Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3822,2,Mod(1,3822)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3822, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3822.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3822.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: | \(30.5188236525\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3822.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | −0.223607 | − | 0.974679i | \(-0.571783\pi\) | ||||
−0.223607 | + | 0.974679i | \(0.571783\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −3.58579 | −1.08116 | −0.540578 | − | 0.841294i | \(-0.681794\pi\) | ||||
−0.540578 | + | 0.841294i | \(0.681794\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.24264 | −1.27153 | −0.635764 | − | 0.771884i | \(-0.719315\pi\) | ||||
−0.635764 | + | 0.771884i | \(0.719315\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 6.65685 | 1.52719 | 0.763594 | − | 0.645697i | \(-0.223433\pi\) | ||||
0.763594 | + | 0.645697i | \(0.223433\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.58579 | −0.764492 | ||||||||
\(23\) | −7.82843 | −1.63234 | −0.816170 | − | 0.577812i | \(-0.803907\pi\) | ||||
−0.816170 | + | 0.577812i | \(0.803907\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.48528 | −1.76137 | −0.880686 | − | 0.473700i | \(-0.842918\pi\) | ||||
−0.880686 | + | 0.473700i | \(0.842918\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −1.41421 | −0.254000 | −0.127000 | − | 0.991903i | \(-0.540535\pi\) | ||||
−0.127000 | + | 0.991903i | \(0.540535\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.58579 | −0.624205 | ||||||||
\(34\) | −5.24264 | −0.899105 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.58579 | −0.918298 | −0.459149 | − | 0.888359i | \(-0.651846\pi\) | ||||
−0.459149 | + | 0.888359i | \(0.651846\pi\) | |||||||
\(38\) | 6.65685 | 1.07988 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −10.8284 | −1.69112 | −0.845558 | − | 0.533883i | \(-0.820732\pi\) | ||||
−0.845558 | + | 0.533883i | \(0.820732\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.65685 | 0.405166 | 0.202583 | − | 0.979265i | \(-0.435066\pi\) | ||||
0.202583 | + | 0.979265i | \(0.435066\pi\) | |||||||
\(44\) | −3.58579 | −0.540578 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −7.82843 | −1.15424 | ||||||||
\(47\) | 6.00000 | 0.875190 | 0.437595 | − | 0.899172i | \(-0.355830\pi\) | ||||
0.437595 | + | 0.899172i | \(0.355830\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.00000 | −0.565685 | ||||||||
\(51\) | −5.24264 | −0.734117 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 5.65685 | 0.777029 | 0.388514 | − | 0.921443i | \(-0.372988\pi\) | ||||
0.388514 | + | 0.921443i | \(0.372988\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 3.58579 | 0.483507 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.65685 | 0.881722 | ||||||||
\(58\) | −9.48528 | −1.24548 | ||||||||
\(59\) | 3.07107 | 0.399819 | 0.199909 | − | 0.979814i | \(-0.435935\pi\) | ||||
0.199909 | + | 0.979814i | \(0.435935\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 7.58579 | 0.971260 | 0.485630 | − | 0.874164i | \(-0.338590\pi\) | ||||
0.485630 | + | 0.874164i | \(0.338590\pi\) | |||||||
\(62\) | −1.41421 | −0.179605 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | −3.58579 | −0.441380 | ||||||||
\(67\) | 15.5563 | 1.90051 | 0.950255 | − | 0.311472i | \(-0.100822\pi\) | ||||
0.950255 | + | 0.311472i | \(0.100822\pi\) | |||||||
\(68\) | −5.24264 | −0.635764 | ||||||||
\(69\) | −7.82843 | −0.942432 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.2426 | −1.69029 | −0.845145 | − | 0.534537i | \(-0.820486\pi\) | ||||
−0.845145 | + | 0.534537i | \(0.820486\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 11.0000 | 1.28745 | 0.643726 | − | 0.765256i | \(-0.277388\pi\) | ||||
0.643726 | + | 0.765256i | \(0.277388\pi\) | |||||||
\(74\) | −5.58579 | −0.649334 | ||||||||
\(75\) | −4.00000 | −0.461880 | ||||||||
\(76\) | 6.65685 | 0.763594 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | −6.24264 | −0.702352 | −0.351176 | − | 0.936309i | \(-0.614218\pi\) | ||||
−0.351176 | + | 0.936309i | \(0.614218\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.8284 | −1.19580 | ||||||||
\(83\) | 7.65685 | 0.840449 | 0.420224 | − | 0.907420i | \(-0.361951\pi\) | ||||
0.420224 | + | 0.907420i | \(0.361951\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.24264 | 0.568644 | ||||||||
\(86\) | 2.65685 | 0.286496 | ||||||||
\(87\) | −9.48528 | −1.01693 | ||||||||
\(88\) | −3.58579 | −0.382246 | ||||||||
\(89\) | −5.75736 | −0.610279 | −0.305139 | − | 0.952308i | \(-0.598703\pi\) | ||||
−0.305139 | + | 0.952308i | \(0.598703\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.82843 | −0.816170 | ||||||||
\(93\) | −1.41421 | −0.146647 | ||||||||
\(94\) | 6.00000 | 0.618853 | ||||||||
\(95\) | −6.65685 | −0.682979 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −15.3137 | −1.55487 | −0.777436 | − | 0.628962i | \(-0.783480\pi\) | ||||
−0.777436 | + | 0.628962i | \(0.783480\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.58579 | −0.360385 | ||||||||
\(100\) | −4.00000 | −0.400000 | ||||||||
\(101\) | −15.4142 | −1.53377 | −0.766886 | − | 0.641784i | \(-0.778195\pi\) | ||||
−0.766886 | + | 0.641784i | \(0.778195\pi\) | |||||||
\(102\) | −5.24264 | −0.519099 | ||||||||
\(103\) | 4.41421 | 0.434945 | 0.217473 | − | 0.976066i | \(-0.430219\pi\) | ||||
0.217473 | + | 0.976066i | \(0.430219\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.65685 | 0.549442 | ||||||||
\(107\) | 13.5563 | 1.31054 | 0.655271 | − | 0.755394i | \(-0.272554\pi\) | ||||
0.655271 | + | 0.755394i | \(0.272554\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −18.8995 | −1.81024 | −0.905122 | − | 0.425153i | \(-0.860220\pi\) | ||||
−0.905122 | + | 0.425153i | \(0.860220\pi\) | |||||||
\(110\) | 3.58579 | 0.341891 | ||||||||
\(111\) | −5.58579 | −0.530179 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.41421 | 0.697471 | 0.348735 | − | 0.937221i | \(-0.386611\pi\) | ||||
0.348735 | + | 0.937221i | \(0.386611\pi\) | |||||||
\(114\) | 6.65685 | 0.623472 | ||||||||
\(115\) | 7.82843 | 0.730005 | ||||||||
\(116\) | −9.48528 | −0.880686 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 3.07107 | 0.282715 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 1.85786 | 0.168897 | ||||||||
\(122\) | 7.58579 | 0.686785 | ||||||||
\(123\) | −10.8284 | −0.976366 | ||||||||
\(124\) | −1.41421 | −0.127000 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.7279 | −1.66183 | −0.830917 | − | 0.556396i | \(-0.812184\pi\) | ||||
