Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2583,2,Mod(1,2583)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2583, 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("2583.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2583 = 3^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2583.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: | \(20.6253588421\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.633117.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 6x^{3} + 4x^{2} + 6x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 287) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.45719\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2583.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.45719 | 1.73750 | 0.868748 | − | 0.495255i | \(-0.164925\pi\) | ||||
0.868748 | + | 0.495255i | \(0.164925\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.03778 | 2.01889 | ||||||||
\(5\) | 2.26685 | 1.01376 | 0.506882 | − | 0.862015i | \(-0.330798\pi\) | ||||
0.506882 | + | 0.862015i | \(0.330798\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 5.00722 | 1.77032 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.57007 | 1.76141 | ||||||||
\(11\) | 5.41988 | 1.63415 | 0.817077 | − | 0.576528i | \(-0.195593\pi\) | ||||
0.817077 | + | 0.576528i | \(0.195593\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.23628 | 0.897584 | 0.448792 | − | 0.893636i | \(-0.351854\pi\) | ||||
0.448792 | + | 0.893636i | \(0.351854\pi\) | |||||||
\(14\) | 2.45719 | 0.656712 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.22813 | 1.05703 | ||||||||
\(17\) | −2.83206 | −0.686876 | −0.343438 | − | 0.939175i | \(-0.611592\pi\) | ||||
−0.343438 | + | 0.939175i | \(0.611592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.32097 | −0.991298 | −0.495649 | − | 0.868523i | \(-0.665070\pi\) | ||||
−0.495649 | + | 0.868523i | \(0.665070\pi\) | |||||||
\(20\) | 9.15303 | 2.04668 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 13.3177 | 2.83934 | ||||||||
\(23\) | −6.99907 | −1.45941 | −0.729703 | − | 0.683764i | \(-0.760342\pi\) | ||||
−0.729703 | + | 0.683764i | \(0.760342\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.138589 | 0.0277177 | ||||||||
\(26\) | 7.95216 | 1.55955 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.03778 | 0.763069 | ||||||||
\(29\) | −8.06741 | −1.49808 | −0.749040 | − | 0.662524i | \(-0.769485\pi\) | ||||
−0.749040 | + | 0.662524i | \(0.769485\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.18123 | 1.64900 | 0.824498 | − | 0.565864i | \(-0.191457\pi\) | ||||
0.824498 | + | 0.565864i | \(0.191457\pi\) | |||||||
\(32\) | 0.374872 | 0.0662686 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.95892 | −1.19344 | ||||||||
\(35\) | 2.26685 | 0.383167 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.0469023 | −0.00771068 | −0.00385534 | − | 0.999993i | \(-0.501227\pi\) | ||||
−0.00385534 | + | 0.999993i | \(0.501227\pi\) | |||||||
\(38\) | −10.6174 | −1.72238 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 11.3506 | 1.79469 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.31281 | −0.962695 | −0.481348 | − | 0.876530i | \(-0.659852\pi\) | ||||
−0.481348 | + | 0.876530i | \(0.659852\pi\) | |||||||
\(44\) | 21.8843 | 3.29918 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −17.1980 | −2.53571 | ||||||||
\(47\) | −5.26448 | −0.767903 | −0.383952 | − | 0.923353i | \(-0.625437\pi\) | ||||
−0.383952 | + | 0.923353i | \(0.625437\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.340538 | 0.0481594 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 13.0674 | 1.81212 | ||||||||
\(53\) | −6.43622 | −0.884082 | −0.442041 | − | 0.896995i | \(-0.645745\pi\) | ||||
−0.442041 | + | 0.896995i | \(0.645745\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.2860 | 1.65665 | ||||||||
\(56\) | 5.00722 | 0.669118 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −19.8232 | −2.60291 | ||||||||
\(59\) | −2.45253 | −0.319292 | −0.159646 | − | 0.987174i | \(-0.551035\pi\) | ||||
−0.159646 | + | 0.987174i | \(0.551035\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.28319 | 0.676443 | 0.338221 | − | 0.941067i | \(-0.390175\pi\) | ||||
0.338221 | + | 0.941067i | \(0.390175\pi\) | |||||||
\(62\) | 22.5600 | 2.86513 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.53512 | −0.941891 | ||||||||
\(65\) | 7.33615 | 0.909938 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.78423 | −1.07316 | −0.536582 | − | 0.843848i | \(-0.680285\pi\) | ||||
−0.536582 | + | 0.843848i | \(0.680285\pi\) | |||||||
\(68\) | −11.4353 | −1.38673 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.57007 | 0.665751 | ||||||||
\(71\) | 12.1364 | 1.44033 | 0.720165 | − | 0.693802i | \(-0.244066\pi\) | ||||
0.720165 | + | 0.693802i | \(0.244066\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.42993 | 0.284402 | 0.142201 | − | 0.989838i | \(-0.454582\pi\) | ||||
0.142201 | + | 0.989838i | \(0.454582\pi\) | |||||||
\(74\) | −0.115248 | −0.0133973 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −17.4471 | −2.00132 | ||||||||
\(77\) | 5.41988 | 0.617652 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.92882 | 0.554536 | 0.277268 | − | 0.960793i | \(-0.410571\pi\) | ||||
0.277268 | + | 0.960793i | \(0.410571\pi\) | |||||||
\(80\) | 9.58451 | 1.07158 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.45719 | 0.271351 | ||||||||
\(83\) | 1.63593 | 0.179567 | 0.0897833 | − | 0.995961i | \(-0.471383\pi\) | ||||
0.0897833 | + | 0.995961i | \(0.471383\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.41985 | −0.696330 | ||||||||
\(86\) | −15.5118 | −1.67268 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 27.1385 | 2.89298 | ||||||||
\(89\) | −1.68625 | −0.178742 | −0.0893712 | − | 0.995998i | \(-0.528486\pi\) | ||||
−0.0893712 | + | 0.995998i | \(0.528486\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.23628 | 0.339255 | ||||||||
\(92\) | −28.2607 | −2.94638 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.9358 | −1.33423 | ||||||||
\(95\) | −9.79497 | −1.00494 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.8278 | 1.91168 | 0.955838 | − | 0.293894i | \(-0.0949512\pi\) | ||||
0.955838 | + | 0.293894i | \(0.0949512\pi\) | |||||||
\(98\) | 2.45719 | 0.248214 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.559591 | 0.0559591 | ||||||||
\(101\) | −7.44903 | −0.741207 | −0.370603 | − | 0.928791i | \(-0.620849\pi\) | ||||
−0.370603 | + | 0.928791i | \(0.620849\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.68672 | 0.363264 | 0.181632 | − | 0.983367i | \(-0.441862\pi\) | ||||
0.181632 | + | 0.983367i | \(0.441862\pi\) | |||||||
\(104\) | 16.2048 | 1.58901 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.8150 | −1.53609 | ||||||||
