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 | 1.1 | ||
Root | \(1.61803\) 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 | ||||||||
\(3\) | −3.23607 | −1.86834 | −0.934172 | − | 0.356822i | \(-0.883860\pi\) | ||||
−0.934172 | + | 0.356822i | \(0.883860\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 3.23607 | 1.32112 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.47214 | 2.49071 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −3.23607 | −0.934172 | ||||||||
\(13\) | −4.47214 | −1.24035 | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −3.23607 | −0.835549 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | −7.47214 | −1.76120 | ||||||||
\(19\) | 5.23607 | 1.20124 | 0.600618 | − | 0.799536i | \(-0.294921\pi\) | ||||
0.600618 | + | 0.799536i | \(0.294921\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −3.23607 | −0.706168 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.23607 | −1.50882 | −0.754412 | − | 0.656401i | \(-0.772078\pi\) | ||||
−0.754412 | + | 0.656401i | \(0.772078\pi\) | |||||||
\(24\) | 3.23607 | 0.660560 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.47214 | 0.877058 | ||||||||
\(27\) | −14.4721 | −2.78516 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 1.23607 | 0.229532 | 0.114766 | − | 0.993393i | \(-0.463388\pi\) | ||||
0.114766 | + | 0.993393i | \(0.463388\pi\) | |||||||
\(30\) | 3.23607 | 0.590822 | ||||||||
\(31\) | 8.94427 | 1.60644 | 0.803219 | − | 0.595683i | \(-0.203119\pi\) | ||||
0.803219 | + | 0.595683i | \(0.203119\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 7.47214 | 1.24536 | ||||||||
\(37\) | −3.23607 | −0.532006 | −0.266003 | − | 0.963972i | \(-0.585703\pi\) | ||||
−0.266003 | + | 0.963972i | \(0.585703\pi\) | |||||||
\(38\) | −5.23607 | −0.849402 | ||||||||
\(39\) | 14.4721 | 2.31740 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 7.70820 | 1.20382 | 0.601910 | − | 0.798564i | \(-0.294407\pi\) | ||||
0.601910 | + | 0.798564i | \(0.294407\pi\) | |||||||
\(42\) | 3.23607 | 0.499336 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.47214 | 1.11388 | ||||||||
\(46\) | 7.23607 | 1.06690 | ||||||||
\(47\) | 0.472136 | 0.0688681 | 0.0344341 | − | 0.999407i | \(-0.489037\pi\) | ||||
0.0344341 | + | 0.999407i | \(0.489037\pi\) | |||||||
\(48\) | −3.23607 | −0.467086 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 6.47214 | 0.906280 | ||||||||
\(52\) | −4.47214 | −0.620174 | ||||||||
\(53\) | −0.763932 | −0.104934 | −0.0524671 | − | 0.998623i | \(-0.516708\pi\) | ||||
−0.0524671 | + | 0.998623i | \(0.516708\pi\) | |||||||
\(54\) | 14.4721 | 1.96941 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −16.9443 | −2.24432 | ||||||||
\(58\) | −1.23607 | −0.162304 | ||||||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | −3.23607 | −0.417775 | ||||||||
\(61\) | −14.4721 | −1.85297 | −0.926484 | − | 0.376335i | \(-0.877184\pi\) | ||||
−0.926484 | + | 0.376335i | \(0.877184\pi\) | |||||||
\(62\) | −8.94427 | −1.13592 | ||||||||
\(63\) | 7.47214 | 0.941401 | ||||||||
\(64\) | 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 | ||||||||
\(69\) | 23.4164 | 2.81900 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | −7.47214 | −0.880600 | ||||||||
\(73\) | 8.47214 | 0.991589 | 0.495794 | − | 0.868440i | \(-0.334877\pi\) | ||||
0.495794 | + | 0.868440i | \(0.334877\pi\) | |||||||
\(74\) | 3.23607 | 0.376185 | ||||||||
\(75\) | −3.23607 | −0.373669 | ||||||||
\(76\) | 5.23607 | 0.600618 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −14.4721 | −1.63865 | ||||||||
\(79\) | −5.23607 | −0.589104 | −0.294552 | − | 0.955636i | \(-0.595170\pi\) | ||||
−0.294552 | + | 0.955636i | \(0.595170\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 24.4164 | 2.71293 | ||||||||
\(82\) | −7.70820 | −0.851229 | ||||||||
\(83\) | −8.00000 | −0.878114 | −0.439057 | − | 0.898459i | \(-0.644687\pi\) | ||||
−0.439057 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(84\) | −3.23607 | −0.353084 | ||||||||
\(85\) | −2.00000 | −0.216930 | ||||||||
\(86\) | −8.00000 | −0.862662 | ||||||||
\(87\) | −4.00000 | −0.428845 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.9443 | −1.58409 | −0.792045 | − | 0.610463i | \(-0.790983\pi\) | ||||
−0.792045 | + | 0.610463i | \(0.790983\pi\) | |||||||
\(90\) | −7.47214 | −0.787632 | ||||||||
\(91\) | −4.47214 | −0.468807 | ||||||||
\(92\) | −7.23607 | −0.754412 | ||||||||
\(93\) | −28.9443 | −3.00138 | ||||||||
\(94\) | −0.472136 | −0.0486971 | ||||||||
\(95\) | 5.23607 | 0.537209 | ||||||||
\(96\) | 3.23607 | 0.330280 | ||||||||
\(97\) | 1.70820 | 0.173442 | 0.0867209 | − | 0.996233i | \(-0.472361\pi\) | ||||
0.0867209 | + | 0.996233i | \(0.472361\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 7.41641 | 0.737960 | 0.368980 | − | 0.929437i | \(-0.379707\pi\) | ||||
0.368980 | + | 0.929437i | \(0.379707\pi\) | |||||||
\(102\) | −6.47214 | −0.640837 | ||||||||
\(103\) | 14.0000 | 1.37946 | 0.689730 | − | 0.724066i | \(-0.257729\pi\) | ||||
0.689730 | + | 0.724066i | \(0.257729\pi\) | |||||||
\(104\) | 4.47214 | 0.438529 | ||||||||
\(105\) | −3.23607 | −0.315808 | ||||||||
\(106\) | 0.763932 | 0.0741996 | ||||||||
\(107\) | 16.0000 | 1.54678 | 0.773389 | − | 0.633932i | \(-0.218560\pi\) | ||||
0.773389 | + | 0.633932i | \(0.218560\pi\) | |||||||
\(108\) | −14.4721 | −1.39258 | ||||||||
\(109\) | −15.7082 | −1.50457 | −0.752287 | − | 0.658836i | \(-0.771049\pi\) | ||||
−0.752287 | + | 0.658836i | \(0.771049\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.4721 | 0.993971 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 10.9443 | 1.02955 | 0.514775 | − | 0.857325i | \(-0.327875\pi\) | ||||
0.514775 | + | 0.857325i | \(0.327875\pi\) | |||||||
\(114\) | 16.9443 | 1.58698 | ||||||||
\(115\) | −7.23607 | −0.674767 | ||||||||
\(116\) | 1.23607 | 0.114766 | ||||||||
\(117\) | −33.4164 | −3.08935 | ||||||||
\(118\) | 8.00000 | 0.736460 | ||||||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | 3.23607 | 0.295411 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 14.4721 | 1.31025 | ||||||||
\(123\) | −24.9443 | −2.24915 | ||||||||
\(124\) | 8.94427 | 0.803219 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −7.47214 | −0.665671 | ||||||||
\(127\) | 5.52786 | 0.490519 | 0.245259 | − | 0.969458i | \(-0.421127\pi\) | ||||
0.245259 | + | 0.969458i | \(0.421127\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −25.8885 | −2.27936 | ||||||||
\(130\) | 4.47214 | 0.392232 | ||||||||
\(131\) | −6.18034 | −0.539979 | −0.269989 | − | 0.962863i | \(-0.587020\pi\) | ||||
−0.269989 | + | 0.962863i | \(0.587020\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.23607 | 0.454025 | ||||||||
\(134\) | 6.00000 | 0.518321 | ||||||||
\(135\) | −14.4721 | −1.24556 | ||||||||
