Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1250,2,Mod(1,1250)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1250, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1250.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1250 = 2 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1250.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: | \(9.98130025266\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.7625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 9x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 50) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.96645\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1250.1 |
$q$-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 | ||||||||
\(3\) | 2.96645 | 1.71268 | 0.856340 | − | 0.516413i | \(-0.172733\pi\) | ||||
0.856340 | + | 0.516413i | \(0.172733\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.96645 | 1.21105 | ||||||||
\(7\) | 1.83337 | 0.692947 | 0.346474 | − | 0.938060i | \(-0.387379\pi\) | ||||
0.346474 | + | 0.938060i | \(0.387379\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 5.79981 | 1.93327 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.83337 | −0.552781 | −0.276390 | − | 0.961045i | \(-0.589138\pi\) | ||||
−0.276390 | + | 0.961045i | \(0.589138\pi\) | |||||||
\(12\) | 2.96645 | 0.856340 | ||||||||
\(13\) | −2.41785 | −0.670590 | −0.335295 | − | 0.942113i | \(-0.608836\pi\) | ||||
−0.335295 | + | 0.942113i | \(0.608836\pi\) | |||||||
\(14\) | 1.83337 | 0.489988 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.78467 | 0.675381 | 0.337691 | − | 0.941257i | \(-0.390354\pi\) | ||||
0.337691 | + | 0.941257i | \(0.390354\pi\) | |||||||
\(18\) | 5.79981 | 1.36703 | ||||||||
\(19\) | −1.67232 | −0.383657 | −0.191829 | − | 0.981428i | \(-0.561442\pi\) | ||||
−0.191829 | + | 0.981428i | \(0.561442\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.43858 | 1.18680 | ||||||||
\(22\) | −1.83337 | −0.390875 | ||||||||
\(23\) | −7.76626 | −1.61938 | −0.809689 | − | 0.586860i | \(-0.800364\pi\) | ||||
−0.809689 | + | 0.586860i | \(0.800364\pi\) | |||||||
\(24\) | 2.96645 | 0.605524 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.41785 | −0.474179 | ||||||||
\(27\) | 8.30550 | 1.59839 | ||||||||
\(28\) | 1.83337 | 0.346474 | ||||||||
\(29\) | 7.58448 | 1.40840 | 0.704201 | − | 0.710000i | \(-0.251305\pi\) | ||||
0.704201 | + | 0.710000i | \(0.251305\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.29413 | −0.950853 | −0.475427 | − | 0.879755i | \(-0.657706\pi\) | ||||
−0.475427 | + | 0.879755i | \(0.657706\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −5.43858 | −0.946736 | ||||||||
\(34\) | 2.78467 | 0.477567 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.79981 | 0.966636 | ||||||||
\(37\) | −1.31486 | −0.216162 | −0.108081 | − | 0.994142i | \(-0.534471\pi\) | ||||
−0.108081 | + | 0.994142i | \(0.534471\pi\) | |||||||
\(38\) | −1.67232 | −0.271286 | ||||||||
\(39\) | −7.17242 | −1.14851 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.51505 | 0.548958 | 0.274479 | − | 0.961593i | \(-0.411495\pi\) | ||||
0.274479 | + | 0.961593i | \(0.411495\pi\) | |||||||
\(42\) | 5.43858 | 0.839192 | ||||||||
\(43\) | −4.30550 | −0.656583 | −0.328291 | − | 0.944576i | \(-0.606473\pi\) | ||||
−0.328291 | + | 0.944576i | \(0.606473\pi\) | |||||||
\(44\) | −1.83337 | −0.276390 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.76626 | −1.14507 | ||||||||
\(47\) | 1.83337 | 0.267424 | 0.133712 | − | 0.991020i | \(-0.457310\pi\) | ||||
0.133712 | + | 0.991020i | \(0.457310\pi\) | |||||||
\(48\) | 2.96645 | 0.428170 | ||||||||
\(49\) | −3.63877 | −0.519824 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.26057 | 1.15671 | ||||||||
\(52\) | −2.41785 | −0.335295 | ||||||||
\(53\) | −6.51738 | −0.895231 | −0.447615 | − | 0.894226i | \(-0.647727\pi\) | ||||
−0.447615 | + | 0.894226i | \(0.647727\pi\) | |||||||
\(54\) | 8.30550 | 1.13024 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.83337 | 0.244994 | ||||||||
\(57\) | −4.96086 | −0.657082 | ||||||||
\(58\) | 7.58448 | 0.995891 | ||||||||
\(59\) | −9.06039 | −1.17956 | −0.589781 | − | 0.807563i | \(-0.700786\pi\) | ||||
−0.589781 | + | 0.807563i | \(0.700786\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.58794 | 0.331351 | 0.165676 | − | 0.986180i | \(-0.447019\pi\) | ||||
0.165676 | + | 0.986180i | \(0.447019\pi\) | |||||||
\(62\) | −5.29413 | −0.672355 | ||||||||
\(63\) | 10.6332 | 1.33965 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.43858 | −0.669443 | ||||||||
\(67\) | 9.50010 | 1.16062 | 0.580311 | − | 0.814395i | \(-0.302931\pi\) | ||||
0.580311 | + | 0.814395i | \(0.302931\pi\) | |||||||
\(68\) | 2.78467 | 0.337691 | ||||||||
\(69\) | −23.0382 | −2.77347 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.305502 | 0.0362564 | 0.0181282 | − | 0.999836i | \(-0.494229\pi\) | ||||
0.0181282 | + | 0.999836i | \(0.494229\pi\) | |||||||
\(72\) | 5.79981 | 0.683515 | ||||||||
\(73\) | 14.9480 | 1.74954 | 0.874768 | − | 0.484542i | \(-0.161014\pi\) | ||||
0.874768 | + | 0.484542i | \(0.161014\pi\) | |||||||
\(74\) | −1.31486 | −0.152850 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.67232 | −0.191829 | ||||||||
\(77\) | −3.36123 | −0.383048 | ||||||||
\(78\) | −7.17242 | −0.812117 | ||||||||
\(79\) | −3.46076 | −0.389366 | −0.194683 | − | 0.980866i | \(-0.562368\pi\) | ||||
−0.194683 | + | 0.980866i | \(0.562368\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.23840 | 0.804266 | ||||||||
\(82\) | 3.51505 | 0.388172 | ||||||||
\(83\) | −6.37261 | −0.699484 | −0.349742 | − | 0.936846i | \(-0.613731\pi\) | ||||
−0.349742 | + | 0.936846i | \(0.613731\pi\) | |||||||
\(84\) | 5.43858 | 0.593398 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.30550 | −0.464274 | ||||||||
\(87\) | 22.4990 | 2.41214 | ||||||||
\(88\) | −1.83337 | −0.195437 | ||||||||
\(89\) | −3.32045 | −0.351967 | −0.175984 | − | 0.984393i | \(-0.556311\pi\) | ||||
−0.175984 | + | 0.984393i | \(0.556311\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.43280 | −0.464684 | ||||||||
\(92\) | −7.76626 | −0.809689 | ||||||||
\(93\) | −15.7047 | −1.62851 | ||||||||
\(94\) | 1.83337 | 0.189097 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.96645 | 0.302762 | ||||||||
\(97\) | 11.0902 | 1.12604 | 0.563018 | − | 0.826445i | \(-0.309640\pi\) | ||||
0.563018 | + | 0.826445i | \(0.309640\pi\) | |||||||
\(98\) | −3.63877 | −0.367571 | ||||||||
\(99\) | −10.6332 | −1.06867 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.1807 | −1.31152 | −0.655762 | − | 0.754968i | \(-0.727653\pi\) | ||||
−0.655762 | + | 0.754968i | \(0.727653\pi\) | |||||||
\(102\) | 8.26057 | 0.817919 | ||||||||
\(103\) | −2.63318 | −0.259455 | −0.129727 | − | 0.991550i | \(-0.541410\pi\) | ||||
−0.129727 | + | 0.991550i | \(0.541410\pi\) | |||||||
\(104\) | −2.41785 | −0.237089 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.51738 | −0.633024 | ||||||||
\(107\) | 18.8045 | 1.81790 | 0.908949 | − | 0.416908i | \(-0.136886\pi\) | ||||
0.908949 | + | 0.416908i | \(0.136886\pi\) | |||||||
