Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.40 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 3.27981 | 1.89360 | 0.946799 | − | 0.321825i | \(-0.104296\pi\) | ||||
0.946799 | + | 0.321825i | \(0.104296\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.91132 | −0.854769 | −0.427384 | − | 0.904070i | \(-0.640565\pi\) | ||||
−0.427384 | + | 0.904070i | \(0.640565\pi\) | |||||||
\(6\) | −3.27981 | −1.33898 | ||||||||
\(7\) | 1.09804 | 0.415022 | 0.207511 | − | 0.978233i | \(-0.433464\pi\) | ||||
0.207511 | + | 0.978233i | \(0.433464\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.75714 | 2.58571 | ||||||||
\(10\) | 1.91132 | 0.604413 | ||||||||
\(11\) | −3.44938 | −1.04003 | −0.520014 | − | 0.854158i | \(-0.674073\pi\) | ||||
−0.520014 | + | 0.854158i | \(0.674073\pi\) | |||||||
\(12\) | 3.27981 | 0.946799 | ||||||||
\(13\) | −2.45581 | −0.681120 | −0.340560 | − | 0.940223i | \(-0.610617\pi\) | ||||
−0.340560 | + | 0.940223i | \(0.610617\pi\) | |||||||
\(14\) | −1.09804 | −0.293465 | ||||||||
\(15\) | −6.26877 | −1.61859 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.97426 | −1.44897 | −0.724485 | − | 0.689290i | \(-0.757923\pi\) | ||||
−0.724485 | + | 0.689290i | \(0.757923\pi\) | |||||||
\(18\) | −7.75714 | −1.82838 | ||||||||
\(19\) | −1.07537 | −0.246707 | −0.123354 | − | 0.992363i | \(-0.539365\pi\) | ||||
−0.123354 | + | 0.992363i | \(0.539365\pi\) | |||||||
\(20\) | −1.91132 | −0.427384 | ||||||||
\(21\) | 3.60137 | 0.785884 | ||||||||
\(22\) | 3.44938 | 0.735411 | ||||||||
\(23\) | −5.86835 | −1.22364 | −0.611818 | − | 0.790999i | \(-0.709561\pi\) | ||||
−0.611818 | + | 0.790999i | \(0.709561\pi\) | |||||||
\(24\) | −3.27981 | −0.669488 | ||||||||
\(25\) | −1.34685 | −0.269371 | ||||||||
\(26\) | 2.45581 | 0.481625 | ||||||||
\(27\) | 15.6025 | 3.00270 | ||||||||
\(28\) | 1.09804 | 0.207511 | ||||||||
\(29\) | −1.05773 | −0.196415 | −0.0982074 | − | 0.995166i | \(-0.531311\pi\) | ||||
−0.0982074 | + | 0.995166i | \(0.531311\pi\) | |||||||
\(30\) | 6.26877 | 1.14451 | ||||||||
\(31\) | −0.801680 | −0.143986 | −0.0719930 | − | 0.997405i | \(-0.522936\pi\) | ||||
−0.0719930 | + | 0.997405i | \(0.522936\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −11.3133 | −1.96940 | ||||||||
\(34\) | 5.97426 | 1.02458 | ||||||||
\(35\) | −2.09871 | −0.354748 | ||||||||
\(36\) | 7.75714 | 1.29286 | ||||||||
\(37\) | 11.0412 | 1.81516 | 0.907581 | − | 0.419877i | \(-0.137927\pi\) | ||||
0.907581 | + | 0.419877i | \(0.137927\pi\) | |||||||
\(38\) | 1.07537 | 0.174448 | ||||||||
\(39\) | −8.05460 | −1.28977 | ||||||||
\(40\) | 1.91132 | 0.302206 | ||||||||
\(41\) | −1.22406 | −0.191167 | −0.0955834 | − | 0.995421i | \(-0.530472\pi\) | ||||
−0.0955834 | + | 0.995421i | \(0.530472\pi\) | |||||||
\(42\) | −3.60137 | −0.555704 | ||||||||
\(43\) | 4.23670 | 0.646091 | 0.323045 | − | 0.946383i | \(-0.395293\pi\) | ||||
0.323045 | + | 0.946383i | \(0.395293\pi\) | |||||||
\(44\) | −3.44938 | −0.520014 | ||||||||
\(45\) | −14.8264 | −2.21019 | ||||||||
\(46\) | 5.86835 | 0.865241 | ||||||||
\(47\) | −2.09540 | −0.305646 | −0.152823 | − | 0.988254i | \(-0.548836\pi\) | ||||
−0.152823 | + | 0.988254i | \(0.548836\pi\) | |||||||
\(48\) | 3.27981 | 0.473400 | ||||||||
\(49\) | −5.79430 | −0.827757 | ||||||||
\(50\) | 1.34685 | 0.190474 | ||||||||
\(51\) | −19.5944 | −2.74377 | ||||||||
\(52\) | −2.45581 | −0.340560 | ||||||||
\(53\) | −13.0772 | −1.79629 | −0.898144 | − | 0.439702i | \(-0.855084\pi\) | ||||
−0.898144 | + | 0.439702i | \(0.855084\pi\) | |||||||
\(54\) | −15.6025 | −2.12323 | ||||||||
\(55\) | 6.59288 | 0.888984 | ||||||||
\(56\) | −1.09804 | −0.146732 | ||||||||
\(57\) | −3.52701 | −0.467164 | ||||||||
\(58\) | 1.05773 | 0.138886 | ||||||||
\(59\) | −4.64292 | −0.604457 | −0.302228 | − | 0.953236i | \(-0.597730\pi\) | ||||
−0.302228 | + | 0.953236i | \(0.597730\pi\) | |||||||
\(60\) | −6.26877 | −0.809294 | ||||||||
\(61\) | 9.17375 | 1.17458 | 0.587289 | − | 0.809377i | \(-0.300195\pi\) | ||||
0.587289 | + | 0.809377i | \(0.300195\pi\) | |||||||
\(62\) | 0.801680 | 0.101813 | ||||||||
\(63\) | 8.51768 | 1.07313 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.69385 | 0.582200 | ||||||||
\(66\) | 11.3133 | 1.39257 | ||||||||
\(67\) | −7.02213 | −0.857890 | −0.428945 | − | 0.903331i | \(-0.641115\pi\) | ||||
−0.428945 | + | 0.903331i | \(0.641115\pi\) | |||||||
\(68\) | −5.97426 | −0.724485 | ||||||||
\(69\) | −19.2471 | −2.31707 | ||||||||
\(70\) | 2.09871 | 0.250844 | ||||||||
\(71\) | −7.43171 | −0.881982 | −0.440991 | − | 0.897511i | \(-0.645373\pi\) | ||||
−0.440991 | + | 0.897511i | \(0.645373\pi\) | |||||||
\(72\) | −7.75714 | −0.914188 | ||||||||
\(73\) | −10.8441 | −1.26921 | −0.634603 | − | 0.772838i | \(-0.718836\pi\) | ||||
−0.634603 | + | 0.772838i | \(0.718836\pi\) | |||||||
\(74\) | −11.0412 | −1.28351 | ||||||||
\(75\) | −4.41742 | −0.510080 | ||||||||
\(76\) | −1.07537 | −0.123354 | ||||||||
\(77\) | −3.78758 | −0.431634 | ||||||||
\(78\) | 8.05460 | 0.912004 | ||||||||
\(79\) | −2.91328 | −0.327770 | −0.163885 | − | 0.986479i | \(-0.552403\pi\) | ||||
−0.163885 | + | 0.986479i | \(0.552403\pi\) | |||||||
\(80\) | −1.91132 | −0.213692 | ||||||||
\(81\) | 27.9018 | 3.10020 | ||||||||
\(82\) | 1.22406 | 0.135175 | ||||||||
\(83\) | −11.0335 | −1.21109 | −0.605544 | − | 0.795811i | \(-0.707045\pi\) | ||||
−0.605544 | + | 0.795811i | \(0.707045\pi\) | |||||||
\(84\) | 3.60137 | 0.392942 | ||||||||
\(85\) | 11.4187 | 1.23853 | ||||||||
\(86\) | −4.23670 | −0.456855 | ||||||||
\(87\) | −3.46914 | −0.371931 | ||||||||
\(88\) | 3.44938 | 0.367706 | ||||||||
\(89\) | 3.10254 | 0.328869 | 0.164435 | − | 0.986388i | \(-0.447420\pi\) | ||||
0.164435 | + | 0.986388i | \(0.447420\pi\) | |||||||
\(90\) | 14.8264 | 1.56284 | ||||||||
\(91\) | −2.69659 | −0.282680 | ||||||||
\(92\) | −5.86835 | −0.611818 | ||||||||
\(93\) | −2.62936 | −0.272652 | ||||||||
\(94\) | 2.09540 | 0.216124 | ||||||||
\(95\) | 2.05538 | 0.210878 | ||||||||
\(96\) | −3.27981 | −0.334744 | ||||||||
\(97\) | 2.04540 | 0.207678 | 0.103839 | − | 0.994594i | \(-0.466887\pi\) | ||||
0.103839 | + | 0.994594i | \(0.466887\pi\) | |||||||
\(98\) | 5.79430 | 0.585313 | ||||||||
\(99\) | −26.7574 | −2.68922 | ||||||||
\(100\) | −1.34685 | −0.134685 | ||||||||
\(101\) | −3.98337 | −0.396360 | −0.198180 | − | 0.980166i | \(-0.563503\pi\) | ||||
−0.198180 | + | 0.980166i | \(0.563503\pi\) | |||||||
\(102\) | 19.5944 | 1.94014 | ||||||||
\(103\) | −8.36098 | −0.823831 | −0.411916 | − | 0.911222i | \(-0.635140\pi\) | ||||
−0.411916 | + | 0.911222i | \(0.635140\pi\) | |||||||
\(104\) | 2.45581 | 0.240812 | ||||||||
\(105\) | −6.88338 | −0.671749 | ||||||||
\(106\) | 13.0772 | 1.27017 | ||||||||
\(107\) | 17.1374 | 1.65673 | 0.828367 | − | 0.560186i | \(-0.189270\pi\) | ||||
0.828367 | + | 0.560186i | \(0.189270\pi\) | |||||||
\(108\) | 15.6025 | 1.50135 | ||||||||
\(109\) | −17.6410 | −1.68970 | −0.844849 | − | 0.535004i | \(-0.820310\pi\) | ||||
−0.844849 | + | 0.535004i | \(0.820310\pi\) | |||||||
\(110\) | −6.59288 | −0.628606 | ||||||||
\(111\) | 36.2130 | 3.43719 | ||||||||
