Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4002,2,Mod(1,4002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4002, 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("4002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4002.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: | \(31.9561308889\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.2389280.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 11x^{3} + 7x^{2} + 26x - 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(3.13869\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4002.1 |
$q$-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 | ||||||||
\(5\) | 3.53070 | 1.57898 | 0.789489 | − | 0.613765i | \(-0.210346\pi\) | ||||
0.789489 | + | 0.613765i | \(0.210346\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.614480 | −0.232251 | −0.116126 | − | 0.993235i | \(-0.537048\pi\) | ||||
−0.116126 | + | 0.993235i | \(0.537048\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.53070 | −1.11651 | ||||||||
\(11\) | 0.607988 | 0.183315 | 0.0916577 | − | 0.995791i | \(-0.470783\pi\) | ||||
0.0916577 | + | 0.995791i | \(0.470783\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −5.13869 | −1.42522 | −0.712608 | − | 0.701562i | \(-0.752486\pi\) | ||||
−0.712608 | + | 0.701562i | \(0.752486\pi\) | |||||||
\(14\) | 0.614480 | 0.164227 | ||||||||
\(15\) | −3.53070 | −0.911623 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.89186 | −1.18645 | −0.593225 | − | 0.805037i | \(-0.702146\pi\) | ||||
−0.593225 | + | 0.805037i | \(0.702146\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 4.89186 | 1.12227 | 0.561135 | − | 0.827724i | \(-0.310365\pi\) | ||||
0.561135 | + | 0.827724i | \(0.310365\pi\) | |||||||
\(20\) | 3.53070 | 0.789489 | ||||||||
\(21\) | 0.614480 | 0.134090 | ||||||||
\(22\) | −0.607988 | −0.129624 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 7.46585 | 1.49317 | ||||||||
\(26\) | 5.13869 | 1.00778 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.614480 | −0.116126 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 3.53070 | 0.644615 | ||||||||
\(31\) | −0.273696 | −0.0491572 | −0.0245786 | − | 0.999698i | \(-0.507824\pi\) | ||||
−0.0245786 | + | 0.999698i | \(0.507824\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.607988 | −0.105837 | ||||||||
\(34\) | 4.89186 | 0.838947 | ||||||||
\(35\) | −2.16954 | −0.366720 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.09540 | −0.837678 | −0.418839 | − | 0.908060i | \(-0.637563\pi\) | ||||
−0.418839 | + | 0.908060i | \(0.637563\pi\) | |||||||
\(38\) | −4.89186 | −0.793564 | ||||||||
\(39\) | 5.13869 | 0.822849 | ||||||||
\(40\) | −3.53070 | −0.558253 | ||||||||
\(41\) | 5.34872 | 0.835330 | 0.417665 | − | 0.908601i | \(-0.362849\pi\) | ||||
0.417665 | + | 0.908601i | \(0.362849\pi\) | |||||||
\(42\) | −0.614480 | −0.0948163 | ||||||||
\(43\) | −1.78997 | −0.272968 | −0.136484 | − | 0.990642i | \(-0.543580\pi\) | ||||
−0.136484 | + | 0.990642i | \(0.543580\pi\) | |||||||
\(44\) | 0.607988 | 0.0916577 | ||||||||
\(45\) | 3.53070 | 0.526326 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −11.4953 | −1.67677 | −0.838384 | − | 0.545080i | \(-0.816499\pi\) | ||||
−0.838384 | + | 0.545080i | \(0.816499\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.62241 | −0.946059 | ||||||||
\(50\) | −7.46585 | −1.05583 | ||||||||
\(51\) | 4.89186 | 0.684997 | ||||||||
\(52\) | −5.13869 | −0.712608 | ||||||||
\(53\) | 1.81684 | 0.249562 | 0.124781 | − | 0.992184i | \(-0.460177\pi\) | ||||
0.124781 | + | 0.992184i | \(0.460177\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 2.14663 | 0.289451 | ||||||||
\(56\) | 0.614480 | 0.0821133 | ||||||||
\(57\) | −4.89186 | −0.647943 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | −2.87293 | −0.374024 | −0.187012 | − | 0.982358i | \(-0.559880\pi\) | ||||
−0.187012 | + | 0.982358i | \(0.559880\pi\) | |||||||
\(60\) | −3.53070 | −0.455812 | ||||||||
\(61\) | 12.9700 | 1.66063 | 0.830316 | − | 0.557293i | \(-0.188160\pi\) | ||||
0.830316 | + | 0.557293i | \(0.188160\pi\) | |||||||
\(62\) | 0.273696 | 0.0347594 | ||||||||
\(63\) | −0.614480 | −0.0774171 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −18.1432 | −2.25038 | ||||||||
\(66\) | 0.607988 | 0.0748382 | ||||||||
\(67\) | −11.7945 | −1.44092 | −0.720461 | − | 0.693495i | \(-0.756070\pi\) | ||||
−0.720461 | + | 0.693495i | \(0.756070\pi\) | |||||||
\(68\) | −4.89186 | −0.593225 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 2.16954 | 0.259310 | ||||||||
\(71\) | −7.92271 | −0.940253 | −0.470127 | − | 0.882599i | \(-0.655792\pi\) | ||||
−0.470127 | + | 0.882599i | \(0.655792\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −6.01561 | −0.704074 | −0.352037 | − | 0.935986i | \(-0.614511\pi\) | ||||
−0.352037 | + | 0.935986i | \(0.614511\pi\) | |||||||
\(74\) | 5.09540 | 0.592328 | ||||||||
\(75\) | −7.46585 | −0.862083 | ||||||||
\(76\) | 4.89186 | 0.561135 | ||||||||
\(77\) | −0.373596 | −0.0425753 | ||||||||
\(78\) | −5.13869 | −0.581842 | ||||||||
\(79\) | 0.712684 | 0.0801832 | 0.0400916 | − | 0.999196i | \(-0.487235\pi\) | ||||
0.0400916 | + | 0.999196i | \(0.487235\pi\) | |||||||
\(80\) | 3.53070 | 0.394744 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.34872 | −0.590667 | ||||||||
\(83\) | −12.8507 | −1.41055 | −0.705276 | − | 0.708933i | \(-0.749177\pi\) | ||||
−0.705276 | + | 0.708933i | \(0.749177\pi\) | |||||||
\(84\) | 0.614480 | 0.0670452 | ||||||||
\(85\) | −17.2717 | −1.87338 | ||||||||
\(86\) | 1.78997 | 0.193018 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | −0.607988 | −0.0648118 | ||||||||
\(89\) | 13.0889 | 1.38742 | 0.693711 | − | 0.720254i | \(-0.255975\pi\) | ||||
0.693711 | + | 0.720254i | \(0.255975\pi\) | |||||||
\(90\) | −3.53070 | −0.372169 | ||||||||
\(91\) | 3.15762 | 0.331008 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 0.273696 | 0.0283809 | ||||||||
\(94\) | 11.4953 | 1.18565 | ||||||||
\(95\) | 17.2717 | 1.77204 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −5.81684 | −0.590610 | −0.295305 | − | 0.955403i | \(-0.595421\pi\) | ||||
−0.295305 | + | 0.955403i | \(0.595421\pi\) | |||||||
\(98\) | 6.62241 | 0.668965 | ||||||||
\(99\) | 0.607988 | 0.0611051 | ||||||||
\(100\) | 7.46585 | 0.746585 | ||||||||
\(101\) | −10.9403 | −1.08860 | −0.544299 | − | 0.838891i | \(-0.683204\pi\) | ||||
−0.544299 | + | 0.838891i | \(0.683204\pi\) | |||||||
\(102\) | −4.89186 | −0.484366 | ||||||||
\(103\) | −1.01643 | −0.100152 | −0.0500758 | − | 0.998745i | \(-0.515946\pi\) | ||||
−0.0500758 | + | 0.998745i | \(0.515946\pi\) | |||||||
\(104\) | 5.13869 | 0.503890 | ||||||||
\(105\) | 2.16954 | 0.211726 | ||||||||
\(106\) | −1.81684 | −0.176467 | ||||||||
\(107\) | −12.7064 | −1.22838 | −0.614189 | − | 0.789159i | \(-0.710517\pi\) | ||||
−0.614189 | + | 0.789159i | \(0.710517\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 0.0431107 | 0.00412925 | 0.00206463 | − | 0.999998i | \(-0.499343\pi\) | ||||
0.00206463 | + | 0.999998i | \(0.499343\pi\) | |||||||
\(110\) | −2.14663 | −0.204673 | ||||||||
\(111\) | 5.09540 | 0.483634 | ||||||||
