Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3864,2,Mod(1,3864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3864.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(30.8541953410\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 11x^{4} + 23x^{3} + 9x^{2} - 23x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.35141\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3864.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.60318 | −1.16418 | −0.582089 | − | 0.813125i | \(-0.697764\pi\) | ||||
−0.582089 | + | 0.813125i | \(0.697764\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.69569 | 1.11429 | 0.557146 | − | 0.830414i | \(-0.311896\pi\) | ||||
0.557146 | + | 0.830414i | \(0.311896\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.98292 | −1.65936 | −0.829681 | − | 0.558238i | \(-0.811478\pi\) | ||||
−0.829681 | + | 0.558238i | \(0.811478\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.60318 | 0.672139 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.23227 | −1.26901 | −0.634506 | − | 0.772918i | \(-0.718797\pi\) | ||||
−0.634506 | + | 0.772918i | \(0.718797\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.69569 | 0.847850 | 0.423925 | − | 0.905697i | \(-0.360652\pi\) | ||||
0.423925 | + | 0.905697i | \(0.360652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.77655 | 0.355311 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.36825 | −0.811164 | −0.405582 | − | 0.914059i | \(-0.632931\pi\) | ||||
−0.405582 | + | 0.914059i | \(0.632931\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00295 | 0.718950 | 0.359475 | − | 0.933155i | \(-0.382956\pi\) | ||||
0.359475 | + | 0.933155i | \(0.382956\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.69569 | −0.643337 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.60318 | 0.440018 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.22079 | −1.35149 | −0.675745 | − | 0.737136i | \(-0.736178\pi\) | ||||
−0.675745 | + | 0.737136i | \(0.736178\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.98292 | 0.958033 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.55101 | 1.02310 | 0.511548 | − | 0.859255i | \(-0.329072\pi\) | ||||
0.511548 | + | 0.859255i | \(0.329072\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.60613 | −1.31242 | −0.656211 | − | 0.754577i | \(-0.727842\pi\) | ||||
−0.656211 | + | 0.754577i | \(0.727842\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.60318 | −0.388059 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.68126 | −0.391102 | −0.195551 | − | 0.980693i | \(-0.562650\pi\) | ||||
−0.195551 | + | 0.980693i | \(0.562650\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.23227 | 0.732665 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.3133 | 1.55400 | 0.777001 | − | 0.629500i | \(-0.216740\pi\) | ||||
0.777001 | + | 0.629500i | \(0.216740\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.62055 | −1.29724 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.69569 | −0.489506 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.6671 | −1.90950 | −0.954749 | − | 0.297414i | \(-0.903876\pi\) | ||||
−0.954749 | + | 0.297414i | \(0.903876\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.08103 | 0.522522 | 0.261261 | − | 0.965268i | \(-0.415862\pi\) | ||||
0.261261 | + | 0.965268i | \(0.415862\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.5746 | 1.93179 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.79098 | 0.463142 | 0.231571 | − | 0.972818i | \(-0.425613\pi\) | ||||
0.231571 | + | 0.972818i | \(0.425613\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.77377 | −0.210508 | −0.105254 | − | 0.994445i | \(-0.533566\pi\) | ||||
−0.105254 | + | 0.994445i | \(0.533566\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.52720 | 0.178745 | 0.0893724 | − | 0.995998i | \(-0.471514\pi\) | ||||
0.0893724 | + | 0.995998i | \(0.471514\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.77655 | −0.205139 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.69569 | −0.421163 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.97409 | 0.222102 | 0.111051 | − | 0.993815i | \(-0.464578\pi\) | ||||
0.111051 | + | 0.993815i | \(0.464578\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.08481 | −0.777659 | −0.388829 | − | 0.921310i | \(-0.627120\pi\) | ||||
−0.388829 | + | 0.921310i | \(0.627120\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.6206 | 1.47736 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.36825 | 0.468326 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.9801 | 1.37589 | 0.687946 | − | 0.725762i | \(-0.258513\pi\) | ||||
0.687946 | + | 0.725762i | \(0.258513\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.98292 | 0.627180 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.00295 | −0.415086 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.62055 | −0.987048 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.66060 | 0.168609 | 0.0843043 | − | 0.996440i | \(-0.473133\pi\) | ||||
0.0843043 | + | 0.996440i | \(0.473133\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.69569 | 0.371431 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.46076 | −0.344359 | −0.172179 | − | 0.985066i | \(-0.555081\pi\) | ||||
−0.172179 | + | 0.985066i | \(0.555081\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.6471 | −1.83735 | −0.918676 | − | 0.395011i | \(-0.870741\pi\) | ||||
−0.918676 | + | 0.395011i | \(0.870741\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.60318 | −0.254044 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.8097 | 1.62506 | 0.812528 | − | 0.582922i | \(-0.198091\pi\) | ||||
0.812528 | + | 0.582922i | \(0.198091\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.58022 | −0.821836 | −0.410918 | − | 0.911672i | \(-0.634792\pi\) | ||||
−0.410918 | + | 0.911672i | \(0.634792\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.22079 | 0.780283 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.6119 | 0.998282 | 0.499141 | − | 0.866521i | \(-0.333649\pi\) | ||||
