Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [89,2,Mod(1,89)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(89, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("89.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 89 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 89.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: | \(0.710668577989\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.535120.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 6x^{3} + 4x^{2} + 4x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.34526\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 89.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.09813 | −1.48360 | −0.741800 | − | 0.670621i | \(-0.766028\pi\) | ||||
−0.741800 | + | 0.670621i | \(0.766028\pi\) | |||||||
\(3\) | 2.34526 | 1.35404 | 0.677020 | − | 0.735965i | \(-0.263271\pi\) | ||||
0.677020 | + | 0.735965i | \(0.263271\pi\) | |||||||
\(4\) | 2.40214 | 1.20107 | ||||||||
\(5\) | −0.402140 | −0.179842 | −0.0899212 | − | 0.995949i | \(-0.528662\pi\) | ||||
−0.0899212 | + | 0.995949i | \(0.528662\pi\) | |||||||
\(6\) | −4.92067 | −2.00885 | ||||||||
\(7\) | 0.678986 | 0.256633 | 0.128316 | − | 0.991733i | \(-0.459043\pi\) | ||||
0.128316 | + | 0.991733i | \(0.459043\pi\) | |||||||
\(8\) | −0.843741 | −0.298308 | ||||||||
\(9\) | 2.50027 | 0.833423 | ||||||||
\(10\) | 0.843741 | 0.266814 | ||||||||
\(11\) | 0.745613 | 0.224811 | 0.112405 | − | 0.993662i | \(-0.464144\pi\) | ||||
0.112405 | + | 0.993662i | \(0.464144\pi\) | |||||||
\(12\) | 5.63365 | 1.62630 | ||||||||
\(13\) | 6.09267 | 1.68980 | 0.844901 | − | 0.534922i | \(-0.179659\pi\) | ||||
0.844901 | + | 0.534922i | \(0.179659\pi\) | |||||||
\(14\) | −1.42460 | −0.380740 | ||||||||
\(15\) | −0.943125 | −0.243514 | ||||||||
\(16\) | −3.03400 | −0.758501 | ||||||||
\(17\) | −6.59240 | −1.59889 | −0.799446 | − | 0.600738i | \(-0.794874\pi\) | ||||
−0.799446 | + | 0.600738i | \(0.794874\pi\) | |||||||
\(18\) | −5.24588 | −1.23647 | ||||||||
\(19\) | 0.827996 | 0.189955 | 0.0949776 | − | 0.995479i | \(-0.469722\pi\) | ||||
0.0949776 | + | 0.995479i | \(0.469722\pi\) | |||||||
\(20\) | −0.965997 | −0.216003 | ||||||||
\(21\) | 1.59240 | 0.347491 | ||||||||
\(22\) | −1.56439 | −0.333530 | ||||||||
\(23\) | −7.71478 | −1.60864 | −0.804322 | − | 0.594194i | \(-0.797471\pi\) | ||||
−0.804322 | + | 0.594194i | \(0.797471\pi\) | |||||||
\(24\) | −1.97880 | −0.403920 | ||||||||
\(25\) | −4.83828 | −0.967657 | ||||||||
\(26\) | −12.7832 | −2.50699 | ||||||||
\(27\) | −1.17200 | −0.225552 | ||||||||
\(28\) | 1.63102 | 0.308234 | ||||||||
\(29\) | 6.24042 | 1.15882 | 0.579409 | − | 0.815037i | \(-0.303284\pi\) | ||||
0.579409 | + | 0.815037i | \(0.303284\pi\) | |||||||
\(30\) | 1.97880 | 0.361277 | ||||||||
\(31\) | 0.400348 | 0.0719047 | 0.0359524 | − | 0.999354i | \(-0.488554\pi\) | ||||
0.0359524 | + | 0.999354i | \(0.488554\pi\) | |||||||
\(32\) | 8.05321 | 1.42362 | ||||||||
\(33\) | 1.74866 | 0.304403 | ||||||||
\(34\) | 13.8317 | 2.37212 | ||||||||
\(35\) | −0.273047 | −0.0461534 | ||||||||
\(36\) | 6.00599 | 1.00100 | ||||||||
\(37\) | −9.34706 | −1.53665 | −0.768323 | − | 0.640062i | \(-0.778909\pi\) | ||||
−0.768323 | + | 0.640062i | \(0.778909\pi\) | |||||||
\(38\) | −1.73724 | −0.281818 | ||||||||
\(39\) | 14.2889 | 2.28806 | ||||||||
\(40\) | 0.339302 | 0.0536484 | ||||||||
\(41\) | 1.89641 | 0.296170 | 0.148085 | − | 0.988975i | \(-0.452689\pi\) | ||||
0.148085 | + | 0.988975i | \(0.452689\pi\) | |||||||
\(42\) | −3.34106 | −0.515537 | ||||||||
\(43\) | −2.27864 | −0.347489 | −0.173744 | − | 0.984791i | \(-0.555587\pi\) | ||||
−0.173744 | + | 0.984791i | \(0.555587\pi\) | |||||||
\(44\) | 1.79107 | 0.270014 | ||||||||
\(45\) | −1.00546 | −0.149885 | ||||||||
\(46\) | 16.1866 | 2.38658 | ||||||||
\(47\) | 3.45064 | 0.503328 | 0.251664 | − | 0.967815i | \(-0.419022\pi\) | ||||
0.251664 | + | 0.967815i | \(0.419022\pi\) | |||||||
\(48\) | −7.11554 | −1.02704 | ||||||||
\(49\) | −6.53898 | −0.934140 | ||||||||
\(50\) | 10.1513 | 1.43562 | ||||||||
\(51\) | −15.4609 | −2.16496 | ||||||||
\(52\) | 14.6354 | 2.02957 | ||||||||
\(53\) | 1.33802 | 0.183791 | 0.0918953 | − | 0.995769i | \(-0.470707\pi\) | ||||
0.0918953 | + | 0.995769i | \(0.470707\pi\) | |||||||
\(54\) | 2.45902 | 0.334630 | ||||||||
\(55\) | −0.299841 | −0.0404306 | ||||||||
\(56\) | −0.572888 | −0.0765554 | ||||||||
\(57\) | 1.94187 | 0.257207 | ||||||||
\(58\) | −13.0932 | −1.71922 | ||||||||
\(59\) | 3.53177 | 0.459797 | 0.229899 | − | 0.973215i | \(-0.426161\pi\) | ||||
0.229899 | + | 0.973215i | \(0.426161\pi\) | |||||||
\(60\) | −2.26552 | −0.292477 | ||||||||
\(61\) | 0.597860 | 0.0765481 | 0.0382741 | − | 0.999267i | \(-0.487814\pi\) | ||||
0.0382741 | + | 0.999267i | \(0.487814\pi\) | |||||||
\(62\) | −0.839982 | −0.106678 | ||||||||
\(63\) | 1.69765 | 0.213883 | ||||||||
\(64\) | −10.8287 | −1.35358 | ||||||||
\(65\) | −2.45011 | −0.303898 | ||||||||
\(66\) | −3.66891 | −0.451612 | ||||||||
\(67\) | 10.4367 | 1.27504 | 0.637522 | − | 0.770432i | \(-0.279960\pi\) | ||||
0.637522 | + | 0.770432i | \(0.279960\pi\) | |||||||
\(68\) | −15.8359 | −1.92038 | ||||||||
\(69\) | −18.0932 | −2.17817 | ||||||||
\(70\) | 0.572888 | 0.0684733 | ||||||||
\(71\) | 12.6941 | 1.50651 | 0.753257 | − | 0.657726i | \(-0.228482\pi\) | ||||
0.753257 | + | 0.657726i | \(0.228482\pi\) | |||||||
\(72\) | −2.10958 | −0.248616 | ||||||||
\(73\) | −10.4361 | −1.22146 | −0.610729 | − | 0.791840i | \(-0.709124\pi\) | ||||
−0.610729 | + | 0.791840i | \(0.709124\pi\) | |||||||
\(74\) | 19.6113 | 2.27977 | ||||||||
\(75\) | −11.3471 | −1.31025 | ||||||||
\(76\) | 1.98896 | 0.228149 | ||||||||
\(77\) | 0.506261 | 0.0576938 | ||||||||
\(78\) | −29.9800 | −3.39457 | ||||||||
\(79\) | 17.3471 | 1.95170 | 0.975848 | − | 0.218450i | \(-0.0701000\pi\) | ||||
0.975848 | + | 0.218450i | \(0.0701000\pi\) | |||||||
\(80\) | 1.22009 | 0.136411 | ||||||||
\(81\) | −10.2495 | −1.13883 | ||||||||
\(82\) | −3.97892 | −0.439398 | ||||||||
\(83\) | −1.12476 | −0.123458 | −0.0617291 | − | 0.998093i | \(-0.519661\pi\) | ||||
−0.0617291 | + | 0.998093i | \(0.519661\pi\) | |||||||
\(84\) | 3.82517 | 0.417361 | ||||||||
\(85\) | 2.65107 | 0.287549 | ||||||||
\(86\) | 4.78087 | 0.515535 | ||||||||
\(87\) | 14.6354 | 1.56908 | ||||||||
\(88\) | −0.629105 | −0.0670628 | ||||||||
\(89\) | 1.00000 | 0.106000 | ||||||||
\(90\) | 2.10958 | 0.222369 | ||||||||
\(91\) | 4.13684 | 0.433658 | ||||||||
\(92\) | −18.5320 | −1.93209 | ||||||||
\(93\) | 0.938923 | 0.0973618 | ||||||||
\(94\) | −7.23989 | −0.746737 | ||||||||
\(95\) | −0.332970 | −0.0341620 | ||||||||
\(96\) | 18.8869 | 1.92764 | ||||||||
\(97\) | 7.63786 | 0.775507 | 0.387753 | − | 0.921763i | \(-0.373251\pi\) | ||||
0.387753 | + | 0.921763i | \(0.373251\pi\) | |||||||
\(98\) | 13.7196 | 1.38589 | ||||||||
\(99\) | 1.86423 | 0.187362 | ||||||||
\(100\) | −11.6222 | −1.16222 | ||||||||
\(101\) | 9.00487 | 0.896018 | 0.448009 | − | 0.894029i | \(-0.352133\pi\) | ||||
0.448009 | + | 0.894029i | \(0.352133\pi\) | |||||||
\(102\) | 32.4390 | 3.21194 | ||||||||
\(103\) | 3.56269 | 0.351043 | 0.175521 | − | 0.984476i | \(-0.443839\pi\) | ||||
0.175521 | + | 0.984476i | \(0.443839\pi\) | |||||||
\(104\) | −5.14064 | −0.504081 | ||||||||
