Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.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: | \(61.7083906820\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.24197.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 6x^{2} - x + 2 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 483) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.27460\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.39532 | 1.07122 | 0.535610 | − | 0.844465i | \(-0.320082\pi\) | ||||
0.535610 | + | 0.844465i | \(0.320082\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.56912 | 1.37764 | 0.688821 | − | 0.724931i | \(-0.258129\pi\) | ||||
0.688821 | + | 0.724931i | \(0.258129\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.05307 | 1.40147 | 0.700735 | − | 0.713421i | \(-0.252855\pi\) | ||||
0.700735 | + | 0.713421i | \(0.252855\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.39532 | 0.618470 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.44840 | −0.351288 | −0.175644 | − | 0.984454i | \(-0.556201\pi\) | ||||
−0.175644 | + | 0.984454i | \(0.556201\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.98008 | −0.454261 | −0.227130 | − | 0.973864i | \(-0.572934\pi\) | ||||
−0.227130 | + | 0.973864i | \(0.572934\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.737570 | 0.147514 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.68985 | 0.685187 | 0.342594 | − | 0.939484i | \(-0.388695\pi\) | ||||
0.342594 | + | 0.939484i | \(0.388695\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.44840 | 0.619350 | 0.309675 | − | 0.950842i | \(-0.399780\pi\) | ||||
0.309675 | + | 0.950842i | \(0.399780\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.56912 | 0.795382 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.39532 | −0.404883 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.99759 | −0.657201 | −0.328600 | − | 0.944469i | \(-0.606577\pi\) | ||||
−0.328600 | + | 0.944469i | \(0.606577\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.05307 | 0.809140 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.77848 | 0.277751 | 0.138876 | − | 0.990310i | \(-0.455651\pi\) | ||||
0.138876 | + | 0.990310i | \(0.455651\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.25467 | 0.191336 | 0.0956680 | − | 0.995413i | \(-0.469501\pi\) | ||||
0.0956680 | + | 0.995413i | \(0.469501\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.39532 | 0.357074 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.87928 | −0.419986 | −0.209993 | − | 0.977703i | \(-0.567344\pi\) | ||||
−0.209993 | + | 0.977703i | \(0.567344\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.44840 | −0.202816 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.4128 | −1.43031 | −0.715157 | − | 0.698964i | \(-0.753645\pi\) | ||||
−0.715157 | + | 0.698964i | \(0.753645\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.9445 | 1.47576 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.98008 | −0.262267 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.1315 | 1.83977 | 0.919885 | − | 0.392188i | \(-0.128282\pi\) | ||||
0.919885 | + | 0.392188i | \(0.128282\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.37540 | 1.07236 | 0.536180 | − | 0.844104i | \(-0.319867\pi\) | ||||
0.536180 | + | 0.844104i | \(0.319867\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.1037 | 1.50128 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.73517 | 0.945001 | 0.472500 | − | 0.881330i | \(-0.343352\pi\) | ||||
0.472500 | + | 0.881330i | \(0.343352\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.946925 | 0.112379 | 0.0561897 | − | 0.998420i | \(-0.482105\pi\) | ||||
0.0561897 | + | 0.998420i | \(0.482105\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.86711 | 0.452611 | 0.226305 | − | 0.974056i | \(-0.427335\pi\) | ||||
0.226305 | + | 0.974056i | \(0.427335\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.737570 | 0.0851673 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.56912 | −0.520700 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.23904 | −0.476930 | −0.238465 | − | 0.971151i | \(-0.576644\pi\) | ||||
−0.238465 | + | 0.971151i | \(0.576644\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.8281 | −1.18854 | −0.594269 | − | 0.804267i | \(-0.702558\pi\) | ||||
−0.594269 | + | 0.804267i | \(0.702558\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.46938 | −0.376307 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.68985 | 0.395593 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.262430 | 0.0278175 | 0.0139087 | − | 0.999903i | \(-0.495573\pi\) | ||||
0.0139087 | + | 0.999903i | \(0.495573\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.05307 | −0.529706 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.44840 | 0.357582 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.74292 | −0.486613 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.20695 | −0.731755 | −0.365877 | − | 0.930663i | \(-0.619231\pi\) | ||||
−0.365877 | + | 0.930663i | \(0.619231\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.56912 | 0.459214 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.26684 | −0.822582 | −0.411291 | − | 0.911504i | \(-0.634922\pi\) | ||||
−0.411291 | + | 0.911504i | \(0.634922\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.2619 | 1.89793 | 0.948966 | − | 0.315378i | \(-0.102131\pi\) | ||||
0.948966 | + | 0.315378i | \(0.102131\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.39532 | −0.233760 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.0531 | 1.06854 | 0.534271 | − | 0.845314i | \(-0.320586\pi\) | ||||
0.534271 | + | 0.845314i | \(0.320586\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.9047 | 1.23604 | 0.618022 | − | 0.786161i | \(-0.287934\pi\) | ||||
0.618022 | + | 0.786161i | \(0.287934\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.99759 | −0.379435 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.25708 | −0.118256 | −0.0591281 | − | 0.998250i | \(-0.518832\pi\) | ||||
