Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.46 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.52977 | 1.08171 | 0.540854 | − | 0.841117i | \(-0.318101\pi\) | ||||
0.540854 | + | 0.841117i | \(0.318101\pi\) | |||||||
\(3\) | 0.0640431 | 0.0369753 | 0.0184877 | − | 0.999829i | \(-0.494115\pi\) | ||||
0.0184877 | + | 0.999829i | \(0.494115\pi\) | |||||||
\(4\) | 0.340181 | 0.170091 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.0979709 | 0.0399965 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.53913 | −0.897719 | ||||||||
\(9\) | −2.99590 | −0.998633 | ||||||||
\(10\) | −1.52977 | −0.483754 | ||||||||
\(11\) | −6.33328 | −1.90956 | −0.954778 | − | 0.297319i | \(-0.903907\pi\) | ||||
−0.954778 | + | 0.297319i | \(0.903907\pi\) | |||||||
\(12\) | 0.0217863 | 0.00628916 | ||||||||
\(13\) | −2.98935 | −0.829095 | −0.414548 | − | 0.910028i | \(-0.636060\pi\) | ||||
−0.414548 | + | 0.910028i | \(0.636060\pi\) | |||||||
\(14\) | −1.52977 | −0.408847 | ||||||||
\(15\) | −0.0640431 | −0.0165359 | ||||||||
\(16\) | −4.56464 | −1.14116 | ||||||||
\(17\) | −3.87195 | −0.939086 | −0.469543 | − | 0.882910i | \(-0.655581\pi\) | ||||
−0.469543 | + | 0.882910i | \(0.655581\pi\) | |||||||
\(18\) | −4.58302 | −1.08023 | ||||||||
\(19\) | 0.248126 | 0.0569239 | 0.0284620 | − | 0.999595i | \(-0.490939\pi\) | ||||
0.0284620 | + | 0.999595i | \(0.490939\pi\) | |||||||
\(20\) | −0.340181 | −0.0760669 | ||||||||
\(21\) | −0.0640431 | −0.0139754 | ||||||||
\(22\) | −9.68843 | −2.06558 | ||||||||
\(23\) | 4.03259 | 0.840853 | 0.420427 | − | 0.907327i | \(-0.361880\pi\) | ||||
0.420427 | + | 0.907327i | \(0.361880\pi\) | |||||||
\(24\) | −0.162614 | −0.0331934 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.57300 | −0.896839 | ||||||||
\(27\) | −0.383996 | −0.0739001 | ||||||||
\(28\) | −0.340181 | −0.0642882 | ||||||||
\(29\) | −2.72647 | −0.506293 | −0.253147 | − | 0.967428i | \(-0.581466\pi\) | ||||
−0.253147 | + | 0.967428i | \(0.581466\pi\) | |||||||
\(30\) | −0.0979709 | −0.0178870 | ||||||||
\(31\) | 6.29609 | 1.13081 | 0.565405 | − | 0.824813i | \(-0.308720\pi\) | ||||
0.565405 | + | 0.824813i | \(0.308720\pi\) | |||||||
\(32\) | −1.90456 | −0.336682 | ||||||||
\(33\) | −0.405603 | −0.0706064 | ||||||||
\(34\) | −5.92318 | −1.01582 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −1.01915 | −0.169858 | ||||||||
\(37\) | −1.45340 | −0.238938 | −0.119469 | − | 0.992838i | \(-0.538119\pi\) | ||||
−0.119469 | + | 0.992838i | \(0.538119\pi\) | |||||||
\(38\) | 0.379574 | 0.0615750 | ||||||||
\(39\) | −0.191447 | −0.0306561 | ||||||||
\(40\) | 2.53913 | 0.401472 | ||||||||
\(41\) | −6.94726 | −1.08498 | −0.542490 | − | 0.840063i | \(-0.682518\pi\) | ||||
−0.542490 | + | 0.840063i | \(0.682518\pi\) | |||||||
\(42\) | −0.0979709 | −0.0151172 | ||||||||
\(43\) | 3.71626 | 0.566725 | 0.283362 | − | 0.959013i | \(-0.408550\pi\) | ||||
0.283362 | + | 0.959013i | \(0.408550\pi\) | |||||||
\(44\) | −2.15446 | −0.324798 | ||||||||
\(45\) | 2.99590 | 0.446602 | ||||||||
\(46\) | 6.16892 | 0.909557 | ||||||||
\(47\) | 0.165459 | 0.0241346 | 0.0120673 | − | 0.999927i | \(-0.496159\pi\) | ||||
0.0120673 | + | 0.999927i | \(0.496159\pi\) | |||||||
\(48\) | −0.292334 | −0.0421947 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.52977 | 0.216341 | ||||||||
\(51\) | −0.247972 | −0.0347230 | ||||||||
\(52\) | −1.01692 | −0.141021 | ||||||||
\(53\) | −3.32221 | −0.456341 | −0.228171 | − | 0.973621i | \(-0.573274\pi\) | ||||
−0.228171 | + | 0.973621i | \(0.573274\pi\) | |||||||
\(54\) | −0.587424 | −0.0799382 | ||||||||
\(55\) | 6.33328 | 0.853980 | ||||||||
\(56\) | 2.53913 | 0.339306 | ||||||||
\(57\) | 0.0158907 | 0.00210478 | ||||||||
\(58\) | −4.17086 | −0.547661 | ||||||||
\(59\) | −10.7987 | −1.40587 | −0.702937 | − | 0.711252i | \(-0.748128\pi\) | ||||
−0.702937 | + | 0.711252i | \(0.748128\pi\) | |||||||
\(60\) | −0.0217863 | −0.00281260 | ||||||||
\(61\) | 2.79025 | 0.357255 | 0.178628 | − | 0.983917i | \(-0.442834\pi\) | ||||
0.178628 | + | 0.983917i | \(0.442834\pi\) | |||||||
\(62\) | 9.63154 | 1.22321 | ||||||||
\(63\) | 2.99590 | 0.377448 | ||||||||
\(64\) | 6.21575 | 0.776969 | ||||||||
\(65\) | 2.98935 | 0.370783 | ||||||||
\(66\) | −0.620477 | −0.0763755 | ||||||||
\(67\) | −5.18520 | −0.633473 | −0.316736 | − | 0.948514i | \(-0.602587\pi\) | ||||
−0.316736 | + | 0.948514i | \(0.602587\pi\) | |||||||
\(68\) | −1.31717 | −0.159730 | ||||||||
\(69\) | 0.258260 | 0.0310908 | ||||||||
\(70\) | 1.52977 | 0.182842 | ||||||||
\(71\) | −6.62897 | −0.786714 | −0.393357 | − | 0.919386i | \(-0.628686\pi\) | ||||
−0.393357 | + | 0.919386i | \(0.628686\pi\) | |||||||
\(72\) | 7.60698 | 0.896492 | ||||||||
\(73\) | 8.86780 | 1.03790 | 0.518949 | − | 0.854805i | \(-0.326324\pi\) | ||||
0.518949 | + | 0.854805i | \(0.326324\pi\) | |||||||
\(74\) | −2.22336 | −0.258461 | ||||||||
\(75\) | 0.0640431 | 0.00739506 | ||||||||
\(76\) | 0.0844077 | 0.00968223 | ||||||||
\(77\) | 6.33328 | 0.721744 | ||||||||
\(78\) | −0.292869 | −0.0331609 | ||||||||
\(79\) | 15.8461 | 1.78282 | 0.891411 | − | 0.453197i | \(-0.149716\pi\) | ||||
0.891411 | + | 0.453197i | \(0.149716\pi\) | |||||||
\(80\) | 4.56464 | 0.510342 | ||||||||
\(81\) | 8.96310 | 0.995900 | ||||||||
\(82\) | −10.6277 | −1.17363 | ||||||||
\(83\) | −13.7034 | −1.50414 | −0.752070 | − | 0.659083i | \(-0.770945\pi\) | ||||
−0.752070 | + | 0.659083i | \(0.770945\pi\) | |||||||
\(84\) | −0.0217863 | −0.00237708 | ||||||||
\(85\) | 3.87195 | 0.419972 | ||||||||
\(86\) | 5.68501 | 0.613030 | ||||||||
\(87\) | −0.174612 | −0.0187204 | ||||||||
\(88\) | 16.0810 | 1.71424 | ||||||||
\(89\) | 4.87365 | 0.516606 | 0.258303 | − | 0.966064i | \(-0.416837\pi\) | ||||
0.258303 | + | 0.966064i | \(0.416837\pi\) | |||||||
\(90\) | 4.58302 | 0.483093 | ||||||||
\(91\) | 2.98935 | 0.313369 | ||||||||
\(92\) | 1.37181 | 0.143021 | ||||||||
\(93\) | 0.403221 | 0.0418121 | ||||||||
\(94\) | 0.253113 | 0.0261066 | ||||||||
\(95\) | −0.248126 | −0.0254572 | ||||||||
\(96\) | −0.121974 | −0.0124489 | ||||||||
\(97\) | 2.59750 | 0.263736 | 0.131868 | − | 0.991267i | \(-0.457903\pi\) | ||||
0.131868 | + | 0.991267i | \(0.457903\pi\) | |||||||
\(98\) | 1.52977 | 0.154530 | ||||||||
\(99\) | 18.9739 | 1.90695 | ||||||||
\(100\) | 0.340181 | 0.0340181 | ||||||||
\(101\) | −15.2588 | −1.51831 | −0.759153 | − | 0.650912i | \(-0.774387\pi\) | ||||
−0.759153 | + | 0.650912i | \(0.774387\pi\) | |||||||
\(102\) | −0.379339 | −0.0375601 | ||||||||
\(103\) | −3.84827 | −0.379181 | −0.189591 | − | 0.981863i | \(-0.560716\pi\) | ||||
−0.189591 | + | 0.981863i | \(0.560716\pi\) | |||||||
\(104\) | 7.59035 | 0.744295 | ||||||||
\(105\) | 0.0640431 | 0.00624997 | ||||||||
\(106\) | −5.08221 | −0.493627 | ||||||||
\(107\) | 0.128746 | 0.0124463 | 0.00622317 | − | 0.999981i | \(-0.498019\pi\) | ||||
0.00622317 | + | 0.999981i | \(0.498019\pi\) | |||||||
\(108\) | −0.130628 | −0.0125697 | ||||||||
\(109\) | 4.66644 | 0.446964 | 0.223482 | − | 0.974708i | \(-0.428258\pi\) | ||||
0.223482 | + | 0.974708i | \(0.428258\pi\) | |||||||
\(110\) | 9.68843 | 0.923756 | ||||||||
\(111\) | −0.0930804 | −0.00883480 | ||||||||
\(112\) | 4.56464 | 0.431318 | ||||||||
