Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 21 x^{10} + 116 x^{9} + 106 x^{8} - 774 x^{7} - 63 x^{6} + 2013 x^{5} - 417 x^{4} - 2249 x^{3} + 761 x^{2} + 910 x - 375 \) |
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 | 1.12 | ||
Root | \(4.25305\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.25305 | 1.90202 | 0.951011 | − | 0.309158i | \(-0.100047\pi\) | ||||
0.951011 | + | 0.309158i | \(0.100047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.10378 | 0.795156 | 0.397578 | − | 0.917568i | \(-0.369851\pi\) | ||||
0.397578 | + | 0.917568i | \(0.369851\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.25305 | −1.34493 | ||||||||
\(11\) | −4.67709 | −1.41020 | −0.705098 | − | 0.709110i | \(-0.749097\pi\) | ||||
−0.705098 | + | 0.709110i | \(0.749097\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.547094 | 0.151736 | 0.0758682 | − | 0.997118i | \(-0.475827\pi\) | ||||
0.0758682 | + | 0.997118i | \(0.475827\pi\) | |||||||
\(14\) | −2.10378 | −0.562260 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.524967 | −0.127323 | −0.0636616 | − | 0.997972i | \(-0.520278\pi\) | ||||
−0.0636616 | + | 0.997972i | \(0.520278\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.11080 | −1.86074 | −0.930372 | − | 0.366617i | \(-0.880516\pi\) | ||||
−0.930372 | + | 0.366617i | \(0.880516\pi\) | |||||||
\(20\) | 4.25305 | 0.951011 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.67709 | 0.997159 | ||||||||
\(23\) | 6.00153 | 1.25141 | 0.625703 | − | 0.780061i | \(-0.284812\pi\) | ||||
0.625703 | + | 0.780061i | \(0.284812\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.0884 | 2.61768 | ||||||||
\(26\) | −0.547094 | −0.107294 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.10378 | 0.397578 | ||||||||
\(29\) | 8.07750 | 1.49995 | 0.749977 | − | 0.661464i | \(-0.230065\pi\) | ||||
0.749977 | + | 0.661464i | \(0.230065\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.87410 | 0.875414 | 0.437707 | − | 0.899118i | \(-0.355791\pi\) | ||||
0.437707 | + | 0.899118i | \(0.355791\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.524967 | 0.0900311 | ||||||||
\(35\) | 8.94750 | 1.51240 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.1411 | −1.66718 | −0.833591 | − | 0.552382i | \(-0.813719\pi\) | ||||
−0.833591 | + | 0.552382i | \(0.813719\pi\) | |||||||
\(38\) | 8.11080 | 1.31574 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.25305 | −0.672466 | ||||||||
\(41\) | −2.58901 | −0.404336 | −0.202168 | − | 0.979351i | \(-0.564799\pi\) | ||||
−0.202168 | + | 0.979351i | \(0.564799\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.72324 | 1.17778 | 0.588892 | − | 0.808212i | \(-0.299564\pi\) | ||||
0.588892 | + | 0.808212i | \(0.299564\pi\) | |||||||
\(44\) | −4.67709 | −0.705098 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00153 | −0.884878 | ||||||||
\(47\) | −5.67930 | −0.828412 | −0.414206 | − | 0.910183i | \(-0.635941\pi\) | ||||
−0.414206 | + | 0.910183i | \(0.635941\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.57409 | −0.367727 | ||||||||
\(50\) | −13.0884 | −1.85098 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.547094 | 0.0758682 | ||||||||
\(53\) | −0.544241 | −0.0747573 | −0.0373786 | − | 0.999301i | \(-0.511901\pi\) | ||||
−0.0373786 | + | 0.999301i | \(0.511901\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19.8919 | −2.68222 | ||||||||
\(56\) | −2.10378 | −0.281130 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.07750 | −1.06063 | ||||||||
\(59\) | 7.68172 | 1.00007 | 0.500037 | − | 0.866004i | \(-0.333320\pi\) | ||||
0.500037 | + | 0.866004i | \(0.333320\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.68590 | 0.471931 | 0.235966 | − | 0.971761i | \(-0.424175\pi\) | ||||
0.235966 | + | 0.971761i | \(0.424175\pi\) | |||||||
\(62\) | −4.87410 | −0.619011 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.32682 | 0.288606 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.0374969 | 0.00458098 | 0.00229049 | − | 0.999997i | \(-0.499271\pi\) | ||||
0.00229049 | + | 0.999997i | \(0.499271\pi\) | |||||||
\(68\) | −0.524967 | −0.0636616 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.94750 | −1.06943 | ||||||||
\(71\) | 13.0756 | 1.55179 | 0.775894 | − | 0.630863i | \(-0.217299\pi\) | ||||
0.775894 | + | 0.630863i | \(0.217299\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.3053 | 1.67431 | 0.837155 | − | 0.546965i | \(-0.184217\pi\) | ||||
0.837155 | + | 0.546965i | \(0.184217\pi\) | |||||||
\(74\) | 10.1411 | 1.17888 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.11080 | −0.930372 | ||||||||
\(77\) | −9.83959 | −1.12133 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.75832 | −0.535353 | −0.267676 | − | 0.963509i | \(-0.586256\pi\) | ||||
−0.267676 | + | 0.963509i | \(0.586256\pi\) | |||||||
\(80\) | 4.25305 | 0.475505 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.58901 | 0.285909 | ||||||||
\(83\) | −7.02674 | −0.771284 | −0.385642 | − | 0.922648i | \(-0.626020\pi\) | ||||
−0.385642 | + | 0.922648i | \(0.626020\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.23271 | −0.242172 | ||||||||
\(86\) | −7.72324 | −0.832818 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.67709 | 0.498579 | ||||||||
\(89\) | −15.5764 | −1.65110 | −0.825548 | − | 0.564332i | \(-0.809134\pi\) | ||||
−0.825548 | + | 0.564332i | \(0.809134\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.15097 | 0.120654 | ||||||||
\(92\) | 6.00153 | 0.625703 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.67930 | 0.585776 | ||||||||
\(95\) | −34.4956 | −3.53917 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.91148 | 0.904823 | 0.452412 | − | 0.891809i | \(-0.350564\pi\) | ||||
0.452412 | + | 0.891809i | \(0.350564\pi\) | |||||||
\(98\) | 2.57409 | 0.260022 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 13.0884 | 1.30884 | ||||||||
\(101\) | 10.7801 | 1.07266 | 0.536329 | − | 0.844009i | \(-0.319810\pi\) | ||||
0.536329 | + | 0.844009i | \(0.319810\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.83807 | 0.181110 | 0.0905552 | − | 0.995891i | \(-0.471136\pi\) | ||||
0.0905552 | + | 0.995891i | \(0.471136\pi\) | |||||||
\(104\) | −0.547094 | −0.0536469 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.544241 | 0.0528614 | ||||||||
\(107\) | 17.1840 | 1.66124 | 0.830619 | − | 0.556841i | \(-0.187987\pi\) | ||||
0.830619 | + | 0.556841i | \(0.187987\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.72734 | −0.357015 | −0.178507 | − | 0.983939i | \(-0.557127\pi\) | ||||
−0.178507 | + | 0.983939i | \(0.557127\pi\) | |||||||
