Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 11 x^{16} + 123 x^{15} - 35 x^{14} - 982 x^{13} + 988 x^{12} + 3872 x^{11} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 5 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.55461\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.55461 | −1.80638 | −0.903190 | − | 0.429241i | \(-0.858781\pi\) | ||||
−0.903190 | + | 0.429241i | \(0.858781\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.52602 | 2.26301 | ||||||||
\(5\) | 2.12871 | 0.951987 | 0.475993 | − | 0.879449i | \(-0.342089\pi\) | ||||
0.475993 | + | 0.879449i | \(0.342089\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −6.45298 | −2.28147 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.43801 | −1.71965 | ||||||||
\(11\) | 4.13995 | 1.24824 | 0.624121 | − | 0.781328i | \(-0.285457\pi\) | ||||
0.624121 | + | 0.781328i | \(0.285457\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.75071 | −1.31761 | −0.658805 | − | 0.752313i | \(-0.728938\pi\) | ||||
−0.658805 | + | 0.752313i | \(0.728938\pi\) | |||||||
\(14\) | −2.55461 | −0.682747 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7.43278 | 1.85820 | ||||||||
\(17\) | 1.32611 | 0.321630 | 0.160815 | − | 0.986985i | \(-0.448588\pi\) | ||||
0.160815 | + | 0.986985i | \(0.448588\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.03962 | −1.15617 | −0.578083 | − | 0.815978i | \(-0.696199\pi\) | ||||
−0.578083 | + | 0.815978i | \(0.696199\pi\) | |||||||
\(20\) | 9.63456 | 2.15435 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −10.5759 | −2.25480 | ||||||||
\(23\) | −0.634865 | −0.132378 | −0.0661892 | − | 0.997807i | \(-0.521084\pi\) | ||||
−0.0661892 | + | 0.997807i | \(0.521084\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.468604 | −0.0937208 | ||||||||
\(26\) | 12.1362 | 2.38011 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.52602 | 0.855336 | ||||||||
\(29\) | 6.95445 | 1.29141 | 0.645705 | − | 0.763587i | \(-0.276564\pi\) | ||||
0.645705 | + | 0.763587i | \(0.276564\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.31737 | −0.595817 | −0.297908 | − | 0.954594i | \(-0.596289\pi\) | ||||
−0.297908 | + | 0.954594i | \(0.596289\pi\) | |||||||
\(32\) | −6.08189 | −1.07514 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.38770 | −0.580986 | ||||||||
\(35\) | 2.12871 | 0.359817 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.32426 | 1.20410 | 0.602051 | − | 0.798458i | \(-0.294350\pi\) | ||||
0.602051 | + | 0.798458i | \(0.294350\pi\) | |||||||
\(38\) | 12.8742 | 2.08848 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −13.7365 | −2.17193 | ||||||||
\(41\) | −4.92704 | −0.769475 | −0.384737 | − | 0.923026i | \(-0.625708\pi\) | ||||
−0.384737 | + | 0.923026i | \(0.625708\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.118376 | −0.0180521 | −0.00902606 | − | 0.999959i | \(-0.502873\pi\) | ||||
−0.00902606 | + | 0.999959i | \(0.502873\pi\) | |||||||
\(44\) | 18.7375 | 2.82478 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.62183 | 0.239126 | ||||||||
\(47\) | −10.6971 | −1.56034 | −0.780169 | − | 0.625568i | \(-0.784867\pi\) | ||||
−0.780169 | + | 0.625568i | \(0.784867\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.19710 | 0.169295 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −21.5018 | −2.98176 | ||||||||
\(53\) | −4.29353 | −0.589762 | −0.294881 | − | 0.955534i | \(-0.595280\pi\) | ||||
−0.294881 | + | 0.955534i | \(0.595280\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.81274 | 1.18831 | ||||||||
\(56\) | −6.45298 | −0.862315 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −17.7659 | −2.33278 | ||||||||
\(59\) | 9.53007 | 1.24071 | 0.620355 | − | 0.784321i | \(-0.286989\pi\) | ||||
0.620355 | + | 0.784321i | \(0.286989\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.70203 | −1.24222 | −0.621109 | − | 0.783724i | \(-0.713318\pi\) | ||||
−0.621109 | + | 0.783724i | \(0.713318\pi\) | |||||||
\(62\) | 8.47457 | 1.07627 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.671262 | 0.0839078 | ||||||||
\(65\) | −10.1129 | −1.25435 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.95734 | 0.361297 | 0.180648 | − | 0.983548i | \(-0.442180\pi\) | ||||
0.180648 | + | 0.983548i | \(0.442180\pi\) | |||||||
\(68\) | 6.00202 | 0.727851 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.43801 | −0.649967 | ||||||||
\(71\) | −1.45245 | −0.172375 | −0.0861873 | − | 0.996279i | \(-0.527468\pi\) | ||||
−0.0861873 | + | 0.996279i | \(0.527468\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.08465 | 0.829195 | 0.414598 | − | 0.910005i | \(-0.363922\pi\) | ||||
0.414598 | + | 0.910005i | \(0.363922\pi\) | |||||||
\(74\) | −18.7106 | −2.17506 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −22.8094 | −2.61641 | ||||||||
\(77\) | 4.13995 | 0.471791 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.36766 | 0.603909 | 0.301954 | − | 0.953322i | \(-0.402361\pi\) | ||||
0.301954 | + | 0.953322i | \(0.402361\pi\) | |||||||
\(80\) | 15.8222 | 1.76898 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 12.5867 | 1.38996 | ||||||||
\(83\) | 10.4852 | 1.15090 | 0.575451 | − | 0.817836i | \(-0.304826\pi\) | ||||
0.575451 | + | 0.817836i | \(0.304826\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.82291 | 0.306188 | ||||||||
\(86\) | 0.302403 | 0.0326090 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −26.7150 | −2.84783 | ||||||||
\(89\) | 3.15112 | 0.334018 | 0.167009 | − | 0.985955i | \(-0.446589\pi\) | ||||
0.167009 | + | 0.985955i | \(0.446589\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.75071 | −0.498010 | ||||||||
\(92\) | −2.87341 | −0.299574 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 27.3270 | 2.81856 | ||||||||
\(95\) | −10.7279 | −1.10066 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.7425 | −1.69994 | −0.849970 | − | 0.526831i | \(-0.823380\pi\) | ||||
−0.849970 | + | 0.526831i | \(0.823380\pi\) | |||||||
\(98\) | −2.55461 | −0.258054 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.12091 | −0.212091 | ||||||||
\(101\) | 18.6303 | 1.85378 | 0.926891 | − | 0.375331i | \(-0.122471\pi\) | ||||
0.926891 | + | 0.375331i | \(0.122471\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.48405 | 0.737426 | 0.368713 | − | 0.929543i | \(-0.379799\pi\) | ||||
0.368713 | + | 0.929543i | \(0.379799\pi\) | |||||||
\(104\) | 30.6562 | 3.00609 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.9683 | 1.06533 | ||||||||
\(107\) | 11.2137 | 1.08407 | 0.542035 | − | 0.840356i | \(-0.317654\pi\) | ||||
0.542035 | + | 0.840356i | \(0.317654\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.85001 | 0.368765 | 0.184382 | − | 0.982855i | \(-0.440972\pi\) | ||||
