Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 48 x^{13} + 44 x^{12} + 872 x^{11} - 707 x^{10} - 7580 x^{9} + 5112 x^{8} + 33191 x^{7} - 16428 x^{6} - 71361 x^{5} + 21747 x^{4} + 65434 x^{3} - 11840 x^{2} + \cdots + 2048 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.113262\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.113262 | −0.0506522 | −0.0253261 | − | 0.999679i | \(-0.508062\pi\) | ||||
−0.0253261 | + | 0.999679i | \(0.508062\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.75034 | 0.661568 | 0.330784 | − | 0.943707i | \(-0.392687\pi\) | ||||
0.330784 | + | 0.943707i | \(0.392687\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.113262 | −0.0358165 | ||||||||
\(11\) | 3.65617 | 1.10238 | 0.551188 | − | 0.834381i | \(-0.314175\pi\) | ||||
0.551188 | + | 0.834381i | \(0.314175\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 1.75034 | 0.467799 | ||||||||
\(15\) | 0.113262 | 0.0292441 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.05562 | 1.46870 | 0.734352 | − | 0.678769i | \(-0.237486\pi\) | ||||
0.734352 | + | 0.678769i | \(0.237486\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −7.50794 | −1.72244 | −0.861220 | − | 0.508232i | \(-0.830299\pi\) | ||||
−0.861220 | + | 0.508232i | \(0.830299\pi\) | |||||||
\(20\) | −0.113262 | −0.0253261 | ||||||||
\(21\) | −1.75034 | −0.381956 | ||||||||
\(22\) | 3.65617 | 0.779497 | ||||||||
\(23\) | 5.43702 | 1.13370 | 0.566848 | − | 0.823822i | \(-0.308163\pi\) | ||||
0.566848 | + | 0.823822i | \(0.308163\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.98717 | −0.997434 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.75034 | 0.330784 | ||||||||
\(29\) | 9.14306 | 1.69782 | 0.848912 | − | 0.528534i | \(-0.177258\pi\) | ||||
0.848912 | + | 0.528534i | \(0.177258\pi\) | |||||||
\(30\) | 0.113262 | 0.0206787 | ||||||||
\(31\) | 4.35795 | 0.782710 | 0.391355 | − | 0.920240i | \(-0.372006\pi\) | ||||
0.391355 | + | 0.920240i | \(0.372006\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.65617 | −0.636457 | ||||||||
\(34\) | 6.05562 | 1.03853 | ||||||||
\(35\) | −0.198247 | −0.0335099 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.0304744 | 0.00500996 | 0.00250498 | − | 0.999997i | \(-0.499203\pi\) | ||||
0.00250498 | + | 0.999997i | \(0.499203\pi\) | |||||||
\(38\) | −7.50794 | −1.21795 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −0.113262 | −0.0179083 | ||||||||
\(41\) | 5.21159 | 0.813914 | 0.406957 | − | 0.913447i | \(-0.366590\pi\) | ||||
0.406957 | + | 0.913447i | \(0.366590\pi\) | |||||||
\(42\) | −1.75034 | −0.270084 | ||||||||
\(43\) | 6.58092 | 1.00358 | 0.501791 | − | 0.864989i | \(-0.332675\pi\) | ||||
0.501791 | + | 0.864989i | \(0.332675\pi\) | |||||||
\(44\) | 3.65617 | 0.551188 | ||||||||
\(45\) | −0.113262 | −0.0168841 | ||||||||
\(46\) | 5.43702 | 0.801644 | ||||||||
\(47\) | −11.8201 | −1.72414 | −0.862068 | − | 0.506792i | \(-0.830831\pi\) | ||||
−0.862068 | + | 0.506792i | \(0.830831\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −3.93630 | −0.562328 | ||||||||
\(50\) | −4.98717 | −0.705293 | ||||||||
\(51\) | −6.05562 | −0.847957 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −3.10712 | −0.426796 | −0.213398 | − | 0.976965i | \(-0.568453\pi\) | ||||
−0.213398 | + | 0.976965i | \(0.568453\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −0.414104 | −0.0558378 | ||||||||
\(56\) | 1.75034 | 0.233899 | ||||||||
\(57\) | 7.50794 | 0.994451 | ||||||||
\(58\) | 9.14306 | 1.20054 | ||||||||
\(59\) | 6.97905 | 0.908595 | 0.454298 | − | 0.890850i | \(-0.349890\pi\) | ||||
0.454298 | + | 0.890850i | \(0.349890\pi\) | |||||||
\(60\) | 0.113262 | 0.0146220 | ||||||||
\(61\) | 10.2132 | 1.30767 | 0.653833 | − | 0.756639i | \(-0.273160\pi\) | ||||
0.653833 | + | 0.756639i | \(0.273160\pi\) | |||||||
\(62\) | 4.35795 | 0.553460 | ||||||||
\(63\) | 1.75034 | 0.220523 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.113262 | 0.0140484 | ||||||||
\(66\) | −3.65617 | −0.450043 | ||||||||
\(67\) | −12.1648 | −1.48617 | −0.743085 | − | 0.669197i | \(-0.766638\pi\) | ||||
−0.743085 | + | 0.669197i | \(0.766638\pi\) | |||||||
\(68\) | 6.05562 | 0.734352 | ||||||||
\(69\) | −5.43702 | −0.654540 | ||||||||
\(70\) | −0.198247 | −0.0236951 | ||||||||
\(71\) | −5.75511 | −0.683006 | −0.341503 | − | 0.939881i | \(-0.610936\pi\) | ||||
−0.341503 | + | 0.939881i | \(0.610936\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −6.79650 | −0.795470 | −0.397735 | − | 0.917500i | \(-0.630204\pi\) | ||||
−0.397735 | + | 0.917500i | \(0.630204\pi\) | |||||||
\(74\) | 0.0304744 | 0.00354257 | ||||||||
\(75\) | 4.98717 | 0.575869 | ||||||||
\(76\) | −7.50794 | −0.861220 | ||||||||
\(77\) | 6.39954 | 0.729296 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −5.30030 | −0.596330 | −0.298165 | − | 0.954514i | \(-0.596375\pi\) | ||||
−0.298165 | + | 0.954514i | \(0.596375\pi\) | |||||||
\(80\) | −0.113262 | −0.0126631 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.21159 | 0.575524 | ||||||||
\(83\) | 11.0499 | 1.21288 | 0.606442 | − | 0.795128i | \(-0.292596\pi\) | ||||
0.606442 | + | 0.795128i | \(0.292596\pi\) | |||||||
\(84\) | −1.75034 | −0.190978 | ||||||||
\(85\) | −0.685871 | −0.0743932 | ||||||||
\(86\) | 6.58092 | 0.709639 | ||||||||
\(87\) | −9.14306 | −0.980239 | ||||||||
\(88\) | 3.65617 | 0.389749 | ||||||||
\(89\) | 10.4079 | 1.10324 | 0.551619 | − | 0.834096i | \(-0.314010\pi\) | ||||
0.551619 | + | 0.834096i | \(0.314010\pi\) | |||||||
\(90\) | −0.113262 | −0.0119388 | ||||||||
\(91\) | −1.75034 | −0.183486 | ||||||||
\(92\) | 5.43702 | 0.566848 | ||||||||
\(93\) | −4.35795 | −0.451898 | ||||||||
\(94\) | −11.8201 | −1.21915 | ||||||||
\(95\) | 0.850363 | 0.0872454 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 10.1090 | 1.02641 | 0.513207 | − | 0.858265i | \(-0.328457\pi\) | ||||
0.513207 | + | 0.858265i | \(0.328457\pi\) | |||||||
\(98\) | −3.93630 | −0.397626 | ||||||||
\(99\) | 3.65617 | 0.367459 | ||||||||
\(100\) | −4.98717 | −0.498717 | ||||||||
\(101\) | −1.08143 | −0.107606 | −0.0538030 | − | 0.998552i | \(-0.517134\pi\) | ||||
−0.0538030 | + | 0.998552i | \(0.517134\pi\) | |||||||
\(102\) | −6.05562 | −0.599596 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0.198247 | 0.0193469 | ||||||||
\(106\) | −3.10712 | −0.301790 | ||||||||
\(107\) | 2.13304 | 0.206209 | 0.103105 | − | 0.994671i | \(-0.467122\pi\) | ||||
0.103105 | + | 0.994671i | \(0.467122\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −2.39240 | −0.229150 | −0.114575 | − | 0.993415i | \(-0.536551\pi\) | ||||
−0.114575 | + | 0.993415i | \(0.536551\pi\) | |||||||
\(110\) | −0.414104 | −0.0394833 | ||||||||
\(111\) | −0.0304744 | −0.00289250 | ||||||||
\(112\) | 1.75034 | 0.165392 | ||||||||
\(113\) | 1.47065 | 0.138347 | 0.0691736 | − | 0.997605i | \(-0.477964\pi\) | ||||
0.0691736 | + | 0.997605i | \(0.477964\pi\) | |||||||
\(114\) | 7.50794 | 0.703183 | ||||||||
\(115\) | −0.615806 | −0.0574242 | ||||||||
\(116\) | 9.14306 | 0.848912 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 6.97905 | 0.642474 | ||||||||
