Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.23607 | 0.713644 | 0.356822 | − | 0.934172i | \(-0.383860\pi\) | ||||
0.356822 | + | 0.934172i | \(0.383860\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.23607 | 0.504623 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.47214 | −0.490712 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.23607 | 0.356822 | ||||||||
\(13\) | −4.47214 | −1.24035 | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 1.23607 | 0.319151 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | −1.47214 | −0.346986 | ||||||||
\(19\) | −0.763932 | −0.175258 | −0.0876290 | − | 0.996153i | \(-0.527929\pi\) | ||||
−0.0876290 | + | 0.996153i | \(0.527929\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −1.23607 | −0.269732 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.76393 | −0.576320 | −0.288160 | − | 0.957582i | \(-0.593043\pi\) | ||||
−0.288160 | + | 0.957582i | \(0.593043\pi\) | |||||||
\(24\) | 1.23607 | 0.252311 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.47214 | −0.877058 | ||||||||
\(27\) | −5.52786 | −1.06384 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 3.23607 | 0.600923 | 0.300461 | − | 0.953794i | \(-0.402859\pi\) | ||||
0.300461 | + | 0.953794i | \(0.402859\pi\) | |||||||
\(30\) | 1.23607 | 0.225674 | ||||||||
\(31\) | −8.94427 | −1.60644 | −0.803219 | − | 0.595683i | \(-0.796881\pi\) | ||||
−0.803219 | + | 0.595683i | \(0.796881\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −1.47214 | −0.245356 | ||||||||
\(37\) | 1.23607 | 0.203208 | 0.101604 | − | 0.994825i | \(-0.467602\pi\) | ||||
0.101604 | + | 0.994825i | \(0.467602\pi\) | |||||||
\(38\) | −0.763932 | −0.123926 | ||||||||
\(39\) | −5.52786 | −0.885167 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 5.70820 | 0.891472 | 0.445736 | − | 0.895165i | \(-0.352942\pi\) | ||||
0.445736 | + | 0.895165i | \(0.352942\pi\) | |||||||
\(42\) | −1.23607 | −0.190729 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.47214 | −0.219453 | ||||||||
\(46\) | −2.76393 | −0.407520 | ||||||||
\(47\) | −8.47214 | −1.23579 | −0.617894 | − | 0.786261i | \(-0.712014\pi\) | ||||
−0.617894 | + | 0.786261i | \(0.712014\pi\) | |||||||
\(48\) | 1.23607 | 0.178411 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 2.47214 | 0.346168 | ||||||||
\(52\) | −4.47214 | −0.620174 | ||||||||
\(53\) | −5.23607 | −0.719229 | −0.359615 | − | 0.933101i | \(-0.617092\pi\) | ||||
−0.359615 | + | 0.933101i | \(0.617092\pi\) | |||||||
\(54\) | −5.52786 | −0.752247 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −0.944272 | −0.125072 | ||||||||
\(58\) | 3.23607 | 0.424917 | ||||||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 1.23607 | 0.159576 | ||||||||
\(61\) | 5.52786 | 0.707770 | 0.353885 | − | 0.935289i | \(-0.384860\pi\) | ||||
0.353885 | + | 0.935289i | \(0.384860\pi\) | |||||||
\(62\) | −8.94427 | −1.13592 | ||||||||
\(63\) | 1.47214 | 0.185472 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.47214 | −0.554700 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.00000 | −0.733017 | −0.366508 | − | 0.930415i | \(-0.619447\pi\) | ||||
−0.366508 | + | 0.930415i | \(0.619447\pi\) | |||||||
\(68\) | 2.00000 | 0.242536 | ||||||||
\(69\) | −3.41641 | −0.411287 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | −1.47214 | −0.173493 | ||||||||
\(73\) | 0.472136 | 0.0552593 | 0.0276297 | − | 0.999618i | \(-0.491204\pi\) | ||||
0.0276297 | + | 0.999618i | \(0.491204\pi\) | |||||||
\(74\) | 1.23607 | 0.143690 | ||||||||
\(75\) | 1.23607 | 0.142729 | ||||||||
\(76\) | −0.763932 | −0.0876290 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.52786 | −0.625907 | ||||||||
\(79\) | 0.763932 | 0.0859491 | 0.0429745 | − | 0.999076i | \(-0.486317\pi\) | ||||
0.0429745 | + | 0.999076i | \(0.486317\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −2.41641 | −0.268490 | ||||||||
\(82\) | 5.70820 | 0.630366 | ||||||||
\(83\) | 8.00000 | 0.878114 | 0.439057 | − | 0.898459i | \(-0.355313\pi\) | ||||
0.439057 | + | 0.898459i | \(0.355313\pi\) | |||||||
\(84\) | −1.23607 | −0.134866 | ||||||||
\(85\) | 2.00000 | 0.216930 | ||||||||
\(86\) | −8.00000 | −0.862662 | ||||||||
\(87\) | 4.00000 | 0.428845 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.94427 | 0.312092 | 0.156046 | − | 0.987750i | \(-0.450125\pi\) | ||||
0.156046 | + | 0.987750i | \(0.450125\pi\) | |||||||
\(90\) | −1.47214 | −0.155177 | ||||||||
\(91\) | 4.47214 | 0.468807 | ||||||||
\(92\) | −2.76393 | −0.288160 | ||||||||
\(93\) | −11.0557 | −1.14643 | ||||||||
\(94\) | −8.47214 | −0.873834 | ||||||||
\(95\) | −0.763932 | −0.0783778 | ||||||||
\(96\) | 1.23607 | 0.126156 | ||||||||
\(97\) | −11.7082 | −1.18879 | −0.594394 | − | 0.804174i | \(-0.702608\pi\) | ||||
−0.594394 | + | 0.804174i | \(0.702608\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 19.4164 | 1.93200 | 0.966002 | − | 0.258533i | \(-0.0832391\pi\) | ||||
0.966002 | + | 0.258533i | \(0.0832391\pi\) | |||||||
\(102\) | 2.47214 | 0.244778 | ||||||||
\(103\) | 14.0000 | 1.37946 | 0.689730 | − | 0.724066i | \(-0.257729\pi\) | ||||
0.689730 | + | 0.724066i | \(0.257729\pi\) | |||||||
\(104\) | −4.47214 | −0.438529 | ||||||||
\(105\) | −1.23607 | −0.120628 | ||||||||
\(106\) | −5.23607 | −0.508572 | ||||||||
\(107\) | −16.0000 | −1.54678 | −0.773389 | − | 0.633932i | \(-0.781440\pi\) | ||||
−0.773389 | + | 0.633932i | \(0.781440\pi\) | |||||||
\(108\) | −5.52786 | −0.531919 | ||||||||
\(109\) | 2.29180 | 0.219514 | 0.109757 | − | 0.993958i | \(-0.464993\pi\) | ||||
0.109757 | + | 0.993958i | \(0.464993\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.52786 | 0.145018 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −6.94427 | −0.653262 | −0.326631 | − | 0.945152i | \(-0.605913\pi\) | ||||
−0.326631 | + | 0.945152i | \(0.605913\pi\) | |||||||
\(114\) | −0.944272 | −0.0884392 | ||||||||
\(115\) | −2.76393 | −0.257738 | ||||||||
\(116\) | 3.23607 | 0.300461 | ||||||||
\(117\) | 6.58359 | 0.608653 | ||||||||
\(118\) | −8.00000 | −0.736460 | ||||||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | 1.23607 | 0.112837 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 5.52786 | 0.500469 | ||||||||
\(123\) | 7.05573 | 0.636194 | ||||||||
\(124\) | −8.94427 | −0.803219 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 1.47214 | 0.131148 | ||||||||
\(127\) | −14.4721 | −1.28419 | −0.642097 | − | 0.766623i | \(-0.721935\pi\) | ||||
−0.642097 | + | 0.766623i | \(0.721935\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −9.88854 | −0.870638 | ||||||||
\(130\) | −4.47214 | −0.392232 | ||||||||
\(131\) | −16.1803 | −1.41368 | −0.706841 | − | 0.707372i | \(-0.749881\pi\) | ||||
−0.706841 | + | 0.707372i | \(0.749881\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.763932 | 0.0662413 | ||||||||
