 | −0.0904508 | ||||||||
\(321\) | 0.236068 | 0.0131760 | ||||||||
\(322\) | −26.5623 | −1.48026 | ||||||||
\(323\) | 0.527864 | 0.0293711 | ||||||||
\(324\) | 0.618034 | 0.0343352 | ||||||||
\(325\) | −30.2705 | −1.67911 | ||||||||
\(326\) | −24.7082 | −1.36846 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −13.2918 | −0.733917 | ||||||||
\(329\) | −1.85410 | −0.102220 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.5967 | −1.24203 | −0.621015 | − | 0.783799i | \(-0.713279\pi\) | ||||
−0.621015 | + | 0.783799i | \(0.713279\pi\) | |||||||
\(332\) | −7.85410 | −0.431050 | ||||||||
\(333\) | −4.23607 | −0.232135 | ||||||||
\(334\) | −30.7984 | −1.68521 | ||||||||
\(335\) | −4.03444 | −0.220425 | ||||||||
\(336\) | −14.5623 | −0.794439 | ||||||||
\(337\) | −13.7082 | −0.746733 | −0.373367 | − | 0.927684i | \(-0.621797\pi\) | ||||
−0.373367 | + | 0.927684i | \(0.621797\pi\) | |||||||
\(338\) | 41.8885 | 2.27844 | ||||||||
\(339\) | −12.7082 | −0.690215 | ||||||||
\(340\) | 0.145898 | 0.00791243 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1.38197 | −0.0747282 | ||||||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | −3.94427 | −0.212661 | ||||||||
\(345\) | 2.09017 | 0.112531 | ||||||||
\(346\) | 28.5066 | 1.53252 | ||||||||
\(347\) | −3.05573 | −0.164040 | −0.0820200 | − | 0.996631i | \(-0.526137\pi\) | ||||
−0.0820200 | + | 0.996631i | \(0.526137\pi\) | |||||||
\(348\) | −2.76393 | −0.148162 | ||||||||
\(349\) | 30.1246 | 1.61253 | 0.806267 | − | 0.591552i | \(-0.201485\pi\) | ||||
0.806267 | + | 0.591552i | \(0.201485\pi\) | |||||||
\(350\) | −23.5623 | −1.25946 | ||||||||
\(351\) | 6.23607 | 0.332857 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.52786 | −0.0813200 | −0.0406600 | − | 0.999173i | \(-0.512946\pi\) | ||||
−0.0406600 | + | 0.999173i | \(0.512946\pi\) | |||||||
\(354\) | −8.61803 | −0.458043 | ||||||||
\(355\) | −5.56231 | −0.295217 | ||||||||
\(356\) | 5.85410 | 0.310267 | ||||||||
\(357\) | −1.85410 | −0.0981295 | ||||||||
\(358\) | 3.61803 | 0.191219 | ||||||||
\(359\) | −17.2361 | −0.909685 | −0.454842 | − | 0.890572i | \(-0.650304\pi\) | ||||
−0.454842 | + | 0.890572i | \(0.650304\pi\) | |||||||
\(360\) | 0.854102 | 0.0450151 | ||||||||
\(361\) | −18.2705 | −0.961606 | ||||||||
\(362\) | −13.7984 | −0.725226 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 11.5623 | 0.606029 | ||||||||
\(365\) | −0.472136 | −0.0247127 | ||||||||
\(366\) | 1.85410 | 0.0969155 | ||||||||
\(367\) | −14.5623 | −0.760146 | −0.380073 | − | 0.924956i | \(-0.624101\pi\) | ||||
−0.380073 | + | 0.924956i | \(0.624101\pi\) | |||||||
\(368\) | 26.5623 | 1.38466 | ||||||||
\(369\) | 5.94427 | 0.309446 | ||||||||
\(370\) | 2.61803 | 0.136105 | ||||||||
\(371\) | −22.1459 | −1.14976 | ||||||||
\(372\) | −2.38197 | −0.123499 | ||||||||
\(373\) | 22.4164 | 1.16068 | 0.580339 | − | 0.814375i | \(-0.302920\pi\) | ||||
0.580339 | + | 0.814375i | \(0.302920\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.76393 | 0.194369 | ||||||||
\(376\) | 1.38197 | 0.0712695 | ||||||||
\(377\) | −27.8885 | −1.43633 | ||||||||
\(378\) | 4.85410 | 0.249668 | ||||||||
\(379\) | 28.4164 | 1.45965 | 0.729826 | − | 0.683633i | \(-0.239601\pi\) | ||||
0.729826 | + | 0.683633i | \(0.239601\pi\) | |||||||
\(380\) | 0.201626 | 0.0103432 | ||||||||
\(381\) | 9.70820 | 0.497366 | ||||||||
\(382\) | 2.38197 | 0.121872 | ||||||||
\(383\) | −8.88854 | −0.454183 | −0.227092 | − | 0.973873i | \(-0.572922\pi\) | ||||
−0.227092 | + | 0.973873i | \(0.572922\pi\) | |||||||
\(384\) | 13.6180 | 0.694942 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.52786 | 0.128665 | ||||||||
\(387\) | 1.76393 | 0.0896657 | ||||||||
\(388\) | 9.29180 | 0.471719 | ||||||||
\(389\) | −9.27051 | −0.470034 | −0.235017 | − | 0.971991i | \(-0.575515\pi\) | ||||
−0.235017 | + | 0.971991i | \(0.575515\pi\) | |||||||
\(390\) | −3.85410 | −0.195160 | ||||||||
\(391\) | 3.38197 | 0.171033 | ||||||||
\(392\) | −4.47214 | −0.225877 | ||||||||
\(393\) | −13.8541 | −0.698847 | ||||||||
\(394\) | 43.0689 | 2.16978 | ||||||||
\(395\) | −0.201626 | −0.0101449 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.2918 | −1.26936 | −0.634679 | − | 0.772776i | \(-0.718868\pi\) | ||||
−0.634679 | + | 0.772776i | \(0.718868\pi\) | |||||||
\(398\) | −5.32624 | −0.266980 | ||||||||
\(399\) | −2.56231 | −0.128276 | ||||||||
\(400\) | 23.5623 | 1.17812 | ||||||||
\(401\) | −14.9098 | −0.744561 | −0.372281 | − | 0.928120i | \(-0.621424\pi\) | ||||
−0.372281 | + | 0.928120i | \(0.621424\pi\) | |||||||
\(402\) | 17.0902 | 0.852380 | ||||||||
\(403\) | −24.0344 | −1.19724 | ||||||||