\(110\) | 19.8919 | 1.89662 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.10378 | 0.198789 | ||||||||
\(113\) | 20.5365 | 1.93191 | 0.965955 | − | 0.258712i | \(-0.0832979\pi\) | ||||
0.965955 | + | 0.258712i | \(0.0832979\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 25.5248 | 2.38020 | ||||||||
\(116\) | 8.07750 | 0.749977 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.68172 | −0.707160 | ||||||||
\(119\) | −1.10442 | −0.101242 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.8752 | 0.988652 | ||||||||
\(122\) | −3.68590 | −0.333706 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.87410 | 0.437707 | ||||||||
\(125\) | 34.4005 | 3.07687 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.7968 | −1.57921 | −0.789606 | − | 0.613614i | \(-0.789715\pi\) | ||||
−0.789606 | + | 0.613614i | \(0.789715\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.32682 | −0.204075 | ||||||||
\(131\) | 19.4735 | 1.70141 | 0.850704 | − | 0.525645i | \(-0.176176\pi\) | ||||
0.850704 | + | 0.525645i | \(0.176176\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.0634 | −1.47958 | ||||||||
\(134\) | −0.0374969 | −0.00323924 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.524967 | 0.0450156 | ||||||||
\(137\) | 8.78583 | 0.750624 | 0.375312 | − | 0.926899i | \(-0.377536\pi\) | ||||
0.375312 | + | 0.926899i | \(0.377536\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.73608 | 0.232071 | 0.116036 | − | 0.993245i | \(-0.462981\pi\) | ||||
0.116036 | + | 0.993245i | \(0.462981\pi\) | |||||||
\(140\) | 8.94750 | 0.756202 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.0756 | −1.09728 | ||||||||
\(143\) | −2.55881 | −0.213978 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 34.3540 | 2.85294 | ||||||||
\(146\) | −14.3053 | −1.18392 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.1411 | −0.833591 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.34994 | 0.191235 | 0.0956175 | − | 0.995418i | \(-0.469517\pi\) | ||||
0.0956175 | + | 0.995418i | \(0.469517\pi\) | |||||||
\(152\) | 8.11080 | 0.657872 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 9.83959 | 0.792897 | ||||||||
\(155\) | 20.7298 | 1.66506 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.88317 | 0.469528 | 0.234764 | − | 0.972052i | \(-0.424568\pi\) | ||||
0.234764 | + | 0.972052i | \(0.424568\pi\) | |||||||
\(158\) | 4.75832 | 0.378552 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.25305 | −0.336233 | ||||||||
\(161\) | 12.6259 | 0.995063 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.559443 | 0.0438190 | 0.0219095 | − | 0.999760i | \(-0.493025\pi\) | ||||
0.0219095 | + | 0.999760i | \(0.493025\pi\) | |||||||
\(164\) | −2.58901 | −0.202168 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.02674 | 0.545380 | ||||||||
\(167\) | 12.8886 | 0.997349 | 0.498674 | − | 0.866789i | \(-0.333820\pi\) | ||||
0.498674 | + | 0.866789i | \(0.333820\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7007 | −0.976976 | ||||||||
\(170\) | 2.23271 | 0.171241 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.72324 | 0.588892 | ||||||||
\(173\) | 15.4812 | 1.17701 | 0.588506 | − | 0.808493i | \(-0.299716\pi\) | ||||
0.588506 | + | 0.808493i | \(0.299716\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 27.5352 | 2.08147 | ||||||||
\(176\) | −4.67709 | −0.352549 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 15.5764 | 1.16750 | ||||||||
\(179\) | −18.5958 | −1.38991 | −0.694957 | − | 0.719051i | \(-0.744577\pi\) | ||||
−0.694957 | + | 0.719051i | \(0.744577\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.7960 | 0.951123 | 0.475561 | − | 0.879683i | \(-0.342245\pi\) | ||||
0.475561 | + | 0.879683i | \(0.342245\pi\) | |||||||
\(182\) | −1.15097 | −0.0853154 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.00153 | −0.442439 | ||||||||
\(185\) | −43.1305 | −3.17102 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.45532 | 0.179551 | ||||||||
\(188\) | −5.67930 | −0.414206 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 34.4956 | 2.50257 | ||||||||
\(191\) | −5.71191 | −0.413300 | −0.206650 | − | 0.978415i | \(-0.566256\pi\) | ||||
−0.206650 | + | 0.978415i | \(0.566256\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.85587 | 0.421515 | 0.210758 | − | 0.977538i | \(-0.432407\pi\) | ||||
0.210758 | + | 0.977538i | \(0.432407\pi\) | |||||||
\(194\) | −8.91148 | −0.639807 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.57409 | −0.183864 | ||||||||
\(197\) | 20.7385 | 1.47756 | 0.738778 | − | 0.673949i | \(-0.235403\pi\) | ||||
0.738778 | + | 0.673949i | \(0.235403\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.14505 | −0.0811706 | −0.0405853 | − | 0.999176i | \(-0.512922\pi\) | ||||
−0.0405853 | + | 0.999176i | \(0.512922\pi\) | |||||||
\(200\) | −13.0884 | −0.925491 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.7801 | −0.758484 | ||||||||
\(203\) | 16.9933 | 1.19270 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.0112 | −0.769055 | ||||||||
\(206\) | −1.83807 | −0.128064 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.547094 | 0.0379341 | ||||||||
\(209\) | 37.9349 | 2.62401 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.55721 | 0.244888 | 0.122444 | − | 0.992475i | \(-0.460927\pi\) | ||||
0.122444 | + | 0.992475i | \(0.460927\pi\) | |||||||
\(212\) | −0.544241 | −0.0373786 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −17.1840 | −1.17467 | ||||||||
\(215\) | 32.8473 | 2.24017 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.2540 | 0.696090 | ||||||||
\(218\) | 3.72734 | 0.252447 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −19.8919 | −1.34111 | ||||||||
\(221\) | −0.287206 | −0.0193196 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.36433 | −0.359222 | −0.179611 | − | 0.983738i | \(-0.557484\pi\) | ||||
−0.179611 | + | 0.983738i | \(0.557484\pi\) | |||||||
\(224\) | −2.10378 | −0.140565 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −20.5365 | −1.36607 | ||||||||
\(227\) | 11.7698 | 0.781188 | 0.390594 | − | 0.920563i | \(-0.372270\pi\) | ||||
0.390594 | + | 0.920563i | \(0.372270\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.6187 | −1.56077 | −0.780384 | − | 0.625301i | \(-0.784976\pi\) | ||||
−0.780384 | + | 0.625301i | \(0.784976\pi\) | |||||||
\(230\) | −25.5248 | −1.68306 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.07750 | −0.530314 | ||||||||
\(233\) | 27.4243 | 1.79662 | 0.898312 | − | 0.439358i | \(-0.144794\pi\) | ||||
0.898312 | + | 0.439358i | \(0.144794\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.1544 | −1.57566 | ||||||||
