Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.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: | \(64.0959177025\) |
Analytic rank: | \(1\) |
Dimension: | \(149\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.27388 | −1.60788 | −0.803938 | − | 0.594713i | \(-0.797266\pi\) | ||||
−0.803938 | + | 0.594713i | \(0.797266\pi\) | |||||||
\(3\) | 0.787573 | 0.454706 | 0.227353 | − | 0.973812i | \(-0.426993\pi\) | ||||
0.227353 | + | 0.973812i | \(0.426993\pi\) | |||||||
\(4\) | 3.17053 | 1.58527 | ||||||||
\(5\) | −4.28008 | −1.91411 | −0.957056 | − | 0.289904i | \(-0.906376\pi\) | ||||
−0.957056 | + | 0.289904i | \(0.906376\pi\) | |||||||
\(6\) | −1.79085 | −0.731110 | ||||||||
\(7\) | 1.25028 | 0.472560 | 0.236280 | − | 0.971685i | \(-0.424072\pi\) | ||||
0.236280 | + | 0.971685i | \(0.424072\pi\) | |||||||
\(8\) | −2.66164 | −0.941034 | ||||||||
\(9\) | −2.37973 | −0.793243 | ||||||||
\(10\) | 9.73239 | 3.07765 | ||||||||
\(11\) | 2.44033 | 0.735787 | 0.367894 | − | 0.929868i | \(-0.380079\pi\) | ||||
0.367894 | + | 0.929868i | \(0.380079\pi\) | |||||||
\(12\) | 2.49702 | 0.720829 | ||||||||
\(13\) | 2.67145 | 0.740928 | 0.370464 | − | 0.928847i | \(-0.379199\pi\) | ||||
0.370464 | + | 0.928847i | \(0.379199\pi\) | |||||||
\(14\) | −2.84298 | −0.759818 | ||||||||
\(15\) | −3.37088 | −0.870357 | ||||||||
\(16\) | −0.288799 | −0.0721997 | ||||||||
\(17\) | 2.63677 | 0.639512 | 0.319756 | − | 0.947500i | \(-0.396399\pi\) | ||||
0.319756 | + | 0.947500i | \(0.396399\pi\) | |||||||
\(18\) | 5.41122 | 1.27544 | ||||||||
\(19\) | −3.45020 | −0.791530 | −0.395765 | − | 0.918352i | \(-0.629520\pi\) | ||||
−0.395765 | + | 0.918352i | \(0.629520\pi\) | |||||||
\(20\) | −13.5701 | −3.03437 | ||||||||
\(21\) | 0.984684 | 0.214876 | ||||||||
\(22\) | −5.54902 | −1.18305 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −2.09624 | −0.427893 | ||||||||
\(25\) | 13.3191 | 2.66382 | ||||||||
\(26\) | −6.07456 | −1.19132 | ||||||||
\(27\) | −4.23693 | −0.815398 | ||||||||
\(28\) | 3.96404 | 0.749133 | ||||||||
\(29\) | 7.37128 | 1.36881 | 0.684406 | − | 0.729101i | \(-0.260062\pi\) | ||||
0.684406 | + | 0.729101i | \(0.260062\pi\) | |||||||
\(30\) | 7.66497 | 1.39943 | ||||||||
\(31\) | −9.30618 | −1.67144 | −0.835719 | − | 0.549157i | \(-0.814949\pi\) | ||||
−0.835719 | + | 0.549157i | \(0.814949\pi\) | |||||||
\(32\) | 5.97998 | 1.05712 | ||||||||
\(33\) | 1.92194 | 0.334567 | ||||||||
\(34\) | −5.99571 | −1.02826 | ||||||||
\(35\) | −5.35129 | −0.904533 | ||||||||
\(36\) | −7.54500 | −1.25750 | ||||||||
\(37\) | −6.59241 | −1.08379 | −0.541893 | − | 0.840448i | \(-0.682292\pi\) | ||||
−0.541893 | + | 0.840448i | \(0.682292\pi\) | |||||||
\(38\) | 7.84534 | 1.27268 | ||||||||
\(39\) | 2.10396 | 0.336904 | ||||||||
\(40\) | 11.3921 | 1.80124 | ||||||||
\(41\) | 2.90291 | 0.453358 | 0.226679 | − | 0.973969i | \(-0.427213\pi\) | ||||
0.226679 | + | 0.973969i | \(0.427213\pi\) | |||||||
\(42\) | −2.23905 | −0.345494 | ||||||||
\(43\) | −8.50068 | −1.29634 | −0.648171 | − | 0.761495i | \(-0.724466\pi\) | ||||
−0.648171 | + | 0.761495i | \(0.724466\pi\) | |||||||
\(44\) | 7.73714 | 1.16642 | ||||||||
\(45\) | 10.1854 | 1.51835 | ||||||||
\(46\) | 2.27388 | 0.335265 | ||||||||
\(47\) | 3.14677 | 0.459004 | 0.229502 | − | 0.973308i | \(-0.426290\pi\) | ||||
0.229502 | + | 0.973308i | \(0.426290\pi\) | |||||||
\(48\) | −0.227450 | −0.0328296 | ||||||||
\(49\) | −5.43681 | −0.776687 | ||||||||
\(50\) | −30.2861 | −4.28309 | ||||||||
\(51\) | 2.07665 | 0.290790 | ||||||||
\(52\) | 8.46992 | 1.17457 | ||||||||
\(53\) | 6.05340 | 0.831499 | 0.415750 | − | 0.909479i | \(-0.363519\pi\) | ||||
0.415750 | + | 0.909479i | \(0.363519\pi\) | |||||||
\(54\) | 9.63427 | 1.31106 | ||||||||
\(55\) | −10.4448 | −1.40838 | ||||||||
\(56\) | −3.32779 | −0.444695 | ||||||||
\(57\) | −2.71728 | −0.359913 | ||||||||
\(58\) | −16.7614 | −2.20088 | ||||||||
\(59\) | 3.90287 | 0.508110 | 0.254055 | − | 0.967190i | \(-0.418236\pi\) | ||||
0.254055 | + | 0.967190i | \(0.418236\pi\) | |||||||
\(60\) | −10.6875 | −1.37975 | ||||||||
\(61\) | 0.783546 | 0.100323 | 0.0501614 | − | 0.998741i | \(-0.484026\pi\) | ||||
0.0501614 | + | 0.998741i | \(0.484026\pi\) | |||||||
\(62\) | 21.1611 | 2.68747 | ||||||||
\(63\) | −2.97532 | −0.374855 | ||||||||
\(64\) | −13.0202 | −1.62752 | ||||||||
\(65\) | −11.4340 | −1.41822 | ||||||||
\(66\) | −4.37026 | −0.537941 | ||||||||
\(67\) | 6.43593 | 0.786274 | 0.393137 | − | 0.919480i | \(-0.371390\pi\) | ||||
0.393137 | + | 0.919480i | \(0.371390\pi\) | |||||||
\(68\) | 8.35997 | 1.01380 | ||||||||
\(69\) | −0.787573 | −0.0948127 | ||||||||
\(70\) | 12.1682 | 1.45438 | ||||||||
\(71\) | 0.619609 | 0.0735340 | 0.0367670 | − | 0.999324i | \(-0.488294\pi\) | ||||
0.0367670 | + | 0.999324i | \(0.488294\pi\) | |||||||
\(72\) | 6.33399 | 0.746468 | ||||||||
\(73\) | 11.0559 | 1.29400 | 0.647000 | − | 0.762490i | \(-0.276023\pi\) | ||||
0.647000 | + | 0.762490i | \(0.276023\pi\) | |||||||
\(74\) | 14.9903 | 1.74259 | ||||||||
\(75\) | 10.4898 | 1.21125 | ||||||||
\(76\) | −10.9390 | −1.25478 | ||||||||
\(77\) | 3.05109 | 0.347704 | ||||||||
\(78\) | −4.78416 | −0.541700 | ||||||||
\(79\) | −6.19070 | −0.696508 | −0.348254 | − | 0.937400i | \(-0.613225\pi\) | ||||
−0.348254 | + | 0.937400i | \(0.613225\pi\) | |||||||
\(80\) | 1.23608 | 0.138198 | ||||||||
\(81\) | 3.80229 | 0.422477 | ||||||||
\(82\) | −6.60087 | −0.728944 | ||||||||
\(83\) | −13.5113 | −1.48306 | −0.741530 | − | 0.670919i | \(-0.765900\pi\) | ||||
−0.741530 | + | 0.670919i | \(0.765900\pi\) | |||||||
\(84\) | 3.12197 | 0.340635 | ||||||||
\(85\) | −11.2856 | −1.22410 | ||||||||
\(86\) | 19.3295 | 2.08436 | ||||||||
\(87\) | 5.80542 | 0.622406 | ||||||||
\(88\) | −6.49529 | −0.692400 | ||||||||
\(89\) | −1.31530 | −0.139421 | −0.0697107 | − | 0.997567i | \(-0.522208\pi\) | ||||
−0.0697107 | + | 0.997567i | \(0.522208\pi\) | |||||||
\(90\) | −23.1605 | −2.44133 | ||||||||
\(91\) | 3.34006 | 0.350133 | ||||||||
\(92\) | −3.17053 | −0.330551 | ||||||||
\(93\) | −7.32930 | −0.760013 | ||||||||
\(94\) | −7.15538 | −0.738022 | ||||||||
\(95\) | 14.7671 | 1.51508 | ||||||||
\(96\) | 4.70968 | 0.480679 | ||||||||
\(97\) | 0.201416 | 0.0204507 | 0.0102254 | − | 0.999948i | \(-0.496745\pi\) | ||||
0.0102254 | + | 0.999948i | \(0.496745\pi\) | |||||||
\(98\) | 12.3626 | 1.24882 | ||||||||
\(99\) | −5.80732 | −0.583658 | ||||||||
\(100\) | 42.2286 | 4.22286 | ||||||||
\(101\) | −2.20421 | −0.219327 | −0.109664 | − | 0.993969i | \(-0.534977\pi\) | ||||
−0.109664 | + | 0.993969i | \(0.534977\pi\) | |||||||
\(102\) | −4.72206 | −0.467553 | ||||||||
\(103\) | −6.69109 | −0.659292 | −0.329646 | − | 0.944105i | \(-0.606929\pi\) | ||||
−0.329646 | + | 0.944105i | \(0.606929\pi\) | |||||||
\(104\) | −7.11046 | −0.697238 | ||||||||
\(105\) | −4.21453 | −0.411296 | ||||||||
\(106\) | −13.7647 | −1.33695 | ||||||||
\(107\) | 15.4984 | 1.49829 | 0.749145 | − | 0.662406i | \(-0.230465\pi\) | ||||
0.749145 | + | 0.662406i | \(0.230465\pi\) | |||||||
\(108\) | −13.4333 | −1.29262 | ||||||||
\(109\) | 0.0936218 | 0.00896734 | 0.00448367 | − | 0.999990i | \(-0.498573\pi\) | ||||