0.184382 | + | 0.982855i | \(0.440972\pi\) | |||||||
\(110\) | −22.5131 | −2.14654 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.43278 | 0.702332 | ||||||||
\(113\) | −4.76521 | −0.448273 | −0.224137 | − | 0.974558i | \(-0.571956\pi\) | ||||
−0.224137 | + | 0.974558i | \(0.571956\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.35144 | −0.126023 | ||||||||
\(116\) | 31.4759 | 2.92247 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −24.3456 | −2.24119 | ||||||||
\(119\) | 1.32611 | 0.121565 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.13918 | 0.558107 | ||||||||
\(122\) | 24.7849 | 2.24392 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −15.0145 | −1.34834 | ||||||||
\(125\) | −11.6411 | −1.04121 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 10.4490 | 0.923567 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 25.8344 | 2.26583 | ||||||||
\(131\) | 11.0346 | 0.964098 | 0.482049 | − | 0.876144i | \(-0.339893\pi\) | ||||
0.482049 | + | 0.876144i | \(0.339893\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.03962 | −0.436990 | ||||||||
\(134\) | −7.55485 | −0.652639 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.55738 | −0.733790 | ||||||||
\(137\) | 10.6933 | 0.913589 | 0.456794 | − | 0.889572i | \(-0.348997\pi\) | ||||
0.456794 | + | 0.889572i | \(0.348997\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.73393 | −0.316708 | −0.158354 | − | 0.987382i | \(-0.550619\pi\) | ||||
−0.158354 | + | 0.987382i | \(0.550619\pi\) | |||||||
\(140\) | 9.63456 | 0.814269 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.71045 | 0.311374 | ||||||||
\(143\) | −19.6677 | −1.64470 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.8040 | 1.22940 | ||||||||
\(146\) | −18.0985 | −1.49784 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 33.1497 | 2.72489 | ||||||||
\(149\) | 11.4885 | 0.941174 | 0.470587 | − | 0.882354i | \(-0.344042\pi\) | ||||
0.470587 | + | 0.882354i | \(0.344042\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.9894 | 1.05707 | 0.528533 | − | 0.848913i | \(-0.322742\pi\) | ||||
0.528533 | + | 0.848913i | \(0.322742\pi\) | |||||||
\(152\) | 32.5205 | 2.63776 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.5759 | −0.852234 | ||||||||
\(155\) | −7.06171 | −0.567210 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.6471 | 1.00934 | 0.504672 | − | 0.863311i | \(-0.331613\pi\) | ||||
0.504672 | + | 0.863311i | \(0.331613\pi\) | |||||||
\(158\) | −13.7123 | −1.09089 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −12.9466 | −1.02352 | ||||||||
\(161\) | −0.634865 | −0.0500344 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.11310 | 0.478815 | 0.239407 | − | 0.970919i | \(-0.423047\pi\) | ||||
0.239407 | + | 0.970919i | \(0.423047\pi\) | |||||||
\(164\) | −22.2999 | −1.74133 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −26.7856 | −2.07897 | ||||||||
\(167\) | −18.3586 | −1.42063 | −0.710314 | − | 0.703885i | \(-0.751447\pi\) | ||||
−0.710314 | + | 0.703885i | \(0.751447\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.56928 | 0.736098 | ||||||||
\(170\) | −7.21143 | −0.553091 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.535770 | −0.0408521 | ||||||||
\(173\) | −18.7445 | −1.42512 | −0.712558 | − | 0.701613i | \(-0.752464\pi\) | ||||
−0.712558 | + | 0.701613i | \(0.752464\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.468604 | −0.0354231 | ||||||||
\(176\) | 30.7713 | 2.31948 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.04987 | −0.603363 | ||||||||
\(179\) | −2.99701 | −0.224007 | −0.112004 | − | 0.993708i | \(-0.535727\pi\) | ||||
−0.112004 | + | 0.993708i | \(0.535727\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.4052 | 1.81402 | 0.907012 | − | 0.421105i | \(-0.138358\pi\) | ||||
0.907012 | + | 0.421105i | \(0.138358\pi\) | |||||||
\(182\) | 12.1362 | 0.899595 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.09677 | 0.302018 | ||||||||
\(185\) | 15.5912 | 1.14629 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.49005 | 0.401472 | ||||||||
\(188\) | −48.4154 | −3.53106 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 27.4055 | 1.98820 | ||||||||
\(191\) | 15.5134 | 1.12251 | 0.561254 | − | 0.827643i | \(-0.310319\pi\) | ||||
0.561254 | + | 0.827643i | \(0.310319\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.3101 | 1.67789 | 0.838947 | − | 0.544213i | \(-0.183172\pi\) | ||||
0.838947 | + | 0.544213i | \(0.183172\pi\) | |||||||
\(194\) | 42.7704 | 3.07074 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.52602 | 0.323287 | ||||||||
\(197\) | 22.0204 | 1.56889 | 0.784444 | − | 0.620200i | \(-0.212949\pi\) | ||||
0.784444 | + | 0.620200i | \(0.212949\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.90444 | −0.135002 | −0.0675011 | − | 0.997719i | \(-0.521503\pi\) | ||||
−0.0675011 | + | 0.997719i | \(0.521503\pi\) | |||||||
\(200\) | 3.02389 | 0.213821 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −47.5930 | −3.34863 | ||||||||
\(203\) | 6.95445 | 0.488107 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.4882 | −0.732530 | ||||||||
\(206\) | −19.1188 | −1.33207 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −35.3110 | −2.44838 | ||||||||
\(209\) | −20.8637 | −1.44318 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.5624 | 1.00252 | 0.501260 | − | 0.865297i | \(-0.332870\pi\) | ||||
0.501260 | + | 0.865297i | \(0.332870\pi\) | |||||||
\(212\) | −19.4326 | −1.33464 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −28.6466 | −1.95824 | ||||||||
\(215\) | −0.251987 | −0.0171854 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.31737 | −0.225198 | ||||||||
\(218\) | −9.83527 | −0.666129 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 39.8866 | 2.68915 | ||||||||
\(221\) | −6.29999 | −0.423783 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.83408 | 0.189784 | 0.0948919 | − | 0.995488i | \(-0.469749\pi\) | ||||
0.0948919 | + | 0.995488i | \(0.469749\pi\) | |||||||
\(224\) | −6.08189 | −0.406363 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.1732 | 0.809751 | ||||||||
\(227\) | −1.45824 | −0.0967865 | −0.0483933 | − | 0.998828i | \(-0.515410\pi\) | ||||
−0.0483933 | + | 0.998828i | \(0.515410\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.1581 | 1.39817 | 0.699084 | − | 0.715040i | \(-0.253591\pi\) | ||||
0.699084 | + | 0.715040i | \(0.253591\pi\) | |||||||
\(230\) | 3.45240 | 0.227645 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −44.8769 | −2.94631 | ||||||||
\(233\) | 9.49469 | 0.622018 | 0.311009 | − | 0.950407i | \(-0.399333\pi\) | ||||
