Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 5 x^{10} - 31 x^{9} + 168 x^{8} + 300 x^{7} - 1928 x^{6} - 736 x^{5} + 8532 x^{4} - 2065 x^{3} + \cdots + 576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.31499\) 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 | ||||||||
\(5\) | −1.31499 | −0.588083 | −0.294042 | − | 0.955793i | \(-0.595000\pi\) | ||||
−0.294042 | + | 0.955793i | \(0.595000\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 3.43679 | 1.29898 | 0.649492 | − | 0.760369i | \(-0.274982\pi\) | ||||
0.649492 | + | 0.760369i | \(0.274982\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.31499 | −0.415837 | ||||||||
\(11\) | −3.11170 | −0.938213 | −0.469107 | − | 0.883142i | \(-0.655424\pi\) | ||||
−0.469107 | + | 0.883142i | \(0.655424\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 3.43679 | 0.918520 | ||||||||
\(15\) | −1.31499 | −0.339530 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.00690 | 1.45689 | 0.728444 | − | 0.685106i | \(-0.240244\pi\) | ||||
0.728444 | + | 0.685106i | \(0.240244\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 2.43679 | 0.559037 | 0.279519 | − | 0.960140i | \(-0.409825\pi\) | ||||
0.279519 | + | 0.960140i | \(0.409825\pi\) | |||||||
\(20\) | −1.31499 | −0.294042 | ||||||||
\(21\) | 3.43679 | 0.749968 | ||||||||
\(22\) | −3.11170 | −0.663417 | ||||||||
\(23\) | 5.59372 | 1.16637 | 0.583186 | − | 0.812339i | \(-0.301806\pi\) | ||||
0.583186 | + | 0.812339i | \(0.301806\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −3.27079 | −0.654158 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.43679 | 0.649492 | ||||||||
\(29\) | 6.46722 | 1.20093 | 0.600466 | − | 0.799650i | \(-0.294982\pi\) | ||||
0.600466 | + | 0.799650i | \(0.294982\pi\) | |||||||
\(30\) | −1.31499 | −0.240084 | ||||||||
\(31\) | −2.43679 | −0.437660 | −0.218830 | − | 0.975763i | \(-0.570224\pi\) | ||||
−0.218830 | + | 0.975763i | \(0.570224\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.11170 | −0.541678 | ||||||||
\(34\) | 6.00690 | 1.03017 | ||||||||
\(35\) | −4.51935 | −0.763910 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.81393 | 0.462608 | 0.231304 | − | 0.972882i | \(-0.425701\pi\) | ||||
0.231304 | + | 0.972882i | \(0.425701\pi\) | |||||||
\(38\) | 2.43679 | 0.395299 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −1.31499 | −0.207919 | ||||||||
\(41\) | 0.544657 | 0.0850612 | 0.0425306 | − | 0.999095i | \(-0.486458\pi\) | ||||
0.0425306 | + | 0.999095i | \(0.486458\pi\) | |||||||
\(42\) | 3.43679 | 0.530308 | ||||||||
\(43\) | −12.8675 | −1.96227 | −0.981135 | − | 0.193323i | \(-0.938073\pi\) | ||||
−0.981135 | + | 0.193323i | \(0.938073\pi\) | |||||||
\(44\) | −3.11170 | −0.469107 | ||||||||
\(45\) | −1.31499 | −0.196028 | ||||||||
\(46\) | 5.59372 | 0.824749 | ||||||||
\(47\) | −5.36242 | −0.782189 | −0.391095 | − | 0.920350i | \(-0.627903\pi\) | ||||
−0.391095 | + | 0.920350i | \(0.627903\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 4.81150 | 0.687357 | ||||||||
\(50\) | −3.27079 | −0.462560 | ||||||||
\(51\) | 6.00690 | 0.841134 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 10.1760 | 1.39778 | 0.698888 | − | 0.715231i | \(-0.253679\pi\) | ||||
0.698888 | + | 0.715231i | \(0.253679\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 4.09187 | 0.551747 | ||||||||
\(56\) | 3.43679 | 0.459260 | ||||||||
\(57\) | 2.43679 | 0.322760 | ||||||||
\(58\) | 6.46722 | 0.849188 | ||||||||
\(59\) | −4.51171 | −0.587375 | −0.293688 | − | 0.955901i | \(-0.594883\pi\) | ||||
−0.293688 | + | 0.955901i | \(0.594883\pi\) | |||||||
\(60\) | −1.31499 | −0.169765 | ||||||||
\(61\) | 13.8024 | 1.76722 | 0.883610 | − | 0.468224i | \(-0.155106\pi\) | ||||
0.883610 | + | 0.468224i | \(0.155106\pi\) | |||||||
\(62\) | −2.43679 | −0.309472 | ||||||||
\(63\) | 3.43679 | 0.432994 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.31499 | −0.163105 | ||||||||
\(66\) | −3.11170 | −0.383024 | ||||||||
\(67\) | −14.5505 | −1.77763 | −0.888813 | − | 0.458271i | \(-0.848469\pi\) | ||||
−0.888813 | + | 0.458271i | \(0.848469\pi\) | |||||||
\(68\) | 6.00690 | 0.728444 | ||||||||
\(69\) | 5.59372 | 0.673405 | ||||||||
\(70\) | −4.51935 | −0.540166 | ||||||||
\(71\) | −9.93655 | −1.17925 | −0.589626 | − | 0.807676i | \(-0.700725\pi\) | ||||
−0.589626 | + | 0.807676i | \(0.700725\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −2.55975 | −0.299596 | −0.149798 | − | 0.988717i | \(-0.547862\pi\) | ||||
−0.149798 | + | 0.988717i | \(0.547862\pi\) | |||||||
\(74\) | 2.81393 | 0.327113 | ||||||||
\(75\) | −3.27079 | −0.377679 | ||||||||
\(76\) | 2.43679 | 0.279519 | ||||||||
\(77\) | −10.6943 | −1.21872 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 12.3825 | 1.39314 | 0.696570 | − | 0.717489i | \(-0.254709\pi\) | ||||
0.696570 | + | 0.717489i | \(0.254709\pi\) | |||||||
\(80\) | −1.31499 | −0.147021 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.544657 | 0.0601474 | ||||||||
\(83\) | 8.21206 | 0.901391 | 0.450695 | − | 0.892678i | \(-0.351176\pi\) | ||||
0.450695 | + | 0.892678i | \(0.351176\pi\) | |||||||
\(84\) | 3.43679 | 0.374984 | ||||||||
\(85\) | −7.89903 | −0.856771 | ||||||||
\(86\) | −12.8675 | −1.38753 | ||||||||
\(87\) | 6.46722 | 0.693359 | ||||||||
\(88\) | −3.11170 | −0.331708 | ||||||||
\(89\) | −1.59953 | −0.169550 | −0.0847749 | − | 0.996400i | \(-0.527017\pi\) | ||||
−0.0847749 | + | 0.996400i | \(0.527017\pi\) | |||||||
\(90\) | −1.31499 | −0.138612 | ||||||||
\(91\) | 3.43679 | 0.360273 | ||||||||
\(92\) | 5.59372 | 0.583186 | ||||||||
\(93\) | −2.43679 | −0.252683 | ||||||||
\(94\) | −5.36242 | −0.553091 | ||||||||
\(95\) | −3.20436 | −0.328760 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 9.40912 | 0.955351 | 0.477676 | − | 0.878536i | \(-0.341479\pi\) | ||||
0.477676 | + | 0.878536i | \(0.341479\pi\) | |||||||
\(98\) | 4.81150 | 0.486035 | ||||||||
\(99\) | −3.11170 | −0.312738 | ||||||||
\(100\) | −3.27079 | −0.327079 | ||||||||
\(101\) | 13.2699 | 1.32041 | 0.660203 | − | 0.751087i | \(-0.270470\pi\) | ||||
0.660203 | + | 0.751087i | \(0.270470\pi\) | |||||||
\(102\) | 6.00690 | 0.594772 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −4.51935 | −0.441044 | ||||||||
\(106\) | 10.1760 | 0.988377 | ||||||||
\(107\) | −0.861674 | −0.0833012 | −0.0416506 | − | 0.999132i | \(-0.513262\pi\) | ||||
−0.0416506 | + | 0.999132i | \(0.513262\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 0.888682 | 0.0851203 | 0.0425602 | − | 0.999094i | \(-0.486449\pi\) | ||||
0.0425602 | + | 0.999094i | \(0.486449\pi\) | |||||||
\(110\) | 4.09187 | 0.390144 | ||||||||
\(111\) | 2.81393 | 0.267087 | ||||||||
\(112\) | 3.43679 | 0.324746 | ||||||||
\(113\) | −6.57570 | −0.618590 | −0.309295 | − | 0.950966i | \(-0.600093\pi\) | ||||
−0.309295 | + | 0.950966i | \(0.600093\pi\) | |||||||
\(114\) | 2.43679 | 0.228226 | ||||||||
\(115\) | −7.35571 | −0.685923 | ||||||||
\(116\) | 6.46722 | 0.600466 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −4.51171 | −0.415337 | ||||||||