−0.0591281 | + | 0.998250i | \(0.518832\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.39532 | 0.223365 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.05307 | 0.467157 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.44840 | 0.132774 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.87687 | 0.897897 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.77848 | 0.160360 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.2099 | −0.913201 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.3385 | −1.71601 | −0.858007 | − | 0.513638i | \(-0.828297\pi\) | ||||
−0.858007 | + | 0.513638i | \(0.828297\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.25467 | 0.110468 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.4659 | −1.70075 | −0.850373 | − | 0.526181i | \(-0.823623\pi\) | ||||
−0.850373 | + | 0.526181i | \(0.823623\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.98008 | 0.171694 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.39532 | 0.206157 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.4980 | 1.75126 | 0.875632 | − | 0.482980i | \(-0.160446\pi\) | ||||
0.875632 | + | 0.482980i | \(0.160446\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.0507 | −1.78549 | −0.892747 | − | 0.450558i | \(-0.851225\pi\) | ||||
−0.892747 | + | 0.450558i | \(0.851225\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.87928 | −0.242479 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.0881 | 1.93072 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.83837 | 0.733987 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.1159 | −1.56604 | −0.783018 | − | 0.621999i | \(-0.786321\pi\) | ||||
−0.783018 | + | 0.621999i | \(0.786321\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.2542 | −1.48550 | −0.742751 | − | 0.669568i | \(-0.766479\pi\) | ||||
−0.742751 | + | 0.669568i | \(0.766479\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.44840 | −0.117096 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.26002 | 0.663461 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.63783 | 0.529756 | 0.264878 | − | 0.964282i | \(-0.414668\pi\) | ||||
0.264878 | + | 0.964282i | \(0.414668\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.4128 | −0.825792 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.1080 | −1.65331 | −0.826655 | − | 0.562710i | \(-0.809759\pi\) | ||||
−0.826655 | + | 0.562710i | \(0.809759\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.9445 | 0.852030 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.01217 | 0.0783240 | 0.0391620 | − | 0.999233i | \(-0.487531\pi\) | ||||
0.0391620 | + | 0.999233i | \(0.487531\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5336 | 0.964120 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.98008 | −0.151420 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.2069 | 1.15616 | 0.578081 | − | 0.815979i | \(-0.303802\pi\) | ||||
0.578081 | + | 0.815979i | \(0.303802\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.737570 | −0.0557551 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.1315 | 1.06219 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.1491 | −1.35652 | −0.678262 | − | 0.734820i | \(-0.737267\pi\) | ||||
−0.678262 | + | 0.734820i | \(0.737267\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5866 | 0.786899 | 0.393449 | − | 0.919346i | \(-0.371282\pi\) | ||||
0.393449 | + | 0.919346i | \(0.371282\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.37540 | 0.619127 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.57553 | −0.704007 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.61790 | −0.483949 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.8004 | 1.43271 | 0.716354 | − | 0.697737i | \(-0.245810\pi\) | ||||
0.716354 | + | 0.697737i | \(0.245810\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.4956 | 1.61927 | 0.809635 | − | 0.586934i | \(-0.199665\pi\) | ||||
0.809635 | + | 0.586934i | \(0.199665\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.1037 | 0.866767 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.67338 | 0.119224 | 0.0596118 | − | 0.998222i | \(-0.481014\pi\) | ||||
0.0596118 | + | 0.998222i | \(0.481014\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.82380 | −0.412838 | −0.206419 | − | 0.978464i | \(-0.566181\pi\) | ||||
−0.206419 | + | 0.978464i | \(0.566181\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.73517 | 0.545596 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.68985 | −0.258976 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.26002 | 0.297533 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.04721 | −0.625808 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.2809 | 0.983138 | 0.491569 | − | 0.870839i | \(-0.336424\pi\) | ||||
0.491569 | + | 0.870839i | \(0.336424\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.946925 | 0.0648822 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.00535 | 0.204963 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.44840 | −0.234092 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.86711 | 0.261315 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.31886 | −0.492320 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.0031 | 1.33950 | 0.669752 | − | 0.742585i | \(-0.266400\pi\) | ||||
0.669752 | + | 0.742585i | \(0.266400\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.737570 | 0.0491714 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.4547 | −1.22488 | −0.612441 | − | 0.790517i | \(-0.709812\pi\) | ||||
−0.612441 | + | 0.790517i | \(0.709812\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.2299 | −1.13859 | −0.569293 | − | 0.822135i | \(-0.692783\pi\) | ||||
−0.569293 | + | 0.822135i | \(0.692783\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.56912 | −0.300626 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.2844 | −1.06682 | −0.533412 | − | 0.845856i | \(-0.679090\pi\) | ||||
−0.533412 | + | 0.845856i | \(0.679090\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.89679 | −0.449897 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.23904 | −0.275355 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.1539 | 1.69175 | 0.845877 | − | 0.533378i | \(-0.179078\pi\) | ||||
0.845877 | + | 0.533378i | \(0.179078\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.67527 | 0.558823 | 0.279412 | − | 0.960171i | \(-0.409861\pi\) | ||||
