Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8021,2,Mod(1,8021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8021, 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("8021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8021 = 13 \cdot 617 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8021.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: | \(64.0480074613\) |
Analytic rank: | \(0\) |
Dimension: | \(169\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8021.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.46202 | −1.74091 | −0.870455 | − | 0.492247i | \(-0.836176\pi\) | ||||
−0.870455 | + | 0.492247i | \(0.836176\pi\) | |||||||
\(3\) | 0.861982 | 0.497666 | 0.248833 | − | 0.968546i | \(-0.419953\pi\) | ||||
0.248833 | + | 0.968546i | \(0.419953\pi\) | |||||||
\(4\) | 4.06154 | 2.03077 | ||||||||
\(5\) | 2.09605 | 0.937381 | 0.468690 | − | 0.883363i | \(-0.344726\pi\) | ||||
0.468690 | + | 0.883363i | \(0.344726\pi\) | |||||||
\(6\) | −2.12222 | −0.866392 | ||||||||
\(7\) | 1.61995 | 0.612282 | 0.306141 | − | 0.951986i | \(-0.400962\pi\) | ||||
0.306141 | + | 0.951986i | \(0.400962\pi\) | |||||||
\(8\) | −5.07555 | −1.79448 | ||||||||
\(9\) | −2.25699 | −0.752329 | ||||||||
\(10\) | −5.16051 | −1.63190 | ||||||||
\(11\) | 1.07211 | 0.323254 | 0.161627 | − | 0.986852i | \(-0.448326\pi\) | ||||
0.161627 | + | 0.986852i | \(0.448326\pi\) | |||||||
\(12\) | 3.50098 | 1.01064 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −3.98834 | −1.06593 | ||||||||
\(15\) | 1.80676 | 0.466502 | ||||||||
\(16\) | 4.37303 | 1.09326 | ||||||||
\(17\) | 6.24773 | 1.51530 | 0.757648 | − | 0.652663i | \(-0.226348\pi\) | ||||
0.757648 | + | 0.652663i | \(0.226348\pi\) | |||||||
\(18\) | 5.55674 | 1.30974 | ||||||||
\(19\) | −1.80627 | −0.414388 | −0.207194 | − | 0.978300i | \(-0.566433\pi\) | ||||
−0.207194 | + | 0.978300i | \(0.566433\pi\) | |||||||
\(20\) | 8.51318 | 1.90360 | ||||||||
\(21\) | 1.39636 | 0.304712 | ||||||||
\(22\) | −2.63956 | −0.562757 | ||||||||
\(23\) | −5.74920 | −1.19879 | −0.599396 | − | 0.800453i | \(-0.704592\pi\) | ||||
−0.599396 | + | 0.800453i | \(0.704592\pi\) | |||||||
\(24\) | −4.37504 | −0.893051 | ||||||||
\(25\) | −0.606588 | −0.121318 | ||||||||
\(26\) | 2.46202 | 0.482842 | ||||||||
\(27\) | −4.53143 | −0.872074 | ||||||||
\(28\) | 6.57947 | 1.24340 | ||||||||
\(29\) | 9.80731 | 1.82117 | 0.910586 | − | 0.413320i | \(-0.135631\pi\) | ||||
0.910586 | + | 0.413320i | \(0.135631\pi\) | |||||||
\(30\) | −4.44827 | −0.812139 | ||||||||
\(31\) | 7.54571 | 1.35525 | 0.677625 | − | 0.735408i | \(-0.263009\pi\) | ||||
0.677625 | + | 0.735408i | \(0.263009\pi\) | |||||||
\(32\) | −0.615376 | −0.108784 | ||||||||
\(33\) | 0.924142 | 0.160873 | ||||||||
\(34\) | −15.3820 | −2.63800 | ||||||||
\(35\) | 3.39548 | 0.573941 | ||||||||
\(36\) | −9.16684 | −1.52781 | ||||||||
\(37\) | −9.42892 | −1.55010 | −0.775052 | − | 0.631897i | \(-0.782277\pi\) | ||||
−0.775052 | + | 0.631897i | \(0.782277\pi\) | |||||||
\(38\) | 4.44708 | 0.721412 | ||||||||
\(39\) | −0.861982 | −0.138028 | ||||||||
\(40\) | −10.6386 | −1.68211 | ||||||||
\(41\) | 10.5896 | 1.65382 | 0.826909 | − | 0.562336i | \(-0.190097\pi\) | ||||
0.826909 | + | 0.562336i | \(0.190097\pi\) | |||||||
\(42\) | −3.43788 | −0.530476 | ||||||||
\(43\) | 4.69034 | 0.715271 | 0.357635 | − | 0.933861i | \(-0.383583\pi\) | ||||
0.357635 | + | 0.933861i | \(0.383583\pi\) | |||||||
\(44\) | 4.35443 | 0.656455 | ||||||||
\(45\) | −4.73075 | −0.705218 | ||||||||
\(46\) | 14.1546 | 2.08699 | ||||||||
\(47\) | −0.665416 | −0.0970609 | −0.0485304 | − | 0.998822i | \(-0.515454\pi\) | ||||
−0.0485304 | + | 0.998822i | \(0.515454\pi\) | |||||||
\(48\) | 3.76947 | 0.544077 | ||||||||
\(49\) | −4.37578 | −0.625111 | ||||||||
\(50\) | 1.49343 | 0.211203 | ||||||||
\(51\) | 5.38543 | 0.754111 | ||||||||
\(52\) | −4.06154 | −0.563234 | ||||||||
\(53\) | 9.02049 | 1.23906 | 0.619530 | − | 0.784973i | \(-0.287323\pi\) | ||||
0.619530 | + | 0.784973i | \(0.287323\pi\) | |||||||
\(54\) | 11.1565 | 1.51820 | ||||||||
\(55\) | 2.24720 | 0.303012 | ||||||||
\(56\) | −8.22212 | −1.09873 | ||||||||
\(57\) | −1.55698 | −0.206227 | ||||||||
\(58\) | −24.1458 | −3.17050 | ||||||||
\(59\) | −11.8134 | −1.53798 | −0.768988 | − | 0.639264i | \(-0.779239\pi\) | ||||
−0.768988 | + | 0.639264i | \(0.779239\pi\) | |||||||
\(60\) | 7.33821 | 0.947359 | ||||||||
\(61\) | 10.7395 | 1.37505 | 0.687526 | − | 0.726160i | \(-0.258697\pi\) | ||||
0.687526 | + | 0.726160i | \(0.258697\pi\) | |||||||
\(62\) | −18.5777 | −2.35937 | ||||||||
\(63\) | −3.65620 | −0.460637 | ||||||||
\(64\) | −7.23099 | −0.903873 | ||||||||
\(65\) | −2.09605 | −0.259983 | ||||||||
\(66\) | −2.27526 | −0.280065 | ||||||||
\(67\) | 11.3257 | 1.38365 | 0.691825 | − | 0.722065i | \(-0.256807\pi\) | ||||
0.691825 | + | 0.722065i | \(0.256807\pi\) | |||||||
\(68\) | 25.3754 | 3.07722 | ||||||||
\(69\) | −4.95571 | −0.596597 | ||||||||
\(70\) | −8.35974 | −0.999180 | ||||||||
\(71\) | 11.9453 | 1.41765 | 0.708825 | − | 0.705384i | \(-0.249225\pi\) | ||||
0.708825 | + | 0.705384i | \(0.249225\pi\) | |||||||
\(72\) | 11.4555 | 1.35004 | ||||||||
\(73\) | −10.9238 | −1.27853 | −0.639265 | − | 0.768987i | \(-0.720761\pi\) | ||||
−0.639265 | + | 0.768987i | \(0.720761\pi\) | |||||||
\(74\) | 23.2142 | 2.69859 | ||||||||
\(75\) | −0.522869 | −0.0603757 | ||||||||
\(76\) | −7.33626 | −0.841526 | ||||||||
\(77\) | 1.73676 | 0.197923 | ||||||||
\(78\) | 2.12222 | 0.240294 | ||||||||
\(79\) | −6.27932 | −0.706479 | −0.353239 | − | 0.935533i | \(-0.614920\pi\) | ||||
−0.353239 | + | 0.935533i | \(0.614920\pi\) | |||||||
\(80\) | 9.16607 | 1.02480 | ||||||||
\(81\) | 2.86495 | 0.318327 | ||||||||
\(82\) | −26.0718 | −2.87915 | ||||||||
\(83\) | −8.99398 | −0.987217 | −0.493609 | − | 0.869684i | \(-0.664322\pi\) | ||||
−0.493609 | + | 0.869684i | \(0.664322\pi\) | |||||||
\(84\) | 5.67139 | 0.618799 | ||||||||
\(85\) | 13.0955 | 1.42041 | ||||||||
\(86\) | −11.5477 | −1.24522 | ||||||||
\(87\) | 8.45373 | 0.906335 | ||||||||
\(88\) | −5.44156 | −0.580073 | ||||||||
\(89\) | −15.3562 | −1.62776 | −0.813878 | − | 0.581036i | \(-0.802648\pi\) | ||||
−0.813878 | + | 0.581036i | \(0.802648\pi\) | |||||||
\(90\) | 11.6472 | 1.22772 | ||||||||
\(91\) | −1.61995 | −0.169816 | ||||||||
\(92\) | −23.3506 | −2.43447 | ||||||||
\(93\) | 6.50427 | 0.674461 | ||||||||
\(94\) | 1.63827 | 0.168974 | ||||||||
\(95\) | −3.78604 | −0.388439 | ||||||||
\(96\) | −0.530444 | −0.0541382 | ||||||||
\(97\) | 10.6377 | 1.08009 | 0.540046 | − | 0.841635i | \(-0.318407\pi\) | ||||
0.540046 | + | 0.841635i | \(0.318407\pi\) | |||||||
\(98\) | 10.7732 | 1.08826 | ||||||||
\(99\) | −2.41974 | −0.243193 | ||||||||
\(100\) | −2.46368 | −0.246368 | ||||||||
\(101\) | 12.6119 | 1.25493 | 0.627467 | − | 0.778643i | \(-0.284092\pi\) | ||||
0.627467 | + | 0.778643i | \(0.284092\pi\) | |||||||
\(102\) | −13.2590 | −1.31284 | ||||||||
\(103\) | 5.86005 | 0.577407 | 0.288704 | − | 0.957418i | \(-0.406776\pi\) | ||||
0.288704 | + | 0.957418i | \(0.406776\pi\) | |||||||
\(104\) | 5.07555 | 0.497699 | ||||||||
\(105\) | 2.92685 | 0.285631 | ||||||||
