Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(16.0738859269\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} + \cdots - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(-2.54331\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.54331 | 1.79840 | 0.899198 | − | 0.437543i | \(-0.144151\pi\) | ||||
0.899198 | + | 0.437543i | \(0.144151\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.46845 | 2.23422 | ||||||||
\(5\) | 0.329781 | 0.147482 | 0.0737412 | − | 0.997277i | \(-0.476506\pi\) | ||||
0.0737412 | + | 0.997277i | \(0.476506\pi\) | |||||||
\(6\) | −2.54331 | −1.03830 | ||||||||
\(7\) | 0.595463 | 0.225064 | 0.112532 | − | 0.993648i | \(-0.464104\pi\) | ||||
0.112532 | + | 0.993648i | \(0.464104\pi\) | |||||||
\(8\) | 6.27804 | 2.21962 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.838736 | 0.265232 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −4.46845 | −1.28993 | ||||||||
\(13\) | 0.0829823 | 0.0230152 | 0.0115076 | − | 0.999934i | \(-0.496337\pi\) | ||||
0.0115076 | + | 0.999934i | \(0.496337\pi\) | |||||||
\(14\) | 1.51445 | 0.404754 | ||||||||
\(15\) | −0.329781 | −0.0851490 | ||||||||
\(16\) | 7.03014 | 1.75754 | ||||||||
\(17\) | 6.96049 | 1.68817 | 0.844083 | − | 0.536213i | \(-0.180146\pi\) | ||||
0.844083 | + | 0.536213i | \(0.180146\pi\) | |||||||
\(18\) | 2.54331 | 0.599465 | ||||||||
\(19\) | 1.08146 | 0.248105 | 0.124052 | − | 0.992276i | \(-0.460411\pi\) | ||||
0.124052 | + | 0.992276i | \(0.460411\pi\) | |||||||
\(20\) | 1.47361 | 0.329509 | ||||||||
\(21\) | −0.595463 | −0.129941 | ||||||||
\(22\) | −2.54331 | −0.542237 | ||||||||
\(23\) | 3.20203 | 0.667669 | 0.333835 | − | 0.942632i | \(-0.391657\pi\) | ||||
0.333835 | + | 0.942632i | \(0.391657\pi\) | |||||||
\(24\) | −6.27804 | −1.28150 | ||||||||
\(25\) | −4.89124 | −0.978249 | ||||||||
\(26\) | 0.211050 | 0.0413903 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.66080 | 0.502844 | ||||||||
\(29\) | 8.72957 | 1.62104 | 0.810521 | − | 0.585710i | \(-0.199184\pi\) | ||||
0.810521 | + | 0.585710i | \(0.199184\pi\) | |||||||
\(30\) | −0.838736 | −0.153132 | ||||||||
\(31\) | −3.05943 | −0.549489 | −0.274745 | − | 0.961517i | \(-0.588593\pi\) | ||||
−0.274745 | + | 0.961517i | \(0.588593\pi\) | |||||||
\(32\) | 5.32378 | 0.941119 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 17.7027 | 3.03599 | ||||||||
\(35\) | 0.196372 | 0.0331930 | ||||||||
\(36\) | 4.46845 | 0.744742 | ||||||||
\(37\) | −5.63463 | −0.926328 | −0.463164 | − | 0.886273i | \(-0.653286\pi\) | ||||
−0.463164 | + | 0.886273i | \(0.653286\pi\) | |||||||
\(38\) | 2.75050 | 0.446190 | ||||||||
\(39\) | −0.0829823 | −0.0132878 | ||||||||
\(40\) | 2.07038 | 0.327355 | ||||||||
\(41\) | −0.0715670 | −0.0111769 | −0.00558844 | − | 0.999984i | \(-0.501779\pi\) | ||||
−0.00558844 | + | 0.999984i | \(0.501779\pi\) | |||||||
\(42\) | −1.51445 | −0.233685 | ||||||||
\(43\) | 11.3684 | 1.73366 | 0.866831 | − | 0.498603i | \(-0.166153\pi\) | ||||
0.866831 | + | 0.498603i | \(0.166153\pi\) | |||||||
\(44\) | −4.46845 | −0.673644 | ||||||||
\(45\) | 0.329781 | 0.0491608 | ||||||||
\(46\) | 8.14377 | 1.20073 | ||||||||
\(47\) | 11.2549 | 1.64169 | 0.820845 | − | 0.571151i | \(-0.193503\pi\) | ||||
0.820845 | + | 0.571151i | \(0.193503\pi\) | |||||||
\(48\) | −7.03014 | −1.01471 | ||||||||
\(49\) | −6.64542 | −0.949346 | ||||||||
\(50\) | −12.4400 | −1.75928 | ||||||||
\(51\) | −6.96049 | −0.974663 | ||||||||
\(52\) | 0.370802 | 0.0514210 | ||||||||
\(53\) | −8.24041 | −1.13191 | −0.565954 | − | 0.824437i | \(-0.691492\pi\) | ||||
−0.565954 | + | 0.824437i | \(0.691492\pi\) | |||||||
\(54\) | −2.54331 | −0.346101 | ||||||||
\(55\) | −0.329781 | −0.0444676 | ||||||||
\(56\) | 3.73835 | 0.499557 | ||||||||
\(57\) | −1.08146 | −0.143243 | ||||||||
\(58\) | 22.2021 | 2.91527 | ||||||||
\(59\) | −0.674261 | −0.0877813 | −0.0438907 | − | 0.999036i | \(-0.513975\pi\) | ||||
−0.0438907 | + | 0.999036i | \(0.513975\pi\) | |||||||
\(60\) | −1.47361 | −0.190242 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | −7.78108 | −0.988199 | ||||||||
\(63\) | 0.595463 | 0.0750213 | ||||||||
\(64\) | −0.520247 | −0.0650309 | ||||||||
\(65\) | 0.0273660 | 0.00339433 | ||||||||
\(66\) | 2.54331 | 0.313060 | ||||||||
\(67\) | 0.140859 | 0.0172087 | 0.00860433 | − | 0.999963i | \(-0.497261\pi\) | ||||
0.00860433 | + | 0.999963i | \(0.497261\pi\) | |||||||
\(68\) | 31.1026 | 3.77174 | ||||||||
\(69\) | −3.20203 | −0.385479 | ||||||||
\(70\) | 0.499437 | 0.0596941 | ||||||||
\(71\) | −12.8499 | −1.52500 | −0.762500 | − | 0.646988i | \(-0.776028\pi\) | ||||
−0.762500 | + | 0.646988i | \(0.776028\pi\) | |||||||
\(72\) | 6.27804 | 0.739875 | ||||||||
\(73\) | −1.10649 | −0.129505 | −0.0647527 | − | 0.997901i | \(-0.520626\pi\) | ||||
−0.0647527 | + | 0.997901i | \(0.520626\pi\) | |||||||
\(74\) | −14.3306 | −1.66590 | ||||||||
\(75\) | 4.89124 | 0.564792 | ||||||||
\(76\) | 4.83247 | 0.554322 | ||||||||
\(77\) | −0.595463 | −0.0678594 | ||||||||
\(78\) | −0.211050 | −0.0238967 | ||||||||
\(79\) | 14.9245 | 1.67913 | 0.839567 | − | 0.543256i | \(-0.182809\pi\) | ||||
0.839567 | + | 0.543256i | \(0.182809\pi\) | |||||||
\(80\) | 2.31841 | 0.259206 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.182017 | −0.0201005 | ||||||||
\(83\) | −1.08794 | −0.119417 | −0.0597087 | − | 0.998216i | \(-0.519017\pi\) | ||||
−0.0597087 | + | 0.998216i | \(0.519017\pi\) | |||||||
\(84\) | −2.66080 | −0.290317 | ||||||||
\(85\) | 2.29543 | 0.248975 | ||||||||
\(86\) | 28.9134 | 3.11781 | ||||||||
\(87\) | −8.72957 | −0.935909 | ||||||||
\(88\) | −6.27804 | −0.669242 | ||||||||
\(89\) | −1.53437 | −0.162642 | −0.0813212 | − | 0.996688i | \(-0.525914\pi\) | ||||
−0.0813212 | + | 0.996688i | \(0.525914\pi\) | |||||||
\(90\) | 0.838736 | 0.0884106 | ||||||||
\(91\) | 0.0494129 | 0.00517988 | ||||||||
\(92\) | 14.3081 | 1.49172 | ||||||||
\(93\) | 3.05943 | 0.317248 | ||||||||
\(94\) | 28.6246 | 2.95241 | ||||||||
\(95\) | 0.356646 | 0.0365911 | ||||||||
\(96\) | −5.32378 | −0.543356 | ||||||||
\(97\) | −8.74805 | −0.888230 | −0.444115 | − | 0.895970i | \(-0.646482\pi\) | ||||
−0.444115 | + | 0.895970i | \(0.646482\pi\) | |||||||
\(98\) | −16.9014 | −1.70730 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −21.8563 | −2.18563 | ||||||||
\(101\) | 9.88085 | 0.983181 | 0.491590 | − | 0.870827i | \(-0.336416\pi\) | ||||
0.491590 | + | 0.870827i | \(0.336416\pi\) | |||||||
\(102\) | −17.7027 | −1.75283 | ||||||||
\(103\) | −7.23771 | −0.713153 | −0.356577 | − | 0.934266i | \(-0.616056\pi\) | ||||
−0.356577 | + | 0.934266i | \(0.616056\pi\) | |||||||
\(104\) | 0.520967 | 0.0510850 | ||||||||
\(105\) | −0.196372 | −0.0191640 | ||||||||
\(106\) | −20.9580 | −2.03562 | ||||||||
\(107\) | −16.9166 | −1.63539 | −0.817695 | − | 0.575652i | \(-0.804748\pi\) | ||||
−0.817695 | + | 0.575652i | \(0.804748\pi\) | |||||||
\(108\) | −4.46845 | −0.429977 | ||||||||
\(109\) | 5.79446 | 0.555008 | 0.277504 | − | 0.960724i | \(-0.410493\pi\) | ||||
0.277504 | + | 0.960724i | \(0.410493\pi\) | |||||||
\(110\) | −0.838736 | −0.0799704 | ||||||||
\(111\) | 5.63463 | 0.534816 | ||||||||
\(112\) | 4.18619 | 0.395558 | ||||||||