\(112\) | −0.614480 | −0.0580629 | ||||||||
\(113\) | 12.5541 | 1.18099 | 0.590496 | − | 0.807040i | \(-0.298932\pi\) | ||||
0.590496 | + | 0.807040i | \(0.298932\pi\) | |||||||
\(114\) | 4.89186 | 0.458165 | ||||||||
\(115\) | −3.53070 | −0.329240 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | −5.13869 | −0.475072 | ||||||||
\(118\) | 2.87293 | 0.264475 | ||||||||
\(119\) | 3.00595 | 0.275555 | ||||||||
\(120\) | 3.53070 | 0.322307 | ||||||||
\(121\) | −10.6304 | −0.966395 | ||||||||
\(122\) | −12.9700 | −1.17424 | ||||||||
\(123\) | −5.34872 | −0.482278 | ||||||||
\(124\) | −0.273696 | −0.0245786 | ||||||||
\(125\) | 8.70619 | 0.778706 | ||||||||
\(126\) | 0.614480 | 0.0547422 | ||||||||
\(127\) | −2.60917 | −0.231526 | −0.115763 | − | 0.993277i | \(-0.536931\pi\) | ||||
−0.115763 | + | 0.993277i | \(0.536931\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.78997 | 0.157598 | ||||||||
\(130\) | 18.1432 | 1.59126 | ||||||||
\(131\) | −5.35403 | −0.467784 | −0.233892 | − | 0.972263i | \(-0.575146\pi\) | ||||
−0.233892 | + | 0.972263i | \(0.575146\pi\) | |||||||
\(132\) | −0.607988 | −0.0529186 | ||||||||
\(133\) | −3.00595 | −0.260649 | ||||||||
\(134\) | 11.7945 | 1.01889 | ||||||||
\(135\) | −3.53070 | −0.303874 | ||||||||
\(136\) | 4.89186 | 0.419473 | ||||||||
\(137\) | 12.1503 | 1.03807 | 0.519035 | − | 0.854753i | \(-0.326291\pi\) | ||||
0.519035 | + | 0.854753i | \(0.326291\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −7.67652 | −0.651114 | −0.325557 | − | 0.945522i | \(-0.605552\pi\) | ||||
−0.325557 | + | 0.945522i | \(0.605552\pi\) | |||||||
\(140\) | −2.16954 | −0.183360 | ||||||||
\(141\) | 11.4953 | 0.968083 | ||||||||
\(142\) | 7.92271 | 0.664859 | ||||||||
\(143\) | −3.12426 | −0.261264 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −3.53070 | −0.293209 | ||||||||
\(146\) | 6.01561 | 0.497855 | ||||||||
\(147\) | 6.62241 | 0.546208 | ||||||||
\(148\) | −5.09540 | −0.418839 | ||||||||
\(149\) | 12.9587 | 1.06162 | 0.530809 | − | 0.847492i | \(-0.321888\pi\) | ||||
0.530809 | + | 0.847492i | \(0.321888\pi\) | |||||||
\(150\) | 7.46585 | 0.609584 | ||||||||
\(151\) | 2.37558 | 0.193322 | 0.0966612 | − | 0.995317i | \(-0.469184\pi\) | ||||
0.0966612 | + | 0.995317i | \(0.469184\pi\) | |||||||
\(152\) | −4.89186 | −0.396782 | ||||||||
\(153\) | −4.89186 | −0.395483 | ||||||||
\(154\) | 0.373596 | 0.0301053 | ||||||||
\(155\) | −0.966339 | −0.0776182 | ||||||||
\(156\) | 5.13869 | 0.411424 | ||||||||
\(157\) | 20.0757 | 1.60222 | 0.801108 | − | 0.598520i | \(-0.204244\pi\) | ||||
0.801108 | + | 0.598520i | \(0.204244\pi\) | |||||||
\(158\) | −0.712684 | −0.0566981 | ||||||||
\(159\) | −1.81684 | −0.144084 | ||||||||
\(160\) | −3.53070 | −0.279126 | ||||||||
\(161\) | 0.614480 | 0.0484278 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 17.0816 | 1.33793 | 0.668967 | − | 0.743292i | \(-0.266737\pi\) | ||||
0.668967 | + | 0.743292i | \(0.266737\pi\) | |||||||
\(164\) | 5.34872 | 0.417665 | ||||||||
\(165\) | −2.14663 | −0.167115 | ||||||||
\(166\) | 12.8507 | 0.997411 | ||||||||
\(167\) | 21.0475 | 1.62870 | 0.814351 | − | 0.580372i | \(-0.197093\pi\) | ||||
0.814351 | + | 0.580372i | \(0.197093\pi\) | |||||||
\(168\) | −0.614480 | −0.0474081 | ||||||||
\(169\) | 13.4061 | 1.03124 | ||||||||
\(170\) | 17.2717 | 1.32468 | ||||||||
\(171\) | 4.89186 | 0.374090 | ||||||||
\(172\) | −1.78997 | −0.136484 | ||||||||
\(173\) | 5.91740 | 0.449892 | 0.224946 | − | 0.974371i | \(-0.427779\pi\) | ||||
0.224946 | + | 0.974371i | \(0.427779\pi\) | |||||||
\(174\) | −1.00000 | −0.0758098 | ||||||||
\(175\) | −4.58761 | −0.346791 | ||||||||
\(176\) | 0.607988 | 0.0458288 | ||||||||
\(177\) | 2.87293 | 0.215943 | ||||||||
\(178\) | −13.0889 | −0.981055 | ||||||||
\(179\) | 22.0310 | 1.64667 | 0.823336 | − | 0.567554i | \(-0.192110\pi\) | ||||
0.823336 | + | 0.567554i | \(0.192110\pi\) | |||||||
\(180\) | 3.53070 | 0.263163 | ||||||||
\(181\) | −13.2542 | −0.985177 | −0.492588 | − | 0.870262i | \(-0.663949\pi\) | ||||
−0.492588 | + | 0.870262i | \(0.663949\pi\) | |||||||
\(182\) | −3.15762 | −0.234058 | ||||||||
\(183\) | −12.9700 | −0.958766 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −17.9903 | −1.32268 | ||||||||
\(186\) | −0.273696 | −0.0200684 | ||||||||
\(187\) | −2.97419 | −0.217495 | ||||||||
\(188\) | −11.4953 | −0.838384 | ||||||||
\(189\) | 0.614480 | 0.0446968 | ||||||||
\(190\) | −17.2717 | −1.25302 | ||||||||
\(191\) | −19.0549 | −1.37877 | −0.689383 | − | 0.724398i | \(-0.742118\pi\) | ||||
−0.689383 | + | 0.724398i | \(0.742118\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −8.39147 | −0.604031 | −0.302016 | − | 0.953303i | \(-0.597659\pi\) | ||||
−0.302016 | + | 0.953303i | \(0.597659\pi\) | |||||||
\(194\) | 5.81684 | 0.417624 | ||||||||
\(195\) | 18.1432 | 1.29926 | ||||||||
\(196\) | −6.62241 | −0.473030 | ||||||||
\(197\) | −22.0222 | −1.56902 | −0.784510 | − | 0.620116i | \(-0.787085\pi\) | ||||
−0.784510 | + | 0.620116i | \(0.787085\pi\) | |||||||
\(198\) | −0.607988 | −0.0432078 | ||||||||
\(199\) | −21.8887 | −1.55165 | −0.775824 | − | 0.630950i | \(-0.782665\pi\) | ||||
−0.775824 | + | 0.630950i | \(0.782665\pi\) | |||||||
\(200\) | −7.46585 | −0.527916 | ||||||||
\(201\) | 11.7945 | 0.831917 | ||||||||
\(202\) | 10.9403 | 0.769755 | ||||||||
\(203\) | 0.614480 | 0.0431280 | ||||||||
\(204\) | 4.89186 | 0.342499 | ||||||||
\(205\) | 18.8847 | 1.31897 | ||||||||
\(206\) | 1.01643 | 0.0708179 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −5.13869 | −0.356304 | ||||||||
\(209\) | 2.97419 | 0.205729 | ||||||||
\(210\) | −2.16954 | −0.149713 | ||||||||
\(211\) | −2.97950 | −0.205117 | −0.102559 | − | 0.994727i | \(-0.532703\pi\) | ||||
−0.102559 | + | 0.994727i | \(0.532703\pi\) | |||||||
\(212\) | 1.81684 | 0.124781 | ||||||||
\(213\) | 7.92271 | 0.542855 | ||||||||
\(214\) | 12.7064 | 0.868594 | ||||||||
\(215\) | −6.31985 | −0.431010 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0.168181 | 0.0114168 | ||||||||
\(218\) | −0.0431107 | −0.00291982 | ||||||||
\(219\) | 6.01561 | 0.406497 | ||||||||
\(220\) | 2.14663 | 0.144725 | ||||||||
\(221\) | 25.1377 | 1.69095 | ||||||||
\(222\) | −5.09540 | −0.341981 | ||||||||
\(223\) | −9.51458 | −0.637143 | −0.318572 | − | 0.947899i | \(-0.603203\pi\) | ||||
−0.318572 | + | 0.947899i | \(0.603203\pi\) | |||||||
\(224\) | 0.614480 | 0.0410566 | ||||||||
\(225\) | 7.46585 | 0.497724 | ||||||||
\(226\) | −12.5541 | −0.835088 | ||||||||
\(227\) | −1.55081 | −0.102931 | −0.0514655 | − | 0.998675i | \(-0.516389\pi\) | ||||
−0.0514655 | + | 0.998675i | \(0.516389\pi\) | |||||||
\(228\) | −4.89186 | −0.323971 | ||||||||
\(229\) | −16.4316 | −1.08583 | −0.542914 | − | 0.839788i | \(-0.682679\pi\) | ||||
−0.542914 | + | 0.839788i | \(0.682679\pi\) | |||||||
\(230\) | 3.53070 | 0.232808 | ||||||||
\(231\) | 0.373596 | 0.0245808 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | −4.59050 | −0.300734 | −0.150367 | − | 0.988630i | \(-0.548045\pi\) | ||||
−0.150367 | + | 0.988630i | \(0.548045\pi\) | |||||||
\(234\) | 5.13869 | 0.335927 | ||||||||
