Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(1,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("605.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.404.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.210756\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.74483 | −1.94089 | −0.970443 | − | 0.241332i | \(-0.922416\pi\) | ||||
−0.970443 | + | 0.241332i | \(0.922416\pi\) | |||||||
\(3\) | −0.210756 | −0.121680 | −0.0608400 | − | 0.998148i | \(-0.519378\pi\) | ||||
−0.0608400 | + | 0.998148i | \(0.519378\pi\) | |||||||
\(4\) | 5.53407 | 2.76704 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.578488 | 0.236167 | ||||||||
\(7\) | −2.32331 | −0.878130 | −0.439065 | − | 0.898455i | \(-0.644690\pi\) | ||||
−0.439065 | + | 0.898455i | \(0.644690\pi\) | |||||||
\(8\) | −9.70041 | −3.42961 | ||||||||
\(9\) | −2.95558 | −0.985194 | ||||||||
\(10\) | 2.74483 | 0.867990 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.16634 | −0.336693 | ||||||||
\(13\) | −0.534070 | −0.148124 | −0.0740622 | − | 0.997254i | \(-0.523596\pi\) | ||||
−0.0740622 | + | 0.997254i | \(0.523596\pi\) | |||||||
\(14\) | 6.37709 | 1.70435 | ||||||||
\(15\) | 0.210756 | 0.0544169 | ||||||||
\(16\) | 15.5578 | 3.88945 | ||||||||
\(17\) | 2.42151 | 0.587303 | 0.293651 | − | 0.955913i | \(-0.405130\pi\) | ||||
0.293651 | + | 0.955913i | \(0.405130\pi\) | |||||||
\(18\) | 8.11256 | 1.91215 | ||||||||
\(19\) | 4.95558 | 1.13689 | 0.568444 | − | 0.822722i | \(-0.307546\pi\) | ||||
0.568444 | + | 0.822722i | \(0.307546\pi\) | |||||||
\(20\) | −5.53407 | −1.23746 | ||||||||
\(21\) | 0.489652 | 0.106851 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.53407 | −0.945419 | −0.472709 | − | 0.881218i | \(-0.656724\pi\) | ||||
−0.472709 | + | 0.881218i | \(0.656724\pi\) | |||||||
\(24\) | 2.04442 | 0.417315 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.46593 | 0.287492 | ||||||||
\(27\) | 1.25517 | 0.241558 | ||||||||
\(28\) | −12.8574 | −2.42982 | ||||||||
\(29\) | −5.48965 | −1.01940 | −0.509701 | − | 0.860351i | \(-0.670244\pi\) | ||||
−0.509701 | + | 0.860351i | \(0.670244\pi\) | |||||||
\(30\) | −0.578488 | −0.105617 | ||||||||
\(31\) | 1.04442 | 0.187583 | 0.0937915 | − | 0.995592i | \(-0.470101\pi\) | ||||
0.0937915 | + | 0.995592i | \(0.470101\pi\) | |||||||
\(32\) | −23.3026 | −4.11936 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.64663 | −1.13989 | ||||||||
\(35\) | 2.32331 | 0.392712 | ||||||||
\(36\) | −16.3564 | −2.72607 | ||||||||
\(37\) | 7.48965 | 1.23129 | 0.615646 | − | 0.788023i | \(-0.288895\pi\) | ||||
0.615646 | + | 0.788023i | \(0.288895\pi\) | |||||||
\(38\) | −13.6022 | −2.20657 | ||||||||
\(39\) | 0.112558 | 0.0180238 | ||||||||
\(40\) | 9.70041 | 1.53377 | ||||||||
\(41\) | 10.6022 | 1.65579 | 0.827894 | − | 0.560885i | \(-0.189539\pi\) | ||||
0.827894 | + | 0.560885i | \(0.189539\pi\) | |||||||
\(42\) | −1.34401 | −0.207385 | ||||||||
\(43\) | 4.32331 | 0.659299 | 0.329650 | − | 0.944103i | \(-0.393069\pi\) | ||||
0.329650 | + | 0.944103i | \(0.393069\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.95558 | 0.440592 | ||||||||
\(46\) | 12.4452 | 1.83495 | ||||||||
\(47\) | 6.76855 | 0.987294 | 0.493647 | − | 0.869662i | \(-0.335663\pi\) | ||||
0.493647 | + | 0.869662i | \(0.335663\pi\) | |||||||
\(48\) | −3.27890 | −0.473268 | ||||||||
\(49\) | −1.60221 | −0.228887 | ||||||||
\(50\) | −2.74483 | −0.388177 | ||||||||
\(51\) | −0.510348 | −0.0714630 | ||||||||
\(52\) | −2.95558 | −0.409865 | ||||||||
\(53\) | −4.53407 | −0.622802 | −0.311401 | − | 0.950279i | \(-0.600798\pi\) | ||||
−0.311401 | + | 0.950279i | \(0.600798\pi\) | |||||||
\(54\) | −3.44523 | −0.468837 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 22.5371 | 3.01165 | ||||||||
\(57\) | −1.04442 | −0.138337 | ||||||||
\(58\) | 15.0681 | 1.97854 | ||||||||
\(59\) | −6.44523 | −0.839098 | −0.419549 | − | 0.907733i | \(-0.637812\pi\) | ||||
−0.419549 | + | 0.907733i | \(0.637812\pi\) | |||||||
\(60\) | 1.16634 | 0.150574 | ||||||||
\(61\) | 6.79861 | 0.870472 | 0.435236 | − | 0.900316i | \(-0.356665\pi\) | ||||
0.435236 | + | 0.900316i | \(0.356665\pi\) | |||||||
\(62\) | −2.86675 | −0.364077 | ||||||||
\(63\) | 6.86675 | 0.865129 | ||||||||
\(64\) | 32.8461 | 4.10576 | ||||||||
\(65\) | 0.534070 | 0.0662433 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.721104 | 0.0880968 | 0.0440484 | − | 0.999029i | \(-0.485974\pi\) | ||||
0.0440484 | + | 0.999029i | \(0.485974\pi\) | |||||||
\(68\) | 13.4008 | 1.62509 | ||||||||
\(69\) | 0.955582 | 0.115039 | ||||||||
\(70\) | −6.37709 | −0.762208 | ||||||||
\(71\) | 4.53407 | 0.538095 | 0.269048 | − | 0.963127i | \(-0.413291\pi\) | ||||
0.269048 | + | 0.963127i | \(0.413291\pi\) | |||||||
\(72\) | 28.6704 | 3.37883 | ||||||||
\(73\) | 1.06814 | 0.125016 | 0.0625082 | − | 0.998044i | \(-0.480090\pi\) | ||||
0.0625082 | + | 0.998044i | \(0.480090\pi\) | |||||||
\(74\) | −20.5578 | −2.38979 | ||||||||
\(75\) | −0.210756 | −0.0243360 | ||||||||
\(76\) | 27.4245 | 3.14581 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.308953 | −0.0349821 | ||||||||
\(79\) | 4.64663 | 0.522787 | 0.261393 | − | 0.965232i | \(-0.415818\pi\) | ||||
0.261393 | + | 0.965232i | \(0.415818\pi\) | |||||||
\(80\) | −15.5578 | −1.73941 | ||||||||
\(81\) | 8.60221 | 0.955801 | ||||||||
\(82\) | −29.1012 | −3.21369 | ||||||||
\(83\) | 13.6022 | 1.49304 | 0.746518 | − | 0.665365i | \(-0.231724\pi\) | ||||
0.746518 | + | 0.665365i | \(0.231724\pi\) | |||||||
\(84\) | 2.70977 | 0.295660 | ||||||||
\(85\) | −2.42151 | −0.262650 | ||||||||
\(86\) | −11.8667 | −1.27962 | ||||||||
\(87\) | 1.15698 | 0.124041 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.7148 | 1.34776 | 0.673881 | − | 0.738840i | \(-0.264626\pi\) | ||||
0.673881 | + | 0.738840i | \(0.264626\pi\) | |||||||
\(90\) | −8.11256 | −0.855139 | ||||||||
\(91\) | 1.24081 | 0.130073 | ||||||||
\(92\) | −25.0919 | −2.61601 | ||||||||
\(93\) | −0.220117 | −0.0228251 | ||||||||
\(94\) | −18.5785 | −1.91622 | ||||||||
\(95\) | −4.95558 | −0.508432 | ||||||||
\(96\) | 4.91116 | 0.501244 | ||||||||
\(97\) | 4.75919 | 0.483222 | 0.241611 | − | 0.970373i | \(-0.422324\pi\) | ||||
0.241611 | + | 0.970373i | \(0.422324\pi\) | |||||||
\(98\) | 4.39779 | 0.444244 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.53407 | 0.553407 | ||||||||
\(101\) | −6.57849 | −0.654584 | −0.327292 | − | 0.944923i | \(-0.606136\pi\) | ||||
−0.327292 | + | 0.944923i | \(0.606136\pi\) | |||||||
\(102\) | 1.40082 | 0.138701 | ||||||||
\(103\) | 16.3564 | 1.61164 | 0.805822 | − | 0.592158i | \(-0.201724\pi\) | ||||
0.805822 | + | 0.592158i | \(0.201724\pi\) | |||||||
\(104\) | 5.18070 | 0.508009 | ||||||||
\(105\) | −0.489652 | −0.0477852 | ||||||||
\(106\) | 12.4452 | 1.20879 | ||||||||
\(107\) | 10.2108 | 0.987111 | 0.493556 | − | 0.869714i | \(-0.335697\pi\) | ||||
0.493556 | + | 0.869714i | \(0.335697\pi\) | |||||||
\(108\) | 6.94622 | 0.668400 | ||||||||
\(109\) | −12.0919 | −1.15819 | −0.579095 | − | 0.815260i | \(-0.696594\pi\) | ||||
−0.579095 | + | 0.815260i | \(0.696594\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.57849 | −0.149823 | ||||||||
\(112\) | −36.1456 | −3.41544 | ||||||||