\(236\) | 7.68172 | 0.500037 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.10442 | 0.0715888 | ||||||||
\(239\) | −19.9867 | −1.29283 | −0.646416 | − | 0.762985i | \(-0.723733\pi\) | ||||
−0.646416 | + | 0.762985i | \(0.723733\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.69539 | 0.109209 | 0.0546047 | − | 0.998508i | \(-0.482610\pi\) | ||||
0.0546047 | + | 0.998508i | \(0.482610\pi\) | |||||||
\(242\) | −10.8752 | −0.699082 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.68590 | 0.235966 | ||||||||
\(245\) | −10.9477 | −0.699425 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.43736 | −0.282343 | ||||||||
\(248\) | −4.87410 | −0.309505 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −34.4005 | −2.17568 | ||||||||
\(251\) | −25.2458 | −1.59350 | −0.796752 | − | 0.604307i | \(-0.793450\pi\) | ||||
−0.796752 | + | 0.604307i | \(0.793450\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.0697 | −1.76473 | ||||||||
\(254\) | 17.7968 | 1.11667 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.0313 | −1.37428 | −0.687138 | − | 0.726527i | \(-0.741133\pi\) | ||||
−0.687138 | + | 0.726527i | \(0.741133\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.3346 | −1.32567 | ||||||||
\(260\) | 2.32682 | 0.144303 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −19.4735 | −1.20308 | ||||||||
\(263\) | −28.4131 | −1.75203 | −0.876013 | − | 0.482287i | \(-0.839806\pi\) | ||||
−0.876013 | + | 0.482287i | \(0.839806\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.31468 | −0.142190 | ||||||||
\(266\) | 17.0634 | 1.04622 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.0374969 | 0.00229049 | ||||||||
\(269\) | 16.6698 | 1.01638 | 0.508189 | − | 0.861245i | \(-0.330315\pi\) | ||||
0.508189 | + | 0.861245i | \(0.330315\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.61463 | 0.523302 | 0.261651 | − | 0.965163i | \(-0.415733\pi\) | ||||
0.261651 | + | 0.965163i | \(0.415733\pi\) | |||||||
\(272\) | −0.524967 | −0.0318308 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.78583 | −0.530771 | ||||||||
\(275\) | −61.2157 | −3.69145 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.78762 | 0.287660 | 0.143830 | − | 0.989602i | \(-0.454058\pi\) | ||||
0.143830 | + | 0.989602i | \(0.454058\pi\) | |||||||
\(278\) | −2.73608 | −0.164099 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.94750 | −0.534715 | ||||||||
\(281\) | 1.93881 | 0.115660 | 0.0578298 | − | 0.998326i | \(-0.481582\pi\) | ||||
0.0578298 | + | 0.998326i | \(0.481582\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.3283 | −1.68394 | −0.841972 | − | 0.539521i | \(-0.818606\pi\) | ||||
−0.841972 | + | 0.539521i | \(0.818606\pi\) | |||||||
\(284\) | 13.0756 | 0.775894 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.55881 | 0.151305 | ||||||||
\(287\) | −5.44672 | −0.321510 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7244 | −0.983789 | ||||||||
\(290\) | −34.3540 | −2.01734 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.3053 | 0.837155 | ||||||||
\(293\) | 24.7952 | 1.44855 | 0.724275 | − | 0.689511i | \(-0.242174\pi\) | ||||
0.724275 | + | 0.689511i | \(0.242174\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 32.6707 | 1.90216 | ||||||||
\(296\) | 10.1411 | 0.589438 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | 3.28340 | 0.189884 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.2480 | 0.936521 | ||||||||
\(302\) | −2.34994 | −0.135224 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.11080 | −0.465186 | ||||||||
\(305\) | 15.6763 | 0.897623 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.6307 | −0.892093 | −0.446046 | − | 0.895010i | \(-0.647168\pi\) | ||||
−0.446046 | + | 0.895010i | \(0.647168\pi\) | |||||||
\(308\) | −9.83959 | −0.560663 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −20.7298 | −1.17737 | ||||||||
\(311\) | −0.803622 | −0.0455692 | −0.0227846 | − | 0.999740i | \(-0.507253\pi\) | ||||
−0.0227846 | + | 0.999740i | \(0.507253\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.3580 | −1.15070 | −0.575350 | − | 0.817907i | \(-0.695134\pi\) | ||||
−0.575350 | + | 0.817907i | \(0.695134\pi\) | |||||||
\(314\) | −5.88317 | −0.332006 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.75832 | −0.267676 | ||||||||
\(317\) | 23.4979 | 1.31977 | 0.659886 | − | 0.751365i | \(-0.270604\pi\) | ||||
0.659886 | + | 0.751365i | \(0.270604\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −37.7792 | −2.11523 | ||||||||
\(320\) | 4.25305 | 0.237753 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.6259 | −0.703616 | ||||||||
\(323\) | 4.25790 | 0.236916 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.16059 | 0.397198 | ||||||||
\(326\) | −0.559443 | −0.0309847 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.58901 | 0.142954 | ||||||||
\(329\) | −11.9480 | −0.658716 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.55426 | 0.195360 | 0.0976799 | − | 0.995218i | \(-0.468858\pi\) | ||||
0.0976799 | + | 0.995218i | \(0.468858\pi\) | |||||||
\(332\) | −7.02674 | −0.385642 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.8886 | −0.705232 | ||||||||
\(335\) | 0.159476 | 0.00871312 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.3744 | 1.27328 | 0.636642 | − | 0.771159i | \(-0.280323\pi\) | ||||
0.636642 | + | 0.771159i | \(0.280323\pi\) | |||||||
\(338\) | 12.7007 | 0.690826 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.23271 | −0.121086 | ||||||||
\(341\) | −22.7966 | −1.23450 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1418 | −1.08756 | ||||||||
\(344\) | −7.72324 | −0.416409 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.4812 | −0.832274 | ||||||||
\(347\) | −14.6186 | −0.784768 | −0.392384 | − | 0.919801i | \(-0.628350\pi\) | ||||
−0.392384 | + | 0.919801i | \(0.628350\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.9685 | 1.06889 | 0.534443 | − | 0.845204i | \(-0.320521\pi\) | ||||
0.534443 | + | 0.845204i | \(0.320521\pi\) | |||||||
\(350\) | −27.5352 | −1.47182 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.67709 | 0.249290 | ||||||||
\(353\) | 32.4912 | 1.72933 | 0.864667 | − | 0.502346i | \(-0.167530\pi\) | ||||
0.864667 | + | 0.502346i | \(0.167530\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 55.6112 | 2.95153 | ||||||||
\(356\) | −15.5764 | −0.825548 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.5958 | 0.982818 | ||||||||
\(359\) | 11.0126 | 0.581222 | 0.290611 | − | 0.956841i | \(-0.406141\pi\) | ||||
0.290611 | + | 0.956841i | \(0.406141\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 46.7850 | 2.46237 | ||||||||
\(362\) | −12.7960 | −0.672545 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.15097 | 0.0603271 | ||||||||