\(113\) | −12.3271 | −1.15964 | −0.579818 | − | 0.814746i | \(-0.696876\pi\) | ||||
−0.579818 | + | 0.814746i | \(0.696876\pi\) | |||||||
\(114\) | −2.75050 | −0.257608 | ||||||||
\(115\) | 1.05597 | 0.0984695 | ||||||||
\(116\) | 39.0077 | 3.62177 | ||||||||
\(117\) | 0.0829823 | 0.00767172 | ||||||||
\(118\) | −1.71486 | −0.157865 | ||||||||
\(119\) | 4.14471 | 0.379945 | ||||||||
\(120\) | −2.07038 | −0.188999 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.54331 | 0.230261 | ||||||||
\(123\) | 0.0715670 | 0.00645298 | ||||||||
\(124\) | −13.6709 | −1.22768 | ||||||||
\(125\) | −3.26194 | −0.291757 | ||||||||
\(126\) | 1.51445 | 0.134918 | ||||||||
\(127\) | −7.99339 | −0.709299 | −0.354649 | − | 0.934999i | \(-0.615400\pi\) | ||||
−0.354649 | + | 0.934999i | \(0.615400\pi\) | |||||||
\(128\) | −11.9707 | −1.05807 | ||||||||
\(129\) | −11.3684 | −1.00093 | ||||||||
\(130\) | 0.0696003 | 0.00610435 | ||||||||
\(131\) | −15.8726 | −1.38680 | −0.693398 | − | 0.720555i | \(-0.743887\pi\) | ||||
−0.693398 | + | 0.720555i | \(0.743887\pi\) | |||||||
\(132\) | 4.46845 | 0.388929 | ||||||||
\(133\) | 0.643972 | 0.0558395 | ||||||||
\(134\) | 0.358249 | 0.0309480 | ||||||||
\(135\) | −0.329781 | −0.0283830 | ||||||||
\(136\) | 43.6982 | 3.74709 | ||||||||
\(137\) | −16.9666 | −1.44956 | −0.724778 | − | 0.688983i | \(-0.758058\pi\) | ||||
−0.724778 | + | 0.688983i | \(0.758058\pi\) | |||||||
\(138\) | −8.14377 | −0.693243 | ||||||||
\(139\) | 15.7351 | 1.33463 | 0.667315 | − | 0.744775i | \(-0.267443\pi\) | ||||
0.667315 | + | 0.744775i | \(0.267443\pi\) | |||||||
\(140\) | 0.877480 | 0.0741606 | ||||||||
\(141\) | −11.2549 | −0.947830 | ||||||||
\(142\) | −32.6813 | −2.74255 | ||||||||
\(143\) | −0.0829823 | −0.00693933 | ||||||||
\(144\) | 7.03014 | 0.585845 | ||||||||
\(145\) | 2.87885 | 0.239075 | ||||||||
\(146\) | −2.81416 | −0.232902 | ||||||||
\(147\) | 6.64542 | 0.548105 | ||||||||
\(148\) | −25.1781 | −2.06963 | ||||||||
\(149\) | −15.3791 | −1.25990 | −0.629950 | − | 0.776635i | \(-0.716925\pi\) | ||||
−0.629950 | + | 0.776635i | \(0.716925\pi\) | |||||||
\(150\) | 12.4400 | 1.01572 | ||||||||
\(151\) | 16.5708 | 1.34851 | 0.674257 | − | 0.738497i | \(-0.264464\pi\) | ||||
0.674257 | + | 0.738497i | \(0.264464\pi\) | |||||||
\(152\) | 6.78948 | 0.550699 | ||||||||
\(153\) | 6.96049 | 0.562722 | ||||||||
\(154\) | −1.51445 | −0.122038 | ||||||||
\(155\) | −1.00894 | −0.0810400 | ||||||||
\(156\) | −0.370802 | −0.0296879 | ||||||||
\(157\) | −6.06333 | −0.483907 | −0.241953 | − | 0.970288i | \(-0.577788\pi\) | ||||
−0.241953 | + | 0.970288i | \(0.577788\pi\) | |||||||
\(158\) | 37.9576 | 3.01975 | ||||||||
\(159\) | 8.24041 | 0.653507 | ||||||||
\(160\) | 1.75568 | 0.138799 | ||||||||
\(161\) | 1.90669 | 0.150268 | ||||||||
\(162\) | 2.54331 | 0.199822 | ||||||||
\(163\) | 17.8621 | 1.39907 | 0.699535 | − | 0.714598i | \(-0.253390\pi\) | ||||
0.699535 | + | 0.714598i | \(0.253390\pi\) | |||||||
\(164\) | −0.319793 | −0.0249717 | ||||||||
\(165\) | 0.329781 | 0.0256734 | ||||||||
\(166\) | −2.76698 | −0.214759 | ||||||||
\(167\) | 21.2052 | 1.64091 | 0.820455 | − | 0.571711i | \(-0.193720\pi\) | ||||
0.820455 | + | 0.571711i | \(0.193720\pi\) | |||||||
\(168\) | −3.73835 | −0.288420 | ||||||||
\(169\) | −12.9931 | −0.999470 | ||||||||
\(170\) | 5.83801 | 0.447755 | ||||||||
\(171\) | 1.08146 | 0.0827016 | ||||||||
\(172\) | 50.7990 | 3.87339 | ||||||||
\(173\) | 2.96793 | 0.225647 | 0.112824 | − | 0.993615i | \(-0.464010\pi\) | ||||
0.112824 | + | 0.993615i | \(0.464010\pi\) | |||||||
\(174\) | −22.2021 | −1.68313 | ||||||||
\(175\) | −2.91256 | −0.220169 | ||||||||
\(176\) | −7.03014 | −0.529917 | ||||||||
\(177\) | 0.674261 | 0.0506806 | ||||||||
\(178\) | −3.90237 | −0.292495 | ||||||||
\(179\) | 1.16838 | 0.0873291 | 0.0436646 | − | 0.999046i | \(-0.486097\pi\) | ||||
0.0436646 | + | 0.999046i | \(0.486097\pi\) | |||||||
\(180\) | 1.47361 | 0.109836 | ||||||||
\(181\) | −11.0228 | −0.819318 | −0.409659 | − | 0.912239i | \(-0.634352\pi\) | ||||
−0.409659 | + | 0.912239i | \(0.634352\pi\) | |||||||
\(182\) | 0.125673 | 0.00931548 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | 20.1025 | 1.48197 | ||||||||
\(185\) | −1.85819 | −0.136617 | ||||||||
\(186\) | 7.78108 | 0.570537 | ||||||||
\(187\) | −6.96049 | −0.509001 | ||||||||
\(188\) | 50.2918 | 3.66790 | ||||||||
\(189\) | −0.595463 | −0.0433136 | ||||||||
\(190\) | 0.907063 | 0.0658052 | ||||||||
\(191\) | −15.3640 | −1.11170 | −0.555849 | − | 0.831283i | \(-0.687607\pi\) | ||||
−0.555849 | + | 0.831283i | \(0.687607\pi\) | |||||||
\(192\) | 0.520247 | 0.0375456 | ||||||||
\(193\) | −11.1185 | −0.800324 | −0.400162 | − | 0.916444i | \(-0.631046\pi\) | ||||
−0.400162 | + | 0.916444i | \(0.631046\pi\) | |||||||
\(194\) | −22.2490 | −1.59739 | ||||||||
\(195\) | −0.0273660 | −0.00195972 | ||||||||
\(196\) | −29.6947 | −2.12105 | ||||||||
\(197\) | −17.7144 | −1.26210 | −0.631050 | − | 0.775742i | \(-0.717376\pi\) | ||||
−0.631050 | + | 0.775742i | \(0.717376\pi\) | |||||||
\(198\) | −2.54331 | −0.180746 | ||||||||
\(199\) | 24.5173 | 1.73798 | 0.868992 | − | 0.494826i | \(-0.164768\pi\) | ||||
0.868992 | + | 0.494826i | \(0.164768\pi\) | |||||||
\(200\) | −30.7074 | −2.17134 | ||||||||
\(201\) | −0.140859 | −0.00993542 | ||||||||
\(202\) | 25.1301 | 1.76815 | ||||||||
\(203\) | 5.19814 | 0.364838 | ||||||||
\(204\) | −31.1026 | −2.17762 | ||||||||
\(205\) | −0.0236014 | −0.00164839 | ||||||||
\(206\) | −18.4078 | −1.28253 | ||||||||
\(207\) | 3.20203 | 0.222556 | ||||||||
\(208\) | 0.583378 | 0.0404500 | ||||||||
\(209\) | −1.08146 | −0.0748064 | ||||||||
\(210\) | −0.499437 | −0.0344644 | ||||||||
\(211\) | 9.34349 | 0.643232 | 0.321616 | − | 0.946870i | \(-0.395774\pi\) | ||||
0.321616 | + | 0.946870i | \(0.395774\pi\) | |||||||
\(212\) | −36.8219 | −2.52894 | ||||||||
\(213\) | 12.8499 | 0.880459 | ||||||||
\(214\) | −43.0243 | −2.94108 | ||||||||
\(215\) | 3.74907 | 0.255685 | ||||||||
\(216\) | −6.27804 | −0.427167 | ||||||||
\(217\) | −1.82178 | −0.123670 | ||||||||
\(218\) | 14.7371 | 0.998124 | ||||||||
\(219\) | 1.10649 | 0.0747700 | ||||||||
\(220\) | −1.47361 | −0.0993507 | ||||||||
\(221\) | 0.577597 | 0.0388534 | ||||||||
\(222\) | 14.3306 | 0.961810 | ||||||||
\(223\) | −23.8528 | −1.59730 | −0.798652 | − | 0.601793i | \(-0.794453\pi\) | ||||
−0.798652 | + | 0.601793i | \(0.794453\pi\) | |||||||
\(224\) | 3.17011 | 0.211812 | ||||||||
\(225\) | −4.89124 | −0.326083 | ||||||||
\(226\) | −31.3517 | −2.08548 | ||||||||
\(227\) | 4.98647 | 0.330964 | 0.165482 | − | 0.986213i | \(-0.447082\pi\) | ||||
0.165482 | + | 0.986213i | \(0.447082\pi\) | |||||||
\(228\) | −4.83247 | −0.320038 | ||||||||
\(229\) | 0.915859 | 0.0605217 | 0.0302608 | − | 0.999542i | \(-0.490366\pi\) | ||||
0.0302608 | + | 0.999542i | \(0.490366\pi\) | |||||||
\(230\) | 2.68566 | 0.177087 | ||||||||
\(231\) | 0.595463 | 0.0391786 | ||||||||
\(232\) | 54.8046 | 3.59810 | ||||||||
\(233\) | 7.32305 | 0.479749 | 0.239875 | − | 0.970804i | \(-0.422894\pi\) | ||||
0.239875 | + | 0.970804i | \(0.422894\pi\) | |||||||
\(234\) | 0.211050 | 0.0137968 | ||||||||
\(235\) | 3.71164 | 0.242120 | ||||||||
