Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6010,2,Mod(1,6010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6010, 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("6010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6010 = 2 \cdot 5 \cdot 601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6010.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: | \(47.9900916148\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + 164 x^{7} + 2332 x^{6} - 440 x^{5} - 1344 x^{4} + 244 x^{3} + 295 x^{2} + \cdots - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.624714\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6010.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.62471 | −0.938029 | −0.469015 | − | 0.883190i | \(-0.655391\pi\) | ||||
−0.469015 | + | 0.883190i | \(0.655391\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.62471 | −0.663287 | ||||||||
\(7\) | −0.333284 | −0.125969 | −0.0629847 | − | 0.998014i | \(-0.520062\pi\) | ||||
−0.0629847 | + | 0.998014i | \(0.520062\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.360304 | −0.120101 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −2.68771 | −0.810375 | −0.405187 | − | 0.914234i | \(-0.632794\pi\) | ||||
−0.405187 | + | 0.914234i | \(0.632794\pi\) | |||||||
\(12\) | −1.62471 | −0.469015 | ||||||||
\(13\) | 1.45394 | 0.403251 | 0.201625 | − | 0.979463i | \(-0.435378\pi\) | ||||
0.201625 | + | 0.979463i | \(0.435378\pi\) | |||||||
\(14\) | −0.333284 | −0.0890739 | ||||||||
\(15\) | −1.62471 | −0.419499 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.11004 | −0.996830 | −0.498415 | − | 0.866939i | \(-0.666084\pi\) | ||||
−0.498415 | + | 0.866939i | \(0.666084\pi\) | |||||||
\(18\) | −0.360304 | −0.0849244 | ||||||||
\(19\) | 8.34271 | 1.91395 | 0.956975 | − | 0.290172i | \(-0.0937124\pi\) | ||||
0.956975 | + | 0.290172i | \(0.0937124\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0.541491 | 0.118163 | ||||||||
\(22\) | −2.68771 | −0.573022 | ||||||||
\(23\) | −4.74671 | −0.989757 | −0.494878 | − | 0.868962i | \(-0.664787\pi\) | ||||
−0.494878 | + | 0.868962i | \(0.664787\pi\) | |||||||
\(24\) | −1.62471 | −0.331643 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.45394 | 0.285141 | ||||||||
\(27\) | 5.45953 | 1.05069 | ||||||||
\(28\) | −0.333284 | −0.0629847 | ||||||||
\(29\) | −1.44606 | −0.268527 | −0.134264 | − | 0.990946i | \(-0.542867\pi\) | ||||
−0.134264 | + | 0.990946i | \(0.542867\pi\) | |||||||
\(30\) | −1.62471 | −0.296631 | ||||||||
\(31\) | −3.92911 | −0.705689 | −0.352844 | − | 0.935682i | \(-0.614785\pi\) | ||||
−0.352844 | + | 0.935682i | \(0.614785\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.36676 | 0.760155 | ||||||||
\(34\) | −4.11004 | −0.704865 | ||||||||
\(35\) | −0.333284 | −0.0563353 | ||||||||
\(36\) | −0.360304 | −0.0600506 | ||||||||
\(37\) | 3.53964 | 0.581913 | 0.290956 | − | 0.956736i | \(-0.406027\pi\) | ||||
0.290956 | + | 0.956736i | \(0.406027\pi\) | |||||||
\(38\) | 8.34271 | 1.35337 | ||||||||
\(39\) | −2.36224 | −0.378261 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 2.16999 | 0.338896 | 0.169448 | − | 0.985539i | \(-0.445801\pi\) | ||||
0.169448 | + | 0.985539i | \(0.445801\pi\) | |||||||
\(42\) | 0.541491 | 0.0835539 | ||||||||
\(43\) | −5.62222 | −0.857381 | −0.428690 | − | 0.903451i | \(-0.641025\pi\) | ||||
−0.428690 | + | 0.903451i | \(0.641025\pi\) | |||||||
\(44\) | −2.68771 | −0.405187 | ||||||||
\(45\) | −0.360304 | −0.0537109 | ||||||||
\(46\) | −4.74671 | −0.699864 | ||||||||
\(47\) | 6.48708 | 0.946238 | 0.473119 | − | 0.880999i | \(-0.343128\pi\) | ||||
0.473119 | + | 0.880999i | \(0.343128\pi\) | |||||||
\(48\) | −1.62471 | −0.234507 | ||||||||
\(49\) | −6.88892 | −0.984132 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 6.67763 | 0.935056 | ||||||||
\(52\) | 1.45394 | 0.201625 | ||||||||
\(53\) | −5.31846 | −0.730547 | −0.365273 | − | 0.930900i | \(-0.619025\pi\) | ||||
−0.365273 | + | 0.930900i | \(0.619025\pi\) | |||||||
\(54\) | 5.45953 | 0.742948 | ||||||||
\(55\) | −2.68771 | −0.362411 | ||||||||
\(56\) | −0.333284 | −0.0445369 | ||||||||
\(57\) | −13.5545 | −1.79534 | ||||||||
\(58\) | −1.44606 | −0.189877 | ||||||||
\(59\) | −3.43978 | −0.447822 | −0.223911 | − | 0.974610i | \(-0.571882\pi\) | ||||
−0.223911 | + | 0.974610i | \(0.571882\pi\) | |||||||
\(60\) | −1.62471 | −0.209750 | ||||||||
\(61\) | −8.19878 | −1.04975 | −0.524873 | − | 0.851181i | \(-0.675887\pi\) | ||||
−0.524873 | + | 0.851181i | \(0.675887\pi\) | |||||||
\(62\) | −3.92911 | −0.498997 | ||||||||
\(63\) | 0.120083 | 0.0151291 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.45394 | 0.180339 | ||||||||
\(66\) | 4.36676 | 0.537511 | ||||||||
\(67\) | 3.23813 | 0.395600 | 0.197800 | − | 0.980242i | \(-0.436620\pi\) | ||||
0.197800 | + | 0.980242i | \(0.436620\pi\) | |||||||
\(68\) | −4.11004 | −0.498415 | ||||||||
\(69\) | 7.71204 | 0.928421 | ||||||||
\(70\) | −0.333284 | −0.0398350 | ||||||||
\(71\) | 0.556242 | 0.0660137 | 0.0330069 | − | 0.999455i | \(-0.489492\pi\) | ||||
0.0330069 | + | 0.999455i | \(0.489492\pi\) | |||||||
\(72\) | −0.360304 | −0.0424622 | ||||||||
\(73\) | 12.1155 | 1.41801 | 0.709007 | − | 0.705201i | \(-0.249143\pi\) | ||||
0.709007 | + | 0.705201i | \(0.249143\pi\) | |||||||
\(74\) | 3.53964 | 0.411475 | ||||||||
\(75\) | −1.62471 | −0.187606 | ||||||||
\(76\) | 8.34271 | 0.956975 | ||||||||
\(77\) | 0.895770 | 0.102083 | ||||||||
\(78\) | −2.36224 | −0.267471 | ||||||||
\(79\) | 2.81119 | 0.316283 | 0.158142 | − | 0.987416i | \(-0.449450\pi\) | ||||
0.158142 | + | 0.987416i | \(0.449450\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −7.78927 | −0.865474 | ||||||||
\(82\) | 2.16999 | 0.239636 | ||||||||
\(83\) | −5.47476 | −0.600933 | −0.300466 | − | 0.953792i | \(-0.597142\pi\) | ||||
−0.300466 | + | 0.953792i | \(0.597142\pi\) | |||||||
\(84\) | 0.541491 | 0.0590815 | ||||||||
\(85\) | −4.11004 | −0.445796 | ||||||||
\(86\) | −5.62222 | −0.606260 | ||||||||
\(87\) | 2.34944 | 0.251886 | ||||||||
\(88\) | −2.68771 | −0.286511 | ||||||||
\(89\) | −11.3071 | −1.19855 | −0.599276 | − | 0.800542i | \(-0.704545\pi\) | ||||
−0.599276 | + | 0.800542i | \(0.704545\pi\) | |||||||
\(90\) | −0.360304 | −0.0379793 | ||||||||
\(91\) | −0.484576 | −0.0507973 | ||||||||
\(92\) | −4.74671 | −0.494878 | ||||||||
\(93\) | 6.38368 | 0.661956 | ||||||||
\(94\) | 6.48708 | 0.669091 | ||||||||
\(95\) | 8.34271 | 0.855944 | ||||||||
\(96\) | −1.62471 | −0.165822 | ||||||||
\(97\) | 13.6146 | 1.38235 | 0.691174 | − | 0.722688i | \(-0.257094\pi\) | ||||
0.691174 | + | 0.722688i | \(0.257094\pi\) | |||||||
\(98\) | −6.88892 | −0.695886 | ||||||||
\(99\) | 0.968392 | 0.0973270 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −11.3537 | −1.12973 | −0.564865 | − | 0.825183i | \(-0.691072\pi\) | ||||
−0.564865 | + | 0.825183i | \(0.691072\pi\) | |||||||
\(102\) | 6.67763 | 0.661184 | ||||||||
\(103\) | −12.9895 | −1.27990 | −0.639948 | − | 0.768418i | \(-0.721044\pi\) | ||||
−0.639948 | + | 0.768418i | \(0.721044\pi\) | |||||||
\(104\) | 1.45394 | 0.142571 | ||||||||
\(105\) | 0.541491 | 0.0528441 | ||||||||
\(106\) | −5.31846 | −0.516575 | ||||||||