\(134\) | −6.00000 | −0.518321 | ||||||||
\(135\) | −5.52786 | −0.475763 | ||||||||
\(136\) | 2.00000 | 0.171499 | ||||||||
\(137\) | 15.8885 | 1.35745 | 0.678725 | − | 0.734393i | \(-0.262533\pi\) | ||||
0.678725 | + | 0.734393i | \(0.262533\pi\) | |||||||
\(138\) | −3.41641 | −0.290824 | ||||||||
\(139\) | −8.18034 | −0.693847 | −0.346924 | − | 0.937893i | \(-0.612774\pi\) | ||||
−0.346924 | + | 0.937893i | \(0.612774\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −10.4721 | −0.881913 | ||||||||
\(142\) | −8.00000 | −0.671345 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.47214 | −0.122678 | ||||||||
\(145\) | 3.23607 | 0.268741 | ||||||||
\(146\) | 0.472136 | 0.0390742 | ||||||||
\(147\) | 1.23607 | 0.101949 | ||||||||
\(148\) | 1.23607 | 0.101604 | ||||||||
\(149\) | −5.70820 | −0.467634 | −0.233817 | − | 0.972281i | \(-0.575122\pi\) | ||||
−0.233817 | + | 0.972281i | \(0.575122\pi\) | |||||||
\(150\) | 1.23607 | 0.100925 | ||||||||
\(151\) | −6.29180 | −0.512019 | −0.256010 | − | 0.966674i | \(-0.582408\pi\) | ||||
−0.256010 | + | 0.966674i | \(0.582408\pi\) | |||||||
\(152\) | −0.763932 | −0.0619631 | ||||||||
\(153\) | −2.94427 | −0.238030 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.94427 | −0.718421 | ||||||||
\(156\) | −5.52786 | −0.442583 | ||||||||
\(157\) | −16.4721 | −1.31462 | −0.657310 | − | 0.753620i | \(-0.728306\pi\) | ||||
−0.657310 | + | 0.753620i | \(0.728306\pi\) | |||||||
\(158\) | 0.763932 | 0.0607752 | ||||||||
\(159\) | −6.47214 | −0.513274 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 2.76393 | 0.217828 | ||||||||
\(162\) | −2.41641 | −0.189851 | ||||||||
\(163\) | −2.94427 | −0.230613 | −0.115307 | − | 0.993330i | \(-0.536785\pi\) | ||||
−0.115307 | + | 0.993330i | \(0.536785\pi\) | |||||||
\(164\) | 5.70820 | 0.445736 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.00000 | 0.620920 | ||||||||
\(167\) | 12.9443 | 1.00166 | 0.500829 | − | 0.865546i | \(-0.333029\pi\) | ||||
0.500829 | + | 0.865546i | \(0.333029\pi\) | |||||||
\(168\) | −1.23607 | −0.0953647 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 2.00000 | 0.153393 | ||||||||
\(171\) | 1.12461 | 0.0860012 | ||||||||
\(172\) | −8.00000 | −0.609994 | ||||||||
\(173\) | 3.52786 | 0.268219 | 0.134109 | − | 0.990967i | \(-0.457183\pi\) | ||||
0.134109 | + | 0.990967i | \(0.457183\pi\) | |||||||
\(174\) | 4.00000 | 0.303239 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.88854 | −0.743268 | ||||||||
\(178\) | 2.94427 | 0.220683 | ||||||||
\(179\) | 9.52786 | 0.712146 | 0.356073 | − | 0.934458i | \(-0.384115\pi\) | ||||
0.356073 | + | 0.934458i | \(0.384115\pi\) | |||||||
\(180\) | −1.47214 | −0.109727 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 4.47214 | 0.331497 | ||||||||
\(183\) | 6.83282 | 0.505096 | ||||||||
\(184\) | −2.76393 | −0.203760 | ||||||||
\(185\) | 1.23607 | 0.0908775 | ||||||||
\(186\) | −11.0557 | −0.810645 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −8.47214 | −0.617894 | ||||||||
\(189\) | 5.52786 | 0.402093 | ||||||||
\(190\) | −0.763932 | −0.0554215 | ||||||||
\(191\) | −2.47214 | −0.178877 | −0.0894387 | − | 0.995992i | \(-0.528507\pi\) | ||||
−0.0894387 | + | 0.995992i | \(0.528507\pi\) | |||||||
\(192\) | 1.23607 | 0.0892055 | ||||||||
\(193\) | −9.05573 | −0.651846 | −0.325923 | − | 0.945396i | \(-0.605675\pi\) | ||||
−0.325923 | + | 0.945396i | \(0.605675\pi\) | |||||||
\(194\) | −11.7082 | −0.840600 | ||||||||
\(195\) | −5.52786 | −0.395859 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 5.41641 | 0.385903 | 0.192952 | − | 0.981208i | \(-0.438194\pi\) | ||||
0.192952 | + | 0.981208i | \(0.438194\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.4721 | −1.02590 | −0.512951 | − | 0.858418i | \(-0.671448\pi\) | ||||
−0.512951 | + | 0.858418i | \(0.671448\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −7.41641 | −0.523113 | ||||||||
\(202\) | 19.4164 | 1.36613 | ||||||||
\(203\) | −3.23607 | −0.227127 | ||||||||
\(204\) | 2.47214 | 0.173084 | ||||||||
\(205\) | 5.70820 | 0.398678 | ||||||||
\(206\) | 14.0000 | 0.975426 | ||||||||
\(207\) | 4.06888 | 0.282807 | ||||||||
\(208\) | −4.47214 | −0.310087 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.23607 | −0.0852968 | ||||||||
\(211\) | 21.8885 | 1.50687 | 0.753435 | − | 0.657523i | \(-0.228396\pi\) | ||||
0.753435 | + | 0.657523i | \(0.228396\pi\) | |||||||
\(212\) | −5.23607 | −0.359615 | ||||||||
\(213\) | −9.88854 | −0.677552 | ||||||||
\(214\) | −16.0000 | −1.09374 | ||||||||
\(215\) | −8.00000 | −0.545595 | ||||||||
\(216\) | −5.52786 | −0.376124 | ||||||||
\(217\) | 8.94427 | 0.607177 | ||||||||
\(218\) | 2.29180 | 0.155220 | ||||||||
\(219\) | 0.583592 | 0.0394355 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.94427 | −0.601657 | ||||||||
\(222\) | 1.52786 | 0.102544 | ||||||||
\(223\) | −18.9443 | −1.26860 | −0.634301 | − | 0.773086i | \(-0.718712\pi\) | ||||
−0.634301 | + | 0.773086i | \(0.718712\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −1.47214 | −0.0981424 | ||||||||
\(226\) | −6.94427 | −0.461926 | ||||||||
\(227\) | 1.52786 | 0.101408 | 0.0507039 | − | 0.998714i | \(-0.483854\pi\) | ||||
0.0507039 | + | 0.998714i | \(0.483854\pi\) | |||||||
\(228\) | −0.944272 | −0.0625359 | ||||||||
\(229\) | −11.5279 | −0.761783 | −0.380891 | − | 0.924620i | \(-0.624383\pi\) | ||||
−0.380891 | + | 0.924620i | \(0.624383\pi\) | |||||||
\(230\) | −2.76393 | −0.182248 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.23607 | 0.212458 | ||||||||
\(233\) | −2.94427 | −0.192886 | −0.0964428 | − | 0.995339i | \(-0.530746\pi\) | ||||
−0.0964428 | + | 0.995339i | \(0.530746\pi\) | |||||||
\(234\) | 6.58359 | 0.430383 | ||||||||
\(235\) | −8.47214 | −0.552661 | ||||||||
\(236\) | −8.00000 | −0.520756 | ||||||||
\(237\) | 0.944272 | 0.0613371 | ||||||||
\(238\) | −2.00000 | −0.129641 | ||||||||
\(239\) | 7.23607 | 0.468062 | 0.234031 | − | 0.972229i | \(-0.424808\pi\) | ||||
0.234031 | + | 0.972229i | \(0.424808\pi\) | |||||||
\(240\) | 1.23607 | 0.0797878 | ||||||||
\(241\) | −17.1246 | −1.10309 | −0.551547 | − | 0.834144i | \(-0.685962\pi\) | ||||
−0.551547 | + | 0.834144i | \(0.685962\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5967 | 0.872232 | ||||||||
\(244\) | 5.52786 | 0.353885 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 7.05573 | 0.449857 | ||||||||
\(247\) | 3.41641 | 0.217381 | ||||||||
\(248\) | −8.94427 | −0.567962 | ||||||||
\(249\) | 9.88854 | 0.626661 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −5.52786 | −0.348916 | −0.174458 | − | 0.984665i | \(-0.555817\pi\) | ||||
−0.174458 | + | 0.984665i | \(0.555817\pi\) | |||||||
\(252\) | 1.47214 | 0.0927358 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −14.4721 | −0.908063 | ||||||||
