Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.28 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.91950 | 1.35729 | 0.678647 | − | 0.734464i | \(-0.262567\pi\) | ||||
0.678647 | + | 0.734464i | \(0.262567\pi\) | |||||||
\(3\) | −0.260789 | −0.150566 | −0.0752832 | − | 0.997162i | \(-0.523986\pi\) | ||||
−0.0752832 | + | 0.997162i | \(0.523986\pi\) | |||||||
\(4\) | 1.68450 | 0.842248 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.500585 | −0.204363 | ||||||||
\(7\) | −5.05939 | −1.91227 | −0.956135 | − | 0.292927i | \(-0.905371\pi\) | ||||
−0.956135 | + | 0.292927i | \(0.905371\pi\) | |||||||
\(8\) | −0.605613 | −0.214116 | ||||||||
\(9\) | −2.93199 | −0.977330 | ||||||||
\(10\) | 1.91950 | 0.607000 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.439297 | −0.126814 | ||||||||
\(13\) | −1.62207 | −0.449881 | −0.224941 | − | 0.974372i | \(-0.572219\pi\) | ||||
−0.224941 | + | 0.974372i | \(0.572219\pi\) | |||||||
\(14\) | −9.71152 | −2.59551 | ||||||||
\(15\) | −0.260789 | −0.0673353 | ||||||||
\(16\) | −4.53147 | −1.13287 | ||||||||
\(17\) | 8.05028 | 1.95248 | 0.976240 | − | 0.216691i | \(-0.0695264\pi\) | ||||
0.976240 | + | 0.216691i | \(0.0695264\pi\) | |||||||
\(18\) | −5.62796 | −1.32652 | ||||||||
\(19\) | 2.76332 | 0.633948 | 0.316974 | − | 0.948434i | \(-0.397333\pi\) | ||||
0.316974 | + | 0.948434i | \(0.397333\pi\) | |||||||
\(20\) | 1.68450 | 0.376665 | ||||||||
\(21\) | 1.31943 | 0.287923 | ||||||||
\(22\) | 1.91950 | 0.409240 | ||||||||
\(23\) | 6.01036 | 1.25325 | 0.626624 | − | 0.779322i | \(-0.284436\pi\) | ||||
0.626624 | + | 0.779322i | \(0.284436\pi\) | |||||||
\(24\) | 0.157937 | 0.0322387 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.11357 | −0.610621 | ||||||||
\(27\) | 1.54700 | 0.297719 | ||||||||
\(28\) | −8.52252 | −1.61060 | ||||||||
\(29\) | 9.05396 | 1.68128 | 0.840639 | − | 0.541596i | \(-0.182180\pi\) | ||||
0.840639 | + | 0.541596i | \(0.182180\pi\) | |||||||
\(30\) | −0.500585 | −0.0913938 | ||||||||
\(31\) | 3.49816 | 0.628289 | 0.314144 | − | 0.949375i | \(-0.398282\pi\) | ||||
0.314144 | + | 0.949375i | \(0.398282\pi\) | |||||||
\(32\) | −7.48694 | −1.32352 | ||||||||
\(33\) | −0.260789 | −0.0453975 | ||||||||
\(34\) | 15.4526 | 2.65009 | ||||||||
\(35\) | −5.05939 | −0.855193 | ||||||||
\(36\) | −4.93892 | −0.823154 | ||||||||
\(37\) | −2.75291 | −0.452576 | −0.226288 | − | 0.974060i | \(-0.572659\pi\) | ||||
−0.226288 | + | 0.974060i | \(0.572659\pi\) | |||||||
\(38\) | 5.30419 | 0.860454 | ||||||||
\(39\) | 0.423017 | 0.0677370 | ||||||||
\(40\) | −0.605613 | −0.0957558 | ||||||||
\(41\) | −2.96672 | −0.463324 | −0.231662 | − | 0.972796i | \(-0.574416\pi\) | ||||
−0.231662 | + | 0.972796i | \(0.574416\pi\) | |||||||
\(42\) | 2.53265 | 0.390797 | ||||||||
\(43\) | −8.50985 | −1.29774 | −0.648870 | − | 0.760899i | \(-0.724758\pi\) | ||||
−0.648870 | + | 0.760899i | \(0.724758\pi\) | |||||||
\(44\) | 1.68450 | 0.253947 | ||||||||
\(45\) | −2.93199 | −0.437075 | ||||||||
\(46\) | 11.5369 | 1.70102 | ||||||||
\(47\) | −1.94959 | −0.284377 | −0.142189 | − | 0.989840i | \(-0.545414\pi\) | ||||
−0.142189 | + | 0.989840i | \(0.545414\pi\) | |||||||
\(48\) | 1.18175 | 0.170572 | ||||||||
\(49\) | 18.5974 | 2.65678 | ||||||||
\(50\) | 1.91950 | 0.271459 | ||||||||
\(51\) | −2.09942 | −0.293978 | ||||||||
\(52\) | −2.73237 | −0.378911 | ||||||||
\(53\) | 8.90378 | 1.22303 | 0.611514 | − | 0.791234i | \(-0.290561\pi\) | ||||
0.611514 | + | 0.791234i | \(0.290561\pi\) | |||||||
\(54\) | 2.96946 | 0.404093 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 3.06403 | 0.409448 | ||||||||
\(57\) | −0.720641 | −0.0954512 | ||||||||
\(58\) | 17.3791 | 2.28199 | ||||||||
\(59\) | −8.85846 | −1.15327 | −0.576637 | − | 0.817001i | \(-0.695635\pi\) | ||||
−0.576637 | + | 0.817001i | \(0.695635\pi\) | |||||||
\(60\) | −0.439297 | −0.0567130 | ||||||||
\(61\) | 8.65733 | 1.10846 | 0.554229 | − | 0.832364i | \(-0.313013\pi\) | ||||
0.554229 | + | 0.832364i | \(0.313013\pi\) | |||||||
\(62\) | 6.71474 | 0.852773 | ||||||||
\(63\) | 14.8341 | 1.86892 | ||||||||
\(64\) | −5.30828 | −0.663535 | ||||||||
\(65\) | −1.62207 | −0.201193 | ||||||||
\(66\) | −0.500585 | −0.0616177 | ||||||||
\(67\) | −4.09260 | −0.499991 | −0.249996 | − | 0.968247i | \(-0.580429\pi\) | ||||
−0.249996 | + | 0.968247i | \(0.580429\pi\) | |||||||
\(68\) | 13.5607 | 1.64447 | ||||||||
\(69\) | −1.56743 | −0.188697 | ||||||||
\(70\) | −9.71152 | −1.16075 | ||||||||
\(71\) | 0.239302 | 0.0283999 | 0.0141999 | − | 0.999899i | \(-0.495480\pi\) | ||||
0.0141999 | + | 0.999899i | \(0.495480\pi\) | |||||||
\(72\) | 1.77565 | 0.209262 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | −5.28422 | −0.614279 | ||||||||
\(75\) | −0.260789 | −0.0301133 | ||||||||
\(76\) | 4.65479 | 0.533941 | ||||||||
\(77\) | −5.05939 | −0.576571 | ||||||||
\(78\) | 0.811983 | 0.0919390 | ||||||||
\(79\) | 0.231708 | 0.0260692 | 0.0130346 | − | 0.999915i | \(-0.495851\pi\) | ||||
0.0130346 | + | 0.999915i | \(0.495851\pi\) | |||||||
\(80\) | −4.53147 | −0.506633 | ||||||||
\(81\) | 8.39253 | 0.932503 | ||||||||
\(82\) | −5.69463 | −0.628867 | ||||||||
\(83\) | 16.6802 | 1.83089 | 0.915443 | − | 0.402447i | \(-0.131840\pi\) | ||||
0.915443 | + | 0.402447i | \(0.131840\pi\) | |||||||
\(84\) | 2.22258 | 0.242503 | ||||||||
\(85\) | 8.05028 | 0.873176 | ||||||||
\(86\) | −16.3347 | −1.76142 | ||||||||
\(87\) | −2.36117 | −0.253144 | ||||||||
\(88\) | −0.605613 | −0.0645585 | ||||||||
\(89\) | 16.9646 | 1.79825 | 0.899124 | − | 0.437694i | \(-0.144205\pi\) | ||||
0.899124 | + | 0.437694i | \(0.144205\pi\) | |||||||
\(90\) | −5.62796 | −0.593240 | ||||||||
\(91\) | 8.20668 | 0.860294 | ||||||||
\(92\) | 10.1244 | 1.05554 | ||||||||
\(93\) | −0.912281 | −0.0945991 | ||||||||
\(94\) | −3.74225 | −0.385984 | ||||||||
\(95\) | 2.76332 | 0.283510 | ||||||||
\(96\) | 1.95251 | 0.199277 | ||||||||
\(97\) | −2.05323 | −0.208474 | −0.104237 | − | 0.994552i | \(-0.533240\pi\) | ||||
−0.104237 | + | 0.994552i | \(0.533240\pi\) | |||||||
\(98\) | 35.6978 | 3.60603 | ||||||||
\(99\) | −2.93199 | −0.294676 | ||||||||
\(100\) | 1.68450 | 0.168450 | ||||||||
\(101\) | 2.37103 | 0.235927 | 0.117963 | − | 0.993018i | \(-0.462363\pi\) | ||||
0.117963 | + | 0.993018i | \(0.462363\pi\) | |||||||
\(102\) | −4.02985 | −0.399014 | ||||||||
\(103\) | −3.30328 | −0.325482 | −0.162741 | − | 0.986669i | \(-0.552033\pi\) | ||||
−0.162741 | + | 0.986669i | \(0.552033\pi\) | |||||||
\(104\) | 0.982346 | 0.0963269 | ||||||||
\(105\) | 1.31943 | 0.128763 | ||||||||
\(106\) | 17.0908 | 1.66001 | ||||||||
\(107\) | −0.293542 | −0.0283778 | −0.0141889 | − | 0.999899i | \(-0.504517\pi\) | ||||
−0.0141889 | + | 0.999899i | \(0.504517\pi\) | |||||||
\(108\) | 2.60591 | 0.250753 | ||||||||
\(109\) | 14.8598 | 1.42331 | 0.711655 | − | 0.702529i | \(-0.247946\pi\) | ||||
0.711655 | + | 0.702529i | \(0.247946\pi\) | |||||||
\(110\) | 1.91950 | 0.183018 | ||||||||
\(111\) | 0.717928 | 0.0681427 | ||||||||
\(112\) | 22.9265 | 2.16635 | ||||||||
\(113\) | 7.21829 | 0.679039 | 0.339520 | − | 0.940599i | \(-0.389735\pi\) | ||||
