Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4527,2,Mod(1,4527)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4527, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4527.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4527 = 3^{2} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4527.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: | \(36.1482769950\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 503) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.208270\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4527.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.17266 | −0.829195 | −0.414598 | − | 0.910005i | \(-0.636078\pi\) | ||||
−0.414598 | + | 0.910005i | \(0.636078\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.624870 | −0.312435 | ||||||||
\(5\) | −0.178789 | −0.0799568 | −0.0399784 | − | 0.999201i | \(-0.512729\pi\) | ||||
−0.0399784 | + | 0.999201i | \(0.512729\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0809018 | −0.0305780 | −0.0152890 | − | 0.999883i | \(-0.504867\pi\) | ||||
−0.0152890 | + | 0.999883i | \(0.504867\pi\) | |||||||
\(8\) | 3.07808 | 1.08827 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.209658 | 0.0662998 | ||||||||
\(11\) | 4.30391 | 1.29768 | 0.648839 | − | 0.760926i | \(-0.275255\pi\) | ||||
0.648839 | + | 0.760926i | \(0.275255\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.10019 | 0.305139 | 0.152569 | − | 0.988293i | \(-0.451245\pi\) | ||||
0.152569 | + | 0.988293i | \(0.451245\pi\) | |||||||
\(14\) | 0.0948703 | 0.0253551 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.35980 | −0.589950 | ||||||||
\(17\) | 3.06504 | 0.743381 | 0.371690 | − | 0.928357i | \(-0.378778\pi\) | ||||
0.371690 | + | 0.928357i | \(0.378778\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.15853 | −0.495200 | −0.247600 | − | 0.968862i | \(-0.579642\pi\) | ||||
−0.247600 | + | 0.968862i | \(0.579642\pi\) | |||||||
\(20\) | 0.111720 | 0.0249813 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.04702 | −1.07603 | ||||||||
\(23\) | −9.15620 | −1.90920 | −0.954600 | − | 0.297892i | \(-0.903716\pi\) | ||||
−0.954600 | + | 0.297892i | \(0.903716\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96803 | −0.993607 | ||||||||
\(26\) | −1.29015 | −0.253020 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.0505531 | 0.00955364 | ||||||||
\(29\) | 6.17849 | 1.14732 | 0.573658 | − | 0.819095i | \(-0.305524\pi\) | ||||
0.573658 | + | 0.819095i | \(0.305524\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.82812 | −1.76518 | −0.882591 | − | 0.470141i | \(-0.844203\pi\) | ||||
−0.882591 | + | 0.470141i | \(0.844203\pi\) | |||||||
\(32\) | −3.38892 | −0.599082 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.59425 | −0.616408 | ||||||||
\(35\) | 0.0144643 | 0.00244492 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.08321 | 0.671275 | 0.335637 | − | 0.941991i | \(-0.391048\pi\) | ||||
0.335637 | + | 0.941991i | \(0.391048\pi\) | |||||||
\(38\) | 2.53122 | 0.410618 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.550326 | −0.0870141 | ||||||||
\(41\) | −4.58598 | −0.716210 | −0.358105 | − | 0.933681i | \(-0.616577\pi\) | ||||
−0.358105 | + | 0.933681i | \(0.616577\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.03126 | 0.309764 | 0.154882 | − | 0.987933i | \(-0.450500\pi\) | ||||
0.154882 | + | 0.987933i | \(0.450500\pi\) | |||||||
\(44\) | −2.68938 | −0.405440 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.7371 | 1.58310 | ||||||||
\(47\) | 5.12836 | 0.748049 | 0.374024 | − | 0.927419i | \(-0.377978\pi\) | ||||
0.374024 | + | 0.927419i | \(0.377978\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99345 | −0.999065 | ||||||||
\(50\) | 5.82581 | 0.823894 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.687477 | −0.0953359 | ||||||||
\(53\) | −2.69017 | −0.369523 | −0.184761 | − | 0.982783i | \(-0.559151\pi\) | ||||
−0.184761 | + | 0.982783i | \(0.559151\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.769491 | −0.103758 | ||||||||
\(56\) | −0.249022 | −0.0332770 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.24527 | −0.951350 | ||||||||
\(59\) | −9.21598 | −1.19982 | −0.599909 | − | 0.800068i | \(-0.704797\pi\) | ||||
−0.599909 | + | 0.800068i | \(0.704797\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.0554 | −1.79961 | −0.899805 | − | 0.436291i | \(-0.856292\pi\) | ||||
−0.899805 | + | 0.436291i | \(0.856292\pi\) | |||||||
\(62\) | 11.5250 | 1.46368 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.69364 | 1.08671 | ||||||||
\(65\) | −0.196702 | −0.0243979 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.62801 | 0.687570 | 0.343785 | − | 0.939048i | \(-0.388291\pi\) | ||||
0.343785 | + | 0.939048i | \(0.388291\pi\) | |||||||
\(68\) | −1.91525 | −0.232258 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.0169617 | −0.00202732 | ||||||||
\(71\) | 4.88191 | 0.579376 | 0.289688 | − | 0.957121i | \(-0.406448\pi\) | ||||
0.289688 | + | 0.957121i | \(0.406448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.9754 | 1.28457 | 0.642286 | − | 0.766465i | \(-0.277986\pi\) | ||||
0.642286 | + | 0.766465i | \(0.277986\pi\) | |||||||
\(74\) | −4.78821 | −0.556618 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.34880 | 0.154718 | ||||||||
\(77\) | −0.348194 | −0.0396804 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.4356 | 1.96166 | 0.980828 | − | 0.194874i | \(-0.0624299\pi\) | ||||
0.980828 | + | 0.194874i | \(0.0624299\pi\) | |||||||
\(80\) | 0.421905 | 0.0471705 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.37780 | 0.593878 | ||||||||
\(83\) | 2.48372 | 0.272624 | 0.136312 | − | 0.990666i | \(-0.456475\pi\) | ||||
0.136312 | + | 0.990666i | \(0.456475\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.547994 | −0.0594383 | ||||||||
\(86\) | −2.38198 | −0.256855 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 13.2478 | 1.41222 | ||||||||
\(89\) | −5.57230 | −0.590662 | −0.295331 | − | 0.955395i | \(-0.595430\pi\) | ||||
−0.295331 | + | 0.955395i | \(0.595430\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0890076 | −0.00933053 | ||||||||
\(92\) | 5.72143 | 0.596500 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.01382 | −0.620279 | ||||||||
\(95\) | 0.385920 | 0.0395946 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.9731 | −1.41876 | −0.709379 | − | 0.704828i | \(-0.751024\pi\) | ||||
−0.709379 | + | 0.704828i | \(0.751024\pi\) | |||||||
\(98\) | 8.20094 | 0.828420 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.10437 | 0.310437 | ||||||||
\(101\) | 7.98379 | 0.794417 | 0.397208 | − | 0.917728i | \(-0.369979\pi\) | ||||
0.397208 | + | 0.917728i | \(0.369979\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.5314 | 1.03769 | 0.518846 | − | 0.854868i | \(-0.326362\pi\) | ||||
