Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} - 19 x^{12} + 36 x^{11} + 134 x^{10} - 237 x^{9} - 438 x^{8} + 716 x^{7} + 662 x^{6} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.64093\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.64093 | −1.16032 | −0.580158 | − | 0.814504i | \(-0.697009\pi\) | ||||
−0.580158 | + | 0.814504i | \(0.697009\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.692668 | 0.346334 | ||||||||
\(5\) | 0.0817657 | 0.0365667 | 0.0182834 | − | 0.999833i | \(-0.494180\pi\) | ||||
0.0182834 | + | 0.999833i | \(0.494180\pi\) | |||||||
\(6\) | −1.64093 | −0.669909 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.14525 | 0.758459 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.134172 | −0.0424290 | ||||||||
\(11\) | −4.94328 | −1.49046 | −0.745228 | − | 0.666810i | \(-0.767659\pi\) | ||||
−0.745228 | + | 0.666810i | \(0.767659\pi\) | |||||||
\(12\) | 0.692668 | 0.199956 | ||||||||
\(13\) | 1.23171 | 0.341616 | 0.170808 | − | 0.985304i | \(-0.445362\pi\) | ||||
0.170808 | + | 0.985304i | \(0.445362\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0817657 | 0.0211118 | ||||||||
\(16\) | −4.90555 | −1.22639 | ||||||||
\(17\) | −0.810235 | −0.196511 | −0.0982555 | − | 0.995161i | \(-0.531326\pi\) | ||||
−0.0982555 | + | 0.995161i | \(0.531326\pi\) | |||||||
\(18\) | −1.64093 | −0.386772 | ||||||||
\(19\) | 6.55953 | 1.50486 | 0.752430 | − | 0.658673i | \(-0.228882\pi\) | ||||
0.752430 | + | 0.658673i | \(0.228882\pi\) | |||||||
\(20\) | 0.0566365 | 0.0126643 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.11161 | 1.72940 | ||||||||
\(23\) | −5.53945 | −1.15506 | −0.577528 | − | 0.816371i | \(-0.695983\pi\) | ||||
−0.577528 | + | 0.816371i | \(0.695983\pi\) | |||||||
\(24\) | 2.14525 | 0.437897 | ||||||||
\(25\) | −4.99331 | −0.998663 | ||||||||
\(26\) | −2.02116 | −0.396382 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0447280 | −0.00830578 | −0.00415289 | − | 0.999991i | \(-0.501322\pi\) | ||||
−0.00415289 | + | 0.999991i | \(0.501322\pi\) | |||||||
\(30\) | −0.134172 | −0.0244964 | ||||||||
\(31\) | 7.20734 | 1.29448 | 0.647238 | − | 0.762288i | \(-0.275924\pi\) | ||||
0.647238 | + | 0.762288i | \(0.275924\pi\) | |||||||
\(32\) | 3.75919 | 0.664537 | ||||||||
\(33\) | −4.94328 | −0.860515 | ||||||||
\(34\) | 1.32954 | 0.228015 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.692668 | 0.115445 | ||||||||
\(37\) | 5.22958 | 0.859737 | 0.429869 | − | 0.902891i | \(-0.358560\pi\) | ||||
0.429869 | + | 0.902891i | \(0.358560\pi\) | |||||||
\(38\) | −10.7638 | −1.74611 | ||||||||
\(39\) | 1.23171 | 0.197232 | ||||||||
\(40\) | 0.175408 | 0.0277344 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.64881 | −1.31893 | −0.659466 | − | 0.751735i | \(-0.729217\pi\) | ||||
−0.659466 | + | 0.751735i | \(0.729217\pi\) | |||||||
\(44\) | −3.42405 | −0.516195 | ||||||||
\(45\) | 0.0817657 | 0.0121889 | ||||||||
\(46\) | 9.08988 | 1.34023 | ||||||||
\(47\) | 10.9081 | 1.59111 | 0.795556 | − | 0.605881i | \(-0.207179\pi\) | ||||
0.795556 | + | 0.605881i | \(0.207179\pi\) | |||||||
\(48\) | −4.90555 | −0.708055 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 8.19370 | 1.15876 | ||||||||
\(51\) | −0.810235 | −0.113456 | ||||||||
\(52\) | 0.853167 | 0.118313 | ||||||||
\(53\) | −5.99240 | −0.823120 | −0.411560 | − | 0.911383i | \(-0.635016\pi\) | ||||
−0.411560 | + | 0.911383i | \(0.635016\pi\) | |||||||
\(54\) | −1.64093 | −0.223303 | ||||||||
\(55\) | −0.404191 | −0.0545011 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.55953 | 0.868831 | ||||||||
\(58\) | 0.0733957 | 0.00963733 | ||||||||
\(59\) | −4.34053 | −0.565089 | −0.282544 | − | 0.959254i | \(-0.591178\pi\) | ||||
−0.282544 | + | 0.959254i | \(0.591178\pi\) | |||||||
\(60\) | 0.0566365 | 0.00731174 | ||||||||
\(61\) | 1.13380 | 0.145168 | 0.0725842 | − | 0.997362i | \(-0.476875\pi\) | ||||
0.0725842 | + | 0.997362i | \(0.476875\pi\) | |||||||
\(62\) | −11.8268 | −1.50200 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.64251 | 0.455314 | ||||||||
\(65\) | 0.100712 | 0.0124918 | ||||||||
\(66\) | 8.11161 | 0.998470 | ||||||||
\(67\) | −2.70626 | −0.330622 | −0.165311 | − | 0.986241i | \(-0.552863\pi\) | ||||
−0.165311 | + | 0.986241i | \(0.552863\pi\) | |||||||
\(68\) | −0.561224 | −0.0680584 | ||||||||
\(69\) | −5.53945 | −0.666872 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.56029 | −0.659885 | −0.329943 | − | 0.944001i | \(-0.607029\pi\) | ||||
−0.329943 | + | 0.944001i | \(0.607029\pi\) | |||||||
\(72\) | 2.14525 | 0.252820 | ||||||||
\(73\) | −14.5072 | −1.69794 | −0.848972 | − | 0.528438i | \(-0.822778\pi\) | ||||
−0.848972 | + | 0.528438i | \(0.822778\pi\) | |||||||
\(74\) | −8.58140 | −0.997567 | ||||||||
\(75\) | −4.99331 | −0.576578 | ||||||||
\(76\) | 4.54357 | 0.521184 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.02116 | −0.228851 | ||||||||
\(79\) | 15.5574 | 1.75034 | 0.875171 | − | 0.483813i | \(-0.160749\pi\) | ||||
0.875171 | + | 0.483813i | \(0.160749\pi\) | |||||||
\(80\) | −0.401106 | −0.0448450 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.64093 | 0.181211 | ||||||||
\(83\) | 9.02538 | 0.990664 | 0.495332 | − | 0.868704i | \(-0.335046\pi\) | ||||
0.495332 | + | 0.868704i | \(0.335046\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0662495 | −0.00718577 | ||||||||
\(86\) | 14.1921 | 1.53038 | ||||||||
\(87\) | −0.0447280 | −0.00479534 | ||||||||
\(88\) | −10.6046 | −1.13045 | ||||||||
\(89\) | 7.38768 | 0.783093 | 0.391546 | − | 0.920158i | \(-0.371940\pi\) | ||||
0.391546 | + | 0.920158i | \(0.371940\pi\) | |||||||
\(90\) | −0.134172 | −0.0141430 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.83700 | −0.400035 | ||||||||
\(93\) | 7.20734 | 0.747366 | ||||||||
\(94\) | −17.8995 | −1.84619 | ||||||||
\(95\) | 0.536345 | 0.0550278 | ||||||||
\(96\) | 3.75919 | 0.383671 | ||||||||
\(97\) | 5.44556 | 0.552912 | 0.276456 | − | 0.961027i | \(-0.410840\pi\) | ||||
0.276456 | + | 0.961027i | \(0.410840\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.94328 | −0.496819 | ||||||||
\(100\) | −3.45871 | −0.345871 | ||||||||
\(101\) | −3.78486 | −0.376607 | −0.188304 | − | 0.982111i | \(-0.560299\pi\) | ||||
−0.188304 | + | 0.982111i | \(0.560299\pi\) | |||||||
\(102\) | 1.32954 | 0.131644 | ||||||||
\(103\) | −19.1368 | −1.88561 | −0.942804 | − | 0.333349i | \(-0.891821\pi\) | ||||
−0.942804 | + | 0.333349i | \(0.891821\pi\) | |||||||
\(104\) | 2.64233 | 0.259102 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.83314 | 0.955079 | ||||||||
\(107\) | −13.5411 | −1.30907 | −0.654534 | − | 0.756032i | \(-0.727135\pi\) | ||||
−0.654534 | + | 0.756032i | \(0.727135\pi\) | |||||||
\(108\) | 0.692668 | 0.0666520 | ||||||||
\(109\) | 0.705015 | 0.0675282 | 0.0337641 | − | 0.999430i | \(-0.489251\pi\) | ||||
0.0337641 | + | 0.999430i | \(0.489251\pi\) | |||||||
\(110\) | 0.663251 | 0.0632385 | ||||||||
\(111\) | 5.22958 | 0.496370 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.6339 | −1.09443 | −0.547213 | − | 0.836993i | \(-0.684311\pi\) | ||||
