Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4018,2,Mod(1,4018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4018, 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("4018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4018 = 2 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4018.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: | \(32.0838915322\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, a_2, a_3]\) |
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 | \(\chi\) | \(=\) | 4018.1 |
$q$-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 | ||||||||
\(3\) | −0.414214 | −0.239146 | −0.119573 | − | 0.992825i | \(-0.538153\pi\) | ||||
−0.119573 | + | 0.992825i | \(0.538153\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | −0.223607 | − | 0.974679i | \(-0.571783\pi\) | ||||
−0.223607 | + | 0.974679i | \(0.571783\pi\) | |||||||
\(6\) | −0.414214 | −0.169102 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0.585786 | 0.176621 | 0.0883106 | − | 0.996093i | \(-0.471853\pi\) | ||||
0.0883106 | + | 0.996093i | \(0.471853\pi\) | |||||||
\(12\) | −0.414214 | −0.119573 | ||||||||
\(13\) | 6.24264 | 1.73140 | 0.865699 | − | 0.500566i | \(-0.166875\pi\) | ||||
0.865699 | + | 0.500566i | \(0.166875\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.414214 | 0.106949 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.17157 | 0.526684 | 0.263342 | − | 0.964703i | \(-0.415175\pi\) | ||||
0.263342 | + | 0.964703i | \(0.415175\pi\) | |||||||
\(18\) | −2.82843 | −0.666667 | ||||||||
\(19\) | −2.82843 | −0.648886 | −0.324443 | − | 0.945905i | \(-0.605177\pi\) | ||||
−0.324443 | + | 0.945905i | \(0.605177\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.585786 | 0.124890 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | −0.414214 | −0.0845510 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 6.24264 | 1.22428 | ||||||||
\(27\) | 2.41421 | 0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.82843 | 0.710921 | 0.355461 | − | 0.934691i | \(-0.384324\pi\) | ||||
0.355461 | + | 0.934691i | \(0.384324\pi\) | |||||||
\(30\) | 0.414214 | 0.0756247 | ||||||||
\(31\) | 8.41421 | 1.51124 | 0.755619 | − | 0.655012i | \(-0.227336\pi\) | ||||
0.755619 | + | 0.655012i | \(0.227336\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.242641 | −0.0422383 | ||||||||
\(34\) | 2.17157 | 0.372422 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.82843 | −0.471405 | ||||||||
\(37\) | −1.41421 | −0.232495 | −0.116248 | − | 0.993220i | \(-0.537087\pi\) | ||||
−0.116248 | + | 0.993220i | \(0.537087\pi\) | |||||||
\(38\) | −2.82843 | −0.458831 | ||||||||
\(39\) | −2.58579 | −0.414057 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.07107 | −0.925829 | −0.462915 | − | 0.886403i | \(-0.653196\pi\) | ||||
−0.462915 | + | 0.886403i | \(0.653196\pi\) | |||||||
\(44\) | 0.585786 | 0.0883106 | ||||||||
\(45\) | 2.82843 | 0.421637 | ||||||||
\(46\) | −4.00000 | −0.589768 | ||||||||
\(47\) | 8.58579 | 1.25237 | 0.626183 | − | 0.779676i | \(-0.284616\pi\) | ||||
0.626183 | + | 0.779676i | \(0.284616\pi\) | |||||||
\(48\) | −0.414214 | −0.0597866 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.00000 | −0.565685 | ||||||||
\(51\) | −0.899495 | −0.125954 | ||||||||
\(52\) | 6.24264 | 0.865699 | ||||||||
\(53\) | 8.65685 | 1.18911 | 0.594555 | − | 0.804055i | \(-0.297328\pi\) | ||||
0.594555 | + | 0.804055i | \(0.297328\pi\) | |||||||
\(54\) | 2.41421 | 0.328533 | ||||||||
\(55\) | −0.585786 | −0.0789874 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.17157 | 0.155179 | ||||||||
\(58\) | 3.82843 | 0.502697 | ||||||||
\(59\) | −4.82843 | −0.628608 | −0.314304 | − | 0.949322i | \(-0.601771\pi\) | ||||
−0.314304 | + | 0.949322i | \(0.601771\pi\) | |||||||
\(60\) | 0.414214 | 0.0534747 | ||||||||
\(61\) | 2.65685 | 0.340175 | 0.170088 | − | 0.985429i | \(-0.445595\pi\) | ||||
0.170088 | + | 0.985429i | \(0.445595\pi\) | |||||||
\(62\) | 8.41421 | 1.06861 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.24264 | −0.774304 | ||||||||
\(66\) | −0.242641 | −0.0298670 | ||||||||
\(67\) | 3.17157 | 0.387469 | 0.193735 | − | 0.981054i | \(-0.437940\pi\) | ||||
0.193735 | + | 0.981054i | \(0.437940\pi\) | |||||||
\(68\) | 2.17157 | 0.263342 | ||||||||
\(69\) | 1.65685 | 0.199462 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.24264 | 0.147474 | 0.0737372 | − | 0.997278i | \(-0.476507\pi\) | ||||
0.0737372 | + | 0.997278i | \(0.476507\pi\) | |||||||
\(72\) | −2.82843 | −0.333333 | ||||||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | −1.41421 | −0.164399 | ||||||||
\(75\) | 1.65685 | 0.191317 | ||||||||
\(76\) | −2.82843 | −0.324443 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.58579 | −0.292783 | ||||||||
\(79\) | −3.24264 | −0.364826 | −0.182413 | − | 0.983222i | \(-0.558391\pi\) | ||||
−0.182413 | + | 0.983222i | \(0.558391\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | −1.00000 | −0.110432 | ||||||||
\(83\) | 1.07107 | 0.117565 | 0.0587825 | − | 0.998271i | \(-0.481278\pi\) | ||||
0.0587825 | + | 0.998271i | \(0.481278\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.17157 | −0.235540 | ||||||||
\(86\) | −6.07107 | −0.654660 | ||||||||
\(87\) | −1.58579 | −0.170014 | ||||||||
\(88\) | 0.585786 | 0.0624450 | ||||||||
\(89\) | 7.82843 | 0.829812 | 0.414906 | − | 0.909864i | \(-0.363815\pi\) | ||||
0.414906 | + | 0.909864i | \(0.363815\pi\) | |||||||
\(90\) | 2.82843 | 0.298142 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.00000 | −0.417029 | ||||||||
\(93\) | −3.48528 | −0.361407 | ||||||||
\(94\) | 8.58579 | 0.885556 | ||||||||
\(95\) | 2.82843 | 0.290191 | ||||||||
\(96\) | −0.414214 | −0.0422755 | ||||||||
\(97\) | 12.1716 | 1.23584 | 0.617918 | − | 0.786243i | \(-0.287976\pi\) | ||||
0.617918 | + | 0.786243i | \(0.287976\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.65685 | −0.166520 | ||||||||
\(100\) | −4.00000 | −0.400000 | ||||||||
\(101\) | 0.343146 | 0.0341443 | 0.0170721 | − | 0.999854i | \(-0.494566\pi\) | ||||
0.0170721 | + | 0.999854i | \(0.494566\pi\) | |||||||
\(102\) | −0.899495 | −0.0890633 | ||||||||
\(103\) | 8.89949 | 0.876893 | 0.438447 | − | 0.898757i | \(-0.355529\pi\) | ||||
0.438447 | + | 0.898757i | \(0.355529\pi\) | |||||||
\(104\) | 6.24264 | 0.612141 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.65685 | 0.840828 | ||||||||
\(107\) | 12.8995 | 1.24704 | 0.623521 | − | 0.781807i | \(-0.285702\pi\) | ||||
0.623521 | + | 0.781807i | \(0.285702\pi\) | |||||||
\(108\) | 2.41421 | 0.232308 | ||||||||
\(109\) | 14.1421 | 1.35457 | 0.677285 | − | 0.735720i | \(-0.263156\pi\) | ||||
0.677285 | + | 0.735720i | \(0.263156\pi\) | |||||||
\(110\) | −0.585786 | −0.0558525 | ||||||||
\(111\) | 0.585786 | 0.0556004 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.00000 | −0.470360 | −0.235180 | − | 0.971952i | \(-0.575568\pi\) | ||||
−0.235180 | + | 0.971952i | \(0.575568\pi\) | |||||||
