Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 11 x^{16} + 123 x^{15} - 35 x^{14} - 982 x^{13} + 988 x^{12} + 3872 x^{11} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 5 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(2.59597\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.59597 | 1.83563 | 0.917813 | − | 0.397013i | \(-0.129953\pi\) | ||||
0.917813 | + | 0.397013i | \(0.129953\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.73905 | 2.36952 | ||||||||
\(5\) | 1.63234 | 0.730005 | 0.365002 | − | 0.931007i | \(-0.381068\pi\) | ||||
0.365002 | + | 0.931007i | \(0.381068\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 7.11048 | 2.51393 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.23750 | 1.34002 | ||||||||
\(11\) | −4.79599 | −1.44604 | −0.723022 | − | 0.690825i | \(-0.757248\pi\) | ||||
−0.723022 | + | 0.690825i | \(0.757248\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.263712 | 0.0731405 | 0.0365702 | − | 0.999331i | \(-0.488357\pi\) | ||||
0.0365702 | + | 0.999331i | \(0.488357\pi\) | |||||||
\(14\) | 2.59597 | 0.693802 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 8.98048 | 2.24512 | ||||||||
\(17\) | 5.12058 | 1.24192 | 0.620961 | − | 0.783841i | \(-0.286742\pi\) | ||||
0.620961 | + | 0.783841i | \(0.286742\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.93565 | 1.36173 | 0.680866 | − | 0.732408i | \(-0.261604\pi\) | ||||
0.680866 | + | 0.732408i | \(0.261604\pi\) | |||||||
\(20\) | 7.73574 | 1.72976 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −12.4502 | −2.65440 | ||||||||
\(23\) | 4.10470 | 0.855889 | 0.427944 | − | 0.903805i | \(-0.359238\pi\) | ||||
0.427944 | + | 0.903805i | \(0.359238\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.33547 | −0.467093 | ||||||||
\(26\) | 0.684587 | 0.134259 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.73905 | 0.895596 | ||||||||
\(29\) | −0.459771 | −0.0853773 | −0.0426886 | − | 0.999088i | \(-0.513592\pi\) | ||||
−0.0426886 | + | 0.999088i | \(0.513592\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.24495 | −1.66044 | −0.830221 | − | 0.557434i | \(-0.811786\pi\) | ||||
−0.830221 | + | 0.557434i | \(0.811786\pi\) | |||||||
\(32\) | 9.09207 | 1.60727 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 13.2929 | 2.27971 | ||||||||
\(35\) | 1.63234 | 0.275916 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.64452 | 1.09235 | 0.546176 | − | 0.837670i | \(-0.316083\pi\) | ||||
0.546176 | + | 0.837670i | \(0.316083\pi\) | |||||||
\(38\) | 15.4088 | 2.49963 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 11.6067 | 1.83518 | ||||||||
\(41\) | 3.43282 | 0.536116 | 0.268058 | − | 0.963403i | \(-0.413618\pi\) | ||||
0.268058 | + | 0.963403i | \(0.413618\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.33770 | 0.356497 | 0.178248 | − | 0.983986i | \(-0.442957\pi\) | ||||
0.178248 | + | 0.983986i | \(0.442957\pi\) | |||||||
\(44\) | −22.7284 | −3.42644 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.6557 | 1.57109 | ||||||||
\(47\) | 5.69134 | 0.830167 | 0.415083 | − | 0.909783i | \(-0.363752\pi\) | ||||
0.415083 | + | 0.909783i | \(0.363752\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −6.06280 | −0.857409 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.24974 | 0.173308 | ||||||||
\(53\) | −2.55281 | −0.350656 | −0.175328 | − | 0.984510i | \(-0.556099\pi\) | ||||
−0.175328 | + | 0.984510i | \(0.556099\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.82868 | −1.05562 | ||||||||
\(56\) | 7.11048 | 0.950178 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.19355 | −0.156721 | ||||||||
\(59\) | 13.3394 | 1.73664 | 0.868320 | − | 0.496005i | \(-0.165200\pi\) | ||||
0.868320 | + | 0.496005i | \(0.165200\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9442 | 1.40126 | 0.700631 | − | 0.713524i | \(-0.252902\pi\) | ||||
0.700631 | + | 0.713524i | \(0.252902\pi\) | |||||||
\(62\) | −23.9996 | −3.04795 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.64176 | 0.705220 | ||||||||
\(65\) | 0.430467 | 0.0533929 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.34491 | 0.164307 | 0.0821535 | − | 0.996620i | \(-0.473820\pi\) | ||||
0.0821535 | + | 0.996620i | \(0.473820\pi\) | |||||||
\(68\) | 24.2667 | 2.94276 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.23750 | 0.506478 | ||||||||
\(71\) | −5.05046 | −0.599379 | −0.299690 | − | 0.954037i | \(-0.596883\pi\) | ||||
−0.299690 | + | 0.954037i | \(0.596883\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.4455 | −1.92480 | −0.962401 | − | 0.271634i | \(-0.912436\pi\) | ||||
−0.962401 | + | 0.271634i | \(0.912436\pi\) | |||||||
\(74\) | 17.2490 | 2.00515 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 28.1293 | 3.22666 | ||||||||
\(77\) | −4.79599 | −0.546554 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.111124 | −0.0125025 | −0.00625124 | − | 0.999980i | \(-0.501990\pi\) | ||||
−0.00625124 | + | 0.999980i | \(0.501990\pi\) | |||||||
\(80\) | 14.6592 | 1.63895 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.91149 | 0.984109 | ||||||||
\(83\) | −6.65678 | −0.730676 | −0.365338 | − | 0.930875i | \(-0.619047\pi\) | ||||
−0.365338 | + | 0.930875i | \(0.619047\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.35852 | 0.906609 | ||||||||
\(86\) | 6.06861 | 0.654395 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −34.1018 | −3.63526 | ||||||||
\(89\) | −11.2897 | −1.19671 | −0.598353 | − | 0.801233i | \(-0.704178\pi\) | ||||
−0.598353 | + | 0.801233i | \(0.704178\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.263712 | 0.0276445 | ||||||||
\(92\) | 19.4524 | 2.02805 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 14.7745 | 1.52388 | ||||||||
\(95\) | 9.68900 | 0.994070 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.51451 | −0.559913 | −0.279957 | − | 0.960013i | \(-0.590320\pi\) | ||||
−0.279957 | + | 0.960013i | \(0.590320\pi\) | |||||||
\(98\) | 2.59597 | 0.262232 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −11.0679 | −1.10679 | ||||||||
\(101\) | −0.809406 | −0.0805389 | −0.0402694 | − | 0.999189i | \(-0.512822\pi\) | ||||
−0.0402694 | + | 0.999189i | \(0.512822\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.13235 | −0.505705 | −0.252853 | − | 0.967505i | \(-0.581369\pi\) | ||||
−0.252853 | + | 0.967505i | \(0.581369\pi\) | |||||||
\(104\) | 1.87512 | 0.183870 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.62702 | −0.643673 | ||||||||
\(107\) | 17.1879 | 1.66161 | 0.830807 | − | 0.556560i | \(-0.187879\pi\) | ||||
0.830807 | + | 0.556560i | \(0.187879\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.44424 | 0.808812 | 0.404406 | − | 0.914580i | \(-0.367478\pi\) | ||||