\(236\) | −3.01290 | −0.196123 | ||||||||
\(237\) | −14.9245 | −0.969448 | ||||||||
\(238\) | 10.5413 | 0.683292 | ||||||||
\(239\) | −24.5442 | −1.58763 | −0.793817 | − | 0.608157i | \(-0.791909\pi\) | ||||
−0.793817 | + | 0.608157i | \(0.791909\pi\) | |||||||
\(240\) | −2.31841 | −0.149652 | ||||||||
\(241\) | 18.3505 | 1.18206 | 0.591031 | − | 0.806649i | \(-0.298721\pi\) | ||||
0.591031 | + | 0.806649i | \(0.298721\pi\) | |||||||
\(242\) | 2.54331 | 0.163490 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.46845 | 0.286063 | ||||||||
\(245\) | −2.19153 | −0.140012 | ||||||||
\(246\) | 0.182017 | 0.0116050 | ||||||||
\(247\) | 0.0897424 | 0.00571017 | ||||||||
\(248\) | −19.2072 | −1.21966 | ||||||||
\(249\) | 1.08794 | 0.0689456 | ||||||||
\(250\) | −8.29614 | −0.524694 | ||||||||
\(251\) | 2.34673 | 0.148125 | 0.0740623 | − | 0.997254i | \(-0.476404\pi\) | ||||
0.0740623 | + | 0.997254i | \(0.476404\pi\) | |||||||
\(252\) | 2.66080 | 0.167615 | ||||||||
\(253\) | −3.20203 | −0.201310 | ||||||||
\(254\) | −20.3297 | −1.27560 | ||||||||
\(255\) | −2.29543 | −0.143746 | ||||||||
\(256\) | −29.4048 | −1.83780 | ||||||||
\(257\) | −2.07933 | −0.129705 | −0.0648527 | − | 0.997895i | \(-0.520658\pi\) | ||||
−0.0648527 | + | 0.997895i | \(0.520658\pi\) | |||||||
\(258\) | −28.9134 | −1.80007 | ||||||||
\(259\) | −3.35522 | −0.208483 | ||||||||
\(260\) | 0.122283 | 0.00758370 | ||||||||
\(261\) | 8.72957 | 0.540347 | ||||||||
\(262\) | −40.3690 | −2.49401 | ||||||||
\(263\) | −24.1181 | −1.48718 | −0.743591 | − | 0.668634i | \(-0.766879\pi\) | ||||
−0.743591 | + | 0.668634i | \(0.766879\pi\) | |||||||
\(264\) | 6.27804 | 0.386387 | ||||||||
\(265\) | −2.71753 | −0.166936 | ||||||||
\(266\) | 1.63782 | 0.100421 | ||||||||
\(267\) | 1.53437 | 0.0939016 | ||||||||
\(268\) | 0.629421 | 0.0384480 | ||||||||
\(269\) | −13.9942 | −0.853243 | −0.426622 | − | 0.904430i | \(-0.640296\pi\) | ||||
−0.426622 | + | 0.904430i | \(0.640296\pi\) | |||||||
\(270\) | −0.838736 | −0.0510439 | ||||||||
\(271\) | −24.2791 | −1.47485 | −0.737426 | − | 0.675428i | \(-0.763959\pi\) | ||||
−0.737426 | + | 0.675428i | \(0.763959\pi\) | |||||||
\(272\) | 48.9332 | 2.96701 | ||||||||
\(273\) | −0.0494129 | −0.00299061 | ||||||||
\(274\) | −43.1514 | −2.60687 | ||||||||
\(275\) | 4.89124 | 0.294953 | ||||||||
\(276\) | −14.3081 | −0.861247 | ||||||||
\(277\) | −16.3119 | −0.980085 | −0.490043 | − | 0.871699i | \(-0.663019\pi\) | ||||
−0.490043 | + | 0.871699i | \(0.663019\pi\) | |||||||
\(278\) | 40.0192 | 2.40019 | ||||||||
\(279\) | −3.05943 | −0.183163 | ||||||||
\(280\) | 1.23283 | 0.0736759 | ||||||||
\(281\) | 13.7085 | 0.817778 | 0.408889 | − | 0.912584i | \(-0.365916\pi\) | ||||
0.408889 | + | 0.912584i | \(0.365916\pi\) | |||||||
\(282\) | −28.6246 | −1.70457 | ||||||||
\(283\) | 31.0223 | 1.84409 | 0.922043 | − | 0.387087i | \(-0.126519\pi\) | ||||
0.922043 | + | 0.387087i | \(0.126519\pi\) | |||||||
\(284\) | −57.4190 | −3.40719 | ||||||||
\(285\) | −0.356646 | −0.0211259 | ||||||||
\(286\) | −0.211050 | −0.0124797 | ||||||||
\(287\) | −0.0426155 | −0.00251551 | ||||||||
\(288\) | 5.32378 | 0.313706 | ||||||||
\(289\) | 31.4484 | 1.84990 | ||||||||
\(290\) | 7.32181 | 0.429951 | ||||||||
\(291\) | 8.74805 | 0.512820 | ||||||||
\(292\) | −4.94431 | −0.289344 | ||||||||
\(293\) | 4.76769 | 0.278531 | 0.139266 | − | 0.990255i | \(-0.455526\pi\) | ||||
0.139266 | + | 0.990255i | \(0.455526\pi\) | |||||||
\(294\) | 16.9014 | 0.985710 | ||||||||
\(295\) | −0.222358 | −0.0129462 | ||||||||
\(296\) | −35.3745 | −2.05610 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | −39.1138 | −2.26580 | ||||||||
\(299\) | 0.265712 | 0.0153665 | ||||||||
\(300\) | 21.8563 | 1.26187 | ||||||||
\(301\) | 6.76945 | 0.390185 | ||||||||
\(302\) | 42.1448 | 2.42516 | ||||||||
\(303\) | −9.88085 | −0.567640 | ||||||||
\(304\) | 7.60284 | 0.436053 | ||||||||
\(305\) | 0.329781 | 0.0188832 | ||||||||
\(306\) | 17.7027 | 1.01200 | ||||||||
\(307\) | −9.09194 | −0.518905 | −0.259452 | − | 0.965756i | \(-0.583542\pi\) | ||||
−0.259452 | + | 0.965756i | \(0.583542\pi\) | |||||||
\(308\) | −2.66080 | −0.151613 | ||||||||
\(309\) | 7.23771 | 0.411739 | ||||||||
\(310\) | −2.56605 | −0.145742 | ||||||||
\(311\) | 0.130155 | 0.00738041 | 0.00369020 | − | 0.999993i | \(-0.498825\pi\) | ||||
0.00369020 | + | 0.999993i | \(0.498825\pi\) | |||||||
\(312\) | −0.520967 | −0.0294939 | ||||||||
\(313\) | −18.8073 | −1.06305 | −0.531526 | − | 0.847042i | \(-0.678381\pi\) | ||||
−0.531526 | + | 0.847042i | \(0.678381\pi\) | |||||||
\(314\) | −15.4210 | −0.870255 | ||||||||
\(315\) | 0.196372 | 0.0110643 | ||||||||
\(316\) | 66.6892 | 3.75156 | ||||||||
\(317\) | 21.5314 | 1.20932 | 0.604661 | − | 0.796483i | \(-0.293308\pi\) | ||||
0.604661 | + | 0.796483i | \(0.293308\pi\) | |||||||
\(318\) | 20.9580 | 1.17526 | ||||||||
\(319\) | −8.72957 | −0.488762 | ||||||||
\(320\) | −0.171568 | −0.00959092 | ||||||||
\(321\) | 16.9166 | 0.944193 | ||||||||
\(322\) | 4.84931 | 0.270242 | ||||||||
\(323\) | 7.52751 | 0.418842 | ||||||||
\(324\) | 4.46845 | 0.248247 | ||||||||
\(325\) | −0.405887 | −0.0225146 | ||||||||
\(326\) | 45.4290 | 2.51608 | ||||||||
\(327\) | −5.79446 | −0.320434 | ||||||||
\(328\) | −0.449301 | −0.0248085 | ||||||||
\(329\) | 6.70186 | 0.369485 | ||||||||
\(330\) | 0.838736 | 0.0461709 | ||||||||
\(331\) | −5.77423 | −0.317380 | −0.158690 | − | 0.987328i | \(-0.550727\pi\) | ||||
−0.158690 | + | 0.987328i | \(0.550727\pi\) | |||||||
\(332\) | −4.86142 | −0.266805 | ||||||||
\(333\) | −5.63463 | −0.308776 | ||||||||
\(334\) | 53.9316 | 2.95100 | ||||||||
\(335\) | 0.0464526 | 0.00253797 | ||||||||
\(336\) | −4.18619 | −0.228376 | ||||||||
\(337\) | −16.2916 | −0.887462 | −0.443731 | − | 0.896160i | \(-0.646345\pi\) | ||||
−0.443731 | + | 0.896160i | \(0.646345\pi\) | |||||||
\(338\) | −33.0456 | −1.79744 | ||||||||
\(339\) | 12.3271 | 0.669517 | ||||||||
\(340\) | 10.2570 | 0.556266 | ||||||||
\(341\) | 3.05943 | 0.165677 | ||||||||
\(342\) | 2.75050 | 0.148730 | ||||||||
\(343\) | −8.12535 | −0.438728 | ||||||||
\(344\) | 71.3712 | 3.84808 | ||||||||
\(345\) | −1.05597 | −0.0568514 | ||||||||
\(346\) | 7.54837 | 0.405803 | ||||||||
\(347\) | −18.5188 | −0.994143 | −0.497072 | − | 0.867710i | \(-0.665591\pi\) | ||||
−0.497072 | + | 0.867710i | \(0.665591\pi\) | |||||||
\(348\) | −39.0077 | −2.09103 | ||||||||
\(349\) | 9.92712 | 0.531387 | 0.265693 | − | 0.964058i | \(-0.414399\pi\) | ||||
0.265693 | + | 0.964058i | \(0.414399\pi\) | |||||||
\(350\) | −7.40755 | −0.395950 | ||||||||
\(351\) | −0.0829823 | −0.00442927 | ||||||||
\(352\) | −5.32378 | −0.283758 | ||||||||
\(353\) | 14.8318 | 0.789415 | 0.394707 | − | 0.918807i | \(-0.370846\pi\) | ||||
0.394707 | + | 0.918807i | \(0.370846\pi\) | |||||||
\(354\) | 1.71486 | 0.0911437 | ||||||||
\(355\) | −4.23764 | −0.224911 | ||||||||
\(356\) | −6.85623 | −0.363380 | ||||||||
\(357\) | −4.14471 | −0.219362 | ||||||||
\(358\) | 2.97157 | 0.157052 | ||||||||
\(359\) | 27.5857 | 1.45592 | 0.727959 | − | 0.685621i | \(-0.240469\pi\) | ||||
0.727959 | + | 0.685621i | \(0.240469\pi\) | |||||||
\(360\) | 2.07038 | 0.109118 | ||||||||