0.339520 | + | 0.940599i | \(0.389735\pi\) | |||||||
\(114\) | −1.38327 | −0.129555 | ||||||||
\(115\) | 6.01036 | 0.560469 | ||||||||
\(116\) | 15.2513 | 1.41605 | ||||||||
\(117\) | 4.75589 | 0.439682 | ||||||||
\(118\) | −17.0038 | −1.56533 | ||||||||
\(119\) | −40.7295 | −3.73367 | ||||||||
\(120\) | 0.157937 | 0.0144176 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 16.6178 | 1.50450 | ||||||||
\(123\) | 0.773687 | 0.0697610 | ||||||||
\(124\) | 5.89264 | 0.529175 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 28.4741 | 2.53667 | ||||||||
\(127\) | 14.1325 | 1.25405 | 0.627026 | − | 0.778998i | \(-0.284272\pi\) | ||||
0.627026 | + | 0.778998i | \(0.284272\pi\) | |||||||
\(128\) | 4.78462 | 0.422904 | ||||||||
\(129\) | 2.21927 | 0.195396 | ||||||||
\(130\) | −3.11357 | −0.273078 | ||||||||
\(131\) | −22.2478 | −1.94380 | −0.971899 | − | 0.235396i | \(-0.924361\pi\) | ||||
−0.971899 | + | 0.235396i | \(0.924361\pi\) | |||||||
\(132\) | −0.439297 | −0.0382359 | ||||||||
\(133\) | −13.9807 | −1.21228 | ||||||||
\(134\) | −7.85577 | −0.678635 | ||||||||
\(135\) | 1.54700 | 0.133144 | ||||||||
\(136\) | −4.87535 | −0.418058 | ||||||||
\(137\) | −3.39120 | −0.289729 | −0.144865 | − | 0.989451i | \(-0.546275\pi\) | ||||
−0.144865 | + | 0.989451i | \(0.546275\pi\) | |||||||
\(138\) | −3.00870 | −0.256117 | ||||||||
\(139\) | −13.3808 | −1.13494 | −0.567472 | − | 0.823393i | \(-0.692079\pi\) | ||||
−0.567472 | + | 0.823393i | \(0.692079\pi\) | |||||||
\(140\) | −8.52252 | −0.720284 | ||||||||
\(141\) | 0.508432 | 0.0428177 | ||||||||
\(142\) | 0.459341 | 0.0385470 | ||||||||
\(143\) | −1.62207 | −0.135644 | ||||||||
\(144\) | 13.2862 | 1.10718 | ||||||||
\(145\) | 9.05396 | 0.751890 | ||||||||
\(146\) | 1.91950 | 0.158859 | ||||||||
\(147\) | −4.85000 | −0.400021 | ||||||||
\(148\) | −4.63727 | −0.381181 | ||||||||
\(149\) | −12.3339 | −1.01043 | −0.505214 | − | 0.862994i | \(-0.668587\pi\) | ||||
−0.505214 | + | 0.862994i | \(0.668587\pi\) | |||||||
\(150\) | −0.500585 | −0.0408726 | ||||||||
\(151\) | 13.3710 | 1.08811 | 0.544056 | − | 0.839049i | \(-0.316888\pi\) | ||||
0.544056 | + | 0.839049i | \(0.316888\pi\) | |||||||
\(152\) | −1.67350 | −0.135739 | ||||||||
\(153\) | −23.6033 | −1.90822 | ||||||||
\(154\) | −9.71152 | −0.782576 | ||||||||
\(155\) | 3.49816 | 0.280979 | ||||||||
\(156\) | 0.712570 | 0.0570513 | ||||||||
\(157\) | −19.5703 | −1.56188 | −0.780938 | − | 0.624608i | \(-0.785259\pi\) | ||||
−0.780938 | + | 0.624608i | \(0.785259\pi\) | |||||||
\(158\) | 0.444765 | 0.0353836 | ||||||||
\(159\) | −2.32200 | −0.184147 | ||||||||
\(160\) | −7.48694 | −0.591895 | ||||||||
\(161\) | −30.4088 | −2.39655 | ||||||||
\(162\) | 16.1095 | 1.26568 | ||||||||
\(163\) | 5.77977 | 0.452706 | 0.226353 | − | 0.974045i | \(-0.427320\pi\) | ||||
0.226353 | + | 0.974045i | \(0.427320\pi\) | |||||||
\(164\) | −4.99743 | −0.390233 | ||||||||
\(165\) | −0.260789 | −0.0203024 | ||||||||
\(166\) | 32.0177 | 2.48505 | ||||||||
\(167\) | 9.08740 | 0.703204 | 0.351602 | − | 0.936150i | \(-0.385637\pi\) | ||||
0.351602 | + | 0.936150i | \(0.385637\pi\) | |||||||
\(168\) | −0.799064 | −0.0616491 | ||||||||
\(169\) | −10.3689 | −0.797607 | ||||||||
\(170\) | 15.4526 | 1.18516 | ||||||||
\(171\) | −8.10201 | −0.619576 | ||||||||
\(172\) | −14.3348 | −1.09302 | ||||||||
\(173\) | −22.1123 | −1.68116 | −0.840582 | − | 0.541685i | \(-0.817787\pi\) | ||||
−0.840582 | + | 0.541685i | \(0.817787\pi\) | |||||||
\(174\) | −4.53227 | −0.343591 | ||||||||
\(175\) | −5.05939 | −0.382454 | ||||||||
\(176\) | −4.53147 | −0.341572 | ||||||||
\(177\) | 2.31018 | 0.173644 | ||||||||
\(178\) | 32.5637 | 2.44075 | ||||||||
\(179\) | 18.4166 | 1.37652 | 0.688262 | − | 0.725462i | \(-0.258374\pi\) | ||||
0.688262 | + | 0.725462i | \(0.258374\pi\) | |||||||
\(180\) | −4.93892 | −0.368126 | ||||||||
\(181\) | −5.15509 | −0.383175 | −0.191588 | − | 0.981476i | \(-0.561364\pi\) | ||||
−0.191588 | + | 0.981476i | \(0.561364\pi\) | |||||||
\(182\) | 15.7528 | 1.16767 | ||||||||
\(183\) | −2.25773 | −0.166896 | ||||||||
\(184\) | −3.63995 | −0.268341 | ||||||||
\(185\) | −2.75291 | −0.202398 | ||||||||
\(186\) | −1.75113 | −0.128399 | ||||||||
\(187\) | 8.05028 | 0.588695 | ||||||||
\(188\) | −3.28408 | −0.239516 | ||||||||
\(189\) | −7.82685 | −0.569320 | ||||||||
\(190\) | 5.30419 | 0.384807 | ||||||||
\(191\) | 3.36000 | 0.243121 | 0.121561 | − | 0.992584i | \(-0.461210\pi\) | ||||
0.121561 | + | 0.992584i | \(0.461210\pi\) | |||||||
\(192\) | 1.38434 | 0.0999061 | ||||||||
\(193\) | 20.2514 | 1.45773 | 0.728863 | − | 0.684660i | \(-0.240049\pi\) | ||||
0.728863 | + | 0.684660i | \(0.240049\pi\) | |||||||
\(194\) | −3.94118 | −0.282960 | ||||||||
\(195\) | 0.423017 | 0.0302929 | ||||||||
\(196\) | 31.3273 | 2.23766 | ||||||||
\(197\) | −14.3042 | −1.01913 | −0.509565 | − | 0.860432i | \(-0.670194\pi\) | ||||
−0.509565 | + | 0.860432i | \(0.670194\pi\) | |||||||
\(198\) | −5.62796 | −0.399962 | ||||||||
\(199\) | −10.2846 | −0.729058 | −0.364529 | − | 0.931192i | \(-0.618770\pi\) | ||||
−0.364529 | + | 0.931192i | \(0.618770\pi\) | |||||||
\(200\) | −0.605613 | −0.0428233 | ||||||||
\(201\) | 1.06730 | 0.0752818 | ||||||||
\(202\) | 4.55121 | 0.320222 | ||||||||
\(203\) | −45.8075 | −3.21506 | ||||||||
\(204\) | −3.53647 | −0.247602 | ||||||||
\(205\) | −2.96672 | −0.207205 | ||||||||
\(206\) | −6.34066 | −0.441774 | ||||||||
\(207\) | −17.6223 | −1.22484 | ||||||||
\(208\) | 7.35035 | 0.509655 | ||||||||
\(209\) | 2.76332 | 0.191142 | ||||||||
\(210\) | 2.53265 | 0.174770 | ||||||||
\(211\) | 2.08830 | 0.143764 | 0.0718822 | − | 0.997413i | \(-0.477099\pi\) | ||||
0.0718822 | + | 0.997413i | \(0.477099\pi\) | |||||||
\(212\) | 14.9984 | 1.03009 | ||||||||
\(213\) | −0.0624071 | −0.00427607 | ||||||||
\(214\) | −0.563455 | −0.0385170 | ||||||||
\(215\) | −8.50985 | −0.580367 | ||||||||
\(216\) | −0.936880 | −0.0637466 | ||||||||
\(217\) | −17.6986 | −1.20146 | ||||||||
\(218\) | 28.5234 | 1.93185 | ||||||||
\(219\) | −0.260789 | −0.0176225 | ||||||||
\(220\) | 1.68450 | 0.113569 | ||||||||
\(221\) | −13.0581 | −0.878384 | ||||||||
\(222\) | 1.37807 | 0.0924897 | ||||||||
\(223\) | 26.4461 | 1.77096 | 0.885482 | − | 0.464674i | \(-0.153829\pi\) | ||||
0.885482 | + | 0.464674i | \(0.153829\pi\) | |||||||
\(224\) | 37.8794 | 2.53092 | ||||||||
\(225\) | −2.93199 | −0.195466 | ||||||||
\(226\) | 13.8555 | 0.921656 | ||||||||
\(227\) | −11.0178 | −0.731276 | −0.365638 | − | 0.930757i | \(-0.619149\pi\) | ||||
−0.365638 | + | 0.930757i | \(0.619149\pi\) | |||||||
\(228\) | −1.21392 | −0.0803936 | ||||||||
\(229\) | 12.8889 | 0.851719 | 0.425860 | − | 0.904789i | \(-0.359972\pi\) | ||||
0.425860 | + | 0.904789i | \(0.359972\pi\) | |||||||
\(230\) | 11.5369 | 0.760721 | ||||||||
\(231\) | 1.31943 | 0.0868122 | ||||||||
\(232\) | −5.48319 | −0.359989 | ||||||||
\(233\) | 1.64458 | 0.107740 | 0.0538700 | − | 0.998548i | \(-0.482844\pi\) | ||||
0.0538700 | + | 0.998548i | \(0.482844\pi\) | |||||||
\(234\) | 9.12895 | 0.596778 | ||||||||
\(235\) | −1.94959 | −0.127177 | ||||||||
\(236\) | −14.9220 | −0.971342 | ||||||||
\(237\) | −0.0604269 | −0.00392515 | ||||||||