\(113\) | −10.8430 | −1.02003 | −0.510013 | − | 0.860167i | \(-0.670359\pi\) | ||||
−0.510013 | + | 0.860167i | \(0.670359\pi\) | |||||||
\(114\) | 2.86675 | 0.268495 | ||||||||
\(115\) | 4.53407 | 0.422804 | ||||||||
\(116\) | −30.3801 | −2.82072 | ||||||||
\(117\) | 1.57849 | 0.145931 | ||||||||
\(118\) | 17.6910 | 1.62859 | ||||||||
\(119\) | −5.62593 | −0.515728 | ||||||||
\(120\) | −2.04442 | −0.186629 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −18.6610 | −1.68949 | ||||||||
\(123\) | −2.23448 | −0.201476 | ||||||||
\(124\) | 5.77988 | 0.519049 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −18.8480 | −1.67912 | ||||||||
\(127\) | −8.12192 | −0.720704 | −0.360352 | − | 0.932816i | \(-0.617343\pi\) | ||||
−0.360352 | + | 0.932816i | \(0.617343\pi\) | |||||||
\(128\) | −43.5515 | −3.84944 | ||||||||
\(129\) | −0.911164 | −0.0802235 | ||||||||
\(130\) | −1.46593 | −0.128571 | ||||||||
\(131\) | 5.79861 | 0.506627 | 0.253313 | − | 0.967384i | \(-0.418480\pi\) | ||||
0.253313 | + | 0.967384i | \(0.418480\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.5134 | −0.998336 | ||||||||
\(134\) | −1.97930 | −0.170986 | ||||||||
\(135\) | −1.25517 | −0.108028 | ||||||||
\(136\) | −23.4897 | −2.01422 | ||||||||
\(137\) | 8.86675 | 0.757537 | 0.378769 | − | 0.925491i | \(-0.376348\pi\) | ||||
0.378769 | + | 0.925491i | \(0.376348\pi\) | |||||||
\(138\) | −2.62291 | −0.223277 | ||||||||
\(139\) | −16.8667 | −1.43062 | −0.715309 | − | 0.698808i | \(-0.753714\pi\) | ||||
−0.715309 | + | 0.698808i | \(0.753714\pi\) | |||||||
\(140\) | 12.8574 | 1.08665 | ||||||||
\(141\) | −1.42651 | −0.120134 | ||||||||
\(142\) | −12.4452 | −1.04438 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −45.9823 | −3.83186 | ||||||||
\(145\) | 5.48965 | 0.455891 | ||||||||
\(146\) | −2.93186 | −0.242642 | ||||||||
\(147\) | 0.337675 | 0.0278510 | ||||||||
\(148\) | 41.4483 | 3.40703 | ||||||||
\(149\) | 4.46593 | 0.365863 | 0.182932 | − | 0.983126i | \(-0.441441\pi\) | ||||
0.182932 | + | 0.983126i | \(0.441441\pi\) | |||||||
\(150\) | 0.578488 | 0.0472334 | ||||||||
\(151\) | −11.5134 | −0.936945 | −0.468473 | − | 0.883478i | \(-0.655196\pi\) | ||||
−0.468473 | + | 0.883478i | \(0.655196\pi\) | |||||||
\(152\) | −48.0712 | −3.89909 | ||||||||
\(153\) | −7.15698 | −0.578607 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.04442 | −0.0838897 | ||||||||
\(156\) | 0.622906 | 0.0498724 | ||||||||
\(157\) | −5.91116 | −0.471762 | −0.235881 | − | 0.971782i | \(-0.575798\pi\) | ||||
−0.235881 | + | 0.971782i | \(0.575798\pi\) | |||||||
\(158\) | −12.7542 | −1.01467 | ||||||||
\(159\) | 0.955582 | 0.0757826 | ||||||||
\(160\) | 23.3026 | 1.84223 | ||||||||
\(161\) | 10.5341 | 0.830201 | ||||||||
\(162\) | −23.6116 | −1.85510 | ||||||||
\(163\) | 23.4990 | 1.84058 | 0.920292 | − | 0.391231i | \(-0.127951\pi\) | ||||
0.920292 | + | 0.391231i | \(0.127951\pi\) | |||||||
\(164\) | 58.6734 | 4.58162 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −37.3357 | −2.89781 | ||||||||
\(167\) | 14.2345 | 1.10150 | 0.550748 | − | 0.834671i | \(-0.314342\pi\) | ||||
0.550748 | + | 0.834671i | \(0.314342\pi\) | |||||||
\(168\) | −4.74983 | −0.366457 | ||||||||
\(169\) | −12.7148 | −0.978059 | ||||||||
\(170\) | 6.64663 | 0.509773 | ||||||||
\(171\) | −14.6466 | −1.12006 | ||||||||
\(172\) | 23.9255 | 1.82430 | ||||||||
\(173\) | −6.44523 | −0.490022 | −0.245011 | − | 0.969520i | \(-0.578792\pi\) | ||||
−0.245011 | + | 0.969520i | \(0.578792\pi\) | |||||||
\(174\) | −3.17570 | −0.240749 | ||||||||
\(175\) | −2.32331 | −0.175626 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.35837 | 0.102101 | ||||||||
\(178\) | −34.8998 | −2.61585 | ||||||||
\(179\) | 16.9793 | 1.26909 | 0.634546 | − | 0.772885i | \(-0.281187\pi\) | ||||
0.634546 | + | 0.772885i | \(0.281187\pi\) | |||||||
\(180\) | 16.3564 | 1.21913 | ||||||||
\(181\) | 4.48965 | 0.333713 | 0.166857 | − | 0.985981i | \(-0.446638\pi\) | ||||
0.166857 | + | 0.985981i | \(0.446638\pi\) | |||||||
\(182\) | −3.40582 | −0.252456 | ||||||||
\(183\) | −1.43285 | −0.105919 | ||||||||
\(184\) | 43.9823 | 3.24242 | ||||||||
\(185\) | −7.48965 | −0.550650 | ||||||||
\(186\) | 0.604184 | 0.0443009 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 37.4576 | 2.73188 | ||||||||
\(189\) | −2.91616 | −0.212120 | ||||||||
\(190\) | 13.6022 | 0.986808 | ||||||||
\(191\) | −2.75919 | −0.199648 | −0.0998239 | − | 0.995005i | \(-0.531828\pi\) | ||||
−0.0998239 | + | 0.995005i | \(0.531828\pi\) | |||||||
\(192\) | −6.92250 | −0.499588 | ||||||||
\(193\) | 11.8036 | 0.849642 | 0.424821 | − | 0.905277i | \(-0.360337\pi\) | ||||
0.424821 | + | 0.905277i | \(0.360337\pi\) | |||||||
\(194\) | −13.0631 | −0.937879 | ||||||||
\(195\) | −0.112558 | −0.00806048 | ||||||||
\(196\) | −8.86675 | −0.633339 | ||||||||
\(197\) | −6.51035 | −0.463843 | −0.231922 | − | 0.972734i | \(-0.574501\pi\) | ||||
−0.231922 | + | 0.972734i | \(0.574501\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.9586 | 1.69838 | 0.849190 | − | 0.528087i | \(-0.177090\pi\) | ||||
0.849190 | + | 0.528087i | \(0.177090\pi\) | |||||||
\(200\) | −9.70041 | −0.685922 | ||||||||
\(201\) | −0.151977 | −0.0107196 | ||||||||
\(202\) | 18.0568 | 1.27047 | ||||||||
\(203\) | 12.7542 | 0.895168 | ||||||||
\(204\) | −2.82430 | −0.197741 | ||||||||
\(205\) | −10.6022 | −0.740491 | ||||||||
\(206\) | −44.8955 | −3.12802 | ||||||||
\(207\) | 13.4008 | 0.931421 | ||||||||
\(208\) | −8.30895 | −0.576122 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.34401 | 0.0927455 | ||||||||
\(211\) | −16.8667 | −1.16115 | −0.580577 | − | 0.814205i | \(-0.697173\pi\) | ||||
−0.580577 | + | 0.814205i | \(0.697173\pi\) | |||||||
\(212\) | −25.0919 | −1.72332 | ||||||||
\(213\) | −0.955582 | −0.0654754 | ||||||||
\(214\) | −28.0267 | −1.91587 | ||||||||
\(215\) | −4.32331 | −0.294848 | ||||||||
\(216\) | −12.1757 | −0.828451 | ||||||||
\(217\) | −2.42651 | −0.164722 | ||||||||
\(218\) | 33.1901 | 2.24791 | ||||||||
\(219\) | −0.225117 | −0.0152120 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.29326 | −0.0869939 | ||||||||
\(222\) | 4.33268 | 0.290790 | ||||||||
\(223\) | −25.0174 | −1.67529 | −0.837644 | − | 0.546216i | \(-0.816068\pi\) | ||||
−0.837644 | + | 0.546216i | \(0.816068\pi\) | |||||||
\(224\) | 54.1393 | 3.61733 | ||||||||
\(225\) | −2.95558 | −0.197039 | ||||||||
\(226\) | 29.7622 | 1.97975 | ||||||||
\(227\) | 4.00936 | 0.266111 | 0.133055 | − | 0.991109i | \(-0.457521\pi\) | ||||
0.133055 | + | 0.991109i | \(0.457521\pi\) | |||||||
\(228\) | −5.77988 | −0.382782 | ||||||||
\(229\) | −17.3327 | −1.14538 | −0.572688 | − | 0.819774i | \(-0.694099\pi\) | ||||
−0.572688 | + | 0.819774i | \(0.694099\pi\) | |||||||
\(230\) | −12.4452 | −0.820614 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 53.2519 | 3.49616 | ||||||||
\(233\) | 2.11256 | 0.138398 | 0.0691992 | − | 0.997603i | \(-0.477956\pi\) | ||||
0.0691992 | + | 0.997603i | \(0.477956\pi\) | |||||||
\(234\) | −4.33268 | −0.283236 | ||||||||
\(235\) | −6.76855 | −0.441531 | ||||||||
\(236\) | −35.6684 | −2.32181 | ||||||||
\(237\) | −0.979304 | −0.0636127 | ||||||||
\(238\) | 15.4422 | 1.00097 | ||||||||
