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: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3864) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.11491\) 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 | ||||||||
\(5\) | −1.47283 | −0.658671 | −0.329336 | − | 0.944213i | \(-0.606825\pi\) | ||||
−0.329336 | + | 0.944213i | \(0.606825\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.64207 | 0.495104 | 0.247552 | − | 0.968875i | \(-0.420374\pi\) | ||||
0.247552 | + | 0.968875i | \(0.420374\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.169240 | −0.0469387 | −0.0234693 | − | 0.999725i | \(-0.507471\pi\) | ||||
−0.0234693 | + | 0.999725i | \(0.507471\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.47283 | 0.380284 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.58774 | 0.627619 | 0.313810 | − | 0.949486i | \(-0.398395\pi\) | ||||
0.313810 | + | 0.949486i | \(0.398395\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.87189 | −0.888272 | −0.444136 | − | 0.895959i | \(-0.646489\pi\) | ||||
−0.444136 | + | 0.895959i | \(0.646489\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.83076 | −0.566152 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.357926 | −0.0664653 | −0.0332326 | − | 0.999448i | \(-0.510580\pi\) | ||||
−0.0332326 | + | 0.999448i | \(0.510580\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.87189 | 0.695412 | 0.347706 | − | 0.937604i | \(-0.386961\pi\) | ||||
0.347706 | + | 0.937604i | \(0.386961\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.64207 | −0.285848 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.47283 | −0.248954 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.35793 | −0.716439 | −0.358219 | − | 0.933637i | \(-0.616616\pi\) | ||||
−0.358219 | + | 0.933637i | \(0.616616\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.169240 | 0.0271000 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.87189 | −1.54173 | −0.770865 | − | 0.636999i | \(-0.780176\pi\) | ||||
−0.770865 | + | 0.636999i | \(0.780176\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.11491 | 0.780016 | 0.390008 | − | 0.920811i | \(-0.372472\pi\) | ||||
0.390008 | + | 0.920811i | \(0.372472\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.47283 | −0.219557 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.79811 | −1.28334 | −0.641668 | − | 0.766982i | \(-0.721757\pi\) | ||||
−0.641668 | + | 0.766982i | \(0.721757\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.58774 | −0.362356 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.5940 | 1.86728 | 0.933639 | − | 0.358216i | \(-0.116615\pi\) | ||||
0.933639 | + | 0.358216i | \(0.116615\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.41850 | −0.326111 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.87189 | 0.512844 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.47283 | 0.972880 | 0.486440 | − | 0.873714i | \(-0.338295\pi\) | ||||
0.486440 | + | 0.873714i | \(0.338295\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.11491 | −0.398823 | −0.199412 | − | 0.979916i | \(-0.563903\pi\) | ||||
−0.199412 | + | 0.979916i | \(0.563903\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.249262 | 0.0309171 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.1623 | 1.24152 | 0.620760 | − | 0.784001i | \(-0.286824\pi\) | ||||
0.620760 | + | 0.784001i | \(0.286824\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.2361 | −1.57083 | −0.785416 | − | 0.618969i | \(-0.787551\pi\) | ||||
−0.785416 | + | 0.618969i | \(0.787551\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.3579 | −1.44639 | −0.723193 | − | 0.690646i | \(-0.757326\pi\) | ||||
−0.723193 | + | 0.690646i | \(0.757326\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.83076 | 0.326868 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.64207 | 0.187132 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.587741 | −0.0661261 | −0.0330630 | − | 0.999453i | \(-0.510526\pi\) | ||||
−0.0330630 | + | 0.999453i | \(0.510526\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.10170 | 0.669749 | 0.334875 | − | 0.942263i | \(-0.391306\pi\) | ||||
0.334875 | + | 0.942263i | \(0.391306\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.81131 | −0.413395 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.357926 | 0.0383737 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.5202 | −1.53914 | −0.769569 | − | 0.638563i | \(-0.779529\pi\) | ||||
−0.769569 | + | 0.638563i | \(0.779529\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.169240 | −0.0177411 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.87189 | −0.401496 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.70265 | 0.585079 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.81756 | 0.489149 | 0.244574 | − | 0.969631i | \(-0.421352\pi\) | ||||
0.244574 | + | 0.969631i | \(0.421352\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.64207 | 0.165035 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.09546 | −0.507017 | −0.253509 | − | 0.967333i | \(-0.581585\pi\) | ||||
−0.253509 | + | 0.967333i | \(0.581585\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.45963 | 0.439420 | 0.219710 | − | 0.975565i | \(-0.429489\pi\) | ||||
0.219710 | + | 0.975565i | \(0.429489\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.47283 | 0.143734 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.77643 | 0.848449 | 0.424225 | − | 0.905557i | \(-0.360547\pi\) | ||||
0.424225 | + | 0.905557i | \(0.360547\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.32528 | 0.701634 | 0.350817 | − | 0.936444i | \(-0.385904\pi\) | ||||
0.350817 | + | 0.936444i | \(0.385904\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.35793 | 0.413636 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.4464 | −1.82937 | −0.914683 | − | 0.404172i | \(-0.867560\pi\) | ||||
−0.914683 | + | 0.404172i | \(0.867560\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.47283 | −0.137342 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.169240 | −0.0156462 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.58774 | 0.237218 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.30359 | −0.754872 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.87189 | 0.890118 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.5334 | 1.03158 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.7764 | 1.48867 | 0.744334 | − | 0.667808i | \(-0.232767\pi\) | ||||