\(107\) | 8.58781 | 0.830215 | 0.415108 | − | 0.909772i | \(-0.363744\pi\) | ||||
0.415108 | + | 0.909772i | \(0.363744\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.91912 | −0.279601 | −0.139800 | − | 0.990180i | \(-0.544646\pi\) | ||||
−0.139800 | + | 0.990180i | \(0.544646\pi\) | |||||||
\(110\) | 30.1891 | 2.87842 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.22813 | 0.399521 | ||||||||
\(113\) | 7.03990 | 0.662258 | 0.331129 | − | 0.943585i | \(-0.392570\pi\) | ||||
0.331129 | + | 0.943585i | \(0.392570\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.8658 | −1.47949 | ||||||||
\(116\) | −32.5745 | −3.02446 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.02633 | −0.554768 | ||||||||
\(119\) | −2.83206 | −0.259615 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.3751 | 1.67046 | ||||||||
\(122\) | 12.9818 | 1.17532 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 37.0718 | 3.32915 | ||||||||
\(125\) | −11.0201 | −0.985665 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.1099 | 1.69573 | 0.847863 | − | 0.530216i | \(-0.177889\pi\) | ||||
0.847863 | + | 0.530216i | \(0.177889\pi\) | |||||||
\(128\) | −19.2650 | −1.70280 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 18.0263 | 1.58101 | ||||||||
\(131\) | −9.99440 | −0.873215 | −0.436608 | − | 0.899652i | \(-0.643820\pi\) | ||||
−0.436608 | + | 0.899652i | \(0.643820\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.32097 | −0.374676 | ||||||||
\(134\) | −21.5845 | −1.86462 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −14.1808 | −1.21599 | ||||||||
\(137\) | −4.66385 | −0.398459 | −0.199230 | − | 0.979953i | \(-0.563844\pi\) | ||||
−0.199230 | + | 0.979953i | \(0.563844\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.3954 | −0.881725 | −0.440862 | − | 0.897575i | \(-0.645327\pi\) | ||||
−0.440862 | + | 0.897575i | \(0.645327\pi\) | |||||||
\(140\) | 9.15303 | 0.773572 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 29.8215 | 2.50257 | ||||||||
\(143\) | 17.5403 | 1.46679 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.2876 | −1.51870 | ||||||||
\(146\) | 5.97080 | 0.494147 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.189381 | −0.0155670 | ||||||||
\(149\) | −6.23050 | −0.510422 | −0.255211 | − | 0.966885i | \(-0.582145\pi\) | ||||
−0.255211 | + | 0.966885i | \(0.582145\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.1548 | −1.72156 | −0.860778 | − | 0.508981i | \(-0.830022\pi\) | ||||
−0.860778 | + | 0.508981i | \(0.830022\pi\) | |||||||
\(152\) | −21.6360 | −1.75492 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 13.3177 | 1.07317 | ||||||||
\(155\) | 20.8124 | 1.67169 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.4912 | 1.63538 | 0.817688 | − | 0.575662i | \(-0.195255\pi\) | ||||
0.817688 | + | 0.575662i | \(0.195255\pi\) | |||||||
\(158\) | 12.1111 | 0.963504 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.849777 | 0.0671808 | ||||||||
\(161\) | −6.99907 | −0.551604 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.63497 | −0.128060 | −0.0640302 | − | 0.997948i | \(-0.520395\pi\) | ||||
−0.0640302 | + | 0.997948i | \(0.520395\pi\) | |||||||
\(164\) | 4.03778 | 0.315298 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.01979 | 0.311996 | ||||||||
\(167\) | 19.8243 | 1.53405 | 0.767026 | − | 0.641616i | \(-0.221736\pi\) | ||||
0.767026 | + | 0.641616i | \(0.221736\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.52647 | −0.194344 | ||||||||
\(170\) | −15.7748 | −1.20987 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −25.4898 | −1.94358 | ||||||||
\(173\) | 9.31394 | 0.708126 | 0.354063 | − | 0.935222i | \(-0.384800\pi\) | ||||
0.354063 | + | 0.935222i | \(0.384800\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.138589 | 0.0104763 | ||||||||
\(176\) | 22.9159 | 1.72735 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.14344 | −0.310564 | ||||||||
\(179\) | 17.3459 | 1.29649 | 0.648245 | − | 0.761432i | \(-0.275503\pi\) | ||||
0.648245 | + | 0.761432i | \(0.275503\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.1355 | 0.753364 | 0.376682 | − | 0.926343i | \(-0.377065\pi\) | ||||
0.376682 | + | 0.926343i | \(0.377065\pi\) | |||||||
\(182\) | 7.95216 | 0.589454 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −35.0459 | −2.58362 | ||||||||
\(185\) | −0.106320 | −0.00781681 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.3494 | −1.12246 | ||||||||
\(188\) | −21.2568 | −1.55031 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −24.0681 | −1.74608 | ||||||||
\(191\) | −18.1959 | −1.31661 | −0.658306 | − | 0.752750i | \(-0.728727\pi\) | ||||
−0.658306 | + | 0.752750i | \(0.728727\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.29950 | 0.0935398 | 0.0467699 | − | 0.998906i | \(-0.485107\pi\) | ||||
0.0467699 | + | 0.998906i | \(0.485107\pi\) | |||||||
\(194\) | 46.2635 | 3.32153 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.03778 | 0.288413 | ||||||||
\(197\) | −5.64679 | −0.402317 | −0.201159 | − | 0.979559i | \(-0.564471\pi\) | ||||
−0.201159 | + | 0.979559i | \(0.564471\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.5069 | −0.815699 | −0.407850 | − | 0.913049i | \(-0.633721\pi\) | ||||
−0.407850 | + | 0.913049i | \(0.633721\pi\) | |||||||
\(200\) | 0.693943 | 0.0490692 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −18.3037 | −1.28784 | ||||||||
\(203\) | −8.06741 | −0.566221 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.26685 | 0.158323 | ||||||||
\(206\) | 9.05898 | 0.631169 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 13.6834 | 0.948775 | ||||||||
\(209\) | −23.4191 | −1.61993 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.92599 | −0.683333 | −0.341667 | − | 0.939821i | \(-0.610991\pi\) | ||||
−0.341667 | + | 0.939821i | \(0.610991\pi\) | |||||||
\(212\) | −25.9880 | −1.78487 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 21.1019 | 1.44250 | ||||||||
\(215\) | −14.3102 | −0.975946 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.18123 | 0.623262 | ||||||||
\(218\) | −7.17282 | −0.485805 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 49.6083 | 3.34459 | ||||||||
\(221\) | −9.16536 | −0.616529 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.8232 | −0.791738 | −0.395869 | − | 0.918307i | \(-0.629557\pi\) | ||||
−0.395869 | + | 0.918307i | \(0.629557\pi\) | |||||||
\(224\) | 0.374872 | 0.0250472 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.2984 | 1.15067 | ||||||||
\(227\) | −1.60275 | −0.106378 | −0.0531892 | − | 0.998584i | \(-0.516939\pi\) | ||||
−0.0531892 | + | 0.998584i | \(0.516939\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.93349 | −0.656423 | −0.328212 | − | 0.944604i | \(-0.606446\pi\) | ||||
