Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3850,2,Mod(1,3850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3850, 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("3850.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3850.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(30.7424047782\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.81361\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3850.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.81361 | −1.62444 | −0.812218 | − | 0.583354i | \(-0.801740\pi\) | ||||
−0.812218 | + | 0.583354i | \(0.801740\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.81361 | 1.14865 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 4.91638 | 1.63879 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −2.81361 | −0.812218 | ||||||||
\(13\) | 4.91638 | 1.36356 | 0.681779 | − | 0.731558i | \(-0.261206\pi\) | ||||
0.681779 | + | 0.731558i | \(0.261206\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.81361 | −1.16747 | −0.583736 | − | 0.811944i | \(-0.698410\pi\) | ||||
−0.583736 | + | 0.811944i | \(0.698410\pi\) | |||||||
\(18\) | −4.91638 | −1.15880 | ||||||||
\(19\) | 1.28917 | 0.295756 | 0.147878 | − | 0.989006i | \(-0.452756\pi\) | ||||
0.147878 | + | 0.989006i | \(0.452756\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.81361 | −0.613979 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −7.49472 | −1.56276 | −0.781378 | − | 0.624057i | \(-0.785483\pi\) | ||||
−0.781378 | + | 0.624057i | \(0.785483\pi\) | |||||||
\(24\) | 2.81361 | 0.574325 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.91638 | −0.964182 | ||||||||
\(27\) | −5.39194 | −1.03768 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −1.86751 | −0.346787 | −0.173394 | − | 0.984853i | \(-0.555473\pi\) | ||||
−0.173394 | + | 0.984853i | \(0.555473\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.15165 | 1.64369 | 0.821843 | − | 0.569715i | \(-0.192946\pi\) | ||||
0.821843 | + | 0.569715i | \(0.192946\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.81361 | −0.489786 | ||||||||
\(34\) | 4.81361 | 0.825527 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.91638 | 0.819397 | ||||||||
\(37\) | −6.75971 | −1.11129 | −0.555645 | − | 0.831420i | \(-0.687528\pi\) | ||||
−0.555645 | + | 0.831420i | \(0.687528\pi\) | |||||||
\(38\) | −1.28917 | −0.209131 | ||||||||
\(39\) | −13.8328 | −2.21501 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.4111 | −1.93829 | −0.969144 | − | 0.246495i | \(-0.920721\pi\) | ||||
−0.969144 | + | 0.246495i | \(0.920721\pi\) | |||||||
\(42\) | 2.81361 | 0.434149 | ||||||||
\(43\) | 2.62721 | 0.400646 | 0.200323 | − | 0.979730i | \(-0.435801\pi\) | ||||
0.200323 | + | 0.979730i | \(0.435801\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.49472 | 1.10504 | ||||||||
\(47\) | −11.0192 | −1.60731 | −0.803655 | − | 0.595096i | \(-0.797114\pi\) | ||||
−0.803655 | + | 0.595096i | \(0.797114\pi\) | |||||||
\(48\) | −2.81361 | −0.406109 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.5436 | 1.89648 | ||||||||
\(52\) | 4.91638 | 0.681779 | ||||||||
\(53\) | 9.74914 | 1.33915 | 0.669574 | − | 0.742745i | \(-0.266477\pi\) | ||||
0.669574 | + | 0.742745i | \(0.266477\pi\) | |||||||
\(54\) | 5.39194 | 0.733751 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −3.62721 | −0.480436 | ||||||||
\(58\) | 1.86751 | 0.245216 | ||||||||
\(59\) | 1.39194 | 0.181216 | 0.0906078 | − | 0.995887i | \(-0.471119\pi\) | ||||
0.0906078 | + | 0.995887i | \(0.471119\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.57834 | 0.842270 | 0.421135 | − | 0.906998i | \(-0.361632\pi\) | ||||
0.421135 | + | 0.906998i | \(0.361632\pi\) | |||||||
\(62\) | −9.15165 | −1.16226 | ||||||||
\(63\) | 4.91638 | 0.619406 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.81361 | 0.346331 | ||||||||
\(67\) | −3.62721 | −0.443135 | −0.221567 | − | 0.975145i | \(-0.571117\pi\) | ||||
−0.221567 | + | 0.975145i | \(0.571117\pi\) | |||||||
\(68\) | −4.81361 | −0.583736 | ||||||||
\(69\) | 21.0872 | 2.53860 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.338044 | −0.0401185 | −0.0200592 | − | 0.999799i | \(-0.506385\pi\) | ||||
−0.0200592 | + | 0.999799i | \(0.506385\pi\) | |||||||
\(72\) | −4.91638 | −0.579401 | ||||||||
\(73\) | 13.6952 | 1.60291 | 0.801454 | − | 0.598057i | \(-0.204060\pi\) | ||||
0.801454 | + | 0.598057i | \(0.204060\pi\) | |||||||
\(74\) | 6.75971 | 0.785800 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.28917 | 0.147878 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 13.8328 | 1.56625 | ||||||||
\(79\) | −6.28917 | −0.707587 | −0.353793 | − | 0.935324i | \(-0.615108\pi\) | ||||
−0.353793 | + | 0.935324i | \(0.615108\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.421663 | 0.0468514 | ||||||||
\(82\) | 12.4111 | 1.37058 | ||||||||
\(83\) | −9.75971 | −1.07127 | −0.535634 | − | 0.844451i | \(-0.679927\pi\) | ||||
−0.535634 | + | 0.844451i | \(0.679927\pi\) | |||||||
\(84\) | −2.81361 | −0.306990 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.62721 | −0.283300 | ||||||||
\(87\) | 5.25443 | 0.563334 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −6.71083 | −0.711347 | −0.355673 | − | 0.934610i | \(-0.615748\pi\) | ||||
−0.355673 | + | 0.934610i | \(0.615748\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.91638 | 0.515377 | ||||||||
\(92\) | −7.49472 | −0.781378 | ||||||||
\(93\) | −25.7491 | −2.67006 | ||||||||
\(94\) | 11.0192 | 1.13654 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.81361 | 0.287163 | ||||||||
\(97\) | 0.338044 | 0.0343232 | 0.0171616 | − | 0.999853i | \(-0.494537\pi\) | ||||
0.0171616 | + | 0.999853i | \(0.494537\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 4.91638 | 0.494115 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.5139 | 1.64319 | 0.821596 | − | 0.570070i | \(-0.193084\pi\) | ||||
0.821596 | + | 0.570070i | \(0.193084\pi\) | |||||||
\(102\) | −13.5436 | −1.34102 | ||||||||
\(103\) | −5.83779 | −0.575214 | −0.287607 | − | 0.957748i | \(-0.592860\pi\) | ||||
−0.287607 | + | 0.957748i | \(0.592860\pi\) | |||||||
\(104\) | −4.91638 | −0.482091 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.74914 | −0.946921 | ||||||||
\(107\) | 0.0488759 | 0.00472501 | 0.00236251 | − | 0.999997i | \(-0.499248\pi\) | ||||
0.00236251 | + | 0.999997i | \(0.499248\pi\) | |||||||
\(108\) | −5.39194 | −0.518840 | ||||||||
\(109\) | 0.240293 | 0.0230159 | 0.0115079 | − | 0.999934i | \(-0.496337\pi\) | ||||
0.0115079 | + | 0.999934i | \(0.496337\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 19.0192 | 1.80522 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 21.0036 | 1.97585 | 0.987925 | − | 0.154934i | \(-0.0495164\pi\) | ||||
0.987925 | + | 0.154934i | \(0.0495164\pi\) | |||||||
