Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8959,2,Mod(1,8959)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8959, 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("8959.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8959 = 17^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8959.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: | \(71.5379751709\) |
Analytic rank: | \(1\) |
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 31) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8959.1 |
$q$-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 | \(0.306144\pi\) | |||||||
\(3\) | 3.23607 | 1.86834 | 0.934172 | − | 0.356822i | \(-0.116140\pi\) | ||||
0.934172 | + | 0.356822i | \(0.116140\pi\) | |||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | −1.00000 | −0.447214 | −0.223607 | − | 0.974679i | \(-0.571783\pi\) | ||||
−0.223607 | + | 0.974679i | \(0.571783\pi\) | |||||||
\(6\) | 5.23607 | 2.13762 | ||||||||
\(7\) | −0.236068 | −0.0892253 | −0.0446127 | − | 0.999004i | \(-0.514205\pi\) | ||||
−0.0446127 | + | 0.999004i | \(0.514205\pi\) | |||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | 7.47214 | 2.49071 | ||||||||
\(10\) | −1.61803 | −0.511667 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 2.00000 | 0.577350 | ||||||||
\(13\) | −3.23607 | −0.897524 | −0.448762 | − | 0.893651i | \(-0.648135\pi\) | ||||
−0.448762 | + | 0.893651i | \(0.648135\pi\) | |||||||
\(14\) | −0.381966 | −0.102085 | ||||||||
\(15\) | −3.23607 | −0.835549 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 12.0902 | 2.84968 | ||||||||
\(19\) | −2.23607 | −0.512989 | −0.256495 | − | 0.966546i | \(-0.582568\pi\) | ||||
−0.256495 | + | 0.966546i | \(0.582568\pi\) | |||||||
\(20\) | −0.618034 | −0.138197 | ||||||||
\(21\) | −0.763932 | −0.166704 | ||||||||
\(22\) | −3.23607 | −0.689932 | ||||||||
\(23\) | −5.70820 | −1.19024 | −0.595121 | − | 0.803636i | \(-0.702896\pi\) | ||||
−0.595121 | + | 0.803636i | \(0.702896\pi\) | |||||||
\(24\) | −7.23607 | −1.47706 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | −5.23607 | −1.02688 | ||||||||
\(27\) | 14.4721 | 2.78516 | ||||||||
\(28\) | −0.145898 | −0.0275721 | ||||||||
\(29\) | −2.76393 | −0.513249 | −0.256625 | − | 0.966511i | \(-0.582610\pi\) | ||||
−0.256625 | + | 0.966511i | \(0.582610\pi\) | |||||||
\(30\) | −5.23607 | −0.955971 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | −3.38197 | −0.597853 | ||||||||
\(33\) | −6.47214 | −1.12665 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.236068 | 0.0399028 | ||||||||
\(36\) | 4.61803 | 0.769672 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | −3.61803 | −0.586923 | ||||||||
\(39\) | −10.4721 | −1.67688 | ||||||||
\(40\) | 2.23607 | 0.353553 | ||||||||
\(41\) | −7.00000 | −1.09322 | −0.546608 | − | 0.837389i | \(-0.684081\pi\) | ||||
−0.546608 | + | 0.837389i | \(0.684081\pi\) | |||||||
\(42\) | −1.23607 | −0.190729 | ||||||||
\(43\) | 1.23607 | 0.188499 | 0.0942493 | − | 0.995549i | \(-0.469955\pi\) | ||||
0.0942493 | + | 0.995549i | \(0.469955\pi\) | |||||||
\(44\) | −1.23607 | −0.186344 | ||||||||
\(45\) | −7.47214 | −1.11388 | ||||||||
\(46\) | −9.23607 | −1.36178 | ||||||||
\(47\) | 2.47214 | 0.360598 | 0.180299 | − | 0.983612i | \(-0.442293\pi\) | ||||
0.180299 | + | 0.983612i | \(0.442293\pi\) | |||||||
\(48\) | −15.7082 | −2.26728 | ||||||||
\(49\) | −6.94427 | −0.992039 | ||||||||
\(50\) | −6.47214 | −0.915298 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.00000 | −0.277350 | ||||||||
\(53\) | −10.4721 | −1.43846 | −0.719229 | − | 0.694773i | \(-0.755505\pi\) | ||||
−0.719229 | + | 0.694773i | \(0.755505\pi\) | |||||||
\(54\) | 23.4164 | 3.18657 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0.527864 | 0.0705388 | ||||||||
\(57\) | −7.23607 | −0.958441 | ||||||||
\(58\) | −4.47214 | −0.587220 | ||||||||
\(59\) | 2.23607 | 0.291111 | 0.145556 | − | 0.989350i | \(-0.453503\pi\) | ||||
0.145556 | + | 0.989350i | \(0.453503\pi\) | |||||||
\(60\) | −2.00000 | −0.258199 | ||||||||
\(61\) | −8.18034 | −1.04739 | −0.523693 | − | 0.851907i | \(-0.675446\pi\) | ||||
−0.523693 | + | 0.851907i | \(0.675446\pi\) | |||||||
\(62\) | −1.61803 | −0.205491 | ||||||||
\(63\) | −1.76393 | −0.222235 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | 3.23607 | 0.401385 | ||||||||
\(66\) | −10.4721 | −1.28903 | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −18.4721 | −2.22378 | ||||||||
\(70\) | 0.381966 | 0.0456537 | ||||||||
\(71\) | 9.18034 | 1.08951 | 0.544753 | − | 0.838597i | \(-0.316623\pi\) | ||||
0.544753 | + | 0.838597i | \(0.316623\pi\) | |||||||
\(72\) | −16.7082 | −1.96908 | ||||||||
\(73\) | −8.47214 | −0.991589 | −0.495794 | − | 0.868440i | \(-0.665123\pi\) | ||||
−0.495794 | + | 0.868440i | \(0.665123\pi\) | |||||||
\(74\) | 3.23607 | 0.376185 | ||||||||
\(75\) | −12.9443 | −1.49468 | ||||||||
\(76\) | −1.38197 | −0.158522 | ||||||||
\(77\) | 0.472136 | 0.0538049 | ||||||||
\(78\) | −16.9443 | −1.91856 | ||||||||
\(79\) | 11.7082 | 1.31728 | 0.658638 | − | 0.752460i | \(-0.271133\pi\) | ||||
0.658638 | + | 0.752460i | \(0.271133\pi\) | |||||||
\(80\) | 4.85410 | 0.542705 | ||||||||
\(81\) | 24.4164 | 2.71293 | ||||||||
\(82\) | −11.3262 | −1.25077 | ||||||||
\(83\) | −14.9443 | −1.64035 | −0.820173 | − | 0.572115i | \(-0.806123\pi\) | ||||
−0.820173 | + | 0.572115i | \(0.806123\pi\) | |||||||
\(84\) | −0.472136 | −0.0515143 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.00000 | 0.215666 | ||||||||
\(87\) | −8.94427 | −0.958927 | ||||||||
\(88\) | 4.47214 | 0.476731 | ||||||||
\(89\) | 11.7082 | 1.24107 | 0.620534 | − | 0.784180i | \(-0.286916\pi\) | ||||
0.620534 | + | 0.784180i | \(0.286916\pi\) | |||||||
\(90\) | −12.0902 | −1.27442 | ||||||||
\(91\) | 0.763932 | 0.0800818 | ||||||||
\(92\) | −3.52786 | −0.367805 | ||||||||
\(93\) | −3.23607 | −0.335565 | ||||||||
\(94\) | 4.00000 | 0.412568 | ||||||||
\(95\) | 2.23607 | 0.229416 | ||||||||
\(96\) | −10.9443 | −1.11700 | ||||||||
\(97\) | 15.9443 | 1.61890 | 0.809448 | − | 0.587192i | \(-0.199767\pi\) | ||||
0.809448 | + | 0.587192i | \(0.199767\pi\) | |||||||
\(98\) | −11.2361 | −1.13501 | ||||||||
\(99\) | −14.9443 | −1.50196 | ||||||||
\(100\) | −2.47214 | −0.247214 | ||||||||
\(101\) | −3.00000 | −0.298511 | −0.149256 | − | 0.988799i | \(-0.547688\pi\) | ||||
−0.149256 | + | 0.988799i | \(0.547688\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.23607 | 0.614458 | 0.307229 | − | 0.951636i | \(-0.400598\pi\) | ||||
0.307229 | + | 0.951636i | \(0.400598\pi\) | |||||||
\(104\) | 7.23607 | 0.709555 | ||||||||
\(105\) | 0.763932 | 0.0745521 | ||||||||
\(106\) | −16.9443 | −1.64577 | ||||||||
\(107\) | −5.76393 | −0.557220 | −0.278610 | − | 0.960404i | \(-0.589874\pi\) | ||||
−0.278610 | + | 0.960404i | \(0.589874\pi\) | |||||||
\(108\) | 8.94427 | 0.860663 | ||||||||
\(109\) | 13.9443 | 1.33562 | 0.667810 | − | 0.744332i | \(-0.267232\pi\) | ||||
0.667810 | + | 0.744332i | \(0.267232\pi\) | |||||||
\(110\) | 3.23607 | 0.308547 | ||||||||