\(361\) | −17.8304 | −0.938444 | ||||||||
\(362\) | −28.0344 | −1.47346 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0.220799 | 0.0115730 | ||||||||
\(365\) | −0.364900 | −0.0190998 | ||||||||
\(366\) | −2.54331 | −0.132941 | ||||||||
\(367\) | −25.3367 | −1.32256 | −0.661281 | − | 0.750138i | \(-0.729987\pi\) | ||||
−0.661281 | + | 0.750138i | \(0.729987\pi\) | |||||||
\(368\) | 22.5107 | 1.17345 | ||||||||
\(369\) | −0.0715670 | −0.00372563 | ||||||||
\(370\) | −4.72597 | −0.245692 | ||||||||
\(371\) | −4.90686 | −0.254752 | ||||||||
\(372\) | 13.6709 | 0.708803 | ||||||||
\(373\) | 22.9549 | 1.18856 | 0.594281 | − | 0.804258i | \(-0.297437\pi\) | ||||
0.594281 | + | 0.804258i | \(0.297437\pi\) | |||||||
\(374\) | −17.7027 | −0.915385 | ||||||||
\(375\) | 3.26194 | 0.168446 | ||||||||
\(376\) | 70.6585 | 3.64393 | ||||||||
\(377\) | 0.724400 | 0.0373085 | ||||||||
\(378\) | −1.51445 | −0.0778949 | ||||||||
\(379\) | −2.82059 | −0.144884 | −0.0724420 | − | 0.997373i | \(-0.523079\pi\) | ||||
−0.0724420 | + | 0.997373i | \(0.523079\pi\) | |||||||
\(380\) | 1.59365 | 0.0817527 | ||||||||
\(381\) | 7.99339 | 0.409514 | ||||||||
\(382\) | −39.0754 | −1.99927 | ||||||||
\(383\) | 25.6130 | 1.30876 | 0.654382 | − | 0.756164i | \(-0.272929\pi\) | ||||
0.654382 | + | 0.756164i | \(0.272929\pi\) | |||||||
\(384\) | 11.9707 | 0.610877 | ||||||||
\(385\) | −0.196372 | −0.0100081 | ||||||||
\(386\) | −28.2777 | −1.43930 | ||||||||
\(387\) | 11.3684 | 0.577887 | ||||||||
\(388\) | −39.0902 | −1.98450 | ||||||||
\(389\) | −2.02580 | −0.102712 | −0.0513562 | − | 0.998680i | \(-0.516354\pi\) | ||||
−0.0513562 | + | 0.998680i | \(0.516354\pi\) | |||||||
\(390\) | −0.0696003 | −0.00352435 | ||||||||
\(391\) | 22.2877 | 1.12714 | ||||||||
\(392\) | −41.7203 | −2.10719 | ||||||||
\(393\) | 15.8726 | 0.800667 | ||||||||
\(394\) | −45.0533 | −2.26975 | ||||||||
\(395\) | 4.92180 | 0.247643 | ||||||||
\(396\) | −4.46845 | −0.224548 | ||||||||
\(397\) | 1.07995 | 0.0542011 | 0.0271006 | − | 0.999633i | \(-0.491373\pi\) | ||||
0.0271006 | + | 0.999633i | \(0.491373\pi\) | |||||||
\(398\) | 62.3552 | 3.12558 | ||||||||
\(399\) | −0.643972 | −0.0322389 | ||||||||
\(400\) | −34.3861 | −1.71931 | ||||||||
\(401\) | 3.50052 | 0.174807 | 0.0874037 | − | 0.996173i | \(-0.472143\pi\) | ||||
0.0874037 | + | 0.996173i | \(0.472143\pi\) | |||||||
\(402\) | −0.358249 | −0.0178678 | ||||||||
\(403\) | −0.253878 | −0.0126466 | ||||||||
\(404\) | 44.1521 | 2.19665 | ||||||||
\(405\) | 0.329781 | 0.0163869 | ||||||||
\(406\) | 13.2205 | 0.656123 | ||||||||
\(407\) | 5.63463 | 0.279298 | ||||||||
\(408\) | −43.6982 | −2.16339 | ||||||||
\(409\) | −27.1693 | −1.34344 | −0.671719 | − | 0.740806i | \(-0.734444\pi\) | ||||
−0.671719 | + | 0.740806i | \(0.734444\pi\) | |||||||
\(410\) | −0.0600258 | −0.00296446 | ||||||||
\(411\) | 16.9666 | 0.836901 | ||||||||
\(412\) | −32.3414 | −1.59334 | ||||||||
\(413\) | −0.401498 | −0.0197564 | ||||||||
\(414\) | 8.14377 | 0.400244 | ||||||||
\(415\) | −0.358783 | −0.0176120 | ||||||||
\(416\) | 0.441779 | 0.0216600 | ||||||||
\(417\) | −15.7351 | −0.770549 | ||||||||
\(418\) | −2.75050 | −0.134531 | ||||||||
\(419\) | −15.6757 | −0.765810 | −0.382905 | − | 0.923788i | \(-0.625076\pi\) | ||||
−0.382905 | + | 0.923788i | \(0.625076\pi\) | |||||||
\(420\) | −0.877480 | −0.0428166 | ||||||||
\(421\) | −1.40707 | −0.0685762 | −0.0342881 | − | 0.999412i | \(-0.510916\pi\) | ||||
−0.0342881 | + | 0.999412i | \(0.510916\pi\) | |||||||
\(422\) | 23.7634 | 1.15679 | ||||||||
\(423\) | 11.2549 | 0.547230 | ||||||||
\(424\) | −51.7337 | −2.51241 | ||||||||
\(425\) | −34.0454 | −1.65145 | ||||||||
\(426\) | 32.6813 | 1.58341 | ||||||||
\(427\) | 0.595463 | 0.0288165 | ||||||||
\(428\) | −75.5910 | −3.65383 | ||||||||
\(429\) | 0.0829823 | 0.00400642 | ||||||||
\(430\) | 9.53507 | 0.459822 | ||||||||
\(431\) | −23.5382 | −1.13379 | −0.566897 | − | 0.823789i | \(-0.691856\pi\) | ||||
−0.566897 | + | 0.823789i | \(0.691856\pi\) | |||||||
\(432\) | −7.03014 | −0.338238 | ||||||||
\(433\) | 29.2710 | 1.40668 | 0.703338 | − | 0.710856i | \(-0.251692\pi\) | ||||
0.703338 | + | 0.710856i | \(0.251692\pi\) | |||||||
\(434\) | −4.63335 | −0.222408 | ||||||||
\(435\) | −2.87885 | −0.138030 | ||||||||
\(436\) | 25.8922 | 1.24001 | ||||||||
\(437\) | 3.46288 | 0.165652 | ||||||||
\(438\) | 2.81416 | 0.134466 | ||||||||
\(439\) | −17.0691 | −0.814664 | −0.407332 | − | 0.913280i | \(-0.633541\pi\) | ||||
−0.407332 | + | 0.913280i | \(0.633541\pi\) | |||||||
\(440\) | −2.07038 | −0.0987014 | ||||||||
\(441\) | −6.64542 | −0.316449 | ||||||||
\(442\) | 1.46901 | 0.0698738 | ||||||||
\(443\) | −32.9257 | −1.56435 | −0.782173 | − | 0.623061i | \(-0.785889\pi\) | ||||
−0.782173 | + | 0.623061i | \(0.785889\pi\) | |||||||
\(444\) | 25.1781 | 1.19490 | ||||||||
\(445\) | −0.506004 | −0.0239869 | ||||||||
\(446\) | −60.6653 | −2.87258 | ||||||||
\(447\) | 15.3791 | 0.727404 | ||||||||
\(448\) | −0.309788 | −0.0146361 | ||||||||
\(449\) | −30.7700 | −1.45213 | −0.726064 | − | 0.687627i | \(-0.758652\pi\) | ||||
−0.726064 | + | 0.687627i | \(0.758652\pi\) | |||||||
\(450\) | −12.4400 | −0.586426 | ||||||||
\(451\) | 0.0715670 | 0.00336996 | ||||||||
\(452\) | −55.0831 | −2.59089 | ||||||||
\(453\) | −16.5708 | −0.778565 | ||||||||
\(454\) | 12.6822 | 0.595204 | ||||||||
\(455\) | 0.0162954 | 0.000763942 0 | ||||||||
\(456\) | −6.78948 | −0.317946 | ||||||||
\(457\) | −11.8994 | −0.556632 | −0.278316 | − | 0.960490i | \(-0.589776\pi\) | ||||
−0.278316 | + | 0.960490i | \(0.589776\pi\) | |||||||
\(458\) | 2.32932 | 0.108842 | ||||||||
\(459\) | −6.96049 | −0.324888 | ||||||||
\(460\) | 4.71854 | 0.220003 | ||||||||
\(461\) | 9.53778 | 0.444218 | 0.222109 | − | 0.975022i | \(-0.428706\pi\) | ||||
0.222109 | + | 0.975022i | \(0.428706\pi\) | |||||||
\(462\) | 1.51445 | 0.0704586 | ||||||||
\(463\) | 22.8038 | 1.05978 | 0.529890 | − | 0.848066i | \(-0.322233\pi\) | ||||
0.529890 | + | 0.848066i | \(0.322233\pi\) | |||||||
\(464\) | 61.3701 | 2.84904 | ||||||||
\(465\) | 1.00894 | 0.0467885 | ||||||||
\(466\) | 18.6248 | 0.862778 | ||||||||
\(467\) | 41.0776 | 1.90084 | 0.950422 | − | 0.310962i | \(-0.100651\pi\) | ||||
0.950422 | + | 0.310962i | \(0.100651\pi\) | |||||||
\(468\) | 0.370802 | 0.0171403 | ||||||||
\(469\) | 0.0838763 | 0.00387305 | ||||||||
\(470\) | 9.43986 | 0.435428 | ||||||||
\(471\) | 6.06333 | 0.279384 | ||||||||
\(472\) | −4.23304 | −0.194842 | ||||||||
\(473\) | −11.3684 | −0.522719 | ||||||||
\(474\) | −37.9576 | −1.74345 | ||||||||
\(475\) | −5.28970 | −0.242708 | ||||||||
\(476\) | 18.5204 | 0.848883 | ||||||||
\(477\) | −8.24041 | −0.377303 | ||||||||
\(478\) | −62.4237 | −2.85519 | ||||||||
\(479\) | −11.8369 | −0.540841 | −0.270421 | − | 0.962742i | \(-0.587163\pi\) | ||||
−0.270421 | + | 0.962742i | \(0.587163\pi\) | |||||||
\(480\) | −1.75568 | −0.0801354 | ||||||||
\(481\) | −0.467575 | −0.0213196 | ||||||||
\(482\) | 46.6712 | 2.12581 | ||||||||
\(483\) | −1.90669 | −0.0867574 | ||||||||
\(484\) | 4.46845 | 0.203111 | ||||||||
\(485\) | −2.88494 | −0.130998 | ||||||||
\(486\) | −2.54331 | −0.115367 | ||||||||
