Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6762,2,Mod(1,6762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6762, 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("6762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6762.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: | \(53.9948418468\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.16448.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.87996\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6762.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.879961 | −0.393530 | −0.196765 | − | 0.980451i | \(-0.563044\pi\) | ||||
−0.196765 | + | 0.980451i | \(0.563044\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.879961 | −0.278268 | ||||||||
\(11\) | −4.07288 | −1.22802 | −0.614010 | − | 0.789298i | \(-0.710444\pi\) | ||||
−0.614010 | + | 0.789298i | \(0.710444\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 2.22129 | 0.616076 | 0.308038 | − | 0.951374i | \(-0.400328\pi\) | ||||
0.308038 | + | 0.951374i | \(0.400328\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.879961 | 0.227205 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.75992 | 1.88206 | 0.941029 | − | 0.338327i | \(-0.109861\pi\) | ||||
0.941029 | + | 0.338327i | \(0.109861\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 0.585786 | 0.134389 | 0.0671943 | − | 0.997740i | \(-0.478595\pi\) | ||||
0.0671943 | + | 0.997740i | \(0.478595\pi\) | |||||||
\(20\) | −0.879961 | −0.196765 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.07288 | −0.868341 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.22567 | −0.845134 | ||||||||
\(26\) | 2.22129 | 0.435632 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.60713 | 0.855523 | 0.427762 | − | 0.903892i | \(-0.359302\pi\) | ||||
0.427762 | + | 0.903892i | \(0.359302\pi\) | |||||||
\(30\) | 0.879961 | 0.160658 | ||||||||
\(31\) | 0.585786 | 0.105210 | 0.0526052 | − | 0.998615i | \(-0.483248\pi\) | ||||
0.0526052 | + | 0.998615i | \(0.483248\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.07288 | 0.708997 | ||||||||
\(34\) | 7.75992 | 1.33082 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.53863 | 0.581747 | 0.290873 | − | 0.956762i | \(-0.406054\pi\) | ||||
0.290873 | + | 0.956762i | \(0.406054\pi\) | |||||||
\(38\) | 0.585786 | 0.0950271 | ||||||||
\(39\) | −2.22129 | −0.355692 | ||||||||
\(40\) | −0.879961 | −0.139134 | ||||||||
\(41\) | −0.124413 | −0.0194301 | −0.00971505 | − | 0.999953i | \(-0.503092\pi\) | ||||
−0.00971505 | + | 0.999953i | \(0.503092\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.85158 | −0.892358 | −0.446179 | − | 0.894944i | \(-0.647216\pi\) | ||||
−0.446179 | + | 0.894944i | \(0.647216\pi\) | |||||||
\(44\) | −4.07288 | −0.614010 | ||||||||
\(45\) | −0.879961 | −0.131177 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 0.0515337 | 0.00751696 | 0.00375848 | − | 0.999993i | \(-0.498804\pi\) | ||||
0.00375848 | + | 0.999993i | \(0.498804\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.22567 | −0.597600 | ||||||||
\(51\) | −7.75992 | −1.08661 | ||||||||
\(52\) | 2.22129 | 0.308038 | ||||||||
\(53\) | −7.34390 | −1.00876 | −0.504381 | − | 0.863481i | \(-0.668279\pi\) | ||||
−0.504381 | + | 0.863481i | \(0.668279\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 3.58397 | 0.483263 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.585786 | −0.0775893 | ||||||||
\(58\) | 4.60713 | 0.604946 | ||||||||
\(59\) | −4.90131 | −0.638096 | −0.319048 | − | 0.947739i | \(-0.603363\pi\) | ||||
−0.319048 | + | 0.947739i | \(0.603363\pi\) | |||||||
\(60\) | 0.879961 | 0.113602 | ||||||||
\(61\) | 2.14320 | 0.274408 | 0.137204 | − | 0.990543i | \(-0.456188\pi\) | ||||
0.137204 | + | 0.990543i | \(0.456188\pi\) | |||||||
\(62\) | 0.585786 | 0.0743950 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.95465 | −0.242445 | ||||||||
\(66\) | 4.07288 | 0.501337 | ||||||||
\(67\) | −8.58835 | −1.04923 | −0.524617 | − | 0.851338i | \(-0.675791\pi\) | ||||
−0.524617 | + | 0.851338i | \(0.675791\pi\) | |||||||
\(68\) | 7.75992 | 0.941029 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.07288 | 0.483362 | 0.241681 | − | 0.970356i | \(-0.422301\pi\) | ||||
0.241681 | + | 0.970356i | \(0.422301\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 4.97162 | 0.581885 | 0.290942 | − | 0.956741i | \(-0.406031\pi\) | ||||
0.290942 | + | 0.956741i | \(0.406031\pi\) | |||||||
\(74\) | 3.53863 | 0.411357 | ||||||||
\(75\) | 4.22567 | 0.487938 | ||||||||
\(76\) | 0.585786 | 0.0671943 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.22129 | −0.251512 | ||||||||
\(79\) | −1.92712 | −0.216818 | −0.108409 | − | 0.994106i | \(-0.534576\pi\) | ||||
−0.108409 | + | 0.994106i | \(0.534576\pi\) | |||||||
\(80\) | −0.879961 | −0.0983826 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.124413 | −0.0137392 | ||||||||
\(83\) | 6.99819 | 0.768151 | 0.384075 | − | 0.923302i | \(-0.374520\pi\) | ||||
0.384075 | + | 0.923302i | \(0.374520\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.82843 | −0.740647 | ||||||||
\(86\) | −5.85158 | −0.630993 | ||||||||
\(87\) | −4.60713 | −0.493936 | ||||||||
\(88\) | −4.07288 | −0.434170 | ||||||||
\(89\) | 10.4587 | 1.10862 | 0.554311 | − | 0.832310i | \(-0.312982\pi\) | ||||
0.554311 | + | 0.832310i | \(0.312982\pi\) | |||||||
\(90\) | −0.879961 | −0.0927560 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −0.585786 | −0.0607432 | ||||||||
\(94\) | 0.0515337 | 0.00531530 | ||||||||
\(95\) | −0.515469 | −0.0528860 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 17.5084 | 1.77771 | 0.888856 | − | 0.458186i | \(-0.151501\pi\) | ||||
0.888856 | + | 0.458186i | \(0.151501\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.07288 | −0.409340 | ||||||||
\(100\) | −4.22567 | −0.422567 | ||||||||
\(101\) | −4.41240 | −0.439050 | −0.219525 | − | 0.975607i | \(-0.570451\pi\) | ||||
−0.219525 | + | 0.975607i | \(0.570451\pi\) | |||||||
\(102\) | −7.75992 | −0.768347 | ||||||||
\(103\) | 3.77871 | 0.372327 | 0.186163 | − | 0.982519i | \(-0.440395\pi\) | ||||
0.186163 | + | 0.982519i | \(0.440395\pi\) | |||||||
\(104\) | 2.22129 | 0.217816 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.34390 | −0.713302 | ||||||||
\(107\) | −3.61416 | −0.349394 | −0.174697 | − | 0.984622i | \(-0.555895\pi\) | ||||
−0.174697 | + | 0.984622i | \(0.555895\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 6.42381 | 0.615289 | 0.307645 | − | 0.951501i | \(-0.400459\pi\) | ||||
0.307645 | + | 0.951501i | \(0.400459\pi\) | |||||||
\(110\) | 3.58397 | 0.341719 | ||||||||
\(111\) | −3.53863 | −0.335872 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.6115 | 1.28046 | 0.640231 | − | 0.768182i | \(-0.278838\pi\) | ||||
0.640231 | + | 0.768182i | \(0.278838\pi\) | |||||||
\(114\) | −0.585786 | −0.0548639 | ||||||||
\(115\) | 0.879961 | 0.0820568 | ||||||||