−0.830917 | + | 0.556396i | \(0.812184\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.65685 | 0.233923 | ||||||||
\(130\) | 1.00000 | 0.0877058 | ||||||||
\(131\) | 19.7279 | 1.72364 | 0.861818 | − | 0.507217i | \(-0.169326\pi\) | ||||
0.861818 | + | 0.507217i | \(0.169326\pi\) | |||||||
\(132\) | −3.58579 | −0.312103 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 15.5563 | 1.34386 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −5.24264 | −0.449553 | ||||||||
\(137\) | −3.58579 | −0.306354 | −0.153177 | − | 0.988199i | \(-0.548951\pi\) | ||||
−0.153177 | + | 0.988199i | \(0.548951\pi\) | |||||||
\(138\) | −7.82843 | −0.666400 | ||||||||
\(139\) | −19.7990 | −1.67933 | −0.839664 | − | 0.543106i | \(-0.817248\pi\) | ||||
−0.839664 | + | 0.543106i | \(0.817248\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | −14.2426 | −1.19522 | ||||||||
\(143\) | 3.58579 | 0.299859 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 9.48528 | 0.787710 | ||||||||
\(146\) | 11.0000 | 0.910366 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.58579 | −0.459149 | ||||||||
\(149\) | −8.48528 | −0.695141 | −0.347571 | − | 0.937654i | \(-0.612993\pi\) | ||||
−0.347571 | + | 0.937654i | \(0.612993\pi\) | |||||||
\(150\) | −4.00000 | −0.326599 | ||||||||
\(151\) | −3.58579 | −0.291807 | −0.145904 | − | 0.989299i | \(-0.546609\pi\) | ||||
−0.145904 | + | 0.989299i | \(0.546609\pi\) | |||||||
\(152\) | 6.65685 | 0.539942 | ||||||||
\(153\) | −5.24264 | −0.423842 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.41421 | 0.113592 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 5.58579 | 0.445794 | 0.222897 | − | 0.974842i | \(-0.428449\pi\) | ||||
0.222897 | + | 0.974842i | \(0.428449\pi\) | |||||||
\(158\) | −6.24264 | −0.496638 | ||||||||
\(159\) | 5.65685 | 0.448618 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −11.6569 | −0.913035 | −0.456518 | − | 0.889714i | \(-0.650903\pi\) | ||||
−0.456518 | + | 0.889714i | \(0.650903\pi\) | |||||||
\(164\) | −10.8284 | −0.845558 | ||||||||
\(165\) | 3.58579 | 0.279153 | ||||||||
\(166\) | 7.65685 | 0.594287 | ||||||||
\(167\) | −5.14214 | −0.397910 | −0.198955 | − | 0.980009i | \(-0.563755\pi\) | ||||
−0.198955 | + | 0.980009i | \(0.563755\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 5.24264 | 0.402092 | ||||||||
\(171\) | 6.65685 | 0.509062 | ||||||||
\(172\) | 2.65685 | 0.202583 | ||||||||
\(173\) | 1.89949 | 0.144416 | 0.0722080 | − | 0.997390i | \(-0.476995\pi\) | ||||
0.0722080 | + | 0.997390i | \(0.476995\pi\) | |||||||
\(174\) | −9.48528 | −0.719077 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.58579 | −0.270289 | ||||||||
\(177\) | 3.07107 | 0.230836 | ||||||||
\(178\) | −5.75736 | −0.431532 | ||||||||
\(179\) | −25.8995 | −1.93582 | −0.967910 | − | 0.251299i | \(-0.919142\pi\) | ||||
−0.967910 | + | 0.251299i | \(0.919142\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 17.1716 | 1.27635 | 0.638176 | − | 0.769890i | \(-0.279689\pi\) | ||||
0.638176 | + | 0.769890i | \(0.279689\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.58579 | 0.560757 | ||||||||
\(184\) | −7.82843 | −0.577119 | ||||||||
\(185\) | 5.58579 | 0.410675 | ||||||||
\(186\) | −1.41421 | −0.103695 | ||||||||
\(187\) | 18.7990 | 1.37472 | ||||||||
\(188\) | 6.00000 | 0.437595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.65685 | −0.482939 | ||||||||
\(191\) | 11.9706 | 0.866160 | 0.433080 | − | 0.901356i | \(-0.357427\pi\) | ||||
0.433080 | + | 0.901356i | \(0.357427\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 14.2426 | 1.02521 | 0.512604 | − | 0.858625i | \(-0.328681\pi\) | ||||
0.512604 | + | 0.858625i | \(0.328681\pi\) | |||||||
\(194\) | −15.3137 | −1.09946 | ||||||||
\(195\) | 1.00000 | 0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.41421 | 0.528241 | 0.264120 | − | 0.964490i | \(-0.414918\pi\) | ||||
0.264120 | + | 0.964490i | \(0.414918\pi\) | |||||||
\(198\) | −3.58579 | −0.254831 | ||||||||
\(199\) | 14.5563 | 1.03187 | 0.515936 | − | 0.856627i | \(-0.327444\pi\) | ||||
0.515936 | + | 0.856627i | \(0.327444\pi\) | |||||||
\(200\) | −4.00000 | −0.282843 | ||||||||
\(201\) | 15.5563 | 1.09726 | ||||||||
\(202\) | −15.4142 | −1.08454 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5.24264 | −0.367058 | ||||||||
\(205\) | 10.8284 | 0.756290 | ||||||||
\(206\) | 4.41421 | 0.307553 | ||||||||
\(207\) | −7.82843 | −0.544113 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −23.8701 | −1.65113 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.34315 | 0.0924660 | 0.0462330 | − | 0.998931i | \(-0.485278\pi\) | ||||
0.0462330 | + | 0.998931i | \(0.485278\pi\) | |||||||
\(212\) | 5.65685 | 0.388514 | ||||||||
\(213\) | −14.2426 | −0.975890 | ||||||||
\(214\) | 13.5563 | 0.926693 | ||||||||
\(215\) | −2.65685 | −0.181196 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −18.8995 | −1.28004 | ||||||||
\(219\) | 11.0000 | 0.743311 | ||||||||
\(220\) | 3.58579 | 0.241754 | ||||||||
\(221\) | 5.24264 | 0.352658 | ||||||||
\(222\) | −5.58579 | −0.374893 | ||||||||
\(223\) | −14.0000 | −0.937509 | −0.468755 | − | 0.883328i | \(-0.655297\pi\) | ||||
−0.468755 | + | 0.883328i | \(0.655297\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | 7.41421 | 0.493186 | ||||||||
\(227\) | −9.07107 | −0.602068 | −0.301034 | − | 0.953613i | \(-0.597332\pi\) | ||||
−0.301034 | + | 0.953613i | \(0.597332\pi\) | |||||||
\(228\) | 6.65685 | 0.440861 | ||||||||
\(229\) | 15.8995 | 1.05067 | 0.525334 | − | 0.850896i | \(-0.323940\pi\) | ||||
0.525334 | + | 0.850896i | \(0.323940\pi\) | |||||||
\(230\) | 7.82843 | 0.516191 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.48528 | −0.622739 | ||||||||
\(233\) | 22.1421 | 1.45058 | 0.725290 | − | 0.688444i | \(-0.241706\pi\) | ||||
0.725290 | + | 0.688444i | \(0.241706\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −6.00000 | −0.391397 | ||||||||
\(236\) | 3.07107 | 0.199909 | ||||||||
\(237\) | −6.24264 | −0.405503 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.3848 | 1.05984 | 0.529922 | − | 0.848047i | \(-0.322221\pi\) | ||||
0.529922 | + | 0.848047i | \(0.322221\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −18.9706 | −1.22200 | −0.611001 | − | 0.791630i | \(-0.709233\pi\) | ||||
−0.611001 | + | 0.791630i | \(0.709233\pi\) | |||||||
\(242\) | 1.85786 | 0.119428 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 7.58579 | 0.485630 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −10.8284 | −0.690395 | ||||||||
\(247\) | −6.65685 | −0.423565 | ||||||||
\(248\) | −1.41421 | −0.0898027 | ||||||||
\(249\) | 7.65685 | 0.485233 | ||||||||
\(250\) | 9.00000 | 0.569210 | ||||||||
