Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 6 x^{13} - 29 x^{12} + 207 x^{11} + 269 x^{10} - 2601 x^{9} - 847 x^{8} + 14851 x^{7} + \cdots - 2048 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.57230\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.57230 | −1.15037 | −0.575185 | − | 0.818024i | \(-0.695070\pi\) | ||||
−0.575185 | + | 0.818024i | \(0.695070\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −4.81484 | −1.81984 | −0.909919 | − | 0.414786i | \(-0.863857\pi\) | ||||
−0.909919 | + | 0.414786i | \(0.863857\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.57230 | 0.813434 | ||||||||
\(11\) | 1.68147 | 0.506983 | 0.253491 | − | 0.967338i | \(-0.418421\pi\) | ||||
0.253491 | + | 0.967338i | \(0.418421\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 4.81484 | 1.28682 | ||||||||
\(15\) | −2.57230 | −0.664166 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.18217 | 1.49940 | 0.749698 | − | 0.661780i | \(-0.230199\pi\) | ||||
0.749698 | + | 0.661780i | \(0.230199\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 0.771079 | 0.176898 | 0.0884488 | − | 0.996081i | \(-0.471809\pi\) | ||||
0.0884488 | + | 0.996081i | \(0.471809\pi\) | |||||||
\(20\) | −2.57230 | −0.575185 | ||||||||
\(21\) | −4.81484 | −1.05068 | ||||||||
\(22\) | −1.68147 | −0.358491 | ||||||||
\(23\) | −2.46234 | −0.513432 | −0.256716 | − | 0.966487i | \(-0.582641\pi\) | ||||
−0.256716 | + | 0.966487i | \(0.582641\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.61675 | 0.323350 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.81484 | −0.909919 | ||||||||
\(29\) | −4.09908 | −0.761179 | −0.380590 | − | 0.924744i | \(-0.624279\pi\) | ||||
−0.380590 | + | 0.924744i | \(0.624279\pi\) | |||||||
\(30\) | 2.57230 | 0.469636 | ||||||||
\(31\) | −7.36712 | −1.32317 | −0.661587 | − | 0.749868i | \(-0.730117\pi\) | ||||
−0.661587 | + | 0.749868i | \(0.730117\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.68147 | 0.292707 | ||||||||
\(34\) | −6.18217 | −1.06023 | ||||||||
\(35\) | 12.3852 | 2.09349 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 7.10946 | 1.16879 | 0.584394 | − | 0.811470i | \(-0.301332\pi\) | ||||
0.584394 | + | 0.811470i | \(0.301332\pi\) | |||||||
\(38\) | −0.771079 | −0.125085 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 2.57230 | 0.406717 | ||||||||
\(41\) | 11.9672 | 1.86897 | 0.934484 | − | 0.356005i | \(-0.115861\pi\) | ||||
0.934484 | + | 0.356005i | \(0.115861\pi\) | |||||||
\(42\) | 4.81484 | 0.742946 | ||||||||
\(43\) | 4.87285 | 0.743103 | 0.371551 | − | 0.928412i | \(-0.378826\pi\) | ||||
0.371551 | + | 0.928412i | \(0.378826\pi\) | |||||||
\(44\) | 1.68147 | 0.253491 | ||||||||
\(45\) | −2.57230 | −0.383456 | ||||||||
\(46\) | 2.46234 | 0.363052 | ||||||||
\(47\) | −7.45264 | −1.08708 | −0.543539 | − | 0.839384i | \(-0.682916\pi\) | ||||
−0.543539 | + | 0.839384i | \(0.682916\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 16.1827 | 2.31181 | ||||||||
\(50\) | −1.61675 | −0.228643 | ||||||||
\(51\) | 6.18217 | 0.865677 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 4.54055 | 0.623692 | 0.311846 | − | 0.950133i | \(-0.399053\pi\) | ||||
0.311846 | + | 0.950133i | \(0.399053\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −4.32526 | −0.583217 | ||||||||
\(56\) | 4.81484 | 0.643410 | ||||||||
\(57\) | 0.771079 | 0.102132 | ||||||||
\(58\) | 4.09908 | 0.538235 | ||||||||
\(59\) | −5.91864 | −0.770541 | −0.385271 | − | 0.922804i | \(-0.625892\pi\) | ||||
−0.385271 | + | 0.922804i | \(0.625892\pi\) | |||||||
\(60\) | −2.57230 | −0.332083 | ||||||||
\(61\) | −0.0881773 | −0.0112900 | −0.00564498 | − | 0.999984i | \(-0.501797\pi\) | ||||
−0.00564498 | + | 0.999984i | \(0.501797\pi\) | |||||||
\(62\) | 7.36712 | 0.935626 | ||||||||
\(63\) | −4.81484 | −0.606613 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.57230 | 0.319055 | ||||||||
\(66\) | −1.68147 | −0.206975 | ||||||||
\(67\) | −9.81599 | −1.19921 | −0.599607 | − | 0.800295i | \(-0.704676\pi\) | ||||
−0.599607 | + | 0.800295i | \(0.704676\pi\) | |||||||
\(68\) | 6.18217 | 0.749698 | ||||||||
\(69\) | −2.46234 | −0.296430 | ||||||||
\(70\) | −12.3852 | −1.48032 | ||||||||
\(71\) | −6.15722 | −0.730727 | −0.365364 | − | 0.930865i | \(-0.619055\pi\) | ||||
−0.365364 | + | 0.930865i | \(0.619055\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 16.5077 | 1.93207 | 0.966037 | − | 0.258402i | \(-0.0831959\pi\) | ||||
0.966037 | + | 0.258402i | \(0.0831959\pi\) | |||||||
\(74\) | −7.10946 | −0.826458 | ||||||||
\(75\) | 1.61675 | 0.186686 | ||||||||
\(76\) | 0.771079 | 0.0884488 | ||||||||
\(77\) | −8.09602 | −0.922627 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −3.92812 | −0.441948 | −0.220974 | − | 0.975280i | \(-0.570924\pi\) | ||||
−0.220974 | + | 0.975280i | \(0.570924\pi\) | |||||||
\(80\) | −2.57230 | −0.287592 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −11.9672 | −1.32156 | ||||||||
\(83\) | −1.22361 | −0.134309 | −0.0671545 | − | 0.997743i | \(-0.521392\pi\) | ||||
−0.0671545 | + | 0.997743i | \(0.521392\pi\) | |||||||
\(84\) | −4.81484 | −0.525342 | ||||||||
\(85\) | −15.9024 | −1.72486 | ||||||||
\(86\) | −4.87285 | −0.525453 | ||||||||
\(87\) | −4.09908 | −0.439467 | ||||||||
\(88\) | −1.68147 | −0.179245 | ||||||||
\(89\) | 6.45570 | 0.684303 | 0.342152 | − | 0.939645i | \(-0.388844\pi\) | ||||
0.342152 | + | 0.939645i | \(0.388844\pi\) | |||||||
\(90\) | 2.57230 | 0.271145 | ||||||||
\(91\) | 4.81484 | 0.504732 | ||||||||
\(92\) | −2.46234 | −0.256716 | ||||||||
\(93\) | −7.36712 | −0.763935 | ||||||||
\(94\) | 7.45264 | 0.768681 | ||||||||
\(95\) | −1.98345 | −0.203498 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −8.09177 | −0.821595 | −0.410797 | − | 0.911727i | \(-0.634750\pi\) | ||||
−0.410797 | + | 0.911727i | \(0.634750\pi\) | |||||||
\(98\) | −16.1827 | −1.63470 | ||||||||
\(99\) | 1.68147 | 0.168994 | ||||||||
\(100\) | 1.61675 | 0.161675 | ||||||||
\(101\) | 6.68754 | 0.665435 | 0.332718 | − | 0.943027i | \(-0.392034\pi\) | ||||
0.332718 | + | 0.943027i | \(0.392034\pi\) | |||||||
\(102\) | −6.18217 | −0.612126 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 12.3852 | 1.20867 | ||||||||
\(106\) | −4.54055 | −0.441017 | ||||||||
\(107\) | 9.93787 | 0.960730 | 0.480365 | − | 0.877069i | \(-0.340504\pi\) | ||||
0.480365 | + | 0.877069i | \(0.340504\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 10.9229 | 1.04623 | 0.523113 | − | 0.852263i | \(-0.324771\pi\) | ||||
0.523113 | + | 0.852263i | \(0.324771\pi\) | |||||||
\(110\) | 4.32526 | 0.412397 | ||||||||
\(111\) | 7.10946 | 0.674800 | ||||||||
\(112\) | −4.81484 | −0.454960 | ||||||||
\(113\) | 2.41897 | 0.227557 | 0.113779 | − | 0.993506i | \(-0.463705\pi\) | ||||
0.113779 | + | 0.993506i | \(0.463705\pi\) | |||||||
\(114\) | −0.771079 | −0.0722181 | ||||||||
\(115\) | 6.33388 | 0.590637 | ||||||||
\(116\) | −4.09908 | −0.380590 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 5.91864 | 0.544855 | ||||||||
\(119\) | −29.7661 | −2.72866 | ||||||||