\(238\) | −78.1805 | −5.06769 | ||||||||
\(239\) | 11.8217 | 0.764685 | 0.382343 | − | 0.924021i | \(-0.375117\pi\) | ||||
0.382343 | + | 0.924021i | \(0.375117\pi\) | |||||||
\(240\) | 1.18175 | 0.0762819 | ||||||||
\(241\) | 21.1752 | 1.36401 | 0.682007 | − | 0.731345i | \(-0.261107\pi\) | ||||
0.682007 | + | 0.731345i | \(0.261107\pi\) | |||||||
\(242\) | 1.91950 | 0.123390 | ||||||||
\(243\) | −6.82966 | −0.438123 | ||||||||
\(244\) | 14.5832 | 0.933595 | ||||||||
\(245\) | 18.5974 | 1.18815 | ||||||||
\(246\) | 1.48510 | 0.0946862 | ||||||||
\(247\) | −4.48229 | −0.285201 | ||||||||
\(248\) | −2.11853 | −0.134527 | ||||||||
\(249\) | −4.35000 | −0.275670 | ||||||||
\(250\) | 1.91950 | 0.121400 | ||||||||
\(251\) | 16.6286 | 1.04959 | 0.524794 | − | 0.851229i | \(-0.324142\pi\) | ||||
0.524794 | + | 0.851229i | \(0.324142\pi\) | |||||||
\(252\) | 24.9879 | 1.57409 | ||||||||
\(253\) | 6.01036 | 0.377868 | ||||||||
\(254\) | 27.1273 | 1.70212 | ||||||||
\(255\) | −2.09942 | −0.131471 | ||||||||
\(256\) | 19.8007 | 1.23754 | ||||||||
\(257\) | −29.6351 | −1.84859 | −0.924294 | − | 0.381682i | \(-0.875345\pi\) | ||||
−0.924294 | + | 0.381682i | \(0.875345\pi\) | |||||||
\(258\) | 4.25990 | 0.265210 | ||||||||
\(259\) | 13.9281 | 0.865447 | ||||||||
\(260\) | −2.73237 | −0.169454 | ||||||||
\(261\) | −26.5461 | −1.64316 | ||||||||
\(262\) | −42.7047 | −2.63831 | ||||||||
\(263\) | −9.47055 | −0.583979 | −0.291990 | − | 0.956421i | \(-0.594317\pi\) | ||||
−0.291990 | + | 0.956421i | \(0.594317\pi\) | |||||||
\(264\) | 0.157937 | 0.00972034 | ||||||||
\(265\) | 8.90378 | 0.546955 | ||||||||
\(266\) | −26.8360 | −1.64542 | ||||||||
\(267\) | −4.42418 | −0.270756 | ||||||||
\(268\) | −6.89397 | −0.421116 | ||||||||
\(269\) | 14.7519 | 0.899439 | 0.449719 | − | 0.893170i | \(-0.351524\pi\) | ||||
0.449719 | + | 0.893170i | \(0.351524\pi\) | |||||||
\(270\) | 2.96946 | 0.180716 | ||||||||
\(271\) | −0.504336 | −0.0306362 | −0.0153181 | − | 0.999883i | \(-0.504876\pi\) | ||||
−0.0153181 | + | 0.999883i | \(0.504876\pi\) | |||||||
\(272\) | −36.4796 | −2.21190 | ||||||||
\(273\) | −2.14021 | −0.129531 | ||||||||
\(274\) | −6.50941 | −0.393248 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −2.64033 | −0.158929 | ||||||||
\(277\) | 3.17052 | 0.190498 | 0.0952489 | − | 0.995453i | \(-0.469635\pi\) | ||||
0.0952489 | + | 0.995453i | \(0.469635\pi\) | |||||||
\(278\) | −25.6845 | −1.54045 | ||||||||
\(279\) | −10.2566 | −0.614045 | ||||||||
\(280\) | 3.06403 | 0.183111 | ||||||||
\(281\) | −18.6576 | −1.11302 | −0.556508 | − | 0.830842i | \(-0.687859\pi\) | ||||
−0.556508 | + | 0.830842i | \(0.687859\pi\) | |||||||
\(282\) | 0.975936 | 0.0581162 | ||||||||
\(283\) | −2.36183 | −0.140396 | −0.0701980 | − | 0.997533i | \(-0.522363\pi\) | ||||
−0.0701980 | + | 0.997533i | \(0.522363\pi\) | |||||||
\(284\) | 0.403103 | 0.0239197 | ||||||||
\(285\) | −0.720641 | −0.0426871 | ||||||||
\(286\) | −3.11357 | −0.184109 | ||||||||
\(287\) | 15.0098 | 0.886000 | ||||||||
\(288\) | 21.9516 | 1.29351 | ||||||||
\(289\) | 47.8071 | 2.81218 | ||||||||
\(290\) | 17.3791 | 1.02054 | ||||||||
\(291\) | 0.535459 | 0.0313891 | ||||||||
\(292\) | 1.68450 | 0.0985776 | ||||||||
\(293\) | −1.04737 | −0.0611879 | −0.0305940 | − | 0.999532i | \(-0.509740\pi\) | ||||
−0.0305940 | + | 0.999532i | \(0.509740\pi\) | |||||||
\(294\) | −9.30959 | −0.542946 | ||||||||
\(295\) | −8.85846 | −0.515759 | ||||||||
\(296\) | 1.66720 | 0.0969039 | ||||||||
\(297\) | 1.54700 | 0.0897658 | ||||||||
\(298\) | −23.6749 | −1.37145 | ||||||||
\(299\) | −9.74922 | −0.563812 | ||||||||
\(300\) | −0.439297 | −0.0253628 | ||||||||
\(301\) | 43.0547 | 2.48163 | ||||||||
\(302\) | 25.6656 | 1.47689 | ||||||||
\(303\) | −0.618338 | −0.0355226 | ||||||||
\(304\) | −12.5219 | −0.718178 | ||||||||
\(305\) | 8.65733 | 0.495717 | ||||||||
\(306\) | −45.3067 | −2.59001 | ||||||||
\(307\) | 17.6897 | 1.00960 | 0.504802 | − | 0.863235i | \(-0.331565\pi\) | ||||
0.504802 | + | 0.863235i | \(0.331565\pi\) | |||||||
\(308\) | −8.52252 | −0.485616 | ||||||||
\(309\) | 0.861457 | 0.0490066 | ||||||||
\(310\) | 6.71474 | 0.381372 | ||||||||
\(311\) | 12.6987 | 0.720077 | 0.360039 | − | 0.932937i | \(-0.382763\pi\) | ||||
0.360039 | + | 0.932937i | \(0.382763\pi\) | |||||||
\(312\) | −0.256184 | −0.0145036 | ||||||||
\(313\) | −6.00541 | −0.339446 | −0.169723 | − | 0.985492i | \(-0.554287\pi\) | ||||
−0.169723 | + | 0.985492i | \(0.554287\pi\) | |||||||
\(314\) | −37.5652 | −2.11993 | ||||||||
\(315\) | 14.8341 | 0.835806 | ||||||||
\(316\) | 0.390312 | 0.0219568 | ||||||||
\(317\) | 6.17630 | 0.346895 | 0.173448 | − | 0.984843i | \(-0.444509\pi\) | ||||
0.173448 | + | 0.984843i | \(0.444509\pi\) | |||||||
\(318\) | −4.45709 | −0.249941 | ||||||||
\(319\) | 9.05396 | 0.506924 | ||||||||
\(320\) | −5.30828 | −0.296742 | ||||||||
\(321\) | 0.0765524 | 0.00427274 | ||||||||
\(322\) | −58.3697 | −3.25282 | ||||||||
\(323\) | 22.2455 | 1.23777 | ||||||||
\(324\) | 14.1372 | 0.785399 | ||||||||
\(325\) | −1.62207 | −0.0899762 | ||||||||
\(326\) | 11.0943 | 0.614456 | ||||||||
\(327\) | −3.87526 | −0.214303 | ||||||||
\(328\) | 1.79668 | 0.0992052 | ||||||||
\(329\) | 9.86375 | 0.543806 | ||||||||
\(330\) | −0.500585 | −0.0275563 | ||||||||
\(331\) | −28.4197 | −1.56209 | −0.781045 | − | 0.624475i | \(-0.785313\pi\) | ||||
−0.781045 | + | 0.624475i | \(0.785313\pi\) | |||||||
\(332\) | 28.0977 | 1.54206 | ||||||||
\(333\) | 8.07151 | 0.442316 | ||||||||
\(334\) | 17.4433 | 0.954455 | ||||||||
\(335\) | −4.09260 | −0.223603 | ||||||||
\(336\) | −5.97896 | −0.326179 | ||||||||
\(337\) | 7.52437 | 0.409879 | 0.204939 | − | 0.978775i | \(-0.434300\pi\) | ||||
0.204939 | + | 0.978775i | \(0.434300\pi\) | |||||||
\(338\) | −19.9031 | −1.08259 | ||||||||
\(339\) | −1.88245 | −0.102240 | ||||||||
\(340\) | 13.5607 | 0.735430 | ||||||||
\(341\) | 3.49816 | 0.189436 | ||||||||
\(342\) | −15.5518 | −0.840947 | ||||||||
\(343\) | −58.6759 | −3.16820 | ||||||||
\(344\) | 5.15367 | 0.277867 | ||||||||
\(345\) | −1.56743 | −0.0843878 | ||||||||
\(346\) | −42.4446 | −2.28183 | ||||||||
\(347\) | −14.9875 | −0.804572 | −0.402286 | − | 0.915514i | \(-0.631784\pi\) | ||||
−0.402286 | + | 0.915514i | \(0.631784\pi\) | |||||||
\(348\) | −3.97738 | −0.213210 | ||||||||
\(349\) | 2.33812 | 0.125157 | 0.0625784 | − | 0.998040i | \(-0.480068\pi\) | ||||
0.0625784 | + | 0.998040i | \(0.480068\pi\) | |||||||
\(350\) | −9.71152 | −0.519103 | ||||||||
\(351\) | −2.50933 | −0.133938 | ||||||||
\(352\) | −7.48694 | −0.399055 | ||||||||
\(353\) | 23.8996 | 1.27205 | 0.636024 | − | 0.771669i | \(-0.280578\pi\) | ||||
0.636024 | + | 0.771669i | \(0.280578\pi\) | |||||||
\(354\) | 4.43441 | 0.235686 | ||||||||
\(355\) | 0.239302 | 0.0127008 | ||||||||
\(356\) | 28.5769 | 1.51457 | ||||||||
\(357\) | 10.6218 | 0.562165 | ||||||||
\(358\) | 35.3508 | 1.86835 | ||||||||
\(359\) | 28.4313 | 1.50055 | 0.750273 | − | 0.661128i | \(-0.229922\pi\) | ||||
0.750273 | + | 0.661128i | \(0.229922\pi\) | |||||||
\(360\) | 1.77565 | 0.0935850 | ||||||||
\(361\) | −11.3641 | −0.598110 | ||||||||