\(136\) | 2.00000 | 0.171499 | ||||||||
\(137\) | −19.8885 | −1.69919 | −0.849596 | − | 0.527433i | \(-0.823154\pi\) | ||||
−0.849596 | + | 0.527433i | \(0.823154\pi\) | |||||||
\(138\) | −23.4164 | −1.99334 | ||||||||
\(139\) | −14.1803 | −1.20276 | −0.601380 | − | 0.798963i | \(-0.705382\pi\) | ||||
−0.601380 | + | 0.798963i | \(0.705382\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | −1.52786 | −0.128669 | ||||||||
\(142\) | 8.00000 | 0.671345 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 7.47214 | 0.622678 | ||||||||
\(145\) | 1.23607 | 0.102650 | ||||||||
\(146\) | −8.47214 | −0.701159 | ||||||||
\(147\) | −3.23607 | −0.266906 | ||||||||
\(148\) | −3.23607 | −0.266003 | ||||||||
\(149\) | −7.70820 | −0.631481 | −0.315740 | − | 0.948846i | \(-0.602253\pi\) | ||||
−0.315740 | + | 0.948846i | \(0.602253\pi\) | |||||||
\(150\) | 3.23607 | 0.264224 | ||||||||
\(151\) | 19.7082 | 1.60383 | 0.801915 | − | 0.597438i | \(-0.203814\pi\) | ||||
0.801915 | + | 0.597438i | \(0.203814\pi\) | |||||||
\(152\) | −5.23607 | −0.424701 | ||||||||
\(153\) | −14.9443 | −1.20817 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.94427 | 0.718421 | ||||||||
\(156\) | 14.4721 | 1.15870 | ||||||||
\(157\) | −7.52786 | −0.600789 | −0.300394 | − | 0.953815i | \(-0.597118\pi\) | ||||
−0.300394 | + | 0.953815i | \(0.597118\pi\) | |||||||
\(158\) | 5.23607 | 0.416559 | ||||||||
\(159\) | 2.47214 | 0.196053 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −7.23607 | −0.570282 | ||||||||
\(162\) | −24.4164 | −1.91833 | ||||||||
\(163\) | 14.9443 | 1.17053 | 0.585263 | − | 0.810844i | \(-0.300991\pi\) | ||||
0.585263 | + | 0.810844i | \(0.300991\pi\) | |||||||
\(164\) | 7.70820 | 0.601910 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.00000 | 0.620920 | ||||||||
\(167\) | 4.94427 | 0.382599 | 0.191300 | − | 0.981532i | \(-0.438730\pi\) | ||||
0.191300 | + | 0.981532i | \(0.438730\pi\) | |||||||
\(168\) | 3.23607 | 0.249668 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 2.00000 | 0.153393 | ||||||||
\(171\) | 39.1246 | 2.99193 | ||||||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | −12.4721 | −0.948239 | −0.474119 | − | 0.880461i | \(-0.657234\pi\) | ||||
−0.474119 | + | 0.880461i | \(0.657234\pi\) | |||||||
\(174\) | 4.00000 | 0.303239 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 25.8885 | 1.94590 | ||||||||
\(178\) | 14.9443 | 1.12012 | ||||||||
\(179\) | 18.4721 | 1.38067 | 0.690336 | − | 0.723489i | \(-0.257463\pi\) | ||||
0.690336 | + | 0.723489i | \(0.257463\pi\) | |||||||
\(180\) | 7.47214 | 0.556940 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 4.47214 | 0.331497 | ||||||||
\(183\) | 46.8328 | 3.46198 | ||||||||
\(184\) | 7.23607 | 0.533450 | ||||||||
\(185\) | −3.23607 | −0.237920 | ||||||||
\(186\) | 28.9443 | 2.12230 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.472136 | 0.0344341 | ||||||||
\(189\) | −14.4721 | −1.05269 | ||||||||
\(190\) | −5.23607 | −0.379864 | ||||||||
\(191\) | 6.47214 | 0.468307 | 0.234154 | − | 0.972200i | \(-0.424768\pi\) | ||||
0.234154 | + | 0.972200i | \(0.424768\pi\) | |||||||
\(192\) | −3.23607 | −0.233543 | ||||||||
\(193\) | 26.9443 | 1.93949 | 0.969746 | − | 0.244118i | \(-0.0784984\pi\) | ||||
0.969746 | + | 0.244118i | \(0.0784984\pi\) | |||||||
\(194\) | −1.70820 | −0.122642 | ||||||||
\(195\) | 14.4721 | 1.03637 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 21.4164 | 1.52586 | 0.762928 | − | 0.646484i | \(-0.223761\pi\) | ||||
0.762928 | + | 0.646484i | \(0.223761\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.52786 | −0.391860 | −0.195930 | − | 0.980618i | \(-0.562773\pi\) | ||||
−0.195930 | + | 0.980618i | \(0.562773\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 19.4164 | 1.36953 | ||||||||
\(202\) | −7.41641 | −0.521817 | ||||||||
\(203\) | 1.23607 | 0.0867550 | ||||||||
\(204\) | 6.47214 | 0.453140 | ||||||||
\(205\) | 7.70820 | 0.538364 | ||||||||
\(206\) | −14.0000 | −0.975426 | ||||||||
\(207\) | −54.0689 | −3.75805 | ||||||||
\(208\) | −4.47214 | −0.310087 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.23607 | 0.223310 | ||||||||
\(211\) | 13.8885 | 0.956127 | 0.478063 | − | 0.878325i | \(-0.341339\pi\) | ||||
0.478063 | + | 0.878325i | \(0.341339\pi\) | |||||||
\(212\) | −0.763932 | −0.0524671 | ||||||||
\(213\) | 25.8885 | 1.77385 | ||||||||
\(214\) | −16.0000 | −1.09374 | ||||||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | 14.4721 | 0.984704 | ||||||||
\(217\) | 8.94427 | 0.607177 | ||||||||
\(218\) | 15.7082 | 1.06389 | ||||||||
\(219\) | −27.4164 | −1.85263 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.94427 | 0.601657 | ||||||||
\(222\) | −10.4721 | −0.702844 | ||||||||
\(223\) | −1.05573 | −0.0706968 | −0.0353484 | − | 0.999375i | \(-0.511254\pi\) | ||||
−0.0353484 | + | 0.999375i | \(0.511254\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 7.47214 | 0.498142 | ||||||||
\(226\) | −10.9443 | −0.728002 | ||||||||
\(227\) | −10.4721 | −0.695060 | −0.347530 | − | 0.937669i | \(-0.612980\pi\) | ||||
−0.347530 | + | 0.937669i | \(0.612980\pi\) | |||||||
\(228\) | −16.9443 | −1.12216 | ||||||||
\(229\) | −20.4721 | −1.35284 | −0.676418 | − | 0.736518i | \(-0.736469\pi\) | ||||
−0.676418 | + | 0.736518i | \(0.736469\pi\) | |||||||
\(230\) | 7.23607 | 0.477132 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.23607 | −0.0811518 | ||||||||
\(233\) | −14.9443 | −0.979032 | −0.489516 | − | 0.871994i | \(-0.662826\pi\) | ||||
−0.489516 | + | 0.871994i | \(0.662826\pi\) | |||||||
\(234\) | 33.4164 | 2.18450 | ||||||||
\(235\) | 0.472136 | 0.0307988 | ||||||||
\(236\) | −8.00000 | −0.520756 | ||||||||
\(237\) | 16.9443 | 1.10065 | ||||||||
\(238\) | 2.00000 | 0.129641 | ||||||||
\(239\) | −2.76393 | −0.178784 | −0.0893920 | − | 0.995997i | \(-0.528492\pi\) | ||||
−0.0893920 | + | 0.995997i | \(0.528492\pi\) | |||||||
\(240\) | −3.23607 | −0.208887 | ||||||||
\(241\) | −23.1246 | −1.48959 | −0.744794 | − | 0.667295i | \(-0.767452\pi\) | ||||
−0.744794 | + | 0.667295i | \(0.767452\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −35.5967 | −2.28353 | ||||||||
\(244\) | −14.4721 | −0.926484 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 24.9443 | 1.59039 | ||||||||
\(247\) | −23.4164 | −1.48995 | ||||||||
\(248\) | −8.94427 | −0.567962 | ||||||||
\(249\) | 25.8885 | 1.64062 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −14.4721 | −0.913473 | −0.456737 | − | 0.889602i | \(-0.650982\pi\) | ||||
−0.456737 | + | 0.889602i | \(0.650982\pi\) | |||||||
\(252\) | 7.47214 | 0.470700 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −5.52786 | −0.346849 | ||||||||
\(255\) | 6.47214 | 0.405301 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −25.1246 | −1.56723 | −0.783615 | − | 0.621247i | \(-0.786627\pi\) | ||||