\(108\) | 8.30550 | 0.799197 | ||||||||
\(109\) | 10.3093 | 0.987449 | 0.493725 | − | 0.869618i | \(-0.335635\pi\) | ||||
0.493725 | + | 0.869618i | \(0.335635\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.90047 | −0.370216 | ||||||||
\(112\) | 1.83337 | 0.173237 | ||||||||
\(113\) | 6.05662 | 0.569759 | 0.284879 | − | 0.958563i | \(-0.408046\pi\) | ||||
0.284879 | + | 0.958563i | \(0.408046\pi\) | |||||||
\(114\) | −4.96086 | −0.464627 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.58448 | 0.704201 | ||||||||
\(117\) | −14.0231 | −1.29643 | ||||||||
\(118\) | −9.06039 | −0.834076 | ||||||||
\(119\) | 5.10532 | 0.468003 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.63877 | −0.694434 | ||||||||
\(122\) | 2.58794 | 0.234301 | ||||||||
\(123\) | 10.4272 | 0.940190 | ||||||||
\(124\) | −5.29413 | −0.475427 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 10.6332 | 0.947279 | ||||||||
\(127\) | 0.333269 | 0.0295728 | 0.0147864 | − | 0.999891i | \(-0.495293\pi\) | ||||
0.0147864 | + | 0.999891i | \(0.495293\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −12.7720 | −1.12452 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.17801 | −0.452405 | −0.226202 | − | 0.974080i | \(-0.572631\pi\) | ||||
−0.226202 | + | 0.974080i | \(0.572631\pi\) | |||||||
\(132\) | −5.43858 | −0.473368 | ||||||||
\(133\) | −3.06598 | −0.265854 | ||||||||
\(134\) | 9.50010 | 0.820683 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.78467 | 0.238783 | ||||||||
\(137\) | −19.5232 | −1.66798 | −0.833988 | − | 0.551782i | \(-0.813948\pi\) | ||||
−0.833988 | + | 0.551782i | \(0.813948\pi\) | |||||||
\(138\) | −23.0382 | −1.96114 | ||||||||
\(139\) | −7.95507 | −0.674740 | −0.337370 | − | 0.941372i | \(-0.609537\pi\) | ||||
−0.337370 | + | 0.941372i | \(0.609537\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.43858 | 0.458011 | ||||||||
\(142\) | 0.305502 | 0.0256371 | ||||||||
\(143\) | 4.43280 | 0.370689 | ||||||||
\(144\) | 5.79981 | 0.483318 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 14.9480 | 1.23711 | ||||||||
\(147\) | −10.7942 | −0.890292 | ||||||||
\(148\) | −1.31486 | −0.108081 | ||||||||
\(149\) | −1.67955 | −0.137594 | −0.0687969 | − | 0.997631i | \(-0.521916\pi\) | ||||
−0.0687969 | + | 0.997631i | \(0.521916\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.2664 | −1.73063 | −0.865316 | − | 0.501227i | \(-0.832882\pi\) | ||||
−0.865316 | + | 0.501227i | \(0.832882\pi\) | |||||||
\(152\) | −1.67232 | −0.135643 | ||||||||
\(153\) | 16.1506 | 1.30570 | ||||||||
\(154\) | −3.36123 | −0.270856 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.17242 | −0.574253 | ||||||||
\(157\) | 10.4514 | 0.834113 | 0.417056 | − | 0.908881i | \(-0.363062\pi\) | ||||
0.417056 | + | 0.908881i | \(0.363062\pi\) | |||||||
\(158\) | −3.46076 | −0.275323 | ||||||||
\(159\) | −19.3335 | −1.53324 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.2384 | −1.12214 | ||||||||
\(162\) | 7.23840 | 0.568702 | ||||||||
\(163\) | 10.4106 | 0.815423 | 0.407711 | − | 0.913111i | \(-0.366327\pi\) | ||||
0.407711 | + | 0.913111i | \(0.366327\pi\) | |||||||
\(164\) | 3.51505 | 0.274479 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.37261 | −0.494610 | ||||||||
\(167\) | 2.12171 | 0.164183 | 0.0820913 | − | 0.996625i | \(-0.473840\pi\) | ||||
0.0820913 | + | 0.996625i | \(0.473840\pi\) | |||||||
\(168\) | 5.43858 | 0.419596 | ||||||||
\(169\) | −7.15401 | −0.550309 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.69916 | −0.741713 | ||||||||
\(172\) | −4.30550 | −0.328291 | ||||||||
\(173\) | −18.1147 | −1.37723 | −0.688617 | − | 0.725126i | \(-0.741782\pi\) | ||||
−0.688617 | + | 0.725126i | \(0.741782\pi\) | |||||||
\(174\) | 22.4990 | 1.70564 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.83337 | −0.138195 | ||||||||
\(177\) | −26.8772 | −2.02021 | ||||||||
\(178\) | −3.32045 | −0.248878 | ||||||||
\(179\) | 10.5605 | 0.789328 | 0.394664 | − | 0.918826i | \(-0.370861\pi\) | ||||
0.394664 | + | 0.918826i | \(0.370861\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.1561 | 1.34954 | 0.674768 | − | 0.738030i | \(-0.264244\pi\) | ||||
0.674768 | + | 0.738030i | \(0.264244\pi\) | |||||||
\(182\) | −4.43280 | −0.328581 | ||||||||
\(183\) | 7.67698 | 0.567499 | ||||||||
\(184\) | −7.76626 | −0.572536 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −15.7047 | −1.15153 | ||||||||
\(187\) | −5.10532 | −0.373338 | ||||||||
\(188\) | 1.83337 | 0.133712 | ||||||||
\(189\) | 15.2270 | 1.10760 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.9051 | −1.58500 | −0.792500 | − | 0.609872i | \(-0.791221\pi\) | ||||
−0.792500 | + | 0.609872i | \(0.791221\pi\) | |||||||
\(192\) | 2.96645 | 0.214085 | ||||||||
\(193\) | 27.4248 | 1.97408 | 0.987041 | − | 0.160465i | \(-0.0512995\pi\) | ||||
0.987041 | + | 0.160465i | \(0.0512995\pi\) | |||||||
\(194\) | 11.0902 | 0.796228 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.63877 | −0.259912 | ||||||||
\(197\) | −1.12372 | −0.0800619 | −0.0400309 | − | 0.999198i | \(-0.512746\pi\) | ||||
−0.0400309 | + | 0.999198i | \(0.512746\pi\) | |||||||
\(198\) | −10.6332 | −0.755667 | ||||||||
\(199\) | 25.4992 | 1.80759 | 0.903794 | − | 0.427968i | \(-0.140770\pi\) | ||||
0.903794 | + | 0.427968i | \(0.140770\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 28.1815 | 1.98777 | ||||||||
\(202\) | −13.1807 | −0.927388 | ||||||||
\(203\) | 13.9051 | 0.975949 | ||||||||
\(204\) | 8.26057 | 0.578356 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.63318 | −0.183462 | ||||||||
\(207\) | −45.0429 | −3.13070 | ||||||||
\(208\) | −2.41785 | −0.167648 | ||||||||
\(209\) | 3.06598 | 0.212078 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.3044 | 1.46665 | 0.733327 | − | 0.679876i | \(-0.237967\pi\) | ||||
0.733327 | + | 0.679876i | \(0.237967\pi\) | |||||||
\(212\) | −6.51738 | −0.447615 | ||||||||
\(213\) | 0.906255 | 0.0620956 | ||||||||
\(214\) | 18.8045 | 1.28545 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8.30550 | 0.565118 | ||||||||
\(217\) | −9.70607 | −0.658891 | ||||||||
\(218\) | 10.3093 | 0.698232 | ||||||||
\(219\) | 44.3426 | 2.99639 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.73290 | −0.452904 | ||||||||
\(222\) | −3.90047 | −0.261782 | ||||||||
\(223\) | 3.24511 | 0.217309 | 0.108654 | − | 0.994080i | \(-0.465346\pi\) | ||||
0.108654 | + | 0.994080i | \(0.465346\pi\) | |||||||
\(224\) | 1.83337 | 0.122497 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.05662 | 0.402880 | ||||||||
\(227\) | 16.3773 | 1.08700 | 0.543499 | − | 0.839410i | \(-0.317099\pi\) | ||||
0.543499 | + | 0.839410i | \(0.317099\pi\) | |||||||
\(228\) | −4.96086 | −0.328541 | ||||||||
\(229\) | −5.08998 | −0.336355 | −0.168178 | − | 0.985757i | \(-0.553788\pi\) | ||||
−0.168178 | + | 0.985757i | \(0.553788\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.97091 | −0.656038 | ||||||||
\(232\) | 7.58448 | 0.497946 | ||||||||
\(233\) | −1.66296 | −0.108944 | −0.0544721 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544721 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(234\) | −14.0231 | −0.916716 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.06039 | −0.589781 | ||||||||