−0.328212 | + | 0.944604i | \(0.606446\pi\) | |||||||
\(230\) | −38.9853 | −2.57061 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −40.3953 | −2.65208 | ||||||||
\(233\) | 7.91248 | 0.518364 | 0.259182 | − | 0.965829i | \(-0.416547\pi\) | ||||
0.259182 | + | 0.965829i | \(0.416547\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.9338 | −0.778473 | ||||||||
\(236\) | −9.90278 | −0.644616 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.95892 | −0.451079 | ||||||||
\(239\) | −27.1893 | −1.75873 | −0.879365 | − | 0.476148i | \(-0.842033\pi\) | ||||
−0.879365 | + | 0.476148i | \(0.842033\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.4014 | 1.24975 | 0.624877 | − | 0.780723i | \(-0.285149\pi\) | ||||
0.624877 | + | 0.780723i | \(0.285149\pi\) | |||||||
\(242\) | 45.1510 | 2.90242 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 21.3324 | 1.36566 | ||||||||
\(245\) | 2.26685 | 0.144823 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.9839 | −0.889773 | ||||||||
\(248\) | 45.9724 | 2.91925 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −27.0784 | −1.71259 | ||||||||
\(251\) | −27.4697 | −1.73387 | −0.866935 | − | 0.498421i | \(-0.833913\pi\) | ||||
−0.866935 | + | 0.498421i | \(0.833913\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −37.9341 | −2.38489 | ||||||||
\(254\) | 46.9566 | 2.94632 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.2675 | −2.01672 | ||||||||
\(257\) | −21.6328 | −1.34942 | −0.674710 | − | 0.738083i | \(-0.735731\pi\) | ||||
−0.674710 | + | 0.738083i | \(0.735731\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.0469023 | −0.00291436 | ||||||||
\(260\) | 29.6218 | 1.83707 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −24.5581 | −1.51721 | ||||||||
\(263\) | 9.84482 | 0.607058 | 0.303529 | − | 0.952822i | \(-0.401835\pi\) | ||||
0.303529 | + | 0.952822i | \(0.401835\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.5899 | −0.896251 | ||||||||
\(266\) | −10.6174 | −0.650997 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −35.4688 | −2.16660 | ||||||||
\(269\) | 26.0627 | 1.58907 | 0.794535 | − | 0.607219i | \(-0.207715\pi\) | ||||
0.794535 | + | 0.607219i | \(0.207715\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.4506 | 1.54602 | 0.773008 | − | 0.634396i | \(-0.218751\pi\) | ||||
0.773008 | + | 0.634396i | \(0.218751\pi\) | |||||||
\(272\) | −11.9743 | −0.726050 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.4600 | −0.692321 | ||||||||
\(275\) | 0.751133 | 0.0452950 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.3678 | 1.76454 | 0.882270 | − | 0.470743i | \(-0.156014\pi\) | ||||
0.882270 | + | 0.470743i | \(0.156014\pi\) | |||||||
\(278\) | −25.5434 | −1.53199 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 11.3506 | 0.678328 | ||||||||
\(281\) | −24.2120 | −1.44437 | −0.722184 | − | 0.691701i | \(-0.756861\pi\) | ||||
−0.722184 | + | 0.691701i | \(0.756861\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.91251 | 0.529794 | 0.264897 | − | 0.964277i | \(-0.414662\pi\) | ||||
0.264897 | + | 0.964277i | \(0.414662\pi\) | |||||||
\(284\) | 49.0043 | 2.90787 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 43.0997 | 2.54854 | ||||||||
\(287\) | 1.00000 | 0.0590281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.97942 | −0.528201 | ||||||||
\(290\) | −44.9361 | −2.63874 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.81153 | 0.574176 | ||||||||
\(293\) | 8.79238 | 0.513656 | 0.256828 | − | 0.966457i | \(-0.417323\pi\) | ||||
0.256828 | + | 0.966457i | \(0.417323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.55950 | −0.323687 | ||||||||
\(296\) | −0.234850 | −0.0136504 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.3095 | −0.886856 | ||||||||
\(299\) | −22.6510 | −1.30994 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.31281 | −0.363865 | ||||||||
\(302\) | −51.9814 | −2.99120 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −18.2696 | −1.04783 | ||||||||
\(305\) | 11.9762 | 0.685753 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.4509 | 1.45256 | 0.726281 | − | 0.687398i | \(-0.241247\pi\) | ||||
0.726281 | + | 0.687398i | \(0.241247\pi\) | |||||||
\(308\) | 21.8843 | 1.24697 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 51.1401 | 2.90456 | ||||||||
\(311\) | 8.20774 | 0.465418 | 0.232709 | − | 0.972546i | \(-0.425241\pi\) | ||||
0.232709 | + | 0.972546i | \(0.425241\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.84025 | 0.443157 | 0.221578 | − | 0.975143i | \(-0.428879\pi\) | ||||
0.221578 | + | 0.975143i | \(0.428879\pi\) | |||||||
\(314\) | 50.3508 | 2.84146 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.9015 | 1.11955 | ||||||||
\(317\) | −32.4359 | −1.82178 | −0.910891 | − | 0.412647i | \(-0.864604\pi\) | ||||
−0.910891 | + | 0.412647i | \(0.864604\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −43.7244 | −2.44810 | ||||||||
\(320\) | −17.0810 | −0.954855 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −17.1980 | −0.958409 | ||||||||
\(323\) | 12.2373 | 0.680899 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.448512 | 0.0248790 | ||||||||
\(326\) | −4.01742 | −0.222504 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.00722 | 0.276478 | ||||||||
\(329\) | −5.26448 | −0.290240 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.8576 | 0.761685 | 0.380843 | − | 0.924640i | \(-0.375634\pi\) | ||||
0.380843 | + | 0.924640i | \(0.375634\pi\) | |||||||
\(332\) | 6.60553 | 0.362526 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 48.7121 | 2.66541 | ||||||||
\(335\) | −19.9125 | −1.08794 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.6080 | 1.01364 | 0.506822 | − | 0.862050i | \(-0.330820\pi\) | ||||
0.506822 | + | 0.862050i | \(0.330820\pi\) | |||||||
\(338\) | −6.20802 | −0.337672 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −25.9220 | −1.40582 | ||||||||
\(341\) | 49.7611 | 2.69472 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −31.6097 | −1.70428 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.8861 | 1.23037 | ||||||||
\(347\) | −23.3306 | −1.25245 | −0.626225 | − | 0.779642i | \(-0.715401\pi\) | ||||
−0.626225 | + | 0.779642i | \(0.715401\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.59571 | −0.299531 | −0.149766 | − | 0.988722i | \(-0.547852\pi\) | ||||
−0.149766 | + | 0.988722i | \(0.547852\pi\) | |||||||
\(350\) | 0.340538 | 0.0182025 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.03176 | 0.108293 | ||||||||
\(353\) | 19.4280 | 1.03405 | 0.517023 | − | 0.855971i | \(-0.327040\pi\) | ||||
0.517023 | + | 0.855971i | \(0.327040\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 27.5114 | 1.46016 | ||||||||