−0.783615 | + | 0.621247i | \(0.786627\pi\) | |||||||
\(258\) | 25.8885 | 1.61175 | ||||||||
\(259\) | −3.23607 | −0.201079 | ||||||||
\(260\) | −4.47214 | −0.277350 | ||||||||
\(261\) | 9.23607 | 0.571698 | ||||||||
\(262\) | 6.18034 | 0.381823 | ||||||||
\(263\) | 28.3607 | 1.74879 | 0.874397 | − | 0.485211i | \(-0.161257\pi\) | ||||
0.874397 | + | 0.485211i | \(0.161257\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.763932 | −0.0469280 | ||||||||
\(266\) | −5.23607 | −0.321044 | ||||||||
\(267\) | 48.3607 | 2.95963 | ||||||||
\(268\) | −6.00000 | −0.366508 | ||||||||
\(269\) | −3.52786 | −0.215098 | −0.107549 | − | 0.994200i | \(-0.534300\pi\) | ||||
−0.107549 | + | 0.994200i | \(0.534300\pi\) | |||||||
\(270\) | 14.4721 | 0.880746 | ||||||||
\(271\) | 2.47214 | 0.150172 | 0.0750858 | − | 0.997177i | \(-0.476077\pi\) | ||||
0.0750858 | + | 0.997177i | \(0.476077\pi\) | |||||||
\(272\) | −2.00000 | −0.121268 | ||||||||
\(273\) | 14.4721 | 0.875894 | ||||||||
\(274\) | 19.8885 | 1.20151 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 23.4164 | 1.40950 | ||||||||
\(277\) | 20.4721 | 1.23005 | 0.615026 | − | 0.788507i | \(-0.289146\pi\) | ||||
0.615026 | + | 0.788507i | \(0.289146\pi\) | |||||||
\(278\) | 14.1803 | 0.850480 | ||||||||
\(279\) | 66.8328 | 4.00118 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 16.3607 | 0.975996 | 0.487998 | − | 0.872845i | \(-0.337727\pi\) | ||||
0.487998 | + | 0.872845i | \(0.337727\pi\) | |||||||
\(282\) | 1.52786 | 0.0909830 | ||||||||
\(283\) | −7.41641 | −0.440860 | −0.220430 | − | 0.975403i | \(-0.570746\pi\) | ||||
−0.220430 | + | 0.975403i | \(0.570746\pi\) | |||||||
\(284\) | −8.00000 | −0.474713 | ||||||||
\(285\) | −16.9443 | −1.00369 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.70820 | 0.455001 | ||||||||
\(288\) | −7.47214 | −0.440300 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | −1.23607 | −0.0725844 | ||||||||
\(291\) | −5.52786 | −0.324049 | ||||||||
\(292\) | 8.47214 | 0.495794 | ||||||||
\(293\) | 8.47214 | 0.494947 | 0.247474 | − | 0.968895i | \(-0.420400\pi\) | ||||
0.247474 | + | 0.968895i | \(0.420400\pi\) | |||||||
\(294\) | 3.23607 | 0.188731 | ||||||||
\(295\) | −8.00000 | −0.465778 | ||||||||
\(296\) | 3.23607 | 0.188093 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.70820 | 0.446524 | ||||||||
\(299\) | 32.3607 | 1.87147 | ||||||||
\(300\) | −3.23607 | −0.186834 | ||||||||
\(301\) | 8.00000 | 0.461112 | ||||||||
\(302\) | −19.7082 | −1.13408 | ||||||||
\(303\) | −24.0000 | −1.37876 | ||||||||
\(304\) | 5.23607 | 0.300309 | ||||||||
\(305\) | −14.4721 | −0.828672 | ||||||||
\(306\) | 14.9443 | 0.854307 | ||||||||
\(307\) | −18.4721 | −1.05426 | −0.527130 | − | 0.849785i | \(-0.676732\pi\) | ||||
−0.527130 | + | 0.849785i | \(0.676732\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −45.3050 | −2.57731 | ||||||||
\(310\) | −8.94427 | −0.508001 | ||||||||
\(311\) | −22.8328 | −1.29473 | −0.647365 | − | 0.762180i | \(-0.724129\pi\) | ||||
−0.647365 | + | 0.762180i | \(0.724129\pi\) | |||||||
\(312\) | −14.4721 | −0.819323 | ||||||||
\(313\) | 10.6525 | 0.602114 | 0.301057 | − | 0.953606i | \(-0.402661\pi\) | ||||
0.301057 | + | 0.953606i | \(0.402661\pi\) | |||||||
\(314\) | 7.52786 | 0.424822 | ||||||||
\(315\) | 7.47214 | 0.421007 | ||||||||
\(316\) | −5.23607 | −0.294552 | ||||||||
\(317\) | −20.1803 | −1.13344 | −0.566720 | − | 0.823910i | \(-0.691788\pi\) | ||||
−0.566720 | + | 0.823910i | \(0.691788\pi\) | |||||||
\(318\) | −2.47214 | −0.138631 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −51.7771 | −2.88992 | ||||||||
\(322\) | 7.23607 | 0.403250 | ||||||||
\(323\) | −10.4721 | −0.582685 | ||||||||
\(324\) | 24.4164 | 1.35647 | ||||||||
\(325\) | −4.47214 | −0.248069 | ||||||||
\(326\) | −14.9443 | −0.827687 | ||||||||
\(327\) | 50.8328 | 2.81106 | ||||||||
\(328\) | −7.70820 | −0.425614 | ||||||||
\(329\) | 0.472136 | 0.0260297 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.4164 | 0.627503 | 0.313751 | − | 0.949505i | \(-0.398414\pi\) | ||||
0.313751 | + | 0.949505i | \(0.398414\pi\) | |||||||
\(332\) | −8.00000 | −0.439057 | ||||||||
\(333\) | −24.1803 | −1.32507 | ||||||||
\(334\) | −4.94427 | −0.270539 | ||||||||
\(335\) | −6.00000 | −0.327815 | ||||||||
\(336\) | −3.23607 | −0.176542 | ||||||||
\(337\) | 24.8328 | 1.35273 | 0.676365 | − | 0.736567i | \(-0.263554\pi\) | ||||
0.676365 | + | 0.736567i | \(0.263554\pi\) | |||||||
\(338\) | −7.00000 | −0.380750 | ||||||||
\(339\) | −35.4164 | −1.92356 | ||||||||
\(340\) | −2.00000 | −0.108465 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −39.1246 | −2.11562 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | 23.4164 | 1.26070 | ||||||||
\(346\) | 12.4721 | 0.670506 | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | −4.00000 | −0.214423 | ||||||||
\(349\) | 7.05573 | 0.377684 | 0.188842 | − | 0.982007i | \(-0.439527\pi\) | ||||
0.188842 | + | 0.982007i | \(0.439527\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 64.7214 | 3.45457 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.2361 | −1.23673 | −0.618366 | − | 0.785891i | \(-0.712205\pi\) | ||||
−0.618366 | + | 0.785891i | \(0.712205\pi\) | |||||||
\(354\) | −25.8885 | −1.37596 | ||||||||
\(355\) | −8.00000 | −0.424596 | ||||||||
\(356\) | −14.9443 | −0.792045 | ||||||||
\(357\) | 6.47214 | 0.342542 | ||||||||
\(358\) | −18.4721 | −0.976283 | ||||||||
\(359\) | −10.1803 | −0.537298 | −0.268649 | − | 0.963238i | \(-0.586577\pi\) | ||||
−0.268649 | + | 0.963238i | \(0.586577\pi\) | |||||||
\(360\) | −7.47214 | −0.393816 | ||||||||
\(361\) | 8.41641 | 0.442969 | ||||||||
\(362\) | −14.0000 | −0.735824 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.47214 | −0.234404 | ||||||||
\(365\) | 8.47214 | 0.443452 | ||||||||
\(366\) | −46.8328 | −2.44799 | ||||||||
\(367\) | −24.8328 | −1.29626 | −0.648131 | − | 0.761529i | \(-0.724449\pi\) | ||||
−0.648131 | + | 0.761529i | \(0.724449\pi\) | |||||||
\(368\) | −7.23607 | −0.377206 | ||||||||
\(369\) | 57.5967 | 2.99837 | ||||||||
\(370\) | 3.23607 | 0.168235 | ||||||||
\(371\) | −0.763932 | −0.0396614 | ||||||||
\(372\) | −28.9443 | −1.50069 | ||||||||
\(373\) | −6.36068 | −0.329344 | −0.164672 | − | 0.986348i | \(-0.552656\pi\) | ||||
−0.164672 | + | 0.986348i | \(0.552656\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.23607 | −0.167110 | ||||||||
\(376\) | −0.472136 | −0.0243486 | ||||||||
\(377\) | −5.52786 | −0.284699 | ||||||||
\(378\) | 14.4721 | 0.744366 | ||||||||
\(379\) | 12.9443 | 0.664903 | 0.332451 | − | 0.943120i | \(-0.392124\pi\) | ||||
0.332451 | + | 0.943120i | \(0.392124\pi\) | |||||||
\(380\) | 5.23607 | 0.268605 | ||||||||