0.279412 | + | 0.960171i | \(0.409861\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.39532 | 0.153032 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.0055 | −0.636633 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.8281 | −0.686202 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.22888 | −0.582522 | −0.291261 | − | 0.956644i | \(-0.594075\pi\) | ||||
−0.291261 | + | 0.956644i | \(0.594075\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.56912 | 0.287258 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.46938 | −0.217261 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.7606 | 1.10787 | 0.553937 | − | 0.832559i | \(-0.313125\pi\) | ||||
0.553937 | + | 0.832559i | \(0.313125\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.99759 | 0.248398 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.68985 | 0.228396 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.2721 | 0.633403 | 0.316702 | − | 0.948525i | \(-0.397425\pi\) | ||||
0.316702 | + | 0.948525i | \(0.397425\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.9421 | −1.53218 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.262430 | 0.0160604 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.5312 | −1.06889 | −0.534447 | − | 0.845202i | \(-0.679480\pi\) | ||||
−0.534447 | + | 0.845202i | \(0.679480\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.1602 | −1.28539 | −0.642695 | − | 0.766123i | \(-0.722184\pi\) | ||||
−0.642695 | + | 0.766123i | \(0.722184\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.05307 | −0.305826 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.37005 | 0.203222 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.92941 | 0.176011 | 0.0880055 | − | 0.996120i | \(-0.471951\pi\) | ||||
0.0880055 | + | 0.996120i | \(0.471951\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.44840 | 0.206450 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.8655 | −1.60266 | −0.801332 | − | 0.598220i | \(-0.795875\pi\) | ||||
−0.801332 | + | 0.598220i | \(0.795875\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.0584 | 1.31124 | 0.655619 | − | 0.755092i | \(-0.272408\pi\) | ||||
0.655619 | + | 0.755092i | \(0.272408\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.74292 | −0.280946 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.77848 | −0.104980 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.9021 | −0.876597 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.20695 | −0.422479 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.7537 | 1.38771 | 0.693854 | − | 0.720116i | \(-0.255911\pi\) | ||||
0.693854 | + | 0.720116i | \(0.255911\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 33.8496 | 1.97080 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.56912 | 0.265127 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.05307 | 0.292227 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.25467 | −0.0723182 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.26684 | −0.474918 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.0618 | 1.14873 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.61015 | −0.548480 | −0.274240 | − | 0.961661i | \(-0.588426\pi\) | ||||
−0.274240 | + | 0.961661i | \(0.588426\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.2619 | 1.09577 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.5642 | −0.769155 | −0.384577 | − | 0.923093i | \(-0.625653\pi\) | ||||
−0.384577 | + | 0.923093i | \(0.625653\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.23168 | 0.0696189 | 0.0348095 | − | 0.999394i | \(-0.488918\pi\) | ||||
0.0348095 | + | 0.999394i | \(0.488918\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.39532 | −0.134961 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.0584 | 0.901931 | 0.450965 | − | 0.892541i | \(-0.351080\pi\) | ||||
0.450965 | + | 0.892541i | \(0.351080\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.8594 | 0.943942 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.0531 | 0.616922 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.86794 | 0.159576 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.72700 | 0.206737 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.9047 | 0.713630 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.87928 | 0.158740 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.5424 | 0.689391 | 0.344696 | − | 0.938714i | \(-0.387982\pi\) | ||||
0.344696 | + | 0.938714i | \(0.387982\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.99759 | −0.219067 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.5282 | 1.01230 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.62661 | 0.524395 | 0.262197 | − | 0.965014i | \(-0.415553\pi\) | ||||
0.262197 | + | 0.965014i | \(0.415553\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.25708 | −0.0682752 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.7561 | 0.853243 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.39532 | 0.128960 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.94199 | 0.533714 | 0.266857 | − | 0.963736i | \(-0.414015\pi\) | ||||
0.266857 | + | 0.963736i | \(0.414015\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.7274 | −0.681283 | −0.340641 | − | 0.940193i | \(-0.610644\pi\) | ||||
−0.340641 | + | 0.940193i | \(0.610644\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.05307 | 0.269713 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.67433 | −0.0891159 | −0.0445579 | − | 0.999007i | \(-0.514188\pi\) | ||||
−0.0445579 | + | 0.999007i | \(0.514188\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.26819 | 0.120383 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.44840 | 0.0766573 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 36.9662 | 1.95100 | 0.975500 | − | 0.220001i | \(-0.0706060\pi\) | ||||
0.975500 | + | 0.220001i | \(0.0706060\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0793 | −0.793647 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.87687 | 0.518401 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.26297 | 0.484846 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.5080 | 1.17491 | 0.587454 | − | 0.809258i | \(-0.300130\pi\) | ||||