\(119\) | 10.5994 | 0.971647 | ||||||||
\(120\) | 0.113262 | 0.0103393 | ||||||||
\(121\) | 2.36755 | 0.215232 | ||||||||
\(122\) | 10.2132 | 0.924659 | ||||||||
\(123\) | −5.21159 | −0.469913 | ||||||||
\(124\) | 4.35795 | 0.391355 | ||||||||
\(125\) | 1.13117 | 0.101174 | ||||||||
\(126\) | 1.75034 | 0.155933 | ||||||||
\(127\) | −5.04339 | −0.447528 | −0.223764 | − | 0.974643i | \(-0.571835\pi\) | ||||
−0.223764 | + | 0.974643i | \(0.571835\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −6.58092 | −0.579418 | ||||||||
\(130\) | 0.113262 | 0.00993372 | ||||||||
\(131\) | −4.59698 | −0.401640 | −0.200820 | − | 0.979628i | \(-0.564361\pi\) | ||||
−0.200820 | + | 0.979628i | \(0.564361\pi\) | |||||||
\(132\) | −3.65617 | −0.318228 | ||||||||
\(133\) | −13.1415 | −1.13951 | ||||||||
\(134\) | −12.1648 | −1.05088 | ||||||||
\(135\) | 0.113262 | 0.00974803 | ||||||||
\(136\) | 6.05562 | 0.519265 | ||||||||
\(137\) | 15.0484 | 1.28567 | 0.642836 | − | 0.766004i | \(-0.277758\pi\) | ||||
0.642836 | + | 0.766004i | \(0.277758\pi\) | |||||||
\(138\) | −5.43702 | −0.462830 | ||||||||
\(139\) | 5.89502 | 0.500009 | 0.250004 | − | 0.968245i | \(-0.419568\pi\) | ||||
0.250004 | + | 0.968245i | \(0.419568\pi\) | |||||||
\(140\) | −0.198247 | −0.0167549 | ||||||||
\(141\) | 11.8201 | 0.995431 | ||||||||
\(142\) | −5.75511 | −0.482958 | ||||||||
\(143\) | −3.65617 | −0.305744 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.03556 | −0.0859986 | ||||||||
\(146\) | −6.79650 | −0.562483 | ||||||||
\(147\) | 3.93630 | 0.324660 | ||||||||
\(148\) | 0.0304744 | 0.00250498 | ||||||||
\(149\) | 0.0191072 | 0.00156532 | 0.000782660 | − | 1.00000i | \(-0.499751\pi\) | ||||
0.000782660 | 1.00000i | \(0.499751\pi\) | ||||||||
\(150\) | 4.98717 | 0.407201 | ||||||||
\(151\) | −2.37037 | −0.192898 | −0.0964488 | − | 0.995338i | \(-0.530748\pi\) | ||||
−0.0964488 | + | 0.995338i | \(0.530748\pi\) | |||||||
\(152\) | −7.50794 | −0.608975 | ||||||||
\(153\) | 6.05562 | 0.489568 | ||||||||
\(154\) | 6.39954 | 0.515690 | ||||||||
\(155\) | −0.493589 | −0.0396460 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −18.0051 | −1.43697 | −0.718483 | − | 0.695544i | \(-0.755163\pi\) | ||||
−0.718483 | + | 0.695544i | \(0.755163\pi\) | |||||||
\(158\) | −5.30030 | −0.421669 | ||||||||
\(159\) | 3.10712 | 0.246411 | ||||||||
\(160\) | −0.113262 | −0.00895413 | ||||||||
\(161\) | 9.51665 | 0.750017 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 17.8749 | 1.40007 | 0.700034 | − | 0.714109i | \(-0.253168\pi\) | ||||
0.700034 | + | 0.714109i | \(0.253168\pi\) | |||||||
\(164\) | 5.21159 | 0.406957 | ||||||||
\(165\) | 0.414104 | 0.0322380 | ||||||||
\(166\) | 11.0499 | 0.857638 | ||||||||
\(167\) | 4.42869 | 0.342702 | 0.171351 | − | 0.985210i | \(-0.445187\pi\) | ||||
0.171351 | + | 0.985210i | \(0.445187\pi\) | |||||||
\(168\) | −1.75034 | −0.135042 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −0.685871 | −0.0526039 | ||||||||
\(171\) | −7.50794 | −0.574147 | ||||||||
\(172\) | 6.58092 | 0.501791 | ||||||||
\(173\) | 9.46262 | 0.719430 | 0.359715 | − | 0.933062i | \(-0.382874\pi\) | ||||
0.359715 | + | 0.933062i | \(0.382874\pi\) | |||||||
\(174\) | −9.14306 | −0.693134 | ||||||||
\(175\) | −8.72926 | −0.659870 | ||||||||
\(176\) | 3.65617 | 0.275594 | ||||||||
\(177\) | −6.97905 | −0.524578 | ||||||||
\(178\) | 10.4079 | 0.780107 | ||||||||
\(179\) | 11.2831 | 0.843339 | 0.421669 | − | 0.906750i | \(-0.361444\pi\) | ||||
0.421669 | + | 0.906750i | \(0.361444\pi\) | |||||||
\(180\) | −0.113262 | −0.00844204 | ||||||||
\(181\) | −17.1528 | −1.27496 | −0.637480 | − | 0.770467i | \(-0.720023\pi\) | ||||
−0.637480 | + | 0.770467i | \(0.720023\pi\) | |||||||
\(182\) | −1.75034 | −0.129744 | ||||||||
\(183\) | −10.2132 | −0.754981 | ||||||||
\(184\) | 5.43702 | 0.400822 | ||||||||
\(185\) | −0.00345158 | −0.000253765 0 | ||||||||
\(186\) | −4.35795 | −0.319540 | ||||||||
\(187\) | 22.1404 | 1.61906 | ||||||||
\(188\) | −11.8201 | −0.862068 | ||||||||
\(189\) | −1.75034 | −0.127319 | ||||||||
\(190\) | 0.850363 | 0.0616918 | ||||||||
\(191\) | 3.75731 | 0.271870 | 0.135935 | − | 0.990718i | \(-0.456596\pi\) | ||||
0.135935 | + | 0.990718i | \(0.456596\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −4.89362 | −0.352250 | −0.176125 | − | 0.984368i | \(-0.556356\pi\) | ||||
−0.176125 | + | 0.984368i | \(0.556356\pi\) | |||||||
\(194\) | 10.1090 | 0.725785 | ||||||||
\(195\) | −0.113262 | −0.00811085 | ||||||||
\(196\) | −3.93630 | −0.281164 | ||||||||
\(197\) | −24.9189 | −1.77540 | −0.887698 | − | 0.460426i | \(-0.847697\pi\) | ||||
−0.887698 | + | 0.460426i | \(0.847697\pi\) | |||||||
\(198\) | 3.65617 | 0.259832 | ||||||||
\(199\) | 12.8498 | 0.910900 | 0.455450 | − | 0.890261i | \(-0.349478\pi\) | ||||
0.455450 | + | 0.890261i | \(0.349478\pi\) | |||||||
\(200\) | −4.98717 | −0.352646 | ||||||||
\(201\) | 12.1648 | 0.858041 | ||||||||
\(202\) | −1.08143 | −0.0760889 | ||||||||
\(203\) | 16.0035 | 1.12323 | ||||||||
\(204\) | −6.05562 | −0.423978 | ||||||||
\(205\) | −0.590274 | −0.0412266 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | 5.43702 | 0.377899 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −27.4503 | −1.89878 | ||||||||
\(210\) | 0.198247 | 0.0136803 | ||||||||
\(211\) | 16.3252 | 1.12388 | 0.561938 | − | 0.827180i | \(-0.310056\pi\) | ||||
0.561938 | + | 0.827180i | \(0.310056\pi\) | |||||||
\(212\) | −3.10712 | −0.213398 | ||||||||
\(213\) | 5.75511 | 0.394333 | ||||||||
\(214\) | 2.13304 | 0.145812 | ||||||||
\(215\) | −0.745368 | −0.0508336 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 7.62790 | 0.517816 | ||||||||
\(218\) | −2.39240 | −0.162033 | ||||||||
\(219\) | 6.79650 | 0.459265 | ||||||||
\(220\) | −0.414104 | −0.0279189 | ||||||||
\(221\) | −6.05562 | −0.407345 | ||||||||
\(222\) | −0.0304744 | −0.00204531 | ||||||||
\(223\) | −14.1757 | −0.949273 | −0.474637 | − | 0.880182i | \(-0.657420\pi\) | ||||
−0.474637 | + | 0.880182i | \(0.657420\pi\) | |||||||
\(224\) | 1.75034 | 0.116950 | ||||||||
\(225\) | −4.98717 | −0.332478 | ||||||||
\(226\) | 1.47065 | 0.0978263 | ||||||||
\(227\) | 7.24312 | 0.480743 | 0.240371 | − | 0.970681i | \(-0.422731\pi\) | ||||
0.240371 | + | 0.970681i | \(0.422731\pi\) | |||||||
\(228\) | 7.50794 | 0.497226 | ||||||||
\(229\) | −1.26769 | −0.0837713 | −0.0418857 | − | 0.999122i | \(-0.513337\pi\) | ||||
−0.0418857 | + | 0.999122i | \(0.513337\pi\) | |||||||
\(230\) | −0.615806 | −0.0406051 | ||||||||
\(231\) | −6.39954 | −0.421059 | ||||||||
\(232\) | 9.14306 | 0.600272 | ||||||||
\(233\) | −8.23879 | −0.539741 | −0.269871 | − | 0.962897i | \(-0.586981\pi\) | ||||
−0.269871 | + | 0.962897i | \(0.586981\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 1.33876 | 0.0873314 | ||||||||
\(236\) | 6.97905 | 0.454298 | ||||||||
\(237\) | 5.30030 | 0.344291 | ||||||||
\(238\) | 10.5994 | 0.687058 | ||||||||
\(239\) | −2.25279 | −0.145721 | −0.0728606 | − | 0.997342i | \(-0.523213\pi\) | ||||
−0.0728606 | + | 0.997342i | \(0.523213\pi\) | |||||||
\(240\) | 0.113262 | 0.00731102 | ||||||||