\(381\) | −17.8885 | −0.916458 | ||||||||
\(382\) | −6.47214 | −0.331143 | ||||||||
\(383\) | 31.8885 | 1.62943 | 0.814714 | − | 0.579863i | \(-0.196894\pi\) | ||||
0.814714 | + | 0.579863i | \(0.196894\pi\) | |||||||
\(384\) | 3.23607 | 0.165140 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −26.9443 | −1.37143 | ||||||||
\(387\) | 59.7771 | 3.03864 | ||||||||
\(388\) | 1.70820 | 0.0867209 | ||||||||
\(389\) | −6.36068 | −0.322499 | −0.161250 | − | 0.986914i | \(-0.551552\pi\) | ||||
−0.161250 | + | 0.986914i | \(0.551552\pi\) | |||||||
\(390\) | −14.4721 | −0.732825 | ||||||||
\(391\) | 14.4721 | 0.731887 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 20.0000 | 1.00887 | ||||||||
\(394\) | −21.4164 | −1.07894 | ||||||||
\(395\) | −5.23607 | −0.263455 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.41641 | −0.0710875 | −0.0355437 | − | 0.999368i | \(-0.511316\pi\) | ||||
−0.0355437 | + | 0.999368i | \(0.511316\pi\) | |||||||
\(398\) | 5.52786 | 0.277087 | ||||||||
\(399\) | −16.9443 | −0.848275 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −12.4721 | −0.622829 | −0.311414 | − | 0.950274i | \(-0.600803\pi\) | ||||
−0.311414 | + | 0.950274i | \(0.600803\pi\) | |||||||
\(402\) | −19.4164 | −0.968402 | ||||||||
\(403\) | −40.0000 | −1.99254 | ||||||||
\(404\) | 7.41641 | 0.368980 | ||||||||
\(405\) | 24.4164 | 1.21326 | ||||||||
\(406\) | −1.23607 | −0.0613450 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −6.47214 | −0.320418 | ||||||||
\(409\) | −9.23607 | −0.456694 | −0.228347 | − | 0.973580i | \(-0.573332\pi\) | ||||
−0.228347 | + | 0.973580i | \(0.573332\pi\) | |||||||
\(410\) | −7.70820 | −0.380681 | ||||||||
\(411\) | 64.3607 | 3.17468 | ||||||||
\(412\) | 14.0000 | 0.689730 | ||||||||
\(413\) | −8.00000 | −0.393654 | ||||||||
\(414\) | 54.0689 | 2.65734 | ||||||||
\(415\) | −8.00000 | −0.392705 | ||||||||
\(416\) | 4.47214 | 0.219265 | ||||||||
\(417\) | 45.8885 | 2.24717 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.41641 | −0.166902 | −0.0834512 | − | 0.996512i | \(-0.526594\pi\) | ||||
−0.0834512 | + | 0.996512i | \(0.526594\pi\) | |||||||
\(420\) | −3.23607 | −0.157904 | ||||||||
\(421\) | −31.3050 | −1.52571 | −0.762855 | − | 0.646570i | \(-0.776203\pi\) | ||||
−0.762855 | + | 0.646570i | \(0.776203\pi\) | |||||||
\(422\) | −13.8885 | −0.676084 | ||||||||
\(423\) | 3.52786 | 0.171531 | ||||||||
\(424\) | 0.763932 | 0.0370998 | ||||||||
\(425\) | −2.00000 | −0.0970143 | ||||||||
\(426\) | −25.8885 | −1.25430 | ||||||||
\(427\) | −14.4721 | −0.700356 | ||||||||
\(428\) | 16.0000 | 0.773389 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.00000 | −0.385794 | ||||||||
\(431\) | 28.6525 | 1.38014 | 0.690071 | − | 0.723742i | \(-0.257579\pi\) | ||||
0.690071 | + | 0.723742i | \(0.257579\pi\) | |||||||
\(432\) | −14.4721 | −0.696291 | ||||||||
\(433\) | −0.763932 | −0.0367122 | −0.0183561 | − | 0.999832i | \(-0.505843\pi\) | ||||
−0.0183561 | + | 0.999832i | \(0.505843\pi\) | |||||||
\(434\) | −8.94427 | −0.429339 | ||||||||
\(435\) | −4.00000 | −0.191785 | ||||||||
\(436\) | −15.7082 | −0.752287 | ||||||||
\(437\) | −37.8885 | −1.81245 | ||||||||
\(438\) | 27.4164 | 1.31001 | ||||||||
\(439\) | 7.41641 | 0.353966 | 0.176983 | − | 0.984214i | \(-0.443366\pi\) | ||||
0.176983 | + | 0.984214i | \(0.443366\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.47214 | 0.355816 | ||||||||
\(442\) | −8.94427 | −0.425436 | ||||||||
\(443\) | 14.9443 | 0.710024 | 0.355012 | − | 0.934862i | \(-0.384477\pi\) | ||||
0.355012 | + | 0.934862i | \(0.384477\pi\) | |||||||
\(444\) | 10.4721 | 0.496986 | ||||||||
\(445\) | −14.9443 | −0.708426 | ||||||||
\(446\) | 1.05573 | 0.0499902 | ||||||||
\(447\) | 24.9443 | 1.17982 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 26.3607 | 1.24404 | 0.622019 | − | 0.783002i | \(-0.286313\pi\) | ||||
0.622019 | + | 0.783002i | \(0.286313\pi\) | |||||||
\(450\) | −7.47214 | −0.352240 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 10.9443 | 0.514775 | ||||||||
\(453\) | −63.7771 | −2.99651 | ||||||||
\(454\) | 10.4721 | 0.491482 | ||||||||
\(455\) | −4.47214 | −0.209657 | ||||||||
\(456\) | 16.9443 | 0.793488 | ||||||||
\(457\) | −30.9443 | −1.44751 | −0.723756 | − | 0.690056i | \(-0.757586\pi\) | ||||
−0.723756 | + | 0.690056i | \(0.757586\pi\) | |||||||
\(458\) | 20.4721 | 0.956600 | ||||||||
\(459\) | 28.9443 | 1.35100 | ||||||||
\(460\) | −7.23607 | −0.337383 | ||||||||
\(461\) | −3.05573 | −0.142319 | −0.0711597 | − | 0.997465i | \(-0.522670\pi\) | ||||
−0.0711597 | + | 0.997465i | \(0.522670\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.29180 | −0.106509 | −0.0532544 | − | 0.998581i | \(-0.516959\pi\) | ||||
−0.0532544 | + | 0.998581i | \(0.516959\pi\) | |||||||
\(464\) | 1.23607 | 0.0573830 | ||||||||
\(465\) | −28.9443 | −1.34226 | ||||||||
\(466\) | 14.9443 | 0.692280 | ||||||||
\(467\) | 36.1803 | 1.67423 | 0.837113 | − | 0.547030i | \(-0.184242\pi\) | ||||
0.837113 | + | 0.547030i | \(0.184242\pi\) | |||||||
\(468\) | −33.4164 | −1.54467 | ||||||||
\(469\) | −6.00000 | −0.277054 | ||||||||
\(470\) | −0.472136 | −0.0217780 | ||||||||
\(471\) | 24.3607 | 1.12248 | ||||||||
\(472\) | 8.00000 | 0.368230 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −16.9443 | −0.778276 | ||||||||
\(475\) | 5.23607 | 0.240247 | ||||||||
\(476\) | −2.00000 | −0.0916698 | ||||||||
\(477\) | −5.70820 | −0.261361 | ||||||||
\(478\) | 2.76393 | 0.126419 | ||||||||
\(479\) | −29.8885 | −1.36564 | −0.682821 | − | 0.730586i | \(-0.739247\pi\) | ||||
−0.682821 | + | 0.730586i | \(0.739247\pi\) | |||||||
\(480\) | 3.23607 | 0.147706 | ||||||||
\(481\) | 14.4721 | 0.659873 | ||||||||
\(482\) | 23.1246 | 1.05330 | ||||||||
\(483\) | 23.4164 | 1.06548 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.70820 | 0.0775655 | ||||||||
\(486\) | 35.5967 | 1.61470 | ||||||||
\(487\) | −34.0689 | −1.54381 | −0.771904 | − | 0.635739i | \(-0.780696\pi\) | ||||
−0.771904 | + | 0.635739i | \(0.780696\pi\) | |||||||
\(488\) | 14.4721 | 0.655123 | ||||||||
\(489\) | −48.3607 | −2.18695 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 8.00000 | 0.361035 | 0.180517 | − | 0.983572i | \(-0.442223\pi\) | ||||
0.180517 | + | 0.983572i | \(0.442223\pi\) | |||||||
\(492\) | −24.9443 | −1.12457 | ||||||||
\(493\) | −2.47214 | −0.111339 | ||||||||
\(494\) | 23.4164 | 1.05355 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.94427 | 0.401610 | ||||||||
\(497\) | −8.00000 | −0.358849 | ||||||||
\(498\) | −25.8885 | −1.16009 | ||||||||
\(499\) | −29.3050 | −1.31187 | −0.655935 | − | 0.754817i | \(-0.727725\pi\) | ||||
−0.655935 | + | 0.754817i | \(0.727725\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −16.0000 | −0.714827 | ||||||||