0.587454 | + | 0.809258i | \(0.300130\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.77848 | 0.0925838 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.4128 | 0.540608 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.5896 | 1.22142 | 0.610711 | − | 0.791853i | \(-0.290884\pi\) | ||||
0.610711 | + | 0.791853i | \(0.290884\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.2099 | −0.527237 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.6451 | 0.960270 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.93664 | −0.356311 | −0.178156 | − | 0.984002i | \(-0.557013\pi\) | ||||
−0.178156 | + | 0.984002i | \(0.557013\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.3385 | −0.990741 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.8281 | 1.16646 | 0.583230 | − | 0.812307i | \(-0.301788\pi\) | ||||
0.583230 | + | 0.812307i | \(0.301788\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.9445 | −0.557784 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.25467 | 0.0637787 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.1350 | 0.818077 | 0.409039 | − | 0.912517i | \(-0.365864\pi\) | ||||
0.409039 | + | 0.912517i | \(0.365864\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.44840 | −0.0732486 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.4659 | −0.981926 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.1539 | −0.510897 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.5687 | 0.931938 | 0.465969 | − | 0.884801i | \(-0.345706\pi\) | ||||
0.465969 | + | 0.884801i | \(0.345706\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.98008 | 0.0991278 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.22928 | −0.361013 | −0.180506 | − | 0.983574i | \(-0.557774\pi\) | ||||
−0.180506 | + | 0.983574i | \(0.557774\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.4250 | 0.868002 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.39532 | 0.119025 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.2655 | −0.905387 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.7912 | 0.879717 | 0.439859 | − | 0.898067i | \(-0.355029\pi\) | ||||
0.439859 | + | 0.898067i | \(0.355029\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.4980 | 1.01109 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.1315 | −0.695368 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25.9368 | −1.27319 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.0507 | −1.03086 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.7937 | 0.820426 | 0.410213 | − | 0.911990i | \(-0.365454\pi\) | ||||
0.410213 | + | 0.911990i | \(0.365454\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.1194 | −0.541925 | −0.270963 | − | 0.962590i | \(-0.587342\pi\) | ||||
−0.270963 | + | 0.962590i | \(0.587342\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.87928 | −0.139995 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.06829 | −0.0518199 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.37540 | −0.405314 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 23.0881 | 1.11470 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −35.8516 | −1.72691 | −0.863456 | − | 0.504424i | \(-0.831705\pi\) | ||||
−0.863456 | + | 0.504424i | \(0.831705\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.2199 | 0.635310 | 0.317655 | − | 0.948206i | \(-0.397105\pi\) | ||||
0.317655 | + | 0.948206i | \(0.397105\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.83837 | 0.423767 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.98008 | −0.0947199 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.2898 | 1.35020 | 0.675100 | − | 0.737726i | \(-0.264100\pi\) | ||||
0.675100 | + | 0.737726i | \(0.264100\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.7781 | −1.12973 | −0.564865 | − | 0.825183i | \(-0.691072\pi\) | ||||
−0.564865 | + | 0.825183i | \(0.691072\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.628604 | 0.0297987 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.1159 | −0.904152 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.97578 | −0.140436 | −0.0702179 | − | 0.997532i | \(-0.522369\pi\) | ||||
−0.0702179 | + | 0.997532i | \(0.522369\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.12607 | 0.382642 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.2542 | −0.857655 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.1037 | −0.567432 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.4381 | −0.909277 | −0.454638 | − | 0.890676i | \(-0.650231\pi\) | ||||
−0.454638 | + | 0.890676i | \(0.650231\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.44840 | −0.0676054 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.92877 | −0.229556 | −0.114778 | − | 0.993391i | \(-0.536616\pi\) | ||||
−0.114778 | + | 0.993391i | \(0.536616\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.27983 | −0.152427 | −0.0762133 | − | 0.997092i | \(-0.524283\pi\) | ||||
−0.0762133 | + | 0.997092i | \(0.524283\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.26002 | 0.383049 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.04520 | −0.140915 | −0.0704575 | − | 0.997515i | \(-0.522446\pi\) | ||||
−0.0704575 | + | 0.997515i | \(0.522446\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.73517 | −0.357177 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.63783 | 0.305855 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.73276 | 0.263593 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.46045 | −0.0670098 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.4128 | −0.476771 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.10080 | −0.141679 | −0.0708396 | − | 0.997488i | \(-0.522568\pi\) | ||||
−0.0708396 | + | 0.997488i | \(0.522568\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.2001 | −0.921047 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.2630 | −0.783871 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.5634 | −0.795872 | −0.397936 | − | 0.917413i | \(-0.630273\pi\) | ||||
−0.397936 | + | 0.917413i | \(0.630273\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21.1080 | −0.954538 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.6646 | −1.47413 | −0.737066 | − | 0.675821i | \(-0.763789\pi\) | ||||