\(241\) | 13.8985 | 0.895284 | 0.447642 | − | 0.894213i | \(-0.352264\pi\) | ||||
0.447642 | + | 0.894213i | \(0.352264\pi\) | |||||||
\(242\) | 2.36755 | 0.152192 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 10.2132 | 0.653833 | ||||||||
\(245\) | 0.445832 | 0.0284832 | ||||||||
\(246\) | −5.21159 | −0.332279 | ||||||||
\(247\) | 7.50794 | 0.477719 | ||||||||
\(248\) | 4.35795 | 0.276730 | ||||||||
\(249\) | −11.0499 | −0.700259 | ||||||||
\(250\) | 1.13117 | 0.0715412 | ||||||||
\(251\) | −28.5671 | −1.80314 | −0.901568 | − | 0.432637i | \(-0.857583\pi\) | ||||
−0.901568 | + | 0.432637i | \(0.857583\pi\) | |||||||
\(252\) | 1.75034 | 0.110261 | ||||||||
\(253\) | 19.8786 | 1.24976 | ||||||||
\(254\) | −5.04339 | −0.316450 | ||||||||
\(255\) | 0.685871 | 0.0429509 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.5467 | −1.09453 | −0.547265 | − | 0.836959i | \(-0.684331\pi\) | ||||
−0.547265 | + | 0.836959i | \(0.684331\pi\) | |||||||
\(258\) | −6.58092 | −0.409710 | ||||||||
\(259\) | 0.0533406 | 0.00331442 | ||||||||
\(260\) | 0.113262 | 0.00702420 | ||||||||
\(261\) | 9.14306 | 0.565942 | ||||||||
\(262\) | −4.59698 | −0.284002 | ||||||||
\(263\) | −9.97158 | −0.614874 | −0.307437 | − | 0.951568i | \(-0.599471\pi\) | ||||
−0.307437 | + | 0.951568i | \(0.599471\pi\) | |||||||
\(264\) | −3.65617 | −0.225021 | ||||||||
\(265\) | 0.351918 | 0.0216182 | ||||||||
\(266\) | −13.1415 | −0.805756 | ||||||||
\(267\) | −10.4079 | −0.636955 | ||||||||
\(268\) | −12.1648 | −0.743085 | ||||||||
\(269\) | −5.46710 | −0.333335 | −0.166668 | − | 0.986013i | \(-0.553301\pi\) | ||||
−0.166668 | + | 0.986013i | \(0.553301\pi\) | |||||||
\(270\) | 0.113262 | 0.00689289 | ||||||||
\(271\) | 22.8053 | 1.38533 | 0.692663 | − | 0.721262i | \(-0.256438\pi\) | ||||
0.692663 | + | 0.721262i | \(0.256438\pi\) | |||||||
\(272\) | 6.05562 | 0.367176 | ||||||||
\(273\) | 1.75034 | 0.105936 | ||||||||
\(274\) | 15.0484 | 0.909107 | ||||||||
\(275\) | −18.2339 | −1.09955 | ||||||||
\(276\) | −5.43702 | −0.327270 | ||||||||
\(277\) | 24.2026 | 1.45419 | 0.727096 | − | 0.686536i | \(-0.240870\pi\) | ||||
0.727096 | + | 0.686536i | \(0.240870\pi\) | |||||||
\(278\) | 5.89502 | 0.353560 | ||||||||
\(279\) | 4.35795 | 0.260903 | ||||||||
\(280\) | −0.198247 | −0.0118475 | ||||||||
\(281\) | −4.92762 | −0.293957 | −0.146979 | − | 0.989140i | \(-0.546955\pi\) | ||||
−0.146979 | + | 0.989140i | \(0.546955\pi\) | |||||||
\(282\) | 11.8201 | 0.703876 | ||||||||
\(283\) | −10.6051 | −0.630409 | −0.315205 | − | 0.949024i | \(-0.602073\pi\) | ||||
−0.315205 | + | 0.949024i | \(0.602073\pi\) | |||||||
\(284\) | −5.75511 | −0.341503 | ||||||||
\(285\) | −0.850363 | −0.0503712 | ||||||||
\(286\) | −3.65617 | −0.216194 | ||||||||
\(287\) | 9.12208 | 0.538459 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 19.6706 | 1.15709 | ||||||||
\(290\) | −1.03556 | −0.0608102 | ||||||||
\(291\) | −10.1090 | −0.592601 | ||||||||
\(292\) | −6.79650 | −0.397735 | ||||||||
\(293\) | 20.3878 | 1.19107 | 0.595533 | − | 0.803331i | \(-0.296941\pi\) | ||||
0.595533 | + | 0.803331i | \(0.296941\pi\) | |||||||
\(294\) | 3.93630 | 0.229570 | ||||||||
\(295\) | −0.790460 | −0.0460224 | ||||||||
\(296\) | 0.0304744 | 0.00177129 | ||||||||
\(297\) | −3.65617 | −0.212152 | ||||||||
\(298\) | 0.0191072 | 0.00110685 | ||||||||
\(299\) | −5.43702 | −0.314431 | ||||||||
\(300\) | 4.98717 | 0.287934 | ||||||||
\(301\) | 11.5189 | 0.663937 | ||||||||
\(302\) | −2.37037 | −0.136399 | ||||||||
\(303\) | 1.08143 | 0.0621263 | ||||||||
\(304\) | −7.50794 | −0.430610 | ||||||||
\(305\) | −1.15676 | −0.0662362 | ||||||||
\(306\) | 6.05562 | 0.346177 | ||||||||
\(307\) | 5.60226 | 0.319738 | 0.159869 | − | 0.987138i | \(-0.448893\pi\) | ||||
0.159869 | + | 0.987138i | \(0.448893\pi\) | |||||||
\(308\) | 6.39954 | 0.364648 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −0.493589 | −0.0280340 | ||||||||
\(311\) | −18.0590 | −1.02403 | −0.512015 | − | 0.858976i | \(-0.671101\pi\) | ||||
−0.512015 | + | 0.858976i | \(0.671101\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −4.76033 | −0.269070 | −0.134535 | − | 0.990909i | \(-0.542954\pi\) | ||||
−0.134535 | + | 0.990909i | \(0.542954\pi\) | |||||||
\(314\) | −18.0051 | −1.01609 | ||||||||
\(315\) | −0.198247 | −0.0111700 | ||||||||
\(316\) | −5.30030 | −0.298165 | ||||||||
\(317\) | 27.1745 | 1.52627 | 0.763136 | − | 0.646238i | \(-0.223659\pi\) | ||||
0.763136 | + | 0.646238i | \(0.223659\pi\) | |||||||
\(318\) | 3.10712 | 0.174239 | ||||||||
\(319\) | 33.4286 | 1.87164 | ||||||||
\(320\) | −0.113262 | −0.00633153 | ||||||||
\(321\) | −2.13304 | −0.119055 | ||||||||
\(322\) | 9.51665 | 0.530342 | ||||||||
\(323\) | −45.4653 | −2.52976 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 4.98717 | 0.276639 | ||||||||
\(326\) | 17.8749 | 0.989998 | ||||||||
\(327\) | 2.39240 | 0.132300 | ||||||||
\(328\) | 5.21159 | 0.287762 | ||||||||
\(329\) | −20.6892 | −1.14063 | ||||||||
\(330\) | 0.414104 | 0.0227957 | ||||||||
\(331\) | 28.1489 | 1.54720 | 0.773601 | − | 0.633673i | \(-0.218453\pi\) | ||||
0.773601 | + | 0.633673i | \(0.218453\pi\) | |||||||
\(332\) | 11.0499 | 0.606442 | ||||||||
\(333\) | 0.0304744 | 0.00166999 | ||||||||
\(334\) | 4.42869 | 0.242327 | ||||||||
\(335\) | 1.37781 | 0.0752778 | ||||||||
\(336\) | −1.75034 | −0.0954890 | ||||||||
\(337\) | −9.70607 | −0.528723 | −0.264362 | − | 0.964424i | \(-0.585161\pi\) | ||||
−0.264362 | + | 0.964424i | \(0.585161\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −1.47065 | −0.0798748 | ||||||||
\(340\) | −0.685871 | −0.0371966 | ||||||||
\(341\) | 15.9334 | 0.862841 | ||||||||
\(342\) | −7.50794 | −0.405983 | ||||||||
\(343\) | −19.1423 | −1.03359 | ||||||||
\(344\) | 6.58092 | 0.354820 | ||||||||
\(345\) | 0.615806 | 0.0331539 | ||||||||
\(346\) | 9.46262 | 0.508714 | ||||||||
\(347\) | 0.347167 | 0.0186369 | 0.00931844 | − | 0.999957i | \(-0.497034\pi\) | ||||
0.00931844 | + | 0.999957i | \(0.497034\pi\) | |||||||
\(348\) | −9.14306 | −0.490120 | ||||||||
\(349\) | 15.1633 | 0.811672 | 0.405836 | − | 0.913946i | \(-0.366980\pi\) | ||||
0.405836 | + | 0.913946i | \(0.366980\pi\) | |||||||
\(350\) | −8.72926 | −0.466599 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 3.65617 | 0.194874 | ||||||||
\(353\) | 23.8881 | 1.27144 | 0.635718 | − | 0.771921i | \(-0.280704\pi\) | ||||
0.635718 | + | 0.771921i | \(0.280704\pi\) | |||||||
\(354\) | −6.97905 | −0.370932 | ||||||||
\(355\) | 0.651834 | 0.0345958 | ||||||||
\(356\) | 10.4079 | 0.551619 | ||||||||
\(357\) | −10.5994 | −0.560981 | ||||||||
\(358\) | 11.2831 | 0.596331 | ||||||||
\(359\) | 21.9488 | 1.15841 | 0.579206 | − | 0.815181i | \(-0.303363\pi\) | ||||
0.579206 | + | 0.815181i | \(0.303363\pi\) | |||||||
\(360\) | −0.113262 | −0.00596942 | ||||||||
\(361\) | 37.3692 | 1.96680 | ||||||||
\(362\) | −17.1528 | −0.901533 | ||||||||
\(363\) | −2.36755 | −0.124264 | ||||||||
\(364\) | −1.75034 | −0.0917429 | ||||||||
\(365\) | 0.769784 | 0.0402923 | ||||||||
\(366\) | −10.2132 | −0.533852 | ||||||||