−0.547213 | + | 0.836993i | \(0.684311\pi\) | |||||||
\(114\) | −10.7638 | −1.00812 | ||||||||
\(115\) | −0.452937 | −0.0422366 | ||||||||
\(116\) | −0.0309816 | −0.00287657 | ||||||||
\(117\) | 1.23171 | 0.113872 | ||||||||
\(118\) | 7.12253 | 0.655682 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.175408 | 0.0160125 | ||||||||
\(121\) | 13.4360 | 1.22146 | ||||||||
\(122\) | −1.86049 | −0.168441 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | 4.99229 | 0.448321 | ||||||||
\(125\) | −0.817110 | −0.0730846 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.52451 | −0.224014 | −0.112007 | − | 0.993707i | \(-0.535728\pi\) | ||||
−0.112007 | + | 0.993707i | \(0.535728\pi\) | |||||||
\(128\) | −13.4955 | −1.19284 | ||||||||
\(129\) | −8.64881 | −0.761485 | ||||||||
\(130\) | −0.165262 | −0.0144944 | ||||||||
\(131\) | −10.8567 | −0.948553 | −0.474277 | − | 0.880376i | \(-0.657290\pi\) | ||||
−0.474277 | + | 0.880376i | \(0.657290\pi\) | |||||||
\(132\) | −3.42405 | −0.298025 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.44080 | 0.383626 | ||||||||
\(135\) | 0.0817657 | 0.00703727 | ||||||||
\(136\) | −1.73816 | −0.149046 | ||||||||
\(137\) | −10.3736 | −0.886277 | −0.443138 | − | 0.896453i | \(-0.646135\pi\) | ||||
−0.443138 | + | 0.896453i | \(0.646135\pi\) | |||||||
\(138\) | 9.08988 | 0.773782 | ||||||||
\(139\) | −3.46799 | −0.294151 | −0.147075 | − | 0.989125i | \(-0.546986\pi\) | ||||
−0.147075 | + | 0.989125i | \(0.546986\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.9081 | 0.918628 | ||||||||
\(142\) | 9.12408 | 0.765676 | ||||||||
\(143\) | −6.08870 | −0.509163 | ||||||||
\(144\) | −4.90555 | −0.408796 | ||||||||
\(145\) | −0.00365722 | −0.000303715 0 | ||||||||
\(146\) | 23.8054 | 1.97015 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.62236 | 0.297756 | ||||||||
\(149\) | 22.9065 | 1.87657 | 0.938287 | − | 0.345857i | \(-0.112412\pi\) | ||||
0.938287 | + | 0.345857i | \(0.112412\pi\) | |||||||
\(150\) | 8.19370 | 0.669013 | ||||||||
\(151\) | −22.3577 | −1.81945 | −0.909724 | − | 0.415214i | \(-0.863707\pi\) | ||||
−0.909724 | + | 0.415214i | \(0.863707\pi\) | |||||||
\(152\) | 14.0718 | 1.14137 | ||||||||
\(153\) | −0.810235 | −0.0655037 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.589313 | 0.0473348 | ||||||||
\(156\) | 0.853167 | 0.0683081 | ||||||||
\(157\) | 12.9470 | 1.03328 | 0.516640 | − | 0.856203i | \(-0.327182\pi\) | ||||
0.516640 | + | 0.856203i | \(0.327182\pi\) | |||||||
\(158\) | −25.5287 | −2.03095 | ||||||||
\(159\) | −5.99240 | −0.475228 | ||||||||
\(160\) | 0.307373 | 0.0242999 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.64093 | −0.128924 | ||||||||
\(163\) | 2.36528 | 0.185263 | 0.0926313 | − | 0.995700i | \(-0.470472\pi\) | ||||
0.0926313 | + | 0.995700i | \(0.470472\pi\) | |||||||
\(164\) | −0.692668 | −0.0540883 | ||||||||
\(165\) | −0.404191 | −0.0314662 | ||||||||
\(166\) | −14.8101 | −1.14948 | ||||||||
\(167\) | 14.7792 | 1.14365 | 0.571824 | − | 0.820377i | \(-0.306236\pi\) | ||||
0.571824 | + | 0.820377i | \(0.306236\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4829 | −0.883299 | ||||||||
\(170\) | 0.108711 | 0.00833776 | ||||||||
\(171\) | 6.55953 | 0.501620 | ||||||||
\(172\) | −5.99075 | −0.456790 | ||||||||
\(173\) | −10.5024 | −0.798479 | −0.399239 | − | 0.916847i | \(-0.630726\pi\) | ||||
−0.399239 | + | 0.916847i | \(0.630726\pi\) | |||||||
\(174\) | 0.0733957 | 0.00556411 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 24.2495 | 1.82788 | ||||||||
\(177\) | −4.34053 | −0.326254 | ||||||||
\(178\) | −12.1227 | −0.908635 | ||||||||
\(179\) | −6.55231 | −0.489743 | −0.244871 | − | 0.969556i | \(-0.578746\pi\) | ||||
−0.244871 | + | 0.969556i | \(0.578746\pi\) | |||||||
\(180\) | 0.0566365 | 0.00422143 | ||||||||
\(181\) | −2.05872 | −0.153023 | −0.0765115 | − | 0.997069i | \(-0.524378\pi\) | ||||
−0.0765115 | + | 0.997069i | \(0.524378\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.13380 | 0.0838130 | ||||||||
\(184\) | −11.8835 | −0.876063 | ||||||||
\(185\) | 0.427600 | 0.0314378 | ||||||||
\(186\) | −11.8268 | −0.867181 | ||||||||
\(187\) | 4.00522 | 0.292891 | ||||||||
\(188\) | 7.55569 | 0.551056 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.880107 | −0.0638496 | ||||||||
\(191\) | −18.4559 | −1.33542 | −0.667712 | − | 0.744419i | \(-0.732726\pi\) | ||||
−0.667712 | + | 0.744419i | \(0.732726\pi\) | |||||||
\(192\) | 3.64251 | 0.262875 | ||||||||
\(193\) | 22.7365 | 1.63661 | 0.818304 | − | 0.574786i | \(-0.194915\pi\) | ||||
0.818304 | + | 0.574786i | \(0.194915\pi\) | |||||||
\(194\) | −8.93580 | −0.641553 | ||||||||
\(195\) | 0.100712 | 0.00721213 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.89397 | 0.134940 | 0.0674698 | − | 0.997721i | \(-0.478507\pi\) | ||||
0.0674698 | + | 0.997721i | \(0.478507\pi\) | |||||||
\(198\) | 8.11161 | 0.576467 | ||||||||
\(199\) | 20.6802 | 1.46598 | 0.732989 | − | 0.680241i | \(-0.238125\pi\) | ||||
0.732989 | + | 0.680241i | \(0.238125\pi\) | |||||||
\(200\) | −10.7119 | −0.757445 | ||||||||
\(201\) | −2.70626 | −0.190885 | ||||||||
\(202\) | 6.21070 | 0.436984 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.561224 | −0.0392935 | ||||||||
\(205\) | −0.0817657 | −0.00571077 | ||||||||
\(206\) | 31.4023 | 2.18790 | ||||||||
\(207\) | −5.53945 | −0.385019 | ||||||||
\(208\) | −6.04222 | −0.418953 | ||||||||
\(209\) | −32.4256 | −2.24293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.73506 | −0.601346 | −0.300673 | − | 0.953727i | \(-0.597211\pi\) | ||||
−0.300673 | + | 0.953727i | \(0.597211\pi\) | |||||||
\(212\) | −4.15074 | −0.285074 | ||||||||
\(213\) | −5.56029 | −0.380985 | ||||||||
\(214\) | 22.2201 | 1.51893 | ||||||||
\(215\) | −0.707176 | −0.0482290 | ||||||||
\(216\) | 2.14525 | 0.145966 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.15688 | −0.0783541 | ||||||||
\(219\) | −14.5072 | −0.980308 | ||||||||
\(220\) | −0.279970 | −0.0188756 | ||||||||
\(221\) | −0.997977 | −0.0671312 | ||||||||
\(222\) | −8.58140 | −0.575946 | ||||||||
\(223\) | 12.8945 | 0.863483 | 0.431741 | − | 0.901997i | \(-0.357899\pi\) | ||||
0.431741 | + | 0.901997i | \(0.357899\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.99331 | −0.332888 | ||||||||
\(226\) | 19.0905 | 1.26988 | ||||||||
\(227\) | −18.9009 | −1.25450 | −0.627248 | − | 0.778820i | \(-0.715819\pi\) | ||||
−0.627248 | + | 0.778820i | \(0.715819\pi\) | |||||||
\(228\) | 4.54357 | 0.300905 | ||||||||
\(229\) | −1.43656 | −0.0949305 | −0.0474652 | − | 0.998873i | \(-0.515114\pi\) | ||||
−0.0474652 | + | 0.998873i | \(0.515114\pi\) | |||||||
\(230\) | 0.743241 | 0.0490078 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.0959526 | −0.00629960 | ||||||||
\(233\) | −14.7809 | −0.968331 | −0.484166 | − | 0.874976i | \(-0.660877\pi\) | ||||
−0.484166 | + | 0.874976i | \(0.660877\pi\) | |||||||
\(234\) | −2.02116 | −0.132127 | ||||||||
\(235\) | 0.891909 | 0.0581817 | ||||||||