0.744334 | + | 0.667808i | \(0.232767\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.11491 | −0.450342 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.1949 | 1.32759 | 0.663794 | − | 0.747916i | \(-0.268945\pi\) | ||||
0.663794 | + | 0.747916i | \(0.268945\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.87189 | −0.335735 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.47283 | 0.126761 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.4247 | 1.31782 | 0.658912 | − | 0.752220i | \(-0.271017\pi\) | ||||
0.658912 | + | 0.752220i | \(0.271017\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.18869 | 0.355280 | 0.177640 | − | 0.984096i | \(-0.443154\pi\) | ||||
0.177640 | + | 0.984096i | \(0.443154\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.79811 | 0.740934 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.277904 | −0.0232395 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.527166 | 0.0437788 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.51396 | 0.615568 | 0.307784 | − | 0.951456i | \(-0.400413\pi\) | ||||
0.307784 | + | 0.951456i | \(0.400413\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.5808 | −1.67484 | −0.837420 | − | 0.546560i | \(-0.815937\pi\) | ||||
−0.837420 | + | 0.546560i | \(0.815937\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.58774 | 0.209206 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.70265 | −0.458048 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.5808 | −1.48291 | −0.741454 | − | 0.671004i | \(-0.765863\pi\) | ||||
−0.741454 | + | 0.671004i | \(0.765863\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.5940 | −1.07807 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.5940 | 1.22142 | 0.610708 | − | 0.791856i | \(-0.290885\pi\) | ||||
0.610708 | + | 0.791856i | \(0.290885\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.41850 | 0.188280 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.98055 | −0.462789 | −0.231395 | − | 0.972860i | \(-0.574329\pi\) | ||||
−0.231395 | + | 0.972860i | \(0.574329\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9714 | −0.997797 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.87189 | −0.296091 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.3315 | 1.08961 | 0.544803 | − | 0.838564i | \(-0.316605\pi\) | ||||
0.544803 | + | 0.838564i | \(0.316605\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.83076 | −0.213985 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.47283 | −0.561693 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.6219 | −1.39187 | −0.695933 | − | 0.718106i | \(-0.745009\pi\) | ||||
−0.695933 | + | 0.718106i | \(0.745009\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.07378 | −0.674449 | −0.337224 | − | 0.941424i | \(-0.609488\pi\) | ||||
−0.337224 | + | 0.941424i | \(0.609488\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.11491 | 0.230261 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.41850 | 0.471898 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.24926 | 0.310737 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.5808 | 1.48917 | 0.744587 | − | 0.667526i | \(-0.232647\pi\) | ||||
0.744587 | + | 0.667526i | \(0.232647\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.6615 | −1.27130 | −0.635652 | − | 0.771976i | \(-0.719269\pi\) | ||||
−0.635652 | + | 0.771976i | \(0.719269\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.249262 | −0.0178500 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.5591 | −1.60727 | −0.803635 | − | 0.595123i | \(-0.797103\pi\) | ||||
−0.803635 | + | 0.595123i | \(0.797103\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.64832 | 0.329510 | 0.164755 | − | 0.986334i | \(-0.447317\pi\) | ||||
0.164755 | + | 0.986334i | \(0.447317\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.1623 | −0.716792 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.357926 | −0.0251215 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.5397 | 1.01549 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.35793 | −0.439787 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.8844 | −1.50658 | −0.753291 | − | 0.657687i | \(-0.771535\pi\) | ||||
−0.753291 | + | 0.657687i | \(0.771535\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.2361 | 0.906920 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.53341 | −0.513774 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.87189 | 0.262841 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.3579 | 0.835071 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.437949 | −0.0294596 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.56606 | −0.573626 | −0.286813 | − | 0.957987i | \(-0.592596\pi\) | ||||
−0.286813 | + | 0.957987i | \(0.592596\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.83076 | −0.188717 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.74154 | −0.646569 | −0.323284 | − | 0.946302i | \(-0.604787\pi\) | ||||
−0.323284 | + | 0.946302i | \(0.604787\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.04113 | −0.531373 | −0.265686 | − | 0.964060i | \(-0.585599\pi\) | ||||
−0.265686 | + | 0.964060i | \(0.585599\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.64207 | −0.108041 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −27.5676 | −1.80601 | −0.903006 | − | 0.429628i | \(-0.858645\pi\) | ||||
−0.903006 | + | 0.429628i | \(0.858645\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.9582 | 0.845297 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.587741 | 0.0381779 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.0147 | 1.29464 | 0.647322 | − | 0.762216i | \(-0.275889\pi\) | ||||
0.647322 | + | 0.762216i | \(0.275889\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.99304 | 0.386046 | 0.193023 | − | 0.981194i | \(-0.438171\pi\) | ||||