\(235\) | −40.5866 | −2.64758 | ||||||||
\(236\) | −2.87293 | −0.187012 | ||||||||
\(237\) | −0.712684 | −0.0462938 | ||||||||
\(238\) | −3.00595 | −0.194847 | ||||||||
\(239\) | −23.5054 | −1.52044 | −0.760219 | − | 0.649667i | \(-0.774908\pi\) | ||||
−0.760219 | + | 0.649667i | \(0.774908\pi\) | |||||||
\(240\) | −3.53070 | −0.227906 | ||||||||
\(241\) | −15.9841 | −1.02963 | −0.514814 | − | 0.857302i | \(-0.672139\pi\) | ||||
−0.514814 | + | 0.857302i | \(0.672139\pi\) | |||||||
\(242\) | 10.6304 | 0.683345 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 12.9700 | 0.830316 | ||||||||
\(245\) | −23.3818 | −1.49381 | ||||||||
\(246\) | 5.34872 | 0.341022 | ||||||||
\(247\) | −25.1377 | −1.59948 | ||||||||
\(248\) | 0.273696 | 0.0173797 | ||||||||
\(249\) | 12.8507 | 0.814382 | ||||||||
\(250\) | −8.70619 | −0.550628 | ||||||||
\(251\) | 28.3752 | 1.79103 | 0.895513 | − | 0.445036i | \(-0.146809\pi\) | ||||
0.895513 | + | 0.445036i | \(0.146809\pi\) | |||||||
\(252\) | −0.614480 | −0.0387086 | ||||||||
\(253\) | −0.607988 | −0.0382239 | ||||||||
\(254\) | 2.60917 | 0.163714 | ||||||||
\(255\) | 17.2717 | 1.08160 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 29.2724 | 1.82597 | 0.912983 | − | 0.407999i | \(-0.133773\pi\) | ||||
0.912983 | + | 0.407999i | \(0.133773\pi\) | |||||||
\(258\) | −1.78997 | −0.111439 | ||||||||
\(259\) | 3.13102 | 0.194552 | ||||||||
\(260\) | −18.1432 | −1.12519 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 5.35403 | 0.330773 | ||||||||
\(263\) | 9.93539 | 0.612642 | 0.306321 | − | 0.951928i | \(-0.400902\pi\) | ||||
0.306321 | + | 0.951928i | \(0.400902\pi\) | |||||||
\(264\) | 0.607988 | 0.0374191 | ||||||||
\(265\) | 6.41471 | 0.394052 | ||||||||
\(266\) | 3.00595 | 0.184306 | ||||||||
\(267\) | −13.0889 | −0.801028 | ||||||||
\(268\) | −11.7945 | −0.720461 | ||||||||
\(269\) | −17.7327 | −1.08118 | −0.540590 | − | 0.841286i | \(-0.681799\pi\) | ||||
−0.540590 | + | 0.841286i | \(0.681799\pi\) | |||||||
\(270\) | 3.53070 | 0.214872 | ||||||||
\(271\) | −15.1509 | −0.920354 | −0.460177 | − | 0.887827i | \(-0.652214\pi\) | ||||
−0.460177 | + | 0.887827i | \(0.652214\pi\) | |||||||
\(272\) | −4.89186 | −0.296613 | ||||||||
\(273\) | −3.15762 | −0.191108 | ||||||||
\(274\) | −12.1503 | −0.734027 | ||||||||
\(275\) | 4.53915 | 0.273721 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | −23.4648 | −1.40986 | −0.704931 | − | 0.709275i | \(-0.749022\pi\) | ||||
−0.704931 | + | 0.709275i | \(0.749022\pi\) | |||||||
\(278\) | 7.67652 | 0.460407 | ||||||||
\(279\) | −0.273696 | −0.0163857 | ||||||||
\(280\) | 2.16954 | 0.129655 | ||||||||
\(281\) | 13.7591 | 0.820799 | 0.410400 | − | 0.911906i | \(-0.365389\pi\) | ||||
0.410400 | + | 0.911906i | \(0.365389\pi\) | |||||||
\(282\) | −11.4953 | −0.684538 | ||||||||
\(283\) | −21.6445 | −1.28663 | −0.643316 | − | 0.765600i | \(-0.722442\pi\) | ||||
−0.643316 | + | 0.765600i | \(0.722442\pi\) | |||||||
\(284\) | −7.92271 | −0.470127 | ||||||||
\(285\) | −17.2717 | −1.02309 | ||||||||
\(286\) | 3.12426 | 0.184742 | ||||||||
\(287\) | −3.28668 | −0.194006 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 6.93029 | 0.407664 | ||||||||
\(290\) | 3.53070 | 0.207330 | ||||||||
\(291\) | 5.81684 | 0.340989 | ||||||||
\(292\) | −6.01561 | −0.352037 | ||||||||
\(293\) | 2.54450 | 0.148651 | 0.0743257 | − | 0.997234i | \(-0.476320\pi\) | ||||
0.0743257 | + | 0.997234i | \(0.476320\pi\) | |||||||
\(294\) | −6.62241 | −0.386227 | ||||||||
\(295\) | −10.1435 | −0.590575 | ||||||||
\(296\) | 5.09540 | 0.296164 | ||||||||
\(297\) | −0.607988 | −0.0352791 | ||||||||
\(298\) | −12.9587 | −0.750677 | ||||||||
\(299\) | 5.13869 | 0.297178 | ||||||||
\(300\) | −7.46585 | −0.431041 | ||||||||
\(301\) | 1.09990 | 0.0633972 | ||||||||
\(302\) | −2.37558 | −0.136700 | ||||||||
\(303\) | 10.9403 | 0.628503 | ||||||||
\(304\) | 4.89186 | 0.280567 | ||||||||
\(305\) | 45.7930 | 2.62210 | ||||||||
\(306\) | 4.89186 | 0.279649 | ||||||||
\(307\) | −22.7296 | −1.29725 | −0.648624 | − | 0.761109i | \(-0.724655\pi\) | ||||
−0.648624 | + | 0.761109i | \(0.724655\pi\) | |||||||
\(308\) | −0.373596 | −0.0212876 | ||||||||
\(309\) | 1.01643 | 0.0578225 | ||||||||
\(310\) | 0.966339 | 0.0548843 | ||||||||
\(311\) | 9.02765 | 0.511911 | 0.255955 | − | 0.966689i | \(-0.417610\pi\) | ||||
0.255955 | + | 0.966689i | \(0.417610\pi\) | |||||||
\(312\) | −5.13869 | −0.290921 | ||||||||
\(313\) | −13.2001 | −0.746113 | −0.373057 | − | 0.927809i | \(-0.621690\pi\) | ||||
−0.373057 | + | 0.927809i | \(0.621690\pi\) | |||||||
\(314\) | −20.0757 | −1.13294 | ||||||||
\(315\) | −2.16954 | −0.122240 | ||||||||
\(316\) | 0.712684 | 0.0400916 | ||||||||
\(317\) | 11.6125 | 0.652222 | 0.326111 | − | 0.945332i | \(-0.394262\pi\) | ||||
0.326111 | + | 0.945332i | \(0.394262\pi\) | |||||||
\(318\) | 1.81684 | 0.101883 | ||||||||
\(319\) | −0.607988 | −0.0340408 | ||||||||
\(320\) | 3.53070 | 0.197372 | ||||||||
\(321\) | 12.7064 | 0.709204 | ||||||||
\(322\) | −0.614480 | −0.0342436 | ||||||||
\(323\) | −23.9303 | −1.33152 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −38.3647 | −2.12809 | ||||||||
\(326\) | −17.0816 | −0.946062 | ||||||||
\(327\) | −0.0431107 | −0.00238402 | ||||||||
\(328\) | −5.34872 | −0.295334 | ||||||||
\(329\) | 7.06365 | 0.389432 | ||||||||
\(330\) | 2.14663 | 0.118168 | ||||||||
\(331\) | −8.36260 | −0.459650 | −0.229825 | − | 0.973232i | \(-0.573815\pi\) | ||||
−0.229825 | + | 0.973232i | \(0.573815\pi\) | |||||||
\(332\) | −12.8507 | −0.705276 | ||||||||
\(333\) | −5.09540 | −0.279226 | ||||||||
\(334\) | −21.0475 | −1.15167 | ||||||||
\(335\) | −41.6427 | −2.27518 | ||||||||
\(336\) | 0.614480 | 0.0335226 | ||||||||
\(337\) | 25.3392 | 1.38031 | 0.690156 | − | 0.723660i | \(-0.257542\pi\) | ||||
0.690156 | + | 0.723660i | \(0.257542\pi\) | |||||||
\(338\) | −13.4061 | −0.729198 | ||||||||
\(339\) | −12.5541 | −0.681846 | ||||||||
\(340\) | −17.2717 | −0.936689 | ||||||||
\(341\) | −0.166404 | −0.00901128 | ||||||||
\(342\) | −4.89186 | −0.264521 | ||||||||
\(343\) | 8.37070 | 0.451975 | ||||||||
\(344\) | 1.78997 | 0.0965088 | ||||||||
\(345\) | 3.53070 | 0.190087 | ||||||||
\(346\) | −5.91740 | −0.318122 | ||||||||
\(347\) | 8.48741 | 0.455628 | 0.227814 | − | 0.973705i | \(-0.426842\pi\) | ||||
0.227814 | + | 0.973705i | \(0.426842\pi\) | |||||||
\(348\) | 1.00000 | 0.0536056 | ||||||||
\(349\) | −29.5570 | −1.58215 | −0.791075 | − | 0.611719i | \(-0.790478\pi\) | ||||
−0.791075 | + | 0.611719i | \(0.790478\pi\) | |||||||
\(350\) | 4.58761 | 0.245218 | ||||||||
\(351\) | 5.13869 | 0.274283 | ||||||||
\(352\) | −0.607988 | −0.0324059 | ||||||||
\(353\) | 33.7901 | 1.79846 | 0.899232 | − | 0.437472i | \(-0.144126\pi\) | ||||
0.899232 | + | 0.437472i | \(0.144126\pi\) | |||||||
\(354\) | −2.87293 | −0.152694 | ||||||||
\(355\) | −27.9727 | −1.48464 | ||||||||
\(356\) | 13.0889 | 0.693711 | ||||||||
\(357\) | −3.00595 | −0.159092 | ||||||||
\(358\) | −22.0310 | −1.16437 | ||||||||
\(359\) | −22.9516 | −1.21134 | −0.605669 | − | 0.795717i | \(-0.707094\pi\) | ||||
−0.605669 | + | 0.795717i | \(0.707094\pi\) | |||||||
