Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.19898000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 10x^{4} + 7x^{3} + 24x^{2} - 15x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-2.18328\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 2.18328 | 1.26052 | 0.630260 | − | 0.776384i | \(-0.282948\pi\) | ||||
0.630260 | + | 0.776384i | \(0.282948\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.18328 | −0.891322 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.76673 | 0.588911 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.18328 | 0.630260 | ||||||||
\(13\) | 2.53263 | 0.702425 | 0.351212 | − | 0.936296i | \(-0.385769\pi\) | ||||
0.351212 | + | 0.936296i | \(0.385769\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 2.18328 | 0.563722 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.73813 | −1.39170 | −0.695850 | − | 0.718187i | \(-0.744972\pi\) | ||||
−0.695850 | + | 0.718187i | \(0.744972\pi\) | |||||||
\(18\) | −1.76673 | −0.416423 | ||||||||
\(19\) | −2.24060 | −0.514029 | −0.257014 | − | 0.966408i | \(-0.582739\pi\) | ||||
−0.257014 | + | 0.966408i | \(0.582739\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 2.18328 | 0.476432 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.51489 | −0.524390 | −0.262195 | − | 0.965015i | \(-0.584446\pi\) | ||||
−0.262195 | + | 0.965015i | \(0.584446\pi\) | |||||||
\(24\) | −2.18328 | −0.445661 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.53263 | −0.496689 | ||||||||
\(27\) | −2.69257 | −0.518186 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −8.62000 | −1.60069 | −0.800347 | − | 0.599537i | \(-0.795351\pi\) | ||||
−0.800347 | + | 0.599537i | \(0.795351\pi\) | |||||||
\(30\) | −2.18328 | −0.398611 | ||||||||
\(31\) | 1.84089 | 0.330634 | 0.165317 | − | 0.986240i | \(-0.447135\pi\) | ||||
0.165317 | + | 0.986240i | \(0.447135\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.73813 | 0.984080 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 1.76673 | 0.294455 | ||||||||
\(37\) | −4.63124 | −0.761372 | −0.380686 | − | 0.924704i | \(-0.624312\pi\) | ||||
−0.380686 | + | 0.924704i | \(0.624312\pi\) | |||||||
\(38\) | 2.24060 | 0.363473 | ||||||||
\(39\) | 5.52945 | 0.885421 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −10.5523 | −1.64800 | −0.823999 | − | 0.566591i | \(-0.808262\pi\) | ||||
−0.823999 | + | 0.566591i | \(0.808262\pi\) | |||||||
\(42\) | −2.18328 | −0.336888 | ||||||||
\(43\) | −2.18804 | −0.333672 | −0.166836 | − | 0.985985i | \(-0.553355\pi\) | ||||
−0.166836 | + | 0.985985i | \(0.553355\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.76673 | 0.263369 | ||||||||
\(46\) | 2.51489 | 0.370800 | ||||||||
\(47\) | 3.22482 | 0.470389 | 0.235194 | − | 0.971948i | \(-0.424427\pi\) | ||||
0.235194 | + | 0.971948i | \(0.424427\pi\) | |||||||
\(48\) | 2.18328 | 0.315130 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −12.5280 | −1.75427 | ||||||||
\(52\) | 2.53263 | 0.351212 | ||||||||
\(53\) | −4.01746 | −0.551841 | −0.275920 | − | 0.961180i | \(-0.588983\pi\) | ||||
−0.275920 | + | 0.961180i | \(0.588983\pi\) | |||||||
\(54\) | 2.69257 | 0.366413 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −4.89187 | −0.647944 | ||||||||
\(58\) | 8.62000 | 1.13186 | ||||||||
\(59\) | 2.01405 | 0.262207 | 0.131103 | − | 0.991369i | \(-0.458148\pi\) | ||||
0.131103 | + | 0.991369i | \(0.458148\pi\) | |||||||
\(60\) | 2.18328 | 0.281861 | ||||||||
\(61\) | −0.268235 | −0.0343440 | −0.0171720 | − | 0.999853i | \(-0.505466\pi\) | ||||
−0.0171720 | + | 0.999853i | \(0.505466\pi\) | |||||||
\(62\) | −1.84089 | −0.233793 | ||||||||
\(63\) | 1.76673 | 0.222587 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.53263 | 0.314134 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.86233 | 0.471859 | 0.235929 | − | 0.971770i | \(-0.424187\pi\) | ||||
0.235929 | + | 0.971770i | \(0.424187\pi\) | |||||||
\(68\) | −5.73813 | −0.695850 | ||||||||
\(69\) | −5.49071 | −0.661004 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −9.55514 | −1.13399 | −0.566993 | − | 0.823723i | \(-0.691893\pi\) | ||||
−0.566993 | + | 0.823723i | \(0.691893\pi\) | |||||||
\(72\) | −1.76673 | −0.208211 | ||||||||
\(73\) | −11.4258 | −1.33729 | −0.668647 | − | 0.743580i | \(-0.733126\pi\) | ||||
−0.668647 | + | 0.743580i | \(0.733126\pi\) | |||||||
\(74\) | 4.63124 | 0.538371 | ||||||||
\(75\) | 2.18328 | 0.252104 | ||||||||
\(76\) | −2.24060 | −0.257014 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.52945 | −0.626087 | ||||||||
\(79\) | −11.7534 | −1.32236 | −0.661182 | − | 0.750225i | \(-0.729945\pi\) | ||||
−0.661182 | + | 0.750225i | \(0.729945\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −11.1789 | −1.24209 | ||||||||
\(82\) | 10.5523 | 1.16531 | ||||||||
\(83\) | −7.34851 | −0.806604 | −0.403302 | − | 0.915067i | \(-0.632138\pi\) | ||||
−0.403302 | + | 0.915067i | \(0.632138\pi\) | |||||||
\(84\) | 2.18328 | 0.238216 | ||||||||
\(85\) | −5.73813 | −0.622387 | ||||||||
\(86\) | 2.18804 | 0.235942 | ||||||||
\(87\) | −18.8199 | −2.01771 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.65397 | −0.281321 | −0.140660 | − | 0.990058i | \(-0.544923\pi\) | ||||
−0.140660 | + | 0.990058i | \(0.544923\pi\) | |||||||
\(90\) | −1.76673 | −0.186230 | ||||||||
\(91\) | 2.53263 | 0.265492 | ||||||||
\(92\) | −2.51489 | −0.262195 | ||||||||
\(93\) | 4.01919 | 0.416771 | ||||||||
\(94\) | −3.22482 | −0.332615 | ||||||||
\(95\) | −2.24060 | −0.229881 | ||||||||
\(96\) | −2.18328 | −0.222831 | ||||||||
\(97\) | 16.5045 | 1.67578 | 0.837891 | − | 0.545838i | \(-0.183789\pi\) | ||||
0.837891 | + | 0.545838i | \(0.183789\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 16.0478 | 1.59682 | 0.798408 | − | 0.602116i | \(-0.205676\pi\) | ||||
0.798408 | + | 0.602116i | \(0.205676\pi\) | |||||||
\(102\) | 12.5280 | 1.24045 | ||||||||
\(103\) | −12.9029 | −1.27136 | −0.635680 | − | 0.771953i | \(-0.719280\pi\) | ||||
−0.635680 | + | 0.771953i | \(0.719280\pi\) | |||||||
\(104\) | −2.53263 | −0.248345 | ||||||||
\(105\) | 2.18328 | 0.213067 | ||||||||
\(106\) | 4.01746 | 0.390210 | ||||||||
\(107\) | −6.74567 | −0.652129 | −0.326064 | − | 0.945348i | \(-0.605723\pi\) | ||||
−0.326064 | + | 0.945348i | \(0.605723\pi\) | |||||||
\(108\) | −2.69257 | −0.259093 | ||||||||
\(109\) | 18.6864 | 1.78983 | 0.894916 | − | 0.446235i | \(-0.147235\pi\) | ||||
0.894916 | + | 0.446235i | \(0.147235\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.1113 | −0.959725 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 7.56433 | 0.711593 | 0.355796 | − | 0.934564i | \(-0.384210\pi\) | ||||
0.355796 | + | 0.934564i | \(0.384210\pi\) | |||||||
\(114\) | 4.89187 | 0.458165 | ||||||||
\(115\) | −2.51489 | −0.234514 | ||||||||
\(116\) | −8.62000 | −0.800347 | ||||||||
\(117\) | 4.47448 | 0.413666 | ||||||||
\(118\) | −2.01405 | −0.185408 | ||||||||
\(119\) | −5.73813 | −0.526013 | ||||||||