\(237\) | −10.2662 | −0.666859 | ||||||||
\(238\) | 5.10532 | 0.330928 | ||||||||
\(239\) | 12.7998 | 0.827951 | 0.413976 | − | 0.910288i | \(-0.364140\pi\) | ||||
0.413976 | + | 0.910288i | \(0.364140\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.395477 | 0.0254749 | 0.0127375 | − | 0.999919i | \(-0.495945\pi\) | ||||
0.0127375 | + | 0.999919i | \(0.495945\pi\) | |||||||
\(242\) | −7.63877 | −0.491039 | ||||||||
\(243\) | −3.44417 | −0.220944 | ||||||||
\(244\) | 2.58794 | 0.165676 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.4272 | 0.664815 | ||||||||
\(247\) | 4.04342 | 0.257277 | ||||||||
\(248\) | −5.29413 | −0.336177 | ||||||||
\(249\) | −18.9040 | −1.19799 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.36589 | 0.591170 | 0.295585 | − | 0.955316i | \(-0.404485\pi\) | ||||
0.295585 | + | 0.955316i | \(0.404485\pi\) | |||||||
\(252\) | 10.6332 | 0.669827 | ||||||||
\(253\) | 14.2384 | 0.895160 | ||||||||
\(254\) | 0.333269 | 0.0209111 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.97926 | −0.310598 | −0.155299 | − | 0.987868i | \(-0.549634\pi\) | ||||
−0.155299 | + | 0.987868i | \(0.549634\pi\) | |||||||
\(258\) | −12.7720 | −0.795153 | ||||||||
\(259\) | −2.41062 | −0.149789 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 43.9886 | 2.72282 | ||||||||
\(262\) | −5.17801 | −0.319899 | ||||||||
\(263\) | −19.8112 | −1.22161 | −0.610805 | − | 0.791781i | \(-0.709154\pi\) | ||||
−0.610805 | + | 0.791781i | \(0.709154\pi\) | |||||||
\(264\) | −5.43858 | −0.334722 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.06598 | −0.187987 | ||||||||
\(267\) | −9.84995 | −0.602807 | ||||||||
\(268\) | 9.50010 | 0.580311 | ||||||||
\(269\) | 14.7939 | 0.902001 | 0.451000 | − | 0.892524i | \(-0.351067\pi\) | ||||
0.451000 | + | 0.892524i | \(0.351067\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.5564 | −0.762747 | −0.381374 | − | 0.924421i | \(-0.624549\pi\) | ||||
−0.381374 | + | 0.924421i | \(0.624549\pi\) | |||||||
\(272\) | 2.78467 | 0.168845 | ||||||||
\(273\) | −13.1497 | −0.795854 | ||||||||
\(274\) | −19.5232 | −1.17944 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −23.0382 | −1.38674 | ||||||||
\(277\) | −6.33183 | −0.380443 | −0.190221 | − | 0.981741i | \(-0.560921\pi\) | ||||
−0.190221 | + | 0.981741i | \(0.560921\pi\) | |||||||
\(278\) | −7.95507 | −0.477114 | ||||||||
\(279\) | −30.7049 | −1.83826 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.0892 | −1.19842 | −0.599212 | − | 0.800591i | \(-0.704519\pi\) | ||||
−0.599212 | + | 0.800591i | \(0.704519\pi\) | |||||||
\(282\) | 5.43858 | 0.323863 | ||||||||
\(283\) | 1.81678 | 0.107996 | 0.0539982 | − | 0.998541i | \(-0.482803\pi\) | ||||
0.0539982 | + | 0.998541i | \(0.482803\pi\) | |||||||
\(284\) | 0.305502 | 0.0181282 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.43280 | 0.262117 | ||||||||
\(287\) | 6.44437 | 0.380399 | ||||||||
\(288\) | 5.79981 | 0.341757 | ||||||||
\(289\) | −9.24562 | −0.543860 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 32.8984 | 1.92854 | ||||||||
\(292\) | 14.9480 | 0.874768 | ||||||||
\(293\) | −6.85931 | −0.400725 | −0.200363 | − | 0.979722i | \(-0.564212\pi\) | ||||
−0.200363 | + | 0.979722i | \(0.564212\pi\) | |||||||
\(294\) | −10.7942 | −0.629532 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.31486 | −0.0764248 | ||||||||
\(297\) | −15.2270 | −0.883561 | ||||||||
\(298\) | −1.67955 | −0.0972936 | ||||||||
\(299\) | 18.7776 | 1.08594 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.89356 | −0.454977 | ||||||||
\(302\) | −21.2664 | −1.22374 | ||||||||
\(303\) | −39.0997 | −2.24622 | ||||||||
\(304\) | −1.67232 | −0.0959143 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 16.1506 | 0.923266 | ||||||||
\(307\) | −2.89526 | −0.165241 | −0.0826206 | − | 0.996581i | \(-0.526329\pi\) | ||||
−0.0826206 | + | 0.996581i | \(0.526329\pi\) | |||||||
\(308\) | −3.36123 | −0.191524 | ||||||||
\(309\) | −7.81119 | −0.444363 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.6490 | −1.17090 | −0.585449 | − | 0.810709i | \(-0.699082\pi\) | ||||
−0.585449 | + | 0.810709i | \(0.699082\pi\) | |||||||
\(312\) | −7.17242 | −0.406058 | ||||||||
\(313\) | 16.4272 | 0.928521 | 0.464260 | − | 0.885699i | \(-0.346320\pi\) | ||||
0.464260 | + | 0.885699i | \(0.346320\pi\) | |||||||
\(314\) | 10.4514 | 0.589807 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.46076 | −0.194683 | ||||||||
\(317\) | 16.5059 | 0.927063 | 0.463531 | − | 0.886081i | \(-0.346582\pi\) | ||||
0.463531 | + | 0.886081i | \(0.346582\pi\) | |||||||
\(318\) | −19.3335 | −1.08417 | ||||||||
\(319\) | −13.9051 | −0.778538 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 55.7825 | 3.11348 | ||||||||
\(322\) | −14.2384 | −0.793475 | ||||||||
\(323\) | −4.65686 | −0.259115 | ||||||||
\(324\) | 7.23840 | 0.402133 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.4106 | 0.576591 | ||||||||
\(327\) | 30.5819 | 1.69118 | ||||||||
\(328\) | 3.51505 | 0.194086 | ||||||||
\(329\) | 3.36123 | 0.185311 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.4710 | 1.50994 | 0.754972 | − | 0.655757i | \(-0.227651\pi\) | ||||
0.754972 | + | 0.655757i | \(0.227651\pi\) | |||||||
\(332\) | −6.37261 | −0.349742 | ||||||||
\(333\) | −7.62595 | −0.417900 | ||||||||
\(334\) | 2.12171 | 0.116095 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.43858 | 0.296699 | ||||||||
\(337\) | −2.74521 | −0.149541 | −0.0747706 | − | 0.997201i | \(-0.523822\pi\) | ||||
−0.0747706 | + | 0.997201i | \(0.523822\pi\) | |||||||
\(338\) | −7.15401 | −0.389127 | ||||||||
\(339\) | 17.9666 | 0.975814 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.70607 | 0.525613 | ||||||||
\(342\) | −9.69916 | −0.524470 | ||||||||
\(343\) | −19.5048 | −1.05316 | ||||||||
\(344\) | −4.30550 | −0.232137 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.1147 | −0.973851 | ||||||||
\(347\) | −21.3391 | −1.14554 | −0.572770 | − | 0.819716i | \(-0.694131\pi\) | ||||
−0.572770 | + | 0.819716i | \(0.694131\pi\) | |||||||
\(348\) | 22.4990 | 1.20607 | ||||||||
\(349\) | −16.7650 | −0.897411 | −0.448705 | − | 0.893680i | \(-0.648115\pi\) | ||||
−0.448705 | + | 0.893680i | \(0.648115\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.0814 | −1.07187 | ||||||||
\(352\) | −1.83337 | −0.0977187 | ||||||||
\(353\) | 2.98862 | 0.159068 | 0.0795342 | − | 0.996832i | \(-0.474657\pi\) | ||||
0.0795342 | + | 0.996832i | \(0.474657\pi\) | |||||||
\(354\) | −26.8772 | −1.42851 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.32045 | −0.175984 | ||||||||
\(357\) | 15.1447 | 0.801540 | ||||||||
\(358\) | 10.5605 | 0.558139 | ||||||||
\(359\) | 6.70494 | 0.353873 | 0.176937 | − | 0.984222i | \(-0.443381\pi\) | ||||
0.176937 | + | 0.984222i | \(0.443381\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.2033 | −0.852807 | ||||||||
\(362\) | 18.1561 | 0.954266 | ||||||||
\(363\) | −22.6600 | −1.18934 | ||||||||
\(364\) | −4.43280 | −0.232342 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7.67698 | 0.401282 | ||||||||
