Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, 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("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} + \cdots - 108 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(2.70316\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.70316 | 1.91142 | 0.955711 | − | 0.294305i | \(-0.0950882\pi\) | ||||
0.955711 | + | 0.294305i | \(0.0950882\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.30708 | 2.65354 | ||||||||
\(5\) | 2.79988 | 1.25214 | 0.626072 | − | 0.779765i | \(-0.284662\pi\) | ||||
0.626072 | + | 0.779765i | \(0.284662\pi\) | |||||||
\(6\) | −2.70316 | −1.10356 | ||||||||
\(7\) | 0.880738 | 0.332888 | 0.166444 | − | 0.986051i | \(-0.446772\pi\) | ||||
0.166444 | + | 0.986051i | \(0.446772\pi\) | |||||||
\(8\) | 8.93955 | 3.16061 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 7.56852 | 2.39338 | ||||||||
\(11\) | −5.67616 | −1.71143 | −0.855713 | − | 0.517451i | \(-0.826881\pi\) | ||||
−0.855713 | + | 0.517451i | \(0.826881\pi\) | |||||||
\(12\) | −5.30708 | −1.53202 | ||||||||
\(13\) | −3.71641 | −1.03075 | −0.515373 | − | 0.856966i | \(-0.672347\pi\) | ||||
−0.515373 | + | 0.856966i | \(0.672347\pi\) | |||||||
\(14\) | 2.38078 | 0.636289 | ||||||||
\(15\) | −2.79988 | −0.722926 | ||||||||
\(16\) | 13.5509 | 3.38772 | ||||||||
\(17\) | 4.80704 | 1.16588 | 0.582939 | − | 0.812516i | \(-0.301903\pi\) | ||||
0.582939 | + | 0.812516i | \(0.301903\pi\) | |||||||
\(18\) | 2.70316 | 0.637141 | ||||||||
\(19\) | 6.68378 | 1.53336 | 0.766682 | − | 0.642027i | \(-0.221907\pi\) | ||||
0.766682 | + | 0.642027i | \(0.221907\pi\) | |||||||
\(20\) | 14.8592 | 3.32261 | ||||||||
\(21\) | −0.880738 | −0.192193 | ||||||||
\(22\) | −15.3436 | −3.27126 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −8.93955 | −1.82478 | ||||||||
\(25\) | 2.83932 | 0.567865 | ||||||||
\(26\) | −10.0460 | −1.97019 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.67414 | 0.883330 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −7.56852 | −1.38182 | ||||||||
\(31\) | 0.779005 | 0.139913 | 0.0699567 | − | 0.997550i | \(-0.477714\pi\) | ||||
0.0699567 | + | 0.997550i | \(0.477714\pi\) | |||||||
\(32\) | 18.7511 | 3.31476 | ||||||||
\(33\) | 5.67616 | 0.988092 | ||||||||
\(34\) | 12.9942 | 2.22849 | ||||||||
\(35\) | 2.46596 | 0.416823 | ||||||||
\(36\) | 5.30708 | 0.884513 | ||||||||
\(37\) | −8.14977 | −1.33981 | −0.669907 | − | 0.742445i | \(-0.733666\pi\) | ||||
−0.669907 | + | 0.742445i | \(0.733666\pi\) | |||||||
\(38\) | 18.0673 | 2.93091 | ||||||||
\(39\) | 3.71641 | 0.595101 | ||||||||
\(40\) | 25.0297 | 3.95754 | ||||||||
\(41\) | 6.06174 | 0.946686 | 0.473343 | − | 0.880878i | \(-0.343047\pi\) | ||||
0.473343 | + | 0.880878i | \(0.343047\pi\) | |||||||
\(42\) | −2.38078 | −0.367362 | ||||||||
\(43\) | 9.54562 | 1.45569 | 0.727847 | − | 0.685740i | \(-0.240521\pi\) | ||||
0.727847 | + | 0.685740i | \(0.240521\pi\) | |||||||
\(44\) | −30.1238 | −4.54133 | ||||||||
\(45\) | 2.79988 | 0.417381 | ||||||||
\(46\) | 2.70316 | 0.398559 | ||||||||
\(47\) | −7.68018 | −1.12027 | −0.560135 | − | 0.828402i | \(-0.689251\pi\) | ||||
−0.560135 | + | 0.828402i | \(0.689251\pi\) | |||||||
\(48\) | −13.5509 | −1.95590 | ||||||||
\(49\) | −6.22430 | −0.889186 | ||||||||
\(50\) | 7.67515 | 1.08543 | ||||||||
\(51\) | −4.80704 | −0.673120 | ||||||||
\(52\) | −19.7233 | −2.73512 | ||||||||
\(53\) | −9.73506 | −1.33721 | −0.668607 | − | 0.743616i | \(-0.733109\pi\) | ||||
−0.668607 | + | 0.743616i | \(0.733109\pi\) | |||||||
\(54\) | −2.70316 | −0.367854 | ||||||||
\(55\) | −15.8926 | −2.14295 | ||||||||
\(56\) | 7.87341 | 1.05213 | ||||||||
\(57\) | −6.68378 | −0.885288 | ||||||||
\(58\) | −2.70316 | −0.354942 | ||||||||
\(59\) | 5.14558 | 0.669898 | 0.334949 | − | 0.942236i | \(-0.391281\pi\) | ||||
0.334949 | + | 0.942236i | \(0.391281\pi\) | |||||||
\(60\) | −14.8592 | −1.91831 | ||||||||
\(61\) | −7.99562 | −1.02373 | −0.511867 | − | 0.859065i | \(-0.671046\pi\) | ||||
−0.511867 | + | 0.859065i | \(0.671046\pi\) | |||||||
\(62\) | 2.10578 | 0.267434 | ||||||||
\(63\) | 0.880738 | 0.110963 | ||||||||
\(64\) | 23.5855 | 2.94819 | ||||||||
\(65\) | −10.4055 | −1.29064 | ||||||||
\(66\) | 15.3436 | 1.88866 | ||||||||
\(67\) | −8.36073 | −1.02143 | −0.510713 | − | 0.859751i | \(-0.670619\pi\) | ||||
−0.510713 | + | 0.859751i | \(0.670619\pi\) | |||||||
\(68\) | 25.5113 | 3.09370 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 6.66589 | 0.796726 | ||||||||
\(71\) | 8.52656 | 1.01192 | 0.505958 | − | 0.862558i | \(-0.331139\pi\) | ||||
0.505958 | + | 0.862558i | \(0.331139\pi\) | |||||||
\(72\) | 8.93955 | 1.05354 | ||||||||
\(73\) | −12.6677 | −1.48264 | −0.741321 | − | 0.671150i | \(-0.765801\pi\) | ||||
−0.741321 | + | 0.671150i | \(0.765801\pi\) | |||||||
\(74\) | −22.0301 | −2.56095 | ||||||||
\(75\) | −2.83932 | −0.327857 | ||||||||
\(76\) | 35.4713 | 4.06884 | ||||||||
\(77\) | −4.99921 | −0.569713 | ||||||||
\(78\) | 10.0460 | 1.13749 | ||||||||
\(79\) | 15.1051 | 1.69945 | 0.849726 | − | 0.527224i | \(-0.176767\pi\) | ||||
0.849726 | + | 0.527224i | \(0.176767\pi\) | |||||||
\(80\) | 37.9409 | 4.24192 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 16.3859 | 1.80952 | ||||||||
\(83\) | −0.302272 | −0.0331786 | −0.0165893 | − | 0.999862i | \(-0.505281\pi\) | ||||
−0.0165893 | + | 0.999862i | \(0.505281\pi\) | |||||||
\(84\) | −4.67414 | −0.509991 | ||||||||
\(85\) | 13.4591 | 1.45985 | ||||||||
\(86\) | 25.8033 | 2.78245 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | −50.7423 | −5.40915 | ||||||||
\(89\) | −10.7142 | −1.13570 | −0.567852 | − | 0.823131i | \(-0.692225\pi\) | ||||
−0.567852 | + | 0.823131i | \(0.692225\pi\) | |||||||
\(90\) | 7.56852 | 0.797792 | ||||||||
\(91\) | −3.27318 | −0.343123 | ||||||||
\(92\) | 5.30708 | 0.553301 | ||||||||
\(93\) | −0.779005 | −0.0807791 | ||||||||
\(94\) | −20.7608 | −2.14131 | ||||||||
\(95\) | 18.7138 | 1.91999 | ||||||||
\(96\) | −18.7511 | −1.91378 | ||||||||
\(97\) | −0.884027 | −0.0897593 | −0.0448797 | − | 0.998992i | \(-0.514290\pi\) | ||||
−0.0448797 | + | 0.998992i | \(0.514290\pi\) | |||||||
\(98\) | −16.8253 | −1.69961 | ||||||||
\(99\) | −5.67616 | −0.570475 | ||||||||
\(100\) | 15.0685 | 1.50685 | ||||||||
\(101\) | −1.36093 | −0.135418 | −0.0677089 | − | 0.997705i | \(-0.521569\pi\) | ||||
−0.0677089 | + | 0.997705i | \(0.521569\pi\) | |||||||
\(102\) | −12.9942 | −1.28662 | ||||||||
\(103\) | −5.31264 | −0.523470 | −0.261735 | − | 0.965140i | \(-0.584295\pi\) | ||||
−0.261735 | + | 0.965140i | \(0.584295\pi\) | |||||||
\(104\) | −33.2230 | −3.25779 | ||||||||
\(105\) | −2.46596 | −0.240653 | ||||||||
\(106\) | −26.3154 | −2.55598 | ||||||||
\(107\) | 7.83080 | 0.757032 | 0.378516 | − | 0.925595i | \(-0.376434\pi\) | ||||
0.378516 | + | 0.925595i | \(0.376434\pi\) | |||||||
\(108\) | −5.30708 | −0.510674 | ||||||||
\(109\) | 11.2420 | 1.07679 | 0.538393 | − | 0.842694i | \(-0.319032\pi\) | ||||
0.538393 | + | 0.842694i | \(0.319032\pi\) | |||||||
\(110\) | −42.9601 | −4.09609 | ||||||||
\(111\) | 8.14977 | 0.773542 | ||||||||