0.499141 | + | 0.866521i | \(0.333649\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.60318 | 0.242748 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.98292 | −0.553121 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.23227 | 0.479642 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.65813 | 0.241648 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.55101 | −0.590685 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.39122 | 0.750533 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.1427 | 1.07749 | 0.538746 | − | 0.842469i | \(-0.318898\pi\) | ||||
0.538746 | + | 0.842469i | \(0.318898\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.60613 | 0.757727 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.54823 | −0.659492 | −0.329746 | − | 0.944070i | \(-0.606963\pi\) | ||||
−0.329746 | + | 0.944070i | \(0.606963\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.69569 | −0.320457 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.60318 | 0.224046 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.65535 | 0.568605 | 0.284303 | − | 0.958735i | \(-0.408238\pi\) | ||||
0.284303 | + | 0.958735i | \(0.408238\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.4114 | 0.967903 | 0.483952 | − | 0.875095i | \(-0.339201\pi\) | ||||
0.483952 | + | 0.875095i | \(0.339201\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.68126 | 0.225803 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −22.1110 | −1.84902 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.3714 | 0.944339 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.7718 | 1.37400 | 0.687000 | − | 0.726658i | \(-0.258927\pi\) | ||||
0.687000 | + | 0.726658i | \(0.258927\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.95065 | 0.484257 | 0.242129 | − | 0.970244i | \(-0.422154\pi\) | ||||
0.242129 | + | 0.970244i | \(0.422154\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.23227 | −0.423004 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.4204 | −0.836986 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.765909 | 0.0611262 | 0.0305631 | − | 0.999533i | \(-0.490270\pi\) | ||||
0.0305631 | + | 0.999533i | \(0.490270\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.3133 | −0.897203 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.5339 | 0.981733 | 0.490866 | − | 0.871235i | \(-0.336680\pi\) | ||||
0.490866 | + | 0.871235i | \(0.336680\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.62055 | 0.748959 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.18570 | 0.478664 | 0.239332 | − | 0.970938i | \(-0.423072\pi\) | ||||
0.239332 | + | 0.970938i | \(0.423072\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.7953 | 1.75348 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.69569 | 0.282617 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.41729 | −0.563926 | −0.281963 | − | 0.959425i | \(-0.590986\pi\) | ||||
−0.281963 | + | 0.959425i | \(0.590986\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.77655 | −0.134295 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.6671 | 1.10245 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.1053 | 1.57748 | 0.788742 | − | 0.614725i | \(-0.210733\pi\) | ||||
0.788742 | + | 0.614725i | \(0.210733\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.30657 | 0.171446 | 0.0857231 | − | 0.996319i | \(-0.472680\pi\) | ||||
0.0857231 | + | 0.996319i | \(0.472680\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.08103 | −0.301678 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.4002 | 1.57337 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.3369 | −1.41405 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.0754 | 0.801390 | 0.400695 | − | 0.916212i | \(-0.368769\pi\) | ||||
0.400695 | + | 0.916212i | \(0.368769\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.8092 | −1.49788 | −0.748938 | − | 0.662640i | \(-0.769436\pi\) | ||||
−0.748938 | + | 0.662640i | \(0.769436\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −15.5746 | −1.11532 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.99412 | 0.569557 | 0.284779 | − | 0.958593i | \(-0.408080\pi\) | ||||
0.284779 | + | 0.958593i | \(0.408080\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.9881 | −1.41692 | −0.708460 | − | 0.705751i | \(-0.750610\pi\) | ||||
−0.708460 | + | 0.705751i | \(0.750610\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.79098 | −0.267395 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.36825 | 0.306591 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.0535 | −1.19107 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.6581 | 0.944753 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.0383 | 1.31065 | 0.655326 | − | 0.755346i | \(-0.272531\pi\) | ||||
0.655326 | + | 0.755346i | \(0.272531\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.77377 | 0.121537 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 22.4033 | 1.52789 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00295 | −0.271738 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.52720 | −0.103198 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 31.3042 | 2.10575 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.0349 | −0.738952 | −0.369476 | − | 0.929240i | \(-0.620463\pi\) | ||||
−0.369476 | + | 0.929240i | \(0.620463\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.77655 | 0.118437 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.18514 | 0.277778 | 0.138889 | − | 0.990308i | \(-0.455647\pi\) | ||||
0.138889 | + | 0.990308i | \(0.455647\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.15714 | 0.472957 | 0.236478 | − | 0.971637i | \(-0.424007\pi\) | ||||
0.236478 | + | 0.971637i | \(0.424007\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.69569 | 0.243159 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 29.1064 | 1.90683 | 0.953413 | − | 0.301667i | \(-0.0975432\pi\) | ||||
0.953413 | + | 0.301667i | \(0.0975432\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.97982 | 0.455313 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.97409 | −0.128231 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.6094 | 1.78590 | 0.892950 | − | 0.450155i | \(-0.148631\pi\) | ||||
0.892950 | + | 0.450155i | \(0.148631\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.9424 | 0.898108 | 0.449054 | − | 0.893505i | \(-0.351761\pi\) | ||||