\(120\) | 2.57230 | 0.234818 | ||||||||
\(121\) | −8.17265 | −0.742969 | ||||||||
\(122\) | 0.0881773 | 0.00798320 | ||||||||
\(123\) | 11.9672 | 1.07905 | ||||||||
\(124\) | −7.36712 | −0.661587 | ||||||||
\(125\) | 8.70275 | 0.778398 | ||||||||
\(126\) | 4.81484 | 0.428940 | ||||||||
\(127\) | 18.6336 | 1.65346 | 0.826731 | − | 0.562598i | \(-0.190198\pi\) | ||||
0.826731 | + | 0.562598i | \(0.190198\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 4.87285 | 0.429031 | ||||||||
\(130\) | −2.57230 | −0.225606 | ||||||||
\(131\) | −15.8374 | −1.38372 | −0.691861 | − | 0.722030i | \(-0.743209\pi\) | ||||
−0.691861 | + | 0.722030i | \(0.743209\pi\) | |||||||
\(132\) | 1.68147 | 0.146353 | ||||||||
\(133\) | −3.71262 | −0.321925 | ||||||||
\(134\) | 9.81599 | 0.847973 | ||||||||
\(135\) | −2.57230 | −0.221389 | ||||||||
\(136\) | −6.18217 | −0.530116 | ||||||||
\(137\) | −2.03436 | −0.173807 | −0.0869034 | − | 0.996217i | \(-0.527697\pi\) | ||||
−0.0869034 | + | 0.996217i | \(0.527697\pi\) | |||||||
\(138\) | 2.46234 | 0.209608 | ||||||||
\(139\) | 1.34700 | 0.114251 | 0.0571254 | − | 0.998367i | \(-0.481807\pi\) | ||||
0.0571254 | + | 0.998367i | \(0.481807\pi\) | |||||||
\(140\) | 12.3852 | 1.04674 | ||||||||
\(141\) | −7.45264 | −0.627625 | ||||||||
\(142\) | 6.15722 | 0.516702 | ||||||||
\(143\) | −1.68147 | −0.140612 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 10.5441 | 0.875638 | ||||||||
\(146\) | −16.5077 | −1.36618 | ||||||||
\(147\) | 16.1827 | 1.33472 | ||||||||
\(148\) | 7.10946 | 0.584394 | ||||||||
\(149\) | −16.3859 | −1.34239 | −0.671194 | − | 0.741282i | \(-0.734218\pi\) | ||||
−0.671194 | + | 0.741282i | \(0.734218\pi\) | |||||||
\(150\) | −1.61675 | −0.132007 | ||||||||
\(151\) | 19.8000 | 1.61130 | 0.805650 | − | 0.592392i | \(-0.201816\pi\) | ||||
0.805650 | + | 0.592392i | \(0.201816\pi\) | |||||||
\(152\) | −0.771079 | −0.0625427 | ||||||||
\(153\) | 6.18217 | 0.499799 | ||||||||
\(154\) | 8.09602 | 0.652396 | ||||||||
\(155\) | 18.9505 | 1.52214 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 16.4161 | 1.31015 | 0.655073 | − | 0.755566i | \(-0.272638\pi\) | ||||
0.655073 | + | 0.755566i | \(0.272638\pi\) | |||||||
\(158\) | 3.92812 | 0.312504 | ||||||||
\(159\) | 4.54055 | 0.360089 | ||||||||
\(160\) | 2.57230 | 0.203359 | ||||||||
\(161\) | 11.8557 | 0.934364 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −17.7158 | −1.38761 | −0.693803 | − | 0.720165i | \(-0.744066\pi\) | ||||
−0.693803 | + | 0.720165i | \(0.744066\pi\) | |||||||
\(164\) | 11.9672 | 0.934484 | ||||||||
\(165\) | −4.32526 | −0.336721 | ||||||||
\(166\) | 1.22361 | 0.0949708 | ||||||||
\(167\) | −15.7136 | −1.21595 | −0.607977 | − | 0.793954i | \(-0.708019\pi\) | ||||
−0.607977 | + | 0.793954i | \(0.708019\pi\) | |||||||
\(168\) | 4.81484 | 0.371473 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 15.9024 | 1.21966 | ||||||||
\(171\) | 0.771079 | 0.0589659 | ||||||||
\(172\) | 4.87285 | 0.371551 | ||||||||
\(173\) | 8.65865 | 0.658305 | 0.329153 | − | 0.944277i | \(-0.393237\pi\) | ||||
0.329153 | + | 0.944277i | \(0.393237\pi\) | |||||||
\(174\) | 4.09908 | 0.310750 | ||||||||
\(175\) | −7.78439 | −0.588444 | ||||||||
\(176\) | 1.68147 | 0.126746 | ||||||||
\(177\) | −5.91864 | −0.444872 | ||||||||
\(178\) | −6.45570 | −0.483875 | ||||||||
\(179\) | −16.8361 | −1.25839 | −0.629196 | − | 0.777247i | \(-0.716616\pi\) | ||||
−0.629196 | + | 0.777247i | \(0.716616\pi\) | |||||||
\(180\) | −2.57230 | −0.191728 | ||||||||
\(181\) | 0.312325 | 0.0232149 | 0.0116075 | − | 0.999933i | \(-0.496305\pi\) | ||||
0.0116075 | + | 0.999933i | \(0.496305\pi\) | |||||||
\(182\) | −4.81484 | −0.356900 | ||||||||
\(183\) | −0.0881773 | −0.00651826 | ||||||||
\(184\) | 2.46234 | 0.181526 | ||||||||
\(185\) | −18.2877 | −1.34454 | ||||||||
\(186\) | 7.36712 | 0.540184 | ||||||||
\(187\) | 10.3951 | 0.760168 | ||||||||
\(188\) | −7.45264 | −0.543539 | ||||||||
\(189\) | −4.81484 | −0.350228 | ||||||||
\(190\) | 1.98345 | 0.143895 | ||||||||
\(191\) | 12.0110 | 0.869084 | 0.434542 | − | 0.900652i | \(-0.356910\pi\) | ||||
0.434542 | + | 0.900652i | \(0.356910\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −12.2193 | −0.879564 | −0.439782 | − | 0.898104i | \(-0.644944\pi\) | ||||
−0.439782 | + | 0.898104i | \(0.644944\pi\) | |||||||
\(194\) | 8.09177 | 0.580955 | ||||||||
\(195\) | 2.57230 | 0.184207 | ||||||||
\(196\) | 16.1827 | 1.15591 | ||||||||
\(197\) | 5.75541 | 0.410056 | 0.205028 | − | 0.978756i | \(-0.434271\pi\) | ||||
0.205028 | + | 0.978756i | \(0.434271\pi\) | |||||||
\(198\) | −1.68147 | −0.119497 | ||||||||
\(199\) | −24.5893 | −1.74309 | −0.871544 | − | 0.490317i | \(-0.836881\pi\) | ||||
−0.871544 | + | 0.490317i | \(0.836881\pi\) | |||||||
\(200\) | −1.61675 | −0.114321 | ||||||||
\(201\) | −9.81599 | −0.692367 | ||||||||
\(202\) | −6.68754 | −0.470534 | ||||||||
\(203\) | 19.7364 | 1.38522 | ||||||||
\(204\) | 6.18217 | 0.432838 | ||||||||
\(205\) | −30.7834 | −2.15000 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | −2.46234 | −0.171144 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 1.29655 | 0.0896840 | ||||||||
\(210\) | −12.3852 | −0.854662 | ||||||||
\(211\) | 7.63512 | 0.525623 | 0.262812 | − | 0.964847i | \(-0.415350\pi\) | ||||
0.262812 | + | 0.964847i | \(0.415350\pi\) | |||||||
\(212\) | 4.54055 | 0.311846 | ||||||||
\(213\) | −6.15722 | −0.421886 | ||||||||
\(214\) | −9.93787 | −0.679339 | ||||||||
\(215\) | −12.5345 | −0.854843 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 35.4715 | 2.40796 | ||||||||
\(218\) | −10.9229 | −0.739793 | ||||||||
\(219\) | 16.5077 | 1.11548 | ||||||||
\(220\) | −4.32526 | −0.291609 | ||||||||
\(221\) | −6.18217 | −0.415858 | ||||||||
\(222\) | −7.10946 | −0.477156 | ||||||||
\(223\) | 3.09337 | 0.207148 | 0.103574 | − | 0.994622i | \(-0.466972\pi\) | ||||
0.103574 | + | 0.994622i | \(0.466972\pi\) | |||||||
\(224\) | 4.81484 | 0.321705 | ||||||||
\(225\) | 1.61675 | 0.107783 | ||||||||
\(226\) | −2.41897 | −0.160907 | ||||||||
\(227\) | −24.1516 | −1.60300 | −0.801499 | − | 0.597996i | \(-0.795964\pi\) | ||||
−0.801499 | + | 0.597996i | \(0.795964\pi\) | |||||||
\(228\) | 0.771079 | 0.0510659 | ||||||||
\(229\) | −9.02543 | −0.596417 | −0.298209 | − | 0.954501i | \(-0.596389\pi\) | ||||
−0.298209 | + | 0.954501i | \(0.596389\pi\) | |||||||
\(230\) | −6.33388 | −0.417643 | ||||||||
\(231\) | −8.09602 | −0.532679 | ||||||||
\(232\) | 4.09908 | 0.269118 | ||||||||
\(233\) | −19.8825 | −1.30255 | −0.651274 | − | 0.758843i | \(-0.725765\pi\) | ||||
−0.651274 | + | 0.758843i | \(0.725765\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | 19.1704 | 1.25054 | ||||||||
\(236\) | −5.91864 | −0.385271 | ||||||||
\(237\) | −3.92812 | −0.255159 | ||||||||
\(238\) | 29.7661 | 1.92945 | ||||||||
\(239\) | −21.7455 | −1.40660 | −0.703301 | − | 0.710893i | \(-0.748291\pi\) | ||||
−0.703301 | + | 0.710893i | \(0.748291\pi\) | |||||||
\(240\) | −2.57230 | −0.166042 | ||||||||
\(241\) | −29.9056 | −1.92639 | −0.963195 | − | 0.268805i | \(-0.913371\pi\) | ||||