\(112\) | 11.9348 | 1.12773 | ||||||||
\(113\) | −17.4918 | −1.64549 | −0.822745 | − | 0.568411i | \(-0.807558\pi\) | ||||
−0.822745 | + | 0.568411i | \(0.807558\pi\) | |||||||
\(114\) | −18.0673 | −1.69216 | ||||||||
\(115\) | 2.79988 | 0.261090 | ||||||||
\(116\) | −5.30708 | −0.492750 | ||||||||
\(117\) | −3.71641 | −0.343582 | ||||||||
\(118\) | 13.9093 | 1.28046 | ||||||||
\(119\) | 4.23374 | 0.388106 | ||||||||
\(120\) | −25.0297 | −2.28489 | ||||||||
\(121\) | 21.2188 | 1.92898 | ||||||||
\(122\) | −21.6134 | −1.95679 | ||||||||
\(123\) | −6.06174 | −0.546569 | ||||||||
\(124\) | 4.13424 | 0.371266 | ||||||||
\(125\) | −6.04963 | −0.541095 | ||||||||
\(126\) | 2.38078 | 0.212096 | ||||||||
\(127\) | 0.206399 | 0.0183149 | 0.00915747 | − | 0.999958i | \(-0.497085\pi\) | ||||
0.00915747 | + | 0.999958i | \(0.497085\pi\) | |||||||
\(128\) | 26.2532 | 2.32048 | ||||||||
\(129\) | −9.54562 | −0.840445 | ||||||||
\(130\) | −28.1277 | −2.46696 | ||||||||
\(131\) | 9.50384 | 0.830354 | 0.415177 | − | 0.909741i | \(-0.363720\pi\) | ||||
0.415177 | + | 0.909741i | \(0.363720\pi\) | |||||||
\(132\) | 30.1238 | 2.62194 | ||||||||
\(133\) | 5.88666 | 0.510438 | ||||||||
\(134\) | −22.6004 | −1.95238 | ||||||||
\(135\) | −2.79988 | −0.240975 | ||||||||
\(136\) | 42.9728 | 3.68488 | ||||||||
\(137\) | 4.27725 | 0.365430 | 0.182715 | − | 0.983166i | \(-0.441511\pi\) | ||||
0.182715 | + | 0.983166i | \(0.441511\pi\) | |||||||
\(138\) | −2.70316 | −0.230108 | ||||||||
\(139\) | −9.47109 | −0.803327 | −0.401663 | − | 0.915787i | \(-0.631568\pi\) | ||||
−0.401663 | + | 0.915787i | \(0.631568\pi\) | |||||||
\(140\) | 13.0870 | 1.10606 | ||||||||
\(141\) | 7.68018 | 0.646788 | ||||||||
\(142\) | 23.0487 | 1.93420 | ||||||||
\(143\) | 21.0949 | 1.76405 | ||||||||
\(144\) | 13.5509 | 1.12924 | ||||||||
\(145\) | −2.79988 | −0.232517 | ||||||||
\(146\) | −34.2428 | −2.83396 | ||||||||
\(147\) | 6.22430 | 0.513372 | ||||||||
\(148\) | −43.2514 | −3.55525 | ||||||||
\(149\) | −20.3448 | −1.66671 | −0.833354 | − | 0.552740i | \(-0.813582\pi\) | ||||
−0.833354 | + | 0.552740i | \(0.813582\pi\) | |||||||
\(150\) | −7.67515 | −0.626673 | ||||||||
\(151\) | −14.3715 | −1.16953 | −0.584766 | − | 0.811202i | \(-0.698814\pi\) | ||||
−0.584766 | + | 0.811202i | \(0.698814\pi\) | |||||||
\(152\) | 59.7500 | 4.84636 | ||||||||
\(153\) | 4.80704 | 0.388626 | ||||||||
\(154\) | −13.5137 | −1.08896 | ||||||||
\(155\) | 2.18112 | 0.175192 | ||||||||
\(156\) | 19.7233 | 1.57912 | ||||||||
\(157\) | −18.9351 | −1.51118 | −0.755592 | − | 0.655043i | \(-0.772651\pi\) | ||||
−0.755592 | + | 0.655043i | \(0.772651\pi\) | |||||||
\(158\) | 40.8314 | 3.24837 | ||||||||
\(159\) | 9.73506 | 0.772041 | ||||||||
\(160\) | 52.5009 | 4.15056 | ||||||||
\(161\) | 0.880738 | 0.0694119 | ||||||||
\(162\) | 2.70316 | 0.212380 | ||||||||
\(163\) | 12.4920 | 0.978447 | 0.489224 | − | 0.872158i | \(-0.337280\pi\) | ||||
0.489224 | + | 0.872158i | \(0.337280\pi\) | |||||||
\(164\) | 32.1701 | 2.51207 | ||||||||
\(165\) | 15.8926 | 1.23723 | ||||||||
\(166\) | −0.817089 | −0.0634184 | ||||||||
\(167\) | 8.77674 | 0.679165 | 0.339582 | − | 0.940576i | \(-0.389714\pi\) | ||||
0.339582 | + | 0.940576i | \(0.389714\pi\) | |||||||
\(168\) | −7.87341 | −0.607447 | ||||||||
\(169\) | 0.811682 | 0.0624371 | ||||||||
\(170\) | 36.3822 | 2.79038 | ||||||||
\(171\) | 6.68378 | 0.511121 | ||||||||
\(172\) | 50.6593 | 3.86274 | ||||||||
\(173\) | 14.7668 | 1.12270 | 0.561351 | − | 0.827578i | \(-0.310282\pi\) | ||||
0.561351 | + | 0.827578i | \(0.310282\pi\) | |||||||
\(174\) | 2.70316 | 0.204926 | ||||||||
\(175\) | 2.50070 | 0.189035 | ||||||||
\(176\) | −76.9170 | −5.79784 | ||||||||
\(177\) | −5.14558 | −0.386766 | ||||||||
\(178\) | −28.9622 | −2.17081 | ||||||||
\(179\) | −7.96536 | −0.595359 | −0.297679 | − | 0.954666i | \(-0.596213\pi\) | ||||
−0.297679 | + | 0.954666i | \(0.596213\pi\) | |||||||
\(180\) | 14.8592 | 1.10754 | ||||||||
\(181\) | 10.2864 | 0.764579 | 0.382289 | − | 0.924043i | \(-0.375136\pi\) | ||||
0.382289 | + | 0.924043i | \(0.375136\pi\) | |||||||
\(182\) | −8.84794 | −0.655853 | ||||||||
\(183\) | 7.99562 | 0.591053 | ||||||||
\(184\) | 8.93955 | 0.659033 | ||||||||
\(185\) | −22.8184 | −1.67764 | ||||||||
\(186\) | −2.10578 | −0.154403 | ||||||||
\(187\) | −27.2855 | −1.99531 | ||||||||
\(188\) | −40.7593 | −2.97268 | ||||||||
\(189\) | −0.880738 | −0.0640643 | ||||||||
\(190\) | 50.5863 | 3.66992 | ||||||||
\(191\) | 23.0537 | 1.66811 | 0.834054 | − | 0.551683i | \(-0.186014\pi\) | ||||
0.834054 | + | 0.551683i | \(0.186014\pi\) | |||||||
\(192\) | −23.5855 | −1.70214 | ||||||||
\(193\) | 5.67387 | 0.408414 | 0.204207 | − | 0.978928i | \(-0.434538\pi\) | ||||
0.204207 | + | 0.978928i | \(0.434538\pi\) | |||||||
\(194\) | −2.38967 | −0.171568 | ||||||||
\(195\) | 10.4055 | 0.745153 | ||||||||
\(196\) | −33.0328 | −2.35949 | ||||||||
\(197\) | 7.96762 | 0.567669 | 0.283835 | − | 0.958873i | \(-0.408393\pi\) | ||||
0.283835 | + | 0.958873i | \(0.408393\pi\) | |||||||
\(198\) | −15.3436 | −1.09042 | ||||||||
\(199\) | −6.95306 | −0.492889 | −0.246445 | − | 0.969157i | \(-0.579262\pi\) | ||||
−0.246445 | + | 0.969157i | \(0.579262\pi\) | |||||||
\(200\) | 25.3823 | 1.79480 | ||||||||
\(201\) | 8.36073 | 0.589721 | ||||||||
\(202\) | −3.67882 | −0.258841 | ||||||||
\(203\) | −0.880738 | −0.0618157 | ||||||||
\(204\) | −25.5113 | −1.78615 | ||||||||
\(205\) | 16.9722 | 1.18539 | ||||||||
\(206\) | −14.3609 | −1.00057 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −50.3607 | −3.49188 | ||||||||
\(209\) | −37.9382 | −2.62424 | ||||||||
\(210\) | −6.66589 | −0.459990 | ||||||||
\(211\) | 5.75864 | 0.396441 | 0.198221 | − | 0.980157i | \(-0.436484\pi\) | ||||
0.198221 | + | 0.980157i | \(0.436484\pi\) | |||||||
\(212\) | −51.6647 | −3.54835 | ||||||||
\(213\) | −8.52656 | −0.584230 | ||||||||
\(214\) | 21.1679 | 1.44701 | ||||||||
\(215\) | 26.7266 | 1.82274 | ||||||||
\(216\) | −8.93955 | −0.608260 | ||||||||
\(217\) | 0.686100 | 0.0465755 | ||||||||
\(218\) | 30.3889 | 2.05819 | ||||||||
\(219\) | 12.6677 | 0.856004 | ||||||||
\(220\) | −84.3430 | −5.68640 | ||||||||
\(221\) | −17.8649 | −1.20172 | ||||||||
\(222\) | 22.0301 | 1.47857 | ||||||||
\(223\) | 12.0916 | 0.809713 | 0.404856 | − | 0.914380i | \(-0.367322\pi\) | ||||
0.404856 | + | 0.914380i | \(0.367322\pi\) | |||||||
\(224\) | 16.5148 | 1.10344 | ||||||||
\(225\) | 2.83932 | 0.189288 | ||||||||
\(226\) | −47.2831 | −3.14523 | ||||||||
\(227\) | −27.0451 | −1.79505 | −0.897523 | − | 0.440968i | \(-0.854635\pi\) | ||||
−0.897523 | + | 0.440968i | \(0.854635\pi\) | |||||||
\(228\) | −35.4713 | −2.34914 | ||||||||
\(229\) | −5.32014 | −0.351565 | −0.175782 | − | 0.984429i | \(-0.556245\pi\) | ||||
−0.175782 | + | 0.984429i | \(0.556245\pi\) | |||||||
\(230\) | 7.56852 | 0.499054 | ||||||||
\(231\) | 4.99921 | 0.328924 | ||||||||
\(232\) | −8.93955 | −0.586911 | ||||||||
\(233\) | 23.8743 | 1.56406 | 0.782028 | − | 0.623244i | \(-0.214186\pi\) | ||||
0.782028 | + | 0.623244i | \(0.214186\pi\) | |||||||
\(234\) | −10.0460 | −0.656730 | ||||||||
