Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8013,2,Mod(1,8013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8013 = 3 \cdot 2671 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8013.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: | \(63.9841271397\) |
Analytic rank: | \(0\) |
Dimension: | \(106\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.43314 | −1.72049 | −0.860244 | − | 0.509883i | \(-0.829689\pi\) | ||||
−0.860244 | + | 0.509883i | \(0.829689\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.92015 | 1.96008 | ||||||||
\(5\) | 4.32607 | 1.93468 | 0.967338 | − | 0.253492i | \(-0.0815791\pi\) | ||||
0.967338 | + | 0.253492i | \(0.0815791\pi\) | |||||||
\(6\) | 2.43314 | 0.993324 | ||||||||
\(7\) | 4.27561 | 1.61603 | 0.808014 | − | 0.589163i | \(-0.200542\pi\) | ||||
0.808014 | + | 0.589163i | \(0.200542\pi\) | |||||||
\(8\) | −4.67199 | −1.65180 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −10.5259 | −3.32858 | ||||||||
\(11\) | 4.41643 | 1.33160 | 0.665802 | − | 0.746128i | \(-0.268089\pi\) | ||||
0.665802 | + | 0.746128i | \(0.268089\pi\) | |||||||
\(12\) | −3.92015 | −1.13165 | ||||||||
\(13\) | −3.10182 | −0.860289 | −0.430145 | − | 0.902760i | \(-0.641537\pi\) | ||||
−0.430145 | + | 0.902760i | \(0.641537\pi\) | |||||||
\(14\) | −10.4031 | −2.78036 | ||||||||
\(15\) | −4.32607 | −1.11699 | ||||||||
\(16\) | 3.52729 | 0.881822 | ||||||||
\(17\) | 2.22761 | 0.540274 | 0.270137 | − | 0.962822i | \(-0.412931\pi\) | ||||
0.270137 | + | 0.962822i | \(0.412931\pi\) | |||||||
\(18\) | −2.43314 | −0.573496 | ||||||||
\(19\) | 6.20974 | 1.42461 | 0.712306 | − | 0.701869i | \(-0.247651\pi\) | ||||
0.712306 | + | 0.701869i | \(0.247651\pi\) | |||||||
\(20\) | 16.9588 | 3.79211 | ||||||||
\(21\) | −4.27561 | −0.933015 | ||||||||
\(22\) | −10.7458 | −2.29101 | ||||||||
\(23\) | 1.57714 | 0.328856 | 0.164428 | − | 0.986389i | \(-0.447422\pi\) | ||||
0.164428 | + | 0.986389i | \(0.447422\pi\) | |||||||
\(24\) | 4.67199 | 0.953666 | ||||||||
\(25\) | 13.7148 | 2.74297 | ||||||||
\(26\) | 7.54714 | 1.48012 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 16.7610 | 3.16754 | ||||||||
\(29\) | −8.59536 | −1.59612 | −0.798060 | − | 0.602579i | \(-0.794140\pi\) | ||||
−0.798060 | + | 0.602579i | \(0.794140\pi\) | |||||||
\(30\) | 10.5259 | 1.92176 | ||||||||
\(31\) | −2.78902 | −0.500923 | −0.250462 | − | 0.968127i | \(-0.580582\pi\) | ||||
−0.250462 | + | 0.968127i | \(0.580582\pi\) | |||||||
\(32\) | 0.761613 | 0.134635 | ||||||||
\(33\) | −4.41643 | −0.768802 | ||||||||
\(34\) | −5.42007 | −0.929534 | ||||||||
\(35\) | 18.4966 | 3.12649 | ||||||||
\(36\) | 3.92015 | 0.653359 | ||||||||
\(37\) | 3.92642 | 0.645499 | 0.322749 | − | 0.946484i | \(-0.395393\pi\) | ||||
0.322749 | + | 0.946484i | \(0.395393\pi\) | |||||||
\(38\) | −15.1091 | −2.45103 | ||||||||
\(39\) | 3.10182 | 0.496688 | ||||||||
\(40\) | −20.2113 | −3.19569 | ||||||||
\(41\) | 4.06953 | 0.635553 | 0.317777 | − | 0.948166i | \(-0.397064\pi\) | ||||
0.317777 | + | 0.948166i | \(0.397064\pi\) | |||||||
\(42\) | 10.4031 | 1.60524 | ||||||||
\(43\) | −8.21929 | −1.25343 | −0.626715 | − | 0.779249i | \(-0.715601\pi\) | ||||
−0.626715 | + | 0.779249i | \(0.715601\pi\) | |||||||
\(44\) | 17.3131 | 2.61005 | ||||||||
\(45\) | 4.32607 | 0.644892 | ||||||||
\(46\) | −3.83740 | −0.565793 | ||||||||
\(47\) | −4.10099 | −0.598191 | −0.299095 | − | 0.954223i | \(-0.596685\pi\) | ||||
−0.299095 | + | 0.954223i | \(0.596685\pi\) | |||||||
\(48\) | −3.52729 | −0.509120 | ||||||||
\(49\) | 11.2808 | 1.61155 | ||||||||
\(50\) | −33.3701 | −4.71924 | ||||||||
\(51\) | −2.22761 | −0.311927 | ||||||||
\(52\) | −12.1596 | −1.68623 | ||||||||
\(53\) | −5.52229 | −0.758545 | −0.379273 | − | 0.925285i | \(-0.623826\pi\) | ||||
−0.379273 | + | 0.925285i | \(0.623826\pi\) | |||||||
\(54\) | 2.43314 | 0.331108 | ||||||||
\(55\) | 19.1058 | 2.57622 | ||||||||
\(56\) | −19.9756 | −2.66935 | ||||||||
\(57\) | −6.20974 | −0.822500 | ||||||||
\(58\) | 20.9137 | 2.74610 | ||||||||
\(59\) | −8.78197 | −1.14331 | −0.571657 | − | 0.820492i | \(-0.693699\pi\) | ||||
−0.571657 | + | 0.820492i | \(0.693699\pi\) | |||||||
\(60\) | −16.9588 | −2.18938 | ||||||||
\(61\) | −12.8871 | −1.65003 | −0.825015 | − | 0.565111i | \(-0.808833\pi\) | ||||
−0.825015 | + | 0.565111i | \(0.808833\pi\) | |||||||
\(62\) | 6.78607 | 0.861832 | ||||||||
\(63\) | 4.27561 | 0.538676 | ||||||||
\(64\) | −8.90768 | −1.11346 | ||||||||
\(65\) | −13.4187 | −1.66438 | ||||||||
\(66\) | 10.7458 | 1.32271 | ||||||||
\(67\) | 4.05528 | 0.495431 | 0.247716 | − | 0.968833i | \(-0.420320\pi\) | ||||
0.247716 | + | 0.968833i | \(0.420320\pi\) | |||||||
\(68\) | 8.73256 | 1.05898 | ||||||||
\(69\) | −1.57714 | −0.189865 | ||||||||
\(70\) | −45.0047 | −5.37909 | ||||||||
\(71\) | −2.48373 | −0.294764 | −0.147382 | − | 0.989080i | \(-0.547085\pi\) | ||||
−0.147382 | + | 0.989080i | \(0.547085\pi\) | |||||||
\(72\) | −4.67199 | −0.550599 | ||||||||
\(73\) | 0.913035 | 0.106863 | 0.0534314 | − | 0.998572i | \(-0.482984\pi\) | ||||
0.0534314 | + | 0.998572i | \(0.482984\pi\) | |||||||
\(74\) | −9.55350 | −1.11057 | ||||||||
\(75\) | −13.7148 | −1.58365 | ||||||||
\(76\) | 24.3431 | 2.79235 | ||||||||
\(77\) | 18.8829 | 2.15191 | ||||||||
\(78\) | −7.54714 | −0.854546 | ||||||||
\(79\) | −13.3802 | −1.50539 | −0.752697 | − | 0.658367i | \(-0.771248\pi\) | ||||
−0.752697 | + | 0.658367i | \(0.771248\pi\) | |||||||
\(80\) | 15.2593 | 1.70604 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.90171 | −1.09346 | ||||||||
\(83\) | 12.3204 | 1.35234 | 0.676171 | − | 0.736745i | \(-0.263638\pi\) | ||||
0.676171 | + | 0.736745i | \(0.263638\pi\) | |||||||
\(84\) | −16.7610 | −1.82878 | ||||||||
\(85\) | 9.63677 | 1.04525 | ||||||||
\(86\) | 19.9986 | 2.15651 | ||||||||
\(87\) | 8.59536 | 0.921520 | ||||||||
\(88\) | −20.6335 | −2.19954 | ||||||||
\(89\) | 13.8184 | 1.46475 | 0.732374 | − | 0.680903i | \(-0.238412\pi\) | ||||
0.732374 | + | 0.680903i | \(0.238412\pi\) | |||||||
\(90\) | −10.5259 | −1.10953 | ||||||||
\(91\) | −13.2622 | −1.39025 | ||||||||
\(92\) | 6.18263 | 0.644583 | ||||||||
\(93\) | 2.78902 | 0.289208 | ||||||||
\(94\) | 9.97827 | 1.02918 | ||||||||
\(95\) | 26.8637 | 2.75616 | ||||||||
\(96\) | −0.761613 | −0.0777318 | ||||||||
\(97\) | −0.475066 | −0.0482357 | −0.0241178 | − | 0.999709i | \(-0.507678\pi\) | ||||
−0.0241178 | + | 0.999709i | \(0.507678\pi\) | |||||||
\(98\) | −27.4478 | −2.77265 | ||||||||
\(99\) | 4.41643 | 0.443868 | ||||||||
\(100\) | 53.7642 | 5.37642 | ||||||||
\(101\) | −0.687244 | −0.0683834 | −0.0341917 | − | 0.999415i | \(-0.510886\pi\) | ||||
−0.0341917 | + | 0.999415i | \(0.510886\pi\) | |||||||
\(102\) | 5.42007 | 0.536667 | ||||||||
\(103\) | −6.80191 | −0.670212 | −0.335106 | − | 0.942180i | \(-0.608772\pi\) | ||||
−0.335106 | + | 0.942180i | \(0.608772\pi\) | |||||||
\(104\) | 14.4917 | 1.42102 | ||||||||
\(105\) | −18.4966 | −1.80508 | ||||||||
\(106\) | 13.4365 | 1.30507 | ||||||||
\(107\) | 7.16048 | 0.692230 | 0.346115 | − | 0.938192i | \(-0.387501\pi\) | ||||
0.346115 | + | 0.938192i | \(0.387501\pi\) | |||||||