\(362\) | −9.89522 | −0.520081 | ||||||||
\(363\) | −0.260789 | −0.0136879 | ||||||||
\(364\) | 13.8241 | 0.724580 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | −4.33373 | −0.226527 | ||||||||
\(367\) | 10.7479 | 0.561037 | 0.280519 | − | 0.959849i | \(-0.409494\pi\) | ||||
0.280519 | + | 0.959849i | \(0.409494\pi\) | |||||||
\(368\) | −27.2358 | −1.41976 | ||||||||
\(369\) | 8.69839 | 0.452820 | ||||||||
\(370\) | −5.28422 | −0.274714 | ||||||||
\(371\) | −45.0477 | −2.33876 | ||||||||
\(372\) | −1.53673 | −0.0796759 | ||||||||
\(373\) | −1.85363 | −0.0959771 | −0.0479885 | − | 0.998848i | \(-0.515281\pi\) | ||||
−0.0479885 | + | 0.998848i | \(0.515281\pi\) | |||||||
\(374\) | 15.4526 | 0.799032 | ||||||||
\(375\) | −0.260789 | −0.0134671 | ||||||||
\(376\) | 1.18070 | 0.0608898 | ||||||||
\(377\) | −14.6861 | −0.756375 | ||||||||
\(378\) | −15.0237 | −0.772734 | ||||||||
\(379\) | −18.2285 | −0.936335 | −0.468167 | − | 0.883640i | \(-0.655086\pi\) | ||||
−0.468167 | + | 0.883640i | \(0.655086\pi\) | |||||||
\(380\) | 4.65479 | 0.238786 | ||||||||
\(381\) | −3.68558 | −0.188818 | ||||||||
\(382\) | 6.44953 | 0.329987 | ||||||||
\(383\) | −15.9244 | −0.813699 | −0.406849 | − | 0.913495i | \(-0.633373\pi\) | ||||
−0.406849 | + | 0.913495i | \(0.633373\pi\) | |||||||
\(384\) | −1.24777 | −0.0636752 | ||||||||
\(385\) | −5.05939 | −0.257850 | ||||||||
\(386\) | 38.8726 | 1.97856 | ||||||||
\(387\) | 24.9508 | 1.26832 | ||||||||
\(388\) | −3.45865 | −0.175587 | ||||||||
\(389\) | −0.186606 | −0.00946132 | −0.00473066 | − | 0.999989i | \(-0.501506\pi\) | ||||
−0.00473066 | + | 0.999989i | \(0.501506\pi\) | |||||||
\(390\) | 0.811983 | 0.0411164 | ||||||||
\(391\) | 48.3851 | 2.44694 | ||||||||
\(392\) | −11.2628 | −0.568859 | ||||||||
\(393\) | 5.80197 | 0.292671 | ||||||||
\(394\) | −27.4569 | −1.38326 | ||||||||
\(395\) | 0.231708 | 0.0116585 | ||||||||
\(396\) | −4.93892 | −0.248190 | ||||||||
\(397\) | −29.9531 | −1.50330 | −0.751652 | − | 0.659560i | \(-0.770742\pi\) | ||||
−0.751652 | + | 0.659560i | \(0.770742\pi\) | |||||||
\(398\) | −19.7414 | −0.989546 | ||||||||
\(399\) | 3.64600 | 0.182529 | ||||||||
\(400\) | −4.53147 | −0.226573 | ||||||||
\(401\) | 0.923651 | 0.0461249 | 0.0230625 | − | 0.999734i | \(-0.492658\pi\) | ||||
0.0230625 | + | 0.999734i | \(0.492658\pi\) | |||||||
\(402\) | 2.04869 | 0.102180 | ||||||||
\(403\) | −5.67426 | −0.282655 | ||||||||
\(404\) | 3.99399 | 0.198709 | ||||||||
\(405\) | 8.39253 | 0.417028 | ||||||||
\(406\) | −87.9277 | −4.36378 | ||||||||
\(407\) | −2.75291 | −0.136457 | ||||||||
\(408\) | 1.27144 | 0.0629455 | ||||||||
\(409\) | 17.1161 | 0.846335 | 0.423167 | − | 0.906052i | \(-0.360918\pi\) | ||||
0.423167 | + | 0.906052i | \(0.360918\pi\) | |||||||
\(410\) | −5.69463 | −0.281238 | ||||||||
\(411\) | 0.884385 | 0.0436235 | ||||||||
\(412\) | −5.56436 | −0.274136 | ||||||||
\(413\) | 44.8184 | 2.20537 | ||||||||
\(414\) | −33.8261 | −1.66246 | ||||||||
\(415\) | 16.6802 | 0.818797 | ||||||||
\(416\) | 12.1443 | 0.595425 | ||||||||
\(417\) | 3.48956 | 0.170884 | ||||||||
\(418\) | 5.30419 | 0.259437 | ||||||||
\(419\) | 26.1991 | 1.27991 | 0.639954 | − | 0.768413i | \(-0.278953\pi\) | ||||
0.639954 | + | 0.768413i | \(0.278953\pi\) | |||||||
\(420\) | 2.22258 | 0.108451 | ||||||||
\(421\) | −10.0051 | −0.487621 | −0.243810 | − | 0.969823i | \(-0.578397\pi\) | ||||
−0.243810 | + | 0.969823i | \(0.578397\pi\) | |||||||
\(422\) | 4.00850 | 0.195131 | ||||||||
\(423\) | 5.71619 | 0.277930 | ||||||||
\(424\) | −5.39224 | −0.261870 | ||||||||
\(425\) | 8.05028 | 0.390496 | ||||||||
\(426\) | −0.119791 | −0.00580388 | ||||||||
\(427\) | −43.8008 | −2.11967 | ||||||||
\(428\) | −0.494470 | −0.0239011 | ||||||||
\(429\) | 0.423017 | 0.0204235 | ||||||||
\(430\) | −16.3347 | −0.787729 | ||||||||
\(431\) | −21.3432 | −1.02806 | −0.514032 | − | 0.857771i | \(-0.671849\pi\) | ||||
−0.514032 | + | 0.857771i | \(0.671849\pi\) | |||||||
\(432\) | −7.01016 | −0.337276 | ||||||||
\(433\) | −21.9708 | −1.05585 | −0.527925 | − | 0.849291i | \(-0.677030\pi\) | ||||
−0.527925 | + | 0.849291i | \(0.677030\pi\) | |||||||
\(434\) | −33.9725 | −1.63073 | ||||||||
\(435\) | −2.36117 | −0.113209 | ||||||||
\(436\) | 25.0312 | 1.19878 | ||||||||
\(437\) | 16.6085 | 0.794493 | ||||||||
\(438\) | −0.500585 | −0.0239189 | ||||||||
\(439\) | 11.0330 | 0.526575 | 0.263287 | − | 0.964717i | \(-0.415193\pi\) | ||||
0.263287 | + | 0.964717i | \(0.415193\pi\) | |||||||
\(440\) | −0.605613 | −0.0288714 | ||||||||
\(441\) | −54.5275 | −2.59655 | ||||||||
\(442\) | −25.0651 | −1.19223 | ||||||||
\(443\) | −12.1571 | −0.577599 | −0.288800 | − | 0.957390i | \(-0.593256\pi\) | ||||
−0.288800 | + | 0.957390i | \(0.593256\pi\) | |||||||
\(444\) | 1.20935 | 0.0573930 | ||||||||
\(445\) | 16.9646 | 0.804201 | ||||||||
\(446\) | 50.7634 | 2.40372 | ||||||||
\(447\) | 3.21653 | 0.152137 | ||||||||
\(448\) | 26.8567 | 1.26886 | ||||||||
\(449\) | −10.5329 | −0.497077 | −0.248538 | − | 0.968622i | \(-0.579950\pi\) | ||||
−0.248538 | + | 0.968622i | \(0.579950\pi\) | |||||||
\(450\) | −5.62796 | −0.265305 | ||||||||
\(451\) | −2.96672 | −0.139697 | ||||||||
\(452\) | 12.1592 | 0.571919 | ||||||||
\(453\) | −3.48699 | −0.163833 | ||||||||
\(454\) | −21.1487 | −0.992557 | ||||||||
\(455\) | 8.20668 | 0.384735 | ||||||||
\(456\) | 0.436429 | 0.0204377 | ||||||||
\(457\) | −4.23915 | −0.198299 | −0.0991496 | − | 0.995073i | \(-0.531612\pi\) | ||||
−0.0991496 | + | 0.995073i | \(0.531612\pi\) | |||||||
\(458\) | 24.7402 | 1.15603 | ||||||||
\(459\) | 12.4537 | 0.581291 | ||||||||
\(460\) | 10.1244 | 0.472054 | ||||||||
\(461\) | −4.53169 | −0.211062 | −0.105531 | − | 0.994416i | \(-0.533654\pi\) | ||||
−0.105531 | + | 0.994416i | \(0.533654\pi\) | |||||||
\(462\) | 2.53265 | 0.117830 | ||||||||
\(463\) | 35.5819 | 1.65363 | 0.826815 | − | 0.562473i | \(-0.190150\pi\) | ||||
0.826815 | + | 0.562473i | \(0.190150\pi\) | |||||||
\(464\) | −41.0277 | −1.90466 | ||||||||
\(465\) | −0.912281 | −0.0423060 | ||||||||
\(466\) | 3.15678 | 0.146235 | ||||||||
\(467\) | −35.5349 | −1.64436 | −0.822180 | − | 0.569228i | \(-0.807242\pi\) | ||||
−0.822180 | + | 0.569228i | \(0.807242\pi\) | |||||||
\(468\) | 8.01127 | 0.370321 | ||||||||
\(469\) | 20.7061 | 0.956118 | ||||||||
\(470\) | −3.74225 | −0.172617 | ||||||||
\(471\) | 5.10370 | 0.235166 | ||||||||
\(472\) | 5.36479 | 0.246935 | ||||||||
\(473\) | −8.50985 | −0.391283 | ||||||||
\(474\) | −0.115990 | −0.00532758 | ||||||||
\(475\) | 2.76332 | 0.126790 | ||||||||
\(476\) | −68.6087 | −3.14467 | ||||||||
\(477\) | −26.1058 | −1.19530 | ||||||||
\(478\) | 22.6919 | 1.03790 | ||||||||
\(479\) | −26.0127 | −1.18855 | −0.594274 | − | 0.804262i | \(-0.702561\pi\) | ||||
−0.594274 | + | 0.804262i | \(0.702561\pi\) | |||||||
\(480\) | 1.95251 | 0.0891194 | ||||||||
\(481\) | 4.46541 | 0.203605 | ||||||||
\(482\) | 40.6459 | 1.85137 | ||||||||
\(483\) | 7.93026 | 0.360839 | ||||||||
\(484\) | 1.68450 | 0.0765680 | ||||||||
\(485\) | −2.05323 | −0.0932323 | ||||||||
\(486\) | −13.1096 | −0.594662 | ||||||||
\(487\) | −40.5386 | −1.83698 | −0.918490 | − | 0.395443i | \(-0.870591\pi\) | ||||
