Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 8x^{6} + 28x^{5} + 9x^{4} - 64x^{3} + 17x^{2} + 23x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 501) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.459587\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 | ||||||||
\(5\) | −2.63865 | −1.18004 | −0.590020 | − | 0.807388i | \(-0.700880\pi\) | ||||
−0.590020 | + | 0.807388i | \(0.700880\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.604857 | 0.228614 | 0.114307 | − | 0.993445i | \(-0.463535\pi\) | ||||
0.114307 | + | 0.993445i | \(0.463535\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.18757 | −1.26260 | −0.631301 | − | 0.775538i | \(-0.717479\pi\) | ||||
−0.631301 | + | 0.775538i | \(0.717479\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.588099 | −0.163109 | −0.0815547 | − | 0.996669i | \(-0.525989\pi\) | ||||
−0.0815547 | + | 0.996669i | \(0.525989\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.63865 | 0.681297 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.13576 | 0.760534 | 0.380267 | − | 0.924877i | \(-0.375832\pi\) | ||||
0.380267 | + | 0.924877i | \(0.375832\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.33284 | −0.764607 | −0.382303 | − | 0.924037i | \(-0.624869\pi\) | ||||
−0.382303 | + | 0.924037i | \(0.624869\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.604857 | −0.131991 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.06079 | −0.429705 | −0.214852 | − | 0.976647i | \(-0.568927\pi\) | ||||
−0.214852 | + | 0.976647i | \(0.568927\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.96248 | 0.392495 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.1474 | 1.88432 | 0.942162 | − | 0.335158i | \(-0.108790\pi\) | ||||
0.942162 | + | 0.335158i | \(0.108790\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00945 | 0.181303 | 0.0906515 | − | 0.995883i | \(-0.471105\pi\) | ||||
0.0906515 | + | 0.995883i | \(0.471105\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.18757 | 0.728963 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.59601 | −0.269774 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.963871 | −0.158459 | −0.0792297 | − | 0.996856i | \(-0.525246\pi\) | ||||
−0.0792297 | + | 0.996856i | \(0.525246\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.588099 | 0.0941713 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0988 | 1.57717 | 0.788585 | − | 0.614926i | \(-0.210814\pi\) | ||||
0.788585 | + | 0.614926i | \(0.210814\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.46622 | 0.223596 | 0.111798 | − | 0.993731i | \(-0.464339\pi\) | ||||
0.111798 | + | 0.993731i | \(0.464339\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.63865 | −0.393347 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.81359 | 0.556270 | 0.278135 | − | 0.960542i | \(-0.410284\pi\) | ||||
0.278135 | + | 0.960542i | \(0.410284\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.63415 | −0.947735 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.13576 | −0.439094 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.52878 | −0.347354 | −0.173677 | − | 0.984803i | \(-0.555565\pi\) | ||||
−0.173677 | + | 0.984803i | \(0.555565\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.0495 | 1.48992 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.33284 | 0.441446 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.70087 | 0.481812 | 0.240906 | − | 0.970548i | \(-0.422555\pi\) | ||||
0.240906 | + | 0.970548i | \(0.422555\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.962658 | 0.123256 | 0.0616279 | − | 0.998099i | \(-0.480371\pi\) | ||||
0.0616279 | + | 0.998099i | \(0.480371\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.604857 | 0.0762048 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.55179 | 0.192476 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.12872 | 0.748742 | 0.374371 | − | 0.927279i | \(-0.377859\pi\) | ||||
0.374371 | + | 0.927279i | \(0.377859\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.06079 | 0.248090 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.34451 | −0.515599 | −0.257799 | − | 0.966198i | \(-0.582997\pi\) | ||||
−0.257799 | + | 0.966198i | \(0.582997\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.8707 | 1.62344 | 0.811721 | − | 0.584046i | \(-0.198531\pi\) | ||||
0.811721 | + | 0.584046i | \(0.198531\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.96248 | −0.226607 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.53288 | −0.288649 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.16426 | −1.03106 | −0.515530 | − | 0.856872i | \(-0.672405\pi\) | ||||
−0.515530 | + | 0.856872i | \(0.672405\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.6712 | −1.72013 | −0.860067 | − | 0.510182i | \(-0.829578\pi\) | ||||
−0.860067 | + | 0.510182i | \(0.829578\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.27418 | −0.897461 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.1474 | −1.08791 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.57911 | 0.591384 | 0.295692 | − | 0.955283i | \(-0.404450\pi\) | ||||
0.295692 | + | 0.955283i | \(0.404450\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.355716 | −0.0372892 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.00945 | −0.104675 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.79421 | 0.902267 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.60693 | −0.670832 | −0.335416 | − | 0.942070i | \(-0.608877\pi\) | ||||
−0.335416 | + | 0.942070i | \(0.608877\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.18757 | −0.420867 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.212823 | 0.0211767 | 0.0105883 | − | 0.999944i | \(-0.496630\pi\) | ||||
0.0105883 | + | 0.999944i | \(0.496630\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.50031 | 0.147830 | 0.0739150 | − | 0.997265i | \(-0.476451\pi\) | ||||
0.0739150 | + | 0.997265i | \(0.476451\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.59601 | 0.155754 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.70835 | 0.745194 | 0.372597 | − | 0.927993i | \(-0.378467\pi\) | ||||
0.372597 | + | 0.927993i | \(0.378467\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.3144 | −1.84998 | −0.924991 | − | 0.379988i | \(-0.875928\pi\) | ||||