\(356\) | −6.80872 | −0.360862 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 42.6221 | 2.25265 | ||||||||
\(359\) | −14.3127 | −0.755398 | −0.377699 | − | 0.925929i | \(-0.623285\pi\) | ||||
−0.377699 | + | 0.925929i | \(0.623285\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.329226 | −0.0173277 | ||||||||
\(362\) | 24.9048 | 1.30897 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13.0674 | 0.684918 | ||||||||
\(365\) | 5.50827 | 0.288316 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.2458 | −1.10902 | −0.554512 | − | 0.832176i | \(-0.687095\pi\) | ||||
−0.554512 | + | 0.832176i | \(0.687095\pi\) | |||||||
\(368\) | −29.5929 | −1.54264 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.261249 | −0.0135817 | ||||||||
\(371\) | −6.43622 | −0.334152 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.2272 | 1.46155 | 0.730774 | − | 0.682620i | \(-0.239160\pi\) | ||||
0.730774 | + | 0.682620i | \(0.239160\pi\) | |||||||
\(374\) | −37.7165 | −1.95027 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −26.3604 | −1.35943 | ||||||||
\(377\) | −26.1084 | −1.34465 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.57635 | −0.440538 | −0.220269 | − | 0.975439i | \(-0.570693\pi\) | ||||
−0.220269 | + | 0.975439i | \(0.570693\pi\) | |||||||
\(380\) | −39.5500 | −2.02887 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −44.7109 | −2.28761 | ||||||||
\(383\) | −2.63393 | −0.134588 | −0.0672938 | − | 0.997733i | \(-0.521436\pi\) | ||||
−0.0672938 | + | 0.997733i | \(0.521436\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.2860 | 0.626154 | ||||||||
\(386\) | 3.19311 | 0.162525 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 76.0227 | 3.85947 | ||||||||
\(389\) | 13.2656 | 0.672595 | 0.336298 | − | 0.941756i | \(-0.390825\pi\) | ||||
0.336298 | + | 0.941756i | \(0.390825\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.8218 | 1.00243 | ||||||||
\(392\) | 5.00722 | 0.252903 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.8752 | −0.699025 | ||||||||
\(395\) | 11.1729 | 0.562169 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.28602 | 0.114732 | 0.0573661 | − | 0.998353i | \(-0.481730\pi\) | ||||
0.0573661 | + | 0.998353i | \(0.481730\pi\) | |||||||
\(398\) | −28.2745 | −1.41727 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.585970 | 0.0292985 | ||||||||
\(401\) | −2.79191 | −0.139421 | −0.0697107 | − | 0.997567i | \(-0.522208\pi\) | ||||
−0.0697107 | + | 0.997567i | \(0.522208\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.7130 | 1.48011 | ||||||||
\(404\) | −30.0776 | −1.49642 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −19.8232 | −0.983807 | ||||||||
\(407\) | −0.254204 | −0.0126004 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.8769 | −0.537826 | −0.268913 | − | 0.963164i | \(-0.586664\pi\) | ||||
−0.268913 | + | 0.963164i | \(0.586664\pi\) | |||||||
\(410\) | 5.57007 | 0.275086 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.8862 | 0.733390 | ||||||||
\(413\) | −2.45253 | −0.120681 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.70840 | 0.182038 | ||||||||
\(416\) | 1.21319 | 0.0594816 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −57.5452 | −2.81463 | ||||||||
\(419\) | 24.9047 | 1.21668 | 0.608338 | − | 0.793678i | \(-0.291836\pi\) | ||||
0.608338 | + | 0.793678i | \(0.291836\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.16405 | −0.349155 | −0.174577 | − | 0.984643i | \(-0.555856\pi\) | ||||
−0.174577 | + | 0.984643i | \(0.555856\pi\) | |||||||
\(422\) | −24.3900 | −1.18729 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −32.2276 | −1.56511 | ||||||||
\(425\) | −0.392491 | −0.0190386 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.28319 | 0.255671 | ||||||||
\(428\) | 34.6757 | 1.67611 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −35.1628 | −1.69570 | ||||||||
\(431\) | 14.6538 | 0.705850 | 0.352925 | − | 0.935652i | \(-0.385187\pi\) | ||||
0.352925 | + | 0.935652i | \(0.385187\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.4173 | −1.41370 | −0.706851 | − | 0.707362i | \(-0.749885\pi\) | ||||
−0.706851 | + | 0.707362i | \(0.749885\pi\) | |||||||
\(434\) | 22.5600 | 1.08292 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.7868 | −0.564483 | ||||||||
\(437\) | 30.2427 | 1.44671 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.5607 | 1.26767 | 0.633837 | − | 0.773466i | \(-0.281479\pi\) | ||||
0.633837 | + | 0.773466i | \(0.281479\pi\) | |||||||
\(440\) | 61.5188 | 2.93280 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −22.5210 | −1.07122 | ||||||||
\(443\) | 12.2373 | 0.581409 | 0.290705 | − | 0.956813i | \(-0.406110\pi\) | ||||
0.290705 | + | 0.956813i | \(0.406110\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.82247 | −0.181203 | ||||||||
\(446\) | −29.0518 | −1.37564 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.53512 | −0.356001 | ||||||||
\(449\) | 23.4334 | 1.10589 | 0.552944 | − | 0.833218i | \(-0.313504\pi\) | ||||
0.552944 | + | 0.833218i | \(0.313504\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.41988 | 0.255212 | ||||||||
\(452\) | 28.4256 | 1.33703 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.93826 | −0.184832 | ||||||||
\(455\) | 7.33615 | 0.343924 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.25626 | −0.386212 | −0.193106 | − | 0.981178i | \(-0.561856\pi\) | ||||
−0.193106 | + | 0.981178i | \(0.561856\pi\) | |||||||
\(458\) | −24.4085 | −1.14053 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −64.0627 | −2.98694 | ||||||||
\(461\) | 8.79238 | 0.409502 | 0.204751 | − | 0.978814i | \(-0.434362\pi\) | ||||
0.204751 | + | 0.978814i | \(0.434362\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.8884 | 1.71435 | 0.857175 | − | 0.515025i | \(-0.172217\pi\) | ||||
0.857175 | + | 0.515025i | \(0.172217\pi\) | |||||||
\(464\) | −34.1100 | −1.58352 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.4425 | 0.900655 | ||||||||
\(467\) | 21.8803 | 1.01250 | 0.506250 | − | 0.862387i | \(-0.331031\pi\) | ||||
0.506250 | + | 0.862387i | \(0.331031\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.78423 | −0.405618 | ||||||||
\(470\) | −29.3235 | −1.35259 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.2803 | −0.565249 | ||||||||
\(473\) | −34.2147 | −1.57319 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.598837 | −0.0274765 | ||||||||
\(476\) | −11.4353 | −0.524134 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −66.8093 | −3.05579 | ||||||||
\(479\) | −34.3678 | −1.57030 | −0.785152 | − | 0.619303i | \(-0.787415\pi\) | ||||
−0.785152 | + | 0.619303i | \(0.787415\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.151789 | −0.00692098 | ||||||||
\(482\) | 47.6729 | 2.17144 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 74.1945 | 3.37248 | ||||||||
