Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2175,2,Mod(1,2175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2175, 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("2175.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2175 = 3 \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2175.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: | \(17.3674624396\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 10x^{5} + 19x^{4} + 24x^{3} - 44x^{2} - 3x + 14 \) |
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 | 1.2 | ||
Root | \(2.26695\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2175.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.26695 | −1.60298 | −0.801489 | − | 0.598010i | \(-0.795958\pi\) | ||||
−0.801489 | + | 0.598010i | \(0.795958\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.13907 | 1.56954 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.26695 | 0.925480 | ||||||||
\(7\) | −0.159887 | −0.0604316 | −0.0302158 | − | 0.999543i | \(-0.509619\pi\) | ||||
−0.0302158 | + | 0.999543i | \(0.509619\pi\) | |||||||
\(8\) | −2.58223 | −0.912955 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.24930 | −0.979701 | −0.489851 | − | 0.871806i | \(-0.662949\pi\) | ||||
−0.489851 | + | 0.871806i | \(0.662949\pi\) | |||||||
\(12\) | −3.13907 | −0.906173 | ||||||||
\(13\) | −7.05679 | −1.95720 | −0.978600 | − | 0.205770i | \(-0.934030\pi\) | ||||
−0.978600 | + | 0.205770i | \(0.934030\pi\) | |||||||
\(14\) | 0.362456 | 0.0968704 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.424361 | −0.106090 | ||||||||
\(17\) | −7.63808 | −1.85251 | −0.926254 | − | 0.376901i | \(-0.876990\pi\) | ||||
−0.926254 | + | 0.376901i | \(0.876990\pi\) | |||||||
\(18\) | −2.26695 | −0.534326 | ||||||||
\(19\) | −3.99028 | −0.915432 | −0.457716 | − | 0.889098i | \(-0.651332\pi\) | ||||
−0.457716 | + | 0.889098i | \(0.651332\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.159887 | 0.0348902 | ||||||||
\(22\) | 7.36601 | 1.57044 | ||||||||
\(23\) | −2.06402 | −0.430377 | −0.215189 | − | 0.976572i | \(-0.569037\pi\) | ||||
−0.215189 | + | 0.976572i | \(0.569037\pi\) | |||||||
\(24\) | 2.58223 | 0.527095 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 15.9974 | 3.13735 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.501897 | −0.0948496 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.2044 | 1.83277 | 0.916383 | − | 0.400303i | \(-0.131095\pi\) | ||||
0.916383 | + | 0.400303i | \(0.131095\pi\) | |||||||
\(32\) | 6.12646 | 1.08302 | ||||||||
\(33\) | 3.24930 | 0.565631 | ||||||||
\(34\) | 17.3152 | 2.96953 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.13907 | 0.523179 | ||||||||
\(37\) | 4.27815 | 0.703323 | 0.351662 | − | 0.936127i | \(-0.385617\pi\) | ||||
0.351662 | + | 0.936127i | \(0.385617\pi\) | |||||||
\(38\) | 9.04576 | 1.46742 | ||||||||
\(39\) | 7.05679 | 1.12999 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.12330 | −0.800125 | −0.400063 | − | 0.916488i | \(-0.631012\pi\) | ||||
−0.400063 | + | 0.916488i | \(0.631012\pi\) | |||||||
\(42\) | −0.362456 | −0.0559282 | ||||||||
\(43\) | 3.94180 | 0.601118 | 0.300559 | − | 0.953763i | \(-0.402827\pi\) | ||||
0.300559 | + | 0.953763i | \(0.402827\pi\) | |||||||
\(44\) | −10.1998 | −1.53768 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.67903 | 0.689885 | ||||||||
\(47\) | −5.61626 | −0.819215 | −0.409608 | − | 0.912262i | \(-0.634334\pi\) | ||||
−0.409608 | + | 0.912262i | \(0.634334\pi\) | |||||||
\(48\) | 0.424361 | 0.0612513 | ||||||||
\(49\) | −6.97444 | −0.996348 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.63808 | 1.06955 | ||||||||
\(52\) | −22.1518 | −3.07190 | ||||||||
\(53\) | −12.0822 | −1.65962 | −0.829808 | − | 0.558049i | \(-0.811550\pi\) | ||||
−0.829808 | + | 0.558049i | \(0.811550\pi\) | |||||||
\(54\) | 2.26695 | 0.308493 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.412864 | 0.0551713 | ||||||||
\(57\) | 3.99028 | 0.528525 | ||||||||
\(58\) | 2.26695 | 0.297665 | ||||||||
\(59\) | −7.06781 | −0.920151 | −0.460075 | − | 0.887880i | \(-0.652178\pi\) | ||||
−0.460075 | + | 0.887880i | \(0.652178\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4310 | 1.46359 | 0.731796 | − | 0.681524i | \(-0.238682\pi\) | ||||
0.731796 | + | 0.681524i | \(0.238682\pi\) | |||||||
\(62\) | −23.1329 | −2.93788 | ||||||||
\(63\) | −0.159887 | −0.0201439 | ||||||||
\(64\) | −13.0397 | −1.62996 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.36601 | −0.906694 | ||||||||
\(67\) | 14.9512 | 1.82658 | 0.913289 | − | 0.407311i | \(-0.133534\pi\) | ||||
0.913289 | + | 0.407311i | \(0.133534\pi\) | |||||||
\(68\) | −23.9765 | −2.90758 | ||||||||
\(69\) | 2.06402 | 0.248478 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.43347 | 0.407478 | 0.203739 | − | 0.979025i | \(-0.434691\pi\) | ||||
0.203739 | + | 0.979025i | \(0.434691\pi\) | |||||||
\(72\) | −2.58223 | −0.304318 | ||||||||
\(73\) | 12.0772 | 1.41353 | 0.706764 | − | 0.707449i | \(-0.250154\pi\) | ||||
0.706764 | + | 0.707449i | \(0.250154\pi\) | |||||||
\(74\) | −9.69836 | −1.12741 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.5258 | −1.43680 | ||||||||
\(77\) | 0.519521 | 0.0592049 | ||||||||
\(78\) | −15.9974 | −1.81135 | ||||||||
\(79\) | −12.7441 | −1.43383 | −0.716913 | − | 0.697163i | \(-0.754446\pi\) | ||||
−0.716913 | + | 0.697163i | \(0.754446\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.6143 | 1.28258 | ||||||||
\(83\) | 2.59792 | 0.285159 | 0.142580 | − | 0.989783i | \(-0.454460\pi\) | ||||
0.142580 | + | 0.989783i | \(0.454460\pi\) | |||||||
\(84\) | 0.501897 | 0.0547614 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.93586 | −0.963579 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 8.39044 | 0.894423 | ||||||||
\(89\) | 4.33165 | 0.459154 | 0.229577 | − | 0.973290i | \(-0.426266\pi\) | ||||
0.229577 | + | 0.973290i | \(0.426266\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.12829 | 0.118277 | ||||||||
\(92\) | −6.47910 | −0.675493 | ||||||||
\(93\) | −10.2044 | −1.05815 | ||||||||
\(94\) | 12.7318 | 1.31318 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −6.12646 | −0.625279 | ||||||||
\(97\) | 3.88355 | 0.394315 | 0.197158 | − | 0.980372i | \(-0.436829\pi\) | ||||
0.197158 | + | 0.980372i | \(0.436829\pi\) | |||||||
\(98\) | 15.8107 | 1.59712 | ||||||||
\(99\) | −3.24930 | −0.326567 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.4045 | 1.53280 | 0.766400 | − | 0.642363i | \(-0.222046\pi\) | ||||
0.766400 | + | 0.642363i | \(0.222046\pi\) | |||||||
\(102\) | −17.3152 | −1.71446 | ||||||||
\(103\) | −7.68484 | −0.757210 | −0.378605 | − | 0.925558i | \(-0.623596\pi\) | ||||
−0.378605 | + | 0.925558i | \(0.623596\pi\) | |||||||
\(104\) | 18.2222 | 1.78684 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 27.3897 | 2.66033 | ||||||||
\(107\) | 4.60924 | 0.445592 | 0.222796 | − | 0.974865i | \(-0.428482\pi\) | ||||
0.222796 | + | 0.974865i | \(0.428482\pi\) | |||||||
