Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0509119 | 0.0360001 | 0.0180001 | − | 0.999838i | \(-0.494270\pi\) | ||||
0.0180001 | + | 0.999838i | \(0.494270\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.99741 | −0.998704 | ||||||||
\(5\) | 3.95784 | 1.77000 | 0.885000 | − | 0.465590i | \(-0.154158\pi\) | ||||
0.885000 | + | 0.465590i | \(0.154158\pi\) | |||||||
\(6\) | 0.0509119 | 0.0207847 | ||||||||
\(7\) | 1.89285 | 0.715431 | 0.357715 | − | 0.933831i | \(-0.383556\pi\) | ||||
0.357715 | + | 0.933831i | \(0.383556\pi\) | |||||||
\(8\) | −0.203515 | −0.0719536 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.201501 | 0.0637202 | ||||||||
\(11\) | 5.26878 | 1.58860 | 0.794298 | − | 0.607528i | \(-0.207839\pi\) | ||||
0.794298 | + | 0.607528i | \(0.207839\pi\) | |||||||
\(12\) | −1.99741 | −0.576602 | ||||||||
\(13\) | −2.15571 | −0.597887 | −0.298944 | − | 0.954271i | \(-0.596634\pi\) | ||||
−0.298944 | + | 0.954271i | \(0.596634\pi\) | |||||||
\(14\) | 0.0963686 | 0.0257556 | ||||||||
\(15\) | 3.95784 | 1.02191 | ||||||||
\(16\) | 3.98445 | 0.996114 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0.0509119 | 0.0120000 | ||||||||
\(19\) | 3.28525 | 0.753688 | 0.376844 | − | 0.926277i | \(-0.377009\pi\) | ||||
0.376844 | + | 0.926277i | \(0.377009\pi\) | |||||||
\(20\) | −7.90542 | −1.76771 | ||||||||
\(21\) | 1.89285 | 0.413054 | ||||||||
\(22\) | 0.268243 | 0.0571897 | ||||||||
\(23\) | −2.60175 | −0.542501 | −0.271251 | − | 0.962509i | \(-0.587437\pi\) | ||||
−0.271251 | + | 0.962509i | \(0.587437\pi\) | |||||||
\(24\) | −0.203515 | −0.0415424 | ||||||||
\(25\) | 10.6645 | 2.13290 | ||||||||
\(26\) | −0.109751 | −0.0215240 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.78080 | −0.714504 | ||||||||
\(29\) | 1.79464 | 0.333256 | 0.166628 | − | 0.986020i | \(-0.446712\pi\) | ||||
0.166628 | + | 0.986020i | \(0.446712\pi\) | |||||||
\(30\) | 0.201501 | 0.0367889 | ||||||||
\(31\) | 1.06539 | 0.191350 | 0.0956749 | − | 0.995413i | \(-0.469499\pi\) | ||||
0.0956749 | + | 0.995413i | \(0.469499\pi\) | |||||||
\(32\) | 0.609887 | 0.107814 | ||||||||
\(33\) | 5.26878 | 0.917176 | ||||||||
\(34\) | 0.0509119 | 0.00873131 | ||||||||
\(35\) | 7.49161 | 1.26631 | ||||||||
\(36\) | −1.99741 | −0.332901 | ||||||||
\(37\) | −6.27633 | −1.03182 | −0.515911 | − | 0.856642i | \(-0.672547\pi\) | ||||
−0.515911 | + | 0.856642i | \(0.672547\pi\) | |||||||
\(38\) | 0.167258 | 0.0271328 | ||||||||
\(39\) | −2.15571 | −0.345190 | ||||||||
\(40\) | −0.805482 | −0.127358 | ||||||||
\(41\) | 8.76444 | 1.36878 | 0.684388 | − | 0.729118i | \(-0.260070\pi\) | ||||
0.684388 | + | 0.729118i | \(0.260070\pi\) | |||||||
\(42\) | 0.0963686 | 0.0148700 | ||||||||
\(43\) | −10.2465 | −1.56258 | −0.781291 | − | 0.624167i | \(-0.785438\pi\) | ||||
−0.781291 | + | 0.624167i | \(0.785438\pi\) | |||||||
\(44\) | −10.5239 | −1.58654 | ||||||||
\(45\) | 3.95784 | 0.590000 | ||||||||
\(46\) | −0.132460 | −0.0195301 | ||||||||
\(47\) | 6.79563 | 0.991244 | 0.495622 | − | 0.868538i | \(-0.334940\pi\) | ||||
0.495622 | + | 0.868538i | \(0.334940\pi\) | |||||||
\(48\) | 3.98445 | 0.575106 | ||||||||
\(49\) | −3.41711 | −0.488159 | ||||||||
\(50\) | 0.542950 | 0.0767847 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 4.30584 | 0.597113 | ||||||||
\(53\) | −6.84440 | −0.940150 | −0.470075 | − | 0.882626i | \(-0.655773\pi\) | ||||
−0.470075 | + | 0.882626i | \(0.655773\pi\) | |||||||
\(54\) | 0.0509119 | 0.00692823 | ||||||||
\(55\) | 20.8530 | 2.81182 | ||||||||
\(56\) | −0.385225 | −0.0514778 | ||||||||
\(57\) | 3.28525 | 0.435142 | ||||||||
\(58\) | 0.0913684 | 0.0119973 | ||||||||
\(59\) | −13.4533 | −1.75147 | −0.875736 | − | 0.482791i | \(-0.839623\pi\) | ||||
−0.875736 | + | 0.482791i | \(0.839623\pi\) | |||||||
\(60\) | −7.90542 | −1.02059 | ||||||||
\(61\) | 10.8439 | 1.38842 | 0.694210 | − | 0.719773i | \(-0.255754\pi\) | ||||
0.694210 | + | 0.719773i | \(0.255754\pi\) | |||||||
\(62\) | 0.0542410 | 0.00688862 | ||||||||
\(63\) | 1.89285 | 0.238477 | ||||||||
\(64\) | −7.93786 | −0.992232 | ||||||||
\(65\) | −8.53197 | −1.05826 | ||||||||
\(66\) | 0.268243 | 0.0330185 | ||||||||
\(67\) | 10.6925 | 1.30630 | 0.653150 | − | 0.757228i | \(-0.273447\pi\) | ||||
0.653150 | + | 0.757228i | \(0.273447\pi\) | |||||||
\(68\) | −1.99741 | −0.242221 | ||||||||
\(69\) | −2.60175 | −0.313213 | ||||||||
\(70\) | 0.381412 | 0.0455874 | ||||||||
\(71\) | −0.635598 | −0.0754316 | −0.0377158 | − | 0.999289i | \(-0.512008\pi\) | ||||
−0.0377158 | + | 0.999289i | \(0.512008\pi\) | |||||||
\(72\) | −0.203515 | −0.0239845 | ||||||||
\(73\) | −3.45288 | −0.404129 | −0.202064 | − | 0.979372i | \(-0.564765\pi\) | ||||
−0.202064 | + | 0.979372i | \(0.564765\pi\) | |||||||
\(74\) | −0.319540 | −0.0371457 | ||||||||
\(75\) | 10.6645 | 1.23143 | ||||||||
\(76\) | −6.56198 | −0.752711 | ||||||||
\(77\) | 9.97301 | 1.13653 | ||||||||
\(78\) | −0.109751 | −0.0124269 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | 15.7698 | 1.76312 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.446214 | 0.0492761 | ||||||||
\(83\) | −12.9078 | −1.41682 | −0.708410 | − | 0.705801i | \(-0.750587\pi\) | ||||
−0.708410 | + | 0.705801i | \(0.750587\pi\) | |||||||
\(84\) | −3.78080 | −0.412519 | ||||||||
\(85\) | 3.95784 | 0.429288 | ||||||||
\(86\) | −0.521670 | −0.0562531 | ||||||||
\(87\) | 1.79464 | 0.192405 | ||||||||
\(88\) | −1.07228 | −0.114305 | ||||||||
\(89\) | −6.91898 | −0.733411 | −0.366705 | − | 0.930337i | \(-0.619514\pi\) | ||||
−0.366705 | + | 0.930337i | \(0.619514\pi\) | |||||||
\(90\) | 0.201501 | 0.0212401 | ||||||||
\(91\) | −4.08045 | −0.427747 | ||||||||
\(92\) | 5.19675 | 0.541798 | ||||||||
\(93\) | 1.06539 | 0.110476 | ||||||||
\(94\) | 0.345978 | 0.0356849 | ||||||||
\(95\) | 13.0025 | 1.33403 | ||||||||
\(96\) | 0.609887 | 0.0622463 | ||||||||
\(97\) | 2.23271 | 0.226697 | 0.113349 | − | 0.993555i | \(-0.463842\pi\) | ||||
0.113349 | + | 0.993555i | \(0.463842\pi\) | |||||||
\(98\) | −0.173972 | −0.0175738 | ||||||||
\(99\) | 5.26878 | 0.529532 | ||||||||
\(100\) | −21.3014 | −2.13014 | ||||||||
\(101\) | −7.71317 | −0.767490 | −0.383745 | − | 0.923439i | \(-0.625366\pi\) | ||||
−0.383745 | + | 0.923439i | \(0.625366\pi\) | |||||||
\(102\) | 0.0509119 | 0.00504103 | ||||||||
\(103\) | 6.30662 | 0.621410 | 0.310705 | − | 0.950506i | \(-0.399435\pi\) | ||||
0.310705 | + | 0.950506i | \(0.399435\pi\) | |||||||
\(104\) | 0.438721 | 0.0430201 | ||||||||
\(105\) | 7.49161 | 0.731106 | ||||||||
\(106\) | −0.348461 | −0.0338455 | ||||||||
\(107\) | −18.0287 | −1.74290 | −0.871450 | − | 0.490484i | \(-0.836820\pi\) | ||||
−0.871450 | + | 0.490484i | \(0.836820\pi\) | |||||||
\(108\) | −1.99741 | −0.192201 | ||||||||
\(109\) | 15.0394 | 1.44051 | 0.720256 | − | 0.693709i | \(-0.244024\pi\) | ||||
0.720256 | + | 0.693709i | \(0.244024\pi\) | |||||||
\(110\) | 1.06166 | 0.101226 | ||||||||
\(111\) | −6.27633 | −0.595723 | ||||||||
\(112\) | 7.54198 | 0.712650 | ||||||||
\(113\) | −1.47464 | −0.138722 | −0.0693610 | − | 0.997592i | \(-0.522096\pi\) | ||||
−0.0693610 | + | 0.997592i | \(0.522096\pi\) | |||||||
\(114\) | 0.167258 | 0.0156652 | ||||||||
