Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7605,2,Mod(1,7605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7605, 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("7605.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7605.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: | \(60.7262307372\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.3352656.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 6x^{3} + 10x^{2} + 6x - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 585) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.63209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7605.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.63209 | −1.86117 | −0.930584 | − | 0.366079i | \(-0.880700\pi\) | ||||
−0.930584 | + | 0.366079i | \(0.880700\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.92789 | 2.46394 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.08975 | −0.411887 | −0.205943 | − | 0.978564i | \(-0.566026\pi\) | ||||
−0.205943 | + | 0.978564i | \(0.566026\pi\) | |||||||
\(8\) | −7.70645 | −2.72464 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.63209 | 0.832339 | ||||||||
\(11\) | −4.72184 | −1.42369 | −0.711844 | − | 0.702338i | \(-0.752140\pi\) | ||||
−0.711844 | + | 0.702338i | \(0.752140\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.86832 | 0.766590 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 10.4283 | 2.60707 | ||||||||
\(17\) | 5.22369 | 1.26693 | 0.633465 | − | 0.773771i | \(-0.281632\pi\) | ||||
0.633465 | + | 0.773771i | \(0.281632\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.92789 | −0.671703 | −0.335852 | − | 0.941915i | \(-0.609024\pi\) | ||||
−0.335852 | + | 0.941915i | \(0.609024\pi\) | |||||||
\(20\) | −4.92789 | −1.10191 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 12.4283 | 2.64972 | ||||||||
\(23\) | −7.70645 | −1.60691 | −0.803453 | − | 0.595368i | \(-0.797006\pi\) | ||||
−0.803453 | + | 0.595368i | \(0.797006\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.37017 | −1.01487 | ||||||||
\(29\) | 1.31118 | 0.243480 | 0.121740 | − | 0.992562i | \(-0.461153\pi\) | ||||
0.121740 | + | 0.992562i | \(0.461153\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.32091 | 0.416847 | 0.208423 | − | 0.978039i | \(-0.433167\pi\) | ||||
0.208423 | + | 0.978039i | \(0.433167\pi\) | |||||||
\(32\) | −12.0353 | −2.12756 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −13.7492 | −2.35797 | ||||||||
\(35\) | 1.08975 | 0.184201 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.4283 | 1.71440 | 0.857200 | − | 0.514983i | \(-0.172202\pi\) | ||||
0.857200 | + | 0.514983i | \(0.172202\pi\) | |||||||
\(38\) | 7.70645 | 1.25015 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.70645 | 1.21850 | ||||||||
\(41\) | −4.98745 | −0.778910 | −0.389455 | − | 0.921046i | \(-0.627337\pi\) | ||||
−0.389455 | + | 0.921046i | \(0.627337\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.96838 | 0.910169 | 0.455084 | − | 0.890448i | \(-0.349609\pi\) | ||||
0.455084 | + | 0.890448i | \(0.349609\pi\) | |||||||
\(44\) | −23.2687 | −3.50789 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 20.2841 | 2.99072 | ||||||||
\(47\) | 8.51804 | 1.24248 | 0.621242 | − | 0.783619i | \(-0.286628\pi\) | ||||
0.621242 | + | 0.783619i | \(0.286628\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.81244 | −0.830349 | ||||||||
\(50\) | −2.63209 | −0.372233 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.67627 | −1.32914 | −0.664569 | − | 0.747227i | \(-0.731385\pi\) | ||||
−0.664569 | + | 0.747227i | \(0.731385\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.72184 | 0.636693 | ||||||||
\(56\) | 8.39811 | 1.12224 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.45115 | −0.453158 | ||||||||
\(59\) | 3.16696 | 0.412302 | 0.206151 | − | 0.978520i | \(-0.433906\pi\) | ||||
0.206151 | + | 0.978520i | \(0.433906\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.32091 | 0.809309 | 0.404655 | − | 0.914470i | \(-0.367392\pi\) | ||||
0.404655 | + | 0.914470i | \(0.367392\pi\) | |||||||
\(62\) | −6.10883 | −0.775822 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 10.8213 | 1.35266 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.57536 | 0.192461 | 0.0962303 | − | 0.995359i | \(-0.469321\pi\) | ||||
0.0962303 | + | 0.995359i | \(0.469321\pi\) | |||||||
\(68\) | 25.7417 | 3.12164 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.86832 | −0.342830 | ||||||||
\(71\) | 6.00225 | 0.712336 | 0.356168 | − | 0.934422i | \(-0.384083\pi\) | ||||
0.356168 | + | 0.934422i | \(0.384083\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.3098 | −1.44075 | −0.720374 | − | 0.693586i | \(-0.756030\pi\) | ||||
−0.720374 | + | 0.693586i | \(0.756030\pi\) | |||||||
\(74\) | −27.4482 | −3.19079 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.4283 | −1.65504 | ||||||||
\(77\) | 5.14562 | 0.586398 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.04333 | −0.342401 | −0.171201 | − | 0.985236i | \(-0.554765\pi\) | ||||
−0.171201 | + | 0.985236i | \(0.554765\pi\) | |||||||
\(80\) | −10.4283 | −1.16592 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 13.1274 | 1.44968 | ||||||||
\(83\) | 1.40782 | 0.154528 | 0.0772640 | − | 0.997011i | \(-0.475382\pi\) | ||||
0.0772640 | + | 0.997011i | \(0.475382\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.22369 | −0.566588 | ||||||||
\(86\) | −15.7093 | −1.69398 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 36.3886 | 3.87904 | ||||||||
\(89\) | 8.67483 | 0.919530 | 0.459765 | − | 0.888041i | \(-0.347934\pi\) | ||||
0.459765 | + | 0.888041i | \(0.347934\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −37.9765 | −3.95933 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −22.4202 | −2.31247 | ||||||||
\(95\) | 2.92789 | 0.300395 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.0324 | 1.12017 | 0.560087 | − | 0.828434i | \(-0.310768\pi\) | ||||
0.560087 | + | 0.828434i | \(0.310768\pi\) | |||||||
\(98\) | 15.2989 | 1.54542 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.92789 | 0.492789 | ||||||||
\(101\) | −9.21492 | −0.916918 | −0.458459 | − | 0.888715i | \(-0.651598\pi\) | ||||
−0.458459 | + | 0.888715i | \(0.651598\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.8586 | 1.46406 | 0.732031 | − | 0.681271i | \(-0.238572\pi\) | ||||
0.732031 | + | 0.681271i | \(0.238572\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 25.4688 | 2.47375 | ||||||||
\(107\) | 6.89487 | 0.666552 | 0.333276 | − | 0.942829i | \(-0.391846\pi\) | ||||