\(365\) | 60.8412 | 3.18457 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.4535 | −1.69406 | −0.847031 | − | 0.531544i | \(-0.821612\pi\) | ||||
−0.847031 | + | 0.531544i | \(0.821612\pi\) | |||||||
\(368\) | 6.00153 | 0.312852 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 43.1305 | 2.24225 | ||||||||
\(371\) | −1.14497 | −0.0594437 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.06417 | 0.417547 | 0.208773 | − | 0.977964i | \(-0.433053\pi\) | ||||
0.208773 | + | 0.977964i | \(0.433053\pi\) | |||||||
\(374\) | −2.45532 | −0.126962 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.67930 | 0.292888 | ||||||||
\(377\) | 4.41915 | 0.227598 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.31863 | 0.119100 | 0.0595499 | − | 0.998225i | \(-0.481033\pi\) | ||||
0.0595499 | + | 0.998225i | \(0.481033\pi\) | |||||||
\(380\) | −34.4956 | −1.76959 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.71191 | 0.292247 | ||||||||
\(383\) | 32.0190 | 1.63610 | 0.818048 | − | 0.575150i | \(-0.195056\pi\) | ||||
0.818048 | + | 0.575150i | \(0.195056\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −41.8483 | −2.13278 | ||||||||
\(386\) | −5.85587 | −0.298056 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.91148 | 0.452412 | ||||||||
\(389\) | 5.77502 | 0.292805 | 0.146403 | − | 0.989225i | \(-0.453231\pi\) | ||||
0.146403 | + | 0.989225i | \(0.453231\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.15061 | −0.159333 | ||||||||
\(392\) | 2.57409 | 0.130011 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −20.7385 | −1.04479 | ||||||||
\(395\) | −20.2374 | −1.01825 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.60163 | 0.0803833 | 0.0401917 | − | 0.999192i | \(-0.487203\pi\) | ||||
0.0401917 | + | 0.999192i | \(0.487203\pi\) | |||||||
\(398\) | 1.14505 | 0.0573963 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.0884 | 0.654421 | ||||||||
\(401\) | 32.9876 | 1.64732 | 0.823662 | − | 0.567081i | \(-0.191928\pi\) | ||||
0.823662 | + | 0.567081i | \(0.191928\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.66659 | 0.132832 | ||||||||
\(404\) | 10.7801 | 0.536329 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16.9933 | −0.843364 | ||||||||
\(407\) | 47.4307 | 2.35105 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.9325 | −1.03504 | −0.517522 | − | 0.855670i | \(-0.673145\pi\) | ||||
−0.517522 | + | 0.855670i | \(0.673145\pi\) | |||||||
\(410\) | 11.0112 | 0.543804 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.83807 | 0.0905552 | ||||||||
\(413\) | 16.1607 | 0.795215 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −29.8850 | −1.46700 | ||||||||
\(416\) | −0.547094 | −0.0268235 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −37.9349 | −1.85546 | ||||||||
\(419\) | −18.6183 | −0.909562 | −0.454781 | − | 0.890603i | \(-0.650282\pi\) | ||||
−0.454781 | + | 0.890603i | \(0.650282\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.0112 | −1.41392 | −0.706960 | − | 0.707254i | \(-0.749934\pi\) | ||||
−0.706960 | + | 0.707254i | \(0.749934\pi\) | |||||||
\(422\) | −3.55721 | −0.173162 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.544241 | 0.0264307 | ||||||||
\(425\) | −6.87099 | −0.333292 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.75434 | 0.375259 | ||||||||
\(428\) | 17.1840 | 0.830619 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −32.8473 | −1.58404 | ||||||||
\(431\) | −20.0767 | −0.967059 | −0.483530 | − | 0.875328i | \(-0.660645\pi\) | ||||
−0.483530 | + | 0.875328i | \(0.660645\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.1410 | −1.25626 | −0.628129 | − | 0.778109i | \(-0.716179\pi\) | ||||
−0.628129 | + | 0.778109i | \(0.716179\pi\) | |||||||
\(434\) | −10.2540 | −0.492210 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.72734 | −0.178507 | ||||||||
\(437\) | −48.6772 | −2.32855 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.54942 | 0.0739497 | 0.0369749 | − | 0.999316i | \(-0.488228\pi\) | ||||
0.0369749 | + | 0.999316i | \(0.488228\pi\) | |||||||
\(440\) | 19.8919 | 0.948309 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.287206 | 0.0136610 | ||||||||
\(443\) | −7.35831 | −0.349604 | −0.174802 | − | 0.984604i | \(-0.555929\pi\) | ||||
−0.174802 | + | 0.984604i | \(0.555929\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −66.2472 | −3.14042 | ||||||||
\(446\) | 5.36433 | 0.254008 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.10378 | 0.0993945 | ||||||||
\(449\) | 5.07130 | 0.239330 | 0.119665 | − | 0.992814i | \(-0.461818\pi\) | ||||
0.119665 | + | 0.992814i | \(0.461818\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.1090 | 0.570193 | ||||||||
\(452\) | 20.5365 | 0.965955 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.7698 | −0.552383 | ||||||||
\(455\) | 4.89512 | 0.229487 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.68190 | 0.312566 | 0.156283 | − | 0.987712i | \(-0.450049\pi\) | ||||
0.156283 | + | 0.987712i | \(0.450049\pi\) | |||||||
\(458\) | 23.6187 | 1.10363 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 25.5248 | 1.19010 | ||||||||
\(461\) | −17.6016 | −0.819788 | −0.409894 | − | 0.912133i | \(-0.634434\pi\) | ||||
−0.409894 | + | 0.912133i | \(0.634434\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.1244 | 0.563467 | 0.281734 | − | 0.959493i | \(-0.409091\pi\) | ||||
0.281734 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(464\) | 8.07750 | 0.374988 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.4243 | −1.27041 | ||||||||
\(467\) | −32.6155 | −1.50927 | −0.754633 | − | 0.656147i | \(-0.772185\pi\) | ||||
−0.754633 | + | 0.656147i | \(0.772185\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.0788855 | 0.00364259 | ||||||||
\(470\) | 24.1544 | 1.11416 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.68172 | −0.353580 | ||||||||
\(473\) | −36.1223 | −1.66090 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −106.158 | −4.87084 | ||||||||
\(476\) | −1.10442 | −0.0506209 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 19.9867 | 0.914171 | ||||||||
\(479\) | 26.8635 | 1.22742 | 0.613712 | − | 0.789530i | \(-0.289675\pi\) | ||||
0.613712 | + | 0.789530i | \(0.289675\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.54812 | −0.252972 | ||||||||
\(482\) | −1.69539 | −0.0772227 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.8752 | 0.494326 | ||||||||
\(485\) | 37.9009 | 1.72099 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.2025 | 1.59518 | 0.797590 | − | 0.603201i | \(-0.206108\pi\) | ||||
0.797590 | + | 0.603201i | \(0.206108\pi\) | |||||||
