Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [209,2,Mod(1,209)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(209, 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("209.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 209 = 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 209.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: | \(1.66887340224\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 209.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | 0.414214 | 0.239146 | 0.119573 | − | 0.992825i | \(-0.461847\pi\) | ||||
0.119573 | + | 0.992825i | \(0.461847\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | −0.223607 | − | 0.974679i | \(-0.571783\pi\) | ||||
−0.223607 | + | 0.974679i | \(0.571783\pi\) | |||||||
\(6\) | −0.585786 | −0.239146 | ||||||||
\(7\) | −0.585786 | −0.221406 | −0.110703 | − | 0.993854i | \(-0.535310\pi\) | ||||
−0.110703 | + | 0.993854i | \(0.535310\pi\) | |||||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | 1.41421 | 0.447214 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.24264 | −1.73140 | −0.865699 | − | 0.500566i | \(-0.833125\pi\) | ||||
−0.865699 | + | 0.500566i | \(0.833125\pi\) | |||||||
\(14\) | 0.828427 | 0.221406 | ||||||||
\(15\) | −0.414214 | −0.106949 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 0.585786 | 0.142074 | 0.0710370 | − | 0.997474i | \(-0.477369\pi\) | ||||
0.0710370 | + | 0.997474i | \(0.477369\pi\) | |||||||
\(18\) | 4.00000 | 0.942809 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.242641 | −0.0529485 | ||||||||
\(22\) | 1.41421 | 0.301511 | ||||||||
\(23\) | −3.00000 | −0.625543 | −0.312772 | − | 0.949828i | \(-0.601257\pi\) | ||||
−0.312772 | + | 0.949828i | \(0.601257\pi\) | |||||||
\(24\) | 1.17157 | 0.239146 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 8.82843 | 1.73140 | ||||||||
\(27\) | −2.41421 | −0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.24264 | 0.416448 | 0.208224 | − | 0.978081i | \(-0.433232\pi\) | ||||
0.208224 | + | 0.978081i | \(0.433232\pi\) | |||||||
\(30\) | 0.585786 | 0.106949 | ||||||||
\(31\) | −3.58579 | −0.644026 | −0.322013 | − | 0.946735i | \(-0.604360\pi\) | ||||
−0.322013 | + | 0.946735i | \(0.604360\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.414214 | −0.0721053 | ||||||||
\(34\) | −0.828427 | −0.142074 | ||||||||
\(35\) | 0.585786 | 0.0990160 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.07107 | −0.669279 | −0.334640 | − | 0.942346i | \(-0.608615\pi\) | ||||
−0.334640 | + | 0.942346i | \(0.608615\pi\) | |||||||
\(38\) | 1.41421 | 0.229416 | ||||||||
\(39\) | −2.58579 | −0.414057 | ||||||||
\(40\) | −2.82843 | −0.447214 | ||||||||
\(41\) | 9.65685 | 1.50815 | 0.754074 | − | 0.656790i | \(-0.228086\pi\) | ||||
0.754074 | + | 0.656790i | \(0.228086\pi\) | |||||||
\(42\) | 0.343146 | 0.0529485 | ||||||||
\(43\) | 11.6569 | 1.77765 | 0.888827 | − | 0.458243i | \(-0.151521\pi\) | ||||
0.888827 | + | 0.458243i | \(0.151521\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.82843 | 0.421637 | ||||||||
\(46\) | 4.24264 | 0.625543 | ||||||||
\(47\) | 3.17157 | 0.462621 | 0.231311 | − | 0.972880i | \(-0.425699\pi\) | ||||
0.231311 | + | 0.972880i | \(0.425699\pi\) | |||||||
\(48\) | −1.65685 | −0.239146 | ||||||||
\(49\) | −6.65685 | −0.950979 | ||||||||
\(50\) | 5.65685 | 0.800000 | ||||||||
\(51\) | 0.242641 | 0.0339765 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.4853 | 1.71499 | 0.857493 | − | 0.514496i | \(-0.172021\pi\) | ||||
0.857493 | + | 0.514496i | \(0.172021\pi\) | |||||||
\(54\) | 3.41421 | 0.464616 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | −1.65685 | −0.221406 | ||||||||
\(57\) | −0.414214 | −0.0548639 | ||||||||
\(58\) | −3.17157 | −0.416448 | ||||||||
\(59\) | −4.41421 | −0.574682 | −0.287341 | − | 0.957828i | \(-0.592771\pi\) | ||||
−0.287341 | + | 0.957828i | \(0.592771\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.07107 | 0.393210 | 0.196605 | − | 0.980483i | \(-0.437008\pi\) | ||||
0.196605 | + | 0.980483i | \(0.437008\pi\) | |||||||
\(62\) | 5.07107 | 0.644026 | ||||||||
\(63\) | 1.65685 | 0.208744 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 6.24264 | 0.774304 | ||||||||
\(66\) | 0.585786 | 0.0721053 | ||||||||
\(67\) | −7.58579 | −0.926751 | −0.463376 | − | 0.886162i | \(-0.653362\pi\) | ||||
−0.463376 | + | 0.886162i | \(0.653362\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.24264 | −0.149596 | ||||||||
\(70\) | −0.828427 | −0.0990160 | ||||||||
\(71\) | −9.58579 | −1.13762 | −0.568812 | − | 0.822468i | \(-0.692597\pi\) | ||||
−0.568812 | + | 0.822468i | \(0.692597\pi\) | |||||||
\(72\) | −8.00000 | −0.942809 | ||||||||
\(73\) | 12.4853 | 1.46129 | 0.730646 | − | 0.682757i | \(-0.239219\pi\) | ||||
0.730646 | + | 0.682757i | \(0.239219\pi\) | |||||||
\(74\) | 5.75736 | 0.669279 | ||||||||
\(75\) | −1.65685 | −0.191317 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.585786 | 0.0667566 | ||||||||
\(78\) | 3.65685 | 0.414057 | ||||||||
\(79\) | −17.4142 | −1.95925 | −0.979626 | − | 0.200830i | \(-0.935636\pi\) | ||||
−0.979626 | + | 0.200830i | \(0.935636\pi\) | |||||||
\(80\) | 4.00000 | 0.447214 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | −13.6569 | −1.50815 | ||||||||
\(83\) | 0.585786 | 0.0642984 | 0.0321492 | − | 0.999483i | \(-0.489765\pi\) | ||||
0.0321492 | + | 0.999483i | \(0.489765\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.585786 | −0.0635375 | ||||||||
\(86\) | −16.4853 | −1.77765 | ||||||||
\(87\) | 0.928932 | 0.0995920 | ||||||||
\(88\) | −2.82843 | −0.301511 | ||||||||
\(89\) | −14.8995 | −1.57934 | −0.789672 | − | 0.613530i | \(-0.789749\pi\) | ||||
−0.789672 | + | 0.613530i | \(0.789749\pi\) | |||||||
\(90\) | −4.00000 | −0.421637 | ||||||||
\(91\) | 3.65685 | 0.383342 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.48528 | −0.154017 | ||||||||
\(94\) | −4.48528 | −0.462621 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.414214 | −0.0420570 | −0.0210285 | − | 0.999779i | \(-0.506694\pi\) | ||||
−0.0210285 | + | 0.999779i | \(0.506694\pi\) | |||||||
\(98\) | 9.41421 | 0.950979 | ||||||||
\(99\) | 2.82843 | 0.284268 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.24264 | −0.223151 | −0.111576 | − | 0.993756i | \(-0.535590\pi\) | ||||
−0.111576 | + | 0.993756i | \(0.535590\pi\) | |||||||
\(102\) | −0.343146 | −0.0339765 | ||||||||
\(103\) | 2.34315 | 0.230877 | 0.115439 | − | 0.993315i | \(-0.463173\pi\) | ||||
0.115439 | + | 0.993315i | \(0.463173\pi\) | |||||||
\(104\) | −17.6569 | −1.73140 | ||||||||
\(105\) | 0.242641 | 0.0236793 | ||||||||
\(106\) | −17.6569 | −1.71499 | ||||||||
\(107\) | 4.34315 | 0.419868 | 0.209934 | − | 0.977716i | \(-0.432675\pi\) | ||||
0.209934 | + | 0.977716i | \(0.432675\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.6569 | −1.11652 | −0.558262 | − | 0.829665i | \(-0.688532\pi\) | ||||
−0.558262 | + | 0.829665i | \(0.688532\pi\) | |||||||
\(110\) | −1.41421 | −0.134840 | ||||||||