\(113\) | 1.34578 | 0.126600 | 0.0633002 | − | 0.997995i | \(-0.479837\pi\) | ||||
0.0633002 | + | 0.997995i | \(0.479837\pi\) | |||||||
\(114\) | 0.0243091 | 0.00227676 | ||||||||
\(115\) | −4.03259 | −0.376041 | ||||||||
\(116\) | −0.927495 | −0.0861158 | ||||||||
\(117\) | 8.95578 | 0.827962 | ||||||||
\(118\) | −16.5195 | −1.52074 | ||||||||
\(119\) | 3.87195 | 0.354941 | ||||||||
\(120\) | 0.162614 | 0.0148446 | ||||||||
\(121\) | 29.1105 | 2.64641 | ||||||||
\(122\) | 4.26843 | 0.386446 | ||||||||
\(123\) | −0.444924 | −0.0401174 | ||||||||
\(124\) | 2.14181 | 0.192340 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 4.58302 | 0.408288 | ||||||||
\(127\) | −2.40677 | −0.213566 | −0.106783 | − | 0.994282i | \(-0.534055\pi\) | ||||
−0.106783 | + | 0.994282i | \(0.534055\pi\) | |||||||
\(128\) | 13.3178 | 1.17713 | ||||||||
\(129\) | 0.238001 | 0.0209548 | ||||||||
\(130\) | 4.57300 | 0.401078 | ||||||||
\(131\) | 1.25416 | 0.109576 | 0.0547881 | − | 0.998498i | \(-0.482552\pi\) | ||||
0.0547881 | + | 0.998498i | \(0.482552\pi\) | |||||||
\(132\) | −0.137979 | −0.0120095 | ||||||||
\(133\) | −0.248126 | −0.0215152 | ||||||||
\(134\) | −7.93213 | −0.685232 | ||||||||
\(135\) | 0.383996 | 0.0330491 | ||||||||
\(136\) | 9.83140 | 0.843035 | ||||||||
\(137\) | 0.743203 | 0.0634961 | 0.0317481 | − | 0.999496i | \(-0.489893\pi\) | ||||
0.0317481 | + | 0.999496i | \(0.489893\pi\) | |||||||
\(138\) | 0.395077 | 0.0336311 | ||||||||
\(139\) | 10.7094 | 0.908358 | 0.454179 | − | 0.890910i | \(-0.349933\pi\) | ||||
0.454179 | + | 0.890910i | \(0.349933\pi\) | |||||||
\(140\) | 0.340181 | 0.0287506 | ||||||||
\(141\) | 0.0105965 | 0.000892385 0 | ||||||||
\(142\) | −10.1408 | −0.850994 | ||||||||
\(143\) | 18.9324 | 1.58320 | ||||||||
\(144\) | 13.6752 | 1.13960 | ||||||||
\(145\) | 2.72647 | 0.226421 | ||||||||
\(146\) | 13.5657 | 1.12270 | ||||||||
\(147\) | 0.0640431 | 0.00528219 | ||||||||
\(148\) | −0.494420 | −0.0406411 | ||||||||
\(149\) | −19.5430 | −1.60103 | −0.800513 | − | 0.599315i | \(-0.795440\pi\) | ||||
−0.800513 | + | 0.599315i | \(0.795440\pi\) | |||||||
\(150\) | 0.0979709 | 0.00799929 | ||||||||
\(151\) | 10.4567 | 0.850955 | 0.425478 | − | 0.904969i | \(-0.360106\pi\) | ||||
0.425478 | + | 0.904969i | \(0.360106\pi\) | |||||||
\(152\) | −0.630024 | −0.0511017 | ||||||||
\(153\) | 11.6000 | 0.937802 | ||||||||
\(154\) | 9.68843 | 0.780716 | ||||||||
\(155\) | −6.29609 | −0.505714 | ||||||||
\(156\) | −0.0651267 | −0.00521431 | ||||||||
\(157\) | −2.10666 | −0.168130 | −0.0840648 | − | 0.996460i | \(-0.526790\pi\) | ||||
−0.0840648 | + | 0.996460i | \(0.526790\pi\) | |||||||
\(158\) | 24.2408 | 1.92849 | ||||||||
\(159\) | −0.212765 | −0.0168734 | ||||||||
\(160\) | 1.90456 | 0.150569 | ||||||||
\(161\) | −4.03259 | −0.317813 | ||||||||
\(162\) | 13.7114 | 1.07727 | ||||||||
\(163\) | 3.71513 | 0.290991 | 0.145496 | − | 0.989359i | \(-0.453522\pi\) | ||||
0.145496 | + | 0.989359i | \(0.453522\pi\) | |||||||
\(164\) | −2.36333 | −0.184545 | ||||||||
\(165\) | 0.405603 | 0.0315762 | ||||||||
\(166\) | −20.9629 | −1.62704 | ||||||||
\(167\) | 17.5534 | 1.35832 | 0.679162 | − | 0.733988i | \(-0.262343\pi\) | ||||
0.679162 | + | 0.733988i | \(0.262343\pi\) | |||||||
\(168\) | 0.162614 | 0.0125459 | ||||||||
\(169\) | −4.06381 | −0.312601 | ||||||||
\(170\) | 5.92318 | 0.454287 | ||||||||
\(171\) | −0.743359 | −0.0568461 | ||||||||
\(172\) | 1.26420 | 0.0963946 | ||||||||
\(173\) | −18.7357 | −1.42445 | −0.712226 | − | 0.701950i | \(-0.752313\pi\) | ||||
−0.712226 | + | 0.701950i | \(0.752313\pi\) | |||||||
\(174\) | −0.267115 | −0.0202499 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 28.9091 | 2.17911 | ||||||||
\(177\) | −0.691584 | −0.0519826 | ||||||||
\(178\) | 7.45554 | 0.558816 | ||||||||
\(179\) | −25.0619 | −1.87321 | −0.936606 | − | 0.350384i | \(-0.886051\pi\) | ||||
−0.936606 | + | 0.350384i | \(0.886051\pi\) | |||||||
\(180\) | 1.01915 | 0.0759629 | ||||||||
\(181\) | −6.58458 | −0.489428 | −0.244714 | − | 0.969595i | \(-0.578694\pi\) | ||||
−0.244714 | + | 0.969595i | \(0.578694\pi\) | |||||||
\(182\) | 4.57300 | 0.338973 | ||||||||
\(183\) | 0.178697 | 0.0132096 | ||||||||
\(184\) | −10.2393 | −0.754850 | ||||||||
\(185\) | 1.45340 | 0.106856 | ||||||||
\(186\) | 0.616834 | 0.0452284 | ||||||||
\(187\) | 24.5222 | 1.79324 | ||||||||
\(188\) | 0.0562860 | 0.00410508 | ||||||||
\(189\) | 0.383996 | 0.0279316 | ||||||||
\(190\) | −0.379574 | −0.0275372 | ||||||||
\(191\) | 25.9927 | 1.88077 | 0.940383 | − | 0.340117i | \(-0.110467\pi\) | ||||
0.940383 | + | 0.340117i | \(0.110467\pi\) | |||||||
\(192\) | 0.398076 | 0.0287287 | ||||||||
\(193\) | −11.0098 | −0.792502 | −0.396251 | − | 0.918142i | \(-0.629689\pi\) | ||||
−0.396251 | + | 0.918142i | \(0.629689\pi\) | |||||||
\(194\) | 3.97356 | 0.285285 | ||||||||
\(195\) | 0.191447 | 0.0137098 | ||||||||
\(196\) | 0.340181 | 0.0242987 | ||||||||
\(197\) | 21.1177 | 1.50458 | 0.752288 | − | 0.658835i | \(-0.228950\pi\) | ||||
0.752288 | + | 0.658835i | \(0.228950\pi\) | |||||||
\(198\) | 29.0256 | 2.06276 | ||||||||
\(199\) | −0.983055 | −0.0696869 | −0.0348434 | − | 0.999393i | \(-0.511093\pi\) | ||||
−0.0348434 | + | 0.999393i | \(0.511093\pi\) | |||||||
\(200\) | −2.53913 | −0.179544 | ||||||||
\(201\) | −0.332076 | −0.0234228 | ||||||||
\(202\) | −23.3424 | −1.64236 | ||||||||
\(203\) | 2.72647 | 0.191361 | ||||||||
\(204\) | −0.0843554 | −0.00590606 | ||||||||
\(205\) | 6.94726 | 0.485217 | ||||||||
\(206\) | −5.88695 | −0.410163 | ||||||||
\(207\) | −12.0812 | −0.839704 | ||||||||
\(208\) | 13.6453 | 0.946130 | ||||||||
\(209\) | −1.57145 | −0.108699 | ||||||||
\(210\) | 0.0979709 | 0.00676064 | ||||||||
\(211\) | −13.7715 | −0.948068 | −0.474034 | − | 0.880507i | \(-0.657203\pi\) | ||||
−0.474034 | + | 0.880507i | \(0.657203\pi\) | |||||||
\(212\) | −1.13015 | −0.0776194 | ||||||||
\(213\) | −0.424540 | −0.0290890 | ||||||||
\(214\) | 0.196951 | 0.0134633 | ||||||||
\(215\) | −3.71626 | −0.253447 | ||||||||
\(216\) | 0.975017 | 0.0663415 | ||||||||
\(217\) | −6.29609 | −0.427406 | ||||||||
\(218\) | 7.13856 | 0.483485 | ||||||||
\(219\) | 0.567922 | 0.0383766 | ||||||||
\(220\) | 2.15446 | 0.145254 | ||||||||
\(221\) | 11.5746 | 0.778592 | ||||||||
\(222\) | −0.142391 | −0.00955667 | ||||||||
\(223\) | −15.1545 | −1.01482 | −0.507411 | − | 0.861704i | \(-0.669397\pi\) | ||||
−0.507411 | + | 0.861704i | \(0.669397\pi\) | |||||||
\(224\) | 1.90456 | 0.127254 | ||||||||
\(225\) | −2.99590 | −0.199727 | ||||||||
\(226\) | 2.05873 | 0.136945 | ||||||||
\(227\) | 11.8269 | 0.784978 | 0.392489 | − | 0.919757i | \(-0.371614\pi\) | ||||
0.392489 | + | 0.919757i | \(0.371614\pi\) | |||||||
\(228\) | 0.00540573 | 0.000358004 0 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | −6.16892 | −0.406766 | ||||||||
\(231\) | 0.405603 | 0.0266867 | ||||||||
\(232\) | 6.92288 | 0.454509 | ||||||||
\(233\) | −26.1105 | −1.71055 | −0.855277 | − | 0.518170i | \(-0.826613\pi\) | ||||
−0.855277 | + | 0.518170i | \(0.826613\pi\) | |||||||
\(234\) | 13.7002 | 0.895612 | ||||||||
\(235\) | −0.165459 | −0.0107933 | ||||||||
\(236\) | −3.67352 | −0.239126 | ||||||||
\(237\) | 1.01483 | 0.0659204 | ||||||||