\(108\) | −3.13907 | −0.302058 | ||||||||
\(109\) | −14.4509 | −1.38415 | −0.692073 | − | 0.721827i | \(-0.743302\pi\) | ||||
−0.692073 | + | 0.721827i | \(0.743302\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.27815 | −0.406064 | ||||||||
\(112\) | 0.0678498 | 0.00641120 | ||||||||
\(113\) | 4.08614 | 0.384392 | 0.192196 | − | 0.981357i | \(-0.438439\pi\) | ||||
0.192196 | + | 0.981357i | \(0.438439\pi\) | |||||||
\(114\) | −9.04576 | −0.847213 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.13907 | −0.291456 | ||||||||
\(117\) | −7.05679 | −0.652400 | ||||||||
\(118\) | 16.0224 | 1.47498 | ||||||||
\(119\) | 1.22123 | 0.111950 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.442038 | −0.0401853 | ||||||||
\(122\) | −25.9136 | −2.34610 | ||||||||
\(123\) | 5.12330 | 0.461952 | ||||||||
\(124\) | 32.0324 | 2.87659 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.362456 | 0.0322901 | ||||||||
\(127\) | 3.69650 | 0.328011 | 0.164006 | − | 0.986459i | \(-0.447559\pi\) | ||||
0.164006 | + | 0.986459i | \(0.447559\pi\) | |||||||
\(128\) | 17.3074 | 1.52977 | ||||||||
\(129\) | −3.94180 | −0.347056 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.92811 | −0.867423 | −0.433712 | − | 0.901052i | \(-0.642796\pi\) | ||||
−0.433712 | + | 0.901052i | \(0.642796\pi\) | |||||||
\(132\) | 10.1998 | 0.887779 | ||||||||
\(133\) | 0.637993 | 0.0553210 | ||||||||
\(134\) | −33.8936 | −2.92797 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 19.7233 | 1.69126 | ||||||||
\(137\) | −3.82810 | −0.327057 | −0.163528 | − | 0.986539i | \(-0.552288\pi\) | ||||
−0.163528 | + | 0.986539i | \(0.552288\pi\) | |||||||
\(138\) | −4.67903 | −0.398305 | ||||||||
\(139\) | −2.06987 | −0.175564 | −0.0877822 | − | 0.996140i | \(-0.527978\pi\) | ||||
−0.0877822 | + | 0.996140i | \(0.527978\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.61626 | 0.472974 | ||||||||
\(142\) | −7.78351 | −0.653177 | ||||||||
\(143\) | 22.9296 | 1.91747 | ||||||||
\(144\) | −0.424361 | −0.0353634 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −27.3784 | −2.26585 | ||||||||
\(147\) | 6.97444 | 0.575242 | ||||||||
\(148\) | 13.4294 | 1.10389 | ||||||||
\(149\) | −1.46609 | −0.120107 | −0.0600536 | − | 0.998195i | \(-0.519127\pi\) | ||||
−0.0600536 | + | 0.998195i | \(0.519127\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.1279 | −1.63799 | −0.818995 | − | 0.573801i | \(-0.805468\pi\) | ||||
−0.818995 | + | 0.573801i | \(0.805468\pi\) | |||||||
\(152\) | 10.3038 | 0.835748 | ||||||||
\(153\) | −7.63808 | −0.617502 | ||||||||
\(154\) | −1.17773 | −0.0949041 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 22.1518 | 1.77356 | ||||||||
\(157\) | −7.09106 | −0.565928 | −0.282964 | − | 0.959131i | \(-0.591318\pi\) | ||||
−0.282964 | + | 0.959131i | \(0.591318\pi\) | |||||||
\(158\) | 28.8903 | 2.29839 | ||||||||
\(159\) | 12.0822 | 0.958180 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.330009 | 0.0260084 | ||||||||
\(162\) | −2.26695 | −0.178109 | ||||||||
\(163\) | 6.58715 | 0.515946 | 0.257973 | − | 0.966152i | \(-0.416945\pi\) | ||||
0.257973 | + | 0.966152i | \(0.416945\pi\) | |||||||
\(164\) | −16.0824 | −1.25583 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.88937 | −0.457104 | ||||||||
\(167\) | 10.6638 | 0.825192 | 0.412596 | − | 0.910914i | \(-0.364622\pi\) | ||||
0.412596 | + | 0.910914i | \(0.364622\pi\) | |||||||
\(168\) | −0.412864 | −0.0318532 | ||||||||
\(169\) | 36.7983 | 2.83063 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.99028 | −0.305144 | ||||||||
\(172\) | 12.3736 | 0.943477 | ||||||||
\(173\) | 13.8799 | 1.05527 | 0.527633 | − | 0.849472i | \(-0.323080\pi\) | ||||
0.527633 | + | 0.849472i | \(0.323080\pi\) | |||||||
\(174\) | −2.26695 | −0.171857 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.37888 | 0.103937 | ||||||||
\(177\) | 7.06781 | 0.531249 | ||||||||
\(178\) | −9.81965 | −0.736014 | ||||||||
\(179\) | −11.1105 | −0.830439 | −0.415219 | − | 0.909721i | \(-0.636295\pi\) | ||||
−0.415219 | + | 0.909721i | \(0.636295\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.9453 | 0.813557 | 0.406778 | − | 0.913527i | \(-0.366652\pi\) | ||||
0.406778 | + | 0.913527i | \(0.366652\pi\) | |||||||
\(182\) | −2.55777 | −0.189595 | ||||||||
\(183\) | −11.4310 | −0.845005 | ||||||||
\(184\) | 5.32976 | 0.392915 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 23.1329 | 1.69619 | ||||||||
\(187\) | 24.8184 | 1.81490 | ||||||||
\(188\) | −17.6298 | −1.28579 | ||||||||
\(189\) | 0.159887 | 0.0116301 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.1472 | 1.31309 | 0.656544 | − | 0.754287i | \(-0.272017\pi\) | ||||
0.656544 | + | 0.754287i | \(0.272017\pi\) | |||||||
\(192\) | 13.0397 | 0.941058 | ||||||||
\(193\) | 17.3305 | 1.24747 | 0.623737 | − | 0.781634i | \(-0.285614\pi\) | ||||
0.623737 | + | 0.781634i | \(0.285614\pi\) | |||||||
\(194\) | −8.80383 | −0.632078 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −21.8933 | −1.56381 | ||||||||
\(197\) | 10.4273 | 0.742915 | 0.371458 | − | 0.928450i | \(-0.378858\pi\) | ||||
0.371458 | + | 0.928450i | \(0.378858\pi\) | |||||||
\(198\) | 7.36601 | 0.523480 | ||||||||
\(199\) | 11.5570 | 0.819256 | 0.409628 | − | 0.912253i | \(-0.365659\pi\) | ||||
0.409628 | + | 0.912253i | \(0.365659\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.9512 | −1.05458 | ||||||||
\(202\) | −34.9212 | −2.45704 | ||||||||
\(203\) | 0.159887 | 0.0112219 | ||||||||
\(204\) | 23.9765 | 1.67869 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 17.4212 | 1.21379 | ||||||||
\(207\) | −2.06402 | −0.143459 | ||||||||
\(208\) | 2.99463 | 0.207640 | ||||||||
\(209\) | 12.9656 | 0.896850 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.1616 | −1.45682 | −0.728412 | − | 0.685140i | \(-0.759741\pi\) | ||||
−0.728412 | + | 0.685140i | \(0.759741\pi\) | |||||||
\(212\) | −37.9269 | −2.60483 | ||||||||
\(213\) | −3.43347 | −0.235257 | ||||||||
\(214\) | −10.4489 | −0.714274 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.58223 | 0.175698 | ||||||||
\(217\) | −1.63155 | −0.110757 | ||||||||
\(218\) | 32.7595 | 2.21876 | ||||||||
\(219\) | −12.0772 | −0.816101 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 53.9003 | 3.62573 | ||||||||
\(222\) | 9.69836 | 0.650911 | ||||||||
\(223\) | −9.46925 | −0.634108 | −0.317054 | − | 0.948408i | \(-0.602694\pi\) | ||||
−0.317054 | + | 0.948408i | \(0.602694\pi\) | |||||||
\(224\) | −0.979541 | −0.0654483 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.26310 | −0.616172 | ||||||||
\(227\) | −22.4030 | −1.48694 | −0.743471 | − | 0.668768i | \(-0.766822\pi\) | ||||
−0.743471 | + | 0.668768i | \(0.766822\pi\) | |||||||
\(228\) | 12.5258 | 0.829539 | ||||||||
\(229\) | 2.03117 | 0.134223 | 0.0671117 | − | 0.997745i | \(-0.478622\pi\) | ||||
0.0671117 | + | 0.997745i | \(0.478622\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.519521 | −0.0341820 | ||||||||