\(105\) | −0.640369 | −0.0624936 | ||||||||
\(106\) | −2.80733 | −0.272672 | ||||||||
\(107\) | −16.5438 | −1.59935 | −0.799677 | − | 0.600430i | \(-0.794996\pi\) | ||||
−0.799677 | + | 0.600430i | \(0.794996\pi\) | |||||||
\(108\) | −2.81532 | −0.270904 | ||||||||
\(109\) | −14.0770 | −1.34834 | −0.674168 | − | 0.738578i | \(-0.735498\pi\) | ||||
−0.674168 | + | 0.738578i | \(0.735498\pi\) | |||||||
\(110\) | 0.629105 | 0.0599828 | ||||||||
\(111\) | −21.9213 | −2.08068 | ||||||||
\(112\) | −2.06005 | −0.194656 | ||||||||
\(113\) | −5.27389 | −0.496126 | −0.248063 | − | 0.968744i | \(-0.579794\pi\) | ||||
−0.248063 | + | 0.968744i | \(0.579794\pi\) | |||||||
\(114\) | −4.07429 | −0.381592 | ||||||||
\(115\) | 3.10242 | 0.289302 | ||||||||
\(116\) | 14.9904 | 1.39182 | ||||||||
\(117\) | 15.2333 | 1.40832 | ||||||||
\(118\) | −7.41010 | −0.682155 | ||||||||
\(119\) | −4.47615 | −0.410328 | ||||||||
\(120\) | 0.795753 | 0.0726420 | ||||||||
\(121\) | −10.4441 | −0.949460 | ||||||||
\(122\) | −1.25439 | −0.113567 | ||||||||
\(123\) | 4.44759 | 0.401026 | ||||||||
\(124\) | 0.961693 | 0.0863626 | ||||||||
\(125\) | 3.95637 | 0.353868 | ||||||||
\(126\) | −3.56188 | −0.317318 | ||||||||
\(127\) | 0.193928 | 0.0172084 | 0.00860418 | − | 0.999963i | \(-0.497261\pi\) | ||||
0.00860418 | + | 0.999963i | \(0.497261\pi\) | |||||||
\(128\) | 6.61348 | 0.584555 | ||||||||
\(129\) | −5.34401 | −0.470514 | ||||||||
\(130\) | 5.14064 | 0.450864 | ||||||||
\(131\) | 16.6694 | 1.45642 | 0.728208 | − | 0.685356i | \(-0.240353\pi\) | ||||
0.728208 | + | 0.685356i | \(0.240353\pi\) | |||||||
\(132\) | 4.20053 | 0.365609 | ||||||||
\(133\) | 0.562197 | 0.0487487 | ||||||||
\(134\) | −21.8975 | −1.89165 | ||||||||
\(135\) | 0.471310 | 0.0405639 | ||||||||
\(136\) | 5.56228 | 0.476962 | ||||||||
\(137\) | −13.6911 | −1.16971 | −0.584853 | − | 0.811139i | \(-0.698848\pi\) | ||||
−0.584853 | + | 0.811139i | \(0.698848\pi\) | |||||||
\(138\) | 37.9619 | 3.23153 | ||||||||
\(139\) | −2.19626 | −0.186284 | −0.0931420 | − | 0.995653i | \(-0.529691\pi\) | ||||
−0.0931420 | + | 0.995653i | \(0.529691\pi\) | |||||||
\(140\) | −0.655898 | −0.0554335 | ||||||||
\(141\) | 8.09267 | 0.681526 | ||||||||
\(142\) | −26.6339 | −2.23506 | ||||||||
\(143\) | 4.54278 | 0.379886 | ||||||||
\(144\) | −7.58582 | −0.632152 | ||||||||
\(145\) | −2.50952 | −0.208405 | ||||||||
\(146\) | 21.8964 | 1.81216 | ||||||||
\(147\) | −15.3356 | −1.26486 | ||||||||
\(148\) | −22.4529 | −1.84562 | ||||||||
\(149\) | 6.59353 | 0.540163 | 0.270081 | − | 0.962838i | \(-0.412949\pi\) | ||||
0.270081 | + | 0.962838i | \(0.412949\pi\) | |||||||
\(150\) | 23.8076 | 1.94388 | ||||||||
\(151\) | 3.18418 | 0.259125 | 0.129562 | − | 0.991571i | \(-0.458643\pi\) | ||||
0.129562 | + | 0.991571i | \(0.458643\pi\) | |||||||
\(152\) | −0.698614 | −0.0566651 | ||||||||
\(153\) | −16.4828 | −1.33255 | ||||||||
\(154\) | −1.06220 | −0.0855946 | ||||||||
\(155\) | −0.160996 | −0.0129315 | ||||||||
\(156\) | 34.3240 | 2.74812 | ||||||||
\(157\) | 10.4063 | 0.830510 | 0.415255 | − | 0.909705i | \(-0.363692\pi\) | ||||
0.415255 | + | 0.909705i | \(0.363692\pi\) | |||||||
\(158\) | −36.3963 | −2.89554 | ||||||||
\(159\) | 3.13800 | 0.248860 | ||||||||
\(160\) | −3.23852 | −0.256027 | ||||||||
\(161\) | −5.23823 | −0.412830 | ||||||||
\(162\) | 21.5047 | 1.68957 | ||||||||
\(163\) | 10.6512 | 0.834266 | 0.417133 | − | 0.908845i | \(-0.363035\pi\) | ||||
0.417133 | + | 0.908845i | \(0.363035\pi\) | |||||||
\(164\) | 4.55545 | 0.355721 | ||||||||
\(165\) | −0.703207 | −0.0547446 | ||||||||
\(166\) | 2.35989 | 0.183163 | ||||||||
\(167\) | −1.85225 | −0.143331 | −0.0716656 | − | 0.997429i | \(-0.522831\pi\) | ||||
−0.0716656 | + | 0.997429i | \(0.522831\pi\) | |||||||
\(168\) | −1.34358 | −0.103659 | ||||||||
\(169\) | 24.1206 | 1.85543 | ||||||||
\(170\) | −5.56228 | −0.426607 | ||||||||
\(171\) | 2.07021 | 0.158313 | ||||||||
\(172\) | −5.47361 | −0.417359 | ||||||||
\(173\) | 15.1853 | 1.15452 | 0.577260 | − | 0.816560i | \(-0.304122\pi\) | ||||
0.577260 | + | 0.816560i | \(0.304122\pi\) | |||||||
\(174\) | −30.7070 | −2.32789 | ||||||||
\(175\) | −3.28513 | −0.248332 | ||||||||
\(176\) | −2.26219 | −0.170519 | ||||||||
\(177\) | 8.28293 | 0.622583 | ||||||||
\(178\) | −2.09813 | −0.157261 | ||||||||
\(179\) | 17.9782 | 1.34375 | 0.671876 | − | 0.740664i | \(-0.265489\pi\) | ||||
0.671876 | + | 0.740664i | \(0.265489\pi\) | |||||||
\(180\) | −2.41525 | −0.180022 | ||||||||
\(181\) | −18.3834 | −1.36643 | −0.683214 | − | 0.730218i | \(-0.739419\pi\) | ||||
−0.683214 | + | 0.730218i | \(0.739419\pi\) | |||||||
\(182\) | −8.67961 | −0.643376 | ||||||||
\(183\) | 1.40214 | 0.103649 | ||||||||
\(184\) | 6.50928 | 0.479870 | ||||||||
\(185\) | 3.75883 | 0.276354 | ||||||||
\(186\) | −1.96998 | −0.144446 | ||||||||
\(187\) | −4.91538 | −0.359448 | ||||||||
\(188\) | 8.28893 | 0.604532 | ||||||||
\(189\) | −0.795775 | −0.0578841 | ||||||||
\(190\) | 0.698614 | 0.0506828 | ||||||||
\(191\) | 6.13884 | 0.444191 | 0.222096 | − | 0.975025i | \(-0.428710\pi\) | ||||
0.222096 | + | 0.975025i | \(0.428710\pi\) | |||||||
\(192\) | −25.3961 | −1.83280 | ||||||||
\(193\) | 8.69486 | 0.625870 | 0.312935 | − | 0.949775i | \(-0.398688\pi\) | ||||
0.312935 | + | 0.949775i | \(0.398688\pi\) | |||||||
\(194\) | −16.0252 | −1.15054 | ||||||||
\(195\) | −5.74615 | −0.411490 | ||||||||
\(196\) | −15.7075 | −1.12197 | ||||||||
\(197\) | −23.6990 | −1.68848 | −0.844241 | − | 0.535963i | \(-0.819949\pi\) | ||||
−0.844241 | + | 0.535963i | \(0.819949\pi\) | |||||||
\(198\) | −3.91140 | −0.277971 | ||||||||
\(199\) | −4.36867 | −0.309687 | −0.154843 | − | 0.987939i | \(-0.549487\pi\) | ||||
−0.154843 | + | 0.987939i | \(0.549487\pi\) | |||||||
\(200\) | 4.08226 | 0.288659 | ||||||||
\(201\) | 24.4768 | 1.72646 | ||||||||
\(202\) | −18.8934 | −1.32933 | ||||||||
\(203\) | 4.23716 | 0.297390 | ||||||||
\(204\) | −37.1393 | −2.60027 | ||||||||
\(205\) | −0.762624 | −0.0532640 | ||||||||
\(206\) | −7.47499 | −0.520807 | ||||||||
\(207\) | −19.2890 | −1.34068 | ||||||||
\(208\) | −18.4852 | −1.28172 | ||||||||
\(209\) | 0.617365 | 0.0427040 | ||||||||
\(210\) | 1.34358 | 0.0927155 | ||||||||
\(211\) | −16.1958 | −1.11497 | −0.557483 | − | 0.830188i | \(-0.688233\pi\) | ||||
−0.557483 | + | 0.830188i | \(0.688233\pi\) | |||||||
\(212\) | 3.21410 | 0.220745 | ||||||||
\(213\) | 29.7711 | 2.03988 | ||||||||
\(214\) | 34.7111 | 2.37280 | ||||||||
\(215\) | 0.916331 | 0.0624933 | ||||||||
\(216\) | 0.988868 | 0.0672840 | ||||||||
\(217\) | 0.271831 | 0.0184531 | ||||||||
\(218\) | 29.5354 | 2.00039 | ||||||||
\(219\) | −24.4755 | −1.65390 | ||||||||
\(220\) | −0.720260 | −0.0485599 | ||||||||
\(221\) | −40.1653 | −2.70181 | ||||||||
\(222\) | 45.9937 | 3.08690 | ||||||||
\(223\) | 16.0452 | 1.07447 | 0.537234 | − | 0.843433i | \(-0.319469\pi\) | ||||
0.537234 | + | 0.843433i | \(0.319469\pi\) | |||||||
\(224\) | 5.46802 | 0.365347 | ||||||||
\(225\) | −12.0970 | −0.806467 | ||||||||
\(226\) | 11.0653 | 0.736053 | ||||||||
\(227\) | 0.986788 | 0.0654954 | 0.0327477 | − | 0.999464i | \(-0.489574\pi\) | ||||
0.0327477 | + | 0.999464i | \(0.489574\pi\) | |||||||
\(228\) | 4.66464 | 0.308923 | ||||||||
\(229\) | 1.64149 | 0.108473 | 0.0542364 | − | 0.998528i | \(-0.482728\pi\) | ||||