0.404406 | + | 0.914580i | \(0.367478\pi\) | |||||||
\(110\) | −20.3230 | −1.93772 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.98048 | 0.848575 | ||||||||
\(113\) | 2.27777 | 0.214275 | 0.107137 | − | 0.994244i | \(-0.465832\pi\) | ||||
0.107137 | + | 0.994244i | \(0.465832\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.70026 | 0.624803 | ||||||||
\(116\) | −2.17888 | −0.202303 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 34.6286 | 3.18782 | ||||||||
\(119\) | 5.12058 | 0.469403 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.0015 | 1.09105 | ||||||||
\(122\) | 28.4108 | 2.57219 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −43.8123 | −3.93446 | ||||||||
\(125\) | −11.9740 | −1.07098 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | −3.53831 | −0.312745 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.11748 | 0.0980094 | ||||||||
\(131\) | −7.70860 | −0.673503 | −0.336752 | − | 0.941593i | \(-0.609328\pi\) | ||||
−0.336752 | + | 0.941593i | \(0.609328\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.93565 | 0.514686 | ||||||||
\(134\) | 3.49134 | 0.301606 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 36.4098 | 3.12211 | ||||||||
\(137\) | 2.92001 | 0.249473 | 0.124737 | − | 0.992190i | \(-0.460191\pi\) | ||||
0.124737 | + | 0.992190i | \(0.460191\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.52119 | 0.129026 | 0.0645130 | − | 0.997917i | \(-0.479451\pi\) | ||||
0.0645130 | + | 0.997917i | \(0.479451\pi\) | |||||||
\(140\) | 7.73574 | 0.653789 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.1108 | −1.10024 | ||||||||
\(143\) | −1.26476 | −0.105764 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.750502 | −0.0623258 | ||||||||
\(146\) | −42.6920 | −3.53322 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 31.4887 | 2.58835 | ||||||||
\(149\) | −12.0258 | −0.985195 | −0.492598 | − | 0.870257i | \(-0.663953\pi\) | ||||
−0.492598 | + | 0.870257i | \(0.663953\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.51556 | 0.367471 | 0.183736 | − | 0.982976i | \(-0.441181\pi\) | ||||
0.183736 | + | 0.982976i | \(0.441181\pi\) | |||||||
\(152\) | 42.2053 | 3.42330 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −12.4502 | −1.00327 | ||||||||
\(155\) | −15.0909 | −1.21213 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.59506 | 0.207109 | 0.103554 | − | 0.994624i | \(-0.466978\pi\) | ||||
0.103554 | + | 0.994624i | \(0.466978\pi\) | |||||||
\(158\) | −0.288475 | −0.0229499 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 14.8413 | 1.17331 | ||||||||
\(161\) | 4.10470 | 0.323495 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.3837 | 1.59658 | 0.798288 | − | 0.602275i | \(-0.205739\pi\) | ||||
0.798288 | + | 0.602275i | \(0.205739\pi\) | |||||||
\(164\) | 16.2683 | 1.27034 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.2808 | −1.34125 | ||||||||
\(167\) | −7.15571 | −0.553726 | −0.276863 | − | 0.960909i | \(-0.589295\pi\) | ||||
−0.276863 | + | 0.960909i | \(0.589295\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9305 | −0.994650 | ||||||||
\(170\) | 21.6985 | 1.66420 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.0785 | 0.844727 | ||||||||
\(173\) | 9.08892 | 0.691018 | 0.345509 | − | 0.938415i | \(-0.387706\pi\) | ||||
0.345509 | + | 0.938415i | \(0.387706\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.33547 | −0.176545 | ||||||||
\(176\) | −43.0703 | −3.24654 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −29.3077 | −2.19670 | ||||||||
\(179\) | 19.6649 | 1.46982 | 0.734912 | − | 0.678162i | \(-0.237223\pi\) | ||||
0.734912 | + | 0.678162i | \(0.237223\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.64241 | 0.419397 | 0.209699 | − | 0.977766i | \(-0.432752\pi\) | ||||
0.209699 | + | 0.977766i | \(0.432752\pi\) | |||||||
\(182\) | 0.684587 | 0.0507450 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 29.1864 | 2.15165 | ||||||||
\(185\) | 10.8461 | 0.797422 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −24.5582 | −1.79588 | ||||||||
\(188\) | 26.9715 | 1.96710 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 25.1523 | 1.82474 | ||||||||
\(191\) | 14.5073 | 1.04971 | 0.524855 | − | 0.851192i | \(-0.324119\pi\) | ||||
0.524855 | + | 0.851192i | \(0.324119\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.6112 | −0.979753 | −0.489877 | − | 0.871792i | \(-0.662958\pi\) | ||||
−0.489877 | + | 0.871792i | \(0.662958\pi\) | |||||||
\(194\) | −14.3155 | −1.02779 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.73905 | 0.338503 | ||||||||
\(197\) | −6.88652 | −0.490644 | −0.245322 | − | 0.969442i | \(-0.578894\pi\) | ||||
−0.245322 | + | 0.969442i | \(0.578894\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.0663 | −1.77690 | −0.888451 | − | 0.458972i | \(-0.848218\pi\) | ||||
−0.888451 | + | 0.458972i | \(0.848218\pi\) | |||||||
\(200\) | −16.6063 | −1.17424 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.10119 | −0.147839 | ||||||||
\(203\) | −0.459771 | −0.0322696 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.60353 | 0.391367 | ||||||||
\(206\) | −13.3234 | −0.928286 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.36826 | 0.164209 | ||||||||
\(209\) | −28.4673 | −1.96913 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.2975 | −1.53502 | −0.767512 | − | 0.641035i | \(-0.778505\pi\) | ||||
−0.767512 | + | 0.641035i | \(0.778505\pi\) | |||||||
\(212\) | −12.0979 | −0.830887 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 44.6192 | 3.05010 | ||||||||
\(215\) | 3.81593 | 0.260244 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.24495 | −0.627588 | ||||||||
\(218\) | 21.9210 | 1.48468 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −37.1005 | −2.50131 | ||||||||
\(221\) | 1.35036 | 0.0908348 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.15329 | −0.612950 | −0.306475 | − | 0.951879i | \(-0.599150\pi\) | ||||
−0.306475 | + | 0.951879i | \(0.599150\pi\) | |||||||
\(224\) | 9.09207 | 0.607489 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.91303 | 0.393329 | ||||||||
\(227\) | −18.4647 | −1.22554 | −0.612771 | − | 0.790260i | \(-0.709945\pi\) | ||||
−0.612771 | + | 0.790260i | \(0.709945\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.5708 | −1.42544 | −0.712721 | − | 0.701448i | \(-0.752537\pi\) | ||||
−0.712721 | + | 0.701448i | \(0.752537\pi\) | |||||||
\(230\) | 17.3937 | 1.14690 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.26919 | −0.214633 | ||||||||
\(233\) | 8.86474 | 0.580749 | 0.290374 | − | 0.956913i | \(-0.406220\pi\) | ||||