\(255\) | 2.47214 | 0.154811 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.1246 | 0.943447 | 0.471724 | − | 0.881746i | \(-0.343632\pi\) | ||||
0.471724 | + | 0.881746i | \(0.343632\pi\) | |||||||
\(258\) | −9.88854 | −0.615634 | ||||||||
\(259\) | −1.23607 | −0.0768055 | ||||||||
\(260\) | −4.47214 | −0.277350 | ||||||||
\(261\) | −4.76393 | −0.294880 | ||||||||
\(262\) | −16.1803 | −0.999625 | ||||||||
\(263\) | 16.3607 | 1.00884 | 0.504421 | − | 0.863458i | \(-0.331706\pi\) | ||||
0.504421 | + | 0.863458i | \(0.331706\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.23607 | −0.321649 | ||||||||
\(266\) | 0.763932 | 0.0468397 | ||||||||
\(267\) | 3.63932 | 0.222723 | ||||||||
\(268\) | −6.00000 | −0.366508 | ||||||||
\(269\) | −12.4721 | −0.760440 | −0.380220 | − | 0.924896i | \(-0.624152\pi\) | ||||
−0.380220 | + | 0.924896i | \(0.624152\pi\) | |||||||
\(270\) | −5.52786 | −0.336415 | ||||||||
\(271\) | 6.47214 | 0.393154 | 0.196577 | − | 0.980488i | \(-0.437017\pi\) | ||||
0.196577 | + | 0.980488i | \(0.437017\pi\) | |||||||
\(272\) | 2.00000 | 0.121268 | ||||||||
\(273\) | 5.52786 | 0.334562 | ||||||||
\(274\) | 15.8885 | 0.959862 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.41641 | −0.205644 | ||||||||
\(277\) | −11.5279 | −0.692642 | −0.346321 | − | 0.938116i | \(-0.612569\pi\) | ||||
−0.346321 | + | 0.938116i | \(0.612569\pi\) | |||||||
\(278\) | −8.18034 | −0.490624 | ||||||||
\(279\) | 13.1672 | 0.788299 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 28.3607 | 1.69186 | 0.845928 | − | 0.533297i | \(-0.179047\pi\) | ||||
0.845928 | + | 0.533297i | \(0.179047\pi\) | |||||||
\(282\) | −10.4721 | −0.623607 | ||||||||
\(283\) | −19.4164 | −1.15419 | −0.577093 | − | 0.816679i | \(-0.695813\pi\) | ||||
−0.577093 | + | 0.816679i | \(0.695813\pi\) | |||||||
\(284\) | −8.00000 | −0.474713 | ||||||||
\(285\) | −0.944272 | −0.0559338 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.70820 | −0.336945 | ||||||||
\(288\) | −1.47214 | −0.0867464 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 3.23607 | 0.190028 | ||||||||
\(291\) | −14.4721 | −0.848372 | ||||||||
\(292\) | 0.472136 | 0.0276297 | ||||||||
\(293\) | 0.472136 | 0.0275825 | 0.0137912 | − | 0.999905i | \(-0.495610\pi\) | ||||
0.0137912 | + | 0.999905i | \(0.495610\pi\) | |||||||
\(294\) | 1.23607 | 0.0720889 | ||||||||
\(295\) | −8.00000 | −0.465778 | ||||||||
\(296\) | 1.23607 | 0.0718450 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.70820 | −0.330667 | ||||||||
\(299\) | 12.3607 | 0.714837 | ||||||||
\(300\) | 1.23607 | 0.0713644 | ||||||||
\(301\) | 8.00000 | 0.461112 | ||||||||
\(302\) | −6.29180 | −0.362052 | ||||||||
\(303\) | 24.0000 | 1.37876 | ||||||||
\(304\) | −0.763932 | −0.0438145 | ||||||||
\(305\) | 5.52786 | 0.316525 | ||||||||
\(306\) | −2.94427 | −0.168313 | ||||||||
\(307\) | 9.52786 | 0.543784 | 0.271892 | − | 0.962328i | \(-0.412351\pi\) | ||||
0.271892 | + | 0.962328i | \(0.412351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.3050 | 0.984444 | ||||||||
\(310\) | −8.94427 | −0.508001 | ||||||||
\(311\) | 30.8328 | 1.74837 | 0.874184 | − | 0.485594i | \(-0.161397\pi\) | ||||
0.874184 | + | 0.485594i | \(0.161397\pi\) | |||||||
\(312\) | −5.52786 | −0.312954 | ||||||||
\(313\) | −20.6525 | −1.16735 | −0.583673 | − | 0.811988i | \(-0.698385\pi\) | ||||
−0.583673 | + | 0.811988i | \(0.698385\pi\) | |||||||
\(314\) | −16.4721 | −0.929576 | ||||||||
\(315\) | 1.47214 | 0.0829455 | ||||||||
\(316\) | 0.763932 | 0.0429745 | ||||||||
\(317\) | 2.18034 | 0.122460 | 0.0612300 | − | 0.998124i | \(-0.480498\pi\) | ||||
0.0612300 | + | 0.998124i | \(0.480498\pi\) | |||||||
\(318\) | −6.47214 | −0.362939 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −19.7771 | −1.10385 | ||||||||
\(322\) | 2.76393 | 0.154028 | ||||||||
\(323\) | −1.52786 | −0.0850126 | ||||||||
\(324\) | −2.41641 | −0.134245 | ||||||||
\(325\) | −4.47214 | −0.248069 | ||||||||
\(326\) | −2.94427 | −0.163068 | ||||||||
\(327\) | 2.83282 | 0.156655 | ||||||||
\(328\) | 5.70820 | 0.315183 | ||||||||
\(329\) | 8.47214 | 0.467084 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.4164 | −0.847362 | −0.423681 | − | 0.905811i | \(-0.639262\pi\) | ||||
−0.423681 | + | 0.905811i | \(0.639262\pi\) | |||||||
\(332\) | 8.00000 | 0.439057 | ||||||||
\(333\) | −1.81966 | −0.0997168 | ||||||||
\(334\) | 12.9443 | 0.708279 | ||||||||
\(335\) | −6.00000 | −0.327815 | ||||||||
\(336\) | −1.23607 | −0.0674330 | ||||||||
\(337\) | 28.8328 | 1.57062 | 0.785312 | − | 0.619100i | \(-0.212503\pi\) | ||||
0.785312 | + | 0.619100i | \(0.212503\pi\) | |||||||
\(338\) | 7.00000 | 0.380750 | ||||||||
\(339\) | −8.58359 | −0.466197 | ||||||||
\(340\) | 2.00000 | 0.108465 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.12461 | 0.0608120 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | −3.41641 | −0.183933 | ||||||||
\(346\) | 3.52786 | 0.189659 | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 4.00000 | 0.214423 | ||||||||
\(349\) | −24.9443 | −1.33524 | −0.667618 | − | 0.744504i | \(-0.732686\pi\) | ||||
−0.667618 | + | 0.744504i | \(0.732686\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 24.7214 | 1.31953 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.7639 | −0.998703 | −0.499352 | − | 0.866399i | \(-0.666428\pi\) | ||||
−0.499352 | + | 0.866399i | \(0.666428\pi\) | |||||||
\(354\) | −9.88854 | −0.525570 | ||||||||
\(355\) | −8.00000 | −0.424596 | ||||||||
\(356\) | 2.94427 | 0.156046 | ||||||||
\(357\) | −2.47214 | −0.130839 | ||||||||
\(358\) | 9.52786 | 0.503563 | ||||||||
\(359\) | −12.1803 | −0.642854 | −0.321427 | − | 0.946934i | \(-0.604162\pi\) | ||||
−0.321427 | + | 0.946934i | \(0.604162\pi\) | |||||||
\(360\) | −1.47214 | −0.0775884 | ||||||||
\(361\) | −18.4164 | −0.969285 | ||||||||
\(362\) | 14.0000 | 0.735824 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.47214 | 0.234404 | ||||||||
\(365\) | 0.472136 | 0.0247127 | ||||||||
\(366\) | 6.83282 | 0.357157 | ||||||||
\(367\) | 28.8328 | 1.50506 | 0.752530 | − | 0.658558i | \(-0.228833\pi\) | ||||
0.752530 | + | 0.658558i | \(0.228833\pi\) | |||||||
\(368\) | −2.76393 | −0.144080 | ||||||||
\(369\) | −8.40325 | −0.437456 | ||||||||
\(370\) | 1.23607 | 0.0642601 | ||||||||
\(371\) | 5.23607 | 0.271843 | ||||||||
\(372\) | −11.0557 | −0.573213 | ||||||||
\(373\) | −38.3607 | −1.98624 | −0.993120 | − | 0.117098i | \(-0.962641\pi\) | ||||
−0.993120 | + | 0.117098i | \(0.962641\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.23607 | 0.0638303 | ||||||||
\(376\) | −8.47214 | −0.436917 | ||||||||
\(377\) | −14.4721 | −0.745353 | ||||||||
\(378\) | 5.52786 | 0.284323 | ||||||||
\(379\) | −4.94427 | −0.253970 | −0.126985 | − | 0.991905i | \(-0.540530\pi\) | ||||