0.193023 | + | 0.981194i | \(0.438171\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.47283 | −0.0940959 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.655277 | 0.0416943 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.10170 | −0.386680 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.2687 | −0.900633 | −0.450316 | − | 0.892869i | \(-0.648689\pi\) | ||||
−0.450316 | + | 0.892869i | \(0.648689\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.64207 | 0.103236 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.81131 | 0.238674 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 31.0015 | 1.93382 | 0.966911 | − | 0.255115i | \(-0.0821133\pi\) | ||||
0.966911 | + | 0.255115i | \(0.0821133\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.35793 | −0.270788 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.357926 | −0.0221551 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.65456 | 0.472000 | 0.236000 | − | 0.971753i | \(-0.424163\pi\) | ||||
0.236000 | + | 0.971753i | \(0.424163\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.0217 | −1.22992 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.5202 | 0.888622 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.72210 | 0.348882 | 0.174441 | − | 0.984668i | \(-0.444188\pi\) | ||||
0.174441 | + | 0.984668i | \(0.444188\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.22134 | −0.0741910 | −0.0370955 | − | 0.999312i | \(-0.511811\pi\) | ||||
−0.0370955 | + | 0.999312i | \(0.511811\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.169240 | 0.0102429 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.64832 | −0.280304 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.8587 | −0.892772 | −0.446386 | − | 0.894841i | \(-0.647289\pi\) | ||||
−0.446386 | + | 0.894841i | \(0.647289\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.87189 | 0.231804 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.7981 | 1.12140 | 0.560701 | − | 0.828019i | \(-0.310532\pi\) | ||||
0.560701 | + | 0.828019i | \(0.310532\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.3378 | −1.62506 | −0.812531 | − | 0.582918i | \(-0.801911\pi\) | ||||
−0.812531 | + | 0.582918i | \(0.801911\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.70265 | −0.337796 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.87189 | −0.582719 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.3036 | −0.606094 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.81756 | −0.282410 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.82452 | 0.515534 | 0.257767 | − | 0.966207i | \(-0.417013\pi\) | ||||
0.257767 | + | 0.966207i | \(0.417013\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.0062 | −0.640808 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.64207 | −0.0952828 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.169240 | −0.00978739 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.11491 | 0.294818 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.09546 | 0.292727 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.58774 | 0.262693 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.6825 | −1.75114 | −0.875571 | − | 0.483090i | \(-0.839515\pi\) | ||||
−0.875571 | + | 0.483090i | \(0.839515\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.45963 | −0.253699 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.2097 | 1.31610 | 0.658049 | − | 0.752975i | \(-0.271382\pi\) | ||||
0.658049 | + | 0.752975i | \(0.271382\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.9582 | −1.52376 | −0.761882 | − | 0.647715i | \(-0.775725\pi\) | ||||
−0.761882 | + | 0.647715i | \(0.775725\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.47283 | −0.0829848 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.6483 | 1.04739 | 0.523697 | − | 0.851905i | \(-0.324552\pi\) | ||||
0.523697 | + | 0.851905i | \(0.324552\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.587741 | −0.0329072 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.77643 | −0.489852 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.0194 | −0.557497 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.479077 | 0.0265744 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.32528 | −0.405089 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.79811 | −0.485055 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.42074 | −0.242986 | −0.121493 | − | 0.992592i | \(-0.538768\pi\) | ||||
−0.121493 | + | 0.992592i | \(0.538768\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.35793 | −0.238813 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.9673 | −0.817754 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.91302 | −0.213156 | −0.106578 | − | 0.994304i | \(-0.533989\pi\) | ||||
−0.106578 | + | 0.994304i | \(0.533989\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.4464 | 1.05618 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.35793 | 0.344301 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.47283 | 0.0792947 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.8719 | −0.852048 | −0.426024 | − | 0.904712i | \(-0.640086\pi\) | ||||
−0.426024 | + | 0.904712i | \(0.640086\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.0411 | −0.644547 | −0.322273 | − | 0.946647i | \(-0.604447\pi\) | ||||
−0.322273 | + | 0.946647i | \(0.604447\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.169240 | 0.00903335 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.83299 | 0.0975605 | 0.0487802 | − | 0.998810i | \(-0.484467\pi\) | ||||
0.0487802 | + | 0.998810i | \(0.484467\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.4945 | 1.03466 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.58774 | −0.136958 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.4185 | 0.972091 | 0.486046 | − | 0.873933i | \(-0.338439\pi\) | ||||
0.486046 | + | 0.873933i | \(0.338439\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.00848 | −0.210973 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.30359 | 0.435826 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.2012 | 0.952693 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.0885 | −1.20521 | −0.602605 | − | 0.798040i | \(-0.705871\pi\) | ||||
−0.602605 | + | 0.798040i | \(0.705871\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.87189 | −0.513910 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.5940 | 0.705765 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.8455 | −1.85601 | −0.928004 | − | 0.372569i | \(-0.878477\pi\) | ||||