−0.737066 | + | 0.675821i | \(0.763789\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.34436 | −0.240698 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.9445 | 0.491920 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.946925 | −0.0424754 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.9084 | 0.756926 | 0.378463 | − | 0.925616i | \(-0.376453\pi\) | ||||
0.378463 | + | 0.925616i | \(0.376453\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.01217 | 0.0452204 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.22582 | 0.411359 | 0.205679 | − | 0.978619i | \(-0.434060\pi\) | ||||
0.205679 | + | 0.978619i | \(0.434060\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.8018 | −0.881167 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.5336 | 0.556635 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.4362 | −0.551226 | −0.275613 | − | 0.961269i | \(-0.588881\pi\) | ||||
−0.275613 | + | 0.961269i | \(0.588881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.86711 | −0.171071 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.98008 | −0.0874225 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 46.1385 | 2.03310 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.1558 | −0.578590 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.2069 | 0.667511 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.2123 | −1.14838 | −0.574191 | − | 0.818721i | \(-0.694683\pi\) | ||||
−0.574191 | + | 0.818721i | \(0.694683\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.3309 | −1.10764 | −0.553822 | − | 0.832635i | \(-0.686831\pi\) | ||||
−0.553822 | + | 0.832635i | \(0.686831\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.737570 | −0.0321902 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.99465 | −0.217570 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.1315 | 0.613257 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.98677 | 0.389260 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.4757 | 1.14464 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.1491 | −0.783190 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.56912 | 0.196806 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.2940 | −0.700534 | −0.350267 | − | 0.936650i | \(-0.613909\pi\) | ||||
−0.350267 | + | 0.936650i | \(0.613909\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.5866 | 0.454316 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.9109 | 1.32408 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.1461 | −0.562087 | −0.281044 | − | 0.959695i | \(-0.590681\pi\) | ||||
−0.281044 | + | 0.959695i | \(0.590681\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.37540 | 0.357453 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.30617 | −0.311253 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.23904 | 0.180262 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.57553 | −0.406459 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.28424 | 0.0544150 | 0.0272075 | − | 0.999630i | \(-0.491339\pi\) | ||||
0.0272075 | + | 0.999630i | \(0.491339\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.33996 | 0.268152 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.61790 | −0.279408 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.02181 | 0.0430642 | 0.0215321 | − | 0.999768i | \(-0.493146\pi\) | ||||
0.0215321 | + | 0.999768i | \(0.493146\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.01111 | −0.126678 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.9943 | −0.628592 | −0.314296 | − | 0.949325i | \(-0.601768\pi\) | ||||
−0.314296 | + | 0.949325i | \(0.601768\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.3179 | 0.641035 | 0.320517 | − | 0.947243i | \(-0.396143\pi\) | ||||
0.320517 | + | 0.947243i | \(0.396143\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.8004 | 0.827174 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.737570 | 0.0307588 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.4091 | −1.51573 | −0.757865 | − | 0.652411i | \(-0.773757\pi\) | ||||
−0.757865 | + | 0.652411i | \(0.773757\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.4956 | 0.934885 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.8281 | 0.449225 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −47.5775 | −1.97046 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.1037 | 0.500428 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.1484 | 1.32691 | 0.663454 | − | 0.748217i | \(-0.269090\pi\) | ||||
0.663454 | + | 0.748217i | \(0.269090\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.82809 | −0.281346 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.67338 | 0.0688338 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.6719 | 1.30061 | 0.650305 | − | 0.759673i | \(-0.274641\pi\) | ||||
0.650305 | + | 0.759673i | \(0.274641\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.46938 | 0.142231 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.82380 | −0.238352 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.0114 | 1.47138 | 0.735692 | − | 0.677316i | \(-0.236857\pi\) | ||||
0.735692 | + | 0.677316i | \(0.236857\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.4295 | −1.36362 | −0.681810 | − | 0.731530i | \(-0.738807\pi\) | ||||
−0.681810 | + | 0.731530i | \(0.738807\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.73517 | 0.315000 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.6583 | 0.961846 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.510803 | −0.0207329 | −0.0103664 | − | 0.999946i | \(-0.503300\pi\) | ||||
−0.0103664 | + | 0.999946i | \(0.503300\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.68985 | −0.149520 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.5492 | −0.588598 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.7444 | −1.20137 | −0.600683 | − | 0.799488i | \(-0.705104\pi\) | ||||
−0.600683 | + | 0.799488i | \(0.705104\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.26002 | 0.171781 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.2312 | −0.733959 | −0.366980 | − | 0.930229i | \(-0.619608\pi\) | ||||
−0.366980 | + | 0.930229i | \(0.619608\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.3889 | −1.26163 | −0.630814 | − | 0.775934i | \(-0.717279\pi\) | ||||