\(236\) | −3.00655 | −0.195709 | ||||||||
\(237\) | 15.5574 | 1.01056 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.03844 | −0.0671712 | −0.0335856 | − | 0.999436i | \(-0.510693\pi\) | ||||
−0.0335856 | + | 0.999436i | \(0.510693\pi\) | |||||||
\(240\) | −0.401106 | −0.0258913 | ||||||||
\(241\) | −24.3864 | −1.57087 | −0.785433 | − | 0.618947i | \(-0.787559\pi\) | ||||
−0.785433 | + | 0.618947i | \(0.787559\pi\) | |||||||
\(242\) | −22.0477 | −1.41728 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.785347 | 0.0502767 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.64093 | 0.104622 | ||||||||
\(247\) | 8.07945 | 0.514083 | ||||||||
\(248\) | 15.4615 | 0.981808 | ||||||||
\(249\) | 9.02538 | 0.571960 | ||||||||
\(250\) | 1.34083 | 0.0848012 | ||||||||
\(251\) | −10.4072 | −0.656898 | −0.328449 | − | 0.944522i | \(-0.606526\pi\) | ||||
−0.328449 | + | 0.944522i | \(0.606526\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.3831 | 1.72156 | ||||||||
\(254\) | 4.14255 | 0.259927 | ||||||||
\(255\) | −0.0662495 | −0.00414870 | ||||||||
\(256\) | 14.8602 | 0.928764 | ||||||||
\(257\) | 18.1220 | 1.13042 | 0.565210 | − | 0.824947i | \(-0.308795\pi\) | ||||
0.565210 | + | 0.824947i | \(0.308795\pi\) | |||||||
\(258\) | 14.1921 | 0.883564 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.0697598 | 0.00432632 | ||||||||
\(261\) | −0.0447280 | −0.00276859 | ||||||||
\(262\) | 17.8151 | 1.10062 | ||||||||
\(263\) | −2.84868 | −0.175657 | −0.0878284 | − | 0.996136i | \(-0.527993\pi\) | ||||
−0.0878284 | + | 0.996136i | \(0.527993\pi\) | |||||||
\(264\) | −10.6046 | −0.652666 | ||||||||
\(265\) | −0.489973 | −0.0300988 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.38768 | 0.452119 | ||||||||
\(268\) | −1.87454 | −0.114506 | ||||||||
\(269\) | −7.26180 | −0.442760 | −0.221380 | − | 0.975188i | \(-0.571056\pi\) | ||||
−0.221380 | + | 0.975188i | \(0.571056\pi\) | |||||||
\(270\) | −0.134172 | −0.00816546 | ||||||||
\(271\) | 4.19299 | 0.254706 | 0.127353 | − | 0.991857i | \(-0.459352\pi\) | ||||
0.127353 | + | 0.991857i | \(0.459352\pi\) | |||||||
\(272\) | 3.97465 | 0.240998 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.0224 | 1.02836 | ||||||||
\(275\) | 24.6834 | 1.48846 | ||||||||
\(276\) | −3.83700 | −0.230960 | ||||||||
\(277\) | 8.00920 | 0.481226 | 0.240613 | − | 0.970621i | \(-0.422652\pi\) | ||||
0.240613 | + | 0.970621i | \(0.422652\pi\) | |||||||
\(278\) | 5.69074 | 0.341308 | ||||||||
\(279\) | 7.20734 | 0.431492 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.19975 | −0.131226 | −0.0656131 | − | 0.997845i | \(-0.520900\pi\) | ||||
−0.0656131 | + | 0.997845i | \(0.520900\pi\) | |||||||
\(282\) | −17.8995 | −1.06590 | ||||||||
\(283\) | −3.83526 | −0.227983 | −0.113991 | − | 0.993482i | \(-0.536364\pi\) | ||||
−0.113991 | + | 0.993482i | \(0.536364\pi\) | |||||||
\(284\) | −3.85144 | −0.228541 | ||||||||
\(285\) | 0.536345 | 0.0317703 | ||||||||
\(286\) | 9.99117 | 0.590790 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.75919 | 0.221512 | ||||||||
\(289\) | −16.3435 | −0.961383 | ||||||||
\(290\) | 0.00600125 | 0.000352406 0 | ||||||||
\(291\) | 5.44556 | 0.319224 | ||||||||
\(292\) | −10.0487 | −0.588055 | ||||||||
\(293\) | −7.82147 | −0.456935 | −0.228468 | − | 0.973552i | \(-0.573371\pi\) | ||||
−0.228468 | + | 0.973552i | \(0.573371\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.354907 | −0.0206635 | ||||||||
\(296\) | 11.2187 | 0.652076 | ||||||||
\(297\) | −4.94328 | −0.286838 | ||||||||
\(298\) | −37.5881 | −2.17742 | ||||||||
\(299\) | −6.82301 | −0.394585 | ||||||||
\(300\) | −3.45871 | −0.199689 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 36.6876 | 2.11113 | ||||||||
\(303\) | −3.78486 | −0.217434 | ||||||||
\(304\) | −32.1781 | −1.84554 | ||||||||
\(305\) | 0.0927060 | 0.00530833 | ||||||||
\(306\) | 1.32954 | 0.0760050 | ||||||||
\(307\) | 1.95055 | 0.111324 | 0.0556619 | − | 0.998450i | \(-0.482273\pi\) | ||||
0.0556619 | + | 0.998450i | \(0.482273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.1368 | −1.08866 | ||||||||
\(310\) | −0.967025 | −0.0549233 | ||||||||
\(311\) | 25.3798 | 1.43916 | 0.719578 | − | 0.694412i | \(-0.244336\pi\) | ||||
0.719578 | + | 0.694412i | \(0.244336\pi\) | |||||||
\(312\) | 2.64233 | 0.149592 | ||||||||
\(313\) | −16.7300 | −0.945636 | −0.472818 | − | 0.881160i | \(-0.656763\pi\) | ||||
−0.472818 | + | 0.881160i | \(0.656763\pi\) | |||||||
\(314\) | −21.2451 | −1.19893 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.7761 | 0.606203 | ||||||||
\(317\) | −27.1439 | −1.52455 | −0.762277 | − | 0.647250i | \(-0.775919\pi\) | ||||
−0.762277 | + | 0.647250i | \(0.775919\pi\) | |||||||
\(318\) | 9.83314 | 0.551415 | ||||||||
\(319\) | 0.221103 | 0.0123794 | ||||||||
\(320\) | 0.297832 | 0.0166493 | ||||||||
\(321\) | −13.5411 | −0.755791 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.31476 | −0.295721 | ||||||||
\(324\) | 0.692668 | 0.0384815 | ||||||||
\(325\) | −6.15033 | −0.341159 | ||||||||
\(326\) | −3.88126 | −0.214963 | ||||||||
\(327\) | 0.705015 | 0.0389874 | ||||||||
\(328\) | −2.14525 | −0.118451 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.663251 | 0.0365108 | ||||||||
\(331\) | −1.13038 | −0.0621311 | −0.0310656 | − | 0.999517i | \(-0.509890\pi\) | ||||
−0.0310656 | + | 0.999517i | \(0.509890\pi\) | |||||||
\(332\) | 6.25159 | 0.343101 | ||||||||
\(333\) | 5.22958 | 0.286579 | ||||||||
\(334\) | −24.2517 | −1.32699 | ||||||||
\(335\) | −0.221279 | −0.0120898 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.0417 | 1.47306 | 0.736529 | − | 0.676406i | \(-0.236464\pi\) | ||||
0.736529 | + | 0.676406i | \(0.236464\pi\) | |||||||
\(338\) | 18.8427 | 1.02491 | ||||||||
\(339\) | −11.6339 | −0.631867 | ||||||||
\(340\) | −0.0458889 | −0.00248867 | ||||||||
\(341\) | −35.6279 | −1.92936 | ||||||||
\(342\) | −10.7638 | −0.582037 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −18.5538 | −1.00036 | ||||||||
\(345\) | −0.452937 | −0.0243853 | ||||||||
\(346\) | 17.2337 | 0.926488 | ||||||||
\(347\) | −17.4737 | −0.938039 | −0.469020 | − | 0.883188i | \(-0.655393\pi\) | ||||
−0.469020 | + | 0.883188i | \(0.655393\pi\) | |||||||
\(348\) | −0.0309816 | −0.00166079 | ||||||||
\(349\) | 22.4220 | 1.20022 | 0.600112 | − | 0.799916i | \(-0.295123\pi\) | ||||
0.600112 | + | 0.799916i | \(0.295123\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.23171 | 0.0657439 | ||||||||
\(352\) | −18.5827 | −0.990463 | ||||||||
\(353\) | −9.96215 | −0.530232 | −0.265116 | − | 0.964217i | \(-0.585410\pi\) | ||||
−0.265116 | + | 0.964217i | \(0.585410\pi\) | |||||||
\(354\) | 7.12253 | 0.378558 | ||||||||
\(355\) | −0.454641 | −0.0241299 | ||||||||
\(356\) | 5.11721 | 0.271212 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.7519 | 0.568256 | ||||||||
\(359\) | −21.0085 | −1.10879 | −0.554394 | − | 0.832254i | \(-0.687050\pi\) | ||||
−0.554394 | + | 0.832254i | \(0.687050\pi\) | |||||||
\(360\) | 0.175408 | 0.00924480 | ||||||||
\(361\) | 24.0274 | 1.26460 | ||||||||