\(111\) | 6.47214 | 0.614308 | ||||||||
\(112\) | 1.14590 | 0.108277 | ||||||||
\(113\) | −3.47214 | −0.326631 | −0.163316 | − | 0.986574i | \(-0.552219\pi\) | ||||
−0.163316 | + | 0.986574i | \(0.552219\pi\) | |||||||
\(114\) | −11.7082 | −1.09657 | ||||||||
\(115\) | 5.70820 | 0.532293 | ||||||||
\(116\) | −1.70820 | −0.158603 | ||||||||
\(117\) | −24.1803 | −2.23547 | ||||||||
\(118\) | 3.61803 | 0.333067 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 7.23607 | 0.660560 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −13.2361 | −1.19834 | ||||||||
\(123\) | −22.6525 | −2.04250 | ||||||||
\(124\) | −0.618034 | −0.0555011 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | −2.85410 | −0.254264 | ||||||||
\(127\) | 12.4721 | 1.10672 | 0.553362 | − | 0.832941i | \(-0.313345\pi\) | ||||
0.553362 | + | 0.832941i | \(0.313345\pi\) | |||||||
\(128\) | 13.6180 | 1.20368 | ||||||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 5.23607 | 0.459234 | ||||||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | −4.00000 | −0.348155 | ||||||||
\(133\) | 0.527864 | 0.0457716 | ||||||||
\(134\) | 12.9443 | 1.11821 | ||||||||
\(135\) | −14.4721 | −1.24556 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.29180 | 0.537544 | 0.268772 | − | 0.963204i | \(-0.413382\pi\) | ||||
0.268772 | + | 0.963204i | \(0.413382\pi\) | |||||||
\(138\) | −29.8885 | −2.54428 | ||||||||
\(139\) | −13.4164 | −1.13796 | −0.568982 | − | 0.822350i | \(-0.692663\pi\) | ||||
−0.568982 | + | 0.822350i | \(0.692663\pi\) | |||||||
\(140\) | 0.145898 | 0.0123306 | ||||||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | 14.8541 | 1.24653 | ||||||||
\(143\) | 6.47214 | 0.541227 | ||||||||
\(144\) | −36.2705 | −3.02254 | ||||||||
\(145\) | 2.76393 | 0.229532 | ||||||||
\(146\) | −13.7082 | −1.13450 | ||||||||
\(147\) | −22.4721 | −1.85347 | ||||||||
\(148\) | 1.23607 | 0.101604 | ||||||||
\(149\) | 10.0000 | 0.819232 | 0.409616 | − | 0.912258i | \(-0.365663\pi\) | ||||
0.409616 | + | 0.912258i | \(0.365663\pi\) | |||||||
\(150\) | −20.9443 | −1.71009 | ||||||||
\(151\) | −14.1803 | −1.15398 | −0.576990 | − | 0.816751i | \(-0.695773\pi\) | ||||
−0.576990 | + | 0.816751i | \(0.695773\pi\) | |||||||
\(152\) | 5.00000 | 0.405554 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.763932 | 0.0615594 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | −6.47214 | −0.518186 | ||||||||
\(157\) | 20.8885 | 1.66709 | 0.833544 | − | 0.552454i | \(-0.186308\pi\) | ||||
0.833544 | + | 0.552454i | \(0.186308\pi\) | |||||||
\(158\) | 18.9443 | 1.50713 | ||||||||
\(159\) | −33.8885 | −2.68754 | ||||||||
\(160\) | 3.38197 | 0.267368 | ||||||||
\(161\) | 1.34752 | 0.106200 | ||||||||
\(162\) | 39.5066 | 3.10393 | ||||||||
\(163\) | −10.7082 | −0.838731 | −0.419366 | − | 0.907817i | \(-0.637747\pi\) | ||||
−0.419366 | + | 0.907817i | \(0.637747\pi\) | |||||||
\(164\) | −4.32624 | −0.337822 | ||||||||
\(165\) | 6.47214 | 0.503855 | ||||||||
\(166\) | −24.1803 | −1.87676 | ||||||||
\(167\) | 6.47214 | 0.500829 | 0.250414 | − | 0.968139i | \(-0.419433\pi\) | ||||
0.250414 | + | 0.968139i | \(0.419433\pi\) | |||||||
\(168\) | 1.70820 | 0.131791 | ||||||||
\(169\) | −2.52786 | −0.194451 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.7082 | −1.27771 | ||||||||
\(172\) | 0.763932 | 0.0582493 | ||||||||
\(173\) | −2.94427 | −0.223849 | −0.111924 | − | 0.993717i | \(-0.535701\pi\) | ||||
−0.111924 | + | 0.993717i | \(0.535701\pi\) | |||||||
\(174\) | −14.4721 | −1.09713 | ||||||||
\(175\) | 0.944272 | 0.0713802 | ||||||||
\(176\) | 9.70820 | 0.731783 | ||||||||
\(177\) | 7.23607 | 0.543896 | ||||||||
\(178\) | 18.9443 | 1.41993 | ||||||||
\(179\) | 1.70820 | 0.127677 | 0.0638386 | − | 0.997960i | \(-0.479666\pi\) | ||||
0.0638386 | + | 0.997960i | \(0.479666\pi\) | |||||||
\(180\) | −4.61803 | −0.344208 | ||||||||
\(181\) | 4.18034 | 0.310722 | 0.155361 | − | 0.987858i | \(-0.450346\pi\) | ||||
0.155361 | + | 0.987858i | \(0.450346\pi\) | |||||||
\(182\) | 1.23607 | 0.0916235 | ||||||||
\(183\) | −26.4721 | −1.95688 | ||||||||
\(184\) | 12.7639 | 0.940970 | ||||||||
\(185\) | −2.00000 | −0.147043 | ||||||||
\(186\) | −5.23607 | −0.383927 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.52786 | 0.111431 | ||||||||
\(189\) | −3.41641 | −0.248507 | ||||||||
\(190\) | 3.61803 | 0.262480 | ||||||||
\(191\) | −19.1803 | −1.38784 | −0.693920 | − | 0.720052i | \(-0.744118\pi\) | ||||
−0.693920 | + | 0.720052i | \(0.744118\pi\) | |||||||
\(192\) | 13.7082 | 0.989304 | ||||||||
\(193\) | −3.47214 | −0.249930 | −0.124965 | − | 0.992161i | \(-0.539882\pi\) | ||||
−0.124965 | + | 0.992161i | \(0.539882\pi\) | |||||||
\(194\) | 25.7984 | 1.85222 | ||||||||
\(195\) | 10.4721 | 0.749925 | ||||||||
\(196\) | −4.29180 | −0.306557 | ||||||||
\(197\) | −11.4164 | −0.813385 | −0.406693 | − | 0.913565i | \(-0.633318\pi\) | ||||
−0.406693 | + | 0.913565i | \(0.633318\pi\) | |||||||
\(198\) | −24.1803 | −1.71842 | ||||||||
\(199\) | 18.9443 | 1.34292 | 0.671462 | − | 0.741039i | \(-0.265667\pi\) | ||||
0.671462 | + | 0.741039i | \(0.265667\pi\) | |||||||
\(200\) | 8.94427 | 0.632456 | ||||||||
\(201\) | 25.8885 | 1.82604 | ||||||||
\(202\) | −4.85410 | −0.341533 | ||||||||
\(203\) | 0.652476 | 0.0457948 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.00000 | 0.488901 | ||||||||
\(206\) | 10.0902 | 0.703015 | ||||||||
\(207\) | −42.6525 | −2.96455 | ||||||||
\(208\) | 15.7082 | 1.08917 | ||||||||
\(209\) | 4.47214 | 0.309344 | ||||||||
\(210\) | 1.23607 | 0.0852968 | ||||||||
\(211\) | −23.1803 | −1.59580 | −0.797900 | − | 0.602790i | \(-0.794056\pi\) | ||||
−0.797900 | + | 0.602790i | \(0.794056\pi\) | |||||||
\(212\) | −6.47214 | −0.444508 | ||||||||
\(213\) | 29.7082 | 2.03557 | ||||||||
\(214\) | −9.32624 | −0.637528 | ||||||||
\(215\) | −1.23607 | −0.0842991 | ||||||||
\(216\) | −32.3607 | −2.20187 | ||||||||
\(217\) | 0.236068 | 0.0160253 | ||||||||
\(218\) | 22.5623 | 1.52811 | ||||||||
\(219\) | −27.4164 | −1.85263 | ||||||||
\(220\) | 1.23607 | 0.0833357 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 10.4721 | 0.702844 | ||||||||
\(223\) | 4.00000 | 0.267860 | 0.133930 | − | 0.990991i | \(-0.457240\pi\) | ||||
0.133930 | + | 0.990991i | \(0.457240\pi\) | |||||||
\(224\) | 0.798374 | 0.0533436 | ||||||||
\(225\) | −29.8885 | −1.99257 | ||||||||
\(226\) | −5.61803 | −0.373706 | ||||||||
\(227\) | 6.47214 | 0.429571 | 0.214785 | − | 0.976661i | \(-0.431095\pi\) | ||||
0.214785 | + | 0.976661i | \(0.431095\pi\) | |||||||
\(228\) | −4.47214 | −0.296174 | ||||||||
\(229\) | −13.4164 | −0.886581 | −0.443291 | − | 0.896378i | \(-0.646189\pi\) | ||||
−0.443291 | + | 0.896378i | \(0.646189\pi\) | |||||||
\(230\) | 9.23607 | 0.609008 | ||||||||
\(231\) | 1.52786 | 0.100526 | ||||||||
\(232\) | 6.18034 | 0.405759 | ||||||||
\(233\) | −17.9443 | −1.17557 | −0.587784 | − | 0.809018i | \(-0.700000\pi\) | ||||
−0.587784 | + | 0.809018i | \(0.700000\pi\) | |||||||
\(234\) | −39.1246 | −2.55766 | ||||||||