\(114\) | 1.17157 | 0.109728 | ||||||||
\(115\) | 4.00000 | 0.373002 | ||||||||
\(116\) | 3.82843 | 0.355461 | ||||||||
\(117\) | −17.6569 | −1.63238 | ||||||||
\(118\) | −4.82843 | −0.444493 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.414214 | 0.0378124 | ||||||||
\(121\) | −10.6569 | −0.968805 | ||||||||
\(122\) | 2.65685 | 0.240540 | ||||||||
\(123\) | 0.414214 | 0.0373484 | ||||||||
\(124\) | 8.41421 | 0.755619 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.75736 | −0.510883 | −0.255442 | − | 0.966825i | \(-0.582221\pi\) | ||||
−0.255442 | + | 0.966825i | \(0.582221\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.51472 | 0.221409 | ||||||||
\(130\) | −6.24264 | −0.547516 | ||||||||
\(131\) | −0.242641 | −0.0211996 | −0.0105998 | − | 0.999944i | \(-0.503374\pi\) | ||||
−0.0105998 | + | 0.999944i | \(0.503374\pi\) | |||||||
\(132\) | −0.242641 | −0.0211192 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.17157 | 0.273982 | ||||||||
\(135\) | −2.41421 | −0.207782 | ||||||||
\(136\) | 2.17157 | 0.186211 | ||||||||
\(137\) | 1.65685 | 0.141555 | 0.0707773 | − | 0.997492i | \(-0.477452\pi\) | ||||
0.0707773 | + | 0.997492i | \(0.477452\pi\) | |||||||
\(138\) | 1.65685 | 0.141041 | ||||||||
\(139\) | 1.51472 | 0.128477 | 0.0642384 | − | 0.997935i | \(-0.479538\pi\) | ||||
0.0642384 | + | 0.997935i | \(0.479538\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.55635 | −0.299499 | ||||||||
\(142\) | 1.24264 | 0.104280 | ||||||||
\(143\) | 3.65685 | 0.305802 | ||||||||
\(144\) | −2.82843 | −0.235702 | ||||||||
\(145\) | −3.82843 | −0.317934 | ||||||||
\(146\) | 4.00000 | 0.331042 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.41421 | −0.116248 | ||||||||
\(149\) | 20.6569 | 1.69228 | 0.846138 | − | 0.532964i | \(-0.178922\pi\) | ||||
0.846138 | + | 0.532964i | \(0.178922\pi\) | |||||||
\(150\) | 1.65685 | 0.135282 | ||||||||
\(151\) | 20.0711 | 1.63336 | 0.816680 | − | 0.577091i | \(-0.195812\pi\) | ||||
0.816680 | + | 0.577091i | \(0.195812\pi\) | |||||||
\(152\) | −2.82843 | −0.229416 | ||||||||
\(153\) | −6.14214 | −0.496562 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.41421 | −0.675846 | ||||||||
\(156\) | −2.58579 | −0.207029 | ||||||||
\(157\) | −13.6569 | −1.08994 | −0.544968 | − | 0.838457i | \(-0.683458\pi\) | ||||
−0.544968 | + | 0.838457i | \(0.683458\pi\) | |||||||
\(158\) | −3.24264 | −0.257971 | ||||||||
\(159\) | −3.58579 | −0.284371 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.48528 | 0.588099 | ||||||||
\(163\) | −25.3137 | −1.98272 | −0.991361 | − | 0.131159i | \(-0.958130\pi\) | ||||
−0.991361 | + | 0.131159i | \(0.958130\pi\) | |||||||
\(164\) | −1.00000 | −0.0780869 | ||||||||
\(165\) | 0.242641 | 0.0188896 | ||||||||
\(166\) | 1.07107 | 0.0831310 | ||||||||
\(167\) | 24.9706 | 1.93228 | 0.966140 | − | 0.258018i | \(-0.0830694\pi\) | ||||
0.966140 | + | 0.258018i | \(0.0830694\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.9706 | 1.99774 | ||||||||
\(170\) | −2.17157 | −0.166552 | ||||||||
\(171\) | 8.00000 | 0.611775 | ||||||||
\(172\) | −6.07107 | −0.462915 | ||||||||
\(173\) | −9.82843 | −0.747241 | −0.373621 | − | 0.927582i | \(-0.621884\pi\) | ||||
−0.373621 | + | 0.927582i | \(0.621884\pi\) | |||||||
\(174\) | −1.58579 | −0.120218 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.585786 | 0.0441553 | ||||||||
\(177\) | 2.00000 | 0.150329 | ||||||||
\(178\) | 7.82843 | 0.586765 | ||||||||
\(179\) | 4.24264 | 0.317110 | 0.158555 | − | 0.987350i | \(-0.449317\pi\) | ||||
0.158555 | + | 0.987350i | \(0.449317\pi\) | |||||||
\(180\) | 2.82843 | 0.210819 | ||||||||
\(181\) | 9.89949 | 0.735824 | 0.367912 | − | 0.929861i | \(-0.380073\pi\) | ||||
0.367912 | + | 0.929861i | \(0.380073\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.10051 | −0.0813517 | ||||||||
\(184\) | −4.00000 | −0.294884 | ||||||||
\(185\) | 1.41421 | 0.103975 | ||||||||
\(186\) | −3.48528 | −0.255553 | ||||||||
\(187\) | 1.27208 | 0.0930236 | ||||||||
\(188\) | 8.58579 | 0.626183 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.82843 | 0.205196 | ||||||||
\(191\) | −3.24264 | −0.234629 | −0.117315 | − | 0.993095i | \(-0.537429\pi\) | ||||
−0.117315 | + | 0.993095i | \(0.537429\pi\) | |||||||
\(192\) | −0.414214 | −0.0298933 | ||||||||
\(193\) | 7.89949 | 0.568618 | 0.284309 | − | 0.958733i | \(-0.408236\pi\) | ||||
0.284309 | + | 0.958733i | \(0.408236\pi\) | |||||||
\(194\) | 12.1716 | 0.873868 | ||||||||
\(195\) | 2.58579 | 0.185172 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.3137 | 1.66103 | 0.830516 | − | 0.556994i | \(-0.188045\pi\) | ||||
0.830516 | + | 0.556994i | \(0.188045\pi\) | |||||||
\(198\) | −1.65685 | −0.117748 | ||||||||
\(199\) | 11.3137 | 0.802008 | 0.401004 | − | 0.916076i | \(-0.368661\pi\) | ||||
0.401004 | + | 0.916076i | \(0.368661\pi\) | |||||||
\(200\) | −4.00000 | −0.282843 | ||||||||
\(201\) | −1.31371 | −0.0926619 | ||||||||
\(202\) | 0.343146 | 0.0241437 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.899495 | −0.0629772 | ||||||||
\(205\) | 1.00000 | 0.0698430 | ||||||||
\(206\) | 8.89949 | 0.620057 | ||||||||
\(207\) | 11.3137 | 0.786357 | ||||||||
\(208\) | 6.24264 | 0.432849 | ||||||||
\(209\) | −1.65685 | −0.114607 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.65685 | −0.114063 | −0.0570313 | − | 0.998372i | \(-0.518163\pi\) | ||||
−0.0570313 | + | 0.998372i | \(0.518163\pi\) | |||||||
\(212\) | 8.65685 | 0.594555 | ||||||||
\(213\) | −0.514719 | −0.0352679 | ||||||||
\(214\) | 12.8995 | 0.881791 | ||||||||
\(215\) | 6.07107 | 0.414043 | ||||||||
\(216\) | 2.41421 | 0.164266 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 14.1421 | 0.957826 | ||||||||
\(219\) | −1.65685 | −0.111960 | ||||||||
\(220\) | −0.585786 | −0.0394937 | ||||||||
\(221\) | 13.5563 | 0.911899 | ||||||||
\(222\) | 0.585786 | 0.0393154 | ||||||||
\(223\) | −27.8701 | −1.86632 | −0.933159 | − | 0.359465i | \(-0.882959\pi\) | ||||
−0.933159 | + | 0.359465i | \(0.882959\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.3137 | 0.754247 | ||||||||
\(226\) | −5.00000 | −0.332595 | ||||||||
\(227\) | −7.72792 | −0.512920 | −0.256460 | − | 0.966555i | \(-0.582556\pi\) | ||||
−0.256460 | + | 0.966555i | \(0.582556\pi\) | |||||||
\(228\) | 1.17157 | 0.0775893 | ||||||||
\(229\) | 3.41421 | 0.225618 | 0.112809 | − | 0.993617i | \(-0.464015\pi\) | ||||
0.112809 | + | 0.993617i | \(0.464015\pi\) | |||||||
\(230\) | 4.00000 | 0.263752 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.82843 | 0.251349 | ||||||||
\(233\) | −24.2426 | −1.58819 | −0.794094 | − | 0.607795i | \(-0.792054\pi\) | ||||
−0.794094 | + | 0.607795i | \(0.792054\pi\) | |||||||
\(234\) | −17.6569 | −1.15426 | ||||||||
\(235\) | −8.58579 | −0.560075 | ||||||||
\(236\) | −4.82843 | −0.314304 | ||||||||
\(237\) | 1.34315 | 0.0872467 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.51472 | 0.227348 | 0.113674 | − | 0.993518i | \(-0.463738\pi\) | ||||