\(235\) | −21.5036 | −1.40274 | ||||||||
\(236\) | 27.3080 | 1.77760 | ||||||||
\(237\) | −15.1051 | −0.981179 | ||||||||
\(238\) | 11.4445 | 0.741836 | ||||||||
\(239\) | −8.24781 | −0.533506 | −0.266753 | − | 0.963765i | \(-0.585951\pi\) | ||||
−0.266753 | + | 0.963765i | \(0.585951\pi\) | |||||||
\(240\) | −37.9409 | −2.44907 | ||||||||
\(241\) | 10.5594 | 0.680192 | 0.340096 | − | 0.940391i | \(-0.389540\pi\) | ||||
0.340096 | + | 0.940391i | \(0.389540\pi\) | |||||||
\(242\) | 57.3577 | 3.68709 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −42.4334 | −2.71652 | ||||||||
\(245\) | −17.4273 | −1.11339 | ||||||||
\(246\) | −16.3859 | −1.04472 | ||||||||
\(247\) | −24.8396 | −1.58051 | ||||||||
\(248\) | 6.96396 | 0.442212 | ||||||||
\(249\) | 0.302272 | 0.0191557 | ||||||||
\(250\) | −16.3531 | −1.03426 | ||||||||
\(251\) | −15.9674 | −1.00785 | −0.503927 | − | 0.863746i | \(-0.668112\pi\) | ||||
−0.503927 | + | 0.863746i | \(0.668112\pi\) | |||||||
\(252\) | 4.67414 | 0.294443 | ||||||||
\(253\) | −5.67616 | −0.356857 | ||||||||
\(254\) | 0.557929 | 0.0350076 | ||||||||
\(255\) | −13.4591 | −0.842843 | ||||||||
\(256\) | 23.7956 | 1.48722 | ||||||||
\(257\) | −5.13834 | −0.320521 | −0.160260 | − | 0.987075i | \(-0.551233\pi\) | ||||
−0.160260 | + | 0.987075i | \(0.551233\pi\) | |||||||
\(258\) | −25.8033 | −1.60645 | ||||||||
\(259\) | −7.17782 | −0.446008 | ||||||||
\(260\) | −55.2227 | −3.42477 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 25.6904 | 1.58716 | ||||||||
\(263\) | 22.1102 | 1.36337 | 0.681687 | − | 0.731644i | \(-0.261246\pi\) | ||||
0.681687 | + | 0.731644i | \(0.261246\pi\) | |||||||
\(264\) | 50.7423 | 3.12297 | ||||||||
\(265\) | −27.2570 | −1.67438 | ||||||||
\(266\) | 15.9126 | 0.975663 | ||||||||
\(267\) | 10.7142 | 0.655699 | ||||||||
\(268\) | −44.3710 | −2.71039 | ||||||||
\(269\) | 20.1023 | 1.22566 | 0.612828 | − | 0.790216i | \(-0.290032\pi\) | ||||
0.612828 | + | 0.790216i | \(0.290032\pi\) | |||||||
\(270\) | −7.56852 | −0.460606 | ||||||||
\(271\) | 6.90145 | 0.419233 | 0.209617 | − | 0.977784i | \(-0.432778\pi\) | ||||
0.209617 | + | 0.977784i | \(0.432778\pi\) | |||||||
\(272\) | 65.1397 | 3.94967 | ||||||||
\(273\) | 3.27318 | 0.198102 | ||||||||
\(274\) | 11.5621 | 0.698491 | ||||||||
\(275\) | −16.1165 | −0.971859 | ||||||||
\(276\) | −5.30708 | −0.319448 | ||||||||
\(277\) | 24.5794 | 1.47683 | 0.738416 | − | 0.674345i | \(-0.235574\pi\) | ||||
0.738416 | + | 0.674345i | \(0.235574\pi\) | |||||||
\(278\) | −25.6019 | −1.53550 | ||||||||
\(279\) | 0.779005 | 0.0466378 | ||||||||
\(280\) | 22.0446 | 1.31742 | ||||||||
\(281\) | −17.2690 | −1.03018 | −0.515090 | − | 0.857136i | \(-0.672241\pi\) | ||||
−0.515090 | + | 0.857136i | \(0.672241\pi\) | |||||||
\(282\) | 20.7608 | 1.23629 | ||||||||
\(283\) | −7.22081 | −0.429232 | −0.214616 | − | 0.976698i | \(-0.568850\pi\) | ||||
−0.214616 | + | 0.976698i | \(0.568850\pi\) | |||||||
\(284\) | 45.2511 | 2.68516 | ||||||||
\(285\) | −18.7138 | −1.10851 | ||||||||
\(286\) | 57.0229 | 3.37184 | ||||||||
\(287\) | 5.33881 | 0.315140 | ||||||||
\(288\) | 18.7511 | 1.10492 | ||||||||
\(289\) | 6.10760 | 0.359271 | ||||||||
\(290\) | −7.56852 | −0.444439 | ||||||||
\(291\) | 0.884027 | 0.0518226 | ||||||||
\(292\) | −67.2285 | −3.93425 | ||||||||
\(293\) | −18.2359 | −1.06535 | −0.532677 | − | 0.846319i | \(-0.678814\pi\) | ||||
−0.532677 | + | 0.846319i | \(0.678814\pi\) | |||||||
\(294\) | 16.8253 | 0.981270 | ||||||||
\(295\) | 14.4070 | 0.838809 | ||||||||
\(296\) | −72.8553 | −4.23463 | ||||||||
\(297\) | 5.67616 | 0.329364 | ||||||||
\(298\) | −54.9951 | −3.18578 | ||||||||
\(299\) | −3.71641 | −0.214925 | ||||||||
\(300\) | −15.0685 | −0.869981 | ||||||||
\(301\) | 8.40720 | 0.484583 | ||||||||
\(302\) | −38.8484 | −2.23547 | ||||||||
\(303\) | 1.36093 | 0.0781835 | ||||||||
\(304\) | 90.5712 | 5.19461 | ||||||||
\(305\) | −22.3868 | −1.28186 | ||||||||
\(306\) | 12.9942 | 0.742828 | ||||||||
\(307\) | −14.8966 | −0.850193 | −0.425097 | − | 0.905148i | \(-0.639760\pi\) | ||||
−0.425097 | + | 0.905148i | \(0.639760\pi\) | |||||||
\(308\) | −26.5312 | −1.51175 | ||||||||
\(309\) | 5.31264 | 0.302226 | ||||||||
\(310\) | 5.89592 | 0.334866 | ||||||||
\(311\) | −1.07620 | −0.0610259 | −0.0305129 | − | 0.999534i | \(-0.509714\pi\) | ||||
−0.0305129 | + | 0.999534i | \(0.509714\pi\) | |||||||
\(312\) | 33.2230 | 1.88088 | ||||||||
\(313\) | −24.6270 | −1.39200 | −0.696000 | − | 0.718042i | \(-0.745039\pi\) | ||||
−0.696000 | + | 0.718042i | \(0.745039\pi\) | |||||||
\(314\) | −51.1846 | −2.88851 | ||||||||
\(315\) | 2.46596 | 0.138941 | ||||||||
\(316\) | 80.1637 | 4.50956 | ||||||||
\(317\) | 10.3442 | 0.580988 | 0.290494 | − | 0.956877i | \(-0.406180\pi\) | ||||
0.290494 | + | 0.956877i | \(0.406180\pi\) | |||||||
\(318\) | 26.3154 | 1.47570 | ||||||||
\(319\) | 5.67616 | 0.317804 | ||||||||
\(320\) | 66.0367 | 3.69156 | ||||||||
\(321\) | −7.83080 | −0.437073 | ||||||||
\(322\) | 2.38078 | 0.132676 | ||||||||
\(323\) | 32.1292 | 1.78771 | ||||||||
\(324\) | 5.30708 | 0.294838 | ||||||||
\(325\) | −10.5521 | −0.585324 | ||||||||
\(326\) | 33.7678 | 1.87023 | ||||||||
\(327\) | −11.2420 | −0.621683 | ||||||||
\(328\) | 54.1893 | 2.99210 | ||||||||
\(329\) | −6.76423 | −0.372924 | ||||||||
\(330\) | 42.9601 | 2.36488 | ||||||||
\(331\) | −14.0821 | −0.774025 | −0.387012 | − | 0.922075i | \(-0.626493\pi\) | ||||
−0.387012 | + | 0.922075i | \(0.626493\pi\) | |||||||
\(332\) | −1.60418 | −0.0880408 | ||||||||
\(333\) | −8.14977 | −0.446605 | ||||||||
\(334\) | 23.7249 | 1.29817 | ||||||||
\(335\) | −23.4090 | −1.27897 | ||||||||
\(336\) | −11.9348 | −0.651096 | ||||||||
\(337\) | −0.569964 | −0.0310479 | −0.0155240 | − | 0.999879i | \(-0.504942\pi\) | ||||
−0.0155240 | + | 0.999879i | \(0.504942\pi\) | |||||||
\(338\) | 2.19411 | 0.119344 | ||||||||
\(339\) | 17.4918 | 0.950024 | ||||||||
\(340\) | 71.4286 | 3.87376 | ||||||||
\(341\) | −4.42176 | −0.239452 | ||||||||
\(342\) | 18.0673 | 0.976969 | ||||||||
\(343\) | −11.6471 | −0.628887 | ||||||||
\(344\) | 85.3336 | 4.60088 | ||||||||
\(345\) | −2.79988 | −0.150740 | ||||||||
\(346\) | 39.9171 | 2.14596 | ||||||||
\(347\) | −12.4225 | −0.666877 | −0.333438 | − | 0.942772i | \(-0.608209\pi\) | ||||
−0.333438 | + | 0.942772i | \(0.608209\pi\) | |||||||
\(348\) | 5.30708 | 0.284489 | ||||||||
\(349\) | −28.4638 | −1.52363 | −0.761816 | − | 0.647793i | \(-0.775692\pi\) | ||||
−0.761816 | + | 0.647793i | \(0.775692\pi\) | |||||||
\(350\) | 6.75980 | 0.361326 | ||||||||
\(351\) | 3.71641 | 0.198367 | ||||||||
\(352\) | −106.434 | −5.67297 | ||||||||
\(353\) | 27.0042 | 1.43729 | 0.718644 | − | 0.695378i | \(-0.244763\pi\) | ||||
0.718644 | + | 0.695378i | \(0.244763\pi\) | |||||||
\(354\) | −13.9093 | −0.739273 | ||||||||
\(355\) | 23.8733 | 1.26706 | ||||||||
\(356\) | −56.8611 | −3.01363 | ||||||||
\(357\) | −4.23374 | −0.224073 | ||||||||
\(358\) | −21.5316 | −1.13798 | ||||||||
\(359\) | 14.0693 | 0.742551 | 0.371276 | − | 0.928523i | \(-0.378921\pi\) | ||||
0.371276 | + | 0.928523i | \(0.378921\pi\) | |||||||
