Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6080,2,Mod(1,6080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6080.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6080 = 2^{6} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6080.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: | \(48.5490444289\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3040) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.08613\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6080.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.08613 | −1.78178 | −0.890889 | − | 0.454221i | \(-0.849918\pi\) | ||||
−0.890889 | + | 0.454221i | \(0.849918\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.648061 | −0.244944 | −0.122472 | − | 0.992472i | \(-0.539082\pi\) | ||||
−0.122472 | + | 0.992472i | \(0.539082\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.52420 | 2.17473 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.35194 | −0.407625 | −0.203813 | − | 0.979010i | \(-0.565333\pi\) | ||||
−0.203813 | + | 0.979010i | \(0.565333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.43807 | −1.23090 | −0.615449 | − | 0.788176i | \(-0.711025\pi\) | ||||
−0.615449 | + | 0.788176i | \(0.711025\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.08613 | −0.796835 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.35194 | −0.698928 | −0.349464 | − | 0.936950i | \(-0.613636\pi\) | ||||
−0.349464 | + | 0.936950i | \(0.613636\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −10.8761 | −2.09311 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.17226 | 0.774769 | 0.387385 | − | 0.921918i | \(-0.373379\pi\) | ||||
0.387385 | + | 0.921918i | \(0.373379\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.17226 | 0.749360 | 0.374680 | − | 0.927154i | \(-0.377753\pi\) | ||||
0.374680 | + | 0.927154i | \(0.377753\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.17226 | 0.726297 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.648061 | −0.109542 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.43807 | 0.400816 | 0.200408 | − | 0.979713i | \(-0.435773\pi\) | ||||
0.200408 | + | 0.979713i | \(0.435773\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.6965 | 2.19319 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.1723 | 1.58864 | 0.794320 | − | 0.607499i | \(-0.207827\pi\) | ||||
0.794320 | + | 0.607499i | \(0.207827\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.82032 | −1.04009 | −0.520045 | − | 0.854139i | \(-0.674085\pi\) | ||||
−0.520045 | + | 0.854139i | \(0.674085\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.52420 | 0.972570 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.648061 | −0.0945294 | −0.0472647 | − | 0.998882i | \(-0.515050\pi\) | ||||
−0.0472647 | + | 0.998882i | \(0.515050\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.58002 | −0.940002 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.17226 | −0.864289 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.43807 | −0.884337 | −0.442168 | − | 0.896932i | \(-0.645791\pi\) | ||||
−0.442168 | + | 0.896932i | \(0.645791\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.35194 | −0.182295 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.08613 | −0.408768 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.3445 | −1.34674 | −0.673371 | − | 0.739305i | \(-0.735154\pi\) | ||||
−0.673371 | + | 0.739305i | \(0.735154\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.11644 | 0.270983 | 0.135491 | − | 0.990779i | \(-0.456739\pi\) | ||||
0.135491 | + | 0.990779i | \(0.456739\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.22808 | −0.532688 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.43807 | −0.550475 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.1345 | 1.48247 | 0.741234 | − | 0.671246i | \(-0.234241\pi\) | ||||
0.741234 | + | 0.671246i | \(0.234241\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.3445 | 1.24533 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.82774 | −0.454269 | −0.227135 | − | 0.973863i | \(-0.572936\pi\) | ||||
−0.227135 | + | 0.973863i | \(0.572936\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.17226 | −0.488326 | −0.244163 | − | 0.969734i | \(-0.578513\pi\) | ||||
−0.244163 | + | 0.969734i | \(0.578513\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.08613 | −0.356356 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.876139 | 0.0998453 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | 0.225018 | 0.112509 | − | 0.993651i | \(-0.464111\pi\) | ||||
0.112509 | + | 0.993651i | \(0.464111\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 13.9926 | 1.55473 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.52420 | −1.04542 | −0.522708 | − | 0.852512i | \(-0.675078\pi\) | ||||
−0.522708 | + | 0.852512i | \(0.675078\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | 0.216930 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.8761 | −1.38047 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.82774 | 0.405740 | 0.202870 | − | 0.979206i | \(-0.434973\pi\) | ||||
0.202870 | + | 0.979206i | \(0.434973\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.87614 | 0.301501 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.8761 | −1.33519 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.73419 | 0.785288 | 0.392644 | − | 0.919691i | \(-0.371560\pi\) | ||||
0.392644 | + | 0.919691i | \(0.371560\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.82032 | −0.886476 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.35194 | 0.134523 | 0.0672615 | − | 0.997735i | \(-0.478574\pi\) | ||||
0.0672615 | + | 0.997735i | \(0.478574\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.79001 | −0.373441 | −0.186720 | − | 0.982413i | \(-0.559786\pi\) | ||||
−0.186720 | + | 0.982413i | \(0.559786\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.00000 | 0.195180 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.55451 | 0.826996 | 0.413498 | − | 0.910505i | \(-0.364307\pi\) | ||||
0.413498 | + | 0.910505i | \(0.364307\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.04840 | 0.675114 | 0.337557 | − | 0.941305i | \(-0.390399\pi\) | ||||
0.337557 | + | 0.941305i | \(0.390399\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.52420 | −0.714165 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.6103 | 1.75071 | 0.875356 | − | 0.483478i | \(-0.160627\pi\) | ||||