0.113674 | + | 0.993518i | \(0.463738\pi\) | |||||||
\(240\) | 0.414214 | 0.0267374 | ||||||||
\(241\) | −21.4142 | −1.37941 | −0.689705 | − | 0.724090i | \(-0.742260\pi\) | ||||
−0.689705 | + | 0.724090i | \(0.742260\pi\) | |||||||
\(242\) | −10.6569 | −0.685049 | ||||||||
\(243\) | −10.3431 | −0.663513 | ||||||||
\(244\) | 2.65685 | 0.170088 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.414214 | 0.0264093 | ||||||||
\(247\) | −17.6569 | −1.12348 | ||||||||
\(248\) | 8.41421 | 0.534303 | ||||||||
\(249\) | −0.443651 | −0.0281152 | ||||||||
\(250\) | 9.00000 | 0.569210 | ||||||||
\(251\) | −12.9289 | −0.816067 | −0.408033 | − | 0.912967i | \(-0.633785\pi\) | ||||
−0.408033 | + | 0.912967i | \(0.633785\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.34315 | −0.147312 | ||||||||
\(254\) | −5.75736 | −0.361249 | ||||||||
\(255\) | 0.899495 | 0.0563286 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 25.4853 | 1.58973 | 0.794864 | − | 0.606788i | \(-0.207542\pi\) | ||||
0.794864 | + | 0.606788i | \(0.207542\pi\) | |||||||
\(258\) | 2.51472 | 0.156560 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6.24264 | −0.387152 | ||||||||
\(261\) | −10.8284 | −0.670263 | ||||||||
\(262\) | −0.242641 | −0.0149904 | ||||||||
\(263\) | 8.97056 | 0.553149 | 0.276574 | − | 0.960993i | \(-0.410801\pi\) | ||||
0.276574 | + | 0.960993i | \(0.410801\pi\) | |||||||
\(264\) | −0.242641 | −0.0149335 | ||||||||
\(265\) | −8.65685 | −0.531786 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.24264 | −0.198446 | ||||||||
\(268\) | 3.17157 | 0.193735 | ||||||||
\(269\) | −2.68629 | −0.163786 | −0.0818930 | − | 0.996641i | \(-0.526097\pi\) | ||||
−0.0818930 | + | 0.996641i | \(0.526097\pi\) | |||||||
\(270\) | −2.41421 | −0.146924 | ||||||||
\(271\) | 6.00000 | 0.364474 | 0.182237 | − | 0.983255i | \(-0.441666\pi\) | ||||
0.182237 | + | 0.983255i | \(0.441666\pi\) | |||||||
\(272\) | 2.17157 | 0.131671 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.65685 | 0.100094 | ||||||||
\(275\) | −2.34315 | −0.141297 | ||||||||
\(276\) | 1.65685 | 0.0997309 | ||||||||
\(277\) | −12.3431 | −0.741628 | −0.370814 | − | 0.928707i | \(-0.620921\pi\) | ||||
−0.370814 | + | 0.928707i | \(0.620921\pi\) | |||||||
\(278\) | 1.51472 | 0.0908468 | ||||||||
\(279\) | −23.7990 | −1.42481 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.0000 | −1.55103 | −0.775515 | − | 0.631329i | \(-0.782510\pi\) | ||||
−0.775515 | + | 0.631329i | \(0.782510\pi\) | |||||||
\(282\) | −3.55635 | −0.211778 | ||||||||
\(283\) | −22.4853 | −1.33661 | −0.668306 | − | 0.743887i | \(-0.732980\pi\) | ||||
−0.668306 | + | 0.743887i | \(0.732980\pi\) | |||||||
\(284\) | 1.24264 | 0.0737372 | ||||||||
\(285\) | −1.17157 | −0.0693980 | ||||||||
\(286\) | 3.65685 | 0.216234 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.82843 | −0.166667 | ||||||||
\(289\) | −12.2843 | −0.722604 | ||||||||
\(290\) | −3.82843 | −0.224813 | ||||||||
\(291\) | −5.04163 | −0.295546 | ||||||||
\(292\) | 4.00000 | 0.234082 | ||||||||
\(293\) | 14.0000 | 0.817889 | 0.408944 | − | 0.912559i | \(-0.365897\pi\) | ||||
0.408944 | + | 0.912559i | \(0.365897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.82843 | 0.281122 | ||||||||
\(296\) | −1.41421 | −0.0821995 | ||||||||
\(297\) | 1.41421 | 0.0820610 | ||||||||
\(298\) | 20.6569 | 1.19662 | ||||||||
\(299\) | −24.9706 | −1.44408 | ||||||||
\(300\) | 1.65685 | 0.0956585 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 20.0711 | 1.15496 | ||||||||
\(303\) | −0.142136 | −0.00816548 | ||||||||
\(304\) | −2.82843 | −0.162221 | ||||||||
\(305\) | −2.65685 | −0.152131 | ||||||||
\(306\) | −6.14214 | −0.351123 | ||||||||
\(307\) | 24.9706 | 1.42515 | 0.712573 | − | 0.701598i | \(-0.247530\pi\) | ||||
0.712573 | + | 0.701598i | \(0.247530\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.68629 | −0.209706 | ||||||||
\(310\) | −8.41421 | −0.477895 | ||||||||
\(311\) | 5.51472 | 0.312711 | 0.156356 | − | 0.987701i | \(-0.450025\pi\) | ||||
0.156356 | + | 0.987701i | \(0.450025\pi\) | |||||||
\(312\) | −2.58579 | −0.146391 | ||||||||
\(313\) | −4.97056 | −0.280953 | −0.140476 | − | 0.990084i | \(-0.544863\pi\) | ||||
−0.140476 | + | 0.990084i | \(0.544863\pi\) | |||||||
\(314\) | −13.6569 | −0.770701 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.24264 | −0.182413 | ||||||||
\(317\) | −21.6569 | −1.21637 | −0.608185 | − | 0.793795i | \(-0.708102\pi\) | ||||
−0.608185 | + | 0.793795i | \(0.708102\pi\) | |||||||
\(318\) | −3.58579 | −0.201081 | ||||||||
\(319\) | 2.24264 | 0.125564 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −5.34315 | −0.298225 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.14214 | −0.341758 | ||||||||
\(324\) | 7.48528 | 0.415849 | ||||||||
\(325\) | −24.9706 | −1.38512 | ||||||||
\(326\) | −25.3137 | −1.40200 | ||||||||
\(327\) | −5.85786 | −0.323941 | ||||||||
\(328\) | −1.00000 | −0.0552158 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.242641 | 0.0133569 | ||||||||
\(331\) | −16.0416 | −0.881728 | −0.440864 | − | 0.897574i | \(-0.645328\pi\) | ||||
−0.440864 | + | 0.897574i | \(0.645328\pi\) | |||||||
\(332\) | 1.07107 | 0.0587825 | ||||||||
\(333\) | 4.00000 | 0.219199 | ||||||||
\(334\) | 24.9706 | 1.36633 | ||||||||
\(335\) | −3.17157 | −0.173282 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.65685 | −0.471569 | −0.235784 | − | 0.971805i | \(-0.575766\pi\) | ||||
−0.235784 | + | 0.971805i | \(0.575766\pi\) | |||||||
\(338\) | 25.9706 | 1.41261 | ||||||||
\(339\) | 2.07107 | 0.112485 | ||||||||
\(340\) | −2.17157 | −0.117770 | ||||||||
\(341\) | 4.92893 | 0.266917 | ||||||||
\(342\) | 8.00000 | 0.432590 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.07107 | −0.327330 | ||||||||
\(345\) | −1.65685 | −0.0892020 | ||||||||
\(346\) | −9.82843 | −0.528380 | ||||||||
\(347\) | −5.65685 | −0.303676 | −0.151838 | − | 0.988405i | \(-0.548519\pi\) | ||||
−0.151838 | + | 0.988405i | \(0.548519\pi\) | |||||||
\(348\) | −1.58579 | −0.0850071 | ||||||||
\(349\) | 19.7990 | 1.05982 | 0.529908 | − | 0.848055i | \(-0.322227\pi\) | ||||
0.529908 | + | 0.848055i | \(0.322227\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.0711 | 0.804434 | ||||||||
\(352\) | 0.585786 | 0.0312225 | ||||||||
\(353\) | −6.34315 | −0.337612 | −0.168806 | − | 0.985649i | \(-0.553991\pi\) | ||||
−0.168806 | + | 0.985649i | \(0.553991\pi\) | |||||||
\(354\) | 2.00000 | 0.106299 | ||||||||
\(355\) | −1.24264 | −0.0659525 | ||||||||
\(356\) | 7.82843 | 0.414906 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.24264 | 0.224231 | ||||||||
\(359\) | 18.3848 | 0.970311 | 0.485156 | − | 0.874428i | \(-0.338763\pi\) | ||||
0.485156 | + | 0.874428i | \(0.338763\pi\) | |||||||
\(360\) | 2.82843 | 0.149071 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 9.89949 | 0.520306 | ||||||||