\(239\) | −23.9349 | −1.54822 | −0.774110 | − | 0.633052i | \(-0.781802\pi\) | ||||
−0.774110 | + | 0.633052i | \(0.781802\pi\) | |||||||
\(240\) | 3.27890 | 0.211652 | ||||||||
\(241\) | −14.5134 | −0.934889 | −0.467444 | − | 0.884023i | \(-0.654825\pi\) | ||||
−0.467444 | + | 0.884023i | \(0.654825\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.57849 | −0.357860 | ||||||||
\(244\) | 37.6240 | 2.40863 | ||||||||
\(245\) | 1.60221 | 0.102361 | ||||||||
\(246\) | 6.13325 | 0.391042 | ||||||||
\(247\) | −2.64663 | −0.168401 | ||||||||
\(248\) | −10.1313 | −0.643337 | ||||||||
\(249\) | −2.86675 | −0.181673 | ||||||||
\(250\) | 2.74483 | 0.173598 | ||||||||
\(251\) | 28.8066 | 1.81826 | 0.909129 | − | 0.416514i | \(-0.136748\pi\) | ||||
0.909129 | + | 0.416514i | \(0.136748\pi\) | |||||||
\(252\) | 38.0011 | 2.39384 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 22.2933 | 1.39880 | ||||||||
\(255\) | 0.510348 | 0.0319592 | ||||||||
\(256\) | 53.8491 | 3.36557 | ||||||||
\(257\) | −27.6497 | −1.72474 | −0.862369 | − | 0.506280i | \(-0.831020\pi\) | ||||
−0.862369 | + | 0.506280i | \(0.831020\pi\) | |||||||
\(258\) | 2.50099 | 0.155705 | ||||||||
\(259\) | −17.4008 | −1.08123 | ||||||||
\(260\) | 2.95558 | 0.183297 | ||||||||
\(261\) | 16.2251 | 1.00431 | ||||||||
\(262\) | −15.9162 | −0.983304 | ||||||||
\(263\) | 3.13325 | 0.193205 | 0.0966024 | − | 0.995323i | \(-0.469202\pi\) | ||||
0.0966024 | + | 0.995323i | \(0.469202\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.53407 | 0.278526 | ||||||||
\(266\) | 31.6022 | 1.93766 | ||||||||
\(267\) | −2.67971 | −0.163996 | ||||||||
\(268\) | 3.99064 | 0.243767 | ||||||||
\(269\) | 18.0030 | 1.09766 | 0.548832 | − | 0.835933i | \(-0.315073\pi\) | ||||
0.548832 | + | 0.835933i | \(0.315073\pi\) | |||||||
\(270\) | 3.44523 | 0.209670 | ||||||||
\(271\) | 20.3327 | 1.23512 | 0.617561 | − | 0.786523i | \(-0.288121\pi\) | ||||
0.617561 | + | 0.786523i | \(0.288121\pi\) | |||||||
\(272\) | 37.6734 | 2.28428 | ||||||||
\(273\) | −0.261509 | −0.0158272 | ||||||||
\(274\) | −24.3377 | −1.47029 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.28826 | 0.318316 | ||||||||
\(277\) | −25.4897 | −1.53152 | −0.765762 | − | 0.643124i | \(-0.777638\pi\) | ||||
−0.765762 | + | 0.643124i | \(0.777638\pi\) | |||||||
\(278\) | 46.2963 | 2.77667 | ||||||||
\(279\) | −3.08686 | −0.184806 | ||||||||
\(280\) | −22.5371 | −1.34685 | ||||||||
\(281\) | 18.2726 | 1.09005 | 0.545025 | − | 0.838420i | \(-0.316520\pi\) | ||||
0.545025 | + | 0.838420i | \(0.316520\pi\) | |||||||
\(282\) | 3.91553 | 0.233166 | ||||||||
\(283\) | −11.0538 | −0.657079 | −0.328539 | − | 0.944490i | \(-0.606556\pi\) | ||||
−0.328539 | + | 0.944490i | \(0.606556\pi\) | |||||||
\(284\) | 25.0919 | 1.48893 | ||||||||
\(285\) | 1.04442 | 0.0618660 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −24.6323 | −1.45400 | ||||||||
\(288\) | 68.8728 | 4.05837 | ||||||||
\(289\) | −11.1363 | −0.655075 | ||||||||
\(290\) | −15.0681 | −0.884832 | ||||||||
\(291\) | −1.00303 | −0.0587985 | ||||||||
\(292\) | 5.91116 | 0.345925 | ||||||||
\(293\) | 27.1393 | 1.58550 | 0.792748 | − | 0.609550i | \(-0.208650\pi\) | ||||
0.792748 | + | 0.609550i | \(0.208650\pi\) | |||||||
\(294\) | −0.926860 | −0.0540556 | ||||||||
\(295\) | 6.44523 | 0.375256 | ||||||||
\(296\) | −72.6527 | −4.22285 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.2582 | −0.710098 | ||||||||
\(299\) | 2.42151 | 0.140040 | ||||||||
\(300\) | −1.16634 | −0.0673385 | ||||||||
\(301\) | −10.0444 | −0.578951 | ||||||||
\(302\) | 31.6022 | 1.81850 | ||||||||
\(303\) | 1.38646 | 0.0796498 | ||||||||
\(304\) | 77.0979 | 4.42187 | ||||||||
\(305\) | −6.79861 | −0.389287 | ||||||||
\(306\) | 19.6447 | 1.12301 | ||||||||
\(307\) | 11.7385 | 0.669951 | 0.334976 | − | 0.942227i | \(-0.391272\pi\) | ||||
0.334976 | + | 0.942227i | \(0.391272\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.44721 | −0.196105 | ||||||||
\(310\) | 2.86675 | 0.162820 | ||||||||
\(311\) | 10.6416 | 0.603431 | 0.301716 | − | 0.953398i | \(-0.402441\pi\) | ||||
0.301716 | + | 0.953398i | \(0.402441\pi\) | |||||||
\(312\) | −1.09186 | −0.0618146 | ||||||||
\(313\) | −27.1807 | −1.53634 | −0.768172 | − | 0.640244i | \(-0.778833\pi\) | ||||
−0.768172 | + | 0.640244i | \(0.778833\pi\) | |||||||
\(314\) | 16.2251 | 0.915636 | ||||||||
\(315\) | −6.86675 | −0.386897 | ||||||||
\(316\) | 25.7148 | 1.44657 | ||||||||
\(317\) | 4.97930 | 0.279666 | 0.139833 | − | 0.990175i | \(-0.455343\pi\) | ||||
0.139833 | + | 0.990175i | \(0.455343\pi\) | |||||||
\(318\) | −2.62291 | −0.147085 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −32.8461 | −1.83615 | ||||||||
\(321\) | −2.15198 | −0.120112 | ||||||||
\(322\) | −28.9142 | −1.61132 | ||||||||
\(323\) | 12.0000 | 0.667698 | ||||||||
\(324\) | 47.6052 | 2.64474 | ||||||||
\(325\) | −0.534070 | −0.0296249 | ||||||||
\(326\) | −64.5007 | −3.57236 | ||||||||
\(327\) | 2.54843 | 0.140929 | ||||||||
\(328\) | −102.846 | −5.67871 | ||||||||
\(329\) | −15.7255 | −0.866973 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.55477 | 0.415247 | 0.207624 | − | 0.978209i | \(-0.433427\pi\) | ||||
0.207624 | + | 0.978209i | \(0.433427\pi\) | |||||||
\(332\) | 75.2756 | 4.13128 | ||||||||
\(333\) | −22.1363 | −1.21306 | ||||||||
\(334\) | −39.0712 | −2.13788 | ||||||||
\(335\) | −0.721104 | −0.0393981 | ||||||||
\(336\) | 7.61791 | 0.415591 | ||||||||
\(337\) | 3.69105 | 0.201064 | 0.100532 | − | 0.994934i | \(-0.467946\pi\) | ||||
0.100532 | + | 0.994934i | \(0.467946\pi\) | |||||||
\(338\) | 34.8998 | 1.89830 | ||||||||
\(339\) | 2.28523 | 0.124117 | ||||||||
\(340\) | −13.4008 | −0.726761 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 40.2024 | 2.17390 | ||||||||
\(343\) | 19.9856 | 1.07912 | ||||||||
\(344\) | −41.9379 | −2.26114 | ||||||||
\(345\) | −0.955582 | −0.0514468 | ||||||||
\(346\) | 17.6910 | 0.951077 | ||||||||
\(347\) | −15.7655 | −0.846338 | −0.423169 | − | 0.906051i | \(-0.639082\pi\) | ||||
−0.423169 | + | 0.906051i | \(0.639082\pi\) | |||||||
\(348\) | 6.40279 | 0.343226 | ||||||||
\(349\) | −10.5578 | −0.565146 | −0.282573 | − | 0.959246i | \(-0.591188\pi\) | ||||
−0.282573 | + | 0.959246i | \(0.591188\pi\) | |||||||
\(350\) | 6.37709 | 0.340870 | ||||||||
\(351\) | −0.670351 | −0.0357807 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.5528 | −1.30681 | −0.653407 | − | 0.757007i | \(-0.726661\pi\) | ||||
−0.653407 | + | 0.757007i | \(0.726661\pi\) | |||||||
\(354\) | −3.72849 | −0.198167 | ||||||||
\(355\) | −4.53407 | −0.240643 | ||||||||
\(356\) | 70.3644 | 3.72931 | ||||||||
\(357\) | 1.18570 | 0.0627538 | ||||||||
\(358\) | −46.6052 | −2.46316 | ||||||||
\(359\) | −16.6704 | −0.879827 | −0.439914 | − | 0.898040i | \(-0.644991\pi\) | ||||
−0.439914 | + | 0.898040i | \(0.644991\pi\) | |||||||
\(360\) | −28.6704 | −1.51106 | ||||||||
\(361\) | 5.55779 | 0.292515 | ||||||||
\(362\) | −12.3233 | −0.647699 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.86675 | 0.359915 | ||||||||
\(365\) | −1.06814 | −0.0559090 | ||||||||
\(366\) | 3.93291 | 0.205577 | ||||||||
\(367\) | 15.2789 | 0.797552 | 0.398776 | − | 0.917048i | \(-0.369435\pi\) | ||||