0.518846 | + | 0.854868i | \(0.326362\pi\) | |||||||
\(104\) | 3.38648 | 0.332072 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.15465 | 0.306407 | ||||||||
\(107\) | 3.31671 | 0.320638 | 0.160319 | − | 0.987065i | \(-0.448748\pi\) | ||||
0.160319 | + | 0.987065i | \(0.448748\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.7956 | −1.22559 | −0.612797 | − | 0.790240i | \(-0.709956\pi\) | ||||
−0.612797 | + | 0.790240i | \(0.709956\pi\) | |||||||
\(110\) | 0.902350 | 0.0860357 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.190912 | 0.0180395 | ||||||||
\(113\) | 4.42086 | 0.415880 | 0.207940 | − | 0.978142i | \(-0.433324\pi\) | ||||
0.207940 | + | 0.978142i | \(0.433324\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.63702 | 0.152653 | ||||||||
\(116\) | −3.86075 | −0.358462 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.8072 | 0.994884 | ||||||||
\(119\) | −0.247967 | −0.0227311 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.52364 | 0.683967 | ||||||||
\(122\) | 16.4822 | 1.49223 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.14130 | 0.551505 | ||||||||
\(125\) | 1.78217 | 0.159402 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.5071 | −1.55351 | −0.776753 | − | 0.629806i | \(-0.783135\pi\) | ||||
−0.776753 | + | 0.629806i | \(0.783135\pi\) | |||||||
\(128\) | −3.41685 | −0.302010 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.230665 | 0.0202306 | ||||||||
\(131\) | −11.8336 | −1.03390 | −0.516952 | − | 0.856014i | \(-0.672934\pi\) | ||||
−0.516952 | + | 0.856014i | \(0.672934\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.174629 | 0.0151422 | ||||||||
\(134\) | −6.59973 | −0.570130 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.43443 | 0.808995 | ||||||||
\(137\) | 2.19499 | 0.187530 | 0.0937651 | − | 0.995594i | \(-0.470110\pi\) | ||||
0.0937651 | + | 0.995594i | \(0.470110\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.11773 | 0.518899 | 0.259450 | − | 0.965757i | \(-0.416459\pi\) | ||||
0.259450 | + | 0.965757i | \(0.416459\pi\) | |||||||
\(140\) | −0.00903832 | −0.000763878 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.72482 | −0.480416 | ||||||||
\(143\) | 4.73513 | 0.395972 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.10464 | −0.0917357 | ||||||||
\(146\) | −12.8704 | −1.06516 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.55147 | −0.209730 | ||||||||
\(149\) | 17.3950 | 1.42505 | 0.712526 | − | 0.701646i | \(-0.247551\pi\) | ||||
0.712526 | + | 0.701646i | \(0.247551\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.9595 | −1.78704 | −0.893520 | − | 0.449024i | \(-0.851772\pi\) | ||||
−0.893520 | + | 0.449024i | \(0.851772\pi\) | |||||||
\(152\) | −6.64411 | −0.538909 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.408313 | 0.0329028 | ||||||||
\(155\) | 1.75716 | 0.141138 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.5736 | −1.56214 | −0.781070 | − | 0.624444i | \(-0.785326\pi\) | ||||
−0.781070 | + | 0.624444i | \(0.785326\pi\) | |||||||
\(158\) | −20.4460 | −1.62660 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.605900 | 0.0479006 | ||||||||
\(161\) | 0.740753 | 0.0583795 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.2549 | −1.11653 | −0.558265 | − | 0.829663i | \(-0.688533\pi\) | ||||
−0.558265 | + | 0.829663i | \(0.688533\pi\) | |||||||
\(164\) | 2.86564 | 0.223769 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.91256 | −0.226058 | ||||||||
\(167\) | 19.3555 | 1.49777 | 0.748886 | − | 0.662698i | \(-0.230589\pi\) | ||||
0.748886 | + | 0.662698i | \(0.230589\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.7896 | −0.906890 | ||||||||
\(170\) | 0.642611 | 0.0492860 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.26927 | −0.0967811 | ||||||||
\(173\) | −24.1751 | −1.83800 | −0.919000 | − | 0.394258i | \(-0.871002\pi\) | ||||
−0.919000 | + | 0.394258i | \(0.871002\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.401923 | 0.0303825 | ||||||||
\(176\) | −10.1564 | −0.765564 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.53441 | 0.489775 | ||||||||
\(179\) | −11.7844 | −0.880807 | −0.440403 | − | 0.897800i | \(-0.645165\pi\) | ||||
−0.440403 | + | 0.897800i | \(0.645165\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.193747 | 0.0144011 | 0.00720054 | − | 0.999974i | \(-0.497708\pi\) | ||||
0.00720054 | + | 0.999974i | \(0.497708\pi\) | |||||||
\(182\) | 0.104376 | 0.00773683 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −28.1835 | −2.07771 | ||||||||
\(185\) | −0.730031 | −0.0536730 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.1916 | 0.964669 | ||||||||
\(188\) | −3.20456 | −0.233716 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.452553 | −0.0328317 | ||||||||
\(191\) | 20.0106 | 1.44791 | 0.723957 | − | 0.689845i | \(-0.242321\pi\) | ||||
0.723957 | + | 0.689845i | \(0.242321\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.4429 | −1.18358 | −0.591792 | − | 0.806091i | \(-0.701579\pi\) | ||||
−0.591792 | + | 0.806091i | \(0.701579\pi\) | |||||||
\(194\) | 16.3857 | 1.17643 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.37000 | 0.312143 | ||||||||
\(197\) | −24.3311 | −1.73352 | −0.866761 | − | 0.498723i | \(-0.833802\pi\) | ||||
−0.866761 | + | 0.498723i | \(0.833802\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.2467 | −1.15170 | −0.575851 | − | 0.817555i | \(-0.695329\pi\) | ||||
−0.575851 | + | 0.817555i | \(0.695329\pi\) | |||||||
\(200\) | −15.2920 | −1.08131 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.36226 | −0.658727 | ||||||||
\(203\) | −0.499851 | −0.0350827 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.819922 | 0.0572659 | ||||||||
\(206\) | −12.3498 | −0.860449 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.59623 | −0.180016 | ||||||||
\(209\) | −9.29010 | −0.642610 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.5844 | 0.935189 | 0.467594 | − | 0.883943i | \(-0.345121\pi\) | ||||
0.467594 | + | 0.883943i | \(0.345121\pi\) | |||||||
\(212\) | 1.68100 | 0.115452 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.88937 | −0.265872 | ||||||||
\(215\) | −0.363166 | −0.0247677 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.795113 | 0.0539758 | ||||||||
\(218\) | 15.0049 | 1.01626 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.480831 | 0.0324176 | ||||||||
\(221\) | 3.37213 | 0.226834 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.6725 | 1.65219 | 0.826096 | − | 0.563530i | \(-0.190557\pi\) | ||||
0.826096 | + | 0.563530i | \(0.190557\pi\) | |||||||
\(224\) | 0.274169 | 0.0183187 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.18417 | −0.344846 | ||||||||
\(227\) | −17.9854 | −1.19373 | −0.596866 | − | 0.802341i | \(-0.703588\pi\) | ||||