0.449054 | + | 0.893505i | \(0.351761\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.60318 | −0.166311 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.1110 | −1.40689 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.08481 | 0.448982 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.89996 | −0.246163 | −0.123082 | − | 0.992397i | \(-0.539278\pi\) | ||||
−0.123082 | + | 0.992397i | \(0.539278\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.69569 | −0.232346 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −13.6206 | −0.852952 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.0968 | 1.00409 | 0.502044 | − | 0.864842i | \(-0.332581\pi\) | ||||
0.502044 | + | 0.864842i | \(0.332581\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.22079 | 0.510815 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.36825 | −0.270388 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.2875 | 1.55929 | 0.779647 | − | 0.626219i | \(-0.215398\pi\) | ||||
0.779647 | + | 0.626219i | \(0.215398\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −29.4506 | −1.80913 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.9801 | −0.794371 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.45589 | −0.576535 | −0.288268 | − | 0.957550i | \(-0.593079\pi\) | ||||
−0.288268 | + | 0.957550i | \(0.593079\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.941543 | 0.0571947 | 0.0285973 | − | 0.999591i | \(-0.490896\pi\) | ||||
0.0285973 | + | 0.999591i | \(0.490896\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.98292 | −0.362103 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.56559 | 0.395920 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.8705 | −1.07374 | −0.536868 | − | 0.843666i | \(-0.680393\pi\) | ||||
−0.536868 | + | 0.843666i | \(0.680393\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.00295 | 0.239650 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.79086 | 0.464764 | 0.232382 | − | 0.972625i | \(-0.425348\pi\) | ||||
0.232382 | + | 0.972625i | \(0.425348\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.7680 | −1.05620 | −0.528099 | − | 0.849183i | \(-0.677095\pi\) | ||||
−0.528099 | + | 0.849183i | \(0.677095\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.62055 | 0.569872 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.55101 | −0.386694 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.3767 | 0.610393 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.66060 | −0.0973463 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.0142620 | 0.000833194 0 | 0.000416597 | − | 1.00000i | \(-0.499867\pi\) | ||||
0.000416597 | 1.00000i | \(0.499867\pi\) | ||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 38.1812 | 2.22299 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.69569 | −0.214446 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.98292 | 0.346001 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.60613 | 0.496049 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.46076 | 0.198816 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.6237 | −0.608309 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.1566 | 1.32162 | 0.660808 | − | 0.750555i | \(-0.270214\pi\) | ||||
0.660808 | + | 0.750555i | \(0.270214\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.6471 | 1.06080 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.20295 | 0.295032 | 0.147516 | − | 0.989060i | \(-0.452872\pi\) | ||||
0.147516 | + | 0.989060i | \(0.452872\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.56663 | 0.258121 | 0.129061 | − | 0.991637i | \(-0.458804\pi\) | ||||
0.129061 | + | 0.991637i | \(0.458804\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.60318 | 0.146673 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.7700 | −1.39122 | −0.695611 | − | 0.718419i | \(-0.744866\pi\) | ||||
−0.695611 | + | 0.718419i | \(0.744866\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.1437 | −0.903874 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.8097 | −0.938227 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.3369 | −1.07593 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.6290 | −0.589589 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.58022 | 0.474487 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.68126 | 0.147823 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.3320 | 1.61223 | 0.806116 | − | 0.591758i | \(-0.201566\pi\) | ||||
0.806116 | + | 0.591758i | \(0.201566\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.22079 | −0.450497 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.86861 | −0.539180 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.5910 | −1.01271 | −0.506357 | − | 0.862324i | \(-0.669008\pi\) | ||||
−0.506357 | + | 0.862324i | \(0.669008\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.6119 | −0.576358 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.7937 | 0.801121 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.60318 | −0.140151 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.7773 | −1.38380 | −0.691899 | − | 0.721995i | \(-0.743225\pi\) | ||||
−0.691899 | + | 0.721995i | \(0.743225\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.7869 | −1.11269 | −0.556347 | − | 0.830950i | \(-0.687798\pi\) | ||||
−0.556347 | + | 0.830950i | \(0.687798\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.98292 | 0.319344 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.3198 | 1.13474 | 0.567368 | − | 0.823464i | \(-0.307962\pi\) | ||||
0.567368 | + | 0.823464i | \(0.307962\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.61745 | 0.245069 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.23227 | −0.276921 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.09577 | −0.110610 | −0.0553051 | − | 0.998469i | \(-0.517613\pi\) | ||||
−0.0553051 | + | 0.998469i | \(0.517613\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.34187 | −0.281151 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.65813 | −0.139516 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.97557 | −0.208091 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.05801 | −0.472824 | −0.236412 | − | 0.971653i | \(-0.575972\pi\) | ||||
