Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6043,2,Mod(1,6043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6043, 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("6043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6043 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6043.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: | \(48.2535979415\) |
Analytic rank: | \(1\) |
Dimension: | \(243\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.82300 | −1.99616 | −0.998081 | − | 0.0619204i | \(-0.980278\pi\) | ||||
−0.998081 | + | 0.0619204i | \(0.980278\pi\) | |||||||
\(3\) | 0.597654 | 0.345056 | 0.172528 | − | 0.985005i | \(-0.444807\pi\) | ||||
0.172528 | + | 0.985005i | \(0.444807\pi\) | |||||||
\(4\) | 5.96933 | 2.98466 | ||||||||
\(5\) | −3.72082 | −1.66400 | −0.832000 | − | 0.554775i | \(-0.812804\pi\) | ||||
−0.832000 | + | 0.554775i | \(0.812804\pi\) | |||||||
\(6\) | −1.68718 | −0.688787 | ||||||||
\(7\) | −3.33856 | −1.26186 | −0.630929 | − | 0.775840i | \(-0.717326\pi\) | ||||
−0.630929 | + | 0.775840i | \(0.717326\pi\) | |||||||
\(8\) | −11.2054 | −3.96171 | ||||||||
\(9\) | −2.64281 | −0.880937 | ||||||||
\(10\) | 10.5039 | 3.32162 | ||||||||
\(11\) | −1.73054 | −0.521778 | −0.260889 | − | 0.965369i | \(-0.584016\pi\) | ||||
−0.260889 | + | 0.965369i | \(0.584016\pi\) | |||||||
\(12\) | 3.56759 | 1.02988 | ||||||||
\(13\) | −1.21237 | −0.336252 | −0.168126 | − | 0.985766i | \(-0.553771\pi\) | ||||
−0.168126 | + | 0.985766i | \(0.553771\pi\) | |||||||
\(14\) | 9.42477 | 2.51887 | ||||||||
\(15\) | −2.22376 | −0.574173 | ||||||||
\(16\) | 19.6942 | 4.92355 | ||||||||
\(17\) | −7.55550 | −1.83248 | −0.916239 | − | 0.400631i | \(-0.868791\pi\) | ||||
−0.916239 | + | 0.400631i | \(0.868791\pi\) | |||||||
\(18\) | 7.46065 | 1.75849 | ||||||||
\(19\) | −6.19875 | −1.42209 | −0.711045 | − | 0.703146i | \(-0.751778\pi\) | ||||
−0.711045 | + | 0.703146i | \(0.751778\pi\) | |||||||
\(20\) | −22.2108 | −4.96648 | ||||||||
\(21\) | −1.99531 | −0.435412 | ||||||||
\(22\) | 4.88532 | 1.04155 | ||||||||
\(23\) | 8.01885 | 1.67205 | 0.836023 | − | 0.548695i | \(-0.184875\pi\) | ||||
0.836023 | + | 0.548695i | \(0.184875\pi\) | |||||||
\(24\) | −6.69696 | −1.36701 | ||||||||
\(25\) | 8.84449 | 1.76890 | ||||||||
\(26\) | 3.42253 | 0.671213 | ||||||||
\(27\) | −3.37245 | −0.649028 | ||||||||
\(28\) | −19.9290 | −3.76622 | ||||||||
\(29\) | 6.45469 | 1.19861 | 0.599303 | − | 0.800522i | \(-0.295445\pi\) | ||||
0.599303 | + | 0.800522i | \(0.295445\pi\) | |||||||
\(30\) | 6.27768 | 1.14614 | ||||||||
\(31\) | 4.24692 | 0.762769 | 0.381385 | − | 0.924416i | \(-0.375447\pi\) | ||||
0.381385 | + | 0.924416i | \(0.375447\pi\) | |||||||
\(32\) | −33.1859 | −5.86650 | ||||||||
\(33\) | −1.03426 | −0.180042 | ||||||||
\(34\) | 21.3292 | 3.65792 | ||||||||
\(35\) | 12.4222 | 2.09973 | ||||||||
\(36\) | −15.7758 | −2.62930 | ||||||||
\(37\) | 8.67346 | 1.42591 | 0.712954 | − | 0.701210i | \(-0.247357\pi\) | ||||
0.712954 | + | 0.701210i | \(0.247357\pi\) | |||||||
\(38\) | 17.4991 | 2.83872 | ||||||||
\(39\) | −0.724579 | −0.116026 | ||||||||
\(40\) | 41.6933 | 6.59229 | ||||||||
\(41\) | −2.29649 | −0.358652 | −0.179326 | − | 0.983790i | \(-0.557392\pi\) | ||||
−0.179326 | + | 0.983790i | \(0.557392\pi\) | |||||||
\(42\) | 5.63275 | 0.869152 | ||||||||
\(43\) | 7.95868 | 1.21369 | 0.606844 | − | 0.794821i | \(-0.292435\pi\) | ||||
0.606844 | + | 0.794821i | \(0.292435\pi\) | |||||||
\(44\) | −10.3302 | −1.55733 | ||||||||
\(45\) | 9.83342 | 1.46588 | ||||||||
\(46\) | −22.6372 | −3.33767 | ||||||||
\(47\) | −10.5821 | −1.54356 | −0.771779 | − | 0.635891i | \(-0.780633\pi\) | ||||
−0.771779 | + | 0.635891i | \(0.780633\pi\) | |||||||
\(48\) | 11.7703 | 1.69890 | ||||||||
\(49\) | 4.14601 | 0.592287 | ||||||||
\(50\) | −24.9680 | −3.53101 | ||||||||
\(51\) | −4.51558 | −0.632307 | ||||||||
\(52\) | −7.23705 | −1.00360 | ||||||||
\(53\) | 4.25553 | 0.584542 | 0.292271 | − | 0.956336i | \(-0.405589\pi\) | ||||
0.292271 | + | 0.956336i | \(0.405589\pi\) | |||||||
\(54\) | 9.52042 | 1.29557 | ||||||||
\(55\) | 6.43903 | 0.868238 | ||||||||
\(56\) | 37.4100 | 4.99912 | ||||||||
\(57\) | −3.70471 | −0.490700 | ||||||||
\(58\) | −18.2216 | −2.39261 | ||||||||
\(59\) | −5.23318 | −0.681302 | −0.340651 | − | 0.940190i | \(-0.610648\pi\) | ||||
−0.340651 | + | 0.940190i | \(0.610648\pi\) | |||||||
\(60\) | −13.2744 | −1.71371 | ||||||||
\(61\) | −1.36840 | −0.175205 | −0.0876027 | − | 0.996155i | \(-0.527921\pi\) | ||||
−0.0876027 | + | 0.996155i | \(0.527921\pi\) | |||||||
\(62\) | −11.9891 | −1.52261 | ||||||||
\(63\) | 8.82319 | 1.11162 | ||||||||
\(64\) | 54.2955 | 6.78693 | ||||||||
\(65\) | 4.51102 | 0.559523 | ||||||||
\(66\) | 2.91973 | 0.359394 | ||||||||
\(67\) | 5.26621 | 0.643370 | 0.321685 | − | 0.946847i | \(-0.395751\pi\) | ||||
0.321685 | + | 0.946847i | \(0.395751\pi\) | |||||||
\(68\) | −45.1013 | −5.46933 | ||||||||
\(69\) | 4.79250 | 0.576949 | ||||||||
\(70\) | −35.0678 | −4.19141 | ||||||||
\(71\) | 5.76859 | 0.684606 | 0.342303 | − | 0.939590i | \(-0.388793\pi\) | ||||
0.342303 | + | 0.939590i | \(0.388793\pi\) | |||||||
\(72\) | 29.6138 | 3.49002 | ||||||||
\(73\) | 1.11339 | 0.130312 | 0.0651561 | − | 0.997875i | \(-0.479245\pi\) | ||||
0.0651561 | + | 0.997875i | \(0.479245\pi\) | |||||||
\(74\) | −24.4852 | −2.84634 | ||||||||
\(75\) | 5.28595 | 0.610368 | ||||||||
\(76\) | −37.0023 | −4.24446 | ||||||||
\(77\) | 5.77752 | 0.658410 | ||||||||
\(78\) | 2.04549 | 0.231606 | ||||||||
\(79\) | 3.44428 | 0.387511 | 0.193756 | − | 0.981050i | \(-0.437933\pi\) | ||||
0.193756 | + | 0.981050i | \(0.437933\pi\) | |||||||
\(80\) | −73.2786 | −8.19279 | ||||||||
\(81\) | 5.91287 | 0.656986 | ||||||||
\(82\) | 6.48299 | 0.715927 | ||||||||
\(83\) | 13.3730 | 1.46788 | 0.733939 | − | 0.679215i | \(-0.237680\pi\) | ||||
0.733939 | + | 0.679215i | \(0.237680\pi\) | |||||||
\(84\) | −11.9106 | −1.29956 | ||||||||
\(85\) | 28.1127 | 3.04925 | ||||||||
\(86\) | −22.4674 | −2.42272 | ||||||||
\(87\) | 3.85767 | 0.413586 | ||||||||
\(88\) | 19.3914 | 2.06713 | ||||||||
\(89\) | −3.08598 | −0.327113 | −0.163556 | − | 0.986534i | \(-0.552297\pi\) | ||||
−0.163556 | + | 0.986534i | \(0.552297\pi\) | |||||||
\(90\) | −27.7597 | −2.92613 | ||||||||
\(91\) | 4.04758 | 0.424302 | ||||||||
\(92\) | 47.8671 | 4.99049 | ||||||||
\(93\) | 2.53819 | 0.263198 | ||||||||
\(94\) | 29.8733 | 3.08119 | ||||||||
\(95\) | 23.0644 | 2.36636 | ||||||||
\(96\) | −19.8337 | −2.02427 | ||||||||
\(97\) | 1.27250 | 0.129202 | 0.0646012 | − | 0.997911i | \(-0.479422\pi\) | ||||
0.0646012 | + | 0.997911i | \(0.479422\pi\) | |||||||
\(98\) | −11.7042 | −1.18230 | ||||||||
\(99\) | 4.57349 | 0.459653 | ||||||||
\(100\) | 52.7957 | 5.27957 | ||||||||
\(101\) | −1.77204 | −0.176325 | −0.0881623 | − | 0.996106i | \(-0.528099\pi\) | ||||
−0.0881623 | + | 0.996106i | \(0.528099\pi\) | |||||||
\(102\) | 12.7475 | 1.26219 | ||||||||
\(103\) | 0.372412 | 0.0366949 | 0.0183474 | − | 0.999832i | \(-0.494160\pi\) | ||||
0.0183474 | + | 0.999832i | \(0.494160\pi\) | |||||||
\(104\) | 13.5851 | 1.33213 | ||||||||
\(105\) | 7.42417 | 0.724525 | ||||||||