\(360\) | −3.53070 | −0.186084 | ||||||||
\(361\) | 4.93029 | 0.259489 | ||||||||
\(362\) | 13.2542 | 0.696625 | ||||||||
\(363\) | 10.6304 | 0.557949 | ||||||||
\(364\) | 3.15762 | 0.165504 | ||||||||
\(365\) | −21.2393 | −1.11172 | ||||||||
\(366\) | 12.9700 | 0.677950 | ||||||||
\(367\) | 33.3095 | 1.73874 | 0.869372 | − | 0.494158i | \(-0.164524\pi\) | ||||
0.869372 | + | 0.494158i | \(0.164524\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 5.34872 | 0.278443 | ||||||||
\(370\) | 17.9903 | 0.935273 | ||||||||
\(371\) | −1.11641 | −0.0579610 | ||||||||
\(372\) | 0.273696 | 0.0141905 | ||||||||
\(373\) | 26.3647 | 1.36511 | 0.682556 | − | 0.730833i | \(-0.260868\pi\) | ||||
0.682556 | + | 0.730833i | \(0.260868\pi\) | |||||||
\(374\) | 2.97419 | 0.153792 | ||||||||
\(375\) | −8.70619 | −0.449586 | ||||||||
\(376\) | 11.4953 | 0.592827 | ||||||||
\(377\) | 5.13869 | 0.264656 | ||||||||
\(378\) | −0.614480 | −0.0316054 | ||||||||
\(379\) | −21.6448 | −1.11182 | −0.555908 | − | 0.831244i | \(-0.687629\pi\) | ||||
−0.555908 | + | 0.831244i | \(0.687629\pi\) | |||||||
\(380\) | 17.2717 | 0.886019 | ||||||||
\(381\) | 2.60917 | 0.133672 | ||||||||
\(382\) | 19.0549 | 0.974934 | ||||||||
\(383\) | −11.0030 | −0.562229 | −0.281115 | − | 0.959674i | \(-0.590704\pi\) | ||||
−0.281115 | + | 0.959674i | \(0.590704\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −1.31906 | −0.0672254 | ||||||||
\(386\) | 8.39147 | 0.427114 | ||||||||
\(387\) | −1.78997 | −0.0909893 | ||||||||
\(388\) | −5.81684 | −0.295305 | ||||||||
\(389\) | 23.3305 | 1.18291 | 0.591453 | − | 0.806340i | \(-0.298555\pi\) | ||||
0.591453 | + | 0.806340i | \(0.298555\pi\) | |||||||
\(390\) | −18.1432 | −0.918716 | ||||||||
\(391\) | 4.89186 | 0.247392 | ||||||||
\(392\) | 6.62241 | 0.334482 | ||||||||
\(393\) | 5.35403 | 0.270075 | ||||||||
\(394\) | 22.0222 | 1.10946 | ||||||||
\(395\) | 2.51627 | 0.126608 | ||||||||
\(396\) | 0.607988 | 0.0305526 | ||||||||
\(397\) | 6.09884 | 0.306092 | 0.153046 | − | 0.988219i | \(-0.451092\pi\) | ||||
0.153046 | + | 0.988219i | \(0.451092\pi\) | |||||||
\(398\) | 21.8887 | 1.09718 | ||||||||
\(399\) | 3.00595 | 0.150486 | ||||||||
\(400\) | 7.46585 | 0.373293 | ||||||||
\(401\) | −21.2632 | −1.06183 | −0.530917 | − | 0.847424i | \(-0.678152\pi\) | ||||
−0.530917 | + | 0.847424i | \(0.678152\pi\) | |||||||
\(402\) | −11.7945 | −0.588254 | ||||||||
\(403\) | 1.40644 | 0.0700597 | ||||||||
\(404\) | −10.9403 | −0.544299 | ||||||||
\(405\) | 3.53070 | 0.175442 | ||||||||
\(406\) | −0.614480 | −0.0304961 | ||||||||
\(407\) | −3.09794 | −0.153559 | ||||||||
\(408\) | −4.89186 | −0.242183 | ||||||||
\(409\) | −15.1812 | −0.750663 | −0.375332 | − | 0.926891i | \(-0.622471\pi\) | ||||
−0.375332 | + | 0.926891i | \(0.622471\pi\) | |||||||
\(410\) | −18.8847 | −0.932650 | ||||||||
\(411\) | −12.1503 | −0.599331 | ||||||||
\(412\) | −1.01643 | −0.0500758 | ||||||||
\(413\) | 1.76536 | 0.0868675 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | −45.3721 | −2.22723 | ||||||||
\(416\) | 5.13869 | 0.251945 | ||||||||
\(417\) | 7.67652 | 0.375921 | ||||||||
\(418\) | −2.97419 | −0.145473 | ||||||||
\(419\) | −13.2146 | −0.645576 | −0.322788 | − | 0.946471i | \(-0.604620\pi\) | ||||
−0.322788 | + | 0.946471i | \(0.604620\pi\) | |||||||
\(420\) | 2.16954 | 0.105863 | ||||||||
\(421\) | −19.6648 | −0.958402 | −0.479201 | − | 0.877705i | \(-0.659074\pi\) | ||||
−0.479201 | + | 0.877705i | \(0.659074\pi\) | |||||||
\(422\) | 2.97950 | 0.145040 | ||||||||
\(423\) | −11.4953 | −0.558923 | ||||||||
\(424\) | −1.81684 | −0.0882334 | ||||||||
\(425\) | −36.5219 | −1.77157 | ||||||||
\(426\) | −7.92271 | −0.383857 | ||||||||
\(427\) | −7.96977 | −0.385684 | ||||||||
\(428\) | −12.7064 | −0.614189 | ||||||||
\(429\) | 3.12426 | 0.150841 | ||||||||
\(430\) | 6.31985 | 0.304770 | ||||||||
\(431\) | 0.429690 | 0.0206974 | 0.0103487 | − | 0.999946i | \(-0.496706\pi\) | ||||
0.0103487 | + | 0.999946i | \(0.496706\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 6.61312 | 0.317806 | 0.158903 | − | 0.987294i | \(-0.449204\pi\) | ||||
0.158903 | + | 0.987294i | \(0.449204\pi\) | |||||||
\(434\) | −0.168181 | −0.00807292 | ||||||||
\(435\) | 3.53070 | 0.169284 | ||||||||
\(436\) | 0.0431107 | 0.00206463 | ||||||||
\(437\) | −4.89186 | −0.234009 | ||||||||
\(438\) | −6.01561 | −0.287437 | ||||||||
\(439\) | −1.50559 | −0.0718577 | −0.0359288 | − | 0.999354i | \(-0.511439\pi\) | ||||
−0.0359288 | + | 0.999354i | \(0.511439\pi\) | |||||||
\(440\) | −2.14663 | −0.102336 | ||||||||
\(441\) | −6.62241 | −0.315353 | ||||||||
\(442\) | −25.1377 | −1.19568 | ||||||||
\(443\) | −24.0942 | −1.14475 | −0.572375 | − | 0.819992i | \(-0.693978\pi\) | ||||
−0.572375 | + | 0.819992i | \(0.693978\pi\) | |||||||
\(444\) | 5.09540 | 0.241817 | ||||||||
\(445\) | 46.2130 | 2.19071 | ||||||||
\(446\) | 9.51458 | 0.450528 | ||||||||
\(447\) | −12.9587 | −0.612925 | ||||||||
\(448\) | −0.614480 | −0.0290314 | ||||||||
\(449\) | 30.6301 | 1.44553 | 0.722763 | − | 0.691096i | \(-0.242872\pi\) | ||||
0.722763 | + | 0.691096i | \(0.242872\pi\) | |||||||
\(450\) | −7.46585 | −0.351944 | ||||||||
\(451\) | 3.25196 | 0.153129 | ||||||||
\(452\) | 12.5541 | 0.590496 | ||||||||
\(453\) | −2.37558 | −0.111615 | ||||||||
\(454\) | 1.55081 | 0.0727833 | ||||||||
\(455\) | 11.1486 | 0.522655 | ||||||||
\(456\) | 4.89186 | 0.229082 | ||||||||
\(457\) | −39.2943 | −1.83811 | −0.919055 | − | 0.394129i | \(-0.871046\pi\) | ||||
−0.919055 | + | 0.394129i | \(0.871046\pi\) | |||||||
\(458\) | 16.4316 | 0.767796 | ||||||||
\(459\) | 4.89186 | 0.228332 | ||||||||
\(460\) | −3.53070 | −0.164620 | ||||||||
\(461\) | 15.6924 | 0.730870 | 0.365435 | − | 0.930837i | \(-0.380920\pi\) | ||||
0.365435 | + | 0.930837i | \(0.380920\pi\) | |||||||
\(462\) | −0.373596 | −0.0173813 | ||||||||
\(463\) | −5.09452 | −0.236762 | −0.118381 | − | 0.992968i | \(-0.537770\pi\) | ||||
−0.118381 | + | 0.992968i | \(0.537770\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | 0.966339 | 0.0448129 | ||||||||
\(466\) | 4.59050 | 0.212651 | ||||||||
\(467\) | −20.3616 | −0.942221 | −0.471111 | − | 0.882074i | \(-0.656147\pi\) | ||||
−0.471111 | + | 0.882074i | \(0.656147\pi\) | |||||||
\(468\) | −5.13869 | −0.237536 | ||||||||
\(469\) | 7.24746 | 0.334656 | ||||||||
\(470\) | 40.5866 | 1.87212 | ||||||||
\(471\) | −20.0757 | −0.925040 | ||||||||
\(472\) | 2.87293 | 0.132237 | ||||||||
\(473\) | −1.08828 | −0.0500392 | ||||||||
\(474\) | 0.712684 | 0.0327347 | ||||||||
\(475\) | 36.5219 | 1.67574 | ||||||||
\(476\) | 3.00595 | 0.137777 | ||||||||
\(477\) | 1.81684 | 0.0831872 | ||||||||
\(478\) | 23.5054 | 1.07511 | ||||||||
\(479\) | 13.9805 | 0.638786 | 0.319393 | − | 0.947622i | \(-0.396521\pi\) | ||||
0.319393 | + | 0.947622i | \(0.396521\pi\) | |||||||
\(480\) | 3.53070 | 0.161154 | ||||||||
\(481\) | 26.1837 | 1.19387 | ||||||||
\(482\) | 15.9841 | 0.728057 | ||||||||
\(483\) | −0.614480 | −0.0279598 | ||||||||
\(484\) | −10.6304 | −0.483198 | ||||||||
\(485\) | −20.5375 | −0.932560 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 12.4420 | 0.563802 | 0.281901 | − | 0.959443i | \(-0.409035\pi\) | ||||