\(119\) | 20.6444 | 1.89247 | ||||||||
\(120\) | −1.31499 | −0.120042 | ||||||||
\(121\) | −1.31732 | −0.119756 | ||||||||
\(122\) | 13.8024 | 1.24961 | ||||||||
\(123\) | 0.544657 | 0.0491101 | ||||||||
\(124\) | −2.43679 | −0.218830 | ||||||||
\(125\) | 10.8760 | 0.972782 | ||||||||
\(126\) | 3.43679 | 0.306173 | ||||||||
\(127\) | 16.4226 | 1.45727 | 0.728637 | − | 0.684901i | \(-0.240154\pi\) | ||||
0.728637 | + | 0.684901i | \(0.240154\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −12.8675 | −1.13292 | ||||||||
\(130\) | −1.31499 | −0.115333 | ||||||||
\(131\) | −10.8094 | −0.944422 | −0.472211 | − | 0.881485i | \(-0.656544\pi\) | ||||
−0.472211 | + | 0.881485i | \(0.656544\pi\) | |||||||
\(132\) | −3.11170 | −0.270839 | ||||||||
\(133\) | 8.37472 | 0.726180 | ||||||||
\(134\) | −14.5505 | −1.25697 | ||||||||
\(135\) | −1.31499 | −0.113177 | ||||||||
\(136\) | 6.00690 | 0.515087 | ||||||||
\(137\) | −10.6942 | −0.913669 | −0.456834 | − | 0.889552i | \(-0.651017\pi\) | ||||
−0.456834 | + | 0.889552i | \(0.651017\pi\) | |||||||
\(138\) | 5.59372 | 0.476169 | ||||||||
\(139\) | −20.9071 | −1.77331 | −0.886657 | − | 0.462427i | \(-0.846979\pi\) | ||||
−0.886657 | + | 0.462427i | \(0.846979\pi\) | |||||||
\(140\) | −4.51935 | −0.381955 | ||||||||
\(141\) | −5.36242 | −0.451597 | ||||||||
\(142\) | −9.93655 | −0.833857 | ||||||||
\(143\) | −3.11170 | −0.260213 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −8.50435 | −0.706248 | ||||||||
\(146\) | −2.55975 | −0.211846 | ||||||||
\(147\) | 4.81150 | 0.396846 | ||||||||
\(148\) | 2.81393 | 0.231304 | ||||||||
\(149\) | 5.57577 | 0.456785 | 0.228393 | − | 0.973569i | \(-0.426653\pi\) | ||||
0.228393 | + | 0.973569i | \(0.426653\pi\) | |||||||
\(150\) | −3.27079 | −0.267059 | ||||||||
\(151\) | −14.9584 | −1.21730 | −0.608649 | − | 0.793440i | \(-0.708288\pi\) | ||||
−0.608649 | + | 0.793440i | \(0.708288\pi\) | |||||||
\(152\) | 2.43679 | 0.197649 | ||||||||
\(153\) | 6.00690 | 0.485629 | ||||||||
\(154\) | −10.6943 | −0.861767 | ||||||||
\(155\) | 3.20436 | 0.257380 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | 22.7031 | 1.81190 | 0.905951 | − | 0.423384i | \(-0.139158\pi\) | ||||
0.905951 | + | 0.423384i | \(0.139158\pi\) | |||||||
\(158\) | 12.3825 | 0.985098 | ||||||||
\(159\) | 10.1760 | 0.807007 | ||||||||
\(160\) | −1.31499 | −0.103959 | ||||||||
\(161\) | 19.2244 | 1.51510 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 3.89555 | 0.305123 | 0.152562 | − | 0.988294i | \(-0.451248\pi\) | ||||
0.152562 | + | 0.988294i | \(0.451248\pi\) | |||||||
\(164\) | 0.544657 | 0.0425306 | ||||||||
\(165\) | 4.09187 | 0.318551 | ||||||||
\(166\) | 8.21206 | 0.637379 | ||||||||
\(167\) | −5.44190 | −0.421107 | −0.210553 | − | 0.977582i | \(-0.567527\pi\) | ||||
−0.210553 | + | 0.977582i | \(0.567527\pi\) | |||||||
\(168\) | 3.43679 | 0.265154 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −7.89903 | −0.605828 | ||||||||
\(171\) | 2.43679 | 0.186346 | ||||||||
\(172\) | −12.8675 | −0.981135 | ||||||||
\(173\) | 20.1657 | 1.53317 | 0.766583 | − | 0.642145i | \(-0.221955\pi\) | ||||
0.766583 | + | 0.642145i | \(0.221955\pi\) | |||||||
\(174\) | 6.46722 | 0.490279 | ||||||||
\(175\) | −11.2410 | −0.849741 | ||||||||
\(176\) | −3.11170 | −0.234553 | ||||||||
\(177\) | −4.51171 | −0.339121 | ||||||||
\(178\) | −1.59953 | −0.119890 | ||||||||
\(179\) | 11.0633 | 0.826912 | 0.413456 | − | 0.910524i | \(-0.364322\pi\) | ||||
0.413456 | + | 0.910524i | \(0.364322\pi\) | |||||||
\(180\) | −1.31499 | −0.0980138 | ||||||||
\(181\) | 0.606839 | 0.0451060 | 0.0225530 | − | 0.999746i | \(-0.492821\pi\) | ||||
0.0225530 | + | 0.999746i | \(0.492821\pi\) | |||||||
\(182\) | 3.43679 | 0.254752 | ||||||||
\(183\) | 13.8024 | 1.02030 | ||||||||
\(184\) | 5.59372 | 0.412374 | ||||||||
\(185\) | −3.70030 | −0.272052 | ||||||||
\(186\) | −2.43679 | −0.178674 | ||||||||
\(187\) | −18.6917 | −1.36687 | ||||||||
\(188\) | −5.36242 | −0.391095 | ||||||||
\(189\) | 3.43679 | 0.249989 | ||||||||
\(190\) | −3.20436 | −0.232469 | ||||||||
\(191\) | 6.43044 | 0.465291 | 0.232645 | − | 0.972562i | \(-0.425262\pi\) | ||||
0.232645 | + | 0.972562i | \(0.425262\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −21.8446 | −1.57241 | −0.786205 | − | 0.617966i | \(-0.787957\pi\) | ||||
−0.786205 | + | 0.617966i | \(0.787957\pi\) | |||||||
\(194\) | 9.40912 | 0.675535 | ||||||||
\(195\) | −1.31499 | −0.0941686 | ||||||||
\(196\) | 4.81150 | 0.343679 | ||||||||
\(197\) | 16.8084 | 1.19755 | 0.598775 | − | 0.800917i | \(-0.295654\pi\) | ||||
0.598775 | + | 0.800917i | \(0.295654\pi\) | |||||||
\(198\) | −3.11170 | −0.221139 | ||||||||
\(199\) | 27.6236 | 1.95819 | 0.979094 | − | 0.203410i | \(-0.0652023\pi\) | ||||
0.979094 | + | 0.203410i | \(0.0652023\pi\) | |||||||
\(200\) | −3.27079 | −0.231280 | ||||||||
\(201\) | −14.5505 | −1.02631 | ||||||||
\(202\) | 13.2699 | 0.933668 | ||||||||
\(203\) | 22.2265 | 1.55999 | ||||||||
\(204\) | 6.00690 | 0.420567 | ||||||||
\(205\) | −0.716221 | −0.0500231 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | 5.59372 | 0.388790 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −7.58255 | −0.524496 | ||||||||
\(210\) | −4.51935 | −0.311865 | ||||||||
\(211\) | −0.511831 | −0.0352359 | −0.0176180 | − | 0.999845i | \(-0.505608\pi\) | ||||
−0.0176180 | + | 0.999845i | \(0.505608\pi\) | |||||||
\(212\) | 10.1760 | 0.698888 | ||||||||
\(213\) | −9.93655 | −0.680841 | ||||||||
\(214\) | −0.861674 | −0.0589028 | ||||||||
\(215\) | 16.9206 | 1.15398 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −8.37472 | −0.568513 | ||||||||
\(218\) | 0.888682 | 0.0601892 | ||||||||
\(219\) | −2.55975 | −0.172972 | ||||||||
\(220\) | 4.09187 | 0.275874 | ||||||||
\(221\) | 6.00690 | 0.404068 | ||||||||
\(222\) | 2.81393 | 0.188859 | ||||||||
\(223\) | −14.3697 | −0.962264 | −0.481132 | − | 0.876648i | \(-0.659774\pi\) | ||||
−0.481132 | + | 0.876648i | \(0.659774\pi\) | |||||||
\(224\) | 3.43679 | 0.229630 | ||||||||
\(225\) | −3.27079 | −0.218053 | ||||||||
\(226\) | −6.57570 | −0.437409 | ||||||||
\(227\) | 26.2398 | 1.74160 | 0.870799 | − | 0.491639i | \(-0.163602\pi\) | ||||
0.870799 | + | 0.491639i | \(0.163602\pi\) | |||||||
\(228\) | 2.43679 | 0.161380 | ||||||||
\(229\) | 19.1941 | 1.26838 | 0.634192 | − | 0.773175i | \(-0.281333\pi\) | ||||
0.634192 | + | 0.773175i | \(0.281333\pi\) | |||||||
\(230\) | −7.35571 | −0.485021 | ||||||||
\(231\) | −10.6943 | −0.703630 | ||||||||
\(232\) | 6.46722 | 0.424594 | ||||||||
\(233\) | 7.61515 | 0.498885 | 0.249443 | − | 0.968390i | \(-0.419753\pi\) | ||||
0.249443 | + | 0.968390i | \(0.419753\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | 7.05155 | 0.459992 | ||||||||
\(236\) | −4.51171 | −0.293688 | ||||||||
\(237\) | 12.3825 | 0.804329 | ||||||||
\(238\) | 20.6444 | 1.33818 | ||||||||
\(239\) | 22.9290 | 1.48316 | 0.741578 | − | 0.670867i | \(-0.234078\pi\) | ||||
0.741578 | + | 0.670867i | \(0.234078\pi\) | |||||||
\(240\) | −1.31499 | −0.0848825 | ||||||||
