Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, 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("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.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: | \(32.0200112105\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-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 | ||||||||
\(3\) | −1.18460 | −0.683927 | −0.341963 | − | 0.939713i | \(-0.611092\pi\) | ||||
−0.341963 | + | 0.939713i | \(0.611092\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.18460 | −0.483609 | ||||||||
\(7\) | 4.68706 | 1.77154 | 0.885770 | − | 0.464124i | \(-0.153631\pi\) | ||||
0.885770 | + | 0.464124i | \(0.153631\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.59673 | −0.532244 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.20462 | 0.363208 | 0.181604 | − | 0.983372i | \(-0.441871\pi\) | ||||
0.181604 | + | 0.983372i | \(0.441871\pi\) | |||||||
\(12\) | −1.18460 | −0.341963 | ||||||||
\(13\) | 5.57551 | 1.54637 | 0.773185 | − | 0.634181i | \(-0.218663\pi\) | ||||
0.773185 | + | 0.634181i | \(0.218663\pi\) | |||||||
\(14\) | 4.68706 | 1.25267 | ||||||||
\(15\) | 1.18460 | 0.305861 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.07141 | 1.23000 | 0.614998 | − | 0.788528i | \(-0.289157\pi\) | ||||
0.614998 | + | 0.788528i | \(0.289157\pi\) | |||||||
\(18\) | −1.59673 | −0.376354 | ||||||||
\(19\) | 7.66277 | 1.75796 | 0.878980 | − | 0.476859i | \(-0.158225\pi\) | ||||
0.878980 | + | 0.476859i | \(0.158225\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −5.55227 | −1.21160 | ||||||||
\(22\) | 1.20462 | 0.256827 | ||||||||
\(23\) | −6.33980 | −1.32194 | −0.660970 | − | 0.750412i | \(-0.729855\pi\) | ||||
−0.660970 | + | 0.750412i | \(0.729855\pi\) | |||||||
\(24\) | −1.18460 | −0.241805 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.57551 | 1.09345 | ||||||||
\(27\) | 5.44527 | 1.04794 | ||||||||
\(28\) | 4.68706 | 0.885770 | ||||||||
\(29\) | −0.292065 | −0.0542351 | −0.0271176 | − | 0.999632i | \(-0.508633\pi\) | ||||
−0.0271176 | + | 0.999632i | \(0.508633\pi\) | |||||||
\(30\) | 1.18460 | 0.216277 | ||||||||
\(31\) | −8.91920 | −1.60194 | −0.800968 | − | 0.598708i | \(-0.795681\pi\) | ||||
−0.800968 | + | 0.598708i | \(0.795681\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.42699 | −0.248407 | ||||||||
\(34\) | 5.07141 | 0.869739 | ||||||||
\(35\) | −4.68706 | −0.792257 | ||||||||
\(36\) | −1.59673 | −0.266122 | ||||||||
\(37\) | −4.02531 | −0.661757 | −0.330879 | − | 0.943673i | \(-0.607345\pi\) | ||||
−0.330879 | + | 0.943673i | \(0.607345\pi\) | |||||||
\(38\) | 7.66277 | 1.24306 | ||||||||
\(39\) | −6.60473 | −1.05760 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −4.54836 | −0.710335 | −0.355168 | − | 0.934803i | \(-0.615576\pi\) | ||||
−0.355168 | + | 0.934803i | \(0.615576\pi\) | |||||||
\(42\) | −5.55227 | −0.856733 | ||||||||
\(43\) | 3.79335 | 0.578480 | 0.289240 | − | 0.957257i | \(-0.406597\pi\) | ||||
0.289240 | + | 0.957257i | \(0.406597\pi\) | |||||||
\(44\) | 1.20462 | 0.181604 | ||||||||
\(45\) | 1.59673 | 0.238027 | ||||||||
\(46\) | −6.33980 | −0.934753 | ||||||||
\(47\) | −6.89121 | −1.00519 | −0.502593 | − | 0.864523i | \(-0.667621\pi\) | ||||
−0.502593 | + | 0.864523i | \(0.667621\pi\) | |||||||
\(48\) | −1.18460 | −0.170982 | ||||||||
\(49\) | 14.9685 | 2.13836 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −6.00757 | −0.841228 | ||||||||
\(52\) | 5.57551 | 0.773185 | ||||||||
\(53\) | −2.85791 | −0.392565 | −0.196282 | − | 0.980547i | \(-0.562887\pi\) | ||||
−0.196282 | + | 0.980547i | \(0.562887\pi\) | |||||||
\(54\) | 5.44527 | 0.741007 | ||||||||
\(55\) | −1.20462 | −0.162431 | ||||||||
\(56\) | 4.68706 | 0.626334 | ||||||||
\(57\) | −9.07728 | −1.20232 | ||||||||
\(58\) | −0.292065 | −0.0383500 | ||||||||
\(59\) | 12.5998 | 1.64035 | 0.820175 | − | 0.572113i | \(-0.193876\pi\) | ||||
0.820175 | + | 0.572113i | \(0.193876\pi\) | |||||||
\(60\) | 1.18460 | 0.152931 | ||||||||
\(61\) | 8.87868 | 1.13680 | 0.568400 | − | 0.822753i | \(-0.307563\pi\) | ||||
0.568400 | + | 0.822753i | \(0.307563\pi\) | |||||||
\(62\) | −8.91920 | −1.13274 | ||||||||
\(63\) | −7.48398 | −0.942893 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.57551 | −0.691557 | ||||||||
\(66\) | −1.42699 | −0.175651 | ||||||||
\(67\) | −12.8489 | −1.56974 | −0.784872 | − | 0.619658i | \(-0.787271\pi\) | ||||
−0.784872 | + | 0.619658i | \(0.787271\pi\) | |||||||
\(68\) | 5.07141 | 0.614998 | ||||||||
\(69\) | 7.51010 | 0.904110 | ||||||||
\(70\) | −4.68706 | −0.560210 | ||||||||
\(71\) | 5.98862 | 0.710719 | 0.355359 | − | 0.934730i | \(-0.384358\pi\) | ||||
0.355359 | + | 0.934730i | \(0.384358\pi\) | |||||||
\(72\) | −1.59673 | −0.188177 | ||||||||
\(73\) | −16.0837 | −1.88245 | −0.941225 | − | 0.337780i | \(-0.890324\pi\) | ||||
−0.941225 | + | 0.337780i | \(0.890324\pi\) | |||||||
\(74\) | −4.02531 | −0.467933 | ||||||||
\(75\) | −1.18460 | −0.136785 | ||||||||
\(76\) | 7.66277 | 0.878980 | ||||||||
\(77\) | 5.64614 | 0.643438 | ||||||||
\(78\) | −6.60473 | −0.747838 | ||||||||
\(79\) | 14.3384 | 1.61320 | 0.806598 | − | 0.591100i | \(-0.201306\pi\) | ||||
0.806598 | + | 0.591100i | \(0.201306\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −1.66024 | −0.184471 | ||||||||
\(82\) | −4.54836 | −0.502283 | ||||||||
\(83\) | 1.14337 | 0.125501 | 0.0627505 | − | 0.998029i | \(-0.480013\pi\) | ||||
0.0627505 | + | 0.998029i | \(0.480013\pi\) | |||||||
\(84\) | −5.55227 | −0.605802 | ||||||||
\(85\) | −5.07141 | −0.550071 | ||||||||
\(86\) | 3.79335 | 0.409047 | ||||||||
\(87\) | 0.345979 | 0.0370928 | ||||||||
\(88\) | 1.20462 | 0.128413 | ||||||||
\(89\) | −13.0424 | −1.38250 | −0.691248 | − | 0.722618i | \(-0.742939\pi\) | ||||
−0.691248 | + | 0.722618i | \(0.742939\pi\) | |||||||
\(90\) | 1.59673 | 0.168310 | ||||||||
\(91\) | 26.1327 | 2.73946 | ||||||||
\(92\) | −6.33980 | −0.660970 | ||||||||
\(93\) | 10.5656 | 1.09561 | ||||||||
\(94\) | −6.89121 | −0.710774 | ||||||||
\(95\) | −7.66277 | −0.786183 | ||||||||
\(96\) | −1.18460 | −0.120902 | ||||||||
\(97\) | 16.9850 | 1.72456 | 0.862281 | − | 0.506430i | \(-0.169035\pi\) | ||||
0.862281 | + | 0.506430i | \(0.169035\pi\) | |||||||
\(98\) | 14.9685 | 1.51205 | ||||||||
\(99\) | −1.92346 | −0.193315 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 8.26350 | 0.822249 | 0.411124 | − | 0.911579i | \(-0.365136\pi\) | ||||
0.411124 | + | 0.911579i | \(0.365136\pi\) | |||||||
\(102\) | −6.00757 | −0.594838 | ||||||||
\(103\) | 3.12024 | 0.307447 | 0.153723 | − | 0.988114i | \(-0.450874\pi\) | ||||
0.153723 | + | 0.988114i | \(0.450874\pi\) | |||||||
\(104\) | 5.57551 | 0.546724 | ||||||||
\(105\) | 5.55227 | 0.541846 | ||||||||
\(106\) | −2.85791 | −0.277585 | ||||||||
\(107\) | −10.8774 | −1.05155 | −0.525777 | − | 0.850623i | \(-0.676225\pi\) | ||||
−0.525777 | + | 0.850623i | \(0.676225\pi\) | |||||||
\(108\) | 5.44527 | 0.523971 | ||||||||
\(109\) | −2.49420 | −0.238901 | −0.119450 | − | 0.992840i | \(-0.538113\pi\) | ||||
−0.119450 | + | 0.992840i | \(0.538113\pi\) | |||||||
\(110\) | −1.20462 | −0.114856 | ||||||||