\(108\) | −3.92015 | −0.377217 | ||||||||
\(109\) | 15.8253 | 1.51579 | 0.757894 | − | 0.652378i | \(-0.226229\pi\) | ||||
0.757894 | + | 0.652378i | \(0.226229\pi\) | |||||||
\(110\) | −46.4870 | −4.43236 | ||||||||
\(111\) | −3.92642 | −0.372679 | ||||||||
\(112\) | 15.0813 | 1.42505 | ||||||||
\(113\) | 4.14186 | 0.389633 | 0.194817 | − | 0.980840i | \(-0.437589\pi\) | ||||
0.194817 | + | 0.980840i | \(0.437589\pi\) | |||||||
\(114\) | 15.1091 | 1.41510 | ||||||||
\(115\) | 6.82281 | 0.636230 | ||||||||
\(116\) | −33.6951 | −3.12851 | ||||||||
\(117\) | −3.10182 | −0.286763 | ||||||||
\(118\) | 21.3677 | 1.96706 | ||||||||
\(119\) | 9.52438 | 0.873098 | ||||||||
\(120\) | 20.2113 | 1.84503 | ||||||||
\(121\) | 8.50488 | 0.773171 | ||||||||
\(122\) | 31.3562 | 2.83885 | ||||||||
\(123\) | −4.06953 | −0.366937 | ||||||||
\(124\) | −10.9334 | −0.981847 | ||||||||
\(125\) | 37.7010 | 3.37208 | ||||||||
\(126\) | −10.4031 | −0.926786 | ||||||||
\(127\) | 13.3891 | 1.18809 | 0.594045 | − | 0.804431i | \(-0.297530\pi\) | ||||
0.594045 | + | 0.804431i | \(0.297530\pi\) | |||||||
\(128\) | 20.1504 | 1.78106 | ||||||||
\(129\) | 8.21929 | 0.723668 | ||||||||
\(130\) | 32.6494 | 2.86355 | ||||||||
\(131\) | −2.23789 | −0.195526 | −0.0977629 | − | 0.995210i | \(-0.531169\pi\) | ||||
−0.0977629 | + | 0.995210i | \(0.531169\pi\) | |||||||
\(132\) | −17.3131 | −1.50691 | ||||||||
\(133\) | 26.5504 | 2.30222 | ||||||||
\(134\) | −9.86704 | −0.852383 | ||||||||
\(135\) | −4.32607 | −0.372328 | ||||||||
\(136\) | −10.4074 | −0.892423 | ||||||||
\(137\) | −5.49567 | −0.469527 | −0.234763 | − | 0.972053i | \(-0.575432\pi\) | ||||
−0.234763 | + | 0.972053i | \(0.575432\pi\) | |||||||
\(138\) | 3.83740 | 0.326661 | ||||||||
\(139\) | −12.3433 | −1.04695 | −0.523474 | − | 0.852041i | \(-0.675364\pi\) | ||||
−0.523474 | + | 0.852041i | \(0.675364\pi\) | |||||||
\(140\) | 72.5094 | 6.12816 | ||||||||
\(141\) | 4.10099 | 0.345366 | ||||||||
\(142\) | 6.04324 | 0.507138 | ||||||||
\(143\) | −13.6990 | −1.14557 | ||||||||
\(144\) | 3.52729 | 0.293941 | ||||||||
\(145\) | −37.1841 | −3.08797 | ||||||||
\(146\) | −2.22154 | −0.183856 | ||||||||
\(147\) | −11.2808 | −0.930428 | ||||||||
\(148\) | 15.3921 | 1.26523 | ||||||||
\(149\) | 15.6789 | 1.28446 | 0.642232 | − | 0.766510i | \(-0.278009\pi\) | ||||
0.642232 | + | 0.766510i | \(0.278009\pi\) | |||||||
\(150\) | 33.3701 | 2.72465 | ||||||||
\(151\) | −5.53514 | −0.450444 | −0.225222 | − | 0.974308i | \(-0.572311\pi\) | ||||
−0.225222 | + | 0.974308i | \(0.572311\pi\) | |||||||
\(152\) | −29.0119 | −2.35317 | ||||||||
\(153\) | 2.22761 | 0.180091 | ||||||||
\(154\) | −45.9448 | −3.70234 | ||||||||
\(155\) | −12.0655 | −0.969123 | ||||||||
\(156\) | 12.1596 | 0.973547 | ||||||||
\(157\) | −2.45042 | −0.195565 | −0.0977823 | − | 0.995208i | \(-0.531175\pi\) | ||||
−0.0977823 | + | 0.995208i | \(0.531175\pi\) | |||||||
\(158\) | 32.5559 | 2.59001 | ||||||||
\(159\) | 5.52229 | 0.437946 | ||||||||
\(160\) | 3.29479 | 0.260476 | ||||||||
\(161\) | 6.74324 | 0.531441 | ||||||||
\(162\) | −2.43314 | −0.191165 | ||||||||
\(163\) | 16.7975 | 1.31568 | 0.657840 | − | 0.753158i | \(-0.271470\pi\) | ||||
0.657840 | + | 0.753158i | \(0.271470\pi\) | |||||||
\(164\) | 15.9532 | 1.24573 | ||||||||
\(165\) | −19.1058 | −1.48738 | ||||||||
\(166\) | −29.9773 | −2.32669 | ||||||||
\(167\) | 11.4013 | 0.882256 | 0.441128 | − | 0.897444i | \(-0.354579\pi\) | ||||
0.441128 | + | 0.897444i | \(0.354579\pi\) | |||||||
\(168\) | 19.9756 | 1.54115 | ||||||||
\(169\) | −3.37873 | −0.259902 | ||||||||
\(170\) | −23.4476 | −1.79835 | ||||||||
\(171\) | 6.20974 | 0.474871 | ||||||||
\(172\) | −32.2208 | −2.45682 | ||||||||
\(173\) | 15.4104 | 1.17163 | 0.585816 | − | 0.810444i | \(-0.300774\pi\) | ||||
0.585816 | + | 0.810444i | \(0.300774\pi\) | |||||||
\(174\) | −20.9137 | −1.58546 | ||||||||
\(175\) | 58.6393 | 4.43272 | ||||||||
\(176\) | 15.5780 | 1.17424 | ||||||||
\(177\) | 8.78197 | 0.660093 | ||||||||
\(178\) | −33.6221 | −2.52008 | ||||||||
\(179\) | −7.82666 | −0.584992 | −0.292496 | − | 0.956267i | \(-0.594486\pi\) | ||||
−0.292496 | + | 0.956267i | \(0.594486\pi\) | |||||||
\(180\) | 16.9588 | 1.26404 | ||||||||
\(181\) | 5.73370 | 0.426182 | 0.213091 | − | 0.977032i | \(-0.431647\pi\) | ||||
0.213091 | + | 0.977032i | \(0.431647\pi\) | |||||||
\(182\) | 32.2687 | 2.39191 | ||||||||
\(183\) | 12.8871 | 0.952645 | ||||||||
\(184\) | −7.36838 | −0.543204 | ||||||||
\(185\) | 16.9859 | 1.24883 | ||||||||
\(186\) | −6.78607 | −0.497579 | ||||||||
\(187\) | 9.83807 | 0.719431 | ||||||||
\(188\) | −16.0765 | −1.17250 | ||||||||
\(189\) | −4.27561 | −0.311005 | ||||||||
\(190\) | −65.3632 | −4.74194 | ||||||||
\(191\) | 26.7017 | 1.93207 | 0.966033 | − | 0.258417i | \(-0.0832010\pi\) | ||||
0.966033 | + | 0.258417i | \(0.0832010\pi\) | |||||||
\(192\) | 8.90768 | 0.642857 | ||||||||
\(193\) | 5.01994 | 0.361343 | 0.180672 | − | 0.983543i | \(-0.442173\pi\) | ||||
0.180672 | + | 0.983543i | \(0.442173\pi\) | |||||||
\(194\) | 1.15590 | 0.0829889 | ||||||||
\(195\) | 13.4187 | 0.960931 | ||||||||
\(196\) | 44.2226 | 3.15876 | ||||||||
\(197\) | 5.40340 | 0.384976 | 0.192488 | − | 0.981299i | \(-0.438344\pi\) | ||||
0.192488 | + | 0.981299i | \(0.438344\pi\) | |||||||
\(198\) | −10.7458 | −0.763670 | ||||||||
\(199\) | −6.84587 | −0.485291 | −0.242645 | − | 0.970115i | \(-0.578015\pi\) | ||||
−0.242645 | + | 0.970115i | \(0.578015\pi\) | |||||||
\(200\) | −64.0756 | −4.53083 | ||||||||
\(201\) | −4.05528 | −0.286037 | ||||||||
\(202\) | 1.67216 | 0.117653 | ||||||||
\(203\) | −36.7504 | −2.57937 | ||||||||
\(204\) | −8.73256 | −0.611401 | ||||||||
\(205\) | 17.6050 | 1.22959 | ||||||||
\(206\) | 16.5500 | 1.15309 | ||||||||
\(207\) | 1.57714 | 0.109619 | ||||||||
\(208\) | −10.9410 | −0.758622 | ||||||||
\(209\) | 27.4249 | 1.89702 | ||||||||
\(210\) | 45.0047 | 3.10562 | ||||||||
\(211\) | −2.07753 | −0.143023 | −0.0715117 | − | 0.997440i | \(-0.522782\pi\) | ||||
−0.0715117 | + | 0.997440i | \(0.522782\pi\) | |||||||
\(212\) | −21.6482 | −1.48681 | ||||||||
\(213\) | 2.48373 | 0.170182 | ||||||||
\(214\) | −17.4224 | −1.19097 | ||||||||
\(215\) | −35.5572 | −2.42498 | ||||||||
\(216\) | 4.67199 | 0.317889 | ||||||||
\(217\) | −11.9248 | −0.809506 | ||||||||
\(218\) | −38.5051 | −2.60789 | ||||||||
\(219\) | −0.913035 | −0.0616972 | ||||||||
\(220\) | 74.8975 | 5.04959 | ||||||||
\(221\) | −6.90963 | −0.464792 | ||||||||
\(222\) | 9.55350 | 0.641189 | ||||||||
\(223\) | −16.3319 | −1.09367 | −0.546834 | − | 0.837241i | \(-0.684167\pi\) | ||||
−0.546834 | + | 0.837241i | \(0.684167\pi\) | |||||||
\(224\) | 3.25636 | 0.217575 | ||||||||
\(225\) | 13.7148 | 0.914323 | ||||||||
\(226\) | −10.0777 | −0.670359 | ||||||||
\(227\) | 10.2045 | 0.677299 | 0.338650 | − | 0.940913i | \(-0.390030\pi\) | ||||
0.338650 | + | 0.940913i | \(0.390030\pi\) | |||||||
\(228\) | −24.3431 | −1.61216 | ||||||||
\(229\) | 13.8003 | 0.911952 | 0.455976 | − | 0.889992i | \(-0.349290\pi\) | ||||
0.455976 | + | 0.889992i | \(0.349290\pi\) | |||||||
\(230\) | −16.6008 | −1.09463 | ||||||||
\(231\) | −18.8829 | −1.24241 | ||||||||