\(115\) | −10.2973 | −0.960228 | ||||||||
\(116\) | −3.58462 | −0.332824 | ||||||||
\(117\) | −2.15571 | −0.199296 | ||||||||
\(118\) | −0.684933 | −0.0630532 | ||||||||
\(119\) | 1.89285 | 0.173517 | ||||||||
\(120\) | −0.805482 | −0.0735301 | ||||||||
\(121\) | 16.7600 | 1.52364 | ||||||||
\(122\) | 0.552083 | 0.0499833 | ||||||||
\(123\) | 8.76444 | 0.790263 | ||||||||
\(124\) | −2.12802 | −0.191102 | ||||||||
\(125\) | 22.4192 | 2.00524 | ||||||||
\(126\) | 0.0963686 | 0.00858520 | ||||||||
\(127\) | −3.07151 | −0.272553 | −0.136276 | − | 0.990671i | \(-0.543514\pi\) | ||||
−0.136276 | + | 0.990671i | \(0.543514\pi\) | |||||||
\(128\) | −1.62391 | −0.143534 | ||||||||
\(129\) | −10.2465 | −0.902157 | ||||||||
\(130\) | −0.434379 | −0.0380975 | ||||||||
\(131\) | 7.42141 | 0.648412 | 0.324206 | − | 0.945987i | \(-0.394903\pi\) | ||||
0.324206 | + | 0.945987i | \(0.394903\pi\) | |||||||
\(132\) | −10.5239 | −0.915988 | ||||||||
\(133\) | 6.21849 | 0.539211 | ||||||||
\(134\) | 0.544377 | 0.0470270 | ||||||||
\(135\) | 3.95784 | 0.340637 | ||||||||
\(136\) | −0.203515 | −0.0174513 | ||||||||
\(137\) | −20.7596 | −1.77361 | −0.886805 | − | 0.462144i | \(-0.847080\pi\) | ||||
−0.886805 | + | 0.462144i | \(0.847080\pi\) | |||||||
\(138\) | −0.132460 | −0.0112757 | ||||||||
\(139\) | −6.99991 | −0.593725 | −0.296862 | − | 0.954920i | \(-0.595940\pi\) | ||||
−0.296862 | + | 0.954920i | \(0.595940\pi\) | |||||||
\(140\) | −14.9638 | −1.26467 | ||||||||
\(141\) | 6.79563 | 0.572295 | ||||||||
\(142\) | −0.0323595 | −0.00271555 | ||||||||
\(143\) | −11.3580 | −0.949802 | ||||||||
\(144\) | 3.98445 | 0.332038 | ||||||||
\(145\) | 7.10289 | 0.589863 | ||||||||
\(146\) | −0.175792 | −0.0145487 | ||||||||
\(147\) | −3.41711 | −0.281839 | ||||||||
\(148\) | 12.5364 | 1.03049 | ||||||||
\(149\) | −2.52004 | −0.206449 | −0.103225 | − | 0.994658i | \(-0.532916\pi\) | ||||
−0.103225 | + | 0.994658i | \(0.532916\pi\) | |||||||
\(150\) | 0.542950 | 0.0443317 | ||||||||
\(151\) | 2.39953 | 0.195271 | 0.0976357 | − | 0.995222i | \(-0.468872\pi\) | ||||
0.0976357 | + | 0.995222i | \(0.468872\pi\) | |||||||
\(152\) | −0.668599 | −0.0542305 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 0.507745 | 0.0409152 | ||||||||
\(155\) | 4.21665 | 0.338689 | ||||||||
\(156\) | 4.30584 | 0.344743 | ||||||||
\(157\) | −7.13021 | −0.569053 | −0.284526 | − | 0.958668i | \(-0.591836\pi\) | ||||
−0.284526 | + | 0.958668i | \(0.591836\pi\) | |||||||
\(158\) | 0.0509119 | 0.00405033 | ||||||||
\(159\) | −6.84440 | −0.542796 | ||||||||
\(160\) | 2.41384 | 0.190830 | ||||||||
\(161\) | −4.92472 | −0.388122 | ||||||||
\(162\) | 0.0509119 | 0.00400001 | ||||||||
\(163\) | 9.18135 | 0.719139 | 0.359570 | − | 0.933118i | \(-0.382924\pi\) | ||||
0.359570 | + | 0.933118i | \(0.382924\pi\) | |||||||
\(164\) | −17.5062 | −1.36700 | ||||||||
\(165\) | 20.8530 | 1.62340 | ||||||||
\(166\) | −0.657162 | −0.0510057 | ||||||||
\(167\) | 11.7414 | 0.908574 | 0.454287 | − | 0.890855i | \(-0.349894\pi\) | ||||
0.454287 | + | 0.890855i | \(0.349894\pi\) | |||||||
\(168\) | −0.385225 | −0.0297207 | ||||||||
\(169\) | −8.35290 | −0.642531 | ||||||||
\(170\) | 0.201501 | 0.0154544 | ||||||||
\(171\) | 3.28525 | 0.251229 | ||||||||
\(172\) | 20.4665 | 1.56056 | ||||||||
\(173\) | −17.3164 | −1.31654 | −0.658270 | − | 0.752782i | \(-0.728711\pi\) | ||||
−0.658270 | + | 0.752782i | \(0.728711\pi\) | |||||||
\(174\) | 0.0913684 | 0.00692662 | ||||||||
\(175\) | 20.1863 | 1.52594 | ||||||||
\(176\) | 20.9932 | 1.58242 | ||||||||
\(177\) | −13.4533 | −1.01121 | ||||||||
\(178\) | −0.352258 | −0.0264029 | ||||||||
\(179\) | 23.2880 | 1.74063 | 0.870314 | − | 0.492497i | \(-0.163916\pi\) | ||||
0.870314 | + | 0.492497i | \(0.163916\pi\) | |||||||
\(180\) | −7.90542 | −0.589236 | ||||||||
\(181\) | 1.61698 | 0.120189 | 0.0600946 | − | 0.998193i | \(-0.480860\pi\) | ||||
0.0600946 | + | 0.998193i | \(0.480860\pi\) | |||||||
\(182\) | −0.207743 | −0.0153989 | ||||||||
\(183\) | 10.8439 | 0.801604 | ||||||||
\(184\) | 0.529496 | 0.0390349 | ||||||||
\(185\) | −24.8407 | −1.82633 | ||||||||
\(186\) | 0.0542410 | 0.00397714 | ||||||||
\(187\) | 5.26878 | 0.385291 | ||||||||
\(188\) | −13.5736 | −0.989960 | ||||||||
\(189\) | 1.89285 | 0.137685 | ||||||||
\(190\) | 0.661981 | 0.0480252 | ||||||||
\(191\) | −8.53278 | −0.617410 | −0.308705 | − | 0.951158i | \(-0.599896\pi\) | ||||
−0.308705 | + | 0.951158i | \(0.599896\pi\) | |||||||
\(192\) | −7.93786 | −0.572866 | ||||||||
\(193\) | −21.0273 | −1.51358 | −0.756790 | − | 0.653658i | \(-0.773233\pi\) | ||||
−0.756790 | + | 0.653658i | \(0.773233\pi\) | |||||||
\(194\) | 0.113671 | 0.00816113 | ||||||||
\(195\) | −8.53197 | −0.610987 | ||||||||
\(196\) | 6.82537 | 0.487526 | ||||||||
\(197\) | 18.1465 | 1.29288 | 0.646441 | − | 0.762964i | \(-0.276256\pi\) | ||||
0.646441 | + | 0.762964i | \(0.276256\pi\) | |||||||
\(198\) | 0.268243 | 0.0190632 | ||||||||
\(199\) | −8.58119 | −0.608305 | −0.304152 | − | 0.952623i | \(-0.598373\pi\) | ||||
−0.304152 | + | 0.952623i | \(0.598373\pi\) | |||||||
\(200\) | −2.17039 | −0.153470 | ||||||||
\(201\) | 10.6925 | 0.754193 | ||||||||
\(202\) | −0.392692 | −0.0276297 | ||||||||
\(203\) | 3.39698 | 0.238422 | ||||||||
\(204\) | −1.99741 | −0.139847 | ||||||||
\(205\) | 34.6883 | 2.42273 | ||||||||
\(206\) | 0.321082 | 0.0223708 | ||||||||
\(207\) | −2.60175 | −0.180834 | ||||||||
\(208\) | −8.58934 | −0.595564 | ||||||||
\(209\) | 17.3092 | 1.19731 | ||||||||
\(210\) | 0.381412 | 0.0263199 | ||||||||
\(211\) | 24.2509 | 1.66950 | 0.834749 | − | 0.550631i | \(-0.185613\pi\) | ||||
0.834749 | + | 0.550631i | \(0.185613\pi\) | |||||||
\(212\) | 13.6711 | 0.938932 | ||||||||
\(213\) | −0.635598 | −0.0435505 | ||||||||
\(214\) | −0.917875 | −0.0627446 | ||||||||
\(215\) | −40.5542 | −2.76577 | ||||||||
\(216\) | −0.203515 | −0.0138475 | ||||||||
\(217\) | 2.01663 | 0.136898 | ||||||||
\(218\) | 0.765683 | 0.0518586 | ||||||||
\(219\) | −3.45288 | −0.233324 | ||||||||
\(220\) | −41.6519 | −2.80817 | ||||||||
\(221\) | −2.15571 | −0.145009 | ||||||||
\(222\) | −0.319540 | −0.0214461 | ||||||||
\(223\) | −9.47539 | −0.634519 | −0.317260 | − | 0.948339i | \(-0.602763\pi\) | ||||
−0.317260 | + | 0.948339i | \(0.602763\pi\) | |||||||
\(224\) | 1.15443 | 0.0771333 | ||||||||
\(225\) | 10.6645 | 0.710967 | ||||||||
\(226\) | −0.0750764 | −0.00499401 | ||||||||
\(227\) | −15.6787 | −1.04063 | −0.520317 | − | 0.853973i | \(-0.674186\pi\) | ||||
−0.520317 | + | 0.853973i | \(0.674186\pi\) | |||||||
\(228\) | −6.56198 | −0.434578 | ||||||||
\(229\) | 18.9379 | 1.25145 | 0.625727 | − | 0.780042i | \(-0.284802\pi\) | ||||
0.625727 | + | 0.780042i | \(0.284802\pi\) | |||||||
\(230\) | −0.524255 | −0.0345683 | ||||||||
\(231\) | 9.97301 | 0.656176 | ||||||||
\(232\) | −0.365237 | −0.0239790 | ||||||||
\(233\) | 28.1117 | 1.84166 | 0.920829 | − | 0.389967i | \(-0.127514\pi\) | ||||
0.920829 | + | 0.389967i | \(0.127514\pi\) | |||||||
\(234\) | −0.109751 | −0.00717467 | ||||||||
\(235\) | 26.8960 | 1.75450 | ||||||||
\(236\) | 26.8717 | 1.74920 | ||||||||
\(237\) | 1.00000 | 0.0649570 | ||||||||
\(238\) | 0.0963686 | 0.00624665 | ||||||||