\(232\) | 2.58223 | 0.169532 | ||||||||
\(233\) | −11.0704 | −0.725249 | −0.362624 | − | 0.931935i | \(-0.618119\pi\) | ||||
−0.362624 | + | 0.931935i | \(0.618119\pi\) | |||||||
\(234\) | 15.9974 | 1.04578 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −22.1864 | −1.44421 | ||||||||
\(237\) | 12.7441 | 0.827820 | ||||||||
\(238\) | −2.76847 | −0.179453 | ||||||||
\(239\) | −2.24098 | −0.144957 | −0.0724786 | − | 0.997370i | \(-0.523091\pi\) | ||||
−0.0724786 | + | 0.997370i | \(0.523091\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.4838 | 0.932986 | 0.466493 | − | 0.884525i | \(-0.345517\pi\) | ||||
0.466493 | + | 0.884525i | \(0.345517\pi\) | |||||||
\(242\) | 1.00208 | 0.0644161 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 35.8828 | 2.29716 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.6143 | −0.740499 | ||||||||
\(247\) | 28.1585 | 1.79168 | ||||||||
\(248\) | −26.3501 | −1.67323 | ||||||||
\(249\) | −2.59792 | −0.164637 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.2044 | −1.02281 | −0.511407 | − | 0.859339i | \(-0.670875\pi\) | ||||
−0.511407 | + | 0.859339i | \(0.670875\pi\) | |||||||
\(252\) | −0.501897 | −0.0316165 | ||||||||
\(253\) | 6.70661 | 0.421641 | ||||||||
\(254\) | −8.37978 | −0.525794 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.1557 | −0.822232 | ||||||||
\(257\) | 3.36942 | 0.210178 | 0.105089 | − | 0.994463i | \(-0.466487\pi\) | ||||
0.105089 | + | 0.994463i | \(0.466487\pi\) | |||||||
\(258\) | 8.93586 | 0.556323 | ||||||||
\(259\) | −0.684020 | −0.0425029 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 22.5066 | 1.39046 | ||||||||
\(263\) | −1.79671 | −0.110790 | −0.0553950 | − | 0.998465i | \(-0.517642\pi\) | ||||
−0.0553950 | + | 0.998465i | \(0.517642\pi\) | |||||||
\(264\) | −8.39044 | −0.516396 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.44630 | −0.0886783 | ||||||||
\(267\) | −4.33165 | −0.265093 | ||||||||
\(268\) | 46.9329 | 2.86688 | ||||||||
\(269\) | −0.117055 | −0.00713699 | −0.00356849 | − | 0.999994i | \(-0.501136\pi\) | ||||
−0.00356849 | + | 0.999994i | \(0.501136\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.06294 | −0.246806 | −0.123403 | − | 0.992357i | \(-0.539381\pi\) | ||||
−0.123403 | + | 0.992357i | \(0.539381\pi\) | |||||||
\(272\) | 3.24131 | 0.196533 | ||||||||
\(273\) | −1.12829 | −0.0682871 | ||||||||
\(274\) | 8.67813 | 0.524265 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.47910 | 0.389996 | ||||||||
\(277\) | 12.5436 | 0.753674 | 0.376837 | − | 0.926279i | \(-0.377012\pi\) | ||||
0.376837 | + | 0.926279i | \(0.377012\pi\) | |||||||
\(278\) | 4.69231 | 0.281426 | ||||||||
\(279\) | 10.2044 | 0.610922 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.83163 | −0.168921 | −0.0844605 | − | 0.996427i | \(-0.526917\pi\) | ||||
−0.0844605 | + | 0.996427i | \(0.526917\pi\) | |||||||
\(282\) | −12.7318 | −0.758167 | ||||||||
\(283\) | −28.2249 | −1.67780 | −0.838898 | − | 0.544288i | \(-0.816800\pi\) | ||||
−0.838898 | + | 0.544288i | \(0.816800\pi\) | |||||||
\(284\) | 10.7779 | 0.639551 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −51.9804 | −3.07366 | ||||||||
\(287\) | 0.819148 | 0.0483528 | ||||||||
\(288\) | 6.12646 | 0.361005 | ||||||||
\(289\) | 41.3403 | 2.43178 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.88355 | −0.227658 | ||||||||
\(292\) | 37.9112 | 2.21859 | ||||||||
\(293\) | −21.9337 | −1.28138 | −0.640691 | − | 0.767799i | \(-0.721352\pi\) | ||||
−0.640691 | + | 0.767799i | \(0.721352\pi\) | |||||||
\(294\) | −15.8107 | −0.922100 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −11.0472 | −0.642103 | ||||||||
\(297\) | 3.24930 | 0.188544 | ||||||||
\(298\) | 3.32357 | 0.192529 | ||||||||
\(299\) | 14.5653 | 0.842335 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.630241 | −0.0363265 | ||||||||
\(302\) | 45.6291 | 2.62566 | ||||||||
\(303\) | −15.4045 | −0.884963 | ||||||||
\(304\) | 1.69332 | 0.0971185 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 17.3152 | 0.989843 | ||||||||
\(307\) | 0.461574 | 0.0263434 | 0.0131717 | − | 0.999913i | \(-0.495807\pi\) | ||||
0.0131717 | + | 0.999913i | \(0.495807\pi\) | |||||||
\(308\) | 1.63081 | 0.0929243 | ||||||||
\(309\) | 7.68484 | 0.437175 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.5507 | 1.56226 | 0.781128 | − | 0.624371i | \(-0.214645\pi\) | ||||
0.781128 | + | 0.624371i | \(0.214645\pi\) | |||||||
\(312\) | −18.2222 | −1.03163 | ||||||||
\(313\) | −14.9121 | −0.842882 | −0.421441 | − | 0.906856i | \(-0.638476\pi\) | ||||
−0.421441 | + | 0.906856i | \(0.638476\pi\) | |||||||
\(314\) | 16.0751 | 0.907170 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −40.0048 | −2.25044 | ||||||||
\(317\) | 22.9266 | 1.28769 | 0.643843 | − | 0.765157i | \(-0.277339\pi\) | ||||
0.643843 | + | 0.765157i | \(0.277339\pi\) | |||||||
\(318\) | −27.3897 | −1.53594 | ||||||||
\(319\) | 3.24930 | 0.181926 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.60924 | −0.257263 | ||||||||
\(322\) | −0.748115 | −0.0416908 | ||||||||
\(323\) | 30.4781 | 1.69584 | ||||||||
\(324\) | 3.13907 | 0.174393 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14.9328 | −0.827049 | ||||||||
\(327\) | 14.4509 | 0.799137 | ||||||||
\(328\) | 13.2295 | 0.730478 | ||||||||
\(329\) | 0.897966 | 0.0495065 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.23147 | −0.177618 | −0.0888088 | − | 0.996049i | \(-0.528306\pi\) | ||||
−0.0888088 | + | 0.996049i | \(0.528306\pi\) | |||||||
\(332\) | 8.15507 | 0.447568 | ||||||||
\(333\) | 4.27815 | 0.234441 | ||||||||
\(334\) | −24.1744 | −1.32277 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.0678498 | −0.00370151 | ||||||||
\(337\) | −28.8026 | −1.56898 | −0.784489 | − | 0.620143i | \(-0.787075\pi\) | ||||
−0.784489 | + | 0.620143i | \(0.787075\pi\) | |||||||
\(338\) | −83.4199 | −4.53744 | ||||||||
\(339\) | −4.08614 | −0.221929 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −33.1572 | −1.79556 | ||||||||
\(342\) | 9.04576 | 0.489139 | ||||||||
\(343\) | 2.23433 | 0.120642 | ||||||||
\(344\) | −10.1786 | −0.548794 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −31.4650 | −1.69157 | ||||||||
\(347\) | 16.4175 | 0.881337 | 0.440669 | − | 0.897670i | \(-0.354741\pi\) | ||||
0.440669 | + | 0.897670i | \(0.354741\pi\) | |||||||
\(348\) | 3.13907 | 0.168272 | ||||||||
\(349\) | −18.2107 | −0.974796 | −0.487398 | − | 0.873180i | \(-0.662054\pi\) | ||||
−0.487398 | + | 0.873180i | \(0.662054\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.05679 | 0.376663 | ||||||||
\(352\) | −19.9067 | −1.06103 | ||||||||
\(353\) | 18.8790 | 1.00483 | 0.502414 | − | 0.864627i | \(-0.332445\pi\) | ||||
0.502414 | + | 0.864627i | \(0.332445\pi\) | |||||||
\(354\) | −16.0224 | −0.851581 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.5974 | 0.720660 | ||||||||
\(357\) | −1.22123 | −0.0646343 | ||||||||
\(358\) | 25.1870 | 1.33117 | ||||||||
