Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, 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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.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: | \(64.1677830643\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 37 x^{13} + 39 x^{12} + 537 x^{11} - 616 x^{10} - 3853 x^{9} + 4929 x^{8} + \cdots + 3381 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1148) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-2.11769\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-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 | ||||||||
\(3\) | 2.11769 | 1.22265 | 0.611324 | − | 0.791380i | \(-0.290637\pi\) | ||||
0.611324 | + | 0.791380i | \(0.290637\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.93656 | 1.76049 | 0.880243 | − | 0.474524i | \(-0.157380\pi\) | ||||
0.880243 | + | 0.474524i | \(0.157380\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.48461 | 0.494869 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.13020 | 1.24530 | 0.622652 | − | 0.782499i | \(-0.286055\pi\) | ||||
0.622652 | + | 0.782499i | \(0.286055\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.64438 | 0.456070 | 0.228035 | − | 0.973653i | \(-0.426770\pi\) | ||||
0.228035 | + | 0.973653i | \(0.426770\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.33642 | 2.15245 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.20325 | −1.26197 | −0.630987 | − | 0.775794i | \(-0.717350\pi\) | ||||
−0.630987 | + | 0.775794i | \(0.717350\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.58422 | −1.51052 | −0.755262 | − | 0.655423i | \(-0.772490\pi\) | ||||
−0.755262 | + | 0.655423i | \(0.772490\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.17263 | 1.49560 | 0.747798 | − | 0.663926i | \(-0.231111\pi\) | ||||
0.747798 | + | 0.663926i | \(0.231111\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.4965 | 2.09931 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.20913 | −0.617598 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.38888 | −1.74347 | −0.871736 | − | 0.489976i | \(-0.837006\pi\) | ||||
−0.871736 | + | 0.489976i | \(0.837006\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.46362 | 1.16090 | 0.580450 | − | 0.814296i | \(-0.302877\pi\) | ||||
0.580450 | + | 0.814296i | \(0.302877\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.74649 | 1.52257 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.3246 | 1.86175 | 0.930873 | − | 0.365343i | \(-0.119048\pi\) | ||||
0.930873 | + | 0.365343i | \(0.119048\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.48230 | 0.557614 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.742453 | −0.113223 | −0.0566115 | − | 0.998396i | \(-0.518030\pi\) | ||||
−0.0566115 | + | 0.998396i | \(0.518030\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.84425 | 0.871209 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.264604 | 0.0385964 | 0.0192982 | − | 0.999814i | \(-0.493857\pi\) | ||||
0.0192982 | + | 0.999814i | \(0.493857\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.0189 | −1.54295 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.838544 | −0.115183 | −0.0575914 | − | 0.998340i | \(-0.518342\pi\) | ||||
−0.0575914 | + | 0.998340i | \(0.518342\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.2588 | 2.19234 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −13.9433 | −1.84684 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.28576 | −0.688148 | −0.344074 | − | 0.938943i | \(-0.611807\pi\) | ||||
−0.344074 | + | 0.938943i | \(0.611807\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.56825 | 0.328831 | 0.164415 | − | 0.986391i | \(-0.447426\pi\) | ||||
0.164415 | + | 0.986391i | \(0.447426\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.47323 | 0.802905 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.9381 | 1.58064 | 0.790318 | − | 0.612697i | \(-0.209915\pi\) | ||||
0.790318 | + | 0.612697i | \(0.209915\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 15.1894 | 1.82859 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.81754 | 0.690415 | 0.345207 | − | 0.938526i | \(-0.387809\pi\) | ||||
0.345207 | + | 0.938526i | \(0.387809\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.4835 | 1.46109 | 0.730544 | − | 0.682866i | \(-0.239267\pi\) | ||||
0.730544 | + | 0.682866i | \(0.239267\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 22.2284 | 2.56672 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.51028 | 0.282429 | 0.141214 | − | 0.989979i | \(-0.454899\pi\) | ||||
0.141214 | + | 0.989979i | \(0.454899\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2498 | −1.24997 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.61393 | −0.945501 | −0.472751 | − | 0.881196i | \(-0.656739\pi\) | ||||
−0.472751 | + | 0.881196i | \(0.656739\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.4829 | −2.22169 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −19.8827 | −2.13165 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.18149 | 0.125238 | 0.0626190 | − | 0.998038i | \(-0.480055\pi\) | ||||
0.0626190 | + | 0.998038i | \(0.480055\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.6879 | 1.41937 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −25.9192 | −2.65926 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.32575 | 0.642283 | 0.321141 | − | 0.947031i | \(-0.395934\pi\) | ||||
0.321141 | + | 0.947031i | \(0.395934\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.13173 | 0.616262 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.1843 | 1.31189 | 0.655946 | − | 0.754808i | \(-0.272270\pi\) | ||||
0.655946 | + | 0.754808i | \(0.272270\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.8507 | 1.56182 | 0.780909 | − | 0.624645i | \(-0.214756\pi\) | ||||