\(114\) | 3.62721 | 0.339720 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.86751 | −0.173394 | ||||||||
\(117\) | 24.1708 | 2.23459 | ||||||||
\(118\) | −1.39194 | −0.128139 | ||||||||
\(119\) | −4.81361 | −0.441263 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −6.57834 | −0.595575 | ||||||||
\(123\) | 34.9200 | 3.14863 | ||||||||
\(124\) | 9.15165 | 0.821843 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.91638 | −0.437986 | ||||||||
\(127\) | −4.96526 | −0.440595 | −0.220298 | − | 0.975433i | \(-0.570703\pi\) | ||||
−0.220298 | + | 0.975433i | \(0.570703\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −7.39194 | −0.650824 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.1325 | 1.06002 | 0.530010 | − | 0.847991i | \(-0.322188\pi\) | ||||
0.530010 | + | 0.847991i | \(0.322188\pi\) | |||||||
\(132\) | −2.81361 | −0.244893 | ||||||||
\(133\) | 1.28917 | 0.111785 | ||||||||
\(134\) | 3.62721 | 0.313343 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.81361 | 0.412763 | ||||||||
\(137\) | 16.7491 | 1.43098 | 0.715488 | − | 0.698625i | \(-0.246204\pi\) | ||||
0.715488 | + | 0.698625i | \(0.246204\pi\) | |||||||
\(138\) | −21.0872 | −1.79506 | ||||||||
\(139\) | −22.5819 | −1.91537 | −0.957686 | − | 0.287814i | \(-0.907071\pi\) | ||||
−0.957686 | + | 0.287814i | \(0.907071\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 31.0036 | 2.61097 | ||||||||
\(142\) | 0.338044 | 0.0283681 | ||||||||
\(143\) | 4.91638 | 0.411128 | ||||||||
\(144\) | 4.91638 | 0.409698 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −13.6952 | −1.13343 | ||||||||
\(147\) | −2.81361 | −0.232062 | ||||||||
\(148\) | −6.75971 | −0.555645 | ||||||||
\(149\) | −13.4217 | −1.09955 | −0.549773 | − | 0.835314i | \(-0.685286\pi\) | ||||
−0.549773 | + | 0.835314i | \(0.685286\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.2544 | −1.24139 | −0.620694 | − | 0.784053i | \(-0.713149\pi\) | ||||
−0.620694 | + | 0.784053i | \(0.713149\pi\) | |||||||
\(152\) | −1.28917 | −0.104565 | ||||||||
\(153\) | −23.6655 | −1.91324 | ||||||||
\(154\) | −1.00000 | −0.0805823 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −13.8328 | −1.10751 | ||||||||
\(157\) | 8.50885 | 0.679080 | 0.339540 | − | 0.940592i | \(-0.389729\pi\) | ||||
0.339540 | + | 0.940592i | \(0.389729\pi\) | |||||||
\(158\) | 6.28917 | 0.500339 | ||||||||
\(159\) | −27.4303 | −2.17536 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.49472 | −0.590667 | ||||||||
\(162\) | −0.421663 | −0.0331290 | ||||||||
\(163\) | −15.7250 | −1.23167 | −0.615837 | − | 0.787873i | \(-0.711182\pi\) | ||||
−0.615837 | + | 0.787873i | \(0.711182\pi\) | |||||||
\(164\) | −12.4111 | −0.969144 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.75971 | 0.757500 | ||||||||
\(167\) | 14.6167 | 1.13107 | 0.565535 | − | 0.824724i | \(-0.308670\pi\) | ||||
0.565535 | + | 0.824724i | \(0.308670\pi\) | |||||||
\(168\) | 2.81361 | 0.217074 | ||||||||
\(169\) | 11.1708 | 0.859293 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.33804 | 0.484682 | ||||||||
\(172\) | 2.62721 | 0.200323 | ||||||||
\(173\) | −3.08362 | −0.234443 | −0.117222 | − | 0.993106i | \(-0.537399\pi\) | ||||
−0.117222 | + | 0.993106i | \(0.537399\pi\) | |||||||
\(174\) | −5.25443 | −0.398337 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −3.91638 | −0.294373 | ||||||||
\(178\) | 6.71083 | 0.502998 | ||||||||
\(179\) | −17.0489 | −1.27429 | −0.637146 | − | 0.770743i | \(-0.719885\pi\) | ||||
−0.637146 | + | 0.770743i | \(0.719885\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.0872 | −0.824104 | −0.412052 | − | 0.911160i | \(-0.635188\pi\) | ||||
−0.412052 | + | 0.911160i | \(0.635188\pi\) | |||||||
\(182\) | −4.91638 | −0.364426 | ||||||||
\(183\) | −18.5089 | −1.36821 | ||||||||
\(184\) | 7.49472 | 0.552518 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 25.7491 | 1.88802 | ||||||||
\(187\) | −4.81361 | −0.352006 | ||||||||
\(188\) | −11.0192 | −0.803655 | ||||||||
\(189\) | −5.39194 | −0.392206 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.55416 | −0.112455 | −0.0562274 | − | 0.998418i | \(-0.517907\pi\) | ||||
−0.0562274 | + | 0.998418i | \(0.517907\pi\) | |||||||
\(192\) | −2.81361 | −0.203055 | ||||||||
\(193\) | −12.9894 | −0.935000 | −0.467500 | − | 0.883993i | \(-0.654845\pi\) | ||||
−0.467500 | + | 0.883993i | \(0.654845\pi\) | |||||||
\(194\) | −0.338044 | −0.0242702 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 0.710831 | 0.0506446 | 0.0253223 | − | 0.999679i | \(-0.491939\pi\) | ||||
0.0253223 | + | 0.999679i | \(0.491939\pi\) | |||||||
\(198\) | −4.91638 | −0.349392 | ||||||||
\(199\) | 15.2197 | 1.07889 | 0.539447 | − | 0.842019i | \(-0.318633\pi\) | ||||
0.539447 | + | 0.842019i | \(0.318633\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.2056 | 0.719844 | ||||||||
\(202\) | −16.5139 | −1.16191 | ||||||||
\(203\) | −1.86751 | −0.131073 | ||||||||
\(204\) | 13.5436 | 0.948241 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.83779 | 0.406738 | ||||||||
\(207\) | −36.8469 | −2.56104 | ||||||||
\(208\) | 4.91638 | 0.340890 | ||||||||
\(209\) | 1.28917 | 0.0891737 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0242 | −0.827779 | −0.413889 | − | 0.910327i | \(-0.635830\pi\) | ||||
−0.413889 | + | 0.910327i | \(0.635830\pi\) | |||||||
\(212\) | 9.74914 | 0.669574 | ||||||||
\(213\) | 0.951124 | 0.0651699 | ||||||||
\(214\) | −0.0488759 | −0.00334109 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.39194 | 0.366875 | ||||||||
\(217\) | 9.15165 | 0.621255 | ||||||||
\(218\) | −0.240293 | −0.0162747 | ||||||||
\(219\) | −38.5330 | −2.60382 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.6655 | −1.59192 | ||||||||
\(222\) | −19.0192 | −1.27648 | ||||||||
\(223\) | −6.03831 | −0.404355 | −0.202178 | − | 0.979349i | \(-0.564802\pi\) | ||||
−0.202178 | + | 0.979349i | \(0.564802\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −21.0036 | −1.39714 | ||||||||
\(227\) | −4.60303 | −0.305514 | −0.152757 | − | 0.988264i | \(-0.548815\pi\) | ||||
−0.152757 | + | 0.988264i | \(0.548815\pi\) | |||||||
\(228\) | −3.62721 | −0.240218 | ||||||||
\(229\) | −5.42166 | −0.358274 | −0.179137 | − | 0.983824i | \(-0.557330\pi\) | ||||
−0.179137 | + | 0.983824i | \(0.557330\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.81361 | −0.185122 | ||||||||
\(232\) | 1.86751 | 0.122608 | ||||||||
\(233\) | 2.57834 | 0.168912 | 0.0844562 | − | 0.996427i | \(-0.473085\pi\) | ||||
0.0844562 | + | 0.996427i | \(0.473085\pi\) | |||||||
\(234\) | −24.1708 | −1.58010 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.39194 | 0.0906078 | ||||||||
\(237\) | 17.6952 | 1.14943 | ||||||||
\(238\) | 4.81361 | 0.312020 | ||||||||
\(239\) | −21.0630 | −1.36245 | −0.681226 | − | 0.732073i | \(-0.738553\pi\) | ||||