\(367\) | 4.01659 | 0.209664 | 0.104832 | − | 0.994490i | \(-0.466570\pi\) | ||||
0.104832 | + | 0.994490i | \(0.466570\pi\) | |||||||
\(368\) | −7.76626 | −0.404844 | ||||||||
\(369\) | 20.3866 | 1.06129 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.9487 | −0.620348 | ||||||||
\(372\) | −15.7047 | −0.814253 | ||||||||
\(373\) | 26.5832 | 1.37643 | 0.688214 | − | 0.725508i | \(-0.258395\pi\) | ||||
0.688214 | + | 0.725508i | \(0.258395\pi\) | |||||||
\(374\) | −5.10532 | −0.263990 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.83337 | 0.0945486 | ||||||||
\(377\) | −18.3381 | −0.944461 | ||||||||
\(378\) | 15.2270 | 0.783193 | ||||||||
\(379\) | −15.6278 | −0.802745 | −0.401373 | − | 0.915915i | \(-0.631467\pi\) | ||||
−0.401373 | + | 0.915915i | \(0.631467\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.988624 | 0.0506487 | ||||||||
\(382\) | −21.9051 | −1.12076 | ||||||||
\(383\) | 13.4455 | 0.687033 | 0.343516 | − | 0.939147i | \(-0.388382\pi\) | ||||
0.343516 | + | 0.939147i | \(0.388382\pi\) | |||||||
\(384\) | 2.96645 | 0.151381 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 27.4248 | 1.39589 | ||||||||
\(387\) | −24.9711 | −1.26935 | ||||||||
\(388\) | 11.0902 | 0.563018 | ||||||||
\(389\) | −25.1116 | −1.27321 | −0.636605 | − | 0.771190i | \(-0.719662\pi\) | ||||
−0.636605 | + | 0.771190i | \(0.719662\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.6265 | −1.09370 | ||||||||
\(392\) | −3.63877 | −0.183786 | ||||||||
\(393\) | −15.3603 | −0.774825 | ||||||||
\(394\) | −1.12372 | −0.0566123 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −10.6332 | −0.534337 | ||||||||
\(397\) | 3.51819 | 0.176573 | 0.0882864 | − | 0.996095i | \(-0.471861\pi\) | ||||
0.0882864 | + | 0.996095i | \(0.471861\pi\) | |||||||
\(398\) | 25.4992 | 1.27816 | ||||||||
\(399\) | −9.09507 | −0.455323 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.8696 | 1.49161 | 0.745807 | − | 0.666162i | \(-0.232064\pi\) | ||||
0.745807 | + | 0.666162i | \(0.232064\pi\) | |||||||
\(402\) | 28.1815 | 1.40557 | ||||||||
\(403\) | 12.8004 | 0.637633 | ||||||||
\(404\) | −13.1807 | −0.655762 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.9051 | 0.690100 | ||||||||
\(407\) | 2.41062 | 0.119490 | ||||||||
\(408\) | 8.26057 | 0.408959 | ||||||||
\(409\) | −38.7628 | −1.91670 | −0.958348 | − | 0.285604i | \(-0.907806\pi\) | ||||
−0.958348 | + | 0.285604i | \(0.907806\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −57.9144 | −2.85671 | ||||||||
\(412\) | −2.63318 | −0.129727 | ||||||||
\(413\) | −16.6110 | −0.817374 | ||||||||
\(414\) | −45.0429 | −2.21374 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.41785 | −0.118545 | ||||||||
\(417\) | −23.5983 | −1.15561 | ||||||||
\(418\) | 3.06598 | 0.149962 | ||||||||
\(419\) | −18.9103 | −0.923830 | −0.461915 | − | 0.886924i | \(-0.652838\pi\) | ||||
−0.461915 | + | 0.886924i | \(0.652838\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.0532 | −1.07481 | −0.537403 | − | 0.843326i | \(-0.680594\pi\) | ||||
−0.537403 | + | 0.843326i | \(0.680594\pi\) | |||||||
\(422\) | 21.3044 | 1.03708 | ||||||||
\(423\) | 10.6332 | 0.517003 | ||||||||
\(424\) | −6.51738 | −0.316512 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.906255 | 0.0439082 | ||||||||
\(427\) | 4.74464 | 0.229609 | ||||||||
\(428\) | 18.8045 | 0.908949 | ||||||||
\(429\) | 13.1497 | 0.634872 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.20578 | −0.443427 | −0.221713 | − | 0.975112i | \(-0.571165\pi\) | ||||
−0.221713 | + | 0.975112i | \(0.571165\pi\) | |||||||
\(432\) | 8.30550 | 0.399599 | ||||||||
\(433\) | 34.7972 | 1.67225 | 0.836125 | − | 0.548540i | \(-0.184816\pi\) | ||||
0.836125 | + | 0.548540i | \(0.184816\pi\) | |||||||
\(434\) | −9.70607 | −0.465906 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.3093 | 0.493725 | ||||||||
\(437\) | 12.9877 | 0.621286 | ||||||||
\(438\) | 44.3426 | 2.11877 | ||||||||
\(439\) | −8.34985 | −0.398517 | −0.199258 | − | 0.979947i | \(-0.563853\pi\) | ||||
−0.199258 | + | 0.979947i | \(0.563853\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −21.1042 | −1.00496 | ||||||||
\(442\) | −6.73290 | −0.320252 | ||||||||
\(443\) | −1.19887 | −0.0569599 | −0.0284799 | − | 0.999594i | \(-0.509067\pi\) | ||||
−0.0284799 | + | 0.999594i | \(0.509067\pi\) | |||||||
\(444\) | −3.90047 | −0.185108 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.24511 | 0.153661 | ||||||||
\(447\) | −4.98229 | −0.235654 | ||||||||
\(448\) | 1.83337 | 0.0866184 | ||||||||
\(449\) | 32.7953 | 1.54771 | 0.773853 | − | 0.633365i | \(-0.218327\pi\) | ||||
0.773853 | + | 0.633365i | \(0.218327\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.44437 | −0.303453 | ||||||||
\(452\) | 6.05662 | 0.284879 | ||||||||
\(453\) | −63.0855 | −2.96402 | ||||||||
\(454\) | 16.3773 | 0.768623 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.96086 | −0.232313 | ||||||||
\(457\) | 19.7884 | 0.925664 | 0.462832 | − | 0.886446i | \(-0.346833\pi\) | ||||
0.462832 | + | 0.886446i | \(0.346833\pi\) | |||||||
\(458\) | −5.08998 | −0.237839 | ||||||||
\(459\) | 23.1281 | 1.07953 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.39976 | 0.437790 | 0.218895 | − | 0.975748i | \(-0.429755\pi\) | ||||
0.218895 | + | 0.975748i | \(0.429755\pi\) | |||||||
\(462\) | −9.97091 | −0.463889 | ||||||||
\(463\) | 17.7329 | 0.824118 | 0.412059 | − | 0.911157i | \(-0.364810\pi\) | ||||
0.412059 | + | 0.911157i | \(0.364810\pi\) | |||||||
\(464\) | 7.58448 | 0.352101 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.66296 | −0.0770352 | ||||||||
\(467\) | 21.8608 | 1.01160 | 0.505798 | − | 0.862652i | \(-0.331198\pi\) | ||||
0.505798 | + | 0.862652i | \(0.331198\pi\) | |||||||
\(468\) | −14.0231 | −0.648216 | ||||||||
\(469\) | 17.4172 | 0.804249 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 31.0035 | 1.42857 | ||||||||
\(472\) | −9.06039 | −0.417038 | ||||||||
\(473\) | 7.89356 | 0.362946 | ||||||||
\(474\) | −10.2662 | −0.471541 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.10532 | 0.234002 | ||||||||
\(477\) | −37.7996 | −1.73072 | ||||||||
\(478\) | 12.7998 | 0.585450 | ||||||||
\(479\) | −6.11052 | −0.279197 | −0.139598 | − | 0.990208i | \(-0.544581\pi\) | ||||
−0.139598 | + | 0.990208i | \(0.544581\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.17914 | 0.144956 | ||||||||
\(482\) | 0.395477 | 0.0180135 | ||||||||
\(483\) | −42.2375 | −1.92187 | ||||||||
\(484\) | −7.63877 | −0.347217 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.44417 | −0.156231 | ||||||||
\(487\) | 5.06189 | 0.229376 | 0.114688 | − | 0.993402i | \(-0.463413\pi\) | ||||
0.114688 | + | 0.993402i | \(0.463413\pi\) | |||||||
\(488\) | 2.58794 | 0.117150 | ||||||||
\(489\) | 30.8826 | 1.39656 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.38228 | 0.107511 | 0.0537554 | − | 0.998554i | \(-0.482881\pi\) | ||||
0.0537554 | + | 0.998554i | \(0.482881\pi\) | |||||||
\(492\) | 10.4272 | 0.470095 | ||||||||
\(493\) | 21.1203 | 0.951209 | ||||||||