0.780909 | + | 0.624645i | \(0.214756\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.98270 | 0.771717 | 0.385858 | − | 0.922558i | \(-0.373905\pi\) | ||||
0.385858 | + | 0.922558i | \(0.373905\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.0240 | 1.15169 | 0.575847 | − | 0.817557i | \(-0.304672\pi\) | ||||
0.575847 | + | 0.817557i | \(0.304672\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 23.9819 | 2.27626 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.6408 | −1.75358 | −0.876788 | − | 0.480876i | \(-0.840319\pi\) | ||||
−0.876788 | + | 0.480876i | \(0.840319\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 28.2355 | 2.63298 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.44126 | 0.225695 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.05859 | 0.550781 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.11769 | −0.190946 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 21.6375 | 1.93532 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.15387 | −0.368596 | −0.184298 | − | 0.982870i | \(-0.559001\pi\) | ||||
−0.184298 | + | 0.982870i | \(0.559001\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.57228 | −0.138432 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.5045 | −0.917786 | −0.458893 | − | 0.888492i | \(-0.651754\pi\) | ||||
−0.458893 | + | 0.888492i | \(0.651754\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.6330 | −1.08727 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.41888 | 0.121223 | 0.0606117 | − | 0.998161i | \(-0.480695\pi\) | ||||
0.0606117 | + | 0.998161i | \(0.480695\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.3332 | −0.876448 | −0.438224 | − | 0.898866i | \(-0.644392\pi\) | ||||
−0.438224 | + | 0.898866i | \(0.644392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.560348 | 0.0471898 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.79165 | 0.567946 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −36.9599 | −3.06936 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.28402 | 0.105191 | 0.0525954 | − | 0.998616i | \(-0.483251\pi\) | ||||
0.0525954 | + | 0.998616i | \(0.483251\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.45601 | 0.525382 | 0.262691 | − | 0.964880i | \(-0.415390\pi\) | ||||
0.262691 | + | 0.964880i | \(0.415390\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.72478 | −0.624511 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.4444 | 2.04375 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.2843 | −1.29963 | −0.649815 | − | 0.760093i | \(-0.725154\pi\) | ||||
−0.649815 | + | 0.760093i | \(0.725154\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.77577 | −0.140828 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.33662 | 0.104692 | 0.0523459 | − | 0.998629i | \(-0.483330\pi\) | ||||
0.0523459 | + | 0.998629i | \(0.483330\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 34.4311 | 2.68046 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.64888 | 0.746653 | 0.373326 | − | 0.927700i | \(-0.378217\pi\) | ||||
0.373326 | + | 0.927700i | \(0.378217\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.2960 | −0.792000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.77498 | −0.747511 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.394838 | 0.0300190 | 0.0150095 | − | 0.999887i | \(-0.495222\pi\) | ||||
0.0150095 | + | 0.999887i | \(0.495222\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.1936 | −0.841362 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.95229 | −0.594382 | −0.297191 | − | 0.954818i | \(-0.596050\pi\) | ||||
−0.297191 | + | 0.954818i | \(0.596050\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.47729 | 0.184135 | 0.0920677 | − | 0.995753i | \(-0.470652\pi\) | ||||
0.0920677 | + | 0.995753i | \(0.470652\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.43875 | 0.402044 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 44.5799 | 3.27758 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.4905 | −1.57154 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.03672 | 0.581517 | 0.290758 | − | 0.956797i | \(-0.406092\pi\) | ||||
0.290758 | + | 0.956797i | \(0.406092\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.7700 | −1.35109 | −0.675547 | − | 0.737317i | \(-0.736092\pi\) | ||||
−0.675547 | + | 0.737317i | \(0.736092\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.7083 | 0.981670 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.9468 | 0.779924 | 0.389962 | − | 0.920831i | \(-0.372488\pi\) | ||||
0.389962 | + | 0.920831i | \(0.372488\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.8786 | −1.48004 | −0.740022 | − | 0.672583i | \(-0.765185\pi\) | ||||
−0.740022 | + | 0.672583i | \(0.765185\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 27.3988 | 1.93256 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.93656 | −0.274942 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.6485 | 0.740124 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −27.1942 | −1.88106 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.44265 | 0.305845 | 0.152922 | − | 0.988238i | \(-0.451132\pi\) | ||||
0.152922 | + | 0.988238i | \(0.451132\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.3197 | 0.844134 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.92271 | −0.199327 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 26.4362 | 1.78640 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.55614 | −0.575549 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.49744 | 0.635995 | 0.317998 | − | 0.948091i | \(-0.396990\pi\) | ||||
0.317998 | + | 0.948091i | \(0.396990\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.5832 | 1.03888 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.6954 | −0.842621 | −0.421311 | − | 0.906916i | \(-0.638430\pi\) | ||||