\(363\) | 4.41421 | 0.231686 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.00000 | −0.209370 | ||||||||
\(366\) | −1.10051 | −0.0575243 | ||||||||
\(367\) | 3.24264 | 0.169264 | 0.0846322 | − | 0.996412i | \(-0.473028\pi\) | ||||
0.0846322 | + | 0.996412i | \(0.473028\pi\) | |||||||
\(368\) | −4.00000 | −0.208514 | ||||||||
\(369\) | 2.82843 | 0.147242 | ||||||||
\(370\) | 1.41421 | 0.0735215 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.48528 | −0.180703 | ||||||||
\(373\) | −11.7574 | −0.608773 | −0.304386 | − | 0.952549i | \(-0.598451\pi\) | ||||
−0.304386 | + | 0.952549i | \(0.598451\pi\) | |||||||
\(374\) | 1.27208 | 0.0657776 | ||||||||
\(375\) | −3.72792 | −0.192509 | ||||||||
\(376\) | 8.58579 | 0.442778 | ||||||||
\(377\) | 23.8995 | 1.23089 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.3848 | −1.40666 | −0.703331 | − | 0.710863i | \(-0.748305\pi\) | ||||
−0.703331 | + | 0.710863i | \(0.748305\pi\) | |||||||
\(380\) | 2.82843 | 0.145095 | ||||||||
\(381\) | 2.38478 | 0.122176 | ||||||||
\(382\) | −3.24264 | −0.165908 | ||||||||
\(383\) | 10.7279 | 0.548171 | 0.274086 | − | 0.961705i | \(-0.411625\pi\) | ||||
0.274086 | + | 0.961705i | \(0.411625\pi\) | |||||||
\(384\) | −0.414214 | −0.0211377 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.89949 | 0.402074 | ||||||||
\(387\) | 17.1716 | 0.872880 | ||||||||
\(388\) | 12.1716 | 0.617918 | ||||||||
\(389\) | −2.00000 | −0.101404 | −0.0507020 | − | 0.998714i | \(-0.516146\pi\) | ||||
−0.0507020 | + | 0.998714i | \(0.516146\pi\) | |||||||
\(390\) | 2.58579 | 0.130936 | ||||||||
\(391\) | −8.68629 | −0.439285 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.100505 | 0.00506981 | ||||||||
\(394\) | 23.3137 | 1.17453 | ||||||||
\(395\) | 3.24264 | 0.163155 | ||||||||
\(396\) | −1.65685 | −0.0832601 | ||||||||
\(397\) | 8.58579 | 0.430908 | 0.215454 | − | 0.976514i | \(-0.430877\pi\) | ||||
0.215454 | + | 0.976514i | \(0.430877\pi\) | |||||||
\(398\) | 11.3137 | 0.567105 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | 13.9706 | 0.697657 | 0.348828 | − | 0.937187i | \(-0.386580\pi\) | ||||
0.348828 | + | 0.937187i | \(0.386580\pi\) | |||||||
\(402\) | −1.31371 | −0.0655218 | ||||||||
\(403\) | 52.5269 | 2.61655 | ||||||||
\(404\) | 0.343146 | 0.0170721 | ||||||||
\(405\) | −7.48528 | −0.371947 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.828427 | −0.0410636 | ||||||||
\(408\) | −0.899495 | −0.0445316 | ||||||||
\(409\) | −14.1005 | −0.697225 | −0.348613 | − | 0.937267i | \(-0.613347\pi\) | ||||
−0.348613 | + | 0.937267i | \(0.613347\pi\) | |||||||
\(410\) | 1.00000 | 0.0493865 | ||||||||
\(411\) | −0.686292 | −0.0338523 | ||||||||
\(412\) | 8.89949 | 0.438447 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 11.3137 | 0.556038 | ||||||||
\(415\) | −1.07107 | −0.0525767 | ||||||||
\(416\) | 6.24264 | 0.306071 | ||||||||
\(417\) | −0.627417 | −0.0307247 | ||||||||
\(418\) | −1.65685 | −0.0810394 | ||||||||
\(419\) | −20.2426 | −0.988918 | −0.494459 | − | 0.869201i | \(-0.664634\pi\) | ||||
−0.494459 | + | 0.869201i | \(0.664634\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.1127 | 1.76003 | 0.880013 | − | 0.474950i | \(-0.157534\pi\) | ||||
0.880013 | + | 0.474950i | \(0.157534\pi\) | |||||||
\(422\) | −1.65685 | −0.0806544 | ||||||||
\(423\) | −24.2843 | −1.18074 | ||||||||
\(424\) | 8.65685 | 0.420414 | ||||||||
\(425\) | −8.68629 | −0.421347 | ||||||||
\(426\) | −0.514719 | −0.0249382 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.8995 | 0.623521 | ||||||||
\(429\) | −1.51472 | −0.0731313 | ||||||||
\(430\) | 6.07107 | 0.292773 | ||||||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | 2.41421 | 0.116154 | ||||||||
\(433\) | 24.9706 | 1.20001 | 0.600004 | − | 0.799997i | \(-0.295166\pi\) | ||||
0.600004 | + | 0.799997i | \(0.295166\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.58579 | 0.0760326 | ||||||||
\(436\) | 14.1421 | 0.677285 | ||||||||
\(437\) | 11.3137 | 0.541208 | ||||||||
\(438\) | −1.65685 | −0.0791676 | ||||||||
\(439\) | −9.51472 | −0.454113 | −0.227056 | − | 0.973882i | \(-0.572910\pi\) | ||||
−0.227056 | + | 0.973882i | \(0.572910\pi\) | |||||||
\(440\) | −0.585786 | −0.0279263 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.5563 | 0.644810 | ||||||||
\(443\) | 9.24264 | 0.439131 | 0.219566 | − | 0.975598i | \(-0.429536\pi\) | ||||
0.219566 | + | 0.975598i | \(0.429536\pi\) | |||||||
\(444\) | 0.585786 | 0.0278002 | ||||||||
\(445\) | −7.82843 | −0.371103 | ||||||||
\(446\) | −27.8701 | −1.31969 | ||||||||
\(447\) | −8.55635 | −0.404701 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.1716 | 0.668798 | 0.334399 | − | 0.942432i | \(-0.391467\pi\) | ||||
0.334399 | + | 0.942432i | \(0.391467\pi\) | |||||||
\(450\) | 11.3137 | 0.533333 | ||||||||
\(451\) | −0.585786 | −0.0275836 | ||||||||
\(452\) | −5.00000 | −0.235180 | ||||||||
\(453\) | −8.31371 | −0.390612 | ||||||||
\(454\) | −7.72792 | −0.362689 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.17157 | 0.0548639 | ||||||||
\(457\) | −36.7279 | −1.71806 | −0.859030 | − | 0.511925i | \(-0.828932\pi\) | ||||
−0.859030 | + | 0.511925i | \(0.828932\pi\) | |||||||
\(458\) | 3.41421 | 0.159536 | ||||||||
\(459\) | 5.24264 | 0.244706 | ||||||||
\(460\) | 4.00000 | 0.186501 | ||||||||
\(461\) | −31.9706 | −1.48902 | −0.744509 | − | 0.667613i | \(-0.767316\pi\) | ||||
−0.744509 | + | 0.667613i | \(0.767316\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.65685 | 0.262896 | 0.131448 | − | 0.991323i | \(-0.458037\pi\) | ||||
0.131448 | + | 0.991323i | \(0.458037\pi\) | |||||||
\(464\) | 3.82843 | 0.177730 | ||||||||
\(465\) | 3.48528 | 0.161626 | ||||||||
\(466\) | −24.2426 | −1.12302 | ||||||||
\(467\) | −34.4853 | −1.59579 | −0.797894 | − | 0.602797i | \(-0.794053\pi\) | ||||
−0.797894 | + | 0.602797i | \(0.794053\pi\) | |||||||
\(468\) | −17.6569 | −0.816188 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −8.58579 | −0.396033 | ||||||||
\(471\) | 5.65685 | 0.260654 | ||||||||
\(472\) | −4.82843 | −0.222246 | ||||||||
\(473\) | −3.55635 | −0.163521 | ||||||||
\(474\) | 1.34315 | 0.0616927 | ||||||||
\(475\) | 11.3137 | 0.519109 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.4853 | −1.12110 | ||||||||
\(478\) | 3.51472 | 0.160759 | ||||||||
\(479\) | 35.2132 | 1.60893 | 0.804466 | − | 0.593998i | \(-0.202451\pi\) | ||||
0.804466 | + | 0.593998i | \(0.202451\pi\) | |||||||
\(480\) | 0.414214 | 0.0189062 | ||||||||
\(481\) | −8.82843 | −0.402542 | ||||||||
\(482\) | −21.4142 | −0.975391 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.6569 | −0.484402 | ||||||||
\(485\) | −12.1716 | −0.552683 | ||||||||
\(486\) | −10.3431 | −0.469175 | ||||||||
\(487\) | −18.5858 | −0.842202 | −0.421101 | − | 0.907014i | \(-0.638356\pi\) | ||||
−0.421101 | + | 0.907014i | \(0.638356\pi\) | |||||||
\(488\) | 2.65685 | 0.120270 | ||||||||