0.0542364 | + | 0.998528i | \(0.482728\pi\) | |||||||
\(230\) | −6.50928 | −0.429209 | ||||||||
\(231\) | 1.18732 | 0.0781197 | ||||||||
\(232\) | −5.26530 | −0.345684 | ||||||||
\(233\) | 18.6930 | 1.22462 | 0.612311 | − | 0.790617i | \(-0.290240\pi\) | ||||
0.612311 | + | 0.790617i | \(0.290240\pi\) | |||||||
\(234\) | −31.9614 | −2.08938 | ||||||||
\(235\) | −1.38764 | −0.0905197 | ||||||||
\(236\) | 8.48380 | 0.552248 | ||||||||
\(237\) | 40.6834 | 2.64267 | ||||||||
\(238\) | 9.39153 | 0.608763 | ||||||||
\(239\) | −10.2061 | −0.660178 | −0.330089 | − | 0.943950i | \(-0.607079\pi\) | ||||
−0.330089 | + | 0.943950i | \(0.607079\pi\) | |||||||
\(240\) | 2.86144 | 0.184705 | ||||||||
\(241\) | 14.0238 | 0.903355 | 0.451677 | − | 0.892181i | \(-0.350826\pi\) | ||||
0.451677 | + | 0.892181i | \(0.350826\pi\) | |||||||
\(242\) | 21.9130 | 1.40862 | ||||||||
\(243\) | −20.5217 | −1.31647 | ||||||||
\(244\) | 1.43614 | 0.0919397 | ||||||||
\(245\) | 2.62958 | 0.167998 | ||||||||
\(246\) | −9.33162 | −0.594962 | ||||||||
\(247\) | 5.04470 | 0.320987 | ||||||||
\(248\) | −0.337790 | −0.0214497 | ||||||||
\(249\) | −2.63786 | −0.167167 | ||||||||
\(250\) | −8.30096 | −0.524999 | ||||||||
\(251\) | −18.7723 | −1.18490 | −0.592448 | − | 0.805609i | \(-0.701838\pi\) | ||||
−0.592448 | + | 0.805609i | \(0.701838\pi\) | |||||||
\(252\) | 4.07799 | 0.256889 | ||||||||
\(253\) | −5.75224 | −0.361640 | ||||||||
\(254\) | −0.406886 | −0.0255303 | ||||||||
\(255\) | 6.21746 | 0.389352 | ||||||||
\(256\) | 7.78138 | 0.486336 | ||||||||
\(257\) | −3.94845 | −0.246298 | −0.123149 | − | 0.992388i | \(-0.539299\pi\) | ||||
−0.123149 | + | 0.992388i | \(0.539299\pi\) | |||||||
\(258\) | 11.2124 | 0.698054 | ||||||||
\(259\) | −6.34652 | −0.394354 | ||||||||
\(260\) | −5.88550 | −0.365003 | ||||||||
\(261\) | 15.6027 | 0.965785 | ||||||||
\(262\) | −34.9746 | −2.16074 | ||||||||
\(263\) | −6.91803 | −0.426584 | −0.213292 | − | 0.976988i | \(-0.568419\pi\) | ||||
−0.213292 | + | 0.976988i | \(0.568419\pi\) | |||||||
\(264\) | −1.47542 | −0.0908057 | ||||||||
\(265\) | −0.538070 | −0.0330534 | ||||||||
\(266\) | −1.17956 | −0.0723236 | ||||||||
\(267\) | 2.34526 | 0.143528 | ||||||||
\(268\) | 25.0704 | 1.53142 | ||||||||
\(269\) | −21.1692 | −1.29071 | −0.645354 | − | 0.763884i | \(-0.723290\pi\) | ||||
−0.645354 | + | 0.763884i | \(0.723290\pi\) | |||||||
\(270\) | −0.988868 | −0.0601806 | ||||||||
\(271\) | 2.36402 | 0.143604 | 0.0718019 | − | 0.997419i | \(-0.477125\pi\) | ||||
0.0718019 | + | 0.997419i | \(0.477125\pi\) | |||||||
\(272\) | 20.0014 | 1.21276 | ||||||||
\(273\) | 9.70198 | 0.587191 | ||||||||
\(274\) | 28.7256 | 1.73538 | ||||||||
\(275\) | −3.60749 | −0.217540 | ||||||||
\(276\) | −43.4624 | −2.61613 | ||||||||
\(277\) | 26.2166 | 1.57520 | 0.787600 | − | 0.616187i | \(-0.211323\pi\) | ||||
0.787600 | + | 0.616187i | \(0.211323\pi\) | |||||||
\(278\) | 4.60802 | 0.276371 | ||||||||
\(279\) | 1.00098 | 0.0599270 | ||||||||
\(280\) | 0.230381 | 0.0137679 | ||||||||
\(281\) | 13.3303 | 0.795220 | 0.397610 | − | 0.917555i | \(-0.369840\pi\) | ||||
0.397610 | + | 0.917555i | \(0.369840\pi\) | |||||||
\(282\) | −16.9795 | −1.01111 | ||||||||
\(283\) | −7.39449 | −0.439557 | −0.219778 | − | 0.975550i | \(-0.570533\pi\) | ||||
−0.219778 | + | 0.975550i | \(0.570533\pi\) | |||||||
\(284\) | 30.4930 | 1.80943 | ||||||||
\(285\) | −0.780903 | −0.0462567 | ||||||||
\(286\) | −9.53133 | −0.563599 | ||||||||
\(287\) | 1.28764 | 0.0760069 | ||||||||
\(288\) | 20.1352 | 1.18648 | ||||||||
\(289\) | 26.4598 | 1.55646 | ||||||||
\(290\) | 5.26530 | 0.309189 | ||||||||
\(291\) | 17.9128 | 1.05007 | ||||||||
\(292\) | −25.0691 | −1.46706 | ||||||||
\(293\) | 19.3032 | 1.12771 | 0.563853 | − | 0.825875i | \(-0.309319\pi\) | ||||
0.563853 | + | 0.825875i | \(0.309319\pi\) | |||||||
\(294\) | 32.1761 | 1.87655 | ||||||||
\(295\) | −1.42027 | −0.0826910 | ||||||||
\(296\) | 7.88650 | 0.458393 | ||||||||
\(297\) | −0.873862 | −0.0507066 | ||||||||
\(298\) | −13.8341 | −0.801386 | ||||||||
\(299\) | −47.0036 | −2.71829 | ||||||||
\(300\) | −27.2572 | −1.57370 | ||||||||
\(301\) | −1.54716 | −0.0891770 | ||||||||
\(302\) | −6.68081 | −0.384437 | ||||||||
\(303\) | 21.1188 | 1.21324 | ||||||||
\(304\) | −2.51214 | −0.144081 | ||||||||
\(305\) | −0.240423 | −0.0137666 | ||||||||
\(306\) | 34.5830 | 1.97698 | ||||||||
\(307\) | 24.8020 | 1.41552 | 0.707761 | − | 0.706452i | \(-0.249705\pi\) | ||||
0.707761 | + | 0.706452i | \(0.249705\pi\) | |||||||
\(308\) | 1.21611 | 0.0692943 | ||||||||
\(309\) | 8.35546 | 0.475326 | ||||||||
\(310\) | 0.337790 | 0.0191852 | ||||||||
\(311\) | 13.5042 | 0.765750 | 0.382875 | − | 0.923800i | \(-0.374934\pi\) | ||||
0.382875 | + | 0.923800i | \(0.374934\pi\) | |||||||
\(312\) | −12.0562 | −0.682545 | ||||||||
\(313\) | −8.16150 | −0.461315 | −0.230658 | − | 0.973035i | \(-0.574088\pi\) | ||||
−0.230658 | + | 0.973035i | \(0.574088\pi\) | |||||||
\(314\) | −21.8337 | −1.23214 | ||||||||
\(315\) | −0.682692 | −0.0384653 | ||||||||
\(316\) | 41.6701 | 2.34412 | ||||||||
\(317\) | −11.9353 | −0.670353 | −0.335176 | − | 0.942155i | \(-0.608796\pi\) | ||||
−0.335176 | + | 0.942155i | \(0.608796\pi\) | |||||||
\(318\) | −6.58393 | −0.369208 | ||||||||
\(319\) | 4.65294 | 0.260515 | ||||||||
\(320\) | 4.35464 | 0.243432 | ||||||||
\(321\) | −38.7997 | −2.16559 | ||||||||
\(322\) | 10.9905 | 0.612475 | ||||||||
\(323\) | −5.45848 | −0.303718 | ||||||||
\(324\) | −24.6206 | −1.36781 | ||||||||
\(325\) | −29.4781 | −1.63515 | ||||||||
\(326\) | −22.3476 | −1.23772 | ||||||||
\(327\) | −33.0144 | −1.82570 | ||||||||
\(328\) | −1.60008 | −0.0883498 | ||||||||
\(329\) | 2.34294 | 0.129170 | ||||||||
\(330\) | 1.47542 | 0.0812190 | ||||||||
\(331\) | 22.0853 | 1.21392 | 0.606960 | − | 0.794732i | \(-0.292389\pi\) | ||||
0.606960 | + | 0.794732i | \(0.292389\pi\) | |||||||
\(332\) | −2.70183 | −0.148282 | ||||||||
\(333\) | −23.3701 | −1.28068 | ||||||||
\(334\) | 3.88625 | 0.212646 | ||||||||
\(335\) | −4.19701 | −0.229307 | ||||||||
\(336\) | −4.83135 | −0.263572 | ||||||||
\(337\) | 11.1800 | 0.609016 | 0.304508 | − | 0.952510i | \(-0.401508\pi\) | ||||
0.304508 | + | 0.952510i | \(0.401508\pi\) | |||||||
\(338\) | −50.6082 | −2.75272 | ||||||||
\(339\) | −12.3687 | −0.671774 | ||||||||
\(340\) | 6.36824 | 0.345366 | ||||||||
\(341\) | 0.298505 | 0.0161650 | ||||||||
\(342\) | −4.34357 | −0.234873 | ||||||||
\(343\) | −9.19278 | −0.496363 | ||||||||
\(344\) | 1.92258 | 0.103659 | ||||||||
\(345\) | 7.27600 | 0.391727 | ||||||||
\(346\) | −31.8608 | −1.71285 | ||||||||
\(347\) | −9.49198 | −0.509556 | −0.254778 | − | 0.967000i | \(-0.582002\pi\) | ||||
−0.254778 | + | 0.967000i | \(0.582002\pi\) | |||||||
\(348\) | 35.1564 | 1.88458 | ||||||||
\(349\) | −24.2009 | −1.29545 | −0.647723 | − | 0.761876i | \(-0.724278\pi\) | ||||
−0.647723 | + | 0.761876i | \(0.724278\pi\) | |||||||
\(350\) | 6.89262 | 0.368426 | ||||||||
\(351\) | −7.14064 | −0.381139 | ||||||||
\(352\) | 6.00458 | 0.320045 | ||||||||
\(353\) | −1.04797 | −0.0557776 | −0.0278888 | − | 0.999611i | \(-0.508878\pi\) | ||||
−0.0278888 | + | 0.999611i | \(0.508878\pi\) | |||||||
\(354\) | −17.3786 | −0.923665 | ||||||||
\(355\) | −5.10481 | −0.270935 | ||||||||
\(356\) | 2.40214 | 0.127313 | ||||||||