−0.421311 | + | 0.906916i | \(0.638430\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.2558 | −0.875966 | −0.437983 | − | 0.898983i | \(-0.644307\pi\) | ||||
−0.437983 | + | 0.898983i | \(0.644307\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.8763 | 0.778042 | 0.389021 | − | 0.921229i | \(-0.372813\pi\) | ||||
0.389021 | + | 0.921229i | \(0.372813\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.04163 | 0.0679484 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.31600 | 0.345311 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.4170 | −1.45004 | −0.725018 | − | 0.688730i | \(-0.758169\pi\) | ||||
−0.725018 | + | 0.688730i | \(0.758169\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.0278 | −1.61218 | −0.806092 | − | 0.591791i | \(-0.798421\pi\) | ||||
−0.806092 | + | 0.591791i | \(0.798421\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.1961 | −0.910680 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.8270 | −0.688905 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.2416 | −1.15602 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.08571 | −0.131649 | −0.0658244 | − | 0.997831i | \(-0.520968\pi\) | ||||
−0.0658244 | + | 0.997831i | \(0.520968\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 29.6244 | 1.86247 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −43.3765 | −2.71634 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.9277 | −1.18068 | −0.590339 | − | 0.807156i | \(-0.701006\pi\) | ||||
−0.590339 | + | 0.807156i | \(0.701006\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.9388 | −0.862790 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.16279 | −0.318351 | −0.159175 | − | 0.987250i | \(-0.550884\pi\) | ||||
−0.159175 | + | 0.987250i | \(0.550884\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.30098 | −0.202778 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.50204 | 0.153122 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.40064 | 0.390254 | 0.195127 | − | 0.980778i | \(-0.437488\pi\) | ||||
0.195127 | + | 0.980778i | \(0.437488\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −31.9665 | −1.94183 | −0.970915 | − | 0.239425i | \(-0.923041\pi\) | ||||
−0.970915 | + | 0.239425i | \(0.923041\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 43.3529 | 2.61428 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.0243 | 1.44348 | 0.721740 | − | 0.692165i | \(-0.243343\pi\) | ||||
0.721740 | + | 0.692165i | \(0.243343\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.59593 | 0.574493 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.6948 | −0.816965 | −0.408483 | − | 0.912766i | \(-0.633942\pi\) | ||||
−0.408483 | + | 0.912766i | \(0.633942\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.1506 | −0.841165 | −0.420582 | − | 0.907254i | \(-0.638174\pi\) | ||||
−0.420582 | + | 0.907254i | \(0.638174\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −54.8888 | −3.25133 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.0738 | 0.592577 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.3960 | 0.785286 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.12691 | 0.241097 | 0.120548 | − | 0.992707i | \(-0.461535\pi\) | ||||
0.120548 | + | 0.992707i | \(0.461535\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.8077 | −1.21147 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.2544 | −0.769097 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.7946 | 0.682097 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 27.9203 | 1.60398 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.1101 | 0.578901 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.97471 | 0.340995 | 0.170497 | − | 0.985358i | \(-0.445463\pi\) | ||||
0.170497 | + | 0.985358i | \(0.445463\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 33.5669 | 1.90955 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.1431 | 0.915390 | 0.457695 | − | 0.889109i | \(-0.348675\pi\) | ||||
0.457695 | + | 0.889109i | \(0.348675\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.74303 | −0.437662 | −0.218831 | − | 0.975763i | \(-0.570224\pi\) | ||||
−0.218831 | + | 0.975763i | \(0.570224\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.3917 | −1.36997 | −0.684987 | − | 0.728556i | \(-0.740192\pi\) | ||||
−0.684987 | + | 0.728556i | \(0.740192\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −38.7780 | −2.17115 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.9049 | 0.943538 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 34.2594 | 1.90624 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.2604 | 0.957432 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 25.4632 | 1.40812 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.4302 | −1.34281 | −0.671403 | − | 0.741092i | \(-0.734308\pi\) | ||||
−0.671403 | + | 0.741092i | \(0.734308\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.8125 | 0.921320 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 50.9315 | 2.78269 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.3432 | 0.563428 | 0.281714 | − | 0.959498i | \(-0.409097\pi\) | ||||
0.281714 | + | 0.959498i | \(0.409097\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −39.4754 | −2.14401 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.6961 | 1.44567 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 59.7940 | 3.21920 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.4882 | −1.26091 | −0.630457 | − | 0.776224i | \(-0.717133\pi\) | ||||
−0.630457 | + | 0.776224i | \(0.717133\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.54452 | 0.296791 | 0.148396 | − | 0.988928i | \(-0.452589\pi\) | ||||
0.148396 | + | 0.988928i | \(0.452589\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.27705 | −0.281668 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.44192 | −0.183195 | −0.0915974 | − | 0.995796i | \(-0.529197\pi\) | ||||