0.333276 | + | 0.942829i | \(0.391846\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.5790 | 1.39642 | 0.698208 | − | 0.715895i | \(-0.253981\pi\) | ||||
0.698208 | + | 0.715895i | \(0.253981\pi\) | |||||||
\(110\) | −12.4283 | −1.18499 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −11.3642 | −1.07382 | ||||||||
\(113\) | 13.2938 | 1.25057 | 0.625286 | − | 0.780395i | \(-0.284982\pi\) | ||||
0.625286 | + | 0.780395i | \(0.284982\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.70645 | 0.718631 | ||||||||
\(116\) | 6.46136 | 0.599922 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.33570 | −0.767364 | ||||||||
\(119\) | −5.69251 | −0.521832 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.2958 | 1.02689 | ||||||||
\(122\) | −16.6372 | −1.50626 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 11.4372 | 1.02709 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.4548 | 1.37139 | 0.685696 | − | 0.727888i | \(-0.259498\pi\) | ||||
0.685696 | + | 0.727888i | \(0.259498\pi\) | |||||||
\(128\) | −4.41210 | −0.389978 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.48870 | −0.741661 | −0.370831 | − | 0.928701i | \(-0.620927\pi\) | ||||
−0.370831 | + | 0.928701i | \(0.620927\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.19067 | 0.276666 | ||||||||
\(134\) | −4.14648 | −0.358201 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −40.2561 | −3.45193 | ||||||||
\(137\) | 5.72185 | 0.488851 | 0.244426 | − | 0.969668i | \(-0.421401\pi\) | ||||
0.244426 | + | 0.969668i | \(0.421401\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.3938 | −1.56014 | −0.780072 | − | 0.625689i | \(-0.784818\pi\) | ||||
−0.780072 | + | 0.625689i | \(0.784818\pi\) | |||||||
\(140\) | 5.37017 | 0.453862 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −15.7985 | −1.32578 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.31118 | −0.108888 | ||||||||
\(146\) | 32.4004 | 2.68147 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 51.3894 | 4.22419 | ||||||||
\(149\) | −22.6603 | −1.85640 | −0.928202 | − | 0.372076i | \(-0.878646\pi\) | ||||
−0.928202 | + | 0.372076i | \(0.878646\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.26871 | 0.184625 | 0.0923125 | − | 0.995730i | \(-0.470574\pi\) | ||||
0.0923125 | + | 0.995730i | \(0.470574\pi\) | |||||||
\(152\) | 22.5636 | 1.83015 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −13.5437 | −1.09139 | ||||||||
\(155\) | −2.32091 | −0.186420 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.8934 | −1.10882 | −0.554409 | − | 0.832245i | \(-0.687056\pi\) | ||||
−0.554409 | + | 0.832245i | \(0.687056\pi\) | |||||||
\(158\) | 8.01031 | 0.637266 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.0353 | 0.951472 | ||||||||
\(161\) | 8.39811 | 0.661864 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24.6218 | −1.92853 | −0.964264 | − | 0.264943i | \(-0.914647\pi\) | ||||
−0.964264 | + | 0.264943i | \(0.914647\pi\) | |||||||
\(164\) | −24.5776 | −1.91919 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.70550 | −0.287603 | ||||||||
\(167\) | −3.79988 | −0.294044 | −0.147022 | − | 0.989133i | \(-0.546969\pi\) | ||||
−0.147022 | + | 0.989133i | \(0.546969\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 13.7492 | 1.05452 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 29.4115 | 2.24260 | ||||||||
\(173\) | 18.0803 | 1.37462 | 0.687309 | − | 0.726365i | \(-0.258792\pi\) | ||||
0.687309 | + | 0.726365i | \(0.258792\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.08975 | −0.0823774 | ||||||||
\(176\) | −49.2407 | −3.71166 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −22.8329 | −1.71140 | ||||||||
\(179\) | 25.6449 | 1.91679 | 0.958394 | − | 0.285448i | \(-0.0921425\pi\) | ||||
0.958394 | + | 0.285448i | \(0.0921425\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.0957 | −1.41937 | −0.709686 | − | 0.704518i | \(-0.751163\pi\) | ||||
−0.709686 | + | 0.704518i | \(0.751163\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 59.3894 | 4.37825 | ||||||||
\(185\) | −10.4283 | −0.766703 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −24.6654 | −1.80371 | ||||||||
\(188\) | 41.9759 | 3.06141 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.70645 | −0.559085 | ||||||||
\(191\) | −24.1538 | −1.74771 | −0.873853 | − | 0.486190i | \(-0.838386\pi\) | ||||
−0.873853 | + | 0.486190i | \(0.838386\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.7956 | −0.921049 | −0.460524 | − | 0.887647i | \(-0.652339\pi\) | ||||
−0.460524 | + | 0.887647i | \(0.652339\pi\) | |||||||
\(194\) | −29.0383 | −2.08483 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −28.6431 | −2.04593 | ||||||||
\(197\) | −0.652546 | −0.0464920 | −0.0232460 | − | 0.999730i | \(-0.507400\pi\) | ||||
−0.0232460 | + | 0.999730i | \(0.507400\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.38779 | −0.452818 | −0.226409 | − | 0.974032i | \(-0.572699\pi\) | ||||
−0.226409 | + | 0.974032i | \(0.572699\pi\) | |||||||
\(200\) | −7.70645 | −0.544929 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 24.2545 | 1.70654 | ||||||||
\(203\) | −1.42886 | −0.100286 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.98745 | 0.348339 | ||||||||
\(206\) | −39.1092 | −2.72487 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.8250 | 0.956296 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.4976 | −1.20458 | −0.602292 | − | 0.798276i | \(-0.705746\pi\) | ||||
−0.602292 | + | 0.798276i | \(0.705746\pi\) | |||||||
\(212\) | −47.6836 | −3.27492 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.1479 | −1.24056 | ||||||||
\(215\) | −5.96838 | −0.407040 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.52921 | −0.171694 | ||||||||
\(218\) | −38.3732 | −2.59896 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 23.2687 | 1.56877 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.65350 | 0.177692 | 0.0888458 | − | 0.996045i | \(-0.471682\pi\) | ||||
0.0888458 | + | 0.996045i | \(0.471682\pi\) | |||||||
\(224\) | 13.1154 | 0.876312 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −34.9904 | −2.32753 | ||||||||
\(227\) | 5.10964 | 0.339139 | 0.169569 | − | 0.985518i | \(-0.445762\pi\) | ||||
0.169569 | + | 0.985518i | \(0.445762\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.2929 | −1.14275 | −0.571375 | − | 0.820689i | \(-0.693590\pi\) | ||||
−0.571375 | + | 0.820689i | \(0.693590\pi\) | |||||||
\(230\) | −20.2841 | −1.33749 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.1046 | −0.663397 | ||||||||