−0.918490 | + | 0.395443i | \(0.870591\pi\) | |||||||
\(488\) | −5.24299 | −0.237339 | ||||||||
\(489\) | −1.50730 | −0.0681624 | ||||||||
\(490\) | 35.6978 | 1.61266 | ||||||||
\(491\) | 12.5485 | 0.566307 | 0.283153 | − | 0.959075i | \(-0.408619\pi\) | ||||
0.283153 | + | 0.959075i | \(0.408619\pi\) | |||||||
\(492\) | 1.30327 | 0.0587560 | ||||||||
\(493\) | 72.8869 | 3.28266 | ||||||||
\(494\) | −8.60377 | −0.387102 | ||||||||
\(495\) | −2.93199 | −0.131783 | ||||||||
\(496\) | −15.8518 | −0.711767 | ||||||||
\(497\) | −1.21072 | −0.0543082 | ||||||||
\(498\) | −8.34984 | −0.374165 | ||||||||
\(499\) | 14.2569 | 0.638228 | 0.319114 | − | 0.947716i | \(-0.396615\pi\) | ||||
0.319114 | + | 0.947716i | \(0.396615\pi\) | |||||||
\(500\) | 1.68450 | 0.0753329 | ||||||||
\(501\) | −2.36989 | −0.105879 | ||||||||
\(502\) | 31.9187 | 1.42460 | ||||||||
\(503\) | 9.76277 | 0.435300 | 0.217650 | − | 0.976027i | \(-0.430161\pi\) | ||||
0.217650 | + | 0.976027i | \(0.430161\pi\) | |||||||
\(504\) | −8.98370 | −0.400166 | ||||||||
\(505\) | 2.37103 | 0.105510 | ||||||||
\(506\) | 11.5369 | 0.512878 | ||||||||
\(507\) | 2.70409 | 0.120093 | ||||||||
\(508\) | 23.8060 | 1.05622 | ||||||||
\(509\) | −31.2400 | −1.38469 | −0.692344 | − | 0.721567i | \(-0.743422\pi\) | ||||
−0.692344 | + | 0.721567i | \(0.743422\pi\) | |||||||
\(510\) | −4.02985 | −0.178445 | ||||||||
\(511\) | −5.05939 | −0.223814 | ||||||||
\(512\) | 28.4382 | 1.25680 | ||||||||
\(513\) | 4.27483 | 0.188739 | ||||||||
\(514\) | −56.8847 | −2.50908 | ||||||||
\(515\) | −3.30328 | −0.145560 | ||||||||
\(516\) | 3.73835 | 0.164572 | ||||||||
\(517\) | −1.94959 | −0.0857430 | ||||||||
\(518\) | 26.7350 | 1.17467 | ||||||||
\(519\) | 5.76662 | 0.253127 | ||||||||
\(520\) | 0.982346 | 0.0430787 | ||||||||
\(521\) | 40.3474 | 1.76765 | 0.883826 | − | 0.467817i | \(-0.154959\pi\) | ||||
0.883826 | + | 0.467817i | \(0.154959\pi\) | |||||||
\(522\) | −50.9554 | −2.23026 | ||||||||
\(523\) | 36.5074 | 1.59636 | 0.798178 | − | 0.602421i | \(-0.205797\pi\) | ||||
0.798178 | + | 0.602421i | \(0.205797\pi\) | |||||||
\(524\) | −37.4763 | −1.63716 | ||||||||
\(525\) | 1.31943 | 0.0575847 | ||||||||
\(526\) | −18.1788 | −0.792632 | ||||||||
\(527\) | 28.1612 | 1.22672 | ||||||||
\(528\) | 1.18175 | 0.0514293 | ||||||||
\(529\) | 13.1244 | 0.570628 | ||||||||
\(530\) | 17.0908 | 0.742378 | ||||||||
\(531\) | 25.9729 | 1.12713 | ||||||||
\(532\) | −23.5504 | −1.02104 | ||||||||
\(533\) | 4.81223 | 0.208441 | ||||||||
\(534\) | −8.49224 | −0.367495 | ||||||||
\(535\) | −0.293542 | −0.0126909 | ||||||||
\(536\) | 2.47853 | 0.107056 | ||||||||
\(537\) | −4.80285 | −0.207258 | ||||||||
\(538\) | 28.3163 | 1.22080 | ||||||||
\(539\) | 18.5974 | 0.801048 | ||||||||
\(540\) | 2.60591 | 0.112140 | ||||||||
\(541\) | 33.3113 | 1.43216 | 0.716082 | − | 0.698016i | \(-0.245934\pi\) | ||||
0.716082 | + | 0.698016i | \(0.245934\pi\) | |||||||
\(542\) | −0.968075 | −0.0415824 | ||||||||
\(543\) | 1.34439 | 0.0576933 | ||||||||
\(544\) | −60.2720 | −2.58414 | ||||||||
\(545\) | 14.8598 | 0.636523 | ||||||||
\(546\) | −4.10814 | −0.175812 | ||||||||
\(547\) | 12.0433 | 0.514935 | 0.257468 | − | 0.966287i | \(-0.417112\pi\) | ||||
0.257468 | + | 0.966287i | \(0.417112\pi\) | |||||||
\(548\) | −5.71245 | −0.244024 | ||||||||
\(549\) | −25.3832 | −1.08333 | ||||||||
\(550\) | 1.91950 | 0.0818479 | ||||||||
\(551\) | 25.0189 | 1.06584 | ||||||||
\(552\) | 0.949258 | 0.0404031 | ||||||||
\(553\) | −1.17230 | −0.0498514 | ||||||||
\(554\) | 6.08582 | 0.258562 | ||||||||
\(555\) | 0.717928 | 0.0304743 | ||||||||
\(556\) | −22.5399 | −0.955904 | ||||||||
\(557\) | −7.13074 | −0.302139 | −0.151070 | − | 0.988523i | \(-0.548272\pi\) | ||||
−0.151070 | + | 0.988523i | \(0.548272\pi\) | |||||||
\(558\) | −19.6875 | −0.833440 | ||||||||
\(559\) | 13.8036 | 0.583829 | ||||||||
\(560\) | 22.9265 | 0.968820 | ||||||||
\(561\) | −2.09942 | −0.0886377 | ||||||||
\(562\) | −35.8132 | −1.51069 | ||||||||
\(563\) | 6.82712 | 0.287729 | 0.143864 | − | 0.989597i | \(-0.454047\pi\) | ||||
0.143864 | + | 0.989597i | \(0.454047\pi\) | |||||||
\(564\) | 0.856451 | 0.0360631 | ||||||||
\(565\) | 7.21829 | 0.303676 | ||||||||
\(566\) | −4.53353 | −0.190559 | ||||||||
\(567\) | −42.4611 | −1.78320 | ||||||||
\(568\) | −0.144924 | −0.00608088 | ||||||||
\(569\) | 34.9467 | 1.46504 | 0.732520 | − | 0.680745i | \(-0.238344\pi\) | ||||
0.732520 | + | 0.680745i | \(0.238344\pi\) | |||||||
\(570\) | −1.38327 | −0.0579389 | ||||||||
\(571\) | −28.3733 | −1.18739 | −0.593694 | − | 0.804691i | \(-0.702331\pi\) | ||||
−0.593694 | + | 0.804691i | \(0.702331\pi\) | |||||||
\(572\) | −2.73237 | −0.114246 | ||||||||
\(573\) | −0.876250 | −0.0366059 | ||||||||
\(574\) | 28.8114 | 1.20256 | ||||||||
\(575\) | 6.01036 | 0.250649 | ||||||||
\(576\) | 15.5638 | 0.648493 | ||||||||
\(577\) | 25.9918 | 1.08205 | 0.541027 | − | 0.841005i | \(-0.318036\pi\) | ||||
0.541027 | + | 0.841005i | \(0.318036\pi\) | |||||||
\(578\) | 91.7658 | 3.81696 | ||||||||
\(579\) | −5.28132 | −0.219484 | ||||||||
\(580\) | 15.2513 | 0.633278 | ||||||||
\(581\) | −84.3915 | −3.50115 | ||||||||
\(582\) | 1.02781 | 0.0426043 | ||||||||
\(583\) | 8.90378 | 0.368757 | ||||||||
\(584\) | −0.605613 | −0.0250604 | ||||||||
\(585\) | 4.75589 | 0.196632 | ||||||||
\(586\) | −2.01043 | −0.0830500 | ||||||||
\(587\) | 16.3037 | 0.672924 | 0.336462 | − | 0.941697i | \(-0.390770\pi\) | ||||
0.336462 | + | 0.941697i | \(0.390770\pi\) | |||||||
\(588\) | −8.16980 | −0.336917 | ||||||||
\(589\) | 9.66653 | 0.398302 | ||||||||
\(590\) | −17.0038 | −0.700037 | ||||||||
\(591\) | 3.73037 | 0.153447 | ||||||||
\(592\) | 12.4747 | 0.512708 | ||||||||
\(593\) | 29.7094 | 1.22002 | 0.610009 | − | 0.792394i | \(-0.291166\pi\) | ||||
0.610009 | + | 0.792394i | \(0.291166\pi\) | |||||||
\(594\) | 2.96946 | 0.121839 | ||||||||
\(595\) | −40.7295 | −1.66975 | ||||||||
\(596\) | −20.7763 | −0.851031 | ||||||||
\(597\) | 2.68211 | 0.109772 | ||||||||
\(598\) | −18.7137 | −0.765259 | ||||||||
\(599\) | 29.5739 | 1.20836 | 0.604179 | − | 0.796848i | \(-0.293501\pi\) | ||||
0.604179 | + | 0.796848i | \(0.293501\pi\) | |||||||
\(600\) | 0.157937 | 0.00644774 | ||||||||
\(601\) | 33.3005 | 1.35835 | 0.679177 | − | 0.733975i | \(-0.262337\pi\) | ||||
0.679177 | + | 0.733975i | \(0.262337\pi\) | |||||||
\(602\) | 82.6436 | 3.36830 | ||||||||
\(603\) | 11.9995 | 0.488656 | ||||||||
\(604\) | 22.5233 | 0.916460 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −1.18690 | −0.0482146 | ||||||||
\(607\) | −43.5409 | −1.76727 | −0.883635 | − | 0.468176i | \(-0.844911\pi\) | ||||
−0.883635 | + | 0.468176i | \(0.844911\pi\) | |||||||
\(608\) | −20.6888 | −0.839041 | ||||||||
\(609\) | 11.9461 | 0.484079 | ||||||||
\(610\) | 16.6178 | 0.672834 | ||||||||
\(611\) | 3.16237 | 0.127936 | ||||||||
\(612\) | −39.7597 | −1.60719 | ||||||||
\(613\) | 43.0817 | 1.74005 | 0.870026 | − | 0.493006i | \(-0.164102\pi\) | ||||
0.870026 | + | 0.493006i | \(0.164102\pi\) | |||||||
\(614\) | 33.9554 | 1.37033 | ||||||||
\(615\) | 0.773687 | 0.0311981 | ||||||||