−0.126985 | + | 0.991905i | \(0.540530\pi\) | |||||||
\(380\) | −0.763932 | −0.0391889 | ||||||||
\(381\) | −17.8885 | −0.916458 | ||||||||
\(382\) | −2.47214 | −0.126485 | ||||||||
\(383\) | −3.88854 | −0.198695 | −0.0993477 | − | 0.995053i | \(-0.531676\pi\) | ||||
−0.0993477 | + | 0.995053i | \(0.531676\pi\) | |||||||
\(384\) | 1.23607 | 0.0630778 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.05573 | −0.460924 | ||||||||
\(387\) | 11.7771 | 0.598663 | ||||||||
\(388\) | −11.7082 | −0.594394 | ||||||||
\(389\) | 38.3607 | 1.94496 | 0.972482 | − | 0.232979i | \(-0.0748472\pi\) | ||||
0.972482 | + | 0.232979i | \(0.0748472\pi\) | |||||||
\(390\) | −5.52786 | −0.279914 | ||||||||
\(391\) | −5.52786 | −0.279556 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −20.0000 | −1.00887 | ||||||||
\(394\) | 5.41641 | 0.272875 | ||||||||
\(395\) | 0.763932 | 0.0384376 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.4164 | 1.27561 | 0.637806 | − | 0.770197i | \(-0.279842\pi\) | ||||
0.637806 | + | 0.770197i | \(0.279842\pi\) | |||||||
\(398\) | −14.4721 | −0.725423 | ||||||||
\(399\) | 0.944272 | 0.0472727 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −3.52786 | −0.176173 | −0.0880866 | − | 0.996113i | \(-0.528075\pi\) | ||||
−0.0880866 | + | 0.996113i | \(0.528075\pi\) | |||||||
\(402\) | −7.41641 | −0.369897 | ||||||||
\(403\) | 40.0000 | 1.99254 | ||||||||
\(404\) | 19.4164 | 0.966002 | ||||||||
\(405\) | −2.41641 | −0.120072 | ||||||||
\(406\) | −3.23607 | −0.160603 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.47214 | 0.122389 | ||||||||
\(409\) | 4.76393 | 0.235561 | 0.117781 | − | 0.993040i | \(-0.462422\pi\) | ||||
0.117781 | + | 0.993040i | \(0.462422\pi\) | |||||||
\(410\) | 5.70820 | 0.281908 | ||||||||
\(411\) | 19.6393 | 0.968736 | ||||||||
\(412\) | 14.0000 | 0.689730 | ||||||||
\(413\) | 8.00000 | 0.393654 | ||||||||
\(414\) | 4.06888 | 0.199975 | ||||||||
\(415\) | 8.00000 | 0.392705 | ||||||||
\(416\) | −4.47214 | −0.219265 | ||||||||
\(417\) | −10.1115 | −0.495160 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.4164 | 1.14397 | 0.571983 | − | 0.820265i | \(-0.306174\pi\) | ||||
0.571983 | + | 0.820265i | \(0.306174\pi\) | |||||||
\(420\) | −1.23607 | −0.0603139 | ||||||||
\(421\) | 31.3050 | 1.52571 | 0.762855 | − | 0.646570i | \(-0.223797\pi\) | ||||
0.762855 | + | 0.646570i | \(0.223797\pi\) | |||||||
\(422\) | 21.8885 | 1.06552 | ||||||||
\(423\) | 12.4721 | 0.606416 | ||||||||
\(424\) | −5.23607 | −0.254286 | ||||||||
\(425\) | 2.00000 | 0.0970143 | ||||||||
\(426\) | −9.88854 | −0.479102 | ||||||||
\(427\) | −5.52786 | −0.267512 | ||||||||
\(428\) | −16.0000 | −0.773389 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.00000 | −0.385794 | ||||||||
\(431\) | 2.65248 | 0.127765 | 0.0638826 | − | 0.997957i | \(-0.479652\pi\) | ||||
0.0638826 | + | 0.997957i | \(0.479652\pi\) | |||||||
\(432\) | −5.52786 | −0.265959 | ||||||||
\(433\) | −5.23607 | −0.251629 | −0.125815 | − | 0.992054i | \(-0.540154\pi\) | ||||
−0.125815 | + | 0.992054i | \(0.540154\pi\) | |||||||
\(434\) | 8.94427 | 0.429339 | ||||||||
\(435\) | 4.00000 | 0.191785 | ||||||||
\(436\) | 2.29180 | 0.109757 | ||||||||
\(437\) | 2.11146 | 0.101005 | ||||||||
\(438\) | 0.583592 | 0.0278851 | ||||||||
\(439\) | 19.4164 | 0.926695 | 0.463347 | − | 0.886177i | \(-0.346648\pi\) | ||||
0.463347 | + | 0.886177i | \(0.346648\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.47214 | −0.0701017 | ||||||||
\(442\) | −8.94427 | −0.425436 | ||||||||
\(443\) | −2.94427 | −0.139887 | −0.0699433 | − | 0.997551i | \(-0.522282\pi\) | ||||
−0.0699433 | + | 0.997551i | \(0.522282\pi\) | |||||||
\(444\) | 1.52786 | 0.0725092 | ||||||||
\(445\) | 2.94427 | 0.139572 | ||||||||
\(446\) | −18.9443 | −0.897037 | ||||||||
\(447\) | −7.05573 | −0.333724 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −18.3607 | −0.866494 | −0.433247 | − | 0.901275i | \(-0.642632\pi\) | ||||
−0.433247 | + | 0.901275i | \(0.642632\pi\) | |||||||
\(450\) | −1.47214 | −0.0693972 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −6.94427 | −0.326631 | ||||||||
\(453\) | −7.77709 | −0.365399 | ||||||||
\(454\) | 1.52786 | 0.0717062 | ||||||||
\(455\) | 4.47214 | 0.209657 | ||||||||
\(456\) | −0.944272 | −0.0442196 | ||||||||
\(457\) | 13.0557 | 0.610721 | 0.305361 | − | 0.952237i | \(-0.401223\pi\) | ||||
0.305361 | + | 0.952237i | \(0.401223\pi\) | |||||||
\(458\) | −11.5279 | −0.538662 | ||||||||
\(459\) | −11.0557 | −0.516037 | ||||||||
\(460\) | −2.76393 | −0.128869 | ||||||||
\(461\) | 20.9443 | 0.975472 | 0.487736 | − | 0.872991i | \(-0.337823\pi\) | ||||
0.487736 | + | 0.872991i | \(0.337823\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.7082 | −0.730022 | −0.365011 | − | 0.931003i | \(-0.618935\pi\) | ||||
−0.365011 | + | 0.931003i | \(0.618935\pi\) | |||||||
\(464\) | 3.23607 | 0.150231 | ||||||||
\(465\) | −11.0557 | −0.512697 | ||||||||
\(466\) | −2.94427 | −0.136391 | ||||||||
\(467\) | 13.8197 | 0.639498 | 0.319749 | − | 0.947502i | \(-0.396401\pi\) | ||||
0.319749 | + | 0.947502i | \(0.396401\pi\) | |||||||
\(468\) | 6.58359 | 0.304327 | ||||||||
\(469\) | 6.00000 | 0.277054 | ||||||||
\(470\) | −8.47214 | −0.390790 | ||||||||
\(471\) | −20.3607 | −0.938171 | ||||||||
\(472\) | −8.00000 | −0.368230 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0.944272 | 0.0433718 | ||||||||
\(475\) | −0.763932 | −0.0350516 | ||||||||
\(476\) | −2.00000 | −0.0916698 | ||||||||
\(477\) | 7.70820 | 0.352934 | ||||||||
\(478\) | 7.23607 | 0.330970 | ||||||||
\(479\) | −5.88854 | −0.269054 | −0.134527 | − | 0.990910i | \(-0.542952\pi\) | ||||
−0.134527 | + | 0.990910i | \(0.542952\pi\) | |||||||
\(480\) | 1.23607 | 0.0564185 | ||||||||
\(481\) | −5.52786 | −0.252049 | ||||||||
\(482\) | −17.1246 | −0.780005 | ||||||||
\(483\) | 3.41641 | 0.155452 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.7082 | −0.531642 | ||||||||
\(486\) | 13.5967 | 0.616761 | ||||||||
\(487\) | 24.0689 | 1.09067 | 0.545333 | − | 0.838220i | \(-0.316403\pi\) | ||||
0.545333 | + | 0.838220i | \(0.316403\pi\) | |||||||
\(488\) | 5.52786 | 0.250235 | ||||||||
\(489\) | −3.63932 | −0.164576 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | −8.00000 | −0.361035 | −0.180517 | − | 0.983572i | \(-0.557777\pi\) | ||||
−0.180517 | + | 0.983572i | \(0.557777\pi\) | |||||||
\(492\) | 7.05573 | 0.318097 | ||||||||
\(493\) | 6.47214 | 0.291490 | ||||||||
\(494\) | 3.41641 | 0.153711 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.94427 | −0.401610 | ||||||||
\(497\) | 8.00000 | 0.358849 | ||||||||
\(498\) | 9.88854 | 0.443116 | ||||||||
\(499\) | 33.3050 | 1.49093 | 0.745467 | − | 0.666542i | \(-0.232226\pi\) | ||||
0.745467 | + | 0.666542i | \(0.232226\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 16.0000 | 0.714827 | ||||||||