0.311009 | + | 0.950407i | \(0.399333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.7711 | −1.48542 | ||||||||
\(236\) | 43.1332 | 2.80774 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.38770 | −0.219592 | ||||||||
\(239\) | 25.7367 | 1.66477 | 0.832384 | − | 0.554199i | \(-0.186975\pi\) | ||||
0.832384 | + | 0.554199i | \(0.186975\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.7397 | 1.07830 | 0.539149 | − | 0.842211i | \(-0.318746\pi\) | ||||
0.539149 | + | 0.842211i | \(0.318746\pi\) | |||||||
\(242\) | −15.6832 | −1.00815 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −43.9115 | −2.81115 | ||||||||
\(245\) | 2.12871 | 0.135998 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.9418 | 1.52338 | ||||||||
\(248\) | 21.4069 | 1.35934 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 29.7383 | 1.88082 | ||||||||
\(251\) | 5.36016 | 0.338330 | 0.169165 | − | 0.985588i | \(-0.445893\pi\) | ||||
0.169165 | + | 0.985588i | \(0.445893\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.62831 | −0.165240 | ||||||||
\(254\) | −2.55461 | −0.160290 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −28.0355 | −1.75222 | ||||||||
\(257\) | −13.1565 | −0.820678 | −0.410339 | − | 0.911933i | \(-0.634590\pi\) | ||||
−0.410339 | + | 0.911933i | \(0.634590\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.32426 | 0.455108 | ||||||||
\(260\) | −45.7710 | −2.83860 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −28.1891 | −1.74153 | ||||||||
\(263\) | 15.6935 | 0.967702 | 0.483851 | − | 0.875150i | \(-0.339238\pi\) | ||||
0.483851 | + | 0.875150i | \(0.339238\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.13968 | −0.561446 | ||||||||
\(266\) | 12.8742 | 0.789370 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.3850 | 0.817618 | ||||||||
\(269\) | 28.0155 | 1.70813 | 0.854067 | − | 0.520163i | \(-0.174129\pi\) | ||||
0.854067 | + | 0.520163i | \(0.174129\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.4489 | −1.18143 | −0.590717 | − | 0.806879i | \(-0.701155\pi\) | ||||
−0.590717 | + | 0.806879i | \(0.701155\pi\) | |||||||
\(272\) | 9.85672 | 0.597652 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −27.3171 | −1.65029 | ||||||||
\(275\) | −1.94000 | −0.116986 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.0931 | −0.906858 | −0.453429 | − | 0.891292i | \(-0.649799\pi\) | ||||
−0.453429 | + | 0.891292i | \(0.649799\pi\) | |||||||
\(278\) | 9.53872 | 0.572094 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −13.7365 | −0.820913 | ||||||||
\(281\) | 15.7060 | 0.936943 | 0.468471 | − | 0.883479i | \(-0.344805\pi\) | ||||
0.468471 | + | 0.883479i | \(0.344805\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.8370 | 1.77363 | 0.886813 | − | 0.462129i | \(-0.152914\pi\) | ||||
0.886813 | + | 0.462129i | \(0.152914\pi\) | |||||||
\(284\) | −6.57383 | −0.390085 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 50.2433 | 2.97095 | ||||||||
\(287\) | −4.92704 | −0.290834 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.2414 | −0.896554 | ||||||||
\(290\) | −37.8184 | −2.22077 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 32.0652 | 1.87648 | ||||||||
\(293\) | −17.2017 | −1.00493 | −0.502467 | − | 0.864596i | \(-0.667574\pi\) | ||||
−0.502467 | + | 0.864596i | \(0.667574\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.2867 | 1.18114 | ||||||||
\(296\) | −47.2633 | −2.74712 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −29.3486 | −1.70012 | ||||||||
\(299\) | 3.01606 | 0.174423 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.118376 | −0.00682306 | ||||||||
\(302\) | −33.1829 | −1.90946 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −37.4584 | −2.14838 | ||||||||
\(305\) | −20.6528 | −1.18258 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.9522 | −0.796294 | −0.398147 | − | 0.917322i | \(-0.630347\pi\) | ||||
−0.398147 | + | 0.917322i | \(0.630347\pi\) | |||||||
\(308\) | 18.7375 | 1.06767 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 18.0399 | 1.02460 | ||||||||
\(311\) | −4.04310 | −0.229263 | −0.114632 | − | 0.993408i | \(-0.536569\pi\) | ||||
−0.114632 | + | 0.993408i | \(0.536569\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.51810 | 0.198855 | 0.0994274 | − | 0.995045i | \(-0.468299\pi\) | ||||
0.0994274 | + | 0.995045i | \(0.468299\pi\) | |||||||
\(314\) | −32.3082 | −1.82326 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.2941 | 1.36665 | ||||||||
\(317\) | 11.1408 | 0.625731 | 0.312865 | − | 0.949797i | \(-0.398711\pi\) | ||||
0.312865 | + | 0.949797i | \(0.398711\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28.7911 | 1.61199 | ||||||||
\(320\) | 1.42892 | 0.0798791 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.62183 | 0.0903811 | ||||||||
\(323\) | −6.68311 | −0.371858 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.22620 | 0.123487 | ||||||||
\(326\) | −15.6166 | −0.864921 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 31.7941 | 1.75553 | ||||||||
\(329\) | −10.6971 | −0.589753 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.8759 | 1.36730 | 0.683650 | − | 0.729810i | \(-0.260391\pi\) | ||||
0.683650 | + | 0.729810i | \(0.260391\pi\) | |||||||
\(332\) | 47.4563 | 2.60450 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 46.8989 | 2.56619 | ||||||||
\(335\) | 6.29532 | 0.343950 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.4887 | −1.44293 | −0.721465 | − | 0.692451i | \(-0.756531\pi\) | ||||
−0.721465 | + | 0.692451i | \(0.756531\pi\) | |||||||
\(338\) | −24.4457 | −1.32967 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.7765 | 0.692905 | ||||||||
\(341\) | −13.7337 | −0.743723 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0.763875 | 0.0411854 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 47.8848 | 2.57430 | ||||||||
\(347\) | −22.3607 | −1.20039 | −0.600193 | − | 0.799855i | \(-0.704910\pi\) | ||||
−0.600193 | + | 0.799855i | \(0.704910\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.65405 | 0.356183 | 0.178092 | − | 0.984014i | \(-0.443008\pi\) | ||||
0.178092 | + | 0.984014i | \(0.443008\pi\) | |||||||
\(350\) | 1.19710 | 0.0639876 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −25.1787 | −1.34203 | ||||||||
\(353\) | −5.95514 | −0.316960 | −0.158480 | − | 0.987362i | \(-0.550659\pi\) | ||||
−0.158480 | + | 0.987362i | \(0.550659\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.09185 | −0.164098 | ||||||||
\(356\) | 14.2620 | 0.755885 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.65618 | 0.404642 | ||||||||
\(359\) | 2.04929 | 0.108158 | 0.0540788 | − | 0.998537i | \(-0.482778\pi\) | ||||