\(367\) | 9.65935 | 0.504214 | 0.252107 | − | 0.967699i | \(-0.418876\pi\) | ||||
0.252107 | + | 0.967699i | \(0.418876\pi\) | |||||||
\(368\) | 5.43702 | 0.283424 | ||||||||
\(369\) | 5.21159 | 0.271305 | ||||||||
\(370\) | −0.00345158 | −0.000179439 0 | ||||||||
\(371\) | −5.43853 | −0.282354 | ||||||||
\(372\) | −4.35795 | −0.225949 | ||||||||
\(373\) | 33.1269 | 1.71525 | 0.857623 | − | 0.514279i | \(-0.171940\pi\) | ||||
0.857623 | + | 0.514279i | \(0.171940\pi\) | |||||||
\(374\) | 22.1404 | 1.14485 | ||||||||
\(375\) | −1.13117 | −0.0584131 | ||||||||
\(376\) | −11.8201 | −0.609574 | ||||||||
\(377\) | −9.14306 | −0.470892 | ||||||||
\(378\) | −1.75034 | −0.0900279 | ||||||||
\(379\) | −13.3594 | −0.686225 | −0.343113 | − | 0.939294i | \(-0.611481\pi\) | ||||
−0.343113 | + | 0.939294i | \(0.611481\pi\) | |||||||
\(380\) | 0.850363 | 0.0436227 | ||||||||
\(381\) | 5.04339 | 0.258381 | ||||||||
\(382\) | 3.75731 | 0.192241 | ||||||||
\(383\) | 19.2044 | 0.981297 | 0.490649 | − | 0.871357i | \(-0.336760\pi\) | ||||
0.490649 | + | 0.871357i | \(0.336760\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −0.724824 | −0.0369405 | ||||||||
\(386\) | −4.89362 | −0.249079 | ||||||||
\(387\) | 6.58092 | 0.334527 | ||||||||
\(388\) | 10.1090 | 0.513207 | ||||||||
\(389\) | 27.5591 | 1.39730 | 0.698651 | − | 0.715463i | \(-0.253784\pi\) | ||||
0.698651 | + | 0.715463i | \(0.253784\pi\) | |||||||
\(390\) | −0.113262 | −0.00573524 | ||||||||
\(391\) | 32.9245 | 1.66507 | ||||||||
\(392\) | −3.93630 | −0.198813 | ||||||||
\(393\) | 4.59698 | 0.231887 | ||||||||
\(394\) | −24.9189 | −1.25539 | ||||||||
\(395\) | 0.600321 | 0.0302054 | ||||||||
\(396\) | 3.65617 | 0.183729 | ||||||||
\(397\) | 12.6689 | 0.635834 | 0.317917 | − | 0.948119i | \(-0.397017\pi\) | ||||
0.317917 | + | 0.948119i | \(0.397017\pi\) | |||||||
\(398\) | 12.8498 | 0.644104 | ||||||||
\(399\) | 13.1415 | 0.657897 | ||||||||
\(400\) | −4.98717 | −0.249359 | ||||||||
\(401\) | 5.67991 | 0.283641 | 0.141821 | − | 0.989892i | \(-0.454704\pi\) | ||||
0.141821 | + | 0.989892i | \(0.454704\pi\) | |||||||
\(402\) | 12.1648 | 0.606726 | ||||||||
\(403\) | −4.35795 | −0.217085 | ||||||||
\(404\) | −1.08143 | −0.0538030 | ||||||||
\(405\) | −0.113262 | −0.00562803 | ||||||||
\(406\) | 16.0035 | 0.794240 | ||||||||
\(407\) | 0.111419 | 0.00552285 | ||||||||
\(408\) | −6.05562 | −0.299798 | ||||||||
\(409\) | −26.1681 | −1.29393 | −0.646965 | − | 0.762520i | \(-0.723962\pi\) | ||||
−0.646965 | + | 0.762520i | \(0.723962\pi\) | |||||||
\(410\) | −0.590274 | −0.0291516 | ||||||||
\(411\) | −15.0484 | −0.742283 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 12.2157 | 0.601097 | ||||||||
\(414\) | 5.43702 | 0.267215 | ||||||||
\(415\) | −1.25153 | −0.0614353 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −5.89502 | −0.288680 | ||||||||
\(418\) | −27.4503 | −1.34264 | ||||||||
\(419\) | −28.2916 | −1.38214 | −0.691068 | − | 0.722790i | \(-0.742859\pi\) | ||||
−0.691068 | + | 0.722790i | \(0.742859\pi\) | |||||||
\(420\) | 0.198247 | 0.00967347 | ||||||||
\(421\) | 10.1314 | 0.493776 | 0.246888 | − | 0.969044i | \(-0.420592\pi\) | ||||
0.246888 | + | 0.969044i | \(0.420592\pi\) | |||||||
\(422\) | 16.3252 | 0.794700 | ||||||||
\(423\) | −11.8201 | −0.574712 | ||||||||
\(424\) | −3.10712 | −0.150895 | ||||||||
\(425\) | −30.2004 | −1.46494 | ||||||||
\(426\) | 5.75511 | 0.278836 | ||||||||
\(427\) | 17.8766 | 0.865109 | ||||||||
\(428\) | 2.13304 | 0.103105 | ||||||||
\(429\) | 3.65617 | 0.176521 | ||||||||
\(430\) | −0.745368 | −0.0359448 | ||||||||
\(431\) | 38.4390 | 1.85154 | 0.925771 | − | 0.378084i | \(-0.123417\pi\) | ||||
0.925771 | + | 0.378084i | \(0.123417\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −23.8800 | −1.14760 | −0.573800 | − | 0.818995i | \(-0.694531\pi\) | ||||
−0.573800 | + | 0.818995i | \(0.694531\pi\) | |||||||
\(434\) | 7.62790 | 0.366151 | ||||||||
\(435\) | 1.03556 | 0.0496513 | ||||||||
\(436\) | −2.39240 | −0.114575 | ||||||||
\(437\) | −40.8208 | −1.95272 | ||||||||
\(438\) | 6.79650 | 0.324749 | ||||||||
\(439\) | −36.5348 | −1.74371 | −0.871856 | − | 0.489763i | \(-0.837083\pi\) | ||||
−0.871856 | + | 0.489763i | \(0.837083\pi\) | |||||||
\(440\) | −0.414104 | −0.0197416 | ||||||||
\(441\) | −3.93630 | −0.187443 | ||||||||
\(442\) | −6.05562 | −0.288037 | ||||||||
\(443\) | 39.2216 | 1.86347 | 0.931737 | − | 0.363134i | \(-0.118293\pi\) | ||||
0.931737 | + | 0.363134i | \(0.118293\pi\) | |||||||
\(444\) | −0.0304744 | −0.00144625 | ||||||||
\(445\) | −1.17882 | −0.0558815 | ||||||||
\(446\) | −14.1757 | −0.671237 | ||||||||
\(447\) | −0.0191072 | −0.000903738 0 | ||||||||
\(448\) | 1.75034 | 0.0826959 | ||||||||
\(449\) | 7.10810 | 0.335452 | 0.167726 | − | 0.985834i | \(-0.446358\pi\) | ||||
0.167726 | + | 0.985834i | \(0.446358\pi\) | |||||||
\(450\) | −4.98717 | −0.235098 | ||||||||
\(451\) | 19.0544 | 0.897239 | ||||||||
\(452\) | 1.47065 | 0.0691736 | ||||||||
\(453\) | 2.37037 | 0.111369 | ||||||||
\(454\) | 7.24312 | 0.339936 | ||||||||
\(455\) | 0.198247 | 0.00929396 | ||||||||
\(456\) | 7.50794 | 0.351592 | ||||||||
\(457\) | 3.49794 | 0.163627 | 0.0818133 | − | 0.996648i | \(-0.473929\pi\) | ||||
0.0818133 | + | 0.996648i | \(0.473929\pi\) | |||||||
\(458\) | −1.26769 | −0.0592353 | ||||||||
\(459\) | −6.05562 | −0.282652 | ||||||||
\(460\) | −0.615806 | −0.0287121 | ||||||||
\(461\) | −16.7541 | −0.780317 | −0.390159 | − | 0.920748i | \(-0.627580\pi\) | ||||
−0.390159 | + | 0.920748i | \(0.627580\pi\) | |||||||
\(462\) | −6.39954 | −0.297734 | ||||||||
\(463\) | 34.6202 | 1.60894 | 0.804469 | − | 0.593995i | \(-0.202450\pi\) | ||||
0.804469 | + | 0.593995i | \(0.202450\pi\) | |||||||
\(464\) | 9.14306 | 0.424456 | ||||||||
\(465\) | 0.493589 | 0.0228896 | ||||||||
\(466\) | −8.23879 | −0.381655 | ||||||||
\(467\) | 27.0423 | 1.25137 | 0.625685 | − | 0.780076i | \(-0.284820\pi\) | ||||
0.625685 | + | 0.780076i | \(0.284820\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −21.2926 | −0.983202 | ||||||||
\(470\) | 1.33876 | 0.0617526 | ||||||||
\(471\) | 18.0051 | 0.829633 | ||||||||
\(472\) | 6.97905 | 0.321237 | ||||||||
\(473\) | 24.0610 | 1.10632 | ||||||||
\(474\) | 5.30030 | 0.243451 | ||||||||
\(475\) | 37.4434 | 1.71802 | ||||||||
\(476\) | 10.5994 | 0.485824 | ||||||||
\(477\) | −3.10712 | −0.142265 | ||||||||
\(478\) | −2.25279 | −0.103040 | ||||||||
\(479\) | −3.48706 | −0.159328 | −0.0796640 | − | 0.996822i | \(-0.525385\pi\) | ||||
−0.0796640 | + | 0.996822i | \(0.525385\pi\) | |||||||
\(480\) | 0.113262 | 0.00516967 | ||||||||
\(481\) | −0.0304744 | −0.00138951 | ||||||||
\(482\) | 13.8985 | 0.633061 | ||||||||
\(483\) | −9.51665 | −0.433022 | ||||||||
\(484\) | 2.36755 | 0.107616 | ||||||||
\(485\) | −1.14496 | −0.0519902 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −25.2054 | −1.14217 | −0.571084 | − | 0.820892i | \(-0.693477\pi\) | ||||
−0.571084 | + | 0.820892i | \(0.693477\pi\) | |||||||
\(488\) | 10.2132 | 0.462330 | ||||||||
\(489\) | −17.8749 | −0.808330 | ||||||||
\(490\) | 0.445832 | 0.0201407 | ||||||||