−0.630814 | + | 0.775934i | \(0.717279\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.262430 | −0.0105140 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.1438 | −1.12575 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.04721 | −0.361311 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.79011 | 0.230867 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.9030 | −1.70794 | −0.853970 | − | 0.520322i | \(-0.825812\pi\) | ||||
−0.853970 | + | 0.520322i | \(0.825812\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.2809 | 0.567615 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −46.3219 | −1.83823 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.05307 | 0.200210 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.946925 | 0.0374598 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.8505 | −0.784049 | −0.392025 | − | 0.919955i | \(-0.628225\pi\) | ||||
−0.392025 | + | 0.919955i | \(0.628225\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.5457 | −1.04686 | −0.523431 | − | 0.852068i | \(-0.675348\pi\) | ||||
−0.523431 | + | 0.852068i | \(0.675348\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.00535 | 0.118336 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.0117 | −1.17988 | −0.589940 | − | 0.807447i | \(-0.700849\pi\) | ||||
−0.589940 | + | 0.807447i | \(0.700849\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 64.5687 | 2.53454 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.44840 | −0.135153 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.41083 | 0.172609 | 0.0863046 | − | 0.996269i | \(-0.472494\pi\) | ||||
0.0863046 | + | 0.996269i | \(0.472494\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −46.6271 | −1.82187 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.86711 | 0.150870 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.2147 | 1.17700 | 0.588499 | − | 0.808498i | \(-0.299719\pi\) | ||||
0.588499 | + | 0.808498i | \(0.299719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.8322 | 0.732488 | 0.366244 | − | 0.930519i | \(-0.380644\pi\) | ||||
0.366244 | + | 0.930519i | \(0.380644\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.31886 | −0.284241 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.74292 | 0.183923 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.68985 | 0.142871 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.0031 | 0.773363 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.2682 | 1.47733 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.0208 | −0.656102 | −0.328051 | − | 0.944660i | \(-0.606392\pi\) | ||||
−0.328051 | + | 0.944660i | \(0.606392\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.737570 | 0.0283891 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.4116 | 1.28411 | 0.642056 | − | 0.766657i | \(-0.278082\pi\) | ||||
0.642056 | + | 0.766657i | \(0.278082\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.20695 | 0.276577 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.4547 | −0.707186 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.95082 | 0.380758 | 0.190379 | − | 0.981711i | \(-0.439028\pi\) | ||||
0.190379 | + | 0.981711i | \(0.439028\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 49.0993 | 1.87599 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.2299 | −0.657363 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −52.6169 | −2.00454 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.7795 | −0.828533 | −0.414266 | − | 0.910156i | \(-0.635962\pi\) | ||||
−0.414266 | + | 0.910156i | \(0.635962\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.56912 | −0.173567 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −50.4231 | −1.91266 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.57594 | −0.0975707 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.2844 | −0.615931 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.4292 | 0.658291 | 0.329146 | − | 0.944279i | \(-0.393239\pi\) | ||||
0.329146 | + | 0.944279i | \(0.393239\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.91554 | 0.298540 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.89679 | −0.259748 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.26684 | 0.310907 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.6266 | 1.11265 | 0.556325 | − | 0.830965i | \(-0.312211\pi\) | ||||
0.556325 | + | 0.830965i | \(0.312211\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.23904 | −0.158977 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.44840 | 0.129143 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 55.3035 | 2.06823 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 26.1539 | 0.976734 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.1492 | 0.639558 | 0.319779 | − | 0.947492i | \(-0.396391\pi\) | ||||
0.319779 | + | 0.947492i | \(0.396391\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.2619 | −0.717351 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.67527 | 0.322637 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.72152 | 0.101075 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −48.6199 | −1.80321 | −0.901606 | − | 0.432557i | \(-0.857611\pi\) | ||||
−0.901606 | + | 0.432557i | \(0.857611\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.81727 | −0.0672141 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.3216 | −1.45238 | −0.726189 | − | 0.687495i | \(-0.758710\pi\) | ||||
−0.726189 | + | 0.687495i | \(0.758710\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.39532 | 0.0883528 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.3429 | 1.30187 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.5818 | −0.757115 | −0.378557 | − | 0.925578i | \(-0.623580\pi\) | ||||
−0.378557 | + | 0.925578i | \(0.623580\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.0055 | −0.367560 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.0313 | 1.39523 | 0.697616 | − | 0.716472i | \(-0.254244\pi\) | ||||
0.697616 | + | 0.716472i | \(0.254244\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −45.7888 | −1.67757 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.8281 | −0.396179 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.0531 | −0.403871 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.3146 | 1.39812 | 0.699060 | − | 0.715063i | \(-0.253602\pi\) | ||||