\(489\) | 10.4853 | 0.474161 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.8701 | 0.716206 | 0.358103 | − | 0.933682i | \(-0.383424\pi\) | ||||
0.358103 | + | 0.933682i | \(0.383424\pi\) | |||||||
\(492\) | 0.414214 | 0.0186742 | ||||||||
\(493\) | 8.31371 | 0.374431 | ||||||||
\(494\) | −17.6569 | −0.794419 | ||||||||
\(495\) | 1.65685 | 0.0744701 | ||||||||
\(496\) | 8.41421 | 0.377809 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.443651 | −0.0198805 | ||||||||
\(499\) | 22.4853 | 1.00658 | 0.503290 | − | 0.864118i | \(-0.332123\pi\) | ||||
0.503290 | + | 0.864118i | \(0.332123\pi\) | |||||||
\(500\) | 9.00000 | 0.402492 | ||||||||
\(501\) | −10.3431 | −0.462098 | ||||||||
\(502\) | −12.9289 | −0.577046 | ||||||||
\(503\) | −10.3431 | −0.461178 | −0.230589 | − | 0.973051i | \(-0.574065\pi\) | ||||
−0.230589 | + | 0.973051i | \(0.574065\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.343146 | −0.0152698 | ||||||||
\(506\) | −2.34315 | −0.104166 | ||||||||
\(507\) | −10.7574 | −0.477751 | ||||||||
\(508\) | −5.75736 | −0.255442 | ||||||||
\(509\) | 27.3137 | 1.21066 | 0.605329 | − | 0.795975i | \(-0.293041\pi\) | ||||
0.605329 | + | 0.795975i | \(0.293041\pi\) | |||||||
\(510\) | 0.899495 | 0.0398303 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.82843 | −0.301482 | ||||||||
\(514\) | 25.4853 | 1.12411 | ||||||||
\(515\) | −8.89949 | −0.392159 | ||||||||
\(516\) | 2.51472 | 0.110704 | ||||||||
\(517\) | 5.02944 | 0.221194 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.07107 | 0.178700 | ||||||||
\(520\) | −6.24264 | −0.273758 | ||||||||
\(521\) | 9.17157 | 0.401814 | 0.200907 | − | 0.979610i | \(-0.435611\pi\) | ||||
0.200907 | + | 0.979610i | \(0.435611\pi\) | |||||||
\(522\) | −10.8284 | −0.473947 | ||||||||
\(523\) | −15.3137 | −0.669622 | −0.334811 | − | 0.942285i | \(-0.608672\pi\) | ||||
−0.334811 | + | 0.942285i | \(0.608672\pi\) | |||||||
\(524\) | −0.242641 | −0.0105998 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.97056 | 0.391135 | ||||||||
\(527\) | 18.2721 | 0.795944 | ||||||||
\(528\) | −0.242641 | −0.0105596 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | −8.65685 | −0.376030 | ||||||||
\(531\) | 13.6569 | 0.592657 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.24264 | −0.270399 | ||||||||
\(534\) | −3.24264 | −0.140323 | ||||||||
\(535\) | −12.8995 | −0.557694 | ||||||||
\(536\) | 3.17157 | 0.136991 | ||||||||
\(537\) | −1.75736 | −0.0758357 | ||||||||
\(538\) | −2.68629 | −0.115814 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.41421 | −0.103891 | ||||||||
\(541\) | −18.0000 | −0.773880 | −0.386940 | − | 0.922105i | \(-0.626468\pi\) | ||||
−0.386940 | + | 0.922105i | \(0.626468\pi\) | |||||||
\(542\) | 6.00000 | 0.257722 | ||||||||
\(543\) | −4.10051 | −0.175970 | ||||||||
\(544\) | 2.17157 | 0.0931054 | ||||||||
\(545\) | −14.1421 | −0.605783 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.7990 | 0.932058 | 0.466029 | − | 0.884770i | \(-0.345684\pi\) | ||||
0.466029 | + | 0.884770i | \(0.345684\pi\) | |||||||
\(548\) | 1.65685 | 0.0707773 | ||||||||
\(549\) | −7.51472 | −0.320720 | ||||||||
\(550\) | −2.34315 | −0.0999121 | ||||||||
\(551\) | −10.8284 | −0.461307 | ||||||||
\(552\) | 1.65685 | 0.0705204 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −12.3431 | −0.524410 | ||||||||
\(555\) | −0.585786 | −0.0248652 | ||||||||
\(556\) | 1.51472 | 0.0642384 | ||||||||
\(557\) | −0.798990 | −0.0338543 | −0.0169271 | − | 0.999857i | \(-0.505388\pi\) | ||||
−0.0169271 | + | 0.999857i | \(0.505388\pi\) | |||||||
\(558\) | −23.7990 | −1.00749 | ||||||||
\(559\) | −37.8995 | −1.60298 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.526912 | −0.0222462 | ||||||||
\(562\) | −26.0000 | −1.09674 | ||||||||
\(563\) | −31.9411 | −1.34616 | −0.673079 | − | 0.739571i | \(-0.735029\pi\) | ||||
−0.673079 | + | 0.739571i | \(0.735029\pi\) | |||||||
\(564\) | −3.55635 | −0.149749 | ||||||||
\(565\) | 5.00000 | 0.210352 | ||||||||
\(566\) | −22.4853 | −0.945127 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.24264 | 0.0521400 | ||||||||
\(569\) | 22.1716 | 0.929481 | 0.464740 | − | 0.885447i | \(-0.346148\pi\) | ||||
0.464740 | + | 0.885447i | \(0.346148\pi\) | |||||||
\(570\) | −1.17157 | −0.0490718 | ||||||||
\(571\) | −45.2548 | −1.89386 | −0.946928 | − | 0.321446i | \(-0.895831\pi\) | ||||
−0.946928 | + | 0.321446i | \(0.895831\pi\) | |||||||
\(572\) | 3.65685 | 0.152901 | ||||||||
\(573\) | 1.34315 | 0.0561107 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.0000 | 0.667246 | ||||||||
\(576\) | −2.82843 | −0.117851 | ||||||||
\(577\) | −6.34315 | −0.264069 | −0.132034 | − | 0.991245i | \(-0.542151\pi\) | ||||
−0.132034 | + | 0.991245i | \(0.542151\pi\) | |||||||
\(578\) | −12.2843 | −0.510958 | ||||||||
\(579\) | −3.27208 | −0.135983 | ||||||||
\(580\) | −3.82843 | −0.158967 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5.04163 | −0.208982 | ||||||||
\(583\) | 5.07107 | 0.210022 | ||||||||
\(584\) | 4.00000 | 0.165521 | ||||||||
\(585\) | 17.6569 | 0.730021 | ||||||||
\(586\) | 14.0000 | 0.578335 | ||||||||
\(587\) | 11.1005 | 0.458167 | 0.229083 | − | 0.973407i | \(-0.426427\pi\) | ||||
0.229083 | + | 0.973407i | \(0.426427\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.7990 | −0.980620 | ||||||||
\(590\) | 4.82843 | 0.198783 | ||||||||
\(591\) | −9.65685 | −0.397230 | ||||||||
\(592\) | −1.41421 | −0.0581238 | ||||||||
\(593\) | 27.0000 | 1.10876 | 0.554379 | − | 0.832265i | \(-0.312956\pi\) | ||||
0.554379 | + | 0.832265i | \(0.312956\pi\) | |||||||
\(594\) | 1.41421 | 0.0580259 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20.6569 | 0.846138 | ||||||||
\(597\) | −4.68629 | −0.191797 | ||||||||
\(598\) | −24.9706 | −1.02112 | ||||||||
\(599\) | −47.8406 | −1.95471 | −0.977357 | − | 0.211595i | \(-0.932134\pi\) | ||||
−0.977357 | + | 0.211595i | \(0.932134\pi\) | |||||||
\(600\) | 1.65685 | 0.0676408 | ||||||||
\(601\) | −0.313708 | −0.0127964 | −0.00639822 | − | 0.999980i | \(-0.502037\pi\) | ||||
−0.00639822 | + | 0.999980i | \(0.502037\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.97056 | −0.365310 | ||||||||
\(604\) | 20.0711 | 0.816680 | ||||||||
\(605\) | 10.6569 | 0.433263 | ||||||||
\(606\) | −0.142136 | −0.00577387 | ||||||||
\(607\) | 7.38478 | 0.299739 | 0.149869 | − | 0.988706i | \(-0.452115\pi\) | ||||
0.149869 | + | 0.988706i | \(0.452115\pi\) | |||||||
\(608\) | −2.82843 | −0.114708 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.65685 | −0.107573 | ||||||||
\(611\) | 53.5980 | 2.16834 | ||||||||
\(612\) | −6.14214 | −0.248281 | ||||||||
\(613\) | 38.0416 | 1.53649 | 0.768243 | − | 0.640158i | \(-0.221131\pi\) | ||||
0.768243 | + | 0.640158i | \(0.221131\pi\) | |||||||
\(614\) | 24.9706 | 1.00773 | ||||||||
\(615\) | −0.414214 | −0.0167027 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.7990 | −1.28018 | −0.640090 | − | 0.768300i | \(-0.721103\pi\) | ||||