\(241\) | 13.1026 | 0.844014 | 0.422007 | − | 0.906593i | \(-0.361326\pi\) | ||||
0.422007 | + | 0.906593i | \(0.361326\pi\) | |||||||
\(242\) | −1.31732 | −0.0846804 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 13.8024 | 0.883610 | ||||||||
\(245\) | −6.32709 | −0.404223 | ||||||||
\(246\) | 0.544657 | 0.0347261 | ||||||||
\(247\) | 2.43679 | 0.155049 | ||||||||
\(248\) | −2.43679 | −0.154736 | ||||||||
\(249\) | 8.21206 | 0.520418 | ||||||||
\(250\) | 10.8760 | 0.687861 | ||||||||
\(251\) | 15.6751 | 0.989404 | 0.494702 | − | 0.869063i | \(-0.335277\pi\) | ||||
0.494702 | + | 0.869063i | \(0.335277\pi\) | |||||||
\(252\) | 3.43679 | 0.216497 | ||||||||
\(253\) | −17.4060 | −1.09430 | ||||||||
\(254\) | 16.4226 | 1.03045 | ||||||||
\(255\) | −7.89903 | −0.494657 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.32596 | −0.332224 | −0.166112 | − | 0.986107i | \(-0.553121\pi\) | ||||
−0.166112 | + | 0.986107i | \(0.553121\pi\) | |||||||
\(258\) | −12.8675 | −0.801093 | ||||||||
\(259\) | 9.67088 | 0.600919 | ||||||||
\(260\) | −1.31499 | −0.0815524 | ||||||||
\(261\) | 6.46722 | 0.400311 | ||||||||
\(262\) | −10.8094 | −0.667807 | ||||||||
\(263\) | −19.1914 | −1.18339 | −0.591697 | − | 0.806160i | \(-0.701542\pi\) | ||||
−0.591697 | + | 0.806160i | \(0.701542\pi\) | |||||||
\(264\) | −3.11170 | −0.191512 | ||||||||
\(265\) | −13.3813 | −0.822008 | ||||||||
\(266\) | 8.37472 | 0.513487 | ||||||||
\(267\) | −1.59953 | −0.0978896 | ||||||||
\(268\) | −14.5505 | −0.888813 | ||||||||
\(269\) | −20.8026 | −1.26836 | −0.634179 | − | 0.773187i | \(-0.718662\pi\) | ||||
−0.634179 | + | 0.773187i | \(0.718662\pi\) | |||||||
\(270\) | −1.31499 | −0.0800280 | ||||||||
\(271\) | −18.4540 | −1.12100 | −0.560501 | − | 0.828153i | \(-0.689392\pi\) | ||||
−0.560501 | + | 0.828153i | \(0.689392\pi\) | |||||||
\(272\) | 6.00690 | 0.364222 | ||||||||
\(273\) | 3.43679 | 0.208004 | ||||||||
\(274\) | −10.6942 | −0.646061 | ||||||||
\(275\) | 10.1777 | 0.613740 | ||||||||
\(276\) | 5.59372 | 0.336702 | ||||||||
\(277\) | −16.1807 | −0.972205 | −0.486103 | − | 0.873902i | \(-0.661582\pi\) | ||||
−0.486103 | + | 0.873902i | \(0.661582\pi\) | |||||||
\(278\) | −20.9071 | −1.25392 | ||||||||
\(279\) | −2.43679 | −0.145887 | ||||||||
\(280\) | −4.51935 | −0.270083 | ||||||||
\(281\) | 20.1897 | 1.20441 | 0.602207 | − | 0.798340i | \(-0.294288\pi\) | ||||
0.602207 | + | 0.798340i | \(0.294288\pi\) | |||||||
\(282\) | −5.36242 | −0.319327 | ||||||||
\(283\) | −21.2857 | −1.26530 | −0.632652 | − | 0.774436i | \(-0.718034\pi\) | ||||
−0.632652 | + | 0.774436i | \(0.718034\pi\) | |||||||
\(284\) | −9.93655 | −0.589626 | ||||||||
\(285\) | −3.20436 | −0.189810 | ||||||||
\(286\) | −3.11170 | −0.183999 | ||||||||
\(287\) | 1.87187 | 0.110493 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 19.0828 | 1.12252 | ||||||||
\(290\) | −8.50435 | −0.499393 | ||||||||
\(291\) | 9.40912 | 0.551572 | ||||||||
\(292\) | −2.55975 | −0.149798 | ||||||||
\(293\) | 23.1886 | 1.35469 | 0.677345 | − | 0.735666i | \(-0.263131\pi\) | ||||
0.677345 | + | 0.735666i | \(0.263131\pi\) | |||||||
\(294\) | 4.81150 | 0.280613 | ||||||||
\(295\) | 5.93287 | 0.345425 | ||||||||
\(296\) | 2.81393 | 0.163556 | ||||||||
\(297\) | −3.11170 | −0.180559 | ||||||||
\(298\) | 5.57577 | 0.322996 | ||||||||
\(299\) | 5.59372 | 0.323493 | ||||||||
\(300\) | −3.27079 | −0.188839 | ||||||||
\(301\) | −44.2227 | −2.54896 | ||||||||
\(302\) | −14.9584 | −0.860760 | ||||||||
\(303\) | 13.2699 | 0.762337 | ||||||||
\(304\) | 2.43679 | 0.139759 | ||||||||
\(305\) | −18.1501 | −1.03927 | ||||||||
\(306\) | 6.00690 | 0.343392 | ||||||||
\(307\) | −24.3962 | −1.39236 | −0.696182 | − | 0.717865i | \(-0.745119\pi\) | ||||
−0.696182 | + | 0.717865i | \(0.745119\pi\) | |||||||
\(308\) | −10.6943 | −0.609362 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 3.20436 | 0.181995 | ||||||||
\(311\) | −27.1959 | −1.54214 | −0.771068 | − | 0.636753i | \(-0.780277\pi\) | ||||
−0.771068 | + | 0.636753i | \(0.780277\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 2.70927 | 0.153137 | 0.0765684 | − | 0.997064i | \(-0.475604\pi\) | ||||
0.0765684 | + | 0.997064i | \(0.475604\pi\) | |||||||
\(314\) | 22.7031 | 1.28121 | ||||||||
\(315\) | −4.51935 | −0.254637 | ||||||||
\(316\) | 12.3825 | 0.696570 | ||||||||
\(317\) | −27.6179 | −1.55117 | −0.775587 | − | 0.631241i | \(-0.782546\pi\) | ||||
−0.775587 | + | 0.631241i | \(0.782546\pi\) | |||||||
\(318\) | 10.1760 | 0.570640 | ||||||||
\(319\) | −20.1241 | −1.12673 | ||||||||
\(320\) | −1.31499 | −0.0735104 | ||||||||
\(321\) | −0.861674 | −0.0480940 | ||||||||
\(322\) | 19.2244 | 1.07134 | ||||||||
\(323\) | 14.6375 | 0.814454 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −3.27079 | −0.181431 | ||||||||
\(326\) | 3.89555 | 0.215755 | ||||||||
\(327\) | 0.888682 | 0.0491442 | ||||||||
\(328\) | 0.544657 | 0.0300737 | ||||||||
\(329\) | −18.4295 | −1.01605 | ||||||||
\(330\) | 4.09187 | 0.225250 | ||||||||
\(331\) | −2.45599 | −0.134993 | −0.0674966 | − | 0.997720i | \(-0.521501\pi\) | ||||
−0.0674966 | + | 0.997720i | \(0.521501\pi\) | |||||||
\(332\) | 8.21206 | 0.450695 | ||||||||
\(333\) | 2.81393 | 0.154203 | ||||||||
\(334\) | −5.44190 | −0.297767 | ||||||||
\(335\) | 19.1338 | 1.04539 | ||||||||
\(336\) | 3.43679 | 0.187492 | ||||||||
\(337\) | −12.6506 | −0.689122 | −0.344561 | − | 0.938764i | \(-0.611972\pi\) | ||||
−0.344561 | + | 0.938764i | \(0.611972\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −6.57570 | −0.357143 | ||||||||
\(340\) | −7.89903 | −0.428385 | ||||||||
\(341\) | 7.58255 | 0.410618 | ||||||||
\(342\) | 2.43679 | 0.131766 | ||||||||
\(343\) | −7.52140 | −0.406117 | ||||||||
\(344\) | −12.8675 | −0.693767 | ||||||||
\(345\) | −7.35571 | −0.396018 | ||||||||
\(346\) | 20.1657 | 1.08411 | ||||||||
\(347\) | −7.26365 | −0.389933 | −0.194967 | − | 0.980810i | \(-0.562460\pi\) | ||||
−0.194967 | + | 0.980810i | \(0.562460\pi\) | |||||||
\(348\) | 6.46722 | 0.346679 | ||||||||
\(349\) | 1.47059 | 0.0787191 | 0.0393595 | − | 0.999225i | \(-0.487468\pi\) | ||||
0.0393595 | + | 0.999225i | \(0.487468\pi\) | |||||||
\(350\) | −11.2410 | −0.600857 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −3.11170 | −0.165854 | ||||||||
\(353\) | 31.5648 | 1.68003 | 0.840014 | − | 0.542565i | \(-0.182547\pi\) | ||||
0.840014 | + | 0.542565i | \(0.182547\pi\) | |||||||
\(354\) | −4.51171 | −0.239795 | ||||||||
\(355\) | 13.0665 | 0.693498 | ||||||||
\(356\) | −1.59953 | −0.0847749 | ||||||||
\(357\) | 20.6444 | 1.09262 | ||||||||
\(358\) | 11.0633 | 0.584715 | ||||||||
\(359\) | 3.69648 | 0.195092 | 0.0975462 | − | 0.995231i | \(-0.468901\pi\) | ||||
0.0975462 | + | 0.995231i | \(0.468901\pi\) | |||||||
\(360\) | −1.31499 | −0.0693062 | ||||||||
\(361\) | −13.0621 | −0.687477 | ||||||||
\(362\) | 0.606839 | 0.0318947 | ||||||||
\(363\) | −1.31732 | −0.0691413 | ||||||||
\(364\) | 3.43679 | 0.180137 | ||||||||
\(365\) | 3.36605 | 0.176187 | ||||||||
\(366\) | 13.8024 | 0.721464 | ||||||||