0.875356 | + | 0.483478i | \(0.160627\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.35194 | −0.312570 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −28.9549 | −2.67688 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.29612 | −0.118815 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.17226 | −0.833842 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −31.3929 | −2.83060 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.79001 | 0.158838 | 0.0794188 | − | 0.996841i | \(-0.474694\pi\) | ||||
0.0794188 | + | 0.996841i | \(0.474694\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 21.0484 | 1.85321 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.2207 | 1.50458 | 0.752288 | − | 0.658834i | \(-0.228950\pi\) | ||||
0.752288 | + | 0.658834i | \(0.228950\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.648061 | −0.0561940 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.8761 | −0.936069 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.1116 | 0.863895 | 0.431948 | − | 0.901899i | \(-0.357827\pi\) | ||||
0.431948 | + | 0.901899i | \(0.357827\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.69646 | 0.822443 | 0.411222 | − | 0.911535i | \(-0.365102\pi\) | ||||
0.411222 | + | 0.911535i | \(0.365102\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.00000 | 0.168430 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.00000 | 0.501745 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.17226 | 0.346487 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 20.3068 | 1.67488 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.88356 | −0.482000 | −0.241000 | − | 0.970525i | \(-0.577475\pi\) | ||||
−0.241000 | + | 0.970525i | \(0.577475\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.6284 | 1.51596 | 0.757980 | − | 0.652278i | \(-0.226187\pi\) | ||||
0.757980 | + | 0.652278i | \(0.226187\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.0484 | 1.05490 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.17226 | 0.335124 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.3929 | 1.38811 | 0.694053 | − | 0.719924i | \(-0.255823\pi\) | ||||
0.694053 | + | 0.719924i | \(0.255823\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19.8687 | 1.57569 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.17226 | 0.171198 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.17968 | −0.0923996 | −0.0461998 | − | 0.998932i | \(-0.514711\pi\) | ||||
−0.0461998 | + | 0.998932i | \(0.514711\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.17226 | 0.324810 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.7268 | −1.91342 | −0.956708 | − | 0.291051i | \(-0.905995\pi\) | ||||
−0.956708 | + | 0.291051i | \(0.905995\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.69646 | 0.515112 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.52420 | 0.498918 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.2026 | −1.30789 | −0.653944 | − | 0.756543i | \(-0.726887\pi\) | ||||
−0.653944 | + | 0.756543i | \(0.726887\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.648061 | −0.0489888 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 31.9245 | 2.39960 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.00000 | −0.448461 | −0.224231 | − | 0.974536i | \(-0.571987\pi\) | ||||
−0.224231 | + | 0.974536i | \(0.571987\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.0968 | −1.19647 | −0.598233 | − | 0.801322i | \(-0.704130\pi\) | ||||
−0.598233 | + | 0.801322i | \(0.704130\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.53162 | −0.482831 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.43807 | 0.179250 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.70388 | −0.197727 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.04840 | 0.512696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.111635 | 0.00807764 | 0.00403882 | − | 0.999992i | \(-0.498714\pi\) | ||||
0.00403882 | + | 0.999992i | \(0.498714\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.01809 | −0.433191 | −0.216596 | − | 0.976261i | \(-0.569495\pi\) | ||||
−0.216596 | + | 0.976261i | \(0.569495\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.6965 | 0.980824 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.7645 | −1.05193 | −0.525964 | − | 0.850507i | \(-0.676295\pi\) | ||||
−0.525964 | + | 0.850507i | \(0.676295\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.75228 | 0.691321 | 0.345660 | − | 0.938360i | \(-0.387655\pi\) | ||||
0.345660 | + | 0.938360i | \(0.387655\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −37.4487 | −2.64143 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.70388 | −0.189775 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.1723 | 0.710461 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −21.8687 | −1.51998 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.35194 | −0.0935156 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.87614 | −0.335687 | −0.167844 | − | 0.985814i | \(-0.553680\pi\) | ||||
−0.167844 | + | 0.985814i | \(0.553680\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.8129 | 0.809407 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.82032 | −0.465142 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.70388 | −0.183551 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.8761 | 0.870089 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.87614 | −0.597074 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.8384 | −1.39544 | −0.697721 | − | 0.716369i | \(-0.745803\pi\) | ||||
−0.697721 | + | 0.716369i | \(0.745803\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.52420 | 0.434947 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.3552 | 1.68288 | 0.841441 | − | 0.540348i | \(-0.181707\pi\) | ||||
0.841441 | + | 0.540348i | \(0.181707\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.0410 | −1.72084 | −0.860418 | − | 0.509589i | \(-0.829798\pi\) | ||||
−0.860418 | + | 0.509589i | \(0.829798\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.70388 | −0.177902 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.1090 | −0.989825 | −0.494913 | − | 0.868943i | \(-0.664800\pi\) | ||||
−0.494913 | + | 0.868943i | \(0.664800\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.648061 | −0.0422748 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.17226 | −0.400931 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.9878 | −1.35759 | −0.678793 | − | 0.734330i | \(-0.737497\pi\) | ||||
