Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,2,Mod(1,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.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: | \(1.14186074890\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.1957.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.06150\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 143.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.57641 | 1.82180 | 0.910900 | − | 0.412627i | \(-0.135389\pi\) | ||||
0.910900 | + | 0.412627i | \(0.135389\pi\) | |||||||
\(3\) | −0.188279 | −0.108703 | −0.0543514 | − | 0.998522i | \(-0.517309\pi\) | ||||
−0.0543514 | + | 0.998522i | \(0.517309\pi\) | |||||||
\(4\) | 4.63791 | 2.31896 | ||||||||
\(5\) | −4.12300 | −1.84386 | −0.921930 | − | 0.387356i | \(-0.873389\pi\) | ||||
−0.921930 | + | 0.387356i | \(0.873389\pi\) | |||||||
\(6\) | −0.485084 | −0.198035 | ||||||||
\(7\) | 2.15845 | 0.815816 | 0.407908 | − | 0.913023i | \(-0.366258\pi\) | ||||
0.407908 | + | 0.913023i | \(0.366258\pi\) | |||||||
\(8\) | 6.79636 | 2.40288 | ||||||||
\(9\) | −2.96455 | −0.988184 | ||||||||
\(10\) | −10.6226 | −3.35915 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.873220 | −0.252077 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 5.56105 | 1.48625 | ||||||||
\(15\) | 0.776272 | 0.200433 | ||||||||
\(16\) | 8.23442 | 2.05860 | ||||||||
\(17\) | −3.09317 | −0.750203 | −0.375101 | − | 0.926984i | \(-0.622392\pi\) | ||||
−0.375101 | + | 0.926984i | \(0.622392\pi\) | |||||||
\(18\) | −7.63791 | −1.80027 | ||||||||
\(19\) | −2.68783 | −0.616631 | −0.308316 | − | 0.951284i | \(-0.599765\pi\) | ||||
−0.308316 | + | 0.951284i | \(0.599765\pi\) | |||||||
\(20\) | −19.1221 | −4.27583 | ||||||||
\(21\) | −0.406389 | −0.0886814 | ||||||||
\(22\) | 2.57641 | 0.549294 | ||||||||
\(23\) | 3.31128 | 0.690449 | 0.345224 | − | 0.938520i | \(-0.387803\pi\) | ||||
0.345224 | + | 0.938520i | \(0.387803\pi\) | |||||||
\(24\) | −1.27961 | −0.261199 | ||||||||
\(25\) | 11.9991 | 2.39982 | ||||||||
\(26\) | −2.57641 | −0.505277 | ||||||||
\(27\) | 1.12300 | 0.216121 | ||||||||
\(28\) | 10.0107 | 1.89184 | ||||||||
\(29\) | −3.34673 | −0.621471 | −0.310736 | − | 0.950496i | \(-0.600575\pi\) | ||||
−0.310736 | + | 0.950496i | \(0.600575\pi\) | |||||||
\(30\) | 2.00000 | 0.365148 | ||||||||
\(31\) | 9.96928 | 1.79054 | 0.895268 | − | 0.445529i | \(-0.146984\pi\) | ||||
0.895268 | + | 0.445529i | \(0.146984\pi\) | |||||||
\(32\) | 7.62255 | 1.34749 | ||||||||
\(33\) | −0.188279 | −0.0327751 | ||||||||
\(34\) | −7.96928 | −1.36672 | ||||||||
\(35\) | −8.89927 | −1.50425 | ||||||||
\(36\) | −13.7493 | −2.29156 | ||||||||
\(37\) | 2.05966 | 0.338607 | 0.169303 | − | 0.985564i | \(-0.445848\pi\) | ||||
0.169303 | + | 0.985564i | \(0.445848\pi\) | |||||||
\(38\) | −6.92497 | −1.12338 | ||||||||
\(39\) | 0.188279 | 0.0301487 | ||||||||
\(40\) | −28.0214 | −4.43057 | ||||||||
\(41\) | 9.49394 | 1.48270 | 0.741352 | − | 0.671116i | \(-0.234185\pi\) | ||||
0.741352 | + | 0.671116i | \(0.234185\pi\) | |||||||
\(42\) | −1.04703 | −0.161560 | ||||||||
\(43\) | 2.84717 | 0.434189 | 0.217095 | − | 0.976151i | \(-0.430342\pi\) | ||||
0.217095 | + | 0.976151i | \(0.430342\pi\) | |||||||
\(44\) | 4.63791 | 0.699192 | ||||||||
\(45\) | 12.2228 | 1.82207 | ||||||||
\(46\) | 8.53122 | 1.25786 | ||||||||
\(47\) | −9.46972 | −1.38130 | −0.690651 | − | 0.723189i | \(-0.742676\pi\) | ||||
−0.690651 | + | 0.723189i | \(0.742676\pi\) | |||||||
\(48\) | −1.55036 | −0.223776 | ||||||||
\(49\) | −2.34111 | −0.334444 | ||||||||
\(50\) | 30.9147 | 4.37200 | ||||||||
\(51\) | 0.582377 | 0.0815491 | ||||||||
\(52\) | −4.63791 | −0.643163 | ||||||||
\(53\) | −5.34111 | −0.733658 | −0.366829 | − | 0.930288i | \(-0.619557\pi\) | ||||
−0.366829 | + | 0.930288i | \(0.619557\pi\) | |||||||
\(54\) | 2.89331 | 0.393729 | ||||||||
\(55\) | −4.12300 | −0.555945 | ||||||||
\(56\) | 14.6696 | 1.96031 | ||||||||
\(57\) | 0.506062 | 0.0670295 | ||||||||
\(58\) | −8.62255 | −1.13220 | ||||||||
\(59\) | 4.62255 | 0.601805 | 0.300903 | − | 0.953655i | \(-0.402712\pi\) | ||||
0.300903 | + | 0.953655i | \(0.402712\pi\) | |||||||
\(60\) | 3.60028 | 0.464795 | ||||||||
\(61\) | −0.193895 | −0.0248258 | −0.0124129 | − | 0.999923i | \(-0.503951\pi\) | ||||
−0.0124129 | + | 0.999923i | \(0.503951\pi\) | |||||||
\(62\) | 25.6850 | 3.26200 | ||||||||
\(63\) | −6.39883 | −0.806176 | ||||||||
\(64\) | 3.17003 | 0.396253 | ||||||||
\(65\) | 4.12300 | 0.511395 | ||||||||
\(66\) | −0.485084 | −0.0597097 | ||||||||
\(67\) | −5.78662 | −0.706948 | −0.353474 | − | 0.935444i | \(-0.615000\pi\) | ||||
−0.353474 | + | 0.935444i | \(0.615000\pi\) | |||||||
\(68\) | −14.3458 | −1.73969 | ||||||||
\(69\) | −0.623443 | −0.0750537 | ||||||||
\(70\) | −22.9282 | −2.74045 | ||||||||
\(71\) | −3.78295 | −0.448953 | −0.224477 | − | 0.974479i | \(-0.572067\pi\) | ||||
−0.224477 | + | 0.974479i | \(0.572067\pi\) | |||||||
\(72\) | −20.1482 | −2.37448 | ||||||||
\(73\) | 7.47534 | 0.874922 | 0.437461 | − | 0.899237i | \(-0.355878\pi\) | ||||
0.437461 | + | 0.899237i | \(0.355878\pi\) | |||||||
\(74\) | 5.30655 | 0.616874 | ||||||||
\(75\) | −2.25918 | −0.260867 | ||||||||
\(76\) | −12.4659 | −1.42994 | ||||||||
\(77\) | 2.15845 | 0.245978 | ||||||||
\(78\) | 0.485084 | 0.0549249 | ||||||||
\(79\) | −17.2049 | −1.93571 | −0.967853 | − | 0.251517i | \(-0.919071\pi\) | ||||
−0.967853 | + | 0.251517i | \(0.919071\pi\) | |||||||
\(80\) | −33.9505 | −3.79578 | ||||||||
\(81\) | 8.68222 | 0.964691 | ||||||||
\(82\) | 24.4603 | 2.70119 | ||||||||
\(83\) | −0.218111 | −0.0239408 | −0.0119704 | − | 0.999928i | \(-0.503810\pi\) | ||||
−0.0119704 | + | 0.999928i | \(0.503810\pi\) | |||||||
\(84\) | −1.88480 | −0.205648 | ||||||||
\(85\) | 12.7531 | 1.38327 | ||||||||
\(86\) | 7.33549 | 0.791006 | ||||||||
\(87\) | 0.630117 | 0.0675556 | ||||||||
\(88\) | 6.79636 | 0.724494 | ||||||||
\(89\) | −1.52939 | −0.162115 | −0.0810574 | − | 0.996709i | \(-0.525830\pi\) | ||||
−0.0810574 | + | 0.996709i | \(0.525830\pi\) | |||||||
\(90\) | 31.4911 | 3.31945 | ||||||||
\(91\) | −2.15845 | −0.226267 | ||||||||
\(92\) | 15.3574 | 1.60112 | ||||||||
\(93\) | −1.87700 | −0.194636 | ||||||||
\(94\) | −24.3979 | −2.51645 | ||||||||
\(95\) | 11.0819 | 1.13698 | ||||||||
\(96\) | −1.43516 | −0.146476 | ||||||||
\(97\) | 12.1462 | 1.23326 | 0.616628 | − | 0.787255i | \(-0.288498\pi\) | ||||
0.616628 | + | 0.787255i | \(0.288498\pi\) | |||||||
\(98\) | −6.03167 | −0.609290 | ||||||||
\(99\) | −2.96455 | −0.297949 | ||||||||
\(100\) | 55.6508 | 5.56508 | ||||||||
\(101\) | −13.2162 | −1.31506 | −0.657529 | − | 0.753429i | \(-0.728398\pi\) | ||||
−0.657529 | + | 0.753429i | \(0.728398\pi\) | |||||||
\(102\) | 1.50044 | 0.148566 | ||||||||
\(103\) | −4.61783 | −0.455008 | −0.227504 | − | 0.973777i | \(-0.573056\pi\) | ||||
−0.227504 | + | 0.973777i | \(0.573056\pi\) | |||||||
\(104\) | −6.79636 | −0.666438 | ||||||||
\(105\) | 1.67554 | 0.163516 | ||||||||
\(106\) | −13.7609 | −1.33658 | ||||||||
\(107\) | 10.3458 | 1.00017 | 0.500085 | − | 0.865976i | \(-0.333302\pi\) | ||||
0.500085 | + | 0.865976i | \(0.333302\pi\) | |||||||
\(108\) | 5.20837 | 0.501175 | ||||||||
\(109\) | 6.83032 | 0.654226 | 0.327113 | − | 0.944985i | \(-0.393924\pi\) | ||||