\(491\) | −24.3399 | −1.09844 | −0.549221 | − | 0.835677i | \(-0.685076\pi\) | ||||
−0.549221 | + | 0.835677i | \(0.685076\pi\) | |||||||
\(492\) | −5.21159 | −0.234957 | ||||||||
\(493\) | 55.3670 | 2.49360 | ||||||||
\(494\) | 7.50794 | 0.337798 | ||||||||
\(495\) | −0.414104 | −0.0186126 | ||||||||
\(496\) | 4.35795 | 0.195678 | ||||||||
\(497\) | −10.0734 | −0.451854 | ||||||||
\(498\) | −11.0499 | −0.495158 | ||||||||
\(499\) | 4.90624 | 0.219633 | 0.109817 | − | 0.993952i | \(-0.464974\pi\) | ||||
0.109817 | + | 0.993952i | \(0.464974\pi\) | |||||||
\(500\) | 1.13117 | 0.0505872 | ||||||||
\(501\) | −4.42869 | −0.197859 | ||||||||
\(502\) | −28.5671 | −1.27501 | ||||||||
\(503\) | −11.7912 | −0.525745 | −0.262872 | − | 0.964831i | \(-0.584670\pi\) | ||||
−0.262872 | + | 0.964831i | \(0.584670\pi\) | |||||||
\(504\) | 1.75034 | 0.0779665 | ||||||||
\(505\) | 0.122484 | 0.00545048 | ||||||||
\(506\) | 19.8786 | 0.883713 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −5.04339 | −0.223764 | ||||||||
\(509\) | 9.02388 | 0.399976 | 0.199988 | − | 0.979798i | \(-0.435910\pi\) | ||||
0.199988 | + | 0.979798i | \(0.435910\pi\) | |||||||
\(510\) | 0.685871 | 0.0303709 | ||||||||
\(511\) | −11.8962 | −0.526257 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 7.50794 | 0.331484 | ||||||||
\(514\) | −17.5467 | −0.773950 | ||||||||
\(515\) | 0.113262 | 0.00499091 | ||||||||
\(516\) | −6.58092 | −0.289709 | ||||||||
\(517\) | −43.2162 | −1.90065 | ||||||||
\(518\) | 0.0533406 | 0.00234365 | ||||||||
\(519\) | −9.46262 | −0.415363 | ||||||||
\(520\) | 0.113262 | 0.00496686 | ||||||||
\(521\) | −19.5572 | −0.856818 | −0.428409 | − | 0.903585i | \(-0.640926\pi\) | ||||
−0.428409 | + | 0.903585i | \(0.640926\pi\) | |||||||
\(522\) | 9.14306 | 0.400181 | ||||||||
\(523\) | −13.6811 | −0.598232 | −0.299116 | − | 0.954217i | \(-0.596692\pi\) | ||||
−0.299116 | + | 0.954217i | \(0.596692\pi\) | |||||||
\(524\) | −4.59698 | −0.200820 | ||||||||
\(525\) | 8.72926 | 0.380976 | ||||||||
\(526\) | −9.97158 | −0.434782 | ||||||||
\(527\) | 26.3901 | 1.14957 | ||||||||
\(528\) | −3.65617 | −0.159114 | ||||||||
\(529\) | 6.56116 | 0.285268 | ||||||||
\(530\) | 0.351918 | 0.0152863 | ||||||||
\(531\) | 6.97905 | 0.302865 | ||||||||
\(532\) | −13.1415 | −0.569755 | ||||||||
\(533\) | −5.21159 | −0.225739 | ||||||||
\(534\) | −10.4079 | −0.450395 | ||||||||
\(535\) | −0.241593 | −0.0104450 | ||||||||
\(536\) | −12.1648 | −0.525441 | ||||||||
\(537\) | −11.2831 | −0.486902 | ||||||||
\(538\) | −5.46710 | −0.235704 | ||||||||
\(539\) | −14.3918 | −0.619897 | ||||||||
\(540\) | 0.113262 | 0.00487401 | ||||||||
\(541\) | 28.2190 | 1.21323 | 0.606615 | − | 0.794996i | \(-0.292527\pi\) | ||||
0.606615 | + | 0.794996i | \(0.292527\pi\) | |||||||
\(542\) | 22.8053 | 0.979573 | ||||||||
\(543\) | 17.1528 | 0.736099 | ||||||||
\(544\) | 6.05562 | 0.259633 | ||||||||
\(545\) | 0.270967 | 0.0116070 | ||||||||
\(546\) | 1.75034 | 0.0749078 | ||||||||
\(547\) | 23.1882 | 0.991457 | 0.495729 | − | 0.868477i | \(-0.334901\pi\) | ||||
0.495729 | + | 0.868477i | \(0.334901\pi\) | |||||||
\(548\) | 15.0484 | 0.642836 | ||||||||
\(549\) | 10.2132 | 0.435889 | ||||||||
\(550\) | −18.2339 | −0.777497 | ||||||||
\(551\) | −68.6456 | −2.92440 | ||||||||
\(552\) | −5.43702 | −0.231415 | ||||||||
\(553\) | −9.27734 | −0.394513 | ||||||||
\(554\) | 24.2026 | 1.02827 | ||||||||
\(555\) | 0.00345158 | 0.000146512 0 | ||||||||
\(556\) | 5.89502 | 0.250004 | ||||||||
\(557\) | 31.6205 | 1.33981 | 0.669903 | − | 0.742449i | \(-0.266336\pi\) | ||||
0.669903 | + | 0.742449i | \(0.266336\pi\) | |||||||
\(558\) | 4.35795 | 0.184487 | ||||||||
\(559\) | −6.58092 | −0.278343 | ||||||||
\(560\) | −0.198247 | −0.00837747 | ||||||||
\(561\) | −22.1404 | −0.934767 | ||||||||
\(562\) | −4.92762 | −0.207859 | ||||||||
\(563\) | −43.7292 | −1.84297 | −0.921483 | − | 0.388419i | \(-0.873021\pi\) | ||||
−0.921483 | + | 0.388419i | \(0.873021\pi\) | |||||||
\(564\) | 11.8201 | 0.497715 | ||||||||
\(565\) | −0.166569 | −0.00700760 | ||||||||
\(566\) | −10.6051 | −0.445767 | ||||||||
\(567\) | 1.75034 | 0.0735075 | ||||||||
\(568\) | −5.75511 | −0.241479 | ||||||||
\(569\) | 47.0223 | 1.97128 | 0.985639 | − | 0.168867i | \(-0.0540109\pi\) | ||||
0.985639 | + | 0.168867i | \(0.0540109\pi\) | |||||||
\(570\) | −0.850363 | −0.0356178 | ||||||||
\(571\) | −28.0637 | −1.17443 | −0.587214 | − | 0.809432i | \(-0.699775\pi\) | ||||
−0.587214 | + | 0.809432i | \(0.699775\pi\) | |||||||
\(572\) | −3.65617 | −0.152872 | ||||||||
\(573\) | −3.75731 | −0.156964 | ||||||||
\(574\) | 9.12208 | 0.380748 | ||||||||
\(575\) | −27.1153 | −1.13079 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −8.71369 | −0.362756 | −0.181378 | − | 0.983413i | \(-0.558056\pi\) | ||||
−0.181378 | + | 0.983413i | \(0.558056\pi\) | |||||||
\(578\) | 19.6706 | 0.818188 | ||||||||
\(579\) | 4.89362 | 0.203372 | ||||||||
\(580\) | −1.03556 | −0.0429993 | ||||||||
\(581\) | 19.3411 | 0.802404 | ||||||||
\(582\) | −10.1090 | −0.419032 | ||||||||
\(583\) | −11.3602 | −0.470489 | ||||||||
\(584\) | −6.79650 | −0.281241 | ||||||||
\(585\) | 0.113262 | 0.00468280 | ||||||||
\(586\) | 20.3878 | 0.842211 | ||||||||
\(587\) | −29.4117 | −1.21395 | −0.606976 | − | 0.794721i | \(-0.707617\pi\) | ||||
−0.606976 | + | 0.794721i | \(0.707617\pi\) | |||||||
\(588\) | 3.93630 | 0.162330 | ||||||||
\(589\) | −32.7192 | −1.34817 | ||||||||
\(590\) | −0.790460 | −0.0325427 | ||||||||
\(591\) | 24.9189 | 1.02503 | ||||||||
\(592\) | 0.0304744 | 0.00125249 | ||||||||
\(593\) | −31.1387 | −1.27871 | −0.639357 | − | 0.768910i | \(-0.720800\pi\) | ||||
−0.639357 | + | 0.768910i | \(0.720800\pi\) | |||||||
\(594\) | −3.65617 | −0.150014 | ||||||||
\(595\) | −1.20051 | −0.0492161 | ||||||||
\(596\) | 0.0191072 | 0.000782660 0 | ||||||||
\(597\) | −12.8498 | −0.525908 | ||||||||
\(598\) | −5.43702 | −0.222336 | ||||||||
\(599\) | 3.34070 | 0.136497 | 0.0682486 | − | 0.997668i | \(-0.478259\pi\) | ||||
0.0682486 | + | 0.997668i | \(0.478259\pi\) | |||||||
\(600\) | 4.98717 | 0.203600 | ||||||||
\(601\) | 29.2746 | 1.19413 | 0.597067 | − | 0.802191i | \(-0.296332\pi\) | ||||
0.597067 | + | 0.802191i | \(0.296332\pi\) | |||||||
\(602\) | 11.5189 | 0.469474 | ||||||||
\(603\) | −12.1648 | −0.495390 | ||||||||
\(604\) | −2.37037 | −0.0964488 | ||||||||
\(605\) | −0.268153 | −0.0109020 | ||||||||
\(606\) | 1.08143 | 0.0439300 | ||||||||
\(607\) | −38.4815 | −1.56192 | −0.780958 | − | 0.624584i | \(-0.785269\pi\) | ||||
−0.780958 | + | 0.624584i | \(0.785269\pi\) | |||||||
\(608\) | −7.50794 | −0.304487 | ||||||||
\(609\) | −16.0035 | −0.648495 | ||||||||
\(610\) | −1.15676 | −0.0468360 | ||||||||
\(611\) | 11.8201 | 0.478190 | ||||||||
\(612\) | 6.05562 | 0.244784 | ||||||||
\(613\) | 25.6048 | 1.03417 | 0.517084 | − | 0.855935i | \(-0.327017\pi\) | ||||
0.517084 | + | 0.855935i | \(0.327017\pi\) | |||||||
\(614\) | 5.60226 | 0.226089 | ||||||||
\(615\) | 0.590274 | 0.0238022 | ||||||||
\(616\) | 6.39954 | 0.257845 | ||||||||
\(617\) | −5.82731 | −0.234599 | −0.117299 | − | 0.993097i | \(-0.537424\pi\) | ||||