\(239\) | 24.0586 | 1.55622 | 0.778110 | − | 0.628128i | \(-0.216179\pi\) | ||||
0.778110 | + | 0.628128i | \(0.216179\pi\) | |||||||
\(240\) | 15.7698 | 1.01794 | ||||||||
\(241\) | 11.1814 | 0.720258 | 0.360129 | − | 0.932902i | \(-0.382733\pi\) | ||||
0.360129 | + | 0.932902i | \(0.382733\pi\) | |||||||
\(242\) | 0.853284 | 0.0548511 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −21.6597 | −1.38662 | ||||||||
\(245\) | −13.5244 | −0.864042 | ||||||||
\(246\) | 0.446214 | 0.0284496 | ||||||||
\(247\) | −7.08205 | −0.450620 | ||||||||
\(248\) | −0.216823 | −0.0137683 | ||||||||
\(249\) | −12.9078 | −0.818001 | ||||||||
\(250\) | 1.14140 | 0.0721888 | ||||||||
\(251\) | 13.3467 | 0.842437 | 0.421218 | − | 0.906959i | \(-0.361603\pi\) | ||||
0.421218 | + | 0.906959i | \(0.361603\pi\) | |||||||
\(252\) | −3.78080 | −0.238168 | ||||||||
\(253\) | −13.7080 | −0.861816 | ||||||||
\(254\) | −0.156377 | −0.00981194 | ||||||||
\(255\) | 3.95784 | 0.247850 | ||||||||
\(256\) | 15.7930 | 0.987065 | ||||||||
\(257\) | 16.1906 | 1.00994 | 0.504971 | − | 0.863137i | \(-0.331503\pi\) | ||||
0.504971 | + | 0.863137i | \(0.331503\pi\) | |||||||
\(258\) | −0.521670 | −0.0324778 | ||||||||
\(259\) | −11.8802 | −0.738197 | ||||||||
\(260\) | 17.0418 | 1.05689 | ||||||||
\(261\) | 1.79464 | 0.111085 | ||||||||
\(262\) | 0.377838 | 0.0233429 | ||||||||
\(263\) | −17.8736 | −1.10214 | −0.551068 | − | 0.834460i | \(-0.685779\pi\) | ||||
−0.551068 | + | 0.834460i | \(0.685779\pi\) | |||||||
\(264\) | −1.07228 | −0.0659941 | ||||||||
\(265\) | −27.0890 | −1.66407 | ||||||||
\(266\) | 0.316595 | 0.0194117 | ||||||||
\(267\) | −6.91898 | −0.423435 | ||||||||
\(268\) | −21.3573 | −1.30461 | ||||||||
\(269\) | 15.7614 | 0.960992 | 0.480496 | − | 0.876997i | \(-0.340457\pi\) | ||||
0.480496 | + | 0.876997i | \(0.340457\pi\) | |||||||
\(270\) | 0.201501 | 0.0122630 | ||||||||
\(271\) | −17.7427 | −1.07779 | −0.538897 | − | 0.842372i | \(-0.681159\pi\) | ||||
−0.538897 | + | 0.842372i | \(0.681159\pi\) | |||||||
\(272\) | 3.98445 | 0.241593 | ||||||||
\(273\) | −4.08045 | −0.246960 | ||||||||
\(274\) | −1.05691 | −0.0638502 | ||||||||
\(275\) | 56.1889 | 3.38832 | ||||||||
\(276\) | 5.19675 | 0.312807 | ||||||||
\(277\) | −14.7538 | −0.886471 | −0.443235 | − | 0.896405i | \(-0.646169\pi\) | ||||
−0.443235 | + | 0.896405i | \(0.646169\pi\) | |||||||
\(278\) | −0.356378 | −0.0213742 | ||||||||
\(279\) | 1.06539 | 0.0637833 | ||||||||
\(280\) | −1.52466 | −0.0911158 | ||||||||
\(281\) | −32.3269 | −1.92846 | −0.964230 | − | 0.265066i | \(-0.914606\pi\) | ||||
−0.964230 | + | 0.265066i | \(0.914606\pi\) | |||||||
\(282\) | 0.345978 | 0.0206027 | ||||||||
\(283\) | −15.7050 | −0.933565 | −0.466782 | − | 0.884372i | \(-0.654587\pi\) | ||||
−0.466782 | + | 0.884372i | \(0.654587\pi\) | |||||||
\(284\) | 1.26955 | 0.0753339 | ||||||||
\(285\) | 13.0025 | 0.770201 | ||||||||
\(286\) | −0.578256 | −0.0341930 | ||||||||
\(287\) | 16.5898 | 0.979264 | ||||||||
\(288\) | 0.609887 | 0.0359379 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0.361622 | 0.0212352 | ||||||||
\(291\) | 2.23271 | 0.130884 | ||||||||
\(292\) | 6.89681 | 0.403605 | ||||||||
\(293\) | −10.2116 | −0.596570 | −0.298285 | − | 0.954477i | \(-0.596415\pi\) | ||||
−0.298285 | + | 0.954477i | \(0.596415\pi\) | |||||||
\(294\) | −0.173972 | −0.0101462 | ||||||||
\(295\) | −53.2461 | −3.10011 | ||||||||
\(296\) | 1.27733 | 0.0742433 | ||||||||
\(297\) | 5.26878 | 0.305725 | ||||||||
\(298\) | −0.128300 | −0.00743221 | ||||||||
\(299\) | 5.60862 | 0.324355 | ||||||||
\(300\) | −21.3014 | −1.22984 | ||||||||
\(301\) | −19.3952 | −1.11792 | ||||||||
\(302\) | 0.122165 | 0.00702979 | ||||||||
\(303\) | −7.71317 | −0.443110 | ||||||||
\(304\) | 13.0899 | 0.750758 | ||||||||
\(305\) | 42.9185 | 2.45750 | ||||||||
\(306\) | 0.0509119 | 0.00291044 | ||||||||
\(307\) | −10.2616 | −0.585660 | −0.292830 | − | 0.956165i | \(-0.594597\pi\) | ||||
−0.292830 | + | 0.956165i | \(0.594597\pi\) | |||||||
\(308\) | −19.9202 | −1.13506 | ||||||||
\(309\) | 6.30662 | 0.358771 | ||||||||
\(310\) | 0.214677 | 0.0121929 | ||||||||
\(311\) | −3.07625 | −0.174438 | −0.0872191 | − | 0.996189i | \(-0.527798\pi\) | ||||
−0.0872191 | + | 0.996189i | \(0.527798\pi\) | |||||||
\(312\) | 0.438721 | 0.0248377 | ||||||||
\(313\) | −6.77918 | −0.383182 | −0.191591 | − | 0.981475i | \(-0.561365\pi\) | ||||
−0.191591 | + | 0.981475i | \(0.561365\pi\) | |||||||
\(314\) | −0.363012 | −0.0204860 | ||||||||
\(315\) | 7.49161 | 0.422104 | ||||||||
\(316\) | −1.99741 | −0.112363 | ||||||||
\(317\) | 27.8869 | 1.56628 | 0.783142 | − | 0.621842i | \(-0.213616\pi\) | ||||
0.783142 | + | 0.621842i | \(0.213616\pi\) | |||||||
\(318\) | −0.348461 | −0.0195407 | ||||||||
\(319\) | 9.45555 | 0.529409 | ||||||||
\(320\) | −31.4168 | −1.75625 | ||||||||
\(321\) | −18.0287 | −1.00626 | ||||||||
\(322\) | −0.250727 | −0.0139724 | ||||||||
\(323\) | 3.28525 | 0.182796 | ||||||||
\(324\) | −1.99741 | −0.110967 | ||||||||
\(325\) | −22.9896 | −1.27524 | ||||||||
\(326\) | 0.467440 | 0.0258891 | ||||||||
\(327\) | 15.0394 | 0.831680 | ||||||||
\(328\) | −1.78370 | −0.0984883 | ||||||||
\(329\) | 12.8631 | 0.709167 | ||||||||
\(330\) | 1.06166 | 0.0584427 | ||||||||
\(331\) | 28.0154 | 1.53986 | 0.769932 | − | 0.638126i | \(-0.220290\pi\) | ||||
0.769932 | + | 0.638126i | \(0.220290\pi\) | |||||||
\(332\) | 25.7822 | 1.41498 | ||||||||
\(333\) | −6.27633 | −0.343941 | ||||||||
\(334\) | 0.597775 | 0.0327088 | ||||||||
\(335\) | 42.3193 | 2.31215 | ||||||||
\(336\) | 7.54198 | 0.411449 | ||||||||
\(337\) | −26.2695 | −1.43099 | −0.715495 | − | 0.698618i | \(-0.753799\pi\) | ||||
−0.715495 | + | 0.698618i | \(0.753799\pi\) | |||||||
\(338\) | −0.425262 | −0.0231312 | ||||||||
\(339\) | −1.47464 | −0.0800912 | ||||||||
\(340\) | −7.90542 | −0.428732 | ||||||||
\(341\) | 5.61330 | 0.303978 | ||||||||
\(342\) | 0.167258 | 0.00904428 | ||||||||
\(343\) | −19.7180 | −1.06467 | ||||||||
\(344\) | 2.08533 | 0.112433 | ||||||||
\(345\) | −10.2973 | −0.554388 | ||||||||
\(346\) | −0.881609 | −0.0473956 | ||||||||
\(347\) | −1.44253 | −0.0774390 | −0.0387195 | − | 0.999250i | \(-0.512328\pi\) | ||||
−0.0387195 | + | 0.999250i | \(0.512328\pi\) | |||||||
\(348\) | −3.58462 | −0.192156 | ||||||||
\(349\) | 17.5904 | 0.941595 | 0.470797 | − | 0.882241i | \(-0.343966\pi\) | ||||
0.470797 | + | 0.882241i | \(0.343966\pi\) | |||||||
\(350\) | 1.02772 | 0.0549342 | ||||||||
\(351\) | −2.15571 | −0.115063 | ||||||||
\(352\) | 3.21336 | 0.171273 | ||||||||
\(353\) | 35.2617 | 1.87679 | 0.938394 | − | 0.345566i | \(-0.112313\pi\) | ||||
0.938394 | + | 0.345566i | \(0.112313\pi\) | |||||||
\(354\) | −0.684933 | −0.0364038 | ||||||||
\(355\) | −2.51560 | −0.133514 | ||||||||
\(356\) | 13.8200 | 0.732460 | ||||||||
\(357\) | 1.89285 | 0.100180 | ||||||||
\(358\) | 1.18564 | 0.0626628 | ||||||||
\(359\) | 27.6109 | 1.45725 | 0.728623 | − | 0.684915i | \(-0.240161\pi\) | ||||
0.728623 | + | 0.684915i | \(0.240161\pi\) | |||||||
\(360\) | −0.805482 | −0.0424526 | ||||||||
\(361\) | −8.20715 | −0.431955 | ||||||||
\(362\) | 0.0823235 | 0.00432683 | ||||||||