\(232\) | 40.1575 | 2.63647 | ||||||||
\(233\) | 18.9576 | 1.24195 | 0.620976 | − | 0.783829i | \(-0.286736\pi\) | ||||
0.620976 | + | 0.783829i | \(0.286736\pi\) | |||||||
\(234\) | 7.54714 | 0.493372 | ||||||||
\(235\) | −17.7411 | −1.15730 | ||||||||
\(236\) | −34.4266 | −2.24098 | ||||||||
\(237\) | 13.3802 | 0.869140 | ||||||||
\(238\) | −23.1741 | −1.50215 | ||||||||
\(239\) | −4.74569 | −0.306973 | −0.153487 | − | 0.988151i | \(-0.549050\pi\) | ||||
−0.153487 | + | 0.988151i | \(0.549050\pi\) | |||||||
\(240\) | −15.2593 | −0.984982 | ||||||||
\(241\) | −2.14957 | −0.138466 | −0.0692329 | − | 0.997601i | \(-0.522055\pi\) | ||||
−0.0692329 | + | 0.997601i | \(0.522055\pi\) | |||||||
\(242\) | −20.6935 | −1.33023 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −50.5196 | −3.23418 | ||||||||
\(245\) | 48.8017 | 3.11782 | ||||||||
\(246\) | 9.90171 | 0.631310 | ||||||||
\(247\) | −19.2615 | −1.22558 | ||||||||
\(248\) | 13.0303 | 0.827424 | ||||||||
\(249\) | −12.3204 | −0.780775 | ||||||||
\(250\) | −91.7316 | −5.80161 | ||||||||
\(251\) | −1.07911 | −0.0681129 | −0.0340564 | − | 0.999420i | \(-0.510843\pi\) | ||||
−0.0340564 | + | 0.999420i | \(0.510843\pi\) | |||||||
\(252\) | 16.7610 | 1.05585 | ||||||||
\(253\) | 6.96533 | 0.437907 | ||||||||
\(254\) | −32.5775 | −2.04410 | ||||||||
\(255\) | −9.63677 | −0.603478 | ||||||||
\(256\) | −31.2132 | −1.95083 | ||||||||
\(257\) | 19.0965 | 1.19121 | 0.595603 | − | 0.803279i | \(-0.296913\pi\) | ||||
0.595603 | + | 0.803279i | \(0.296913\pi\) | |||||||
\(258\) | −19.9986 | −1.24506 | ||||||||
\(259\) | 16.7878 | 1.04314 | ||||||||
\(260\) | −52.6032 | −3.26231 | ||||||||
\(261\) | −8.59536 | −0.532040 | ||||||||
\(262\) | 5.44510 | 0.336400 | ||||||||
\(263\) | 21.0525 | 1.29815 | 0.649077 | − | 0.760723i | \(-0.275155\pi\) | ||||
0.649077 | + | 0.760723i | \(0.275155\pi\) | |||||||
\(264\) | 20.6335 | 1.26991 | ||||||||
\(265\) | −23.8898 | −1.46754 | ||||||||
\(266\) | −64.6008 | −3.96093 | ||||||||
\(267\) | −13.8184 | −0.845673 | ||||||||
\(268\) | 15.8973 | 0.971082 | ||||||||
\(269\) | 2.84626 | 0.173539 | 0.0867697 | − | 0.996228i | \(-0.472346\pi\) | ||||
0.0867697 | + | 0.996228i | \(0.472346\pi\) | |||||||
\(270\) | 10.5259 | 0.640586 | ||||||||
\(271\) | 0.859074 | 0.0521850 | 0.0260925 | − | 0.999660i | \(-0.491694\pi\) | ||||
0.0260925 | + | 0.999660i | \(0.491694\pi\) | |||||||
\(272\) | 7.85741 | 0.476425 | ||||||||
\(273\) | 13.2622 | 0.802663 | ||||||||
\(274\) | 13.3717 | 0.807814 | ||||||||
\(275\) | 60.5707 | 3.65255 | ||||||||
\(276\) | −6.18263 | −0.372150 | ||||||||
\(277\) | −14.5325 | −0.873173 | −0.436586 | − | 0.899662i | \(-0.643813\pi\) | ||||
−0.436586 | + | 0.899662i | \(0.643813\pi\) | |||||||
\(278\) | 30.0330 | 1.80126 | ||||||||
\(279\) | −2.78902 | −0.166974 | ||||||||
\(280\) | −86.4158 | −5.16433 | ||||||||
\(281\) | 28.0433 | 1.67292 | 0.836462 | − | 0.548025i | \(-0.184620\pi\) | ||||
0.836462 | + | 0.548025i | \(0.184620\pi\) | |||||||
\(282\) | −9.97827 | −0.594197 | ||||||||
\(283\) | −3.01509 | −0.179229 | −0.0896143 | − | 0.995977i | \(-0.528563\pi\) | ||||
−0.0896143 | + | 0.995977i | \(0.528563\pi\) | |||||||
\(284\) | −9.73658 | −0.577760 | ||||||||
\(285\) | −26.8637 | −1.59127 | ||||||||
\(286\) | 33.3315 | 1.97093 | ||||||||
\(287\) | 17.3997 | 1.02707 | ||||||||
\(288\) | 0.761613 | 0.0448785 | ||||||||
\(289\) | −12.0378 | −0.708104 | ||||||||
\(290\) | 90.4740 | 5.31282 | ||||||||
\(291\) | 0.475066 | 0.0278489 | ||||||||
\(292\) | 3.57924 | 0.209459 | ||||||||
\(293\) | −28.0077 | −1.63623 | −0.818113 | − | 0.575057i | \(-0.804980\pi\) | ||||
−0.818113 | + | 0.575057i | \(0.804980\pi\) | |||||||
\(294\) | 27.4478 | 1.60079 | ||||||||
\(295\) | −37.9914 | −2.21194 | ||||||||
\(296\) | −18.3442 | −1.06623 | ||||||||
\(297\) | −4.41643 | −0.256267 | ||||||||
\(298\) | −38.1488 | −2.20990 | ||||||||
\(299\) | −4.89200 | −0.282912 | ||||||||
\(300\) | −53.7642 | −3.10408 | ||||||||
\(301\) | −35.1425 | −2.02558 | ||||||||
\(302\) | 13.4678 | 0.774982 | ||||||||
\(303\) | 0.687244 | 0.0394812 | ||||||||
\(304\) | 21.9035 | 1.25625 | ||||||||
\(305\) | −55.7506 | −3.19227 | ||||||||
\(306\) | −5.42007 | −0.309845 | ||||||||
\(307\) | 31.6001 | 1.80351 | 0.901756 | − | 0.432246i | \(-0.142279\pi\) | ||||
0.901756 | + | 0.432246i | \(0.142279\pi\) | |||||||
\(308\) | 74.0240 | 4.21791 | ||||||||
\(309\) | 6.80191 | 0.386947 | ||||||||
\(310\) | 29.3570 | 1.66736 | ||||||||
\(311\) | −7.14550 | −0.405184 | −0.202592 | − | 0.979263i | \(-0.564937\pi\) | ||||
−0.202592 | + | 0.979263i | \(0.564937\pi\) | |||||||
\(312\) | −14.4917 | −0.820429 | ||||||||
\(313\) | 2.29485 | 0.129713 | 0.0648563 | − | 0.997895i | \(-0.479341\pi\) | ||||
0.0648563 | + | 0.997895i | \(0.479341\pi\) | |||||||
\(314\) | 5.96220 | 0.336466 | ||||||||
\(315\) | 18.4966 | 1.04216 | ||||||||
\(316\) | −52.4526 | −2.95069 | ||||||||
\(317\) | −4.72896 | −0.265605 | −0.132802 | − | 0.991143i | \(-0.542398\pi\) | ||||
−0.132802 | + | 0.991143i | \(0.542398\pi\) | |||||||
\(318\) | −13.4365 | −0.753481 | ||||||||
\(319\) | −37.9609 | −2.12540 | ||||||||
\(320\) | −38.5352 | −2.15418 | ||||||||
\(321\) | −7.16048 | −0.399659 | ||||||||
\(322\) | −16.4072 | −0.914338 | ||||||||
\(323\) | 13.8329 | 0.769681 | ||||||||
\(324\) | 3.92015 | 0.217786 | ||||||||
\(325\) | −42.5409 | −2.35975 | ||||||||
\(326\) | −40.8706 | −2.26361 | ||||||||
\(327\) | −15.8253 | −0.875140 | ||||||||
\(328\) | −19.0128 | −1.04981 | ||||||||
\(329\) | −17.5342 | −0.966694 | ||||||||
\(330\) | 46.4870 | 2.55902 | ||||||||
\(331\) | −27.8375 | −1.53009 | −0.765043 | − | 0.643980i | \(-0.777282\pi\) | ||||
−0.765043 | + | 0.643980i | \(0.777282\pi\) | |||||||
\(332\) | 48.2979 | 2.65069 | ||||||||
\(333\) | 3.92642 | 0.215166 | ||||||||
\(334\) | −27.7408 | −1.51791 | ||||||||
\(335\) | 17.5434 | 0.958498 | ||||||||
\(336\) | −15.0813 | −0.822753 | ||||||||
\(337\) | −29.0543 | −1.58269 | −0.791346 | − | 0.611369i | \(-0.790619\pi\) | ||||
−0.791346 | + | 0.611369i | \(0.790619\pi\) | |||||||
\(338\) | 8.22090 | 0.447158 | ||||||||
\(339\) | −4.14186 | −0.224955 | ||||||||
\(340\) | 37.7776 | 2.04878 | ||||||||
\(341\) | −12.3175 | −0.667031 | ||||||||
\(342\) | −15.1091 | −0.817009 | ||||||||
\(343\) | 18.3032 | 0.988281 | ||||||||
\(344\) | 38.4004 | 2.07041 | ||||||||
\(345\) | −6.82281 | −0.367328 | ||||||||
\(346\) | −37.4956 | −2.01578 | ||||||||
\(347\) | 20.9222 | 1.12316 | 0.561581 | − | 0.827421i | \(-0.310193\pi\) | ||||
0.561581 | + | 0.827421i | \(0.310193\pi\) | |||||||
\(348\) | 33.6951 | 1.80625 | ||||||||
\(349\) | 14.6284 | 0.783038 | 0.391519 | − | 0.920170i | \(-0.371950\pi\) | ||||
0.391519 | + | 0.920170i | \(0.371950\pi\) | |||||||
\(350\) | −142.677 | −7.62643 | ||||||||
\(351\) | 3.10182 | 0.165563 | ||||||||
\(352\) | 3.36361 | 0.179281 | ||||||||
\(353\) | −23.4035 | −1.24564 | −0.622822 | − | 0.782363i | \(-0.714014\pi\) | ||||
−0.622822 | + | 0.782363i | \(0.714014\pi\) | |||||||
\(354\) | −21.3677 | −1.13568 | ||||||||
\(355\) | −10.7448 | −0.570273 | ||||||||
\(356\) | 54.1702 | 2.87102 | ||||||||