0.327113 | + | 0.944985i | \(0.393924\pi\) | |||||||
\(110\) | −10.6226 | −1.01282 | ||||||||
\(111\) | −0.387791 | −0.0368075 | ||||||||
\(112\) | 17.7735 | 1.67944 | ||||||||
\(113\) | −7.40077 | −0.696206 | −0.348103 | − | 0.937456i | \(-0.613174\pi\) | ||||
−0.348103 | + | 0.937456i | \(0.613174\pi\) | |||||||
\(114\) | 1.30382 | 0.122114 | ||||||||
\(115\) | −13.6524 | −1.27309 | ||||||||
\(116\) | −15.5218 | −1.44117 | ||||||||
\(117\) | 2.96455 | 0.274073 | ||||||||
\(118\) | 11.9096 | 1.09637 | ||||||||
\(119\) | −6.67643 | −0.612028 | ||||||||
\(120\) | 5.27583 | 0.481615 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.499555 | −0.0452276 | ||||||||
\(123\) | −1.78751 | −0.161174 | ||||||||
\(124\) | 46.2367 | 4.15217 | ||||||||
\(125\) | −28.8573 | −2.58108 | ||||||||
\(126\) | −16.4860 | −1.46869 | ||||||||
\(127\) | 8.40550 | 0.745867 | 0.372934 | − | 0.927858i | \(-0.378352\pi\) | ||||
0.372934 | + | 0.927858i | \(0.378352\pi\) | |||||||
\(128\) | −7.07780 | −0.625595 | ||||||||
\(129\) | −0.536061 | −0.0471976 | ||||||||
\(130\) | 10.6226 | 0.931660 | ||||||||
\(131\) | −0.630117 | −0.0550536 | −0.0275268 | − | 0.999621i | \(-0.508763\pi\) | ||||
−0.0275268 | + | 0.999621i | \(0.508763\pi\) | |||||||
\(132\) | −0.873220 | −0.0760041 | ||||||||
\(133\) | −5.80155 | −0.503058 | ||||||||
\(134\) | −14.9087 | −1.28792 | ||||||||
\(135\) | −4.63012 | −0.398497 | ||||||||
\(136\) | −21.0223 | −1.80264 | ||||||||
\(137\) | 4.81645 | 0.411497 | 0.205748 | − | 0.978605i | \(-0.434037\pi\) | ||||
0.205748 | + | 0.978605i | \(0.434037\pi\) | |||||||
\(138\) | −1.60625 | −0.136733 | ||||||||
\(139\) | −10.5592 | −0.895621 | −0.447811 | − | 0.894128i | \(-0.647796\pi\) | ||||
−0.447811 | + | 0.894128i | \(0.647796\pi\) | |||||||
\(140\) | −41.2740 | −3.48829 | ||||||||
\(141\) | 1.78295 | 0.150151 | ||||||||
\(142\) | −9.74644 | −0.817903 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | −24.4113 | −2.03428 | ||||||||
\(145\) | 13.7985 | 1.14591 | ||||||||
\(146\) | 19.2596 | 1.59393 | ||||||||
\(147\) | 0.440781 | 0.0363550 | ||||||||
\(148\) | 9.55254 | 0.785214 | ||||||||
\(149\) | −2.80049 | −0.229425 | −0.114712 | − | 0.993399i | \(-0.536595\pi\) | ||||
−0.114712 | + | 0.993399i | \(0.536595\pi\) | |||||||
\(150\) | −5.82058 | −0.475248 | ||||||||
\(151\) | −8.24600 | −0.671050 | −0.335525 | − | 0.942031i | \(-0.608914\pi\) | ||||
−0.335525 | + | 0.942031i | \(0.608914\pi\) | |||||||
\(152\) | −18.2675 | −1.48169 | ||||||||
\(153\) | 9.16985 | 0.741338 | ||||||||
\(154\) | 5.56105 | 0.448122 | ||||||||
\(155\) | −41.1033 | −3.30150 | ||||||||
\(156\) | 0.873220 | 0.0699136 | ||||||||
\(157\) | −13.2918 | −1.06080 | −0.530400 | − | 0.847747i | \(-0.677958\pi\) | ||||
−0.530400 | + | 0.847747i | \(0.677958\pi\) | |||||||
\(158\) | −44.3270 | −3.52647 | ||||||||
\(159\) | 1.00562 | 0.0797506 | ||||||||
\(160\) | −31.4278 | −2.48458 | ||||||||
\(161\) | 7.14721 | 0.563279 | ||||||||
\(162\) | 22.3690 | 1.75747 | ||||||||
\(163\) | −2.85084 | −0.223295 | −0.111647 | − | 0.993748i | \(-0.535613\pi\) | ||||
−0.111647 | + | 0.993748i | \(0.535613\pi\) | |||||||
\(164\) | 44.0321 | 3.43833 | ||||||||
\(165\) | 0.776272 | 0.0604327 | ||||||||
\(166\) | −0.561944 | −0.0436153 | ||||||||
\(167\) | −1.30093 | −0.100669 | −0.0503346 | − | 0.998732i | \(-0.516029\pi\) | ||||
−0.0503346 | + | 0.998732i | \(0.516029\pi\) | |||||||
\(168\) | −2.76197 | −0.213091 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 32.8573 | 2.52004 | ||||||||
\(171\) | 7.96822 | 0.609345 | ||||||||
\(172\) | 13.2049 | 1.00687 | ||||||||
\(173\) | 8.52850 | 0.648410 | 0.324205 | − | 0.945987i | \(-0.394903\pi\) | ||||
0.324205 | + | 0.945987i | \(0.394903\pi\) | |||||||
\(174\) | 1.62344 | 0.123073 | ||||||||
\(175\) | 25.8994 | 1.95781 | ||||||||
\(176\) | 8.23442 | 0.620692 | ||||||||
\(177\) | −0.870328 | −0.0654179 | ||||||||
\(178\) | −3.94034 | −0.295341 | ||||||||
\(179\) | 19.3048 | 1.44291 | 0.721453 | − | 0.692463i | \(-0.243475\pi\) | ||||
0.721453 | + | 0.692463i | \(0.243475\pi\) | |||||||
\(180\) | 56.6885 | 4.22531 | ||||||||
\(181\) | −26.3402 | −1.95785 | −0.978927 | − | 0.204213i | \(-0.934537\pi\) | ||||
−0.978927 | + | 0.204213i | \(0.934537\pi\) | |||||||
\(182\) | −5.56105 | −0.412213 | ||||||||
\(183\) | 0.0365064 | 0.00269863 | ||||||||
\(184\) | 22.5046 | 1.65906 | ||||||||
\(185\) | −8.49199 | −0.624344 | ||||||||
\(186\) | −4.83594 | −0.354588 | ||||||||
\(187\) | −3.09317 | −0.226195 | ||||||||
\(188\) | −43.9198 | −3.20318 | ||||||||
\(189\) | 2.42393 | 0.176315 | ||||||||
\(190\) | 28.5517 | 2.07135 | ||||||||
\(191\) | −1.86015 | −0.134596 | −0.0672979 | − | 0.997733i | \(-0.521438\pi\) | ||||
−0.0672979 | + | 0.997733i | \(0.521438\pi\) | |||||||
\(192\) | −0.596848 | −0.0430738 | ||||||||
\(193\) | 16.4239 | 1.18222 | 0.591110 | − | 0.806591i | \(-0.298690\pi\) | ||||
0.591110 | + | 0.806591i | \(0.298690\pi\) | |||||||
\(194\) | 31.2935 | 2.24674 | ||||||||
\(195\) | −0.776272 | −0.0555900 | ||||||||
\(196\) | −10.8579 | −0.775561 | ||||||||
\(197\) | −17.5929 | −1.25344 | −0.626721 | − | 0.779244i | \(-0.715603\pi\) | ||||
−0.626721 | + | 0.779244i | \(0.715603\pi\) | |||||||
\(198\) | −7.63791 | −0.542803 | ||||||||
\(199\) | 0.434274 | 0.0307849 | 0.0153924 | − | 0.999882i | \(-0.495100\pi\) | ||||
0.0153924 | + | 0.999882i | \(0.495100\pi\) | |||||||
\(200\) | 81.5503 | 5.76648 | ||||||||
\(201\) | 1.08950 | 0.0768471 | ||||||||
\(202\) | −34.0503 | −2.39577 | ||||||||
\(203\) | −7.22373 | −0.507006 | ||||||||
\(204\) | 2.70101 | 0.189109 | ||||||||
\(205\) | −39.1435 | −2.73390 | ||||||||
\(206\) | −11.8974 | −0.828934 | ||||||||
\(207\) | −9.81645 | −0.682290 | ||||||||
\(208\) | −8.23442 | −0.570954 | ||||||||
\(209\) | −2.68783 | −0.185921 | ||||||||
\(210\) | 4.31689 | 0.297894 | ||||||||
\(211\) | 4.04018 | 0.278137 | 0.139069 | − | 0.990283i | \(-0.455589\pi\) | ||||
0.139069 | + | 0.990283i | \(0.455589\pi\) | |||||||
\(212\) | −24.7716 | −1.70132 | ||||||||
\(213\) | 0.712248 | 0.0488024 | ||||||||
\(214\) | 26.6552 | 1.82211 | ||||||||
\(215\) | −11.7389 | −0.800585 | ||||||||
\(216\) | 7.63230 | 0.519312 | ||||||||
\(217\) | 21.5182 | 1.46075 | ||||||||
\(218\) | 17.5977 | 1.19187 | ||||||||
\(219\) | −1.40745 | −0.0951065 | ||||||||
\(220\) | −19.1221 | −1.28921 | ||||||||
\(221\) | 3.09317 | 0.208069 | ||||||||
\(222\) | −0.999110 | −0.0670559 | ||||||||
\(223\) | 21.4390 | 1.43566 | 0.717831 | − | 0.696218i | \(-0.245135\pi\) | ||||
0.717831 | + | 0.696218i | \(0.245135\pi\) | |||||||
\(224\) | 16.4529 | 1.09930 | ||||||||
\(225\) | −35.5720 | −2.37147 | ||||||||
\(226\) | −19.0675 | −1.26835 | ||||||||
\(227\) | 18.8647 | 1.25209 | 0.626047 | − | 0.779785i | \(-0.284672\pi\) | ||||
0.626047 | + | 0.779785i | \(0.284672\pi\) | |||||||
\(228\) | 2.34707 | 0.155439 | ||||||||
\(229\) | 13.3048 | 0.879204 | 0.439602 | − | 0.898193i | \(-0.355120\pi\) | ||||
0.439602 | + | 0.898193i | \(0.355120\pi\) | |||||||
\(230\) | −35.1742 | −2.31932 | ||||||||
\(231\) | −0.406389 | −0.0267385 | ||||||||
\(232\) | −22.7456 | −1.49332 | ||||||||
\(233\) | 21.3160 | 1.39646 | 0.698229 | − | 0.715875i | \(-0.253972\pi\) | ||||
0.698229 | + | 0.715875i | \(0.253972\pi\) | |||||||