−0.0915974 | + | 0.995796i | \(0.529197\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.9011 | 1.21546 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.62296 | −0.402324 | −0.201162 | − | 0.979558i | \(-0.564472\pi\) | ||||
−0.201162 | + | 0.979558i | \(0.564472\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.3520 | 1.28168 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.8302 | 0.673411 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 49.1422 | 2.57222 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.7933 | 0.667806 | 0.333903 | − | 0.942607i | \(-0.391634\pi\) | ||||
0.333903 | + | 0.942607i | \(0.391634\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.48461 | −0.0772855 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 37.4785 | 1.94056 | 0.970281 | − | 0.241979i | \(-0.0777965\pi\) | ||||
0.970281 | + | 0.241979i | \(0.0777965\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 45.8215 | 2.36621 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.4389 | −0.795146 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.08847 | −0.466844 | −0.233422 | − | 0.972376i | \(-0.574992\pi\) | ||||
−0.233422 | + | 0.972376i | \(0.574992\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.79660 | −0.450663 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.3554 | 0.733524 | 0.366762 | − | 0.930315i | \(-0.380466\pi\) | ||||
0.366762 | + | 0.930315i | \(0.380466\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.10225 | −0.0560305 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.6068 | −1.34902 | −0.674510 | − | 0.738265i | \(-0.735645\pi\) | ||||
−0.674510 | + | 0.738265i | \(0.735645\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −37.3210 | −1.88740 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22.2453 | −1.12213 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.88189 | 0.497212 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.0384 | 1.50758 | 0.753792 | − | 0.657113i | \(-0.228223\pi\) | ||||
0.753792 | + | 0.657113i | \(0.228223\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.8185 | 0.739999 | 0.369999 | − | 0.929032i | \(-0.379358\pi\) | ||||
0.369999 | + | 0.929032i | \(0.379358\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.6287 | 0.529452 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −44.2854 | −2.20056 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 46.7727 | 2.31844 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.6040 | −0.919908 | −0.459954 | − | 0.887943i | \(-0.652134\pi\) | ||||
−0.459954 | + | 0.887943i | \(0.652134\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.00475 | 0.148214 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −33.9093 | −1.66454 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.8824 | −1.07159 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.89906 | −0.0927751 | −0.0463875 | − | 0.998924i | \(-0.514771\pi\) | ||||
−0.0463875 | + | 0.998924i | \(0.514771\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.78259 | 0.281826 | 0.140913 | − | 0.990022i | \(-0.454996\pi\) | ||||
0.140913 | + | 0.990022i | \(0.454996\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.392832 | 0.0191002 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −54.6161 | −2.64927 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.3826 | 0.694398 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.9485 | −1.34623 | −0.673117 | − | 0.739536i | \(-0.735045\pi\) | ||||
−0.673117 | + | 0.739536i | \(0.735045\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.1725 | 0.584975 | 0.292487 | − | 0.956269i | \(-0.405517\pi\) | ||||
0.292487 | + | 0.956269i | \(0.405517\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −78.2697 | −3.75274 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −47.2262 | −2.25913 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.3773 | −0.495284 | −0.247642 | − | 0.968852i | \(-0.579656\pi\) | ||||
−0.247642 | + | 0.968852i | \(0.579656\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −38.9198 | −1.84913 | −0.924567 | − | 0.381020i | \(-0.875573\pi\) | ||||
−0.924567 | + | 0.381020i | \(0.875573\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.65103 | 0.220480 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.71915 | 0.128611 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.8233 | −0.510783 | −0.255391 | − | 0.966838i | \(-0.582204\pi\) | ||||
−0.255391 | + | 0.966838i | \(0.582204\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.13020 | −0.194484 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.6718 | 0.642358 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.2417 | −0.479086 | −0.239543 | − | 0.970886i | \(-0.576998\pi\) | ||||
−0.239543 | + | 0.970886i | \(0.576998\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.6979 | 0.779392 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.4368 | −1.13814 | −0.569068 | − | 0.822290i | \(-0.692696\pi\) | ||||
−0.569068 | + | 0.822290i | \(0.692696\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.0456 | −0.978072 | −0.489036 | − | 0.872264i | \(-0.662651\pi\) | ||||
−0.489036 | + | 0.872264i | \(0.662651\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 53.8834 | 2.49878 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.2601 | −0.567329 | −0.283664 | − | 0.958924i | \(-0.591550\pi\) | ||||
−0.283664 | + | 0.958924i | \(0.591550\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −34.4851 | −1.58899 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.06648 | −0.140997 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −69.1116 | −3.17106 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.24491 | −0.0570004 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.7134 | −1.03780 | −0.518902 | − | 0.854834i | \(-0.673659\pi\) | ||||