\(357\) | −9.52438 | −0.504083 | ||||||||
\(358\) | 19.0433 | 1.00647 | ||||||||
\(359\) | 23.9181 | 1.26235 | 0.631174 | − | 0.775641i | \(-0.282573\pi\) | ||||
0.631174 | + | 0.775641i | \(0.282573\pi\) | |||||||
\(360\) | −20.2113 | −1.06523 | ||||||||
\(361\) | 19.5609 | 1.02952 | ||||||||
\(362\) | −13.9509 | −0.733241 | ||||||||
\(363\) | −8.50488 | −0.446391 | ||||||||
\(364\) | −51.9897 | −2.72500 | ||||||||
\(365\) | 3.94985 | 0.206745 | ||||||||
\(366\) | −31.3562 | −1.63901 | ||||||||
\(367\) | −22.3516 | −1.16675 | −0.583373 | − | 0.812205i | \(-0.698267\pi\) | ||||
−0.583373 | + | 0.812205i | \(0.698267\pi\) | |||||||
\(368\) | 5.56302 | 0.289993 | ||||||||
\(369\) | 4.06953 | 0.211851 | ||||||||
\(370\) | −41.3291 | −2.14860 | ||||||||
\(371\) | −23.6112 | −1.22583 | ||||||||
\(372\) | 10.9334 | 0.566870 | ||||||||
\(373\) | −13.6008 | −0.704222 | −0.352111 | − | 0.935958i | \(-0.614536\pi\) | ||||
−0.352111 | + | 0.935958i | \(0.614536\pi\) | |||||||
\(374\) | −23.9374 | −1.23777 | ||||||||
\(375\) | −37.7010 | −1.94687 | ||||||||
\(376\) | 19.1598 | 0.988090 | ||||||||
\(377\) | 26.6613 | 1.37312 | ||||||||
\(378\) | 10.4031 | 0.535080 | ||||||||
\(379\) | 23.7741 | 1.22119 | 0.610596 | − | 0.791942i | \(-0.290930\pi\) | ||||
0.610596 | + | 0.791942i | \(0.290930\pi\) | |||||||
\(380\) | 105.310 | 5.40229 | ||||||||
\(381\) | −13.3891 | −0.685945 | ||||||||
\(382\) | −64.9689 | −3.32410 | ||||||||
\(383\) | 30.8995 | 1.57889 | 0.789446 | − | 0.613820i | \(-0.210368\pi\) | ||||
0.789446 | + | 0.613820i | \(0.210368\pi\) | |||||||
\(384\) | −20.1504 | −1.02829 | ||||||||
\(385\) | 81.6889 | 4.16325 | ||||||||
\(386\) | −12.2142 | −0.621686 | ||||||||
\(387\) | −8.21929 | −0.417810 | ||||||||
\(388\) | −1.86233 | −0.0945456 | ||||||||
\(389\) | 13.5985 | 0.689472 | 0.344736 | − | 0.938700i | \(-0.387968\pi\) | ||||
0.344736 | + | 0.938700i | \(0.387968\pi\) | |||||||
\(390\) | −32.6494 | −1.65327 | ||||||||
\(391\) | 3.51325 | 0.177673 | ||||||||
\(392\) | −52.7040 | −2.66195 | ||||||||
\(393\) | 2.23789 | 0.112887 | ||||||||
\(394\) | −13.1472 | −0.662347 | ||||||||
\(395\) | −57.8838 | −2.91245 | ||||||||
\(396\) | 17.3131 | 0.870015 | ||||||||
\(397\) | −13.2920 | −0.667105 | −0.333553 | − | 0.942731i | \(-0.608248\pi\) | ||||
−0.333553 | + | 0.942731i | \(0.608248\pi\) | |||||||
\(398\) | 16.6569 | 0.834936 | ||||||||
\(399\) | −26.5504 | −1.32918 | ||||||||
\(400\) | 48.3762 | 2.41881 | ||||||||
\(401\) | −38.1202 | −1.90363 | −0.951816 | − | 0.306670i | \(-0.900785\pi\) | ||||
−0.951816 | + | 0.306670i | \(0.900785\pi\) | |||||||
\(402\) | 9.86704 | 0.492123 | ||||||||
\(403\) | 8.65104 | 0.430939 | ||||||||
\(404\) | −2.69410 | −0.134037 | ||||||||
\(405\) | 4.32607 | 0.214964 | ||||||||
\(406\) | 89.4188 | 4.43778 | ||||||||
\(407\) | 17.3408 | 0.859549 | ||||||||
\(408\) | 10.4074 | 0.515241 | ||||||||
\(409\) | −32.4502 | −1.60456 | −0.802281 | − | 0.596947i | \(-0.796380\pi\) | ||||
−0.802281 | + | 0.596947i | \(0.796380\pi\) | |||||||
\(410\) | −42.8355 | −2.11549 | ||||||||
\(411\) | 5.49567 | 0.271081 | ||||||||
\(412\) | −26.6645 | −1.31367 | ||||||||
\(413\) | −37.5483 | −1.84763 | ||||||||
\(414\) | −3.83740 | −0.188598 | ||||||||
\(415\) | 53.2989 | 2.61634 | ||||||||
\(416\) | −2.36239 | −0.115825 | ||||||||
\(417\) | 12.3433 | 0.604456 | ||||||||
\(418\) | −66.7285 | −3.26380 | ||||||||
\(419\) | −28.2342 | −1.37933 | −0.689665 | − | 0.724128i | \(-0.742242\pi\) | ||||
−0.689665 | + | 0.724128i | \(0.742242\pi\) | |||||||
\(420\) | −72.5094 | −3.53809 | ||||||||
\(421\) | 22.3706 | 1.09028 | 0.545138 | − | 0.838346i | \(-0.316477\pi\) | ||||
0.545138 | + | 0.838346i | \(0.316477\pi\) | |||||||
\(422\) | 5.05492 | 0.246070 | ||||||||
\(423\) | −4.10099 | −0.199397 | ||||||||
\(424\) | 25.8001 | 1.25296 | ||||||||
\(425\) | 30.5513 | 1.48195 | ||||||||
\(426\) | −6.04324 | −0.292796 | ||||||||
\(427\) | −55.1004 | −2.66650 | ||||||||
\(428\) | 28.0702 | 1.35682 | ||||||||
\(429\) | 13.6990 | 0.661393 | ||||||||
\(430\) | 86.5154 | 4.17214 | ||||||||
\(431\) | −28.5174 | −1.37364 | −0.686818 | − | 0.726829i | \(-0.740993\pi\) | ||||
−0.686818 | + | 0.726829i | \(0.740993\pi\) | |||||||
\(432\) | −3.52729 | −0.169707 | ||||||||
\(433\) | −26.3546 | −1.26652 | −0.633261 | − | 0.773938i | \(-0.718284\pi\) | ||||
−0.633261 | + | 0.773938i | \(0.718284\pi\) | |||||||
\(434\) | 29.0146 | 1.39274 | ||||||||
\(435\) | 37.1841 | 1.78284 | ||||||||
\(436\) | 62.0375 | 2.97106 | ||||||||
\(437\) | 9.79363 | 0.468493 | ||||||||
\(438\) | 2.22154 | 0.106149 | ||||||||
\(439\) | 15.2254 | 0.726667 | 0.363333 | − | 0.931659i | \(-0.381639\pi\) | ||||
0.363333 | + | 0.931659i | \(0.381639\pi\) | |||||||
\(440\) | −89.2620 | −4.25540 | ||||||||
\(441\) | 11.2808 | 0.537183 | ||||||||
\(442\) | 16.8121 | 0.799669 | ||||||||
\(443\) | −10.4840 | −0.498109 | −0.249054 | − | 0.968490i | \(-0.580120\pi\) | ||||
−0.249054 | + | 0.968490i | \(0.580120\pi\) | |||||||
\(444\) | −15.3921 | −0.730479 | ||||||||
\(445\) | 59.7793 | 2.83381 | ||||||||
\(446\) | 39.7378 | 1.88164 | ||||||||
\(447\) | −15.6789 | −0.741585 | ||||||||
\(448\) | −38.0858 | −1.79938 | ||||||||
\(449\) | −5.42350 | −0.255951 | −0.127975 | − | 0.991777i | \(-0.540848\pi\) | ||||
−0.127975 | + | 0.991777i | \(0.540848\pi\) | |||||||
\(450\) | −33.3701 | −1.57308 | ||||||||
\(451\) | 17.9728 | 0.846306 | ||||||||
\(452\) | 16.2367 | 0.763710 | ||||||||
\(453\) | 5.53514 | 0.260064 | ||||||||
\(454\) | −24.8290 | −1.16528 | ||||||||
\(455\) | −57.3730 | −2.68969 | ||||||||
\(456\) | 29.0119 | 1.35860 | ||||||||
\(457\) | 1.72894 | 0.0808765 | 0.0404383 | − | 0.999182i | \(-0.487125\pi\) | ||||
0.0404383 | + | 0.999182i | \(0.487125\pi\) | |||||||
\(458\) | −33.5781 | −1.56900 | ||||||||
\(459\) | −2.22761 | −0.103976 | ||||||||
\(460\) | 26.7464 | 1.24706 | ||||||||
\(461\) | 18.0135 | 0.838973 | 0.419487 | − | 0.907762i | \(-0.362210\pi\) | ||||
0.419487 | + | 0.907762i | \(0.362210\pi\) | |||||||
\(462\) | 45.9448 | 2.13754 | ||||||||
\(463\) | 35.4777 | 1.64879 | 0.824393 | − | 0.566017i | \(-0.191516\pi\) | ||||
0.824393 | + | 0.566017i | \(0.191516\pi\) | |||||||
\(464\) | −30.3183 | −1.40749 | ||||||||
\(465\) | 12.0655 | 0.559524 | ||||||||
\(466\) | −46.1264 | −2.13676 | ||||||||
\(467\) | 16.8773 | 0.780988 | 0.390494 | − | 0.920606i | \(-0.372304\pi\) | ||||
0.390494 | + | 0.920606i | \(0.372304\pi\) | |||||||
\(468\) | −12.1596 | −0.562078 | ||||||||
\(469\) | 17.3388 | 0.800631 | ||||||||
\(470\) | 43.1666 | 1.99113 | ||||||||
\(471\) | 2.45042 | 0.112909 | ||||||||
\(472\) | 41.0293 | 1.88852 | ||||||||
\(473\) | −36.2999 | −1.66907 | ||||||||
\(474\) | −32.5559 | −1.49534 | ||||||||
\(475\) | 85.1656 | 3.90767 | ||||||||
\(476\) | 37.3370 | 1.71134 | ||||||||
\(477\) | −5.52229 | −0.252848 | ||||||||
\(478\) | 11.5469 | 0.528143 | ||||||||
\(479\) | −33.1887 | −1.51643 | −0.758215 | − | 0.652004i | \(-0.773928\pi\) | ||||
−0.758215 | + | 0.652004i | \(0.773928\pi\) | |||||||
\(480\) | −3.29479 | −0.150386 | ||||||||
\(481\) | −12.1790 | −0.555316 | ||||||||
\(482\) | 5.23019 | 0.238229 | ||||||||