\(111\) | −1.68629 | −0.160056 | ||||||||
\(112\) | 2.34315 | 0.221406 | ||||||||
\(113\) | −6.41421 | −0.603398 | −0.301699 | − | 0.953403i | \(-0.597554\pi\) | ||||
−0.301699 | + | 0.953403i | \(0.597554\pi\) | |||||||
\(114\) | 0.585786 | 0.0548639 | ||||||||
\(115\) | 3.00000 | 0.279751 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17.6569 | 1.63238 | ||||||||
\(118\) | 6.24264 | 0.574682 | ||||||||
\(119\) | −0.343146 | −0.0314561 | ||||||||
\(120\) | −1.17157 | −0.106949 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −4.34315 | −0.393210 | ||||||||
\(123\) | 4.00000 | 0.360668 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | −2.34315 | −0.208744 | ||||||||
\(127\) | −16.5858 | −1.47175 | −0.735875 | − | 0.677117i | \(-0.763229\pi\) | ||||
−0.735875 | + | 0.677117i | \(0.763229\pi\) | |||||||
\(128\) | −11.3137 | −1.00000 | ||||||||
\(129\) | 4.82843 | 0.425119 | ||||||||
\(130\) | −8.82843 | −0.774304 | ||||||||
\(131\) | −2.48528 | −0.217140 | −0.108570 | − | 0.994089i | \(-0.534627\pi\) | ||||
−0.108570 | + | 0.994089i | \(0.534627\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.585786 | 0.0507941 | ||||||||
\(134\) | 10.7279 | 0.926751 | ||||||||
\(135\) | 2.41421 | 0.207782 | ||||||||
\(136\) | 1.65685 | 0.142074 | ||||||||
\(137\) | 8.65685 | 0.739605 | 0.369802 | − | 0.929110i | \(-0.379425\pi\) | ||||
0.369802 | + | 0.929110i | \(0.379425\pi\) | |||||||
\(138\) | 1.75736 | 0.149596 | ||||||||
\(139\) | −16.3848 | −1.38974 | −0.694869 | − | 0.719136i | \(-0.744538\pi\) | ||||
−0.694869 | + | 0.719136i | \(0.744538\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.31371 | 0.110634 | ||||||||
\(142\) | 13.5563 | 1.13762 | ||||||||
\(143\) | 6.24264 | 0.522036 | ||||||||
\(144\) | 11.3137 | 0.942809 | ||||||||
\(145\) | −2.24264 | −0.186241 | ||||||||
\(146\) | −17.6569 | −1.46129 | ||||||||
\(147\) | −2.75736 | −0.227423 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.31371 | −0.107623 | −0.0538116 | − | 0.998551i | \(-0.517137\pi\) | ||||
−0.0538116 | + | 0.998551i | \(0.517137\pi\) | |||||||
\(150\) | 2.34315 | 0.191317 | ||||||||
\(151\) | 6.48528 | 0.527765 | 0.263882 | − | 0.964555i | \(-0.414997\pi\) | ||||
0.263882 | + | 0.964555i | \(0.414997\pi\) | |||||||
\(152\) | −2.82843 | −0.229416 | ||||||||
\(153\) | −1.65685 | −0.133949 | ||||||||
\(154\) | −0.828427 | −0.0667566 | ||||||||
\(155\) | 3.58579 | 0.288017 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.00000 | 0.399043 | 0.199522 | − | 0.979893i | \(-0.436061\pi\) | ||||
0.199522 | + | 0.979893i | \(0.436061\pi\) | |||||||
\(158\) | 24.6274 | 1.95925 | ||||||||
\(159\) | 5.17157 | 0.410132 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.75736 | 0.138499 | ||||||||
\(162\) | −10.5858 | −0.831698 | ||||||||
\(163\) | 8.14214 | 0.637741 | 0.318871 | − | 0.947798i | \(-0.396696\pi\) | ||||
0.318871 | + | 0.947798i | \(0.396696\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.414214 | 0.0322465 | ||||||||
\(166\) | −0.828427 | −0.0642984 | ||||||||
\(167\) | 6.72792 | 0.520622 | 0.260311 | − | 0.965525i | \(-0.416175\pi\) | ||||
0.260311 | + | 0.965525i | \(0.416175\pi\) | |||||||
\(168\) | −0.686292 | −0.0529485 | ||||||||
\(169\) | 25.9706 | 1.99774 | ||||||||
\(170\) | 0.828427 | 0.0635375 | ||||||||
\(171\) | 2.82843 | 0.216295 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.8995 | −1.36087 | −0.680437 | − | 0.732807i | \(-0.738210\pi\) | ||||
−0.680437 | + | 0.732807i | \(0.738210\pi\) | |||||||
\(174\) | −1.31371 | −0.0995920 | ||||||||
\(175\) | 2.34315 | 0.177125 | ||||||||
\(176\) | 4.00000 | 0.301511 | ||||||||
\(177\) | −1.82843 | −0.137433 | ||||||||
\(178\) | 21.0711 | 1.57934 | ||||||||
\(179\) | 1.92893 | 0.144175 | 0.0720876 | − | 0.997398i | \(-0.477034\pi\) | ||||
0.0720876 | + | 0.997398i | \(0.477034\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3848 | 1.29220 | 0.646100 | − | 0.763253i | \(-0.276399\pi\) | ||||
0.646100 | + | 0.763253i | \(0.276399\pi\) | |||||||
\(182\) | −5.17157 | −0.383342 | ||||||||
\(183\) | 1.27208 | 0.0940347 | ||||||||
\(184\) | −8.48528 | −0.625543 | ||||||||
\(185\) | 4.07107 | 0.299311 | ||||||||
\(186\) | 2.10051 | 0.154017 | ||||||||
\(187\) | −0.585786 | −0.0428369 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.41421 | 0.102869 | ||||||||
\(190\) | −1.41421 | −0.102598 | ||||||||
\(191\) | −14.3137 | −1.03570 | −0.517852 | − | 0.855470i | \(-0.673268\pi\) | ||||
−0.517852 | + | 0.855470i | \(0.673268\pi\) | |||||||
\(192\) | 3.31371 | 0.239146 | ||||||||
\(193\) | 6.82843 | 0.491521 | 0.245760 | − | 0.969331i | \(-0.420962\pi\) | ||||
0.245760 | + | 0.969331i | \(0.420962\pi\) | |||||||
\(194\) | 0.585786 | 0.0420570 | ||||||||
\(195\) | 2.58579 | 0.185172 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.89949 | −0.277828 | −0.138914 | − | 0.990304i | \(-0.544361\pi\) | ||||
−0.138914 | + | 0.990304i | \(0.544361\pi\) | |||||||
\(198\) | −4.00000 | −0.284268 | ||||||||
\(199\) | −16.1421 | −1.14429 | −0.572143 | − | 0.820154i | \(-0.693888\pi\) | ||||
−0.572143 | + | 0.820154i | \(0.693888\pi\) | |||||||
\(200\) | −11.3137 | −0.800000 | ||||||||
\(201\) | −3.14214 | −0.221629 | ||||||||
\(202\) | 3.17157 | 0.223151 | ||||||||
\(203\) | −1.31371 | −0.0922043 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.65685 | −0.674464 | ||||||||
\(206\) | −3.31371 | −0.230877 | ||||||||
\(207\) | 8.48528 | 0.589768 | ||||||||
\(208\) | 24.9706 | 1.73140 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | −0.343146 | −0.0236793 | ||||||||
\(211\) | −15.4142 | −1.06116 | −0.530579 | − | 0.847635i | \(-0.678026\pi\) | ||||
−0.530579 | + | 0.847635i | \(0.678026\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.97056 | −0.272058 | ||||||||
\(214\) | −6.14214 | −0.419868 | ||||||||
\(215\) | −11.6569 | −0.794991 | ||||||||
\(216\) | −6.82843 | −0.464616 | ||||||||
\(217\) | 2.10051 | 0.142592 | ||||||||
\(218\) | 16.4853 | 1.11652 | ||||||||
\(219\) | 5.17157 | 0.349463 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.65685 | −0.245987 | ||||||||
\(222\) | 2.38478 | 0.160056 | ||||||||
\(223\) | −13.5858 | −0.909772 | −0.454886 | − | 0.890550i | \(-0.650320\pi\) | ||||
−0.454886 | + | 0.890550i | \(0.650320\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.3137 | 0.754247 | ||||||||
\(226\) | 9.07107 | 0.603398 | ||||||||
\(227\) | 19.0711 | 1.26579 | 0.632896 | − | 0.774237i | \(-0.281866\pi\) | ||||
0.632896 | + | 0.774237i | \(0.281866\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.31371 | 0.549385 | 0.274693 | − | 0.961532i | \(-0.411424\pi\) | ||||
0.274693 | + | 0.961532i | \(0.411424\pi\) | |||||||
\(230\) | −4.24264 | −0.279751 | ||||||||
\(231\) | 0.242641 | 0.0159646 | ||||||||
\(232\) | 6.34315 | 0.416448 | ||||||||
\(233\) | 8.24264 | 0.539993 | 0.269997 | − | 0.962861i | \(-0.412977\pi\) | ||||
0.269997 | + | 0.962861i | \(0.412977\pi\) | |||||||
\(234\) | −24.9706 | −1.63238 | ||||||||