\(357\) | −10.4978 | −0.555600 | ||||||||
\(358\) | −37.7205 | −1.99359 | ||||||||
\(359\) | 30.8654 | 1.62901 | 0.814507 | − | 0.580154i | \(-0.197008\pi\) | ||||
0.814507 | + | 0.580154i | \(0.197008\pi\) | |||||||
\(360\) | 0.848346 | 0.0447118 | ||||||||
\(361\) | −18.3144 | −0.963917 | ||||||||
\(362\) | 38.5708 | 2.02723 | ||||||||
\(363\) | −24.4941 | −1.28561 | ||||||||
\(364\) | 9.93726 | 0.520854 | ||||||||
\(365\) | 4.19679 | 0.219670 | ||||||||
\(366\) | −2.94187 | −0.153774 | ||||||||
\(367\) | −29.8753 | −1.55948 | −0.779740 | − | 0.626104i | \(-0.784649\pi\) | ||||
−0.779740 | + | 0.626104i | \(0.784649\pi\) | |||||||
\(368\) | 23.4067 | 1.22016 | ||||||||
\(369\) | 4.74154 | 0.246835 | ||||||||
\(370\) | −7.88650 | −0.409999 | ||||||||
\(371\) | 0.908494 | 0.0471667 | ||||||||
\(372\) | 2.25542 | 0.116938 | ||||||||
\(373\) | 16.8287 | 0.871355 | 0.435677 | − | 0.900103i | \(-0.356509\pi\) | ||||
0.435677 | + | 0.900103i | \(0.356509\pi\) | |||||||
\(374\) | 10.3131 | 0.533278 | ||||||||
\(375\) | 9.27873 | 0.479152 | ||||||||
\(376\) | −2.91145 | −0.150147 | ||||||||
\(377\) | 38.0208 | 1.95817 | ||||||||
\(378\) | 1.66964 | 0.0858769 | ||||||||
\(379\) | −13.6608 | −0.701707 | −0.350853 | − | 0.936430i | \(-0.614108\pi\) | ||||
−0.350853 | + | 0.936430i | \(0.614108\pi\) | |||||||
\(380\) | −0.799841 | −0.0410310 | ||||||||
\(381\) | 0.454813 | 0.0233008 | ||||||||
\(382\) | −12.8801 | −0.659002 | ||||||||
\(383\) | −25.6318 | −1.30972 | −0.654861 | − | 0.755749i | \(-0.727273\pi\) | ||||
−0.654861 | + | 0.755749i | \(0.727273\pi\) | |||||||
\(384\) | 15.5104 | 0.791510 | ||||||||
\(385\) | −0.203588 | −0.0103758 | ||||||||
\(386\) | −18.2429 | −0.928541 | ||||||||
\(387\) | −5.69720 | −0.289605 | ||||||||
\(388\) | 18.3472 | 0.931438 | ||||||||
\(389\) | 14.5801 | 0.739240 | 0.369620 | − | 0.929183i | \(-0.379488\pi\) | ||||
0.369620 | + | 0.929183i | \(0.379488\pi\) | |||||||
\(390\) | 12.0562 | 0.610487 | ||||||||
\(391\) | 50.8589 | 2.57205 | ||||||||
\(392\) | 5.51720 | 0.278661 | ||||||||
\(393\) | 39.0943 | 1.97205 | ||||||||
\(394\) | 49.7235 | 2.50503 | ||||||||
\(395\) | −6.97595 | −0.350998 | ||||||||
\(396\) | 4.47815 | 0.225035 | ||||||||
\(397\) | −27.9706 | −1.40380 | −0.701902 | − | 0.712274i | \(-0.747665\pi\) | ||||
−0.701902 | + | 0.712274i | \(0.747665\pi\) | |||||||
\(398\) | 9.16603 | 0.459452 | ||||||||
\(399\) | 1.31850 | 0.0660077 | ||||||||
\(400\) | 14.6794 | 0.733968 | ||||||||
\(401\) | −17.9848 | −0.898116 | −0.449058 | − | 0.893503i | \(-0.648240\pi\) | ||||
−0.449058 | + | 0.893503i | \(0.648240\pi\) | |||||||
\(402\) | −51.3554 | −2.56137 | ||||||||
\(403\) | 2.43919 | 0.121505 | ||||||||
\(404\) | 21.6310 | 1.07618 | ||||||||
\(405\) | 4.12172 | 0.204810 | ||||||||
\(406\) | −8.89010 | −0.441208 | ||||||||
\(407\) | −6.96929 | −0.345455 | ||||||||
\(408\) | 13.0450 | 0.645825 | ||||||||
\(409\) | 16.9540 | 0.838323 | 0.419162 | − | 0.907912i | \(-0.362324\pi\) | ||||
0.419162 | + | 0.907912i | \(0.362324\pi\) | |||||||
\(410\) | 1.60008 | 0.0790225 | ||||||||
\(411\) | −32.1092 | −1.58383 | ||||||||
\(412\) | 8.55809 | 0.421627 | ||||||||
\(413\) | 2.39802 | 0.117999 | ||||||||
\(414\) | 40.4708 | 1.98903 | ||||||||
\(415\) | 0.452310 | 0.0222030 | ||||||||
\(416\) | 49.0655 | 2.40564 | ||||||||
\(417\) | −5.15080 | −0.252236 | ||||||||
\(418\) | −1.29531 | −0.0633557 | ||||||||
\(419\) | −15.4330 | −0.753952 | −0.376976 | − | 0.926223i | \(-0.623036\pi\) | ||||
−0.376976 | + | 0.926223i | \(0.623036\pi\) | |||||||
\(420\) | −1.53826 | −0.0750592 | ||||||||
\(421\) | −9.47448 | −0.461758 | −0.230879 | − | 0.972982i | \(-0.574160\pi\) | ||||
−0.230879 | + | 0.972982i | \(0.574160\pi\) | |||||||
\(422\) | 33.9809 | 1.65416 | ||||||||
\(423\) | 8.62753 | 0.419485 | ||||||||
\(424\) | −1.12894 | −0.0548261 | ||||||||
\(425\) | 31.8959 | 1.54718 | ||||||||
\(426\) | −62.4635 | −3.02637 | ||||||||
\(427\) | 0.405939 | 0.0196447 | ||||||||
\(428\) | −39.7406 | −1.92094 | ||||||||
\(429\) | 10.6540 | 0.514381 | ||||||||
\(430\) | −1.92258 | −0.0927151 | ||||||||
\(431\) | 19.7151 | 0.949643 | 0.474822 | − | 0.880082i | \(-0.342513\pi\) | ||||
0.474822 | + | 0.880082i | \(0.342513\pi\) | |||||||
\(432\) | 3.55587 | 0.171082 | ||||||||
\(433\) | −20.9780 | −1.00814 | −0.504070 | − | 0.863663i | \(-0.668164\pi\) | ||||
−0.504070 | + | 0.863663i | \(0.668164\pi\) | |||||||
\(434\) | −0.570336 | −0.0273770 | ||||||||
\(435\) | −5.88550 | −0.282188 | ||||||||
\(436\) | −33.8150 | −1.61945 | ||||||||
\(437\) | −6.38780 | −0.305570 | ||||||||
\(438\) | 51.3528 | 2.45373 | ||||||||
\(439\) | 23.2780 | 1.11100 | 0.555500 | − | 0.831516i | \(-0.312527\pi\) | ||||
0.555500 | + | 0.831516i | \(0.312527\pi\) | |||||||
\(440\) | 0.252988 | 0.0120607 | ||||||||
\(441\) | −16.3492 | −0.778533 | ||||||||
\(442\) | 84.2720 | 4.00841 | ||||||||
\(443\) | −8.53700 | −0.405605 | −0.202803 | − | 0.979220i | \(-0.565005\pi\) | ||||
−0.202803 | + | 0.979220i | \(0.565005\pi\) | |||||||
\(444\) | −52.6581 | −2.49904 | ||||||||
\(445\) | −0.402140 | −0.0190633 | ||||||||
\(446\) | −33.6650 | −1.59408 | ||||||||
\(447\) | 15.4636 | 0.731402 | ||||||||
\(448\) | −7.35251 | −0.347373 | ||||||||
\(449\) | 10.7725 | 0.508386 | 0.254193 | − | 0.967154i | \(-0.418190\pi\) | ||||
0.254193 | + | 0.967154i | \(0.418190\pi\) | |||||||
\(450\) | 25.3811 | 1.19647 | ||||||||
\(451\) | 1.41399 | 0.0665823 | ||||||||
\(452\) | −12.6686 | −0.595882 | ||||||||
\(453\) | 7.46774 | 0.350865 | ||||||||
\(454\) | −2.07041 | −0.0971690 | ||||||||
\(455\) | −1.66359 | −0.0779902 | ||||||||
\(456\) | −1.63843 | −0.0767267 | ||||||||
\(457\) | −31.0724 | −1.45351 | −0.726753 | − | 0.686899i | \(-0.758971\pi\) | ||||
−0.726753 | + | 0.686899i | \(0.758971\pi\) | |||||||
\(458\) | −3.44406 | −0.160930 | ||||||||
\(459\) | 7.72632 | 0.360634 | ||||||||
\(460\) | 7.45245 | 0.347472 | ||||||||
\(461\) | −23.8796 | −1.11218 | −0.556092 | − | 0.831121i | \(-0.687700\pi\) | ||||
−0.556092 | + | 0.831121i | \(0.687700\pi\) | |||||||
\(462\) | −2.49114 | −0.115898 | ||||||||
\(463\) | 12.8814 | 0.598649 | 0.299324 | − | 0.954151i | \(-0.403239\pi\) | ||||
0.299324 | + | 0.954151i | \(0.403239\pi\) | |||||||
\(464\) | −18.9335 | −0.878964 | ||||||||
\(465\) | −0.377579 | −0.0175098 | ||||||||
\(466\) | −39.2204 | −1.81685 | ||||||||
\(467\) | 4.98245 | 0.230560 | 0.115280 | − | 0.993333i | \(-0.463223\pi\) | ||||
0.115280 | + | 0.993333i | \(0.463223\pi\) | |||||||
\(468\) | 36.5925 | 1.69149 | ||||||||
\(469\) | 7.08636 | 0.327218 | ||||||||
\(470\) | 2.91145 | 0.134295 | ||||||||
\(471\) | 24.4054 | 1.12454 | ||||||||
\(472\) | −2.97990 | −0.137161 | ||||||||
\(473\) | −1.69898 | −0.0781193 | ||||||||
\(474\) | −85.3591 | −3.92067 | ||||||||
\(475\) | −4.00608 | −0.183811 | ||||||||
\(476\) | −10.7523 | −0.492833 | ||||||||
\(477\) | 3.34540 | 0.153175 | ||||||||
\(478\) | 21.4137 | 0.979440 | ||||||||
\(479\) | −29.9376 | −1.36788 | −0.683941 | − | 0.729537i | \(-0.739736\pi\) | ||||
−0.683941 | + | 0.729537i | \(0.739736\pi\) | |||||||
\(480\) | −7.59518 | −0.346671 | ||||||||
\(481\) | −56.9485 | −2.59663 | ||||||||
\(482\) | −29.4238 | −1.34022 | ||||||||
\(483\) | −12.2850 | −0.558988 | ||||||||
\(484\) | −25.0881 | −1.14037 | ||||||||
\(485\) | −3.07149 | −0.139469 | ||||||||