\(106\) | −12.0134 | −1.16684 | ||||||||
\(107\) | −6.35637 | −0.614493 | −0.307247 | − | 0.951630i | \(-0.599408\pi\) | ||||
−0.307247 | + | 0.951630i | \(0.599408\pi\) | |||||||
\(108\) | −20.1312 | −1.93713 | ||||||||
\(109\) | 15.2256 | 1.45835 | 0.729173 | − | 0.684329i | \(-0.239905\pi\) | ||||
0.729173 | + | 0.684329i | \(0.239905\pi\) | |||||||
\(110\) | −18.1774 | −1.73314 | ||||||||
\(111\) | 5.18373 | 0.492018 | ||||||||
\(112\) | −65.7504 | −6.21283 | ||||||||
\(113\) | −16.6095 | −1.56249 | −0.781245 | − | 0.624224i | \(-0.785415\pi\) | ||||
−0.781245 | + | 0.624224i | \(0.785415\pi\) | |||||||
\(114\) | 10.4584 | 0.979517 | ||||||||
\(115\) | −29.8367 | −2.78228 | ||||||||
\(116\) | 38.5302 | 3.57743 | ||||||||
\(117\) | 3.20407 | 0.296216 | ||||||||
\(118\) | 14.7733 | 1.35999 | ||||||||
\(119\) | 25.2245 | 2.31233 | ||||||||
\(120\) | 24.9182 | 2.27471 | ||||||||
\(121\) | −8.00523 | −0.727748 | ||||||||
\(122\) | 3.86299 | 0.349738 | ||||||||
\(123\) | −1.37251 | −0.123755 | ||||||||
\(124\) | 25.3513 | 2.27661 | ||||||||
\(125\) | −14.3047 | −1.27945 | ||||||||
\(126\) | −24.9079 | −2.21897 | ||||||||
\(127\) | −11.2761 | −1.00059 | −0.500295 | − | 0.865855i | \(-0.666775\pi\) | ||||
−0.500295 | + | 0.865855i | \(0.666775\pi\) | |||||||
\(128\) | −86.9042 | −7.68132 | ||||||||
\(129\) | 4.75654 | 0.418790 | ||||||||
\(130\) | −12.7346 | −1.11690 | ||||||||
\(131\) | 19.3041 | 1.68661 | 0.843303 | − | 0.537439i | \(-0.180608\pi\) | ||||
0.843303 | + | 0.537439i | \(0.180608\pi\) | |||||||
\(132\) | −6.17386 | −0.537366 | ||||||||
\(133\) | 20.6949 | 1.79448 | ||||||||
\(134\) | −14.8665 | −1.28427 | ||||||||
\(135\) | 12.5483 | 1.07998 | ||||||||
\(136\) | 84.6625 | 7.25975 | ||||||||
\(137\) | 3.76816 | 0.321935 | 0.160968 | − | 0.986960i | \(-0.448538\pi\) | ||||
0.160968 | + | 0.986960i | \(0.448538\pi\) | |||||||
\(138\) | −13.5292 | −1.15168 | ||||||||
\(139\) | 1.08513 | 0.0920393 | 0.0460196 | − | 0.998941i | \(-0.485346\pi\) | ||||
0.0460196 | + | 0.998941i | \(0.485346\pi\) | |||||||
\(140\) | 74.1521 | 6.26700 | ||||||||
\(141\) | −6.32444 | −0.532614 | ||||||||
\(142\) | −16.2847 | −1.36658 | ||||||||
\(143\) | 2.09806 | 0.175449 | ||||||||
\(144\) | −52.0480 | −4.33734 | ||||||||
\(145\) | −24.0167 | −1.99448 | ||||||||
\(146\) | −3.14309 | −0.260124 | ||||||||
\(147\) | 2.47788 | 0.204372 | ||||||||
\(148\) | 51.7747 | 4.25586 | ||||||||
\(149\) | 8.21163 | 0.672723 | 0.336361 | − | 0.941733i | \(-0.390804\pi\) | ||||
0.336361 | + | 0.941733i | \(0.390804\pi\) | |||||||
\(150\) | −14.9222 | −1.21839 | ||||||||
\(151\) | −8.21335 | −0.668393 | −0.334197 | − | 0.942503i | \(-0.608465\pi\) | ||||
−0.334197 | + | 0.942503i | \(0.608465\pi\) | |||||||
\(152\) | 69.4595 | 5.63391 | ||||||||
\(153\) | 19.9678 | 1.61430 | ||||||||
\(154\) | −16.3099 | −1.31429 | ||||||||
\(155\) | −15.8020 | −1.26925 | ||||||||
\(156\) | −4.32525 | −0.346297 | ||||||||
\(157\) | −11.5434 | −0.921261 | −0.460630 | − | 0.887592i | \(-0.652377\pi\) | ||||
−0.460630 | + | 0.887592i | \(0.652377\pi\) | |||||||
\(158\) | −9.72319 | −0.773536 | ||||||||
\(159\) | 2.54333 | 0.201699 | ||||||||
\(160\) | 123.479 | 9.76186 | ||||||||
\(161\) | −26.7714 | −2.10988 | ||||||||
\(162\) | −16.6920 | −1.31145 | ||||||||
\(163\) | −22.6897 | −1.77719 | −0.888595 | − | 0.458692i | \(-0.848318\pi\) | ||||
−0.888595 | + | 0.458692i | \(0.848318\pi\) | |||||||
\(164\) | −13.7085 | −1.07045 | ||||||||
\(165\) | 3.84831 | 0.299591 | ||||||||
\(166\) | −37.7520 | −2.93012 | ||||||||
\(167\) | 3.23533 | 0.250357 | 0.125179 | − | 0.992134i | \(-0.460050\pi\) | ||||
0.125179 | + | 0.992134i | \(0.460050\pi\) | |||||||
\(168\) | 22.3582 | 1.72497 | ||||||||
\(169\) | −11.5302 | −0.886935 | ||||||||
\(170\) | −79.3620 | −6.08679 | ||||||||
\(171\) | 16.3821 | 1.25277 | ||||||||
\(172\) | 47.5080 | 3.62245 | ||||||||
\(173\) | −18.1779 | −1.38204 | −0.691022 | − | 0.722834i | \(-0.742839\pi\) | ||||
−0.691022 | + | 0.722834i | \(0.742839\pi\) | |||||||
\(174\) | −10.8902 | −0.825584 | ||||||||
\(175\) | −29.5279 | −2.23210 | ||||||||
\(176\) | −34.0816 | −2.56900 | ||||||||
\(177\) | −3.12763 | −0.235087 | ||||||||
\(178\) | 8.71171 | 0.652970 | ||||||||
\(179\) | 16.1170 | 1.20464 | 0.602320 | − | 0.798255i | \(-0.294243\pi\) | ||||
0.602320 | + | 0.798255i | \(0.294243\pi\) | |||||||
\(180\) | 58.6989 | 4.37516 | ||||||||
\(181\) | 17.3754 | 1.29150 | 0.645750 | − | 0.763549i | \(-0.276545\pi\) | ||||
0.645750 | + | 0.763549i | \(0.276545\pi\) | |||||||
\(182\) | −11.4263 | −0.846976 | ||||||||
\(183\) | −0.817828 | −0.0604556 | ||||||||
\(184\) | −89.8544 | −6.62416 | ||||||||
\(185\) | −32.2724 | −2.37271 | ||||||||
\(186\) | −7.16531 | −0.525386 | ||||||||
\(187\) | 13.0751 | 0.956147 | ||||||||
\(188\) | −63.1680 | −4.60700 | ||||||||
\(189\) | 11.2591 | 0.818982 | ||||||||
\(190\) | −65.1108 | −4.72364 | ||||||||
\(191\) | −5.75282 | −0.416259 | −0.208130 | − | 0.978101i | \(-0.566738\pi\) | ||||
−0.208130 | + | 0.978101i | \(0.566738\pi\) | |||||||
\(192\) | 32.4499 | 2.34187 | ||||||||
\(193\) | −8.77184 | −0.631411 | −0.315705 | − | 0.948857i | \(-0.602241\pi\) | ||||
−0.315705 | + | 0.948857i | \(0.602241\pi\) | |||||||
\(194\) | −3.59226 | −0.257909 | ||||||||
\(195\) | 2.69603 | 0.193067 | ||||||||
\(196\) | 24.7489 | 1.76778 | ||||||||
\(197\) | −13.6434 | −0.972054 | −0.486027 | − | 0.873944i | \(-0.661554\pi\) | ||||
−0.486027 | + | 0.873944i | \(0.661554\pi\) | |||||||
\(198\) | −12.9110 | −0.917542 | ||||||||
\(199\) | −7.47762 | −0.530075 | −0.265037 | − | 0.964238i | \(-0.585384\pi\) | ||||
−0.265037 | + | 0.964238i | \(0.585384\pi\) | |||||||
\(200\) | −99.1061 | −7.00786 | ||||||||
\(201\) | 3.14737 | 0.221998 | ||||||||
\(202\) | 5.00247 | 0.351973 | ||||||||
\(203\) | −21.5494 | −1.51247 | ||||||||
\(204\) | −26.9550 | −1.88722 | ||||||||
\(205\) | 8.54483 | 0.596797 | ||||||||
\(206\) | −1.05132 | −0.0732489 | ||||||||
\(207\) | −21.1923 | −1.47297 | ||||||||
\(208\) | −23.8767 | −1.65555 | ||||||||
\(209\) | 10.7272 | 0.742015 | ||||||||
\(210\) | −20.9584 | −1.44627 | ||||||||
\(211\) | −2.47957 | −0.170701 | −0.0853503 | − | 0.996351i | \(-0.527201\pi\) | ||||
−0.0853503 | + | 0.996351i | \(0.527201\pi\) | |||||||
\(212\) | 25.4026 | 1.74466 | ||||||||
\(213\) | 3.44762 | 0.236227 | ||||||||
\(214\) | 17.9440 | 1.22663 | ||||||||
\(215\) | −29.6128 | −2.01958 | ||||||||
\(216\) | 37.7897 | 2.57126 | ||||||||
\(217\) | −14.1786 | −0.962507 | ||||||||
\(218\) | −42.9818 | −2.91110 | ||||||||
\(219\) | 0.665421 | 0.0449650 | ||||||||
\(220\) | 38.4367 | 2.59140 | ||||||||
\(221\) | 9.16008 | 0.616174 | ||||||||
\(222\) | −14.6337 | −0.982148 | ||||||||
\(223\) | −3.29777 | −0.220835 | −0.110417 | − | 0.993885i | \(-0.535219\pi\) | ||||
−0.110417 | + | 0.993885i | \(0.535219\pi\) | |||||||
\(224\) | 110.793 | 7.40269 | ||||||||
\(225\) | −23.3743 | −1.55829 | ||||||||
\(226\) | 46.8886 | 3.11898 | ||||||||
\(227\) | −4.54764 | −0.301838 | −0.150919 | − | 0.988546i | \(-0.548223\pi\) | ||||
−0.150919 | + | 0.988546i | \(0.548223\pi\) | |||||||
\(228\) | −22.1146 | −1.46458 | ||||||||