\(487\) | 23.2203 | 1.05221 | 0.526105 | − | 0.850420i | \(-0.323652\pi\) | ||||
0.526105 | + | 0.850420i | \(0.323652\pi\) | |||||||
\(488\) | 6.27804 | 0.284194 | ||||||||
\(489\) | −17.8621 | −0.807754 | ||||||||
\(490\) | −5.57376 | −0.251797 | ||||||||
\(491\) | −10.6561 | −0.480901 | −0.240451 | − | 0.970661i | \(-0.577295\pi\) | ||||
−0.240451 | + | 0.970661i | \(0.577295\pi\) | |||||||
\(492\) | 0.319793 | 0.0144174 | ||||||||
\(493\) | 60.7621 | 2.73659 | ||||||||
\(494\) | 0.228243 | 0.0102691 | ||||||||
\(495\) | −0.329781 | −0.0148225 | ||||||||
\(496\) | −21.5082 | −0.965747 | ||||||||
\(497\) | −7.65163 | −0.343223 | ||||||||
\(498\) | 2.76698 | 0.123991 | ||||||||
\(499\) | 41.6152 | 1.86295 | 0.931475 | − | 0.363804i | \(-0.118522\pi\) | ||||
0.931475 | + | 0.363804i | \(0.118522\pi\) | |||||||
\(500\) | −14.5758 | −0.651851 | ||||||||
\(501\) | −21.2052 | −0.947380 | ||||||||
\(502\) | 5.96848 | 0.266386 | ||||||||
\(503\) | 31.7709 | 1.41660 | 0.708298 | − | 0.705914i | \(-0.249463\pi\) | ||||
0.708298 | + | 0.705914i | \(0.249463\pi\) | |||||||
\(504\) | 3.73835 | 0.166519 | ||||||||
\(505\) | 3.25851 | 0.145002 | ||||||||
\(506\) | −8.14377 | −0.362035 | ||||||||
\(507\) | 12.9931 | 0.577044 | ||||||||
\(508\) | −35.7181 | −1.58473 | ||||||||
\(509\) | 29.3708 | 1.30184 | 0.650920 | − | 0.759147i | \(-0.274383\pi\) | ||||
0.650920 | + | 0.759147i | \(0.274383\pi\) | |||||||
\(510\) | −5.83801 | −0.258511 | ||||||||
\(511\) | −0.658877 | −0.0291470 | ||||||||
\(512\) | −50.8442 | −2.24702 | ||||||||
\(513\) | −1.08146 | −0.0477478 | ||||||||
\(514\) | −5.28840 | −0.233261 | ||||||||
\(515\) | −2.38686 | −0.105178 | ||||||||
\(516\) | −50.7990 | −2.23630 | ||||||||
\(517\) | −11.2549 | −0.494988 | ||||||||
\(518\) | −8.53338 | −0.374935 | ||||||||
\(519\) | −2.96793 | −0.130278 | ||||||||
\(520\) | 0.171805 | 0.00753414 | ||||||||
\(521\) | −3.61714 | −0.158470 | −0.0792350 | − | 0.996856i | \(-0.525248\pi\) | ||||
−0.0792350 | + | 0.996856i | \(0.525248\pi\) | |||||||
\(522\) | 22.2021 | 0.971757 | ||||||||
\(523\) | −21.7716 | −0.952004 | −0.476002 | − | 0.879444i | \(-0.657914\pi\) | ||||
−0.476002 | + | 0.879444i | \(0.657914\pi\) | |||||||
\(524\) | −70.9259 | −3.09841 | ||||||||
\(525\) | 2.91256 | 0.127114 | ||||||||
\(526\) | −61.3398 | −2.67454 | ||||||||
\(527\) | −21.2951 | −0.927629 | ||||||||
\(528\) | 7.03014 | 0.305948 | ||||||||
\(529\) | −12.7470 | −0.554218 | ||||||||
\(530\) | −6.91153 | −0.300218 | ||||||||
\(531\) | −0.674261 | −0.0292604 | ||||||||
\(532\) | 2.87756 | 0.124758 | ||||||||
\(533\) | −0.00593879 | −0.000257238 0 | ||||||||
\(534\) | 3.90237 | 0.168872 | ||||||||
\(535\) | −5.57877 | −0.241191 | ||||||||
\(536\) | 0.884319 | 0.0381967 | ||||||||
\(537\) | −1.16838 | −0.0504195 | ||||||||
\(538\) | −35.5917 | −1.53447 | ||||||||
\(539\) | 6.64542 | 0.286239 | ||||||||
\(540\) | −1.47361 | −0.0634140 | ||||||||
\(541\) | 39.5580 | 1.70073 | 0.850366 | − | 0.526191i | \(-0.176380\pi\) | ||||
0.850366 | + | 0.526191i | \(0.176380\pi\) | |||||||
\(542\) | −61.7494 | −2.65236 | ||||||||
\(543\) | 11.0228 | 0.473034 | ||||||||
\(544\) | 37.0561 | 1.58877 | ||||||||
\(545\) | 1.91090 | 0.0818540 | ||||||||
\(546\) | −0.125673 | −0.00537829 | ||||||||
\(547\) | 22.9213 | 0.980046 | 0.490023 | − | 0.871710i | \(-0.336988\pi\) | ||||
0.490023 | + | 0.871710i | \(0.336988\pi\) | |||||||
\(548\) | −75.8144 | −3.23863 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | 12.4400 | 0.530442 | ||||||||
\(551\) | 9.44072 | 0.402188 | ||||||||
\(552\) | −20.1025 | −0.855618 | ||||||||
\(553\) | 8.88697 | 0.377913 | ||||||||
\(554\) | −41.4862 | −1.76258 | ||||||||
\(555\) | 1.85819 | 0.0788759 | ||||||||
\(556\) | 70.3113 | 2.98186 | ||||||||
\(557\) | 4.36360 | 0.184892 | 0.0924458 | − | 0.995718i | \(-0.470532\pi\) | ||||
0.0924458 | + | 0.995718i | \(0.470532\pi\) | |||||||
\(558\) | −7.78108 | −0.329400 | ||||||||
\(559\) | 0.943374 | 0.0399005 | ||||||||
\(560\) | 1.38053 | 0.0583378 | ||||||||
\(561\) | 6.96049 | 0.293872 | ||||||||
\(562\) | 34.8649 | 1.47069 | ||||||||
\(563\) | 7.88133 | 0.332158 | 0.166079 | − | 0.986112i | \(-0.446889\pi\) | ||||
0.166079 | + | 0.986112i | \(0.446889\pi\) | |||||||
\(564\) | −50.2918 | −2.11767 | ||||||||
\(565\) | −4.06524 | −0.171026 | ||||||||
\(566\) | 78.8995 | 3.31640 | ||||||||
\(567\) | 0.595463 | 0.0250071 | ||||||||
\(568\) | −80.6721 | −3.38493 | ||||||||
\(569\) | 19.5591 | 0.819961 | 0.409980 | − | 0.912094i | \(-0.365536\pi\) | ||||
0.409980 | + | 0.912094i | \(0.365536\pi\) | |||||||
\(570\) | −0.907063 | −0.0379927 | ||||||||
\(571\) | 37.0732 | 1.55147 | 0.775733 | − | 0.631061i | \(-0.217380\pi\) | ||||
0.775733 | + | 0.631061i | \(0.217380\pi\) | |||||||
\(572\) | −0.370802 | −0.0155040 | ||||||||
\(573\) | 15.3640 | 0.641840 | ||||||||
\(574\) | −0.108385 | −0.00452389 | ||||||||
\(575\) | −15.6619 | −0.653147 | ||||||||
\(576\) | −0.520247 | −0.0216770 | ||||||||
\(577\) | 20.2481 | 0.842941 | 0.421471 | − | 0.906842i | \(-0.361514\pi\) | ||||
0.421471 | + | 0.906842i | \(0.361514\pi\) | |||||||
\(578\) | 79.9831 | 3.32686 | ||||||||
\(579\) | 11.1185 | 0.462067 | ||||||||
\(580\) | 12.8640 | 0.534147 | ||||||||
\(581\) | −0.647830 | −0.0268765 | ||||||||
\(582\) | 22.2490 | 0.922252 | ||||||||
\(583\) | 8.24041 | 0.341283 | ||||||||
\(584\) | −6.94662 | −0.287453 | ||||||||
\(585\) | 0.0273660 | 0.00113144 | ||||||||
\(586\) | 12.1257 | 0.500910 | ||||||||
\(587\) | −14.4483 | −0.596343 | −0.298172 | − | 0.954512i | \(-0.596377\pi\) | ||||
−0.298172 | + | 0.954512i | \(0.596377\pi\) | |||||||
\(588\) | 29.6947 | 1.22459 | ||||||||
\(589\) | −3.30866 | −0.136331 | ||||||||
\(590\) | −0.565527 | −0.0232824 | ||||||||
\(591\) | 17.7144 | 0.728674 | ||||||||
\(592\) | −39.6123 | −1.62805 | ||||||||
\(593\) | −14.6070 | −0.599839 | −0.299920 | − | 0.953964i | \(-0.596960\pi\) | ||||
−0.299920 | + | 0.953964i | \(0.596960\pi\) | |||||||
\(594\) | 2.54331 | 0.104353 | ||||||||
\(595\) | 1.36685 | 0.0560353 | ||||||||
\(596\) | −68.7205 | −2.81490 | ||||||||
\(597\) | −24.5173 | −1.00343 | ||||||||
\(598\) | 0.675789 | 0.0276351 | ||||||||
\(599\) | 3.38693 | 0.138386 | 0.0691932 | − | 0.997603i | \(-0.477958\pi\) | ||||
0.0691932 | + | 0.997603i | \(0.477958\pi\) | |||||||
\(600\) | 30.7074 | 1.25363 | ||||||||
\(601\) | 25.0307 | 1.02102 | 0.510512 | − | 0.859871i | \(-0.329456\pi\) | ||||
0.510512 | + | 0.859871i | \(0.329456\pi\) | |||||||
\(602\) | 17.2168 | 0.701706 | ||||||||
\(603\) | 0.140859 | 0.00573622 | ||||||||
\(604\) | 74.0459 | 3.01288 | ||||||||
\(605\) | 0.329781 | 0.0134075 | ||||||||
\(606\) | −25.1301 | −1.02084 | ||||||||
\(607\) | 41.4522 | 1.68249 | 0.841246 | − | 0.540652i | \(-0.181822\pi\) | ||||
0.841246 | + | 0.540652i | \(0.181822\pi\) | |||||||
\(608\) | 5.75747 | 0.233496 | ||||||||
\(609\) | −5.19814 | −0.210639 | ||||||||
\(610\) | 0.838736 | 0.0339594 | ||||||||
\(611\) | 0.933954 | 0.0377837 | ||||||||
\(612\) | 31.1026 | 1.25725 | ||||||||
\(613\) | −22.4905 | −0.908383 | −0.454191 | − | 0.890904i | \(-0.650072\pi\) | ||||
−0.454191 | + | 0.890904i | \(0.650072\pi\) | |||||||
\(614\) | −23.1237 | −0.933195 | ||||||||