\(362\) | 3.37822 | 0.177555 | ||||||||
\(363\) | 13.4360 | 0.705209 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.18619 | −0.0620882 | ||||||||
\(366\) | −1.86049 | −0.0972496 | ||||||||
\(367\) | −31.8537 | −1.66275 | −0.831376 | − | 0.555711i | \(-0.812446\pi\) | ||||
−0.831376 | + | 0.555711i | \(0.812446\pi\) | |||||||
\(368\) | 27.1740 | 1.41655 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | −0.701664 | −0.0364778 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.99229 | 0.258838 | ||||||||
\(373\) | −22.2169 | −1.15035 | −0.575175 | − | 0.818031i | \(-0.695066\pi\) | ||||
−0.575175 | + | 0.818031i | \(0.695066\pi\) | |||||||
\(374\) | −6.57231 | −0.339846 | ||||||||
\(375\) | −0.817110 | −0.0421954 | ||||||||
\(376\) | 23.4006 | 1.20679 | ||||||||
\(377\) | −0.0550920 | −0.00283738 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0974 | 1.44327 | 0.721633 | − | 0.692276i | \(-0.243392\pi\) | ||||
0.721633 | + | 0.692276i | \(0.243392\pi\) | |||||||
\(380\) | 0.371509 | 0.0190580 | ||||||||
\(381\) | −2.52451 | −0.129334 | ||||||||
\(382\) | 30.2850 | 1.54952 | ||||||||
\(383\) | 7.97911 | 0.407714 | 0.203857 | − | 0.979001i | \(-0.434652\pi\) | ||||
0.203857 | + | 0.979001i | \(0.434652\pi\) | |||||||
\(384\) | −13.4955 | −0.688689 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −37.3091 | −1.89898 | ||||||||
\(387\) | −8.64881 | −0.439644 | ||||||||
\(388\) | 3.77196 | 0.191492 | ||||||||
\(389\) | −34.4544 | −1.74691 | −0.873453 | − | 0.486908i | \(-0.838125\pi\) | ||||
−0.873453 | + | 0.486908i | \(0.838125\pi\) | |||||||
\(390\) | −0.165262 | −0.00836835 | ||||||||
\(391\) | 4.48826 | 0.226981 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.8567 | −0.547647 | ||||||||
\(394\) | −3.10788 | −0.156573 | ||||||||
\(395\) | 1.27206 | 0.0640043 | ||||||||
\(396\) | −3.42405 | −0.172065 | ||||||||
\(397\) | −23.1863 | −1.16369 | −0.581843 | − | 0.813301i | \(-0.697668\pi\) | ||||
−0.581843 | + | 0.813301i | \(0.697668\pi\) | |||||||
\(398\) | −33.9348 | −1.70100 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 24.4949 | 1.22475 | ||||||||
\(401\) | −10.7495 | −0.536804 | −0.268402 | − | 0.963307i | \(-0.586496\pi\) | ||||
−0.268402 | + | 0.963307i | \(0.586496\pi\) | |||||||
\(402\) | 4.44080 | 0.221487 | ||||||||
\(403\) | 8.87737 | 0.442213 | ||||||||
\(404\) | −2.62165 | −0.130432 | ||||||||
\(405\) | 0.0817657 | 0.00406297 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.8513 | −1.28140 | ||||||||
\(408\) | −1.73816 | −0.0860515 | ||||||||
\(409\) | −15.6989 | −0.776261 | −0.388130 | − | 0.921604i | \(-0.626879\pi\) | ||||
−0.388130 | + | 0.921604i | \(0.626879\pi\) | |||||||
\(410\) | 0.134172 | 0.00662629 | ||||||||
\(411\) | −10.3736 | −0.511692 | ||||||||
\(412\) | −13.2555 | −0.653050 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 9.08988 | 0.446743 | ||||||||
\(415\) | 0.737967 | 0.0362254 | ||||||||
\(416\) | 4.63024 | 0.227016 | ||||||||
\(417\) | −3.46799 | −0.169828 | ||||||||
\(418\) | 53.2083 | 2.60250 | ||||||||
\(419\) | −27.5809 | −1.34741 | −0.673707 | − | 0.738999i | \(-0.735299\pi\) | ||||
−0.673707 | + | 0.738999i | \(0.735299\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.8712 | 1.21215 | 0.606075 | − | 0.795408i | \(-0.292743\pi\) | ||||
0.606075 | + | 0.795408i | \(0.292743\pi\) | |||||||
\(422\) | 14.3337 | 0.697752 | ||||||||
\(423\) | 10.9081 | 0.530370 | ||||||||
\(424\) | −12.8552 | −0.624303 | ||||||||
\(425\) | 4.04576 | 0.196248 | ||||||||
\(426\) | 9.12408 | 0.442063 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −9.37949 | −0.453375 | ||||||||
\(429\) | −6.08870 | −0.293965 | ||||||||
\(430\) | 1.16043 | 0.0559609 | ||||||||
\(431\) | 38.0558 | 1.83308 | 0.916541 | − | 0.399942i | \(-0.130970\pi\) | ||||
0.916541 | + | 0.399942i | \(0.130970\pi\) | |||||||
\(432\) | −4.90555 | −0.236018 | ||||||||
\(433\) | 21.6978 | 1.04273 | 0.521365 | − | 0.853334i | \(-0.325423\pi\) | ||||
0.521365 | + | 0.853334i | \(0.325423\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.00365722 | −0.000175350 0 | ||||||||
\(436\) | 0.488341 | 0.0233873 | ||||||||
\(437\) | −36.3362 | −1.73820 | ||||||||
\(438\) | 23.8054 | 1.13747 | ||||||||
\(439\) | −36.9921 | −1.76554 | −0.882769 | − | 0.469807i | \(-0.844323\pi\) | ||||
−0.882769 | + | 0.469807i | \(0.844323\pi\) | |||||||
\(440\) | −0.867090 | −0.0413369 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.63762 | 0.0778934 | ||||||||
\(443\) | 10.9047 | 0.518100 | 0.259050 | − | 0.965864i | \(-0.416591\pi\) | ||||
0.259050 | + | 0.965864i | \(0.416591\pi\) | |||||||
\(444\) | 3.62236 | 0.171910 | ||||||||
\(445\) | 0.604059 | 0.0286352 | ||||||||
\(446\) | −21.1591 | −1.00191 | ||||||||
\(447\) | 22.9065 | 1.08344 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.3090 | −1.33599 | −0.667993 | − | 0.744168i | \(-0.732846\pi\) | ||||
−0.667993 | + | 0.744168i | \(0.732846\pi\) | |||||||
\(450\) | 8.19370 | 0.386255 | ||||||||
\(451\) | 4.94328 | 0.232770 | ||||||||
\(452\) | −8.05843 | −0.379037 | ||||||||
\(453\) | −22.3577 | −1.05046 | ||||||||
\(454\) | 31.0151 | 1.45561 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 14.0718 | 0.658973 | ||||||||
\(457\) | 0.0300373 | 0.00140509 | 0.000702543 | − | 1.00000i | \(-0.499776\pi\) | ||||
0.000702543 | 1.00000i | \(0.499776\pi\) | ||||||||
\(458\) | 2.35730 | 0.110149 | ||||||||
\(459\) | −0.810235 | −0.0378186 | ||||||||
\(460\) | −0.313735 | −0.0146280 | ||||||||
\(461\) | −33.9313 | −1.58034 | −0.790169 | − | 0.612889i | \(-0.790007\pi\) | ||||
−0.790169 | + | 0.612889i | \(0.790007\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.9962 | 1.39404 | 0.697020 | − | 0.717052i | \(-0.254509\pi\) | ||||
0.697020 | + | 0.717052i | \(0.254509\pi\) | |||||||
\(464\) | 0.219415 | 0.0101861 | ||||||||
\(465\) | 0.589313 | 0.0273288 | ||||||||
\(466\) | 24.2546 | 1.12357 | ||||||||
\(467\) | −16.3034 | −0.754429 | −0.377215 | − | 0.926126i | \(-0.623118\pi\) | ||||
−0.377215 | + | 0.926126i | \(0.623118\pi\) | |||||||
\(468\) | 0.853167 | 0.0394377 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.46356 | −0.0675092 | ||||||||
\(471\) | 12.9470 | 0.596565 | ||||||||
\(472\) | −9.31151 | −0.428597 | ||||||||
\(473\) | 42.7535 | 1.96581 | ||||||||
\(474\) | −25.5287 | −1.17257 | ||||||||
\(475\) | −32.7538 | −1.50285 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.99240 | −0.274373 | ||||||||
\(478\) | 1.70401 | 0.0779398 | ||||||||
\(479\) | 1.76809 | 0.0807862 | 0.0403931 | − | 0.999184i | \(-0.487139\pi\) | ||||
0.0403931 | + | 0.999184i | \(0.487139\pi\) | |||||||
\(480\) | 0.307373 | 0.0140296 | ||||||||
\(481\) | 6.44134 | 0.293700 | ||||||||
\(482\) | 40.0165 | 1.82270 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.30671 | 0.423032 | ||||||||
\(485\) | 0.445260 | 0.0202182 | ||||||||
\(486\) | −1.64093 | −0.0744343 | ||||||||
\(487\) | 12.5458 | 0.568503 | 0.284252 | − | 0.958750i | \(-0.408255\pi\) | ||||
0.284252 | + | 0.958750i | \(0.408255\pi\) | |||||||