\(238\) | 5.92318 | 0.383942 | ||||||||
\(239\) | −8.58088 | −0.555051 | −0.277526 | − | 0.960718i | \(-0.589514\pi\) | ||||
−0.277526 | + | 0.960718i | \(0.589514\pi\) | |||||||
\(240\) | 0.292334 | 0.0188701 | ||||||||
\(241\) | 7.57526 | 0.487966 | 0.243983 | − | 0.969780i | \(-0.421546\pi\) | ||||
0.243983 | + | 0.969780i | \(0.421546\pi\) | |||||||
\(242\) | 44.5322 | 2.86264 | ||||||||
\(243\) | 1.72601 | 0.110724 | ||||||||
\(244\) | 0.949192 | 0.0607658 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −0.680629 | −0.0433953 | ||||||||
\(247\) | −0.741734 | −0.0471954 | ||||||||
\(248\) | −15.9866 | −1.01515 | ||||||||
\(249\) | −0.877607 | −0.0556161 | ||||||||
\(250\) | −1.52977 | −0.0967508 | ||||||||
\(251\) | 0.889480 | 0.0561435 | 0.0280717 | − | 0.999606i | \(-0.491063\pi\) | ||||
0.0280717 | + | 0.999606i | \(0.491063\pi\) | |||||||
\(252\) | 1.01915 | 0.0642003 | ||||||||
\(253\) | −25.5395 | −1.60566 | ||||||||
\(254\) | −3.68179 | −0.231016 | ||||||||
\(255\) | 0.247972 | 0.0155286 | ||||||||
\(256\) | 7.94154 | 0.496346 | ||||||||
\(257\) | −8.95767 | −0.558764 | −0.279382 | − | 0.960180i | \(-0.590130\pi\) | ||||
−0.279382 | + | 0.960180i | \(0.590130\pi\) | |||||||
\(258\) | 0.364086 | 0.0226670 | ||||||||
\(259\) | 1.45340 | 0.0903100 | ||||||||
\(260\) | 1.01692 | 0.0630667 | ||||||||
\(261\) | 8.16824 | 0.505601 | ||||||||
\(262\) | 1.91856 | 0.118529 | ||||||||
\(263\) | −9.02758 | −0.556664 | −0.278332 | − | 0.960485i | \(-0.589782\pi\) | ||||
−0.278332 | + | 0.960485i | \(0.589782\pi\) | |||||||
\(264\) | 1.02988 | 0.0633847 | ||||||||
\(265\) | 3.32221 | 0.204082 | ||||||||
\(266\) | −0.379574 | −0.0232732 | ||||||||
\(267\) | 0.312124 | 0.0191017 | ||||||||
\(268\) | −1.76391 | −0.107748 | ||||||||
\(269\) | −3.20915 | −0.195665 | −0.0978325 | − | 0.995203i | \(-0.531191\pi\) | ||||
−0.0978325 | + | 0.995203i | \(0.531191\pi\) | |||||||
\(270\) | 0.587424 | 0.0357495 | ||||||||
\(271\) | 15.0040 | 0.911431 | 0.455715 | − | 0.890126i | \(-0.349384\pi\) | ||||
0.455715 | + | 0.890126i | \(0.349384\pi\) | |||||||
\(272\) | 17.6741 | 1.07165 | ||||||||
\(273\) | 0.191447 | 0.0115869 | ||||||||
\(274\) | 1.13693 | 0.0686842 | ||||||||
\(275\) | −6.33328 | −0.381911 | ||||||||
\(276\) | 0.0878551 | 0.00528826 | ||||||||
\(277\) | 2.50666 | 0.150611 | 0.0753053 | − | 0.997161i | \(-0.476007\pi\) | ||||
0.0753053 | + | 0.997161i | \(0.476007\pi\) | |||||||
\(278\) | 16.3828 | 0.982577 | ||||||||
\(279\) | −18.8624 | −1.12926 | ||||||||
\(280\) | −2.53913 | −0.151742 | ||||||||
\(281\) | −8.57990 | −0.511834 | −0.255917 | − | 0.966699i | \(-0.582377\pi\) | ||||
−0.255917 | + | 0.966699i | \(0.582377\pi\) | |||||||
\(282\) | 0.0162101 | 0.000965300 0 | ||||||||
\(283\) | 25.9387 | 1.54190 | 0.770949 | − | 0.636897i | \(-0.219782\pi\) | ||||
0.770949 | + | 0.636897i | \(0.219782\pi\) | |||||||
\(284\) | −2.25505 | −0.133813 | ||||||||
\(285\) | −0.0158907 | −0.000941286 0 | ||||||||
\(286\) | 28.9621 | 1.71256 | ||||||||
\(287\) | 6.94726 | 0.410084 | ||||||||
\(288\) | 5.70587 | 0.336222 | ||||||||
\(289\) | −2.00799 | −0.118117 | ||||||||
\(290\) | 4.17086 | 0.244922 | ||||||||
\(291\) | 0.166352 | 0.00975172 | ||||||||
\(292\) | 3.01666 | 0.176537 | ||||||||
\(293\) | 0.0470215 | 0.00274702 | 0.00137351 | − | 0.999999i | \(-0.499563\pi\) | ||||
0.00137351 | + | 0.999999i | \(0.499563\pi\) | |||||||
\(294\) | 0.0979709 | 0.00571378 | ||||||||
\(295\) | 10.7987 | 0.628726 | ||||||||
\(296\) | 3.69038 | 0.214499 | ||||||||
\(297\) | 2.43196 | 0.141116 | ||||||||
\(298\) | −29.8962 | −1.73184 | ||||||||
\(299\) | −12.0548 | −0.697147 | ||||||||
\(300\) | 0.0217863 | 0.00125783 | ||||||||
\(301\) | −3.71626 | −0.214202 | ||||||||
\(302\) | 15.9963 | 0.920484 | ||||||||
\(303\) | −0.977220 | −0.0561398 | ||||||||
\(304\) | −1.13260 | −0.0649593 | ||||||||
\(305\) | −2.79025 | −0.159769 | ||||||||
\(306\) | 17.7452 | 1.01443 | ||||||||
\(307\) | −28.3458 | −1.61778 | −0.808891 | − | 0.587958i | \(-0.799932\pi\) | ||||
−0.808891 | + | 0.587958i | \(0.799932\pi\) | |||||||
\(308\) | 2.15446 | 0.122762 | ||||||||
\(309\) | −0.246455 | −0.0140203 | ||||||||
\(310\) | −9.63154 | −0.547034 | ||||||||
\(311\) | 29.4770 | 1.67149 | 0.835743 | − | 0.549120i | \(-0.185037\pi\) | ||||
0.835743 | + | 0.549120i | \(0.185037\pi\) | |||||||
\(312\) | 0.486109 | 0.0275205 | ||||||||
\(313\) | −19.3373 | −1.09301 | −0.546503 | − | 0.837457i | \(-0.684041\pi\) | ||||
−0.546503 | + | 0.837457i | \(0.684041\pi\) | |||||||
\(314\) | −3.22269 | −0.181867 | ||||||||
\(315\) | −2.99590 | −0.168800 | ||||||||
\(316\) | 5.39053 | 0.303241 | ||||||||
\(317\) | −14.1393 | −0.794141 | −0.397071 | − | 0.917788i | \(-0.629973\pi\) | ||||
−0.397071 | + | 0.917788i | \(0.629973\pi\) | |||||||
\(318\) | −0.325480 | −0.0182520 | ||||||||
\(319\) | 17.2675 | 0.966796 | ||||||||
\(320\) | −6.21575 | −0.347471 | ||||||||
\(321\) | 0.00824529 | 0.000460207 0 | ||||||||
\(322\) | −6.16892 | −0.343780 | ||||||||
\(323\) | −0.960731 | −0.0534565 | ||||||||
\(324\) | 3.04908 | 0.169393 | ||||||||
\(325\) | −2.98935 | −0.165819 | ||||||||
\(326\) | 5.68328 | 0.314768 | ||||||||
\(327\) | 0.298854 | 0.0165266 | ||||||||
\(328\) | 17.6400 | 0.974006 | ||||||||
\(329\) | −0.165459 | −0.00912203 | ||||||||
\(330\) | 0.620477 | 0.0341562 | ||||||||
\(331\) | 5.63435 | 0.309692 | 0.154846 | − | 0.987939i | \(-0.450512\pi\) | ||||
0.154846 | + | 0.987939i | \(0.450512\pi\) | |||||||
\(332\) | −4.66163 | −0.255840 | ||||||||
\(333\) | 4.35424 | 0.238611 | ||||||||
\(334\) | 26.8526 | 1.46931 | ||||||||
\(335\) | 5.18520 | 0.283298 | ||||||||
\(336\) | 0.292334 | 0.0159481 | ||||||||
\(337\) | 8.30947 | 0.452646 | 0.226323 | − | 0.974052i | \(-0.427330\pi\) | ||||
0.226323 | + | 0.974052i | \(0.427330\pi\) | |||||||
\(338\) | −6.21667 | −0.338143 | ||||||||
\(339\) | 0.0861880 | 0.00468109 | ||||||||
\(340\) | 1.31717 | 0.0714333 | ||||||||
\(341\) | −39.8749 | −2.15935 | ||||||||
\(342\) | −1.13717 | −0.0614909 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −9.43608 | −0.508759 | ||||||||
\(345\) | −0.258260 | −0.0139042 | ||||||||
\(346\) | −28.6613 | −1.54084 | ||||||||
\(347\) | −3.02638 | −0.162464 | −0.0812322 | − | 0.996695i | \(-0.525886\pi\) | ||||
−0.0812322 | + | 0.996695i | \(0.525886\pi\) | |||||||
\(348\) | −0.0593997 | −0.00318416 | ||||||||
\(349\) | 0.603670 | 0.0323137 | 0.0161569 | − | 0.999869i | \(-0.494857\pi\) | ||||
0.0161569 | + | 0.999869i | \(0.494857\pi\) | |||||||
\(350\) | −1.52977 | −0.0817694 | ||||||||
\(351\) | 1.14790 | 0.0612702 | ||||||||
\(352\) | 12.0621 | 0.642913 | ||||||||
\(353\) | 0.153802 | 0.00818607 | 0.00409304 | − | 0.999992i | \(-0.498697\pi\) | ||||
0.00409304 | + | 0.999992i | \(0.498697\pi\) | |||||||
\(354\) | −1.05796 | −0.0562300 | ||||||||
\(355\) | 6.62897 | 0.351829 | ||||||||
\(356\) | 1.65792 | 0.0878698 | ||||||||
\(357\) | 0.247972 | 0.0131241 | ||||||||
\(358\) | −38.3388 | −2.02627 | ||||||||
\(359\) | 8.18487 | 0.431981 | 0.215990 | − | 0.976395i | \(-0.430702\pi\) | ||||
0.215990 | + | 0.976395i | \(0.430702\pi\) | |||||||
\(360\) | −7.60698 | −0.400923 | ||||||||
\(361\) | −18.9384 | −0.996760 | ||||||||
\(362\) | −10.0729 | −0.529418 | ||||||||