−0.924991 | + | 0.379988i | \(0.875928\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.963871 | 0.0914866 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.91046 | 0.273793 | 0.136896 | − | 0.990585i | \(-0.456287\pi\) | ||||
0.136896 | + | 0.990585i | \(0.456287\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.43771 | 0.507069 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.588099 | −0.0543698 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.89669 | 0.173869 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.53578 | 0.594162 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.0988 | −0.910580 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.01496 | 0.716880 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.5989 | 1.02923 | 0.514617 | − | 0.857420i | \(-0.327934\pi\) | ||||
0.514617 | + | 0.857420i | \(0.327934\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.46622 | −0.129093 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.26258 | 0.721905 | 0.360952 | − | 0.932584i | \(-0.382452\pi\) | ||||
0.360952 | + | 0.932584i | \(0.382452\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.01589 | −0.174800 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.63865 | 0.227099 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.10912 | 0.521937 | 0.260969 | − | 0.965347i | \(-0.415958\pi\) | ||||
0.260969 | + | 0.965347i | \(0.415958\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.8050 | −1.25574 | −0.627872 | − | 0.778317i | \(-0.716074\pi\) | ||||
−0.627872 | + | 0.778317i | \(0.716074\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.81359 | −0.321163 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.46271 | 0.205942 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26.7754 | −2.22358 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.63415 | 0.547175 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.27551 | 0.596033 | 0.298017 | − | 0.954561i | \(-0.403675\pi\) | ||||
0.298017 | + | 0.954561i | \(0.403675\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.77287 | 0.551168 | 0.275584 | − | 0.961277i | \(-0.411129\pi\) | ||||
0.275584 | + | 0.961277i | \(0.411129\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.13576 | 0.253511 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.66359 | −0.213945 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.7559 | −1.09784 | −0.548919 | − | 0.835875i | \(-0.684961\pi\) | ||||
−0.548919 | + | 0.835875i | \(0.684961\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.52878 | 0.200545 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.24648 | −0.0982367 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.7400 | −0.841222 | −0.420611 | − | 0.907241i | \(-0.638184\pi\) | ||||
−0.420611 | + | 0.907241i | \(0.638184\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.0495 | −0.860206 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6541 | −0.973395 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.33284 | −0.254869 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.63924 | 0.124629 | 0.0623145 | − | 0.998057i | \(-0.480152\pi\) | ||||
0.0623145 | + | 0.998057i | \(0.480152\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.18702 | 0.0897300 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.70087 | −0.278175 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.0432 | 1.42336 | 0.711678 | − | 0.702505i | \(-0.247935\pi\) | ||||
0.711678 | + | 0.702505i | \(0.247935\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.7592 | 1.09704 | 0.548520 | − | 0.836138i | \(-0.315192\pi\) | ||||
0.548520 | + | 0.836138i | \(0.315192\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.962658 | −0.0711617 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.54332 | 0.186989 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.1312 | −0.960251 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.604857 | −0.0439968 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.24196 | 0.596367 | 0.298184 | − | 0.954508i | \(-0.403619\pi\) | ||||
0.298184 | + | 0.954508i | \(0.403619\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.4363 | 0.895186 | 0.447593 | − | 0.894237i | \(-0.352281\pi\) | ||||
0.447593 | + | 0.894237i | \(0.352281\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.55179 | −0.111126 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.4826 | −1.31683 | −0.658415 | − | 0.752655i | \(-0.728773\pi\) | ||||
−0.658415 | + | 0.752655i | \(0.728773\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.83561 | −0.342787 | −0.171394 | − | 0.985203i | \(-0.554827\pi\) | ||||
−0.171394 | + | 0.985203i | \(0.554827\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.12872 | −0.432287 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.13772 | 0.430783 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −26.6472 | −1.86112 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.06079 | −0.143235 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.9565 | 0.965394 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.4148 | −1.74963 | −0.874814 | − | 0.484459i | \(-0.839016\pi\) | ||||
−0.874814 | + | 0.484459i | \(0.839016\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.34451 | 0.297681 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.86883 | −0.263852 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.610574 | 0.0414485 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.8707 | −0.937294 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.84414 | −0.124050 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.4950 | −0.903692 | −0.451846 | − | 0.892096i | \(-0.649234\pi\) | ||||
−0.451846 | + | 0.892096i | \(0.649234\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.96248 | 0.130832 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.1793 | −1.47209 | −0.736047 | − | 0.676930i | \(-0.763310\pi\) | ||||
−0.736047 | + | 0.676930i | \(0.763310\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.65236 | −0.571764 | −0.285882 | − | 0.958265i | \(-0.592287\pi\) | ||||
−0.285882 | + | 0.958265i | \(0.592287\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.53288 | 0.166651 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.2852 | −1.00136 | −0.500682 | − | 0.865631i | \(-0.666917\pi\) | ||||
−0.500682 | + | 0.865631i | \(0.666917\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.0627 | −0.656421 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.16426 | 0.595282 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.8813 | 1.93286 | 0.966430 | − | 0.256930i | \(-0.0827111\pi\) | ||||