0.398776 | + | 0.917048i | \(0.369435\pi\) | |||||||
\(368\) | −70.5401 | −3.67716 | ||||||||
\(369\) | −31.3357 | −1.63127 | ||||||||
\(370\) | 20.5578 | 1.06875 | ||||||||
\(371\) | 10.5341 | 0.546902 | ||||||||
\(372\) | −1.21814 | −0.0631578 | ||||||||
\(373\) | 17.8461 | 0.924033 | 0.462017 | − | 0.886871i | \(-0.347126\pi\) | ||||
0.462017 | + | 0.886871i | \(0.347126\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.210756 | 0.0108834 | ||||||||
\(376\) | −65.6577 | −3.38604 | ||||||||
\(377\) | 2.93186 | 0.150998 | ||||||||
\(378\) | 8.00436 | 0.411700 | ||||||||
\(379\) | 1.89244 | 0.0972082 | 0.0486041 | − | 0.998818i | \(-0.484523\pi\) | ||||
0.0486041 | + | 0.998818i | \(0.484523\pi\) | |||||||
\(380\) | −27.4245 | −1.40685 | ||||||||
\(381\) | 1.71174 | 0.0876952 | ||||||||
\(382\) | 7.57349 | 0.387493 | ||||||||
\(383\) | 5.31698 | 0.271685 | 0.135842 | − | 0.990730i | \(-0.456626\pi\) | ||||
0.135842 | + | 0.990730i | \(0.456626\pi\) | |||||||
\(384\) | 9.17873 | 0.468400 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −32.3988 | −1.64906 | ||||||||
\(387\) | −12.7779 | −0.649538 | ||||||||
\(388\) | 26.3377 | 1.33709 | ||||||||
\(389\) | −26.8273 | −1.36020 | −0.680100 | − | 0.733120i | \(-0.738064\pi\) | ||||
−0.680100 | + | 0.733120i | \(0.738064\pi\) | |||||||
\(390\) | 0.308953 | 0.0156445 | ||||||||
\(391\) | −10.9793 | −0.555247 | ||||||||
\(392\) | 15.5421 | 0.784994 | ||||||||
\(393\) | −1.22209 | −0.0616463 | ||||||||
\(394\) | 17.8698 | 0.900266 | ||||||||
\(395\) | −4.64663 | −0.233797 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.5972 | 1.58582 | 0.792909 | − | 0.609340i | \(-0.208565\pi\) | ||||
0.792909 | + | 0.609340i | \(0.208565\pi\) | |||||||
\(398\) | −65.7622 | −3.29636 | ||||||||
\(399\) | 2.42651 | 0.121478 | ||||||||
\(400\) | 15.5578 | 0.777890 | ||||||||
\(401\) | −3.13628 | −0.156618 | −0.0783092 | − | 0.996929i | \(-0.524952\pi\) | ||||
−0.0783092 | + | 0.996929i | \(0.524952\pi\) | |||||||
\(402\) | 0.417150 | 0.0208056 | ||||||||
\(403\) | −0.557793 | −0.0277856 | ||||||||
\(404\) | −36.4058 | −1.81126 | ||||||||
\(405\) | −8.60221 | −0.427447 | ||||||||
\(406\) | −35.0080 | −1.73742 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 4.95058 | 0.245090 | ||||||||
\(409\) | 0.424538 | 0.0209921 | 0.0104960 | − | 0.999945i | \(-0.496659\pi\) | ||||
0.0104960 | + | 0.999945i | \(0.496659\pi\) | |||||||
\(410\) | 29.1012 | 1.43721 | ||||||||
\(411\) | −1.86872 | −0.0921771 | ||||||||
\(412\) | 90.5175 | 4.45947 | ||||||||
\(413\) | 14.9743 | 0.736837 | ||||||||
\(414\) | −36.7829 | −1.80778 | ||||||||
\(415\) | −13.6022 | −0.667706 | ||||||||
\(416\) | 12.4452 | 0.610178 | ||||||||
\(417\) | 3.55477 | 0.174078 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.71174 | 0.327890 | 0.163945 | − | 0.986469i | \(-0.447578\pi\) | ||||
0.163945 | + | 0.986469i | \(0.447578\pi\) | |||||||
\(420\) | −2.70977 | −0.132223 | ||||||||
\(421\) | 2.77988 | 0.135483 | 0.0677416 | − | 0.997703i | \(-0.478421\pi\) | ||||
0.0677416 | + | 0.997703i | \(0.478421\pi\) | |||||||
\(422\) | 46.2963 | 2.25367 | ||||||||
\(423\) | −20.0050 | −0.972676 | ||||||||
\(424\) | 43.9823 | 2.13597 | ||||||||
\(425\) | 2.42151 | 0.117461 | ||||||||
\(426\) | 2.62291 | 0.127080 | ||||||||
\(427\) | −15.7953 | −0.764388 | ||||||||
\(428\) | 56.5070 | 2.73137 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.8667 | 0.572265 | ||||||||
\(431\) | 16.1964 | 0.780153 | 0.390076 | − | 0.920782i | \(-0.372449\pi\) | ||||
0.390076 | + | 0.920782i | \(0.372449\pi\) | |||||||
\(432\) | 19.5277 | 0.939529 | ||||||||
\(433\) | 7.82733 | 0.376157 | 0.188079 | − | 0.982154i | \(-0.439774\pi\) | ||||
0.188079 | + | 0.982154i | \(0.439774\pi\) | |||||||
\(434\) | 6.66035 | 0.319707 | ||||||||
\(435\) | −1.15698 | −0.0554728 | ||||||||
\(436\) | −66.9172 | −3.20475 | ||||||||
\(437\) | −22.4690 | −1.07484 | ||||||||
\(438\) | 0.617907 | 0.0295247 | ||||||||
\(439\) | 20.7355 | 0.989650 | 0.494825 | − | 0.868993i | \(-0.335232\pi\) | ||||
0.494825 | + | 0.868993i | \(0.335232\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.73546 | 0.225498 | ||||||||
\(442\) | 3.54977 | 0.168845 | ||||||||
\(443\) | 5.30262 | 0.251935 | 0.125968 | − | 0.992034i | \(-0.459796\pi\) | ||||
0.125968 | + | 0.992034i | \(0.459796\pi\) | |||||||
\(444\) | −8.73546 | −0.414567 | ||||||||
\(445\) | −12.7148 | −0.602738 | ||||||||
\(446\) | 68.6684 | 3.25154 | ||||||||
\(447\) | −0.941221 | −0.0445182 | ||||||||
\(448\) | −76.3117 | −3.60539 | ||||||||
\(449\) | −30.0030 | −1.41593 | −0.707965 | − | 0.706247i | \(-0.750387\pi\) | ||||
−0.707965 | + | 0.706247i | \(0.750387\pi\) | |||||||
\(450\) | 8.11256 | 0.382430 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −60.0061 | −2.82245 | ||||||||
\(453\) | 2.42651 | 0.114007 | ||||||||
\(454\) | −11.0050 | −0.516490 | ||||||||
\(455\) | −1.24081 | −0.0581702 | ||||||||
\(456\) | 10.1313 | 0.474441 | ||||||||
\(457\) | 37.5134 | 1.75480 | 0.877401 | − | 0.479758i | \(-0.159276\pi\) | ||||
0.877401 | + | 0.479758i | \(0.159276\pi\) | |||||||
\(458\) | 47.5752 | 2.22304 | ||||||||
\(459\) | 3.03942 | 0.141868 | ||||||||
\(460\) | 25.0919 | 1.16991 | ||||||||
\(461\) | 15.7829 | 0.735083 | 0.367542 | − | 0.930007i | \(-0.380200\pi\) | ||||
0.367542 | + | 0.930007i | \(0.380200\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.5672 | −0.769941 | −0.384970 | − | 0.922929i | \(-0.625788\pi\) | ||||
−0.384970 | + | 0.922929i | \(0.625788\pi\) | |||||||
\(464\) | −85.4069 | −3.96491 | ||||||||
\(465\) | 0.220117 | 0.0102077 | ||||||||
\(466\) | −5.79861 | −0.268615 | ||||||||
\(467\) | 3.70041 | 0.171234 | 0.0856172 | − | 0.996328i | \(-0.472714\pi\) | ||||
0.0856172 | + | 0.996328i | \(0.472714\pi\) | |||||||
\(468\) | 8.73546 | 0.403797 | ||||||||
\(469\) | −1.67535 | −0.0773605 | ||||||||
\(470\) | 18.5785 | 0.856962 | ||||||||
\(471\) | 1.24581 | 0.0574040 | ||||||||
\(472\) | 62.5214 | 2.87778 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 2.68802 | 0.123465 | ||||||||
\(475\) | 4.95558 | 0.227378 | ||||||||
\(476\) | −31.1343 | −1.42704 | ||||||||
\(477\) | 13.4008 | 0.613581 | ||||||||
\(478\) | 65.6971 | 3.00492 | ||||||||
\(479\) | 1.26454 | 0.0577781 | 0.0288890 | − | 0.999583i | \(-0.490803\pi\) | ||||
0.0288890 | + | 0.999583i | \(0.490803\pi\) | |||||||
\(480\) | −4.91116 | −0.224163 | ||||||||
\(481\) | −4.00000 | −0.182384 | ||||||||
\(482\) | 39.8367 | 1.81451 | ||||||||
\(483\) | −2.22012 | −0.101019 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.75919 | −0.216104 | ||||||||
\(486\) | 15.3120 | 0.694566 | ||||||||
\(487\) | 21.6022 | 0.978890 | 0.489445 | − | 0.872034i | \(-0.337199\pi\) | ||||
0.489445 | + | 0.872034i | \(0.337199\pi\) | |||||||
\(488\) | −65.9492 | −2.98538 | ||||||||
\(489\) | −4.95256 | −0.223962 | ||||||||
\(490\) | −4.39779 | −0.198672 | ||||||||
\(491\) | 25.5371 | 1.15247 | 0.576237 | − | 0.817283i | \(-0.304521\pi\) | ||||
0.576237 | + | 0.817283i | \(0.304521\pi\) | |||||||
\(492\) | −12.3658 | −0.557491 | ||||||||
\(493\) | −13.2933 | −0.598698 | ||||||||
\(494\) | 7.26454 | 0.326847 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.2488 | 0.729594 | ||||||||