\(502\) | −5.52786 | −0.246721 | ||||||||
\(503\) | 14.8328 | 0.661363 | 0.330681 | − | 0.943742i | \(-0.392721\pi\) | ||||
0.330681 | + | 0.943742i | \(0.392721\pi\) | |||||||
\(504\) | 1.47214 | 0.0655741 | ||||||||
\(505\) | 19.4164 | 0.864019 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.65248 | 0.384270 | ||||||||
\(508\) | −14.4721 | −0.642097 | ||||||||
\(509\) | 6.94427 | 0.307799 | 0.153900 | − | 0.988086i | \(-0.450817\pi\) | ||||
0.153900 | + | 0.988086i | \(0.450817\pi\) | |||||||
\(510\) | 2.47214 | 0.109468 | ||||||||
\(511\) | −0.472136 | −0.0208861 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.22291 | 0.186446 | ||||||||
\(514\) | 15.1246 | 0.667118 | ||||||||
\(515\) | 14.0000 | 0.616914 | ||||||||
\(516\) | −9.88854 | −0.435319 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.23607 | −0.0543097 | ||||||||
\(519\) | 4.36068 | 0.191413 | ||||||||
\(520\) | −4.47214 | −0.196116 | ||||||||
\(521\) | 8.47214 | 0.371171 | 0.185586 | − | 0.982628i | \(-0.440582\pi\) | ||||
0.185586 | + | 0.982628i | \(0.440582\pi\) | |||||||
\(522\) | −4.76393 | −0.208512 | ||||||||
\(523\) | −30.4721 | −1.33245 | −0.666227 | − | 0.745749i | \(-0.732092\pi\) | ||||
−0.666227 | + | 0.745749i | \(0.732092\pi\) | |||||||
\(524\) | −16.1803 | −0.706841 | ||||||||
\(525\) | −1.23607 | −0.0539464 | ||||||||
\(526\) | 16.3607 | 0.713360 | ||||||||
\(527\) | −17.8885 | −0.779237 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.3607 | −0.667856 | ||||||||
\(530\) | −5.23607 | −0.227440 | ||||||||
\(531\) | 11.7771 | 0.511082 | ||||||||
\(532\) | 0.763932 | 0.0331207 | ||||||||
\(533\) | −25.5279 | −1.10573 | ||||||||
\(534\) | 3.63932 | 0.157489 | ||||||||
\(535\) | −16.0000 | −0.691740 | ||||||||
\(536\) | −6.00000 | −0.259161 | ||||||||
\(537\) | 11.7771 | 0.508219 | ||||||||
\(538\) | −12.4721 | −0.537712 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.52786 | −0.237881 | ||||||||
\(541\) | −15.2361 | −0.655050 | −0.327525 | − | 0.944843i | \(-0.606215\pi\) | ||||
−0.327525 | + | 0.944843i | \(0.606215\pi\) | |||||||
\(542\) | 6.47214 | 0.278002 | ||||||||
\(543\) | 17.3050 | 0.742627 | ||||||||
\(544\) | 2.00000 | 0.0857493 | ||||||||
\(545\) | 2.29180 | 0.0981698 | ||||||||
\(546\) | 5.52786 | 0.236571 | ||||||||
\(547\) | −7.05573 | −0.301681 | −0.150841 | − | 0.988558i | \(-0.548198\pi\) | ||||
−0.150841 | + | 0.988558i | \(0.548198\pi\) | |||||||
\(548\) | 15.8885 | 0.678725 | ||||||||
\(549\) | −8.13777 | −0.347311 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.47214 | −0.105317 | ||||||||
\(552\) | −3.41641 | −0.145412 | ||||||||
\(553\) | −0.763932 | −0.0324857 | ||||||||
\(554\) | −11.5279 | −0.489772 | ||||||||
\(555\) | 1.52786 | 0.0648542 | ||||||||
\(556\) | −8.18034 | −0.346924 | ||||||||
\(557\) | 24.8328 | 1.05220 | 0.526100 | − | 0.850423i | \(-0.323654\pi\) | ||||
0.526100 | + | 0.850423i | \(0.323654\pi\) | |||||||
\(558\) | 13.1672 | 0.557411 | ||||||||
\(559\) | 35.7771 | 1.51321 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 28.3607 | 1.19632 | ||||||||
\(563\) | 14.8328 | 0.625129 | 0.312564 | − | 0.949897i | \(-0.398812\pi\) | ||||
0.312564 | + | 0.949897i | \(0.398812\pi\) | |||||||
\(564\) | −10.4721 | −0.440956 | ||||||||
\(565\) | −6.94427 | −0.292148 | ||||||||
\(566\) | −19.4164 | −0.816132 | ||||||||
\(567\) | 2.41641 | 0.101480 | ||||||||
\(568\) | −8.00000 | −0.335673 | ||||||||
\(569\) | −46.8328 | −1.96333 | −0.981667 | − | 0.190605i | \(-0.938955\pi\) | ||||
−0.981667 | + | 0.190605i | \(0.938955\pi\) | |||||||
\(570\) | −0.944272 | −0.0395512 | ||||||||
\(571\) | 27.4164 | 1.14734 | 0.573670 | − | 0.819086i | \(-0.305519\pi\) | ||||
0.573670 | + | 0.819086i | \(0.305519\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.05573 | −0.127655 | ||||||||
\(574\) | −5.70820 | −0.238256 | ||||||||
\(575\) | −2.76393 | −0.115264 | ||||||||
\(576\) | −1.47214 | −0.0613390 | ||||||||
\(577\) | −11.7082 | −0.487419 | −0.243709 | − | 0.969848i | \(-0.578364\pi\) | ||||
−0.243709 | + | 0.969848i | \(0.578364\pi\) | |||||||
\(578\) | −13.0000 | −0.540729 | ||||||||
\(579\) | −11.1935 | −0.465186 | ||||||||
\(580\) | 3.23607 | 0.134370 | ||||||||
\(581\) | −8.00000 | −0.331896 | ||||||||
\(582\) | −14.4721 | −0.599889 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0.472136 | 0.0195371 | ||||||||
\(585\) | 6.58359 | 0.272198 | ||||||||
\(586\) | 0.472136 | 0.0195038 | ||||||||
\(587\) | −0.291796 | −0.0120437 | −0.00602186 | − | 0.999982i | \(-0.501917\pi\) | ||||
−0.00602186 | + | 0.999982i | \(0.501917\pi\) | |||||||
\(588\) | 1.23607 | 0.0509746 | ||||||||
\(589\) | 6.83282 | 0.281541 | ||||||||
\(590\) | −8.00000 | −0.329355 | ||||||||
\(591\) | 6.69505 | 0.275397 | ||||||||
\(592\) | 1.23607 | 0.0508021 | ||||||||
\(593\) | −6.36068 | −0.261202 | −0.130601 | − | 0.991435i | \(-0.541691\pi\) | ||||
−0.130601 | + | 0.991435i | \(0.541691\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.00000 | −0.0819920 | ||||||||
\(596\) | −5.70820 | −0.233817 | ||||||||
\(597\) | −17.8885 | −0.732129 | ||||||||
\(598\) | 12.3607 | 0.505466 | ||||||||
\(599\) | −17.8885 | −0.730906 | −0.365453 | − | 0.930830i | \(-0.619086\pi\) | ||||
−0.365453 | + | 0.930830i | \(0.619086\pi\) | |||||||
\(600\) | 1.23607 | 0.0504623 | ||||||||
\(601\) | 18.2918 | 0.746138 | 0.373069 | − | 0.927804i | \(-0.378305\pi\) | ||||
0.373069 | + | 0.927804i | \(0.378305\pi\) | |||||||
\(602\) | 8.00000 | 0.326056 | ||||||||
\(603\) | 8.83282 | 0.359700 | ||||||||
\(604\) | −6.29180 | −0.256010 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 24.0000 | 0.974933 | ||||||||
\(607\) | 34.8328 | 1.41382 | 0.706910 | − | 0.707303i | \(-0.250088\pi\) | ||||
0.706910 | + | 0.707303i | \(0.250088\pi\) | |||||||
\(608\) | −0.763932 | −0.0309815 | ||||||||
\(609\) | −4.00000 | −0.162088 | ||||||||
\(610\) | 5.52786 | 0.223817 | ||||||||
\(611\) | 37.8885 | 1.53281 | ||||||||
\(612\) | −2.94427 | −0.119015 | ||||||||
\(613\) | 26.0000 | 1.05013 | 0.525065 | − | 0.851062i | \(-0.324041\pi\) | ||||
0.525065 | + | 0.851062i | \(0.324041\pi\) | |||||||
\(614\) | 9.52786 | 0.384513 | ||||||||
\(615\) | 7.05573 | 0.284514 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.4721 | −1.62935 | −0.814673 | − | 0.579920i | \(-0.803084\pi\) | ||||
−0.814673 | + | 0.579920i | \(0.803084\pi\) | |||||||
\(618\) | 17.3050 | 0.696107 | ||||||||
\(619\) | 10.4721 | 0.420911 | 0.210455 | − | 0.977603i | \(-0.432505\pi\) | ||||
0.210455 | + | 0.977603i | \(0.432505\pi\) | |||||||
\(620\) | −8.94427 | −0.359211 | ||||||||
\(621\) | 15.2786 | 0.613111 | ||||||||
\(622\) | 30.8328 | 1.23628 | ||||||||
\(623\) | −2.94427 | −0.117960 | ||||||||
