Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5239,2,Mod(1,5239)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5239, 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("5239.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5239 = 13^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5239.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: | \(41.8336256189\) |
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 | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5239.1 |
$q$-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 | \(-0.693856\pi\) | ||||
−0.572061 | + | 0.820211i | \(0.693856\pi\) | |||||||
\(3\) | −3.23607 | −1.86834 | −0.934172 | − | 0.356822i | \(-0.883860\pi\) | ||||
−0.934172 | + | 0.356822i | \(0.883860\pi\) | |||||||
\(4\) | 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 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.381966 | 0.102085 | ||||||||
\(15\) | 3.23607 | 0.835549 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | 0.763932 | 0.185281 | 0.0926404 | − | 0.995700i | \(-0.470469\pi\) | ||||
0.0926404 | + | 0.995700i | \(0.470469\pi\) | |||||||
\(18\) | −12.0902 | −2.84968 | ||||||||
\(19\) | 2.23607 | 0.512989 | 0.256495 | − | 0.966546i | \(-0.417432\pi\) | ||||
0.256495 | + | 0.966546i | \(0.417432\pi\) | |||||||
\(20\) | −0.618034 | −0.138197 | ||||||||
\(21\) | 0.763932 | 0.166704 | ||||||||
\(22\) | 3.23607 | 0.689932 | ||||||||
\(23\) | 5.70820 | 1.19024 | 0.595121 | − | 0.803636i | \(-0.297104\pi\) | ||||
0.595121 | + | 0.803636i | \(0.297104\pi\) | |||||||
\(24\) | −7.23607 | −1.47706 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −14.4721 | −2.78516 | ||||||||
\(28\) | −0.145898 | −0.0275721 | ||||||||
\(29\) | 2.76393 | 0.513249 | 0.256625 | − | 0.966511i | \(-0.417390\pi\) | ||||
0.256625 | + | 0.966511i | \(0.417390\pi\) | |||||||
\(30\) | −5.23607 | −0.955971 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 3.38197 | 0.597853 | ||||||||
\(33\) | 6.47214 | 1.12665 | ||||||||
\(34\) | −1.23607 | −0.211984 | ||||||||
\(35\) | 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 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −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 | \(-0.557707\pi\) | ||||
−0.180299 | + | 0.983612i | \(0.557707\pi\) | |||||||
\(48\) | 15.7082 | 2.26728 | ||||||||
\(49\) | −6.94427 | −0.992039 | ||||||||
\(50\) | 6.47214 | 0.915298 | ||||||||
\(51\) | −2.47214 | −0.346168 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −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 | \(-0.546497\pi\) | ||||
−0.145556 | + | 0.989350i | \(0.546497\pi\) | |||||||
\(60\) | 2.00000 | 0.258199 | ||||||||
\(61\) | 8.18034 | 1.04739 | 0.523693 | − | 0.851907i | \(-0.324554\pi\) | ||||
0.523693 | + | 0.851907i | \(0.324554\pi\) | |||||||
\(62\) | 1.61803 | 0.205491 | ||||||||
\(63\) | −1.76393 | −0.222235 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −10.4721 | −1.28903 | ||||||||
\(67\) | −8.00000 | −0.977356 | −0.488678 | − | 0.872464i | \(-0.662521\pi\) | ||||
−0.488678 | + | 0.872464i | \(0.662521\pi\) | |||||||
\(68\) | 0.472136 | 0.0572549 | ||||||||
\(69\) | −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 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.7082 | −1.31728 | −0.658638 | − | 0.752460i | \(-0.728867\pi\) | ||||
−0.658638 | + | 0.752460i | \(0.728867\pi\) | |||||||
\(80\) | 4.85410 | 0.542705 | ||||||||
\(81\) | 24.4164 | 2.71293 | ||||||||
\(82\) | 11.3262 | 1.25077 | ||||||||
\(83\) | 14.9443 | 1.64035 | 0.820173 | − | 0.572115i | \(-0.193877\pi\) | ||||
0.820173 | + | 0.572115i | \(0.193877\pi\) | |||||||
\(84\) | 0.472136 | 0.0515143 | ||||||||
\(85\) | −0.763932 | −0.0828601 | ||||||||