0.00448367 | + | 0.999990i | \(0.498573\pi\) | |||||||
\(110\) | 23.7503 | 2.26450 | ||||||||
\(111\) | −5.19200 | −0.492803 | ||||||||
\(112\) | −0.361079 | −0.0341187 | ||||||||
\(113\) | −15.2000 | −1.42990 | −0.714948 | − | 0.699178i | \(-0.753550\pi\) | ||||
−0.714948 | + | 0.699178i | \(0.753550\pi\) | |||||||
\(114\) | 6.17878 | 0.578695 | ||||||||
\(115\) | 4.28008 | 0.399120 | ||||||||
\(116\) | 23.3709 | 2.16993 | ||||||||
\(117\) | −6.35733 | −0.587736 | ||||||||
\(118\) | −8.87465 | −0.816978 | ||||||||
\(119\) | 3.29670 | 0.302208 | ||||||||
\(120\) | 8.97208 | 0.819035 | ||||||||
\(121\) | −5.04479 | −0.458617 | ||||||||
\(122\) | −1.78169 | −0.161307 | ||||||||
\(123\) | 2.28625 | 0.206145 | ||||||||
\(124\) | −29.5055 | −2.64967 | ||||||||
\(125\) | −35.6065 | −3.18474 | ||||||||
\(126\) | 6.76552 | 0.602720 | ||||||||
\(127\) | 12.8681 | 1.14186 | 0.570928 | − | 0.821000i | \(-0.306584\pi\) | ||||
0.570928 | + | 0.821000i | \(0.306584\pi\) | |||||||
\(128\) | 17.6463 | 1.55973 | ||||||||
\(129\) | −6.69491 | −0.589454 | ||||||||
\(130\) | 25.9996 | 2.28032 | ||||||||
\(131\) | −2.56745 | −0.224319 | −0.112160 | − | 0.993690i | \(-0.535777\pi\) | ||||
−0.112160 | + | 0.993690i | \(0.535777\pi\) | |||||||
\(132\) | 6.09356 | 0.530377 | ||||||||
\(133\) | −4.31370 | −0.374045 | ||||||||
\(134\) | −14.6345 | −1.26423 | ||||||||
\(135\) | 18.1344 | 1.56076 | ||||||||
\(136\) | −7.01816 | −0.601802 | ||||||||
\(137\) | 1.71935 | 0.146894 | 0.0734470 | − | 0.997299i | \(-0.476600\pi\) | ||||
0.0734470 | + | 0.997299i | \(0.476600\pi\) | |||||||
\(138\) | 1.79085 | 0.152447 | ||||||||
\(139\) | 21.4823 | 1.82210 | 0.911051 | − | 0.412294i | \(-0.135272\pi\) | ||||
0.911051 | + | 0.412294i | \(0.135272\pi\) | |||||||
\(140\) | −16.9664 | −1.43392 | ||||||||
\(141\) | 2.47831 | 0.208712 | ||||||||
\(142\) | −1.40892 | −0.118234 | ||||||||
\(143\) | 6.51923 | 0.545165 | ||||||||
\(144\) | 0.687263 | 0.0572719 | ||||||||
\(145\) | −31.5497 | −2.62006 | ||||||||
\(146\) | −25.1399 | −2.08059 | ||||||||
\(147\) | −4.28188 | −0.353164 | ||||||||
\(148\) | −20.9014 | −1.71809 | ||||||||
\(149\) | 3.15103 | 0.258142 | 0.129071 | − | 0.991635i | \(-0.458800\pi\) | ||||
0.129071 | + | 0.991635i | \(0.458800\pi\) | |||||||
\(150\) | −23.8525 | −1.94755 | ||||||||
\(151\) | 11.9695 | 0.974061 | 0.487031 | − | 0.873385i | \(-0.338080\pi\) | ||||
0.487031 | + | 0.873385i | \(0.338080\pi\) | |||||||
\(152\) | 9.18320 | 0.744856 | ||||||||
\(153\) | −6.27481 | −0.507288 | ||||||||
\(154\) | −6.93781 | −0.559064 | ||||||||
\(155\) | 39.8312 | 3.19932 | ||||||||
\(156\) | 6.67068 | 0.534082 | ||||||||
\(157\) | 16.0992 | 1.28485 | 0.642427 | − | 0.766347i | \(-0.277928\pi\) | ||||
0.642427 | + | 0.766347i | \(0.277928\pi\) | |||||||
\(158\) | 14.0769 | 1.11990 | ||||||||
\(159\) | 4.76750 | 0.378087 | ||||||||
\(160\) | −25.5948 | −2.02345 | ||||||||
\(161\) | −1.25028 | −0.0985356 | ||||||||
\(162\) | −8.64596 | −0.679291 | ||||||||
\(163\) | −0.269021 | −0.0210714 | −0.0105357 | − | 0.999944i | \(-0.503354\pi\) | ||||
−0.0105357 | + | 0.999944i | \(0.503354\pi\) | |||||||
\(164\) | 9.20376 | 0.718693 | ||||||||
\(165\) | −8.22606 | −0.640398 | ||||||||
\(166\) | 30.7231 | 2.38458 | ||||||||
\(167\) | 10.3717 | 0.802584 | 0.401292 | − | 0.915950i | \(-0.368561\pi\) | ||||
0.401292 | + | 0.915950i | \(0.368561\pi\) | |||||||
\(168\) | −2.62088 | −0.202205 | ||||||||
\(169\) | −5.86334 | −0.451026 | ||||||||
\(170\) | 25.6621 | 1.96820 | ||||||||
\(171\) | 8.21053 | 0.627875 | ||||||||
\(172\) | −26.9517 | −2.05505 | ||||||||
\(173\) | 17.7835 | 1.35205 | 0.676026 | − | 0.736878i | \(-0.263701\pi\) | ||||
0.676026 | + | 0.736878i | \(0.263701\pi\) | |||||||
\(174\) | −13.2008 | −1.00075 | ||||||||
\(175\) | 16.6526 | 1.25882 | ||||||||
\(176\) | −0.704765 | −0.0531236 | ||||||||
\(177\) | 3.07379 | 0.231041 | ||||||||
\(178\) | 2.99083 | 0.224172 | ||||||||
\(179\) | 22.9220 | 1.71327 | 0.856634 | − | 0.515925i | \(-0.172552\pi\) | ||||
0.856634 | + | 0.515925i | \(0.172552\pi\) | |||||||
\(180\) | 32.2932 | 2.40700 | ||||||||
\(181\) | −19.5684 | −1.45451 | −0.727255 | − | 0.686367i | \(-0.759204\pi\) | ||||
−0.727255 | + | 0.686367i | \(0.759204\pi\) | |||||||
\(182\) | −7.59488 | −0.562970 | ||||||||
\(183\) | 0.617100 | 0.0456173 | ||||||||
\(184\) | 2.66164 | 0.196219 | ||||||||
\(185\) | 28.2161 | 2.07449 | ||||||||
\(186\) | 16.6659 | 1.22201 | ||||||||
\(187\) | 6.43460 | 0.470544 | ||||||||
\(188\) | 9.97694 | 0.727643 | ||||||||
\(189\) | −5.29733 | −0.385324 | ||||||||
\(190\) | −33.5787 | −2.43605 | ||||||||
\(191\) | −16.5236 | −1.19561 | −0.597804 | − | 0.801642i | \(-0.703960\pi\) | ||||
−0.597804 | + | 0.801642i | \(0.703960\pi\) | |||||||
\(192\) | −10.2543 | −0.740043 | ||||||||
\(193\) | −0.896292 | −0.0645165 | −0.0322583 | − | 0.999480i | \(-0.510270\pi\) | ||||
−0.0322583 | + | 0.999480i | \(0.510270\pi\) | |||||||
\(194\) | −0.457997 | −0.0328823 | ||||||||
\(195\) | −9.00514 | −0.644872 | ||||||||
\(196\) | −17.2376 | −1.23125 | ||||||||
\(197\) | 5.69587 | 0.405814 | 0.202907 | − | 0.979198i | \(-0.434961\pi\) | ||||
0.202907 | + | 0.979198i | \(0.434961\pi\) | |||||||
\(198\) | 13.2052 | 0.938449 | ||||||||
\(199\) | −5.86630 | −0.415851 | −0.207926 | − | 0.978145i | \(-0.566671\pi\) | ||||
−0.207926 | + | 0.978145i | \(0.566671\pi\) | |||||||
\(200\) | −35.4507 | −2.50675 | ||||||||
\(201\) | 5.06876 | 0.357523 | ||||||||
\(202\) | 5.01211 | 0.352651 | ||||||||
\(203\) | 9.21613 | 0.646846 | ||||||||
\(204\) | 6.58409 | 0.460978 | ||||||||
\(205\) | −12.4247 | −0.867778 | ||||||||
\(206\) | 15.2147 | 1.06006 | ||||||||
\(207\) | 2.37973 | 0.165403 | ||||||||
\(208\) | −0.771513 | −0.0534948 | ||||||||
\(209\) | −8.41962 | −0.582397 | ||||||||
\(210\) | 9.58334 | 0.661313 | ||||||||
\(211\) | 11.7676 | 0.810116 | 0.405058 | − | 0.914291i | \(-0.367251\pi\) | ||||
0.405058 | + | 0.914291i | \(0.367251\pi\) | |||||||
\(212\) | 19.1925 | 1.31815 | ||||||||
\(213\) | 0.487987 | 0.0334363 | ||||||||
\(214\) | −35.2416 | −2.40906 | ||||||||
\(215\) | 36.3836 | 2.48134 | ||||||||
\(216\) | 11.2772 | 0.767317 | ||||||||
\(217\) | −11.6353 | −0.789855 | ||||||||
\(218\) | −0.212885 | −0.0144184 | ||||||||
\(219\) | 8.70737 | 0.588389 | ||||||||
\(220\) | −33.1156 | −2.23265 | ||||||||
\(221\) | 7.04402 | 0.473832 | ||||||||
\(222\) | 11.8060 | 0.792367 | ||||||||
\(223\) | 25.3383 | 1.69678 | 0.848390 | − | 0.529372i | \(-0.177572\pi\) | ||||
0.848390 | + | 0.529372i | \(0.177572\pi\) | |||||||
\(224\) | 7.47663 | 0.499554 | ||||||||
\(225\) | −31.6959 | −2.11306 | ||||||||
\(226\) | 34.5630 | 2.29909 | ||||||||
\(227\) | −22.1634 | −1.47104 | −0.735519 | − | 0.677504i | \(-0.763062\pi\) | ||||
−0.735519 | + | 0.677504i | \(0.763062\pi\) | |||||||
\(228\) | −8.61523 | −0.570557 | ||||||||
\(229\) | 0.975720 | 0.0644774 | 0.0322387 | − | 0.999480i | \(-0.489736\pi\) | ||||
0.0322387 | + | 0.999480i | \(0.489736\pi\) | |||||||
\(230\) | −9.73239 | −0.641735 | ||||||||
\(231\) | 2.40295 | 0.158103 | ||||||||
\(232\) | −19.6197 | −1.28810 | ||||||||