\(502\) | 14.4721 | 0.645923 | ||||||||
\(503\) | 38.8328 | 1.73147 | 0.865735 | − | 0.500503i | \(-0.166852\pi\) | ||||
0.865735 | + | 0.500503i | \(0.166852\pi\) | |||||||
\(504\) | −7.47214 | −0.332835 | ||||||||
\(505\) | 7.41641 | 0.330026 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22.6525 | −1.00603 | ||||||||
\(508\) | 5.52786 | 0.245259 | ||||||||
\(509\) | −10.9443 | −0.485096 | −0.242548 | − | 0.970139i | \(-0.577983\pi\) | ||||
−0.242548 | + | 0.970139i | \(0.577983\pi\) | |||||||
\(510\) | −6.47214 | −0.286591 | ||||||||
\(511\) | 8.47214 | 0.374785 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −75.7771 | −3.34564 | ||||||||
\(514\) | 25.1246 | 1.10820 | ||||||||
\(515\) | 14.0000 | 0.616914 | ||||||||
\(516\) | −25.8885 | −1.13968 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.23607 | 0.142185 | ||||||||
\(519\) | 40.3607 | 1.77164 | ||||||||
\(520\) | 4.47214 | 0.196116 | ||||||||
\(521\) | −0.472136 | −0.0206847 | −0.0103423 | − | 0.999947i | \(-0.503292\pi\) | ||||
−0.0103423 | + | 0.999947i | \(0.503292\pi\) | |||||||
\(522\) | −9.23607 | −0.404252 | ||||||||
\(523\) | 21.5279 | 0.941348 | 0.470674 | − | 0.882307i | \(-0.344011\pi\) | ||||
0.470674 | + | 0.882307i | \(0.344011\pi\) | |||||||
\(524\) | −6.18034 | −0.269989 | ||||||||
\(525\) | −3.23607 | −0.141234 | ||||||||
\(526\) | −28.3607 | −1.23658 | ||||||||
\(527\) | −17.8885 | −0.779237 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 29.3607 | 1.27655 | ||||||||
\(530\) | 0.763932 | 0.0331831 | ||||||||
\(531\) | −59.7771 | −2.59410 | ||||||||
\(532\) | 5.23607 | 0.227012 | ||||||||
\(533\) | −34.4721 | −1.49315 | ||||||||
\(534\) | −48.3607 | −2.09277 | ||||||||
\(535\) | 16.0000 | 0.691740 | ||||||||
\(536\) | 6.00000 | 0.259161 | ||||||||
\(537\) | −59.7771 | −2.57957 | ||||||||
\(538\) | 3.52786 | 0.152097 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −14.4721 | −0.622782 | ||||||||
\(541\) | 10.7639 | 0.462778 | 0.231389 | − | 0.972861i | \(-0.425673\pi\) | ||||
0.231389 | + | 0.972861i | \(0.425673\pi\) | |||||||
\(542\) | −2.47214 | −0.106187 | ||||||||
\(543\) | −45.3050 | −1.94422 | ||||||||
\(544\) | 2.00000 | 0.0857493 | ||||||||
\(545\) | −15.7082 | −0.672866 | ||||||||
\(546\) | −14.4721 | −0.619350 | ||||||||
\(547\) | 24.9443 | 1.06654 | 0.533270 | − | 0.845945i | \(-0.320963\pi\) | ||||
0.533270 | + | 0.845945i | \(0.320963\pi\) | |||||||
\(548\) | −19.8885 | −0.849596 | ||||||||
\(549\) | −108.138 | −4.61521 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.47214 | 0.275722 | ||||||||
\(552\) | −23.4164 | −0.996669 | ||||||||
\(553\) | −5.23607 | −0.222660 | ||||||||
\(554\) | −20.4721 | −0.869778 | ||||||||
\(555\) | 10.4721 | 0.444517 | ||||||||
\(556\) | −14.1803 | −0.601380 | ||||||||
\(557\) | 28.8328 | 1.22169 | 0.610843 | − | 0.791752i | \(-0.290831\pi\) | ||||
0.610843 | + | 0.791752i | \(0.290831\pi\) | |||||||
\(558\) | −66.8328 | −2.82926 | ||||||||
\(559\) | −35.7771 | −1.51321 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.3607 | −0.690134 | ||||||||
\(563\) | 38.8328 | 1.63661 | 0.818304 | − | 0.574786i | \(-0.194915\pi\) | ||||
0.818304 | + | 0.574786i | \(0.194915\pi\) | |||||||
\(564\) | −1.52786 | −0.0643347 | ||||||||
\(565\) | 10.9443 | 0.460429 | ||||||||
\(566\) | 7.41641 | 0.311735 | ||||||||
\(567\) | 24.4164 | 1.02539 | ||||||||
\(568\) | 8.00000 | 0.335673 | ||||||||
\(569\) | −6.83282 | −0.286447 | −0.143223 | − | 0.989690i | \(-0.545747\pi\) | ||||
−0.143223 | + | 0.989690i | \(0.545747\pi\) | |||||||
\(570\) | 16.9443 | 0.709717 | ||||||||
\(571\) | −0.583592 | −0.0244226 | −0.0122113 | − | 0.999925i | \(-0.503887\pi\) | ||||
−0.0122113 | + | 0.999925i | \(0.503887\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.9443 | −0.874960 | ||||||||
\(574\) | −7.70820 | −0.321734 | ||||||||
\(575\) | −7.23607 | −0.301765 | ||||||||
\(576\) | 7.47214 | 0.311339 | ||||||||
\(577\) | 1.70820 | 0.0711135 | 0.0355567 | − | 0.999368i | \(-0.488680\pi\) | ||||
0.0355567 | + | 0.999368i | \(0.488680\pi\) | |||||||
\(578\) | 13.0000 | 0.540729 | ||||||||
\(579\) | −87.1935 | −3.62364 | ||||||||
\(580\) | 1.23607 | 0.0513249 | ||||||||
\(581\) | −8.00000 | −0.331896 | ||||||||
\(582\) | 5.52786 | 0.229137 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −8.47214 | −0.350579 | ||||||||
\(585\) | −33.4164 | −1.38160 | ||||||||
\(586\) | −8.47214 | −0.349981 | ||||||||
\(587\) | −13.7082 | −0.565798 | −0.282899 | − | 0.959150i | \(-0.591296\pi\) | ||||
−0.282899 | + | 0.959150i | \(0.591296\pi\) | |||||||
\(588\) | −3.23607 | −0.133453 | ||||||||
\(589\) | 46.8328 | 1.92971 | ||||||||
\(590\) | 8.00000 | 0.329355 | ||||||||
\(591\) | −69.3050 | −2.85082 | ||||||||
\(592\) | −3.23607 | −0.133002 | ||||||||
\(593\) | −38.3607 | −1.57528 | −0.787642 | − | 0.616133i | \(-0.788698\pi\) | ||||
−0.787642 | + | 0.616133i | \(0.788698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.00000 | −0.0819920 | ||||||||
\(596\) | −7.70820 | −0.315740 | ||||||||
\(597\) | 17.8885 | 0.732129 | ||||||||
\(598\) | −32.3607 | −1.32333 | ||||||||
\(599\) | 17.8885 | 0.730906 | 0.365453 | − | 0.930830i | \(-0.380914\pi\) | ||||
0.365453 | + | 0.930830i | \(0.380914\pi\) | |||||||
\(600\) | 3.23607 | 0.132112 | ||||||||
\(601\) | −31.7082 | −1.29340 | −0.646702 | − | 0.762743i | \(-0.723852\pi\) | ||||
−0.646702 | + | 0.762743i | \(0.723852\pi\) | |||||||
\(602\) | −8.00000 | −0.326056 | ||||||||
\(603\) | −44.8328 | −1.82573 | ||||||||
\(604\) | 19.7082 | 0.801915 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 24.0000 | 0.974933 | ||||||||
\(607\) | 18.8328 | 0.764400 | 0.382200 | − | 0.924080i | \(-0.375166\pi\) | ||||
0.382200 | + | 0.924080i | \(0.375166\pi\) | |||||||
\(608\) | −5.23607 | −0.212351 | ||||||||
\(609\) | −4.00000 | −0.162088 | ||||||||
\(610\) | 14.4721 | 0.585960 | ||||||||
\(611\) | −2.11146 | −0.0854204 | ||||||||
\(612\) | −14.9443 | −0.604086 | ||||||||
\(613\) | −26.0000 | −1.05013 | −0.525065 | − | 0.851062i | \(-0.675959\pi\) | ||||
−0.525065 | + | 0.851062i | \(0.675959\pi\) | |||||||
\(614\) | 18.4721 | 0.745475 | ||||||||
\(615\) | −24.9443 | −1.00585 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.5279 | −1.26926 | −0.634632 | − | 0.772814i | \(-0.718848\pi\) | ||||
−0.634632 | + | 0.772814i | \(0.718848\pi\) | |||||||
\(618\) | 45.3050 | 1.82243 | ||||||||
\(619\) | 1.52786 | 0.0614100 | 0.0307050 | − | 0.999528i | \(-0.490225\pi\) | ||||
0.0307050 | + | 0.999528i | \(0.490225\pi\) | |||||||
\(620\) | 8.94427 | 0.359211 | ||||||||
\(621\) | 104.721 | 4.20232 | ||||||||
\(622\) | 22.8328 | 0.915513 | ||||||||
\(623\) | −14.9443 | −0.598730 | ||||||||
\(624\) | 14.4721 | 0.579349 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −10.6525 | −0.425759 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.52786 | −0.300394 | ||||||||