\(251\) | −24.5563 | −1.54998 | −0.774992 | − | 0.631972i | \(-0.782246\pi\) | ||||
−0.774992 | + | 0.631972i | \(0.782246\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28.0711 | 1.76481 | ||||||||
\(254\) | −18.7279 | −1.17509 | ||||||||
\(255\) | 5.24264 | 0.328307 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.82843 | 0.176432 | 0.0882162 | − | 0.996101i | \(-0.471883\pi\) | ||||
0.0882162 | + | 0.996101i | \(0.471883\pi\) | |||||||
\(258\) | 2.65685 | 0.165409 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.00000 | 0.0620174 | ||||||||
\(261\) | −9.48528 | −0.587124 | ||||||||
\(262\) | 19.7279 | 1.21880 | ||||||||
\(263\) | −18.6274 | −1.14862 | −0.574308 | − | 0.818639i | \(-0.694729\pi\) | ||||
−0.574308 | + | 0.818639i | \(0.694729\pi\) | |||||||
\(264\) | −3.58579 | −0.220690 | ||||||||
\(265\) | −5.65685 | −0.347498 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.75736 | −0.352345 | ||||||||
\(268\) | 15.5563 | 0.950255 | ||||||||
\(269\) | 29.2132 | 1.78116 | 0.890580 | − | 0.454826i | \(-0.150299\pi\) | ||||
0.890580 | + | 0.454826i | \(0.150299\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −8.38478 | −0.509339 | −0.254669 | − | 0.967028i | \(-0.581967\pi\) | ||||
−0.254669 | + | 0.967028i | \(0.581967\pi\) | |||||||
\(272\) | −5.24264 | −0.317882 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.58579 | −0.216625 | ||||||||
\(275\) | 14.3431 | 0.864924 | ||||||||
\(276\) | −7.82843 | −0.471216 | ||||||||
\(277\) | −7.41421 | −0.445477 | −0.222738 | − | 0.974878i | \(-0.571500\pi\) | ||||
−0.222738 | + | 0.974878i | \(0.571500\pi\) | |||||||
\(278\) | −19.7990 | −1.18746 | ||||||||
\(279\) | −1.41421 | −0.0846668 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.97056 | −0.415829 | −0.207914 | − | 0.978147i | \(-0.566668\pi\) | ||||
−0.207914 | + | 0.978147i | \(0.566668\pi\) | |||||||
\(282\) | 6.00000 | 0.357295 | ||||||||
\(283\) | 8.48528 | 0.504398 | 0.252199 | − | 0.967675i | \(-0.418846\pi\) | ||||
0.252199 | + | 0.967675i | \(0.418846\pi\) | |||||||
\(284\) | −14.2426 | −0.845145 | ||||||||
\(285\) | −6.65685 | −0.394318 | ||||||||
\(286\) | 3.58579 | 0.212032 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 10.4853 | 0.616781 | ||||||||
\(290\) | 9.48528 | 0.556995 | ||||||||
\(291\) | −15.3137 | −0.897705 | ||||||||
\(292\) | 11.0000 | 0.643726 | ||||||||
\(293\) | 19.7990 | 1.15667 | 0.578335 | − | 0.815800i | \(-0.303703\pi\) | ||||
0.578335 | + | 0.815800i | \(0.303703\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.07107 | −0.178804 | ||||||||
\(296\) | −5.58579 | −0.324667 | ||||||||
\(297\) | −3.58579 | −0.208068 | ||||||||
\(298\) | −8.48528 | −0.491539 | ||||||||
\(299\) | 7.82843 | 0.452730 | ||||||||
\(300\) | −4.00000 | −0.230940 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.58579 | −0.206339 | ||||||||
\(303\) | −15.4142 | −0.885523 | ||||||||
\(304\) | 6.65685 | 0.381797 | ||||||||
\(305\) | −7.58579 | −0.434361 | ||||||||
\(306\) | −5.24264 | −0.299702 | ||||||||
\(307\) | −1.31371 | −0.0749773 | −0.0374887 | − | 0.999297i | \(-0.511936\pi\) | ||||
−0.0374887 | + | 0.999297i | \(0.511936\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.41421 | 0.251116 | ||||||||
\(310\) | 1.41421 | 0.0803219 | ||||||||
\(311\) | 7.17157 | 0.406663 | 0.203331 | − | 0.979110i | \(-0.434823\pi\) | ||||
0.203331 | + | 0.979110i | \(0.434823\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | −3.89949 | −0.220412 | −0.110206 | − | 0.993909i | \(-0.535151\pi\) | ||||
−0.110206 | + | 0.993909i | \(0.535151\pi\) | |||||||
\(314\) | 5.58579 | 0.315224 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.24264 | −0.351176 | ||||||||
\(317\) | −12.5858 | −0.706888 | −0.353444 | − | 0.935456i | \(-0.614990\pi\) | ||||
−0.353444 | + | 0.935456i | \(0.614990\pi\) | |||||||
\(318\) | 5.65685 | 0.317221 | ||||||||
\(319\) | 34.0122 | 1.90432 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 13.5563 | 0.756642 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −34.8995 | −1.94186 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 4.00000 | 0.221880 | ||||||||
\(326\) | −11.6569 | −0.645613 | ||||||||
\(327\) | −18.8995 | −1.04514 | ||||||||
\(328\) | −10.8284 | −0.597900 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.58579 | 0.197391 | ||||||||
\(331\) | 12.2426 | 0.672916 | 0.336458 | − | 0.941698i | \(-0.390771\pi\) | ||||
0.336458 | + | 0.941698i | \(0.390771\pi\) | |||||||
\(332\) | 7.65685 | 0.420224 | ||||||||
\(333\) | −5.58579 | −0.306099 | ||||||||
\(334\) | −5.14214 | −0.281365 | ||||||||
\(335\) | −15.5563 | −0.849934 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.1716 | −1.20776 | −0.603881 | − | 0.797074i | \(-0.706380\pi\) | ||||
−0.603881 | + | 0.797074i | \(0.706380\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | 7.41421 | 0.402685 | ||||||||
\(340\) | 5.24264 | 0.284322 | ||||||||
\(341\) | 5.07107 | 0.274614 | ||||||||
\(342\) | 6.65685 | 0.359961 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.65685 | 0.143248 | ||||||||
\(345\) | 7.82843 | 0.421468 | ||||||||
\(346\) | 1.89949 | 0.102117 | ||||||||
\(347\) | −10.5858 | −0.568275 | −0.284137 | − | 0.958784i | \(-0.591707\pi\) | ||||
−0.284137 | + | 0.958784i | \(0.591707\pi\) | |||||||
\(348\) | −9.48528 | −0.508464 | ||||||||
\(349\) | −4.10051 | −0.219495 | −0.109748 | − | 0.993959i | \(-0.535004\pi\) | ||||
−0.109748 | + | 0.993959i | \(0.535004\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −3.58579 | −0.191123 | ||||||||
\(353\) | −20.8284 | −1.10859 | −0.554293 | − | 0.832322i | \(-0.687011\pi\) | ||||
−0.554293 | + | 0.832322i | \(0.687011\pi\) | |||||||
\(354\) | 3.07107 | 0.163225 | ||||||||
\(355\) | 14.2426 | 0.755921 | ||||||||
\(356\) | −5.75736 | −0.305139 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −25.8995 | −1.36883 | ||||||||
\(359\) | 22.1421 | 1.16862 | 0.584309 | − | 0.811532i | \(-0.301366\pi\) | ||||
0.584309 | + | 0.811532i | \(0.301366\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 25.3137 | 1.33230 | ||||||||
\(362\) | 17.1716 | 0.902518 | ||||||||
\(363\) | 1.85786 | 0.0975126 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.0000 | −0.575766 | ||||||||
\(366\) | 7.58579 | 0.396515 | ||||||||
\(367\) | −17.6569 | −0.921680 | −0.460840 | − | 0.887483i | \(-0.652452\pi\) | ||||
−0.460840 | + | 0.887483i | \(0.652452\pi\) | |||||||
\(368\) | −7.82843 | −0.408085 | ||||||||
\(369\) | −10.8284 | −0.563705 | ||||||||
\(370\) | 5.58579 | 0.290391 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.41421 | −0.0733236 | ||||||||
\(373\) | −22.8701 | −1.18417 | −0.592083 | − | 0.805877i | \(-0.701694\pi\) | ||||