0.290374 | + | 0.956913i | \(0.406220\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.29020 | 0.606026 | ||||||||
\(236\) | 63.2160 | 4.11501 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 13.2929 | 0.861648 | ||||||||
\(239\) | −20.1987 | −1.30654 | −0.653272 | − | 0.757124i | \(-0.726604\pi\) | ||||
−0.653272 | + | 0.757124i | \(0.726604\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.276725 | 0.0178254 | 0.00891272 | − | 0.999960i | \(-0.497163\pi\) | ||||
0.00891272 | + | 0.999960i | \(0.497163\pi\) | |||||||
\(242\) | 31.1555 | 2.00275 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 51.8651 | 3.32032 | ||||||||
\(245\) | 1.63234 | 0.104286 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.56530 | 0.0995977 | ||||||||
\(248\) | −65.7360 | −4.17424 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −31.0840 | −1.96593 | ||||||||
\(251\) | 23.2801 | 1.46942 | 0.734712 | − | 0.678379i | \(-0.237317\pi\) | ||||
0.734712 | + | 0.678379i | \(0.237317\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.6861 | −1.23765 | ||||||||
\(254\) | 2.59597 | 0.162885 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −20.4689 | −1.27930 | ||||||||
\(257\) | −23.4788 | −1.46457 | −0.732285 | − | 0.680998i | \(-0.761546\pi\) | ||||
−0.732285 | + | 0.680998i | \(0.761546\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.64452 | 0.412870 | ||||||||
\(260\) | 2.04000 | 0.126516 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −20.0113 | −1.23630 | ||||||||
\(263\) | 2.69710 | 0.166310 | 0.0831551 | − | 0.996537i | \(-0.473500\pi\) | ||||
0.0831551 | + | 0.996537i | \(0.473500\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.16706 | −0.255980 | ||||||||
\(266\) | 15.4088 | 0.944772 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.37360 | 0.389329 | ||||||||
\(269\) | 4.37198 | 0.266565 | 0.133282 | − | 0.991078i | \(-0.457448\pi\) | ||||
0.133282 | + | 0.991078i | \(0.457448\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.85747 | −0.538053 | −0.269026 | − | 0.963133i | \(-0.586702\pi\) | ||||
−0.269026 | + | 0.963133i | \(0.586702\pi\) | |||||||
\(272\) | 45.9852 | 2.78826 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.58024 | 0.457939 | ||||||||
\(275\) | 11.2009 | 0.675438 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.4438 | −1.16826 | −0.584131 | − | 0.811659i | \(-0.698565\pi\) | ||||
−0.584131 | + | 0.811659i | \(0.698565\pi\) | |||||||
\(278\) | 3.94897 | 0.236843 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 11.6067 | 0.693634 | ||||||||
\(281\) | 0.140909 | 0.00840591 | 0.00420295 | − | 0.999991i | \(-0.498662\pi\) | ||||
0.00420295 | + | 0.999991i | \(0.498662\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.7659 | 1.35329 | 0.676645 | − | 0.736309i | \(-0.263433\pi\) | ||||
0.676645 | + | 0.736309i | \(0.263433\pi\) | |||||||
\(284\) | −23.9344 | −1.42024 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.28327 | −0.194144 | ||||||||
\(287\) | 3.43282 | 0.202633 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.22031 | 0.542371 | ||||||||
\(290\) | −1.94828 | −0.114407 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −77.9361 | −4.56086 | ||||||||
\(293\) | 29.5536 | 1.72654 | 0.863271 | − | 0.504741i | \(-0.168412\pi\) | ||||
0.863271 | + | 0.504741i | \(0.168412\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.7744 | 1.26775 | ||||||||
\(296\) | 47.2457 | 2.74610 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −31.2187 | −1.80845 | ||||||||
\(299\) | 1.08246 | 0.0626001 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.33770 | 0.134743 | ||||||||
\(302\) | 11.7223 | 0.674540 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 53.3050 | 3.05725 | ||||||||
\(305\) | 17.8647 | 1.02293 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.4005 | −0.993097 | −0.496549 | − | 0.868009i | \(-0.665400\pi\) | ||||
−0.496549 | + | 0.868009i | \(0.665400\pi\) | |||||||
\(308\) | −22.7284 | −1.29507 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −39.1755 | −2.22502 | ||||||||
\(311\) | 17.8934 | 1.01464 | 0.507322 | − | 0.861757i | \(-0.330635\pi\) | ||||
0.507322 | + | 0.861757i | \(0.330635\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.0691 | −0.738712 | −0.369356 | − | 0.929288i | \(-0.620422\pi\) | ||||
−0.369356 | + | 0.929288i | \(0.620422\pi\) | |||||||
\(314\) | 6.73670 | 0.380174 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.526624 | −0.0296249 | ||||||||
\(317\) | 24.7771 | 1.39162 | 0.695809 | − | 0.718226i | \(-0.255046\pi\) | ||||
0.695809 | + | 0.718226i | \(0.255046\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.20505 | 0.123459 | ||||||||
\(320\) | 9.20927 | 0.514814 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.6557 | 0.593817 | ||||||||
\(323\) | 30.3940 | 1.69117 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.615890 | −0.0341634 | ||||||||
\(326\) | 52.9155 | 2.93072 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 24.4090 | 1.34776 | ||||||||
\(329\) | 5.69134 | 0.313774 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.3948 | −0.791210 | −0.395605 | − | 0.918421i | \(-0.629465\pi\) | ||||
−0.395605 | + | 0.918421i | \(0.629465\pi\) | |||||||
\(332\) | −31.5468 | −1.73136 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −18.5760 | −1.01643 | ||||||||
\(335\) | 2.19535 | 0.119945 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.13837 | −0.443325 | −0.221663 | − | 0.975123i | \(-0.571148\pi\) | ||||
−0.221663 | + | 0.975123i | \(0.571148\pi\) | |||||||
\(338\) | −33.5670 | −1.82581 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 39.6114 | 2.14823 | ||||||||
\(341\) | 44.3387 | 2.40107 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 16.6222 | 0.896209 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 23.5946 | 1.26845 | ||||||||
\(347\) | 23.6307 | 1.26856 | 0.634280 | − | 0.773103i | \(-0.281297\pi\) | ||||
0.634280 | + | 0.773103i | \(0.281297\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.0018 | −1.44537 | −0.722686 | − | 0.691176i | \(-0.757093\pi\) | ||||
−0.722686 | + | 0.691176i | \(0.757093\pi\) | |||||||
\(350\) | −6.06280 | −0.324070 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −43.6055 | −2.32418 | ||||||||
\(353\) | −20.7847 | −1.10626 | −0.553130 | − | 0.833095i | \(-0.686567\pi\) | ||||
−0.553130 | + | 0.833095i | \(0.686567\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.24406 | −0.437549 | ||||||||
\(356\) | −53.5024 | −2.83562 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 51.0495 | 2.69805 | ||||||||
\(359\) | 7.34347 | 0.387574 | 0.193787 | − | 0.981044i | \(-0.437923\pi\) | ||||