−0.678793 | + | 0.734330i | \(0.737497\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.87614 | −0.571762 | −0.285881 | − | 0.958265i | \(-0.592286\pi\) | ||||
−0.285881 | + | 0.958265i | \(0.592286\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.5545 | −0.677072 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.58002 | −0.420382 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.43807 | −0.282388 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 29.3929 | 1.86270 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.11164 | −0.259524 | −0.129762 | − | 0.991545i | \(-0.541421\pi\) | ||||
−0.129762 | + | 0.991545i | \(0.541421\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.53162 | 0.284900 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.17226 | −0.386522 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.37483 | −0.335273 | −0.167636 | − | 0.985849i | \(-0.553613\pi\) | ||||
−0.167636 | + | 0.985849i | \(0.553613\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.58002 | −0.0981775 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 27.2207 | 1.68492 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.58482 | −0.467700 | −0.233850 | − | 0.972273i | \(-0.575133\pi\) | ||||
−0.233850 | + | 0.972273i | \(0.575133\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.43807 | −0.395487 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.8129 | −0.722938 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.81551 | 0.171665 | 0.0858324 | − | 0.996310i | \(-0.472645\pi\) | ||||
0.0858324 | + | 0.996310i | \(0.472645\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.7449 | −1.01718 | −0.508589 | − | 0.861009i | \(-0.669833\pi\) | ||||
−0.508589 | + | 0.861009i | \(0.669833\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.87614 | −0.537208 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.35194 | −0.0815250 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.0484 | −1.50501 | −0.752506 | − | 0.658585i | \(-0.771155\pi\) | ||||
−0.752506 | + | 0.658585i | \(0.771155\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 27.2207 | 1.62966 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.8613 | −1.60241 | −0.801205 | − | 0.598389i | \(-0.795808\pi\) | ||||
−0.801205 | + | 0.598389i | \(0.795808\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.5242 | 1.27948 | 0.639740 | − | 0.768591i | \(-0.279042\pi\) | ||||
0.639740 | + | 0.768591i | \(0.279042\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.08613 | −0.182807 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.59224 | −0.389128 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.8687 | −1.39921 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.6710 | −1.09077 | −0.545384 | − | 0.838186i | \(-0.683616\pi\) | ||||
−0.545384 | + | 0.838186i | \(0.683616\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.3445 | −0.602281 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.7039 | 0.853206 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.8761 | 0.860309 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.41998 | 0.254764 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.17226 | −0.239690 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.11644 | 0.121187 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.3068 | 0.588240 | 0.294120 | − | 0.955769i | \(-0.404974\pi\) | ||||
0.294120 | + | 0.955769i | \(0.404974\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.6965 | 0.665388 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.4003 | −0.703159 | −0.351579 | − | 0.936158i | \(-0.614355\pi\) | ||||
−0.351579 | + | 0.936158i | \(0.614355\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.4535 | −1.55177 | −0.775883 | − | 0.630877i | \(-0.782695\pi\) | ||||
−0.775883 | + | 0.630877i | \(0.782695\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.22808 | −0.238225 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 34.1149 | 1.91608 | 0.958041 | − | 0.286630i | \(-0.0925350\pi\) | ||||
0.958041 | + | 0.286630i | \(0.0925350\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.64064 | −0.315815 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −26.4003 | −1.47352 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.00000 | 0.111283 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.43807 | −0.246180 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.7523 | −1.20290 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.419983 | 0.0231544 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.2691 | 0.894228 | 0.447114 | − | 0.894477i | \(-0.352452\pi\) | ||||
0.447114 | + | 0.894477i | \(0.352452\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.9065 | 0.871668 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.1345 | 0.662980 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.0665 | 1.25651 | 0.628256 | − | 0.778007i | \(-0.283769\pi\) | ||||
0.628256 | + | 0.778007i | \(0.283769\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −57.4339 | −3.11938 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.64064 | −0.305458 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.80068 | 0.475192 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.3445 | 0.556930 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.4003 | −1.41724 | −0.708622 | − | 0.705588i | \(-0.750683\pi\) | ||||
−0.708622 | + | 0.705588i | \(0.750683\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.4535 | 1.89778 | 0.948892 | − | 0.315600i | \(-0.102206\pi\) | ||||
0.948892 | + | 0.315600i | \(0.102206\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 48.2691 | 2.57641 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.0336 | −1.01305 | −0.506527 | − | 0.862224i | \(-0.669071\pi\) | ||||
−0.506527 | + | 0.862224i | \(0.669071\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.82774 | −0.203155 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.00000 | 0.211702 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.16745 | −0.219950 | −0.109975 | − | 0.993934i | \(-0.535077\pi\) | ||||
−0.109975 | + | 0.993934i | \(0.535077\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.3068 | 1.48572 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.17226 | −0.218386 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −34.3249 | −1.79174 | −0.895872 | − | 0.444312i | \(-0.853448\pi\) | ||||