\(486\) | 43.0571 | 1.95311 | ||||||||
\(487\) | 21.5179 | 0.975069 | 0.487535 | − | 0.873104i | \(-0.337896\pi\) | ||||
0.487535 | + | 0.873104i | \(0.337896\pi\) | |||||||
\(488\) | −0.504439 | −0.0228349 | ||||||||
\(489\) | 24.9799 | 1.12963 | ||||||||
\(490\) | −5.51720 | −0.249242 | ||||||||
\(491\) | 22.2920 | 1.00602 | 0.503012 | − | 0.864279i | \(-0.332225\pi\) | ||||
0.503012 | + | 0.864279i | \(0.332225\pi\) | |||||||
\(492\) | 10.6837 | 0.481660 | ||||||||
\(493\) | −41.1394 | −1.85282 | ||||||||
\(494\) | −10.5844 | −0.476216 | ||||||||
\(495\) | −0.749683 | −0.0336957 | ||||||||
\(496\) | −1.21466 | −0.0545398 | ||||||||
\(497\) | 8.61913 | 0.386621 | ||||||||
\(498\) | 5.53456 | 0.248010 | ||||||||
\(499\) | 35.9789 | 1.61063 | 0.805317 | − | 0.592844i | \(-0.201995\pi\) | ||||
0.805317 | + | 0.592844i | \(0.201995\pi\) | |||||||
\(500\) | 9.50375 | 0.425021 | ||||||||
\(501\) | −4.34401 | −0.194076 | ||||||||
\(502\) | 39.3867 | 1.75791 | ||||||||
\(503\) | −12.7057 | −0.566517 | −0.283259 | − | 0.959044i | \(-0.591415\pi\) | ||||
−0.283259 | + | 0.959044i | \(0.591415\pi\) | |||||||
\(504\) | −1.43237 | −0.0638030 | ||||||||
\(505\) | −3.62122 | −0.161142 | ||||||||
\(506\) | 12.0689 | 0.536530 | ||||||||
\(507\) | 56.5693 | 2.51233 | ||||||||
\(508\) | 0.465843 | 0.0206684 | ||||||||
\(509\) | −22.2317 | −0.985403 | −0.492701 | − | 0.870198i | \(-0.663991\pi\) | ||||
−0.492701 | + | 0.870198i | \(0.663991\pi\) | |||||||
\(510\) | −13.0450 | −0.577643 | ||||||||
\(511\) | −7.08600 | −0.313466 | ||||||||
\(512\) | −29.5533 | −1.30608 | ||||||||
\(513\) | −0.970414 | −0.0428448 | ||||||||
\(514\) | 8.28435 | 0.365407 | ||||||||
\(515\) | −1.43270 | −0.0631324 | ||||||||
\(516\) | −12.8371 | −0.565120 | ||||||||
\(517\) | 2.57285 | 0.113154 | ||||||||
\(518\) | 13.3158 | 0.585063 | ||||||||
\(519\) | 35.6136 | 1.56327 | ||||||||
\(520\) | 2.06726 | 0.0906552 | ||||||||
\(521\) | 15.2116 | 0.666433 | 0.333216 | − | 0.942850i | \(-0.391866\pi\) | ||||
0.333216 | + | 0.942850i | \(0.391866\pi\) | |||||||
\(522\) | −32.7365 | −1.43284 | ||||||||
\(523\) | 23.2905 | 1.01842 | 0.509212 | − | 0.860641i | \(-0.329937\pi\) | ||||
0.509212 | + | 0.860641i | \(0.329937\pi\) | |||||||
\(524\) | 40.0424 | 1.74926 | ||||||||
\(525\) | −7.70449 | −0.336252 | ||||||||
\(526\) | 14.5149 | 0.632880 | ||||||||
\(527\) | −2.63926 | −0.114968 | ||||||||
\(528\) | −5.30544 | −0.230890 | ||||||||
\(529\) | 36.5178 | 1.58773 | ||||||||
\(530\) | 1.12894 | 0.0490380 | ||||||||
\(531\) | 8.83037 | 0.383205 | ||||||||
\(532\) | 1.35048 | 0.0585506 | ||||||||
\(533\) | 11.5542 | 0.500469 | ||||||||
\(534\) | −4.92067 | −0.212938 | ||||||||
\(535\) | 6.65294 | 0.287632 | ||||||||
\(536\) | −8.80586 | −0.380355 | ||||||||
\(537\) | 42.1636 | 1.81949 | ||||||||
\(538\) | 44.4156 | 1.91489 | ||||||||
\(539\) | −4.87555 | −0.210005 | ||||||||
\(540\) | 1.13215 | 0.0487201 | ||||||||
\(541\) | −9.20513 | −0.395760 | −0.197880 | − | 0.980226i | \(-0.563406\pi\) | ||||
−0.197880 | + | 0.980226i | \(0.563406\pi\) | |||||||
\(542\) | −4.96001 | −0.213051 | ||||||||
\(543\) | −43.1140 | −1.85020 | ||||||||
\(544\) | −53.0900 | −2.27621 | ||||||||
\(545\) | 5.66094 | 0.242488 | ||||||||
\(546\) | −20.3560 | −0.871156 | ||||||||
\(547\) | −25.6044 | −1.09477 | −0.547383 | − | 0.836882i | \(-0.684376\pi\) | ||||
−0.547383 | + | 0.836882i | \(0.684376\pi\) | |||||||
\(548\) | −32.8879 | −1.40490 | ||||||||
\(549\) | 1.49481 | 0.0637969 | ||||||||
\(550\) | 7.56897 | 0.322742 | ||||||||
\(551\) | 5.16704 | 0.220123 | ||||||||
\(552\) | 15.2660 | 0.649763 | ||||||||
\(553\) | 11.7784 | 0.500869 | ||||||||
\(554\) | −55.0057 | −2.33697 | ||||||||
\(555\) | 8.81544 | 0.374195 | ||||||||
\(556\) | −5.27571 | −0.223740 | ||||||||
\(557\) | −13.0483 | −0.552874 | −0.276437 | − | 0.961032i | \(-0.589154\pi\) | ||||
−0.276437 | + | 0.961032i | \(0.589154\pi\) | |||||||
\(558\) | −2.10018 | −0.0889077 | ||||||||
\(559\) | −13.8830 | −0.587188 | ||||||||
\(560\) | 0.828427 | 0.0350074 | ||||||||
\(561\) | −11.5279 | −0.486707 | ||||||||
\(562\) | −27.9687 | −1.17979 | ||||||||
\(563\) | 38.2429 | 1.61175 | 0.805874 | − | 0.592087i | \(-0.201696\pi\) | ||||
0.805874 | + | 0.592087i | \(0.201696\pi\) | |||||||
\(564\) | 19.4397 | 0.818560 | ||||||||
\(565\) | 2.12084 | 0.0892245 | ||||||||
\(566\) | 15.5146 | 0.652126 | ||||||||
\(567\) | −6.95924 | −0.292261 | ||||||||
\(568\) | −10.7105 | −0.449405 | ||||||||
\(569\) | −23.2615 | −0.975174 | −0.487587 | − | 0.873074i | \(-0.662123\pi\) | ||||
−0.487587 | + | 0.873074i | \(0.662123\pi\) | |||||||
\(570\) | 1.63843 | 0.0686265 | ||||||||
\(571\) | −1.38815 | −0.0580921 | −0.0290461 | − | 0.999578i | \(-0.509247\pi\) | ||||
−0.0290461 | + | 0.999578i | \(0.509247\pi\) | |||||||
\(572\) | 10.9124 | 0.456270 | ||||||||
\(573\) | 14.3972 | 0.601452 | ||||||||
\(574\) | −2.70163 | −0.112764 | ||||||||
\(575\) | 37.3263 | 1.55661 | ||||||||
\(576\) | −27.0745 | −1.12811 | ||||||||
\(577\) | 32.3652 | 1.34738 | 0.673690 | − | 0.739014i | \(-0.264708\pi\) | ||||
0.673690 | + | 0.739014i | \(0.264708\pi\) | |||||||
\(578\) | −55.5160 | −2.30916 | ||||||||
\(579\) | 20.3918 | 0.847453 | ||||||||
\(580\) | −6.02823 | −0.250309 | ||||||||
\(581\) | −0.763695 | −0.0316834 | ||||||||
\(582\) | −37.5833 | −1.55788 | ||||||||
\(583\) | 0.997642 | 0.0413181 | ||||||||
\(584\) | 8.80540 | 0.364370 | ||||||||
\(585\) | −6.12592 | −0.253276 | ||||||||
\(586\) | −40.5006 | −1.67306 | ||||||||
\(587\) | −40.5897 | −1.67532 | −0.837658 | − | 0.546195i | \(-0.816076\pi\) | ||||
−0.837658 | + | 0.546195i | \(0.816076\pi\) | |||||||
\(588\) | −36.8383 | −1.51919 | ||||||||
\(589\) | 0.331487 | 0.0136587 | ||||||||
\(590\) | 2.97990 | 0.122680 | ||||||||
\(591\) | −55.5804 | −2.28627 | ||||||||
\(592\) | 28.3590 | 1.16555 | ||||||||
\(593\) | 5.60774 | 0.230282 | 0.115141 | − | 0.993349i | \(-0.463268\pi\) | ||||
0.115141 | + | 0.993349i | \(0.463268\pi\) | |||||||
\(594\) | 1.83347 | 0.0752284 | ||||||||
\(595\) | 1.80004 | 0.0737944 | ||||||||
\(596\) | 15.8386 | 0.648773 | ||||||||
\(597\) | −10.2457 | −0.419328 | ||||||||
\(598\) | 98.6196 | 4.03285 | ||||||||
\(599\) | −15.2969 | −0.625015 | −0.312508 | − | 0.949915i | \(-0.601169\pi\) | ||||
−0.312508 | + | 0.949915i | \(0.601169\pi\) | |||||||
\(600\) | 9.57398 | 0.390856 | ||||||||
\(601\) | −29.4967 | −1.20319 | −0.601597 | − | 0.798799i | \(-0.705469\pi\) | ||||
−0.601597 | + | 0.798799i | \(0.705469\pi\) | |||||||
\(602\) | 3.24615 | 0.132303 | ||||||||
\(603\) | 26.0945 | 1.06265 | ||||||||
\(604\) | 7.64884 | 0.311227 | ||||||||
\(605\) | 4.19997 | 0.170753 | ||||||||
\(606\) | −44.3100 | −1.79997 | ||||||||
\(607\) | −2.66519 | −0.108177 | −0.0540885 | − | 0.998536i | \(-0.517225\pi\) | ||||
−0.0540885 | + | 0.998536i | \(0.517225\pi\) | |||||||
\(608\) | 6.66802 | 0.270424 | ||||||||
\(609\) | 9.93726 | 0.402678 | ||||||||
\(610\) | 0.504439 | 0.0204241 | ||||||||
\(611\) | 21.0236 | 0.850525 | ||||||||
\(612\) | −39.5939 | −1.60049 | ||||||||
\(613\) | 17.2285 | 0.695853 | 0.347927 | − | 0.937522i | \(-0.386886\pi\) | ||||
0.347927 | + | 0.937522i | \(0.386886\pi\) | |||||||
\(614\) | −52.0377 | −2.10007 | ||||||||
\(615\) | −1.78856 | −0.0721215 | ||||||||
\(616\) | −0.427153 | −0.0172105 | ||||||||