−0.117299 | + | 0.993097i | \(0.537424\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | −9.74174 | −0.391554 | −0.195777 | − | 0.980648i | \(-0.562723\pi\) | ||||
−0.195777 | + | 0.980648i | \(0.562723\pi\) | |||||||
\(620\) | −0.493589 | −0.0198230 | ||||||||
\(621\) | −5.43702 | −0.218180 | ||||||||
\(622\) | −18.0590 | −0.724099 | ||||||||
\(623\) | 18.2174 | 0.729866 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 24.8077 | 0.992310 | ||||||||
\(626\) | −4.76033 | −0.190261 | ||||||||
\(627\) | 27.4503 | 1.09626 | ||||||||
\(628\) | −18.0051 | −0.718483 | ||||||||
\(629\) | 0.184541 | 0.00735815 | ||||||||
\(630\) | −0.198247 | −0.00789835 | ||||||||
\(631\) | 10.6825 | 0.425262 | 0.212631 | − | 0.977133i | \(-0.431797\pi\) | ||||
0.212631 | + | 0.977133i | \(0.431797\pi\) | |||||||
\(632\) | −5.30030 | −0.210835 | ||||||||
\(633\) | −16.3252 | −0.648870 | ||||||||
\(634\) | 27.1745 | 1.07924 | ||||||||
\(635\) | 0.571223 | 0.0226683 | ||||||||
\(636\) | 3.10712 | 0.123205 | ||||||||
\(637\) | 3.93630 | 0.155962 | ||||||||
\(638\) | 33.4286 | 1.32345 | ||||||||
\(639\) | −5.75511 | −0.227669 | ||||||||
\(640\) | −0.113262 | −0.00447707 | ||||||||
\(641\) | −6.41802 | −0.253497 | −0.126748 | − | 0.991935i | \(-0.540454\pi\) | ||||
−0.126748 | + | 0.991935i | \(0.540454\pi\) | |||||||
\(642\) | −2.13304 | −0.0841846 | ||||||||
\(643\) | −20.5851 | −0.811798 | −0.405899 | − | 0.913918i | \(-0.633041\pi\) | ||||
−0.405899 | + | 0.913918i | \(0.633041\pi\) | |||||||
\(644\) | 9.51665 | 0.375008 | ||||||||
\(645\) | 0.745368 | 0.0293488 | ||||||||
\(646\) | −45.4653 | −1.78881 | ||||||||
\(647\) | −3.21383 | −0.126349 | −0.0631744 | − | 0.998003i | \(-0.520122\pi\) | ||||
−0.0631744 | + | 0.998003i | \(0.520122\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 25.5166 | 1.00161 | ||||||||
\(650\) | 4.98717 | 0.195613 | ||||||||
\(651\) | −7.62790 | −0.298961 | ||||||||
\(652\) | 17.8749 | 0.700034 | ||||||||
\(653\) | 8.29517 | 0.324615 | 0.162307 | − | 0.986740i | \(-0.448106\pi\) | ||||
0.162307 | + | 0.986740i | \(0.448106\pi\) | |||||||
\(654\) | 2.39240 | 0.0935501 | ||||||||
\(655\) | 0.520662 | 0.0203440 | ||||||||
\(656\) | 5.21159 | 0.203479 | ||||||||
\(657\) | −6.79650 | −0.265157 | ||||||||
\(658\) | −20.6892 | −0.806549 | ||||||||
\(659\) | −8.89655 | −0.346560 | −0.173280 | − | 0.984873i | \(-0.555437\pi\) | ||||
−0.173280 | + | 0.984873i | \(0.555437\pi\) | |||||||
\(660\) | 0.414104 | 0.0161190 | ||||||||
\(661\) | 18.4665 | 0.718264 | 0.359132 | − | 0.933287i | \(-0.383073\pi\) | ||||
0.359132 | + | 0.933287i | \(0.383073\pi\) | |||||||
\(662\) | 28.1489 | 1.09404 | ||||||||
\(663\) | 6.05562 | 0.235181 | ||||||||
\(664\) | 11.0499 | 0.428819 | ||||||||
\(665\) | 1.48843 | 0.0577187 | ||||||||
\(666\) | 0.0304744 | 0.00118086 | ||||||||
\(667\) | 49.7110 | 1.92482 | ||||||||
\(668\) | 4.42869 | 0.171351 | ||||||||
\(669\) | 14.1757 | 0.548063 | ||||||||
\(670\) | 1.37781 | 0.0532295 | ||||||||
\(671\) | 37.3411 | 1.44154 | ||||||||
\(672\) | −1.75034 | −0.0675210 | ||||||||
\(673\) | −18.1098 | −0.698082 | −0.349041 | − | 0.937107i | \(-0.613493\pi\) | ||||
−0.349041 | + | 0.937107i | \(0.613493\pi\) | |||||||
\(674\) | −9.70607 | −0.373864 | ||||||||
\(675\) | 4.98717 | 0.191956 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 19.9368 | 0.766234 | 0.383117 | − | 0.923700i | \(-0.374851\pi\) | ||||
0.383117 | + | 0.923700i | \(0.374851\pi\) | |||||||
\(678\) | −1.47065 | −0.0564800 | ||||||||
\(679\) | 17.6942 | 0.679042 | ||||||||
\(680\) | −0.685871 | −0.0263020 | ||||||||
\(681\) | −7.24312 | −0.277557 | ||||||||
\(682\) | 15.9334 | 0.610120 | ||||||||
\(683\) | −36.6572 | −1.40265 | −0.701324 | − | 0.712843i | \(-0.747407\pi\) | ||||
−0.701324 | + | 0.712843i | \(0.747407\pi\) | |||||||
\(684\) | −7.50794 | −0.287073 | ||||||||
\(685\) | −1.70441 | −0.0651221 | ||||||||
\(686\) | −19.1423 | −0.730855 | ||||||||
\(687\) | 1.26769 | 0.0483654 | ||||||||
\(688\) | 6.58092 | 0.250895 | ||||||||
\(689\) | 3.10712 | 0.118372 | ||||||||
\(690\) | 0.615806 | 0.0234434 | ||||||||
\(691\) | 28.4139 | 1.08092 | 0.540459 | − | 0.841371i | \(-0.318251\pi\) | ||||
0.540459 | + | 0.841371i | \(0.318251\pi\) | |||||||
\(692\) | 9.46262 | 0.359715 | ||||||||
\(693\) | 6.39954 | 0.243099 | ||||||||
\(694\) | 0.347167 | 0.0131783 | ||||||||
\(695\) | −0.667680 | −0.0253266 | ||||||||
\(696\) | −9.14306 | −0.346567 | ||||||||
\(697\) | 31.5594 | 1.19540 | ||||||||
\(698\) | 15.1633 | 0.573939 | ||||||||
\(699\) | 8.23879 | 0.311620 | ||||||||
\(700\) | −8.72926 | −0.329935 | ||||||||
\(701\) | −1.07339 | −0.0405413 | −0.0202706 | − | 0.999795i | \(-0.506453\pi\) | ||||
−0.0202706 | + | 0.999795i | \(0.506453\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −0.228800 | −0.00862935 | ||||||||
\(704\) | 3.65617 | 0.137797 | ||||||||
\(705\) | −1.33876 | −0.0504208 | ||||||||
\(706\) | 23.8881 | 0.899041 | ||||||||
\(707\) | −1.89287 | −0.0711886 | ||||||||
\(708\) | −6.97905 | −0.262289 | ||||||||
\(709\) | −38.6959 | −1.45325 | −0.726627 | − | 0.687032i | \(-0.758913\pi\) | ||||
−0.726627 | + | 0.687032i | \(0.758913\pi\) | |||||||
\(710\) | 0.651834 | 0.0244629 | ||||||||
\(711\) | −5.30030 | −0.198777 | ||||||||
\(712\) | 10.4079 | 0.390054 | ||||||||
\(713\) | 23.6942 | 0.887356 | ||||||||
\(714\) | −10.5994 | −0.396673 | ||||||||
\(715\) | 0.414104 | 0.0154866 | ||||||||
\(716\) | 11.2831 | 0.421669 | ||||||||
\(717\) | 2.25279 | 0.0841321 | ||||||||
\(718\) | 21.9488 | 0.819121 | ||||||||
\(719\) | −27.6041 | −1.02946 | −0.514730 | − | 0.857352i | \(-0.672108\pi\) | ||||
−0.514730 | + | 0.857352i | \(0.672108\pi\) | |||||||
\(720\) | −0.113262 | −0.00422102 | ||||||||
\(721\) | −1.75034 | −0.0651862 | ||||||||
\(722\) | 37.3692 | 1.39074 | ||||||||
\(723\) | −13.8985 | −0.516892 | ||||||||
\(724\) | −17.1528 | −0.637480 | ||||||||
\(725\) | −45.5980 | −1.69347 | ||||||||
\(726\) | −2.36755 | −0.0878680 | ||||||||
\(727\) | −28.5672 | −1.05950 | −0.529750 | − | 0.848154i | \(-0.677714\pi\) | ||||
−0.529750 | + | 0.848154i | \(0.677714\pi\) | |||||||
\(728\) | −1.75034 | −0.0648720 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.769784 | 0.0284910 | ||||||||
\(731\) | 39.8516 | 1.47396 | ||||||||
\(732\) | −10.2132 | −0.377491 | ||||||||
\(733\) | 37.3573 | 1.37983 | 0.689913 | − | 0.723893i | \(-0.257649\pi\) | ||||
0.689913 | + | 0.723893i | \(0.257649\pi\) | |||||||
\(734\) | 9.65935 | 0.356533 | ||||||||
\(735\) | −0.445832 | −0.0164448 | ||||||||
\(736\) | 5.43702 | 0.200411 | ||||||||
\(737\) | −44.4766 | −1.63832 | ||||||||
\(738\) | 5.21159 | 0.191841 | ||||||||
\(739\) | 10.8084 | 0.397595 | 0.198798 | − | 0.980041i | \(-0.436296\pi\) | ||||
0.198798 | + | 0.980041i | \(0.436296\pi\) | |||||||
\(740\) | −0.00345158 | −0.000126883 0 | ||||||||
\(741\) | −7.50794 | −0.275811 | ||||||||
\(742\) | −5.43853 | −0.199655 | ||||||||
\(743\) | −33.2240 | −1.21887 | −0.609435 | − | 0.792836i | \(-0.708604\pi\) | ||||
−0.609435 | + | 0.792836i | \(0.708604\pi\) | |||||||
\(744\) | −4.35795 | −0.159770 | ||||||||