\(116\) | 4.60713 | 0.427762 | ||||||||
\(117\) | 2.22129 | 0.205359 | ||||||||
\(118\) | −4.90131 | −0.451202 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.879961 | 0.0803291 | ||||||||
\(121\) | 5.58835 | 0.508032 | ||||||||
\(122\) | 2.14320 | 0.194036 | ||||||||
\(123\) | 0.124413 | 0.0112180 | ||||||||
\(124\) | 0.585786 | 0.0526052 | ||||||||
\(125\) | 8.11823 | 0.726116 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.92446 | 0.525711 | 0.262856 | − | 0.964835i | \(-0.415336\pi\) | ||||
0.262856 | + | 0.964835i | \(0.415336\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 5.85158 | 0.515203 | ||||||||
\(130\) | −1.95465 | −0.171434 | ||||||||
\(131\) | 6.76430 | 0.590999 | 0.295500 | − | 0.955343i | \(-0.404514\pi\) | ||||
0.295500 | + | 0.955343i | \(0.404514\pi\) | |||||||
\(132\) | 4.07288 | 0.354499 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.58835 | −0.741920 | ||||||||
\(135\) | 0.879961 | 0.0757350 | ||||||||
\(136\) | 7.75992 | 0.665408 | ||||||||
\(137\) | 5.56881 | 0.475776 | 0.237888 | − | 0.971293i | \(-0.423545\pi\) | ||||
0.237888 | + | 0.971293i | \(0.423545\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | 12.8258 | 1.08787 | 0.543934 | − | 0.839128i | \(-0.316934\pi\) | ||||
0.543934 | + | 0.839128i | \(0.316934\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.0515337 | −0.00433992 | ||||||||
\(142\) | 4.07288 | 0.341788 | ||||||||
\(143\) | −9.04707 | −0.756554 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −4.05410 | −0.336674 | ||||||||
\(146\) | 4.97162 | 0.411455 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.53863 | 0.290873 | ||||||||
\(149\) | 13.9322 | 1.14137 | 0.570687 | − | 0.821168i | \(-0.306677\pi\) | ||||
0.570687 | + | 0.821168i | \(0.306677\pi\) | |||||||
\(150\) | 4.22567 | 0.345024 | ||||||||
\(151\) | 1.15279 | 0.0938127 | 0.0469063 | − | 0.998899i | \(-0.485064\pi\) | ||||
0.0469063 | + | 0.998899i | \(0.485064\pi\) | |||||||
\(152\) | 0.585786 | 0.0475136 | ||||||||
\(153\) | 7.75992 | 0.627352 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.515469 | −0.0414035 | ||||||||
\(156\) | −2.22129 | −0.177846 | ||||||||
\(157\) | 15.6970 | 1.25276 | 0.626378 | − | 0.779520i | \(-0.284537\pi\) | ||||
0.626378 | + | 0.779520i | \(0.284537\pi\) | |||||||
\(158\) | −1.92712 | −0.153313 | ||||||||
\(159\) | 7.34390 | 0.582409 | ||||||||
\(160\) | −0.879961 | −0.0695670 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −8.48528 | −0.664619 | −0.332309 | − | 0.943170i | \(-0.607828\pi\) | ||||
−0.332309 | + | 0.943170i | \(0.607828\pi\) | |||||||
\(164\) | −0.124413 | −0.00971505 | ||||||||
\(165\) | −3.58397 | −0.279012 | ||||||||
\(166\) | 6.99819 | 0.543165 | ||||||||
\(167\) | 19.0409 | 1.47343 | 0.736714 | − | 0.676205i | \(-0.236377\pi\) | ||||
0.736714 | + | 0.676205i | \(0.236377\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.06585 | −0.620450 | ||||||||
\(170\) | −6.82843 | −0.523716 | ||||||||
\(171\) | 0.585786 | 0.0447962 | ||||||||
\(172\) | −5.85158 | −0.446179 | ||||||||
\(173\) | −12.0087 | −0.913008 | −0.456504 | − | 0.889721i | \(-0.650899\pi\) | ||||
−0.456504 | + | 0.889721i | \(0.650899\pi\) | |||||||
\(174\) | −4.60713 | −0.349266 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.07288 | −0.307005 | ||||||||
\(177\) | 4.90131 | 0.368405 | ||||||||
\(178\) | 10.4587 | 0.783914 | ||||||||
\(179\) | 10.6461 | 0.795725 | 0.397862 | − | 0.917445i | \(-0.369752\pi\) | ||||
0.397862 | + | 0.917445i | \(0.369752\pi\) | |||||||
\(180\) | −0.879961 | −0.0655884 | ||||||||
\(181\) | −21.5385 | −1.60095 | −0.800473 | − | 0.599368i | \(-0.795418\pi\) | ||||
−0.800473 | + | 0.599368i | \(0.795418\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.14320 | −0.158430 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −3.11385 | −0.228935 | ||||||||
\(186\) | −0.585786 | −0.0429519 | ||||||||
\(187\) | −31.6052 | −2.31120 | ||||||||
\(188\) | 0.0515337 | 0.00375848 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.515469 | −0.0373961 | ||||||||
\(191\) | 25.2194 | 1.82481 | 0.912405 | − | 0.409287i | \(-0.134223\pi\) | ||||
0.912405 | + | 0.409287i | \(0.134223\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −7.50844 | −0.540469 | −0.270235 | − | 0.962794i | \(-0.587101\pi\) | ||||
−0.270235 | + | 0.962794i | \(0.587101\pi\) | |||||||
\(194\) | 17.5084 | 1.25703 | ||||||||
\(195\) | 1.95465 | 0.139976 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.66388 | 0.474782 | 0.237391 | − | 0.971414i | \(-0.423708\pi\) | ||||
0.237391 | + | 0.971414i | \(0.423708\pi\) | |||||||
\(198\) | −4.07288 | −0.289447 | ||||||||
\(199\) | −4.80964 | −0.340947 | −0.170473 | − | 0.985362i | \(-0.554530\pi\) | ||||
−0.170473 | + | 0.985362i | \(0.554530\pi\) | |||||||
\(200\) | −4.22567 | −0.298800 | ||||||||
\(201\) | 8.58835 | 0.605775 | ||||||||
\(202\) | −4.41240 | −0.310456 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7.75992 | −0.543303 | ||||||||
\(205\) | 0.109479 | 0.00764634 | ||||||||
\(206\) | 3.77871 | 0.263275 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 2.22129 | 0.154019 | ||||||||
\(209\) | −2.38584 | −0.165032 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.79824 | 0.330324 | 0.165162 | − | 0.986266i | \(-0.447185\pi\) | ||||
0.165162 | + | 0.986266i | \(0.447185\pi\) | |||||||
\(212\) | −7.34390 | −0.504381 | ||||||||
\(213\) | −4.07288 | −0.279069 | ||||||||
\(214\) | −3.61416 | −0.247059 | ||||||||
\(215\) | 5.14917 | 0.351170 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.42381 | 0.435075 | ||||||||
\(219\) | −4.97162 | −0.335951 | ||||||||
\(220\) | 3.58397 | 0.241632 | ||||||||
\(221\) | 17.2371 | 1.15949 | ||||||||
\(222\) | −3.53863 | −0.237497 | ||||||||
\(223\) | −14.5983 | −0.977574 | −0.488787 | − | 0.872403i | \(-0.662560\pi\) | ||||
−0.488787 | + | 0.872403i | \(0.662560\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.22567 | −0.281711 | ||||||||
\(226\) | 13.6115 | 0.905424 | ||||||||
\(227\) | −9.39543 | −0.623597 | −0.311798 | − | 0.950148i | \(-0.600931\pi\) | ||||
−0.311798 | + | 0.950148i | \(0.600931\pi\) | |||||||
\(228\) | −0.585786 | −0.0387947 | ||||||||
\(229\) | 7.14757 | 0.472325 | 0.236162 | − | 0.971714i | \(-0.424110\pi\) | ||||
0.236162 | + | 0.971714i | \(0.424110\pi\) | |||||||
\(230\) | 0.879961 | 0.0580229 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.60713 | 0.302473 | ||||||||
\(233\) | 15.3439 | 1.00521 | 0.502606 | − | 0.864516i | \(-0.332375\pi\) | ||||
0.502606 | + | 0.864516i | \(0.332375\pi\) | |||||||
\(234\) | 2.22129 | 0.145211 | ||||||||
\(235\) | −0.0453476 | −0.00295815 | ||||||||
\(236\) | −4.90131 | −0.319048 | ||||||||
\(237\) | 1.92712 | 0.125180 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.7687 | 1.14936 | 0.574680 | − | 0.818378i | \(-0.305127\pi\) | ||||
0.574680 | + | 0.818378i | \(0.305127\pi\) | |||||||