\(235\) | −3.17157 | −0.206891 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.21320 | −0.468548 | ||||||||
\(238\) | 0.485281 | 0.0314561 | ||||||||
\(239\) | 6.00000 | 0.388108 | 0.194054 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(240\) | 1.65685 | 0.106949 | ||||||||
\(241\) | 16.9706 | 1.09317 | 0.546585 | − | 0.837404i | \(-0.315928\pi\) | ||||
0.546585 | + | 0.837404i | \(0.315928\pi\) | |||||||
\(242\) | −1.41421 | −0.0909091 | ||||||||
\(243\) | 10.3431 | 0.663513 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.65685 | 0.425291 | ||||||||
\(246\) | −5.65685 | −0.360668 | ||||||||
\(247\) | 6.24264 | 0.397210 | ||||||||
\(248\) | −10.1421 | −0.644026 | ||||||||
\(249\) | 0.242641 | 0.0153767 | ||||||||
\(250\) | −12.7279 | −0.804984 | ||||||||
\(251\) | −22.6569 | −1.43009 | −0.715044 | − | 0.699079i | \(-0.753593\pi\) | ||||
−0.715044 | + | 0.699079i | \(0.753593\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.00000 | 0.188608 | ||||||||
\(254\) | 23.4558 | 1.47175 | ||||||||
\(255\) | −0.242641 | −0.0151947 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.8284 | −1.54875 | −0.774377 | − | 0.632724i | \(-0.781937\pi\) | ||||
−0.774377 | + | 0.632724i | \(0.781937\pi\) | |||||||
\(258\) | −6.82843 | −0.425119 | ||||||||
\(259\) | 2.38478 | 0.148183 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.34315 | −0.392631 | ||||||||
\(262\) | 3.51472 | 0.217140 | ||||||||
\(263\) | −26.4853 | −1.63315 | −0.816576 | − | 0.577238i | \(-0.804131\pi\) | ||||
−0.816576 | + | 0.577238i | \(0.804131\pi\) | |||||||
\(264\) | −1.17157 | −0.0721053 | ||||||||
\(265\) | −12.4853 | −0.766965 | ||||||||
\(266\) | −0.828427 | −0.0507941 | ||||||||
\(267\) | −6.17157 | −0.377694 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.00000 | −0.121942 | −0.0609711 | − | 0.998140i | \(-0.519420\pi\) | ||||
−0.0609711 | + | 0.998140i | \(0.519420\pi\) | |||||||
\(270\) | −3.41421 | −0.207782 | ||||||||
\(271\) | −22.1421 | −1.34504 | −0.672519 | − | 0.740079i | \(-0.734788\pi\) | ||||
−0.672519 | + | 0.740079i | \(0.734788\pi\) | |||||||
\(272\) | −2.34315 | −0.142074 | ||||||||
\(273\) | 1.51472 | 0.0916749 | ||||||||
\(274\) | −12.2426 | −0.739605 | ||||||||
\(275\) | 4.00000 | 0.241209 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.4853 | 0.870336 | 0.435168 | − | 0.900349i | \(-0.356689\pi\) | ||||
0.435168 | + | 0.900349i | \(0.356689\pi\) | |||||||
\(278\) | 23.1716 | 1.38974 | ||||||||
\(279\) | 10.1421 | 0.607194 | ||||||||
\(280\) | 1.65685 | 0.0990160 | ||||||||
\(281\) | 12.3431 | 0.736330 | 0.368165 | − | 0.929760i | \(-0.379986\pi\) | ||||
0.368165 | + | 0.929760i | \(0.379986\pi\) | |||||||
\(282\) | −1.85786 | −0.110634 | ||||||||
\(283\) | 8.72792 | 0.518821 | 0.259411 | − | 0.965767i | \(-0.416472\pi\) | ||||
0.259411 | + | 0.965767i | \(0.416472\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.414214 | 0.0245359 | ||||||||
\(286\) | −8.82843 | −0.522036 | ||||||||
\(287\) | −5.65685 | −0.333914 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6569 | −0.979815 | ||||||||
\(290\) | 3.17157 | 0.186241 | ||||||||
\(291\) | −0.171573 | −0.0100578 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.6985 | 1.61816 | 0.809081 | − | 0.587697i | \(-0.199965\pi\) | ||||
0.809081 | + | 0.587697i | \(0.199965\pi\) | |||||||
\(294\) | 3.89949 | 0.227423 | ||||||||
\(295\) | 4.41421 | 0.257005 | ||||||||
\(296\) | −11.5147 | −0.669279 | ||||||||
\(297\) | 2.41421 | 0.140087 | ||||||||
\(298\) | 1.85786 | 0.107623 | ||||||||
\(299\) | 18.7279 | 1.08306 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.82843 | −0.393584 | ||||||||
\(302\) | −9.17157 | −0.527765 | ||||||||
\(303\) | −0.928932 | −0.0533658 | ||||||||
\(304\) | 4.00000 | 0.229416 | ||||||||
\(305\) | −3.07107 | −0.175849 | ||||||||
\(306\) | 2.34315 | 0.133949 | ||||||||
\(307\) | 4.58579 | 0.261725 | 0.130862 | − | 0.991401i | \(-0.458225\pi\) | ||||
0.130862 | + | 0.991401i | \(0.458225\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.970563 | 0.0552134 | ||||||||
\(310\) | −5.07107 | −0.288017 | ||||||||
\(311\) | −0.343146 | −0.0194580 | −0.00972901 | − | 0.999953i | \(-0.503097\pi\) | ||||
−0.00972901 | + | 0.999953i | \(0.503097\pi\) | |||||||
\(312\) | −7.31371 | −0.414057 | ||||||||
\(313\) | 19.9706 | 1.12880 | 0.564401 | − | 0.825500i | \(-0.309107\pi\) | ||||
0.564401 | + | 0.825500i | \(0.309107\pi\) | |||||||
\(314\) | −7.07107 | −0.399043 | ||||||||
\(315\) | −1.65685 | −0.0933532 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.5858 | −1.43704 | −0.718520 | − | 0.695506i | \(-0.755180\pi\) | ||||
−0.718520 | + | 0.695506i | \(0.755180\pi\) | |||||||
\(318\) | −7.31371 | −0.410132 | ||||||||
\(319\) | −2.24264 | −0.125564 | ||||||||
\(320\) | −8.00000 | −0.447214 | ||||||||
\(321\) | 1.79899 | 0.100410 | ||||||||
\(322\) | −2.48528 | −0.138499 | ||||||||
\(323\) | −0.585786 | −0.0325940 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.9706 | 1.38512 | ||||||||
\(326\) | −11.5147 | −0.637741 | ||||||||
\(327\) | −4.82843 | −0.267013 | ||||||||
\(328\) | 27.3137 | 1.50815 | ||||||||
\(329\) | −1.85786 | −0.102427 | ||||||||
\(330\) | −0.585786 | −0.0322465 | ||||||||
\(331\) | −8.21320 | −0.451438 | −0.225719 | − | 0.974192i | \(-0.572473\pi\) | ||||
−0.225719 | + | 0.974192i | \(0.572473\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.5147 | 0.631003 | ||||||||
\(334\) | −9.51472 | −0.520622 | ||||||||
\(335\) | 7.58579 | 0.414456 | ||||||||
\(336\) | 0.970563 | 0.0529485 | ||||||||
\(337\) | −8.72792 | −0.475440 | −0.237720 | − | 0.971334i | \(-0.576400\pi\) | ||||
−0.237720 | + | 0.971334i | \(0.576400\pi\) | |||||||
\(338\) | −36.7279 | −1.99774 | ||||||||
\(339\) | −2.65685 | −0.144301 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.58579 | 0.194181 | ||||||||
\(342\) | −4.00000 | −0.216295 | ||||||||
\(343\) | 8.00000 | 0.431959 | ||||||||
\(344\) | 32.9706 | 1.77765 | ||||||||
\(345\) | 1.24264 | 0.0669015 | ||||||||
\(346\) | 25.3137 | 1.36087 | ||||||||
\(347\) | −25.6985 | −1.37957 | −0.689783 | − | 0.724016i | \(-0.742294\pi\) | ||||
−0.689783 | + | 0.724016i | \(0.742294\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.2132 | −1.02846 | −0.514230 | − | 0.857653i | \(-0.671922\pi\) | ||||
−0.514230 | + | 0.857653i | \(0.671922\pi\) | |||||||
\(350\) | −3.31371 | −0.177125 | ||||||||
\(351\) | 15.0711 | 0.804434 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.68629 | −0.0897522 | −0.0448761 | − | 0.998993i | \(-0.514289\pi\) | ||||
−0.0448761 | + | 0.998993i | \(0.514289\pi\) | |||||||
\(354\) | 2.58579 | 0.137433 | ||||||||
\(355\) | 9.58579 | 0.508761 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.142136 | −0.00752261 | ||||||||
\(358\) | −2.72792 | −0.144175 | ||||||||
\(359\) | −0.485281 | −0.0256122 | −0.0128061 | − | 0.999918i | \(-0.504076\pi\) | ||||
−0.0128061 | + | 0.999918i | \(0.504076\pi\) | |||||||
\(360\) | 8.00000 | 0.421637 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −24.5858 | −1.29220 | ||||||||