\(234\) | 7.63791 | 0.499306 | ||||||||
\(235\) | 39.0436 | 2.54693 | ||||||||
\(236\) | 21.4390 | 1.39556 | ||||||||
\(237\) | 3.23932 | 0.210417 | ||||||||
\(238\) | −17.2013 | −1.11499 | ||||||||
\(239\) | 13.9123 | 0.899909 | 0.449954 | − | 0.893052i | \(-0.351440\pi\) | ||||
0.449954 | + | 0.893052i | \(0.351440\pi\) | |||||||
\(240\) | 6.39215 | 0.412612 | ||||||||
\(241\) | 0.565726 | 0.0364416 | 0.0182208 | − | 0.999834i | \(-0.494200\pi\) | ||||
0.0182208 | + | 0.999834i | \(0.494200\pi\) | |||||||
\(242\) | 2.57641 | 0.165618 | ||||||||
\(243\) | −5.00367 | −0.320986 | ||||||||
\(244\) | −0.899270 | −0.0575699 | ||||||||
\(245\) | 9.65238 | 0.616668 | ||||||||
\(246\) | −4.60536 | −0.293627 | ||||||||
\(247\) | 2.68783 | 0.171023 | ||||||||
\(248\) | 67.7548 | 4.30243 | ||||||||
\(249\) | 0.0410656 | 0.00260243 | ||||||||
\(250\) | −74.3484 | −4.70221 | ||||||||
\(251\) | 12.4985 | 0.788898 | 0.394449 | − | 0.918918i | \(-0.370935\pi\) | ||||
0.394449 | + | 0.918918i | \(0.370935\pi\) | |||||||
\(252\) | −29.6772 | −1.86949 | ||||||||
\(253\) | 3.31128 | 0.208178 | ||||||||
\(254\) | 21.6561 | 1.35882 | ||||||||
\(255\) | −2.40114 | −0.150365 | ||||||||
\(256\) | −24.5754 | −1.53596 | ||||||||
\(257\) | 14.7640 | 0.920952 | 0.460476 | − | 0.887672i | \(-0.347679\pi\) | ||||
0.460476 | + | 0.887672i | \(0.347679\pi\) | |||||||
\(258\) | −1.38112 | −0.0859846 | ||||||||
\(259\) | 4.44568 | 0.276241 | ||||||||
\(260\) | 19.1221 | 1.18590 | ||||||||
\(261\) | 9.92154 | 0.614128 | ||||||||
\(262\) | −1.62344 | −0.100297 | ||||||||
\(263\) | −15.8445 | −0.977014 | −0.488507 | − | 0.872560i | \(-0.662458\pi\) | ||||
−0.488507 | + | 0.872560i | \(0.662458\pi\) | |||||||
\(264\) | −1.27961 | −0.0787545 | ||||||||
\(265\) | 22.0214 | 1.35276 | ||||||||
\(266\) | −14.9472 | −0.916471 | ||||||||
\(267\) | 0.287951 | 0.0176223 | ||||||||
\(268\) | −26.8378 | −1.63938 | ||||||||
\(269\) | −2.34289 | −0.142848 | −0.0714242 | − | 0.997446i | \(-0.522754\pi\) | ||||
−0.0714242 | + | 0.997446i | \(0.522754\pi\) | |||||||
\(270\) | −11.9291 | −0.725982 | ||||||||
\(271\) | 26.0038 | 1.57962 | 0.789810 | − | 0.613351i | \(-0.210179\pi\) | ||||
0.789810 | + | 0.613351i | \(0.210179\pi\) | |||||||
\(272\) | −25.4704 | −1.54437 | ||||||||
\(273\) | 0.406389 | 0.0245958 | ||||||||
\(274\) | 12.4092 | 0.749665 | ||||||||
\(275\) | 11.9991 | 0.723574 | ||||||||
\(276\) | −2.89147 | −0.174046 | ||||||||
\(277\) | 28.0019 | 1.68247 | 0.841235 | − | 0.540669i | \(-0.181829\pi\) | ||||
0.841235 | + | 0.540669i | \(0.181829\pi\) | |||||||
\(278\) | −27.2049 | −1.63164 | ||||||||
\(279\) | −29.5544 | −1.76938 | ||||||||
\(280\) | −60.4826 | −3.61453 | ||||||||
\(281\) | −20.4632 | −1.22073 | −0.610367 | − | 0.792119i | \(-0.708978\pi\) | ||||
−0.610367 | + | 0.792119i | \(0.708978\pi\) | |||||||
\(282\) | 4.59361 | 0.273546 | ||||||||
\(283\) | −9.17810 | −0.545582 | −0.272791 | − | 0.962073i | \(-0.587947\pi\) | ||||
−0.272791 | + | 0.962073i | \(0.587947\pi\) | |||||||
\(284\) | −17.5450 | −1.04110 | ||||||||
\(285\) | −2.08649 | −0.123593 | ||||||||
\(286\) | −2.57641 | −0.152347 | ||||||||
\(287\) | 20.4922 | 1.20961 | ||||||||
\(288\) | −22.5974 | −1.33157 | ||||||||
\(289\) | −7.43233 | −0.437196 | ||||||||
\(290\) | 35.5508 | 2.08761 | ||||||||
\(291\) | −2.28686 | −0.134058 | ||||||||
\(292\) | 34.6700 | 2.02891 | ||||||||
\(293\) | 18.7380 | 1.09468 | 0.547342 | − | 0.836909i | \(-0.315640\pi\) | ||||
0.547342 | + | 0.836909i | \(0.315640\pi\) | |||||||
\(294\) | 1.13563 | 0.0662315 | ||||||||
\(295\) | −19.0588 | −1.10964 | ||||||||
\(296\) | 13.9982 | 0.813630 | ||||||||
\(297\) | 1.12300 | 0.0651629 | ||||||||
\(298\) | −7.21522 | −0.417966 | ||||||||
\(299\) | −3.31128 | −0.191496 | ||||||||
\(300\) | −10.4779 | −0.604940 | ||||||||
\(301\) | 6.14546 | 0.354219 | ||||||||
\(302\) | −21.2451 | −1.22252 | ||||||||
\(303\) | 2.48832 | 0.142950 | ||||||||
\(304\) | −22.1327 | −1.26940 | ||||||||
\(305\) | 0.799430 | 0.0457752 | ||||||||
\(306\) | 23.6253 | 1.35057 | ||||||||
\(307\) | 3.49288 | 0.199349 | 0.0996746 | − | 0.995020i | \(-0.468220\pi\) | ||||
0.0996746 | + | 0.995020i | \(0.468220\pi\) | |||||||
\(308\) | 10.0107 | 0.570412 | ||||||||
\(309\) | 0.869438 | 0.0494606 | ||||||||
\(310\) | −105.899 | −6.01467 | ||||||||
\(311\) | −4.19951 | −0.238132 | −0.119066 | − | 0.992886i | \(-0.537990\pi\) | ||||
−0.119066 | + | 0.992886i | \(0.537990\pi\) | |||||||
\(312\) | 1.27961 | 0.0724436 | ||||||||
\(313\) | −12.4678 | −0.704720 | −0.352360 | − | 0.935864i | \(-0.614621\pi\) | ||||
−0.352360 | + | 0.935864i | \(0.614621\pi\) | |||||||
\(314\) | −34.2452 | −1.93257 | ||||||||
\(315\) | 26.3823 | 1.48648 | ||||||||
\(316\) | −79.7950 | −4.48882 | ||||||||
\(317\) | −8.27494 | −0.464767 | −0.232383 | − | 0.972624i | \(-0.574652\pi\) | ||||
−0.232383 | + | 0.972624i | \(0.574652\pi\) | |||||||
\(318\) | 2.59089 | 0.145290 | ||||||||
\(319\) | −3.34673 | −0.187381 | ||||||||
\(320\) | −13.0700 | −0.730636 | ||||||||
\(321\) | −1.94790 | −0.108721 | ||||||||
\(322\) | 18.4142 | 1.02618 | ||||||||
\(323\) | 8.31391 | 0.462599 | ||||||||
\(324\) | 40.2674 | 2.23708 | ||||||||
\(325\) | −11.9991 | −0.665591 | ||||||||
\(326\) | −7.34495 | −0.406799 | ||||||||
\(327\) | −1.28600 | −0.0711162 | ||||||||
\(328\) | 64.5242 | 3.56275 | ||||||||
\(329\) | −20.4399 | −1.12689 | ||||||||
\(330\) | 2.00000 | 0.110096 | ||||||||
\(331\) | −23.5852 | −1.29636 | −0.648179 | − | 0.761488i | \(-0.724469\pi\) | ||||
−0.648179 | + | 0.761488i | \(0.724469\pi\) | |||||||
\(332\) | −1.01158 | −0.0555176 | ||||||||
\(333\) | −6.10598 | −0.334606 | ||||||||
\(334\) | −3.35174 | −0.183399 | ||||||||
\(335\) | 23.8582 | 1.30351 | ||||||||
\(336\) | −3.34638 | −0.182560 | ||||||||
\(337\) | 0.664508 | 0.0361981 | 0.0180990 | − | 0.999836i | \(-0.494239\pi\) | ||||
0.0180990 | + | 0.999836i | \(0.494239\pi\) | |||||||
\(338\) | 2.57641 | 0.140138 | ||||||||
\(339\) | 1.39341 | 0.0756795 | ||||||||
\(340\) | 59.1478 | 3.20774 | ||||||||
\(341\) | 9.96928 | 0.539867 | ||||||||
\(342\) | 20.5294 | 1.11011 | ||||||||
\(343\) | −20.1623 | −1.08866 | ||||||||
\(344\) | 19.3504 | 1.04330 | ||||||||
\(345\) | 2.57045 | 0.138389 | ||||||||
\(346\) | 21.9729 | 1.18127 | ||||||||
\(347\) | −1.33916 | −0.0718899 | −0.0359450 | − | 0.999354i | \(-0.511444\pi\) | ||||
−0.0359450 | + | 0.999354i | \(0.511444\pi\) | |||||||
\(348\) | 2.92243 | 0.156659 | ||||||||
\(349\) | −1.48448 | −0.0794626 | −0.0397313 | − | 0.999210i | \(-0.512650\pi\) | ||||
−0.0397313 | + | 0.999210i | \(0.512650\pi\) | |||||||
\(350\) | 66.7277 | 3.56675 | ||||||||
\(351\) | −1.12300 | −0.0599412 | ||||||||
\(352\) | 7.62255 | 0.406283 | ||||||||
\(353\) | 6.04843 | 0.321925 | 0.160963 | − | 0.986960i | \(-0.448540\pi\) | ||||
0.160963 | + | 0.986960i | \(0.448540\pi\) | |||||||
\(354\) | −2.24233 | −0.119178 | ||||||||
\(355\) | 15.5971 | 0.827807 | ||||||||
\(356\) | −7.09317 | −0.375937 | ||||||||
\(357\) | 1.25703 | 0.0665291 | ||||||||
\(358\) | 49.7371 | 2.62869 | ||||||||
\(359\) | −16.7101 | −0.881925 | −0.440963 | − | 0.897525i | \(-0.645363\pi\) | ||||
−0.440963 | + | 0.897525i | \(0.645363\pi\) | |||||||
\(360\) | 83.0708 | 4.37822 | ||||||||
\(361\) | −11.7756 | −0.619766 | ||||||||