0.193787 | + | 0.981044i | \(0.437923\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.2320 | 0.854314 | ||||||||
\(362\) | 14.6475 | 0.769856 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.24974 | 0.0655043 | ||||||||
\(365\) | −26.8447 | −1.40511 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.27104 | 0.170747 | 0.0853735 | − | 0.996349i | \(-0.472792\pi\) | ||||
0.0853735 | + | 0.996349i | \(0.472792\pi\) | |||||||
\(368\) | 36.8621 | 1.92157 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 28.1562 | 1.46377 | ||||||||
\(371\) | −2.55281 | −0.132535 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.7576 | −1.59257 | −0.796284 | − | 0.604923i | \(-0.793204\pi\) | ||||
−0.796284 | + | 0.604923i | \(0.793204\pi\) | |||||||
\(374\) | −63.7524 | −3.29656 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 40.4681 | 2.08698 | ||||||||
\(377\) | −0.121247 | −0.00624453 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.1652 | 0.830353 | 0.415176 | − | 0.909741i | \(-0.363720\pi\) | ||||
0.415176 | + | 0.909741i | \(0.363720\pi\) | |||||||
\(380\) | 45.9166 | 2.35547 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 37.6604 | 1.92688 | ||||||||
\(383\) | −10.0448 | −0.513263 | −0.256632 | − | 0.966509i | \(-0.582613\pi\) | ||||
−0.256632 | + | 0.966509i | \(0.582613\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.82868 | −0.398987 | ||||||||
\(386\) | −35.3341 | −1.79846 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −26.1335 | −1.32673 | ||||||||
\(389\) | −29.6168 | −1.50163 | −0.750816 | − | 0.660511i | \(-0.770340\pi\) | ||||
−0.750816 | + | 0.660511i | \(0.770340\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.0184 | 1.06295 | ||||||||
\(392\) | 7.11048 | 0.359133 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.8772 | −0.900640 | ||||||||
\(395\) | −0.181393 | −0.00912687 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.0564815 | 0.00283472 | 0.00141736 | − | 0.999999i | \(-0.499549\pi\) | ||||
0.00141736 | + | 0.999999i | \(0.499549\pi\) | |||||||
\(398\) | −65.0713 | −3.26173 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20.9736 | −1.04868 | ||||||||
\(401\) | 13.6688 | 0.682587 | 0.341294 | − | 0.939957i | \(-0.389135\pi\) | ||||
0.341294 | + | 0.939957i | \(0.389135\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.43800 | −0.121446 | ||||||||
\(404\) | −3.83581 | −0.190839 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.19355 | −0.0592349 | ||||||||
\(407\) | −31.8670 | −1.57959 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −37.5240 | −1.85544 | −0.927722 | − | 0.373272i | \(-0.878236\pi\) | ||||
−0.927722 | + | 0.373272i | \(0.878236\pi\) | |||||||
\(410\) | 14.5466 | 0.718404 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −24.3224 | −1.19828 | ||||||||
\(413\) | 13.3394 | 0.656388 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.8661 | −0.533397 | ||||||||
\(416\) | 2.39769 | 0.117556 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −73.9002 | −3.61458 | ||||||||
\(419\) | −9.96006 | −0.486581 | −0.243290 | − | 0.969954i | \(-0.578227\pi\) | ||||
−0.243290 | + | 0.969954i | \(0.578227\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.917111 | −0.0446973 | −0.0223486 | − | 0.999750i | \(-0.507114\pi\) | ||||
−0.0223486 | + | 0.999750i | \(0.507114\pi\) | |||||||
\(422\) | −57.8836 | −2.81773 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −18.1517 | −0.881526 | ||||||||
\(425\) | −11.9589 | −0.580094 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.9442 | 0.529627 | ||||||||
\(428\) | 81.4542 | 3.93724 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.90603 | 0.477711 | ||||||||
\(431\) | 28.8257 | 1.38848 | 0.694242 | − | 0.719741i | \(-0.255740\pi\) | ||||
0.694242 | + | 0.719741i | \(0.255740\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.4309 | −1.41436 | −0.707178 | − | 0.707035i | \(-0.750032\pi\) | ||||
−0.707178 | + | 0.707035i | \(0.750032\pi\) | |||||||
\(434\) | −23.9996 | −1.15202 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 40.0177 | 1.91650 | ||||||||
\(437\) | 24.3641 | 1.16549 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.0634 | −1.00530 | −0.502650 | − | 0.864490i | \(-0.667642\pi\) | ||||
−0.502650 | + | 0.864490i | \(0.667642\pi\) | |||||||
\(440\) | −55.6657 | −2.65376 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.50548 | 0.166739 | ||||||||
\(443\) | −37.1991 | −1.76738 | −0.883691 | − | 0.468071i | \(-0.844949\pi\) | ||||
−0.883691 | + | 0.468071i | \(0.844949\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.4286 | −0.873600 | ||||||||
\(446\) | −23.7617 | −1.12515 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.64176 | 0.266548 | ||||||||
\(449\) | −20.6942 | −0.976621 | −0.488310 | − | 0.872670i | \(-0.662387\pi\) | ||||
−0.488310 | + | 0.872670i | \(0.662387\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.4638 | −0.775248 | ||||||||
\(452\) | 10.7945 | 0.507729 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −47.9337 | −2.24964 | ||||||||
\(455\) | 0.430467 | 0.0201806 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.9339 | 1.40025 | 0.700124 | − | 0.714021i | \(-0.253128\pi\) | ||||
0.700124 | + | 0.714021i | \(0.253128\pi\) | |||||||
\(458\) | −55.9972 | −2.61658 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 31.7529 | 1.48048 | ||||||||
\(461\) | −22.9494 | −1.06886 | −0.534429 | − | 0.845213i | \(-0.679473\pi\) | ||||
−0.534429 | + | 0.845213i | \(0.679473\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.6390 | −0.680333 | −0.340167 | − | 0.940365i | \(-0.610484\pi\) | ||||
−0.340167 | + | 0.940365i | \(0.610484\pi\) | |||||||
\(464\) | −4.12896 | −0.191682 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 23.0126 | 1.06604 | ||||||||
\(467\) | −2.88366 | −0.133440 | −0.0667200 | − | 0.997772i | \(-0.521253\pi\) | ||||
−0.0667200 | + | 0.997772i | \(0.521253\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.34491 | 0.0621022 | ||||||||
\(470\) | 24.1171 | 1.11244 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 94.8494 | 4.36580 | ||||||||
\(473\) | −11.2116 | −0.515510 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.8625 | −0.636056 | ||||||||
\(476\) | 24.2667 | 1.11226 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −52.4351 | −2.39833 | ||||||||
\(479\) | −9.17227 | −0.419092 | −0.209546 | − | 0.977799i | \(-0.567199\pi\) | ||||
−0.209546 | + | 0.977799i | \(0.567199\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.75224 | 0.0798952 | ||||||||
\(482\) | 0.718370 | 0.0327209 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 56.8757 | 2.58526 | ||||||||