−0.596866 | + | 0.802341i | \(0.703588\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.8558 | 1.04778 | 0.523891 | − | 0.851786i | \(-0.324480\pi\) | ||||
0.523891 | + | 0.851786i | \(0.324480\pi\) | |||||||
\(230\) | −1.91967 | −0.126579 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 19.0179 | 1.24858 | ||||||||
\(233\) | −2.33607 | −0.153041 | −0.0765205 | − | 0.997068i | \(-0.524381\pi\) | ||||
−0.0765205 | + | 0.997068i | \(0.524381\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.916894 | −0.0598115 | ||||||||
\(236\) | 5.75879 | 0.374865 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.290781 | 0.0188485 | ||||||||
\(239\) | −4.84852 | −0.313625 | −0.156812 | − | 0.987628i | \(-0.550122\pi\) | ||||
−0.156812 | + | 0.987628i | \(0.550122\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.42679 | −0.220739 | −0.110369 | − | 0.993891i | \(-0.535203\pi\) | ||||
−0.110369 | + | 0.993891i | \(0.535203\pi\) | |||||||
\(242\) | −8.82267 | −0.567143 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.78280 | 0.562261 | ||||||||
\(245\) | 1.25035 | 0.0798820 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.37480 | −0.151105 | ||||||||
\(248\) | −30.2517 | −1.92099 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.08988 | −0.132176 | ||||||||
\(251\) | 25.7166 | 1.62321 | 0.811607 | − | 0.584204i | \(-0.198593\pi\) | ||||
0.811607 | + | 0.584204i | \(0.198593\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −39.4074 | −2.47753 | ||||||||
\(254\) | 20.5299 | 1.28816 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.3805 | −0.836280 | ||||||||
\(257\) | 24.1897 | 1.50891 | 0.754457 | − | 0.656350i | \(-0.227900\pi\) | ||||
0.754457 | + | 0.656350i | \(0.227900\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.330339 | −0.0205262 | ||||||||
\(260\) | 0.122913 | 0.00762275 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.8768 | 0.857309 | ||||||||
\(263\) | −18.1779 | −1.12089 | −0.560447 | − | 0.828190i | \(-0.689371\pi\) | ||||
−0.560447 | + | 0.828190i | \(0.689371\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.480972 | 0.0295458 | ||||||||
\(266\) | −0.204780 | −0.0125559 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.51677 | −0.214821 | ||||||||
\(269\) | 5.69010 | 0.346931 | 0.173466 | − | 0.984840i | \(-0.444503\pi\) | ||||
0.173466 | + | 0.984840i | \(0.444503\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.4138 | 0.997069 | 0.498535 | − | 0.866870i | \(-0.333872\pi\) | ||||
0.498535 | + | 0.866870i | \(0.333872\pi\) | |||||||
\(272\) | −7.23287 | −0.438557 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.57397 | −0.155499 | ||||||||
\(275\) | −21.3820 | −1.28938 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.4497 | −1.58921 | −0.794605 | − | 0.607127i | \(-0.792322\pi\) | ||||
−0.794605 | + | 0.607127i | \(0.792322\pi\) | |||||||
\(278\) | −7.17402 | −0.430269 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.0445223 | 0.00266072 | ||||||||
\(281\) | −3.32607 | −0.198417 | −0.0992084 | − | 0.995067i | \(-0.531631\pi\) | ||||
−0.0992084 | + | 0.995067i | \(0.531631\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.9817 | −1.30668 | −0.653339 | − | 0.757065i | \(-0.726633\pi\) | ||||
−0.653339 | + | 0.757065i | \(0.726633\pi\) | |||||||
\(284\) | −3.05056 | −0.181017 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.55270 | −0.328338 | ||||||||
\(287\) | 0.371014 | 0.0219003 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.60555 | −0.447385 | ||||||||
\(290\) | 1.29537 | 0.0760669 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.85819 | −0.401345 | ||||||||
\(293\) | 6.54118 | 0.382140 | 0.191070 | − | 0.981576i | \(-0.438804\pi\) | ||||
0.191070 | + | 0.981576i | \(0.438804\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.64771 | 0.0959336 | ||||||||
\(296\) | 12.5684 | 0.730525 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.3984 | −1.18165 | ||||||||
\(299\) | −10.0736 | −0.582570 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.164333 | −0.00947197 | ||||||||
\(302\) | 25.7510 | 1.48181 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.09369 | 0.292143 | ||||||||
\(305\) | 2.51295 | 0.143891 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.6985 | 0.895959 | 0.447980 | − | 0.894044i | \(-0.352144\pi\) | ||||
0.447980 | + | 0.894044i | \(0.352144\pi\) | |||||||
\(308\) | 0.217576 | 0.0123975 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.06055 | −0.117031 | ||||||||
\(311\) | −25.6166 | −1.45258 | −0.726292 | − | 0.687386i | \(-0.758758\pi\) | ||||
−0.726292 | + | 0.687386i | \(0.758758\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.69793 | 0.209019 | 0.104510 | − | 0.994524i | \(-0.466673\pi\) | ||||
0.104510 | + | 0.994524i | \(0.466673\pi\) | |||||||
\(314\) | 22.9531 | 1.29532 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.8950 | −0.612890 | ||||||||
\(317\) | −19.0196 | −1.06825 | −0.534124 | − | 0.845406i | \(-0.679359\pi\) | ||||
−0.534124 | + | 0.845406i | \(0.679359\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 26.5917 | 1.48885 | ||||||||
\(320\) | −1.55433 | −0.0868894 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.868651 | −0.0484080 | ||||||||
\(323\) | −6.61597 | −0.368122 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.46580 | −0.303188 | ||||||||
\(326\) | 16.7161 | 0.925822 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −14.1160 | −0.779427 | ||||||||
\(329\) | −0.414894 | −0.0228738 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.74934 | −0.261048 | −0.130524 | − | 0.991445i | \(-0.541666\pi\) | ||||
−0.130524 | + | 0.991445i | \(0.541666\pi\) | |||||||
\(332\) | −1.55200 | −0.0851771 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −22.6974 | −1.24195 | ||||||||
\(335\) | −1.00622 | −0.0549759 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.8451 | −1.62576 | −0.812882 | − | 0.582428i | \(-0.802103\pi\) | ||||
−0.812882 | + | 0.582428i | \(0.802103\pi\) | |||||||
\(338\) | 13.8252 | 0.751989 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.342425 | 0.0185706 | ||||||||
\(341\) | −42.2993 | −2.29064 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.13210 | 0.0611274 | ||||||||
\(344\) | 6.25238 | 0.337105 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 28.3492 | 1.52406 | ||||||||
\(347\) | −15.3781 | −0.825540 | −0.412770 | − | 0.910835i | \(-0.635439\pi\) | ||||
−0.412770 | + | 0.910835i | \(0.635439\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.64130 | 0.355501 | 0.177750 | − | 0.984076i | \(-0.443118\pi\) | ||||
0.177750 | + | 0.984076i | \(0.443118\pi\) | |||||||
\(350\) | −0.471319 | −0.0251930 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −14.5856 | −0.777415 | ||||||||