\(240\) | 0.879961 | 0.0568012 | ||||||||
\(241\) | 5.07629 | 0.326992 | 0.163496 | − | 0.986544i | \(-0.447723\pi\) | ||||
0.163496 | + | 0.986544i | \(0.447723\pi\) | |||||||
\(242\) | 5.58835 | 0.359233 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 2.14320 | 0.137204 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.124413 | 0.00793231 | ||||||||
\(247\) | 1.30120 | 0.0827936 | ||||||||
\(248\) | 0.585786 | 0.0371975 | ||||||||
\(249\) | −6.99819 | −0.443492 | ||||||||
\(250\) | 8.11823 | 0.513442 | ||||||||
\(251\) | 13.7473 | 0.867723 | 0.433862 | − | 0.900979i | \(-0.357151\pi\) | ||||
0.433862 | + | 0.900979i | \(0.357151\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.07288 | 0.256060 | ||||||||
\(254\) | 5.92446 | 0.371734 | ||||||||
\(255\) | 6.82843 | 0.427613 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.0069 | 0.686594 | 0.343297 | − | 0.939227i | \(-0.388456\pi\) | ||||
0.343297 | + | 0.939227i | \(0.388456\pi\) | |||||||
\(258\) | 5.85158 | 0.364304 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.95465 | −0.121222 | ||||||||
\(261\) | 4.60713 | 0.285174 | ||||||||
\(262\) | 6.76430 | 0.417900 | ||||||||
\(263\) | −26.7153 | −1.64734 | −0.823669 | − | 0.567071i | \(-0.808076\pi\) | ||||
−0.823669 | + | 0.567071i | \(0.808076\pi\) | |||||||
\(264\) | 4.07288 | 0.250668 | ||||||||
\(265\) | 6.46234 | 0.396978 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.4587 | −0.640063 | ||||||||
\(268\) | −8.58835 | −0.524617 | ||||||||
\(269\) | 17.1693 | 1.04683 | 0.523416 | − | 0.852077i | \(-0.324657\pi\) | ||||
0.523416 | + | 0.852077i | \(0.324657\pi\) | |||||||
\(270\) | 0.879961 | 0.0535527 | ||||||||
\(271\) | −17.5260 | −1.06463 | −0.532315 | − | 0.846546i | \(-0.678678\pi\) | ||||
−0.532315 | + | 0.846546i | \(0.678678\pi\) | |||||||
\(272\) | 7.75992 | 0.470514 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.56881 | 0.336424 | ||||||||
\(275\) | 17.2106 | 1.03784 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | −5.00075 | −0.300466 | −0.150233 | − | 0.988651i | \(-0.548002\pi\) | ||||
−0.150233 | + | 0.988651i | \(0.548002\pi\) | |||||||
\(278\) | 12.8258 | 0.769239 | ||||||||
\(279\) | 0.585786 | 0.0350701 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.73676 | 0.282572 | 0.141286 | − | 0.989969i | \(-0.454876\pi\) | ||||
0.141286 | + | 0.989969i | \(0.454876\pi\) | |||||||
\(282\) | −0.0515337 | −0.00306879 | ||||||||
\(283\) | −5.12101 | −0.304412 | −0.152206 | − | 0.988349i | \(-0.548638\pi\) | ||||
−0.152206 | + | 0.988349i | \(0.548638\pi\) | |||||||
\(284\) | 4.07288 | 0.241681 | ||||||||
\(285\) | 0.515469 | 0.0305338 | ||||||||
\(286\) | −9.04707 | −0.534964 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 43.2164 | 2.54214 | ||||||||
\(290\) | −4.05410 | −0.238065 | ||||||||
\(291\) | −17.5084 | −1.02636 | ||||||||
\(292\) | 4.97162 | 0.290942 | ||||||||
\(293\) | 9.45315 | 0.552259 | 0.276129 | − | 0.961120i | \(-0.410948\pi\) | ||||
0.276129 | + | 0.961120i | \(0.410948\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.31296 | 0.251110 | ||||||||
\(296\) | 3.53863 | 0.205679 | ||||||||
\(297\) | 4.07288 | 0.236332 | ||||||||
\(298\) | 13.9322 | 0.807073 | ||||||||
\(299\) | −2.22129 | −0.128461 | ||||||||
\(300\) | 4.22567 | 0.243969 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.15279 | 0.0663356 | ||||||||
\(303\) | 4.41240 | 0.253486 | ||||||||
\(304\) | 0.585786 | 0.0335972 | ||||||||
\(305\) | −1.88593 | −0.107988 | ||||||||
\(306\) | 7.75992 | 0.443605 | ||||||||
\(307\) | 29.8036 | 1.70098 | 0.850490 | − | 0.525991i | \(-0.176305\pi\) | ||||
0.850490 | + | 0.525991i | \(0.176305\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.77871 | −0.214963 | ||||||||
\(310\) | −0.515469 | −0.0292767 | ||||||||
\(311\) | −18.5983 | −1.05461 | −0.527306 | − | 0.849675i | \(-0.676798\pi\) | ||||
−0.527306 | + | 0.849675i | \(0.676798\pi\) | |||||||
\(312\) | −2.22129 | −0.125756 | ||||||||
\(313\) | 17.1803 | 0.971089 | 0.485545 | − | 0.874212i | \(-0.338621\pi\) | ||||
0.485545 | + | 0.874212i | \(0.338621\pi\) | |||||||
\(314\) | 15.6970 | 0.885832 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.92712 | −0.108409 | ||||||||
\(317\) | 2.45775 | 0.138041 | 0.0690205 | − | 0.997615i | \(-0.478013\pi\) | ||||
0.0690205 | + | 0.997615i | \(0.478013\pi\) | |||||||
\(318\) | 7.34390 | 0.411825 | ||||||||
\(319\) | −18.7643 | −1.05060 | ||||||||
\(320\) | −0.879961 | −0.0491913 | ||||||||
\(321\) | 3.61416 | 0.201723 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.54566 | 0.252927 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −9.38646 | −0.520667 | ||||||||
\(326\) | −8.48528 | −0.469956 | ||||||||
\(327\) | −6.42381 | −0.355237 | ||||||||
\(328\) | −0.124413 | −0.00686958 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.58397 | −0.197291 | ||||||||
\(331\) | 19.4595 | 1.06959 | 0.534795 | − | 0.844982i | \(-0.320389\pi\) | ||||
0.534795 | + | 0.844982i | \(0.320389\pi\) | |||||||
\(332\) | 6.99819 | 0.384075 | ||||||||
\(333\) | 3.53863 | 0.193916 | ||||||||
\(334\) | 19.0409 | 1.04187 | ||||||||
\(335\) | 7.55741 | 0.412905 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.0213 | 1.41747 | 0.708734 | − | 0.705476i | \(-0.249267\pi\) | ||||
0.708734 | + | 0.705476i | \(0.249267\pi\) | |||||||
\(338\) | −8.06585 | −0.438724 | ||||||||
\(339\) | −13.6115 | −0.739276 | ||||||||
\(340\) | −6.82843 | −0.370323 | ||||||||
\(341\) | −2.38584 | −0.129200 | ||||||||
\(342\) | 0.585786 | 0.0316757 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.85158 | −0.315496 | ||||||||
\(345\) | −0.879961 | −0.0473755 | ||||||||
\(346\) | −12.0087 | −0.645594 | ||||||||
\(347\) | −31.4229 | −1.68687 | −0.843434 | − | 0.537233i | \(-0.819470\pi\) | ||||
−0.843434 | + | 0.537233i | \(0.819470\pi\) | |||||||
\(348\) | −4.60713 | −0.246968 | ||||||||
\(349\) | −13.3688 | −0.715614 | −0.357807 | − | 0.933796i | \(-0.616475\pi\) | ||||
−0.357807 | + | 0.933796i | \(0.616475\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.22129 | −0.118564 | ||||||||
\(352\) | −4.07288 | −0.217085 | ||||||||
\(353\) | −15.8005 | −0.840973 | −0.420487 | − | 0.907299i | \(-0.638141\pi\) | ||||
−0.420487 | + | 0.907299i | \(0.638141\pi\) | |||||||
\(354\) | 4.90131 | 0.260502 | ||||||||
\(355\) | −3.58397 | −0.190218 | ||||||||
\(356\) | 10.4587 | 0.554311 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.6461 | 0.562662 | ||||||||
\(359\) | 26.9642 | 1.42311 | 0.711557 | − | 0.702629i | \(-0.247990\pi\) | ||||
0.711557 | + | 0.702629i | \(0.247990\pi\) | |||||||
\(360\) | −0.879961 | −0.0463780 | ||||||||
\(361\) | −18.6569 | −0.981940 | ||||||||
\(362\) | −21.5385 | −1.13204 | ||||||||
\(363\) | −5.58835 | −0.293312 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.37483 | −0.228989 | ||||||||
\(366\) | −2.14320 | −0.112027 | ||||||||