\(233\) | 2.40701 | 0.157688 | 0.0788441 | − | 0.996887i | \(-0.474877\pi\) | ||||
0.0788441 | + | 0.996887i | \(0.474877\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.51804 | −0.555656 | ||||||||
\(236\) | 15.6064 | 1.01589 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 14.9832 | 0.971216 | ||||||||
\(239\) | −8.83530 | −0.571508 | −0.285754 | − | 0.958303i | \(-0.592244\pi\) | ||||
−0.285754 | + | 0.958303i | \(0.592244\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.54054 | 0.550145 | 0.275072 | − | 0.961424i | \(-0.411298\pi\) | ||||
0.275072 | + | 0.961424i | \(0.411298\pi\) | |||||||
\(242\) | −29.7314 | −1.91121 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 31.1487 | 1.99409 | ||||||||
\(245\) | 5.81244 | 0.371343 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −17.8860 | −1.13576 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.63209 | 0.166468 | ||||||||
\(251\) | 2.54513 | 0.160647 | 0.0803237 | − | 0.996769i | \(-0.474405\pi\) | ||||
0.0803237 | + | 0.996769i | \(0.474405\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 36.3886 | 2.28773 | ||||||||
\(254\) | −40.6784 | −2.55239 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.0296 | −0.626850 | ||||||||
\(257\) | 12.0513 | 0.751737 | 0.375868 | − | 0.926673i | \(-0.377344\pi\) | ||||
0.375868 | + | 0.926673i | \(0.377344\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.3642 | −0.706139 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 22.3430 | 1.38036 | ||||||||
\(263\) | −10.4729 | −0.645788 | −0.322894 | − | 0.946435i | \(-0.604656\pi\) | ||||
−0.322894 | + | 0.946435i | \(0.604656\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.67627 | 0.594409 | ||||||||
\(266\) | −8.39811 | −0.514921 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.76318 | 0.474212 | ||||||||
\(269\) | 8.92325 | 0.544060 | 0.272030 | − | 0.962289i | \(-0.412305\pi\) | ||||
0.272030 | + | 0.962289i | \(0.412305\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.77479 | −0.411539 | −0.205770 | − | 0.978600i | \(-0.565970\pi\) | ||||
−0.205770 | + | 0.978600i | \(0.565970\pi\) | |||||||
\(272\) | 54.4741 | 3.30298 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.0604 | −0.909834 | ||||||||
\(275\) | −4.72184 | −0.284738 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.63658 | −0.338669 | −0.169335 | − | 0.985559i | \(-0.554162\pi\) | ||||
−0.169335 | + | 0.985559i | \(0.554162\pi\) | |||||||
\(278\) | 48.4142 | 2.90369 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.39811 | −0.501883 | ||||||||
\(281\) | 12.5297 | 0.747456 | 0.373728 | − | 0.927538i | \(-0.378079\pi\) | ||||
0.373728 | + | 0.927538i | \(0.378079\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.3442 | 1.50656 | 0.753279 | − | 0.657701i | \(-0.228471\pi\) | ||||
0.753279 | + | 0.657701i | \(0.228471\pi\) | |||||||
\(284\) | 29.5784 | 1.75516 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.43508 | 0.320823 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.2869 | 0.605111 | ||||||||
\(290\) | 3.45115 | 0.202658 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −60.6611 | −3.54992 | ||||||||
\(293\) | −17.8455 | −1.04254 | −0.521272 | − | 0.853391i | \(-0.674542\pi\) | ||||
−0.521272 | + | 0.853391i | \(0.674542\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.16696 | −0.184387 | ||||||||
\(296\) | −80.3652 | −4.67113 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 59.6439 | 3.45508 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.50404 | −0.374887 | ||||||||
\(302\) | −5.97144 | −0.343618 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −30.5329 | −1.75118 | ||||||||
\(305\) | −6.32091 | −0.361934 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.0377 | −0.572880 | −0.286440 | − | 0.958098i | \(-0.592472\pi\) | ||||
−0.286440 | + | 0.958098i | \(0.592472\pi\) | |||||||
\(308\) | 25.3571 | 1.44485 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.10883 | 0.346958 | ||||||||
\(311\) | 8.76317 | 0.496914 | 0.248457 | − | 0.968643i | \(-0.420077\pi\) | ||||
0.248457 | + | 0.968643i | \(0.420077\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.37893 | 0.247512 | 0.123756 | − | 0.992313i | \(-0.460506\pi\) | ||||
0.123756 | + | 0.992313i | \(0.460506\pi\) | |||||||
\(314\) | 36.5688 | 2.06369 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.9972 | −0.843657 | ||||||||
\(317\) | −11.7036 | −0.657338 | −0.328669 | − | 0.944445i | \(-0.606600\pi\) | ||||
−0.328669 | + | 0.944445i | \(0.606600\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.19119 | −0.346640 | ||||||||
\(320\) | −10.8213 | −0.604930 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −22.1046 | −1.23184 | ||||||||
\(323\) | −15.2944 | −0.851001 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 64.8067 | 3.58931 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 38.4356 | 2.12225 | ||||||||
\(329\) | −9.28254 | −0.511763 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.7232 | 0.699332 | 0.349666 | − | 0.936874i | \(-0.386295\pi\) | ||||
0.349666 | + | 0.936874i | \(0.386295\pi\) | |||||||
\(332\) | 6.93757 | 0.380748 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.0016 | 0.547265 | ||||||||
\(335\) | −1.57536 | −0.0860710 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.03730 | −0.219926 | −0.109963 | − | 0.993936i | \(-0.535073\pi\) | ||||
−0.109963 | + | 0.993936i | \(0.535073\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −25.7417 | −1.39604 | ||||||||
\(341\) | −10.9589 | −0.593460 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.9624 | 0.753897 | ||||||||
\(344\) | −45.9950 | −2.47989 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −47.5889 | −2.55839 | ||||||||
\(347\) | 0.344344 | 0.0184854 | 0.00924268 | − | 0.999957i | \(-0.497058\pi\) | ||||
0.00924268 | + | 0.999957i | \(0.497058\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.6402 | 1.85425 | 0.927125 | − | 0.374752i | \(-0.122272\pi\) | ||||
0.927125 | + | 0.374752i | \(0.122272\pi\) | |||||||
\(350\) | 2.86832 | 0.153318 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 56.8286 | 3.02898 | ||||||||
\(353\) | 17.8402 | 0.949541 | 0.474770 | − | 0.880110i | \(-0.342531\pi\) | ||||
0.474770 | + | 0.880110i | \(0.342531\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00225 | −0.318567 | ||||||||
\(356\) | 42.7486 | 2.26567 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −67.4996 | −3.56746 | ||||||||