\(106\) | −22.2086 | −2.15709 | ||||||||
\(107\) | −2.16873 | −0.209659 | −0.104830 | − | 0.994490i | \(-0.533430\pi\) | ||||
−0.104830 | + | 0.994490i | \(0.533430\pi\) | |||||||
\(108\) | −18.4046 | −1.77098 | ||||||||
\(109\) | 0.841927 | 0.0806420 | 0.0403210 | − | 0.999187i | \(-0.487162\pi\) | ||||
0.0403210 | + | 0.999187i | \(0.487162\pi\) | |||||||
\(110\) | −5.53265 | −0.527517 | ||||||||
\(111\) | −8.12756 | −0.771434 | ||||||||
\(112\) | 7.08407 | 0.669381 | ||||||||
\(113\) | −17.7325 | −1.66813 | −0.834066 | − | 0.551665i | \(-0.813993\pi\) | ||||
−0.834066 | + | 0.551665i | \(0.813993\pi\) | |||||||
\(114\) | 3.83331 | 0.359022 | ||||||||
\(115\) | −12.0506 | −1.12372 | ||||||||
\(116\) | 39.8328 | 3.69838 | ||||||||
\(117\) | 2.25699 | 0.208658 | ||||||||
\(118\) | 29.0849 | 2.67748 | ||||||||
\(119\) | 10.1210 | 0.927788 | ||||||||
\(120\) | −9.17028 | −0.837128 | ||||||||
\(121\) | −9.85057 | −0.895507 | ||||||||
\(122\) | −26.4409 | −2.39384 | ||||||||
\(123\) | 9.12805 | 0.823048 | ||||||||
\(124\) | 30.6472 | 2.75220 | ||||||||
\(125\) | −11.7517 | −1.05110 | ||||||||
\(126\) | 9.00162 | 0.801928 | ||||||||
\(127\) | 11.6863 | 1.03699 | 0.518495 | − | 0.855081i | \(-0.326493\pi\) | ||||
0.518495 | + | 0.855081i | \(0.326493\pi\) | |||||||
\(128\) | 19.0336 | 1.68235 | ||||||||
\(129\) | 4.04299 | 0.355966 | ||||||||
\(130\) | 5.16051 | 0.452606 | ||||||||
\(131\) | −1.73191 | −0.151317 | −0.0756587 | − | 0.997134i | \(-0.524106\pi\) | ||||
−0.0756587 | + | 0.997134i | \(0.524106\pi\) | |||||||
\(132\) | 3.75344 | 0.326695 | ||||||||
\(133\) | −2.92607 | −0.253722 | ||||||||
\(134\) | −27.8840 | −2.40881 | ||||||||
\(135\) | −9.49809 | −0.817465 | ||||||||
\(136\) | −31.7107 | −2.71917 | ||||||||
\(137\) | −16.6916 | −1.42606 | −0.713030 | − | 0.701134i | \(-0.752678\pi\) | ||||
−0.713030 | + | 0.701134i | \(0.752678\pi\) | |||||||
\(138\) | 12.2011 | 1.03862 | ||||||||
\(139\) | 7.90555 | 0.670540 | 0.335270 | − | 0.942122i | \(-0.391172\pi\) | ||||
0.335270 | + | 0.942122i | \(0.391172\pi\) | |||||||
\(140\) | 13.7909 | 1.16554 | ||||||||
\(141\) | −0.573577 | −0.0483039 | ||||||||
\(142\) | −29.4097 | −2.46800 | ||||||||
\(143\) | −1.07211 | −0.0896546 | ||||||||
\(144\) | −9.86986 | −0.822489 | ||||||||
\(145\) | 20.5566 | 1.70713 | ||||||||
\(146\) | 26.8945 | 2.22581 | ||||||||
\(147\) | −3.77184 | −0.311096 | ||||||||
\(148\) | −38.2959 | −3.14791 | ||||||||
\(149\) | −1.40742 | −0.115300 | −0.0576501 | − | 0.998337i | \(-0.518361\pi\) | ||||
−0.0576501 | + | 0.998337i | \(0.518361\pi\) | |||||||
\(150\) | 1.28731 | 0.105109 | ||||||||
\(151\) | 21.6425 | 1.76124 | 0.880622 | − | 0.473820i | \(-0.157125\pi\) | ||||
0.880622 | + | 0.473820i | \(0.157125\pi\) | |||||||
\(152\) | 9.16784 | 0.743610 | ||||||||
\(153\) | −14.1010 | −1.14000 | ||||||||
\(154\) | −4.27595 | −0.344566 | ||||||||
\(155\) | 15.8162 | 1.27038 | ||||||||
\(156\) | −3.50098 | −0.280302 | ||||||||
\(157\) | 0.753749 | 0.0601557 | 0.0300778 | − | 0.999548i | \(-0.490424\pi\) | ||||
0.0300778 | + | 0.999548i | \(0.490424\pi\) | |||||||
\(158\) | 15.4598 | 1.22992 | ||||||||
\(159\) | 7.77550 | 0.616638 | ||||||||
\(160\) | −1.28986 | −0.101972 | ||||||||
\(161\) | −9.31339 | −0.733998 | ||||||||
\(162\) | −7.05355 | −0.554180 | ||||||||
\(163\) | 15.5877 | 1.22092 | 0.610460 | − | 0.792047i | \(-0.290985\pi\) | ||||
0.610460 | + | 0.792047i | \(0.290985\pi\) | |||||||
\(164\) | 43.0101 | 3.35852 | ||||||||
\(165\) | 1.93705 | 0.150799 | ||||||||
\(166\) | 22.1434 | 1.71866 | ||||||||
\(167\) | 18.3639 | 1.42104 | 0.710519 | − | 0.703678i | \(-0.248460\pi\) | ||||
0.710519 | + | 0.703678i | \(0.248460\pi\) | |||||||
\(168\) | −7.08732 | −0.546799 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −32.2414 | −2.47281 | ||||||||
\(171\) | 4.07674 | 0.311756 | ||||||||
\(172\) | 19.0500 | 1.45255 | ||||||||
\(173\) | 17.4467 | 1.32645 | 0.663225 | − | 0.748420i | \(-0.269187\pi\) | ||||
0.663225 | + | 0.748420i | \(0.269187\pi\) | |||||||
\(174\) | −20.8132 | −1.57785 | ||||||||
\(175\) | −0.982640 | −0.0742806 | ||||||||
\(176\) | 4.68838 | 0.353400 | ||||||||
\(177\) | −10.1830 | −0.765398 | ||||||||
\(178\) | 37.8073 | 2.83378 | ||||||||
\(179\) | −20.7614 | −1.55178 | −0.775890 | − | 0.630868i | \(-0.782699\pi\) | ||||
−0.775890 | + | 0.630868i | \(0.782699\pi\) | |||||||
\(180\) | −19.2141 | −1.43214 | ||||||||
\(181\) | 4.87190 | 0.362125 | 0.181063 | − | 0.983472i | \(-0.442046\pi\) | ||||
0.181063 | + | 0.983472i | \(0.442046\pi\) | |||||||
\(182\) | 3.98834 | 0.295635 | ||||||||
\(183\) | 9.25726 | 0.684316 | ||||||||
\(184\) | 29.1804 | 2.15121 | ||||||||
\(185\) | −19.7635 | −1.45304 | ||||||||
\(186\) | −16.0136 | −1.17418 | ||||||||
\(187\) | 6.69827 | 0.489826 | ||||||||
\(188\) | −2.70261 | −0.197108 | ||||||||
\(189\) | −7.34067 | −0.533955 | ||||||||
\(190\) | 9.32129 | 0.676238 | ||||||||
\(191\) | −11.7213 | −0.848126 | −0.424063 | − | 0.905633i | \(-0.639397\pi\) | ||||
−0.424063 | + | 0.905633i | \(0.639397\pi\) | |||||||
\(192\) | −6.23298 | −0.449827 | ||||||||
\(193\) | 13.1345 | 0.945446 | 0.472723 | − | 0.881211i | \(-0.343271\pi\) | ||||
0.472723 | + | 0.881211i | \(0.343271\pi\) | |||||||
\(194\) | −26.1902 | −1.88034 | ||||||||
\(195\) | −1.80676 | −0.129384 | ||||||||
\(196\) | −17.7724 | −1.26946 | ||||||||
\(197\) | −0.426539 | −0.0303897 | −0.0151948 | − | 0.999885i | \(-0.504837\pi\) | ||||
−0.0151948 | + | 0.999885i | \(0.504837\pi\) | |||||||
\(198\) | 5.95746 | 0.423378 | ||||||||
\(199\) | 13.8782 | 0.983801 | 0.491900 | − | 0.870652i | \(-0.336302\pi\) | ||||
0.491900 | + | 0.870652i | \(0.336302\pi\) | |||||||
\(200\) | 3.07877 | 0.217702 | ||||||||
\(201\) | 9.76253 | 0.688595 | ||||||||
\(202\) | −31.0508 | −2.18473 | ||||||||
\(203\) | 15.8873 | 1.11507 | ||||||||
\(204\) | 21.8731 | 1.53143 | ||||||||
\(205\) | 22.1963 | 1.55026 | ||||||||
\(206\) | −14.4275 | −1.00521 | ||||||||
\(207\) | 12.9759 | 0.901885 | ||||||||
\(208\) | −4.37303 | −0.303215 | ||||||||
\(209\) | −1.93653 | −0.133953 | ||||||||
\(210\) | −7.20595 | −0.497258 | ||||||||
\(211\) | 5.25818 | 0.361988 | 0.180994 | − | 0.983484i | \(-0.442069\pi\) | ||||
0.180994 | + | 0.983484i | \(0.442069\pi\) | |||||||
\(212\) | 36.6371 | 2.51625 | ||||||||
\(213\) | 10.2967 | 0.705516 | ||||||||
\(214\) | 5.33946 | 0.364998 | ||||||||
\(215\) | 9.83118 | 0.670481 | ||||||||
\(216\) | 22.9995 | 1.56492 | ||||||||
\(217\) | 12.2236 | 0.829795 | ||||||||
\(218\) | −2.07284 | −0.140390 | ||||||||
\(219\) | −9.41609 | −0.636280 | ||||||||
\(220\) | 9.12709 | 0.615348 | ||||||||
\(221\) | −6.24773 | −0.420268 | ||||||||
\(222\) | 20.0102 | 1.34300 | ||||||||
\(223\) | 8.56762 | 0.573730 | 0.286865 | − | 0.957971i | \(-0.407387\pi\) | ||||
0.286865 | + | 0.957971i | \(0.407387\pi\) | |||||||
\(224\) | −0.996876 | −0.0666066 | ||||||||
\(225\) | 1.36906 | 0.0912708 | ||||||||
\(226\) | 43.6577 | 2.90407 | ||||||||
\(227\) | −11.4062 | −0.757056 | −0.378528 | − | 0.925590i | \(-0.623570\pi\) | ||||
−0.378528 | + | 0.925590i | \(0.623570\pi\) | |||||||
\(228\) | −6.32372 | −0.418799 | ||||||||
\(229\) | 20.1646 | 1.33252 | 0.666258 | − | 0.745721i | \(-0.267895\pi\) | ||||