\(367\) | 5.67201 | 0.296077 | 0.148038 | − | 0.988982i | \(-0.452704\pi\) | ||||
0.148038 | + | 0.988982i | \(0.452704\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −0.124413 | −0.00647670 | ||||||||
\(370\) | −3.11385 | −0.161882 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.585786 | −0.0303716 | ||||||||
\(373\) | 7.49704 | 0.388182 | 0.194091 | − | 0.980984i | \(-0.437824\pi\) | ||||
0.194091 | + | 0.980984i | \(0.437824\pi\) | |||||||
\(374\) | −31.6052 | −1.63427 | ||||||||
\(375\) | −8.11823 | −0.419223 | ||||||||
\(376\) | 0.0515337 | 0.00265765 | ||||||||
\(377\) | 10.2338 | 0.527067 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.24273 | −0.115202 | −0.0576008 | − | 0.998340i | \(-0.518345\pi\) | ||||
−0.0576008 | + | 0.998340i | \(0.518345\pi\) | |||||||
\(380\) | −0.515469 | −0.0264430 | ||||||||
\(381\) | −5.92446 | −0.303520 | ||||||||
\(382\) | 25.2194 | 1.29034 | ||||||||
\(383\) | 24.0693 | 1.22988 | 0.614941 | − | 0.788573i | \(-0.289180\pi\) | ||||
0.614941 | + | 0.788573i | \(0.289180\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.50844 | −0.382169 | ||||||||
\(387\) | −5.85158 | −0.297453 | ||||||||
\(388\) | 17.5084 | 0.888856 | ||||||||
\(389\) | −11.9021 | −0.603458 | −0.301729 | − | 0.953394i | \(-0.597564\pi\) | ||||
−0.301729 | + | 0.953394i | \(0.597564\pi\) | |||||||
\(390\) | 1.95465 | 0.0989777 | ||||||||
\(391\) | −7.75992 | −0.392436 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.76430 | −0.341214 | ||||||||
\(394\) | 6.66388 | 0.335722 | ||||||||
\(395\) | 1.69579 | 0.0853245 | ||||||||
\(396\) | −4.07288 | −0.204670 | ||||||||
\(397\) | −12.7305 | −0.638925 | −0.319462 | − | 0.947599i | \(-0.603502\pi\) | ||||
−0.319462 | + | 0.947599i | \(0.603502\pi\) | |||||||
\(398\) | −4.80964 | −0.241086 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.22567 | −0.211283 | ||||||||
\(401\) | −24.8032 | −1.23861 | −0.619307 | − | 0.785149i | \(-0.712586\pi\) | ||||
−0.619307 | + | 0.785149i | \(0.712586\pi\) | |||||||
\(402\) | 8.58835 | 0.428348 | ||||||||
\(403\) | 1.30120 | 0.0648176 | ||||||||
\(404\) | −4.41240 | −0.219525 | ||||||||
\(405\) | −0.879961 | −0.0437256 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.4124 | −0.714396 | ||||||||
\(408\) | −7.75992 | −0.384173 | ||||||||
\(409\) | −13.1174 | −0.648613 | −0.324306 | − | 0.945952i | \(-0.605131\pi\) | ||||
−0.324306 | + | 0.945952i | \(0.605131\pi\) | |||||||
\(410\) | 0.109479 | 0.00540678 | ||||||||
\(411\) | −5.56881 | −0.274689 | ||||||||
\(412\) | 3.77871 | 0.186163 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | −6.15813 | −0.302291 | ||||||||
\(416\) | 2.22129 | 0.108908 | ||||||||
\(417\) | −12.8258 | −0.628081 | ||||||||
\(418\) | −2.38584 | −0.116695 | ||||||||
\(419\) | 31.2417 | 1.52626 | 0.763129 | − | 0.646247i | \(-0.223662\pi\) | ||||
0.763129 | + | 0.646247i | \(0.223662\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.1129 | −1.85751 | −0.928755 | − | 0.370694i | \(-0.879120\pi\) | ||||
−0.928755 | + | 0.370694i | \(0.879120\pi\) | |||||||
\(422\) | 4.79824 | 0.233575 | ||||||||
\(423\) | 0.0515337 | 0.00250565 | ||||||||
\(424\) | −7.34390 | −0.356651 | ||||||||
\(425\) | −32.7909 | −1.59059 | ||||||||
\(426\) | −4.07288 | −0.197332 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.61416 | −0.174697 | ||||||||
\(429\) | 9.04707 | 0.436796 | ||||||||
\(430\) | 5.14917 | 0.248315 | ||||||||
\(431\) | 29.4031 | 1.41630 | 0.708149 | − | 0.706063i | \(-0.249530\pi\) | ||||
0.708149 | + | 0.706063i | \(0.249530\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −14.8309 | −0.712727 | −0.356364 | − | 0.934347i | \(-0.615984\pi\) | ||||
−0.356364 | + | 0.934347i | \(0.615984\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.05410 | 0.194379 | ||||||||
\(436\) | 6.42381 | 0.307645 | ||||||||
\(437\) | −0.585786 | −0.0280220 | ||||||||
\(438\) | −4.97162 | −0.237553 | ||||||||
\(439\) | 0.299392 | 0.0142892 | 0.00714461 | − | 0.999974i | \(-0.497726\pi\) | ||||
0.00714461 | + | 0.999974i | \(0.497726\pi\) | |||||||
\(440\) | 3.58397 | 0.170859 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 17.2371 | 0.819884 | ||||||||
\(443\) | 10.5202 | 0.499829 | 0.249915 | − | 0.968268i | \(-0.419597\pi\) | ||||
0.249915 | + | 0.968268i | \(0.419597\pi\) | |||||||
\(444\) | −3.53863 | −0.167936 | ||||||||
\(445\) | −9.20326 | −0.436276 | ||||||||
\(446\) | −14.5983 | −0.691249 | ||||||||
\(447\) | −13.9322 | −0.658973 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −40.9505 | −1.93257 | −0.966287 | − | 0.257469i | \(-0.917112\pi\) | ||||
−0.966287 | + | 0.257469i | \(0.917112\pi\) | |||||||
\(450\) | −4.22567 | −0.199200 | ||||||||
\(451\) | 0.506721 | 0.0238605 | ||||||||
\(452\) | 13.6115 | 0.640231 | ||||||||
\(453\) | −1.15279 | −0.0541628 | ||||||||
\(454\) | −9.39543 | −0.440949 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.585786 | −0.0274320 | ||||||||
\(457\) | 15.1539 | 0.708869 | 0.354435 | − | 0.935081i | \(-0.384673\pi\) | ||||
0.354435 | + | 0.935081i | \(0.384673\pi\) | |||||||
\(458\) | 7.14757 | 0.333984 | ||||||||
\(459\) | −7.75992 | −0.362202 | ||||||||
\(460\) | 0.879961 | 0.0410284 | ||||||||
\(461\) | 22.0089 | 1.02506 | 0.512528 | − | 0.858671i | \(-0.328709\pi\) | ||||
0.512528 | + | 0.858671i | \(0.328709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.83546 | −0.0853009 | −0.0426505 | − | 0.999090i | \(-0.513580\pi\) | ||||
−0.0426505 | + | 0.999090i | \(0.513580\pi\) | |||||||
\(464\) | 4.60713 | 0.213881 | ||||||||
\(465\) | 0.515469 | 0.0239043 | ||||||||
\(466\) | 15.3439 | 0.710792 | ||||||||
\(467\) | −22.4586 | −1.03926 | −0.519631 | − | 0.854391i | \(-0.673930\pi\) | ||||
−0.519631 | + | 0.854391i | \(0.673930\pi\) | |||||||
\(468\) | 2.22129 | 0.102679 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.0453476 | −0.00209173 | ||||||||
\(471\) | −15.6970 | −0.723279 | ||||||||
\(472\) | −4.90131 | −0.225601 | ||||||||
\(473\) | 23.8328 | 1.09583 | ||||||||
\(474\) | 1.92712 | 0.0885156 | ||||||||
\(475\) | −2.47534 | −0.113576 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.34390 | −0.336254 | ||||||||
\(478\) | 17.7687 | 0.812720 | ||||||||
\(479\) | −19.6760 | −0.899021 | −0.449511 | − | 0.893275i | \(-0.648402\pi\) | ||||
−0.449511 | + | 0.893275i | \(0.648402\pi\) | |||||||
\(480\) | 0.879961 | 0.0401645 | ||||||||
\(481\) | 7.86033 | 0.358400 | ||||||||
\(482\) | 5.07629 | 0.231218 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.58835 | 0.254016 | ||||||||
\(485\) | −15.4067 | −0.699584 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −6.01154 | −0.272409 | −0.136204 | − | 0.990681i | \(-0.543490\pi\) | ||||
−0.136204 | + | 0.990681i | \(0.543490\pi\) | |||||||
\(488\) | 2.14320 | 0.0970180 | ||||||||