\(362\) | −67.8633 | −3.56682 | ||||||||
\(363\) | −0.188279 | −0.00988207 | ||||||||
\(364\) | −10.0107 | −0.524703 | ||||||||
\(365\) | −30.8208 | −1.61323 | ||||||||
\(366\) | 0.0940556 | 0.00491636 | ||||||||
\(367\) | 18.2943 | 0.954953 | 0.477476 | − | 0.878645i | \(-0.341552\pi\) | ||||
0.477476 | + | 0.878645i | \(0.341552\pi\) | |||||||
\(368\) | 27.2664 | 1.42136 | ||||||||
\(369\) | −28.1453 | −1.46518 | ||||||||
\(370\) | −21.8789 | −1.13743 | ||||||||
\(371\) | −11.5285 | −0.598530 | ||||||||
\(372\) | −8.70537 | −0.451353 | ||||||||
\(373\) | 16.5748 | 0.858211 | 0.429106 | − | 0.903254i | \(-0.358829\pi\) | ||||
0.429106 | + | 0.903254i | \(0.358829\pi\) | |||||||
\(374\) | −7.96928 | −0.412082 | ||||||||
\(375\) | 5.43322 | 0.280570 | ||||||||
\(376\) | −64.3596 | −3.31910 | ||||||||
\(377\) | 3.34673 | 0.172365 | ||||||||
\(378\) | 6.24505 | 0.321211 | ||||||||
\(379\) | −26.9952 | −1.38665 | −0.693326 | − | 0.720625i | \(-0.743855\pi\) | ||||
−0.693326 | + | 0.720625i | \(0.743855\pi\) | |||||||
\(380\) | 51.3970 | 2.63661 | ||||||||
\(381\) | −1.58258 | −0.0810778 | ||||||||
\(382\) | −4.79252 | −0.245207 | ||||||||
\(383\) | 9.35039 | 0.477783 | 0.238891 | − | 0.971046i | \(-0.423216\pi\) | ||||
0.238891 | + | 0.971046i | \(0.423216\pi\) | |||||||
\(384\) | 1.33260 | 0.0680039 | ||||||||
\(385\) | −8.89927 | −0.453549 | ||||||||
\(386\) | 42.3149 | 2.15377 | ||||||||
\(387\) | −8.44058 | −0.429059 | ||||||||
\(388\) | 56.3328 | 2.85987 | ||||||||
\(389\) | 17.8258 | 0.903802 | 0.451901 | − | 0.892068i | \(-0.350746\pi\) | ||||
0.451901 | + | 0.892068i | \(0.350746\pi\) | |||||||
\(390\) | −2.00000 | −0.101274 | ||||||||
\(391\) | −10.2423 | −0.517977 | ||||||||
\(392\) | −15.9110 | −0.803628 | ||||||||
\(393\) | 0.118638 | 0.00598447 | ||||||||
\(394\) | −45.3266 | −2.28352 | ||||||||
\(395\) | 70.9359 | 3.56917 | ||||||||
\(396\) | −13.7493 | −0.690930 | ||||||||
\(397\) | 36.0101 | 1.80730 | 0.903649 | − | 0.428275i | \(-0.140878\pi\) | ||||
0.903649 | + | 0.428275i | \(0.140878\pi\) | |||||||
\(398\) | 1.11887 | 0.0560839 | ||||||||
\(399\) | 1.09231 | 0.0546838 | ||||||||
\(400\) | 98.8057 | 4.94028 | ||||||||
\(401\) | 23.4604 | 1.17156 | 0.585778 | − | 0.810472i | \(-0.300789\pi\) | ||||
0.585778 | + | 0.810472i | \(0.300789\pi\) | |||||||
\(402\) | 2.80699 | 0.140000 | ||||||||
\(403\) | −9.96928 | −0.496605 | ||||||||
\(404\) | −61.2954 | −3.04956 | ||||||||
\(405\) | −35.7968 | −1.77876 | ||||||||
\(406\) | −18.6113 | −0.923664 | ||||||||
\(407\) | 2.05966 | 0.102094 | ||||||||
\(408\) | 3.95804 | 0.195952 | ||||||||
\(409\) | 14.8798 | 0.735758 | 0.367879 | − | 0.929874i | \(-0.380084\pi\) | ||||
0.367879 | + | 0.929874i | \(0.380084\pi\) | |||||||
\(410\) | −100.850 | −4.98062 | ||||||||
\(411\) | −0.906834 | −0.0447308 | ||||||||
\(412\) | −21.4171 | −1.05514 | ||||||||
\(413\) | 9.97753 | 0.490962 | ||||||||
\(414\) | −25.2912 | −1.24300 | ||||||||
\(415\) | 0.899270 | 0.0441434 | ||||||||
\(416\) | −7.62255 | −0.373726 | ||||||||
\(417\) | 1.98808 | 0.0973565 | ||||||||
\(418\) | −6.92497 | −0.338712 | ||||||||
\(419\) | −27.9935 | −1.36757 | −0.683786 | − | 0.729683i | \(-0.739668\pi\) | ||||
−0.683786 | + | 0.729683i | \(0.739668\pi\) | |||||||
\(420\) | 7.77102 | 0.379187 | ||||||||
\(421\) | −13.3185 | −0.649103 | −0.324551 | − | 0.945868i | \(-0.605213\pi\) | ||||
−0.324551 | + | 0.945868i | \(0.605213\pi\) | |||||||
\(422\) | 10.4092 | 0.506710 | ||||||||
\(423\) | 28.0735 | 1.36498 | ||||||||
\(424\) | −36.3001 | −1.76289 | ||||||||
\(425\) | −37.1152 | −1.80035 | ||||||||
\(426\) | 1.83505 | 0.0889083 | ||||||||
\(427\) | −0.418513 | −0.0202533 | ||||||||
\(428\) | 47.9831 | 2.31935 | ||||||||
\(429\) | 0.188279 | 0.00909018 | ||||||||
\(430\) | −30.2442 | −1.45851 | ||||||||
\(431\) | 12.2181 | 0.588526 | 0.294263 | − | 0.955725i | \(-0.404926\pi\) | ||||
0.294263 | + | 0.955725i | \(0.404926\pi\) | |||||||
\(432\) | 9.24723 | 0.444908 | ||||||||
\(433\) | −27.2663 | −1.31034 | −0.655168 | − | 0.755483i | \(-0.727402\pi\) | ||||
−0.655168 | + | 0.755483i | \(0.727402\pi\) | |||||||
\(434\) | 55.4397 | 2.66119 | ||||||||
\(435\) | −2.59797 | −0.124563 | ||||||||
\(436\) | 31.6784 | 1.51712 | ||||||||
\(437\) | −8.90016 | −0.425752 | ||||||||
\(438\) | −3.62617 | −0.173265 | ||||||||
\(439\) | −34.0428 | −1.62477 | −0.812386 | − | 0.583120i | \(-0.801832\pi\) | ||||
−0.812386 | + | 0.583120i | \(0.801832\pi\) | |||||||
\(440\) | −28.0214 | −1.33587 | ||||||||
\(441\) | 6.94034 | 0.330492 | ||||||||
\(442\) | 7.96928 | 0.379060 | ||||||||
\(443\) | −39.2983 | −1.86712 | −0.933558 | − | 0.358425i | \(-0.883314\pi\) | ||||
−0.933558 | + | 0.358425i | \(0.883314\pi\) | |||||||
\(444\) | −1.79854 | −0.0853549 | ||||||||
\(445\) | 6.30566 | 0.298917 | ||||||||
\(446\) | 55.2358 | 2.61549 | ||||||||
\(447\) | 0.527272 | 0.0249391 | ||||||||
\(448\) | 6.84233 | 0.323270 | ||||||||
\(449\) | 14.8508 | 0.700854 | 0.350427 | − | 0.936590i | \(-0.386036\pi\) | ||||
0.350427 | + | 0.936590i | \(0.386036\pi\) | |||||||
\(450\) | −91.6482 | −4.32034 | ||||||||
\(451\) | 9.49394 | 0.447052 | ||||||||
\(452\) | −34.3241 | −1.61447 | ||||||||
\(453\) | 1.55254 | 0.0729449 | ||||||||
\(454\) | 48.6033 | 2.28107 | ||||||||
\(455\) | 8.89927 | 0.417204 | ||||||||
\(456\) | 3.43938 | 0.161064 | ||||||||
\(457\) | 19.7213 | 0.922525 | 0.461263 | − | 0.887264i | \(-0.347397\pi\) | ||||
0.461263 | + | 0.887264i | \(0.347397\pi\) | |||||||
\(458\) | 34.2786 | 1.60173 | ||||||||
\(459\) | −3.47362 | −0.162135 | ||||||||
\(460\) | −63.3186 | −2.95224 | ||||||||
\(461\) | −29.8161 | −1.38867 | −0.694337 | − | 0.719650i | \(-0.744302\pi\) | ||||
−0.694337 | + | 0.719650i | \(0.744302\pi\) | |||||||
\(462\) | −1.04703 | −0.0487121 | ||||||||
\(463\) | −16.5769 | −0.770395 | −0.385198 | − | 0.922834i | \(-0.625867\pi\) | ||||
−0.385198 | + | 0.922834i | \(0.625867\pi\) | |||||||
\(464\) | −27.5583 | −1.27936 | ||||||||
\(465\) | 7.73888 | 0.358882 | ||||||||
\(466\) | 54.9189 | 2.54407 | ||||||||
\(467\) | −1.67187 | −0.0773651 | −0.0386825 | − | 0.999252i | \(-0.512316\pi\) | ||||
−0.0386825 | + | 0.999252i | \(0.512316\pi\) | |||||||
\(468\) | 13.7493 | 0.635563 | ||||||||
\(469\) | −12.4901 | −0.576739 | ||||||||
\(470\) | 100.593 | 4.63999 | ||||||||
\(471\) | 2.50256 | 0.115312 | ||||||||
\(472\) | 31.4165 | 1.44606 | ||||||||
\(473\) | 2.84717 | 0.130913 | ||||||||
\(474\) | 8.34584 | 0.383337 | ||||||||
\(475\) | −32.2516 | −1.47981 | ||||||||
\(476\) | −30.9647 | −1.41927 | ||||||||
\(477\) | 15.8340 | 0.724989 | ||||||||
\(478\) | 35.8437 | 1.63945 | ||||||||
\(479\) | −20.0579 | −0.916468 | −0.458234 | − | 0.888832i | \(-0.651518\pi\) | ||||
−0.458234 | + | 0.888832i | \(0.651518\pi\) | |||||||
\(480\) | 5.91718 | 0.270081 | ||||||||
\(481\) | −2.05966 | −0.0939126 | ||||||||
\(482\) | 1.45754 | 0.0663893 | ||||||||
\(483\) | −1.34567 | −0.0612300 | ||||||||
\(484\) | 4.63791 | 0.210814 | ||||||||
\(485\) | −50.0786 | −2.27395 | ||||||||
\(486\) | −12.8915 | −0.584772 | ||||||||
\(487\) | 4.74733 | 0.215122 | 0.107561 | − | 0.994198i | \(-0.465696\pi\) | ||||
0.107561 | + | 0.994198i | \(0.465696\pi\) | |||||||
\(488\) | −1.31778 | −0.0596532 | ||||||||