−0.640090 | + | 0.768300i | \(0.721103\pi\) | |||||||
\(618\) | −3.68629 | −0.148284 | ||||||||
\(619\) | −11.0711 | −0.444984 | −0.222492 | − | 0.974935i | \(-0.571419\pi\) | ||||
−0.222492 | + | 0.974935i | \(0.571419\pi\) | |||||||
\(620\) | −8.41421 | −0.337923 | ||||||||
\(621\) | −9.65685 | −0.387516 | ||||||||
\(622\) | 5.51472 | 0.221120 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.58579 | −0.103514 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | −4.97056 | −0.198664 | ||||||||
\(627\) | 0.686292 | 0.0274078 | ||||||||
\(628\) | −13.6569 | −0.544968 | ||||||||
\(629\) | −3.07107 | −0.122451 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.2132 | 0.764866 | 0.382433 | − | 0.923983i | \(-0.375086\pi\) | ||||
0.382433 | + | 0.923983i | \(0.375086\pi\) | |||||||
\(632\) | −3.24264 | −0.128985 | ||||||||
\(633\) | 0.686292 | 0.0272776 | ||||||||
\(634\) | −21.6569 | −0.860104 | ||||||||
\(635\) | 5.75736 | 0.228474 | ||||||||
\(636\) | −3.58579 | −0.142186 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.24264 | 0.0887870 | ||||||||
\(639\) | −3.51472 | −0.139040 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 18.8701 | 0.745322 | 0.372661 | − | 0.927967i | \(-0.378445\pi\) | ||||
0.372661 | + | 0.927967i | \(0.378445\pi\) | |||||||
\(642\) | −5.34315 | −0.210877 | ||||||||
\(643\) | 6.55635 | 0.258557 | 0.129279 | − | 0.991608i | \(-0.458734\pi\) | ||||
0.129279 | + | 0.991608i | \(0.458734\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.51472 | −0.0990169 | ||||||||
\(646\) | −6.14214 | −0.241659 | ||||||||
\(647\) | −11.3848 | −0.447582 | −0.223791 | − | 0.974637i | \(-0.571843\pi\) | ||||
−0.223791 | + | 0.974637i | \(0.571843\pi\) | |||||||
\(648\) | 7.48528 | 0.294050 | ||||||||
\(649\) | −2.82843 | −0.111025 | ||||||||
\(650\) | −24.9706 | −0.979426 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −25.3137 | −0.991361 | ||||||||
\(653\) | −25.6274 | −1.00288 | −0.501439 | − | 0.865193i | \(-0.667196\pi\) | ||||
−0.501439 | + | 0.865193i | \(0.667196\pi\) | |||||||
\(654\) | −5.85786 | −0.229061 | ||||||||
\(655\) | 0.242641 | 0.00948076 | ||||||||
\(656\) | −1.00000 | −0.0390434 | ||||||||
\(657\) | −11.3137 | −0.441390 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.37258 | 0.0534682 | 0.0267341 | − | 0.999643i | \(-0.491489\pi\) | ||||
0.0267341 | + | 0.999643i | \(0.491489\pi\) | |||||||
\(660\) | 0.242641 | 0.00944478 | ||||||||
\(661\) | −33.4558 | −1.30128 | −0.650641 | − | 0.759386i | \(-0.725500\pi\) | ||||
−0.650641 | + | 0.759386i | \(0.725500\pi\) | |||||||
\(662\) | −16.0416 | −0.623476 | ||||||||
\(663\) | −5.61522 | −0.218077 | ||||||||
\(664\) | 1.07107 | 0.0415655 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.00000 | 0.154997 | ||||||||
\(667\) | −15.3137 | −0.592949 | ||||||||
\(668\) | 24.9706 | 0.966140 | ||||||||
\(669\) | 11.5442 | 0.446323 | ||||||||
\(670\) | −3.17157 | −0.122529 | ||||||||
\(671\) | 1.55635 | 0.0600822 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.5563 | 0.599653 | 0.299827 | − | 0.953994i | \(-0.403071\pi\) | ||||
0.299827 | + | 0.953994i | \(0.403071\pi\) | |||||||
\(674\) | −8.65685 | −0.333450 | ||||||||
\(675\) | −9.65685 | −0.371692 | ||||||||
\(676\) | 25.9706 | 0.998868 | ||||||||
\(677\) | 11.7990 | 0.453472 | 0.226736 | − | 0.973956i | \(-0.427195\pi\) | ||||
0.226736 | + | 0.973956i | \(0.427195\pi\) | |||||||
\(678\) | 2.07107 | 0.0795389 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.17157 | −0.0832760 | ||||||||
\(681\) | 3.20101 | 0.122663 | ||||||||
\(682\) | 4.92893 | 0.188739 | ||||||||
\(683\) | 1.65685 | 0.0633978 | 0.0316989 | − | 0.999497i | \(-0.489908\pi\) | ||||
0.0316989 | + | 0.999497i | \(0.489908\pi\) | |||||||
\(684\) | 8.00000 | 0.305888 | ||||||||
\(685\) | −1.65685 | −0.0633051 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.41421 | −0.0539556 | ||||||||
\(688\) | −6.07107 | −0.231457 | ||||||||
\(689\) | 54.0416 | 2.05882 | ||||||||
\(690\) | −1.65685 | −0.0630754 | ||||||||
\(691\) | −19.7279 | −0.750486 | −0.375243 | − | 0.926927i | \(-0.622441\pi\) | ||||
−0.375243 | + | 0.926927i | \(0.622441\pi\) | |||||||
\(692\) | −9.82843 | −0.373621 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.65685 | −0.214731 | ||||||||
\(695\) | −1.51472 | −0.0574566 | ||||||||
\(696\) | −1.58579 | −0.0601091 | ||||||||
\(697\) | −2.17157 | −0.0822542 | ||||||||
\(698\) | 19.7990 | 0.749403 | ||||||||
\(699\) | 10.0416 | 0.379809 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.97056 | −0.338813 | −0.169407 | − | 0.985546i | \(-0.554185\pi\) | ||||
−0.169407 | + | 0.985546i | \(0.554185\pi\) | |||||||
\(702\) | 15.0711 | 0.568821 | ||||||||
\(703\) | 4.00000 | 0.150863 | ||||||||
\(704\) | 0.585786 | 0.0220777 | ||||||||
\(705\) | 3.55635 | 0.133940 | ||||||||
\(706\) | −6.34315 | −0.238727 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.00000 | 0.0751646 | ||||||||
\(709\) | 22.7990 | 0.856234 | 0.428117 | − | 0.903723i | \(-0.359177\pi\) | ||||
0.428117 | + | 0.903723i | \(0.359177\pi\) | |||||||
\(710\) | −1.24264 | −0.0466355 | ||||||||
\(711\) | 9.17157 | 0.343961 | ||||||||
\(712\) | 7.82843 | 0.293383 | ||||||||
\(713\) | −33.6569 | −1.26046 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.65685 | −0.136759 | ||||||||
\(716\) | 4.24264 | 0.158555 | ||||||||
\(717\) | −1.45584 | −0.0543695 | ||||||||
\(718\) | 18.3848 | 0.686114 | ||||||||
\(719\) | −27.3553 | −1.02018 | −0.510091 | − | 0.860120i | \(-0.670388\pi\) | ||||
−0.510091 | + | 0.860120i | \(0.670388\pi\) | |||||||
\(720\) | 2.82843 | 0.105409 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −11.0000 | −0.409378 | ||||||||
\(723\) | 8.87006 | 0.329881 | ||||||||
\(724\) | 9.89949 | 0.367912 | ||||||||
\(725\) | −15.3137 | −0.568737 | ||||||||
\(726\) | 4.41421 | 0.163827 | ||||||||
\(727\) | −43.0711 | −1.59742 | −0.798709 | − | 0.601718i | \(-0.794483\pi\) | ||||
−0.798709 | + | 0.601718i | \(0.794483\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | −4.00000 | −0.148047 | ||||||||
\(731\) | −13.1838 | −0.487619 | ||||||||
\(732\) | −1.10051 | −0.0406758 | ||||||||
\(733\) | −23.8284 | −0.880123 | −0.440062 | − | 0.897968i | \(-0.645043\pi\) | ||||
−0.440062 | + | 0.897968i | \(0.645043\pi\) | |||||||
\(734\) | 3.24264 | 0.119688 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.00000 | −0.147442 | ||||||||
\(737\) | 1.85786 | 0.0684353 | ||||||||
\(738\) | 2.82843 | 0.104116 | ||||||||
\(739\) | 18.5563 | 0.682606 | 0.341303 | − | 0.939953i | \(-0.389132\pi\) | ||||
0.341303 | + | 0.939953i | \(0.389132\pi\) | |||||||
\(740\) | 1.41421 | 0.0519875 | ||||||||
\(741\) | 7.31371 | 0.268676 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.9411 | −1.24518 | −0.622590 | − | 0.782549i | \(-0.713919\pi\) | ||||
−0.622590 | + | 0.782549i | \(0.713919\pi\) | |||||||
\(744\) | −3.48528 | −0.127777 | ||||||||