−0.963195 | + | 0.268805i | \(0.913371\pi\) | |||||||
\(242\) | 8.17265 | 0.525358 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.0881773 | −0.00564498 | ||||||||
\(245\) | −41.6268 | −2.65944 | ||||||||
\(246\) | −11.9672 | −0.763003 | ||||||||
\(247\) | −0.771079 | −0.0490626 | ||||||||
\(248\) | 7.36712 | 0.467813 | ||||||||
\(249\) | −1.22361 | −0.0775433 | ||||||||
\(250\) | −8.70275 | −0.550410 | ||||||||
\(251\) | −10.3576 | −0.653769 | −0.326884 | − | 0.945064i | \(-0.605999\pi\) | ||||
−0.326884 | + | 0.945064i | \(0.605999\pi\) | |||||||
\(252\) | −4.81484 | −0.303306 | ||||||||
\(253\) | −4.14035 | −0.260301 | ||||||||
\(254\) | −18.6336 | −1.16917 | ||||||||
\(255\) | −15.9024 | −0.995848 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.58228 | −0.161078 | −0.0805392 | − | 0.996751i | \(-0.525664\pi\) | ||||
−0.0805392 | + | 0.996751i | \(0.525664\pi\) | |||||||
\(258\) | −4.87285 | −0.303370 | ||||||||
\(259\) | −34.2309 | −2.12700 | ||||||||
\(260\) | 2.57230 | 0.159528 | ||||||||
\(261\) | −4.09908 | −0.253726 | ||||||||
\(262\) | 15.8374 | 0.978440 | ||||||||
\(263\) | −19.9903 | −1.23265 | −0.616326 | − | 0.787491i | \(-0.711380\pi\) | ||||
−0.616326 | + | 0.787491i | \(0.711380\pi\) | |||||||
\(264\) | −1.68147 | −0.103487 | ||||||||
\(265\) | −11.6797 | −0.717476 | ||||||||
\(266\) | 3.71262 | 0.227635 | ||||||||
\(267\) | 6.45570 | 0.395083 | ||||||||
\(268\) | −9.81599 | −0.599607 | ||||||||
\(269\) | −1.69478 | −0.103333 | −0.0516663 | − | 0.998664i | \(-0.516453\pi\) | ||||
−0.0516663 | + | 0.998664i | \(0.516453\pi\) | |||||||
\(270\) | 2.57230 | 0.156545 | ||||||||
\(271\) | 24.7894 | 1.50585 | 0.752924 | − | 0.658107i | \(-0.228643\pi\) | ||||
0.752924 | + | 0.658107i | \(0.228643\pi\) | |||||||
\(272\) | 6.18217 | 0.374849 | ||||||||
\(273\) | 4.81484 | 0.291407 | ||||||||
\(274\) | 2.03436 | 0.122900 | ||||||||
\(275\) | 2.71852 | 0.163933 | ||||||||
\(276\) | −2.46234 | −0.148215 | ||||||||
\(277\) | −3.08089 | −0.185113 | −0.0925565 | − | 0.995707i | \(-0.529504\pi\) | ||||
−0.0925565 | + | 0.995707i | \(0.529504\pi\) | |||||||
\(278\) | −1.34700 | −0.0807875 | ||||||||
\(279\) | −7.36712 | −0.441058 | ||||||||
\(280\) | −12.3852 | −0.740159 | ||||||||
\(281\) | −3.29557 | −0.196597 | −0.0982986 | − | 0.995157i | \(-0.531340\pi\) | ||||
−0.0982986 | + | 0.995157i | \(0.531340\pi\) | |||||||
\(282\) | 7.45264 | 0.443798 | ||||||||
\(283\) | 24.9865 | 1.48529 | 0.742646 | − | 0.669684i | \(-0.233570\pi\) | ||||
0.742646 | + | 0.669684i | \(0.233570\pi\) | |||||||
\(284\) | −6.15722 | −0.365364 | ||||||||
\(285\) | −1.98345 | −0.117489 | ||||||||
\(286\) | 1.68147 | 0.0994275 | ||||||||
\(287\) | −57.6203 | −3.40122 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 21.2192 | 1.24819 | ||||||||
\(290\) | −10.5441 | −0.619169 | ||||||||
\(291\) | −8.09177 | −0.474348 | ||||||||
\(292\) | 16.5077 | 0.966037 | ||||||||
\(293\) | −9.62707 | −0.562419 | −0.281210 | − | 0.959646i | \(-0.590736\pi\) | ||||
−0.281210 | + | 0.959646i | \(0.590736\pi\) | |||||||
\(294\) | −16.1827 | −0.943793 | ||||||||
\(295\) | 15.2245 | 0.886407 | ||||||||
\(296\) | −7.10946 | −0.413229 | ||||||||
\(297\) | 1.68147 | 0.0975689 | ||||||||
\(298\) | 16.3859 | 0.949211 | ||||||||
\(299\) | 2.46234 | 0.142401 | ||||||||
\(300\) | 1.61675 | 0.0933431 | ||||||||
\(301\) | −23.4620 | −1.35233 | ||||||||
\(302\) | −19.8000 | −1.13936 | ||||||||
\(303\) | 6.68754 | 0.384189 | ||||||||
\(304\) | 0.771079 | 0.0442244 | ||||||||
\(305\) | 0.226819 | 0.0129876 | ||||||||
\(306\) | −6.18217 | −0.353411 | ||||||||
\(307\) | −20.2738 | −1.15709 | −0.578545 | − | 0.815651i | \(-0.696379\pi\) | ||||
−0.578545 | + | 0.815651i | \(0.696379\pi\) | |||||||
\(308\) | −8.09602 | −0.461313 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −18.9505 | −1.07632 | ||||||||
\(311\) | −32.4947 | −1.84260 | −0.921302 | − | 0.388847i | \(-0.872873\pi\) | ||||
−0.921302 | + | 0.388847i | \(0.872873\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 7.50820 | 0.424389 | 0.212194 | − | 0.977227i | \(-0.431939\pi\) | ||||
0.212194 | + | 0.977227i | \(0.431939\pi\) | |||||||
\(314\) | −16.4161 | −0.926413 | ||||||||
\(315\) | 12.3852 | 0.697829 | ||||||||
\(316\) | −3.92812 | −0.220974 | ||||||||
\(317\) | −2.86805 | −0.161086 | −0.0805429 | − | 0.996751i | \(-0.525665\pi\) | ||||
−0.0805429 | + | 0.996751i | \(0.525665\pi\) | |||||||
\(318\) | −4.54055 | −0.254621 | ||||||||
\(319\) | −6.89248 | −0.385905 | ||||||||
\(320\) | −2.57230 | −0.143796 | ||||||||
\(321\) | 9.93787 | 0.554678 | ||||||||
\(322\) | −11.8557 | −0.660695 | ||||||||
\(323\) | 4.76694 | 0.265240 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −1.61675 | −0.0896811 | ||||||||
\(326\) | 17.7158 | 0.981186 | ||||||||
\(327\) | 10.9229 | 0.604039 | ||||||||
\(328\) | −11.9672 | −0.660780 | ||||||||
\(329\) | 35.8832 | 1.97831 | ||||||||
\(330\) | 4.32526 | 0.238098 | ||||||||
\(331\) | 26.5172 | 1.45752 | 0.728758 | − | 0.684772i | \(-0.240098\pi\) | ||||
0.728758 | + | 0.684772i | \(0.240098\pi\) | |||||||
\(332\) | −1.22361 | −0.0671545 | ||||||||
\(333\) | 7.10946 | 0.389596 | ||||||||
\(334\) | 15.7136 | 0.859810 | ||||||||
\(335\) | 25.2497 | 1.37954 | ||||||||
\(336\) | −4.81484 | −0.262671 | ||||||||
\(337\) | −14.6616 | −0.798668 | −0.399334 | − | 0.916806i | \(-0.630759\pi\) | ||||
−0.399334 | + | 0.916806i | \(0.630759\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 2.41897 | 0.131380 | ||||||||
\(340\) | −15.9024 | −0.862430 | ||||||||
\(341\) | −12.3876 | −0.670827 | ||||||||
\(342\) | −0.771079 | −0.0416952 | ||||||||
\(343\) | −44.2131 | −2.38728 | ||||||||
\(344\) | −4.87285 | −0.262727 | ||||||||
\(345\) | 6.33388 | 0.341004 | ||||||||
\(346\) | −8.65865 | −0.465492 | ||||||||
\(347\) | 2.56359 | 0.137621 | 0.0688103 | − | 0.997630i | \(-0.478080\pi\) | ||||
0.0688103 | + | 0.997630i | \(0.478080\pi\) | |||||||
\(348\) | −4.09908 | −0.219734 | ||||||||
\(349\) | −24.6663 | −1.32035 | −0.660177 | − | 0.751110i | \(-0.729519\pi\) | ||||
−0.660177 | + | 0.751110i | \(0.729519\pi\) | |||||||
\(350\) | 7.78439 | 0.416093 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −1.68147 | −0.0896227 | ||||||||
\(353\) | 11.7074 | 0.623122 | 0.311561 | − | 0.950226i | \(-0.399148\pi\) | ||||
0.311561 | + | 0.950226i | \(0.399148\pi\) | |||||||
\(354\) | 5.91864 | 0.314572 | ||||||||
\(355\) | 15.8382 | 0.840607 | ||||||||
\(356\) | 6.45570 | 0.342152 | ||||||||
\(357\) | −29.7661 | −1.57539 | ||||||||
\(358\) | 16.8361 | 0.889817 | ||||||||
\(359\) | −2.53080 | −0.133570 | −0.0667851 | − | 0.997767i | \(-0.521274\pi\) | ||||
−0.0667851 | + | 0.997767i | \(0.521274\pi\) | |||||||
\(360\) | 2.57230 | 0.135572 | ||||||||
\(361\) | −18.4054 | −0.968707 | ||||||||
\(362\) | −0.312325 | −0.0164154 | ||||||||
\(363\) | −8.17265 | −0.428953 | ||||||||
\(364\) | 4.81484 | 0.252366 | ||||||||
\(365\) | −42.4627 | −2.22260 | ||||||||
\(366\) | 0.0881773 | 0.00460910 | ||||||||