\(360\) | 25.0297 | 1.31918 | ||||||||
\(361\) | 25.6729 | 1.35120 | ||||||||
\(362\) | 27.8057 | 1.46143 | ||||||||
\(363\) | −21.2188 | −1.11370 | ||||||||
\(364\) | −17.3710 | −0.910489 | ||||||||
\(365\) | −35.4680 | −1.85648 | ||||||||
\(366\) | 21.6134 | 1.12975 | ||||||||
\(367\) | 34.8397 | 1.81862 | 0.909310 | − | 0.416120i | \(-0.136610\pi\) | ||||
0.909310 | + | 0.416120i | \(0.136610\pi\) | |||||||
\(368\) | 13.5509 | 0.706389 | ||||||||
\(369\) | 6.06174 | 0.315562 | ||||||||
\(370\) | −61.6817 | −3.20668 | ||||||||
\(371\) | −8.57404 | −0.445142 | ||||||||
\(372\) | −4.13424 | −0.214350 | ||||||||
\(373\) | 22.0794 | 1.14323 | 0.571613 | − | 0.820523i | \(-0.306318\pi\) | ||||
0.571613 | + | 0.820523i | \(0.306318\pi\) | |||||||
\(374\) | −73.7571 | −3.81389 | ||||||||
\(375\) | 6.04963 | 0.312402 | ||||||||
\(376\) | −68.6574 | −3.54073 | ||||||||
\(377\) | 3.71641 | 0.191405 | ||||||||
\(378\) | −2.38078 | −0.122454 | ||||||||
\(379\) | −7.46769 | −0.383590 | −0.191795 | − | 0.981435i | \(-0.561431\pi\) | ||||
−0.191795 | + | 0.981435i | \(0.561431\pi\) | |||||||
\(380\) | 99.3154 | 5.09477 | ||||||||
\(381\) | −0.206399 | −0.0105741 | ||||||||
\(382\) | 62.3178 | 3.18846 | ||||||||
\(383\) | −30.9640 | −1.58218 | −0.791092 | − | 0.611697i | \(-0.790487\pi\) | ||||
−0.791092 | + | 0.611697i | \(0.790487\pi\) | |||||||
\(384\) | −26.2532 | −1.33973 | ||||||||
\(385\) | −13.9972 | −0.713363 | ||||||||
\(386\) | 15.3374 | 0.780652 | ||||||||
\(387\) | 9.54562 | 0.485231 | ||||||||
\(388\) | −4.69160 | −0.238180 | ||||||||
\(389\) | −20.5067 | −1.03973 | −0.519864 | − | 0.854249i | \(-0.674018\pi\) | ||||
−0.519864 | + | 0.854249i | \(0.674018\pi\) | |||||||
\(390\) | 28.1277 | 1.42430 | ||||||||
\(391\) | 4.80704 | 0.243102 | ||||||||
\(392\) | −55.6425 | −2.81037 | ||||||||
\(393\) | −9.50384 | −0.479405 | ||||||||
\(394\) | 21.5378 | 1.08506 | ||||||||
\(395\) | 42.2924 | 2.12796 | ||||||||
\(396\) | −30.1238 | −1.51378 | ||||||||
\(397\) | −18.4473 | −0.925843 | −0.462922 | − | 0.886399i | \(-0.653199\pi\) | ||||
−0.462922 | + | 0.886399i | \(0.653199\pi\) | |||||||
\(398\) | −18.7952 | −0.942120 | ||||||||
\(399\) | −5.88666 | −0.294701 | ||||||||
\(400\) | 38.4754 | 1.92377 | ||||||||
\(401\) | −15.7291 | −0.785475 | −0.392738 | − | 0.919651i | \(-0.628472\pi\) | ||||
−0.392738 | + | 0.919651i | \(0.628472\pi\) | |||||||
\(402\) | 22.6004 | 1.12721 | ||||||||
\(403\) | −2.89510 | −0.144215 | ||||||||
\(404\) | −7.22257 | −0.359336 | ||||||||
\(405\) | 2.79988 | 0.139127 | ||||||||
\(406\) | −2.38078 | −0.118156 | ||||||||
\(407\) | 46.2594 | 2.29299 | ||||||||
\(408\) | −42.9728 | −2.12747 | ||||||||
\(409\) | −7.14903 | −0.353497 | −0.176748 | − | 0.984256i | \(-0.556558\pi\) | ||||
−0.176748 | + | 0.984256i | \(0.556558\pi\) | |||||||
\(410\) | 45.8785 | 2.26578 | ||||||||
\(411\) | −4.27725 | −0.210981 | ||||||||
\(412\) | −28.1946 | −1.38905 | ||||||||
\(413\) | 4.53191 | 0.223001 | ||||||||
\(414\) | 2.70316 | 0.132853 | ||||||||
\(415\) | −0.846325 | −0.0415444 | ||||||||
\(416\) | −69.6869 | −3.41668 | ||||||||
\(417\) | 9.47109 | 0.463801 | ||||||||
\(418\) | −102.553 | −5.01603 | ||||||||
\(419\) | −14.7980 | −0.722928 | −0.361464 | − | 0.932386i | \(-0.617723\pi\) | ||||
−0.361464 | + | 0.932386i | \(0.617723\pi\) | |||||||
\(420\) | −13.0870 | −0.638582 | ||||||||
\(421\) | 6.98352 | 0.340356 | 0.170178 | − | 0.985413i | \(-0.445566\pi\) | ||||
0.170178 | + | 0.985413i | \(0.445566\pi\) | |||||||
\(422\) | 15.5665 | 0.757767 | ||||||||
\(423\) | −7.68018 | −0.373423 | ||||||||
\(424\) | −87.0271 | −4.22641 | ||||||||
\(425\) | 13.6487 | 0.662061 | ||||||||
\(426\) | −23.0487 | −1.11671 | ||||||||
\(427\) | −7.04205 | −0.340789 | ||||||||
\(428\) | 41.5586 | 2.00881 | ||||||||
\(429\) | −21.0949 | −1.01847 | ||||||||
\(430\) | 72.2463 | 3.48402 | ||||||||
\(431\) | 18.2431 | 0.878737 | 0.439368 | − | 0.898307i | \(-0.355202\pi\) | ||||
0.439368 | + | 0.898307i | \(0.355202\pi\) | |||||||
\(432\) | −13.5509 | −0.651968 | ||||||||
\(433\) | −6.54148 | −0.314364 | −0.157182 | − | 0.987570i | \(-0.550241\pi\) | ||||
−0.157182 | + | 0.987570i | \(0.550241\pi\) | |||||||
\(434\) | 1.85464 | 0.0890255 | ||||||||
\(435\) | 2.79988 | 0.134244 | ||||||||
\(436\) | 59.6620 | 2.85729 | ||||||||
\(437\) | 6.68378 | 0.319728 | ||||||||
\(438\) | 34.2428 | 1.63619 | ||||||||
\(439\) | −24.9232 | −1.18952 | −0.594760 | − | 0.803904i | \(-0.702753\pi\) | ||||
−0.594760 | + | 0.803904i | \(0.702753\pi\) | |||||||
\(440\) | −142.072 | −6.77303 | ||||||||
\(441\) | −6.22430 | −0.296395 | ||||||||
\(442\) | −48.2917 | −2.29700 | ||||||||
\(443\) | −31.7227 | −1.50719 | −0.753594 | − | 0.657340i | \(-0.771682\pi\) | ||||
−0.753594 | + | 0.657340i | \(0.771682\pi\) | |||||||
\(444\) | 43.2514 | 2.05262 | ||||||||
\(445\) | −29.9985 | −1.42207 | ||||||||
\(446\) | 32.6855 | 1.54770 | ||||||||
\(447\) | 20.3448 | 0.962274 | ||||||||
\(448\) | 20.7727 | 0.981417 | ||||||||
\(449\) | 27.6235 | 1.30363 | 0.651816 | − | 0.758377i | \(-0.274008\pi\) | ||||
0.651816 | + | 0.758377i | \(0.274008\pi\) | |||||||
\(450\) | 7.67515 | 0.361810 | ||||||||
\(451\) | −34.4074 | −1.62018 | ||||||||
\(452\) | −92.8303 | −4.36637 | ||||||||
\(453\) | 14.3715 | 0.675230 | ||||||||
\(454\) | −73.1072 | −3.43109 | ||||||||
\(455\) | −9.16452 | −0.429639 | ||||||||
\(456\) | −59.7500 | −2.79805 | ||||||||
\(457\) | 3.37558 | 0.157903 | 0.0789516 | − | 0.996878i | \(-0.474843\pi\) | ||||
0.0789516 | + | 0.996878i | \(0.474843\pi\) | |||||||
\(458\) | −14.3812 | −0.671989 | ||||||||
\(459\) | −4.80704 | −0.224373 | ||||||||
\(460\) | 14.8592 | 0.692812 | ||||||||
\(461\) | 39.9849 | 1.86228 | 0.931140 | − | 0.364661i | \(-0.118815\pi\) | ||||
0.931140 | + | 0.364661i | \(0.118815\pi\) | |||||||
\(462\) | 13.5137 | 0.628713 | ||||||||
\(463\) | 9.18722 | 0.426966 | 0.213483 | − | 0.976947i | \(-0.431519\pi\) | ||||
0.213483 | + | 0.976947i | \(0.431519\pi\) | |||||||
\(464\) | −13.5509 | −0.629085 | ||||||||
\(465\) | −2.18112 | −0.101147 | ||||||||
\(466\) | 64.5360 | 2.98957 | ||||||||
\(467\) | 13.0823 | 0.605378 | 0.302689 | − | 0.953089i | \(-0.402116\pi\) | ||||
0.302689 | + | 0.953089i | \(0.402116\pi\) | |||||||
\(468\) | −19.7233 | −0.911708 | ||||||||
\(469\) | −7.36362 | −0.340020 | ||||||||
\(470\) | −58.1276 | −2.68123 | ||||||||
\(471\) | 18.9351 | 0.872482 | ||||||||
\(472\) | 45.9992 | 2.11729 | ||||||||
\(473\) | −54.1825 | −2.49131 | ||||||||
\(474\) | −40.8314 | −1.87545 | ||||||||
\(475\) | 18.9774 | 0.870743 | ||||||||
\(476\) | 22.4688 | 1.02986 | ||||||||
\(477\) | −9.73506 | −0.445738 | ||||||||
\(478\) | −22.2951 | −1.01976 | ||||||||
\(479\) | 41.5385 | 1.89794 | 0.948972 | − | 0.315361i | \(-0.102125\pi\) | ||||
0.948972 | + | 0.315361i | \(0.102125\pi\) | |||||||
\(480\) | −52.5009 | −2.39633 | ||||||||
\(481\) | 30.2879 | 1.38101 | ||||||||
\(482\) | 28.5438 | 1.30013 | ||||||||
\(483\) | −0.880738 | −0.0400750 | ||||||||
\(484\) | 112.610 | 5.11862 | ||||||||
\(485\) | −2.47517 | −0.112392 | ||||||||
\(486\) | −2.70316 | −0.122618 | ||||||||