\(363\) | 1.86432 | 0.0978517 | ||||||||
\(364\) | 1.01692 | 0.0533011 | ||||||||
\(365\) | −8.86780 | −0.464162 | ||||||||
\(366\) | 0.273364 | 0.0142890 | ||||||||
\(367\) | 15.1388 | 0.790240 | 0.395120 | − | 0.918629i | \(-0.370703\pi\) | ||||
0.395120 | + | 0.918629i | \(0.370703\pi\) | |||||||
\(368\) | −18.4073 | −0.959548 | ||||||||
\(369\) | 20.8133 | 1.08350 | ||||||||
\(370\) | 2.22336 | 0.115587 | ||||||||
\(371\) | 3.32221 | 0.172481 | ||||||||
\(372\) | 0.137168 | 0.00711184 | ||||||||
\(373\) | −32.6744 | −1.69182 | −0.845909 | − | 0.533327i | \(-0.820941\pi\) | ||||
−0.845909 | + | 0.533327i | \(0.820941\pi\) | |||||||
\(374\) | 37.5131 | 1.93976 | ||||||||
\(375\) | −0.0640431 | −0.00330717 | ||||||||
\(376\) | −0.420122 | −0.0216661 | ||||||||
\(377\) | 8.15037 | 0.419766 | ||||||||
\(378\) | 0.587424 | 0.0302138 | ||||||||
\(379\) | −11.1445 | −0.572455 | −0.286228 | − | 0.958162i | \(-0.592401\pi\) | ||||
−0.286228 | + | 0.958162i | \(0.592401\pi\) | |||||||
\(380\) | −0.0844077 | −0.00433003 | ||||||||
\(381\) | −0.154137 | −0.00789667 | ||||||||
\(382\) | 39.7627 | 2.03444 | ||||||||
\(383\) | 1.36490 | 0.0697431 | 0.0348715 | − | 0.999392i | \(-0.488898\pi\) | ||||
0.0348715 | + | 0.999392i | \(0.488898\pi\) | |||||||
\(384\) | 0.852911 | 0.0435249 | ||||||||
\(385\) | −6.33328 | −0.322774 | ||||||||
\(386\) | −16.8424 | −0.857255 | ||||||||
\(387\) | −11.1335 | −0.565950 | ||||||||
\(388\) | 0.883620 | 0.0448590 | ||||||||
\(389\) | 16.8374 | 0.853688 | 0.426844 | − | 0.904325i | \(-0.359625\pi\) | ||||
0.426844 | + | 0.904325i | \(0.359625\pi\) | |||||||
\(390\) | 0.292869 | 0.0148300 | ||||||||
\(391\) | −15.6140 | −0.789633 | ||||||||
\(392\) | −2.53913 | −0.128246 | ||||||||
\(393\) | 0.0803201 | 0.00405161 | ||||||||
\(394\) | 32.3052 | 1.62751 | ||||||||
\(395\) | −15.8461 | −0.797302 | ||||||||
\(396\) | 6.45456 | 0.324354 | ||||||||
\(397\) | −0.437439 | −0.0219544 | −0.0109772 | − | 0.999940i | \(-0.503494\pi\) | ||||
−0.0109772 | + | 0.999940i | \(0.503494\pi\) | |||||||
\(398\) | −1.50384 | −0.0753808 | ||||||||
\(399\) | −0.0158907 | −0.000795532 0 | ||||||||
\(400\) | −4.56464 | −0.228232 | ||||||||
\(401\) | 5.85288 | 0.292279 | 0.146139 | − | 0.989264i | \(-0.453315\pi\) | ||||
0.146139 | + | 0.989264i | \(0.453315\pi\) | |||||||
\(402\) | −0.507999 | −0.0253367 | ||||||||
\(403\) | −18.8212 | −0.937550 | ||||||||
\(404\) | −5.19075 | −0.258250 | ||||||||
\(405\) | −8.96310 | −0.445380 | ||||||||
\(406\) | 4.17086 | 0.206997 | ||||||||
\(407\) | 9.20480 | 0.456265 | ||||||||
\(408\) | 0.629633 | 0.0311715 | ||||||||
\(409\) | 22.6847 | 1.12169 | 0.560844 | − | 0.827922i | \(-0.310477\pi\) | ||||
0.560844 | + | 0.827922i | \(0.310477\pi\) | |||||||
\(410\) | 10.6277 | 0.524863 | ||||||||
\(411\) | 0.0475971 | 0.00234779 | ||||||||
\(412\) | −1.30911 | −0.0644952 | ||||||||
\(413\) | 10.7987 | 0.531370 | ||||||||
\(414\) | −18.4814 | −0.908313 | ||||||||
\(415\) | 13.7034 | 0.672672 | ||||||||
\(416\) | 5.69339 | 0.279141 | ||||||||
\(417\) | 0.685862 | 0.0335868 | ||||||||
\(418\) | −2.40395 | −0.117581 | ||||||||
\(419\) | −3.34462 | −0.163395 | −0.0816976 | − | 0.996657i | \(-0.526034\pi\) | ||||
−0.0816976 | + | 0.996657i | \(0.526034\pi\) | |||||||
\(420\) | 0.0217863 | 0.00106306 | ||||||||
\(421\) | −21.3930 | −1.04263 | −0.521315 | − | 0.853364i | \(-0.674558\pi\) | ||||
−0.521315 | + | 0.853364i | \(0.674558\pi\) | |||||||
\(422\) | −21.0671 | −1.02553 | ||||||||
\(423\) | −0.495697 | −0.0241016 | ||||||||
\(424\) | 8.43554 | 0.409666 | ||||||||
\(425\) | −3.87195 | −0.187817 | ||||||||
\(426\) | −0.649446 | −0.0314658 | ||||||||
\(427\) | −2.79025 | −0.135030 | ||||||||
\(428\) | 0.0437969 | 0.00211700 | ||||||||
\(429\) | 1.21249 | 0.0585395 | ||||||||
\(430\) | −5.68501 | −0.274155 | ||||||||
\(431\) | 8.21306 | 0.395609 | 0.197805 | − | 0.980241i | \(-0.436619\pi\) | ||||
0.197805 | + | 0.980241i | \(0.436619\pi\) | |||||||
\(432\) | 1.75280 | 0.0843318 | ||||||||
\(433\) | 14.5906 | 0.701181 | 0.350591 | − | 0.936529i | \(-0.385981\pi\) | ||||
0.350591 | + | 0.936529i | \(0.385981\pi\) | |||||||
\(434\) | −9.63154 | −0.462328 | ||||||||
\(435\) | 0.174612 | 0.00837200 | ||||||||
\(436\) | 1.58744 | 0.0760245 | ||||||||
\(437\) | 1.00059 | 0.0478647 | ||||||||
\(438\) | 0.868787 | 0.0415122 | ||||||||
\(439\) | −2.38669 | −0.113910 | −0.0569552 | − | 0.998377i | \(-0.518139\pi\) | ||||
−0.0569552 | + | 0.998377i | \(0.518139\pi\) | |||||||
\(440\) | −16.0810 | −0.766634 | ||||||||
\(441\) | −2.99590 | −0.142662 | ||||||||
\(442\) | 17.7064 | 0.842209 | ||||||||
\(443\) | −25.8584 | −1.22857 | −0.614284 | − | 0.789085i | \(-0.710555\pi\) | ||||
−0.614284 | + | 0.789085i | \(0.710555\pi\) | |||||||
\(444\) | −0.0316642 | −0.00150272 | ||||||||
\(445\) | −4.87365 | −0.231033 | ||||||||
\(446\) | −23.1829 | −1.09774 | ||||||||
\(447\) | −1.25160 | −0.0591984 | ||||||||
\(448\) | −6.21575 | −0.293666 | ||||||||
\(449\) | 10.9602 | 0.517246 | 0.258623 | − | 0.965978i | \(-0.416731\pi\) | ||||
0.258623 | + | 0.965978i | \(0.416731\pi\) | |||||||
\(450\) | −4.58302 | −0.216046 | ||||||||
\(451\) | 43.9989 | 2.07183 | ||||||||
\(452\) | 0.457810 | 0.0215336 | ||||||||
\(453\) | 0.669680 | 0.0314643 | ||||||||
\(454\) | 18.0924 | 0.849116 | ||||||||
\(455\) | −2.98935 | −0.140143 | ||||||||
\(456\) | −0.0403487 | −0.00188950 | ||||||||
\(457\) | 3.61489 | 0.169097 | 0.0845487 | − | 0.996419i | \(-0.473055\pi\) | ||||
0.0845487 | + | 0.996419i | \(0.473055\pi\) | |||||||
\(458\) | 1.52977 | 0.0714812 | ||||||||
\(459\) | 1.48681 | 0.0693985 | ||||||||
\(460\) | −1.37181 | −0.0639611 | ||||||||
\(461\) | 32.1627 | 1.49797 | 0.748984 | − | 0.662588i | \(-0.230542\pi\) | ||||
0.748984 | + | 0.662588i | \(0.230542\pi\) | |||||||
\(462\) | 0.620477 | 0.0288672 | ||||||||
\(463\) | 14.6125 | 0.679103 | 0.339551 | − | 0.940588i | \(-0.389725\pi\) | ||||
0.339551 | + | 0.940588i | \(0.389725\pi\) | |||||||
\(464\) | 12.4454 | 0.577762 | ||||||||
\(465\) | −0.403221 | −0.0186989 | ||||||||
\(466\) | −39.9429 | −1.85032 | ||||||||
\(467\) | 15.1468 | 0.700912 | 0.350456 | − | 0.936579i | \(-0.386027\pi\) | ||||
0.350456 | + | 0.936579i | \(0.386027\pi\) | |||||||
\(468\) | 3.04659 | 0.140829 | ||||||||
\(469\) | 5.18520 | 0.239430 | ||||||||
\(470\) | −0.253113 | −0.0116752 | ||||||||
\(471\) | −0.134917 | −0.00621665 | ||||||||
\(472\) | 27.4194 | 1.26208 | ||||||||
\(473\) | −23.5361 | −1.08219 | ||||||||
\(474\) | 1.55245 | 0.0713065 | ||||||||
\(475\) | 0.248126 | 0.0113848 | ||||||||
\(476\) | 1.31717 | 0.0603722 | ||||||||
\(477\) | 9.95301 | 0.455717 | ||||||||
\(478\) | −13.1267 | −0.600403 | ||||||||
\(479\) | −6.58694 | −0.300965 | −0.150482 | − | 0.988613i | \(-0.548083\pi\) | ||||
−0.150482 | + | 0.988613i | \(0.548083\pi\) | |||||||
\(480\) | 0.121974 | 0.00556733 | ||||||||
\(481\) | 4.34472 | 0.198102 | ||||||||
\(482\) | 11.5884 | 0.527836 | ||||||||
\(483\) | −0.258260 | −0.0117512 | ||||||||
\(484\) | 9.90284 | 0.450129 | ||||||||
\(485\) | −2.59750 | −0.117946 | ||||||||
\(486\) | 2.64039 | 0.119771 | ||||||||
\(487\) | 30.5299 | 1.38344 | 0.691722 | − | 0.722164i | \(-0.256852\pi\) | ||||