\(483\) | −6.74324 | −0.306828 | ||||||||
\(484\) | 33.3404 | 1.51547 | ||||||||
\(485\) | −2.05517 | −0.0933204 | ||||||||
\(486\) | 2.43314 | 0.110369 | ||||||||
\(487\) | 38.5119 | 1.74514 | 0.872570 | − | 0.488489i | \(-0.162452\pi\) | ||||
0.872570 | + | 0.488489i | \(0.162452\pi\) | |||||||
\(488\) | 60.2086 | 2.72552 | ||||||||
\(489\) | −16.7975 | −0.759608 | ||||||||
\(490\) | −118.741 | −5.36418 | ||||||||
\(491\) | −17.3939 | −0.784977 | −0.392488 | − | 0.919757i | \(-0.628386\pi\) | ||||
−0.392488 | + | 0.919757i | \(0.628386\pi\) | |||||||
\(492\) | −15.9532 | −0.719224 | ||||||||
\(493\) | −19.1471 | −0.862342 | ||||||||
\(494\) | 46.8658 | 2.10859 | ||||||||
\(495\) | 19.1058 | 0.858741 | ||||||||
\(496\) | −9.83768 | −0.441725 | ||||||||
\(497\) | −10.6194 | −0.476347 | ||||||||
\(498\) | 29.9773 | 1.34331 | ||||||||
\(499\) | 24.7114 | 1.10624 | 0.553118 | − | 0.833103i | \(-0.313438\pi\) | ||||
0.553118 | + | 0.833103i | \(0.313438\pi\) | |||||||
\(500\) | 147.793 | 6.60953 | ||||||||
\(501\) | −11.4013 | −0.509371 | ||||||||
\(502\) | 2.62562 | 0.117187 | ||||||||
\(503\) | −2.75301 | −0.122751 | −0.0613753 | − | 0.998115i | \(-0.519549\pi\) | ||||
−0.0613753 | + | 0.998115i | \(0.519549\pi\) | |||||||
\(504\) | −19.9756 | −0.889785 | ||||||||
\(505\) | −2.97306 | −0.132300 | ||||||||
\(506\) | −16.9476 | −0.753413 | ||||||||
\(507\) | 3.37873 | 0.150055 | ||||||||
\(508\) | 52.4873 | 2.32875 | ||||||||
\(509\) | 37.2596 | 1.65150 | 0.825751 | − | 0.564035i | \(-0.190752\pi\) | ||||
0.825751 | + | 0.564035i | \(0.190752\pi\) | |||||||
\(510\) | 23.4476 | 1.03828 | ||||||||
\(511\) | 3.90378 | 0.172693 | ||||||||
\(512\) | 35.6453 | 1.57532 | ||||||||
\(513\) | −6.20974 | −0.274167 | ||||||||
\(514\) | −46.4643 | −2.04945 | ||||||||
\(515\) | −29.4255 | −1.29664 | ||||||||
\(516\) | 32.2208 | 1.41844 | ||||||||
\(517\) | −18.1117 | −0.796554 | ||||||||
\(518\) | −40.8471 | −1.79472 | ||||||||
\(519\) | −15.4104 | −0.676442 | ||||||||
\(520\) | 62.6919 | 2.74922 | ||||||||
\(521\) | −39.5184 | −1.73133 | −0.865666 | − | 0.500621i | \(-0.833105\pi\) | ||||
−0.865666 | + | 0.500621i | \(0.833105\pi\) | |||||||
\(522\) | 20.9137 | 0.915367 | ||||||||
\(523\) | 4.09491 | 0.179058 | 0.0895289 | − | 0.995984i | \(-0.471464\pi\) | ||||
0.0895289 | + | 0.995984i | \(0.471464\pi\) | |||||||
\(524\) | −8.77289 | −0.383245 | ||||||||
\(525\) | −58.6393 | −2.55923 | ||||||||
\(526\) | −51.2236 | −2.23346 | ||||||||
\(527\) | −6.21284 | −0.270636 | ||||||||
\(528\) | −15.5780 | −0.677947 | ||||||||
\(529\) | −20.5126 | −0.891853 | ||||||||
\(530\) | 58.1271 | 2.52488 | ||||||||
\(531\) | −8.78197 | −0.381105 | ||||||||
\(532\) | 104.082 | 4.51252 | ||||||||
\(533\) | −12.6229 | −0.546760 | ||||||||
\(534\) | 33.6221 | 1.45497 | ||||||||
\(535\) | 30.9767 | 1.33924 | ||||||||
\(536\) | −18.9462 | −0.818352 | ||||||||
\(537\) | 7.82666 | 0.337745 | ||||||||
\(538\) | −6.92533 | −0.298572 | ||||||||
\(539\) | 49.8211 | 2.14595 | ||||||||
\(540\) | −16.9588 | −0.729792 | ||||||||
\(541\) | 13.3054 | 0.572043 | 0.286022 | − | 0.958223i | \(-0.407667\pi\) | ||||
0.286022 | + | 0.958223i | \(0.407667\pi\) | |||||||
\(542\) | −2.09024 | −0.0897837 | ||||||||
\(543\) | −5.73370 | −0.246057 | ||||||||
\(544\) | 1.69657 | 0.0727400 | ||||||||
\(545\) | 68.4612 | 2.93256 | ||||||||
\(546\) | −32.2687 | −1.38097 | ||||||||
\(547\) | 30.5954 | 1.30817 | 0.654083 | − | 0.756423i | \(-0.273055\pi\) | ||||
0.654083 | + | 0.756423i | \(0.273055\pi\) | |||||||
\(548\) | −21.5439 | −0.920308 | ||||||||
\(549\) | −12.8871 | −0.550010 | ||||||||
\(550\) | −147.377 | −6.28416 | ||||||||
\(551\) | −53.3750 | −2.27385 | ||||||||
\(552\) | 7.36838 | 0.313619 | ||||||||
\(553\) | −57.2087 | −2.43276 | ||||||||
\(554\) | 35.3595 | 1.50228 | ||||||||
\(555\) | −16.9859 | −0.721012 | ||||||||
\(556\) | −48.3878 | −2.05210 | ||||||||
\(557\) | 8.92849 | 0.378312 | 0.189156 | − | 0.981947i | \(-0.439425\pi\) | ||||
0.189156 | + | 0.981947i | \(0.439425\pi\) | |||||||
\(558\) | 6.78607 | 0.287277 | ||||||||
\(559\) | 25.4947 | 1.07831 | ||||||||
\(560\) | 65.2427 | 2.75701 | ||||||||
\(561\) | −9.83807 | −0.415364 | ||||||||
\(562\) | −68.2332 | −2.87824 | ||||||||
\(563\) | 17.1704 | 0.723648 | 0.361824 | − | 0.932246i | \(-0.382154\pi\) | ||||
0.361824 | + | 0.932246i | \(0.382154\pi\) | |||||||
\(564\) | 16.0765 | 0.676943 | ||||||||
\(565\) | 17.9179 | 0.753813 | ||||||||
\(566\) | 7.33613 | 0.308360 | ||||||||
\(567\) | 4.27561 | 0.179559 | ||||||||
\(568\) | 11.6039 | 0.486891 | ||||||||
\(569\) | 33.4025 | 1.40030 | 0.700152 | − | 0.713994i | \(-0.253115\pi\) | ||||
0.700152 | + | 0.713994i | \(0.253115\pi\) | |||||||
\(570\) | 65.3632 | 2.73776 | ||||||||
\(571\) | −43.8389 | −1.83460 | −0.917301 | − | 0.398195i | \(-0.869637\pi\) | ||||
−0.917301 | + | 0.398195i | \(0.869637\pi\) | |||||||
\(572\) | −53.7020 | −2.24540 | ||||||||
\(573\) | −26.7017 | −1.11548 | ||||||||
\(574\) | −42.3359 | −1.76706 | ||||||||
\(575\) | 21.6302 | 0.902042 | ||||||||
\(576\) | −8.90768 | −0.371153 | ||||||||
\(577\) | 23.1444 | 0.963513 | 0.481757 | − | 0.876305i | \(-0.339999\pi\) | ||||
0.481757 | + | 0.876305i | \(0.339999\pi\) | |||||||
\(578\) | 29.2895 | 1.21828 | ||||||||
\(579\) | −5.01994 | −0.208622 | ||||||||
\(580\) | −145.767 | −6.05266 | ||||||||
\(581\) | 52.6773 | 2.18542 | ||||||||
\(582\) | −1.15590 | −0.0479136 | ||||||||
\(583\) | −24.3888 | −1.01008 | ||||||||
\(584\) | −4.26569 | −0.176516 | ||||||||
\(585\) | −13.4187 | −0.554794 | ||||||||
\(586\) | 68.1465 | 2.81511 | ||||||||
\(587\) | 22.3416 | 0.922135 | 0.461068 | − | 0.887365i | \(-0.347467\pi\) | ||||
0.461068 | + | 0.887365i | \(0.347467\pi\) | |||||||
\(588\) | −44.2226 | −1.82371 | ||||||||
\(589\) | −17.3191 | −0.713621 | ||||||||
\(590\) | 92.4381 | 3.80562 | ||||||||
\(591\) | −5.40340 | −0.222266 | ||||||||
\(592\) | 13.8496 | 0.569215 | ||||||||
\(593\) | 30.0817 | 1.23531 | 0.617654 | − | 0.786450i | \(-0.288083\pi\) | ||||
0.617654 | + | 0.786450i | \(0.288083\pi\) | |||||||
\(594\) | 10.7458 | 0.440905 | ||||||||
\(595\) | 41.2031 | 1.68916 | ||||||||
\(596\) | 61.4636 | 2.51765 | ||||||||
\(597\) | 6.84587 | 0.280183 | ||||||||
\(598\) | 11.9029 | 0.486746 | ||||||||
\(599\) | −38.4851 | −1.57246 | −0.786230 | − | 0.617934i | \(-0.787970\pi\) | ||||
−0.786230 | + | 0.617934i | \(0.787970\pi\) | |||||||
\(600\) | 64.0756 | 2.61588 | ||||||||
\(601\) | −40.4580 | −1.65031 | −0.825157 | − | 0.564903i | \(-0.808914\pi\) | ||||
−0.825157 | + | 0.564903i | \(0.808914\pi\) | |||||||
\(602\) | 85.5064 | 3.48498 | ||||||||
\(603\) | 4.05528 | 0.165144 | ||||||||
\(604\) | −21.6986 | −0.882904 | ||||||||
\(605\) | 36.7927 | 1.49583 | ||||||||
\(606\) | −1.67216 | −0.0679268 | ||||||||
\(607\) | 4.84177 | 0.196521 | 0.0982607 | − | 0.995161i | \(-0.468672\pi\) | ||||
0.0982607 | + | 0.995161i | \(0.468672\pi\) | |||||||
\(608\) | 4.72942 | 0.191803 | ||||||||
\(609\) | 36.7504 | 1.48920 | ||||||||
\(610\) | 135.649 | 5.49226 | ||||||||
\(611\) | 12.7205 | 0.514617 | ||||||||
\(612\) | 8.73256 | 0.352993 | ||||||||