\(107\) | −11.8474 | −1.14533 | −0.572664 | − | 0.819790i | \(-0.694090\pi\) | ||||
−0.572664 | + | 0.819790i | \(0.694090\pi\) | |||||||
\(108\) | 5.45953 | 0.525344 | ||||||||
\(109\) | −15.6620 | −1.50015 | −0.750073 | − | 0.661355i | \(-0.769982\pi\) | ||||
−0.750073 | + | 0.661355i | \(0.769982\pi\) | |||||||
\(110\) | −2.68771 | −0.256263 | ||||||||
\(111\) | −5.75090 | −0.545851 | ||||||||
\(112\) | −0.333284 | −0.0314924 | ||||||||
\(113\) | −3.77807 | −0.355411 | −0.177705 | − | 0.984084i | \(-0.556867\pi\) | ||||
−0.177705 | + | 0.984084i | \(0.556867\pi\) | |||||||
\(114\) | −13.5545 | −1.26950 | ||||||||
\(115\) | −4.74671 | −0.442633 | ||||||||
\(116\) | −1.44606 | −0.134264 | ||||||||
\(117\) | −0.523861 | −0.0484309 | ||||||||
\(118\) | −3.43978 | −0.316658 | ||||||||
\(119\) | 1.36981 | 0.125570 | ||||||||
\(120\) | −1.62471 | −0.148315 | ||||||||
\(121\) | −3.77622 | −0.343292 | ||||||||
\(122\) | −8.19878 | −0.742282 | ||||||||
\(123\) | −3.52562 | −0.317894 | ||||||||
\(124\) | −3.92911 | −0.352844 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.120083 | 0.0106979 | ||||||||
\(127\) | −18.1828 | −1.61346 | −0.806729 | − | 0.590921i | \(-0.798764\pi\) | ||||
−0.806729 | + | 0.590921i | \(0.798764\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 9.13450 | 0.804248 | ||||||||
\(130\) | 1.45394 | 0.127519 | ||||||||
\(131\) | −16.2325 | −1.41824 | −0.709119 | − | 0.705088i | \(-0.750907\pi\) | ||||
−0.709119 | + | 0.705088i | \(0.750907\pi\) | |||||||
\(132\) | 4.36676 | 0.380078 | ||||||||
\(133\) | −2.78049 | −0.241099 | ||||||||
\(134\) | 3.23813 | 0.279732 | ||||||||
\(135\) | 5.45953 | 0.469882 | ||||||||
\(136\) | −4.11004 | −0.352433 | ||||||||
\(137\) | 13.9834 | 1.19468 | 0.597341 | − | 0.801988i | \(-0.296224\pi\) | ||||
0.597341 | + | 0.801988i | \(0.296224\pi\) | |||||||
\(138\) | 7.71204 | 0.656493 | ||||||||
\(139\) | 13.7715 | 1.16808 | 0.584040 | − | 0.811725i | \(-0.301471\pi\) | ||||
0.584040 | + | 0.811725i | \(0.301471\pi\) | |||||||
\(140\) | −0.333284 | −0.0281676 | ||||||||
\(141\) | −10.5396 | −0.887599 | ||||||||
\(142\) | 0.556242 | 0.0466788 | ||||||||
\(143\) | −3.90777 | −0.326784 | ||||||||
\(144\) | −0.360304 | −0.0300253 | ||||||||
\(145\) | −1.44606 | −0.120089 | ||||||||
\(146\) | 12.1155 | 1.00269 | ||||||||
\(147\) | 11.1925 | 0.923144 | ||||||||
\(148\) | 3.53964 | 0.290956 | ||||||||
\(149\) | −7.71007 | −0.631634 | −0.315817 | − | 0.948820i | \(-0.602279\pi\) | ||||
−0.315817 | + | 0.948820i | \(0.602279\pi\) | |||||||
\(150\) | −1.62471 | −0.132657 | ||||||||
\(151\) | 16.0886 | 1.30927 | 0.654635 | − | 0.755945i | \(-0.272822\pi\) | ||||
0.654635 | + | 0.755945i | \(0.272822\pi\) | |||||||
\(152\) | 8.34271 | 0.676683 | ||||||||
\(153\) | 1.48086 | 0.119721 | ||||||||
\(154\) | 0.895770 | 0.0721832 | ||||||||
\(155\) | −3.92911 | −0.315593 | ||||||||
\(156\) | −2.36224 | −0.189131 | ||||||||
\(157\) | −1.65930 | −0.132426 | −0.0662132 | − | 0.997805i | \(-0.521092\pi\) | ||||
−0.0662132 | + | 0.997805i | \(0.521092\pi\) | |||||||
\(158\) | 2.81119 | 0.223646 | ||||||||
\(159\) | 8.64098 | 0.685274 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 1.58200 | 0.124679 | ||||||||
\(162\) | −7.78927 | −0.611983 | ||||||||
\(163\) | 2.60909 | 0.204360 | 0.102180 | − | 0.994766i | \(-0.467418\pi\) | ||||
0.102180 | + | 0.994766i | \(0.467418\pi\) | |||||||
\(164\) | 2.16999 | 0.169448 | ||||||||
\(165\) | 4.36676 | 0.339952 | ||||||||
\(166\) | −5.47476 | −0.424924 | ||||||||
\(167\) | −0.268612 | −0.0207858 | −0.0103929 | − | 0.999946i | \(-0.503308\pi\) | ||||
−0.0103929 | + | 0.999946i | \(0.503308\pi\) | |||||||
\(168\) | 0.541491 | 0.0417769 | ||||||||
\(169\) | −10.8861 | −0.837389 | ||||||||
\(170\) | −4.11004 | −0.315225 | ||||||||
\(171\) | −3.00591 | −0.229868 | ||||||||
\(172\) | −5.62222 | −0.428690 | ||||||||
\(173\) | −11.6388 | −0.884882 | −0.442441 | − | 0.896798i | \(-0.645887\pi\) | ||||
−0.442441 | + | 0.896798i | \(0.645887\pi\) | |||||||
\(174\) | 2.34944 | 0.178110 | ||||||||
\(175\) | −0.333284 | −0.0251939 | ||||||||
\(176\) | −2.68771 | −0.202594 | ||||||||
\(177\) | 5.58867 | 0.420070 | ||||||||
\(178\) | −11.3071 | −0.847504 | ||||||||
\(179\) | 6.79330 | 0.507755 | 0.253878 | − | 0.967236i | \(-0.418294\pi\) | ||||
0.253878 | + | 0.967236i | \(0.418294\pi\) | |||||||
\(180\) | −0.360304 | −0.0268555 | ||||||||
\(181\) | 0.611592 | 0.0454593 | 0.0227296 | − | 0.999742i | \(-0.492764\pi\) | ||||
0.0227296 | + | 0.999742i | \(0.492764\pi\) | |||||||
\(182\) | −0.484576 | −0.0359191 | ||||||||
\(183\) | 13.3207 | 0.984692 | ||||||||
\(184\) | −4.74671 | −0.349932 | ||||||||
\(185\) | 3.53964 | 0.260239 | ||||||||
\(186\) | 6.38368 | 0.468074 | ||||||||
\(187\) | 11.0466 | 0.807806 | ||||||||
\(188\) | 6.48708 | 0.473119 | ||||||||
\(189\) | −1.81957 | −0.132355 | ||||||||
\(190\) | 8.34271 | 0.605244 | ||||||||
\(191\) | −23.5883 | −1.70679 | −0.853396 | − | 0.521263i | \(-0.825461\pi\) | ||||
−0.853396 | + | 0.521263i | \(0.825461\pi\) | |||||||
\(192\) | −1.62471 | −0.117254 | ||||||||
\(193\) | −8.93664 | −0.643274 | −0.321637 | − | 0.946863i | \(-0.604233\pi\) | ||||
−0.321637 | + | 0.946863i | \(0.604233\pi\) | |||||||
\(194\) | 13.6146 | 0.977468 | ||||||||
\(195\) | −2.36224 | −0.169164 | ||||||||
\(196\) | −6.88892 | −0.492066 | ||||||||
\(197\) | −16.9345 | −1.20653 | −0.603266 | − | 0.797540i | \(-0.706134\pi\) | ||||
−0.603266 | + | 0.797540i | \(0.706134\pi\) | |||||||
\(198\) | 0.968392 | 0.0688206 | ||||||||
\(199\) | 10.3990 | 0.737169 | 0.368584 | − | 0.929594i | \(-0.379843\pi\) | ||||
0.368584 | + | 0.929594i | \(0.379843\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −5.26103 | −0.371085 | ||||||||
\(202\) | −11.3537 | −0.798840 | ||||||||
\(203\) | 0.481949 | 0.0338262 | ||||||||
\(204\) | 6.67763 | 0.467528 | ||||||||
\(205\) | 2.16999 | 0.151559 | ||||||||
\(206\) | −12.9895 | −0.905024 | ||||||||
\(207\) | 1.71026 | 0.118871 | ||||||||
\(208\) | 1.45394 | 0.100813 | ||||||||
\(209\) | −22.4228 | −1.55102 | ||||||||
\(210\) | 0.541491 | 0.0373664 | ||||||||
\(211\) | 4.69539 | 0.323244 | 0.161622 | − | 0.986853i | \(-0.448328\pi\) | ||||
0.161622 | + | 0.986853i | \(0.448328\pi\) | |||||||
\(212\) | −5.31846 | −0.365273 | ||||||||
\(213\) | −0.903734 | −0.0619228 | ||||||||
\(214\) | −11.8474 | −0.809869 | ||||||||
\(215\) | −5.62222 | −0.383432 | ||||||||
\(216\) | 5.45953 | 0.371474 | ||||||||
\(217\) | 1.30951 | 0.0888952 | ||||||||
\(218\) | −15.6620 | −1.06076 | ||||||||
\(219\) | −19.6843 | −1.33014 | ||||||||
\(220\) | −2.68771 | −0.181205 | ||||||||
\(221\) | −5.97575 | −0.401973 | ||||||||
\(222\) | −5.75090 | −0.385975 | ||||||||
\(223\) | 15.9530 | 1.06829 | 0.534145 | − | 0.845393i | \(-0.320634\pi\) | ||||
0.534145 | + | 0.845393i | \(0.320634\pi\) | |||||||
\(224\) | −0.333284 | −0.0222685 | ||||||||
\(225\) | −0.360304 | −0.0240202 | ||||||||
\(226\) | −3.77807 | −0.251313 | ||||||||
\(227\) | 19.0713 | 1.26581 | 0.632904 | − | 0.774230i | \(-0.281863\pi\) | ||||
0.632904 | + | 0.774230i | \(0.281863\pi\) | |||||||
\(228\) | −13.5545 | −0.897670 | ||||||||
\(229\) | −17.3615 | −1.14728 | −0.573639 | − | 0.819109i | \(-0.694469\pi\) | ||||