\(120\) | −2.18328 | −0.199306 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0.268235 | 0.0242849 | ||||||||
\(123\) | −23.0388 | −2.07733 | ||||||||
\(124\) | 1.84089 | 0.165317 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.76673 | −0.157393 | ||||||||
\(127\) | −10.7426 | −0.953249 | −0.476625 | − | 0.879107i | \(-0.658140\pi\) | ||||
−0.476625 | + | 0.879107i | \(0.658140\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.77710 | −0.420601 | ||||||||
\(130\) | −2.53263 | −0.222126 | ||||||||
\(131\) | −17.0221 | −1.48723 | −0.743613 | − | 0.668610i | \(-0.766890\pi\) | ||||
−0.743613 | + | 0.668610i | \(0.766890\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.24060 | −0.194285 | ||||||||
\(134\) | −3.86233 | −0.333654 | ||||||||
\(135\) | −2.69257 | −0.231740 | ||||||||
\(136\) | 5.73813 | 0.492040 | ||||||||
\(137\) | −12.4777 | −1.06604 | −0.533019 | − | 0.846103i | \(-0.678943\pi\) | ||||
−0.533019 | + | 0.846103i | \(0.678943\pi\) | |||||||
\(138\) | 5.49071 | 0.467401 | ||||||||
\(139\) | 17.3812 | 1.47426 | 0.737129 | − | 0.675752i | \(-0.236181\pi\) | ||||
0.737129 | + | 0.675752i | \(0.236181\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 7.04070 | 0.592934 | ||||||||
\(142\) | 9.55514 | 0.801849 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.76673 | 0.147228 | ||||||||
\(145\) | −8.62000 | −0.715852 | ||||||||
\(146\) | 11.4258 | 0.945610 | ||||||||
\(147\) | 2.18328 | 0.180074 | ||||||||
\(148\) | −4.63124 | −0.380686 | ||||||||
\(149\) | −1.49206 | −0.122235 | −0.0611173 | − | 0.998131i | \(-0.519466\pi\) | ||||
−0.0611173 | + | 0.998131i | \(0.519466\pi\) | |||||||
\(150\) | −2.18328 | −0.178264 | ||||||||
\(151\) | −7.99555 | −0.650668 | −0.325334 | − | 0.945599i | \(-0.605477\pi\) | ||||
−0.325334 | + | 0.945599i | \(0.605477\pi\) | |||||||
\(152\) | 2.24060 | 0.181737 | ||||||||
\(153\) | −10.1377 | −0.819587 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.84089 | 0.147864 | ||||||||
\(156\) | 5.52945 | 0.442710 | ||||||||
\(157\) | 2.05173 | 0.163746 | 0.0818729 | − | 0.996643i | \(-0.473910\pi\) | ||||
0.0818729 | + | 0.996643i | \(0.473910\pi\) | |||||||
\(158\) | 11.7534 | 0.935053 | ||||||||
\(159\) | −8.77126 | −0.695606 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −2.51489 | −0.198201 | ||||||||
\(162\) | 11.1789 | 0.878294 | ||||||||
\(163\) | 20.6976 | 1.62116 | 0.810579 | − | 0.585629i | \(-0.199152\pi\) | ||||
0.810579 | + | 0.585629i | \(0.199152\pi\) | |||||||
\(164\) | −10.5523 | −0.823999 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.34851 | 0.570355 | ||||||||
\(167\) | 1.32050 | 0.102183 | 0.0510917 | − | 0.998694i | \(-0.483730\pi\) | ||||
0.0510917 | + | 0.998694i | \(0.483730\pi\) | |||||||
\(168\) | −2.18328 | −0.168444 | ||||||||
\(169\) | −6.58579 | −0.506599 | ||||||||
\(170\) | 5.73813 | 0.440094 | ||||||||
\(171\) | −3.95854 | −0.302717 | ||||||||
\(172\) | −2.18804 | −0.166836 | ||||||||
\(173\) | 15.7029 | 1.19387 | 0.596933 | − | 0.802291i | \(-0.296386\pi\) | ||||
0.596933 | + | 0.802291i | \(0.296386\pi\) | |||||||
\(174\) | 18.8199 | 1.42673 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.39724 | 0.330517 | ||||||||
\(178\) | 2.65397 | 0.198924 | ||||||||
\(179\) | 4.65497 | 0.347929 | 0.173964 | − | 0.984752i | \(-0.444342\pi\) | ||||
0.173964 | + | 0.984752i | \(0.444342\pi\) | |||||||
\(180\) | 1.76673 | 0.131684 | ||||||||
\(181\) | −5.90450 | −0.438878 | −0.219439 | − | 0.975626i | \(-0.570423\pi\) | ||||
−0.219439 | + | 0.975626i | \(0.570423\pi\) | |||||||
\(182\) | −2.53263 | −0.187731 | ||||||||
\(183\) | −0.585633 | −0.0432913 | ||||||||
\(184\) | 2.51489 | 0.185400 | ||||||||
\(185\) | −4.63124 | −0.340496 | ||||||||
\(186\) | −4.01919 | −0.294701 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.22482 | 0.235194 | ||||||||
\(189\) | −2.69257 | −0.195856 | ||||||||
\(190\) | 2.24060 | 0.162550 | ||||||||
\(191\) | −5.93400 | −0.429369 | −0.214685 | − | 0.976683i | \(-0.568872\pi\) | ||||
−0.214685 | + | 0.976683i | \(0.568872\pi\) | |||||||
\(192\) | 2.18328 | 0.157565 | ||||||||
\(193\) | 10.8377 | 0.780113 | 0.390056 | − | 0.920791i | \(-0.372456\pi\) | ||||
0.390056 | + | 0.920791i | \(0.372456\pi\) | |||||||
\(194\) | −16.5045 | −1.18496 | ||||||||
\(195\) | 5.52945 | 0.395972 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 12.0176 | 0.856216 | 0.428108 | − | 0.903728i | \(-0.359180\pi\) | ||||
0.428108 | + | 0.903728i | \(0.359180\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.4014 | 1.30444 | 0.652220 | − | 0.758030i | \(-0.273838\pi\) | ||||
0.652220 | + | 0.758030i | \(0.273838\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 8.43256 | 0.594787 | ||||||||
\(202\) | −16.0478 | −1.12912 | ||||||||
\(203\) | −8.62000 | −0.605005 | ||||||||
\(204\) | −12.5280 | −0.877133 | ||||||||
\(205\) | −10.5523 | −0.737007 | ||||||||
\(206\) | 12.9029 | 0.898987 | ||||||||
\(207\) | −4.44313 | −0.308819 | ||||||||
\(208\) | 2.53263 | 0.175606 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −2.18328 | −0.150661 | ||||||||
\(211\) | 20.0422 | 1.37976 | 0.689880 | − | 0.723924i | \(-0.257663\pi\) | ||||
0.689880 | + | 0.723924i | \(0.257663\pi\) | |||||||
\(212\) | −4.01746 | −0.275920 | ||||||||
\(213\) | −20.8616 | −1.42941 | ||||||||
\(214\) | 6.74567 | 0.461125 | ||||||||
\(215\) | −2.18804 | −0.149223 | ||||||||
\(216\) | 2.69257 | 0.183206 | ||||||||
\(217\) | 1.84089 | 0.124968 | ||||||||
\(218\) | −18.6864 | −1.26560 | ||||||||
\(219\) | −24.9459 | −1.68569 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.5325 | −0.977565 | ||||||||
\(222\) | 10.1113 | 0.678628 | ||||||||
\(223\) | 11.8000 | 0.790185 | 0.395092 | − | 0.918641i | \(-0.370713\pi\) | ||||
0.395092 | + | 0.918641i | \(0.370713\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 1.76673 | 0.117782 | ||||||||
\(226\) | −7.56433 | −0.503172 | ||||||||
\(227\) | 0.990121 | 0.0657166 | 0.0328583 | − | 0.999460i | \(-0.489539\pi\) | ||||
0.0328583 | + | 0.999460i | \(0.489539\pi\) | |||||||
\(228\) | −4.89187 | −0.323972 | ||||||||
\(229\) | 18.3559 | 1.21299 | 0.606495 | − | 0.795087i | \(-0.292575\pi\) | ||||
0.606495 | + | 0.795087i | \(0.292575\pi\) | |||||||
\(230\) | 2.51489 | 0.165827 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.62000 | 0.565931 | ||||||||
\(233\) | −17.3650 | −1.13762 | −0.568809 | − | 0.822470i | \(-0.692596\pi\) | ||||
−0.568809 | + | 0.822470i | \(0.692596\pi\) | |||||||
\(234\) | −4.47448 | −0.292506 | ||||||||
\(235\) | 3.22482 | 0.210364 | ||||||||
\(236\) | 2.01405 | 0.131103 | ||||||||
\(237\) | −25.6611 | −1.66687 | ||||||||
\(238\) | 5.73813 | 0.371947 | ||||||||
\(239\) | 8.92113 | 0.577060 | 0.288530 | − | 0.957471i | \(-0.406834\pi\) | ||||
0.288530 | + | 0.957471i | \(0.406834\pi\) | |||||||
\(240\) | 2.18328 | 0.140930 | ||||||||
\(241\) | −0.896696 | −0.0577613 | −0.0288806 | − | 0.999583i | \(-0.509194\pi\) | ||||