−0.518902 | + | 0.854834i | \(0.673659\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.6219 | 0.849087 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 24.9017 | 1.13073 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.5514 | −1.29379 | −0.646893 | − | 0.762581i | \(-0.723932\pi\) | ||||
−0.646893 | + | 0.762581i | \(0.723932\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.83054 | 0.128001 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.49643 | 0.383438 | 0.191719 | − | 0.981450i | \(-0.438594\pi\) | ||||
0.191719 | + | 0.981450i | \(0.438594\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 48.8527 | 2.20021 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 24.1379 | 1.08492 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.05158 | −0.360438 | −0.180219 | − | 0.983627i | \(-0.557681\pi\) | ||||
−0.180219 | + | 0.983627i | \(0.557681\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.4333 | 0.912893 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.3484 | −1.39776 | −0.698879 | − | 0.715240i | \(-0.746317\pi\) | ||||
−0.698879 | + | 0.715240i | \(0.746317\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 51.9010 | 2.30957 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.8037 | −0.968337 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.98621 | 0.176686 | 0.0883429 | − | 0.996090i | \(-0.471843\pi\) | ||||
0.0883429 | + | 0.996090i | \(0.471843\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 21.1296 | 0.932897 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 62.3974 | 2.74956 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.09287 | 0.0480642 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.836144 | 0.0367026 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −42.5988 | −1.86629 | −0.933144 | − | 0.359503i | \(-0.882946\pi\) | ||||
−0.933144 | + | 0.359503i | \(0.882946\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.4853 | −0.589673 | −0.294836 | − | 0.955548i | \(-0.595265\pi\) | ||||
−0.294836 | + | 0.955548i | \(0.595265\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −33.6318 | −1.46502 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28.4466 | 1.23681 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.84728 | −0.340543 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.64438 | −0.0712262 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31.4244 | 1.35860 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.8405 | −0.726720 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.8373 | 1.36879 | 0.684395 | − | 0.729111i | \(-0.260066\pi\) | ||||
0.684395 | + | 0.729111i | \(0.260066\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.24613 | 0.225133 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 47.3334 | 2.02754 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.2689 | −1.25145 | −0.625723 | − | 0.780045i | \(-0.715196\pi\) | ||||
−0.625723 | + | 0.780045i | \(0.715196\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.81284 | 0.162728 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 61.8185 | 2.63356 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 94.4063 | 4.00732 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.63655 | 0.323571 | 0.161785 | − | 0.986826i | \(-0.448275\pi\) | ||||
0.161785 | + | 0.986826i | \(0.448275\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.22088 | −0.0516377 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −45.5102 | −1.92144 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.77861 | 0.0749593 | 0.0374797 | − | 0.999297i | \(-0.488067\pi\) | ||||
0.0374797 | + | 0.999297i | \(0.488067\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −73.3806 | −3.08715 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.83946 | 0.370570 | 0.185285 | − | 0.982685i | \(-0.440679\pi\) | ||||
0.185285 | + | 0.982685i | \(0.440679\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.50457 | 0.272208 | 0.136104 | − | 0.990695i | \(-0.456542\pi\) | ||||
0.136104 | + | 0.990695i | \(0.456542\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.0193 | 0.710990 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 75.2878 | 3.13972 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.7240 | −1.07090 | −0.535452 | − | 0.844566i | \(-0.679859\pi\) | ||||
−0.535452 | + | 0.844566i | \(0.679859\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −39.7490 | −1.65191 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.46336 | −0.143438 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.61019 | 0.397333 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.1254 | −1.11959 | −0.559794 | − | 0.828632i | \(-0.689120\pi\) | ||||
−0.559794 | + | 0.828632i | \(0.689120\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.5579 | −1.75357 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.1818 | 0.953573 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.0630 | 1.02921 | 0.514607 | − | 0.857426i | \(-0.327938\pi\) | ||||
0.514607 | + | 0.857426i | \(0.327938\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −44.2143 | −1.80957 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.8368 | 0.810510 | 0.405255 | − | 0.914204i | \(-0.367183\pi\) | ||||
0.405255 | + | 0.914204i | \(0.367183\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.3130 | −0.787792 | −0.393896 | − | 0.919155i | \(-0.628873\pi\) | ||||
−0.393896 | + | 0.919155i | \(0.628873\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.2079 | 0.782208 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.8500 | 0.969641 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.9873 | −0.608318 | −0.304159 | − | 0.952621i | \(-0.598375\pi\) | ||||
−0.304159 | + | 0.952621i | \(0.598375\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.435110 | 0.0176027 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.2933 | 0.456131 | 0.228066 | − | 0.973646i | \(-0.426760\pi\) | ||||