\(489\) | 8.48528 | 0.383718 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.2401 | 1.18420 | 0.592099 | − | 0.805865i | \(-0.298299\pi\) | ||||
0.592099 | + | 0.805865i | \(0.298299\pi\) | |||||||
\(492\) | 0.124413 | 0.00560899 | ||||||||
\(493\) | 35.7510 | 1.61014 | ||||||||
\(494\) | 1.30120 | 0.0585440 | ||||||||
\(495\) | 3.58397 | 0.161088 | ||||||||
\(496\) | 0.585786 | 0.0263026 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6.99819 | −0.313596 | ||||||||
\(499\) | −6.49934 | −0.290950 | −0.145475 | − | 0.989362i | \(-0.546471\pi\) | ||||
−0.145475 | + | 0.989362i | \(0.546471\pi\) | |||||||
\(500\) | 8.11823 | 0.363058 | ||||||||
\(501\) | −19.0409 | −0.850684 | ||||||||
\(502\) | 13.7473 | 0.613573 | ||||||||
\(503\) | −34.4071 | −1.53414 | −0.767068 | − | 0.641566i | \(-0.778285\pi\) | ||||
−0.767068 | + | 0.641566i | \(0.778285\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.88274 | 0.172780 | ||||||||
\(506\) | 4.07288 | 0.181062 | ||||||||
\(507\) | 8.06585 | 0.358217 | ||||||||
\(508\) | 5.92446 | 0.262856 | ||||||||
\(509\) | −7.76368 | −0.344119 | −0.172059 | − | 0.985087i | \(-0.555042\pi\) | ||||
−0.172059 | + | 0.985087i | \(0.555042\pi\) | |||||||
\(510\) | 6.82843 | 0.302368 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.585786 | −0.0258631 | ||||||||
\(514\) | 11.0069 | 0.485495 | ||||||||
\(515\) | −3.32511 | −0.146522 | ||||||||
\(516\) | 5.85158 | 0.257602 | ||||||||
\(517\) | −0.209891 | −0.00923098 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.0087 | 0.527126 | ||||||||
\(520\) | −1.95465 | −0.0857172 | ||||||||
\(521\) | 31.7347 | 1.39032 | 0.695162 | − | 0.718853i | \(-0.255333\pi\) | ||||
0.695162 | + | 0.718853i | \(0.255333\pi\) | |||||||
\(522\) | 4.60713 | 0.201649 | ||||||||
\(523\) | 0.0771298 | 0.00337265 | 0.00168632 | − | 0.999999i | \(-0.499463\pi\) | ||||
0.00168632 | + | 0.999999i | \(0.499463\pi\) | |||||||
\(524\) | 6.76430 | 0.295500 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −26.7153 | −1.16484 | ||||||||
\(527\) | 4.54566 | 0.198012 | ||||||||
\(528\) | 4.07288 | 0.177249 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 6.46234 | 0.280706 | ||||||||
\(531\) | −4.90131 | −0.212699 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.276359 | −0.0119704 | ||||||||
\(534\) | −10.4587 | −0.452593 | ||||||||
\(535\) | 3.18032 | 0.137497 | ||||||||
\(536\) | −8.58835 | −0.370960 | ||||||||
\(537\) | −10.6461 | −0.459412 | ||||||||
\(538\) | 17.1693 | 0.740222 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.879961 | 0.0378675 | ||||||||
\(541\) | 10.9550 | 0.470992 | 0.235496 | − | 0.971875i | \(-0.424328\pi\) | ||||
0.235496 | + | 0.971875i | \(0.424328\pi\) | |||||||
\(542\) | −17.5260 | −0.752807 | ||||||||
\(543\) | 21.5385 | 0.924307 | ||||||||
\(544\) | 7.75992 | 0.332704 | ||||||||
\(545\) | −5.65270 | −0.242135 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.9490 | −1.49431 | −0.747155 | − | 0.664649i | \(-0.768581\pi\) | ||||
−0.747155 | + | 0.664649i | \(0.768581\pi\) | |||||||
\(548\) | 5.56881 | 0.237888 | ||||||||
\(549\) | 2.14320 | 0.0914694 | ||||||||
\(550\) | 17.2106 | 0.733864 | ||||||||
\(551\) | 2.69880 | 0.114973 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5.00075 | −0.212462 | ||||||||
\(555\) | 3.11385 | 0.132176 | ||||||||
\(556\) | 12.8258 | 0.543934 | ||||||||
\(557\) | 9.65685 | 0.409174 | 0.204587 | − | 0.978848i | \(-0.434415\pi\) | ||||
0.204587 | + | 0.978848i | \(0.434415\pi\) | |||||||
\(558\) | 0.585786 | 0.0247983 | ||||||||
\(559\) | −12.9981 | −0.549761 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 31.6052 | 1.33437 | ||||||||
\(562\) | 4.73676 | 0.199808 | ||||||||
\(563\) | −23.7010 | −0.998878 | −0.499439 | − | 0.866349i | \(-0.666461\pi\) | ||||
−0.499439 | + | 0.866349i | \(0.666461\pi\) | |||||||
\(564\) | −0.0515337 | −0.00216996 | ||||||||
\(565\) | −11.9776 | −0.503901 | ||||||||
\(566\) | −5.12101 | −0.215252 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.07288 | 0.170894 | ||||||||
\(569\) | 20.8825 | 0.875441 | 0.437720 | − | 0.899111i | \(-0.355786\pi\) | ||||
0.437720 | + | 0.899111i | \(0.355786\pi\) | |||||||
\(570\) | 0.515469 | 0.0215906 | ||||||||
\(571\) | 0.686292 | 0.0287204 | 0.0143602 | − | 0.999897i | \(-0.495429\pi\) | ||||
0.0143602 | + | 0.999897i | \(0.495429\pi\) | |||||||
\(572\) | −9.04707 | −0.378277 | ||||||||
\(573\) | −25.2194 | −1.05356 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.22567 | 0.176223 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 29.9707 | 1.24770 | 0.623848 | − | 0.781546i | \(-0.285568\pi\) | ||||
0.623848 | + | 0.781546i | \(0.285568\pi\) | |||||||
\(578\) | 43.2164 | 1.79756 | ||||||||
\(579\) | 7.50844 | 0.312040 | ||||||||
\(580\) | −4.05410 | −0.168337 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −17.5084 | −0.725748 | ||||||||
\(583\) | 29.9108 | 1.23878 | ||||||||
\(584\) | 4.97162 | 0.205727 | ||||||||
\(585\) | −1.95465 | −0.0808149 | ||||||||
\(586\) | 9.45315 | 0.390506 | ||||||||
\(587\) | 24.2577 | 1.00122 | 0.500611 | − | 0.865672i | \(-0.333109\pi\) | ||||
0.500611 | + | 0.865672i | \(0.333109\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.343146 | 0.0141391 | ||||||||
\(590\) | 4.31296 | 0.177562 | ||||||||
\(591\) | −6.66388 | −0.274116 | ||||||||
\(592\) | 3.53863 | 0.145437 | ||||||||
\(593\) | 20.7179 | 0.850782 | 0.425391 | − | 0.905010i | \(-0.360137\pi\) | ||||
0.425391 | + | 0.905010i | \(0.360137\pi\) | |||||||
\(594\) | 4.07288 | 0.167112 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 13.9322 | 0.570687 | ||||||||
\(597\) | 4.80964 | 0.196846 | ||||||||
\(598\) | −2.22129 | −0.0908355 | ||||||||
\(599\) | 29.9322 | 1.22300 | 0.611499 | − | 0.791245i | \(-0.290567\pi\) | ||||
0.611499 | + | 0.791245i | \(0.290567\pi\) | |||||||
\(600\) | 4.22567 | 0.172512 | ||||||||
\(601\) | 23.2985 | 0.950364 | 0.475182 | − | 0.879888i | \(-0.342382\pi\) | ||||
0.475182 | + | 0.879888i | \(0.342382\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.58835 | −0.349745 | ||||||||
\(604\) | 1.15279 | 0.0469063 | ||||||||
\(605\) | −4.91753 | −0.199926 | ||||||||
\(606\) | 4.41240 | 0.179242 | ||||||||
\(607\) | −21.6809 | −0.879999 | −0.439999 | − | 0.897998i | \(-0.645021\pi\) | ||||
−0.439999 | + | 0.897998i | \(0.645021\pi\) | |||||||
\(608\) | 0.585786 | 0.0237568 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.88593 | −0.0763590 | ||||||||
\(611\) | 0.114472 | 0.00463102 | ||||||||
\(612\) | 7.75992 | 0.313676 | ||||||||
\(613\) | −30.9746 | −1.25105 | −0.625526 | − | 0.780203i | \(-0.715116\pi\) | ||||
−0.625526 | + | 0.780203i | \(0.715116\pi\) | |||||||
\(614\) | 29.8036 | 1.20277 | ||||||||
\(615\) | −0.109479 | −0.00441462 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.6274 | −0.508361 | −0.254180 | − | 0.967157i | \(-0.581806\pi\) | ||||
−0.254180 | + | 0.967157i | \(0.581806\pi\) | |||||||
\(618\) | −3.77871 | −0.152002 | ||||||||