0.0540788 | + | 0.998537i | \(0.482778\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.39772 | 0.336722 | ||||||||
\(362\) | −62.3457 | −3.27682 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −21.5018 | −1.12700 | ||||||||
\(365\) | 15.0811 | 0.789383 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.1828 | −0.896936 | −0.448468 | − | 0.893799i | \(-0.648030\pi\) | ||||
−0.448468 | + | 0.893799i | \(0.648030\pi\) | |||||||
\(368\) | −4.71881 | −0.245985 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −39.8294 | −2.07063 | ||||||||
\(371\) | −4.29353 | −0.222909 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.0837 | 0.677449 | 0.338725 | − | 0.940886i | \(-0.390005\pi\) | ||||
0.338725 | + | 0.940886i | \(0.390005\pi\) | |||||||
\(374\) | −14.0249 | −0.725211 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 69.0284 | 3.55987 | ||||||||
\(377\) | −33.0386 | −1.70157 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.7955 | −1.06819 | −0.534096 | − | 0.845424i | \(-0.679348\pi\) | ||||
−0.534096 | + | 0.845424i | \(0.679348\pi\) | |||||||
\(380\) | −48.5545 | −2.49079 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −39.6306 | −2.02768 | ||||||||
\(383\) | −6.61047 | −0.337779 | −0.168890 | − | 0.985635i | \(-0.554018\pi\) | ||||
−0.168890 | + | 0.985635i | \(0.554018\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.81274 | 0.449139 | ||||||||
\(386\) | −59.5480 | −3.03091 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −75.7767 | −3.84698 | ||||||||
\(389\) | −7.82979 | −0.396986 | −0.198493 | − | 0.980102i | \(-0.563605\pi\) | ||||
−0.198493 | + | 0.980102i | \(0.563605\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.841904 | −0.0425769 | ||||||||
\(392\) | −6.45298 | −0.325924 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −56.2534 | −2.83401 | ||||||||
\(395\) | 11.4262 | 0.574913 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.8727 | −1.19814 | −0.599068 | − | 0.800698i | \(-0.704462\pi\) | ||||
−0.599068 | + | 0.800698i | \(0.704462\pi\) | |||||||
\(398\) | 4.86509 | 0.243865 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.48303 | −0.174152 | ||||||||
\(401\) | −19.4992 | −0.973741 | −0.486871 | − | 0.873474i | \(-0.661862\pi\) | ||||
−0.486871 | + | 0.873474i | \(0.661862\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.7599 | 0.785055 | ||||||||
\(404\) | 84.3209 | 4.19512 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.7659 | −0.881706 | ||||||||
\(407\) | 30.3221 | 1.50301 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.3931 | −1.30505 | −0.652526 | − | 0.757766i | \(-0.726291\pi\) | ||||
−0.652526 | + | 0.757766i | \(0.726291\pi\) | |||||||
\(410\) | 26.7933 | 1.32323 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 33.8729 | 1.66880 | ||||||||
\(413\) | 9.53007 | 0.468944 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.3200 | 1.09564 | ||||||||
\(416\) | 28.8933 | 1.41661 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 53.2987 | 2.60692 | ||||||||
\(419\) | 21.2813 | 1.03966 | 0.519831 | − | 0.854269i | \(-0.325995\pi\) | ||||
0.519831 | + | 0.854269i | \(0.325995\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.10895 | 0.346469 | 0.173235 | − | 0.984881i | \(-0.444578\pi\) | ||||
0.173235 | + | 0.984881i | \(0.444578\pi\) | |||||||
\(422\) | −37.2013 | −1.81093 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 27.7061 | 1.34553 | ||||||||
\(425\) | −0.621422 | −0.0301434 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.70203 | −0.469514 | ||||||||
\(428\) | 50.7535 | 2.45326 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.643728 | 0.0310433 | ||||||||
\(431\) | −22.4856 | −1.08309 | −0.541546 | − | 0.840671i | \(-0.682161\pi\) | ||||
−0.541546 | + | 0.840671i | \(0.682161\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.4030 | −1.17273 | −0.586367 | − | 0.810046i | \(-0.699442\pi\) | ||||
−0.586367 | + | 0.810046i | \(0.699442\pi\) | |||||||
\(434\) | 8.47457 | 0.406792 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.4252 | 0.834517 | ||||||||
\(437\) | 3.19947 | 0.153052 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.99162 | −0.429147 | −0.214573 | − | 0.976708i | \(-0.568836\pi\) | ||||
−0.214573 | + | 0.976708i | \(0.568836\pi\) | |||||||
\(440\) | −56.8684 | −2.71109 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.0940 | 0.765513 | ||||||||
\(443\) | −3.16638 | −0.150439 | −0.0752196 | − | 0.997167i | \(-0.523966\pi\) | ||||
−0.0752196 | + | 0.997167i | \(0.523966\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.70781 | 0.317981 | ||||||||
\(446\) | −7.23995 | −0.342822 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.671262 | 0.0317142 | ||||||||
\(449\) | 3.58210 | 0.169050 | 0.0845248 | − | 0.996421i | \(-0.473063\pi\) | ||||
0.0845248 | + | 0.996421i | \(0.473063\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.3977 | −0.960490 | ||||||||
\(452\) | −21.5674 | −1.01445 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.72522 | 0.174833 | ||||||||
\(455\) | −10.1129 | −0.474099 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.8800 | −0.602500 | −0.301250 | − | 0.953545i | \(-0.597404\pi\) | ||||
−0.301250 | + | 0.953545i | \(0.597404\pi\) | |||||||
\(458\) | −54.0507 | −2.52562 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.11665 | −0.285190 | ||||||||
\(461\) | 17.0189 | 0.792648 | 0.396324 | − | 0.918111i | \(-0.370286\pi\) | ||||
0.396324 | + | 0.918111i | \(0.370286\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.4544 | −1.22944 | −0.614721 | − | 0.788745i | \(-0.710731\pi\) | ||||
−0.614721 | + | 0.788745i | \(0.710731\pi\) | |||||||
\(464\) | 51.6909 | 2.39969 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.2552 | −1.12360 | ||||||||
\(467\) | −22.8012 | −1.05511 | −0.527557 | − | 0.849520i | \(-0.676892\pi\) | ||||
−0.527557 | + | 0.849520i | \(0.676892\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.95734 | 0.136557 | ||||||||
\(470\) | 58.1712 | 2.68324 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −61.4973 | −2.83064 | ||||||||
\(473\) | −0.490069 | −0.0225334 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.36158 | 0.108357 | ||||||||
\(476\) | 6.00202 | 0.275102 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −65.7471 | −3.00720 | ||||||||
\(479\) | 10.8867 | 0.497424 | 0.248712 | − | 0.968578i | \(-0.419993\pi\) | ||||
0.248712 | + | 0.968578i | \(0.419993\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.7955 | −1.58654 | ||||||||
\(482\) | −42.7633 | −1.94781 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 27.7860 | 1.26300 | ||||||||