\(367\) | −7.08638 | −0.369906 | −0.184953 | − | 0.982747i | \(-0.559213\pi\) | ||||
−0.184953 | + | 0.982747i | \(0.559213\pi\) | |||||||
\(368\) | 5.59372 | 0.291593 | ||||||||
\(369\) | 0.544657 | 0.0283537 | ||||||||
\(370\) | −3.70030 | −0.192370 | ||||||||
\(371\) | 34.9726 | 1.81569 | ||||||||
\(372\) | −2.43679 | −0.126342 | ||||||||
\(373\) | 9.77642 | 0.506204 | 0.253102 | − | 0.967440i | \(-0.418549\pi\) | ||||
0.253102 | + | 0.967440i | \(0.418549\pi\) | |||||||
\(374\) | −18.6917 | −0.966523 | ||||||||
\(375\) | 10.8760 | 0.561636 | ||||||||
\(376\) | −5.36242 | −0.276546 | ||||||||
\(377\) | 6.46722 | 0.333079 | ||||||||
\(378\) | 3.43679 | 0.176769 | ||||||||
\(379\) | 18.2285 | 0.936333 | 0.468167 | − | 0.883640i | \(-0.344915\pi\) | ||||
0.468167 | + | 0.883640i | \(0.344915\pi\) | |||||||
\(380\) | −3.20436 | −0.164380 | ||||||||
\(381\) | 16.4226 | 0.841357 | ||||||||
\(382\) | 6.43044 | 0.329010 | ||||||||
\(383\) | −3.84084 | −0.196258 | −0.0981288 | − | 0.995174i | \(-0.531286\pi\) | ||||
−0.0981288 | + | 0.995174i | \(0.531286\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 14.0629 | 0.716710 | ||||||||
\(386\) | −21.8446 | −1.11186 | ||||||||
\(387\) | −12.8675 | −0.654090 | ||||||||
\(388\) | 9.40912 | 0.477676 | ||||||||
\(389\) | −27.5604 | −1.39737 | −0.698685 | − | 0.715429i | \(-0.746231\pi\) | ||||
−0.698685 | + | 0.715429i | \(0.746231\pi\) | |||||||
\(390\) | −1.31499 | −0.0665873 | ||||||||
\(391\) | 33.6009 | 1.69927 | ||||||||
\(392\) | 4.81150 | 0.243018 | ||||||||
\(393\) | −10.8094 | −0.545262 | ||||||||
\(394\) | 16.8084 | 0.846796 | ||||||||
\(395\) | −16.2829 | −0.819282 | ||||||||
\(396\) | −3.11170 | −0.156369 | ||||||||
\(397\) | −37.5736 | −1.88576 | −0.942882 | − | 0.333128i | \(-0.891896\pi\) | ||||
−0.942882 | + | 0.333128i | \(0.891896\pi\) | |||||||
\(398\) | 27.6236 | 1.38465 | ||||||||
\(399\) | 8.37472 | 0.419260 | ||||||||
\(400\) | −3.27079 | −0.163540 | ||||||||
\(401\) | −30.7512 | −1.53564 | −0.767820 | − | 0.640666i | \(-0.778658\pi\) | ||||
−0.767820 | + | 0.640666i | \(0.778658\pi\) | |||||||
\(402\) | −14.5505 | −0.725713 | ||||||||
\(403\) | −2.43679 | −0.121385 | ||||||||
\(404\) | 13.2699 | 0.660203 | ||||||||
\(405\) | −1.31499 | −0.0653426 | ||||||||
\(406\) | 22.2265 | 1.10308 | ||||||||
\(407\) | −8.75611 | −0.434024 | ||||||||
\(408\) | 6.00690 | 0.297386 | ||||||||
\(409\) | 25.0321 | 1.23776 | 0.618879 | − | 0.785486i | \(-0.287587\pi\) | ||||
0.618879 | + | 0.785486i | \(0.287587\pi\) | |||||||
\(410\) | −0.716221 | −0.0353716 | ||||||||
\(411\) | −10.6942 | −0.527507 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | −15.5058 | −0.762990 | ||||||||
\(414\) | 5.59372 | 0.274916 | ||||||||
\(415\) | −10.7988 | −0.530092 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | −20.9071 | −1.02382 | ||||||||
\(418\) | −7.58255 | −0.370875 | ||||||||
\(419\) | 1.04667 | 0.0511332 | 0.0255666 | − | 0.999673i | \(-0.491861\pi\) | ||||
0.0255666 | + | 0.999673i | \(0.491861\pi\) | |||||||
\(420\) | −4.51935 | −0.220522 | ||||||||
\(421\) | −12.7139 | −0.619638 | −0.309819 | − | 0.950796i | \(-0.600268\pi\) | ||||
−0.309819 | + | 0.950796i | \(0.600268\pi\) | |||||||
\(422\) | −0.511831 | −0.0249156 | ||||||||
\(423\) | −5.36242 | −0.260730 | ||||||||
\(424\) | 10.1760 | 0.494189 | ||||||||
\(425\) | −19.6473 | −0.953035 | ||||||||
\(426\) | −9.93655 | −0.481428 | ||||||||
\(427\) | 47.4360 | 2.29559 | ||||||||
\(428\) | −0.861674 | −0.0416506 | ||||||||
\(429\) | −3.11170 | −0.150234 | ||||||||
\(430\) | 16.9206 | 0.815985 | ||||||||
\(431\) | 0.741467 | 0.0357152 | 0.0178576 | − | 0.999841i | \(-0.494315\pi\) | ||||
0.0178576 | + | 0.999841i | \(0.494315\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −31.1023 | −1.49468 | −0.747341 | − | 0.664440i | \(-0.768670\pi\) | ||||
−0.747341 | + | 0.664440i | \(0.768670\pi\) | |||||||
\(434\) | −8.37472 | −0.401999 | ||||||||
\(435\) | −8.50435 | −0.407753 | ||||||||
\(436\) | 0.888682 | 0.0425602 | ||||||||
\(437\) | 13.6307 | 0.652045 | ||||||||
\(438\) | −2.55975 | −0.122309 | ||||||||
\(439\) | −38.0269 | −1.81492 | −0.907462 | − | 0.420134i | \(-0.861983\pi\) | ||||
−0.907462 | + | 0.420134i | \(0.861983\pi\) | |||||||
\(440\) | 4.09187 | 0.195072 | ||||||||
\(441\) | 4.81150 | 0.229119 | ||||||||
\(442\) | 6.00690 | 0.285719 | ||||||||
\(443\) | 38.2558 | 1.81759 | 0.908793 | − | 0.417248i | \(-0.137005\pi\) | ||||
0.908793 | + | 0.417248i | \(0.137005\pi\) | |||||||
\(444\) | 2.81393 | 0.133543 | ||||||||
\(445\) | 2.10337 | 0.0997094 | ||||||||
\(446\) | −14.3697 | −0.680423 | ||||||||
\(447\) | 5.57577 | 0.263725 | ||||||||
\(448\) | 3.43679 | 0.162373 | ||||||||
\(449\) | 23.8234 | 1.12429 | 0.562147 | − | 0.827037i | \(-0.309976\pi\) | ||||
0.562147 | + | 0.827037i | \(0.309976\pi\) | |||||||
\(450\) | −3.27079 | −0.154187 | ||||||||
\(451\) | −1.69481 | −0.0798055 | ||||||||
\(452\) | −6.57570 | −0.309295 | ||||||||
\(453\) | −14.9584 | −0.702807 | ||||||||
\(454\) | 26.2398 | 1.23150 | ||||||||
\(455\) | −4.51935 | −0.211871 | ||||||||
\(456\) | 2.43679 | 0.114113 | ||||||||
\(457\) | −19.3293 | −0.904185 | −0.452092 | − | 0.891971i | \(-0.649322\pi\) | ||||
−0.452092 | + | 0.891971i | \(0.649322\pi\) | |||||||
\(458\) | 19.1941 | 0.896884 | ||||||||
\(459\) | 6.00690 | 0.280378 | ||||||||
\(460\) | −7.35571 | −0.342962 | ||||||||
\(461\) | 0.682323 | 0.0317789 | 0.0158895 | − | 0.999874i | \(-0.494942\pi\) | ||||
0.0158895 | + | 0.999874i | \(0.494942\pi\) | |||||||
\(462\) | −10.6943 | −0.497542 | ||||||||
\(463\) | −21.9563 | −1.02040 | −0.510198 | − | 0.860057i | \(-0.670428\pi\) | ||||
−0.510198 | + | 0.860057i | \(0.670428\pi\) | |||||||
\(464\) | 6.46722 | 0.300233 | ||||||||
\(465\) | 3.20436 | 0.148599 | ||||||||
\(466\) | 7.61515 | 0.352765 | ||||||||
\(467\) | −16.6653 | −0.771180 | −0.385590 | − | 0.922670i | \(-0.626002\pi\) | ||||
−0.385590 | + | 0.922670i | \(0.626002\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −50.0069 | −2.30911 | ||||||||
\(470\) | 7.05155 | 0.325264 | ||||||||
\(471\) | 22.7031 | 1.04610 | ||||||||
\(472\) | −4.51171 | −0.207668 | ||||||||
\(473\) | 40.0397 | 1.84103 | ||||||||
\(474\) | 12.3825 | 0.568747 | ||||||||
\(475\) | −7.97022 | −0.365699 | ||||||||
\(476\) | 20.6444 | 0.946236 | ||||||||
\(477\) | 10.1760 | 0.465925 | ||||||||
\(478\) | 22.9290 | 1.04875 | ||||||||
\(479\) | −16.7942 | −0.767344 | −0.383672 | − | 0.923469i | \(-0.625341\pi\) | ||||
−0.383672 | + | 0.923469i | \(0.625341\pi\) | |||||||
\(480\) | −1.31499 | −0.0600210 | ||||||||
\(481\) | 2.81393 | 0.128304 | ||||||||
\(482\) | 13.1026 | 0.596808 | ||||||||
\(483\) | 19.2244 | 0.874741 | ||||||||
\(484\) | −1.31732 | −0.0598781 | ||||||||
\(485\) | −12.3729 | −0.561826 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −16.0914 | −0.729171 | −0.364585 | − | 0.931170i | \(-0.618789\pi\) | ||||
−0.364585 | + | 0.931170i | \(0.618789\pi\) | |||||||
\(488\) | 13.8024 | 0.624806 | ||||||||
\(489\) | 3.89555 | 0.176163 | ||||||||
\(490\) | −6.32709 | −0.285829 | ||||||||