\(485\) | −9.00155 | −0.408739 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.2962 | −1.19160 | −0.595798 | − | 0.803134i | \(-0.703164\pi\) | ||||
−0.595798 | + | 0.803134i | \(0.703164\pi\) | |||||||
\(488\) | 77.8185 | 3.52268 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.23750 | 0.191431 | ||||||||
\(491\) | −14.2675 | −0.643882 | −0.321941 | − | 0.946760i | \(-0.604335\pi\) | ||||
−0.321941 | + | 0.946760i | \(0.604335\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.35429 | −0.106032 | ||||||||
\(494\) | 4.06347 | 0.182824 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −83.0241 | −3.72789 | ||||||||
\(497\) | −5.05046 | −0.226544 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.6638 | 1.41747 | 0.708734 | − | 0.705476i | \(-0.249267\pi\) | ||||
0.708734 | + | 0.705476i | \(0.249267\pi\) | |||||||
\(500\) | −56.7452 | −2.53772 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 60.4343 | 2.69731 | ||||||||
\(503\) | 38.6248 | 1.72219 | 0.861097 | − | 0.508441i | \(-0.169778\pi\) | ||||
0.861097 | + | 0.508441i | \(0.169778\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.32123 | −0.0587937 | ||||||||
\(506\) | −51.1044 | −2.27187 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.73905 | 0.210261 | ||||||||
\(509\) | 15.2747 | 0.677040 | 0.338520 | − | 0.940959i | \(-0.390074\pi\) | ||||
0.338520 | + | 0.940959i | \(0.390074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.4455 | −0.727507 | ||||||||
\(512\) | −46.0599 | −2.03558 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −60.9503 | −2.68840 | ||||||||
\(515\) | −8.37773 | −0.369167 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.2956 | −1.20046 | ||||||||
\(518\) | 17.2490 | 0.757876 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.06083 | 0.134226 | ||||||||
\(521\) | −10.6429 | −0.466273 | −0.233136 | − | 0.972444i | \(-0.574899\pi\) | ||||
−0.233136 | + | 0.972444i | \(0.574899\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.1697 | 1.23178 | 0.615888 | − | 0.787834i | \(-0.288797\pi\) | ||||
0.615888 | + | 0.787834i | \(0.288797\pi\) | |||||||
\(524\) | −36.5314 | −1.59588 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.00158 | 0.305283 | ||||||||
\(527\) | −47.3395 | −2.06214 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.15146 | −0.267455 | ||||||||
\(530\) | −10.8175 | −0.469884 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 28.1293 | 1.21956 | ||||||||
\(533\) | 0.905275 | 0.0392118 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28.0565 | 1.21299 | ||||||||
\(536\) | 9.56296 | 0.413057 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11.3495 | 0.489313 | ||||||||
\(539\) | −4.79599 | −0.206578 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.9718 | 0.514708 | 0.257354 | − | 0.966317i | \(-0.417149\pi\) | ||||
0.257354 | + | 0.966317i | \(0.417149\pi\) | |||||||
\(542\) | −22.9937 | −0.987664 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 46.5566 | 1.99610 | ||||||||
\(545\) | 13.7839 | 0.590436 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.6453 | 1.65235 | 0.826177 | − | 0.563410i | \(-0.190511\pi\) | ||||
0.826177 | + | 0.563410i | \(0.190511\pi\) | |||||||
\(548\) | 13.8381 | 0.591132 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 29.0771 | 1.23985 | ||||||||
\(551\) | −2.72904 | −0.116261 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.111124 | −0.00472549 | ||||||||
\(554\) | −50.4754 | −2.14449 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.20901 | 0.305730 | ||||||||
\(557\) | 27.9185 | 1.18295 | 0.591473 | − | 0.806325i | \(-0.298547\pi\) | ||||
0.591473 | + | 0.806325i | \(0.298547\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.616480 | 0.0260743 | ||||||||
\(560\) | 14.6592 | 0.619464 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.365794 | 0.0154301 | ||||||||
\(563\) | −17.5654 | −0.740292 | −0.370146 | − | 0.928974i | \(-0.620692\pi\) | ||||
−0.370146 | + | 0.928974i | \(0.620692\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.71810 | 0.156422 | ||||||||
\(566\) | 59.0994 | 2.48413 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −35.9112 | −1.50680 | ||||||||
\(569\) | 6.23445 | 0.261362 | 0.130681 | − | 0.991424i | \(-0.458284\pi\) | ||||
0.130681 | + | 0.991424i | \(0.458284\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.2350 | 0.428321 | 0.214161 | − | 0.976798i | \(-0.431298\pi\) | ||||
0.214161 | + | 0.976798i | \(0.431298\pi\) | |||||||
\(572\) | −5.99375 | −0.250611 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.91149 | 0.371958 | ||||||||
\(575\) | −9.58639 | −0.399780 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.56718 | −0.273395 | −0.136698 | − | 0.990613i | \(-0.543649\pi\) | ||||
−0.136698 | + | 0.990613i | \(0.543649\pi\) | |||||||
\(578\) | 23.9356 | 0.995591 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.55666 | −0.147682 | ||||||||
\(581\) | −6.65678 | −0.276170 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.2433 | 0.507064 | ||||||||
\(584\) | −116.935 | −4.83882 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 76.7202 | 3.16928 | ||||||||
\(587\) | 3.47722 | 0.143520 | 0.0717602 | − | 0.997422i | \(-0.477138\pi\) | ||||
0.0717602 | + | 0.997422i | \(0.477138\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −54.8748 | −2.26108 | ||||||||
\(590\) | 56.5256 | 2.32712 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 59.6709 | 2.45246 | ||||||||
\(593\) | 18.0049 | 0.739372 | 0.369686 | − | 0.929157i | \(-0.379465\pi\) | ||||
0.369686 | + | 0.929157i | \(0.379465\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.35852 | 0.342666 | ||||||||
\(596\) | −56.9910 | −2.33444 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.81002 | 0.114910 | ||||||||
\(599\) | −5.91219 | −0.241565 | −0.120783 | − | 0.992679i | \(-0.538540\pi\) | ||||
−0.120783 | + | 0.992679i | \(0.538540\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.32532 | −0.339597 | −0.169799 | − | 0.985479i | \(-0.554312\pi\) | ||||
−0.169799 | + | 0.985479i | \(0.554312\pi\) | |||||||
\(602\) | 6.06861 | 0.247338 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 21.3995 | 0.870732 | ||||||||
\(605\) | 19.5905 | 0.796468 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.2488 | 0.497163 | 0.248581 | − | 0.968611i | \(-0.420036\pi\) | ||||
0.248581 | + | 0.968611i | \(0.420036\pi\) | |||||||
\(608\) | 53.9673 | 2.18867 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 46.3761 | 1.87771 | ||||||||
\(611\) | 1.50087 | 0.0607188 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.93637 | 0.239768 | 0.119884 | − | 0.992788i | \(-0.461748\pi\) | ||||