\(485\) | −35.6398 | −1.61832 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.0508 | −0.772645 | −0.386323 | − | 0.922364i | \(-0.626255\pi\) | ||||
−0.386323 | + | 0.922364i | \(0.626255\pi\) | |||||||
\(488\) | 62.6070 | 2.83408 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.43801 | −0.245664 | ||||||||
\(491\) | 27.2143 | 1.22817 | 0.614083 | − | 0.789241i | \(-0.289526\pi\) | ||||
0.614083 | + | 0.789241i | \(0.289526\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.22240 | 0.415356 | ||||||||
\(494\) | −61.1618 | −2.75180 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −24.6573 | −1.10714 | ||||||||
\(497\) | −1.45245 | −0.0651515 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.74789 | 0.167779 | 0.0838893 | − | 0.996475i | \(-0.473266\pi\) | ||||
0.0838893 | + | 0.996475i | \(0.473266\pi\) | |||||||
\(500\) | −52.6876 | −2.35626 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.6931 | −0.611152 | ||||||||
\(503\) | 3.01178 | 0.134289 | 0.0671443 | − | 0.997743i | \(-0.478611\pi\) | ||||
0.0671443 | + | 0.997743i | \(0.478611\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.6584 | 1.76478 | ||||||||
\(506\) | 6.71429 | 0.298487 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.52602 | 0.200809 | ||||||||
\(509\) | −22.0551 | −0.977576 | −0.488788 | − | 0.872402i | \(-0.662561\pi\) | ||||
−0.488788 | + | 0.872402i | \(0.662561\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.08465 | 0.313406 | ||||||||
\(512\) | 50.7218 | 2.24161 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 33.6096 | 1.48246 | ||||||||
\(515\) | 15.9314 | 0.702020 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −44.2856 | −1.94768 | ||||||||
\(518\) | −18.7106 | −0.822097 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 65.2582 | 2.86176 | ||||||||
\(521\) | −3.30328 | −0.144719 | −0.0723596 | − | 0.997379i | \(-0.523053\pi\) | ||||
−0.0723596 | + | 0.997379i | \(0.523053\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.4263 | 1.28672 | 0.643362 | − | 0.765562i | \(-0.277539\pi\) | ||||
0.643362 | + | 0.765562i | \(0.277539\pi\) | |||||||
\(524\) | 49.9428 | 2.18176 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −40.0907 | −1.74804 | ||||||||
\(527\) | −4.39921 | −0.191633 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5969 | −0.982476 | ||||||||
\(530\) | 23.3483 | 1.01418 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −22.8094 | −0.988912 | ||||||||
\(533\) | 23.4070 | 1.01387 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.8707 | 1.03202 | ||||||||
\(536\) | −19.0837 | −0.824288 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −71.5686 | −3.08554 | ||||||||
\(539\) | 4.13995 | 0.178320 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.5971 | 1.18649 | 0.593246 | − | 0.805021i | \(-0.297846\pi\) | ||||
0.593246 | + | 0.805021i | \(0.297846\pi\) | |||||||
\(542\) | 49.6842 | 2.13412 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8.06528 | −0.345796 | ||||||||
\(545\) | 8.19556 | 0.351059 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.48013 | −0.0632860 | −0.0316430 | − | 0.999499i | \(-0.510074\pi\) | ||||
−0.0316430 | + | 0.999499i | \(0.510074\pi\) | |||||||
\(548\) | 48.3980 | 2.06746 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.95593 | 0.211321 | ||||||||
\(551\) | −35.0478 | −1.49308 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.36766 | 0.228256 | ||||||||
\(554\) | 38.5570 | 1.63813 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.8998 | −0.716712 | ||||||||
\(557\) | 38.4105 | 1.62751 | 0.813753 | − | 0.581211i | \(-0.197421\pi\) | ||||
0.813753 | + | 0.581211i | \(0.197421\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.562369 | 0.0237857 | ||||||||
\(560\) | 15.8222 | 0.668611 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −40.1227 | −1.69247 | ||||||||
\(563\) | −43.0432 | −1.81406 | −0.907028 | − | 0.421070i | \(-0.861655\pi\) | ||||
−0.907028 | + | 0.421070i | \(0.861655\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.1437 | −0.426750 | ||||||||
\(566\) | −76.2218 | −3.20384 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.37265 | 0.393268 | ||||||||
\(569\) | 1.66577 | 0.0698327 | 0.0349163 | − | 0.999390i | \(-0.488884\pi\) | ||||
0.0349163 | + | 0.999390i | \(0.488884\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.4302 | 1.39901 | 0.699505 | − | 0.714627i | \(-0.253404\pi\) | ||||
0.699505 | + | 0.714627i | \(0.253404\pi\) | |||||||
\(572\) | −89.0164 | −3.72196 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.5867 | 0.525357 | ||||||||
\(575\) | 0.297500 | 0.0124066 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.3687 | −0.473286 | −0.236643 | − | 0.971597i | \(-0.576047\pi\) | ||||
−0.236643 | + | 0.971597i | \(0.576047\pi\) | |||||||
\(578\) | 38.9358 | 1.61952 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 67.0031 | 2.78215 | ||||||||
\(581\) | 10.4852 | 0.435000 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.7750 | −0.736165 | ||||||||
\(584\) | −45.7171 | −1.89179 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 43.9436 | 1.81529 | ||||||||
\(587\) | 29.5488 | 1.21961 | 0.609805 | − | 0.792551i | \(-0.291248\pi\) | ||||
0.609805 | + | 0.792551i | \(0.291248\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.7183 | 0.688864 | ||||||||
\(590\) | −51.8246 | −2.13359 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 54.4397 | 2.23746 | ||||||||
\(593\) | 22.9545 | 0.942628 | 0.471314 | − | 0.881966i | \(-0.343780\pi\) | ||||
0.471314 | + | 0.881966i | \(0.343780\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.82291 | 0.115728 | ||||||||
\(596\) | 51.9971 | 2.12988 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.70485 | −0.315075 | ||||||||
\(599\) | −39.1632 | −1.60016 | −0.800082 | − | 0.599890i | \(-0.795211\pi\) | ||||
−0.800082 | + | 0.599890i | \(0.795211\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.5220 | −0.673947 | −0.336973 | − | 0.941514i | \(-0.609403\pi\) | ||||
−0.336973 | + | 0.941514i | \(0.609403\pi\) | |||||||
\(602\) | 0.302403 | 0.0123250 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 58.7904 | 2.39215 | ||||||||
\(605\) | 13.0685 | 0.531311 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.46104 | 0.221657 | 0.110828 | − | 0.993840i | \(-0.464650\pi\) | ||||
0.110828 | + | 0.993840i | \(0.464650\pi\) | |||||||
\(608\) | 30.6504 | 1.24304 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 52.7597 | 2.13618 | ||||||||
\(611\) | 50.8191 | 2.05592 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.0546 | −0.890779 | −0.445389 | − | 0.895337i | \(-0.646935\pi\) | ||||
