Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9216,2,Mod(1,9216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9216.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9216 = 2^{10} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9216.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: | \(73.5901305028\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4352.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 48) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.334904\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9216.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.473626 | 0.211812 | 0.105906 | − | 0.994376i | \(-0.466226\pi\) | ||||
0.105906 | + | 0.994376i | \(0.466226\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.55765 | 1.72263 | 0.861314 | − | 0.508072i | \(-0.169642\pi\) | ||||
0.861314 | + | 0.508072i | \(0.169642\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.49824 | −1.05476 | −0.527379 | − | 0.849630i | \(-0.676825\pi\) | ||||
−0.527379 | + | 0.849630i | \(0.676825\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0840215 | −0.0233034 | −0.0116517 | − | 0.999932i | \(-0.503709\pi\) | ||||
−0.0116517 | + | 0.999932i | \(0.503709\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.61706 | 0.877266 | 0.438633 | − | 0.898666i | \(-0.355463\pi\) | ||||
0.438633 | + | 0.898666i | \(0.355463\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.61706 | 0.829810 | 0.414905 | − | 0.909865i | \(-0.363815\pi\) | ||||
0.414905 | + | 0.909865i | \(0.363815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.82843 | −0.589768 | −0.294884 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294884 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.77568 | −0.955136 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.30205 | −1.35596 | −0.677979 | − | 0.735082i | \(-0.737144\pi\) | ||||
−0.677979 | + | 0.735082i | \(0.737144\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.557647 | −0.100156 | −0.0500782 | − | 0.998745i | \(-0.515947\pi\) | ||||
−0.0500782 | + | 0.998745i | \(0.515947\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.15862 | 0.364873 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.20285 | 1.01974 | 0.509871 | − | 0.860251i | \(-0.329693\pi\) | ||||
0.509871 | + | 0.860251i | \(0.329693\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.27391 | 1.44834 | 0.724171 | − | 0.689620i | \(-0.242223\pi\) | ||||
0.724171 | + | 0.689620i | \(0.242223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.27744 | 0.347307 | 0.173653 | − | 0.984807i | \(-0.444443\pi\) | ||||
0.173653 | + | 0.984807i | \(0.444443\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.7721 | 1.96745 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.697947 | −0.0958704 | −0.0479352 | − | 0.998850i | \(-0.515264\pi\) | ||||
−0.0479352 | + | 0.998850i | \(0.515264\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.65685 | −0.223410 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.65685 | −0.736460 | −0.368230 | − | 0.929735i | \(-0.620036\pi\) | ||||
−0.368230 | + | 0.929735i | \(0.620036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.85970 | −0.494184 | −0.247092 | − | 0.968992i | \(-0.579475\pi\) | ||||
−0.247092 | + | 0.968992i | \(0.579475\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0397948 | −0.00493593 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.33962 | −0.652338 | −0.326169 | − | 0.945311i | \(-0.605758\pi\) | ||||
−0.326169 | + | 0.945311i | \(0.605758\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.11529 | 1.08179 | 0.540893 | − | 0.841091i | \(-0.318086\pi\) | ||||
0.540893 | + | 0.841091i | \(0.318086\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.541560 | −0.0633848 | −0.0316924 | − | 0.999498i | \(-0.510090\pi\) | ||||
−0.0316924 | + | 0.999498i | \(0.510090\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15.9437 | −1.81696 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.9937 | 1.23689 | 0.618445 | − | 0.785828i | \(-0.287763\pi\) | ||||
0.618445 | + | 0.785828i | \(0.287763\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.0496 | 1.65191 | 0.825954 | − | 0.563738i | \(-0.190637\pi\) | ||||
0.825954 | + | 0.563738i | \(0.190637\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.71313 | 0.185815 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.6533 | 1.55325 | 0.776625 | − | 0.629964i | \(-0.216930\pi\) | ||||
0.776625 | + | 0.629964i | \(0.216930\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.382941 | −0.0401431 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.71313 | 0.175764 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.31724 | 0.438349 | 0.219175 | − | 0.975686i | \(-0.429664\pi\) | ||||
0.219175 | + | 0.975686i | \(0.429664\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.641669 | 0.0638484 | 0.0319242 | − | 0.999490i | \(-0.489836\pi\) | ||||
0.0319242 | + | 0.999490i | \(0.489836\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.33686 | −0.131724 | −0.0658622 | − | 0.997829i | \(-0.520980\pi\) | ||||
−0.0658622 | + | 0.997829i | \(0.520980\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.57373 | 0.828854 | 0.414427 | − | 0.910083i | \(-0.363982\pi\) | ||||