\(86\) | −2.00000 | −0.215666 | ||||||||
\(87\) | −8.94427 | −0.958927 | ||||||||
\(88\) | −4.47214 | −0.476731 | ||||||||
\(89\) | −11.7082 | −1.24107 | −0.620534 | − | 0.784180i | \(-0.713084\pi\) | ||||
−0.620534 | + | 0.784180i | \(0.713084\pi\) | |||||||
\(90\) | 12.0902 | 1.27442 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 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 | \(0.547688\pi\) | |||||||
\(102\) | 4.00000 | 0.396059 | ||||||||
\(103\) | 6.23607 | 0.614458 | 0.307229 | − | 0.951636i | \(-0.400598\pi\) | ||||
0.307229 | + | 0.951636i | \(0.400598\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.763932 | −0.0745521 | ||||||||
\(106\) | 16.9443 | 1.64577 | ||||||||
\(107\) | 5.76393 | 0.557220 | 0.278610 | − | 0.960404i | \(-0.410126\pi\) | ||||
0.278610 | + | 0.960404i | \(0.410126\pi\) | |||||||
\(108\) | −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 | \(-0.447781\pi\) | ||||
0.163316 | + | 0.986574i | \(0.447781\pi\) | |||||||
\(114\) | 11.7082 | 1.09657 | ||||||||
\(115\) | −5.70820 | −0.532293 | ||||||||
\(116\) | 1.70820 | 0.158603 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.61803 | 0.333067 | ||||||||
\(119\) | −0.180340 | −0.0165317 | ||||||||
\(120\) | 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 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | 4.00000 | 0.348155 | ||||||||
\(133\) | −0.527864 | −0.0457716 | ||||||||
\(134\) | 12.9443 | 1.11821 | ||||||||
\(135\) | 14.4721 | 1.24556 | ||||||||
\(136\) | 1.70820 | 0.146477 | ||||||||
\(137\) | −6.29180 | −0.537544 | −0.268772 | − | 0.963204i | \(-0.586618\pi\) | ||||
−0.268772 | + | 0.963204i | \(0.586618\pi\) | |||||||
\(138\) | 29.8885 | 2.54428 | ||||||||
\(139\) | 13.4164 | 1.13796 | 0.568982 | − | 0.822350i | \(-0.307337\pi\) | ||||
0.568982 | + | 0.822350i | \(0.307337\pi\) | |||||||
\(140\) | 0.145898 | 0.0123306 | ||||||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | −14.8541 | −1.24653 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −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 | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | −20.9443 | −1.71009 | ||||||||
\(151\) | 14.1803 | 1.15398 | 0.576990 | − | 0.816751i | \(-0.304227\pi\) | ||||
0.576990 | + | 0.816751i | \(0.304227\pi\) | |||||||
\(152\) | 5.00000 | 0.405554 | ||||||||
\(153\) | 5.70820 | 0.461481 | ||||||||
\(154\) | −0.763932 | −0.0615594 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 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 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.23607 | 0.0948021 | ||||||||
\(171\) | 16.7082 | 1.27771 | ||||||||
\(172\) | 0.763932 | 0.0582493 | ||||||||
\(173\) | 2.94427 | 0.223849 | 0.111924 | − | 0.993717i | \(-0.464299\pi\) | ||||
0.111924 | + | 0.993717i | \(0.464299\pi\) | |||||||
\(174\) | 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 | \(-0.549654\pi\) | ||||
−0.155361 | + | 0.987858i | \(0.549654\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −26.4721 | −1.95688 | ||||||||
\(184\) | 12.7639 | 0.940970 | ||||||||
\(185\) | −2.00000 | −0.147043 | ||||||||
\(186\) | −5.23607 | −0.383927 | ||||||||
\(187\) | −1.52786 | −0.111728 | ||||||||
\(188\) | −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 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −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 | \(-0.734333\pi\) | ||||
−0.671462 | + | 0.741039i | \(0.734333\pi\) | |||||||
\(200\) | −8.94427 | −0.632456 | ||||||||
\(201\) | 25.8885 | 1.82604 | ||||||||
\(202\) | 4.85410 | 0.341533 | ||||||||
\(203\) | −0.652476 | −0.0457948 | ||||||||
\(204\) | −1.52786 | −0.106972 | ||||||||
\(205\) | 7.00000 | 0.488901 | ||||||||