\(613\) | −9.92711 | −0.400952 | −0.200476 | − | 0.979699i | \(-0.564249\pi\) | ||||
−0.200476 | + | 0.979699i | \(0.564249\pi\) | |||||||
\(614\) | −76.8873 | −3.10292 | ||||||||
\(615\) | −17.6050 | −0.709904 | ||||||||
\(616\) | −88.2210 | −3.55452 | ||||||||
\(617\) | −29.5188 | −1.18838 | −0.594190 | − | 0.804325i | \(-0.702527\pi\) | ||||
−0.594190 | + | 0.804325i | \(0.702527\pi\) | |||||||
\(618\) | −16.5500 | −0.665737 | ||||||||
\(619\) | −3.48114 | −0.139919 | −0.0699595 | − | 0.997550i | \(-0.522287\pi\) | ||||
−0.0699595 | + | 0.997550i | \(0.522287\pi\) | |||||||
\(620\) | −47.2985 | −1.89956 | ||||||||
\(621\) | −1.57714 | −0.0632884 | ||||||||
\(622\) | 17.3860 | 0.697115 | ||||||||
\(623\) | 59.0821 | 2.36707 | ||||||||
\(624\) | 10.9410 | 0.437991 | ||||||||
\(625\) | 94.5226 | 3.78090 | ||||||||
\(626\) | −5.58369 | −0.223169 | ||||||||
\(627\) | −27.4249 | −1.09525 | ||||||||
\(628\) | −9.60601 | −0.383321 | ||||||||
\(629\) | 8.74651 | 0.348746 | ||||||||
\(630\) | −45.0047 | −1.79303 | ||||||||
\(631\) | −31.8075 | −1.26624 | −0.633118 | − | 0.774055i | \(-0.718225\pi\) | ||||
−0.633118 | + | 0.774055i | \(0.718225\pi\) | |||||||
\(632\) | 62.5123 | 2.48661 | ||||||||
\(633\) | 2.07753 | 0.0825746 | ||||||||
\(634\) | 11.5062 | 0.456970 | ||||||||
\(635\) | 57.9221 | 2.29857 | ||||||||
\(636\) | 21.6482 | 0.858408 | ||||||||
\(637\) | −34.9911 | −1.38640 | ||||||||
\(638\) | 92.3639 | 3.65672 | ||||||||
\(639\) | −2.48373 | −0.0982547 | ||||||||
\(640\) | 87.1718 | 3.44577 | ||||||||
\(641\) | −46.2740 | −1.82771 | −0.913856 | − | 0.406039i | \(-0.866910\pi\) | ||||
−0.913856 | + | 0.406039i | \(0.866910\pi\) | |||||||
\(642\) | 17.4224 | 0.687608 | ||||||||
\(643\) | 4.72986 | 0.186528 | 0.0932638 | − | 0.995641i | \(-0.470270\pi\) | ||||
0.0932638 | + | 0.995641i | \(0.470270\pi\) | |||||||
\(644\) | 26.4345 | 1.04167 | ||||||||
\(645\) | 35.5572 | 1.40006 | ||||||||
\(646\) | −33.6572 | −1.32423 | ||||||||
\(647\) | −27.7209 | −1.08982 | −0.544911 | − | 0.838494i | \(-0.683436\pi\) | ||||
−0.544911 | + | 0.838494i | \(0.683436\pi\) | |||||||
\(648\) | −4.67199 | −0.183533 | ||||||||
\(649\) | −38.7850 | −1.52244 | ||||||||
\(650\) | 103.508 | 4.05991 | ||||||||
\(651\) | 11.9248 | 0.467369 | ||||||||
\(652\) | 65.8487 | 2.57883 | ||||||||
\(653\) | −25.5695 | −1.00061 | −0.500305 | − | 0.865849i | \(-0.666779\pi\) | ||||
−0.500305 | + | 0.865849i | \(0.666779\pi\) | |||||||
\(654\) | 38.5051 | 1.50567 | ||||||||
\(655\) | −9.68128 | −0.378279 | ||||||||
\(656\) | 14.3544 | 0.560445 | ||||||||
\(657\) | 0.913035 | 0.0356209 | ||||||||
\(658\) | 42.6632 | 1.66318 | ||||||||
\(659\) | 47.1520 | 1.83678 | 0.918391 | − | 0.395673i | \(-0.129489\pi\) | ||||
0.918391 | + | 0.395673i | \(0.129489\pi\) | |||||||
\(660\) | −74.8975 | −2.91538 | ||||||||
\(661\) | −18.8904 | −0.734752 | −0.367376 | − | 0.930072i | \(-0.619744\pi\) | ||||
−0.367376 | + | 0.930072i | \(0.619744\pi\) | |||||||
\(662\) | 67.7323 | 2.63249 | ||||||||
\(663\) | 6.90963 | 0.268348 | ||||||||
\(664\) | −57.5609 | −2.23380 | ||||||||
\(665\) | 114.859 | 4.45404 | ||||||||
\(666\) | −9.55350 | −0.370191 | ||||||||
\(667\) | −13.5561 | −0.524894 | ||||||||
\(668\) | 44.6947 | 1.72929 | ||||||||
\(669\) | 16.3319 | 0.631429 | ||||||||
\(670\) | −42.6855 | −1.64908 | ||||||||
\(671\) | −56.9152 | −2.19719 | ||||||||
\(672\) | −3.25636 | −0.125617 | ||||||||
\(673\) | 10.3173 | 0.397702 | 0.198851 | − | 0.980030i | \(-0.436279\pi\) | ||||
0.198851 | + | 0.980030i | \(0.436279\pi\) | |||||||
\(674\) | 70.6932 | 2.72300 | ||||||||
\(675\) | −13.7148 | −0.527884 | ||||||||
\(676\) | −13.2451 | −0.509428 | ||||||||
\(677\) | −37.8576 | −1.45499 | −0.727493 | − | 0.686115i | \(-0.759315\pi\) | ||||
−0.727493 | + | 0.686115i | \(0.759315\pi\) | |||||||
\(678\) | 10.0777 | 0.387032 | ||||||||
\(679\) | −2.03120 | −0.0779503 | ||||||||
\(680\) | −45.0229 | −1.72655 | ||||||||
\(681\) | −10.2045 | −0.391039 | ||||||||
\(682\) | 29.9702 | 1.14762 | ||||||||
\(683\) | −19.5701 | −0.748830 | −0.374415 | − | 0.927261i | \(-0.622156\pi\) | ||||
−0.374415 | + | 0.927261i | \(0.622156\pi\) | |||||||
\(684\) | 24.3431 | 0.930783 | ||||||||
\(685\) | −23.7746 | −0.908381 | ||||||||
\(686\) | −44.5342 | −1.70033 | ||||||||
\(687\) | −13.8003 | −0.526516 | ||||||||
\(688\) | −28.9918 | −1.10530 | ||||||||
\(689\) | 17.1291 | 0.652569 | ||||||||
\(690\) | 16.6008 | 0.631983 | ||||||||
\(691\) | 29.9143 | 1.13799 | 0.568997 | − | 0.822340i | \(-0.307332\pi\) | ||||
0.568997 | + | 0.822340i | \(0.307332\pi\) | |||||||
\(692\) | 60.4112 | 2.29649 | ||||||||
\(693\) | 18.8829 | 0.717304 | ||||||||
\(694\) | −50.9066 | −1.93239 | ||||||||
\(695\) | −53.3981 | −2.02551 | ||||||||
\(696\) | −40.1575 | −1.52216 | ||||||||
\(697\) | 9.06530 | 0.343373 | ||||||||
\(698\) | −35.5928 | −1.34721 | ||||||||
\(699\) | −18.9576 | −0.717041 | ||||||||
\(700\) | 229.875 | 8.68846 | ||||||||
\(701\) | −42.8417 | −1.61811 | −0.809054 | − | 0.587734i | \(-0.800020\pi\) | ||||
−0.809054 | + | 0.587734i | \(0.800020\pi\) | |||||||
\(702\) | −7.54714 | −0.284849 | ||||||||
\(703\) | 24.3820 | 0.919586 | ||||||||
\(704\) | −39.3402 | −1.48269 | ||||||||
\(705\) | 17.7411 | 0.668170 | ||||||||
\(706\) | 56.9440 | 2.14311 | ||||||||
\(707\) | −2.93839 | −0.110510 | ||||||||
\(708\) | 34.4266 | 1.29383 | ||||||||
\(709\) | −1.33886 | −0.0502820 | −0.0251410 | − | 0.999684i | \(-0.508003\pi\) | ||||
−0.0251410 | + | 0.999684i | \(0.508003\pi\) | |||||||
\(710\) | 26.1435 | 0.981147 | ||||||||
\(711\) | −13.3802 | −0.501798 | ||||||||
\(712\) | −64.5595 | −2.41947 | ||||||||
\(713\) | −4.39868 | −0.164732 | ||||||||
\(714\) | 23.1741 | 0.867269 | ||||||||
\(715\) | −59.2626 | −2.21630 | ||||||||
\(716\) | −30.6817 | −1.14663 | ||||||||
\(717\) | 4.74569 | 0.177231 | ||||||||
\(718\) | −58.1959 | −2.17185 | ||||||||
\(719\) | 28.3780 | 1.05832 | 0.529160 | − | 0.848522i | \(-0.322507\pi\) | ||||
0.529160 | + | 0.848522i | \(0.322507\pi\) | |||||||
\(720\) | 15.2593 | 0.568679 | ||||||||
\(721\) | −29.0823 | −1.08308 | ||||||||
\(722\) | −47.5943 | −1.77128 | ||||||||
\(723\) | 2.14957 | 0.0799433 | ||||||||
\(724\) | 22.4770 | 0.835350 | ||||||||
\(725\) | −117.884 | −4.37810 | ||||||||
\(726\) | 20.6935 | 0.768009 | ||||||||
\(727\) | −37.0819 | −1.37529 | −0.687646 | − | 0.726046i | \(-0.741356\pi\) | ||||
−0.687646 | + | 0.726046i | \(0.741356\pi\) | |||||||
\(728\) | 61.9607 | 2.29642 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −9.61052 | −0.355701 | ||||||||
\(731\) | −18.3093 | −0.677195 | ||||||||
\(732\) | 50.5196 | 1.86726 | ||||||||
\(733\) | −46.2021 | −1.70651 | −0.853256 | − | 0.521492i | \(-0.825376\pi\) | ||||
−0.853256 | + | 0.521492i | \(0.825376\pi\) | |||||||
\(734\) | 54.3846 | 2.00737 | ||||||||
\(735\) | −48.8017 | −1.80008 | ||||||||
\(736\) | 1.20117 | 0.0442757 | ||||||||
\(737\) | 17.9099 | 0.659718 | ||||||||
\(738\) | −9.90171 | −0.364487 | ||||||||
\(739\) | 16.5828 | 0.610008 | 0.305004 | − | 0.952351i | \(-0.401342\pi\) | ||||
0.305004 | + | 0.952351i | \(0.401342\pi\) | |||||||
\(740\) | 66.5874 | 2.44780 | ||||||||
\(741\) | 19.2615 | 0.707588 | ||||||||