\(494\) | 4.04342 | 0.181922 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.29413 | −0.237713 | ||||||||
\(497\) | 0.560096 | 0.0251237 | ||||||||
\(498\) | −18.9040 | −0.847109 | ||||||||
\(499\) | −0.0503313 | −0.00225314 | −0.00112657 | − | 0.999999i | \(-0.500359\pi\) | ||||
−0.00112657 | + | 0.999999i | \(0.500359\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.29393 | 0.281192 | ||||||||
\(502\) | 9.36589 | 0.418020 | ||||||||
\(503\) | −5.41082 | −0.241256 | −0.120628 | − | 0.992698i | \(-0.538491\pi\) | ||||
−0.120628 | + | 0.992698i | \(0.538491\pi\) | |||||||
\(504\) | 10.6332 | 0.473639 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 14.2384 | 0.632974 | ||||||||
\(507\) | −21.2220 | −0.942502 | ||||||||
\(508\) | 0.333269 | 0.0147864 | ||||||||
\(509\) | 18.9463 | 0.839779 | 0.419890 | − | 0.907575i | \(-0.362069\pi\) | ||||
0.419890 | + | 0.907575i | \(0.362069\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.4052 | 1.21234 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −13.8895 | −0.613235 | ||||||||
\(514\) | −4.97926 | −0.219626 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −12.7720 | −0.562258 | ||||||||
\(517\) | −3.36123 | −0.147827 | ||||||||
\(518\) | −2.41062 | −0.105917 | ||||||||
\(519\) | −53.7362 | −2.35876 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.4191 | 1.68317 | 0.841585 | − | 0.540125i | \(-0.181623\pi\) | ||||
0.841585 | + | 0.540125i | \(0.181623\pi\) | |||||||
\(522\) | 43.9886 | 1.92533 | ||||||||
\(523\) | −12.2666 | −0.536379 | −0.268189 | − | 0.963366i | \(-0.586425\pi\) | ||||
−0.268189 | + | 0.963366i | \(0.586425\pi\) | |||||||
\(524\) | −5.17801 | −0.226202 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.8112 | −0.863809 | ||||||||
\(527\) | −14.7424 | −0.642188 | ||||||||
\(528\) | −5.43858 | −0.236684 | ||||||||
\(529\) | 37.3148 | 1.62238 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −52.5486 | −2.28041 | ||||||||
\(532\) | −3.06598 | −0.132927 | ||||||||
\(533\) | −8.49885 | −0.368126 | ||||||||
\(534\) | −9.84995 | −0.426249 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.50010 | 0.410342 | ||||||||
\(537\) | 31.3271 | 1.35187 | ||||||||
\(538\) | 14.7939 | 0.637811 | ||||||||
\(539\) | 6.67120 | 0.287349 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.0273 | 1.80690 | 0.903448 | − | 0.428697i | \(-0.141027\pi\) | ||||
0.903448 | + | 0.428697i | \(0.141027\pi\) | |||||||
\(542\) | −12.5564 | −0.539344 | ||||||||
\(543\) | 53.8593 | 2.31132 | ||||||||
\(544\) | 2.78467 | 0.119392 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −13.1497 | −0.562754 | ||||||||
\(547\) | 19.3715 | 0.828265 | 0.414132 | − | 0.910217i | \(-0.364085\pi\) | ||||
0.414132 | + | 0.910217i | \(0.364085\pi\) | |||||||
\(548\) | −19.5232 | −0.833988 | ||||||||
\(549\) | 15.0096 | 0.640592 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.6837 | −0.540344 | ||||||||
\(552\) | −23.0382 | −0.980571 | ||||||||
\(553\) | −6.34484 | −0.269810 | ||||||||
\(554\) | −6.33183 | −0.269014 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.95507 | −0.337370 | ||||||||
\(557\) | 8.54685 | 0.362142 | 0.181071 | − | 0.983470i | \(-0.442044\pi\) | ||||
0.181071 | + | 0.983470i | \(0.442044\pi\) | |||||||
\(558\) | −30.7049 | −1.29984 | ||||||||
\(559\) | 10.4100 | 0.440298 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.1447 | −0.639408 | ||||||||
\(562\) | −20.0892 | −0.847413 | ||||||||
\(563\) | −23.4598 | −0.988714 | −0.494357 | − | 0.869259i | \(-0.664596\pi\) | ||||
−0.494357 | + | 0.869259i | \(0.664596\pi\) | |||||||
\(564\) | 5.43858 | 0.229006 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.81678 | 0.0763650 | ||||||||
\(567\) | 13.2706 | 0.557314 | ||||||||
\(568\) | 0.305502 | 0.0128186 | ||||||||
\(569\) | −7.10054 | −0.297670 | −0.148835 | − | 0.988862i | \(-0.547552\pi\) | ||||
−0.148835 | + | 0.988862i | \(0.547552\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.9620 | −0.500593 | −0.250297 | − | 0.968169i | \(-0.580528\pi\) | ||||
−0.250297 | + | 0.968169i | \(0.580528\pi\) | |||||||
\(572\) | 4.43280 | 0.185345 | ||||||||
\(573\) | −64.9804 | −2.71460 | ||||||||
\(574\) | 6.44437 | 0.268983 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.79981 | 0.241659 | ||||||||
\(577\) | 41.5696 | 1.73057 | 0.865283 | − | 0.501284i | \(-0.167139\pi\) | ||||
0.865283 | + | 0.501284i | \(0.167139\pi\) | |||||||
\(578\) | −9.24562 | −0.384567 | ||||||||
\(579\) | 81.3544 | 3.38097 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.6833 | −0.484706 | ||||||||
\(582\) | 32.8984 | 1.36368 | ||||||||
\(583\) | 11.9487 | 0.494866 | ||||||||
\(584\) | 14.9480 | 0.618554 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.85931 | −0.283356 | ||||||||
\(587\) | 19.1275 | 0.789476 | 0.394738 | − | 0.918794i | \(-0.370835\pi\) | ||||
0.394738 | + | 0.918794i | \(0.370835\pi\) | |||||||
\(588\) | −10.7942 | −0.445146 | ||||||||
\(589\) | 8.85348 | 0.364801 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.33346 | −0.137120 | ||||||||
\(592\) | −1.31486 | −0.0540405 | ||||||||
\(593\) | 0.538428 | 0.0221106 | 0.0110553 | − | 0.999939i | \(-0.496481\pi\) | ||||
0.0110553 | + | 0.999939i | \(0.496481\pi\) | |||||||
\(594\) | −15.2270 | −0.624772 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.67955 | −0.0687969 | ||||||||
\(597\) | 75.6419 | 3.09582 | ||||||||
\(598\) | 18.7776 | 0.767875 | ||||||||
\(599\) | −38.4209 | −1.56983 | −0.784917 | − | 0.619601i | \(-0.787295\pi\) | ||||
−0.784917 | + | 0.619601i | \(0.787295\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.6034 | 0.799639 | 0.399820 | − | 0.916594i | \(-0.369073\pi\) | ||||
0.399820 | + | 0.916594i | \(0.369073\pi\) | |||||||
\(602\) | −7.89356 | −0.321717 | ||||||||
\(603\) | 55.0988 | 2.24380 | ||||||||
\(604\) | −21.2664 | −0.865316 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −39.0997 | −1.58832 | ||||||||
\(607\) | −32.4415 | −1.31676 | −0.658381 | − | 0.752685i | \(-0.728758\pi\) | ||||
−0.658381 | + | 0.752685i | \(0.728758\pi\) | |||||||
\(608\) | −1.67232 | −0.0678216 | ||||||||
\(609\) | 41.2488 | 1.67149 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.43280 | −0.179332 | ||||||||
\(612\) | 16.1506 | 0.652848 | ||||||||
\(613\) | −23.4703 | −0.947957 | −0.473979 | − | 0.880536i | \(-0.657183\pi\) | ||||
−0.473979 | + | 0.880536i | \(0.657183\pi\) | |||||||
\(614\) | −2.89526 | −0.116843 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.36123 | −0.135428 | ||||||||
\(617\) | 17.4133 | 0.701032 | 0.350516 | − | 0.936557i | \(-0.386006\pi\) | ||||
0.350516 | + | 0.936557i | \(0.386006\pi\) | |||||||
\(618\) | −7.81119 | −0.314212 | ||||||||
\(619\) | 12.5832 | 0.505763 | 0.252881 | − | 0.967497i | \(-0.418622\pi\) | ||||
0.252881 | + | 0.967497i | \(0.418622\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −64.5027 | −2.58840 | ||||||||
\(622\) | −20.6490 | −0.827950 | ||||||||
\(623\) | −6.08760 | −0.243895 | ||||||||
\(624\) | −7.17242 | −0.287127 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.4272 | 0.656563 | ||||||||
\(627\) | 9.09507 | 0.363222 | ||||||||
\(628\) | 10.4514 | 0.417056 | ||||||||