−0.928004 | + | 0.372569i | \(0.878477\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.5334 | −0.595583 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.0605754 | 0.00311979 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.1087 | −0.519247 | −0.259624 | − | 0.965710i | \(-0.583598\pi\) | ||||
−0.259624 | + | 0.965710i | \(0.583598\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.7764 | −0.859482 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.8565 | −1.57669 | −0.788345 | − | 0.615233i | \(-0.789062\pi\) | ||||
−0.788345 | + | 0.615233i | \(0.789062\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.41850 | −0.123258 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.11491 | 0.260005 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.16701 | 0.109872 | 0.0549358 | − | 0.998490i | \(-0.482505\pi\) | ||||
0.0549358 | + | 0.998490i | \(0.482505\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.58774 | 0.130868 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.1949 | −0.766483 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.865646 | 0.0435554 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −31.7563 | −1.59380 | −0.796901 | − | 0.604110i | \(-0.793529\pi\) | ||||
−0.796901 | + | 0.604110i | \(0.793529\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.87189 | 0.193837 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.84396 | −0.341771 | −0.170886 | − | 0.985291i | \(-0.554663\pi\) | ||||
−0.170886 | + | 0.985291i | \(0.554663\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.655277 | −0.0326417 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.47283 | −0.0731857 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.15604 | −0.354712 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.50700 | 0.173410 | 0.0867050 | − | 0.996234i | \(-0.472366\pi\) | ||||
0.0867050 | + | 0.996234i | \(0.472366\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.4247 | −0.760847 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.47283 | 0.367714 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.98680 | −0.441144 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.18869 | −0.205121 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −37.3114 | −1.82278 | −0.911389 | − | 0.411545i | \(-0.864989\pi\) | ||||
−0.911389 | + | 0.411545i | \(0.864989\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.03265 | 0.147802 | 0.0739012 | − | 0.997266i | \(-0.476455\pi\) | ||||
0.0739012 | + | 0.997266i | \(0.476455\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.79811 | −0.427779 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.32528 | −0.355328 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.11491 | −0.150741 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.277904 | 0.0134173 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.0995 | −1.16083 | −0.580415 | − | 0.814321i | \(-0.697110\pi\) | ||||
−0.580415 | + | 0.814321i | \(0.697110\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.6087 | 0.846220 | 0.423110 | − | 0.906078i | \(-0.360938\pi\) | ||||
0.423110 | + | 0.906078i | \(0.360938\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.527166 | −0.0252757 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.87189 | −0.185218 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.2617 | −1.25340 | −0.626702 | − | 0.779259i | \(-0.715596\pi\) | ||||
−0.626702 | + | 0.779259i | \(0.715596\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.13659 | −0.434092 | −0.217046 | − | 0.976161i | \(-0.569642\pi\) | ||||
−0.217046 | + | 0.976161i | \(0.569642\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.3859 | 1.01379 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.51396 | −0.355398 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.46035 | −0.163304 | −0.0816519 | − | 0.996661i | \(-0.526020\pi\) | ||||
−0.0816519 | + | 0.996661i | \(0.526020\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.2104 | −0.763316 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.5808 | 0.966969 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.249262 | 0.0116856 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5132 | 0.678901 | 0.339450 | − | 0.940624i | \(-0.389759\pi\) | ||||
0.339450 | + | 0.940624i | \(0.389759\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.58774 | −0.120785 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.4185 | −0.578387 | −0.289194 | − | 0.957271i | \(-0.593387\pi\) | ||||
−0.289194 | + | 0.957271i | \(0.593387\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.3315 | −0.758990 | −0.379495 | − | 0.925194i | \(-0.623902\pi\) | ||||
−0.379495 | + | 0.925194i | \(0.623902\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.70265 | 0.264454 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.81756 | 0.130381 | 0.0651905 | − | 0.997873i | \(-0.479234\pi\) | ||||
0.0651905 | + | 0.997873i | \(0.479234\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.1623 | 0.469250 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.5808 | 0.856157 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.39905 | 0.386189 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.9604 | 0.502897 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.5940 | 0.622426 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.3594 | −1.61561 | −0.807807 | − | 0.589447i | \(-0.799346\pi\) | ||||
−0.807807 | + | 0.589447i | \(0.799346\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.737534 | 0.0336287 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.09546 | −0.322188 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.80507 | −0.217739 | −0.108869 | − | 0.994056i | \(-0.534723\pi\) | ||||
−0.108869 | + | 0.994056i | \(0.534723\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.5940 | −0.705184 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.0202 | 1.89635 | 0.948174 | − | 0.317753i | \(-0.102928\pi\) | ||||