\(485\) | 42.6798 | 1.93799 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.9585 | 0.723146 | 0.361573 | − | 0.932344i | \(-0.382240\pi\) | ||||
0.361573 | + | 0.932344i | \(0.382240\pi\) | |||||||
\(488\) | 26.4541 | 1.19752 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.57007 | 0.251630 | ||||||||
\(491\) | 1.69863 | 0.0766581 | 0.0383290 | − | 0.999265i | \(-0.487796\pi\) | ||||
0.0383290 | + | 0.999265i | \(0.487796\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.8474 | 1.02900 | ||||||||
\(494\) | −34.3611 | −1.54598 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 38.8194 | 1.74304 | ||||||||
\(497\) | 12.1364 | 0.544394 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.0520 | −1.03195 | −0.515975 | − | 0.856604i | \(-0.672570\pi\) | ||||
−0.515975 | + | 0.856604i | \(0.672570\pi\) | |||||||
\(500\) | −44.4967 | −1.98995 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −67.4982 | −3.01259 | ||||||||
\(503\) | −34.6937 | −1.54692 | −0.773458 | − | 0.633848i | \(-0.781474\pi\) | ||||
−0.773458 | + | 0.633848i | \(0.781474\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.8858 | −0.751409 | ||||||||
\(506\) | −93.2112 | −4.14374 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 77.1615 | 3.42349 | ||||||||
\(509\) | 7.41125 | 0.328498 | 0.164249 | − | 0.986419i | \(-0.447480\pi\) | ||||
0.164249 | + | 0.986419i | \(0.447480\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.42993 | 0.107494 | ||||||||
\(512\) | −40.7573 | −1.80124 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −53.1560 | −2.34461 | ||||||||
\(515\) | 8.35723 | 0.368264 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.5328 | −1.25487 | ||||||||
\(518\) | −0.115248 | −0.00506370 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 36.7337 | 1.61088 | ||||||||
\(521\) | 24.2278 | 1.06144 | 0.530719 | − | 0.847548i | \(-0.321922\pi\) | ||||
0.530719 | + | 0.847548i | \(0.321922\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −43.3265 | −1.89454 | −0.947268 | − | 0.320442i | \(-0.896169\pi\) | ||||
−0.947268 | + | 0.320442i | \(0.896169\pi\) | |||||||
\(524\) | −40.3552 | −1.76293 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.1906 | 1.05476 | ||||||||
\(527\) | −26.0018 | −1.13266 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.9869 | 1.12987 | ||||||||
\(530\) | −35.8502 | −1.55723 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −17.4471 | −0.756429 | ||||||||
\(533\) | 3.23628 | 0.140179 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.4672 | 0.841643 | ||||||||
\(536\) | −43.9846 | −1.89984 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 64.0410 | 2.76100 | ||||||||
\(539\) | 5.41988 | 0.233451 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.7180 | −0.546788 | −0.273394 | − | 0.961902i | \(-0.588146\pi\) | ||||
−0.273394 | + | 0.961902i | \(0.588146\pi\) | |||||||
\(542\) | 62.5370 | 2.68620 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.06166 | −0.0455183 | ||||||||
\(545\) | −6.61718 | −0.283449 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.71489 | −0.201594 | −0.100797 | − | 0.994907i | \(-0.532139\pi\) | ||||
−0.100797 | + | 0.994907i | \(0.532139\pi\) | |||||||
\(548\) | −18.8316 | −0.804446 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.84568 | 0.0786999 | ||||||||
\(551\) | 34.8590 | 1.48504 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.92882 | 0.209595 | ||||||||
\(554\) | 72.1623 | 3.06588 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −41.9743 | −1.78011 | ||||||||
\(557\) | 11.0756 | 0.469288 | 0.234644 | − | 0.972081i | \(-0.424608\pi\) | ||||
0.234644 | + | 0.972081i | \(0.424608\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.4301 | −0.864099 | ||||||||
\(560\) | 9.58451 | 0.405020 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −59.4935 | −2.50958 | ||||||||
\(563\) | −24.9735 | −1.05251 | −0.526255 | − | 0.850327i | \(-0.676404\pi\) | ||||
−0.526255 | + | 0.850327i | \(0.676404\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.9584 | 0.671374 | ||||||||
\(566\) | 21.8997 | 0.920515 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 60.7698 | 2.54985 | ||||||||
\(569\) | −3.14116 | −0.131684 | −0.0658422 | − | 0.997830i | \(-0.520973\pi\) | ||||
−0.0658422 | + | 0.997830i | \(0.520973\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.13418 | 0.298556 | 0.149278 | − | 0.988795i | \(-0.452305\pi\) | ||||
0.149278 | + | 0.988795i | \(0.452305\pi\) | |||||||
\(572\) | 70.8238 | 2.96129 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.45719 | 0.102561 | ||||||||
\(575\) | −0.969990 | −0.0404514 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.41995 | 0.184005 | 0.0920024 | − | 0.995759i | \(-0.470673\pi\) | ||||
0.0920024 | + | 0.995759i | \(0.470673\pi\) | |||||||
\(578\) | −22.0642 | −0.917748 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −73.8413 | −3.06609 | ||||||||
\(581\) | 1.63593 | 0.0678698 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −34.8835 | −1.44473 | ||||||||
\(584\) | 12.1672 | 0.503482 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.6046 | 0.892476 | ||||||||
\(587\) | −29.7123 | −1.22636 | −0.613178 | − | 0.789944i | \(-0.710109\pi\) | ||||
−0.613178 | + | 0.789944i | \(0.710109\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −39.6718 | −1.63465 | ||||||||
\(590\) | −13.6608 | −0.562404 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.198309 | −0.00815044 | ||||||||
\(593\) | 14.3020 | 0.587315 | 0.293657 | − | 0.955911i | \(-0.405128\pi\) | ||||
0.293657 | + | 0.955911i | \(0.405128\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.41985 | −0.263188 | ||||||||
\(596\) | −25.1574 | −1.03049 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −55.6577 | −2.27601 | ||||||||
\(599\) | −38.6159 | −1.57780 | −0.788902 | − | 0.614518i | \(-0.789350\pi\) | ||||
−0.788902 | + | 0.614518i | \(0.789350\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.04839 | 0.0835557 | 0.0417779 | − | 0.999127i | \(-0.486698\pi\) | ||||
0.0417779 | + | 0.999127i | \(0.486698\pi\) | |||||||
\(602\) | −15.5118 | −0.632213 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −85.4186 | −3.47563 | ||||||||
\(605\) | 41.6534 | 1.69345 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.79770 | 0.235321 | 0.117661 | − | 0.993054i | \(-0.462460\pi\) | ||||
0.117661 | + | 0.993054i | \(0.462460\pi\) | |||||||
\(608\) | −1.61981 | −0.0656920 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 29.4277 | 1.19149 | ||||||||
\(611\) | −17.0373 | −0.689257 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 45.3061 | 1.82989 | 0.914947 | − | 0.403573i | \(-0.132232\pi\) | ||||
0.914947 | + | 0.403573i | \(0.132232\pi\) | |||||||