\(616\) | 3.06403 | 0.123453 | ||||||||
\(617\) | 5.40838 | 0.217733 | 0.108867 | − | 0.994056i | \(-0.465278\pi\) | ||||
0.108867 | + | 0.994056i | \(0.465278\pi\) | |||||||
\(618\) | 1.65357 | 0.0665164 | ||||||||
\(619\) | 24.5407 | 0.986373 | 0.493186 | − | 0.869924i | \(-0.335832\pi\) | ||||
0.493186 | + | 0.869924i | \(0.335832\pi\) | |||||||
\(620\) | 5.89264 | 0.236654 | ||||||||
\(621\) | 9.29800 | 0.373116 | ||||||||
\(622\) | 24.3752 | 0.977357 | ||||||||
\(623\) | −85.8307 | −3.43874 | ||||||||
\(624\) | −1.91689 | −0.0767369 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −11.5274 | −0.460728 | ||||||||
\(627\) | −0.720641 | −0.0287796 | ||||||||
\(628\) | −32.9660 | −1.31549 | ||||||||
\(629\) | −22.1617 | −0.883646 | ||||||||
\(630\) | 28.4741 | 1.13443 | ||||||||
\(631\) | 5.18828 | 0.206542 | 0.103271 | − | 0.994653i | \(-0.467069\pi\) | ||||
0.103271 | + | 0.994653i | \(0.467069\pi\) | |||||||
\(632\) | −0.140326 | −0.00558185 | ||||||||
\(633\) | −0.544605 | −0.0216461 | ||||||||
\(634\) | 11.8554 | 0.470839 | ||||||||
\(635\) | 14.1325 | 0.560829 | ||||||||
\(636\) | −3.91140 | −0.155097 | ||||||||
\(637\) | −30.1663 | −1.19523 | ||||||||
\(638\) | 17.3791 | 0.688045 | ||||||||
\(639\) | −0.701630 | −0.0277561 | ||||||||
\(640\) | 4.78462 | 0.189129 | ||||||||
\(641\) | 6.78306 | 0.267915 | 0.133957 | − | 0.990987i | \(-0.457231\pi\) | ||||
0.133957 | + | 0.990987i | \(0.457231\pi\) | |||||||
\(642\) | 0.146943 | 0.00579936 | ||||||||
\(643\) | 44.0325 | 1.73647 | 0.868236 | − | 0.496151i | \(-0.165254\pi\) | ||||
0.868236 | + | 0.496151i | \(0.165254\pi\) | |||||||
\(644\) | −51.2234 | −2.01849 | ||||||||
\(645\) | 2.21927 | 0.0873838 | ||||||||
\(646\) | 42.7003 | 1.68002 | ||||||||
\(647\) | −35.2216 | −1.38470 | −0.692352 | − | 0.721560i | \(-0.743425\pi\) | ||||
−0.692352 | + | 0.721560i | \(0.743425\pi\) | |||||||
\(648\) | −5.08262 | −0.199664 | ||||||||
\(649\) | −8.85846 | −0.347725 | ||||||||
\(650\) | −3.11357 | −0.122124 | ||||||||
\(651\) | 4.61559 | 0.180899 | ||||||||
\(652\) | 9.73599 | 0.381291 | ||||||||
\(653\) | −12.0554 | −0.471765 | −0.235882 | − | 0.971782i | \(-0.575798\pi\) | ||||
−0.235882 | + | 0.971782i | \(0.575798\pi\) | |||||||
\(654\) | −7.43858 | −0.290872 | ||||||||
\(655\) | −22.2478 | −0.869293 | ||||||||
\(656\) | 13.4436 | 0.524884 | ||||||||
\(657\) | −2.93199 | −0.114388 | ||||||||
\(658\) | 18.9335 | 0.738105 | ||||||||
\(659\) | −6.40438 | −0.249479 | −0.124740 | − | 0.992190i | \(-0.539810\pi\) | ||||
−0.124740 | + | 0.992190i | \(0.539810\pi\) | |||||||
\(660\) | −0.439297 | −0.0170996 | ||||||||
\(661\) | −32.3306 | −1.25751 | −0.628757 | − | 0.777602i | \(-0.716436\pi\) | ||||
−0.628757 | + | 0.777602i | \(0.716436\pi\) | |||||||
\(662\) | −54.5518 | −2.12021 | ||||||||
\(663\) | 3.40541 | 0.132255 | ||||||||
\(664\) | −10.1017 | −0.392023 | ||||||||
\(665\) | −13.9807 | −0.542148 | ||||||||
\(666\) | 15.4933 | 0.600353 | ||||||||
\(667\) | 54.4176 | 2.10706 | ||||||||
\(668\) | 15.3077 | 0.592272 | ||||||||
\(669\) | −6.89685 | −0.266647 | ||||||||
\(670\) | −7.85577 | −0.303495 | ||||||||
\(671\) | 8.65733 | 0.334212 | ||||||||
\(672\) | −9.87850 | −0.381072 | ||||||||
\(673\) | −14.0369 | −0.541082 | −0.270541 | − | 0.962708i | \(-0.587203\pi\) | ||||
−0.270541 | + | 0.962708i | \(0.587203\pi\) | |||||||
\(674\) | 14.4431 | 0.556326 | ||||||||
\(675\) | 1.54700 | 0.0595439 | ||||||||
\(676\) | −17.4663 | −0.671783 | ||||||||
\(677\) | 19.9621 | 0.767208 | 0.383604 | − | 0.923498i | \(-0.374683\pi\) | ||||
0.383604 | + | 0.923498i | \(0.374683\pi\) | |||||||
\(678\) | −3.61336 | −0.138770 | ||||||||
\(679\) | 10.3881 | 0.398658 | ||||||||
\(680\) | −4.87535 | −0.186961 | ||||||||
\(681\) | 2.87331 | 0.110106 | ||||||||
\(682\) | 6.71474 | 0.257121 | ||||||||
\(683\) | −6.63806 | −0.253998 | −0.126999 | − | 0.991903i | \(-0.540535\pi\) | ||||
−0.126999 | + | 0.991903i | \(0.540535\pi\) | |||||||
\(684\) | −13.6478 | −0.521837 | ||||||||
\(685\) | −3.39120 | −0.129571 | ||||||||
\(686\) | −112.629 | −4.30018 | ||||||||
\(687\) | −3.36127 | −0.128240 | ||||||||
\(688\) | 38.5621 | 1.47017 | ||||||||
\(689\) | −14.4425 | −0.550217 | ||||||||
\(690\) | −3.00870 | −0.114539 | ||||||||
\(691\) | 6.91495 | 0.263057 | 0.131529 | − | 0.991312i | \(-0.458011\pi\) | ||||
0.131529 | + | 0.991312i | \(0.458011\pi\) | |||||||
\(692\) | −37.2480 | −1.41596 | ||||||||
\(693\) | 14.8341 | 0.563500 | ||||||||
\(694\) | −28.7686 | −1.09204 | ||||||||
\(695\) | −13.3808 | −0.507563 | ||||||||
\(696\) | 1.42995 | 0.0542022 | ||||||||
\(697\) | −23.8829 | −0.904631 | ||||||||
\(698\) | 4.48804 | 0.169875 | ||||||||
\(699\) | −0.428888 | −0.0162220 | ||||||||
\(700\) | −8.52252 | −0.322121 | ||||||||
\(701\) | 26.8781 | 1.01517 | 0.507585 | − | 0.861602i | \(-0.330538\pi\) | ||||
0.507585 | + | 0.861602i | \(0.330538\pi\) | |||||||
\(702\) | −4.81667 | −0.181794 | ||||||||
\(703\) | −7.60716 | −0.286910 | ||||||||
\(704\) | −5.30828 | −0.200063 | ||||||||
\(705\) | 0.508432 | 0.0191486 | ||||||||
\(706\) | 45.8754 | 1.72654 | ||||||||
\(707\) | −11.9960 | −0.451155 | ||||||||
\(708\) | 3.89150 | 0.146251 | ||||||||
\(709\) | 3.08730 | 0.115946 | 0.0579729 | − | 0.998318i | \(-0.481536\pi\) | ||||
0.0579729 | + | 0.998318i | \(0.481536\pi\) | |||||||
\(710\) | 0.459341 | 0.0172387 | ||||||||
\(711\) | −0.679367 | −0.0254782 | ||||||||
\(712\) | −10.2740 | −0.385034 | ||||||||
\(713\) | 21.0252 | 0.787401 | ||||||||
\(714\) | 20.3886 | 0.763023 | ||||||||
\(715\) | −1.62207 | −0.0606619 | ||||||||
\(716\) | 31.0227 | 1.15937 | ||||||||
\(717\) | −3.08298 | −0.115136 | ||||||||
\(718\) | 54.5740 | 2.03668 | ||||||||
\(719\) | −5.54758 | −0.206890 | −0.103445 | − | 0.994635i | \(-0.532987\pi\) | ||||
−0.103445 | + | 0.994635i | \(0.532987\pi\) | |||||||
\(720\) | 13.2862 | 0.495148 | ||||||||
\(721\) | 16.7126 | 0.622409 | ||||||||
\(722\) | −21.8134 | −0.811811 | ||||||||
\(723\) | −5.52225 | −0.205375 | ||||||||
\(724\) | −8.68373 | −0.322728 | ||||||||
\(725\) | 9.05396 | 0.336256 | ||||||||
\(726\) | −0.500585 | −0.0185784 | ||||||||
\(727\) | −2.51174 | −0.0931553 | −0.0465777 | − | 0.998915i | \(-0.514831\pi\) | ||||
−0.0465777 | + | 0.998915i | \(0.514831\pi\) | |||||||
\(728\) | −4.97007 | −0.184203 | ||||||||
\(729\) | −23.3965 | −0.866537 | ||||||||
\(730\) | 1.91950 | 0.0710440 | ||||||||
\(731\) | −68.5067 | −2.53381 | ||||||||
\(732\) | −3.80314 | −0.140568 | ||||||||
\(733\) | 34.6386 | 1.27941 | 0.639704 | − | 0.768622i | \(-0.279057\pi\) | ||||
0.639704 | + | 0.768622i | \(0.279057\pi\) | |||||||
\(734\) | 20.6307 | 0.761493 | ||||||||
\(735\) | −4.85000 | −0.178895 | ||||||||
\(736\) | −44.9992 | −1.65869 | ||||||||
\(737\) | −4.09260 | −0.150753 | ||||||||
\(738\) | 16.6966 | 0.614610 | ||||||||
\(739\) | −24.1154 | −0.887098 | −0.443549 | − | 0.896250i | \(-0.646281\pi\) | ||||
−0.443549 | + | 0.896250i | \(0.646281\pi\) | |||||||
\(740\) | −4.63727 | −0.170469 | ||||||||
\(741\) | 1.16893 | 0.0429417 | ||||||||
\(742\) | −86.4692 | −3.17438 | ||||||||
\(743\) | −34.9553 | −1.28239 | −0.641193 | − | 0.767380i | \(-0.721560\pi\) | ||||