\(404\) | −1.85410 | −0.0922450 | ||||||||
\(405\) | −0.381966 | −0.0189800 | ||||||||
\(406\) | −21.7082 | −1.07736 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.38197 | 0.0684175 | ||||||||
\(409\) | −28.9443 | −1.43120 | −0.715601 | − | 0.698509i | \(-0.753847\pi\) | ||||
−0.715601 | + | 0.698509i | \(0.753847\pi\) | |||||||
\(410\) | −3.67376 | −0.181434 | ||||||||
\(411\) | −1.47214 | −0.0726151 | ||||||||
\(412\) | −3.70820 | −0.182690 | ||||||||
\(413\) | −15.9787 | −0.786261 | ||||||||
\(414\) | −8.85410 | −0.435155 | ||||||||
\(415\) | 4.85410 | 0.238278 | ||||||||
\(416\) | −21.0902 | −1.03403 | ||||||||
\(417\) | 5.85410 | 0.286677 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.5066 | −1.05067 | −0.525333 | − | 0.850897i | \(-0.676059\pi\) | ||||
−0.525333 | + | 0.850897i | \(0.676059\pi\) | |||||||
\(420\) | −0.708204 | −0.0345568 | ||||||||
\(421\) | −3.72949 | −0.181764 | −0.0908821 | − | 0.995862i | \(-0.528969\pi\) | ||||
−0.0908821 | + | 0.995862i | \(0.528969\pi\) | |||||||
\(422\) | 18.2361 | 0.887718 | ||||||||
\(423\) | −0.618034 | −0.0300498 | ||||||||
\(424\) | 16.5066 | 0.801630 | ||||||||
\(425\) | 3.00000 | 0.145521 | ||||||||
\(426\) | 23.5623 | 1.14160 | ||||||||
\(427\) | 3.43769 | 0.166362 | ||||||||
\(428\) | 0.145898 | 0.00705225 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.09017 | −0.0525727 | ||||||||
\(431\) | −1.49342 | −0.0719356 | −0.0359678 | − | 0.999353i | \(-0.511451\pi\) | ||||
−0.0359678 | + | 0.999353i | \(0.511451\pi\) | |||||||
\(432\) | −4.85410 | −0.233543 | ||||||||
\(433\) | −6.00000 | −0.288342 | −0.144171 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144171 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(434\) | −18.7082 | −0.898023 | ||||||||
\(435\) | 1.70820 | 0.0819021 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.67376 | 0.223576 | ||||||||
\(438\) | 2.00000 | 0.0955637 | ||||||||
\(439\) | 16.7082 | 0.797439 | 0.398720 | − | 0.917073i | \(-0.369455\pi\) | ||||
0.398720 | + | 0.917073i | \(0.369455\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.00000 | 0.0952381 | ||||||||
\(442\) | −6.23607 | −0.296620 | ||||||||
\(443\) | −0.875388 | −0.0415909 | −0.0207955 | − | 0.999784i | \(-0.506620\pi\) | ||||
−0.0207955 | + | 0.999784i | \(0.506620\pi\) | |||||||
\(444\) | −2.61803 | −0.124246 | ||||||||
\(445\) | −3.61803 | −0.171511 | ||||||||
\(446\) | −20.5623 | −0.973653 | ||||||||
\(447\) | 15.0000 | 0.709476 | ||||||||
\(448\) | 12.7082 | 0.600406 | ||||||||
\(449\) | −15.5279 | −0.732805 | −0.366403 | − | 0.930456i | \(-0.619411\pi\) | ||||
−0.366403 | + | 0.930456i | \(0.619411\pi\) | |||||||
\(450\) | −7.85410 | −0.370246 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −7.85410 | −0.369426 | ||||||||
\(453\) | 2.00000 | 0.0939682 | ||||||||
\(454\) | 17.6180 | 0.826855 | ||||||||
\(455\) | −7.14590 | −0.335005 | ||||||||
\(456\) | 1.90983 | 0.0894360 | ||||||||
\(457\) | 32.7984 | 1.53424 | 0.767122 | − | 0.641502i | \(-0.221688\pi\) | ||||
0.767122 | + | 0.641502i | \(0.221688\pi\) | |||||||
\(458\) | 16.1803 | 0.756058 | ||||||||
\(459\) | −0.618034 | −0.0288474 | ||||||||
\(460\) | 1.29180 | 0.0602303 | ||||||||
\(461\) | −9.90983 | −0.461547 | −0.230773 | − | 0.973008i | \(-0.574126\pi\) | ||||
−0.230773 | + | 0.973008i | \(0.574126\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.79837 | 0.408895 | 0.204448 | − | 0.978878i | \(-0.434460\pi\) | ||||
0.204448 | + | 0.978878i | \(0.434460\pi\) | |||||||
\(464\) | 21.7082 | 1.00778 | ||||||||
\(465\) | 1.47214 | 0.0682687 | ||||||||
\(466\) | 14.0344 | 0.650133 | ||||||||
\(467\) | −14.2361 | −0.658767 | −0.329383 | − | 0.944196i | \(-0.606841\pi\) | ||||
−0.329383 | + | 0.944196i | \(0.606841\pi\) | |||||||
\(468\) | 3.85410 | 0.178156 | ||||||||
\(469\) | 31.6869 | 1.46317 | ||||||||
\(470\) | 0.381966 | 0.0176188 | ||||||||
\(471\) | 9.70820 | 0.447330 | ||||||||
\(472\) | 11.9098 | 0.548194 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0.854102 | 0.0392302 | ||||||||
\(475\) | 4.14590 | 0.190227 | ||||||||
\(476\) | −1.14590 | −0.0525222 | ||||||||
\(477\) | −7.38197 | −0.337997 | ||||||||
\(478\) | −28.4164 | −1.29974 | ||||||||
\(479\) | −16.9098 | −0.772630 | −0.386315 | − | 0.922367i | \(-0.626252\pi\) | ||||
−0.386315 | + | 0.922367i | \(0.626252\pi\) | |||||||
\(480\) | 1.29180 | 0.0589622 | ||||||||
\(481\) | −26.4164 | −1.20448 | ||||||||
\(482\) | 27.7082 | 1.26207 | ||||||||
\(483\) | −16.4164 | −0.746972 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.74265 | −0.260760 | ||||||||
\(486\) | 1.61803 | 0.0733955 | ||||||||
\(487\) | 39.1803 | 1.77543 | 0.887715 | − | 0.460393i | \(-0.152291\pi\) | ||||