\(111\) | 4.76837 | 0.452593 | ||||||||
\(112\) | 4.68706 | 0.442885 | ||||||||
\(113\) | 2.93612 | 0.276207 | 0.138103 | − | 0.990418i | \(-0.455899\pi\) | ||||
0.138103 | + | 0.990418i | \(0.455899\pi\) | |||||||
\(114\) | −9.07728 | −0.850165 | ||||||||
\(115\) | 6.33980 | 0.591189 | ||||||||
\(116\) | −0.292065 | −0.0271176 | ||||||||
\(117\) | −8.90261 | −0.823046 | ||||||||
\(118\) | 12.5998 | 1.15990 | ||||||||
\(119\) | 23.7700 | 2.17899 | ||||||||
\(120\) | 1.18460 | 0.108138 | ||||||||
\(121\) | −9.54888 | −0.868080 | ||||||||
\(122\) | 8.87868 | 0.803838 | ||||||||
\(123\) | 5.38797 | 0.485817 | ||||||||
\(124\) | −8.91920 | −0.800968 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −7.48398 | −0.666726 | ||||||||
\(127\) | 3.65155 | 0.324023 | 0.162011 | − | 0.986789i | \(-0.448202\pi\) | ||||
0.162011 | + | 0.986789i | \(0.448202\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −4.49358 | −0.395638 | ||||||||
\(130\) | −5.57551 | −0.489005 | ||||||||
\(131\) | 15.9192 | 1.39087 | 0.695435 | − | 0.718589i | \(-0.255212\pi\) | ||||
0.695435 | + | 0.718589i | \(0.255212\pi\) | |||||||
\(132\) | −1.42699 | −0.124204 | ||||||||
\(133\) | 35.9158 | 3.11430 | ||||||||
\(134\) | −12.8489 | −1.10998 | ||||||||
\(135\) | −5.44527 | −0.468654 | ||||||||
\(136\) | 5.07141 | 0.434870 | ||||||||
\(137\) | 1.83255 | 0.156565 | 0.0782827 | − | 0.996931i | \(-0.475056\pi\) | ||||
0.0782827 | + | 0.996931i | \(0.475056\pi\) | |||||||
\(138\) | 7.51010 | 0.639302 | ||||||||
\(139\) | −1.09285 | −0.0926946 | −0.0463473 | − | 0.998925i | \(-0.514758\pi\) | ||||
−0.0463473 | + | 0.998925i | \(0.514758\pi\) | |||||||
\(140\) | −4.68706 | −0.396129 | ||||||||
\(141\) | 8.16330 | 0.687474 | ||||||||
\(142\) | 5.98862 | 0.502554 | ||||||||
\(143\) | 6.71640 | 0.561653 | ||||||||
\(144\) | −1.59673 | −0.133061 | ||||||||
\(145\) | 0.292065 | 0.0242547 | ||||||||
\(146\) | −16.0837 | −1.33109 | ||||||||
\(147\) | −17.7316 | −1.46248 | ||||||||
\(148\) | −4.02531 | −0.330879 | ||||||||
\(149\) | −12.2217 | −1.00124 | −0.500621 | − | 0.865667i | \(-0.666895\pi\) | ||||
−0.500621 | + | 0.865667i | \(0.666895\pi\) | |||||||
\(150\) | −1.18460 | −0.0967218 | ||||||||
\(151\) | 3.85740 | 0.313911 | 0.156955 | − | 0.987606i | \(-0.449832\pi\) | ||||
0.156955 | + | 0.987606i | \(0.449832\pi\) | |||||||
\(152\) | 7.66277 | 0.621532 | ||||||||
\(153\) | −8.09769 | −0.654659 | ||||||||
\(154\) | 5.64614 | 0.454979 | ||||||||
\(155\) | 8.91920 | 0.716407 | ||||||||
\(156\) | −6.60473 | −0.528801 | ||||||||
\(157\) | 23.1416 | 1.84690 | 0.923449 | − | 0.383721i | \(-0.125357\pi\) | ||||
0.923449 | + | 0.383721i | \(0.125357\pi\) | |||||||
\(158\) | 14.3384 | 1.14070 | ||||||||
\(159\) | 3.38547 | 0.268485 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −29.7150 | −2.34187 | ||||||||
\(162\) | −1.66024 | −0.130441 | ||||||||
\(163\) | 11.2345 | 0.879952 | 0.439976 | − | 0.898010i | \(-0.354987\pi\) | ||||
0.439976 | + | 0.898010i | \(0.354987\pi\) | |||||||
\(164\) | −4.54836 | −0.355168 | ||||||||
\(165\) | 1.42699 | 0.111091 | ||||||||
\(166\) | 1.14337 | 0.0887427 | ||||||||
\(167\) | 17.0849 | 1.32207 | 0.661036 | − | 0.750354i | \(-0.270117\pi\) | ||||
0.661036 | + | 0.750354i | \(0.270117\pi\) | |||||||
\(168\) | −5.55227 | −0.428367 | ||||||||
\(169\) | 18.0863 | 1.39126 | ||||||||
\(170\) | −5.07141 | −0.388959 | ||||||||
\(171\) | −12.2354 | −0.935664 | ||||||||
\(172\) | 3.79335 | 0.289240 | ||||||||
\(173\) | 10.9413 | 0.831851 | 0.415925 | − | 0.909399i | \(-0.363458\pi\) | ||||
0.415925 | + | 0.909399i | \(0.363458\pi\) | |||||||
\(174\) | 0.345979 | 0.0262286 | ||||||||
\(175\) | 4.68706 | 0.354308 | ||||||||
\(176\) | 1.20462 | 0.0908020 | ||||||||
\(177\) | −14.9256 | −1.12188 | ||||||||
\(178\) | −13.0424 | −0.977572 | ||||||||
\(179\) | −17.3319 | −1.29545 | −0.647724 | − | 0.761875i | \(-0.724279\pi\) | ||||
−0.647724 | + | 0.761875i | \(0.724279\pi\) | |||||||
\(180\) | 1.59673 | 0.119013 | ||||||||
\(181\) | −23.4315 | −1.74165 | −0.870823 | − | 0.491597i | \(-0.836413\pi\) | ||||
−0.870823 | + | 0.491597i | \(0.836413\pi\) | |||||||
\(182\) | 26.1327 | 1.93709 | ||||||||
\(183\) | −10.5176 | −0.777487 | ||||||||
\(184\) | −6.33980 | −0.467376 | ||||||||
\(185\) | 4.02531 | 0.295947 | ||||||||
\(186\) | 10.5656 | 0.774710 | ||||||||
\(187\) | 6.10914 | 0.446745 | ||||||||
\(188\) | −6.89121 | −0.502593 | ||||||||
\(189\) | 25.5223 | 1.85647 | ||||||||
\(190\) | −7.66277 | −0.555916 | ||||||||
\(191\) | −1.46888 | −0.106285 | −0.0531423 | − | 0.998587i | \(-0.516924\pi\) | ||||
−0.0531423 | + | 0.998587i | \(0.516924\pi\) | |||||||
\(192\) | −1.18460 | −0.0854908 | ||||||||
\(193\) | −5.91331 | −0.425649 | −0.212825 | − | 0.977090i | \(-0.568266\pi\) | ||||
−0.212825 | + | 0.977090i | \(0.568266\pi\) | |||||||
\(194\) | 16.9850 | 1.21945 | ||||||||
\(195\) | 6.60473 | 0.472974 | ||||||||
\(196\) | 14.9685 | 1.06918 | ||||||||
\(197\) | −18.2523 | −1.30042 | −0.650211 | − | 0.759754i | \(-0.725319\pi\) | ||||
−0.650211 | + | 0.759754i | \(0.725319\pi\) | |||||||
\(198\) | −1.92346 | −0.136695 | ||||||||
\(199\) | 18.6917 | 1.32502 | 0.662511 | − | 0.749053i | \(-0.269491\pi\) | ||||
0.662511 | + | 0.749053i | \(0.269491\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 15.2208 | 1.07359 | ||||||||
\(202\) | 8.26350 | 0.581418 | ||||||||
\(203\) | −1.36893 | −0.0960797 | ||||||||
\(204\) | −6.00757 | −0.420614 | ||||||||
\(205\) | 4.54836 | 0.317672 | ||||||||
\(206\) | 3.12024 | 0.217398 | ||||||||
\(207\) | 10.1230 | 0.703595 | ||||||||
\(208\) | 5.57551 | 0.386592 | ||||||||
\(209\) | 9.23075 | 0.638505 | ||||||||
\(210\) | 5.55227 | 0.383143 | ||||||||
\(211\) | −0.232000 | −0.0159715 | −0.00798577 | − | 0.999968i | \(-0.502542\pi\) | ||||
−0.00798577 | + | 0.999968i | \(0.502542\pi\) | |||||||
\(212\) | −2.85791 | −0.196282 | ||||||||
\(213\) | −7.09410 | −0.486080 | ||||||||
\(214\) | −10.8774 | −0.743561 | ||||||||
\(215\) | −3.79335 | −0.258704 | ||||||||
\(216\) | 5.44527 | 0.370504 | ||||||||
\(217\) | −41.8048 | −2.83789 | ||||||||
\(218\) | −2.49420 | −0.168928 | ||||||||
\(219\) | 19.0526 | 1.28746 | ||||||||
\(220\) | −1.20462 | −0.0812157 | ||||||||
\(221\) | 28.2757 | 1.90203 | ||||||||
\(222\) | 4.76837 | 0.320032 | ||||||||
\(223\) | 21.6531 | 1.45000 | 0.724999 | − | 0.688750i | \(-0.241840\pi\) | ||||
0.724999 | + | 0.688750i | \(0.241840\pi\) | |||||||
\(224\) | 4.68706 | 0.313167 | ||||||||
\(225\) | −1.59673 | −0.106449 | ||||||||
\(226\) | 2.93612 | 0.195308 | ||||||||
\(227\) | −16.5630 | −1.09933 | −0.549663 | − | 0.835387i | \(-0.685244\pi\) | ||||
−0.549663 | + | 0.835387i | \(0.685244\pi\) | |||||||
\(228\) | −9.07728 | −0.601158 | ||||||||
\(229\) | −9.48459 | −0.626760 | −0.313380 | − | 0.949628i | \(-0.601461\pi\) | ||||
−0.313380 | + | 0.949628i | \(0.601461\pi\) | |||||||
\(230\) | 6.33980 | 0.418034 | ||||||||
\(231\) | −6.68839 | −0.440064 | ||||||||
\(232\) | −0.292065 | −0.0191750 | ||||||||
\(233\) | 22.7987 | 1.49359 | 0.746796 | − | 0.665053i | \(-0.231591\pi\) | ||||
0.746796 | + | 0.665053i | \(0.231591\pi\) | |||||||