\(363\) | 16.7600 | 0.879673 | ||||||||
\(364\) | 8.15032 | 0.427193 | ||||||||
\(365\) | −13.6659 | −0.715308 | ||||||||
\(366\) | 0.552083 | 0.0288579 | ||||||||
\(367\) | −12.7400 | −0.665022 | −0.332511 | − | 0.943099i | \(-0.607896\pi\) | ||||
−0.332511 | + | 0.943099i | \(0.607896\pi\) | |||||||
\(368\) | −10.3665 | −0.540393 | ||||||||
\(369\) | 8.76444 | 0.456258 | ||||||||
\(370\) | −1.26469 | −0.0657480 | ||||||||
\(371\) | −12.9554 | −0.672612 | ||||||||
\(372\) | −2.12802 | −0.110333 | ||||||||
\(373\) | 14.7130 | 0.761808 | 0.380904 | − | 0.924615i | \(-0.375613\pi\) | ||||
0.380904 | + | 0.924615i | \(0.375613\pi\) | |||||||
\(374\) | 0.268243 | 0.0138705 | ||||||||
\(375\) | 22.4192 | 1.15772 | ||||||||
\(376\) | −1.38302 | −0.0713236 | ||||||||
\(377\) | −3.86873 | −0.199250 | ||||||||
\(378\) | 0.0963686 | 0.00495667 | ||||||||
\(379\) | 4.68446 | 0.240625 | 0.120312 | − | 0.992736i | \(-0.461610\pi\) | ||||
0.120312 | + | 0.992736i | \(0.461610\pi\) | |||||||
\(380\) | −25.9713 | −1.33230 | ||||||||
\(381\) | −3.07151 | −0.157358 | ||||||||
\(382\) | −0.434420 | −0.0222269 | ||||||||
\(383\) | 27.1546 | 1.38753 | 0.693767 | − | 0.720199i | \(-0.255950\pi\) | ||||
0.693767 | + | 0.720199i | \(0.255950\pi\) | |||||||
\(384\) | −1.62391 | −0.0828696 | ||||||||
\(385\) | 39.4716 | 2.01166 | ||||||||
\(386\) | −1.07054 | −0.0544891 | ||||||||
\(387\) | −10.2465 | −0.520861 | ||||||||
\(388\) | −4.45963 | −0.226404 | ||||||||
\(389\) | −7.35108 | −0.372715 | −0.186357 | − | 0.982482i | \(-0.559668\pi\) | ||||
−0.186357 | + | 0.982482i | \(0.559668\pi\) | |||||||
\(390\) | −0.434379 | −0.0219956 | ||||||||
\(391\) | −2.60175 | −0.131576 | ||||||||
\(392\) | 0.695435 | 0.0351248 | ||||||||
\(393\) | 7.42141 | 0.374361 | ||||||||
\(394\) | 0.923871 | 0.0465439 | ||||||||
\(395\) | 3.95784 | 0.199141 | ||||||||
\(396\) | −10.5239 | −0.528846 | ||||||||
\(397\) | 1.86641 | 0.0936722 | 0.0468361 | − | 0.998903i | \(-0.485086\pi\) | ||||
0.0468361 | + | 0.998903i | \(0.485086\pi\) | |||||||
\(398\) | −0.436884 | −0.0218990 | ||||||||
\(399\) | 6.21849 | 0.311314 | ||||||||
\(400\) | 42.4923 | 2.12461 | ||||||||
\(401\) | 15.5893 | 0.778491 | 0.389246 | − | 0.921134i | \(-0.372736\pi\) | ||||
0.389246 | + | 0.921134i | \(0.372736\pi\) | |||||||
\(402\) | 0.544377 | 0.0271510 | ||||||||
\(403\) | −2.29668 | −0.114406 | ||||||||
\(404\) | 15.4064 | 0.766495 | ||||||||
\(405\) | 3.95784 | 0.196667 | ||||||||
\(406\) | 0.172947 | 0.00858321 | ||||||||
\(407\) | −33.0686 | −1.63915 | ||||||||
\(408\) | −0.203515 | −0.0100755 | ||||||||
\(409\) | 19.8656 | 0.982291 | 0.491145 | − | 0.871078i | \(-0.336578\pi\) | ||||
0.491145 | + | 0.871078i | \(0.336578\pi\) | |||||||
\(410\) | 1.76604 | 0.0872187 | ||||||||
\(411\) | −20.7596 | −1.02399 | ||||||||
\(412\) | −12.5969 | −0.620605 | ||||||||
\(413\) | −25.4651 | −1.25306 | ||||||||
\(414\) | −0.132460 | −0.00651004 | ||||||||
\(415\) | −51.0872 | −2.50777 | ||||||||
\(416\) | −1.31474 | −0.0644605 | ||||||||
\(417\) | −6.99991 | −0.342787 | ||||||||
\(418\) | 0.881246 | 0.0431031 | ||||||||
\(419\) | 24.8173 | 1.21241 | 0.606203 | − | 0.795310i | \(-0.292692\pi\) | ||||
0.606203 | + | 0.795310i | \(0.292692\pi\) | |||||||
\(420\) | −14.9638 | −0.730158 | ||||||||
\(421\) | 0.949942 | 0.0462974 | 0.0231487 | − | 0.999732i | \(-0.492631\pi\) | ||||
0.0231487 | + | 0.999732i | \(0.492631\pi\) | |||||||
\(422\) | 1.23466 | 0.0601021 | ||||||||
\(423\) | 6.79563 | 0.330415 | ||||||||
\(424\) | 1.39294 | 0.0676472 | ||||||||
\(425\) | 10.6645 | 0.517305 | ||||||||
\(426\) | −0.0323595 | −0.00156782 | ||||||||
\(427\) | 20.5259 | 0.993318 | ||||||||
\(428\) | 36.0107 | 1.74064 | ||||||||
\(429\) | −11.3580 | −0.548368 | ||||||||
\(430\) | −2.06469 | −0.0995681 | ||||||||
\(431\) | −37.6436 | −1.81323 | −0.906613 | − | 0.421962i | \(-0.861341\pi\) | ||||
−0.906613 | + | 0.421962i | \(0.861341\pi\) | |||||||
\(432\) | 3.98445 | 0.191702 | ||||||||
\(433\) | 26.7637 | 1.28618 | 0.643090 | − | 0.765791i | \(-0.277652\pi\) | ||||
0.643090 | + | 0.765791i | \(0.277652\pi\) | |||||||
\(434\) | 0.102670 | 0.00492833 | ||||||||
\(435\) | 7.10289 | 0.340558 | ||||||||
\(436\) | −30.0398 | −1.43864 | ||||||||
\(437\) | −8.54738 | −0.408877 | ||||||||
\(438\) | −0.175792 | −0.00839969 | ||||||||
\(439\) | 36.4366 | 1.73902 | 0.869512 | − | 0.493912i | \(-0.164433\pi\) | ||||
0.869512 | + | 0.493912i | \(0.164433\pi\) | |||||||
\(440\) | −4.24391 | −0.202320 | ||||||||
\(441\) | −3.41711 | −0.162720 | ||||||||
\(442\) | −0.109751 | −0.00522034 | ||||||||
\(443\) | 11.0897 | 0.526889 | 0.263444 | − | 0.964675i | \(-0.415141\pi\) | ||||
0.263444 | + | 0.964675i | \(0.415141\pi\) | |||||||
\(444\) | 12.5364 | 0.594951 | ||||||||
\(445\) | −27.3842 | −1.29814 | ||||||||
\(446\) | −0.482410 | −0.0228428 | ||||||||
\(447\) | −2.52004 | −0.119194 | ||||||||
\(448\) | −15.0252 | −0.709873 | ||||||||
\(449\) | −14.4035 | −0.679745 | −0.339872 | − | 0.940472i | \(-0.610384\pi\) | ||||
−0.339872 | + | 0.940472i | \(0.610384\pi\) | |||||||
\(450\) | 0.542950 | 0.0255949 | ||||||||
\(451\) | 46.1779 | 2.17443 | ||||||||
\(452\) | 2.94545 | 0.138542 | ||||||||
\(453\) | 2.39953 | 0.112740 | ||||||||
\(454\) | −0.798234 | −0.0374630 | ||||||||
\(455\) | −16.1498 | −0.757112 | ||||||||
\(456\) | −0.668599 | −0.0313100 | ||||||||
\(457\) | 2.53031 | 0.118363 | 0.0591815 | − | 0.998247i | \(-0.481151\pi\) | ||||
0.0591815 | + | 0.998247i | \(0.481151\pi\) | |||||||
\(458\) | 0.964166 | 0.0450525 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 20.5679 | 0.958983 | ||||||||
\(461\) | −26.2235 | −1.22135 | −0.610675 | − | 0.791881i | \(-0.709102\pi\) | ||||
−0.610675 | + | 0.791881i | \(0.709102\pi\) | |||||||
\(462\) | 0.507745 | 0.0236224 | ||||||||
\(463\) | −33.4646 | −1.55523 | −0.777617 | − | 0.628739i | \(-0.783572\pi\) | ||||
−0.777617 | + | 0.628739i | \(0.783572\pi\) | |||||||
\(464\) | 7.15066 | 0.331961 | ||||||||
\(465\) | 4.21665 | 0.195542 | ||||||||
\(466\) | 1.43122 | 0.0662999 | ||||||||
\(467\) | −8.60118 | −0.398015 | −0.199008 | − | 0.979998i | \(-0.563772\pi\) | ||||
−0.199008 | + | 0.979998i | \(0.563772\pi\) | |||||||
\(468\) | 4.30584 | 0.199038 | ||||||||
\(469\) | 20.2394 | 0.934567 | ||||||||
\(470\) | 1.36933 | 0.0631623 | ||||||||
\(471\) | −7.13021 | −0.328543 | ||||||||
\(472\) | 2.73796 | 0.126025 | ||||||||
\(473\) | −53.9867 | −2.48231 | ||||||||
\(474\) | 0.0509119 | 0.00233846 | ||||||||
\(475\) | 35.0356 | 1.60754 | ||||||||
\(476\) | −3.78080 | −0.173293 | ||||||||
\(477\) | −6.84440 | −0.313383 | ||||||||
\(478\) | 1.22487 | 0.0560241 | ||||||||
\(479\) | −22.0804 | −1.00888 | −0.504439 | − | 0.863447i | \(-0.668301\pi\) | ||||
−0.504439 | + | 0.863447i | \(0.668301\pi\) | |||||||
\(480\) | 2.41384 | 0.110176 | ||||||||
\(481\) | 13.5300 | 0.616914 | ||||||||
\(482\) | 0.569267 | 0.0259294 | ||||||||
\(483\) | −4.92472 | −0.224082 | ||||||||
\(484\) | −33.4766 | −1.52166 | ||||||||
\(485\) | 8.83671 | 0.401255 | ||||||||
\(486\) | 0.0509119 | 0.00230941 | ||||||||
\(487\) | −3.82625 | −0.173384 | −0.0866920 | − | 0.996235i | \(-0.527630\pi\) | ||||