\(488\) | 2.43228 | 0.110104 | ||||||||
\(489\) | 2.36528 | 0.106961 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.480203 | −0.0216713 | −0.0108356 | − | 0.999941i | \(-0.503449\pi\) | ||||
−0.0108356 | + | 0.999941i | \(0.503449\pi\) | |||||||
\(492\) | −0.692668 | −0.0312279 | ||||||||
\(493\) | 0.0362402 | 0.00163218 | ||||||||
\(494\) | −13.2579 | −0.596499 | ||||||||
\(495\) | −0.404191 | −0.0181670 | ||||||||
\(496\) | −35.3559 | −1.58753 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −14.8101 | −0.663655 | ||||||||
\(499\) | 44.0725 | 1.97296 | 0.986479 | − | 0.163889i | \(-0.0524038\pi\) | ||||
0.986479 | + | 0.163889i | \(0.0524038\pi\) | |||||||
\(500\) | −0.565986 | −0.0253117 | ||||||||
\(501\) | 14.7792 | 0.660285 | ||||||||
\(502\) | 17.0776 | 0.762209 | ||||||||
\(503\) | −28.8604 | −1.28682 | −0.643411 | − | 0.765521i | \(-0.722481\pi\) | ||||
−0.643411 | + | 0.765521i | \(0.722481\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.309471 | −0.0137713 | ||||||||
\(506\) | −44.9339 | −1.99755 | ||||||||
\(507\) | −11.4829 | −0.509973 | ||||||||
\(508\) | −1.74864 | −0.0775836 | ||||||||
\(509\) | 29.3896 | 1.30267 | 0.651336 | − | 0.758789i | \(-0.274209\pi\) | ||||
0.651336 | + | 0.758789i | \(0.274209\pi\) | |||||||
\(510\) | 0.108711 | 0.00481381 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 2.60635 | 0.115185 | ||||||||
\(513\) | 6.55953 | 0.289610 | ||||||||
\(514\) | −29.7371 | −1.31165 | ||||||||
\(515\) | −1.56474 | −0.0689505 | ||||||||
\(516\) | −5.99075 | −0.263728 | ||||||||
\(517\) | −53.9219 | −2.37148 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.5024 | −0.461002 | ||||||||
\(520\) | 0.216052 | 0.00947450 | ||||||||
\(521\) | −4.09206 | −0.179277 | −0.0896383 | − | 0.995974i | \(-0.528571\pi\) | ||||
−0.0896383 | + | 0.995974i | \(0.528571\pi\) | |||||||
\(522\) | 0.0733957 | 0.00321244 | ||||||||
\(523\) | −7.40617 | −0.323849 | −0.161925 | − | 0.986803i | \(-0.551770\pi\) | ||||
−0.161925 | + | 0.986803i | \(0.551770\pi\) | |||||||
\(524\) | −7.52008 | −0.328516 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.67449 | 0.203818 | ||||||||
\(527\) | −5.83964 | −0.254379 | ||||||||
\(528\) | 24.2495 | 1.05532 | ||||||||
\(529\) | 7.68555 | 0.334154 | ||||||||
\(530\) | 0.804014 | 0.0349241 | ||||||||
\(531\) | −4.34053 | −0.188363 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.23171 | −0.0533514 | ||||||||
\(534\) | −12.1227 | −0.524601 | ||||||||
\(535\) | −1.10720 | −0.0478684 | ||||||||
\(536\) | −5.80560 | −0.250764 | ||||||||
\(537\) | −6.55231 | −0.282753 | ||||||||
\(538\) | 11.9161 | 0.513742 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.0566365 | 0.00243725 | ||||||||
\(541\) | −31.6011 | −1.35864 | −0.679319 | − | 0.733843i | \(-0.737725\pi\) | ||||
−0.679319 | + | 0.733843i | \(0.737725\pi\) | |||||||
\(542\) | −6.88043 | −0.295540 | ||||||||
\(543\) | −2.05872 | −0.0883479 | ||||||||
\(544\) | −3.04583 | −0.130589 | ||||||||
\(545\) | 0.0576461 | 0.00246929 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.6853 | −0.585143 | −0.292571 | − | 0.956244i | \(-0.594511\pi\) | ||||
−0.292571 | + | 0.956244i | \(0.594511\pi\) | |||||||
\(548\) | −7.18546 | −0.306948 | ||||||||
\(549\) | 1.13380 | 0.0483894 | ||||||||
\(550\) | −40.5038 | −1.72709 | ||||||||
\(551\) | −0.293394 | −0.0124990 | ||||||||
\(552\) | −11.8835 | −0.505795 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −13.1426 | −0.558374 | ||||||||
\(555\) | 0.427600 | 0.0181506 | ||||||||
\(556\) | −2.40216 | −0.101874 | ||||||||
\(557\) | 4.80505 | 0.203597 | 0.101798 | − | 0.994805i | \(-0.467540\pi\) | ||||
0.101798 | + | 0.994805i | \(0.467540\pi\) | |||||||
\(558\) | −11.8268 | −0.500667 | ||||||||
\(559\) | −10.6528 | −0.450567 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.00522 | 0.169101 | ||||||||
\(562\) | 3.60965 | 0.152264 | ||||||||
\(563\) | 8.15180 | 0.343558 | 0.171779 | − | 0.985136i | \(-0.445049\pi\) | ||||
0.171779 | + | 0.985136i | \(0.445049\pi\) | |||||||
\(564\) | 7.55569 | 0.318152 | ||||||||
\(565\) | −0.951255 | −0.0400196 | ||||||||
\(566\) | 6.29341 | 0.264532 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.9282 | −0.500496 | ||||||||
\(569\) | −34.3425 | −1.43971 | −0.719857 | − | 0.694122i | \(-0.755793\pi\) | ||||
−0.719857 | + | 0.694122i | \(0.755793\pi\) | |||||||
\(570\) | −0.880107 | −0.0368636 | ||||||||
\(571\) | −8.17313 | −0.342035 | −0.171017 | − | 0.985268i | \(-0.554705\pi\) | ||||
−0.171017 | + | 0.985268i | \(0.554705\pi\) | |||||||
\(572\) | −4.21745 | −0.176340 | ||||||||
\(573\) | −18.4559 | −0.771008 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27.6602 | 1.15351 | ||||||||
\(576\) | 3.64251 | 0.151771 | ||||||||
\(577\) | −1.24503 | −0.0518312 | −0.0259156 | − | 0.999664i | \(-0.508250\pi\) | ||||
−0.0259156 | + | 0.999664i | \(0.508250\pi\) | |||||||
\(578\) | 26.8187 | 1.11551 | ||||||||
\(579\) | 22.7365 | 0.944896 | ||||||||
\(580\) | −0.00253323 | −0.000105187 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −8.93580 | −0.370401 | ||||||||
\(583\) | 29.6221 | 1.22682 | ||||||||
\(584\) | −31.1216 | −1.28782 | ||||||||
\(585\) | 0.100712 | 0.00416392 | ||||||||
\(586\) | 12.8345 | 0.530189 | ||||||||
\(587\) | 9.16561 | 0.378305 | 0.189153 | − | 0.981948i | \(-0.439426\pi\) | ||||
0.189153 | + | 0.981948i | \(0.439426\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 47.2768 | 1.94800 | ||||||||
\(590\) | 0.582379 | 0.0239761 | ||||||||
\(591\) | 1.89397 | 0.0779074 | ||||||||
\(592\) | −25.6539 | −1.05437 | ||||||||
\(593\) | 19.9726 | 0.820177 | 0.410089 | − | 0.912046i | \(-0.365498\pi\) | ||||
0.410089 | + | 0.912046i | \(0.365498\pi\) | |||||||
\(594\) | 8.11161 | 0.332823 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.8666 | 0.649921 | ||||||||
\(597\) | 20.6802 | 0.846382 | ||||||||
\(598\) | 11.1961 | 0.457844 | ||||||||
\(599\) | −9.37301 | −0.382971 | −0.191485 | − | 0.981495i | \(-0.561330\pi\) | ||||
−0.191485 | + | 0.981495i | \(0.561330\pi\) | |||||||
\(600\) | −10.7119 | −0.437311 | ||||||||
\(601\) | 1.48167 | 0.0604388 | 0.0302194 | − | 0.999543i | \(-0.490379\pi\) | ||||
0.0302194 | + | 0.999543i | \(0.490379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.70626 | −0.110207 | ||||||||
\(604\) | −15.4865 | −0.630136 | ||||||||
\(605\) | 1.09861 | 0.0446647 | ||||||||
\(606\) | 6.21070 | 0.252293 | ||||||||
\(607\) | −23.5439 | −0.955617 | −0.477809 | − | 0.878464i | \(-0.658569\pi\) | ||||
−0.477809 | + | 0.878464i | \(0.658569\pi\) | |||||||
\(608\) | 24.6585 | 1.00003 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.152125 | −0.00615934 | ||||||||
\(611\) | 13.4357 | 0.543548 | ||||||||
\(612\) | −0.561224 | −0.0226861 | ||||||||
\(613\) | −23.4070 | −0.945401 | −0.472700 | − | 0.881223i | \(-0.656721\pi\) | ||||
−0.472700 | + | 0.881223i | \(0.656721\pi\) | |||||||
\(614\) | −3.20073 | −0.129171 | ||||||||
\(615\) | −0.0817657 | −0.00329711 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.4731 | −1.30732 | −0.653658 | − | 0.756790i | \(-0.726767\pi\) | ||||