\(234\) | −8.90261 | −0.581982 | ||||||||
\(235\) | 6.89121 | 0.449533 | ||||||||
\(236\) | 12.5998 | 0.820175 | ||||||||
\(237\) | −16.9852 | −1.10331 | ||||||||
\(238\) | 23.7700 | 1.54078 | ||||||||
\(239\) | −5.11597 | −0.330925 | −0.165462 | − | 0.986216i | \(-0.552912\pi\) | ||||
−0.165462 | + | 0.986216i | \(0.552912\pi\) | |||||||
\(240\) | 1.18460 | 0.0764653 | ||||||||
\(241\) | −19.7206 | −1.27032 | −0.635158 | − | 0.772382i | \(-0.719065\pi\) | ||||
−0.635158 | + | 0.772382i | \(0.719065\pi\) | |||||||
\(242\) | −9.54888 | −0.613825 | ||||||||
\(243\) | −14.3691 | −0.921778 | ||||||||
\(244\) | 8.87868 | 0.568400 | ||||||||
\(245\) | −14.9685 | −0.956302 | ||||||||
\(246\) | 5.38797 | 0.343525 | ||||||||
\(247\) | 42.7239 | 2.71845 | ||||||||
\(248\) | −8.91920 | −0.566370 | ||||||||
\(249\) | −1.35443 | −0.0858335 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −9.93945 | −0.627372 | −0.313686 | − | 0.949527i | \(-0.601564\pi\) | ||||
−0.313686 | + | 0.949527i | \(0.601564\pi\) | |||||||
\(252\) | −7.48398 | −0.471446 | ||||||||
\(253\) | −7.63708 | −0.480139 | ||||||||
\(254\) | 3.65155 | 0.229119 | ||||||||
\(255\) | 6.00757 | 0.376208 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.61811 | 0.225691 | 0.112846 | − | 0.993613i | \(-0.464003\pi\) | ||||
0.112846 | + | 0.993613i | \(0.464003\pi\) | |||||||
\(258\) | −4.49358 | −0.279758 | ||||||||
\(259\) | −18.8669 | −1.17233 | ||||||||
\(260\) | −5.57551 | −0.345779 | ||||||||
\(261\) | 0.466350 | 0.0288663 | ||||||||
\(262\) | 15.9192 | 0.983494 | ||||||||
\(263\) | −26.6289 | −1.64201 | −0.821003 | − | 0.570924i | \(-0.806585\pi\) | ||||
−0.821003 | + | 0.570924i | \(0.806585\pi\) | |||||||
\(264\) | −1.42699 | −0.0878253 | ||||||||
\(265\) | 2.85791 | 0.175560 | ||||||||
\(266\) | 35.9158 | 2.20214 | ||||||||
\(267\) | 15.4500 | 0.945525 | ||||||||
\(268\) | −12.8489 | −0.784872 | ||||||||
\(269\) | −18.7041 | −1.14041 | −0.570204 | − | 0.821503i | \(-0.693136\pi\) | ||||
−0.570204 | + | 0.821503i | \(0.693136\pi\) | |||||||
\(270\) | −5.44527 | −0.331389 | ||||||||
\(271\) | −26.8851 | −1.63316 | −0.816578 | − | 0.577235i | \(-0.804132\pi\) | ||||
−0.816578 | + | 0.577235i | \(0.804132\pi\) | |||||||
\(272\) | 5.07141 | 0.307499 | ||||||||
\(273\) | −30.9567 | −1.87359 | ||||||||
\(274\) | 1.83255 | 0.110708 | ||||||||
\(275\) | 1.20462 | 0.0726416 | ||||||||
\(276\) | 7.51010 | 0.452055 | ||||||||
\(277\) | 2.71702 | 0.163250 | 0.0816248 | − | 0.996663i | \(-0.473989\pi\) | ||||
0.0816248 | + | 0.996663i | \(0.473989\pi\) | |||||||
\(278\) | −1.09285 | −0.0655450 | ||||||||
\(279\) | 14.2416 | 0.852621 | ||||||||
\(280\) | −4.68706 | −0.280105 | ||||||||
\(281\) | 25.7351 | 1.53523 | 0.767614 | − | 0.640912i | \(-0.221444\pi\) | ||||
0.767614 | + | 0.640912i | \(0.221444\pi\) | |||||||
\(282\) | 8.16330 | 0.486118 | ||||||||
\(283\) | −9.30846 | −0.553330 | −0.276665 | − | 0.960966i | \(-0.589229\pi\) | ||||
−0.276665 | + | 0.960966i | \(0.589229\pi\) | |||||||
\(284\) | 5.98862 | 0.355359 | ||||||||
\(285\) | 9.07728 | 0.537692 | ||||||||
\(286\) | 6.71640 | 0.397149 | ||||||||
\(287\) | −21.3184 | −1.25839 | ||||||||
\(288\) | −1.59673 | −0.0940884 | ||||||||
\(289\) | 8.71917 | 0.512893 | ||||||||
\(290\) | 0.292065 | 0.0171506 | ||||||||
\(291\) | −20.1203 | −1.17947 | ||||||||
\(292\) | −16.0837 | −0.941225 | ||||||||
\(293\) | 17.9029 | 1.04590 | 0.522948 | − | 0.852365i | \(-0.324832\pi\) | ||||
0.522948 | + | 0.852365i | \(0.324832\pi\) | |||||||
\(294\) | −17.7316 | −1.03413 | ||||||||
\(295\) | −12.5998 | −0.733587 | ||||||||
\(296\) | −4.02531 | −0.233966 | ||||||||
\(297\) | 6.55950 | 0.380621 | ||||||||
\(298\) | −12.2217 | −0.707985 | ||||||||
\(299\) | −35.3476 | −2.04421 | ||||||||
\(300\) | −1.18460 | −0.0683927 | ||||||||
\(301\) | 17.7796 | 1.02480 | ||||||||
\(302\) | 3.85740 | 0.221968 | ||||||||
\(303\) | −9.78890 | −0.562358 | ||||||||
\(304\) | 7.66277 | 0.439490 | ||||||||
\(305\) | −8.87868 | −0.508392 | ||||||||
\(306\) | −8.09769 | −0.462914 | ||||||||
\(307\) | −3.00095 | −0.171273 | −0.0856366 | − | 0.996326i | \(-0.527292\pi\) | ||||
−0.0856366 | + | 0.996326i | \(0.527292\pi\) | |||||||
\(308\) | 5.64614 | 0.321719 | ||||||||
\(309\) | −3.69623 | −0.210271 | ||||||||
\(310\) | 8.91920 | 0.506576 | ||||||||
\(311\) | −21.9134 | −1.24260 | −0.621298 | − | 0.783575i | \(-0.713394\pi\) | ||||
−0.621298 | + | 0.783575i | \(0.713394\pi\) | |||||||
\(312\) | −6.60473 | −0.373919 | ||||||||
\(313\) | 29.3208 | 1.65731 | 0.828655 | − | 0.559759i | \(-0.189106\pi\) | ||||
0.828655 | + | 0.559759i | \(0.189106\pi\) | |||||||
\(314\) | 23.1416 | 1.30595 | ||||||||
\(315\) | 7.48398 | 0.421674 | ||||||||
\(316\) | 14.3384 | 0.806598 | ||||||||
\(317\) | −14.9234 | −0.838182 | −0.419091 | − | 0.907944i | \(-0.637651\pi\) | ||||
−0.419091 | + | 0.907944i | \(0.637651\pi\) | |||||||
\(318\) | 3.38547 | 0.189848 | ||||||||
\(319\) | −0.351829 | −0.0196986 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 12.8853 | 0.719185 | ||||||||
\(322\) | −29.7150 | −1.65595 | ||||||||
\(323\) | 38.8610 | 2.16228 | ||||||||
\(324\) | −1.66024 | −0.0922357 | ||||||||
\(325\) | 5.57551 | 0.309274 | ||||||||
\(326\) | 11.2345 | 0.622220 | ||||||||
\(327\) | 2.95462 | 0.163391 | ||||||||
\(328\) | −4.54836 | −0.251141 | ||||||||
\(329\) | −32.2995 | −1.78073 | ||||||||
\(330\) | 1.42699 | 0.0785533 | ||||||||
\(331\) | −15.9878 | −0.878769 | −0.439385 | − | 0.898299i | \(-0.644803\pi\) | ||||
−0.439385 | + | 0.898299i | \(0.644803\pi\) | |||||||
\(332\) | 1.14337 | 0.0627505 | ||||||||
\(333\) | 6.42735 | 0.352217 | ||||||||
\(334\) | 17.0849 | 0.934846 | ||||||||
\(335\) | 12.8489 | 0.702011 | ||||||||
\(336\) | −5.55227 | −0.302901 | ||||||||
\(337\) | −3.70069 | −0.201590 | −0.100795 | − | 0.994907i | \(-0.532139\pi\) | ||||
−0.100795 | + | 0.994907i | \(0.532139\pi\) | |||||||
\(338\) | 18.0863 | 0.983768 | ||||||||
\(339\) | −3.47811 | −0.188905 | ||||||||
\(340\) | −5.07141 | −0.275036 | ||||||||
\(341\) | −10.7443 | −0.581835 | ||||||||
\(342\) | −12.2354 | −0.661614 | ||||||||
\(343\) | 37.3488 | 2.01665 | ||||||||
\(344\) | 3.79335 | 0.204524 | ||||||||
\(345\) | −7.51010 | −0.404330 | ||||||||
\(346\) | 10.9413 | 0.588207 | ||||||||
\(347\) | −33.9042 | −1.82007 | −0.910036 | − | 0.414529i | \(-0.863946\pi\) | ||||
−0.910036 | + | 0.414529i | \(0.863946\pi\) | |||||||
\(348\) | 0.345979 | 0.0185464 | ||||||||
\(349\) | 6.93106 | 0.371011 | 0.185506 | − | 0.982643i | \(-0.440608\pi\) | ||||
0.185506 | + | 0.982643i | \(0.440608\pi\) | |||||||
\(350\) | 4.68706 | 0.250534 | ||||||||
\(351\) | 30.3602 | 1.62051 | ||||||||
\(352\) | 1.20462 | 0.0642067 | ||||||||
\(353\) | 15.2625 | 0.812340 | 0.406170 | − | 0.913798i | \(-0.366864\pi\) | ||||
0.406170 | + | 0.913798i | \(0.366864\pi\) | |||||||
\(354\) | −14.9256 | −0.793288 | ||||||||
\(355\) | −5.98862 | −0.317843 | ||||||||
\(356\) | −13.0424 | −0.691248 | ||||||||
\(357\) | −28.1578 | −1.49027 | ||||||||
\(358\) | −17.3319 | −0.916020 | ||||||||
\(359\) | 30.4397 | 1.60655 | 0.803274 | − | 0.595610i | \(-0.203090\pi\) | ||||