\(229\) | 17.3129 | 1.14407 | 0.572034 | − | 0.820230i | \(-0.306154\pi\) | ||||
0.572034 | + | 0.820230i | \(0.306154\pi\) | |||||||
\(230\) | 84.2289 | 5.55389 | ||||||||
\(231\) | 3.45296 | 0.227188 | ||||||||
\(232\) | −72.3274 | −4.74853 | ||||||||
\(233\) | −19.5186 | −1.27871 | −0.639354 | − | 0.768912i | \(-0.720798\pi\) | ||||
−0.639354 | + | 0.768912i | \(0.720798\pi\) | |||||||
\(234\) | −9.04509 | −0.591296 | ||||||||
\(235\) | 39.3741 | 2.56848 | ||||||||
\(236\) | −31.2386 | −2.03346 | ||||||||
\(237\) | 2.05849 | 0.133713 | ||||||||
\(238\) | −71.2089 | −4.61578 | ||||||||
\(239\) | −7.38447 | −0.477661 | −0.238831 | − | 0.971061i | \(-0.576764\pi\) | ||||
−0.238831 | + | 0.971061i | \(0.576764\pi\) | |||||||
\(240\) | −43.7952 | −2.82697 | ||||||||
\(241\) | −6.31482 | −0.406773 | −0.203387 | − | 0.979099i | \(-0.565195\pi\) | ||||
−0.203387 | + | 0.979099i | \(0.565195\pi\) | |||||||
\(242\) | 22.5988 | 1.45270 | ||||||||
\(243\) | 13.6512 | 0.875725 | ||||||||
\(244\) | −8.16841 | −0.522929 | ||||||||
\(245\) | −15.4266 | −0.985567 | ||||||||
\(246\) | 3.87459 | 0.247035 | ||||||||
\(247\) | 7.51519 | 0.478180 | ||||||||
\(248\) | −47.5885 | −3.02187 | ||||||||
\(249\) | 7.99243 | 0.506500 | ||||||||
\(250\) | 40.3820 | 2.55398 | ||||||||
\(251\) | −0.528208 | −0.0333402 | −0.0166701 | − | 0.999861i | \(-0.505307\pi\) | ||||
−0.0166701 | + | 0.999861i | \(0.505307\pi\) | |||||||
\(252\) | 52.6685 | 3.31780 | ||||||||
\(253\) | −13.8769 | −0.872436 | ||||||||
\(254\) | 31.8323 | 1.99734 | ||||||||
\(255\) | 16.8016 | 1.05216 | ||||||||
\(256\) | 136.740 | 8.54622 | ||||||||
\(257\) | 13.1701 | 0.821525 | 0.410763 | − | 0.911742i | \(-0.365262\pi\) | ||||
0.410763 | + | 0.911742i | \(0.365262\pi\) | |||||||
\(258\) | −13.4277 | −0.835972 | ||||||||
\(259\) | −28.9569 | −1.79930 | ||||||||
\(260\) | 26.9277 | 1.66999 | ||||||||
\(261\) | −17.0585 | −1.05590 | ||||||||
\(262\) | −54.4954 | −3.36674 | ||||||||
\(263\) | −15.1334 | −0.933167 | −0.466583 | − | 0.884477i | \(-0.654515\pi\) | ||||
−0.466583 | + | 0.884477i | \(0.654515\pi\) | |||||||
\(264\) | 11.5894 | 0.713276 | ||||||||
\(265\) | −15.8340 | −0.972678 | ||||||||
\(266\) | −58.4217 | −3.58207 | ||||||||
\(267\) | −1.84435 | −0.112872 | ||||||||
\(268\) | 31.4357 | 1.92024 | ||||||||
\(269\) | 15.7393 | 0.959640 | 0.479820 | − | 0.877367i | \(-0.340702\pi\) | ||||
0.479820 | + | 0.877367i | \(0.340702\pi\) | |||||||
\(270\) | −35.4238 | −2.15582 | ||||||||
\(271\) | 13.7742 | 0.836725 | 0.418363 | − | 0.908280i | \(-0.362604\pi\) | ||||
0.418363 | + | 0.908280i | \(0.362604\pi\) | |||||||
\(272\) | −148.800 | −9.02231 | ||||||||
\(273\) | 2.41905 | 0.146408 | ||||||||
\(274\) | −10.6375 | −0.642635 | ||||||||
\(275\) | −15.3058 | −0.922972 | ||||||||
\(276\) | 28.6080 | 1.72200 | ||||||||
\(277\) | 25.3440 | 1.52277 | 0.761386 | − | 0.648299i | \(-0.224519\pi\) | ||||
0.761386 | + | 0.648299i | \(0.224519\pi\) | |||||||
\(278\) | −3.06331 | −0.183725 | ||||||||
\(279\) | −11.2238 | −0.671951 | ||||||||
\(280\) | −139.196 | −8.31854 | ||||||||
\(281\) | 4.04188 | 0.241118 | 0.120559 | − | 0.992706i | \(-0.461531\pi\) | ||||
0.120559 | + | 0.992706i | \(0.461531\pi\) | |||||||
\(282\) | 17.8539 | 1.06318 | ||||||||
\(283\) | −26.5549 | −1.57853 | −0.789263 | − | 0.614055i | \(-0.789537\pi\) | ||||
−0.789263 | + | 0.614055i | \(0.789537\pi\) | |||||||
\(284\) | 34.4346 | 2.04332 | ||||||||
\(285\) | 13.7845 | 0.816526 | ||||||||
\(286\) | −5.92282 | −0.350224 | ||||||||
\(287\) | 7.66698 | 0.452568 | ||||||||
\(288\) | 87.7041 | 5.16801 | ||||||||
\(289\) | 40.0856 | 2.35798 | ||||||||
\(290\) | 67.7992 | 3.98131 | ||||||||
\(291\) | 0.760513 | 0.0445820 | ||||||||
\(292\) | 6.64618 | 0.388938 | ||||||||
\(293\) | −8.96609 | −0.523805 | −0.261902 | − | 0.965094i | \(-0.584350\pi\) | ||||
−0.261902 | + | 0.965094i | \(0.584350\pi\) | |||||||
\(294\) | −6.99506 | −0.407960 | ||||||||
\(295\) | 19.4717 | 1.13369 | ||||||||
\(296\) | −97.1897 | −5.64904 | ||||||||
\(297\) | 5.83616 | 0.338648 | ||||||||
\(298\) | −23.1814 | −1.34286 | ||||||||
\(299\) | −9.72183 | −0.562228 | ||||||||
\(300\) | 31.5535 | 1.82174 | ||||||||
\(301\) | −26.5706 | −1.53150 | ||||||||
\(302\) | 23.1863 | 1.33422 | ||||||||
\(303\) | −1.05907 | −0.0608418 | ||||||||
\(304\) | −122.079 | −7.00173 | ||||||||
\(305\) | 5.09156 | 0.291542 | ||||||||
\(306\) | −56.3690 | −3.22240 | ||||||||
\(307\) | −23.9312 | −1.36583 | −0.682913 | − | 0.730499i | \(-0.739287\pi\) | ||||
−0.682913 | + | 0.730499i | \(0.739287\pi\) | |||||||
\(308\) | 34.4879 | 1.96513 | ||||||||
\(309\) | 0.222574 | 0.0126618 | ||||||||
\(310\) | 44.6091 | 2.53363 | ||||||||
\(311\) | 26.5395 | 1.50492 | 0.752460 | − | 0.658639i | \(-0.228867\pi\) | ||||
0.752460 | + | 0.658639i | \(0.228867\pi\) | |||||||
\(312\) | 8.11921 | 0.459660 | ||||||||
\(313\) | −8.99460 | −0.508405 | −0.254202 | − | 0.967151i | \(-0.581813\pi\) | ||||
−0.254202 | + | 0.967151i | \(0.581813\pi\) | |||||||
\(314\) | 32.5869 | 1.83899 | ||||||||
\(315\) | −32.8295 | −1.84973 | ||||||||
\(316\) | 20.5600 | 1.15659 | ||||||||
\(317\) | 21.1187 | 1.18614 | 0.593071 | − | 0.805150i | \(-0.297915\pi\) | ||||
0.593071 | + | 0.805150i | \(0.297915\pi\) | |||||||
\(318\) | −7.17983 | −0.402625 | ||||||||
\(319\) | −11.1701 | −0.625406 | ||||||||
\(320\) | −202.024 | −11.2935 | ||||||||
\(321\) | −3.79891 | −0.212034 | ||||||||
\(322\) | 75.5757 | 4.21167 | ||||||||
\(323\) | 46.8347 | 2.60595 | ||||||||
\(324\) | 35.2959 | 1.96088 | ||||||||
\(325\) | −10.7228 | −0.594795 | ||||||||
\(326\) | 64.0529 | 3.54756 | ||||||||
\(327\) | 9.09963 | 0.503211 | ||||||||
\(328\) | 25.7331 | 1.42087 | ||||||||
\(329\) | 35.3290 | 1.94775 | ||||||||
\(330\) | −10.8638 | −0.598032 | ||||||||
\(331\) | 18.1325 | 0.996655 | 0.498327 | − | 0.866989i | \(-0.333948\pi\) | ||||
0.498327 | + | 0.866989i | \(0.333948\pi\) | |||||||
\(332\) | 79.8279 | 4.38112 | ||||||||
\(333\) | −22.9223 | −1.25613 | ||||||||
\(334\) | −9.13334 | −0.499754 | ||||||||
\(335\) | −19.5946 | −1.07057 | ||||||||
\(336\) | −39.2960 | −2.14377 | ||||||||
\(337\) | −0.844951 | −0.0460274 | −0.0230137 | − | 0.999735i | \(-0.507326\pi\) | ||||
−0.0230137 | + | 0.999735i | \(0.507326\pi\) | |||||||
\(338\) | 32.5496 | 1.77047 | ||||||||
\(339\) | −9.92673 | −0.539146 | ||||||||
\(340\) | 167.814 | 9.10097 | ||||||||
\(341\) | −7.34947 | −0.397996 | ||||||||
\(342\) | −46.2467 | −2.50073 | ||||||||
\(343\) | 9.52822 | 0.514476 | ||||||||
\(344\) | −89.1803 | −4.80828 | ||||||||
\(345\) | −17.8320 | −0.960043 | ||||||||
\(346\) | 51.3163 | 2.75878 | ||||||||
\(347\) | −10.0944 | −0.541897 | −0.270949 | − | 0.962594i | \(-0.587337\pi\) | ||||
−0.270949 | + | 0.962594i | \(0.587337\pi\) | |||||||
\(348\) | 23.0277 | 1.23441 | ||||||||
\(349\) | 28.3075 | 1.51527 | 0.757633 | − | 0.652681i | \(-0.226356\pi\) | ||||
0.757633 | + | 0.652681i | \(0.226356\pi\) | |||||||
\(350\) | 83.3573 | 4.45563 | ||||||||
\(351\) | 4.08866 | 0.218237 | ||||||||
\(352\) | 57.4296 | 3.06101 | ||||||||
\(353\) | 26.3891 | 1.40455 | 0.702275 | − | 0.711906i | \(-0.252168\pi\) | ||||
0.702275 | + | 0.711906i | \(0.252168\pi\) | |||||||