−0.573639 | + | 0.819109i | \(0.694469\pi\) | |||||||
\(230\) | −4.74671 | −0.312989 | ||||||||
\(231\) | −1.45537 | −0.0957564 | ||||||||
\(232\) | −1.44606 | −0.0949386 | ||||||||
\(233\) | 12.4461 | 0.815369 | 0.407684 | − | 0.913123i | \(-0.366336\pi\) | ||||
0.407684 | + | 0.913123i | \(0.366336\pi\) | |||||||
\(234\) | −0.523861 | −0.0342458 | ||||||||
\(235\) | 6.48708 | 0.423170 | ||||||||
\(236\) | −3.43978 | −0.223911 | ||||||||
\(237\) | −4.56737 | −0.296683 | ||||||||
\(238\) | 1.36981 | 0.0887915 | ||||||||
\(239\) | 19.8560 | 1.28438 | 0.642189 | − | 0.766546i | \(-0.278026\pi\) | ||||
0.642189 | + | 0.766546i | \(0.278026\pi\) | |||||||
\(240\) | −1.62471 | −0.104875 | ||||||||
\(241\) | 13.1376 | 0.846270 | 0.423135 | − | 0.906067i | \(-0.360930\pi\) | ||||
0.423135 | + | 0.906067i | \(0.360930\pi\) | |||||||
\(242\) | −3.77622 | −0.242744 | ||||||||
\(243\) | −3.72326 | −0.238847 | ||||||||
\(244\) | −8.19878 | −0.524873 | ||||||||
\(245\) | −6.88892 | −0.440117 | ||||||||
\(246\) | −3.52562 | −0.224785 | ||||||||
\(247\) | 12.1298 | 0.771802 | ||||||||
\(248\) | −3.92911 | −0.249499 | ||||||||
\(249\) | 8.89492 | 0.563693 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 9.77582 | 0.617044 | 0.308522 | − | 0.951217i | \(-0.400166\pi\) | ||||
0.308522 | + | 0.951217i | \(0.400166\pi\) | |||||||
\(252\) | 0.120083 | 0.00756454 | ||||||||
\(253\) | 12.7578 | 0.802074 | ||||||||
\(254\) | −18.1828 | −1.14089 | ||||||||
\(255\) | 6.67763 | 0.418170 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.08949 | −0.566987 | −0.283493 | − | 0.958974i | \(-0.591493\pi\) | ||||
−0.283493 | + | 0.958974i | \(0.591493\pi\) | |||||||
\(258\) | 9.13450 | 0.568689 | ||||||||
\(259\) | −1.17970 | −0.0733033 | ||||||||
\(260\) | 1.45394 | 0.0901697 | ||||||||
\(261\) | 0.521022 | 0.0322504 | ||||||||
\(262\) | −16.2325 | −1.00285 | ||||||||
\(263\) | −22.2251 | −1.37046 | −0.685230 | − | 0.728327i | \(-0.740298\pi\) | ||||
−0.685230 | + | 0.728327i | \(0.740298\pi\) | |||||||
\(264\) | 4.36676 | 0.268756 | ||||||||
\(265\) | −5.31846 | −0.326711 | ||||||||
\(266\) | −2.78049 | −0.170483 | ||||||||
\(267\) | 18.3708 | 1.12428 | ||||||||
\(268\) | 3.23813 | 0.197800 | ||||||||
\(269\) | −20.4234 | −1.24523 | −0.622617 | − | 0.782526i | \(-0.713931\pi\) | ||||
−0.622617 | + | 0.782526i | \(0.713931\pi\) | |||||||
\(270\) | 5.45953 | 0.332257 | ||||||||
\(271\) | 2.62739 | 0.159603 | 0.0798014 | − | 0.996811i | \(-0.474571\pi\) | ||||
0.0798014 | + | 0.996811i | \(0.474571\pi\) | |||||||
\(272\) | −4.11004 | −0.249208 | ||||||||
\(273\) | 0.787297 | 0.0476494 | ||||||||
\(274\) | 13.9834 | 0.844767 | ||||||||
\(275\) | −2.68771 | −0.162075 | ||||||||
\(276\) | 7.71204 | 0.464210 | ||||||||
\(277\) | 10.6123 | 0.637631 | 0.318816 | − | 0.947817i | \(-0.396715\pi\) | ||||
0.318816 | + | 0.947817i | \(0.396715\pi\) | |||||||
\(278\) | 13.7715 | 0.825957 | ||||||||
\(279\) | 1.41567 | 0.0847541 | ||||||||
\(280\) | −0.333284 | −0.0199175 | ||||||||
\(281\) | −26.4013 | −1.57497 | −0.787483 | − | 0.616336i | \(-0.788616\pi\) | ||||
−0.787483 | + | 0.616336i | \(0.788616\pi\) | |||||||
\(282\) | −10.5396 | −0.627627 | ||||||||
\(283\) | −0.0558568 | −0.00332034 | −0.00166017 | − | 0.999999i | \(-0.500528\pi\) | ||||
−0.00166017 | + | 0.999999i | \(0.500528\pi\) | |||||||
\(284\) | 0.556242 | 0.0330069 | ||||||||
\(285\) | −13.5545 | −0.802901 | ||||||||
\(286\) | −3.90777 | −0.231072 | ||||||||
\(287\) | −0.723224 | −0.0426906 | ||||||||
\(288\) | −0.360304 | −0.0212311 | ||||||||
\(289\) | −0.107604 | −0.00632965 | ||||||||
\(290\) | −1.44606 | −0.0849157 | ||||||||
\(291\) | −22.1198 | −1.29668 | ||||||||
\(292\) | 12.1155 | 0.709007 | ||||||||
\(293\) | 30.4694 | 1.78004 | 0.890020 | − | 0.455921i | \(-0.150690\pi\) | ||||
0.890020 | + | 0.455921i | \(0.150690\pi\) | |||||||
\(294\) | 11.1925 | 0.652762 | ||||||||
\(295\) | −3.43978 | −0.200272 | ||||||||
\(296\) | 3.53964 | 0.205737 | ||||||||
\(297\) | −14.6736 | −0.851451 | ||||||||
\(298\) | −7.71007 | −0.446633 | ||||||||
\(299\) | −6.90144 | −0.399120 | ||||||||
\(300\) | −1.62471 | −0.0938029 | ||||||||
\(301\) | 1.87380 | 0.108004 | ||||||||
\(302\) | 16.0886 | 0.925794 | ||||||||
\(303\) | 18.4464 | 1.05972 | ||||||||
\(304\) | 8.34271 | 0.478487 | ||||||||
\(305\) | −8.19878 | −0.469461 | ||||||||
\(306\) | 1.48086 | 0.0846552 | ||||||||
\(307\) | −8.88609 | −0.507156 | −0.253578 | − | 0.967315i | \(-0.581607\pi\) | ||||
−0.253578 | + | 0.967315i | \(0.581607\pi\) | |||||||
\(308\) | 0.895770 | 0.0510413 | ||||||||
\(309\) | 21.1043 | 1.20058 | ||||||||
\(310\) | −3.92911 | −0.223158 | ||||||||
\(311\) | −3.17282 | −0.179914 | −0.0899570 | − | 0.995946i | \(-0.528673\pi\) | ||||
−0.0899570 | + | 0.995946i | \(0.528673\pi\) | |||||||
\(312\) | −2.36224 | −0.133736 | ||||||||
\(313\) | 13.4188 | 0.758476 | 0.379238 | − | 0.925299i | \(-0.376186\pi\) | ||||
0.379238 | + | 0.925299i | \(0.376186\pi\) | |||||||
\(314\) | −1.65930 | −0.0936397 | ||||||||
\(315\) | 0.120083 | 0.00676593 | ||||||||
\(316\) | 2.81119 | 0.158142 | ||||||||
\(317\) | −33.6522 | −1.89009 | −0.945047 | − | 0.326935i | \(-0.893984\pi\) | ||||
−0.945047 | + | 0.326935i | \(0.893984\pi\) | |||||||
\(318\) | 8.64098 | 0.484562 | ||||||||
\(319\) | 3.88660 | 0.217608 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 19.2486 | 1.07435 | ||||||||
\(322\) | 1.58200 | 0.0881615 | ||||||||
\(323\) | −34.2888 | −1.90788 | ||||||||
\(324\) | −7.78927 | −0.432737 | ||||||||
\(325\) | 1.45394 | 0.0806502 | ||||||||
\(326\) | 2.60909 | 0.144504 | ||||||||
\(327\) | 25.4463 | 1.40718 | ||||||||
\(328\) | 2.16999 | 0.119818 | ||||||||
\(329\) | −2.16204 | −0.119197 | ||||||||
\(330\) | 4.36676 | 0.240382 | ||||||||
\(331\) | −8.64239 | −0.475029 | −0.237514 | − | 0.971384i | \(-0.576333\pi\) | ||||
−0.237514 | + | 0.971384i | \(0.576333\pi\) | |||||||
\(332\) | −5.47476 | −0.300466 | ||||||||
\(333\) | −1.27534 | −0.0698885 | ||||||||
\(334\) | −0.268612 | −0.0146978 | ||||||||
\(335\) | 3.23813 | 0.176918 | ||||||||
\(336\) | 0.541491 | 0.0295408 | ||||||||
\(337\) | −14.0322 | −0.764383 | −0.382192 | − | 0.924083i | \(-0.624831\pi\) | ||||
−0.382192 | + | 0.924083i | \(0.624831\pi\) | |||||||
\(338\) | −10.8861 | −0.592123 | ||||||||
\(339\) | 6.13828 | 0.333386 | ||||||||
\(340\) | −4.11004 | −0.222898 | ||||||||
\(341\) | 10.5603 | 0.571872 | ||||||||
\(342\) | −3.00591 | −0.162541 | ||||||||
\(343\) | 4.62895 | 0.249940 | ||||||||
\(344\) | −5.62222 | −0.303130 | ||||||||
\(345\) | 7.71204 | 0.415202 | ||||||||
\(346\) | −11.6388 | −0.625706 | ||||||||
\(347\) | −27.7738 | −1.49098 | −0.745489 | − | 0.666518i | \(-0.767784\pi\) | ||||
−0.745489 | + | 0.666518i | \(0.767784\pi\) | |||||||
\(348\) | 2.34944 | 0.125943 | ||||||||
\(349\) | −0.464225 | −0.0248494 | −0.0124247 | − | 0.999923i | \(-0.503955\pi\) | ||||
−0.0124247 | + | 0.999923i | \(0.503955\pi\) | |||||||
\(350\) | −0.333284 | −0.0178148 | ||||||||
\(351\) | 7.93784 | 0.423691 | ||||||||
\(352\) | −2.68771 | −0.143255 | ||||||||
\(353\) | −30.2986 | −1.61263 | −0.806316 | − | 0.591485i | \(-0.798542\pi\) | ||||
−0.806316 | + | 0.591485i | \(0.798542\pi\) | |||||||