\(367\) | 5.13485 | 0.268037 | 0.134018 | − | 0.990979i | \(-0.457212\pi\) | ||||
0.134018 | + | 0.990979i | \(0.457212\pi\) | |||||||
\(368\) | −2.46234 | −0.128358 | ||||||||
\(369\) | 11.9672 | 0.622989 | ||||||||
\(370\) | 18.2877 | 0.950732 | ||||||||
\(371\) | −21.8620 | −1.13502 | ||||||||
\(372\) | −7.36712 | −0.381968 | ||||||||
\(373\) | −33.0765 | −1.71263 | −0.856317 | − | 0.516450i | \(-0.827253\pi\) | ||||
−0.856317 | + | 0.516450i | \(0.827253\pi\) | |||||||
\(374\) | −10.3951 | −0.537520 | ||||||||
\(375\) | 8.70275 | 0.449408 | ||||||||
\(376\) | 7.45264 | 0.384340 | ||||||||
\(377\) | 4.09908 | 0.211113 | ||||||||
\(378\) | 4.81484 | 0.247649 | ||||||||
\(379\) | −15.1628 | −0.778859 | −0.389430 | − | 0.921056i | \(-0.627328\pi\) | ||||
−0.389430 | + | 0.921056i | \(0.627328\pi\) | |||||||
\(380\) | −1.98345 | −0.101749 | ||||||||
\(381\) | 18.6336 | 0.954627 | ||||||||
\(382\) | −12.0110 | −0.614535 | ||||||||
\(383\) | −31.7073 | −1.62017 | −0.810085 | − | 0.586313i | \(-0.800579\pi\) | ||||
−0.810085 | + | 0.586313i | \(0.800579\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 20.8254 | 1.06136 | ||||||||
\(386\) | 12.2193 | 0.621946 | ||||||||
\(387\) | 4.87285 | 0.247701 | ||||||||
\(388\) | −8.09177 | −0.410797 | ||||||||
\(389\) | −23.6651 | −1.19987 | −0.599934 | − | 0.800050i | \(-0.704806\pi\) | ||||
−0.599934 | + | 0.800050i | \(0.704806\pi\) | |||||||
\(390\) | −2.57230 | −0.130254 | ||||||||
\(391\) | −15.2226 | −0.769838 | ||||||||
\(392\) | −16.1827 | −0.817349 | ||||||||
\(393\) | −15.8374 | −0.798893 | ||||||||
\(394\) | −5.75541 | −0.289953 | ||||||||
\(395\) | 10.1043 | 0.508403 | ||||||||
\(396\) | 1.68147 | 0.0844971 | ||||||||
\(397\) | 25.1755 | 1.26352 | 0.631762 | − | 0.775163i | \(-0.282332\pi\) | ||||
0.631762 | + | 0.775163i | \(0.282332\pi\) | |||||||
\(398\) | 24.5893 | 1.23255 | ||||||||
\(399\) | −3.71262 | −0.185863 | ||||||||
\(400\) | 1.61675 | 0.0808375 | ||||||||
\(401\) | −15.0419 | −0.751158 | −0.375579 | − | 0.926790i | \(-0.622556\pi\) | ||||
−0.375579 | + | 0.926790i | \(0.622556\pi\) | |||||||
\(402\) | 9.81599 | 0.489577 | ||||||||
\(403\) | 7.36712 | 0.366983 | ||||||||
\(404\) | 6.68754 | 0.332718 | ||||||||
\(405\) | −2.57230 | −0.127819 | ||||||||
\(406\) | −19.7364 | −0.979501 | ||||||||
\(407\) | 11.9544 | 0.592555 | ||||||||
\(408\) | −6.18217 | −0.306063 | ||||||||
\(409\) | 20.1039 | 0.994072 | 0.497036 | − | 0.867730i | \(-0.334422\pi\) | ||||
0.497036 | + | 0.867730i | \(0.334422\pi\) | |||||||
\(410\) | 30.7834 | 1.52028 | ||||||||
\(411\) | −2.03436 | −0.100347 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | 28.4973 | 1.40226 | ||||||||
\(414\) | 2.46234 | 0.121017 | ||||||||
\(415\) | 3.14750 | 0.154505 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 1.34700 | 0.0659627 | ||||||||
\(418\) | −1.29655 | −0.0634162 | ||||||||
\(419\) | −34.5445 | −1.68761 | −0.843805 | − | 0.536650i | \(-0.819690\pi\) | ||||
−0.843805 | + | 0.536650i | \(0.819690\pi\) | |||||||
\(420\) | 12.3852 | 0.604337 | ||||||||
\(421\) | 4.53726 | 0.221132 | 0.110566 | − | 0.993869i | \(-0.464734\pi\) | ||||
0.110566 | + | 0.993869i | \(0.464734\pi\) | |||||||
\(422\) | −7.63512 | −0.371672 | ||||||||
\(423\) | −7.45264 | −0.362360 | ||||||||
\(424\) | −4.54055 | −0.220508 | ||||||||
\(425\) | 9.99501 | 0.484829 | ||||||||
\(426\) | 6.15722 | 0.298318 | ||||||||
\(427\) | 0.424560 | 0.0205459 | ||||||||
\(428\) | 9.93787 | 0.480365 | ||||||||
\(429\) | −1.68147 | −0.0811822 | ||||||||
\(430\) | 12.5345 | 0.604465 | ||||||||
\(431\) | 8.15170 | 0.392653 | 0.196327 | − | 0.980539i | \(-0.437099\pi\) | ||||
0.196327 | + | 0.980539i | \(0.437099\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −24.1238 | −1.15931 | −0.579657 | − | 0.814860i | \(-0.696814\pi\) | ||||
−0.579657 | + | 0.814860i | \(0.696814\pi\) | |||||||
\(434\) | −35.4715 | −1.70269 | ||||||||
\(435\) | 10.5441 | 0.505550 | ||||||||
\(436\) | 10.9229 | 0.523113 | ||||||||
\(437\) | −1.89865 | −0.0908249 | ||||||||
\(438\) | −16.5077 | −0.788766 | ||||||||
\(439\) | 34.3120 | 1.63762 | 0.818810 | − | 0.574065i | \(-0.194634\pi\) | ||||
0.818810 | + | 0.574065i | \(0.194634\pi\) | |||||||
\(440\) | 4.32526 | 0.206198 | ||||||||
\(441\) | 16.1827 | 0.770604 | ||||||||
\(442\) | 6.18217 | 0.294056 | ||||||||
\(443\) | 13.8306 | 0.657112 | 0.328556 | − | 0.944484i | \(-0.393438\pi\) | ||||
0.328556 | + | 0.944484i | \(0.393438\pi\) | |||||||
\(444\) | 7.10946 | 0.337400 | ||||||||
\(445\) | −16.6060 | −0.787201 | ||||||||
\(446\) | −3.09337 | −0.146476 | ||||||||
\(447\) | −16.3859 | −0.775028 | ||||||||
\(448\) | −4.81484 | −0.227480 | ||||||||
\(449\) | 1.18499 | 0.0559229 | 0.0279615 | − | 0.999609i | \(-0.491098\pi\) | ||||
0.0279615 | + | 0.999609i | \(0.491098\pi\) | |||||||
\(450\) | −1.61675 | −0.0762143 | ||||||||
\(451\) | 20.1226 | 0.947535 | ||||||||
\(452\) | 2.41897 | 0.113779 | ||||||||
\(453\) | 19.8000 | 0.930284 | ||||||||
\(454\) | 24.1516 | 1.13349 | ||||||||
\(455\) | −12.3852 | −0.580629 | ||||||||
\(456\) | −0.771079 | −0.0361091 | ||||||||
\(457\) | 10.8635 | 0.508171 | 0.254086 | − | 0.967182i | \(-0.418225\pi\) | ||||
0.254086 | + | 0.967182i | \(0.418225\pi\) | |||||||
\(458\) | 9.02543 | 0.421731 | ||||||||
\(459\) | 6.18217 | 0.288559 | ||||||||
\(460\) | 6.33388 | 0.295318 | ||||||||
\(461\) | −22.7229 | −1.05831 | −0.529155 | − | 0.848525i | \(-0.677491\pi\) | ||||
−0.529155 | + | 0.848525i | \(0.677491\pi\) | |||||||
\(462\) | 8.09602 | 0.376661 | ||||||||
\(463\) | −24.7743 | −1.15136 | −0.575679 | − | 0.817676i | \(-0.695262\pi\) | ||||
−0.575679 | + | 0.817676i | \(0.695262\pi\) | |||||||
\(464\) | −4.09908 | −0.190295 | ||||||||
\(465\) | 18.9505 | 0.878808 | ||||||||
\(466\) | 19.8825 | 0.921041 | ||||||||
\(467\) | 10.2797 | 0.475686 | 0.237843 | − | 0.971304i | \(-0.423560\pi\) | ||||
0.237843 | + | 0.971304i | \(0.423560\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 47.2624 | 2.18238 | ||||||||
\(470\) | −19.1704 | −0.884267 | ||||||||
\(471\) | 16.4161 | 0.756413 | ||||||||
\(472\) | 5.91864 | 0.272427 | ||||||||
\(473\) | 8.19356 | 0.376740 | ||||||||
\(474\) | 3.92812 | 0.180424 | ||||||||
\(475\) | 1.24664 | 0.0571998 | ||||||||
\(476\) | −29.7661 | −1.36433 | ||||||||
\(477\) | 4.54055 | 0.207897 | ||||||||
\(478\) | 21.7455 | 0.994617 | ||||||||
\(479\) | −17.4984 | −0.799522 | −0.399761 | − | 0.916619i | \(-0.630907\pi\) | ||||
−0.399761 | + | 0.916619i | \(0.630907\pi\) | |||||||
\(480\) | 2.57230 | 0.117409 | ||||||||
\(481\) | −7.10946 | −0.324163 | ||||||||
\(482\) | 29.9056 | 1.36216 | ||||||||
\(483\) | 11.8557 | 0.539455 | ||||||||
\(484\) | −8.17265 | −0.371484 | ||||||||
\(485\) | 20.8145 | 0.945137 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 31.5809 | 1.43107 | 0.715534 | − | 0.698578i | \(-0.246184\pi\) | ||||
0.715534 | + | 0.698578i | \(0.246184\pi\) | |||||||
\(488\) | 0.0881773 | 0.00399160 | ||||||||
\(489\) | −17.7158 | −0.801135 | ||||||||
\(490\) | 41.6268 | 1.88051 | ||||||||