\(359\) | 7.22285 | 0.381207 | 0.190604 | − | 0.981667i | \(-0.438955\pi\) | ||||
0.190604 | + | 0.981667i | \(0.438955\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.4275 | −0.548815 | ||||||||
\(362\) | 50.2616 | 2.64169 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.3098 | 0.644322 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.7505 | −1.55296 | −0.776481 | − | 0.630141i | \(-0.782997\pi\) | ||||
−0.776481 | + | 0.630141i | \(0.782997\pi\) | |||||||
\(368\) | −80.3652 | −4.18932 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 27.4482 | 1.42696 | ||||||||
\(371\) | 10.5447 | 0.547455 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.84177 | 0.198919 | 0.0994597 | − | 0.995042i | \(-0.468289\pi\) | ||||
0.0994597 | + | 0.995042i | \(0.468289\pi\) | |||||||
\(374\) | 64.9215 | 3.35701 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −65.6439 | −3.38533 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.1026 | −1.59763 | −0.798816 | − | 0.601576i | \(-0.794540\pi\) | ||||
−0.798816 | + | 0.601576i | \(0.794540\pi\) | |||||||
\(380\) | 14.4283 | 0.740156 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 63.5749 | 3.25277 | ||||||||
\(383\) | −12.9609 | −0.662271 | −0.331136 | − | 0.943583i | \(-0.607432\pi\) | ||||
−0.331136 | + | 0.943583i | \(0.607432\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.14562 | −0.262245 | ||||||||
\(386\) | 33.6792 | 1.71423 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 54.3666 | 2.76005 | ||||||||
\(389\) | 14.1302 | 0.716432 | 0.358216 | − | 0.933639i | \(-0.383385\pi\) | ||||
0.358216 | + | 0.933639i | \(0.383385\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −40.2561 | −2.03584 | ||||||||
\(392\) | 44.7933 | 2.26241 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.71756 | 0.0865294 | ||||||||
\(395\) | 3.04333 | 0.153126 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.3100 | 1.42084 | 0.710419 | − | 0.703779i | \(-0.248505\pi\) | ||||
0.710419 | + | 0.703779i | \(0.248505\pi\) | |||||||
\(398\) | 16.8132 | 0.842770 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.4283 | 0.521415 | ||||||||
\(401\) | −4.43551 | −0.221499 | −0.110749 | − | 0.993848i | \(-0.535325\pi\) | ||||
−0.110749 | + | 0.993848i | \(0.535325\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −45.4101 | −2.25923 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.76089 | 0.186650 | ||||||||
\(407\) | −49.2407 | −2.44077 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.96839 | 0.443459 | 0.221729 | − | 0.975108i | \(-0.428830\pi\) | ||||
0.221729 | + | 0.975108i | \(0.428830\pi\) | |||||||
\(410\) | −13.1274 | −0.648317 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 73.2216 | 3.60737 | ||||||||
\(413\) | −3.45119 | −0.169822 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.40782 | −0.0691071 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −36.3886 | −1.77983 | ||||||||
\(419\) | −34.3921 | −1.68016 | −0.840081 | − | 0.542461i | \(-0.817493\pi\) | ||||
−0.840081 | + | 0.542461i | \(0.817493\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.1940 | −0.984198 | −0.492099 | − | 0.870539i | \(-0.663770\pi\) | ||||
−0.492099 | + | 0.870539i | \(0.663770\pi\) | |||||||
\(422\) | 46.0552 | 2.24193 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 74.5698 | 3.62143 | ||||||||
\(425\) | 5.22369 | 0.253386 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.88821 | −0.333344 | ||||||||
\(428\) | 33.9771 | 1.64235 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 15.7093 | 0.757569 | ||||||||
\(431\) | −20.7692 | −1.00042 | −0.500208 | − | 0.865905i | \(-0.666743\pi\) | ||||
−0.500208 | + | 0.865905i | \(0.666743\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.6923 | 1.76332 | 0.881661 | − | 0.471884i | \(-0.156426\pi\) | ||||
0.881661 | + | 0.471884i | \(0.156426\pi\) | |||||||
\(434\) | 6.65710 | 0.319551 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 71.8437 | 3.44069 | ||||||||
\(437\) | 22.5636 | 1.07936 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.2986 | −0.968800 | −0.484400 | − | 0.874847i | \(-0.660962\pi\) | ||||
−0.484400 | + | 0.874847i | \(0.660962\pi\) | |||||||
\(440\) | −36.3886 | −1.73476 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.0068 | −0.475439 | −0.237720 | − | 0.971334i | \(-0.576400\pi\) | ||||
−0.237720 | + | 0.971334i | \(0.576400\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.67483 | −0.411226 | ||||||||
\(446\) | −6.98425 | −0.330714 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −11.7925 | −0.557145 | ||||||||
\(449\) | 10.5636 | 0.498528 | 0.249264 | − | 0.968436i | \(-0.419811\pi\) | ||||
0.249264 | + | 0.968436i | \(0.419811\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.5500 | 1.10892 | ||||||||
\(452\) | 65.5102 | 3.08134 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.4490 | −0.631194 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.81290 | 0.225138 | 0.112569 | − | 0.993644i | \(-0.464092\pi\) | ||||
0.112569 | + | 0.993644i | \(0.464092\pi\) | |||||||
\(458\) | 45.5165 | 2.12685 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 37.9765 | 1.77067 | ||||||||
\(461\) | 19.5639 | 0.911181 | 0.455591 | − | 0.890189i | \(-0.349428\pi\) | ||||
0.455591 | + | 0.890189i | \(0.349428\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.03118 | −0.0479230 | −0.0239615 | − | 0.999713i | \(-0.507628\pi\) | ||||
−0.0239615 | + | 0.999713i | \(0.507628\pi\) | |||||||
\(464\) | 13.6734 | 0.634771 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.33545 | −0.293484 | ||||||||
\(467\) | 12.4884 | 0.577896 | 0.288948 | − | 0.957345i | \(-0.406694\pi\) | ||||
0.288948 | + | 0.957345i | \(0.406694\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.71675 | −0.0792720 | ||||||||
\(470\) | 22.4202 | 1.03417 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −24.4060 | −1.12338 | ||||||||
\(473\) | −28.1817 | −1.29580 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.92789 | −0.134341 | ||||||||
\(476\) | −28.0521 | −1.28576 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 23.2553 | 1.06367 | ||||||||
\(479\) | −6.64403 | −0.303574 | −0.151787 | − | 0.988413i | \(-0.548503\pi\) | ||||
−0.151787 | + | 0.988413i | \(0.548503\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −22.4795 | −1.02391 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 55.6642 | 2.53019 | ||||||||
\(485\) | −11.0324 | −0.500957 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.826873 | −0.0374692 | −0.0187346 | − | 0.999824i | \(-0.505964\pi\) | ||||