\(745\) | −0.00216411 | −7.92870e−5 0 | ||||||||
\(746\) | 33.1269 | 1.21286 | ||||||||
\(747\) | 11.0499 | 0.404295 | ||||||||
\(748\) | 22.1404 | 0.809532 | ||||||||
\(749\) | 3.73356 | 0.136421 | ||||||||
\(750\) | −1.13117 | −0.0413043 | ||||||||
\(751\) | −6.10923 | −0.222929 | −0.111465 | − | 0.993768i | \(-0.535554\pi\) | ||||
−0.111465 | + | 0.993768i | \(0.535554\pi\) | |||||||
\(752\) | −11.8201 | −0.431034 | ||||||||
\(753\) | 28.5671 | 1.04104 | ||||||||
\(754\) | −9.14306 | −0.332971 | ||||||||
\(755\) | 0.268472 | 0.00977069 | ||||||||
\(756\) | −1.75034 | −0.0636594 | ||||||||
\(757\) | −22.2939 | −0.810287 | −0.405143 | − | 0.914253i | \(-0.632778\pi\) | ||||
−0.405143 | + | 0.914253i | \(0.632778\pi\) | |||||||
\(758\) | −13.3594 | −0.485235 | ||||||||
\(759\) | −19.8786 | −0.721549 | ||||||||
\(760\) | 0.850363 | 0.0308459 | ||||||||
\(761\) | −20.1551 | −0.730622 | −0.365311 | − | 0.930886i | \(-0.619037\pi\) | ||||
−0.365311 | + | 0.930886i | \(0.619037\pi\) | |||||||
\(762\) | 5.04339 | 0.182703 | ||||||||
\(763\) | −4.18751 | −0.151598 | ||||||||
\(764\) | 3.75731 | 0.135935 | ||||||||
\(765\) | −0.685871 | −0.0247977 | ||||||||
\(766\) | 19.2044 | 0.693882 | ||||||||
\(767\) | −6.97905 | −0.251999 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 20.5590 | 0.741378 | 0.370689 | − | 0.928757i | \(-0.379122\pi\) | ||||
0.370689 | + | 0.928757i | \(0.379122\pi\) | |||||||
\(770\) | −0.724824 | −0.0261208 | ||||||||
\(771\) | 17.5467 | 0.631927 | ||||||||
\(772\) | −4.89362 | −0.176125 | ||||||||
\(773\) | 18.1145 | 0.651532 | 0.325766 | − | 0.945450i | \(-0.394378\pi\) | ||||
0.325766 | + | 0.945450i | \(0.394378\pi\) | |||||||
\(774\) | 6.58092 | 0.236546 | ||||||||
\(775\) | −21.7338 | −0.780702 | ||||||||
\(776\) | 10.1090 | 0.362892 | ||||||||
\(777\) | −0.0533406 | −0.00191358 | ||||||||
\(778\) | 27.5591 | 0.988042 | ||||||||
\(779\) | −39.1283 | −1.40192 | ||||||||
\(780\) | −0.113262 | −0.00405542 | ||||||||
\(781\) | −21.0416 | −0.752929 | ||||||||
\(782\) | 32.9245 | 1.17738 | ||||||||
\(783\) | −9.14306 | −0.326746 | ||||||||
\(784\) | −3.93630 | −0.140582 | ||||||||
\(785\) | 2.03929 | 0.0727856 | ||||||||
\(786\) | 4.59698 | 0.163969 | ||||||||
\(787\) | −5.64316 | −0.201157 | −0.100579 | − | 0.994929i | \(-0.532069\pi\) | ||||
−0.100579 | + | 0.994929i | \(0.532069\pi\) | |||||||
\(788\) | −24.9189 | −0.887698 | ||||||||
\(789\) | 9.97158 | 0.354998 | ||||||||
\(790\) | 0.600321 | 0.0213585 | ||||||||
\(791\) | 2.57414 | 0.0915260 | ||||||||
\(792\) | 3.65617 | 0.129916 | ||||||||
\(793\) | −10.2132 | −0.362681 | ||||||||
\(794\) | 12.6689 | 0.449603 | ||||||||
\(795\) | −0.351918 | −0.0124813 | ||||||||
\(796\) | 12.8498 | 0.455450 | ||||||||
\(797\) | 0.839598 | 0.0297401 | 0.0148700 | − | 0.999889i | \(-0.495267\pi\) | ||||
0.0148700 | + | 0.999889i | \(0.495267\pi\) | |||||||
\(798\) | 13.1415 | 0.465203 | ||||||||
\(799\) | −71.5780 | −2.53225 | ||||||||
\(800\) | −4.98717 | −0.176323 | ||||||||
\(801\) | 10.4079 | 0.367746 | ||||||||
\(802\) | 5.67991 | 0.200565 | ||||||||
\(803\) | −24.8491 | −0.876907 | ||||||||
\(804\) | 12.1648 | 0.429020 | ||||||||
\(805\) | −1.07787 | −0.0379900 | ||||||||
\(806\) | −4.35795 | −0.153502 | ||||||||
\(807\) | 5.46710 | 0.192451 | ||||||||
\(808\) | −1.08143 | −0.0380445 | ||||||||
\(809\) | −40.2280 | −1.41434 | −0.707171 | − | 0.707043i | \(-0.750029\pi\) | ||||
−0.707171 | + | 0.707043i | \(0.750029\pi\) | |||||||
\(810\) | −0.113262 | −0.00397961 | ||||||||
\(811\) | −40.4036 | −1.41876 | −0.709381 | − | 0.704826i | \(-0.751025\pi\) | ||||
−0.709381 | + | 0.704826i | \(0.751025\pi\) | |||||||
\(812\) | 16.0035 | 0.561613 | ||||||||
\(813\) | −22.8053 | −0.799818 | ||||||||
\(814\) | 0.111419 | 0.00390525 | ||||||||
\(815\) | −2.02454 | −0.0709166 | ||||||||
\(816\) | −6.05562 | −0.211989 | ||||||||
\(817\) | −49.4092 | −1.72861 | ||||||||
\(818\) | −26.1681 | −0.914946 | ||||||||
\(819\) | −1.75034 | −0.0611619 | ||||||||
\(820\) | −0.590274 | −0.0206133 | ||||||||
\(821\) | −21.7903 | −0.760487 | −0.380244 | − | 0.924886i | \(-0.624160\pi\) | ||||
−0.380244 | + | 0.924886i | \(0.624160\pi\) | |||||||
\(822\) | −15.0484 | −0.524873 | ||||||||
\(823\) | −16.4108 | −0.572044 | −0.286022 | − | 0.958223i | \(-0.592333\pi\) | ||||
−0.286022 | + | 0.958223i | \(0.592333\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 18.2339 | 0.634824 | ||||||||
\(826\) | 12.2157 | 0.425040 | ||||||||
\(827\) | 17.7950 | 0.618794 | 0.309397 | − | 0.950933i | \(-0.399873\pi\) | ||||
0.309397 | + | 0.950933i | \(0.399873\pi\) | |||||||
\(828\) | 5.43702 | 0.188949 | ||||||||
\(829\) | −52.2100 | −1.81333 | −0.906665 | − | 0.421852i | \(-0.861380\pi\) | ||||
−0.906665 | + | 0.421852i | \(0.861380\pi\) | |||||||
\(830\) | −1.25153 | −0.0434413 | ||||||||
\(831\) | −24.2026 | −0.839578 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −23.8367 | −0.825894 | ||||||||
\(834\) | −5.89502 | −0.204128 | ||||||||
\(835\) | −0.501601 | −0.0173586 | ||||||||
\(836\) | −27.4503 | −0.949388 | ||||||||
\(837\) | −4.35795 | −0.150633 | ||||||||
\(838\) | −28.2916 | −0.977318 | ||||||||
\(839\) | 15.9315 | 0.550017 | 0.275009 | − | 0.961442i | \(-0.411319\pi\) | ||||
0.275009 | + | 0.961442i | \(0.411319\pi\) | |||||||
\(840\) | 0.198247 | 0.00684017 | ||||||||
\(841\) | 54.5956 | 1.88261 | ||||||||
\(842\) | 10.1314 | 0.349153 | ||||||||
\(843\) | 4.92762 | 0.169716 | ||||||||
\(844\) | 16.3252 | 0.561938 | ||||||||
\(845\) | −0.113262 | −0.00389633 | ||||||||
\(846\) | −11.8201 | −0.406383 | ||||||||
\(847\) | 4.14402 | 0.142390 | ||||||||
\(848\) | −3.10712 | −0.106699 | ||||||||
\(849\) | 10.6051 | 0.363967 | ||||||||
\(850\) | −30.2004 | −1.03587 | ||||||||
\(851\) | 0.165690 | 0.00567977 | ||||||||
\(852\) | 5.75511 | 0.197167 | ||||||||
\(853\) | −14.9322 | −0.511269 | −0.255634 | − | 0.966774i | \(-0.582284\pi\) | ||||
−0.255634 | + | 0.966774i | \(0.582284\pi\) | |||||||
\(854\) | 17.8766 | 0.611724 | ||||||||
\(855\) | 0.850363 | 0.0290818 | ||||||||
\(856\) | 2.13304 | 0.0729060 | ||||||||
\(857\) | −54.0921 | −1.84775 | −0.923876 | − | 0.382692i | \(-0.874997\pi\) | ||||
−0.923876 | + | 0.382692i | \(0.874997\pi\) | |||||||
\(858\) | 3.65617 | 0.124819 | ||||||||
\(859\) | −21.9404 | −0.748596 | −0.374298 | − | 0.927309i | \(-0.622116\pi\) | ||||
−0.374298 | + | 0.927309i | \(0.622116\pi\) | |||||||
\(860\) | −0.745368 | −0.0254168 | ||||||||
\(861\) | −9.12208 | −0.310880 | ||||||||
\(862\) | 38.4390 | 1.30924 | ||||||||
\(863\) | 5.05710 | 0.172146 | 0.0860729 | − | 0.996289i | \(-0.472568\pi\) | ||||
0.0860729 | + | 0.996289i | \(0.472568\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −1.07175 | −0.0364407 | ||||||||
\(866\) | −23.8800 | −0.811476 | ||||||||
\(867\) | −19.6706 | −0.668048 | ||||||||
\(868\) | 7.62790 | 0.258908 | ||||||||
\(869\) | −19.3788 | −0.657380 | ||||||||
\(870\) | 1.03556 | 0.0351088 | ||||||||
\(871\) | 12.1648 | 0.412189 | ||||||||
\(872\) | −2.39240 | −0.0810167 | ||||||||
\(873\) | 10.1090 | 0.342138 | ||||||||
\(874\) | −40.8208 | −1.38078 | ||||||||