\(354\) | 8.82931 | 0.469272 | ||||||||
\(355\) | −21.4639 | −1.13918 | ||||||||
\(356\) | −18.4212 | −0.976322 | ||||||||
\(357\) | 15.0755 | 0.797883 | ||||||||
\(358\) | −45.4982 | −2.40466 | ||||||||
\(359\) | 13.9218 | 0.734765 | 0.367383 | − | 0.930070i | \(-0.380254\pi\) | ||||
0.367383 | + | 0.930070i | \(0.380254\pi\) | |||||||
\(360\) | −110.187 | −5.80739 | ||||||||
\(361\) | 19.4245 | 1.02234 | ||||||||
\(362\) | −49.0507 | −2.57805 | ||||||||
\(363\) | −4.78436 | −0.251114 | ||||||||
\(364\) | 24.1613 | 1.26640 | ||||||||
\(365\) | −4.14272 | −0.216840 | ||||||||
\(366\) | 2.30873 | 0.120679 | ||||||||
\(367\) | 25.1195 | 1.31123 | 0.655614 | − | 0.755096i | \(-0.272410\pi\) | ||||
0.655614 | + | 0.755096i | \(0.272410\pi\) | |||||||
\(368\) | 157.925 | 8.23240 | ||||||||
\(369\) | 6.06919 | 0.315949 | ||||||||
\(370\) | 91.1049 | 4.73632 | ||||||||
\(371\) | −14.2074 | −0.737609 | ||||||||
\(372\) | 15.1513 | 0.785557 | ||||||||
\(373\) | 7.89929 | 0.409010 | 0.204505 | − | 0.978866i | \(-0.434442\pi\) | ||||
0.204505 | + | 0.978866i | \(0.434442\pi\) | |||||||
\(374\) | −36.9110 | −1.90862 | ||||||||
\(375\) | −8.54923 | −0.441481 | ||||||||
\(376\) | 118.577 | 6.11513 | ||||||||
\(377\) | −7.82549 | −0.403033 | ||||||||
\(378\) | −31.7845 | −1.63482 | ||||||||
\(379\) | 20.3577 | 1.04570 | 0.522852 | − | 0.852424i | \(-0.324868\pi\) | ||||
0.522852 | + | 0.852424i | \(0.324868\pi\) | |||||||
\(380\) | 137.679 | 7.06278 | ||||||||
\(381\) | −6.73919 | −0.345259 | ||||||||
\(382\) | 16.2402 | 0.830921 | ||||||||
\(383\) | −10.6099 | −0.542143 | −0.271072 | − | 0.962559i | \(-0.587378\pi\) | ||||
−0.271072 | + | 0.962559i | \(0.587378\pi\) | |||||||
\(384\) | −51.9386 | −2.65048 | ||||||||
\(385\) | −21.4971 | −1.09559 | ||||||||
\(386\) | 24.7629 | 1.26040 | ||||||||
\(387\) | −21.0333 | −1.06918 | ||||||||
\(388\) | 7.59595 | 0.385626 | ||||||||
\(389\) | 20.3903 | 1.03383 | 0.516915 | − | 0.856037i | \(-0.327080\pi\) | ||||
0.516915 | + | 0.856037i | \(0.327080\pi\) | |||||||
\(390\) | −7.61089 | −0.385392 | ||||||||
\(391\) | −60.5864 | −3.06399 | ||||||||
\(392\) | −46.4578 | −2.34647 | ||||||||
\(393\) | 11.5372 | 0.581973 | ||||||||
\(394\) | 38.5154 | 1.94038 | ||||||||
\(395\) | −12.8155 | −0.644819 | ||||||||
\(396\) | 27.3007 | 1.37191 | ||||||||
\(397\) | −17.7947 | −0.893088 | −0.446544 | − | 0.894762i | \(-0.647345\pi\) | ||||
−0.446544 | + | 0.894762i | \(0.647345\pi\) | |||||||
\(398\) | 21.1093 | 1.05812 | ||||||||
\(399\) | 12.3684 | 0.619194 | ||||||||
\(400\) | 174.185 | 8.70926 | ||||||||
\(401\) | −34.5031 | −1.72300 | −0.861500 | − | 0.507757i | \(-0.830475\pi\) | ||||
−0.861500 | + | 0.507757i | \(0.830475\pi\) | |||||||
\(402\) | −8.88502 | −0.443145 | ||||||||
\(403\) | −5.14885 | −0.256482 | ||||||||
\(404\) | −10.5779 | −0.526270 | ||||||||
\(405\) | −22.0007 | −1.09322 | ||||||||
\(406\) | 60.8339 | 3.01914 | ||||||||
\(407\) | −15.0098 | −0.744007 | ||||||||
\(408\) | 50.5989 | 2.50502 | ||||||||
\(409\) | 2.00565 | 0.0991728 | 0.0495864 | − | 0.998770i | \(-0.484210\pi\) | ||||
0.0495864 | + | 0.998770i | \(0.484210\pi\) | |||||||
\(410\) | −24.1220 | −1.19130 | ||||||||
\(411\) | 2.25205 | 0.111086 | ||||||||
\(412\) | 2.22305 | 0.109522 | ||||||||
\(413\) | 17.4713 | 0.859707 | ||||||||
\(414\) | 59.8258 | 2.94028 | ||||||||
\(415\) | −49.7585 | −2.44255 | ||||||||
\(416\) | 40.2337 | 1.97262 | ||||||||
\(417\) | 0.648531 | 0.0317587 | ||||||||
\(418\) | −30.2828 | −1.48118 | ||||||||
\(419\) | −27.7507 | −1.35571 | −0.677856 | − | 0.735195i | \(-0.737091\pi\) | ||||
−0.677856 | + | 0.735195i | \(0.737091\pi\) | |||||||
\(420\) | 44.3173 | 2.16246 | ||||||||
\(421\) | −23.6872 | −1.15444 | −0.577221 | − | 0.816588i | \(-0.695863\pi\) | ||||
−0.577221 | + | 0.816588i | \(0.695863\pi\) | |||||||
\(422\) | 6.99982 | 0.340746 | ||||||||
\(423\) | 27.9665 | 1.35978 | ||||||||
\(424\) | −47.6849 | −2.31579 | ||||||||
\(425\) | −66.8246 | −3.24147 | ||||||||
\(426\) | −9.73264 | −0.471548 | ||||||||
\(427\) | 4.56848 | 0.221084 | ||||||||
\(428\) | −37.9432 | −1.83406 | ||||||||
\(429\) | 1.25391 | 0.0605395 | ||||||||
\(430\) | 83.5969 | 4.03140 | ||||||||
\(431\) | 36.8142 | 1.77328 | 0.886639 | − | 0.462462i | \(-0.153034\pi\) | ||||
0.886639 | + | 0.462462i | \(0.153034\pi\) | |||||||
\(432\) | −66.4177 | −3.19552 | ||||||||
\(433\) | 32.0131 | 1.53845 | 0.769225 | − | 0.638978i | \(-0.220643\pi\) | ||||
0.769225 | + | 0.638978i | \(0.220643\pi\) | |||||||
\(434\) | 40.0262 | 1.92132 | ||||||||
\(435\) | −14.3537 | −0.688207 | ||||||||
\(436\) | 90.8865 | 4.35267 | ||||||||
\(437\) | −49.7068 | −2.37780 | ||||||||
\(438\) | −1.87848 | −0.0897574 | ||||||||
\(439\) | 25.7334 | 1.22819 | 0.614094 | − | 0.789233i | \(-0.289522\pi\) | ||||
0.614094 | + | 0.789233i | \(0.289522\pi\) | |||||||
\(440\) | −72.1519 | −3.43971 | ||||||||
\(441\) | −10.9571 | −0.521768 | ||||||||
\(442\) | −25.8589 | −1.22998 | ||||||||
\(443\) | 7.64228 | 0.363095 | 0.181548 | − | 0.983382i | \(-0.441889\pi\) | ||||
0.181548 | + | 0.983382i | \(0.441889\pi\) | |||||||
\(444\) | 30.9434 | 1.46851 | ||||||||
\(445\) | 11.4824 | 0.544316 | ||||||||
\(446\) | 9.30960 | 0.440822 | ||||||||
\(447\) | 4.90771 | 0.232127 | ||||||||
\(448\) | −181.269 | −8.56415 | ||||||||
\(449\) | 15.3349 | 0.723698 | 0.361849 | − | 0.932237i | \(-0.382146\pi\) | ||||
0.361849 | + | 0.932237i | \(0.382146\pi\) | |||||||
\(450\) | 65.9857 | 3.11059 | ||||||||
\(451\) | 3.97417 | 0.187136 | ||||||||
\(452\) | −99.1475 | −4.66351 | ||||||||
\(453\) | −4.90874 | −0.230633 | ||||||||
\(454\) | 12.8380 | 0.602517 | ||||||||
\(455\) | −15.0603 | −0.706039 | ||||||||
\(456\) | 41.5127 | 1.94401 | ||||||||
\(457\) | 12.9652 | 0.606486 | 0.303243 | − | 0.952913i | \(-0.401931\pi\) | ||||
0.303243 | + | 0.952913i | \(0.401931\pi\) | |||||||
\(458\) | −48.8743 | −2.28375 | ||||||||
\(459\) | 25.4805 | 1.18933 | ||||||||
\(460\) | −178.105 | −8.30418 | ||||||||
\(461\) | −16.7791 | −0.781480 | −0.390740 | − | 0.920501i | \(-0.627781\pi\) | ||||
−0.390740 | + | 0.920501i | \(0.627781\pi\) | |||||||
\(462\) | −9.74770 | −0.453504 | ||||||||
\(463\) | −14.2076 | −0.660283 | −0.330141 | − | 0.943931i | \(-0.607096\pi\) | ||||
−0.330141 | + | 0.943931i | \(0.607096\pi\) | |||||||
\(464\) | 127.120 | 5.90140 | ||||||||
\(465\) | −9.44414 | −0.437962 | ||||||||
\(466\) | 55.1011 | 2.55251 | ||||||||
\(467\) | −26.9571 | −1.24742 | −0.623712 | − | 0.781654i | \(-0.714376\pi\) | ||||
−0.623712 | + | 0.781654i | \(0.714376\pi\) | |||||||
\(468\) | 19.1261 | 0.884106 | ||||||||
\(469\) | −17.5816 | −0.811842 | ||||||||
\(470\) | −111.153 | −5.12711 | ||||||||
\(471\) | −6.89894 | −0.317886 | ||||||||
\(472\) | 58.6399 | 2.69912 | ||||||||
\(473\) | −13.7728 | −0.633275 | ||||||||
\(474\) | −5.81111 | −0.266913 | ||||||||
\(475\) | −54.8248 | −2.51553 | ||||||||
\(476\) | 150.573 | 6.90152 | ||||||||
\(477\) | −11.2466 | −0.514944 | ||||||||
\(478\) | 20.8463 | 0.953490 | ||||||||
\(479\) | −26.5811 | −1.21452 | −0.607261 | − | 0.794502i | \(-0.707732\pi\) | ||||
−0.607261 | + | 0.794502i | \(0.707732\pi\) | |||||||