−0.0187346 | + | 0.999824i | \(0.505964\pi\) | |||||||
\(488\) | −48.7118 | −2.20508 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −15.2989 | −0.691132 | ||||||||
\(491\) | 12.8198 | 0.578550 | 0.289275 | − | 0.957246i | \(-0.406586\pi\) | ||||
0.289275 | + | 0.957246i | \(0.406586\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.84920 | 0.308473 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 24.2031 | 1.08675 | ||||||||
\(497\) | −6.54096 | −0.293402 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.8651 | −0.889283 | −0.444642 | − | 0.895709i | \(-0.646669\pi\) | ||||
−0.444642 | + | 0.895709i | \(0.646669\pi\) | |||||||
\(500\) | −4.92789 | −0.220382 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.69901 | −0.298992 | ||||||||
\(503\) | 18.7090 | 0.834194 | 0.417097 | − | 0.908862i | \(-0.363048\pi\) | ||||
0.417097 | + | 0.908862i | \(0.363048\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.21492 | 0.410058 | ||||||||
\(506\) | −95.7781 | −4.25785 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 76.1595 | 3.37903 | ||||||||
\(509\) | 10.0362 | 0.444848 | 0.222424 | − | 0.974950i | \(-0.428603\pi\) | ||||
0.222424 | + | 0.974950i | \(0.428603\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.4146 | 0.593425 | ||||||||
\(512\) | 35.2230 | 1.55665 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −31.7200 | −1.39911 | ||||||||
\(515\) | −14.8586 | −0.654749 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −40.2208 | −1.76891 | ||||||||
\(518\) | 29.9117 | 1.31424 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.06270 | −0.0903687 | −0.0451844 | − | 0.998979i | \(-0.514388\pi\) | ||||
−0.0451844 | + | 0.998979i | \(0.514388\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.0369 | −1.40088 | −0.700438 | − | 0.713713i | \(-0.747012\pi\) | ||||
−0.700438 | + | 0.713713i | \(0.747012\pi\) | |||||||
\(524\) | −41.8314 | −1.82741 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.5656 | 1.20192 | ||||||||
\(527\) | 12.1237 | 0.528116 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 36.3894 | 1.58215 | ||||||||
\(530\) | −25.4688 | −1.10629 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 15.7232 | 0.681689 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.89487 | −0.298091 | ||||||||
\(536\) | −12.1404 | −0.524386 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −23.4868 | −1.01259 | ||||||||
\(539\) | 27.4454 | 1.18216 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.1795 | 0.480644 | 0.240322 | − | 0.970693i | \(-0.422747\pi\) | ||||
0.240322 | + | 0.970693i | \(0.422747\pi\) | |||||||
\(542\) | 17.8318 | 0.765943 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −62.8685 | −2.69546 | ||||||||
\(545\) | −14.5790 | −0.624496 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.0903080 | −0.00386129 | −0.00193064 | − | 0.999998i | \(-0.500615\pi\) | ||||
−0.00193064 | + | 0.999998i | \(0.500615\pi\) | |||||||
\(548\) | 28.1967 | 1.20450 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12.4283 | 0.529944 | ||||||||
\(551\) | −3.83899 | −0.163547 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.31647 | 0.141031 | ||||||||
\(554\) | 14.8360 | 0.630320 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −90.6427 | −3.84411 | ||||||||
\(557\) | 28.1241 | 1.19166 | 0.595829 | − | 0.803111i | \(-0.296824\pi\) | ||||
0.595829 | + | 0.803111i | \(0.296824\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 11.3642 | 0.480227 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −32.9791 | −1.39114 | ||||||||
\(563\) | −23.6557 | −0.996967 | −0.498484 | − | 0.866899i | \(-0.666110\pi\) | ||||
−0.498484 | + | 0.866899i | \(0.666110\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.2938 | −0.559273 | ||||||||
\(566\) | −66.7082 | −2.80396 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −46.2561 | −1.94086 | ||||||||
\(569\) | −9.76686 | −0.409448 | −0.204724 | − | 0.978820i | \(-0.565630\pi\) | ||||
−0.204724 | + | 0.978820i | \(0.565630\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.9688 | −0.877518 | −0.438759 | − | 0.898605i | \(-0.644582\pi\) | ||||
−0.438759 | + | 0.898605i | \(0.644582\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −14.3056 | −0.597105 | ||||||||
\(575\) | −7.70645 | −0.321381 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.22602 | 0.300823 | 0.150412 | − | 0.988623i | \(-0.451940\pi\) | ||||
0.150412 | + | 0.988623i | \(0.451940\pi\) | |||||||
\(578\) | −27.0760 | −1.12621 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.46136 | −0.268293 | ||||||||
\(581\) | −1.53417 | −0.0636481 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 45.6898 | 1.89228 | ||||||||
\(584\) | 94.8646 | 3.92552 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 46.9708 | 1.94035 | ||||||||
\(587\) | −24.1904 | −0.998443 | −0.499221 | − | 0.866475i | \(-0.666381\pi\) | ||||
−0.499221 | + | 0.866475i | \(0.666381\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.79535 | −0.279997 | ||||||||
\(590\) | 8.33570 | 0.343176 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 108.749 | 4.46957 | ||||||||
\(593\) | −10.5786 | −0.434410 | −0.217205 | − | 0.976126i | \(-0.569694\pi\) | ||||
−0.217205 | + | 0.976126i | \(0.569694\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.69251 | 0.233370 | ||||||||
\(596\) | −111.667 | −4.57408 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.8978 | 1.05816 | 0.529078 | − | 0.848573i | \(-0.322538\pi\) | ||||
0.529078 | + | 0.848573i | \(0.322538\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.3046 | −0.624289 | −0.312144 | − | 0.950035i | \(-0.601047\pi\) | ||||
−0.312144 | + | 0.950035i | \(0.601047\pi\) | |||||||
\(602\) | 17.1192 | 0.697727 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.1799 | 0.454905 | ||||||||
\(605\) | −11.2958 | −0.459238 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.9448 | −1.58072 | −0.790360 | − | 0.612643i | \(-0.790107\pi\) | ||||
−0.790360 | + | 0.612643i | \(0.790107\pi\) | |||||||
\(608\) | 35.2379 | 1.42909 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.6372 | 0.673620 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −40.5599 | −1.63820 | −0.819100 | − | 0.573651i | \(-0.805527\pi\) | ||||
−0.819100 | + | 0.573651i | \(0.805527\pi\) | |||||||
\(614\) | 26.4200 | 1.06623 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −39.6545 | −1.59773 | ||||||||
\(617\) | −31.6607 | −1.27461 | −0.637307 | − | 0.770610i | \(-0.719952\pi\) | ||||