−0.653658 | + | 0.756790i | \(0.726767\pi\) | |||||||
\(618\) | 31.4023 | 1.26318 | ||||||||
\(619\) | 9.07557 | 0.364778 | 0.182389 | − | 0.983226i | \(-0.441617\pi\) | ||||
0.182389 | + | 0.983226i | \(0.441617\pi\) | |||||||
\(620\) | 0.408198 | 0.0163936 | ||||||||
\(621\) | −5.53945 | −0.222291 | ||||||||
\(622\) | −41.6466 | −1.66987 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.04222 | −0.241883 | ||||||||
\(625\) | 24.8998 | 0.995990 | ||||||||
\(626\) | 27.4528 | 1.09724 | ||||||||
\(627\) | −32.4256 | −1.29495 | ||||||||
\(628\) | 8.96795 | 0.357860 | ||||||||
\(629\) | −4.23719 | −0.168948 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.18697 | −0.166681 | −0.0833404 | − | 0.996521i | \(-0.526559\pi\) | ||||
−0.0833404 | + | 0.996521i | \(0.526559\pi\) | |||||||
\(632\) | 33.3744 | 1.32756 | ||||||||
\(633\) | −8.73506 | −0.347187 | ||||||||
\(634\) | 44.5414 | 1.76897 | ||||||||
\(635\) | −0.206418 | −0.00819145 | ||||||||
\(636\) | −4.15074 | −0.164588 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.362816 | −0.0143640 | ||||||||
\(639\) | −5.56029 | −0.219962 | ||||||||
\(640\) | −1.10347 | −0.0436184 | ||||||||
\(641\) | −28.6487 | −1.13156 | −0.565778 | − | 0.824558i | \(-0.691424\pi\) | ||||
−0.565778 | + | 0.824558i | \(0.691424\pi\) | |||||||
\(642\) | 22.2201 | 0.876957 | ||||||||
\(643\) | −26.3904 | −1.04073 | −0.520367 | − | 0.853943i | \(-0.674205\pi\) | ||||
−0.520367 | + | 0.853943i | \(0.674205\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.707176 | −0.0278450 | ||||||||
\(646\) | 8.72118 | 0.343130 | ||||||||
\(647\) | 16.5423 | 0.650344 | 0.325172 | − | 0.945655i | \(-0.394578\pi\) | ||||
0.325172 | + | 0.945655i | \(0.394578\pi\) | |||||||
\(648\) | 2.14525 | 0.0842733 | ||||||||
\(649\) | 21.4565 | 0.842240 | ||||||||
\(650\) | 10.0923 | 0.395852 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.63835 | 0.0641627 | ||||||||
\(653\) | 37.0887 | 1.45139 | 0.725697 | − | 0.688015i | \(-0.241518\pi\) | ||||
0.725697 | + | 0.688015i | \(0.241518\pi\) | |||||||
\(654\) | −1.15688 | −0.0452377 | ||||||||
\(655\) | −0.887705 | −0.0346855 | ||||||||
\(656\) | 4.90555 | 0.191529 | ||||||||
\(657\) | −14.5072 | −0.565981 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.20478 | −0.163795 | −0.0818975 | − | 0.996641i | \(-0.526098\pi\) | ||||
−0.0818975 | + | 0.996641i | \(0.526098\pi\) | |||||||
\(660\) | −0.279970 | −0.0108978 | ||||||||
\(661\) | 11.6207 | 0.451994 | 0.225997 | − | 0.974128i | \(-0.427436\pi\) | ||||
0.225997 | + | 0.974128i | \(0.427436\pi\) | |||||||
\(662\) | 1.85488 | 0.0720918 | ||||||||
\(663\) | −0.997977 | −0.0387582 | ||||||||
\(664\) | 19.3617 | 0.751379 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.58140 | −0.332522 | ||||||||
\(667\) | 0.247769 | 0.00959364 | ||||||||
\(668\) | 10.2371 | 0.396084 | ||||||||
\(669\) | 12.8945 | 0.498532 | ||||||||
\(670\) | 0.363105 | 0.0140280 | ||||||||
\(671\) | −5.60470 | −0.216367 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.7947 | −1.30269 | −0.651346 | − | 0.758781i | \(-0.725795\pi\) | ||||
−0.651346 | + | 0.758781i | \(0.725795\pi\) | |||||||
\(674\) | −44.3737 | −1.70921 | ||||||||
\(675\) | −4.99331 | −0.192193 | ||||||||
\(676\) | −7.95382 | −0.305916 | ||||||||
\(677\) | 22.3305 | 0.858229 | 0.429115 | − | 0.903250i | \(-0.358826\pi\) | ||||
0.429115 | + | 0.903250i | \(0.358826\pi\) | |||||||
\(678\) | 19.0905 | 0.733166 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.142122 | −0.00545011 | ||||||||
\(681\) | −18.9009 | −0.724283 | ||||||||
\(682\) | 58.4631 | 2.23867 | ||||||||
\(683\) | 1.70074 | 0.0650769 | 0.0325385 | − | 0.999470i | \(-0.489641\pi\) | ||||
0.0325385 | + | 0.999470i | \(0.489641\pi\) | |||||||
\(684\) | 4.54357 | 0.173728 | ||||||||
\(685\) | −0.848205 | −0.0324082 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.43656 | −0.0548081 | ||||||||
\(688\) | 42.4271 | 1.61752 | ||||||||
\(689\) | −7.38091 | −0.281190 | ||||||||
\(690\) | 0.743241 | 0.0282947 | ||||||||
\(691\) | 18.1625 | 0.690934 | 0.345467 | − | 0.938431i | \(-0.387721\pi\) | ||||
0.345467 | + | 0.938431i | \(0.387721\pi\) | |||||||
\(692\) | −7.27464 | −0.276540 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.6733 | 1.08842 | ||||||||
\(695\) | −0.283562 | −0.0107561 | ||||||||
\(696\) | −0.0959526 | −0.00363707 | ||||||||
\(697\) | 0.810235 | 0.0306899 | ||||||||
\(698\) | −36.7931 | −1.39264 | ||||||||
\(699\) | −14.7809 | −0.559066 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.2740 | −0.614662 | −0.307331 | − | 0.951603i | \(-0.599436\pi\) | ||||
−0.307331 | + | 0.951603i | \(0.599436\pi\) | |||||||
\(702\) | −2.02116 | −0.0762838 | ||||||||
\(703\) | 34.3036 | 1.29378 | ||||||||
\(704\) | −18.0060 | −0.678625 | ||||||||
\(705\) | 0.891909 | 0.0335912 | ||||||||
\(706\) | 16.3472 | 0.615236 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.00655 | −0.112993 | ||||||||
\(709\) | −29.3971 | −1.10403 | −0.552016 | − | 0.833833i | \(-0.686141\pi\) | ||||
−0.552016 | + | 0.833833i | \(0.686141\pi\) | |||||||
\(710\) | 0.746037 | 0.0279983 | ||||||||
\(711\) | 15.5574 | 0.583447 | ||||||||
\(712\) | 15.8484 | 0.593944 | ||||||||
\(713\) | −39.9247 | −1.49519 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.497847 | −0.0186184 | ||||||||
\(716\) | −4.53857 | −0.169614 | ||||||||
\(717\) | −1.03844 | −0.0387813 | ||||||||
\(718\) | 34.4736 | 1.28655 | ||||||||
\(719\) | −21.6187 | −0.806240 | −0.403120 | − | 0.915147i | \(-0.632074\pi\) | ||||
−0.403120 | + | 0.915147i | \(0.632074\pi\) | |||||||
\(720\) | −0.401106 | −0.0149483 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −39.4274 | −1.46734 | ||||||||
\(723\) | −24.3864 | −0.906939 | ||||||||
\(724\) | −1.42601 | −0.0529971 | ||||||||
\(725\) | 0.223341 | 0.00829467 | ||||||||
\(726\) | −22.0477 | −0.818266 | ||||||||
\(727\) | −30.5668 | −1.13366 | −0.566830 | − | 0.823834i | \(-0.691831\pi\) | ||||
−0.566830 | + | 0.823834i | \(0.691831\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.94647 | 0.0720420 | ||||||||
\(731\) | 7.00757 | 0.259184 | ||||||||
\(732\) | 0.785347 | 0.0290273 | ||||||||
\(733\) | −6.44019 | −0.237874 | −0.118937 | − | 0.992902i | \(-0.537949\pi\) | ||||
−0.118937 | + | 0.992902i | \(0.537949\pi\) | |||||||
\(734\) | 52.2699 | 1.92932 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20.8239 | −0.767577 | ||||||||
\(737\) | 13.3778 | 0.492778 | ||||||||
\(738\) | 1.64093 | 0.0604037 | ||||||||
\(739\) | −17.7546 | −0.653114 | −0.326557 | − | 0.945178i | \(-0.605889\pi\) | ||||
−0.326557 | + | 0.945178i | \(0.605889\pi\) | |||||||
\(740\) | 0.296185 | 0.0108880 | ||||||||
\(741\) | 8.07945 | 0.296806 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.7838 | −0.505678 | −0.252839 | − | 0.967508i | \(-0.581364\pi\) | ||||
−0.252839 | + | 0.967508i | \(0.581364\pi\) | |||||||
\(744\) | 15.4615 | 0.566847 | ||||||||
\(745\) | 1.87297 | 0.0686202 | ||||||||