0.228066 | + | 0.973646i | \(0.426760\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.33642 | −0.336157 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 46.4782 | 1.87114 | 0.935572 | − | 0.353137i | \(-0.114885\pi\) | ||||
0.935572 | + | 0.353137i | \(0.114885\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.4425 | −1.46475 | −0.732374 | − | 0.680902i | \(-0.761588\pi\) | ||||
−0.732374 | + | 0.680902i | \(0.761588\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −23.0179 | −0.923677 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 32.6946 | 1.30779 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −57.5888 | −2.29988 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −58.9245 | −2.34947 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.2500 | −0.607095 | −0.303547 | − | 0.952816i | \(-0.598171\pi\) | ||||
−0.303547 | + | 0.952816i | \(0.598171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.40816 | 0.373941 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.3520 | −0.648908 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.63675 | 0.341665 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.4291 | 0.846398 | 0.423199 | − | 0.906037i | \(-0.360907\pi\) | ||||
0.423199 | + | 0.906037i | \(0.360907\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.2975 | 1.03707 | 0.518536 | − | 0.855056i | \(-0.326477\pi\) | ||||
0.518536 | + | 0.855056i | \(0.326477\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.18940 | −0.243707 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.6289 | 0.653749 | 0.326875 | − | 0.945068i | \(-0.394005\pi\) | ||||
0.326875 | + | 0.945068i | \(0.394005\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.8313 | −0.856953 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.05664 | −0.276148 | −0.138074 | − | 0.990422i | \(-0.544091\pi\) | ||||
−0.138074 | + | 0.990422i | \(0.544091\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −41.3518 | −1.61575 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.5331 | 0.723046 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 45.2945 | 1.76442 | 0.882211 | − | 0.470854i | \(-0.156054\pi\) | ||||
0.882211 | + | 0.470854i | \(0.156054\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.1854 | −1.56303 | −0.781516 | − | 0.623886i | \(-0.785553\pi\) | ||||
−0.781516 | + | 0.623886i | \(0.785553\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18.1193 | −0.703693 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −67.3430 | −2.60753 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.1126 | 0.777599 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.6074 | 0.409494 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.5616 | 0.599856 | 0.299928 | − | 0.953962i | \(-0.403037\pi\) | ||||
0.299928 | + | 0.953962i | \(0.403037\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −33.6848 | −1.29653 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.4420 | 1.01625 | 0.508124 | − | 0.861284i | \(-0.330339\pi\) | ||||
0.508124 | + | 0.861284i | \(0.330339\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.8848 | −1.03023 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.07364 | −0.0410817 | −0.0205408 | − | 0.999789i | \(-0.506539\pi\) | ||||
−0.0205408 | + | 0.999789i | \(0.506539\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.58553 | 0.213412 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.0716 | −1.07100 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.37889 | −0.0525315 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.62945 | 0.328280 | 0.164140 | − | 0.986437i | \(-0.447515\pi\) | ||||
0.164140 | + | 0.986437i | \(0.447515\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −40.6772 | −1.54297 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.20325 | 0.197087 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.1503 | 0.951272 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.1873 | −1.66893 | −0.834465 | − | 0.551061i | \(-0.814223\pi\) | ||||
−0.834465 | + | 0.551061i | \(0.814223\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −74.5634 | −2.81221 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.20585 | 0.0830770 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.9496 | 0.636554 | 0.318277 | − | 0.947998i | \(-0.396896\pi\) | ||||
0.318277 | + | 0.947998i | \(0.396896\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.72678 | 0.139765 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 46.3611 | 1.73624 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 26.7358 | 0.999860 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −47.4723 | −1.77288 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.8173 | 0.776355 | 0.388177 | − | 0.921585i | \(-0.373105\pi\) | ||||
0.388177 | + | 0.921585i | \(0.373105\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −53.0011 | −1.97113 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −98.5508 | −3.66008 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.51361 | 0.278664 | 0.139332 | − | 0.990246i | \(-0.455504\pi\) | ||||
0.139332 | + | 0.990246i | \(0.455504\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.68636 | 0.136532 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.86317 | 0.142884 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.7527 | 0.914261 | 0.457131 | − | 0.889400i | \(-0.348877\pi\) | ||||
0.457131 | + | 0.889400i | \(0.348877\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 53.4369 | 1.96837 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.3640 | 1.33767 | 0.668836 | − | 0.743410i | \(-0.266793\pi\) | ||||
0.668836 | + | 0.743410i | \(0.266793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.9282 | −0.842289 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.7748 | −0.431976 | −0.215988 | − | 0.976396i | \(-0.569297\pi\) | ||||