\(488\) | −3.68590 | −0.166853 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10.9477 | 0.494568 | ||||||||
\(491\) | 13.8169 | 0.623548 | 0.311774 | − | 0.950156i | \(-0.399077\pi\) | ||||
0.311774 | + | 0.950156i | \(0.399077\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.24042 | −0.190979 | ||||||||
\(494\) | 4.43736 | 0.199646 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.87410 | 0.218853 | ||||||||
\(497\) | 27.5082 | 1.23391 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.5985 | −1.32501 | −0.662505 | − | 0.749057i | \(-0.730507\pi\) | ||||
−0.662505 | + | 0.749057i | \(0.730507\pi\) | |||||||
\(500\) | 34.4005 | 1.53844 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 25.2458 | 1.12678 | ||||||||
\(503\) | −11.1481 | −0.497070 | −0.248535 | − | 0.968623i | \(-0.579949\pi\) | ||||
−0.248535 | + | 0.968623i | \(0.579949\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 45.8482 | 2.04022 | ||||||||
\(506\) | 28.0697 | 1.24785 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −17.7968 | −0.789606 | ||||||||
\(509\) | −22.5150 | −0.997962 | −0.498981 | − | 0.866613i | \(-0.666292\pi\) | ||||
−0.498981 | + | 0.866613i | \(0.666292\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.0953 | 1.33134 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 22.0313 | 0.971759 | ||||||||
\(515\) | 7.81740 | 0.344476 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.5626 | 1.16822 | ||||||||
\(518\) | 21.3346 | 0.937390 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.32682 | −0.102038 | ||||||||
\(521\) | −41.1084 | −1.80099 | −0.900496 | − | 0.434864i | \(-0.856797\pi\) | ||||
−0.900496 | + | 0.434864i | \(0.856797\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.70738 | 0.380747 | 0.190374 | − | 0.981712i | \(-0.439030\pi\) | ||||
0.190374 | + | 0.981712i | \(0.439030\pi\) | |||||||
\(524\) | 19.4735 | 0.850704 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28.4131 | 1.23887 | ||||||||
\(527\) | −2.55874 | −0.111460 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0184 | 0.566018 | ||||||||
\(530\) | 2.31468 | 0.100543 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −17.0634 | −0.739791 | ||||||||
\(533\) | −1.41643 | −0.0613525 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 73.0843 | 3.15971 | ||||||||
\(536\) | −0.0374969 | −0.00161962 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.6698 | −0.718688 | ||||||||
\(539\) | 12.0393 | 0.518567 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.3238 | −0.572836 | −0.286418 | − | 0.958105i | \(-0.592465\pi\) | ||||
−0.286418 | + | 0.958105i | \(0.592465\pi\) | |||||||
\(542\) | −8.61463 | −0.370030 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.524967 | 0.0225078 | ||||||||
\(545\) | −15.8526 | −0.679049 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.3966 | −1.08588 | −0.542940 | − | 0.839771i | \(-0.682689\pi\) | ||||
−0.542940 | + | 0.839771i | \(0.682689\pi\) | |||||||
\(548\) | 8.78583 | 0.375312 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 61.2157 | 2.61025 | ||||||||
\(551\) | −65.5149 | −2.79103 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.0105 | −0.425689 | ||||||||
\(554\) | −4.78762 | −0.203407 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.73608 | 0.116036 | ||||||||
\(557\) | 24.2298 | 1.02665 | 0.513325 | − | 0.858194i | \(-0.328413\pi\) | ||||
0.513325 | + | 0.858194i | \(0.328413\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.22534 | 0.178713 | ||||||||
\(560\) | 8.94750 | 0.378101 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.93881 | −0.0817837 | ||||||||
\(563\) | −2.60064 | −0.109604 | −0.0548019 | − | 0.998497i | \(-0.517453\pi\) | ||||
−0.0548019 | + | 0.998497i | \(0.517453\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 87.3426 | 3.67453 | ||||||||
\(566\) | 28.3283 | 1.19073 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13.0756 | −0.548640 | ||||||||
\(569\) | 0.0803760 | 0.00336954 | 0.00168477 | − | 0.999999i | \(-0.499464\pi\) | ||||
0.00168477 | + | 0.999999i | \(0.499464\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.9549 | −1.12803 | −0.564013 | − | 0.825766i | \(-0.690743\pi\) | ||||
−0.564013 | + | 0.825766i | \(0.690743\pi\) | |||||||
\(572\) | −2.55881 | −0.106989 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.44672 | 0.227342 | ||||||||
\(575\) | 78.5506 | 3.27579 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.8989 | −0.786772 | −0.393386 | − | 0.919373i | \(-0.628696\pi\) | ||||
−0.393386 | + | 0.919373i | \(0.628696\pi\) | |||||||
\(578\) | 16.7244 | 0.695644 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 34.3540 | 1.42647 | ||||||||
\(581\) | −14.7827 | −0.613291 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.54546 | 0.105422 | ||||||||
\(584\) | −14.3053 | −0.591958 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.7952 | −1.02428 | ||||||||
\(587\) | −6.24700 | −0.257841 | −0.128921 | − | 0.991655i | \(-0.541151\pi\) | ||||
−0.128921 | + | 0.991655i | \(0.541151\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −39.5328 | −1.62892 | ||||||||
\(590\) | −32.6707 | −1.34503 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10.1411 | −0.416796 | ||||||||
\(593\) | −30.7455 | −1.26257 | −0.631283 | − | 0.775553i | \(-0.717471\pi\) | ||||
−0.631283 | + | 0.775553i | \(0.717471\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.69714 | −0.192564 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.28340 | −0.134268 | ||||||||
\(599\) | 34.6147 | 1.41432 | 0.707158 | − | 0.707055i | \(-0.249977\pi\) | ||||
0.707158 | + | 0.707055i | \(0.249977\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.2891 | 0.419702 | 0.209851 | − | 0.977733i | \(-0.432702\pi\) | ||||
0.209851 | + | 0.977733i | \(0.432702\pi\) | |||||||
\(602\) | −16.2480 | −0.662220 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.34994 | 0.0956175 | ||||||||
\(605\) | 46.2526 | 1.88044 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.5414 | 1.56435 | 0.782173 | − | 0.623062i | \(-0.214111\pi\) | ||||
0.782173 | + | 0.623062i | \(0.214111\pi\) | |||||||
\(608\) | 8.11080 | 0.328936 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15.6763 | −0.634715 | ||||||||
\(611\) | −3.10711 | −0.125700 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.4761 | 0.463517 | 0.231759 | − | 0.972773i | \(-0.425552\pi\) | ||||
0.231759 | + | 0.972773i | \(0.425552\pi\) | |||||||
\(614\) | 15.6307 | 0.630805 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.83959 | 0.396448 | ||||||||
\(617\) | 8.32005 | 0.334952 | 0.167476 | − | 0.985876i | \(-0.446438\pi\) | ||||