\(746\) | 36.4565 | 1.33477 | ||||||||
\(747\) | 9.02538 | 0.330221 | ||||||||
\(748\) | 2.77429 | 0.101438 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.34083 | 0.0489600 | ||||||||
\(751\) | −31.6129 | −1.15357 | −0.576785 | − | 0.816896i | \(-0.695693\pi\) | ||||
−0.576785 | + | 0.816896i | \(0.695693\pi\) | |||||||
\(752\) | −53.5102 | −1.95132 | ||||||||
\(753\) | −10.4072 | −0.379260 | ||||||||
\(754\) | 0.0904024 | 0.00329226 | ||||||||
\(755\) | −1.82810 | −0.0665313 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.1875 | 0.915454 | 0.457727 | − | 0.889093i | \(-0.348664\pi\) | ||||
0.457727 | + | 0.889093i | \(0.348664\pi\) | |||||||
\(758\) | −46.1060 | −1.67464 | ||||||||
\(759\) | 27.3831 | 0.993943 | ||||||||
\(760\) | 1.15059 | 0.0417363 | ||||||||
\(761\) | −24.5389 | −0.889534 | −0.444767 | − | 0.895646i | \(-0.646714\pi\) | ||||
−0.444767 | + | 0.895646i | \(0.646714\pi\) | |||||||
\(762\) | 4.14255 | 0.150069 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12.7838 | −0.462503 | ||||||||
\(765\) | −0.0662495 | −0.00239526 | ||||||||
\(766\) | −13.0932 | −0.473077 | ||||||||
\(767\) | −5.34629 | −0.193043 | ||||||||
\(768\) | 14.8602 | 0.536222 | ||||||||
\(769\) | 27.2252 | 0.981766 | 0.490883 | − | 0.871226i | \(-0.336674\pi\) | ||||
0.490883 | + | 0.871226i | \(0.336674\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.1220 | 0.652649 | ||||||||
\(772\) | 15.7488 | 0.566813 | ||||||||
\(773\) | −39.2782 | −1.41274 | −0.706369 | − | 0.707844i | \(-0.749668\pi\) | ||||
−0.706369 | + | 0.707844i | \(0.749668\pi\) | |||||||
\(774\) | 14.1921 | 0.510126 | ||||||||
\(775\) | −35.9885 | −1.29275 | ||||||||
\(776\) | 11.6821 | 0.419362 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 56.5374 | 2.02696 | ||||||||
\(779\) | −6.55953 | −0.235019 | ||||||||
\(780\) | 0.0697598 | 0.00249780 | ||||||||
\(781\) | 27.4861 | 0.983530 | ||||||||
\(782\) | −7.36495 | −0.263370 | ||||||||
\(783\) | −0.0447280 | −0.00159845 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.05862 | 0.0377837 | ||||||||
\(786\) | 17.8151 | 0.635444 | ||||||||
\(787\) | −54.3409 | −1.93704 | −0.968522 | − | 0.248927i | \(-0.919922\pi\) | ||||
−0.968522 | + | 0.248927i | \(0.919922\pi\) | |||||||
\(788\) | 1.31189 | 0.0467341 | ||||||||
\(789\) | −2.84868 | −0.101416 | ||||||||
\(790\) | −2.08737 | −0.0742652 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −10.6046 | −0.376817 | ||||||||
\(793\) | 1.39652 | 0.0495918 | ||||||||
\(794\) | 38.0472 | 1.35024 | ||||||||
\(795\) | −0.489973 | −0.0173775 | ||||||||
\(796\) | 14.3245 | 0.507718 | ||||||||
\(797\) | −45.0852 | −1.59700 | −0.798500 | − | 0.601995i | \(-0.794373\pi\) | ||||
−0.798500 | + | 0.601995i | \(0.794373\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.83814 | −0.312671 | ||||||||
\(800\) | −18.7708 | −0.663648 | ||||||||
\(801\) | 7.38768 | 0.261031 | ||||||||
\(802\) | 17.6392 | 0.622862 | ||||||||
\(803\) | 71.7134 | 2.53071 | ||||||||
\(804\) | −1.87454 | −0.0661099 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.5672 | −0.513107 | ||||||||
\(807\) | −7.26180 | −0.255628 | ||||||||
\(808\) | −8.11945 | −0.285641 | ||||||||
\(809\) | 44.8906 | 1.57827 | 0.789135 | − | 0.614220i | \(-0.210529\pi\) | ||||
0.789135 | + | 0.614220i | \(0.210529\pi\) | |||||||
\(810\) | −0.134172 | −0.00471433 | ||||||||
\(811\) | 43.9625 | 1.54373 | 0.771865 | − | 0.635786i | \(-0.219324\pi\) | ||||
0.771865 | + | 0.635786i | \(0.219324\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.19299 | 0.147055 | ||||||||
\(814\) | 42.4203 | 1.48683 | ||||||||
\(815\) | 0.193398 | 0.00677445 | ||||||||
\(816\) | 3.97465 | 0.139141 | ||||||||
\(817\) | −56.7321 | −1.98481 | ||||||||
\(818\) | 25.7609 | 0.900708 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.0566365 | −0.00197783 | ||||||||
\(821\) | −9.16765 | −0.319953 | −0.159977 | − | 0.987121i | \(-0.551142\pi\) | ||||
−0.159977 | + | 0.987121i | \(0.551142\pi\) | |||||||
\(822\) | 17.0224 | 0.593725 | ||||||||
\(823\) | −8.42471 | −0.293667 | −0.146834 | − | 0.989161i | \(-0.546908\pi\) | ||||
−0.146834 | + | 0.989161i | \(0.546908\pi\) | |||||||
\(824\) | −41.0532 | −1.43016 | ||||||||
\(825\) | 24.6834 | 0.859364 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.2599 | 1.67816 | 0.839080 | − | 0.544008i | \(-0.183094\pi\) | ||||
0.839080 | + | 0.544008i | \(0.183094\pi\) | |||||||
\(828\) | −3.83700 | −0.133345 | ||||||||
\(829\) | 0.597727 | 0.0207599 | 0.0103800 | − | 0.999946i | \(-0.496696\pi\) | ||||
0.0103800 | + | 0.999946i | \(0.496696\pi\) | |||||||
\(830\) | −1.21096 | −0.0420329 | ||||||||
\(831\) | 8.00920 | 0.277836 | ||||||||
\(832\) | 4.48652 | 0.155542 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 5.69074 | 0.197054 | ||||||||
\(835\) | 1.20843 | 0.0418195 | ||||||||
\(836\) | −22.4602 | −0.776801 | ||||||||
\(837\) | 7.20734 | 0.249122 | ||||||||
\(838\) | 45.2584 | 1.56343 | ||||||||
\(839\) | 12.7920 | 0.441630 | 0.220815 | − | 0.975316i | \(-0.429128\pi\) | ||||
0.220815 | + | 0.975316i | \(0.429128\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9980 | −0.999931 | ||||||||
\(842\) | −40.8121 | −1.40648 | ||||||||
\(843\) | −2.19975 | −0.0757635 | ||||||||
\(844\) | −6.05049 | −0.208267 | ||||||||
\(845\) | −0.938906 | −0.0322994 | ||||||||
\(846\) | −17.8995 | −0.615397 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 29.3960 | 1.00946 | ||||||||
\(849\) | −3.83526 | −0.131626 | ||||||||
\(850\) | −6.63883 | −0.227710 | ||||||||
\(851\) | −28.9690 | −0.993045 | ||||||||
\(852\) | −3.85144 | −0.131948 | ||||||||
\(853\) | −14.5985 | −0.499841 | −0.249921 | − | 0.968266i | \(-0.580405\pi\) | ||||
−0.249921 | + | 0.968266i | \(0.580405\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.536345 | 0.0183426 | ||||||||
\(856\) | −29.0490 | −0.992875 | ||||||||
\(857\) | −7.40299 | −0.252881 | −0.126441 | − | 0.991974i | \(-0.540355\pi\) | ||||
−0.126441 | + | 0.991974i | \(0.540355\pi\) | |||||||
\(858\) | 9.99117 | 0.341093 | ||||||||
\(859\) | −43.1440 | −1.47206 | −0.736028 | − | 0.676951i | \(-0.763301\pi\) | ||||
−0.736028 | + | 0.676951i | \(0.763301\pi\) | |||||||
\(860\) | −0.489838 | −0.0167033 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −62.4470 | −2.12695 | ||||||||
\(863\) | 27.0789 | 0.921776 | 0.460888 | − | 0.887458i | \(-0.347531\pi\) | ||||
0.460888 | + | 0.887458i | \(0.347531\pi\) | |||||||
\(864\) | 3.75919 | 0.127890 | ||||||||
\(865\) | −0.858732 | −0.0291978 | ||||||||
\(866\) | −35.6047 | −1.20990 | ||||||||
\(867\) | −16.3435 | −0.555055 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −76.9045 | −2.60881 | ||||||||
\(870\) | 0.00600125 | 0.000203462 0 | ||||||||
\(871\) | −3.33333 | −0.112946 | ||||||||
\(872\) | 1.51243 | 0.0512174 | ||||||||
\(873\) | 5.44556 | 0.184304 | ||||||||
\(874\) | 59.6253 | 2.01686 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.0487 | −0.339514 | ||||||||
\(877\) | 33.0013 | 1.11438 | 0.557188 | − | 0.830387i | \(-0.311880\pi\) | ||||