\(206\) | −10.0902 | −0.703015 | ||||||||
\(207\) | 42.6525 | 2.96455 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.47214 | −0.309344 | ||||||||
\(210\) | 1.23607 | 0.0852968 | ||||||||
\(211\) | 23.1803 | 1.59580 | 0.797900 | − | 0.602790i | \(-0.205944\pi\) | ||||
0.797900 | + | 0.602790i | \(0.205944\pi\) | |||||||
\(212\) | −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 | \(-0.542760\pi\) | ||||
−0.133930 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(224\) | −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 | \(-0.353811\pi\) | ||||
0.443291 | + | 0.896378i | \(0.353811\pi\) | |||||||
\(230\) | 9.23607 | 0.609008 | ||||||||
\(231\) | −1.52786 | −0.100526 | ||||||||
\(232\) | 6.18034 | 0.405759 | ||||||||
\(233\) | 17.9443 | 1.17557 | 0.587784 | − | 0.809018i | \(-0.300000\pi\) | ||||
0.587784 | + | 0.809018i | \(0.300000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.47214 | 0.161264 | ||||||||
\(236\) | −1.38197 | −0.0899583 | ||||||||
\(237\) | 37.8885 | 2.46113 | ||||||||
\(238\) | 0.291796 | 0.0189143 | ||||||||
\(239\) | 11.7082 | 0.757341 | 0.378670 | − | 0.925532i | \(-0.376381\pi\) | ||||
0.378670 | + | 0.925532i | \(0.376381\pi\) | |||||||
\(240\) | −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 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −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 | ||||||||
\(255\) | 2.47214 | 0.154811 | ||||||||
\(256\) | 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 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 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 | \(-0.609426\pi\) | ||||
−0.337040 | + | 0.941490i | \(0.609426\pi\) | |||||||
\(270\) | −23.4164 | −1.42508 | ||||||||
\(271\) | 14.1803 | 0.861394 | 0.430697 | − | 0.902497i | \(-0.358268\pi\) | ||||
0.430697 | + | 0.902497i | \(0.358268\pi\) | |||||||
\(272\) | −3.70820 | −0.224843 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.1803 | 0.615017 | ||||||||
\(275\) | 8.00000 | 0.482418 | ||||||||
\(276\) | −11.4164 | −0.687187 | ||||||||
\(277\) | −12.6525 | −0.760214 | −0.380107 | − | 0.924943i | \(-0.624113\pi\) | ||||
−0.380107 | + | 0.924943i | \(0.624113\pi\) | |||||||
\(278\) | −21.7082 | −1.30197 | ||||||||
\(279\) | −7.47214 | −0.447345 | ||||||||
\(280\) | 0.527864 | 0.0315459 | ||||||||
\(281\) | −17.0000 | −1.01413 | −0.507067 | − | 0.861906i | \(-0.669271\pi\) | ||||
−0.507067 | + | 0.861906i | \(0.669271\pi\) | |||||||
\(282\) | −12.9443 | −0.770820 | ||||||||
\(283\) | −13.8885 | −0.825588 | −0.412794 | − | 0.910824i | \(-0.635447\pi\) | ||||
−0.412794 | + | 0.910824i | \(0.635447\pi\) | |||||||
\(284\) | 5.67376 | 0.336676 | ||||||||
\(285\) | 7.23607 | 0.428628 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.65248 | 0.0975426 | ||||||||
\(288\) | 25.2705 | 1.48908 | ||||||||
\(289\) | −16.4164 | −0.965671 | ||||||||
\(290\) | 4.47214 | 0.262613 | ||||||||
\(291\) | −51.5967 | −3.02465 | ||||||||
\(292\) | −5.23607 | −0.306418 | ||||||||
\(293\) | 0.472136 | 0.0275825 | 0.0137912 | − | 0.999905i | \(-0.495610\pi\) | ||||
0.0137912 | + | 0.999905i | \(0.495610\pi\) | |||||||
\(294\) | −36.3607 | −2.12060 | ||||||||
\(295\) | 2.23607 | 0.130189 | ||||||||
\(296\) | 4.47214 | 0.259938 | ||||||||
\(297\) | 28.9443 | 1.67952 | ||||||||
\(298\) | 16.1803 | 0.937302 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 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 | ||||||||
\(306\) | −9.23607 | −0.527991 | ||||||||
\(307\) | 28.7082 | 1.63846 | 0.819232 | − | 0.573462i | \(-0.194400\pi\) | ||||
0.819232 | + | 0.573462i | \(0.194400\pi\) | |||||||
\(308\) | 0.291796 | 0.0166266 | ||||||||
\(309\) | −20.1803 | −1.14802 | ||||||||