0.119884 | + | 0.992788i | \(0.461748\pi\) | |||||||
\(614\) | −45.1711 | −1.82296 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −34.1018 | −1.37400 | ||||||||
\(617\) | 44.2173 | 1.78012 | 0.890061 | − | 0.455841i | \(-0.150662\pi\) | ||||
0.890061 | + | 0.455841i | \(0.150662\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.2653 | −1.21647 | −0.608233 | − | 0.793759i | \(-0.708121\pi\) | ||||
−0.608233 | + | 0.793759i | \(0.708121\pi\) | |||||||
\(620\) | −71.5165 | −2.87217 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 46.4508 | 1.86251 | ||||||||
\(623\) | −11.2897 | −0.452312 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.86826 | −0.314730 | ||||||||
\(626\) | −33.9271 | −1.35600 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.2981 | 0.490749 | ||||||||
\(629\) | 34.0238 | 1.35662 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.4959 | 1.49269 | 0.746344 | − | 0.665561i | \(-0.231808\pi\) | ||||
0.746344 | + | 0.665561i | \(0.231808\pi\) | |||||||
\(632\) | −0.790148 | −0.0314304 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 64.3205 | 2.55449 | ||||||||
\(635\) | 1.63234 | 0.0647774 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.263712 | 0.0104486 | ||||||||
\(638\) | 5.72425 | 0.226625 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.77572 | −0.228305 | ||||||||
\(641\) | −20.9319 | −0.826762 | −0.413381 | − | 0.910558i | \(-0.635652\pi\) | ||||
−0.413381 | + | 0.910558i | \(0.635652\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.0230 | 1.65723 | 0.828613 | − | 0.559821i | \(-0.189130\pi\) | ||||
0.828613 | + | 0.559821i | \(0.189130\pi\) | |||||||
\(644\) | 19.4524 | 0.766530 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 78.9017 | 3.10435 | ||||||||
\(647\) | −7.99073 | −0.314148 | −0.157074 | − | 0.987587i | \(-0.550206\pi\) | ||||
−0.157074 | + | 0.987587i | \(0.550206\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −63.9755 | −2.51126 | ||||||||
\(650\) | −1.59883 | −0.0627113 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 96.5995 | 3.78313 | ||||||||
\(653\) | 6.91364 | 0.270552 | 0.135276 | − | 0.990808i | \(-0.456808\pi\) | ||||
0.135276 | + | 0.990808i | \(0.456808\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.5831 | −0.491661 | ||||||||
\(656\) | 30.8284 | 1.20364 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 14.7745 | 0.575971 | ||||||||
\(659\) | −29.0812 | −1.13284 | −0.566421 | − | 0.824116i | \(-0.691672\pi\) | ||||
−0.566421 | + | 0.824116i | \(0.691672\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.8242 | −1.19892 | −0.599461 | − | 0.800404i | \(-0.704618\pi\) | ||||
−0.599461 | + | 0.800404i | \(0.704618\pi\) | |||||||
\(662\) | −37.3685 | −1.45237 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −47.3329 | −1.83687 | ||||||||
\(665\) | 9.68900 | 0.375723 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.88722 | −0.0730734 | ||||||||
\(668\) | −33.9113 | −1.31207 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.69906 | 0.220174 | ||||||||
\(671\) | −52.4883 | −2.02629 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.7018 | 0.990733 | 0.495366 | − | 0.868684i | \(-0.335034\pi\) | ||||
0.495366 | + | 0.868684i | \(0.335034\pi\) | |||||||
\(674\) | −21.1270 | −0.813780 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −61.2780 | −2.35685 | ||||||||
\(677\) | 21.9171 | 0.842342 | 0.421171 | − | 0.906981i | \(-0.361619\pi\) | ||||
0.421171 | + | 0.906981i | \(0.361619\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.51451 | −0.211627 | ||||||||
\(680\) | 59.4331 | 2.27916 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 115.102 | 4.40747 | ||||||||
\(683\) | −16.0446 | −0.613931 | −0.306966 | − | 0.951721i | \(-0.599314\pi\) | ||||
−0.306966 | + | 0.951721i | \(0.599314\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.76644 | 0.182116 | ||||||||
\(686\) | 2.59597 | 0.0991145 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20.9937 | 0.800377 | ||||||||
\(689\) | −0.673207 | −0.0256471 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.0457 | −0.420199 | −0.210099 | − | 0.977680i | \(-0.567379\pi\) | ||||
−0.210099 | + | 0.977680i | \(0.567379\pi\) | |||||||
\(692\) | 43.0728 | 1.63738 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 61.3444 | 2.32860 | ||||||||
\(695\) | 2.48310 | 0.0941895 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.5780 | 0.665815 | ||||||||
\(698\) | −70.0958 | −2.65316 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11.0679 | −0.418327 | ||||||||
\(701\) | 7.99153 | 0.301836 | 0.150918 | − | 0.988546i | \(-0.451777\pi\) | ||||
0.150918 | + | 0.988546i | \(0.451777\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 39.4395 | 1.48749 | ||||||||
\(704\) | −27.0578 | −1.01978 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −53.9565 | −2.03068 | ||||||||
\(707\) | −0.809406 | −0.0304408 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.5416 | 0.395900 | 0.197950 | − | 0.980212i | \(-0.436572\pi\) | ||||
0.197950 | + | 0.980212i | \(0.436572\pi\) | |||||||
\(710\) | −21.4013 | −0.803177 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −80.2751 | −3.00844 | ||||||||
\(713\) | −37.9477 | −1.42115 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.06452 | −0.0772085 | ||||||||
\(716\) | 93.1929 | 3.48278 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.0634 | 0.711440 | ||||||||
\(719\) | 25.0664 | 0.934820 | 0.467410 | − | 0.884041i | \(-0.345187\pi\) | ||||
0.467410 | + | 0.884041i | \(0.345187\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.13235 | −0.191139 | ||||||||
\(722\) | 42.1376 | 1.56820 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 26.7397 | 0.993771 | ||||||||
\(725\) | 1.07378 | 0.0398792 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.6940 | −0.804588 | −0.402294 | − | 0.915511i | \(-0.631787\pi\) | ||||
−0.402294 | + | 0.915511i | \(0.631787\pi\) | |||||||
\(728\) | 1.87512 | 0.0694964 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −69.6879 | −2.57926 | ||||||||
\(731\) | 11.9704 | 0.442741 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.1204 | 0.780099 | 0.390050 | − | 0.920794i | \(-0.372458\pi\) | ||||
0.390050 | + | 0.920794i | \(0.372458\pi\) | |||||||
\(734\) | 8.49152 | 0.313428 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 37.3202 | 1.37564 | ||||||||
\(737\) | −6.45018 | −0.237595 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.2759 | −1.11372 | −0.556858 | − | 0.830608i | \(-0.687993\pi\) | ||||
−0.556858 | + | 0.830608i | \(0.687993\pi\) | |||||||
\(740\) | 51.4002 | 1.88951 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.62702 | −0.243286 | ||||||||