0.281901 | + | 0.959443i | \(0.409035\pi\) | |||||||
\(488\) | −12.9700 | −0.587122 | ||||||||
\(489\) | −17.0816 | −0.772456 | ||||||||
\(490\) | 23.3818 | 1.05628 | ||||||||
\(491\) | −39.8690 | −1.79926 | −0.899632 | − | 0.436648i | \(-0.856165\pi\) | ||||
−0.899632 | + | 0.436648i | \(0.856165\pi\) | |||||||
\(492\) | −5.34872 | −0.241139 | ||||||||
\(493\) | 4.89186 | 0.220318 | ||||||||
\(494\) | 25.1377 | 1.13100 | ||||||||
\(495\) | 2.14663 | 0.0964836 | ||||||||
\(496\) | −0.273696 | −0.0122893 | ||||||||
\(497\) | 4.86835 | 0.218375 | ||||||||
\(498\) | −12.8507 | −0.575855 | ||||||||
\(499\) | −24.2777 | −1.08682 | −0.543410 | − | 0.839467i | \(-0.682867\pi\) | ||||
−0.543410 | + | 0.839467i | \(0.682867\pi\) | |||||||
\(500\) | 8.70619 | 0.389353 | ||||||||
\(501\) | −21.0475 | −0.940332 | ||||||||
\(502\) | −28.3752 | −1.26645 | ||||||||
\(503\) | −26.7528 | −1.19285 | −0.596424 | − | 0.802669i | \(-0.703412\pi\) | ||||
−0.596424 | + | 0.802669i | \(0.703412\pi\) | |||||||
\(504\) | 0.614480 | 0.0273711 | ||||||||
\(505\) | −38.6269 | −1.71887 | ||||||||
\(506\) | 0.607988 | 0.0270284 | ||||||||
\(507\) | −13.4061 | −0.595387 | ||||||||
\(508\) | −2.60917 | −0.115763 | ||||||||
\(509\) | −15.3597 | −0.680805 | −0.340403 | − | 0.940280i | \(-0.610563\pi\) | ||||
−0.340403 | + | 0.940280i | \(0.610563\pi\) | |||||||
\(510\) | −17.2717 | −0.764804 | ||||||||
\(511\) | 3.69647 | 0.163522 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.89186 | −0.215981 | ||||||||
\(514\) | −29.2724 | −1.29115 | ||||||||
\(515\) | −3.58870 | −0.158137 | ||||||||
\(516\) | 1.78997 | 0.0787991 | ||||||||
\(517\) | −6.98903 | −0.307377 | ||||||||
\(518\) | −3.13102 | −0.137569 | ||||||||
\(519\) | −5.91740 | −0.259745 | ||||||||
\(520\) | 18.1432 | 0.795631 | ||||||||
\(521\) | 40.3188 | 1.76640 | 0.883198 | − | 0.469000i | \(-0.155385\pi\) | ||||
0.883198 | + | 0.469000i | \(0.155385\pi\) | |||||||
\(522\) | 1.00000 | 0.0437688 | ||||||||
\(523\) | 27.0512 | 1.18287 | 0.591433 | − | 0.806354i | \(-0.298562\pi\) | ||||
0.591433 | + | 0.806354i | \(0.298562\pi\) | |||||||
\(524\) | −5.35403 | −0.233892 | ||||||||
\(525\) | 4.58761 | 0.200220 | ||||||||
\(526\) | −9.93539 | −0.433204 | ||||||||
\(527\) | 1.33888 | 0.0583226 | ||||||||
\(528\) | −0.607988 | −0.0264593 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −6.41471 | −0.278637 | ||||||||
\(531\) | −2.87293 | −0.124675 | ||||||||
\(532\) | −3.00595 | −0.130324 | ||||||||
\(533\) | −27.4854 | −1.19053 | ||||||||
\(534\) | 13.0889 | 0.566412 | ||||||||
\(535\) | −44.8626 | −1.93958 | ||||||||
\(536\) | 11.7945 | 0.509443 | ||||||||
\(537\) | −22.0310 | −0.950707 | ||||||||
\(538\) | 17.7327 | 0.764509 | ||||||||
\(539\) | −4.02635 | −0.173427 | ||||||||
\(540\) | −3.53070 | −0.151937 | ||||||||
\(541\) | −29.0227 | −1.24778 | −0.623891 | − | 0.781512i | \(-0.714449\pi\) | ||||
−0.623891 | + | 0.781512i | \(0.714449\pi\) | |||||||
\(542\) | 15.1509 | 0.650789 | ||||||||
\(543\) | 13.2542 | 0.568792 | ||||||||
\(544\) | 4.89186 | 0.209737 | ||||||||
\(545\) | 0.152211 | 0.00652000 | ||||||||
\(546\) | 3.15762 | 0.135134 | ||||||||
\(547\) | 23.7088 | 1.01372 | 0.506858 | − | 0.862029i | \(-0.330807\pi\) | ||||
0.506858 | + | 0.862029i | \(0.330807\pi\) | |||||||
\(548\) | 12.1503 | 0.519035 | ||||||||
\(549\) | 12.9700 | 0.553544 | ||||||||
\(550\) | −4.53915 | −0.193550 | ||||||||
\(551\) | −4.89186 | −0.208400 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | −0.437930 | −0.0186227 | ||||||||
\(554\) | 23.4648 | 0.996924 | ||||||||
\(555\) | 17.9903 | 0.763647 | ||||||||
\(556\) | −7.67652 | −0.325557 | ||||||||
\(557\) | 11.4860 | 0.486675 | 0.243338 | − | 0.969942i | \(-0.421758\pi\) | ||||
0.243338 | + | 0.969942i | \(0.421758\pi\) | |||||||
\(558\) | 0.273696 | 0.0115865 | ||||||||
\(559\) | 9.19811 | 0.389038 | ||||||||
\(560\) | −2.16954 | −0.0916800 | ||||||||
\(561\) | 2.97419 | 0.125571 | ||||||||
\(562\) | −13.7591 | −0.580393 | ||||||||
\(563\) | −31.2272 | −1.31607 | −0.658035 | − | 0.752988i | \(-0.728612\pi\) | ||||
−0.658035 | + | 0.752988i | \(0.728612\pi\) | |||||||
\(564\) | 11.4953 | 0.484041 | ||||||||
\(565\) | 44.3249 | 1.86476 | ||||||||
\(566\) | 21.6445 | 0.909787 | ||||||||
\(567\) | −0.614480 | −0.0258057 | ||||||||
\(568\) | 7.92271 | 0.332430 | ||||||||
\(569\) | 26.8003 | 1.12353 | 0.561763 | − | 0.827298i | \(-0.310123\pi\) | ||||
0.561763 | + | 0.827298i | \(0.310123\pi\) | |||||||
\(570\) | 17.2717 | 0.723432 | ||||||||
\(571\) | 11.2327 | 0.470074 | 0.235037 | − | 0.971986i | \(-0.424479\pi\) | ||||
0.235037 | + | 0.971986i | \(0.424479\pi\) | |||||||
\(572\) | −3.12426 | −0.130632 | ||||||||
\(573\) | 19.0549 | 0.796030 | ||||||||
\(574\) | 3.28668 | 0.137183 | ||||||||
\(575\) | −7.46585 | −0.311348 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −35.5509 | −1.48000 | −0.740002 | − | 0.672605i | \(-0.765175\pi\) | ||||
−0.740002 | + | 0.672605i | \(0.765175\pi\) | |||||||
\(578\) | −6.93029 | −0.288262 | ||||||||
\(579\) | 8.39147 | 0.348738 | ||||||||
\(580\) | −3.53070 | −0.146604 | ||||||||
\(581\) | 7.89651 | 0.327603 | ||||||||
\(582\) | −5.81684 | −0.241116 | ||||||||
\(583\) | 1.10462 | 0.0457485 | ||||||||
\(584\) | 6.01561 | 0.248928 | ||||||||
\(585\) | −18.1432 | −0.750128 | ||||||||
\(586\) | −2.54450 | −0.105112 | ||||||||
\(587\) | 10.1849 | 0.420376 | 0.210188 | − | 0.977661i | \(-0.432592\pi\) | ||||
0.210188 | + | 0.977661i | \(0.432592\pi\) | |||||||
\(588\) | 6.62241 | 0.273104 | ||||||||
\(589\) | −1.33888 | −0.0551677 | ||||||||
\(590\) | 10.1435 | 0.417599 | ||||||||
\(591\) | 22.0222 | 0.905874 | ||||||||
\(592\) | −5.09540 | −0.209420 | ||||||||
\(593\) | −16.9833 | −0.697421 | −0.348711 | − | 0.937230i | \(-0.613380\pi\) | ||||
−0.348711 | + | 0.937230i | \(0.613380\pi\) | |||||||
\(594\) | 0.607988 | 0.0249461 | ||||||||
\(595\) | 10.6131 | 0.435095 | ||||||||
\(596\) | 12.9587 | 0.530809 | ||||||||
\(597\) | 21.8887 | 0.895844 | ||||||||
\(598\) | −5.13869 | −0.210137 | ||||||||
\(599\) | −6.57201 | −0.268525 | −0.134262 | − | 0.990946i | \(-0.542867\pi\) | ||||
−0.134262 | + | 0.990946i | \(0.542867\pi\) | |||||||
\(600\) | 7.46585 | 0.304792 | ||||||||
\(601\) | 22.6191 | 0.922652 | 0.461326 | − | 0.887231i | \(-0.347374\pi\) | ||||
0.461326 | + | 0.887231i | \(0.347374\pi\) | |||||||
\(602\) | −1.09990 | −0.0448286 | ||||||||
\(603\) | −11.7945 | −0.480308 | ||||||||
\(604\) | 2.37558 | 0.0966612 | ||||||||
\(605\) | −37.5326 | −1.52592 | ||||||||
\(606\) | −10.9403 | −0.444418 | ||||||||
\(607\) | −46.2754 | −1.87826 | −0.939130 | − | 0.343562i | \(-0.888366\pi\) | ||||
−0.939130 | + | 0.343562i | \(0.888366\pi\) | |||||||
\(608\) | −4.89186 | −0.198391 | ||||||||
\(609\) | −0.614480 | −0.0249000 | ||||||||
\(610\) | −45.7930 | −1.85411 | ||||||||
\(611\) | 59.0710 | 2.38976 | ||||||||
\(612\) | −4.89186 | −0.197742 | ||||||||
\(613\) | 28.0254 | 1.13193 | 0.565967 | − | 0.824428i | \(-0.308503\pi\) | ||||
0.565967 | + | 0.824428i | \(0.308503\pi\) | |||||||
\(614\) | 22.7296 | 0.917293 | ||||||||