\(363\) | 0.414214 | 0.0217406 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.4853 | −0.653509 | ||||||||
\(366\) | −1.79899 | −0.0940347 | ||||||||
\(367\) | −4.17157 | −0.217754 | −0.108877 | − | 0.994055i | \(-0.534726\pi\) | ||||
−0.108877 | + | 0.994055i | \(0.534726\pi\) | |||||||
\(368\) | 12.0000 | 0.625543 | ||||||||
\(369\) | −27.3137 | −1.42189 | ||||||||
\(370\) | −5.75736 | −0.299311 | ||||||||
\(371\) | −7.31371 | −0.379709 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.3137 | −1.31069 | −0.655347 | − | 0.755328i | \(-0.727478\pi\) | ||||
−0.655347 | + | 0.755328i | \(0.727478\pi\) | |||||||
\(374\) | 0.828427 | 0.0428369 | ||||||||
\(375\) | 3.72792 | 0.192509 | ||||||||
\(376\) | 8.97056 | 0.462621 | ||||||||
\(377\) | −14.0000 | −0.721037 | ||||||||
\(378\) | −2.00000 | −0.102869 | ||||||||
\(379\) | 28.6985 | 1.47414 | 0.737071 | − | 0.675815i | \(-0.236208\pi\) | ||||
0.737071 | + | 0.675815i | \(0.236208\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.87006 | −0.351964 | ||||||||
\(382\) | 20.2426 | 1.03570 | ||||||||
\(383\) | −31.5269 | −1.61095 | −0.805475 | − | 0.592630i | \(-0.798090\pi\) | ||||
−0.805475 | + | 0.592630i | \(0.798090\pi\) | |||||||
\(384\) | −4.68629 | −0.239146 | ||||||||
\(385\) | −0.585786 | −0.0298544 | ||||||||
\(386\) | −9.65685 | −0.491521 | ||||||||
\(387\) | −32.9706 | −1.67599 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.68629 | −0.288306 | −0.144153 | − | 0.989555i | \(-0.546046\pi\) | ||||
−0.144153 | + | 0.989555i | \(0.546046\pi\) | |||||||
\(390\) | −3.65685 | −0.185172 | ||||||||
\(391\) | −1.75736 | −0.0888735 | ||||||||
\(392\) | −18.8284 | −0.950979 | ||||||||
\(393\) | −1.02944 | −0.0519282 | ||||||||
\(394\) | 5.51472 | 0.277828 | ||||||||
\(395\) | 17.4142 | 0.876204 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.0000 | 1.30490 | 0.652451 | − | 0.757831i | \(-0.273741\pi\) | ||||
0.652451 | + | 0.757831i | \(0.273741\pi\) | |||||||
\(398\) | 22.8284 | 1.14429 | ||||||||
\(399\) | 0.242641 | 0.0121472 | ||||||||
\(400\) | 16.0000 | 0.800000 | ||||||||
\(401\) | −1.02944 | −0.0514076 | −0.0257038 | − | 0.999670i | \(-0.508183\pi\) | ||||
−0.0257038 | + | 0.999670i | \(0.508183\pi\) | |||||||
\(402\) | 4.44365 | 0.221629 | ||||||||
\(403\) | 22.3848 | 1.11507 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.48528 | −0.371947 | ||||||||
\(406\) | 1.85786 | 0.0922043 | ||||||||
\(407\) | 4.07107 | 0.201795 | ||||||||
\(408\) | 0.686292 | 0.0339765 | ||||||||
\(409\) | −24.7279 | −1.22272 | −0.611359 | − | 0.791354i | \(-0.709377\pi\) | ||||
−0.611359 | + | 0.791354i | \(0.709377\pi\) | |||||||
\(410\) | 13.6569 | 0.674464 | ||||||||
\(411\) | 3.58579 | 0.176874 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.58579 | 0.127238 | ||||||||
\(414\) | −12.0000 | −0.589768 | ||||||||
\(415\) | −0.585786 | −0.0287551 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.78680 | −0.332351 | ||||||||
\(418\) | −1.41421 | −0.0691714 | ||||||||
\(419\) | 23.4558 | 1.14589 | 0.572946 | − | 0.819593i | \(-0.305800\pi\) | ||||
0.572946 | + | 0.819593i | \(0.305800\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.142136 | 0.00692727 | 0.00346363 | − | 0.999994i | \(-0.498897\pi\) | ||||
0.00346363 | + | 0.999994i | \(0.498897\pi\) | |||||||
\(422\) | 21.7990 | 1.06116 | ||||||||
\(423\) | −8.97056 | −0.436164 | ||||||||
\(424\) | 35.3137 | 1.71499 | ||||||||
\(425\) | −2.34315 | −0.113659 | ||||||||
\(426\) | 5.61522 | 0.272058 | ||||||||
\(427\) | −1.79899 | −0.0870592 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.58579 | 0.124843 | ||||||||
\(430\) | 16.4853 | 0.794991 | ||||||||
\(431\) | 13.5147 | 0.650981 | 0.325491 | − | 0.945545i | \(-0.394471\pi\) | ||||
0.325491 | + | 0.945545i | \(0.394471\pi\) | |||||||
\(432\) | 9.65685 | 0.464616 | ||||||||
\(433\) | −25.3848 | −1.21991 | −0.609957 | − | 0.792434i | \(-0.708813\pi\) | ||||
−0.609957 | + | 0.792434i | \(0.708813\pi\) | |||||||
\(434\) | −2.97056 | −0.142592 | ||||||||
\(435\) | −0.928932 | −0.0445389 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.00000 | 0.143509 | ||||||||
\(438\) | −7.31371 | −0.349463 | ||||||||
\(439\) | −5.75736 | −0.274784 | −0.137392 | − | 0.990517i | \(-0.543872\pi\) | ||||
−0.137392 | + | 0.990517i | \(0.543872\pi\) | |||||||
\(440\) | 2.82843 | 0.134840 | ||||||||
\(441\) | 18.8284 | 0.896592 | ||||||||
\(442\) | 5.17157 | 0.245987 | ||||||||
\(443\) | 21.9706 | 1.04385 | 0.521926 | − | 0.852990i | \(-0.325214\pi\) | ||||
0.521926 | + | 0.852990i | \(0.325214\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.8995 | 0.706304 | ||||||||
\(446\) | 19.2132 | 0.909772 | ||||||||
\(447\) | −0.544156 | −0.0257377 | ||||||||
\(448\) | −4.68629 | −0.221406 | ||||||||
\(449\) | 23.3848 | 1.10360 | 0.551798 | − | 0.833978i | \(-0.313942\pi\) | ||||
0.551798 | + | 0.833978i | \(0.313942\pi\) | |||||||
\(450\) | −16.0000 | −0.754247 | ||||||||
\(451\) | −9.65685 | −0.454724 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.68629 | 0.126213 | ||||||||
\(454\) | −26.9706 | −1.26579 | ||||||||
\(455\) | −3.65685 | −0.171436 | ||||||||
\(456\) | −1.17157 | −0.0548639 | ||||||||
\(457\) | 31.0711 | 1.45344 | 0.726722 | − | 0.686932i | \(-0.241043\pi\) | ||||
0.726722 | + | 0.686932i | \(0.241043\pi\) | |||||||
\(458\) | −11.7574 | −0.549385 | ||||||||
\(459\) | −1.41421 | −0.0660098 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.9706 | −0.976696 | −0.488348 | − | 0.872649i | \(-0.662400\pi\) | ||||
−0.488348 | + | 0.872649i | \(0.662400\pi\) | |||||||
\(462\) | −0.343146 | −0.0159646 | ||||||||
\(463\) | −38.4558 | −1.78719 | −0.893597 | − | 0.448870i | \(-0.851827\pi\) | ||||
−0.893597 | + | 0.448870i | \(0.851827\pi\) | |||||||
\(464\) | −8.97056 | −0.416448 | ||||||||
\(465\) | 1.48528 | 0.0688783 | ||||||||
\(466\) | −11.6569 | −0.539993 | ||||||||
\(467\) | 32.3137 | 1.49530 | 0.747650 | − | 0.664093i | \(-0.231182\pi\) | ||||
0.747650 | + | 0.664093i | \(0.231182\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.44365 | 0.205189 | ||||||||
\(470\) | 4.48528 | 0.206891 | ||||||||
\(471\) | 2.07107 | 0.0954298 | ||||||||
\(472\) | −12.4853 | −0.574682 | ||||||||
\(473\) | −11.6569 | −0.535983 | ||||||||
\(474\) | 10.2010 | 0.468548 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −35.3137 | −1.61690 | ||||||||
\(478\) | −8.48528 | −0.388108 | ||||||||
\(479\) | 24.5269 | 1.12066 | 0.560332 | − | 0.828268i | \(-0.310674\pi\) | ||||
0.560332 | + | 0.828268i | \(0.310674\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.4142 | 1.15879 | ||||||||
\(482\) | −24.0000 | −1.09317 | ||||||||
\(483\) | 0.727922 | 0.0331216 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.414214 | 0.0188085 | ||||||||
\(486\) | −14.6274 | −0.663513 | ||||||||
\(487\) | −18.5563 | −0.840868 | −0.420434 | − | 0.907323i | \(-0.638122\pi\) | ||||
−0.420434 | + | 0.907323i | \(0.638122\pi\) | |||||||
\(488\) | 8.68629 | 0.393210 | ||||||||