\(310\) | −1.61803 | −0.0918982 | ||||||||
\(311\) | −29.1803 | −1.65467 | −0.827333 | − | 0.561712i | \(-0.810143\pi\) | ||||
−0.827333 | + | 0.561712i | \(0.810143\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.7639 | 0.947553 | 0.473777 | − | 0.880645i | \(-0.342890\pi\) | ||||
0.473777 | + | 0.880645i | \(0.342890\pi\) | |||||||
\(314\) | −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 | ||||||||
\(323\) | 1.70820 | 0.0950470 | ||||||||
\(324\) | 15.0902 | 0.838343 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 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 | \(-0.517505\pi\) | ||||
−0.0549650 | + | 0.998488i | \(0.517505\pi\) | |||||||
\(332\) | 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 | \(-0.631727\pi\) | ||||
−0.402121 | + | 0.915586i | \(0.631727\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.2361 | −0.610259 | ||||||||
\(340\) | −0.472136 | −0.0256052 | ||||||||
\(341\) | 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 | \(-0.275173\pi\) | ||||
0.649034 | + | 0.760759i | \(0.275173\pi\) | |||||||
\(348\) | −5.52786 | −0.296325 | ||||||||
\(349\) | 7.88854 | 0.422264 | 0.211132 | − | 0.977458i | \(-0.432285\pi\) | ||||
0.211132 | + | 0.977458i | \(0.432285\pi\) | |||||||
\(350\) | −1.52786 | −0.0816678 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.76393 | −0.360519 | ||||||||
\(353\) | −7.41641 | −0.394736 | −0.197368 | − | 0.980330i | \(-0.563239\pi\) | ||||
−0.197368 | + | 0.980330i | \(0.563239\pi\) | |||||||
\(354\) | −11.7082 | −0.622284 | ||||||||
\(355\) | −9.18034 | −0.487242 | ||||||||
\(356\) | −7.23607 | −0.383511 | ||||||||
\(357\) | 0.583592 | 0.0308870 | ||||||||
\(358\) | −2.76393 | −0.146078 | ||||||||
\(359\) | −22.2361 | −1.17357 | −0.586787 | − | 0.809741i | \(-0.699608\pi\) | ||||
−0.586787 | + | 0.809741i | \(0.699608\pi\) | |||||||
\(360\) | −16.7082 | −0.880600 | ||||||||
\(361\) | −14.0000 | −0.736842 | ||||||||
\(362\) | 6.76393 | 0.355504 | ||||||||
\(363\) | 22.6525 | 1.18895 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.47214 | 0.443452 | ||||||||
\(366\) | 42.8328 | 2.23891 | ||||||||
\(367\) | 18.0000 | 0.939592 | 0.469796 | − | 0.882775i | \(-0.344327\pi\) | ||||
0.469796 | + | 0.882775i | \(0.344327\pi\) | |||||||
\(368\) | −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 | \(0.336306\pi\) | |||||||
\(374\) | 2.47214 | 0.127831 | ||||||||
\(375\) | −29.1246 | −1.50399 | ||||||||
\(376\) | −5.52786 | −0.285078 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −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 | \(-0.291039\pi\) | ||||
0.610324 | + | 0.792152i | \(0.291039\pi\) | |||||||
\(384\) | 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 | \(0.649822\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.36068 | 0.220529 | ||||||||
\(392\) | −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 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1.85410 | −0.0922450 | ||||||||
\(405\) | −24.4164 | −1.21326 | ||||||||
\(406\) | 1.05573 | 0.0523949 | ||||||||
\(407\) | −4.00000 | −0.198273 | ||||||||
\(408\) | −5.52786 | −0.273670 | ||||||||
\(409\) | 3.81966 | 0.188870 | 0.0944350 | − | 0.995531i | \(-0.469896\pi\) | ||||
0.0944350 | + | 0.995531i | \(0.469896\pi\) | |||||||
\(410\) | −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 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −43.4164 | −2.12611 | ||||||||
\(418\) | 7.23607 | 0.353928 | ||||||||
\(419\) | −10.1246 | −0.494620 | −0.247310 | − | 0.968936i | \(-0.579547\pi\) | ||||
−0.247310 | + | 0.968936i | \(0.579547\pi\) | |||||||
\(420\) | −0.472136 | −0.0230379 | ||||||||
\(421\) | −29.3607 | −1.43095 | −0.715476 | − | 0.698637i | \(-0.753790\pi\) | ||||