0.699060 | + | 0.715063i | \(0.253602\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.22888 | −0.336319 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −43.7246 | −1.59130 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.4278 | −0.924190 | −0.462095 | − | 0.886830i | \(-0.652902\pi\) | ||||
−0.462095 | + | 0.886830i | \(0.652902\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.56912 | 0.165849 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.3205 | 1.67912 | 0.839558 | − | 0.543271i | \(-0.182814\pi\) | ||||
0.839558 | + | 0.543271i | \(0.182814\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.9047 | −0.467180 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.46938 | −0.125436 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 71.4078 | 2.57838 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.92806 | 0.105588 | 0.0527942 | − | 0.998605i | \(-0.483187\pi\) | ||||
0.0527942 | + | 0.998605i | \(0.483187\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.7606 | 0.639631 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.848652 | 0.0305239 | 0.0152619 | − | 0.999884i | \(-0.495142\pi\) | ||||
0.0152619 | + | 0.999884i | \(0.495142\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.54344 | 0.0913629 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.99759 | 0.143413 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.52152 | −0.126171 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.32662 | 0.154818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.68985 | 0.131864 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.8997 | 0.567486 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.3118 | −1.11614 | −0.558072 | − | 0.829793i | \(-0.688459\pi\) | ||||
−0.558072 | + | 0.829793i | \(0.688459\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.2721 | 0.365695 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.25708 | 0.0446966 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.3215 | 1.50288 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −24.9421 | −0.884606 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.66393 | 0.165205 | 0.0826025 | − | 0.996583i | \(-0.473677\pi\) | ||||
0.0826025 | + | 0.996583i | \(0.473677\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.17034 | 0.147536 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.262430 | 0.00927250 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.6693 | 0.623535 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.39532 | −0.0844240 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.5312 | −0.617126 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.2106 | 0.921516 | 0.460758 | − | 0.887526i | \(-0.347578\pi\) | ||||
0.460758 | + | 0.887526i | \(0.347578\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.2107 | 1.23642 | 0.618208 | − | 0.786015i | \(-0.287859\pi\) | ||||
0.618208 | + | 0.786015i | \(0.287859\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.1602 | −0.742120 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −50.5606 | −1.77106 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.48435 | −0.0869164 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.05307 | −0.176569 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.9369 | 1.07970 | 0.539852 | − | 0.841760i | \(-0.318480\pi\) | ||||
0.539852 | + | 0.841760i | \(0.318480\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.7770 | 0.619668 | 0.309834 | − | 0.950791i | \(-0.399727\pi\) | ||||
0.309834 | + | 0.950791i | \(0.399727\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.37005 | 0.117330 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.40509 | 0.118406 | 0.0592032 | − | 0.998246i | \(-0.481144\pi\) | ||||
0.0592032 | + | 0.998246i | \(0.481144\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.475680 | 0.0165210 | 0.00826052 | − | 0.999966i | \(-0.497371\pi\) | ||||
0.00826052 | + | 0.999966i | \(0.497371\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.92941 | 0.101620 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.44840 | −0.0501840 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.42447 | 0.0839023 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.44840 | 0.119194 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.4804 | 0.534442 | 0.267221 | − | 0.963635i | \(-0.413895\pi\) | ||||
0.267221 | + | 0.963635i | \(0.413895\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.3850 | −0.530519 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26.8655 | −0.925298 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30.0219 | 1.03279 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.87687 | −0.339373 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.0584 | 0.757043 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.99759 | −0.137036 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.6583 | 0.810044 | 0.405022 | − | 0.914307i | \(-0.367264\pi\) | ||||
0.405022 | + | 0.914307i | \(0.367264\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.74292 | −0.162204 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.2346 | −0.349608 | −0.174804 | − | 0.984603i | \(-0.555929\pi\) | ||||
−0.174804 | + | 0.984603i | \(0.555929\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.4043 | 1.31034 | 0.655169 | − | 0.755483i | \(-0.272598\pi\) | ||||
0.655169 | + | 0.755483i | \(0.272598\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.77848 | −0.0606103 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.5209 | −1.14106 | −0.570532 | − | 0.821275i | \(-0.693263\pi\) | ||||
−0.570532 | + | 0.821275i | \(0.693263\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.4255 | 1.23851 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.9021 | −0.506103 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.3687 | −0.657038 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 39.0864 | 1.32439 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.20695 | −0.243918 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.2099 | 0.345157 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −52.7392 | −1.78088 | −0.890438 | − | 0.455105i | \(-0.849602\pi\) | ||||
−0.890438 | + | 0.455105i | \(0.849602\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.7537 | 0.801194 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.1890 | 0.646495 | 0.323247 | − | 0.946314i | \(-0.395225\pi\) | ||||