−0.681226 | + | 0.732073i | \(0.738553\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.0192 | 1.35396 | 0.676981 | − | 0.736000i | \(-0.263288\pi\) | ||||
0.676981 | + | 0.736000i | \(0.263288\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 14.9894 | 0.961573 | ||||||||
\(244\) | 6.57834 | 0.421135 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −34.9200 | −2.22641 | ||||||||
\(247\) | 6.33804 | 0.403280 | ||||||||
\(248\) | −9.15165 | −0.581130 | ||||||||
\(249\) | 27.4600 | 1.74021 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.4897 | −1.73513 | −0.867567 | − | 0.497320i | \(-0.834317\pi\) | ||||
−0.867567 | + | 0.497320i | \(0.834317\pi\) | |||||||
\(252\) | 4.91638 | 0.309703 | ||||||||
\(253\) | −7.49472 | −0.471189 | ||||||||
\(254\) | 4.96526 | 0.311548 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.23025 | 0.513389 | 0.256694 | − | 0.966493i | \(-0.417367\pi\) | ||||
0.256694 | + | 0.966493i | \(0.417367\pi\) | |||||||
\(258\) | 7.39194 | 0.460202 | ||||||||
\(259\) | −6.75971 | −0.420028 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.18137 | −0.568313 | ||||||||
\(262\) | −12.1325 | −0.749548 | ||||||||
\(263\) | −8.96526 | −0.552821 | −0.276411 | − | 0.961040i | \(-0.589145\pi\) | ||||
−0.276411 | + | 0.961040i | \(0.589145\pi\) | |||||||
\(264\) | 2.81361 | 0.173166 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.28917 | −0.0790440 | ||||||||
\(267\) | 18.8816 | 1.15554 | ||||||||
\(268\) | −3.62721 | −0.221567 | ||||||||
\(269\) | 7.56777 | 0.461415 | 0.230708 | − | 0.973023i | \(-0.425896\pi\) | ||||
0.230708 | + | 0.973023i | \(0.425896\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.6167 | 1.25237 | 0.626186 | − | 0.779674i | \(-0.284615\pi\) | ||||
0.626186 | + | 0.779674i | \(0.284615\pi\) | |||||||
\(272\) | −4.81361 | −0.291868 | ||||||||
\(273\) | −13.8328 | −0.837197 | ||||||||
\(274\) | −16.7491 | −1.01185 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 21.0872 | 1.26930 | ||||||||
\(277\) | −22.3517 | −1.34298 | −0.671491 | − | 0.741013i | \(-0.734346\pi\) | ||||
−0.671491 | + | 0.741013i | \(0.734346\pi\) | |||||||
\(278\) | 22.5819 | 1.35437 | ||||||||
\(279\) | 44.9930 | 2.69366 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.20555 | −0.370192 | −0.185096 | − | 0.982720i | \(-0.559260\pi\) | ||||
−0.185096 | + | 0.982720i | \(0.559260\pi\) | |||||||
\(282\) | −31.0036 | −1.84624 | ||||||||
\(283\) | 10.6761 | 0.634628 | 0.317314 | − | 0.948321i | \(-0.397219\pi\) | ||||
0.317314 | + | 0.948321i | \(0.397219\pi\) | |||||||
\(284\) | −0.338044 | −0.0200592 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.91638 | −0.290712 | ||||||||
\(287\) | −12.4111 | −0.732604 | ||||||||
\(288\) | −4.91638 | −0.289701 | ||||||||
\(289\) | 6.17081 | 0.362989 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.951124 | −0.0557559 | ||||||||
\(292\) | 13.6952 | 0.801454 | ||||||||
\(293\) | 12.2736 | 0.717030 | 0.358515 | − | 0.933524i | \(-0.383283\pi\) | ||||
0.358515 | + | 0.933524i | \(0.383283\pi\) | |||||||
\(294\) | 2.81361 | 0.164093 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.75971 | 0.392900 | ||||||||
\(297\) | −5.39194 | −0.312872 | ||||||||
\(298\) | 13.4217 | 0.777496 | ||||||||
\(299\) | −36.8469 | −2.13091 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.62721 | 0.151430 | ||||||||
\(302\) | 15.2544 | 0.877794 | ||||||||
\(303\) | −46.4635 | −2.66926 | ||||||||
\(304\) | 1.28917 | 0.0739389 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 23.6655 | 1.35287 | ||||||||
\(307\) | −19.2544 | −1.09891 | −0.549454 | − | 0.835524i | \(-0.685164\pi\) | ||||
−0.549454 | + | 0.835524i | \(0.685164\pi\) | |||||||
\(308\) | 1.00000 | 0.0569803 | ||||||||
\(309\) | 16.4252 | 0.934399 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.36725 | −0.0775295 | −0.0387647 | − | 0.999248i | \(-0.512342\pi\) | ||||
−0.0387647 | + | 0.999248i | \(0.512342\pi\) | |||||||
\(312\) | 13.8328 | 0.783126 | ||||||||
\(313\) | 32.2822 | 1.82470 | 0.912348 | − | 0.409415i | \(-0.134267\pi\) | ||||
0.912348 | + | 0.409415i | \(0.134267\pi\) | |||||||
\(314\) | −8.50885 | −0.480182 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.28917 | −0.353793 | ||||||||
\(317\) | −11.3380 | −0.636808 | −0.318404 | − | 0.947955i | \(-0.603147\pi\) | ||||
−0.318404 | + | 0.947955i | \(0.603147\pi\) | |||||||
\(318\) | 27.4303 | 1.53821 | ||||||||
\(319\) | −1.86751 | −0.104560 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.137518 | −0.00767548 | ||||||||
\(322\) | 7.49472 | 0.417664 | ||||||||
\(323\) | −6.20555 | −0.345286 | ||||||||
\(324\) | 0.421663 | 0.0234257 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.7250 | 0.870925 | ||||||||
\(327\) | −0.676089 | −0.0373878 | ||||||||
\(328\) | 12.4111 | 0.685288 | ||||||||
\(329\) | −11.0192 | −0.607506 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.7144 | −1.79815 | −0.899073 | − | 0.437799i | \(-0.855758\pi\) | ||||
−0.899073 | + | 0.437799i | \(0.855758\pi\) | |||||||
\(332\) | −9.75971 | −0.535634 | ||||||||
\(333\) | −33.2333 | −1.82117 | ||||||||
\(334\) | −14.6167 | −0.799788 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.81361 | −0.153495 | ||||||||
\(337\) | −18.5472 | −1.01033 | −0.505164 | − | 0.863023i | \(-0.668568\pi\) | ||||
−0.505164 | + | 0.863023i | \(0.668568\pi\) | |||||||
\(338\) | −11.1708 | −0.607612 | ||||||||
\(339\) | −59.0958 | −3.20964 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.15165 | 0.495590 | ||||||||
\(342\) | −6.33804 | −0.342722 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −2.62721 | −0.141650 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.08362 | 0.165776 | ||||||||
\(347\) | −6.28917 | −0.337620 | −0.168810 | − | 0.985649i | \(-0.553992\pi\) | ||||
−0.168810 | + | 0.985649i | \(0.553992\pi\) | |||||||
\(348\) | 5.25443 | 0.281667 | ||||||||
\(349\) | −23.2283 | −1.24338 | −0.621691 | − | 0.783263i | \(-0.713554\pi\) | ||||
−0.621691 | + | 0.783263i | \(0.713554\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.5089 | −1.41494 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 9.21968 | 0.490714 | 0.245357 | − | 0.969433i | \(-0.421095\pi\) | ||||
0.245357 | + | 0.969433i | \(0.421095\pi\) | |||||||
\(354\) | 3.91638 | 0.208153 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.71083 | −0.355673 | ||||||||
\(357\) | 13.5436 | 0.716803 | ||||||||
\(358\) | 17.0489 | 0.901061 | ||||||||
\(359\) | 28.0766 | 1.48183 | 0.740914 | − | 0.671600i | \(-0.234393\pi\) | ||||
0.740914 | + | 0.671600i | \(0.234393\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.3380 | −0.912529 | ||||||||
\(362\) | 11.0872 | 0.582730 | ||||||||
\(363\) | −2.81361 | −0.147676 | ||||||||
\(364\) | 4.91638 | 0.257688 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 18.5089 | 0.967473 | ||||||||