−0.715476 | + | 0.698637i | \(0.753790\pi\) | |||||||
\(422\) | −37.5066 | −1.82579 | ||||||||
\(423\) | −18.4721 | −0.898146 | ||||||||
\(424\) | −23.4164 | −1.13720 | ||||||||
\(425\) | −3.05573 | −0.148225 | ||||||||
\(426\) | 48.0689 | 2.32895 | ||||||||
\(427\) | −1.93112 | −0.0934533 | ||||||||
\(428\) | 3.56231 | 0.172191 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | \(-0.508967\pi\) | ||||
−0.0281673 | + | 0.999603i | \(0.508967\pi\) | |||||||
\(440\) | 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 | 0 | ||||||||
\(456\) | −16.1803 | −0.757714 | ||||||||
\(457\) | 3.05573 | 0.142941 | 0.0714705 | − | 0.997443i | \(-0.477231\pi\) | ||||
0.0714705 | + | 0.997443i | \(0.477231\pi\) | |||||||
\(458\) | −21.7082 | −1.01436 | ||||||||
\(459\) | −11.0557 | −0.516037 | ||||||||
\(460\) | −3.52786 | −0.164488 | ||||||||
\(461\) | −34.3607 | −1.60034 | −0.800168 | − | 0.599776i | \(-0.795256\pi\) | ||||
−0.800168 | + | 0.599776i | \(0.795256\pi\) | |||||||
\(462\) | 2.47214 | 0.115014 | ||||||||
\(463\) | 2.58359 | 0.120070 | 0.0600349 | − | 0.998196i | \(-0.480879\pi\) | ||||
0.0600349 | + | 0.998196i | \(0.480879\pi\) | |||||||
\(464\) | −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 | \(0.465256\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 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 | ||||||||
\(476\) | −0.111456 | −0.00510859 | ||||||||
\(477\) | −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 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 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 | ||||||||
\(493\) | 2.11146 | 0.0950952 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 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 | \(-0.270103\pi\) | ||||
0.661069 | + | 0.750325i | \(0.270103\pi\) | |||||||
\(504\) | −3.94427 | −0.175692 | ||||||||
\(505\) | 3.00000 | 0.133498 | ||||||||
\(506\) | 18.4721 | 0.821187 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.70820 | 0.341996 | ||||||||
\(509\) | −29.5967 | −1.31185 | −0.655926 | − | 0.754825i | \(-0.727722\pi\) | ||||
−0.655926 | + | 0.754825i | \(0.727722\pi\) | |||||||
\(510\) | −4.00000 | −0.177123 | ||||||||
\(511\) | 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 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.00000 | 0.0876216 | 0.0438108 | − | 0.999040i | \(-0.486050\pi\) | ||||
0.0438108 | + | 0.999040i | \(0.486050\pi\) | |||||||
\(522\) | −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 | ||||||||
\(527\) | −0.763932 | −0.0332774 | ||||||||
\(528\) | −31.4164 | −1.36722 | ||||||||
\(529\) | 9.58359 | 0.416678 | ||||||||
\(530\) | −16.9443 | −0.736012 | ||||||||
\(531\) | −16.7082 | −0.725074 | ||||||||
\(532\) | −0.326238 | −0.0141442 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −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 | ||||||||
\(544\) | 2.58359 | 0.110771 | ||||||||
\(545\) | −13.9443 | −0.597307 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.1246 | −0.518411 | −0.259205 | − | 0.965822i | \(-0.583461\pi\) | ||||
−0.259205 | + | 0.965822i | \(0.583461\pi\) | |||||||
\(548\) | −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 | \(-0.418179\pi\) | ||||
0.254228 | + | 0.967144i | \(0.418179\pi\) | |||||||
\(558\) | 12.0902 | 0.511818 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.14590 | −0.0484230 | ||||||||
\(561\) | 4.94427 | 0.208747 | ||||||||
\(562\) | 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 | \(-0.299264\pi\) | ||||
0.589655 | + | 0.807655i | \(0.299264\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 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 | \(-0.295102\pi\) | ||||