−0.236412 | + | 0.971653i | \(0.575972\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.55101 | 0.341032 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.3133 | −0.587357 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.3958 | −1.36672 | −0.683360 | − | 0.730081i | \(-0.739482\pi\) | ||||
−0.683360 | + | 0.730081i | \(0.739482\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.39122 | −0.433321 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.1349 | 1.34602 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.1640 | −1.70352 | −0.851761 | − | 0.523931i | \(-0.824465\pi\) | ||||
−0.851761 | + | 0.523931i | \(0.824465\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.1427 | −0.622090 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.5507 | 0.998996 | 0.499498 | − | 0.866315i | \(-0.333518\pi\) | ||||
0.499498 | + | 0.866315i | \(0.333518\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.62055 | 0.490309 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.60613 | −0.437474 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −37.9492 | −1.92410 | −0.962050 | − | 0.272872i | \(-0.912027\pi\) | ||||
−0.962050 | + | 0.272872i | \(0.912027\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.23227 | 0.264607 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.54823 | 0.380758 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.13891 | −0.258567 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.4074 | 0.923842 | 0.461921 | − | 0.886921i | \(-0.347160\pi\) | ||||
0.461921 | + | 0.886921i | \(0.347160\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.69569 | 0.185016 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.2788 | 1.31230 | 0.656151 | − | 0.754629i | \(-0.272183\pi\) | ||||
0.656151 | + | 0.754629i | \(0.272183\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.9493 | −1.19300 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.60318 | −0.129353 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −30.3815 | −1.50596 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.3366 | −0.659453 | −0.329727 | − | 0.944076i | \(-0.606957\pi\) | ||||
−0.329727 | + | 0.944076i | \(0.606957\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.65535 | −0.328284 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.6671 | 0.721722 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.4430 | 0.905334 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.4114 | −0.558819 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.9845 | −0.780895 | −0.390447 | − | 0.920625i | \(-0.627680\pi\) | ||||
−0.390447 | + | 0.920625i | \(0.627680\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.2583 | 1.27975 | 0.639875 | − | 0.768479i | \(-0.278986\pi\) | ||||
0.639875 | + | 0.768479i | \(0.278986\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.68126 | −0.130367 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.29541 | −0.450894 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.08103 | −0.197495 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 22.1110 | 1.06753 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.7663 | −1.53013 | −0.765065 | − | 0.643953i | \(-0.777293\pi\) | ||||
−0.765065 | + | 0.643953i | \(0.777293\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.4136 | 1.12518 | 0.562592 | − | 0.826735i | \(-0.309804\pi\) | ||||
0.562592 | + | 0.826735i | \(0.309804\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.3714 | −0.545215 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.69569 | −0.176789 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.2881 | −0.777389 | −0.388695 | − | 0.921367i | \(-0.627074\pi\) | ||||
−0.388695 | + | 0.921367i | \(0.627074\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.05460 | −0.0501055 | −0.0250528 | − | 0.999686i | \(-0.507975\pi\) | ||||
−0.0250528 | + | 0.999686i | \(0.507975\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −33.7896 | −1.60178 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.7718 | −0.793279 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.9276 | 1.41237 | 0.706185 | − | 0.708028i | \(-0.250415\pi\) | ||||
0.706185 | + | 0.708028i | \(0.250415\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.2105 | 1.14003 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.95065 | −0.279586 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −15.5746 | −0.730149 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.4004 | 0.813957 | 0.406979 | − | 0.913438i | \(-0.366582\pi\) | ||||
0.406979 | + | 0.913438i | \(0.366582\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.23227 | 0.244222 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.07921 | −0.0968384 | −0.0484192 | − | 0.998827i | \(-0.515418\pi\) | ||||
−0.0484192 | + | 0.998827i | \(0.515418\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.63990 | 0.0762127 | 0.0381063 | − | 0.999274i | \(-0.487867\pi\) | ||||
0.0381063 | + | 0.999274i | \(0.487867\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.4204 | 0.483234 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.7952 | −1.23994 | −0.619968 | − | 0.784627i | \(-0.712854\pi\) | ||||
−0.619968 | + | 0.784627i | \(0.712854\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.79098 | −0.175051 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.765909 | −0.0352912 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −31.8056 | −1.46242 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.56559 | 0.301250 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.3133 | 0.518000 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.159110 | 0.00726991 | 0.00363496 | − | 0.999993i | \(-0.498843\pi\) | ||||
0.00363496 | + | 0.999993i | \(0.498843\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 49.1843 | 2.24261 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.32285 | −0.196291 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.32562 | 0.331956 | 0.165978 | − | 0.986129i | \(-0.446922\pi\) | ||||
0.165978 | + | 0.986129i | \(0.446922\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.5339 | −0.566804 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.9361 | −0.989961 | −0.494981 | − | 0.868904i | \(-0.664825\pi\) | ||||