\(367\) | −6.87807 | −0.359032 | −0.179516 | − | 0.983755i | \(-0.557453\pi\) | ||||
−0.179516 | + | 0.983755i | \(0.557453\pi\) | |||||||
\(368\) | −7.49472 | −0.390689 | ||||||||
\(369\) | −61.0177 | −3.17645 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.74914 | 0.506150 | ||||||||
\(372\) | −25.7491 | −1.33503 | ||||||||
\(373\) | −10.3627 | −0.536562 | −0.268281 | − | 0.963341i | \(-0.586456\pi\) | ||||
−0.268281 | + | 0.963341i | \(0.586456\pi\) | |||||||
\(374\) | 4.81361 | 0.248906 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.0192 | 0.568270 | ||||||||
\(377\) | −9.18137 | −0.472865 | ||||||||
\(378\) | 5.39194 | 0.277332 | ||||||||
\(379\) | −32.4494 | −1.66681 | −0.833407 | − | 0.552659i | \(-0.813613\pi\) | ||||
−0.833407 | + | 0.552659i | \(0.813613\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.9703 | 0.715719 | ||||||||
\(382\) | 1.55416 | 0.0795176 | ||||||||
\(383\) | −30.7194 | −1.56969 | −0.784845 | − | 0.619693i | \(-0.787257\pi\) | ||||
−0.784845 | + | 0.619693i | \(0.787257\pi\) | |||||||
\(384\) | 2.81361 | 0.143581 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.9894 | 0.661145 | ||||||||
\(387\) | 12.9164 | 0.656577 | ||||||||
\(388\) | 0.338044 | 0.0171616 | ||||||||
\(389\) | −29.3169 | −1.48643 | −0.743213 | − | 0.669054i | \(-0.766699\pi\) | ||||
−0.743213 | + | 0.669054i | \(0.766699\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.0766 | 1.82447 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −34.1361 | −1.72194 | ||||||||
\(394\) | −0.710831 | −0.0358112 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.91638 | 0.247057 | ||||||||
\(397\) | −22.1955 | −1.11396 | −0.556980 | − | 0.830526i | \(-0.688040\pi\) | ||||
−0.556980 | + | 0.830526i | \(0.688040\pi\) | |||||||
\(398\) | −15.2197 | −0.762894 | ||||||||
\(399\) | −3.62721 | −0.181588 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.2544 | −1.01146 | −0.505729 | − | 0.862692i | \(-0.668776\pi\) | ||||
−0.505729 | + | 0.862692i | \(0.668776\pi\) | |||||||
\(402\) | −10.2056 | −0.509007 | ||||||||
\(403\) | 44.9930 | 2.24126 | ||||||||
\(404\) | 16.5139 | 0.821596 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.86751 | 0.0926827 | ||||||||
\(407\) | −6.75971 | −0.335066 | ||||||||
\(408\) | −13.5436 | −0.670508 | ||||||||
\(409\) | −22.1658 | −1.09603 | −0.548014 | − | 0.836469i | \(-0.684616\pi\) | ||||
−0.548014 | + | 0.836469i | \(0.684616\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −47.1255 | −2.32453 | ||||||||
\(412\) | −5.83779 | −0.287607 | ||||||||
\(413\) | 1.39194 | 0.0684931 | ||||||||
\(414\) | 36.8469 | 1.81093 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.91638 | −0.241045 | ||||||||
\(417\) | 63.5366 | 3.11140 | ||||||||
\(418\) | −1.28917 | −0.0630553 | ||||||||
\(419\) | 36.5769 | 1.78690 | 0.893449 | − | 0.449165i | \(-0.148278\pi\) | ||||
0.893449 | + | 0.449165i | \(0.148278\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.94108 | −0.143339 | −0.0716697 | − | 0.997428i | \(-0.522833\pi\) | ||||
−0.0716697 | + | 0.997428i | \(0.522833\pi\) | |||||||
\(422\) | 12.0242 | 0.585328 | ||||||||
\(423\) | −54.1744 | −2.63405 | ||||||||
\(424\) | −9.74914 | −0.473460 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.951124 | −0.0460821 | ||||||||
\(427\) | 6.57834 | 0.318348 | ||||||||
\(428\) | 0.0488759 | 0.00236251 | ||||||||
\(429\) | −13.8328 | −0.667852 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.53303 | 0.314685 | 0.157343 | − | 0.987544i | \(-0.449707\pi\) | ||||
0.157343 | + | 0.987544i | \(0.449707\pi\) | |||||||
\(432\) | −5.39194 | −0.259420 | ||||||||
\(433\) | 16.0347 | 0.770581 | 0.385290 | − | 0.922795i | \(-0.374101\pi\) | ||||
0.385290 | + | 0.922795i | \(0.374101\pi\) | |||||||
\(434\) | −9.15165 | −0.439293 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.240293 | 0.0115079 | ||||||||
\(437\) | −9.66196 | −0.462194 | ||||||||
\(438\) | 38.5330 | 1.84118 | ||||||||
\(439\) | −14.2650 | −0.680831 | −0.340415 | − | 0.940275i | \(-0.610568\pi\) | ||||
−0.340415 | + | 0.940275i | \(0.610568\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.91638 | 0.234113 | ||||||||
\(442\) | 23.6655 | 1.12565 | ||||||||
\(443\) | −13.9022 | −0.660516 | −0.330258 | − | 0.943891i | \(-0.607136\pi\) | ||||
−0.330258 | + | 0.943891i | \(0.607136\pi\) | |||||||
\(444\) | 19.0192 | 0.902609 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.03831 | 0.285922 | ||||||||
\(447\) | 37.7633 | 1.78614 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 11.5089 | 0.543136 | 0.271568 | − | 0.962419i | \(-0.412458\pi\) | ||||
0.271568 | + | 0.962419i | \(0.412458\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.4111 | −0.584416 | ||||||||
\(452\) | 21.0036 | 0.987925 | ||||||||
\(453\) | 42.9200 | 2.01656 | ||||||||
\(454\) | 4.60303 | 0.216031 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.62721 | 0.169860 | ||||||||
\(457\) | −17.4600 | −0.816743 | −0.408372 | − | 0.912816i | \(-0.633903\pi\) | ||||
−0.408372 | + | 0.912816i | \(0.633903\pi\) | |||||||
\(458\) | 5.42166 | 0.253338 | ||||||||
\(459\) | 25.9547 | 1.21146 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.35363 | 0.435642 | 0.217821 | − | 0.975989i | \(-0.430105\pi\) | ||||
0.217821 | + | 0.975989i | \(0.430105\pi\) | |||||||
\(462\) | 2.81361 | 0.130901 | ||||||||
\(463\) | 16.3380 | 0.759293 | 0.379647 | − | 0.925132i | \(-0.376046\pi\) | ||||
0.379647 | + | 0.925132i | \(0.376046\pi\) | |||||||
\(464\) | −1.86751 | −0.0866968 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.57834 | −0.119439 | ||||||||
\(467\) | 3.55918 | 0.164699 | 0.0823496 | − | 0.996604i | \(-0.473758\pi\) | ||||
0.0823496 | + | 0.996604i | \(0.473758\pi\) | |||||||
\(468\) | 24.1708 | 1.11730 | ||||||||
\(469\) | −3.62721 | −0.167489 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.9406 | −1.10312 | ||||||||
\(472\) | −1.39194 | −0.0640694 | ||||||||
\(473\) | 2.62721 | 0.120799 | ||||||||
\(474\) | −17.6952 | −0.812770 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.81361 | −0.220631 | ||||||||
\(477\) | 47.9305 | 2.19459 | ||||||||
\(478\) | 21.0630 | 0.963400 | ||||||||
\(479\) | −38.7144 | −1.76891 | −0.884453 | − | 0.466629i | \(-0.845468\pi\) | ||||
−0.884453 | + | 0.466629i | \(0.845468\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.2333 | −1.51531 | ||||||||
\(482\) | −21.0192 | −0.957396 | ||||||||
\(483\) | 21.0872 | 0.959500 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −14.9894 | −0.679935 | ||||||||
\(487\) | −14.8781 | −0.674190 | −0.337095 | − | 0.941471i | \(-0.609444\pi\) | ||||
−0.337095 | + | 0.941471i | \(0.609444\pi\) | |||||||
\(488\) | −6.57834 | −0.297787 | ||||||||