0.600163 | + | 0.799878i | \(0.295102\pi\) | |||||||
\(578\) | 26.5623 | 1.10485 | ||||||||
\(579\) | 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 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.763932 | −0.0315577 | ||||||||
\(587\) | 6.47214 | 0.267134 | 0.133567 | − | 0.991040i | \(-0.457357\pi\) | ||||
0.133567 | + | 0.991040i | \(0.457357\pi\) | |||||||
\(588\) | 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 | \(-0.457207\pi\) | ||||
0.134034 | + | 0.990977i | \(0.457207\pi\) | |||||||
\(594\) | −46.8328 | −1.92157 | ||||||||
\(595\) | 0.180340 | 0.00739321 | ||||||||
\(596\) | −6.18034 | −0.253157 | ||||||||
\(597\) | 61.3050 | 2.50904 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −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 | \(-0.285956\pi\) | ||||
0.622897 | + | 0.782304i | \(0.285956\pi\) | |||||||
\(602\) | 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 | \(-0.349261\pi\) | ||||
0.456058 | + | 0.889950i | \(0.349261\pi\) | |||||||
\(608\) | 7.56231 | 0.306692 | ||||||||
\(609\) | 2.11146 | 0.0855605 | ||||||||
\(610\) | 13.2361 | 0.535913 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 3.52786 | 0.142605 | ||||||||
\(613\) | 43.8885 | 1.77264 | 0.886321 | − | 0.463072i | \(-0.153253\pi\) | ||||
0.886321 | + | 0.463072i | \(0.153253\pi\) | |||||||
\(614\) | −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 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | −27.1246 | −1.08412 | ||||||||
\(627\) | 14.4721 | 0.577961 | ||||||||
\(628\) | 12.9098 | 0.515158 | ||||||||
\(629\) | 1.52786 | 0.0609199 | ||||||||
\(630\) | −2.85410 | −0.113710 | ||||||||
\(631\) | −34.3607 | −1.36788 | −0.683939 | − | 0.729540i | \(-0.739734\pi\) | ||||
−0.683939 | + | 0.729540i | \(0.739734\pi\) | |||||||
\(632\) | −26.1803 | −1.04140 | ||||||||
\(633\) | −75.0132 | −2.98151 | ||||||||
\(634\) | 6.56231 | 0.260622 | ||||||||
\(635\) | −12.4721 | −0.494942 | ||||||||
\(636\) | 20.9443 | 0.830494 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 8.94427 | 0.354107 | ||||||||
\(639\) | 68.5967 | 2.71365 | ||||||||
\(640\) | 13.6180 | 0.538300 | ||||||||
\(641\) | 12.0000 | 0.473972 | 0.236986 | − | 0.971513i | \(-0.423841\pi\) | ||||
0.236986 | + | 0.971513i | \(0.423841\pi\) | |||||||
\(642\) | 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 | ||||||||
\(646\) | −2.76393 | −0.108745 | ||||||||
\(647\) | −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 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.763932 | −0.0299409 | ||||||||
\(652\) | −6.61803 | −0.259182 | ||||||||
\(653\) | −47.3050 | −1.85119 | −0.925593 | − | 0.378521i | \(-0.876433\pi\) | ||||
−0.925593 | + | 0.378521i | \(0.876433\pi\) | |||||||
\(654\) | 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 | \(-0.496042\pi\) | ||||
0.0124333 | + | 0.999923i | \(0.496042\pi\) | |||||||
\(662\) | 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 | \(-0.688887\pi\) | ||||
−0.559187 | + | 0.829041i | \(0.688887\pi\) | |||||||
\(674\) | 23.8885 | 0.920152 | ||||||||
\(675\) | 57.8885 | 2.22813 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −46.7214 | −1.79565 | −0.897824 | − | 0.440355i | \(-0.854853\pi\) | ||||
−0.897824 | + | 0.440355i | \(0.854853\pi\) | |||||||
\(678\) | 18.1803 | 0.698212 | ||||||||
\(679\) | −3.76393 | −0.144446 | ||||||||
\(680\) | −1.70820 | −0.0655066 | ||||||||
\(681\) | −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 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −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 | ||||||||
\(697\) | −5.34752 | −0.202552 | ||||||||