\(233\) | 21.7967 | 1.42795 | 0.713974 | − | 0.700172i | \(-0.246893\pi\) | ||||
0.713974 | + | 0.700172i | \(0.246893\pi\) | |||||||
\(234\) | 14.4558 | 0.945006 | ||||||||
\(235\) | −13.4684 | −0.878585 | ||||||||
\(236\) | 12.3742 | 0.805489 | ||||||||
\(237\) | −4.87563 | −0.316706 | ||||||||
\(238\) | −7.49629 | −0.485912 | ||||||||
\(239\) | −25.1787 | −1.62868 | −0.814338 | − | 0.580391i | \(-0.802900\pi\) | ||||
−0.814338 | + | 0.580391i | \(0.802900\pi\) | |||||||
\(240\) | 0.973506 | 0.0628396 | ||||||||
\(241\) | −24.6809 | −1.58984 | −0.794919 | − | 0.606716i | \(-0.792487\pi\) | ||||
−0.794919 | + | 0.606716i | \(0.792487\pi\) | |||||||
\(242\) | 11.4712 | 0.737400 | ||||||||
\(243\) | 15.7054 | 1.00750 | ||||||||
\(244\) | 2.48426 | 0.159038 | ||||||||
\(245\) | 23.2700 | 1.48667 | ||||||||
\(246\) | −5.19867 | −0.331455 | ||||||||
\(247\) | −9.21704 | −0.586466 | ||||||||
\(248\) | 24.7697 | 1.57288 | ||||||||
\(249\) | −10.6412 | −0.674356 | ||||||||
\(250\) | 80.9648 | 5.12067 | ||||||||
\(251\) | 28.2330 | 1.78205 | 0.891024 | − | 0.453956i | \(-0.149988\pi\) | ||||
0.891024 | + | 0.453956i | \(0.149988\pi\) | |||||||
\(252\) | −9.43334 | −0.594244 | ||||||||
\(253\) | −2.44033 | −0.153422 | ||||||||
\(254\) | −29.2604 | −1.83596 | ||||||||
\(255\) | −8.88824 | −0.556603 | ||||||||
\(256\) | −14.0853 | −0.880331 | ||||||||
\(257\) | 14.8114 | 0.923912 | 0.461956 | − | 0.886903i | \(-0.347148\pi\) | ||||
0.461956 | + | 0.886903i | \(0.347148\pi\) | |||||||
\(258\) | 15.2234 | 0.947769 | ||||||||
\(259\) | −8.24234 | −0.512154 | ||||||||
\(260\) | −36.2520 | −2.24825 | ||||||||
\(261\) | −17.5416 | −1.08580 | ||||||||
\(262\) | 5.83808 | 0.360678 | ||||||||
\(263\) | −16.3895 | −1.01062 | −0.505309 | − | 0.862939i | \(-0.668621\pi\) | ||||
−0.505309 | + | 0.862939i | \(0.668621\pi\) | |||||||
\(264\) | −5.11552 | −0.314838 | ||||||||
\(265\) | −25.9091 | −1.59158 | ||||||||
\(266\) | 9.80884 | 0.601419 | ||||||||
\(267\) | −1.03589 | −0.0633957 | ||||||||
\(268\) | 20.4053 | 1.24645 | ||||||||
\(269\) | −24.4249 | −1.48921 | −0.744605 | − | 0.667505i | \(-0.767362\pi\) | ||||
−0.744605 | + | 0.667505i | \(0.767362\pi\) | |||||||
\(270\) | −41.2355 | −2.50951 | ||||||||
\(271\) | −8.50273 | −0.516504 | −0.258252 | − | 0.966078i | \(-0.583146\pi\) | ||||
−0.258252 | + | 0.966078i | \(0.583146\pi\) | |||||||
\(272\) | −0.761498 | −0.0461726 | ||||||||
\(273\) | 2.63054 | 0.159207 | ||||||||
\(274\) | −3.90960 | −0.236187 | ||||||||
\(275\) | 32.5030 | 1.96001 | ||||||||
\(276\) | −2.49702 | −0.150303 | ||||||||
\(277\) | −22.8741 | −1.37437 | −0.687186 | − | 0.726481i | \(-0.741154\pi\) | ||||
−0.687186 | + | 0.726481i | \(0.741154\pi\) | |||||||
\(278\) | −48.8481 | −2.92971 | ||||||||
\(279\) | 22.1462 | 1.32586 | ||||||||
\(280\) | 14.2432 | 0.851196 | ||||||||
\(281\) | −10.3974 | −0.620259 | −0.310129 | − | 0.950694i | \(-0.600372\pi\) | ||||
−0.310129 | + | 0.950694i | \(0.600372\pi\) | |||||||
\(282\) | −5.63539 | −0.335583 | ||||||||
\(283\) | −7.61323 | −0.452559 | −0.226280 | − | 0.974062i | \(-0.572656\pi\) | ||||
−0.226280 | + | 0.974062i | \(0.572656\pi\) | |||||||
\(284\) | 1.96449 | 0.116571 | ||||||||
\(285\) | 11.6302 | 0.688913 | ||||||||
\(286\) | −14.8239 | −0.876558 | ||||||||
\(287\) | 3.62944 | 0.214239 | ||||||||
\(288\) | −14.2307 | −0.838554 | ||||||||
\(289\) | −10.0474 | −0.591025 | ||||||||
\(290\) | 71.7402 | 4.21273 | ||||||||
\(291\) | 0.158630 | 0.00929907 | ||||||||
\(292\) | 35.0532 | 2.05133 | ||||||||
\(293\) | 27.1230 | 1.58454 | 0.792270 | − | 0.610170i | \(-0.208899\pi\) | ||||
0.792270 | + | 0.610170i | \(0.208899\pi\) | |||||||
\(294\) | 9.73649 | 0.567844 | ||||||||
\(295\) | −16.7046 | −0.972579 | ||||||||
\(296\) | 17.5467 | 1.01988 | ||||||||
\(297\) | −10.3395 | −0.599959 | ||||||||
\(298\) | −7.16505 | −0.415060 | ||||||||
\(299\) | −2.67145 | −0.154494 | ||||||||
\(300\) | 33.2581 | 1.92016 | ||||||||
\(301\) | −10.6282 | −0.612600 | ||||||||
\(302\) | −27.2171 | −1.56617 | ||||||||
\(303\) | −1.73598 | −0.0997293 | ||||||||
\(304\) | 0.996414 | 0.0571482 | ||||||||
\(305\) | −3.35364 | −0.192029 | ||||||||
\(306\) | 14.2682 | 0.815656 | ||||||||
\(307\) | −19.8534 | −1.13309 | −0.566547 | − | 0.824029i | \(-0.691721\pi\) | ||||
−0.566547 | + | 0.824029i | \(0.691721\pi\) | |||||||
\(308\) | 9.67356 | 0.551202 | ||||||||
\(309\) | −5.26972 | −0.299784 | ||||||||
\(310\) | −90.5714 | −5.14411 | ||||||||
\(311\) | −6.48325 | −0.367632 | −0.183816 | − | 0.982961i | \(-0.558845\pi\) | ||||
−0.183816 | + | 0.982961i | \(0.558845\pi\) | |||||||
\(312\) | −5.60001 | −0.317038 | ||||||||
\(313\) | −10.6090 | −0.599656 | −0.299828 | − | 0.953993i | \(-0.596929\pi\) | ||||
−0.299828 | + | 0.953993i | \(0.596929\pi\) | |||||||
\(314\) | −36.6076 | −2.06588 | ||||||||
\(315\) | 12.7346 | 0.717514 | ||||||||
\(316\) | −19.6278 | −1.10415 | ||||||||
\(317\) | −17.2767 | −0.970356 | −0.485178 | − | 0.874415i | \(-0.661245\pi\) | ||||
−0.485178 | + | 0.874415i | \(0.661245\pi\) | |||||||
\(318\) | −10.8407 | −0.607917 | ||||||||
\(319\) | 17.9883 | 1.00715 | ||||||||
\(320\) | 55.7274 | 3.11526 | ||||||||
\(321\) | 12.2062 | 0.681281 | ||||||||
\(322\) | 2.84298 | 0.158433 | ||||||||
\(323\) | −9.09739 | −0.506192 | ||||||||
\(324\) | 12.0553 | 0.669738 | ||||||||
\(325\) | 35.5814 | 1.97370 | ||||||||
\(326\) | 0.611722 | 0.0338802 | ||||||||
\(327\) | 0.0737340 | 0.00407750 | ||||||||
\(328\) | −7.72652 | −0.426625 | ||||||||
\(329\) | 3.93434 | 0.216907 | ||||||||
\(330\) | 18.7051 | 1.02968 | ||||||||
\(331\) | −27.1881 | −1.49439 | −0.747196 | − | 0.664604i | \(-0.768600\pi\) | ||||
−0.747196 | + | 0.664604i | \(0.768600\pi\) | |||||||
\(332\) | −42.8381 | −2.35104 | ||||||||
\(333\) | 15.6881 | 0.859705 | ||||||||
\(334\) | −23.5839 | −1.29045 | ||||||||
\(335\) | −27.5463 | −1.50502 | ||||||||
\(336\) | −0.284376 | −0.0155140 | ||||||||
\(337\) | 4.48772 | 0.244462 | 0.122231 | − | 0.992502i | \(-0.460995\pi\) | ||||
0.122231 | + | 0.992502i | \(0.460995\pi\) | |||||||
\(338\) | 13.3325 | 0.725194 | ||||||||
\(339\) | −11.9711 | −0.650182 | ||||||||
\(340\) | −35.7814 | −1.94052 | ||||||||
\(341\) | −22.7101 | −1.22982 | ||||||||
\(342\) | −18.6698 | −1.00955 | ||||||||
\(343\) | −15.5495 | −0.839591 | ||||||||
\(344\) | 22.6258 | 1.21990 | ||||||||
\(345\) | 3.37088 | 0.181482 | ||||||||
\(346\) | −40.4375 | −2.17393 | ||||||||
\(347\) | 1.50060 | 0.0805564 | 0.0402782 | − | 0.999189i | \(-0.487176\pi\) | ||||
0.0402782 | + | 0.999189i | \(0.487176\pi\) | |||||||
\(348\) | 18.4063 | 0.986679 | ||||||||
\(349\) | −1.00000 | −0.0535288 | ||||||||
\(350\) | −37.8659 | −2.02402 | ||||||||
\(351\) | −11.3188 | −0.604151 | ||||||||
\(352\) | 14.5931 | 0.777817 | ||||||||
\(353\) | 15.8373 | 0.842934 | 0.421467 | − | 0.906844i | \(-0.361515\pi\) | ||||
0.421467 | + | 0.906844i | \(0.361515\pi\) | |||||||
\(354\) | −6.98944 | −0.371484 | ||||||||
\(355\) | −2.65198 | −0.140752 | ||||||||
\(356\) | −4.17020 | −0.221020 | ||||||||
\(357\) | 2.59639 | 0.137416 | ||||||||
\(358\) | −52.1218 | −2.75472 | ||||||||
\(359\) | −25.7781 | −1.36052 | −0.680258 | − | 0.732972i | \(-0.738132\pi\) | ||||