0.414427 | + | 0.910083i | \(0.363982\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.08402 | 0.774309 | 0.387154 | − | 0.922015i | \(-0.373458\pi\) | ||||
0.387154 | + | 0.922015i | \(0.373458\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.55136 | −0.898516 | −0.449258 | − | 0.893402i | \(-0.648312\pi\) | ||||
−0.449258 | + | 0.893402i | \(0.648312\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.33962 | −0.124920 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.4853 | 1.51120 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.23765 | 0.112514 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.63001 | −0.414121 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.09921 | 0.452481 | 0.226241 | − | 0.974071i | \(-0.427356\pi\) | ||||
0.226241 | + | 0.974071i | \(0.427356\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.99647 | 0.261803 | 0.130901 | − | 0.991395i | \(-0.458213\pi\) | ||||
0.130901 | + | 0.991395i | \(0.458213\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.4853 | 1.42946 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.37941 | 0.288723 | 0.144361 | − | 0.989525i | \(-0.453887\pi\) | ||||
0.144361 | + | 0.989525i | \(0.453887\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.31724 | −0.705459 | −0.352729 | − | 0.935725i | \(-0.614746\pi\) | ||||
−0.352729 | + | 0.935725i | \(0.614746\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.293927 | 0.0245794 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.45844 | −0.287208 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.1305 | −1.15761 | −0.578807 | − | 0.815465i | \(-0.696482\pi\) | ||||
−0.578807 | + | 0.815465i | \(0.696482\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.97685 | 0.811905 | 0.405952 | − | 0.913894i | \(-0.366940\pi\) | ||||
0.405952 | + | 0.913894i | \(0.366940\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.264116 | −0.0212143 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.8562 | 1.82412 | 0.912060 | − | 0.410056i | \(-0.134491\pi\) | ||||
0.912060 | + | 0.410056i | \(0.134491\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.8910 | −1.01595 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.6135 | 0.831316 | 0.415658 | − | 0.909521i | \(-0.363551\pi\) | ||||
0.415658 | + | 0.909521i | \(0.363551\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.83822 | −0.451775 | −0.225888 | − | 0.974153i | \(-0.572528\pi\) | ||||
−0.225888 | + | 0.974153i | \(0.572528\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9929 | −0.999457 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.12695 | 0.389795 | 0.194897 | − | 0.980824i | \(-0.437563\pi\) | ||||
0.194897 | + | 0.980824i | \(0.437563\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.7659 | −1.64534 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.1286 | −0.981279 | −0.490640 | − | 0.871363i | \(-0.663237\pi\) | ||||
−0.490640 | + | 0.871363i | \(0.663237\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.3181 | 1.13859 | 0.569294 | − | 0.822134i | \(-0.307217\pi\) | ||||
0.569294 | + | 0.822134i | \(0.307217\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.93783 | 0.215993 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.6533 | −0.925303 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.63001 | 0.624446 | 0.312223 | − | 0.950009i | \(-0.398926\pi\) | ||||
0.312223 | + | 0.950009i | \(0.398926\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.4514 | 0.824288 | 0.412144 | − | 0.911119i | \(-0.364780\pi\) | ||||
0.412144 | + | 0.911119i | \(0.364780\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.5925 | −0.754681 | −0.377340 | − | 0.926075i | \(-0.623161\pi\) | ||||
−0.377340 | + | 0.926075i | \(0.623161\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.68000 | 0.260868 | 0.130434 | − | 0.991457i | \(-0.458363\pi\) | ||||
0.130434 | + | 0.991457i | \(0.458363\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −33.2802 | −2.33581 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.39236 | 0.306776 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.6533 | −0.875249 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.3102 | 0.985153 | 0.492577 | − | 0.870269i | \(-0.336055\pi\) | ||||
0.492577 | + | 0.870269i | \(0.336055\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.07866 | 0.0735637 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.54156 | −0.172532 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.303911 | −0.0204433 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.86156 | −0.325554 | −0.162777 | − | 0.986663i | \(-0.552045\pi\) | ||||
−0.162777 | + | 0.986663i | \(0.552045\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.0496 | 0.998877 | 0.499438 | − | 0.866349i | \(-0.333540\pi\) | ||||
0.499438 | + | 0.866349i | \(0.333540\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.5264 | −1.88507 | −0.942537 | − | 0.334101i | \(-0.891567\pi\) | ||||
−0.942537 | + | 0.334101i | \(0.891567\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.5702 | −0.889014 | −0.444507 | − | 0.895775i | \(-0.646621\pi\) | ||||
−0.444507 | + | 0.895775i | \(0.646621\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.33962 | 0.0873869 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.3629 | 1.89933 | 0.949665 | − | 0.313267i | \(-0.101424\pi\) | ||||