0.803274 | + | 0.595610i | \(0.203090\pi\) | |||||||
\(360\) | 1.59673 | 0.0841552 | ||||||||
\(361\) | 39.7180 | 2.09042 | ||||||||
\(362\) | −23.4315 | −1.23153 | ||||||||
\(363\) | 11.3116 | 0.593703 | ||||||||
\(364\) | 26.1327 | 1.36973 | ||||||||
\(365\) | 16.0837 | 0.841857 | ||||||||
\(366\) | −10.5176 | −0.549766 | ||||||||
\(367\) | −5.26652 | −0.274910 | −0.137455 | − | 0.990508i | \(-0.543892\pi\) | ||||
−0.137455 | + | 0.990508i | \(0.543892\pi\) | |||||||
\(368\) | −6.33980 | −0.330485 | ||||||||
\(369\) | 7.26253 | 0.378072 | ||||||||
\(370\) | 4.02531 | 0.209266 | ||||||||
\(371\) | −13.3952 | −0.695445 | ||||||||
\(372\) | 10.5656 | 0.547803 | ||||||||
\(373\) | 26.4681 | 1.37047 | 0.685233 | − | 0.728324i | \(-0.259700\pi\) | ||||
0.685233 | + | 0.728324i | \(0.259700\pi\) | |||||||
\(374\) | 6.10914 | 0.315896 | ||||||||
\(375\) | 1.18460 | 0.0611723 | ||||||||
\(376\) | −6.89121 | −0.355387 | ||||||||
\(377\) | −1.62841 | −0.0838675 | ||||||||
\(378\) | 25.5223 | 1.31272 | ||||||||
\(379\) | 22.3660 | 1.14886 | 0.574432 | − | 0.818552i | \(-0.305223\pi\) | ||||
0.574432 | + | 0.818552i | \(0.305223\pi\) | |||||||
\(380\) | −7.66277 | −0.393092 | ||||||||
\(381\) | −4.32561 | −0.221608 | ||||||||
\(382\) | −1.46888 | −0.0751545 | ||||||||
\(383\) | 14.5128 | 0.741571 | 0.370786 | − | 0.928718i | \(-0.379088\pi\) | ||||
0.370786 | + | 0.928718i | \(0.379088\pi\) | |||||||
\(384\) | −1.18460 | −0.0604511 | ||||||||
\(385\) | −5.64614 | −0.287754 | ||||||||
\(386\) | −5.91331 | −0.300979 | ||||||||
\(387\) | −6.05697 | −0.307893 | ||||||||
\(388\) | 16.9850 | 0.862281 | ||||||||
\(389\) | 7.81183 | 0.396076 | 0.198038 | − | 0.980194i | \(-0.436543\pi\) | ||||
0.198038 | + | 0.980194i | \(0.436543\pi\) | |||||||
\(390\) | 6.60473 | 0.334443 | ||||||||
\(391\) | −32.1517 | −1.62598 | ||||||||
\(392\) | 14.9685 | 0.756023 | ||||||||
\(393\) | −18.8579 | −0.951253 | ||||||||
\(394\) | −18.2523 | −0.919537 | ||||||||
\(395\) | −14.3384 | −0.721443 | ||||||||
\(396\) | −1.92346 | −0.0966577 | ||||||||
\(397\) | 0.904128 | 0.0453769 | 0.0226884 | − | 0.999743i | \(-0.492777\pi\) | ||||
0.0226884 | + | 0.999743i | \(0.492777\pi\) | |||||||
\(398\) | 18.6917 | 0.936931 | ||||||||
\(399\) | −42.5457 | −2.12995 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 15.2208 | 0.759142 | ||||||||
\(403\) | −49.7291 | −2.47718 | ||||||||
\(404\) | 8.26350 | 0.411124 | ||||||||
\(405\) | 1.66024 | 0.0824981 | ||||||||
\(406\) | −1.36893 | −0.0679386 | ||||||||
\(407\) | −4.84899 | −0.240355 | ||||||||
\(408\) | −6.00757 | −0.297419 | ||||||||
\(409\) | 17.0960 | 0.845344 | 0.422672 | − | 0.906283i | \(-0.361092\pi\) | ||||
0.422672 | + | 0.906283i | \(0.361092\pi\) | |||||||
\(410\) | 4.54836 | 0.224628 | ||||||||
\(411\) | −2.17083 | −0.107079 | ||||||||
\(412\) | 3.12024 | 0.153723 | ||||||||
\(413\) | 59.0558 | 2.90595 | ||||||||
\(414\) | 10.1230 | 0.497517 | ||||||||
\(415\) | −1.14337 | −0.0561258 | ||||||||
\(416\) | 5.57551 | 0.273362 | ||||||||
\(417\) | 1.29459 | 0.0633963 | ||||||||
\(418\) | 9.23075 | 0.451491 | ||||||||
\(419\) | 24.7515 | 1.20919 | 0.604595 | − | 0.796533i | \(-0.293335\pi\) | ||||
0.604595 | + | 0.796533i | \(0.293335\pi\) | |||||||
\(420\) | 5.55227 | 0.270923 | ||||||||
\(421\) | 13.3166 | 0.649011 | 0.324506 | − | 0.945884i | \(-0.394802\pi\) | ||||
0.324506 | + | 0.945884i | \(0.394802\pi\) | |||||||
\(422\) | −0.232000 | −0.0112936 | ||||||||
\(423\) | 11.0034 | 0.535005 | ||||||||
\(424\) | −2.85791 | −0.138793 | ||||||||
\(425\) | 5.07141 | 0.245999 | ||||||||
\(426\) | −7.09410 | −0.343710 | ||||||||
\(427\) | 41.6149 | 2.01389 | ||||||||
\(428\) | −10.8774 | −0.525777 | ||||||||
\(429\) | −7.95621 | −0.384130 | ||||||||
\(430\) | −3.79335 | −0.182932 | ||||||||
\(431\) | 12.8500 | 0.618963 | 0.309482 | − | 0.950905i | \(-0.399844\pi\) | ||||
0.309482 | + | 0.950905i | \(0.399844\pi\) | |||||||
\(432\) | 5.44527 | 0.261986 | ||||||||
\(433\) | 18.4111 | 0.884780 | 0.442390 | − | 0.896823i | \(-0.354131\pi\) | ||||
0.442390 | + | 0.896823i | \(0.354131\pi\) | |||||||
\(434\) | −41.8048 | −2.00669 | ||||||||
\(435\) | −0.345979 | −0.0165884 | ||||||||
\(436\) | −2.49420 | −0.119450 | ||||||||
\(437\) | −48.5804 | −2.32392 | ||||||||
\(438\) | 19.0526 | 0.910370 | ||||||||
\(439\) | −16.7436 | −0.799126 | −0.399563 | − | 0.916706i | \(-0.630838\pi\) | ||||
−0.399563 | + | 0.916706i | \(0.630838\pi\) | |||||||
\(440\) | −1.20462 | −0.0574282 | ||||||||
\(441\) | −23.9007 | −1.13813 | ||||||||
\(442\) | 28.2757 | 1.34494 | ||||||||
\(443\) | −1.70027 | −0.0807823 | −0.0403912 | − | 0.999184i | \(-0.512860\pi\) | ||||
−0.0403912 | + | 0.999184i | \(0.512860\pi\) | |||||||
\(444\) | 4.76837 | 0.226297 | ||||||||
\(445\) | 13.0424 | 0.618271 | ||||||||
\(446\) | 21.6531 | 1.02530 | ||||||||
\(447\) | 14.4778 | 0.684776 | ||||||||
\(448\) | 4.68706 | 0.221443 | ||||||||
\(449\) | −33.7537 | −1.59293 | −0.796467 | − | 0.604682i | \(-0.793300\pi\) | ||||
−0.796467 | + | 0.604682i | \(0.793300\pi\) | |||||||
\(450\) | −1.59673 | −0.0752707 | ||||||||
\(451\) | −5.47907 | −0.257999 | ||||||||
\(452\) | 2.93612 | 0.138103 | ||||||||
\(453\) | −4.56946 | −0.214692 | ||||||||
\(454\) | −16.5630 | −0.777341 | ||||||||
\(455\) | −26.1327 | −1.22512 | ||||||||
\(456\) | −9.07728 | −0.425083 | ||||||||
\(457\) | 20.4483 | 0.956533 | 0.478266 | − | 0.878215i | \(-0.341265\pi\) | ||||
0.478266 | + | 0.878215i | \(0.341265\pi\) | |||||||
\(458\) | −9.48459 | −0.443186 | ||||||||
\(459\) | 27.6152 | 1.28897 | ||||||||
\(460\) | 6.33980 | 0.295595 | ||||||||
\(461\) | 1.18525 | 0.0552025 | 0.0276013 | − | 0.999619i | \(-0.491213\pi\) | ||||
0.0276013 | + | 0.999619i | \(0.491213\pi\) | |||||||
\(462\) | −6.68839 | −0.311172 | ||||||||
\(463\) | −10.3889 | −0.482814 | −0.241407 | − | 0.970424i | \(-0.577609\pi\) | ||||
−0.241407 | + | 0.970424i | \(0.577609\pi\) | |||||||
\(464\) | −0.292065 | −0.0135588 | ||||||||
\(465\) | −10.5656 | −0.489970 | ||||||||
\(466\) | 22.7987 | 1.05613 | ||||||||
\(467\) | −13.1057 | −0.606459 | −0.303230 | − | 0.952918i | \(-0.598065\pi\) | ||||
−0.303230 | + | 0.952918i | \(0.598065\pi\) | |||||||
\(468\) | −8.90261 | −0.411523 | ||||||||
\(469\) | −60.2235 | −2.78086 | ||||||||
\(470\) | 6.89121 | 0.317868 | ||||||||
\(471\) | −27.4134 | −1.26314 | ||||||||
\(472\) | 12.5998 | 0.579951 | ||||||||
\(473\) | 4.56956 | 0.210109 | ||||||||
\(474\) | −16.9852 | −0.780156 | ||||||||
\(475\) | 7.66277 | 0.351592 | ||||||||
\(476\) | 23.7700 | 1.08949 | ||||||||
\(477\) | 4.56333 | 0.208940 | ||||||||
\(478\) | −5.11597 | −0.233999 | ||||||||
\(479\) | −8.41221 | −0.384363 | −0.192182 | − | 0.981359i | \(-0.561556\pi\) | ||||
−0.192182 | + | 0.981359i | \(0.561556\pi\) | |||||||
\(480\) | 1.18460 | 0.0540691 | ||||||||
\(481\) | −22.4432 | −1.02332 | ||||||||
\(482\) | −19.7206 | −0.898249 | ||||||||
\(483\) | 35.2003 | 1.60167 | ||||||||
\(484\) | −9.54888 | −0.434040 | ||||||||
\(485\) | −16.9850 | −0.771248 | ||||||||
\(486\) | −14.3691 | −0.651795 | ||||||||
\(487\) | 27.3511 | 1.23940 | 0.619698 | − | 0.784840i | \(-0.287255\pi\) | ||||