0.167476 | + | 0.985876i | \(0.446438\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.0989 | −0.807841 | −0.403921 | − | 0.914794i | \(-0.632353\pi\) | ||||
−0.403921 | + | 0.914794i | \(0.632353\pi\) | |||||||
\(620\) | 20.7298 | 0.832528 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.803622 | 0.0322223 | ||||||||
\(623\) | −32.7694 | −1.31288 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 80.8647 | 3.23459 | ||||||||
\(626\) | 20.3580 | 0.813668 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.88317 | 0.234764 | ||||||||
\(629\) | 5.32373 | 0.212271 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.8280 | −0.789339 | −0.394670 | − | 0.918823i | \(-0.629141\pi\) | ||||
−0.394670 | + | 0.918823i | \(0.629141\pi\) | |||||||
\(632\) | 4.75832 | 0.189276 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −23.4979 | −0.933220 | ||||||||
\(635\) | −75.6907 | −3.00370 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.40827 | −0.0557976 | ||||||||
\(638\) | 37.7792 | 1.49569 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.25305 | −0.168117 | ||||||||
\(641\) | −14.5984 | −0.576600 | −0.288300 | − | 0.957540i | \(-0.593090\pi\) | ||||
−0.288300 | + | 0.957540i | \(0.593090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.63135 | 0.261515 | 0.130757 | − | 0.991414i | \(-0.458259\pi\) | ||||
0.130757 | + | 0.991414i | \(0.458259\pi\) | |||||||
\(644\) | 12.6259 | 0.497532 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.25790 | −0.167525 | ||||||||
\(647\) | −10.4522 | −0.410917 | −0.205458 | − | 0.978666i | \(-0.565869\pi\) | ||||
−0.205458 | + | 0.978666i | \(0.565869\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −35.9281 | −1.41030 | ||||||||
\(650\) | −7.16059 | −0.280862 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.559443 | 0.0219095 | ||||||||
\(653\) | −9.33999 | −0.365502 | −0.182751 | − | 0.983159i | \(-0.558500\pi\) | ||||
−0.182751 | + | 0.983159i | \(0.558500\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 82.8217 | 3.23611 | ||||||||
\(656\) | −2.58901 | −0.101084 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11.9480 | 0.465783 | ||||||||
\(659\) | −29.1535 | −1.13566 | −0.567830 | − | 0.823146i | \(-0.692217\pi\) | ||||
−0.567830 | + | 0.823146i | \(0.692217\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.9644 | −0.971004 | −0.485502 | − | 0.874236i | \(-0.661363\pi\) | ||||
−0.485502 | + | 0.874236i | \(0.661363\pi\) | |||||||
\(662\) | −3.55426 | −0.138140 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.02674 | 0.272690 | ||||||||
\(665\) | −72.5713 | −2.81420 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.4774 | 1.87705 | ||||||||
\(668\) | 12.8886 | 0.498674 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.159476 | −0.00616111 | ||||||||
\(671\) | −17.2393 | −0.665515 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0978 | 0.774712 | 0.387356 | − | 0.921930i | \(-0.373389\pi\) | ||||
0.387356 | + | 0.921930i | \(0.373389\pi\) | |||||||
\(674\) | −23.3744 | −0.900348 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.7007 | −0.488488 | ||||||||
\(677\) | −45.6993 | −1.75637 | −0.878184 | − | 0.478323i | \(-0.841245\pi\) | ||||
−0.878184 | + | 0.478323i | \(0.841245\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.7478 | 0.719475 | ||||||||
\(680\) | 2.23271 | 0.0856206 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 22.7966 | 0.872927 | ||||||||
\(683\) | −35.2201 | −1.34766 | −0.673830 | − | 0.738886i | \(-0.735352\pi\) | ||||
−0.673830 | + | 0.738886i | \(0.735352\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 37.3666 | 1.42770 | ||||||||
\(686\) | 20.1418 | 0.769018 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.72324 | 0.294446 | ||||||||
\(689\) | −0.297751 | −0.0113434 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.6521 | −0.709558 | −0.354779 | − | 0.934950i | \(-0.615444\pi\) | ||||
−0.354779 | + | 0.934950i | \(0.615444\pi\) | |||||||
\(692\) | 15.4812 | 0.588506 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.6186 | 0.554915 | ||||||||
\(695\) | 11.6367 | 0.441404 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.35915 | 0.0514813 | ||||||||
\(698\) | −19.9685 | −0.755817 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 27.5352 | 1.04073 | ||||||||
\(701\) | 46.3334 | 1.74999 | 0.874995 | − | 0.484133i | \(-0.160865\pi\) | ||||
0.874995 | + | 0.484133i | \(0.160865\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 82.2522 | 3.10220 | ||||||||
\(704\) | −4.67709 | −0.176274 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −32.4912 | −1.22282 | ||||||||
\(707\) | 22.6790 | 0.852931 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.62028 | −0.211074 | −0.105537 | − | 0.994415i | \(-0.533656\pi\) | ||||
−0.105537 | + | 0.994415i | \(0.533656\pi\) | |||||||
\(710\) | −55.6112 | −2.08705 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.5764 | 0.583750 | ||||||||
\(713\) | 29.2521 | 1.09550 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.8827 | −0.406991 | ||||||||
\(716\) | −18.5958 | −0.694957 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.0126 | −0.410986 | ||||||||
\(719\) | −1.38058 | −0.0514870 | −0.0257435 | − | 0.999669i | \(-0.508195\pi\) | ||||
−0.0257435 | + | 0.999669i | \(0.508195\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.86690 | 0.144011 | ||||||||
\(722\) | −46.7850 | −1.74116 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.7960 | 0.475561 | ||||||||
\(725\) | 105.722 | 3.92641 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.6994 | 1.24984 | 0.624920 | − | 0.780689i | \(-0.285131\pi\) | ||||
0.624920 | + | 0.780689i | \(0.285131\pi\) | |||||||
\(728\) | −1.15097 | −0.0426577 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −60.8412 | −2.25183 | ||||||||
\(731\) | −4.05445 | −0.149959 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.43137 | 0.237548 | 0.118774 | − | 0.992921i | \(-0.462104\pi\) | ||||
0.118774 | + | 0.992921i | \(0.462104\pi\) | |||||||
\(734\) | 32.4535 | 1.19788 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.00153 | −0.221220 | ||||||||
\(737\) | −0.175377 | −0.00646008 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.37703 | −0.161012 | −0.0805058 | − | 0.996754i | \(-0.525654\pi\) | ||||
−0.0805058 | + | 0.996754i | \(0.525654\pi\) | |||||||
\(740\) | −43.1305 | −1.58551 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.14497 | 0.0420330 | ||||||||
\(743\) | −29.5010 | −1.08229 | −0.541144 | − | 0.840930i | \(-0.682009\pi\) | ||||