\(354\) | 5.58867 | 0.297034 | ||||||||
\(355\) | 0.556242 | 0.0295222 | ||||||||
\(356\) | −11.3071 | −0.599276 | ||||||||
\(357\) | −2.22555 | −0.117788 | ||||||||
\(358\) | 6.79330 | 0.359037 | ||||||||
\(359\) | −8.38256 | −0.442414 | −0.221207 | − | 0.975227i | \(-0.571000\pi\) | ||||
−0.221207 | + | 0.975227i | \(0.571000\pi\) | |||||||
\(360\) | −0.360304 | −0.0189897 | ||||||||
\(361\) | 50.6008 | 2.66320 | ||||||||
\(362\) | 0.611592 | 0.0321446 | ||||||||
\(363\) | 6.13527 | 0.322018 | ||||||||
\(364\) | −0.484576 | −0.0253987 | ||||||||
\(365\) | 12.1155 | 0.634155 | ||||||||
\(366\) | 13.3207 | 0.696283 | ||||||||
\(367\) | −15.7099 | −0.820051 | −0.410025 | − | 0.912074i | \(-0.634480\pi\) | ||||
−0.410025 | + | 0.912074i | \(0.634480\pi\) | |||||||
\(368\) | −4.74671 | −0.247439 | ||||||||
\(369\) | −0.781857 | −0.0407018 | ||||||||
\(370\) | 3.53964 | 0.184017 | ||||||||
\(371\) | 1.77256 | 0.0920266 | ||||||||
\(372\) | 6.38368 | 0.330978 | ||||||||
\(373\) | −19.8047 | −1.02545 | −0.512723 | − | 0.858554i | \(-0.671363\pi\) | ||||
−0.512723 | + | 0.858554i | \(0.671363\pi\) | |||||||
\(374\) | 11.0466 | 0.571205 | ||||||||
\(375\) | −1.62471 | −0.0838999 | ||||||||
\(376\) | 6.48708 | 0.334546 | ||||||||
\(377\) | −2.10249 | −0.108284 | ||||||||
\(378\) | −1.81957 | −0.0935888 | ||||||||
\(379\) | −0.485721 | −0.0249498 | −0.0124749 | − | 0.999922i | \(-0.503971\pi\) | ||||
−0.0124749 | + | 0.999922i | \(0.503971\pi\) | |||||||
\(380\) | 8.34271 | 0.427972 | ||||||||
\(381\) | 29.5418 | 1.51347 | ||||||||
\(382\) | −23.5883 | −1.20688 | ||||||||
\(383\) | 34.4148 | 1.75851 | 0.879256 | − | 0.476349i | \(-0.158040\pi\) | ||||
0.879256 | + | 0.476349i | \(0.158040\pi\) | |||||||
\(384\) | −1.62471 | −0.0829109 | ||||||||
\(385\) | 0.895770 | 0.0456527 | ||||||||
\(386\) | −8.93664 | −0.454863 | ||||||||
\(387\) | 2.02571 | 0.102972 | ||||||||
\(388\) | 13.6146 | 0.691174 | ||||||||
\(389\) | −12.7219 | −0.645025 | −0.322512 | − | 0.946565i | \(-0.604527\pi\) | ||||
−0.322512 | + | 0.946565i | \(0.604527\pi\) | |||||||
\(390\) | −2.36224 | −0.119617 | ||||||||
\(391\) | 19.5091 | 0.986619 | ||||||||
\(392\) | −6.88892 | −0.347943 | ||||||||
\(393\) | 26.3732 | 1.33035 | ||||||||
\(394\) | −16.9345 | −0.853148 | ||||||||
\(395\) | 2.81119 | 0.141446 | ||||||||
\(396\) | 0.968392 | 0.0486635 | ||||||||
\(397\) | −15.6156 | −0.783726 | −0.391863 | − | 0.920024i | \(-0.628169\pi\) | ||||
−0.391863 | + | 0.920024i | \(0.628169\pi\) | |||||||
\(398\) | 10.3990 | 0.521257 | ||||||||
\(399\) | 4.51750 | 0.226158 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −12.8988 | −0.644133 | −0.322067 | − | 0.946717i | \(-0.604377\pi\) | ||||
−0.322067 | + | 0.946717i | \(0.604377\pi\) | |||||||
\(402\) | −5.26103 | −0.262396 | ||||||||
\(403\) | −5.71269 | −0.284570 | ||||||||
\(404\) | −11.3537 | −0.564865 | ||||||||
\(405\) | −7.78927 | −0.387052 | ||||||||
\(406\) | 0.481949 | 0.0239187 | ||||||||
\(407\) | −9.51352 | −0.471568 | ||||||||
\(408\) | 6.67763 | 0.330592 | ||||||||
\(409\) | −8.25106 | −0.407988 | −0.203994 | − | 0.978972i | \(-0.565392\pi\) | ||||
−0.203994 | + | 0.978972i | \(0.565392\pi\) | |||||||
\(410\) | 2.16999 | 0.107168 | ||||||||
\(411\) | −22.7190 | −1.12065 | ||||||||
\(412\) | −12.9895 | −0.639948 | ||||||||
\(413\) | 1.14642 | 0.0564119 | ||||||||
\(414\) | 1.71026 | 0.0840545 | ||||||||
\(415\) | −5.47476 | −0.268745 | ||||||||
\(416\) | 1.45394 | 0.0712854 | ||||||||
\(417\) | −22.3747 | −1.09569 | ||||||||
\(418\) | −22.4228 | −1.09673 | ||||||||
\(419\) | 23.2358 | 1.13514 | 0.567571 | − | 0.823324i | \(-0.307883\pi\) | ||||
0.567571 | + | 0.823324i | \(0.307883\pi\) | |||||||
\(420\) | 0.541491 | 0.0264221 | ||||||||
\(421\) | −18.8075 | −0.916620 | −0.458310 | − | 0.888792i | \(-0.651545\pi\) | ||||
−0.458310 | + | 0.888792i | \(0.651545\pi\) | |||||||
\(422\) | 4.69539 | 0.228568 | ||||||||
\(423\) | −2.33732 | −0.113644 | ||||||||
\(424\) | −5.31846 | −0.258287 | ||||||||
\(425\) | −4.11004 | −0.199366 | ||||||||
\(426\) | −0.903734 | −0.0437860 | ||||||||
\(427\) | 2.73252 | 0.132236 | ||||||||
\(428\) | −11.8474 | −0.572664 | ||||||||
\(429\) | 6.34902 | 0.306533 | ||||||||
\(430\) | −5.62222 | −0.271128 | ||||||||
\(431\) | −30.4849 | −1.46841 | −0.734203 | − | 0.678930i | \(-0.762444\pi\) | ||||
−0.734203 | + | 0.678930i | \(0.762444\pi\) | |||||||
\(432\) | 5.45953 | 0.262672 | ||||||||
\(433\) | 27.9441 | 1.34291 | 0.671455 | − | 0.741046i | \(-0.265670\pi\) | ||||
0.671455 | + | 0.741046i | \(0.265670\pi\) | |||||||
\(434\) | 1.30951 | 0.0628584 | ||||||||
\(435\) | 2.34944 | 0.112647 | ||||||||
\(436\) | −15.6620 | −0.750073 | ||||||||
\(437\) | −39.6004 | −1.89434 | ||||||||
\(438\) | −19.6843 | −0.940550 | ||||||||
\(439\) | −28.9237 | −1.38045 | −0.690227 | − | 0.723593i | \(-0.742489\pi\) | ||||
−0.690227 | + | 0.723593i | \(0.742489\pi\) | |||||||
\(440\) | −2.68771 | −0.128132 | ||||||||
\(441\) | 2.48210 | 0.118195 | ||||||||
\(442\) | −5.97575 | −0.284238 | ||||||||
\(443\) | 24.7452 | 1.17568 | 0.587839 | − | 0.808978i | \(-0.299979\pi\) | ||||
0.587839 | + | 0.808978i | \(0.299979\pi\) | |||||||
\(444\) | −5.75090 | −0.272926 | ||||||||
\(445\) | −11.3071 | −0.536009 | ||||||||
\(446\) | 15.9530 | 0.755395 | ||||||||
\(447\) | 12.5267 | 0.592491 | ||||||||
\(448\) | −0.333284 | −0.0157462 | ||||||||
\(449\) | 9.52218 | 0.449380 | 0.224690 | − | 0.974430i | \(-0.427863\pi\) | ||||
0.224690 | + | 0.974430i | \(0.427863\pi\) | |||||||
\(450\) | −0.360304 | −0.0169849 | ||||||||
\(451\) | −5.83231 | −0.274633 | ||||||||
\(452\) | −3.77807 | −0.177705 | ||||||||
\(453\) | −26.1394 | −1.22813 | ||||||||
\(454\) | 19.0713 | 0.895062 | ||||||||
\(455\) | −0.484576 | −0.0227173 | ||||||||
\(456\) | −13.5545 | −0.634749 | ||||||||
\(457\) | −37.8541 | −1.77074 | −0.885371 | − | 0.464885i | \(-0.846096\pi\) | ||||
−0.885371 | + | 0.464885i | \(0.846096\pi\) | |||||||
\(458\) | −17.3615 | −0.811247 | ||||||||
\(459\) | −22.4389 | −1.04736 | ||||||||
\(460\) | −4.74671 | −0.221316 | ||||||||
\(461\) | −3.49481 | −0.162769 | −0.0813847 | − | 0.996683i | \(-0.525934\pi\) | ||||
−0.0813847 | + | 0.996683i | \(0.525934\pi\) | |||||||
\(462\) | −1.45537 | −0.0677100 | ||||||||
\(463\) | 28.8258 | 1.33965 | 0.669825 | − | 0.742519i | \(-0.266369\pi\) | ||||
0.669825 | + | 0.742519i | \(0.266369\pi\) | |||||||
\(464\) | −1.44606 | −0.0671318 | ||||||||
\(465\) | 6.38368 | 0.296036 | ||||||||
\(466\) | 12.4461 | 0.576553 | ||||||||
\(467\) | −40.6843 | −1.88264 | −0.941322 | − | 0.337510i | \(-0.890415\pi\) | ||||
−0.941322 | + | 0.337510i | \(0.890415\pi\) | |||||||
\(468\) | −0.523861 | −0.0242155 | ||||||||
\(469\) | −1.07922 | −0.0498336 | ||||||||
\(470\) | 6.48708 | 0.299227 | ||||||||
\(471\) | 2.69589 | 0.124220 | ||||||||
\(472\) | −3.43978 | −0.158329 | ||||||||
\(473\) | 15.1109 | 0.694800 | ||||||||
\(474\) | −4.56737 | −0.209786 | ||||||||
\(475\) | 8.34271 | 0.382790 | ||||||||
\(476\) | 1.36981 | 0.0627851 | ||||||||
\(477\) | 1.91626 | 0.0877396 | ||||||||
\(478\) | 19.8560 | 0.908193 | ||||||||
\(479\) | 35.4903 | 1.62159 | 0.810797 | − | 0.585327i | \(-0.199034\pi\) | ||||
0.810797 | + | 0.585327i | \(0.199034\pi\) | |||||||