\(353\) | 33.7272 | 1.79512 | 0.897558 | − | 0.440896i | \(-0.145339\pi\) | ||||
0.897558 | + | 0.440896i | \(0.145339\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.872830 | −0.0463250 | ||||||||
\(356\) | 3.48196 | 0.184544 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.8191 | 0.730361 | ||||||||
\(359\) | 27.2110 | 1.43614 | 0.718071 | − | 0.695970i | \(-0.245025\pi\) | ||||
0.718071 | + | 0.695970i | \(0.245025\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.3408 | −0.754777 | ||||||||
\(362\) | −0.227199 | −0.0119413 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.0556181 | 0.00291518 | ||||||||
\(365\) | −1.96228 | −0.102710 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.0523 | 0.733525 | 0.366763 | − | 0.930315i | \(-0.380466\pi\) | ||||
0.366763 | + | 0.930315i | \(0.380466\pi\) | |||||||
\(368\) | 21.6068 | 1.12633 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.856078 | 0.0445054 | ||||||||
\(371\) | 0.217639 | 0.0112993 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.8673 | 1.02869 | 0.514345 | − | 0.857584i | \(-0.328035\pi\) | ||||
0.514345 | + | 0.857584i | \(0.328035\pi\) | |||||||
\(374\) | −15.4693 | −0.799899 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.7855 | 0.814075 | ||||||||
\(377\) | 6.79753 | 0.350091 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.4863 | −0.846844 | −0.423422 | − | 0.905933i | \(-0.639171\pi\) | ||||
−0.423422 | + | 0.905933i | \(0.639171\pi\) | |||||||
\(380\) | −0.241150 | −0.0123707 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −23.4656 | −1.20060 | ||||||||
\(383\) | −22.2392 | −1.13637 | −0.568186 | − | 0.822900i | \(-0.692355\pi\) | ||||
−0.568186 | + | 0.822900i | \(0.692355\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0622532 | 0.00317272 | ||||||||
\(386\) | 19.2819 | 0.981422 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.73139 | 0.443269 | ||||||||
\(389\) | 10.3650 | 0.525528 | 0.262764 | − | 0.964860i | \(-0.415366\pi\) | ||||
0.262764 | + | 0.964860i | \(0.415366\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.0641 | −1.41926 | ||||||||
\(392\) | −21.5264 | −1.08725 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 28.5322 | 1.43743 | ||||||||
\(395\) | −3.11729 | −0.156848 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.54363 | −0.127661 | −0.0638306 | − | 0.997961i | \(-0.520332\pi\) | ||||
−0.0638306 | + | 0.997961i | \(0.520332\pi\) | |||||||
\(398\) | 19.0519 | 0.954985 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.7236 | 0.586178 | ||||||||
\(401\) | −12.4246 | −0.620455 | −0.310227 | − | 0.950662i | \(-0.600405\pi\) | ||||
−0.310227 | + | 0.950662i | \(0.600405\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.8128 | −0.538625 | ||||||||
\(404\) | −4.98883 | −0.248203 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.586155 | 0.0290904 | ||||||||
\(407\) | 17.5738 | 0.871098 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.3575 | 0.709932 | 0.354966 | − | 0.934879i | \(-0.384492\pi\) | ||||
0.354966 | + | 0.934879i | \(0.384492\pi\) | |||||||
\(410\) | −0.961490 | −0.0474846 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.58076 | −0.324211 | ||||||||
\(413\) | 0.745589 | 0.0366880 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.444061 | −0.0217981 | ||||||||
\(416\) | −3.72846 | −0.182803 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.8941 | 0.532849 | ||||||||
\(419\) | −15.6860 | −0.766309 | −0.383155 | − | 0.923684i | \(-0.625162\pi\) | ||||
−0.383155 | + | 0.923684i | \(0.625162\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.689920 | 0.0336247 | 0.0168123 | − | 0.999859i | \(-0.494648\pi\) | ||||
0.0168123 | + | 0.999859i | \(0.494648\pi\) | |||||||
\(422\) | −15.9299 | −0.775454 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.28054 | −0.402139 | ||||||||
\(425\) | −15.2272 | −0.738628 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.13711 | 0.0550285 | ||||||||
\(428\) | −2.07251 | −0.100179 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.425870 | 0.0205373 | ||||||||
\(431\) | −29.0858 | −1.40102 | −0.700508 | − | 0.713645i | \(-0.747043\pi\) | ||||
−0.700508 | + | 0.713645i | \(0.747043\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.1169 | 0.870643 | 0.435321 | − | 0.900275i | \(-0.356635\pi\) | ||||
0.435321 | + | 0.900275i | \(0.356635\pi\) | |||||||
\(434\) | −0.932396 | −0.0447565 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.99557 | 0.382918 | ||||||||
\(437\) | 19.7639 | 0.945435 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.25712 | 0.155454 | 0.0777270 | − | 0.996975i | \(-0.475234\pi\) | ||||
0.0777270 | + | 0.996975i | \(0.475234\pi\) | |||||||
\(440\) | −2.36855 | −0.112916 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.95436 | −0.188090 | ||||||||
\(443\) | 21.5717 | 1.02490 | 0.512451 | − | 0.858717i | \(-0.328738\pi\) | ||||
0.512451 | + | 0.858717i | \(0.328738\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.996264 | 0.0472274 | ||||||||
\(446\) | −28.9324 | −1.36999 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.703331 | −0.0332293 | ||||||||
\(449\) | −18.9612 | −0.894834 | −0.447417 | − | 0.894325i | \(-0.647656\pi\) | ||||
−0.447417 | + | 0.894325i | \(0.647656\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.7377 | −0.929410 | ||||||||
\(452\) | −2.76246 | −0.129935 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.0907 | 0.989837 | ||||||||
\(455\) | 0.0159136 | 0.000746039 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.18789 | 0.195901 | 0.0979506 | − | 0.995191i | \(-0.468771\pi\) | ||||
0.0979506 | + | 0.995191i | \(0.468771\pi\) | |||||||
\(458\) | −18.5935 | −0.868815 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.02293 | −0.0476942 | ||||||||
\(461\) | −13.7101 | −0.638543 | −0.319271 | − | 0.947663i | \(-0.603438\pi\) | ||||
−0.319271 | + | 0.947663i | \(0.603438\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.87808 | 0.226703 | 0.113352 | − | 0.993555i | \(-0.463841\pi\) | ||||
0.113352 | + | 0.993555i | \(0.463841\pi\) | |||||||
\(464\) | −14.5800 | −0.676859 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.73941 | 0.126901 | ||||||||
\(467\) | −12.3373 | −0.570904 | −0.285452 | − | 0.958393i | \(-0.592144\pi\) | ||||
−0.285452 | + | 0.958393i | \(0.592144\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.455316 | −0.0210245 | ||||||||
\(470\) | 1.07520 | 0.0495955 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −28.3675 | −1.30572 | ||||||||
\(473\) | 8.74236 | 0.401974 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.7236 | 0.492034 | ||||||||
\(476\) | 0.154947 | 0.00710199 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.68566 | 0.260056 | ||||||||