\(489\) | 3.37258 | 0.152513 | ||||||||
\(490\) | −9.41421 | −0.425291 | ||||||||
\(491\) | 36.2426 | 1.63561 | 0.817804 | − | 0.575497i | \(-0.195191\pi\) | ||||
0.817804 | + | 0.575497i | \(0.195191\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.31371 | 0.0591665 | ||||||||
\(494\) | −8.82843 | −0.397210 | ||||||||
\(495\) | −2.82843 | −0.127128 | ||||||||
\(496\) | 14.3431 | 0.644026 | ||||||||
\(497\) | 5.61522 | 0.251877 | ||||||||
\(498\) | −0.343146 | −0.0153767 | ||||||||
\(499\) | 12.6274 | 0.565281 | 0.282640 | − | 0.959226i | \(-0.408790\pi\) | ||||
0.282640 | + | 0.959226i | \(0.408790\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.78680 | 0.124505 | ||||||||
\(502\) | 32.0416 | 1.43009 | ||||||||
\(503\) | 0.142136 | 0.00633751 | 0.00316876 | − | 0.999995i | \(-0.498991\pi\) | ||||
0.00316876 | + | 0.999995i | \(0.498991\pi\) | |||||||
\(504\) | 4.68629 | 0.208744 | ||||||||
\(505\) | 2.24264 | 0.0997962 | ||||||||
\(506\) | −4.24264 | −0.188608 | ||||||||
\(507\) | 10.7574 | 0.477751 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.2132 | 1.51647 | 0.758237 | − | 0.651979i | \(-0.226061\pi\) | ||||
0.758237 | + | 0.651979i | \(0.226061\pi\) | |||||||
\(510\) | 0.343146 | 0.0151947 | ||||||||
\(511\) | −7.31371 | −0.323539 | ||||||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | 2.41421 | 0.106590 | ||||||||
\(514\) | 35.1127 | 1.54875 | ||||||||
\(515\) | −2.34315 | −0.103251 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.17157 | −0.139486 | ||||||||
\(518\) | −3.37258 | −0.148183 | ||||||||
\(519\) | −7.41421 | −0.325448 | ||||||||
\(520\) | 17.6569 | 0.774304 | ||||||||
\(521\) | −30.5563 | −1.33870 | −0.669349 | − | 0.742948i | \(-0.733427\pi\) | ||||
−0.669349 | + | 0.742948i | \(0.733427\pi\) | |||||||
\(522\) | 8.97056 | 0.392631 | ||||||||
\(523\) | 13.6569 | 0.597173 | 0.298586 | − | 0.954383i | \(-0.403485\pi\) | ||||
0.298586 | + | 0.954383i | \(0.403485\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.970563 | 0.0423588 | ||||||||
\(526\) | 37.4558 | 1.63315 | ||||||||
\(527\) | −2.10051 | −0.0914994 | ||||||||
\(528\) | 1.65685 | 0.0721053 | ||||||||
\(529\) | −14.0000 | −0.608696 | ||||||||
\(530\) | 17.6569 | 0.766965 | ||||||||
\(531\) | 12.4853 | 0.541815 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −60.2843 | −2.61120 | ||||||||
\(534\) | 8.72792 | 0.377694 | ||||||||
\(535\) | −4.34315 | −0.187771 | ||||||||
\(536\) | −21.4558 | −0.926751 | ||||||||
\(537\) | 0.798990 | 0.0344790 | ||||||||
\(538\) | 2.82843 | 0.121942 | ||||||||
\(539\) | 6.65685 | 0.286731 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.2132 | −1.42795 | −0.713974 | − | 0.700173i | \(-0.753106\pi\) | ||||
−0.713974 | + | 0.700173i | \(0.753106\pi\) | |||||||
\(542\) | 31.3137 | 1.34504 | ||||||||
\(543\) | 7.20101 | 0.309025 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.6569 | 0.499325 | ||||||||
\(546\) | −2.14214 | −0.0916749 | ||||||||
\(547\) | 10.7279 | 0.458693 | 0.229346 | − | 0.973345i | \(-0.426341\pi\) | ||||
0.229346 | + | 0.973345i | \(0.426341\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.68629 | −0.370722 | ||||||||
\(550\) | −5.65685 | −0.241209 | ||||||||
\(551\) | −2.24264 | −0.0955397 | ||||||||
\(552\) | −3.51472 | −0.149596 | ||||||||
\(553\) | 10.2010 | 0.433791 | ||||||||
\(554\) | −20.4853 | −0.870336 | ||||||||
\(555\) | 1.68629 | 0.0715791 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.9411 | 1.69236 | 0.846180 | − | 0.532897i | \(-0.178897\pi\) | ||||
0.846180 | + | 0.532897i | \(0.178897\pi\) | |||||||
\(558\) | −14.3431 | −0.607194 | ||||||||
\(559\) | −72.7696 | −3.07782 | ||||||||
\(560\) | −2.34315 | −0.0990160 | ||||||||
\(561\) | −0.242641 | −0.0102443 | ||||||||
\(562\) | −17.4558 | −0.736330 | ||||||||
\(563\) | 19.2132 | 0.809740 | 0.404870 | − | 0.914374i | \(-0.367317\pi\) | ||||
0.404870 | + | 0.914374i | \(0.367317\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.41421 | 0.269848 | ||||||||
\(566\) | −12.3431 | −0.518821 | ||||||||
\(567\) | −4.38478 | −0.184143 | ||||||||
\(568\) | −27.1127 | −1.13762 | ||||||||
\(569\) | −17.7574 | −0.744427 | −0.372214 | − | 0.928147i | \(-0.621401\pi\) | ||||
−0.372214 | + | 0.928147i | \(0.621401\pi\) | |||||||
\(570\) | −0.585786 | −0.0245359 | ||||||||
\(571\) | −25.6985 | −1.07545 | −0.537724 | − | 0.843121i | \(-0.680716\pi\) | ||||
−0.537724 | + | 0.843121i | \(0.680716\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.92893 | −0.247685 | ||||||||
\(574\) | 8.00000 | 0.333914 | ||||||||
\(575\) | 12.0000 | 0.500435 | ||||||||
\(576\) | −22.6274 | −0.942809 | ||||||||
\(577\) | −3.97056 | −0.165297 | −0.0826483 | − | 0.996579i | \(-0.526338\pi\) | ||||
−0.0826483 | + | 0.996579i | \(0.526338\pi\) | |||||||
\(578\) | 23.5563 | 0.979815 | ||||||||
\(579\) | 2.82843 | 0.117545 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.343146 | −0.0142361 | ||||||||
\(582\) | 0.242641 | 0.0100578 | ||||||||
\(583\) | −12.4853 | −0.517088 | ||||||||
\(584\) | 35.3137 | 1.46129 | ||||||||
\(585\) | −17.6569 | −0.730021 | ||||||||
\(586\) | −39.1716 | −1.61816 | ||||||||
\(587\) | −3.65685 | −0.150935 | −0.0754673 | − | 0.997148i | \(-0.524045\pi\) | ||||
−0.0754673 | + | 0.997148i | \(0.524045\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.58579 | 0.147750 | ||||||||
\(590\) | −6.24264 | −0.257005 | ||||||||
\(591\) | −1.61522 | −0.0664414 | ||||||||
\(592\) | 16.2843 | 0.669279 | ||||||||
\(593\) | 3.02944 | 0.124404 | 0.0622020 | − | 0.998064i | \(-0.480188\pi\) | ||||
0.0622020 | + | 0.998064i | \(0.480188\pi\) | |||||||
\(594\) | −3.41421 | −0.140087 | ||||||||
\(595\) | 0.343146 | 0.0140676 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.68629 | −0.273652 | ||||||||
\(598\) | −26.4853 | −1.08306 | ||||||||
\(599\) | −9.31371 | −0.380548 | −0.190274 | − | 0.981731i | \(-0.560938\pi\) | ||||
−0.190274 | + | 0.981731i | \(0.560938\pi\) | |||||||
\(600\) | −4.68629 | −0.191317 | ||||||||
\(601\) | −19.5563 | −0.797720 | −0.398860 | − | 0.917012i | \(-0.630594\pi\) | ||||
−0.398860 | + | 0.917012i | \(0.630594\pi\) | |||||||
\(602\) | 9.65685 | 0.393584 | ||||||||
\(603\) | 21.4558 | 0.873750 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 1.31371 | 0.0533658 | ||||||||
\(607\) | −21.8995 | −0.888873 | −0.444437 | − | 0.895810i | \(-0.646596\pi\) | ||||
−0.444437 | + | 0.895810i | \(0.646596\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.544156 | −0.0220503 | ||||||||
\(610\) | 4.34315 | 0.175849 | ||||||||
\(611\) | −19.7990 | −0.800981 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.5858 | −0.427556 | −0.213778 | − | 0.976882i | \(-0.568577\pi\) | ||||
−0.213778 | + | 0.976882i | \(0.568577\pi\) | |||||||
\(614\) | −6.48528 | −0.261725 | ||||||||
\(615\) | −4.00000 | −0.161296 | ||||||||
\(616\) | 1.65685 | 0.0667566 | ||||||||
\(617\) | 17.1716 | 0.691301 | 0.345651 | − | 0.938363i | \(-0.387658\pi\) | ||||
0.345651 | + | 0.938363i | \(0.387658\pi\) | |||||||