\(480\) | −1.62471 | −0.0741577 | ||||||||
\(481\) | 5.14643 | 0.234657 | ||||||||
\(482\) | 13.1376 | 0.598403 | ||||||||
\(483\) | −2.57030 | −0.116953 | ||||||||
\(484\) | −3.77622 | −0.171646 | ||||||||
\(485\) | 13.6146 | 0.618205 | ||||||||
\(486\) | −3.72326 | −0.168891 | ||||||||
\(487\) | 8.70620 | 0.394515 | 0.197258 | − | 0.980352i | \(-0.436796\pi\) | ||||
0.197258 | + | 0.980352i | \(0.436796\pi\) | |||||||
\(488\) | −8.19878 | −0.371141 | ||||||||
\(489\) | −4.23902 | −0.191695 | ||||||||
\(490\) | −6.88892 | −0.311210 | ||||||||
\(491\) | 23.0004 | 1.03800 | 0.518998 | − | 0.854776i | \(-0.326305\pi\) | ||||
0.518998 | + | 0.854776i | \(0.326305\pi\) | |||||||
\(492\) | −3.52562 | −0.158947 | ||||||||
\(493\) | 5.94337 | 0.267676 | ||||||||
\(494\) | 12.1298 | 0.545746 | ||||||||
\(495\) | 0.968392 | 0.0435260 | ||||||||
\(496\) | −3.92911 | −0.176422 | ||||||||
\(497\) | −0.185386 | −0.00831572 | ||||||||
\(498\) | 8.89492 | 0.398591 | ||||||||
\(499\) | 21.6725 | 0.970196 | 0.485098 | − | 0.874460i | \(-0.338784\pi\) | ||||
0.485098 | + | 0.874460i | \(0.338784\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0.436418 | 0.0194977 | ||||||||
\(502\) | 9.77582 | 0.436316 | ||||||||
\(503\) | −40.7529 | −1.81708 | −0.908541 | − | 0.417796i | \(-0.862803\pi\) | ||||
−0.908541 | + | 0.417796i | \(0.862803\pi\) | |||||||
\(504\) | 0.120083 | 0.00534894 | ||||||||
\(505\) | −11.3537 | −0.505231 | ||||||||
\(506\) | 12.7578 | 0.567152 | ||||||||
\(507\) | 17.6867 | 0.785495 | ||||||||
\(508\) | −18.1828 | −0.806729 | ||||||||
\(509\) | 8.50319 | 0.376897 | 0.188449 | − | 0.982083i | \(-0.439654\pi\) | ||||
0.188449 | + | 0.982083i | \(0.439654\pi\) | |||||||
\(510\) | 6.67763 | 0.295691 | ||||||||
\(511\) | −4.03791 | −0.178627 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 45.5473 | 2.01096 | ||||||||
\(514\) | −9.08949 | −0.400920 | ||||||||
\(515\) | −12.9895 | −0.572387 | ||||||||
\(516\) | 9.13450 | 0.402124 | ||||||||
\(517\) | −17.4354 | −0.766807 | ||||||||
\(518\) | −1.17970 | −0.0518332 | ||||||||
\(519\) | 18.9097 | 0.830046 | ||||||||
\(520\) | 1.45394 | 0.0637596 | ||||||||
\(521\) | 34.9279 | 1.53022 | 0.765110 | − | 0.643899i | \(-0.222684\pi\) | ||||
0.765110 | + | 0.643899i | \(0.222684\pi\) | |||||||
\(522\) | 0.521022 | 0.0228045 | ||||||||
\(523\) | 6.43054 | 0.281188 | 0.140594 | − | 0.990067i | \(-0.455099\pi\) | ||||
0.140594 | + | 0.990067i | \(0.455099\pi\) | |||||||
\(524\) | −16.2325 | −0.709119 | ||||||||
\(525\) | 0.541491 | 0.0236326 | ||||||||
\(526\) | −22.2251 | −0.969062 | ||||||||
\(527\) | 16.1488 | 0.703452 | ||||||||
\(528\) | 4.36676 | 0.190039 | ||||||||
\(529\) | −0.468773 | −0.0203815 | ||||||||
\(530\) | −5.31846 | −0.231019 | ||||||||
\(531\) | 1.23937 | 0.0537840 | ||||||||
\(532\) | −2.78049 | −0.120550 | ||||||||
\(533\) | 3.15505 | 0.136660 | ||||||||
\(534\) | 18.3708 | 0.794984 | ||||||||
\(535\) | −11.8474 | −0.512206 | ||||||||
\(536\) | 3.23813 | 0.139866 | ||||||||
\(537\) | −11.0372 | −0.476289 | ||||||||
\(538\) | −20.4234 | −0.880514 | ||||||||
\(539\) | 18.5154 | 0.797516 | ||||||||
\(540\) | 5.45953 | 0.234941 | ||||||||
\(541\) | −34.8380 | −1.49780 | −0.748901 | − | 0.662682i | \(-0.769418\pi\) | ||||
−0.748901 | + | 0.662682i | \(0.769418\pi\) | |||||||
\(542\) | 2.62739 | 0.112856 | ||||||||
\(543\) | −0.993662 | −0.0426421 | ||||||||
\(544\) | −4.11004 | −0.176216 | ||||||||
\(545\) | −15.6620 | −0.670886 | ||||||||
\(546\) | 0.787297 | 0.0336932 | ||||||||
\(547\) | 42.9689 | 1.83722 | 0.918608 | − | 0.395169i | \(-0.129314\pi\) | ||||
0.918608 | + | 0.395169i | \(0.129314\pi\) | |||||||
\(548\) | 13.9834 | 0.597341 | ||||||||
\(549\) | 2.95405 | 0.126076 | ||||||||
\(550\) | −2.68771 | −0.114604 | ||||||||
\(551\) | −12.0641 | −0.513947 | ||||||||
\(552\) | 7.71204 | 0.328246 | ||||||||
\(553\) | −0.936923 | −0.0398420 | ||||||||
\(554\) | 10.6123 | 0.450873 | ||||||||
\(555\) | −5.75090 | −0.244112 | ||||||||
\(556\) | 13.7715 | 0.584040 | ||||||||
\(557\) | −11.6767 | −0.494759 | −0.247380 | − | 0.968919i | \(-0.579569\pi\) | ||||
−0.247380 | + | 0.968919i | \(0.579569\pi\) | |||||||
\(558\) | 1.41567 | 0.0599302 | ||||||||
\(559\) | −8.17438 | −0.345740 | ||||||||
\(560\) | −0.333284 | −0.0140838 | ||||||||
\(561\) | −17.9475 | −0.757746 | ||||||||
\(562\) | −26.4013 | −1.11367 | ||||||||
\(563\) | 42.0773 | 1.77335 | 0.886674 | − | 0.462395i | \(-0.153010\pi\) | ||||
0.886674 | + | 0.462395i | \(0.153010\pi\) | |||||||
\(564\) | −10.5396 | −0.443799 | ||||||||
\(565\) | −3.77807 | −0.158945 | ||||||||
\(566\) | −0.0558568 | −0.00234784 | ||||||||
\(567\) | 2.59604 | 0.109023 | ||||||||
\(568\) | 0.556242 | 0.0233394 | ||||||||
\(569\) | −13.3817 | −0.560990 | −0.280495 | − | 0.959855i | \(-0.590499\pi\) | ||||
−0.280495 | + | 0.959855i | \(0.590499\pi\) | |||||||
\(570\) | −13.5545 | −0.567736 | ||||||||
\(571\) | −38.9405 | −1.62961 | −0.814804 | − | 0.579737i | \(-0.803155\pi\) | ||||
−0.814804 | + | 0.579737i | \(0.803155\pi\) | |||||||
\(572\) | −3.90777 | −0.163392 | ||||||||
\(573\) | 38.3243 | 1.60102 | ||||||||
\(574\) | −0.723224 | −0.0301868 | ||||||||
\(575\) | −4.74671 | −0.197951 | ||||||||
\(576\) | −0.360304 | −0.0150127 | ||||||||
\(577\) | −17.2284 | −0.717226 | −0.358613 | − | 0.933486i | \(-0.616750\pi\) | ||||
−0.358613 | + | 0.933486i | \(0.616750\pi\) | |||||||
\(578\) | −0.107604 | −0.00447574 | ||||||||
\(579\) | 14.5195 | 0.603410 | ||||||||
\(580\) | −1.44606 | −0.0600445 | ||||||||
\(581\) | 1.82465 | 0.0756992 | ||||||||
\(582\) | −22.1198 | −0.916894 | ||||||||
\(583\) | 14.2945 | 0.592017 | ||||||||
\(584\) | 12.1155 | 0.501344 | ||||||||
\(585\) | −0.523861 | −0.0216590 | ||||||||
\(586\) | 30.4694 | 1.25868 | ||||||||
\(587\) | 6.29000 | 0.259616 | 0.129808 | − | 0.991539i | \(-0.458564\pi\) | ||||
0.129808 | + | 0.991539i | \(0.458564\pi\) | |||||||
\(588\) | 11.1925 | 0.461572 | ||||||||
\(589\) | −32.7794 | −1.35065 | ||||||||
\(590\) | −3.43978 | −0.141614 | ||||||||
\(591\) | 27.5137 | 1.13176 | ||||||||
\(592\) | 3.53964 | 0.145478 | ||||||||
\(593\) | 15.8226 | 0.649756 | 0.324878 | − | 0.945756i | \(-0.394677\pi\) | ||||
0.324878 | + | 0.945756i | \(0.394677\pi\) | |||||||
\(594\) | −14.6736 | −0.602067 | ||||||||
\(595\) | 1.36981 | 0.0561567 | ||||||||
\(596\) | −7.71007 | −0.315817 | ||||||||
\(597\) | −16.8955 | −0.691486 | ||||||||
\(598\) | −6.90144 | −0.282221 | ||||||||
\(599\) | −17.7875 | −0.726776 | −0.363388 | − | 0.931638i | \(-0.618380\pi\) | ||||
−0.363388 | + | 0.931638i | \(0.618380\pi\) | |||||||
\(600\) | −1.62471 | −0.0663287 | ||||||||
\(601\) | −1.00000 | −0.0407909 | ||||||||
\(602\) | 1.87380 | 0.0763702 | ||||||||
\(603\) | −1.16671 | −0.0475121 | ||||||||
\(604\) | 16.0886 | 0.654635 | ||||||||
\(605\) | −3.77622 | −0.153525 | ||||||||
\(606\) | 18.4464 | 0.749336 | ||||||||
\(607\) | −26.1579 | −1.06172 | −0.530858 | − | 0.847461i | \(-0.678130\pi\) | ||||
−0.530858 | + | 0.847461i | \(0.678130\pi\) | |||||||
\(608\) | 8.34271 | 0.338342 | ||||||||
\(609\) | −0.783030 | −0.0317300 | ||||||||
\(610\) | −8.19878 | −0.331959 | ||||||||
\(611\) | 9.43184 | 0.381571 | ||||||||