−0.0866920 | + | 0.996235i | \(0.527630\pi\) | |||||||
\(488\) | −2.20690 | −0.0999018 | ||||||||
\(489\) | 9.18135 | 0.415195 | ||||||||
\(490\) | −0.688552 | −0.0311056 | ||||||||
\(491\) | −17.9562 | −0.810353 | −0.405177 | − | 0.914238i | \(-0.632790\pi\) | ||||
−0.405177 | + | 0.914238i | \(0.632790\pi\) | |||||||
\(492\) | −17.5062 | −0.789239 | ||||||||
\(493\) | 1.79464 | 0.0808264 | ||||||||
\(494\) | −0.360561 | −0.0162224 | ||||||||
\(495\) | 20.8530 | 0.937272 | ||||||||
\(496\) | 4.24500 | 0.190606 | ||||||||
\(497\) | −1.20309 | −0.0539661 | ||||||||
\(498\) | −0.657162 | −0.0294481 | ||||||||
\(499\) | −20.8933 | −0.935311 | −0.467656 | − | 0.883911i | \(-0.654901\pi\) | ||||
−0.467656 | + | 0.883911i | \(0.654901\pi\) | |||||||
\(500\) | −44.7804 | −2.00264 | ||||||||
\(501\) | 11.7414 | 0.524566 | ||||||||
\(502\) | 0.679506 | 0.0303278 | ||||||||
\(503\) | −36.3950 | −1.62277 | −0.811386 | − | 0.584511i | \(-0.801286\pi\) | ||||
−0.811386 | + | 0.584511i | \(0.801286\pi\) | |||||||
\(504\) | −0.385225 | −0.0171593 | ||||||||
\(505\) | −30.5275 | −1.35846 | ||||||||
\(506\) | −0.697901 | −0.0310255 | ||||||||
\(507\) | −8.35290 | −0.370965 | ||||||||
\(508\) | 6.13507 | 0.272200 | ||||||||
\(509\) | −27.7110 | −1.22827 | −0.614133 | − | 0.789202i | \(-0.710494\pi\) | ||||
−0.614133 | + | 0.789202i | \(0.710494\pi\) | |||||||
\(510\) | 0.201501 | 0.00892262 | ||||||||
\(511\) | −6.53579 | −0.289126 | ||||||||
\(512\) | 4.05186 | 0.179069 | ||||||||
\(513\) | 3.28525 | 0.145047 | ||||||||
\(514\) | 0.824293 | 0.0363580 | ||||||||
\(515\) | 24.9606 | 1.09990 | ||||||||
\(516\) | 20.4665 | 0.900988 | ||||||||
\(517\) | 35.8047 | 1.57469 | ||||||||
\(518\) | −0.604841 | −0.0265752 | ||||||||
\(519\) | −17.3164 | −0.760104 | ||||||||
\(520\) | 1.73639 | 0.0761457 | ||||||||
\(521\) | 15.1921 | 0.665580 | 0.332790 | − | 0.943001i | \(-0.392010\pi\) | ||||
0.332790 | + | 0.943001i | \(0.392010\pi\) | |||||||
\(522\) | 0.0913684 | 0.00399909 | ||||||||
\(523\) | −13.9690 | −0.610822 | −0.305411 | − | 0.952221i | \(-0.598794\pi\) | ||||
−0.305411 | + | 0.952221i | \(0.598794\pi\) | |||||||
\(524\) | −14.8236 | −0.647571 | ||||||||
\(525\) | 20.1863 | 0.881004 | ||||||||
\(526\) | −0.909980 | −0.0396770 | ||||||||
\(527\) | 1.06539 | 0.0464091 | ||||||||
\(528\) | 20.9932 | 0.913612 | ||||||||
\(529\) | −16.2309 | −0.705692 | ||||||||
\(530\) | −1.37915 | −0.0599066 | ||||||||
\(531\) | −13.4533 | −0.583824 | ||||||||
\(532\) | −12.4209 | −0.538512 | ||||||||
\(533\) | −18.8936 | −0.818374 | ||||||||
\(534\) | −0.352258 | −0.0152437 | ||||||||
\(535\) | −71.3547 | −3.08493 | ||||||||
\(536\) | −2.17610 | −0.0939930 | ||||||||
\(537\) | 23.2880 | 1.00495 | ||||||||
\(538\) | 0.802444 | 0.0345958 | ||||||||
\(539\) | −18.0040 | −0.775487 | ||||||||
\(540\) | −7.90542 | −0.340195 | ||||||||
\(541\) | −2.79015 | −0.119958 | −0.0599790 | − | 0.998200i | \(-0.519103\pi\) | ||||
−0.0599790 | + | 0.998200i | \(0.519103\pi\) | |||||||
\(542\) | −0.903316 | −0.0388007 | ||||||||
\(543\) | 1.61698 | 0.0693913 | ||||||||
\(544\) | 0.609887 | 0.0261487 | ||||||||
\(545\) | 59.5235 | 2.54971 | ||||||||
\(546\) | −0.207743 | −0.00889059 | ||||||||
\(547\) | 13.7464 | 0.587755 | 0.293877 | − | 0.955843i | \(-0.405054\pi\) | ||||
0.293877 | + | 0.955843i | \(0.405054\pi\) | |||||||
\(548\) | 41.4653 | 1.77131 | ||||||||
\(549\) | 10.8439 | 0.462807 | ||||||||
\(550\) | 2.86068 | 0.121980 | ||||||||
\(551\) | 5.89583 | 0.251171 | ||||||||
\(552\) | 0.529496 | 0.0225368 | ||||||||
\(553\) | 1.89285 | 0.0804922 | ||||||||
\(554\) | −0.751144 | −0.0319131 | ||||||||
\(555\) | −24.8407 | −1.05443 | ||||||||
\(556\) | 13.9817 | 0.592955 | ||||||||
\(557\) | 20.9519 | 0.887762 | 0.443881 | − | 0.896086i | \(-0.353601\pi\) | ||||
0.443881 | + | 0.896086i | \(0.353601\pi\) | |||||||
\(558\) | 0.0542410 | 0.00229621 | ||||||||
\(559\) | 22.0886 | 0.934248 | ||||||||
\(560\) | 29.8500 | 1.26139 | ||||||||
\(561\) | 5.26878 | 0.222448 | ||||||||
\(562\) | −1.64582 | −0.0694248 | ||||||||
\(563\) | 42.8573 | 1.80622 | 0.903109 | − | 0.429411i | \(-0.141279\pi\) | ||||
0.903109 | + | 0.429411i | \(0.141279\pi\) | |||||||
\(564\) | −13.5736 | −0.571553 | ||||||||
\(565\) | −5.83637 | −0.245538 | ||||||||
\(566\) | −0.799570 | −0.0336084 | ||||||||
\(567\) | 1.89285 | 0.0794923 | ||||||||
\(568\) | 0.129354 | 0.00542758 | ||||||||
\(569\) | 4.96177 | 0.208008 | 0.104004 | − | 0.994577i | \(-0.466834\pi\) | ||||
0.104004 | + | 0.994577i | \(0.466834\pi\) | |||||||
\(570\) | 0.661981 | 0.0277273 | ||||||||
\(571\) | 4.32863 | 0.181147 | 0.0905737 | − | 0.995890i | \(-0.471130\pi\) | ||||
0.0905737 | + | 0.995890i | \(0.471130\pi\) | |||||||
\(572\) | 22.6865 | 0.948571 | ||||||||
\(573\) | −8.53278 | −0.356462 | ||||||||
\(574\) | 0.844617 | 0.0352536 | ||||||||
\(575\) | −27.7463 | −1.15710 | ||||||||
\(576\) | −7.93786 | −0.330744 | ||||||||
\(577\) | −40.8018 | −1.69860 | −0.849301 | − | 0.527909i | \(-0.822976\pi\) | ||||
−0.849301 | + | 0.527909i | \(0.822976\pi\) | |||||||
\(578\) | 0.0509119 | 0.00211765 | ||||||||
\(579\) | −21.0273 | −0.873866 | ||||||||
\(580\) | −14.1874 | −0.589099 | ||||||||
\(581\) | −24.4326 | −1.01364 | ||||||||
\(582\) | 0.113671 | 0.00471183 | ||||||||
\(583\) | −36.0616 | −1.49352 | ||||||||
\(584\) | 0.702714 | 0.0290785 | ||||||||
\(585\) | −8.53197 | −0.352754 | ||||||||
\(586\) | −0.519893 | −0.0214766 | ||||||||
\(587\) | −36.6535 | −1.51285 | −0.756427 | − | 0.654079i | \(-0.773057\pi\) | ||||
−0.756427 | + | 0.654079i | \(0.773057\pi\) | |||||||
\(588\) | 6.82537 | 0.281473 | ||||||||
\(589\) | 3.50007 | 0.144218 | ||||||||
\(590\) | −2.71086 | −0.111604 | ||||||||
\(591\) | 18.1465 | 0.746446 | ||||||||
\(592\) | −25.0078 | −1.02781 | ||||||||
\(593\) | 1.21468 | 0.0498807 | 0.0249404 | − | 0.999689i | \(-0.492060\pi\) | ||||
0.0249404 | + | 0.999689i | \(0.492060\pi\) | |||||||
\(594\) | 0.268243 | 0.0110062 | ||||||||
\(595\) | 7.49161 | 0.307126 | ||||||||
\(596\) | 5.03354 | 0.206182 | ||||||||
\(597\) | −8.58119 | −0.351205 | ||||||||
\(598\) | 0.285545 | 0.0116768 | ||||||||
\(599\) | 10.0949 | 0.412466 | 0.206233 | − | 0.978503i | \(-0.433879\pi\) | ||||
0.206233 | + | 0.978503i | \(0.433879\pi\) | |||||||
\(600\) | −2.17039 | −0.0886059 | ||||||||
\(601\) | −17.6006 | −0.717943 | −0.358972 | − | 0.933348i | \(-0.616873\pi\) | ||||
−0.358972 | + | 0.933348i | \(0.616873\pi\) | |||||||
\(602\) | −0.987444 | −0.0402452 | ||||||||
\(603\) | 10.6925 | 0.435433 | ||||||||
\(604\) | −4.79285 | −0.195018 | ||||||||
\(605\) | 66.3335 | 2.69684 | ||||||||
\(606\) | −0.392692 | −0.0159520 | ||||||||
\(607\) | −7.07116 | −0.287010 | −0.143505 | − | 0.989650i | \(-0.545837\pi\) | ||||
−0.143505 | + | 0.989650i | \(0.545837\pi\) | |||||||
\(608\) | 2.00363 | 0.0812579 | ||||||||
\(609\) | 3.39698 | 0.137653 | ||||||||
\(610\) | 2.18506 | 0.0884704 | ||||||||
\(611\) | −14.6494 | −0.592652 | ||||||||
\(612\) | −1.99741 | −0.0807404 | ||||||||
\(613\) | −24.6259 | −0.994631 | −0.497315 | − | 0.867570i | \(-0.665681\pi\) | ||||
−0.497315 | + | 0.867570i | \(0.665681\pi\) | |||||||
\(614\) | −0.522436 | −0.0210838 | ||||||||