\(619\) | 35.4672 | 1.42555 | 0.712773 | − | 0.701395i | \(-0.247439\pi\) | ||||
0.712773 | + | 0.701395i | \(0.247439\pi\) | |||||||
\(620\) | −0.515469 | −0.0207017 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −18.5983 | −0.745724 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.22129 | −0.0889230 | ||||||||
\(625\) | 13.9846 | 0.559385 | ||||||||
\(626\) | 17.1803 | 0.686664 | ||||||||
\(627\) | 2.38584 | 0.0952812 | ||||||||
\(628\) | 15.6970 | 0.626378 | ||||||||
\(629\) | 27.4595 | 1.09488 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.3025 | −0.648993 | −0.324497 | − | 0.945887i | \(-0.605195\pi\) | ||||
−0.324497 | + | 0.945887i | \(0.605195\pi\) | |||||||
\(632\) | −1.92712 | −0.0766567 | ||||||||
\(633\) | −4.79824 | −0.190713 | ||||||||
\(634\) | 2.45775 | 0.0976097 | ||||||||
\(635\) | −5.21330 | −0.206883 | ||||||||
\(636\) | 7.34390 | 0.291204 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −18.7643 | −0.742886 | ||||||||
\(639\) | 4.07288 | 0.161121 | ||||||||
\(640\) | −0.879961 | −0.0347835 | ||||||||
\(641\) | −13.8228 | −0.545966 | −0.272983 | − | 0.962019i | \(-0.588010\pi\) | ||||
−0.272983 | + | 0.962019i | \(0.588010\pi\) | |||||||
\(642\) | 3.61416 | 0.142640 | ||||||||
\(643\) | −26.9502 | −1.06281 | −0.531406 | − | 0.847117i | \(-0.678336\pi\) | ||||
−0.531406 | + | 0.847117i | \(0.678336\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.14917 | −0.202748 | ||||||||
\(646\) | 4.54566 | 0.178846 | ||||||||
\(647\) | 25.4495 | 1.00052 | 0.500262 | − | 0.865874i | \(-0.333237\pi\) | ||||
0.500262 | + | 0.865874i | \(0.333237\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 19.9624 | 0.783594 | ||||||||
\(650\) | −9.38646 | −0.368167 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.48528 | −0.332309 | ||||||||
\(653\) | −29.2277 | −1.14377 | −0.571885 | − | 0.820334i | \(-0.693788\pi\) | ||||
−0.571885 | + | 0.820334i | \(0.693788\pi\) | |||||||
\(654\) | −6.42381 | −0.251191 | ||||||||
\(655\) | −5.95232 | −0.232576 | ||||||||
\(656\) | −0.124413 | −0.00485753 | ||||||||
\(657\) | 4.97162 | 0.193962 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.6958 | 0.689330 | 0.344665 | − | 0.938726i | \(-0.387992\pi\) | ||||
0.344665 | + | 0.938726i | \(0.387992\pi\) | |||||||
\(660\) | −3.58397 | −0.139506 | ||||||||
\(661\) | −4.52334 | −0.175938 | −0.0879688 | − | 0.996123i | \(-0.528038\pi\) | ||||
−0.0879688 | + | 0.996123i | \(0.528038\pi\) | |||||||
\(662\) | 19.4595 | 0.756314 | ||||||||
\(663\) | −17.2371 | −0.669432 | ||||||||
\(664\) | 6.99819 | 0.271582 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.53863 | 0.137119 | ||||||||
\(667\) | −4.60713 | −0.178389 | ||||||||
\(668\) | 19.0409 | 0.736714 | ||||||||
\(669\) | 14.5983 | 0.564403 | ||||||||
\(670\) | 7.55741 | 0.291968 | ||||||||
\(671\) | −8.72898 | −0.336979 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.9679 | −1.57920 | −0.789598 | − | 0.613624i | \(-0.789711\pi\) | ||||
−0.789598 | + | 0.613624i | \(0.789711\pi\) | |||||||
\(674\) | 26.0213 | 1.00230 | ||||||||
\(675\) | 4.22567 | 0.162646 | ||||||||
\(676\) | −8.06585 | −0.310225 | ||||||||
\(677\) | 8.96787 | 0.344663 | 0.172332 | − | 0.985039i | \(-0.444870\pi\) | ||||
0.172332 | + | 0.985039i | \(0.444870\pi\) | |||||||
\(678\) | −13.6115 | −0.522747 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.82843 | −0.261858 | ||||||||
\(681\) | 9.39543 | 0.360034 | ||||||||
\(682\) | −2.38584 | −0.0913584 | ||||||||
\(683\) | 41.3579 | 1.58252 | 0.791258 | − | 0.611482i | \(-0.209426\pi\) | ||||
0.791258 | + | 0.611482i | \(0.209426\pi\) | |||||||
\(684\) | 0.585786 | 0.0223981 | ||||||||
\(685\) | −4.90034 | −0.187232 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.14757 | −0.272697 | ||||||||
\(688\) | −5.85158 | −0.223090 | ||||||||
\(689\) | −16.3130 | −0.621474 | ||||||||
\(690\) | −0.879961 | −0.0334995 | ||||||||
\(691\) | −29.6028 | −1.12614 | −0.563071 | − | 0.826409i | \(-0.690380\pi\) | ||||
−0.563071 | + | 0.826409i | \(0.690380\pi\) | |||||||
\(692\) | −12.0087 | −0.456504 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −31.4229 | −1.19280 | ||||||||
\(695\) | −11.2862 | −0.428109 | ||||||||
\(696\) | −4.60713 | −0.174633 | ||||||||
\(697\) | −0.965438 | −0.0365686 | ||||||||
\(698\) | −13.3688 | −0.506016 | ||||||||
\(699\) | −15.3439 | −0.580359 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.4306 | 1.18712 | 0.593560 | − | 0.804790i | \(-0.297722\pi\) | ||||
0.593560 | + | 0.804790i | \(0.297722\pi\) | |||||||
\(702\) | −2.22129 | −0.0838374 | ||||||||
\(703\) | 2.07288 | 0.0781801 | ||||||||
\(704\) | −4.07288 | −0.153502 | ||||||||
\(705\) | 0.0453476 | 0.00170789 | ||||||||
\(706\) | −15.8005 | −0.594658 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.90131 | 0.184202 | ||||||||
\(709\) | 46.0250 | 1.72851 | 0.864253 | − | 0.503058i | \(-0.167792\pi\) | ||||
0.864253 | + | 0.503058i | \(0.167792\pi\) | |||||||
\(710\) | −3.58397 | −0.134504 | ||||||||
\(711\) | −1.92712 | −0.0722727 | ||||||||
\(712\) | 10.4587 | 0.391957 | ||||||||
\(713\) | −0.585786 | −0.0219379 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.96106 | 0.297727 | ||||||||
\(716\) | 10.6461 | 0.397862 | ||||||||
\(717\) | −17.7687 | −0.663583 | ||||||||
\(718\) | 26.9642 | 1.00629 | ||||||||
\(719\) | −18.3195 | −0.683204 | −0.341602 | − | 0.939845i | \(-0.610969\pi\) | ||||
−0.341602 | + | 0.939845i | \(0.610969\pi\) | |||||||
\(720\) | −0.879961 | −0.0327942 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −18.6569 | −0.694336 | ||||||||
\(723\) | −5.07629 | −0.188789 | ||||||||
\(724\) | −21.5385 | −0.800473 | ||||||||
\(725\) | −19.4682 | −0.723031 | ||||||||
\(726\) | −5.58835 | −0.207403 | ||||||||
\(727\) | −3.36365 | −0.124751 | −0.0623754 | − | 0.998053i | \(-0.519868\pi\) | ||||
−0.0623754 | + | 0.998053i | \(0.519868\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.37483 | −0.161920 | ||||||||
\(731\) | −45.4078 | −1.67947 | ||||||||
\(732\) | −2.14320 | −0.0792148 | ||||||||
\(733\) | 18.5909 | 0.686671 | 0.343335 | − | 0.939213i | \(-0.388443\pi\) | ||||
0.343335 | + | 0.939213i | \(0.388443\pi\) | |||||||
\(734\) | 5.67201 | 0.209358 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 34.9793 | 1.28848 | ||||||||
\(738\) | −0.124413 | −0.00457972 | ||||||||
\(739\) | 13.9802 | 0.514272 | 0.257136 | − | 0.966375i | \(-0.417221\pi\) | ||||
0.257136 | + | 0.966375i | \(0.417221\pi\) | |||||||
\(740\) | −3.11385 | −0.114468 | ||||||||
\(741\) | −1.30120 | −0.0478009 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.7015 | 1.08964 | 0.544821 | − | 0.838552i | \(-0.316598\pi\) | ||||
0.544821 | + | 0.838552i | \(0.316598\pi\) | |||||||
\(744\) | −0.585786 | −0.0214760 | ||||||||
\(745\) | −12.2598 | −0.449165 | ||||||||
\(746\) | 7.49704 | 0.274486 | ||||||||