−0.592083 | + | 0.805877i | \(0.701694\pi\) | |||||||
\(374\) | 18.7990 | 0.972073 | ||||||||
\(375\) | 9.00000 | 0.464758 | ||||||||
\(376\) | 6.00000 | 0.309426 | ||||||||
\(377\) | 9.48528 | 0.488517 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.89949 | −0.405770 | −0.202885 | − | 0.979203i | \(-0.565032\pi\) | ||||
−0.202885 | + | 0.979203i | \(0.565032\pi\) | |||||||
\(380\) | −6.65685 | −0.341489 | ||||||||
\(381\) | −18.7279 | −0.959461 | ||||||||
\(382\) | 11.9706 | 0.612467 | ||||||||
\(383\) | 0.313708 | 0.0160298 | 0.00801488 | − | 0.999968i | \(-0.497449\pi\) | ||||
0.00801488 | + | 0.999968i | \(0.497449\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.2426 | 0.724931 | ||||||||
\(387\) | 2.65685 | 0.135055 | ||||||||
\(388\) | −15.3137 | −0.777436 | ||||||||
\(389\) | 18.3431 | 0.930034 | 0.465017 | − | 0.885302i | \(-0.346048\pi\) | ||||
0.465017 | + | 0.885302i | \(0.346048\pi\) | |||||||
\(390\) | 1.00000 | 0.0506370 | ||||||||
\(391\) | 41.0416 | 2.07556 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.7279 | 0.995142 | ||||||||
\(394\) | 7.41421 | 0.373523 | ||||||||
\(395\) | 6.24264 | 0.314101 | ||||||||
\(396\) | −3.58579 | −0.180193 | ||||||||
\(397\) | −0.343146 | −0.0172220 | −0.00861100 | − | 0.999963i | \(-0.502741\pi\) | ||||
−0.00861100 | + | 0.999963i | \(0.502741\pi\) | |||||||
\(398\) | 14.5563 | 0.729644 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | 15.7990 | 0.788964 | 0.394482 | − | 0.918904i | \(-0.370924\pi\) | ||||
0.394482 | + | 0.918904i | \(0.370924\pi\) | |||||||
\(402\) | 15.5563 | 0.775880 | ||||||||
\(403\) | 1.41421 | 0.0704470 | ||||||||
\(404\) | −15.4142 | −0.766886 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.0294 | 0.992822 | ||||||||
\(408\) | −5.24264 | −0.259549 | ||||||||
\(409\) | 30.7990 | 1.52291 | 0.761456 | − | 0.648217i | \(-0.224485\pi\) | ||||
0.761456 | + | 0.648217i | \(0.224485\pi\) | |||||||
\(410\) | 10.8284 | 0.534778 | ||||||||
\(411\) | −3.58579 | −0.176874 | ||||||||
\(412\) | 4.41421 | 0.217473 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −7.82843 | −0.384746 | ||||||||
\(415\) | −7.65685 | −0.375860 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −19.7990 | −0.969561 | ||||||||
\(418\) | −23.8701 | −1.16752 | ||||||||
\(419\) | 7.92893 | 0.387354 | 0.193677 | − | 0.981065i | \(-0.437959\pi\) | ||||
0.193677 | + | 0.981065i | \(0.437959\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.4558 | 0.753272 | 0.376636 | − | 0.926361i | \(-0.377081\pi\) | ||||
0.376636 | + | 0.926361i | \(0.377081\pi\) | |||||||
\(422\) | 1.34315 | 0.0653833 | ||||||||
\(423\) | 6.00000 | 0.291730 | ||||||||
\(424\) | 5.65685 | 0.274721 | ||||||||
\(425\) | 20.9706 | 1.01722 | ||||||||
\(426\) | −14.2426 | −0.690058 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 13.5563 | 0.655271 | ||||||||
\(429\) | 3.58579 | 0.173123 | ||||||||
\(430\) | −2.65685 | −0.128125 | ||||||||
\(431\) | 30.4853 | 1.46842 | 0.734212 | − | 0.678920i | \(-0.237552\pi\) | ||||
0.734212 | + | 0.678920i | \(0.237552\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.48528 | 0.454784 | ||||||||
\(436\) | −18.8995 | −0.905122 | ||||||||
\(437\) | −52.1127 | −2.49289 | ||||||||
\(438\) | 11.0000 | 0.525600 | ||||||||
\(439\) | 12.0711 | 0.576121 | 0.288060 | − | 0.957612i | \(-0.406990\pi\) | ||||
0.288060 | + | 0.957612i | \(0.406990\pi\) | |||||||
\(440\) | 3.58579 | 0.170946 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.24264 | 0.249367 | ||||||||
\(443\) | 29.7990 | 1.41579 | 0.707896 | − | 0.706316i | \(-0.249644\pi\) | ||||
0.707896 | + | 0.706316i | \(0.249644\pi\) | |||||||
\(444\) | −5.58579 | −0.265090 | ||||||||
\(445\) | 5.75736 | 0.272925 | ||||||||
\(446\) | −14.0000 | −0.662919 | ||||||||
\(447\) | −8.48528 | −0.401340 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.0416 | −1.27617 | −0.638087 | − | 0.769965i | \(-0.720274\pi\) | ||||
−0.638087 | + | 0.769965i | \(0.720274\pi\) | |||||||
\(450\) | −4.00000 | −0.188562 | ||||||||
\(451\) | 38.8284 | 1.82836 | ||||||||
\(452\) | 7.41421 | 0.348735 | ||||||||
\(453\) | −3.58579 | −0.168475 | ||||||||
\(454\) | −9.07107 | −0.425726 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.65685 | 0.311736 | ||||||||
\(457\) | −19.6985 | −0.921456 | −0.460728 | − | 0.887541i | \(-0.652412\pi\) | ||||
−0.460728 | + | 0.887541i | \(0.652412\pi\) | |||||||
\(458\) | 15.8995 | 0.742935 | ||||||||
\(459\) | −5.24264 | −0.244706 | ||||||||
\(460\) | 7.82843 | 0.365002 | ||||||||
\(461\) | −16.5147 | −0.769167 | −0.384584 | − | 0.923090i | \(-0.625655\pi\) | ||||
−0.384584 | + | 0.923090i | \(0.625655\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.92893 | 0.461437 | 0.230718 | − | 0.973021i | \(-0.425892\pi\) | ||||
0.230718 | + | 0.973021i | \(0.425892\pi\) | |||||||
\(464\) | −9.48528 | −0.440343 | ||||||||
\(465\) | 1.41421 | 0.0655826 | ||||||||
\(466\) | 22.1421 | 1.02571 | ||||||||
\(467\) | 7.58579 | 0.351028 | 0.175514 | − | 0.984477i | \(-0.443841\pi\) | ||||
0.175514 | + | 0.984477i | \(0.443841\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.00000 | −0.276759 | ||||||||
\(471\) | 5.58579 | 0.257379 | ||||||||
\(472\) | 3.07107 | 0.141357 | ||||||||
\(473\) | −9.52691 | −0.438048 | ||||||||
\(474\) | −6.24264 | −0.286734 | ||||||||
\(475\) | −26.6274 | −1.22175 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.65685 | 0.259010 | ||||||||
\(478\) | 16.3848 | 0.749422 | ||||||||
\(479\) | −4.85786 | −0.221961 | −0.110981 | − | 0.993823i | \(-0.535399\pi\) | ||||
−0.110981 | + | 0.993823i | \(0.535399\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 5.58579 | 0.254690 | ||||||||
\(482\) | −18.9706 | −0.864085 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.85786 | 0.0844484 | ||||||||
\(485\) | 15.3137 | 0.695360 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 19.6569 | 0.890737 | 0.445369 | − | 0.895347i | \(-0.353073\pi\) | ||||
0.445369 | + | 0.895347i | \(0.353073\pi\) | |||||||
\(488\) | 7.58579 | 0.343392 | ||||||||
\(489\) | −11.6569 | −0.527141 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.1716 | 0.865201 | 0.432600 | − | 0.901586i | \(-0.357596\pi\) | ||||
0.432600 | + | 0.901586i | \(0.357596\pi\) | |||||||
\(492\) | −10.8284 | −0.488183 | ||||||||
\(493\) | 49.7279 | 2.23963 | ||||||||
\(494\) | −6.65685 | −0.299506 | ||||||||
\(495\) | 3.58579 | 0.161169 | ||||||||
\(496\) | −1.41421 | −0.0635001 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.65685 | 0.343112 | ||||||||
\(499\) | −26.0416 | −1.16578 | −0.582892 | − | 0.812550i | \(-0.698079\pi\) | ||||