\(489\) | 0.536752 | 0.0242728 | ||||||||
\(490\) | 24.8685 | 1.12345 | ||||||||
\(491\) | 42.4522 | 1.91584 | 0.957919 | − | 0.287037i | \(-0.0926704\pi\) | ||||
0.957919 | + | 0.287037i | \(0.0926704\pi\) | |||||||
\(492\) | −8.29030 | −0.373756 | ||||||||
\(493\) | 10.3520 | 0.466230 | ||||||||
\(494\) | 6.92497 | 0.311569 | ||||||||
\(495\) | 12.2228 | 0.549376 | ||||||||
\(496\) | 82.0912 | 3.68600 | ||||||||
\(497\) | −8.16529 | −0.366263 | ||||||||
\(498\) | 0.105802 | 0.00474110 | ||||||||
\(499\) | −20.6880 | −0.926122 | −0.463061 | − | 0.886326i | \(-0.653249\pi\) | ||||
−0.463061 | + | 0.886326i | \(0.653249\pi\) | |||||||
\(500\) | −133.838 | −5.98541 | ||||||||
\(501\) | 0.244938 | 0.0109430 | ||||||||
\(502\) | 32.2013 | 1.43722 | ||||||||
\(503\) | 3.88526 | 0.173235 | 0.0866175 | − | 0.996242i | \(-0.472394\pi\) | ||||
0.0866175 | + | 0.996242i | \(0.472394\pi\) | |||||||
\(504\) | −43.4887 | −1.93714 | ||||||||
\(505\) | 54.4902 | 2.42478 | ||||||||
\(506\) | 8.53122 | 0.379259 | ||||||||
\(507\) | −0.188279 | −0.00836175 | ||||||||
\(508\) | 38.9840 | 1.72963 | ||||||||
\(509\) | 4.35776 | 0.193154 | 0.0965771 | − | 0.995326i | \(-0.469211\pi\) | ||||
0.0965771 | + | 0.995326i | \(0.469211\pi\) | |||||||
\(510\) | −6.18633 | −0.273935 | ||||||||
\(511\) | 16.1351 | 0.713776 | ||||||||
\(512\) | −49.1608 | −2.17262 | ||||||||
\(513\) | −3.01843 | −0.133267 | ||||||||
\(514\) | 38.0381 | 1.67779 | ||||||||
\(515\) | 19.0393 | 0.838971 | ||||||||
\(516\) | −2.48621 | −0.109449 | ||||||||
\(517\) | −9.46972 | −0.416478 | ||||||||
\(518\) | 11.4539 | 0.503256 | ||||||||
\(519\) | −1.60573 | −0.0704839 | ||||||||
\(520\) | 28.0214 | 1.22882 | ||||||||
\(521\) | −21.4185 | −0.938360 | −0.469180 | − | 0.883103i | \(-0.655450\pi\) | ||||
−0.469180 | + | 0.883103i | \(0.655450\pi\) | |||||||
\(522\) | 25.5620 | 1.11882 | ||||||||
\(523\) | 27.8835 | 1.21926 | 0.609630 | − | 0.792686i | \(-0.291318\pi\) | ||||
0.609630 | + | 0.792686i | \(0.291318\pi\) | |||||||
\(524\) | −2.92243 | −0.127667 | ||||||||
\(525\) | −4.87631 | −0.212820 | ||||||||
\(526\) | −40.8220 | −1.77992 | ||||||||
\(527\) | −30.8366 | −1.34326 | ||||||||
\(528\) | −1.55036 | −0.0674710 | ||||||||
\(529\) | −12.0354 | −0.523280 | ||||||||
\(530\) | 56.7362 | 2.46446 | ||||||||
\(531\) | −13.7038 | −0.594694 | ||||||||
\(532\) | −26.9071 | −1.16657 | ||||||||
\(533\) | −9.49394 | −0.411228 | ||||||||
\(534\) | 0.741881 | 0.0321043 | ||||||||
\(535\) | −42.6559 | −1.84417 | ||||||||
\(536\) | −39.3279 | −1.69871 | ||||||||
\(537\) | −3.63468 | −0.156848 | ||||||||
\(538\) | −6.03625 | −0.260241 | ||||||||
\(539\) | −2.34111 | −0.100839 | ||||||||
\(540\) | −21.4741 | −0.924097 | ||||||||
\(541\) | 16.1874 | 0.695950 | 0.347975 | − | 0.937504i | \(-0.386869\pi\) | ||||
0.347975 | + | 0.937504i | \(0.386869\pi\) | |||||||
\(542\) | 66.9967 | 2.87775 | ||||||||
\(543\) | 4.95930 | 0.212824 | ||||||||
\(544\) | −23.5778 | −1.01089 | ||||||||
\(545\) | −28.1614 | −1.20630 | ||||||||
\(546\) | 1.04703 | 0.0448087 | ||||||||
\(547\) | −16.5264 | −0.706617 | −0.353309 | − | 0.935507i | \(-0.614943\pi\) | ||||
−0.353309 | + | 0.935507i | \(0.614943\pi\) | |||||||
\(548\) | 22.3383 | 0.954244 | ||||||||
\(549\) | 0.574813 | 0.0245324 | ||||||||
\(550\) | 30.9147 | 1.31821 | ||||||||
\(551\) | 8.99544 | 0.383219 | ||||||||
\(552\) | −4.23714 | −0.180345 | ||||||||
\(553\) | −37.1359 | −1.57918 | ||||||||
\(554\) | 72.1445 | 3.06513 | ||||||||
\(555\) | 1.59886 | 0.0678679 | ||||||||
\(556\) | −48.9727 | −2.07691 | ||||||||
\(557\) | −27.0075 | −1.14434 | −0.572172 | − | 0.820133i | \(-0.693899\pi\) | ||||
−0.572172 | + | 0.820133i | \(0.693899\pi\) | |||||||
\(558\) | −76.1445 | −3.22345 | ||||||||
\(559\) | −2.84717 | −0.120422 | ||||||||
\(560\) | −73.2803 | −3.09666 | ||||||||
\(561\) | 0.582377 | 0.0245880 | ||||||||
\(562\) | −52.7217 | −2.22393 | ||||||||
\(563\) | 37.7276 | 1.59003 | 0.795015 | − | 0.606589i | \(-0.207463\pi\) | ||||
0.795015 | + | 0.606589i | \(0.207463\pi\) | |||||||
\(564\) | 8.26915 | 0.348194 | ||||||||
\(565\) | 30.5134 | 1.28371 | ||||||||
\(566\) | −23.6466 | −0.993941 | ||||||||
\(567\) | 18.7401 | 0.787010 | ||||||||
\(568\) | −25.7103 | −1.07878 | ||||||||
\(569\) | −7.39694 | −0.310096 | −0.155048 | − | 0.987907i | \(-0.549553\pi\) | ||||
−0.155048 | + | 0.987907i | \(0.549553\pi\) | |||||||
\(570\) | −5.37567 | −0.225162 | ||||||||
\(571\) | 24.3578 | 1.01934 | 0.509670 | − | 0.860370i | \(-0.329767\pi\) | ||||
0.509670 | + | 0.860370i | \(0.329767\pi\) | |||||||
\(572\) | −4.63791 | −0.193921 | ||||||||
\(573\) | 0.350227 | 0.0146309 | ||||||||
\(574\) | 52.7963 | 2.20368 | ||||||||
\(575\) | 39.7324 | 1.65695 | ||||||||
\(576\) | −9.39770 | −0.391571 | ||||||||
\(577\) | 4.42797 | 0.184339 | 0.0921693 | − | 0.995743i | \(-0.470620\pi\) | ||||
0.0921693 | + | 0.995743i | \(0.470620\pi\) | |||||||
\(578\) | −19.1488 | −0.796483 | ||||||||
\(579\) | −3.09228 | −0.128511 | ||||||||
\(580\) | 63.9964 | 2.65731 | ||||||||
\(581\) | −0.470780 | −0.0195313 | ||||||||
\(582\) | −5.89191 | −0.244227 | ||||||||
\(583\) | −5.34111 | −0.221206 | ||||||||
\(584\) | 50.8051 | 2.10233 | ||||||||
\(585\) | −12.2228 | −0.505352 | ||||||||
\(586\) | 48.2768 | 1.99430 | ||||||||
\(587\) | 9.80799 | 0.404819 | 0.202410 | − | 0.979301i | \(-0.435123\pi\) | ||||
0.202410 | + | 0.979301i | \(0.435123\pi\) | |||||||
\(588\) | 2.04430 | 0.0843056 | ||||||||
\(589\) | −26.7958 | −1.10410 | ||||||||
\(590\) | −49.1033 | −2.02155 | ||||||||
\(591\) | 3.31237 | 0.136253 | ||||||||
\(592\) | 16.9601 | 0.697057 | ||||||||
\(593\) | 23.4213 | 0.961796 | 0.480898 | − | 0.876777i | \(-0.340311\pi\) | ||||
0.480898 | + | 0.876777i | \(0.340311\pi\) | |||||||
\(594\) | 2.89331 | 0.118714 | ||||||||
\(595\) | 27.5269 | 1.12849 | ||||||||
\(596\) | −12.9884 | −0.532026 | ||||||||
\(597\) | −0.0817645 | −0.00334640 | ||||||||
\(598\) | −8.53122 | −0.348868 | ||||||||
\(599\) | −2.61327 | −0.106775 | −0.0533876 | − | 0.998574i | \(-0.517002\pi\) | ||||
−0.0533876 | + | 0.998574i | \(0.517002\pi\) | |||||||
\(600\) | −15.3542 | −0.626832 | ||||||||
\(601\) | −27.4904 | −1.12136 | −0.560679 | − | 0.828034i | \(-0.689460\pi\) | ||||
−0.560679 | + | 0.828034i | \(0.689460\pi\) | |||||||
\(602\) | 15.8333 | 0.645316 | ||||||||
\(603\) | 17.1547 | 0.698594 | ||||||||
\(604\) | −38.2442 | −1.55614 | ||||||||
\(605\) | −4.12300 | −0.167624 | ||||||||
\(606\) | 6.41095 | 0.260427 | ||||||||
\(607\) | 35.0458 | 1.42246 | 0.711232 | − | 0.702958i | \(-0.248138\pi\) | ||||
0.711232 | + | 0.702958i | \(0.248138\pi\) | |||||||
\(608\) | −20.4882 | −0.830904 | ||||||||
\(609\) | 1.36007 | 0.0551130 | ||||||||
\(610\) | 2.05966 | 0.0833934 | ||||||||
\(611\) | 9.46972 | 0.383104 | ||||||||
\(612\) | 42.5290 | 1.71913 | ||||||||
\(613\) | −15.8368 | −0.639641 | −0.319821 | − | 0.947478i | \(-0.603623\pi\) | ||||
−0.319821 | + | 0.947478i | \(0.603623\pi\) | |||||||
\(614\) | 8.99911 | 0.363175 | ||||||||
\(615\) | 7.36988 | 0.297182 | ||||||||
\(616\) | 14.6696 | 0.591054 | ||||||||
\(617\) | 19.0168 | 0.765588 | 0.382794 | − | 0.923834i | \(-0.374962\pi\) | ||||
0.382794 | + | 0.923834i | \(0.374962\pi\) | |||||||
\(618\) | 2.24003 | 0.0901074 | ||||||||