\(698\) | −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 | \(0.457798\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 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 | ||||||||
\(714\) | −0.944272 | −0.0353385 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.05573 | 0.0394544 | ||||||||
\(717\) | −37.8885 | −1.41497 | ||||||||
\(718\) | 35.9787 | 1.34271 | ||||||||
\(719\) | −13.8197 | −0.515386 | −0.257693 | − | 0.966227i | \(-0.582962\pi\) | ||||
−0.257693 | + | 0.966227i | \(0.582962\pi\) | |||||||
\(720\) | 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 | \(0.806200\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 41.9443 | 1.55349 | ||||||||
\(730\) | −13.7082 | −0.507363 | ||||||||
\(731\) | 0.944272 | 0.0349252 | ||||||||
\(732\) | −16.3607 | −0.604708 | ||||||||
\(733\) | −3.47214 | −0.128246 | −0.0641231 | − | 0.997942i | \(-0.520425\pi\) | ||||
−0.0641231 | + | 0.997942i | \(0.520425\pi\) | |||||||
\(734\) | −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 | \(-0.536262\pi\) | ||||
−0.113674 | + | 0.993518i | \(0.536262\pi\) | |||||||
\(740\) | −1.23607 | −0.0454388 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −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 | ||||||||
\(748\) | −0.944272 | −0.0345260 | ||||||||
\(749\) | −1.36068 | −0.0497182 | ||||||||
\(750\) | 47.1246 | 1.72075 | ||||||||
\(751\) | −21.5410 | −0.786043 | −0.393021 | − | 0.919529i | \(-0.628570\pi\) | ||||
−0.393021 | + | 0.919529i | \(0.628570\pi\) | |||||||
\(752\) | 12.0000 | 0.437595 | ||||||||
\(753\) | 5.88854 | 0.214590 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −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 | \(-0.511541\pi\) | ||||
−0.0362500 | + | 0.999343i | \(0.511541\pi\) | |||||||
\(762\) | 65.3050 | 2.36575 | ||||||||
\(763\) | −3.29180 | −0.119171 | ||||||||
\(764\) | −11.8541 | −0.428866 | ||||||||
\(765\) | −5.70820 | −0.206381 | ||||||||
\(766\) | −38.6525 | −1.39657 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −43.8885 | −1.58369 | ||||||||
\(769\) | 47.3607 | 1.70787 | 0.853935 | − | 0.520380i | \(-0.174210\pi\) | ||||
0.853935 | + | 0.520380i | \(0.174210\pi\) | |||||||
\(770\) | 0.763932 | 0.0275302 | ||||||||
\(771\) | −6.29180 | −0.226594 | ||||||||
\(772\) | −2.14590 | −0.0772326 | ||||||||
\(773\) | 11.1246 | 0.400124 | 0.200062 | − | 0.979783i | \(-0.435886\pi\) | ||||
0.200062 | + | 0.979783i | \(0.435886\pi\) | |||||||
\(774\) | −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 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.3607 | −0.656997 | ||||||||
\(782\) | −7.05573 | −0.252312 | ||||||||
\(783\) | −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 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −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 | ||||||||
\(799\) | −1.88854 | −0.0668119 | ||||||||
\(800\) | −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 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 35.7771 | 1.25941 | ||||||||
\(808\) | −6.70820 | −0.235994 | ||||||||
\(809\) | 23.4164 | 0.823277 | 0.411639 | − | 0.911347i | \(-0.364957\pi\) | ||||
0.411639 | + | 0.911347i | \(0.364957\pi\) | |||||||
\(810\) | 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 | ||||||||
\(816\) | 12.0000 | 0.420084 | ||||||||
\(817\) | 2.76393 | 0.0966977 | ||||||||
\(818\) | −6.18034 | −0.216091 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 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 | \(-0.580132\pi\) | ||||
−0.249090 | + | 0.968480i | \(0.580132\pi\) | |||||||
\(824\) | 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 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.30495 | −0.183806 | ||||||||