\(480\) | 73.7976 | 3.36839 | ||||||||
\(481\) | −10.5155 | −0.479464 | ||||||||
\(482\) | 17.8267 | 0.811985 | ||||||||
\(483\) | −16.0001 | −0.728028 | ||||||||
\(484\) | −47.7858 | −2.17208 | ||||||||
\(485\) | −4.73473 | −0.214993 | ||||||||
\(486\) | −38.5373 | −1.74809 | ||||||||
\(487\) | 0.891424 | 0.0403943 | 0.0201971 | − | 0.999796i | \(-0.493571\pi\) | ||||
0.0201971 | + | 0.999796i | \(0.493571\pi\) | |||||||
\(488\) | 15.3335 | 0.694113 | ||||||||
\(489\) | −13.5606 | −0.613230 | ||||||||
\(490\) | 43.5492 | 1.96735 | ||||||||
\(491\) | 2.99797 | 0.135296 | 0.0676482 | − | 0.997709i | \(-0.478450\pi\) | ||||
0.0676482 | + | 0.997709i | \(0.478450\pi\) | |||||||
\(492\) | −8.19294 | −0.369366 | ||||||||
\(493\) | −48.7684 | −2.19642 | ||||||||
\(494\) | −21.2154 | −0.954525 | ||||||||
\(495\) | −17.0171 | −0.764863 | ||||||||
\(496\) | 83.6397 | 3.75554 | ||||||||
\(497\) | −19.2588 | −0.863876 | ||||||||
\(498\) | −22.5626 | −1.01106 | ||||||||
\(499\) | 3.85489 | 0.172569 | 0.0862843 | − | 0.996271i | \(-0.472501\pi\) | ||||
0.0862843 | + | 0.996271i | \(0.472501\pi\) | |||||||
\(500\) | −85.3892 | −3.81872 | ||||||||
\(501\) | 1.93361 | 0.0863873 | ||||||||
\(502\) | 1.49113 | 0.0665525 | ||||||||
\(503\) | −22.6365 | −1.00931 | −0.504656 | − | 0.863321i | \(-0.668381\pi\) | ||||
−0.504656 | + | 0.863321i | \(0.668381\pi\) | |||||||
\(504\) | −98.8674 | −4.40391 | ||||||||
\(505\) | 6.59344 | 0.293404 | ||||||||
\(506\) | 39.1746 | 1.74152 | ||||||||
\(507\) | −6.89104 | −0.306042 | ||||||||
\(508\) | −67.3105 | −2.98642 | ||||||||
\(509\) | −4.37885 | −0.194089 | −0.0970446 | − | 0.995280i | \(-0.530939\pi\) | ||||
−0.0970446 | + | 0.995280i | \(0.530939\pi\) | |||||||
\(510\) | −47.4310 | −2.10028 | ||||||||
\(511\) | −3.71712 | −0.164436 | ||||||||
\(512\) | −212.207 | −9.37833 | ||||||||
\(513\) | 20.9050 | 0.922976 | ||||||||
\(514\) | −37.1791 | −1.63990 | ||||||||
\(515\) | −1.38568 | −0.0610603 | ||||||||
\(516\) | 28.3933 | 1.24995 | ||||||||
\(517\) | 18.3128 | 0.805394 | ||||||||
\(518\) | 81.7454 | 3.59168 | ||||||||
\(519\) | −10.8641 | −0.476882 | ||||||||
\(520\) | −50.5478 | −2.21667 | ||||||||
\(521\) | −1.64330 | −0.0719944 | −0.0359972 | − | 0.999352i | \(-0.511461\pi\) | ||||
−0.0359972 | + | 0.999352i | \(0.511461\pi\) | |||||||
\(522\) | 48.1562 | 2.10774 | ||||||||
\(523\) | 34.8130 | 1.52227 | 0.761133 | − | 0.648596i | \(-0.224644\pi\) | ||||
0.761133 | + | 0.648596i | \(0.224644\pi\) | |||||||
\(524\) | 115.232 | 5.03395 | ||||||||
\(525\) | −17.6475 | −0.770199 | ||||||||
\(526\) | 42.7216 | 1.86275 | ||||||||
\(527\) | −32.0876 | −1.39776 | ||||||||
\(528\) | −20.3690 | −0.886448 | ||||||||
\(529\) | 41.3019 | 1.79573 | ||||||||
\(530\) | 44.6995 | 1.94162 | ||||||||
\(531\) | 13.8303 | 0.600184 | ||||||||
\(532\) | 123.535 | 5.35591 | ||||||||
\(533\) | 2.78420 | 0.120597 | ||||||||
\(534\) | 5.20659 | 0.225311 | ||||||||
\(535\) | 23.6509 | 1.02252 | ||||||||
\(536\) | −59.0100 | −2.54884 | ||||||||
\(537\) | 9.63238 | 0.415668 | ||||||||
\(538\) | −44.4319 | −1.91560 | ||||||||
\(539\) | −7.17484 | −0.309042 | ||||||||
\(540\) | 74.9047 | 3.22339 | ||||||||
\(541\) | 17.6864 | 0.760397 | 0.380198 | − | 0.924905i | \(-0.375856\pi\) | ||||
0.380198 | + | 0.924905i | \(0.375856\pi\) | |||||||
\(542\) | −38.8847 | −1.67024 | ||||||||
\(543\) | 10.3845 | 0.445640 | ||||||||
\(544\) | 250.736 | 10.7502 | ||||||||
\(545\) | −56.6516 | −2.42669 | ||||||||
\(546\) | −6.82899 | −0.292254 | ||||||||
\(547\) | −29.2416 | −1.25028 | −0.625141 | − | 0.780512i | \(-0.714959\pi\) | ||||
−0.625141 | + | 0.780512i | \(0.714959\pi\) | |||||||
\(548\) | 22.4934 | 0.960869 | ||||||||
\(549\) | 3.61641 | 0.154345 | ||||||||
\(550\) | 43.2081 | 1.84240 | ||||||||
\(551\) | −40.0110 | −1.70453 | ||||||||
\(552\) | −53.7019 | −2.28570 | ||||||||
\(553\) | −11.4989 | −0.488985 | ||||||||
\(554\) | −71.5460 | −3.03970 | ||||||||
\(555\) | −19.2877 | −0.818718 | ||||||||
\(556\) | 6.47748 | 0.274706 | ||||||||
\(557\) | −11.4800 | −0.486424 | −0.243212 | − | 0.969973i | \(-0.578201\pi\) | ||||
−0.243212 | + | 0.969973i | \(0.578201\pi\) | |||||||
\(558\) | 31.6848 | 1.34132 | ||||||||
\(559\) | −9.64888 | −0.408104 | ||||||||
\(560\) | 244.645 | 10.3381 | ||||||||
\(561\) | 7.81439 | 0.329924 | ||||||||
\(562\) | −11.4102 | −0.481311 | ||||||||
\(563\) | 30.5148 | 1.28604 | 0.643022 | − | 0.765848i | \(-0.277680\pi\) | ||||
0.643022 | + | 0.765848i | \(0.277680\pi\) | |||||||
\(564\) | −37.7526 | −1.58967 | ||||||||
\(565\) | 61.8009 | 2.59998 | ||||||||
\(566\) | 74.9645 | 3.15099 | ||||||||
\(567\) | −19.7405 | −0.829023 | ||||||||
\(568\) | −64.6394 | −2.71221 | ||||||||
\(569\) | 26.0219 | 1.09090 | 0.545448 | − | 0.838145i | \(-0.316360\pi\) | ||||
0.545448 | + | 0.838145i | \(0.316360\pi\) | |||||||
\(570\) | −38.9138 | −1.62992 | ||||||||
\(571\) | 14.5536 | 0.609051 | 0.304526 | − | 0.952504i | \(-0.401502\pi\) | ||||
0.304526 | + | 0.952504i | \(0.401502\pi\) | |||||||
\(572\) | 12.5240 | 0.523655 | ||||||||
\(573\) | −3.43820 | −0.143633 | ||||||||
\(574\) | −21.6439 | −0.903398 | ||||||||
\(575\) | 70.9226 | 2.95768 | ||||||||
\(576\) | −143.493 | −5.97886 | ||||||||
\(577\) | 35.6134 | 1.48261 | 0.741304 | − | 0.671170i | \(-0.234208\pi\) | ||||
0.741304 | + | 0.671170i | \(0.234208\pi\) | |||||||
\(578\) | −113.162 | −4.70691 | ||||||||
\(579\) | −5.24252 | −0.217872 | ||||||||
\(580\) | −143.364 | −5.95285 | ||||||||
\(581\) | −44.6466 | −1.85226 | ||||||||
\(582\) | −2.14693 | −0.0889930 | ||||||||
\(583\) | −7.36437 | −0.305001 | ||||||||
\(584\) | −12.4760 | −0.516259 | ||||||||
\(585\) | −11.9218 | −0.492904 | ||||||||
\(586\) | 25.3113 | 1.04560 | ||||||||
\(587\) | 39.6508 | 1.63656 | 0.818282 | − | 0.574817i | \(-0.194927\pi\) | ||||
0.818282 | + | 0.574817i | \(0.194927\pi\) | |||||||
\(588\) | 14.7913 | 0.609982 | ||||||||
\(589\) | −26.3256 | −1.08473 | ||||||||
\(590\) | −54.9687 | −2.26302 | ||||||||
\(591\) | −8.15405 | −0.335413 | ||||||||
\(592\) | 170.817 | 7.02054 | ||||||||
\(593\) | 17.3506 | 0.712504 | 0.356252 | − | 0.934390i | \(-0.384054\pi\) | ||||
0.356252 | + | 0.934390i | \(0.384054\pi\) | |||||||
\(594\) | −16.4755 | −0.675997 | ||||||||
\(595\) | −93.8559 | −3.84772 | ||||||||
\(596\) | 49.0179 | 2.00785 | ||||||||
\(597\) | −4.46903 | −0.182905 | ||||||||
\(598\) | 27.4447 | 1.12230 | ||||||||
\(599\) | −12.0996 | −0.494378 | −0.247189 | − | 0.968967i | \(-0.579507\pi\) | ||||
−0.247189 | + | 0.968967i | \(0.579507\pi\) | |||||||
\(600\) | −59.2312 | −2.41810 | ||||||||
\(601\) | −9.13920 | −0.372796 | −0.186398 | − | 0.982474i | \(-0.559681\pi\) | ||||
−0.186398 | + | 0.982474i | \(0.559681\pi\) | |||||||
\(602\) | 75.0087 | 3.05713 | ||||||||
\(603\) | −13.9176 | −0.566768 | ||||||||
\(604\) | −49.0282 | −1.99493 | ||||||||
\(605\) | 29.7860 | 1.21097 | ||||||||
\(606\) | 2.98975 | 0.121450 | ||||||||
\(607\) | −11.7739 | −0.477888 | −0.238944 | − | 0.971033i | \(-0.576801\pi\) | ||||
−0.238944 | + | 0.971033i | \(0.576801\pi\) | |||||||
\(608\) | 205.711 | 8.34269 | ||||||||
\(609\) | −12.8791 | −0.521887 | ||||||||
\(610\) | −14.3735 | −0.581965 | ||||||||