\(875\) | 1.97993 | 0.0669338 | ||||||||
\(876\) | 6.79650 | 0.229633 | ||||||||
\(877\) | −6.50539 | −0.219671 | −0.109836 | − | 0.993950i | \(-0.535032\pi\) | ||||
−0.109836 | + | 0.993950i | \(0.535032\pi\) | |||||||
\(878\) | −36.5348 | −1.23299 | ||||||||
\(879\) | −20.3878 | −0.687663 | ||||||||
\(880\) | −0.414104 | −0.0139594 | ||||||||
\(881\) | 52.8066 | 1.77910 | 0.889549 | − | 0.456839i | \(-0.151019\pi\) | ||||
0.889549 | + | 0.456839i | \(0.151019\pi\) | |||||||
\(882\) | −3.93630 | −0.132542 | ||||||||
\(883\) | −10.8432 | −0.364902 | −0.182451 | − | 0.983215i | \(-0.558403\pi\) | ||||
−0.182451 | + | 0.983215i | \(0.558403\pi\) | |||||||
\(884\) | −6.05562 | −0.203673 | ||||||||
\(885\) | 0.790460 | 0.0265710 | ||||||||
\(886\) | 39.2216 | 1.31768 | ||||||||
\(887\) | −13.2482 | −0.444830 | −0.222415 | − | 0.974952i | \(-0.571394\pi\) | ||||
−0.222415 | + | 0.974952i | \(0.571394\pi\) | |||||||
\(888\) | −0.0304744 | −0.00102265 | ||||||||
\(889\) | −8.82766 | −0.296070 | ||||||||
\(890\) | −1.17882 | −0.0395142 | ||||||||
\(891\) | 3.65617 | 0.122486 | ||||||||
\(892\) | −14.1757 | −0.474637 | ||||||||
\(893\) | 88.7446 | 2.96972 | ||||||||
\(894\) | −0.0191072 | −0.000639039 0 | ||||||||
\(895\) | −1.27794 | −0.0427170 | ||||||||
\(896\) | 1.75034 | 0.0584749 | ||||||||
\(897\) | 5.43702 | 0.181537 | ||||||||
\(898\) | 7.10810 | 0.237200 | ||||||||
\(899\) | 39.8450 | 1.32890 | ||||||||
\(900\) | −4.98717 | −0.166239 | ||||||||
\(901\) | −18.8156 | −0.626837 | ||||||||
\(902\) | 19.0544 | 0.634444 | ||||||||
\(903\) | −11.5189 | −0.383324 | ||||||||
\(904\) | 1.47065 | 0.0489131 | ||||||||
\(905\) | 1.94276 | 0.0645796 | ||||||||
\(906\) | 2.37037 | 0.0787501 | ||||||||
\(907\) | 54.2853 | 1.80251 | 0.901257 | − | 0.433285i | \(-0.142646\pi\) | ||||
0.901257 | + | 0.433285i | \(0.142646\pi\) | |||||||
\(908\) | 7.24312 | 0.240371 | ||||||||
\(909\) | −1.08143 | −0.0358687 | ||||||||
\(910\) | 0.198247 | 0.00657183 | ||||||||
\(911\) | −13.2915 | −0.440366 | −0.220183 | − | 0.975459i | \(-0.570665\pi\) | ||||
−0.220183 | + | 0.975459i | \(0.570665\pi\) | |||||||
\(912\) | 7.50794 | 0.248613 | ||||||||
\(913\) | 40.4002 | 1.33705 | ||||||||
\(914\) | 3.49794 | 0.115702 | ||||||||
\(915\) | 1.15676 | 0.0382415 | ||||||||
\(916\) | −1.26769 | −0.0418857 | ||||||||
\(917\) | −8.04629 | −0.265712 | ||||||||
\(918\) | −6.05562 | −0.199865 | ||||||||
\(919\) | −33.7921 | −1.11470 | −0.557349 | − | 0.830278i | \(-0.688182\pi\) | ||||
−0.557349 | + | 0.830278i | \(0.688182\pi\) | |||||||
\(920\) | −0.615806 | −0.0203025 | ||||||||
\(921\) | −5.60226 | −0.184601 | ||||||||
\(922\) | −16.7541 | −0.551768 | ||||||||
\(923\) | 5.75511 | 0.189432 | ||||||||
\(924\) | −6.39954 | −0.210530 | ||||||||
\(925\) | −0.151981 | −0.00499710 | ||||||||
\(926\) | 34.6202 | 1.13769 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 9.14306 | 0.300136 | ||||||||
\(929\) | −25.0860 | −0.823045 | −0.411523 | − | 0.911400i | \(-0.635003\pi\) | ||||
−0.411523 | + | 0.911400i | \(0.635003\pi\) | |||||||
\(930\) | 0.493589 | 0.0161854 | ||||||||
\(931\) | 29.5535 | 0.968577 | ||||||||
\(932\) | −8.23879 | −0.269871 | ||||||||
\(933\) | 18.0590 | 0.591224 | ||||||||
\(934\) | 27.0423 | 0.884852 | ||||||||
\(935\) | −2.50766 | −0.0820092 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −10.6702 | −0.348579 | −0.174289 | − | 0.984694i | \(-0.555763\pi\) | ||||
−0.174289 | + | 0.984694i | \(0.555763\pi\) | |||||||
\(938\) | −21.2926 | −0.695229 | ||||||||
\(939\) | 4.76033 | 0.155348 | ||||||||
\(940\) | 1.33876 | 0.0436657 | ||||||||
\(941\) | −37.8436 | −1.23367 | −0.616833 | − | 0.787094i | \(-0.711585\pi\) | ||||
−0.616833 | + | 0.787094i | \(0.711585\pi\) | |||||||
\(942\) | 18.0051 | 0.586639 | ||||||||
\(943\) | 28.3355 | 0.922731 | ||||||||
\(944\) | 6.97905 | 0.227149 | ||||||||
\(945\) | 0.198247 | 0.00644898 | ||||||||
\(946\) | 24.0610 | 0.782289 | ||||||||
\(947\) | −21.8642 | −0.710492 | −0.355246 | − | 0.934773i | \(-0.615603\pi\) | ||||
−0.355246 | + | 0.934773i | \(0.615603\pi\) | |||||||
\(948\) | 5.30030 | 0.172146 | ||||||||
\(949\) | 6.79650 | 0.220624 | ||||||||
\(950\) | 37.4434 | 1.21482 | ||||||||
\(951\) | −27.1745 | −0.881193 | ||||||||
\(952\) | 10.5994 | 0.343529 | ||||||||
\(953\) | −9.56399 | −0.309808 | −0.154904 | − | 0.987930i | \(-0.549507\pi\) | ||||
−0.154904 | + | 0.987930i | \(0.549507\pi\) | |||||||
\(954\) | −3.10712 | −0.100597 | ||||||||
\(955\) | −0.425560 | −0.0137708 | ||||||||
\(956\) | −2.25279 | −0.0728606 | ||||||||
\(957\) | −33.4286 | −1.08059 | ||||||||
\(958\) | −3.48706 | −0.112662 | ||||||||
\(959\) | 26.3399 | 0.850559 | ||||||||
\(960\) | 0.113262 | 0.00365551 | ||||||||
\(961\) | −12.0083 | −0.387365 | ||||||||
\(962\) | −0.0304744 | −0.000982533 0 | ||||||||
\(963\) | 2.13304 | 0.0687364 | ||||||||
\(964\) | 13.8985 | 0.447642 | ||||||||
\(965\) | 0.554260 | 0.0178423 | ||||||||
\(966\) | −9.51665 | −0.306193 | ||||||||
\(967\) | −43.1439 | −1.38741 | −0.693707 | − | 0.720257i | \(-0.744024\pi\) | ||||
−0.693707 | + | 0.720257i | \(0.744024\pi\) | |||||||
\(968\) | 2.36755 | 0.0760959 | ||||||||
\(969\) | 45.4653 | 1.46056 | ||||||||
\(970\) | −1.14496 | −0.0367626 | ||||||||
\(971\) | 36.1333 | 1.15957 | 0.579786 | − | 0.814769i | \(-0.303136\pi\) | ||||
0.579786 | + | 0.814769i | \(0.303136\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 10.3183 | 0.330790 | ||||||||
\(974\) | −25.2054 | −0.807634 | ||||||||
\(975\) | −4.98717 | −0.159717 | ||||||||
\(976\) | 10.2132 | 0.326916 | ||||||||
\(977\) | −32.7260 | −1.04700 | −0.523499 | − | 0.852026i | \(-0.675374\pi\) | ||||
−0.523499 | + | 0.852026i | \(0.675374\pi\) | |||||||
\(978\) | −17.8749 | −0.571575 | ||||||||
\(979\) | 38.0531 | 1.21618 | ||||||||
\(980\) | 0.445832 | 0.0142416 | ||||||||
\(981\) | −2.39240 | −0.0763833 | ||||||||
\(982\) | −24.3399 | −0.776716 | ||||||||
\(983\) | −0.489890 | −0.0156251 | −0.00781253 | − | 0.999969i | \(-0.502487\pi\) | ||||
−0.00781253 | + | 0.999969i | \(0.502487\pi\) | |||||||
\(984\) | −5.21159 | −0.166140 | ||||||||
\(985\) | 2.82236 | 0.0899278 | ||||||||
\(986\) | 55.3670 | 1.76324 | ||||||||
\(987\) | 20.6892 | 0.658545 | ||||||||
\(988\) | 7.50794 | 0.238860 | ||||||||
\(989\) | 35.7806 | 1.13776 | ||||||||
\(990\) | −0.414104 | −0.0131611 | ||||||||
\(991\) | 17.5448 | 0.557329 | 0.278665 | − | 0.960388i | \(-0.410108\pi\) | ||||
0.278665 | + | 0.960388i | \(0.410108\pi\) | |||||||
\(992\) | 4.35795 | 0.138365 | ||||||||
\(993\) | −28.1489 | −0.893278 | ||||||||
\(994\) | −10.0734 | −0.319509 | ||||||||
\(995\) | −1.45539 | −0.0461391 | ||||||||
\(996\) | −11.0499 | −0.350129 | ||||||||
\(997\) | −31.7460 | −1.00541 | −0.502703 | − | 0.864459i | \(-0.667661\pi\) | ||||
−0.502703 | + | 0.864459i | \(0.667661\pi\) | |||||||
\(998\) | 4.90624 | 0.155304 | ||||||||
\(999\) | −0.0304744 | −0.000964167 0 |
(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 | 8034.2.a.bc.1.8 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.bc.1.8 | ✓ | 15 | 1.1 | even | 1 | trivial |