−0.641193 | + | 0.767380i | \(0.721560\pi\) | |||||||
\(744\) | 0.552489 | 0.0202552 | ||||||||
\(745\) | −12.3339 | −0.451877 | ||||||||
\(746\) | −3.55804 | −0.130269 | ||||||||
\(747\) | −48.9061 | −1.78938 | ||||||||
\(748\) | 13.5607 | 0.495827 | ||||||||
\(749\) | 1.48514 | 0.0542659 | ||||||||
\(750\) | −0.500585 | −0.0182788 | ||||||||
\(751\) | −11.1374 | −0.406408 | −0.203204 | − | 0.979136i | \(-0.565135\pi\) | ||||
−0.203204 | + | 0.979136i | \(0.565135\pi\) | |||||||
\(752\) | 8.83451 | 0.322162 | ||||||||
\(753\) | −4.33655 | −0.158033 | ||||||||
\(754\) | −28.1901 | −1.02662 | ||||||||
\(755\) | 13.3710 | 0.486619 | ||||||||
\(756\) | −13.1843 | −0.479508 | ||||||||
\(757\) | −7.09223 | −0.257771 | −0.128886 | − | 0.991659i | \(-0.541140\pi\) | ||||
−0.128886 | + | 0.991659i | \(0.541140\pi\) | |||||||
\(758\) | −34.9897 | −1.27088 | ||||||||
\(759\) | −1.56743 | −0.0568942 | ||||||||
\(760\) | −1.67350 | −0.0607042 | ||||||||
\(761\) | 8.13384 | 0.294852 | 0.147426 | − | 0.989073i | \(-0.452901\pi\) | ||||
0.147426 | + | 0.989073i | \(0.452901\pi\) | |||||||
\(762\) | −7.07449 | −0.256282 | ||||||||
\(763\) | −75.1815 | −2.72175 | ||||||||
\(764\) | 5.65990 | 0.204768 | ||||||||
\(765\) | −23.6033 | −0.853381 | ||||||||
\(766\) | −30.5669 | −1.10443 | ||||||||
\(767\) | 14.3690 | 0.518836 | ||||||||
\(768\) | −5.16378 | −0.186332 | ||||||||
\(769\) | 1.31148 | 0.0472932 | 0.0236466 | − | 0.999720i | \(-0.492472\pi\) | ||||
0.0236466 | + | 0.999720i | \(0.492472\pi\) | |||||||
\(770\) | −9.71152 | −0.349979 | ||||||||
\(771\) | 7.72850 | 0.278335 | ||||||||
\(772\) | 34.1133 | 1.22777 | ||||||||
\(773\) | −12.7660 | −0.459162 | −0.229581 | − | 0.973290i | \(-0.573736\pi\) | ||||
−0.229581 | + | 0.973290i | \(0.573736\pi\) | |||||||
\(774\) | 47.8932 | 1.72148 | ||||||||
\(775\) | 3.49816 | 0.125658 | ||||||||
\(776\) | 1.24346 | 0.0446377 | ||||||||
\(777\) | −3.63228 | −0.130307 | ||||||||
\(778\) | −0.358192 | −0.0128418 | ||||||||
\(779\) | −8.19798 | −0.293723 | ||||||||
\(780\) | 0.712570 | 0.0255141 | ||||||||
\(781\) | 0.239302 | 0.00856289 | ||||||||
\(782\) | 92.8754 | 3.32122 | ||||||||
\(783\) | 14.0064 | 0.500549 | ||||||||
\(784\) | −84.2736 | −3.00977 | ||||||||
\(785\) | −19.5703 | −0.698493 | ||||||||
\(786\) | 11.1369 | 0.397240 | ||||||||
\(787\) | −40.5526 | −1.44554 | −0.722771 | − | 0.691087i | \(-0.757132\pi\) | ||||
−0.722771 | + | 0.691087i | \(0.757132\pi\) | |||||||
\(788\) | −24.0953 | −0.858361 | ||||||||
\(789\) | 2.46981 | 0.0879276 | ||||||||
\(790\) | 0.444765 | 0.0158240 | ||||||||
\(791\) | −36.5201 | −1.29851 | ||||||||
\(792\) | 1.77565 | 0.0630950 | ||||||||
\(793\) | −14.0428 | −0.498674 | ||||||||
\(794\) | −57.4951 | −2.04042 | ||||||||
\(795\) | −2.32200 | −0.0823530 | ||||||||
\(796\) | −17.3244 | −0.614047 | ||||||||
\(797\) | −23.8325 | −0.844191 | −0.422096 | − | 0.906551i | \(-0.638705\pi\) | ||||
−0.422096 | + | 0.906551i | \(0.638705\pi\) | |||||||
\(798\) | 6.99852 | 0.247745 | ||||||||
\(799\) | −15.6948 | −0.555241 | ||||||||
\(800\) | −7.48694 | −0.264703 | ||||||||
\(801\) | −49.7401 | −1.75748 | ||||||||
\(802\) | 1.77295 | 0.0626051 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | 1.79787 | 0.0634060 | ||||||||
\(805\) | −30.4088 | −1.07177 | ||||||||
\(806\) | −10.8918 | −0.383646 | ||||||||
\(807\) | −3.84713 | −0.135425 | ||||||||
\(808\) | −1.43593 | −0.0505157 | ||||||||
\(809\) | 16.0244 | 0.563390 | 0.281695 | − | 0.959504i | \(-0.409103\pi\) | ||||
0.281695 | + | 0.959504i | \(0.409103\pi\) | |||||||
\(810\) | 16.1095 | 0.566030 | ||||||||
\(811\) | 47.9010 | 1.68203 | 0.841015 | − | 0.541012i | \(-0.181959\pi\) | ||||
0.841015 | + | 0.541012i | \(0.181959\pi\) | |||||||
\(812\) | −77.1625 | −2.70787 | ||||||||
\(813\) | 0.131525 | 0.00461279 | ||||||||
\(814\) | −5.28422 | −0.185212 | ||||||||
\(815\) | 5.77977 | 0.202457 | ||||||||
\(816\) | 9.51346 | 0.333038 | ||||||||
\(817\) | −23.5154 | −0.822700 | ||||||||
\(818\) | 32.8543 | 1.14873 | ||||||||
\(819\) | −24.0619 | −0.840791 | ||||||||
\(820\) | −4.99743 | −0.174518 | ||||||||
\(821\) | 11.4420 | 0.399327 | 0.199664 | − | 0.979865i | \(-0.436015\pi\) | ||||
0.199664 | + | 0.979865i | \(0.436015\pi\) | |||||||
\(822\) | 1.69758 | 0.0592099 | ||||||||
\(823\) | −20.1196 | −0.701325 | −0.350662 | − | 0.936502i | \(-0.614044\pi\) | ||||
−0.350662 | + | 0.936502i | \(0.614044\pi\) | |||||||
\(824\) | 2.00051 | 0.0696910 | ||||||||
\(825\) | −0.260789 | −0.00907949 | ||||||||
\(826\) | 86.0291 | 2.99333 | ||||||||
\(827\) | −16.5886 | −0.576843 | −0.288422 | − | 0.957503i | \(-0.593130\pi\) | ||||
−0.288422 | + | 0.957503i | \(0.593130\pi\) | |||||||
\(828\) | −29.6847 | −1.03161 | ||||||||
\(829\) | 42.7293 | 1.48405 | 0.742025 | − | 0.670372i | \(-0.233865\pi\) | ||||
0.742025 | + | 0.670372i | \(0.233865\pi\) | |||||||
\(830\) | 32.0177 | 1.11135 | ||||||||
\(831\) | −0.826834 | −0.0286826 | ||||||||
\(832\) | 8.61040 | 0.298512 | ||||||||
\(833\) | 149.715 | 5.18730 | ||||||||
\(834\) | 6.69822 | 0.231940 | ||||||||
\(835\) | 9.08740 | 0.314482 | ||||||||
\(836\) | 4.65479 | 0.160989 | ||||||||
\(837\) | 5.41164 | 0.187054 | ||||||||
\(838\) | 50.2892 | 1.73721 | ||||||||
\(839\) | −28.0798 | −0.969422 | −0.484711 | − | 0.874674i | \(-0.661075\pi\) | ||||
−0.484711 | + | 0.874674i | \(0.661075\pi\) | |||||||
\(840\) | −0.799064 | −0.0275703 | ||||||||
\(841\) | 52.9742 | 1.82669 | ||||||||
\(842\) | −19.2049 | −0.661845 | ||||||||
\(843\) | 4.86568 | 0.167583 | ||||||||
\(844\) | 3.51773 | 0.121085 | ||||||||
\(845\) | −10.3689 | −0.356701 | ||||||||
\(846\) | 10.9722 | 0.377233 | ||||||||
\(847\) | −5.05939 | −0.173843 | ||||||||
\(848\) | −40.3472 | −1.38553 | ||||||||
\(849\) | 0.615937 | 0.0211389 | ||||||||
\(850\) | 15.4526 | 0.530018 | ||||||||
\(851\) | −16.5460 | −0.567189 | ||||||||
\(852\) | −0.105125 | −0.00360151 | ||||||||
\(853\) | 31.9888 | 1.09528 | 0.547638 | − | 0.836715i | \(-0.315527\pi\) | ||||
0.547638 | + | 0.836715i | \(0.315527\pi\) | |||||||
\(854\) | −84.0758 | −2.87701 | ||||||||
\(855\) | −8.10201 | −0.277083 | ||||||||
\(856\) | 0.177773 | 0.00607615 | ||||||||
\(857\) | 36.5653 | 1.24905 | 0.624524 | − | 0.781006i | \(-0.285293\pi\) | ||||
0.624524 | + | 0.781006i | \(0.285293\pi\) | |||||||
\(858\) | 0.811983 | 0.0277206 | ||||||||
\(859\) | −9.29029 | −0.316981 | −0.158490 | − | 0.987361i | \(-0.550663\pi\) | ||||
−0.158490 | + | 0.987361i | \(0.550663\pi\) | |||||||
\(860\) | −14.3348 | −0.488813 | ||||||||
\(861\) | −3.91438 | −0.133402 | ||||||||
\(862\) | −40.9683 | −1.39539 | ||||||||
\(863\) | −11.2880 | −0.384248 | −0.192124 | − | 0.981371i | \(-0.561538\pi\) | ||||
−0.192124 | + | 0.981371i | \(0.561538\pi\) | |||||||
\(864\) | −11.5823 | −0.394037 | ||||||||
\(865\) | −22.1123 | −0.751839 | ||||||||
\(866\) | −42.1731 | −1.43310 | ||||||||
\(867\) | −12.4675 | −0.423420 | ||||||||
\(868\) | −29.8132 | −1.01192 | ||||||||
\(869\) | 0.231708 | 0.00786017 | ||||||||
\(870\) | −4.53227 | −0.153658 | ||||||||
\(871\) | 6.63849 | 0.224937 | ||||||||
\(872\) | −8.99928 | −0.304754 | ||||||||