−0.895872 | + | 0.444312i | \(0.853448\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 66.3659 | 3.45487 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.17226 | 0.216613 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.32905 | 0.0688153 | 0.0344077 | − | 0.999408i | \(-0.489046\pi\) | ||||
0.0344077 | + | 0.999408i | \(0.489046\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.08613 | −0.159367 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.5168 | −0.953663 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.5922 | −0.544087 | −0.272043 | − | 0.962285i | \(-0.587699\pi\) | ||||
−0.272043 | + | 0.962285i | \(0.587699\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.52420 | −0.283013 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.38225 | 0.121727 | 0.0608637 | − | 0.998146i | \(-0.480615\pi\) | ||||
0.0608637 | + | 0.998146i | \(0.480615\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.876139 | 0.0446522 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −44.4971 | −2.26192 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.3323 | −1.18299 | −0.591497 | − | 0.806307i | \(-0.701463\pi\) | ||||
−0.591497 | + | 0.806307i | \(0.701463\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.70388 | −0.339030 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −53.1452 | −2.68082 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.00000 | 0.100631 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.3807 | −1.72552 | −0.862759 | − | 0.505616i | \(-0.831265\pi\) | ||||
−0.862759 | + | 0.505616i | \(0.831265\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.00000 | 0.100125 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.3297 | 1.21497 | 0.607483 | − | 0.794333i | \(-0.292179\pi\) | ||||
0.607483 | + | 0.794333i | \(0.292179\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.5168 | −0.922387 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.9926 | 0.695297 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.29612 | −0.163383 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.75228 | −0.482219 | −0.241110 | − | 0.970498i | \(-0.577511\pi\) | ||||
−0.241110 | + | 0.970498i | \(0.577511\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −31.2058 | −1.53927 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.70388 | 0.329876 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.52420 | −0.467525 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −29.9245 | −1.46541 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.51678 | −0.318366 | −0.159183 | − | 0.987249i | \(-0.550886\pi\) | ||||
−0.159183 | + | 0.987249i | \(0.550886\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.40515 | −0.117220 | −0.0586098 | − | 0.998281i | \(-0.518667\pi\) | ||||
−0.0586098 | + | 0.998281i | \(0.518667\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.22808 | −0.205576 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.00000 | 0.0970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.37158 | −0.0663756 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.5168 | −0.893999 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.1090 | 0.631439 | 0.315720 | − | 0.948852i | \(-0.397754\pi\) | ||||
0.315720 | + | 0.948852i | \(0.397754\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.8942 | −1.00411 | −0.502056 | − | 0.864835i | \(-0.667423\pi\) | ||||
−0.502056 | + | 0.864835i | \(0.667423\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.8761 | −0.617364 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.35194 | −0.160345 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −41.3929 | −1.97558 | −0.987788 | − | 0.155803i | \(-0.950203\pi\) | ||||
−0.987788 | + | 0.155803i | \(0.950203\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −42.9293 | −2.04425 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.0558 | −0.477766 | −0.238883 | − | 0.971048i | \(-0.576781\pi\) | ||||
−0.238883 | + | 0.971048i | \(0.576781\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.82774 | 0.181452 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.1574 | 0.858817 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.1116 | 0.571583 | 0.285792 | − | 0.958292i | \(-0.407743\pi\) | ||||
0.285792 | + | 0.958292i | \(0.407743\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.7523 | −0.647569 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −57.4897 | −2.70110 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.87614 | 0.134835 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.9123 | −1.44602 | −0.723008 | − | 0.690839i | \(-0.757241\pi\) | ||||
−0.723008 | + | 0.690839i | \(0.757241\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −21.7523 | −1.01531 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.00000 | 0.279448 | 0.139724 | − | 0.990190i | \(-0.455378\pi\) | ||||
0.139724 | + | 0.990190i | \(0.455378\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.0894 | 1.44485 | 0.722423 | − | 0.691451i | \(-0.243028\pi\) | ||||
0.722423 | + | 0.691451i | \(0.243028\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.8761 | −0.597117 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.0410 | 0.557190 | 0.278595 | − | 0.960409i | \(-0.410131\pi\) | ||||
0.278595 | + | 0.960409i | \(0.410131\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.86391 | −0.363122 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −53.6768 | −2.47330 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.22066 | 0.423966 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −42.0032 | −1.92320 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.3035 | 0.470781 | 0.235390 | − | 0.971901i | \(-0.424363\pi\) | ||||
0.235390 | + | 0.971901i | \(0.424363\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.8203 | −0.493364 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.70388 | −0.305037 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.73419 | 0.351192 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.4939 | −1.01930 | −0.509648 | − | 0.860383i | \(-0.670224\pi\) | ||||
−0.509648 | + | 0.860383i | \(0.670224\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.64064 | 0.164636 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.6162 | 1.60734 | 0.803668 | − | 0.595078i | \(-0.202879\pi\) | ||||