0.949665 | + | 0.313267i | \(0.101424\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.0063 | −1.54638 | −0.773190 | − | 0.634175i | \(-0.781340\pi\) | ||||
−0.773190 | + | 0.634175i | \(0.781340\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.52284 | 0.416729 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.303911 | −0.0193374 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.2837 | −1.40654 | −0.703268 | − | 0.710925i | \(-0.748276\pi\) | ||||
−0.703268 | + | 0.710925i | \(0.748276\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.89450 | 0.622062 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.66038 | −0.540220 | −0.270110 | − | 0.962829i | \(-0.587060\pi\) | ||||
−0.270110 | + | 0.962829i | \(0.587060\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28.2704 | 1.75664 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.3208 | 0.821394 | 0.410697 | − | 0.911772i | \(-0.365285\pi\) | ||||
0.410697 | + | 0.911772i | \(0.365285\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.330566 | −0.0203065 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.5058 | 1.00638 | 0.503188 | − | 0.864177i | \(-0.332160\pi\) | ||||
0.503188 | + | 0.864177i | \(0.332160\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.9769 | 1.33500 | 0.667499 | − | 0.744610i | \(-0.267365\pi\) | ||||
0.667499 | + | 0.744610i | \(0.267365\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.7064 | 1.00744 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.4862 | 0.930475 | 0.465237 | − | 0.885186i | \(-0.345969\pi\) | ||||
0.465237 | + | 0.885186i | \(0.345969\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.8910 | −1.36556 | −0.682780 | − | 0.730624i | \(-0.739229\pi\) | ||||
−0.682780 | + | 0.730624i | \(0.739229\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.34315 | 0.377061 | 0.188530 | − | 0.982067i | \(-0.439628\pi\) | ||||
0.188530 | + | 0.982067i | \(0.439628\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 42.2672 | 2.49496 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.91688 | −0.230405 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −30.5783 | −1.78641 | −0.893203 | − | 0.449654i | \(-0.851547\pi\) | ||||
−0.893203 | + | 0.449654i | \(0.851547\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.67923 | −0.155991 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.237649 | 0.0137436 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.3798 | 0.598281 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.82805 | −0.104674 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.1286 | −0.977582 | −0.488791 | − | 0.872401i | \(-0.662562\pi\) | ||||
−0.488791 | + | 0.872401i | \(0.662562\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.8651 | 1.52338 | 0.761689 | − | 0.647943i | \(-0.224370\pi\) | ||||
0.761689 | + | 0.647943i | \(0.224370\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.6890 | −1.11289 | −0.556445 | − | 0.830885i | \(-0.687835\pi\) | ||||
−0.556445 | + | 0.830885i | \(0.687835\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.1860 | 1.69541 | 0.847706 | − | 0.530466i | \(-0.177983\pi\) | ||||
0.847706 | + | 0.530466i | \(0.177983\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.5443 | 1.43021 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.0831 | 0.727964 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.401260 | 0.0222579 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.8910 | 0.710702 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.7784 | −1.14209 | −0.571043 | − | 0.820920i | \(-0.693461\pi\) | ||||
−0.571043 | + | 0.820920i | \(0.693461\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.52898 | −0.138173 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.0098 | 1.25342 | 0.626712 | − | 0.779251i | \(-0.284400\pi\) | ||||
0.626712 | + | 0.779251i | \(0.284400\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.95078 | 0.105641 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 30.8651 | 1.66656 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.4186 | 0.827716 | 0.413858 | − | 0.910341i | \(-0.364181\pi\) | ||||
0.413858 | + | 0.910341i | \(0.364181\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.3638 | −1.51828 | −0.759140 | − | 0.650927i | \(-0.774380\pi\) | ||||
−0.759140 | + | 0.650927i | \(0.774380\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.2117 | 0.649965 | 0.324983 | − | 0.945720i | \(-0.394642\pi\) | ||||
0.324983 | + | 0.945720i | \(0.394642\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.31724 | 0.229135 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.4780 | 1.76690 | 0.883452 | − | 0.468522i | \(-0.155214\pi\) | ||||
0.883452 | + | 0.468522i | \(0.155214\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.91688 | −0.311415 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.256497 | −0.0134256 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.702379 | 0.0366639 | 0.0183319 | − | 0.999832i | \(-0.494164\pi\) | ||||
0.0183319 | + | 0.999832i | \(0.494164\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.18100 | −0.165149 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.8132 | −1.38834 | −0.694168 | − | 0.719813i | \(-0.744227\pi\) | ||||