\(112\) | 1.09804 | 0.103755 | ||||||||
\(113\) | 10.3617 | 0.974746 | 0.487373 | − | 0.873194i | \(-0.337955\pi\) | ||||
0.487373 | + | 0.873194i | \(0.337955\pi\) | |||||||
\(114\) | 3.52701 | 0.330335 | ||||||||
\(115\) | 11.2163 | 1.04593 | ||||||||
\(116\) | −1.05773 | −0.0982074 | ||||||||
\(117\) | −19.0501 | −1.76118 | ||||||||
\(118\) | 4.64292 | 0.427415 | ||||||||
\(119\) | −6.56000 | −0.601354 | ||||||||
\(120\) | 6.26877 | 0.572257 | ||||||||
\(121\) | 0.898254 | 0.0816595 | ||||||||
\(122\) | −9.17375 | −0.830552 | ||||||||
\(123\) | −4.01470 | −0.361993 | ||||||||
\(124\) | −0.801680 | −0.0719930 | ||||||||
\(125\) | 12.1309 | 1.08502 | ||||||||
\(126\) | −8.51768 | −0.758816 | ||||||||
\(127\) | 11.5199 | 1.02222 | 0.511112 | − | 0.859514i | \(-0.329234\pi\) | ||||
0.511112 | + | 0.859514i | \(0.329234\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 13.8956 | 1.22344 | ||||||||
\(130\) | −4.69385 | −0.411678 | ||||||||
\(131\) | 16.2852 | 1.42284 | 0.711420 | − | 0.702767i | \(-0.248052\pi\) | ||||
0.711420 | + | 0.702767i | \(0.248052\pi\) | |||||||
\(132\) | −11.3133 | −0.984698 | ||||||||
\(133\) | −1.18081 | −0.102389 | ||||||||
\(134\) | 7.02213 | 0.606620 | ||||||||
\(135\) | −29.8214 | −2.56662 | ||||||||
\(136\) | 5.97426 | 0.512289 | ||||||||
\(137\) | 1.52041 | 0.129897 | 0.0649487 | − | 0.997889i | \(-0.479312\pi\) | ||||
0.0649487 | + | 0.997889i | \(0.479312\pi\) | |||||||
\(138\) | 19.2471 | 1.63842 | ||||||||
\(139\) | 19.7483 | 1.67503 | 0.837515 | − | 0.546414i | \(-0.184007\pi\) | ||||
0.837515 | + | 0.546414i | \(0.184007\pi\) | |||||||
\(140\) | −2.09871 | −0.177374 | ||||||||
\(141\) | −6.87252 | −0.578771 | ||||||||
\(142\) | 7.43171 | 0.623656 | ||||||||
\(143\) | 8.47105 | 0.708385 | ||||||||
\(144\) | 7.75714 | 0.646428 | ||||||||
\(145\) | 2.02165 | 0.167889 | ||||||||
\(146\) | 10.8441 | 0.897464 | ||||||||
\(147\) | −19.0042 | −1.56744 | ||||||||
\(148\) | 11.0412 | 0.907581 | ||||||||
\(149\) | 16.3947 | 1.34311 | 0.671554 | − | 0.740956i | \(-0.265627\pi\) | ||||
0.671554 | + | 0.740956i | \(0.265627\pi\) | |||||||
\(150\) | 4.41742 | 0.360681 | ||||||||
\(151\) | −5.05534 | −0.411398 | −0.205699 | − | 0.978615i | \(-0.565947\pi\) | ||||
−0.205699 | + | 0.978615i | \(0.565947\pi\) | |||||||
\(152\) | 1.07537 | 0.0872242 | ||||||||
\(153\) | −46.3432 | −3.74662 | ||||||||
\(154\) | 3.78758 | 0.305212 | ||||||||
\(155\) | 1.53227 | 0.123075 | ||||||||
\(156\) | −8.05460 | −0.644884 | ||||||||
\(157\) | −8.49219 | −0.677751 | −0.338875 | − | 0.940831i | \(-0.610046\pi\) | ||||
−0.338875 | + | 0.940831i | \(0.610046\pi\) | |||||||
\(158\) | 2.91328 | 0.231768 | ||||||||
\(159\) | −42.8906 | −3.40145 | ||||||||
\(160\) | 1.91132 | 0.151103 | ||||||||
\(161\) | −6.44371 | −0.507835 | ||||||||
\(162\) | −27.9018 | −2.19217 | ||||||||
\(163\) | −6.78097 | −0.531127 | −0.265563 | − | 0.964093i | \(-0.585558\pi\) | ||||
−0.265563 | + | 0.964093i | \(0.585558\pi\) | |||||||
\(164\) | −1.22406 | −0.0955834 | ||||||||
\(165\) | 21.6234 | 1.68338 | ||||||||
\(166\) | 11.0335 | 0.856369 | ||||||||
\(167\) | 12.2107 | 0.944895 | 0.472447 | − | 0.881359i | \(-0.343371\pi\) | ||||
0.472447 | + | 0.881359i | \(0.343371\pi\) | |||||||
\(168\) | −3.60137 | −0.277852 | ||||||||
\(169\) | −6.96898 | −0.536075 | ||||||||
\(170\) | −11.4187 | −0.875776 | ||||||||
\(171\) | −8.34181 | −0.637914 | ||||||||
\(172\) | 4.23670 | 0.323045 | ||||||||
\(173\) | −25.2030 | −1.91615 | −0.958074 | − | 0.286522i | \(-0.907501\pi\) | ||||
−0.958074 | + | 0.286522i | \(0.907501\pi\) | |||||||
\(174\) | 3.46914 | 0.262995 | ||||||||
\(175\) | −1.47890 | −0.111795 | ||||||||
\(176\) | −3.44938 | −0.260007 | ||||||||
\(177\) | −15.2279 | −1.14460 | ||||||||
\(178\) | −3.10254 | −0.232546 | ||||||||
\(179\) | 0.0966408 | 0.00722327 | 0.00361163 | − | 0.999993i | \(-0.498850\pi\) | ||||
0.00361163 | + | 0.999993i | \(0.498850\pi\) | |||||||
\(180\) | −14.8264 | −1.10509 | ||||||||
\(181\) | −13.5853 | −1.00979 | −0.504895 | − | 0.863181i | \(-0.668469\pi\) | ||||
−0.504895 | + | 0.863181i | \(0.668469\pi\) | |||||||
\(182\) | 2.69659 | 0.199885 | ||||||||
\(183\) | 30.0881 | 2.22418 | ||||||||
\(184\) | 5.86835 | 0.432620 | ||||||||
\(185\) | −21.1033 | −1.55154 | ||||||||
\(186\) | 2.62936 | 0.192794 | ||||||||
\(187\) | 20.6075 | 1.50697 | ||||||||
\(188\) | −2.09540 | −0.152823 | ||||||||
\(189\) | 17.1322 | 1.24619 | ||||||||
\(190\) | −2.05538 | −0.149113 | ||||||||
\(191\) | −6.59808 | −0.477420 | −0.238710 | − | 0.971091i | \(-0.576725\pi\) | ||||
−0.238710 | + | 0.971091i | \(0.576725\pi\) | |||||||
\(192\) | 3.27981 | 0.236700 | ||||||||
\(193\) | 18.1038 | 1.30314 | 0.651569 | − | 0.758590i | \(-0.274111\pi\) | ||||
0.651569 | + | 0.758590i | \(0.274111\pi\) | |||||||
\(194\) | −2.04540 | −0.146851 | ||||||||
\(195\) | 15.3949 | 1.10245 | ||||||||
\(196\) | −5.79430 | −0.413878 | ||||||||
\(197\) | −19.5243 | −1.39105 | −0.695523 | − | 0.718503i | \(-0.744827\pi\) | ||||
−0.695523 | + | 0.718503i | \(0.744827\pi\) | |||||||
\(198\) | 26.7574 | 1.90156 | ||||||||
\(199\) | −8.31380 | −0.589350 | −0.294675 | − | 0.955598i | \(-0.595211\pi\) | ||||
−0.294675 | + | 0.955598i | \(0.595211\pi\) | |||||||
\(200\) | 1.34685 | 0.0952369 | ||||||||
\(201\) | −23.0312 | −1.62450 | ||||||||
\(202\) | 3.98337 | 0.280269 | ||||||||
\(203\) | −1.16143 | −0.0815164 | ||||||||
\(204\) | −19.5944 | −1.37188 | ||||||||
\(205\) | 2.33958 | 0.163403 | ||||||||
\(206\) | 8.36098 | 0.582537 | ||||||||
\(207\) | −45.5216 | −3.16397 | ||||||||
\(208\) | −2.45581 | −0.170280 | ||||||||
\(209\) | 3.70937 | 0.256583 | ||||||||
\(210\) | 6.88338 | 0.474998 | ||||||||
\(211\) | −10.8425 | −0.746431 | −0.373215 | − | 0.927745i | \(-0.621745\pi\) | ||||
−0.373215 | + | 0.927745i | \(0.621745\pi\) | |||||||
\(212\) | −13.0772 | −0.898144 | ||||||||
\(213\) | −24.3746 | −1.67012 | ||||||||
\(214\) | −17.1374 | −1.17149 | ||||||||
\(215\) | −8.09770 | −0.552258 | ||||||||
\(216\) | −15.6025 | −1.06162 | ||||||||
\(217\) | −0.880280 | −0.0597573 | ||||||||
\(218\) | 17.6410 | 1.19480 | ||||||||
\(219\) | −35.5666 | −2.40337 | ||||||||
\(220\) | 6.59288 | 0.444492 | ||||||||
\(221\) | 14.6717 | 0.986924 | ||||||||
\(222\) | −36.2130 | −2.43046 | ||||||||
\(223\) | −1.51293 | −0.101313 | −0.0506567 | − | 0.998716i | \(-0.516131\pi\) | ||||
−0.0506567 | + | 0.998716i | \(0.516131\pi\) | |||||||
\(224\) | −1.09804 | −0.0733662 | ||||||||
\(225\) | −10.4477 | −0.696515 | ||||||||
\(226\) | −10.3617 | −0.689250 | ||||||||
\(227\) | 10.8934 | 0.723019 | 0.361510 | − | 0.932368i | \(-0.382261\pi\) | ||||
0.361510 | + | 0.932368i | \(0.382261\pi\) | |||||||
\(228\) | −3.52701 | −0.233582 | ||||||||
\(229\) | −7.10403 | −0.469447 | −0.234724 | − | 0.972062i | \(-0.575419\pi\) | ||||
−0.234724 | + | 0.972062i | \(0.575419\pi\) | |||||||
\(230\) | −11.2163 | −0.739581 | ||||||||
\(231\) | −12.4225 | −0.817342 | ||||||||
\(232\) | 1.05773 | 0.0694431 | ||||||||
\(233\) | 29.5080 | 1.93314 | 0.966568 | − | 0.256410i | \(-0.0825397\pi\) | ||||
0.966568 | + | 0.256410i | \(0.0825397\pi\) | |||||||