−0.0288806 | + | 0.999583i | \(0.509194\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.3289 | −1.04750 | ||||||||
\(244\) | −0.268235 | −0.0171720 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 23.0388 | 1.46890 | ||||||||
\(247\) | −5.67461 | −0.361067 | ||||||||
\(248\) | −1.84089 | −0.116897 | ||||||||
\(249\) | −16.0439 | −1.01674 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −22.4978 | −1.42005 | −0.710026 | − | 0.704176i | \(-0.751317\pi\) | ||||
−0.710026 | + | 0.704176i | \(0.751317\pi\) | |||||||
\(252\) | 1.76673 | 0.111294 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 10.7426 | 0.674049 | ||||||||
\(255\) | −12.5280 | −0.784531 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −24.9449 | −1.55602 | −0.778009 | − | 0.628254i | \(-0.783770\pi\) | ||||
−0.778009 | + | 0.628254i | \(0.783770\pi\) | |||||||
\(258\) | 4.77710 | 0.297410 | ||||||||
\(259\) | −4.63124 | −0.287772 | ||||||||
\(260\) | 2.53263 | 0.157067 | ||||||||
\(261\) | −15.2292 | −0.942666 | ||||||||
\(262\) | 17.0221 | 1.05163 | ||||||||
\(263\) | 6.25594 | 0.385758 | 0.192879 | − | 0.981223i | \(-0.438218\pi\) | ||||
0.192879 | + | 0.981223i | \(0.438218\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.01746 | −0.246791 | ||||||||
\(266\) | 2.24060 | 0.137380 | ||||||||
\(267\) | −5.79438 | −0.354610 | ||||||||
\(268\) | 3.86233 | 0.235929 | ||||||||
\(269\) | −13.0673 | −0.796727 | −0.398364 | − | 0.917228i | \(-0.630422\pi\) | ||||
−0.398364 | + | 0.917228i | \(0.630422\pi\) | |||||||
\(270\) | 2.69257 | 0.163865 | ||||||||
\(271\) | −24.3157 | −1.47707 | −0.738535 | − | 0.674215i | \(-0.764482\pi\) | ||||
−0.738535 | + | 0.674215i | \(0.764482\pi\) | |||||||
\(272\) | −5.73813 | −0.347925 | ||||||||
\(273\) | 5.52945 | 0.334658 | ||||||||
\(274\) | 12.4777 | 0.753803 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.49071 | −0.330502 | ||||||||
\(277\) | −13.4094 | −0.805696 | −0.402848 | − | 0.915267i | \(-0.631980\pi\) | ||||
−0.402848 | + | 0.915267i | \(0.631980\pi\) | |||||||
\(278\) | −17.3812 | −1.04246 | ||||||||
\(279\) | 3.25236 | 0.194714 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 12.7398 | 0.759993 | 0.379997 | − | 0.924988i | \(-0.375925\pi\) | ||||
0.379997 | + | 0.924988i | \(0.375925\pi\) | |||||||
\(282\) | −7.04070 | −0.419268 | ||||||||
\(283\) | −13.7495 | −0.817325 | −0.408662 | − | 0.912686i | \(-0.634005\pi\) | ||||
−0.408662 | + | 0.912686i | \(0.634005\pi\) | |||||||
\(284\) | −9.55514 | −0.566993 | ||||||||
\(285\) | −4.89187 | −0.289769 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.5523 | −0.622885 | ||||||||
\(288\) | −1.76673 | −0.104106 | ||||||||
\(289\) | 15.9261 | 0.936828 | ||||||||
\(290\) | 8.62000 | 0.506184 | ||||||||
\(291\) | 36.0341 | 2.11236 | ||||||||
\(292\) | −11.4258 | −0.668647 | ||||||||
\(293\) | 16.6376 | 0.971982 | 0.485991 | − | 0.873964i | \(-0.338459\pi\) | ||||
0.485991 | + | 0.873964i | \(0.338459\pi\) | |||||||
\(294\) | −2.18328 | −0.127332 | ||||||||
\(295\) | 2.01405 | 0.117262 | ||||||||
\(296\) | 4.63124 | 0.269186 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.49206 | 0.0864329 | ||||||||
\(299\) | −6.36928 | −0.368345 | ||||||||
\(300\) | 2.18328 | 0.126052 | ||||||||
\(301\) | −2.18804 | −0.126116 | ||||||||
\(302\) | 7.99555 | 0.460092 | ||||||||
\(303\) | 35.0369 | 2.01282 | ||||||||
\(304\) | −2.24060 | −0.128507 | ||||||||
\(305\) | −0.268235 | −0.0153591 | ||||||||
\(306\) | 10.1377 | 0.579536 | ||||||||
\(307\) | 5.56226 | 0.317455 | 0.158728 | − | 0.987322i | \(-0.449261\pi\) | ||||
0.158728 | + | 0.987322i | \(0.449261\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −28.1707 | −1.60258 | ||||||||
\(310\) | −1.84089 | −0.104556 | ||||||||
\(311\) | 17.9179 | 1.01603 | 0.508014 | − | 0.861349i | \(-0.330380\pi\) | ||||
0.508014 | + | 0.861349i | \(0.330380\pi\) | |||||||
\(312\) | −5.52945 | −0.313043 | ||||||||
\(313\) | 5.15478 | 0.291365 | 0.145683 | − | 0.989331i | \(-0.453462\pi\) | ||||
0.145683 | + | 0.989331i | \(0.453462\pi\) | |||||||
\(314\) | −2.05173 | −0.115786 | ||||||||
\(315\) | 1.76673 | 0.0995441 | ||||||||
\(316\) | −11.7534 | −0.661182 | ||||||||
\(317\) | 28.4614 | 1.59855 | 0.799275 | − | 0.600965i | \(-0.205217\pi\) | ||||
0.799275 | + | 0.600965i | \(0.205217\pi\) | |||||||
\(318\) | 8.77126 | 0.491868 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −14.7277 | −0.822021 | ||||||||
\(322\) | 2.51489 | 0.140149 | ||||||||
\(323\) | 12.8568 | 0.715374 | ||||||||
\(324\) | −11.1789 | −0.621047 | ||||||||
\(325\) | 2.53263 | 0.140485 | ||||||||
\(326\) | −20.6976 | −1.14633 | ||||||||
\(327\) | 40.7977 | 2.25612 | ||||||||
\(328\) | 10.5523 | 0.582655 | ||||||||
\(329\) | 3.22482 | 0.177790 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.8572 | −1.36627 | −0.683136 | − | 0.730291i | \(-0.739385\pi\) | ||||
−0.683136 | + | 0.730291i | \(0.739385\pi\) | |||||||
\(332\) | −7.34851 | −0.403302 | ||||||||
\(333\) | −8.18217 | −0.448380 | ||||||||
\(334\) | −1.32050 | −0.0722546 | ||||||||
\(335\) | 3.86233 | 0.211022 | ||||||||
\(336\) | 2.18328 | 0.119108 | ||||||||
\(337\) | −15.6474 | −0.852369 | −0.426184 | − | 0.904636i | \(-0.640142\pi\) | ||||
−0.426184 | + | 0.904636i | \(0.640142\pi\) | |||||||
\(338\) | 6.58579 | 0.358220 | ||||||||
\(339\) | 16.5151 | 0.896977 | ||||||||
\(340\) | −5.73813 | −0.311194 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 3.95854 | 0.214053 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 2.18804 | 0.117971 | ||||||||
\(345\) | −5.49071 | −0.295610 | ||||||||
\(346\) | −15.7029 | −0.844191 | ||||||||
\(347\) | 14.6646 | 0.787239 | 0.393620 | − | 0.919273i | \(-0.371223\pi\) | ||||
0.393620 | + | 0.919273i | \(0.371223\pi\) | |||||||
\(348\) | −18.8199 | −1.00885 | ||||||||
\(349\) | 26.9763 | 1.44401 | 0.722004 | − | 0.691889i | \(-0.243221\pi\) | ||||
0.722004 | + | 0.691889i | \(0.243221\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −6.81929 | −0.363987 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.77463 | 0.254128 | 0.127064 | − | 0.991895i | \(-0.459445\pi\) | ||||
0.127064 | + | 0.991895i | \(0.459445\pi\) | |||||||
\(354\) | −4.39724 | −0.233711 | ||||||||
\(355\) | −9.55514 | −0.507134 | ||||||||
\(356\) | −2.65397 | −0.140660 | ||||||||
\(357\) | −12.5280 | −0.663050 | ||||||||
\(358\) | −4.65497 | −0.246023 | ||||||||
\(359\) | 34.0982 | 1.79963 | 0.899816 | − | 0.436269i | \(-0.143700\pi\) | ||||
0.899816 | + | 0.436269i | \(0.143700\pi\) | |||||||
\(360\) | −1.76673 | −0.0931150 | ||||||||
\(361\) | −13.9797 | −0.735774 | ||||||||
\(362\) | 5.90450 | 0.310334 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.53263 | 0.132746 | ||||||||
\(365\) | −11.4258 | −0.598056 | ||||||||
\(366\) | 0.585633 | 0.0306115 | ||||||||
\(367\) | −9.98965 | −0.521455 | −0.260728 | − | 0.965412i | \(-0.583962\pi\) | ||||
−0.260728 | + | 0.965412i | \(0.583962\pi\) | |||||||
\(368\) | −2.51489 | −0.131098 | ||||||||