\(479\) | 3.56361 | 0.162826 | 0.0814128 | − | 0.996680i | \(-0.474057\pi\) | ||||
0.0814128 | + | 0.996680i | \(0.474057\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.49231 | 0.204832 | ||||||||
\(482\) | 4.01846 | 0.183036 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.70130 | −0.213695 | ||||||||
\(485\) | 2.49824 | 0.113439 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.09262 | −0.230769 | −0.115384 | − | 0.993321i | \(-0.536810\pi\) | ||||
−0.115384 | + | 0.993321i | \(0.536810\pi\) | |||||||
\(488\) | −43.2637 | −1.95845 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.46624 | −0.0662378 | ||||||||
\(491\) | −27.1049 | −1.22323 | −0.611614 | − | 0.791156i | \(-0.709479\pi\) | ||||
−0.611614 | + | 0.791156i | \(0.709479\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.9373 | 0.852893 | ||||||||
\(494\) | 2.78483 | 0.125295 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.1924 | 1.04137 | ||||||||
\(497\) | −0.394955 | −0.0177162 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.49778 | −0.201348 | −0.100674 | − | 0.994919i | \(-0.532100\pi\) | ||||
−0.100674 | + | 0.994919i | \(0.532100\pi\) | |||||||
\(500\) | −1.11363 | −0.0498028 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −30.1568 | −1.34596 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.42741 | −0.0635190 | ||||||||
\(506\) | 46.2115 | 2.05435 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.9397 | 0.485369 | ||||||||
\(509\) | 9.92656 | 0.439987 | 0.219993 | − | 0.975501i | \(-0.429396\pi\) | ||||
0.219993 | + | 0.975501i | \(0.429396\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.887929 | −0.0392797 | ||||||||
\(512\) | 22.5244 | 0.995449 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −28.3663 | −1.25118 | ||||||||
\(515\) | −1.88290 | −0.0829704 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.0720 | 0.970726 | ||||||||
\(518\) | 0.387375 | 0.0170203 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.605464 | −0.0265514 | ||||||||
\(521\) | 8.65790 | 0.379309 | 0.189655 | − | 0.981851i | \(-0.439263\pi\) | ||||
0.189655 | + | 0.981851i | \(0.439263\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.7111 | 0.774451 | 0.387226 | − | 0.921985i | \(-0.373433\pi\) | ||||
0.387226 | + | 0.921985i | \(0.373433\pi\) | |||||||
\(524\) | 7.39445 | 0.323028 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.3164 | 0.929441 | ||||||||
\(527\) | −30.1236 | −1.31220 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 60.8360 | 2.64504 | ||||||||
\(530\) | −0.564016 | −0.0244993 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.109120 | −0.00473096 | ||||||||
\(533\) | −5.04547 | −0.218543 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.592990 | −0.0256372 | ||||||||
\(536\) | 17.3234 | 0.748259 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.67255 | −0.287674 | ||||||||
\(539\) | −30.0992 | −1.29646 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.8187 | −0.465131 | −0.232565 | − | 0.972581i | \(-0.574712\pi\) | ||||
−0.232565 | + | 0.972581i | \(0.574712\pi\) | |||||||
\(542\) | −19.2478 | −0.826765 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10.3872 | −0.445346 | ||||||||
\(545\) | 2.28771 | 0.0979945 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.1188 | −1.41606 | −0.708028 | − | 0.706184i | \(-0.750415\pi\) | ||||
−0.708028 | + | 0.706184i | \(0.750415\pi\) | |||||||
\(548\) | −1.37158 | −0.0585910 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 25.0738 | 1.06915 | ||||||||
\(551\) | −13.3364 | −0.568151 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.41057 | −0.0599835 | ||||||||
\(554\) | 31.0165 | 1.31777 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.82279 | −0.162122 | ||||||||
\(557\) | −12.3324 | −0.522541 | −0.261270 | − | 0.965266i | \(-0.584141\pi\) | ||||
−0.261270 | + | 0.965266i | \(0.584141\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.23478 | 0.0945210 | ||||||||
\(560\) | −0.0341329 | −0.00144238 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.90035 | 0.164526 | ||||||||
\(563\) | −29.3356 | −1.23635 | −0.618174 | − | 0.786041i | \(-0.712127\pi\) | ||||
−0.618174 | + | 0.786041i | \(0.712127\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.790400 | −0.0332524 | ||||||||
\(566\) | 25.7771 | 1.08349 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.0269 | 0.630514 | ||||||||
\(569\) | −0.339405 | −0.0142286 | −0.00711431 | − | 0.999975i | \(-0.502265\pi\) | ||||
−0.00711431 | + | 0.999975i | \(0.502265\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.5993 | −0.694658 | −0.347329 | − | 0.937743i | \(-0.612911\pi\) | ||||
−0.347329 | + | 0.937743i | \(0.612911\pi\) | |||||||
\(572\) | −2.95884 | −0.123715 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.435073 | −0.0181596 | ||||||||
\(575\) | 45.4883 | 1.89699 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.0207 | −0.791840 | −0.395920 | − | 0.918285i | \(-0.629574\pi\) | ||||
−0.395920 | + | 0.918285i | \(0.629574\pi\) | |||||||
\(578\) | 8.91872 | 0.370970 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.690259 | 0.0286614 | ||||||||
\(581\) | −0.200937 | −0.00833629 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.5782 | −0.479522 | ||||||||
\(584\) | 33.7831 | 1.39796 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.67058 | −0.316869 | ||||||||
\(587\) | −29.3939 | −1.21322 | −0.606609 | − | 0.795000i | \(-0.707471\pi\) | ||||
−0.606609 | + | 0.795000i | \(0.707471\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.2143 | 0.874118 | ||||||||
\(590\) | −1.93221 | −0.0795477 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.63554 | −0.396018 | ||||||||
\(593\) | 21.6941 | 0.890871 | 0.445436 | − | 0.895314i | \(-0.353049\pi\) | ||||
0.445436 | + | 0.895314i | \(0.353049\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.0443337 | 0.00181751 | ||||||||
\(596\) | −10.8696 | −0.445236 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 11.8129 | 0.483065 | ||||||||
\(599\) | 7.41054 | 0.302786 | 0.151393 | − | 0.988474i | \(-0.451624\pi\) | ||||
0.151393 | + | 0.988474i | \(0.451624\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.7208 | −0.722848 | −0.361424 | − | 0.932402i | \(-0.617709\pi\) | ||||
−0.361424 | + | 0.932402i | \(0.617709\pi\) | |||||||
\(602\) | 0.192706 | 0.00785411 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.7218 | 0.558333 | ||||||||
\(605\) | −1.34514 | −0.0546878 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.0318 | 1.50307 | 0.751536 | − | 0.659692i | \(-0.229313\pi\) | ||||
0.751536 | + | 0.659692i | \(0.229313\pi\) | |||||||
\(608\) | 7.31507 | 0.296665 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.94683 | −0.119314 | ||||||||