\(742\) | 57.4492 | 2.10903 | ||||||||
\(743\) | 12.5815 | 0.461571 | 0.230785 | − | 0.973005i | \(-0.425870\pi\) | ||||
0.230785 | + | 0.973005i | \(0.425870\pi\) | |||||||
\(744\) | −13.0303 | −0.477713 | ||||||||
\(745\) | 67.8278 | 2.48502 | ||||||||
\(746\) | 33.0926 | 1.21160 | ||||||||
\(747\) | 12.3204 | 0.450780 | ||||||||
\(748\) | 38.5667 | 1.41014 | ||||||||
\(749\) | 30.6154 | 1.11866 | ||||||||
\(750\) | 91.7316 | 3.34956 | ||||||||
\(751\) | 18.2752 | 0.666873 | 0.333437 | − | 0.942773i | \(-0.391792\pi\) | ||||
0.333437 | + | 0.942773i | \(0.391792\pi\) | |||||||
\(752\) | −14.4654 | −0.527498 | ||||||||
\(753\) | 1.07911 | 0.0393250 | ||||||||
\(754\) | −64.8705 | −2.36244 | ||||||||
\(755\) | −23.9454 | −0.871462 | ||||||||
\(756\) | −16.7610 | −0.609593 | ||||||||
\(757\) | −37.5022 | −1.36304 | −0.681520 | − | 0.731800i | \(-0.738681\pi\) | ||||
−0.681520 | + | 0.731800i | \(0.738681\pi\) | |||||||
\(758\) | −57.8455 | −2.10104 | ||||||||
\(759\) | −6.96533 | −0.252826 | ||||||||
\(760\) | −125.507 | −4.55262 | ||||||||
\(761\) | −34.5732 | −1.25328 | −0.626638 | − | 0.779310i | \(-0.715570\pi\) | ||||
−0.626638 | + | 0.779310i | \(0.715570\pi\) | |||||||
\(762\) | 32.5775 | 1.18016 | ||||||||
\(763\) | 67.6627 | 2.44956 | ||||||||
\(764\) | 104.675 | 3.78700 | ||||||||
\(765\) | 9.63677 | 0.348418 | ||||||||
\(766\) | −75.1828 | −2.71646 | ||||||||
\(767\) | 27.2401 | 0.983581 | ||||||||
\(768\) | 31.2132 | 1.12631 | ||||||||
\(769\) | −42.7129 | −1.54026 | −0.770132 | − | 0.637884i | \(-0.779810\pi\) | ||||
−0.770132 | + | 0.637884i | \(0.779810\pi\) | |||||||
\(770\) | −198.760 | −7.16282 | ||||||||
\(771\) | −19.0965 | −0.687743 | ||||||||
\(772\) | 19.6789 | 0.708260 | ||||||||
\(773\) | 24.0764 | 0.865970 | 0.432985 | − | 0.901401i | \(-0.357460\pi\) | ||||
0.432985 | + | 0.901401i | \(0.357460\pi\) | |||||||
\(774\) | 19.9986 | 0.718836 | ||||||||
\(775\) | −38.2510 | −1.37402 | ||||||||
\(776\) | 2.21951 | 0.0796756 | ||||||||
\(777\) | −16.7878 | −0.602260 | ||||||||
\(778\) | −33.0870 | −1.18623 | ||||||||
\(779\) | 25.2707 | 0.905417 | ||||||||
\(780\) | 52.6032 | 1.88350 | ||||||||
\(781\) | −10.9692 | −0.392509 | ||||||||
\(782\) | −8.54821 | −0.305683 | ||||||||
\(783\) | 8.59536 | 0.307173 | ||||||||
\(784\) | 39.7908 | 1.42110 | ||||||||
\(785\) | −10.6007 | −0.378354 | ||||||||
\(786\) | −5.44510 | −0.194220 | ||||||||
\(787\) | 40.7181 | 1.45144 | 0.725721 | − | 0.687989i | \(-0.241506\pi\) | ||||
0.725721 | + | 0.687989i | \(0.241506\pi\) | |||||||
\(788\) | 21.1821 | 0.754582 | ||||||||
\(789\) | −21.0525 | −0.749489 | ||||||||
\(790\) | 140.839 | 5.01083 | ||||||||
\(791\) | 17.7090 | 0.629658 | ||||||||
\(792\) | −20.6335 | −0.733181 | ||||||||
\(793\) | 39.9736 | 1.41950 | ||||||||
\(794\) | 32.3412 | 1.14775 | ||||||||
\(795\) | 23.8898 | 0.847284 | ||||||||
\(796\) | −26.8368 | −0.951206 | ||||||||
\(797\) | 48.0936 | 1.70356 | 0.851782 | − | 0.523897i | \(-0.175522\pi\) | ||||
0.851782 | + | 0.523897i | \(0.175522\pi\) | |||||||
\(798\) | 64.6008 | 2.28684 | ||||||||
\(799\) | −9.13539 | −0.323187 | ||||||||
\(800\) | 10.4454 | 0.369301 | ||||||||
\(801\) | 13.8184 | 0.488249 | ||||||||
\(802\) | 92.7516 | 3.27517 | ||||||||
\(803\) | 4.03236 | 0.142299 | ||||||||
\(804\) | −15.8973 | −0.560655 | ||||||||
\(805\) | 29.1717 | 1.02817 | ||||||||
\(806\) | −21.0491 | −0.741425 | ||||||||
\(807\) | −2.84626 | −0.100193 | ||||||||
\(808\) | 3.21080 | 0.112956 | ||||||||
\(809\) | −15.9086 | −0.559315 | −0.279657 | − | 0.960100i | \(-0.590221\pi\) | ||||
−0.279657 | + | 0.960100i | \(0.590221\pi\) | |||||||
\(810\) | −10.5259 | −0.369843 | ||||||||
\(811\) | −2.74419 | −0.0963614 | −0.0481807 | − | 0.998839i | \(-0.515342\pi\) | ||||
−0.0481807 | + | 0.998839i | \(0.515342\pi\) | |||||||
\(812\) | −144.067 | −5.05577 | ||||||||
\(813\) | −0.859074 | −0.0301290 | ||||||||
\(814\) | −42.1924 | −1.47884 | ||||||||
\(815\) | 72.6670 | 2.54541 | ||||||||
\(816\) | −7.85741 | −0.275064 | ||||||||
\(817\) | −51.0396 | −1.78565 | ||||||||
\(818\) | 78.9559 | 2.76063 | ||||||||
\(819\) | −13.2622 | −0.463418 | ||||||||
\(820\) | 69.0144 | 2.41009 | ||||||||
\(821\) | −1.10716 | −0.0386402 | −0.0193201 | − | 0.999813i | \(-0.506150\pi\) | ||||
−0.0193201 | + | 0.999813i | \(0.506150\pi\) | |||||||
\(822\) | −13.3717 | −0.466392 | ||||||||
\(823\) | −3.11513 | −0.108587 | −0.0542933 | − | 0.998525i | \(-0.517291\pi\) | ||||
−0.0542933 | + | 0.998525i | \(0.517291\pi\) | |||||||
\(824\) | 31.7785 | 1.10705 | ||||||||
\(825\) | −60.5707 | −2.10880 | ||||||||
\(826\) | 91.3600 | 3.17882 | ||||||||
\(827\) | −33.4492 | −1.16314 | −0.581572 | − | 0.813495i | \(-0.697562\pi\) | ||||
−0.581572 | + | 0.813495i | \(0.697562\pi\) | |||||||
\(828\) | 6.18263 | 0.214861 | ||||||||
\(829\) | −43.6230 | −1.51509 | −0.757544 | − | 0.652784i | \(-0.773601\pi\) | ||||
−0.757544 | + | 0.652784i | \(0.773601\pi\) | |||||||
\(830\) | −129.684 | −4.50138 | ||||||||
\(831\) | 14.5325 | 0.504127 | ||||||||
\(832\) | 27.6300 | 0.957898 | ||||||||
\(833\) | 25.1293 | 0.870678 | ||||||||
\(834\) | −30.0330 | −1.03996 | ||||||||
\(835\) | 49.3226 | 1.70688 | ||||||||
\(836\) | 107.510 | 3.71830 | ||||||||
\(837\) | 2.78902 | 0.0964027 | ||||||||
\(838\) | 68.6976 | 2.37312 | ||||||||
\(839\) | −1.76697 | −0.0610026 | −0.0305013 | − | 0.999535i | \(-0.509710\pi\) | ||||
−0.0305013 | + | 0.999535i | \(0.509710\pi\) | |||||||
\(840\) | 86.4158 | 2.98163 | ||||||||
\(841\) | 44.8803 | 1.54760 | ||||||||
\(842\) | −54.4307 | −1.87581 | ||||||||
\(843\) | −28.0433 | −0.965863 | ||||||||
\(844\) | −8.14425 | −0.280337 | ||||||||
\(845\) | −14.6166 | −0.502826 | ||||||||
\(846\) | 9.97827 | 0.343060 | ||||||||
\(847\) | 36.3636 | 1.24947 | ||||||||
\(848\) | −19.4787 | −0.668902 | ||||||||
\(849\) | 3.01509 | 0.103478 | ||||||||
\(850\) | −74.3354 | −2.54968 | ||||||||
\(851\) | 6.19251 | 0.212276 | ||||||||
\(852\) | 9.73658 | 0.333570 | ||||||||
\(853\) | −2.18049 | −0.0746584 | −0.0373292 | − | 0.999303i | \(-0.511885\pi\) | ||||
−0.0373292 | + | 0.999303i | \(0.511885\pi\) | |||||||
\(854\) | 134.067 | 4.58767 | ||||||||
\(855\) | 26.8637 | 0.918721 | ||||||||
\(856\) | −33.4537 | −1.14342 | ||||||||
\(857\) | −26.3557 | −0.900295 | −0.450147 | − | 0.892954i | \(-0.648629\pi\) | ||||
−0.450147 | + | 0.892954i | \(0.648629\pi\) | |||||||
\(858\) | −33.3315 | −1.13792 | ||||||||
\(859\) | −18.2241 | −0.621799 | −0.310900 | − | 0.950443i | \(-0.600630\pi\) | ||||
−0.310900 | + | 0.950443i | \(0.600630\pi\) | |||||||
\(860\) | −139.389 | −4.75314 | ||||||||
\(861\) | −17.3997 | −0.592981 | ||||||||
\(862\) | 69.3868 | 2.36332 | ||||||||
\(863\) | −39.2193 | −1.33504 | −0.667521 | − | 0.744591i | \(-0.732644\pi\) | ||||
−0.667521 | + | 0.744591i | \(0.732644\pi\) | |||||||
\(864\) | −0.761613 | −0.0259106 | ||||||||
\(865\) | 66.6665 | 2.26673 | ||||||||
\(866\) | 64.1243 | 2.17903 | ||||||||
\(867\) | 12.0378 | 0.408824 | ||||||||
\(868\) | −46.7469 | −1.58669 | ||||||||
\(869\) | −59.0929 | −2.00459 | ||||||||
\(870\) | −90.4740 | −3.06736 | ||||||||
\(871\) | −12.5787 | −0.426214 | ||||||||