\(359\) | 14.4500 | 0.762640 | 0.381320 | − | 0.924443i | \(-0.375470\pi\) | ||||
0.381320 | + | 0.924443i | \(0.375470\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.07770 | −0.161984 | ||||||||
\(362\) | −24.8125 | −1.30411 | ||||||||
\(363\) | 0.442038 | 0.0232010 | ||||||||
\(364\) | 3.54178 | 0.185640 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 25.9136 | 1.35452 | ||||||||
\(367\) | 21.1171 | 1.10231 | 0.551153 | − | 0.834404i | \(-0.314188\pi\) | ||||
0.551153 | + | 0.834404i | \(0.314188\pi\) | |||||||
\(368\) | 0.875889 | 0.0456589 | ||||||||
\(369\) | −5.12330 | −0.266708 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.93178 | 0.100293 | ||||||||
\(372\) | −32.0324 | −1.66080 | ||||||||
\(373\) | 17.1185 | 0.886361 | 0.443181 | − | 0.896432i | \(-0.353850\pi\) | ||||
0.443181 | + | 0.896432i | \(0.353850\pi\) | |||||||
\(374\) | −56.2622 | −2.90925 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 14.5025 | 0.747907 | ||||||||
\(377\) | 7.05679 | 0.363443 | ||||||||
\(378\) | −0.362456 | −0.0186427 | ||||||||
\(379\) | −0.206688 | −0.0106169 | −0.00530844 | − | 0.999986i | \(-0.501690\pi\) | ||||
−0.00530844 | + | 0.999986i | \(0.501690\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.69650 | −0.189377 | ||||||||
\(382\) | −41.1389 | −2.10485 | ||||||||
\(383\) | −16.3701 | −0.836474 | −0.418237 | − | 0.908338i | \(-0.637352\pi\) | ||||
−0.418237 | + | 0.908338i | \(0.637352\pi\) | |||||||
\(384\) | −17.3074 | −0.883215 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −39.2873 | −1.99967 | ||||||||
\(387\) | 3.94180 | 0.200373 | ||||||||
\(388\) | 12.1908 | 0.618892 | ||||||||
\(389\) | 11.7627 | 0.596393 | 0.298197 | − | 0.954504i | \(-0.403615\pi\) | ||||
0.298197 | + | 0.954504i | \(0.403615\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.7651 | 0.797277 | ||||||||
\(392\) | 18.0096 | 0.909621 | ||||||||
\(393\) | 9.92811 | 0.500807 | ||||||||
\(394\) | −23.6382 | −1.19088 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −10.1998 | −0.512559 | ||||||||
\(397\) | 4.96134 | 0.249002 | 0.124501 | − | 0.992219i | \(-0.460267\pi\) | ||||
0.124501 | + | 0.992219i | \(0.460267\pi\) | |||||||
\(398\) | −26.1992 | −1.31325 | ||||||||
\(399\) | −0.637993 | −0.0319396 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.1967 | 1.80758 | 0.903789 | − | 0.427979i | \(-0.140774\pi\) | ||||
0.903789 | + | 0.427979i | \(0.140774\pi\) | |||||||
\(402\) | 33.8936 | 1.69046 | ||||||||
\(403\) | −72.0103 | −3.58709 | ||||||||
\(404\) | 48.3557 | 2.40579 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.362456 | −0.0179884 | ||||||||
\(407\) | −13.9010 | −0.689047 | ||||||||
\(408\) | −19.7233 | −0.976447 | ||||||||
\(409\) | −16.1607 | −0.799094 | −0.399547 | − | 0.916713i | \(-0.630832\pi\) | ||||
−0.399547 | + | 0.916713i | \(0.630832\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.82810 | 0.188826 | ||||||||
\(412\) | −24.1233 | −1.18847 | ||||||||
\(413\) | 1.13005 | 0.0556061 | ||||||||
\(414\) | 4.67903 | 0.229962 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −43.2331 | −2.11968 | ||||||||
\(417\) | 2.06987 | 0.101362 | ||||||||
\(418\) | −29.3924 | −1.43763 | ||||||||
\(419\) | −33.5544 | −1.63924 | −0.819621 | − | 0.572906i | \(-0.805816\pi\) | ||||
−0.819621 | + | 0.572906i | \(0.805816\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.9847 | 1.31515 | 0.657577 | − | 0.753388i | \(-0.271582\pi\) | ||||
0.657577 | + | 0.753388i | \(0.271582\pi\) | |||||||
\(422\) | 47.9723 | 2.33526 | ||||||||
\(423\) | −5.61626 | −0.273072 | ||||||||
\(424\) | 31.1990 | 1.51515 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.78351 | 0.377112 | ||||||||
\(427\) | −1.82767 | −0.0884471 | ||||||||
\(428\) | 14.4687 | 0.699373 | ||||||||
\(429\) | −22.9296 | −1.10705 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.832366 | 0.0400937 | 0.0200468 | − | 0.999799i | \(-0.493618\pi\) | ||||
0.0200468 | + | 0.999799i | \(0.493618\pi\) | |||||||
\(432\) | 0.424361 | 0.0204171 | ||||||||
\(433\) | 22.5647 | 1.08439 | 0.542195 | − | 0.840253i | \(-0.317593\pi\) | ||||
0.542195 | + | 0.840253i | \(0.317593\pi\) | |||||||
\(434\) | 3.69865 | 0.177541 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −45.3625 | −2.17247 | ||||||||
\(437\) | 8.23600 | 0.393981 | ||||||||
\(438\) | 27.3784 | 1.30819 | ||||||||
\(439\) | 23.9583 | 1.14347 | 0.571734 | − | 0.820439i | \(-0.306271\pi\) | ||||
0.571734 | + | 0.820439i | \(0.306271\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.97444 | −0.332116 | ||||||||
\(442\) | −122.190 | −5.81196 | ||||||||
\(443\) | −17.4925 | −0.831092 | −0.415546 | − | 0.909572i | \(-0.636409\pi\) | ||||
−0.415546 | + | 0.909572i | \(0.636409\pi\) | |||||||
\(444\) | −13.4294 | −0.637332 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 21.4663 | 1.01646 | ||||||||
\(447\) | 1.46609 | 0.0693439 | ||||||||
\(448\) | 2.08487 | 0.0985010 | ||||||||
\(449\) | 4.22200 | 0.199249 | 0.0996243 | − | 0.995025i | \(-0.468236\pi\) | ||||
0.0996243 | + | 0.995025i | \(0.468236\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.6471 | 0.783884 | ||||||||
\(452\) | 12.8267 | 0.603318 | ||||||||
\(453\) | 20.1279 | 0.945694 | ||||||||
\(454\) | 50.7866 | 2.38353 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −10.3038 | −0.482520 | ||||||||
\(457\) | 1.28562 | 0.0601389 | 0.0300694 | − | 0.999548i | \(-0.490427\pi\) | ||||
0.0300694 | + | 0.999548i | \(0.490427\pi\) | |||||||
\(458\) | −4.60456 | −0.215157 | ||||||||
\(459\) | 7.63808 | 0.356515 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.8534 | −1.11097 | −0.555483 | − | 0.831528i | \(-0.687466\pi\) | ||||
−0.555483 | + | 0.831528i | \(0.687466\pi\) | |||||||
\(462\) | 1.17773 | 0.0547929 | ||||||||
\(463\) | −14.1402 | −0.657152 | −0.328576 | − | 0.944478i | \(-0.606569\pi\) | ||||
−0.328576 | + | 0.944478i | \(0.606569\pi\) | |||||||
\(464\) | 0.424361 | 0.0197005 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 25.0962 | 1.16256 | ||||||||
\(467\) | −7.06487 | −0.326923 | −0.163462 | − | 0.986550i | \(-0.552266\pi\) | ||||
−0.163462 | + | 0.986550i | \(0.552266\pi\) | |||||||
\(468\) | −22.1518 | −1.02397 | ||||||||
\(469\) | −2.39050 | −0.110383 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.09106 | 0.326739 | ||||||||
\(472\) | 18.2507 | 0.840056 | ||||||||
\(473\) | −12.8081 | −0.588916 | ||||||||
\(474\) | −28.8903 | −1.32698 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.83353 | 0.175710 | ||||||||
\(477\) | −12.0822 | −0.553205 | ||||||||
\(478\) | 5.08020 | 0.232363 | ||||||||
\(479\) | 22.9561 | 1.04889 | 0.524444 | − | 0.851445i | \(-0.324273\pi\) | ||||
0.524444 | + | 0.851445i | \(0.324273\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.1900 | −1.37654 | ||||||||
\(482\) | −32.8342 | −1.49556 | ||||||||
\(483\) | −0.330009 | −0.0150159 | ||||||||
\(484\) | −1.38759 | −0.0630723 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.26695 | 0.102831 | ||||||||