\(619\) | −26.7417 | −1.07484 | −0.537419 | − | 0.843315i | \(-0.680601\pi\) | ||||
−0.537419 | + | 0.843315i | \(0.680601\pi\) | |||||||
\(620\) | −190.634 | −7.65603 | ||||||||
\(621\) | 3.71856 | 0.149221 | ||||||||
\(622\) | −10.8197 | −0.433830 | ||||||||
\(623\) | −3.30110 | −0.132256 | ||||||||
\(624\) | 1.55036 | 0.0620643 | ||||||||
\(625\) | 58.9831 | 2.35932 | ||||||||
\(626\) | −32.1222 | −1.28386 | ||||||||
\(627\) | 0.506062 | 0.0202102 | ||||||||
\(628\) | −61.6462 | −2.45995 | ||||||||
\(629\) | −6.37088 | −0.254024 | ||||||||
\(630\) | 67.9719 | 2.70806 | ||||||||
\(631\) | −39.8528 | −1.58651 | −0.793257 | − | 0.608888i | \(-0.791616\pi\) | ||||
−0.793257 | + | 0.608888i | \(0.791616\pi\) | |||||||
\(632\) | −116.931 | −4.65126 | ||||||||
\(633\) | −0.760679 | −0.0302343 | ||||||||
\(634\) | −21.3197 | −0.846712 | ||||||||
\(635\) | −34.6559 | −1.37528 | ||||||||
\(636\) | 4.66396 | 0.184938 | ||||||||
\(637\) | 2.34111 | 0.0927581 | ||||||||
\(638\) | −8.62255 | −0.341370 | ||||||||
\(639\) | 11.2147 | 0.443648 | ||||||||
\(640\) | 29.1818 | 1.15351 | ||||||||
\(641\) | 9.85468 | 0.389236 | 0.194618 | − | 0.980879i | \(-0.437653\pi\) | ||||
0.194618 | + | 0.980879i | \(0.437653\pi\) | |||||||
\(642\) | −5.01860 | −0.198068 | ||||||||
\(643\) | 10.3078 | 0.406499 | 0.203249 | − | 0.979127i | \(-0.434850\pi\) | ||||
0.203249 | + | 0.979127i | \(0.434850\pi\) | |||||||
\(644\) | 33.1482 | 1.30622 | ||||||||
\(645\) | 2.21018 | 0.0870257 | ||||||||
\(646\) | 21.4201 | 0.842762 | ||||||||
\(647\) | −24.4455 | −0.961052 | −0.480526 | − | 0.876980i | \(-0.659554\pi\) | ||||
−0.480526 | + | 0.876980i | \(0.659554\pi\) | |||||||
\(648\) | 59.0075 | 2.31803 | ||||||||
\(649\) | 4.62255 | 0.181451 | ||||||||
\(650\) | −30.9147 | −1.21257 | ||||||||
\(651\) | −4.05141 | −0.158787 | ||||||||
\(652\) | −13.2219 | −0.517811 | ||||||||
\(653\) | 26.5723 | 1.03986 | 0.519928 | − | 0.854210i | \(-0.325959\pi\) | ||||
0.519928 | + | 0.854210i | \(0.325959\pi\) | |||||||
\(654\) | −3.31328 | −0.129559 | ||||||||
\(655\) | 2.59797 | 0.101511 | ||||||||
\(656\) | 78.1770 | 3.05230 | ||||||||
\(657\) | −22.1610 | −0.864584 | ||||||||
\(658\) | −52.6616 | −2.05296 | ||||||||
\(659\) | 22.5480 | 0.878345 | 0.439172 | − | 0.898403i | \(-0.355272\pi\) | ||||
0.439172 | + | 0.898403i | \(0.355272\pi\) | |||||||
\(660\) | 3.60028 | 0.140141 | ||||||||
\(661\) | −44.8824 | −1.74572 | −0.872861 | − | 0.487969i | \(-0.837738\pi\) | ||||
−0.872861 | + | 0.487969i | \(0.837738\pi\) | |||||||
\(662\) | −60.7651 | −2.36170 | ||||||||
\(663\) | −0.582377 | −0.0226177 | ||||||||
\(664\) | −1.48236 | −0.0575267 | ||||||||
\(665\) | 23.9198 | 0.927568 | ||||||||
\(666\) | −15.7315 | −0.609585 | ||||||||
\(667\) | −11.0819 | −0.429094 | ||||||||
\(668\) | −6.03361 | −0.233448 | ||||||||
\(669\) | −4.03651 | −0.156060 | ||||||||
\(670\) | 61.4686 | 2.37474 | ||||||||
\(671\) | −0.193895 | −0.00748525 | ||||||||
\(672\) | −3.09772 | −0.119497 | ||||||||
\(673\) | −0.766928 | −0.0295629 | −0.0147815 | − | 0.999891i | \(-0.504705\pi\) | ||||
−0.0147815 | + | 0.999891i | \(0.504705\pi\) | |||||||
\(674\) | 1.71205 | 0.0659457 | ||||||||
\(675\) | 13.4750 | 0.518652 | ||||||||
\(676\) | 4.63791 | 0.178381 | ||||||||
\(677\) | 22.6545 | 0.870682 | 0.435341 | − | 0.900266i | \(-0.356628\pi\) | ||||
0.435341 | + | 0.900266i | \(0.356628\pi\) | |||||||
\(678\) | 3.59000 | 0.137873 | ||||||||
\(679\) | 26.2168 | 1.00611 | ||||||||
\(680\) | 86.6748 | 3.32383 | ||||||||
\(681\) | −3.55182 | −0.136106 | ||||||||
\(682\) | 25.6850 | 0.983529 | ||||||||
\(683\) | 6.69712 | 0.256258 | 0.128129 | − | 0.991757i | \(-0.459103\pi\) | ||||
0.128129 | + | 0.991757i | \(0.459103\pi\) | |||||||
\(684\) | 36.9559 | 1.41304 | ||||||||
\(685\) | −19.8582 | −0.758743 | ||||||||
\(686\) | −51.9464 | −1.98332 | ||||||||
\(687\) | −2.50500 | −0.0955719 | ||||||||
\(688\) | 23.4448 | 0.893824 | ||||||||
\(689\) | 5.34111 | 0.203480 | ||||||||
\(690\) | 6.62255 | 0.252116 | ||||||||
\(691\) | −22.1563 | −0.842865 | −0.421433 | − | 0.906860i | \(-0.638473\pi\) | ||||
−0.421433 | + | 0.906860i | \(0.638473\pi\) | |||||||
\(692\) | 39.5544 | 1.50363 | ||||||||
\(693\) | −6.39883 | −0.243071 | ||||||||
\(694\) | −3.45023 | −0.130969 | ||||||||
\(695\) | 43.5356 | 1.65140 | ||||||||
\(696\) | 4.28250 | 0.162328 | ||||||||
\(697\) | −29.3663 | −1.11233 | ||||||||
\(698\) | −3.82465 | −0.144765 | ||||||||
\(699\) | −4.01335 | −0.151799 | ||||||||
\(700\) | 120.119 | 4.54009 | ||||||||
\(701\) | 14.7084 | 0.555527 | 0.277763 | − | 0.960650i | \(-0.410407\pi\) | ||||
0.277763 | + | 0.960650i | \(0.410407\pi\) | |||||||
\(702\) | −2.89331 | −0.109201 | ||||||||
\(703\) | −5.53603 | −0.208796 | ||||||||
\(704\) | 3.17003 | 0.119475 | ||||||||
\(705\) | −7.35109 | −0.276858 | ||||||||
\(706\) | 15.5833 | 0.586484 | ||||||||
\(707\) | −28.5264 | −1.07285 | ||||||||
\(708\) | −4.03651 | −0.151701 | ||||||||
\(709\) | 28.8284 | 1.08267 | 0.541336 | − | 0.840806i | \(-0.317919\pi\) | ||||
0.541336 | + | 0.840806i | \(0.317919\pi\) | |||||||
\(710\) | 40.1846 | 1.50810 | ||||||||
\(711\) | 51.0049 | 1.91283 | ||||||||
\(712\) | −10.3943 | −0.389542 | ||||||||
\(713\) | 33.0110 | 1.23627 | ||||||||
\(714\) | 3.23863 | 0.121203 | ||||||||
\(715\) | 4.12300 | 0.154191 | ||||||||
\(716\) | 89.5339 | 3.34604 | ||||||||
\(717\) | −2.61938 | −0.0978225 | ||||||||
\(718\) | −43.0522 | −1.60669 | ||||||||
\(719\) | −8.10420 | −0.302236 | −0.151118 | − | 0.988516i | \(-0.548287\pi\) | ||||
−0.151118 | + | 0.988516i | \(0.548287\pi\) | |||||||
\(720\) | 100.648 | 3.75093 | ||||||||
\(721\) | −9.96733 | −0.371203 | ||||||||
\(722\) | −30.3387 | −1.12909 | ||||||||
\(723\) | −0.106514 | −0.00396130 | ||||||||
\(724\) | −122.164 | −4.54018 | ||||||||
\(725\) | −40.1577 | −1.49142 | ||||||||
\(726\) | −0.485084 | −0.0180032 | ||||||||
\(727\) | −19.1116 | −0.708810 | −0.354405 | − | 0.935092i | \(-0.615317\pi\) | ||||
−0.354405 | + | 0.935092i | \(0.615317\pi\) | |||||||
\(728\) | −14.6696 | −0.543691 | ||||||||
\(729\) | −25.1046 | −0.929799 | ||||||||
\(730\) | −79.4072 | −2.93899 | ||||||||
\(731\) | −8.80677 | −0.325730 | ||||||||
\(732\) | 0.169313 | 0.00625800 | ||||||||
\(733\) | −27.4827 | −1.01510 | −0.507548 | − | 0.861623i | \(-0.669448\pi\) | ||||
−0.507548 | + | 0.861623i | \(0.669448\pi\) | |||||||
\(734\) | 47.1336 | 1.73973 | ||||||||
\(735\) | −1.81734 | −0.0670335 | ||||||||
\(736\) | 25.2404 | 0.930373 | ||||||||
\(737\) | −5.78662 | −0.213153 | ||||||||
\(738\) | −72.5139 | −2.66927 | ||||||||
\(739\) | −3.99458 | −0.146943 | −0.0734715 | − | 0.997297i | \(-0.523408\pi\) | ||||
−0.0734715 | + | 0.997297i | \(0.523408\pi\) | |||||||
\(740\) | −39.3851 | −1.44783 | ||||||||
\(741\) | −0.506062 | −0.0185906 | ||||||||
\(742\) | −29.7022 | −1.09040 | ||||||||
\(743\) | 27.9386 | 1.02497 | 0.512483 | − | 0.858697i | \(-0.328726\pi\) | ||||
0.512483 | + | 0.858697i | \(0.328726\pi\) | |||||||
\(744\) | −12.7568 | −0.467686 | ||||||||
\(745\) | 11.5464 | 0.423028 | ||||||||
\(746\) | 42.7036 | 1.56349 | ||||||||
\(747\) | 0.646601 | 0.0236579 | ||||||||
\(748\) | −14.3458 | −0.524536 | ||||||||
\(749\) | 22.3309 | 0.815955 | ||||||||
\(750\) | 13.9982 | 0.511143 | ||||||||