0.619698 | + | 0.784840i | \(0.287255\pi\) | |||||||
\(488\) | 8.87868 | 0.401919 | ||||||||
\(489\) | −13.3083 | −0.601822 | ||||||||
\(490\) | −14.9685 | −0.676208 | ||||||||
\(491\) | −12.8040 | −0.577835 | −0.288918 | − | 0.957354i | \(-0.593295\pi\) | ||||
−0.288918 | + | 0.957354i | \(0.593295\pi\) | |||||||
\(492\) | 5.38797 | 0.242909 | ||||||||
\(493\) | −1.48118 | −0.0667090 | ||||||||
\(494\) | 42.7239 | 1.92224 | ||||||||
\(495\) | 1.92346 | 0.0864533 | ||||||||
\(496\) | −8.91920 | −0.400484 | ||||||||
\(497\) | 28.0690 | 1.25907 | ||||||||
\(498\) | −1.35443 | −0.0606935 | ||||||||
\(499\) | −30.6213 | −1.37080 | −0.685398 | − | 0.728168i | \(-0.740372\pi\) | ||||
−0.685398 | + | 0.728168i | \(0.740372\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −20.2387 | −0.904200 | ||||||||
\(502\) | −9.93945 | −0.443619 | ||||||||
\(503\) | 0.215284 | 0.00959906 | 0.00479953 | − | 0.999988i | \(-0.498472\pi\) | ||||
0.00479953 | + | 0.999988i | \(0.498472\pi\) | |||||||
\(504\) | −7.48398 | −0.333363 | ||||||||
\(505\) | −8.26350 | −0.367721 | ||||||||
\(506\) | −7.63708 | −0.339509 | ||||||||
\(507\) | −21.4250 | −0.951518 | ||||||||
\(508\) | 3.65155 | 0.162011 | ||||||||
\(509\) | −10.4650 | −0.463853 | −0.231926 | − | 0.972733i | \(-0.574503\pi\) | ||||
−0.231926 | + | 0.972733i | \(0.574503\pi\) | |||||||
\(510\) | 6.00757 | 0.266020 | ||||||||
\(511\) | −75.3850 | −3.33484 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 41.7258 | 1.84224 | ||||||||
\(514\) | 3.61811 | 0.159588 | ||||||||
\(515\) | −3.12024 | −0.137494 | ||||||||
\(516\) | −4.49358 | −0.197819 | ||||||||
\(517\) | −8.30132 | −0.365092 | ||||||||
\(518\) | −18.8669 | −0.828962 | ||||||||
\(519\) | −12.9610 | −0.568925 | ||||||||
\(520\) | −5.57551 | −0.244502 | ||||||||
\(521\) | −25.7634 | −1.12871 | −0.564357 | − | 0.825531i | \(-0.690876\pi\) | ||||
−0.564357 | + | 0.825531i | \(0.690876\pi\) | |||||||
\(522\) | 0.466350 | 0.0204116 | ||||||||
\(523\) | −10.5026 | −0.459245 | −0.229622 | − | 0.973280i | \(-0.573749\pi\) | ||||
−0.229622 | + | 0.973280i | \(0.573749\pi\) | |||||||
\(524\) | 15.9192 | 0.695435 | ||||||||
\(525\) | −5.55227 | −0.242321 | ||||||||
\(526\) | −26.6289 | −1.16107 | ||||||||
\(527\) | −45.2329 | −1.97038 | ||||||||
\(528\) | −1.42699 | −0.0621019 | ||||||||
\(529\) | 17.1931 | 0.747525 | ||||||||
\(530\) | 2.85791 | 0.124140 | ||||||||
\(531\) | −20.1185 | −0.873067 | ||||||||
\(532\) | 35.9158 | 1.55715 | ||||||||
\(533\) | −25.3595 | −1.09844 | ||||||||
\(534\) | 15.4500 | 0.668587 | ||||||||
\(535\) | 10.8774 | 0.470269 | ||||||||
\(536\) | −12.8489 | −0.554988 | ||||||||
\(537\) | 20.5313 | 0.885991 | ||||||||
\(538\) | −18.7041 | −0.806390 | ||||||||
\(539\) | 18.0314 | 0.776668 | ||||||||
\(540\) | −5.44527 | −0.234327 | ||||||||
\(541\) | 6.91127 | 0.297139 | 0.148569 | − | 0.988902i | \(-0.452533\pi\) | ||||
0.148569 | + | 0.988902i | \(0.452533\pi\) | |||||||
\(542\) | −26.8851 | −1.15482 | ||||||||
\(543\) | 27.7568 | 1.19116 | ||||||||
\(544\) | 5.07141 | 0.217435 | ||||||||
\(545\) | 2.49420 | 0.106840 | ||||||||
\(546\) | −30.9567 | −1.32483 | ||||||||
\(547\) | −29.1689 | −1.24717 | −0.623587 | − | 0.781754i | \(-0.714325\pi\) | ||||
−0.623587 | + | 0.781754i | \(0.714325\pi\) | |||||||
\(548\) | 1.83255 | 0.0782827 | ||||||||
\(549\) | −14.1769 | −0.605055 | ||||||||
\(550\) | 1.20462 | 0.0513653 | ||||||||
\(551\) | −2.23803 | −0.0953431 | ||||||||
\(552\) | 7.51010 | 0.319651 | ||||||||
\(553\) | 67.2049 | 2.85784 | ||||||||
\(554\) | 2.71702 | 0.115435 | ||||||||
\(555\) | −4.76837 | −0.202406 | ||||||||
\(556\) | −1.09285 | −0.0463473 | ||||||||
\(557\) | 34.2643 | 1.45182 | 0.725912 | − | 0.687788i | \(-0.241418\pi\) | ||||
0.725912 | + | 0.687788i | \(0.241418\pi\) | |||||||
\(558\) | 14.2416 | 0.602894 | ||||||||
\(559\) | 21.1499 | 0.894544 | ||||||||
\(560\) | −4.68706 | −0.198064 | ||||||||
\(561\) | −7.23686 | −0.305540 | ||||||||
\(562\) | 25.7351 | 1.08557 | ||||||||
\(563\) | −29.8364 | −1.25745 | −0.628727 | − | 0.777626i | \(-0.716424\pi\) | ||||
−0.628727 | + | 0.777626i | \(0.716424\pi\) | |||||||
\(564\) | 8.16330 | 0.343737 | ||||||||
\(565\) | −2.93612 | −0.123523 | ||||||||
\(566\) | −9.30846 | −0.391264 | ||||||||
\(567\) | −7.78165 | −0.326799 | ||||||||
\(568\) | 5.98862 | 0.251277 | ||||||||
\(569\) | 6.27332 | 0.262991 | 0.131496 | − | 0.991317i | \(-0.458022\pi\) | ||||
0.131496 | + | 0.991317i | \(0.458022\pi\) | |||||||
\(570\) | 9.07728 | 0.380205 | ||||||||
\(571\) | −2.18579 | −0.0914723 | −0.0457362 | − | 0.998954i | \(-0.514563\pi\) | ||||
−0.0457362 | + | 0.998954i | \(0.514563\pi\) | |||||||
\(572\) | 6.71640 | 0.280827 | ||||||||
\(573\) | 1.74003 | 0.0726908 | ||||||||
\(574\) | −21.3184 | −0.889815 | ||||||||
\(575\) | −6.33980 | −0.264388 | ||||||||
\(576\) | −1.59673 | −0.0665306 | ||||||||
\(577\) | −46.4721 | −1.93466 | −0.967330 | − | 0.253519i | \(-0.918412\pi\) | ||||
−0.967330 | + | 0.253519i | \(0.918412\pi\) | |||||||
\(578\) | 8.71917 | 0.362670 | ||||||||
\(579\) | 7.00488 | 0.291113 | ||||||||
\(580\) | 0.292065 | 0.0121273 | ||||||||
\(581\) | 5.35904 | 0.222330 | ||||||||
\(582\) | −20.1203 | −0.834014 | ||||||||
\(583\) | −3.44271 | −0.142583 | ||||||||
\(584\) | −16.0837 | −0.665547 | ||||||||
\(585\) | 8.90261 | 0.368078 | ||||||||
\(586\) | 17.9029 | 0.739560 | ||||||||
\(587\) | −4.77144 | −0.196939 | −0.0984693 | − | 0.995140i | \(-0.531395\pi\) | ||||
−0.0984693 | + | 0.995140i | \(0.531395\pi\) | |||||||
\(588\) | −17.7316 | −0.731240 | ||||||||
\(589\) | −68.3457 | −2.81614 | ||||||||
\(590\) | −12.5998 | −0.518724 | ||||||||
\(591\) | 21.6216 | 0.889393 | ||||||||
\(592\) | −4.02531 | −0.165439 | ||||||||
\(593\) | −37.2715 | −1.53056 | −0.765278 | − | 0.643700i | \(-0.777398\pi\) | ||||
−0.765278 | + | 0.643700i | \(0.777398\pi\) | |||||||
\(594\) | 6.55950 | 0.269140 | ||||||||
\(595\) | −23.7700 | −0.974474 | ||||||||
\(596\) | −12.2217 | −0.500621 | ||||||||
\(597\) | −22.1421 | −0.906217 | ||||||||
\(598\) | −35.3476 | −1.44547 | ||||||||
\(599\) | 13.3274 | 0.544544 | 0.272272 | − | 0.962220i | \(-0.412225\pi\) | ||||
0.272272 | + | 0.962220i | \(0.412225\pi\) | |||||||
\(600\) | −1.18460 | −0.0483609 | ||||||||
\(601\) | 4.28792 | 0.174908 | 0.0874540 | − | 0.996169i | \(-0.472127\pi\) | ||||
0.0874540 | + | 0.996169i | \(0.472127\pi\) | |||||||
\(602\) | 17.7796 | 0.724644 | ||||||||
\(603\) | 20.5163 | 0.835487 | ||||||||
\(604\) | 3.85740 | 0.156955 | ||||||||
\(605\) | 9.54888 | 0.388217 | ||||||||
\(606\) | −9.78890 | −0.397647 | ||||||||
\(607\) | −14.5854 | −0.592003 | −0.296001 | − | 0.955188i | \(-0.595653\pi\) | ||||
−0.296001 | + | 0.955188i | \(0.595653\pi\) | |||||||
\(608\) | 7.66277 | 0.310766 | ||||||||
\(609\) | 1.62162 | 0.0657115 | ||||||||
\(610\) | −8.87868 | −0.359487 | ||||||||
\(611\) | −38.4221 | −1.55439 | ||||||||
\(612\) | −8.09769 | −0.327330 | ||||||||
\(613\) | −9.89125 | −0.399504 | −0.199752 | − | 0.979847i | \(-0.564014\pi\) | ||||
−0.199752 | + | 0.979847i | \(0.564014\pi\) | |||||||
\(614\) | −3.00095 | −0.121108 | ||||||||