0.557188 | + | 0.830387i | \(0.311880\pi\) | |||||||
\(878\) | 60.7017 | 2.04858 | ||||||||
\(879\) | −7.82147 | −0.263812 | ||||||||
\(880\) | 1.98278 | 0.0668394 | ||||||||
\(881\) | −22.3933 | −0.754451 | −0.377225 | − | 0.926122i | \(-0.623122\pi\) | ||||
−0.377225 | + | 0.926122i | \(0.623122\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.8447 | 0.432257 | 0.216129 | − | 0.976365i | \(-0.430657\pi\) | ||||
0.216129 | + | 0.976365i | \(0.430657\pi\) | |||||||
\(884\) | −0.691266 | −0.0232498 | ||||||||
\(885\) | −0.354907 | −0.0119301 | ||||||||
\(886\) | −17.8940 | −0.601160 | ||||||||
\(887\) | −26.8473 | −0.901445 | −0.450722 | − | 0.892664i | \(-0.648834\pi\) | ||||
−0.450722 | + | 0.892664i | \(0.648834\pi\) | |||||||
\(888\) | 11.2187 | 0.376476 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.991222 | −0.0332258 | ||||||||
\(891\) | −4.94328 | −0.165606 | ||||||||
\(892\) | 8.93164 | 0.299053 | ||||||||
\(893\) | 71.5520 | 2.39440 | ||||||||
\(894\) | −37.5881 | −1.25713 | ||||||||
\(895\) | −0.535754 | −0.0179083 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.82301 | −0.227814 | ||||||||
\(898\) | 46.4533 | 1.55017 | ||||||||
\(899\) | −0.322370 | −0.0107516 | ||||||||
\(900\) | −3.45871 | −0.115290 | ||||||||
\(901\) | 4.85526 | 0.161752 | ||||||||
\(902\) | −8.11161 | −0.270087 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −24.9576 | −0.830078 | ||||||||
\(905\) | −0.168332 | −0.00559556 | ||||||||
\(906\) | 36.6876 | 1.21886 | ||||||||
\(907\) | −32.9319 | −1.09349 | −0.546743 | − | 0.837300i | \(-0.684133\pi\) | ||||
−0.546743 | + | 0.837300i | \(0.684133\pi\) | |||||||
\(908\) | −13.0920 | −0.434474 | ||||||||
\(909\) | −3.78486 | −0.125536 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.75669 | −0.0582018 | −0.0291009 | − | 0.999576i | \(-0.509264\pi\) | ||||
−0.0291009 | + | 0.999576i | \(0.509264\pi\) | |||||||
\(912\) | −32.1781 | −1.06552 | ||||||||
\(913\) | −44.6150 | −1.47654 | ||||||||
\(914\) | −0.0492893 | −0.00163034 | ||||||||
\(915\) | 0.0927060 | 0.00306477 | ||||||||
\(916\) | −0.995058 | −0.0328776 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.32954 | 0.0438815 | ||||||||
\(919\) | −31.1103 | −1.02623 | −0.513117 | − | 0.858319i | \(-0.671509\pi\) | ||||
−0.513117 | + | 0.858319i | \(0.671509\pi\) | |||||||
\(920\) | −0.971663 | −0.0320348 | ||||||||
\(921\) | 1.95055 | 0.0642728 | ||||||||
\(922\) | 55.6790 | 1.83369 | ||||||||
\(923\) | −6.84868 | −0.225427 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −26.1129 | −0.858588 | ||||||||
\(926\) | −49.2217 | −1.61753 | ||||||||
\(927\) | −19.1368 | −0.628536 | ||||||||
\(928\) | −0.168141 | −0.00551950 | ||||||||
\(929\) | −14.9878 | −0.491734 | −0.245867 | − | 0.969304i | \(-0.579073\pi\) | ||||
−0.245867 | + | 0.969304i | \(0.579073\pi\) | |||||||
\(930\) | −0.967025 | −0.0317100 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.2383 | −0.335366 | ||||||||
\(933\) | 25.3798 | 0.830897 | ||||||||
\(934\) | 26.7527 | 0.875376 | ||||||||
\(935\) | 0.327490 | 0.0107101 | ||||||||
\(936\) | 2.64233 | 0.0863672 | ||||||||
\(937\) | −46.7766 | −1.52812 | −0.764062 | − | 0.645143i | \(-0.776798\pi\) | ||||
−0.764062 | + | 0.645143i | \(0.776798\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.7300 | −0.545963 | ||||||||
\(940\) | 0.617797 | 0.0201503 | ||||||||
\(941\) | −1.19448 | −0.0389391 | −0.0194695 | − | 0.999810i | \(-0.506198\pi\) | ||||
−0.0194695 | + | 0.999810i | \(0.506198\pi\) | |||||||
\(942\) | −21.2451 | −0.692204 | ||||||||
\(943\) | 5.53945 | 0.180389 | ||||||||
\(944\) | 21.2927 | 0.693018 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −70.1557 | −2.28096 | ||||||||
\(947\) | 0.760030 | 0.0246977 | 0.0123488 | − | 0.999924i | \(-0.496069\pi\) | ||||
0.0123488 | + | 0.999924i | \(0.496069\pi\) | |||||||
\(948\) | 10.7761 | 0.349991 | ||||||||
\(949\) | −17.8687 | −0.580044 | ||||||||
\(950\) | 53.7468 | 1.74378 | ||||||||
\(951\) | −27.1439 | −0.880202 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.9749 | −1.48927 | −0.744637 | − | 0.667470i | \(-0.767377\pi\) | ||||
−0.744637 | + | 0.667470i | \(0.767377\pi\) | |||||||
\(954\) | 9.83314 | 0.318360 | ||||||||
\(955\) | −1.50906 | −0.0488321 | ||||||||
\(956\) | −0.719295 | −0.0232636 | ||||||||
\(957\) | 0.221103 | 0.00714725 | ||||||||
\(958\) | −2.90132 | −0.0937376 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.297832 | 0.00961250 | ||||||||
\(961\) | 20.9458 | 0.675670 | ||||||||
\(962\) | −10.5698 | −0.340784 | ||||||||
\(963\) | −13.5411 | −0.436356 | ||||||||
\(964\) | −16.8917 | −0.544044 | ||||||||
\(965\) | 1.85906 | 0.0598454 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.1637 | 0.648421 | 0.324211 | − | 0.945985i | \(-0.394901\pi\) | ||||
0.324211 | + | 0.945985i | \(0.394901\pi\) | |||||||
\(968\) | 28.8236 | 0.926427 | ||||||||
\(969\) | −5.31476 | −0.170735 | ||||||||
\(970\) | −0.730642 | −0.0234595 | ||||||||
\(971\) | −35.0294 | −1.12415 | −0.562074 | − | 0.827087i | \(-0.689996\pi\) | ||||
−0.562074 | + | 0.827087i | \(0.689996\pi\) | |||||||
\(972\) | 0.692668 | 0.0222173 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −20.5868 | −0.659644 | ||||||||
\(975\) | −6.15033 | −0.196968 | ||||||||
\(976\) | −5.56191 | −0.178033 | ||||||||
\(977\) | −58.3885 | −1.86801 | −0.934006 | − | 0.357257i | \(-0.883712\pi\) | ||||
−0.934006 | + | 0.357257i | \(0.883712\pi\) | |||||||
\(978\) | −3.88126 | −0.124109 | ||||||||
\(979\) | −36.5194 | −1.16717 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.705015 | 0.0225094 | ||||||||
\(982\) | 0.787983 | 0.0251455 | ||||||||
\(983\) | 36.7120 | 1.17093 | 0.585465 | − | 0.810698i | \(-0.300912\pi\) | ||||
0.585465 | + | 0.810698i | \(0.300912\pi\) | |||||||
\(984\) | −2.14525 | −0.0683880 | ||||||||
\(985\) | 0.154862 | 0.00493430 | ||||||||
\(986\) | −0.0594678 | −0.00189384 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.59638 | 0.178044 | ||||||||
\(989\) | 47.9097 | 1.52344 | ||||||||
\(990\) | 0.663251 | 0.0210795 | ||||||||
\(991\) | 25.4394 | 0.808108 | 0.404054 | − | 0.914735i | \(-0.367601\pi\) | ||||
0.404054 | + | 0.914735i | \(0.367601\pi\) | |||||||
\(992\) | 27.0938 | 0.860228 | ||||||||
\(993\) | −1.13038 | −0.0358714 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.69093 | 0.0536060 | ||||||||
\(996\) | 6.25159 | 0.198089 | ||||||||
\(997\) | −23.9681 | −0.759076 | −0.379538 | − | 0.925176i | \(-0.623917\pi\) | ||||
−0.379538 | + | 0.925176i | \(0.623917\pi\) | |||||||
\(998\) | −72.3202 | −2.28925 | ||||||||
\(999\) | 5.22958 | 0.165457 |
(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 | 6027.2.a.bk.1.4 | 14 | ||
7.3 | odd | 6 | 861.2.i.g.247.11 | ✓ | 28 | ||
7.5 | odd | 6 | 861.2.i.g.739.11 | yes | 28 | ||
7.6 | odd | 2 | 6027.2.a.bj.1.4 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.g.247.11 | ✓ | 28 | 7.3 | odd | 6 | ||
861.2.i.g.739.11 | yes | 28 | 7.5 | odd | 6 | ||
6027.2.a.bj.1.4 | 14 | 7.6 | odd | 2 | |||
6027.2.a.bk.1.4 | 14 | 1.1 | even | 1 | trivial |