0.887715 | + | 0.460393i | \(0.152291\pi\) | |||||||
\(488\) | −2.56231 | −0.115990 | ||||||||
\(489\) | −15.2705 | −0.690556 | ||||||||
\(490\) | −1.23607 | −0.0558399 | ||||||||
\(491\) | −26.2148 | −1.18306 | −0.591528 | − | 0.806284i | \(-0.701475\pi\) | ||||
−0.591528 | + | 0.806284i | \(0.701475\pi\) | |||||||
\(492\) | 3.67376 | 0.165626 | ||||||||
\(493\) | 2.76393 | 0.124481 | ||||||||
\(494\) | −8.61803 | −0.387744 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.7082 | 0.840023 | ||||||||
\(497\) | 43.6869 | 1.95963 | ||||||||
\(498\) | −20.5623 | −0.921419 | ||||||||
\(499\) | 2.56231 | 0.114705 | 0.0573523 | − | 0.998354i | \(-0.481734\pi\) | ||||
0.0573523 | + | 0.998354i | \(0.481734\pi\) | |||||||
\(500\) | 2.32624 | 0.104033 | ||||||||
\(501\) | −19.0344 | −0.850396 | ||||||||
\(502\) | 27.1803 | 1.21312 | ||||||||
\(503\) | −30.0689 | −1.34071 | −0.670353 | − | 0.742043i | \(-0.733857\pi\) | ||||
−0.670353 | + | 0.742043i | \(0.733857\pi\) | |||||||
\(504\) | −6.70820 | −0.298807 | ||||||||
\(505\) | 1.14590 | 0.0509918 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.8885 | 1.14975 | ||||||||
\(508\) | 6.00000 | 0.266207 | ||||||||
\(509\) | 21.3820 | 0.947739 | 0.473869 | − | 0.880595i | \(-0.342857\pi\) | ||||
0.473869 | + | 0.880595i | \(0.342857\pi\) | |||||||
\(510\) | 0.381966 | 0.0169137 | ||||||||
\(511\) | 3.70820 | 0.164041 | ||||||||
\(512\) | −5.29180 | −0.233867 | ||||||||
\(513\) | −0.854102 | −0.0377095 | ||||||||
\(514\) | −44.2148 | −1.95023 | ||||||||
\(515\) | 2.29180 | 0.100989 | ||||||||
\(516\) | 1.09017 | 0.0479921 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −20.5623 | −0.903456 | ||||||||
\(519\) | 17.6180 | 0.773346 | ||||||||
\(520\) | 5.32624 | 0.233571 | ||||||||
\(521\) | 38.8328 | 1.70130 | 0.850648 | − | 0.525735i | \(-0.176210\pi\) | ||||
0.850648 | + | 0.525735i | \(0.176210\pi\) | |||||||
\(522\) | −7.23607 | −0.316714 | ||||||||
\(523\) | 34.9787 | 1.52951 | 0.764756 | − | 0.644320i | \(-0.222859\pi\) | ||||
0.764756 | + | 0.644320i | \(0.222859\pi\) | |||||||
\(524\) | −8.56231 | −0.374046 | ||||||||
\(525\) | −14.5623 | −0.635551 | ||||||||
\(526\) | −1.09017 | −0.0475337 | ||||||||
\(527\) | 2.38197 | 0.103760 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.94427 | 0.301925 | ||||||||
\(530\) | 4.56231 | 0.198174 | ||||||||
\(531\) | −5.32624 | −0.231139 | ||||||||
\(532\) | −1.58359 | −0.0686574 | ||||||||
\(533\) | 37.0689 | 1.60563 | ||||||||
\(534\) | 15.3262 | 0.663231 | ||||||||
\(535\) | −0.0901699 | −0.00389839 | ||||||||
\(536\) | −23.6180 | −1.02014 | ||||||||
\(537\) | 2.23607 | 0.0964935 | ||||||||
\(538\) | 39.5967 | 1.70714 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.236068 | −0.0101587 | ||||||||
\(541\) | −0.562306 | −0.0241754 | −0.0120877 | − | 0.999927i | \(-0.503848\pi\) | ||||
−0.0120877 | + | 0.999927i | \(0.503848\pi\) | |||||||
\(542\) | 10.1459 | 0.435804 | ||||||||
\(543\) | −8.52786 | −0.365966 | ||||||||
\(544\) | 2.09017 | 0.0896153 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 30.2705 | 1.29546 | ||||||||
\(547\) | 19.3820 | 0.828713 | 0.414357 | − | 0.910115i | \(-0.364007\pi\) | ||||
0.414357 | + | 0.910115i | \(0.364007\pi\) | |||||||
\(548\) | −0.909830 | −0.0388660 | ||||||||
\(549\) | 1.14590 | 0.0489057 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.81966 | 0.162723 | ||||||||
\(552\) | 12.2361 | 0.520802 | ||||||||
\(553\) | 1.58359 | 0.0673412 | ||||||||
\(554\) | 16.8885 | 0.717525 | ||||||||
\(555\) | 1.61803 | 0.0686817 | ||||||||
\(556\) | 3.61803 | 0.153439 | ||||||||
\(557\) | 26.0902 | 1.10548 | 0.552738 | − | 0.833355i | \(-0.313583\pi\) | ||||
0.552738 | + | 0.833355i | \(0.313583\pi\) | |||||||
\(558\) | −6.23607 | −0.263994 | ||||||||
\(559\) | 11.0000 | 0.465250 | ||||||||
\(560\) | 5.56231 | 0.235050 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.47214 | −0.357375 | ||||||||
\(563\) | 26.8885 | 1.13322 | 0.566609 | − | 0.823987i | \(-0.308255\pi\) | ||||
0.566609 | + | 0.823987i | \(0.308255\pi\) | |||||||
\(564\) | −0.381966 | −0.0160837 | ||||||||
\(565\) | 4.85410 | 0.204214 | ||||||||
\(566\) | −35.8885 | −1.50851 | ||||||||
\(567\) | 3.00000 | 0.125988 | ||||||||
\(568\) | −32.5623 | −1.36628 | ||||||||
\(569\) | 34.0689 | 1.42824 | 0.714121 | − | 0.700022i | \(-0.246827\pi\) | ||||
0.714121 | + | 0.700022i | \(0.246827\pi\) | |||||||
\(570\) | 0.527864 | 0.0221098 | ||||||||
\(571\) | −25.6869 | −1.07496 | −0.537482 | − | 0.843275i | \(-0.680624\pi\) | ||||
−0.537482 | + | 0.843275i | \(0.680624\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.47214 | 0.0614994 | ||||||||