\(624\) | −5.52786 | −0.221292 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −20.6525 | −0.825439 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −16.4721 | −0.657310 | ||||||||
\(629\) | 2.47214 | 0.0985705 | ||||||||
\(630\) | 1.47214 | 0.0586513 | ||||||||
\(631\) | −38.8328 | −1.54591 | −0.772955 | − | 0.634461i | \(-0.781222\pi\) | ||||
−0.772955 | + | 0.634461i | \(0.781222\pi\) | |||||||
\(632\) | 0.763932 | 0.0303876 | ||||||||
\(633\) | 27.0557 | 1.07537 | ||||||||
\(634\) | 2.18034 | 0.0865924 | ||||||||
\(635\) | −14.4721 | −0.574309 | ||||||||
\(636\) | −6.47214 | −0.256637 | ||||||||
\(637\) | −4.47214 | −0.177192 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.7771 | 0.465894 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 2.00000 | 0.0789953 | 0.0394976 | − | 0.999220i | \(-0.487424\pi\) | ||||
0.0394976 | + | 0.999220i | \(0.487424\pi\) | |||||||
\(642\) | −19.7771 | −0.780539 | ||||||||
\(643\) | −25.8197 | −1.01823 | −0.509114 | − | 0.860699i | \(-0.670027\pi\) | ||||
−0.509114 | + | 0.860699i | \(0.670027\pi\) | |||||||
\(644\) | 2.76393 | 0.108914 | ||||||||
\(645\) | −9.88854 | −0.389361 | ||||||||
\(646\) | −1.52786 | −0.0601130 | ||||||||
\(647\) | −30.0000 | −1.17942 | −0.589711 | − | 0.807614i | \(-0.700758\pi\) | ||||
−0.589711 | + | 0.807614i | \(0.700758\pi\) | |||||||
\(648\) | −2.41641 | −0.0949255 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.47214 | −0.175412 | ||||||||
\(651\) | 11.0557 | 0.433308 | ||||||||
\(652\) | −2.94427 | −0.115307 | ||||||||
\(653\) | 33.5967 | 1.31474 | 0.657371 | − | 0.753567i | \(-0.271668\pi\) | ||||
0.657371 | + | 0.753567i | \(0.271668\pi\) | |||||||
\(654\) | 2.83282 | 0.110772 | ||||||||
\(655\) | −16.1803 | −0.632218 | ||||||||
\(656\) | 5.70820 | 0.222868 | ||||||||
\(657\) | −0.695048 | −0.0271164 | ||||||||
\(658\) | 8.47214 | 0.330278 | ||||||||
\(659\) | −12.3607 | −0.481504 | −0.240752 | − | 0.970587i | \(-0.577394\pi\) | ||||
−0.240752 | + | 0.970587i | \(0.577394\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.9443 | 0.581265 | 0.290632 | − | 0.956835i | \(-0.406134\pi\) | ||||
0.290632 | + | 0.956835i | \(0.406134\pi\) | |||||||
\(662\) | −15.4164 | −0.599176 | ||||||||
\(663\) | −11.0557 | −0.429369 | ||||||||
\(664\) | 8.00000 | 0.310460 | ||||||||
\(665\) | 0.763932 | 0.0296240 | ||||||||
\(666\) | −1.81966 | −0.0705104 | ||||||||
\(667\) | −8.94427 | −0.346324 | ||||||||
\(668\) | 12.9443 | 0.500829 | ||||||||
\(669\) | −23.4164 | −0.905331 | ||||||||
\(670\) | −6.00000 | −0.231800 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.23607 | −0.0476824 | ||||||||
\(673\) | −11.8885 | −0.458270 | −0.229135 | − | 0.973395i | \(-0.573590\pi\) | ||||
−0.229135 | + | 0.973395i | \(0.573590\pi\) | |||||||
\(674\) | 28.8328 | 1.11060 | ||||||||
\(675\) | −5.52786 | −0.212768 | ||||||||
\(676\) | 7.00000 | 0.269231 | ||||||||
\(677\) | 23.5279 | 0.904249 | 0.452125 | − | 0.891955i | \(-0.350666\pi\) | ||||
0.452125 | + | 0.891955i | \(0.350666\pi\) | |||||||
\(678\) | −8.58359 | −0.329651 | ||||||||
\(679\) | 11.7082 | 0.449320 | ||||||||
\(680\) | 2.00000 | 0.0766965 | ||||||||
\(681\) | 1.88854 | 0.0723692 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −48.4721 | −1.85473 | −0.927367 | − | 0.374152i | \(-0.877934\pi\) | ||||
−0.927367 | + | 0.374152i | \(0.877934\pi\) | |||||||
\(684\) | 1.12461 | 0.0430006 | ||||||||
\(685\) | 15.8885 | 0.607070 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −14.2492 | −0.543642 | ||||||||
\(688\) | −8.00000 | −0.304997 | ||||||||
\(689\) | 23.4164 | 0.892094 | ||||||||
\(690\) | −3.41641 | −0.130060 | ||||||||
\(691\) | −36.3607 | −1.38323 | −0.691613 | − | 0.722269i | \(-0.743099\pi\) | ||||
−0.691613 | + | 0.722269i | \(0.743099\pi\) | |||||||
\(692\) | 3.52786 | 0.134109 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.18034 | −0.310298 | ||||||||
\(696\) | 4.00000 | 0.151620 | ||||||||
\(697\) | 11.4164 | 0.432427 | ||||||||
\(698\) | −24.9443 | −0.944155 | ||||||||
\(699\) | −3.63932 | −0.137652 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | 9.70820 | 0.366674 | 0.183337 | − | 0.983050i | \(-0.441310\pi\) | ||||
0.183337 | + | 0.983050i | \(0.441310\pi\) | |||||||
\(702\) | 24.7214 | 0.933048 | ||||||||
\(703\) | −0.944272 | −0.0356139 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.4721 | −0.394403 | ||||||||
\(706\) | −18.7639 | −0.706190 | ||||||||
\(707\) | −19.4164 | −0.730229 | ||||||||
\(708\) | −9.88854 | −0.371634 | ||||||||
\(709\) | 14.9443 | 0.561244 | 0.280622 | − | 0.959818i | \(-0.409459\pi\) | ||||
0.280622 | + | 0.959818i | \(0.409459\pi\) | |||||||
\(710\) | −8.00000 | −0.300235 | ||||||||
\(711\) | −1.12461 | −0.0421762 | ||||||||
\(712\) | 2.94427 | 0.110341 | ||||||||
\(713\) | 24.7214 | 0.925822 | ||||||||
\(714\) | −2.47214 | −0.0925174 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.52786 | 0.356073 | ||||||||
\(717\) | 8.94427 | 0.334030 | ||||||||
\(718\) | −12.1803 | −0.454566 | ||||||||
\(719\) | 12.3607 | 0.460976 | 0.230488 | − | 0.973075i | \(-0.425968\pi\) | ||||
0.230488 | + | 0.973075i | \(0.425968\pi\) | |||||||
\(720\) | −1.47214 | −0.0548633 | ||||||||
\(721\) | −14.0000 | −0.521387 | ||||||||
\(722\) | −18.4164 | −0.685388 | ||||||||
\(723\) | −21.1672 | −0.787216 | ||||||||
\(724\) | 14.0000 | 0.520306 | ||||||||
\(725\) | 3.23607 | 0.120185 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.3607 | 0.384256 | 0.192128 | − | 0.981370i | \(-0.438461\pi\) | ||||
0.192128 | + | 0.981370i | \(0.438461\pi\) | |||||||
\(728\) | 4.47214 | 0.165748 | ||||||||
\(729\) | 24.0557 | 0.890953 | ||||||||
\(730\) | 0.472136 | 0.0174745 | ||||||||
\(731\) | −16.0000 | −0.591781 | ||||||||
\(732\) | 6.83282 | 0.252548 | ||||||||
\(733\) | 36.2492 | 1.33890 | 0.669448 | − | 0.742859i | \(-0.266531\pi\) | ||||
0.669448 | + | 0.742859i | \(0.266531\pi\) | |||||||
\(734\) | 28.8328 | 1.06424 | ||||||||
\(735\) | 1.23607 | 0.0455931 | ||||||||
\(736\) | −2.76393 | −0.101880 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −8.40325 | −0.309328 | ||||||||
\(739\) | −44.7214 | −1.64510 | −0.822551 | − | 0.568691i | \(-0.807450\pi\) | ||||
−0.822551 | + | 0.568691i | \(0.807450\pi\) | |||||||
\(740\) | 1.23607 | 0.0454388 | ||||||||
\(741\) | 4.22291 | 0.155133 | ||||||||
\(742\) | 5.23607 | 0.192222 | ||||||||
\(743\) | 38.4721 | 1.41141 | 0.705703 | − | 0.708508i | \(-0.250631\pi\) | ||||
0.705703 | + | 0.708508i | \(0.250631\pi\) | |||||||
\(744\) | −11.0557 | −0.405323 | ||||||||
\(745\) | −5.70820 | −0.209132 | ||||||||
\(746\) | −38.3607 | −1.40448 | ||||||||
\(747\) | −11.7771 | −0.430901 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.0000 | 0.584627 | ||||||||
\(750\) | 1.23607 | 0.0451348 | ||||||||
\(751\) | 6.11146 | 0.223010 | 0.111505 | − | 0.993764i | \(-0.464433\pi\) | ||||