\(234\) | 19.0501 | 1.24534 | ||||||||
\(235\) | 4.00499 | 0.261257 | ||||||||
\(236\) | −4.64292 | −0.302228 | ||||||||
\(237\) | −9.55500 | −0.620664 | ||||||||
\(238\) | 6.56000 | 0.425222 | ||||||||
\(239\) | 4.21162 | 0.272427 | 0.136214 | − | 0.990679i | \(-0.456507\pi\) | ||||
0.136214 | + | 0.990679i | \(0.456507\pi\) | |||||||
\(240\) | −6.26877 | −0.404647 | ||||||||
\(241\) | 19.4162 | 1.25071 | 0.625355 | − | 0.780341i | \(-0.284954\pi\) | ||||
0.625355 | + | 0.780341i | \(0.284954\pi\) | |||||||
\(242\) | −0.898254 | −0.0577420 | ||||||||
\(243\) | 44.7051 | 2.86783 | ||||||||
\(244\) | 9.17375 | 0.587289 | ||||||||
\(245\) | 11.0748 | 0.707541 | ||||||||
\(246\) | 4.01470 | 0.255968 | ||||||||
\(247\) | 2.64091 | 0.168037 | ||||||||
\(248\) | 0.801680 | 0.0509067 | ||||||||
\(249\) | −36.1879 | −2.29332 | ||||||||
\(250\) | −12.1309 | −0.767224 | ||||||||
\(251\) | 6.06301 | 0.382694 | 0.191347 | − | 0.981522i | \(-0.438714\pi\) | ||||
0.191347 | + | 0.981522i | \(0.438714\pi\) | |||||||
\(252\) | 8.51768 | 0.536564 | ||||||||
\(253\) | 20.2422 | 1.27262 | ||||||||
\(254\) | −11.5199 | −0.722821 | ||||||||
\(255\) | 37.4512 | 2.34529 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.25432 | −0.265377 | −0.132689 | − | 0.991158i | \(-0.542361\pi\) | ||||
−0.132689 | + | 0.991158i | \(0.542361\pi\) | |||||||
\(258\) | −13.8956 | −0.865100 | ||||||||
\(259\) | 12.1237 | 0.753332 | ||||||||
\(260\) | 4.69385 | 0.291100 | ||||||||
\(261\) | −8.20493 | −0.507872 | ||||||||
\(262\) | −16.2852 | −1.00610 | ||||||||
\(263\) | −12.7094 | −0.783696 | −0.391848 | − | 0.920030i | \(-0.628164\pi\) | ||||
−0.391848 | + | 0.920030i | \(0.628164\pi\) | |||||||
\(264\) | 11.3133 | 0.696287 | ||||||||
\(265\) | 24.9947 | 1.53541 | ||||||||
\(266\) | 1.18081 | 0.0723999 | ||||||||
\(267\) | 10.1758 | 0.622746 | ||||||||
\(268\) | −7.02213 | −0.428945 | ||||||||
\(269\) | 8.03286 | 0.489772 | 0.244886 | − | 0.969552i | \(-0.421249\pi\) | ||||
0.244886 | + | 0.969552i | \(0.421249\pi\) | |||||||
\(270\) | 29.8214 | 1.81487 | ||||||||
\(271\) | −17.8576 | −1.08477 | −0.542385 | − | 0.840130i | \(-0.682479\pi\) | ||||
−0.542385 | + | 0.840130i | \(0.682479\pi\) | |||||||
\(272\) | −5.97426 | −0.362243 | ||||||||
\(273\) | −8.84431 | −0.535282 | ||||||||
\(274\) | −1.52041 | −0.0918513 | ||||||||
\(275\) | 4.64581 | 0.280153 | ||||||||
\(276\) | −19.2471 | −1.15854 | ||||||||
\(277\) | 29.7703 | 1.78873 | 0.894363 | − | 0.447341i | \(-0.147629\pi\) | ||||
0.894363 | + | 0.447341i | \(0.147629\pi\) | |||||||
\(278\) | −19.7483 | −1.18443 | ||||||||
\(279\) | −6.21874 | −0.372306 | ||||||||
\(280\) | 2.09871 | 0.125422 | ||||||||
\(281\) | −7.91897 | −0.472406 | −0.236203 | − | 0.971704i | \(-0.575903\pi\) | ||||
−0.236203 | + | 0.971704i | \(0.575903\pi\) | |||||||
\(282\) | 6.87252 | 0.409253 | ||||||||
\(283\) | 28.2406 | 1.67873 | 0.839365 | − | 0.543568i | \(-0.182927\pi\) | ||||
0.839365 | + | 0.543568i | \(0.182927\pi\) | |||||||
\(284\) | −7.43171 | −0.440991 | ||||||||
\(285\) | 6.74125 | 0.399317 | ||||||||
\(286\) | −8.47105 | −0.500904 | ||||||||
\(287\) | −1.34408 | −0.0793384 | ||||||||
\(288\) | −7.75714 | −0.457094 | ||||||||
\(289\) | 18.6918 | 1.09952 | ||||||||
\(290\) | −2.02165 | −0.118716 | ||||||||
\(291\) | 6.70851 | 0.393260 | ||||||||
\(292\) | −10.8441 | −0.634603 | ||||||||
\(293\) | −17.5694 | −1.02641 | −0.513207 | − | 0.858265i | \(-0.671543\pi\) | ||||
−0.513207 | + | 0.858265i | \(0.671543\pi\) | |||||||
\(294\) | 19.0042 | 1.10835 | ||||||||
\(295\) | 8.87411 | 0.516670 | ||||||||
\(296\) | −11.0412 | −0.641757 | ||||||||
\(297\) | −53.8191 | −3.12290 | ||||||||
\(298\) | −16.3947 | −0.949721 | ||||||||
\(299\) | 14.4116 | 0.833443 | ||||||||
\(300\) | −4.41742 | −0.255040 | ||||||||
\(301\) | 4.65209 | 0.268142 | ||||||||
\(302\) | 5.05534 | 0.290902 | ||||||||
\(303\) | −13.0647 | −0.750546 | ||||||||
\(304\) | −1.07537 | −0.0616768 | ||||||||
\(305\) | −17.5340 | −1.00399 | ||||||||
\(306\) | 46.3432 | 2.64926 | ||||||||
\(307\) | 4.50149 | 0.256914 | 0.128457 | − | 0.991715i | \(-0.458998\pi\) | ||||
0.128457 | + | 0.991715i | \(0.458998\pi\) | |||||||
\(308\) | −3.78758 | −0.215817 | ||||||||
\(309\) | −27.4224 | −1.56001 | ||||||||
\(310\) | −1.53227 | −0.0870269 | ||||||||
\(311\) | −13.2750 | −0.752754 | −0.376377 | − | 0.926467i | \(-0.622830\pi\) | ||||
−0.376377 | + | 0.926467i | \(0.622830\pi\) | |||||||
\(312\) | 8.05460 | 0.456002 | ||||||||
\(313\) | 18.2654 | 1.03242 | 0.516212 | − | 0.856461i | \(-0.327342\pi\) | ||||
0.516212 | + | 0.856461i | \(0.327342\pi\) | |||||||
\(314\) | 8.49219 | 0.479242 | ||||||||
\(315\) | −16.2800 | −0.917275 | ||||||||
\(316\) | −2.91328 | −0.163885 | ||||||||
\(317\) | −4.82884 | −0.271215 | −0.135607 | − | 0.990763i | \(-0.543299\pi\) | ||||
−0.135607 | + | 0.990763i | \(0.543299\pi\) | |||||||
\(318\) | 42.8906 | 2.40519 | ||||||||
\(319\) | 3.64850 | 0.204277 | ||||||||
\(320\) | −1.91132 | −0.106846 | ||||||||
\(321\) | 56.2074 | 3.13719 | ||||||||
\(322\) | 6.44371 | 0.359094 | ||||||||
\(323\) | 6.42455 | 0.357472 | ||||||||
\(324\) | 27.9018 | 1.55010 | ||||||||
\(325\) | 3.30762 | 0.183474 | ||||||||
\(326\) | 6.78097 | 0.375563 | ||||||||
\(327\) | −57.8590 | −3.19961 | ||||||||
\(328\) | 1.22406 | 0.0675877 | ||||||||
\(329\) | −2.30085 | −0.126850 | ||||||||
\(330\) | −21.6234 | −1.19033 | ||||||||
\(331\) | −19.8008 | −1.08835 | −0.544176 | − | 0.838971i | \(-0.683158\pi\) | ||||
−0.544176 | + | 0.838971i | \(0.683158\pi\) | |||||||
\(332\) | −11.0335 | −0.605544 | ||||||||
\(333\) | 85.6482 | 4.69349 | ||||||||
\(334\) | −12.2107 | −0.668142 | ||||||||
\(335\) | 13.4215 | 0.733297 | ||||||||
\(336\) | 3.60137 | 0.196471 | ||||||||
\(337\) | 13.4066 | 0.730305 | 0.365153 | − | 0.930948i | \(-0.381017\pi\) | ||||
0.365153 | + | 0.930948i | \(0.381017\pi\) | |||||||
\(338\) | 6.96898 | 0.379062 | ||||||||
\(339\) | 33.9844 | 1.84578 | ||||||||
\(340\) | 11.4187 | 0.619267 | ||||||||
\(341\) | 2.76530 | 0.149750 | ||||||||
\(342\) | 8.34181 | 0.451073 | ||||||||
\(343\) | −14.0487 | −0.758559 | ||||||||
\(344\) | −4.23670 | −0.228428 | ||||||||
\(345\) | 36.7873 | 1.98056 | ||||||||
\(346\) | 25.2030 | 1.35492 | ||||||||
\(347\) | −6.21002 | −0.333371 | −0.166686 | − | 0.986010i | \(-0.553307\pi\) | ||||
−0.166686 | + | 0.986010i | \(0.553307\pi\) | |||||||
\(348\) | −3.46914 | −0.185965 | ||||||||
\(349\) | −3.71651 | −0.198940 | −0.0994701 | − | 0.995041i | \(-0.531715\pi\) | ||||
−0.0994701 | + | 0.995041i | \(0.531715\pi\) | |||||||
\(350\) | 1.47890 | 0.0790507 | ||||||||
\(351\) | −38.3169 | −2.04520 | ||||||||
\(352\) | 3.44938 | 0.183853 | ||||||||
\(353\) | 1.59932 | 0.0851232 | 0.0425616 | − | 0.999094i | \(-0.486448\pi\) | ||||
0.0425616 | + | 0.999094i | \(0.486448\pi\) | |||||||
\(354\) | 15.2279 | 0.809353 | ||||||||
\(355\) | 14.2044 | 0.753891 | ||||||||
\(356\) | 3.10254 | 0.164435 | ||||||||
\(357\) | −21.5155 | −1.13872 | ||||||||
\(358\) | −0.0966408 | −0.00510762 | ||||||||
\(359\) | −13.9365 | −0.735543 | −0.367771 | − | 0.929916i | \(-0.619879\pi\) | ||||