\(491\) | 15.1300 | 0.682808 | 0.341404 | − | 0.939917i | \(-0.389098\pi\) | ||||
0.341404 | + | 0.939917i | \(0.389098\pi\) | |||||||
\(492\) | 11.9672 | 0.539525 | ||||||||
\(493\) | −25.3412 | −1.14131 | ||||||||
\(494\) | 0.771079 | 0.0346925 | ||||||||
\(495\) | −4.32526 | −0.194406 | ||||||||
\(496\) | −7.36712 | −0.330794 | ||||||||
\(497\) | 29.6460 | 1.32981 | ||||||||
\(498\) | 1.22361 | 0.0548314 | ||||||||
\(499\) | 6.31066 | 0.282504 | 0.141252 | − | 0.989974i | \(-0.454887\pi\) | ||||
0.141252 | + | 0.989974i | \(0.454887\pi\) | |||||||
\(500\) | 8.70275 | 0.389199 | ||||||||
\(501\) | −15.7136 | −0.702032 | ||||||||
\(502\) | 10.3576 | 0.462284 | ||||||||
\(503\) | −23.6215 | −1.05323 | −0.526615 | − | 0.850104i | \(-0.676539\pi\) | ||||
−0.526615 | + | 0.850104i | \(0.676539\pi\) | |||||||
\(504\) | 4.81484 | 0.214470 | ||||||||
\(505\) | −17.2024 | −0.765496 | ||||||||
\(506\) | 4.14035 | 0.184061 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 18.6336 | 0.826731 | ||||||||
\(509\) | −4.56360 | −0.202278 | −0.101139 | − | 0.994872i | \(-0.532249\pi\) | ||||
−0.101139 | + | 0.994872i | \(0.532249\pi\) | |||||||
\(510\) | 15.9024 | 0.704171 | ||||||||
\(511\) | −79.4817 | −3.51606 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.771079 | 0.0340440 | ||||||||
\(514\) | 2.58228 | 0.113900 | ||||||||
\(515\) | −2.57230 | −0.113349 | ||||||||
\(516\) | 4.87285 | 0.214515 | ||||||||
\(517\) | −12.5314 | −0.551130 | ||||||||
\(518\) | 34.2309 | 1.50402 | ||||||||
\(519\) | 8.65865 | 0.380073 | ||||||||
\(520\) | −2.57230 | −0.112803 | ||||||||
\(521\) | −8.52013 | −0.373274 | −0.186637 | − | 0.982429i | \(-0.559759\pi\) | ||||
−0.186637 | + | 0.982429i | \(0.559759\pi\) | |||||||
\(522\) | 4.09908 | 0.179412 | ||||||||
\(523\) | −21.2892 | −0.930913 | −0.465457 | − | 0.885071i | \(-0.654110\pi\) | ||||
−0.465457 | + | 0.885071i | \(0.654110\pi\) | |||||||
\(524\) | −15.8374 | −0.691861 | ||||||||
\(525\) | −7.78439 | −0.339739 | ||||||||
\(526\) | 19.9903 | 0.871617 | ||||||||
\(527\) | −45.5448 | −1.98396 | ||||||||
\(528\) | 1.68147 | 0.0731767 | ||||||||
\(529\) | −16.9369 | −0.736387 | ||||||||
\(530\) | 11.6797 | 0.507332 | ||||||||
\(531\) | −5.91864 | −0.256847 | ||||||||
\(532\) | −3.71262 | −0.160963 | ||||||||
\(533\) | −11.9672 | −0.518359 | ||||||||
\(534\) | −6.45570 | −0.279366 | ||||||||
\(535\) | −25.5632 | −1.10519 | ||||||||
\(536\) | 9.81599 | 0.423986 | ||||||||
\(537\) | −16.8361 | −0.726533 | ||||||||
\(538\) | 1.69478 | 0.0730672 | ||||||||
\(539\) | 27.2107 | 1.17205 | ||||||||
\(540\) | −2.57230 | −0.110694 | ||||||||
\(541\) | −4.95665 | −0.213103 | −0.106552 | − | 0.994307i | \(-0.533981\pi\) | ||||
−0.106552 | + | 0.994307i | \(0.533981\pi\) | |||||||
\(542\) | −24.7894 | −1.06480 | ||||||||
\(543\) | 0.312325 | 0.0134031 | ||||||||
\(544\) | −6.18217 | −0.265058 | ||||||||
\(545\) | −28.0971 | −1.20355 | ||||||||
\(546\) | −4.81484 | −0.206056 | ||||||||
\(547\) | 20.1699 | 0.862404 | 0.431202 | − | 0.902255i | \(-0.358090\pi\) | ||||
0.431202 | + | 0.902255i | \(0.358090\pi\) | |||||||
\(548\) | −2.03436 | −0.0869034 | ||||||||
\(549\) | −0.0881773 | −0.00376332 | ||||||||
\(550\) | −2.71852 | −0.115918 | ||||||||
\(551\) | −3.16071 | −0.134651 | ||||||||
\(552\) | 2.46234 | 0.104804 | ||||||||
\(553\) | 18.9133 | 0.804274 | ||||||||
\(554\) | 3.08089 | 0.130895 | ||||||||
\(555\) | −18.2877 | −0.776269 | ||||||||
\(556\) | 1.34700 | 0.0571254 | ||||||||
\(557\) | 9.97975 | 0.422856 | 0.211428 | − | 0.977394i | \(-0.432189\pi\) | ||||
0.211428 | + | 0.977394i | \(0.432189\pi\) | |||||||
\(558\) | 7.36712 | 0.311875 | ||||||||
\(559\) | −4.87285 | −0.206100 | ||||||||
\(560\) | 12.3852 | 0.523372 | ||||||||
\(561\) | 10.3951 | 0.438883 | ||||||||
\(562\) | 3.29557 | 0.139015 | ||||||||
\(563\) | 1.13095 | 0.0476638 | 0.0238319 | − | 0.999716i | \(-0.492413\pi\) | ||||
0.0238319 | + | 0.999716i | \(0.492413\pi\) | |||||||
\(564\) | −7.45264 | −0.313813 | ||||||||
\(565\) | −6.22232 | −0.261775 | ||||||||
\(566\) | −24.9865 | −1.05026 | ||||||||
\(567\) | −4.81484 | −0.202204 | ||||||||
\(568\) | 6.15722 | 0.258351 | ||||||||
\(569\) | 29.9381 | 1.25507 | 0.627535 | − | 0.778589i | \(-0.284064\pi\) | ||||
0.627535 | + | 0.778589i | \(0.284064\pi\) | |||||||
\(570\) | 1.98345 | 0.0830775 | ||||||||
\(571\) | 1.46445 | 0.0612854 | 0.0306427 | − | 0.999530i | \(-0.490245\pi\) | ||||
0.0306427 | + | 0.999530i | \(0.490245\pi\) | |||||||
\(572\) | −1.68147 | −0.0703059 | ||||||||
\(573\) | 12.0110 | 0.501766 | ||||||||
\(574\) | 57.6203 | 2.40503 | ||||||||
\(575\) | −3.98098 | −0.166018 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 42.4814 | 1.76852 | 0.884262 | − | 0.466990i | \(-0.154662\pi\) | ||||
0.884262 | + | 0.466990i | \(0.154662\pi\) | |||||||
\(578\) | −21.2192 | −0.882602 | ||||||||
\(579\) | −12.2193 | −0.507817 | ||||||||
\(580\) | 10.5441 | 0.437819 | ||||||||
\(581\) | 5.89150 | 0.244421 | ||||||||
\(582\) | 8.09177 | 0.335415 | ||||||||
\(583\) | 7.63480 | 0.316201 | ||||||||
\(584\) | −16.5077 | −0.683092 | ||||||||
\(585\) | 2.57230 | 0.106352 | ||||||||
\(586\) | 9.62707 | 0.397691 | ||||||||
\(587\) | −30.5500 | −1.26093 | −0.630466 | − | 0.776217i | \(-0.717136\pi\) | ||||
−0.630466 | + | 0.776217i | \(0.717136\pi\) | |||||||
\(588\) | 16.1827 | 0.667362 | ||||||||
\(589\) | −5.68063 | −0.234066 | ||||||||
\(590\) | −15.2245 | −0.626784 | ||||||||
\(591\) | 5.75541 | 0.236746 | ||||||||
\(592\) | 7.10946 | 0.292197 | ||||||||
\(593\) | −43.2197 | −1.77482 | −0.887411 | − | 0.460979i | \(-0.847498\pi\) | ||||
−0.887411 | + | 0.460979i | \(0.847498\pi\) | |||||||
\(594\) | −1.68147 | −0.0689916 | ||||||||
\(595\) | 76.5676 | 3.13896 | ||||||||
\(596\) | −16.3859 | −0.671194 | ||||||||
\(597\) | −24.5893 | −1.00637 | ||||||||
\(598\) | −2.46234 | −0.100692 | ||||||||
\(599\) | 36.4711 | 1.49017 | 0.745085 | − | 0.666970i | \(-0.232409\pi\) | ||||
0.745085 | + | 0.666970i | \(0.232409\pi\) | |||||||
\(600\) | −1.61675 | −0.0660035 | ||||||||
\(601\) | −22.2340 | −0.906944 | −0.453472 | − | 0.891271i | \(-0.649815\pi\) | ||||
−0.453472 | + | 0.891271i | \(0.649815\pi\) | |||||||
\(602\) | 23.4620 | 0.956240 | ||||||||
\(603\) | −9.81599 | −0.399738 | ||||||||
\(604\) | 19.8000 | 0.805650 | ||||||||
\(605\) | 21.0226 | 0.854688 | ||||||||
\(606\) | −6.68754 | −0.271663 | ||||||||
\(607\) | 25.0935 | 1.01851 | 0.509257 | − | 0.860614i | \(-0.329920\pi\) | ||||
0.509257 | + | 0.860614i | \(0.329920\pi\) | |||||||
\(608\) | −0.771079 | −0.0312714 | ||||||||
\(609\) | 19.7364 | 0.799759 | ||||||||
\(610\) | −0.226819 | −0.00918363 | ||||||||
\(611\) | 7.45264 | 0.301501 | ||||||||
\(612\) | 6.18217 | 0.249899 | ||||||||
\(613\) | 13.6964 | 0.553193 | 0.276597 | − | 0.960986i | \(-0.410793\pi\) | ||||
0.276597 | + | 0.960986i | \(0.410793\pi\) | |||||||
\(614\) | 20.2738 | 0.818186 | ||||||||
\(615\) | −30.7834 | −1.24131 | ||||||||
\(616\) | 8.09602 | 0.326198 | ||||||||
\(617\) | 27.3265 | 1.10012 | 0.550061 | − | 0.835124i | \(-0.314604\pi\) | ||||