\(614\) | 62.5378 | 2.52382 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 27.1385 | 1.09344 | ||||||||
\(617\) | 22.8349 | 0.919300 | 0.459650 | − | 0.888100i | \(-0.347975\pi\) | ||||
0.459650 | + | 0.888100i | \(0.347975\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.2514 | 0.613007 | 0.306503 | − | 0.951870i | \(-0.400841\pi\) | ||||
0.306503 | + | 0.951870i | \(0.400841\pi\) | |||||||
\(620\) | 84.0360 | 3.37497 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.1680 | 0.808662 | ||||||||
\(623\) | −1.68625 | −0.0675583 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.6737 | −1.02695 | ||||||||
\(626\) | 19.2650 | 0.769983 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 82.7390 | 3.30165 | ||||||||
\(629\) | 0.132830 | 0.00529628 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.2426 | −1.60203 | −0.801016 | − | 0.598643i | \(-0.795707\pi\) | ||||
−0.801016 | + | 0.598643i | \(0.795707\pi\) | |||||||
\(632\) | 24.6797 | 0.981706 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −79.7012 | −3.16534 | ||||||||
\(635\) | 43.3191 | 1.71907 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.23628 | 0.128226 | ||||||||
\(638\) | −107.439 | −4.25355 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −43.6707 | −1.72624 | ||||||||
\(641\) | −8.41075 | −0.332205 | −0.166102 | − | 0.986109i | \(-0.553118\pi\) | ||||
−0.166102 | + | 0.986109i | \(0.553118\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.9146 | −0.943101 | −0.471550 | − | 0.881839i | \(-0.656305\pi\) | ||||
−0.471550 | + | 0.881839i | \(0.656305\pi\) | |||||||
\(644\) | −28.2607 | −1.11363 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 30.0693 | 1.18306 | ||||||||
\(647\) | −10.9669 | −0.431152 | −0.215576 | − | 0.976487i | \(-0.569163\pi\) | ||||
−0.215576 | + | 0.976487i | \(0.569163\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.2924 | −0.521772 | ||||||||
\(650\) | 1.10208 | 0.0432271 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.60164 | −0.258540 | ||||||||
\(653\) | −29.3523 | −1.14865 | −0.574323 | − | 0.818629i | \(-0.694735\pi\) | ||||
−0.574323 | + | 0.818629i | \(0.694735\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.6558 | −0.885234 | ||||||||
\(656\) | 4.22813 | 0.165081 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.9358 | −0.504291 | ||||||||
\(659\) | 12.7905 | 0.498245 | 0.249123 | − | 0.968472i | \(-0.419858\pi\) | ||||
0.249123 | + | 0.968472i | \(0.419858\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.1159 | 0.587942 | 0.293971 | − | 0.955814i | \(-0.405023\pi\) | ||||
0.293971 | + | 0.955814i | \(0.405023\pi\) | |||||||
\(662\) | 34.0509 | 1.32342 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.19146 | 0.317890 | ||||||||
\(665\) | −9.79497 | −0.379833 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 56.4643 | 2.18631 | ||||||||
\(668\) | 80.0463 | 3.09708 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −48.9288 | −1.89028 | ||||||||
\(671\) | 28.6342 | 1.10541 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.3101 | 0.397425 | 0.198713 | − | 0.980058i | \(-0.436324\pi\) | ||||
0.198713 | + | 0.980058i | \(0.436324\pi\) | |||||||
\(674\) | 45.7235 | 1.76120 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.2013 | −0.392359 | ||||||||
\(677\) | 1.97105 | 0.0757535 | 0.0378768 | − | 0.999282i | \(-0.487941\pi\) | ||||
0.0378768 | + | 0.999282i | \(0.487941\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.8278 | 0.722546 | ||||||||
\(680\) | −32.1456 | −1.23273 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 122.273 | 4.68206 | ||||||||
\(683\) | 9.53970 | 0.365026 | 0.182513 | − | 0.983203i | \(-0.441577\pi\) | ||||
0.182513 | + | 0.983203i | \(0.441577\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.5722 | −0.403944 | ||||||||
\(686\) | 2.45719 | 0.0938160 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −26.6914 | −1.01760 | ||||||||
\(689\) | −20.8294 | −0.793538 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.3915 | 0.623562 | 0.311781 | − | 0.950154i | \(-0.399075\pi\) | ||||
0.311781 | + | 0.950154i | \(0.399075\pi\) | |||||||
\(692\) | 37.6077 | 1.42963 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −57.3276 | −2.17613 | ||||||||
\(695\) | −23.5647 | −0.893861 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.83206 | −0.107272 | ||||||||
\(698\) | −13.7497 | −0.520434 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.559591 | 0.0211505 | ||||||||
\(701\) | −12.1383 | −0.458457 | −0.229229 | − | 0.973373i | \(-0.573620\pi\) | ||||
−0.229229 | + | 0.973373i | \(0.573620\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.202663 | 0.00764359 | ||||||||
\(704\) | −40.8394 | −1.53919 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 47.7382 | 1.79665 | ||||||||
\(707\) | −7.44903 | −0.280150 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.6150 | −1.11222 | −0.556108 | − | 0.831110i | \(-0.687706\pi\) | ||||
−0.556108 | + | 0.831110i | \(0.687706\pi\) | |||||||
\(710\) | 67.6008 | 2.53701 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.44344 | −0.316431 | ||||||||
\(713\) | −64.2600 | −2.40656 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 39.7611 | 1.48698 | ||||||||
\(716\) | 70.0388 | 2.61747 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −35.1691 | −1.31250 | ||||||||
\(719\) | −42.0273 | −1.56735 | −0.783676 | − | 0.621169i | \(-0.786658\pi\) | ||||
−0.783676 | + | 0.621169i | \(0.786658\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.68672 | 0.137301 | ||||||||
\(722\) | −0.808971 | −0.0301068 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 40.9249 | 1.52096 | ||||||||
\(725\) | −1.11805 | −0.0415234 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.0718 | −1.52327 | −0.761635 | − | 0.648007i | \(-0.775603\pi\) | ||||
−0.761635 | + | 0.648007i | \(0.775603\pi\) | |||||||
\(728\) | 16.2048 | 0.600589 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13.5349 | 0.500948 | ||||||||
\(731\) | 17.8783 | 0.661252 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.51418 | 0.351414 | 0.175707 | − | 0.984442i | \(-0.443779\pi\) | ||||
0.175707 | + | 0.984442i | \(0.443779\pi\) | |||||||
\(734\) | −52.2051 | −1.92693 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.62375 | −0.0967128 | ||||||||
\(737\) | −47.6094 | −1.75372 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.4606 | −1.67230 | −0.836148 | − | 0.548504i | \(-0.815197\pi\) | ||||
−0.836148 | + | 0.548504i | \(0.815197\pi\) | |||||||
\(740\) | −0.429298 | −0.0157813 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.8150 | −0.580587 | ||||||||
\(743\) | 51.1920 | 1.87805 | 0.939027 | − | 0.343845i | \(-0.111729\pi\) | ||||