−0.680258 | + | 0.732972i | \(0.738132\pi\) | |||||||
\(360\) | −27.1100 | −1.42882 | ||||||||
\(361\) | −7.09614 | −0.373481 | ||||||||
\(362\) | 44.4963 | 2.33867 | ||||||||
\(363\) | −3.97314 | −0.208536 | ||||||||
\(364\) | 10.5897 | 0.555053 | ||||||||
\(365\) | −47.3204 | −2.47686 | ||||||||
\(366\) | −1.40321 | −0.0733470 | ||||||||
\(367\) | −9.60812 | −0.501540 | −0.250770 | − | 0.968047i | \(-0.580684\pi\) | ||||
−0.250770 | + | 0.968047i | \(0.580684\pi\) | |||||||
\(368\) | 0.288799 | 0.0150547 | ||||||||
\(369\) | −6.90814 | −0.359623 | ||||||||
\(370\) | −64.1599 | −3.33552 | ||||||||
\(371\) | 7.56843 | 0.392933 | ||||||||
\(372\) | −23.2378 | −1.20482 | ||||||||
\(373\) | −0.209451 | −0.0108450 | −0.00542248 | − | 0.999985i | \(-0.501726\pi\) | ||||
−0.00542248 | + | 0.999985i | \(0.501726\pi\) | |||||||
\(374\) | −14.6315 | −0.756577 | ||||||||
\(375\) | −28.0427 | −1.44812 | ||||||||
\(376\) | −8.37559 | −0.431938 | ||||||||
\(377\) | 19.6920 | 1.01419 | ||||||||
\(378\) | 12.0455 | 0.619554 | ||||||||
\(379\) | −18.0633 | −0.927849 | −0.463925 | − | 0.885875i | \(-0.653559\pi\) | ||||
−0.463925 | + | 0.885875i | \(0.653559\pi\) | |||||||
\(380\) | 46.8196 | 2.40180 | ||||||||
\(381\) | 10.1345 | 0.519208 | ||||||||
\(382\) | 37.5728 | 1.92239 | ||||||||
\(383\) | 19.0299 | 0.972384 | 0.486192 | − | 0.873852i | \(-0.338386\pi\) | ||||
0.486192 | + | 0.873852i | \(0.338386\pi\) | |||||||
\(384\) | 13.8978 | 0.709218 | ||||||||
\(385\) | −13.0589 | −0.665543 | ||||||||
\(386\) | 2.03806 | 0.103735 | ||||||||
\(387\) | 20.2293 | 1.02831 | ||||||||
\(388\) | 0.638597 | 0.0324199 | ||||||||
\(389\) | 27.6343 | 1.40111 | 0.700556 | − | 0.713597i | \(-0.252935\pi\) | ||||
0.700556 | + | 0.713597i | \(0.252935\pi\) | |||||||
\(390\) | 20.4766 | 1.03687 | ||||||||
\(391\) | −2.63677 | −0.133347 | ||||||||
\(392\) | 14.4709 | 0.730888 | ||||||||
\(393\) | −2.02206 | −0.101999 | ||||||||
\(394\) | −12.9517 | −0.652498 | ||||||||
\(395\) | 26.4967 | 1.33319 | ||||||||
\(396\) | −18.4123 | −0.925252 | ||||||||
\(397\) | −34.8216 | −1.74764 | −0.873822 | − | 0.486245i | \(-0.838366\pi\) | ||||
−0.873822 | + | 0.486245i | \(0.838366\pi\) | |||||||
\(398\) | 13.3393 | 0.668637 | ||||||||
\(399\) | −3.39736 | −0.170081 | ||||||||
\(400\) | −3.84655 | −0.192327 | ||||||||
\(401\) | 21.5855 | 1.07793 | 0.538964 | − | 0.842329i | \(-0.318816\pi\) | ||||
0.538964 | + | 0.842329i | \(0.318816\pi\) | |||||||
\(402\) | −11.5258 | −0.574853 | ||||||||
\(403\) | −24.8610 | −1.23842 | ||||||||
\(404\) | −6.98852 | −0.347692 | ||||||||
\(405\) | −16.2741 | −0.808668 | ||||||||
\(406\) | −20.9564 | −1.04005 | ||||||||
\(407\) | −16.0877 | −0.797435 | ||||||||
\(408\) | −5.52731 | −0.273643 | ||||||||
\(409\) | 23.6939 | 1.17159 | 0.585794 | − | 0.810460i | \(-0.300783\pi\) | ||||
0.585794 | + | 0.810460i | \(0.300783\pi\) | |||||||
\(410\) | 28.2523 | 1.39528 | ||||||||
\(411\) | 1.35411 | 0.0667935 | ||||||||
\(412\) | −21.2143 | −1.04515 | ||||||||
\(413\) | 4.87966 | 0.240113 | ||||||||
\(414\) | −5.41122 | −0.265947 | ||||||||
\(415\) | 57.8296 | 2.83874 | ||||||||
\(416\) | 15.9752 | 0.783251 | ||||||||
\(417\) | 16.9189 | 0.828520 | ||||||||
\(418\) | 19.1452 | 0.936423 | ||||||||
\(419\) | 16.6173 | 0.811808 | 0.405904 | − | 0.913916i | \(-0.366957\pi\) | ||||
0.405904 | + | 0.913916i | \(0.366957\pi\) | |||||||
\(420\) | −13.3623 | −0.652013 | ||||||||
\(421\) | 8.12051 | 0.395769 | 0.197885 | − | 0.980225i | \(-0.436593\pi\) | ||||
0.197885 | + | 0.980225i | \(0.436593\pi\) | |||||||
\(422\) | −26.7582 | −1.30257 | ||||||||
\(423\) | −7.48847 | −0.364102 | ||||||||
\(424\) | −16.1120 | −0.782469 | ||||||||
\(425\) | 35.1195 | 1.70354 | ||||||||
\(426\) | −1.10962 | −0.0537615 | ||||||||
\(427\) | 0.979650 | 0.0474086 | ||||||||
\(428\) | 49.1382 | 2.37519 | ||||||||
\(429\) | 5.13437 | 0.247890 | ||||||||
\(430\) | −82.7320 | −3.98969 | ||||||||
\(431\) | 10.8759 | 0.523873 | 0.261937 | − | 0.965085i | \(-0.415639\pi\) | ||||
0.261937 | + | 0.965085i | \(0.415639\pi\) | |||||||
\(432\) | 1.22362 | 0.0588715 | ||||||||
\(433\) | 35.2088 | 1.69203 | 0.846014 | − | 0.533161i | \(-0.178996\pi\) | ||||
0.846014 | + | 0.533161i | \(0.178996\pi\) | |||||||
\(434\) | 26.4573 | 1.26999 | ||||||||
\(435\) | −24.8477 | −1.19135 | ||||||||
\(436\) | 0.296831 | 0.0142156 | ||||||||
\(437\) | 3.45020 | 0.165045 | ||||||||
\(438\) | −19.7995 | −0.946057 | ||||||||
\(439\) | 25.8833 | 1.23534 | 0.617670 | − | 0.786437i | \(-0.288077\pi\) | ||||
0.617670 | + | 0.786437i | \(0.288077\pi\) | |||||||
\(440\) | 27.8004 | 1.32533 | ||||||||
\(441\) | 12.9381 | 0.616101 | ||||||||
\(442\) | −16.0172 | −0.761863 | ||||||||
\(443\) | −35.1901 | −1.67193 | −0.835965 | − | 0.548782i | \(-0.815092\pi\) | ||||
−0.835965 | + | 0.548782i | \(0.815092\pi\) | |||||||
\(444\) | −16.4614 | −0.781224 | ||||||||
\(445\) | 5.62959 | 0.266868 | ||||||||
\(446\) | −57.6163 | −2.72821 | ||||||||
\(447\) | 2.48166 | 0.117379 | ||||||||
\(448\) | −16.2788 | −0.769102 | ||||||||
\(449\) | −8.97668 | −0.423636 | −0.211818 | − | 0.977309i | \(-0.567938\pi\) | ||||
−0.211818 | + | 0.977309i | \(0.567938\pi\) | |||||||
\(450\) | 72.0726 | 3.39753 | ||||||||
\(451\) | 7.08406 | 0.333575 | ||||||||
\(452\) | −48.1921 | −2.26676 | ||||||||
\(453\) | 9.42683 | 0.442911 | ||||||||
\(454\) | 50.3970 | 2.36525 | ||||||||
\(455\) | −14.2957 | −0.670193 | ||||||||
\(456\) | 7.23244 | 0.338690 | ||||||||
\(457\) | −17.6964 | −0.827803 | −0.413902 | − | 0.910322i | \(-0.635834\pi\) | ||||
−0.413902 | + | 0.910322i | \(0.635834\pi\) | |||||||
\(458\) | −2.21867 | −0.103672 | ||||||||
\(459\) | −11.1718 | −0.521456 | ||||||||
\(460\) | 13.5701 | 0.632711 | ||||||||
\(461\) | −11.3698 | −0.529542 | −0.264771 | − | 0.964311i | \(-0.585296\pi\) | ||||
−0.264771 | + | 0.964311i | \(0.585296\pi\) | |||||||
\(462\) | −5.46403 | −0.254210 | ||||||||
\(463\) | 33.8439 | 1.57286 | 0.786431 | − | 0.617679i | \(-0.211927\pi\) | ||||
0.786431 | + | 0.617679i | \(0.211927\pi\) | |||||||
\(464\) | −2.12882 | −0.0988279 | ||||||||
\(465\) | 31.3700 | 1.45475 | ||||||||
\(466\) | −49.5630 | −2.29596 | ||||||||
\(467\) | −4.76103 | −0.220314 | −0.110157 | − | 0.993914i | \(-0.535135\pi\) | ||||
−0.110157 | + | 0.993914i | \(0.535135\pi\) | |||||||
\(468\) | −20.1561 | −0.931717 | ||||||||
\(469\) | 8.04669 | 0.371562 | ||||||||
\(470\) | 30.6256 | 1.41266 | ||||||||
\(471\) | 12.6793 | 0.584230 | ||||||||
\(472\) | −10.3880 | −0.478149 | ||||||||
\(473\) | −20.7445 | −0.953832 | ||||||||
\(474\) | 11.0866 | 0.509224 | ||||||||
\(475\) | −45.9536 | −2.10849 | ||||||||
\(476\) | 10.4523 | 0.479079 | ||||||||
\(477\) | −14.4055 | −0.659581 | ||||||||
\(478\) | 57.2534 | 2.61871 | ||||||||
\(479\) | −3.63253 | −0.165975 | −0.0829874 | − | 0.996551i | \(-0.526446\pi\) | ||||
−0.0829874 | + | 0.996551i | \(0.526446\pi\) | |||||||
\(480\) | −20.1578 | −0.920074 | ||||||||
\(481\) | −17.6113 | −0.803007 | ||||||||
\(482\) | 56.1214 | 2.55626 | ||||||||
\(483\) | −0.984684 | −0.0448047 | ||||||||
\(484\) | −15.9947 | −0.727030 | ||||||||