\(618\) | −1.37258 | −0.0552134 | ||||||||
\(619\) | 6.51472 | 0.261849 | 0.130924 | − | 0.991392i | \(-0.458206\pi\) | ||||
0.130924 | + | 0.991392i | \(0.458206\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.24264 | 0.290637 | ||||||||
\(622\) | 0.485281 | 0.0194580 | ||||||||
\(623\) | 8.72792 | 0.349677 | ||||||||
\(624\) | 10.3431 | 0.414057 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | −28.2426 | −1.12880 | ||||||||
\(627\) | 0.414214 | 0.0165421 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.38478 | −0.0950873 | ||||||||
\(630\) | 2.34315 | 0.0933532 | ||||||||
\(631\) | −41.9706 | −1.67082 | −0.835411 | − | 0.549626i | \(-0.814770\pi\) | ||||
−0.835411 | + | 0.549626i | \(0.814770\pi\) | |||||||
\(632\) | −49.2548 | −1.95925 | ||||||||
\(633\) | −6.38478 | −0.253772 | ||||||||
\(634\) | 36.1838 | 1.43704 | ||||||||
\(635\) | 16.5858 | 0.658187 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 41.5563 | 1.64652 | ||||||||
\(638\) | 3.17157 | 0.125564 | ||||||||
\(639\) | 27.1127 | 1.07256 | ||||||||
\(640\) | 11.3137 | 0.447214 | ||||||||
\(641\) | −18.8995 | −0.746485 | −0.373243 | − | 0.927734i | \(-0.621754\pi\) | ||||
−0.373243 | + | 0.927734i | \(0.621754\pi\) | |||||||
\(642\) | −2.54416 | −0.100410 | ||||||||
\(643\) | 13.3431 | 0.526202 | 0.263101 | − | 0.964768i | \(-0.415255\pi\) | ||||
0.263101 | + | 0.964768i | \(0.415255\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.82843 | −0.190119 | ||||||||
\(646\) | 0.828427 | 0.0325940 | ||||||||
\(647\) | 36.9411 | 1.45231 | 0.726153 | − | 0.687533i | \(-0.241307\pi\) | ||||
0.726153 | + | 0.687533i | \(0.241307\pi\) | |||||||
\(648\) | 21.1716 | 0.831698 | ||||||||
\(649\) | 4.41421 | 0.173273 | ||||||||
\(650\) | −35.3137 | −1.38512 | ||||||||
\(651\) | 0.870058 | 0.0341002 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.4853 | −0.997316 | −0.498658 | − | 0.866799i | \(-0.666174\pi\) | ||||
−0.498658 | + | 0.866799i | \(0.666174\pi\) | |||||||
\(654\) | 6.82843 | 0.267013 | ||||||||
\(655\) | 2.48528 | 0.0971080 | ||||||||
\(656\) | −38.6274 | −1.50815 | ||||||||
\(657\) | −35.3137 | −1.37772 | ||||||||
\(658\) | 2.62742 | 0.102427 | ||||||||
\(659\) | −17.7990 | −0.693350 | −0.346675 | − | 0.937985i | \(-0.612689\pi\) | ||||
−0.346675 | + | 0.937985i | \(0.612689\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.87006 | 0.150528 | 0.0752639 | − | 0.997164i | \(-0.476020\pi\) | ||||
0.0752639 | + | 0.997164i | \(0.476020\pi\) | |||||||
\(662\) | 11.6152 | 0.451438 | ||||||||
\(663\) | −1.51472 | −0.0588268 | ||||||||
\(664\) | 1.65685 | 0.0642984 | ||||||||
\(665\) | −0.585786 | −0.0227158 | ||||||||
\(666\) | −16.2843 | −0.631003 | ||||||||
\(667\) | −6.72792 | −0.260506 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.62742 | −0.217569 | ||||||||
\(670\) | −10.7279 | −0.414456 | ||||||||
\(671\) | −3.07107 | −0.118557 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.1421 | −1.23899 | −0.619494 | − | 0.785001i | \(-0.712662\pi\) | ||||
−0.619494 | + | 0.785001i | \(0.712662\pi\) | |||||||
\(674\) | 12.3431 | 0.475440 | ||||||||
\(675\) | 9.65685 | 0.371692 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.31371 | −0.0504899 | −0.0252450 | − | 0.999681i | \(-0.508037\pi\) | ||||
−0.0252450 | + | 0.999681i | \(0.508037\pi\) | |||||||
\(678\) | 3.75736 | 0.144301 | ||||||||
\(679\) | 0.242641 | 0.00931169 | ||||||||
\(680\) | −1.65685 | −0.0635375 | ||||||||
\(681\) | 7.89949 | 0.302709 | ||||||||
\(682\) | −5.07107 | −0.194181 | ||||||||
\(683\) | −39.1127 | −1.49661 | −0.748303 | − | 0.663357i | \(-0.769131\pi\) | ||||
−0.748303 | + | 0.663357i | \(0.769131\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.65685 | −0.330761 | ||||||||
\(686\) | −11.3137 | −0.431959 | ||||||||
\(687\) | 3.44365 | 0.131383 | ||||||||
\(688\) | −46.6274 | −1.77765 | ||||||||
\(689\) | −77.9411 | −2.96932 | ||||||||
\(690\) | −1.75736 | −0.0669015 | ||||||||
\(691\) | −7.97056 | −0.303214 | −0.151607 | − | 0.988441i | \(-0.548445\pi\) | ||||
−0.151607 | + | 0.988441i | \(0.548445\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.65685 | −0.0629387 | ||||||||
\(694\) | 36.3431 | 1.37957 | ||||||||
\(695\) | 16.3848 | 0.621510 | ||||||||
\(696\) | 2.62742 | 0.0995920 | ||||||||
\(697\) | 5.65685 | 0.214269 | ||||||||
\(698\) | 27.1716 | 1.02846 | ||||||||
\(699\) | 3.41421 | 0.129137 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.3137 | 0.805008 | 0.402504 | − | 0.915418i | \(-0.368140\pi\) | ||||
0.402504 | + | 0.915418i | \(0.368140\pi\) | |||||||
\(702\) | −21.3137 | −0.804434 | ||||||||
\(703\) | 4.07107 | 0.153543 | ||||||||
\(704\) | −8.00000 | −0.301511 | ||||||||
\(705\) | −1.31371 | −0.0494771 | ||||||||
\(706\) | 2.38478 | 0.0897522 | ||||||||
\(707\) | 1.31371 | 0.0494071 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.2843 | 1.17491 | 0.587453 | − | 0.809258i | \(-0.300131\pi\) | ||||
0.587453 | + | 0.809258i | \(0.300131\pi\) | |||||||
\(710\) | −13.5563 | −0.508761 | ||||||||
\(711\) | 49.2548 | 1.84720 | ||||||||
\(712\) | −42.1421 | −1.57934 | ||||||||
\(713\) | 10.7574 | 0.402866 | ||||||||
\(714\) | 0.201010 | 0.00752261 | ||||||||
\(715\) | −6.24264 | −0.233462 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.48528 | 0.0928145 | ||||||||
\(718\) | 0.686292 | 0.0256122 | ||||||||
\(719\) | 43.9706 | 1.63983 | 0.819913 | − | 0.572489i | \(-0.194022\pi\) | ||||
0.819913 | + | 0.572489i | \(0.194022\pi\) | |||||||
\(720\) | −11.3137 | −0.421637 | ||||||||
\(721\) | −1.37258 | −0.0511177 | ||||||||
\(722\) | −1.41421 | −0.0526316 | ||||||||
\(723\) | 7.02944 | 0.261428 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.97056 | −0.333158 | ||||||||
\(726\) | −0.585786 | −0.0217406 | ||||||||
\(727\) | 44.1127 | 1.63605 | 0.818025 | − | 0.575183i | \(-0.195069\pi\) | ||||
0.818025 | + | 0.575183i | \(0.195069\pi\) | |||||||
\(728\) | 10.3431 | 0.383342 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | 17.6569 | 0.653509 | ||||||||
\(731\) | 6.82843 | 0.252559 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.5858 | 0.390995 | 0.195497 | − | 0.980704i | \(-0.437368\pi\) | ||||
0.195497 | + | 0.980704i | \(0.437368\pi\) | |||||||
\(734\) | 5.89949 | 0.217754 | ||||||||
\(735\) | 2.75736 | 0.101707 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.58579 | 0.279426 | ||||||||
\(738\) | 38.6274 | 1.42189 | ||||||||
\(739\) | −24.5858 | −0.904403 | −0.452201 | − | 0.891916i | \(-0.649361\pi\) | ||||
−0.452201 | + | 0.891916i | \(0.649361\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.58579 | 0.0949912 | ||||||||
\(742\) | 10.3431 | 0.379709 | ||||||||
\(743\) | −21.0711 | −0.773023 | −0.386511 | − | 0.922285i | \(-0.626320\pi\) | ||||
−0.386511 | + | 0.922285i | \(0.626320\pi\) | |||||||
\(744\) | −4.20101 | −0.154017 | ||||||||
\(745\) | 1.31371 | 0.0481306 | ||||||||
\(746\) | 35.7990 | 1.31069 | ||||||||
\(747\) | −1.65685 | −0.0606211 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.54416 | −0.0929614 | ||||||||