\(615\) | −5.38797 | −0.217264 | ||||||||
\(616\) | 5.64614 | 0.227490 | ||||||||
\(617\) | −13.1860 | −0.530846 | −0.265423 | − | 0.964132i | \(-0.585512\pi\) | ||||
−0.265423 | + | 0.964132i | \(0.585512\pi\) | |||||||
\(618\) | −3.69623 | −0.148684 | ||||||||
\(619\) | −27.7389 | −1.11492 | −0.557460 | − | 0.830204i | \(-0.688224\pi\) | ||||
−0.557460 | + | 0.830204i | \(0.688224\pi\) | |||||||
\(620\) | 8.91920 | 0.358204 | ||||||||
\(621\) | −34.5219 | −1.38532 | ||||||||
\(622\) | −21.9134 | −0.878648 | ||||||||
\(623\) | −61.1306 | −2.44915 | ||||||||
\(624\) | −6.60473 | −0.264401 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 29.3208 | 1.17190 | ||||||||
\(627\) | −10.9347 | −0.436690 | ||||||||
\(628\) | 23.1416 | 0.923449 | ||||||||
\(629\) | −20.4140 | −0.813959 | ||||||||
\(630\) | 7.48398 | 0.298169 | ||||||||
\(631\) | 2.70915 | 0.107850 | 0.0539248 | − | 0.998545i | \(-0.482827\pi\) | ||||
0.0539248 | + | 0.998545i | \(0.482827\pi\) | |||||||
\(632\) | 14.3384 | 0.570351 | ||||||||
\(633\) | 0.274826 | 0.0109234 | ||||||||
\(634\) | −14.9234 | −0.592684 | ||||||||
\(635\) | −3.65155 | −0.144907 | ||||||||
\(636\) | 3.38547 | 0.134243 | ||||||||
\(637\) | 83.4571 | 3.30669 | ||||||||
\(638\) | −0.351829 | −0.0139290 | ||||||||
\(639\) | −9.56224 | −0.378276 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −2.54312 | −0.100447 | −0.0502237 | − | 0.998738i | \(-0.515993\pi\) | ||||
−0.0502237 | + | 0.998738i | \(0.515993\pi\) | |||||||
\(642\) | 12.8853 | 0.508541 | ||||||||
\(643\) | −24.8187 | −0.978752 | −0.489376 | − | 0.872073i | \(-0.662775\pi\) | ||||
−0.489376 | + | 0.872073i | \(0.662775\pi\) | |||||||
\(644\) | −29.7150 | −1.17094 | ||||||||
\(645\) | 4.49358 | 0.176935 | ||||||||
\(646\) | 38.8610 | 1.52897 | ||||||||
\(647\) | 0.270701 | 0.0106423 | 0.00532117 | − | 0.999986i | \(-0.498306\pi\) | ||||
0.00532117 | + | 0.999986i | \(0.498306\pi\) | |||||||
\(648\) | −1.66024 | −0.0652205 | ||||||||
\(649\) | 15.1780 | 0.595788 | ||||||||
\(650\) | 5.57551 | 0.218690 | ||||||||
\(651\) | 49.5218 | 1.94091 | ||||||||
\(652\) | 11.2345 | 0.439976 | ||||||||
\(653\) | −11.1525 | −0.436429 | −0.218215 | − | 0.975901i | \(-0.570023\pi\) | ||||
−0.218215 | + | 0.975901i | \(0.570023\pi\) | |||||||
\(654\) | 2.95462 | 0.115535 | ||||||||
\(655\) | −15.9192 | −0.622016 | ||||||||
\(656\) | −4.54836 | −0.177584 | ||||||||
\(657\) | 25.6813 | 1.00192 | ||||||||
\(658\) | −32.2995 | −1.25917 | ||||||||
\(659\) | 16.5271 | 0.643805 | 0.321903 | − | 0.946773i | \(-0.395678\pi\) | ||||
0.321903 | + | 0.946773i | \(0.395678\pi\) | |||||||
\(660\) | 1.42699 | 0.0555456 | ||||||||
\(661\) | −2.99653 | −0.116551 | −0.0582757 | − | 0.998301i | \(-0.518560\pi\) | ||||
−0.0582757 | + | 0.998301i | \(0.518560\pi\) | |||||||
\(662\) | −15.9878 | −0.621384 | ||||||||
\(663\) | −33.4953 | −1.30085 | ||||||||
\(664\) | 1.14337 | 0.0443713 | ||||||||
\(665\) | −35.9158 | −1.39276 | ||||||||
\(666\) | 6.42735 | 0.249055 | ||||||||
\(667\) | 1.85163 | 0.0716955 | ||||||||
\(668\) | 17.0849 | 0.661036 | ||||||||
\(669\) | −25.6502 | −0.991693 | ||||||||
\(670\) | 12.8489 | 0.496396 | ||||||||
\(671\) | 10.6955 | 0.412894 | ||||||||
\(672\) | −5.55227 | −0.214183 | ||||||||
\(673\) | −2.88930 | −0.111374 | −0.0556872 | − | 0.998448i | \(-0.517735\pi\) | ||||
−0.0556872 | + | 0.998448i | \(0.517735\pi\) | |||||||
\(674\) | −3.70069 | −0.142545 | ||||||||
\(675\) | 5.44527 | 0.209589 | ||||||||
\(676\) | 18.0863 | 0.695629 | ||||||||
\(677\) | −7.70902 | −0.296282 | −0.148141 | − | 0.988966i | \(-0.547329\pi\) | ||||
−0.148141 | + | 0.988966i | \(0.547329\pi\) | |||||||
\(678\) | −3.47811 | −0.133576 | ||||||||
\(679\) | 79.6095 | 3.05513 | ||||||||
\(680\) | −5.07141 | −0.194480 | ||||||||
\(681\) | 19.6205 | 0.751858 | ||||||||
\(682\) | −10.7443 | −0.411420 | ||||||||
\(683\) | 7.21850 | 0.276208 | 0.138104 | − | 0.990418i | \(-0.455899\pi\) | ||||
0.138104 | + | 0.990418i | \(0.455899\pi\) | |||||||
\(684\) | −12.2354 | −0.467832 | ||||||||
\(685\) | −1.83255 | −0.0700182 | ||||||||
\(686\) | 37.3488 | 1.42598 | ||||||||
\(687\) | 11.2354 | 0.428658 | ||||||||
\(688\) | 3.79335 | 0.144620 | ||||||||
\(689\) | −15.9343 | −0.607050 | ||||||||
\(690\) | −7.51010 | −0.285905 | ||||||||
\(691\) | 11.8567 | 0.451050 | 0.225525 | − | 0.974237i | \(-0.427590\pi\) | ||||
0.225525 | + | 0.974237i | \(0.427590\pi\) | |||||||
\(692\) | 10.9413 | 0.415925 | ||||||||
\(693\) | −9.01538 | −0.342466 | ||||||||
\(694\) | −33.9042 | −1.28699 | ||||||||
\(695\) | 1.09285 | 0.0414543 | ||||||||
\(696\) | 0.345979 | 0.0131143 | ||||||||
\(697\) | −23.0666 | −0.873710 | ||||||||
\(698\) | 6.93106 | 0.262345 | ||||||||
\(699\) | −27.0072 | −1.02151 | ||||||||
\(700\) | 4.68706 | 0.177154 | ||||||||
\(701\) | −41.8618 | −1.58110 | −0.790549 | − | 0.612399i | \(-0.790205\pi\) | ||||
−0.790549 | + | 0.612399i | \(0.790205\pi\) | |||||||
\(702\) | 30.3602 | 1.14587 | ||||||||
\(703\) | −30.8450 | −1.16334 | ||||||||
\(704\) | 1.20462 | 0.0454010 | ||||||||
\(705\) | −8.16330 | −0.307448 | ||||||||
\(706\) | 15.2625 | 0.574411 | ||||||||
\(707\) | 38.7315 | 1.45665 | ||||||||
\(708\) | −14.9256 | −0.560939 | ||||||||
\(709\) | −3.07129 | −0.115345 | −0.0576724 | − | 0.998336i | \(-0.518368\pi\) | ||||
−0.0576724 | + | 0.998336i | \(0.518368\pi\) | |||||||
\(710\) | −5.98862 | −0.224749 | ||||||||
\(711\) | −22.8946 | −0.858615 | ||||||||
\(712\) | −13.0424 | −0.488786 | ||||||||
\(713\) | 56.5459 | 2.11766 | ||||||||
\(714\) | −28.1578 | −1.05378 | ||||||||
\(715\) | −6.71640 | −0.251179 | ||||||||
\(716\) | −17.3319 | −0.647724 | ||||||||
\(717\) | 6.06036 | 0.226328 | ||||||||
\(718\) | 30.4397 | 1.13600 | ||||||||
\(719\) | 27.6940 | 1.03281 | 0.516407 | − | 0.856343i | \(-0.327269\pi\) | ||||
0.516407 | + | 0.856343i | \(0.327269\pi\) | |||||||
\(720\) | 1.59673 | 0.0595067 | ||||||||
\(721\) | 14.6248 | 0.544654 | ||||||||
\(722\) | 39.7180 | 1.47815 | ||||||||
\(723\) | 23.3609 | 0.868803 | ||||||||
\(724\) | −23.4315 | −0.870823 | ||||||||
\(725\) | −0.292065 | −0.0108470 | ||||||||
\(726\) | 11.3116 | 0.419811 | ||||||||
\(727\) | −31.2593 | −1.15934 | −0.579671 | − | 0.814851i | \(-0.696819\pi\) | ||||
−0.579671 | + | 0.814851i | \(0.696819\pi\) | |||||||
\(728\) | 26.1327 | 0.968544 | ||||||||
\(729\) | 22.0023 | 0.814900 | ||||||||
\(730\) | 16.0837 | 0.595283 | ||||||||
\(731\) | 19.2376 | 0.711529 | ||||||||
\(732\) | −10.5176 | −0.388744 | ||||||||
\(733\) | 16.7522 | 0.618757 | 0.309379 | − | 0.950939i | \(-0.399879\pi\) | ||||
0.309379 | + | 0.950939i | \(0.399879\pi\) | |||||||
\(734\) | −5.26652 | −0.194391 | ||||||||
\(735\) | 17.7316 | 0.654041 | ||||||||
\(736\) | −6.33980 | −0.233688 | ||||||||
\(737\) | −15.4781 | −0.570143 | ||||||||
\(738\) | 7.26253 | 0.267337 | ||||||||
\(739\) | −0.974682 | −0.0358542 | −0.0179271 | − | 0.999839i | \(-0.505707\pi\) | ||||
−0.0179271 | + | 0.999839i | \(0.505707\pi\) | |||||||
\(740\) | 4.02531 | 0.147973 | ||||||||
\(741\) | −50.6105 | −1.85922 | ||||||||
\(742\) | −13.3952 | −0.491754 | ||||||||
\(743\) | −25.1796 | −0.923751 | −0.461876 | − | 0.886945i | \(-0.652823\pi\) | ||||