\(574\) | 28.8541 | 1.20435 | ||||||||
\(575\) | 26.5623 | 1.10772 | ||||||||
\(576\) | 4.23607 | 0.176503 | ||||||||
\(577\) | 15.2361 | 0.634286 | 0.317143 | − | 0.948378i | \(-0.397277\pi\) | ||||
0.317143 | + | 0.948378i | \(0.397277\pi\) | |||||||
\(578\) | −26.8885 | −1.11842 | ||||||||
\(579\) | 1.56231 | 0.0649272 | ||||||||
\(580\) | 1.05573 | 0.0438367 | ||||||||
\(581\) | −38.1246 | −1.58168 | ||||||||
\(582\) | 24.3262 | 1.00836 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.76393 | −0.114372 | ||||||||
\(585\) | −2.38197 | −0.0984822 | ||||||||
\(586\) | 29.0344 | 1.19940 | ||||||||
\(587\) | 24.3050 | 1.00317 | 0.501586 | − | 0.865108i | \(-0.332750\pi\) | ||||
0.501586 | + | 0.865108i | \(0.332750\pi\) | |||||||
\(588\) | 1.23607 | 0.0509746 | ||||||||
\(589\) | 3.29180 | 0.135636 | ||||||||
\(590\) | 3.29180 | 0.135521 | ||||||||
\(591\) | 26.6180 | 1.09492 | ||||||||
\(592\) | 20.5623 | 0.845106 | ||||||||
\(593\) | −29.2148 | −1.19971 | −0.599854 | − | 0.800110i | \(-0.704775\pi\) | ||||
−0.599854 | + | 0.800110i | \(0.704775\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.708204 | 0.0290335 | ||||||||
\(596\) | 9.27051 | 0.379735 | ||||||||
\(597\) | −3.29180 | −0.134724 | ||||||||
\(598\) | −55.2148 | −2.25790 | ||||||||
\(599\) | −21.7082 | −0.886973 | −0.443487 | − | 0.896281i | \(-0.646259\pi\) | ||||
−0.443487 | + | 0.896281i | \(0.646259\pi\) | |||||||
\(600\) | 10.8541 | 0.443117 | ||||||||
\(601\) | −19.8328 | −0.808997 | −0.404499 | − | 0.914539i | \(-0.632554\pi\) | ||||
−0.404499 | + | 0.914539i | \(0.632554\pi\) | |||||||
\(602\) | 8.56231 | 0.348974 | ||||||||
\(603\) | 10.5623 | 0.430130 | ||||||||
\(604\) | 1.23607 | 0.0502949 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.85410 | −0.197184 | ||||||||
\(607\) | −2.32624 | −0.0944191 | −0.0472095 | − | 0.998885i | \(-0.515033\pi\) | ||||
−0.0472095 | + | 0.998885i | \(0.515033\pi\) | |||||||
\(608\) | 2.88854 | 0.117146 | ||||||||
\(609\) | −13.4164 | −0.543660 | ||||||||
\(610\) | −0.708204 | −0.0286743 | ||||||||
\(611\) | −3.85410 | −0.155920 | ||||||||
\(612\) | −0.381966 | −0.0154401 | ||||||||
\(613\) | 3.34752 | 0.135205 | 0.0676026 | − | 0.997712i | \(-0.478465\pi\) | ||||
0.0676026 | + | 0.997712i | \(0.478465\pi\) | |||||||
\(614\) | −31.6525 | −1.27739 | ||||||||
\(615\) | −2.27051 | −0.0915558 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 46.4164 | 1.86865 | 0.934327 | − | 0.356417i | \(-0.116002\pi\) | ||||
0.934327 | + | 0.356417i | \(0.116002\pi\) | |||||||
\(618\) | −9.70820 | −0.390521 | ||||||||
\(619\) | −31.1803 | −1.25324 | −0.626622 | − | 0.779323i | \(-0.715563\pi\) | ||||
−0.626622 | + | 0.779323i | \(0.715563\pi\) | |||||||
\(620\) | 0.909830 | 0.0365397 | ||||||||
\(621\) | −5.47214 | −0.219589 | ||||||||
\(622\) | 18.5623 | 0.744281 | ||||||||
\(623\) | 28.4164 | 1.13848 | ||||||||
\(624\) | −30.2705 | −1.21179 | ||||||||
\(625\) | 22.8328 | 0.913313 | ||||||||
\(626\) | −45.0344 | −1.79994 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.00000 | 0.239426 | ||||||||
\(629\) | 2.61803 | 0.104388 | ||||||||
\(630\) | −1.85410 | −0.0738692 | ||||||||
\(631\) | 12.7295 | 0.506753 | 0.253377 | − | 0.967368i | \(-0.418459\pi\) | ||||
0.253377 | + | 0.967368i | \(0.418459\pi\) | |||||||
\(632\) | −1.18034 | −0.0469514 | ||||||||
\(633\) | 11.2705 | 0.447963 | ||||||||
\(634\) | 41.0344 | 1.62969 | ||||||||
\(635\) | −3.70820 | −0.147156 | ||||||||
\(636\) | −4.56231 | −0.180907 | ||||||||
\(637\) | 12.4721 | 0.494164 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.5623 | 0.576076 | ||||||||
\(640\) | −5.20163 | −0.205612 | ||||||||
\(641\) | −6.74265 | −0.266318 | −0.133159 | − | 0.991095i | \(-0.542512\pi\) | ||||
−0.133159 | + | 0.991095i | \(0.542512\pi\) | |||||||
\(642\) | 0.381966 | 0.0150750 | ||||||||
\(643\) | −18.4377 | −0.727112 | −0.363556 | − | 0.931572i | \(-0.618437\pi\) | ||||
−0.363556 | + | 0.931572i | \(0.618437\pi\) | |||||||
\(644\) | −10.1459 | −0.399804 | ||||||||
\(645\) | −0.673762 | −0.0265294 | ||||||||
\(646\) | 0.854102 | 0.0336042 | ||||||||
\(647\) | 3.20163 | 0.125869 | 0.0629345 | − | 0.998018i | \(-0.479954\pi\) | ||||
0.0629345 | + | 0.998018i | \(0.479954\pi\) | |||||||
\(648\) | −2.23607 | −0.0878410 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −48.9787 | −1.92110 | ||||||||
\(651\) | −11.5623 | −0.453162 | ||||||||
\(652\) | −9.43769 | −0.369609 | ||||||||
\(653\) | 21.9656 | 0.859579 | 0.429789 | − | 0.902929i | \(-0.358588\pi\) | ||||
0.429789 | + | 0.902929i | \(0.358588\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.29180 | 0.206768 | ||||||||