\(617\) | 18.2907 | 0.736355 | 0.368177 | − | 0.929756i | \(-0.379982\pi\) | ||||
0.368177 | + | 0.929756i | \(0.379982\pi\) | |||||||
\(618\) | −17.5308 | −0.705193 | ||||||||
\(619\) | 41.6253 | 1.67306 | 0.836532 | − | 0.547919i | \(-0.184580\pi\) | ||||
0.836532 | + | 0.547919i | \(0.184580\pi\) | |||||||
\(620\) | −0.386735 | −0.0155317 | ||||||||
\(621\) | 9.04176 | 0.362833 | ||||||||
\(622\) | −28.3334 | −1.13607 | ||||||||
\(623\) | 0.678986 | 0.0272030 | ||||||||
\(624\) | −43.3526 | −1.73549 | ||||||||
\(625\) | 22.6004 | 0.904016 | ||||||||
\(626\) | 17.1239 | 0.684408 | ||||||||
\(627\) | 1.44788 | 0.0578229 | ||||||||
\(628\) | 24.9973 | 0.997500 | ||||||||
\(629\) | 61.6196 | 2.45693 | ||||||||
\(630\) | 1.43237 | 0.0570672 | ||||||||
\(631\) | 35.5147 | 1.41382 | 0.706909 | − | 0.707304i | \(-0.250089\pi\) | ||||
0.706909 | + | 0.707304i | \(0.250089\pi\) | |||||||
\(632\) | −14.6364 | −0.582206 | ||||||||
\(633\) | −37.9835 | −1.50971 | ||||||||
\(634\) | 25.0418 | 0.994535 | ||||||||
\(635\) | −0.0779864 | −0.00309479 | ||||||||
\(636\) | 7.53792 | 0.298898 | ||||||||
\(637\) | −39.8398 | −1.57851 | ||||||||
\(638\) | −9.76247 | −0.386500 | ||||||||
\(639\) | 31.7387 | 1.25556 | ||||||||
\(640\) | −2.65955 | −0.105128 | ||||||||
\(641\) | −6.95752 | −0.274805 | −0.137403 | − | 0.990515i | \(-0.543875\pi\) | ||||
−0.137403 | + | 0.990515i | \(0.543875\pi\) | |||||||
\(642\) | 81.4067 | 3.21287 | ||||||||
\(643\) | −27.1280 | −1.06982 | −0.534911 | − | 0.844908i | \(-0.679655\pi\) | ||||
−0.534911 | + | 0.844908i | \(0.679655\pi\) | |||||||
\(644\) | −12.5830 | −0.495838 | ||||||||
\(645\) | 2.14904 | 0.0846184 | ||||||||
\(646\) | 11.4526 | 0.450596 | ||||||||
\(647\) | −42.4343 | −1.66826 | −0.834132 | − | 0.551564i | \(-0.814031\pi\) | ||||
−0.834132 | + | 0.551564i | \(0.814031\pi\) | |||||||
\(648\) | 8.64789 | 0.339721 | ||||||||
\(649\) | 2.63333 | 0.103367 | ||||||||
\(650\) | 61.8487 | 2.42591 | ||||||||
\(651\) | 0.637516 | 0.0249862 | ||||||||
\(652\) | 25.5857 | 1.00201 | ||||||||
\(653\) | 5.57983 | 0.218356 | 0.109178 | − | 0.994022i | \(-0.465178\pi\) | ||||
0.109178 | + | 0.994022i | \(0.465178\pi\) | |||||||
\(654\) | 69.2684 | 2.70861 | ||||||||
\(655\) | −6.70345 | −0.261926 | ||||||||
\(656\) | −5.75373 | −0.224645 | ||||||||
\(657\) | −26.0932 | −1.01799 | ||||||||
\(658\) | −4.91578 | −0.191637 | ||||||||
\(659\) | −19.1324 | −0.745291 | −0.372646 | − | 0.927974i | \(-0.621549\pi\) | ||||
−0.372646 | + | 0.927974i | \(0.621549\pi\) | |||||||
\(660\) | −1.68920 | −0.0657520 | ||||||||
\(661\) | 10.5218 | 0.409252 | 0.204626 | − | 0.978840i | \(-0.434402\pi\) | ||||
0.204626 | + | 0.978840i | \(0.434402\pi\) | |||||||
\(662\) | −46.3379 | −1.80097 | ||||||||
\(663\) | −94.1983 | −3.65836 | ||||||||
\(664\) | 0.949005 | 0.0368285 | ||||||||
\(665\) | −0.226082 | −0.00876709 | ||||||||
\(666\) | 49.0335 | 1.90001 | ||||||||
\(667\) | −48.1435 | −1.86412 | ||||||||
\(668\) | −4.44936 | −0.172151 | ||||||||
\(669\) | 37.6303 | 1.45487 | ||||||||
\(670\) | 8.80586 | 0.340200 | ||||||||
\(671\) | 0.445772 | 0.0172089 | ||||||||
\(672\) | 12.8239 | 0.494695 | ||||||||
\(673\) | −34.9240 | −1.34622 | −0.673111 | − | 0.739542i | \(-0.735042\pi\) | ||||
−0.673111 | + | 0.739542i | \(0.735042\pi\) | |||||||
\(674\) | −23.4572 | −0.903536 | ||||||||
\(675\) | 5.67049 | 0.218257 | ||||||||
\(676\) | 57.9411 | 2.22850 | ||||||||
\(677\) | −19.8302 | −0.762135 | −0.381067 | − | 0.924547i | \(-0.624443\pi\) | ||||
−0.381067 | + | 0.924547i | \(0.624443\pi\) | |||||||
\(678\) | 25.9511 | 0.996644 | ||||||||
\(679\) | 5.18600 | 0.199020 | ||||||||
\(680\) | −2.23682 | −0.0857780 | ||||||||
\(681\) | 2.31428 | 0.0886834 | ||||||||
\(682\) | −0.626302 | −0.0239823 | ||||||||
\(683\) | 5.91731 | 0.226420 | 0.113210 | − | 0.993571i | \(-0.463887\pi\) | ||||
0.113210 | + | 0.993571i | \(0.463887\pi\) | |||||||
\(684\) | 4.97294 | 0.190145 | ||||||||
\(685\) | 5.50573 | 0.210363 | ||||||||
\(686\) | 19.2876 | 0.736405 | ||||||||
\(687\) | 3.84973 | 0.146877 | ||||||||
\(688\) | 6.91339 | 0.263571 | ||||||||
\(689\) | 8.15209 | 0.310570 | ||||||||
\(690\) | −15.2660 | −0.581166 | ||||||||
\(691\) | −34.9975 | −1.33137 | −0.665685 | − | 0.746233i | \(-0.731860\pi\) | ||||
−0.665685 | + | 0.746233i | \(0.731860\pi\) | |||||||
\(692\) | 36.4773 | 1.38666 | ||||||||
\(693\) | 1.26579 | 0.0480833 | ||||||||
\(694\) | 19.9154 | 0.755978 | ||||||||
\(695\) | 0.883202 | 0.0335018 | ||||||||
\(696\) | −12.3485 | −0.468070 | ||||||||
\(697\) | −12.5019 | −0.473544 | ||||||||
\(698\) | 50.7766 | 1.92192 | ||||||||
\(699\) | 43.8401 | 1.65819 | ||||||||
\(700\) | −7.89133 | −0.298264 | ||||||||
\(701\) | 2.61006 | 0.0985807 | 0.0492903 | − | 0.998784i | \(-0.484304\pi\) | ||||
0.0492903 | + | 0.998784i | \(0.484304\pi\) | |||||||
\(702\) | 14.9820 | 0.565458 | ||||||||
\(703\) | −7.73932 | −0.291894 | ||||||||
\(704\) | −8.07399 | −0.304300 | ||||||||
\(705\) | −3.25439 | −0.122567 | ||||||||
\(706\) | 2.19877 | 0.0827517 | ||||||||
\(707\) | 6.11418 | 0.229947 | ||||||||
\(708\) | 19.8968 | 0.747766 | ||||||||
\(709\) | −5.18047 | −0.194557 | −0.0972783 | − | 0.995257i | \(-0.531014\pi\) | ||||
−0.0972783 | + | 0.995257i | \(0.531014\pi\) | |||||||
\(710\) | 10.7105 | 0.401960 | ||||||||
\(711\) | 43.3723 | 1.62659 | ||||||||
\(712\) | −0.843741 | −0.0316205 | ||||||||
\(713\) | −3.08860 | −0.115669 | ||||||||
\(714\) | 22.0256 | 0.824289 | ||||||||
\(715\) | −1.82683 | −0.0683197 | ||||||||
\(716\) | 43.1861 | 1.61394 | ||||||||
\(717\) | −23.9360 | −0.893907 | ||||||||
\(718\) | −64.7595 | −2.41680 | ||||||||
\(719\) | −22.7700 | −0.849177 | −0.424588 | − | 0.905386i | \(-0.639581\pi\) | ||||
−0.424588 | + | 0.905386i | \(0.639581\pi\) | |||||||
\(720\) | 3.05056 | 0.113688 | ||||||||
\(721\) | 2.41902 | 0.0900890 | ||||||||
\(722\) | 38.4260 | 1.43007 | ||||||||
\(723\) | 32.8896 | 1.22318 | ||||||||
\(724\) | −44.1595 | −1.64118 | ||||||||
\(725\) | −30.1929 | −1.12134 | ||||||||
\(726\) | 51.3917 | 1.90733 | ||||||||
\(727\) | −21.9526 | −0.814175 | −0.407088 | − | 0.913389i | \(-0.633456\pi\) | ||||
−0.407088 | + | 0.913389i | \(0.633456\pi\) | |||||||
\(728\) | −3.49042 | −0.129364 | ||||||||
\(729\) | −17.3804 | −0.643719 | ||||||||
\(730\) | −8.80540 | −0.325903 | ||||||||
\(731\) | 15.0217 | 0.555597 | ||||||||
\(732\) | 3.36814 | 0.124490 | ||||||||
\(733\) | −14.0420 | −0.518652 | −0.259326 | − | 0.965790i | \(-0.583500\pi\) | ||||
−0.259326 | + | 0.965790i | \(0.583500\pi\) | |||||||
\(734\) | 62.6823 | 2.31364 | ||||||||
\(735\) | 6.16707 | 0.227476 | ||||||||
\(736\) | −62.1287 | −2.29010 | ||||||||
\(737\) | 7.78173 | 0.286644 | ||||||||
\(738\) | −9.94837 | −0.366204 | ||||||||
\(739\) | −32.5728 | −1.19821 | −0.599106 | − | 0.800670i | \(-0.704477\pi\) | ||||
−0.599106 | + | 0.800670i | \(0.704477\pi\) | |||||||
\(740\) | 9.02923 | 0.331921 | ||||||||
\(741\) | 11.8312 | 0.434629 | ||||||||
\(742\) | −1.90614 | −0.0699765 | ||||||||
\(743\) | 29.7292 | 1.09066 | 0.545330 | − | 0.838221i | \(-0.316404\pi\) | ||||
0.545330 | + | 0.838221i | \(0.316404\pi\) | |||||||
\(744\) | −0.792208 | −0.0290438 | ||||||||
\(745\) | −2.65152 | −0.0971442 | ||||||||
\(746\) | −35.3087 | −1.29274 | ||||||||
\(747\) | −2.81220 | −0.102893 | ||||||||