−0.367771 | + | 0.929916i | \(0.619879\pi\) | |||||||
\(360\) | 14.8264 | 0.781419 | ||||||||
\(361\) | −17.8436 | −0.939136 | ||||||||
\(362\) | 13.5853 | 0.714029 | ||||||||
\(363\) | 2.94610 | 0.154630 | ||||||||
\(364\) | −2.69659 | −0.141340 | ||||||||
\(365\) | 20.7266 | 1.08488 | ||||||||
\(366\) | −30.0881 | −1.57273 | ||||||||
\(367\) | −26.7668 | −1.39722 | −0.698608 | − | 0.715505i | \(-0.746197\pi\) | ||||
−0.698608 | + | 0.715505i | \(0.746197\pi\) | |||||||
\(368\) | −5.86835 | −0.305909 | ||||||||
\(369\) | −9.49524 | −0.494303 | ||||||||
\(370\) | 21.1033 | 1.09711 | ||||||||
\(371\) | −14.3593 | −0.745498 | ||||||||
\(372\) | −2.62936 | −0.136326 | ||||||||
\(373\) | 26.4820 | 1.37119 | 0.685593 | − | 0.727985i | \(-0.259543\pi\) | ||||
0.685593 | + | 0.727985i | \(0.259543\pi\) | |||||||
\(374\) | −20.6075 | −1.06559 | ||||||||
\(375\) | 39.7869 | 2.05459 | ||||||||
\(376\) | 2.09540 | 0.108062 | ||||||||
\(377\) | 2.59758 | 0.133782 | ||||||||
\(378\) | −17.1322 | −0.881187 | ||||||||
\(379\) | −20.3489 | −1.04525 | −0.522627 | − | 0.852561i | \(-0.675048\pi\) | ||||
−0.522627 | + | 0.852561i | \(0.675048\pi\) | |||||||
\(380\) | 2.05538 | 0.105439 | ||||||||
\(381\) | 37.7830 | 1.93568 | ||||||||
\(382\) | 6.59808 | 0.337587 | ||||||||
\(383\) | 8.44791 | 0.431668 | 0.215834 | − | 0.976430i | \(-0.430753\pi\) | ||||
0.215834 | + | 0.976430i | \(0.430753\pi\) | |||||||
\(384\) | −3.27981 | −0.167372 | ||||||||
\(385\) | 7.23927 | 0.368948 | ||||||||
\(386\) | −18.1038 | −0.921457 | ||||||||
\(387\) | 32.8647 | 1.67061 | ||||||||
\(388\) | 2.04540 | 0.103839 | ||||||||
\(389\) | 28.8520 | 1.46285 | 0.731427 | − | 0.681920i | \(-0.238855\pi\) | ||||
0.731427 | + | 0.681920i | \(0.238855\pi\) | |||||||
\(390\) | −15.3949 | −0.779552 | ||||||||
\(391\) | 35.0590 | 1.77301 | ||||||||
\(392\) | 5.79430 | 0.292656 | ||||||||
\(393\) | 53.4122 | 2.69429 | ||||||||
\(394\) | 19.5243 | 0.983619 | ||||||||
\(395\) | 5.56821 | 0.280167 | ||||||||
\(396\) | −26.7574 | −1.34461 | ||||||||
\(397\) | −10.2395 | −0.513905 | −0.256953 | − | 0.966424i | \(-0.582718\pi\) | ||||
−0.256953 | + | 0.966424i | \(0.582718\pi\) | |||||||
\(398\) | 8.31380 | 0.416733 | ||||||||
\(399\) | −3.87282 | −0.193883 | ||||||||
\(400\) | −1.34685 | −0.0673427 | ||||||||
\(401\) | −29.9424 | −1.49525 | −0.747625 | − | 0.664121i | \(-0.768806\pi\) | ||||
−0.747625 | + | 0.664121i | \(0.768806\pi\) | |||||||
\(402\) | 23.0312 | 1.14869 | ||||||||
\(403\) | 1.96878 | 0.0980718 | ||||||||
\(404\) | −3.98337 | −0.198180 | ||||||||
\(405\) | −53.3293 | −2.64995 | ||||||||
\(406\) | 1.16143 | 0.0576408 | ||||||||
\(407\) | −38.0854 | −1.88782 | ||||||||
\(408\) | 19.5944 | 0.970069 | ||||||||
\(409\) | −7.40367 | −0.366088 | −0.183044 | − | 0.983105i | \(-0.558595\pi\) | ||||
−0.183044 | + | 0.983105i | \(0.558595\pi\) | |||||||
\(410\) | −2.33958 | −0.115544 | ||||||||
\(411\) | 4.98665 | 0.245973 | ||||||||
\(412\) | −8.36098 | −0.411916 | ||||||||
\(413\) | −5.09813 | −0.250863 | ||||||||
\(414\) | 45.5216 | 2.23726 | ||||||||
\(415\) | 21.0886 | 1.03520 | ||||||||
\(416\) | 2.45581 | 0.120406 | ||||||||
\(417\) | 64.7707 | 3.17184 | ||||||||
\(418\) | −3.70937 | −0.181431 | ||||||||
\(419\) | 4.67884 | 0.228576 | 0.114288 | − | 0.993448i | \(-0.463541\pi\) | ||||
0.114288 | + | 0.993448i | \(0.463541\pi\) | |||||||
\(420\) | −6.88338 | −0.335875 | ||||||||
\(421\) | 1.46039 | 0.0711752 | 0.0355876 | − | 0.999367i | \(-0.488670\pi\) | ||||
0.0355876 | + | 0.999367i | \(0.488670\pi\) | |||||||
\(422\) | 10.8425 | 0.527806 | ||||||||
\(423\) | −16.2543 | −0.790313 | ||||||||
\(424\) | 13.0772 | 0.635084 | ||||||||
\(425\) | 8.04645 | 0.390310 | ||||||||
\(426\) | 24.3746 | 1.18095 | ||||||||
\(427\) | 10.0732 | 0.487475 | ||||||||
\(428\) | 17.1374 | 0.828367 | ||||||||
\(429\) | 27.7834 | 1.34140 | ||||||||
\(430\) | 8.09770 | 0.390506 | ||||||||
\(431\) | −24.5944 | −1.18467 | −0.592336 | − | 0.805691i | \(-0.701794\pi\) | ||||
−0.592336 | + | 0.805691i | \(0.701794\pi\) | |||||||
\(432\) | 15.6025 | 0.750676 | ||||||||
\(433\) | 13.4899 | 0.648284 | 0.324142 | − | 0.946008i | \(-0.394924\pi\) | ||||
0.324142 | + | 0.946008i | \(0.394924\pi\) | |||||||
\(434\) | 0.880280 | 0.0422548 | ||||||||
\(435\) | 6.63064 | 0.317915 | ||||||||
\(436\) | −17.6410 | −0.844849 | ||||||||
\(437\) | 6.31066 | 0.301880 | ||||||||
\(438\) | 35.5666 | 1.69944 | ||||||||
\(439\) | −28.2774 | −1.34961 | −0.674804 | − | 0.737997i | \(-0.735772\pi\) | ||||
−0.674804 | + | 0.737997i | \(0.735772\pi\) | |||||||
\(440\) | −6.59288 | −0.314303 | ||||||||
\(441\) | −44.9472 | −2.14034 | ||||||||
\(442\) | −14.6717 | −0.697860 | ||||||||
\(443\) | 17.9594 | 0.853278 | 0.426639 | − | 0.904422i | \(-0.359698\pi\) | ||||
0.426639 | + | 0.904422i | \(0.359698\pi\) | |||||||
\(444\) | 36.2130 | 1.71859 | ||||||||
\(445\) | −5.92996 | −0.281107 | ||||||||
\(446\) | 1.51293 | 0.0716394 | ||||||||
\(447\) | 53.7715 | 2.54331 | ||||||||
\(448\) | 1.09804 | 0.0518777 | ||||||||
\(449\) | 32.7174 | 1.54403 | 0.772014 | − | 0.635605i | \(-0.219249\pi\) | ||||
0.772014 | + | 0.635605i | \(0.219249\pi\) | |||||||
\(450\) | 10.4477 | 0.492511 | ||||||||
\(451\) | 4.22227 | 0.198819 | ||||||||
\(452\) | 10.3617 | 0.487373 | ||||||||
\(453\) | −16.5805 | −0.779022 | ||||||||
\(454\) | −10.8934 | −0.511252 | ||||||||
\(455\) | 5.15405 | 0.241626 | ||||||||
\(456\) | 3.52701 | 0.165168 | ||||||||
\(457\) | −40.8658 | −1.91162 | −0.955811 | − | 0.293981i | \(-0.905020\pi\) | ||||
−0.955811 | + | 0.293981i | \(0.905020\pi\) | |||||||
\(458\) | 7.10403 | 0.331949 | ||||||||
\(459\) | −93.2134 | −4.35083 | ||||||||
\(460\) | 11.2163 | 0.522963 | ||||||||
\(461\) | 7.24778 | 0.337563 | 0.168781 | − | 0.985654i | \(-0.446017\pi\) | ||||
0.168781 | + | 0.985654i | \(0.446017\pi\) | |||||||
\(462\) | 12.4225 | 0.577948 | ||||||||
\(463\) | −26.8102 | −1.24597 | −0.622987 | − | 0.782232i | \(-0.714081\pi\) | ||||
−0.622987 | + | 0.782232i | \(0.714081\pi\) | |||||||
\(464\) | −1.05773 | −0.0491037 | ||||||||
\(465\) | 5.02554 | 0.233054 | ||||||||
\(466\) | −29.5080 | −1.36693 | ||||||||
\(467\) | −40.4222 | −1.87052 | −0.935258 | − | 0.353966i | \(-0.884833\pi\) | ||||
−0.935258 | + | 0.353966i | \(0.884833\pi\) | |||||||
\(468\) | −19.0501 | −0.880591 | ||||||||
\(469\) | −7.71061 | −0.356043 | ||||||||
\(470\) | −4.00499 | −0.184736 | ||||||||
\(471\) | −27.8528 | −1.28339 | ||||||||
\(472\) | 4.64292 | 0.213708 | ||||||||
\(473\) | −14.6140 | −0.671953 | ||||||||
\(474\) | 9.55500 | 0.438876 | ||||||||
\(475\) | 1.44837 | 0.0664557 | ||||||||
\(476\) | −6.56000 | −0.300677 | ||||||||
\(477\) | −101.441 | −4.64469 | ||||||||
\(478\) | −4.21162 | −0.192635 | ||||||||
\(479\) | −42.7351 | −1.95262 | −0.976308 | − | 0.216384i | \(-0.930574\pi\) | ||||
−0.976308 | + | 0.216384i | \(0.930574\pi\) | |||||||
\(480\) | 6.26877 | 0.286129 | ||||||||
\(481\) | −27.1151 | −1.23634 | ||||||||
\(482\) | −19.4162 | −0.884385 | ||||||||
\(483\) | −21.1341 | −0.961636 | ||||||||
\(484\) | 0.898254 | 0.0408297 | ||||||||
\(485\) | −3.90941 | −0.177517 | ||||||||