0.666258 | + | 0.745721i | \(0.267895\pi\) | |||||||
\(230\) | 29.6688 | 1.95630 | ||||||||
\(231\) | 1.49706 | 0.0984993 | ||||||||
\(232\) | −49.7775 | −3.26805 | ||||||||
\(233\) | −15.0511 | −0.986033 | −0.493017 | − | 0.870020i | \(-0.664106\pi\) | ||||
−0.493017 | + | 0.870020i | \(0.664106\pi\) | |||||||
\(234\) | −5.55674 | −0.363256 | ||||||||
\(235\) | −1.39474 | −0.0909830 | ||||||||
\(236\) | −47.9806 | −3.12327 | ||||||||
\(237\) | −5.41266 | −0.351590 | ||||||||
\(238\) | −24.9180 | −1.61520 | ||||||||
\(239\) | 7.02165 | 0.454193 | 0.227096 | − | 0.973872i | \(-0.427077\pi\) | ||||
0.227096 | + | 0.973872i | \(0.427077\pi\) | |||||||
\(240\) | 7.90099 | 0.510007 | ||||||||
\(241\) | 22.7870 | 1.46784 | 0.733918 | − | 0.679238i | \(-0.237689\pi\) | ||||
0.733918 | + | 0.679238i | \(0.237689\pi\) | |||||||
\(242\) | 24.2523 | 1.55900 | ||||||||
\(243\) | 16.0638 | 1.03049 | ||||||||
\(244\) | 43.6189 | 2.79241 | ||||||||
\(245\) | −9.17183 | −0.585967 | ||||||||
\(246\) | −22.4734 | −1.43285 | ||||||||
\(247\) | 1.80627 | 0.114930 | ||||||||
\(248\) | −38.2986 | −2.43197 | ||||||||
\(249\) | −7.75265 | −0.491304 | ||||||||
\(250\) | 28.9328 | 1.82987 | ||||||||
\(251\) | −11.4825 | −0.724770 | −0.362385 | − | 0.932028i | \(-0.618037\pi\) | ||||
−0.362385 | + | 0.932028i | \(0.618037\pi\) | |||||||
\(252\) | −14.8498 | −0.935448 | ||||||||
\(253\) | −6.16379 | −0.387514 | ||||||||
\(254\) | −28.7718 | −1.80531 | ||||||||
\(255\) | 11.2881 | 0.706889 | ||||||||
\(256\) | −32.3991 | −2.02494 | ||||||||
\(257\) | 5.34673 | 0.333520 | 0.166760 | − | 0.985998i | \(-0.446670\pi\) | ||||
0.166760 | + | 0.985998i | \(0.446670\pi\) | |||||||
\(258\) | −9.95393 | −0.619704 | ||||||||
\(259\) | −15.2743 | −0.949101 | ||||||||
\(260\) | −8.51318 | −0.527965 | ||||||||
\(261\) | −22.1350 | −1.37012 | ||||||||
\(262\) | 4.26399 | 0.263430 | ||||||||
\(263\) | 4.46814 | 0.275518 | 0.137759 | − | 0.990466i | \(-0.456010\pi\) | ||||
0.137759 | + | 0.990466i | \(0.456010\pi\) | |||||||
\(264\) | −4.69053 | −0.288682 | ||||||||
\(265\) | 18.9074 | 1.16147 | ||||||||
\(266\) | 7.20403 | 0.441708 | ||||||||
\(267\) | −13.2368 | −0.810078 | ||||||||
\(268\) | 45.9996 | 2.80988 | ||||||||
\(269\) | −13.1416 | −0.801259 | −0.400629 | − | 0.916240i | \(-0.631208\pi\) | ||||
−0.400629 | + | 0.916240i | \(0.631208\pi\) | |||||||
\(270\) | 23.3845 | 1.42313 | ||||||||
\(271\) | 17.7967 | 1.08107 | 0.540536 | − | 0.841321i | \(-0.318222\pi\) | ||||
0.540536 | + | 0.841321i | \(0.318222\pi\) | |||||||
\(272\) | 27.3215 | 1.65661 | ||||||||
\(273\) | −1.39636 | −0.0845118 | ||||||||
\(274\) | 41.0950 | 2.48264 | ||||||||
\(275\) | −0.650331 | −0.0392164 | ||||||||
\(276\) | −20.1278 | −1.21155 | ||||||||
\(277\) | 9.66624 | 0.580788 | 0.290394 | − | 0.956907i | \(-0.406214\pi\) | ||||
0.290394 | + | 0.956907i | \(0.406214\pi\) | |||||||
\(278\) | −19.4636 | −1.16735 | ||||||||
\(279\) | −17.0306 | −1.01959 | ||||||||
\(280\) | −17.2339 | −1.02993 | ||||||||
\(281\) | 11.0466 | 0.658986 | 0.329493 | − | 0.944158i | \(-0.393122\pi\) | ||||
0.329493 | + | 0.944158i | \(0.393122\pi\) | |||||||
\(282\) | 1.41216 | 0.0840927 | ||||||||
\(283\) | 6.46084 | 0.384057 | 0.192029 | − | 0.981389i | \(-0.438493\pi\) | ||||
0.192029 | + | 0.981389i | \(0.438493\pi\) | |||||||
\(284\) | 48.5165 | 2.87892 | ||||||||
\(285\) | −3.26350 | −0.193313 | ||||||||
\(286\) | 2.63956 | 0.156081 | ||||||||
\(287\) | 17.1546 | 1.01260 | ||||||||
\(288\) | 1.38890 | 0.0818415 | ||||||||
\(289\) | 22.0341 | 1.29612 | ||||||||
\(290\) | −50.6107 | −2.97196 | ||||||||
\(291\) | 9.16949 | 0.537525 | ||||||||
\(292\) | −44.3673 | −2.59640 | ||||||||
\(293\) | 30.0930 | 1.75805 | 0.879027 | − | 0.476772i | \(-0.158193\pi\) | ||||
0.879027 | + | 0.476772i | \(0.158193\pi\) | |||||||
\(294\) | 9.28635 | 0.541591 | ||||||||
\(295\) | −24.7615 | −1.44167 | ||||||||
\(296\) | 47.8570 | 2.78163 | ||||||||
\(297\) | −4.85820 | −0.281902 | ||||||||
\(298\) | 3.46509 | 0.200727 | ||||||||
\(299\) | 5.74920 | 0.332485 | ||||||||
\(300\) | −2.12365 | −0.122609 | ||||||||
\(301\) | 7.59810 | 0.437947 | ||||||||
\(302\) | −53.2843 | −3.06617 | ||||||||
\(303\) | 10.8713 | 0.624538 | ||||||||
\(304\) | −7.89889 | −0.453032 | ||||||||
\(305\) | 22.5105 | 1.28895 | ||||||||
\(306\) | 34.7170 | 1.98464 | ||||||||
\(307\) | −34.5629 | −1.97261 | −0.986304 | − | 0.164939i | \(-0.947257\pi\) | ||||
−0.986304 | + | 0.164939i | \(0.947257\pi\) | |||||||
\(308\) | 7.05394 | 0.401935 | ||||||||
\(309\) | 5.05126 | 0.287356 | ||||||||
\(310\) | −38.9397 | −2.21163 | ||||||||
\(311\) | 25.6949 | 1.45703 | 0.728513 | − | 0.685032i | \(-0.240212\pi\) | ||||
0.728513 | + | 0.685032i | \(0.240212\pi\) | |||||||
\(312\) | 4.37504 | 0.247688 | ||||||||
\(313\) | −1.76797 | −0.0999316 | −0.0499658 | − | 0.998751i | \(-0.515911\pi\) | ||||
−0.0499658 | + | 0.998751i | \(0.515911\pi\) | |||||||
\(314\) | −1.85574 | −0.104726 | ||||||||
\(315\) | −7.66356 | −0.431792 | ||||||||
\(316\) | −25.5037 | −1.43470 | ||||||||
\(317\) | −2.90409 | −0.163110 | −0.0815551 | − | 0.996669i | \(-0.525989\pi\) | ||||
−0.0815551 | + | 0.996669i | \(0.525989\pi\) | |||||||
\(318\) | −19.1434 | −1.07351 | ||||||||
\(319\) | 10.5145 | 0.588701 | ||||||||
\(320\) | −15.1565 | −0.847273 | ||||||||
\(321\) | −1.86941 | −0.104340 | ||||||||
\(322\) | 22.9298 | 1.27783 | ||||||||
\(323\) | −11.2851 | −0.627920 | ||||||||
\(324\) | 11.6361 | 0.646450 | ||||||||
\(325\) | 0.606588 | 0.0336475 | ||||||||
\(326\) | −38.3771 | −2.12551 | ||||||||
\(327\) | 0.725726 | 0.0401328 | ||||||||
\(328\) | −53.7481 | −2.96774 | ||||||||
\(329\) | −1.07794 | −0.0594286 | ||||||||
\(330\) | −4.76904 | −0.262527 | ||||||||
\(331\) | 29.1426 | 1.60182 | 0.800910 | − | 0.598784i | \(-0.204349\pi\) | ||||
0.800910 | + | 0.598784i | \(0.204349\pi\) | |||||||
\(332\) | −36.5294 | −2.00481 | ||||||||
\(333\) | 21.2809 | 1.16619 | ||||||||
\(334\) | −45.2122 | −2.47390 | ||||||||
\(335\) | 23.7391 | 1.29701 | ||||||||
\(336\) | 6.10634 | 0.333128 | ||||||||
\(337\) | −24.4145 | −1.32994 | −0.664970 | − | 0.746870i | \(-0.731556\pi\) | ||||
−0.664970 | + | 0.746870i | \(0.731556\pi\) | |||||||
\(338\) | −2.46202 | −0.133916 | ||||||||
\(339\) | −15.2851 | −0.830172 | ||||||||
\(340\) | 53.1880 | 2.88452 | ||||||||
\(341\) | 8.08985 | 0.438090 | ||||||||
\(342\) | −10.0370 | −0.542739 | ||||||||
\(343\) | −18.4281 | −0.995026 | ||||||||
\(344\) | −23.8061 | −1.28354 | ||||||||
\(345\) | −10.3874 | −0.559239 | ||||||||
\(346\) | −42.9542 | −2.30923 | ||||||||
\(347\) | −1.02741 | −0.0551541 | −0.0275770 | − | 0.999620i | \(-0.508779\pi\) | ||||
−0.0275770 | + | 0.999620i | \(0.508779\pi\) | |||||||
\(348\) | 34.3352 | 1.84056 | ||||||||
\(349\) | −35.5121 | −1.90092 | −0.950460 | − | 0.310846i | \(-0.899388\pi\) | ||||
−0.950460 | + | 0.310846i | \(0.899388\pi\) | |||||||
\(350\) | 2.41928 | 0.129316 | ||||||||
\(351\) | 4.53143 | 0.241870 | ||||||||
\(352\) | −0.659753 | −0.0351649 | ||||||||
\(353\) | 19.9986 | 1.06442 | 0.532208 | − | 0.846614i | \(-0.321363\pi\) | ||||
0.532208 | + | 0.846614i | \(0.321363\pi\) | |||||||