\(656\) | −28.8541 | −1.12656 | ||||||||
\(657\) | 1.23607 | 0.0482236 | ||||||||
\(658\) | −3.00000 | −0.116952 | ||||||||
\(659\) | 20.6525 | 0.804506 | 0.402253 | − | 0.915528i | \(-0.368227\pi\) | ||||
0.402253 | + | 0.915528i | \(0.368227\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.0902 | −0.820313 | −0.410156 | − | 0.912015i | \(-0.634526\pi\) | ||||
−0.410156 | + | 0.912015i | \(0.634526\pi\) | |||||||
\(662\) | −36.5623 | −1.42103 | ||||||||
\(663\) | −3.85410 | −0.149681 | ||||||||
\(664\) | 28.4164 | 1.10277 | ||||||||
\(665\) | 0.978714 | 0.0379529 | ||||||||
\(666\) | −6.85410 | −0.265591 | ||||||||
\(667\) | 24.4721 | 0.947565 | ||||||||
\(668\) | −11.7639 | −0.455160 | ||||||||
\(669\) | −12.7082 | −0.491328 | ||||||||
\(670\) | −6.52786 | −0.252193 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −10.1459 | −0.391387 | ||||||||
\(673\) | −14.4164 | −0.555712 | −0.277856 | − | 0.960623i | \(-0.589624\pi\) | ||||
−0.277856 | + | 0.960623i | \(0.589624\pi\) | |||||||
\(674\) | −22.1803 | −0.854355 | ||||||||
\(675\) | −4.85410 | −0.186834 | ||||||||
\(676\) | 16.0000 | 0.615385 | ||||||||
\(677\) | 22.4721 | 0.863674 | 0.431837 | − | 0.901952i | \(-0.357866\pi\) | ||||
0.431837 | + | 0.901952i | \(0.357866\pi\) | |||||||
\(678\) | −20.5623 | −0.789691 | ||||||||
\(679\) | 45.1033 | 1.73091 | ||||||||
\(680\) | −0.527864 | −0.0202427 | ||||||||
\(681\) | 10.8885 | 0.417250 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.8885 | −1.48803 | −0.744014 | − | 0.668164i | \(-0.767081\pi\) | ||||
−0.744014 | + | 0.668164i | \(0.767081\pi\) | |||||||
\(684\) | −0.527864 | −0.0201834 | ||||||||
\(685\) | 0.562306 | 0.0214846 | ||||||||
\(686\) | −24.2705 | −0.926652 | ||||||||
\(687\) | 10.0000 | 0.381524 | ||||||||
\(688\) | −8.56231 | −0.326435 | ||||||||
\(689\) | −46.0344 | −1.75377 | ||||||||
\(690\) | 3.38197 | 0.128749 | ||||||||
\(691\) | −39.7082 | −1.51057 | −0.755286 | − | 0.655396i | \(-0.772502\pi\) | ||||
−0.755286 | + | 0.655396i | \(0.772502\pi\) | |||||||
\(692\) | 10.8885 | 0.413920 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.94427 | −0.187682 | ||||||||
\(695\) | −2.23607 | −0.0848189 | ||||||||
\(696\) | 10.0000 | 0.379049 | ||||||||
\(697\) | −3.67376 | −0.139154 | ||||||||
\(698\) | 48.7426 | 1.84494 | ||||||||
\(699\) | 8.67376 | 0.328072 | ||||||||
\(700\) | −9.00000 | −0.340168 | ||||||||
\(701\) | 49.6869 | 1.87665 | 0.938324 | − | 0.345756i | \(-0.112377\pi\) | ||||
0.938324 | + | 0.345756i | \(0.112377\pi\) | |||||||
\(702\) | 10.0902 | 0.380829 | ||||||||
\(703\) | 3.61803 | 0.136457 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.236068 | 0.00889083 | ||||||||
\(706\) | −2.47214 | −0.0930401 | ||||||||
\(707\) | −9.00000 | −0.338480 | ||||||||
\(708\) | −3.29180 | −0.123713 | ||||||||
\(709\) | 6.25735 | 0.235000 | 0.117500 | − | 0.993073i | \(-0.462512\pi\) | ||||
0.117500 | + | 0.993073i | \(0.462512\pi\) | |||||||
\(710\) | −9.00000 | −0.337764 | ||||||||
\(711\) | 0.527864 | 0.0197964 | ||||||||
\(712\) | −21.1803 | −0.793767 | ||||||||
\(713\) | 21.0902 | 0.789833 | ||||||||
\(714\) | −3.00000 | −0.112272 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.38197 | 0.0516465 | ||||||||
\(717\) | −17.5623 | −0.655876 | ||||||||
\(718\) | −27.8885 | −1.04079 | ||||||||
\(719\) | −28.4164 | −1.05975 | −0.529877 | − | 0.848075i | \(-0.677762\pi\) | ||||
−0.529877 | + | 0.848075i | \(0.677762\pi\) | |||||||
\(720\) | 1.85410 | 0.0690983 | ||||||||
\(721\) | −18.0000 | −0.670355 | ||||||||
\(722\) | −29.5623 | −1.10020 | ||||||||
\(723\) | 17.1246 | 0.636871 | ||||||||
\(724\) | −5.27051 | −0.195877 | ||||||||
\(725\) | 21.7082 | 0.806222 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.1459 | 1.19223 | 0.596113 | − | 0.802901i | \(-0.296711\pi\) | ||||
0.596113 | + | 0.802901i | \(0.296711\pi\) | |||||||
\(728\) | −41.8328 | −1.55043 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.763932 | −0.0282744 | ||||||||
\(731\) | −1.09017 | −0.0403214 | ||||||||
\(732\) | 0.708204 | 0.0261760 | ||||||||
\(733\) | −24.2918 | −0.897238 | −0.448619 | − | 0.893723i | \(-0.648084\pi\) | ||||
−0.448619 | + | 0.893723i | \(0.648084\pi\) | |||||||
\(734\) | −23.5623 | −0.869701 | ||||||||
\(735\) | −0.763932 | −0.0281781 | ||||||||
\(736\) | 18.5066 | 0.682162 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 9.61803 | 0.354045 | ||||||||
\(739\) | −25.0000 | −0.919640 | −0.459820 | − | 0.888012i | \(-0.652086\pi\) | ||||
−0.459820 | + | 0.888012i | \(0.652086\pi\) | |||||||
\(740\) | 1.00000 | 0.0367607 | ||||||||
\(741\) | −5.32624 | −0.195664 | ||||||||