\(369\) | −18.6432 | −0.970524 | ||||||||
\(370\) | 4.63124 | 0.240767 | ||||||||
\(371\) | −4.01746 | −0.208576 | ||||||||
\(372\) | 4.01919 | 0.208385 | ||||||||
\(373\) | −0.510916 | −0.0264542 | −0.0132271 | − | 0.999913i | \(-0.504210\pi\) | ||||
−0.0132271 | + | 0.999913i | \(0.504210\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.18328 | 0.112744 | ||||||||
\(376\) | −3.22482 | −0.166307 | ||||||||
\(377\) | −21.8313 | −1.12437 | ||||||||
\(378\) | 2.69257 | 0.138491 | ||||||||
\(379\) | 5.31376 | 0.272949 | 0.136475 | − | 0.990644i | \(-0.456423\pi\) | ||||
0.136475 | + | 0.990644i | \(0.456423\pi\) | |||||||
\(380\) | −2.24060 | −0.114940 | ||||||||
\(381\) | −23.4541 | −1.20159 | ||||||||
\(382\) | 5.93400 | 0.303610 | ||||||||
\(383\) | 23.5202 | 1.20183 | 0.600914 | − | 0.799314i | \(-0.294803\pi\) | ||||
0.600914 | + | 0.799314i | \(0.294803\pi\) | |||||||
\(384\) | −2.18328 | −0.111415 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.8377 | −0.551623 | ||||||||
\(387\) | −3.86567 | −0.196503 | ||||||||
\(388\) | 16.5045 | 0.837891 | ||||||||
\(389\) | 9.18397 | 0.465646 | 0.232823 | − | 0.972519i | \(-0.425204\pi\) | ||||
0.232823 | + | 0.972519i | \(0.425204\pi\) | |||||||
\(390\) | −5.52945 | −0.279995 | ||||||||
\(391\) | 14.4307 | 0.729794 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −37.1641 | −1.87468 | ||||||||
\(394\) | −12.0176 | −0.605436 | ||||||||
\(395\) | −11.7534 | −0.591380 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −31.5709 | −1.58450 | −0.792248 | − | 0.610199i | \(-0.791089\pi\) | ||||
−0.792248 | + | 0.610199i | \(0.791089\pi\) | |||||||
\(398\) | −18.4014 | −0.922378 | ||||||||
\(399\) | −4.89187 | −0.244900 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −10.6804 | −0.533354 | −0.266677 | − | 0.963786i | \(-0.585926\pi\) | ||||
−0.266677 | + | 0.963786i | \(0.585926\pi\) | |||||||
\(402\) | −8.43256 | −0.420578 | ||||||||
\(403\) | 4.66229 | 0.232245 | ||||||||
\(404\) | 16.0478 | 0.798408 | ||||||||
\(405\) | −11.1789 | −0.555482 | ||||||||
\(406\) | 8.62000 | 0.427803 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 12.5280 | 0.620227 | ||||||||
\(409\) | −23.5770 | −1.16581 | −0.582903 | − | 0.812542i | \(-0.698083\pi\) | ||||
−0.582903 | + | 0.812542i | \(0.698083\pi\) | |||||||
\(410\) | 10.5523 | 0.521143 | ||||||||
\(411\) | −27.2423 | −1.34376 | ||||||||
\(412\) | −12.9029 | −0.635680 | ||||||||
\(413\) | 2.01405 | 0.0991048 | ||||||||
\(414\) | 4.44313 | 0.218368 | ||||||||
\(415\) | −7.34851 | −0.360724 | ||||||||
\(416\) | −2.53263 | −0.124172 | ||||||||
\(417\) | 37.9482 | 1.85833 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.9235 | −0.777915 | −0.388958 | − | 0.921256i | \(-0.627165\pi\) | ||||
−0.388958 | + | 0.921256i | \(0.627165\pi\) | |||||||
\(420\) | 2.18328 | 0.106533 | ||||||||
\(421\) | −39.8602 | −1.94267 | −0.971333 | − | 0.237722i | \(-0.923599\pi\) | ||||
−0.971333 | + | 0.237722i | \(0.923599\pi\) | |||||||
\(422\) | −20.0422 | −0.975638 | ||||||||
\(423\) | 5.69740 | 0.277017 | ||||||||
\(424\) | 4.01746 | 0.195105 | ||||||||
\(425\) | −5.73813 | −0.278340 | ||||||||
\(426\) | 20.8616 | 1.01075 | ||||||||
\(427\) | −0.268235 | −0.0129808 | ||||||||
\(428\) | −6.74567 | −0.326064 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.18804 | 0.105516 | ||||||||
\(431\) | −17.5909 | −0.847325 | −0.423662 | − | 0.905820i | \(-0.639256\pi\) | ||||
−0.423662 | + | 0.905820i | \(0.639256\pi\) | |||||||
\(432\) | −2.69257 | −0.129547 | ||||||||
\(433\) | 20.5443 | 0.987296 | 0.493648 | − | 0.869662i | \(-0.335663\pi\) | ||||
0.493648 | + | 0.869662i | \(0.335663\pi\) | |||||||
\(434\) | −1.84089 | −0.0883656 | ||||||||
\(435\) | −18.8199 | −0.902346 | ||||||||
\(436\) | 18.6864 | 0.894916 | ||||||||
\(437\) | 5.63485 | 0.269552 | ||||||||
\(438\) | 24.9459 | 1.19196 | ||||||||
\(439\) | 22.4200 | 1.07005 | 0.535023 | − | 0.844837i | \(-0.320303\pi\) | ||||
0.535023 | + | 0.844837i | \(0.320303\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.76673 | 0.0841301 | ||||||||
\(442\) | 14.5325 | 0.691243 | ||||||||
\(443\) | 7.63516 | 0.362757 | 0.181379 | − | 0.983413i | \(-0.441944\pi\) | ||||
0.181379 | + | 0.983413i | \(0.441944\pi\) | |||||||
\(444\) | −10.1113 | −0.479862 | ||||||||
\(445\) | −2.65397 | −0.125810 | ||||||||
\(446\) | −11.8000 | −0.558745 | ||||||||
\(447\) | −3.25760 | −0.154079 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −0.652470 | −0.0307920 | −0.0153960 | − | 0.999881i | \(-0.504901\pi\) | ||||
−0.0153960 | + | 0.999881i | \(0.504901\pi\) | |||||||
\(450\) | −1.76673 | −0.0832846 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 7.56433 | 0.355796 | ||||||||
\(453\) | −17.4566 | −0.820181 | ||||||||
\(454\) | −0.990121 | −0.0464687 | ||||||||
\(455\) | 2.53263 | 0.118731 | ||||||||
\(456\) | 4.89187 | 0.229083 | ||||||||
\(457\) | 30.5691 | 1.42996 | 0.714981 | − | 0.699144i | \(-0.246435\pi\) | ||||
0.714981 | + | 0.699144i | \(0.246435\pi\) | |||||||
\(458\) | −18.3559 | −0.857714 | ||||||||
\(459\) | 15.4503 | 0.721160 | ||||||||
\(460\) | −2.51489 | −0.117257 | ||||||||
\(461\) | −3.55735 | −0.165682 | −0.0828412 | − | 0.996563i | \(-0.526399\pi\) | ||||
−0.0828412 | + | 0.996563i | \(0.526399\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.57677 | 0.305648 | 0.152824 | − | 0.988253i | \(-0.451163\pi\) | ||||
0.152824 | + | 0.988253i | \(0.451163\pi\) | |||||||
\(464\) | −8.62000 | −0.400173 | ||||||||
\(465\) | 4.01919 | 0.186385 | ||||||||
\(466\) | 17.3650 | 0.804418 | ||||||||
\(467\) | −18.3935 | −0.851150 | −0.425575 | − | 0.904923i | \(-0.639928\pi\) | ||||
−0.425575 | + | 0.904923i | \(0.639928\pi\) | |||||||
\(468\) | 4.47448 | 0.206833 | ||||||||
\(469\) | 3.86233 | 0.178346 | ||||||||
\(470\) | −3.22482 | −0.148750 | ||||||||
\(471\) | 4.47951 | 0.206405 | ||||||||
\(472\) | −2.01405 | −0.0927040 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 25.6611 | 1.17865 | ||||||||
\(475\) | −2.24060 | −0.102806 | ||||||||
\(476\) | −5.73813 | −0.263007 | ||||||||
\(477\) | −7.09778 | −0.324985 | ||||||||
\(478\) | −8.92113 | −0.408043 | ||||||||
\(479\) | 33.1011 | 1.51243 | 0.756213 | − | 0.654325i | \(-0.227047\pi\) | ||||
0.756213 | + | 0.654325i | \(0.227047\pi\) | |||||||
\(480\) | −2.18328 | −0.0996529 | ||||||||
\(481\) | −11.7292 | −0.534807 | ||||||||
\(482\) | 0.896696 | 0.0408434 | ||||||||
\(483\) | −5.49071 | −0.249836 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.5045 | 0.749432 | ||||||||
\(486\) | 16.3289 | 0.740694 | ||||||||
\(487\) | −15.5981 | −0.706819 | −0.353410 | − | 0.935469i | \(-0.614978\pi\) | ||||
−0.353410 | + | 0.935469i | \(0.614978\pi\) | |||||||
\(488\) | 0.268235 | 0.0121424 | ||||||||
\(489\) | 45.1887 | 2.04350 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | −41.6636 | −1.88025 | −0.940127 | − | 0.340825i | \(-0.889294\pi\) | ||||
−0.940127 | + | 0.340825i | \(0.889294\pi\) | |||||||
\(492\) | −23.0388 | −1.03867 | ||||||||