\(354\) | 25.0706 | 1.33249 | ||||||||
\(355\) | 25.0380 | 1.32888 | ||||||||
\(356\) | −62.3699 | −3.30560 | ||||||||
\(357\) | 8.72410 | 0.461729 | ||||||||
\(358\) | 51.1150 | 2.70151 | ||||||||
\(359\) | −4.33805 | −0.228954 | −0.114477 | − | 0.993426i | \(-0.536519\pi\) | ||||
−0.114477 | + | 0.993426i | \(0.536519\pi\) | |||||||
\(360\) | 24.0112 | 1.26550 | ||||||||
\(361\) | −15.7374 | −0.828283 | ||||||||
\(362\) | −11.9947 | −0.630428 | ||||||||
\(363\) | −8.49102 | −0.445663 | ||||||||
\(364\) | −6.57947 | −0.344858 | ||||||||
\(365\) | −22.8967 | −1.19847 | ||||||||
\(366\) | −22.7915 | −1.19133 | ||||||||
\(367\) | 28.2747 | 1.47593 | 0.737965 | − | 0.674839i | \(-0.235787\pi\) | ||||
0.737965 | + | 0.674839i | \(0.235787\pi\) | |||||||
\(368\) | −25.1414 | −1.31059 | ||||||||
\(369\) | −23.9006 | −1.24421 | ||||||||
\(370\) | 48.6580 | 2.52961 | ||||||||
\(371\) | 14.6127 | 0.758654 | ||||||||
\(372\) | 26.4174 | 1.36968 | ||||||||
\(373\) | −36.1735 | −1.87299 | −0.936495 | − | 0.350680i | \(-0.885951\pi\) | ||||
−0.936495 | + | 0.350680i | \(0.885951\pi\) | |||||||
\(374\) | −16.4913 | −0.852743 | ||||||||
\(375\) | −10.1297 | −0.523097 | ||||||||
\(376\) | 3.37735 | 0.174174 | ||||||||
\(377\) | −9.80731 | −0.505102 | ||||||||
\(378\) | 18.0729 | 0.929568 | ||||||||
\(379\) | −2.35542 | −0.120990 | −0.0604948 | − | 0.998169i | \(-0.519268\pi\) | ||||
−0.0604948 | + | 0.998169i | \(0.519268\pi\) | |||||||
\(380\) | −15.3771 | −0.788830 | ||||||||
\(381\) | 10.0734 | 0.516074 | ||||||||
\(382\) | 28.8582 | 1.47651 | ||||||||
\(383\) | 25.7036 | 1.31339 | 0.656697 | − | 0.754155i | \(-0.271953\pi\) | ||||
0.656697 | + | 0.754155i | \(0.271953\pi\) | |||||||
\(384\) | 16.4066 | 0.837247 | ||||||||
\(385\) | 3.64034 | 0.185529 | ||||||||
\(386\) | −32.3375 | −1.64594 | ||||||||
\(387\) | −10.5860 | −0.538119 | ||||||||
\(388\) | 43.2053 | 2.19342 | ||||||||
\(389\) | 1.38616 | 0.0702811 | 0.0351405 | − | 0.999382i | \(-0.488812\pi\) | ||||
0.0351405 | + | 0.999382i | \(0.488812\pi\) | |||||||
\(390\) | 4.44827 | 0.225247 | ||||||||
\(391\) | −35.9194 | −1.81652 | ||||||||
\(392\) | 22.2095 | 1.12175 | ||||||||
\(393\) | −1.49287 | −0.0753055 | ||||||||
\(394\) | 1.05015 | 0.0529057 | ||||||||
\(395\) | −13.1617 | −0.662239 | ||||||||
\(396\) | −9.82789 | −0.493870 | ||||||||
\(397\) | −29.4951 | −1.48032 | −0.740159 | − | 0.672432i | \(-0.765250\pi\) | ||||
−0.740159 | + | 0.672432i | \(0.765250\pi\) | |||||||
\(398\) | −34.1684 | −1.71271 | ||||||||
\(399\) | −2.52222 | −0.126269 | ||||||||
\(400\) | −2.65263 | −0.132631 | ||||||||
\(401\) | −1.76600 | −0.0881898 | −0.0440949 | − | 0.999027i | \(-0.514040\pi\) | ||||
−0.0440949 | + | 0.999027i | \(0.514040\pi\) | |||||||
\(402\) | −24.0355 | −1.19878 | ||||||||
\(403\) | −7.54571 | −0.375879 | ||||||||
\(404\) | 51.2239 | 2.54848 | ||||||||
\(405\) | 6.00506 | 0.298394 | ||||||||
\(406\) | −39.1149 | −1.94124 | ||||||||
\(407\) | −10.1089 | −0.501078 | ||||||||
\(408\) | −27.3340 | −1.35324 | ||||||||
\(409\) | −1.60684 | −0.0794530 | −0.0397265 | − | 0.999211i | \(-0.512649\pi\) | ||||
−0.0397265 | + | 0.999211i | \(0.512649\pi\) | |||||||
\(410\) | −54.6477 | −2.69886 | ||||||||
\(411\) | −14.3879 | −0.709701 | ||||||||
\(412\) | 23.8008 | 1.17258 | ||||||||
\(413\) | −19.1371 | −0.941674 | ||||||||
\(414\) | −31.9468 | −1.57010 | ||||||||
\(415\) | −18.8518 | −0.925398 | ||||||||
\(416\) | 0.615376 | 0.0301713 | ||||||||
\(417\) | 6.81445 | 0.333705 | ||||||||
\(418\) | 4.76778 | 0.233200 | ||||||||
\(419\) | −5.08871 | −0.248600 | −0.124300 | − | 0.992245i | \(-0.539668\pi\) | ||||
−0.124300 | + | 0.992245i | \(0.539668\pi\) | |||||||
\(420\) | 11.8875 | 0.580051 | ||||||||
\(421\) | −5.77609 | −0.281509 | −0.140755 | − | 0.990045i | \(-0.544953\pi\) | ||||
−0.140755 | + | 0.990045i | \(0.544953\pi\) | |||||||
\(422\) | −12.9457 | −0.630189 | ||||||||
\(423\) | 1.50183 | 0.0730217 | ||||||||
\(424\) | −45.7840 | −2.22347 | ||||||||
\(425\) | −3.78980 | −0.183832 | ||||||||
\(426\) | −25.3506 | −1.22824 | ||||||||
\(427\) | 17.3974 | 0.841919 | ||||||||
\(428\) | −8.80840 | −0.425770 | ||||||||
\(429\) | −0.924142 | −0.0446180 | ||||||||
\(430\) | −24.2046 | −1.16725 | ||||||||
\(431\) | −11.2740 | −0.543047 | −0.271524 | − | 0.962432i | \(-0.587528\pi\) | ||||
−0.271524 | + | 0.962432i | \(0.587528\pi\) | |||||||
\(432\) | −19.8161 | −0.953401 | ||||||||
\(433\) | 18.7754 | 0.902288 | 0.451144 | − | 0.892451i | \(-0.351016\pi\) | ||||
0.451144 | + | 0.892451i | \(0.351016\pi\) | |||||||
\(434\) | −30.0948 | −1.44460 | ||||||||
\(435\) | 17.7194 | 0.849581 | ||||||||
\(436\) | 3.41952 | 0.163765 | ||||||||
\(437\) | 10.3846 | 0.496764 | ||||||||
\(438\) | 23.1826 | 1.10771 | ||||||||
\(439\) | −14.2188 | −0.678628 | −0.339314 | − | 0.940673i | \(-0.610195\pi\) | ||||
−0.339314 | + | 0.940673i | \(0.610195\pi\) | |||||||
\(440\) | −11.4058 | −0.543749 | ||||||||
\(441\) | 9.87607 | 0.470289 | ||||||||
\(442\) | 15.3820 | 0.731648 | ||||||||
\(443\) | −19.1794 | −0.911242 | −0.455621 | − | 0.890174i | \(-0.650583\pi\) | ||||
−0.455621 | + | 0.890174i | \(0.650583\pi\) | |||||||
\(444\) | −33.0104 | −1.56661 | ||||||||
\(445\) | −32.1873 | −1.52583 | ||||||||
\(446\) | −21.0936 | −0.998813 | ||||||||
\(447\) | −1.21317 | −0.0573809 | ||||||||
\(448\) | −11.7138 | −0.553425 | ||||||||
\(449\) | 25.7033 | 1.21301 | 0.606506 | − | 0.795079i | \(-0.292571\pi\) | ||||
0.606506 | + | 0.795079i | \(0.292571\pi\) | |||||||
\(450\) | −3.37066 | −0.158894 | ||||||||
\(451\) | 11.3532 | 0.534603 | ||||||||
\(452\) | −72.0212 | −3.38759 | ||||||||
\(453\) | 18.6555 | 0.876511 | ||||||||
\(454\) | 28.0823 | 1.31797 | ||||||||
\(455\) | −3.39548 | −0.159183 | ||||||||
\(456\) | 7.90252 | 0.370069 | ||||||||
\(457\) | 0.891689 | 0.0417115 | 0.0208557 | − | 0.999782i | \(-0.493361\pi\) | ||||
0.0208557 | + | 0.999782i | \(0.493361\pi\) | |||||||
\(458\) | −49.6457 | −2.31979 | ||||||||
\(459\) | −28.3111 | −1.32145 | ||||||||
\(460\) | −48.9440 | −2.28202 | ||||||||
\(461\) | −25.9204 | −1.20723 | −0.603616 | − | 0.797275i | \(-0.706274\pi\) | ||||
−0.603616 | + | 0.797275i | \(0.706274\pi\) | |||||||
\(462\) | −3.68579 | −0.171479 | ||||||||
\(463\) | −9.50406 | −0.441691 | −0.220846 | − | 0.975309i | \(-0.570882\pi\) | ||||
−0.220846 | + | 0.975309i | \(0.570882\pi\) | |||||||
\(464\) | 42.8876 | 1.99101 | ||||||||
\(465\) | 13.6333 | 0.632227 | ||||||||
\(466\) | 37.0562 | 1.71660 | ||||||||
\(467\) | −24.5471 | −1.13590 | −0.567952 | − | 0.823062i | \(-0.692264\pi\) | ||||
−0.567952 | + | 0.823062i | \(0.692264\pi\) | |||||||
\(468\) | 9.16684 | 0.423737 | ||||||||
\(469\) | 18.3470 | 0.847184 | ||||||||
\(470\) | 3.43388 | 0.158393 | ||||||||
\(471\) | 0.649718 | 0.0299374 | ||||||||
\(472\) | 59.9596 | 2.75986 | ||||||||
\(473\) | 5.02858 | 0.231214 | ||||||||
\(474\) | 13.3261 | 0.612087 | ||||||||
\(475\) | 1.09567 | 0.0502726 | ||||||||
\(476\) | 41.1068 | 1.88412 | ||||||||
\(477\) | −20.3591 | −0.932180 | ||||||||
\(478\) | −17.2874 | −0.790709 | ||||||||
\(479\) | −0.560322 | −0.0256018 | −0.0128009 | − | 0.999918i | \(-0.504075\pi\) | ||||