−0.215988 | + | 0.976396i | \(0.569297\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.05462 | 0.185187 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.7883 | −0.467899 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.08643 | −0.0761350 | −0.0380675 | − | 0.999275i | \(-0.512120\pi\) | ||||
−0.0380675 | + | 0.999275i | \(0.512120\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.41688 | −0.160960 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.4145 | 0.924928 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.7156 | −1.47983 | −0.739917 | − | 0.672698i | \(-0.765135\pi\) | ||||
−0.739917 | + | 0.672698i | \(0.765135\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 62.7353 | 2.27715 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.7790 | −0.716989 | −0.358495 | − | 0.933532i | \(-0.616710\pi\) | ||||
−0.358495 | + | 0.933532i | \(0.616710\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −30.4091 | −1.09944 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.69183 | −0.313844 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.9578 | 0.900003 | 0.450001 | − | 0.893028i | \(-0.351423\pi\) | ||||
0.450001 | + | 0.893028i | \(0.351423\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40.0830 | −1.44355 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.6827 | 0.492133 | 0.246067 | − | 0.969253i | \(-0.420862\pi\) | ||||
0.246067 | + | 0.969253i | \(0.420862\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 67.8456 | 2.43709 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.58422 | 0.235904 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0276 | 0.859776 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30.1302 | 1.07676 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −64.1042 | −2.28798 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.7902 | 0.384630 | 0.192315 | − | 0.981333i | \(-0.438401\pi\) | ||||
0.192315 | + | 0.981333i | \(0.438401\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.9332 | −0.389231 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.22319 | 0.149970 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.99045 | −0.247926 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.70563 | −0.131260 | −0.0656301 | − | 0.997844i | \(-0.520906\pi\) | ||||
−0.0656301 | + | 0.997844i | \(0.520906\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.37680 | −0.0487076 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.75405 | 0.0619764 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 51.5595 | 1.81950 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.5546 | 0.477144 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.1550 | 0.743769 | 0.371884 | − | 0.928279i | \(-0.378712\pi\) | ||||
0.371884 | + | 0.928279i | \(0.378712\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.1506 | 0.426667 | 0.213333 | − | 0.976979i | \(-0.431568\pi\) | ||||
0.213333 | + | 0.976979i | \(0.431568\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −67.6952 | −2.37417 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.26167 | 0.184308 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.88848 | 0.171026 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.2915 | 0.533675 | 0.266838 | − | 0.963741i | \(-0.414021\pi\) | ||||
0.266838 | + | 0.963741i | \(0.414021\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 57.1962 | 1.99373 | 0.996867 | − | 0.0791017i | \(-0.0252052\pi\) | ||||
0.996867 | + | 0.0791017i | \(0.0252052\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 91.8079 | 3.19634 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29.1296 | −1.01294 | −0.506469 | − | 0.862258i | \(-0.669049\pi\) | ||||
−0.506469 | + | 0.862258i | \(0.669049\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.4260 | −0.744155 | −0.372077 | − | 0.928202i | \(-0.621354\pi\) | ||||
−0.372077 | + | 0.928202i | \(0.621354\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 50.8759 | 1.76487 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 37.9834 | 1.31447 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −20.7426 | −0.716969 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.9582 | −0.481891 | −0.240945 | − | 0.970539i | \(-0.577457\pi\) | ||||
−0.240945 | + | 0.970539i | \(0.577457\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.1511 | 2.03969 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −29.0014 | −0.998861 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −40.5309 | −1.39430 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29.9665 | −1.02845 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 81.2269 | 2.78442 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.9836 | 0.376070 | 0.188035 | − | 0.982162i | \(-0.439788\pi\) | ||||
0.188035 | + | 0.982162i | \(0.439788\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −38.4798 | −1.31598 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.9320 | 1.19325 | 0.596627 | − | 0.802519i | \(-0.296507\pi\) | ||||
0.596627 | + | 0.802519i | \(0.296507\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.09973 | 0.139881 | 0.0699405 | − | 0.997551i | \(-0.477719\pi\) | ||||
0.0699405 | + | 0.997551i | \(0.477719\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.6514 | 0.396618 | 0.198309 | − | 0.980140i | \(-0.436455\pi\) | ||||
0.198309 | + | 0.980140i | \(0.436455\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.55431 | 0.0528480 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.3332 | 0.724513 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.3680 | 0.351710 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.2752 | 0.720881 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.39125 | 0.317846 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.8783 | 0.671243 | 0.335621 | − | 0.941997i | \(-0.391054\pi\) | ||||