\(873\) | 6.02004 | 0.203748 | ||||||||
\(874\) | 31.8801 | 1.07836 | ||||||||
\(875\) | −5.05939 | −0.171039 | ||||||||
\(876\) | −0.439297 | −0.0148425 | ||||||||
\(877\) | −2.78097 | −0.0939067 | −0.0469534 | − | 0.998897i | \(-0.514951\pi\) | ||||
−0.0469534 | + | 0.998897i | \(0.514951\pi\) | |||||||
\(878\) | 21.1778 | 0.714717 | ||||||||
\(879\) | 0.273142 | 0.00921284 | ||||||||
\(880\) | −4.53147 | −0.152756 | ||||||||
\(881\) | −7.67817 | −0.258684 | −0.129342 | − | 0.991600i | \(-0.541287\pi\) | ||||
−0.129342 | + | 0.991600i | \(0.541287\pi\) | |||||||
\(882\) | −104.666 | −3.52428 | ||||||||
\(883\) | −8.38796 | −0.282277 | −0.141139 | − | 0.989990i | \(-0.545076\pi\) | ||||
−0.141139 | + | 0.989990i | \(0.545076\pi\) | |||||||
\(884\) | −21.9963 | −0.739817 | ||||||||
\(885\) | 2.31018 | 0.0776560 | ||||||||
\(886\) | −23.3355 | −0.783972 | ||||||||
\(887\) | 0.678209 | 0.0227720 | 0.0113860 | − | 0.999935i | \(-0.496376\pi\) | ||||
0.0113860 | + | 0.999935i | \(0.496376\pi\) | |||||||
\(888\) | −0.434786 | −0.0145905 | ||||||||
\(889\) | −71.5016 | −2.39809 | ||||||||
\(890\) | 32.5637 | 1.09154 | ||||||||
\(891\) | 8.39253 | 0.281160 | ||||||||
\(892\) | 44.5484 | 1.49159 | ||||||||
\(893\) | −5.38734 | −0.180280 | ||||||||
\(894\) | 6.17414 | 0.206494 | ||||||||
\(895\) | 18.4166 | 0.615600 | ||||||||
\(896\) | −24.2072 | −0.808707 | ||||||||
\(897\) | 2.54249 | 0.0848911 | ||||||||
\(898\) | −20.2179 | −0.674679 | ||||||||
\(899\) | 31.6722 | 1.05633 | ||||||||
\(900\) | −4.93892 | −0.164631 | ||||||||
\(901\) | 71.6779 | 2.38794 | ||||||||
\(902\) | −5.69463 | −0.189611 | ||||||||
\(903\) | −11.2282 | −0.373650 | ||||||||
\(904\) | −4.37149 | −0.145393 | ||||||||
\(905\) | −5.15509 | −0.171361 | ||||||||
\(906\) | −6.69329 | −0.222370 | ||||||||
\(907\) | −31.6705 | −1.05160 | −0.525801 | − | 0.850608i | \(-0.676234\pi\) | ||||
−0.525801 | + | 0.850608i | \(0.676234\pi\) | |||||||
\(908\) | −18.5594 | −0.615916 | ||||||||
\(909\) | −6.95184 | −0.230578 | ||||||||
\(910\) | 15.7528 | 0.522199 | ||||||||
\(911\) | −22.6435 | −0.750213 | −0.375107 | − | 0.926982i | \(-0.622394\pi\) | ||||
−0.375107 | + | 0.926982i | \(0.622394\pi\) | |||||||
\(912\) | 3.26556 | 0.108134 | ||||||||
\(913\) | 16.6802 | 0.552033 | ||||||||
\(914\) | −8.13707 | −0.269150 | ||||||||
\(915\) | −2.25773 | −0.0746383 | ||||||||
\(916\) | 21.7112 | 0.717359 | ||||||||
\(917\) | 112.560 | 3.71707 | ||||||||
\(918\) | 23.9050 | 0.788983 | ||||||||
\(919\) | −20.7185 | −0.683439 | −0.341720 | − | 0.939802i | \(-0.611009\pi\) | ||||
−0.341720 | + | 0.939802i | \(0.611009\pi\) | |||||||
\(920\) | −3.63995 | −0.120006 | ||||||||
\(921\) | −4.61327 | −0.152012 | ||||||||
\(922\) | −8.69860 | −0.286473 | ||||||||
\(923\) | −0.388164 | −0.0127766 | ||||||||
\(924\) | 2.22258 | 0.0731174 | ||||||||
\(925\) | −2.75291 | −0.0905152 | ||||||||
\(926\) | 68.2996 | 2.24446 | ||||||||
\(927\) | 9.68518 | 0.318103 | ||||||||
\(928\) | −67.7865 | −2.22520 | ||||||||
\(929\) | 7.04258 | 0.231059 | 0.115530 | − | 0.993304i | \(-0.463143\pi\) | ||||
0.115530 | + | 0.993304i | \(0.463143\pi\) | |||||||
\(930\) | −1.75113 | −0.0574217 | ||||||||
\(931\) | 51.3905 | 1.68426 | ||||||||
\(932\) | 2.77029 | 0.0907438 | ||||||||
\(933\) | −3.31168 | −0.108419 | ||||||||
\(934\) | −68.2094 | −2.23188 | ||||||||
\(935\) | 8.05028 | 0.263272 | ||||||||
\(936\) | −2.88023 | −0.0941432 | ||||||||
\(937\) | 30.7631 | 1.00499 | 0.502493 | − | 0.864581i | \(-0.332416\pi\) | ||||
0.502493 | + | 0.864581i | \(0.332416\pi\) | |||||||
\(938\) | 39.7454 | 1.29773 | ||||||||
\(939\) | 1.56614 | 0.0511091 | ||||||||
\(940\) | −3.28408 | −0.107115 | ||||||||
\(941\) | −19.5241 | −0.636469 | −0.318235 | − | 0.948012i | \(-0.603090\pi\) | ||||
−0.318235 | + | 0.948012i | \(0.603090\pi\) | |||||||
\(942\) | 9.79657 | 0.319190 | ||||||||
\(943\) | −17.8311 | −0.580659 | ||||||||
\(944\) | 40.1418 | 1.30650 | ||||||||
\(945\) | −7.82685 | −0.254607 | ||||||||
\(946\) | −16.3347 | −0.531087 | ||||||||
\(947\) | 44.0813 | 1.43245 | 0.716226 | − | 0.697869i | \(-0.245868\pi\) | ||||
0.716226 | + | 0.697869i | \(0.245868\pi\) | |||||||
\(948\) | −0.101789 | −0.00330595 | ||||||||
\(949\) | −1.62207 | −0.0526546 | ||||||||
\(950\) | 5.30419 | 0.172091 | ||||||||
\(951\) | −1.61071 | −0.0522308 | ||||||||
\(952\) | 24.6663 | 0.799440 | ||||||||
\(953\) | 34.2161 | 1.10837 | 0.554185 | − | 0.832394i | \(-0.313030\pi\) | ||||
0.554185 | + | 0.832394i | \(0.313030\pi\) | |||||||
\(954\) | −50.1101 | −1.62238 | ||||||||
\(955\) | 3.36000 | 0.108727 | ||||||||
\(956\) | 19.9137 | 0.644054 | ||||||||
\(957\) | −2.36117 | −0.0763257 | ||||||||
\(958\) | −49.9314 | −1.61321 | ||||||||
\(959\) | 17.1574 | 0.554041 | ||||||||
\(960\) | 1.38434 | 0.0446794 | ||||||||
\(961\) | −18.7629 | −0.605253 | ||||||||
\(962\) | 8.57138 | 0.276352 | ||||||||
\(963\) | 0.860662 | 0.0277344 | ||||||||
\(964\) | 35.6695 | 1.14884 | ||||||||
\(965\) | 20.2514 | 0.651915 | ||||||||
\(966\) | 15.2222 | 0.489765 | ||||||||
\(967\) | −29.8521 | −0.959978 | −0.479989 | − | 0.877274i | \(-0.659359\pi\) | ||||
−0.479989 | + | 0.877274i | \(0.659359\pi\) | |||||||
\(968\) | −0.605613 | −0.0194651 | ||||||||
\(969\) | −5.80136 | −0.186367 | ||||||||
\(970\) | −3.94118 | −0.126544 | ||||||||
\(971\) | −35.3502 | −1.13444 | −0.567221 | − | 0.823565i | \(-0.691982\pi\) | ||||
−0.567221 | + | 0.823565i | \(0.691982\pi\) | |||||||
\(972\) | −11.5045 | −0.369008 | ||||||||
\(973\) | 67.6987 | 2.17032 | ||||||||
\(974\) | −77.8141 | −2.49332 | ||||||||
\(975\) | 0.423017 | 0.0135474 | ||||||||
\(976\) | −39.2304 | −1.25573 | ||||||||
\(977\) | −40.1721 | −1.28522 | −0.642610 | − | 0.766193i | \(-0.722148\pi\) | ||||
−0.642610 | + | 0.766193i | \(0.722148\pi\) | |||||||
\(978\) | −2.89326 | −0.0925164 | ||||||||
\(979\) | 16.9646 | 0.542192 | ||||||||
\(980\) | 31.3273 | 1.00071 | ||||||||
\(981\) | −43.5687 | −1.39104 | ||||||||
\(982\) | 24.0869 | 0.768645 | ||||||||
\(983\) | −15.6324 | −0.498597 | −0.249298 | − | 0.968427i | \(-0.580200\pi\) | ||||
−0.249298 | + | 0.968427i | \(0.580200\pi\) | |||||||
\(984\) | −0.468555 | −0.0149370 | ||||||||
\(985\) | −14.3042 | −0.455769 | ||||||||
\(986\) | 139.907 | 4.45554 | ||||||||
\(987\) | −2.57235 | −0.0818789 | ||||||||
\(988\) | −7.55039 | −0.240210 | ||||||||
\(989\) | −51.1473 | −1.62639 | ||||||||
\(990\) | −5.62796 | −0.178868 | ||||||||
\(991\) | −2.27823 | −0.0723703 | −0.0361852 | − | 0.999345i | \(-0.511521\pi\) | ||||
−0.0361852 | + | 0.999345i | \(0.511521\pi\) | |||||||
\(992\) | −26.1905 | −0.831551 | ||||||||
\(993\) | 7.41154 | 0.235198 | ||||||||
\(994\) | −2.32398 | −0.0737123 | ||||||||
\(995\) | −10.2846 | −0.326044 | ||||||||
\(996\) | −7.32755 | −0.232182 | ||||||||
\(997\) | −12.1301 | −0.384163 | −0.192082 | − | 0.981379i | \(-0.561524\pi\) | ||||
−0.192082 | + | 0.981379i | \(0.561524\pi\) | |||||||
\(998\) | 27.3662 | 0.866263 | ||||||||
\(999\) | −4.25874 | −0.134741 |
(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 | 4015.2.a.h.1.28 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.h.1.28 | ✓ | 37 | 1.1 | even | 1 | trivial |