0.939027 | + | 0.343845i | \(0.111729\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.1236 | −0.517448 | ||||||||
\(746\) | 69.3595 | 2.53943 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −61.9777 | −2.26613 | ||||||||
\(749\) | 8.58781 | 0.313792 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.2359 | −1.17631 | −0.588153 | − | 0.808750i | \(-0.700145\pi\) | ||||
−0.588153 | + | 0.808750i | \(0.700145\pi\) | |||||||
\(752\) | −22.2589 | −0.811698 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −64.1534 | −2.33633 | ||||||||
\(755\) | −47.9547 | −1.74525 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.3465 | −0.957581 | −0.478790 | − | 0.877929i | \(-0.658925\pi\) | ||||
−0.478790 | + | 0.877929i | \(0.658925\pi\) | |||||||
\(758\) | −21.0737 | −0.765432 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −49.0456 | −1.77907 | ||||||||
\(761\) | 30.0811 | 1.09044 | 0.545219 | − | 0.838293i | \(-0.316446\pi\) | ||||
0.545219 | + | 0.838293i | \(0.316446\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.91912 | −0.105679 | ||||||||
\(764\) | −73.4713 | −2.65810 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.47207 | −0.233845 | ||||||||
\(767\) | −7.93707 | −0.286591 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.608700 | −0.0219503 | −0.0109751 | − | 0.999940i | \(-0.503494\pi\) | ||||
−0.0109751 | + | 0.999940i | \(0.503494\pi\) | |||||||
\(770\) | 30.1891 | 1.08794 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.24708 | 0.188847 | ||||||||
\(773\) | 8.67944 | 0.312178 | 0.156089 | − | 0.987743i | \(-0.450111\pi\) | ||||
0.156089 | + | 0.987743i | \(0.450111\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.27241 | 0.0457064 | ||||||||
\(776\) | 94.2751 | 3.38428 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 32.5962 | 1.16863 | ||||||||
\(779\) | −4.32097 | −0.154815 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 65.7780 | 2.35372 | ||||||||
\(782\) | 48.7059 | 1.74172 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.22813 | 0.151005 | ||||||||
\(785\) | 46.4504 | 1.65789 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.2640 | 1.22138 | 0.610689 | − | 0.791870i | \(-0.290892\pi\) | ||||
0.610689 | + | 0.791870i | \(0.290892\pi\) | |||||||
\(788\) | −22.8005 | −0.812235 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 27.4539 | 0.976766 | ||||||||
\(791\) | 7.03990 | 0.250310 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.0979 | 0.607164 | ||||||||
\(794\) | 5.61719 | 0.199347 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −46.4622 | −1.64681 | ||||||||
\(797\) | −13.1568 | −0.466036 | −0.233018 | − | 0.972472i | \(-0.574860\pi\) | ||||
−0.233018 | + | 0.972472i | \(0.574860\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.9093 | 0.527454 | ||||||||
\(800\) | 0.0519530 | 0.00183681 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.86026 | −0.242244 | ||||||||
\(803\) | 13.1699 | 0.464756 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.8658 | −0.559196 | ||||||||
\(806\) | 73.0106 | 2.57169 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −37.2990 | −1.31217 | ||||||||
\(809\) | 2.04798 | 0.0720033 | 0.0360017 | − | 0.999352i | \(-0.488538\pi\) | ||||
0.0360017 | + | 0.999352i | \(0.488538\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.48050 | 0.192446 | 0.0962232 | − | 0.995360i | \(-0.469324\pi\) | ||||
0.0962232 | + | 0.995360i | \(0.469324\pi\) | |||||||
\(812\) | −32.5745 | −1.14314 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.624629 | −0.0218932 | ||||||||
\(815\) | −3.70622 | −0.129823 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.2775 | 0.954318 | ||||||||
\(818\) | −26.7265 | −0.934471 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.15303 | 0.319638 | ||||||||
\(821\) | 1.55848 | 0.0543913 | 0.0271957 | − | 0.999630i | \(-0.491342\pi\) | ||||
0.0271957 | + | 0.999630i | \(0.491342\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.3703 | 1.37236 | 0.686182 | − | 0.727430i | \(-0.259286\pi\) | ||||
0.686182 | + | 0.727430i | \(0.259286\pi\) | |||||||
\(824\) | 18.4602 | 0.643093 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.02633 | −0.209683 | ||||||||
\(827\) | 26.3888 | 0.917628 | 0.458814 | − | 0.888532i | \(-0.348274\pi\) | ||||
0.458814 | + | 0.888532i | \(0.348274\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.0610 | 1.56503 | 0.782517 | − | 0.622629i | \(-0.213935\pi\) | ||||
0.782517 | + | 0.622629i | \(0.213935\pi\) | |||||||
\(830\) | 9.11224 | 0.316291 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −24.3858 | −0.845425 | ||||||||
\(833\) | −2.83206 | −0.0981251 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 44.9387 | 1.55517 | ||||||||
\(836\) | −94.5613 | −3.27047 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 61.1957 | 2.11397 | ||||||||
\(839\) | 42.0761 | 1.45263 | 0.726314 | − | 0.687363i | \(-0.241232\pi\) | ||||
0.726314 | + | 0.687363i | \(0.241232\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.0831 | 1.24425 | ||||||||
\(842\) | −17.6034 | −0.606655 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −40.0790 | −1.37958 | ||||||||
\(845\) | −5.72712 | −0.197019 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.3751 | 0.631375 | ||||||||
\(848\) | −27.2131 | −0.934503 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.964426 | −0.0330795 | ||||||||
\(851\) | 0.328272 | 0.0112530 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.2803 | −0.694384 | −0.347192 | − | 0.937794i | \(-0.612865\pi\) | ||||
−0.347192 | + | 0.937794i | \(0.612865\pi\) | |||||||
\(854\) | 12.9818 | 0.444228 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 43.0011 | 1.46975 | ||||||||
\(857\) | 49.2604 | 1.68270 | 0.841351 | − | 0.540490i | \(-0.181761\pi\) | ||||
0.841351 | + | 0.540490i | \(0.181761\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.7326 | −0.434430 | −0.217215 | − | 0.976124i | \(-0.569697\pi\) | ||||
−0.217215 | + | 0.976124i | \(0.569697\pi\) | |||||||
\(860\) | −57.7814 | −1.97033 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 36.0072 | 1.22641 | ||||||||
\(863\) | 14.7535 | 0.502216 | 0.251108 | − | 0.967959i | \(-0.419205\pi\) | ||||
0.251108 | + | 0.967959i | \(0.419205\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.1133 | 0.717872 | ||||||||
\(866\) | −72.2838 | −2.45630 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 37.0718 | 1.25830 | ||||||||
\(869\) | 26.7136 | 0.906197 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.4282 | −0.963254 | ||||||||
\(872\) | −14.6167 | −0.494982 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 74.3122 | 2.51365 | ||||||||
\(875\) | −11.0201 | −0.372546 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.7432 | −0.700450 | −0.350225 | − | 0.936666i | \(-0.613895\pi\) | ||||