\(235\) | −2.47214 | −0.161264 | ||||||||
\(236\) | 1.38197 | 0.0899583 | ||||||||
\(237\) | 37.8885 | 2.46113 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.7082 | −0.757341 | −0.378670 | − | 0.925532i | \(-0.623619\pi\) | ||||
−0.378670 | + | 0.925532i | \(0.623619\pi\) | |||||||
\(240\) | 15.7082 | 1.01396 | ||||||||
\(241\) | −14.3607 | −0.925053 | −0.462526 | − | 0.886606i | \(-0.653057\pi\) | ||||
−0.462526 | + | 0.886606i | \(0.653057\pi\) | |||||||
\(242\) | −11.3262 | −0.728078 | ||||||||
\(243\) | 35.5967 | 2.28353 | ||||||||
\(244\) | −5.05573 | −0.323660 | ||||||||
\(245\) | 6.94427 | 0.443653 | ||||||||
\(246\) | −36.6525 | −2.33688 | ||||||||
\(247\) | 7.23607 | 0.460420 | ||||||||
\(248\) | 2.23607 | 0.141990 | ||||||||
\(249\) | −48.3607 | −3.06473 | ||||||||
\(250\) | 14.5623 | 0.921001 | ||||||||
\(251\) | −1.81966 | −0.114856 | −0.0574280 | − | 0.998350i | \(-0.518290\pi\) | ||||
−0.0574280 | + | 0.998350i | \(0.518290\pi\) | |||||||
\(252\) | −1.09017 | −0.0686743 | ||||||||
\(253\) | 11.4164 | 0.717743 | ||||||||
\(254\) | 20.1803 | 1.26623 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 1.94427 | 0.121280 | 0.0606402 | − | 0.998160i | \(-0.480686\pi\) | ||||
0.0606402 | + | 0.998160i | \(0.480686\pi\) | |||||||
\(258\) | 6.47214 | 0.402938 | ||||||||
\(259\) | −0.472136 | −0.0293371 | ||||||||
\(260\) | 2.00000 | 0.124035 | ||||||||
\(261\) | −20.6525 | −1.27836 | ||||||||
\(262\) | −19.4164 | −1.19955 | ||||||||
\(263\) | −23.2361 | −1.43280 | −0.716399 | − | 0.697691i | \(-0.754211\pi\) | ||||
−0.716399 | + | 0.697691i | \(0.754211\pi\) | |||||||
\(264\) | 14.4721 | 0.890698 | ||||||||
\(265\) | 10.4721 | 0.643298 | ||||||||
\(266\) | 0.854102 | 0.0523684 | ||||||||
\(267\) | 37.8885 | 2.31874 | ||||||||
\(268\) | 4.94427 | 0.302019 | ||||||||
\(269\) | 11.0557 | 0.674080 | 0.337040 | − | 0.941490i | \(-0.390574\pi\) | ||||
0.337040 | + | 0.941490i | \(0.390574\pi\) | |||||||
\(270\) | −23.4164 | −1.42508 | ||||||||
\(271\) | −14.1803 | −0.861394 | −0.430697 | − | 0.902497i | \(-0.641732\pi\) | ||||
−0.430697 | + | 0.902497i | \(0.641732\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.47214 | 0.149620 | ||||||||
\(274\) | 10.1803 | 0.615017 | ||||||||
\(275\) | 8.00000 | 0.482418 | ||||||||
\(276\) | −11.4164 | −0.687187 | ||||||||
\(277\) | 12.6525 | 0.760214 | 0.380107 | − | 0.924943i | \(-0.375887\pi\) | ||||
0.380107 | + | 0.924943i | \(0.375887\pi\) | |||||||
\(278\) | −21.7082 | −1.30197 | ||||||||
\(279\) | −7.47214 | −0.447345 | ||||||||
\(280\) | −0.527864 | −0.0315459 | ||||||||
\(281\) | 17.0000 | 1.01413 | 0.507067 | − | 0.861906i | \(-0.330729\pi\) | ||||
0.507067 | + | 0.861906i | \(0.330729\pi\) | |||||||
\(282\) | 12.9443 | 0.770820 | ||||||||
\(283\) | 13.8885 | 0.825588 | 0.412794 | − | 0.910824i | \(-0.364553\pi\) | ||||
0.412794 | + | 0.910824i | \(0.364553\pi\) | |||||||
\(284\) | 5.67376 | 0.336676 | ||||||||
\(285\) | 7.23607 | 0.428628 | ||||||||
\(286\) | 10.4721 | 0.619230 | ||||||||
\(287\) | 1.65248 | 0.0975426 | ||||||||
\(288\) | −25.2705 | −1.48908 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 4.47214 | 0.262613 | ||||||||
\(291\) | 51.5967 | 3.02465 | ||||||||
\(292\) | −5.23607 | −0.306418 | ||||||||
\(293\) | −0.472136 | −0.0275825 | −0.0137912 | − | 0.999905i | \(-0.504390\pi\) | ||||
−0.0137912 | + | 0.999905i | \(0.504390\pi\) | |||||||
\(294\) | −36.3607 | −2.12060 | ||||||||
\(295\) | −2.23607 | −0.130189 | ||||||||
\(296\) | −4.47214 | −0.259938 | ||||||||
\(297\) | −28.9443 | −1.67952 | ||||||||
\(298\) | 16.1803 | 0.937302 | ||||||||
\(299\) | 18.4721 | 1.06827 | ||||||||
\(300\) | −8.00000 | −0.461880 | ||||||||
\(301\) | −0.291796 | −0.0168188 | ||||||||
\(302\) | −22.9443 | −1.32029 | ||||||||
\(303\) | −9.70820 | −0.557722 | ||||||||
\(304\) | 10.8541 | 0.622525 | ||||||||
\(305\) | 8.18034 | 0.468405 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.7082 | −1.63846 | −0.819232 | − | 0.573462i | \(-0.805600\pi\) | ||||
−0.819232 | + | 0.573462i | \(0.805600\pi\) | |||||||
\(308\) | 0.291796 | 0.0166266 | ||||||||
\(309\) | 20.1803 | 1.14802 | ||||||||
\(310\) | 1.61803 | 0.0918982 | ||||||||
\(311\) | 29.1803 | 1.65467 | 0.827333 | − | 0.561712i | \(-0.189857\pi\) | ||||
0.827333 | + | 0.561712i | \(0.189857\pi\) | |||||||
\(312\) | 23.4164 | 1.32569 | ||||||||
\(313\) | −16.7639 | −0.947553 | −0.473777 | − | 0.880645i | \(-0.657110\pi\) | ||||
−0.473777 | + | 0.880645i | \(0.657110\pi\) | |||||||
\(314\) | 33.7984 | 1.90735 | ||||||||
\(315\) | 1.76393 | 0.0993863 | ||||||||
\(316\) | 7.23607 | 0.407061 | ||||||||
\(317\) | −4.05573 | −0.227792 | −0.113896 | − | 0.993493i | \(-0.536333\pi\) | ||||
−0.113896 | + | 0.993493i | \(0.536333\pi\) | |||||||
\(318\) | −54.8328 | −3.07487 | ||||||||
\(319\) | 5.52786 | 0.309501 | ||||||||
\(320\) | −4.23607 | −0.236803 | ||||||||
\(321\) | −18.6525 | −1.04108 | ||||||||
\(322\) | 2.18034 | 0.121506 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 15.0902 | 0.838343 | ||||||||
\(325\) | 12.9443 | 0.718019 | ||||||||
\(326\) | −17.3262 | −0.959612 | ||||||||
\(327\) | 45.1246 | 2.49540 | ||||||||
\(328\) | 15.6525 | 0.864263 | ||||||||
\(329\) | −0.583592 | −0.0321745 | ||||||||
\(330\) | 10.4721 | 0.576472 | ||||||||
\(331\) | 2.00000 | 0.109930 | 0.0549650 | − | 0.998488i | \(-0.482495\pi\) | ||||
0.0549650 | + | 0.998488i | \(0.482495\pi\) | |||||||
\(332\) | −9.23607 | −0.506895 | ||||||||
\(333\) | 14.9443 | 0.818941 | ||||||||
\(334\) | 10.4721 | 0.573010 | ||||||||
\(335\) | −8.00000 | −0.437087 | ||||||||
\(336\) | 3.70820 | 0.202299 | ||||||||
\(337\) | 14.7639 | 0.804243 | 0.402121 | − | 0.915586i | \(-0.368273\pi\) | ||||
0.402121 | + | 0.915586i | \(0.368273\pi\) | |||||||
\(338\) | −4.09017 | −0.222476 | ||||||||
\(339\) | −11.2361 | −0.610259 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00000 | 0.108306 | ||||||||
\(342\) | −27.0344 | −1.46186 | ||||||||
\(343\) | 3.29180 | 0.177740 | ||||||||
\(344\) | −2.76393 | −0.149021 | ||||||||
\(345\) | 18.4721 | 0.994506 | ||||||||
\(346\) | −4.76393 | −0.256111 | ||||||||
\(347\) | −24.1803 | −1.29807 | −0.649034 | − | 0.760759i | \(-0.724827\pi\) | ||||
−0.649034 | + | 0.760759i | \(0.724827\pi\) | |||||||
\(348\) | −5.52786 | −0.296325 | ||||||||
\(349\) | −7.88854 | −0.422264 | −0.211132 | − | 0.977458i | \(-0.567715\pi\) | ||||
−0.211132 | + | 0.977458i | \(0.567715\pi\) | |||||||
\(350\) | 1.52786 | 0.0816678 | ||||||||
\(351\) | −46.8328 | −2.49975 | ||||||||
\(352\) | 6.76393 | 0.360519 | ||||||||
\(353\) | 7.41641 | 0.394736 | 0.197368 | − | 0.980330i | \(-0.436761\pi\) | ||||
0.197368 | + | 0.980330i | \(0.436761\pi\) | |||||||
\(354\) | 11.7082 | 0.622284 | ||||||||
\(355\) | −9.18034 | −0.487242 | ||||||||
\(356\) | 7.23607 | 0.383511 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.76393 | 0.146078 | ||||||||
\(359\) | 22.2361 | 1.17357 | 0.586787 | − | 0.809741i | \(-0.300392\pi\) | ||||
0.586787 | + | 0.809741i | \(0.300392\pi\) | |||||||