0.803668 | + | 0.595078i | \(0.202879\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.34452 | 0.375818 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.82032 | −0.396444 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.48061 | 0.111270 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.0558176 | 0.00249874 | 0.00124937 | − | 0.999999i | \(-0.499602\pi\) | ||||
0.00124937 | + | 0.999999i | \(0.499602\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 76.3100 | 3.40928 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.8081 | 1.06155 | 0.530775 | − | 0.847513i | \(-0.321901\pi\) | ||||
0.530775 | + | 0.847513i | \(0.321901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.35194 | 0.0601605 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.6661 | −0.917816 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.5316 | −0.466806 | −0.233403 | − | 0.972380i | \(-0.574986\pi\) | ||||
−0.233403 | + | 0.972380i | \(0.574986\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.70388 | 0.119613 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.8761 | −0.480193 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.79001 | −0.167008 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.876139 | 0.0385325 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 53.0894 | 2.33037 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.2961 | −0.494892 | −0.247446 | − | 0.968902i | \(-0.579591\pi\) | ||||
−0.247446 | + | 0.968902i | \(0.579591\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.0861 | 0.484763 | 0.242381 | − | 0.970181i | \(-0.422071\pi\) | ||||
0.242381 | + | 0.970181i | \(0.422071\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.00000 | 0.0872872 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.34452 | 0.363493 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.7645 | −0.511500 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −67.4897 | −2.92880 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −45.1452 | −1.95546 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.55451 | 0.369844 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.5168 | 0.799058 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.89578 | 0.383169 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.8565 | −0.724717 | −0.362359 | − | 0.932039i | \(-0.618028\pi\) | ||||
−0.362359 | + | 0.932039i | \(0.618028\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 49.6768 | 2.13184 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.04840 | 0.301920 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.6151 | −0.710412 | −0.355206 | − | 0.934788i | \(-0.615589\pi\) | ||||
−0.355206 | + | 0.934788i | \(0.615589\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.8081 | 0.589315 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.17226 | 0.177744 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.29612 | −0.0551167 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.52420 | −0.319384 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.4562 | −1.62944 | −0.814720 | − | 0.579855i | \(-0.803109\pi\) | ||||
−0.814720 | + | 0.579855i | \(0.803109\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.2691 | 1.28024 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.34452 | 0.352306 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −40.4184 | −1.70343 | −0.851717 | − | 0.524002i | \(-0.824438\pi\) | ||||
−0.851717 | + | 0.524002i | \(0.824438\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.6103 | 0.782942 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.06804 | −0.380822 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.9368 | 1.12925 | 0.564624 | − | 0.825348i | \(-0.309021\pi\) | ||||
0.564624 | + | 0.825348i | \(0.309021\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.4636 | 0.898223 | 0.449111 | − | 0.893476i | \(-0.351741\pi\) | ||||
0.449111 | + | 0.893476i | \(0.351741\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.344521 | −0.0143926 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.35194 | −0.139786 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.8613 | −0.535423 | −0.267712 | − | 0.963499i | \(-0.586267\pi\) | ||||
−0.267712 | + | 0.963499i | \(0.586267\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.5726 | 0.771851 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.17226 | 0.256069 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.70388 | 0.360478 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −28.9549 | −1.19714 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.8687 | 0.572423 | 0.286212 | − | 0.958166i | \(-0.407604\pi\) | ||||
0.286212 | + | 0.958166i | \(0.407604\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.17226 | 0.171915 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 45.5652 | 1.87430 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.9368 | −0.859770 | −0.429885 | − | 0.902884i | \(-0.641446\pi\) | ||||
−0.429885 | + | 0.902884i | \(0.641446\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.29612 | −0.0531358 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −30.0968 | −1.23178 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.703878 | −0.0287597 | −0.0143798 | − | 0.999897i | \(-0.504577\pi\) | ||||
−0.0143798 | + | 0.999897i | \(0.504577\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.22066 | 0.212955 | 0.106478 | − | 0.994315i | \(-0.466043\pi\) | ||||
0.106478 | + | 0.994315i | \(0.466043\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 79.1681 | 3.22397 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.17226 | −0.372905 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.1345 | −0.654880 | −0.327440 | − | 0.944872i | \(-0.606186\pi\) | ||||
−0.327440 | + | 0.944872i | \(0.606186\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.34452 | 0.338137 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.87614 | 0.116356 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.3323 | 0.780824 | 0.390412 | − | 0.920640i | \(-0.372333\pi\) | ||||
0.390412 | + | 0.920640i | \(0.372333\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −31.3929 | −1.26588 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.01223 | 0.0407507 | 0.0203753 | − | 0.999792i | \(-0.493514\pi\) | ||||