\(487\) | 22.4277 | 1.01630 | 0.508148 | − | 0.861270i | \(-0.330330\pi\) | ||||
0.508148 | + | 0.861270i | \(0.330330\pi\) | |||||||
\(488\) | −71.4773 | −3.23563 | ||||||||
\(489\) | −12.4920 | −0.564907 | ||||||||
\(490\) | −47.1088 | −2.12816 | ||||||||
\(491\) | 13.8826 | 0.626513 | 0.313256 | − | 0.949669i | \(-0.398580\pi\) | ||||
0.313256 | + | 0.949669i | \(0.398580\pi\) | |||||||
\(492\) | −32.1701 | −1.45034 | ||||||||
\(493\) | −4.80704 | −0.216498 | ||||||||
\(494\) | −67.1455 | −3.02102 | ||||||||
\(495\) | −15.8926 | −0.714317 | ||||||||
\(496\) | 10.5562 | 0.473988 | ||||||||
\(497\) | 7.50967 | 0.336855 | ||||||||
\(498\) | 0.817089 | 0.0366146 | ||||||||
\(499\) | −10.9367 | −0.489592 | −0.244796 | − | 0.969575i | \(-0.578721\pi\) | ||||
−0.244796 | + | 0.969575i | \(0.578721\pi\) | |||||||
\(500\) | −32.1059 | −1.43582 | ||||||||
\(501\) | −8.77674 | −0.392116 | ||||||||
\(502\) | −43.1625 | −1.92644 | ||||||||
\(503\) | −3.54058 | −0.157867 | −0.0789334 | − | 0.996880i | \(-0.525151\pi\) | ||||
−0.0789334 | + | 0.996880i | \(0.525151\pi\) | |||||||
\(504\) | 7.87341 | 0.350709 | ||||||||
\(505\) | −3.81044 | −0.169563 | ||||||||
\(506\) | −15.3436 | −0.682105 | ||||||||
\(507\) | −0.811682 | −0.0360481 | ||||||||
\(508\) | 1.09537 | 0.0485994 | ||||||||
\(509\) | 12.3607 | 0.547878 | 0.273939 | − | 0.961747i | \(-0.411673\pi\) | ||||
0.273939 | + | 0.961747i | \(0.411673\pi\) | |||||||
\(510\) | −36.3822 | −1.61103 | ||||||||
\(511\) | −11.1569 | −0.493554 | ||||||||
\(512\) | 11.8168 | 0.522233 | ||||||||
\(513\) | −6.68378 | −0.295096 | ||||||||
\(514\) | −13.8898 | −0.612651 | ||||||||
\(515\) | −14.8748 | −0.655460 | ||||||||
\(516\) | −50.6593 | −2.23015 | ||||||||
\(517\) | 43.5939 | 1.91726 | ||||||||
\(518\) | −19.4028 | −0.852509 | ||||||||
\(519\) | −14.7668 | −0.648192 | ||||||||
\(520\) | −93.0205 | −4.07922 | ||||||||
\(521\) | 34.5365 | 1.51307 | 0.756535 | − | 0.653953i | \(-0.226891\pi\) | ||||
0.756535 | + | 0.653953i | \(0.226891\pi\) | |||||||
\(522\) | −2.70316 | −0.118314 | ||||||||
\(523\) | 31.4234 | 1.37405 | 0.687024 | − | 0.726634i | \(-0.258917\pi\) | ||||
0.687024 | + | 0.726634i | \(0.258917\pi\) | |||||||
\(524\) | 50.4376 | 2.20338 | ||||||||
\(525\) | −2.50070 | −0.109140 | ||||||||
\(526\) | 59.7675 | 2.60599 | ||||||||
\(527\) | 3.74471 | 0.163122 | ||||||||
\(528\) | 76.9170 | 3.34738 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −73.6801 | −3.20046 | ||||||||
\(531\) | 5.14558 | 0.223299 | ||||||||
\(532\) | 31.2409 | 1.35447 | ||||||||
\(533\) | −22.5279 | −0.975792 | ||||||||
\(534\) | 28.9622 | 1.25332 | ||||||||
\(535\) | 21.9253 | 0.947913 | ||||||||
\(536\) | −74.7412 | −3.22833 | ||||||||
\(537\) | 7.96536 | 0.343730 | ||||||||
\(538\) | 54.3396 | 2.34275 | ||||||||
\(539\) | 35.3301 | 1.52178 | ||||||||
\(540\) | −14.8592 | −0.639437 | ||||||||
\(541\) | 28.3717 | 1.21980 | 0.609898 | − | 0.792480i | \(-0.291210\pi\) | ||||
0.609898 | + | 0.792480i | \(0.291210\pi\) | |||||||
\(542\) | 18.6557 | 0.801332 | ||||||||
\(543\) | −10.2864 | −0.441430 | ||||||||
\(544\) | 90.1374 | 3.86461 | ||||||||
\(545\) | 31.4762 | 1.34829 | ||||||||
\(546\) | 8.84794 | 0.378657 | ||||||||
\(547\) | 20.4656 | 0.875046 | 0.437523 | − | 0.899207i | \(-0.355856\pi\) | ||||
0.437523 | + | 0.899207i | \(0.355856\pi\) | |||||||
\(548\) | 22.6997 | 0.969682 | ||||||||
\(549\) | −7.99562 | −0.341245 | ||||||||
\(550\) | −43.5653 | −1.85763 | ||||||||
\(551\) | −6.68378 | −0.284738 | ||||||||
\(552\) | −8.93955 | −0.380493 | ||||||||
\(553\) | 13.3036 | 0.565727 | ||||||||
\(554\) | 66.4420 | 2.82285 | ||||||||
\(555\) | 22.8184 | 0.968586 | ||||||||
\(556\) | −50.2638 | −2.13166 | ||||||||
\(557\) | 33.3630 | 1.41363 | 0.706817 | − | 0.707396i | \(-0.250130\pi\) | ||||
0.706817 | + | 0.707396i | \(0.250130\pi\) | |||||||
\(558\) | 2.10578 | 0.0891446 | ||||||||
\(559\) | −35.4754 | −1.50045 | ||||||||
\(560\) | 33.4160 | 1.41208 | ||||||||
\(561\) | 27.2855 | 1.15199 | ||||||||
\(562\) | −46.6808 | −1.96911 | ||||||||
\(563\) | 21.5508 | 0.908257 | 0.454129 | − | 0.890936i | \(-0.349951\pi\) | ||||
0.454129 | + | 0.890936i | \(0.349951\pi\) | |||||||
\(564\) | 40.7593 | 1.71628 | ||||||||
\(565\) | −48.9749 | −2.06039 | ||||||||
\(566\) | −19.5190 | −0.820445 | ||||||||
\(567\) | 0.880738 | 0.0369875 | ||||||||
\(568\) | 76.2236 | 3.19827 | ||||||||
\(569\) | 12.9510 | 0.542934 | 0.271467 | − | 0.962448i | \(-0.412491\pi\) | ||||
0.271467 | + | 0.962448i | \(0.412491\pi\) | |||||||
\(570\) | −50.5863 | −2.11883 | ||||||||
\(571\) | 3.76335 | 0.157491 | 0.0787456 | − | 0.996895i | \(-0.474909\pi\) | ||||
0.0787456 | + | 0.996895i | \(0.474909\pi\) | |||||||
\(572\) | 111.952 | 4.68096 | ||||||||
\(573\) | −23.0537 | −0.963082 | ||||||||
\(574\) | 14.4317 | 0.602366 | ||||||||
\(575\) | 2.83932 | 0.118408 | ||||||||
\(576\) | 23.5855 | 0.982731 | ||||||||
\(577\) | 9.05091 | 0.376794 | 0.188397 | − | 0.982093i | \(-0.439671\pi\) | ||||
0.188397 | + | 0.982093i | \(0.439671\pi\) | |||||||
\(578\) | 16.5098 | 0.686718 | ||||||||
\(579\) | −5.67387 | −0.235798 | ||||||||
\(580\) | −14.8592 | −0.616993 | ||||||||
\(581\) | −0.266222 | −0.0110448 | ||||||||
\(582\) | 2.38967 | 0.0990549 | ||||||||
\(583\) | 55.2578 | 2.28854 | ||||||||
\(584\) | −113.244 | −4.68605 | ||||||||
\(585\) | −10.4055 | −0.430214 | ||||||||
\(586\) | −49.2946 | −2.03634 | ||||||||
\(587\) | −7.59812 | −0.313608 | −0.156804 | − | 0.987630i | \(-0.550119\pi\) | ||||
−0.156804 | + | 0.987630i | \(0.550119\pi\) | |||||||
\(588\) | 33.0328 | 1.36225 | ||||||||
\(589\) | 5.20670 | 0.214538 | ||||||||
\(590\) | 38.9445 | 1.60332 | ||||||||
\(591\) | −7.96762 | −0.327744 | ||||||||
\(592\) | −110.437 | −4.53892 | ||||||||
\(593\) | 7.95422 | 0.326641 | 0.163320 | − | 0.986573i | \(-0.447780\pi\) | ||||
0.163320 | + | 0.986573i | \(0.447780\pi\) | |||||||
\(594\) | 15.3436 | 0.629554 | ||||||||
\(595\) | 11.8540 | 0.485965 | ||||||||
\(596\) | −107.971 | −4.42267 | ||||||||
\(597\) | 6.95306 | 0.284570 | ||||||||
\(598\) | −10.0460 | −0.410813 | ||||||||
\(599\) | 31.2856 | 1.27830 | 0.639148 | − | 0.769084i | \(-0.279287\pi\) | ||||
0.639148 | + | 0.769084i | \(0.279287\pi\) | |||||||
\(600\) | −25.3823 | −1.03623 | ||||||||
\(601\) | 14.4217 | 0.588274 | 0.294137 | − | 0.955763i | \(-0.404968\pi\) | ||||
0.294137 | + | 0.955763i | \(0.404968\pi\) | |||||||
\(602\) | 22.7260 | 0.926242 | ||||||||
\(603\) | −8.36073 | −0.340475 | ||||||||
\(604\) | −76.2704 | −3.10340 | ||||||||
\(605\) | 59.4100 | 2.41536 | ||||||||
\(606\) | 3.67882 | 0.149442 | ||||||||
\(607\) | −27.1287 | −1.10112 | −0.550560 | − | 0.834796i | \(-0.685586\pi\) | ||||
−0.550560 | + | 0.834796i | \(0.685586\pi\) | |||||||
\(608\) | 125.328 | 5.08274 | ||||||||
\(609\) | 0.880738 | 0.0356893 | ||||||||
\(610\) | −60.5150 | −2.45018 | ||||||||
\(611\) | 28.5427 | 1.15471 | ||||||||
\(612\) | 25.5113 | 1.03123 | ||||||||
\(613\) | −7.58210 | −0.306238 | −0.153119 | − | 0.988208i | \(-0.548932\pi\) | ||||
−0.153119 | + | 0.988208i | \(0.548932\pi\) | |||||||
\(614\) | −40.2679 | −1.62508 | ||||||||