\(611\) | 12.8294 | 0.519024 | ||||||||
\(612\) | 119.194 | 4.81813 | ||||||||
\(613\) | 25.4704 | 1.02874 | 0.514370 | − | 0.857568i | \(-0.328026\pi\) | ||||
0.514370 | + | 0.857568i | \(0.328026\pi\) | |||||||
\(614\) | 67.5578 | 2.72641 | ||||||||
\(615\) | 5.10685 | 0.205928 | ||||||||
\(616\) | −64.7395 | −2.60843 | ||||||||
\(617\) | −18.4710 | −0.743616 | −0.371808 | − | 0.928310i | \(-0.621262\pi\) | ||||
−0.371808 | + | 0.928310i | \(0.621262\pi\) | |||||||
\(618\) | −0.628325 | −0.0252749 | ||||||||
\(619\) | −6.14925 | −0.247159 | −0.123580 | − | 0.992335i | \(-0.539437\pi\) | ||||
−0.123580 | + | 0.992335i | \(0.539437\pi\) | |||||||
\(620\) | −94.3274 | −3.78828 | ||||||||
\(621\) | −27.0431 | −1.08520 | ||||||||
\(622\) | −74.9211 | −3.00406 | ||||||||
\(623\) | 10.3027 | 0.412770 | ||||||||
\(624\) | −14.2700 | −0.571258 | ||||||||
\(625\) | 9.00257 | 0.360103 | ||||||||
\(626\) | 25.3917 | 1.01486 | ||||||||
\(627\) | 6.41115 | 0.256036 | ||||||||
\(628\) | −68.9061 | −2.74965 | ||||||||
\(629\) | −65.5324 | −2.61295 | ||||||||
\(630\) | 92.6776 | 3.69237 | ||||||||
\(631\) | −22.6156 | −0.900314 | −0.450157 | − | 0.892949i | \(-0.648632\pi\) | ||||
−0.450157 | + | 0.892949i | \(0.648632\pi\) | |||||||
\(632\) | −38.5945 | −1.53521 | ||||||||
\(633\) | −1.48193 | −0.0589012 | ||||||||
\(634\) | −59.6180 | −2.36773 | ||||||||
\(635\) | 41.9562 | 1.66498 | ||||||||
\(636\) | 15.1820 | 0.602005 | ||||||||
\(637\) | −5.02651 | −0.199158 | ||||||||
\(638\) | 31.5332 | 1.24841 | ||||||||
\(639\) | −15.2453 | −0.603094 | ||||||||
\(640\) | 323.355 | 12.7817 | ||||||||
\(641\) | 22.1009 | 0.872931 | 0.436466 | − | 0.899721i | \(-0.356230\pi\) | ||||
0.436466 | + | 0.899721i | \(0.356230\pi\) | |||||||
\(642\) | 10.7243 | 0.423255 | ||||||||
\(643\) | −6.33196 | −0.249708 | −0.124854 | − | 0.992175i | \(-0.539846\pi\) | ||||
−0.124854 | + | 0.992175i | \(0.539846\pi\) | |||||||
\(644\) | −159.807 | −6.29730 | ||||||||
\(645\) | −17.6982 | −0.696866 | ||||||||
\(646\) | −132.214 | −5.20190 | ||||||||
\(647\) | 37.1000 | 1.45855 | 0.729275 | − | 0.684221i | \(-0.239858\pi\) | ||||
0.729275 | + | 0.684221i | \(0.239858\pi\) | |||||||
\(648\) | −66.2561 | −2.60279 | ||||||||
\(649\) | 9.05624 | 0.355488 | ||||||||
\(650\) | 30.2705 | 1.18731 | ||||||||
\(651\) | −8.47391 | −0.332119 | ||||||||
\(652\) | −135.442 | −5.30432 | ||||||||
\(653\) | 19.0530 | 0.745603 | 0.372802 | − | 0.927911i | \(-0.378397\pi\) | ||||
0.372802 | + | 0.927911i | \(0.378397\pi\) | |||||||
\(654\) | −25.6883 | −1.00449 | ||||||||
\(655\) | −71.8270 | −2.80651 | ||||||||
\(656\) | −45.2276 | −1.76584 | ||||||||
\(657\) | −2.94247 | −0.114797 | ||||||||
\(658\) | −99.7338 | −3.88803 | ||||||||
\(659\) | −31.2605 | −1.21773 | −0.608867 | − | 0.793272i | \(-0.708376\pi\) | ||||
−0.608867 | + | 0.793272i | \(0.708376\pi\) | |||||||
\(660\) | 22.9718 | 0.894177 | ||||||||
\(661\) | −15.6698 | −0.609485 | −0.304742 | − | 0.952435i | \(-0.598570\pi\) | ||||
−0.304742 | + | 0.952435i | \(0.598570\pi\) | |||||||
\(662\) | −51.1882 | −1.98948 | ||||||||
\(663\) | 5.47456 | 0.212614 | ||||||||
\(664\) | −149.850 | −5.81531 | ||||||||
\(665\) | −77.0020 | −2.98601 | ||||||||
\(666\) | 64.7097 | 2.50745 | ||||||||
\(667\) | 51.7592 | 2.00412 | ||||||||
\(668\) | 19.3127 | 0.747233 | ||||||||
\(669\) | −1.97093 | −0.0762004 | ||||||||
\(670\) | 55.3156 | 2.13703 | ||||||||
\(671\) | 2.36807 | 0.0914183 | ||||||||
\(672\) | 66.2161 | 2.55434 | ||||||||
\(673\) | 17.8506 | 0.688091 | 0.344046 | − | 0.938953i | \(-0.388202\pi\) | ||||
0.344046 | + | 0.938953i | \(0.388202\pi\) | |||||||
\(674\) | 2.38530 | 0.0918782 | ||||||||
\(675\) | −29.8276 | −1.14806 | ||||||||
\(676\) | −68.8273 | −2.64720 | ||||||||
\(677\) | 17.8879 | 0.687487 | 0.343744 | − | 0.939064i | \(-0.388305\pi\) | ||||
0.343744 | + | 0.939064i | \(0.388305\pi\) | |||||||
\(678\) | 28.0232 | 1.07622 | ||||||||
\(679\) | −4.24831 | −0.163035 | ||||||||
\(680\) | −315.014 | −12.0802 | ||||||||
\(681\) | −2.71792 | −0.104151 | ||||||||
\(682\) | 20.7476 | 0.794465 | ||||||||
\(683\) | 32.2057 | 1.23232 | 0.616158 | − | 0.787622i | \(-0.288688\pi\) | ||||
0.616158 | + | 0.787622i | \(0.288688\pi\) | |||||||
\(684\) | 97.7902 | 3.73910 | ||||||||
\(685\) | −14.0206 | −0.535701 | ||||||||
\(686\) | −26.8982 | −1.02698 | ||||||||
\(687\) | 10.3471 | 0.394768 | ||||||||
\(688\) | 156.740 | 5.97565 | ||||||||
\(689\) | −5.15928 | −0.196553 | ||||||||
\(690\) | 50.3398 | 1.91640 | ||||||||
\(691\) | 16.6742 | 0.634318 | 0.317159 | − | 0.948372i | \(-0.397271\pi\) | ||||
0.317159 | + | 0.948372i | \(0.397271\pi\) | |||||||
\(692\) | −108.510 | −4.12493 | ||||||||
\(693\) | −15.2689 | −0.580017 | ||||||||
\(694\) | 28.4966 | 1.08172 | ||||||||
\(695\) | −4.03756 | −0.153153 | ||||||||
\(696\) | −43.2268 | −1.63851 | ||||||||
\(697\) | 17.3511 | 0.657222 | ||||||||
\(698\) | −79.9121 | −3.02472 | ||||||||
\(699\) | −11.6654 | −0.441226 | ||||||||
\(700\) | −176.262 | −6.66207 | ||||||||
\(701\) | 19.4301 | 0.733866 | 0.366933 | − | 0.930247i | \(-0.380408\pi\) | ||||
0.366933 | + | 0.930247i | \(0.380408\pi\) | |||||||
\(702\) | −11.5423 | −0.435636 | ||||||||
\(703\) | −53.7646 | −2.02777 | ||||||||
\(704\) | −93.9605 | −3.54127 | ||||||||
\(705\) | 23.5321 | 0.886269 | ||||||||
\(706\) | −74.4964 | −2.80371 | ||||||||
\(707\) | 5.91607 | 0.222497 | ||||||||
\(708\) | −18.6699 | −0.701656 | ||||||||
\(709\) | 8.64155 | 0.324540 | 0.162270 | − | 0.986746i | \(-0.448118\pi\) | ||||
0.162270 | + | 0.986746i | \(0.448118\pi\) | |||||||
\(710\) | 60.5925 | 2.27400 | ||||||||
\(711\) | −9.10257 | −0.341373 | ||||||||
\(712\) | 34.5796 | 1.29593 | ||||||||
\(713\) | 34.0554 | 1.27538 | ||||||||
\(714\) | −42.5583 | −1.59270 | ||||||||
\(715\) | −7.80650 | −0.291947 | ||||||||
\(716\) | 96.2076 | 3.59545 | ||||||||
\(717\) | −4.41336 | −0.164820 | ||||||||
\(718\) | −39.3013 | −1.46671 | ||||||||
\(719\) | 30.7036 | 1.14505 | 0.572526 | − | 0.819887i | \(-0.305964\pi\) | ||||
0.572526 | + | 0.819887i | \(0.305964\pi\) | |||||||
\(720\) | 193.661 | 7.21733 | ||||||||
\(721\) | −1.24332 | −0.0463037 | ||||||||
\(722\) | −54.8352 | −2.04076 | ||||||||
\(723\) | −3.77408 | −0.140359 | ||||||||
\(724\) | 103.719 | 3.85470 | ||||||||
\(725\) | 57.0884 | 2.12021 | ||||||||
\(726\) | 13.5062 | 0.501264 | ||||||||
\(727\) | −43.7061 | −1.62097 | −0.810484 | − | 0.585761i | \(-0.800796\pi\) | ||||
−0.810484 | + | 0.585761i | \(0.800796\pi\) | |||||||
\(728\) | −45.3548 | −1.68096 | ||||||||
\(729\) | −9.57992 | −0.354812 | ||||||||
\(730\) | 11.6949 | 0.432847 | ||||||||
\(731\) | −60.1318 | −2.22406 | ||||||||
\(732\) | −4.88189 | −0.180440 | ||||||||
\(733\) | −4.07363 | −0.150463 | −0.0752314 | − | 0.997166i | \(-0.523970\pi\) | ||||
−0.0752314 | + | 0.997166i | \(0.523970\pi\) | |||||||
\(734\) | −70.9124 | −2.61742 | ||||||||
\(735\) | −9.21974 | −0.340075 | ||||||||
\(736\) | −266.113 | −9.80905 | ||||||||
\(737\) | −9.11339 | −0.335696 | ||||||||
\(738\) | −17.1333 | −0.630686 | ||||||||
\(739\) | −27.6548 | −1.01730 | −0.508648 | − | 0.860974i | \(-0.669855\pi\) | ||||
−0.508648 | + | 0.860974i | \(0.669855\pi\) | |||||||