−0.637307 | + | 0.770610i | \(0.719952\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.4523 | −0.741661 | −0.370831 | − | 0.928700i | \(-0.620927\pi\) | ||||
−0.370831 | + | 0.928700i | \(0.620927\pi\) | |||||||
\(620\) | −11.4372 | −0.459327 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −23.0654 | −0.924839 | ||||||||
\(623\) | −9.45340 | −0.378742 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −11.5257 | −0.460661 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −68.4653 | −2.73206 | ||||||||
\(629\) | 54.4741 | 2.17203 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.5073 | −1.33390 | −0.666952 | − | 0.745101i | \(-0.732401\pi\) | ||||
−0.666952 | + | 0.745101i | \(0.732401\pi\) | |||||||
\(632\) | 23.4533 | 0.932921 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 30.8048 | 1.22342 | ||||||||
\(635\) | −15.4548 | −0.613305 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.2958 | 0.645155 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.41210 | 0.174403 | ||||||||
\(641\) | 15.9434 | 0.629726 | 0.314863 | − | 0.949137i | \(-0.398041\pi\) | ||||
0.314863 | + | 0.949137i | \(0.398041\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.7201 | 0.580506 | 0.290253 | − | 0.956950i | \(-0.406261\pi\) | ||||
0.290253 | + | 0.956950i | \(0.406261\pi\) | |||||||
\(644\) | 41.3849 | 1.63079 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 40.2561 | 1.58385 | ||||||||
\(647\) | −37.0838 | −1.45791 | −0.728957 | − | 0.684559i | \(-0.759995\pi\) | ||||
−0.728957 | + | 0.684559i | \(0.759995\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.9538 | −0.586990 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −121.333 | −4.75178 | ||||||||
\(653\) | −20.5706 | −0.804988 | −0.402494 | − | 0.915423i | \(-0.631857\pi\) | ||||
−0.402494 | + | 0.915423i | \(0.631857\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.48870 | 0.331681 | ||||||||
\(656\) | −52.0106 | −2.03067 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 24.4325 | 0.952476 | ||||||||
\(659\) | 29.6632 | 1.15552 | 0.577758 | − | 0.816208i | \(-0.303928\pi\) | ||||
0.577758 | + | 0.816208i | \(0.303928\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.1054 | 0.626427 | 0.313213 | − | 0.949683i | \(-0.398595\pi\) | ||||
0.313213 | + | 0.949683i | \(0.398595\pi\) | |||||||
\(662\) | −33.4887 | −1.30157 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.8493 | −0.421034 | ||||||||
\(665\) | −3.19067 | −0.123729 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.1046 | −0.391250 | ||||||||
\(668\) | −18.7254 | −0.724507 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.14648 | 0.160193 | ||||||||
\(671\) | −29.8463 | −1.15220 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.06634 | 0.272387 | 0.136194 | − | 0.990682i | \(-0.456513\pi\) | ||||
0.136194 | + | 0.990682i | \(0.456513\pi\) | |||||||
\(674\) | 10.6265 | 0.409319 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.6740 | −0.909866 | −0.454933 | − | 0.890526i | \(-0.650337\pi\) | ||||
−0.454933 | + | 0.890526i | \(0.650337\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0226 | −0.461385 | ||||||||
\(680\) | 40.2561 | 1.54375 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 28.8449 | 1.10453 | ||||||||
\(683\) | 20.1994 | 0.772909 | 0.386454 | − | 0.922309i | \(-0.373700\pi\) | ||||
0.386454 | + | 0.922309i | \(0.373700\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.72185 | −0.218621 | ||||||||
\(686\) | −36.7502 | −1.40313 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 62.2400 | 2.37288 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.1378 | 1.18454 | 0.592269 | − | 0.805740i | \(-0.298232\pi\) | ||||
0.592269 | + | 0.805740i | \(0.298232\pi\) | |||||||
\(692\) | 89.0975 | 3.38698 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.906344 | −0.0344044 | ||||||||
\(695\) | 18.3938 | 0.697718 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.0529 | −0.986824 | ||||||||
\(698\) | −91.1762 | −3.45107 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.37017 | −0.202973 | ||||||||
\(701\) | 24.0928 | 0.909974 | 0.454987 | − | 0.890498i | \(-0.349644\pi\) | ||||
0.454987 | + | 0.890498i | \(0.349644\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.5329 | −1.15157 | ||||||||
\(704\) | −51.0965 | −1.92577 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −46.9571 | −1.76725 | ||||||||
\(707\) | 10.0420 | 0.377667 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.78080 | −0.179547 | −0.0897734 | − | 0.995962i | \(-0.528614\pi\) | ||||
−0.0897734 | + | 0.995962i | \(0.528614\pi\) | |||||||
\(710\) | 15.7985 | 0.592906 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −66.8522 | −2.50539 | ||||||||
\(713\) | −17.8860 | −0.669834 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 126.375 | 4.72286 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19.0112 | −0.709490 | ||||||||
\(719\) | −13.5084 | −0.503779 | −0.251889 | − | 0.967756i | \(-0.581052\pi\) | ||||
−0.251889 | + | 0.967756i | \(0.581052\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.1922 | −0.603028 | ||||||||
\(722\) | 27.4460 | 1.02144 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −94.1014 | −3.49725 | ||||||||
\(725\) | 1.31118 | 0.0486961 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.06108 | −0.224793 | −0.112397 | − | 0.993663i | \(-0.535853\pi\) | ||||
−0.112397 | + | 0.993663i | \(0.535853\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −32.4004 | −1.19919 | ||||||||
\(731\) | 31.1769 | 1.15312 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.63897 | −0.208280 | −0.104140 | − | 0.994563i | \(-0.533209\pi\) | ||||
−0.104140 | + | 0.994563i | \(0.533209\pi\) | |||||||
\(734\) | 78.3059 | 2.89032 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 92.7493 | 3.41878 | ||||||||
\(737\) | −7.43858 | −0.274004 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.12716 | 0.115035 | 0.0575173 | − | 0.998345i | \(-0.481682\pi\) | ||||
0.0575173 | + | 0.998345i | \(0.481682\pi\) | |||||||
\(740\) | −51.3894 | −1.88911 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −27.7546 | −1.01890 | ||||||||
\(743\) | −48.7893 | −1.78991 | −0.894953 | − | 0.446161i | \(-0.852791\pi\) | ||||
−0.894953 | + | 0.446161i | \(0.852791\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.6603 | 0.830209 | ||||||||
\(746\) | −10.1119 | −0.370222 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −121.548 | −4.44425 | ||||||||