\(486\) | −44.7051 | −2.02786 | ||||||||
\(487\) | 29.2596 | 1.32588 | 0.662939 | − | 0.748673i | \(-0.269309\pi\) | ||||
0.662939 | + | 0.748673i | \(0.269309\pi\) | |||||||
\(488\) | −9.17375 | −0.415276 | ||||||||
\(489\) | −22.2403 | −1.00574 | ||||||||
\(490\) | −11.0748 | −0.500307 | ||||||||
\(491\) | −2.36499 | −0.106730 | −0.0533652 | − | 0.998575i | \(-0.516995\pi\) | ||||
−0.0533652 | + | 0.998575i | \(0.516995\pi\) | |||||||
\(492\) | −4.01470 | −0.180997 | ||||||||
\(493\) | 6.31913 | 0.284599 | ||||||||
\(494\) | −2.64091 | −0.118820 | ||||||||
\(495\) | 51.1419 | 2.29866 | ||||||||
\(496\) | −0.801680 | −0.0359965 | ||||||||
\(497\) | −8.16035 | −0.366042 | ||||||||
\(498\) | 36.1879 | 1.62162 | ||||||||
\(499\) | 27.2837 | 1.22138 | 0.610692 | − | 0.791868i | \(-0.290891\pi\) | ||||
0.610692 | + | 0.791868i | \(0.290891\pi\) | |||||||
\(500\) | 12.1309 | 0.542509 | ||||||||
\(501\) | 40.0489 | 1.78925 | ||||||||
\(502\) | −6.06301 | −0.270606 | ||||||||
\(503\) | 10.8000 | 0.481550 | 0.240775 | − | 0.970581i | \(-0.422598\pi\) | ||||
0.240775 | + | 0.970581i | \(0.422598\pi\) | |||||||
\(504\) | −8.51768 | −0.379408 | ||||||||
\(505\) | 7.61349 | 0.338796 | ||||||||
\(506\) | −20.2422 | −0.899875 | ||||||||
\(507\) | −22.8569 | −1.01511 | ||||||||
\(508\) | 11.5199 | 0.511112 | ||||||||
\(509\) | −8.32214 | −0.368872 | −0.184436 | − | 0.982844i | \(-0.559046\pi\) | ||||
−0.184436 | + | 0.982844i | \(0.559046\pi\) | |||||||
\(510\) | −37.4512 | −1.65837 | ||||||||
\(511\) | −11.9073 | −0.526748 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −16.7785 | −0.740789 | ||||||||
\(514\) | 4.25432 | 0.187650 | ||||||||
\(515\) | 15.9805 | 0.704185 | ||||||||
\(516\) | 13.8956 | 0.611718 | ||||||||
\(517\) | 7.22785 | 0.317881 | ||||||||
\(518\) | −12.1237 | −0.532686 | ||||||||
\(519\) | −82.6609 | −3.62841 | ||||||||
\(520\) | −4.69385 | −0.205839 | ||||||||
\(521\) | 6.05714 | 0.265368 | 0.132684 | − | 0.991158i | \(-0.457640\pi\) | ||||
0.132684 | + | 0.991158i | \(0.457640\pi\) | |||||||
\(522\) | 8.20493 | 0.359120 | ||||||||
\(523\) | 11.0178 | 0.481775 | 0.240887 | − | 0.970553i | \(-0.422562\pi\) | ||||
0.240887 | + | 0.970553i | \(0.422562\pi\) | |||||||
\(524\) | 16.2852 | 0.711420 | ||||||||
\(525\) | −4.85052 | −0.211694 | ||||||||
\(526\) | 12.7094 | 0.554157 | ||||||||
\(527\) | 4.78944 | 0.208631 | ||||||||
\(528\) | −11.3133 | −0.492349 | ||||||||
\(529\) | 11.4375 | 0.497283 | ||||||||
\(530\) | −24.9947 | −1.08570 | ||||||||
\(531\) | −36.0158 | −1.56295 | ||||||||
\(532\) | −1.18081 | −0.0511944 | ||||||||
\(533\) | 3.00608 | 0.130208 | ||||||||
\(534\) | −10.1758 | −0.440348 | ||||||||
\(535\) | −32.7551 | −1.41612 | ||||||||
\(536\) | 7.02213 | 0.303310 | ||||||||
\(537\) | 0.316963 | 0.0136780 | ||||||||
\(538\) | −8.03286 | −0.346321 | ||||||||
\(539\) | 19.9868 | 0.860891 | ||||||||
\(540\) | −29.8214 | −1.28331 | ||||||||
\(541\) | −21.1166 | −0.907874 | −0.453937 | − | 0.891034i | \(-0.649981\pi\) | ||||
−0.453937 | + | 0.891034i | \(0.649981\pi\) | |||||||
\(542\) | 17.8576 | 0.767049 | ||||||||
\(543\) | −44.5573 | −1.91214 | ||||||||
\(544\) | 5.97426 | 0.256144 | ||||||||
\(545\) | 33.7176 | 1.44430 | ||||||||
\(546\) | 8.84431 | 0.378501 | ||||||||
\(547\) | 17.3197 | 0.740537 | 0.370268 | − | 0.928925i | \(-0.379266\pi\) | ||||
0.370268 | + | 0.928925i | \(0.379266\pi\) | |||||||
\(548\) | 1.52041 | 0.0649487 | ||||||||
\(549\) | 71.1621 | 3.03712 | ||||||||
\(550\) | −4.64581 | −0.198098 | ||||||||
\(551\) | 1.13745 | 0.0484570 | ||||||||
\(552\) | 19.2471 | 0.819209 | ||||||||
\(553\) | −3.19891 | −0.136032 | ||||||||
\(554\) | −29.7703 | −1.26482 | ||||||||
\(555\) | −69.2147 | −2.93800 | ||||||||
\(556\) | 19.7483 | 0.837515 | ||||||||
\(557\) | −2.45081 | −0.103844 | −0.0519221 | − | 0.998651i | \(-0.516535\pi\) | ||||
−0.0519221 | + | 0.998651i | \(0.516535\pi\) | |||||||
\(558\) | 6.21874 | 0.263260 | ||||||||
\(559\) | −10.4046 | −0.440066 | ||||||||
\(560\) | −2.09871 | −0.0886869 | ||||||||
\(561\) | 67.5887 | 2.85360 | ||||||||
\(562\) | 7.91897 | 0.334042 | ||||||||
\(563\) | −6.66243 | −0.280788 | −0.140394 | − | 0.990096i | \(-0.544837\pi\) | ||||
−0.140394 | + | 0.990096i | \(0.544837\pi\) | |||||||
\(564\) | −6.87252 | −0.289385 | ||||||||
\(565\) | −19.8045 | −0.833183 | ||||||||
\(566\) | −28.2406 | −1.18704 | ||||||||
\(567\) | 30.6374 | 1.28665 | ||||||||
\(568\) | 7.43171 | 0.311828 | ||||||||
\(569\) | 20.2085 | 0.847183 | 0.423591 | − | 0.905853i | \(-0.360769\pi\) | ||||
0.423591 | + | 0.905853i | \(0.360769\pi\) | |||||||
\(570\) | −6.74125 | −0.282360 | ||||||||
\(571\) | 32.9979 | 1.38092 | 0.690459 | − | 0.723371i | \(-0.257408\pi\) | ||||
0.690459 | + | 0.723371i | \(0.257408\pi\) | |||||||
\(572\) | 8.47105 | 0.354192 | ||||||||
\(573\) | −21.6404 | −0.904042 | ||||||||
\(574\) | 1.34408 | 0.0561007 | ||||||||
\(575\) | 7.90380 | 0.329611 | ||||||||
\(576\) | 7.75714 | 0.323214 | ||||||||
\(577\) | −5.58644 | −0.232567 | −0.116283 | − | 0.993216i | \(-0.537098\pi\) | ||||
−0.116283 | + | 0.993216i | \(0.537098\pi\) | |||||||
\(578\) | −18.6918 | −0.777476 | ||||||||
\(579\) | 59.3769 | 2.46762 | ||||||||
\(580\) | 2.02165 | 0.0839446 | ||||||||
\(581\) | −12.1153 | −0.502628 | ||||||||
\(582\) | −6.70851 | −0.278077 | ||||||||
\(583\) | 45.1082 | 1.86819 | ||||||||
\(584\) | 10.8441 | 0.448732 | ||||||||
\(585\) | 36.4108 | 1.50540 | ||||||||
\(586\) | 17.5694 | 0.725784 | ||||||||
\(587\) | 24.8405 | 1.02528 | 0.512638 | − | 0.858605i | \(-0.328668\pi\) | ||||
0.512638 | + | 0.858605i | \(0.328668\pi\) | |||||||
\(588\) | −19.0042 | −0.783720 | ||||||||
\(589\) | 0.862104 | 0.0355224 | ||||||||
\(590\) | −8.87411 | −0.365341 | ||||||||
\(591\) | −64.0359 | −2.63408 | ||||||||
\(592\) | 11.0412 | 0.453791 | ||||||||
\(593\) | 26.3962 | 1.08396 | 0.541981 | − | 0.840390i | \(-0.317674\pi\) | ||||
0.541981 | + | 0.840390i | \(0.317674\pi\) | |||||||
\(594\) | 53.8191 | 2.20822 | ||||||||
\(595\) | 12.5383 | 0.514019 | ||||||||
\(596\) | 16.3947 | 0.671554 | ||||||||
\(597\) | −27.2677 | −1.11599 | ||||||||
\(598\) | −14.4116 | −0.589333 | ||||||||
\(599\) | −23.6993 | −0.968327 | −0.484163 | − | 0.874978i | \(-0.660876\pi\) | ||||
−0.484163 | + | 0.874978i | \(0.660876\pi\) | |||||||
\(600\) | 4.41742 | 0.180340 | ||||||||
\(601\) | 32.7696 | 1.33670 | 0.668351 | − | 0.743846i | \(-0.267001\pi\) | ||||
0.668351 | + | 0.743846i | \(0.267001\pi\) | |||||||
\(602\) | −4.65209 | −0.189605 | ||||||||
\(603\) | −54.4717 | −2.21826 | ||||||||
\(604\) | −5.05534 | −0.205699 | ||||||||
\(605\) | −1.71685 | −0.0698000 | ||||||||
\(606\) | 13.0647 | 0.530716 | ||||||||
\(607\) | 21.8414 | 0.886516 | 0.443258 | − | 0.896394i | \(-0.353823\pi\) | ||||
0.443258 | + | 0.896394i | \(0.353823\pi\) | |||||||
\(608\) | 1.07537 | 0.0436121 | ||||||||
\(609\) | −3.80927 | −0.154359 | ||||||||
\(610\) | 17.5340 | 0.709930 | ||||||||
\(611\) | 5.14592 | 0.208182 | ||||||||
\(612\) | −46.3432 | −1.87331 | ||||||||
\(613\) | −15.6341 | −0.631453 | −0.315727 | − | 0.948850i | \(-0.602248\pi\) | ||||
−0.315727 | + | 0.948850i | \(0.602248\pi\) | |||||||