\(629\) | −3.66145 | −0.145992 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.7362 | 1.66149 | 0.830747 | − | 0.556650i | \(-0.187914\pi\) | ||||
0.830747 | + | 0.556650i | \(0.187914\pi\) | |||||||
\(632\) | −3.46076 | −0.137662 | ||||||||
\(633\) | 63.1983 | 2.51191 | ||||||||
\(634\) | 16.5059 | 0.655532 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −19.3335 | −0.766622 | ||||||||
\(637\) | 8.79799 | 0.348589 | ||||||||
\(638\) | −13.9051 | −0.550509 | ||||||||
\(639\) | 1.77185 | 0.0700934 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.3981 | −0.568692 | −0.284346 | − | 0.958722i | \(-0.591776\pi\) | ||||
−0.284346 | + | 0.958722i | \(0.591776\pi\) | |||||||
\(642\) | 55.7825 | 2.20156 | ||||||||
\(643\) | 30.1666 | 1.18966 | 0.594828 | − | 0.803853i | \(-0.297220\pi\) | ||||
0.594828 | + | 0.803853i | \(0.297220\pi\) | |||||||
\(644\) | −14.2384 | −0.561071 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.65686 | −0.183222 | ||||||||
\(647\) | −10.6878 | −0.420180 | −0.210090 | − | 0.977682i | \(-0.567376\pi\) | ||||
−0.210090 | + | 0.977682i | \(0.567376\pi\) | |||||||
\(648\) | 7.23840 | 0.284351 | ||||||||
\(649\) | 16.6110 | 0.652039 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −28.7925 | −1.12847 | ||||||||
\(652\) | 10.4106 | 0.407711 | ||||||||
\(653\) | 10.1658 | 0.397819 | 0.198910 | − | 0.980018i | \(-0.436260\pi\) | ||||
0.198910 | + | 0.980018i | \(0.436260\pi\) | |||||||
\(654\) | 30.5819 | 1.19585 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.51505 | 0.137240 | ||||||||
\(657\) | 86.6959 | 3.38233 | ||||||||
\(658\) | 3.36123 | 0.131034 | ||||||||
\(659\) | 31.1202 | 1.21227 | 0.606136 | − | 0.795361i | \(-0.292719\pi\) | ||||
0.606136 | + | 0.795361i | \(0.292719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.4641 | 1.61277 | 0.806383 | − | 0.591393i | \(-0.201422\pi\) | ||||
0.806383 | + | 0.591393i | \(0.201422\pi\) | |||||||
\(662\) | 27.4710 | 1.06769 | ||||||||
\(663\) | −19.9728 | −0.775680 | ||||||||
\(664\) | −6.37261 | −0.247305 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.62595 | −0.295500 | ||||||||
\(667\) | −58.9031 | −2.28074 | ||||||||
\(668\) | 2.12171 | 0.0820913 | ||||||||
\(669\) | 9.62646 | 0.372181 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.74464 | −0.183165 | ||||||||
\(672\) | 5.43858 | 0.209798 | ||||||||
\(673\) | 2.14497 | 0.0826824 | 0.0413412 | − | 0.999145i | \(-0.486837\pi\) | ||||
0.0413412 | + | 0.999145i | \(0.486837\pi\) | |||||||
\(674\) | −2.74521 | −0.105742 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.15401 | −0.275154 | ||||||||
\(677\) | 41.5482 | 1.59683 | 0.798413 | − | 0.602110i | \(-0.205673\pi\) | ||||
0.798413 | + | 0.602110i | \(0.205673\pi\) | |||||||
\(678\) | 17.9666 | 0.690005 | ||||||||
\(679\) | 20.3323 | 0.780283 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 48.5823 | 1.86168 | ||||||||
\(682\) | 9.70607 | 0.371665 | ||||||||
\(683\) | −28.8309 | −1.10318 | −0.551592 | − | 0.834114i | \(-0.685980\pi\) | ||||
−0.551592 | + | 0.834114i | \(0.685980\pi\) | |||||||
\(684\) | −9.69916 | −0.370857 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −19.5048 | −0.744695 | ||||||||
\(687\) | −15.0991 | −0.576068 | ||||||||
\(688\) | −4.30550 | −0.164146 | ||||||||
\(689\) | 15.7580 | 0.600333 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −49.2045 | −1.87183 | −0.935914 | − | 0.352230i | \(-0.885424\pi\) | ||||
−0.935914 | + | 0.352230i | \(0.885424\pi\) | |||||||
\(692\) | −18.1147 | −0.688617 | ||||||||
\(693\) | −19.4945 | −0.740535 | ||||||||
\(694\) | −21.3391 | −0.810019 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 22.4990 | 0.852821 | ||||||||
\(697\) | 9.78824 | 0.370756 | ||||||||
\(698\) | −16.7650 | −0.634565 | ||||||||
\(699\) | −4.93309 | −0.186587 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.9783 | −0.943419 | −0.471709 | − | 0.881754i | \(-0.656363\pi\) | ||||
−0.471709 | + | 0.881754i | \(0.656363\pi\) | |||||||
\(702\) | −20.0814 | −0.757925 | ||||||||
\(703\) | 2.19887 | 0.0829321 | ||||||||
\(704\) | −1.83337 | −0.0690976 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.98862 | 0.112478 | ||||||||
\(707\) | −24.1650 | −0.908817 | ||||||||
\(708\) | −26.8772 | −1.01011 | ||||||||
\(709\) | 9.79239 | 0.367761 | 0.183881 | − | 0.982949i | \(-0.441134\pi\) | ||||
0.183881 | + | 0.982949i | \(0.441134\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.0718 | −0.752750 | ||||||||
\(712\) | −3.32045 | −0.124439 | ||||||||
\(713\) | 41.1156 | 1.53979 | ||||||||
\(714\) | 15.1447 | 0.566774 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.5605 | 0.394664 | ||||||||
\(717\) | 37.9700 | 1.41801 | ||||||||
\(718\) | 6.70494 | 0.250226 | ||||||||
\(719\) | −8.58417 | −0.320135 | −0.160068 | − | 0.987106i | \(-0.551171\pi\) | ||||
−0.160068 | + | 0.987106i | \(0.551171\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.82758 | −0.179788 | ||||||||
\(722\) | −16.2033 | −0.603026 | ||||||||
\(723\) | 1.17316 | 0.0436304 | ||||||||
\(724\) | 18.1561 | 0.674768 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −22.6600 | −0.840992 | ||||||||
\(727\) | −24.0162 | −0.890713 | −0.445356 | − | 0.895353i | \(-0.646923\pi\) | ||||
−0.445356 | + | 0.895353i | \(0.646923\pi\) | |||||||
\(728\) | −4.43280 | −0.164290 | ||||||||
\(729\) | −31.9322 | −1.18267 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.9894 | −0.443444 | ||||||||
\(732\) | 7.67698 | 0.283749 | ||||||||
\(733\) | −19.0091 | −0.702118 | −0.351059 | − | 0.936353i | \(-0.614178\pi\) | ||||
−0.351059 | + | 0.936353i | \(0.614178\pi\) | |||||||
\(734\) | 4.01659 | 0.148255 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.76626 | −0.286268 | ||||||||
\(737\) | −17.4172 | −0.641569 | ||||||||
\(738\) | 20.3866 | 0.750442 | ||||||||
\(739\) | −20.7920 | −0.764845 | −0.382423 | − | 0.923988i | \(-0.624910\pi\) | ||||
−0.382423 | + | 0.923988i | \(0.624910\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.9946 | 0.440633 | ||||||||
\(742\) | −11.9487 | −0.438652 | ||||||||
\(743\) | 6.53365 | 0.239696 | 0.119848 | − | 0.992792i | \(-0.461759\pi\) | ||||
0.119848 | + | 0.992792i | \(0.461759\pi\) | |||||||
\(744\) | −15.7047 | −0.575764 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 26.5832 | 0.973281 | ||||||||
\(747\) | −36.9599 | −1.35229 | ||||||||
\(748\) | −5.10532 | −0.186669 | ||||||||
\(749\) | 34.4755 | 1.25971 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.9879 | 1.02129 | 0.510646 | − | 0.859791i | \(-0.329406\pi\) | ||||
0.510646 | + | 0.859791i | \(0.329406\pi\) | |||||||
\(752\) | 1.83337 | 0.0668560 | ||||||||
\(753\) | 27.7834 | 1.01248 | ||||||||
\(754\) | −18.3381 | −0.667835 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 15.2270 | 0.553801 | ||||||||
\(757\) | 4.48558 | 0.163031 | 0.0815156 | − | 0.996672i | \(-0.474024\pi\) | ||||
0.0815156 | + | 0.996672i | \(0.474024\pi\) | |||||||
\(758\) | −15.6278 | −0.567627 | ||||||||
\(759\) | 42.2375 | 1.53312 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.449070 | 0.0162788 | 0.00813939 | − | 0.999967i | \(-0.497409\pi\) | ||||