\(612\) | 1.48086 | 0.0598603 | ||||||||
\(613\) | −20.1097 | −0.812224 | −0.406112 | − | 0.913823i | \(-0.633116\pi\) | ||||
−0.406112 | + | 0.913823i | \(0.633116\pi\) | |||||||
\(614\) | −8.88609 | −0.358614 | ||||||||
\(615\) | −3.52562 | −0.142167 | ||||||||
\(616\) | 0.895770 | 0.0360916 | ||||||||
\(617\) | 35.7908 | 1.44088 | 0.720442 | − | 0.693516i | \(-0.243939\pi\) | ||||
0.720442 | + | 0.693516i | \(0.243939\pi\) | |||||||
\(618\) | 21.1043 | 0.848938 | ||||||||
\(619\) | −43.9013 | −1.76454 | −0.882271 | − | 0.470742i | \(-0.843986\pi\) | ||||
−0.882271 | + | 0.470742i | \(0.843986\pi\) | |||||||
\(620\) | −3.92911 | −0.157797 | ||||||||
\(621\) | −25.9148 | −1.03993 | ||||||||
\(622\) | −3.17282 | −0.127218 | ||||||||
\(623\) | 3.76848 | 0.150981 | ||||||||
\(624\) | −2.36224 | −0.0945653 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 13.4188 | 0.536324 | ||||||||
\(627\) | 36.4306 | 1.45490 | ||||||||
\(628\) | −1.65930 | −0.0662132 | ||||||||
\(629\) | −14.5480 | −0.580068 | ||||||||
\(630\) | 0.120083 | 0.00478424 | ||||||||
\(631\) | −2.74625 | −0.109326 | −0.0546631 | − | 0.998505i | \(-0.517408\pi\) | ||||
−0.0546631 | + | 0.998505i | \(0.517408\pi\) | |||||||
\(632\) | 2.81119 | 0.111823 | ||||||||
\(633\) | −7.62866 | −0.303212 | ||||||||
\(634\) | −33.6522 | −1.33650 | ||||||||
\(635\) | −18.1828 | −0.721561 | ||||||||
\(636\) | 8.64098 | 0.342637 | ||||||||
\(637\) | −10.0161 | −0.396852 | ||||||||
\(638\) | 3.88660 | 0.153872 | ||||||||
\(639\) | −0.200416 | −0.00792833 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −24.5608 | −0.970093 | −0.485046 | − | 0.874488i | \(-0.661197\pi\) | ||||
−0.485046 | + | 0.874488i | \(0.661197\pi\) | |||||||
\(642\) | 19.2486 | 0.759681 | ||||||||
\(643\) | 33.6868 | 1.32848 | 0.664240 | − | 0.747520i | \(-0.268755\pi\) | ||||
0.664240 | + | 0.747520i | \(0.268755\pi\) | |||||||
\(644\) | 1.58200 | 0.0623396 | ||||||||
\(645\) | 9.13450 | 0.359671 | ||||||||
\(646\) | −34.2888 | −1.34908 | ||||||||
\(647\) | 1.86914 | 0.0734834 | 0.0367417 | − | 0.999325i | \(-0.488302\pi\) | ||||
0.0367417 | + | 0.999325i | \(0.488302\pi\) | |||||||
\(648\) | −7.78927 | −0.305991 | ||||||||
\(649\) | 9.24514 | 0.362904 | ||||||||
\(650\) | 1.45394 | 0.0570283 | ||||||||
\(651\) | −2.12758 | −0.0833863 | ||||||||
\(652\) | 2.60909 | 0.102180 | ||||||||
\(653\) | 41.9660 | 1.64226 | 0.821128 | − | 0.570743i | \(-0.193345\pi\) | ||||
0.821128 | + | 0.570743i | \(0.193345\pi\) | |||||||
\(654\) | 25.4463 | 0.995027 | ||||||||
\(655\) | −16.2325 | −0.634256 | ||||||||
\(656\) | 2.16999 | 0.0847240 | ||||||||
\(657\) | −4.36527 | −0.170305 | ||||||||
\(658\) | −2.16204 | −0.0842851 | ||||||||
\(659\) | 48.4170 | 1.88606 | 0.943030 | − | 0.332707i | \(-0.107962\pi\) | ||||
0.943030 | + | 0.332707i | \(0.107962\pi\) | |||||||
\(660\) | 4.36676 | 0.169976 | ||||||||
\(661\) | −41.8331 | −1.62712 | −0.813559 | − | 0.581483i | \(-0.802473\pi\) | ||||
−0.813559 | + | 0.581483i | \(0.802473\pi\) | |||||||
\(662\) | −8.64239 | −0.335896 | ||||||||
\(663\) | 9.70889 | 0.377062 | ||||||||
\(664\) | −5.47476 | −0.212462 | ||||||||
\(665\) | −2.78049 | −0.107823 | ||||||||
\(666\) | −1.27534 | −0.0494186 | ||||||||
\(667\) | 6.86403 | 0.265776 | ||||||||
\(668\) | −0.268612 | −0.0103929 | ||||||||
\(669\) | −25.9190 | −1.00209 | ||||||||
\(670\) | 3.23813 | 0.125100 | ||||||||
\(671\) | 22.0359 | 0.850688 | ||||||||
\(672\) | 0.541491 | 0.0208885 | ||||||||
\(673\) | 47.3383 | 1.82476 | 0.912378 | − | 0.409349i | \(-0.134244\pi\) | ||||
0.912378 | + | 0.409349i | \(0.134244\pi\) | |||||||
\(674\) | −14.0322 | −0.540500 | ||||||||
\(675\) | 5.45953 | 0.210138 | ||||||||
\(676\) | −10.8861 | −0.418694 | ||||||||
\(677\) | 33.6319 | 1.29258 | 0.646289 | − | 0.763093i | \(-0.276320\pi\) | ||||
0.646289 | + | 0.763093i | \(0.276320\pi\) | |||||||
\(678\) | 6.13828 | 0.235739 | ||||||||
\(679\) | −4.53751 | −0.174134 | ||||||||
\(680\) | −4.11004 | −0.157613 | ||||||||
\(681\) | −30.9855 | −1.18737 | ||||||||
\(682\) | 10.5603 | 0.404375 | ||||||||
\(683\) | −21.0748 | −0.806405 | −0.403203 | − | 0.915111i | \(-0.632103\pi\) | ||||
−0.403203 | + | 0.915111i | \(0.632103\pi\) | |||||||
\(684\) | −3.00591 | −0.114934 | ||||||||
\(685\) | 13.9834 | 0.534278 | ||||||||
\(686\) | 4.62895 | 0.176734 | ||||||||
\(687\) | 28.2074 | 1.07618 | ||||||||
\(688\) | −5.62222 | −0.214345 | ||||||||
\(689\) | −7.73274 | −0.294594 | ||||||||
\(690\) | 7.71204 | 0.293592 | ||||||||
\(691\) | 19.7067 | 0.749679 | 0.374839 | − | 0.927090i | \(-0.377698\pi\) | ||||
0.374839 | + | 0.927090i | \(0.377698\pi\) | |||||||
\(692\) | −11.6388 | −0.442441 | ||||||||
\(693\) | −0.322749 | −0.0122602 | ||||||||
\(694\) | −27.7738 | −1.05428 | ||||||||
\(695\) | 13.7715 | 0.522381 | ||||||||
\(696\) | 2.34944 | 0.0890552 | ||||||||
\(697\) | −8.91875 | −0.337822 | ||||||||
\(698\) | −0.464225 | −0.0175712 | ||||||||
\(699\) | −20.2213 | −0.764840 | ||||||||
\(700\) | −0.333284 | −0.0125969 | ||||||||
\(701\) | 22.4682 | 0.848611 | 0.424305 | − | 0.905519i | \(-0.360518\pi\) | ||||
0.424305 | + | 0.905519i | \(0.360518\pi\) | |||||||
\(702\) | 7.93784 | 0.299595 | ||||||||
\(703\) | 29.5302 | 1.11375 | ||||||||
\(704\) | −2.68771 | −0.101297 | ||||||||
\(705\) | −10.5396 | −0.396946 | ||||||||
\(706\) | −30.2986 | −1.14030 | ||||||||
\(707\) | 3.78399 | 0.142312 | ||||||||
\(708\) | 5.58867 | 0.210035 | ||||||||
\(709\) | 1.04779 | 0.0393504 | 0.0196752 | − | 0.999806i | \(-0.493737\pi\) | ||||
0.0196752 | + | 0.999806i | \(0.493737\pi\) | |||||||
\(710\) | 0.556242 | 0.0208754 | ||||||||
\(711\) | −1.01288 | −0.0379860 | ||||||||
\(712\) | −11.3071 | −0.423752 | ||||||||
\(713\) | 18.6503 | 0.698460 | ||||||||
\(714\) | −2.22555 | −0.0832890 | ||||||||
\(715\) | −3.90777 | −0.146142 | ||||||||
\(716\) | 6.79330 | 0.253878 | ||||||||
\(717\) | −32.2603 | −1.20478 | ||||||||
\(718\) | −8.38256 | −0.312834 | ||||||||
\(719\) | 27.4040 | 1.02200 | 0.510998 | − | 0.859582i | \(-0.329276\pi\) | ||||
0.510998 | + | 0.859582i | \(0.329276\pi\) | |||||||
\(720\) | −0.360304 | −0.0134277 | ||||||||
\(721\) | 4.32920 | 0.161228 | ||||||||
\(722\) | 50.6008 | 1.88317 | ||||||||
\(723\) | −21.3449 | −0.793826 | ||||||||
\(724\) | 0.611592 | 0.0227296 | ||||||||
\(725\) | −1.44606 | −0.0537054 | ||||||||
\(726\) | 6.13527 | 0.227701 | ||||||||
\(727\) | 26.9437 | 0.999287 | 0.499644 | − | 0.866231i | \(-0.333464\pi\) | ||||
0.499644 | + | 0.866231i | \(0.333464\pi\) | |||||||
\(728\) | −0.484576 | −0.0179596 | ||||||||
\(729\) | 29.4170 | 1.08952 | ||||||||
\(730\) | 12.1155 | 0.448415 | ||||||||
\(731\) | 23.1075 | 0.854663 | ||||||||
\(732\) | 13.3207 | 0.492346 | ||||||||
\(733\) | −7.56912 | −0.279572 | −0.139786 | − | 0.990182i | \(-0.544641\pi\) | ||||
−0.139786 | + | 0.990182i | \(0.544641\pi\) | |||||||
\(734\) | −15.7099 | −0.579864 | ||||||||
\(735\) | 11.1925 | 0.412843 | ||||||||
\(736\) | −4.74671 | −0.174966 | ||||||||
\(737\) | −8.70315 | −0.320585 | ||||||||
\(738\) | −0.781857 | −0.0287805 | ||||||||
\(739\) | 33.0602 | 1.21614 | 0.608069 | − | 0.793884i | \(-0.291944\pi\) | ||||
0.608069 | + | 0.793884i | \(0.291944\pi\) | |||||||
\(740\) | 3.53964 | 0.130120 | ||||||||