\(493\) | 49.4626 | 2.22768 | ||||||||
\(494\) | 5.67461 | 0.255313 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.84089 | 0.0826585 | ||||||||
\(497\) | −9.55514 | −0.428606 | ||||||||
\(498\) | 16.0439 | 0.718944 | ||||||||
\(499\) | −2.45110 | −0.109726 | −0.0548631 | − | 0.998494i | \(-0.517472\pi\) | ||||
−0.0548631 | + | 0.998494i | \(0.517472\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 2.88303 | 0.128804 | ||||||||
\(502\) | 22.4978 | 1.00413 | ||||||||
\(503\) | −6.68855 | −0.298228 | −0.149114 | − | 0.988820i | \(-0.547642\pi\) | ||||
−0.149114 | + | 0.988820i | \(0.547642\pi\) | |||||||
\(504\) | −1.76673 | −0.0786965 | ||||||||
\(505\) | 16.0478 | 0.714118 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.3787 | −0.638579 | ||||||||
\(508\) | −10.7426 | −0.476625 | ||||||||
\(509\) | −14.0762 | −0.623917 | −0.311959 | − | 0.950096i | \(-0.600985\pi\) | ||||
−0.311959 | + | 0.950096i | \(0.600985\pi\) | |||||||
\(510\) | 12.5280 | 0.554747 | ||||||||
\(511\) | −11.4258 | −0.505450 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 6.03298 | 0.266363 | ||||||||
\(514\) | 24.9449 | 1.10027 | ||||||||
\(515\) | −12.9029 | −0.568570 | ||||||||
\(516\) | −4.77710 | −0.210300 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 4.63124 | 0.203485 | ||||||||
\(519\) | 34.2838 | 1.50489 | ||||||||
\(520\) | −2.53263 | −0.111063 | ||||||||
\(521\) | 41.6989 | 1.82686 | 0.913431 | − | 0.406993i | \(-0.133423\pi\) | ||||
0.913431 | + | 0.406993i | \(0.133423\pi\) | |||||||
\(522\) | 15.2292 | 0.666565 | ||||||||
\(523\) | 10.6960 | 0.467703 | 0.233851 | − | 0.972272i | \(-0.424867\pi\) | ||||
0.233851 | + | 0.972272i | \(0.424867\pi\) | |||||||
\(524\) | −17.0221 | −0.743613 | ||||||||
\(525\) | 2.18328 | 0.0952864 | ||||||||
\(526\) | −6.25594 | −0.272772 | ||||||||
\(527\) | −10.5633 | −0.460143 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.6753 | −0.725015 | ||||||||
\(530\) | 4.01746 | 0.174507 | ||||||||
\(531\) | 3.55828 | 0.154416 | ||||||||
\(532\) | −2.24060 | −0.0971423 | ||||||||
\(533\) | −26.7252 | −1.15759 | ||||||||
\(534\) | 5.79438 | 0.250747 | ||||||||
\(535\) | −6.74567 | −0.291641 | ||||||||
\(536\) | −3.86233 | −0.166827 | ||||||||
\(537\) | 10.1631 | 0.438571 | ||||||||
\(538\) | 13.0673 | 0.563371 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.69257 | −0.115870 | ||||||||
\(541\) | 9.64911 | 0.414847 | 0.207424 | − | 0.978251i | \(-0.433492\pi\) | ||||
0.207424 | + | 0.978251i | \(0.433492\pi\) | |||||||
\(542\) | 24.3157 | 1.04445 | ||||||||
\(543\) | −12.8912 | −0.553215 | ||||||||
\(544\) | 5.73813 | 0.246020 | ||||||||
\(545\) | 18.6864 | 0.800437 | ||||||||
\(546\) | −5.52945 | −0.236639 | ||||||||
\(547\) | 14.8545 | 0.635133 | 0.317567 | − | 0.948236i | \(-0.397134\pi\) | ||||
0.317567 | + | 0.948236i | \(0.397134\pi\) | |||||||
\(548\) | −12.4777 | −0.533019 | ||||||||
\(549\) | −0.473900 | −0.0202255 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.3140 | 0.822803 | ||||||||
\(552\) | 5.49071 | 0.233700 | ||||||||
\(553\) | −11.7534 | −0.499807 | ||||||||
\(554\) | 13.4094 | 0.569713 | ||||||||
\(555\) | −10.1113 | −0.429202 | ||||||||
\(556\) | 17.3812 | 0.737129 | ||||||||
\(557\) | 39.9349 | 1.69210 | 0.846048 | − | 0.533106i | \(-0.178975\pi\) | ||||
0.846048 | + | 0.533106i | \(0.178975\pi\) | |||||||
\(558\) | −3.25236 | −0.137683 | ||||||||
\(559\) | −5.54148 | −0.234380 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.7398 | −0.537396 | ||||||||
\(563\) | 4.06409 | 0.171281 | 0.0856405 | − | 0.996326i | \(-0.472706\pi\) | ||||
0.0856405 | + | 0.996326i | \(0.472706\pi\) | |||||||
\(564\) | 7.04070 | 0.296467 | ||||||||
\(565\) | 7.56433 | 0.318234 | ||||||||
\(566\) | 13.7495 | 0.577936 | ||||||||
\(567\) | −11.1789 | −0.469468 | ||||||||
\(568\) | 9.55514 | 0.400925 | ||||||||
\(569\) | 31.8994 | 1.33729 | 0.668647 | − | 0.743580i | \(-0.266874\pi\) | ||||
0.668647 | + | 0.743580i | \(0.266874\pi\) | |||||||
\(570\) | 4.89187 | 0.204898 | ||||||||
\(571\) | 20.3883 | 0.853222 | 0.426611 | − | 0.904435i | \(-0.359707\pi\) | ||||
0.426611 | + | 0.904435i | \(0.359707\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.9556 | −0.541229 | ||||||||
\(574\) | 10.5523 | 0.440446 | ||||||||
\(575\) | −2.51489 | −0.104878 | ||||||||
\(576\) | 1.76673 | 0.0736139 | ||||||||
\(577\) | −26.0450 | −1.08427 | −0.542134 | − | 0.840292i | \(-0.682383\pi\) | ||||
−0.542134 | + | 0.840292i | \(0.682383\pi\) | |||||||
\(578\) | −15.9261 | −0.662438 | ||||||||
\(579\) | 23.6617 | 0.983348 | ||||||||
\(580\) | −8.62000 | −0.357926 | ||||||||
\(581\) | −7.34851 | −0.304867 | ||||||||
\(582\) | −36.0341 | −1.49366 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 11.4258 | 0.472805 | ||||||||
\(585\) | 4.47448 | 0.184997 | ||||||||
\(586\) | −16.6376 | −0.687295 | ||||||||
\(587\) | −38.9847 | −1.60907 | −0.804536 | − | 0.593904i | \(-0.797586\pi\) | ||||
−0.804536 | + | 0.593904i | \(0.797586\pi\) | |||||||
\(588\) | 2.18328 | 0.0900371 | ||||||||
\(589\) | −4.12470 | −0.169955 | ||||||||
\(590\) | −2.01405 | −0.0829170 | ||||||||
\(591\) | 26.2378 | 1.07928 | ||||||||
\(592\) | −4.63124 | −0.190343 | ||||||||
\(593\) | −0.526179 | −0.0216076 | −0.0108038 | − | 0.999942i | \(-0.503439\pi\) | ||||
−0.0108038 | + | 0.999942i | \(0.503439\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.73813 | −0.235240 | ||||||||
\(596\) | −1.49206 | −0.0611173 | ||||||||
\(597\) | 40.1755 | 1.64427 | ||||||||
\(598\) | 6.36928 | 0.260459 | ||||||||
\(599\) | −12.3903 | −0.506256 | −0.253128 | − | 0.967433i | \(-0.581459\pi\) | ||||
−0.253128 | + | 0.967433i | \(0.581459\pi\) | |||||||
\(600\) | −2.18328 | −0.0891322 | ||||||||
\(601\) | 26.8732 | 1.09618 | 0.548091 | − | 0.836418i | \(-0.315355\pi\) | ||||
0.548091 | + | 0.836418i | \(0.315355\pi\) | |||||||
\(602\) | 2.18804 | 0.0891777 | ||||||||
\(603\) | 6.82370 | 0.277883 | ||||||||
\(604\) | −7.99555 | −0.325334 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −35.0369 | −1.42328 | ||||||||
\(607\) | −36.1325 | −1.46657 | −0.733286 | − | 0.679920i | \(-0.762014\pi\) | ||||
−0.733286 | + | 0.679920i | \(0.762014\pi\) | |||||||
\(608\) | 2.24060 | 0.0908683 | ||||||||
\(609\) | −18.8199 | −0.762621 | ||||||||
\(610\) | 0.268235 | 0.0108605 | ||||||||
\(611\) | 8.16728 | 0.330413 | ||||||||
\(612\) | −10.1377 | −0.409794 | ||||||||
\(613\) | −33.2590 | −1.34332 | −0.671659 | − | 0.740860i | \(-0.734418\pi\) | ||||
−0.671659 | + | 0.740860i | \(0.734418\pi\) | |||||||
\(614\) | −5.56226 | −0.224475 | ||||||||
\(615\) | −23.0388 | −0.929012 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.1415 | −1.09267 | −0.546337 | − | 0.837565i | \(-0.683978\pi\) | ||||
−0.546337 | + | 0.837565i | \(0.683978\pi\) | |||||||
\(618\) | 28.1707 | 1.13319 | ||||||||
\(619\) | 2.93234 | 0.117861 | 0.0589303 | − | 0.998262i | \(-0.481231\pi\) | ||||
0.0589303 | + | 0.998262i | \(0.481231\pi\) | |||||||