\(489\) | 44.2439 | 2.00078 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.2927 | 0.554764 | 0.277382 | − | 0.960760i | \(-0.410533\pi\) | ||||
0.277382 | + | 0.960760i | \(0.410533\pi\) | |||||||
\(492\) | 34.9200 | 1.57431 | ||||||||
\(493\) | 8.98944 | 0.404864 | ||||||||
\(494\) | −6.33804 | −0.285162 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.15165 | 0.410921 | ||||||||
\(497\) | −0.338044 | −0.0151634 | ||||||||
\(498\) | −27.4600 | −1.23051 | ||||||||
\(499\) | 20.0383 | 0.897038 | 0.448519 | − | 0.893773i | \(-0.351952\pi\) | ||||
0.448519 | + | 0.893773i | \(0.351952\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −41.1255 | −1.83735 | ||||||||
\(502\) | 27.4897 | 1.22693 | ||||||||
\(503\) | 37.6061 | 1.67677 | 0.838386 | − | 0.545077i | \(-0.183499\pi\) | ||||
0.838386 | + | 0.545077i | \(0.183499\pi\) | |||||||
\(504\) | −4.91638 | −0.218993 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.49472 | 0.333181 | ||||||||
\(507\) | −31.4303 | −1.39587 | ||||||||
\(508\) | −4.96526 | −0.220298 | ||||||||
\(509\) | −6.04836 | −0.268089 | −0.134044 | − | 0.990975i | \(-0.542796\pi\) | ||||
−0.134044 | + | 0.990975i | \(0.542796\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.6952 | 0.605842 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.95112 | −0.306900 | ||||||||
\(514\) | −8.23025 | −0.363021 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.39194 | −0.325412 | ||||||||
\(517\) | −11.0192 | −0.484622 | ||||||||
\(518\) | 6.75971 | 0.297004 | ||||||||
\(519\) | 8.67609 | 0.380838 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.90582 | 0.346360 | 0.173180 | − | 0.984890i | \(-0.444596\pi\) | ||||
0.173180 | + | 0.984890i | \(0.444596\pi\) | |||||||
\(522\) | 9.18137 | 0.401858 | ||||||||
\(523\) | −12.6413 | −0.552767 | −0.276384 | − | 0.961047i | \(-0.589136\pi\) | ||||
−0.276384 | + | 0.961047i | \(0.589136\pi\) | |||||||
\(524\) | 12.1325 | 0.530010 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.96526 | 0.390904 | ||||||||
\(527\) | −44.0524 | −1.91895 | ||||||||
\(528\) | −2.81361 | −0.122447 | ||||||||
\(529\) | 33.1708 | 1.44221 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.84333 | 0.296975 | ||||||||
\(532\) | 1.28917 | 0.0558925 | ||||||||
\(533\) | −61.0177 | −2.64297 | ||||||||
\(534\) | −18.8816 | −0.817088 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.62721 | 0.156672 | ||||||||
\(537\) | 47.9688 | 2.07001 | ||||||||
\(538\) | −7.56777 | −0.326270 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.7980 | −1.79704 | −0.898519 | − | 0.438935i | \(-0.855356\pi\) | ||||
−0.898519 | + | 0.438935i | \(0.855356\pi\) | |||||||
\(542\) | −20.6167 | −0.885561 | ||||||||
\(543\) | 31.1950 | 1.33871 | ||||||||
\(544\) | 4.81361 | 0.206382 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 13.8328 | 0.591988 | ||||||||
\(547\) | 3.63778 | 0.155540 | 0.0777700 | − | 0.996971i | \(-0.475220\pi\) | ||||
0.0777700 | + | 0.996971i | \(0.475220\pi\) | |||||||
\(548\) | 16.7491 | 0.715488 | ||||||||
\(549\) | 32.3416 | 1.38031 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.40753 | −0.102564 | ||||||||
\(552\) | −21.0872 | −0.897530 | ||||||||
\(553\) | −6.28917 | −0.267443 | ||||||||
\(554\) | 22.3517 | 0.949631 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −22.5819 | −0.957686 | ||||||||
\(557\) | −24.8852 | −1.05442 | −0.527210 | − | 0.849735i | \(-0.676762\pi\) | ||||
−0.527210 | + | 0.849735i | \(0.676762\pi\) | |||||||
\(558\) | −44.9930 | −1.90471 | ||||||||
\(559\) | 12.9164 | 0.546305 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.5436 | 0.571811 | ||||||||
\(562\) | 6.20555 | 0.261765 | ||||||||
\(563\) | 5.10831 | 0.215290 | 0.107645 | − | 0.994189i | \(-0.465669\pi\) | ||||
0.107645 | + | 0.994189i | \(0.465669\pi\) | |||||||
\(564\) | 31.0036 | 1.30549 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10.6761 | −0.448749 | ||||||||
\(567\) | 0.421663 | 0.0177082 | ||||||||
\(568\) | 0.338044 | 0.0141840 | ||||||||
\(569\) | 21.4116 | 0.897622 | 0.448811 | − | 0.893627i | \(-0.351848\pi\) | ||||
0.448811 | + | 0.893627i | \(0.351848\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.85746 | −0.412522 | −0.206261 | − | 0.978497i | \(-0.566130\pi\) | ||||
−0.206261 | + | 0.978497i | \(0.566130\pi\) | |||||||
\(572\) | 4.91638 | 0.205564 | ||||||||
\(573\) | 4.37279 | 0.182676 | ||||||||
\(574\) | 12.4111 | 0.518029 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.91638 | 0.204849 | ||||||||
\(577\) | −5.77332 | −0.240347 | −0.120173 | − | 0.992753i | \(-0.538345\pi\) | ||||
−0.120173 | + | 0.992753i | \(0.538345\pi\) | |||||||
\(578\) | −6.17081 | −0.256672 | ||||||||
\(579\) | 36.5472 | 1.51885 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.75971 | −0.404901 | ||||||||
\(582\) | 0.951124 | 0.0394254 | ||||||||
\(583\) | 9.74914 | 0.403768 | ||||||||
\(584\) | −13.6952 | −0.566713 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.2736 | −0.507017 | ||||||||
\(587\) | −28.1361 | −1.16130 | −0.580650 | − | 0.814153i | \(-0.697201\pi\) | ||||
−0.580650 | + | 0.814153i | \(0.697201\pi\) | |||||||
\(588\) | −2.81361 | −0.116031 | ||||||||
\(589\) | 11.7980 | 0.486129 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.00000 | −0.0822690 | ||||||||
\(592\) | −6.75971 | −0.277822 | ||||||||
\(593\) | −20.8917 | −0.857919 | −0.428959 | − | 0.903324i | \(-0.641120\pi\) | ||||
−0.428959 | + | 0.903324i | \(0.641120\pi\) | |||||||
\(594\) | 5.39194 | 0.221234 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13.4217 | −0.549773 | ||||||||
\(597\) | −42.8222 | −1.75260 | ||||||||
\(598\) | 36.8469 | 1.50678 | ||||||||
\(599\) | 38.7839 | 1.58467 | 0.792333 | − | 0.610088i | \(-0.208866\pi\) | ||||
0.792333 | + | 0.610088i | \(0.208866\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.0857 | 1.67592 | 0.837961 | − | 0.545730i | \(-0.183748\pi\) | ||||
0.837961 | + | 0.545730i | \(0.183748\pi\) | |||||||
\(602\) | −2.62721 | −0.107077 | ||||||||
\(603\) | −17.8328 | −0.726206 | ||||||||
\(604\) | −15.2544 | −0.620694 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 46.4635 | 1.88745 | ||||||||
\(607\) | 9.36222 | 0.380001 | 0.190000 | − | 0.981784i | \(-0.439151\pi\) | ||||
0.190000 | + | 0.981784i | \(0.439151\pi\) | |||||||
\(608\) | −1.28917 | −0.0522827 | ||||||||
\(609\) | 5.25443 | 0.212920 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −54.1744 | −2.19166 | ||||||||
\(612\) | −23.6655 | −0.956622 | ||||||||
\(613\) | 10.4705 | 0.422901 | 0.211451 | − | 0.977389i | \(-0.432181\pi\) | ||||
0.211451 | + | 0.977389i | \(0.432181\pi\) | |||||||
\(614\) | 19.2544 | 0.777045 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.00000 | −0.0402911 | ||||||||
\(617\) | −15.9200 | −0.640913 | −0.320457 | − | 0.947263i | \(-0.603836\pi\) | ||||
−0.320457 | + | 0.947263i | \(0.603836\pi\) | |||||||