\(741\) | −19.7075 | −0.723973 | ||||||||
\(742\) | 1.77256 | 0.0650727 | ||||||||
\(743\) | 49.0273 | 1.79864 | 0.899318 | − | 0.437294i | \(-0.144063\pi\) | ||||
0.899318 | + | 0.437294i | \(0.144063\pi\) | |||||||
\(744\) | 6.38368 | 0.234037 | ||||||||
\(745\) | −7.71007 | −0.282475 | ||||||||
\(746\) | −19.8047 | −0.725100 | ||||||||
\(747\) | 1.97258 | 0.0721728 | ||||||||
\(748\) | 11.0466 | 0.403903 | ||||||||
\(749\) | 3.94854 | 0.144276 | ||||||||
\(750\) | −1.62471 | −0.0593262 | ||||||||
\(751\) | −17.1169 | −0.624604 | −0.312302 | − | 0.949983i | \(-0.601100\pi\) | ||||
−0.312302 | + | 0.949983i | \(0.601100\pi\) | |||||||
\(752\) | 6.48708 | 0.236559 | ||||||||
\(753\) | −15.8829 | −0.578806 | ||||||||
\(754\) | −2.10249 | −0.0765682 | ||||||||
\(755\) | 16.0886 | 0.585524 | ||||||||
\(756\) | −1.81957 | −0.0661773 | ||||||||
\(757\) | 29.7065 | 1.07970 | 0.539850 | − | 0.841761i | \(-0.318481\pi\) | ||||
0.539850 | + | 0.841761i | \(0.318481\pi\) | |||||||
\(758\) | −0.485721 | −0.0176422 | ||||||||
\(759\) | −20.7277 | −0.752369 | ||||||||
\(760\) | 8.34271 | 0.302622 | ||||||||
\(761\) | −49.7109 | −1.80202 | −0.901009 | − | 0.433801i | \(-0.857172\pi\) | ||||
−0.901009 | + | 0.433801i | \(0.857172\pi\) | |||||||
\(762\) | 29.5418 | 1.07019 | ||||||||
\(763\) | 5.21989 | 0.188973 | ||||||||
\(764\) | −23.5883 | −0.853396 | ||||||||
\(765\) | 1.48086 | 0.0535406 | ||||||||
\(766\) | 34.4148 | 1.24346 | ||||||||
\(767\) | −5.00125 | −0.180585 | ||||||||
\(768\) | −1.62471 | −0.0586268 | ||||||||
\(769\) | 10.4087 | 0.375346 | 0.187673 | − | 0.982232i | \(-0.439906\pi\) | ||||
0.187673 | + | 0.982232i | \(0.439906\pi\) | |||||||
\(770\) | 0.895770 | 0.0322813 | ||||||||
\(771\) | 14.7678 | 0.531850 | ||||||||
\(772\) | −8.93664 | −0.321637 | ||||||||
\(773\) | 34.6792 | 1.24733 | 0.623663 | − | 0.781694i | \(-0.285644\pi\) | ||||
0.623663 | + | 0.781694i | \(0.285644\pi\) | |||||||
\(774\) | 2.02571 | 0.0728125 | ||||||||
\(775\) | −3.92911 | −0.141138 | ||||||||
\(776\) | 13.6146 | 0.488734 | ||||||||
\(777\) | 1.91668 | 0.0687606 | ||||||||
\(778\) | −12.7219 | −0.456101 | ||||||||
\(779\) | 18.1036 | 0.648630 | ||||||||
\(780\) | −2.36224 | −0.0845818 | ||||||||
\(781\) | −1.49502 | −0.0534959 | ||||||||
\(782\) | 19.5091 | 0.697645 | ||||||||
\(783\) | −7.89482 | −0.282138 | ||||||||
\(784\) | −6.88892 | −0.246033 | ||||||||
\(785\) | −1.65930 | −0.0592229 | ||||||||
\(786\) | 26.3732 | 0.940699 | ||||||||
\(787\) | 42.9333 | 1.53041 | 0.765203 | − | 0.643789i | \(-0.222639\pi\) | ||||
0.765203 | + | 0.643789i | \(0.222639\pi\) | |||||||
\(788\) | −16.9345 | −0.603266 | ||||||||
\(789\) | 36.1095 | 1.28553 | ||||||||
\(790\) | 2.81119 | 0.100018 | ||||||||
\(791\) | 1.25917 | 0.0447709 | ||||||||
\(792\) | 0.968392 | 0.0344103 | ||||||||
\(793\) | −11.9205 | −0.423311 | ||||||||
\(794\) | −15.6156 | −0.554178 | ||||||||
\(795\) | 8.64098 | 0.306464 | ||||||||
\(796\) | 10.3990 | 0.368584 | ||||||||
\(797\) | 27.0481 | 0.958092 | 0.479046 | − | 0.877790i | \(-0.340983\pi\) | ||||
0.479046 | + | 0.877790i | \(0.340983\pi\) | |||||||
\(798\) | 4.51750 | 0.159918 | ||||||||
\(799\) | −26.6621 | −0.943238 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 4.07400 | 0.143948 | ||||||||
\(802\) | −12.8988 | −0.455471 | ||||||||
\(803\) | −32.5630 | −1.14912 | ||||||||
\(804\) | −5.26103 | −0.185542 | ||||||||
\(805\) | 1.58200 | 0.0557582 | ||||||||
\(806\) | −5.71269 | −0.201221 | ||||||||
\(807\) | 33.1821 | 1.16807 | ||||||||
\(808\) | −11.3537 | −0.399420 | ||||||||
\(809\) | 26.6791 | 0.937987 | 0.468993 | − | 0.883202i | \(-0.344617\pi\) | ||||
0.468993 | + | 0.883202i | \(0.344617\pi\) | |||||||
\(810\) | −7.78927 | −0.273687 | ||||||||
\(811\) | −24.3470 | −0.854938 | −0.427469 | − | 0.904030i | \(-0.640595\pi\) | ||||
−0.427469 | + | 0.904030i | \(0.640595\pi\) | |||||||
\(812\) | 0.481949 | 0.0169131 | ||||||||
\(813\) | −4.26876 | −0.149712 | ||||||||
\(814\) | −9.51352 | −0.333449 | ||||||||
\(815\) | 2.60909 | 0.0913924 | ||||||||
\(816\) | 6.67763 | 0.233764 | ||||||||
\(817\) | −46.9046 | −1.64098 | ||||||||
\(818\) | −8.25106 | −0.288491 | ||||||||
\(819\) | 0.174594 | 0.00610082 | ||||||||
\(820\) | 2.16999 | 0.0757795 | ||||||||
\(821\) | −14.8525 | −0.518355 | −0.259178 | − | 0.965830i | \(-0.583452\pi\) | ||||
−0.259178 | + | 0.965830i | \(0.583452\pi\) | |||||||
\(822\) | −22.7190 | −0.792416 | ||||||||
\(823\) | 52.8539 | 1.84237 | 0.921186 | − | 0.389122i | \(-0.127222\pi\) | ||||
0.921186 | + | 0.389122i | \(0.127222\pi\) | |||||||
\(824\) | −12.9895 | −0.452512 | ||||||||
\(825\) | 4.36676 | 0.152031 | ||||||||
\(826\) | 1.14642 | 0.0398892 | ||||||||
\(827\) | 21.1336 | 0.734889 | 0.367444 | − | 0.930045i | \(-0.380233\pi\) | ||||
0.367444 | + | 0.930045i | \(0.380233\pi\) | |||||||
\(828\) | 1.71026 | 0.0594355 | ||||||||
\(829\) | −8.20142 | −0.284847 | −0.142424 | − | 0.989806i | \(-0.545490\pi\) | ||||
−0.142424 | + | 0.989806i | \(0.545490\pi\) | |||||||
\(830\) | −5.47476 | −0.190032 | ||||||||
\(831\) | −17.2420 | −0.598117 | ||||||||
\(832\) | 1.45394 | 0.0504064 | ||||||||
\(833\) | 28.3137 | 0.981012 | ||||||||
\(834\) | −22.3747 | −0.774772 | ||||||||
\(835\) | −0.268612 | −0.00929571 | ||||||||
\(836\) | −22.4228 | −0.775508 | ||||||||
\(837\) | −21.4511 | −0.741458 | ||||||||
\(838\) | 23.2358 | 0.802667 | ||||||||
\(839\) | −25.2567 | −0.871957 | −0.435978 | − | 0.899957i | \(-0.643598\pi\) | ||||
−0.435978 | + | 0.899957i | \(0.643598\pi\) | |||||||
\(840\) | 0.541491 | 0.0186832 | ||||||||
\(841\) | −26.9089 | −0.927893 | ||||||||
\(842\) | −18.8075 | −0.648148 | ||||||||
\(843\) | 42.8945 | 1.47736 | ||||||||
\(844\) | 4.69539 | 0.161622 | ||||||||
\(845\) | −10.8861 | −0.374492 | ||||||||
\(846\) | −2.33732 | −0.0803587 | ||||||||
\(847\) | 1.25855 | 0.0432444 | ||||||||
\(848\) | −5.31846 | −0.182637 | ||||||||
\(849\) | 0.0907514 | 0.00311458 | ||||||||
\(850\) | −4.11004 | −0.140973 | ||||||||
\(851\) | −16.8016 | −0.575952 | ||||||||
\(852\) | −0.903734 | −0.0309614 | ||||||||
\(853\) | 43.7081 | 1.49654 | 0.748269 | − | 0.663396i | \(-0.230885\pi\) | ||||
0.748269 | + | 0.663396i | \(0.230885\pi\) | |||||||
\(854\) | 2.73252 | 0.0935049 | ||||||||
\(855\) | −3.00591 | −0.102800 | ||||||||
\(856\) | −11.8474 | −0.404935 | ||||||||
\(857\) | −39.6884 | −1.35573 | −0.677866 | − | 0.735186i | \(-0.737095\pi\) | ||||
−0.677866 | + | 0.735186i | \(0.737095\pi\) | |||||||
\(858\) | 6.34902 | 0.216752 | ||||||||
\(859\) | −54.3917 | −1.85582 | −0.927911 | − | 0.372801i | \(-0.878397\pi\) | ||||
−0.927911 | + | 0.372801i | \(0.878397\pi\) | |||||||
\(860\) | −5.62222 | −0.191716 | ||||||||
\(861\) | 1.17503 | 0.0400450 | ||||||||
\(862\) | −30.4849 | −1.03832 | ||||||||
\(863\) | 44.3274 | 1.50892 | 0.754461 | − | 0.656345i | \(-0.227898\pi\) | ||||
0.754461 | + | 0.656345i | \(0.227898\pi\) | |||||||
\(864\) | 5.45953 | 0.185737 | ||||||||
\(865\) | −11.6388 | −0.395731 | ||||||||
\(866\) | 27.9441 | 0.949580 | ||||||||
\(867\) | 0.174826 | 0.00593740 | ||||||||
\(868\) | 1.30951 | 0.0444476 | ||||||||
\(869\) | −7.55565 | −0.256308 | ||||||||
\(870\) | 2.34944 | 0.0796534 | ||||||||