\(740\) | −192.644 | −7.08175 | ||||||||
\(741\) | 4.49148 | 0.164999 | ||||||||
\(742\) | 40.1074 | 1.47239 | ||||||||
\(743\) | 23.7394 | 0.870914 | 0.435457 | − | 0.900210i | \(-0.356587\pi\) | ||||
0.435457 | + | 0.900210i | \(0.356587\pi\) | |||||||
\(744\) | −28.4414 | −1.04271 | ||||||||
\(745\) | −30.5540 | −1.11941 | ||||||||
\(746\) | −22.2997 | −0.816450 | ||||||||
\(747\) | −35.3423 | −1.29311 | ||||||||
\(748\) | 78.0496 | 2.85378 | ||||||||
\(749\) | 21.2211 | 0.775403 | ||||||||
\(750\) | 24.1345 | 0.881267 | ||||||||
\(751\) | 23.5186 | 0.858207 | 0.429103 | − | 0.903255i | \(-0.358830\pi\) | ||||
0.429103 | + | 0.903255i | \(0.358830\pi\) | |||||||
\(752\) | −208.406 | −7.59979 | ||||||||
\(753\) | −0.315686 | −0.0115042 | ||||||||
\(754\) | 22.0913 | 0.804519 | ||||||||
\(755\) | 30.5604 | 1.11221 | ||||||||
\(756\) | 67.2095 | 2.44438 | ||||||||
\(757\) | −16.6457 | −0.604998 | −0.302499 | − | 0.953150i | \(-0.597821\pi\) | ||||
−0.302499 | + | 0.953150i | \(0.597821\pi\) | |||||||
\(758\) | −57.4697 | −2.08739 | ||||||||
\(759\) | −8.29361 | −0.301039 | ||||||||
\(760\) | −258.446 | −9.37483 | ||||||||
\(761\) | −14.4908 | −0.525290 | −0.262645 | − | 0.964892i | \(-0.584595\pi\) | ||||
−0.262645 | + | 0.964892i | \(0.584595\pi\) | |||||||
\(762\) | 19.0247 | 0.689193 | ||||||||
\(763\) | −50.8316 | −1.84023 | ||||||||
\(764\) | −34.3405 | −1.24239 | ||||||||
\(765\) | −74.2964 | −2.68619 | ||||||||
\(766\) | 29.9519 | 1.08221 | ||||||||
\(767\) | 6.34457 | 0.229089 | ||||||||
\(768\) | 81.7230 | 2.94892 | ||||||||
\(769\) | 16.7576 | 0.604294 | 0.302147 | − | 0.953261i | \(-0.402297\pi\) | ||||
0.302147 | + | 0.953261i | \(0.402297\pi\) | |||||||
\(770\) | 60.6863 | 2.18698 | ||||||||
\(771\) | 7.87114 | 0.283472 | ||||||||
\(772\) | −52.3620 | −1.88455 | ||||||||
\(773\) | 7.02025 | 0.252501 | 0.126250 | − | 0.991998i | \(-0.459706\pi\) | ||||
0.126250 | + | 0.991998i | \(0.459706\pi\) | |||||||
\(774\) | 59.3769 | 2.13426 | ||||||||
\(775\) | 37.5619 | 1.34926 | ||||||||
\(776\) | −14.2588 | −0.511863 | ||||||||
\(777\) | −17.3062 | −0.620857 | ||||||||
\(778\) | −57.5619 | −2.06369 | ||||||||
\(779\) | 14.2354 | 0.510035 | ||||||||
\(780\) | 16.0935 | 0.576239 | ||||||||
\(781\) | −9.98278 | −0.357212 | ||||||||
\(782\) | 171.035 | 6.11622 | ||||||||
\(783\) | −21.7681 | −0.777929 | ||||||||
\(784\) | 81.6524 | 2.91616 | ||||||||
\(785\) | 42.9508 | 1.53298 | ||||||||
\(786\) | −32.5694 | −1.16171 | ||||||||
\(787\) | 8.73854 | 0.311495 | 0.155748 | − | 0.987797i | \(-0.450221\pi\) | ||||
0.155748 | + | 0.987797i | \(0.450221\pi\) | |||||||
\(788\) | −81.4421 | −2.90125 | ||||||||
\(789\) | −9.04455 | −0.321995 | ||||||||
\(790\) | 36.1782 | 1.28716 | ||||||||
\(791\) | 55.4519 | 1.97164 | ||||||||
\(792\) | −51.2478 | −1.82101 | ||||||||
\(793\) | 1.65901 | 0.0589131 | ||||||||
\(794\) | 50.2343 | 1.78275 | ||||||||
\(795\) | −9.46328 | −0.335628 | ||||||||
\(796\) | −44.6364 | −1.58209 | ||||||||
\(797\) | −13.4158 | −0.475211 | −0.237606 | − | 0.971362i | \(-0.576363\pi\) | ||||
−0.237606 | + | 0.971362i | \(0.576363\pi\) | |||||||
\(798\) | −34.9160 | −1.23601 | ||||||||
\(799\) | 79.9531 | 2.82854 | ||||||||
\(800\) | −293.513 | −10.3772 | ||||||||
\(801\) | 8.15565 | 0.288166 | ||||||||
\(802\) | 97.4021 | 3.43939 | ||||||||
\(803\) | −1.92676 | −0.0679940 | ||||||||
\(804\) | 18.7877 | 0.662590 | ||||||||
\(805\) | 99.6116 | 3.51085 | ||||||||
\(806\) | 14.5352 | 0.511981 | ||||||||
\(807\) | 9.40664 | 0.331129 | ||||||||
\(808\) | 19.8564 | 0.698547 | ||||||||
\(809\) | 25.8973 | 0.910501 | 0.455251 | − | 0.890363i | \(-0.349550\pi\) | ||||
0.455251 | + | 0.890363i | \(0.349550\pi\) | |||||||
\(810\) | 62.1080 | 2.18225 | ||||||||
\(811\) | −46.1281 | −1.61978 | −0.809889 | − | 0.586583i | \(-0.800473\pi\) | ||||
−0.809889 | + | 0.586583i | \(0.800473\pi\) | |||||||
\(812\) | −128.635 | −4.51422 | ||||||||
\(813\) | 8.23223 | 0.288717 | ||||||||
\(814\) | 42.3726 | 1.48516 | ||||||||
\(815\) | 84.4241 | 2.95725 | ||||||||
\(816\) | −88.9307 | −3.11320 | ||||||||
\(817\) | −49.3338 | −1.72597 | ||||||||
\(818\) | −5.66194 | −0.197965 | ||||||||
\(819\) | −10.6970 | −0.373783 | ||||||||
\(820\) | 51.0069 | 1.78124 | ||||||||
\(821\) | −26.7987 | −0.935279 | −0.467640 | − | 0.883919i | \(-0.654896\pi\) | ||||
−0.467640 | + | 0.883919i | \(0.654896\pi\) | |||||||
\(822\) | −6.35755 | −0.221745 | ||||||||
\(823\) | −29.5607 | −1.03042 | −0.515210 | − | 0.857064i | \(-0.672286\pi\) | ||||
−0.515210 | + | 0.857064i | \(0.672286\pi\) | |||||||
\(824\) | −4.17303 | −0.145374 | ||||||||
\(825\) | −9.14755 | −0.318477 | ||||||||
\(826\) | −49.3215 | −1.71612 | ||||||||
\(827\) | 37.6739 | 1.31005 | 0.655025 | − | 0.755607i | \(-0.272658\pi\) | ||||
0.655025 | + | 0.755607i | \(0.272658\pi\) | |||||||
\(828\) | −126.504 | −4.39631 | ||||||||
\(829\) | −42.5447 | −1.47764 | −0.738820 | − | 0.673903i | \(-0.764616\pi\) | ||||
−0.738820 | + | 0.673903i | \(0.764616\pi\) | |||||||
\(830\) | 140.468 | 4.87573 | ||||||||
\(831\) | 15.1469 | 0.525441 | ||||||||
\(832\) | −65.8263 | −2.28212 | ||||||||
\(833\) | −31.3252 | −1.08535 | ||||||||
\(834\) | −1.83080 | −0.0633955 | ||||||||
\(835\) | −12.0381 | −0.416595 | ||||||||
\(836\) | 64.0341 | 2.21466 | ||||||||
\(837\) | −14.3225 | −0.495059 | ||||||||
\(838\) | 78.3403 | 2.70622 | ||||||||
\(839\) | −31.2272 | −1.07808 | −0.539042 | − | 0.842279i | \(-0.681213\pi\) | ||||
−0.539042 | + | 0.842279i | \(0.681213\pi\) | |||||||
\(840\) | −83.1909 | −2.87036 | ||||||||
\(841\) | 12.6630 | 0.436656 | ||||||||
\(842\) | 66.8689 | 2.30446 | ||||||||
\(843\) | 2.41565 | 0.0831993 | ||||||||
\(844\) | −14.8014 | −0.509484 | ||||||||
\(845\) | 42.9016 | 1.47586 | ||||||||
\(846\) | −78.9494 | −2.71434 | ||||||||
\(847\) | 26.7260 | 0.918315 | ||||||||
\(848\) | 83.8093 | 2.87802 | ||||||||
\(849\) | −15.8707 | −0.544680 | ||||||||
\(850\) | 188.646 | 6.47050 | ||||||||
\(851\) | 69.5512 | 2.38418 | ||||||||
\(852\) | 20.5800 | 0.705059 | ||||||||
\(853\) | −45.0494 | −1.54246 | −0.771230 | − | 0.636556i | \(-0.780358\pi\) | ||||
−0.771230 | + | 0.636556i | \(0.780358\pi\) | |||||||
\(854\) | −12.8968 | −0.441320 | ||||||||
\(855\) | −60.9548 | −2.08461 | ||||||||
\(856\) | 71.2257 | 2.43444 | ||||||||
\(857\) | 53.3004 | 1.82071 | 0.910354 | − | 0.413831i | \(-0.135810\pi\) | ||||
0.910354 | + | 0.413831i | \(0.135810\pi\) | |||||||
\(858\) | −3.53980 | −0.120847 | ||||||||
\(859\) | 10.3211 | 0.352151 | 0.176076 | − | 0.984377i | \(-0.443660\pi\) | ||||
0.176076 | + | 0.984377i | \(0.443660\pi\) | |||||||
\(860\) | −176.769 | −6.02776 | ||||||||
\(861\) | 4.58220 | 0.156161 | ||||||||
\(862\) | −103.927 | −3.53975 | ||||||||
\(863\) | 20.3151 | 0.691535 | 0.345767 | − | 0.938320i | \(-0.387619\pi\) | ||||
0.345767 | + | 0.938320i | \(0.387619\pi\) | |||||||
\(864\) | 111.918 | 3.80752 | ||||||||
\(865\) | 67.6368 | 2.29972 | ||||||||
\(866\) | −90.3729 | −3.07100 | ||||||||
\(867\) | 23.9573 | 0.813634 | ||||||||
\(868\) | −84.6368 | −2.87276 | ||||||||
\(869\) | −5.96046 | −0.202195 | ||||||||
\(870\) | 40.5205 | 1.37377 | ||||||||