\(485\) | −0.862079 | −0.0391450 | ||||||||
\(486\) | −35.7121 | −1.61994 | ||||||||
\(487\) | 2.27769 | 0.103212 | 0.0516060 | − | 0.998668i | \(-0.483566\pi\) | ||||
0.0516060 | + | 0.998668i | \(0.483566\pi\) | |||||||
\(488\) | −2.08552 | −0.0944071 | ||||||||
\(489\) | −0.211874 | −0.00958127 | ||||||||
\(490\) | −52.9132 | −2.39037 | ||||||||
\(491\) | −28.9331 | −1.30573 | −0.652866 | − | 0.757473i | \(-0.726434\pi\) | ||||
−0.652866 | + | 0.757473i | \(0.726434\pi\) | |||||||
\(492\) | 7.24864 | 0.326794 | ||||||||
\(493\) | 19.4364 | 0.875371 | ||||||||
\(494\) | 20.9584 | 0.942965 | ||||||||
\(495\) | 24.8558 | 1.11719 | ||||||||
\(496\) | 2.68761 | 0.120677 | ||||||||
\(497\) | 0.774682 | 0.0347493 | ||||||||
\(498\) | 24.1967 | 1.08428 | ||||||||
\(499\) | −26.9272 | −1.20543 | −0.602714 | − | 0.797957i | \(-0.705914\pi\) | ||||
−0.602714 | + | 0.797957i | \(0.705914\pi\) | |||||||
\(500\) | −112.891 | −5.04866 | ||||||||
\(501\) | 8.16845 | 0.364939 | ||||||||
\(502\) | −64.1984 | −2.86531 | ||||||||
\(503\) | −27.2625 | −1.21558 | −0.607788 | − | 0.794099i | \(-0.707943\pi\) | ||||
−0.607788 | + | 0.794099i | \(0.707943\pi\) | |||||||
\(504\) | 7.91924 | 0.352751 | ||||||||
\(505\) | 9.43421 | 0.419817 | ||||||||
\(506\) | 5.54902 | 0.246684 | ||||||||
\(507\) | −4.61781 | −0.205084 | ||||||||
\(508\) | 40.7985 | 1.81014 | ||||||||
\(509\) | −18.0179 | −0.798628 | −0.399314 | − | 0.916814i | \(-0.630752\pi\) | ||||
−0.399314 | + | 0.916814i | \(0.630752\pi\) | |||||||
\(510\) | 20.2108 | 0.894949 | ||||||||
\(511\) | 13.8230 | 0.611493 | ||||||||
\(512\) | −3.26437 | −0.144266 | ||||||||
\(513\) | 14.6182 | 0.645411 | ||||||||
\(514\) | −33.6794 | −1.48554 | ||||||||
\(515\) | 28.6384 | 1.26196 | ||||||||
\(516\) | −21.2264 | −0.934441 | ||||||||
\(517\) | 7.67916 | 0.337729 | ||||||||
\(518\) | 18.7421 | 0.823480 | ||||||||
\(519\) | 14.0058 | 0.614786 | ||||||||
\(520\) | 30.4334 | 1.33459 | ||||||||
\(521\) | −16.7772 | −0.735024 | −0.367512 | − | 0.930019i | \(-0.619790\pi\) | ||||
−0.367512 | + | 0.930019i | \(0.619790\pi\) | |||||||
\(522\) | 39.8876 | 1.74583 | ||||||||
\(523\) | −11.3706 | −0.497200 | −0.248600 | − | 0.968606i | \(-0.579970\pi\) | ||||
−0.248600 | + | 0.968606i | \(0.579970\pi\) | |||||||
\(524\) | −8.14018 | −0.355606 | ||||||||
\(525\) | 13.1151 | 0.572391 | ||||||||
\(526\) | 37.2677 | 1.62495 | ||||||||
\(527\) | −24.5383 | −1.06890 | ||||||||
\(528\) | −0.555054 | −0.0241556 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 58.9141 | 2.55907 | ||||||||
\(531\) | −9.28777 | −0.403055 | ||||||||
\(532\) | −13.6767 | −0.592961 | ||||||||
\(533\) | 7.75499 | 0.335906 | ||||||||
\(534\) | 2.35550 | 0.101932 | ||||||||
\(535\) | −66.3346 | −2.86789 | ||||||||
\(536\) | −17.1302 | −0.739910 | ||||||||
\(537\) | 18.0527 | 0.779033 | ||||||||
\(538\) | 55.5392 | 2.39447 | ||||||||
\(539\) | −13.2676 | −0.571476 | ||||||||
\(540\) | 57.4957 | 2.47422 | ||||||||
\(541\) | −16.3138 | −0.701384 | −0.350692 | − | 0.936491i | \(-0.614054\pi\) | ||||
−0.350692 | + | 0.936491i | \(0.614054\pi\) | |||||||
\(542\) | 19.3342 | 0.830474 | ||||||||
\(543\) | −15.4116 | −0.661374 | ||||||||
\(544\) | 15.7679 | 0.676042 | ||||||||
\(545\) | −0.400709 | −0.0171645 | ||||||||
\(546\) | −5.98153 | −0.255986 | ||||||||
\(547\) | −38.2131 | −1.63387 | −0.816937 | − | 0.576727i | \(-0.804330\pi\) | ||||
−0.816937 | + | 0.576727i | \(0.804330\pi\) | |||||||
\(548\) | 5.45125 | 0.232866 | ||||||||
\(549\) | −1.86463 | −0.0795803 | ||||||||
\(550\) | −73.9080 | −3.15145 | ||||||||
\(551\) | −25.4324 | −1.08345 | ||||||||
\(552\) | 2.09624 | 0.0892219 | ||||||||
\(553\) | −7.74009 | −0.329142 | ||||||||
\(554\) | 52.0130 | 2.20982 | ||||||||
\(555\) | 22.2222 | 0.943280 | ||||||||
\(556\) | 68.1102 | 2.88851 | ||||||||
\(557\) | −37.9355 | −1.60738 | −0.803688 | − | 0.595050i | \(-0.797132\pi\) | ||||
−0.803688 | + | 0.595050i | \(0.797132\pi\) | |||||||
\(558\) | −50.3577 | −2.13181 | ||||||||
\(559\) | −22.7092 | −0.960496 | ||||||||
\(560\) | 1.54545 | 0.0653070 | ||||||||
\(561\) | 5.06772 | 0.213959 | ||||||||
\(562\) | 23.6425 | 0.997299 | ||||||||
\(563\) | 27.1671 | 1.14496 | 0.572478 | − | 0.819920i | \(-0.305982\pi\) | ||||
0.572478 | + | 0.819920i | \(0.305982\pi\) | |||||||
\(564\) | 7.85757 | 0.330863 | ||||||||
\(565\) | 65.0572 | 2.73698 | ||||||||
\(566\) | 17.3116 | 0.727659 | ||||||||
\(567\) | 4.75392 | 0.199646 | ||||||||
\(568\) | −1.64918 | −0.0691980 | ||||||||
\(569\) | 2.64363 | 0.110827 | 0.0554133 | − | 0.998464i | \(-0.482352\pi\) | ||||
0.0554133 | + | 0.998464i | \(0.482352\pi\) | |||||||
\(570\) | −26.4457 | −1.10769 | ||||||||
\(571\) | 24.1686 | 1.01143 | 0.505713 | − | 0.862702i | \(-0.331230\pi\) | ||||
0.505713 | + | 0.862702i | \(0.331230\pi\) | |||||||
\(572\) | 20.6694 | 0.864231 | ||||||||
\(573\) | −13.0136 | −0.543650 | ||||||||
\(574\) | −8.25291 | −0.344470 | ||||||||
\(575\) | −13.3191 | −0.555445 | ||||||||
\(576\) | 30.9845 | 1.29102 | ||||||||
\(577\) | −26.7917 | −1.11535 | −0.557676 | − | 0.830059i | \(-0.688307\pi\) | ||||
−0.557676 | + | 0.830059i | \(0.688307\pi\) | |||||||
\(578\) | 22.8466 | 0.950295 | ||||||||
\(579\) | −0.705896 | −0.0293360 | ||||||||
\(580\) | −100.029 | −4.15349 | ||||||||
\(581\) | −16.8929 | −0.700835 | ||||||||
\(582\) | −0.360706 | −0.0149518 | ||||||||
\(583\) | 14.7723 | 0.611806 | ||||||||
\(584\) | −29.4270 | −1.21770 | ||||||||
\(585\) | 27.2099 | 1.12499 | ||||||||
\(586\) | −61.6744 | −2.54775 | ||||||||
\(587\) | −21.7750 | −0.898752 | −0.449376 | − | 0.893343i | \(-0.648354\pi\) | ||||
−0.449376 | + | 0.893343i | \(0.648354\pi\) | |||||||
\(588\) | −13.5758 | −0.559858 | ||||||||
\(589\) | 32.1081 | 1.32299 | ||||||||
\(590\) | 37.9842 | 1.56379 | ||||||||
\(591\) | 4.48591 | 0.184526 | ||||||||
\(592\) | 1.90388 | 0.0782490 | ||||||||
\(593\) | −17.0690 | −0.700940 | −0.350470 | − | 0.936574i | \(-0.613978\pi\) | ||||
−0.350470 | + | 0.936574i | \(0.613978\pi\) | |||||||
\(594\) | 23.5108 | 0.964660 | ||||||||
\(595\) | −14.1101 | −0.578459 | ||||||||
\(596\) | 9.99042 | 0.409224 | ||||||||
\(597\) | −4.62014 | −0.189090 | ||||||||
\(598\) | 6.07456 | 0.248407 | ||||||||
\(599\) | −37.5141 | −1.53278 | −0.766392 | − | 0.642373i | \(-0.777950\pi\) | ||||
−0.766392 | + | 0.642373i | \(0.777950\pi\) | |||||||
\(600\) | −27.9201 | −1.13983 | ||||||||
\(601\) | −35.0311 | −1.42895 | −0.714474 | − | 0.699662i | \(-0.753334\pi\) | ||||
−0.714474 | + | 0.699662i | \(0.753334\pi\) | |||||||
\(602\) | 24.1673 | 0.984984 | ||||||||
\(603\) | −15.3158 | −0.623706 | ||||||||
\(604\) | 37.9496 | 1.54415 | ||||||||
\(605\) | 21.5921 | 0.877845 | ||||||||
\(606\) | 3.94741 | 0.160352 | ||||||||
\(607\) | −33.6012 | −1.36383 | −0.681915 | − | 0.731431i | \(-0.738853\pi\) | ||||
−0.681915 | + | 0.731431i | \(0.738853\pi\) | |||||||
\(608\) | −20.6321 | −0.836743 | ||||||||
\(609\) | 7.25838 | 0.294124 | ||||||||
\(610\) | 7.62578 | 0.308759 | ||||||||
\(611\) | 8.40646 | 0.340089 | ||||||||
\(612\) | −19.8945 | −0.804186 | ||||||||
\(613\) | 16.5942 | 0.670234 | 0.335117 | − | 0.942177i | \(-0.391224\pi\) | ||||