\(615\) | 34.6883 | 1.39877 | ||||||||
\(616\) | −2.02966 | −0.0817774 | ||||||||
\(617\) | −44.2311 | −1.78068 | −0.890338 | − | 0.455300i | \(-0.849532\pi\) | ||||
−0.890338 | + | 0.455300i | \(0.849532\pi\) | |||||||
\(618\) | 0.321082 | 0.0129158 | ||||||||
\(619\) | −21.7895 | −0.875794 | −0.437897 | − | 0.899025i | \(-0.644277\pi\) | ||||
−0.437897 | + | 0.899025i | \(0.644277\pi\) | |||||||
\(620\) | −8.42236 | −0.338250 | ||||||||
\(621\) | −2.60175 | −0.104404 | ||||||||
\(622\) | −0.156618 | −0.00627979 | ||||||||
\(623\) | −13.0966 | −0.524705 | ||||||||
\(624\) | −8.58934 | −0.343849 | ||||||||
\(625\) | 35.4092 | 1.41637 | ||||||||
\(626\) | −0.345141 | −0.0137946 | ||||||||
\(627\) | 17.3092 | 0.691264 | ||||||||
\(628\) | 14.2419 | 0.568315 | ||||||||
\(629\) | −6.27633 | −0.250254 | ||||||||
\(630\) | 0.381412 | 0.0151958 | ||||||||
\(631\) | −16.6559 | −0.663062 | −0.331531 | − | 0.943444i | \(-0.607565\pi\) | ||||
−0.331531 | + | 0.943444i | \(0.607565\pi\) | |||||||
\(632\) | −0.203515 | −0.00809541 | ||||||||
\(633\) | 24.2509 | 0.963885 | ||||||||
\(634\) | 1.41977 | 0.0563865 | ||||||||
\(635\) | −12.1566 | −0.482419 | ||||||||
\(636\) | 13.6711 | 0.542093 | ||||||||
\(637\) | 7.36632 | 0.291864 | ||||||||
\(638\) | 0.481400 | 0.0190588 | ||||||||
\(639\) | −0.635598 | −0.0251439 | ||||||||
\(640\) | −6.42716 | −0.254056 | ||||||||
\(641\) | 39.3415 | 1.55390 | 0.776949 | − | 0.629564i | \(-0.216766\pi\) | ||||
0.776949 | + | 0.629564i | \(0.216766\pi\) | |||||||
\(642\) | −0.917875 | −0.0362256 | ||||||||
\(643\) | −29.6872 | −1.17075 | −0.585374 | − | 0.810763i | \(-0.699052\pi\) | ||||
−0.585374 | + | 0.810763i | \(0.699052\pi\) | |||||||
\(644\) | 9.83667 | 0.387619 | ||||||||
\(645\) | −40.5542 | −1.59682 | ||||||||
\(646\) | 0.167258 | 0.00658068 | ||||||||
\(647\) | 10.7626 | 0.423123 | 0.211562 | − | 0.977365i | \(-0.432145\pi\) | ||||
0.211562 | + | 0.977365i | \(0.432145\pi\) | |||||||
\(648\) | −0.203515 | −0.00799484 | ||||||||
\(649\) | −70.8825 | −2.78238 | ||||||||
\(650\) | −1.17044 | −0.0459086 | ||||||||
\(651\) | 2.01663 | 0.0790378 | ||||||||
\(652\) | −18.3389 | −0.718207 | ||||||||
\(653\) | −41.0151 | −1.60505 | −0.802523 | − | 0.596621i | \(-0.796510\pi\) | ||||
−0.802523 | + | 0.596621i | \(0.796510\pi\) | |||||||
\(654\) | 0.765683 | 0.0299406 | ||||||||
\(655\) | 29.3728 | 1.14769 | ||||||||
\(656\) | 34.9215 | 1.36346 | ||||||||
\(657\) | −3.45288 | −0.134710 | ||||||||
\(658\) | 0.654885 | 0.0255301 | ||||||||
\(659\) | −41.0426 | −1.59879 | −0.799397 | − | 0.600804i | \(-0.794847\pi\) | ||||
−0.799397 | + | 0.600804i | \(0.794847\pi\) | |||||||
\(660\) | −41.6519 | −1.62130 | ||||||||
\(661\) | −14.7998 | −0.575645 | −0.287822 | − | 0.957684i | \(-0.592931\pi\) | ||||
−0.287822 | + | 0.957684i | \(0.592931\pi\) | |||||||
\(662\) | 1.42632 | 0.0554353 | ||||||||
\(663\) | −2.15571 | −0.0837210 | ||||||||
\(664\) | 2.62695 | 0.101945 | ||||||||
\(665\) | 24.6118 | 0.954404 | ||||||||
\(666\) | −0.319540 | −0.0123819 | ||||||||
\(667\) | −4.66919 | −0.180792 | ||||||||
\(668\) | −23.4523 | −0.907397 | ||||||||
\(669\) | −9.47539 | −0.366340 | ||||||||
\(670\) | 2.15456 | 0.0832378 | ||||||||
\(671\) | 57.1341 | 2.20564 | ||||||||
\(672\) | 1.15443 | 0.0445329 | ||||||||
\(673\) | 50.4582 | 1.94502 | 0.972510 | − | 0.232862i | \(-0.0748092\pi\) | ||||
0.972510 | + | 0.232862i | \(0.0748092\pi\) | |||||||
\(674\) | −1.33743 | −0.0515158 | ||||||||
\(675\) | 10.6645 | 0.410477 | ||||||||
\(676\) | 16.6841 | 0.641698 | ||||||||
\(677\) | −16.6894 | −0.641425 | −0.320713 | − | 0.947177i | \(-0.603922\pi\) | ||||
−0.320713 | + | 0.947177i | \(0.603922\pi\) | |||||||
\(678\) | −0.0750764 | −0.00288329 | ||||||||
\(679\) | 4.22619 | 0.162186 | ||||||||
\(680\) | −0.805482 | −0.0308888 | ||||||||
\(681\) | −15.6787 | −0.600811 | ||||||||
\(682\) | 0.285784 | 0.0109432 | ||||||||
\(683\) | 17.3496 | 0.663865 | 0.331932 | − | 0.943303i | \(-0.392299\pi\) | ||||
0.331932 | + | 0.943303i | \(0.392299\pi\) | |||||||
\(684\) | −6.56198 | −0.250904 | ||||||||
\(685\) | −82.1631 | −3.13929 | ||||||||
\(686\) | −1.00388 | −0.0383284 | ||||||||
\(687\) | 18.9379 | 0.722528 | ||||||||
\(688\) | −40.8269 | −1.55651 | ||||||||
\(689\) | 14.7546 | 0.562104 | ||||||||
\(690\) | −0.524255 | −0.0199580 | ||||||||
\(691\) | −31.5049 | −1.19850 | −0.599251 | − | 0.800562i | \(-0.704535\pi\) | ||||
−0.599251 | + | 0.800562i | \(0.704535\pi\) | |||||||
\(692\) | 34.5879 | 1.31483 | ||||||||
\(693\) | 9.97301 | 0.378843 | ||||||||
\(694\) | −0.0734418 | −0.00278781 | ||||||||
\(695\) | −27.7045 | −1.05089 | ||||||||
\(696\) | −0.365237 | −0.0138443 | ||||||||
\(697\) | 8.76444 | 0.331977 | ||||||||
\(698\) | 0.895562 | 0.0338975 | ||||||||
\(699\) | 28.1117 | 1.06328 | ||||||||
\(700\) | −40.3203 | −1.52397 | ||||||||
\(701\) | −16.8050 | −0.634715 | −0.317357 | − | 0.948306i | \(-0.602795\pi\) | ||||
−0.317357 | + | 0.948306i | \(0.602795\pi\) | |||||||
\(702\) | −0.109751 | −0.00414230 | ||||||||
\(703\) | −20.6193 | −0.777672 | ||||||||
\(704\) | −41.8228 | −1.57626 | ||||||||
\(705\) | 26.8960 | 1.01296 | ||||||||
\(706\) | 1.79524 | 0.0675646 | ||||||||
\(707\) | −14.5999 | −0.549086 | ||||||||
\(708\) | 26.8717 | 1.00990 | ||||||||
\(709\) | −34.7618 | −1.30551 | −0.652753 | − | 0.757571i | \(-0.726386\pi\) | ||||
−0.652753 | + | 0.757571i | \(0.726386\pi\) | |||||||
\(710\) | −0.128074 | −0.00480652 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | 1.40812 | 0.0527715 | ||||||||
\(713\) | −2.77188 | −0.103808 | ||||||||
\(714\) | 0.0963686 | 0.00360650 | ||||||||
\(715\) | −44.9531 | −1.68115 | ||||||||
\(716\) | −46.5157 | −1.73837 | ||||||||
\(717\) | 24.0586 | 0.898484 | ||||||||
\(718\) | 1.40572 | 0.0524610 | ||||||||
\(719\) | 2.59739 | 0.0968663 | 0.0484332 | − | 0.998826i | \(-0.484577\pi\) | ||||
0.0484332 | + | 0.998826i | \(0.484577\pi\) | |||||||
\(720\) | 15.7698 | 0.587707 | ||||||||
\(721\) | 11.9375 | 0.444576 | ||||||||
\(722\) | −0.417841 | −0.0155504 | ||||||||
\(723\) | 11.1814 | 0.415841 | ||||||||
\(724\) | −3.22977 | −0.120034 | ||||||||
\(725\) | 19.1389 | 0.710802 | ||||||||
\(726\) | 0.853284 | 0.0316683 | ||||||||
\(727\) | 27.1767 | 1.00793 | 0.503964 | − | 0.863724i | \(-0.331874\pi\) | ||||
0.503964 | + | 0.863724i | \(0.331874\pi\) | |||||||
\(728\) | 0.830434 | 0.0307779 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.695759 | −0.0257512 | ||||||||
\(731\) | −10.2465 | −0.378982 | ||||||||
\(732\) | −21.6597 | −0.800565 | ||||||||
\(733\) | 11.0733 | 0.409001 | 0.204501 | − | 0.978866i | \(-0.434443\pi\) | ||||
0.204501 | + | 0.978866i | \(0.434443\pi\) | |||||||
\(734\) | −0.648617 | −0.0239409 | ||||||||
\(735\) | −13.5244 | −0.498855 | ||||||||
\(736\) | −1.58677 | −0.0584891 | ||||||||
\(737\) | 56.3366 | 2.07518 | ||||||||
\(738\) | 0.446214 | 0.0164254 | ||||||||
\(739\) | 39.7289 | 1.46145 | 0.730725 | − | 0.682672i | \(-0.239182\pi\) | ||||
0.730725 | + | 0.682672i | \(0.239182\pi\) | |||||||
\(740\) | 49.6171 | 1.82396 | ||||||||
\(741\) | −7.08205 | −0.260166 | ||||||||
\(742\) | −0.659585 | −0.0242141 | ||||||||
\(743\) | 10.0844 | 0.369959 | 0.184980 | − | 0.982742i | \(-0.440778\pi\) | ||||