\(748\) | −11.8074 | −0.431723 | ||||||||
\(749\) | −11.2330 | −0.410446 | ||||||||
\(750\) | −19.4680 | −0.710869 | ||||||||
\(751\) | 38.1761 | 1.39307 | 0.696533 | − | 0.717525i | \(-0.254725\pi\) | ||||
0.696533 | + | 0.717525i | \(0.254725\pi\) | |||||||
\(752\) | −10.4693 | −0.381775 | ||||||||
\(753\) | −44.0260 | −1.60440 | ||||||||
\(754\) | −79.7726 | −2.90515 | ||||||||
\(755\) | −1.28048 | −0.0466016 | ||||||||
\(756\) | −1.91156 | −0.0695228 | ||||||||
\(757\) | −29.0793 | −1.05691 | −0.528453 | − | 0.848962i | \(-0.677228\pi\) | ||||
−0.528453 | + | 0.848962i | \(0.677228\pi\) | |||||||
\(758\) | 28.6620 | 1.04105 | ||||||||
\(759\) | −13.4905 | −0.489675 | ||||||||
\(760\) | 0.280941 | 0.0101908 | ||||||||
\(761\) | −33.0769 | −1.19904 | −0.599519 | − | 0.800361i | \(-0.704641\pi\) | ||||
−0.599519 | + | 0.800361i | \(0.704641\pi\) | |||||||
\(762\) | −0.954257 | −0.0345691 | ||||||||
\(763\) | −9.55812 | −0.346027 | ||||||||
\(764\) | 14.7464 | 0.533505 | ||||||||
\(765\) | 6.62838 | 0.239650 | ||||||||
\(766\) | 53.7787 | 1.94310 | ||||||||
\(767\) | 21.5179 | 0.776966 | ||||||||
\(768\) | 18.2494 | 0.658518 | ||||||||
\(769\) | −12.4613 | −0.449367 | −0.224683 | − | 0.974432i | \(-0.572135\pi\) | ||||
−0.224683 | + | 0.974432i | \(0.572135\pi\) | |||||||
\(770\) | 0.427153 | 0.0153935 | ||||||||
\(771\) | −9.26016 | −0.333497 | ||||||||
\(772\) | 20.8863 | 0.751714 | ||||||||
\(773\) | 3.92483 | 0.141166 | 0.0705831 | − | 0.997506i | \(-0.477514\pi\) | ||||
0.0705831 | + | 0.997506i | \(0.477514\pi\) | |||||||
\(774\) | 11.9535 | 0.429658 | ||||||||
\(775\) | −1.93700 | −0.0695791 | ||||||||
\(776\) | −6.44437 | −0.231340 | ||||||||
\(777\) | −14.8843 | −0.533970 | ||||||||
\(778\) | −30.5909 | −1.09674 | ||||||||
\(779\) | 1.57022 | 0.0562591 | ||||||||
\(780\) | −13.8031 | −0.494229 | ||||||||
\(781\) | 9.46490 | 0.338681 | ||||||||
\(782\) | −106.709 | −3.81589 | ||||||||
\(783\) | −7.31380 | −0.261374 | ||||||||
\(784\) | 19.8393 | 0.708546 | ||||||||
\(785\) | −4.18477 | −0.149361 | ||||||||
\(786\) | −82.0248 | −2.92573 | ||||||||
\(787\) | −22.9047 | −0.816465 | −0.408233 | − | 0.912878i | \(-0.633855\pi\) | ||||
−0.408233 | + | 0.912878i | \(0.633855\pi\) | |||||||
\(788\) | −56.9283 | −2.02799 | ||||||||
\(789\) | −16.2246 | −0.577612 | ||||||||
\(790\) | 14.6364 | 0.520741 | ||||||||
\(791\) | −3.58090 | −0.127322 | ||||||||
\(792\) | −1.57293 | −0.0558916 | ||||||||
\(793\) | 3.64256 | 0.129351 | ||||||||
\(794\) | 58.6858 | 2.08268 | ||||||||
\(795\) | −1.26192 | −0.0447555 | ||||||||
\(796\) | −10.4942 | −0.371956 | ||||||||
\(797\) | 11.5045 | 0.407509 | 0.203755 | − | 0.979022i | \(-0.434686\pi\) | ||||
0.203755 | + | 0.979022i | \(0.434686\pi\) | |||||||
\(798\) | −2.76639 | −0.0979290 | ||||||||
\(799\) | −22.7480 | −0.804767 | ||||||||
\(800\) | −38.9637 | −1.37758 | ||||||||
\(801\) | 2.50027 | 0.0883426 | ||||||||
\(802\) | 37.7343 | 1.33244 | ||||||||
\(803\) | −7.78133 | −0.274597 | ||||||||
\(804\) | 58.7966 | 2.07360 | ||||||||
\(805\) | 2.10650 | 0.0742444 | ||||||||
\(806\) | −5.11773 | −0.180265 | ||||||||
\(807\) | −49.6473 | −1.74767 | ||||||||
\(808\) | −7.59778 | −0.267289 | ||||||||
\(809\) | −11.6004 | −0.407850 | −0.203925 | − | 0.978987i | \(-0.565370\pi\) | ||||
−0.203925 | + | 0.978987i | \(0.565370\pi\) | |||||||
\(810\) | −8.64789 | −0.303856 | ||||||||
\(811\) | −45.9245 | −1.61263 | −0.806313 | − | 0.591489i | \(-0.798540\pi\) | ||||
−0.806313 | + | 0.591489i | \(0.798540\pi\) | |||||||
\(812\) | 10.1783 | 0.357187 | ||||||||
\(813\) | 5.54425 | 0.194445 | ||||||||
\(814\) | 14.6225 | 0.512517 | ||||||||
\(815\) | −4.28327 | −0.150037 | ||||||||
\(816\) | 46.9085 | 1.64213 | ||||||||
\(817\) | −1.88670 | −0.0660073 | ||||||||
\(818\) | −35.5717 | −1.24374 | ||||||||
\(819\) | 10.3432 | 0.361421 | ||||||||
\(820\) | −1.83193 | −0.0639738 | ||||||||
\(821\) | 29.3695 | 1.02500 | 0.512501 | − | 0.858687i | \(-0.328719\pi\) | ||||
0.512501 | + | 0.858687i | \(0.328719\pi\) | |||||||
\(822\) | 67.3692 | 2.34977 | ||||||||
\(823\) | −7.09029 | −0.247152 | −0.123576 | − | 0.992335i | \(-0.539436\pi\) | ||||
−0.123576 | + | 0.992335i | \(0.539436\pi\) | |||||||
\(824\) | −3.00599 | −0.104719 | ||||||||
\(825\) | −8.46052 | −0.294557 | ||||||||
\(826\) | −5.03136 | −0.175063 | ||||||||
\(827\) | 5.07055 | 0.176320 | 0.0881601 | − | 0.996106i | \(-0.471901\pi\) | ||||
0.0881601 | + | 0.996106i | \(0.471901\pi\) | |||||||
\(828\) | −46.3349 | −1.61025 | ||||||||
\(829\) | −5.34123 | −0.185508 | −0.0927542 | − | 0.995689i | \(-0.529567\pi\) | ||||
−0.0927542 | + | 0.995689i | \(0.529567\pi\) | |||||||
\(830\) | −0.949005 | −0.0329404 | ||||||||
\(831\) | 61.4848 | 2.13288 | ||||||||
\(832\) | −65.9754 | −2.28729 | ||||||||
\(833\) | 43.1076 | 1.49359 | ||||||||
\(834\) | 10.8070 | 0.374217 | ||||||||
\(835\) | 0.744862 | 0.0257770 | ||||||||
\(836\) | 1.48300 | 0.0512905 | ||||||||
\(837\) | −0.469210 | −0.0162183 | ||||||||
\(838\) | 32.3804 | 1.11856 | ||||||||
\(839\) | 30.9654 | 1.06904 | 0.534522 | − | 0.845154i | \(-0.320492\pi\) | ||||
0.534522 | + | 0.845154i | \(0.320492\pi\) | |||||||
\(840\) | 0.540305 | 0.0186423 | ||||||||
\(841\) | 9.94288 | 0.342858 | ||||||||
\(842\) | 19.8787 | 0.685064 | ||||||||
\(843\) | 31.2631 | 1.07676 | ||||||||
\(844\) | −38.9046 | −1.33915 | ||||||||
\(845\) | −9.69987 | −0.333686 | ||||||||
\(846\) | −18.1017 | −0.622348 | ||||||||
\(847\) | −7.09137 | −0.243662 | ||||||||
\(848\) | −4.05954 | −0.139405 | ||||||||
\(849\) | −17.3420 | −0.595177 | ||||||||
\(850\) | −66.9217 | −2.29540 | ||||||||
\(851\) | 72.1105 | 2.47192 | ||||||||
\(852\) | 71.5143 | 2.45004 | ||||||||
\(853\) | 21.7707 | 0.745414 | 0.372707 | − | 0.927949i | \(-0.378430\pi\) | ||||
0.372707 | + | 0.927949i | \(0.378430\pi\) | |||||||
\(854\) | −0.851711 | −0.0291450 | ||||||||
\(855\) | −0.832515 | −0.0284714 | ||||||||
\(856\) | 13.9587 | 0.477099 | ||||||||
\(857\) | 43.2636 | 1.47786 | 0.738929 | − | 0.673784i | \(-0.235332\pi\) | ||||
0.738929 | + | 0.673784i | \(0.235332\pi\) | |||||||
\(858\) | −22.3535 | −0.763135 | ||||||||
\(859\) | −25.8029 | −0.880385 | −0.440192 | − | 0.897904i | \(-0.645090\pi\) | ||||
−0.440192 | + | 0.897904i | \(0.645090\pi\) | |||||||
\(860\) | 2.20116 | 0.0750588 | ||||||||
\(861\) | 3.01985 | 0.102916 | ||||||||
\(862\) | −41.3648 | −1.40889 | ||||||||
\(863\) | −7.49398 | −0.255098 | −0.127549 | − | 0.991832i | \(-0.540711\pi\) | ||||
−0.127549 | + | 0.991832i | \(0.540711\pi\) | |||||||
\(864\) | −9.43840 | −0.321101 | ||||||||
\(865\) | −6.10663 | −0.207632 | ||||||||
\(866\) | 44.0146 | 1.49568 | ||||||||
\(867\) | 62.0552 | 2.10750 | ||||||||
\(868\) | 0.652976 | 0.0221635 | ||||||||
\(869\) | 12.9342 | 0.438763 | ||||||||
\(870\) | 12.3485 | 0.418654 | ||||||||
\(871\) | 63.5872 | 2.15457 | ||||||||
\(872\) | 11.8774 | 0.402219 | ||||||||
\(873\) | 19.0967 | 0.646325 | ||||||||
\(874\) | 13.4024 | 0.453344 | ||||||||
\(875\) | 2.68632 | 0.0908141 | ||||||||
\(876\) | −58.7936 | −1.98645 | ||||||||
\(877\) | 27.2811 | 0.921216 | 0.460608 | − | 0.887604i | \(-0.347631\pi\) | ||||
0.460608 | + | 0.887604i | \(0.347631\pi\) | |||||||
\(878\) | −48.8403 | −1.64828 | ||||||||
\(879\) | 45.2711 | 1.52696 | ||||||||
\(880\) | 0.909719 | 0.0306666 | ||||||||