−0.582892 | + | 0.812550i | \(0.698079\pi\) | |||||||
\(500\) | 9.00000 | 0.402492 | ||||||||
\(501\) | −5.14214 | −0.229734 | ||||||||
\(502\) | −24.5563 | −1.09600 | ||||||||
\(503\) | −14.3848 | −0.641385 | −0.320693 | − | 0.947183i | \(-0.603916\pi\) | ||||
−0.320693 | + | 0.947183i | \(0.603916\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.4142 | 0.685924 | ||||||||
\(506\) | 28.0711 | 1.24791 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −18.7279 | −0.830917 | ||||||||
\(509\) | −20.7990 | −0.921899 | −0.460950 | − | 0.887426i | \(-0.652491\pi\) | ||||
−0.460950 | + | 0.887426i | \(0.652491\pi\) | |||||||
\(510\) | 5.24264 | 0.232148 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 6.65685 | 0.293907 | ||||||||
\(514\) | 2.82843 | 0.124757 | ||||||||
\(515\) | −4.41421 | −0.194513 | ||||||||
\(516\) | 2.65685 | 0.116961 | ||||||||
\(517\) | −21.5147 | −0.946216 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.89949 | 0.0833786 | ||||||||
\(520\) | 1.00000 | 0.0438529 | ||||||||
\(521\) | −0.757359 | −0.0331805 | −0.0165903 | − | 0.999862i | \(-0.505281\pi\) | ||||
−0.0165903 | + | 0.999862i | \(0.505281\pi\) | |||||||
\(522\) | −9.48528 | −0.415159 | ||||||||
\(523\) | 22.2426 | 0.972603 | 0.486301 | − | 0.873791i | \(-0.338346\pi\) | ||||
0.486301 | + | 0.873791i | \(0.338346\pi\) | |||||||
\(524\) | 19.7279 | 0.861818 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.6274 | −0.812194 | ||||||||
\(527\) | 7.41421 | 0.322968 | ||||||||
\(528\) | −3.58579 | −0.156051 | ||||||||
\(529\) | 38.2843 | 1.66453 | ||||||||
\(530\) | −5.65685 | −0.245718 | ||||||||
\(531\) | 3.07107 | 0.133273 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.8284 | 0.469031 | ||||||||
\(534\) | −5.75736 | −0.249145 | ||||||||
\(535\) | −13.5563 | −0.586092 | ||||||||
\(536\) | 15.5563 | 0.671932 | ||||||||
\(537\) | −25.8995 | −1.11765 | ||||||||
\(538\) | 29.2132 | 1.25947 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −25.3848 | −1.09138 | −0.545688 | − | 0.837988i | \(-0.683732\pi\) | ||||
−0.545688 | + | 0.837988i | \(0.683732\pi\) | |||||||
\(542\) | −8.38478 | −0.360157 | ||||||||
\(543\) | 17.1716 | 0.736903 | ||||||||
\(544\) | −5.24264 | −0.224776 | ||||||||
\(545\) | 18.8995 | 0.809565 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.4853 | 1.47448 | 0.737242 | − | 0.675629i | \(-0.236128\pi\) | ||||
0.737242 | + | 0.675629i | \(0.236128\pi\) | |||||||
\(548\) | −3.58579 | −0.153177 | ||||||||
\(549\) | 7.58579 | 0.323753 | ||||||||
\(550\) | 14.3431 | 0.611594 | ||||||||
\(551\) | −63.1421 | −2.68995 | ||||||||
\(552\) | −7.82843 | −0.333200 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −7.41421 | −0.315000 | ||||||||
\(555\) | 5.58579 | 0.237103 | ||||||||
\(556\) | −19.7990 | −0.839664 | ||||||||
\(557\) | −11.5147 | −0.487894 | −0.243947 | − | 0.969789i | \(-0.578442\pi\) | ||||
−0.243947 | + | 0.969789i | \(0.578442\pi\) | |||||||
\(558\) | −1.41421 | −0.0598684 | ||||||||
\(559\) | −2.65685 | −0.112373 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.7990 | 0.793694 | ||||||||
\(562\) | −6.97056 | −0.294035 | ||||||||
\(563\) | −14.7574 | −0.621949 | −0.310974 | − | 0.950418i | \(-0.600655\pi\) | ||||
−0.310974 | + | 0.950418i | \(0.600655\pi\) | |||||||
\(564\) | 6.00000 | 0.252646 | ||||||||
\(565\) | −7.41421 | −0.311918 | ||||||||
\(566\) | 8.48528 | 0.356663 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.2426 | −0.597608 | ||||||||
\(569\) | 29.7990 | 1.24924 | 0.624619 | − | 0.780929i | \(-0.285254\pi\) | ||||
0.624619 | + | 0.780929i | \(0.285254\pi\) | |||||||
\(570\) | −6.65685 | −0.278825 | ||||||||
\(571\) | 0.627417 | 0.0262566 | 0.0131283 | − | 0.999914i | \(-0.495821\pi\) | ||||
0.0131283 | + | 0.999914i | \(0.495821\pi\) | |||||||
\(572\) | 3.58579 | 0.149929 | ||||||||
\(573\) | 11.9706 | 0.500077 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 31.3137 | 1.30587 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −22.1421 | −0.921789 | −0.460895 | − | 0.887455i | \(-0.652471\pi\) | ||||
−0.460895 | + | 0.887455i | \(0.652471\pi\) | |||||||
\(578\) | 10.4853 | 0.436130 | ||||||||
\(579\) | 14.2426 | 0.591904 | ||||||||
\(580\) | 9.48528 | 0.393855 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −15.3137 | −0.634774 | ||||||||
\(583\) | −20.2843 | −0.840089 | ||||||||
\(584\) | 11.0000 | 0.455183 | ||||||||
\(585\) | 1.00000 | 0.0413449 | ||||||||
\(586\) | 19.7990 | 0.817889 | ||||||||
\(587\) | 3.17157 | 0.130905 | 0.0654524 | − | 0.997856i | \(-0.479151\pi\) | ||||
0.0654524 | + | 0.997856i | \(0.479151\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.41421 | −0.387906 | ||||||||
\(590\) | −3.07107 | −0.126434 | ||||||||
\(591\) | 7.41421 | 0.304980 | ||||||||
\(592\) | −5.58579 | −0.229574 | ||||||||
\(593\) | −3.89949 | −0.160133 | −0.0800665 | − | 0.996790i | \(-0.525513\pi\) | ||||
−0.0800665 | + | 0.996790i | \(0.525513\pi\) | |||||||
\(594\) | −3.58579 | −0.147127 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.48528 | −0.347571 | ||||||||
\(597\) | 14.5563 | 0.595752 | ||||||||
\(598\) | 7.82843 | 0.320128 | ||||||||
\(599\) | −24.3137 | −0.993431 | −0.496716 | − | 0.867913i | \(-0.665461\pi\) | ||||
−0.496716 | + | 0.867913i | \(0.665461\pi\) | |||||||
\(600\) | −4.00000 | −0.163299 | ||||||||
\(601\) | 41.4558 | 1.69102 | 0.845510 | − | 0.533960i | \(-0.179297\pi\) | ||||
0.845510 | + | 0.533960i | \(0.179297\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.5563 | 0.633504 | ||||||||
\(604\) | −3.58579 | −0.145904 | ||||||||
\(605\) | −1.85786 | −0.0755329 | ||||||||
\(606\) | −15.4142 | −0.626160 | ||||||||
\(607\) | 5.72792 | 0.232489 | 0.116245 | − | 0.993221i | \(-0.462914\pi\) | ||||
0.116245 | + | 0.993221i | \(0.462914\pi\) | |||||||
\(608\) | 6.65685 | 0.269971 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.58579 | −0.307140 | ||||||||
\(611\) | −6.00000 | −0.242734 | ||||||||
\(612\) | −5.24264 | −0.211921 | ||||||||
\(613\) | −27.8701 | −1.12566 | −0.562831 | − | 0.826572i | \(-0.690288\pi\) | ||||
−0.562831 | + | 0.826572i | \(0.690288\pi\) | |||||||
\(614\) | −1.31371 | −0.0530170 | ||||||||
\(615\) | 10.8284 | 0.436644 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.75736 | 0.272041 | 0.136021 | − | 0.990706i | \(-0.456569\pi\) | ||||
0.136021 | + | 0.990706i | \(0.456569\pi\) | |||||||
\(618\) | 4.41421 | 0.177566 | ||||||||
\(619\) | −20.1716 | −0.810764 | −0.405382 | − | 0.914147i | \(-0.632861\pi\) | ||||
−0.405382 | + | 0.914147i | \(0.632861\pi\) | |||||||
\(620\) | 1.41421 | 0.0567962 | ||||||||
\(621\) | −7.82843 | −0.314144 | ||||||||