\(615\) | 0.0236014 | 0.000951701 0 | ||||||||
\(616\) | −3.73835 | −0.150622 | ||||||||
\(617\) | 19.0197 | 0.765703 | 0.382851 | − | 0.923810i | \(-0.374942\pi\) | ||||
0.382851 | + | 0.923810i | \(0.374942\pi\) | |||||||
\(618\) | 18.4078 | 0.740470 | ||||||||
\(619\) | −19.8223 | −0.796727 | −0.398364 | − | 0.917228i | \(-0.630422\pi\) | ||||
−0.398364 | + | 0.917228i | \(0.630422\pi\) | |||||||
\(620\) | −4.50840 | −0.181062 | ||||||||
\(621\) | −3.20203 | −0.128493 | ||||||||
\(622\) | 0.331025 | 0.0132729 | ||||||||
\(623\) | −0.913658 | −0.0366050 | ||||||||
\(624\) | −0.583378 | −0.0233538 | ||||||||
\(625\) | 23.3805 | 0.935220 | ||||||||
\(626\) | −47.8329 | −1.91179 | ||||||||
\(627\) | 1.08146 | 0.0431895 | ||||||||
\(628\) | −27.0937 | −1.08116 | ||||||||
\(629\) | −39.2198 | −1.56380 | ||||||||
\(630\) | 0.499437 | 0.0198980 | ||||||||
\(631\) | −8.96489 | −0.356886 | −0.178443 | − | 0.983950i | \(-0.557106\pi\) | ||||
−0.178443 | + | 0.983950i | \(0.557106\pi\) | |||||||
\(632\) | 93.6965 | 3.72704 | ||||||||
\(633\) | −9.34349 | −0.371370 | ||||||||
\(634\) | 54.7611 | 2.17484 | ||||||||
\(635\) | −2.63607 | −0.104609 | ||||||||
\(636\) | 36.8219 | 1.46008 | ||||||||
\(637\) | −0.551453 | −0.0218494 | ||||||||
\(638\) | −22.2021 | −0.878988 | ||||||||
\(639\) | −12.8499 | −0.508333 | ||||||||
\(640\) | −3.94771 | −0.156047 | ||||||||
\(641\) | −2.96210 | −0.116996 | −0.0584980 | − | 0.998288i | \(-0.518631\pi\) | ||||
−0.0584980 | + | 0.998288i | \(0.518631\pi\) | |||||||
\(642\) | 43.0243 | 1.69803 | ||||||||
\(643\) | 30.3611 | 1.19733 | 0.598663 | − | 0.801001i | \(-0.295699\pi\) | ||||
0.598663 | + | 0.801001i | \(0.295699\pi\) | |||||||
\(644\) | 8.51995 | 0.335733 | ||||||||
\(645\) | −3.74907 | −0.147620 | ||||||||
\(646\) | 19.1448 | 0.753243 | ||||||||
\(647\) | 44.6983 | 1.75727 | 0.878636 | − | 0.477491i | \(-0.158454\pi\) | ||||
0.878636 | + | 0.477491i | \(0.158454\pi\) | |||||||
\(648\) | 6.27804 | 0.246625 | ||||||||
\(649\) | 0.674261 | 0.0264671 | ||||||||
\(650\) | −1.03230 | −0.0404901 | ||||||||
\(651\) | 1.82178 | 0.0714011 | ||||||||
\(652\) | 79.8161 | 3.12584 | ||||||||
\(653\) | −21.4840 | −0.840733 | −0.420366 | − | 0.907355i | \(-0.638098\pi\) | ||||
−0.420366 | + | 0.907355i | \(0.638098\pi\) | |||||||
\(654\) | −14.7371 | −0.576267 | ||||||||
\(655\) | −5.23448 | −0.204528 | ||||||||
\(656\) | −0.503126 | −0.0196438 | ||||||||
\(657\) | −1.10649 | −0.0431685 | ||||||||
\(658\) | 17.0449 | 0.664481 | ||||||||
\(659\) | −26.1584 | −1.01899 | −0.509493 | − | 0.860475i | \(-0.670167\pi\) | ||||
−0.509493 | + | 0.860475i | \(0.670167\pi\) | |||||||
\(660\) | 1.47361 | 0.0573601 | ||||||||
\(661\) | 49.2767 | 1.91664 | 0.958320 | − | 0.285697i | \(-0.0922249\pi\) | ||||
0.958320 | + | 0.285697i | \(0.0922249\pi\) | |||||||
\(662\) | −14.6857 | −0.570775 | ||||||||
\(663\) | −0.577597 | −0.0224320 | ||||||||
\(664\) | −6.83016 | −0.265061 | ||||||||
\(665\) | 0.212370 | 0.00823534 | ||||||||
\(666\) | −14.3306 | −0.555301 | ||||||||
\(667\) | 27.9523 | 1.08232 | ||||||||
\(668\) | 94.7545 | 3.66616 | ||||||||
\(669\) | 23.8528 | 0.922204 | ||||||||
\(670\) | 0.118143 | 0.00456428 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −3.17011 | −0.122290 | ||||||||
\(673\) | −7.96941 | −0.307198 | −0.153599 | − | 0.988133i | \(-0.549086\pi\) | ||||
−0.153599 | + | 0.988133i | \(0.549086\pi\) | |||||||
\(674\) | −41.4348 | −1.59601 | ||||||||
\(675\) | 4.89124 | 0.188264 | ||||||||
\(676\) | −58.0591 | −2.23304 | ||||||||
\(677\) | 13.0772 | 0.502596 | 0.251298 | − | 0.967910i | \(-0.419143\pi\) | ||||
0.251298 | + | 0.967910i | \(0.419143\pi\) | |||||||
\(678\) | 31.3517 | 1.20406 | ||||||||
\(679\) | −5.20914 | −0.199909 | ||||||||
\(680\) | 14.4108 | 0.552630 | ||||||||
\(681\) | −4.98647 | −0.191082 | ||||||||
\(682\) | 7.78108 | 0.297953 | ||||||||
\(683\) | 29.5060 | 1.12902 | 0.564508 | − | 0.825427i | \(-0.309066\pi\) | ||||
0.564508 | + | 0.825427i | \(0.309066\pi\) | |||||||
\(684\) | 4.83247 | 0.184774 | ||||||||
\(685\) | −5.59526 | −0.213784 | ||||||||
\(686\) | −20.6653 | −0.789006 | ||||||||
\(687\) | −0.915859 | −0.0349422 | ||||||||
\(688\) | 79.9213 | 3.04697 | ||||||||
\(689\) | −0.683809 | −0.0260510 | ||||||||
\(690\) | −2.68566 | −0.102241 | ||||||||
\(691\) | 1.06947 | 0.0406846 | 0.0203423 | − | 0.999793i | \(-0.493524\pi\) | ||||
0.0203423 | + | 0.999793i | \(0.493524\pi\) | |||||||
\(692\) | 13.2620 | 0.504147 | ||||||||
\(693\) | −0.595463 | −0.0226198 | ||||||||
\(694\) | −47.0992 | −1.78786 | ||||||||
\(695\) | 5.18912 | 0.196835 | ||||||||
\(696\) | −54.8046 | −2.07736 | ||||||||
\(697\) | −0.498141 | −0.0188684 | ||||||||
\(698\) | 25.2478 | 0.955643 | ||||||||
\(699\) | −7.32305 | −0.276983 | ||||||||
\(700\) | −13.0146 | −0.491906 | ||||||||
\(701\) | −2.52697 | −0.0954424 | −0.0477212 | − | 0.998861i | \(-0.515196\pi\) | ||||
−0.0477212 | + | 0.998861i | \(0.515196\pi\) | |||||||
\(702\) | −0.211050 | −0.00796558 | ||||||||
\(703\) | −6.09365 | −0.229826 | ||||||||
\(704\) | 0.520247 | 0.0196076 | ||||||||
\(705\) | −3.71164 | −0.139788 | ||||||||
\(706\) | 37.7218 | 1.41968 | ||||||||
\(707\) | 5.88368 | 0.221279 | ||||||||
\(708\) | 3.01290 | 0.113232 | ||||||||
\(709\) | −8.02051 | −0.301217 | −0.150608 | − | 0.988594i | \(-0.548123\pi\) | ||||
−0.150608 | + | 0.988594i | \(0.548123\pi\) | |||||||
\(710\) | −10.7777 | −0.404478 | ||||||||
\(711\) | 14.9245 | 0.559711 | ||||||||
\(712\) | −9.63281 | −0.361005 | ||||||||
\(713\) | −9.79637 | −0.366877 | ||||||||
\(714\) | −10.5413 | −0.394499 | ||||||||
\(715\) | −0.0273660 | −0.00102343 | ||||||||
\(716\) | 5.22087 | 0.195113 | ||||||||
\(717\) | 24.5442 | 0.916621 | ||||||||
\(718\) | 70.1591 | 2.61831 | ||||||||
\(719\) | −17.4383 | −0.650339 | −0.325170 | − | 0.945656i | \(-0.605421\pi\) | ||||
−0.325170 | + | 0.945656i | \(0.605421\pi\) | |||||||
\(720\) | 2.31841 | 0.0864019 | ||||||||
\(721\) | −4.30979 | −0.160505 | ||||||||
\(722\) | −45.3484 | −1.68769 | ||||||||
\(723\) | −18.3505 | −0.682463 | ||||||||
\(724\) | −49.2548 | −1.83054 | ||||||||
\(725\) | −42.6985 | −1.58578 | ||||||||
\(726\) | −2.54331 | −0.0943913 | ||||||||
\(727\) | −21.4232 | −0.794541 | −0.397271 | − | 0.917701i | \(-0.630043\pi\) | ||||
−0.397271 | + | 0.917701i | \(0.630043\pi\) | |||||||
\(728\) | 0.310217 | 0.0114974 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.928057 | −0.0343489 | ||||||||
\(731\) | 79.1294 | 2.92671 | ||||||||
\(732\) | −4.46845 | −0.165159 | ||||||||
\(733\) | 24.8791 | 0.918929 | 0.459464 | − | 0.888196i | \(-0.348041\pi\) | ||||
0.459464 | + | 0.888196i | \(0.348041\pi\) | |||||||
\(734\) | −64.4391 | −2.37849 | ||||||||
\(735\) | 2.19153 | 0.0808359 | ||||||||
\(736\) | 17.0469 | 0.628356 | ||||||||
\(737\) | −0.140859 | −0.00518861 | ||||||||
\(738\) | −0.182017 | −0.00670015 | ||||||||
\(739\) | −3.44825 | −0.126846 | −0.0634230 | − | 0.997987i | \(-0.520202\pi\) | ||||
−0.0634230 | + | 0.997987i | \(0.520202\pi\) | |||||||
\(740\) | −8.30325 | −0.305233 | ||||||||
\(741\) | −0.0897424 | −0.00329677 | ||||||||
\(742\) | −12.4797 | −0.458144 | ||||||||
\(743\) | −18.1232 | −0.664874 | −0.332437 | − | 0.943125i | \(-0.607871\pi\) | ||||