−0.494981 | + | 0.868904i | \(0.664825\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.8559 | 1.02938 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.62055 | −0.432412 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.77377 | 0.0795646 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.9564 | −1.16197 | −0.580985 | − | 0.813915i | \(-0.697332\pi\) | ||||
−0.580985 | + | 0.813915i | \(0.697332\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.18570 | −0.276357 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 41.9105 | 1.86870 | 0.934348 | − | 0.356361i | \(-0.115983\pi\) | ||||
0.934348 | + | 0.356361i | \(0.115983\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.00899 | 0.400895 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22.7953 | −1.01237 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.07380 | 0.0919198 | 0.0459599 | − | 0.998943i | \(-0.485365\pi\) | ||||
0.0459599 | + | 0.998943i | \(0.485365\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.52720 | −0.0675592 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.69569 | −0.163169 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 48.5418 | 2.13901 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.90912 | −0.435803 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.41729 | 0.325583 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.1781 | −1.36594 | −0.682968 | − | 0.730448i | \(-0.739311\pi\) | ||||
−0.682968 | + | 0.730448i | \(0.739311\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.3193 | 0.451234 | 0.225617 | − | 0.974216i | \(-0.427560\pi\) | ||||
0.225617 | + | 0.974216i | \(0.427560\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.77655 | 0.0775351 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.9445 | −0.912357 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.6671 | −0.636499 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −39.1941 | −1.69769 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −43.7587 | −1.89185 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.1053 | −0.910760 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.69569 | 0.159185 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.4970 | 0.795249 | 0.397625 | − | 0.917548i | \(-0.369835\pi\) | ||||
0.397625 | + | 0.917548i | \(0.369835\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.30657 | −0.0989845 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22.3359 | 0.956763 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.3400 | −1.21173 | −0.605865 | − | 0.795568i | \(-0.707173\pi\) | ||||
−0.605865 | + | 0.795568i | \(0.707173\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.08103 | 0.174174 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.1437 | −0.687745 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.97409 | −0.0839469 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −21.4002 | −0.908388 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.0883 | 1.65623 | 0.828113 | − | 0.560561i | \(-0.189415\pi\) | ||||
0.828113 | + | 0.560561i | \(0.189415\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 51.4897 | 2.17778 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.3369 | 0.816403 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.17133 | 0.344380 | 0.172190 | − | 0.985064i | \(-0.444916\pi\) | ||||
0.172190 | + | 0.985064i | \(0.444916\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.6247 | −1.16218 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.6914 | −0.573973 | −0.286987 | − | 0.957935i | \(-0.592654\pi\) | ||||
−0.286987 | + | 0.957935i | \(0.592654\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.35839 | 0.182393 | 0.0911965 | − | 0.995833i | \(-0.470931\pi\) | ||||
0.0911965 | + | 0.995833i | \(0.470931\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.0754 | −0.462683 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.77655 | −0.0740874 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.6108 | 1.69065 | 0.845325 | − | 0.534253i | \(-0.179407\pi\) | ||||
0.845325 | + | 0.534253i | \(0.179407\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.8092 | 0.864799 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.08481 | 0.293927 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 41.8105 | 1.73161 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.5746 | 0.643931 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.2002 | −0.586105 | −0.293053 | − | 0.956096i | \(-0.594671\pi\) | ||||
−0.293053 | + | 0.956096i | \(0.594671\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.7937 | 0.609562 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.99412 | −0.328834 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.16321 | 0.335223 | 0.167612 | − | 0.985853i | \(-0.446395\pi\) | ||||
0.167612 | + | 0.985853i | \(0.446395\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.6206 | −0.558388 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.9881 | 0.818059 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.8584 | −0.443662 | −0.221831 | − | 0.975085i | \(-0.571203\pi\) | ||||
−0.221831 | + | 0.975085i | \(0.571203\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.4217 | 1.24093 | 0.620463 | − | 0.784236i | \(-0.286945\pi\) | ||||
0.620463 | + | 0.784236i | \(0.286945\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.79098 | 0.154381 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.91960 | −0.281322 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.32132 | 0.215986 | 0.107993 | − | 0.994152i | \(-0.465558\pi\) | ||||
0.107993 | + | 0.994152i | \(0.465558\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.36825 | −0.177011 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.0418 | 0.648981 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.4731 | −1.19041 | −0.595203 | − | 0.803575i | \(-0.702928\pi\) | ||||
−0.595203 | + | 0.803575i | \(0.702928\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 17.0535 | 0.687662 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 46.4590 | 1.87037 | 0.935185 | − | 0.354159i | \(-0.115233\pi\) | ||||
0.935185 | + | 0.354159i | \(0.115233\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.26772 | 0.292114 | 0.146057 | − | 0.989276i | \(-0.453342\pi\) | ||||