0.948174 | + | 0.317753i | \(0.102928\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.926221 | −0.0417149 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.41850 | −0.108704 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.2361 | −0.593718 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.1513 | 1.30499 | 0.652496 | − | 0.757792i | \(-0.273722\pi\) | ||||
0.652496 | + | 0.757792i | \(0.273722\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.98055 | 0.267191 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.7151 | 0.522352 | 0.261176 | − | 0.965291i | \(-0.415890\pi\) | ||||
0.261176 | + | 0.965291i | \(0.415890\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.50477 | 0.333958 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.9714 | 0.576078 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.9457 | 0.573807 | 0.286903 | − | 0.957960i | \(-0.407374\pi\) | ||||
0.286903 | + | 0.957960i | \(0.407374\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.3579 | −0.546682 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.87189 | 0.170948 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.56829 | −0.289434 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.4471 | −0.635385 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.3315 | −0.629084 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.5404 | 0.943701 | 0.471850 | − | 0.881679i | \(-0.343586\pi\) | ||||
0.471850 | + | 0.881679i | \(0.343586\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.82452 | 0.298415 | 0.149208 | − | 0.988806i | \(-0.452328\pi\) | ||||
0.149208 | + | 0.988806i | \(0.452328\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.83076 | 0.123545 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.0194 | 0.436454 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.47283 | 0.324293 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.67072 | 0.0723667 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.9262 | −0.558849 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.6219 | 0.803595 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.64207 | 0.0707291 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.9457 | −0.728551 | −0.364276 | − | 0.931291i | \(-0.618683\pi\) | ||||
−0.364276 | + | 0.931291i | \(0.618683\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.07378 | 0.389393 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.7889 | −0.462146 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.2012 | 0.778226 | 0.389113 | − | 0.921190i | \(-0.372782\pi\) | ||||
0.389113 | + | 0.921190i | \(0.372782\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.11491 | −0.132941 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.38585 | 0.0590392 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.587741 | −0.0249933 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.41850 | −0.272450 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.5529 | 1.16745 | 0.583726 | − | 0.811951i | \(-0.301594\pi\) | ||||
0.583726 | + | 0.811951i | \(0.301594\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.865646 | −0.0366129 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.24926 | −0.179404 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −35.7610 | −1.50715 | −0.753573 | − | 0.657364i | \(-0.771671\pi\) | ||||
−0.753573 | + | 0.657364i | \(0.771671\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.6414 | 1.20495 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.9582 | −1.46552 | −0.732761 | − | 0.680486i | \(-0.761769\pi\) | ||||
−0.732761 | + | 0.680486i | \(0.761769\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.6964 | 1.11721 | 0.558605 | − | 0.829434i | \(-0.311337\pi\) | ||||
0.558605 | + | 0.829434i | \(0.311337\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.5808 | −0.859774 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.83076 | −0.118051 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.7299 | −1.90376 | −0.951879 | − | 0.306473i | \(-0.900851\pi\) | ||||
−0.951879 | + | 0.306473i | \(0.900851\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.6615 | 0.733988 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.10170 | 0.253141 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.3223 | 0.924496 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.249262 | 0.0103057 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.2081 | −0.916628 | −0.458314 | − | 0.888790i | \(-0.651546\pi\) | ||||
−0.458314 | + | 0.888790i | \(0.651546\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.9915 | −0.617715 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.5591 | 0.927957 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.3664 | −0.877413 | −0.438707 | − | 0.898630i | \(-0.644563\pi\) | ||||
−0.438707 | + | 0.898630i | \(0.644563\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.81131 | −0.156249 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.64832 | −0.190243 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.31832 | 0.380736 | 0.190368 | − | 0.981713i | \(-0.439032\pi\) | ||||
0.190368 | + | 0.981713i | \(0.439032\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.0257 | −1.42873 | −0.714364 | − | 0.699774i | \(-0.753284\pi\) | ||||
−0.714364 | + | 0.699774i | \(0.753284\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.1623 | 0.413840 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.2298 | 0.497213 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.5356 | 0.874105 | 0.437052 | − | 0.899436i | \(-0.356022\pi\) | ||||
0.437052 | + | 0.899436i | \(0.356022\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.357926 | 0.0145039 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.48899 | 0.0602381 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.8300 | 1.72989 | 0.864945 | − | 0.501867i | \(-0.167353\pi\) | ||||
0.864945 | + | 0.501867i | \(0.167353\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.5397 | −0.586295 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.2904 | −1.46100 | −0.730498 | − | 0.682915i | \(-0.760712\pi\) | ||||
−0.730498 | + | 0.682915i | \(0.760712\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.5481 | −1.10725 | −0.553626 | − | 0.832765i | \(-0.686756\pi\) | ||||