−0.0128009 | + | 0.999918i | \(0.504075\pi\) | |||||||
\(480\) | −1.11183 | −0.0507481 | ||||||||
\(481\) | 9.42892 | 0.429922 | ||||||||
\(482\) | −56.1019 | −2.55537 | ||||||||
\(483\) | −8.02798 | −0.365286 | ||||||||
\(484\) | −40.0085 | −1.81857 | ||||||||
\(485\) | 22.2971 | 1.01246 | ||||||||
\(486\) | −39.5494 | −1.79400 | ||||||||
\(487\) | −17.0160 | −0.771066 | −0.385533 | − | 0.922694i | \(-0.625982\pi\) | ||||
−0.385533 | + | 0.922694i | \(0.625982\pi\) | |||||||
\(488\) | −54.5089 | −2.46750 | ||||||||
\(489\) | 13.4363 | 0.607610 | ||||||||
\(490\) | 22.5812 | 1.02012 | ||||||||
\(491\) | 39.0243 | 1.76114 | 0.880572 | − | 0.473912i | \(-0.157159\pi\) | ||||
0.880572 | + | 0.473912i | \(0.157159\pi\) | |||||||
\(492\) | 37.0739 | 1.67142 | ||||||||
\(493\) | 61.2734 | 2.75961 | ||||||||
\(494\) | −4.44708 | −0.200084 | ||||||||
\(495\) | −5.07190 | −0.227965 | ||||||||
\(496\) | 32.9976 | 1.48164 | ||||||||
\(497\) | 19.3508 | 0.868002 | ||||||||
\(498\) | 19.0872 | 0.855317 | ||||||||
\(499\) | 38.9175 | 1.74219 | 0.871093 | − | 0.491119i | \(-0.163412\pi\) | ||||
0.871093 | + | 0.491119i | \(0.163412\pi\) | |||||||
\(500\) | −47.7299 | −2.13455 | ||||||||
\(501\) | 15.8293 | 0.707202 | ||||||||
\(502\) | 28.2702 | 1.26176 | ||||||||
\(503\) | −3.80123 | −0.169489 | −0.0847443 | − | 0.996403i | \(-0.527007\pi\) | ||||
−0.0847443 | + | 0.996403i | \(0.527007\pi\) | |||||||
\(504\) | 18.5572 | 0.826604 | ||||||||
\(505\) | 26.4352 | 1.17635 | ||||||||
\(506\) | 15.1754 | 0.674628 | ||||||||
\(507\) | 0.861982 | 0.0382820 | ||||||||
\(508\) | 47.4643 | 2.10589 | ||||||||
\(509\) | 38.6940 | 1.71508 | 0.857540 | − | 0.514417i | \(-0.171992\pi\) | ||||
0.857540 | + | 0.514417i | \(0.171992\pi\) | |||||||
\(510\) | −27.7916 | −1.23063 | ||||||||
\(511\) | −17.6959 | −0.782820 | ||||||||
\(512\) | 41.7000 | 1.84290 | ||||||||
\(513\) | 8.18501 | 0.361377 | ||||||||
\(514\) | −13.1637 | −0.580628 | ||||||||
\(515\) | 12.2829 | 0.541251 | ||||||||
\(516\) | 16.4208 | 0.722884 | ||||||||
\(517\) | −0.713401 | −0.0313753 | ||||||||
\(518\) | 37.6057 | 1.65230 | ||||||||
\(519\) | 15.0388 | 0.660129 | ||||||||
\(520\) | 10.6386 | 0.466533 | ||||||||
\(521\) | −17.6906 | −0.775038 | −0.387519 | − | 0.921862i | \(-0.626668\pi\) | ||||
−0.387519 | + | 0.921862i | \(0.626668\pi\) | |||||||
\(522\) | 54.4967 | 2.38526 | ||||||||
\(523\) | −24.0101 | −1.04989 | −0.524943 | − | 0.851137i | \(-0.675913\pi\) | ||||
−0.524943 | + | 0.851137i | \(0.675913\pi\) | |||||||
\(524\) | −7.03421 | −0.307291 | ||||||||
\(525\) | −0.847019 | −0.0369669 | ||||||||
\(526\) | −11.0007 | −0.479652 | ||||||||
\(527\) | 47.1435 | 2.05360 | ||||||||
\(528\) | 4.04130 | 0.175875 | ||||||||
\(529\) | 10.0533 | 0.437100 | ||||||||
\(530\) | −46.5503 | −2.02202 | ||||||||
\(531\) | 26.6627 | 1.15706 | ||||||||
\(532\) | −11.8843 | −0.515251 | ||||||||
\(533\) | −10.5896 | −0.458686 | ||||||||
\(534\) | 32.5892 | 1.41027 | ||||||||
\(535\) | −4.54577 | −0.196531 | ||||||||
\(536\) | −57.4840 | −2.48293 | ||||||||
\(537\) | −17.8960 | −0.772268 | ||||||||
\(538\) | 32.3549 | 1.39492 | ||||||||
\(539\) | −4.69133 | −0.202070 | ||||||||
\(540\) | −38.5769 | −1.66008 | ||||||||
\(541\) | 15.2875 | 0.657259 | 0.328630 | − | 0.944459i | \(-0.393413\pi\) | ||||
0.328630 | + | 0.944459i | \(0.393413\pi\) | |||||||
\(542\) | −43.8158 | −1.88205 | ||||||||
\(543\) | 4.19949 | 0.180217 | ||||||||
\(544\) | −3.84470 | −0.164840 | ||||||||
\(545\) | 1.76472 | 0.0755922 | ||||||||
\(546\) | 3.43788 | 0.147128 | ||||||||
\(547\) | 37.2556 | 1.59294 | 0.796468 | − | 0.604681i | \(-0.206699\pi\) | ||||
0.796468 | + | 0.604681i | \(0.206699\pi\) | |||||||
\(548\) | −67.7936 | −2.89600 | ||||||||
\(549\) | −24.2389 | −1.03449 | ||||||||
\(550\) | 1.60113 | 0.0682723 | ||||||||
\(551\) | −17.7147 | −0.754671 | ||||||||
\(552\) | 25.1530 | 1.07058 | ||||||||
\(553\) | −10.1722 | −0.432564 | ||||||||
\(554\) | −23.7985 | −1.01110 | ||||||||
\(555\) | −17.0357 | −0.723127 | ||||||||
\(556\) | 32.1087 | 1.36171 | ||||||||
\(557\) | 36.5212 | 1.54745 | 0.773726 | − | 0.633521i | \(-0.218391\pi\) | ||||
0.773726 | + | 0.633521i | \(0.218391\pi\) | |||||||
\(558\) | 41.9296 | 1.77502 | ||||||||
\(559\) | −4.69034 | −0.198380 | ||||||||
\(560\) | 14.8485 | 0.627465 | ||||||||
\(561\) | 5.77379 | 0.243770 | ||||||||
\(562\) | −27.1970 | −1.14724 | ||||||||
\(563\) | −30.6850 | −1.29322 | −0.646610 | − | 0.762821i | \(-0.723814\pi\) | ||||
−0.646610 | + | 0.762821i | \(0.723814\pi\) | |||||||
\(564\) | −2.32961 | −0.0980941 | ||||||||
\(565\) | −37.1681 | −1.56367 | ||||||||
\(566\) | −15.9067 | −0.668609 | ||||||||
\(567\) | 4.64106 | 0.194906 | ||||||||
\(568\) | −60.6292 | −2.54394 | ||||||||
\(569\) | 1.20675 | 0.0505896 | 0.0252948 | − | 0.999680i | \(-0.491948\pi\) | ||||
0.0252948 | + | 0.999680i | \(0.491948\pi\) | |||||||
\(570\) | 8.03479 | 0.336540 | ||||||||
\(571\) | 30.3315 | 1.26934 | 0.634668 | − | 0.772785i | \(-0.281137\pi\) | ||||
0.634668 | + | 0.772785i | \(0.281137\pi\) | |||||||
\(572\) | −4.35443 | −0.182068 | ||||||||
\(573\) | −10.1036 | −0.422083 | ||||||||
\(574\) | −42.2349 | −1.76285 | ||||||||
\(575\) | 3.48740 | 0.145435 | ||||||||
\(576\) | 16.3202 | 0.680010 | ||||||||
\(577\) | −7.66150 | −0.318952 | −0.159476 | − | 0.987202i | \(-0.550981\pi\) | ||||
−0.159476 | + | 0.987202i | \(0.550981\pi\) | |||||||
\(578\) | −54.2483 | −2.25643 | ||||||||
\(579\) | 11.3218 | 0.470516 | ||||||||
\(580\) | 83.4914 | 3.46679 | ||||||||
\(581\) | −14.5698 | −0.604455 | ||||||||
\(582\) | −22.5755 | −0.935783 | ||||||||
\(583\) | 9.67098 | 0.400531 | ||||||||
\(584\) | 55.4441 | 2.29429 | ||||||||
\(585\) | 4.73075 | 0.195592 | ||||||||
\(586\) | −74.0897 | −3.06062 | ||||||||
\(587\) | −19.6544 | −0.811223 | −0.405611 | − | 0.914046i | \(-0.632941\pi\) | ||||
−0.405611 | + | 0.914046i | \(0.632941\pi\) | |||||||
\(588\) | −15.3195 | −0.631765 | ||||||||
\(589\) | −13.6296 | −0.561599 | ||||||||
\(590\) | 60.9632 | 2.50982 | ||||||||
\(591\) | −0.367669 | −0.0151239 | ||||||||
\(592\) | −41.2329 | −1.69466 | ||||||||
\(593\) | −17.0040 | −0.698269 | −0.349135 | − | 0.937073i | \(-0.613524\pi\) | ||||
−0.349135 | + | 0.937073i | \(0.613524\pi\) | |||||||
\(594\) | 11.9610 | 0.490765 | ||||||||
\(595\) | 21.2140 | 0.869691 | ||||||||
\(596\) | −5.71628 | −0.234148 | ||||||||
\(597\) | 11.9628 | 0.489604 | ||||||||
\(598\) | −14.1546 | −0.578826 | ||||||||
\(599\) | −0.192914 | −0.00788227 | −0.00394113 | − | 0.999992i | \(-0.501255\pi\) | ||||
−0.00394113 | + | 0.999992i | \(0.501255\pi\) | |||||||
\(600\) | 2.65385 | 0.108343 | ||||||||
\(601\) | −20.0409 | −0.817486 | −0.408743 | − | 0.912650i | \(-0.634033\pi\) | ||||
−0.408743 | + | 0.912650i | \(0.634033\pi\) | |||||||
\(602\) | −18.7067 | −0.762427 | ||||||||
\(603\) | −25.5619 | −1.04096 | ||||||||
\(604\) | 87.9020 | 3.57668 | ||||||||
\(605\) | −20.6473 | −0.839431 | ||||||||
\(606\) | −26.7653 | −1.08726 | ||||||||
\(607\) | −34.4452 | −1.39809 | −0.699043 | − | 0.715080i | \(-0.746390\pi\) | ||||
−0.699043 | + | 0.715080i | \(0.746390\pi\) | |||||||
\(608\) | 1.11154 | 0.0450788 | ||||||||