\(491\) | 18.1187 | 0.817684 | 0.408842 | − | 0.912605i | \(-0.365933\pi\) | ||||
0.408842 | + | 0.912605i | \(0.365933\pi\) | |||||||
\(492\) | 0.544657 | 0.0245551 | ||||||||
\(493\) | 38.8479 | 1.74962 | ||||||||
\(494\) | 2.43679 | 0.109636 | ||||||||
\(495\) | 4.09187 | 0.183916 | ||||||||
\(496\) | −2.43679 | −0.109415 | ||||||||
\(497\) | −34.1498 | −1.53183 | ||||||||
\(498\) | 8.21206 | 0.367991 | ||||||||
\(499\) | 19.5924 | 0.877075 | 0.438537 | − | 0.898713i | \(-0.355497\pi\) | ||||
0.438537 | + | 0.898713i | \(0.355497\pi\) | |||||||
\(500\) | 10.8760 | 0.486391 | ||||||||
\(501\) | −5.44190 | −0.243126 | ||||||||
\(502\) | 15.6751 | 0.699615 | ||||||||
\(503\) | −7.20486 | −0.321249 | −0.160624 | − | 0.987016i | \(-0.551351\pi\) | ||||
−0.160624 | + | 0.987016i | \(0.551351\pi\) | |||||||
\(504\) | 3.43679 | 0.153087 | ||||||||
\(505\) | −17.4499 | −0.776508 | ||||||||
\(506\) | −17.4060 | −0.773790 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 16.4226 | 0.728637 | ||||||||
\(509\) | −25.8878 | −1.14746 | −0.573728 | − | 0.819046i | \(-0.694503\pi\) | ||||
−0.573728 | + | 0.819046i | \(0.694503\pi\) | |||||||
\(510\) | −7.89903 | −0.349775 | ||||||||
\(511\) | −8.79730 | −0.389170 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.43679 | 0.107587 | ||||||||
\(514\) | −5.32596 | −0.234918 | ||||||||
\(515\) | 1.31499 | 0.0579455 | ||||||||
\(516\) | −12.8675 | −0.566459 | ||||||||
\(517\) | 16.6862 | 0.733860 | ||||||||
\(518\) | 9.67088 | 0.424914 | ||||||||
\(519\) | 20.1657 | 0.885174 | ||||||||
\(520\) | −1.31499 | −0.0576663 | ||||||||
\(521\) | 14.5840 | 0.638935 | 0.319467 | − | 0.947597i | \(-0.396496\pi\) | ||||
0.319467 | + | 0.947597i | \(0.396496\pi\) | |||||||
\(522\) | 6.46722 | 0.283063 | ||||||||
\(523\) | −21.4457 | −0.937757 | −0.468879 | − | 0.883263i | \(-0.655342\pi\) | ||||
−0.468879 | + | 0.883263i | \(0.655342\pi\) | |||||||
\(524\) | −10.8094 | −0.472211 | ||||||||
\(525\) | −11.2410 | −0.490598 | ||||||||
\(526\) | −19.1914 | −0.836786 | ||||||||
\(527\) | −14.6375 | −0.637621 | ||||||||
\(528\) | −3.11170 | −0.135419 | ||||||||
\(529\) | 8.28970 | 0.360422 | ||||||||
\(530\) | −13.3813 | −0.581248 | ||||||||
\(531\) | −4.51171 | −0.195792 | ||||||||
\(532\) | 8.37472 | 0.363090 | ||||||||
\(533\) | 0.544657 | 0.0235917 | ||||||||
\(534\) | −1.59953 | −0.0692184 | ||||||||
\(535\) | 1.13310 | 0.0489880 | ||||||||
\(536\) | −14.5505 | −0.628486 | ||||||||
\(537\) | 11.0633 | 0.477418 | ||||||||
\(538\) | −20.8026 | −0.896864 | ||||||||
\(539\) | −14.9720 | −0.644888 | ||||||||
\(540\) | −1.31499 | −0.0565883 | ||||||||
\(541\) | 41.4939 | 1.78396 | 0.891982 | − | 0.452072i | \(-0.149315\pi\) | ||||
0.891982 | + | 0.452072i | \(0.149315\pi\) | |||||||
\(542\) | −18.4540 | −0.792669 | ||||||||
\(543\) | 0.606839 | 0.0260419 | ||||||||
\(544\) | 6.00690 | 0.257544 | ||||||||
\(545\) | −1.16861 | −0.0500578 | ||||||||
\(546\) | 3.43679 | 0.147081 | ||||||||
\(547\) | −28.3172 | −1.21076 | −0.605379 | − | 0.795937i | \(-0.706978\pi\) | ||||
−0.605379 | + | 0.795937i | \(0.706978\pi\) | |||||||
\(548\) | −10.6942 | −0.456834 | ||||||||
\(549\) | 13.8024 | 0.589073 | ||||||||
\(550\) | 10.1777 | 0.433980 | ||||||||
\(551\) | 15.7592 | 0.671366 | ||||||||
\(552\) | 5.59372 | 0.238085 | ||||||||
\(553\) | 42.5560 | 1.80966 | ||||||||
\(554\) | −16.1807 | −0.687453 | ||||||||
\(555\) | −3.70030 | −0.157069 | ||||||||
\(556\) | −20.9071 | −0.886657 | ||||||||
\(557\) | −35.7072 | −1.51296 | −0.756481 | − | 0.654015i | \(-0.773083\pi\) | ||||
−0.756481 | + | 0.654015i | \(0.773083\pi\) | |||||||
\(558\) | −2.43679 | −0.103157 | ||||||||
\(559\) | −12.8675 | −0.544236 | ||||||||
\(560\) | −4.51935 | −0.190977 | ||||||||
\(561\) | −18.6917 | −0.789163 | ||||||||
\(562\) | 20.1897 | 0.851649 | ||||||||
\(563\) | 39.2661 | 1.65487 | 0.827434 | − | 0.561564i | \(-0.189800\pi\) | ||||
0.827434 | + | 0.561564i | \(0.189800\pi\) | |||||||
\(564\) | −5.36242 | −0.225799 | ||||||||
\(565\) | 8.64700 | 0.363782 | ||||||||
\(566\) | −21.2857 | −0.894706 | ||||||||
\(567\) | 3.43679 | 0.144331 | ||||||||
\(568\) | −9.93655 | −0.416928 | ||||||||
\(569\) | −1.78837 | −0.0749722 | −0.0374861 | − | 0.999297i | \(-0.511935\pi\) | ||||
−0.0374861 | + | 0.999297i | \(0.511935\pi\) | |||||||
\(570\) | −3.20436 | −0.134216 | ||||||||
\(571\) | −7.03549 | −0.294426 | −0.147213 | − | 0.989105i | \(-0.547030\pi\) | ||||
−0.147213 | + | 0.989105i | \(0.547030\pi\) | |||||||
\(572\) | −3.11170 | −0.130107 | ||||||||
\(573\) | 6.43044 | 0.268636 | ||||||||
\(574\) | 1.87187 | 0.0781304 | ||||||||
\(575\) | −18.2959 | −0.762991 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −7.86416 | −0.327389 | −0.163695 | − | 0.986511i | \(-0.552341\pi\) | ||||
−0.163695 | + | 0.986511i | \(0.552341\pi\) | |||||||
\(578\) | 19.0828 | 0.793742 | ||||||||
\(579\) | −21.8446 | −0.907831 | ||||||||
\(580\) | −8.50435 | −0.353124 | ||||||||
\(581\) | 28.2231 | 1.17089 | ||||||||
\(582\) | 9.40912 | 0.390021 | ||||||||
\(583\) | −31.6646 | −1.31141 | ||||||||
\(584\) | −2.55975 | −0.105923 | ||||||||
\(585\) | −1.31499 | −0.0543683 | ||||||||
\(586\) | 23.1886 | 0.957910 | ||||||||
\(587\) | −12.7866 | −0.527761 | −0.263881 | − | 0.964555i | \(-0.585002\pi\) | ||||
−0.263881 | + | 0.964555i | \(0.585002\pi\) | |||||||
\(588\) | 4.81150 | 0.198423 | ||||||||
\(589\) | −5.93793 | −0.244668 | ||||||||
\(590\) | 5.93287 | 0.244253 | ||||||||
\(591\) | 16.8084 | 0.691406 | ||||||||
\(592\) | 2.81393 | 0.115652 | ||||||||
\(593\) | −1.44125 | −0.0591851 | −0.0295925 | − | 0.999562i | \(-0.509421\pi\) | ||||
−0.0295925 | + | 0.999562i | \(0.509421\pi\) | |||||||
\(594\) | −3.11170 | −0.127675 | ||||||||
\(595\) | −27.1473 | −1.11293 | ||||||||
\(596\) | 5.57577 | 0.228393 | ||||||||
\(597\) | 27.6236 | 1.13056 | ||||||||
\(598\) | 5.59372 | 0.228744 | ||||||||
\(599\) | −14.1708 | −0.579001 | −0.289501 | − | 0.957178i | \(-0.593489\pi\) | ||||
−0.289501 | + | 0.957178i | \(0.593489\pi\) | |||||||
\(600\) | −3.27079 | −0.133530 | ||||||||
\(601\) | −24.0693 | −0.981809 | −0.490904 | − | 0.871214i | \(-0.663334\pi\) | ||||
−0.490904 | + | 0.871214i | \(0.663334\pi\) | |||||||
\(602\) | −44.2227 | −1.80238 | ||||||||
\(603\) | −14.5505 | −0.592542 | ||||||||
\(604\) | −14.9584 | −0.608649 | ||||||||
\(605\) | 1.73227 | 0.0704266 | ||||||||
\(606\) | 13.2699 | 0.539053 | ||||||||
\(607\) | 39.3859 | 1.59862 | 0.799312 | − | 0.600916i | \(-0.205197\pi\) | ||||
0.799312 | + | 0.600916i | \(0.205197\pi\) | |||||||
\(608\) | 2.43679 | 0.0988247 | ||||||||
\(609\) | 22.2265 | 0.900661 | ||||||||
\(610\) | −18.1501 | −0.734876 | ||||||||
\(611\) | −5.36242 | −0.216940 | ||||||||
\(612\) | 6.00690 | 0.242815 | ||||||||
\(613\) | 13.1418 | 0.530792 | 0.265396 | − | 0.964140i | \(-0.414497\pi\) | ||||
0.265396 | + | 0.964140i | \(0.414497\pi\) | |||||||
\(614\) | −24.3962 | −0.984550 | ||||||||
\(615\) | −0.716221 | −0.0288808 | ||||||||
\(616\) | −10.6943 | −0.430884 | ||||||||
\(617\) | 15.6549 | 0.630244 | 0.315122 | − | 0.949051i | \(-0.397955\pi\) | ||||