−0.553626 | + | 0.832765i | \(0.686756\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.5202 | −0.581740 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.83299 | −0.113320 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.35793 | 0.253911 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.2772 | −0.449651 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.7368 | 0.785710 | 0.392855 | − | 0.919600i | \(-0.371487\pi\) | ||||
0.392855 | + | 0.919600i | \(0.371487\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.8844 | 0.869826 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.7089 | −0.980542 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.169240 | −0.00670552 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.2361 | −0.523610 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.3726 | 1.12065 | 0.560326 | − | 0.828272i | \(-0.310676\pi\) | ||||
0.560326 | + | 0.828272i | \(0.310676\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.8432 | −1.25578 | −0.627888 | − | 0.778304i | \(-0.716080\pi\) | ||||
−0.627888 | + | 0.778304i | \(0.716080\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.53341 | 0.296628 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.91998 | −0.0754821 | −0.0377411 | − | 0.999288i | \(-0.512016\pi\) | ||||
−0.0377411 | + | 0.999288i | \(0.512016\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.2709 | 0.481677 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.87189 | −0.151751 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.40753 | 0.289879 | 0.144940 | − | 0.989441i | \(-0.453701\pi\) | ||||
0.144940 | + | 0.989441i | \(0.453701\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.3796 | −0.874444 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.3579 | −0.482129 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.27719 | −0.283479 | −0.141739 | − | 0.989904i | \(-0.545270\pi\) | ||||
−0.141739 | + | 0.989904i | \(0.545270\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.27719 | 0.360841 | 0.180420 | − | 0.983590i | \(-0.442254\pi\) | ||||
0.180420 | + | 0.983590i | \(0.442254\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.437949 | 0.0170085 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.70265 | 0.221139 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.357926 | −0.0138590 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.56606 | 0.331183 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.11491 | −0.197459 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.6266 | 0.872193 | 0.436096 | − | 0.899900i | \(-0.356361\pi\) | ||||
0.436096 | + | 0.899900i | \(0.356361\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.83076 | 0.108956 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.4938 | −0.941373 | −0.470687 | − | 0.882300i | \(-0.655994\pi\) | ||||
−0.470687 | + | 0.882300i | \(0.655994\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.81756 | 0.184881 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.74154 | 0.373297 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.4402 | 0.858650 | 0.429325 | − | 0.903150i | \(-0.358752\pi\) | ||||
0.429325 | + | 0.903150i | \(0.358752\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.7181 | −0.868013 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.04113 | 0.306788 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.30064 | −0.0876475 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.4798 | −0.436712 | −0.218356 | − | 0.975869i | \(-0.570069\pi\) | ||||
−0.218356 | + | 0.975869i | \(0.570069\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.64207 | 0.0623772 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.16924 | −0.234013 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.5459 | −0.967620 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 27.5676 | 1.04270 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.6204 | 0.438896 | 0.219448 | − | 0.975624i | \(-0.429574\pi\) | ||||
0.219448 | + | 0.975624i | \(0.429574\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.8734 | 0.636393 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.9582 | −0.488032 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.09546 | −0.191635 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −45.5870 | −1.71206 | −0.856028 | − | 0.516929i | \(-0.827075\pi\) | ||||
−0.856028 | + | 0.516929i | \(0.827075\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.587741 | −0.0220420 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.87189 | 0.145003 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.409307 | 0.0153072 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.0147 | −0.747463 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.5195 | 1.17548 | 0.587739 | − | 0.809050i | \(-0.300018\pi\) | ||||
0.587739 | + | 0.809050i | \(0.300018\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.45963 | 0.166085 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.99304 | −0.222884 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.01320 | 0.0376294 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.1560 | −0.562106 | −0.281053 | − | 0.959692i | \(-0.590684\pi\) | ||||
−0.281053 | + | 0.959692i | \(0.590684\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.2361 | 0.489553 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.1491 | 1.66762 | 0.833810 | − | 0.552052i | \(-0.186155\pi\) | ||||
0.833810 | + | 0.552052i | \(0.186155\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.47283 | 0.0543263 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.6872 | 0.614681 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.5055 | −0.607164 | −0.303582 | − | 0.952805i | \(-0.598183\pi\) | ||||
−0.303582 | + | 0.952805i | \(0.598183\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.655277 | −0.0240722 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −53.5537 | −1.96469 | −0.982347 | − | 0.187070i | \(-0.940101\pi\) | ||||
−0.982347 | + | 0.187070i | \(0.940101\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.0668 | −0.405457 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.10170 | 0.223250 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.77643 | 0.320684 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.2570 | −1.03111 | −0.515557 | − | 0.856855i | \(-0.672415\pi\) | ||||