−0.350225 | + | 0.936666i | \(0.613895\pi\) | |||||||
\(878\) | 65.2648 | 2.20258 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 51.9469 | 1.75113 | ||||||||
\(881\) | 19.5041 | 0.657110 | 0.328555 | − | 0.944485i | \(-0.393438\pi\) | ||||
0.328555 | + | 0.944485i | \(0.393438\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.7626 | 0.934286 | 0.467143 | − | 0.884182i | \(-0.345283\pi\) | ||||
0.467143 | + | 0.884182i | \(0.345283\pi\) | |||||||
\(884\) | −37.0077 | −1.24470 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30.0693 | 1.01020 | ||||||||
\(887\) | −35.3228 | −1.18602 | −0.593012 | − | 0.805194i | \(-0.702061\pi\) | ||||
−0.593012 | + | 0.805194i | \(0.702061\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.1099 | 0.640924 | ||||||||
\(890\) | −9.39254 | −0.314839 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −47.7394 | −1.59843 | ||||||||
\(893\) | 22.7476 | 0.761221 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 39.3204 | 1.31434 | ||||||||
\(896\) | −19.2650 | −0.643598 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 57.5802 | 1.92148 | ||||||||
\(899\) | −74.0687 | −2.47033 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.2278 | 0.607255 | ||||||||
\(902\) | 13.3177 | 0.443430 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 35.2503 | 1.17241 | ||||||||
\(905\) | 22.9756 | 0.763734 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.5803 | 0.351312 | 0.175656 | − | 0.984452i | \(-0.443795\pi\) | ||||
0.175656 | + | 0.984452i | \(0.443795\pi\) | |||||||
\(908\) | −6.47156 | −0.214766 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 18.0263 | 0.597567 | ||||||||
\(911\) | 18.0853 | 0.599192 | 0.299596 | − | 0.954066i | \(-0.403148\pi\) | ||||
0.299596 | + | 0.954066i | \(0.403148\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.86654 | 0.293440 | ||||||||
\(914\) | −20.2872 | −0.671041 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −40.1093 | −1.32525 | ||||||||
\(917\) | −9.99440 | −0.330044 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.90775 | 0.326826 | 0.163413 | − | 0.986558i | \(-0.447750\pi\) | ||||
0.163413 | + | 0.986558i | \(0.447750\pi\) | |||||||
\(920\) | −79.4436 | −2.61918 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 21.6046 | 0.711508 | ||||||||
\(923\) | 39.2770 | 1.29282 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.00650012 | −0.000213722 0 | ||||||||
\(926\) | 90.6419 | 2.97868 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.02425 | −0.0992757 | ||||||||
\(929\) | 15.2665 | 0.500878 | 0.250439 | − | 0.968132i | \(-0.419425\pi\) | ||||
0.250439 | + | 0.968132i | \(0.419425\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.32097 | −0.141614 | ||||||||
\(932\) | 31.9489 | 1.04652 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 53.7641 | 1.75921 | ||||||||
\(935\) | −34.7948 | −1.13791 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.2126 | 0.692985 | 0.346492 | − | 0.938053i | \(-0.387373\pi\) | ||||
0.346492 | + | 0.938053i | \(0.387373\pi\) | |||||||
\(938\) | −21.5845 | −0.704759 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −48.1859 | −1.57165 | ||||||||
\(941\) | 34.1282 | 1.11255 | 0.556274 | − | 0.830999i | \(-0.312230\pi\) | ||||
0.556274 | + | 0.830999i | \(0.312230\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.99907 | −0.227921 | ||||||||
\(944\) | −10.3696 | −0.337502 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −84.0720 | −2.73342 | ||||||||
\(947\) | 18.3584 | 0.596567 | 0.298284 | − | 0.954477i | \(-0.403586\pi\) | ||||
0.298284 | + | 0.954477i | \(0.403586\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.86394 | 0.255274 | ||||||||
\(950\) | −1.47146 | −0.0477403 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −14.1808 | −0.459601 | ||||||||
\(953\) | 16.0790 | 0.520849 | 0.260424 | − | 0.965494i | \(-0.416138\pi\) | ||||
0.260424 | + | 0.965494i | \(0.416138\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −41.2474 | −1.33473 | ||||||||
\(956\) | −109.785 | −3.55069 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −84.4482 | −2.72840 | ||||||||
\(959\) | −4.66385 | −0.150603 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53.2949 | 1.71919 | ||||||||
\(962\) | −0.372974 | −0.0120252 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 78.3386 | 2.52312 | ||||||||
\(965\) | 2.94576 | 0.0948273 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.0340 | 1.22309 | 0.611546 | − | 0.791209i | \(-0.290548\pi\) | ||||
0.611546 | + | 0.791209i | \(0.290548\pi\) | |||||||
\(968\) | 92.0080 | 2.95725 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 104.872 | 3.36725 | ||||||||
\(971\) | −60.7488 | −1.94952 | −0.974761 | − | 0.223250i | \(-0.928333\pi\) | ||||
−0.974761 | + | 0.223250i | \(0.928333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.3954 | −0.333261 | ||||||||
\(974\) | 39.2129 | 1.25646 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.3380 | 0.715021 | ||||||||
\(977\) | 4.23580 | 0.135515 | 0.0677576 | − | 0.997702i | \(-0.478416\pi\) | ||||
0.0677576 | + | 0.997702i | \(0.478416\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.13928 | −0.292093 | ||||||||
\(980\) | 9.15303 | 0.292383 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.17386 | 0.133193 | ||||||||
\(983\) | 7.21490 | 0.230120 | 0.115060 | − | 0.993359i | \(-0.463294\pi\) | ||||
0.115060 | + | 0.993359i | \(0.463294\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.8004 | −0.407855 | ||||||||
\(986\) | 56.1404 | 1.78788 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −56.4639 | −1.79636 | ||||||||
\(989\) | 44.1838 | 1.40496 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.9196 | −0.664533 | −0.332267 | − | 0.943186i | \(-0.607813\pi\) | ||||
−0.332267 | + | 0.943186i | \(0.607813\pi\) | |||||||
\(992\) | 3.44178 | 0.109277 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 29.8215 | 0.945882 | ||||||||
\(995\) | −26.0843 | −0.826927 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.4455 | −0.584175 | −0.292088 | − | 0.956392i | \(-0.594350\pi\) | ||||
−0.292088 | + | 0.956392i | \(0.594350\pi\) | |||||||
\(998\) | −56.6432 | −1.79301 | ||||||||
\(999\) | 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 | 2583.2.a.r.1.5 | 5 | ||
3.2 | odd | 2 | 287.2.a.e.1.1 | ✓ | 5 | ||
12.11 | even | 2 | 4592.2.a.bb.1.5 | 5 | |||
15.14 | odd | 2 | 7175.2.a.n.1.5 | 5 | |||
21.20 | even | 2 | 2009.2.a.n.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.a.e.1.1 | ✓ | 5 | 3.2 | odd | 2 | ||
2009.2.a.n.1.1 | 5 | 21.20 | even | 2 | |||
2583.2.a.r.1.5 | 5 | 1.1 | even | 1 | trivial | ||
4592.2.a.bb.1.5 | 5 | 12.11 | even | 2 | |||
7175.2.a.n.1.5 | 5 | 15.14 | odd | 2 |