\(745\) | −20.6569 | −0.756809 | ||||||||
\(746\) | −11.7574 | −0.430468 | ||||||||
\(747\) | −3.02944 | −0.110841 | ||||||||
\(748\) | 1.27208 | 0.0465118 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −3.72792 | −0.136124 | ||||||||
\(751\) | 20.3431 | 0.742332 | 0.371166 | − | 0.928567i | \(-0.378958\pi\) | ||||
0.371166 | + | 0.928567i | \(0.378958\pi\) | |||||||
\(752\) | 8.58579 | 0.313091 | ||||||||
\(753\) | 5.35534 | 0.195159 | ||||||||
\(754\) | 23.8995 | 0.870368 | ||||||||
\(755\) | −20.0711 | −0.730461 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.45584 | 0.161950 | 0.0809752 | − | 0.996716i | \(-0.474197\pi\) | ||||
0.0809752 | + | 0.996716i | \(0.474197\pi\) | |||||||
\(758\) | −27.3848 | −0.994660 | ||||||||
\(759\) | 0.970563 | 0.0352292 | ||||||||
\(760\) | 2.82843 | 0.102598 | ||||||||
\(761\) | −7.55635 | −0.273917 | −0.136959 | − | 0.990577i | \(-0.543733\pi\) | ||||
−0.136959 | + | 0.990577i | \(0.543733\pi\) | |||||||
\(762\) | 2.38478 | 0.0863913 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3.24264 | −0.117315 | ||||||||
\(765\) | 6.14214 | 0.222069 | ||||||||
\(766\) | 10.7279 | 0.387616 | ||||||||
\(767\) | −30.1421 | −1.08837 | ||||||||
\(768\) | −0.414214 | −0.0149466 | ||||||||
\(769\) | 10.9706 | 0.395609 | 0.197804 | − | 0.980242i | \(-0.436619\pi\) | ||||
0.197804 | + | 0.980242i | \(0.436619\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.5563 | −0.380178 | ||||||||
\(772\) | 7.89949 | 0.284309 | ||||||||
\(773\) | −23.5563 | −0.847263 | −0.423631 | − | 0.905835i | \(-0.639245\pi\) | ||||
−0.423631 | + | 0.905835i | \(0.639245\pi\) | |||||||
\(774\) | 17.1716 | 0.617219 | ||||||||
\(775\) | −33.6569 | −1.20899 | ||||||||
\(776\) | 12.1716 | 0.436934 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.00000 | −0.0717035 | ||||||||
\(779\) | 2.82843 | 0.101339 | ||||||||
\(780\) | 2.58579 | 0.0925860 | ||||||||
\(781\) | 0.727922 | 0.0260471 | ||||||||
\(782\) | −8.68629 | −0.310621 | ||||||||
\(783\) | 9.24264 | 0.330305 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.6569 | 0.487434 | ||||||||
\(786\) | 0.100505 | 0.00358490 | ||||||||
\(787\) | 14.3431 | 0.511278 | 0.255639 | − | 0.966772i | \(-0.417714\pi\) | ||||
0.255639 | + | 0.966772i | \(0.417714\pi\) | |||||||
\(788\) | 23.3137 | 0.830516 | ||||||||
\(789\) | −3.71573 | −0.132283 | ||||||||
\(790\) | 3.24264 | 0.115368 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.65685 | −0.0588738 | ||||||||
\(793\) | 16.5858 | 0.588979 | ||||||||
\(794\) | 8.58579 | 0.304698 | ||||||||
\(795\) | 3.58579 | 0.127175 | ||||||||
\(796\) | 11.3137 | 0.401004 | ||||||||
\(797\) | −7.62742 | −0.270177 | −0.135088 | − | 0.990834i | \(-0.543132\pi\) | ||||
−0.135088 | + | 0.990834i | \(0.543132\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.6447 | 0.659601 | ||||||||
\(800\) | −4.00000 | −0.141421 | ||||||||
\(801\) | −22.1421 | −0.782354 | ||||||||
\(802\) | 13.9706 | 0.493318 | ||||||||
\(803\) | 2.34315 | 0.0826878 | ||||||||
\(804\) | −1.31371 | −0.0463309 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 52.5269 | 1.85018 | ||||||||
\(807\) | 1.11270 | 0.0391688 | ||||||||
\(808\) | 0.343146 | 0.0120718 | ||||||||
\(809\) | 4.24264 | 0.149163 | 0.0745817 | − | 0.997215i | \(-0.476238\pi\) | ||||
0.0745817 | + | 0.997215i | \(0.476238\pi\) | |||||||
\(810\) | −7.48528 | −0.263006 | ||||||||
\(811\) | −55.5563 | −1.95085 | −0.975424 | − | 0.220338i | \(-0.929284\pi\) | ||||
−0.975424 | + | 0.220338i | \(0.929284\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.48528 | −0.0871626 | ||||||||
\(814\) | −0.828427 | −0.0290364 | ||||||||
\(815\) | 25.3137 | 0.886701 | ||||||||
\(816\) | −0.899495 | −0.0314886 | ||||||||
\(817\) | 17.1716 | 0.600757 | ||||||||
\(818\) | −14.1005 | −0.493013 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.00000 | 0.0349215 | ||||||||
\(821\) | −10.2426 | −0.357471 | −0.178735 | − | 0.983897i | \(-0.557201\pi\) | ||||
−0.178735 | + | 0.983897i | \(0.557201\pi\) | |||||||
\(822\) | −0.686292 | −0.0239372 | ||||||||
\(823\) | −51.1838 | −1.78415 | −0.892077 | − | 0.451883i | \(-0.850752\pi\) | ||||
−0.892077 | + | 0.451883i | \(0.850752\pi\) | |||||||
\(824\) | 8.89949 | 0.310029 | ||||||||
\(825\) | 0.970563 | 0.0337907 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.4558 | −1.23292 | −0.616460 | − | 0.787386i | \(-0.711434\pi\) | ||||
−0.616460 | + | 0.787386i | \(0.711434\pi\) | |||||||
\(828\) | 11.3137 | 0.393179 | ||||||||
\(829\) | 22.8579 | 0.793886 | 0.396943 | − | 0.917843i | \(-0.370071\pi\) | ||||
0.396943 | + | 0.917843i | \(0.370071\pi\) | |||||||
\(830\) | −1.07107 | −0.0371773 | ||||||||
\(831\) | 5.11270 | 0.177358 | ||||||||
\(832\) | 6.24264 | 0.216425 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.627417 | −0.0217257 | ||||||||
\(835\) | −24.9706 | −0.864142 | ||||||||
\(836\) | −1.65685 | −0.0573035 | ||||||||
\(837\) | 20.3137 | 0.702144 | ||||||||
\(838\) | −20.2426 | −0.699270 | ||||||||
\(839\) | −36.8284 | −1.27146 | −0.635729 | − | 0.771912i | \(-0.719301\pi\) | ||||
−0.635729 | + | 0.771912i | \(0.719301\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.3431 | −0.494591 | ||||||||
\(842\) | 36.1127 | 1.24453 | ||||||||
\(843\) | 10.7696 | 0.370923 | ||||||||
\(844\) | −1.65685 | −0.0570313 | ||||||||
\(845\) | −25.9706 | −0.893415 | ||||||||
\(846\) | −24.2843 | −0.834910 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.65685 | 0.297278 | ||||||||
\(849\) | 9.31371 | 0.319646 | ||||||||
\(850\) | −8.68629 | −0.297937 | ||||||||
\(851\) | 5.65685 | 0.193914 | ||||||||
\(852\) | −0.514719 | −0.0176340 | ||||||||
\(853\) | −21.0000 | −0.719026 | −0.359513 | − | 0.933140i | \(-0.617057\pi\) | ||||
−0.359513 | + | 0.933140i | \(0.617057\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.00000 | −0.273594 | ||||||||
\(856\) | 12.8995 | 0.440896 | ||||||||
\(857\) | 39.9411 | 1.36436 | 0.682181 | − | 0.731183i | \(-0.261031\pi\) | ||||
0.682181 | + | 0.731183i | \(0.261031\pi\) | |||||||
\(858\) | −1.51472 | −0.0517116 | ||||||||
\(859\) | −26.1005 | −0.890538 | −0.445269 | − | 0.895397i | \(-0.646892\pi\) | ||||
−0.445269 | + | 0.895397i | \(0.646892\pi\) | |||||||
\(860\) | 6.07107 | 0.207022 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.0000 | 0.408722 | ||||||||
\(863\) | 23.5563 | 0.801867 | 0.400934 | − | 0.916107i | \(-0.368686\pi\) | ||||
0.400934 | + | 0.916107i | \(0.368686\pi\) | |||||||
\(864\) | 2.41421 | 0.0821332 | ||||||||
\(865\) | 9.82843 | 0.334177 | ||||||||
\(866\) | 24.9706 | 0.848534 | ||||||||
\(867\) | 5.08831 | 0.172808 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.89949 | −0.0644360 | ||||||||
\(870\) | 1.58579 | 0.0537632 | ||||||||
\(871\) | 19.7990 | 0.670863 | ||||||||
\(872\) | 14.1421 | 0.478913 | ||||||||
\(873\) | −34.4264 | −1.16516 | ||||||||
\(874\) | 11.3137 | 0.382692 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.65685 | −0.0559799 | ||||||||