−0.445389 | + | 0.895337i | \(0.646935\pi\) | |||||||
\(614\) | 35.6424 | 1.43841 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −26.7150 | −1.07638 | ||||||||
\(617\) | 42.7536 | 1.72119 | 0.860597 | − | 0.509287i | \(-0.170091\pi\) | ||||
0.860597 | + | 0.509287i | \(0.170091\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.8372 | 1.76197 | 0.880983 | − | 0.473147i | \(-0.156882\pi\) | ||||
0.880983 | + | 0.473147i | \(0.156882\pi\) | |||||||
\(620\) | −31.9614 | −1.28360 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.3285 | 0.414137 | ||||||||
\(623\) | 3.15112 | 0.126247 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4374 | −0.897496 | ||||||||
\(626\) | −8.98736 | −0.359207 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 57.2408 | 2.28415 | ||||||||
\(629\) | 9.71281 | 0.387275 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.7391 | −0.507135 | −0.253568 | − | 0.967318i | \(-0.581604\pi\) | ||||
−0.253568 | + | 0.967318i | \(0.581604\pi\) | |||||||
\(632\) | −34.6374 | −1.37780 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −28.4604 | −1.13031 | ||||||||
\(635\) | 2.12871 | 0.0844752 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.75071 | −0.188230 | ||||||||
\(638\) | −73.5499 | −2.91187 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 22.2428 | 0.879223 | ||||||||
\(641\) | −6.94532 | −0.274323 | −0.137162 | − | 0.990549i | \(-0.543798\pi\) | ||||
−0.137162 | + | 0.990549i | \(0.543798\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.9483 | −1.53597 | −0.767986 | − | 0.640467i | \(-0.778741\pi\) | ||||
−0.767986 | + | 0.640467i | \(0.778741\pi\) | |||||||
\(644\) | −2.87341 | −0.113228 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.0727 | 0.671717 | ||||||||
\(647\) | 24.7855 | 0.974417 | 0.487209 | − | 0.873286i | \(-0.338015\pi\) | ||||
0.487209 | + | 0.873286i | \(0.338015\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 39.4540 | 1.54871 | ||||||||
\(650\) | −5.68707 | −0.223065 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 27.6680 | 1.08356 | ||||||||
\(653\) | 23.6675 | 0.926182 | 0.463091 | − | 0.886311i | \(-0.346740\pi\) | ||||
0.463091 | + | 0.886311i | \(0.346740\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.4895 | 0.917809 | ||||||||
\(656\) | −36.6216 | −1.42983 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 27.3270 | 1.06532 | ||||||||
\(659\) | −13.2866 | −0.517572 | −0.258786 | − | 0.965935i | \(-0.583322\pi\) | ||||
−0.258786 | + | 0.965935i | \(0.583322\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.0055 | −0.855915 | −0.427958 | − | 0.903799i | \(-0.640767\pi\) | ||||
−0.427958 | + | 0.903799i | \(0.640767\pi\) | |||||||
\(662\) | −63.5480 | −2.46986 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −67.6609 | −2.62575 | ||||||||
\(665\) | −10.7279 | −0.416009 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.41514 | −0.170955 | ||||||||
\(668\) | −83.0912 | −3.21489 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −16.0821 | −0.621304 | ||||||||
\(671\) | −40.1659 | −1.55059 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.1513 | 0.930964 | 0.465482 | − | 0.885057i | \(-0.345881\pi\) | ||||
0.465482 | + | 0.885057i | \(0.345881\pi\) | |||||||
\(674\) | 67.6681 | 2.60648 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 43.3107 | 1.66580 | ||||||||
\(677\) | 19.8265 | 0.761993 | 0.380996 | − | 0.924577i | \(-0.375581\pi\) | ||||
0.380996 | + | 0.924577i | \(0.375581\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.7425 | −0.642517 | ||||||||
\(680\) | −18.2162 | −0.698558 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 35.0843 | 1.34345 | ||||||||
\(683\) | −11.5130 | −0.440533 | −0.220267 | − | 0.975440i | \(-0.570693\pi\) | ||||
−0.220267 | + | 0.975440i | \(0.570693\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.7629 | 0.869725 | ||||||||
\(686\) | −2.55461 | −0.0975353 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.879861 | −0.0335444 | ||||||||
\(689\) | 20.3973 | 0.777077 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.79146 | 0.334443 | 0.167222 | − | 0.985919i | \(-0.446520\pi\) | ||||
0.167222 | + | 0.985919i | \(0.446520\pi\) | |||||||
\(692\) | −84.8378 | −3.22505 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 57.1229 | 2.16835 | ||||||||
\(695\) | −7.94844 | −0.301502 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.53382 | −0.247486 | ||||||||
\(698\) | −16.9985 | −0.643402 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.12091 | −0.0801628 | ||||||||
\(701\) | 7.46770 | 0.282051 | 0.141026 | − | 0.990006i | \(-0.454960\pi\) | ||||
0.141026 | + | 0.990006i | \(0.454960\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.9115 | −1.39214 | ||||||||
\(704\) | 2.77899 | 0.104737 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.2130 | 0.572550 | ||||||||
\(707\) | 18.6303 | 0.700664 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.0859 | 1.12990 | 0.564950 | − | 0.825125i | \(-0.308895\pi\) | ||||
0.564950 | + | 0.825125i | \(0.308895\pi\) | |||||||
\(710\) | 7.89846 | 0.296424 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −20.3341 | −0.762052 | ||||||||
\(713\) | 2.10608 | 0.0788733 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −41.8668 | −1.56573 | ||||||||
\(716\) | −13.5645 | −0.506930 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.23514 | −0.195374 | ||||||||
\(719\) | 12.0466 | 0.449261 | 0.224631 | − | 0.974444i | \(-0.427882\pi\) | ||||
0.224631 | + | 0.974444i | \(0.427882\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.48405 | 0.278721 | ||||||||
\(722\) | −16.3437 | −0.608248 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 110.458 | 4.10515 | ||||||||
\(725\) | −3.25888 | −0.121032 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.0016 | 0.445115 | 0.222557 | − | 0.974920i | \(-0.428560\pi\) | ||||
0.222557 | + | 0.974920i | \(0.428560\pi\) | |||||||
\(728\) | 30.6562 | 1.13620 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −38.5264 | −1.42593 | ||||||||
\(731\) | −0.156980 | −0.00580610 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.59393 | −0.0958090 | −0.0479045 | − | 0.998852i | \(-0.515254\pi\) | ||||
−0.0479045 | + | 0.998852i | \(0.515254\pi\) | |||||||
\(734\) | 43.8954 | 1.62021 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.86118 | 0.142325 | ||||||||
\(737\) | 12.2432 | 0.450986 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.97887 | −0.293508 | −0.146754 | − | 0.989173i | \(-0.546883\pi\) | ||||
−0.146754 | + | 0.989173i | \(0.546883\pi\) | |||||||
\(740\) | 70.5661 | 2.59406 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.9683 | 0.402658 | ||||||||