−0.461876 | + | 0.886945i | \(0.652823\pi\) | |||||||
\(744\) | 10.5656 | 0.387355 | ||||||||
\(745\) | 12.2217 | 0.447769 | ||||||||
\(746\) | 26.4681 | 0.969066 | ||||||||
\(747\) | −1.82566 | −0.0667973 | ||||||||
\(748\) | 6.10914 | 0.223372 | ||||||||
\(749\) | −50.9828 | −1.86287 | ||||||||
\(750\) | 1.18460 | 0.0432553 | ||||||||
\(751\) | 24.3111 | 0.887125 | 0.443563 | − | 0.896243i | \(-0.353714\pi\) | ||||
0.443563 | + | 0.896243i | \(0.353714\pi\) | |||||||
\(752\) | −6.89121 | −0.251297 | ||||||||
\(753\) | 11.7742 | 0.429077 | ||||||||
\(754\) | −1.62841 | −0.0593033 | ||||||||
\(755\) | −3.85740 | −0.140385 | ||||||||
\(756\) | 25.5223 | 0.928237 | ||||||||
\(757\) | 18.8631 | 0.685590 | 0.342795 | − | 0.939410i | \(-0.388626\pi\) | ||||
0.342795 | + | 0.939410i | \(0.388626\pi\) | |||||||
\(758\) | 22.3660 | 0.812369 | ||||||||
\(759\) | 9.04685 | 0.328380 | ||||||||
\(760\) | −7.66277 | −0.277958 | ||||||||
\(761\) | 21.2166 | 0.769102 | 0.384551 | − | 0.923104i | \(-0.374356\pi\) | ||||
0.384551 | + | 0.923104i | \(0.374356\pi\) | |||||||
\(762\) | −4.32561 | −0.156700 | ||||||||
\(763\) | −11.6904 | −0.423223 | ||||||||
\(764\) | −1.46888 | −0.0531423 | ||||||||
\(765\) | 8.09769 | 0.292772 | ||||||||
\(766\) | 14.5128 | 0.524370 | ||||||||
\(767\) | 70.2502 | 2.53659 | ||||||||
\(768\) | −1.18460 | −0.0427454 | ||||||||
\(769\) | −1.90537 | −0.0687093 | −0.0343546 | − | 0.999410i | \(-0.510938\pi\) | ||||
−0.0343546 | + | 0.999410i | \(0.510938\pi\) | |||||||
\(770\) | −5.64614 | −0.203473 | ||||||||
\(771\) | −4.28600 | −0.154356 | ||||||||
\(772\) | −5.91331 | −0.212825 | ||||||||
\(773\) | −14.7132 | −0.529197 | −0.264598 | − | 0.964359i | \(-0.585239\pi\) | ||||
−0.264598 | + | 0.964359i | \(0.585239\pi\) | |||||||
\(774\) | −6.05697 | −0.217713 | ||||||||
\(775\) | −8.91920 | −0.320387 | ||||||||
\(776\) | 16.9850 | 0.609725 | ||||||||
\(777\) | 22.3496 | 0.801787 | ||||||||
\(778\) | 7.81183 | 0.280068 | ||||||||
\(779\) | −34.8531 | −1.24874 | ||||||||
\(780\) | 6.60473 | 0.236487 | ||||||||
\(781\) | 7.21404 | 0.258139 | ||||||||
\(782\) | −32.1517 | −1.14974 | ||||||||
\(783\) | −1.59037 | −0.0568353 | ||||||||
\(784\) | 14.9685 | 0.534589 | ||||||||
\(785\) | −23.1416 | −0.825958 | ||||||||
\(786\) | −18.8579 | −0.672638 | ||||||||
\(787\) | −1.05492 | −0.0376038 | −0.0188019 | − | 0.999823i | \(-0.505985\pi\) | ||||
−0.0188019 | + | 0.999823i | \(0.505985\pi\) | |||||||
\(788\) | −18.2523 | −0.650211 | ||||||||
\(789\) | 31.5444 | 1.12301 | ||||||||
\(790\) | −14.3384 | −0.510137 | ||||||||
\(791\) | 13.7617 | 0.489311 | ||||||||
\(792\) | −1.92346 | −0.0683473 | ||||||||
\(793\) | 49.5032 | 1.75791 | ||||||||
\(794\) | 0.904128 | 0.0320863 | ||||||||
\(795\) | −3.38547 | −0.120070 | ||||||||
\(796\) | 18.6917 | 0.662511 | ||||||||
\(797\) | 35.6101 | 1.26137 | 0.630687 | − | 0.776037i | \(-0.282773\pi\) | ||||
0.630687 | + | 0.776037i | \(0.282773\pi\) | |||||||
\(798\) | −42.5457 | −1.50610 | ||||||||
\(799\) | −34.9482 | −1.23638 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 20.8253 | 0.735825 | ||||||||
\(802\) | −1.00000 | −0.0353112 | ||||||||
\(803\) | −19.3748 | −0.683721 | ||||||||
\(804\) | 15.2208 | 0.536795 | ||||||||
\(805\) | 29.7150 | 1.04732 | ||||||||
\(806\) | −49.7291 | −1.75163 | ||||||||
\(807\) | 22.1568 | 0.779955 | ||||||||
\(808\) | 8.26350 | 0.290709 | ||||||||
\(809\) | 1.01998 | 0.0358607 | 0.0179304 | − | 0.999839i | \(-0.494292\pi\) | ||||
0.0179304 | + | 0.999839i | \(0.494292\pi\) | |||||||
\(810\) | 1.66024 | 0.0583350 | ||||||||
\(811\) | 5.54965 | 0.194874 | 0.0974372 | − | 0.995242i | \(-0.468935\pi\) | ||||
0.0974372 | + | 0.995242i | \(0.468935\pi\) | |||||||
\(812\) | −1.36893 | −0.0480399 | ||||||||
\(813\) | 31.8480 | 1.11696 | ||||||||
\(814\) | −4.84899 | −0.169957 | ||||||||
\(815\) | −11.2345 | −0.393526 | ||||||||
\(816\) | −6.00757 | −0.210307 | ||||||||
\(817\) | 29.0675 | 1.01694 | ||||||||
\(818\) | 17.0960 | 0.597749 | ||||||||
\(819\) | −41.7270 | −1.45806 | ||||||||
\(820\) | 4.54836 | 0.158836 | ||||||||
\(821\) | −37.7565 | −1.31771 | −0.658856 | − | 0.752269i | \(-0.728959\pi\) | ||||
−0.658856 | + | 0.752269i | \(0.728959\pi\) | |||||||
\(822\) | −2.17083 | −0.0757164 | ||||||||
\(823\) | −40.4823 | −1.41113 | −0.705563 | − | 0.708647i | \(-0.749306\pi\) | ||||
−0.705563 | + | 0.708647i | \(0.749306\pi\) | |||||||
\(824\) | 3.12024 | 0.108699 | ||||||||
\(825\) | −1.42699 | −0.0496815 | ||||||||
\(826\) | 59.0558 | 2.05481 | ||||||||
\(827\) | −15.9936 | −0.556154 | −0.278077 | − | 0.960559i | \(-0.589697\pi\) | ||||
−0.278077 | + | 0.960559i | \(0.589697\pi\) | |||||||
\(828\) | 10.1230 | 0.351798 | ||||||||
\(829\) | 24.8958 | 0.864666 | 0.432333 | − | 0.901714i | \(-0.357690\pi\) | ||||
0.432333 | + | 0.901714i | \(0.357690\pi\) | |||||||
\(830\) | −1.14337 | −0.0396869 | ||||||||
\(831\) | −3.21856 | −0.111651 | ||||||||
\(832\) | 5.57551 | 0.193296 | ||||||||
\(833\) | 75.9114 | 2.63017 | ||||||||
\(834\) | 1.29459 | 0.0448280 | ||||||||
\(835\) | −17.0849 | −0.591248 | ||||||||
\(836\) | 9.23075 | 0.319252 | ||||||||
\(837\) | −48.5674 | −1.67874 | ||||||||
\(838\) | 24.7515 | 0.855027 | ||||||||
\(839\) | −29.2328 | −1.00923 | −0.504615 | − | 0.863345i | \(-0.668365\pi\) | ||||
−0.504615 | + | 0.863345i | \(0.668365\pi\) | |||||||
\(840\) | 5.55227 | 0.191571 | ||||||||
\(841\) | −28.9147 | −0.997059 | ||||||||
\(842\) | 13.3166 | 0.458920 | ||||||||
\(843\) | −30.4857 | −1.04998 | ||||||||
\(844\) | −0.232000 | −0.00798577 | ||||||||
\(845\) | −18.0863 | −0.622189 | ||||||||
\(846\) | 11.0034 | 0.378306 | ||||||||
\(847\) | −44.7561 | −1.53784 | ||||||||
\(848\) | −2.85791 | −0.0981412 | ||||||||
\(849\) | 11.0268 | 0.378437 | ||||||||
\(850\) | 5.07141 | 0.173948 | ||||||||
\(851\) | 25.5197 | 0.874803 | ||||||||
\(852\) | −7.09410 | −0.243040 | ||||||||
\(853\) | −17.8351 | −0.610662 | −0.305331 | − | 0.952246i | \(-0.598767\pi\) | ||||
−0.305331 | + | 0.952246i | \(0.598767\pi\) | |||||||
\(854\) | 41.6149 | 1.42403 | ||||||||
\(855\) | 12.2354 | 0.418442 | ||||||||
\(856\) | −10.8774 | −0.371780 | ||||||||
\(857\) | −43.6215 | −1.49008 | −0.745042 | − | 0.667018i | \(-0.767571\pi\) | ||||
−0.745042 | + | 0.667018i | \(0.767571\pi\) | |||||||
\(858\) | −7.95621 | −0.271621 | ||||||||
\(859\) | −18.5409 | −0.632608 | −0.316304 | − | 0.948658i | \(-0.602442\pi\) | ||||
−0.316304 | + | 0.948658i | \(0.602442\pi\) | |||||||
\(860\) | −3.79335 | −0.129352 | ||||||||
\(861\) | 25.2537 | 0.860645 | ||||||||
\(862\) | 12.8500 | 0.437673 | ||||||||
\(863\) | −29.5342 | −1.00535 | −0.502677 | − | 0.864474i | \(-0.667652\pi\) | ||||
−0.502677 | + | 0.864474i | \(0.667652\pi\) | |||||||
\(864\) | 5.44527 | 0.185252 | ||||||||
\(865\) | −10.9413 | −0.372015 | ||||||||
\(866\) | 18.4111 | 0.625634 | ||||||||
\(867\) | −10.3287 | −0.350781 | ||||||||
\(868\) | −41.8048 | −1.41895 | ||||||||
\(869\) | 17.2724 | 0.585925 | ||||||||
\(870\) | −0.345979 | −0.0117298 | ||||||||
\(871\) | −71.6392 | −2.42740 | ||||||||
\(872\) | −2.49420 | −0.0844642 | ||||||||