0.111505 | + | 0.993764i | \(0.464433\pi\) | |||||||
\(752\) | −8.47214 | −0.308947 | ||||||||
\(753\) | −6.83282 | −0.249002 | ||||||||
\(754\) | −14.4721 | −0.527044 | ||||||||
\(755\) | −6.29180 | −0.228982 | ||||||||
\(756\) | 5.52786 | 0.201046 | ||||||||
\(757\) | −43.1246 | −1.56739 | −0.783695 | − | 0.621145i | \(-0.786668\pi\) | ||||
−0.783695 | + | 0.621145i | \(0.786668\pi\) | |||||||
\(758\) | −4.94427 | −0.179584 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.763932 | −0.0277107 | ||||||||
\(761\) | −18.0689 | −0.654997 | −0.327498 | − | 0.944852i | \(-0.606206\pi\) | ||||
−0.327498 | + | 0.944852i | \(0.606206\pi\) | |||||||
\(762\) | −17.8885 | −0.648034 | ||||||||
\(763\) | −2.29180 | −0.0829686 | ||||||||
\(764\) | −2.47214 | −0.0894387 | ||||||||
\(765\) | −2.94427 | −0.106450 | ||||||||
\(766\) | −3.88854 | −0.140499 | ||||||||
\(767\) | 35.7771 | 1.29184 | ||||||||
\(768\) | 1.23607 | 0.0446028 | ||||||||
\(769\) | 35.0132 | 1.26261 | 0.631303 | − | 0.775536i | \(-0.282520\pi\) | ||||
0.631303 | + | 0.775536i | \(0.282520\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.6950 | 0.673286 | ||||||||
\(772\) | −9.05573 | −0.325923 | ||||||||
\(773\) | 29.7771 | 1.07101 | 0.535504 | − | 0.844533i | \(-0.320122\pi\) | ||||
0.535504 | + | 0.844533i | \(0.320122\pi\) | |||||||
\(774\) | 11.7771 | 0.423319 | ||||||||
\(775\) | −8.94427 | −0.321288 | ||||||||
\(776\) | −11.7082 | −0.420300 | ||||||||
\(777\) | −1.52786 | −0.0548118 | ||||||||
\(778\) | 38.3607 | 1.37530 | ||||||||
\(779\) | −4.36068 | −0.156238 | ||||||||
\(780\) | −5.52786 | −0.197929 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −5.52786 | −0.197676 | ||||||||
\(783\) | −17.8885 | −0.639284 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −16.4721 | −0.587916 | ||||||||
\(786\) | −20.0000 | −0.713376 | ||||||||
\(787\) | −46.8328 | −1.66941 | −0.834705 | − | 0.550698i | \(-0.814362\pi\) | ||||
−0.834705 | + | 0.550698i | \(0.814362\pi\) | |||||||
\(788\) | 5.41641 | 0.192952 | ||||||||
\(789\) | 20.2229 | 0.719955 | ||||||||
\(790\) | 0.763932 | 0.0271795 | ||||||||
\(791\) | 6.94427 | 0.246910 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.7214 | −0.877881 | ||||||||
\(794\) | 25.4164 | 0.901995 | ||||||||
\(795\) | −6.47214 | −0.229543 | ||||||||
\(796\) | −14.4721 | −0.512951 | ||||||||
\(797\) | −6.58359 | −0.233203 | −0.116601 | − | 0.993179i | \(-0.537200\pi\) | ||||
−0.116601 | + | 0.993179i | \(0.537200\pi\) | |||||||
\(798\) | 0.944272 | 0.0334269 | ||||||||
\(799\) | −16.9443 | −0.599445 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −4.33437 | −0.153147 | ||||||||
\(802\) | −3.52786 | −0.124573 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −7.41641 | −0.261557 | ||||||||
\(805\) | 2.76393 | 0.0974158 | ||||||||
\(806\) | 40.0000 | 1.40894 | ||||||||
\(807\) | −15.4164 | −0.542683 | ||||||||
\(808\) | 19.4164 | 0.683067 | ||||||||
\(809\) | −20.3607 | −0.715843 | −0.357922 | − | 0.933752i | \(-0.616515\pi\) | ||||
−0.357922 | + | 0.933752i | \(0.616515\pi\) | |||||||
\(810\) | −2.41641 | −0.0849039 | ||||||||
\(811\) | −4.18034 | −0.146792 | −0.0733958 | − | 0.997303i | \(-0.523384\pi\) | ||||
−0.0733958 | + | 0.997303i | \(0.523384\pi\) | |||||||
\(812\) | −3.23607 | −0.113564 | ||||||||
\(813\) | 8.00000 | 0.280572 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.94427 | −0.103133 | ||||||||
\(816\) | 2.47214 | 0.0865421 | ||||||||
\(817\) | 6.11146 | 0.213813 | ||||||||
\(818\) | 4.76393 | 0.166567 | ||||||||
\(819\) | −6.58359 | −0.230049 | ||||||||
\(820\) | 5.70820 | 0.199339 | ||||||||
\(821\) | −22.2918 | −0.777989 | −0.388995 | − | 0.921240i | \(-0.627178\pi\) | ||||
−0.388995 | + | 0.921240i | \(0.627178\pi\) | |||||||
\(822\) | 19.6393 | 0.685000 | ||||||||
\(823\) | 37.0132 | 1.29020 | 0.645099 | − | 0.764099i | \(-0.276816\pi\) | ||||
0.645099 | + | 0.764099i | \(0.276816\pi\) | |||||||
\(824\) | 14.0000 | 0.487713 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.00000 | 0.278356 | ||||||||
\(827\) | −39.7771 | −1.38318 | −0.691592 | − | 0.722288i | \(-0.743091\pi\) | ||||
−0.691592 | + | 0.722288i | \(0.743091\pi\) | |||||||
\(828\) | 4.06888 | 0.141403 | ||||||||
\(829\) | −7.52786 | −0.261454 | −0.130727 | − | 0.991418i | \(-0.541731\pi\) | ||||
−0.130727 | + | 0.991418i | \(0.541731\pi\) | |||||||
\(830\) | 8.00000 | 0.277684 | ||||||||
\(831\) | −14.2492 | −0.494300 | ||||||||
\(832\) | −4.47214 | −0.155043 | ||||||||
\(833\) | 2.00000 | 0.0692959 | ||||||||
\(834\) | −10.1115 | −0.350131 | ||||||||
\(835\) | 12.9443 | 0.447955 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 49.4427 | 1.70899 | ||||||||
\(838\) | 23.4164 | 0.808906 | ||||||||
\(839\) | 4.00000 | 0.138095 | 0.0690477 | − | 0.997613i | \(-0.478004\pi\) | ||||
0.0690477 | + | 0.997613i | \(0.478004\pi\) | |||||||
\(840\) | −1.23607 | −0.0426484 | ||||||||
\(841\) | −18.5279 | −0.638892 | ||||||||
\(842\) | 31.3050 | 1.07884 | ||||||||
\(843\) | 35.0557 | 1.20738 | ||||||||
\(844\) | 21.8885 | 0.753435 | ||||||||
\(845\) | 7.00000 | 0.240807 | ||||||||
\(846\) | 12.4721 | 0.428801 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.23607 | −0.179807 | ||||||||
\(849\) | −24.0000 | −0.823678 | ||||||||
\(850\) | 2.00000 | 0.0685994 | ||||||||
\(851\) | −3.41641 | −0.117113 | ||||||||
\(852\) | −9.88854 | −0.338776 | ||||||||
\(853\) | 22.5836 | 0.773247 | 0.386624 | − | 0.922238i | \(-0.373641\pi\) | ||||
0.386624 | + | 0.922238i | \(0.373641\pi\) | |||||||
\(854\) | −5.52786 | −0.189160 | ||||||||
\(855\) | 1.12461 | 0.0384609 | ||||||||
\(856\) | −16.0000 | −0.546869 | ||||||||
\(857\) | 8.47214 | 0.289403 | 0.144701 | − | 0.989475i | \(-0.453778\pi\) | ||||
0.144701 | + | 0.989475i | \(0.453778\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.63932 | 0.124172 | 0.0620860 | − | 0.998071i | \(-0.480225\pi\) | ||||
0.0620860 | + | 0.998071i | \(0.480225\pi\) | |||||||
\(860\) | −8.00000 | −0.272798 | ||||||||
\(861\) | −7.05573 | −0.240459 | ||||||||
\(862\) | 2.65248 | 0.0903437 | ||||||||
\(863\) | −14.7639 | −0.502570 | −0.251285 | − | 0.967913i | \(-0.580853\pi\) | ||||
−0.251285 | + | 0.967913i | \(0.580853\pi\) | |||||||
\(864\) | −5.52786 | −0.188062 | ||||||||
\(865\) | 3.52786 | 0.119951 | ||||||||
\(866\) | −5.23607 | −0.177929 | ||||||||
\(867\) | −16.0689 | −0.545728 | ||||||||
\(868\) | 8.94427 | 0.303588 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 4.00000 | 0.135613 | ||||||||
\(871\) | 26.8328 | 0.909195 | ||||||||
\(872\) | 2.29180 | 0.0776100 | ||||||||
\(873\) | 17.2361 | 0.583353 | ||||||||
\(874\) | 2.11146 | 0.0714211 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0.583592 | 0.0197178 | ||||||||
\(877\) | −27.3050 | −0.922023 | −0.461011 | − | 0.887394i | \(-0.652513\pi\) | ||||