−0.694168 | + | 0.719813i | \(0.744227\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.613530 | 0.0315984 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.51509 | −0.129192 | −0.0645958 | − | 0.997912i | \(-0.520576\pi\) | ||||
−0.0645958 | + | 0.997912i | \(0.520576\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.4880 | −1.30238 | −0.651188 | − | 0.758916i | \(-0.725729\pi\) | ||||
−0.651188 | + | 0.758916i | \(0.725729\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.55136 | −0.384853 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.5532 | 0.839281 | 0.419641 | − | 0.907690i | \(-0.362156\pi\) | ||||
0.419641 | + | 0.907690i | \(0.362156\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.2306 | −0.517383 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.20690 | 0.261988 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.7936 | −0.642094 | −0.321047 | − | 0.947063i | \(-0.604035\pi\) | ||||
−0.321047 | + | 0.947063i | \(0.604035\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0853 | −0.903137 | −0.451568 | − | 0.892237i | \(-0.649135\pi\) | ||||
−0.451568 | + | 0.892237i | \(0.649135\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0468544 | 0.00233398 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.6990 | −1.07558 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.2271 | 1.24740 | 0.623699 | − | 0.781665i | \(-0.285629\pi\) | ||||
0.623699 | + | 0.781665i | \(0.285629\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −25.7819 | −1.26865 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.12787 | 0.349894 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.2571 | 0.501090 | 0.250545 | − | 0.968105i | \(-0.419390\pi\) | ||||
0.250545 | + | 0.968105i | \(0.419390\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.38775 | 0.165109 | 0.0825543 | − | 0.996587i | \(-0.473692\pi\) | ||||
0.0825543 | + | 0.996587i | \(0.473692\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.2739 | −0.837908 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.5912 | −0.851296 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.42454 | −0.213123 | −0.106561 | − | 0.994306i | \(-0.533984\pi\) | ||||
−0.106561 | + | 0.994306i | \(0.533984\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.31371 | −0.351474 | −0.175737 | − | 0.984437i | \(-0.556231\pi\) | ||||
−0.175737 | + | 0.984437i | \(0.556231\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.2306 | −0.489395 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.6533 | −1.41527 | −0.707637 | − | 0.706576i | \(-0.750239\pi\) | ||||
−0.707637 | + | 0.706576i | \(0.750239\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.5743 | −0.692446 | −0.346223 | − | 0.938152i | \(-0.612536\pi\) | ||||
−0.346223 | + | 0.938152i | \(0.612536\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.94019 | 0.328997 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.48844 | 0.306208 | 0.153104 | − | 0.988210i | \(-0.451073\pi\) | ||||
0.153104 | + | 0.988210i | \(0.451073\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.4423 | −1.52765 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.181370 | −0.00850278 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.00353 | −0.421167 | −0.210584 | − | 0.977576i | \(-0.567536\pi\) | ||||
−0.210584 | + | 0.977576i | \(0.567536\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.6783 | −0.963085 | −0.481542 | − | 0.876423i | \(-0.659923\pi\) | ||||
−0.481542 | + | 0.876423i | \(0.659923\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.6435 | 0.866437 | 0.433219 | − | 0.901289i | \(-0.357378\pi\) | ||||
0.433219 | + | 0.901289i | \(0.357378\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.2535 | 1.53879 | 0.769395 | − | 0.638773i | \(-0.220558\pi\) | ||||
0.769395 | + | 0.638773i | \(0.220558\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.3361 | −1.12374 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.96703 | −0.366325 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.2739 | −0.792582 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.08864 | 0.0497412 | 0.0248706 | − | 0.999691i | \(-0.492083\pi\) | ||||
0.0248706 | + | 0.999691i | \(0.492083\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.521173 | −0.0237634 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.04476 | 0.0928476 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.3298 | 1.60095 | 0.800473 | − | 0.599369i | \(-0.204582\pi\) | ||||
0.800473 | + | 0.599369i | \(0.204582\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.2306 | −0.822735 | −0.411367 | − | 0.911470i | \(-0.634949\pi\) | ||||
−0.411367 | + | 0.911470i | \(0.634949\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.4120 | −1.18953 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 41.5443 | 1.86352 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.3361 | 0.910368 | 0.455184 | − | 0.890397i | \(-0.349573\pi\) | ||||
0.455184 | + | 0.890397i | \(0.349573\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.2969 | 1.35087 | 0.675435 | − | 0.737420i | \(-0.263956\pi\) | ||||