−0.541144 | + | 0.840930i | \(0.682009\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.25305 | 0.155820 | ||||||||
\(746\) | −8.06417 | −0.295250 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.45532 | 0.0897753 | ||||||||
\(749\) | 36.1514 | 1.32094 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.4108 | 1.25567 | 0.627834 | − | 0.778347i | \(-0.283942\pi\) | ||||
0.627834 | + | 0.778347i | \(0.283942\pi\) | |||||||
\(752\) | −5.67930 | −0.207103 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.41915 | −0.160936 | ||||||||
\(755\) | 9.99439 | 0.363733 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.1601 | −0.732733 | −0.366366 | − | 0.930471i | \(-0.619398\pi\) | ||||
−0.366366 | + | 0.930471i | \(0.619398\pi\) | |||||||
\(758\) | −2.31863 | −0.0842163 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 34.4956 | 1.25129 | ||||||||
\(761\) | 9.96886 | 0.361371 | 0.180686 | − | 0.983541i | \(-0.442168\pi\) | ||||
0.180686 | + | 0.983541i | \(0.442168\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.84152 | −0.283882 | ||||||||
\(764\) | −5.71191 | −0.206650 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32.0190 | −1.15689 | ||||||||
\(767\) | 4.20262 | 0.151748 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.3004 | 0.840233 | 0.420117 | − | 0.907470i | \(-0.361989\pi\) | ||||
0.420117 | + | 0.907470i | \(0.361989\pi\) | |||||||
\(770\) | 41.8483 | 1.50811 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.85587 | 0.210758 | ||||||||
\(773\) | −24.2668 | −0.872816 | −0.436408 | − | 0.899749i | \(-0.643750\pi\) | ||||
−0.436408 | + | 0.899749i | \(0.643750\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 63.7942 | 2.29156 | ||||||||
\(776\) | −8.91148 | −0.319903 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.77502 | −0.207044 | ||||||||
\(779\) | 20.9990 | 0.752366 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −61.1558 | −2.18833 | ||||||||
\(782\) | 3.15061 | 0.112666 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.57409 | −0.0919318 | ||||||||
\(785\) | 25.0214 | 0.893052 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.1694 | −1.03978 | −0.519889 | − | 0.854234i | \(-0.674027\pi\) | ||||
−0.519889 | + | 0.854234i | \(0.674027\pi\) | |||||||
\(788\) | 20.7385 | 0.738778 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 20.2374 | 0.720013 | ||||||||
\(791\) | 43.2043 | 1.53617 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.01653 | 0.0716092 | ||||||||
\(794\) | −1.60163 | −0.0568396 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.14505 | −0.0405853 | ||||||||
\(797\) | 13.1392 | 0.465414 | 0.232707 | − | 0.972547i | \(-0.425242\pi\) | ||||
0.232707 | + | 0.972547i | \(0.425242\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.98145 | 0.105476 | ||||||||
\(800\) | −13.0884 | −0.462746 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −32.9876 | −1.16483 | ||||||||
\(803\) | −66.9072 | −2.36111 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 53.6987 | 1.89263 | ||||||||
\(806\) | −2.66659 | −0.0939265 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.7801 | −0.379242 | ||||||||
\(809\) | 42.6320 | 1.49886 | 0.749432 | − | 0.662082i | \(-0.230327\pi\) | ||||
0.749432 | + | 0.662082i | \(0.230327\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.8586 | 1.61031 | 0.805156 | − | 0.593063i | \(-0.202081\pi\) | ||||
0.805156 | + | 0.593063i | \(0.202081\pi\) | |||||||
\(812\) | 16.9933 | 0.596348 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −47.4307 | −1.66245 | ||||||||
\(815\) | 2.37934 | 0.0833446 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −62.6416 | −2.19155 | ||||||||
\(818\) | 20.9325 | 0.731886 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.0112 | −0.384528 | ||||||||
\(821\) | −42.4539 | −1.48165 | −0.740825 | − | 0.671698i | \(-0.765565\pi\) | ||||
−0.740825 | + | 0.671698i | \(0.765565\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.96445 | −0.312481 | −0.156241 | − | 0.987719i | \(-0.549937\pi\) | ||||
−0.156241 | + | 0.987719i | \(0.549937\pi\) | |||||||
\(824\) | −1.83807 | −0.0640322 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.1607 | −0.562302 | ||||||||
\(827\) | 16.7639 | 0.582936 | 0.291468 | − | 0.956581i | \(-0.405856\pi\) | ||||
0.291468 | + | 0.956581i | \(0.405856\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.0424 | 1.14761 | 0.573805 | − | 0.818992i | \(-0.305467\pi\) | ||||
0.573805 | + | 0.818992i | \(0.305467\pi\) | |||||||
\(830\) | 29.8850 | 1.03733 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.547094 | 0.0189671 | ||||||||
\(833\) | 1.35131 | 0.0468202 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 54.8158 | 1.89698 | ||||||||
\(836\) | 37.9349 | 1.31201 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18.6183 | 0.643157 | ||||||||
\(839\) | −16.0385 | −0.553712 | −0.276856 | − | 0.960911i | \(-0.589292\pi\) | ||||
−0.276856 | + | 0.960911i | \(0.589292\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.2460 | 1.24986 | ||||||||
\(842\) | 29.0112 | 0.999792 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.55721 | 0.122444 | ||||||||
\(845\) | −54.0166 | −1.85823 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.8790 | 0.786132 | ||||||||
\(848\) | −0.544241 | −0.0186893 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.87099 | 0.235673 | ||||||||
\(851\) | −60.8620 | −2.08632 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.31797 | −0.147845 | −0.0739223 | − | 0.997264i | \(-0.523552\pi\) | ||||
−0.0739223 | + | 0.997264i | \(0.523552\pi\) | |||||||
\(854\) | −7.75434 | −0.265348 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.1840 | −0.587336 | ||||||||
\(857\) | −32.3939 | −1.10656 | −0.553278 | − | 0.832997i | \(-0.686623\pi\) | ||||
−0.553278 | + | 0.832997i | \(0.686623\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.15934 | 0.244274 | 0.122137 | − | 0.992513i | \(-0.461025\pi\) | ||||
0.122137 | + | 0.992513i | \(0.461025\pi\) | |||||||
\(860\) | 32.8473 | 1.12008 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.0767 | 0.683814 | ||||||||
\(863\) | 18.8898 | 0.643016 | 0.321508 | − | 0.946907i | \(-0.395810\pi\) | ||||
0.321508 | + | 0.946907i | \(0.395810\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 65.8422 | 2.23870 | ||||||||
\(866\) | 26.1410 | 0.888308 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10.2540 | 0.348045 | ||||||||
\(869\) | 22.2551 | 0.754952 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.0205143 | 0.000695102 0 | ||||||||
\(872\) | 3.72734 | 0.126224 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 48.6772 | 1.64653 | ||||||||