0.315122 | + | 0.949051i | \(0.397955\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | 4.74807 | 0.190841 | 0.0954204 | − | 0.995437i | \(-0.469580\pi\) | ||||
0.0954204 | + | 0.995437i | \(0.469580\pi\) | |||||||
\(620\) | 3.20436 | 0.128690 | ||||||||
\(621\) | 5.59372 | 0.224468 | ||||||||
\(622\) | −27.1959 | −1.09045 | ||||||||
\(623\) | −5.49724 | −0.220242 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 2.05204 | 0.0820815 | ||||||||
\(626\) | 2.70927 | 0.108284 | ||||||||
\(627\) | −7.58255 | −0.302818 | ||||||||
\(628\) | 22.7031 | 0.905951 | ||||||||
\(629\) | 16.9030 | 0.673967 | ||||||||
\(630\) | −4.51935 | −0.180055 | ||||||||
\(631\) | 5.40691 | 0.215246 | 0.107623 | − | 0.994192i | \(-0.465676\pi\) | ||||
0.107623 | + | 0.994192i | \(0.465676\pi\) | |||||||
\(632\) | 12.3825 | 0.492549 | ||||||||
\(633\) | −0.511831 | −0.0203435 | ||||||||
\(634\) | −27.6179 | −1.09685 | ||||||||
\(635\) | −21.5957 | −0.856998 | ||||||||
\(636\) | 10.1760 | 0.403503 | ||||||||
\(637\) | 4.81150 | 0.190639 | ||||||||
\(638\) | −20.1241 | −0.796719 | ||||||||
\(639\) | −9.93655 | −0.393084 | ||||||||
\(640\) | −1.31499 | −0.0519797 | ||||||||
\(641\) | 12.3293 | 0.486978 | 0.243489 | − | 0.969904i | \(-0.421708\pi\) | ||||
0.243489 | + | 0.969904i | \(0.421708\pi\) | |||||||
\(642\) | −0.861674 | −0.0340076 | ||||||||
\(643\) | −7.50601 | −0.296008 | −0.148004 | − | 0.988987i | \(-0.547285\pi\) | ||||
−0.148004 | + | 0.988987i | \(0.547285\pi\) | |||||||
\(644\) | 19.2244 | 0.757548 | ||||||||
\(645\) | 16.9206 | 0.666249 | ||||||||
\(646\) | 14.6375 | 0.575906 | ||||||||
\(647\) | 2.18457 | 0.0858844 | 0.0429422 | − | 0.999078i | \(-0.486327\pi\) | ||||
0.0429422 | + | 0.999078i | \(0.486327\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 14.0391 | 0.551083 | ||||||||
\(650\) | −3.27079 | −0.128291 | ||||||||
\(651\) | −8.37472 | −0.328231 | ||||||||
\(652\) | 3.89555 | 0.152562 | ||||||||
\(653\) | 27.3469 | 1.07017 | 0.535084 | − | 0.844799i | \(-0.320280\pi\) | ||||
0.535084 | + | 0.844799i | \(0.320280\pi\) | |||||||
\(654\) | 0.888682 | 0.0347502 | ||||||||
\(655\) | 14.2143 | 0.555399 | ||||||||
\(656\) | 0.544657 | 0.0212653 | ||||||||
\(657\) | −2.55975 | −0.0998652 | ||||||||
\(658\) | −18.4295 | −0.718456 | ||||||||
\(659\) | 40.7841 | 1.58872 | 0.794361 | − | 0.607447i | \(-0.207806\pi\) | ||||
0.794361 | + | 0.607447i | \(0.207806\pi\) | |||||||
\(660\) | 4.09187 | 0.159276 | ||||||||
\(661\) | −33.3624 | −1.29765 | −0.648823 | − | 0.760939i | \(-0.724738\pi\) | ||||
−0.648823 | + | 0.760939i | \(0.724738\pi\) | |||||||
\(662\) | −2.45599 | −0.0954546 | ||||||||
\(663\) | 6.00690 | 0.233289 | ||||||||
\(664\) | 8.21206 | 0.318690 | ||||||||
\(665\) | −11.0127 | −0.427054 | ||||||||
\(666\) | 2.81393 | 0.109038 | ||||||||
\(667\) | 36.1758 | 1.40073 | ||||||||
\(668\) | −5.44190 | −0.210553 | ||||||||
\(669\) | −14.3697 | −0.555563 | ||||||||
\(670\) | 19.1338 | 0.739203 | ||||||||
\(671\) | −42.9490 | −1.65803 | ||||||||
\(672\) | 3.43679 | 0.132577 | ||||||||
\(673\) | 32.9787 | 1.27124 | 0.635618 | − | 0.772003i | \(-0.280745\pi\) | ||||
0.635618 | + | 0.772003i | \(0.280745\pi\) | |||||||
\(674\) | −12.6506 | −0.487283 | ||||||||
\(675\) | −3.27079 | −0.125893 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −18.7249 | −0.719656 | −0.359828 | − | 0.933019i | \(-0.617165\pi\) | ||||
−0.359828 | + | 0.933019i | \(0.617165\pi\) | |||||||
\(678\) | −6.57570 | −0.252538 | ||||||||
\(679\) | 32.3371 | 1.24099 | ||||||||
\(680\) | −7.89903 | −0.302914 | ||||||||
\(681\) | 26.2398 | 1.00551 | ||||||||
\(682\) | 7.58255 | 0.290351 | ||||||||
\(683\) | −34.5159 | −1.32072 | −0.660358 | − | 0.750951i | \(-0.729595\pi\) | ||||
−0.660358 | + | 0.750951i | \(0.729595\pi\) | |||||||
\(684\) | 2.43679 | 0.0931729 | ||||||||
\(685\) | 14.0628 | 0.537313 | ||||||||
\(686\) | −7.52140 | −0.287168 | ||||||||
\(687\) | 19.1941 | 0.732302 | ||||||||
\(688\) | −12.8675 | −0.490568 | ||||||||
\(689\) | 10.1760 | 0.387673 | ||||||||
\(690\) | −7.35571 | −0.280027 | ||||||||
\(691\) | −5.75055 | −0.218761 | −0.109381 | − | 0.994000i | \(-0.534887\pi\) | ||||
−0.109381 | + | 0.994000i | \(0.534887\pi\) | |||||||
\(692\) | 20.1657 | 0.766583 | ||||||||
\(693\) | −10.6943 | −0.406241 | ||||||||
\(694\) | −7.26365 | −0.275725 | ||||||||
\(695\) | 27.4927 | 1.04286 | ||||||||
\(696\) | 6.46722 | 0.245139 | ||||||||
\(697\) | 3.27170 | 0.123925 | ||||||||
\(698\) | 1.47059 | 0.0556628 | ||||||||
\(699\) | 7.61515 | 0.288031 | ||||||||
\(700\) | −11.2410 | −0.424870 | ||||||||
\(701\) | 12.9196 | 0.487966 | 0.243983 | − | 0.969779i | \(-0.421546\pi\) | ||||
0.243983 | + | 0.969779i | \(0.421546\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | 6.85695 | 0.258615 | ||||||||
\(704\) | −3.11170 | −0.117277 | ||||||||
\(705\) | 7.05155 | 0.265577 | ||||||||
\(706\) | 31.5648 | 1.18796 | ||||||||
\(707\) | 45.6059 | 1.71518 | ||||||||
\(708\) | −4.51171 | −0.169561 | ||||||||
\(709\) | 21.8796 | 0.821706 | 0.410853 | − | 0.911702i | \(-0.365231\pi\) | ||||
0.410853 | + | 0.911702i | \(0.365231\pi\) | |||||||
\(710\) | 13.0665 | 0.490377 | ||||||||
\(711\) | 12.3825 | 0.464380 | ||||||||
\(712\) | −1.59953 | −0.0599449 | ||||||||
\(713\) | −13.6307 | −0.510474 | ||||||||
\(714\) | 20.6444 | 0.772598 | ||||||||
\(715\) | 4.09187 | 0.153027 | ||||||||
\(716\) | 11.0633 | 0.413456 | ||||||||
\(717\) | 22.9290 | 0.856301 | ||||||||
\(718\) | 3.69648 | 0.137951 | ||||||||
\(719\) | 24.1809 | 0.901796 | 0.450898 | − | 0.892575i | \(-0.351104\pi\) | ||||
0.450898 | + | 0.892575i | \(0.351104\pi\) | |||||||
\(720\) | −1.31499 | −0.0490069 | ||||||||
\(721\) | −3.43679 | −0.127993 | ||||||||
\(722\) | −13.0621 | −0.486120 | ||||||||
\(723\) | 13.1026 | 0.487292 | ||||||||
\(724\) | 0.606839 | 0.0225530 | ||||||||
\(725\) | −21.1529 | −0.785600 | ||||||||
\(726\) | −1.31732 | −0.0488903 | ||||||||
\(727\) | 39.9266 | 1.48080 | 0.740398 | − | 0.672169i | \(-0.234637\pi\) | ||||
0.740398 | + | 0.672169i | \(0.234637\pi\) | |||||||
\(728\) | 3.43679 | 0.127376 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.36605 | 0.124583 | ||||||||
\(731\) | −77.2936 | −2.85881 | ||||||||
\(732\) | 13.8024 | 0.510152 | ||||||||
\(733\) | 52.3822 | 1.93478 | 0.967391 | − | 0.253289i | \(-0.0815123\pi\) | ||||
0.967391 | + | 0.253289i | \(0.0815123\pi\) | |||||||
\(734\) | −7.08638 | −0.261563 | ||||||||
\(735\) | −6.32709 | −0.233378 | ||||||||
\(736\) | 5.59372 | 0.206187 | ||||||||
\(737\) | 45.2768 | 1.66779 | ||||||||
\(738\) | 0.544657 | 0.0200491 | ||||||||
\(739\) | −30.5613 | −1.12422 | −0.562108 | − | 0.827064i | \(-0.690009\pi\) | ||||
−0.562108 | + | 0.827064i | \(0.690009\pi\) | |||||||
\(740\) | −3.70030 | −0.136026 | ||||||||
\(741\) | 2.43679 | 0.0895176 | ||||||||
\(742\) | 34.9726 | 1.28389 | ||||||||
\(743\) | 35.2118 | 1.29179 | 0.645897 | − | 0.763424i | \(-0.276483\pi\) | ||||
0.645897 | + | 0.763424i | \(0.276483\pi\) | |||||||
\(744\) | −2.43679 | −0.0893369 | ||||||||