−0.461011 | + | 0.887394i | \(0.652513\pi\) | |||||||
\(878\) | 19.4164 | 0.655272 | ||||||||
\(879\) | 0.583592 | 0.0196841 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.0557 | 0.709386 | 0.354693 | − | 0.934983i | \(-0.384585\pi\) | ||||
0.354693 | + | 0.934983i | \(0.384585\pi\) | |||||||
\(882\) | −1.47214 | −0.0495694 | ||||||||
\(883\) | −33.4164 | −1.12455 | −0.562276 | − | 0.826950i | \(-0.690074\pi\) | ||||
−0.562276 | + | 0.826950i | \(0.690074\pi\) | |||||||
\(884\) | −8.94427 | −0.300828 | ||||||||
\(885\) | −9.88854 | −0.332400 | ||||||||
\(886\) | −2.94427 | −0.0989147 | ||||||||
\(887\) | 41.8885 | 1.40648 | 0.703240 | − | 0.710953i | \(-0.251736\pi\) | ||||
0.703240 | + | 0.710953i | \(0.251736\pi\) | |||||||
\(888\) | 1.52786 | 0.0512718 | ||||||||
\(889\) | 14.4721 | 0.485380 | ||||||||
\(890\) | 2.94427 | 0.0986922 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.9443 | −0.634301 | ||||||||
\(893\) | 6.47214 | 0.216582 | ||||||||
\(894\) | −7.05573 | −0.235979 | ||||||||
\(895\) | 9.52786 | 0.318481 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 15.2786 | 0.510139 | ||||||||
\(898\) | −18.3607 | −0.612704 | ||||||||
\(899\) | −28.9443 | −0.965346 | ||||||||
\(900\) | −1.47214 | −0.0490712 | ||||||||
\(901\) | −10.4721 | −0.348877 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.88854 | 0.329070 | ||||||||
\(904\) | −6.94427 | −0.230963 | ||||||||
\(905\) | 14.0000 | 0.465376 | ||||||||
\(906\) | −7.77709 | −0.258376 | ||||||||
\(907\) | 24.4721 | 0.812584 | 0.406292 | − | 0.913743i | \(-0.366822\pi\) | ||||
0.406292 | + | 0.913743i | \(0.366822\pi\) | |||||||
\(908\) | 1.52786 | 0.0507039 | ||||||||
\(909\) | −28.5836 | −0.948058 | ||||||||
\(910\) | 4.47214 | 0.148250 | ||||||||
\(911\) | −23.4164 | −0.775820 | −0.387910 | − | 0.921697i | \(-0.626803\pi\) | ||||
−0.387910 | + | 0.921697i | \(0.626803\pi\) | |||||||
\(912\) | −0.944272 | −0.0312680 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 13.0557 | 0.431845 | ||||||||
\(915\) | 6.83282 | 0.225886 | ||||||||
\(916\) | −11.5279 | −0.380891 | ||||||||
\(917\) | 16.1803 | 0.534322 | ||||||||
\(918\) | −11.0557 | −0.364893 | ||||||||
\(919\) | 15.8197 | 0.521842 | 0.260921 | − | 0.965360i | \(-0.415974\pi\) | ||||
0.260921 | + | 0.965360i | \(0.415974\pi\) | |||||||
\(920\) | −2.76393 | −0.0911241 | ||||||||
\(921\) | 11.7771 | 0.388068 | ||||||||
\(922\) | 20.9443 | 0.689763 | ||||||||
\(923\) | 35.7771 | 1.17762 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.23607 | 0.0406417 | ||||||||
\(926\) | −15.7082 | −0.516204 | ||||||||
\(927\) | −20.6099 | −0.676918 | ||||||||
\(928\) | 3.23607 | 0.106229 | ||||||||
\(929\) | −14.3607 | −0.471159 | −0.235579 | − | 0.971855i | \(-0.575699\pi\) | ||||
−0.235579 | + | 0.971855i | \(0.575699\pi\) | |||||||
\(930\) | −11.0557 | −0.362532 | ||||||||
\(931\) | −0.763932 | −0.0250369 | ||||||||
\(932\) | −2.94427 | −0.0964428 | ||||||||
\(933\) | 38.1115 | 1.24771 | ||||||||
\(934\) | 13.8197 | 0.452193 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.58359 | 0.215191 | ||||||||
\(937\) | −13.0557 | −0.426512 | −0.213256 | − | 0.976996i | \(-0.568407\pi\) | ||||
−0.213256 | + | 0.976996i | \(0.568407\pi\) | |||||||
\(938\) | 6.00000 | 0.195907 | ||||||||
\(939\) | −25.5279 | −0.833070 | ||||||||
\(940\) | −8.47214 | −0.276331 | ||||||||
\(941\) | −26.2492 | −0.855700 | −0.427850 | − | 0.903850i | \(-0.640729\pi\) | ||||
−0.427850 | + | 0.903850i | \(0.640729\pi\) | |||||||
\(942\) | −20.3607 | −0.663387 | ||||||||
\(943\) | −15.7771 | −0.513773 | ||||||||
\(944\) | −8.00000 | −0.260378 | ||||||||
\(945\) | 5.52786 | 0.179821 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.5279 | 0.374605 | 0.187303 | − | 0.982302i | \(-0.440025\pi\) | ||||
0.187303 | + | 0.982302i | \(0.440025\pi\) | |||||||
\(948\) | 0.944272 | 0.0306685 | ||||||||
\(949\) | −2.11146 | −0.0685408 | ||||||||
\(950\) | −0.763932 | −0.0247852 | ||||||||
\(951\) | 2.69505 | 0.0873929 | ||||||||
\(952\) | −2.00000 | −0.0648204 | ||||||||
\(953\) | 31.8885 | 1.03297 | 0.516486 | − | 0.856296i | \(-0.327240\pi\) | ||||
0.516486 | + | 0.856296i | \(0.327240\pi\) | |||||||
\(954\) | 7.70820 | 0.249562 | ||||||||
\(955\) | −2.47214 | −0.0799964 | ||||||||
\(956\) | 7.23607 | 0.234031 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.88854 | −0.190250 | ||||||||
\(959\) | −15.8885 | −0.513068 | ||||||||
\(960\) | 1.23607 | 0.0398939 | ||||||||
\(961\) | 49.0000 | 1.58065 | ||||||||
\(962\) | −5.52786 | −0.178225 | ||||||||
\(963\) | 23.5542 | 0.759023 | ||||||||
\(964\) | −17.1246 | −0.551547 | ||||||||
\(965\) | −9.05573 | −0.291514 | ||||||||
\(966\) | 3.41641 | 0.109921 | ||||||||
\(967\) | 29.3050 | 0.942384 | 0.471192 | − | 0.882031i | \(-0.343824\pi\) | ||||
0.471192 | + | 0.882031i | \(0.343824\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.88854 | −0.0606688 | ||||||||
\(970\) | −11.7082 | −0.375928 | ||||||||
\(971\) | 30.8328 | 0.989472 | 0.494736 | − | 0.869043i | \(-0.335265\pi\) | ||||
0.494736 | + | 0.869043i | \(0.335265\pi\) | |||||||
\(972\) | 13.5967 | 0.436116 | ||||||||
\(973\) | 8.18034 | 0.262250 | ||||||||
\(974\) | 24.0689 | 0.771217 | ||||||||
\(975\) | −5.52786 | −0.177033 | ||||||||
\(976\) | 5.52786 | 0.176943 | ||||||||
\(977\) | 52.8328 | 1.69027 | 0.845136 | − | 0.534552i | \(-0.179520\pi\) | ||||
0.845136 | + | 0.534552i | \(0.179520\pi\) | |||||||
\(978\) | −3.63932 | −0.116373 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | −3.37384 | −0.107718 | ||||||||
\(982\) | −8.00000 | −0.255290 | ||||||||
\(983\) | −30.9443 | −0.986969 | −0.493484 | − | 0.869755i | \(-0.664277\pi\) | ||||
−0.493484 | + | 0.869755i | \(0.664277\pi\) | |||||||
\(984\) | 7.05573 | 0.224928 | ||||||||
\(985\) | 5.41641 | 0.172581 | ||||||||
\(986\) | 6.47214 | 0.206115 | ||||||||
\(987\) | 10.4721 | 0.333332 | ||||||||
\(988\) | 3.41641 | 0.108690 | ||||||||
\(989\) | 22.1115 | 0.703103 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.3050 | −0.803838 | −0.401919 | − | 0.915675i | \(-0.631657\pi\) | ||||
−0.401919 | + | 0.915675i | \(0.631657\pi\) | |||||||
\(992\) | −8.94427 | −0.283981 | ||||||||
\(993\) | −19.0557 | −0.604715 | ||||||||
\(994\) | 8.00000 | 0.253745 | ||||||||
\(995\) | −14.4721 | −0.458798 | ||||||||
\(996\) | 9.88854 | 0.313331 | ||||||||
\(997\) | 40.4721 | 1.28177 | 0.640883 | − | 0.767639i | \(-0.278568\pi\) | ||||
0.640883 | + | 0.767639i | \(0.278568\pi\) | |||||||
\(998\) | 33.3050 | 1.05425 | ||||||||
\(999\) | −6.83282 | −0.216181 |
(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 | 8470.2.a.bv.1.2 | yes | 2 | |
11.10 | odd | 2 | 8470.2.a.bj.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.bj.1.2 | ✓ | 2 | 11.10 | odd | 2 | ||
8470.2.a.bv.1.2 | yes | 2 | 1.1 | even | 1 | trivial |