\(747\) | 6.99819 | 0.256050 | ||||||||
\(748\) | −31.6052 | −1.15560 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −8.11823 | −0.296436 | ||||||||
\(751\) | −24.8409 | −0.906458 | −0.453229 | − | 0.891394i | \(-0.649728\pi\) | ||||
−0.453229 | + | 0.891394i | \(0.649728\pi\) | |||||||
\(752\) | 0.0515337 | 0.00187924 | ||||||||
\(753\) | −13.7473 | −0.500980 | ||||||||
\(754\) | 10.2338 | 0.372693 | ||||||||
\(755\) | −1.01441 | −0.0369181 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.9866 | −0.835461 | −0.417730 | − | 0.908571i | \(-0.637174\pi\) | ||||
−0.417730 | + | 0.908571i | \(0.637174\pi\) | |||||||
\(758\) | −2.24273 | −0.0814598 | ||||||||
\(759\) | −4.07288 | −0.147836 | ||||||||
\(760\) | −0.515469 | −0.0186980 | ||||||||
\(761\) | −41.1614 | −1.49210 | −0.746051 | − | 0.665889i | \(-0.768052\pi\) | ||||
−0.746051 | + | 0.665889i | \(0.768052\pi\) | |||||||
\(762\) | −5.92446 | −0.214621 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 25.2194 | 0.912405 | ||||||||
\(765\) | −6.82843 | −0.246882 | ||||||||
\(766\) | 24.0693 | 0.869658 | ||||||||
\(767\) | −10.8872 | −0.393116 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 24.8876 | 0.897472 | 0.448736 | − | 0.893664i | \(-0.351874\pi\) | ||||
0.448736 | + | 0.893664i | \(0.351874\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.0069 | −0.396405 | ||||||||
\(772\) | −7.50844 | −0.270235 | ||||||||
\(773\) | −43.6051 | −1.56837 | −0.784184 | − | 0.620529i | \(-0.786918\pi\) | ||||
−0.784184 | + | 0.620529i | \(0.786918\pi\) | |||||||
\(774\) | −5.85158 | −0.210331 | ||||||||
\(775\) | −2.47534 | −0.0889168 | ||||||||
\(776\) | 17.5084 | 0.628516 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.9021 | −0.426709 | ||||||||
\(779\) | −0.0728797 | −0.00261119 | ||||||||
\(780\) | 1.95465 | 0.0699878 | ||||||||
\(781\) | −16.5883 | −0.593578 | ||||||||
\(782\) | −7.75992 | −0.277494 | ||||||||
\(783\) | −4.60713 | −0.164645 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.8127 | −0.492998 | ||||||||
\(786\) | −6.76430 | −0.241274 | ||||||||
\(787\) | 34.6048 | 1.23353 | 0.616764 | − | 0.787148i | \(-0.288443\pi\) | ||||
0.616764 | + | 0.787148i | \(0.288443\pi\) | |||||||
\(788\) | 6.66388 | 0.237391 | ||||||||
\(789\) | 26.7153 | 0.951091 | ||||||||
\(790\) | 1.69579 | 0.0603335 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.07288 | −0.144723 | ||||||||
\(793\) | 4.76067 | 0.169056 | ||||||||
\(794\) | −12.7305 | −0.451788 | ||||||||
\(795\) | −6.46234 | −0.229196 | ||||||||
\(796\) | −4.80964 | −0.170473 | ||||||||
\(797\) | 38.5951 | 1.36711 | 0.683554 | − | 0.729900i | \(-0.260433\pi\) | ||||
0.683554 | + | 0.729900i | \(0.260433\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.399898 | 0.0141474 | ||||||||
\(800\) | −4.22567 | −0.149400 | ||||||||
\(801\) | 10.4587 | 0.369541 | ||||||||
\(802\) | −24.8032 | −0.875833 | ||||||||
\(803\) | −20.2488 | −0.714566 | ||||||||
\(804\) | 8.58835 | 0.302888 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.30120 | 0.0458330 | ||||||||
\(807\) | −17.1693 | −0.604389 | ||||||||
\(808\) | −4.41240 | −0.155228 | ||||||||
\(809\) | −1.95505 | −0.0687360 | −0.0343680 | − | 0.999409i | \(-0.510942\pi\) | ||||
−0.0343680 | + | 0.999409i | \(0.510942\pi\) | |||||||
\(810\) | −0.879961 | −0.0309187 | ||||||||
\(811\) | −5.50694 | −0.193375 | −0.0966874 | − | 0.995315i | \(-0.530825\pi\) | ||||
−0.0966874 | + | 0.995315i | \(0.530825\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.5260 | 0.614665 | ||||||||
\(814\) | −14.4124 | −0.505154 | ||||||||
\(815\) | 7.46672 | 0.261548 | ||||||||
\(816\) | −7.75992 | −0.271652 | ||||||||
\(817\) | −3.42778 | −0.119923 | ||||||||
\(818\) | −13.1174 | −0.458639 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.109479 | 0.00382317 | ||||||||
\(821\) | −51.6392 | −1.80222 | −0.901110 | − | 0.433591i | \(-0.857246\pi\) | ||||
−0.901110 | + | 0.433591i | \(0.857246\pi\) | |||||||
\(822\) | −5.56881 | −0.194235 | ||||||||
\(823\) | −29.3892 | −1.02444 | −0.512222 | − | 0.858853i | \(-0.671178\pi\) | ||||
−0.512222 | + | 0.858853i | \(0.671178\pi\) | |||||||
\(824\) | 3.77871 | 0.131637 | ||||||||
\(825\) | −17.2106 | −0.599198 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.1112 | −0.664561 | −0.332281 | − | 0.943181i | \(-0.607818\pi\) | ||||
−0.332281 | + | 0.943181i | \(0.607818\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | −5.30858 | −0.184375 | −0.0921874 | − | 0.995742i | \(-0.529386\pi\) | ||||
−0.0921874 | + | 0.995742i | \(0.529386\pi\) | |||||||
\(830\) | −6.15813 | −0.213752 | ||||||||
\(831\) | 5.00075 | 0.173474 | ||||||||
\(832\) | 2.22129 | 0.0770095 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −12.8258 | −0.444120 | ||||||||
\(835\) | −16.7552 | −0.579839 | ||||||||
\(836\) | −2.38584 | −0.0825159 | ||||||||
\(837\) | −0.585786 | −0.0202477 | ||||||||
\(838\) | 31.2417 | 1.07923 | ||||||||
\(839\) | −52.6220 | −1.81671 | −0.908356 | − | 0.418197i | \(-0.862662\pi\) | ||||
−0.908356 | + | 0.418197i | \(0.862662\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.77433 | −0.268080 | ||||||||
\(842\) | −38.1129 | −1.31346 | ||||||||
\(843\) | −4.73676 | −0.163143 | ||||||||
\(844\) | 4.79824 | 0.165162 | ||||||||
\(845\) | 7.09763 | 0.244166 | ||||||||
\(846\) | 0.0515337 | 0.00177177 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.34390 | −0.252190 | ||||||||
\(849\) | 5.12101 | 0.175753 | ||||||||
\(850\) | −32.7909 | −1.12472 | ||||||||
\(851\) | −3.53863 | −0.121303 | ||||||||
\(852\) | −4.07288 | −0.139535 | ||||||||
\(853\) | −25.6808 | −0.879293 | −0.439646 | − | 0.898171i | \(-0.644896\pi\) | ||||
−0.439646 | + | 0.898171i | \(0.644896\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.515469 | −0.0176287 | ||||||||
\(856\) | −3.61416 | −0.123530 | ||||||||
\(857\) | −51.9661 | −1.77513 | −0.887564 | − | 0.460684i | \(-0.847604\pi\) | ||||
−0.887564 | + | 0.460684i | \(0.847604\pi\) | |||||||
\(858\) | 9.04707 | 0.308862 | ||||||||
\(859\) | −14.5806 | −0.497483 | −0.248741 | − | 0.968570i | \(-0.580017\pi\) | ||||
−0.248741 | + | 0.968570i | \(0.580017\pi\) | |||||||
\(860\) | 5.14917 | 0.175585 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 29.4031 | 1.00147 | ||||||||
\(863\) | −28.1046 | −0.956691 | −0.478345 | − | 0.878172i | \(-0.658763\pi\) | ||||
−0.478345 | + | 0.878172i | \(0.658763\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 10.5672 | 0.359297 | ||||||||
\(866\) | −14.8309 | −0.503974 | ||||||||
\(867\) | −43.2164 | −1.46771 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.84893 | 0.266257 | ||||||||
\(870\) | 4.05410 | 0.137447 | ||||||||
\(871\) | −19.0773 | −0.646408 | ||||||||
\(872\) | 6.42381 | 0.217538 | ||||||||
\(873\) | 17.5084 | 0.592571 | ||||||||
\(874\) | −0.585786 | −0.0198145 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.97162 | −0.167976 | ||||||||