\(743\) | 4.32447 | 0.158650 | 0.0793248 | − | 0.996849i | \(-0.474724\pi\) | ||||
0.0793248 | + | 0.996849i | \(0.474724\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.4557 | 0.895986 | ||||||||
\(746\) | −33.4238 | −1.22373 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 24.8480 | 0.908534 | ||||||||
\(749\) | 11.2137 | 0.409740 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.34648 | 0.0856244 | 0.0428122 | − | 0.999083i | \(-0.486368\pi\) | ||||
0.0428122 | + | 0.999083i | \(0.486368\pi\) | |||||||
\(752\) | −79.5095 | −2.89941 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 84.4006 | 3.07369 | ||||||||
\(755\) | 27.6507 | 1.00631 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.4656 | −0.961909 | −0.480954 | − | 0.876746i | \(-0.659710\pi\) | ||||
−0.480954 | + | 0.876746i | \(0.659710\pi\) | |||||||
\(758\) | 53.1243 | 1.92956 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 69.2267 | 2.51111 | ||||||||
\(761\) | 40.6849 | 1.47483 | 0.737414 | − | 0.675441i | \(-0.236047\pi\) | ||||
0.737414 | + | 0.675441i | \(0.236047\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.85001 | 0.139380 | ||||||||
\(764\) | 70.2138 | 2.54025 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.8871 | 0.610157 | ||||||||
\(767\) | −45.2746 | −1.63477 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.94961 | −0.358792 | −0.179396 | − | 0.983777i | \(-0.557414\pi\) | ||||
−0.179396 | + | 0.983777i | \(0.557414\pi\) | |||||||
\(770\) | −22.5131 | −0.811315 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 105.502 | 3.79709 | ||||||||
\(773\) | −31.8949 | −1.14718 | −0.573590 | − | 0.819142i | \(-0.694450\pi\) | ||||
−0.573590 | + | 0.819142i | \(0.694450\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.55453 | 0.0558404 | ||||||||
\(776\) | 108.039 | 3.87837 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.0020 | 0.717108 | ||||||||
\(779\) | 24.8304 | 0.889641 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.01309 | −0.215165 | ||||||||
\(782\) | 2.15073 | 0.0769100 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.43278 | 0.265457 | ||||||||
\(785\) | 26.9219 | 0.960883 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.6972 | −1.37941 | −0.689703 | − | 0.724093i | \(-0.742259\pi\) | ||||
−0.689703 | + | 0.724093i | \(0.742259\pi\) | |||||||
\(788\) | 99.6646 | 3.55040 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −29.1894 | −1.03851 | ||||||||
\(791\) | −4.76521 | −0.169431 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 46.0916 | 1.63676 | ||||||||
\(794\) | 60.9854 | 2.16429 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.61952 | −0.305511 | ||||||||
\(797\) | 9.68211 | 0.342958 | 0.171479 | − | 0.985188i | \(-0.445145\pi\) | ||||
0.171479 | + | 0.985188i | \(0.445145\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.1856 | −0.501852 | ||||||||
\(800\) | 2.85000 | 0.100763 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 49.8127 | 1.75895 | ||||||||
\(803\) | 29.3301 | 1.03504 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.35144 | −0.0476321 | ||||||||
\(806\) | −40.2603 | −1.41811 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −120.221 | −4.22935 | ||||||||
\(809\) | 25.8293 | 0.908111 | 0.454056 | − | 0.890973i | \(-0.349977\pi\) | ||||
0.454056 | + | 0.890973i | \(0.349977\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.7060 | 0.727087 | 0.363544 | − | 0.931577i | \(-0.381567\pi\) | ||||
0.363544 | + | 0.931577i | \(0.381567\pi\) | |||||||
\(812\) | 31.4759 | 1.10459 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −77.4610 | −2.71501 | ||||||||
\(815\) | 13.0130 | 0.455825 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.596568 | 0.0208713 | ||||||||
\(818\) | 67.4239 | 2.35742 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −47.4699 | −1.65772 | ||||||||
\(821\) | 36.0955 | 1.25974 | 0.629871 | − | 0.776700i | \(-0.283108\pi\) | ||||
0.629871 | + | 0.776700i | \(0.283108\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.5252 | 1.58691 | 0.793455 | − | 0.608629i | \(-0.208280\pi\) | ||||
0.793455 | + | 0.608629i | \(0.208280\pi\) | |||||||
\(824\) | −48.2944 | −1.68242 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.3456 | −0.847091 | ||||||||
\(827\) | −19.6678 | −0.683916 | −0.341958 | − | 0.939715i | \(-0.611090\pi\) | ||||
−0.341958 | + | 0.939715i | \(0.611090\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.1390 | −1.60247 | −0.801237 | − | 0.598347i | \(-0.795825\pi\) | ||||
−0.801237 | + | 0.598347i | \(0.795825\pi\) | |||||||
\(830\) | −57.0187 | −1.97915 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.18897 | −0.110558 | ||||||||
\(833\) | 1.32611 | 0.0459471 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −39.0800 | −1.35242 | ||||||||
\(836\) | −94.4296 | −3.26592 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −54.3654 | −1.87802 | ||||||||
\(839\) | 45.6364 | 1.57554 | 0.787772 | − | 0.615966i | \(-0.211234\pi\) | ||||
0.787772 | + | 0.615966i | \(0.211234\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.3644 | 0.667737 | ||||||||
\(842\) | −18.1606 | −0.625855 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 65.9098 | 2.26871 | ||||||||
\(845\) | 20.3702 | 0.700756 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.13918 | 0.210945 | ||||||||
\(848\) | −31.9129 | −1.09589 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.58749 | 0.0544504 | ||||||||
\(851\) | −4.64992 | −0.159397 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.5096 | 0.496799 | 0.248400 | − | 0.968658i | \(-0.420095\pi\) | ||||
0.248400 | + | 0.968658i | \(0.420095\pi\) | |||||||
\(854\) | 24.7849 | 0.848121 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −72.3618 | −2.47328 | ||||||||
\(857\) | −3.03303 | −0.103606 | −0.0518031 | − | 0.998657i | \(-0.516497\pi\) | ||||
−0.0518031 | + | 0.998657i | \(0.516497\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 54.2596 | 1.85131 | 0.925657 | − | 0.378365i | \(-0.123513\pi\) | ||||
0.925657 | + | 0.378365i | \(0.123513\pi\) | |||||||
\(860\) | −1.14050 | −0.0388906 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 57.4418 | 1.95648 | ||||||||
\(863\) | 48.8955 | 1.66442 | 0.832211 | − | 0.554460i | \(-0.187075\pi\) | ||||
0.832211 | + | 0.554460i | \(0.187075\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39.9015 | −1.35669 | ||||||||
\(866\) | 62.3401 | 2.11840 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −15.0145 | −0.509624 | ||||||||
\(869\) | 22.2218 | 0.753824 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.0495 | −0.476049 | ||||||||