\(875\) | 72.3712 | 2.44659 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.1749 | −0.546189 | −0.273094 | − | 0.961987i | \(-0.588047\pi\) | ||||
−0.273094 | + | 0.961987i | \(0.588047\pi\) | |||||||
\(878\) | −1.54942 | −0.0522904 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −19.8919 | −0.670556 | ||||||||
\(881\) | 18.4187 | 0.620540 | 0.310270 | − | 0.950648i | \(-0.399581\pi\) | ||||
0.310270 | + | 0.950648i | \(0.399581\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.7770 | 0.665547 | 0.332774 | − | 0.943007i | \(-0.392015\pi\) | ||||
0.332774 | + | 0.943007i | \(0.392015\pi\) | |||||||
\(884\) | −0.287206 | −0.00965979 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.35831 | 0.247207 | ||||||||
\(887\) | −29.2805 | −0.983143 | −0.491571 | − | 0.870837i | \(-0.663577\pi\) | ||||
−0.491571 | + | 0.870837i | \(0.663577\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37.4407 | −1.25572 | ||||||||
\(890\) | 66.2472 | 2.22061 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.36433 | −0.179611 | ||||||||
\(893\) | 46.0637 | 1.54146 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −79.0888 | −2.64365 | ||||||||
\(896\) | −2.10378 | −0.0702825 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.07130 | −0.169232 | ||||||||
\(899\) | 39.3705 | 1.31308 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.285709 | 0.00951834 | ||||||||
\(902\) | −12.1090 | −0.403187 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −20.5365 | −0.683033 | ||||||||
\(905\) | 54.4222 | 1.80906 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.0299 | 0.366241 | 0.183120 | − | 0.983090i | \(-0.441380\pi\) | ||||
0.183120 | + | 0.983090i | \(0.441380\pi\) | |||||||
\(908\) | 11.7698 | 0.390594 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.89512 | −0.162272 | ||||||||
\(911\) | −46.2825 | −1.53341 | −0.766704 | − | 0.642001i | \(-0.778105\pi\) | ||||
−0.766704 | + | 0.642001i | \(0.778105\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.8647 | 1.08766 | ||||||||
\(914\) | −6.68190 | −0.221018 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −23.6187 | −0.780384 | ||||||||
\(917\) | 40.9680 | 1.35288 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.95357 | 0.0974293 | 0.0487146 | − | 0.998813i | \(-0.484488\pi\) | ||||
0.0487146 | + | 0.998813i | \(0.484488\pi\) | |||||||
\(920\) | −25.5248 | −0.841528 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17.6016 | 0.579678 | ||||||||
\(923\) | 7.15358 | 0.235463 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −132.731 | −4.36416 | ||||||||
\(926\) | −12.1244 | −0.398432 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.07750 | −0.265157 | ||||||||
\(929\) | −48.6223 | −1.59525 | −0.797623 | − | 0.603156i | \(-0.793910\pi\) | ||||
−0.797623 | + | 0.603156i | \(0.793910\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.8779 | 0.684246 | ||||||||
\(932\) | 27.4243 | 0.898312 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 32.6155 | 1.06721 | ||||||||
\(935\) | 10.4426 | 0.341509 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.4395 | 0.406380 | 0.203190 | − | 0.979139i | \(-0.434869\pi\) | ||||
0.203190 | + | 0.979139i | \(0.434869\pi\) | |||||||
\(938\) | −0.0788855 | −0.00257570 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −24.1544 | −0.787828 | ||||||||
\(941\) | −14.0582 | −0.458283 | −0.229142 | − | 0.973393i | \(-0.573592\pi\) | ||||
−0.229142 | + | 0.973393i | \(0.573592\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.5380 | −0.505988 | ||||||||
\(944\) | 7.68172 | 0.250019 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 36.1223 | 1.17444 | ||||||||
\(947\) | −9.24375 | −0.300382 | −0.150191 | − | 0.988657i | \(-0.547989\pi\) | ||||
−0.150191 | + | 0.988657i | \(0.547989\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.82635 | 0.254054 | ||||||||
\(950\) | 106.158 | 3.44421 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.10442 | 0.0357944 | ||||||||
\(953\) | 8.96912 | 0.290538 | 0.145269 | − | 0.989392i | \(-0.453595\pi\) | ||||
0.145269 | + | 0.989392i | \(0.453595\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.2931 | −0.786105 | ||||||||
\(956\) | −19.9867 | −0.646416 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26.8635 | −0.867920 | ||||||||
\(959\) | 18.4835 | 0.596863 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.24318 | −0.233651 | ||||||||
\(962\) | 5.54812 | 0.178879 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.69539 | 0.0546047 | ||||||||
\(965\) | 24.9053 | 0.801731 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.7749 | −0.668074 | −0.334037 | − | 0.942560i | \(-0.608411\pi\) | ||||
−0.334037 | + | 0.942560i | \(0.608411\pi\) | |||||||
\(968\) | −10.8752 | −0.349541 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −37.9009 | −1.21693 | ||||||||
\(971\) | −30.2800 | −0.971731 | −0.485865 | − | 0.874034i | \(-0.661495\pi\) | ||||
−0.485865 | + | 0.874034i | \(0.661495\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.75612 | 0.184533 | ||||||||
\(974\) | −35.2025 | −1.12796 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.68590 | 0.117983 | ||||||||
\(977\) | 3.60470 | 0.115325 | 0.0576623 | − | 0.998336i | \(-0.481635\pi\) | ||||
0.0576623 | + | 0.998336i | \(0.481635\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 72.8522 | 2.32837 | ||||||||
\(980\) | −10.9477 | −0.349713 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.8169 | −0.440915 | ||||||||
\(983\) | 5.97607 | 0.190607 | 0.0953036 | − | 0.995448i | \(-0.469618\pi\) | ||||
0.0953036 | + | 0.995448i | \(0.469618\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 88.2018 | 2.81034 | ||||||||
\(986\) | 4.24042 | 0.135043 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.43736 | −0.141171 | ||||||||
\(989\) | 46.3513 | 1.47389 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.9520 | 0.919691 | 0.459845 | − | 0.887999i | \(-0.347905\pi\) | ||||
0.459845 | + | 0.887999i | \(0.347905\pi\) | |||||||
\(992\) | −4.87410 | −0.154753 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −27.5082 | −0.872509 | ||||||||
\(995\) | −4.86996 | −0.154388 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.17728 | 0.227307 | 0.113653 | − | 0.993520i | \(-0.463745\pi\) | ||||
0.113653 | + | 0.993520i | \(0.463745\pi\) | |||||||
\(998\) | 29.5985 | 0.936924 | ||||||||
\(999\) | 0 | 0 |
(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 | 8046.2.a.l.1.12 | ✓ | 12 | |
3.2 | odd | 2 | 8046.2.a.m.1.1 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.l.1.12 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8046.2.a.m.1.1 | yes | 12 | 3.2 | odd | 2 |