0.335117 | + | 0.942177i | \(0.391224\pi\) | |||||||
\(614\) | 45.1443 | 1.82187 | ||||||||
\(615\) | −9.78536 | −0.394584 | ||||||||
\(616\) | −8.12091 | −0.327201 | ||||||||
\(617\) | 15.9693 | 0.642900 | 0.321450 | − | 0.946927i | \(-0.395830\pi\) | ||||
0.321450 | + | 0.946927i | \(0.395830\pi\) | |||||||
\(618\) | 11.9827 | 0.482015 | ||||||||
\(619\) | 19.4694 | 0.782542 | 0.391271 | − | 0.920275i | \(-0.372035\pi\) | ||||
0.391271 | + | 0.920275i | \(0.372035\pi\) | |||||||
\(620\) | 126.286 | 5.07177 | ||||||||
\(621\) | 4.23693 | 0.170022 | ||||||||
\(622\) | 14.7421 | 0.591106 | ||||||||
\(623\) | −1.64449 | −0.0658850 | ||||||||
\(624\) | −0.607623 | −0.0243244 | ||||||||
\(625\) | 85.8031 | 3.43212 | ||||||||
\(626\) | 24.1236 | 0.964173 | ||||||||
\(627\) | −6.63107 | −0.264819 | ||||||||
\(628\) | 51.0429 | 2.03683 | ||||||||
\(629\) | −17.3827 | −0.693093 | ||||||||
\(630\) | −28.9570 | −1.15367 | ||||||||
\(631\) | 30.9048 | 1.23030 | 0.615151 | − | 0.788410i | \(-0.289095\pi\) | ||||
0.615151 | + | 0.788410i | \(0.289095\pi\) | |||||||
\(632\) | 16.4774 | 0.655438 | ||||||||
\(633\) | 9.26786 | 0.368364 | ||||||||
\(634\) | 39.2851 | 1.56021 | ||||||||
\(635\) | −55.0763 | −2.18564 | ||||||||
\(636\) | 15.1155 | 0.599369 | ||||||||
\(637\) | −14.5242 | −0.575469 | ||||||||
\(638\) | −40.9033 | −1.61938 | ||||||||
\(639\) | −1.47450 | −0.0583303 | ||||||||
\(640\) | −75.5278 | −2.98550 | ||||||||
\(641\) | −13.7208 | −0.541937 | −0.270969 | − | 0.962588i | \(-0.587344\pi\) | ||||
−0.270969 | + | 0.962588i | \(0.587344\pi\) | |||||||
\(642\) | −27.7553 | −1.09542 | ||||||||
\(643\) | 31.7679 | 1.25280 | 0.626402 | − | 0.779500i | \(-0.284527\pi\) | ||||
0.626402 | + | 0.779500i | \(0.284527\pi\) | |||||||
\(644\) | −3.96404 | −0.156205 | ||||||||
\(645\) | 28.6548 | 1.12828 | ||||||||
\(646\) | 20.6864 | 0.813895 | ||||||||
\(647\) | −3.92509 | −0.154311 | −0.0771556 | − | 0.997019i | \(-0.524584\pi\) | ||||
−0.0771556 | + | 0.997019i | \(0.524584\pi\) | |||||||
\(648\) | −10.1204 | −0.397565 | ||||||||
\(649\) | 9.52428 | 0.373861 | ||||||||
\(650\) | −80.9078 | −3.17346 | ||||||||
\(651\) | −9.16365 | −0.359152 | ||||||||
\(652\) | −0.852940 | −0.0334037 | ||||||||
\(653\) | −28.6791 | −1.12230 | −0.561151 | − | 0.827714i | \(-0.689641\pi\) | ||||
−0.561151 | + | 0.827714i | \(0.689641\pi\) | |||||||
\(654\) | −0.167662 | −0.00655611 | ||||||||
\(655\) | 10.9889 | 0.429372 | ||||||||
\(656\) | −0.838357 | −0.0327324 | ||||||||
\(657\) | −26.3101 | −1.02646 | ||||||||
\(658\) | −8.94621 | −0.348760 | ||||||||
\(659\) | 38.8836 | 1.51469 | 0.757345 | − | 0.653015i | \(-0.226496\pi\) | ||||
0.757345 | + | 0.653015i | \(0.226496\pi\) | |||||||
\(660\) | −26.0810 | −1.01520 | ||||||||
\(661\) | 27.5299 | 1.07079 | 0.535394 | − | 0.844602i | \(-0.320163\pi\) | ||||
0.535394 | + | 0.844602i | \(0.320163\pi\) | |||||||
\(662\) | 61.8224 | 2.40280 | ||||||||
\(663\) | 5.54768 | 0.215454 | ||||||||
\(664\) | 35.9624 | 1.39561 | ||||||||
\(665\) | 18.4630 | 0.715964 | ||||||||
\(666\) | −35.6730 | −1.38230 | ||||||||
\(667\) | −7.37128 | −0.285417 | ||||||||
\(668\) | 32.8837 | 1.27231 | ||||||||
\(669\) | 19.9558 | 0.771535 | ||||||||
\(670\) | 62.6370 | 2.41988 | ||||||||
\(671\) | 1.91211 | 0.0738162 | ||||||||
\(672\) | 5.88840 | 0.227150 | ||||||||
\(673\) | 7.96647 | 0.307085 | 0.153542 | − | 0.988142i | \(-0.450932\pi\) | ||||
0.153542 | + | 0.988142i | \(0.450932\pi\) | |||||||
\(674\) | −10.2045 | −0.393064 | ||||||||
\(675\) | −56.4321 | −2.17207 | ||||||||
\(676\) | −18.5899 | −0.714996 | ||||||||
\(677\) | −8.55997 | −0.328987 | −0.164493 | − | 0.986378i | \(-0.552599\pi\) | ||||
−0.164493 | + | 0.986378i | \(0.552599\pi\) | |||||||
\(678\) | 27.2209 | 1.04541 | ||||||||
\(679\) | 0.251826 | 0.00966421 | ||||||||
\(680\) | 30.0383 | 1.15192 | ||||||||
\(681\) | −17.4553 | −0.668889 | ||||||||
\(682\) | 51.6401 | 1.97740 | ||||||||
\(683\) | 13.7651 | 0.526705 | 0.263353 | − | 0.964700i | \(-0.415172\pi\) | ||||
0.263353 | + | 0.964700i | \(0.415172\pi\) | |||||||
\(684\) | 26.0317 | 0.995349 | ||||||||
\(685\) | −7.35896 | −0.281171 | ||||||||
\(686\) | 35.3576 | 1.34996 | ||||||||
\(687\) | 0.768451 | 0.0293182 | ||||||||
\(688\) | 2.45499 | 0.0935956 | ||||||||
\(689\) | 16.1714 | 0.616081 | ||||||||
\(690\) | −7.66497 | −0.291801 | ||||||||
\(691\) | 25.0605 | 0.953348 | 0.476674 | − | 0.879080i | \(-0.341842\pi\) | ||||
0.476674 | + | 0.879080i | \(0.341842\pi\) | |||||||
\(692\) | 56.3830 | 2.14336 | ||||||||
\(693\) | −7.26076 | −0.275813 | ||||||||
\(694\) | −3.41218 | −0.129525 | ||||||||
\(695\) | −91.9459 | −3.48771 | ||||||||
\(696\) | −15.4520 | −0.585705 | ||||||||
\(697\) | 7.65432 | 0.289928 | ||||||||
\(698\) | 2.27388 | 0.0860676 | ||||||||
\(699\) | 17.1665 | 0.649296 | ||||||||
\(700\) | 52.7975 | 1.99556 | ||||||||
\(701\) | −8.87842 | −0.335333 | −0.167667 | − | 0.985844i | \(-0.553623\pi\) | ||||
−0.167667 | + | 0.985844i | \(0.553623\pi\) | |||||||
\(702\) | 25.7375 | 0.971399 | ||||||||
\(703\) | 22.7451 | 0.857848 | ||||||||
\(704\) | −31.7735 | −1.19751 | ||||||||
\(705\) | −10.6074 | −0.399497 | ||||||||
\(706\) | −36.0121 | −1.35533 | ||||||||
\(707\) | −2.75587 | −0.103645 | ||||||||
\(708\) | 9.74556 | 0.366260 | ||||||||
\(709\) | −51.5176 | −1.93479 | −0.967393 | − | 0.253281i | \(-0.918490\pi\) | ||||
−0.967393 | + | 0.253281i | \(0.918490\pi\) | |||||||
\(710\) | 6.03028 | 0.226312 | ||||||||
\(711\) | 14.7322 | 0.552500 | ||||||||
\(712\) | 3.50086 | 0.131200 | ||||||||
\(713\) | 9.30618 | 0.348519 | ||||||||
\(714\) | −5.90388 | −0.220947 | ||||||||
\(715\) | −27.9028 | −1.04351 | ||||||||
\(716\) | 72.6748 | 2.71598 | ||||||||
\(717\) | −19.8301 | −0.740568 | ||||||||
\(718\) | 58.6163 | 2.18754 | ||||||||
\(719\) | 34.8274 | 1.29884 | 0.649421 | − | 0.760429i | \(-0.275011\pi\) | ||||
0.649421 | + | 0.760429i | \(0.275011\pi\) | |||||||
\(720\) | −2.94154 | −0.109625 | ||||||||
\(721\) | −8.36571 | −0.311555 | ||||||||
\(722\) | 16.1358 | 0.600511 | ||||||||
\(723\) | −19.4380 | −0.722908 | ||||||||
\(724\) | −62.0423 | −2.30579 | ||||||||
\(725\) | 98.1788 | 3.64627 | ||||||||
\(726\) | 9.03445 | 0.335300 | ||||||||
\(727\) | 24.1001 | 0.893824 | 0.446912 | − | 0.894578i | \(-0.352524\pi\) | ||||
0.446912 | + | 0.894578i | \(0.352524\pi\) | |||||||
\(728\) | −8.89004 | −0.329487 | ||||||||
\(729\) | 0.962255 | 0.0356391 | ||||||||
\(730\) | 107.601 | 3.98249 | ||||||||
\(731\) | −22.4144 | −0.829026 | ||||||||
\(732\) | 1.95653 | 0.0723156 | ||||||||
\(733\) | −29.0018 | −1.07121 | −0.535604 | − | 0.844469i | \(-0.679916\pi\) | ||||
−0.535604 | + | 0.844469i | \(0.679916\pi\) | |||||||
\(734\) | 21.8477 | 0.806414 | ||||||||
\(735\) | 18.3268 | 0.675995 | ||||||||
\(736\) | −5.97998 | −0.220425 | ||||||||
\(737\) | 15.7058 | 0.578530 | ||||||||
\(738\) | 15.7083 | 0.578230 | ||||||||
\(739\) | −36.0770 | −1.32711 | −0.663557 | − | 0.748126i | \(-0.730954\pi\) | ||||
−0.663557 | + | 0.748126i | \(0.730954\pi\) | |||||||
\(740\) | 89.4599 | 3.28861 | ||||||||
\(741\) | −7.25909 | −0.266669 | ||||||||
\(742\) | −17.2097 | −0.631788 | ||||||||