\(615\) | −16.9722 | −0.684383 | ||||||||
\(616\) | −44.6907 | −1.80064 | ||||||||
\(617\) | 40.3076 | 1.62272 | 0.811361 | − | 0.584546i | \(-0.198727\pi\) | ||||
0.811361 | + | 0.584546i | \(0.198727\pi\) | |||||||
\(618\) | 14.3609 | 0.577681 | ||||||||
\(619\) | 7.17677 | 0.288459 | 0.144229 | − | 0.989544i | \(-0.453930\pi\) | ||||
0.144229 | + | 0.989544i | \(0.453930\pi\) | |||||||
\(620\) | 11.5754 | 0.464878 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −2.90915 | −0.116646 | ||||||||
\(623\) | −9.43642 | −0.378062 | ||||||||
\(624\) | 50.3607 | 2.01604 | ||||||||
\(625\) | −31.1349 | −1.24539 | ||||||||
\(626\) | −66.5707 | −2.66070 | ||||||||
\(627\) | 37.9382 | 1.51510 | ||||||||
\(628\) | −100.490 | −4.00998 | ||||||||
\(629\) | −39.1762 | −1.56206 | ||||||||
\(630\) | 6.66589 | 0.265575 | ||||||||
\(631\) | −13.8537 | −0.551506 | −0.275753 | − | 0.961229i | \(-0.588927\pi\) | ||||
−0.275753 | + | 0.961229i | \(0.588927\pi\) | |||||||
\(632\) | 135.033 | 5.37131 | ||||||||
\(633\) | −5.75864 | −0.228885 | ||||||||
\(634\) | 27.9620 | 1.11051 | ||||||||
\(635\) | 0.577892 | 0.0229329 | ||||||||
\(636\) | 51.6647 | 2.04864 | ||||||||
\(637\) | 23.1320 | 0.916525 | ||||||||
\(638\) | 15.3436 | 0.607457 | ||||||||
\(639\) | 8.52656 | 0.337305 | ||||||||
\(640\) | 73.5058 | 2.90557 | ||||||||
\(641\) | −2.14458 | −0.0847056 | −0.0423528 | − | 0.999103i | \(-0.513485\pi\) | ||||
−0.0423528 | + | 0.999103i | \(0.513485\pi\) | |||||||
\(642\) | −21.1679 | −0.835431 | ||||||||
\(643\) | −48.1250 | −1.89786 | −0.948932 | − | 0.315481i | \(-0.897834\pi\) | ||||
−0.948932 | + | 0.315481i | \(0.897834\pi\) | |||||||
\(644\) | 4.67414 | 0.184187 | ||||||||
\(645\) | −26.7266 | −1.05236 | ||||||||
\(646\) | 86.8503 | 3.41708 | ||||||||
\(647\) | 14.6607 | 0.576370 | 0.288185 | − | 0.957575i | \(-0.406948\pi\) | ||||
0.288185 | + | 0.957575i | \(0.406948\pi\) | |||||||
\(648\) | 8.93955 | 0.351179 | ||||||||
\(649\) | −29.2071 | −1.14648 | ||||||||
\(650\) | −28.5240 | −1.11880 | ||||||||
\(651\) | −0.686100 | −0.0268904 | ||||||||
\(652\) | 66.2959 | 2.59635 | ||||||||
\(653\) | 30.0473 | 1.17584 | 0.587921 | − | 0.808918i | \(-0.299947\pi\) | ||||
0.587921 | + | 0.808918i | \(0.299947\pi\) | |||||||
\(654\) | −30.3889 | −1.18830 | ||||||||
\(655\) | 26.6096 | 1.03972 | ||||||||
\(656\) | 82.1421 | 3.20711 | ||||||||
\(657\) | −12.6677 | −0.494214 | ||||||||
\(658\) | −18.2848 | −0.712816 | ||||||||
\(659\) | 17.5722 | 0.684516 | 0.342258 | − | 0.939606i | \(-0.388808\pi\) | ||||
0.342258 | + | 0.939606i | \(0.388808\pi\) | |||||||
\(660\) | 84.3430 | 3.28305 | ||||||||
\(661\) | −22.2147 | −0.864052 | −0.432026 | − | 0.901861i | \(-0.642201\pi\) | ||||
−0.432026 | + | 0.901861i | \(0.642201\pi\) | |||||||
\(662\) | −38.0663 | −1.47949 | ||||||||
\(663\) | 17.8649 | 0.693815 | ||||||||
\(664\) | −2.70218 | −0.104865 | ||||||||
\(665\) | 16.4819 | 0.639142 | ||||||||
\(666\) | −22.0301 | −0.853650 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 46.5788 | 1.80219 | ||||||||
\(669\) | −12.0916 | −0.467488 | ||||||||
\(670\) | −63.2784 | −2.44466 | ||||||||
\(671\) | 45.3844 | 1.75205 | ||||||||
\(672\) | −16.5148 | −0.637074 | ||||||||
\(673\) | 28.1597 | 1.08547 | 0.542737 | − | 0.839902i | \(-0.317388\pi\) | ||||
0.542737 | + | 0.839902i | \(0.317388\pi\) | |||||||
\(674\) | −1.54070 | −0.0593457 | ||||||||
\(675\) | −2.83932 | −0.109286 | ||||||||
\(676\) | 4.30766 | 0.165679 | ||||||||
\(677\) | 0.245245 | 0.00942553 | 0.00471277 | − | 0.999989i | \(-0.498500\pi\) | ||||
0.00471277 | + | 0.999989i | \(0.498500\pi\) | |||||||
\(678\) | 47.2831 | 1.81590 | ||||||||
\(679\) | −0.778596 | −0.0298798 | ||||||||
\(680\) | 120.319 | 4.61401 | ||||||||
\(681\) | 27.0451 | 1.03637 | ||||||||
\(682\) | −11.9527 | −0.457693 | ||||||||
\(683\) | 28.9636 | 1.10826 | 0.554131 | − | 0.832430i | \(-0.313051\pi\) | ||||
0.554131 | + | 0.832430i | \(0.313051\pi\) | |||||||
\(684\) | 35.4713 | 1.35628 | ||||||||
\(685\) | 11.9758 | 0.457571 | ||||||||
\(686\) | −31.4841 | −1.20207 | ||||||||
\(687\) | 5.32014 | 0.202976 | ||||||||
\(688\) | 129.352 | 4.93149 | ||||||||
\(689\) | 36.1795 | 1.37833 | ||||||||
\(690\) | −7.56852 | −0.288129 | ||||||||
\(691\) | −35.3723 | −1.34563 | −0.672813 | − | 0.739813i | \(-0.734914\pi\) | ||||
−0.672813 | + | 0.739813i | \(0.734914\pi\) | |||||||
\(692\) | 78.3687 | 2.97913 | ||||||||
\(693\) | −4.99921 | −0.189904 | ||||||||
\(694\) | −33.5801 | −1.27468 | ||||||||
\(695\) | −26.5179 | −1.00588 | ||||||||
\(696\) | 8.93955 | 0.338853 | ||||||||
\(697\) | 29.1390 | 1.10372 | ||||||||
\(698\) | −76.9422 | −2.91231 | ||||||||
\(699\) | −23.8743 | −0.903008 | ||||||||
\(700\) | 13.2714 | 0.501612 | ||||||||
\(701\) | 19.9823 | 0.754722 | 0.377361 | − | 0.926066i | \(-0.376832\pi\) | ||||
0.377361 | + | 0.926066i | \(0.376832\pi\) | |||||||
\(702\) | 10.0460 | 0.379164 | ||||||||
\(703\) | −54.4712 | −2.05442 | ||||||||
\(704\) | −133.875 | −5.04561 | ||||||||
\(705\) | 21.5036 | 0.809872 | ||||||||
\(706\) | 72.9966 | 2.74726 | ||||||||
\(707\) | −1.19862 | −0.0450789 | ||||||||
\(708\) | −27.3080 | −1.02630 | ||||||||
\(709\) | −13.0449 | −0.489911 | −0.244956 | − | 0.969534i | \(-0.578773\pi\) | ||||
−0.244956 | + | 0.969534i | \(0.578773\pi\) | |||||||
\(710\) | 64.5334 | 2.42190 | ||||||||
\(711\) | 15.1051 | 0.566484 | ||||||||
\(712\) | −95.7803 | −3.58952 | ||||||||
\(713\) | 0.779005 | 0.0291740 | ||||||||
\(714\) | −11.4445 | −0.428299 | ||||||||
\(715\) | 59.0632 | 2.20884 | ||||||||
\(716\) | −42.2727 | −1.57981 | ||||||||
\(717\) | 8.24781 | 0.308020 | ||||||||
\(718\) | 38.0317 | 1.41933 | ||||||||
\(719\) | 8.19259 | 0.305532 | 0.152766 | − | 0.988262i | \(-0.451182\pi\) | ||||
0.152766 | + | 0.988262i | \(0.451182\pi\) | |||||||
\(720\) | 37.9409 | 1.41397 | ||||||||
\(721\) | −4.67905 | −0.174257 | ||||||||
\(722\) | 69.3978 | 2.58272 | ||||||||
\(723\) | −10.5594 | −0.392709 | ||||||||
\(724\) | 54.5905 | 2.02884 | ||||||||
\(725\) | −2.83932 | −0.105450 | ||||||||
\(726\) | −57.3577 | −2.12874 | ||||||||
\(727\) | −28.0803 | −1.04144 | −0.520721 | − | 0.853727i | \(-0.674337\pi\) | ||||
−0.520721 | + | 0.853727i | \(0.674337\pi\) | |||||||
\(728\) | −29.2608 | −1.08448 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −95.8758 | −3.54852 | ||||||||
\(731\) | 45.8862 | 1.69716 | ||||||||
\(732\) | 42.4334 | 1.56838 | ||||||||
\(733\) | −32.2797 | −1.19228 | −0.596140 | − | 0.802881i | \(-0.703300\pi\) | ||||
−0.596140 | + | 0.802881i | \(0.703300\pi\) | |||||||
\(734\) | 94.1774 | 3.47615 | ||||||||
\(735\) | 17.4273 | 0.642815 | ||||||||
\(736\) | 18.7511 | 0.691176 | ||||||||
\(737\) | 47.4568 | 1.74809 | ||||||||
\(738\) | 16.3859 | 0.603172 | ||||||||
\(739\) | 2.56275 | 0.0942721 | 0.0471361 | − | 0.998888i | \(-0.484991\pi\) | ||||
0.0471361 | + | 0.998888i | \(0.484991\pi\) | |||||||
\(740\) | −121.099 | −4.45168 | ||||||||
\(741\) | 24.8396 | 0.912507 | ||||||||
\(742\) | −23.1770 | −0.850855 | ||||||||
\(743\) | 35.8227 | 1.31421 | 0.657104 | − | 0.753800i | \(-0.271781\pi\) | ||||