\(629\) | 6.47214 | 0.258061 | ||||||||
\(630\) | −7.47214 | −0.297697 | ||||||||
\(631\) | 14.8328 | 0.590485 | 0.295243 | − | 0.955422i | \(-0.404600\pi\) | ||||
0.295243 | + | 0.955422i | \(0.404600\pi\) | |||||||
\(632\) | 5.23607 | 0.208280 | ||||||||
\(633\) | −44.9443 | −1.78637 | ||||||||
\(634\) | 20.1803 | 0.801464 | ||||||||
\(635\) | 5.52786 | 0.219367 | ||||||||
\(636\) | 2.47214 | 0.0980266 | ||||||||
\(637\) | −4.47214 | −0.177192 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −59.7771 | −2.36475 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 2.00000 | 0.0789953 | 0.0394976 | − | 0.999220i | \(-0.487424\pi\) | ||||
0.0394976 | + | 0.999220i | \(0.487424\pi\) | |||||||
\(642\) | 51.7771 | 2.04348 | ||||||||
\(643\) | −48.1803 | −1.90005 | −0.950024 | − | 0.312178i | \(-0.898941\pi\) | ||||
−0.950024 | + | 0.312178i | \(0.898941\pi\) | |||||||
\(644\) | −7.23607 | −0.285141 | ||||||||
\(645\) | −25.8885 | −1.01936 | ||||||||
\(646\) | 10.4721 | 0.412021 | ||||||||
\(647\) | −30.0000 | −1.17942 | −0.589711 | − | 0.807614i | \(-0.700758\pi\) | ||||
−0.589711 | + | 0.807614i | \(0.700758\pi\) | |||||||
\(648\) | −24.4164 | −0.959167 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 4.47214 | 0.175412 | ||||||||
\(651\) | −28.9443 | −1.13442 | ||||||||
\(652\) | 14.9443 | 0.585263 | ||||||||
\(653\) | −15.5967 | −0.610348 | −0.305174 | − | 0.952297i | \(-0.598715\pi\) | ||||
−0.305174 | + | 0.952297i | \(0.598715\pi\) | |||||||
\(654\) | −50.8328 | −1.98772 | ||||||||
\(655\) | −6.18034 | −0.241486 | ||||||||
\(656\) | 7.70820 | 0.300955 | ||||||||
\(657\) | 63.3050 | 2.46976 | ||||||||
\(658\) | −0.472136 | −0.0184058 | ||||||||
\(659\) | −32.3607 | −1.26059 | −0.630297 | − | 0.776354i | \(-0.717067\pi\) | ||||
−0.630297 | + | 0.776354i | \(0.717067\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.94427 | −0.114519 | −0.0572595 | − | 0.998359i | \(-0.518236\pi\) | ||||
−0.0572595 | + | 0.998359i | \(0.518236\pi\) | |||||||
\(662\) | −11.4164 | −0.443711 | ||||||||
\(663\) | −28.9443 | −1.12410 | ||||||||
\(664\) | 8.00000 | 0.310460 | ||||||||
\(665\) | 5.23607 | 0.203046 | ||||||||
\(666\) | 24.1803 | 0.936969 | ||||||||
\(667\) | −8.94427 | −0.346324 | ||||||||
\(668\) | 4.94427 | 0.191300 | ||||||||
\(669\) | 3.41641 | 0.132086 | ||||||||
\(670\) | 6.00000 | 0.231800 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.23607 | 0.124834 | ||||||||
\(673\) | −23.8885 | −0.920836 | −0.460418 | − | 0.887702i | \(-0.652300\pi\) | ||||
−0.460418 | + | 0.887702i | \(0.652300\pi\) | |||||||
\(674\) | −24.8328 | −0.956524 | ||||||||
\(675\) | −14.4721 | −0.557033 | ||||||||
\(676\) | 7.00000 | 0.269231 | ||||||||
\(677\) | −32.4721 | −1.24801 | −0.624003 | − | 0.781422i | \(-0.714495\pi\) | ||||
−0.624003 | + | 0.781422i | \(0.714495\pi\) | |||||||
\(678\) | 35.4164 | 1.36016 | ||||||||
\(679\) | 1.70820 | 0.0655549 | ||||||||
\(680\) | 2.00000 | 0.0766965 | ||||||||
\(681\) | 33.8885 | 1.29861 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −39.5279 | −1.51249 | −0.756246 | − | 0.654288i | \(-0.772969\pi\) | ||||
−0.756246 | + | 0.654288i | \(0.772969\pi\) | |||||||
\(684\) | 39.1246 | 1.49597 | ||||||||
\(685\) | −19.8885 | −0.759902 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 66.2492 | 2.52757 | ||||||||
\(688\) | 8.00000 | 0.304997 | ||||||||
\(689\) | 3.41641 | 0.130155 | ||||||||
\(690\) | −23.4164 | −0.891447 | ||||||||
\(691\) | 8.36068 | 0.318055 | 0.159028 | − | 0.987274i | \(-0.449164\pi\) | ||||
0.159028 | + | 0.987274i | \(0.449164\pi\) | |||||||
\(692\) | −12.4721 | −0.474119 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.1803 | −0.537891 | ||||||||
\(696\) | 4.00000 | 0.151620 | ||||||||
\(697\) | −15.4164 | −0.583938 | ||||||||
\(698\) | −7.05573 | −0.267063 | ||||||||
\(699\) | 48.3607 | 1.82917 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 3.70820 | 0.140057 | 0.0700285 | − | 0.997545i | \(-0.477691\pi\) | ||||
0.0700285 | + | 0.997545i | \(0.477691\pi\) | |||||||
\(702\) | −64.7214 | −2.44275 | ||||||||
\(703\) | −16.9443 | −0.639065 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.52786 | −0.0575427 | ||||||||
\(706\) | 23.2361 | 0.874501 | ||||||||
\(707\) | 7.41641 | 0.278923 | ||||||||
\(708\) | 25.8885 | 0.972951 | ||||||||
\(709\) | −2.94427 | −0.110574 | −0.0552872 | − | 0.998470i | \(-0.517607\pi\) | ||||
−0.0552872 | + | 0.998470i | \(0.517607\pi\) | |||||||
\(710\) | 8.00000 | 0.300235 | ||||||||
\(711\) | −39.1246 | −1.46729 | ||||||||
\(712\) | 14.9443 | 0.560060 | ||||||||
\(713\) | −64.7214 | −2.42383 | ||||||||
\(714\) | −6.47214 | −0.242214 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18.4721 | 0.690336 | ||||||||
\(717\) | 8.94427 | 0.334030 | ||||||||
\(718\) | 10.1803 | 0.379927 | ||||||||
\(719\) | −32.3607 | −1.20685 | −0.603425 | − | 0.797420i | \(-0.706198\pi\) | ||||
−0.603425 | + | 0.797420i | \(0.706198\pi\) | |||||||
\(720\) | 7.47214 | 0.278470 | ||||||||
\(721\) | 14.0000 | 0.521387 | ||||||||
\(722\) | −8.41641 | −0.313226 | ||||||||
\(723\) | 74.8328 | 2.78306 | ||||||||
\(724\) | 14.0000 | 0.520306 | ||||||||
\(725\) | 1.23607 | 0.0459064 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.3607 | −1.27437 | −0.637184 | − | 0.770712i | \(-0.719901\pi\) | ||||
−0.637184 | + | 0.770712i | \(0.719901\pi\) | |||||||
\(728\) | 4.47214 | 0.165748 | ||||||||
\(729\) | 41.9443 | 1.55349 | ||||||||
\(730\) | −8.47214 | −0.313568 | ||||||||
\(731\) | −16.0000 | −0.591781 | ||||||||
\(732\) | 46.8328 | 1.73099 | ||||||||
\(733\) | 44.2492 | 1.63438 | 0.817191 | − | 0.576367i | \(-0.195530\pi\) | ||||
0.817191 | + | 0.576367i | \(0.195530\pi\) | |||||||
\(734\) | 24.8328 | 0.916596 | ||||||||
\(735\) | −3.23607 | −0.119364 | ||||||||
\(736\) | 7.23607 | 0.266725 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −57.5967 | −2.12017 | ||||||||
\(739\) | −44.7214 | −1.64510 | −0.822551 | − | 0.568691i | \(-0.807450\pi\) | ||||
−0.822551 | + | 0.568691i | \(0.807450\pi\) | |||||||
\(740\) | −3.23607 | −0.118960 | ||||||||
\(741\) | 75.7771 | 2.78374 | ||||||||
\(742\) | 0.763932 | 0.0280448 | ||||||||
\(743\) | −29.5279 | −1.08327 | −0.541636 | − | 0.840613i | \(-0.682195\pi\) | ||||
−0.541636 | + | 0.840613i | \(0.682195\pi\) | |||||||
\(744\) | 28.9443 | 1.06115 | ||||||||
\(745\) | −7.70820 | −0.282407 | ||||||||
\(746\) | 6.36068 | 0.232881 | ||||||||
\(747\) | −59.7771 | −2.18713 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.0000 | 0.584627 | ||||||||
\(750\) | 3.23607 | 0.118164 | ||||||||
\(751\) | 41.8885 | 1.52853 | 0.764267 | − | 0.644900i | \(-0.223101\pi\) | ||||
0.764267 | + | 0.644900i | \(0.223101\pi\) | |||||||