\(834\) | 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 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 29.8885 | 1.02759 | ||||||||
\(847\) | 1.65248 | 0.0567797 | ||||||||
\(848\) | 50.8328 | 1.74561 | ||||||||
\(849\) | 44.9443 | 1.54248 | ||||||||
\(850\) | 4.94427 | 0.169587 | ||||||||
\(851\) | 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 | \(-0.899686\pi\) | ||||
−0.950751 | + | 0.309956i | \(0.899686\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 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 | \(-0.446549\pi\) | ||||
0.167133 | + | 0.985934i | \(0.446549\pi\) | |||||||
\(864\) | −48.9443 | −1.66512 | ||||||||
\(865\) | −2.94427 | −0.100108 | ||||||||
\(866\) | −16.4721 | −0.559746 | ||||||||
\(867\) | 53.1246 | 1.80421 | ||||||||
\(868\) | 0.145898 | 0.00495210 | ||||||||
\(869\) | 23.4164 | 0.794347 | ||||||||
\(870\) | −14.4721 | −0.490651 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 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 | \(-0.611438\pi\) | ||||
−0.342984 | + | 0.939341i | \(0.611438\pi\) | |||||||
\(882\) | 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 | \(-0.349839\pi\) | ||||
0.454442 | + | 0.890776i | \(0.349839\pi\) | |||||||
\(888\) | −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 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −50.6525 | −1.69030 | ||||||||
\(899\) | −2.76393 | −0.0921823 | ||||||||
\(900\) | −18.4721 | −0.615738 | ||||||||
\(901\) | −8.00000 | −0.266519 | ||||||||
\(902\) | −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 | \(-0.631814\pi\) | ||||
−0.402373 | + | 0.915476i | \(0.631814\pi\) | |||||||
\(908\) | 4.00000 | 0.132745 | ||||||||
\(909\) | −22.4164 | −0.743505 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.1803 | 0.602342 | 0.301171 | − | 0.953570i | \(-0.402623\pi\) | ||||
0.301171 | + | 0.953570i | \(0.402623\pi\) | |||||||
\(912\) | 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 | ||||||||
\(918\) | 17.8885 | 0.590410 | ||||||||
\(919\) | −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 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −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 | ||||||||
\(935\) | 1.52786 | 0.0499665 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 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 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 14.4721 | 0.469538 | ||||||||
\(951\) | 13.1246 | 0.425595 | ||||||||
\(952\) | −0.403252 | −0.0130695 | ||||||||
\(953\) | 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 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 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 | \(-0.922537\pi\) | ||||
−0.970534 | + | 0.240963i | \(0.922537\pi\) | |||||||
\(968\) | −15.6525 | −0.503090 | ||||||||
\(969\) | −5.52786 | −0.177581 | ||||||||
\(970\) | 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 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −39.7082 | −1.27103 | ||||||||
\(977\) | 47.2492 | 1.51164 | 0.755818 | − | 0.654781i | \(-0.227239\pi\) | ||||
0.755818 | + | 0.654781i | \(0.227239\pi\) | |||||||
\(978\) | −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 | ||||||||
\(986\) | −3.41641 | −0.108801 | ||||||||
\(987\) | −1.88854 | −0.0601130 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.05573 | 0.224359 | ||||||||
\(990\) | −24.1803 | −0.768502 | ||||||||
\(991\) | −16.5410 | −0.525443 | −0.262721 | − | 0.964872i | \(-0.584620\pi\) | ||||
−0.262721 | + | 0.964872i | \(0.584620\pi\) | |||||||
\(992\) | −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 | \(-0.653921\pi\) | ||||
−0.464931 | + | 0.885347i | \(0.653921\pi\) | |||||||
\(998\) | −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 \(a_p\))