\(750\) | −5.27208 | −0.192509 | ||||||||
\(751\) | 34.5563 | 1.26098 | 0.630490 | − | 0.776198i | \(-0.282854\pi\) | ||||
0.630490 | + | 0.776198i | \(0.282854\pi\) | |||||||
\(752\) | −12.6863 | −0.462621 | ||||||||
\(753\) | −9.38478 | −0.342000 | ||||||||
\(754\) | 19.7990 | 0.721037 | ||||||||
\(755\) | −6.48528 | −0.236024 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.9411 | −0.942846 | −0.471423 | − | 0.881907i | \(-0.656260\pi\) | ||||
−0.471423 | + | 0.881907i | \(0.656260\pi\) | |||||||
\(758\) | −40.5858 | −1.47414 | ||||||||
\(759\) | 1.24264 | 0.0451050 | ||||||||
\(760\) | 2.82843 | 0.102598 | ||||||||
\(761\) | 34.1421 | 1.23765 | 0.618826 | − | 0.785528i | \(-0.287609\pi\) | ||||
0.618826 | + | 0.785528i | \(0.287609\pi\) | |||||||
\(762\) | 9.71573 | 0.351964 | ||||||||
\(763\) | 6.82843 | 0.247206 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.65685 | 0.0599037 | ||||||||
\(766\) | 44.5858 | 1.61095 | ||||||||
\(767\) | 27.5563 | 0.995002 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.1421 | 1.08695 | 0.543477 | − | 0.839424i | \(-0.317108\pi\) | ||||
0.543477 | + | 0.839424i | \(0.317108\pi\) | |||||||
\(770\) | 0.828427 | 0.0298544 | ||||||||
\(771\) | −10.2843 | −0.370379 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.34315 | 0.300082 | 0.150041 | − | 0.988680i | \(-0.452059\pi\) | ||||
0.150041 | + | 0.988680i | \(0.452059\pi\) | |||||||
\(774\) | 46.6274 | 1.67599 | ||||||||
\(775\) | 14.3431 | 0.515221 | ||||||||
\(776\) | −1.17157 | −0.0420570 | ||||||||
\(777\) | 0.987807 | 0.0354374 | ||||||||
\(778\) | 8.04163 | 0.288306 | ||||||||
\(779\) | −9.65685 | −0.345993 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.58579 | 0.343006 | ||||||||
\(782\) | 2.48528 | 0.0888735 | ||||||||
\(783\) | −5.41421 | −0.193488 | ||||||||
\(784\) | 26.6274 | 0.950979 | ||||||||
\(785\) | −5.00000 | −0.178458 | ||||||||
\(786\) | 1.45584 | 0.0519282 | ||||||||
\(787\) | 36.0000 | 1.28326 | 0.641631 | − | 0.767014i | \(-0.278258\pi\) | ||||
0.641631 | + | 0.767014i | \(0.278258\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.9706 | −0.390562 | ||||||||
\(790\) | −24.6274 | −0.876204 | ||||||||
\(791\) | 3.75736 | 0.133596 | ||||||||
\(792\) | 8.00000 | 0.284268 | ||||||||
\(793\) | −19.1716 | −0.680803 | ||||||||
\(794\) | −36.7696 | −1.30490 | ||||||||
\(795\) | −5.17157 | −0.183417 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.75736 | −0.168514 | −0.0842572 | − | 0.996444i | \(-0.526852\pi\) | ||||
−0.0842572 | + | 0.996444i | \(0.526852\pi\) | |||||||
\(798\) | −0.343146 | −0.0121472 | ||||||||
\(799\) | 1.85786 | 0.0657265 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 42.1421 | 1.48902 | ||||||||
\(802\) | 1.45584 | 0.0514076 | ||||||||
\(803\) | −12.4853 | −0.440596 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.75736 | −0.0619388 | ||||||||
\(806\) | −31.6569 | −1.11507 | ||||||||
\(807\) | −0.828427 | −0.0291620 | ||||||||
\(808\) | −6.34315 | −0.223151 | ||||||||
\(809\) | 52.4853 | 1.84528 | 0.922642 | − | 0.385657i | \(-0.126025\pi\) | ||||
0.922642 | + | 0.385657i | \(0.126025\pi\) | |||||||
\(810\) | 10.5858 | 0.371947 | ||||||||
\(811\) | 52.2426 | 1.83449 | 0.917244 | − | 0.398327i | \(-0.130409\pi\) | ||||
0.917244 | + | 0.398327i | \(0.130409\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.17157 | −0.321661 | ||||||||
\(814\) | −5.75736 | −0.201795 | ||||||||
\(815\) | −8.14214 | −0.285207 | ||||||||
\(816\) | −0.970563 | −0.0339765 | ||||||||
\(817\) | −11.6569 | −0.407822 | ||||||||
\(818\) | 34.9706 | 1.22272 | ||||||||
\(819\) | −10.3431 | −0.361419 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.5269 | 0.925796 | 0.462898 | − | 0.886412i | \(-0.346810\pi\) | ||||
0.462898 | + | 0.886412i | \(0.346810\pi\) | |||||||
\(822\) | −5.07107 | −0.176874 | ||||||||
\(823\) | −23.0000 | −0.801730 | −0.400865 | − | 0.916137i | \(-0.631290\pi\) | ||||
−0.400865 | + | 0.916137i | \(0.631290\pi\) | |||||||
\(824\) | 6.62742 | 0.230877 | ||||||||
\(825\) | 1.65685 | 0.0576843 | ||||||||
\(826\) | −3.65685 | −0.127238 | ||||||||
\(827\) | 4.10051 | 0.142589 | 0.0712943 | − | 0.997455i | \(-0.477287\pi\) | ||||
0.0712943 | + | 0.997455i | \(0.477287\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.0416 | 0.383492 | 0.191746 | − | 0.981445i | \(-0.438585\pi\) | ||||
0.191746 | + | 0.981445i | \(0.438585\pi\) | |||||||
\(830\) | 0.828427 | 0.0287551 | ||||||||
\(831\) | 6.00000 | 0.208138 | ||||||||
\(832\) | −49.9411 | −1.73140 | ||||||||
\(833\) | −3.89949 | −0.135109 | ||||||||
\(834\) | 9.59798 | 0.332351 | ||||||||
\(835\) | −6.72792 | −0.232829 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.65685 | 0.299225 | ||||||||
\(838\) | −33.1716 | −1.14589 | ||||||||
\(839\) | 40.5563 | 1.40016 | 0.700080 | − | 0.714064i | \(-0.253148\pi\) | ||||
0.700080 | + | 0.714064i | \(0.253148\pi\) | |||||||
\(840\) | 0.686292 | 0.0236793 | ||||||||
\(841\) | −23.9706 | −0.826571 | ||||||||
\(842\) | −0.201010 | −0.00692727 | ||||||||
\(843\) | 5.11270 | 0.176091 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.9706 | −0.893415 | ||||||||
\(846\) | 12.6863 | 0.436164 | ||||||||
\(847\) | −0.585786 | −0.0201279 | ||||||||
\(848\) | −49.9411 | −1.71499 | ||||||||
\(849\) | 3.61522 | 0.124074 | ||||||||
\(850\) | 3.31371 | 0.113659 | ||||||||
\(851\) | 12.2132 | 0.418663 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.0000 | −0.479351 | −0.239675 | − | 0.970853i | \(-0.577041\pi\) | ||||
−0.239675 | + | 0.970853i | \(0.577041\pi\) | |||||||
\(854\) | 2.54416 | 0.0870592 | ||||||||
\(855\) | −2.82843 | −0.0967302 | ||||||||
\(856\) | 12.2843 | 0.419868 | ||||||||
\(857\) | 47.6985 | 1.62935 | 0.814675 | − | 0.579918i | \(-0.196916\pi\) | ||||
0.814675 | + | 0.579918i | \(0.196916\pi\) | |||||||
\(858\) | −3.65685 | −0.124843 | ||||||||
\(859\) | −29.2843 | −0.999166 | −0.499583 | − | 0.866266i | \(-0.666513\pi\) | ||||
−0.499583 | + | 0.866266i | \(0.666513\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.34315 | −0.0798542 | ||||||||
\(862\) | −19.1127 | −0.650981 | ||||||||
\(863\) | 47.5980 | 1.62025 | 0.810127 | − | 0.586254i | \(-0.199398\pi\) | ||||
0.810127 | + | 0.586254i | \(0.199398\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.8995 | 0.608601 | ||||||||
\(866\) | 35.8995 | 1.21991 | ||||||||
\(867\) | −6.89949 | −0.234319 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.4142 | 0.590737 | ||||||||
\(870\) | 1.31371 | 0.0445389 | ||||||||
\(871\) | 47.3553 | 1.60457 | ||||||||
\(872\) | −32.9706 | −1.11652 | ||||||||
\(873\) | 1.17157 | 0.0396517 | ||||||||
\(874\) | −4.24264 | −0.143509 | ||||||||
\(875\) | −5.27208 | −0.178229 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.85786 | −0.332876 | −0.166438 | − | 0.986052i | \(-0.553227\pi\) | ||||
−0.166438 | + | 0.986052i | \(0.553227\pi\) | |||||||
\(878\) | 8.14214 | 0.274784 | ||||||||
\(879\) | 11.4731 | 0.386978 | ||||||||
\(880\) | −4.00000 | −0.134840 | ||||||||