\(871\) | −6.38460 | −0.216334 | ||||||||
\(872\) | −170.609 | −5.77755 | ||||||||
\(873\) | −3.36297 | −0.113819 | ||||||||
\(874\) | 140.322 | 4.74647 | ||||||||
\(875\) | 47.7570 | 1.61448 | ||||||||
\(876\) | 3.97212 | 0.134205 | ||||||||
\(877\) | −32.9289 | −1.11193 | −0.555964 | − | 0.831206i | \(-0.687651\pi\) | ||||
−0.555964 | + | 0.831206i | \(0.687651\pi\) | |||||||
\(878\) | −72.6453 | −2.45166 | ||||||||
\(879\) | −5.35862 | −0.180742 | ||||||||
\(880\) | 126.812 | 4.27482 | ||||||||
\(881\) | −47.1149 | −1.58734 | −0.793671 | − | 0.608347i | \(-0.791833\pi\) | ||||
−0.793671 | + | 0.608347i | \(0.791833\pi\) | |||||||
\(882\) | 30.9319 | 1.04153 | ||||||||
\(883\) | −11.5259 | −0.387876 | −0.193938 | − | 0.981014i | \(-0.562126\pi\) | ||||
−0.193938 | + | 0.981014i | \(0.562126\pi\) | |||||||
\(884\) | 54.6795 | 1.83907 | ||||||||
\(885\) | 11.6374 | 0.391185 | ||||||||
\(886\) | −21.5741 | −0.724797 | ||||||||
\(887\) | −10.4567 | −0.351103 | −0.175552 | − | 0.984470i | \(-0.556171\pi\) | ||||
−0.175552 | + | 0.984470i | \(0.556171\pi\) | |||||||
\(888\) | −58.0858 | −1.94923 | ||||||||
\(889\) | 37.6459 | 1.26260 | ||||||||
\(890\) | −32.4147 | −1.08654 | ||||||||
\(891\) | −10.2325 | −0.342800 | ||||||||
\(892\) | −19.6855 | −0.659118 | ||||||||
\(893\) | 65.5958 | 2.19508 | ||||||||
\(894\) | −13.8545 | −0.463363 | ||||||||
\(895\) | −59.9684 | −2.00452 | ||||||||
\(896\) | 290.135 | 9.69274 | ||||||||
\(897\) | −5.81029 | −0.194000 | ||||||||
\(898\) | −43.2904 | −1.44462 | ||||||||
\(899\) | 27.4126 | 0.914260 | ||||||||
\(900\) | −139.529 | −4.65096 | ||||||||
\(901\) | −32.1527 | −1.07116 | ||||||||
\(902\) | −11.2191 | −0.373555 | ||||||||
\(903\) | −15.8800 | −0.528454 | ||||||||
\(904\) | 186.116 | 6.19013 | ||||||||
\(905\) | −64.6506 | −2.14906 | ||||||||
\(906\) | 13.8574 | 0.460381 | ||||||||
\(907\) | −26.2290 | −0.870921 | −0.435460 | − | 0.900208i | \(-0.643414\pi\) | ||||
−0.435460 | + | 0.900208i | \(0.643414\pi\) | |||||||
\(908\) | −27.1464 | −0.900884 | ||||||||
\(909\) | 4.68317 | 0.155331 | ||||||||
\(910\) | 42.5153 | 1.40937 | ||||||||
\(911\) | −41.5288 | −1.37591 | −0.687955 | − | 0.725754i | \(-0.741491\pi\) | ||||
−0.687955 | + | 0.725754i | \(0.741491\pi\) | |||||||
\(912\) | −72.9613 | −2.41599 | ||||||||
\(913\) | −23.1425 | −0.765906 | ||||||||
\(914\) | −36.6007 | −1.21064 | ||||||||
\(915\) | 3.04299 | 0.100598 | ||||||||
\(916\) | 103.346 | 3.41466 | ||||||||
\(917\) | −64.4479 | −2.12826 | ||||||||
\(918\) | −71.9316 | −2.37410 | ||||||||
\(919\) | −26.5966 | −0.877342 | −0.438671 | − | 0.898648i | \(-0.644551\pi\) | ||||
−0.438671 | + | 0.898648i | \(0.644551\pi\) | |||||||
\(920\) | 334.332 | 11.0226 | ||||||||
\(921\) | −14.3026 | −0.471286 | ||||||||
\(922\) | 47.3674 | 1.55996 | ||||||||
\(923\) | −6.99368 | −0.230200 | ||||||||
\(924\) | 20.6118 | 0.678080 | ||||||||
\(925\) | 76.7124 | 2.52229 | ||||||||
\(926\) | 40.1080 | 1.31803 | ||||||||
\(927\) | −0.984214 | −0.0323258 | ||||||||
\(928\) | −214.205 | −7.03162 | ||||||||
\(929\) | −0.722654 | −0.0237095 | −0.0118548 | − | 0.999930i | \(-0.503774\pi\) | ||||
−0.0118548 | + | 0.999930i | \(0.503774\pi\) | |||||||
\(930\) | 26.6608 | 0.874242 | ||||||||
\(931\) | −25.7001 | −0.842286 | ||||||||
\(932\) | −116.513 | −3.81651 | ||||||||
\(933\) | 15.8615 | 0.519281 | ||||||||
\(934\) | 76.0998 | 2.49006 | ||||||||
\(935\) | −48.6501 | −1.59103 | ||||||||
\(936\) | −35.9029 | −1.17352 | ||||||||
\(937\) | −36.8844 | −1.20496 | −0.602480 | − | 0.798134i | \(-0.705821\pi\) | ||||
−0.602480 | + | 0.798134i | \(0.705821\pi\) | |||||||
\(938\) | 49.6328 | 1.62057 | ||||||||
\(939\) | −5.37566 | −0.175428 | ||||||||
\(940\) | 235.037 | 7.66605 | ||||||||
\(941\) | −42.2118 | −1.37606 | −0.688032 | − | 0.725680i | \(-0.741525\pi\) | ||||
−0.688032 | + | 0.725680i | \(0.741525\pi\) | |||||||
\(942\) | 19.4757 | 0.634553 | ||||||||
\(943\) | −18.4152 | −0.599682 | ||||||||
\(944\) | −103.063 | −3.35443 | ||||||||
\(945\) | −41.8932 | −1.36279 | ||||||||
\(946\) | 38.8807 | 1.26412 | ||||||||
\(947\) | −20.3646 | −0.661759 | −0.330880 | − | 0.943673i | \(-0.607345\pi\) | ||||
−0.330880 | + | 0.943673i | \(0.607345\pi\) | |||||||
\(948\) | 12.2878 | 0.399088 | ||||||||
\(949\) | −1.34984 | −0.0438177 | ||||||||
\(950\) | 154.770 | 5.02141 | ||||||||
\(951\) | 12.6217 | 0.409285 | ||||||||
\(952\) | −282.651 | −9.16078 | ||||||||
\(953\) | −15.2645 | −0.494464 | −0.247232 | − | 0.968956i | \(-0.579521\pi\) | ||||
−0.247232 | + | 0.968956i | \(0.579521\pi\) | |||||||
\(954\) | 31.7490 | 1.02791 | ||||||||
\(955\) | 21.4052 | 0.692656 | ||||||||
\(956\) | −44.0803 | −1.42566 | ||||||||
\(957\) | −6.67586 | −0.215800 | ||||||||
\(958\) | 75.0385 | 2.42438 | ||||||||
\(959\) | −12.5802 | −0.406237 | ||||||||
\(960\) | −120.740 | −3.89687 | ||||||||
\(961\) | −12.9637 | −0.418183 | ||||||||
\(962\) | 29.6852 | 0.957088 | ||||||||
\(963\) | 16.7987 | 0.541329 | ||||||||
\(964\) | −37.6952 | −1.21408 | ||||||||
\(965\) | 32.6384 | 1.05067 | ||||||||
\(966\) | 45.1682 | 1.45326 | ||||||||
\(967\) | 15.5696 | 0.500686 | 0.250343 | − | 0.968157i | \(-0.419457\pi\) | ||||
0.250343 | + | 0.968157i | \(0.419457\pi\) | |||||||
\(968\) | 89.7019 | 2.88313 | ||||||||
\(969\) | 27.9909 | 0.899198 | ||||||||
\(970\) | 13.3661 | 0.429161 | ||||||||
\(971\) | 11.8525 | 0.380366 | 0.190183 | − | 0.981749i | \(-0.439092\pi\) | ||||
0.190183 | + | 0.981749i | \(0.439092\pi\) | |||||||
\(972\) | 81.4885 | 2.61374 | ||||||||
\(973\) | −3.62277 | −0.116141 | ||||||||
\(974\) | −2.51649 | −0.0806335 | ||||||||
\(975\) | −6.40853 | −0.205237 | ||||||||
\(976\) | −26.9495 | −0.862633 | ||||||||
\(977\) | 45.3181 | 1.44985 | 0.724927 | − | 0.688825i | \(-0.241873\pi\) | ||||
0.724927 | + | 0.688825i | \(0.241873\pi\) | |||||||
\(978\) | 38.2815 | 1.22411 | ||||||||
\(979\) | 5.34041 | 0.170680 | ||||||||
\(980\) | −92.0862 | −2.94158 | ||||||||
\(981\) | −40.2383 | −1.28471 | ||||||||
\(982\) | −8.46327 | −0.270074 | ||||||||
\(983\) | 22.1248 | 0.705671 | 0.352835 | − | 0.935685i | \(-0.385218\pi\) | ||||
0.352835 | + | 0.935685i | \(0.385218\pi\) | |||||||
\(984\) | 15.3795 | 0.490281 | ||||||||
\(985\) | 50.7647 | 1.61750 | ||||||||
\(986\) | 137.673 | 4.38441 | ||||||||
\(987\) | 21.1145 | 0.672083 | ||||||||
\(988\) | 44.8606 | 1.42721 | ||||||||
\(989\) | 63.8194 | 2.02934 | ||||||||
\(990\) | 48.0393 | 1.52679 | ||||||||
\(991\) | −30.2114 | −0.959695 | −0.479848 | − | 0.877352i | \(-0.659308\pi\) | ||||
−0.479848 | + | 0.877352i | \(0.659308\pi\) | |||||||
\(992\) | −140.938 | −4.47479 | ||||||||
\(993\) | 10.8370 | 0.343901 | ||||||||
\(994\) | 54.3676 | 1.72444 | ||||||||
\(995\) | 27.8229 | 0.882045 | ||||||||
\(996\) | 47.7094 | 1.51173 | ||||||||
\(997\) | −24.1425 | −0.764601 | −0.382301 | − | 0.924038i | \(-0.624868\pi\) | ||||
−0.382301 | + | 0.924038i | \(0.624868\pi\) | |||||||
\(998\) | −10.8823 | −0.344475 | ||||||||
\(999\) | −29.2508 | −0.925455 |
(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 | 6043.2.a.b.1.1 | ✓ | 243 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6043.2.a.b.1.1 | ✓ | 243 | 1.1 | even | 1 | trivial |