\(360\) | 16.7082 | 0.880600 | ||||||||
\(361\) | −14.0000 | −0.736842 | ||||||||
\(362\) | 6.76393 | 0.355504 | ||||||||
\(363\) | −22.6525 | −1.18895 | ||||||||
\(364\) | 0.472136 | 0.0247466 | ||||||||
\(365\) | 8.47214 | 0.443452 | ||||||||
\(366\) | −42.8328 | −2.23891 | ||||||||
\(367\) | −18.0000 | −0.939592 | −0.469796 | − | 0.882775i | \(-0.655673\pi\) | ||||
−0.469796 | + | 0.882775i | \(0.655673\pi\) | |||||||
\(368\) | 27.7082 | 1.44439 | ||||||||
\(369\) | −52.3050 | −2.72289 | ||||||||
\(370\) | −3.23607 | −0.168235 | ||||||||
\(371\) | 2.47214 | 0.128347 | ||||||||
\(372\) | −2.00000 | −0.103695 | ||||||||
\(373\) | 19.0000 | 0.983783 | 0.491891 | − | 0.870657i | \(-0.336306\pi\) | ||||
0.491891 | + | 0.870657i | \(0.336306\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 29.1246 | 1.50399 | ||||||||
\(376\) | −5.52786 | −0.285078 | ||||||||
\(377\) | 8.94427 | 0.460653 | ||||||||
\(378\) | −5.52786 | −0.284323 | ||||||||
\(379\) | 2.11146 | 0.108458 | 0.0542291 | − | 0.998529i | \(-0.482730\pi\) | ||||
0.0542291 | + | 0.998529i | \(0.482730\pi\) | |||||||
\(380\) | 1.38197 | 0.0708934 | ||||||||
\(381\) | 40.3607 | 2.06774 | ||||||||
\(382\) | −31.0344 | −1.58786 | ||||||||
\(383\) | −23.8885 | −1.22065 | −0.610324 | − | 0.792152i | \(-0.708961\pi\) | ||||
−0.610324 | + | 0.792152i | \(0.708961\pi\) | |||||||
\(384\) | 44.0689 | 2.24888 | ||||||||
\(385\) | −0.472136 | −0.0240623 | ||||||||
\(386\) | −5.61803 | −0.285950 | ||||||||
\(387\) | 9.23607 | 0.469496 | ||||||||
\(388\) | 9.85410 | 0.500266 | ||||||||
\(389\) | −17.8885 | −0.906985 | −0.453493 | − | 0.891260i | \(-0.649822\pi\) | ||||
−0.453493 | + | 0.891260i | \(0.649822\pi\) | |||||||
\(390\) | 16.9443 | 0.858007 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 15.5279 | 0.784276 | ||||||||
\(393\) | −38.8328 | −1.95886 | ||||||||
\(394\) | −18.4721 | −0.930613 | ||||||||
\(395\) | −11.7082 | −0.589104 | ||||||||
\(396\) | −9.23607 | −0.464130 | ||||||||
\(397\) | 7.00000 | 0.351320 | 0.175660 | − | 0.984451i | \(-0.443794\pi\) | ||||
0.175660 | + | 0.984451i | \(0.443794\pi\) | |||||||
\(398\) | 30.6525 | 1.53647 | ||||||||
\(399\) | 1.70820 | 0.0855172 | ||||||||
\(400\) | 19.4164 | 0.970820 | ||||||||
\(401\) | −38.1803 | −1.90664 | −0.953318 | − | 0.301969i | \(-0.902356\pi\) | ||||
−0.953318 | + | 0.301969i | \(0.902356\pi\) | |||||||
\(402\) | 41.8885 | 2.08921 | ||||||||
\(403\) | 3.23607 | 0.161200 | ||||||||
\(404\) | −1.85410 | −0.0922450 | ||||||||
\(405\) | −24.4164 | −1.21326 | ||||||||
\(406\) | 1.05573 | 0.0523949 | ||||||||
\(407\) | −4.00000 | −0.198273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.81966 | −0.188870 | −0.0944350 | − | 0.995531i | \(-0.530104\pi\) | ||||
−0.0944350 | + | 0.995531i | \(0.530104\pi\) | |||||||
\(410\) | 11.3262 | 0.559363 | ||||||||
\(411\) | 20.3607 | 1.00432 | ||||||||
\(412\) | 3.85410 | 0.189878 | ||||||||
\(413\) | −0.527864 | −0.0259745 | ||||||||
\(414\) | −69.0132 | −3.39181 | ||||||||
\(415\) | 14.9443 | 0.733585 | ||||||||
\(416\) | 10.9443 | 0.536587 | ||||||||
\(417\) | −43.4164 | −2.12611 | ||||||||
\(418\) | 7.23607 | 0.353928 | ||||||||
\(419\) | 10.1246 | 0.494620 | 0.247310 | − | 0.968936i | \(-0.420453\pi\) | ||||
0.247310 | + | 0.968936i | \(0.420453\pi\) | |||||||
\(420\) | 0.472136 | 0.0230379 | ||||||||
\(421\) | 29.3607 | 1.43095 | 0.715476 | − | 0.698637i | \(-0.246210\pi\) | ||||
0.715476 | + | 0.698637i | \(0.246210\pi\) | |||||||
\(422\) | −37.5066 | −1.82579 | ||||||||
\(423\) | 18.4721 | 0.898146 | ||||||||
\(424\) | 23.4164 | 1.13720 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 48.0689 | 2.32895 | ||||||||
\(427\) | 1.93112 | 0.0934533 | ||||||||
\(428\) | −3.56231 | −0.172191 | ||||||||
\(429\) | 20.9443 | 1.01120 | ||||||||
\(430\) | −2.00000 | −0.0964486 | ||||||||
\(431\) | −12.0000 | −0.578020 | −0.289010 | − | 0.957326i | \(-0.593326\pi\) | ||||
−0.289010 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(432\) | −70.2492 | −3.37987 | ||||||||
\(433\) | 10.1803 | 0.489236 | 0.244618 | − | 0.969620i | \(-0.421337\pi\) | ||||
0.244618 | + | 0.969620i | \(0.421337\pi\) | |||||||
\(434\) | 0.381966 | 0.0183350 | ||||||||
\(435\) | 8.94427 | 0.428845 | ||||||||
\(436\) | 8.61803 | 0.412729 | ||||||||
\(437\) | 12.7639 | 0.610582 | ||||||||
\(438\) | −44.3607 | −2.11964 | ||||||||
\(439\) | 1.18034 | 0.0563345 | 0.0281673 | − | 0.999603i | \(-0.491033\pi\) | ||||
0.0281673 | + | 0.999603i | \(0.491033\pi\) | |||||||
\(440\) | −4.47214 | −0.213201 | ||||||||
\(441\) | −51.8885 | −2.47088 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.7082 | 1.45899 | 0.729495 | − | 0.683986i | \(-0.239755\pi\) | ||||
0.729495 | + | 0.683986i | \(0.239755\pi\) | |||||||
\(444\) | 4.00000 | 0.189832 | ||||||||
\(445\) | −11.7082 | −0.555022 | ||||||||
\(446\) | 6.47214 | 0.306465 | ||||||||
\(447\) | 32.3607 | 1.53061 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 31.3050 | 1.47737 | 0.738686 | − | 0.674050i | \(-0.235447\pi\) | ||||
0.738686 | + | 0.674050i | \(0.235447\pi\) | |||||||
\(450\) | −48.3607 | −2.27974 | ||||||||
\(451\) | 14.0000 | 0.659234 | ||||||||
\(452\) | −2.14590 | −0.100935 | ||||||||
\(453\) | −45.8885 | −2.15603 | ||||||||
\(454\) | 10.4721 | 0.491482 | ||||||||
\(455\) | −0.763932 | −0.0358137 | ||||||||
\(456\) | 16.1803 | 0.757714 | ||||||||
\(457\) | −3.05573 | −0.142941 | −0.0714705 | − | 0.997443i | \(-0.522769\pi\) | ||||
−0.0714705 | + | 0.997443i | \(0.522769\pi\) | |||||||
\(458\) | −21.7082 | −1.01436 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.52786 | 0.164488 | ||||||||
\(461\) | 34.3607 | 1.60034 | 0.800168 | − | 0.599776i | \(-0.204744\pi\) | ||||
0.800168 | + | 0.599776i | \(0.204744\pi\) | |||||||
\(462\) | 2.47214 | 0.115014 | ||||||||
\(463\) | −2.58359 | −0.120070 | −0.0600349 | − | 0.998196i | \(-0.519121\pi\) | ||||
−0.0600349 | + | 0.998196i | \(0.519121\pi\) | |||||||
\(464\) | 13.4164 | 0.622841 | ||||||||
\(465\) | 3.23607 | 0.150069 | ||||||||
\(466\) | −29.0344 | −1.34499 | ||||||||
\(467\) | 4.70820 | 0.217870 | 0.108935 | − | 0.994049i | \(-0.465256\pi\) | ||||
0.108935 | + | 0.994049i | \(0.465256\pi\) | |||||||
\(468\) | −14.9443 | −0.690799 | ||||||||
\(469\) | −1.88854 | −0.0872049 | ||||||||
\(470\) | −4.00000 | −0.184506 | ||||||||
\(471\) | 67.5967 | 3.11469 | ||||||||
\(472\) | −5.00000 | −0.230144 | ||||||||
\(473\) | −2.47214 | −0.113669 | ||||||||
\(474\) | 61.3050 | 2.81583 | ||||||||
\(475\) | 8.94427 | 0.410391 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −78.2492 | −3.58279 | ||||||||
\(478\) | −18.9443 | −0.866491 | ||||||||
\(479\) | −23.2918 | −1.06423 | −0.532115 | − | 0.846672i | \(-0.678602\pi\) | ||||
−0.532115 | + | 0.846672i | \(0.678602\pi\) | |||||||
\(480\) | 10.9443 | 0.499535 | ||||||||
\(481\) | −6.47214 | −0.295104 | ||||||||
\(482\) | −23.2361 | −1.05837 | ||||||||
\(483\) | 4.36068 | 0.198418 | ||||||||
\(484\) | −4.32624 | −0.196647 | ||||||||
\(485\) | −15.9443 | −0.723992 | ||||||||