\(620\) | 1.84089 | 0.0739320 | ||||||||
\(621\) | 6.77152 | 0.271732 | ||||||||
\(622\) | −17.9179 | −0.718441 | ||||||||
\(623\) | −2.65397 | −0.106329 | ||||||||
\(624\) | 5.52945 | 0.221355 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −5.15478 | −0.206026 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.05173 | 0.0818729 | ||||||||
\(629\) | 26.5747 | 1.05960 | ||||||||
\(630\) | −1.76673 | −0.0703883 | ||||||||
\(631\) | −7.10213 | −0.282731 | −0.141366 | − | 0.989957i | \(-0.545149\pi\) | ||||
−0.141366 | + | 0.989957i | \(0.545149\pi\) | |||||||
\(632\) | 11.7534 | 0.467527 | ||||||||
\(633\) | 43.7578 | 1.73922 | ||||||||
\(634\) | −28.4614 | −1.13035 | ||||||||
\(635\) | −10.7426 | −0.426306 | ||||||||
\(636\) | −8.77126 | −0.347803 | ||||||||
\(637\) | 2.53263 | 0.100346 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.8814 | −0.667817 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 1.60982 | 0.0635842 | 0.0317921 | − | 0.999495i | \(-0.489879\pi\) | ||||
0.0317921 | + | 0.999495i | \(0.489879\pi\) | |||||||
\(642\) | 14.7277 | 0.581257 | ||||||||
\(643\) | −17.9131 | −0.706422 | −0.353211 | − | 0.935544i | \(-0.614910\pi\) | ||||
−0.353211 | + | 0.935544i | \(0.614910\pi\) | |||||||
\(644\) | −2.51489 | −0.0991004 | ||||||||
\(645\) | −4.77710 | −0.188098 | ||||||||
\(646\) | −12.8568 | −0.505846 | ||||||||
\(647\) | −5.38711 | −0.211789 | −0.105895 | − | 0.994377i | \(-0.533771\pi\) | ||||
−0.105895 | + | 0.994377i | \(0.533771\pi\) | |||||||
\(648\) | 11.1789 | 0.439147 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2.53263 | −0.0993379 | ||||||||
\(651\) | 4.01919 | 0.157524 | ||||||||
\(652\) | 20.6976 | 0.810579 | ||||||||
\(653\) | 48.6527 | 1.90393 | 0.951963 | − | 0.306212i | \(-0.0990616\pi\) | ||||
0.951963 | + | 0.306212i | \(0.0990616\pi\) | |||||||
\(654\) | −40.7977 | −1.59532 | ||||||||
\(655\) | −17.0221 | −0.665108 | ||||||||
\(656\) | −10.5523 | −0.411999 | ||||||||
\(657\) | −20.1864 | −0.787547 | ||||||||
\(658\) | −3.22482 | −0.125717 | ||||||||
\(659\) | −29.0793 | −1.13277 | −0.566385 | − | 0.824141i | \(-0.691658\pi\) | ||||
−0.566385 | + | 0.824141i | \(0.691658\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.9160 | −0.541270 | −0.270635 | − | 0.962682i | \(-0.587234\pi\) | ||||
−0.270635 | + | 0.962682i | \(0.587234\pi\) | |||||||
\(662\) | 24.8572 | 0.966101 | ||||||||
\(663\) | −31.7287 | −1.23224 | ||||||||
\(664\) | 7.34851 | 0.285177 | ||||||||
\(665\) | −2.24060 | −0.0868867 | ||||||||
\(666\) | 8.18217 | 0.317053 | ||||||||
\(667\) | 21.6783 | 0.839388 | ||||||||
\(668\) | 1.32050 | 0.0510917 | ||||||||
\(669\) | 25.7627 | 0.996043 | ||||||||
\(670\) | −3.86233 | −0.149215 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −2.18328 | −0.0842220 | ||||||||
\(673\) | −32.6201 | −1.25741 | −0.628707 | − | 0.777642i | \(-0.716415\pi\) | ||||
−0.628707 | + | 0.777642i | \(0.716415\pi\) | |||||||
\(674\) | 15.6474 | 0.602716 | ||||||||
\(675\) | −2.69257 | −0.103637 | ||||||||
\(676\) | −6.58579 | −0.253300 | ||||||||
\(677\) | 37.5887 | 1.44465 | 0.722325 | − | 0.691554i | \(-0.243074\pi\) | ||||
0.722325 | + | 0.691554i | \(0.243074\pi\) | |||||||
\(678\) | −16.5151 | −0.634258 | ||||||||
\(679\) | 16.5045 | 0.633386 | ||||||||
\(680\) | 5.73813 | 0.220047 | ||||||||
\(681\) | 2.16172 | 0.0828372 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.5199 | −0.670380 | −0.335190 | − | 0.942151i | \(-0.608800\pi\) | ||||
−0.335190 | + | 0.942151i | \(0.608800\pi\) | |||||||
\(684\) | −3.95854 | −0.151359 | ||||||||
\(685\) | −12.4777 | −0.476747 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 40.0761 | 1.52900 | ||||||||
\(688\) | −2.18804 | −0.0834181 | ||||||||
\(689\) | −10.1747 | −0.387627 | ||||||||
\(690\) | 5.49071 | 0.209028 | ||||||||
\(691\) | 7.14352 | 0.271752 | 0.135876 | − | 0.990726i | \(-0.456615\pi\) | ||||
0.135876 | + | 0.990726i | \(0.456615\pi\) | |||||||
\(692\) | 15.7029 | 0.596933 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.6646 | −0.556662 | ||||||||
\(695\) | 17.3812 | 0.659308 | ||||||||
\(696\) | 18.8199 | 0.713367 | ||||||||
\(697\) | 60.5506 | 2.29352 | ||||||||
\(698\) | −26.9763 | −1.02107 | ||||||||
\(699\) | −37.9127 | −1.43399 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −38.7733 | −1.46445 | −0.732224 | − | 0.681064i | \(-0.761518\pi\) | ||||
−0.732224 | + | 0.681064i | \(0.761518\pi\) | |||||||
\(702\) | 6.81929 | 0.257378 | ||||||||
\(703\) | 10.3768 | 0.391367 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.04070 | 0.265168 | ||||||||
\(706\) | −4.77463 | −0.179696 | ||||||||
\(707\) | 16.0478 | 0.603540 | ||||||||
\(708\) | 4.39724 | 0.165258 | ||||||||
\(709\) | 30.3511 | 1.13986 | 0.569930 | − | 0.821693i | \(-0.306970\pi\) | ||||
0.569930 | + | 0.821693i | \(0.306970\pi\) | |||||||
\(710\) | 9.55514 | 0.358598 | ||||||||
\(711\) | −20.7652 | −0.778755 | ||||||||
\(712\) | 2.65397 | 0.0994618 | ||||||||
\(713\) | −4.62963 | −0.173381 | ||||||||
\(714\) | 12.5280 | 0.468847 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.65497 | 0.173964 | ||||||||
\(717\) | 19.4774 | 0.727396 | ||||||||
\(718\) | −34.0982 | −1.27253 | ||||||||
\(719\) | 36.0357 | 1.34391 | 0.671953 | − | 0.740594i | \(-0.265456\pi\) | ||||
0.671953 | + | 0.740594i | \(0.265456\pi\) | |||||||
\(720\) | 1.76673 | 0.0658422 | ||||||||
\(721\) | −12.9029 | −0.480529 | ||||||||
\(722\) | 13.9797 | 0.520271 | ||||||||
\(723\) | −1.95774 | −0.0728092 | ||||||||
\(724\) | −5.90450 | −0.219439 | ||||||||
\(725\) | −8.62000 | −0.320139 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.1833 | 1.15653 | 0.578263 | − | 0.815850i | \(-0.303731\pi\) | ||||
0.578263 | + | 0.815850i | \(0.303731\pi\) | |||||||
\(728\) | −2.53263 | −0.0938655 | ||||||||
\(729\) | −2.11408 | −0.0782992 | ||||||||
\(730\) | 11.4258 | 0.422890 | ||||||||
\(731\) | 12.5552 | 0.464372 | ||||||||
\(732\) | −0.585633 | −0.0216456 | ||||||||
\(733\) | −26.0329 | −0.961548 | −0.480774 | − | 0.876844i | \(-0.659644\pi\) | ||||
−0.480774 | + | 0.876844i | \(0.659644\pi\) | |||||||
\(734\) | 9.98965 | 0.368725 | ||||||||
\(735\) | 2.18328 | 0.0805317 | ||||||||
\(736\) | 2.51489 | 0.0927000 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 18.6432 | 0.686264 | ||||||||
\(739\) | 22.4140 | 0.824514 | 0.412257 | − | 0.911068i | \(-0.364741\pi\) | ||||
0.412257 | + | 0.911068i | \(0.364741\pi\) | |||||||
\(740\) | −4.63124 | −0.170248 | ||||||||
\(741\) | −12.3893 | −0.455132 | ||||||||
\(742\) | 4.01746 | 0.147486 | ||||||||
\(743\) | −44.3080 | −1.62550 | −0.812752 | − | 0.582610i | \(-0.802031\pi\) | ||||
−0.812752 | + | 0.582610i | \(0.802031\pi\) | |||||||
\(744\) | −4.01919 | −0.147351 | ||||||||
\(745\) | −1.49206 | −0.0546650 | ||||||||
\(746\) | 0.510916 | 0.0187060 | ||||||||
\(747\) | −12.9828 | −0.475018 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.74567 | −0.246482 | ||||||||