\(881\) | 21.7696 | 0.733435 | 0.366717 | − | 0.930332i | \(-0.380482\pi\) | ||||
0.366717 | + | 0.930332i | \(0.380482\pi\) | |||||||
\(882\) | −26.6274 | −0.896592 | ||||||||
\(883\) | 33.5147 | 1.12786 | 0.563930 | − | 0.825823i | \(-0.309289\pi\) | ||||
0.563930 | + | 0.825823i | \(0.309289\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.82843 | 0.0614619 | ||||||||
\(886\) | −31.0711 | −1.04385 | ||||||||
\(887\) | −51.2548 | −1.72097 | −0.860484 | − | 0.509477i | \(-0.829839\pi\) | ||||
−0.860484 | + | 0.509477i | \(0.829839\pi\) | |||||||
\(888\) | −4.76955 | −0.160056 | ||||||||
\(889\) | 9.71573 | 0.325855 | ||||||||
\(890\) | −21.0711 | −0.706304 | ||||||||
\(891\) | −7.48528 | −0.250766 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.17157 | −0.106133 | ||||||||
\(894\) | 0.769553 | 0.0257377 | ||||||||
\(895\) | −1.92893 | −0.0644771 | ||||||||
\(896\) | 6.62742 | 0.221406 | ||||||||
\(897\) | 7.75736 | 0.259011 | ||||||||
\(898\) | −33.0711 | −1.10360 | ||||||||
\(899\) | −8.04163 | −0.268203 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.31371 | 0.243655 | ||||||||
\(902\) | 13.6569 | 0.454724 | ||||||||
\(903\) | −2.82843 | −0.0941242 | ||||||||
\(904\) | −18.1421 | −0.603398 | ||||||||
\(905\) | −17.3848 | −0.577890 | ||||||||
\(906\) | −3.79899 | −0.126213 | ||||||||
\(907\) | −50.1421 | −1.66494 | −0.832471 | − | 0.554068i | \(-0.813075\pi\) | ||||
−0.832471 | + | 0.554068i | \(0.813075\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.34315 | 0.210389 | ||||||||
\(910\) | 5.17157 | 0.171436 | ||||||||
\(911\) | −46.4264 | −1.53818 | −0.769088 | − | 0.639143i | \(-0.779289\pi\) | ||||
−0.769088 | + | 0.639143i | \(0.779289\pi\) | |||||||
\(912\) | 1.65685 | 0.0548639 | ||||||||
\(913\) | −0.585786 | −0.0193867 | ||||||||
\(914\) | −43.9411 | −1.45344 | ||||||||
\(915\) | −1.27208 | −0.0420536 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.45584 | 0.0480762 | ||||||||
\(918\) | 2.00000 | 0.0660098 | ||||||||
\(919\) | −19.6152 | −0.647047 | −0.323523 | − | 0.946220i | \(-0.604867\pi\) | ||||
−0.323523 | + | 0.946220i | \(0.604867\pi\) | |||||||
\(920\) | 8.48528 | 0.279751 | ||||||||
\(921\) | 1.89949 | 0.0625905 | ||||||||
\(922\) | 29.6569 | 0.976696 | ||||||||
\(923\) | 59.8406 | 1.96968 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.2843 | 0.535424 | ||||||||
\(926\) | 54.3848 | 1.78719 | ||||||||
\(927\) | −6.62742 | −0.217673 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −56.2843 | −1.84663 | −0.923314 | − | 0.384047i | \(-0.874530\pi\) | ||||
−0.923314 | + | 0.384047i | \(0.874530\pi\) | |||||||
\(930\) | −2.10051 | −0.0688783 | ||||||||
\(931\) | 6.65685 | 0.218170 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.142136 | −0.00465331 | ||||||||
\(934\) | −45.6985 | −1.49530 | ||||||||
\(935\) | 0.585786 | 0.0191573 | ||||||||
\(936\) | 49.9411 | 1.63238 | ||||||||
\(937\) | 23.5563 | 0.769552 | 0.384776 | − | 0.923010i | \(-0.374279\pi\) | ||||
0.384776 | + | 0.923010i | \(0.374279\pi\) | |||||||
\(938\) | −6.28427 | −0.205189 | ||||||||
\(939\) | 8.27208 | 0.269949 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.7574 | 0.644072 | 0.322036 | − | 0.946728i | \(-0.395633\pi\) | ||||
0.322036 | + | 0.946728i | \(0.395633\pi\) | |||||||
\(942\) | −2.92893 | −0.0954298 | ||||||||
\(943\) | −28.9706 | −0.943411 | ||||||||
\(944\) | 17.6569 | 0.574682 | ||||||||
\(945\) | −1.41421 | −0.0460044 | ||||||||
\(946\) | 16.4853 | 0.535983 | ||||||||
\(947\) | 5.97056 | 0.194017 | 0.0970086 | − | 0.995284i | \(-0.469073\pi\) | ||||
0.0970086 | + | 0.995284i | \(0.469073\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −77.9411 | −2.53008 | ||||||||
\(950\) | −5.65685 | −0.183533 | ||||||||
\(951\) | −10.5980 | −0.343663 | ||||||||
\(952\) | −0.970563 | −0.0314561 | ||||||||
\(953\) | 25.8995 | 0.838967 | 0.419483 | − | 0.907763i | \(-0.362211\pi\) | ||||
0.419483 | + | 0.907763i | \(0.362211\pi\) | |||||||
\(954\) | 49.9411 | 1.61690 | ||||||||
\(955\) | 14.3137 | 0.463181 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.928932 | −0.0300281 | ||||||||
\(958\) | −34.6863 | −1.12066 | ||||||||
\(959\) | −5.07107 | −0.163753 | ||||||||
\(960\) | −3.31371 | −0.106949 | ||||||||
\(961\) | −18.1421 | −0.585230 | ||||||||
\(962\) | −35.9411 | −1.15879 | ||||||||
\(963\) | −12.2843 | −0.395855 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.82843 | −0.219815 | ||||||||
\(966\) | −1.02944 | −0.0331216 | ||||||||
\(967\) | −27.5563 | −0.886152 | −0.443076 | − | 0.896484i | \(-0.646113\pi\) | ||||
−0.443076 | + | 0.896484i | \(0.646113\pi\) | |||||||
\(968\) | 2.82843 | 0.0909091 | ||||||||
\(969\) | −0.242641 | −0.00779474 | ||||||||
\(970\) | −0.585786 | −0.0188085 | ||||||||
\(971\) | 25.7279 | 0.825648 | 0.412824 | − | 0.910811i | \(-0.364542\pi\) | ||||
0.412824 | + | 0.910811i | \(0.364542\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.59798 | 0.307697 | ||||||||
\(974\) | 26.2426 | 0.840868 | ||||||||
\(975\) | 10.3431 | 0.331246 | ||||||||
\(976\) | −12.2843 | −0.393210 | ||||||||
\(977\) | −44.8406 | −1.43458 | −0.717289 | − | 0.696776i | \(-0.754617\pi\) | ||||
−0.717289 | + | 0.696776i | \(0.754617\pi\) | |||||||
\(978\) | −4.76955 | −0.152513 | ||||||||
\(979\) | 14.8995 | 0.476190 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 32.9706 | 1.05267 | ||||||||
\(982\) | −51.2548 | −1.63561 | ||||||||
\(983\) | 13.1005 | 0.417841 | 0.208921 | − | 0.977933i | \(-0.433005\pi\) | ||||
0.208921 | + | 0.977933i | \(0.433005\pi\) | |||||||
\(984\) | 11.3137 | 0.360668 | ||||||||
\(985\) | 3.89949 | 0.124248 | ||||||||
\(986\) | −1.85786 | −0.0591665 | ||||||||
\(987\) | −0.769553 | −0.0244951 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −34.9706 | −1.11200 | ||||||||
\(990\) | 4.00000 | 0.127128 | ||||||||
\(991\) | −8.68629 | −0.275929 | −0.137965 | − | 0.990437i | \(-0.544056\pi\) | ||||
−0.137965 | + | 0.990437i | \(0.544056\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.40202 | −0.107960 | ||||||||
\(994\) | −7.94113 | −0.251877 | ||||||||
\(995\) | 16.1421 | 0.511740 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.5563 | −1.18942 | −0.594711 | − | 0.803940i | \(-0.702733\pi\) | ||||
−0.594711 | + | 0.803940i | \(0.702733\pi\) | |||||||
\(998\) | −17.8579 | −0.565281 | ||||||||
\(999\) | 9.82843 | 0.310958 |
(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 | 209.2.a.b.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1881.2.a.d.1.2 | 2 | |||
4.3 | odd | 2 | 3344.2.a.n.1.1 | 2 | |||
5.4 | even | 2 | 5225.2.a.f.1.2 | 2 | |||
11.10 | odd | 2 | 2299.2.a.f.1.2 | 2 | |||
19.18 | odd | 2 | 3971.2.a.d.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
209.2.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1881.2.a.d.1.2 | 2 | 3.2 | odd | 2 | |||
2299.2.a.f.1.2 | 2 | 11.10 | odd | 2 | |||
3344.2.a.n.1.1 | 2 | 4.3 | odd | 2 | |||
3971.2.a.d.1.2 | 2 | 19.18 | odd | 2 | |||
5225.2.a.f.1.2 | 2 | 5.4 | even | 2 |