\(881\) | −43.5512 | −1.46728 | −0.733638 | − | 0.679541i | \(-0.762179\pi\) | ||||
−0.733638 | + | 0.679541i | \(0.762179\pi\) | |||||||
\(882\) | 34.3027 | 1.15503 | ||||||||
\(883\) | 3.51915 | 0.118429 | 0.0592145 | − | 0.998245i | \(-0.481140\pi\) | ||||
0.0592145 | + | 0.998245i | \(0.481140\pi\) | |||||||
\(884\) | −96.4827 | −3.24507 | ||||||||
\(885\) | −3.33090 | −0.111967 | ||||||||
\(886\) | 17.9117 | 0.601756 | ||||||||
\(887\) | −21.8519 | −0.733716 | −0.366858 | − | 0.930277i | \(-0.619567\pi\) | ||||
−0.366858 | + | 0.930277i | \(0.619567\pi\) | |||||||
\(888\) | 18.4959 | 0.620683 | ||||||||
\(889\) | 0.131675 | 0.00441623 | ||||||||
\(890\) | 0.843741 | 0.0282823 | ||||||||
\(891\) | −7.64214 | −0.256021 | ||||||||
\(892\) | 38.5429 | 1.29051 | ||||||||
\(893\) | 2.85712 | 0.0956097 | ||||||||
\(894\) | −32.4445 | −1.08511 | ||||||||
\(895\) | −7.22974 | −0.241664 | ||||||||
\(896\) | 4.49046 | 0.150016 | ||||||||
\(897\) | −110.236 | −3.68067 | ||||||||
\(898\) | −22.6021 | −0.754241 | ||||||||
\(899\) | 2.49834 | 0.0833244 | ||||||||
\(900\) | −29.0587 | −0.968623 | ||||||||
\(901\) | −8.82074 | −0.293861 | ||||||||
\(902\) | −2.96674 | −0.0987815 | ||||||||
\(903\) | −3.62851 | −0.120749 | ||||||||
\(904\) | 4.44980 | 0.147998 | ||||||||
\(905\) | 7.39271 | 0.245742 | ||||||||
\(906\) | −15.6683 | −0.520543 | ||||||||
\(907\) | −28.7325 | −0.954045 | −0.477023 | − | 0.878891i | \(-0.658284\pi\) | ||||
−0.477023 | + | 0.878891i | \(0.658284\pi\) | |||||||
\(908\) | 2.37040 | 0.0786646 | ||||||||
\(909\) | 22.5146 | 0.746762 | ||||||||
\(910\) | 3.49042 | 0.115706 | ||||||||
\(911\) | 21.8988 | 0.725540 | 0.362770 | − | 0.931879i | \(-0.381831\pi\) | ||||
0.362770 | + | 0.931879i | \(0.381831\pi\) | |||||||
\(912\) | −5.89164 | −0.195092 | ||||||||
\(913\) | −0.838635 | −0.0277548 | ||||||||
\(914\) | 65.1938 | 2.15642 | ||||||||
\(915\) | −0.563857 | −0.0186405 | ||||||||
\(916\) | 3.94309 | 0.130284 | ||||||||
\(917\) | 11.3183 | 0.373764 | ||||||||
\(918\) | −16.2108 | −0.535037 | ||||||||
\(919\) | −17.1740 | −0.566517 | −0.283258 | − | 0.959044i | \(-0.591415\pi\) | ||||
−0.283258 | + | 0.959044i | \(0.591415\pi\) | |||||||
\(920\) | −2.61764 | −0.0863011 | ||||||||
\(921\) | 58.1672 | 1.91667 | ||||||||
\(922\) | 50.1024 | 1.65004 | ||||||||
\(923\) | 77.3410 | 2.54571 | ||||||||
\(924\) | 2.85210 | 0.0938272 | ||||||||
\(925\) | 45.2237 | 1.48695 | ||||||||
\(926\) | −27.0268 | −0.888155 | ||||||||
\(927\) | 8.90769 | 0.292567 | ||||||||
\(928\) | 50.2554 | 1.64972 | ||||||||
\(929\) | −1.95712 | −0.0642110 | −0.0321055 | − | 0.999484i | \(-0.510221\pi\) | ||||
−0.0321055 | + | 0.999484i | \(0.510221\pi\) | |||||||
\(930\) | 0.792208 | 0.0259775 | ||||||||
\(931\) | −5.41424 | −0.177445 | ||||||||
\(932\) | 44.9033 | 1.47086 | ||||||||
\(933\) | 31.6708 | 1.03686 | ||||||||
\(934\) | −10.4538 | −0.342060 | ||||||||
\(935\) | 1.97667 | 0.0646441 | ||||||||
\(936\) | −12.8530 | −0.420112 | ||||||||
\(937\) | −32.6584 | −1.06690 | −0.533451 | − | 0.845831i | \(-0.679105\pi\) | ||||
−0.533451 | + | 0.845831i | \(0.679105\pi\) | |||||||
\(938\) | −14.8681 | −0.485460 | ||||||||
\(939\) | −19.1409 | −0.624639 | ||||||||
\(940\) | −3.33331 | −0.108721 | ||||||||
\(941\) | 16.2204 | 0.528770 | 0.264385 | − | 0.964417i | \(-0.414831\pi\) | ||||
0.264385 | + | 0.964417i | \(0.414831\pi\) | |||||||
\(942\) | −51.2057 | −1.66837 | ||||||||
\(943\) | −14.6304 | −0.476432 | ||||||||
\(944\) | −10.7154 | −0.348756 | ||||||||
\(945\) | 0.320013 | 0.0104100 | ||||||||
\(946\) | 3.56468 | 0.115898 | ||||||||
\(947\) | 11.5048 | 0.373857 | 0.186929 | − | 0.982374i | \(-0.440147\pi\) | ||||
0.186929 | + | 0.982374i | \(0.440147\pi\) | |||||||
\(948\) | 97.7273 | 3.17404 | ||||||||
\(949\) | −63.5840 | −2.06402 | ||||||||
\(950\) | 8.40526 | 0.272703 | ||||||||
\(951\) | −27.9914 | −0.907684 | ||||||||
\(952\) | 3.77671 | 0.122404 | ||||||||
\(953\) | 39.8366 | 1.29043 | 0.645217 | − | 0.764000i | \(-0.276767\pi\) | ||||
0.645217 | + | 0.764000i | \(0.276767\pi\) | |||||||
\(954\) | −7.01907 | −0.227251 | ||||||||
\(955\) | −2.46868 | −0.0798845 | ||||||||
\(956\) | −24.5165 | −0.792920 | ||||||||
\(957\) | 10.9124 | 0.352747 | ||||||||
\(958\) | 62.8128 | 2.02939 | ||||||||
\(959\) | −9.29604 | −0.300185 | ||||||||
\(960\) | 10.2128 | 0.329616 | ||||||||
\(961\) | −30.8397 | −0.994830 | ||||||||
\(962\) | 119.485 | 3.85236 | ||||||||
\(963\) | −41.3640 | −1.33294 | ||||||||
\(964\) | 33.6872 | 1.08499 | ||||||||
\(965\) | −3.49655 | −0.112558 | ||||||||
\(966\) | 25.7756 | 0.829315 | ||||||||
\(967\) | 32.4694 | 1.04414 | 0.522072 | − | 0.852901i | \(-0.325159\pi\) | ||||
0.522072 | + | 0.852901i | \(0.325159\pi\) | |||||||
\(968\) | 8.81208 | 0.283231 | ||||||||
\(969\) | −12.8016 | −0.411246 | ||||||||
\(970\) | 6.44437 | 0.206916 | ||||||||
\(971\) | −1.97866 | −0.0634981 | −0.0317490 | − | 0.999496i | \(-0.510108\pi\) | ||||
−0.0317490 | + | 0.999496i | \(0.510108\pi\) | |||||||
\(972\) | −49.2960 | −1.58117 | ||||||||
\(973\) | −1.49123 | −0.0478065 | ||||||||
\(974\) | −45.1473 | −1.44661 | ||||||||
\(975\) | −69.1339 | −2.21406 | ||||||||
\(976\) | −1.81391 | −0.0580618 | ||||||||
\(977\) | −51.3643 | −1.64329 | −0.821645 | − | 0.569999i | \(-0.806944\pi\) | ||||
−0.821645 | + | 0.569999i | \(0.806944\pi\) | |||||||
\(978\) | −52.4110 | −1.67592 | ||||||||
\(979\) | 0.745613 | 0.0238299 | ||||||||
\(980\) | 6.31663 | 0.201777 | ||||||||
\(981\) | −35.1964 | −1.12373 | ||||||||
\(982\) | −46.7715 | −1.49254 | ||||||||
\(983\) | −48.3938 | −1.54352 | −0.771761 | − | 0.635913i | \(-0.780624\pi\) | ||||
−0.771761 | + | 0.635913i | \(0.780624\pi\) | |||||||
\(984\) | −3.75262 | −0.119629 | ||||||||
\(985\) | 9.53031 | 0.303661 | ||||||||
\(986\) | 86.3157 | 2.74885 | ||||||||
\(987\) | 5.49481 | 0.174902 | ||||||||
\(988\) | 12.1181 | 0.385528 | ||||||||
\(989\) | 17.5792 | 0.558986 | ||||||||
\(990\) | 1.57293 | 0.0499910 | ||||||||
\(991\) | −0.116520 | −0.00370138 | −0.00185069 | − | 0.999998i | \(-0.500589\pi\) | ||||
−0.00185069 | + | 0.999998i | \(0.500589\pi\) | |||||||
\(992\) | 3.22409 | 0.102365 | ||||||||
\(993\) | 51.7960 | 1.64370 | ||||||||
\(994\) | −18.0840 | −0.573590 | ||||||||
\(995\) | 1.75682 | 0.0556949 | ||||||||
\(996\) | −6.33650 | −0.200780 | ||||||||
\(997\) | −13.0576 | −0.413539 | −0.206770 | − | 0.978390i | \(-0.566295\pi\) | ||||
−0.206770 | + | 0.978390i | \(0.566295\pi\) | |||||||
\(998\) | −75.4882 | −2.38954 | ||||||||
\(999\) | 10.9548 | 0.346594 |
(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 | 89.2.a.c.1.2 | ✓ | 5 | |
3.2 | odd | 2 | 801.2.a.i.1.4 | 5 | |||
4.3 | odd | 2 | 1424.2.a.k.1.1 | 5 | |||
5.4 | even | 2 | 2225.2.a.j.1.4 | 5 | |||
7.6 | odd | 2 | 4361.2.a.i.1.2 | 5 | |||
8.3 | odd | 2 | 5696.2.a.bc.1.5 | 5 | |||
8.5 | even | 2 | 5696.2.a.be.1.1 | 5 | |||
89.88 | even | 2 | 7921.2.a.g.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
89.2.a.c.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial | |
801.2.a.i.1.4 | 5 | 3.2 | odd | 2 | |||
1424.2.a.k.1.1 | 5 | 4.3 | odd | 2 | |||
2225.2.a.j.1.4 | 5 | 5.4 | even | 2 | |||
4361.2.a.i.1.2 | 5 | 7.6 | odd | 2 | |||
5696.2.a.bc.1.5 | 5 | 8.3 | odd | 2 | |||
5696.2.a.be.1.1 | 5 | 8.5 | even | 2 | |||
7921.2.a.g.1.2 | 5 | 89.88 | even | 2 |