\(609\) | 13.6946 | 0.554932 | ||||||||
\(610\) | −55.4213 | −2.24394 | ||||||||
\(611\) | 0.665416 | 0.0269198 | ||||||||
\(612\) | −57.2719 | −2.31508 | ||||||||
\(613\) | 39.1710 | 1.58210 | 0.791050 | − | 0.611751i | \(-0.209535\pi\) | ||||
0.791050 | + | 0.611751i | \(0.209535\pi\) | |||||||
\(614\) | 85.0945 | 3.43413 | ||||||||
\(615\) | 19.1328 | 0.771509 | ||||||||
\(616\) | −8.81504 | −0.355168 | ||||||||
\(617\) | 1.00000 | 0.0402585 | ||||||||
\(618\) | −12.4363 | −0.500261 | ||||||||
\(619\) | −19.1204 | −0.768514 | −0.384257 | − | 0.923226i | \(-0.625542\pi\) | ||||
−0.384257 | + | 0.923226i | \(0.625542\pi\) | |||||||
\(620\) | 64.2380 | 2.57986 | ||||||||
\(621\) | 26.0521 | 1.04543 | ||||||||
\(622\) | −63.2614 | −2.53655 | ||||||||
\(623\) | −24.8762 | −0.996645 | ||||||||
\(624\) | −3.76947 | −0.150900 | ||||||||
\(625\) | −21.5991 | −0.863964 | ||||||||
\(626\) | 4.35278 | 0.173972 | ||||||||
\(627\) | −1.66925 | −0.0666636 | ||||||||
\(628\) | 3.06138 | 0.122162 | ||||||||
\(629\) | −58.9093 | −2.34887 | ||||||||
\(630\) | 18.8678 | 0.751712 | ||||||||
\(631\) | 10.1908 | 0.405691 | 0.202846 | − | 0.979211i | \(-0.434981\pi\) | ||||
0.202846 | + | 0.979211i | \(0.434981\pi\) | |||||||
\(632\) | 31.8710 | 1.26776 | ||||||||
\(633\) | 4.53246 | 0.180149 | ||||||||
\(634\) | 7.14994 | 0.283960 | ||||||||
\(635\) | 24.4950 | 0.972054 | ||||||||
\(636\) | 31.5805 | 1.25225 | ||||||||
\(637\) | 4.37578 | 0.173375 | ||||||||
\(638\) | −25.8870 | −1.02488 | ||||||||
\(639\) | −26.9605 | −1.06654 | ||||||||
\(640\) | 39.8953 | 1.57700 | ||||||||
\(641\) | −31.4730 | −1.24311 | −0.621555 | − | 0.783371i | \(-0.713499\pi\) | ||||
−0.621555 | + | 0.783371i | \(0.713499\pi\) | |||||||
\(642\) | 4.60252 | 0.181647 | ||||||||
\(643\) | 38.9123 | 1.53455 | 0.767275 | − | 0.641318i | \(-0.221612\pi\) | ||||
0.767275 | + | 0.641318i | \(0.221612\pi\) | |||||||
\(644\) | −37.8267 | −1.49058 | ||||||||
\(645\) | 8.47430 | 0.333675 | ||||||||
\(646\) | 27.7842 | 1.09315 | ||||||||
\(647\) | 18.5325 | 0.728586 | 0.364293 | − | 0.931284i | \(-0.381311\pi\) | ||||
0.364293 | + | 0.931284i | \(0.381311\pi\) | |||||||
\(648\) | −14.5412 | −0.571232 | ||||||||
\(649\) | −12.6653 | −0.497157 | ||||||||
\(650\) | −1.49343 | −0.0585772 | ||||||||
\(651\) | 10.5366 | 0.412960 | ||||||||
\(652\) | 63.3099 | 2.47941 | ||||||||
\(653\) | 33.4600 | 1.30939 | 0.654696 | − | 0.755893i | \(-0.272797\pi\) | ||||
0.654696 | + | 0.755893i | \(0.272797\pi\) | |||||||
\(654\) | −1.78675 | −0.0698675 | ||||||||
\(655\) | −3.63016 | −0.141842 | ||||||||
\(656\) | 46.3086 | 1.80805 | ||||||||
\(657\) | 24.6548 | 0.961874 | ||||||||
\(658\) | 2.65390 | 0.103460 | ||||||||
\(659\) | −45.8469 | −1.78594 | −0.892970 | − | 0.450116i | \(-0.851383\pi\) | ||||
−0.892970 | + | 0.450116i | \(0.851383\pi\) | |||||||
\(660\) | 7.86739 | 0.306238 | ||||||||
\(661\) | −6.31898 | −0.245780 | −0.122890 | − | 0.992420i | \(-0.539216\pi\) | ||||
−0.122890 | + | 0.992420i | \(0.539216\pi\) | |||||||
\(662\) | −71.7496 | −2.78863 | ||||||||
\(663\) | −5.38543 | −0.209153 | ||||||||
\(664\) | 45.6494 | 1.77154 | ||||||||
\(665\) | −6.13317 | −0.237834 | ||||||||
\(666\) | −52.3941 | −2.03023 | ||||||||
\(667\) | −56.3842 | −2.18320 | ||||||||
\(668\) | 74.5855 | 2.88580 | ||||||||
\(669\) | 7.38514 | 0.285526 | ||||||||
\(670\) | −58.4462 | −2.25797 | ||||||||
\(671\) | 11.5140 | 0.444491 | ||||||||
\(672\) | −0.859290 | −0.0331478 | ||||||||
\(673\) | 21.2221 | 0.818052 | 0.409026 | − | 0.912523i | \(-0.365869\pi\) | ||||
0.409026 | + | 0.912523i | \(0.365869\pi\) | |||||||
\(674\) | 60.1089 | 2.31531 | ||||||||
\(675\) | 2.74871 | 0.105798 | ||||||||
\(676\) | 4.06154 | 0.156213 | ||||||||
\(677\) | 9.83953 | 0.378164 | 0.189082 | − | 0.981961i | \(-0.439449\pi\) | ||||
0.189082 | + | 0.981961i | \(0.439449\pi\) | |||||||
\(678\) | 37.6322 | 1.44525 | ||||||||
\(679\) | 17.2325 | 0.661321 | ||||||||
\(680\) | −66.4670 | −2.54889 | ||||||||
\(681\) | −9.83194 | −0.376761 | ||||||||
\(682\) | −19.9174 | −0.762676 | ||||||||
\(683\) | 7.92854 | 0.303377 | 0.151688 | − | 0.988428i | \(-0.451529\pi\) | ||||
0.151688 | + | 0.988428i | \(0.451529\pi\) | |||||||
\(684\) | 16.5578 | 0.633104 | ||||||||
\(685\) | −34.9864 | −1.33676 | ||||||||
\(686\) | 45.3704 | 1.73225 | ||||||||
\(687\) | 17.3815 | 0.663147 | ||||||||
\(688\) | 20.5110 | 0.781975 | ||||||||
\(689\) | −9.02049 | −0.343653 | ||||||||
\(690\) | 25.5740 | 0.973585 | ||||||||
\(691\) | −6.72619 | −0.255876 | −0.127938 | − | 0.991782i | \(-0.540836\pi\) | ||||
−0.127938 | + | 0.991782i | \(0.540836\pi\) | |||||||
\(692\) | 70.8606 | 2.69372 | ||||||||
\(693\) | −3.91985 | −0.148903 | ||||||||
\(694\) | 2.52949 | 0.0960183 | ||||||||
\(695\) | 16.5704 | 0.628552 | ||||||||
\(696\) | −42.9073 | −1.62640 | ||||||||
\(697\) | 66.1609 | 2.50602 | ||||||||
\(698\) | 87.4315 | 3.30933 | ||||||||
\(699\) | −12.9738 | −0.490715 | ||||||||
\(700\) | −3.99103 | −0.150847 | ||||||||
\(701\) | −34.3687 | −1.29809 | −0.649045 | − | 0.760750i | \(-0.724831\pi\) | ||||
−0.649045 | + | 0.760750i | \(0.724831\pi\) | |||||||
\(702\) | −11.1565 | −0.421074 | ||||||||
\(703\) | 17.0312 | 0.642344 | ||||||||
\(704\) | −7.75243 | −0.292181 | ||||||||
\(705\) | −1.20224 | −0.0452791 | ||||||||
\(706\) | −49.2368 | −1.85305 | ||||||||
\(707\) | 20.4306 | 0.768374 | ||||||||
\(708\) | −41.3585 | −1.55435 | ||||||||
\(709\) | 12.8276 | 0.481751 | 0.240876 | − | 0.970556i | \(-0.422565\pi\) | ||||
0.240876 | + | 0.970556i | \(0.422565\pi\) | |||||||
\(710\) | −61.6440 | −2.31346 | ||||||||
\(711\) | 14.1723 | 0.531504 | ||||||||
\(712\) | 77.9413 | 2.92097 | ||||||||
\(713\) | −43.3818 | −1.62466 | ||||||||
\(714\) | −21.4789 | −0.803828 | ||||||||
\(715\) | −2.24720 | −0.0840405 | ||||||||
\(716\) | −84.3232 | −3.15131 | ||||||||
\(717\) | 6.05254 | 0.226036 | ||||||||
\(718\) | 10.6804 | 0.398588 | ||||||||
\(719\) | 10.9049 | 0.406683 | 0.203342 | − | 0.979108i | \(-0.434820\pi\) | ||||
0.203342 | + | 0.979108i | \(0.434820\pi\) | |||||||
\(720\) | −20.6877 | −0.770985 | ||||||||
\(721\) | 9.49296 | 0.353536 | ||||||||
\(722\) | 38.7457 | 1.44197 | ||||||||
\(723\) | 19.6420 | 0.730492 | ||||||||
\(724\) | 19.7874 | 0.735393 | ||||||||
\(725\) | −5.94900 | −0.220940 | ||||||||
\(726\) | 20.9051 | 0.775860 | ||||||||
\(727\) | 2.49591 | 0.0925682 | 0.0462841 | − | 0.998928i | \(-0.485262\pi\) | ||||
0.0462841 | + | 0.998928i | \(0.485262\pi\) | |||||||
\(728\) | 8.22212 | 0.304732 | ||||||||
\(729\) | 5.25189 | 0.194515 | ||||||||
\(730\) | 56.3721 | 2.08643 | ||||||||
\(731\) | 29.3040 | 1.08385 | ||||||||
\(732\) | 37.5987 | 1.38969 | ||||||||
\(733\) | −11.4348 | −0.422353 | −0.211176 | − | 0.977448i | \(-0.567729\pi\) | ||||
−0.211176 | + | 0.977448i | \(0.567729\pi\) | |||||||
\(734\) | −69.6129 | −2.56946 | ||||||||
\(735\) | −7.90596 | −0.291616 | ||||||||
\(736\) | 3.53792 | 0.130410 | ||||||||
\(737\) | 12.1424 | 0.447271 | ||||||||
\(738\) | 58.8437 | 2.16607 | ||||||||
\(739\) | 16.6609 | 0.612880 | 0.306440 | − | 0.951890i | \(-0.400862\pi\) | ||||
0.306440 | + | 0.951890i | \(0.400862\pi\) | |||||||
\(740\) | −80.2701 | −2.95079 | ||||||||