0.00813939 | + | 0.999967i | \(0.497409\pi\) | |||||||
\(762\) | 0.988624 | 0.0358141 | ||||||||
\(763\) | 18.9007 | 0.684250 | ||||||||
\(764\) | −21.9051 | −0.792500 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.4455 | 0.485805 | ||||||||
\(767\) | 21.9066 | 0.791003 | ||||||||
\(768\) | 2.96645 | 0.107042 | ||||||||
\(769\) | 20.9864 | 0.756788 | 0.378394 | − | 0.925645i | \(-0.376476\pi\) | ||||
0.378394 | + | 0.925645i | \(0.376476\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.7707 | −0.531955 | ||||||||
\(772\) | 27.4248 | 0.987041 | ||||||||
\(773\) | 35.0412 | 1.26035 | 0.630173 | − | 0.776455i | \(-0.282984\pi\) | ||||
0.630173 | + | 0.776455i | \(0.282984\pi\) | |||||||
\(774\) | −24.9711 | −0.897568 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.0902 | 0.398114 | ||||||||
\(777\) | −7.15099 | −0.256540 | ||||||||
\(778\) | −25.1116 | −0.900295 | ||||||||
\(779\) | −5.87829 | −0.210612 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.560096 | −0.0200418 | ||||||||
\(782\) | −21.6265 | −0.773361 | ||||||||
\(783\) | 62.9929 | 2.25118 | ||||||||
\(784\) | −3.63877 | −0.129956 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −15.3603 | −0.547884 | ||||||||
\(787\) | 39.1993 | 1.39730 | 0.698651 | − | 0.715462i | \(-0.253784\pi\) | ||||
0.698651 | + | 0.715462i | \(0.253784\pi\) | |||||||
\(788\) | −1.12372 | −0.0400309 | ||||||||
\(789\) | −58.7689 | −2.09223 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.1040 | 0.394813 | ||||||||
\(792\) | −10.6332 | −0.377834 | ||||||||
\(793\) | −6.25724 | −0.222201 | ||||||||
\(794\) | 3.51819 | 0.124856 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 25.4992 | 0.903794 | ||||||||
\(797\) | −8.63368 | −0.305821 | −0.152910 | − | 0.988240i | \(-0.548865\pi\) | ||||
−0.152910 | + | 0.988240i | \(0.548865\pi\) | |||||||
\(798\) | −9.09507 | −0.321962 | ||||||||
\(799\) | 5.10532 | 0.180613 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.2580 | −0.680448 | ||||||||
\(802\) | 29.8696 | 1.05473 | ||||||||
\(803\) | −27.4052 | −0.967109 | ||||||||
\(804\) | 28.1815 | 0.993886 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.8004 | 0.450874 | ||||||||
\(807\) | 43.8854 | 1.54484 | ||||||||
\(808\) | −13.1807 | −0.463694 | ||||||||
\(809\) | −45.8972 | −1.61366 | −0.806829 | − | 0.590785i | \(-0.798818\pi\) | ||||
−0.806829 | + | 0.590785i | \(0.798818\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.3940 | 1.38331 | 0.691656 | − | 0.722227i | \(-0.256881\pi\) | ||||
0.691656 | + | 0.722227i | \(0.256881\pi\) | |||||||
\(812\) | 13.9051 | 0.487974 | ||||||||
\(813\) | −37.2479 | −1.30634 | ||||||||
\(814\) | 2.41062 | 0.0844923 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.26057 | 0.289178 | ||||||||
\(817\) | 7.20019 | 0.251903 | ||||||||
\(818\) | −38.7628 | −1.35531 | ||||||||
\(819\) | −25.7094 | −0.898359 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.2766 | 0.951960 | 0.475980 | − | 0.879456i | \(-0.342093\pi\) | ||||
0.475980 | + | 0.879456i | \(0.342093\pi\) | |||||||
\(822\) | −57.9144 | −2.02000 | ||||||||
\(823\) | 6.13887 | 0.213987 | 0.106994 | − | 0.994260i | \(-0.465878\pi\) | ||||
0.106994 | + | 0.994260i | \(0.465878\pi\) | |||||||
\(824\) | −2.63318 | −0.0917311 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.6110 | −0.577971 | ||||||||
\(827\) | 44.0654 | 1.53231 | 0.766153 | − | 0.642659i | \(-0.222169\pi\) | ||||
0.766153 | + | 0.642659i | \(0.222169\pi\) | |||||||
\(828\) | −45.0429 | −1.56535 | ||||||||
\(829\) | 4.69997 | 0.163237 | 0.0816183 | − | 0.996664i | \(-0.473991\pi\) | ||||
0.0816183 | + | 0.996664i | \(0.473991\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.7830 | −0.651576 | ||||||||
\(832\) | −2.41785 | −0.0838238 | ||||||||
\(833\) | −10.1328 | −0.351080 | ||||||||
\(834\) | −23.5983 | −0.817143 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.06598 | 0.106039 | ||||||||
\(837\) | −43.9704 | −1.51984 | ||||||||
\(838\) | −18.9103 | −0.653247 | ||||||||
\(839\) | −46.1940 | −1.59480 | −0.797398 | − | 0.603454i | \(-0.793791\pi\) | ||||
−0.797398 | + | 0.603454i | \(0.793791\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.5244 | 0.983599 | ||||||||
\(842\) | −22.0532 | −0.760002 | ||||||||
\(843\) | −59.5937 | −2.05252 | ||||||||
\(844\) | 21.3044 | 0.733327 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 10.6332 | 0.365576 | ||||||||
\(847\) | −14.0047 | −0.481206 | ||||||||
\(848\) | −6.51738 | −0.223808 | ||||||||
\(849\) | 5.38938 | 0.184963 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.2116 | 0.350048 | ||||||||
\(852\) | 0.906255 | 0.0310478 | ||||||||
\(853\) | 12.6427 | 0.432879 | 0.216439 | − | 0.976296i | \(-0.430556\pi\) | ||||
0.216439 | + | 0.976296i | \(0.430556\pi\) | |||||||
\(854\) | 4.74464 | 0.162358 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.8045 | 0.642724 | ||||||||
\(857\) | −19.4162 | −0.663245 | −0.331623 | − | 0.943412i | \(-0.607596\pi\) | ||||
−0.331623 | + | 0.943412i | \(0.607596\pi\) | |||||||
\(858\) | 13.1497 | 0.448922 | ||||||||
\(859\) | 9.33905 | 0.318644 | 0.159322 | − | 0.987227i | \(-0.449069\pi\) | ||||
0.159322 | + | 0.987227i | \(0.449069\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.1169 | 0.651502 | ||||||||
\(862\) | −9.20578 | −0.313550 | ||||||||
\(863\) | −16.3445 | −0.556372 | −0.278186 | − | 0.960527i | \(-0.589733\pi\) | ||||
−0.278186 | + | 0.960527i | \(0.589733\pi\) | |||||||
\(864\) | 8.30550 | 0.282559 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 34.7972 | 1.18246 | ||||||||
\(867\) | −27.4267 | −0.931458 | ||||||||
\(868\) | −9.70607 | −0.329445 | ||||||||
\(869\) | 6.34484 | 0.215234 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.9698 | −0.778302 | ||||||||
\(872\) | 10.3093 | 0.349116 | ||||||||
\(873\) | 64.3209 | 2.17693 | ||||||||
\(874\) | 12.9877 | 0.439315 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 44.3426 | 1.49820 | ||||||||
\(877\) | −35.5051 | −1.19892 | −0.599461 | − | 0.800404i | \(-0.704618\pi\) | ||||
−0.599461 | + | 0.800404i | \(0.704618\pi\) | |||||||
\(878\) | −8.34985 | −0.281794 | ||||||||
\(879\) | −20.3478 | −0.686314 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.5665 | −1.06350 | −0.531750 | − | 0.846901i | \(-0.678466\pi\) | ||||
−0.531750 | + | 0.846901i | \(0.678466\pi\) | |||||||
\(882\) | −21.1042 | −0.710615 | ||||||||
\(883\) | 34.9303 | 1.17550 | 0.587748 | − | 0.809044i | \(-0.300014\pi\) | ||||
0.587748 | + | 0.809044i | \(0.300014\pi\) | |||||||
\(884\) | −6.73290 | −0.226452 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.19887 | −0.0402767 | ||||||||
\(887\) | −42.9323 | −1.44153 | −0.720764 | − | 0.693181i | \(-0.756209\pi\) | ||||
−0.720764 | + | 0.693181i | \(0.756209\pi\) | |||||||
\(888\) | −3.90047 | −0.130891 | ||||||||
\(889\) | 0.611003 | 0.0204924 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.2706 | −0.444583 | ||||||||
\(892\) | 3.24511 | 0.108654 | ||||||||
\(893\) | −3.06598 | −0.102599 | ||||||||
\(894\) | −4.98229 | −0.166633 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.83337 | 0.0612484 | ||||||||