\(618\) | −16.4252 | −0.660720 | ||||||||
\(619\) | 17.5280 | 0.704510 | 0.352255 | − | 0.935904i | \(-0.385415\pi\) | ||||
0.352255 | + | 0.935904i | \(0.385415\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 40.4111 | 1.62164 | ||||||||
\(622\) | 1.36725 | 0.0548216 | ||||||||
\(623\) | −6.71083 | −0.268864 | ||||||||
\(624\) | −13.8328 | −0.553754 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −32.2822 | −1.29026 | ||||||||
\(627\) | −3.62721 | −0.144857 | ||||||||
\(628\) | 8.50885 | 0.339540 | ||||||||
\(629\) | 32.5386 | 1.29740 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.8122 | 0.908138 | 0.454069 | − | 0.890967i | \(-0.349972\pi\) | ||||
0.454069 | + | 0.890967i | \(0.349972\pi\) | |||||||
\(632\) | 6.28917 | 0.250170 | ||||||||
\(633\) | 33.8313 | 1.34467 | ||||||||
\(634\) | 11.3380 | 0.450291 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −27.4303 | −1.08768 | ||||||||
\(637\) | 4.91638 | 0.194794 | ||||||||
\(638\) | 1.86751 | 0.0739353 | ||||||||
\(639\) | −1.66196 | −0.0657459 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.7350 | 0.424007 | 0.212004 | − | 0.977269i | \(-0.432001\pi\) | ||||
0.212004 | + | 0.977269i | \(0.432001\pi\) | |||||||
\(642\) | 0.137518 | 0.00542739 | ||||||||
\(643\) | −14.2736 | −0.562895 | −0.281448 | − | 0.959577i | \(-0.590815\pi\) | ||||
−0.281448 | + | 0.959577i | \(0.590815\pi\) | |||||||
\(644\) | −7.49472 | −0.295333 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.20555 | 0.244154 | ||||||||
\(647\) | −46.9597 | −1.84618 | −0.923089 | − | 0.384588i | \(-0.874344\pi\) | ||||
−0.923089 | + | 0.384588i | \(0.874344\pi\) | |||||||
\(648\) | −0.421663 | −0.0165645 | ||||||||
\(649\) | 1.39194 | 0.0546386 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25.7491 | −1.00919 | ||||||||
\(652\) | −15.7250 | −0.615837 | ||||||||
\(653\) | −21.9164 | −0.857654 | −0.428827 | − | 0.903387i | \(-0.641073\pi\) | ||||
−0.428827 | + | 0.903387i | \(0.641073\pi\) | |||||||
\(654\) | 0.676089 | 0.0264372 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −12.4111 | −0.484572 | ||||||||
\(657\) | 67.3311 | 2.62683 | ||||||||
\(658\) | 11.0192 | 0.429571 | ||||||||
\(659\) | 12.5819 | 0.490122 | 0.245061 | − | 0.969508i | \(-0.421192\pi\) | ||||
0.245061 | + | 0.969508i | \(0.421192\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.4705 | 0.485048 | 0.242524 | − | 0.970145i | \(-0.422025\pi\) | ||||
0.242524 | + | 0.970145i | \(0.422025\pi\) | |||||||
\(662\) | 32.7144 | 1.27148 | ||||||||
\(663\) | 66.5855 | 2.58597 | ||||||||
\(664\) | 9.75971 | 0.378750 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 33.2333 | 1.28776 | ||||||||
\(667\) | 13.9964 | 0.541944 | ||||||||
\(668\) | 14.6167 | 0.565535 | ||||||||
\(669\) | 16.9894 | 0.656850 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.57834 | 0.253954 | ||||||||
\(672\) | 2.81361 | 0.108537 | ||||||||
\(673\) | 28.4705 | 1.09746 | 0.548729 | − | 0.836000i | \(-0.315112\pi\) | ||||
0.548729 | + | 0.836000i | \(0.315112\pi\) | |||||||
\(674\) | 18.5472 | 0.714410 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.1708 | 0.429646 | ||||||||
\(677\) | 42.1411 | 1.61961 | 0.809807 | − | 0.586697i | \(-0.199572\pi\) | ||||
0.809807 | + | 0.586697i | \(0.199572\pi\) | |||||||
\(678\) | 59.0958 | 2.26956 | ||||||||
\(679\) | 0.338044 | 0.0129730 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.9511 | 0.496288 | ||||||||
\(682\) | −9.15165 | −0.350435 | ||||||||
\(683\) | 1.21611 | 0.0465333 | 0.0232666 | − | 0.999729i | \(-0.492593\pi\) | ||||
0.0232666 | + | 0.999729i | \(0.492593\pi\) | |||||||
\(684\) | 6.33804 | 0.242341 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 15.2544 | 0.581993 | ||||||||
\(688\) | 2.62721 | 0.100162 | ||||||||
\(689\) | 47.9305 | 1.82601 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.4514 | −0.816049 | −0.408025 | − | 0.912971i | \(-0.633782\pi\) | ||||
−0.408025 | + | 0.912971i | \(0.633782\pi\) | |||||||
\(692\) | −3.08362 | −0.117222 | ||||||||
\(693\) | 4.91638 | 0.186758 | ||||||||
\(694\) | 6.28917 | 0.238734 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.25443 | −0.199169 | ||||||||
\(697\) | 59.7422 | 2.26290 | ||||||||
\(698\) | 23.2283 | 0.879203 | ||||||||
\(699\) | −7.25443 | −0.274388 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.3275 | −1.40984 | −0.704920 | − | 0.709287i | \(-0.749017\pi\) | ||||
−0.704920 | + | 0.709287i | \(0.749017\pi\) | |||||||
\(702\) | 26.5089 | 1.00051 | ||||||||
\(703\) | −8.71440 | −0.328670 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.21968 | −0.346987 | ||||||||
\(707\) | 16.5139 | 0.621068 | ||||||||
\(708\) | −3.91638 | −0.147187 | ||||||||
\(709\) | 24.1602 | 0.907357 | 0.453679 | − | 0.891165i | \(-0.350111\pi\) | ||||
0.453679 | + | 0.891165i | \(0.350111\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.9200 | −1.15959 | ||||||||
\(712\) | 6.71083 | 0.251499 | ||||||||
\(713\) | −68.5890 | −2.56868 | ||||||||
\(714\) | −13.5436 | −0.506856 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.0489 | −0.637146 | ||||||||
\(717\) | 59.2630 | 2.21322 | ||||||||
\(718\) | −28.0766 | −1.04781 | ||||||||
\(719\) | 20.8816 | 0.778754 | 0.389377 | − | 0.921079i | \(-0.372690\pi\) | ||||
0.389377 | + | 0.921079i | \(0.372690\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.83779 | −0.217411 | ||||||||
\(722\) | 17.3380 | 0.645255 | ||||||||
\(723\) | −59.1396 | −2.19943 | ||||||||
\(724\) | −11.0872 | −0.412052 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.81361 | 0.104423 | ||||||||
\(727\) | −48.8172 | −1.81053 | −0.905264 | − | 0.424849i | \(-0.860327\pi\) | ||||
−0.905264 | + | 0.424849i | \(0.860327\pi\) | |||||||
\(728\) | −4.91638 | −0.182213 | ||||||||
\(729\) | −43.4394 | −1.60887 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.6464 | −0.467743 | ||||||||
\(732\) | −18.5089 | −0.684107 | ||||||||
\(733\) | −20.6600 | −0.763094 | −0.381547 | − | 0.924349i | \(-0.624609\pi\) | ||||
−0.381547 | + | 0.924349i | \(0.624609\pi\) | |||||||
\(734\) | 6.87807 | 0.253874 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.49472 | 0.276259 | ||||||||
\(737\) | −3.62721 | −0.133610 | ||||||||
\(738\) | 61.0177 | 2.24609 | ||||||||
\(739\) | −8.46355 | −0.311337 | −0.155668 | − | 0.987809i | \(-0.549753\pi\) | ||||
−0.155668 | + | 0.987809i | \(0.549753\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.8328 | −0.655103 | ||||||||
\(742\) | −9.74914 | −0.357902 | ||||||||
\(743\) | 9.27861 | 0.340399 | 0.170200 | − | 0.985410i | \(-0.445559\pi\) | ||||
0.170200 | + | 0.985410i | \(0.445559\pi\) | |||||||
\(744\) | 25.7491 | 0.944009 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.3627 | 0.379407 | ||||||||
\(747\) | −47.9824 | −1.75559 | ||||||||
\(748\) | −4.81361 | −0.176003 | ||||||||