\(741\) | 1.55698 | 0.0571970 | ||||||||
\(742\) | −35.9768 | −1.32075 | ||||||||
\(743\) | 33.5440 | 1.23061 | 0.615305 | − | 0.788289i | \(-0.289033\pi\) | ||||
0.615305 | + | 0.788289i | \(0.289033\pi\) | |||||||
\(744\) | −33.0128 | −1.21031 | ||||||||
\(745\) | −2.95001 | −0.108080 | ||||||||
\(746\) | 89.0598 | 3.26071 | ||||||||
\(747\) | 20.2993 | 0.742712 | ||||||||
\(748\) | 27.2053 | 0.994724 | ||||||||
\(749\) | −3.51323 | −0.128371 | ||||||||
\(750\) | 24.9396 | 0.910665 | ||||||||
\(751\) | −1.89249 | −0.0690578 | −0.0345289 | − | 0.999404i | \(-0.510993\pi\) | ||||
−0.0345289 | + | 0.999404i | \(0.510993\pi\) | |||||||
\(752\) | −2.90988 | −0.106112 | ||||||||
\(753\) | −9.89773 | −0.360693 | ||||||||
\(754\) | 24.1458 | 0.879338 | ||||||||
\(755\) | 45.3637 | 1.65096 | ||||||||
\(756\) | −29.8144 | −1.08434 | ||||||||
\(757\) | 14.6684 | 0.533133 | 0.266567 | − | 0.963817i | \(-0.414111\pi\) | ||||
0.266567 | + | 0.963817i | \(0.414111\pi\) | |||||||
\(758\) | 5.79908 | 0.210632 | ||||||||
\(759\) | −5.31308 | −0.192853 | ||||||||
\(760\) | 19.2162 | 0.697046 | ||||||||
\(761\) | −22.3364 | −0.809695 | −0.404847 | − | 0.914384i | \(-0.632675\pi\) | ||||
−0.404847 | + | 0.914384i | \(0.632675\pi\) | |||||||
\(762\) | −24.8008 | −0.898439 | ||||||||
\(763\) | 1.36388 | 0.0493756 | ||||||||
\(764\) | −47.6067 | −1.72235 | ||||||||
\(765\) | −29.5564 | −1.06861 | ||||||||
\(766\) | −63.2828 | −2.28650 | ||||||||
\(767\) | 11.8134 | 0.426558 | ||||||||
\(768\) | −27.9274 | −1.00774 | ||||||||
\(769\) | 0.408255 | 0.0147221 | 0.00736103 | − | 0.999973i | \(-0.497657\pi\) | ||||
0.00736103 | + | 0.999973i | \(0.497657\pi\) | |||||||
\(770\) | −8.96259 | −0.322989 | ||||||||
\(771\) | 4.60879 | 0.165981 | ||||||||
\(772\) | 53.3465 | 1.91998 | ||||||||
\(773\) | 47.2755 | 1.70038 | 0.850191 | − | 0.526474i | \(-0.176486\pi\) | ||||
0.850191 | + | 0.526474i | \(0.176486\pi\) | |||||||
\(774\) | 26.0630 | 0.936816 | ||||||||
\(775\) | −4.57714 | −0.164416 | ||||||||
\(776\) | −53.9921 | −1.93820 | ||||||||
\(777\) | −13.1662 | −0.472335 | ||||||||
\(778\) | −3.41275 | −0.122353 | ||||||||
\(779\) | −19.1277 | −0.685322 | ||||||||
\(780\) | −7.33821 | −0.262750 | ||||||||
\(781\) | 12.8067 | 0.458261 | ||||||||
\(782\) | 88.4343 | 3.16241 | ||||||||
\(783\) | −44.4411 | −1.58820 | ||||||||
\(784\) | −19.1354 | −0.683407 | ||||||||
\(785\) | 1.57989 | 0.0563888 | ||||||||
\(786\) | 3.67548 | 0.131100 | ||||||||
\(787\) | 7.90451 | 0.281765 | 0.140883 | − | 0.990026i | \(-0.455006\pi\) | ||||
0.140883 | + | 0.990026i | \(0.455006\pi\) | |||||||
\(788\) | −1.73241 | −0.0617144 | ||||||||
\(789\) | 3.85146 | 0.137116 | ||||||||
\(790\) | 32.4045 | 1.15290 | ||||||||
\(791\) | −28.7256 | −1.02137 | ||||||||
\(792\) | 12.2815 | 0.436405 | ||||||||
\(793\) | −10.7395 | −0.381371 | ||||||||
\(794\) | 72.6175 | 2.57710 | ||||||||
\(795\) | 16.2978 | 0.578024 | ||||||||
\(796\) | 56.3669 | 1.99787 | ||||||||
\(797\) | 4.91985 | 0.174270 | 0.0871349 | − | 0.996197i | \(-0.472229\pi\) | ||||
0.0871349 | + | 0.996197i | \(0.472229\pi\) | |||||||
\(798\) | 6.20975 | 0.219823 | ||||||||
\(799\) | −4.15734 | −0.147076 | ||||||||
\(800\) | 0.373280 | 0.0131974 | ||||||||
\(801\) | 34.6588 | 1.22461 | ||||||||
\(802\) | 4.34793 | 0.153531 | ||||||||
\(803\) | −11.7115 | −0.413290 | ||||||||
\(804\) | 39.6509 | 1.39838 | ||||||||
\(805\) | −19.5213 | −0.688036 | ||||||||
\(806\) | 18.5777 | 0.654371 | ||||||||
\(807\) | −11.3278 | −0.398759 | ||||||||
\(808\) | −64.0125 | −2.25195 | ||||||||
\(809\) | 5.74676 | 0.202045 | 0.101023 | − | 0.994884i | \(-0.467789\pi\) | ||||
0.101023 | + | 0.994884i | \(0.467789\pi\) | |||||||
\(810\) | −14.7846 | −0.519477 | ||||||||
\(811\) | 49.6950 | 1.74503 | 0.872514 | − | 0.488589i | \(-0.162488\pi\) | ||||
0.872514 | + | 0.488589i | \(0.162488\pi\) | |||||||
\(812\) | 64.5269 | 2.26445 | ||||||||
\(813\) | 15.3404 | 0.538012 | ||||||||
\(814\) | 24.8882 | 0.872332 | ||||||||
\(815\) | 32.6725 | 1.14447 | ||||||||
\(816\) | 23.5506 | 0.824437 | ||||||||
\(817\) | −8.47205 | −0.296399 | ||||||||
\(818\) | 3.95607 | 0.138321 | ||||||||
\(819\) | 3.65620 | 0.127758 | ||||||||
\(820\) | 90.1511 | 3.14821 | ||||||||
\(821\) | 44.4519 | 1.55138 | 0.775692 | − | 0.631112i | \(-0.217401\pi\) | ||||
0.775692 | + | 0.631112i | \(0.217401\pi\) | |||||||
\(822\) | 35.4232 | 1.23553 | ||||||||
\(823\) | 20.7645 | 0.723805 | 0.361902 | − | 0.932216i | \(-0.382127\pi\) | ||||
0.361902 | + | 0.932216i | \(0.382127\pi\) | |||||||
\(824\) | −29.7430 | −1.03615 | ||||||||
\(825\) | −0.560574 | −0.0195167 | ||||||||
\(826\) | 47.1159 | 1.63937 | ||||||||
\(827\) | 4.87217 | 0.169422 | 0.0847109 | − | 0.996406i | \(-0.473003\pi\) | ||||
0.0847109 | + | 0.996406i | \(0.473003\pi\) | |||||||
\(828\) | 52.7020 | 1.83152 | ||||||||
\(829\) | −3.76033 | −0.130602 | −0.0653009 | − | 0.997866i | \(-0.520801\pi\) | ||||
−0.0653009 | + | 0.997866i | \(0.520801\pi\) | |||||||
\(830\) | 46.4135 | 1.61104 | ||||||||
\(831\) | 8.33213 | 0.289038 | ||||||||
\(832\) | 7.23099 | 0.250689 | ||||||||
\(833\) | −27.3386 | −0.947228 | ||||||||
\(834\) | −16.7773 | −0.580951 | ||||||||
\(835\) | 38.4915 | 1.33205 | ||||||||
\(836\) | −7.86530 | −0.272027 | ||||||||
\(837\) | −34.1929 | −1.18188 | ||||||||
\(838\) | 12.5285 | 0.432790 | ||||||||
\(839\) | 42.5976 | 1.47063 | 0.735317 | − | 0.677723i | \(-0.237033\pi\) | ||||
0.735317 | + | 0.677723i | \(0.237033\pi\) | |||||||
\(840\) | −14.8554 | −0.512558 | ||||||||
\(841\) | 67.1833 | 2.31667 | ||||||||
\(842\) | 14.2208 | 0.490083 | ||||||||
\(843\) | 9.52198 | 0.327955 | ||||||||
\(844\) | 21.3563 | 0.735115 | ||||||||
\(845\) | 2.09605 | 0.0721062 | ||||||||
\(846\) | −3.69755 | −0.127124 | ||||||||
\(847\) | −15.9574 | −0.548303 | ||||||||
\(848\) | 39.4469 | 1.35461 | ||||||||
\(849\) | 5.56913 | 0.191132 | ||||||||
\(850\) | 9.33056 | 0.320035 | ||||||||
\(851\) | 54.2087 | 1.85825 | ||||||||
\(852\) | 41.8203 | 1.43274 | ||||||||
\(853\) | −19.4839 | −0.667115 | −0.333557 | − | 0.942730i | \(-0.608249\pi\) | ||||
−0.333557 | + | 0.942730i | \(0.608249\pi\) | |||||||
\(854\) | −42.8327 | −1.46571 | ||||||||
\(855\) | 8.54503 | 0.292234 | ||||||||
\(856\) | 11.0075 | 0.376229 | ||||||||
\(857\) | −3.07651 | −0.105091 | −0.0525457 | − | 0.998619i | \(-0.516734\pi\) | ||||
−0.0525457 | + | 0.998619i | \(0.516734\pi\) | |||||||
\(858\) | 2.27526 | 0.0776760 | ||||||||
\(859\) | 12.5303 | 0.427527 | 0.213764 | − | 0.976885i | \(-0.431428\pi\) | ||||
0.213764 | + | 0.976885i | \(0.431428\pi\) | |||||||
\(860\) | 39.9297 | 1.36159 | ||||||||
\(861\) | 14.7869 | 0.503938 | ||||||||
\(862\) | 27.7567 | 0.945397 | ||||||||
\(863\) | −3.84060 | −0.130736 | −0.0653678 | − | 0.997861i | \(-0.520822\pi\) | ||||
−0.0653678 | + | 0.997861i | \(0.520822\pi\) | |||||||
\(864\) | 2.78853 | 0.0948679 | ||||||||
\(865\) | 36.5692 | 1.24339 | ||||||||
\(866\) | −46.2254 | −1.57080 | ||||||||
\(867\) | 18.9930 | 0.645036 | ||||||||
\(868\) | 49.6468 | 1.68512 | ||||||||
\(869\) | −6.73214 | −0.228372 | ||||||||
\(870\) | −43.6255 | −1.47904 | ||||||||
\(871\) | −11.3257 | −0.383756 | ||||||||