\(745\) | −7.33211 | −0.268628 | ||||||||
\(746\) | 9.77642 | 0.357940 | ||||||||
\(747\) | 8.21206 | 0.300464 | ||||||||
\(748\) | −18.6917 | −0.683435 | ||||||||
\(749\) | −2.96139 | −0.108207 | ||||||||
\(750\) | 10.8760 | 0.397137 | ||||||||
\(751\) | −22.5006 | −0.821060 | −0.410530 | − | 0.911847i | \(-0.634656\pi\) | ||||
−0.410530 | + | 0.911847i | \(0.634656\pi\) | |||||||
\(752\) | −5.36242 | −0.195547 | ||||||||
\(753\) | 15.6751 | 0.571233 | ||||||||
\(754\) | 6.46722 | 0.235522 | ||||||||
\(755\) | 19.6702 | 0.715872 | ||||||||
\(756\) | 3.43679 | 0.124995 | ||||||||
\(757\) | −21.4959 | −0.781282 | −0.390641 | − | 0.920543i | \(-0.627747\pi\) | ||||
−0.390641 | + | 0.920543i | \(0.627747\pi\) | |||||||
\(758\) | 18.2285 | 0.662088 | ||||||||
\(759\) | −17.4060 | −0.631797 | ||||||||
\(760\) | −3.20436 | −0.116234 | ||||||||
\(761\) | −49.4797 | −1.79364 | −0.896818 | − | 0.442399i | \(-0.854128\pi\) | ||||
−0.896818 | + | 0.442399i | \(0.854128\pi\) | |||||||
\(762\) | 16.4226 | 0.594929 | ||||||||
\(763\) | 3.05421 | 0.110570 | ||||||||
\(764\) | 6.43044 | 0.232645 | ||||||||
\(765\) | −7.89903 | −0.285590 | ||||||||
\(766\) | −3.84084 | −0.138775 | ||||||||
\(767\) | −4.51171 | −0.162909 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −36.1691 | −1.30429 | −0.652145 | − | 0.758094i | \(-0.726131\pi\) | ||||
−0.652145 | + | 0.758094i | \(0.726131\pi\) | |||||||
\(770\) | 14.0629 | 0.506791 | ||||||||
\(771\) | −5.32596 | −0.191810 | ||||||||
\(772\) | −21.8446 | −0.786205 | ||||||||
\(773\) | −1.64867 | −0.0592987 | −0.0296493 | − | 0.999560i | \(-0.509439\pi\) | ||||
−0.0296493 | + | 0.999560i | \(0.509439\pi\) | |||||||
\(774\) | −12.8675 | −0.462512 | ||||||||
\(775\) | 7.97022 | 0.286299 | ||||||||
\(776\) | 9.40912 | 0.337768 | ||||||||
\(777\) | 9.67088 | 0.346941 | ||||||||
\(778\) | −27.5604 | −0.988090 | ||||||||
\(779\) | 1.32721 | 0.0475524 | ||||||||
\(780\) | −1.31499 | −0.0470843 | ||||||||
\(781\) | 30.9196 | 1.10639 | ||||||||
\(782\) | 33.6009 | 1.20157 | ||||||||
\(783\) | 6.46722 | 0.231120 | ||||||||
\(784\) | 4.81150 | 0.171839 | ||||||||
\(785\) | −29.8544 | −1.06555 | ||||||||
\(786\) | −10.8094 | −0.385559 | ||||||||
\(787\) | 8.08810 | 0.288310 | 0.144155 | − | 0.989555i | \(-0.453954\pi\) | ||||
0.144155 | + | 0.989555i | \(0.453954\pi\) | |||||||
\(788\) | 16.8084 | 0.598775 | ||||||||
\(789\) | −19.1914 | −0.683233 | ||||||||
\(790\) | −16.2829 | −0.579320 | ||||||||
\(791\) | −22.5993 | −0.803538 | ||||||||
\(792\) | −3.11170 | −0.110569 | ||||||||
\(793\) | 13.8024 | 0.490139 | ||||||||
\(794\) | −37.5736 | −1.33344 | ||||||||
\(795\) | −13.3813 | −0.474587 | ||||||||
\(796\) | 27.6236 | 0.979094 | ||||||||
\(797\) | 15.3447 | 0.543538 | 0.271769 | − | 0.962363i | \(-0.412391\pi\) | ||||
0.271769 | + | 0.962363i | \(0.412391\pi\) | |||||||
\(798\) | 8.37472 | 0.296462 | ||||||||
\(799\) | −32.2115 | −1.13956 | ||||||||
\(800\) | −3.27079 | −0.115640 | ||||||||
\(801\) | −1.59953 | −0.0565166 | ||||||||
\(802\) | −30.7512 | −1.08586 | ||||||||
\(803\) | 7.96516 | 0.281084 | ||||||||
\(804\) | −14.5505 | −0.513156 | ||||||||
\(805\) | −25.2800 | −0.891003 | ||||||||
\(806\) | −2.43679 | −0.0858321 | ||||||||
\(807\) | −20.8026 | −0.732286 | ||||||||
\(808\) | 13.2699 | 0.466834 | ||||||||
\(809\) | −52.9166 | −1.86045 | −0.930224 | − | 0.366992i | \(-0.880388\pi\) | ||||
−0.930224 | + | 0.366992i | \(0.880388\pi\) | |||||||
\(810\) | −1.31499 | −0.0462042 | ||||||||
\(811\) | −13.6572 | −0.479569 | −0.239785 | − | 0.970826i | \(-0.577077\pi\) | ||||
−0.239785 | + | 0.970826i | \(0.577077\pi\) | |||||||
\(812\) | 22.2265 | 0.779996 | ||||||||
\(813\) | −18.4540 | −0.647211 | ||||||||
\(814\) | −8.75611 | −0.306902 | ||||||||
\(815\) | −5.12262 | −0.179438 | ||||||||
\(816\) | 6.00690 | 0.210284 | ||||||||
\(817\) | −31.3553 | −1.09698 | ||||||||
\(818\) | 25.0321 | 0.875227 | ||||||||
\(819\) | 3.43679 | 0.120091 | ||||||||
\(820\) | −0.716221 | −0.0250115 | ||||||||
\(821\) | −23.2542 | −0.811579 | −0.405789 | − | 0.913967i | \(-0.633003\pi\) | ||||
−0.405789 | + | 0.913967i | \(0.633003\pi\) | |||||||
\(822\) | −10.6942 | −0.373004 | ||||||||
\(823\) | −27.5833 | −0.961494 | −0.480747 | − | 0.876859i | \(-0.659635\pi\) | ||||
−0.480747 | + | 0.876859i | \(0.659635\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 10.1777 | 0.354343 | ||||||||
\(826\) | −15.5058 | −0.539516 | ||||||||
\(827\) | −15.7934 | −0.549191 | −0.274595 | − | 0.961560i | \(-0.588544\pi\) | ||||
−0.274595 | + | 0.961560i | \(0.588544\pi\) | |||||||
\(828\) | 5.59372 | 0.194395 | ||||||||
\(829\) | −36.5604 | −1.26979 | −0.634897 | − | 0.772597i | \(-0.718958\pi\) | ||||
−0.634897 | + | 0.772597i | \(0.718958\pi\) | |||||||
\(830\) | −10.7988 | −0.374832 | ||||||||
\(831\) | −16.1807 | −0.561303 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 28.9022 | 1.00140 | ||||||||
\(834\) | −20.9071 | −0.723953 | ||||||||
\(835\) | 7.15606 | 0.247646 | ||||||||
\(836\) | −7.58255 | −0.262248 | ||||||||
\(837\) | −2.43679 | −0.0842277 | ||||||||
\(838\) | 1.04667 | 0.0361566 | ||||||||
\(839\) | 7.79528 | 0.269123 | 0.134562 | − | 0.990905i | \(-0.457037\pi\) | ||||
0.134562 | + | 0.990905i | \(0.457037\pi\) | |||||||
\(840\) | −4.51935 | −0.155932 | ||||||||
\(841\) | 12.8249 | 0.442239 | ||||||||
\(842\) | −12.7139 | −0.438150 | ||||||||
\(843\) | 20.1897 | 0.695369 | ||||||||
\(844\) | −0.511831 | −0.0176180 | ||||||||
\(845\) | −1.31499 | −0.0452372 | ||||||||
\(846\) | −5.36242 | −0.184364 | ||||||||
\(847\) | −4.52734 | −0.155561 | ||||||||
\(848\) | 10.1760 | 0.349444 | ||||||||
\(849\) | −21.2857 | −0.730524 | ||||||||
\(850\) | −19.6473 | −0.673897 | ||||||||
\(851\) | 15.7403 | 0.539572 | ||||||||
\(852\) | −9.93655 | −0.340421 | ||||||||
\(853\) | 33.3821 | 1.14298 | 0.571491 | − | 0.820609i | \(-0.306365\pi\) | ||||
0.571491 | + | 0.820609i | \(0.306365\pi\) | |||||||
\(854\) | 47.4360 | 1.62323 | ||||||||
\(855\) | −3.20436 | −0.109587 | ||||||||
\(856\) | −0.861674 | −0.0294514 | ||||||||
\(857\) | 10.9659 | 0.374587 | 0.187294 | − | 0.982304i | \(-0.440028\pi\) | ||||
0.187294 | + | 0.982304i | \(0.440028\pi\) | |||||||
\(858\) | −3.11170 | −0.106232 | ||||||||
\(859\) | −22.9068 | −0.781570 | −0.390785 | − | 0.920482i | \(-0.627796\pi\) | ||||
−0.390785 | + | 0.920482i | \(0.627796\pi\) | |||||||
\(860\) | 16.9206 | 0.576989 | ||||||||
\(861\) | 1.87187 | 0.0637932 | ||||||||
\(862\) | 0.741467 | 0.0252545 | ||||||||
\(863\) | 42.8975 | 1.46025 | 0.730125 | − | 0.683314i | \(-0.239462\pi\) | ||||
0.730125 | + | 0.683314i | \(0.239462\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −26.5177 | −0.901629 | ||||||||
\(866\) | −31.1023 | −1.05690 | ||||||||
\(867\) | 19.0828 | 0.648087 | ||||||||
\(868\) | −8.37472 | −0.284256 | ||||||||
\(869\) | −38.5306 | −1.30706 | ||||||||
\(870\) | −8.50435 | −0.288325 | ||||||||
\(871\) | −14.5505 | −0.493025 | ||||||||
\(872\) | 0.888682 | 0.0300946 | ||||||||
\(873\) | 9.40912 | 0.318450 | ||||||||