0.146057 | + | 0.989276i | \(0.453342\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.9801 | −0.520038 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7266 | −1.22906 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.6581 | −0.545453 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 43.0134 | 1.71506 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.6913 | 0.783897 | 0.391948 | − | 0.919987i | \(-0.371801\pi\) | ||||
0.391948 | + | 0.919987i | \(0.371801\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.0383 | −0.756705 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −31.6097 | −1.25439 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.98292 | −0.237052 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.77377 | −0.0701694 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.9126 | −1.41846 | −0.709232 | − | 0.704975i | \(-0.750958\pi\) | ||||
−0.709232 | + | 0.704975i | \(0.750958\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.2297 | −0.600600 | −0.300300 | − | 0.953845i | \(-0.597087\pi\) | ||||
−0.300300 | + | 0.953845i | \(0.597087\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −22.4033 | −0.882129 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.5755 | 1.31999 | 0.659995 | − | 0.751270i | \(-0.270558\pi\) | ||||
0.659995 | + | 0.751270i | \(0.270558\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −54.2052 | −2.12774 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.00295 | 0.156888 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.85635 | 0.111778 | 0.0558889 | − | 0.998437i | \(-0.482201\pi\) | ||||
0.0558889 | + | 0.998437i | \(0.482201\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.6494 | 0.767766 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.52720 | 0.0595816 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.63887 | 0.336523 | 0.168261 | − | 0.985742i | \(-0.446185\pi\) | ||||
0.168261 | + | 0.985742i | \(0.446185\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.2990 | −1.72303 | −0.861516 | − | 0.507731i | \(-0.830484\pi\) | ||||
−0.861516 | + | 0.507731i | \(0.830484\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −31.3042 | −1.21576 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.62055 | 0.373069 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.36825 | 0.169139 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.0349 | 0.426634 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.0822 | 0.582243 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.2449 | 0.626194 | 0.313097 | − | 0.949721i | \(-0.398633\pi\) | ||||
0.313097 | + | 0.949721i | \(0.398633\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.77655 | −0.0683796 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.830668 | −0.0319251 | −0.0159626 | − | 0.999873i | \(-0.505081\pi\) | ||||
−0.0159626 | + | 0.999873i | \(0.505081\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.66060 | −0.0637281 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.18514 | −0.160375 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.4028 | 1.12507 | 0.562534 | − | 0.826774i | \(-0.309826\pi\) | ||||
0.562534 | + | 0.826774i | \(0.309826\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.3251 | −0.661958 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.15714 | −0.273062 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −67.6865 | −2.57865 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.7775 | −1.47516 | −0.737582 | − | 0.675257i | \(-0.764033\pi\) | ||||
−0.737582 | + | 0.675257i | \(0.764033\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.69569 | −0.140388 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29.7060 | −1.12681 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −34.2767 | −1.29832 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −29.1064 | −1.10091 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.8376 | 0.560407 | 0.280203 | − | 0.959941i | \(-0.409598\pi\) | ||||
0.280203 | + | 0.959941i | \(0.409598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.3815 | −1.14586 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.97982 | −0.262875 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.46076 | 0.130155 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.79230 | −0.255090 | −0.127545 | − | 0.991833i | \(-0.540710\pi\) | ||||
−0.127545 | + | 0.991833i | \(0.540710\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.97409 | 0.0740342 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.00295 | −0.149911 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 57.5590 | 2.15258 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.6094 | −1.03109 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.4230 | 0.687063 | 0.343532 | − | 0.939141i | \(-0.388377\pi\) | ||||
0.343532 | + | 0.939141i | \(0.388377\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.6471 | 0.694454 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.9424 | −0.518523 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.76043 | −0.288215 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.9481 | 0.925275 | 0.462637 | − | 0.886548i | \(-0.346903\pi\) | ||||
0.462637 | + | 0.886548i | \(0.346903\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45.0296 | 1.66548 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.1542 | 0.522799 | 0.261399 | − | 0.965231i | \(-0.415816\pi\) | ||||
0.261399 | + | 0.965231i | \(0.415816\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.60318 | 0.0960198 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.0103 | 0.516076 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −46.3978 | −1.70677 | −0.853385 | − | 0.521281i | \(-0.825454\pi\) | ||||
−0.853385 | + | 0.521281i | \(0.825454\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.1110 | 0.812268 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −41.6993 | −1.52980 | −0.764899 | − | 0.644150i | \(-0.777211\pi\) | ||||
−0.764899 | + | 0.644150i | \(0.777211\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −43.6600 | −1.59958 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.08481 | −0.259220 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.8097 | −0.614213 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.29644 | 0.339232 | 0.169616 | − | 0.985510i | \(-0.445747\pi\) | ||||