\(486\) | 57.5967 | 2.61264 | ||||||||
\(487\) | 19.2361 | 0.871669 | 0.435835 | − | 0.900027i | \(-0.356453\pi\) | ||||
0.435835 | + | 0.900027i | \(0.356453\pi\) | |||||||
\(488\) | 18.2918 | 0.828031 | ||||||||
\(489\) | −34.6525 | −1.56704 | ||||||||
\(490\) | 11.2361 | 0.507594 | ||||||||
\(491\) | 4.36068 | 0.196795 | 0.0983974 | − | 0.995147i | \(-0.468628\pi\) | ||||
0.0983974 | + | 0.995147i | \(0.468628\pi\) | |||||||
\(492\) | −14.0000 | −0.631169 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 11.7082 | 0.526777 | ||||||||
\(495\) | 14.9443 | 0.671695 | ||||||||
\(496\) | 4.85410 | 0.217956 | ||||||||
\(497\) | −2.16718 | −0.0972115 | ||||||||
\(498\) | −78.2492 | −3.50643 | ||||||||
\(499\) | 6.58359 | 0.294722 | 0.147361 | − | 0.989083i | \(-0.452922\pi\) | ||||
0.147361 | + | 0.989083i | \(0.452922\pi\) | |||||||
\(500\) | 5.56231 | 0.248754 | ||||||||
\(501\) | 20.9443 | 0.935721 | ||||||||
\(502\) | −2.94427 | −0.131409 | ||||||||
\(503\) | −29.6525 | −1.32214 | −0.661069 | − | 0.750325i | \(-0.729897\pi\) | ||||
−0.661069 | + | 0.750325i | \(0.729897\pi\) | |||||||
\(504\) | 3.94427 | 0.175692 | ||||||||
\(505\) | 3.00000 | 0.133498 | ||||||||
\(506\) | 18.4721 | 0.821187 | ||||||||
\(507\) | −8.18034 | −0.363302 | ||||||||
\(508\) | 7.70820 | 0.341996 | ||||||||
\(509\) | 29.5967 | 1.31185 | 0.655926 | − | 0.754825i | \(-0.272278\pi\) | ||||
0.655926 | + | 0.754825i | \(0.272278\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | 0.0884748 | ||||||||
\(512\) | −5.29180 | −0.233867 | ||||||||
\(513\) | −32.3607 | −1.42876 | ||||||||
\(514\) | 3.14590 | 0.138760 | ||||||||
\(515\) | −6.23607 | −0.274794 | ||||||||
\(516\) | 2.47214 | 0.108830 | ||||||||
\(517\) | −4.94427 | −0.217449 | ||||||||
\(518\) | −0.763932 | −0.0335652 | ||||||||
\(519\) | −9.52786 | −0.418227 | ||||||||
\(520\) | −7.23607 | −0.317323 | ||||||||
\(521\) | −2.00000 | −0.0876216 | −0.0438108 | − | 0.999040i | \(-0.513950\pi\) | ||||
−0.0438108 | + | 0.999040i | \(0.513950\pi\) | |||||||
\(522\) | −33.4164 | −1.46260 | ||||||||
\(523\) | −17.7082 | −0.774326 | −0.387163 | − | 0.922011i | \(-0.626545\pi\) | ||||
−0.387163 | + | 0.922011i | \(0.626545\pi\) | |||||||
\(524\) | −7.41641 | −0.323987 | ||||||||
\(525\) | 3.05573 | 0.133363 | ||||||||
\(526\) | −37.5967 | −1.63930 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 31.4164 | 1.36722 | ||||||||
\(529\) | 9.58359 | 0.416678 | ||||||||
\(530\) | 16.9443 | 0.736012 | ||||||||
\(531\) | 16.7082 | 0.725074 | ||||||||
\(532\) | 0.326238 | 0.0141442 | ||||||||
\(533\) | 22.6525 | 0.981188 | ||||||||
\(534\) | 61.3050 | 2.65292 | ||||||||
\(535\) | 5.76393 | 0.249197 | ||||||||
\(536\) | −17.8885 | −0.772667 | ||||||||
\(537\) | 5.52786 | 0.238545 | ||||||||
\(538\) | 17.8885 | 0.771230 | ||||||||
\(539\) | 13.8885 | 0.598222 | ||||||||
\(540\) | −8.94427 | −0.384900 | ||||||||
\(541\) | 25.3607 | 1.09034 | 0.545170 | − | 0.838325i | \(-0.316465\pi\) | ||||
0.545170 | + | 0.838325i | \(0.316465\pi\) | |||||||
\(542\) | −22.9443 | −0.985541 | ||||||||
\(543\) | 13.5279 | 0.580536 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.9443 | −0.597307 | ||||||||
\(546\) | 4.00000 | 0.171184 | ||||||||
\(547\) | 12.1246 | 0.518411 | 0.259205 | − | 0.965822i | \(-0.416539\pi\) | ||||
0.259205 | + | 0.965822i | \(0.416539\pi\) | |||||||
\(548\) | 3.88854 | 0.166110 | ||||||||
\(549\) | −61.1246 | −2.60873 | ||||||||
\(550\) | 12.9443 | 0.551946 | ||||||||
\(551\) | 6.18034 | 0.263291 | ||||||||
\(552\) | 41.3050 | 1.75806 | ||||||||
\(553\) | −2.76393 | −0.117534 | ||||||||
\(554\) | 20.4721 | 0.869778 | ||||||||
\(555\) | −6.47214 | −0.274727 | ||||||||
\(556\) | −8.29180 | −0.351650 | ||||||||
\(557\) | −12.0000 | −0.508456 | −0.254228 | − | 0.967144i | \(-0.581821\pi\) | ||||
−0.254228 | + | 0.967144i | \(0.581821\pi\) | |||||||
\(558\) | −12.0902 | −0.511818 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | −1.14590 | −0.0484230 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.5066 | 1.16029 | ||||||||
\(563\) | 27.5410 | 1.16072 | 0.580358 | − | 0.814362i | \(-0.302913\pi\) | ||||
0.580358 | + | 0.814362i | \(0.302913\pi\) | |||||||
\(564\) | 4.94427 | 0.208191 | ||||||||
\(565\) | 3.47214 | 0.146074 | ||||||||
\(566\) | 22.4721 | 0.944574 | ||||||||
\(567\) | −5.76393 | −0.242062 | ||||||||
\(568\) | −20.5279 | −0.861330 | ||||||||
\(569\) | 5.52786 | 0.231740 | 0.115870 | − | 0.993264i | \(-0.463034\pi\) | ||||
0.115870 | + | 0.993264i | \(0.463034\pi\) | |||||||
\(570\) | 11.7082 | 0.490403 | ||||||||
\(571\) | −28.1803 | −1.17931 | −0.589655 | − | 0.807655i | \(-0.700736\pi\) | ||||
−0.589655 | + | 0.807655i | \(0.700736\pi\) | |||||||
\(572\) | 4.00000 | 0.167248 | ||||||||
\(573\) | −62.0689 | −2.59296 | ||||||||
\(574\) | 2.67376 | 0.111601 | ||||||||
\(575\) | 22.8328 | 0.952194 | ||||||||
\(576\) | 31.6525 | 1.31885 | ||||||||
\(577\) | −28.8328 | −1.20033 | −0.600163 | − | 0.799878i | \(-0.704898\pi\) | ||||
−0.600163 | + | 0.799878i | \(0.704898\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.2361 | −0.466955 | ||||||||
\(580\) | 1.70820 | 0.0709293 | ||||||||
\(581\) | 3.52786 | 0.146360 | ||||||||
\(582\) | 83.4853 | 3.46058 | ||||||||
\(583\) | 20.9443 | 0.867423 | ||||||||
\(584\) | 18.9443 | 0.783920 | ||||||||
\(585\) | 24.1803 | 0.999734 | ||||||||
\(586\) | −0.763932 | −0.0315577 | ||||||||
\(587\) | −6.47214 | −0.267134 | −0.133567 | − | 0.991040i | \(-0.542643\pi\) | ||||
−0.133567 | + | 0.991040i | \(0.542643\pi\) | |||||||
\(588\) | −13.8885 | −0.572754 | ||||||||
\(589\) | 2.23607 | 0.0921356 | ||||||||
\(590\) | −3.61803 | −0.148952 | ||||||||
\(591\) | −36.9443 | −1.51968 | ||||||||
\(592\) | −9.70820 | −0.399005 | ||||||||
\(593\) | −6.52786 | −0.268067 | −0.134034 | − | 0.990977i | \(-0.542793\pi\) | ||||
−0.134034 | + | 0.990977i | \(0.542793\pi\) | |||||||
\(594\) | −46.8328 | −1.92157 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.18034 | 0.253157 | ||||||||
\(597\) | 61.3050 | 2.50904 | ||||||||
\(598\) | 29.8885 | 1.22223 | ||||||||
\(599\) | −14.5967 | −0.596407 | −0.298203 | − | 0.954502i | \(-0.596387\pi\) | ||||
−0.298203 | + | 0.954502i | \(0.596387\pi\) | |||||||
\(600\) | 28.9443 | 1.18164 | ||||||||
\(601\) | −30.5410 | −1.24579 | −0.622897 | − | 0.782304i | \(-0.714044\pi\) | ||||
−0.622897 | + | 0.782304i | \(0.714044\pi\) | |||||||
\(602\) | −0.472136 | −0.0192428 | ||||||||
\(603\) | 59.7771 | 2.43431 | ||||||||
\(604\) | −8.76393 | −0.356599 | ||||||||
\(605\) | 7.00000 | 0.284590 | ||||||||
\(606\) | −15.7082 | −0.638102 | ||||||||
\(607\) | −22.4721 | −0.912116 | −0.456058 | − | 0.889950i | \(-0.650739\pi\) | ||||
−0.456058 | + | 0.889950i | \(0.650739\pi\) | |||||||
\(608\) | 7.56231 | 0.306692 | ||||||||
\(609\) | 2.11146 | 0.0855605 | ||||||||
\(610\) | 13.2361 | 0.535913 | ||||||||
\(611\) | −8.00000 | −0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −43.8885 | −1.77264 | −0.886321 | − | 0.463072i | \(-0.846747\pi\) | ||||
−0.886321 | + | 0.463072i | \(0.846747\pi\) | |||||||