\(750\) | −2.18328 | −0.0797223 | ||||||||
\(751\) | 39.3682 | 1.43657 | 0.718283 | − | 0.695751i | \(-0.244928\pi\) | ||||
0.718283 | + | 0.695751i | \(0.244928\pi\) | |||||||
\(752\) | 3.22482 | 0.117597 | ||||||||
\(753\) | −49.1192 | −1.79000 | ||||||||
\(754\) | 21.8313 | 0.795048 | ||||||||
\(755\) | −7.99555 | −0.290988 | ||||||||
\(756\) | −2.69257 | −0.0979280 | ||||||||
\(757\) | −33.4097 | −1.21430 | −0.607149 | − | 0.794588i | \(-0.707687\pi\) | ||||
−0.607149 | + | 0.794588i | \(0.707687\pi\) | |||||||
\(758\) | −5.31376 | −0.193004 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.24060 | 0.0812751 | ||||||||
\(761\) | 38.9480 | 1.41186 | 0.705932 | − | 0.708279i | \(-0.250528\pi\) | ||||
0.705932 | + | 0.708279i | \(0.250528\pi\) | |||||||
\(762\) | 23.4541 | 0.849652 | ||||||||
\(763\) | 18.6864 | 0.676493 | ||||||||
\(764\) | −5.93400 | −0.214685 | ||||||||
\(765\) | −10.1377 | −0.366531 | ||||||||
\(766\) | −23.5202 | −0.849821 | ||||||||
\(767\) | 5.10083 | 0.184180 | ||||||||
\(768\) | 2.18328 | 0.0787825 | ||||||||
\(769\) | −0.875099 | −0.0315569 | −0.0157784 | − | 0.999876i | \(-0.505023\pi\) | ||||
−0.0157784 | + | 0.999876i | \(0.505023\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −54.4617 | −1.96139 | ||||||||
\(772\) | 10.8377 | 0.390056 | ||||||||
\(773\) | −22.9131 | −0.824125 | −0.412063 | − | 0.911155i | \(-0.635192\pi\) | ||||
−0.412063 | + | 0.911155i | \(0.635192\pi\) | |||||||
\(774\) | 3.86567 | 0.138949 | ||||||||
\(775\) | 1.84089 | 0.0661268 | ||||||||
\(776\) | −16.5045 | −0.592478 | ||||||||
\(777\) | −10.1113 | −0.362742 | ||||||||
\(778\) | −9.18397 | −0.329261 | ||||||||
\(779\) | 23.6436 | 0.847118 | ||||||||
\(780\) | 5.52945 | 0.197986 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −14.4307 | −0.516042 | ||||||||
\(783\) | 23.2100 | 0.829457 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 2.05173 | 0.0732293 | ||||||||
\(786\) | 37.1641 | 1.32560 | ||||||||
\(787\) | −33.4092 | −1.19091 | −0.595455 | − | 0.803388i | \(-0.703028\pi\) | ||||
−0.595455 | + | 0.803388i | \(0.703028\pi\) | |||||||
\(788\) | 12.0176 | 0.428108 | ||||||||
\(789\) | 13.6585 | 0.486255 | ||||||||
\(790\) | 11.7534 | 0.418168 | ||||||||
\(791\) | 7.56433 | 0.268957 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.679340 | −0.0241241 | ||||||||
\(794\) | 31.5709 | 1.12041 | ||||||||
\(795\) | −8.77126 | −0.311085 | ||||||||
\(796\) | 18.4014 | 0.652220 | ||||||||
\(797\) | −3.43820 | −0.121787 | −0.0608936 | − | 0.998144i | \(-0.519395\pi\) | ||||
−0.0608936 | + | 0.998144i | \(0.519395\pi\) | |||||||
\(798\) | 4.89187 | 0.173170 | ||||||||
\(799\) | −18.5044 | −0.654640 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −4.68886 | −0.165673 | ||||||||
\(802\) | 10.6804 | 0.377138 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 8.43256 | 0.297394 | ||||||||
\(805\) | −2.51489 | −0.0886381 | ||||||||
\(806\) | −4.66229 | −0.164222 | ||||||||
\(807\) | −28.5296 | −1.00429 | ||||||||
\(808\) | −16.0478 | −0.564560 | ||||||||
\(809\) | −35.3314 | −1.24219 | −0.621093 | − | 0.783737i | \(-0.713311\pi\) | ||||
−0.621093 | + | 0.783737i | \(0.713311\pi\) | |||||||
\(810\) | 11.1789 | 0.392785 | ||||||||
\(811\) | 48.6796 | 1.70937 | 0.854686 | − | 0.519145i | \(-0.173749\pi\) | ||||
0.854686 | + | 0.519145i | \(0.173749\pi\) | |||||||
\(812\) | −8.62000 | −0.302503 | ||||||||
\(813\) | −53.0880 | −1.86188 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.6976 | 0.725004 | ||||||||
\(816\) | −12.5280 | −0.438566 | ||||||||
\(817\) | 4.90251 | 0.171517 | ||||||||
\(818\) | 23.5770 | 0.824349 | ||||||||
\(819\) | 4.47448 | 0.156351 | ||||||||
\(820\) | −10.5523 | −0.368504 | ||||||||
\(821\) | 17.1917 | 0.599995 | 0.299997 | − | 0.953940i | \(-0.403014\pi\) | ||||
0.299997 | + | 0.953940i | \(0.403014\pi\) | |||||||
\(822\) | 27.2423 | 0.950184 | ||||||||
\(823\) | −45.8799 | −1.59927 | −0.799636 | − | 0.600485i | \(-0.794974\pi\) | ||||
−0.799636 | + | 0.600485i | \(0.794974\pi\) | |||||||
\(824\) | 12.9029 | 0.449494 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.01405 | −0.0700777 | ||||||||
\(827\) | −27.9645 | −0.972420 | −0.486210 | − | 0.873842i | \(-0.661621\pi\) | ||||
−0.486210 | + | 0.873842i | \(0.661621\pi\) | |||||||
\(828\) | −4.44313 | −0.154410 | ||||||||
\(829\) | −18.8815 | −0.655782 | −0.327891 | − | 0.944715i | \(-0.606338\pi\) | ||||
−0.327891 | + | 0.944715i | \(0.606338\pi\) | |||||||
\(830\) | 7.34851 | 0.255070 | ||||||||
\(831\) | −29.2766 | −1.01560 | ||||||||
\(832\) | 2.53263 | 0.0878031 | ||||||||
\(833\) | −5.73813 | −0.198814 | ||||||||
\(834\) | −37.9482 | −1.31404 | ||||||||
\(835\) | 1.32050 | 0.0456978 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.95674 | −0.171330 | ||||||||
\(838\) | 15.9235 | 0.550069 | ||||||||
\(839\) | −19.7116 | −0.680521 | −0.340261 | − | 0.940331i | \(-0.610515\pi\) | ||||
−0.340261 | + | 0.940331i | \(0.610515\pi\) | |||||||
\(840\) | −2.18328 | −0.0753305 | ||||||||
\(841\) | 45.3044 | 1.56222 | ||||||||
\(842\) | 39.8602 | 1.37367 | ||||||||
\(843\) | 27.8146 | 0.957987 | ||||||||
\(844\) | 20.0422 | 0.689880 | ||||||||
\(845\) | −6.58579 | −0.226558 | ||||||||
\(846\) | −5.69740 | −0.195881 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.01746 | −0.137960 | ||||||||
\(849\) | −30.0191 | −1.03025 | ||||||||
\(850\) | 5.73813 | 0.196816 | ||||||||
\(851\) | 11.6471 | 0.399256 | ||||||||
\(852\) | −20.8616 | −0.714706 | ||||||||
\(853\) | −30.8936 | −1.05778 | −0.528888 | − | 0.848692i | \(-0.677391\pi\) | ||||
−0.528888 | + | 0.848692i | \(0.677391\pi\) | |||||||
\(854\) | 0.268235 | 0.00917881 | ||||||||
\(855\) | −3.95854 | −0.135379 | ||||||||
\(856\) | 6.74567 | 0.230562 | ||||||||
\(857\) | 24.2847 | 0.829550 | 0.414775 | − | 0.909924i | \(-0.363860\pi\) | ||||
0.414775 | + | 0.909924i | \(0.363860\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.0877 | 0.753621 | 0.376811 | − | 0.926290i | \(-0.377021\pi\) | ||||
0.376811 | + | 0.926290i | \(0.377021\pi\) | |||||||
\(860\) | −2.18804 | −0.0746114 | ||||||||
\(861\) | −23.0388 | −0.785159 | ||||||||
\(862\) | 17.5909 | 0.599149 | ||||||||
\(863\) | −14.1052 | −0.480146 | −0.240073 | − | 0.970755i | \(-0.577171\pi\) | ||||
−0.240073 | + | 0.970755i | \(0.577171\pi\) | |||||||
\(864\) | 2.69257 | 0.0916032 | ||||||||
\(865\) | 15.7029 | 0.533913 | ||||||||
\(866\) | −20.5443 | −0.698124 | ||||||||
\(867\) | 34.7712 | 1.18089 | ||||||||
\(868\) | 1.84089 | 0.0624839 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 18.8199 | 0.638055 | ||||||||
\(871\) | 9.78185 | 0.331445 | ||||||||
\(872\) | −18.6864 | −0.632801 | ||||||||
\(873\) | 29.1591 | 0.986886 | ||||||||
\(874\) | −5.63485 | −0.190602 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −24.9459 | −0.842843 | ||||||||
\(877\) | 55.9227 | 1.88838 | 0.944188 | − | 0.329406i | \(-0.106849\pi\) | ||||
0.944188 | + | 0.329406i | \(0.106849\pi\) | |||||||