\(497\) | −10.5341 | −0.472518 | ||||||||
\(498\) | 7.86872 | 0.352606 | ||||||||
\(499\) | 24.3614 | 1.09057 | 0.545283 | − | 0.838252i | \(-0.316422\pi\) | ||||
0.545283 | + | 0.838252i | \(0.316422\pi\) | |||||||
\(500\) | −5.53407 | −0.247491 | ||||||||
\(501\) | −3.00000 | −0.134030 | ||||||||
\(502\) | −79.0692 | −3.52903 | ||||||||
\(503\) | −12.4960 | −0.557169 | −0.278584 | − | 0.960412i | \(-0.589865\pi\) | ||||
−0.278584 | + | 0.960412i | \(0.589865\pi\) | |||||||
\(504\) | −66.6102 | −2.96706 | ||||||||
\(505\) | 6.57849 | 0.292739 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.67971 | 0.119010 | ||||||||
\(508\) | −44.9473 | −1.99421 | ||||||||
\(509\) | 24.4483 | 1.08365 | 0.541825 | − | 0.840491i | \(-0.317734\pi\) | ||||
0.541825 | + | 0.840491i | \(0.317734\pi\) | |||||||
\(510\) | −1.40082 | −0.0620292 | ||||||||
\(511\) | −2.48163 | −0.109781 | ||||||||
\(512\) | −60.7034 | −2.68274 | ||||||||
\(513\) | 6.22012 | 0.274625 | ||||||||
\(514\) | 75.8935 | 3.34752 | ||||||||
\(515\) | −16.3564 | −0.720749 | ||||||||
\(516\) | −5.04245 | −0.221981 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 47.7622 | 2.09855 | ||||||||
\(519\) | 1.35837 | 0.0596259 | ||||||||
\(520\) | −5.18070 | −0.227189 | ||||||||
\(521\) | −0.0394184 | −0.00172695 | −0.000863476 | − | 1.00000i | \(-0.500275\pi\) | ||||
−0.000863476 | 1.00000i | \(0.500275\pi\) | ||||||||
\(522\) | −44.5351 | −1.94925 | ||||||||
\(523\) | −21.0919 | −0.922283 | −0.461141 | − | 0.887327i | \(-0.652560\pi\) | ||||
−0.461141 | + | 0.887327i | \(0.652560\pi\) | |||||||
\(524\) | 32.0899 | 1.40185 | ||||||||
\(525\) | 0.489652 | 0.0213702 | ||||||||
\(526\) | −8.60024 | −0.374988 | ||||||||
\(527\) | 2.52907 | 0.110168 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.44221 | −0.106183 | ||||||||
\(530\) | −12.4452 | −0.540586 | ||||||||
\(531\) | 19.0494 | 0.826674 | ||||||||
\(532\) | −63.7158 | −2.76243 | ||||||||
\(533\) | −5.66232 | −0.245263 | ||||||||
\(534\) | 7.35534 | 0.318297 | ||||||||
\(535\) | −10.2108 | −0.441449 | ||||||||
\(536\) | −6.99500 | −0.302138 | ||||||||
\(537\) | −3.57849 | −0.154423 | ||||||||
\(538\) | −49.4152 | −2.13044 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.94622 | −0.298918 | ||||||||
\(541\) | −33.4402 | −1.43771 | −0.718854 | − | 0.695161i | \(-0.755333\pi\) | ||||
−0.718854 | + | 0.695161i | \(0.755333\pi\) | |||||||
\(542\) | −55.8097 | −2.39723 | ||||||||
\(543\) | −0.946221 | −0.0406062 | ||||||||
\(544\) | −56.4276 | −2.41931 | ||||||||
\(545\) | 12.0919 | 0.517958 | ||||||||
\(546\) | 0.717796 | 0.0307188 | ||||||||
\(547\) | 32.8066 | 1.40271 | 0.701355 | − | 0.712812i | \(-0.252579\pi\) | ||||
0.701355 | + | 0.712812i | \(0.252579\pi\) | |||||||
\(548\) | 49.0692 | 2.09613 | ||||||||
\(549\) | −20.0938 | −0.857584 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.2044 | −1.15895 | ||||||||
\(552\) | −9.26953 | −0.394538 | ||||||||
\(553\) | −10.7956 | −0.459075 | ||||||||
\(554\) | 69.9647 | 2.97251 | ||||||||
\(555\) | 1.57849 | 0.0670031 | ||||||||
\(556\) | −93.3418 | −3.95857 | ||||||||
\(557\) | 28.3327 | 1.20049 | 0.600247 | − | 0.799815i | \(-0.295069\pi\) | ||||
0.600247 | + | 0.799815i | \(0.295069\pi\) | |||||||
\(558\) | 8.47290 | 0.358687 | ||||||||
\(559\) | −2.30895 | −0.0976583 | ||||||||
\(560\) | 36.1456 | 1.52743 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −50.1550 | −2.11566 | ||||||||
\(563\) | 29.0361 | 1.22373 | 0.611863 | − | 0.790964i | \(-0.290420\pi\) | ||||
0.611863 | + | 0.790964i | \(0.290420\pi\) | |||||||
\(564\) | −7.89441 | −0.332415 | ||||||||
\(565\) | 10.8430 | 0.456169 | ||||||||
\(566\) | 30.3407 | 1.27531 | ||||||||
\(567\) | −19.9856 | −0.839318 | ||||||||
\(568\) | −43.9823 | −1.84546 | ||||||||
\(569\) | 28.7098 | 1.20358 | 0.601788 | − | 0.798656i | \(-0.294455\pi\) | ||||
0.601788 | + | 0.798656i | \(0.294455\pi\) | |||||||
\(570\) | −2.86675 | −0.120075 | ||||||||
\(571\) | 0.824301 | 0.0344959 | 0.0172480 | − | 0.999851i | \(-0.494510\pi\) | ||||
0.0172480 | + | 0.999851i | \(0.494510\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.581515 | 0.0242931 | ||||||||
\(574\) | 67.6113 | 2.82204 | ||||||||
\(575\) | −4.53407 | −0.189084 | ||||||||
\(576\) | −97.0792 | −4.04497 | ||||||||
\(577\) | −31.5421 | −1.31311 | −0.656557 | − | 0.754276i | \(-0.727988\pi\) | ||||
−0.656557 | + | 0.754276i | \(0.727988\pi\) | |||||||
\(578\) | 30.5672 | 1.27143 | ||||||||
\(579\) | −2.48768 | −0.103384 | ||||||||
\(580\) | 30.3801 | 1.26147 | ||||||||
\(581\) | −31.6022 | −1.31108 | ||||||||
\(582\) | 2.75313 | 0.114121 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −10.3614 | −0.428758 | ||||||||
\(585\) | −1.57849 | −0.0652625 | ||||||||
\(586\) | −74.4927 | −3.07726 | ||||||||
\(587\) | −26.7735 | −1.10506 | −0.552531 | − | 0.833492i | \(-0.686338\pi\) | ||||
−0.552531 | + | 0.833492i | \(0.686338\pi\) | |||||||
\(588\) | 1.86872 | 0.0770647 | ||||||||
\(589\) | 5.17570 | 0.213261 | ||||||||
\(590\) | −17.6910 | −0.728329 | ||||||||
\(591\) | 1.37209 | 0.0564404 | ||||||||
\(592\) | 116.522 | 4.78904 | ||||||||
\(593\) | −11.0731 | −0.454719 | −0.227360 | − | 0.973811i | \(-0.573009\pi\) | ||||
−0.227360 | + | 0.973811i | \(0.573009\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.62593 | 0.230641 | ||||||||
\(596\) | 24.7148 | 1.01236 | ||||||||
\(597\) | −5.04942 | −0.206659 | ||||||||
\(598\) | −6.64663 | −0.271801 | ||||||||
\(599\) | −11.9349 | −0.487646 | −0.243823 | − | 0.969820i | \(-0.578402\pi\) | ||||
−0.243823 | + | 0.969820i | \(0.578402\pi\) | |||||||
\(600\) | 2.04442 | 0.0834630 | ||||||||
\(601\) | 5.26454 | 0.214745 | 0.107372 | − | 0.994219i | \(-0.465756\pi\) | ||||
0.107372 | + | 0.994219i | \(0.465756\pi\) | |||||||
\(602\) | 27.5702 | 1.12368 | ||||||||
\(603\) | −2.13128 | −0.0867925 | ||||||||
\(604\) | −63.7158 | −2.59256 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.80558 | −0.154591 | ||||||||
\(607\) | 35.8461 | 1.45495 | 0.727473 | − | 0.686136i | \(-0.240695\pi\) | ||||
0.727473 | + | 0.686136i | \(0.240695\pi\) | |||||||
\(608\) | −115.478 | −4.68325 | ||||||||
\(609\) | −2.68802 | −0.108924 | ||||||||
\(610\) | 18.6610 | 0.755561 | ||||||||
\(611\) | −3.61488 | −0.146242 | ||||||||
\(612\) | −39.6072 | −1.60103 | ||||||||
\(613\) | 6.55779 | 0.264867 | 0.132433 | − | 0.991192i | \(-0.457721\pi\) | ||||
0.132433 | + | 0.991192i | \(0.457721\pi\) | |||||||
\(614\) | −32.2201 | −1.30030 | ||||||||
\(615\) | 2.23448 | 0.0901029 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.7986 | 0.716545 | 0.358272 | − | 0.933617i | \(-0.383366\pi\) | ||||
0.358272 | + | 0.933617i | \(0.383366\pi\) | |||||||
\(618\) | 9.46198 | 0.380617 | ||||||||
\(619\) | 44.8905 | 1.80430 | 0.902150 | − | 0.431422i | \(-0.141988\pi\) | ||||
0.902150 | + | 0.431422i | \(0.141988\pi\) | |||||||
\(620\) | −5.77988 | −0.232126 | ||||||||
\(621\) | −5.69105 | −0.228374 | ||||||||
\(622\) | −29.2094 | −1.17119 | ||||||||
\(623\) | −29.5404 | −1.18351 | ||||||||
\(624\) | 1.75116 | 0.0701025 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 74.6063 | 2.98187 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −32.7128 | −1.30538 | ||||||||