\(487\) | 27.0319 | 1.22493 | 0.612467 | − | 0.790496i | \(-0.290177\pi\) | ||||
0.612467 | + | 0.790496i | \(0.290177\pi\) | |||||||
\(488\) | −29.5175 | −1.33619 | ||||||||
\(489\) | −6.58715 | −0.297881 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.5498 | −0.521235 | −0.260617 | − | 0.965442i | \(-0.583926\pi\) | ||||
−0.260617 | + | 0.965442i | \(0.583926\pi\) | |||||||
\(492\) | 16.0824 | 0.725051 | ||||||||
\(493\) | 7.63808 | 0.344002 | ||||||||
\(494\) | −63.8340 | −2.87203 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.33036 | −0.194439 | ||||||||
\(497\) | −0.548966 | −0.0246245 | ||||||||
\(498\) | 5.88937 | 0.263909 | ||||||||
\(499\) | 3.77942 | 0.169190 | 0.0845950 | − | 0.996415i | \(-0.473040\pi\) | ||||
0.0845950 | + | 0.996415i | \(0.473040\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.6638 | −0.476425 | ||||||||
\(502\) | 36.7346 | 1.63955 | ||||||||
\(503\) | 14.7684 | 0.658489 | 0.329244 | − | 0.944245i | \(-0.393206\pi\) | ||||
0.329244 | + | 0.944245i | \(0.393206\pi\) | |||||||
\(504\) | 0.412864 | 0.0183904 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −15.2036 | −0.675881 | ||||||||
\(507\) | −36.7983 | −1.63427 | ||||||||
\(508\) | 11.6036 | 0.514826 | ||||||||
\(509\) | −42.4182 | −1.88015 | −0.940077 | − | 0.340962i | \(-0.889247\pi\) | ||||
−0.940077 | + | 0.340962i | \(0.889247\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.93098 | −0.0854217 | ||||||||
\(512\) | −4.79143 | −0.211753 | ||||||||
\(513\) | 3.99028 | 0.176175 | ||||||||
\(514\) | −7.63831 | −0.336911 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −12.3736 | −0.544717 | ||||||||
\(517\) | 18.2489 | 0.802586 | ||||||||
\(518\) | 1.55064 | 0.0681312 | ||||||||
\(519\) | −13.8799 | −0.609258 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.3409 | 0.891152 | 0.445576 | − | 0.895244i | \(-0.352999\pi\) | ||||
0.445576 | + | 0.895244i | \(0.352999\pi\) | |||||||
\(522\) | 2.26695 | 0.0992218 | ||||||||
\(523\) | −1.52190 | −0.0665481 | −0.0332740 | − | 0.999446i | \(-0.510593\pi\) | ||||
−0.0332740 | + | 0.999446i | \(0.510593\pi\) | |||||||
\(524\) | −31.1651 | −1.36145 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.07306 | 0.177594 | ||||||||
\(527\) | −77.9421 | −3.39521 | ||||||||
\(528\) | −1.37888 | −0.0600080 | ||||||||
\(529\) | −18.7398 | −0.814775 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.06781 | −0.306717 | ||||||||
\(532\) | 2.00271 | 0.0868283 | ||||||||
\(533\) | 36.1540 | 1.56601 | ||||||||
\(534\) | 9.81965 | 0.424938 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −38.6074 | −1.66758 | ||||||||
\(537\) | 11.1105 | 0.479454 | ||||||||
\(538\) | 0.265359 | 0.0114404 | ||||||||
\(539\) | 22.6620 | 0.976123 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.40679 | −0.404430 | −0.202215 | − | 0.979341i | \(-0.564814\pi\) | ||||
−0.202215 | + | 0.979341i | \(0.564814\pi\) | |||||||
\(542\) | 9.21049 | 0.395624 | ||||||||
\(543\) | −10.9453 | −0.469707 | ||||||||
\(544\) | −46.7944 | −2.00629 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.55777 | 0.109463 | ||||||||
\(547\) | −19.7232 | −0.843304 | −0.421652 | − | 0.906758i | \(-0.638550\pi\) | ||||
−0.421652 | + | 0.906758i | \(0.638550\pi\) | |||||||
\(548\) | −12.0167 | −0.513328 | ||||||||
\(549\) | 11.4310 | 0.487864 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.99028 | 0.169991 | ||||||||
\(552\) | −5.32976 | −0.226850 | ||||||||
\(553\) | 2.03762 | 0.0866483 | ||||||||
\(554\) | −28.4358 | −1.20812 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.49749 | −0.275555 | ||||||||
\(557\) | −9.01986 | −0.382184 | −0.191092 | − | 0.981572i | \(-0.561203\pi\) | ||||
−0.191092 | + | 0.981572i | \(0.561203\pi\) | |||||||
\(558\) | −23.1329 | −0.979294 | ||||||||
\(559\) | −27.8164 | −1.17651 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.8184 | −1.04784 | ||||||||
\(562\) | 6.41918 | 0.270777 | ||||||||
\(563\) | −17.5283 | −0.738728 | −0.369364 | − | 0.929285i | \(-0.620424\pi\) | ||||
−0.369364 | + | 0.929285i | \(0.620424\pi\) | |||||||
\(564\) | 17.6298 | 0.742350 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 63.9845 | 2.68947 | ||||||||
\(567\) | −0.159887 | −0.00671462 | ||||||||
\(568\) | −8.86599 | −0.372009 | ||||||||
\(569\) | 32.3981 | 1.35820 | 0.679099 | − | 0.734046i | \(-0.262371\pi\) | ||||
0.679099 | + | 0.734046i | \(0.262371\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.8393 | −0.495458 | −0.247729 | − | 0.968829i | \(-0.579684\pi\) | ||||
−0.247729 | + | 0.968829i | \(0.579684\pi\) | |||||||
\(572\) | 71.9778 | 3.00954 | ||||||||
\(573\) | −18.1472 | −0.758112 | ||||||||
\(574\) | −1.85697 | −0.0775085 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −13.0397 | −0.543320 | ||||||||
\(577\) | 0.192778 | 0.00802545 | 0.00401273 | − | 0.999992i | \(-0.498723\pi\) | ||||
0.00401273 | + | 0.999992i | \(0.498723\pi\) | |||||||
\(578\) | −93.7165 | −3.89809 | ||||||||
\(579\) | −17.3305 | −0.720229 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.415374 | −0.0172326 | ||||||||
\(582\) | 8.80383 | 0.364931 | ||||||||
\(583\) | 39.2587 | 1.62593 | ||||||||
\(584\) | −31.1861 | −1.29049 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 49.7227 | 2.05403 | ||||||||
\(587\) | −34.5089 | −1.42433 | −0.712167 | − | 0.702010i | \(-0.752286\pi\) | ||||
−0.712167 | + | 0.702010i | \(0.752286\pi\) | |||||||
\(588\) | 21.8933 | 0.902863 | ||||||||
\(589\) | −40.7184 | −1.67777 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.4273 | −0.428922 | ||||||||
\(592\) | −1.81548 | −0.0746158 | ||||||||
\(593\) | −2.42748 | −0.0996846 | −0.0498423 | − | 0.998757i | \(-0.515872\pi\) | ||||
−0.0498423 | + | 0.998757i | \(0.515872\pi\) | |||||||
\(594\) | −7.36601 | −0.302231 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.60218 | −0.188513 | ||||||||
\(597\) | −11.5570 | −0.472997 | ||||||||
\(598\) | −33.0189 | −1.35024 | ||||||||
\(599\) | 29.3312 | 1.19844 | 0.599220 | − | 0.800585i | \(-0.295478\pi\) | ||||
0.599220 | + | 0.800585i | \(0.295478\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.5631 | 1.20590 | 0.602952 | − | 0.797778i | \(-0.293991\pi\) | ||||
0.602952 | + | 0.797778i | \(0.293991\pi\) | |||||||
\(602\) | 1.42873 | 0.0582306 | ||||||||
\(603\) | 14.9512 | 0.608860 | ||||||||
\(604\) | −63.1831 | −2.57089 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 34.9212 | 1.41858 | ||||||||
\(607\) | −33.1756 | −1.34656 | −0.673278 | − | 0.739390i | \(-0.735114\pi\) | ||||
−0.673278 | + | 0.739390i | \(0.735114\pi\) | |||||||
\(608\) | −24.4463 | −0.991427 | ||||||||
\(609\) | −0.159887 | −0.00647894 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 39.6327 | 1.60337 | ||||||||
\(612\) | −23.9765 | −0.969193 | ||||||||
\(613\) | 13.9979 | 0.565371 | 0.282686 | − | 0.959213i | \(-0.408775\pi\) | ||||
0.282686 | + | 0.959213i | \(0.408775\pi\) | |||||||
\(614\) | −1.04637 | −0.0422279 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.34152 | −0.0540514 | ||||||||