\(897\) | 55.7029 | 1.85987 | ||||||||
\(898\) | 32.7953 | 1.09439 | ||||||||
\(899\) | −40.1532 | −1.33918 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.1487 | −0.604622 | ||||||||
\(902\) | −6.44437 | −0.214574 | ||||||||
\(903\) | −23.4158 | −0.779230 | ||||||||
\(904\) | 6.05662 | 0.201440 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −63.0855 | −2.09588 | ||||||||
\(907\) | −39.8259 | −1.32240 | −0.661199 | − | 0.750211i | \(-0.729952\pi\) | ||||
−0.661199 | + | 0.750211i | \(0.729952\pi\) | |||||||
\(908\) | 16.3773 | 0.543499 | ||||||||
\(909\) | −76.4453 | −2.53553 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.68984 | −0.0559869 | −0.0279934 | − | 0.999608i | \(-0.508912\pi\) | ||||
−0.0279934 | + | 0.999608i | \(0.508912\pi\) | |||||||
\(912\) | −4.96086 | −0.164270 | ||||||||
\(913\) | 11.6833 | 0.386661 | ||||||||
\(914\) | 19.7884 | 0.654543 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.08998 | −0.168178 | ||||||||
\(917\) | −9.49319 | −0.313493 | ||||||||
\(918\) | 23.1281 | 0.763340 | ||||||||
\(919\) | −29.9144 | −0.986787 | −0.493393 | − | 0.869806i | \(-0.664244\pi\) | ||||
−0.493393 | + | 0.869806i | \(0.664244\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.58864 | −0.283005 | ||||||||
\(922\) | 9.39976 | 0.309564 | ||||||||
\(923\) | −0.738656 | −0.0243132 | ||||||||
\(924\) | −9.97091 | −0.328019 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17.7329 | 0.582739 | ||||||||
\(927\) | −15.2719 | −0.501597 | ||||||||
\(928\) | 7.58448 | 0.248973 | ||||||||
\(929\) | −15.9037 | −0.521783 | −0.260892 | − | 0.965368i | \(-0.584017\pi\) | ||||
−0.260892 | + | 0.965368i | \(0.584017\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.08520 | 0.199434 | ||||||||
\(932\) | −1.66296 | −0.0544721 | ||||||||
\(933\) | −61.2542 | −2.00537 | ||||||||
\(934\) | 21.8608 | 0.715306 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −14.0231 | −0.458358 | ||||||||
\(937\) | 46.2671 | 1.51148 | 0.755739 | − | 0.654872i | \(-0.227278\pi\) | ||||
0.755739 | + | 0.654872i | \(0.227278\pi\) | |||||||
\(938\) | 17.4172 | 0.568690 | ||||||||
\(939\) | 48.7305 | 1.59026 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.6709 | −0.380460 | −0.190230 | − | 0.981740i | \(-0.560923\pi\) | ||||
−0.190230 | + | 0.981740i | \(0.560923\pi\) | |||||||
\(942\) | 31.0035 | 1.01015 | ||||||||
\(943\) | −27.2988 | −0.888971 | ||||||||
\(944\) | −9.06039 | −0.294890 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.89356 | 0.256642 | ||||||||
\(947\) | −2.93363 | −0.0953303 | −0.0476651 | − | 0.998863i | \(-0.515178\pi\) | ||||
−0.0476651 | + | 0.998863i | \(0.515178\pi\) | |||||||
\(948\) | −10.2662 | −0.333430 | ||||||||
\(949\) | −36.1421 | −1.17322 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 48.9638 | 1.58776 | ||||||||
\(952\) | 5.10532 | 0.165464 | ||||||||
\(953\) | −9.93705 | −0.321893 | −0.160946 | − | 0.986963i | \(-0.551455\pi\) | ||||
−0.160946 | + | 0.986963i | \(0.551455\pi\) | |||||||
\(954\) | −37.7996 | −1.22381 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.7998 | 0.413976 | ||||||||
\(957\) | −41.2488 | −1.33339 | ||||||||
\(958\) | −6.11052 | −0.197422 | ||||||||
\(959\) | −35.7931 | −1.15582 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.97223 | −0.0958785 | ||||||||
\(962\) | 3.17914 | 0.102499 | ||||||||
\(963\) | 109.062 | 3.51449 | ||||||||
\(964\) | 0.395477 | 0.0127375 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −42.2375 | −1.35897 | ||||||||
\(967\) | 45.3875 | 1.45956 | 0.729782 | − | 0.683680i | \(-0.239621\pi\) | ||||
0.729782 | + | 0.683680i | \(0.239621\pi\) | |||||||
\(968\) | −7.63877 | −0.245519 | ||||||||
\(969\) | −13.8143 | −0.443781 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.68277 | −0.150277 | −0.0751386 | − | 0.997173i | \(-0.523940\pi\) | ||||
−0.0751386 | + | 0.997173i | \(0.523940\pi\) | |||||||
\(972\) | −3.44417 | −0.110472 | ||||||||
\(973\) | −14.5846 | −0.467559 | ||||||||
\(974\) | 5.06189 | 0.162194 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.58794 | 0.0828379 | ||||||||
\(977\) | 3.20804 | 0.102634 | 0.0513171 | − | 0.998682i | \(-0.483658\pi\) | ||||
0.0513171 | + | 0.998682i | \(0.483658\pi\) | |||||||
\(978\) | 30.8826 | 0.987516 | ||||||||
\(979\) | 6.08760 | 0.194561 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 59.7919 | 1.90901 | ||||||||
\(982\) | 2.38228 | 0.0760216 | ||||||||
\(983\) | 19.5715 | 0.624233 | 0.312117 | − | 0.950044i | \(-0.398962\pi\) | ||||
0.312117 | + | 0.950044i | \(0.398962\pi\) | |||||||
\(984\) | 10.4272 | 0.332407 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 21.1203 | 0.672606 | ||||||||
\(987\) | 9.97091 | 0.317378 | ||||||||
\(988\) | 4.04342 | 0.128638 | ||||||||
\(989\) | 33.4377 | 1.06326 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.2280 | 1.43671 | 0.718357 | − | 0.695674i | \(-0.244894\pi\) | ||||
0.718357 | + | 0.695674i | \(0.244894\pi\) | |||||||
\(992\) | −5.29413 | −0.168089 | ||||||||
\(993\) | 81.4913 | 2.58605 | ||||||||
\(994\) | 0.560096 | 0.0177652 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −18.9040 | −0.598996 | ||||||||
\(997\) | −58.0714 | −1.83914 | −0.919570 | − | 0.392926i | \(-0.871463\pi\) | ||||
−0.919570 | + | 0.392926i | \(0.871463\pi\) | |||||||
\(998\) | −0.0503313 | −0.00159321 | ||||||||
\(999\) | −10.9206 | −0.345512 |
(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 | 1250.2.a.l.1.4 | 4 | ||
4.3 | odd | 2 | 10000.2.a.t.1.1 | 4 | |||
5.2 | odd | 4 | 1250.2.b.e.1249.5 | 8 | |||
5.3 | odd | 4 | 1250.2.b.e.1249.4 | 8 | |||
5.4 | even | 2 | 1250.2.a.f.1.1 | 4 | |||
20.19 | odd | 2 | 10000.2.a.x.1.4 | 4 | |||
25.2 | odd | 20 | 250.2.e.c.149.3 | 16 | |||
25.9 | even | 10 | 250.2.d.d.151.2 | 8 | |||
25.11 | even | 5 | 50.2.d.b.21.1 | ✓ | 8 | ||
25.12 | odd | 20 | 250.2.e.c.99.2 | 16 | |||
25.13 | odd | 20 | 250.2.e.c.99.3 | 16 | |||
25.14 | even | 10 | 250.2.d.d.101.2 | 8 | |||
25.16 | even | 5 | 50.2.d.b.31.1 | yes | 8 | ||
25.23 | odd | 20 | 250.2.e.c.149.2 | 16 | |||
75.11 | odd | 10 | 450.2.h.e.271.1 | 8 | |||
75.41 | odd | 10 | 450.2.h.e.181.1 | 8 | |||
100.11 | odd | 10 | 400.2.u.d.321.2 | 8 | |||
100.91 | odd | 10 | 400.2.u.d.81.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.2.d.b.21.1 | ✓ | 8 | 25.11 | even | 5 | ||
50.2.d.b.31.1 | yes | 8 | 25.16 | even | 5 | ||
250.2.d.d.101.2 | 8 | 25.14 | even | 10 | |||
250.2.d.d.151.2 | 8 | 25.9 | even | 10 | |||
250.2.e.c.99.2 | 16 | 25.12 | odd | 20 | |||
250.2.e.c.99.3 | 16 | 25.13 | odd | 20 | |||
250.2.e.c.149.2 | 16 | 25.23 | odd | 20 | |||
250.2.e.c.149.3 | 16 | 25.2 | odd | 20 | |||
400.2.u.d.81.2 | 8 | 100.91 | odd | 10 | |||
400.2.u.d.321.2 | 8 | 100.11 | odd | 10 | |||
450.2.h.e.181.1 | 8 | 75.41 | odd | 10 | |||
450.2.h.e.271.1 | 8 | 75.11 | odd | 10 | |||
1250.2.a.f.1.1 | 4 | 5.4 | even | 2 | |||
1250.2.a.l.1.4 | 4 | 1.1 | even | 1 | trivial | ||
1250.2.b.e.1249.4 | 8 | 5.3 | odd | 4 | |||
1250.2.b.e.1249.5 | 8 | 5.2 | odd | 4 | |||
10000.2.a.t.1.1 | 4 | 4.3 | odd | 2 | |||
10000.2.a.x.1.4 | 4 | 20.19 | odd | 2 |