\(614\) | −4.50149 | −0.181666 | ||||||||
\(615\) | 7.67337 | 0.309420 | ||||||||
\(616\) | 3.78758 | 0.152606 | ||||||||
\(617\) | 6.89977 | 0.277774 | 0.138887 | − | 0.990308i | \(-0.455647\pi\) | ||||
0.138887 | + | 0.990308i | \(0.455647\pi\) | |||||||
\(618\) | 27.4224 | 1.10309 | ||||||||
\(619\) | −10.3880 | −0.417530 | −0.208765 | − | 0.977966i | \(-0.566944\pi\) | ||||
−0.208765 | + | 0.977966i | \(0.566944\pi\) | |||||||
\(620\) | 1.53227 | 0.0615373 | ||||||||
\(621\) | −91.5610 | −3.67421 | ||||||||
\(622\) | 13.2750 | 0.532277 | ||||||||
\(623\) | 3.40673 | 0.136488 | ||||||||
\(624\) | −8.05460 | −0.322442 | ||||||||
\(625\) | −16.4517 | −0.658069 | ||||||||
\(626\) | −18.2654 | −0.730033 | ||||||||
\(627\) | 12.1660 | 0.485864 | ||||||||
\(628\) | −8.49219 | −0.338875 | ||||||||
\(629\) | −65.9630 | −2.63012 | ||||||||
\(630\) | 16.2800 | 0.648612 | ||||||||
\(631\) | 3.66725 | 0.145991 | 0.0729954 | − | 0.997332i | \(-0.476744\pi\) | ||||
0.0729954 | + | 0.997332i | \(0.476744\pi\) | |||||||
\(632\) | 2.91328 | 0.115884 | ||||||||
\(633\) | −35.5614 | −1.41344 | ||||||||
\(634\) | 4.82884 | 0.191778 | ||||||||
\(635\) | −22.0182 | −0.873764 | ||||||||
\(636\) | −42.8906 | −1.70072 | ||||||||
\(637\) | 14.2297 | 0.563802 | ||||||||
\(638\) | −3.64850 | −0.144446 | ||||||||
\(639\) | −57.6489 | −2.28055 | ||||||||
\(640\) | 1.91132 | 0.0755516 | ||||||||
\(641\) | 17.2995 | 0.683291 | 0.341645 | − | 0.939829i | \(-0.389016\pi\) | ||||
0.341645 | + | 0.939829i | \(0.389016\pi\) | |||||||
\(642\) | −56.2074 | −2.21833 | ||||||||
\(643\) | 15.4977 | 0.611171 | 0.305585 | − | 0.952165i | \(-0.401148\pi\) | ||||
0.305585 | + | 0.952165i | \(0.401148\pi\) | |||||||
\(644\) | −6.44371 | −0.253918 | ||||||||
\(645\) | −26.5589 | −1.04576 | ||||||||
\(646\) | −6.42455 | −0.252771 | ||||||||
\(647\) | 35.1070 | 1.38020 | 0.690099 | − | 0.723715i | \(-0.257567\pi\) | ||||
0.690099 | + | 0.723715i | \(0.257567\pi\) | |||||||
\(648\) | −27.9018 | −1.09609 | ||||||||
\(649\) | 16.0152 | 0.628652 | ||||||||
\(650\) | −3.30762 | −0.129736 | ||||||||
\(651\) | −2.88715 | −0.113156 | ||||||||
\(652\) | −6.78097 | −0.265563 | ||||||||
\(653\) | −14.7734 | −0.578126 | −0.289063 | − | 0.957310i | \(-0.593344\pi\) | ||||
−0.289063 | + | 0.957310i | \(0.593344\pi\) | |||||||
\(654\) | 57.8590 | 2.26247 | ||||||||
\(655\) | −31.1262 | −1.21620 | ||||||||
\(656\) | −1.22406 | −0.0477917 | ||||||||
\(657\) | −84.1192 | −3.28180 | ||||||||
\(658\) | 2.30085 | 0.0896963 | ||||||||
\(659\) | 5.35530 | 0.208613 | 0.104306 | − | 0.994545i | \(-0.466738\pi\) | ||||
0.104306 | + | 0.994545i | \(0.466738\pi\) | |||||||
\(660\) | 21.6234 | 0.841689 | ||||||||
\(661\) | 19.0949 | 0.742704 | 0.371352 | − | 0.928492i | \(-0.378894\pi\) | ||||
0.371352 | + | 0.928492i | \(0.378894\pi\) | |||||||
\(662\) | 19.8008 | 0.769581 | ||||||||
\(663\) | 48.1203 | 1.86884 | ||||||||
\(664\) | 11.0335 | 0.428185 | ||||||||
\(665\) | 2.25690 | 0.0875188 | ||||||||
\(666\) | −85.6482 | −3.31880 | ||||||||
\(667\) | 6.20711 | 0.240340 | ||||||||
\(668\) | 12.2107 | 0.472447 | ||||||||
\(669\) | −4.96212 | −0.191847 | ||||||||
\(670\) | −13.4215 | −0.518519 | ||||||||
\(671\) | −31.6438 | −1.22159 | ||||||||
\(672\) | −3.60137 | −0.138926 | ||||||||
\(673\) | −20.0851 | −0.774224 | −0.387112 | − | 0.922033i | \(-0.626527\pi\) | ||||
−0.387112 | + | 0.922033i | \(0.626527\pi\) | |||||||
\(674\) | −13.4066 | −0.516404 | ||||||||
\(675\) | −21.0143 | −0.808840 | ||||||||
\(676\) | −6.96898 | −0.268038 | ||||||||
\(677\) | −25.4361 | −0.977590 | −0.488795 | − | 0.872399i | \(-0.662563\pi\) | ||||
−0.488795 | + | 0.872399i | \(0.662563\pi\) | |||||||
\(678\) | −33.9844 | −1.30516 | ||||||||
\(679\) | 2.24594 | 0.0861911 | ||||||||
\(680\) | −11.4187 | −0.437888 | ||||||||
\(681\) | 35.7282 | 1.36911 | ||||||||
\(682\) | −2.76530 | −0.105889 | ||||||||
\(683\) | −48.3779 | −1.85113 | −0.925564 | − | 0.378592i | \(-0.876408\pi\) | ||||
−0.925564 | + | 0.378592i | \(0.876408\pi\) | |||||||
\(684\) | −8.34181 | −0.318957 | ||||||||
\(685\) | −2.90599 | −0.111032 | ||||||||
\(686\) | 14.0487 | 0.536382 | ||||||||
\(687\) | −23.2999 | −0.888945 | ||||||||
\(688\) | 4.23670 | 0.161523 | ||||||||
\(689\) | 32.1151 | 1.22349 | ||||||||
\(690\) | −36.7873 | −1.40047 | ||||||||
\(691\) | −35.7633 | −1.36050 | −0.680249 | − | 0.732981i | \(-0.738128\pi\) | ||||
−0.680249 | + | 0.732981i | \(0.738128\pi\) | |||||||
\(692\) | −25.2030 | −0.958074 | ||||||||
\(693\) | −29.3808 | −1.11608 | ||||||||
\(694\) | 6.21002 | 0.235729 | ||||||||
\(695\) | −37.7454 | −1.43176 | ||||||||
\(696\) | 3.46914 | 0.131497 | ||||||||
\(697\) | 7.31288 | 0.276995 | ||||||||
\(698\) | 3.71651 | 0.140672 | ||||||||
\(699\) | 96.7807 | 3.66058 | ||||||||
\(700\) | −1.47890 | −0.0558973 | ||||||||
\(701\) | −11.3880 | −0.430119 | −0.215060 | − | 0.976601i | \(-0.568995\pi\) | ||||
−0.215060 | + | 0.976601i | \(0.568995\pi\) | |||||||
\(702\) | 38.3169 | 1.44618 | ||||||||
\(703\) | −11.8734 | −0.447814 | ||||||||
\(704\) | −3.44938 | −0.130004 | ||||||||
\(705\) | 13.1356 | 0.494715 | ||||||||
\(706\) | −1.59932 | −0.0601912 | ||||||||
\(707\) | −4.37391 | −0.164498 | ||||||||
\(708\) | −15.2279 | −0.572299 | ||||||||
\(709\) | 34.0180 | 1.27757 | 0.638786 | − | 0.769384i | \(-0.279437\pi\) | ||||
0.638786 | + | 0.769384i | \(0.279437\pi\) | |||||||
\(710\) | −14.2044 | −0.533081 | ||||||||
\(711\) | −22.5987 | −0.847518 | ||||||||
\(712\) | −3.10254 | −0.116273 | ||||||||
\(713\) | 4.70454 | 0.176186 | ||||||||
\(714\) | 21.5155 | 0.805199 | ||||||||
\(715\) | −16.1909 | −0.605505 | ||||||||
\(716\) | 0.0966408 | 0.00361163 | ||||||||
\(717\) | 13.8133 | 0.515868 | ||||||||
\(718\) | 13.9365 | 0.520107 | ||||||||
\(719\) | 30.1708 | 1.12518 | 0.562590 | − | 0.826736i | \(-0.309805\pi\) | ||||
0.562590 | + | 0.826736i | \(0.309805\pi\) | |||||||
\(720\) | −14.8264 | −0.552547 | ||||||||
\(721\) | −9.18072 | −0.341908 | ||||||||
\(722\) | 17.8436 | 0.664069 | ||||||||
\(723\) | 63.6815 | 2.36834 | ||||||||
\(724\) | −13.5853 | −0.504895 | ||||||||
\(725\) | 1.42460 | 0.0529084 | ||||||||
\(726\) | −2.94610 | −0.109340 | ||||||||
\(727\) | −0.182495 | −0.00676835 | −0.00338418 | − | 0.999994i | \(-0.501077\pi\) | ||||
−0.00338418 | + | 0.999994i | \(0.501077\pi\) | |||||||
\(728\) | 2.69659 | 0.0999424 | ||||||||
\(729\) | 62.9186 | 2.33032 | ||||||||
\(730\) | −20.7266 | −0.767124 | ||||||||
\(731\) | −25.3112 | −0.936167 | ||||||||
\(732\) | 30.0881 | 1.11209 | ||||||||
\(733\) | −2.60018 | −0.0960400 | −0.0480200 | − | 0.998846i | \(-0.515291\pi\) | ||||
−0.0480200 | + | 0.998846i | \(0.515291\pi\) | |||||||
\(734\) | 26.7668 | 0.987981 | ||||||||
\(735\) | 36.3231 | 1.33980 | ||||||||
\(736\) | 5.86835 | 0.216310 | ||||||||
\(737\) | 24.2220 | 0.892230 | ||||||||
\(738\) | 9.49524 | 0.349525 | ||||||||
\(739\) | 3.26112 | 0.119962 | 0.0599812 | − | 0.998200i | \(-0.480896\pi\) | ||||
0.0599812 | + | 0.998200i | \(0.480896\pi\) | |||||||
\(740\) | −21.1033 | −0.775772 | ||||||||
\(741\) | 8.66169 | 0.318195 | ||||||||
\(742\) | 14.3593 | 0.527147 | ||||||||