\(742\) | −35.8328 | −1.31546 | ||||||||
\(743\) | 12.8197 | 0.470308 | 0.235154 | − | 0.971958i | \(-0.424441\pi\) | ||||
0.235154 | + | 0.971958i | \(0.424441\pi\) | |||||||
\(744\) | 8.61803 | 0.315952 | ||||||||
\(745\) | −5.72949 | −0.209912 | ||||||||
\(746\) | 36.2705 | 1.32796 | ||||||||
\(747\) | −12.7082 | −0.464969 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.708204 | 0.0258772 | ||||||||
\(750\) | 6.09017 | 0.222382 | ||||||||
\(751\) | −52.9230 | −1.93119 | −0.965594 | − | 0.260056i | \(-0.916259\pi\) | ||||
−0.965594 | + | 0.260056i | \(0.916259\pi\) | |||||||
\(752\) | 3.00000 | 0.109399 | ||||||||
\(753\) | 16.7984 | 0.612167 | ||||||||
\(754\) | −45.1246 | −1.64334 | ||||||||
\(755\) | −0.763932 | −0.0278023 | ||||||||
\(756\) | 1.85410 | 0.0674330 | ||||||||
\(757\) | −15.9443 | −0.579504 | −0.289752 | − | 0.957102i | \(-0.593573\pi\) | ||||
−0.289752 | + | 0.957102i | \(0.593573\pi\) | |||||||
\(758\) | 45.9787 | 1.67002 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.729490 | −0.0264614 | ||||||||
\(761\) | 4.88854 | 0.177210 | 0.0886048 | − | 0.996067i | \(-0.471759\pi\) | ||||
0.0886048 | + | 0.996067i | \(0.471759\pi\) | |||||||
\(762\) | 15.7082 | 0.569048 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.909830 | 0.0329165 | ||||||||
\(765\) | 0.236068 | 0.00853506 | ||||||||
\(766\) | −14.3820 | −0.519642 | ||||||||
\(767\) | −33.2148 | −1.19932 | ||||||||
\(768\) | 13.5623 | 0.489388 | ||||||||
\(769\) | −47.6869 | −1.71963 | −0.859817 | − | 0.510602i | \(-0.829423\pi\) | ||||
−0.859817 | + | 0.510602i | \(0.829423\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.3262 | −0.984130 | ||||||||
\(772\) | 0.965558 | 0.0347512 | ||||||||
\(773\) | 49.2492 | 1.77137 | 0.885686 | − | 0.464285i | \(-0.153689\pi\) | ||||
0.885686 | + | 0.464285i | \(0.153689\pi\) | |||||||
\(774\) | 2.85410 | 0.102589 | ||||||||
\(775\) | 18.7082 | 0.672019 | ||||||||
\(776\) | −33.6180 | −1.20682 | ||||||||
\(777\) | −12.7082 | −0.455904 | ||||||||
\(778\) | −15.0000 | −0.537776 | ||||||||
\(779\) | −5.07701 | −0.181903 | ||||||||
\(780\) | −1.47214 | −0.0527109 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 5.47214 | 0.195683 | ||||||||
\(783\) | −4.47214 | −0.159821 | ||||||||
\(784\) | −9.70820 | −0.346722 | ||||||||
\(785\) | −3.70820 | −0.132351 | ||||||||
\(786\) | −22.4164 | −0.799567 | ||||||||
\(787\) | −23.7082 | −0.845106 | −0.422553 | − | 0.906338i | \(-0.638866\pi\) | ||||
−0.422553 | + | 0.906338i | \(0.638866\pi\) | |||||||
\(788\) | 16.4508 | 0.586037 | ||||||||
\(789\) | −0.673762 | −0.0239866 | ||||||||
\(790\) | −0.326238 | −0.0116070 | ||||||||
\(791\) | −38.1246 | −1.35556 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.14590 | 0.253758 | ||||||||
\(794\) | −40.9230 | −1.45230 | ||||||||
\(795\) | 2.81966 | 0.100003 | ||||||||
\(796\) | −2.03444 | −0.0721089 | ||||||||
\(797\) | 15.2361 | 0.539689 | 0.269845 | − | 0.962904i | \(-0.413028\pi\) | ||||
0.269845 | + | 0.962904i | \(0.413028\pi\) | |||||||
\(798\) | −4.14590 | −0.146763 | ||||||||
\(799\) | 0.381966 | 0.0135130 | ||||||||
\(800\) | 16.4164 | 0.580408 | ||||||||
\(801\) | 9.47214 | 0.334681 | ||||||||
\(802\) | −24.1246 | −0.851870 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 6.52786 | 0.230220 | ||||||||
\(805\) | 6.27051 | 0.221006 | ||||||||
\(806\) | −38.8885 | −1.36979 | ||||||||
\(807\) | 24.4721 | 0.861460 | ||||||||
\(808\) | 6.70820 | 0.235994 | ||||||||
\(809\) | 25.3262 | 0.890423 | 0.445212 | − | 0.895425i | \(-0.353128\pi\) | ||||
0.445212 | + | 0.895425i | \(0.353128\pi\) | |||||||
\(810\) | −0.618034 | −0.0217155 | ||||||||
\(811\) | 45.7426 | 1.60624 | 0.803121 | − | 0.595816i | \(-0.203171\pi\) | ||||
0.803121 | + | 0.595816i | \(0.203171\pi\) | |||||||
\(812\) | −8.29180 | −0.290985 | ||||||||
\(813\) | 6.27051 | 0.219916 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.83282 | 0.204315 | ||||||||
\(816\) | 3.00000 | 0.105021 | ||||||||
\(817\) | −1.50658 | −0.0527085 | ||||||||
\(818\) | −46.8328 | −1.63747 | ||||||||
\(819\) | 18.7082 | 0.653718 | ||||||||
\(820\) | −1.40325 | −0.0490037 | ||||||||
\(821\) | 13.5836 | 0.474071 | 0.237035 | − | 0.971501i | \(-0.423824\pi\) | ||||
0.237035 | + | 0.971501i | \(0.423824\pi\) | |||||||
\(822\) | −2.38197 | −0.0830806 | ||||||||
\(823\) | −26.5279 | −0.924703 | −0.462352 | − | 0.886697i | \(-0.652994\pi\) | ||||
−0.462352 | + | 0.886697i | \(0.652994\pi\) | |||||||
\(824\) | 13.4164 | 0.467383 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −25.8541 | −0.899579 | ||||||||
\(827\) | 12.8754 | 0.447721 | 0.223861 | − | 0.974621i | \(-0.428134\pi\) | ||||