\(617\) | 29.9344 | 1.20511 | 0.602556 | − | 0.798077i | \(-0.294149\pi\) | ||||
0.602556 | + | 0.798077i | \(0.294149\pi\) | |||||||
\(618\) | −17.4212 | −0.700782 | ||||||||
\(619\) | −14.9032 | −0.599009 | −0.299505 | − | 0.954095i | \(-0.596821\pi\) | ||||
−0.299505 | + | 0.954095i | \(0.596821\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.06402 | 0.0828261 | ||||||||
\(622\) | −62.4561 | −2.50426 | ||||||||
\(623\) | −0.692574 | −0.0277474 | ||||||||
\(624\) | −2.99463 | −0.119881 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 33.8050 | 1.35112 | ||||||||
\(627\) | −12.9656 | −0.517796 | ||||||||
\(628\) | −22.2594 | −0.888245 | ||||||||
\(629\) | −32.6769 | −1.30291 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.8643 | −1.14907 | −0.574534 | − | 0.818480i | \(-0.694817\pi\) | ||||
−0.574534 | + | 0.818480i | \(0.694817\pi\) | |||||||
\(632\) | 32.9082 | 1.30902 | ||||||||
\(633\) | 21.1616 | 0.841097 | ||||||||
\(634\) | −51.9735 | −2.06413 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 37.9269 | 1.50390 | ||||||||
\(637\) | 49.2171 | 1.95005 | ||||||||
\(638\) | −7.36601 | −0.291623 | ||||||||
\(639\) | 3.43347 | 0.135826 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 44.0167 | 1.73856 | 0.869278 | − | 0.494324i | \(-0.164585\pi\) | ||||
0.869278 | + | 0.494324i | \(0.164585\pi\) | |||||||
\(642\) | 10.4489 | 0.412386 | ||||||||
\(643\) | 29.6239 | 1.16825 | 0.584125 | − | 0.811663i | \(-0.301438\pi\) | ||||
0.584125 | + | 0.811663i | \(0.301438\pi\) | |||||||
\(644\) | 1.03592 | 0.0408211 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −69.0923 | −2.71840 | ||||||||
\(647\) | 39.3943 | 1.54875 | 0.774375 | − | 0.632727i | \(-0.218064\pi\) | ||||
0.774375 | + | 0.632727i | \(0.218064\pi\) | |||||||
\(648\) | −2.58223 | −0.101439 | ||||||||
\(649\) | 22.9654 | 0.901473 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.63155 | 0.0639455 | ||||||||
\(652\) | 20.6776 | 0.809796 | ||||||||
\(653\) | −22.3518 | −0.874692 | −0.437346 | − | 0.899293i | \(-0.644082\pi\) | ||||
−0.437346 | + | 0.899293i | \(0.644082\pi\) | |||||||
\(654\) | −32.7595 | −1.28100 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.17413 | 0.0848855 | ||||||||
\(657\) | 12.0772 | 0.471176 | ||||||||
\(658\) | −2.03565 | −0.0793577 | ||||||||
\(659\) | 42.1979 | 1.64380 | 0.821898 | − | 0.569634i | \(-0.192915\pi\) | ||||
0.821898 | + | 0.569634i | \(0.192915\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.38035 | 0.325958 | 0.162979 | − | 0.986630i | \(-0.447890\pi\) | ||||
0.162979 | + | 0.986630i | \(0.447890\pi\) | |||||||
\(662\) | 7.32559 | 0.284717 | ||||||||
\(663\) | −53.9003 | −2.09332 | ||||||||
\(664\) | −6.70843 | −0.260337 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.69836 | −0.375804 | ||||||||
\(667\) | 2.06402 | 0.0799191 | ||||||||
\(668\) | 33.4746 | 1.29517 | ||||||||
\(669\) | 9.46925 | 0.366102 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −37.1428 | −1.43388 | ||||||||
\(672\) | 0.979541 | 0.0377866 | ||||||||
\(673\) | 3.13725 | 0.120932 | 0.0604660 | − | 0.998170i | \(-0.480741\pi\) | ||||
0.0604660 | + | 0.998170i | \(0.480741\pi\) | |||||||
\(674\) | 65.2941 | 2.51504 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 115.512 | 4.44279 | ||||||||
\(677\) | −16.2776 | −0.625600 | −0.312800 | − | 0.949819i | \(-0.601267\pi\) | ||||
−0.312800 | + | 0.949819i | \(0.601267\pi\) | |||||||
\(678\) | 9.26310 | 0.355747 | ||||||||
\(679\) | −0.620929 | −0.0238291 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.4030 | 0.858486 | ||||||||
\(682\) | 75.1658 | 2.87825 | ||||||||
\(683\) | 1.78249 | 0.0682050 | 0.0341025 | − | 0.999418i | \(-0.489143\pi\) | ||||
0.0341025 | + | 0.999418i | \(0.489143\pi\) | |||||||
\(684\) | −12.5258 | −0.478935 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.06512 | −0.193387 | ||||||||
\(687\) | −2.03117 | −0.0774939 | ||||||||
\(688\) | −1.67275 | −0.0637728 | ||||||||
\(689\) | 85.2614 | 3.24820 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.8504 | −0.793187 | −0.396594 | − | 0.917994i | \(-0.629808\pi\) | ||||
−0.396594 | + | 0.917994i | \(0.629808\pi\) | |||||||
\(692\) | 43.5699 | 1.65628 | ||||||||
\(693\) | 0.519521 | 0.0197350 | ||||||||
\(694\) | −37.2177 | −1.41276 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.58223 | −0.0978791 | ||||||||
\(697\) | 39.1322 | 1.48224 | ||||||||
\(698\) | 41.2828 | 1.56258 | ||||||||
\(699\) | 11.0704 | 0.418722 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.5504 | 1.22941 | 0.614707 | − | 0.788756i | \(-0.289274\pi\) | ||||
0.614707 | + | 0.788756i | \(0.289274\pi\) | |||||||
\(702\) | −15.9974 | −0.603783 | ||||||||
\(703\) | −17.0710 | −0.643845 | ||||||||
\(704\) | 42.3698 | 1.59687 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −42.7978 | −1.61072 | ||||||||
\(707\) | −2.46297 | −0.0926295 | ||||||||
\(708\) | 22.1864 | 0.833815 | ||||||||
\(709\) | 5.93195 | 0.222779 | 0.111390 | − | 0.993777i | \(-0.464470\pi\) | ||||
0.111390 | + | 0.993777i | \(0.464470\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.7441 | −0.477942 | ||||||||
\(712\) | −11.1853 | −0.419187 | ||||||||
\(713\) | −21.0621 | −0.788781 | ||||||||
\(714\) | 2.76847 | 0.103607 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −34.8767 | −1.30340 | ||||||||
\(717\) | 2.24098 | 0.0836911 | ||||||||
\(718\) | −32.7574 | −1.22250 | ||||||||
\(719\) | −13.5279 | −0.504505 | −0.252252 | − | 0.967661i | \(-0.581171\pi\) | ||||
−0.252252 | + | 0.967661i | \(0.581171\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.22871 | 0.0457594 | ||||||||
\(722\) | 6.97701 | 0.259657 | ||||||||
\(723\) | −14.4838 | −0.538660 | ||||||||
\(724\) | 34.3581 | 1.27691 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.00208 | −0.0371907 | ||||||||
\(727\) | 12.7407 | 0.472525 | 0.236263 | − | 0.971689i | \(-0.424077\pi\) | ||||
0.236263 | + | 0.971689i | \(0.424077\pi\) | |||||||
\(728\) | −2.91350 | −0.107981 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.1078 | −1.11358 | ||||||||
\(732\) | −35.8828 | −1.32627 | ||||||||
\(733\) | −30.9422 | −1.14288 | −0.571438 | − | 0.820645i | \(-0.693614\pi\) | ||||
−0.571438 | + | 0.820645i | \(0.693614\pi\) | |||||||
\(734\) | −47.8716 | −1.76697 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.6451 | −0.466105 | ||||||||
\(737\) | −48.5809 | −1.78950 | ||||||||
\(738\) | 11.6143 | 0.427528 | ||||||||
\(739\) | 35.0047 | 1.28767 | 0.643834 | − | 0.765166i | \(-0.277343\pi\) | ||||
0.643834 | + | 0.765166i | \(0.277343\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −28.1585 | −1.03443 | ||||||||
\(742\) | −4.37926 | −0.160768 | ||||||||
\(743\) | 12.5515 | 0.460468 | 0.230234 | − | 0.973135i | \(-0.426051\pi\) | ||||
0.230234 | + | 0.973135i | \(0.426051\pi\) | |||||||
\(744\) | 26.3501 | 0.966041 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −38.8068 | −1.42082 | ||||||||