\(871\) | 4.70805 | 0.159526 | ||||||||
\(872\) | −15.6620 | −0.530382 | ||||||||
\(873\) | −4.90537 | −0.166022 | ||||||||
\(874\) | −39.6004 | −1.33950 | ||||||||
\(875\) | −0.333284 | −0.0112671 | ||||||||
\(876\) | −19.6843 | −0.665069 | ||||||||
\(877\) | 16.6593 | 0.562544 | 0.281272 | − | 0.959628i | \(-0.409244\pi\) | ||||
0.281272 | + | 0.959628i | \(0.409244\pi\) | |||||||
\(878\) | −28.9237 | −0.976128 | ||||||||
\(879\) | −49.5040 | −1.66973 | ||||||||
\(880\) | −2.68771 | −0.0906027 | ||||||||
\(881\) | −18.5108 | −0.623645 | −0.311823 | − | 0.950140i | \(-0.600939\pi\) | ||||
−0.311823 | + | 0.950140i | \(0.600939\pi\) | |||||||
\(882\) | 2.48210 | 0.0835768 | ||||||||
\(883\) | 15.4100 | 0.518586 | 0.259293 | − | 0.965799i | \(-0.416510\pi\) | ||||
0.259293 | + | 0.965799i | \(0.416510\pi\) | |||||||
\(884\) | −5.97575 | −0.200986 | ||||||||
\(885\) | 5.58867 | 0.187861 | ||||||||
\(886\) | 24.7452 | 0.831330 | ||||||||
\(887\) | −56.8466 | −1.90872 | −0.954361 | − | 0.298654i | \(-0.903462\pi\) | ||||
−0.954361 | + | 0.298654i | \(0.903462\pi\) | |||||||
\(888\) | −5.75090 | −0.192988 | ||||||||
\(889\) | 6.06002 | 0.203247 | ||||||||
\(890\) | −11.3071 | −0.379015 | ||||||||
\(891\) | 20.9353 | 0.701359 | ||||||||
\(892\) | 15.9530 | 0.534145 | ||||||||
\(893\) | 54.1198 | 1.81105 | ||||||||
\(894\) | 12.5267 | 0.418954 | ||||||||
\(895\) | 6.79330 | 0.227075 | ||||||||
\(896\) | −0.333284 | −0.0111342 | ||||||||
\(897\) | 11.2129 | 0.374387 | ||||||||
\(898\) | 9.52218 | 0.317759 | ||||||||
\(899\) | 5.68173 | 0.189496 | ||||||||
\(900\) | −0.360304 | −0.0120101 | ||||||||
\(901\) | 21.8591 | 0.728231 | ||||||||
\(902\) | −5.83231 | −0.194195 | ||||||||
\(903\) | −3.04438 | −0.101311 | ||||||||
\(904\) | −3.77807 | −0.125657 | ||||||||
\(905\) | 0.611592 | 0.0203300 | ||||||||
\(906\) | −26.1394 | −0.868422 | ||||||||
\(907\) | 48.0315 | 1.59486 | 0.797430 | − | 0.603412i | \(-0.206193\pi\) | ||||
0.797430 | + | 0.603412i | \(0.206193\pi\) | |||||||
\(908\) | 19.0713 | 0.632904 | ||||||||
\(909\) | 4.09076 | 0.135682 | ||||||||
\(910\) | −0.484576 | −0.0160635 | ||||||||
\(911\) | 21.8425 | 0.723675 | 0.361838 | − | 0.932241i | \(-0.382149\pi\) | ||||
0.361838 | + | 0.932241i | \(0.382149\pi\) | |||||||
\(912\) | −13.5545 | −0.448835 | ||||||||
\(913\) | 14.7146 | 0.486981 | ||||||||
\(914\) | −37.8541 | −1.25210 | ||||||||
\(915\) | 13.3207 | 0.440368 | ||||||||
\(916\) | −17.3615 | −0.573639 | ||||||||
\(917\) | 5.41003 | 0.178655 | ||||||||
\(918\) | −22.4389 | −0.740593 | ||||||||
\(919\) | 38.0442 | 1.25496 | 0.627482 | − | 0.778631i | \(-0.284086\pi\) | ||||
0.627482 | + | 0.778631i | \(0.284086\pi\) | |||||||
\(920\) | −4.74671 | −0.156494 | ||||||||
\(921\) | 14.4374 | 0.475727 | ||||||||
\(922\) | −3.49481 | −0.115095 | ||||||||
\(923\) | 0.808743 | 0.0266201 | ||||||||
\(924\) | −1.45537 | −0.0478782 | ||||||||
\(925\) | 3.53964 | 0.116383 | ||||||||
\(926\) | 28.8258 | 0.947275 | ||||||||
\(927\) | 4.68018 | 0.153717 | ||||||||
\(928\) | −1.44606 | −0.0474693 | ||||||||
\(929\) | −34.7468 | −1.14001 | −0.570003 | − | 0.821643i | \(-0.693058\pi\) | ||||
−0.570003 | + | 0.821643i | \(0.693058\pi\) | |||||||
\(930\) | 6.38368 | 0.209329 | ||||||||
\(931\) | −57.4723 | −1.88358 | ||||||||
\(932\) | 12.4461 | 0.407684 | ||||||||
\(933\) | 5.15492 | 0.168765 | ||||||||
\(934\) | −40.6843 | −1.33123 | ||||||||
\(935\) | 11.0466 | 0.361262 | ||||||||
\(936\) | −0.523861 | −0.0171229 | ||||||||
\(937\) | 12.6504 | 0.413270 | 0.206635 | − | 0.978418i | \(-0.433749\pi\) | ||||
0.206635 | + | 0.978418i | \(0.433749\pi\) | |||||||
\(938\) | −1.07922 | −0.0352377 | ||||||||
\(939\) | −21.8017 | −0.711473 | ||||||||
\(940\) | 6.48708 | 0.211585 | ||||||||
\(941\) | −8.09526 | −0.263898 | −0.131949 | − | 0.991257i | \(-0.542124\pi\) | ||||
−0.131949 | + | 0.991257i | \(0.542124\pi\) | |||||||
\(942\) | 2.69589 | 0.0878367 | ||||||||
\(943\) | −10.3003 | −0.335425 | ||||||||
\(944\) | −3.43978 | −0.111955 | ||||||||
\(945\) | −1.81957 | −0.0591908 | ||||||||
\(946\) | 15.1109 | 0.491298 | ||||||||
\(947\) | 12.9704 | 0.421480 | 0.210740 | − | 0.977542i | \(-0.432413\pi\) | ||||
0.210740 | + | 0.977542i | \(0.432413\pi\) | |||||||
\(948\) | −4.56737 | −0.148341 | ||||||||
\(949\) | 17.6153 | 0.571816 | ||||||||
\(950\) | 8.34271 | 0.270673 | ||||||||
\(951\) | 54.6751 | 1.77296 | ||||||||
\(952\) | 1.36981 | 0.0443958 | ||||||||
\(953\) | −19.2288 | −0.622881 | −0.311441 | − | 0.950266i | \(-0.600811\pi\) | ||||
−0.311441 | + | 0.950266i | \(0.600811\pi\) | |||||||
\(954\) | 1.91626 | 0.0620413 | ||||||||
\(955\) | −23.5883 | −0.763301 | ||||||||
\(956\) | 19.8560 | 0.642189 | ||||||||
\(957\) | −6.31461 | −0.204122 | ||||||||
\(958\) | 35.4903 | 1.14664 | ||||||||
\(959\) | −4.66044 | −0.150493 | ||||||||
\(960\) | −1.62471 | −0.0524374 | ||||||||
\(961\) | −15.5621 | −0.502004 | ||||||||
\(962\) | 5.14643 | 0.165928 | ||||||||
\(963\) | 4.26865 | 0.137555 | ||||||||
\(964\) | 13.1376 | 0.423135 | ||||||||
\(965\) | −8.93664 | −0.287681 | ||||||||
\(966\) | −2.57030 | −0.0826980 | ||||||||
\(967\) | −36.0112 | −1.15804 | −0.579021 | − | 0.815313i | \(-0.696565\pi\) | ||||
−0.579021 | + | 0.815313i | \(0.696565\pi\) | |||||||
\(968\) | −3.77622 | −0.121372 | ||||||||
\(969\) | 55.7096 | 1.78965 | ||||||||
\(970\) | 13.6146 | 0.437137 | ||||||||
\(971\) | 34.8909 | 1.11970 | 0.559852 | − | 0.828593i | \(-0.310858\pi\) | ||||
0.559852 | + | 0.828593i | \(0.310858\pi\) | |||||||
\(972\) | −3.72326 | −0.119424 | ||||||||
\(973\) | −4.58981 | −0.147142 | ||||||||
\(974\) | 8.70620 | 0.278965 | ||||||||
\(975\) | −2.36224 | −0.0756522 | ||||||||
\(976\) | −8.19878 | −0.262436 | ||||||||
\(977\) | 0.795280 | 0.0254433 | 0.0127216 | − | 0.999919i | \(-0.495950\pi\) | ||||
0.0127216 | + | 0.999919i | \(0.495950\pi\) | |||||||
\(978\) | −4.23902 | −0.135549 | ||||||||
\(979\) | 30.3902 | 0.971277 | ||||||||
\(980\) | −6.88892 | −0.220059 | ||||||||
\(981\) | 5.64307 | 0.180169 | ||||||||
\(982\) | 23.0004 | 0.733973 | ||||||||
\(983\) | 31.1377 | 0.993140 | 0.496570 | − | 0.867997i | \(-0.334593\pi\) | ||||
0.496570 | + | 0.867997i | \(0.334593\pi\) | |||||||
\(984\) | −3.52562 | −0.112393 | ||||||||
\(985\) | −16.9345 | −0.539578 | ||||||||
\(986\) | 5.94337 | 0.189275 | ||||||||
\(987\) | 3.51270 | 0.111810 | ||||||||
\(988\) | 12.1298 | 0.385901 | ||||||||
\(989\) | 26.6870 | 0.848598 | ||||||||
\(990\) | 0.968392 | 0.0307775 | ||||||||
\(991\) | 24.0845 | 0.765070 | 0.382535 | − | 0.923941i | \(-0.375051\pi\) | ||||
0.382535 | + | 0.923941i | \(0.375051\pi\) | |||||||
\(992\) | −3.92911 | −0.124749 | ||||||||
\(993\) | 14.0414 | 0.445591 | ||||||||
\(994\) | −0.185386 | −0.00588010 | ||||||||
\(995\) | 10.3990 | 0.329672 | ||||||||
\(996\) | 8.89492 | 0.281846 | ||||||||
\(997\) | 1.06741 | 0.0338052 | 0.0169026 | − | 0.999857i | \(-0.494619\pi\) | ||||
0.0169026 | + | 0.999857i | \(0.494619\pi\) | |||||||
\(998\) | 21.6725 | 0.686032 | ||||||||
\(999\) | 19.3248 | 0.611409 |
(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 | 6010.2.a.c.1.6 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6010.2.a.c.1.6 | ✓ | 16 | 1.1 | even | 1 | trivial |