\(743\) | −20.1265 | −0.738370 | −0.369185 | − | 0.929356i | \(-0.620363\pi\) | ||||
−0.369185 | + | 0.929356i | \(0.620363\pi\) | |||||||
\(744\) | 19.5080 | 0.715197 | ||||||||
\(745\) | −13.4866 | −0.494113 | ||||||||
\(746\) | 0.476267 | 0.0174374 | ||||||||
\(747\) | 32.1533 | 1.17643 | ||||||||
\(748\) | 20.4011 | 0.745938 | ||||||||
\(749\) | 19.3773 | 0.708032 | ||||||||
\(750\) | 63.7657 | 2.32840 | ||||||||
\(751\) | 39.9246 | 1.45687 | 0.728435 | − | 0.685115i | \(-0.240248\pi\) | ||||
0.728435 | + | 0.685115i | \(0.240248\pi\) | |||||||
\(752\) | −0.908785 | −0.0331400 | ||||||||
\(753\) | 22.2355 | 0.810307 | ||||||||
\(754\) | −44.7773 | −1.63069 | ||||||||
\(755\) | −51.2303 | −1.86446 | ||||||||
\(756\) | −16.7954 | −0.610841 | ||||||||
\(757\) | −43.2244 | −1.57102 | −0.785508 | − | 0.618851i | \(-0.787598\pi\) | ||||
−0.785508 | + | 0.618851i | \(0.787598\pi\) | |||||||
\(758\) | 41.0738 | 1.49187 | ||||||||
\(759\) | −1.92194 | −0.0697619 | ||||||||
\(760\) | −39.3049 | −1.42574 | ||||||||
\(761\) | −1.59654 | −0.0578746 | −0.0289373 | − | 0.999581i | \(-0.509212\pi\) | ||||
−0.0289373 | + | 0.999581i | \(0.509212\pi\) | |||||||
\(762\) | −23.0447 | −0.834822 | ||||||||
\(763\) | 0.117053 | 0.00423761 | ||||||||
\(764\) | −52.3887 | −1.89536 | ||||||||
\(765\) | 26.8567 | 0.971006 | ||||||||
\(766\) | −43.2718 | −1.56347 | ||||||||
\(767\) | 10.4263 | 0.376473 | ||||||||
\(768\) | −11.0932 | −0.400292 | ||||||||
\(769\) | 27.4309 | 0.989182 | 0.494591 | − | 0.869126i | \(-0.335318\pi\) | ||||
0.494591 | + | 0.869126i | \(0.335318\pi\) | |||||||
\(770\) | 29.6944 | 1.07011 | ||||||||
\(771\) | 11.6651 | 0.420108 | ||||||||
\(772\) | −2.84172 | −0.102276 | ||||||||
\(773\) | 11.5095 | 0.413969 | 0.206984 | − | 0.978344i | \(-0.433635\pi\) | ||||
0.206984 | + | 0.978344i | \(0.433635\pi\) | |||||||
\(774\) | −45.9990 | −1.65340 | ||||||||
\(775\) | −123.950 | −4.45241 | ||||||||
\(776\) | −0.536099 | −0.0192448 | ||||||||
\(777\) | −6.49144 | −0.232879 | ||||||||
\(778\) | −62.8370 | −2.25282 | ||||||||
\(779\) | −10.0156 | −0.358847 | ||||||||
\(780\) | −28.5511 | −1.02229 | ||||||||
\(781\) | 1.51205 | 0.0541054 | ||||||||
\(782\) | 5.99571 | 0.214406 | ||||||||
\(783\) | −31.2316 | −1.11613 | ||||||||
\(784\) | 1.57014 | 0.0560766 | ||||||||
\(785\) | −68.9058 | −2.45935 | ||||||||
\(786\) | 4.59791 | 0.164002 | ||||||||
\(787\) | 13.3807 | 0.476969 | 0.238485 | − | 0.971146i | \(-0.423349\pi\) | ||||
0.238485 | + | 0.971146i | \(0.423349\pi\) | |||||||
\(788\) | 18.0589 | 0.643323 | ||||||||
\(789\) | −12.9079 | −0.459533 | ||||||||
\(790\) | −60.2503 | −2.14361 | ||||||||
\(791\) | −19.0042 | −0.675712 | ||||||||
\(792\) | 15.4570 | 0.549242 | ||||||||
\(793\) | 2.09321 | 0.0743320 | ||||||||
\(794\) | 79.1801 | 2.81000 | ||||||||
\(795\) | −20.4053 | −0.723701 | ||||||||
\(796\) | −18.5993 | −0.659235 | ||||||||
\(797\) | −34.4601 | −1.22064 | −0.610320 | − | 0.792155i | \(-0.708959\pi\) | ||||
−0.610320 | + | 0.792155i | \(0.708959\pi\) | |||||||
\(798\) | 7.72518 | 0.273468 | ||||||||
\(799\) | 8.29733 | 0.293538 | ||||||||
\(800\) | 79.6481 | 2.81598 | ||||||||
\(801\) | 3.13006 | 0.110595 | ||||||||
\(802\) | −49.0828 | −1.73317 | ||||||||
\(803\) | 26.9802 | 0.952109 | ||||||||
\(804\) | 16.0707 | 0.566769 | ||||||||
\(805\) | 5.35129 | 0.188608 | ||||||||
\(806\) | 56.5310 | 1.99122 | ||||||||
\(807\) | −19.2364 | −0.677153 | ||||||||
\(808\) | 5.86683 | 0.206394 | ||||||||
\(809\) | 18.4374 | 0.648223 | 0.324112 | − | 0.946019i | \(-0.394935\pi\) | ||||
0.324112 | + | 0.946019i | \(0.394935\pi\) | |||||||
\(810\) | 37.0054 | 1.30024 | ||||||||
\(811\) | 1.02712 | 0.0360672 | 0.0180336 | − | 0.999837i | \(-0.494259\pi\) | ||||
0.0180336 | + | 0.999837i | \(0.494259\pi\) | |||||||
\(812\) | 29.2200 | 1.02542 | ||||||||
\(813\) | −6.69652 | −0.234857 | ||||||||
\(814\) | 36.5814 | 1.28218 | ||||||||
\(815\) | 1.15143 | 0.0403329 | ||||||||
\(816\) | −0.599735 | −0.0209949 | ||||||||
\(817\) | 29.3290 | 1.02609 | ||||||||
\(818\) | −53.8771 | −1.88377 | ||||||||
\(819\) | −7.94842 | −0.277740 | ||||||||
\(820\) | −39.3929 | −1.37566 | ||||||||
\(821\) | −8.34345 | −0.291188 | −0.145594 | − | 0.989344i | \(-0.546509\pi\) | ||||
−0.145594 | + | 0.989344i | \(0.546509\pi\) | |||||||
\(822\) | −3.07909 | −0.107396 | ||||||||
\(823\) | −9.78040 | −0.340923 | −0.170462 | − | 0.985364i | \(-0.554526\pi\) | ||||
−0.170462 | + | 0.985364i | \(0.554526\pi\) | |||||||
\(824\) | 17.8093 | 0.620416 | ||||||||
\(825\) | 25.5985 | 0.891226 | ||||||||
\(826\) | −11.0958 | −0.386071 | ||||||||
\(827\) | −23.1805 | −0.806064 | −0.403032 | − | 0.915186i | \(-0.632044\pi\) | ||||
−0.403032 | + | 0.915186i | \(0.632044\pi\) | |||||||
\(828\) | 7.54500 | 0.262207 | ||||||||
\(829\) | −46.2579 | −1.60660 | −0.803302 | − | 0.595572i | \(-0.796925\pi\) | ||||
−0.803302 | + | 0.595572i | \(0.796925\pi\) | |||||||
\(830\) | −131.498 | −4.56435 | ||||||||
\(831\) | −18.0150 | −0.624935 | ||||||||
\(832\) | −34.7828 | −1.20588 | ||||||||
\(833\) | −14.3356 | −0.496700 | ||||||||
\(834\) | −38.4714 | −1.33216 | ||||||||
\(835\) | −44.3916 | −1.53623 | ||||||||
\(836\) | −26.6947 | −0.923254 | ||||||||
\(837\) | 39.4296 | 1.36289 | ||||||||
\(838\) | −37.7857 | −1.30529 | ||||||||
\(839\) | −8.14768 | −0.281289 | −0.140645 | − | 0.990060i | \(-0.544917\pi\) | ||||
−0.140645 | + | 0.990060i | \(0.544917\pi\) | |||||||
\(840\) | 11.2176 | 0.387043 | ||||||||
\(841\) | 25.3357 | 0.873645 | ||||||||
\(842\) | −18.4651 | −0.636348 | ||||||||
\(843\) | −8.18874 | −0.282035 | ||||||||
\(844\) | 37.3096 | 1.28425 | ||||||||
\(845\) | 25.0956 | 0.863314 | ||||||||
\(846\) | 17.0279 | 0.585430 | ||||||||
\(847\) | −6.30738 | −0.216724 | ||||||||
\(848\) | −1.74822 | −0.0600340 | ||||||||
\(849\) | −5.99597 | −0.205781 | ||||||||
\(850\) | −79.8575 | −2.73909 | ||||||||
\(851\) | 6.59241 | 0.225985 | ||||||||
\(852\) | 1.54718 | 0.0530055 | ||||||||
\(853\) | −25.2300 | −0.863859 | −0.431930 | − | 0.901907i | \(-0.642167\pi\) | ||||
−0.431930 | + | 0.901907i | \(0.642167\pi\) | |||||||
\(854\) | −2.22761 | −0.0762271 | ||||||||
\(855\) | −35.1418 | −1.20182 | ||||||||
\(856\) | −41.2513 | −1.40994 | ||||||||
\(857\) | −7.64134 | −0.261023 | −0.130512 | − | 0.991447i | \(-0.541662\pi\) | ||||
−0.130512 | + | 0.991447i | \(0.541662\pi\) | |||||||
\(858\) | −11.6749 | −0.398576 | ||||||||
\(859\) | 26.3385 | 0.898658 | 0.449329 | − | 0.893366i | \(-0.351663\pi\) | ||||
0.449329 | + | 0.893366i | \(0.351663\pi\) | |||||||
\(860\) | 115.355 | 3.93359 | ||||||||
\(861\) | 2.85845 | 0.0974157 | ||||||||
\(862\) | −24.7305 | −0.842324 | ||||||||
\(863\) | −44.3325 | −1.50909 | −0.754547 | − | 0.656246i | \(-0.772144\pi\) | ||||
−0.754547 | + | 0.656246i | \(0.772144\pi\) | |||||||
\(864\) | −25.3368 | −0.861975 | ||||||||
\(865\) | −76.1147 | −2.58798 | ||||||||
\(866\) | −80.0606 | −2.72057 | ||||||||
\(867\) | −7.91308 | −0.268742 | ||||||||
\(868\) | −36.8901 | −1.25213 | ||||||||
\(869\) | −15.1073 | −0.512482 | ||||||||
\(870\) | 56.5006 | 1.91555 | ||||||||
\(871\) | 17.1933 | 0.582572 | ||||||||