\(615\) | −18.8847 | −0.761506 | ||||||||
\(616\) | 0.373596 | 0.0150526 | ||||||||
\(617\) | 1.50461 | 0.0605735 | 0.0302867 | − | 0.999541i | \(-0.490358\pi\) | ||||
0.0302867 | + | 0.999541i | \(0.490358\pi\) | |||||||
\(618\) | −1.01643 | −0.0408867 | ||||||||
\(619\) | 39.3600 | 1.58201 | 0.791007 | − | 0.611808i | \(-0.209557\pi\) | ||||
0.791007 | + | 0.611808i | \(0.209557\pi\) | |||||||
\(620\) | −0.966339 | −0.0388091 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −9.02765 | −0.361976 | ||||||||
\(623\) | −8.04286 | −0.322231 | ||||||||
\(624\) | 5.13869 | 0.205712 | ||||||||
\(625\) | −6.59030 | −0.263612 | ||||||||
\(626\) | 13.2001 | 0.527582 | ||||||||
\(627\) | −2.97419 | −0.118778 | ||||||||
\(628\) | 20.0757 | 0.801108 | ||||||||
\(629\) | 24.9260 | 0.993863 | ||||||||
\(630\) | 2.16954 | 0.0864367 | ||||||||
\(631\) | −32.7818 | −1.30502 | −0.652512 | − | 0.757779i | \(-0.726285\pi\) | ||||
−0.652512 | + | 0.757779i | \(0.726285\pi\) | |||||||
\(632\) | −0.712684 | −0.0283491 | ||||||||
\(633\) | 2.97950 | 0.118425 | ||||||||
\(634\) | −11.6125 | −0.461190 | ||||||||
\(635\) | −9.21220 | −0.365575 | ||||||||
\(636\) | −1.81684 | −0.0720422 | ||||||||
\(637\) | 34.0305 | 1.34834 | ||||||||
\(638\) | 0.607988 | 0.0240705 | ||||||||
\(639\) | −7.92271 | −0.313418 | ||||||||
\(640\) | −3.53070 | −0.139563 | ||||||||
\(641\) | 1.29342 | 0.0510871 | 0.0255435 | − | 0.999674i | \(-0.491868\pi\) | ||||
0.0255435 | + | 0.999674i | \(0.491868\pi\) | |||||||
\(642\) | −12.7064 | −0.501483 | ||||||||
\(643\) | 21.7254 | 0.856765 | 0.428382 | − | 0.903598i | \(-0.359084\pi\) | ||||
0.428382 | + | 0.903598i | \(0.359084\pi\) | |||||||
\(644\) | 0.614480 | 0.0242139 | ||||||||
\(645\) | 6.31985 | 0.248844 | ||||||||
\(646\) | 23.9303 | 0.941525 | ||||||||
\(647\) | 39.2877 | 1.54456 | 0.772280 | − | 0.635282i | \(-0.219116\pi\) | ||||
0.772280 | + | 0.635282i | \(0.219116\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −1.74671 | −0.0685643 | ||||||||
\(650\) | 38.3647 | 1.50479 | ||||||||
\(651\) | −0.168181 | −0.00659151 | ||||||||
\(652\) | 17.0816 | 0.668967 | ||||||||
\(653\) | −16.1028 | −0.630151 | −0.315075 | − | 0.949067i | \(-0.602030\pi\) | ||||
−0.315075 | + | 0.949067i | \(0.602030\pi\) | |||||||
\(654\) | 0.0431107 | 0.00168576 | ||||||||
\(655\) | −18.9035 | −0.738620 | ||||||||
\(656\) | 5.34872 | 0.208832 | ||||||||
\(657\) | −6.01561 | −0.234691 | ||||||||
\(658\) | −7.06365 | −0.275370 | ||||||||
\(659\) | −35.7836 | −1.39393 | −0.696966 | − | 0.717104i | \(-0.745467\pi\) | ||||
−0.696966 | + | 0.717104i | \(0.745467\pi\) | |||||||
\(660\) | −2.14663 | −0.0835573 | ||||||||
\(661\) | 48.0343 | 1.86832 | 0.934160 | − | 0.356856i | \(-0.116151\pi\) | ||||
0.934160 | + | 0.356856i | \(0.116151\pi\) | |||||||
\(662\) | 8.36260 | 0.325022 | ||||||||
\(663\) | −25.1377 | −0.976269 | ||||||||
\(664\) | 12.8507 | 0.498705 | ||||||||
\(665\) | −10.6131 | −0.411558 | ||||||||
\(666\) | 5.09540 | 0.197443 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 21.0475 | 0.814351 | ||||||||
\(669\) | 9.51458 | 0.367855 | ||||||||
\(670\) | 41.6427 | 1.60880 | ||||||||
\(671\) | 7.88558 | 0.304419 | ||||||||
\(672\) | −0.614480 | −0.0237041 | ||||||||
\(673\) | 19.1801 | 0.739339 | 0.369670 | − | 0.929163i | \(-0.379471\pi\) | ||||
0.369670 | + | 0.929163i | \(0.379471\pi\) | |||||||
\(674\) | −25.3392 | −0.976028 | ||||||||
\(675\) | −7.46585 | −0.287361 | ||||||||
\(676\) | 13.4061 | 0.515621 | ||||||||
\(677\) | 14.7763 | 0.567899 | 0.283950 | − | 0.958839i | \(-0.408355\pi\) | ||||
0.283950 | + | 0.958839i | \(0.408355\pi\) | |||||||
\(678\) | 12.5541 | 0.482138 | ||||||||
\(679\) | 3.57433 | 0.137170 | ||||||||
\(680\) | 17.2717 | 0.662339 | ||||||||
\(681\) | 1.55081 | 0.0594273 | ||||||||
\(682\) | 0.166404 | 0.00637193 | ||||||||
\(683\) | −20.3985 | −0.780528 | −0.390264 | − | 0.920703i | \(-0.627616\pi\) | ||||
−0.390264 | + | 0.920703i | \(0.627616\pi\) | |||||||
\(684\) | 4.89186 | 0.187045 | ||||||||
\(685\) | 42.8991 | 1.63909 | ||||||||
\(686\) | −8.37070 | −0.319595 | ||||||||
\(687\) | 16.4316 | 0.626903 | ||||||||
\(688\) | −1.78997 | −0.0682420 | ||||||||
\(689\) | −9.33616 | −0.355679 | ||||||||
\(690\) | −3.53070 | −0.134412 | ||||||||
\(691\) | −11.2648 | −0.428534 | −0.214267 | − | 0.976775i | \(-0.568736\pi\) | ||||
−0.214267 | + | 0.976775i | \(0.568736\pi\) | |||||||
\(692\) | 5.91740 | 0.224946 | ||||||||
\(693\) | −0.373596 | −0.0141918 | ||||||||
\(694\) | −8.48741 | −0.322178 | ||||||||
\(695\) | −27.1035 | −1.02809 | ||||||||
\(696\) | −1.00000 | −0.0379049 | ||||||||
\(697\) | −26.1652 | −0.991077 | ||||||||
\(698\) | 29.5570 | 1.11875 | ||||||||
\(699\) | 4.59050 | 0.173629 | ||||||||
\(700\) | −4.58761 | −0.173396 | ||||||||
\(701\) | −36.1628 | −1.36585 | −0.682925 | − | 0.730489i | \(-0.739292\pi\) | ||||
−0.682925 | + | 0.730489i | \(0.739292\pi\) | |||||||
\(702\) | −5.13869 | −0.193947 | ||||||||
\(703\) | −24.9260 | −0.940101 | ||||||||
\(704\) | 0.607988 | 0.0229144 | ||||||||
\(705\) | 40.5866 | 1.52858 | ||||||||
\(706\) | −33.7901 | −1.27171 | ||||||||
\(707\) | 6.72258 | 0.252829 | ||||||||
\(708\) | 2.87293 | 0.107971 | ||||||||
\(709\) | 16.3670 | 0.614674 | 0.307337 | − | 0.951601i | \(-0.400562\pi\) | ||||
0.307337 | + | 0.951601i | \(0.400562\pi\) | |||||||
\(710\) | 27.9727 | 1.04980 | ||||||||
\(711\) | 0.712684 | 0.0267277 | ||||||||
\(712\) | −13.0889 | −0.490527 | ||||||||
\(713\) | 0.273696 | 0.0102500 | ||||||||
\(714\) | 3.00595 | 0.112495 | ||||||||
\(715\) | −11.0308 | −0.412530 | ||||||||
\(716\) | 22.0310 | 0.823336 | ||||||||
\(717\) | 23.5054 | 0.877825 | ||||||||
\(718\) | 22.9516 | 0.856545 | ||||||||
\(719\) | −6.20987 | −0.231589 | −0.115795 | − | 0.993273i | \(-0.536941\pi\) | ||||
−0.115795 | + | 0.993273i | \(0.536941\pi\) | |||||||
\(720\) | 3.53070 | 0.131581 | ||||||||
\(721\) | 0.624574 | 0.0232603 | ||||||||
\(722\) | −4.93029 | −0.183486 | ||||||||
\(723\) | 15.9841 | 0.594456 | ||||||||
\(724\) | −13.2542 | −0.492588 | ||||||||
\(725\) | −7.46585 | −0.277275 | ||||||||
\(726\) | −10.6304 | −0.394529 | ||||||||
\(727\) | −20.1469 | −0.747208 | −0.373604 | − | 0.927588i | \(-0.621878\pi\) | ||||
−0.373604 | + | 0.927588i | \(0.621878\pi\) | |||||||
\(728\) | −3.15762 | −0.117029 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 21.2393 | 0.786102 | ||||||||
\(731\) | 8.75629 | 0.323863 | ||||||||
\(732\) | −12.9700 | −0.479383 | ||||||||
\(733\) | 35.2928 | 1.30357 | 0.651785 | − | 0.758404i | \(-0.274020\pi\) | ||||
0.651785 | + | 0.758404i | \(0.274020\pi\) | |||||||
\(734\) | −33.3095 | −1.22948 | ||||||||
\(735\) | 23.3818 | 0.862450 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −7.17089 | −0.264143 | ||||||||
\(738\) | −5.34872 | −0.196889 | ||||||||
\(739\) | 36.5798 | 1.34561 | 0.672805 | − | 0.739820i | \(-0.265090\pi\) | ||||
0.672805 | + | 0.739820i | \(0.265090\pi\) | |||||||
\(740\) | −17.9903 | −0.661338 | ||||||||
\(741\) | 25.1377 | 0.923458 | ||||||||
\(742\) | 1.11641 | 0.0409847 | ||||||||