\(629\) | 18.1363 | 0.723141 | ||||||||
\(630\) | 18.8480 | 0.750923 | ||||||||
\(631\) | 21.9112 | 0.872270 | 0.436135 | − | 0.899881i | \(-0.356347\pi\) | ||||
0.436135 | + | 0.899881i | \(0.356347\pi\) | |||||||
\(632\) | −45.0742 | −1.79296 | ||||||||
\(633\) | 3.55477 | 0.141289 | ||||||||
\(634\) | −13.6673 | −0.542799 | ||||||||
\(635\) | 8.12192 | 0.322309 | ||||||||
\(636\) | 5.28826 | 0.209693 | ||||||||
\(637\) | 0.855693 | 0.0339038 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.4008 | −0.530128 | ||||||||
\(640\) | 43.5515 | 1.72152 | ||||||||
\(641\) | 35.7335 | 1.41139 | 0.705694 | − | 0.708517i | \(-0.250635\pi\) | ||||
0.705694 | + | 0.708517i | \(0.250635\pi\) | |||||||
\(642\) | 5.90680 | 0.233123 | ||||||||
\(643\) | 0.412150 | 0.0162536 | 0.00812681 | − | 0.999967i | \(-0.497413\pi\) | ||||
0.00812681 | + | 0.999967i | \(0.497413\pi\) | |||||||
\(644\) | 58.2963 | 2.29720 | ||||||||
\(645\) | 0.911164 | 0.0358770 | ||||||||
\(646\) | −32.9379 | −1.29592 | ||||||||
\(647\) | −16.5484 | −0.650586 | −0.325293 | − | 0.945613i | \(-0.605463\pi\) | ||||
−0.325293 | + | 0.945613i | \(0.605463\pi\) | |||||||
\(648\) | −83.4450 | −3.27803 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.46593 | 0.0574985 | ||||||||
\(651\) | 0.511402 | 0.0200434 | ||||||||
\(652\) | 130.045 | 5.09296 | ||||||||
\(653\) | 11.0080 | 0.430777 | 0.215389 | − | 0.976528i | \(-0.430898\pi\) | ||||
0.215389 | + | 0.976528i | \(0.430898\pi\) | |||||||
\(654\) | −6.99500 | −0.273526 | ||||||||
\(655\) | −5.79861 | −0.226570 | ||||||||
\(656\) | 164.947 | 6.44010 | ||||||||
\(657\) | −3.15698 | −0.123165 | ||||||||
\(658\) | 43.1637 | 1.68269 | ||||||||
\(659\) | 42.9980 | 1.67497 | 0.837483 | − | 0.546464i | \(-0.184026\pi\) | ||||
0.837483 | + | 0.546464i | \(0.184026\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.4927 | 0.758177 | 0.379089 | − | 0.925360i | \(-0.376238\pi\) | ||||
0.379089 | + | 0.925360i | \(0.376238\pi\) | |||||||
\(662\) | −20.7365 | −0.805948 | ||||||||
\(663\) | 0.272562 | 0.0105854 | ||||||||
\(664\) | −131.947 | −5.12054 | ||||||||
\(665\) | 11.5134 | 0.446470 | ||||||||
\(666\) | 60.7602 | 2.35441 | ||||||||
\(667\) | 24.8905 | 0.963763 | ||||||||
\(668\) | 78.7746 | 3.04788 | ||||||||
\(669\) | 5.27256 | 0.203849 | ||||||||
\(670\) | 1.97930 | 0.0764672 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −11.4102 | −0.440157 | ||||||||
\(673\) | −6.80663 | −0.262376 | −0.131188 | − | 0.991357i | \(-0.541879\pi\) | ||||
−0.131188 | + | 0.991357i | \(0.541879\pi\) | |||||||
\(674\) | −10.1313 | −0.390242 | ||||||||
\(675\) | 1.25517 | 0.0483117 | ||||||||
\(676\) | −70.3644 | −2.70632 | ||||||||
\(677\) | −1.02070 | −0.0392285 | −0.0196143 | − | 0.999808i | \(-0.506244\pi\) | ||||
−0.0196143 | + | 0.999808i | \(0.506244\pi\) | |||||||
\(678\) | −6.27256 | −0.240896 | ||||||||
\(679\) | −11.0571 | −0.424332 | ||||||||
\(680\) | 23.4897 | 0.900787 | ||||||||
\(681\) | −0.844996 | −0.0323803 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.09820 | 0.0802853 | 0.0401426 | − | 0.999194i | \(-0.487219\pi\) | ||||
0.0401426 | + | 0.999194i | \(0.487219\pi\) | |||||||
\(684\) | −81.0555 | −3.09923 | ||||||||
\(685\) | −8.86675 | −0.338781 | ||||||||
\(686\) | −54.8571 | −2.09445 | ||||||||
\(687\) | 3.65296 | 0.139369 | ||||||||
\(688\) | 67.2612 | 2.56431 | ||||||||
\(689\) | 2.42151 | 0.0922523 | ||||||||
\(690\) | 2.62291 | 0.0998523 | ||||||||
\(691\) | 11.9950 | 0.456311 | 0.228156 | − | 0.973625i | \(-0.426730\pi\) | ||||
0.228156 | + | 0.973625i | \(0.426730\pi\) | |||||||
\(692\) | −35.6684 | −1.35591 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 43.2736 | 1.64264 | ||||||||
\(695\) | 16.8667 | 0.639792 | ||||||||
\(696\) | −11.2231 | −0.425412 | ||||||||
\(697\) | 25.6734 | 0.972449 | ||||||||
\(698\) | 28.9793 | 1.09688 | ||||||||
\(699\) | −0.445234 | −0.0168403 | ||||||||
\(700\) | −12.8574 | −0.485963 | ||||||||
\(701\) | 29.3594 | 1.10889 | 0.554445 | − | 0.832220i | \(-0.312931\pi\) | ||||
0.554445 | + | 0.832220i | \(0.312931\pi\) | |||||||
\(702\) | 1.84000 | 0.0694462 | ||||||||
\(703\) | 37.1156 | 1.39984 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.42651 | 0.0537255 | ||||||||
\(706\) | 67.3931 | 2.53637 | ||||||||
\(707\) | 15.2839 | 0.574810 | ||||||||
\(708\) | 7.51732 | 0.282518 | ||||||||
\(709\) | −37.5451 | −1.41004 | −0.705018 | − | 0.709189i | \(-0.749061\pi\) | ||||
−0.705018 | + | 0.709189i | \(0.749061\pi\) | |||||||
\(710\) | 12.4452 | 0.467061 | ||||||||
\(711\) | −13.7335 | −0.515046 | ||||||||
\(712\) | −123.338 | −4.62230 | ||||||||
\(713\) | −4.73546 | −0.177345 | ||||||||
\(714\) | −3.25454 | −0.121798 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 93.9647 | 3.51162 | ||||||||
\(717\) | 5.04442 | 0.188387 | ||||||||
\(718\) | 45.7572 | 1.70764 | ||||||||
\(719\) | −3.99500 | −0.148988 | −0.0744942 | − | 0.997221i | \(-0.523734\pi\) | ||||
−0.0744942 | + | 0.997221i | \(0.523734\pi\) | |||||||
\(720\) | 45.9823 | 1.71366 | ||||||||
\(721\) | −38.0011 | −1.41523 | ||||||||
\(722\) | −15.2552 | −0.567739 | ||||||||
\(723\) | 3.05878 | 0.113757 | ||||||||
\(724\) | 24.8461 | 0.923396 | ||||||||
\(725\) | −5.48965 | −0.203881 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.4990 | −0.945706 | −0.472853 | − | 0.881141i | \(-0.656776\pi\) | ||||
−0.472853 | + | 0.881141i | \(0.656776\pi\) | |||||||
\(728\) | −12.0364 | −0.446098 | ||||||||
\(729\) | −24.6309 | −0.912257 | ||||||||
\(730\) | 2.93186 | 0.108513 | ||||||||
\(731\) | 10.4690 | 0.387208 | ||||||||
\(732\) | −7.92947 | −0.293082 | ||||||||
\(733\) | −36.2024 | −1.33717 | −0.668584 | − | 0.743637i | \(-0.733099\pi\) | ||||
−0.668584 | + | 0.743637i | \(0.733099\pi\) | |||||||
\(734\) | −41.9379 | −1.54796 | ||||||||
\(735\) | −0.337675 | −0.0124553 | ||||||||
\(736\) | 105.656 | 3.89452 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 86.0111 | 3.16611 | ||||||||
\(739\) | −6.06011 | −0.222925 | −0.111462 | − | 0.993769i | \(-0.535553\pi\) | ||||
−0.111462 | + | 0.993769i | \(0.535553\pi\) | |||||||
\(740\) | −41.4483 | −1.52367 | ||||||||
\(741\) | 0.557793 | 0.0204910 | ||||||||
\(742\) | −28.9142 | −1.06147 | ||||||||
\(743\) | 36.2869 | 1.33124 | 0.665619 | − | 0.746292i | \(-0.268168\pi\) | ||||
0.665619 | + | 0.746292i | \(0.268168\pi\) | |||||||
\(744\) | 2.13523 | 0.0782812 | ||||||||
\(745\) | −4.46593 | −0.163619 | ||||||||
\(746\) | −48.9843 | −1.79344 | ||||||||
\(747\) | −40.2024 | −1.47093 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.7228 | −0.866812 | ||||||||
\(750\) | −0.578488 | −0.0211234 | ||||||||
\(751\) | −15.7335 | −0.574123 | −0.287062 | − | 0.957912i | \(-0.592678\pi\) | ||||
−0.287062 | + | 0.957912i | \(0.592678\pi\) | |||||||
\(752\) | 105.304 | 3.84003 | ||||||||
\(753\) | −6.07117 | −0.221246 | ||||||||
\(754\) | −8.04744 | −0.293071 | ||||||||
\(755\) | 11.5134 | 0.419015 | ||||||||
\(756\) | −16.1383 | −0.586943 | ||||||||
\(757\) | −25.1393 | −0.913704 | −0.456852 | − | 0.889543i | \(-0.651023\pi\) | ||||
−0.456852 | + | 0.889543i | \(0.651023\pi\) | |||||||
\(758\) | −5.19442 | −0.188670 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 48.0712 | 1.74372 | ||||||||