0.169616 | + | 0.985510i | \(0.445747\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.89996 | 0.142122 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.4906 | −0.563761 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.81280 | −0.138578 | −0.0692892 | − | 0.997597i | \(-0.522073\pi\) | ||||
−0.0692892 | + | 0.997597i | \(0.522073\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.69569 | 0.134145 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.5275 | −1.75912 | −0.879560 | − | 0.475788i | \(-0.842163\pi\) | ||||
−0.879560 | + | 0.475788i | \(0.842163\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.58022 | 0.310625 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.6206 | 0.492452 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 87.7522 | 3.16855 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.1402 | 0.798398 | 0.399199 | − | 0.916864i | \(-0.369288\pi\) | ||||
0.399199 | + | 0.916864i | \(0.369288\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.0968 | −0.579711 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.18180 | −0.0425062 | −0.0212531 | − | 0.999774i | \(-0.506766\pi\) | ||||
−0.0212531 | + | 0.999774i | \(0.506766\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.11145 | 0.255451 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.22079 | −0.294919 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.2105 | 0.867431 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.55532 | −0.234568 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.36825 | 0.156109 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.99380 | −0.0711617 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.7670 | 1.41754 | 0.708770 | − | 0.705440i | \(-0.249251\pi\) | ||||
0.708770 | + | 0.705440i | \(0.249251\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.2875 | −0.900259 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.6119 | −0.377315 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.4164 | −0.867053 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 29.4506 | 1.04450 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.93837 | −0.245770 | −0.122885 | − | 0.992421i | \(-0.539215\pi\) | ||||
−0.122885 | + | 0.992421i | \(0.539215\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.0291 | 0.496314 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.9801 | 0.458631 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.64405 | 0.199174 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.60318 | −0.0917501 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.45589 | 0.332863 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.71075 | 0.0601468 | 0.0300734 | − | 0.999548i | \(-0.490426\pi\) | ||||
0.0300734 | + | 0.999548i | \(0.490426\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.63104 | −0.0572737 | −0.0286368 | − | 0.999590i | \(-0.509117\pi\) | ||||
−0.0286368 | + | 0.999590i | \(0.509117\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.941543 | −0.0330214 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −32.6281 | −1.14291 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.8056 | −1.11274 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.98292 | 0.209060 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.1679 | 0.634066 | 0.317033 | − | 0.948415i | \(-0.397313\pi\) | ||||
0.317033 | + | 0.948415i | \(0.397313\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.2847 | −0.776797 | −0.388398 | − | 0.921492i | \(-0.626972\pi\) | ||||
−0.388398 | + | 0.921492i | \(0.626972\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.56559 | −0.228585 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.2556 | −0.460942 | −0.230471 | − | 0.973079i | \(-0.574027\pi\) | ||||
−0.230471 | + | 0.973079i | \(0.574027\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.1676 | 0.422599 | 0.211300 | − | 0.977421i | \(-0.432230\pi\) | ||||
0.211300 | + | 0.977421i | \(0.432230\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.8705 | 0.619922 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.23227 | −0.181288 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.1025 | −0.557250 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.00295 | −0.138362 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.07369 | 0.0370679 | 0.0185340 | − | 0.999828i | \(-0.494100\pi\) | ||||
0.0185340 | + | 0.999828i | \(0.494100\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.91837 | −0.342013 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.79086 | −0.268331 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −59.3403 | −2.04137 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.65813 | −0.0913345 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.7680 | 0.609797 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.22079 | 0.281805 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.4834 | 1.18069 | 0.590344 | − | 0.807152i | \(-0.298992\pi\) | ||||
0.590344 | + | 0.807152i | \(0.298992\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.62055 | −0.329016 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34.8518 | −1.19052 | −0.595258 | − | 0.803535i | \(-0.702950\pi\) | ||||
−0.595258 | + | 0.803535i | \(0.702950\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.0040 | −0.784886 | −0.392443 | − | 0.919776i | \(-0.628370\pi\) | ||||
−0.392443 | + | 0.919776i | \(0.628370\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.55101 | 0.223258 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.40516 | 0.286115 | 0.143057 | − | 0.989714i | \(-0.454307\pi\) | ||||
0.143057 | + | 0.989714i | \(0.454307\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.3086 | 0.656511 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.3767 | −0.352410 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.29563 | 0.247487 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.6811 | −0.768520 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.66060 | 0.0562029 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.39122 | −0.283675 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.3832 | −0.350615 | −0.175307 | − | 0.984514i | \(-0.556092\pi\) | ||||