0.691722 | + | 0.722164i | \(0.256852\pi\) | |||||||
\(488\) | −7.08483 | −0.320715 | ||||||||
\(489\) | 0.237929 | 0.0107595 | ||||||||
\(490\) | −1.52977 | −0.0691077 | ||||||||
\(491\) | −10.8096 | −0.487829 | −0.243914 | − | 0.969797i | \(-0.578432\pi\) | ||||
−0.243914 | + | 0.969797i | \(0.578432\pi\) | |||||||
\(492\) | −0.151355 | −0.00682360 | ||||||||
\(493\) | 10.5568 | 0.475453 | ||||||||
\(494\) | −1.13468 | −0.0510516 | ||||||||
\(495\) | −18.9739 | −0.852812 | ||||||||
\(496\) | −28.7394 | −1.29044 | ||||||||
\(497\) | 6.62897 | 0.297350 | ||||||||
\(498\) | −1.34253 | −0.0601603 | ||||||||
\(499\) | −12.3086 | −0.551006 | −0.275503 | − | 0.961300i | \(-0.588844\pi\) | ||||
−0.275503 | + | 0.961300i | \(0.588844\pi\) | |||||||
\(500\) | −0.340181 | −0.0152134 | ||||||||
\(501\) | 1.12418 | 0.0502245 | ||||||||
\(502\) | 1.36069 | 0.0607308 | ||||||||
\(503\) | 28.5889 | 1.27471 | 0.637357 | − | 0.770568i | \(-0.280028\pi\) | ||||
0.637357 | + | 0.770568i | \(0.280028\pi\) | |||||||
\(504\) | −7.60698 | −0.338842 | ||||||||
\(505\) | 15.2588 | 0.679007 | ||||||||
\(506\) | −39.0695 | −1.73685 | ||||||||
\(507\) | −0.260259 | −0.0115585 | ||||||||
\(508\) | −0.818737 | −0.0363256 | ||||||||
\(509\) | −28.0096 | −1.24150 | −0.620752 | − | 0.784007i | \(-0.713173\pi\) | ||||
−0.620752 | + | 0.784007i | \(0.713173\pi\) | |||||||
\(510\) | 0.379339 | 0.0167974 | ||||||||
\(511\) | −8.86780 | −0.392288 | ||||||||
\(512\) | −14.4868 | −0.640233 | ||||||||
\(513\) | −0.0952793 | −0.00420668 | ||||||||
\(514\) | −13.7031 | −0.604419 | ||||||||
\(515\) | 3.84827 | 0.169575 | ||||||||
\(516\) | 0.0809635 | 0.00356422 | ||||||||
\(517\) | −1.04790 | −0.0460864 | ||||||||
\(518\) | 2.22336 | 0.0976890 | ||||||||
\(519\) | −1.19990 | −0.0526696 | ||||||||
\(520\) | −7.59035 | −0.332859 | ||||||||
\(521\) | 0.868896 | 0.0380670 | 0.0190335 | − | 0.999819i | \(-0.493941\pi\) | ||||
0.0190335 | + | 0.999819i | \(0.493941\pi\) | |||||||
\(522\) | 12.4955 | 0.546913 | ||||||||
\(523\) | −5.82730 | −0.254810 | −0.127405 | − | 0.991851i | \(-0.540665\pi\) | ||||
−0.127405 | + | 0.991851i | \(0.540665\pi\) | |||||||
\(524\) | 0.426641 | 0.0186379 | ||||||||
\(525\) | −0.0640431 | −0.00279507 | ||||||||
\(526\) | −13.8101 | −0.602148 | ||||||||
\(527\) | −24.3781 | −1.06193 | ||||||||
\(528\) | 1.85143 | 0.0805732 | ||||||||
\(529\) | −6.73822 | −0.292966 | ||||||||
\(530\) | 5.08221 | 0.220757 | ||||||||
\(531\) | 32.3519 | 1.40395 | ||||||||
\(532\) | −0.0844077 | −0.00365954 | ||||||||
\(533\) | 20.7678 | 0.899551 | ||||||||
\(534\) | 0.477476 | 0.0206624 | ||||||||
\(535\) | −0.128746 | −0.00556617 | ||||||||
\(536\) | 13.1659 | 0.568680 | ||||||||
\(537\) | −1.60504 | −0.0692626 | ||||||||
\(538\) | −4.90924 | −0.211652 | ||||||||
\(539\) | −6.33328 | −0.272794 | ||||||||
\(540\) | 0.130628 | 0.00562135 | ||||||||
\(541\) | 25.1358 | 1.08067 | 0.540336 | − | 0.841449i | \(-0.318297\pi\) | ||||
0.540336 | + | 0.841449i | \(0.318297\pi\) | |||||||
\(542\) | 22.9527 | 0.985901 | ||||||||
\(543\) | −0.421697 | −0.0180967 | ||||||||
\(544\) | 7.37437 | 0.316173 | ||||||||
\(545\) | −4.66644 | −0.199889 | ||||||||
\(546\) | 0.292869 | 0.0125336 | ||||||||
\(547\) | 18.6768 | 0.798560 | 0.399280 | − | 0.916829i | \(-0.369260\pi\) | ||||
0.399280 | + | 0.916829i | \(0.369260\pi\) | |||||||
\(548\) | 0.252824 | 0.0108001 | ||||||||
\(549\) | −8.35932 | −0.356767 | ||||||||
\(550\) | −9.68843 | −0.413116 | ||||||||
\(551\) | −0.676508 | −0.0288202 | ||||||||
\(552\) | −0.655755 | −0.0279108 | ||||||||
\(553\) | −15.8461 | −0.673843 | ||||||||
\(554\) | 3.83460 | 0.162917 | ||||||||
\(555\) | 0.0930804 | 0.00395104 | ||||||||
\(556\) | 3.64313 | 0.154503 | ||||||||
\(557\) | 28.3835 | 1.20265 | 0.601325 | − | 0.799005i | \(-0.294640\pi\) | ||||
0.601325 | + | 0.799005i | \(0.294640\pi\) | |||||||
\(558\) | −28.8551 | −1.22153 | ||||||||
\(559\) | −11.1092 | −0.469869 | ||||||||
\(560\) | −4.56464 | −0.192891 | ||||||||
\(561\) | 1.57048 | 0.0663055 | ||||||||
\(562\) | −13.1252 | −0.553654 | ||||||||
\(563\) | −4.23600 | −0.178526 | −0.0892630 | − | 0.996008i | \(-0.528451\pi\) | ||||
−0.0892630 | + | 0.996008i | \(0.528451\pi\) | |||||||
\(564\) | 0.00360473 | 0.000151786 0 | ||||||||
\(565\) | −1.34578 | −0.0566174 | ||||||||
\(566\) | 39.6802 | 1.66788 | ||||||||
\(567\) | −8.96310 | −0.376415 | ||||||||
\(568\) | 16.8318 | 0.706248 | ||||||||
\(569\) | 8.53818 | 0.357939 | 0.178970 | − | 0.983855i | \(-0.442724\pi\) | ||||
0.178970 | + | 0.983855i | \(0.442724\pi\) | |||||||
\(570\) | −0.0243091 | −0.00101820 | ||||||||
\(571\) | −3.36599 | −0.140862 | −0.0704311 | − | 0.997517i | \(-0.522437\pi\) | ||||
−0.0704311 | + | 0.997517i | \(0.522437\pi\) | |||||||
\(572\) | 6.44044 | 0.269288 | ||||||||
\(573\) | 1.66465 | 0.0695419 | ||||||||
\(574\) | 10.6277 | 0.443590 | ||||||||
\(575\) | 4.03259 | 0.168171 | ||||||||
\(576\) | −18.6218 | −0.775906 | ||||||||
\(577\) | −25.2986 | −1.05320 | −0.526598 | − | 0.850114i | \(-0.676533\pi\) | ||||
−0.526598 | + | 0.850114i | \(0.676533\pi\) | |||||||
\(578\) | −3.07176 | −0.127768 | ||||||||
\(579\) | −0.705101 | −0.0293030 | ||||||||
\(580\) | 0.927495 | 0.0385122 | ||||||||
\(581\) | 13.7034 | 0.568512 | ||||||||
\(582\) | 0.254479 | 0.0105485 | ||||||||
\(583\) | 21.0405 | 0.871409 | ||||||||
\(584\) | −22.5165 | −0.931740 | ||||||||
\(585\) | −8.95578 | −0.370276 | ||||||||
\(586\) | 0.0719318 | 0.00297147 | ||||||||
\(587\) | −28.4316 | −1.17350 | −0.586749 | − | 0.809769i | \(-0.699593\pi\) | ||||
−0.586749 | + | 0.809769i | \(0.699593\pi\) | |||||||
\(588\) | 0.0217863 | 0.000898451 0 | ||||||||
\(589\) | 1.56222 | 0.0643702 | ||||||||
\(590\) | 16.5195 | 0.680097 | ||||||||
\(591\) | 1.35244 | 0.0556321 | ||||||||
\(592\) | 6.63426 | 0.272666 | ||||||||
\(593\) | −8.04631 | −0.330422 | −0.165211 | − | 0.986258i | \(-0.552831\pi\) | ||||
−0.165211 | + | 0.986258i | \(0.552831\pi\) | |||||||
\(594\) | 3.72032 | 0.152647 | ||||||||
\(595\) | −3.87195 | −0.158735 | ||||||||
\(596\) | −6.64817 | −0.272320 | ||||||||
\(597\) | −0.0629579 | −0.00257669 | ||||||||
\(598\) | −18.4410 | −0.754110 | ||||||||
\(599\) | 33.0646 | 1.35098 | 0.675492 | − | 0.737367i | \(-0.263931\pi\) | ||||
0.675492 | + | 0.737367i | \(0.263931\pi\) | |||||||
\(600\) | −0.162614 | −0.00663869 | ||||||||
\(601\) | −8.12871 | −0.331577 | −0.165788 | − | 0.986161i | \(-0.553017\pi\) | ||||
−0.165788 | + | 0.986161i | \(0.553017\pi\) | |||||||
\(602\) | −5.68501 | −0.231704 | ||||||||
\(603\) | 15.5343 | 0.632607 | ||||||||
\(604\) | 3.55718 | 0.144740 | ||||||||
\(605\) | −29.1105 | −1.18351 | ||||||||
\(606\) | −1.49492 | −0.0607269 | ||||||||
\(607\) | −29.3624 | −1.19178 | −0.595891 | − | 0.803065i | \(-0.703201\pi\) | ||||
−0.595891 | + | 0.803065i | \(0.703201\pi\) | |||||||
\(608\) | −0.472571 | −0.0191653 | ||||||||
\(609\) | 0.174612 | 0.00707563 | ||||||||
\(610\) | −4.26843 | −0.172824 | ||||||||
\(611\) | −0.494613 | −0.0200099 | ||||||||
\(612\) | 3.94609 | 0.159511 | ||||||||
\(613\) | 19.7545 | 0.797875 | 0.398938 | − | 0.916978i | \(-0.369379\pi\) | ||||
0.398938 | + | 0.916978i | \(0.369379\pi\) | |||||||
\(614\) | −43.3625 | −1.74997 | ||||||||
\(615\) | 0.444924 | 0.0179411 | ||||||||