\(611\) | 5.64219 | 0.228259 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.6348 | 1.52005 | 0.760027 | − | 0.649891i | \(-0.225185\pi\) | ||||
0.760027 | + | 0.649891i | \(0.225185\pi\) | |||||||
\(614\) | −18.4090 | −0.742925 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.07177 | −0.0431828 | ||||||||
\(617\) | 8.73601 | 0.351699 | 0.175849 | − | 0.984417i | \(-0.443733\pi\) | ||||
0.175849 | + | 0.984417i | \(0.443733\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.0846 | 0.686687 | 0.343343 | − | 0.939210i | \(-0.388441\pi\) | ||||
0.343343 | + | 0.939210i | \(0.388441\pi\) | |||||||
\(620\) | −1.09799 | −0.0440965 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 30.0396 | 1.20448 | ||||||||
\(623\) | 0.450809 | 0.0180613 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.5215 | 0.980862 | ||||||||
\(626\) | −4.33641 | −0.173318 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.2309 | 0.488067 | ||||||||
\(629\) | 12.5152 | 0.499013 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.0472 | −1.51464 | −0.757318 | − | 0.653046i | \(-0.773491\pi\) | ||||
−0.757318 | + | 0.653046i | \(0.773491\pi\) | |||||||
\(632\) | 53.6681 | 2.13480 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 22.3035 | 0.885787 | ||||||||
\(635\) | 3.13008 | 0.124213 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.69415 | −0.304853 | ||||||||
\(638\) | −31.1830 | −1.23455 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.610894 | 0.0241477 | ||||||||
\(641\) | −27.5905 | −1.08976 | −0.544879 | − | 0.838514i | \(-0.683425\pi\) | ||||
−0.544879 | + | 0.838514i | \(0.683425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.89268 | 0.271821 | 0.135910 | − | 0.990721i | \(-0.456604\pi\) | ||||
0.135910 | + | 0.990721i | \(0.456604\pi\) | |||||||
\(644\) | −0.462874 | −0.0182398 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.75827 | 0.305245 | ||||||||
\(647\) | −8.60822 | −0.338424 | −0.169212 | − | 0.985580i | \(-0.554122\pi\) | ||||
−0.169212 | + | 0.985580i | \(0.554122\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39.6647 | −1.55698 | ||||||||
\(650\) | 6.40952 | 0.251402 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.90746 | 0.348843 | ||||||||
\(653\) | −3.73378 | −0.146114 | −0.0730571 | − | 0.997328i | \(-0.523276\pi\) | ||||
−0.0730571 | + | 0.997328i | \(0.523276\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.11571 | 0.0826677 | ||||||||
\(656\) | 10.8220 | 0.422528 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.486529 | 0.0189669 | ||||||||
\(659\) | −10.1373 | −0.394893 | −0.197447 | − | 0.980314i | \(-0.563265\pi\) | ||||
−0.197447 | + | 0.980314i | \(0.563265\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.0003 | −0.427863 | −0.213932 | − | 0.976849i | \(-0.568627\pi\) | ||||
−0.213932 | + | 0.976849i | \(0.568627\pi\) | |||||||
\(662\) | 5.56936 | 0.216459 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.64508 | 0.296687 | ||||||||
\(665\) | −0.0312216 | −0.00121072 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −56.5715 | −2.19046 | ||||||||
\(668\) | −12.0947 | −0.467957 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.17996 | 0.0455858 | ||||||||
\(671\) | −60.4932 | −2.33531 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.9940 | −1.73439 | −0.867196 | − | 0.497967i | \(-0.834080\pi\) | ||||
−0.867196 | + | 0.497967i | \(0.834080\pi\) | |||||||
\(674\) | 34.9981 | 1.34808 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.36695 | 0.283344 | ||||||||
\(677\) | −15.4870 | −0.595213 | −0.297607 | − | 0.954689i | \(-0.596188\pi\) | ||||
−0.297607 | + | 0.954689i | \(0.596188\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.13045 | 0.0433828 | ||||||||
\(680\) | −1.68677 | −0.0646846 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 49.6027 | 1.89939 | ||||||||
\(683\) | −33.7255 | −1.29047 | −0.645235 | − | 0.763984i | \(-0.723241\pi\) | ||||
−0.645235 | + | 0.763984i | \(0.723241\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.392439 | −0.0149943 | ||||||||
\(686\) | −1.32756 | −0.0506866 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.79336 | −0.182745 | ||||||||
\(689\) | −2.95970 | −0.112756 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.5728 | 0.516333 | 0.258166 | − | 0.966100i | \(-0.416882\pi\) | ||||
0.258166 | + | 0.966100i | \(0.416882\pi\) | |||||||
\(692\) | 15.1063 | 0.574255 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.0333 | 0.684534 | ||||||||
\(695\) | −1.09378 | −0.0414895 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.0562 | −0.532417 | ||||||||
\(698\) | −7.78799 | −0.294780 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.251149 | −0.00949256 | ||||||||
\(701\) | 34.7789 | 1.31358 | 0.656790 | − | 0.754074i | \(-0.271914\pi\) | ||||
0.656790 | + | 0.754074i | \(0.271914\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.81371 | −0.332415 | ||||||||
\(704\) | 37.4167 | 1.41019 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −39.5505 | −1.48850 | ||||||||
\(707\) | −0.645903 | −0.0242917 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.1752 | −0.870362 | −0.435181 | − | 0.900343i | \(-0.643316\pi\) | ||||
−0.435181 | + | 0.900343i | \(0.643316\pi\) | |||||||
\(710\) | 1.02353 | 0.0384125 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −17.1520 | −0.642797 | ||||||||
\(713\) | 89.9882 | 3.37009 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.846588 | −0.0316606 | ||||||||
\(716\) | 7.36371 | 0.275195 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −31.9092 | −1.19084 | ||||||||
\(719\) | 39.5082 | 1.47341 | 0.736704 | − | 0.676215i | \(-0.236381\pi\) | ||||
0.736704 | + | 0.676215i | \(0.236381\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.852011 | −0.0317305 | ||||||||
\(722\) | 16.8168 | 0.625858 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.121067 | −0.00449940 | ||||||||
\(725\) | −30.6950 | −1.13998 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.75881 | −0.213583 | −0.106791 | − | 0.994281i | \(-0.534058\pi\) | ||||
−0.106791 | + | 0.994281i | \(0.534058\pi\) | |||||||
\(728\) | −0.273972 | −0.0101541 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.30108 | 0.0851669 | ||||||||
\(731\) | 6.22589 | 0.230273 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.9036 | −1.54774 | −0.773872 | − | 0.633343i | \(-0.781682\pi\) | ||||
−0.773872 | + | 0.633343i | \(0.781682\pi\) | |||||||
\(734\) | −16.4786 | −0.608236 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 31.0296 | 1.14377 | ||||||||
\(737\) | 24.2224 | 0.892245 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.5650 | −0.535780 | −0.267890 | − | 0.963449i | \(-0.586326\pi\) | ||||
−0.267890 | + | 0.963449i | \(0.586326\pi\) | |||||||
\(740\) | 0.456174 | 0.0167693 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.255217 | −0.00936931 | ||||||||