\(872\) | −0.249188 | −0.00843857 | ||||||||
\(873\) | −0.479317 | −0.0162224 | ||||||||
\(874\) | −7.84534 | −0.265372 | ||||||||
\(875\) | −44.5179 | −1.50498 | ||||||||
\(876\) | 27.6070 | 0.932753 | ||||||||
\(877\) | −21.9031 | −0.739616 | −0.369808 | − | 0.929108i | \(-0.620577\pi\) | ||||
−0.369808 | + | 0.929108i | \(0.620577\pi\) | |||||||
\(878\) | −58.8554 | −1.98627 | ||||||||
\(879\) | 21.3613 | 0.720500 | ||||||||
\(880\) | 3.01645 | 0.101685 | ||||||||
\(881\) | 38.2893 | 1.29000 | 0.645000 | − | 0.764182i | \(-0.276857\pi\) | ||||
0.645000 | + | 0.764182i | \(0.276857\pi\) | |||||||
\(882\) | −29.4197 | −0.990614 | ||||||||
\(883\) | −3.05985 | −0.102972 | −0.0514860 | − | 0.998674i | \(-0.516396\pi\) | ||||
−0.0514860 | + | 0.998674i | \(0.516396\pi\) | |||||||
\(884\) | 22.3333 | 0.751149 | ||||||||
\(885\) | −13.1561 | −0.442237 | ||||||||
\(886\) | 80.0180 | 2.68826 | ||||||||
\(887\) | −7.29589 | −0.244972 | −0.122486 | − | 0.992470i | \(-0.539087\pi\) | ||||
−0.122486 | + | 0.992470i | \(0.539087\pi\) | |||||||
\(888\) | 13.8193 | 0.463744 | ||||||||
\(889\) | 16.0886 | 0.539595 | ||||||||
\(890\) | −12.8010 | −0.429091 | ||||||||
\(891\) | 9.27885 | 0.310853 | ||||||||
\(892\) | 80.3359 | 2.68985 | ||||||||
\(893\) | −10.8570 | −0.363315 | ||||||||
\(894\) | −5.64300 | −0.188730 | ||||||||
\(895\) | −98.1079 | −3.27939 | ||||||||
\(896\) | 22.0628 | 0.737066 | ||||||||
\(897\) | −2.10396 | −0.0702493 | ||||||||
\(898\) | 20.4119 | 0.681154 | ||||||||
\(899\) | −68.5984 | −2.28788 | ||||||||
\(900\) | −100.493 | −3.34976 | ||||||||
\(901\) | 15.9615 | 0.531753 | ||||||||
\(902\) | −16.1083 | −0.536348 | ||||||||
\(903\) | −8.37049 | −0.278553 | ||||||||
\(904\) | 40.4570 | 1.34558 | ||||||||
\(905\) | 83.7545 | 2.78410 | ||||||||
\(906\) | −21.4355 | −0.712146 | ||||||||
\(907\) | −38.2560 | −1.27027 | −0.635135 | − | 0.772401i | \(-0.719056\pi\) | ||||
−0.635135 | + | 0.772401i | \(0.719056\pi\) | |||||||
\(908\) | −70.2698 | −2.33199 | ||||||||
\(909\) | 5.24542 | 0.173980 | ||||||||
\(910\) | 32.5067 | 1.07759 | ||||||||
\(911\) | 45.1729 | 1.49665 | 0.748323 | − | 0.663335i | \(-0.230860\pi\) | ||||
0.748323 | + | 0.663335i | \(0.230860\pi\) | |||||||
\(912\) | 0.784749 | 0.0259856 | ||||||||
\(913\) | −32.9721 | −1.09122 | ||||||||
\(914\) | 40.2395 | 1.33100 | ||||||||
\(915\) | −2.64124 | −0.0873167 | ||||||||
\(916\) | 3.09355 | 0.102214 | ||||||||
\(917\) | −3.21003 | −0.106004 | ||||||||
\(918\) | 25.4034 | 0.838437 | ||||||||
\(919\) | −37.5627 | −1.23908 | −0.619539 | − | 0.784966i | \(-0.712680\pi\) | ||||
−0.619539 | + | 0.784966i | \(0.712680\pi\) | |||||||
\(920\) | −11.3921 | −0.375585 | ||||||||
\(921\) | −15.6360 | −0.515224 | ||||||||
\(922\) | 25.8535 | 0.851439 | ||||||||
\(923\) | 1.65526 | 0.0544834 | ||||||||
\(924\) | 7.61864 | 0.250635 | ||||||||
\(925\) | −87.8050 | −2.88701 | ||||||||
\(926\) | −76.9571 | −2.52897 | ||||||||
\(927\) | 15.9230 | 0.522979 | ||||||||
\(928\) | 44.0801 | 1.44700 | ||||||||
\(929\) | −45.7850 | −1.50216 | −0.751078 | − | 0.660214i | \(-0.770466\pi\) | ||||
−0.751078 | + | 0.660214i | \(0.770466\pi\) | |||||||
\(930\) | −71.3316 | −2.33906 | ||||||||
\(931\) | 18.7581 | 0.614771 | ||||||||
\(932\) | 69.1070 | 2.26368 | ||||||||
\(933\) | −5.10604 | −0.167164 | ||||||||
\(934\) | 10.8260 | 0.354238 | ||||||||
\(935\) | −27.5406 | −0.900674 | ||||||||
\(936\) | 16.9210 | 0.553079 | ||||||||
\(937\) | −46.4090 | −1.51612 | −0.758059 | − | 0.652186i | \(-0.773852\pi\) | ||||
−0.758059 | + | 0.652186i | \(0.773852\pi\) | |||||||
\(938\) | −18.2972 | −0.597425 | ||||||||
\(939\) | −8.35537 | −0.272667 | ||||||||
\(940\) | −42.7021 | −1.39279 | ||||||||
\(941\) | −44.1426 | −1.43901 | −0.719504 | − | 0.694489i | \(-0.755631\pi\) | ||||
−0.719504 | + | 0.694489i | \(0.755631\pi\) | |||||||
\(942\) | −28.8311 | −0.939369 | ||||||||
\(943\) | −2.90291 | −0.0945318 | ||||||||
\(944\) | −1.12714 | −0.0366854 | ||||||||
\(945\) | 22.6730 | 0.737554 | ||||||||
\(946\) | 47.1704 | 1.53364 | ||||||||
\(947\) | 32.7680 | 1.06482 | 0.532408 | − | 0.846488i | \(-0.321287\pi\) | ||||
0.532408 | + | 0.846488i | \(0.321287\pi\) | |||||||
\(948\) | −15.4583 | −0.502063 | ||||||||
\(949\) | 29.5354 | 0.958761 | ||||||||
\(950\) | 104.493 | 3.39020 | ||||||||
\(951\) | −13.6067 | −0.441226 | ||||||||
\(952\) | −8.77464 | −0.284388 | ||||||||
\(953\) | 24.9222 | 0.807310 | 0.403655 | − | 0.914911i | \(-0.367740\pi\) | ||||
0.403655 | + | 0.914911i | \(0.367740\pi\) | |||||||
\(954\) | 32.7563 | 1.06052 | ||||||||
\(955\) | 70.7226 | 2.28853 | ||||||||
\(956\) | −79.8299 | −2.58188 | ||||||||
\(957\) | 14.1671 | 0.457959 | ||||||||
\(958\) | 8.25995 | 0.266867 | ||||||||
\(959\) | 2.14966 | 0.0694163 | ||||||||
\(960\) | 43.8894 | 1.41652 | ||||||||
\(961\) | 55.6049 | 1.79371 | ||||||||
\(962\) | 40.0460 | 1.29114 | ||||||||
\(963\) | −36.8821 | −1.18851 | ||||||||
\(964\) | −78.2516 | −2.52031 | ||||||||
\(965\) | 3.83621 | 0.123492 | ||||||||
\(966\) | 2.23905 | 0.0720404 | ||||||||
\(967\) | 29.7679 | 0.957272 | 0.478636 | − | 0.878013i | \(-0.341131\pi\) | ||||
0.478636 | + | 0.878013i | \(0.341131\pi\) | |||||||
\(968\) | 13.4274 | 0.431574 | ||||||||
\(969\) | −7.16486 | −0.230169 | ||||||||
\(970\) | 1.96026 | 0.0629403 | ||||||||
\(971\) | −34.6957 | −1.11344 | −0.556718 | − | 0.830701i | \(-0.687940\pi\) | ||||
−0.556718 | + | 0.830701i | \(0.687940\pi\) | |||||||
\(972\) | 49.7944 | 1.59715 | ||||||||
\(973\) | 26.8588 | 0.861053 | ||||||||
\(974\) | −5.17920 | −0.165952 | ||||||||
\(975\) | 28.0229 | 0.897452 | ||||||||
\(976\) | −0.226287 | −0.00724328 | ||||||||
\(977\) | −32.1801 | −1.02953 | −0.514767 | − | 0.857330i | \(-0.672121\pi\) | ||||
−0.514767 | + | 0.857330i | \(0.672121\pi\) | |||||||
\(978\) | 0.481776 | 0.0154055 | ||||||||
\(979\) | −3.20976 | −0.102585 | ||||||||
\(980\) | 73.7782 | 2.35676 | ||||||||
\(981\) | −0.222794 | −0.00711328 | ||||||||
\(982\) | 65.7904 | 2.09946 | ||||||||
\(983\) | −2.63034 | −0.0838948 | −0.0419474 | − | 0.999120i | \(-0.513356\pi\) | ||||
−0.0419474 | + | 0.999120i | \(0.513356\pi\) | |||||||
\(984\) | −6.08520 | −0.193989 | ||||||||
\(985\) | −24.3788 | −0.776773 | ||||||||
\(986\) | −44.1960 | −1.40749 | ||||||||
\(987\) | 3.09858 | 0.0986288 | ||||||||
\(988\) | −29.2229 | −0.929704 | ||||||||
\(989\) | 8.50068 | 0.270306 | ||||||||
\(990\) | −56.5191 | −1.79630 | ||||||||
\(991\) | 43.3282 | 1.37636 | 0.688182 | − | 0.725538i | \(-0.258409\pi\) | ||||
0.688182 | + | 0.725538i | \(0.258409\pi\) | |||||||
\(992\) | −55.6508 | −1.76691 | ||||||||
\(993\) | −21.4126 | −0.679508 | ||||||||
\(994\) | −1.76153 | −0.0558725 | ||||||||
\(995\) | 25.1083 | 0.795986 | ||||||||
\(996\) | −33.7381 | −1.06903 | ||||||||
\(997\) | 21.7317 | 0.688251 | 0.344126 | − | 0.938924i | \(-0.388175\pi\) | ||||
0.344126 | + | 0.938924i | \(0.388175\pi\) | |||||||
\(998\) | 61.2293 | 1.93818 | ||||||||
\(999\) | 27.9316 | 0.883716 |
(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 | 8027.2.a.d.1.17 | ✓ | 149 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8027.2.a.d.1.17 | ✓ | 149 | 1.1 | even | 1 | trivial |