\(743\) | −19.9765 | −0.732868 | −0.366434 | − | 0.930444i | \(-0.619421\pi\) | ||||
−0.366434 | + | 0.930444i | \(0.619421\pi\) | |||||||
\(744\) | −0.273696 | −0.0100342 | ||||||||
\(745\) | 45.7533 | 1.67627 | ||||||||
\(746\) | −26.3647 | −0.965280 | ||||||||
\(747\) | −12.8507 | −0.470184 | ||||||||
\(748\) | −2.97419 | −0.108747 | ||||||||
\(749\) | 7.80784 | 0.285292 | ||||||||
\(750\) | 8.70619 | 0.317905 | ||||||||
\(751\) | 2.50365 | 0.0913596 | 0.0456798 | − | 0.998956i | \(-0.485455\pi\) | ||||
0.0456798 | + | 0.998956i | \(0.485455\pi\) | |||||||
\(752\) | −11.4953 | −0.419192 | ||||||||
\(753\) | −28.3752 | −1.03405 | ||||||||
\(754\) | −5.13869 | −0.187140 | ||||||||
\(755\) | 8.38748 | 0.305252 | ||||||||
\(756\) | 0.614480 | 0.0223484 | ||||||||
\(757\) | 21.2816 | 0.773491 | 0.386746 | − | 0.922186i | \(-0.373599\pi\) | ||||
0.386746 | + | 0.922186i | \(0.373599\pi\) | |||||||
\(758\) | 21.6448 | 0.786173 | ||||||||
\(759\) | 0.607988 | 0.0220686 | ||||||||
\(760\) | −17.2717 | −0.626510 | ||||||||
\(761\) | 1.99861 | 0.0724495 | 0.0362248 | − | 0.999344i | \(-0.488467\pi\) | ||||
0.0362248 | + | 0.999344i | \(0.488467\pi\) | |||||||
\(762\) | −2.60917 | −0.0945202 | ||||||||
\(763\) | −0.0264906 | −0.000959025 0 | ||||||||
\(764\) | −19.0549 | −0.689383 | ||||||||
\(765\) | −17.2717 | −0.624459 | ||||||||
\(766\) | 11.0030 | 0.397556 | ||||||||
\(767\) | 14.7631 | 0.533064 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 38.8605 | 1.40135 | 0.700673 | − | 0.713483i | \(-0.252883\pi\) | ||||
0.700673 | + | 0.713483i | \(0.252883\pi\) | |||||||
\(770\) | 1.31906 | 0.0475355 | ||||||||
\(771\) | −29.2724 | −1.05422 | ||||||||
\(772\) | −8.39147 | −0.302016 | ||||||||
\(773\) | 34.1892 | 1.22970 | 0.614849 | − | 0.788645i | \(-0.289217\pi\) | ||||
0.614849 | + | 0.788645i | \(0.289217\pi\) | |||||||
\(774\) | 1.78997 | 0.0643392 | ||||||||
\(775\) | −2.04337 | −0.0734001 | ||||||||
\(776\) | 5.81684 | 0.208812 | ||||||||
\(777\) | −3.13102 | −0.112325 | ||||||||
\(778\) | −23.3305 | −0.836440 | ||||||||
\(779\) | 26.1652 | 0.937465 | ||||||||
\(780\) | 18.1432 | 0.649630 | ||||||||
\(781\) | −4.81692 | −0.172363 | ||||||||
\(782\) | −4.89186 | −0.174933 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | −6.62241 | −0.236515 | ||||||||
\(785\) | 70.8813 | 2.52986 | ||||||||
\(786\) | −5.35403 | −0.190972 | ||||||||
\(787\) | 12.1130 | 0.431780 | 0.215890 | − | 0.976418i | \(-0.430735\pi\) | ||||
0.215890 | + | 0.976418i | \(0.430735\pi\) | |||||||
\(788\) | −22.0222 | −0.784510 | ||||||||
\(789\) | −9.93539 | −0.353709 | ||||||||
\(790\) | −2.51627 | −0.0895250 | ||||||||
\(791\) | −7.71425 | −0.274287 | ||||||||
\(792\) | −0.607988 | −0.0216039 | ||||||||
\(793\) | −66.6486 | −2.36676 | ||||||||
\(794\) | −6.09884 | −0.216440 | ||||||||
\(795\) | −6.41471 | −0.227506 | ||||||||
\(796\) | −21.8887 | −0.775824 | ||||||||
\(797\) | 19.9628 | 0.707117 | 0.353559 | − | 0.935412i | \(-0.384971\pi\) | ||||
0.353559 | + | 0.935412i | \(0.384971\pi\) | |||||||
\(798\) | −3.00595 | −0.106409 | ||||||||
\(799\) | 56.2336 | 1.98940 | ||||||||
\(800\) | −7.46585 | −0.263958 | ||||||||
\(801\) | 13.0889 | 0.462474 | ||||||||
\(802\) | 21.2632 | 0.750830 | ||||||||
\(803\) | −3.65742 | −0.129068 | ||||||||
\(804\) | 11.7945 | 0.415959 | ||||||||
\(805\) | 2.16954 | 0.0764664 | ||||||||
\(806\) | −1.40644 | −0.0495397 | ||||||||
\(807\) | 17.7327 | 0.624219 | ||||||||
\(808\) | 10.9403 | 0.384878 | ||||||||
\(809\) | 4.77374 | 0.167836 | 0.0839178 | − | 0.996473i | \(-0.473257\pi\) | ||||
0.0839178 | + | 0.996473i | \(0.473257\pi\) | |||||||
\(810\) | −3.53070 | −0.124056 | ||||||||
\(811\) | −9.67652 | −0.339789 | −0.169894 | − | 0.985462i | \(-0.554343\pi\) | ||||
−0.169894 | + | 0.985462i | \(0.554343\pi\) | |||||||
\(812\) | 0.614480 | 0.0215640 | ||||||||
\(813\) | 15.1509 | 0.531367 | ||||||||
\(814\) | 3.09794 | 0.108583 | ||||||||
\(815\) | 60.3100 | 2.11257 | ||||||||
\(816\) | 4.89186 | 0.171249 | ||||||||
\(817\) | −8.75629 | −0.306344 | ||||||||
\(818\) | 15.1812 | 0.530799 | ||||||||
\(819\) | 3.15762 | 0.110336 | ||||||||
\(820\) | 18.8847 | 0.659483 | ||||||||
\(821\) | −16.8899 | −0.589463 | −0.294732 | − | 0.955580i | \(-0.595230\pi\) | ||||
−0.294732 | + | 0.955580i | \(0.595230\pi\) | |||||||
\(822\) | 12.1503 | 0.423791 | ||||||||
\(823\) | −42.2212 | −1.47174 | −0.735870 | − | 0.677123i | \(-0.763226\pi\) | ||||
−0.735870 | + | 0.677123i | \(0.763226\pi\) | |||||||
\(824\) | 1.01643 | 0.0354089 | ||||||||
\(825\) | −4.53915 | −0.158033 | ||||||||
\(826\) | −1.76536 | −0.0614246 | ||||||||
\(827\) | 41.3989 | 1.43958 | 0.719791 | − | 0.694191i | \(-0.244238\pi\) | ||||
0.719791 | + | 0.694191i | \(0.244238\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | −30.6301 | −1.06383 | −0.531914 | − | 0.846799i | \(-0.678527\pi\) | ||||
−0.531914 | + | 0.846799i | \(0.678527\pi\) | |||||||
\(830\) | 45.3721 | 1.57489 | ||||||||
\(831\) | 23.4648 | 0.813985 | ||||||||
\(832\) | −5.13869 | −0.178152 | ||||||||
\(833\) | 32.3959 | 1.12245 | ||||||||
\(834\) | −7.67652 | −0.265816 | ||||||||
\(835\) | 74.3124 | 2.57169 | ||||||||
\(836\) | 2.97419 | 0.102865 | ||||||||
\(837\) | 0.273696 | 0.00946031 | ||||||||
\(838\) | 13.2146 | 0.456491 | ||||||||
\(839\) | 17.4665 | 0.603011 | 0.301506 | − | 0.953464i | \(-0.402511\pi\) | ||||
0.301506 | + | 0.953464i | \(0.402511\pi\) | |||||||
\(840\) | −2.16954 | −0.0748564 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 19.6648 | 0.677693 | ||||||||
\(843\) | −13.7591 | −0.473889 | ||||||||
\(844\) | −2.97950 | −0.102559 | ||||||||
\(845\) | 47.3331 | 1.62831 | ||||||||
\(846\) | 11.4953 | 0.395218 | ||||||||
\(847\) | 6.53213 | 0.224447 | ||||||||
\(848\) | 1.81684 | 0.0623904 | ||||||||
\(849\) | 21.6445 | 0.742838 | ||||||||
\(850\) | 36.5219 | 1.25269 | ||||||||
\(851\) | 5.09540 | 0.174668 | ||||||||
\(852\) | 7.92271 | 0.271428 | ||||||||
\(853\) | −23.8382 | −0.816203 | −0.408102 | − | 0.912937i | \(-0.633809\pi\) | ||||
−0.408102 | + | 0.912937i | \(0.633809\pi\) | |||||||
\(854\) | 7.96977 | 0.272720 | ||||||||
\(855\) | 17.2717 | 0.590680 | ||||||||
\(856\) | 12.7064 | 0.434297 | ||||||||
\(857\) | 25.7558 | 0.879800 | 0.439900 | − | 0.898047i | \(-0.355014\pi\) | ||||
0.439900 | + | 0.898047i | \(0.355014\pi\) | |||||||
\(858\) | −3.12426 | −0.106661 | ||||||||
\(859\) | −56.7124 | −1.93500 | −0.967501 | − | 0.252865i | \(-0.918627\pi\) | ||||
−0.967501 | + | 0.252865i | \(0.918627\pi\) | |||||||
\(860\) | −6.31985 | −0.215505 | ||||||||
\(861\) | 3.28668 | 0.112010 | ||||||||
\(862\) | −0.429690 | −0.0146353 | ||||||||
\(863\) | −24.3205 | −0.827881 | −0.413940 | − | 0.910304i | \(-0.635848\pi\) | ||||
−0.413940 | + | 0.910304i | \(0.635848\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 20.8926 | 0.710369 | ||||||||
\(866\) | −6.61312 | −0.224723 | ||||||||
\(867\) | −6.93029 | −0.235365 | ||||||||
\(868\) | 0.168181 | 0.00570842 | ||||||||
\(869\) | 0.433304 | 0.0146988 | ||||||||
\(870\) | −3.53070 | −0.119702 | ||||||||
\(871\) | 60.6081 | 2.05363 | ||||||||
\(872\) | −0.0431107 | −0.00145991 | ||||||||