\(622\) | 7.17157 | 0.287554 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | −3.89949 | −0.155855 | ||||||||
\(627\) | −23.8701 | −0.953278 | ||||||||
\(628\) | 5.58579 | 0.222897 | ||||||||
\(629\) | 29.2843 | 1.16764 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.0416 | −1.63384 | −0.816921 | − | 0.576750i | \(-0.804321\pi\) | ||||
−0.816921 | + | 0.576750i | \(0.804321\pi\) | |||||||
\(632\) | −6.24264 | −0.248319 | ||||||||
\(633\) | 1.34315 | 0.0533853 | ||||||||
\(634\) | −12.5858 | −0.499845 | ||||||||
\(635\) | 18.7279 | 0.743195 | ||||||||
\(636\) | 5.65685 | 0.224309 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 34.0122 | 1.34656 | ||||||||
\(639\) | −14.2426 | −0.563430 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 9.75736 | 0.385393 | 0.192696 | − | 0.981258i | \(-0.438277\pi\) | ||||
0.192696 | + | 0.981258i | \(0.438277\pi\) | |||||||
\(642\) | 13.5563 | 0.535026 | ||||||||
\(643\) | −28.1127 | −1.10866 | −0.554328 | − | 0.832298i | \(-0.687025\pi\) | ||||
−0.554328 | + | 0.832298i | \(0.687025\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.65685 | −0.104614 | ||||||||
\(646\) | −34.8995 | −1.37310 | ||||||||
\(647\) | −39.3137 | −1.54558 | −0.772791 | − | 0.634661i | \(-0.781140\pi\) | ||||
−0.772791 | + | 0.634661i | \(0.781140\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −11.0122 | −0.432266 | ||||||||
\(650\) | 4.00000 | 0.156893 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.6569 | −0.456518 | ||||||||
\(653\) | 17.0000 | 0.665261 | 0.332631 | − | 0.943057i | \(-0.392064\pi\) | ||||
0.332631 | + | 0.943057i | \(0.392064\pi\) | |||||||
\(654\) | −18.8995 | −0.739029 | ||||||||
\(655\) | −19.7279 | −0.770834 | ||||||||
\(656\) | −10.8284 | −0.422779 | ||||||||
\(657\) | 11.0000 | 0.429151 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.20101 | −0.241557 | −0.120779 | − | 0.992679i | \(-0.538539\pi\) | ||||
−0.120779 | + | 0.992679i | \(0.538539\pi\) | |||||||
\(660\) | 3.58579 | 0.139577 | ||||||||
\(661\) | 11.6569 | 0.453399 | 0.226700 | − | 0.973965i | \(-0.427206\pi\) | ||||
0.226700 | + | 0.973965i | \(0.427206\pi\) | |||||||
\(662\) | 12.2426 | 0.475824 | ||||||||
\(663\) | 5.24264 | 0.203607 | ||||||||
\(664\) | 7.65685 | 0.297144 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.58579 | −0.216445 | ||||||||
\(667\) | 74.2548 | 2.87516 | ||||||||
\(668\) | −5.14214 | −0.198955 | ||||||||
\(669\) | −14.0000 | −0.541271 | ||||||||
\(670\) | −15.5563 | −0.600994 | ||||||||
\(671\) | −27.2010 | −1.05008 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.48528 | −0.365631 | −0.182815 | − | 0.983147i | \(-0.558521\pi\) | ||||
−0.182815 | + | 0.983147i | \(0.558521\pi\) | |||||||
\(674\) | −22.1716 | −0.854017 | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −26.4853 | −1.01791 | −0.508956 | − | 0.860793i | \(-0.669968\pi\) | ||||
−0.508956 | + | 0.860793i | \(0.669968\pi\) | |||||||
\(678\) | 7.41421 | 0.284741 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.24264 | 0.201046 | ||||||||
\(681\) | −9.07107 | −0.347604 | ||||||||
\(682\) | 5.07107 | 0.194181 | ||||||||
\(683\) | 7.24264 | 0.277132 | 0.138566 | − | 0.990353i | \(-0.455751\pi\) | ||||
0.138566 | + | 0.990353i | \(0.455751\pi\) | |||||||
\(684\) | 6.65685 | 0.254531 | ||||||||
\(685\) | 3.58579 | 0.137006 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.8995 | 0.606604 | ||||||||
\(688\) | 2.65685 | 0.101292 | ||||||||
\(689\) | −5.65685 | −0.215509 | ||||||||
\(690\) | 7.82843 | 0.298023 | ||||||||
\(691\) | 4.14214 | 0.157574 | 0.0787871 | − | 0.996891i | \(-0.474895\pi\) | ||||
0.0787871 | + | 0.996891i | \(0.474895\pi\) | |||||||
\(692\) | 1.89949 | 0.0722080 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.5858 | −0.401831 | ||||||||
\(695\) | 19.7990 | 0.751018 | ||||||||
\(696\) | −9.48528 | −0.359539 | ||||||||
\(697\) | 56.7696 | 2.15030 | ||||||||
\(698\) | −4.10051 | −0.155206 | ||||||||
\(699\) | 22.1421 | 0.837492 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.4853 | 1.83126 | 0.915632 | − | 0.402018i | \(-0.131691\pi\) | ||||
0.915632 | + | 0.402018i | \(0.131691\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | −37.1838 | −1.40241 | ||||||||
\(704\) | −3.58579 | −0.135144 | ||||||||
\(705\) | −6.00000 | −0.225973 | ||||||||
\(706\) | −20.8284 | −0.783888 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.07107 | 0.115418 | ||||||||
\(709\) | −19.8579 | −0.745778 | −0.372889 | − | 0.927876i | \(-0.621633\pi\) | ||||
−0.372889 | + | 0.927876i | \(0.621633\pi\) | |||||||
\(710\) | 14.2426 | 0.534517 | ||||||||
\(711\) | −6.24264 | −0.234117 | ||||||||
\(712\) | −5.75736 | −0.215766 | ||||||||
\(713\) | 11.0711 | 0.414615 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.58579 | −0.134101 | ||||||||
\(716\) | −25.8995 | −0.967910 | ||||||||
\(717\) | 16.3848 | 0.611901 | ||||||||
\(718\) | 22.1421 | 0.826337 | ||||||||
\(719\) | 38.8701 | 1.44961 | 0.724804 | − | 0.688955i | \(-0.241930\pi\) | ||||
0.724804 | + | 0.688955i | \(0.241930\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 25.3137 | 0.942079 | ||||||||
\(723\) | −18.9706 | −0.705523 | ||||||||
\(724\) | 17.1716 | 0.638176 | ||||||||
\(725\) | 37.9411 | 1.40910 | ||||||||
\(726\) | 1.85786 | 0.0689518 | ||||||||
\(727\) | 11.8701 | 0.440236 | 0.220118 | − | 0.975473i | \(-0.429356\pi\) | ||||
0.220118 | + | 0.975473i | \(0.429356\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −11.0000 | −0.407128 | ||||||||
\(731\) | −13.9289 | −0.515180 | ||||||||
\(732\) | 7.58579 | 0.280379 | ||||||||
\(733\) | −39.5563 | −1.46105 | −0.730524 | − | 0.682888i | \(-0.760724\pi\) | ||||
−0.730524 | + | 0.682888i | \(0.760724\pi\) | |||||||
\(734\) | −17.6569 | −0.651726 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.82843 | −0.288560 | ||||||||
\(737\) | −55.7817 | −2.05475 | ||||||||
\(738\) | −10.8284 | −0.398600 | ||||||||
\(739\) | 19.6569 | 0.723089 | 0.361545 | − | 0.932355i | \(-0.382250\pi\) | ||||
0.361545 | + | 0.932355i | \(0.382250\pi\) | |||||||
\(740\) | 5.58579 | 0.205338 | ||||||||
\(741\) | −6.65685 | −0.244546 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.2843 | −0.817531 | −0.408765 | − | 0.912640i | \(-0.634041\pi\) | ||||
−0.408765 | + | 0.912640i | \(0.634041\pi\) | |||||||
\(744\) | −1.41421 | −0.0518476 | ||||||||
\(745\) | 8.48528 | 0.310877 | ||||||||
\(746\) | −22.8701 | −0.837332 | ||||||||
\(747\) | 7.65685 | 0.280150 | ||||||||
\(748\) | 18.7990 | 0.687359 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 9.00000 | 0.328634 | ||||||||
\(751\) | 21.2132 | 0.774081 | 0.387040 | − | 0.922063i | \(-0.373497\pi\) | ||||