0.0203753 | + | 0.999792i | \(0.493514\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.8809 | 0.758889 | 0.379445 | − | 0.925214i | \(-0.376115\pi\) | ||||
0.379445 | + | 0.925214i | \(0.376115\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 36.4562 | 1.46294 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.48061 | −0.0993835 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.17226 | 0.166624 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.87614 | 0.194424 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.4636 | −0.695214 | −0.347607 | − | 0.937640i | \(-0.613006\pi\) | ||||
−0.347607 | + | 0.937640i | \(0.613006\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.0484 | 0.598120 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.79001 | 0.0710343 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 29.2026 | 1.15705 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.9729 | −0.987914 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.4051 | −0.884950 | −0.442475 | − | 0.896781i | \(-0.645899\pi\) | ||||
−0.442475 | + | 0.896781i | \(0.645899\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.6332 | −0.892567 | −0.446284 | − | 0.894892i | \(-0.647253\pi\) | ||||
−0.446284 | + | 0.894892i | \(0.647253\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21.0484 | 0.828780 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.8203 | −1.36893 | −0.684464 | − | 0.729047i | \(-0.739964\pi\) | ||||
−0.684464 | + | 0.729047i | \(0.739964\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.9852 | 0.548966 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.34452 | 0.327048 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.1090 | 0.904326 | 0.452163 | − | 0.891935i | \(-0.350653\pi\) | ||||
0.452163 | + | 0.891935i | \(0.350653\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.2207 | 0.672867 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −27.2207 | −1.06198 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.24772 | −0.165468 | −0.0827339 | − | 0.996572i | \(-0.526365\pi\) | ||||
−0.0827339 | + | 0.996572i | \(0.526365\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.15742 | −0.317287 | −0.158644 | − | 0.987336i | \(-0.550712\pi\) | ||||
−0.158644 | + | 0.987336i | \(0.550712\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 27.3929 | 1.06385 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.648061 | −0.0251307 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.9852 | −0.541508 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 64.3100 | 2.48637 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.86130 | −0.110459 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.2239 | 1.51197 | 0.755985 | − | 0.654589i | \(-0.227158\pi\) | ||||
0.755985 | + | 0.654589i | \(0.227158\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.8761 | −0.418623 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.4232 | −1.24613 | −0.623063 | − | 0.782172i | \(-0.714112\pi\) | ||||
−0.623063 | + | 0.782172i | \(0.714112\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.01223 | −0.192352 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −78.2494 | −2.99852 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.6539 | 1.36426 | 0.682130 | − | 0.731231i | \(-0.261054\pi\) | ||||
0.682130 | + | 0.731231i | \(0.261054\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.1116 | 0.386346 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 80.3659 | 3.06615 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.5726 | 1.08853 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.0261 | 1.67483 | 0.837417 | − | 0.546565i | \(-0.184065\pi\) | ||||
0.837417 | + | 0.546565i | \(0.184065\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.71610 | 0.217137 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.69646 | 0.367808 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.3445 | 0.770604 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 46.6284 | 1.76365 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.9023 | −1.09162 | −0.545812 | − | 0.837908i | \(-0.683779\pi\) | ||||
−0.545812 | + | 0.837908i | \(0.683779\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.43807 | 0.0919535 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.00000 | 0.0753244 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.876139 | −0.0329506 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.6433 | 0.399716 | 0.199858 | − | 0.979825i | \(-0.435952\pi\) | ||||
0.199858 | + | 0.979825i | \(0.435952\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.0484 | 0.489353 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.9852 | −0.523748 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000 | 0.224387 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 64.7710 | 2.41892 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −41.4339 | −1.54522 | −0.772612 | − | 0.634879i | \(-0.781050\pi\) | ||||
−0.772612 | + | 0.634879i | \(0.781050\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.45616 | 0.0914720 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 27.3929 | 1.01875 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.17226 | 0.154954 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.72352 | −0.175186 | −0.0875929 | − | 0.996156i | \(-0.527917\pi\) | ||||
−0.0875929 | + | 0.996156i | \(0.527917\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.40515 | −0.348339 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.6406 | −0.504517 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.6917 | −0.653456 | −0.326728 | − | 0.945118i | \(-0.605946\pi\) | ||||
−0.326728 | + | 0.945118i | \(0.605946\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 20.3068 | 0.749027 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.4051 | −0.604291 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.2233 | −0.449640 | −0.224820 | − | 0.974400i | \(-0.572179\pi\) | ||||
−0.224820 | + | 0.974400i | \(0.572179\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.6965 | 0.503152 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.6635 | 0.721385 | 0.360693 | − | 0.932685i | \(-0.382540\pi\) | ||||
0.360693 | + | 0.932685i | \(0.382540\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.88356 | −0.215557 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −62.1378 | −2.27350 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.54384 | −0.202568 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.6768 | −1.52081 | −0.760404 | − | 0.649450i | \(-0.774999\pi\) | ||||