\(614\) | −46.4508 | −1.87460 | ||||||||
\(615\) | 22.6525 | 0.913436 | ||||||||
\(616\) | −1.05573 | −0.0425365 | ||||||||
\(617\) | −32.4721 | −1.30728 | −0.653639 | − | 0.756806i | \(-0.726759\pi\) | ||||
−0.653639 | + | 0.756806i | \(0.726759\pi\) | |||||||
\(618\) | 32.6525 | 1.31348 | ||||||||
\(619\) | −6.18034 | −0.248409 | −0.124204 | − | 0.992257i | \(-0.539638\pi\) | ||||
−0.124204 | + | 0.992257i | \(0.539638\pi\) | |||||||
\(620\) | 0.618034 | 0.0248208 | ||||||||
\(621\) | −82.6099 | −3.31502 | ||||||||
\(622\) | 47.2148 | 1.89314 | ||||||||
\(623\) | −2.76393 | −0.110735 | ||||||||
\(624\) | 50.8328 | 2.03494 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | −27.1246 | −1.08412 | ||||||||
\(627\) | 14.4721 | 0.577961 | ||||||||
\(628\) | 12.9098 | 0.515158 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 2.85410 | 0.113710 | ||||||||
\(631\) | 34.3607 | 1.36788 | 0.683939 | − | 0.729540i | \(-0.260266\pi\) | ||||
0.683939 | + | 0.729540i | \(0.260266\pi\) | |||||||
\(632\) | −26.1803 | −1.04140 | ||||||||
\(633\) | −75.0132 | −2.98151 | ||||||||
\(634\) | −6.56231 | −0.260622 | ||||||||
\(635\) | −12.4721 | −0.494942 | ||||||||
\(636\) | −20.9443 | −0.830494 | ||||||||
\(637\) | 22.4721 | 0.890378 | ||||||||
\(638\) | 8.94427 | 0.354107 | ||||||||
\(639\) | 68.5967 | 2.71365 | ||||||||
\(640\) | −13.6180 | −0.538300 | ||||||||
\(641\) | −12.0000 | −0.473972 | −0.236986 | − | 0.971513i | \(-0.576159\pi\) | ||||
−0.236986 | + | 0.971513i | \(0.576159\pi\) | |||||||
\(642\) | −30.1803 | −1.19112 | ||||||||
\(643\) | −19.5279 | −0.770104 | −0.385052 | − | 0.922895i | \(-0.625816\pi\) | ||||
−0.385052 | + | 0.922895i | \(0.625816\pi\) | |||||||
\(644\) | 0.832816 | 0.0328175 | ||||||||
\(645\) | −4.00000 | −0.157500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.944272 | −0.0371232 | −0.0185616 | − | 0.999828i | \(-0.505909\pi\) | ||||
−0.0185616 | + | 0.999828i | \(0.505909\pi\) | |||||||
\(648\) | −54.5967 | −2.14476 | ||||||||
\(649\) | −4.47214 | −0.175547 | ||||||||
\(650\) | 20.9443 | 0.821502 | ||||||||
\(651\) | 0.763932 | 0.0299409 | ||||||||
\(652\) | −6.61803 | −0.259182 | ||||||||
\(653\) | 47.3050 | 1.85119 | 0.925593 | − | 0.378521i | \(-0.123567\pi\) | ||||
0.925593 | + | 0.378521i | \(0.123567\pi\) | |||||||
\(654\) | 73.0132 | 2.85504 | ||||||||
\(655\) | 12.0000 | 0.468879 | ||||||||
\(656\) | 33.9787 | 1.32665 | ||||||||
\(657\) | −63.3050 | −2.46976 | ||||||||
\(658\) | −0.944272 | −0.0368116 | ||||||||
\(659\) | 25.6525 | 0.999279 | 0.499639 | − | 0.866234i | \(-0.333466\pi\) | ||||
0.499639 | + | 0.866234i | \(0.333466\pi\) | |||||||
\(660\) | 4.00000 | 0.155700 | ||||||||
\(661\) | −0.639320 | −0.0248667 | −0.0124333 | − | 0.999923i | \(-0.503958\pi\) | ||||
−0.0124333 | + | 0.999923i | \(0.503958\pi\) | |||||||
\(662\) | 3.23607 | 0.125773 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 33.4164 | 1.29681 | ||||||||
\(665\) | −0.527864 | −0.0204697 | ||||||||
\(666\) | 24.1803 | 0.936969 | ||||||||
\(667\) | 15.7771 | 0.610891 | ||||||||
\(668\) | 4.00000 | 0.154765 | ||||||||
\(669\) | 12.9443 | 0.500454 | ||||||||
\(670\) | −12.9443 | −0.500081 | ||||||||
\(671\) | 16.3607 | 0.631597 | ||||||||
\(672\) | 2.58359 | 0.0996642 | ||||||||
\(673\) | 29.0132 | 1.11837 | 0.559187 | − | 0.829041i | \(-0.311113\pi\) | ||||
0.559187 | + | 0.829041i | \(0.311113\pi\) | |||||||
\(674\) | 23.8885 | 0.920152 | ||||||||
\(675\) | −57.8885 | −2.22813 | ||||||||
\(676\) | −1.56231 | −0.0600887 | ||||||||
\(677\) | 46.7214 | 1.79565 | 0.897824 | − | 0.440355i | \(-0.145147\pi\) | ||||
0.897824 | + | 0.440355i | \(0.145147\pi\) | |||||||
\(678\) | −18.1803 | −0.698212 | ||||||||
\(679\) | −3.76393 | −0.144446 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.9443 | 0.802586 | ||||||||
\(682\) | 3.23607 | 0.123915 | ||||||||
\(683\) | −5.18034 | −0.198220 | −0.0991101 | − | 0.995076i | \(-0.531600\pi\) | ||||
−0.0991101 | + | 0.995076i | \(0.531600\pi\) | |||||||
\(684\) | −10.3262 | −0.394834 | ||||||||
\(685\) | −6.29180 | −0.240397 | ||||||||
\(686\) | 5.32624 | 0.203357 | ||||||||
\(687\) | −43.4164 | −1.65644 | ||||||||
\(688\) | −6.00000 | −0.228748 | ||||||||
\(689\) | 33.8885 | 1.29105 | ||||||||
\(690\) | 29.8885 | 1.13784 | ||||||||
\(691\) | −3.18034 | −0.120986 | −0.0604929 | − | 0.998169i | \(-0.519267\pi\) | ||||
−0.0604929 | + | 0.998169i | \(0.519267\pi\) | |||||||
\(692\) | −1.81966 | −0.0691731 | ||||||||
\(693\) | 3.52786 | 0.134012 | ||||||||
\(694\) | −39.1246 | −1.48515 | ||||||||
\(695\) | 13.4164 | 0.508913 | ||||||||
\(696\) | 20.0000 | 0.758098 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −12.7639 | −0.483122 | ||||||||
\(699\) | −58.0689 | −2.19637 | ||||||||
\(700\) | 0.583592 | 0.0220577 | ||||||||
\(701\) | 7.00000 | 0.264386 | 0.132193 | − | 0.991224i | \(-0.457798\pi\) | ||||
0.132193 | + | 0.991224i | \(0.457798\pi\) | |||||||
\(702\) | −75.7771 | −2.86002 | ||||||||
\(703\) | −4.47214 | −0.168670 | ||||||||
\(704\) | −8.47214 | −0.319306 | ||||||||
\(705\) | −8.00000 | −0.301297 | ||||||||
\(706\) | 12.0000 | 0.451626 | ||||||||
\(707\) | 0.708204 | 0.0266348 | ||||||||
\(708\) | 4.47214 | 0.168073 | ||||||||
\(709\) | −25.5279 | −0.958719 | −0.479360 | − | 0.877619i | \(-0.659131\pi\) | ||||
−0.479360 | + | 0.877619i | \(0.659131\pi\) | |||||||
\(710\) | −14.8541 | −0.557465 | ||||||||
\(711\) | 87.4853 | 3.28095 | ||||||||
\(712\) | −26.1803 | −0.981150 | ||||||||
\(713\) | 5.70820 | 0.213774 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.47214 | −0.242044 | ||||||||
\(716\) | 1.05573 | 0.0394544 | ||||||||
\(717\) | −37.8885 | −1.41497 | ||||||||
\(718\) | 35.9787 | 1.34271 | ||||||||
\(719\) | 13.8197 | 0.515386 | 0.257693 | − | 0.966227i | \(-0.417038\pi\) | ||||
0.257693 | + | 0.966227i | \(0.417038\pi\) | |||||||
\(720\) | 36.2705 | 1.35172 | ||||||||
\(721\) | −1.47214 | −0.0548252 | ||||||||
\(722\) | −22.6525 | −0.843038 | ||||||||
\(723\) | −46.4721 | −1.72832 | ||||||||
\(724\) | 2.58359 | 0.0960184 | ||||||||
\(725\) | 11.0557 | 0.410599 | ||||||||
\(726\) | −36.6525 | −1.36030 | ||||||||
\(727\) | −44.2361 | −1.64062 | −0.820312 | − | 0.571916i | \(-0.806200\pi\) | ||||
−0.820312 | + | 0.571916i | \(0.806200\pi\) | |||||||
\(728\) | −1.70820 | −0.0633102 | ||||||||
\(729\) | 41.9443 | 1.55349 | ||||||||
\(730\) | 13.7082 | 0.507363 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −16.3607 | −0.604708 | ||||||||
\(733\) | 3.47214 | 0.128246 | 0.0641231 | − | 0.997942i | \(-0.479575\pi\) | ||||
0.0641231 | + | 0.997942i | \(0.479575\pi\) | |||||||
\(734\) | −29.1246 | −1.07501 | ||||||||
\(735\) | 22.4721 | 0.828897 | ||||||||
\(736\) | 19.3050 | 0.711590 | ||||||||
\(737\) | −16.0000 | −0.589368 | ||||||||
\(738\) | −84.6312 | −3.11532 | ||||||||
\(739\) | 6.18034 | 0.227347 | 0.113674 | − | 0.993518i | \(-0.463738\pi\) | ||||
0.113674 | + | 0.993518i | \(0.463738\pi\) | |||||||
\(740\) | −1.23607 | −0.0454388 | ||||||||