\(751\) | −16.3149 | −0.595341 | −0.297670 | − | 0.954669i | \(-0.596210\pi\) | ||||
−0.297670 | + | 0.954669i | \(0.596210\pi\) | |||||||
\(752\) | −77.9776 | −2.84355 | ||||||||
\(753\) | −2.35320 | −0.0857554 | ||||||||
\(754\) | 8.62255 | 0.314015 | ||||||||
\(755\) | 33.9982 | 1.23732 | ||||||||
\(756\) | 11.2420 | 0.408867 | ||||||||
\(757\) | 50.8067 | 1.84660 | 0.923301 | − | 0.384077i | \(-0.125480\pi\) | ||||
0.923301 | + | 0.384077i | \(0.125480\pi\) | |||||||
\(758\) | −69.5509 | −2.52620 | ||||||||
\(759\) | −0.623443 | −0.0226295 | ||||||||
\(760\) | 75.3168 | 2.73203 | ||||||||
\(761\) | −7.06895 | −0.256249 | −0.128125 | − | 0.991758i | \(-0.540896\pi\) | ||||
−0.128125 | + | 0.991758i | \(0.540896\pi\) | |||||||
\(762\) | −4.07737 | −0.147708 | ||||||||
\(763\) | 14.7429 | 0.533728 | ||||||||
\(764\) | −8.62722 | −0.312122 | ||||||||
\(765\) | −37.8073 | −1.36692 | ||||||||
\(766\) | 24.0905 | 0.870425 | ||||||||
\(767\) | −4.62255 | −0.166911 | ||||||||
\(768\) | 4.62703 | 0.166963 | ||||||||
\(769\) | −19.0465 | −0.686834 | −0.343417 | − | 0.939183i | \(-0.611584\pi\) | ||||
−0.343417 | + | 0.939183i | \(0.611584\pi\) | |||||||
\(770\) | −22.9282 | −0.826275 | ||||||||
\(771\) | −2.77974 | −0.100110 | ||||||||
\(772\) | 76.1728 | 2.74152 | ||||||||
\(773\) | −34.6902 | −1.24772 | −0.623861 | − | 0.781536i | \(-0.714437\pi\) | ||||
−0.623861 | + | 0.781536i | \(0.714437\pi\) | |||||||
\(774\) | −21.7464 | −0.781660 | ||||||||
\(775\) | 119.622 | 4.29697 | ||||||||
\(776\) | 82.5496 | 2.96336 | ||||||||
\(777\) | −0.837026 | −0.0300281 | ||||||||
\(778\) | 45.9266 | 1.64655 | ||||||||
\(779\) | −25.5181 | −0.914282 | ||||||||
\(780\) | −3.60028 | −0.128911 | ||||||||
\(781\) | −3.78295 | −0.135364 | ||||||||
\(782\) | −26.3885 | −0.943650 | ||||||||
\(783\) | −3.75836 | −0.134313 | ||||||||
\(784\) | −19.2777 | −0.688488 | ||||||||
\(785\) | 54.8020 | 1.95597 | ||||||||
\(786\) | 0.305660 | 0.0109025 | ||||||||
\(787\) | −29.2246 | −1.04174 | −0.520872 | − | 0.853635i | \(-0.674393\pi\) | ||||
−0.520872 | + | 0.853635i | \(0.674393\pi\) | |||||||
\(788\) | −81.5943 | −2.90668 | ||||||||
\(789\) | 2.98318 | 0.106204 | ||||||||
\(790\) | 182.760 | 6.50232 | ||||||||
\(791\) | −15.9742 | −0.567976 | ||||||||
\(792\) | −20.1482 | −0.715934 | ||||||||
\(793\) | 0.193895 | 0.00688543 | ||||||||
\(794\) | 92.7771 | 3.29254 | ||||||||
\(795\) | −4.14616 | −0.147049 | ||||||||
\(796\) | 2.01413 | 0.0713888 | ||||||||
\(797\) | −3.30655 | −0.117124 | −0.0585620 | − | 0.998284i | \(-0.518652\pi\) | ||||
−0.0585620 | + | 0.998284i | \(0.518652\pi\) | |||||||
\(798\) | 2.81424 | 0.0996229 | ||||||||
\(799\) | 29.2914 | 1.03626 | ||||||||
\(800\) | 91.4638 | 3.23374 | ||||||||
\(801\) | 4.53395 | 0.160199 | ||||||||
\(802\) | 60.4437 | 2.13434 | ||||||||
\(803\) | 7.47534 | 0.263799 | ||||||||
\(804\) | 5.05299 | 0.178205 | ||||||||
\(805\) | −29.4679 | −1.03861 | ||||||||
\(806\) | −25.6850 | −0.904715 | ||||||||
\(807\) | 0.441116 | 0.0155280 | ||||||||
\(808\) | −89.8218 | −3.15992 | ||||||||
\(809\) | −9.10142 | −0.319989 | −0.159994 | − | 0.987118i | \(-0.551148\pi\) | ||||
−0.159994 | + | 0.987118i | \(0.551148\pi\) | |||||||
\(810\) | −92.2273 | −3.24054 | ||||||||
\(811\) | 25.0849 | 0.880849 | 0.440425 | − | 0.897790i | \(-0.354828\pi\) | ||||
0.440425 | + | 0.897790i | \(0.354828\pi\) | |||||||
\(812\) | −33.5030 | −1.17573 | ||||||||
\(813\) | −4.89597 | −0.171709 | ||||||||
\(814\) | 5.30655 | 0.185994 | ||||||||
\(815\) | 11.7540 | 0.411725 | ||||||||
\(816\) | 4.79554 | 0.167877 | ||||||||
\(817\) | −7.65272 | −0.267735 | ||||||||
\(818\) | 38.3365 | 1.34040 | ||||||||
\(819\) | 6.39883 | 0.223593 | ||||||||
\(820\) | −181.544 | −6.33980 | ||||||||
\(821\) | 6.29231 | 0.219603 | 0.109802 | − | 0.993954i | \(-0.464978\pi\) | ||||
0.109802 | + | 0.993954i | \(0.464978\pi\) | |||||||
\(822\) | −2.33638 | −0.0814907 | ||||||||
\(823\) | −32.7466 | −1.14147 | −0.570737 | − | 0.821133i | \(-0.693343\pi\) | ||||
−0.570737 | + | 0.821133i | \(0.693343\pi\) | |||||||
\(824\) | −31.3844 | −1.09333 | ||||||||
\(825\) | −2.25918 | −0.0786544 | ||||||||
\(826\) | 25.7063 | 0.894435 | ||||||||
\(827\) | −6.16948 | −0.214534 | −0.107267 | − | 0.994230i | \(-0.534210\pi\) | ||||
−0.107267 | + | 0.994230i | \(0.534210\pi\) | |||||||
\(828\) | −45.5278 | −1.58220 | ||||||||
\(829\) | 16.0410 | 0.557127 | 0.278564 | − | 0.960418i | \(-0.410142\pi\) | ||||
0.278564 | + | 0.960418i | \(0.410142\pi\) | |||||||
\(830\) | 2.31689 | 0.0804205 | ||||||||
\(831\) | −5.27216 | −0.182889 | ||||||||
\(832\) | −3.17003 | −0.109901 | ||||||||
\(833\) | 7.24144 | 0.250901 | ||||||||
\(834\) | 5.12211 | 0.177364 | ||||||||
\(835\) | 5.36374 | 0.185620 | ||||||||
\(836\) | −12.4659 | −0.431144 | ||||||||
\(837\) | 11.1955 | 0.386972 | ||||||||
\(838\) | −72.1229 | −2.49144 | ||||||||
\(839\) | 27.1837 | 0.938484 | 0.469242 | − | 0.883070i | \(-0.344527\pi\) | ||||
0.469242 | + | 0.883070i | \(0.344527\pi\) | |||||||
\(840\) | 11.3876 | 0.392909 | ||||||||
\(841\) | −17.7994 | −0.613773 | ||||||||
\(842\) | −34.3139 | −1.18254 | ||||||||
\(843\) | 3.85279 | 0.132697 | ||||||||
\(844\) | 18.7380 | 0.644988 | ||||||||
\(845\) | −4.12300 | −0.141835 | ||||||||
\(846\) | 72.3289 | 2.48672 | ||||||||
\(847\) | 2.15845 | 0.0741651 | ||||||||
\(848\) | −43.9809 | −1.51031 | ||||||||
\(849\) | 1.72804 | 0.0593062 | ||||||||
\(850\) | −95.6242 | −3.27988 | ||||||||
\(851\) | 6.82012 | 0.233791 | ||||||||
\(852\) | 3.30335 | 0.113171 | ||||||||
\(853\) | 24.2748 | 0.831152 | 0.415576 | − | 0.909558i | \(-0.363580\pi\) | ||||
0.415576 | + | 0.909558i | \(0.363580\pi\) | |||||||
\(854\) | −1.07826 | −0.0368974 | ||||||||
\(855\) | −32.8530 | −1.12355 | ||||||||
\(856\) | 70.3140 | 2.40328 | ||||||||
\(857\) | 16.7036 | 0.570584 | 0.285292 | − | 0.958441i | \(-0.407909\pi\) | ||||
0.285292 | + | 0.958441i | \(0.407909\pi\) | |||||||
\(858\) | 0.485084 | 0.0165605 | ||||||||
\(859\) | −28.9414 | −0.987468 | −0.493734 | − | 0.869613i | \(-0.664368\pi\) | ||||
−0.493734 | + | 0.869613i | \(0.664368\pi\) | |||||||
\(860\) | −54.4439 | −1.85652 | ||||||||
\(861\) | −3.85824 | −0.131488 | ||||||||
\(862\) | 31.4789 | 1.07218 | ||||||||
\(863\) | −33.6601 | −1.14580 | −0.572901 | − | 0.819625i | \(-0.694182\pi\) | ||||
−0.572901 | + | 0.819625i | \(0.694182\pi\) | |||||||
\(864\) | 8.56011 | 0.291221 | ||||||||
\(865\) | −35.1630 | −1.19558 | ||||||||
\(866\) | −70.2493 | −2.38717 | ||||||||
\(867\) | 1.39935 | 0.0475244 | ||||||||
\(868\) | 99.7993 | 3.38741 | ||||||||
\(869\) | −17.2049 | −0.583637 | ||||||||
\(870\) | −6.69345 | −0.226929 | ||||||||
\(871\) | 5.78662 | 0.196072 | ||||||||
\(872\) | 46.4213 | 1.57202 | ||||||||
\(873\) | −36.0079 | −1.21868 | ||||||||
\(874\) | −22.9305 | −0.775636 | ||||||||
\(875\) | −62.2870 | −2.10568 | ||||||||
\(876\) | −6.52762 | −0.220548 | ||||||||
\(877\) | −56.6214 | −1.91197 | −0.955985 | − | 0.293417i | \(-0.905208\pi\) | ||||
−0.955985 | + | 0.293417i | \(0.905208\pi\) | |||||||
\(878\) | −87.7083 | −2.96001 | ||||||||
\(879\) | −3.52796 | −0.118995 | ||||||||
\(880\) | −33.9505 | −1.14447 | ||||||||
\(881\) | 35.8236 | 1.20693 | 0.603465 | − | 0.797390i | \(-0.293786\pi\) | ||||
0.603465 | + | 0.797390i | \(0.293786\pi\) | |||||||