0.323247 | + | 0.946314i | \(0.395225\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.2985 | 1.12059 | 0.560293 | − | 0.828295i | \(-0.310689\pi\) | ||||
0.560293 | + | 0.828295i | \(0.310689\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 33.8496 | 1.13784 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.8750 | 0.600183 | 0.300092 | − | 0.953910i | \(-0.402983\pi\) | ||||
0.300092 | + | 0.953910i | \(0.402983\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.3385 | 0.648592 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.56912 | 0.153071 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.70118 | 0.190783 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −43.4729 | −1.45314 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.05307 | 0.168717 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.7241 | 0.424371 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.0819 | 0.502452 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.25467 | −0.0417529 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.3584 | 0.842942 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.71166 | −0.222857 | −0.111428 | − | 0.993772i | \(-0.535543\pi\) | ||||
−0.111428 | + | 0.993772i | \(0.535543\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.26684 | −0.274194 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.5404 | 0.481744 | 0.240872 | − | 0.970557i | \(-0.422567\pi\) | ||||
0.240872 | + | 0.970557i | \(0.422567\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −49.4749 | −1.63738 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20.0618 | 0.663222 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.4659 | 0.642821 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.3532 | −0.836325 | −0.418162 | − | 0.908372i | \(-0.637326\pi\) | ||||
−0.418162 | + | 0.908372i | \(0.637326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.61015 | −0.316665 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.78488 | 0.157496 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.94851 | −0.0969463 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.2619 | 0.632644 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 46.6378 | 1.53014 | 0.765069 | − | 0.643948i | \(-0.222705\pi\) | ||||
0.765069 | + | 0.643948i | \(0.222705\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.98008 | −0.0648944 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.5642 | −0.444072 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.8520 | −0.518416 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.8699 | −1.13915 | −0.569576 | − | 0.821939i | \(-0.692892\pi\) | ||||
−0.569576 | + | 0.821939i | \(0.692892\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.23168 | 0.0401945 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.0243 | −0.391982 | −0.195991 | − | 0.980606i | \(-0.562792\pi\) | ||||
−0.195991 | + | 0.980606i | \(0.562792\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.77848 | 0.0579152 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.39532 | −0.0779198 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.4626 | 0.599953 | 0.299977 | − | 0.953947i | \(-0.403021\pi\) | ||||
0.299977 | + | 0.953947i | \(0.403021\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.5408 | 0.634321 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.0584 | 0.520730 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.91601 | 0.288818 | 0.144409 | − | 0.989518i | \(-0.453872\pi\) | ||||
0.144409 | + | 0.989518i | \(0.453872\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 47.4284 | 1.53475 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.8594 | 0.544985 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.4980 | −0.661915 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.1086 | −0.616405 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.0531 | 0.356180 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 53.8842 | 1.73459 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.1091 | 0.357244 | 0.178622 | − | 0.983918i | \(-0.442836\pi\) | ||||
0.178622 | + | 0.983918i | \(0.442836\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.86794 | 0.0921314 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.9226 | −0.607255 | −0.303627 | − | 0.952791i | \(-0.598198\pi\) | ||||
−0.303627 | + | 0.952791i | \(0.598198\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.0507 | 0.674853 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.72700 | 0.119359 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.0219 | 0.544579 | 0.272290 | − | 0.962215i | \(-0.412219\pi\) | ||||
0.272290 | + | 0.962215i | \(0.412219\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.19907 | 0.0383225 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.9047 | 0.412014 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.7249 | −1.20324 | −0.601618 | − | 0.798784i | \(-0.705477\pi\) | ||||
−0.601618 | + | 0.798784i | \(0.705477\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.00829 | 0.127715 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.87928 | 0.0916484 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.25467 | 0.0398963 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.0190 | 1.62067 | 0.810336 | − | 0.585965i | \(-0.199285\pi\) | ||||
0.810336 | + | 0.585965i | \(0.199285\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.5424 | 0.398020 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.9499 | −0.442241 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.6823 | −1.38343 | −0.691717 | − | 0.722169i | \(-0.743145\pi\) | ||||
−0.691717 | + | 0.722169i | \(0.743145\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.99759 | −0.126478 |
(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 | 7728.2.a.cd.1.3 | 4 | ||
4.3 | odd | 2 | 483.2.a.i.1.4 | ✓ | 4 | ||
12.11 | even | 2 | 1449.2.a.p.1.1 | 4 | |||
28.27 | even | 2 | 3381.2.a.w.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.a.i.1.4 | ✓ | 4 | 4.3 | odd | 2 | ||
1449.2.a.p.1.1 | 4 | 12.11 | even | 2 | |||
3381.2.a.w.1.4 | 4 | 28.27 | even | 2 | |||
7728.2.a.cd.1.3 | 4 | 1.1 | even | 1 | trivial |