−0.760404 | + | 0.649450i | \(0.774999\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.6890 | 0.462414 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.6284 | 0.677957 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.6136 | 1.54882 | 0.774408 | − | 0.632686i | \(-0.218048\pi\) | ||||
0.774408 | + | 0.632686i | \(0.218048\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.9852 | −0.507629 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.8809 | −1.11943 | −0.559717 | − | 0.828684i | \(-0.689090\pi\) | ||||
−0.559717 | + | 0.828684i | \(0.689090\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.56779 | −0.165365 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.0484 | 0.471766 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 45.9097 | 1.65770 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.12867 | −0.184945 | −0.0924723 | − | 0.995715i | \(-0.529477\pi\) | ||||
−0.0924723 | + | 0.995715i | \(0.529477\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.5874 | 0.597382 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −42.0787 | −1.51347 | −0.756733 | − | 0.653724i | \(-0.773206\pi\) | ||||
−0.756733 | + | 0.653724i | \(0.773206\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.17226 | 0.149872 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.87614 | 0.174931 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.1723 | 0.364459 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.17487 | 0.185171 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −45.3781 | −1.62168 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.3929 | 0.620780 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.4307 | −1.54814 | −0.774068 | − | 0.633103i | \(-0.781781\pi\) | ||||
−0.774068 | + | 0.633103i | \(0.781781\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 23.4078 | 0.833338 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0606 | −0.428826 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.39292 | −0.333552 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19.8687 | 0.704671 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.0032 | 1.41699 | 0.708494 | − | 0.705717i | \(-0.249375\pi\) | ||||
0.708494 | + | 0.705717i | \(0.249375\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.29612 | −0.0458535 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.9729 | 0.882375 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.64064 | 0.199054 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.17226 | 0.0765621 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.68904 | −0.305869 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.7401 | −1.01045 | −0.505223 | − | 0.862989i | \(-0.668590\pi\) | ||||
−0.505223 | + | 0.862989i | \(0.668590\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0510 | −0.563627 | −0.281814 | − | 0.959469i | \(-0.590936\pi\) | ||||
−0.281814 | + | 0.959469i | \(0.590936\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 51.6768 | 1.81239 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.17968 | −0.0413223 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.82032 | −0.238613 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.7645 | 0.655685 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.82774 | −0.273190 | −0.136595 | − | 0.990627i | \(-0.543616\pi\) | ||||
−0.136595 | + | 0.990627i | \(0.543616\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.78676 | 0.341145 | 0.170572 | − | 0.985345i | \(-0.445438\pi\) | ||||
0.170572 | + | 0.985345i | \(0.445438\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.17226 | 0.145259 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −50.1707 | −1.74461 | −0.872303 | − | 0.488965i | \(-0.837374\pi\) | ||||
−0.872303 | + | 0.488965i | \(0.837374\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.2961 | 0.739645 | 0.369822 | − | 0.929102i | \(-0.379419\pi\) | ||||
0.369822 | + | 0.929102i | \(0.379419\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 77.3026 | 2.68160 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.1600 | −0.455968 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.7268 | −0.855705 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −45.3781 | −1.56850 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.9516 | 1.06857 | 0.534284 | − | 0.845305i | \(-0.320581\pi\) | ||||
0.534284 | + | 0.845305i | \(0.320581\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.5922 | −0.399733 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 82.8975 | 2.85514 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.69646 | 0.230365 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.94418 | 0.204245 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −66.4265 | −2.27975 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.17226 | −0.280141 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.9219 | −1.33266 | −0.666331 | − | 0.745656i | \(-0.732136\pi\) | ||||
−0.666331 | + | 0.745656i | \(0.732136\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.52420 | 0.223123 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 52.1245 | 1.78054 | 0.890270 | − | 0.455434i | \(-0.150516\pi\) | ||||
0.890270 | + | 0.455434i | \(0.150516\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.41998 | 0.150808 | 0.0754039 | − | 0.997153i | \(-0.475975\pi\) | ||||
0.0754039 | + | 0.997153i | \(0.475975\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.3445 | 0.693339 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.4184 | −0.422728 | −0.211364 | − | 0.977407i | \(-0.567791\pi\) | ||||
−0.211364 | + | 0.977407i | \(0.567791\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.2026 | −0.584905 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 40.1197 | 1.36254 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.70388 | −0.0917228 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −53.8539 | −1.82477 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 50.4594 | 1.70779 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.648061 | −0.0219085 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.3020 | −1.36090 | −0.680451 | − | 0.732794i | \(-0.738216\pi\) | ||||