\(882\) | 17.8812 | 0.602091 | ||||||||
\(883\) | −29.2843 | −0.985493 | −0.492747 | − | 0.870173i | \(-0.664007\pi\) | ||||
−0.492747 | + | 0.870173i | \(0.664007\pi\) | |||||||
\(884\) | 14.3458 | 0.482503 | ||||||||
\(885\) | 3.58836 | 0.120621 | ||||||||
\(886\) | −101.249 | −3.40151 | ||||||||
\(887\) | −36.8342 | −1.23677 | −0.618385 | − | 0.785875i | \(-0.712213\pi\) | ||||
−0.618385 | + | 0.785875i | \(0.712213\pi\) | |||||||
\(888\) | −2.63557 | −0.0884438 | ||||||||
\(889\) | 18.1428 | 0.608491 | ||||||||
\(890\) | 16.2460 | 0.544567 | ||||||||
\(891\) | 8.68222 | 0.290865 | ||||||||
\(892\) | 99.4322 | 3.32924 | ||||||||
\(893\) | 25.4530 | 0.851754 | ||||||||
\(894\) | 1.35847 | 0.0454341 | ||||||||
\(895\) | −79.5935 | −2.66052 | ||||||||
\(896\) | −15.2771 | −0.510371 | ||||||||
\(897\) | 0.623443 | 0.0208161 | ||||||||
\(898\) | 38.2619 | 1.27682 | ||||||||
\(899\) | −33.3644 | −1.11277 | ||||||||
\(900\) | −164.980 | −5.49933 | ||||||||
\(901\) | 16.5209 | 0.550392 | ||||||||
\(902\) | 24.4603 | 0.814440 | ||||||||
\(903\) | −1.15706 | −0.0385045 | ||||||||
\(904\) | −50.2983 | −1.67290 | ||||||||
\(905\) | 108.601 | 3.61001 | ||||||||
\(906\) | 4.00000 | 0.132891 | ||||||||
\(907\) | 0.491159 | 0.0163087 | 0.00815433 | − | 0.999967i | \(-0.497404\pi\) | ||||
0.00815433 | + | 0.999967i | \(0.497404\pi\) | |||||||
\(908\) | 87.4929 | 2.90355 | ||||||||
\(909\) | 39.1800 | 1.29952 | ||||||||
\(910\) | 22.9282 | 0.760063 | ||||||||
\(911\) | −44.1275 | −1.46201 | −0.731005 | − | 0.682373i | \(-0.760948\pi\) | ||||
−0.731005 | + | 0.682373i | \(0.760948\pi\) | |||||||
\(912\) | 4.16712 | 0.137987 | ||||||||
\(913\) | −0.218111 | −0.00721841 | ||||||||
\(914\) | 50.8103 | 1.68066 | ||||||||
\(915\) | −0.150516 | −0.00497589 | ||||||||
\(916\) | 61.7064 | 2.03884 | ||||||||
\(917\) | −1.36007 | −0.0449136 | ||||||||
\(918\) | −8.94948 | −0.295377 | ||||||||
\(919\) | −43.8564 | −1.44669 | −0.723345 | − | 0.690487i | \(-0.757396\pi\) | ||||
−0.723345 | + | 0.690487i | \(0.757396\pi\) | |||||||
\(920\) | −92.7865 | −3.05908 | ||||||||
\(921\) | −0.657635 | −0.0216698 | ||||||||
\(922\) | −76.8186 | −2.52989 | ||||||||
\(923\) | 3.78295 | 0.124517 | ||||||||
\(924\) | −1.88480 | −0.0620053 | ||||||||
\(925\) | 24.7141 | 0.812596 | ||||||||
\(926\) | −42.7090 | −1.40351 | ||||||||
\(927\) | 13.6898 | 0.449631 | ||||||||
\(928\) | −25.5106 | −0.837426 | ||||||||
\(929\) | −21.9917 | −0.721526 | −0.360763 | − | 0.932658i | \(-0.617484\pi\) | ||||
−0.360763 | + | 0.932658i | \(0.617484\pi\) | |||||||
\(930\) | 19.9386 | 0.653811 | ||||||||
\(931\) | 6.29251 | 0.206229 | ||||||||
\(932\) | 98.8618 | 3.23833 | ||||||||
\(933\) | 0.790679 | 0.0258857 | ||||||||
\(934\) | −4.30744 | −0.140944 | ||||||||
\(935\) | 12.7531 | 0.417071 | ||||||||
\(936\) | 20.1482 | 0.658563 | ||||||||
\(937\) | −15.9198 | −0.520076 | −0.260038 | − | 0.965598i | \(-0.583735\pi\) | ||||
−0.260038 | + | 0.965598i | \(0.583735\pi\) | |||||||
\(938\) | −32.1797 | −1.05070 | ||||||||
\(939\) | 2.34742 | 0.0766050 | ||||||||
\(940\) | 181.081 | 5.90621 | ||||||||
\(941\) | 7.79435 | 0.254088 | 0.127044 | − | 0.991897i | \(-0.459451\pi\) | ||||
0.127044 | + | 0.991897i | \(0.459451\pi\) | |||||||
\(942\) | 6.44763 | 0.210075 | ||||||||
\(943\) | 31.4371 | 1.02373 | ||||||||
\(944\) | 38.0640 | 1.23888 | ||||||||
\(945\) | −9.99386 | −0.325100 | ||||||||
\(946\) | 7.33549 | 0.238497 | ||||||||
\(947\) | 37.4253 | 1.21616 | 0.608079 | − | 0.793876i | \(-0.291940\pi\) | ||||
0.608079 | + | 0.793876i | \(0.291940\pi\) | |||||||
\(948\) | 15.0237 | 0.487947 | ||||||||
\(949\) | −7.47534 | −0.242660 | ||||||||
\(950\) | −83.0935 | −2.69591 | ||||||||
\(951\) | 1.55799 | 0.0505214 | ||||||||
\(952\) | −45.3754 | −1.47063 | ||||||||
\(953\) | 40.9457 | 1.32636 | 0.663181 | − | 0.748459i | \(-0.269206\pi\) | ||||
0.663181 | + | 0.748459i | \(0.269206\pi\) | |||||||
\(954\) | 40.7949 | 1.32078 | ||||||||
\(955\) | 7.66940 | 0.248176 | ||||||||
\(956\) | 64.5238 | 2.08685 | ||||||||
\(957\) | 0.630117 | 0.0203688 | ||||||||
\(958\) | −51.6774 | −1.66962 | ||||||||
\(959\) | 10.3960 | 0.335706 | ||||||||
\(960\) | 2.46080 | 0.0794221 | ||||||||
\(961\) | 68.3865 | 2.20602 | ||||||||
\(962\) | −5.30655 | −0.171090 | ||||||||
\(963\) | −30.6708 | −0.988351 | ||||||||
\(964\) | 2.62379 | 0.0845065 | ||||||||
\(965\) | −67.7158 | −2.17985 | ||||||||
\(966\) | −3.46700 | −0.111549 | ||||||||
\(967\) | −37.0738 | −1.19221 | −0.596107 | − | 0.802905i | \(-0.703287\pi\) | ||||
−0.596107 | + | 0.802905i | \(0.703287\pi\) | |||||||
\(968\) | 6.79636 | 0.218443 | ||||||||
\(969\) | −1.56533 | −0.0502857 | ||||||||
\(970\) | −129.023 | −4.14268 | ||||||||
\(971\) | −9.13718 | −0.293226 | −0.146613 | − | 0.989194i | \(-0.546837\pi\) | ||||
−0.146613 | + | 0.989194i | \(0.546837\pi\) | |||||||
\(972\) | −23.2066 | −0.744352 | ||||||||
\(973\) | −22.7915 | −0.730662 | ||||||||
\(974\) | 12.2311 | 0.391909 | ||||||||
\(975\) | 2.25918 | 0.0723515 | ||||||||
\(976\) | −1.59662 | −0.0511064 | ||||||||
\(977\) | 24.8647 | 0.795491 | 0.397745 | − | 0.917496i | \(-0.369793\pi\) | ||||
0.397745 | + | 0.917496i | \(0.369793\pi\) | |||||||
\(978\) | 1.38290 | 0.0442202 | ||||||||
\(979\) | −1.52939 | −0.0488794 | ||||||||
\(980\) | 44.7669 | 1.43003 | ||||||||
\(981\) | −20.2488 | −0.646495 | ||||||||
\(982\) | 109.374 | 3.49028 | ||||||||
\(983\) | −22.0037 | −0.701808 | −0.350904 | − | 0.936411i | \(-0.614126\pi\) | ||||
−0.350904 | + | 0.936411i | \(0.614126\pi\) | |||||||
\(984\) | −12.1485 | −0.387281 | ||||||||
\(985\) | 72.5354 | 2.31117 | ||||||||
\(986\) | 26.6710 | 0.849377 | ||||||||
\(987\) | 3.84840 | 0.122496 | ||||||||
\(988\) | 12.4659 | 0.396594 | ||||||||
\(989\) | 9.42777 | 0.299786 | ||||||||
\(990\) | 31.4911 | 1.00085 | ||||||||
\(991\) | 44.3616 | 1.40919 | 0.704596 | − | 0.709608i | \(-0.251128\pi\) | ||||
0.704596 | + | 0.709608i | \(0.251128\pi\) | |||||||
\(992\) | 75.9913 | 2.41273 | ||||||||
\(993\) | 4.44058 | 0.140918 | ||||||||
\(994\) | −21.0372 | −0.667259 | ||||||||
\(995\) | −1.79051 | −0.0567630 | ||||||||
\(996\) | 0.190459 | 0.00603492 | ||||||||
\(997\) | −0.262678 | −0.00831910 | −0.00415955 | − | 0.999991i | \(-0.501324\pi\) | ||||
−0.00415955 | + | 0.999991i | \(0.501324\pi\) | |||||||
\(998\) | −53.3009 | −1.68721 | ||||||||
\(999\) | 2.31300 | 0.0731800 |
(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 | 143.2.a.b.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 1287.2.a.k.1.1 | 4 | |||
4.3 | odd | 2 | 2288.2.a.x.1.3 | 4 | |||
5.4 | even | 2 | 3575.2.a.k.1.1 | 4 | |||
7.6 | odd | 2 | 7007.2.a.n.1.4 | 4 | |||
8.3 | odd | 2 | 9152.2.a.cg.1.2 | 4 | |||
8.5 | even | 2 | 9152.2.a.ch.1.3 | 4 | |||
11.10 | odd | 2 | 1573.2.a.f.1.1 | 4 | |||
13.12 | even | 2 | 1859.2.a.i.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.2.a.b.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1287.2.a.k.1.1 | 4 | 3.2 | odd | 2 | |||
1573.2.a.f.1.1 | 4 | 11.10 | odd | 2 | |||
1859.2.a.i.1.1 | 4 | 13.12 | even | 2 | |||
2288.2.a.x.1.3 | 4 | 4.3 | odd | 2 | |||
3575.2.a.k.1.1 | 4 | 5.4 | even | 2 | |||
7007.2.a.n.1.4 | 4 | 7.6 | odd | 2 | |||
9152.2.a.cg.1.2 | 4 | 8.3 | odd | 2 | |||
9152.2.a.ch.1.3 | 4 | 8.5 | even | 2 |