0.223861 | + | 0.974621i | \(0.428134\pi\) | |||||||
\(828\) | −3.38197 | −0.117531 | ||||||||
\(829\) | −42.6869 | −1.48258 | −0.741289 | − | 0.671186i | \(-0.765785\pi\) | ||||
−0.741289 | + | 0.671186i | \(0.765785\pi\) | |||||||
\(830\) | 7.85410 | 0.272620 | ||||||||
\(831\) | 10.4377 | 0.362080 | ||||||||
\(832\) | 26.4164 | 0.915824 | ||||||||
\(833\) | −1.23607 | −0.0428272 | ||||||||
\(834\) | 9.47214 | 0.327993 | ||||||||
\(835\) | 7.27051 | 0.251606 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.85410 | −0.133217 | ||||||||
\(838\) | −34.7984 | −1.20209 | ||||||||
\(839\) | −23.2918 | −0.804122 | −0.402061 | − | 0.915613i | \(-0.631706\pi\) | ||||
−0.402061 | + | 0.915613i | \(0.631706\pi\) | |||||||
\(840\) | 2.56231 | 0.0884080 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | −6.03444 | −0.207961 | ||||||||
\(843\) | −5.23607 | −0.180340 | ||||||||
\(844\) | 6.96556 | 0.239764 | ||||||||
\(845\) | −9.88854 | −0.340176 | ||||||||
\(846\) | −1.00000 | −0.0343807 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 35.8328 | 1.23050 | ||||||||
\(849\) | −22.1803 | −0.761227 | ||||||||
\(850\) | 4.85410 | 0.166494 | ||||||||
\(851\) | 23.1803 | 0.794612 | ||||||||
\(852\) | 9.00000 | 0.308335 | ||||||||
\(853\) | 7.94427 | 0.272007 | 0.136003 | − | 0.990708i | \(-0.456574\pi\) | ||||
0.136003 | + | 0.990708i | \(0.456574\pi\) | |||||||
\(854\) | 5.56231 | 0.190338 | ||||||||
\(855\) | 0.326238 | 0.0111571 | ||||||||
\(856\) | −0.527864 | −0.0180420 | ||||||||
\(857\) | −41.7214 | −1.42517 | −0.712587 | − | 0.701584i | \(-0.752477\pi\) | ||||
−0.712587 | + | 0.701584i | \(0.752477\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.8885 | 1.46334 | 0.731669 | − | 0.681660i | \(-0.238742\pi\) | ||||
0.731669 | + | 0.681660i | \(0.238742\pi\) | |||||||
\(860\) | −0.416408 | −0.0141994 | ||||||||
\(861\) | 17.8328 | 0.607741 | ||||||||
\(862\) | −2.41641 | −0.0823032 | ||||||||
\(863\) | −23.8885 | −0.813175 | −0.406588 | − | 0.913612i | \(-0.633281\pi\) | ||||
−0.406588 | + | 0.913612i | \(0.633281\pi\) | |||||||
\(864\) | −3.38197 | −0.115057 | ||||||||
\(865\) | −6.72949 | −0.228810 | ||||||||
\(866\) | −9.70820 | −0.329898 | ||||||||
\(867\) | −16.6180 | −0.564378 | ||||||||
\(868\) | −7.14590 | −0.242548 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 2.76393 | 0.0937061 | ||||||||
\(871\) | 65.8673 | 2.23183 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.0344 | 0.508839 | ||||||||
\(874\) | 7.56231 | 0.255799 | ||||||||
\(875\) | 11.2918 | 0.381732 | ||||||||
\(876\) | 0.763932 | 0.0258109 | ||||||||
\(877\) | −20.4164 | −0.689413 | −0.344707 | − | 0.938710i | \(-0.612022\pi\) | ||||
−0.344707 | + | 0.938710i | \(0.612022\pi\) | |||||||
\(878\) | 27.0344 | 0.912368 | ||||||||
\(879\) | 17.9443 | 0.605245 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.0902 | 0.845309 | 0.422655 | − | 0.906291i | \(-0.361098\pi\) | ||||
0.422655 | + | 0.906291i | \(0.361098\pi\) | |||||||
\(882\) | 3.23607 | 0.108964 | ||||||||
\(883\) | 37.4164 | 1.25916 | 0.629581 | − | 0.776935i | \(-0.283226\pi\) | ||||
0.629581 | + | 0.776935i | \(0.283226\pi\) | |||||||
\(884\) | −2.38197 | −0.0801142 | ||||||||
\(885\) | 2.03444 | 0.0683870 | ||||||||
\(886\) | −1.41641 | −0.0475852 | ||||||||
\(887\) | 3.00000 | 0.100730 | 0.0503651 | − | 0.998731i | \(-0.483962\pi\) | ||||
0.0503651 | + | 0.998731i | \(0.483962\pi\) | |||||||
\(888\) | 9.47214 | 0.317864 | ||||||||
\(889\) | 29.1246 | 0.976808 | ||||||||
\(890\) | −5.85410 | −0.196230 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.85410 | −0.262975 | ||||||||
\(893\) | 0.527864 | 0.0176643 | ||||||||
\(894\) | 24.2705 | 0.811727 | ||||||||
\(895\) | −0.854102 | −0.0285495 | ||||||||
\(896\) | 40.8541 | 1.36484 | ||||||||
\(897\) | −34.1246 | −1.13939 | ||||||||
\(898\) | −25.1246 | −0.838419 | ||||||||
\(899\) | 17.2361 | 0.574855 | ||||||||
\(900\) | −3.00000 | −0.100000 | ||||||||
\(901\) | 4.56231 | 0.151992 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.29180 | 0.176100 | ||||||||
\(904\) | 28.4164 | 0.945116 | ||||||||
\(905\) | 3.25735 | 0.108278 | ||||||||
\(906\) | 3.23607 | 0.107511 | ||||||||
\(907\) | 3.97871 | 0.132111 | 0.0660555 | − | 0.997816i | \(-0.478959\pi\) | ||||
0.0660555 | + | 0.997816i | \(0.478959\pi\) | |||||||
\(908\) | 6.72949 | 0.223326 | ||||||||
\(909\) | −3.00000 | −0.0995037 | ||||||||
\(910\) | −11.5623 | −0.383287 | ||||||||
\(911\) | 35.9443 | 1.19089 | 0.595443 | − | 0.803397i | \(-0.296976\pi\) | ||||
0.595443 | + | 0.803397i | \(0.296976\pi\) | |||||||
\(912\) | 4.14590 | 0.137284 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 53.0689 | 1.75536 | ||||||||