\(878\) | −22.4200 | −0.756637 | ||||||||
\(879\) | 36.3247 | 1.22520 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.2057 | −1.55671 | −0.778354 | − | 0.627826i | \(-0.783945\pi\) | ||||
−0.778354 | + | 0.627826i | \(0.783945\pi\) | |||||||
\(882\) | −1.76673 | −0.0594890 | ||||||||
\(883\) | −14.1307 | −0.475536 | −0.237768 | − | 0.971322i | \(-0.576416\pi\) | ||||
−0.237768 | + | 0.971322i | \(0.576416\pi\) | |||||||
\(884\) | −14.5325 | −0.488782 | ||||||||
\(885\) | 4.39724 | 0.147812 | ||||||||
\(886\) | −7.63516 | −0.256508 | ||||||||
\(887\) | −37.6208 | −1.26318 | −0.631591 | − | 0.775302i | \(-0.717598\pi\) | ||||
−0.631591 | + | 0.775302i | \(0.717598\pi\) | |||||||
\(888\) | 10.1113 | 0.339314 | ||||||||
\(889\) | −10.7426 | −0.360294 | ||||||||
\(890\) | 2.65397 | 0.0889614 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.8000 | 0.395092 | ||||||||
\(893\) | −7.22553 | −0.241793 | ||||||||
\(894\) | 3.25760 | 0.108950 | ||||||||
\(895\) | 4.65497 | 0.155598 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −13.9059 | −0.464306 | ||||||||
\(898\) | 0.652470 | 0.0217732 | ||||||||
\(899\) | −15.8685 | −0.529243 | ||||||||
\(900\) | 1.76673 | 0.0588911 | ||||||||
\(901\) | 23.0527 | 0.767997 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.77710 | −0.158972 | ||||||||
\(904\) | −7.56433 | −0.251586 | ||||||||
\(905\) | −5.90450 | −0.196272 | ||||||||
\(906\) | 17.4566 | 0.579955 | ||||||||
\(907\) | −2.97518 | −0.0987893 | −0.0493947 | − | 0.998779i | \(-0.515729\pi\) | ||||
−0.0493947 | + | 0.998779i | \(0.515729\pi\) | |||||||
\(908\) | 0.990121 | 0.0328583 | ||||||||
\(909\) | 28.3522 | 0.940383 | ||||||||
\(910\) | −2.53263 | −0.0839558 | ||||||||
\(911\) | −53.8707 | −1.78481 | −0.892407 | − | 0.451231i | \(-0.850985\pi\) | ||||
−0.892407 | + | 0.451231i | \(0.850985\pi\) | |||||||
\(912\) | −4.89187 | −0.161986 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −30.5691 | −1.01114 | ||||||||
\(915\) | −0.585633 | −0.0193604 | ||||||||
\(916\) | 18.3559 | 0.606495 | ||||||||
\(917\) | −17.0221 | −0.562119 | ||||||||
\(918\) | −15.4503 | −0.509937 | ||||||||
\(919\) | −16.9667 | −0.559678 | −0.279839 | − | 0.960047i | \(-0.590281\pi\) | ||||
−0.279839 | + | 0.960047i | \(0.590281\pi\) | |||||||
\(920\) | 2.51489 | 0.0829134 | ||||||||
\(921\) | 12.1440 | 0.400159 | ||||||||
\(922\) | 3.55735 | 0.117155 | ||||||||
\(923\) | −24.1996 | −0.796540 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.63124 | −0.152274 | ||||||||
\(926\) | −6.57677 | −0.216126 | ||||||||
\(927\) | −22.7960 | −0.748718 | ||||||||
\(928\) | 8.62000 | 0.282965 | ||||||||
\(929\) | 32.3876 | 1.06260 | 0.531301 | − | 0.847183i | \(-0.321703\pi\) | ||||
0.531301 | + | 0.847183i | \(0.321703\pi\) | |||||||
\(930\) | −4.01919 | −0.131794 | ||||||||
\(931\) | −2.24060 | −0.0734327 | ||||||||
\(932\) | −17.3650 | −0.568809 | ||||||||
\(933\) | 39.1198 | 1.28072 | ||||||||
\(934\) | 18.3935 | 0.601854 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.47448 | −0.146253 | ||||||||
\(937\) | −24.1450 | −0.788784 | −0.394392 | − | 0.918942i | \(-0.629045\pi\) | ||||
−0.394392 | + | 0.918942i | \(0.629045\pi\) | |||||||
\(938\) | −3.86233 | −0.126110 | ||||||||
\(939\) | 11.2543 | 0.367272 | ||||||||
\(940\) | 3.22482 | 0.105182 | ||||||||
\(941\) | 40.6046 | 1.32367 | 0.661836 | − | 0.749648i | \(-0.269777\pi\) | ||||
0.661836 | + | 0.749648i | \(0.269777\pi\) | |||||||
\(942\) | −4.47951 | −0.145950 | ||||||||
\(943\) | 26.5379 | 0.864194 | ||||||||
\(944\) | 2.01405 | 0.0655516 | ||||||||
\(945\) | −2.69257 | −0.0875894 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.111103 | 0.00361036 | 0.00180518 | − | 0.999998i | \(-0.499425\pi\) | ||||
0.00180518 | + | 0.999998i | \(0.499425\pi\) | |||||||
\(948\) | −25.6611 | −0.833434 | ||||||||
\(949\) | −28.9374 | −0.939349 | ||||||||
\(950\) | 2.24060 | 0.0726946 | ||||||||
\(951\) | 62.1393 | 2.01500 | ||||||||
\(952\) | 5.73813 | 0.185974 | ||||||||
\(953\) | −7.70395 | −0.249555 | −0.124778 | − | 0.992185i | \(-0.539822\pi\) | ||||
−0.124778 | + | 0.992185i | \(0.539822\pi\) | |||||||
\(954\) | 7.09778 | 0.229799 | ||||||||
\(955\) | −5.93400 | −0.192020 | ||||||||
\(956\) | 8.92113 | 0.288530 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −33.1011 | −1.06945 | ||||||||
\(959\) | −12.4777 | −0.402925 | ||||||||
\(960\) | 2.18328 | 0.0704652 | ||||||||
\(961\) | −27.6111 | −0.890681 | ||||||||
\(962\) | 11.7292 | 0.378165 | ||||||||
\(963\) | −11.9178 | −0.384046 | ||||||||
\(964\) | −0.896696 | −0.0288806 | ||||||||
\(965\) | 10.8377 | 0.348877 | ||||||||
\(966\) | 5.49071 | 0.176661 | ||||||||
\(967\) | 41.8250 | 1.34500 | 0.672501 | − | 0.740096i | \(-0.265220\pi\) | ||||
0.672501 | + | 0.740096i | \(0.265220\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 28.0701 | 0.901743 | ||||||||
\(970\) | −16.5045 | −0.529929 | ||||||||
\(971\) | 37.2897 | 1.19668 | 0.598342 | − | 0.801241i | \(-0.295826\pi\) | ||||
0.598342 | + | 0.801241i | \(0.295826\pi\) | |||||||
\(972\) | −16.3289 | −0.523750 | ||||||||
\(973\) | 17.3812 | 0.557217 | ||||||||
\(974\) | 15.5981 | 0.499797 | ||||||||
\(975\) | 5.52945 | 0.177084 | ||||||||
\(976\) | −0.268235 | −0.00858599 | ||||||||
\(977\) | 2.41139 | 0.0771471 | 0.0385736 | − | 0.999256i | \(-0.487719\pi\) | ||||
0.0385736 | + | 0.999256i | \(0.487719\pi\) | |||||||
\(978\) | −45.1887 | −1.44498 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 33.0139 | 1.05405 | ||||||||
\(982\) | 41.6636 | 1.32954 | ||||||||
\(983\) | −40.4385 | −1.28979 | −0.644894 | − | 0.764272i | \(-0.723098\pi\) | ||||
−0.644894 | + | 0.764272i | \(0.723098\pi\) | |||||||
\(984\) | 23.0388 | 0.734449 | ||||||||
\(985\) | 12.0176 | 0.382911 | ||||||||
\(986\) | −49.4626 | −1.57521 | ||||||||
\(987\) | 7.04070 | 0.224108 | ||||||||
\(988\) | −5.67461 | −0.180533 | ||||||||
\(989\) | 5.50266 | 0.174974 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.7075 | 0.848392 | 0.424196 | − | 0.905570i | \(-0.360557\pi\) | ||||
0.424196 | + | 0.905570i | \(0.360557\pi\) | |||||||
\(992\) | −1.84089 | −0.0584484 | ||||||||
\(993\) | −54.2702 | −1.72221 | ||||||||
\(994\) | 9.55514 | 0.303071 | ||||||||
\(995\) | 18.4014 | 0.583363 | ||||||||
\(996\) | −16.0439 | −0.508370 | ||||||||
\(997\) | −27.3325 | −0.865630 | −0.432815 | − | 0.901483i | \(-0.642480\pi\) | ||||
−0.432815 | + | 0.901483i | \(0.642480\pi\) | |||||||
\(998\) | 2.45110 | 0.0775881 | ||||||||
\(999\) | 12.4700 | 0.394532 |
(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 | 8470.2.a.cw.1.6 | 6 | ||
11.3 | even | 5 | 770.2.n.j.141.1 | yes | 12 | ||
11.4 | even | 5 | 770.2.n.j.71.1 | ✓ | 12 | ||
11.10 | odd | 2 | 8470.2.a.dc.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.j.71.1 | ✓ | 12 | 11.4 | even | 5 | ||
770.2.n.j.141.1 | yes | 12 | 11.3 | even | 5 | ||
8470.2.a.cw.1.6 | 6 | 1.1 | even | 1 | trivial | ||
8470.2.a.dc.1.6 | 6 | 11.10 | odd | 2 |