0.335621 | + | 0.941997i | \(0.391054\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.73952 | 0.294777 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.3176 | 1.15619 | 0.578095 | − | 0.815970i | \(-0.303796\pi\) | ||||
0.578095 | + | 0.815970i | \(0.303796\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.0828 | −0.608535 | −0.304267 | − | 0.952587i | \(-0.598412\pi\) | ||||
−0.304267 | + | 0.952587i | \(0.598412\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −44.0643 | −1.48121 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.8490 | 0.632888 | 0.316444 | − | 0.948611i | \(-0.397511\pi\) | ||||
0.316444 | + | 0.948611i | \(0.397511\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −46.4638 | −1.55660 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.74221 | −0.0583008 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.3047 | −1.04640 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24.9772 | 0.833965 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −60.6862 | −2.02400 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.36315 | 0.145358 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.75201 | 0.324168 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.7374 | 1.12023 | 0.560117 | − | 0.828414i | \(-0.310756\pi\) | ||||
0.560117 | + | 0.828414i | \(0.310756\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.5736 | 0.649214 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.0812 | 1.39421 | 0.697106 | − | 0.716968i | \(-0.254471\pi\) | ||||
0.697106 | + | 0.716968i | \(0.254471\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.5773 | −1.17744 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 21.4100 | 0.707793 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.8624 | −0.754159 | −0.377080 | − | 0.926181i | \(-0.623072\pi\) | ||||
−0.377080 | + | 0.926181i | \(0.623072\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.6526 | 0.416917 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.56627 | 0.314878 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 118.869 | 3.90838 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23.5321 | 0.772895 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.1426 | 1.02176 | 0.510878 | − | 0.859653i | \(-0.329320\pi\) | ||||
0.510878 | + | 0.859653i | \(0.329320\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 34.1860 | 1.11920 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −84.5987 | −2.76667 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.94013 | −0.226724 | −0.113362 | − | 0.993554i | \(-0.536162\pi\) | ||||
−0.113362 | + | 0.993554i | \(0.536162\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.3973 | −0.535106 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.4228 | −0.470171 | −0.235086 | − | 0.971975i | \(-0.575537\pi\) | ||||
−0.235086 | + | 0.971975i | \(0.575537\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.17263 | −0.233573 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.9397 | −0.972909 | −0.486455 | − | 0.873706i | \(-0.661710\pi\) | ||||
−0.486455 | + | 0.873706i | \(0.661710\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.5277 | 0.666358 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −51.6540 | −1.67500 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.521703 | −0.0168996 | −0.00844981 | − | 0.999964i | \(-0.502690\pi\) | ||||
−0.00844981 | + | 0.999964i | \(0.502690\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.6371 | 1.02375 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −82.1198 | −2.65455 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.7784 | 0.347689 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.8512 | 0.381898 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −73.8893 | −2.37858 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.9003 | 0.961529 | 0.480765 | − | 0.876850i | \(-0.340359\pi\) | ||||
0.480765 | + | 0.876850i | \(0.340359\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 72.5507 | 2.33066 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.7863 | 0.538699 | 0.269349 | − | 0.963043i | \(-0.413191\pi\) | ||||
0.269349 | + | 0.963043i | \(0.413191\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 36.5521 | 1.17060 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −57.9457 | −1.85385 | −0.926923 | − | 0.375251i | \(-0.877557\pi\) | ||||
−0.926923 | + | 0.375251i | \(0.877557\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.87981 | 0.155959 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.8510 | 0.569938 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53.6430 | 1.71095 | 0.855473 | − | 0.517847i | \(-0.173266\pi\) | ||||
0.855473 | + | 0.517847i | \(0.173266\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 43.0926 | 1.37304 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.32534 | −0.169336 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.3369 | 0.455428 | 0.227714 | − | 0.973728i | \(-0.426875\pi\) | ||||
0.227714 | + | 0.973728i | \(0.426875\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −51.7356 | −1.64178 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −82.1899 | −2.60559 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.8404 | 0.818373 | 0.409186 | − | 0.912451i | \(-0.365813\pi\) | ||||
0.409186 | + | 0.912451i | \(0.365813\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −36.3420 | −1.14981 |
(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 | 8036.2.a.q.1.11 | 15 | ||
7.2 | even | 3 | 1148.2.i.e.165.5 | ✓ | 30 | ||
7.4 | even | 3 | 1148.2.i.e.821.5 | yes | 30 | ||
7.6 | odd | 2 | 8036.2.a.r.1.5 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.i.e.165.5 | ✓ | 30 | 7.2 | even | 3 | ||
1148.2.i.e.821.5 | yes | 30 | 7.4 | even | 3 | ||
8036.2.a.q.1.11 | 15 | 1.1 | even | 1 | trivial | ||
8036.2.a.r.1.5 | 15 | 7.6 | odd | 2 |