\(915\) | −0.437694 | −0.0144697 | ||||||||
\(916\) | 6.18034 | 0.204204 | ||||||||
\(917\) | −41.5623 | −1.37251 | ||||||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | −46.9574 | −1.54898 | −0.774491 | − | 0.632585i | \(-0.781994\pi\) | ||||
−0.774491 | + | 0.632585i | \(0.781994\pi\) | |||||||
\(920\) | −4.67376 | −0.154089 | ||||||||
\(921\) | −19.5623 | −0.644600 | ||||||||
\(922\) | −16.0344 | −0.528066 | ||||||||
\(923\) | 90.8115 | 2.98910 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.5623 | 0.676084 | ||||||||
\(926\) | 14.2361 | 0.467826 | ||||||||
\(927\) | −6.00000 | −0.197066 | ||||||||
\(928\) | 15.1246 | 0.496490 | ||||||||
\(929\) | 2.88854 | 0.0947700 | 0.0473850 | − | 0.998877i | \(-0.484911\pi\) | ||||
0.0473850 | + | 0.998877i | \(0.484911\pi\) | |||||||
\(930\) | 2.38197 | 0.0781077 | ||||||||
\(931\) | −1.70820 | −0.0559841 | ||||||||
\(932\) | 5.36068 | 0.175595 | ||||||||
\(933\) | 11.4721 | 0.375581 | ||||||||
\(934\) | −23.0344 | −0.753710 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −13.9443 | −0.455783 | ||||||||
\(937\) | 32.5967 | 1.06489 | 0.532445 | − | 0.846465i | \(-0.321273\pi\) | ||||
0.532445 | + | 0.846465i | \(0.321273\pi\) | |||||||
\(938\) | 51.2705 | 1.67404 | ||||||||
\(939\) | −27.8328 | −0.908290 | ||||||||
\(940\) | 0.145898 | 0.00475867 | ||||||||
\(941\) | 33.6312 | 1.09635 | 0.548173 | − | 0.836365i | \(-0.315324\pi\) | ||||
0.548173 | + | 0.836365i | \(0.315324\pi\) | |||||||
\(942\) | 15.7082 | 0.511801 | ||||||||
\(943\) | −32.5279 | −1.05925 | ||||||||
\(944\) | 25.8541 | 0.841479 | ||||||||
\(945\) | −1.14590 | −0.0372761 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.67376 | 0.0868856 | 0.0434428 | − | 0.999056i | \(-0.486167\pi\) | ||||
0.0434428 | + | 0.999056i | \(0.486167\pi\) | |||||||
\(948\) | 0.326238 | 0.0105957 | ||||||||
\(949\) | 7.70820 | 0.250219 | ||||||||
\(950\) | 6.70820 | 0.217643 | ||||||||
\(951\) | 25.3607 | 0.822376 | ||||||||
\(952\) | 4.14590 | 0.134369 | ||||||||
\(953\) | 60.1803 | 1.94943 | 0.974716 | − | 0.223446i | \(-0.0717308\pi\) | ||||
0.974716 | + | 0.223446i | \(0.0717308\pi\) | |||||||
\(954\) | −11.9443 | −0.386710 | ||||||||
\(955\) | −0.562306 | −0.0181958 | ||||||||
\(956\) | −10.8541 | −0.351047 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −27.3607 | −0.883983 | ||||||||
\(959\) | −4.41641 | −0.142613 | ||||||||
\(960\) | −1.61803 | −0.0522218 | ||||||||
\(961\) | −16.1459 | −0.520835 | ||||||||
\(962\) | −42.7426 | −1.37808 | ||||||||
\(963\) | 0.236068 | 0.00760718 | ||||||||
\(964\) | 10.5836 | 0.340875 | ||||||||
\(965\) | −0.596748 | −0.0192100 | ||||||||
\(966\) | −26.5623 | −0.854628 | ||||||||
\(967\) | 25.6869 | 0.826036 | 0.413018 | − | 0.910723i | \(-0.364475\pi\) | ||||
0.413018 | + | 0.910723i | \(0.364475\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.527864 | 0.0169574 | ||||||||
\(970\) | −9.29180 | −0.298342 | ||||||||
\(971\) | −33.7771 | −1.08396 | −0.541979 | − | 0.840392i | \(-0.682325\pi\) | ||||
−0.541979 | + | 0.840392i | \(0.682325\pi\) | |||||||
\(972\) | 0.618034 | 0.0198234 | ||||||||
\(973\) | 17.5623 | 0.563022 | ||||||||
\(974\) | 63.3951 | 2.03131 | ||||||||
\(975\) | −30.2705 | −0.969432 | ||||||||
\(976\) | −5.56231 | −0.178045 | ||||||||
\(977\) | −49.3607 | −1.57919 | −0.789594 | − | 0.613630i | \(-0.789709\pi\) | ||||
−0.789594 | + | 0.613630i | \(0.789709\pi\) | |||||||
\(978\) | −24.7082 | −0.790081 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.472136 | −0.0150818 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −42.4164 | −1.35356 | ||||||||
\(983\) | 35.3050 | 1.12605 | 0.563027 | − | 0.826439i | \(-0.309637\pi\) | ||||
0.563027 | + | 0.826439i | \(0.309637\pi\) | |||||||
\(984\) | −13.2918 | −0.423727 | ||||||||
\(985\) | −10.1672 | −0.323953 | ||||||||
\(986\) | 4.47214 | 0.142422 | ||||||||
\(987\) | −1.85410 | −0.0590167 | ||||||||
\(988\) | −3.29180 | −0.104726 | ||||||||
\(989\) | −9.65248 | −0.306931 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.2705 | −0.389786 | −0.194893 | − | 0.980825i | \(-0.562436\pi\) | ||||
−0.194893 | + | 0.980825i | \(0.562436\pi\) | |||||||
\(992\) | 13.0344 | 0.413844 | ||||||||
\(993\) | −22.5967 | −0.717086 | ||||||||
\(994\) | 70.6869 | 2.24205 | ||||||||
\(995\) | 1.25735 | 0.0398608 | ||||||||
\(996\) | −7.85410 | −0.248867 | ||||||||
\(997\) | 33.9787 | 1.07612 | 0.538058 | − | 0.842908i | \(-0.319158\pi\) | ||||
0.538058 | + | 0.842908i | \(0.319158\pi\) | |||||||
\(998\) | 4.14590 | 0.131236 | ||||||||
\(999\) | −4.23607 | −0.134023 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))