0.966430 | + | 0.256930i | \(0.0827111\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.5171 | 1.12837 | 0.564187 | − | 0.825647i | \(-0.309190\pi\) | ||||
0.564187 | + | 0.825647i | \(0.309190\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.5052 | 1.11837 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.96004 | 0.124715 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.6712 | 0.993119 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.5902 | −0.731567 | −0.365784 | − | 0.930700i | \(-0.619199\pi\) | ||||
−0.365784 | + | 0.930700i | \(0.619199\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.62972 | 0.542546 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.27418 | 0.518149 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.3462 | −0.770137 | −0.385069 | − | 0.922888i | \(-0.625822\pi\) | ||||
−0.385069 | + | 0.922888i | \(0.625822\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.583004 | −0.0362261 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.1474 | 0.628108 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.9134 | 0.672948 | 0.336474 | − | 0.941693i | \(-0.390766\pi\) | ||||
0.336474 | + | 0.941693i | \(0.390766\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.67256 | 0.409892 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.57911 | −0.341436 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.64700 | 0.161391 | 0.0806953 | − | 0.996739i | \(-0.474286\pi\) | ||||
0.0806953 | + | 0.996739i | \(0.474286\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.3534 | −0.932651 | −0.466326 | − | 0.884613i | \(-0.654422\pi\) | ||||
−0.466326 | + | 0.884613i | \(0.654422\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.355716 | 0.0215289 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.21802 | −0.495565 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.8696 | 1.13376 | 0.566881 | − | 0.823800i | \(-0.308150\pi\) | ||||
0.566881 | + | 0.823800i | \(0.308150\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.00945 | 0.0604343 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.41769 | −0.144227 | −0.0721136 | − | 0.997396i | \(-0.522974\pi\) | ||||
−0.0721136 | + | 0.997396i | \(0.522974\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.2449 | 1.02510 | 0.512551 | − | 0.858657i | \(-0.328701\pi\) | ||||
0.512551 | + | 0.858657i | \(0.328701\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.79421 | −0.520924 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.10834 | 0.360564 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.16700 | −0.421588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.60693 | 0.387305 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.14330 | −0.183634 | −0.0918168 | − | 0.995776i | \(-0.529267\pi\) | ||||
−0.0918168 | + | 0.995776i | \(0.529267\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.76531 | −0.568558 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.18757 | 0.242988 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.21195 | 0.0700889 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.886850 | 0.0511172 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.212823 | −0.0122264 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.54012 | −0.145447 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.5662 | −1.57329 | −0.786643 | − | 0.617409i | \(-0.788182\pi\) | ||||
−0.786643 | + | 0.617409i | \(0.788182\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.50031 | −0.0853497 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.97921 | −0.225640 | −0.112820 | − | 0.993615i | \(-0.535988\pi\) | ||||
−0.112820 | + | 0.993615i | \(0.535988\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.9773 | −0.903090 | −0.451545 | − | 0.892248i | \(-0.649127\pi\) | ||||
−0.451545 | + | 0.892248i | \(0.649127\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.59601 | −0.0899247 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.4618 | −1.43008 | −0.715038 | − | 0.699086i | \(-0.753590\pi\) | ||||
−0.715038 | + | 0.699086i | \(0.753590\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −42.4930 | −2.37915 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.70835 | −0.430238 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.4510 | −0.581509 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.15413 | −0.0640197 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.3144 | 1.06809 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.30668 | 0.127171 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.0840 | 1.32378 | 0.661889 | − | 0.749602i | \(-0.269755\pi\) | ||||
0.661889 | + | 0.749602i | \(0.269755\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.963871 | −0.0528198 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.1715 | −0.883546 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.35478 | −0.400641 | −0.200320 | − | 0.979730i | \(-0.564198\pi\) | ||||
−0.200320 | + | 0.979730i | \(0.564198\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.91046 | −0.158074 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.22716 | −0.228913 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.24671 | −0.445280 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.43771 | −0.292756 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.8836 | −1.12109 | −0.560544 | − | 0.828125i | \(-0.689408\pi\) | ||||
−0.560544 | + | 0.828125i | \(0.689408\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.6111 | −1.42446 | −0.712229 | − | 0.701947i | \(-0.752314\pi\) | ||||
−0.712229 | + | 0.701947i | \(0.752314\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.588099 | 0.0313904 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.13148 | 0.113447 | 0.0567237 | − | 0.998390i | \(-0.481935\pi\) | ||||
0.0567237 | + | 0.998390i | \(0.481935\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.4637 | 0.608428 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.89669 | −0.100383 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.5447 | −0.662082 | −0.331041 | − | 0.943616i | \(-0.607400\pi\) | ||||
−0.331041 | + | 0.943616i | \(0.607400\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.89215 | −0.415376 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.53578 | −0.343040 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −36.5999 | −1.91573 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.2125 | 0.950686 | 0.475343 | − | 0.879800i | \(-0.342324\pi\) | ||||
0.475343 | + | 0.879800i | \(0.342324\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.0988 | 0.525723 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.52955 | −0.0794102 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.0633 | 1.24595 | 0.622976 | − | 0.782241i | \(-0.285923\pi\) | ||||
0.622976 | + | 0.782241i | \(0.285923\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.01496 | −0.413891 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.96768 | −0.307351 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.1878 | −0.934243 | −0.467122 | − | 0.884193i | \(-0.654709\pi\) | ||||
−0.467122 | + | 0.884193i | \(0.654709\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.5989 | −0.594228 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.9159 | 1.11985 | 0.559926 | − | 0.828542i | \(-0.310829\pi\) | ||||
0.559926 | + | 0.828542i | \(0.310829\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.68339 | 0.340617 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.46622 | 0.0745319 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.79088 | 0.344311 | 0.172156 | − | 0.985070i | \(-0.444927\pi\) | ||||
0.172156 | + | 0.985070i | \(0.444927\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.46215 | −0.326805 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.26258 | −0.416792 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.1813 | 1.21669 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −36.3338 | −1.82354 | −0.911770 | − | 0.410701i | \(-0.865284\pi\) | ||||
−0.911770 | + | 0.410701i | \(0.865284\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.01589 | 0.100921 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.5238 | −1.32453 | −0.662267 | − | 0.749268i | \(-0.730405\pi\) | ||||
−0.662267 | + | 0.749268i | \(0.730405\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.593658 | −0.0295722 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.63865 | −0.131116 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.03628 | 0.200071 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.5743 | 0.572313 | 0.286157 | − | 0.958183i | \(-0.407622\pi\) | ||||
0.286157 | + | 0.958183i | \(0.407622\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.10912 | −0.301341 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.23850 | 0.110149 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 41.3507 | 2.02983 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.8050 | 0.725004 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.7087 | −1.40251 | −0.701256 | − | 0.712909i | \(-0.747377\pi\) | ||||
−0.701256 | + | 0.712909i | \(0.747377\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.6417 | −1.54212 | −0.771061 | − | 0.636762i | \(-0.780274\pi\) | ||||
−0.771061 | + | 0.636762i | \(0.780274\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.81359 | 0.185423 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.15386 | 0.298506 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.582270 | 0.0281780 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.46271 | −0.118901 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.0921 | −1.30498 | −0.652490 | − | 0.757798i | \(-0.726275\pi\) | ||||
−0.652490 | + | 0.757798i | \(0.726275\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −37.9931 | −1.82583 | −0.912915 | − | 0.408150i | \(-0.866174\pi\) | ||||
−0.912915 | + | 0.408150i | \(0.866174\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 26.7754 | 1.28378 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.86830 | 0.328555 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.8044 | 1.32703 | 0.663516 | − | 0.748162i | \(-0.269063\pi\) | ||||
0.663516 | + | 0.748162i | \(0.269063\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.63415 | −0.315912 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.02886 | 0.333951 | 0.166976 | − | 0.985961i | \(-0.446600\pi\) | ||||
0.166976 | + | 0.985961i | \(0.446600\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.7213 | −0.697857 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.27551 | −0.344120 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.19816 | 0.292509 | 0.146255 | − | 0.989247i | \(-0.453278\pi\) | ||||
0.146255 | + | 0.989247i | \(0.453278\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −42.2895 | −1.99134 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.77287 | −0.318217 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.938610 | 0.0440027 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.9646 | −1.16779 | −0.583897 | − | 0.811828i | \(-0.698473\pi\) | ||||
−0.583897 | + | 0.811828i | \(0.698473\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.13576 | −0.146365 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.7554 | 1.57215 | 0.786073 | − | 0.618134i | \(-0.212111\pi\) | ||||
0.786073 | + | 0.618134i | \(0.212111\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.1602 | −0.797502 | −0.398751 | − | 0.917059i | \(-0.630556\pi\) | ||||
−0.398751 | + | 0.917059i | \(0.630556\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.66359 | 0.123521 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.4137 | −1.08346 | −0.541728 | − | 0.840554i | \(-0.682230\pi\) | ||||
−0.541728 | + | 0.840554i | \(0.682230\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.70700 | 0.171173 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.7559 | 0.633838 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.13989 | −0.282312 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.54063 | −0.300105 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.52878 | −0.115785 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.8820 | −0.588594 | −0.294297 | − | 0.955714i | \(-0.595086\pi\) | ||||
−0.294297 | + | 0.955714i | \(0.595086\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.566852 | 0.0258462 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.24648 | 0.0567170 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.4334 | 0.791609 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 37.7019 | 1.70844 | 0.854218 | − | 0.519915i | \(-0.174037\pi\) | ||||
0.854218 | + | 0.519915i | \(0.174037\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.7400 | 0.485680 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.3330 | 0.556581 | 0.278290 | − | 0.960497i | \(-0.410232\pi\) | ||||
0.278290 | + | 0.960497i | \(0.410232\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.8198 | 1.43309 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.0495 | 0.496640 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.62781 | −0.117873 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.1753 | −0.500274 | −0.250137 | − | 0.968210i | \(-0.580476\pi\) | ||||
−0.250137 | + | 0.968210i | \(0.580476\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.2408 | 1.21461 | 0.607303 | − | 0.794470i | \(-0.292252\pi\) | ||||
0.607303 | + | 0.794470i | \(0.292252\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.561565 | −0.0249893 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.6541 | 0.561990 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.83882 | 0.391774 | 0.195887 | − | 0.980627i | \(-0.437241\pi\) | ||||
0.195887 | + | 0.980627i | \(0.437241\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.38978 | 0.371142 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.33284 | 0.147149 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.95879 | −0.174445 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.9697 | −0.702347 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.63924 | −0.0719545 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.2225 | −1.54312 | −0.771562 | − | 0.636154i | \(-0.780524\pi\) | ||||
−0.771562 | + | 0.636154i | \(0.780524\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.251562 | −0.0110000 | −0.00550001 | − | 0.999985i | \(-0.501751\pi\) | ||||
−0.00550001 | + | 0.999985i | \(0.501751\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.18702 | −0.0518057 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.16540 | 0.137887 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.7531 | −0.815354 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.70087 | 0.160604 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.93911 | −0.257251 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.3396 | −0.879359 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.0432 | −0.821775 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27.7810 | 1.19661 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.5799 | 1.31473 | 0.657366 | − | 0.753572i | \(-0.271671\pi\) | ||||
0.657366 | + | 0.753572i | \(0.271671\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.7592 | −0.633376 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 50.9639 | 2.18305 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.4268 | −0.873388 | −0.436694 | − | 0.899610i | \(-0.643851\pi\) | ||||
−0.436694 | + | 0.899610i | \(0.643851\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.962658 | 0.0410853 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −33.8197 | −1.44077 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.54306 | −0.235715 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.54332 | −0.107958 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.28570 | −0.181591 | −0.0907956 | − | 0.995870i | \(-0.528941\pi\) | ||||
−0.0907956 | + | 0.995870i | \(0.528941\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.862281 | −0.0364706 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.1312 | 0.554401 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.7819 | 1.46588 | 0.732942 | − | 0.680292i | \(-0.238147\pi\) | ||||
0.732942 | + | 0.680292i | \(0.238147\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.67968 | −0.323087 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.604857 | 0.0254016 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.01037 | 0.0423571 | 0.0211785 | − | 0.999776i | \(-0.493258\pi\) | ||||
0.0211785 | + | 0.999776i | \(0.493258\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.17041 | −0.174526 | −0.0872632 | − | 0.996185i | \(-0.527812\pi\) | ||||
−0.0872632 | + | 0.996185i | \(0.527812\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.24196 | −0.344313 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.04426 | −0.168657 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.0426 | −0.917647 | −0.458824 | − | 0.888527i | \(-0.651729\pi\) | ||||
−0.458824 | + | 0.888527i | \(0.651729\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.4363 | −0.516836 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.47881 | −0.393247 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.5894 | 0.438570 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.55179 | 0.0641586 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.82344 | −0.116536 | −0.0582678 | − | 0.998301i | \(-0.518558\pi\) | ||||
−0.0582678 | + | 0.998301i | \(0.518558\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.36435 | −0.138626 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.4826 | 0.760272 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −45.6709 | −1.87548 | −0.937740 | − | 0.347339i | \(-0.887085\pi\) | ||||
−0.937740 | + | 0.347339i | \(0.887085\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.00469 | −0.205172 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.83561 | 0.197908 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.8313 | −1.54575 | −0.772873 | − | 0.634561i | \(-0.781181\pi\) | ||||
−0.772873 | + | 0.634561i | \(0.781181\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.83325 | −0.278734 | −0.139367 | − | 0.990241i | \(-0.544507\pi\) | ||||
−0.139367 | + | 0.990241i | \(0.544507\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.12872 | 0.249581 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.2456 | −0.701135 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.9026 | 0.929587 | 0.464794 | − | 0.885419i | \(-0.346128\pi\) | ||||
0.464794 | + | 0.885419i | \(0.346128\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.13772 | −0.248713 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.24277 | −0.0907329 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.01302 | −0.202474 | −0.101237 | − | 0.994862i | \(-0.532280\pi\) | ||||
−0.101237 | + | 0.994862i | \(0.532280\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 26.6472 | 1.07452 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.2112 | −0.853931 | −0.426966 | − | 0.904268i | \(-0.640417\pi\) | ||||
−0.426966 | + | 0.904268i | \(0.640417\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.4720 | −0.501290 | −0.250645 | − | 0.968079i | \(-0.580643\pi\) | ||||
−0.250645 | + | 0.968079i | \(0.580643\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.06079 | 0.0826967 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.37456 | 0.135199 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.9611 | −1.23844 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.9565 | −0.557370 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.02247 | −0.120514 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.7516 | −1.74172 | −0.870862 | − | 0.491528i | \(-0.836439\pi\) | ||||
−0.870862 | + | 0.491528i | \(0.836439\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.4148 | 1.01015 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30.6054 | −1.21454 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.90154 | 0.154585 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.34451 | −0.171866 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.2570 | 0.563116 | 0.281558 | − | 0.959544i | \(-0.409149\pi\) | ||||
0.281558 | + | 0.959544i | \(0.409149\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.7973 | 1.29340 | 0.646699 | − | 0.762745i | \(-0.276149\pi\) | ||||
0.646699 | + | 0.762745i | \(0.276149\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.86883 | 0.152335 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.71497 | 0.106736 | 0.0533682 | − | 0.998575i | \(-0.483004\pi\) | ||||
0.0533682 | + | 0.998575i | \(0.483004\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.4977 | −0.608337 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.610574 | −0.0239303 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.282536 | 0.0110565 | 0.00552825 | − | 0.999985i | \(-0.498240\pi\) | ||||
0.00552825 | + | 0.999985i | \(0.498240\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.8021 | −0.851877 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.8707 | 0.541147 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.66474 | −0.103804 | −0.0519018 | − | 0.998652i | \(-0.516528\pi\) | ||||
−0.0519018 | + | 0.998652i | \(0.516528\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.1445 | 0.861321 | 0.430660 | − | 0.902514i | \(-0.358281\pi\) | ||||
0.430660 | + | 0.902514i | \(0.358281\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.84414 | 0.0716204 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.31924 | 0.206271 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.9117 | −0.809703 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.4950 | 0.521747 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.03120 | −0.155623 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.6686 | −0.526886 | −0.263443 | − | 0.964675i | \(-0.584858\pi\) | ||||
−0.263443 | + | 0.964675i | \(0.584858\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.96248 | −0.0755358 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.36889 | −0.206343 | −0.103172 | − | 0.994664i | \(-0.532899\pi\) | ||||
−0.103172 | + | 0.994664i | \(0.532899\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.99625 | −0.153362 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.1793 | 0.849914 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.4099 | 1.35492 | 0.677460 | − | 0.735559i | \(-0.263081\pi\) | ||||
0.677460 | + | 0.735559i | \(0.263081\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.1198 | −0.615907 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.65236 | 0.330108 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.48717 | 0.0566567 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.30779 | −0.0877924 | −0.0438962 | − | 0.999036i | \(-0.513977\pi\) | ||||
−0.0438962 | + | 0.999036i | \(0.513977\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.53288 | −0.0962163 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 39.0652 | 1.48183 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.6675 | 1.19949 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.2852 | 0.578138 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.6519 | −0.704474 | −0.352237 | − | 0.935911i | \(-0.614579\pi\) | ||||
−0.352237 | + | 0.935911i | \(0.614579\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.21243 | 0.121159 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.0627 | 0.378985 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.128727 | 0.00484129 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.83611 | −0.331847 | −0.165924 | − | 0.986139i | \(-0.553061\pi\) | ||||
−0.165924 | + | 0.986139i | \(0.553061\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.16426 | −0.343686 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.08027 | −0.0779068 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.49823 | −0.243020 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −29.8813 | −1.11594 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.8566 | −0.665940 | −0.332970 | − | 0.942937i | \(-0.608051\pi\) | ||||
−0.332970 | + | 0.942937i | \(0.608051\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.907473 | 0.0337960 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.5171 | −0.651466 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.9140 | 0.739588 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.2602 | 0.751409 | 0.375704 | − | 0.926740i | \(-0.377401\pi\) | ||||
0.375704 | + | 0.926740i | \(0.377401\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.59770 | 0.170052 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.9048 | −0.624394 | −0.312197 | − | 0.950017i | \(-0.601065\pi\) | ||||
−0.312197 | + | 0.950017i | \(0.601065\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −17.5052 | −0.645689 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.6645 | −0.945363 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.1818 | 1.29418 | 0.647092 | − | 0.762412i | \(-0.275985\pi\) | ||||
0.647092 | + | 0.762412i | \(0.275985\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.96004 | −0.0720040 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.8016 | −1.09331 | −0.546657 | − | 0.837356i | \(-0.684100\pi\) | ||||
−0.546657 | + | 0.837356i | \(0.684100\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.1975 | −0.703343 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.6712 | −0.573378 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.66245 | 0.170362 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.8463 | 1.52699 | 0.763497 | − | 0.645812i | \(-0.223481\pi\) | ||||
0.763497 | + | 0.645812i | \(0.223481\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.5902 | 0.422371 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.8712 | −0.650401 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.1667 | 0.732973 | 0.366486 | − | 0.930423i | \(-0.380561\pi\) | ||||
0.366486 | + | 0.930423i | \(0.380561\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.62972 | −0.313239 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −47.8942 | −1.73616 | −0.868082 | − | 0.496421i | \(-0.834647\pi\) | ||||
−0.868082 | + | 0.496421i | \(0.834647\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.6824 | −0.422933 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.27418 | −0.299154 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.17648 | −0.0785881 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.1859 | 0.439433 | 0.219717 | − | 0.975564i | \(-0.429487\pi\) | ||||
0.219717 | + | 0.975564i | \(0.429487\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.3462 | 0.444639 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 47.6169 | 1.71266 | 0.856331 | − | 0.516427i | \(-0.172738\pi\) | ||||
0.856331 | + | 0.516427i | \(0.172738\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.98103 | 0.0711606 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.583004 | 0.0209151 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −33.6578 | −1.20592 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.1930 | 0.650996 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.1474 | −0.362638 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36.2970 | 1.29549 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.4329 | 0.906586 | 0.453293 | − | 0.891361i | \(-0.350249\pi\) | ||||
0.453293 | + | 0.891361i | \(0.350249\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.9134 | −0.388527 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.76041 | 0.0625930 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.566139 | −0.0201042 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.67256 | −0.236651 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.4752 | 0.477315 | 0.238658 | − | 0.971104i | \(-0.423293\pi\) | ||||
0.238658 | + | 0.971104i | \(0.423293\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.9585 | 0.423062 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.57911 | 0.197128 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −58.0845 | −2.04976 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.28904 | 0.115923 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.64700 | −0.0931789 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.0866 | −0.600732 | −0.300366 | − | 0.953824i | \(-0.597109\pi\) | ||||
−0.300366 | + | 0.953824i | \(0.597109\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.7124 | −0.657080 | −0.328540 | − | 0.944490i | \(-0.606557\pi\) | ||||
−0.328540 | + | 0.944490i | \(0.606557\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.3534 | 0.538466 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.3391 | 0.992676 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.88667 | −0.170963 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.355716 | −0.0124297 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 43.7257 | 1.52604 | 0.763019 | − | 0.646377i | \(-0.223716\pi\) | ||||
0.763019 | + | 0.646377i | \(0.223716\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.6687 | 0.720466 | 0.360233 | − | 0.932862i | \(-0.382697\pi\) | ||||
0.360233 | + | 0.932862i | \(0.382697\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.21802 | 0.286115 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −53.5678 | −1.86274 | −0.931368 | − | 0.364080i | \(-0.881383\pi\) | ||||
−0.931368 | + | 0.364080i | \(0.881383\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.09767 | 0.281244 | 0.140622 | − | 0.990063i | \(-0.455090\pi\) | ||||
0.140622 | + | 0.990063i | \(0.455090\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.8696 | −0.654578 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.8031 | −0.720785 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.63865 | −0.0913143 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.00945 | −0.0348918 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.9455 | −1.24098 | −0.620489 | − | 0.784215i | \(-0.713066\pi\) | ||||
−0.620489 | + | 0.784215i | \(0.713066\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 73.9696 | 2.55068 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.41769 | 0.0832696 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 33.3899 | 1.14865 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.95321 | 0.135834 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.2449 | −0.591842 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.98634 | 0.0680908 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43.1857 | −1.47865 | −0.739325 | − | 0.673348i | \(-0.764855\pi\) | ||||
−0.739325 | + | 0.673348i | \(0.764855\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.79421 | 0.300756 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.1566 | 0.893491 | 0.446746 | − | 0.894661i | \(-0.352583\pi\) | ||||
0.446746 | + | 0.894661i | \(0.352583\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.1284 | −0.516174 | −0.258087 | − | 0.966122i | \(-0.583092\pi\) | ||||
−0.258087 | + | 0.966122i | \(0.583092\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.10834 | −0.208172 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.0990 | −0.513977 | −0.256989 | − | 0.966414i | \(-0.582730\pi\) | ||||
−0.256989 | + | 0.966414i | \(0.582730\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.32538 | −0.147067 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.16700 | 0.243404 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 38.3760 | 1.30182 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.60430 | −0.122127 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.60693 | −0.223611 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.84790 | 0.163889 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43.4986 | −1.46884 | −0.734422 | − | 0.678693i | \(-0.762547\pi\) | ||||