\(747\) | 2.59792 | 0.0950530 | ||||||||
\(748\) | 77.9069 | 2.84856 | ||||||||
\(749\) | −0.736956 | −0.0269278 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.8278 | −1.23439 | −0.617197 | − | 0.786809i | \(-0.711732\pi\) | ||||
−0.617197 | + | 0.786809i | \(0.711732\pi\) | |||||||
\(752\) | 2.38332 | 0.0869108 | ||||||||
\(753\) | 16.2044 | 0.590522 | ||||||||
\(754\) | −15.9974 | −0.582591 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.501897 | 0.0182538 | ||||||||
\(757\) | 6.60568 | 0.240088 | 0.120044 | − | 0.992769i | \(-0.461697\pi\) | ||||
0.120044 | + | 0.992769i | \(0.461697\pi\) | |||||||
\(758\) | 0.468553 | 0.0170186 | ||||||||
\(759\) | −6.70661 | −0.243435 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.8638 | −0.828814 | −0.414407 | − | 0.910092i | \(-0.636011\pi\) | ||||
−0.414407 | + | 0.910092i | \(0.636011\pi\) | |||||||
\(762\) | 8.37978 | 0.303568 | ||||||||
\(763\) | 2.31051 | 0.0836461 | ||||||||
\(764\) | 56.9656 | 2.06094 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 37.1103 | 1.34085 | ||||||||
\(767\) | 49.8760 | 1.80092 | ||||||||
\(768\) | 13.1557 | 0.474716 | ||||||||
\(769\) | −35.0078 | −1.26241 | −0.631206 | − | 0.775615i | \(-0.717440\pi\) | ||||
−0.631206 | + | 0.775615i | \(0.717440\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.36942 | −0.121347 | ||||||||
\(772\) | 54.4016 | 1.95796 | ||||||||
\(773\) | −17.7019 | −0.636691 | −0.318346 | − | 0.947975i | \(-0.603127\pi\) | ||||
−0.318346 | + | 0.947975i | \(0.603127\pi\) | |||||||
\(774\) | −8.93586 | −0.321193 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −10.0282 | −0.359992 | ||||||||
\(777\) | 0.684020 | 0.0245391 | ||||||||
\(778\) | −26.6655 | −0.956005 | ||||||||
\(779\) | 20.4434 | 0.732460 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.1564 | −0.399206 | ||||||||
\(782\) | −35.7388 | −1.27802 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 2.95968 | 0.105703 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −22.5066 | −0.802782 | ||||||||
\(787\) | −5.13176 | −0.182928 | −0.0914638 | − | 0.995808i | \(-0.529155\pi\) | ||||
−0.0914638 | + | 0.995808i | \(0.529155\pi\) | |||||||
\(788\) | 32.7321 | 1.16603 | ||||||||
\(789\) | 1.79671 | 0.0639647 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.653321 | −0.0232294 | ||||||||
\(792\) | 8.39044 | 0.298141 | ||||||||
\(793\) | −80.6662 | −2.86454 | ||||||||
\(794\) | −11.2471 | −0.399145 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 36.2783 | 1.28585 | ||||||||
\(797\) | −27.5492 | −0.975842 | −0.487921 | − | 0.872888i | \(-0.662245\pi\) | ||||
−0.487921 | + | 0.872888i | \(0.662245\pi\) | |||||||
\(798\) | 1.44630 | 0.0511984 | ||||||||
\(799\) | 42.8974 | 1.51760 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.33165 | 0.153051 | ||||||||
\(802\) | −82.0562 | −2.89751 | ||||||||
\(803\) | −39.2424 | −1.38484 | ||||||||
\(804\) | −46.9329 | −1.65520 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 163.244 | 5.75002 | ||||||||
\(807\) | 0.117055 | 0.00412054 | ||||||||
\(808\) | −39.7778 | −1.39938 | ||||||||
\(809\) | −5.51555 | −0.193917 | −0.0969583 | − | 0.995288i | \(-0.530911\pi\) | ||||
−0.0969583 | + | 0.995288i | \(0.530911\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.1711 | −0.602959 | −0.301479 | − | 0.953473i | \(-0.597480\pi\) | ||||
−0.301479 | + | 0.953473i | \(0.597480\pi\) | |||||||
\(812\) | 0.501897 | 0.0176131 | ||||||||
\(813\) | 4.06294 | 0.142493 | ||||||||
\(814\) | 31.5129 | 1.10453 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.24131 | −0.113468 | ||||||||
\(817\) | −15.7288 | −0.550283 | ||||||||
\(818\) | 36.6355 | 1.28093 | ||||||||
\(819\) | 1.12829 | 0.0394256 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.53740 | 0.228157 | 0.114078 | − | 0.993472i | \(-0.463609\pi\) | ||||
0.114078 | + | 0.993472i | \(0.463609\pi\) | |||||||
\(822\) | −8.67813 | −0.302684 | ||||||||
\(823\) | 35.8588 | 1.24996 | 0.624979 | − | 0.780641i | \(-0.285107\pi\) | ||||
0.624979 | + | 0.780641i | \(0.285107\pi\) | |||||||
\(824\) | 19.8440 | 0.691299 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.56177 | −0.0891354 | ||||||||
\(827\) | 2.36177 | 0.0821269 | 0.0410635 | − | 0.999157i | \(-0.486925\pi\) | ||||
0.0410635 | + | 0.999157i | \(0.486925\pi\) | |||||||
\(828\) | −6.47910 | −0.225164 | ||||||||
\(829\) | 54.0332 | 1.87665 | 0.938325 | − | 0.345754i | \(-0.112377\pi\) | ||||
0.938325 | + | 0.345754i | \(0.112377\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.5436 | −0.435134 | ||||||||
\(832\) | 92.0182 | 3.19016 | ||||||||
\(833\) | 53.2713 | 1.84574 | ||||||||
\(834\) | −4.69231 | −0.162481 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 40.7000 | 1.40764 | ||||||||
\(837\) | −10.2044 | −0.352716 | ||||||||
\(838\) | 76.0663 | 2.62767 | ||||||||
\(839\) | 27.6639 | 0.955063 | 0.477532 | − | 0.878615i | \(-0.341532\pi\) | ||||
0.477532 | + | 0.878615i | \(0.341532\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −61.1730 | −2.10816 | ||||||||
\(843\) | 2.83163 | 0.0975266 | ||||||||
\(844\) | −66.4278 | −2.28654 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12.7318 | 0.437728 | ||||||||
\(847\) | 0.0706761 | 0.00242846 | ||||||||
\(848\) | 5.12721 | 0.176069 | ||||||||
\(849\) | 28.2249 | 0.968676 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.83017 | −0.302694 | ||||||||
\(852\) | −10.7779 | −0.369245 | ||||||||
\(853\) | −16.7180 | −0.572413 | −0.286207 | − | 0.958168i | \(-0.592394\pi\) | ||||
−0.286207 | + | 0.958168i | \(0.592394\pi\) | |||||||
\(854\) | 4.14324 | 0.141779 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.9021 | −0.406805 | ||||||||
\(857\) | 50.6304 | 1.72950 | 0.864750 | − | 0.502202i | \(-0.167477\pi\) | ||||
0.864750 | + | 0.502202i | \(0.167477\pi\) | |||||||
\(858\) | 51.9804 | 1.77458 | ||||||||
\(859\) | −23.0473 | −0.786363 | −0.393182 | − | 0.919461i | \(-0.628626\pi\) | ||||
−0.393182 | + | 0.919461i | \(0.628626\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.819148 | −0.0279165 | ||||||||
\(862\) | −1.88693 | −0.0642692 | ||||||||
\(863\) | −45.4971 | −1.54874 | −0.774370 | − | 0.632733i | \(-0.781933\pi\) | ||||
−0.774370 | + | 0.632733i | \(0.781933\pi\) | |||||||
\(864\) | −6.12646 | −0.208426 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −51.1531 | −1.73825 | ||||||||
\(867\) | −41.3403 | −1.40399 | ||||||||
\(868\) | −5.12156 | −0.173837 | ||||||||
\(869\) | 41.4095 | 1.40472 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −105.507 | −3.57498 | ||||||||
\(872\) | 37.3155 | 1.26366 | ||||||||
\(873\) | 3.88355 | 0.131438 | ||||||||
\(874\) | −18.6706 | −0.631543 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −37.9112 | −1.28090 | ||||||||
\(877\) | −6.44199 | −0.217531 | −0.108765 | − | 0.994067i | \(-0.534690\pi\) | ||||
−0.108765 | + | 0.994067i | \(0.534690\pi\) | |||||||
\(878\) | −54.3124 | −1.83295 | ||||||||