0.387040 | + | 0.922063i | \(0.373497\pi\) | |||||||
\(752\) | 6.00000 | 0.218797 | ||||||||
\(753\) | −24.5563 | −0.894883 | ||||||||
\(754\) | 9.48528 | 0.345434 | ||||||||
\(755\) | 3.58579 | 0.130500 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.27208 | −0.191617 | −0.0958085 | − | 0.995400i | \(-0.530544\pi\) | ||||
−0.0958085 | + | 0.995400i | \(0.530544\pi\) | |||||||
\(758\) | −7.89949 | −0.286923 | ||||||||
\(759\) | 28.0711 | 1.01892 | ||||||||
\(760\) | −6.65685 | −0.241469 | ||||||||
\(761\) | −52.0833 | −1.88802 | −0.944008 | − | 0.329922i | \(-0.892978\pi\) | ||||
−0.944008 | + | 0.329922i | \(0.892978\pi\) | |||||||
\(762\) | −18.7279 | −0.678441 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 11.9706 | 0.433080 | ||||||||
\(765\) | 5.24264 | 0.189548 | ||||||||
\(766\) | 0.313708 | 0.0113347 | ||||||||
\(767\) | −3.07107 | −0.110890 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 38.9411 | 1.40425 | 0.702126 | − | 0.712052i | \(-0.252234\pi\) | ||||
0.702126 | + | 0.712052i | \(0.252234\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.82843 | 0.101863 | ||||||||
\(772\) | 14.2426 | 0.512604 | ||||||||
\(773\) | −36.2548 | −1.30400 | −0.651998 | − | 0.758221i | \(-0.726069\pi\) | ||||
−0.651998 | + | 0.758221i | \(0.726069\pi\) | |||||||
\(774\) | 2.65685 | 0.0954987 | ||||||||
\(775\) | 5.65685 | 0.203200 | ||||||||
\(776\) | −15.3137 | −0.549730 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.3431 | 0.657634 | ||||||||
\(779\) | −72.0833 | −2.58265 | ||||||||
\(780\) | 1.00000 | 0.0358057 | ||||||||
\(781\) | 51.0711 | 1.82747 | ||||||||
\(782\) | 41.0416 | 1.46765 | ||||||||
\(783\) | −9.48528 | −0.338976 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.58579 | −0.199365 | ||||||||
\(786\) | 19.7279 | 0.703672 | ||||||||
\(787\) | 19.9706 | 0.711874 | 0.355937 | − | 0.934510i | \(-0.384162\pi\) | ||||
0.355937 | + | 0.934510i | \(0.384162\pi\) | |||||||
\(788\) | 7.41421 | 0.264120 | ||||||||
\(789\) | −18.6274 | −0.663154 | ||||||||
\(790\) | 6.24264 | 0.222103 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.58579 | −0.127415 | ||||||||
\(793\) | −7.58579 | −0.269379 | ||||||||
\(794\) | −0.343146 | −0.0121778 | ||||||||
\(795\) | −5.65685 | −0.200628 | ||||||||
\(796\) | 14.5563 | 0.515936 | ||||||||
\(797\) | −2.24264 | −0.0794384 | −0.0397192 | − | 0.999211i | \(-0.512646\pi\) | ||||
−0.0397192 | + | 0.999211i | \(0.512646\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.4558 | −1.11283 | ||||||||
\(800\) | −4.00000 | −0.141421 | ||||||||
\(801\) | −5.75736 | −0.203426 | ||||||||
\(802\) | 15.7990 | 0.557882 | ||||||||
\(803\) | −39.4437 | −1.39194 | ||||||||
\(804\) | 15.5563 | 0.548630 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.41421 | 0.0498135 | ||||||||
\(807\) | 29.2132 | 1.02835 | ||||||||
\(808\) | −15.4142 | −0.542270 | ||||||||
\(809\) | 16.1005 | 0.566064 | 0.283032 | − | 0.959111i | \(-0.408660\pi\) | ||||
0.283032 | + | 0.959111i | \(0.408660\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −10.1716 | −0.357172 | −0.178586 | − | 0.983924i | \(-0.557152\pi\) | ||||
−0.178586 | + | 0.983924i | \(0.557152\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.38478 | −0.294067 | ||||||||
\(814\) | 20.0294 | 0.702031 | ||||||||
\(815\) | 11.6569 | 0.408322 | ||||||||
\(816\) | −5.24264 | −0.183529 | ||||||||
\(817\) | 17.6863 | 0.618765 | ||||||||
\(818\) | 30.7990 | 1.07686 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.8284 | 0.378145 | ||||||||
\(821\) | 15.7990 | 0.551389 | 0.275694 | − | 0.961245i | \(-0.411092\pi\) | ||||
0.275694 | + | 0.961245i | \(0.411092\pi\) | |||||||
\(822\) | −3.58579 | −0.125069 | ||||||||
\(823\) | −24.0416 | −0.838039 | −0.419019 | − | 0.907977i | \(-0.637626\pi\) | ||||
−0.419019 | + | 0.907977i | \(0.637626\pi\) | |||||||
\(824\) | 4.41421 | 0.153776 | ||||||||
\(825\) | 14.3431 | 0.499364 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.3848 | −1.16090 | −0.580451 | − | 0.814295i | \(-0.697124\pi\) | ||||
−0.580451 | + | 0.814295i | \(0.697124\pi\) | |||||||
\(828\) | −7.82843 | −0.272057 | ||||||||
\(829\) | −45.3848 | −1.57628 | −0.788139 | − | 0.615497i | \(-0.788955\pi\) | ||||
−0.788139 | + | 0.615497i | \(0.788955\pi\) | |||||||
\(830\) | −7.65685 | −0.265773 | ||||||||
\(831\) | −7.41421 | −0.257196 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −19.7990 | −0.685583 | ||||||||
\(835\) | 5.14214 | 0.177951 | ||||||||
\(836\) | −23.8701 | −0.825563 | ||||||||
\(837\) | −1.41421 | −0.0488824 | ||||||||
\(838\) | 7.92893 | 0.273900 | ||||||||
\(839\) | −5.02944 | −0.173635 | −0.0868177 | − | 0.996224i | \(-0.527670\pi\) | ||||
−0.0868177 | + | 0.996224i | \(0.527670\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 60.9706 | 2.10243 | ||||||||
\(842\) | 15.4558 | 0.532644 | ||||||||
\(843\) | −6.97056 | −0.240079 | ||||||||
\(844\) | 1.34315 | 0.0462330 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 6.00000 | 0.206284 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.65685 | 0.194257 | ||||||||
\(849\) | 8.48528 | 0.291214 | ||||||||
\(850\) | 20.9706 | 0.719284 | ||||||||
\(851\) | 43.7279 | 1.49897 | ||||||||
\(852\) | −14.2426 | −0.487945 | ||||||||
\(853\) | −19.0294 | −0.651556 | −0.325778 | − | 0.945446i | \(-0.605626\pi\) | ||||
−0.325778 | + | 0.945446i | \(0.605626\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.65685 | −0.227660 | ||||||||
\(856\) | 13.5563 | 0.463346 | ||||||||
\(857\) | 13.5147 | 0.461654 | 0.230827 | − | 0.972995i | \(-0.425857\pi\) | ||||
0.230827 | + | 0.972995i | \(0.425857\pi\) | |||||||
\(858\) | 3.58579 | 0.122417 | ||||||||
\(859\) | 20.0000 | 0.682391 | 0.341196 | − | 0.939992i | \(-0.389168\pi\) | ||||
0.341196 | + | 0.939992i | \(0.389168\pi\) | |||||||
\(860\) | −2.65685 | −0.0905980 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.4853 | 1.03833 | ||||||||
\(863\) | −18.0000 | −0.612727 | −0.306364 | − | 0.951915i | \(-0.599112\pi\) | ||||
−0.306364 | + | 0.951915i | \(0.599112\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −1.89949 | −0.0645848 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.4853 | 0.356099 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.3848 | 0.759352 | ||||||||
\(870\) | 9.48528 | 0.321581 | ||||||||
\(871\) | −15.5563 | −0.527107 | ||||||||
\(872\) | −18.8995 | −0.640018 | ||||||||
\(873\) | −15.3137 | −0.518291 | ||||||||
\(874\) | −52.1127 | −1.76274 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11.0000 | 0.371656 | ||||||||
\(877\) | −8.48528 | −0.286528 | −0.143264 | − | 0.989685i | \(-0.545760\pi\) | ||||
−0.143264 | + | 0.989685i | \(0.545760\pi\) | |||||||