0.675435 | + | 0.737420i | \(0.263956\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.303911 | 0.0135239 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.9660 | 0.663355 | 0.331677 | − | 0.943393i | \(-0.392385\pi\) | ||||
0.331677 | + | 0.943393i | \(0.392385\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.46824 | −0.109188 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.633169 | −0.0279008 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.89450 | −0.435160 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.9049 | −1.09110 | −0.545551 | − | 0.838078i | \(-0.683680\pi\) | ||||
−0.545551 | + | 0.838078i | \(0.683680\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.2445 | 0.797775 | 0.398888 | − | 0.917000i | \(-0.369396\pi\) | ||||
0.398888 | + | 0.917000i | \(0.369396\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.01704 | −0.0878638 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.779208 | −0.0337513 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.06074 | 0.175561 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −48.1782 | −2.07518 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.8471 | −1.11125 | −0.555627 | − | 0.831432i | \(-0.687522\pi\) | ||||
−0.555627 | + | 0.831432i | \(0.687522\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.82880 | 0.164008 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.4249 | −0.830549 | −0.415275 | − | 0.909696i | \(-0.636315\pi\) | ||||
−0.415275 | + | 0.909696i | \(0.636315\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −26.4120 | −1.12519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 50.1055 | 2.13070 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.9652 | 1.65101 | 0.825504 | − | 0.564397i | \(-0.190891\pi\) | ||||
0.825504 | + | 0.564397i | \(0.190891\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.191354 | −0.00809342 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.1327 | 1.18565 | 0.592826 | − | 0.805330i | \(-0.298012\pi\) | ||||
0.592826 | + | 0.805330i | \(0.298012\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.52377 | −0.190316 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.4849 | 0.565317 | 0.282658 | − | 0.959221i | \(-0.408784\pi\) | ||||
0.282658 | + | 0.959221i | \(0.408784\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.9706 | −0.877591 | −0.438795 | − | 0.898587i | \(-0.644595\pi\) | ||||
−0.438795 | + | 0.898587i | \(0.644595\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.5077 | 0.563308 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.6176 | −0.483648 | −0.241824 | − | 0.970320i | \(-0.577746\pi\) | ||||
−0.241824 | + | 0.970320i | \(0.577746\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 68.5907 | 2.84562 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.44158 | 0.101120 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.0796 | −0.993871 | −0.496936 | − | 0.867787i | \(-0.665541\pi\) | ||||
−0.496936 | + | 0.867787i | \(0.665541\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.01704 | −0.0831108 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 41.5372 | 1.70573 | 0.852865 | − | 0.522132i | \(-0.174863\pi\) | ||||
0.852865 | + | 0.522132i | \(0.174863\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.80785 | 0.320091 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.43160 | 0.262788 | 0.131394 | − | 0.991330i | \(-0.458055\pi\) | ||||
0.131394 | + | 0.991330i | \(0.458055\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.45844 | −0.141073 | −0.0705364 | − | 0.997509i | \(-0.522471\pi\) | ||||
−0.0705364 | + | 0.997509i | \(0.522471\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.586182 | 0.0238317 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.1019 | −1.22180 | −0.610900 | − | 0.791708i | \(-0.709192\pi\) | ||||
−0.610900 | + | 0.791708i | \(0.709192\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.237649 | −0.00961424 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.54246 | 0.143079 | 0.0715393 | − | 0.997438i | \(-0.477209\pi\) | ||||
0.0715393 | + | 0.997438i | \(0.477209\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.9098 | 0.922315 | 0.461157 | − | 0.887318i | \(-0.347434\pi\) | ||||
0.461157 | + | 0.887318i | \(0.347434\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.4612 | 1.62627 | 0.813136 | − | 0.582074i | \(-0.197758\pi\) | ||||
0.813136 | + | 0.582074i | \(0.197758\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 66.7847 | 2.67567 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.6855 | 0.867420 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.4361 | 0.894584 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.1851 | −0.445270 | −0.222635 | − | 0.974902i | \(-0.571466\pi\) | ||||
−0.222635 | + | 0.974902i | \(0.571466\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.41512 | 0.0958409 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.15716 | −0.0458482 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.69312 | 0.264362 | 0.132181 | − | 0.991226i | \(-0.457802\pi\) | ||||
0.132181 | + | 0.991226i | \(0.457802\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.3724 | 1.00059 | 0.500294 | − | 0.865856i | \(-0.333225\pi\) | ||||