\(879\) | 21.9337 | 0.739806 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.3346 | −1.45998 | −0.729990 | − | 0.683458i | \(-0.760475\pi\) | ||||
−0.729990 | + | 0.683458i | \(0.760475\pi\) | |||||||
\(882\) | 15.8107 | 0.532375 | ||||||||
\(883\) | 24.6736 | 0.830333 | 0.415166 | − | 0.909745i | \(-0.363723\pi\) | ||||
0.415166 | + | 0.909745i | \(0.363723\pi\) | |||||||
\(884\) | 169.197 | 5.69072 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 39.6546 | 1.33222 | ||||||||
\(887\) | −37.1527 | −1.24747 | −0.623733 | − | 0.781637i | \(-0.714385\pi\) | ||||
−0.623733 | + | 0.781637i | \(0.714385\pi\) | |||||||
\(888\) | 11.0472 | 0.370718 | ||||||||
\(889\) | −0.591021 | −0.0198222 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.24930 | −0.108856 | ||||||||
\(892\) | −29.7247 | −0.995255 | ||||||||
\(893\) | 22.4104 | 0.749936 | ||||||||
\(894\) | −3.32357 | −0.111157 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.76723 | −0.0924466 | ||||||||
\(897\) | −14.5653 | −0.486322 | ||||||||
\(898\) | −9.57108 | −0.319391 | ||||||||
\(899\) | −10.2044 | −0.340336 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 92.2847 | 3.07445 | ||||||||
\(902\) | −37.7383 | −1.25655 | ||||||||
\(903\) | 0.630241 | 0.0209731 | ||||||||
\(904\) | −10.5514 | −0.350933 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −45.6291 | −1.51593 | ||||||||
\(907\) | −7.49457 | −0.248853 | −0.124427 | − | 0.992229i | \(-0.539709\pi\) | ||||
−0.124427 | + | 0.992229i | \(0.539709\pi\) | |||||||
\(908\) | −70.3248 | −2.33381 | ||||||||
\(909\) | 15.4045 | 0.510934 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.6818 | 1.61290 | 0.806449 | − | 0.591303i | \(-0.201386\pi\) | ||||
0.806449 | + | 0.591303i | \(0.201386\pi\) | |||||||
\(912\) | −1.69332 | −0.0560714 | ||||||||
\(913\) | −8.44143 | −0.279371 | ||||||||
\(914\) | −2.91444 | −0.0964012 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.37598 | 0.210668 | ||||||||
\(917\) | 1.58737 | 0.0524197 | ||||||||
\(918\) | −17.3152 | −0.571486 | ||||||||
\(919\) | −26.1563 | −0.862816 | −0.431408 | − | 0.902157i | \(-0.641983\pi\) | ||||
−0.431408 | + | 0.902157i | \(0.641983\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.461574 | −0.0152094 | ||||||||
\(922\) | 54.0746 | 1.78085 | ||||||||
\(923\) | −24.2293 | −0.797515 | ||||||||
\(924\) | −1.63081 | −0.0536498 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 32.0552 | 1.05340 | ||||||||
\(927\) | −7.68484 | −0.252403 | ||||||||
\(928\) | −6.12646 | −0.201111 | ||||||||
\(929\) | −8.15366 | −0.267513 | −0.133756 | − | 0.991014i | \(-0.542704\pi\) | ||||
−0.133756 | + | 0.991014i | \(0.542704\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.8299 | 0.912089 | ||||||||
\(932\) | −34.7509 | −1.13830 | ||||||||
\(933\) | −27.5507 | −0.901968 | ||||||||
\(934\) | 16.0157 | 0.524051 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 18.2222 | 0.595612 | ||||||||
\(937\) | −41.9169 | −1.36936 | −0.684682 | − | 0.728842i | \(-0.740059\pi\) | ||||
−0.684682 | + | 0.728842i | \(0.740059\pi\) | |||||||
\(938\) | 5.41915 | 0.176941 | ||||||||
\(939\) | 14.9121 | 0.486638 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.4789 | 0.471998 | 0.235999 | − | 0.971753i | \(-0.424164\pi\) | ||||
0.235999 | + | 0.971753i | \(0.424164\pi\) | |||||||
\(942\) | −16.0751 | −0.523755 | ||||||||
\(943\) | 10.5746 | 0.344356 | ||||||||
\(944\) | 2.99931 | 0.0976191 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 29.0353 | 0.944020 | ||||||||
\(947\) | −1.83838 | −0.0597392 | −0.0298696 | − | 0.999554i | \(-0.509509\pi\) | ||||
−0.0298696 | + | 0.999554i | \(0.509509\pi\) | |||||||
\(948\) | 40.0048 | 1.29929 | ||||||||
\(949\) | −85.2262 | −2.76656 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.9266 | −0.743446 | ||||||||
\(952\) | −3.15349 | −0.102205 | ||||||||
\(953\) | 49.5140 | 1.60391 | 0.801957 | − | 0.597382i | \(-0.203792\pi\) | ||||
0.801957 | + | 0.597382i | \(0.203792\pi\) | |||||||
\(954\) | 27.3897 | 0.886776 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.03461 | −0.227516 | ||||||||
\(957\) | −3.24930 | −0.105035 | ||||||||
\(958\) | −52.0403 | −1.68135 | ||||||||
\(959\) | 0.612063 | 0.0197646 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.1299 | 2.35903 | ||||||||
\(962\) | 68.4393 | 2.20657 | ||||||||
\(963\) | 4.60924 | 0.148531 | ||||||||
\(964\) | 45.4658 | 1.46436 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.748115 | 0.0240702 | ||||||||
\(967\) | −5.90299 | −0.189827 | −0.0949137 | − | 0.995486i | \(-0.530258\pi\) | ||||
−0.0949137 | + | 0.995486i | \(0.530258\pi\) | |||||||
\(968\) | 1.14144 | 0.0366874 | ||||||||
\(969\) | −30.4781 | −0.979096 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.7964 | −1.14876 | −0.574380 | − | 0.818588i | \(-0.694757\pi\) | ||||
−0.574380 | + | 0.818588i | \(0.694757\pi\) | |||||||
\(972\) | −3.13907 | −0.100686 | ||||||||
\(973\) | 0.330946 | 0.0106096 | ||||||||
\(974\) | −61.2801 | −1.96354 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.85088 | −0.155273 | ||||||||
\(977\) | 1.79673 | 0.0574825 | 0.0287412 | − | 0.999587i | \(-0.490850\pi\) | ||||
0.0287412 | + | 0.999587i | \(0.490850\pi\) | |||||||
\(978\) | 14.9328 | 0.477497 | ||||||||
\(979\) | −14.0748 | −0.449834 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.4509 | −0.461382 | ||||||||
\(982\) | 26.1828 | 0.835528 | ||||||||
\(983\) | −6.24151 | −0.199073 | −0.0995365 | − | 0.995034i | \(-0.531736\pi\) | ||||
−0.0995365 | + | 0.995034i | \(0.531736\pi\) | |||||||
\(984\) | −13.2295 | −0.421742 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −17.3152 | −0.551427 | ||||||||
\(987\) | −0.897966 | −0.0285826 | ||||||||
\(988\) | 88.3917 | 2.81211 | ||||||||
\(989\) | −8.13593 | −0.258708 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.0410 | 1.30371 | 0.651855 | − | 0.758344i | \(-0.273991\pi\) | ||||
0.651855 | + | 0.758344i | \(0.273991\pi\) | |||||||
\(992\) | 62.5169 | 1.98491 | ||||||||
\(993\) | 3.23147 | 0.102548 | ||||||||
\(994\) | 1.24448 | 0.0394725 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.15507 | −0.258403 | ||||||||
\(997\) | −29.8910 | −0.946657 | −0.473329 | − | 0.880886i | \(-0.656948\pi\) | ||||
−0.473329 | + | 0.880886i | \(0.656948\pi\) | |||||||
\(998\) | −8.56776 | −0.271208 | ||||||||
\(999\) | −4.27815 | −0.135355 |
(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 | 2175.2.a.ba.1.2 | ✓ | 7 | |
3.2 | odd | 2 | 6525.2.a.bx.1.6 | 7 | |||
5.2 | odd | 4 | 2175.2.c.o.349.3 | 14 | |||
5.3 | odd | 4 | 2175.2.c.o.349.12 | 14 | |||
5.4 | even | 2 | 2175.2.a.bb.1.6 | yes | 7 | ||
15.14 | odd | 2 | 6525.2.a.bu.1.2 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2175.2.a.ba.1.2 | ✓ | 7 | 1.1 | even | 1 | trivial | |
2175.2.a.bb.1.6 | yes | 7 | 5.4 | even | 2 | ||
2175.2.c.o.349.3 | 14 | 5.2 | odd | 4 | |||
2175.2.c.o.349.12 | 14 | 5.3 | odd | 4 | |||
6525.2.a.bu.1.2 | 7 | 15.14 | odd | 2 | |||
6525.2.a.bx.1.6 | 7 | 3.2 | odd | 2 |