\(872\) | −4.27324 | −0.144710 | ||||||||
\(873\) | −24.0091 | −0.812584 | ||||||||
\(874\) | −25.5672 | −0.864823 | ||||||||
\(875\) | −19.0371 | −0.643570 | ||||||||
\(876\) | −38.2438 | −1.29214 | ||||||||
\(877\) | −39.8981 | −1.34726 | −0.673631 | − | 0.739068i | \(-0.735266\pi\) | ||||
−0.673631 | + | 0.739068i | \(0.735266\pi\) | |||||||
\(878\) | 35.0071 | 1.18143 | ||||||||
\(879\) | 25.9397 | 0.874923 | ||||||||
\(880\) | 9.82706 | 0.331270 | ||||||||
\(881\) | 2.59734 | 0.0875065 | 0.0437533 | − | 0.999042i | \(-0.486068\pi\) | ||||
0.0437533 | + | 0.999042i | \(0.486068\pi\) | |||||||
\(882\) | −24.3151 | −0.818731 | ||||||||
\(883\) | 0.0735091 | 0.00247378 | 0.00123689 | − | 0.999999i | \(-0.499606\pi\) | ||||
0.00123689 | + | 0.999999i | \(0.499606\pi\) | |||||||
\(884\) | −25.3754 | −0.853467 | ||||||||
\(885\) | −21.3439 | −0.717469 | ||||||||
\(886\) | 47.2201 | 1.58639 | ||||||||
\(887\) | −49.8423 | −1.67354 | −0.836770 | − | 0.547554i | \(-0.815559\pi\) | ||||
−0.836770 | + | 0.547554i | \(0.815559\pi\) | |||||||
\(888\) | 41.2519 | 1.38432 | ||||||||
\(889\) | 18.9311 | 0.634930 | ||||||||
\(890\) | 79.2459 | 2.65633 | ||||||||
\(891\) | 3.07155 | 0.102901 | ||||||||
\(892\) | 34.7977 | 1.16511 | ||||||||
\(893\) | 1.20192 | 0.0402208 | ||||||||
\(894\) | 2.98685 | 0.0998950 | ||||||||
\(895\) | −43.5169 | −1.45461 | ||||||||
\(896\) | 30.8334 | 1.03007 | ||||||||
\(897\) | 4.95571 | 0.165466 | ||||||||
\(898\) | −63.2820 | −2.11175 | ||||||||
\(899\) | 74.0031 | 2.46814 | ||||||||
\(900\) | 5.56050 | 0.185350 | ||||||||
\(901\) | 56.3575 | 1.87754 | ||||||||
\(902\) | −27.9519 | −0.930697 | ||||||||
\(903\) | 6.54943 | 0.217951 | ||||||||
\(904\) | 90.0021 | 2.99343 | ||||||||
\(905\) | 10.2117 | 0.339449 | ||||||||
\(906\) | −45.9301 | −1.52593 | ||||||||
\(907\) | −14.7939 | −0.491222 | −0.245611 | − | 0.969368i | \(-0.578989\pi\) | ||||
−0.245611 | + | 0.969368i | \(0.578989\pi\) | |||||||
\(908\) | −46.3267 | −1.53741 | ||||||||
\(909\) | −28.4650 | −0.944123 | ||||||||
\(910\) | 8.35974 | 0.277123 | ||||||||
\(911\) | −23.1757 | −0.767845 | −0.383923 | − | 0.923365i | \(-0.625427\pi\) | ||||
−0.383923 | + | 0.923365i | \(0.625427\pi\) | |||||||
\(912\) | −6.80870 | −0.225459 | ||||||||
\(913\) | −9.64256 | −0.319122 | ||||||||
\(914\) | −2.19536 | −0.0726159 | ||||||||
\(915\) | 19.4036 | 0.641465 | ||||||||
\(916\) | 81.8994 | 2.70603 | ||||||||
\(917\) | −2.80559 | −0.0926489 | ||||||||
\(918\) | 69.7026 | 2.30053 | ||||||||
\(919\) | −26.9805 | −0.890003 | −0.445002 | − | 0.895530i | \(-0.646797\pi\) | ||||
−0.445002 | + | 0.895530i | \(0.646797\pi\) | |||||||
\(920\) | 61.1634 | 2.01650 | ||||||||
\(921\) | −29.7926 | −0.981699 | ||||||||
\(922\) | 63.8165 | 2.10168 | ||||||||
\(923\) | −11.9453 | −0.393186 | ||||||||
\(924\) | 6.08037 | 0.200030 | ||||||||
\(925\) | 5.71947 | 0.188055 | ||||||||
\(926\) | 23.3992 | 0.768945 | ||||||||
\(927\) | −13.2260 | −0.434400 | ||||||||
\(928\) | −6.03518 | −0.198115 | ||||||||
\(929\) | −39.8449 | −1.30727 | −0.653635 | − | 0.756810i | \(-0.726757\pi\) | ||||
−0.653635 | + | 0.756810i | \(0.726757\pi\) | |||||||
\(930\) | −33.5653 | −1.10065 | ||||||||
\(931\) | 7.90385 | 0.259038 | ||||||||
\(932\) | −61.1308 | −2.00241 | ||||||||
\(933\) | 22.1486 | 0.725112 | ||||||||
\(934\) | 60.4354 | 1.97751 | ||||||||
\(935\) | 14.0399 | 0.459153 | ||||||||
\(936\) | −11.4555 | −0.374433 | ||||||||
\(937\) | 33.7360 | 1.10211 | 0.551053 | − | 0.834470i | \(-0.314226\pi\) | ||||
0.551053 | + | 0.834470i | \(0.314226\pi\) | |||||||
\(938\) | −45.1706 | −1.47487 | ||||||||
\(939\) | −1.52396 | −0.0497325 | ||||||||
\(940\) | −5.66480 | −0.184766 | ||||||||
\(941\) | −41.7588 | −1.36130 | −0.680649 | − | 0.732610i | \(-0.738302\pi\) | ||||
−0.680649 | + | 0.732610i | \(0.738302\pi\) | |||||||
\(942\) | −1.59962 | −0.0521184 | ||||||||
\(943\) | −60.8817 | −1.98258 | ||||||||
\(944\) | −51.6604 | −1.68140 | ||||||||
\(945\) | −15.3864 | −0.500519 | ||||||||
\(946\) | −12.3805 | −0.402523 | ||||||||
\(947\) | 9.92705 | 0.322586 | 0.161293 | − | 0.986907i | \(-0.448434\pi\) | ||||
0.161293 | + | 0.986907i | \(0.448434\pi\) | |||||||
\(948\) | −21.9837 | −0.713999 | ||||||||
\(949\) | 10.9238 | 0.354600 | ||||||||
\(950\) | −2.69755 | −0.0875201 | ||||||||
\(951\) | −2.50328 | −0.0811744 | ||||||||
\(952\) | −51.3695 | −1.66490 | ||||||||
\(953\) | 5.11948 | 0.165836 | 0.0829180 | − | 0.996556i | \(-0.473576\pi\) | ||||
0.0829180 | + | 0.996556i | \(0.473576\pi\) | |||||||
\(954\) | 50.1246 | 1.62284 | ||||||||
\(955\) | −24.5685 | −0.795017 | ||||||||
\(956\) | 28.5187 | 0.922361 | ||||||||
\(957\) | 9.06335 | 0.292976 | ||||||||
\(958\) | 1.37952 | 0.0445704 | ||||||||
\(959\) | −27.0395 | −0.873150 | ||||||||
\(960\) | −13.0646 | −0.421659 | ||||||||
\(961\) | 25.9377 | 0.836702 | ||||||||
\(962\) | −23.2142 | −0.748455 | ||||||||
\(963\) | 4.89480 | 0.157733 | ||||||||
\(964\) | 92.5501 | 2.98084 | ||||||||
\(965\) | 27.5306 | 0.886242 | ||||||||
\(966\) | 19.7650 | 0.635930 | ||||||||
\(967\) | −34.4432 | −1.10762 | −0.553810 | − | 0.832643i | \(-0.686827\pi\) | ||||
−0.553810 | + | 0.832643i | \(0.686827\pi\) | |||||||
\(968\) | 49.9971 | 1.60697 | ||||||||
\(969\) | −9.72756 | −0.312494 | ||||||||
\(970\) | −54.8958 | −1.76260 | ||||||||
\(971\) | 3.50594 | 0.112511 | 0.0562555 | − | 0.998416i | \(-0.482084\pi\) | ||||
0.0562555 | + | 0.998416i | \(0.482084\pi\) | |||||||
\(972\) | 65.2439 | 2.09270 | ||||||||
\(973\) | 12.8066 | 0.410560 | ||||||||
\(974\) | 41.8936 | 1.34236 | ||||||||
\(975\) | 0.522869 | 0.0167452 | ||||||||
\(976\) | 46.9641 | 1.50328 | ||||||||
\(977\) | −45.5511 | −1.45731 | −0.728655 | − | 0.684881i | \(-0.759854\pi\) | ||||
−0.728655 | + | 0.684881i | \(0.759854\pi\) | |||||||
\(978\) | −33.0804 | −1.05779 | ||||||||
\(979\) | −16.4636 | −0.526179 | ||||||||
\(980\) | −37.2518 | −1.18996 | ||||||||
\(981\) | −1.90022 | −0.0606693 | ||||||||
\(982\) | −96.0787 | −3.06599 | ||||||||
\(983\) | −3.30066 | −0.105275 | −0.0526373 | − | 0.998614i | \(-0.516763\pi\) | ||||
−0.0526373 | + | 0.998614i | \(0.516763\pi\) | |||||||
\(984\) | −46.3299 | −1.47694 | ||||||||
\(985\) | −0.894047 | −0.0284867 | ||||||||
\(986\) | −150.856 | −4.80424 | ||||||||
\(987\) | −0.929163 | −0.0295756 | ||||||||
\(988\) | 7.33626 | 0.233397 | ||||||||
\(989\) | −26.9657 | −0.857460 | ||||||||
\(990\) | 12.4871 | 0.396866 | ||||||||
\(991\) | 20.3731 | 0.647174 | 0.323587 | − | 0.946198i | \(-0.395111\pi\) | ||||
0.323587 | + | 0.946198i | \(0.395111\pi\) | |||||||
\(992\) | −4.64345 | −0.147430 | ||||||||
\(993\) | 25.1204 | 0.797171 | ||||||||
\(994\) | −47.6420 | −1.51111 | ||||||||
\(995\) | 29.0894 | 0.922196 | ||||||||
\(996\) | −31.4877 | −0.997726 | ||||||||
\(997\) | 42.5126 | 1.34639 | 0.673193 | − | 0.739467i | \(-0.264922\pi\) | ||||
0.673193 | + | 0.739467i | \(0.264922\pi\) | |||||||
\(998\) | −95.8156 | −3.03299 | ||||||||
\(999\) | 42.7265 | 1.35181 |
(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 | 8021.2.a.c.1.13 | ✓ | 169 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8021.2.a.c.1.13 | ✓ | 169 | 1.1 | even | 1 | trivial |