−0.515557 | + | 0.856855i | \(0.672415\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.2687 | 0.519981 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30.3121 | 1.10317 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.9821 | 0.471841 | 0.235921 | − | 0.971772i | \(-0.424189\pi\) | ||||
0.235921 | + | 0.971772i | \(0.424189\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.64207 | −0.0596035 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.47060 | 0.270809 | 0.135405 | − | 0.990790i | \(-0.456767\pi\) | ||||
0.135405 | + | 0.990790i | \(0.456767\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.32528 | 0.265193 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.81131 | −0.137798 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.26470 | −0.0456657 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.22982 | 0.152531 | 0.0762655 | − | 0.997088i | \(-0.475700\pi\) | ||||
0.0762655 | + | 0.997088i | \(0.475700\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.0015 | −1.11649 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.8565 | −0.462414 | −0.231207 | − | 0.972905i | \(-0.574268\pi\) | ||||
−0.231207 | + | 0.972905i | \(0.574268\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.9604 | −0.393709 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.35793 | 0.156340 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 38.2229 | 1.36948 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.7346 | −0.777725 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.357926 | 0.0127912 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27.3664 | 0.976749 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.03016 | 0.0367212 | 0.0183606 | − | 0.999831i | \(-0.494155\pi\) | ||||
0.0183606 | + | 0.999831i | \(0.494155\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.65456 | −0.272510 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.4464 | −0.691435 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.527166 | 0.0187202 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20.0217 | 0.710096 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.61967 | −0.234481 | −0.117240 | − | 0.993104i | \(-0.537405\pi\) | ||||
−0.117240 | + | 0.993104i | \(0.537405\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.7672 | −0.805447 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.5202 | −0.513046 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20.2926 | −0.716111 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.47283 | −0.0519106 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.72210 | −0.201427 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.2097 | −0.745692 | −0.372846 | − | 0.927893i | \(-0.621618\pi\) | ||||
−0.372846 | + | 0.927893i | \(0.621618\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.0878 | 1.19698 | 0.598492 | − | 0.801129i | \(-0.295767\pi\) | ||||
0.598492 | + | 0.801129i | \(0.295767\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.22134 | 0.0428342 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.9673 | −0.804511 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.8044 | −0.692867 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.169240 | −0.00591371 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.3525 | 1.30361 | 0.651805 | − | 0.758386i | \(-0.274012\pi\) | ||||
0.651805 | + | 0.758386i | \(0.274012\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.7959 | 1.49177 | 0.745885 | − | 0.666075i | \(-0.232027\pi\) | ||||
0.745885 | + | 0.666075i | \(0.232027\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.64832 | 0.161834 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.9993 | −1.07795 | −0.538975 | − | 0.842322i | \(-0.681188\pi\) | ||||
−0.538975 | + | 0.842322i | \(0.681188\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 56.0055 | 1.94515 | 0.972576 | − | 0.232585i | \(-0.0747183\pi\) | ||||
0.972576 | + | 0.232585i | \(0.0747183\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.8587 | 0.515442 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.58774 | 0.0896599 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.80836 | 0.304826 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.87189 | −0.133832 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.6443 | −0.540102 | −0.270051 | − | 0.962846i | \(-0.587040\pi\) | ||||
−0.270051 | + | 0.962846i | \(0.587040\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8719 | −0.995582 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.7981 | −0.647441 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.1047 | 0.657220 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.30359 | −0.285315 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27.3378 | 0.938230 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.35793 | −0.149388 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.55286 | 0.258605 | 0.129302 | − | 0.991605i | \(-0.458726\pi\) | ||||
0.129302 | + | 0.991605i | \(0.458726\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.70265 | 0.195026 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.6894 | −1.25329 | −0.626644 | − | 0.779306i | \(-0.715572\pi\) | ||||
−0.626644 | + | 0.779306i | \(0.715572\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.7438 | −0.673649 | −0.336824 | − | 0.941567i | \(-0.609353\pi\) | ||||
−0.336824 | + | 0.941567i | \(0.609353\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.87189 | 0.336433 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.5947 | 0.701052 | 0.350526 | − | 0.936553i | \(-0.386003\pi\) | ||||
0.350526 | + | 0.936553i | \(0.386003\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.1079 | −0.717692 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.3036 | 0.349928 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.965115 | −0.0327393 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.71986 | −0.0582753 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.81756 | 0.163050 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.5334 | 0.389900 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.8804 | 0.367404 | 0.183702 | − | 0.982982i | \(-0.441192\pi\) | ||||