−0.332437 | + | 0.943125i | \(0.607871\pi\) | |||||||
\(744\) | 19.2072 | 0.704171 | ||||||||
\(745\) | −5.07171 | −0.185813 | ||||||||
\(746\) | 58.3816 | 2.13750 | ||||||||
\(747\) | −1.08794 | −0.0398058 | ||||||||
\(748\) | −31.1026 | −1.13722 | ||||||||
\(749\) | −10.0732 | −0.368067 | ||||||||
\(750\) | 8.29614 | 0.302932 | ||||||||
\(751\) | 12.9982 | 0.474310 | 0.237155 | − | 0.971472i | \(-0.423785\pi\) | ||||
0.237155 | + | 0.971472i | \(0.423785\pi\) | |||||||
\(752\) | 79.1233 | 2.88533 | ||||||||
\(753\) | −2.34673 | −0.0855197 | ||||||||
\(754\) | 1.84238 | 0.0670954 | ||||||||
\(755\) | 5.46474 | 0.198882 | ||||||||
\(756\) | −2.66080 | −0.0967723 | ||||||||
\(757\) | −16.0448 | −0.583158 | −0.291579 | − | 0.956547i | \(-0.594181\pi\) | ||||
−0.291579 | + | 0.956547i | \(0.594181\pi\) | |||||||
\(758\) | −7.17365 | −0.260559 | ||||||||
\(759\) | 3.20203 | 0.116226 | ||||||||
\(760\) | 2.23904 | 0.0812185 | ||||||||
\(761\) | 40.4165 | 1.46510 | 0.732549 | − | 0.680714i | \(-0.238330\pi\) | ||||
0.732549 | + | 0.680714i | \(0.238330\pi\) | |||||||
\(762\) | 20.3297 | 0.736468 | ||||||||
\(763\) | 3.45039 | 0.124912 | ||||||||
\(764\) | −68.6532 | −2.48379 | ||||||||
\(765\) | 2.29543 | 0.0829916 | ||||||||
\(766\) | 65.1419 | 2.35367 | ||||||||
\(767\) | −0.0559518 | −0.00202030 | ||||||||
\(768\) | 29.4048 | 1.06105 | ||||||||
\(769\) | 25.1456 | 0.906774 | 0.453387 | − | 0.891314i | \(-0.350216\pi\) | ||||
0.453387 | + | 0.891314i | \(0.350216\pi\) | |||||||
\(770\) | −0.499437 | −0.0179984 | ||||||||
\(771\) | 2.07933 | 0.0748854 | ||||||||
\(772\) | −49.6822 | −1.78810 | ||||||||
\(773\) | −16.3560 | −0.588284 | −0.294142 | − | 0.955762i | \(-0.595034\pi\) | ||||
−0.294142 | + | 0.955762i | \(0.595034\pi\) | |||||||
\(774\) | 28.9134 | 1.03927 | ||||||||
\(775\) | 14.9644 | 0.537537 | ||||||||
\(776\) | −54.9206 | −1.97154 | ||||||||
\(777\) | 3.35522 | 0.120368 | ||||||||
\(778\) | −5.15226 | −0.184717 | ||||||||
\(779\) | −0.0773971 | −0.00277304 | ||||||||
\(780\) | −0.122283 | −0.00437845 | ||||||||
\(781\) | 12.8499 | 0.459805 | ||||||||
\(782\) | 56.6846 | 2.02704 | ||||||||
\(783\) | −8.72957 | −0.311970 | ||||||||
\(784\) | −46.7183 | −1.66851 | ||||||||
\(785\) | −1.99957 | −0.0713677 | ||||||||
\(786\) | 40.3690 | 1.43992 | ||||||||
\(787\) | 28.0304 | 0.999175 | 0.499588 | − | 0.866263i | \(-0.333485\pi\) | ||||
0.499588 | + | 0.866263i | \(0.333485\pi\) | |||||||
\(788\) | −79.1560 | −2.81981 | ||||||||
\(789\) | 24.1181 | 0.858625 | ||||||||
\(790\) | 12.5177 | 0.445359 | ||||||||
\(791\) | −7.34034 | −0.260992 | ||||||||
\(792\) | −6.27804 | −0.223081 | ||||||||
\(793\) | 0.0829823 | 0.00294679 | ||||||||
\(794\) | 2.74665 | 0.0974751 | ||||||||
\(795\) | 2.71753 | 0.0963808 | ||||||||
\(796\) | 109.554 | 3.88305 | ||||||||
\(797\) | −35.6574 | −1.26305 | −0.631525 | − | 0.775356i | \(-0.717571\pi\) | ||||
−0.631525 | + | 0.775356i | \(0.717571\pi\) | |||||||
\(798\) | −1.63782 | −0.0579783 | ||||||||
\(799\) | 78.3393 | 2.77144 | ||||||||
\(800\) | −26.0399 | −0.920649 | ||||||||
\(801\) | −1.53437 | −0.0542141 | ||||||||
\(802\) | 8.90292 | 0.314373 | ||||||||
\(803\) | 1.10649 | 0.0390473 | ||||||||
\(804\) | −0.629421 | −0.0221980 | ||||||||
\(805\) | 0.628790 | 0.0221619 | ||||||||
\(806\) | −0.645692 | −0.0227435 | ||||||||
\(807\) | 13.9942 | 0.492620 | ||||||||
\(808\) | 62.0324 | 2.18229 | ||||||||
\(809\) | 13.6655 | 0.480452 | 0.240226 | − | 0.970717i | \(-0.422778\pi\) | ||||
0.240226 | + | 0.970717i | \(0.422778\pi\) | |||||||
\(810\) | 0.838736 | 0.0294702 | ||||||||
\(811\) | 47.8791 | 1.68126 | 0.840631 | − | 0.541608i | \(-0.182184\pi\) | ||||
0.840631 | + | 0.541608i | \(0.182184\pi\) | |||||||
\(812\) | 23.2276 | 0.815130 | ||||||||
\(813\) | 24.2791 | 0.851506 | ||||||||
\(814\) | 14.3306 | 0.502289 | ||||||||
\(815\) | 5.89059 | 0.206338 | ||||||||
\(816\) | −48.9332 | −1.71300 | ||||||||
\(817\) | 12.2945 | 0.430130 | ||||||||
\(818\) | −69.1002 | −2.41603 | ||||||||
\(819\) | 0.0494129 | 0.00172663 | ||||||||
\(820\) | −0.105462 | −0.00368288 | ||||||||
\(821\) | 8.04263 | 0.280690 | 0.140345 | − | 0.990103i | \(-0.455179\pi\) | ||||
0.140345 | + | 0.990103i | \(0.455179\pi\) | |||||||
\(822\) | 43.1514 | 1.50508 | ||||||||
\(823\) | 12.4433 | 0.433745 | 0.216872 | − | 0.976200i | \(-0.430414\pi\) | ||||
0.216872 | + | 0.976200i | \(0.430414\pi\) | |||||||
\(824\) | −45.4387 | −1.58293 | ||||||||
\(825\) | −4.89124 | −0.170291 | ||||||||
\(826\) | −1.02114 | −0.0355298 | ||||||||
\(827\) | 12.2012 | 0.424278 | 0.212139 | − | 0.977240i | \(-0.431957\pi\) | ||||
0.212139 | + | 0.977240i | \(0.431957\pi\) | |||||||
\(828\) | 14.3081 | 0.497241 | ||||||||
\(829\) | −21.1707 | −0.735288 | −0.367644 | − | 0.929967i | \(-0.619835\pi\) | ||||
−0.367644 | + | 0.929967i | \(0.619835\pi\) | |||||||
\(830\) | −0.912497 | −0.0316732 | ||||||||
\(831\) | 16.3119 | 0.565852 | ||||||||
\(832\) | −0.0431713 | −0.00149670 | ||||||||
\(833\) | −46.2554 | −1.60265 | ||||||||
\(834\) | −40.0192 | −1.38575 | ||||||||
\(835\) | 6.99307 | 0.242005 | ||||||||
\(836\) | −4.83247 | −0.167134 | ||||||||
\(837\) | 3.05943 | 0.105749 | ||||||||
\(838\) | −39.8683 | −1.37723 | ||||||||
\(839\) | −39.8488 | −1.37573 | −0.687867 | − | 0.725837i | \(-0.741453\pi\) | ||||
−0.687867 | + | 0.725837i | \(0.741453\pi\) | |||||||
\(840\) | −1.23283 | −0.0425368 | ||||||||
\(841\) | 47.2055 | 1.62777 | ||||||||
\(842\) | −3.57861 | −0.123327 | ||||||||
\(843\) | −13.7085 | −0.472144 | ||||||||
\(844\) | 41.7509 | 1.43713 | ||||||||
\(845\) | −4.28488 | −0.147404 | ||||||||
\(846\) | 28.6246 | 0.984136 | ||||||||
\(847\) | 0.595463 | 0.0204604 | ||||||||
\(848\) | −57.9313 | −1.98937 | ||||||||
\(849\) | −31.0223 | −1.06468 | ||||||||
\(850\) | −86.5883 | −2.96995 | ||||||||
\(851\) | −18.0423 | −0.618481 | ||||||||
\(852\) | 57.4190 | 1.96714 | ||||||||
\(853\) | 47.3637 | 1.62170 | 0.810851 | − | 0.585252i | \(-0.199005\pi\) | ||||
0.810851 | + | 0.585252i | \(0.199005\pi\) | |||||||
\(854\) | 1.51445 | 0.0518234 | ||||||||
\(855\) | 0.356646 | 0.0121970 | ||||||||
\(856\) | −106.203 | −3.62995 | ||||||||
\(857\) | 0.0360945 | 0.00123297 | 0.000616483 | − | 1.00000i | \(-0.499804\pi\) | ||||
0.000616483 | 1.00000i | \(0.499804\pi\) | ||||||||
\(858\) | 0.211050 | 0.00720513 | ||||||||
\(859\) | −6.64544 | −0.226740 | −0.113370 | − | 0.993553i | \(-0.536164\pi\) | ||||
−0.113370 | + | 0.993553i | \(0.536164\pi\) | |||||||
\(860\) | 16.7525 | 0.571257 | ||||||||
\(861\) | 0.0426155 | 0.00145233 | ||||||||
\(862\) | −59.8650 | −2.03901 | ||||||||
\(863\) | 29.7608 | 1.01307 | 0.506535 | − | 0.862219i | \(-0.330926\pi\) | ||||
0.506535 | + | 0.862219i | \(0.330926\pi\) | |||||||
\(864\) | −5.32378 | −0.181119 | ||||||||
\(865\) | 0.978765 | 0.0332790 | ||||||||
\(866\) | 74.4454 | 2.52976 | ||||||||
\(867\) | −31.4484 | −1.06804 | ||||||||
\(868\) | −8.14052 | −0.276307 | ||||||||
\(869\) | −14.9245 | −0.506278 | ||||||||
\(870\) | −7.32181 | −0.248233 | ||||||||
\(871\) | 0.0116888 | 0.000396060 0 | ||||||||
\(872\) | 36.3779 | 1.23191 | ||||||||
\(873\) | −8.74805 | −0.296077 | ||||||||