\(761\) | −15.4709 | −0.560821 | −0.280410 | − | 0.959880i | \(-0.590471\pi\) | ||||
−0.280410 | + | 0.959880i | \(0.590471\pi\) | |||||||
\(762\) | −4.69844 | −0.170206 | ||||||||
\(763\) | 28.0932 | 1.01704 | ||||||||
\(764\) | −15.2695 | −0.552432 | ||||||||
\(765\) | 7.15698 | 0.258761 | ||||||||
\(766\) | −14.5942 | −0.527309 | ||||||||
\(767\) | 3.44221 | 0.124291 | ||||||||
\(768\) | −11.3490 | −0.409522 | ||||||||
\(769\) | 17.3220 | 0.624647 | 0.312323 | − | 0.949976i | \(-0.398893\pi\) | ||||
0.312323 | + | 0.949976i | \(0.398893\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.82733 | 0.209866 | ||||||||
\(772\) | 65.3220 | 2.35099 | ||||||||
\(773\) | −22.6991 | −0.816429 | −0.408214 | − | 0.912886i | \(-0.633848\pi\) | ||||
−0.408214 | + | 0.912886i | \(0.633848\pi\) | |||||||
\(774\) | 35.0731 | 1.26068 | ||||||||
\(775\) | 1.04442 | 0.0375166 | ||||||||
\(776\) | −46.1661 | −1.65726 | ||||||||
\(777\) | 3.66732 | 0.131565 | ||||||||
\(778\) | 73.6363 | 2.63999 | ||||||||
\(779\) | 52.5401 | 1.88245 | ||||||||
\(780\) | −0.622906 | −0.0223036 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 30.1363 | 1.07767 | ||||||||
\(783\) | −6.89047 | −0.246245 | ||||||||
\(784\) | −24.9269 | −0.890245 | ||||||||
\(785\) | 5.91116 | 0.210978 | ||||||||
\(786\) | 3.35443 | 0.119648 | ||||||||
\(787\) | 3.10122 | 0.110547 | 0.0552734 | − | 0.998471i | \(-0.482397\pi\) | ||||
0.0552734 | + | 0.998471i | \(0.482397\pi\) | |||||||
\(788\) | −36.0287 | −1.28347 | ||||||||
\(789\) | −0.660352 | −0.0235091 | ||||||||
\(790\) | 12.7542 | 0.453774 | ||||||||
\(791\) | 25.1918 | 0.895716 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.63093 | −0.128938 | ||||||||
\(794\) | −86.7288 | −3.07789 | ||||||||
\(795\) | −0.955582 | −0.0338910 | ||||||||
\(796\) | 132.589 | 4.69948 | ||||||||
\(797\) | −19.0919 | −0.676268 | −0.338134 | − | 0.941098i | \(-0.609796\pi\) | ||||
−0.338134 | + | 0.941098i | \(0.609796\pi\) | |||||||
\(798\) | −6.66035 | −0.235774 | ||||||||
\(799\) | 16.3901 | 0.579841 | ||||||||
\(800\) | −23.3026 | −0.823872 | ||||||||
\(801\) | −37.5795 | −1.32781 | ||||||||
\(802\) | 8.60855 | 0.303978 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.841051 | −0.0296616 | ||||||||
\(805\) | −10.5341 | −0.371277 | ||||||||
\(806\) | 1.53104 | 0.0539287 | ||||||||
\(807\) | −3.79424 | −0.133564 | ||||||||
\(808\) | 63.8140 | 2.24497 | ||||||||
\(809\) | 4.46896 | 0.157120 | 0.0785601 | − | 0.996909i | \(-0.474968\pi\) | ||||
0.0785601 | + | 0.996909i | \(0.474968\pi\) | |||||||
\(810\) | 23.6116 | 0.829626 | ||||||||
\(811\) | −4.86675 | −0.170895 | −0.0854473 | − | 0.996343i | \(-0.527232\pi\) | ||||
−0.0854473 | + | 0.996343i | \(0.527232\pi\) | |||||||
\(812\) | 70.5826 | 2.47696 | ||||||||
\(813\) | −4.28523 | −0.150290 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.4990 | −0.823135 | ||||||||
\(816\) | −7.93989 | −0.277952 | ||||||||
\(817\) | 21.4245 | 0.749550 | ||||||||
\(818\) | −1.16528 | −0.0407432 | ||||||||
\(819\) | −3.66732 | −0.128147 | ||||||||
\(820\) | −58.6734 | −2.04896 | ||||||||
\(821\) | 17.0050 | 0.593479 | 0.296739 | − | 0.954959i | \(-0.404101\pi\) | ||||
0.296739 | + | 0.954959i | \(0.404101\pi\) | |||||||
\(822\) | 5.12931 | 0.178905 | ||||||||
\(823\) | −21.7479 | −0.758082 | −0.379041 | − | 0.925380i | \(-0.623746\pi\) | ||||
−0.379041 | + | 0.925380i | \(0.623746\pi\) | |||||||
\(824\) | −158.664 | −5.52731 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −41.1019 | −1.43012 | ||||||||
\(827\) | −20.7084 | −0.720103 | −0.360051 | − | 0.932932i | \(-0.617241\pi\) | ||||
−0.360051 | + | 0.932932i | \(0.617241\pi\) | |||||||
\(828\) | 74.1611 | 2.57727 | ||||||||
\(829\) | 11.3090 | 0.392776 | 0.196388 | − | 0.980526i | \(-0.437079\pi\) | ||||
0.196388 | + | 0.980526i | \(0.437079\pi\) | |||||||
\(830\) | 37.3357 | 1.29594 | ||||||||
\(831\) | 5.37209 | 0.186356 | ||||||||
\(832\) | −17.5421 | −0.608163 | ||||||||
\(833\) | −3.87977 | −0.134426 | ||||||||
\(834\) | −9.75721 | −0.337865 | ||||||||
\(835\) | −14.2345 | −0.492604 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.31093 | 0.0453122 | ||||||||
\(838\) | −18.4226 | −0.636397 | ||||||||
\(839\) | −43.5084 | −1.50208 | −0.751038 | − | 0.660259i | \(-0.770446\pi\) | ||||
−0.751038 | + | 0.660259i | \(0.770446\pi\) | |||||||
\(840\) | 4.74983 | 0.163885 | ||||||||
\(841\) | 1.13628 | 0.0391821 | ||||||||
\(842\) | −7.63029 | −0.262957 | ||||||||
\(843\) | −3.85105 | −0.132637 | ||||||||
\(844\) | −93.3418 | −3.21296 | ||||||||
\(845\) | 12.7148 | 0.437401 | ||||||||
\(846\) | 54.9102 | 1.88785 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −70.5401 | −2.42236 | ||||||||
\(849\) | 2.32965 | 0.0799533 | ||||||||
\(850\) | −6.64663 | −0.227977 | ||||||||
\(851\) | −33.9586 | −1.16409 | ||||||||
\(852\) | −5.28826 | −0.181173 | ||||||||
\(853\) | −1.11559 | −0.0381969 | −0.0190985 | − | 0.999818i | \(-0.506080\pi\) | ||||
−0.0190985 | + | 0.999818i | \(0.506080\pi\) | |||||||
\(854\) | 43.3553 | 1.48359 | ||||||||
\(855\) | 14.6466 | 0.500904 | ||||||||
\(856\) | −99.0485 | −3.38541 | ||||||||
\(857\) | 7.80361 | 0.266566 | 0.133283 | − | 0.991078i | \(-0.457448\pi\) | ||||
0.133283 | + | 0.991078i | \(0.457448\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.5341 | 1.04181 | 0.520905 | − | 0.853615i | \(-0.325595\pi\) | ||||
0.520905 | + | 0.853615i | \(0.325595\pi\) | |||||||
\(860\) | −23.9255 | −0.815854 | ||||||||
\(861\) | 5.19140 | 0.176922 | ||||||||
\(862\) | −44.4563 | −1.51419 | ||||||||
\(863\) | −4.28959 | −0.146019 | −0.0730097 | − | 0.997331i | \(-0.523260\pi\) | ||||
−0.0730097 | + | 0.997331i | \(0.523260\pi\) | |||||||
\(864\) | −29.2488 | −0.995066 | ||||||||
\(865\) | 6.44523 | 0.219145 | ||||||||
\(866\) | −21.4847 | −0.730078 | ||||||||
\(867\) | 2.34704 | 0.0797095 | ||||||||
\(868\) | −13.4285 | −0.455792 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 3.17570 | 0.107666 | ||||||||
\(871\) | −0.385120 | −0.0130493 | ||||||||
\(872\) | 117.296 | 3.97214 | ||||||||
\(873\) | −14.0662 | −0.476068 | ||||||||
\(874\) | 61.6734 | 2.08613 | ||||||||
\(875\) | 2.32331 | 0.0785424 | ||||||||
\(876\) | −1.24581 | −0.0420921 | ||||||||
\(877\) | 11.3644 | 0.383749 | 0.191875 | − | 0.981419i | \(-0.438543\pi\) | ||||
0.191875 | + | 0.981419i | \(0.438543\pi\) | |||||||
\(878\) | −56.9152 | −1.92080 | ||||||||
\(879\) | −5.71977 | −0.192923 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.3277 | −0.381639 | −0.190820 | − | 0.981625i | \(-0.561115\pi\) | ||||
−0.190820 | + | 0.981625i | \(0.561115\pi\) | |||||||
\(882\) | −12.9980 | −0.437666 | ||||||||
\(883\) | 31.2883 | 1.05293 | 0.526467 | − | 0.850196i | \(-0.323516\pi\) | ||||
0.526467 | + | 0.850196i | \(0.323516\pi\) | |||||||
\(884\) | −7.15698 | −0.240715 | ||||||||
\(885\) | −1.35837 | −0.0456611 | ||||||||
\(886\) | −14.5548 | −0.488977 | ||||||||
\(887\) | −28.2819 | −0.949614 | −0.474807 | − | 0.880090i | \(-0.657482\pi\) | ||||
−0.474807 | + | 0.880090i | \(0.657482\pi\) | |||||||
\(888\) | 15.3120 | 0.513836 | ||||||||
\(889\) | 18.8698 | 0.632872 | ||||||||
\(890\) | 34.8998 | 1.16984 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −138.448 | −4.63558 | ||||||||