\(741\) | 23.4164 | 0.860223 | ||||||||
\(742\) | 4.00000 | 0.146845 | ||||||||
\(743\) | −50.1803 | −1.84094 | −0.920469 | − | 0.390815i | \(-0.872193\pi\) | ||||
−0.920469 | + | 0.390815i | \(0.872193\pi\) | |||||||
\(744\) | 7.23607 | 0.265287 | ||||||||
\(745\) | −10.0000 | −0.366372 | ||||||||
\(746\) | 30.7426 | 1.12557 | ||||||||
\(747\) | −111.666 | −4.08563 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.36068 | 0.0497182 | ||||||||
\(750\) | 47.1246 | 1.72075 | ||||||||
\(751\) | 21.5410 | 0.786043 | 0.393021 | − | 0.919529i | \(-0.371430\pi\) | ||||
0.393021 | + | 0.919529i | \(0.371430\pi\) | |||||||
\(752\) | −12.0000 | −0.437595 | ||||||||
\(753\) | −5.88854 | −0.214590 | ||||||||
\(754\) | 14.4721 | 0.527044 | ||||||||
\(755\) | 14.1803 | 0.516075 | ||||||||
\(756\) | −2.11146 | −0.0767929 | ||||||||
\(757\) | 8.65248 | 0.314480 | 0.157240 | − | 0.987560i | \(-0.449740\pi\) | ||||
0.157240 | + | 0.987560i | \(0.449740\pi\) | |||||||
\(758\) | 3.41641 | 0.124090 | ||||||||
\(759\) | 36.9443 | 1.34099 | ||||||||
\(760\) | −5.00000 | −0.181369 | ||||||||
\(761\) | 2.00000 | 0.0724999 | 0.0362500 | − | 0.999343i | \(-0.488459\pi\) | ||||
0.0362500 | + | 0.999343i | \(0.488459\pi\) | |||||||
\(762\) | 65.3050 | 2.36575 | ||||||||
\(763\) | −3.29180 | −0.119171 | ||||||||
\(764\) | −11.8541 | −0.428866 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −38.6525 | −1.39657 | ||||||||
\(767\) | −7.23607 | −0.261279 | ||||||||
\(768\) | 43.8885 | 1.58369 | ||||||||
\(769\) | −47.3607 | −1.70787 | −0.853935 | − | 0.520380i | \(-0.825790\pi\) | ||||
−0.853935 | + | 0.520380i | \(0.825790\pi\) | |||||||
\(770\) | −0.763932 | −0.0275302 | ||||||||
\(771\) | 6.29180 | 0.226594 | ||||||||
\(772\) | −2.14590 | −0.0772326 | ||||||||
\(773\) | −11.1246 | −0.400124 | −0.200062 | − | 0.979783i | \(-0.564114\pi\) | ||||
−0.200062 | + | 0.979783i | \(0.564114\pi\) | |||||||
\(774\) | 14.9443 | 0.537161 | ||||||||
\(775\) | 4.00000 | 0.143684 | ||||||||
\(776\) | −35.6525 | −1.27985 | ||||||||
\(777\) | −1.52786 | −0.0548118 | ||||||||
\(778\) | −28.9443 | −1.03770 | ||||||||
\(779\) | 15.6525 | 0.560808 | ||||||||
\(780\) | 6.47214 | 0.231740 | ||||||||
\(781\) | −18.3607 | −0.656997 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −40.0000 | −1.42948 | ||||||||
\(784\) | 33.7082 | 1.20386 | ||||||||
\(785\) | −20.8885 | −0.745544 | ||||||||
\(786\) | −62.8328 | −2.24117 | ||||||||
\(787\) | −7.34752 | −0.261911 | −0.130955 | − | 0.991388i | \(-0.541804\pi\) | ||||
−0.130955 | + | 0.991388i | \(0.541804\pi\) | |||||||
\(788\) | −7.05573 | −0.251350 | ||||||||
\(789\) | −75.1935 | −2.67696 | ||||||||
\(790\) | −18.9443 | −0.674007 | ||||||||
\(791\) | 0.819660 | 0.0291438 | ||||||||
\(792\) | 33.4164 | 1.18740 | ||||||||
\(793\) | 26.4721 | 0.940053 | ||||||||
\(794\) | 11.3262 | 0.401953 | ||||||||
\(795\) | 33.8885 | 1.20190 | ||||||||
\(796\) | 11.7082 | 0.414986 | ||||||||
\(797\) | −55.4164 | −1.96295 | −0.981475 | − | 0.191591i | \(-0.938635\pi\) | ||||
−0.981475 | + | 0.191591i | \(0.938635\pi\) | |||||||
\(798\) | 2.76393 | 0.0978421 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 13.5279 | 0.478282 | ||||||||
\(801\) | 87.4853 | 3.09114 | ||||||||
\(802\) | −61.7771 | −2.18142 | ||||||||
\(803\) | 16.9443 | 0.597950 | ||||||||
\(804\) | 16.0000 | 0.564276 | ||||||||
\(805\) | −1.34752 | −0.0474940 | ||||||||
\(806\) | 5.23607 | 0.184433 | ||||||||
\(807\) | 35.7771 | 1.25941 | ||||||||
\(808\) | 6.70820 | 0.235994 | ||||||||
\(809\) | −23.4164 | −0.823277 | −0.411639 | − | 0.911347i | \(-0.635043\pi\) | ||||
−0.411639 | + | 0.911347i | \(0.635043\pi\) | |||||||
\(810\) | −39.5066 | −1.38812 | ||||||||
\(811\) | 28.0000 | 0.983213 | 0.491606 | − | 0.870817i | \(-0.336410\pi\) | ||||
0.491606 | + | 0.870817i | \(0.336410\pi\) | |||||||
\(812\) | 0.403252 | 0.0141514 | ||||||||
\(813\) | −45.8885 | −1.60938 | ||||||||
\(814\) | −6.47214 | −0.226848 | ||||||||
\(815\) | 10.7082 | 0.375092 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.76393 | −0.0966977 | ||||||||
\(818\) | −6.18034 | −0.216091 | ||||||||
\(819\) | 5.70820 | 0.199461 | ||||||||
\(820\) | 4.32624 | 0.151079 | ||||||||
\(821\) | −30.5410 | −1.06589 | −0.532944 | − | 0.846150i | \(-0.678915\pi\) | ||||
−0.532944 | + | 0.846150i | \(0.678915\pi\) | |||||||
\(822\) | 32.9443 | 1.14906 | ||||||||
\(823\) | 14.2918 | 0.498181 | 0.249090 | − | 0.968480i | \(-0.419868\pi\) | ||||
0.249090 | + | 0.968480i | \(0.419868\pi\) | |||||||
\(824\) | −13.9443 | −0.485772 | ||||||||
\(825\) | 25.8885 | 0.901323 | ||||||||
\(826\) | −0.854102 | −0.0297180 | ||||||||
\(827\) | −17.3475 | −0.603233 | −0.301616 | − | 0.953429i | \(-0.597526\pi\) | ||||
−0.301616 | + | 0.953429i | \(0.597526\pi\) | |||||||
\(828\) | −26.3607 | −0.916097 | ||||||||
\(829\) | 16.8328 | 0.584628 | 0.292314 | − | 0.956322i | \(-0.405575\pi\) | ||||
0.292314 | + | 0.956322i | \(0.405575\pi\) | |||||||
\(830\) | 24.1803 | 0.839312 | ||||||||
\(831\) | 40.9443 | 1.42034 | ||||||||
\(832\) | −13.7082 | −0.475246 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −70.2492 | −2.43253 | ||||||||
\(835\) | −6.47214 | −0.223978 | ||||||||
\(836\) | 2.76393 | 0.0955926 | ||||||||
\(837\) | −14.4721 | −0.500230 | ||||||||
\(838\) | 16.3820 | 0.565906 | ||||||||
\(839\) | −28.9443 | −0.999267 | −0.499634 | − | 0.866237i | \(-0.666532\pi\) | ||||
−0.499634 | + | 0.866237i | \(0.666532\pi\) | |||||||
\(840\) | −1.70820 | −0.0589386 | ||||||||
\(841\) | −21.3607 | −0.736575 | ||||||||
\(842\) | 47.5066 | 1.63718 | ||||||||
\(843\) | 55.0132 | 1.89475 | ||||||||
\(844\) | −14.3262 | −0.493129 | ||||||||
\(845\) | 2.52786 | 0.0869612 | ||||||||
\(846\) | 29.8885 | 1.02759 | ||||||||
\(847\) | 1.65248 | 0.0567797 | ||||||||
\(848\) | 50.8328 | 1.74561 | ||||||||
\(849\) | 44.9443 | 1.54248 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.4164 | −0.391349 | ||||||||
\(852\) | 18.3607 | 0.629027 | ||||||||
\(853\) | −10.5836 | −0.362375 | −0.181188 | − | 0.983449i | \(-0.557994\pi\) | ||||
−0.181188 | + | 0.983449i | \(0.557994\pi\) | |||||||
\(854\) | 3.12461 | 0.106922 | ||||||||
\(855\) | 16.7082 | 0.571409 | ||||||||
\(856\) | 12.8885 | 0.440521 | ||||||||
\(857\) | 55.6656 | 1.90150 | 0.950751 | − | 0.309956i | \(-0.100314\pi\) | ||||
0.950751 | + | 0.309956i | \(0.100314\pi\) | |||||||
\(858\) | 33.8885 | 1.15694 | ||||||||
\(859\) | 2.11146 | 0.0720420 | 0.0360210 | − | 0.999351i | \(-0.488532\pi\) | ||||
0.0360210 | + | 0.999351i | \(0.488532\pi\) | |||||||
\(860\) | −0.763932 | −0.0260499 | ||||||||
\(861\) | 5.34752 | 0.182243 | ||||||||
\(862\) | −19.4164 | −0.661325 | ||||||||
\(863\) | −9.81966 | −0.334265 | −0.167133 | − | 0.985934i | \(-0.553451\pi\) | ||||
−0.167133 | + | 0.985934i | \(0.553451\pi\) | |||||||
\(864\) | −48.9443 | −1.66512 | ||||||||
\(865\) | 2.94427 | 0.100108 | ||||||||
\(866\) | 16.4721 | 0.559746 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.145898 | 0.00495210 | ||||||||
\(869\) | −23.4164 | −0.794347 | ||||||||