\(743\) | 46.3530 | 1.70053 | 0.850264 | − | 0.526356i | \(-0.176442\pi\) | ||||
0.850264 | + | 0.526356i | \(0.176442\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.6303 | −0.719197 | ||||||||
\(746\) | −79.8457 | −2.92336 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −116.383 | −4.25537 | ||||||||
\(749\) | 17.1879 | 0.628031 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.3709 | 1.03527 | 0.517634 | − | 0.855602i | \(-0.326813\pi\) | ||||
0.517634 | + | 0.855602i | \(0.326813\pi\) | |||||||
\(752\) | 51.1109 | 1.86382 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.314753 | −0.0114626 | ||||||||
\(755\) | 7.37094 | 0.268256 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.1551 | −1.05966 | −0.529831 | − | 0.848103i | \(-0.677745\pi\) | ||||
−0.529831 | + | 0.848103i | \(0.677745\pi\) | |||||||
\(758\) | 41.9644 | 1.52422 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 68.8934 | 2.49903 | ||||||||
\(761\) | 51.7911 | 1.87743 | 0.938713 | − | 0.344700i | \(-0.112019\pi\) | ||||
0.938713 | + | 0.344700i | \(0.112019\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.44424 | 0.305702 | ||||||||
\(764\) | 68.7507 | 2.48731 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.0759 | −0.942160 | ||||||||
\(767\) | 3.51775 | 0.127019 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.8361 | 1.61683 | 0.808415 | − | 0.588613i | \(-0.200326\pi\) | ||||
0.808415 | + | 0.588613i | \(0.200326\pi\) | |||||||
\(770\) | −20.3230 | −0.732390 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −64.5040 | −2.32155 | ||||||||
\(773\) | 45.1243 | 1.62301 | 0.811504 | − | 0.584347i | \(-0.198649\pi\) | ||||
0.811504 | + | 0.584347i | \(0.198649\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.5913 | 0.775582 | ||||||||
\(776\) | −39.2108 | −1.40758 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −76.8843 | −2.75644 | ||||||||
\(779\) | 20.3760 | 0.730047 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.2219 | 0.866729 | ||||||||
\(782\) | 54.5631 | 1.95117 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.98048 | 0.320731 | ||||||||
\(785\) | 4.23603 | 0.151190 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.6116 | −1.12683 | −0.563416 | − | 0.826173i | \(-0.690513\pi\) | ||||
−0.563416 | + | 0.826173i | \(0.690513\pi\) | |||||||
\(788\) | −32.6355 | −1.16259 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.470890 | −0.0167535 | ||||||||
\(791\) | 2.27777 | 0.0809883 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.88611 | 0.102489 | ||||||||
\(794\) | 0.146624 | 0.00520349 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −118.790 | −4.21041 | ||||||||
\(797\) | −9.37863 | −0.332208 | −0.166104 | − | 0.986108i | \(-0.553119\pi\) | ||||
−0.166104 | + | 0.986108i | \(0.553119\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.1429 | 1.03100 | ||||||||
\(800\) | −21.2342 | −0.750743 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 35.4838 | 1.25297 | ||||||||
\(803\) | 78.8725 | 2.78335 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.70026 | 0.236153 | ||||||||
\(806\) | −6.32897 | −0.222929 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.75526 | −0.202469 | ||||||||
\(809\) | −30.7716 | −1.08187 | −0.540935 | − | 0.841064i | \(-0.681930\pi\) | ||||
−0.540935 | + | 0.841064i | \(0.681930\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.29510 | 0.185936 | 0.0929681 | − | 0.995669i | \(-0.470365\pi\) | ||||
0.0929681 | + | 0.995669i | \(0.470365\pi\) | |||||||
\(812\) | −2.17888 | −0.0764635 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −82.7258 | −2.89954 | ||||||||
\(815\) | 33.2732 | 1.16551 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.8758 | 0.485453 | ||||||||
\(818\) | −97.4111 | −3.40590 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 26.5554 | 0.927354 | ||||||||
\(821\) | 46.7930 | 1.63309 | 0.816543 | − | 0.577284i | \(-0.195888\pi\) | ||||
0.816543 | + | 0.577284i | \(0.195888\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.35491 | −0.326092 | −0.163046 | − | 0.986618i | \(-0.552132\pi\) | ||||
−0.163046 | + | 0.986618i | \(0.552132\pi\) | |||||||
\(824\) | −36.4934 | −1.27131 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 34.6286 | 1.20488 | ||||||||
\(827\) | −40.5945 | −1.41161 | −0.705805 | − | 0.708406i | \(-0.749414\pi\) | ||||
−0.705805 | + | 0.708406i | \(0.749414\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.2936 | −0.392243 | −0.196121 | − | 0.980580i | \(-0.562835\pi\) | ||||
−0.196121 | + | 0.980580i | \(0.562835\pi\) | |||||||
\(830\) | −28.2081 | −0.979118 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.48780 | 0.0515801 | ||||||||
\(833\) | 5.12058 | 0.177417 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.6806 | −0.404222 | ||||||||
\(836\) | −134.908 | −4.66589 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −25.8560 | −0.893180 | ||||||||
\(839\) | −6.00322 | −0.207254 | −0.103627 | − | 0.994616i | \(-0.533045\pi\) | ||||
−0.103627 | + | 0.994616i | \(0.533045\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7886 | −0.992711 | ||||||||
\(842\) | −2.38079 | −0.0820475 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −105.669 | −3.63727 | ||||||||
\(845\) | −21.1069 | −0.726099 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.0015 | 0.412377 | ||||||||
\(848\) | −22.9255 | −0.787264 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −31.0450 | −1.06484 | ||||||||
\(851\) | 27.2737 | 0.934932 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.1151 | 1.47623 | 0.738116 | − | 0.674674i | \(-0.235716\pi\) | ||||
0.738116 | + | 0.674674i | \(0.235716\pi\) | |||||||
\(854\) | 28.4108 | 0.972197 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 122.214 | 4.17719 | ||||||||
\(857\) | −14.7372 | −0.503414 | −0.251707 | − | 0.967803i | \(-0.580992\pi\) | ||||
−0.251707 | + | 0.967803i | \(0.580992\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.1822 | −1.06392 | −0.531961 | − | 0.846769i | \(-0.678545\pi\) | ||||
−0.531961 | + | 0.846769i | \(0.678545\pi\) | |||||||
\(860\) | 18.0839 | 0.616655 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 74.8305 | 2.54874 | ||||||||
\(863\) | 26.3519 | 0.897028 | 0.448514 | − | 0.893776i | \(-0.351953\pi\) | ||||
0.448514 | + | 0.893776i | \(0.351953\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.8362 | 0.504446 | ||||||||
\(866\) | −76.4016 | −2.59623 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −43.8123 | −1.48709 | ||||||||
\(869\) | 0.532952 | 0.0180791 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.354669 | 0.0120175 | ||||||||