0.184980 | + | 0.982742i | \(0.440778\pi\) | |||||||
\(744\) | −0.216823 | −0.00794913 | ||||||||
\(745\) | −9.97391 | −0.365416 | ||||||||
\(746\) | 0.749064 | 0.0274252 | ||||||||
\(747\) | −12.9078 | −0.472273 | ||||||||
\(748\) | −10.5239 | −0.384792 | ||||||||
\(749\) | −34.1257 | −1.24692 | ||||||||
\(750\) | 1.14140 | 0.0416782 | ||||||||
\(751\) | 13.6380 | 0.497659 | 0.248830 | − | 0.968547i | \(-0.419954\pi\) | ||||
0.248830 | + | 0.968547i | \(0.419954\pi\) | |||||||
\(752\) | 27.0769 | 0.987392 | ||||||||
\(753\) | 13.3467 | 0.486381 | ||||||||
\(754\) | −0.196964 | −0.00717301 | ||||||||
\(755\) | 9.49698 | 0.345630 | ||||||||
\(756\) | −3.78080 | −0.137506 | ||||||||
\(757\) | 4.64496 | 0.168824 | 0.0844119 | − | 0.996431i | \(-0.473099\pi\) | ||||
0.0844119 | + | 0.996431i | \(0.473099\pi\) | |||||||
\(758\) | 0.238495 | 0.00866251 | ||||||||
\(759\) | −13.7080 | −0.497570 | ||||||||
\(760\) | −2.64621 | −0.0959881 | ||||||||
\(761\) | 25.3506 | 0.918958 | 0.459479 | − | 0.888189i | \(-0.348036\pi\) | ||||
0.459479 | + | 0.888189i | \(0.348036\pi\) | |||||||
\(762\) | −0.156377 | −0.00566492 | ||||||||
\(763\) | 28.4673 | 1.03059 | ||||||||
\(764\) | 17.0434 | 0.616610 | ||||||||
\(765\) | 3.95784 | 0.143096 | ||||||||
\(766\) | 1.38249 | 0.0499514 | ||||||||
\(767\) | 29.0015 | 1.04718 | ||||||||
\(768\) | 15.7930 | 0.569882 | ||||||||
\(769\) | 26.6305 | 0.960322 | 0.480161 | − | 0.877180i | \(-0.340578\pi\) | ||||
0.480161 | + | 0.877180i | \(0.340578\pi\) | |||||||
\(770\) | 2.00957 | 0.0724200 | ||||||||
\(771\) | 16.1906 | 0.583090 | ||||||||
\(772\) | 42.0001 | 1.51162 | ||||||||
\(773\) | −0.763296 | −0.0274538 | −0.0137269 | − | 0.999906i | \(-0.504370\pi\) | ||||
−0.0137269 | + | 0.999906i | \(0.504370\pi\) | |||||||
\(774\) | −0.521670 | −0.0187510 | ||||||||
\(775\) | 11.3619 | 0.408130 | ||||||||
\(776\) | −0.454391 | −0.0163117 | ||||||||
\(777\) | −11.8802 | −0.426198 | ||||||||
\(778\) | −0.374257 | −0.0134178 | ||||||||
\(779\) | 28.7934 | 1.03163 | ||||||||
\(780\) | 17.0418 | 0.610195 | ||||||||
\(781\) | −3.34883 | −0.119830 | ||||||||
\(782\) | −0.132460 | −0.00473675 | ||||||||
\(783\) | 1.79464 | 0.0641351 | ||||||||
\(784\) | −13.6153 | −0.486262 | ||||||||
\(785\) | −28.2202 | −1.00722 | ||||||||
\(786\) | 0.377838 | 0.0134770 | ||||||||
\(787\) | 11.1190 | 0.396351 | 0.198175 | − | 0.980167i | \(-0.436498\pi\) | ||||
0.198175 | + | 0.980167i | \(0.436498\pi\) | |||||||
\(788\) | −36.2459 | −1.29121 | ||||||||
\(789\) | −17.8736 | −0.636318 | ||||||||
\(790\) | 0.201501 | 0.00716909 | ||||||||
\(791\) | −2.79127 | −0.0992460 | ||||||||
\(792\) | −1.07228 | −0.0381017 | ||||||||
\(793\) | −23.3763 | −0.830119 | ||||||||
\(794\) | 0.0950222 | 0.00337221 | ||||||||
\(795\) | −27.0890 | −0.960749 | ||||||||
\(796\) | 17.1401 | 0.607516 | ||||||||
\(797\) | −46.4224 | −1.64436 | −0.822182 | − | 0.569224i | \(-0.807244\pi\) | ||||
−0.822182 | + | 0.569224i | \(0.807244\pi\) | |||||||
\(798\) | 0.316595 | 0.0112073 | ||||||||
\(799\) | 6.79563 | 0.240412 | ||||||||
\(800\) | 6.50415 | 0.229956 | ||||||||
\(801\) | −6.91898 | −0.244470 | ||||||||
\(802\) | 0.793679 | 0.0280258 | ||||||||
\(803\) | −18.1924 | −0.641998 | ||||||||
\(804\) | −21.3573 | −0.753215 | ||||||||
\(805\) | −19.4913 | −0.686977 | ||||||||
\(806\) | −0.116928 | −0.00411862 | ||||||||
\(807\) | 15.7614 | 0.554829 | ||||||||
\(808\) | 1.56975 | 0.0552236 | ||||||||
\(809\) | −42.7065 | −1.50148 | −0.750741 | − | 0.660597i | \(-0.770303\pi\) | ||||
−0.750741 | + | 0.660597i | \(0.770303\pi\) | |||||||
\(810\) | 0.201501 | 0.00708003 | ||||||||
\(811\) | −28.4024 | −0.997343 | −0.498672 | − | 0.866791i | \(-0.666179\pi\) | ||||
−0.498672 | + | 0.866791i | \(0.666179\pi\) | |||||||
\(812\) | −6.78516 | −0.238113 | ||||||||
\(813\) | −17.7427 | −0.622265 | ||||||||
\(814\) | −1.68358 | −0.0590096 | ||||||||
\(815\) | 36.3383 | 1.27288 | ||||||||
\(816\) | 3.98445 | 0.139484 | ||||||||
\(817\) | −33.6624 | −1.17770 | ||||||||
\(818\) | 1.01139 | 0.0353626 | ||||||||
\(819\) | −4.08045 | −0.142582 | ||||||||
\(820\) | −69.2866 | −2.41959 | ||||||||
\(821\) | 17.2823 | 0.603156 | 0.301578 | − | 0.953441i | \(-0.402487\pi\) | ||||
0.301578 | + | 0.953441i | \(0.402487\pi\) | |||||||
\(822\) | −1.05691 | −0.0368639 | ||||||||
\(823\) | −28.3635 | −0.988688 | −0.494344 | − | 0.869266i | \(-0.664592\pi\) | ||||
−0.494344 | + | 0.869266i | \(0.664592\pi\) | |||||||
\(824\) | −1.28350 | −0.0447127 | ||||||||
\(825\) | 56.1889 | 1.95625 | ||||||||
\(826\) | −1.29648 | −0.0451102 | ||||||||
\(827\) | 42.4452 | 1.47597 | 0.737983 | − | 0.674820i | \(-0.235779\pi\) | ||||
0.737983 | + | 0.674820i | \(0.235779\pi\) | |||||||
\(828\) | 5.19675 | 0.180599 | ||||||||
\(829\) | −32.3382 | −1.12315 | −0.561576 | − | 0.827425i | \(-0.689805\pi\) | ||||
−0.561576 | + | 0.827425i | \(0.689805\pi\) | |||||||
\(830\) | −2.60094 | −0.0902801 | ||||||||
\(831\) | −14.7538 | −0.511804 | ||||||||
\(832\) | 17.1118 | 0.593243 | ||||||||
\(833\) | −3.41711 | −0.118396 | ||||||||
\(834\) | −0.356378 | −0.0123404 | ||||||||
\(835\) | 46.4705 | 1.60818 | ||||||||
\(836\) | −34.5736 | −1.19575 | ||||||||
\(837\) | 1.06539 | 0.0368253 | ||||||||
\(838\) | 1.26350 | 0.0436468 | ||||||||
\(839\) | 13.1367 | 0.453530 | 0.226765 | − | 0.973950i | \(-0.427185\pi\) | ||||
0.226765 | + | 0.973950i | \(0.427185\pi\) | |||||||
\(840\) | −1.52466 | −0.0526057 | ||||||||
\(841\) | −25.7793 | −0.888940 | ||||||||
\(842\) | 0.0483633 | 0.00166671 | ||||||||
\(843\) | −32.3269 | −1.11340 | ||||||||
\(844\) | −48.4389 | −1.66733 | ||||||||
\(845\) | −33.0595 | −1.13728 | ||||||||
\(846\) | 0.345978 | 0.0118950 | ||||||||
\(847\) | 31.7242 | 1.09006 | ||||||||
\(848\) | −27.2712 | −0.936496 | ||||||||
\(849\) | −15.7050 | −0.538994 | ||||||||
\(850\) | 0.542950 | 0.0186230 | ||||||||
\(851\) | 16.3294 | 0.559765 | ||||||||
\(852\) | 1.26955 | 0.0434940 | ||||||||
\(853\) | −23.1614 | −0.793030 | −0.396515 | − | 0.918028i | \(-0.629781\pi\) | ||||
−0.396515 | + | 0.918028i | \(0.629781\pi\) | |||||||
\(854\) | 1.04501 | 0.0357596 | ||||||||
\(855\) | 13.0025 | 0.444676 | ||||||||
\(856\) | 3.66912 | 0.125408 | ||||||||
\(857\) | −20.1442 | −0.688113 | −0.344056 | − | 0.938949i | \(-0.611801\pi\) | ||||
−0.344056 | + | 0.938949i | \(0.611801\pi\) | |||||||
\(858\) | −0.578256 | −0.0197413 | ||||||||
\(859\) | 9.63077 | 0.328598 | 0.164299 | − | 0.986411i | \(-0.447464\pi\) | ||||
0.164299 | + | 0.986411i | \(0.447464\pi\) | |||||||
\(860\) | 81.0032 | 2.76219 | ||||||||
\(861\) | 16.5898 | 0.565378 | ||||||||
\(862\) | −1.91650 | −0.0652764 | ||||||||
\(863\) | 25.8298 | 0.879257 | 0.439629 | − | 0.898180i | \(-0.355110\pi\) | ||||
0.439629 | + | 0.898180i | \(0.355110\pi\) | |||||||
\(864\) | 0.609887 | 0.0207488 | ||||||||
\(865\) | −68.5355 | −2.33028 | ||||||||
\(866\) | 1.36259 | 0.0463026 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −4.02803 | −0.136720 | ||||||||
\(869\) | 5.26878 | 0.178731 | ||||||||
\(870\) | 0.361622 | 0.0122601 | ||||||||
\(871\) | −23.0500 | −0.781021 | ||||||||
\(872\) | −3.06075 | −0.103650 | ||||||||