\(749\) | −7.51368 | −0.274544 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.6808 | −1.63042 | −0.815212 | − | 0.579163i | \(-0.803380\pi\) | ||||
−0.815212 | + | 0.579163i | \(0.803380\pi\) | |||||||
\(752\) | 88.8286 | 3.23925 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.26871 | −0.0825668 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.09782 | −0.330666 | −0.165333 | − | 0.986238i | \(-0.552870\pi\) | ||||
−0.165333 | + | 0.986238i | \(0.552870\pi\) | |||||||
\(758\) | 81.8647 | 2.97346 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −22.5636 | −0.818469 | ||||||||
\(761\) | −30.5748 | −1.10833 | −0.554167 | − | 0.832405i | \(-0.686963\pi\) | ||||
−0.554167 | + | 0.832405i | \(0.686963\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.8875 | −0.575165 | ||||||||
\(764\) | −119.027 | −4.30625 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34.1142 | 1.23260 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.2459 | 0.982514 | 0.491257 | − | 0.871015i | \(-0.336538\pi\) | ||||
0.491257 | + | 0.871015i | \(0.336538\pi\) | |||||||
\(770\) | 13.5437 | 0.488082 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −63.0554 | −2.26941 | ||||||||
\(773\) | 7.33531 | 0.263833 | 0.131916 | − | 0.991261i | \(-0.457887\pi\) | ||||
0.131916 | + | 0.991261i | \(0.457887\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.32091 | 0.0833694 | ||||||||
\(776\) | −85.0210 | −3.05207 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −37.1920 | −1.33340 | ||||||||
\(779\) | 14.6027 | 0.523196 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.3417 | −1.01414 | ||||||||
\(782\) | 105.958 | 3.78904 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −60.6139 | −2.16478 | ||||||||
\(785\) | 13.8934 | 0.495878 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −51.3755 | −1.83134 | −0.915669 | − | 0.401933i | \(-0.868338\pi\) | ||||
−0.915669 | + | 0.401933i | \(0.868338\pi\) | |||||||
\(788\) | −3.21567 | −0.114554 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.01031 | −0.284994 | ||||||||
\(791\) | −14.4869 | −0.515095 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −74.5144 | −2.64442 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −31.4783 | −1.11572 | ||||||||
\(797\) | 35.3318 | 1.25152 | 0.625758 | − | 0.780017i | \(-0.284790\pi\) | ||||
0.625758 | + | 0.780017i | \(0.284790\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44.4956 | 1.57414 | ||||||||
\(800\) | −12.0353 | −0.425511 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11.6746 | 0.412246 | ||||||||
\(803\) | 58.1247 | 2.05118 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.39811 | −0.295995 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 71.0143 | 2.49828 | ||||||||
\(809\) | 31.0435 | 1.09143 | 0.545715 | − | 0.837971i | \(-0.316258\pi\) | ||||
0.545715 | + | 0.837971i | \(0.316258\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.39427 | 0.329878 | 0.164939 | − | 0.986304i | \(-0.447257\pi\) | ||||
0.164939 | + | 0.986304i | \(0.447257\pi\) | |||||||
\(812\) | −7.04126 | −0.247100 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 129.606 | 4.54268 | ||||||||
\(815\) | 24.6218 | 0.862464 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.4747 | −0.611363 | ||||||||
\(818\) | −23.6056 | −0.825350 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 24.5776 | 0.858287 | ||||||||
\(821\) | −6.18635 | −0.215905 | −0.107952 | − | 0.994156i | \(-0.534429\pi\) | ||||
−0.107952 | + | 0.994156i | \(0.534429\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.6710 | 0.790263 | 0.395131 | − | 0.918625i | \(-0.370699\pi\) | ||||
0.395131 | + | 0.918625i | \(0.370699\pi\) | |||||||
\(824\) | −114.507 | −3.98905 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.08384 | 0.316067 | ||||||||
\(827\) | 11.1599 | 0.388066 | 0.194033 | − | 0.980995i | \(-0.437843\pi\) | ||||
0.194033 | + | 0.980995i | \(0.437843\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.7966 | −0.687564 | −0.343782 | − | 0.939049i | \(-0.611708\pi\) | ||||
−0.343782 | + | 0.939049i | \(0.611708\pi\) | |||||||
\(830\) | 3.70550 | 0.128620 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −30.3624 | −1.05199 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.79988 | 0.131500 | ||||||||
\(836\) | 68.1281 | 2.35626 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 90.5229 | 3.12706 | ||||||||
\(839\) | 1.28267 | 0.0442826 | 0.0221413 | − | 0.999755i | \(-0.492952\pi\) | ||||
0.0221413 | + | 0.999755i | \(0.492952\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.2808 | −0.940717 | ||||||||
\(842\) | 53.1525 | 1.83176 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −86.2261 | −2.96803 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.3096 | −0.422961 | ||||||||
\(848\) | −100.907 | −3.46516 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13.7492 | −0.471594 | ||||||||
\(851\) | −80.3652 | −2.75488 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.0390 | 0.412208 | 0.206104 | − | 0.978530i | \(-0.433922\pi\) | ||||
0.206104 | + | 0.978530i | \(0.433922\pi\) | |||||||
\(854\) | 18.1304 | 0.620408 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −53.1350 | −1.81612 | ||||||||
\(857\) | 28.1181 | 0.960497 | 0.480248 | − | 0.877133i | \(-0.340547\pi\) | ||||
0.480248 | + | 0.877133i | \(0.340547\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −50.0048 | −1.70614 | −0.853071 | − | 0.521795i | \(-0.825263\pi\) | ||||
−0.853071 | + | 0.521795i | \(0.825263\pi\) | |||||||
\(860\) | −29.4115 | −1.00292 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 54.6663 | 1.86194 | ||||||||
\(863\) | −41.7180 | −1.42010 | −0.710048 | − | 0.704153i | \(-0.751327\pi\) | ||||
−0.710048 | + | 0.704153i | \(0.751327\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.0803 | −0.614748 | ||||||||
\(866\) | −96.5775 | −3.28184 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.4636 | −0.423044 | ||||||||
\(869\) | 14.3701 | 0.487472 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −112.352 | −3.80473 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −59.3894 | −2.00888 | ||||||||
\(875\) | 1.08975 | 0.0368403 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.2045 | 1.42515 | 0.712573 | − | 0.701598i | \(-0.247530\pi\) | ||||
0.712573 | + | 0.701598i | \(0.247530\pi\) | |||||||
\(878\) | 53.4277 | 1.80310 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 49.2407 | 1.65990 | ||||||||
\(881\) | −49.4623 | −1.66643 | −0.833214 | − | 0.552950i | \(-0.813502\pi\) | ||||