−0.175307 | + | 0.984514i | \(0.556092\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.0142620 | −0.000481045 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.9118 | 1.37835 | 0.689176 | − | 0.724594i | \(-0.257973\pi\) | ||||
0.689176 | + | 0.724594i | \(0.257973\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.1694 | −0.611449 | −0.305725 | − | 0.952120i | \(-0.598899\pi\) | ||||
−0.305725 | + | 0.952120i | \(0.598899\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −38.1812 | −1.28345 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.58708 | 0.0532889 | 0.0266444 | − | 0.999645i | \(-0.491518\pi\) | ||||
0.0266444 | + | 0.999645i | \(0.491518\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.1427 | −0.407253 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.69569 | 0.123810 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.90912 | −0.331596 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −54.9409 | −1.83647 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.98292 | −0.199764 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.4859 | −0.583187 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −59.1943 | −1.97205 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.60613 | −0.286394 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.00442 | −0.199594 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.51319 | −0.249471 | −0.124736 | − | 0.992190i | \(-0.539808\pi\) | ||||
−0.124736 | + | 0.992190i | \(0.539808\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.46076 | −0.114786 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.2129 | −1.56423 | −0.782117 | − | 0.623131i | \(-0.785860\pi\) | ||||
−0.782117 | + | 0.623131i | \(0.785860\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.1833 | −0.866540 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.6237 | 0.351207 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.54823 | 0.249264 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.4159 | −0.871381 | −0.435690 | − | 0.900097i | \(-0.643496\pi\) | ||||
−0.435690 | + | 0.900097i | \(0.643496\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23.1566 | −0.763035 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.6123 | 0.349309 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.6047 | −0.480199 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.6471 | −0.612451 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.8816 | 0.389823 | 0.194911 | − | 0.980821i | \(-0.437558\pi\) | ||||
0.194911 | + | 0.980821i | \(0.437558\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.69569 | 0.121121 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.20295 | −0.170337 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 50.3374 | 1.64621 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.3277 | 1.70947 | 0.854736 | − | 0.519063i | \(-0.173719\pi\) | ||||
0.854736 | + | 0.519063i | \(0.173719\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.56663 | −0.149026 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.10300 | −0.198952 | −0.0994761 | − | 0.995040i | \(-0.531717\pi\) | ||||
−0.0994761 | + | 0.995040i | \(0.531717\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.55101 | −0.213330 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.60318 | −0.0846815 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.77999 | 0.0578417 | 0.0289209 | − | 0.999582i | \(-0.490793\pi\) | ||||
0.0289209 | + | 0.999582i | \(0.490793\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.13709 | −0.296602 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.7700 | 0.803222 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.0788 | 0.974347 | 0.487174 | − | 0.873305i | \(-0.338028\pi\) | ||||
0.487174 | + | 0.873305i | \(0.338028\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.8313 | −0.932960 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.1437 | 0.521852 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.65535 | −0.214913 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.9764 | −0.483111 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.8097 | 0.541685 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 54.1700 | 1.74379 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −62.0094 | −1.99409 | −0.997044 | − | 0.0768279i | \(-0.975521\pi\) | ||||
−0.997044 | + | 0.0768279i | \(0.975521\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19.3369 | 0.621190 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.3406 | 0.331847 | 0.165923 | − | 0.986139i | \(-0.446940\pi\) | ||||
0.165923 | + | 0.986139i | \(0.446940\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.4114 | −0.365833 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.6290 | 0.340399 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32.4038 | −1.03669 | −0.518345 | − | 0.855172i | \(-0.673452\pi\) | ||||
−0.518345 | + | 0.855172i | \(0.673452\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 47.9706 | 1.53315 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.58022 | −0.273945 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51.4249 | −1.64020 | −0.820099 | − | 0.572221i | \(-0.806082\pi\) | ||||
−0.820099 | + | 0.572221i | \(0.806082\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.8101 | −0.663066 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.68126 | −0.0853456 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.60613 | 0.273659 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.14387 | −0.195166 | −0.0975832 | − | 0.995227i | \(-0.531111\pi\) | ||||
−0.0975832 | + | 0.995227i | \(0.531111\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −29.3320 | −0.930822 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 52.0327 | 1.64955 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.8573 | 1.04060 | 0.520300 | − | 0.853984i | \(-0.325820\pi\) | ||||
0.520300 | + | 0.853984i | \(0.325820\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.22079 | 0.260094 |
(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 | 3864.2.a.w.1.1 | ✓ | 6 | |
4.3 | odd | 2 | 7728.2.a.ch.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.a.w.1.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
7728.2.a.ch.1.1 | 6 | 4.3 | odd | 2 |