\(749\) | 0.0488759 | 0.00178589 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.9164 | 0.544306 | 0.272153 | − | 0.962254i | \(-0.412264\pi\) | ||||
0.272153 | + | 0.962254i | \(0.412264\pi\) | |||||||
\(752\) | −11.0192 | −0.401827 | ||||||||
\(753\) | 77.3452 | 2.81862 | ||||||||
\(754\) | 9.18137 | 0.334366 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.39194 | −0.196103 | ||||||||
\(757\) | 22.4736 | 0.816817 | 0.408408 | − | 0.912799i | \(-0.366084\pi\) | ||||
0.408408 | + | 0.912799i | \(0.366084\pi\) | |||||||
\(758\) | 32.4494 | 1.17862 | ||||||||
\(759\) | 21.0872 | 0.765416 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.2836 | 0.590281 | 0.295141 | − | 0.955454i | \(-0.404634\pi\) | ||||
0.295141 | + | 0.955454i | \(0.404634\pi\) | |||||||
\(762\) | −13.9703 | −0.506090 | ||||||||
\(763\) | 0.240293 | 0.00869918 | ||||||||
\(764\) | −1.55416 | −0.0562274 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30.7194 | 1.10994 | ||||||||
\(767\) | 6.84333 | 0.247098 | ||||||||
\(768\) | −2.81361 | −0.101527 | ||||||||
\(769\) | 10.5783 | 0.381465 | 0.190732 | − | 0.981642i | \(-0.438914\pi\) | ||||
0.190732 | + | 0.981642i | \(0.438914\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.1567 | −0.833967 | ||||||||
\(772\) | −12.9894 | −0.467500 | ||||||||
\(773\) | −6.90276 | −0.248275 | −0.124138 | − | 0.992265i | \(-0.539616\pi\) | ||||
−0.124138 | + | 0.992265i | \(0.539616\pi\) | |||||||
\(774\) | −12.9164 | −0.464270 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.338044 | −0.0121351 | ||||||||
\(777\) | 19.0192 | 0.682308 | ||||||||
\(778\) | 29.3169 | 1.05106 | ||||||||
\(779\) | −16.0000 | −0.573259 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.338044 | −0.0120962 | ||||||||
\(782\) | −36.0766 | −1.29010 | ||||||||
\(783\) | 10.0695 | 0.359854 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 34.1361 | 1.21759 | ||||||||
\(787\) | −7.25443 | −0.258592 | −0.129296 | − | 0.991606i | \(-0.541272\pi\) | ||||
−0.129296 | + | 0.991606i | \(0.541272\pi\) | |||||||
\(788\) | 0.710831 | 0.0253223 | ||||||||
\(789\) | 25.2247 | 0.898023 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.0036 | 0.746801 | ||||||||
\(792\) | −4.91638 | −0.174696 | ||||||||
\(793\) | 32.3416 | 1.14848 | ||||||||
\(794\) | 22.1955 | 0.787689 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.2197 | 0.539447 | ||||||||
\(797\) | 35.7733 | 1.26716 | 0.633578 | − | 0.773679i | \(-0.281586\pi\) | ||||
0.633578 | + | 0.773679i | \(0.281586\pi\) | |||||||
\(798\) | 3.62721 | 0.128402 | ||||||||
\(799\) | 53.0419 | 1.87649 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.9930 | −1.16575 | ||||||||
\(802\) | 20.2544 | 0.715209 | ||||||||
\(803\) | 13.6952 | 0.483295 | ||||||||
\(804\) | 10.2056 | 0.359922 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −44.9930 | −1.58481 | ||||||||
\(807\) | −21.2927 | −0.749540 | ||||||||
\(808\) | −16.5139 | −0.580956 | ||||||||
\(809\) | −32.8122 | −1.15361 | −0.576807 | − | 0.816880i | \(-0.695702\pi\) | ||||
−0.576807 | + | 0.816880i | \(0.695702\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.31335 | 0.221692 | 0.110846 | − | 0.993838i | \(-0.464644\pi\) | ||||
0.110846 | + | 0.993838i | \(0.464644\pi\) | |||||||
\(812\) | −1.86751 | −0.0655366 | ||||||||
\(813\) | −58.0071 | −2.03440 | ||||||||
\(814\) | 6.75971 | 0.236928 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 13.5436 | 0.474121 | ||||||||
\(817\) | 3.38692 | 0.118493 | ||||||||
\(818\) | 22.1658 | 0.775008 | ||||||||
\(819\) | 24.1708 | 0.844596 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.5225 | −1.06524 | −0.532621 | − | 0.846354i | \(-0.678793\pi\) | ||||
−0.532621 | + | 0.846354i | \(0.678793\pi\) | |||||||
\(822\) | 47.1255 | 1.64369 | ||||||||
\(823\) | 9.57885 | 0.333898 | 0.166949 | − | 0.985966i | \(-0.446609\pi\) | ||||
0.166949 | + | 0.985966i | \(0.446609\pi\) | |||||||
\(824\) | 5.83779 | 0.203369 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.39194 | −0.0484319 | ||||||||
\(827\) | 44.7250 | 1.55524 | 0.777620 | − | 0.628735i | \(-0.216427\pi\) | ||||
0.777620 | + | 0.628735i | \(0.216427\pi\) | |||||||
\(828\) | −36.8469 | −1.28052 | ||||||||
\(829\) | −38.7910 | −1.34727 | −0.673634 | − | 0.739065i | \(-0.735268\pi\) | ||||
−0.673634 | + | 0.739065i | \(0.735268\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 62.8888 | 2.18159 | ||||||||
\(832\) | 4.91638 | 0.170445 | ||||||||
\(833\) | −4.81361 | −0.166782 | ||||||||
\(834\) | −63.5366 | −2.20009 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.28917 | 0.0445868 | ||||||||
\(837\) | −49.3452 | −1.70562 | ||||||||
\(838\) | −36.5769 | −1.26353 | ||||||||
\(839\) | 24.6861 | 0.852260 | 0.426130 | − | 0.904662i | \(-0.359877\pi\) | ||||
0.426130 | + | 0.904662i | \(0.359877\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.5124 | −0.879739 | ||||||||
\(842\) | 2.94108 | 0.101356 | ||||||||
\(843\) | 17.4600 | 0.601354 | ||||||||
\(844\) | −12.0242 | −0.413889 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 54.1744 | 1.86255 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 9.74914 | 0.334787 | ||||||||
\(849\) | −30.0383 | −1.03091 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 50.6621 | 1.73667 | ||||||||
\(852\) | 0.951124 | 0.0325850 | ||||||||
\(853\) | −4.68468 | −0.160400 | −0.0802002 | − | 0.996779i | \(-0.525556\pi\) | ||||
−0.0802002 | + | 0.996779i | \(0.525556\pi\) | |||||||
\(854\) | −6.57834 | −0.225106 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.0488759 | −0.00167054 | ||||||||
\(857\) | −13.9022 | −0.474892 | −0.237446 | − | 0.971401i | \(-0.576310\pi\) | ||||
−0.237446 | + | 0.971401i | \(0.576310\pi\) | |||||||
\(858\) | 13.8328 | 0.472243 | ||||||||
\(859\) | 25.4585 | 0.868634 | 0.434317 | − | 0.900760i | \(-0.356990\pi\) | ||||
0.434317 | + | 0.900760i | \(0.356990\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 34.9200 | 1.19007 | ||||||||
\(862\) | −6.53303 | −0.222516 | ||||||||
\(863\) | −11.1814 | −0.380618 | −0.190309 | − | 0.981724i | \(-0.560949\pi\) | ||||
−0.190309 | + | 0.981724i | \(0.560949\pi\) | |||||||
\(864\) | 5.39194 | 0.183438 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16.0347 | −0.544883 | ||||||||
\(867\) | −17.3622 | −0.589652 | ||||||||
\(868\) | 9.15165 | 0.310627 | ||||||||
\(869\) | −6.28917 | −0.213345 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.8328 | −0.604240 | ||||||||
\(872\) | −0.240293 | −0.00813734 | ||||||||
\(873\) | 1.66196 | 0.0562487 | ||||||||
\(874\) | 9.66196 | 0.326821 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −38.5330 | −1.30191 | ||||||||
\(877\) | −9.11189 | −0.307687 | −0.153843 | − | 0.988095i | \(-0.549165\pi\) | ||||
−0.153843 | + | 0.988095i | \(0.549165\pi\) | |||||||