\(872\) | −73.9356 | −2.50377 | ||||||||
\(873\) | −0.475066 | −0.0160786 | ||||||||
\(874\) | −23.8292 | −0.806036 | ||||||||
\(875\) | 161.195 | 5.44937 | ||||||||
\(876\) | −3.57924 | −0.120931 | ||||||||
\(877\) | −36.0077 | −1.21589 | −0.607946 | − | 0.793978i | \(-0.708006\pi\) | ||||
−0.607946 | + | 0.793978i | \(0.708006\pi\) | |||||||
\(878\) | −37.0454 | −1.25022 | ||||||||
\(879\) | 28.0077 | 0.944676 | ||||||||
\(880\) | 67.3915 | 2.27177 | ||||||||
\(881\) | −11.6095 | −0.391135 | −0.195567 | − | 0.980690i | \(-0.562655\pi\) | ||||
−0.195567 | + | 0.980690i | \(0.562655\pi\) | |||||||
\(882\) | −27.4478 | −0.924217 | ||||||||
\(883\) | −14.9769 | −0.504014 | −0.252007 | − | 0.967725i | \(-0.581091\pi\) | ||||
−0.252007 | + | 0.967725i | \(0.581091\pi\) | |||||||
\(884\) | −27.0868 | −0.911027 | ||||||||
\(885\) | 37.9914 | 1.27707 | ||||||||
\(886\) | 25.5089 | 0.856989 | ||||||||
\(887\) | −10.1470 | −0.340704 | −0.170352 | − | 0.985383i | \(-0.554491\pi\) | ||||
−0.170352 | + | 0.985383i | \(0.554491\pi\) | |||||||
\(888\) | 18.3442 | 0.615590 | ||||||||
\(889\) | 57.2466 | 1.91999 | ||||||||
\(890\) | −145.451 | −4.87554 | ||||||||
\(891\) | 4.41643 | 0.147956 | ||||||||
\(892\) | −64.0237 | −2.14367 | ||||||||
\(893\) | −25.4661 | −0.852190 | ||||||||
\(894\) | 38.1488 | 1.27589 | ||||||||
\(895\) | −33.8586 | −1.13177 | ||||||||
\(896\) | 86.1552 | 2.87824 | ||||||||
\(897\) | 4.89200 | 0.163339 | ||||||||
\(898\) | 13.1961 | 0.440360 | ||||||||
\(899\) | 23.9727 | 0.799533 | ||||||||
\(900\) | 53.7642 | 1.79214 | ||||||||
\(901\) | −12.3015 | −0.409822 | ||||||||
\(902\) | −43.7303 | −1.45606 | ||||||||
\(903\) | 35.1425 | 1.16947 | ||||||||
\(904\) | −19.3507 | −0.643595 | ||||||||
\(905\) | 24.8043 | 0.824524 | ||||||||
\(906\) | −13.4678 | −0.447436 | ||||||||
\(907\) | 25.5421 | 0.848111 | 0.424056 | − | 0.905636i | \(-0.360606\pi\) | ||||
0.424056 | + | 0.905636i | \(0.360606\pi\) | |||||||
\(908\) | 40.0034 | 1.32756 | ||||||||
\(909\) | −0.687244 | −0.0227945 | ||||||||
\(910\) | 139.596 | 4.62757 | ||||||||
\(911\) | 17.8750 | 0.592226 | 0.296113 | − | 0.955153i | \(-0.404309\pi\) | ||||
0.296113 | + | 0.955153i | \(0.404309\pi\) | |||||||
\(912\) | −21.9035 | −0.725299 | ||||||||
\(913\) | 54.4123 | 1.80078 | ||||||||
\(914\) | −4.20675 | −0.139147 | ||||||||
\(915\) | 55.7506 | 1.84306 | ||||||||
\(916\) | 54.0994 | 1.78749 | ||||||||
\(917\) | −9.56836 | −0.315975 | ||||||||
\(918\) | 5.42007 | 0.178889 | ||||||||
\(919\) | 25.8102 | 0.851399 | 0.425700 | − | 0.904865i | \(-0.360028\pi\) | ||||
0.425700 | + | 0.904865i | \(0.360028\pi\) | |||||||
\(920\) | −31.8761 | −1.05092 | ||||||||
\(921\) | −31.6001 | −1.04126 | ||||||||
\(922\) | −43.8293 | −1.44344 | ||||||||
\(923\) | 7.70407 | 0.253582 | ||||||||
\(924\) | −74.0240 | −2.43521 | ||||||||
\(925\) | 53.8502 | 1.77058 | ||||||||
\(926\) | −86.3220 | −2.83672 | ||||||||
\(927\) | −6.80191 | −0.223404 | ||||||||
\(928\) | −6.54634 | −0.214894 | ||||||||
\(929\) | 51.6803 | 1.69558 | 0.847788 | − | 0.530336i | \(-0.177934\pi\) | ||||
0.847788 | + | 0.530336i | \(0.177934\pi\) | |||||||
\(930\) | −29.3570 | −0.962653 | ||||||||
\(931\) | 70.0511 | 2.29583 | ||||||||
\(932\) | 74.3166 | 2.43432 | ||||||||
\(933\) | 7.14550 | 0.233933 | ||||||||
\(934\) | −41.0647 | −1.34368 | ||||||||
\(935\) | 42.5602 | 1.39187 | ||||||||
\(936\) | 14.4917 | 0.473675 | ||||||||
\(937\) | 25.7958 | 0.842711 | 0.421355 | − | 0.906896i | \(-0.361554\pi\) | ||||
0.421355 | + | 0.906896i | \(0.361554\pi\) | |||||||
\(938\) | −42.1876 | −1.37748 | ||||||||
\(939\) | −2.29485 | −0.0748896 | ||||||||
\(940\) | −69.5480 | −2.26841 | ||||||||
\(941\) | −3.50083 | −0.114124 | −0.0570619 | − | 0.998371i | \(-0.518173\pi\) | ||||
−0.0570619 | + | 0.998371i | \(0.518173\pi\) | |||||||
\(942\) | −5.96220 | −0.194259 | ||||||||
\(943\) | 6.41821 | 0.209006 | ||||||||
\(944\) | −30.9765 | −1.00820 | ||||||||
\(945\) | −18.4966 | −0.601693 | ||||||||
\(946\) | 88.3227 | 2.87162 | ||||||||
\(947\) | −33.5802 | −1.09121 | −0.545605 | − | 0.838043i | \(-0.683700\pi\) | ||||
−0.545605 | + | 0.838043i | \(0.683700\pi\) | |||||||
\(948\) | 52.4526 | 1.70358 | ||||||||
\(949\) | −2.83207 | −0.0919329 | ||||||||
\(950\) | −207.220 | −6.72309 | ||||||||
\(951\) | 4.72896 | 0.153347 | ||||||||
\(952\) | −44.4978 | −1.44218 | ||||||||
\(953\) | −34.8198 | −1.12792 | −0.563962 | − | 0.825801i | \(-0.690724\pi\) | ||||
−0.563962 | + | 0.825801i | \(0.690724\pi\) | |||||||
\(954\) | 13.4365 | 0.435023 | ||||||||
\(955\) | 115.513 | 3.73792 | ||||||||
\(956\) | −18.6038 | −0.601690 | ||||||||
\(957\) | 37.9609 | 1.22710 | ||||||||
\(958\) | 80.7526 | 2.60900 | ||||||||
\(959\) | −23.4973 | −0.758769 | ||||||||
\(960\) | 38.5352 | 1.24372 | ||||||||
\(961\) | −23.2214 | −0.749076 | ||||||||
\(962\) | 29.6332 | 0.955414 | ||||||||
\(963\) | 7.16048 | 0.230743 | ||||||||
\(964\) | −8.42663 | −0.271404 | ||||||||
\(965\) | 21.7166 | 0.699081 | ||||||||
\(966\) | 16.4072 | 0.527893 | ||||||||
\(967\) | −11.4674 | −0.368766 | −0.184383 | − | 0.982854i | \(-0.559029\pi\) | ||||
−0.184383 | + | 0.982854i | \(0.559029\pi\) | |||||||
\(968\) | −39.7347 | −1.27712 | ||||||||
\(969\) | −13.8329 | −0.444376 | ||||||||
\(970\) | 5.00050 | 0.160557 | ||||||||
\(971\) | 38.5464 | 1.23701 | 0.618507 | − | 0.785779i | \(-0.287738\pi\) | ||||
0.618507 | + | 0.785779i | \(0.287738\pi\) | |||||||
\(972\) | −3.92015 | −0.125739 | ||||||||
\(973\) | −52.7753 | −1.69190 | ||||||||
\(974\) | −93.7046 | −3.00249 | ||||||||
\(975\) | 42.5409 | 1.36240 | ||||||||
\(976\) | −45.4566 | −1.45503 | ||||||||
\(977\) | 40.1833 | 1.28558 | 0.642789 | − | 0.766043i | \(-0.277777\pi\) | ||||
0.642789 | + | 0.766043i | \(0.277777\pi\) | |||||||
\(978\) | 40.8706 | 1.30690 | ||||||||
\(979\) | 61.0281 | 1.95047 | ||||||||
\(980\) | 191.310 | 6.11117 | ||||||||
\(981\) | 15.8253 | 0.505262 | ||||||||
\(982\) | 42.3218 | 1.35054 | ||||||||
\(983\) | 29.9943 | 0.956669 | 0.478335 | − | 0.878178i | \(-0.341241\pi\) | ||||
0.478335 | + | 0.878178i | \(0.341241\pi\) | |||||||
\(984\) | 19.0128 | 0.606106 | ||||||||
\(985\) | 23.3755 | 0.744804 | ||||||||
\(986\) | 46.5875 | 1.48365 | ||||||||
\(987\) | 17.5342 | 0.558121 | ||||||||
\(988\) | −75.5080 | −2.40223 | ||||||||
\(989\) | −12.9630 | −0.412198 | ||||||||
\(990\) | −46.4870 | −1.47745 | ||||||||
\(991\) | −45.1315 | −1.43365 | −0.716825 | − | 0.697253i | \(-0.754406\pi\) | ||||
−0.716825 | + | 0.697253i | \(0.754406\pi\) | |||||||
\(992\) | −2.12416 | −0.0674420 | ||||||||
\(993\) | 27.8375 | 0.883395 | ||||||||
\(994\) | 25.8386 | 0.819549 | ||||||||
\(995\) | −29.6157 | −0.938880 | ||||||||
\(996\) | −48.2979 | −1.53038 | ||||||||
\(997\) | −14.5720 | −0.461499 | −0.230749 | − | 0.973013i | \(-0.574118\pi\) | ||||
−0.230749 | + | 0.973013i | \(0.574118\pi\) | |||||||
\(998\) | −60.1263 | −1.90326 | ||||||||
\(999\) | −3.92642 | −0.124226 |
(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 | 8013.2.a.b.1.8 | ✓ | 106 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8013.2.a.b.1.8 | ✓ | 106 | 1.1 | even | 1 | trivial |