0.500294 | + | 0.865856i | \(0.333225\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.72999 | −0.264583 | −0.132292 | − | 0.991211i | \(-0.542234\pi\) | ||||
−0.132292 | + | 0.991211i | \(0.542234\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.7890 | 0.776786 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.0144 | −1.44849 | −0.724243 | − | 0.689545i | \(-0.757810\pi\) | ||||
−0.724243 | + | 0.689545i | \(0.757810\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.41921 | 0.0554529 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.7624 | −0.769832 | −0.384916 | − | 0.922952i | \(-0.625770\pi\) | ||||
−0.384916 | + | 0.922952i | \(0.625770\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.8632 | −0.655904 | −0.327952 | − | 0.944694i | \(-0.606358\pi\) | ||||
−0.327952 | + | 0.944694i | \(0.606358\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.80785 | 0.302776 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.6533 | 0.799700 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.5021 | 0.521244 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.3066 | −1.43807 | −0.719033 | − | 0.694976i | \(-0.755415\pi\) | ||||
−0.719033 | + | 0.694976i | \(0.755415\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.632805 | −0.0243207 | −0.0121603 | − | 0.999926i | \(-0.503871\pi\) | ||||
−0.0121603 | + | 0.999926i | \(0.503871\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.6764 | 0.755113 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.04606 | −0.231346 | −0.115673 | − | 0.993287i | \(-0.536902\pi\) | ||||
−0.115673 | + | 0.993287i | \(0.536902\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.60058 | 0.0611549 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.0586426 | 0.00223410 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.3955 | 1.08021 | 0.540107 | − | 0.841596i | \(-0.318384\pi\) | ||||
0.540107 | + | 0.841596i | \(0.318384\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.93926 | −0.149425 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.5443 | 1.27058 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.7738 | −0.558000 | −0.279000 | − | 0.960291i | \(-0.590003\pi\) | ||||
−0.279000 | + | 0.960291i | \(0.590003\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.4361 | 0.846192 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.92450 | 0.109987 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.7569 | 0.854655 | 0.427327 | − | 0.904097i | \(-0.359455\pi\) | ||||
0.427327 | + | 0.904097i | \(0.359455\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.57726 | 0.0590690 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.139211 | 0.00520621 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.9957 | −1.15594 | −0.577972 | − | 0.816057i | \(-0.696156\pi\) | ||||
−0.577972 | + | 0.816057i | \(0.696156\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.09292 | −0.226912 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 34.8723 | 1.29512 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.1117 | 1.52475 | 0.762375 | − | 0.647135i | \(-0.224033\pi\) | ||||
0.762375 | + | 0.647135i | \(0.224033\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.23765 | 0.304680 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.206562 | −0.00762954 | −0.00381477 | − | 0.999993i | \(-0.501214\pi\) | ||||
−0.00381477 | + | 0.999993i | \(0.501214\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.6792 | 0.688058 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.13215 | 0.0784325 | 0.0392162 | − | 0.999231i | \(-0.487514\pi\) | ||||
0.0392162 | + | 0.999231i | \(0.487514\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.5175 | 1.48644 | 0.743221 | − | 0.669046i | \(-0.233297\pi\) | ||||
0.743221 | + | 0.669046i | \(0.233297\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.69256 | −0.245196 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 39.0761 | 1.42781 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5843 | 0.459208 | 0.229604 | − | 0.973284i | \(-0.426257\pi\) | ||||
0.229604 | + | 0.973284i | \(0.426257\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.72529 | 0.171971 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.6052 | 0.385452 | 0.192726 | − | 0.981253i | \(-0.438267\pi\) | ||||
0.192726 | + | 0.981253i | \(0.438267\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.8182 | −1.55216 | −0.776079 | − | 0.630635i | \(-0.782794\pi\) | ||||
−0.776079 | + | 0.630635i | \(0.782794\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 36.8441 | 1.33385 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.475298 | 0.0171620 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.7455 | 0.459614 | 0.229807 | − | 0.973236i | \(-0.426190\pi\) | ||||
0.229807 | + | 0.973236i | \(0.426190\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.3522 | 1.16363 | 0.581814 | − | 0.813322i | \(-0.302343\pi\) | ||||
0.581814 | + | 0.813322i | \(0.302343\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.66314 | 0.0956630 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33.5443 | 1.20185 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.8874 | −1.14102 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.8253 | 0.386370 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.36056 | 0.262376 | 0.131188 | − | 0.991358i | \(-0.458121\pi\) | ||||