\(743\) | 22.9633 | 0.842440 | 0.421220 | − | 0.906958i | \(-0.361602\pi\) | ||||
0.421220 | + | 0.906958i | \(0.361602\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.11003 | −0.113943 | ||||||||
\(746\) | −23.2976 | −0.852984 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.24306 | −0.301396 | ||||||||
\(749\) | −0.268328 | −0.00980448 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.52609 | −0.311121 | −0.155561 | − | 0.987826i | \(-0.549718\pi\) | ||||
−0.155561 | + | 0.987826i | \(0.549718\pi\) | |||||||
\(752\) | −12.1019 | −0.441311 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.97119 | −0.290294 | ||||||||
\(755\) | 3.92611 | 0.142886 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.7364 | −0.717331 | −0.358665 | − | 0.933466i | \(-0.616768\pi\) | ||||
−0.358665 | + | 0.933466i | \(0.616768\pi\) | |||||||
\(758\) | 19.3328 | 0.702199 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.18789 | 0.0430894 | ||||||||
\(761\) | −44.7253 | −1.62129 | −0.810646 | − | 0.585537i | \(-0.800884\pi\) | ||||
−0.810646 | + | 0.585537i | \(0.800884\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.03519 | 0.0374762 | ||||||||
\(764\) | −12.5040 | −0.452379 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.0791 | 0.942275 | ||||||||
\(767\) | −10.1394 | −0.366111 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.1170 | −1.01393 | −0.506963 | − | 0.861968i | \(-0.669232\pi\) | ||||
−0.506963 | + | 0.861968i | \(0.669232\pi\) | |||||||
\(770\) | −0.0730018 | −0.00263080 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10.2746 | 0.369793 | ||||||||
\(773\) | −34.5978 | −1.24440 | −0.622199 | − | 0.782859i | \(-0.713760\pi\) | ||||
−0.622199 | + | 0.782859i | \(0.713760\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 48.8264 | 1.75390 | ||||||||
\(776\) | −43.0104 | −1.54398 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.1546 | −0.435765 | ||||||||
\(779\) | 9.89897 | 0.354667 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.0113 | 0.751843 | ||||||||
\(782\) | 32.9096 | 1.17685 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 16.5031 | 0.589398 | ||||||||
\(785\) | 3.49953 | 0.124904 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −46.1869 | −1.64639 | −0.823193 | − | 0.567762i | \(-0.807810\pi\) | ||||
−0.823193 | + | 0.567762i | \(0.807810\pi\) | |||||||
\(788\) | 15.2038 | 0.541613 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.65552 | 0.130057 | ||||||||
\(791\) | −0.357656 | −0.0127168 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.4637 | −0.549131 | ||||||||
\(794\) | 2.98282 | 0.105856 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.1521 | 0.359832 | ||||||||
\(797\) | −31.0936 | −1.10139 | −0.550695 | − | 0.834707i | \(-0.685637\pi\) | ||||
−0.550695 | + | 0.834707i | \(0.685637\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.7186 | 0.556085 | ||||||||
\(800\) | 16.8363 | 0.595252 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14.5698 | 0.514478 | ||||||||
\(803\) | 47.2371 | 1.66696 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.132438 | −0.00466784 | ||||||||
\(806\) | 12.6798 | 0.446626 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 24.5747 | 0.864536 | ||||||||
\(809\) | 22.7451 | 0.799676 | 0.399838 | − | 0.916586i | \(-0.369066\pi\) | ||||
0.399838 | + | 0.916586i | \(0.369066\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.2514 | −0.711121 | −0.355561 | − | 0.934653i | \(-0.615710\pi\) | ||||
−0.355561 | + | 0.934653i | \(0.615710\pi\) | |||||||
\(812\) | 0.312342 | 0.0109610 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20.6080 | −0.722311 | ||||||||
\(815\) | 2.54862 | 0.0892741 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.38453 | −0.153395 | ||||||||
\(818\) | −16.8364 | −0.588673 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.512345 | −0.0178918 | ||||||||
\(821\) | −47.0787 | −1.64306 | −0.821529 | − | 0.570167i | \(-0.806879\pi\) | ||||
−0.821529 | + | 0.570167i | \(0.806879\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.97277 | −0.138482 | −0.0692411 | − | 0.997600i | \(-0.522058\pi\) | ||||
−0.0692411 | + | 0.997600i | \(0.522058\pi\) | |||||||
\(824\) | 32.4165 | 1.12928 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.874322 | −0.0304216 | ||||||||
\(827\) | 12.1175 | 0.421366 | 0.210683 | − | 0.977554i | \(-0.432431\pi\) | ||||
0.210683 | + | 0.977554i | \(0.432431\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.0304 | 0.938804 | 0.469402 | − | 0.882985i | \(-0.344470\pi\) | ||||
0.469402 | + | 0.882985i | \(0.344470\pi\) | |||||||
\(830\) | 0.520732 | 0.0180749 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.56468 | 0.331596 | ||||||||
\(833\) | −21.4352 | −0.742686 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.46054 | −0.119757 | ||||||||
\(836\) | 5.80511 | 0.200774 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18.3943 | 0.635420 | ||||||||
\(839\) | 21.4624 | 0.740964 | 0.370482 | − | 0.928840i | \(-0.379193\pi\) | ||||
0.370482 | + | 0.928840i | \(0.379193\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.17374 | 0.316336 | ||||||||
\(842\) | −0.809042 | −0.0278814 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.48848 | −0.292186 | ||||||||
\(845\) | 2.10784 | 0.0725120 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.608676 | −0.0209144 | ||||||||
\(848\) | 6.34825 | 0.218000 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 17.8563 | 0.612467 | ||||||||
\(851\) | −37.3866 | −1.28160 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.5093 | −0.702226 | −0.351113 | − | 0.936333i | \(-0.614197\pi\) | ||||
−0.351113 | + | 0.936333i | \(0.614197\pi\) | |||||||
\(854\) | −1.33344 | −0.0456294 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.2091 | 0.348939 | ||||||||
\(857\) | 23.2772 | 0.795135 | 0.397567 | − | 0.917573i | \(-0.369854\pi\) | ||||
0.397567 | + | 0.917573i | \(0.369854\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.80551 | −0.129842 | −0.0649212 | − | 0.997890i | \(-0.520680\pi\) | ||||
−0.0649212 | + | 0.997890i | \(0.520680\pi\) | |||||||
\(860\) | 0.226932 | 0.00773830 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 34.1078 | 1.16172 | ||||||||
\(863\) | 35.9633 | 1.22420 | 0.612102 | − | 0.790779i | \(-0.290324\pi\) | ||||
0.612102 | + | 0.790779i | \(0.290324\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.32224 | 0.146960 | ||||||||
\(866\) | −21.2450 | −0.721933 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.496842 | −0.0168639 | ||||||||
\(869\) | 75.0412 | 2.54560 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.19189 | 0.209804 | ||||||||
\(872\) | −39.3858 | −1.33377 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −23.1763 | −0.783951 | ||||||||