0.183702 | + | 0.982982i | \(0.441192\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.82452 | −0.297644 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 52.7144 | 1.77599 | 0.887997 | − | 0.459849i | \(-0.152097\pi\) | ||||
0.887997 | + | 0.459849i | \(0.152097\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.616384 | 0.0207430 | 0.0103715 | − | 0.999946i | \(-0.496699\pi\) | ||||
0.0103715 | + | 0.999946i | \(0.496699\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.0062 | 0.369971 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.42698 | 0.115067 | 0.0575334 | − | 0.998344i | \(-0.481676\pi\) | ||||
0.0575334 | + | 0.998344i | \(0.481676\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.7764 | 0.562663 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.64207 | 0.0550115 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34.0653 | 1.13995 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.4270 | 0.916783 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.169240 | 0.00565075 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.38585 | −0.0462207 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 35.1777 | 1.17194 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.11491 | −0.170213 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.3642 | 0.444240 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.2291 | −1.36899 | −0.684495 | − | 0.729018i | \(-0.739977\pi\) | ||||
−0.684495 | + | 0.729018i | \(0.739977\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.09546 | −0.169006 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.7702 | 0.456227 | 0.228113 | − | 0.973635i | \(-0.426744\pi\) | ||||
0.228113 | + | 0.973635i | \(0.426744\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.0194 | 0.331595 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.58774 | −0.151666 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.1949 | 0.501781 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.1406 | 0.862299 | 0.431149 | − | 0.902281i | \(-0.358108\pi\) | ||||
0.431149 | + | 0.902281i | \(0.358108\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.6825 | 1.01102 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.24007 | 0.0737327 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.3362 | 0.405613 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.45963 | 0.146473 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.4853 | 0.639293 | 0.319646 | − | 0.947537i | \(-0.396436\pi\) | ||||
0.319646 | + | 0.947537i | \(0.396436\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.87189 | −0.126896 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.2097 | −0.759850 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.25846 | −0.204673 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.1560 | −0.429789 | −0.214894 | − | 0.976637i | \(-0.568941\pi\) | ||||
−0.214894 | + | 0.976637i | \(0.568941\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.9582 | 0.879746 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.93318 | 0.0956190 | 0.0478095 | − | 0.998856i | \(-0.484776\pi\) | ||||
0.0478095 | + | 0.998856i | \(0.484776\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.87189 | −0.321473 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.47283 | 0.0479113 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.7996 | 0.838375 | 0.419188 | − | 0.907900i | \(-0.362315\pi\) | ||||
0.419188 | + | 0.907900i | \(0.362315\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.09145 | 0.0678914 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.6483 | −0.604713 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.3338 | 1.04739 | 0.523697 | − | 0.851905i | \(-0.324553\pi\) | ||||
0.523697 | + | 0.851905i | \(0.324553\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.3121 | −0.980876 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.587741 | 0.0189990 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.4247 | 0.498091 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.0085 | −0.516403 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.77643 | 0.282816 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.0125 | 0.837372 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49.3400 | −1.58667 | −0.793334 | − | 0.608787i | \(-0.791656\pi\) | ||||
−0.793334 | + | 0.608787i | \(0.791656\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.0194 | 0.321871 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.48131 | −0.143812 | −0.0719061 | − | 0.997411i | \(-0.522908\pi\) | ||||
−0.0719061 | + | 0.997411i | \(0.522908\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.18869 | 0.134283 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.479077 | −0.0153427 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −61.6304 | −1.97173 | −0.985865 | − | 0.167539i | \(-0.946418\pi\) | ||||
−0.985865 | + | 0.167539i | \(0.946418\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.8432 | −0.762033 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.32528 | 0.233878 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.1545 | −0.323879 | −0.161939 | − | 0.986801i | \(-0.551775\pi\) | ||||
−0.161939 | + | 0.986801i | \(0.551775\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 33.2258 | 1.05866 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.79811 | 0.280047 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.11491 | 0.162645 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.1927 | 0.419080 | 0.209540 | − | 0.977800i | \(-0.432803\pi\) | ||||
0.209540 | + | 0.977800i | \(0.432803\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.42074 | 0.140288 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.84620 | −0.217039 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47.2119 | −1.49522 | −0.747608 | − | 0.664141i | \(-0.768798\pi\) | ||||
−0.747608 | + | 0.664141i | \(0.768798\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.35793 | 0.137879 |
(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.bs.1.1 | 3 | ||
4.3 | odd | 2 | 3864.2.a.q.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.a.q.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
7728.2.a.bs.1.1 | 3 | 1.1 | even | 1 | trivial |