0.131188 | + | 0.991358i | \(0.458121\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −43.5317 | −1.54781 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.324298 | 0.0115162 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.0627 | 0.852344 | 0.426172 | − | 0.904642i | \(-0.359862\pi\) | ||||
0.426172 | + | 0.904642i | \(0.359862\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.2306 | 0.361932 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.89450 | 0.0668556 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.10550 | −0.215190 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.83586 | 0.275494 | 0.137747 | − | 0.990467i | \(-0.456014\pi\) | ||||
0.137747 | + | 0.990467i | \(0.456014\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45.7351 | −1.60598 | −0.802988 | − | 0.595995i | \(-0.796758\pi\) | ||||
−0.802988 | + | 0.595995i | \(0.796758\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.02684 | 0.176083 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.23765 | 0.288199 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.3709 | 0.955250 | 0.477625 | − | 0.878564i | \(-0.341498\pi\) | ||||
0.477625 | + | 0.878564i | \(0.341498\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.8560 | −1.00586 | −0.502929 | − | 0.864328i | \(-0.667744\pi\) | ||||
−0.502929 | + | 0.864328i | \(0.667744\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.4227 | 0.501528 | 0.250764 | − | 0.968048i | \(-0.419318\pi\) | ||||
0.250764 | + | 0.968048i | \(0.419318\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.7497 | −0.755400 | −0.377700 | − | 0.925928i | \(-0.623285\pi\) | ||||
−0.377700 | + | 0.925928i | \(0.623285\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 49.8147 | 1.72598 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.76513 | −0.0956914 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.4557 | 1.53478 | 0.767390 | − | 0.641181i | \(-0.221555\pi\) | ||||
0.767390 | + | 0.641181i | \(0.221555\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.3200 | 0.838620 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.15379 | −0.211697 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.64077 | 0.193819 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.5443 | −0.601411 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.5648 | 0.567169 | 0.283585 | − | 0.958947i | \(-0.408476\pi\) | ||||
0.283585 | + | 0.958947i | \(0.408476\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.0888 | 0.652062 | 0.326031 | − | 0.945359i | \(-0.394289\pi\) | ||||
0.326031 | + | 0.945359i | \(0.394289\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −53.9272 | −1.83997 | −0.919987 | − | 0.391949i | \(-0.871801\pi\) | ||||
−0.919987 | + | 0.391949i | \(0.871801\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.64533 | −0.124089 | −0.0620443 | − | 0.998073i | \(-0.519762\pi\) | ||||
−0.0620443 | + | 0.998073i | \(0.519762\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.42826 | 0.0825632 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −38.4586 | −1.30462 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.448643 | 0.0152017 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −21.1020 | −0.713377 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 56.6481 | 1.91287 | 0.956435 | − | 0.291945i | \(-0.0943023\pi\) | ||||
0.956435 | + | 0.291945i | \(0.0943023\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.0118 | −0.674214 | −0.337107 | − | 0.941466i | \(-0.609448\pi\) | ||||
−0.337107 | + | 0.941466i | \(0.609448\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.0292 | −0.505773 | −0.252887 | − | 0.967496i | \(-0.581380\pi\) | ||||
−0.252887 | + | 0.967496i | \(0.581380\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.1180 | 0.876958 | 0.438479 | − | 0.898742i | \(-0.355517\pi\) | ||||
0.438479 | + | 0.898742i | \(0.355517\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.2404 | 0.779458 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.2306 | 0.342354 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.21805 | −0.207847 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.07197 | 0.135808 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.52452 | −0.0841038 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.25507 | 0.241167 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −51.2480 | −1.70166 | −0.850831 | − | 0.525439i | \(-0.823901\pi\) | ||||
−0.850831 | + | 0.525439i | \(0.823901\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.0535 | −0.697533 | −0.348767 | − | 0.937210i | \(-0.613399\pi\) | ||||
−0.348767 | + | 0.937210i | \(0.613399\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −52.6470 | −1.74236 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.6569 | 0.450989 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.8839 | 0.589937 | 0.294968 | − | 0.955507i | \(-0.404691\pi\) | ||||
0.294968 | + | 0.955507i | \(0.404691\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.765881 | −0.0252093 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29.6228 | −0.973992 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.2774 | −0.337192 | −0.168596 | − | 0.985685i | \(-0.553923\pi\) | ||||