\(877\) | 34.3431 | 1.15969 | 0.579843 | − | 0.814728i | \(-0.303114\pi\) | ||||
0.579843 | + | 0.814728i | \(0.303114\pi\) | |||||||
\(878\) | −9.51472 | −0.321106 | ||||||||
\(879\) | −5.79899 | −0.195595 | ||||||||
\(880\) | −0.585786 | −0.0197469 | ||||||||
\(881\) | 53.1543 | 1.79081 | 0.895407 | − | 0.445248i | \(-0.146884\pi\) | ||||
0.895407 | + | 0.445248i | \(0.146884\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.4558 | −1.19318 | −0.596592 | − | 0.802545i | \(-0.703479\pi\) | ||||
−0.596592 | + | 0.802545i | \(0.703479\pi\) | |||||||
\(884\) | 13.5563 | 0.455949 | ||||||||
\(885\) | −2.00000 | −0.0672293 | ||||||||
\(886\) | 9.24264 | 0.310513 | ||||||||
\(887\) | −37.2548 | −1.25089 | −0.625447 | − | 0.780266i | \(-0.715084\pi\) | ||||
−0.625447 | + | 0.780266i | \(0.715084\pi\) | |||||||
\(888\) | 0.585786 | 0.0196577 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −7.82843 | −0.262409 | ||||||||
\(891\) | 4.38478 | 0.146896 | ||||||||
\(892\) | −27.8701 | −0.933159 | ||||||||
\(893\) | −24.2843 | −0.812642 | ||||||||
\(894\) | −8.55635 | −0.286167 | ||||||||
\(895\) | −4.24264 | −0.141816 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.3431 | 0.345348 | ||||||||
\(898\) | 14.1716 | 0.472912 | ||||||||
\(899\) | 32.2132 | 1.07437 | ||||||||
\(900\) | 11.3137 | 0.377124 | ||||||||
\(901\) | 18.7990 | 0.626285 | ||||||||
\(902\) | −0.585786 | −0.0195046 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.00000 | −0.166298 | ||||||||
\(905\) | −9.89949 | −0.329070 | ||||||||
\(906\) | −8.31371 | −0.276204 | ||||||||
\(907\) | 53.2426 | 1.76789 | 0.883946 | − | 0.467588i | \(-0.154877\pi\) | ||||
0.883946 | + | 0.467588i | \(0.154877\pi\) | |||||||
\(908\) | −7.72792 | −0.256460 | ||||||||
\(909\) | −0.970563 | −0.0321915 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.7696 | 0.621863 | 0.310932 | − | 0.950432i | \(-0.399359\pi\) | ||||
0.310932 | + | 0.950432i | \(0.399359\pi\) | |||||||
\(912\) | 1.17157 | 0.0387947 | ||||||||
\(913\) | 0.627417 | 0.0207645 | ||||||||
\(914\) | −36.7279 | −1.21485 | ||||||||
\(915\) | 1.10051 | 0.0363816 | ||||||||
\(916\) | 3.41421 | 0.112809 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.24264 | 0.173033 | ||||||||
\(919\) | −0.213203 | −0.00703293 | −0.00351647 | − | 0.999994i | \(-0.501119\pi\) | ||||
−0.00351647 | + | 0.999994i | \(0.501119\pi\) | |||||||
\(920\) | 4.00000 | 0.131876 | ||||||||
\(921\) | −10.3431 | −0.340818 | ||||||||
\(922\) | −31.9706 | −1.05289 | ||||||||
\(923\) | 7.75736 | 0.255337 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.65685 | 0.185996 | ||||||||
\(926\) | 5.65685 | 0.185896 | ||||||||
\(927\) | −25.1716 | −0.826743 | ||||||||
\(928\) | 3.82843 | 0.125674 | ||||||||
\(929\) | 25.1716 | 0.825853 | 0.412926 | − | 0.910764i | \(-0.364507\pi\) | ||||
0.412926 | + | 0.910764i | \(0.364507\pi\) | |||||||
\(930\) | 3.48528 | 0.114287 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −24.2426 | −0.794094 | ||||||||
\(933\) | −2.28427 | −0.0747837 | ||||||||
\(934\) | −34.4853 | −1.12839 | ||||||||
\(935\) | −1.27208 | −0.0416014 | ||||||||
\(936\) | −17.6569 | −0.577132 | ||||||||
\(937\) | 3.97056 | 0.129713 | 0.0648563 | − | 0.997895i | \(-0.479341\pi\) | ||||
0.0648563 | + | 0.997895i | \(0.479341\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.05887 | 0.0671888 | ||||||||
\(940\) | −8.58579 | −0.280037 | ||||||||
\(941\) | 25.9411 | 0.845657 | 0.422828 | − | 0.906210i | \(-0.361037\pi\) | ||||
0.422828 | + | 0.906210i | \(0.361037\pi\) | |||||||
\(942\) | 5.65685 | 0.184310 | ||||||||
\(943\) | 4.00000 | 0.130258 | ||||||||
\(944\) | −4.82843 | −0.157152 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.55635 | −0.115627 | ||||||||
\(947\) | 40.7696 | 1.32483 | 0.662416 | − | 0.749136i | \(-0.269531\pi\) | ||||
0.662416 | + | 0.749136i | \(0.269531\pi\) | |||||||
\(948\) | 1.34315 | 0.0436233 | ||||||||
\(949\) | 24.9706 | 0.810579 | ||||||||
\(950\) | 11.3137 | 0.367065 | ||||||||
\(951\) | 8.97056 | 0.290890 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.51472 | 0.113853 | 0.0569265 | − | 0.998378i | \(-0.481870\pi\) | ||||
0.0569265 | + | 0.998378i | \(0.481870\pi\) | |||||||
\(954\) | −24.4853 | −0.792740 | ||||||||
\(955\) | 3.24264 | 0.104929 | ||||||||
\(956\) | 3.51472 | 0.113674 | ||||||||
\(957\) | −0.928932 | −0.0300281 | ||||||||
\(958\) | 35.2132 | 1.13769 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.414214 | 0.0133687 | ||||||||
\(961\) | 39.7990 | 1.28384 | ||||||||
\(962\) | −8.82843 | −0.284640 | ||||||||
\(963\) | −36.4853 | −1.17572 | ||||||||
\(964\) | −21.4142 | −0.689705 | ||||||||
\(965\) | −7.89949 | −0.254294 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.0711 | −1.54586 | −0.772931 | − | 0.634490i | \(-0.781210\pi\) | ||||
−0.772931 | + | 0.634490i | \(0.781210\pi\) | |||||||
\(968\) | −10.6569 | −0.342524 | ||||||||
\(969\) | 2.54416 | 0.0817301 | ||||||||
\(970\) | −12.1716 | −0.390806 | ||||||||
\(971\) | 5.24264 | 0.168244 | 0.0841222 | − | 0.996455i | \(-0.473191\pi\) | ||||
0.0841222 | + | 0.996455i | \(0.473191\pi\) | |||||||
\(972\) | −10.3431 | −0.331757 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −18.5858 | −0.595527 | ||||||||
\(975\) | 10.3431 | 0.331246 | ||||||||
\(976\) | 2.65685 | 0.0850438 | ||||||||
\(977\) | −6.28427 | −0.201052 | −0.100526 | − | 0.994934i | \(-0.532053\pi\) | ||||
−0.100526 | + | 0.994934i | \(0.532053\pi\) | |||||||
\(978\) | 10.4853 | 0.335282 | ||||||||
\(979\) | 4.58579 | 0.146562 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −40.0000 | −1.27710 | ||||||||
\(982\) | 15.8701 | 0.506434 | ||||||||
\(983\) | −23.2426 | −0.741325 | −0.370663 | − | 0.928768i | \(-0.620869\pi\) | ||||
−0.370663 | + | 0.928768i | \(0.620869\pi\) | |||||||
\(984\) | 0.414214 | 0.0132046 | ||||||||
\(985\) | −23.3137 | −0.742837 | ||||||||
\(986\) | 8.31371 | 0.264762 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17.6569 | −0.561739 | ||||||||
\(989\) | 24.2843 | 0.772195 | ||||||||
\(990\) | 1.65685 | 0.0526583 | ||||||||
\(991\) | 8.34315 | 0.265029 | 0.132514 | − | 0.991181i | \(-0.457695\pi\) | ||||
0.132514 | + | 0.991181i | \(0.457695\pi\) | |||||||
\(992\) | 8.41421 | 0.267152 | ||||||||
\(993\) | 6.64466 | 0.210862 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.3137 | −0.358669 | ||||||||
\(996\) | −0.443651 | −0.0140576 | ||||||||
\(997\) | 36.2843 | 1.14913 | 0.574567 | − | 0.818457i | \(-0.305170\pi\) | ||||
0.574567 | + | 0.818457i | \(0.305170\pi\) | |||||||
\(998\) | 22.4853 | 0.711759 | ||||||||
\(999\) | −3.41421 | −0.108021 |
(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 | 4018.2.a.bb.1.1 | yes | 2 | |
7.6 | odd | 2 | 4018.2.a.z.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4018.2.a.z.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
4018.2.a.bb.1.1 | yes | 2 | 1.1 | even | 1 | trivial |