\(878\) | 12.0711 | 0.407379 | ||||||||
\(879\) | 19.7990 | 0.667803 | ||||||||
\(880\) | 3.58579 | 0.120877 | ||||||||
\(881\) | −28.2721 | −0.952511 | −0.476255 | − | 0.879307i | \(-0.658006\pi\) | ||||
−0.476255 | + | 0.879307i | \(0.658006\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.5980 | 1.16431 | 0.582157 | − | 0.813076i | \(-0.302209\pi\) | ||||
0.582157 | + | 0.813076i | \(0.302209\pi\) | |||||||
\(884\) | 5.24264 | 0.176329 | ||||||||
\(885\) | −3.07107 | −0.103233 | ||||||||
\(886\) | 29.7990 | 1.00112 | ||||||||
\(887\) | 2.82843 | 0.0949693 | 0.0474846 | − | 0.998872i | \(-0.484879\pi\) | ||||
0.0474846 | + | 0.998872i | \(0.484879\pi\) | |||||||
\(888\) | −5.58579 | −0.187447 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.75736 | 0.192987 | ||||||||
\(891\) | −3.58579 | −0.120128 | ||||||||
\(892\) | −14.0000 | −0.468755 | ||||||||
\(893\) | 39.9411 | 1.33658 | ||||||||
\(894\) | −8.48528 | −0.283790 | ||||||||
\(895\) | 25.8995 | 0.865725 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.82843 | 0.261384 | ||||||||
\(898\) | −27.0416 | −0.902391 | ||||||||
\(899\) | 13.4142 | 0.447389 | ||||||||
\(900\) | −4.00000 | −0.133333 | ||||||||
\(901\) | −29.6569 | −0.988013 | ||||||||
\(902\) | 38.8284 | 1.29285 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.41421 | 0.246593 | ||||||||
\(905\) | −17.1716 | −0.570802 | ||||||||
\(906\) | −3.58579 | −0.119130 | ||||||||
\(907\) | −34.4853 | −1.14506 | −0.572532 | − | 0.819882i | \(-0.694039\pi\) | ||||
−0.572532 | + | 0.819882i | \(0.694039\pi\) | |||||||
\(908\) | −9.07107 | −0.301034 | ||||||||
\(909\) | −15.4142 | −0.511257 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.1716 | −1.19842 | −0.599209 | − | 0.800593i | \(-0.704518\pi\) | ||||
−0.599209 | + | 0.800593i | \(0.704518\pi\) | |||||||
\(912\) | 6.65685 | 0.220430 | ||||||||
\(913\) | −27.4558 | −0.908656 | ||||||||
\(914\) | −19.6985 | −0.651568 | ||||||||
\(915\) | −7.58579 | −0.250778 | ||||||||
\(916\) | 15.8995 | 0.525334 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.24264 | −0.173033 | ||||||||
\(919\) | 33.5147 | 1.10555 | 0.552774 | − | 0.833331i | \(-0.313569\pi\) | ||||
0.552774 | + | 0.833331i | \(0.313569\pi\) | |||||||
\(920\) | 7.82843 | 0.258096 | ||||||||
\(921\) | −1.31371 | −0.0432882 | ||||||||
\(922\) | −16.5147 | −0.543883 | ||||||||
\(923\) | 14.2426 | 0.468802 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.3431 | 0.734638 | ||||||||
\(926\) | 9.92893 | 0.326285 | ||||||||
\(927\) | 4.41421 | 0.144982 | ||||||||
\(928\) | −9.48528 | −0.311370 | ||||||||
\(929\) | 30.8284 | 1.01145 | 0.505724 | − | 0.862695i | \(-0.331225\pi\) | ||||
0.505724 | + | 0.862695i | \(0.331225\pi\) | |||||||
\(930\) | 1.41421 | 0.0463739 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 22.1421 | 0.725290 | ||||||||
\(933\) | 7.17157 | 0.234787 | ||||||||
\(934\) | 7.58579 | 0.248215 | ||||||||
\(935\) | −18.7990 | −0.614793 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 25.2132 | 0.823679 | 0.411840 | − | 0.911256i | \(-0.364886\pi\) | ||||
0.411840 | + | 0.911256i | \(0.364886\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.89949 | −0.127255 | ||||||||
\(940\) | −6.00000 | −0.195698 | ||||||||
\(941\) | −55.9411 | −1.82363 | −0.911814 | − | 0.410603i | \(-0.865318\pi\) | ||||
−0.911814 | + | 0.410603i | \(0.865318\pi\) | |||||||
\(942\) | 5.58579 | 0.181995 | ||||||||
\(943\) | 84.7696 | 2.76048 | ||||||||
\(944\) | 3.07107 | 0.0999547 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.52691 | −0.309747 | ||||||||
\(947\) | −17.7279 | −0.576080 | −0.288040 | − | 0.957618i | \(-0.593004\pi\) | ||||
−0.288040 | + | 0.957618i | \(0.593004\pi\) | |||||||
\(948\) | −6.24264 | −0.202752 | ||||||||
\(949\) | −11.0000 | −0.357075 | ||||||||
\(950\) | −26.6274 | −0.863907 | ||||||||
\(951\) | −12.5858 | −0.408122 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.9411 | 1.09946 | 0.549730 | − | 0.835342i | \(-0.314730\pi\) | ||||
0.549730 | + | 0.835342i | \(0.314730\pi\) | |||||||
\(954\) | 5.65685 | 0.183147 | ||||||||
\(955\) | −11.9706 | −0.387358 | ||||||||
\(956\) | 16.3848 | 0.529922 | ||||||||
\(957\) | 34.0122 | 1.09946 | ||||||||
\(958\) | −4.85786 | −0.156950 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −29.0000 | −0.935484 | ||||||||
\(962\) | 5.58579 | 0.180093 | ||||||||
\(963\) | 13.5563 | 0.436847 | ||||||||
\(964\) | −18.9706 | −0.611001 | ||||||||
\(965\) | −14.2426 | −0.458487 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.4142 | 1.36395 | 0.681975 | − | 0.731376i | \(-0.261121\pi\) | ||||
0.681975 | + | 0.731376i | \(0.261121\pi\) | |||||||
\(968\) | 1.85786 | 0.0597140 | ||||||||
\(969\) | −34.8995 | −1.12113 | ||||||||
\(970\) | 15.3137 | 0.491694 | ||||||||
\(971\) | −27.7990 | −0.892112 | −0.446056 | − | 0.895005i | \(-0.647172\pi\) | ||||
−0.446056 | + | 0.895005i | \(0.647172\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 19.6569 | 0.629846 | ||||||||
\(975\) | 4.00000 | 0.128103 | ||||||||
\(976\) | 7.58579 | 0.242815 | ||||||||
\(977\) | 25.7279 | 0.823109 | 0.411555 | − | 0.911385i | \(-0.364986\pi\) | ||||
0.411555 | + | 0.911385i | \(0.364986\pi\) | |||||||
\(978\) | −11.6569 | −0.372745 | ||||||||
\(979\) | 20.6447 | 0.659806 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.8995 | −0.603414 | ||||||||
\(982\) | 19.1716 | 0.611789 | ||||||||
\(983\) | −33.6274 | −1.07255 | −0.536274 | − | 0.844044i | \(-0.680169\pi\) | ||||
−0.536274 | + | 0.844044i | \(0.680169\pi\) | |||||||
\(984\) | −10.8284 | −0.345198 | ||||||||
\(985\) | −7.41421 | −0.236236 | ||||||||
\(986\) | 49.7279 | 1.58366 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.65685 | −0.211783 | ||||||||
\(989\) | −20.7990 | −0.661369 | ||||||||
\(990\) | 3.58579 | 0.113964 | ||||||||
\(991\) | −8.34315 | −0.265029 | −0.132514 | − | 0.991181i | \(-0.542305\pi\) | ||||
−0.132514 | + | 0.991181i | \(0.542305\pi\) | |||||||
\(992\) | −1.41421 | −0.0449013 | ||||||||
\(993\) | 12.2426 | 0.388508 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.5563 | −0.461467 | ||||||||
\(996\) | 7.65685 | 0.242617 | ||||||||
\(997\) | −43.2548 | −1.36989 | −0.684947 | − | 0.728593i | \(-0.740175\pi\) | ||||
−0.684947 | + | 0.728593i | \(0.740175\pi\) | |||||||
\(998\) | −26.0416 | −0.824333 | ||||||||
\(999\) | −5.58579 | −0.176726 |
(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 | 3822.2.a.br.1.2 | yes | 2 | |
7.6 | odd | 2 | 3822.2.a.bq.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3822.2.a.bq.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
3822.2.a.br.1.2 | yes | 2 | 1.1 | even | 1 | trivial |