\(616\) | −16.0810 | −0.647924 | ||||||||
\(617\) | 3.67101 | 0.147789 | 0.0738947 | − | 0.997266i | \(-0.476457\pi\) | ||||
0.0738947 | + | 0.997266i | \(0.476457\pi\) | |||||||
\(618\) | −0.377018 | −0.0151659 | ||||||||
\(619\) | 18.2966 | 0.735402 | 0.367701 | − | 0.929944i | \(-0.380145\pi\) | ||||
0.367701 | + | 0.929944i | \(0.380145\pi\) | |||||||
\(620\) | −2.14181 | −0.0860172 | ||||||||
\(621\) | −1.54850 | −0.0621391 | ||||||||
\(622\) | 45.0929 | 1.80806 | ||||||||
\(623\) | −4.87365 | −0.195259 | ||||||||
\(624\) | 0.873887 | 0.0349835 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −29.5815 | −1.18231 | ||||||||
\(627\) | −0.100641 | −0.00401920 | ||||||||
\(628\) | −0.716646 | −0.0285973 | ||||||||
\(629\) | 5.62750 | 0.224383 | ||||||||
\(630\) | −4.58302 | −0.182592 | ||||||||
\(631\) | −3.13058 | −0.124626 | −0.0623132 | − | 0.998057i | \(-0.519848\pi\) | ||||
−0.0623132 | + | 0.998057i | \(0.519848\pi\) | |||||||
\(632\) | −40.2353 | −1.60047 | ||||||||
\(633\) | −0.881969 | −0.0350551 | ||||||||
\(634\) | −21.6298 | −0.859029 | ||||||||
\(635\) | 2.40677 | 0.0955097 | ||||||||
\(636\) | −0.0723786 | −0.00287000 | ||||||||
\(637\) | −2.98935 | −0.118442 | ||||||||
\(638\) | 26.4153 | 1.04579 | ||||||||
\(639\) | 19.8597 | 0.785639 | ||||||||
\(640\) | −13.3178 | −0.526431 | ||||||||
\(641\) | −41.1908 | −1.62694 | −0.813470 | − | 0.581607i | \(-0.802424\pi\) | ||||
−0.813470 | + | 0.581607i | \(0.802424\pi\) | |||||||
\(642\) | 0.0126133 | 0.000497809 0 | ||||||||
\(643\) | −23.4393 | −0.924355 | −0.462178 | − | 0.886787i | \(-0.652932\pi\) | ||||
−0.462178 | + | 0.886787i | \(0.652932\pi\) | |||||||
\(644\) | −1.37181 | −0.0540570 | ||||||||
\(645\) | −0.238001 | −0.00937128 | ||||||||
\(646\) | −1.46969 | −0.0578243 | ||||||||
\(647\) | 38.3034 | 1.50586 | 0.752931 | − | 0.658100i | \(-0.228639\pi\) | ||||
0.752931 | + | 0.658100i | \(0.228639\pi\) | |||||||
\(648\) | −22.7585 | −0.894039 | ||||||||
\(649\) | 68.3914 | 2.68460 | ||||||||
\(650\) | −4.57300 | −0.179368 | ||||||||
\(651\) | −0.403221 | −0.0158035 | ||||||||
\(652\) | 1.26382 | 0.0494949 | ||||||||
\(653\) | 5.59820 | 0.219074 | 0.109537 | − | 0.993983i | \(-0.465063\pi\) | ||||
0.109537 | + | 0.993983i | \(0.465063\pi\) | |||||||
\(654\) | 0.457176 | 0.0178770 | ||||||||
\(655\) | −1.25416 | −0.0490039 | ||||||||
\(656\) | 31.7117 | 1.23813 | ||||||||
\(657\) | −26.5670 | −1.03648 | ||||||||
\(658\) | −0.253113 | −0.00986737 | ||||||||
\(659\) | −30.7787 | −1.19897 | −0.599483 | − | 0.800387i | \(-0.704627\pi\) | ||||
−0.599483 | + | 0.800387i | \(0.704627\pi\) | |||||||
\(660\) | 0.137979 | 0.00537081 | ||||||||
\(661\) | 3.01579 | 0.117301 | 0.0586504 | − | 0.998279i | \(-0.481320\pi\) | ||||
0.0586504 | + | 0.998279i | \(0.481320\pi\) | |||||||
\(662\) | 8.61923 | 0.334996 | ||||||||
\(663\) | 0.741274 | 0.0287887 | ||||||||
\(664\) | 34.7947 | 1.35030 | ||||||||
\(665\) | 0.248126 | 0.00962190 | ||||||||
\(666\) | 6.66097 | 0.258107 | ||||||||
\(667\) | −10.9947 | −0.425718 | ||||||||
\(668\) | 5.97135 | 0.231038 | ||||||||
\(669\) | −0.970542 | −0.0375233 | ||||||||
\(670\) | 7.93213 | 0.306445 | ||||||||
\(671\) | −17.6715 | −0.682199 | ||||||||
\(672\) | 0.121974 | 0.00470525 | ||||||||
\(673\) | 11.8958 | 0.458549 | 0.229275 | − | 0.973362i | \(-0.426365\pi\) | ||||
0.229275 | + | 0.973362i | \(0.426365\pi\) | |||||||
\(674\) | 12.7115 | 0.489630 | ||||||||
\(675\) | −0.383996 | −0.0147800 | ||||||||
\(676\) | −1.38243 | −0.0531705 | ||||||||
\(677\) | 35.1701 | 1.35170 | 0.675848 | − | 0.737041i | \(-0.263777\pi\) | ||||
0.675848 | + | 0.737041i | \(0.263777\pi\) | |||||||
\(678\) | 0.131847 | 0.00506357 | ||||||||
\(679\) | −2.59750 | −0.0996828 | ||||||||
\(680\) | −9.83140 | −0.377017 | ||||||||
\(681\) | 0.757430 | 0.0290248 | ||||||||
\(682\) | −60.9992 | −2.33578 | ||||||||
\(683\) | 6.82111 | 0.261002 | 0.130501 | − | 0.991448i | \(-0.458341\pi\) | ||||
0.130501 | + | 0.991448i | \(0.458341\pi\) | |||||||
\(684\) | −0.252877 | −0.00966900 | ||||||||
\(685\) | −0.743203 | −0.0283963 | ||||||||
\(686\) | −1.52977 | −0.0584067 | ||||||||
\(687\) | 0.0640431 | 0.00244340 | ||||||||
\(688\) | −16.9634 | −0.646723 | ||||||||
\(689\) | 9.93124 | 0.378350 | ||||||||
\(690\) | −0.395077 | −0.0150403 | ||||||||
\(691\) | −4.35901 | −0.165825 | −0.0829123 | − | 0.996557i | \(-0.526422\pi\) | ||||
−0.0829123 | + | 0.996557i | \(0.526422\pi\) | |||||||
\(692\) | −6.37355 | −0.242286 | ||||||||
\(693\) | −18.9739 | −0.720758 | ||||||||
\(694\) | −4.62965 | −0.175739 | ||||||||
\(695\) | −10.7094 | −0.406230 | ||||||||
\(696\) | 0.443363 | 0.0168056 | ||||||||
\(697\) | 26.8994 | 1.01889 | ||||||||
\(698\) | 0.923473 | 0.0349540 | ||||||||
\(699\) | −1.67220 | −0.0632483 | ||||||||
\(700\) | −0.340181 | −0.0128576 | ||||||||
\(701\) | 1.07652 | 0.0406598 | 0.0203299 | − | 0.999793i | \(-0.493528\pi\) | ||||
0.0203299 | + | 0.999793i | \(0.493528\pi\) | |||||||
\(702\) | 1.75601 | 0.0662764 | ||||||||
\(703\) | −0.360626 | −0.0136013 | ||||||||
\(704\) | −39.3661 | −1.48367 | ||||||||
\(705\) | −0.0105965 | −0.000399087 0 | ||||||||
\(706\) | 0.235281 | 0.00885493 | ||||||||
\(707\) | 15.2588 | 0.573866 | ||||||||
\(708\) | −0.235264 | −0.00884176 | ||||||||
\(709\) | 27.5885 | 1.03611 | 0.518053 | − | 0.855348i | \(-0.326657\pi\) | ||||
0.518053 | + | 0.855348i | \(0.326657\pi\) | |||||||
\(710\) | 10.1408 | 0.380576 | ||||||||
\(711\) | −47.4732 | −1.78038 | ||||||||
\(712\) | −12.3748 | −0.463767 | ||||||||
\(713\) | 25.3895 | 0.950846 | ||||||||
\(714\) | 0.379339 | 0.0141964 | ||||||||
\(715\) | −18.9324 | −0.708031 | ||||||||
\(716\) | −8.52558 | −0.318616 | ||||||||
\(717\) | −0.549546 | −0.0205232 | ||||||||
\(718\) | 12.5209 | 0.467277 | ||||||||
\(719\) | 47.2367 | 1.76163 | 0.880816 | − | 0.473458i | \(-0.156994\pi\) | ||||
0.880816 | + | 0.473458i | \(0.156994\pi\) | |||||||
\(720\) | −13.6752 | −0.509644 | ||||||||
\(721\) | 3.84827 | 0.143317 | ||||||||
\(722\) | −28.9714 | −1.07820 | ||||||||
\(723\) | 0.485143 | 0.0180427 | ||||||||
\(724\) | −2.23995 | −0.0832471 | ||||||||
\(725\) | −2.72647 | −0.101259 | ||||||||
\(726\) | 2.85198 | 0.105847 | ||||||||
\(727\) | −12.9829 | −0.481510 | −0.240755 | − | 0.970586i | \(-0.577395\pi\) | ||||
−0.240755 | + | 0.970586i | \(0.577395\pi\) | |||||||
\(728\) | −7.59035 | −0.281317 | ||||||||
\(729\) | −26.7788 | −0.991806 | ||||||||
\(730\) | −13.5657 | −0.502087 | ||||||||
\(731\) | −14.3892 | −0.532203 | ||||||||
\(732\) | 0.0607892 | 0.00224684 | ||||||||
\(733\) | 34.5887 | 1.27756 | 0.638781 | − | 0.769389i | \(-0.279439\pi\) | ||||
0.638781 | + | 0.769389i | \(0.279439\pi\) | |||||||
\(734\) | 23.1589 | 0.854809 | ||||||||
\(735\) | −0.0640431 | −0.00236227 | ||||||||
\(736\) | −7.68031 | −0.283100 | ||||||||
\(737\) | 32.8393 | 1.20965 | ||||||||
\(738\) | 31.8394 | 1.17203 | ||||||||
\(739\) | −22.5558 | −0.829728 | −0.414864 | − | 0.909883i | \(-0.636171\pi\) | ||||
−0.414864 | + | 0.909883i | \(0.636171\pi\) | |||||||
\(740\) | 0.494420 | 0.0181752 | ||||||||
\(741\) | −0.0475029 | −0.00174506 | ||||||||
\(742\) | 5.08221 | 0.186574 | ||||||||
\(743\) | −27.7281 | −1.01725 | −0.508623 | − | 0.860989i | \(-0.669845\pi\) | ||||