\(752\) | 0.472136 | 0.0172170 | ||||||||
\(753\) | 46.8328 | 1.70668 | ||||||||
\(754\) | 5.52786 | 0.201313 | ||||||||
\(755\) | 19.7082 | 0.717255 | ||||||||
\(756\) | −14.4721 | −0.526346 | ||||||||
\(757\) | −2.87539 | −0.104508 | −0.0522539 | − | 0.998634i | \(-0.516641\pi\) | ||||
−0.0522539 | + | 0.998634i | \(0.516641\pi\) | |||||||
\(758\) | −12.9443 | −0.470157 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.23607 | −0.189932 | ||||||||
\(761\) | −40.0689 | −1.45250 | −0.726248 | − | 0.687433i | \(-0.758738\pi\) | ||||
−0.726248 | + | 0.687433i | \(0.758738\pi\) | |||||||
\(762\) | 17.8885 | 0.648034 | ||||||||
\(763\) | −15.7082 | −0.568675 | ||||||||
\(764\) | 6.47214 | 0.234154 | ||||||||
\(765\) | −14.9443 | −0.540311 | ||||||||
\(766\) | −31.8885 | −1.15218 | ||||||||
\(767\) | 35.7771 | 1.29184 | ||||||||
\(768\) | −3.23607 | −0.116772 | ||||||||
\(769\) | 41.0132 | 1.47897 | 0.739486 | − | 0.673172i | \(-0.235069\pi\) | ||||
0.739486 | + | 0.673172i | \(0.235069\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 81.3050 | 2.92813 | ||||||||
\(772\) | 26.9443 | 0.969746 | ||||||||
\(773\) | −41.7771 | −1.50262 | −0.751309 | − | 0.659951i | \(-0.770577\pi\) | ||||
−0.751309 | + | 0.659951i | \(0.770577\pi\) | |||||||
\(774\) | −59.7771 | −2.14864 | ||||||||
\(775\) | 8.94427 | 0.321288 | ||||||||
\(776\) | −1.70820 | −0.0613209 | ||||||||
\(777\) | 10.4721 | 0.375686 | ||||||||
\(778\) | 6.36068 | 0.228041 | ||||||||
\(779\) | 40.3607 | 1.44607 | ||||||||
\(780\) | 14.4721 | 0.518186 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −14.4721 | −0.517523 | ||||||||
\(783\) | −17.8885 | −0.639284 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −7.52786 | −0.268681 | ||||||||
\(786\) | −20.0000 | −0.713376 | ||||||||
\(787\) | −6.83282 | −0.243564 | −0.121782 | − | 0.992557i | \(-0.538861\pi\) | ||||
−0.121782 | + | 0.992557i | \(0.538861\pi\) | |||||||
\(788\) | 21.4164 | 0.762928 | ||||||||
\(789\) | −91.7771 | −3.26735 | ||||||||
\(790\) | 5.23607 | 0.186291 | ||||||||
\(791\) | 10.9443 | 0.389134 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 64.7214 | 2.29832 | ||||||||
\(794\) | 1.41641 | 0.0502664 | ||||||||
\(795\) | 2.47214 | 0.0876776 | ||||||||
\(796\) | −5.52786 | −0.195930 | ||||||||
\(797\) | −33.4164 | −1.18367 | −0.591835 | − | 0.806059i | \(-0.701596\pi\) | ||||
−0.591835 | + | 0.806059i | \(0.701596\pi\) | |||||||
\(798\) | 16.9443 | 0.599821 | ||||||||
\(799\) | −0.944272 | −0.0334059 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −111.666 | −3.94551 | ||||||||
\(802\) | 12.4721 | 0.440406 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 19.4164 | 0.684764 | ||||||||
\(805\) | −7.23607 | −0.255038 | ||||||||
\(806\) | 40.0000 | 1.40894 | ||||||||
\(807\) | 11.4164 | 0.401877 | ||||||||
\(808\) | −7.41641 | −0.260908 | ||||||||
\(809\) | −24.3607 | −0.856476 | −0.428238 | − | 0.903666i | \(-0.640865\pi\) | ||||
−0.428238 | + | 0.903666i | \(0.640865\pi\) | |||||||
\(810\) | −24.4164 | −0.857905 | ||||||||
\(811\) | −18.1803 | −0.638398 | −0.319199 | − | 0.947688i | \(-0.603414\pi\) | ||||
−0.319199 | + | 0.947688i | \(0.603414\pi\) | |||||||
\(812\) | 1.23607 | 0.0433775 | ||||||||
\(813\) | −8.00000 | −0.280572 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.9443 | 0.523475 | ||||||||
\(816\) | 6.47214 | 0.226570 | ||||||||
\(817\) | 41.8885 | 1.46549 | ||||||||
\(818\) | 9.23607 | 0.322932 | ||||||||
\(819\) | −33.4164 | −1.16766 | ||||||||
\(820\) | 7.70820 | 0.269182 | ||||||||
\(821\) | 35.7082 | 1.24622 | 0.623112 | − | 0.782132i | \(-0.285868\pi\) | ||||
0.623112 | + | 0.782132i | \(0.285868\pi\) | |||||||
\(822\) | −64.3607 | −2.24484 | ||||||||
\(823\) | −39.0132 | −1.35991 | −0.679957 | − | 0.733252i | \(-0.738001\pi\) | ||||
−0.679957 | + | 0.733252i | \(0.738001\pi\) | |||||||
\(824\) | −14.0000 | −0.487713 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.00000 | 0.278356 | ||||||||
\(827\) | −31.7771 | −1.10500 | −0.552499 | − | 0.833514i | \(-0.686326\pi\) | ||||
−0.552499 | + | 0.833514i | \(0.686326\pi\) | |||||||
\(828\) | −54.0689 | −1.87902 | ||||||||
\(829\) | −16.4721 | −0.572101 | −0.286050 | − | 0.958215i | \(-0.592343\pi\) | ||||
−0.286050 | + | 0.958215i | \(0.592343\pi\) | |||||||
\(830\) | 8.00000 | 0.277684 | ||||||||
\(831\) | −66.2492 | −2.29816 | ||||||||
\(832\) | −4.47214 | −0.155043 | ||||||||
\(833\) | −2.00000 | −0.0692959 | ||||||||
\(834\) | −45.8885 | −1.58899 | ||||||||
\(835\) | 4.94427 | 0.171104 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −129.443 | −4.47419 | ||||||||
\(838\) | 3.41641 | 0.118018 | ||||||||
\(839\) | 4.00000 | 0.138095 | 0.0690477 | − | 0.997613i | \(-0.478004\pi\) | ||||
0.0690477 | + | 0.997613i | \(0.478004\pi\) | |||||||
\(840\) | 3.23607 | 0.111655 | ||||||||
\(841\) | −27.4721 | −0.947315 | ||||||||
\(842\) | 31.3050 | 1.07884 | ||||||||
\(843\) | −52.9443 | −1.82350 | ||||||||
\(844\) | 13.8885 | 0.478063 | ||||||||
\(845\) | 7.00000 | 0.240807 | ||||||||
\(846\) | −3.52786 | −0.121290 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.763932 | −0.0262335 | ||||||||
\(849\) | 24.0000 | 0.823678 | ||||||||
\(850\) | 2.00000 | 0.0685994 | ||||||||
\(851\) | 23.4164 | 0.802704 | ||||||||
\(852\) | 25.8885 | 0.886927 | ||||||||
\(853\) | −49.4164 | −1.69199 | −0.845993 | − | 0.533194i | \(-0.820991\pi\) | ||||
−0.845993 | + | 0.533194i | \(0.820991\pi\) | |||||||
\(854\) | 14.4721 | 0.495226 | ||||||||
\(855\) | 39.1246 | 1.33803 | ||||||||
\(856\) | −16.0000 | −0.546869 | ||||||||
\(857\) | 0.472136 | 0.0161279 | 0.00806393 | − | 0.999967i | \(-0.497433\pi\) | ||||
0.00806393 | + | 0.999967i | \(0.497433\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.3607 | 1.65005 | 0.825023 | − | 0.565100i | \(-0.191162\pi\) | ||||
0.825023 | + | 0.565100i | \(0.191162\pi\) | |||||||
\(860\) | 8.00000 | 0.272798 | ||||||||
\(861\) | −24.9443 | −0.850099 | ||||||||
\(862\) | −28.6525 | −0.975907 | ||||||||
\(863\) | −19.2361 | −0.654803 | −0.327402 | − | 0.944885i | \(-0.606173\pi\) | ||||
−0.327402 | + | 0.944885i | \(0.606173\pi\) | |||||||
\(864\) | 14.4721 | 0.492352 | ||||||||
\(865\) | −12.4721 | −0.424065 | ||||||||
\(866\) | 0.763932 | 0.0259595 | ||||||||
\(867\) | 42.0689 | 1.42873 | ||||||||
\(868\) | 8.94427 | 0.303588 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 4.00000 | 0.135613 | ||||||||
\(871\) | 26.8328 | 0.909195 | ||||||||
\(872\) | 15.7082 | 0.531947 | ||||||||
\(873\) | 12.7639 | 0.431994 | ||||||||
\(874\) | 37.8885 | 1.28160 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −27.4164 | −0.926315 | ||||||||
\(877\) | −35.3050 | −1.19216 | −0.596082 | − | 0.802924i | \(-0.703277\pi\) | ||||
−0.596082 | + | 0.802924i | \(0.703277\pi\) | |||||||