\(873\) | 2.23271 | 0.0755658 | ||||||||
\(874\) | −0.435163 | −0.0147196 | ||||||||
\(875\) | 42.4363 | 1.43461 | ||||||||
\(876\) | 6.89681 | 0.233022 | ||||||||
\(877\) | −0.660738 | −0.0223116 | −0.0111558 | − | 0.999938i | \(-0.503551\pi\) | ||||
−0.0111558 | + | 0.999938i | \(0.503551\pi\) | |||||||
\(878\) | 1.85506 | 0.0626051 | ||||||||
\(879\) | −10.2116 | −0.344430 | ||||||||
\(880\) | 83.0878 | 2.80089 | ||||||||
\(881\) | 25.7400 | 0.867203 | 0.433601 | − | 0.901105i | \(-0.357243\pi\) | ||||
0.433601 | + | 0.901105i | \(0.357243\pi\) | |||||||
\(882\) | −0.173972 | −0.00585793 | ||||||||
\(883\) | 42.7441 | 1.43846 | 0.719228 | − | 0.694775i | \(-0.244496\pi\) | ||||
0.719228 | + | 0.694775i | \(0.244496\pi\) | |||||||
\(884\) | 4.30584 | 0.144821 | ||||||||
\(885\) | −53.2461 | −1.78985 | ||||||||
\(886\) | 0.564599 | 0.0189681 | ||||||||
\(887\) | −41.2625 | −1.38546 | −0.692729 | − | 0.721198i | \(-0.743592\pi\) | ||||
−0.692729 | + | 0.721198i | \(0.743592\pi\) | |||||||
\(888\) | 1.27733 | 0.0428644 | ||||||||
\(889\) | −5.81392 | −0.194993 | ||||||||
\(890\) | −1.39418 | −0.0467331 | ||||||||
\(891\) | 5.26878 | 0.176511 | ||||||||
\(892\) | 18.9262 | 0.633697 | ||||||||
\(893\) | 22.3253 | 0.747089 | ||||||||
\(894\) | −0.128300 | −0.00429099 | ||||||||
\(895\) | 92.1703 | 3.08091 | ||||||||
\(896\) | −3.07381 | −0.102689 | ||||||||
\(897\) | 5.60862 | 0.187266 | ||||||||
\(898\) | −0.733311 | −0.0244709 | ||||||||
\(899\) | 1.91199 | 0.0637685 | ||||||||
\(900\) | −21.3014 | −0.710046 | ||||||||
\(901\) | −6.84440 | −0.228020 | ||||||||
\(902\) | 2.35100 | 0.0782798 | ||||||||
\(903\) | −19.3952 | −0.645431 | ||||||||
\(904\) | 0.300111 | 0.00998155 | ||||||||
\(905\) | 6.39976 | 0.212735 | ||||||||
\(906\) | 0.122165 | 0.00405865 | ||||||||
\(907\) | 16.0894 | 0.534241 | 0.267120 | − | 0.963663i | \(-0.413928\pi\) | ||||
0.267120 | + | 0.963663i | \(0.413928\pi\) | |||||||
\(908\) | 31.3168 | 1.03929 | ||||||||
\(909\) | −7.71317 | −0.255830 | ||||||||
\(910\) | −0.822214 | −0.0272561 | ||||||||
\(911\) | 36.7375 | 1.21717 | 0.608584 | − | 0.793489i | \(-0.291738\pi\) | ||||
0.608584 | + | 0.793489i | \(0.291738\pi\) | |||||||
\(912\) | 13.0899 | 0.433451 | ||||||||
\(913\) | −68.0086 | −2.25075 | ||||||||
\(914\) | 0.128823 | 0.00426109 | ||||||||
\(915\) | 42.9185 | 1.41884 | ||||||||
\(916\) | −37.8268 | −1.24983 | ||||||||
\(917\) | 14.0476 | 0.463894 | ||||||||
\(918\) | 0.0509119 | 0.00168034 | ||||||||
\(919\) | −3.82043 | −0.126024 | −0.0630122 | − | 0.998013i | \(-0.520071\pi\) | ||||
−0.0630122 | + | 0.998013i | \(0.520071\pi\) | |||||||
\(920\) | 2.09566 | 0.0690918 | ||||||||
\(921\) | −10.2616 | −0.338131 | ||||||||
\(922\) | −1.33509 | −0.0439688 | ||||||||
\(923\) | 1.37017 | 0.0450996 | ||||||||
\(924\) | −19.9202 | −0.655326 | ||||||||
\(925\) | −66.9340 | −2.20078 | ||||||||
\(926\) | −1.70375 | −0.0559886 | ||||||||
\(927\) | 6.30662 | 0.207137 | ||||||||
\(928\) | 1.09453 | 0.0359296 | ||||||||
\(929\) | −27.1946 | −0.892227 | −0.446113 | − | 0.894976i | \(-0.647192\pi\) | ||||
−0.446113 | + | 0.894976i | \(0.647192\pi\) | |||||||
\(930\) | 0.214677 | 0.00703955 | ||||||||
\(931\) | −11.2261 | −0.367919 | ||||||||
\(932\) | −56.1505 | −1.83927 | ||||||||
\(933\) | −3.07625 | −0.100712 | ||||||||
\(934\) | −0.437902 | −0.0143286 | ||||||||
\(935\) | 20.8530 | 0.681966 | ||||||||
\(936\) | 0.438721 | 0.0143400 | ||||||||
\(937\) | 34.9947 | 1.14323 | 0.571613 | − | 0.820523i | \(-0.306318\pi\) | ||||
0.571613 | + | 0.820523i | \(0.306318\pi\) | |||||||
\(938\) | 1.03042 | 0.0336445 | ||||||||
\(939\) | −6.77918 | −0.221230 | ||||||||
\(940\) | −53.7223 | −1.75223 | ||||||||
\(941\) | −12.8381 | −0.418509 | −0.209255 | − | 0.977861i | \(-0.567104\pi\) | ||||
−0.209255 | + | 0.977861i | \(0.567104\pi\) | |||||||
\(942\) | −0.363012 | −0.0118276 | ||||||||
\(943\) | −22.8028 | −0.742563 | ||||||||
\(944\) | −53.6041 | −1.74466 | ||||||||
\(945\) | 7.49161 | 0.243702 | ||||||||
\(946\) | −2.74856 | −0.0893635 | ||||||||
\(947\) | 14.2263 | 0.462292 | 0.231146 | − | 0.972919i | \(-0.425752\pi\) | ||||
0.231146 | + | 0.972919i | \(0.425752\pi\) | |||||||
\(948\) | −1.99741 | −0.0648728 | ||||||||
\(949\) | 7.44342 | 0.241624 | ||||||||
\(950\) | 1.78373 | 0.0578717 | ||||||||
\(951\) | 27.8869 | 0.904295 | ||||||||
\(952\) | −0.385225 | −0.0124852 | ||||||||
\(953\) | −5.76547 | −0.186762 | −0.0933810 | − | 0.995630i | \(-0.529767\pi\) | ||||
−0.0933810 | + | 0.995630i | \(0.529767\pi\) | |||||||
\(954\) | −0.348461 | −0.0112818 | ||||||||
\(955\) | −33.7714 | −1.09282 | ||||||||
\(956\) | −48.0548 | −1.55420 | ||||||||
\(957\) | 9.45555 | 0.305655 | ||||||||
\(958\) | −1.12415 | −0.0363197 | ||||||||
\(959\) | −39.2948 | −1.26889 | ||||||||
\(960\) | −31.4168 | −1.01397 | ||||||||
\(961\) | −29.8649 | −0.963385 | ||||||||
\(962\) | 0.688836 | 0.0222090 | ||||||||
\(963\) | −18.0287 | −0.580967 | ||||||||
\(964\) | −22.3338 | −0.719325 | ||||||||
\(965\) | −83.2228 | −2.67904 | ||||||||
\(966\) | −0.250727 | −0.00806700 | ||||||||
\(967\) | 44.3428 | 1.42597 | 0.712984 | − | 0.701181i | \(-0.247343\pi\) | ||||
0.712984 | + | 0.701181i | \(0.247343\pi\) | |||||||
\(968\) | −3.41092 | −0.109631 | ||||||||
\(969\) | 3.28525 | 0.105537 | ||||||||
\(970\) | 0.449894 | 0.0144452 | ||||||||
\(971\) | 46.5023 | 1.49233 | 0.746165 | − | 0.665761i | \(-0.231893\pi\) | ||||
0.746165 | + | 0.665761i | \(0.231893\pi\) | |||||||
\(972\) | −1.99741 | −0.0640669 | ||||||||
\(973\) | −13.2498 | −0.424769 | ||||||||
\(974\) | −0.194802 | −0.00624185 | ||||||||
\(975\) | −22.9896 | −0.736257 | ||||||||
\(976\) | 43.2070 | 1.38302 | ||||||||
\(977\) | 1.00688 | 0.0322129 | 0.0161064 | − | 0.999870i | \(-0.494873\pi\) | ||||
0.0161064 | + | 0.999870i | \(0.494873\pi\) | |||||||
\(978\) | 0.467440 | 0.0149471 | ||||||||
\(979\) | −36.4546 | −1.16509 | ||||||||
\(980\) | 27.0137 | 0.862922 | ||||||||
\(981\) | 15.0394 | 0.480170 | ||||||||
\(982\) | −0.914185 | −0.0291728 | ||||||||
\(983\) | −7.22420 | −0.230416 | −0.115208 | − | 0.993341i | \(-0.536753\pi\) | ||||
−0.115208 | + | 0.993341i | \(0.536753\pi\) | |||||||
\(984\) | −1.78370 | −0.0568622 | ||||||||
\(985\) | 71.8209 | 2.28840 | ||||||||
\(986\) | 0.0913684 | 0.00290976 | ||||||||
\(987\) | 12.8631 | 0.409438 | ||||||||
\(988\) | 14.1458 | 0.450036 | ||||||||
\(989\) | 26.6589 | 0.847703 | ||||||||
\(990\) | 1.06166 | 0.0337419 | ||||||||
\(991\) | −27.3165 | −0.867738 | −0.433869 | − | 0.900976i | \(-0.642852\pi\) | ||||
−0.433869 | + | 0.900976i | \(0.642852\pi\) | |||||||
\(992\) | 0.649768 | 0.0206301 | ||||||||
\(993\) | 28.0154 | 0.889041 | ||||||||
\(994\) | −0.0612517 | −0.00194279 | ||||||||
\(995\) | −33.9630 | −1.07670 | ||||||||
\(996\) | 25.7822 | 0.816941 | ||||||||
\(997\) | −36.6981 | −1.16224 | −0.581120 | − | 0.813818i | \(-0.697385\pi\) | ||||
−0.581120 | + | 0.813818i | \(0.697385\pi\) | |||||||
\(998\) | −1.06372 | −0.0336713 | ||||||||
\(999\) | −6.27633 | −0.198574 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4029.2.a.k.1.16 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.k.1.16 | ✓ | 31 | 1.1 | even | 1 | trivial |