\(877\) | −0.645101 | −0.0217835 | −0.0108917 | − | 0.999941i | \(-0.503467\pi\) | ||||
−0.0108917 | + | 0.999941i | \(0.503467\pi\) | |||||||
\(878\) | 0.299392 | 0.0101040 | ||||||||
\(879\) | −9.45315 | −0.318847 | ||||||||
\(880\) | 3.58397 | 0.120816 | ||||||||
\(881\) | 11.0581 | 0.372556 | 0.186278 | − | 0.982497i | \(-0.440358\pi\) | ||||
0.186278 | + | 0.982497i | \(0.440358\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.56047 | 0.321735 | 0.160868 | − | 0.986976i | \(-0.448571\pi\) | ||||
0.160868 | + | 0.986976i | \(0.448571\pi\) | |||||||
\(884\) | 17.2371 | 0.579746 | ||||||||
\(885\) | −4.31296 | −0.144978 | ||||||||
\(886\) | 10.5202 | 0.353433 | ||||||||
\(887\) | 54.7189 | 1.83728 | 0.918640 | − | 0.395096i | \(-0.129289\pi\) | ||||
0.918640 | + | 0.395096i | \(0.129289\pi\) | |||||||
\(888\) | −3.53863 | −0.118749 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −9.20326 | −0.308494 | ||||||||
\(891\) | −4.07288 | −0.136447 | ||||||||
\(892\) | −14.5983 | −0.488787 | ||||||||
\(893\) | 0.0301877 | 0.00101019 | ||||||||
\(894\) | −13.9322 | −0.465964 | ||||||||
\(895\) | −9.36812 | −0.313142 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.22129 | 0.0741669 | ||||||||
\(898\) | −40.9505 | −1.36654 | ||||||||
\(899\) | 2.69880 | 0.0900099 | ||||||||
\(900\) | −4.22567 | −0.140856 | ||||||||
\(901\) | −56.9881 | −1.89855 | ||||||||
\(902\) | 0.506721 | 0.0168720 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.6115 | 0.452712 | ||||||||
\(905\) | 18.9531 | 0.630021 | ||||||||
\(906\) | −1.15279 | −0.0382989 | ||||||||
\(907\) | −2.58738 | −0.0859126 | −0.0429563 | − | 0.999077i | \(-0.513678\pi\) | ||||
−0.0429563 | + | 0.999077i | \(0.513678\pi\) | |||||||
\(908\) | −9.39543 | −0.311798 | ||||||||
\(909\) | −4.41240 | −0.146350 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.6050 | 1.41157 | 0.705783 | − | 0.708428i | \(-0.250595\pi\) | ||||
0.705783 | + | 0.708428i | \(0.250595\pi\) | |||||||
\(912\) | −0.585786 | −0.0193973 | ||||||||
\(913\) | −28.5028 | −0.943304 | ||||||||
\(914\) | 15.1539 | 0.501246 | ||||||||
\(915\) | 1.88593 | 0.0623469 | ||||||||
\(916\) | 7.14757 | 0.236162 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −7.75992 | −0.256116 | ||||||||
\(919\) | −5.53823 | −0.182689 | −0.0913446 | − | 0.995819i | \(-0.529116\pi\) | ||||
−0.0913446 | + | 0.995819i | \(0.529116\pi\) | |||||||
\(920\) | 0.879961 | 0.0290114 | ||||||||
\(921\) | −29.8036 | −0.982061 | ||||||||
\(922\) | 22.0089 | 0.724824 | ||||||||
\(923\) | 9.04707 | 0.297788 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.9531 | −0.491654 | ||||||||
\(926\) | −1.83546 | −0.0603169 | ||||||||
\(927\) | 3.77871 | 0.124109 | ||||||||
\(928\) | 4.60713 | 0.151237 | ||||||||
\(929\) | −13.9855 | −0.458848 | −0.229424 | − | 0.973327i | \(-0.573684\pi\) | ||||
−0.229424 | + | 0.973327i | \(0.573684\pi\) | |||||||
\(930\) | 0.515469 | 0.0169029 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15.3439 | 0.502606 | ||||||||
\(933\) | 18.5983 | 0.608881 | ||||||||
\(934\) | −22.4586 | −0.734869 | ||||||||
\(935\) | 27.8114 | 0.909529 | ||||||||
\(936\) | 2.22129 | 0.0726053 | ||||||||
\(937\) | −24.5733 | −0.802775 | −0.401388 | − | 0.915908i | \(-0.631472\pi\) | ||||
−0.401388 | + | 0.915908i | \(0.631472\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.1803 | −0.560659 | ||||||||
\(940\) | −0.0453476 | −0.00147908 | ||||||||
\(941\) | 3.20030 | 0.104327 | 0.0521634 | − | 0.998639i | \(-0.483388\pi\) | ||||
0.0521634 | + | 0.998639i | \(0.483388\pi\) | |||||||
\(942\) | −15.6970 | −0.511435 | ||||||||
\(943\) | 0.124413 | 0.00405146 | ||||||||
\(944\) | −4.90131 | −0.159524 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23.8328 | 0.774871 | ||||||||
\(947\) | −2.21392 | −0.0719426 | −0.0359713 | − | 0.999353i | \(-0.511452\pi\) | ||||
−0.0359713 | + | 0.999353i | \(0.511452\pi\) | |||||||
\(948\) | 1.92712 | 0.0625900 | ||||||||
\(949\) | 11.0434 | 0.358485 | ||||||||
\(950\) | −2.47534 | −0.0803106 | ||||||||
\(951\) | −2.45775 | −0.0796980 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.1750 | 1.20422 | 0.602108 | − | 0.798414i | \(-0.294328\pi\) | ||||
0.602108 | + | 0.798414i | \(0.294328\pi\) | |||||||
\(954\) | −7.34390 | −0.237767 | ||||||||
\(955\) | −22.1921 | −0.718119 | ||||||||
\(956\) | 17.7687 | 0.574680 | ||||||||
\(957\) | 18.7643 | 0.606564 | ||||||||
\(958\) | −19.6760 | −0.635704 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.879961 | 0.0284006 | ||||||||
\(961\) | −30.6569 | −0.988931 | ||||||||
\(962\) | 7.86033 | 0.253427 | ||||||||
\(963\) | −3.61416 | −0.116465 | ||||||||
\(964\) | 5.07629 | 0.163496 | ||||||||
\(965\) | 6.60713 | 0.212691 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.5449 | 1.27168 | 0.635838 | − | 0.771822i | \(-0.280654\pi\) | ||||
0.635838 | + | 0.771822i | \(0.280654\pi\) | |||||||
\(968\) | 5.58835 | 0.179616 | ||||||||
\(969\) | −4.54566 | −0.146028 | ||||||||
\(970\) | −15.4067 | −0.494681 | ||||||||
\(971\) | 32.6674 | 1.04835 | 0.524174 | − | 0.851611i | \(-0.324374\pi\) | ||||
0.524174 | + | 0.851611i | \(0.324374\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6.01154 | −0.192622 | ||||||||
\(975\) | 9.38646 | 0.300607 | ||||||||
\(976\) | 2.14320 | 0.0686021 | ||||||||
\(977\) | −42.7155 | −1.36659 | −0.683294 | − | 0.730143i | \(-0.739453\pi\) | ||||
−0.683294 | + | 0.730143i | \(0.739453\pi\) | |||||||
\(978\) | 8.48528 | 0.271329 | ||||||||
\(979\) | −42.5971 | −1.36141 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.42381 | 0.205096 | ||||||||
\(982\) | 26.2401 | 0.837355 | ||||||||
\(983\) | −13.7812 | −0.439551 | −0.219776 | − | 0.975550i | \(-0.570533\pi\) | ||||
−0.219776 | + | 0.975550i | \(0.570533\pi\) | |||||||
\(984\) | 0.124413 | 0.00396615 | ||||||||
\(985\) | −5.86396 | −0.186841 | ||||||||
\(986\) | 35.7510 | 1.13854 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.30120 | 0.0413968 | ||||||||
\(989\) | 5.85158 | 0.186070 | ||||||||
\(990\) | 3.58397 | 0.113906 | ||||||||
\(991\) | 51.1765 | 1.62568 | 0.812838 | − | 0.582490i | \(-0.197922\pi\) | ||||
0.812838 | + | 0.582490i | \(0.197922\pi\) | |||||||
\(992\) | 0.585786 | 0.0185987 | ||||||||
\(993\) | −19.4595 | −0.617528 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.23230 | 0.134173 | ||||||||
\(996\) | −6.99819 | −0.221746 | ||||||||
\(997\) | 41.3363 | 1.30913 | 0.654567 | − | 0.756004i | \(-0.272851\pi\) | ||||
0.654567 | + | 0.756004i | \(0.272851\pi\) | |||||||
\(998\) | −6.49934 | −0.205733 | ||||||||
\(999\) | −3.53863 | −0.111957 |
(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 | 6762.2.a.cn.1.1 | ✓ | 4 | |
7.6 | odd | 2 | 6762.2.a.co.1.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6762.2.a.cn.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
6762.2.a.co.1.4 | yes | 4 | 7.6 | odd | 2 |