\(743\) | 18.9160 | 0.693962 | 0.346981 | − | 0.937872i | \(-0.387207\pi\) | ||||
0.346981 | + | 0.937872i | \(0.387207\pi\) | |||||||
\(744\) | 2.62936 | 0.0963969 | ||||||||
\(745\) | −31.3356 | −1.14805 | ||||||||
\(746\) | −26.4820 | −0.969575 | ||||||||
\(747\) | −85.5888 | −3.13153 | ||||||||
\(748\) | 20.6075 | 0.753486 | ||||||||
\(749\) | 18.8176 | 0.687581 | ||||||||
\(750\) | −39.7869 | −1.45281 | ||||||||
\(751\) | 1.60561 | 0.0585894 | 0.0292947 | − | 0.999571i | \(-0.490674\pi\) | ||||
0.0292947 | + | 0.999571i | \(0.490674\pi\) | |||||||
\(752\) | −2.09540 | −0.0764115 | ||||||||
\(753\) | 19.8855 | 0.724669 | ||||||||
\(754\) | −2.59758 | −0.0945982 | ||||||||
\(755\) | 9.66238 | 0.351650 | ||||||||
\(756\) | 17.1322 | 0.623094 | ||||||||
\(757\) | −48.9088 | −1.77762 | −0.888810 | − | 0.458275i | \(-0.848467\pi\) | ||||
−0.888810 | + | 0.458275i | \(0.848467\pi\) | |||||||
\(758\) | 20.3489 | 0.739107 | ||||||||
\(759\) | 66.3905 | 2.40982 | ||||||||
\(760\) | −2.05538 | −0.0745565 | ||||||||
\(761\) | 38.1912 | 1.38443 | 0.692214 | − | 0.721692i | \(-0.256635\pi\) | ||||
0.692214 | + | 0.721692i | \(0.256635\pi\) | |||||||
\(762\) | −37.7830 | −1.36873 | ||||||||
\(763\) | −19.3706 | −0.701261 | ||||||||
\(764\) | −6.59808 | −0.238710 | ||||||||
\(765\) | 88.5767 | 3.20250 | ||||||||
\(766\) | −8.44791 | −0.305236 | ||||||||
\(767\) | 11.4021 | 0.411708 | ||||||||
\(768\) | 3.27981 | 0.118350 | ||||||||
\(769\) | 39.5368 | 1.42573 | 0.712867 | − | 0.701299i | \(-0.247396\pi\) | ||||
0.712867 | + | 0.701299i | \(0.247396\pi\) | |||||||
\(770\) | −7.23927 | −0.260885 | ||||||||
\(771\) | −13.9534 | −0.502518 | ||||||||
\(772\) | 18.1038 | 0.651569 | ||||||||
\(773\) | −41.0489 | −1.47643 | −0.738213 | − | 0.674568i | \(-0.764330\pi\) | ||||
−0.738213 | + | 0.674568i | \(0.764330\pi\) | |||||||
\(774\) | −32.8647 | −1.18130 | ||||||||
\(775\) | 1.07975 | 0.0387856 | ||||||||
\(776\) | −2.04540 | −0.0734254 | ||||||||
\(777\) | 39.7635 | 1.42651 | ||||||||
\(778\) | −28.8520 | −1.03439 | ||||||||
\(779\) | 1.31632 | 0.0471622 | ||||||||
\(780\) | 15.3949 | 0.551227 | ||||||||
\(781\) | 25.6348 | 0.917287 | ||||||||
\(782\) | −35.0590 | −1.25371 | ||||||||
\(783\) | −16.5032 | −0.589776 | ||||||||
\(784\) | −5.79430 | −0.206939 | ||||||||
\(785\) | 16.2313 | 0.579320 | ||||||||
\(786\) | −53.4122 | −1.90515 | ||||||||
\(787\) | −52.0171 | −1.85421 | −0.927105 | − | 0.374802i | \(-0.877711\pi\) | ||||
−0.927105 | + | 0.374802i | \(0.877711\pi\) | |||||||
\(788\) | −19.5243 | −0.695523 | ||||||||
\(789\) | −41.6845 | −1.48401 | ||||||||
\(790\) | −5.56821 | −0.198108 | ||||||||
\(791\) | 11.3776 | 0.404541 | ||||||||
\(792\) | 26.7574 | 0.950781 | ||||||||
\(793\) | −22.5290 | −0.800029 | ||||||||
\(794\) | 10.2395 | 0.363386 | ||||||||
\(795\) | 81.9777 | 2.90745 | ||||||||
\(796\) | −8.31380 | −0.294675 | ||||||||
\(797\) | −43.7229 | −1.54874 | −0.774372 | − | 0.632730i | \(-0.781934\pi\) | ||||
−0.774372 | + | 0.632730i | \(0.781934\pi\) | |||||||
\(798\) | 3.87282 | 0.137096 | ||||||||
\(799\) | 12.5185 | 0.442872 | ||||||||
\(800\) | 1.34685 | 0.0476184 | ||||||||
\(801\) | 24.0669 | 0.850361 | ||||||||
\(802\) | 29.9424 | 1.05730 | ||||||||
\(803\) | 37.4055 | 1.32001 | ||||||||
\(804\) | −23.0312 | −0.812249 | ||||||||
\(805\) | 12.3160 | 0.434082 | ||||||||
\(806\) | −1.96878 | −0.0693472 | ||||||||
\(807\) | 26.3462 | 0.927431 | ||||||||
\(808\) | 3.98337 | 0.140134 | ||||||||
\(809\) | 45.6733 | 1.60579 | 0.802895 | − | 0.596121i | \(-0.203292\pi\) | ||||
0.802895 | + | 0.596121i | \(0.203292\pi\) | |||||||
\(810\) | 53.3293 | 1.87380 | ||||||||
\(811\) | −33.4049 | −1.17300 | −0.586502 | − | 0.809948i | \(-0.699495\pi\) | ||||
−0.586502 | + | 0.809948i | \(0.699495\pi\) | |||||||
\(812\) | −1.16143 | −0.0407582 | ||||||||
\(813\) | −58.5694 | −2.05412 | ||||||||
\(814\) | 38.0854 | 1.33489 | ||||||||
\(815\) | 12.9606 | 0.453990 | ||||||||
\(816\) | −19.5944 | −0.685942 | ||||||||
\(817\) | −4.55603 | −0.159395 | ||||||||
\(818\) | 7.40367 | 0.258863 | ||||||||
\(819\) | −20.9178 | −0.730929 | ||||||||
\(820\) | 2.33958 | 0.0817017 | ||||||||
\(821\) | 23.1612 | 0.808331 | 0.404165 | − | 0.914686i | \(-0.367562\pi\) | ||||
0.404165 | + | 0.914686i | \(0.367562\pi\) | |||||||
\(822\) | −4.98665 | −0.173929 | ||||||||
\(823\) | 15.2517 | 0.531642 | 0.265821 | − | 0.964022i | \(-0.414357\pi\) | ||||
0.265821 | + | 0.964022i | \(0.414357\pi\) | |||||||
\(824\) | 8.36098 | 0.291268 | ||||||||
\(825\) | 15.2374 | 0.530497 | ||||||||
\(826\) | 5.09813 | 0.177387 | ||||||||
\(827\) | −30.2522 | −1.05197 | −0.525986 | − | 0.850493i | \(-0.676304\pi\) | ||||
−0.525986 | + | 0.850493i | \(0.676304\pi\) | |||||||
\(828\) | −45.5216 | −1.58199 | ||||||||
\(829\) | 33.0136 | 1.14661 | 0.573304 | − | 0.819342i | \(-0.305661\pi\) | ||||
0.573304 | + | 0.819342i | \(0.305661\pi\) | |||||||
\(830\) | −21.0886 | −0.731998 | ||||||||
\(831\) | 97.6410 | 3.38713 | ||||||||
\(832\) | −2.45581 | −0.0851400 | ||||||||
\(833\) | 34.6167 | 1.19940 | ||||||||
\(834\) | −64.7707 | −2.24283 | ||||||||
\(835\) | −23.3386 | −0.807666 | ||||||||
\(836\) | 3.70937 | 0.128291 | ||||||||
\(837\) | −12.5082 | −0.432347 | ||||||||
\(838\) | −4.67884 | −0.161628 | ||||||||
\(839\) | 6.06219 | 0.209290 | 0.104645 | − | 0.994510i | \(-0.466629\pi\) | ||||
0.104645 | + | 0.994510i | \(0.466629\pi\) | |||||||
\(840\) | 6.88338 | 0.237499 | ||||||||
\(841\) | −27.8812 | −0.961421 | ||||||||
\(842\) | −1.46039 | −0.0503284 | ||||||||
\(843\) | −25.9727 | −0.894547 | ||||||||
\(844\) | −10.8425 | −0.373215 | ||||||||
\(845\) | 13.3200 | 0.458220 | ||||||||
\(846\) | 16.2543 | 0.558836 | ||||||||
\(847\) | 0.986323 | 0.0338905 | ||||||||
\(848\) | −13.0772 | −0.449072 | ||||||||
\(849\) | 92.6238 | 3.17884 | ||||||||
\(850\) | −8.04645 | −0.275991 | ||||||||
\(851\) | −64.7936 | −2.22110 | ||||||||
\(852\) | −24.3746 | −0.835060 | ||||||||
\(853\) | 2.88607 | 0.0988170 | 0.0494085 | − | 0.998779i | \(-0.484266\pi\) | ||||
0.0494085 | + | 0.998779i | \(0.484266\pi\) | |||||||
\(854\) | −10.0732 | −0.344697 | ||||||||
\(855\) | 15.9439 | 0.545269 | ||||||||
\(856\) | −17.1374 | −0.585744 | ||||||||
\(857\) | 19.8724 | 0.678829 | 0.339414 | − | 0.940637i | \(-0.389771\pi\) | ||||
0.339414 | + | 0.940637i | \(0.389771\pi\) | |||||||
\(858\) | −27.7834 | −0.948510 | ||||||||
\(859\) | −16.4754 | −0.562134 | −0.281067 | − | 0.959688i | \(-0.590688\pi\) | ||||
−0.281067 | + | 0.959688i | \(0.590688\pi\) | |||||||
\(860\) | −8.09770 | −0.276129 | ||||||||
\(861\) | −4.40832 | −0.150235 | ||||||||
\(862\) | 24.5944 | 0.837689 | ||||||||
\(863\) | −1.94990 | −0.0663754 | −0.0331877 | − | 0.999449i | \(-0.510566\pi\) | ||||
−0.0331877 | + | 0.999449i | \(0.510566\pi\) | |||||||
\(864\) | −15.6025 | −0.530808 | ||||||||
\(865\) | 48.1710 | 1.63786 | ||||||||
\(866\) | −13.4899 | −0.458406 | ||||||||
\(867\) | 61.3055 | 2.08204 | ||||||||
\(868\) | −0.880280 | −0.0298786 | ||||||||
\(869\) | 10.0490 | 0.340890 | ||||||||
\(870\) | −6.63064 | −0.224800 | ||||||||
\(871\) | 17.2450 | 0.584326 | ||||||||