\(872\) | −24.8440 | −0.841326 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.17340 | −0.276469 | ||||||||
\(875\) | −11.6411 | −0.393540 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.9003 | −0.874590 | −0.437295 | − | 0.899318i | \(-0.644063\pi\) | ||||
−0.437295 | + | 0.899318i | \(0.644063\pi\) | |||||||
\(878\) | 22.9701 | 0.775202 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 65.5032 | 2.20811 | ||||||||
\(881\) | 1.06900 | 0.0360156 | 0.0180078 | − | 0.999838i | \(-0.494268\pi\) | ||||
0.0180078 | + | 0.999838i | \(0.494268\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.3081 | −0.986295 | −0.493147 | − | 0.869946i | \(-0.664154\pi\) | ||||
−0.493147 | + | 0.869946i | \(0.664154\pi\) | |||||||
\(884\) | −28.5139 | −0.959025 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.08885 | 0.271750 | ||||||||
\(887\) | 40.0423 | 1.34449 | 0.672244 | − | 0.740330i | \(-0.265331\pi\) | ||||
0.672244 | + | 0.740330i | \(0.265331\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −17.1358 | −0.574394 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.8271 | 0.429482 | ||||||||
\(893\) | 53.9095 | 1.80401 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.37976 | −0.213252 | ||||||||
\(896\) | 10.4490 | 0.349075 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.15085 | −0.305368 | ||||||||
\(899\) | −23.0705 | −0.769443 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.69372 | −0.189685 | ||||||||
\(902\) | 52.1081 | 1.73501 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 30.7498 | 1.02272 | ||||||||
\(905\) | 51.9515 | 1.72693 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.5478 | 0.848302 | 0.424151 | − | 0.905592i | \(-0.360573\pi\) | ||||
0.424151 | + | 0.905592i | \(0.360573\pi\) | |||||||
\(908\) | −6.60000 | −0.219029 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 25.8344 | 0.856403 | ||||||||
\(911\) | −29.3845 | −0.973553 | −0.486777 | − | 0.873526i | \(-0.661827\pi\) | ||||
−0.486777 | + | 0.873526i | \(0.661827\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43.4083 | 1.43660 | ||||||||
\(914\) | 32.9033 | 1.08834 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 95.7619 | 3.16406 | ||||||||
\(917\) | 11.0346 | 0.364395 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.8678 | −0.358494 | −0.179247 | − | 0.983804i | \(-0.557366\pi\) | ||||
−0.179247 | + | 0.983804i | \(0.557366\pi\) | |||||||
\(920\) | 8.72082 | 0.287517 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −43.4766 | −1.43182 | ||||||||
\(923\) | 6.90020 | 0.227123 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.43218 | −0.112849 | ||||||||
\(926\) | 67.5807 | 2.22084 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −42.2962 | −1.38844 | ||||||||
\(929\) | −4.66688 | −0.153115 | −0.0765577 | − | 0.997065i | \(-0.524393\pi\) | ||||
−0.0765577 | + | 0.997065i | \(0.524393\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.03962 | −0.165167 | ||||||||
\(932\) | 42.9731 | 1.40763 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 58.2481 | 1.90594 | ||||||||
\(935\) | 11.6867 | 0.382196 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.0249 | −0.458175 | −0.229088 | − | 0.973406i | \(-0.573574\pi\) | ||||
−0.229088 | + | 0.973406i | \(0.573574\pi\) | |||||||
\(938\) | −7.55485 | −0.246674 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −103.062 | −3.36152 | ||||||||
\(941\) | −46.2542 | −1.50784 | −0.753921 | − | 0.656965i | \(-0.771840\pi\) | ||||
−0.753921 | + | 0.656965i | \(0.771840\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.12801 | 0.101862 | ||||||||
\(944\) | 70.8350 | 2.30548 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.25193 | 0.0407039 | ||||||||
\(947\) | −5.19190 | −0.168714 | −0.0843571 | − | 0.996436i | \(-0.526884\pi\) | ||||
−0.0843571 | + | 0.996436i | \(0.526884\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33.6571 | −1.09256 | ||||||||
\(950\) | −6.03291 | −0.195734 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.55738 | −0.277346 | ||||||||
\(953\) | 31.0054 | 1.00436 | 0.502181 | − | 0.864762i | \(-0.332531\pi\) | ||||
0.502181 | + | 0.864762i | \(0.332531\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 33.0235 | 1.06861 | ||||||||
\(956\) | 116.485 | 3.76738 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −27.8111 | −0.898536 | ||||||||
\(959\) | 10.6933 | 0.345304 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.9951 | −0.645002 | ||||||||
\(962\) | 88.8887 | 2.86589 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 75.7640 | 2.44020 | ||||||||
\(965\) | 49.6203 | 1.59733 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.06932 | 0.195176 | 0.0975881 | − | 0.995227i | \(-0.468887\pi\) | ||||
0.0975881 | + | 0.995227i | \(0.468887\pi\) | |||||||
\(968\) | −39.6159 | −1.27330 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 91.0458 | 2.92330 | ||||||||
\(971\) | 8.98673 | 0.288398 | 0.144199 | − | 0.989549i | \(-0.453939\pi\) | ||||
0.144199 | + | 0.989549i | \(0.453939\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.73393 | −0.119704 | ||||||||
\(974\) | 43.5581 | 1.39569 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −72.1131 | −2.30828 | ||||||||
\(977\) | −55.0884 | −1.76243 | −0.881217 | − | 0.472711i | \(-0.843275\pi\) | ||||
−0.881217 | + | 0.472711i | \(0.843275\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.0455 | 0.416935 | ||||||||
\(980\) | 9.63456 | 0.307765 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −69.5219 | −2.21853 | ||||||||
\(983\) | −59.7557 | −1.90591 | −0.952956 | − | 0.303109i | \(-0.901975\pi\) | ||||
−0.952956 | + | 0.303109i | \(0.901975\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 46.8750 | 1.49356 | ||||||||
\(986\) | −23.5596 | −0.750291 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 108.361 | 3.44742 | ||||||||
\(989\) | 0.0751526 | 0.00238971 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.373535 | −0.0118657 | −0.00593286 | − | 0.999982i | \(-0.501888\pi\) | ||||
−0.00593286 | + | 0.999982i | \(0.501888\pi\) | |||||||
\(992\) | 20.1759 | 0.640584 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.71045 | 0.117688 | ||||||||
\(995\) | −4.05399 | −0.128520 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.3145 | 1.21343 | 0.606716 | − | 0.794919i | \(-0.292487\pi\) | ||||
0.606716 | + | 0.794919i | \(0.292487\pi\) | |||||||
\(998\) | −9.57439 | −0.303072 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.u.1.1 | 18 | ||
3.2 | odd | 2 | 2667.2.a.p.1.18 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.p.1.18 | ✓ | 18 | 3.2 | odd | 2 | ||
8001.2.a.u.1.1 | 18 | 1.1 | even | 1 | trivial |