\(872\) | 60.0426 | 2.03330 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 63.2483 | 2.13941 | ||||||||
\(875\) | −11.9740 | −0.404794 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.9642 | −1.51833 | −0.759167 | − | 0.650896i | \(-0.774393\pi\) | ||||
−0.759167 | + | 0.650896i | \(0.774393\pi\) | |||||||
\(878\) | −54.6798 | −1.84536 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −70.3053 | −2.36999 | ||||||||
\(881\) | −11.3353 | −0.381897 | −0.190949 | − | 0.981600i | \(-0.561156\pi\) | ||||
−0.190949 | + | 0.981600i | \(0.561156\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.7221 | 1.26945 | 0.634724 | − | 0.772739i | \(-0.281114\pi\) | ||||
0.634724 | + | 0.772739i | \(0.281114\pi\) | |||||||
\(884\) | 6.39940 | 0.215235 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −96.5676 | −3.24425 | ||||||||
\(887\) | −5.00523 | −0.168059 | −0.0840295 | − | 0.996463i | \(-0.526779\pi\) | ||||
−0.0840295 | + | 0.996463i | \(0.526779\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −47.8401 | −1.60360 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −43.3779 | −1.45240 | ||||||||
\(893\) | 33.7818 | 1.13046 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.0998 | 1.07298 | ||||||||
\(896\) | −3.53831 | −0.118207 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −53.7215 | −1.79271 | ||||||||
\(899\) | 4.25056 | 0.141764 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.0719 | −0.435487 | ||||||||
\(902\) | −42.7394 | −1.42307 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.1961 | 0.538673 | ||||||||
\(905\) | 9.21033 | 0.306162 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.70559 | −0.0566333 | −0.0283166 | − | 0.999599i | \(-0.509015\pi\) | ||||
−0.0283166 | + | 0.999599i | \(0.509015\pi\) | |||||||
\(908\) | −87.5049 | −2.90395 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.11748 | 0.0370441 | ||||||||
\(911\) | 49.3674 | 1.63561 | 0.817807 | − | 0.575493i | \(-0.195190\pi\) | ||||
0.817807 | + | 0.575493i | \(0.195190\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.9258 | 1.05659 | ||||||||
\(914\) | 77.7074 | 2.57033 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −102.225 | −3.37762 | ||||||||
\(917\) | −7.70860 | −0.254560 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.1970 | −1.32598 | −0.662989 | − | 0.748629i | \(-0.730712\pi\) | ||||
−0.662989 | + | 0.748629i | \(0.730712\pi\) | |||||||
\(920\) | 47.6421 | 1.57071 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −59.5758 | −1.96202 | ||||||||
\(923\) | −1.33186 | −0.0438389 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.5181 | −0.510230 | ||||||||
\(926\) | −38.0024 | −1.24884 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.18027 | −0.137224 | ||||||||
\(929\) | −23.2396 | −0.762465 | −0.381233 | − | 0.924479i | \(-0.624500\pi\) | ||||
−0.381233 | + | 0.924479i | \(0.624500\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.93565 | 0.194533 | ||||||||
\(932\) | 42.0104 | 1.37610 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.48590 | −0.244946 | ||||||||
\(935\) | −40.0874 | −1.31100 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.6176 | 1.06557 | 0.532785 | − | 0.846251i | \(-0.321146\pi\) | ||||
0.532785 | + | 0.846251i | \(0.321146\pi\) | |||||||
\(938\) | 3.49134 | 0.113996 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 44.0267 | 1.43599 | ||||||||
\(941\) | −0.939169 | −0.0306160 | −0.0153080 | − | 0.999883i | \(-0.504873\pi\) | ||||
−0.0153080 | + | 0.999883i | \(0.504873\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.0907 | 0.458856 | ||||||||
\(944\) | 119.794 | 3.89896 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29.1050 | −0.946284 | ||||||||
\(947\) | 3.25233 | 0.105686 | 0.0528432 | − | 0.998603i | \(-0.483172\pi\) | ||||
0.0528432 | + | 0.998603i | \(0.483172\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.33687 | −0.140781 | ||||||||
\(950\) | −35.9866 | −1.16756 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 36.4098 | 1.18005 | ||||||||
\(953\) | −20.1286 | −0.652029 | −0.326015 | − | 0.945365i | \(-0.605706\pi\) | ||||
−0.326015 | + | 0.945365i | \(0.605706\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.6808 | 0.766293 | ||||||||
\(956\) | −95.7225 | −3.09589 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −23.8109 | −0.769296 | ||||||||
\(959\) | 2.92001 | 0.0942919 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 54.4691 | 1.75707 | ||||||||
\(962\) | 4.54875 | 0.146658 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.31141 | 0.0422378 | ||||||||
\(965\) | −22.2180 | −0.715224 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.0528 | −1.48096 | −0.740479 | − | 0.672080i | \(-0.765401\pi\) | ||||
−0.740479 | + | 0.672080i | \(0.765401\pi\) | |||||||
\(968\) | 85.3364 | 2.74282 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −23.3677 | −0.750292 | ||||||||
\(971\) | −15.1771 | −0.487055 | −0.243527 | − | 0.969894i | \(-0.578305\pi\) | ||||
−0.243527 | + | 0.969894i | \(0.578305\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.52119 | 0.0487672 | ||||||||
\(974\) | −68.2641 | −2.18732 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 98.2841 | 3.14600 | ||||||||
\(977\) | 36.8954 | 1.18039 | 0.590194 | − | 0.807261i | \(-0.299051\pi\) | ||||
0.590194 | + | 0.807261i | \(0.299051\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 54.1452 | 1.73049 | ||||||||
\(980\) | 7.73574 | 0.247109 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −37.0379 | −1.18193 | ||||||||
\(983\) | −13.2244 | −0.421794 | −0.210897 | − | 0.977508i | \(-0.567638\pi\) | ||||
−0.210897 | + | 0.977508i | \(0.567638\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.2411 | −0.358173 | ||||||||
\(986\) | −6.11166 | −0.194635 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.41804 | 0.235999 | ||||||||
\(989\) | 9.59557 | 0.305121 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.1367 | 0.734960 | 0.367480 | − | 0.930031i | \(-0.380221\pi\) | ||||
0.367480 | + | 0.930031i | \(0.380221\pi\) | |||||||
\(992\) | −84.0557 | −2.66877 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −13.1108 | −0.415850 | ||||||||
\(995\) | −40.9167 | −1.29715 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.4462 | −1.24927 | −0.624637 | − | 0.780915i | \(-0.714753\pi\) | ||||
−0.624637 | + | 0.780915i | \(0.714753\pi\) | |||||||
\(998\) | 82.1982 | 2.60194 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.u.1.16 | 18 | ||
3.2 | odd | 2 | 2667.2.a.p.1.3 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.p.1.3 | ✓ | 18 | 3.2 | odd | 2 | ||
8001.2.a.u.1.16 | 18 | 1.1 | even | 1 | trivial |