\(878\) | −7.41641 | −0.250292 | ||||||||
\(879\) | −27.4164 | −0.924732 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.9443 | 1.31207 | 0.656033 | − | 0.754732i | \(-0.272233\pi\) | ||||
0.656033 | + | 0.754732i | \(0.272233\pi\) | |||||||
\(882\) | −7.47214 | −0.251600 | ||||||||
\(883\) | −6.58359 | −0.221556 | −0.110778 | − | 0.993845i | \(-0.535334\pi\) | ||||
−0.110778 | + | 0.993845i | \(0.535334\pi\) | |||||||
\(884\) | 8.94427 | 0.300828 | ||||||||
\(885\) | 25.8885 | 0.870234 | ||||||||
\(886\) | −14.9443 | −0.502063 | ||||||||
\(887\) | −6.11146 | −0.205203 | −0.102601 | − | 0.994723i | \(-0.532717\pi\) | ||||
−0.102601 | + | 0.994723i | \(0.532717\pi\) | |||||||
\(888\) | −10.4721 | −0.351422 | ||||||||
\(889\) | 5.52786 | 0.185399 | ||||||||
\(890\) | 14.9443 | 0.500933 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.05573 | −0.0353484 | ||||||||
\(893\) | 2.47214 | 0.0827269 | ||||||||
\(894\) | −24.9443 | −0.834261 | ||||||||
\(895\) | 18.4721 | 0.617455 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −104.721 | −3.49654 | ||||||||
\(898\) | −26.3607 | −0.879667 | ||||||||
\(899\) | 11.0557 | 0.368729 | ||||||||
\(900\) | 7.47214 | 0.249071 | ||||||||
\(901\) | 1.52786 | 0.0509005 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25.8885 | −0.861517 | ||||||||
\(904\) | −10.9443 | −0.364001 | ||||||||
\(905\) | 14.0000 | 0.465376 | ||||||||
\(906\) | 63.7771 | 2.11885 | ||||||||
\(907\) | 15.5279 | 0.515594 | 0.257797 | − | 0.966199i | \(-0.417003\pi\) | ||||
0.257797 | + | 0.966199i | \(0.417003\pi\) | |||||||
\(908\) | −10.4721 | −0.347530 | ||||||||
\(909\) | 55.4164 | 1.83805 | ||||||||
\(910\) | 4.47214 | 0.148250 | ||||||||
\(911\) | 3.41641 | 0.113191 | 0.0565953 | − | 0.998397i | \(-0.481976\pi\) | ||||
0.0565953 | + | 0.998397i | \(0.481976\pi\) | |||||||
\(912\) | −16.9443 | −0.561081 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 30.9443 | 1.02355 | ||||||||
\(915\) | 46.8328 | 1.54825 | ||||||||
\(916\) | −20.4721 | −0.676418 | ||||||||
\(917\) | −6.18034 | −0.204093 | ||||||||
\(918\) | −28.9443 | −0.955303 | ||||||||
\(919\) | −38.1803 | −1.25945 | −0.629727 | − | 0.776817i | \(-0.716833\pi\) | ||||
−0.629727 | + | 0.776817i | \(0.716833\pi\) | |||||||
\(920\) | 7.23607 | 0.238566 | ||||||||
\(921\) | 59.7771 | 1.96972 | ||||||||
\(922\) | 3.05573 | 0.100635 | ||||||||
\(923\) | 35.7771 | 1.17762 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.23607 | −0.106401 | ||||||||
\(926\) | 2.29180 | 0.0753131 | ||||||||
\(927\) | 104.610 | 3.43584 | ||||||||
\(928\) | −1.23607 | −0.0405759 | ||||||||
\(929\) | 30.3607 | 0.996102 | 0.498051 | − | 0.867148i | \(-0.334049\pi\) | ||||
0.498051 | + | 0.867148i | \(0.334049\pi\) | |||||||
\(930\) | 28.9443 | 0.949120 | ||||||||
\(931\) | 5.23607 | 0.171605 | ||||||||
\(932\) | −14.9443 | −0.489516 | ||||||||
\(933\) | 73.8885 | 2.41900 | ||||||||
\(934\) | −36.1803 | −1.18386 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 33.4164 | 1.09225 | ||||||||
\(937\) | 30.9443 | 1.01091 | 0.505453 | − | 0.862854i | \(-0.331326\pi\) | ||||
0.505453 | + | 0.862854i | \(0.331326\pi\) | |||||||
\(938\) | 6.00000 | 0.195907 | ||||||||
\(939\) | −34.4721 | −1.12496 | ||||||||
\(940\) | 0.472136 | 0.0153994 | ||||||||
\(941\) | −54.2492 | −1.76847 | −0.884237 | − | 0.467038i | \(-0.845321\pi\) | ||||
−0.884237 | + | 0.467038i | \(0.845321\pi\) | |||||||
\(942\) | −24.3607 | −0.793714 | ||||||||
\(943\) | −55.7771 | −1.81635 | ||||||||
\(944\) | −8.00000 | −0.260378 | ||||||||
\(945\) | −14.4721 | −0.470779 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.4721 | 0.665255 | 0.332628 | − | 0.943058i | \(-0.392065\pi\) | ||||
0.332628 | + | 0.943058i | \(0.392065\pi\) | |||||||
\(948\) | 16.9443 | 0.550324 | ||||||||
\(949\) | −37.8885 | −1.22991 | ||||||||
\(950\) | −5.23607 | −0.169880 | ||||||||
\(951\) | 65.3050 | 2.11766 | ||||||||
\(952\) | 2.00000 | 0.0648204 | ||||||||
\(953\) | 3.88854 | 0.125962 | 0.0629811 | − | 0.998015i | \(-0.479939\pi\) | ||||
0.0629811 | + | 0.998015i | \(0.479939\pi\) | |||||||
\(954\) | 5.70820 | 0.184810 | ||||||||
\(955\) | 6.47214 | 0.209433 | ||||||||
\(956\) | −2.76393 | −0.0893920 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 29.8885 | 0.965655 | ||||||||
\(959\) | −19.8885 | −0.642235 | ||||||||
\(960\) | −3.23607 | −0.104444 | ||||||||
\(961\) | 49.0000 | 1.58065 | ||||||||
\(962\) | −14.4721 | −0.466600 | ||||||||
\(963\) | 119.554 | 3.85258 | ||||||||
\(964\) | −23.1246 | −0.744794 | ||||||||
\(965\) | 26.9443 | 0.867367 | ||||||||
\(966\) | −23.4164 | −0.753411 | ||||||||
\(967\) | 33.3050 | 1.07102 | 0.535508 | − | 0.844530i | \(-0.320120\pi\) | ||||
0.535508 | + | 0.844530i | \(0.320120\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33.8885 | 1.08866 | ||||||||
\(970\) | −1.70820 | −0.0548471 | ||||||||
\(971\) | −22.8328 | −0.732740 | −0.366370 | − | 0.930469i | \(-0.619400\pi\) | ||||
−0.366370 | + | 0.930469i | \(0.619400\pi\) | |||||||
\(972\) | −35.5967 | −1.14177 | ||||||||
\(973\) | −14.1803 | −0.454601 | ||||||||
\(974\) | 34.0689 | 1.09164 | ||||||||
\(975\) | 14.4721 | 0.463479 | ||||||||
\(976\) | −14.4721 | −0.463242 | ||||||||
\(977\) | −0.832816 | −0.0266441 | −0.0133221 | − | 0.999911i | \(-0.504241\pi\) | ||||
−0.0133221 | + | 0.999911i | \(0.504241\pi\) | |||||||
\(978\) | 48.3607 | 1.54640 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | −117.374 | −3.74746 | ||||||||
\(982\) | −8.00000 | −0.255290 | ||||||||
\(983\) | −13.0557 | −0.416413 | −0.208207 | − | 0.978085i | \(-0.566763\pi\) | ||||
−0.208207 | + | 0.978085i | \(0.566763\pi\) | |||||||
\(984\) | 24.9443 | 0.795194 | ||||||||
\(985\) | 21.4164 | 0.682383 | ||||||||
\(986\) | 2.47214 | 0.0787288 | ||||||||
\(987\) | −1.52786 | −0.0486324 | ||||||||
\(988\) | −23.4164 | −0.744975 | ||||||||
\(989\) | −57.8885 | −1.84075 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.3050 | 1.18503 | 0.592515 | − | 0.805559i | \(-0.298135\pi\) | ||||
0.592515 | + | 0.805559i | \(0.298135\pi\) | |||||||
\(992\) | −8.94427 | −0.283981 | ||||||||
\(993\) | −36.9443 | −1.17239 | ||||||||
\(994\) | 8.00000 | 0.253745 | ||||||||
\(995\) | −5.52786 | −0.175245 | ||||||||
\(996\) | 25.8885 | 0.820310 | ||||||||
\(997\) | −31.5279 | −0.998497 | −0.499249 | − | 0.866459i | \(-0.666391\pi\) | ||||
−0.499249 | + | 0.866459i | \(0.666391\pi\) | |||||||
\(998\) | 29.3050 | 0.927632 | ||||||||
\(999\) | 46.8328 | 1.48172 |
(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.bj.1.1 | ✓ | 2 | |
11.10 | odd | 2 | 8470.2.a.bv.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.bj.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
8470.2.a.bv.1.1 | yes | 2 | 11.10 | odd | 2 |