\(873\) | −5.81684 | −0.196870 | ||||||||
\(874\) | 4.89186 | 0.165470 | ||||||||
\(875\) | −5.34978 | −0.180855 | ||||||||
\(876\) | 6.01561 | 0.203249 | ||||||||
\(877\) | 17.3056 | 0.584367 | 0.292184 | − | 0.956362i | \(-0.405618\pi\) | ||||
0.292184 | + | 0.956362i | \(0.405618\pi\) | |||||||
\(878\) | 1.50559 | 0.0508110 | ||||||||
\(879\) | −2.54450 | −0.0858240 | ||||||||
\(880\) | 2.14663 | 0.0723627 | ||||||||
\(881\) | −7.28454 | −0.245423 | −0.122711 | − | 0.992442i | \(-0.539159\pi\) | ||||
−0.122711 | + | 0.992442i | \(0.539159\pi\) | |||||||
\(882\) | 6.62241 | 0.222988 | ||||||||
\(883\) | 21.8651 | 0.735818 | 0.367909 | − | 0.929862i | \(-0.380074\pi\) | ||||
0.367909 | + | 0.929862i | \(0.380074\pi\) | |||||||
\(884\) | 25.1377 | 0.845474 | ||||||||
\(885\) | 10.1435 | 0.340969 | ||||||||
\(886\) | 24.0942 | 0.809461 | ||||||||
\(887\) | 40.4634 | 1.35863 | 0.679315 | − | 0.733847i | \(-0.262277\pi\) | ||||
0.679315 | + | 0.733847i | \(0.262277\pi\) | |||||||
\(888\) | −5.09540 | −0.170990 | ||||||||
\(889\) | 1.60328 | 0.0537723 | ||||||||
\(890\) | −46.2130 | −1.54906 | ||||||||
\(891\) | 0.607988 | 0.0203684 | ||||||||
\(892\) | −9.51458 | −0.318572 | ||||||||
\(893\) | −56.2336 | −1.88179 | ||||||||
\(894\) | 12.9587 | 0.433404 | ||||||||
\(895\) | 77.7848 | 2.60006 | ||||||||
\(896\) | 0.614480 | 0.0205283 | ||||||||
\(897\) | −5.13869 | −0.171576 | ||||||||
\(898\) | −30.6301 | −1.02214 | ||||||||
\(899\) | 0.273696 | 0.00912827 | ||||||||
\(900\) | 7.46585 | 0.248862 | ||||||||
\(901\) | −8.88771 | −0.296092 | ||||||||
\(902\) | −3.25196 | −0.108278 | ||||||||
\(903\) | −1.09990 | −0.0366024 | ||||||||
\(904\) | −12.5541 | −0.417544 | ||||||||
\(905\) | −46.7966 | −1.55557 | ||||||||
\(906\) | 2.37558 | 0.0789235 | ||||||||
\(907\) | 12.0675 | 0.400694 | 0.200347 | − | 0.979725i | \(-0.435793\pi\) | ||||
0.200347 | + | 0.979725i | \(0.435793\pi\) | |||||||
\(908\) | −1.55081 | −0.0514655 | ||||||||
\(909\) | −10.9403 | −0.362866 | ||||||||
\(910\) | −11.1486 | −0.369573 | ||||||||
\(911\) | 6.97395 | 0.231057 | 0.115529 | − | 0.993304i | \(-0.463144\pi\) | ||||
0.115529 | + | 0.993304i | \(0.463144\pi\) | |||||||
\(912\) | −4.89186 | −0.161986 | ||||||||
\(913\) | −7.81310 | −0.258576 | ||||||||
\(914\) | 39.2943 | 1.29974 | ||||||||
\(915\) | −45.7930 | −1.51387 | ||||||||
\(916\) | −16.4316 | −0.542914 | ||||||||
\(917\) | 3.28994 | 0.108643 | ||||||||
\(918\) | −4.89186 | −0.161455 | ||||||||
\(919\) | 50.0176 | 1.64993 | 0.824965 | − | 0.565184i | \(-0.191195\pi\) | ||||
0.824965 | + | 0.565184i | \(0.191195\pi\) | |||||||
\(920\) | 3.53070 | 0.116404 | ||||||||
\(921\) | 22.7296 | 0.748966 | ||||||||
\(922\) | −15.6924 | −0.516803 | ||||||||
\(923\) | 40.7124 | 1.34006 | ||||||||
\(924\) | 0.373596 | 0.0122904 | ||||||||
\(925\) | −38.0415 | −1.25080 | ||||||||
\(926\) | 5.09452 | 0.167416 | ||||||||
\(927\) | −1.01643 | −0.0333839 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | 35.5627 | 1.16677 | 0.583387 | − | 0.812194i | \(-0.301727\pi\) | ||||
0.583387 | + | 0.812194i | \(0.301727\pi\) | |||||||
\(930\) | −0.966339 | −0.0316875 | ||||||||
\(931\) | −32.3959 | −1.06173 | ||||||||
\(932\) | −4.59050 | −0.150367 | ||||||||
\(933\) | −9.02765 | −0.295552 | ||||||||
\(934\) | 20.3616 | 0.666251 | ||||||||
\(935\) | −10.5010 | −0.343419 | ||||||||
\(936\) | 5.13869 | 0.167963 | ||||||||
\(937\) | −38.4968 | −1.25763 | −0.628817 | − | 0.777553i | \(-0.716461\pi\) | ||||
−0.628817 | + | 0.777553i | \(0.716461\pi\) | |||||||
\(938\) | −7.24746 | −0.236638 | ||||||||
\(939\) | 13.2001 | 0.430769 | ||||||||
\(940\) | −40.5866 | −1.32379 | ||||||||
\(941\) | −39.8828 | −1.30014 | −0.650071 | − | 0.759873i | \(-0.725261\pi\) | ||||
−0.650071 | + | 0.759873i | \(0.725261\pi\) | |||||||
\(942\) | 20.0757 | 0.654102 | ||||||||
\(943\) | −5.34872 | −0.174178 | ||||||||
\(944\) | −2.87293 | −0.0935059 | ||||||||
\(945\) | 2.16954 | 0.0705753 | ||||||||
\(946\) | 1.08828 | 0.0353831 | ||||||||
\(947\) | 12.8926 | 0.418954 | 0.209477 | − | 0.977814i | \(-0.432824\pi\) | ||||
0.209477 | + | 0.977814i | \(0.432824\pi\) | |||||||
\(948\) | −0.712684 | −0.0231469 | ||||||||
\(949\) | 30.9123 | 1.00346 | ||||||||
\(950\) | −36.5219 | −1.18493 | ||||||||
\(951\) | −11.6125 | −0.376560 | ||||||||
\(952\) | −3.00595 | −0.0974233 | ||||||||
\(953\) | −1.94303 | −0.0629411 | −0.0314705 | − | 0.999505i | \(-0.510019\pi\) | ||||
−0.0314705 | + | 0.999505i | \(0.510019\pi\) | |||||||
\(954\) | −1.81684 | −0.0588222 | ||||||||
\(955\) | −67.2772 | −2.17704 | ||||||||
\(956\) | −23.5054 | −0.760219 | ||||||||
\(957\) | 0.607988 | 0.0196535 | ||||||||
\(958\) | −13.9805 | −0.451690 | ||||||||
\(959\) | −7.46612 | −0.241093 | ||||||||
\(960\) | −3.53070 | −0.113953 | ||||||||
\(961\) | −30.9251 | −0.997584 | ||||||||
\(962\) | −26.1837 | −0.844195 | ||||||||
\(963\) | −12.7064 | −0.409459 | ||||||||
\(964\) | −15.9841 | −0.514814 | ||||||||
\(965\) | −29.6278 | −0.953752 | ||||||||
\(966\) | 0.614480 | 0.0197706 | ||||||||
\(967\) | 10.2701 | 0.330265 | 0.165133 | − | 0.986271i | \(-0.447195\pi\) | ||||
0.165133 | + | 0.986271i | \(0.447195\pi\) | |||||||
\(968\) | 10.6304 | 0.341672 | ||||||||
\(969\) | 23.9303 | 0.768752 | ||||||||
\(970\) | 20.5375 | 0.659420 | ||||||||
\(971\) | −6.44342 | −0.206779 | −0.103390 | − | 0.994641i | \(-0.532969\pi\) | ||||
−0.103390 | + | 0.994641i | \(0.532969\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 4.71706 | 0.151222 | ||||||||
\(974\) | −12.4420 | −0.398669 | ||||||||
\(975\) | 38.3647 | 1.22865 | ||||||||
\(976\) | 12.9700 | 0.415158 | ||||||||
\(977\) | −8.47330 | −0.271085 | −0.135543 | − | 0.990772i | \(-0.543278\pi\) | ||||
−0.135543 | + | 0.990772i | \(0.543278\pi\) | |||||||
\(978\) | 17.0816 | 0.546209 | ||||||||
\(979\) | 7.95790 | 0.254336 | ||||||||
\(980\) | −23.3818 | −0.746903 | ||||||||
\(981\) | 0.0431107 | 0.00137642 | ||||||||
\(982\) | 39.8690 | 1.27227 | ||||||||
\(983\) | 26.5393 | 0.846474 | 0.423237 | − | 0.906019i | \(-0.360894\pi\) | ||||
0.423237 | + | 0.906019i | \(0.360894\pi\) | |||||||
\(984\) | 5.34872 | 0.170511 | ||||||||
\(985\) | −77.7540 | −2.47745 | ||||||||
\(986\) | −4.89186 | −0.155789 | ||||||||
\(987\) | −7.06365 | −0.224839 | ||||||||
\(988\) | −25.1377 | −0.799738 | ||||||||
\(989\) | 1.78997 | 0.0569178 | ||||||||
\(990\) | −2.14663 | −0.0682242 | ||||||||
\(991\) | 31.3288 | 0.995191 | 0.497596 | − | 0.867409i | \(-0.334216\pi\) | ||||
0.497596 | + | 0.867409i | \(0.334216\pi\) | |||||||
\(992\) | 0.273696 | 0.00868985 | ||||||||
\(993\) | 8.36260 | 0.265379 | ||||||||
\(994\) | −4.86835 | −0.154415 | ||||||||
\(995\) | −77.2824 | −2.45002 | ||||||||
\(996\) | 12.8507 | 0.407191 | ||||||||
\(997\) | 6.56339 | 0.207865 | 0.103932 | − | 0.994584i | \(-0.466857\pi\) | ||||
0.103932 | + | 0.994584i | \(0.466857\pi\) | |||||||
\(998\) | 24.2777 | 0.768498 | ||||||||
\(999\) | 5.09540 | 0.161211 |
(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 | 4002.2.a.be.1.5 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4002.2.a.be.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial |