Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(1,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.1935333.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 8x^{3} + 10x^{2} + 13x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.60064\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1148.1 |
$q$-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 | ||||||||
\(3\) | 1.60064 | 0.924131 | 0.462066 | − | 0.886846i | \(-0.347108\pi\) | ||||
0.462066 | + | 0.886846i | \(0.347108\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.47347 | −1.10617 | −0.553084 | − | 0.833125i | \(-0.686549\pi\) | ||||
−0.553084 | + | 0.833125i | \(0.686549\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.437946 | −0.145982 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.48567 | 0.447946 | 0.223973 | − | 0.974595i | \(-0.428097\pi\) | ||||
0.223973 | + | 0.974595i | \(0.428097\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.55292 | 0.708052 | 0.354026 | − | 0.935235i | \(-0.384812\pi\) | ||||
0.354026 | + | 0.935235i | \(0.384812\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.95914 | −1.02224 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.00686 | 0.971806 | 0.485903 | − | 0.874013i | \(-0.338491\pi\) | ||||
0.485903 | + | 0.874013i | \(0.338491\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.95228 | 0.447883 | 0.223942 | − | 0.974603i | \(-0.428108\pi\) | ||||
0.223942 | + | 0.974603i | \(0.428108\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.60064 | 0.349289 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.60064 | 0.750786 | 0.375393 | − | 0.926866i | \(-0.377508\pi\) | ||||
0.375393 | + | 0.926866i | \(0.377508\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.11804 | 0.223608 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.50292 | −1.05904 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.95914 | 0.735193 | 0.367596 | − | 0.929985i | \(-0.380181\pi\) | ||||
0.367596 | + | 0.929985i | \(0.380181\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.47347 | 0.803458 | 0.401729 | − | 0.915759i | \(-0.368409\pi\) | ||||
0.401729 | + | 0.915759i | \(0.368409\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.37802 | 0.413961 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.47347 | −0.418092 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.98552 | 1.47721 | 0.738605 | − | 0.674138i | \(-0.235485\pi\) | ||||
0.738605 | + | 0.674138i | \(0.235485\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.08631 | 0.654333 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00686 | −0.306043 | −0.153021 | − | 0.988223i | \(-0.548900\pi\) | ||||
−0.153021 | + | 0.988223i | \(0.548900\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.08324 | 0.161480 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.268535 | −0.0391699 | −0.0195849 | − | 0.999808i | \(-0.506234\pi\) | ||||
−0.0195849 | + | 0.999808i | \(0.506234\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.41354 | 0.898076 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.47347 | 0.339757 | 0.169878 | − | 0.985465i | \(-0.445662\pi\) | ||||
0.169878 | + | 0.985465i | \(0.445662\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.67475 | −0.495503 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.12490 | 0.413903 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.37802 | 0.309592 | 0.154796 | − | 0.987946i | \(-0.450528\pi\) | ||||
0.154796 | + | 0.987946i | \(0.450528\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.24959 | 0.416067 | 0.208034 | − | 0.978122i | \(-0.433294\pi\) | ||||
0.208034 | + | 0.978122i | \(0.433294\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.437946 | −0.0551760 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.31456 | −0.783225 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.16634 | 0.264661 | 0.132331 | − | 0.991206i | \(-0.457754\pi\) | ||||
0.132331 | + | 0.991206i | \(0.457754\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.76334 | 0.693824 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.7397 | −1.74928 | −0.874642 | − | 0.484770i | \(-0.838903\pi\) | ||||
−0.874642 | + | 0.484770i | \(0.838903\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.46127 | 0.639193 | 0.319596 | − | 0.947554i | \(-0.396453\pi\) | ||||
0.319596 | + | 0.947554i | \(0.396453\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.78958 | 0.206643 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.48567 | 0.169308 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.2785 | 1.49394 | 0.746972 | − | 0.664856i | \(-0.231507\pi\) | ||||
0.746972 | + | 0.664856i | \(0.231507\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.49437 | −0.832707 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.73973 | −0.959309 | −0.479655 | − | 0.877457i | \(-0.659238\pi\) | ||||
−0.479655 | + | 0.877457i | \(0.659238\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.91083 | −1.07498 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.33716 | 0.679415 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.21533 | 0.340824 | 0.170412 | − | 0.985373i | \(-0.445490\pi\) | ||||
0.170412 | + | 0.985373i | \(0.445490\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.55292 | 0.267619 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.16042 | 0.742501 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.82889 | −0.495434 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.80193 | −0.284492 | −0.142246 | − | 0.989831i | \(-0.545432\pi\) | ||||
−0.142246 | + | 0.989831i | \(0.545432\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.650642 | −0.0653920 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.48873 | −0.546149 | −0.273075 | − | 0.961993i | \(-0.588041\pi\) | ||||
−0.273075 | + | 0.961993i | \(0.588041\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.72919 | 0.761579 | 0.380790 | − | 0.924662i | \(-0.375652\pi\) | ||||
0.380790 | + | 0.924662i | \(0.375652\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.95914 | −0.386372 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.79965 | −0.754020 | −0.377010 | − | 0.926209i | \(-0.623048\pi\) | ||||
−0.377010 | + | 0.926209i | \(0.623048\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.71699 | −0.451805 | −0.225903 | − | 0.974150i | \(-0.572533\pi\) | ||||
−0.225903 | + | 0.974150i | \(0.572533\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.3826 | 1.36514 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.6308 | −1.47042 | −0.735212 | − | 0.677837i | \(-0.762917\pi\) | ||||
−0.735212 | + | 0.677837i | \(0.762917\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.90607 | −0.830495 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.11804 | −0.103363 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.00686 | 0.367308 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.79279 | −0.799345 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.60064 | 0.144325 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.60190 | 0.858820 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.3227 | −1.53714 | −0.768570 | − | 0.639766i | \(-0.779031\pi\) | ||||
−0.768570 | + | 0.639766i | \(0.779031\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.21226 | −0.282824 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.4445 | −1.43676 | −0.718382 | − | 0.695649i | \(-0.755117\pi\) | ||||
−0.718382 | + | 0.695649i | \(0.755117\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.95228 | 0.169284 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.6113 | 1.17147 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.2859 | −1.30596 | −0.652981 | − | 0.757374i | \(-0.726482\pi\) | ||||
−0.652981 | + | 0.757374i | \(0.726482\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.5342 | 0.893497 | 0.446749 | − | 0.894659i | \(-0.352582\pi\) | ||||
0.446749 | + | 0.894659i | \(0.352582\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.429829 | −0.0361981 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.79279 | 0.317169 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.79279 | −0.813247 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.60064 | 0.132019 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.88015 | −0.154028 | −0.0770141 | − | 0.997030i | \(-0.524539\pi\) | ||||
−0.0770141 | + | 0.997030i | \(0.524539\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.6199 | 1.51526 | 0.757632 | − | 0.652682i | \(-0.226356\pi\) | ||||
0.757632 | + | 0.652682i | \(0.226356\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.75479 | −0.141866 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.0650 | −0.888760 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0357 | 0.800938 | 0.400469 | − | 0.916310i | \(-0.368847\pi\) | ||||
0.400469 | + | 0.916310i | \(0.368847\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.95914 | 0.313980 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.60064 | 0.283770 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2406 | 0.802105 | 0.401053 | − | 0.916055i | \(-0.368644\pi\) | ||||
0.401053 | + | 0.916055i | \(0.368644\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.88196 | −0.457910 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.6040 | 0.975327 | 0.487663 | − | 0.873032i | \(-0.337849\pi\) | ||||
0.487663 | + | 0.873032i | \(0.337849\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.48260 | −0.498662 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.854991 | −0.0653828 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.49180 | −0.265477 | −0.132738 | − | 0.991151i | \(-0.542377\pi\) | ||||
−0.132738 | + | 0.991151i | \(0.542377\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.11804 | 0.0845159 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.80636 | 0.286104 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.29016 | 0.619636 | 0.309818 | − | 0.950796i | \(-0.399732\pi\) | ||||
0.309818 | + | 0.950796i | \(0.399732\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.06371 | 0.0790653 | 0.0395327 | − | 0.999218i | \(-0.487413\pi\) | ||||
0.0395327 | + | 0.999218i | \(0.487413\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.20143 | 0.384501 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −22.2254 | −1.63404 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.95286 | 0.435316 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.50292 | −0.400279 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.79142 | 0.201980 | 0.100990 | − | 0.994887i | \(-0.467799\pi\) | ||||
0.100990 | + | 0.994887i | \(0.467799\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.71894 | 0.195713 | 0.0978567 | − | 0.995201i | \(-0.468801\pi\) | ||||
0.0978567 | + | 0.995201i | \(0.468801\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.1074 | −0.723803 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.5379 | −1.39201 | −0.696007 | − | 0.718035i | \(-0.745042\pi\) | ||||
−0.696007 | + | 0.718035i | \(0.745042\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.7435 | 0.974252 | 0.487126 | − | 0.873332i | \(-0.338045\pi\) | ||||
0.487126 | + | 0.873332i | \(0.338045\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.46754 | 0.244582 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.95914 | 0.277877 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.47347 | −0.172754 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.57689 | −0.109601 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.90044 | 0.200627 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.66211 | 0.665167 | 0.332584 | − | 0.943074i | \(-0.392080\pi\) | ||||
0.332584 | + | 0.943074i | \(0.392080\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −23.5930 | −1.61657 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.96390 | 0.338535 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.47347 | 0.303679 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.74153 | 0.590698 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.2292 | 0.688089 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.3344 | −0.959903 | −0.479952 | − | 0.877295i | \(-0.659346\pi\) | ||||
−0.479952 | + | 0.877295i | \(0.659346\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.489641 | −0.0326427 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.39810 | −0.159167 | −0.0795837 | − | 0.996828i | \(-0.525359\pi\) | ||||
−0.0795837 | + | 0.996828i | \(0.525359\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.26500 | −0.281839 | −0.140920 | − | 0.990021i | \(-0.545006\pi\) | ||||
−0.140920 | + | 0.990021i | \(0.545006\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.37802 | 0.156462 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.8350 | −0.840851 | −0.420425 | − | 0.907327i | \(-0.638119\pi\) | ||||
−0.420425 | + | 0.907327i | \(0.638119\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.664213 | 0.0433285 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 21.2541 | 1.38060 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.6337 | −0.752524 | −0.376262 | − | 0.926513i | \(-0.622791\pi\) | ||||
−0.376262 | + | 0.926513i | \(0.622791\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.7984 | −0.888835 | −0.444417 | − | 0.895820i | \(-0.646589\pi\) | ||||
−0.444417 | + | 0.895820i | \(0.646589\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.51296 | 0.289507 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.47347 | −0.158024 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.98401 | 0.317125 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.9892 | −0.886528 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.12548 | 0.260398 | 0.130199 | − | 0.991488i | \(-0.458438\pi\) | ||||
0.130199 | + | 0.991488i | \(0.458438\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.34936 | 0.336311 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −15.8637 | −0.993423 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.163921 | −0.0102251 | −0.00511255 | − | 0.999987i | \(-0.501627\pi\) | ||||
−0.00511255 | + | 0.999987i | \(0.501627\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.98552 | 0.558333 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.73389 | −0.107325 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.49577 | 0.462209 | 0.231104 | − | 0.972929i | \(-0.425766\pi\) | ||||
0.231104 | + | 0.972929i | \(0.425766\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.11804 | −0.375828 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.14659 | 0.314966 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.1315 | 1.53229 | 0.766146 | − | 0.642666i | \(-0.222172\pi\) | ||||
0.766146 | + | 0.642666i | \(0.222172\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.2978 | −1.05077 | −0.525383 | − | 0.850866i | \(-0.676078\pi\) | ||||
−0.525383 | + | 0.850866i | \(0.676078\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.08631 | 0.247315 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.66104 | 0.100164 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.7894 | −0.888611 | −0.444305 | − | 0.895875i | \(-0.646549\pi\) | ||||
−0.444305 | + | 0.895875i | \(0.646549\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.95914 | −0.117290 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.33132 | −0.318040 | −0.159020 | − | 0.987275i | \(-0.550833\pi\) | ||||
−0.159020 | + | 0.987275i | \(0.550833\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.12743 | 0.364238 | 0.182119 | − | 0.983277i | \(-0.441704\pi\) | ||||
0.182119 | + | 0.983277i | \(0.441704\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.72933 | −0.457846 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.00000 | 0.0590281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.945093 | −0.0555937 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.48488 | −0.262908 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.64544 | 0.505072 | 0.252536 | − | 0.967587i | \(-0.418735\pi\) | ||||
0.252536 | + | 0.967587i | \(0.418735\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.88196 | −0.342461 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.17551 | −0.474391 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.19215 | 0.531596 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.00686 | −0.115673 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.78550 | −0.504714 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.03775 | −0.460240 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.2043 | −0.981902 | −0.490951 | − | 0.871187i | \(-0.663351\pi\) | ||||
−0.490951 | + | 0.871187i | \(0.663351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.3717 | 0.703799 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.3526 | −1.43761 | −0.718807 | − | 0.695210i | \(-0.755312\pi\) | ||||
−0.718807 | + | 0.695210i | \(0.755312\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.22280 | −0.521303 | −0.260652 | − | 0.965433i | \(-0.583937\pi\) | ||||
−0.260652 | + | 0.965433i | \(0.583937\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.08324 | 0.0610339 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.21363 | −0.124330 | −0.0621649 | − | 0.998066i | \(-0.519800\pi\) | ||||
−0.0621649 | + | 0.998066i | \(0.519800\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.88196 | 0.329327 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.4844 | −0.696814 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.82250 | 0.435255 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.85427 | 0.158326 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.55021 | −0.417527 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.268535 | −0.0148048 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.62038 | 0.473819 | 0.236909 | − | 0.971532i | \(-0.423866\pi\) | ||||
0.236909 | + | 0.971532i | \(0.423866\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.93517 | −0.215646 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.35838 | −0.292760 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.79536 | 0.0977994 | 0.0488997 | − | 0.998804i | \(-0.484429\pi\) | ||||
0.0488997 | + | 0.998804i | \(0.484429\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −25.0193 | −1.35886 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.64609 | 0.359906 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −14.2554 | −0.767486 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.35563 | −0.502237 | −0.251118 | − | 0.967956i | \(-0.580798\pi\) | ||||
−0.251118 | + | 0.967956i | \(0.580798\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.5763 | −1.20848 | −0.604240 | − | 0.796802i | \(-0.706523\pi\) | ||||
−0.604240 | + | 0.796802i | \(0.706523\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.0485 | −0.749854 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.2479 | −0.918014 | −0.459007 | − | 0.888433i | \(-0.651795\pi\) | ||||
−0.459007 | + | 0.888433i | \(0.651795\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 36.4582 | 1.93500 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.41354 | 0.339441 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.7449 | −0.672649 | −0.336325 | − | 0.941746i | \(-0.609184\pi\) | ||||
−0.336325 | + | 0.941746i | \(0.609184\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.1886 | −0.799401 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.0741 | −0.738699 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.5083 | −0.707055 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.57951 | −0.447847 | −0.223923 | − | 0.974607i | \(-0.571887\pi\) | ||||
−0.223923 | + | 0.974607i | \(0.571887\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.437946 | −0.0227985 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.47347 | 0.128416 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.1282 | −0.783309 | −0.391655 | − | 0.920112i | \(-0.628097\pi\) | ||||
−0.391655 | + | 0.920112i | \(0.628097\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.3692 | 0.793662 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.1074 | 0.520555 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.7972 | −0.657349 | −0.328675 | − | 0.944443i | \(-0.606602\pi\) | ||||
−0.328675 | + | 0.944443i | \(0.606602\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −27.7274 | −1.42052 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.89743 | 0.505735 | 0.252868 | − | 0.967501i | \(-0.418626\pi\) | ||||
0.252868 | + | 0.967501i | \(0.418626\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.67475 | −0.187283 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.878894 | 0.0446767 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.07916 | 0.460332 | 0.230166 | − | 0.973151i | \(-0.426073\pi\) | ||||
0.230166 | + | 0.973151i | \(0.426073\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.4273 | 0.729618 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −26.3218 | −1.32776 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −32.8438 | −1.65255 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.0487 | 1.15678 | 0.578389 | − | 0.815761i | \(-0.303681\pi\) | ||||
0.578389 | + | 0.815761i | \(0.303681\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.12490 | 0.156441 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.89679 | −0.394347 | −0.197173 | − | 0.980369i | \(-0.563176\pi\) | ||||
−0.197173 | + | 0.980369i | \(0.563176\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.4204 | 0.568891 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.5371 | 0.921114 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.3495 | 0.661710 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.0087 | 0.939921 | 0.469961 | − | 0.882687i | \(-0.344268\pi\) | ||||
0.469961 | + | 0.882687i | \(0.344268\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −24.4672 | −1.20688 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.37802 | 0.117015 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21.6174 | 1.06116 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.8614 | 0.825709 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.2980 | 1.33359 | 0.666796 | − | 0.745240i | \(-0.267665\pi\) | ||||
0.666796 | + | 0.745240i | \(0.267665\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.2599 | −1.47478 | −0.737389 | − | 0.675469i | \(-0.763941\pi\) | ||||
−0.737389 | + | 0.675469i | \(0.763941\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.117604 | 0.00571809 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.47983 | 0.217303 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.24959 | 0.157259 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.07090 | 0.293106 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.4875 | −1.80571 | −0.902855 | − | 0.429944i | \(-0.858533\pi\) | ||||
−0.902855 | + | 0.429944i | \(0.858533\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.5823 | 1.70998 | 0.854989 | − | 0.518646i | \(-0.173564\pi\) | ||||
0.854989 | + | 0.518646i | \(0.173564\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.6748 | −0.751547 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.02945 | 0.336264 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.4665 | 1.64500 | 0.822498 | − | 0.568768i | \(-0.192580\pi\) | ||||
0.822498 | + | 0.568768i | \(0.192580\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.437946 | −0.0208546 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.20825 | 0.152429 | 0.0762143 | − | 0.997091i | \(-0.475717\pi\) | ||||
0.0762143 | + | 0.997091i | \(0.475717\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.95300 | −0.377009 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.00945 | −0.142342 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.5493 | −1.15855 | −0.579276 | − | 0.815131i | \(-0.696665\pi\) | ||||
−0.579276 | + | 0.815131i | \(0.696665\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.48567 | 0.0699574 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 29.8038 | 1.40030 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.31456 | −0.296031 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −38.5083 | −1.80134 | −0.900670 | − | 0.434504i | \(-0.856924\pi\) | ||||
−0.900670 | + | 0.434504i | \(0.856924\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −22.0494 | −1.02918 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.2933 | 1.73692 | 0.868460 | − | 0.495759i | \(-0.165110\pi\) | ||||
0.868460 | + | 0.495759i | \(0.165110\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.1601 | 1.12282 | 0.561408 | − | 0.827539i | \(-0.310260\pi\) | ||||
0.561408 | + | 0.827539i | \(0.310260\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17.7111 | −0.821331 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.64767 | 0.400166 | 0.200083 | − | 0.979779i | \(-0.435879\pi\) | ||||
0.200083 | + | 0.979779i | \(0.435879\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.16634 | 0.100032 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.0636 | 0.740172 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.98152 | −0.137091 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.18272 | 0.100150 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.08324 | −0.0495983 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.3240 | 0.471718 | 0.235859 | − | 0.971787i | \(-0.424210\pi\) | ||||
0.235859 | + | 0.971787i | \(0.424210\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.9393 | 1.04594 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.76334 | 0.262241 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.93047 | 0.314696 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.2407 | 1.59691 | 0.798454 | − | 0.602056i | \(-0.205651\pi\) | ||||
0.798454 | + | 0.602056i | \(0.205651\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.3915 | 0.741251 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.8607 | 1.66350 | 0.831751 | − | 0.555149i | \(-0.187339\pi\) | ||||
0.831751 | + | 0.555149i | \(0.187339\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.8637 | 0.714465 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.60934 | 0.0723345 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.7397 | −0.661167 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.4943 | 1.49941 | 0.749706 | − | 0.661771i | \(-0.230195\pi\) | ||||
0.749706 | + | 0.661771i | \(0.230195\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.1745 | 0.901330 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.8665 | 1.10874 | 0.554370 | − | 0.832270i | \(-0.312959\pi\) | ||||
0.554370 | + | 0.832270i | \(0.312959\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.5762 | 0.604133 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.3763 | −0.460829 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.15050 | 0.272616 | 0.136308 | − | 0.990667i | \(-0.456476\pi\) | ||||
0.136308 | + | 0.990667i | \(0.456476\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.46127 | 0.241592 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.7432 | −0.474325 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.1179 | −0.842435 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.398954 | −0.0175460 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.58912 | −0.245335 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.8734 | 1.26497 | 0.632483 | − | 0.774574i | \(-0.282036\pi\) | ||||
0.632483 | + | 0.774574i | \(0.282036\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.9944 | 0.611931 | 0.305965 | − | 0.952043i | \(-0.401021\pi\) | ||||
0.305965 | + | 0.952043i | \(0.401021\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.78958 | 0.0781037 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.9245 | 0.780805 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.0354 | −0.436321 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.04144 | −0.0451948 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.55292 | 0.110579 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.2922 | 0.834073 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.2696 | 0.572625 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.48567 | 0.0639922 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.42199 | −0.362090 | −0.181045 | − | 0.983475i | \(-0.557948\pi\) | ||||
−0.181045 | + | 0.983475i | \(0.557948\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.70263 | 0.0730667 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.6673 | 0.499773 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.38048 | −0.315566 | −0.157783 | − | 0.987474i | \(-0.550435\pi\) | ||||
−0.157783 | + | 0.987474i | \(0.550435\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.42314 | −0.0607383 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.72933 | 0.329281 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.2785 | 0.564657 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −35.5749 | −1.51007 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.7185 | 0.920242 | 0.460121 | − | 0.887856i | \(-0.347806\pi\) | ||||
0.460121 | + | 0.887856i | \(0.347806\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.12335 | −0.216694 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.52840 | 0.402289 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.3047 | −0.518581 | −0.259291 | − | 0.965799i | \(-0.583489\pi\) | ||||
−0.259291 | + | 0.965799i | \(0.583489\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 38.6623 | 1.62654 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.49437 | −0.314734 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.4711 | 0.690504 | 0.345252 | − | 0.938510i | \(-0.387794\pi\) | ||||
0.345252 | + | 0.938510i | \(0.387794\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.46234 | −0.312289 | −0.156145 | − | 0.987734i | \(-0.549907\pi\) | ||||
−0.156145 | + | 0.987734i | \(0.549907\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.46806 | 0.186656 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.02566 | 0.167882 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.2121 | −0.924703 | −0.462352 | − | 0.886697i | \(-0.652994\pi\) | ||||
−0.462352 | + | 0.886697i | \(0.652994\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.35204 | 0.180865 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.73973 | −0.362585 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.67475 | 0.152193 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.76543 | 0.114337 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.9587 | −1.23653 | −0.618264 | − | 0.785971i | \(-0.712164\pi\) | ||||
−0.618264 | + | 0.785971i | \(0.712164\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.73345 | 0.359856 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −31.2731 | −1.28640 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.60881 | −0.271391 | −0.135696 | − | 0.990751i | \(-0.543327\pi\) | ||||
−0.135696 | + | 0.990751i | \(0.543327\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.91083 | −0.406304 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21.9984 | 0.900337 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.6199 | −0.679071 | −0.339535 | − | 0.940593i | \(-0.610270\pi\) | ||||
−0.339535 | + | 0.940593i | \(0.610270\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.81524 | 0.114836 | 0.0574180 | − | 0.998350i | \(-0.481713\pi\) | ||||
0.0574180 | + | 0.998350i | \(0.481713\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.948741 | −0.0386357 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.7487 | 0.884210 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.70796 | −0.191090 | −0.0955452 | − | 0.995425i | \(-0.530459\pi\) | ||||
−0.0955452 | + | 0.995425i | \(0.530459\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.33716 | 0.256795 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.685549 | −0.0277343 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.5857 | −1.35651 | −0.678257 | − | 0.734825i | \(-0.737264\pi\) | ||||
−0.678257 | + | 0.734825i | \(0.737264\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.95914 | −0.159648 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.1069 | 0.406887 | 0.203443 | − | 0.979087i | \(-0.434787\pi\) | ||||
0.203443 | + | 0.979087i | \(0.434787\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.2098 | −0.611334 | −0.305667 | − | 0.952139i | \(-0.598879\pi\) | ||||
−0.305667 | + | 0.952139i | \(0.598879\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −19.8140 | −0.795110 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.21533 | 0.128819 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.3402 | −1.17361 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.64256 | 0.185406 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 36.0037 | 1.43556 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.8417 | −1.18798 | −0.593990 | − | 0.804473i | \(-0.702448\pi\) | ||||
−0.593990 | + | 0.804473i | \(0.702448\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.4656 | 0.614702 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 42.8471 | 1.70033 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.55292 | 0.101150 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.45520 | 0.255364 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.7674 | −0.780767 | −0.390384 | − | 0.920652i | \(-0.627658\pi\) | ||||
−0.390384 | + | 0.920652i | \(0.627658\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.55248 | −0.297841 | −0.148920 | − | 0.988849i | \(-0.547580\pi\) | ||||
−0.148920 | + | 0.988849i | \(0.547580\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.94542 | 0.312851 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.3795 | 0.919144 | 0.459572 | − | 0.888140i | \(-0.348003\pi\) | ||||
0.459572 | + | 0.888140i | \(0.348003\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.53295 | 0.138680 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.16042 | 0.280639 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.9764 | 1.72093 | 0.860464 | − | 0.509511i | \(-0.170174\pi\) | ||||
0.860464 | + | 0.509511i | \(0.170174\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 40.6750 | 1.58930 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.39174 | −0.0933106 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.3823 | −0.949801 | −0.474901 | − | 0.880039i | \(-0.657516\pi\) | ||||
−0.474901 | + | 0.880039i | \(0.657516\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0954 | 0.548249 | 0.274125 | − | 0.961694i | \(-0.411612\pi\) | ||||
0.274125 | + | 0.961694i | \(0.411612\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.3733 | 0.635885 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.82889 | −0.187256 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.2554 | 0.551972 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22.9443 | −0.887076 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.82781 | 0.186376 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.8755 | 1.53709 | 0.768544 | − | 0.639797i | \(-0.220982\pi\) | ||||
0.768544 | + | 0.639797i | \(0.220982\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.15248 | −0.236809 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.1023 | −1.23379 | −0.616896 | − | 0.787045i | \(-0.711610\pi\) | ||||
−0.616896 | + | 0.787045i | \(0.711610\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.80193 | −0.107528 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.83850 | −0.147092 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.5202 | 0.670391 | 0.335195 | − | 0.942149i | \(-0.391198\pi\) | ||||
0.335195 | + | 0.942149i | \(0.391198\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 37.8092 | 1.44461 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.82674 | −0.260456 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.31456 | 0.240566 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.08090 | 0.155245 | 0.0776225 | − | 0.996983i | \(-0.475267\pi\) | ||||
0.0776225 | + | 0.996983i | \(0.475267\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.650642 | −0.0247158 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −26.0559 | −0.988358 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00686 | 0.151771 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.5443 | −0.777056 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.6923 | −0.781536 | −0.390768 | − | 0.920489i | \(-0.627790\pi\) | ||||
−0.390768 | + | 0.920489i | \(0.627790\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.5422 | 0.661618 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.06317 | 0.0400412 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.48873 | −0.206425 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.7685 | 1.26820 | 0.634102 | − | 0.773250i | \(-0.281370\pi\) | ||||
0.634102 | + | 0.773250i | \(0.281370\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.81524 | −0.218089 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.1074 | 0.603225 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.38134 | −0.350842 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.6215 | −0.695431 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36.2970 | −1.35365 | −0.676825 | − | 0.736144i | \(-0.736645\pi\) | ||||
−0.676825 | + | 0.736144i | \(0.736645\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.72919 | 0.287850 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22.0863 | −0.821400 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.42647 | 0.164395 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.1013 | −0.819691 | −0.409846 | − | 0.912155i | \(-0.634417\pi\) | ||||
−0.409846 | + | 0.912155i | \(0.634417\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.7067 | 1.10025 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.04119 | −0.297414 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.75923 | 0.212722 | 0.106361 | − | 0.994328i | \(-0.466080\pi\) | ||||
0.106361 | + | 0.994328i | \(0.466080\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.95914 | −0.146035 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.21847 | 0.118554 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.2456 | −0.560820 | −0.280410 | − | 0.959880i | \(-0.590470\pi\) | ||||
−0.280410 | + | 0.959880i | \(0.590470\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.97761 | 0.293065 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.62428 | −0.279708 | −0.139854 | − | 0.990172i | \(-0.544663\pi\) | ||||
−0.139854 | + | 0.990172i | \(0.544663\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.65050 | 0.170381 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.82752 | 0.140042 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.79965 | −0.284993 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.6531 | −0.425228 | −0.212614 | − | 0.977136i | \(-0.568198\pi\) | ||||
−0.212614 | + | 0.977136i | \(0.568198\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.60342 | 0.240642 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −46.0557 | −1.67614 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.5722 | −0.493288 | −0.246644 | − | 0.969106i | \(-0.579328\pi\) | ||||
−0.246644 | + | 0.969106i | \(0.579328\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.56241 | 0.310796 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.3416 | −1.35363 | −0.676815 | − | 0.736153i | \(-0.736640\pi\) | ||||
−0.676815 | + | 0.736153i | \(0.736640\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.71699 | −0.170766 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.34040 | 0.156928 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.07090 | 0.219207 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.1074 | 1.26601 | 0.633003 | − | 0.774149i | \(-0.281822\pi\) | ||||
0.633003 | + | 0.774149i | \(0.281822\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.262378 | −0.00944932 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.5320 | −0.666550 | −0.333275 | − | 0.942830i | \(-0.608154\pi\) | ||||
−0.333275 | + | 0.942830i | \(0.608154\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.00151 | 0.179660 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.3826 | 0.515973 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.95228 | 0.0699476 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.8983 | −0.783584 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.7868 | −0.778597 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24.8230 | −0.885972 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.4031 | 1.15505 | 0.577524 | − | 0.816374i | \(-0.304019\pi\) | ||||
0.577524 | + | 0.816374i | \(0.304019\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.9980 | 0.427142 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.6308 | −0.555768 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.29594 | 0.294597 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.79279 | −0.347314 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.8991 | −0.811129 | −0.405565 | − | 0.914066i | \(-0.632925\pi\) | ||||
−0.405565 | + | 0.914066i | \(0.632925\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.07598 | −0.0380655 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.40814 | −0.0497541 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.11363 | 0.286324 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.90607 | −0.313898 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 40.2265 | 1.41604 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.4414 | −0.402259 | −0.201129 | − | 0.979565i | \(-0.564461\pi\) | ||||
−0.201129 | + | 0.979565i | \(0.564461\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.26979 | −0.220162 | −0.110081 | − | 0.993923i | \(-0.535111\pi\) | ||||
−0.110081 | + | 0.993923i | \(0.535111\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.6876 | −0.971046 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.3298 | −0.887264 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.91794 | −0.137071 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.11804 | −0.0390675 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.74037 | −0.270141 | −0.135070 | − | 0.990836i | \(-0.543126\pi\) | ||||
−0.135070 | + | 0.990836i | \(0.543126\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.5868 | −0.891900 | −0.445950 | − | 0.895058i | \(-0.647134\pi\) | ||||
−0.445950 | + | 0.895058i | \(0.647134\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.65872 | 0.0925649 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.3085 | 0.740969 | 0.370484 | − | 0.928839i | \(-0.379192\pi\) | ||||
0.370484 | + | 0.928839i | \(0.379192\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.5631 | 1.23516 | 0.617579 | − | 0.786509i | \(-0.288113\pi\) | ||||
0.617579 | + | 0.786509i | \(0.288113\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.6726 | −0.821193 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.00686 | 0.138829 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.1756 | −1.07888 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −24.6171 | −0.850893 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.7213 | 1.54395 | 0.771976 | − | 0.635652i | \(-0.219269\pi\) | ||||
0.771976 | + | 0.635652i | \(0.219269\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.3252 | −0.459491 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.53353 | −0.293910 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.0345 | 0.551604 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.79279 | −0.302124 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.80782 | 0.336604 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32.3536 | 1.10907 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −51.1574 | −1.75160 | −0.875798 | − | 0.482679i | \(-0.839664\pi\) | ||||
−0.875798 | + | 0.482679i | \(0.839664\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.11479 | 0.0723244 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.0528 | 1.09490 | 0.547452 | − | 0.836837i | \(-0.315598\pi\) | ||||
0.547452 | + | 0.836837i | \(0.315598\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.0209 | 0.819584 | 0.409792 | − | 0.912179i | \(-0.365601\pi\) | ||||
0.409792 | + | 0.912179i | \(0.365601\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.60064 | 0.0545497 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.0819 | 0.581476 | 0.290738 | − | 0.956803i | \(-0.406099\pi\) | ||||
0.290738 | + | 0.956803i | \(0.406099\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.63685 | 0.293662 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.51276 | −0.0513759 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.7274 | 0.669206 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.53050 | 0.187394 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.22709 | 0.0415307 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.60190 | 0.324604 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.8241 | 1.24346 | 0.621730 | − | 0.783231i | \(-0.286430\pi\) | ||||
0.621730 | + | 0.783231i | \(0.286430\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.8383 | 0.466753 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.6341 | −0.695180 | −0.347590 | − | 0.937647i | \(-0.613000\pi\) | ||||
−0.347590 | + | 0.937647i | \(0.613000\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.6324 | 0.929903 | 0.464952 | − | 0.885336i | \(-0.346072\pi\) | ||||
0.464952 | + | 0.885336i | \(0.346072\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.41491 | −0.316479 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.00146 | −0.100779 | −0.0503896 | − | 0.998730i | \(-0.516046\pi\) | ||||
−0.0503896 | + | 0.998730i | \(0.516046\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.3227 | −0.580984 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.1341 | −0.373008 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.524255 | −0.0175435 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.5054 | −0.685421 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.7133 | 0.491264 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.7111 | 0.590697 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.91083 | 0.330178 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.21226 | −0.106897 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.63106 | −0.0874595 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.6479 | 1.38290 | 0.691448 | − | 0.722426i | \(-0.256973\pi\) | ||||
0.691448 | + | 0.722426i | \(0.256973\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.40377 | 0.0797279 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.5434 | −1.07821 | −0.539106 | − | 0.842238i | \(-0.681238\pi\) | ||||
−0.539106 | + | 0.842238i | \(0.681238\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.9843 | −0.429719 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12.8656 | −0.425322 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.4445 | −0.543046 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.91249 | −0.129061 | −0.0645306 | − | 0.997916i | \(-0.520555\pi\) | ||||
−0.0645306 | + | 0.997916i | \(0.520555\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.5379 | −0.907406 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −37.6293 | −1.23858 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.0462 | 0.330316 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.38496 | −0.111177 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.6363 | −0.808291 | −0.404145 | − | 0.914695i | \(-0.632431\pi\) | ||||
−0.404145 | + | 0.914695i | \(0.632431\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.95228 | 0.0639833 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −40.5804 | −1.32854 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.7242 | −0.481533 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.8006 | −0.777530 | −0.388765 | − | 0.921337i | \(-0.627098\pi\) | ||||
−0.388765 | + | 0.921337i | \(0.627098\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.7624 | −0.481753 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.7599 | 1.10054 | 0.550271 | − | 0.834986i | \(-0.314524\pi\) | ||||
0.550271 | + | 0.834986i | \(0.314524\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.60064 | 0.117253 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.6113 | 0.442775 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.7783 | −0.870178 | −0.435089 | − | 0.900387i | \(-0.643283\pi\) | ||||
−0.435089 | + | 0.900387i | \(0.643283\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.9422 | 0.452582 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.54323 | −0.114897 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.41776 | −0.110712 | −0.0553560 | − | 0.998467i | \(-0.517629\pi\) | ||||
−0.0553560 | + | 0.998467i | \(0.517629\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.90449 | −0.223424 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.41491 | 0.304341 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.2859 | −0.493607 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.9881 | −0.354455 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.41582 | 0.110073 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.72520 | −0.216492 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.23940 | 0.297119 | 0.148560 | − | 0.988903i | \(-0.452536\pi\) | ||||
0.148560 | + | 0.988903i | \(0.452536\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.5210 | 0.402233 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.2701 | 0.618406 | 0.309203 | − | 0.950996i | \(-0.399938\pi\) | ||||
0.309203 | + | 0.950996i | \(0.399938\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.5342 | 0.337710 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.56866 | 0.146314 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.89539 | −0.316582 | −0.158291 | − | 0.987393i | \(-0.550598\pi\) | ||||
−0.158291 | + | 0.987393i | \(0.550598\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.77691 | 0.152671 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.06578 | 0.0659554 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.81719 | 0.0579594 | 0.0289797 | − | 0.999580i | \(-0.490774\pi\) | ||||
0.0289797 | + | 0.999580i | \(0.490774\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48.3263 | 1.53980 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.429829 | −0.0136816 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.22598 | −0.229773 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.96926 | 0.221386 | 0.110693 | − | 0.993855i | \(-0.464693\pi\) | ||||
0.110693 | + | 0.993855i | \(0.464693\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.7981 | 0.437871 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −33.9941 | −1.07769 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.3816 | 0.993865 | 0.496932 | − | 0.867789i | \(-0.334460\pi\) | ||||
0.496932 | + | 0.867789i | \(0.334460\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −49.4466 | −1.56442 |
(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 | 1148.2.a.e.1.4 | ✓ | 5 | |
4.3 | odd | 2 | 4592.2.a.bd.1.2 | 5 | |||
7.6 | odd | 2 | 8036.2.a.j.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.a.e.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial | |
4592.2.a.bd.1.2 | 5 | 4.3 | odd | 2 | |||
8036.2.a.j.1.2 | 5 | 7.6 | odd | 2 |