\(893\) | 33.5421 | 1.12244 | ||||||||
\(894\) | 2.58349 | 0.0864048 | ||||||||
\(895\) | −16.9793 | −0.567556 | ||||||||
\(896\) | 101.184 | 3.38031 | ||||||||
\(897\) | −0.510348 | −0.0170400 | ||||||||
\(898\) | 82.3531 | 2.74816 | ||||||||
\(899\) | −5.73349 | −0.191223 | ||||||||
\(900\) | −16.3564 | −0.545213 | ||||||||
\(901\) | −10.9793 | −0.365774 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.11692 | 0.0704467 | ||||||||
\(904\) | 105.182 | 3.49829 | ||||||||
\(905\) | −4.48965 | −0.149241 | ||||||||
\(906\) | −6.66035 | −0.221275 | ||||||||
\(907\) | 33.6166 | 1.11622 | 0.558110 | − | 0.829767i | \(-0.311527\pi\) | ||||
0.558110 | + | 0.829767i | \(0.311527\pi\) | |||||||
\(908\) | 22.1881 | 0.736338 | ||||||||
\(909\) | 19.4433 | 0.644892 | ||||||||
\(910\) | 3.40582 | 0.112902 | ||||||||
\(911\) | 7.53104 | 0.249515 | 0.124757 | − | 0.992187i | \(-0.460185\pi\) | ||||
0.124757 | + | 0.992187i | \(0.460185\pi\) | |||||||
\(912\) | −16.2488 | −0.538053 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −102.968 | −3.40587 | ||||||||
\(915\) | 1.43285 | 0.0473684 | ||||||||
\(916\) | −95.9202 | −3.16929 | ||||||||
\(917\) | −13.4720 | −0.444884 | ||||||||
\(918\) | −8.34267 | −0.275349 | ||||||||
\(919\) | 40.0424 | 1.32088 | 0.660439 | − | 0.750880i | \(-0.270370\pi\) | ||||
0.660439 | + | 0.750880i | \(0.270370\pi\) | |||||||
\(920\) | −43.9823 | −1.45005 | ||||||||
\(921\) | −2.47396 | −0.0815196 | ||||||||
\(922\) | −43.3213 | −1.42671 | ||||||||
\(923\) | −2.42151 | −0.0797050 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.48965 | 0.246258 | ||||||||
\(926\) | 45.4740 | 1.49437 | ||||||||
\(927\) | −48.3427 | −1.58778 | ||||||||
\(928\) | 127.923 | 4.19929 | ||||||||
\(929\) | 51.3407 | 1.68443 | 0.842217 | − | 0.539139i | \(-0.181250\pi\) | ||||
0.842217 | + | 0.539139i | \(0.181250\pi\) | |||||||
\(930\) | −0.604184 | −0.0198120 | ||||||||
\(931\) | −7.93989 | −0.260219 | ||||||||
\(932\) | 11.6910 | 0.382953 | ||||||||
\(933\) | −2.24279 | −0.0734255 | ||||||||
\(934\) | −10.1570 | −0.332346 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −15.3120 | −0.500488 | ||||||||
\(937\) | −35.8510 | −1.17120 | −0.585601 | − | 0.810599i | \(-0.699142\pi\) | ||||
−0.585601 | + | 0.810599i | \(0.699142\pi\) | |||||||
\(938\) | 4.59855 | 0.150148 | ||||||||
\(939\) | 5.72849 | 0.186942 | ||||||||
\(940\) | −37.4576 | −1.22173 | ||||||||
\(941\) | −0.607210 | −0.0197945 | −0.00989724 | − | 0.999951i | \(-0.503150\pi\) | ||||
−0.00989724 | + | 0.999951i | \(0.503150\pi\) | |||||||
\(942\) | −3.41954 | −0.111415 | ||||||||
\(943\) | −48.0712 | −1.56541 | ||||||||
\(944\) | −100.274 | −3.26363 | ||||||||
\(945\) | 2.91616 | 0.0948628 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.3851 | −0.857401 | −0.428701 | − | 0.903447i | \(-0.641028\pi\) | ||||
−0.428701 | + | 0.903447i | \(0.641028\pi\) | |||||||
\(948\) | −5.41954 | −0.176018 | ||||||||
\(949\) | −0.570462 | −0.0185180 | ||||||||
\(950\) | −13.6022 | −0.441314 | ||||||||
\(951\) | −1.04942 | −0.0340297 | ||||||||
\(952\) | 54.5738 | 1.76875 | ||||||||
\(953\) | −35.3594 | −1.14540 | −0.572702 | − | 0.819764i | \(-0.694105\pi\) | ||||
−0.572702 | + | 0.819764i | \(0.694105\pi\) | |||||||
\(954\) | −36.7829 | −1.19089 | ||||||||
\(955\) | 2.75919 | 0.0892852 | ||||||||
\(956\) | −132.457 | −4.28398 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.47093 | −0.112141 | ||||||||
\(959\) | −20.6002 | −0.665216 | ||||||||
\(960\) | 6.92250 | 0.223423 | ||||||||
\(961\) | −29.9092 | −0.964813 | ||||||||
\(962\) | 10.9793 | 0.353987 | ||||||||
\(963\) | −30.1787 | −0.972496 | ||||||||
\(964\) | −80.3180 | −2.58687 | ||||||||
\(965\) | −11.8036 | −0.379971 | ||||||||
\(966\) | 6.09384 | 0.196066 | ||||||||
\(967\) | −3.86872 | −0.124410 | −0.0622048 | − | 0.998063i | \(-0.519813\pi\) | ||||
−0.0622048 | + | 0.998063i | \(0.519813\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.52907 | −0.0812455 | ||||||||
\(970\) | 13.0631 | 0.419432 | ||||||||
\(971\) | 24.1076 | 0.773648 | 0.386824 | − | 0.922153i | \(-0.373572\pi\) | ||||
0.386824 | + | 0.922153i | \(0.373572\pi\) | |||||||
\(972\) | −30.8717 | −0.990212 | ||||||||
\(973\) | 39.1868 | 1.25627 | ||||||||
\(974\) | −59.2943 | −1.89991 | ||||||||
\(975\) | 0.112558 | 0.00360475 | ||||||||
\(976\) | 105.771 | 3.38566 | ||||||||
\(977\) | 10.8143 | 0.345980 | 0.172990 | − | 0.984924i | \(-0.444657\pi\) | ||||
0.172990 | + | 0.984924i | \(0.444657\pi\) | |||||||
\(978\) | 13.5939 | 0.434685 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 8.86675 | 0.283238 | ||||||||
\(981\) | 35.7385 | 1.14104 | ||||||||
\(982\) | −70.0949 | −2.23682 | ||||||||
\(983\) | −38.7084 | −1.23461 | −0.617304 | − | 0.786725i | \(-0.711775\pi\) | ||||
−0.617304 | + | 0.786725i | \(0.711775\pi\) | |||||||
\(984\) | 21.6754 | 0.690985 | ||||||||
\(985\) | 6.51035 | 0.207437 | ||||||||
\(986\) | 36.4877 | 1.16200 | ||||||||
\(987\) | 3.31423 | 0.105493 | ||||||||
\(988\) | −14.6466 | −0.465971 | ||||||||
\(989\) | −19.6022 | −0.623314 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 61.4533 | 1.95213 | 0.976064 | − | 0.217485i | \(-0.0697854\pi\) | ||||
0.976064 | + | 0.217485i | \(0.0697854\pi\) | |||||||
\(992\) | −24.3377 | −0.772722 | ||||||||
\(993\) | −1.59221 | −0.0505273 | ||||||||
\(994\) | 28.9142 | 0.917102 | ||||||||
\(995\) | −23.9586 | −0.759539 | ||||||||
\(996\) | −15.8648 | −0.502695 | ||||||||
\(997\) | −38.3377 | −1.21417 | −0.607083 | − | 0.794638i | \(-0.707661\pi\) | ||||
−0.607083 | + | 0.794638i | \(0.707661\pi\) | |||||||
\(998\) | −66.8678 | −2.11666 | ||||||||
\(999\) | 9.40082 | 0.297429 |
(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 | 605.2.a.h.1.1 | yes | 3 | |
3.2 | odd | 2 | 5445.2.a.bb.1.3 | 3 | |||
4.3 | odd | 2 | 9680.2.a.cb.1.2 | 3 | |||
5.4 | even | 2 | 3025.2.a.p.1.3 | 3 | |||
11.2 | odd | 10 | 605.2.g.p.81.1 | 12 | |||
11.3 | even | 5 | 605.2.g.o.251.1 | 12 | |||
11.4 | even | 5 | 605.2.g.o.511.1 | 12 | |||
11.5 | even | 5 | 605.2.g.o.366.3 | 12 | |||
11.6 | odd | 10 | 605.2.g.p.366.1 | 12 | |||
11.7 | odd | 10 | 605.2.g.p.511.3 | 12 | |||
11.8 | odd | 10 | 605.2.g.p.251.3 | 12 | |||
11.9 | even | 5 | 605.2.g.o.81.3 | 12 | |||
11.10 | odd | 2 | 605.2.a.g.1.3 | ✓ | 3 | ||
33.32 | even | 2 | 5445.2.a.bd.1.1 | 3 | |||
44.43 | even | 2 | 9680.2.a.bz.1.2 | 3 | |||
55.54 | odd | 2 | 3025.2.a.u.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.a.g.1.3 | ✓ | 3 | 11.10 | odd | 2 | ||
605.2.a.h.1.1 | yes | 3 | 1.1 | even | 1 | trivial | |
605.2.g.o.81.3 | 12 | 11.9 | even | 5 | |||
605.2.g.o.251.1 | 12 | 11.3 | even | 5 | |||
605.2.g.o.366.3 | 12 | 11.5 | even | 5 | |||
605.2.g.o.511.1 | 12 | 11.4 | even | 5 | |||
605.2.g.p.81.1 | 12 | 11.2 | odd | 10 | |||
605.2.g.p.251.3 | 12 | 11.8 | odd | 10 | |||
605.2.g.p.366.1 | 12 | 11.6 | odd | 10 | |||
605.2.g.p.511.3 | 12 | 11.7 | odd | 10 | |||
3025.2.a.p.1.3 | 3 | 5.4 | even | 2 | |||
3025.2.a.u.1.1 | 3 | 55.54 | odd | 2 | |||
5445.2.a.bb.1.3 | 3 | 3.2 | odd | 2 | |||
5445.2.a.bd.1.1 | 3 | 33.32 | even | 2 | |||
9680.2.a.bz.1.2 | 3 | 44.43 | even | 2 | |||
9680.2.a.cb.1.2 | 3 | 4.3 | odd | 2 |