\(870\) | 14.4721 | 0.490651 | ||||||||
\(871\) | −25.8885 | −0.877200 | ||||||||
\(872\) | −31.1803 | −1.05590 | ||||||||
\(873\) | 119.138 | 4.03220 | ||||||||
\(874\) | 20.6525 | 0.698580 | ||||||||
\(875\) | −2.12461 | −0.0718250 | ||||||||
\(876\) | −16.9443 | −0.572494 | ||||||||
\(877\) | 18.0557 | 0.609699 | 0.304849 | − | 0.952401i | \(-0.401394\pi\) | ||||
0.304849 | + | 0.952401i | \(0.401394\pi\) | |||||||
\(878\) | 1.90983 | 0.0644536 | ||||||||
\(879\) | −1.52786 | −0.0515336 | ||||||||
\(880\) | −9.70820 | −0.327263 | ||||||||
\(881\) | 20.3607 | 0.685969 | 0.342984 | − | 0.939341i | \(-0.388562\pi\) | ||||
0.342984 | + | 0.939341i | \(0.388562\pi\) | |||||||
\(882\) | −83.9574 | −2.82699 | ||||||||
\(883\) | −31.7771 | −1.06938 | −0.534692 | − | 0.845047i | \(-0.679572\pi\) | ||||
−0.534692 | + | 0.845047i | \(0.679572\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.23607 | −0.243238 | ||||||||
\(886\) | 49.6869 | 1.66926 | ||||||||
\(887\) | −27.0689 | −0.908884 | −0.454442 | − | 0.890776i | \(-0.650161\pi\) | ||||
−0.454442 | + | 0.890776i | \(0.650161\pi\) | |||||||
\(888\) | −14.4721 | −0.485653 | ||||||||
\(889\) | −2.94427 | −0.0987477 | ||||||||
\(890\) | −18.9443 | −0.635013 | ||||||||
\(891\) | −48.8328 | −1.63596 | ||||||||
\(892\) | 2.47214 | 0.0827732 | ||||||||
\(893\) | −5.52786 | −0.184983 | ||||||||
\(894\) | 52.3607 | 1.75120 | ||||||||
\(895\) | −1.70820 | −0.0570990 | ||||||||
\(896\) | −3.21478 | −0.107398 | ||||||||
\(897\) | 59.7771 | 1.99590 | ||||||||
\(898\) | 50.6525 | 1.69030 | ||||||||
\(899\) | 2.76393 | 0.0921823 | ||||||||
\(900\) | −18.4721 | −0.615738 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 22.6525 | 0.754245 | ||||||||
\(903\) | −0.944272 | −0.0314234 | ||||||||
\(904\) | 7.76393 | 0.258225 | ||||||||
\(905\) | −4.18034 | −0.138959 | ||||||||
\(906\) | −74.2492 | −2.46677 | ||||||||
\(907\) | 24.2361 | 0.804745 | 0.402373 | − | 0.915476i | \(-0.368186\pi\) | ||||
0.402373 | + | 0.915476i | \(0.368186\pi\) | |||||||
\(908\) | 4.00000 | 0.132745 | ||||||||
\(909\) | −22.4164 | −0.743505 | ||||||||
\(910\) | −1.23607 | −0.0409753 | ||||||||
\(911\) | −18.1803 | −0.602342 | −0.301171 | − | 0.953570i | \(-0.597377\pi\) | ||||
−0.301171 | + | 0.953570i | \(0.597377\pi\) | |||||||
\(912\) | 35.1246 | 1.16309 | ||||||||
\(913\) | 29.8885 | 0.989166 | ||||||||
\(914\) | −4.94427 | −0.163542 | ||||||||
\(915\) | 26.4721 | 0.875142 | ||||||||
\(916\) | −8.29180 | −0.273969 | ||||||||
\(917\) | 2.83282 | 0.0935478 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.4721 | −0.477392 | −0.238696 | − | 0.971094i | \(-0.576720\pi\) | ||||
−0.238696 | + | 0.971094i | \(0.576720\pi\) | |||||||
\(920\) | −12.7639 | −0.420814 | ||||||||
\(921\) | −92.9017 | −3.06122 | ||||||||
\(922\) | 55.5967 | 1.83098 | ||||||||
\(923\) | −29.7082 | −0.977857 | ||||||||
\(924\) | 0.944272 | 0.0310643 | ||||||||
\(925\) | −8.00000 | −0.263038 | ||||||||
\(926\) | −4.18034 | −0.137374 | ||||||||
\(927\) | 46.5967 | 1.53044 | ||||||||
\(928\) | 9.34752 | 0.306848 | ||||||||
\(929\) | 20.0000 | 0.656179 | 0.328089 | − | 0.944647i | \(-0.393595\pi\) | ||||
0.328089 | + | 0.944647i | \(0.393595\pi\) | |||||||
\(930\) | 5.23607 | 0.171697 | ||||||||
\(931\) | 15.5279 | 0.508905 | ||||||||
\(932\) | −11.0902 | −0.363271 | ||||||||
\(933\) | 94.4296 | 3.09149 | ||||||||
\(934\) | 7.61803 | 0.249270 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 54.0689 | 1.76730 | ||||||||
\(937\) | 9.05573 | 0.295838 | 0.147919 | − | 0.988999i | \(-0.452743\pi\) | ||||
0.147919 | + | 0.988999i | \(0.452743\pi\) | |||||||
\(938\) | −3.05573 | −0.0997731 | ||||||||
\(939\) | −54.2492 | −1.77036 | ||||||||
\(940\) | −1.52786 | −0.0498334 | ||||||||
\(941\) | 38.0000 | 1.23876 | 0.619382 | − | 0.785090i | \(-0.287383\pi\) | ||||
0.619382 | + | 0.785090i | \(0.287383\pi\) | |||||||
\(942\) | 109.374 | 3.56359 | ||||||||
\(943\) | 39.9574 | 1.30119 | ||||||||
\(944\) | −10.8541 | −0.353271 | ||||||||
\(945\) | 3.41641 | 0.111136 | ||||||||
\(946\) | −4.00000 | −0.130051 | ||||||||
\(947\) | 13.0557 | 0.424254 | 0.212127 | − | 0.977242i | \(-0.431961\pi\) | ||||
0.212127 | + | 0.977242i | \(0.431961\pi\) | |||||||
\(948\) | 23.4164 | 0.760530 | ||||||||
\(949\) | 27.4164 | 0.889974 | ||||||||
\(950\) | 14.4721 | 0.469538 | ||||||||
\(951\) | −13.1246 | −0.425595 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.7082 | 1.48063 | 0.740317 | − | 0.672258i | \(-0.234675\pi\) | ||||
0.740317 | + | 0.672258i | \(0.234675\pi\) | |||||||
\(954\) | −126.610 | −4.09915 | ||||||||
\(955\) | 19.1803 | 0.620661 | ||||||||
\(956\) | −7.23607 | −0.234031 | ||||||||
\(957\) | 17.8885 | 0.578254 | ||||||||
\(958\) | −37.6869 | −1.21761 | ||||||||
\(959\) | −1.48529 | −0.0479626 | ||||||||
\(960\) | −13.7082 | −0.442430 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −10.4721 | −0.337635 | ||||||||
\(963\) | −43.0689 | −1.38788 | ||||||||
\(964\) | −8.87539 | −0.285857 | ||||||||
\(965\) | 3.47214 | 0.111772 | ||||||||
\(966\) | 7.05573 | 0.227014 | ||||||||
\(967\) | 60.3607 | 1.94107 | 0.970534 | − | 0.240963i | \(-0.0774632\pi\) | ||||
0.970534 | + | 0.240963i | \(0.0774632\pi\) | |||||||
\(968\) | 15.6525 | 0.503090 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −25.7984 | −0.828336 | ||||||||
\(971\) | −28.0000 | −0.898563 | −0.449281 | − | 0.893390i | \(-0.648320\pi\) | ||||
−0.449281 | + | 0.893390i | \(0.648320\pi\) | |||||||
\(972\) | 22.0000 | 0.705650 | ||||||||
\(973\) | 3.16718 | 0.101535 | ||||||||
\(974\) | 31.1246 | 0.997297 | ||||||||
\(975\) | 41.8885 | 1.34151 | ||||||||
\(976\) | 39.7082 | 1.27103 | ||||||||
\(977\) | −47.2492 | −1.51164 | −0.755818 | − | 0.654781i | \(-0.772761\pi\) | ||||
−0.755818 | + | 0.654781i | \(0.772761\pi\) | |||||||
\(978\) | −56.0689 | −1.79289 | ||||||||
\(979\) | −23.4164 | −0.748392 | ||||||||
\(980\) | 4.29180 | 0.137096 | ||||||||
\(981\) | 104.193 | 3.32664 | ||||||||
\(982\) | 7.05573 | 0.225157 | ||||||||
\(983\) | −39.5279 | −1.26074 | −0.630372 | − | 0.776294i | \(-0.717097\pi\) | ||||
−0.630372 | + | 0.776294i | \(0.717097\pi\) | |||||||
\(984\) | 50.6525 | 1.61474 | ||||||||
\(985\) | 11.4164 | 0.363757 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.88854 | −0.0601130 | ||||||||
\(988\) | 4.47214 | 0.142278 | ||||||||
\(989\) | −7.05573 | −0.224359 | ||||||||
\(990\) | 24.1803 | 0.768502 | ||||||||
\(991\) | 16.5410 | 0.525443 | 0.262721 | − | 0.964872i | \(-0.415380\pi\) | ||||
0.262721 | + | 0.964872i | \(0.415380\pi\) | |||||||
\(992\) | 3.38197 | 0.107378 | ||||||||
\(993\) | 6.47214 | 0.205387 | ||||||||
\(994\) | −3.50658 | −0.111222 | ||||||||
\(995\) | −18.9443 | −0.600574 | ||||||||
\(996\) | −29.8885 | −0.947055 | ||||||||
\(997\) | 29.3607 | 0.929862 | 0.464931 | − | 0.885347i | \(-0.346079\pi\) | ||||
0.464931 | + | 0.885347i | \(0.346079\pi\) | |||||||
\(998\) | 10.6525 | 0.337198 | ||||||||
\(999\) | 28.9443 | 0.915756 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))