\(874\) | 13.6307 | 0.461065 | ||||||||
\(875\) | 37.3786 | 1.26363 | ||||||||
\(876\) | −2.55975 | −0.0864858 | ||||||||
\(877\) | −36.1793 | −1.22169 | −0.610844 | − | 0.791751i | \(-0.709170\pi\) | ||||
−0.610844 | + | 0.791751i | \(0.709170\pi\) | |||||||
\(878\) | −38.0269 | −1.28335 | ||||||||
\(879\) | 23.1886 | 0.782130 | ||||||||
\(880\) | 4.09187 | 0.137937 | ||||||||
\(881\) | −34.7769 | −1.17166 | −0.585832 | − | 0.810433i | \(-0.699232\pi\) | ||||
−0.585832 | + | 0.810433i | \(0.699232\pi\) | |||||||
\(882\) | 4.81150 | 0.162012 | ||||||||
\(883\) | 0.809098 | 0.0272283 | 0.0136142 | − | 0.999907i | \(-0.495666\pi\) | ||||
0.0136142 | + | 0.999907i | \(0.495666\pi\) | |||||||
\(884\) | 6.00690 | 0.202034 | ||||||||
\(885\) | 5.93287 | 0.199431 | ||||||||
\(886\) | 38.2558 | 1.28523 | ||||||||
\(887\) | 3.06854 | 0.103031 | 0.0515157 | − | 0.998672i | \(-0.483595\pi\) | ||||
0.0515157 | + | 0.998672i | \(0.483595\pi\) | |||||||
\(888\) | 2.81393 | 0.0944294 | ||||||||
\(889\) | 56.4411 | 1.89297 | ||||||||
\(890\) | 2.10337 | 0.0705052 | ||||||||
\(891\) | −3.11170 | −0.104246 | ||||||||
\(892\) | −14.3697 | −0.481132 | ||||||||
\(893\) | −13.0671 | −0.437273 | ||||||||
\(894\) | 5.57577 | 0.186482 | ||||||||
\(895\) | −14.5482 | −0.486293 | ||||||||
\(896\) | 3.43679 | 0.114815 | ||||||||
\(897\) | 5.59372 | 0.186769 | ||||||||
\(898\) | 23.8234 | 0.794996 | ||||||||
\(899\) | −15.7592 | −0.525600 | ||||||||
\(900\) | −3.27079 | −0.109026 | ||||||||
\(901\) | 61.1260 | 2.03640 | ||||||||
\(902\) | −1.69481 | −0.0564310 | ||||||||
\(903\) | −44.2227 | −1.47164 | ||||||||
\(904\) | −6.57570 | −0.218705 | ||||||||
\(905\) | −0.797989 | −0.0265261 | ||||||||
\(906\) | −14.9584 | −0.496960 | ||||||||
\(907\) | 0.553149 | 0.0183670 | 0.00918350 | − | 0.999958i | \(-0.497077\pi\) | ||||
0.00918350 | + | 0.999958i | \(0.497077\pi\) | |||||||
\(908\) | 26.2398 | 0.870799 | ||||||||
\(909\) | 13.2699 | 0.440135 | ||||||||
\(910\) | −4.51935 | −0.149815 | ||||||||
\(911\) | 32.7891 | 1.08635 | 0.543176 | − | 0.839619i | \(-0.317222\pi\) | ||||
0.543176 | + | 0.839619i | \(0.317222\pi\) | |||||||
\(912\) | 2.43679 | 0.0806901 | ||||||||
\(913\) | −25.5535 | −0.845696 | ||||||||
\(914\) | −19.3293 | −0.639355 | ||||||||
\(915\) | −18.1501 | −0.600024 | ||||||||
\(916\) | 19.1941 | 0.634192 | ||||||||
\(917\) | −37.1496 | −1.22679 | ||||||||
\(918\) | 6.00690 | 0.198257 | ||||||||
\(919\) | 14.7305 | 0.485913 | 0.242957 | − | 0.970037i | \(-0.421883\pi\) | ||||
0.242957 | + | 0.970037i | \(0.421883\pi\) | |||||||
\(920\) | −7.35571 | −0.242510 | ||||||||
\(921\) | −24.3962 | −0.803882 | ||||||||
\(922\) | 0.682323 | 0.0224711 | ||||||||
\(923\) | −9.93655 | −0.327066 | ||||||||
\(924\) | −10.6943 | −0.351815 | ||||||||
\(925\) | −9.20379 | −0.302619 | ||||||||
\(926\) | −21.9563 | −0.721529 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 6.46722 | 0.212297 | ||||||||
\(929\) | −40.2478 | −1.32049 | −0.660244 | − | 0.751051i | \(-0.729547\pi\) | ||||
−0.660244 | + | 0.751051i | \(0.729547\pi\) | |||||||
\(930\) | 3.20436 | 0.105075 | ||||||||
\(931\) | 11.7246 | 0.384258 | ||||||||
\(932\) | 7.61515 | 0.249443 | ||||||||
\(933\) | −27.1959 | −0.890353 | ||||||||
\(934\) | −16.6653 | −0.545307 | ||||||||
\(935\) | 24.5794 | 0.803833 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | −18.4649 | −0.603223 | −0.301611 | − | 0.953431i | \(-0.597525\pi\) | ||||
−0.301611 | + | 0.953431i | \(0.597525\pi\) | |||||||
\(938\) | −50.0069 | −1.63278 | ||||||||
\(939\) | 2.70927 | 0.0884135 | ||||||||
\(940\) | 7.05155 | 0.229996 | ||||||||
\(941\) | −3.86966 | −0.126147 | −0.0630736 | − | 0.998009i | \(-0.520090\pi\) | ||||
−0.0630736 | + | 0.998009i | \(0.520090\pi\) | |||||||
\(942\) | 22.7031 | 0.739705 | ||||||||
\(943\) | 3.04666 | 0.0992129 | ||||||||
\(944\) | −4.51171 | −0.146844 | ||||||||
\(945\) | −4.51935 | −0.147015 | ||||||||
\(946\) | 40.0397 | 1.30180 | ||||||||
\(947\) | 48.6165 | 1.57983 | 0.789913 | − | 0.613219i | \(-0.210126\pi\) | ||||
0.789913 | + | 0.613219i | \(0.210126\pi\) | |||||||
\(948\) | 12.3825 | 0.402165 | ||||||||
\(949\) | −2.55975 | −0.0830929 | ||||||||
\(950\) | −7.97022 | −0.258588 | ||||||||
\(951\) | −27.6179 | −0.895571 | ||||||||
\(952\) | 20.6444 | 0.669090 | ||||||||
\(953\) | 7.16603 | 0.232131 | 0.116065 | − | 0.993242i | \(-0.462972\pi\) | ||||
0.116065 | + | 0.993242i | \(0.462972\pi\) | |||||||
\(954\) | 10.1760 | 0.329459 | ||||||||
\(955\) | −8.45599 | −0.273630 | ||||||||
\(956\) | 22.9290 | 0.741578 | ||||||||
\(957\) | −20.1241 | −0.650518 | ||||||||
\(958\) | −16.7942 | −0.542594 | ||||||||
\(959\) | −36.7537 | −1.18684 | ||||||||
\(960\) | −1.31499 | −0.0424412 | ||||||||
\(961\) | −25.0621 | −0.808454 | ||||||||
\(962\) | 2.81393 | 0.0907248 | ||||||||
\(963\) | −0.861674 | −0.0277671 | ||||||||
\(964\) | 13.1026 | 0.422007 | ||||||||
\(965\) | 28.7255 | 0.924708 | ||||||||
\(966\) | 19.2244 | 0.618536 | ||||||||
\(967\) | −34.3488 | −1.10458 | −0.552292 | − | 0.833651i | \(-0.686247\pi\) | ||||
−0.552292 | + | 0.833651i | \(0.686247\pi\) | |||||||
\(968\) | −1.31732 | −0.0423402 | ||||||||
\(969\) | 14.6375 | 0.470225 | ||||||||
\(970\) | −12.3729 | −0.397271 | ||||||||
\(971\) | −8.27328 | −0.265502 | −0.132751 | − | 0.991149i | \(-0.542381\pi\) | ||||
−0.132751 | + | 0.991149i | \(0.542381\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −71.8531 | −2.30351 | ||||||||
\(974\) | −16.0914 | −0.515602 | ||||||||
\(975\) | −3.27079 | −0.104749 | ||||||||
\(976\) | 13.8024 | 0.441805 | ||||||||
\(977\) | −3.73445 | −0.119476 | −0.0597379 | − | 0.998214i | \(-0.519026\pi\) | ||||
−0.0597379 | + | 0.998214i | \(0.519026\pi\) | |||||||
\(978\) | 3.89555 | 0.124566 | ||||||||
\(979\) | 4.97726 | 0.159074 | ||||||||
\(980\) | −6.32709 | −0.202112 | ||||||||
\(981\) | 0.888682 | 0.0283734 | ||||||||
\(982\) | 18.1187 | 0.578190 | ||||||||
\(983\) | −41.0686 | −1.30989 | −0.654943 | − | 0.755679i | \(-0.727307\pi\) | ||||
−0.654943 | + | 0.755679i | \(0.727307\pi\) | |||||||
\(984\) | 0.544657 | 0.0173630 | ||||||||
\(985\) | −22.1030 | −0.704259 | ||||||||
\(986\) | 38.8479 | 1.23717 | ||||||||
\(987\) | −18.4295 | −0.586617 | ||||||||
\(988\) | 2.43679 | 0.0775245 | ||||||||
\(989\) | −71.9770 | −2.28874 | ||||||||
\(990\) | 4.09187 | 0.130048 | ||||||||
\(991\) | 56.0647 | 1.78095 | 0.890477 | − | 0.455029i | \(-0.150371\pi\) | ||||
0.890477 | + | 0.455029i | \(0.150371\pi\) | |||||||
\(992\) | −2.43679 | −0.0773681 | ||||||||
\(993\) | −2.45599 | −0.0779384 | ||||||||
\(994\) | −34.1498 | −1.08317 | ||||||||
\(995\) | −36.3249 | −1.15158 | ||||||||
\(996\) | 8.21206 | 0.260209 | ||||||||
\(997\) | −46.8961 | −1.48521 | −0.742607 | − | 0.669727i | \(-0.766411\pi\) | ||||
−0.742607 | + | 0.669727i | \(0.766411\pi\) | |||||||
\(998\) | 19.5924 | 0.620185 | ||||||||
\(999\) | 2.81393 | 0.0890289 |
(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.v.1.4 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.v.1.4 | ✓ | 11 | 1.1 | even | 1 | trivial |