0.550061 | + | 0.835124i | \(0.314604\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | −30.5733 | −1.22885 | −0.614423 | − | 0.788977i | \(-0.710611\pi\) | ||||
−0.614423 | + | 0.788977i | \(0.710611\pi\) | |||||||
\(620\) | 18.9505 | 0.761070 | ||||||||
\(621\) | −2.46234 | −0.0988101 | ||||||||
\(622\) | 32.4947 | 1.30292 | ||||||||
\(623\) | −31.0832 | −1.24532 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −30.4699 | −1.21879 | ||||||||
\(626\) | −7.50820 | −0.300088 | ||||||||
\(627\) | 1.29655 | 0.0517791 | ||||||||
\(628\) | 16.4161 | 0.655073 | ||||||||
\(629\) | 43.9519 | 1.75248 | ||||||||
\(630\) | −12.3852 | −0.493439 | ||||||||
\(631\) | −41.5796 | −1.65526 | −0.827628 | − | 0.561277i | \(-0.810310\pi\) | ||||
−0.827628 | + | 0.561277i | \(0.810310\pi\) | |||||||
\(632\) | 3.92812 | 0.156252 | ||||||||
\(633\) | 7.63512 | 0.303469 | ||||||||
\(634\) | 2.86805 | 0.113905 | ||||||||
\(635\) | −47.9312 | −1.90209 | ||||||||
\(636\) | 4.54055 | 0.180044 | ||||||||
\(637\) | −16.1827 | −0.641181 | ||||||||
\(638\) | 6.89248 | 0.272876 | ||||||||
\(639\) | −6.15722 | −0.243576 | ||||||||
\(640\) | 2.57230 | 0.101679 | ||||||||
\(641\) | 32.9251 | 1.30046 | 0.650232 | − | 0.759736i | \(-0.274672\pi\) | ||||
0.650232 | + | 0.759736i | \(0.274672\pi\) | |||||||
\(642\) | −9.93787 | −0.392216 | ||||||||
\(643\) | −40.5674 | −1.59982 | −0.799911 | − | 0.600119i | \(-0.795120\pi\) | ||||
−0.799911 | + | 0.600119i | \(0.795120\pi\) | |||||||
\(644\) | 11.8557 | 0.467182 | ||||||||
\(645\) | −12.5345 | −0.493544 | ||||||||
\(646\) | −4.76694 | −0.187553 | ||||||||
\(647\) | 3.50592 | 0.137832 | 0.0689160 | − | 0.997622i | \(-0.478046\pi\) | ||||
0.0689160 | + | 0.997622i | \(0.478046\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −9.95202 | −0.390651 | ||||||||
\(650\) | 1.61675 | 0.0634141 | ||||||||
\(651\) | 35.4715 | 1.39024 | ||||||||
\(652\) | −17.7158 | −0.693803 | ||||||||
\(653\) | −23.6156 | −0.924149 | −0.462075 | − | 0.886841i | \(-0.652895\pi\) | ||||
−0.462075 | + | 0.886841i | \(0.652895\pi\) | |||||||
\(654\) | −10.9229 | −0.427120 | ||||||||
\(655\) | 40.7387 | 1.59179 | ||||||||
\(656\) | 11.9672 | 0.467242 | ||||||||
\(657\) | 16.5077 | 0.644025 | ||||||||
\(658\) | −35.8832 | −1.39887 | ||||||||
\(659\) | −10.2901 | −0.400846 | −0.200423 | − | 0.979709i | \(-0.564232\pi\) | ||||
−0.200423 | + | 0.979709i | \(0.564232\pi\) | |||||||
\(660\) | −4.32526 | −0.168360 | ||||||||
\(661\) | 3.85558 | 0.149965 | 0.0749824 | − | 0.997185i | \(-0.476110\pi\) | ||||
0.0749824 | + | 0.997185i | \(0.476110\pi\) | |||||||
\(662\) | −26.5172 | −1.03062 | ||||||||
\(663\) | −6.18217 | −0.240095 | ||||||||
\(664\) | 1.22361 | 0.0474854 | ||||||||
\(665\) | 9.54999 | 0.370333 | ||||||||
\(666\) | −7.10946 | −0.275486 | ||||||||
\(667\) | 10.0933 | 0.390814 | ||||||||
\(668\) | −15.7136 | −0.607977 | ||||||||
\(669\) | 3.09337 | 0.119597 | ||||||||
\(670\) | −25.2497 | −0.975482 | ||||||||
\(671\) | −0.148268 | −0.00572381 | ||||||||
\(672\) | 4.81484 | 0.185736 | ||||||||
\(673\) | 22.6898 | 0.874626 | 0.437313 | − | 0.899309i | \(-0.355930\pi\) | ||||
0.437313 | + | 0.899309i | \(0.355930\pi\) | |||||||
\(674\) | 14.6616 | 0.564743 | ||||||||
\(675\) | 1.61675 | 0.0622287 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 0.215423 | 0.00827938 | 0.00413969 | − | 0.999991i | \(-0.498682\pi\) | ||||
0.00413969 | + | 0.999991i | \(0.498682\pi\) | |||||||
\(678\) | −2.41897 | −0.0928999 | ||||||||
\(679\) | 38.9606 | 1.49517 | ||||||||
\(680\) | 15.9024 | 0.609830 | ||||||||
\(681\) | −24.1516 | −0.925492 | ||||||||
\(682\) | 12.3876 | 0.474346 | ||||||||
\(683\) | −7.30937 | −0.279685 | −0.139843 | − | 0.990174i | \(-0.544660\pi\) | ||||
−0.139843 | + | 0.990174i | \(0.544660\pi\) | |||||||
\(684\) | 0.771079 | 0.0294829 | ||||||||
\(685\) | 5.23298 | 0.199942 | ||||||||
\(686\) | 44.2131 | 1.68807 | ||||||||
\(687\) | −9.02543 | −0.344342 | ||||||||
\(688\) | 4.87285 | 0.185776 | ||||||||
\(689\) | −4.54055 | −0.172981 | ||||||||
\(690\) | −6.33388 | −0.241127 | ||||||||
\(691\) | 39.3684 | 1.49765 | 0.748823 | − | 0.662770i | \(-0.230619\pi\) | ||||
0.748823 | + | 0.662770i | \(0.230619\pi\) | |||||||
\(692\) | 8.65865 | 0.329153 | ||||||||
\(693\) | −8.09602 | −0.307542 | ||||||||
\(694\) | −2.56359 | −0.0973125 | ||||||||
\(695\) | −3.46489 | −0.131431 | ||||||||
\(696\) | 4.09908 | 0.155375 | ||||||||
\(697\) | 73.9835 | 2.80232 | ||||||||
\(698\) | 24.6663 | 0.933632 | ||||||||
\(699\) | −19.8825 | −0.752027 | ||||||||
\(700\) | −7.78439 | −0.294222 | ||||||||
\(701\) | −21.0019 | −0.793232 | −0.396616 | − | 0.917985i | \(-0.629816\pi\) | ||||
−0.396616 | + | 0.917985i | \(0.629816\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | 5.48195 | 0.206756 | ||||||||
\(704\) | 1.68147 | 0.0633728 | ||||||||
\(705\) | 19.1704 | 0.722001 | ||||||||
\(706\) | −11.7074 | −0.440614 | ||||||||
\(707\) | −32.1994 | −1.21098 | ||||||||
\(708\) | −5.91864 | −0.222436 | ||||||||
\(709\) | 0.353263 | 0.0132671 | 0.00663354 | − | 0.999978i | \(-0.497888\pi\) | ||||
0.00663354 | + | 0.999978i | \(0.497888\pi\) | |||||||
\(710\) | −15.8382 | −0.594399 | ||||||||
\(711\) | −3.92812 | −0.147316 | ||||||||
\(712\) | −6.45570 | −0.241938 | ||||||||
\(713\) | 18.1403 | 0.679361 | ||||||||
\(714\) | 29.7661 | 1.11397 | ||||||||
\(715\) | 4.32526 | 0.161755 | ||||||||
\(716\) | −16.8361 | −0.629196 | ||||||||
\(717\) | −21.7455 | −0.812102 | ||||||||
\(718\) | 2.53080 | 0.0944484 | ||||||||
\(719\) | 8.28885 | 0.309122 | 0.154561 | − | 0.987983i | \(-0.450604\pi\) | ||||
0.154561 | + | 0.987983i | \(0.450604\pi\) | |||||||
\(720\) | −2.57230 | −0.0958641 | ||||||||
\(721\) | −4.81484 | −0.179314 | ||||||||
\(722\) | 18.4054 | 0.684979 | ||||||||
\(723\) | −29.9056 | −1.11220 | ||||||||
\(724\) | 0.312325 | 0.0116075 | ||||||||
\(725\) | −6.62718 | −0.246127 | ||||||||
\(726\) | 8.17265 | 0.303316 | ||||||||
\(727\) | 41.0157 | 1.52119 | 0.760594 | − | 0.649228i | \(-0.224908\pi\) | ||||
0.760594 | + | 0.649228i | \(0.224908\pi\) | |||||||
\(728\) | −4.81484 | −0.178450 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 42.4627 | 1.57162 | ||||||||
\(731\) | 30.1248 | 1.11421 | ||||||||
\(732\) | −0.0881773 | −0.00325913 | ||||||||
\(733\) | 2.14522 | 0.0792354 | 0.0396177 | − | 0.999215i | \(-0.487386\pi\) | ||||
0.0396177 | + | 0.999215i | \(0.487386\pi\) | |||||||
\(734\) | −5.13485 | −0.189531 | ||||||||
\(735\) | −41.6268 | −1.53543 | ||||||||
\(736\) | 2.46234 | 0.0907629 | ||||||||
\(737\) | −16.5053 | −0.607981 | ||||||||
\(738\) | −11.9672 | −0.440520 | ||||||||
\(739\) | −27.8164 | −1.02324 | −0.511622 | − | 0.859211i | \(-0.670955\pi\) | ||||
−0.511622 | + | 0.859211i | \(0.670955\pi\) | |||||||
\(740\) | −18.2877 | −0.672269 | ||||||||
\(741\) | −0.771079 | −0.0283263 | ||||||||
\(742\) | 21.8620 | 0.802579 | ||||||||
\(743\) | 43.1157 | 1.58176 | 0.790881 | − | 0.611970i | \(-0.209623\pi\) | ||||
0.790881 | + | 0.611970i | \(0.209623\pi\) | |||||||
\(744\) | 7.36712 | 0.270092 | ||||||||
\(745\) | 42.1496 | 1.54424 | ||||||||
\(746\) | 33.0765 | 1.21102 | ||||||||
\(747\) | −1.22361 | −0.0447696 | ||||||||
\(748\) | 10.3951 | 0.380084 | ||||||||
\(749\) | −47.8492 | −1.74837 | ||||||||
\(750\) | −8.70275 | −0.317780 | ||||||||
\(751\) | 6.62649 | 0.241804 | 0.120902 | − | 0.992664i | \(-0.461421\pi\) | ||||
0.120902 | + | 0.992664i | \(0.461421\pi\) | |||||||
\(752\) | −7.45264 | −0.271770 | ||||||||
\(753\) | −10.3576 | −0.377453 | ||||||||
\(754\) | −4.09908 | −0.149280 | ||||||||
\(755\) | −50.9316 | −1.85359 | ||||||||
\(756\) | −4.81484 | −0.175114 | ||||||||
\(757\) | −0.588080 | −0.0213741 | −0.0106871 | − | 0.999943i | \(-0.503402\pi\) | ||||
−0.0106871 | + | 0.999943i | \(0.503402\pi\) | |||||||
\(758\) | 15.1628 | 0.550737 | ||||||||
\(759\) | −4.14035 | −0.150285 | ||||||||
\(760\) | 1.98345 | 0.0719473 | ||||||||
\(761\) | 27.9768 | 1.01416 | 0.507079 | − | 0.861899i | \(-0.330725\pi\) | ||||
0.507079 | + | 0.861899i | \(0.330725\pi\) | |||||||
\(762\) | −18.6336 | −0.675023 | ||||||||
\(763\) | −52.5921 | −1.90396 | ||||||||
\(764\) | 12.0110 | 0.434542 | ||||||||
\(765\) | −15.9024 | −0.574953 | ||||||||
\(766\) | 31.7073 | 1.14563 | ||||||||
\(767\) | 5.91864 | 0.213710 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 49.9214 | 1.80021 | 0.900106 | − | 0.435670i | \(-0.143489\pi\) | ||||
0.900106 | + | 0.435670i | \(0.143489\pi\) | |||||||
\(770\) | −20.8254 | −0.750496 | ||||||||
\(771\) | −2.58228 | −0.0929987 | ||||||||
\(772\) | −12.2193 | −0.439782 | ||||||||
\(773\) | 0.172234 | 0.00619482 | 0.00309741 | − | 0.999995i | \(-0.499014\pi\) | ||||
0.00309741 | + | 0.999995i | \(0.499014\pi\) | |||||||
\(774\) | −4.87285 | −0.175151 | ||||||||
\(775\) | −11.9108 | −0.427848 | ||||||||
\(776\) | 8.09177 | 0.290478 | ||||||||
\(777\) | −34.2309 | −1.22803 | ||||||||
\(778\) | 23.6651 | 0.848434 | ||||||||
\(779\) | 9.22768 | 0.330616 | ||||||||
\(780\) | 2.57230 | 0.0921033 | ||||||||
\(781\) | −10.3532 | −0.370466 | ||||||||
\(782\) | 15.2226 | 0.544358 | ||||||||
\(783\) | −4.09908 | −0.146489 | ||||||||
\(784\) | 16.1827 | 0.577953 | ||||||||
\(785\) | −42.2271 | −1.50715 | ||||||||
\(786\) | 15.8374 | 0.564902 | ||||||||
\(787\) | 32.4074 | 1.15520 | 0.577599 | − | 0.816321i | \(-0.303990\pi\) | ||||
0.577599 | + | 0.816321i | \(0.303990\pi\) | |||||||
\(788\) | 5.75541 | 0.205028 | ||||||||
\(789\) | −19.9903 | −0.711672 | ||||||||
\(790\) | −10.1043 | −0.359495 | ||||||||
\(791\) | −11.6469 | −0.414118 | ||||||||
\(792\) | −1.68147 | −0.0597485 | ||||||||
\(793\) | 0.0881773 | 0.00313127 | ||||||||
\(794\) | −25.1755 | −0.893446 | ||||||||
\(795\) | −11.6797 | −0.414235 | ||||||||
\(796\) | −24.5893 | −0.871544 | ||||||||
\(797\) | 15.5656 | 0.551363 | 0.275682 | − | 0.961249i | \(-0.411096\pi\) | ||||
0.275682 | + | 0.961249i | \(0.411096\pi\) | |||||||
\(798\) | 3.71262 | 0.131425 | ||||||||
\(799\) | −46.0734 | −1.62996 | ||||||||
\(800\) | −1.61675 | −0.0571607 | ||||||||
\(801\) | 6.45570 | 0.228101 | ||||||||
\(802\) | 15.0419 | 0.531149 | ||||||||
\(803\) | 27.7572 | 0.979529 | ||||||||
\(804\) | −9.81599 | −0.346183 | ||||||||
\(805\) | −30.4966 | −1.07486 | ||||||||
\(806\) | −7.36712 | −0.259496 | ||||||||
\(807\) | −1.69478 | −0.0596591 | ||||||||
\(808\) | −6.68754 | −0.235267 | ||||||||
\(809\) | −45.8293 | −1.61127 | −0.805636 | − | 0.592411i | \(-0.798176\pi\) | ||||
−0.805636 | + | 0.592411i | \(0.798176\pi\) | |||||||
\(810\) | 2.57230 | 0.0903816 | ||||||||
\(811\) | 0.288999 | 0.0101481 | 0.00507406 | − | 0.999987i | \(-0.498385\pi\) | ||||
0.00507406 | + | 0.999987i | \(0.498385\pi\) | |||||||
\(812\) | 19.7364 | 0.692612 | ||||||||
\(813\) | 24.7894 | 0.869402 | ||||||||
\(814\) | −11.9544 | −0.419000 | ||||||||
\(815\) | 45.5703 | 1.59626 | ||||||||
\(816\) | 6.18217 | 0.216419 | ||||||||
\(817\) | 3.75735 | 0.131453 | ||||||||
\(818\) | −20.1039 | −0.702915 | ||||||||
\(819\) | 4.81484 | 0.168244 | ||||||||
\(820\) | −30.7834 | −1.07500 | ||||||||
\(821\) | −32.2067 | −1.12402 | −0.562011 | − | 0.827130i | \(-0.689972\pi\) | ||||
−0.562011 | + | 0.827130i | \(0.689972\pi\) | |||||||
\(822\) | 2.03436 | 0.0709563 | ||||||||
\(823\) | 42.5356 | 1.48270 | 0.741349 | − | 0.671120i | \(-0.234186\pi\) | ||||
0.741349 | + | 0.671120i | \(0.234186\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 2.71852 | 0.0946466 | ||||||||
\(826\) | −28.4973 | −0.991548 | ||||||||
\(827\) | −39.6858 | −1.38001 | −0.690006 | − | 0.723804i | \(-0.742392\pi\) | ||||
−0.690006 | + | 0.723804i | \(0.742392\pi\) | |||||||
\(828\) | −2.46234 | −0.0855721 | ||||||||
\(829\) | −4.07853 | −0.141653 | −0.0708266 | − | 0.997489i | \(-0.522564\pi\) | ||||
−0.0708266 | + | 0.997489i | \(0.522564\pi\) | |||||||
\(830\) | −3.14750 | −0.109251 | ||||||||
\(831\) | −3.08089 | −0.106875 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 100.044 | 3.46632 | ||||||||
\(834\) | −1.34700 | −0.0466427 | ||||||||
\(835\) | 40.4202 | 1.39880 | ||||||||
\(836\) | 1.29655 | 0.0448420 | ||||||||
\(837\) | −7.36712 | −0.254645 | ||||||||
\(838\) | 34.5445 | 1.19332 | ||||||||
\(839\) | 36.1407 | 1.24772 | 0.623858 | − | 0.781538i | \(-0.285564\pi\) | ||||
0.623858 | + | 0.781538i | \(0.285564\pi\) | |||||||
\(840\) | −12.3852 | −0.427331 | ||||||||
\(841\) | −12.1976 | −0.420606 | ||||||||
\(842\) | −4.53726 | −0.156364 | ||||||||
\(843\) | −3.29557 | −0.113505 | ||||||||
\(844\) | 7.63512 | 0.262812 | ||||||||
\(845\) | −2.57230 | −0.0884900 | ||||||||
\(846\) | 7.45264 | 0.256227 | ||||||||
\(847\) | 39.3500 | 1.35208 | ||||||||
\(848\) | 4.54055 | 0.155923 | ||||||||
\(849\) | 24.9865 | 0.857534 | ||||||||
\(850\) | −9.99501 | −0.342826 | ||||||||
\(851\) | −17.5059 | −0.600093 | ||||||||
\(852\) | −6.15722 | −0.210943 | ||||||||
\(853\) | 26.1799 | 0.896383 | 0.448192 | − | 0.893938i | \(-0.352068\pi\) | ||||
0.448192 | + | 0.893938i | \(0.352068\pi\) | |||||||
\(854\) | −0.424560 | −0.0145281 | ||||||||
\(855\) | −1.98345 | −0.0678325 | ||||||||
\(856\) | −9.93787 | −0.339669 | ||||||||
\(857\) | −7.27431 | −0.248486 | −0.124243 | − | 0.992252i | \(-0.539650\pi\) | ||||
−0.124243 | + | 0.992252i | \(0.539650\pi\) | |||||||
\(858\) | 1.68147 | 0.0574045 | ||||||||
\(859\) | 9.31821 | 0.317933 | 0.158967 | − | 0.987284i | \(-0.449184\pi\) | ||||
0.158967 | + | 0.987284i | \(0.449184\pi\) | |||||||
\(860\) | −12.5345 | −0.427421 | ||||||||
\(861\) | −57.6203 | −1.96370 | ||||||||
\(862\) | −8.15170 | −0.277648 | ||||||||
\(863\) | 53.2521 | 1.81272 | 0.906361 | − | 0.422504i | \(-0.138849\pi\) | ||||
0.906361 | + | 0.422504i | \(0.138849\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −22.2727 | −0.757294 | ||||||||
\(866\) | 24.1238 | 0.819759 | ||||||||
\(867\) | 21.2192 | 0.720641 | ||||||||
\(868\) | 35.4715 | 1.20398 | ||||||||
\(869\) | −6.60502 | −0.224060 | ||||||||
\(870\) | −10.5441 | −0.357478 | ||||||||
\(871\) | 9.81599 | 0.332602 | ||||||||
\(872\) | −10.9229 | −0.369897 | ||||||||
\(873\) | −8.09177 | −0.273865 | ||||||||
\(874\) | 1.89865 | 0.0642229 | ||||||||
\(875\) | −41.9023 | −1.41656 | ||||||||
\(876\) | 16.5077 | 0.557742 | ||||||||
\(877\) | 43.1811 | 1.45812 | 0.729061 | − | 0.684449i | \(-0.239957\pi\) | ||||
0.729061 | + | 0.684449i | \(0.239957\pi\) | |||||||
\(878\) | −34.3120 | −1.15797 | ||||||||
\(879\) | −9.62707 | −0.324713 | ||||||||
\(880\) | −4.32526 | −0.145804 | ||||||||
\(881\) | −24.2449 | −0.816831 | −0.408415 | − | 0.912796i | \(-0.633919\pi\) | ||||
−0.408415 | + | 0.912796i | \(0.633919\pi\) | |||||||
\(882\) | −16.1827 | −0.544899 | ||||||||
\(883\) | −32.1646 | −1.08243 | −0.541213 | − | 0.840885i | \(-0.682035\pi\) | ||||
−0.541213 | + | 0.840885i | \(0.682035\pi\) | |||||||
\(884\) | −6.18217 | −0.207929 | ||||||||
\(885\) | 15.2245 | 0.511767 | ||||||||
\(886\) | −13.8306 | −0.464649 | ||||||||
\(887\) | 19.8279 | 0.665757 | 0.332878 | − | 0.942970i | \(-0.391980\pi\) | ||||
0.332878 | + | 0.942970i | \(0.391980\pi\) | |||||||
\(888\) | −7.10946 | −0.238578 | ||||||||
\(889\) | −89.7176 | −3.00903 | ||||||||
\(890\) | 16.6060 | 0.556635 | ||||||||
\(891\) | 1.68147 | 0.0563314 | ||||||||
\(892\) | 3.09337 | 0.103574 | ||||||||
\(893\) | −5.74657 | −0.192302 | ||||||||
\(894\) | 16.3859 | 0.548027 | ||||||||
\(895\) | 43.3076 | 1.44761 | ||||||||
\(896\) | 4.81484 | 0.160852 | ||||||||
\(897\) | 2.46234 | 0.0822150 | ||||||||
\(898\) | −1.18499 | −0.0395435 | ||||||||
\(899\) | 30.1984 | 1.00717 | ||||||||
\(900\) | 1.61675 | 0.0538916 | ||||||||
\(901\) | 28.0704 | 0.935161 | ||||||||
\(902\) | −20.1226 | −0.670008 | ||||||||
\(903\) | −23.4620 | −0.780766 | ||||||||
\(904\) | −2.41897 | −0.0804537 | ||||||||
\(905\) | −0.803394 | −0.0267057 | ||||||||
\(906\) | −19.8000 | −0.657810 | ||||||||
\(907\) | 15.5207 | 0.515358 | 0.257679 | − | 0.966231i | \(-0.417042\pi\) | ||||
0.257679 | + | 0.966231i | \(0.417042\pi\) | |||||||
\(908\) | −24.1516 | −0.801499 | ||||||||
\(909\) | 6.68754 | 0.221812 | ||||||||
\(910\) | 12.3852 | 0.410566 | ||||||||
\(911\) | −2.59413 | −0.0859473 | −0.0429737 | − | 0.999076i | \(-0.513683\pi\) | ||||
−0.0429737 | + | 0.999076i | \(0.513683\pi\) | |||||||
\(912\) | 0.771079 | 0.0255330 | ||||||||
\(913\) | −2.05747 | −0.0680923 | ||||||||
\(914\) | −10.8635 | −0.359331 | ||||||||
\(915\) | 0.226819 | 0.00749840 | ||||||||
\(916\) | −9.02543 | −0.298209 | ||||||||
\(917\) | 76.2547 | 2.51815 | ||||||||
\(918\) | −6.18217 | −0.204042 | ||||||||
\(919\) | −41.1902 | −1.35874 | −0.679370 | − | 0.733796i | \(-0.737747\pi\) | ||||
−0.679370 | + | 0.733796i | \(0.737747\pi\) | |||||||
\(920\) | −6.33388 | −0.208822 | ||||||||
\(921\) | −20.2738 | −0.668046 | ||||||||
\(922\) | 22.7229 | 0.748339 | ||||||||
\(923\) | 6.15722 | 0.202667 | ||||||||
\(924\) | −8.09602 | −0.266339 | ||||||||
\(925\) | 11.4942 | 0.377927 | ||||||||
\(926\) | 24.7743 | 0.814134 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 4.09908 | 0.134559 | ||||||||
\(929\) | −19.9731 | −0.655295 | −0.327647 | − | 0.944800i | \(-0.606256\pi\) | ||||
−0.327647 | + | 0.944800i | \(0.606256\pi\) | |||||||
\(930\) | −18.9505 | −0.621411 | ||||||||
\(931\) | 12.4781 | 0.408954 | ||||||||
\(932\) | −19.8825 | −0.651274 | ||||||||
\(933\) | −32.4947 | −1.06383 | ||||||||
\(934\) | −10.2797 | −0.336361 | ||||||||
\(935\) | −26.7395 | −0.874474 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | −16.4352 | −0.536914 | −0.268457 | − | 0.963292i | \(-0.586514\pi\) | ||||
−0.268457 | + | 0.963292i | \(0.586514\pi\) | |||||||
\(938\) | −47.2624 | −1.54317 | ||||||||
\(939\) | 7.50820 | 0.245021 | ||||||||
\(940\) | 19.1704 | 0.625271 | ||||||||
\(941\) | −7.53303 | −0.245570 | −0.122785 | − | 0.992433i | \(-0.539183\pi\) | ||||
−0.122785 | + | 0.992433i | \(0.539183\pi\) | |||||||
\(942\) | −16.4161 | −0.534865 | ||||||||
\(943\) | −29.4673 | −0.959589 | ||||||||
\(944\) | −5.91864 | −0.192635 | ||||||||
\(945\) | 12.3852 | 0.402892 | ||||||||
\(946\) | −8.19356 | −0.266396 | ||||||||
\(947\) | 55.7249 | 1.81082 | 0.905408 | − | 0.424543i | \(-0.139565\pi\) | ||||
0.905408 | + | 0.424543i | \(0.139565\pi\) | |||||||
\(948\) | −3.92812 | −0.127579 | ||||||||
\(949\) | −16.5077 | −0.535861 | ||||||||
\(950\) | −1.24664 | −0.0404464 | ||||||||
\(951\) | −2.86805 | −0.0930029 | ||||||||
\(952\) | 29.7661 | 0.964726 | ||||||||
\(953\) | −32.8411 | −1.06383 | −0.531913 | − | 0.846799i | \(-0.678527\pi\) | ||||
−0.531913 | + | 0.846799i | \(0.678527\pi\) | |||||||
\(954\) | −4.54055 | −0.147006 | ||||||||
\(955\) | −30.8959 | −0.999767 | ||||||||
\(956\) | −21.7455 | −0.703301 | ||||||||
\(957\) | −6.89248 | −0.222802 | ||||||||
\(958\) | 17.4984 | 0.565348 | ||||||||
\(959\) | 9.79510 | 0.316300 | ||||||||
\(960\) | −2.57230 | −0.0830208 | ||||||||
\(961\) | 23.2745 | 0.750790 | ||||||||
\(962\) | 7.10946 | 0.229218 | ||||||||
\(963\) | 9.93787 | 0.320243 | ||||||||
\(964\) | −29.9056 | −0.963195 | ||||||||
\(965\) | 31.4318 | 1.01182 | ||||||||
\(966\) | −11.8557 | −0.381452 | ||||||||
\(967\) | −25.3198 | −0.814229 | −0.407115 | − | 0.913377i | \(-0.633465\pi\) | ||||
−0.407115 | + | 0.913377i | \(0.633465\pi\) | |||||||
\(968\) | 8.17265 | 0.262679 | ||||||||
\(969\) | 4.76694 | 0.153136 | ||||||||
\(970\) | −20.8145 | −0.668313 | ||||||||
\(971\) | 10.8294 | 0.347531 | 0.173766 | − | 0.984787i | \(-0.444406\pi\) | ||||
0.173766 | + | 0.984787i | \(0.444406\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −6.48558 | −0.207918 | ||||||||
\(974\) | −31.5809 | −1.01192 | ||||||||
\(975\) | −1.61675 | −0.0517774 | ||||||||
\(976\) | −0.0881773 | −0.00282249 | ||||||||
\(977\) | 1.64292 | 0.0525616 | 0.0262808 | − | 0.999655i | \(-0.491634\pi\) | ||||
0.0262808 | + | 0.999655i | \(0.491634\pi\) | |||||||
\(978\) | 17.7158 | 0.566488 | ||||||||
\(979\) | 10.8551 | 0.346930 | ||||||||
\(980\) | −41.6268 | −1.32972 | ||||||||
\(981\) | 10.9229 | 0.348742 | ||||||||
\(982\) | −15.1300 | −0.482818 | ||||||||
\(983\) | 0.103025 | 0.00328598 | 0.00164299 | − | 0.999999i | \(-0.499477\pi\) | ||||
0.00164299 | + | 0.999999i | \(0.499477\pi\) | |||||||
\(984\) | −11.9672 | −0.381502 | ||||||||
\(985\) | −14.8047 | −0.471716 | ||||||||
\(986\) | 25.3412 | 0.807027 | ||||||||
\(987\) | 35.8832 | 1.14218 | ||||||||
\(988\) | −0.771079 | −0.0245313 | ||||||||
\(989\) | −11.9986 | −0.381533 | ||||||||
\(990\) | 4.32526 | 0.137466 | ||||||||
\(991\) | −53.0705 | −1.68584 | −0.842920 | − | 0.538038i | \(-0.819166\pi\) | ||||
−0.842920 | + | 0.538038i | \(0.819166\pi\) | |||||||
\(992\) | 7.36712 | 0.233906 | ||||||||
\(993\) | 26.5172 | 0.841497 | ||||||||
\(994\) | −29.6460 | −0.940315 | ||||||||
\(995\) | 63.2511 | 2.00520 | ||||||||
\(996\) | −1.22361 | −0.0387717 | ||||||||
\(997\) | −27.8641 | −0.882465 | −0.441233 | − | 0.897393i | \(-0.645459\pi\) | ||||
−0.441233 | + | 0.897393i | \(0.645459\pi\) | |||||||
\(998\) | −6.31066 | −0.199761 | ||||||||
\(999\) | 7.10946 | 0.224933 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8034.2.a.bb.1.4 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.bb.1.4 | ✓ | 14 | 1.1 | even | 1 | trivial |