0.657104 | + | 0.753800i | \(0.271781\pi\) | |||||||
\(744\) | −6.96396 | −0.255311 | ||||||||
\(745\) | −56.9629 | −2.08696 | ||||||||
\(746\) | 59.6841 | 2.18519 | ||||||||
\(747\) | −0.302272 | −0.0110595 | ||||||||
\(748\) | −144.806 | −5.29464 | ||||||||
\(749\) | 6.89689 | 0.252007 | ||||||||
\(750\) | 16.3531 | 0.597132 | ||||||||
\(751\) | −42.9765 | −1.56824 | −0.784118 | − | 0.620612i | \(-0.786884\pi\) | ||||
−0.784118 | + | 0.620612i | \(0.786884\pi\) | |||||||
\(752\) | −104.073 | −3.79516 | ||||||||
\(753\) | 15.9674 | 0.581885 | ||||||||
\(754\) | 10.0460 | 0.365855 | ||||||||
\(755\) | −40.2383 | −1.46442 | ||||||||
\(756\) | −4.67414 | −0.169997 | ||||||||
\(757\) | −32.0132 | −1.16354 | −0.581769 | − | 0.813354i | \(-0.697639\pi\) | ||||
−0.581769 | + | 0.813354i | \(0.697639\pi\) | |||||||
\(758\) | −20.1864 | −0.733202 | ||||||||
\(759\) | 5.67616 | 0.206031 | ||||||||
\(760\) | 167.293 | 6.06834 | ||||||||
\(761\) | 11.4559 | 0.415278 | 0.207639 | − | 0.978206i | \(-0.433422\pi\) | ||||
0.207639 | + | 0.978206i | \(0.433422\pi\) | |||||||
\(762\) | −0.557929 | −0.0202116 | ||||||||
\(763\) | 9.90124 | 0.358449 | ||||||||
\(764\) | 122.348 | 4.42639 | ||||||||
\(765\) | 13.4591 | 0.486616 | ||||||||
\(766\) | −83.7005 | −3.02422 | ||||||||
\(767\) | −19.1231 | −0.690495 | ||||||||
\(768\) | −23.7956 | −0.858648 | ||||||||
\(769\) | −0.0983888 | −0.00354799 | −0.00177400 | − | 0.999998i | \(-0.500565\pi\) | ||||
−0.00177400 | + | 0.999998i | \(0.500565\pi\) | |||||||
\(770\) | −37.8366 | −1.36354 | ||||||||
\(771\) | 5.13834 | 0.185053 | ||||||||
\(772\) | 30.1117 | 1.08374 | ||||||||
\(773\) | 12.4020 | 0.446070 | 0.223035 | − | 0.974810i | \(-0.428404\pi\) | ||||
0.223035 | + | 0.974810i | \(0.428404\pi\) | |||||||
\(774\) | 25.8033 | 0.927482 | ||||||||
\(775\) | 2.21185 | 0.0794519 | ||||||||
\(776\) | −7.90281 | −0.283694 | ||||||||
\(777\) | 7.17782 | 0.257503 | ||||||||
\(778\) | −55.4328 | −1.98736 | ||||||||
\(779\) | 40.5153 | 1.45161 | ||||||||
\(780\) | 55.2227 | 1.97729 | ||||||||
\(781\) | −48.3981 | −1.73182 | ||||||||
\(782\) | 12.9942 | 0.464671 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | −84.3449 | −3.01232 | ||||||||
\(785\) | −53.0159 | −1.89222 | ||||||||
\(786\) | −25.6904 | −0.916346 | ||||||||
\(787\) | 26.7197 | 0.952455 | 0.476227 | − | 0.879322i | \(-0.342004\pi\) | ||||
0.476227 | + | 0.879322i | \(0.342004\pi\) | |||||||
\(788\) | 42.2848 | 1.50633 | ||||||||
\(789\) | −22.1102 | −0.787145 | ||||||||
\(790\) | 114.323 | 4.06743 | ||||||||
\(791\) | −15.4057 | −0.547763 | ||||||||
\(792\) | −50.7423 | −1.80305 | ||||||||
\(793\) | 29.7150 | 1.05521 | ||||||||
\(794\) | −49.8660 | −1.76968 | ||||||||
\(795\) | 27.2570 | 0.966706 | ||||||||
\(796\) | −36.9004 | −1.30790 | ||||||||
\(797\) | 20.2834 | 0.718474 | 0.359237 | − | 0.933246i | \(-0.383037\pi\) | ||||
0.359237 | + | 0.933246i | \(0.383037\pi\) | |||||||
\(798\) | −15.9126 | −0.563299 | ||||||||
\(799\) | −36.9189 | −1.30610 | ||||||||
\(800\) | 53.2406 | 1.88234 | ||||||||
\(801\) | −10.7142 | −0.378568 | ||||||||
\(802\) | −42.5184 | −1.50138 | ||||||||
\(803\) | 71.9039 | 2.53743 | ||||||||
\(804\) | 44.3710 | 1.56485 | ||||||||
\(805\) | 2.46596 | 0.0869137 | ||||||||
\(806\) | −7.82592 | −0.275656 | ||||||||
\(807\) | −20.1023 | −0.707633 | ||||||||
\(808\) | −12.1661 | −0.428003 | ||||||||
\(809\) | 35.7621 | 1.25733 | 0.628665 | − | 0.777676i | \(-0.283602\pi\) | ||||
0.628665 | + | 0.777676i | \(0.283602\pi\) | |||||||
\(810\) | 7.56852 | 0.265931 | ||||||||
\(811\) | 26.4097 | 0.927370 | 0.463685 | − | 0.886000i | \(-0.346527\pi\) | ||||
0.463685 | + | 0.886000i | \(0.346527\pi\) | |||||||
\(812\) | −4.67414 | −0.164030 | ||||||||
\(813\) | −6.90145 | −0.242045 | ||||||||
\(814\) | 125.047 | 4.38288 | ||||||||
\(815\) | 34.9760 | 1.22516 | ||||||||
\(816\) | −65.1397 | −2.28034 | ||||||||
\(817\) | 63.8008 | 2.23211 | ||||||||
\(818\) | −19.3250 | −0.675682 | ||||||||
\(819\) | −3.27318 | −0.114374 | ||||||||
\(820\) | 90.0725 | 3.14547 | ||||||||
\(821\) | 21.8673 | 0.763172 | 0.381586 | − | 0.924333i | \(-0.375378\pi\) | ||||
0.381586 | + | 0.924333i | \(0.375378\pi\) | |||||||
\(822\) | −11.5621 | −0.403274 | ||||||||
\(823\) | −33.6657 | −1.17351 | −0.586756 | − | 0.809764i | \(-0.699595\pi\) | ||||
−0.586756 | + | 0.809764i | \(0.699595\pi\) | |||||||
\(824\) | −47.4927 | −1.65449 | ||||||||
\(825\) | 16.1165 | 0.561103 | ||||||||
\(826\) | 12.2505 | 0.426249 | ||||||||
\(827\) | −49.4034 | −1.71793 | −0.858963 | − | 0.512038i | \(-0.828891\pi\) | ||||
−0.858963 | + | 0.512038i | \(0.828891\pi\) | |||||||
\(828\) | 5.30708 | 0.184434 | ||||||||
\(829\) | 3.54310 | 0.123057 | 0.0615285 | − | 0.998105i | \(-0.480402\pi\) | ||||
0.0615285 | + | 0.998105i | \(0.480402\pi\) | |||||||
\(830\) | −2.28775 | −0.0794090 | ||||||||
\(831\) | −24.5794 | −0.852650 | ||||||||
\(832\) | −87.6535 | −3.03884 | ||||||||
\(833\) | −29.9204 | −1.03668 | ||||||||
\(834\) | 25.6019 | 0.886520 | ||||||||
\(835\) | 24.5738 | 0.850412 | ||||||||
\(836\) | −201.341 | −6.96351 | ||||||||
\(837\) | −0.779005 | −0.0269264 | ||||||||
\(838\) | −40.0013 | −1.38182 | ||||||||
\(839\) | −27.3924 | −0.945691 | −0.472846 | − | 0.881145i | \(-0.656773\pi\) | ||||
−0.472846 | + | 0.881145i | \(0.656773\pi\) | |||||||
\(840\) | −22.0446 | −0.760611 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 18.8776 | 0.650564 | ||||||||
\(843\) | 17.2690 | 0.594775 | ||||||||
\(844\) | 30.5615 | 1.05197 | ||||||||
\(845\) | 2.27261 | 0.0781802 | ||||||||
\(846\) | −20.7608 | −0.713770 | ||||||||
\(847\) | 18.6882 | 0.642133 | ||||||||
\(848\) | −131.919 | −4.53011 | ||||||||
\(849\) | 7.22081 | 0.247817 | ||||||||
\(850\) | 36.8947 | 1.26548 | ||||||||
\(851\) | −8.14977 | −0.279371 | ||||||||
\(852\) | −45.2511 | −1.55028 | ||||||||
\(853\) | 18.4109 | 0.630376 | 0.315188 | − | 0.949029i | \(-0.397932\pi\) | ||||
0.315188 | + | 0.949029i | \(0.397932\pi\) | |||||||
\(854\) | −19.0358 | −0.651391 | ||||||||
\(855\) | 18.7138 | 0.639997 | ||||||||
\(856\) | 70.0039 | 2.39268 | ||||||||
\(857\) | 40.3861 | 1.37956 | 0.689782 | − | 0.724018i | \(-0.257707\pi\) | ||||
0.689782 | + | 0.724018i | \(0.257707\pi\) | |||||||
\(858\) | −57.0229 | −1.94673 | ||||||||
\(859\) | 38.5166 | 1.31417 | 0.657085 | − | 0.753816i | \(-0.271789\pi\) | ||||
0.657085 | + | 0.753816i | \(0.271789\pi\) | |||||||
\(860\) | 141.840 | 4.83670 | ||||||||
\(861\) | −5.33881 | −0.181946 | ||||||||
\(862\) | 49.3139 | 1.67964 | ||||||||
\(863\) | 22.4884 | 0.765513 | 0.382756 | − | 0.923849i | \(-0.374975\pi\) | ||||
0.382756 | + | 0.923849i | \(0.374975\pi\) | |||||||
\(864\) | −18.7511 | −0.637927 | ||||||||
\(865\) | 41.3454 | 1.40578 | ||||||||
\(866\) | −17.6827 | −0.600882 | ||||||||
\(867\) | −6.10760 | −0.207425 | ||||||||
\(868\) | 3.64118 | 0.123590 | ||||||||
\(869\) | −85.7387 | −2.90849 | ||||||||
\(870\) | 7.56852 | 0.256597 | ||||||||
\(871\) | 31.0719 | 1.05283 | ||||||||
\(872\) | 100.498 | 3.40330 | ||||||||
\(873\) | −0.884027 | −0.0299198 | ||||||||
\(874\) | 18.0673 | 0.611136 | ||||||||