−0.680451 | + | 0.732794i | \(0.738216\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 57.6210 | 1.94351 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.47580 | −0.150794 | −0.0753968 | − | 0.997154i | \(-0.524022\pi\) | ||||
−0.0753968 | + | 0.997154i | \(0.524022\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.5455 | 0.926981 | 0.463491 | − | 0.886102i | \(-0.346597\pi\) | ||||
0.463491 | + | 0.886102i | \(0.346597\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 31.9245 | 1.07313 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −48.5152 | −1.62898 | −0.814491 | − | 0.580176i | \(-0.802984\pi\) | ||||
−0.814491 | + | 0.580176i | \(0.802984\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.16003 | −0.0389063 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.9171 | −0.633747 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.648061 | −0.0216865 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.00000 | −0.200558 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −45.9097 | −1.53288 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.4078 | 0.580581 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.8761 | −0.428966 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.6406 | −0.453932 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.0968 | −0.535076 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.55451 | 0.151230 | 0.0756150 | − | 0.997137i | \(-0.475908\pi\) | ||||
0.0756150 | + | 0.997137i | \(0.475908\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.82032 | 0.292552 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.298732 | 0.00989745 | 0.00494872 | − | 0.999988i | \(-0.498425\pi\) | ||||
0.00494872 | + | 0.999988i | \(0.498425\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.8761 | 0.426138 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.53162 | −0.215929 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.1600 | −0.368537 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.0754620 | −0.00248926 | −0.00124463 | − | 0.999999i | \(-0.500396\pi\) | ||||
−0.00124463 | + | 0.999999i | \(0.500396\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.8081 | −1.04811 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.9878 | 0.559159 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.43807 | 0.0801632 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.7268 | −0.812134 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.0000 | 0.984268 | 0.492134 | − | 0.870519i | \(-0.336217\pi\) | ||||
0.492134 | + | 0.870519i | \(0.336217\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.58002 | −0.215651 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 38.2691 | 1.25287 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.70388 | −0.0884263 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.9581 | 1.40338 | 0.701690 | − | 0.712482i | \(-0.252429\pi\) | ||||
0.701690 | + | 0.712482i | \(0.252429\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 84.7252 | 2.76490 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.3297 | −0.662729 | −0.331364 | − | 0.943503i | \(-0.607509\pi\) | ||||
−0.331364 | + | 0.943503i | \(0.607509\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34.0968 | −1.11034 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.04840 | 0.229284 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −57.0745 | −1.85467 | −0.927337 | − | 0.374228i | \(-0.877908\pi\) | ||||
−0.927337 | + | 0.374228i | \(0.877908\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.5168 | 0.601080 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −105.283 | −3.41403 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.4594 | 1.44018 | 0.720091 | − | 0.693880i | \(-0.244100\pi\) | ||||
0.720091 | + | 0.693880i | \(0.244100\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.111635 | 0.00361243 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.4078 | 0.562713 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.55295 | −0.211606 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.5922 | −0.438459 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 55.8113 | 1.79850 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.01809 | −0.193729 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.1016 | 1.22527 | 0.612633 | − | 0.790368i | \(-0.290111\pi\) | ||||
0.612633 | + | 0.790368i | \(0.290111\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.17226 | −0.198282 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.3716 | 0.493298 | 0.246649 | − | 0.969105i | \(-0.420671\pi\) | ||||
0.246649 | + | 0.969105i | \(0.420671\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.28390 | −0.201452 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.6965 | 0.438638 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.1271 | 0.803888 | 0.401944 | − | 0.915664i | \(-0.368335\pi\) | ||||
0.401944 | + | 0.915664i | \(0.368335\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.17487 | −0.165390 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.9852 | 1.46819 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.3042 | 0.870868 | 0.435434 | − | 0.900221i | \(-0.356595\pi\) | ||||
0.435434 | + | 0.900221i | \(0.356595\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.7645 | −0.470436 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.29612 | −0.0412560 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.8613 | 0.726947 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.0697 | −1.81288 | −0.906440 | − | 0.422335i | \(-0.861211\pi\) | ||||
−0.906440 | + | 0.422335i | \(0.861211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −50.2084 | −1.59332 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.75228 | 0.309168 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.1213 | −0.573906 | −0.286953 | − | 0.957945i | \(-0.592642\pi\) | ||||
−0.286953 | + | 0.957945i | \(0.592642\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −26.5168 | −0.838954 |
(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 | 6080.2.a.bp.1.1 | 3 | ||
4.3 | odd | 2 | 6080.2.a.bz.1.3 | 3 | |||
8.3 | odd | 2 | 3040.2.a.k.1.1 | ✓ | 3 | ||
8.5 | even | 2 | 3040.2.a.n.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3040.2.a.k.1.1 | ✓ | 3 | 8.3 | odd | 2 | ||
3040.2.a.n.1.3 | yes | 3 | 8.5 | even | 2 | ||
6080.2.a.bp.1.1 | 3 | 1.1 | even | 1 | trivial | ||
6080.2.a.bz.1.3 | 3 | 4.3 | odd | 2 |