\(874\) | 8.80719 | 0.297908 | ||||||||
\(875\) | −1.94237 | −0.0656640 | ||||||||
\(876\) | 4.94431 | 0.167053 | ||||||||
\(877\) | −16.7597 | −0.565934 | −0.282967 | − | 0.959130i | \(-0.591319\pi\) | ||||
−0.282967 | + | 0.959130i | \(0.591319\pi\) | |||||||
\(878\) | −43.4121 | −1.46509 | ||||||||
\(879\) | −4.76769 | −0.160810 | ||||||||
\(880\) | −2.31841 | −0.0781534 | ||||||||
\(881\) | 24.3345 | 0.819851 | 0.409925 | − | 0.912119i | \(-0.365555\pi\) | ||||
0.409925 | + | 0.912119i | \(0.365555\pi\) | |||||||
\(882\) | −16.9014 | −0.569100 | ||||||||
\(883\) | 26.7278 | 0.899461 | 0.449731 | − | 0.893164i | \(-0.351520\pi\) | ||||
0.449731 | + | 0.893164i | \(0.351520\pi\) | |||||||
\(884\) | 2.58096 | 0.0868072 | ||||||||
\(885\) | 0.222358 | 0.00747449 | ||||||||
\(886\) | −83.7404 | −2.81331 | ||||||||
\(887\) | 42.4352 | 1.42484 | 0.712418 | − | 0.701756i | \(-0.247600\pi\) | ||||
0.712418 | + | 0.701756i | \(0.247600\pi\) | |||||||
\(888\) | 35.3745 | 1.18709 | ||||||||
\(889\) | −4.75977 | −0.159638 | ||||||||
\(890\) | −1.28693 | −0.0431379 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −106.585 | −3.56874 | ||||||||
\(893\) | 12.1717 | 0.407311 | ||||||||
\(894\) | 39.1138 | 1.30816 | ||||||||
\(895\) | 0.385311 | 0.0128795 | ||||||||
\(896\) | −7.12812 | −0.238134 | ||||||||
\(897\) | −0.265712 | −0.00887186 | ||||||||
\(898\) | −78.2579 | −2.61150 | ||||||||
\(899\) | −26.7075 | −0.890745 | ||||||||
\(900\) | −21.8563 | −0.728543 | ||||||||
\(901\) | −57.3573 | −1.91085 | ||||||||
\(902\) | 0.182017 | 0.00606052 | ||||||||
\(903\) | −6.76945 | −0.225273 | ||||||||
\(904\) | −77.3901 | −2.57396 | ||||||||
\(905\) | −3.63511 | −0.120835 | ||||||||
\(906\) | −42.1448 | −1.40017 | ||||||||
\(907\) | −7.59234 | −0.252100 | −0.126050 | − | 0.992024i | \(-0.540230\pi\) | ||||
−0.126050 | + | 0.992024i | \(0.540230\pi\) | |||||||
\(908\) | 22.2818 | 0.739448 | ||||||||
\(909\) | 9.88085 | 0.327727 | ||||||||
\(910\) | 0.0414444 | 0.00137387 | ||||||||
\(911\) | −30.6962 | −1.01701 | −0.508505 | − | 0.861059i | \(-0.669802\pi\) | ||||
−0.508505 | + | 0.861059i | \(0.669802\pi\) | |||||||
\(912\) | −7.60284 | −0.251755 | ||||||||
\(913\) | 1.08794 | 0.0360057 | ||||||||
\(914\) | −30.2640 | −1.00104 | ||||||||
\(915\) | −0.329781 | −0.0109022 | ||||||||
\(916\) | 4.09247 | 0.135219 | ||||||||
\(917\) | −9.45155 | −0.312118 | ||||||||
\(918\) | −17.7027 | −0.584276 | ||||||||
\(919\) | −47.5570 | −1.56876 | −0.784380 | − | 0.620281i | \(-0.787019\pi\) | ||||
−0.784380 | + | 0.620281i | \(0.787019\pi\) | |||||||
\(920\) | 6.62941 | 0.218565 | ||||||||
\(921\) | 9.09194 | 0.299590 | ||||||||
\(922\) | 24.2576 | 0.798880 | ||||||||
\(923\) | −1.06631 | −0.0350981 | ||||||||
\(924\) | 2.66080 | 0.0875338 | ||||||||
\(925\) | 27.5604 | 0.906180 | ||||||||
\(926\) | 57.9972 | 1.90590 | ||||||||
\(927\) | −7.23771 | −0.237718 | ||||||||
\(928\) | 46.4743 | 1.52559 | ||||||||
\(929\) | −24.6228 | −0.807847 | −0.403923 | − | 0.914793i | \(-0.632354\pi\) | ||||
−0.403923 | + | 0.914793i | \(0.632354\pi\) | |||||||
\(930\) | 2.56605 | 0.0841442 | ||||||||
\(931\) | −7.18678 | −0.235537 | ||||||||
\(932\) | 32.7227 | 1.07187 | ||||||||
\(933\) | −0.130155 | −0.00426108 | ||||||||
\(934\) | 104.473 | 3.41847 | ||||||||
\(935\) | −2.29543 | −0.0750687 | ||||||||
\(936\) | 0.520967 | 0.0170283 | ||||||||
\(937\) | 13.4835 | 0.440487 | 0.220244 | − | 0.975445i | \(-0.429315\pi\) | ||||
0.220244 | + | 0.975445i | \(0.429315\pi\) | |||||||
\(938\) | 0.213324 | 0.00696527 | ||||||||
\(939\) | 18.8073 | 0.613753 | ||||||||
\(940\) | 16.5853 | 0.540951 | ||||||||
\(941\) | −51.2951 | −1.67217 | −0.836086 | − | 0.548598i | \(-0.815162\pi\) | ||||
−0.836086 | + | 0.548598i | \(0.815162\pi\) | |||||||
\(942\) | 15.4210 | 0.502442 | ||||||||
\(943\) | −0.229160 | −0.00746246 | ||||||||
\(944\) | −4.74015 | −0.154279 | ||||||||
\(945\) | −0.196372 | −0.00638799 | ||||||||
\(946\) | −28.9134 | −0.940054 | ||||||||
\(947\) | 36.6121 | 1.18973 | 0.594867 | − | 0.803824i | \(-0.297205\pi\) | ||||
0.594867 | + | 0.803824i | \(0.297205\pi\) | |||||||
\(948\) | −66.6892 | −2.16597 | ||||||||
\(949\) | −0.0918195 | −0.00298059 | ||||||||
\(950\) | −13.4534 | −0.436485 | ||||||||
\(951\) | −21.5314 | −0.698203 | ||||||||
\(952\) | 26.0207 | 0.843336 | ||||||||
\(953\) | −34.3089 | −1.11137 | −0.555687 | − | 0.831392i | \(-0.687545\pi\) | ||||
−0.555687 | + | 0.831392i | \(0.687545\pi\) | |||||||
\(954\) | −20.9580 | −0.678539 | ||||||||
\(955\) | −5.06675 | −0.163956 | ||||||||
\(956\) | −109.675 | −3.54713 | ||||||||
\(957\) | 8.72957 | 0.282187 | ||||||||
\(958\) | −30.1049 | −0.972646 | ||||||||
\(959\) | −10.1030 | −0.326243 | ||||||||
\(960\) | 0.171568 | 0.00553732 | ||||||||
\(961\) | −21.6399 | −0.698062 | ||||||||
\(962\) | −1.18919 | −0.0383410 | ||||||||
\(963\) | −16.9166 | −0.545130 | ||||||||
\(964\) | 81.9984 | 2.64099 | ||||||||
\(965\) | −3.66665 | −0.118034 | ||||||||
\(966\) | −4.84931 | −0.156024 | ||||||||
\(967\) | 35.6507 | 1.14645 | 0.573225 | − | 0.819398i | \(-0.305692\pi\) | ||||
0.573225 | + | 0.819398i | \(0.305692\pi\) | |||||||
\(968\) | 6.27804 | 0.201784 | ||||||||
\(969\) | −7.52751 | −0.241819 | ||||||||
\(970\) | −7.33730 | −0.235587 | ||||||||
\(971\) | 2.45087 | 0.0786520 | 0.0393260 | − | 0.999226i | \(-0.487479\pi\) | ||||
0.0393260 | + | 0.999226i | \(0.487479\pi\) | |||||||
\(972\) | −4.46845 | −0.143326 | ||||||||
\(973\) | 9.36965 | 0.300377 | ||||||||
\(974\) | 59.0564 | 1.89229 | ||||||||
\(975\) | 0.405887 | 0.0129988 | ||||||||
\(976\) | 7.03014 | 0.225029 | ||||||||
\(977\) | −36.7003 | −1.17415 | −0.587073 | − | 0.809534i | \(-0.699720\pi\) | ||||
−0.587073 | + | 0.809534i | \(0.699720\pi\) | |||||||
\(978\) | −45.4290 | −1.45266 | ||||||||
\(979\) | 1.53437 | 0.0490385 | ||||||||
\(980\) | −9.79275 | −0.312818 | ||||||||
\(981\) | 5.79446 | 0.185003 | ||||||||
\(982\) | −27.1017 | −0.864851 | ||||||||
\(983\) | −34.5193 | −1.10099 | −0.550497 | − | 0.834837i | \(-0.685562\pi\) | ||||
−0.550497 | + | 0.834837i | \(0.685562\pi\) | |||||||
\(984\) | 0.449301 | 0.0143232 | ||||||||
\(985\) | −5.84187 | −0.186138 | ||||||||
\(986\) | 154.537 | 4.92146 | ||||||||
\(987\) | −6.70186 | −0.213322 | ||||||||
\(988\) | 0.401009 | 0.0127578 | ||||||||
\(989\) | 36.4019 | 1.15751 | ||||||||
\(990\) | −0.838736 | −0.0266568 | ||||||||
\(991\) | −36.6557 | −1.16441 | −0.582204 | − | 0.813043i | \(-0.697809\pi\) | ||||
−0.582204 | + | 0.813043i | \(0.697809\pi\) | |||||||
\(992\) | −16.2877 | −0.517135 | ||||||||
\(993\) | 5.77423 | 0.183240 | ||||||||
\(994\) | −19.4605 | −0.617250 | ||||||||
\(995\) | 8.08533 | 0.256322 | ||||||||
\(996\) | 4.86142 | 0.154040 | ||||||||
\(997\) | 17.8981 | 0.566840 | 0.283420 | − | 0.958996i | \(-0.408531\pi\) | ||||
0.283420 | + | 0.958996i | \(0.408531\pi\) | |||||||
\(998\) | 105.840 | 3.35032 | ||||||||
\(999\) | 5.63463 | 0.178272 |
(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 | 2013.2.a.h.1.13 | ✓ | 14 | |
3.2 | odd | 2 | 6039.2.a.j.1.2 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.h.1.13 | ✓ | 14 | 1.1 | even | 1 | trivial | |
6039.2.a.j.1.2 | 14 | 3.2 | odd | 2 |