\(875\) | −5.32814 | −0.180124 | ||||||||
\(876\) | 67.2285 | 2.27144 | ||||||||
\(877\) | −2.78341 | −0.0939892 | −0.0469946 | − | 0.998895i | \(-0.514964\pi\) | ||||
−0.0469946 | + | 0.998895i | \(0.514964\pi\) | |||||||
\(878\) | −67.3714 | −2.27367 | ||||||||
\(879\) | 18.2359 | 0.615082 | ||||||||
\(880\) | −215.358 | −7.25973 | ||||||||
\(881\) | −0.347005 | −0.0116909 | −0.00584544 | − | 0.999983i | \(-0.501861\pi\) | ||||
−0.00584544 | + | 0.999983i | \(0.501861\pi\) | |||||||
\(882\) | −16.8253 | −0.566537 | ||||||||
\(883\) | −31.9999 | −1.07688 | −0.538442 | − | 0.842663i | \(-0.680987\pi\) | ||||
−0.538442 | + | 0.842663i | \(0.680987\pi\) | |||||||
\(884\) | −94.8104 | −3.18882 | ||||||||
\(885\) | −14.4070 | −0.484287 | ||||||||
\(886\) | −85.7514 | −2.88087 | ||||||||
\(887\) | 54.2012 | 1.81990 | 0.909949 | − | 0.414721i | \(-0.136121\pi\) | ||||
0.909949 | + | 0.414721i | \(0.136121\pi\) | |||||||
\(888\) | 72.8553 | 2.44486 | ||||||||
\(889\) | 0.181783 | 0.00609682 | ||||||||
\(890\) | −81.0907 | −2.71817 | ||||||||
\(891\) | −5.67616 | −0.190158 | ||||||||
\(892\) | 64.1710 | 2.14860 | ||||||||
\(893\) | −51.3326 | −1.71778 | ||||||||
\(894\) | 54.9951 | 1.83931 | ||||||||
\(895\) | −22.3020 | −0.745475 | ||||||||
\(896\) | 23.1222 | 0.772459 | ||||||||
\(897\) | 3.71641 | 0.124087 | ||||||||
\(898\) | 74.6706 | 2.49179 | ||||||||
\(899\) | −0.779005 | −0.0259813 | ||||||||
\(900\) | 15.0685 | 0.502284 | ||||||||
\(901\) | −46.7968 | −1.55903 | ||||||||
\(902\) | −93.0088 | −3.09685 | ||||||||
\(903\) | −8.40720 | −0.279774 | ||||||||
\(904\) | −156.369 | −5.20075 | ||||||||
\(905\) | 28.8005 | 0.957363 | ||||||||
\(906\) | 38.8484 | 1.29065 | ||||||||
\(907\) | −8.16651 | −0.271164 | −0.135582 | − | 0.990766i | \(-0.543290\pi\) | ||||
−0.135582 | + | 0.990766i | \(0.543290\pi\) | |||||||
\(908\) | −143.530 | −4.76322 | ||||||||
\(909\) | −1.36093 | −0.0451392 | ||||||||
\(910\) | −24.7732 | −0.821222 | ||||||||
\(911\) | 21.0259 | 0.696618 | 0.348309 | − | 0.937380i | \(-0.386756\pi\) | ||||
0.348309 | + | 0.937380i | \(0.386756\pi\) | |||||||
\(912\) | −90.5712 | −2.99911 | ||||||||
\(913\) | 1.71574 | 0.0567828 | ||||||||
\(914\) | 9.12474 | 0.301820 | ||||||||
\(915\) | 22.3868 | 0.740084 | ||||||||
\(916\) | −28.2344 | −0.932890 | ||||||||
\(917\) | 8.37039 | 0.276415 | ||||||||
\(918\) | −12.9942 | −0.428872 | ||||||||
\(919\) | −12.9335 | −0.426638 | −0.213319 | − | 0.976983i | \(-0.568427\pi\) | ||||
−0.213319 | + | 0.976983i | \(0.568427\pi\) | |||||||
\(920\) | 25.0297 | 0.825204 | ||||||||
\(921\) | 14.8966 | 0.490859 | ||||||||
\(922\) | 108.085 | 3.55961 | ||||||||
\(923\) | −31.6882 | −1.04303 | ||||||||
\(924\) | 26.5312 | 0.872812 | ||||||||
\(925\) | −23.1398 | −0.760833 | ||||||||
\(926\) | 24.8345 | 0.816113 | ||||||||
\(927\) | −5.31264 | −0.174490 | ||||||||
\(928\) | −18.7511 | −0.615536 | ||||||||
\(929\) | −13.5273 | −0.443817 | −0.221909 | − | 0.975067i | \(-0.571229\pi\) | ||||
−0.221909 | + | 0.975067i | \(0.571229\pi\) | |||||||
\(930\) | −5.89592 | −0.193335 | ||||||||
\(931\) | −41.6018 | −1.36344 | ||||||||
\(932\) | 126.703 | 4.15028 | ||||||||
\(933\) | 1.07620 | 0.0352333 | ||||||||
\(934\) | 35.3636 | 1.15713 | ||||||||
\(935\) | −76.3961 | −2.49842 | ||||||||
\(936\) | −33.2230 | −1.08593 | ||||||||
\(937\) | −4.15878 | −0.135862 | −0.0679308 | − | 0.997690i | \(-0.521640\pi\) | ||||
−0.0679308 | + | 0.997690i | \(0.521640\pi\) | |||||||
\(938\) | −19.9050 | −0.649923 | ||||||||
\(939\) | 24.6270 | 0.803671 | ||||||||
\(940\) | −114.121 | −3.72222 | ||||||||
\(941\) | −46.9661 | −1.53105 | −0.765525 | − | 0.643406i | \(-0.777521\pi\) | ||||
−0.765525 | + | 0.643406i | \(0.777521\pi\) | |||||||
\(942\) | 51.1846 | 1.66768 | ||||||||
\(943\) | 6.06174 | 0.197398 | ||||||||
\(944\) | 69.7273 | 2.26943 | ||||||||
\(945\) | −2.46596 | −0.0802177 | ||||||||
\(946\) | −146.464 | −4.76195 | ||||||||
\(947\) | −6.09656 | −0.198112 | −0.0990558 | − | 0.995082i | \(-0.531582\pi\) | ||||
−0.0990558 | + | 0.995082i | \(0.531582\pi\) | |||||||
\(948\) | −80.1637 | −2.60360 | ||||||||
\(949\) | 47.0783 | 1.52823 | ||||||||
\(950\) | 51.2990 | 1.66436 | ||||||||
\(951\) | −10.3442 | −0.335433 | ||||||||
\(952\) | 37.8478 | 1.22665 | ||||||||
\(953\) | −9.32474 | −0.302058 | −0.151029 | − | 0.988529i | \(-0.548259\pi\) | ||||
−0.151029 | + | 0.988529i | \(0.548259\pi\) | |||||||
\(954\) | −26.3154 | −0.851994 | ||||||||
\(955\) | 64.5476 | 2.08871 | ||||||||
\(956\) | −43.7717 | −1.41568 | ||||||||
\(957\) | −5.67616 | −0.183484 | ||||||||
\(958\) | 112.285 | 3.62777 | ||||||||
\(959\) | 3.76713 | 0.121647 | ||||||||
\(960\) | −66.0367 | −2.13132 | ||||||||
\(961\) | −30.3932 | −0.980424 | ||||||||
\(962\) | 81.8730 | 2.63969 | ||||||||
\(963\) | 7.83080 | 0.252344 | ||||||||
\(964\) | 56.0396 | 1.80492 | ||||||||
\(965\) | 15.8862 | 0.511393 | ||||||||
\(966\) | −2.38078 | −0.0766002 | ||||||||
\(967\) | −43.6266 | −1.40294 | −0.701468 | − | 0.712701i | \(-0.747472\pi\) | ||||
−0.701468 | + | 0.712701i | \(0.747472\pi\) | |||||||
\(968\) | 189.686 | 6.09675 | ||||||||
\(969\) | −32.1292 | −1.03214 | ||||||||
\(970\) | −6.69078 | −0.214828 | ||||||||
\(971\) | 19.3929 | 0.622347 | 0.311173 | − | 0.950353i | \(-0.399278\pi\) | ||||
0.311173 | + | 0.950353i | \(0.399278\pi\) | |||||||
\(972\) | −5.30708 | −0.170225 | ||||||||
\(973\) | −8.34155 | −0.267418 | ||||||||
\(974\) | 60.6256 | 1.94257 | ||||||||
\(975\) | 10.5521 | 0.337937 | ||||||||
\(976\) | −108.348 | −3.46813 | ||||||||
\(977\) | −58.1111 | −1.85914 | −0.929569 | − | 0.368649i | \(-0.879820\pi\) | ||||
−0.929569 | + | 0.368649i | \(0.879820\pi\) | |||||||
\(978\) | −33.7678 | −1.07978 | ||||||||
\(979\) | 60.8155 | 1.94367 | ||||||||
\(980\) | −92.4879 | −2.95442 | ||||||||
\(981\) | 11.2420 | 0.358929 | ||||||||
\(982\) | 37.5269 | 1.19753 | ||||||||
\(983\) | 30.4731 | 0.971942 | 0.485971 | − | 0.873975i | \(-0.338466\pi\) | ||||
0.485971 | + | 0.873975i | \(0.338466\pi\) | |||||||
\(984\) | −54.1893 | −1.72749 | ||||||||
\(985\) | 22.3084 | 0.710804 | ||||||||
\(986\) | −12.9942 | −0.413819 | ||||||||
\(987\) | 6.76423 | 0.215308 | ||||||||
\(988\) | −131.826 | −4.19394 | ||||||||
\(989\) | 9.54562 | 0.303533 | ||||||||
\(990\) | −42.9601 | −1.36536 | ||||||||
\(991\) | 11.8870 | 0.377603 | 0.188802 | − | 0.982015i | \(-0.439540\pi\) | ||||
0.188802 | + | 0.982015i | \(0.439540\pi\) | |||||||
\(992\) | 14.6072 | 0.463780 | ||||||||
\(993\) | 14.0821 | 0.446883 | ||||||||
\(994\) | 20.2998 | 0.643872 | ||||||||
\(995\) | −19.4677 | −0.617168 | ||||||||
\(996\) | 1.60418 | 0.0508304 | ||||||||
\(997\) | −33.6336 | −1.06519 | −0.532593 | − | 0.846371i | \(-0.678782\pi\) | ||||
−0.532593 | + | 0.846371i | \(0.678782\pi\) | |||||||
\(998\) | −29.5635 | −0.935818 | ||||||||
\(999\) | 8.14977 | 0.257847 |
(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 | 2001.2.a.l.1.10 | ✓ | 11 | |
3.2 | odd | 2 | 6003.2.a.m.1.2 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.l.1.10 | ✓ | 11 | 1.1 | even | 1 | trivial | |
6003.2.a.m.1.2 | 11 | 3.2 | odd | 2 |