−0.168596 | + | 0.985685i | \(0.553923\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 49.8147 | 1.63261 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.99294 | −0.195990 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.5780 | −0.443574 | −0.221787 | − | 0.975095i | \(-0.571189\pi\) | ||||
−0.221787 | + | 0.975095i | \(0.571189\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.59890 | 0.182519 | 0.0912595 | − | 0.995827i | \(-0.470911\pi\) | ||||
0.0912595 | + | 0.995827i | \(0.470911\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −26.2306 | −0.854186 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.9106 | 1.52439 | 0.762194 | − | 0.647348i | \(-0.224122\pi\) | ||||
0.762194 | + | 0.647348i | \(0.224122\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.0455027 | 0.00147708 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.59115 | −0.181115 | −0.0905576 | − | 0.995891i | \(-0.528865\pi\) | ||||
−0.0905576 | + | 0.995891i | \(0.528865\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.08740 | 0.132265 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.4022 | 0.497362 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6890 | −0.989969 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.42367 | 0.174594 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.7561 | −0.989048 | −0.494524 | − | 0.869164i | \(-0.664658\pi\) | ||||
−0.494524 | + | 0.869164i | \(0.664658\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.3668 | 0.364779 | 0.182389 | − | 0.983226i | \(-0.441617\pi\) | ||||
0.182389 | + | 0.983226i | \(0.441617\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −37.9070 | −1.21524 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.8323 | 0.730471 | 0.365235 | − | 0.930915i | \(-0.380988\pi\) | ||||
0.365235 | + | 0.930915i | \(0.380988\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −51.2608 | −1.63830 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 46.3557 | 1.47852 | 0.739258 | − | 0.673422i | \(-0.235176\pi\) | ||||
0.739258 | + | 0.673422i | \(0.235176\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.01686 | −0.159850 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.44158 | −0.204830 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.43683 | 0.109175 | 0.0545873 | − | 0.998509i | \(-0.482616\pi\) | ||||
0.0545873 | + | 0.998509i | \(0.482616\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.74294 | 0.0552550 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.0320 | −0.982794 | −0.491397 | − | 0.870936i | \(-0.663514\pi\) | ||||
−0.491397 | + | 0.870936i | \(0.663514\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 9216.2.a.y.1.3 | 4 | ||
3.2 | odd | 2 | 3072.2.a.t.1.2 | 4 | |||
4.3 | odd | 2 | 9216.2.a.x.1.3 | 4 | |||
8.3 | odd | 2 | 9216.2.a.bn.1.2 | 4 | |||
8.5 | even | 2 | 9216.2.a.bo.1.2 | 4 | |||
12.11 | even | 2 | 3072.2.a.n.1.2 | 4 | |||
24.5 | odd | 2 | 3072.2.a.i.1.3 | 4 | |||
24.11 | even | 2 | 3072.2.a.o.1.3 | 4 | |||
32.3 | odd | 8 | 1152.2.k.f.289.2 | 8 | |||
32.5 | even | 8 | 144.2.k.b.37.1 | 8 | |||
32.11 | odd | 8 | 1152.2.k.f.865.2 | 8 | |||
32.13 | even | 8 | 144.2.k.b.109.1 | 8 | |||
32.19 | odd | 8 | 576.2.k.b.145.3 | 8 | |||
32.21 | even | 8 | 1152.2.k.c.865.2 | 8 | |||
32.27 | odd | 8 | 576.2.k.b.433.3 | 8 | |||
32.29 | even | 8 | 1152.2.k.c.289.2 | 8 | |||
48.5 | odd | 4 | 3072.2.d.f.1537.2 | 8 | |||
48.11 | even | 4 | 3072.2.d.i.1537.6 | 8 | |||
48.29 | odd | 4 | 3072.2.d.f.1537.7 | 8 | |||
48.35 | even | 4 | 3072.2.d.i.1537.3 | 8 | |||
96.5 | odd | 8 | 48.2.j.a.37.4 | yes | 8 | ||
96.11 | even | 8 | 384.2.j.a.97.2 | 8 | |||
96.29 | odd | 8 | 384.2.j.b.289.4 | 8 | |||
96.35 | even | 8 | 384.2.j.a.289.2 | 8 | |||
96.53 | odd | 8 | 384.2.j.b.97.4 | 8 | |||
96.59 | even | 8 | 192.2.j.a.49.3 | 8 | |||
96.77 | odd | 8 | 48.2.j.a.13.4 | ✓ | 8 | ||
96.83 | even | 8 | 192.2.j.a.145.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.j.a.13.4 | ✓ | 8 | 96.77 | odd | 8 | ||
48.2.j.a.37.4 | yes | 8 | 96.5 | odd | 8 | ||
144.2.k.b.37.1 | 8 | 32.5 | even | 8 | |||
144.2.k.b.109.1 | 8 | 32.13 | even | 8 | |||
192.2.j.a.49.3 | 8 | 96.59 | even | 8 | |||
192.2.j.a.145.3 | 8 | 96.83 | even | 8 | |||
384.2.j.a.97.2 | 8 | 96.11 | even | 8 | |||
384.2.j.a.289.2 | 8 | 96.35 | even | 8 | |||
384.2.j.b.97.4 | 8 | 96.53 | odd | 8 | |||
384.2.j.b.289.4 | 8 | 96.29 | odd | 8 | |||
576.2.k.b.145.3 | 8 | 32.19 | odd | 8 | |||
576.2.k.b.433.3 | 8 | 32.27 | odd | 8 | |||
1152.2.k.c.289.2 | 8 | 32.29 | even | 8 | |||
1152.2.k.c.865.2 | 8 | 32.21 | even | 8 | |||
1152.2.k.f.289.2 | 8 | 32.3 | odd | 8 | |||
1152.2.k.f.865.2 | 8 | 32.11 | odd | 8 | |||
3072.2.a.i.1.3 | 4 | 24.5 | odd | 2 | |||
3072.2.a.n.1.2 | 4 | 12.11 | even | 2 | |||
3072.2.a.o.1.3 | 4 | 24.11 | even | 2 | |||
3072.2.a.t.1.2 | 4 | 3.2 | odd | 2 | |||
3072.2.d.f.1537.2 | 8 | 48.5 | odd | 4 | |||
3072.2.d.f.1537.7 | 8 | 48.29 | odd | 4 | |||
3072.2.d.i.1537.3 | 8 | 48.35 | even | 4 | |||
3072.2.d.i.1537.6 | 8 | 48.11 | even | 4 | |||
9216.2.a.x.1.3 | 4 | 4.3 | odd | 2 | |||
9216.2.a.y.1.3 | 4 | 1.1 | even | 1 | trivial | ||
9216.2.a.bn.1.2 | 4 | 8.3 | odd | 2 | |||
9216.2.a.bo.1.2 | 4 | 8.5 | even | 2 |