\(872\) | 17.6410 | 0.597399 | ||||||||
\(873\) | 15.8664 | 0.536997 | ||||||||
\(874\) | −6.31066 | −0.213461 | ||||||||
\(875\) | 13.3202 | 0.450306 | ||||||||
\(876\) | −35.5666 | −1.20168 | ||||||||
\(877\) | 46.5008 | 1.57022 | 0.785111 | − | 0.619355i | \(-0.212606\pi\) | ||||
0.785111 | + | 0.619355i | \(0.212606\pi\) | |||||||
\(878\) | 28.2774 | 0.954317 | ||||||||
\(879\) | −57.6242 | −1.94361 | ||||||||
\(880\) | 6.59288 | 0.222246 | ||||||||
\(881\) | 21.2602 | 0.716274 | 0.358137 | − | 0.933669i | \(-0.383412\pi\) | ||||
0.358137 | + | 0.933669i | \(0.383412\pi\) | |||||||
\(882\) | 44.9472 | 1.51345 | ||||||||
\(883\) | 8.18177 | 0.275339 | 0.137669 | − | 0.990478i | \(-0.456039\pi\) | ||||
0.137669 | + | 0.990478i | \(0.456039\pi\) | |||||||
\(884\) | 14.6717 | 0.493462 | ||||||||
\(885\) | 29.1054 | 0.978366 | ||||||||
\(886\) | −17.9594 | −0.603359 | ||||||||
\(887\) | 36.7954 | 1.23547 | 0.617734 | − | 0.786387i | \(-0.288051\pi\) | ||||
0.617734 | + | 0.786387i | \(0.288051\pi\) | |||||||
\(888\) | −36.2130 | −1.21523 | ||||||||
\(889\) | 12.6493 | 0.424245 | ||||||||
\(890\) | 5.92996 | 0.198773 | ||||||||
\(891\) | −96.2441 | −3.22430 | ||||||||
\(892\) | −1.51293 | −0.0506567 | ||||||||
\(893\) | 2.25334 | 0.0754051 | ||||||||
\(894\) | −53.7715 | −1.79839 | ||||||||
\(895\) | −0.184711 | −0.00617422 | ||||||||
\(896\) | −1.09804 | −0.0366831 | ||||||||
\(897\) | 47.2672 | 1.57821 | ||||||||
\(898\) | −32.7174 | −1.09179 | ||||||||
\(899\) | 0.847958 | 0.0282810 | ||||||||
\(900\) | −10.4477 | −0.348258 | ||||||||
\(901\) | 78.1264 | 2.60277 | ||||||||
\(902\) | −4.22227 | −0.140586 | ||||||||
\(903\) | 15.2579 | 0.507753 | ||||||||
\(904\) | −10.3617 | −0.344625 | ||||||||
\(905\) | 25.9659 | 0.863137 | ||||||||
\(906\) | 16.5805 | 0.550852 | ||||||||
\(907\) | −55.2478 | −1.83447 | −0.917236 | − | 0.398343i | \(-0.869585\pi\) | ||||
−0.917236 | + | 0.398343i | \(0.869585\pi\) | |||||||
\(908\) | 10.8934 | 0.361510 | ||||||||
\(909\) | −30.8995 | −1.02487 | ||||||||
\(910\) | −5.15405 | −0.170855 | ||||||||
\(911\) | −29.3886 | −0.973689 | −0.486844 | − | 0.873489i | \(-0.661852\pi\) | ||||
−0.486844 | + | 0.873489i | \(0.661852\pi\) | |||||||
\(912\) | −3.52701 | −0.116791 | ||||||||
\(913\) | 38.0589 | 1.25957 | ||||||||
\(914\) | 40.8658 | 1.35172 | ||||||||
\(915\) | −57.5081 | −1.90116 | ||||||||
\(916\) | −7.10403 | −0.234724 | ||||||||
\(917\) | 17.8818 | 0.590510 | ||||||||
\(918\) | 93.2134 | 3.07650 | ||||||||
\(919\) | 40.5393 | 1.33727 | 0.668635 | − | 0.743591i | \(-0.266879\pi\) | ||||
0.668635 | + | 0.743591i | \(0.266879\pi\) | |||||||
\(920\) | −11.2163 | −0.369790 | ||||||||
\(921\) | 14.7640 | 0.486492 | ||||||||
\(922\) | −7.24778 | −0.238693 | ||||||||
\(923\) | 18.2509 | 0.600736 | ||||||||
\(924\) | −12.4225 | −0.408671 | ||||||||
\(925\) | −14.8709 | −0.488951 | ||||||||
\(926\) | 26.8102 | 0.881037 | ||||||||
\(927\) | −64.8573 | −2.13019 | ||||||||
\(928\) | 1.05773 | 0.0347216 | ||||||||
\(929\) | −31.7618 | −1.04207 | −0.521036 | − | 0.853535i | \(-0.674454\pi\) | ||||
−0.521036 | + | 0.853535i | \(0.674454\pi\) | |||||||
\(930\) | −5.02554 | −0.164794 | ||||||||
\(931\) | 6.23103 | 0.204214 | ||||||||
\(932\) | 29.5080 | 0.966568 | ||||||||
\(933\) | −43.5393 | −1.42541 | ||||||||
\(934\) | 40.4222 | 1.32266 | ||||||||
\(935\) | −39.3876 | −1.28811 | ||||||||
\(936\) | 19.0501 | 0.622672 | ||||||||
\(937\) | 7.68717 | 0.251129 | 0.125564 | − | 0.992085i | \(-0.459926\pi\) | ||||
0.125564 | + | 0.992085i | \(0.459926\pi\) | |||||||
\(938\) | 7.71061 | 0.251760 | ||||||||
\(939\) | 59.9071 | 1.95499 | ||||||||
\(940\) | 4.00499 | 0.130628 | ||||||||
\(941\) | −40.2010 | −1.31051 | −0.655257 | − | 0.755406i | \(-0.727440\pi\) | ||||
−0.655257 | + | 0.755406i | \(0.727440\pi\) | |||||||
\(942\) | 27.8528 | 0.907492 | ||||||||
\(943\) | 7.18324 | 0.233918 | ||||||||
\(944\) | −4.64292 | −0.151114 | ||||||||
\(945\) | −32.7452 | −1.06520 | ||||||||
\(946\) | 14.6140 | 0.475143 | ||||||||
\(947\) | 4.60833 | 0.149751 | 0.0748753 | − | 0.997193i | \(-0.476144\pi\) | ||||
0.0748753 | + | 0.997193i | \(0.476144\pi\) | |||||||
\(948\) | −9.55500 | −0.310332 | ||||||||
\(949\) | 26.6311 | 0.864482 | ||||||||
\(950\) | −1.44837 | −0.0469913 | ||||||||
\(951\) | −15.8377 | −0.513572 | ||||||||
\(952\) | 6.56000 | 0.212611 | ||||||||
\(953\) | 16.6350 | 0.538860 | 0.269430 | − | 0.963020i | \(-0.413165\pi\) | ||||
0.269430 | + | 0.963020i | \(0.413165\pi\) | |||||||
\(954\) | 101.441 | 3.28429 | ||||||||
\(955\) | 12.6110 | 0.408084 | ||||||||
\(956\) | 4.21162 | 0.136214 | ||||||||
\(957\) | 11.9664 | 0.386819 | ||||||||
\(958\) | 42.7351 | 1.38071 | ||||||||
\(959\) | 1.66948 | 0.0539102 | ||||||||
\(960\) | −6.26877 | −0.202324 | ||||||||
\(961\) | −30.3573 | −0.979268 | ||||||||
\(962\) | 27.1151 | 0.874227 | ||||||||
\(963\) | 132.937 | 4.28384 | ||||||||
\(964\) | 19.4162 | 0.625355 | ||||||||
\(965\) | −34.6021 | −1.11388 | ||||||||
\(966\) | 21.1341 | 0.679979 | ||||||||
\(967\) | 57.5053 | 1.84924 | 0.924622 | − | 0.380885i | \(-0.124381\pi\) | ||||
0.924622 | + | 0.380885i | \(0.124381\pi\) | |||||||
\(968\) | −0.898254 | −0.0288710 | ||||||||
\(969\) | 21.0713 | 0.676908 | ||||||||
\(970\) | 3.90941 | 0.125524 | ||||||||
\(971\) | 2.47546 | 0.0794413 | 0.0397206 | − | 0.999211i | \(-0.487353\pi\) | ||||
0.0397206 | + | 0.999211i | \(0.487353\pi\) | |||||||
\(972\) | 44.7051 | 1.43392 | ||||||||
\(973\) | 21.6845 | 0.695174 | ||||||||
\(974\) | −29.2596 | −0.937537 | ||||||||
\(975\) | 10.8484 | 0.347426 | ||||||||
\(976\) | 9.17375 | 0.293645 | ||||||||
\(977\) | −55.9403 | −1.78969 | −0.894845 | − | 0.446377i | \(-0.852714\pi\) | ||||
−0.894845 | + | 0.446377i | \(0.852714\pi\) | |||||||
\(978\) | 22.2403 | 0.711166 | ||||||||
\(979\) | −10.7019 | −0.342033 | ||||||||
\(980\) | 11.0748 | 0.353770 | ||||||||
\(981\) | −136.843 | −4.36908 | ||||||||
\(982\) | 2.36499 | 0.0754698 | ||||||||
\(983\) | 5.66670 | 0.180740 | 0.0903698 | − | 0.995908i | \(-0.471195\pi\) | ||||
0.0903698 | + | 0.995908i | \(0.471195\pi\) | |||||||
\(984\) | 4.01470 | 0.127984 | ||||||||
\(985\) | 37.3171 | 1.18902 | ||||||||
\(986\) | −6.31913 | −0.201242 | ||||||||
\(987\) | −7.54633 | −0.240202 | ||||||||
\(988\) | 2.64091 | 0.0840187 | ||||||||
\(989\) | −24.8624 | −0.790580 | ||||||||
\(990\) | −51.1419 | −1.62540 | ||||||||
\(991\) | 17.9190 | 0.569216 | 0.284608 | − | 0.958644i | \(-0.408137\pi\) | ||||
0.284608 | + | 0.958644i | \(0.408137\pi\) | |||||||
\(992\) | 0.801680 | 0.0254534 | ||||||||
\(993\) | −64.9429 | −2.06090 | ||||||||
\(994\) | 8.16035 | 0.258831 | ||||||||
\(995\) | 15.8903 | 0.503758 | ||||||||
\(996\) | −36.1879 | −1.14666 | ||||||||
\(997\) | 30.1813 | 0.955852 | 0.477926 | − | 0.878400i | \(-0.341389\pi\) | ||||
0.477926 | + | 0.878400i | \(0.341389\pi\) | |||||||
\(998\) | −27.2837 | −0.863649 | ||||||||
\(999\) | 172.270 | 5.45040 |
(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 | 4006.2.a.g.1.40 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.g.1.40 | ✓ | 40 | 1.1 | even | 1 | trivial |