−0.833214 | + | 0.552950i | \(0.813502\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.24684 | −0.243876 | −0.121938 | − | 0.992538i | \(-0.538911\pi\) | ||||
−0.121938 | + | 0.992538i | \(0.538911\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 26.3389 | 0.884872 | ||||||||
\(887\) | −26.4616 | −0.888492 | −0.444246 | − | 0.895905i | \(-0.646528\pi\) | ||||
−0.444246 | + | 0.895905i | \(0.646528\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.8419 | −0.564858 | ||||||||
\(890\) | 22.8329 | 0.765361 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.0762 | 0.437822 | ||||||||
\(893\) | −24.9399 | −0.834581 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.6449 | −0.857214 | ||||||||
\(896\) | 4.80808 | 0.160627 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −27.8044 | −0.927844 | ||||||||
\(899\) | 3.04313 | 0.101494 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −50.5458 | −1.68392 | ||||||||
\(902\) | −61.9855 | −2.06389 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −102.448 | −3.40737 | ||||||||
\(905\) | 19.0957 | 0.634762 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.8327 | −0.359695 | −0.179848 | − | 0.983694i | \(-0.557561\pi\) | ||||
−0.179848 | + | 0.983694i | \(0.557561\pi\) | |||||||
\(908\) | 25.1797 | 0.835619 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.47923 | 0.0490092 | 0.0245046 | − | 0.999700i | \(-0.492199\pi\) | ||||
0.0245046 | + | 0.999700i | \(0.492199\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.64749 | −0.220000 | ||||||||
\(914\) | −12.6680 | −0.419020 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −85.2176 | −2.81567 | ||||||||
\(917\) | 9.25056 | 0.305481 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.8120 | −0.818472 | −0.409236 | − | 0.912428i | \(-0.634205\pi\) | ||||
−0.409236 | + | 0.912428i | \(0.634205\pi\) | |||||||
\(920\) | −59.3894 | −1.95801 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −51.4939 | −1.69586 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.4283 | 0.342880 | ||||||||
\(926\) | 2.71416 | 0.0891927 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −15.7804 | −0.518018 | ||||||||
\(929\) | 0.603656 | 0.0198053 | 0.00990266 | − | 0.999951i | \(-0.496848\pi\) | ||||
0.00990266 | + | 0.999951i | \(0.496848\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.0182 | 0.557748 | ||||||||
\(932\) | 11.8614 | 0.388535 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −32.8707 | −1.07556 | ||||||||
\(935\) | 24.6654 | 0.806645 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.64793 | −0.0538355 | −0.0269178 | − | 0.999638i | \(-0.508569\pi\) | ||||
−0.0269178 | + | 0.999638i | \(0.508569\pi\) | |||||||
\(938\) | 4.51863 | 0.147538 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −41.9759 | −1.36910 | ||||||||
\(941\) | −47.2291 | −1.53962 | −0.769812 | − | 0.638271i | \(-0.779650\pi\) | ||||
−0.769812 | + | 0.638271i | \(0.779650\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.4356 | 1.25164 | ||||||||
\(944\) | 33.0259 | 1.07490 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 74.1767 | 2.41169 | ||||||||
\(947\) | −32.1407 | −1.04443 | −0.522217 | − | 0.852813i | \(-0.674895\pi\) | ||||
−0.522217 | + | 0.852813i | \(0.674895\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 7.70645 | 0.250030 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 43.8691 | 1.42181 | ||||||||
\(953\) | 14.6590 | 0.474853 | 0.237427 | − | 0.971405i | \(-0.423696\pi\) | ||||
0.237427 | + | 0.971405i | \(0.423696\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.1538 | 0.781598 | ||||||||
\(956\) | −43.5393 | −1.40816 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.4877 | 0.565001 | ||||||||
\(959\) | −6.23539 | −0.201351 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.6134 | −0.826239 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 42.0868 | 1.35553 | ||||||||
\(965\) | 12.7956 | 0.411906 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.77101 | −0.282057 | −0.141028 | − | 0.990006i | \(-0.545041\pi\) | ||||
−0.141028 | + | 0.990006i | \(0.545041\pi\) | |||||||
\(968\) | −87.0502 | −2.79790 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 29.0383 | 0.932365 | ||||||||
\(971\) | 5.29481 | 0.169919 | 0.0849593 | − | 0.996384i | \(-0.472924\pi\) | ||||
0.0849593 | + | 0.996384i | \(0.472924\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.0447 | 0.642603 | ||||||||
\(974\) | 2.17640 | 0.0697365 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 65.9163 | 2.10993 | ||||||||
\(977\) | −23.2334 | −0.743303 | −0.371651 | − | 0.928372i | \(-0.621208\pi\) | ||||
−0.371651 | + | 0.928372i | \(0.621208\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40.9612 | −1.30912 | ||||||||
\(980\) | 28.6431 | 0.914969 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −33.7429 | −1.07678 | ||||||||
\(983\) | −41.7741 | −1.33239 | −0.666194 | − | 0.745779i | \(-0.732078\pi\) | ||||
−0.666194 | + | 0.745779i | \(0.732078\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.652546 | 0.0207919 | ||||||||
\(986\) | −18.0277 | −0.574119 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −45.9950 | −1.46256 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.6286 | 0.877650 | 0.438825 | − | 0.898573i | \(-0.355395\pi\) | ||||
0.438825 | + | 0.898573i | \(0.355395\pi\) | |||||||
\(992\) | −27.9327 | −0.886865 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 17.2164 | 0.546070 | ||||||||
\(995\) | 6.38779 | 0.202506 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.14898 | −0.289751 | −0.144876 | − | 0.989450i | \(-0.546278\pi\) | ||||
−0.144876 | + | 0.989450i | \(0.546278\pi\) | |||||||
\(998\) | 52.2866 | 1.65510 | ||||||||
\(999\) | 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 | 7605.2.a.cl.1.1 | 5 | ||
3.2 | odd | 2 | 7605.2.a.cn.1.5 | 5 | |||
13.4 | even | 6 | 585.2.j.h.406.1 | ✓ | 10 | ||
13.10 | even | 6 | 585.2.j.h.451.1 | yes | 10 | ||
13.12 | even | 2 | 7605.2.a.co.1.5 | 5 | |||
39.17 | odd | 6 | 585.2.j.i.406.5 | yes | 10 | ||
39.23 | odd | 6 | 585.2.j.i.451.5 | yes | 10 | ||
39.38 | odd | 2 | 7605.2.a.cm.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.j.h.406.1 | ✓ | 10 | 13.4 | even | 6 | ||
585.2.j.h.451.1 | yes | 10 | 13.10 | even | 6 | ||
585.2.j.i.406.5 | yes | 10 | 39.17 | odd | 6 | ||
585.2.j.i.451.5 | yes | 10 | 39.23 | odd | 6 | ||
7605.2.a.cl.1.1 | 5 | 1.1 | even | 1 | trivial | ||
7605.2.a.cm.1.1 | 5 | 39.38 | odd | 2 | |||
7605.2.a.cn.1.5 | 5 | 3.2 | odd | 2 | |||
7605.2.a.co.1.5 | 5 | 13.12 | even | 2 |