\(878\) | 14.2650 | 0.481420 | ||||||||
\(879\) | −34.5330 | −1.16477 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.2786 | 0.952730 | 0.476365 | − | 0.879248i | \(-0.341954\pi\) | ||||
0.476365 | + | 0.879248i | \(0.341954\pi\) | |||||||
\(882\) | −4.91638 | −0.165543 | ||||||||
\(883\) | 43.6061 | 1.46746 | 0.733731 | − | 0.679440i | \(-0.237777\pi\) | ||||
0.733731 | + | 0.679440i | \(0.237777\pi\) | |||||||
\(884\) | −23.6655 | −0.795958 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.9022 | 0.467055 | ||||||||
\(887\) | −22.8505 | −0.767244 | −0.383622 | − | 0.923490i | \(-0.625323\pi\) | ||||
−0.383622 | + | 0.923490i | \(0.625323\pi\) | |||||||
\(888\) | −19.0192 | −0.638241 | ||||||||
\(889\) | −4.96526 | −0.166529 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.421663 | 0.0141262 | ||||||||
\(892\) | −6.03831 | −0.202178 | ||||||||
\(893\) | −14.2056 | −0.475371 | ||||||||
\(894\) | −37.7633 | −1.26299 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 103.673 | 3.46153 | ||||||||
\(898\) | −11.5089 | −0.384055 | ||||||||
\(899\) | −17.0908 | −0.570009 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −46.9285 | −1.56342 | ||||||||
\(902\) | 12.4111 | 0.413244 | ||||||||
\(903\) | −7.39194 | −0.245988 | ||||||||
\(904\) | −21.0036 | −0.698568 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −42.9200 | −1.42592 | ||||||||
\(907\) | −1.78440 | −0.0592501 | −0.0296251 | − | 0.999561i | \(-0.509431\pi\) | ||||
−0.0296251 | + | 0.999561i | \(0.509431\pi\) | |||||||
\(908\) | −4.60303 | −0.152757 | ||||||||
\(909\) | 81.1885 | 2.69285 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.8539 | −0.459000 | −0.229500 | − | 0.973309i | \(-0.573709\pi\) | ||||
−0.229500 | + | 0.973309i | \(0.573709\pi\) | |||||||
\(912\) | −3.62721 | −0.120109 | ||||||||
\(913\) | −9.75971 | −0.322999 | ||||||||
\(914\) | 17.4600 | 0.577525 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.42166 | −0.179137 | ||||||||
\(917\) | 12.1325 | 0.400650 | ||||||||
\(918\) | −25.9547 | −0.856633 | ||||||||
\(919\) | −31.4741 | −1.03824 | −0.519118 | − | 0.854703i | \(-0.673739\pi\) | ||||
−0.519118 | + | 0.854703i | \(0.673739\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 54.1744 | 1.78511 | ||||||||
\(922\) | −9.35363 | −0.308045 | ||||||||
\(923\) | −1.66196 | −0.0547039 | ||||||||
\(924\) | −2.81361 | −0.0925609 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −16.3380 | −0.536901 | ||||||||
\(927\) | −28.7008 | −0.942657 | ||||||||
\(928\) | 1.86751 | 0.0613039 | ||||||||
\(929\) | −45.9341 | −1.50705 | −0.753524 | − | 0.657420i | \(-0.771648\pi\) | ||||
−0.753524 | + | 0.657420i | \(0.771648\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.28917 | 0.0422508 | ||||||||
\(932\) | 2.57834 | 0.0844562 | ||||||||
\(933\) | 3.84690 | 0.125942 | ||||||||
\(934\) | −3.55918 | −0.116460 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −24.1708 | −0.790048 | ||||||||
\(937\) | −20.2141 | −0.660367 | −0.330184 | − | 0.943917i | \(-0.607111\pi\) | ||||
−0.330184 | + | 0.943917i | \(0.607111\pi\) | |||||||
\(938\) | 3.62721 | 0.118433 | ||||||||
\(939\) | −90.8293 | −2.96410 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.3713 | 0.859681 | 0.429840 | − | 0.902905i | \(-0.358570\pi\) | ||||
0.429840 | + | 0.902905i | \(0.358570\pi\) | |||||||
\(942\) | 23.9406 | 0.780026 | ||||||||
\(943\) | 93.0177 | 3.02907 | ||||||||
\(944\) | 1.39194 | 0.0453039 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.62721 | −0.0854181 | ||||||||
\(947\) | 24.1149 | 0.783630 | 0.391815 | − | 0.920044i | \(-0.371847\pi\) | ||||
0.391815 | + | 0.920044i | \(0.371847\pi\) | |||||||
\(948\) | 17.6952 | 0.574715 | ||||||||
\(949\) | 67.3311 | 2.18566 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.9008 | 1.03445 | ||||||||
\(952\) | 4.81361 | 0.156010 | ||||||||
\(953\) | −50.1361 | −1.62407 | −0.812033 | − | 0.583611i | \(-0.801639\pi\) | ||||
−0.812033 | + | 0.583611i | \(0.801639\pi\) | |||||||
\(954\) | −47.9305 | −1.55181 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −21.0630 | −0.681226 | ||||||||
\(957\) | 5.25443 | 0.169851 | ||||||||
\(958\) | 38.7144 | 1.25081 | ||||||||
\(959\) | 16.7491 | 0.540858 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 52.7527 | 1.70170 | ||||||||
\(962\) | 33.2333 | 1.07148 | ||||||||
\(963\) | 0.240293 | 0.00774332 | ||||||||
\(964\) | 21.0192 | 0.676981 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −21.0872 | −0.678469 | ||||||||
\(967\) | 39.9305 | 1.28408 | 0.642039 | − | 0.766672i | \(-0.278089\pi\) | ||||
0.642039 | + | 0.766672i | \(0.278089\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 17.4600 | 0.560895 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.38335 | 0.236943 | 0.118471 | − | 0.992957i | \(-0.462201\pi\) | ||||
0.118471 | + | 0.992957i | \(0.462201\pi\) | |||||||
\(972\) | 14.9894 | 0.480786 | ||||||||
\(973\) | −22.5819 | −0.723943 | ||||||||
\(974\) | 14.8781 | 0.476724 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.57834 | 0.210567 | ||||||||
\(977\) | −10.4111 | −0.333081 | −0.166540 | − | 0.986035i | \(-0.553260\pi\) | ||||
−0.166540 | + | 0.986035i | \(0.553260\pi\) | |||||||
\(978\) | −44.2439 | −1.41476 | ||||||||
\(979\) | −6.71083 | −0.214479 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.18137 | 0.0377183 | ||||||||
\(982\) | −12.2927 | −0.392277 | ||||||||
\(983\) | −6.10278 | −0.194648 | −0.0973241 | − | 0.995253i | \(-0.531028\pi\) | ||||
−0.0973241 | + | 0.995253i | \(0.531028\pi\) | |||||||
\(984\) | −34.9200 | −1.11321 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −8.98944 | −0.286282 | ||||||||
\(987\) | 31.0036 | 0.986855 | ||||||||
\(988\) | 6.33804 | 0.201640 | ||||||||
\(989\) | −19.6902 | −0.626113 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.6550 | −1.29145 | −0.645724 | − | 0.763571i | \(-0.723444\pi\) | ||||
−0.645724 | + | 0.763571i | \(0.723444\pi\) | |||||||
\(992\) | −9.15165 | −0.290565 | ||||||||
\(993\) | 92.0455 | 2.92097 | ||||||||
\(994\) | 0.338044 | 0.0107221 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 27.4600 | 0.870103 | ||||||||
\(997\) | 51.0575 | 1.61701 | 0.808503 | − | 0.588492i | \(-0.200278\pi\) | ||||
0.808503 | + | 0.588492i | \(0.200278\pi\) | |||||||
\(998\) | −20.0383 | −0.634302 | ||||||||
\(999\) | 36.4480 | 1.15316 |
(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 | 3850.2.a.bs.1.1 | ✓ | 3 | |
5.2 | odd | 4 | 3850.2.c.bb.1849.3 | 6 | |||
5.3 | odd | 4 | 3850.2.c.bb.1849.4 | 6 | |||
5.4 | even | 2 | 3850.2.a.bv.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3850.2.a.bs.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
3850.2.a.bv.1.3 | yes | 3 | 5.4 | even | 2 | ||
3850.2.c.bb.1849.3 | 6 | 5.2 | odd | 4 | |||
3850.2.c.bb.1849.4 | 6 | 5.3 | odd | 4 |