\(875\) | −0.144181 | −0.00487421 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.2388 | 0.480810 | 0.240405 | − | 0.970673i | \(-0.422720\pi\) | ||||
0.240405 | + | 0.970673i | \(0.422720\pi\) | |||||||
\(878\) | −3.81949 | −0.128902 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.81584 | 0.0612120 | ||||||||
\(881\) | −27.4845 | −0.925976 | −0.462988 | − | 0.886365i | \(-0.653223\pi\) | ||||
−0.462988 | + | 0.886365i | \(0.653223\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.3360 | 0.818973 | 0.409487 | − | 0.912316i | \(-0.365708\pi\) | ||||
0.409487 | + | 0.912316i | \(0.365708\pi\) | |||||||
\(884\) | −2.10714 | −0.0708709 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −25.2962 | −0.849844 | ||||||||
\(887\) | 26.2023 | 0.879787 | 0.439893 | − | 0.898050i | \(-0.355016\pi\) | ||||
0.439893 | + | 0.898050i | \(0.355016\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.41636 | 0.0475031 | ||||||||
\(890\) | −1.16828 | −0.0391608 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.4171 | −0.516202 | ||||||||
\(893\) | −11.0697 | −0.370434 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.10692 | 0.0704265 | ||||||||
\(896\) | 0.276429 | 0.00923485 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.2350 | 0.741992 | ||||||||
\(899\) | −60.7230 | −2.02522 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.24546 | −0.274696 | ||||||||
\(902\) | 23.1456 | 0.770663 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.6078 | 0.452587 | ||||||||
\(905\) | −0.0346397 | −0.00115146 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 58.2340 | 1.93363 | 0.966814 | − | 0.255482i | \(-0.0822342\pi\) | ||||
0.966814 | + | 0.255482i | \(0.0822342\pi\) | |||||||
\(908\) | 11.2385 | 0.372963 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.0186612 | −0.000618612 0 | ||||||||
\(911\) | 30.4851 | 1.01002 | 0.505008 | − | 0.863114i | \(-0.331489\pi\) | ||||
0.505008 | + | 0.863114i | \(0.331489\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.6897 | 0.353778 | ||||||||
\(914\) | −4.91097 | −0.162440 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.90781 | −0.327363 | ||||||||
\(917\) | 0.957358 | 0.0316148 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.94915 | −0.0972833 | −0.0486417 | − | 0.998816i | \(-0.515489\pi\) | ||||
−0.0486417 | + | 0.998816i | \(0.515489\pi\) | |||||||
\(920\) | 5.03889 | 0.166127 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 16.0773 | 0.529477 | ||||||||
\(923\) | 5.37104 | 0.176790 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.2855 | −0.666983 | ||||||||
\(926\) | −5.72032 | −0.187982 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −20.9384 | −0.687336 | ||||||||
\(929\) | −28.9881 | −0.951070 | −0.475535 | − | 0.879697i | \(-0.657745\pi\) | ||||
−0.475535 | + | 0.879697i | \(0.657745\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.0956 | 0.494737 | ||||||||
\(932\) | 1.45974 | 0.0478153 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 14.4675 | 0.473391 | ||||||||
\(935\) | −2.35852 | −0.0771318 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.5952 | −0.901497 | −0.450748 | − | 0.892651i | \(-0.648843\pi\) | ||||
−0.450748 | + | 0.892651i | \(0.648843\pi\) | |||||||
\(938\) | 0.533930 | 0.0174334 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.572939 | 0.0186872 | ||||||||
\(941\) | −19.2064 | −0.626112 | −0.313056 | − | 0.949735i | \(-0.601353\pi\) | ||||
−0.313056 | + | 0.949735i | \(0.601353\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 41.9902 | 1.36739 | ||||||||
\(944\) | 21.7478 | 0.707832 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.2518 | −0.333315 | ||||||||
\(947\) | 41.2922 | 1.34182 | 0.670908 | − | 0.741541i | \(-0.265905\pi\) | ||||
0.670908 | + | 0.741541i | \(0.265905\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.0750 | 0.391973 | ||||||||
\(950\) | −12.5752 | −0.407992 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.763262 | −0.0247375 | ||||||||
\(953\) | 24.0272 | 0.778317 | 0.389158 | − | 0.921171i | \(-0.372766\pi\) | ||||
0.389158 | + | 0.921171i | \(0.372766\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.57767 | −0.115771 | ||||||||
\(956\) | 3.02969 | 0.0979872 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.17890 | −0.135014 | ||||||||
\(959\) | −0.177578 | −0.00573430 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 65.5920 | 2.11587 | ||||||||
\(962\) | −5.26795 | −0.169846 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.14130 | 0.0689665 | ||||||||
\(965\) | 2.93980 | 0.0946355 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.8553 | −0.349084 | −0.174542 | − | 0.984650i | \(-0.555845\pi\) | ||||
−0.174542 | + | 0.984650i | \(0.555845\pi\) | |||||||
\(968\) | 23.1584 | 0.744338 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.92958 | −0.0940633 | ||||||||
\(971\) | 17.1111 | 0.549122 | 0.274561 | − | 0.961570i | \(-0.411467\pi\) | ||||
0.274561 | + | 0.961570i | \(0.411467\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.494936 | −0.0158669 | ||||||||
\(974\) | 5.97191 | 0.191352 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 33.1679 | 1.06168 | ||||||||
\(977\) | −22.5277 | −0.720726 | −0.360363 | − | 0.932812i | \(-0.617347\pi\) | ||||
−0.360363 | + | 0.932812i | \(0.617347\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.9827 | −0.766489 | ||||||||
\(980\) | −0.781306 | −0.0249579 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 31.7849 | 1.01430 | ||||||||
\(983\) | 27.0618 | 0.863138 | 0.431569 | − | 0.902080i | \(-0.357960\pi\) | ||||
0.431569 | + | 0.902080i | \(0.357960\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.35014 | 0.138607 | ||||||||
\(986\) | −22.2070 | −0.707215 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.48394 | 0.0472104 | ||||||||
\(989\) | −18.5986 | −0.591401 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.8216 | −0.629655 | −0.314827 | − | 0.949149i | \(-0.601947\pi\) | ||||
−0.314827 | + | 0.949149i | \(0.601947\pi\) | |||||||
\(992\) | 33.3067 | 1.05749 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.463148 | 0.0146902 | ||||||||
\(995\) | 2.90473 | 0.0920863 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.1120 | −0.731966 | −0.365983 | − | 0.930622i | \(-0.619267\pi\) | ||||
−0.365983 | + | 0.930622i | \(0.619267\pi\) | |||||||
\(998\) | 5.27436 | 0.166957 | ||||||||
\(999\) | 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 | 4527.2.a.k.1.3 | 10 | ||
3.2 | odd | 2 | 503.2.a.e.1.8 | ✓ | 10 | ||
12.11 | even | 2 | 8048.2.a.p.1.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.e.1.8 | ✓ | 10 | 3.2 | odd | 2 | ||
4527.2.a.k.1.3 | 10 | 1.1 | even | 1 | trivial | ||
8048.2.a.p.1.5 | 10 | 12.11 | even | 2 |