−0.734422 | + | 0.678693i | \(0.762547\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.14330 | 0.106021 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.7969 | 0.464828 | 0.232414 | − | 0.972617i | \(-0.425338\pi\) | ||||
0.232414 | + | 0.972617i | \(0.425338\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.77424 | −0.0933607 | −0.0466804 | − | 0.998910i | \(-0.514864\pi\) | ||||
−0.0466804 | + | 0.998910i | \(0.514864\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.76531 | 0.328257 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42.3348 | −1.42146 | −0.710732 | − | 0.703462i | \(-0.751636\pi\) | ||||
−0.710732 | + | 0.703462i | \(0.751636\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.01565 | 0.235298 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.18757 | −0.140289 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.7101 | −0.425328 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −50.2484 | −1.67962 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.21195 | −0.0404659 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.2433 | 0.341634 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.92964 | −0.264175 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.886850 | −0.0295125 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −38.9443 | −1.29455 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.94687 | 0.263871 | 0.131936 | − | 0.991258i | \(-0.457881\pi\) | ||||
0.131936 | + | 0.991258i | \(0.457881\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.212823 | 0.00705889 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 58.6923 | 1.94456 | 0.972281 | − | 0.233814i | \(-0.0751208\pi\) | ||||
0.972281 | + | 0.233814i | \(0.0751208\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 65.6242 | 2.17184 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.54012 | 0.0839737 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.99768 | 0.165038 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.5200 | −1.27066 | −0.635328 | − | 0.772242i | \(-0.719135\pi\) | ||||
−0.635328 | + | 0.772242i | \(0.719135\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.5662 | 0.908337 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.55501 | 0.0840990 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.89157 | −0.0621946 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.50031 | 0.0492767 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.6862 | 1.26925 | 0.634627 | − | 0.772818i | \(-0.281154\pi\) | ||||
0.634627 | + | 0.772818i | \(0.281154\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.1106 | 0.724645 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.97921 | 0.130274 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 34.6487 | 1.13313 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.9642 | −1.66493 | −0.832463 | − | 0.554080i | \(-0.813070\pi\) | ||||
−0.832463 | + | 0.554080i | \(0.813070\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.9773 | 0.521399 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.6968 | −1.45708 | −0.728538 | − | 0.685006i | \(-0.759800\pi\) | ||||
−0.728538 | + | 0.685006i | \(0.759800\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.8116 | −0.677718 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.59601 | 0.0519181 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.32767 | 0.303109 | 0.151554 | − | 0.988449i | \(-0.451572\pi\) | ||||
0.151554 | + | 0.988449i | \(0.451572\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.15734 | −0.264799 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.4618 | 0.825654 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.95569 | −0.160530 | −0.0802652 | − | 0.996774i | \(-0.525577\pi\) | ||||
−0.0802652 | + | 0.996774i | \(0.525577\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.7477 | −0.703738 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 42.4930 | 1.37360 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.69514 | 0.119322 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.9810 | −0.967129 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.70835 | 0.248398 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −32.8151 | −1.05636 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.4033 | 1.00986 | 0.504931 | − | 0.863159i | \(-0.331518\pi\) | ||||
0.504931 | + | 0.863159i | \(0.331518\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.4510 | 0.335735 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.8079 | 1.24540 | 0.622702 | − | 0.782459i | \(-0.286035\pi\) | ||||
0.622702 | + | 0.782459i | \(0.286035\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.95490 | −0.287081 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.15413 | 0.0369618 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.8665 | 1.17946 | 0.589732 | − | 0.807599i | \(-0.299233\pi\) | ||||
0.589732 | + | 0.807599i | \(0.299233\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.3629 | −0.746682 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.3144 | −0.616661 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.6521 | 0.467330 | 0.233665 | − | 0.972317i | \(-0.424928\pi\) | ||||
0.233665 | + | 0.972317i | \(0.424928\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48.7691 | 1.55391 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.30668 | −0.0734224 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.02157 | −0.0960802 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.2752 | 0.707595 | 0.353797 | − | 0.935322i | \(-0.384890\pi\) | ||||
0.353797 | + | 0.935322i | \(0.384890\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.0840 | −0.764283 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.7595 | 0.404503 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.53346 | 0.206917 | 0.103458 | − | 0.994634i | \(-0.467009\pi\) | ||||
0.103458 | + | 0.994634i | \(0.467009\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.963871 | 0.0304955 |
(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 | 8016.2.a.x.1.1 | 8 | ||
4.3 | odd | 2 | 501.2.a.e.1.3 | ✓ | 8 | ||
12.11 | even | 2 | 1503.2.a.e.1.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
501.2.a.e.1.3 | ✓ | 8 | 4.3 | odd | 2 | ||
1503.2.a.e.1.6 | 8 | 12.11 | even | 2 | |||
8016.2.a.x.1.1 | 8 | 1.1 | even | 1 | trivial |