\(873\) | −27.1205 | −0.917889 | ||||||||
\(874\) | −48.5804 | −1.64326 | ||||||||
\(875\) | −4.68706 | −0.158451 | ||||||||
\(876\) | 19.0526 | 0.643729 | ||||||||
\(877\) | 52.7471 | 1.78114 | 0.890572 | − | 0.454843i | \(-0.150305\pi\) | ||||
0.890572 | + | 0.454843i | \(0.150305\pi\) | |||||||
\(878\) | −16.7436 | −0.565068 | ||||||||
\(879\) | −21.2076 | −0.715316 | ||||||||
\(880\) | −1.20462 | −0.0406079 | ||||||||
\(881\) | 18.4412 | 0.621301 | 0.310651 | − | 0.950524i | \(-0.399453\pi\) | ||||
0.310651 | + | 0.950524i | \(0.399453\pi\) | |||||||
\(882\) | −23.9007 | −0.804779 | ||||||||
\(883\) | −44.0880 | −1.48368 | −0.741840 | − | 0.670577i | \(-0.766046\pi\) | ||||
−0.741840 | + | 0.670577i | \(0.766046\pi\) | |||||||
\(884\) | 28.2757 | 0.951015 | ||||||||
\(885\) | 14.9256 | 0.501719 | ||||||||
\(886\) | −1.70027 | −0.0571217 | ||||||||
\(887\) | −0.646874 | −0.0217199 | −0.0108600 | − | 0.999941i | \(-0.503457\pi\) | ||||
−0.0108600 | + | 0.999941i | \(0.503457\pi\) | |||||||
\(888\) | 4.76837 | 0.160016 | ||||||||
\(889\) | 17.1150 | 0.574020 | ||||||||
\(890\) | 13.0424 | 0.437183 | ||||||||
\(891\) | −1.99997 | −0.0670014 | ||||||||
\(892\) | 21.6531 | 0.724999 | ||||||||
\(893\) | −52.8058 | −1.76708 | ||||||||
\(894\) | 14.4778 | 0.484210 | ||||||||
\(895\) | 17.3319 | 0.579342 | ||||||||
\(896\) | 4.68706 | 0.156584 | ||||||||
\(897\) | 41.8727 | 1.39809 | ||||||||
\(898\) | −33.7537 | −1.12637 | ||||||||
\(899\) | 2.60499 | 0.0868811 | ||||||||
\(900\) | −1.59673 | −0.0532244 | ||||||||
\(901\) | −14.4937 | −0.482853 | ||||||||
\(902\) | −5.47907 | −0.182433 | ||||||||
\(903\) | −21.0617 | −0.700889 | ||||||||
\(904\) | 2.93612 | 0.0976538 | ||||||||
\(905\) | 23.4315 | 0.778888 | ||||||||
\(906\) | −4.56946 | −0.151810 | ||||||||
\(907\) | −27.7674 | −0.922001 | −0.461001 | − | 0.887400i | \(-0.652509\pi\) | ||||
−0.461001 | + | 0.887400i | \(0.652509\pi\) | |||||||
\(908\) | −16.5630 | −0.549663 | ||||||||
\(909\) | −13.1946 | −0.437637 | ||||||||
\(910\) | −26.1327 | −0.866292 | ||||||||
\(911\) | 24.2328 | 0.802867 | 0.401434 | − | 0.915888i | \(-0.368512\pi\) | ||||
0.401434 | + | 0.915888i | \(0.368512\pi\) | |||||||
\(912\) | −9.07728 | −0.300579 | ||||||||
\(913\) | 1.37733 | 0.0455830 | ||||||||
\(914\) | 20.4483 | 0.676371 | ||||||||
\(915\) | 10.5176 | 0.347703 | ||||||||
\(916\) | −9.48459 | −0.313380 | ||||||||
\(917\) | 74.6144 | 2.46398 | ||||||||
\(918\) | 27.6152 | 0.911437 | ||||||||
\(919\) | −24.4364 | −0.806084 | −0.403042 | − | 0.915181i | \(-0.632047\pi\) | ||||
−0.403042 | + | 0.915181i | \(0.632047\pi\) | |||||||
\(920\) | 6.33980 | 0.209017 | ||||||||
\(921\) | 3.55491 | 0.117138 | ||||||||
\(922\) | 1.18525 | 0.0390341 | ||||||||
\(923\) | 33.3897 | 1.09903 | ||||||||
\(924\) | −6.68839 | −0.220032 | ||||||||
\(925\) | −4.02531 | −0.132351 | ||||||||
\(926\) | −10.3889 | −0.341401 | ||||||||
\(927\) | −4.98220 | −0.163637 | ||||||||
\(928\) | −0.292065 | −0.00958750 | ||||||||
\(929\) | −14.2019 | −0.465949 | −0.232974 | − | 0.972483i | \(-0.574846\pi\) | ||||
−0.232974 | + | 0.972483i | \(0.574846\pi\) | |||||||
\(930\) | −10.5656 | −0.346461 | ||||||||
\(931\) | 114.700 | 3.75914 | ||||||||
\(932\) | 22.7987 | 0.746796 | ||||||||
\(933\) | 25.9585 | 0.849844 | ||||||||
\(934\) | −13.1057 | −0.428831 | ||||||||
\(935\) | −6.10914 | −0.199790 | ||||||||
\(936\) | −8.90261 | −0.290991 | ||||||||
\(937\) | −12.5103 | −0.408695 | −0.204348 | − | 0.978898i | \(-0.565507\pi\) | ||||
−0.204348 | + | 0.978898i | \(0.565507\pi\) | |||||||
\(938\) | −60.2235 | −1.96637 | ||||||||
\(939\) | −34.7333 | −1.13348 | ||||||||
\(940\) | 6.89121 | 0.224767 | ||||||||
\(941\) | −2.05386 | −0.0669540 | −0.0334770 | − | 0.999439i | \(-0.510658\pi\) | ||||
−0.0334770 | + | 0.999439i | \(0.510658\pi\) | |||||||
\(942\) | −27.4134 | −0.893177 | ||||||||
\(943\) | 28.8357 | 0.939020 | ||||||||
\(944\) | 12.5998 | 0.410087 | ||||||||
\(945\) | −25.5223 | −0.830240 | ||||||||
\(946\) | 4.56956 | 0.148569 | ||||||||
\(947\) | 44.3966 | 1.44269 | 0.721347 | − | 0.692574i | \(-0.243523\pi\) | ||||
0.721347 | + | 0.692574i | \(0.243523\pi\) | |||||||
\(948\) | −16.9852 | −0.551654 | ||||||||
\(949\) | −89.6747 | −2.91096 | ||||||||
\(950\) | 7.66277 | 0.248613 | ||||||||
\(951\) | 17.6782 | 0.573255 | ||||||||
\(952\) | 23.7700 | 0.770389 | ||||||||
\(953\) | 35.0284 | 1.13468 | 0.567340 | − | 0.823484i | \(-0.307973\pi\) | ||||
0.567340 | + | 0.823484i | \(0.307973\pi\) | |||||||
\(954\) | 4.56333 | 0.147743 | ||||||||
\(955\) | 1.46888 | 0.0475319 | ||||||||
\(956\) | −5.11597 | −0.165462 | ||||||||
\(957\) | 0.416775 | 0.0134724 | ||||||||
\(958\) | −8.41221 | −0.271786 | ||||||||
\(959\) | 8.58927 | 0.277362 | ||||||||
\(960\) | 1.18460 | 0.0382327 | ||||||||
\(961\) | 48.5521 | 1.56620 | ||||||||
\(962\) | −22.4432 | −0.723597 | ||||||||
\(963\) | 17.3682 | 0.559683 | ||||||||
\(964\) | −19.7206 | −0.635158 | ||||||||
\(965\) | 5.91331 | 0.190356 | ||||||||
\(966\) | 35.2003 | 1.13255 | ||||||||
\(967\) | 19.8609 | 0.638685 | 0.319342 | − | 0.947639i | \(-0.396538\pi\) | ||||
0.319342 | + | 0.947639i | \(0.396538\pi\) | |||||||
\(968\) | −9.54888 | −0.306913 | ||||||||
\(969\) | −46.0346 | −1.47884 | ||||||||
\(970\) | −16.9850 | −0.545355 | ||||||||
\(971\) | −52.9437 | −1.69904 | −0.849522 | − | 0.527554i | \(-0.823109\pi\) | ||||
−0.849522 | + | 0.527554i | \(0.823109\pi\) | |||||||
\(972\) | −14.3691 | −0.460889 | ||||||||
\(973\) | −5.12227 | −0.164212 | ||||||||
\(974\) | 27.3511 | 0.876385 | ||||||||
\(975\) | −6.60473 | −0.211521 | ||||||||
\(976\) | 8.87868 | 0.284200 | ||||||||
\(977\) | 15.7034 | 0.502395 | 0.251197 | − | 0.967936i | \(-0.419176\pi\) | ||||
0.251197 | + | 0.967936i | \(0.419176\pi\) | |||||||
\(978\) | −13.3083 | −0.425553 | ||||||||
\(979\) | −15.7112 | −0.502133 | ||||||||
\(980\) | −14.9685 | −0.478151 | ||||||||
\(981\) | 3.98257 | 0.127154 | ||||||||
\(982\) | −12.8040 | −0.408591 | ||||||||
\(983\) | 30.9448 | 0.986987 | 0.493493 | − | 0.869749i | \(-0.335720\pi\) | ||||
0.493493 | + | 0.869749i | \(0.335720\pi\) | |||||||
\(984\) | 5.38797 | 0.171762 | ||||||||
\(985\) | 18.2523 | 0.581566 | ||||||||
\(986\) | −1.48118 | −0.0471704 | ||||||||
\(987\) | 38.2619 | 1.21789 | ||||||||
\(988\) | 42.7239 | 1.35923 | ||||||||
\(989\) | −24.0491 | −0.764716 | ||||||||
\(990\) | 1.92346 | 0.0611317 | ||||||||
\(991\) | −35.9669 | −1.14252 | −0.571262 | − | 0.820768i | \(-0.693546\pi\) | ||||
−0.571262 | + | 0.820768i | \(0.693546\pi\) | |||||||
\(992\) | −8.91920 | −0.283185 | ||||||||
\(993\) | 18.9391 | 0.601013 | ||||||||
\(994\) | 28.0690 | 0.890295 | ||||||||
\(995\) | −18.6917 | −0.592567 | ||||||||
\(996\) | −1.35443 | −0.0429168 | ||||||||
\(997\) | −55.3819 | −1.75396 | −0.876982 | − | 0.480524i | \(-0.840447\pi\) | ||||
−0.876982 | + | 0.480524i | \(0.840447\pi\) | |||||||
\(998\) | −30.6213 | −0.969300 | ||||||||
\(999\) | −21.9189 | −0.693483 |
(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 | 4010.2.a.o.1.9 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.o.1.9 | ✓ | 22 | 1.1 | even | 1 | trivial |