−0.508623 | + | 0.860989i | \(0.669845\pi\) | |||||||
\(744\) | −1.02383 | −0.0375355 | ||||||||
\(745\) | 19.5430 | 0.716001 | ||||||||
\(746\) | −49.9842 | −1.83005 | ||||||||
\(747\) | 41.0539 | 1.50208 | ||||||||
\(748\) | 8.34198 | 0.305013 | ||||||||
\(749\) | −0.128746 | −0.00470427 | ||||||||
\(750\) | −0.0979709 | −0.00357739 | ||||||||
\(751\) | 27.1351 | 0.990174 | 0.495087 | − | 0.868843i | \(-0.335136\pi\) | ||||
0.495087 | + | 0.868843i | \(0.335136\pi\) | |||||||
\(752\) | −0.755259 | −0.0275415 | ||||||||
\(753\) | 0.0569650 | 0.00207592 | ||||||||
\(754\) | 12.4682 | 0.454063 | ||||||||
\(755\) | −10.4567 | −0.380559 | ||||||||
\(756\) | 0.130628 | 0.00475090 | ||||||||
\(757\) | −5.58521 | −0.202998 | −0.101499 | − | 0.994836i | \(-0.532364\pi\) | ||||
−0.101499 | + | 0.994836i | \(0.532364\pi\) | |||||||
\(758\) | −17.0485 | −0.619229 | ||||||||
\(759\) | −1.63563 | −0.0593696 | ||||||||
\(760\) | 0.630024 | 0.0228534 | ||||||||
\(761\) | 22.4624 | 0.814263 | 0.407131 | − | 0.913370i | \(-0.366529\pi\) | ||||
0.407131 | + | 0.913370i | \(0.366529\pi\) | |||||||
\(762\) | −0.235793 | −0.00854189 | ||||||||
\(763\) | −4.66644 | −0.168937 | ||||||||
\(764\) | 8.84223 | 0.319901 | ||||||||
\(765\) | −11.6000 | −0.419398 | ||||||||
\(766\) | 2.08797 | 0.0754416 | ||||||||
\(767\) | 32.2811 | 1.16560 | ||||||||
\(768\) | 0.508601 | 0.0183526 | ||||||||
\(769\) | 44.4172 | 1.60172 | 0.800862 | − | 0.598849i | \(-0.204375\pi\) | ||||
0.800862 | + | 0.598849i | \(0.204375\pi\) | |||||||
\(770\) | −9.68843 | −0.349147 | ||||||||
\(771\) | −0.573677 | −0.0206605 | ||||||||
\(772\) | −3.74532 | −0.134797 | ||||||||
\(773\) | −27.0456 | −0.972763 | −0.486381 | − | 0.873747i | \(-0.661683\pi\) | ||||
−0.486381 | + | 0.873747i | \(0.661683\pi\) | |||||||
\(774\) | −17.0317 | −0.612192 | ||||||||
\(775\) | 6.29609 | 0.226162 | ||||||||
\(776\) | −6.59539 | −0.236761 | ||||||||
\(777\) | 0.0930804 | 0.00333924 | ||||||||
\(778\) | 25.7572 | 0.923441 | ||||||||
\(779\) | −1.72379 | −0.0617613 | ||||||||
\(780\) | 0.0651267 | 0.00233191 | ||||||||
\(781\) | 41.9831 | 1.50227 | ||||||||
\(782\) | −23.8857 | −0.854152 | ||||||||
\(783\) | 1.04695 | 0.0374151 | ||||||||
\(784\) | −4.56464 | −0.163023 | ||||||||
\(785\) | 2.10666 | 0.0751899 | ||||||||
\(786\) | 0.122871 | 0.00438266 | ||||||||
\(787\) | 28.6325 | 1.02064 | 0.510319 | − | 0.859985i | \(-0.329527\pi\) | ||||
0.510319 | + | 0.859985i | \(0.329527\pi\) | |||||||
\(788\) | 7.18385 | 0.255914 | ||||||||
\(789\) | −0.578154 | −0.0205828 | ||||||||
\(790\) | −24.2408 | −0.862447 | ||||||||
\(791\) | −1.34578 | −0.0478505 | ||||||||
\(792\) | −48.1772 | −1.71190 | ||||||||
\(793\) | −8.34104 | −0.296199 | ||||||||
\(794\) | −0.669179 | −0.0237483 | ||||||||
\(795\) | 0.212765 | 0.00754599 | ||||||||
\(796\) | −0.334417 | −0.0118531 | ||||||||
\(797\) | 46.1960 | 1.63635 | 0.818173 | − | 0.574972i | \(-0.194987\pi\) | ||||
0.818173 | + | 0.574972i | \(0.194987\pi\) | |||||||
\(798\) | −0.0243091 | −0.000860533 0 | ||||||||
\(799\) | −0.640648 | −0.0226645 | ||||||||
\(800\) | −1.90456 | −0.0673364 | ||||||||
\(801\) | −14.6010 | −0.515899 | ||||||||
\(802\) | 8.95353 | 0.316160 | ||||||||
\(803\) | −56.1623 | −1.98192 | ||||||||
\(804\) | −0.112966 | −0.00398401 | ||||||||
\(805\) | 4.03259 | 0.142130 | ||||||||
\(806\) | −28.7920 | −1.01415 | ||||||||
\(807\) | −0.205524 | −0.00723478 | ||||||||
\(808\) | 38.7441 | 1.36301 | ||||||||
\(809\) | −11.1772 | −0.392970 | −0.196485 | − | 0.980507i | \(-0.562953\pi\) | ||||
−0.196485 | + | 0.980507i | \(0.562953\pi\) | |||||||
\(810\) | −13.7114 | −0.481771 | ||||||||
\(811\) | −7.73040 | −0.271451 | −0.135726 | − | 0.990746i | \(-0.543337\pi\) | ||||
−0.135726 | + | 0.990746i | \(0.543337\pi\) | |||||||
\(812\) | 0.927495 | 0.0325487 | ||||||||
\(813\) | 0.960906 | 0.0337004 | ||||||||
\(814\) | 14.0812 | 0.493545 | ||||||||
\(815\) | −3.71513 | −0.130135 | ||||||||
\(816\) | 1.13190 | 0.0396245 | ||||||||
\(817\) | 0.922100 | 0.0322602 | ||||||||
\(818\) | 34.7023 | 1.21334 | ||||||||
\(819\) | −8.95578 | −0.312940 | ||||||||
\(820\) | 2.36333 | 0.0825310 | ||||||||
\(821\) | 46.5304 | 1.62392 | 0.811960 | − | 0.583713i | \(-0.198401\pi\) | ||||
0.811960 | + | 0.583713i | \(0.198401\pi\) | |||||||
\(822\) | 0.0728123 | 0.00253962 | ||||||||
\(823\) | −40.0678 | −1.39668 | −0.698338 | − | 0.715768i | \(-0.746077\pi\) | ||||
−0.698338 | + | 0.715768i | \(0.746077\pi\) | |||||||
\(824\) | 9.77126 | 0.340398 | ||||||||
\(825\) | −0.405603 | −0.0141213 | ||||||||
\(826\) | 16.5195 | 0.574787 | ||||||||
\(827\) | −29.0423 | −1.00990 | −0.504951 | − | 0.863148i | \(-0.668489\pi\) | ||||
−0.504951 | + | 0.863148i | \(0.668489\pi\) | |||||||
\(828\) | −4.10981 | −0.142826 | ||||||||
\(829\) | 14.4423 | 0.501603 | 0.250801 | − | 0.968039i | \(-0.419306\pi\) | ||||
0.250801 | + | 0.968039i | \(0.419306\pi\) | |||||||
\(830\) | 20.9629 | 0.727634 | ||||||||
\(831\) | 0.160534 | 0.00556888 | ||||||||
\(832\) | −18.5810 | −0.644181 | ||||||||
\(833\) | −3.87195 | −0.134155 | ||||||||
\(834\) | 1.04921 | 0.0363311 | ||||||||
\(835\) | −17.5534 | −0.607461 | ||||||||
\(836\) | −0.534578 | −0.0184888 | ||||||||
\(837\) | −2.41767 | −0.0835670 | ||||||||
\(838\) | −5.11648 | −0.176746 | ||||||||
\(839\) | −9.18480 | −0.317094 | −0.158547 | − | 0.987351i | \(-0.550681\pi\) | ||||
−0.158547 | + | 0.987351i | \(0.550681\pi\) | |||||||
\(840\) | −0.162614 | −0.00561071 | ||||||||
\(841\) | −21.5663 | −0.743667 | ||||||||
\(842\) | −32.7262 | −1.12782 | ||||||||
\(843\) | −0.549483 | −0.0189252 | ||||||||
\(844\) | −4.68480 | −0.161258 | ||||||||
\(845\) | 4.06381 | 0.139799 | ||||||||
\(846\) | −0.758301 | −0.0260709 | ||||||||
\(847\) | −29.1105 | −1.00025 | ||||||||
\(848\) | 15.1647 | 0.520758 | ||||||||
\(849\) | 1.66120 | 0.0570122 | ||||||||
\(850\) | −5.92318 | −0.203163 | ||||||||
\(851\) | −5.86097 | −0.200912 | ||||||||
\(852\) | −0.144421 | −0.00494777 | ||||||||
\(853\) | −12.7417 | −0.436268 | −0.218134 | − | 0.975919i | \(-0.569997\pi\) | ||||
−0.218134 | + | 0.975919i | \(0.569997\pi\) | |||||||
\(854\) | −4.26843 | −0.146063 | ||||||||
\(855\) | 0.743359 | 0.0254224 | ||||||||
\(856\) | −0.326903 | −0.0111733 | ||||||||
\(857\) | 3.82422 | 0.130633 | 0.0653165 | − | 0.997865i | \(-0.479194\pi\) | ||||
0.0653165 | + | 0.997865i | \(0.479194\pi\) | |||||||
\(858\) | 1.85482 | 0.0633226 | ||||||||
\(859\) | 7.09447 | 0.242060 | 0.121030 | − | 0.992649i | \(-0.461380\pi\) | ||||
0.121030 | + | 0.992649i | \(0.461380\pi\) | |||||||
\(860\) | −1.26420 | −0.0431090 | ||||||||
\(861\) | 0.444924 | 0.0151630 | ||||||||
\(862\) | 12.5641 | 0.427934 | ||||||||
\(863\) | 45.9769 | 1.56507 | 0.782536 | − | 0.622605i | \(-0.213926\pi\) | ||||
0.782536 | + | 0.622605i | \(0.213926\pi\) | |||||||
\(864\) | 0.731344 | 0.0248808 | ||||||||
\(865\) | 18.7357 | 0.637034 | ||||||||
\(866\) | 22.3202 | 0.758473 | ||||||||
\(867\) | −0.128598 | −0.00436742 | ||||||||
\(868\) | −2.14181 | −0.0726978 | ||||||||
\(869\) | −100.358 | −3.40440 | ||||||||
\(870\) | 0.267115 | 0.00905605 | ||||||||
\(871\) | 15.5003 | 0.525209 | ||||||||
\(872\) | −11.8487 | −0.401248 | ||||||||
\(873\) | −7.78184 | −0.263375 | ||||||||
\(874\) | 1.53067 | 0.0517756 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0.193196 | 0.00652750 | ||||||||
\(877\) | 31.9887 | 1.08018 | 0.540091 | − | 0.841607i | \(-0.318390\pi\) | ||||
0.540091 | + | 0.841607i | \(0.318390\pi\) | |||||||
\(878\) | −3.65107 | −0.123218 | ||||||||
\(879\) | 0.00301140 | 0.000101572 0 | ||||||||
\(880\) | −28.9091 | −0.974527 | ||||||||
\(881\) | 0.341666 | 0.0115110 | 0.00575552 | − | 0.999983i | \(-0.498168\pi\) | ||||
0.00575552 | + | 0.999983i | \(0.498168\pi\) | |||||||
\(882\) | −4.58302 | −0.154318 | ||||||||
\(883\) | 10.3447 | 0.348127 | 0.174063 | − | 0.984734i | \(-0.444310\pi\) | ||||
0.174063 | + | 0.984734i | \(0.444310\pi\) | |||||||
\(884\) | 3.93746 | 0.132431 | ||||||||
\(885\) | 0.691584 | 0.0232473 | ||||||||
\(886\) | −39.5572 | −1.32895 | ||||||||
\(887\) | 20.3583 | 0.683565 | 0.341783 | − | 0.939779i | \(-0.388969\pi\) | ||||
0.341783 | + | 0.939779i | \(0.388969\pi\) | |||||||
\(888\) | 0.236343 | 0.00793117 | ||||||||
\(889\) | 2.40677 | 0.0807204 | ||||||||
\(890\) | −7.45554 | −0.249910 | ||||||||
\(891\) | −56.7659 | −1.90173 | ||||||||
\(892\) | −5.15528 | −0.172612 | ||||||||
\(893\) | 0.0410546 | 0.00137384 | ||||||||
\(894\) | −1.91465 | −0.0640354 | ||||||||
\(895\) | 25.0619 | 0.837726 | ||||||||
\(896\) | −13.3178 | −0.444915 | ||||||||
\(897\) | −0.772027 | −0.0257772 | ||||||||
\(898\) | 16.7666 | 0.559509 | ||||||||
\(899\) | −17.1661 | −0.572522 | ||||||||
\(900\) | −1.01915 | −0.0339716 | ||||||||
\(901\) | 12.8634 | 0.428544 | ||||||||
\(902\) | 67.3080 | 2.24111 | ||||||||
\(903\) | −0.238001 | −0.00792018 | ||||||||
\(904\) | −3.41712 | −0.113652 | ||||||||
\(905\) | 6.58458 | 0.218879 | ||||||||
\(906\) | 1.02445 | 0.0340352 | ||||||||
\(907\) | 25.1621 | 0.835492 | 0.417746 | − | 0.908564i | \(-0.362820\pi\) | ||||
0.417746 | + | 0.908564i | \(0.362820\pi\) | |||||||
\(908\) | 4.02328 | 0.133517 | ||||||||
\(909\) | 45.7138 | 1.51623 | ||||||||
\(910\) | −4.57300 | −0.151593 | ||||||||
\(911\) | −18.1865 | −0.602547 | −0.301274 | − | 0.953538i | \(-0.597412\pi\) | ||||
−0.301274 | + | 0.953538i | \(0.597412\pi\) | |||||||
\(912\) | −0.0725355 | −0.00240189 | ||||||||
\(913\) | 86.7873 | 2.87224 | ||||||||
\(914\) | 5.52993 | 0.182914 | ||||||||
\(915\) | −0.178697 | −0.00590753 | ||||||||
\(916\) | 0.340181 | 0.0112399 | ||||||||
\(917\) | −1.25416 | −0.0414159 | ||||||||
\(918\) | 2.27448 | 0.0750689 | ||||||||
\(919\) | 26.5004 | 0.874168 | 0.437084 | − | 0.899421i | \(-0.356011\pi\) | ||||
0.437084 | + | 0.899421i | \(0.356011\pi\) | |||||||
\(920\) | 10.2393 | 0.337579 | ||||||||
\(921\) | −1.81536 | −0.0598180 | ||||||||
\(922\) | 49.2014 | 1.62036 | ||||||||
\(923\) | 19.8163 | 0.652261 | ||||||||
\(924\) | 0.137979 | 0.00453916 | ||||||||
\(925\) | −1.45340 | −0.0477876 | ||||||||
\(926\) | 22.3538 | 0.734590 | ||||||||
\(927\) | 11.5290 | 0.378663 | ||||||||
\(928\) | 5.19273 | 0.170460 | ||||||||
\(929\) | −25.5300 | −0.837613 | −0.418806 | − | 0.908076i | \(-0.637551\pi\) | ||||
−0.418806 | + | 0.908076i | \(0.637551\pi\) | |||||||
\(930\) | −0.616834 | −0.0202268 | ||||||||
\(931\) | 0.248126 | 0.00813199 | ||||||||
\(932\) | −8.88230 | −0.290949 | ||||||||
\(933\) | 1.88780 | 0.0618037 | ||||||||
\(934\) | 23.1711 | 0.758181 | ||||||||
\(935\) | −24.5222 | −0.801960 | ||||||||
\(936\) | −22.7399 | −0.743277 | ||||||||
\(937\) | 1.00053 | 0.0326858 | 0.0163429 | − | 0.999866i | \(-0.494798\pi\) | ||||
0.0163429 | + | 0.999866i | \(0.494798\pi\) | |||||||
\(938\) | 7.93213 | 0.258993 | ||||||||
\(939\) | −1.23842 | −0.0404142 | ||||||||
\(940\) | −0.0562860 | −0.00183585 | ||||||||
\(941\) | 34.1333 | 1.11271 | 0.556356 | − | 0.830944i | \(-0.312199\pi\) | ||||
0.556356 | + | 0.830944i | \(0.312199\pi\) | |||||||
\(942\) | −0.206391 | −0.00672459 | ||||||||
\(943\) | −28.0154 | −0.912308 | ||||||||
\(944\) | 49.2923 | 1.60433 | ||||||||
\(945\) | −0.383996 | −0.0124914 | ||||||||
\(946\) | −36.0048 | −1.17062 | ||||||||
\(947\) | −35.2983 | −1.14704 | −0.573520 | − | 0.819192i | \(-0.694422\pi\) | ||||
−0.573520 | + | 0.819192i | \(0.694422\pi\) | |||||||
\(948\) | 0.345227 | 0.0112124 | ||||||||
\(949\) | −26.5089 | −0.860516 | ||||||||
\(950\) | 0.379574 | 0.0123150 | ||||||||
\(951\) | −0.905524 | −0.0293636 | ||||||||
\(952\) | −9.83140 | −0.318637 | ||||||||
\(953\) | 29.4600 | 0.954302 | 0.477151 | − | 0.878821i | \(-0.341669\pi\) | ||||
0.477151 | + | 0.878821i | \(0.341669\pi\) | |||||||
\(954\) | 15.2258 | 0.492953 | ||||||||
\(955\) | −25.9927 | −0.841104 | ||||||||
\(956\) | −2.91906 | −0.0944090 | ||||||||
\(957\) | 1.10587 | 0.0357476 | ||||||||
\(958\) | −10.0765 | −0.325556 | ||||||||
\(959\) | −0.743203 | −0.0239993 | ||||||||
\(960\) | −0.398076 | −0.0128478 | ||||||||
\(961\) | 8.64072 | 0.278733 | ||||||||
\(962\) | 6.64640 | 0.214289 | ||||||||
\(963\) | −0.385709 | −0.0124293 | ||||||||
\(964\) | 2.57696 | 0.0829984 | ||||||||
\(965\) | 11.0098 | 0.354418 | ||||||||
\(966\) | −0.395077 | −0.0127114 | ||||||||
\(967\) | −17.8398 | −0.573690 | −0.286845 | − | 0.957977i | \(-0.592607\pi\) | ||||
−0.286845 | + | 0.957977i | \(0.592607\pi\) | |||||||
\(968\) | −73.9153 | −2.37573 | ||||||||
\(969\) | −0.0615282 | −0.00197657 | ||||||||
\(970\) | −3.97356 | −0.127583 | ||||||||
\(971\) | −38.5055 | −1.23570 | −0.617851 | − | 0.786296i | \(-0.711996\pi\) | ||||
−0.617851 | + | 0.786296i | \(0.711996\pi\) | |||||||
\(972\) | 0.587157 | 0.0188331 | ||||||||
\(973\) | −10.7094 | −0.343327 | ||||||||
\(974\) | 46.7036 | 1.49648 | ||||||||
\(975\) | −0.191447 | −0.00613121 | ||||||||
\(976\) | −12.7365 | −0.407686 | ||||||||
\(977\) | 6.13402 | 0.196245 | 0.0981223 | − | 0.995174i | \(-0.468716\pi\) | ||||
0.0981223 | + | 0.995174i | \(0.468716\pi\) | |||||||
\(978\) | 0.363975 | 0.0116386 | ||||||||
\(979\) | −30.8662 | −0.986487 | ||||||||
\(980\) | −0.340181 | −0.0108667 | ||||||||
\(981\) | −13.9802 | −0.446353 | ||||||||
\(982\) | −16.5361 | −0.527688 | ||||||||
\(983\) | 40.4504 | 1.29017 | 0.645084 | − | 0.764112i | \(-0.276822\pi\) | ||||
0.645084 | + | 0.764112i | \(0.276822\pi\) | |||||||
\(984\) | 1.12972 | 0.0360142 | ||||||||
\(985\) | −21.1177 | −0.672867 | ||||||||
\(986\) | 16.1494 | 0.514301 | ||||||||
\(987\) | −0.0105965 | −0.000337290 0 | ||||||||
\(988\) | −0.252324 | −0.00802749 | ||||||||
\(989\) | 14.9862 | 0.476532 | ||||||||
\(990\) | −29.0256 | −0.922493 | ||||||||
\(991\) | −59.0067 | −1.87441 | −0.937205 | − | 0.348780i | \(-0.886596\pi\) | ||||
−0.937205 | + | 0.348780i | \(0.886596\pi\) | |||||||
\(992\) | −11.9913 | −0.380724 | ||||||||
\(993\) | 0.360841 | 0.0114510 | ||||||||
\(994\) | 10.1408 | 0.321646 | ||||||||
\(995\) | 0.983055 | 0.0311649 | ||||||||
\(996\) | −0.298545 | −0.00945977 | ||||||||
\(997\) | 56.7998 | 1.79887 | 0.899434 | − | 0.437056i | \(-0.143979\pi\) | ||||
0.899434 | + | 0.437056i | \(0.143979\pi\) | |||||||
\(998\) | −18.8292 | −0.596028 | ||||||||
\(999\) | 0.558101 | 0.0176575 |
(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 | 8015.2.a.l.1.46 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.46 | ✓ | 62 | 1.1 | even | 1 | trivial |