Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.37367 | 1.67844 | 0.839220 | − | 0.543793i | \(-0.183012\pi\) | ||||
0.839220 | + | 0.543793i | \(0.183012\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.63432 | 1.81716 | ||||||||
\(5\) | −3.47491 | −1.55403 | −0.777014 | − | 0.629483i | \(-0.783267\pi\) | ||||
−0.777014 | + | 0.629483i | \(0.783267\pi\) | |||||||
\(6\) | 2.37367 | 0.969047 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.87933 | 1.37155 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −8.24830 | −2.60834 | ||||||||
\(11\) | 1.00968 | 0.304429 | 0.152215 | − | 0.988347i | \(-0.451359\pi\) | ||||
0.152215 | + | 0.988347i | \(0.451359\pi\) | |||||||
\(12\) | 3.63432 | 1.04914 | ||||||||
\(13\) | −3.69507 | −1.02483 | −0.512414 | − | 0.858738i | \(-0.671249\pi\) | ||||
−0.512414 | + | 0.858738i | \(0.671249\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.47491 | −0.897219 | ||||||||
\(16\) | 1.93963 | 0.484907 | ||||||||
\(17\) | 2.26443 | 0.549205 | 0.274602 | − | 0.961558i | \(-0.411454\pi\) | ||||
0.274602 | + | 0.961558i | \(0.411454\pi\) | |||||||
\(18\) | 2.37367 | 0.559480 | ||||||||
\(19\) | 3.08267 | 0.707214 | 0.353607 | − | 0.935394i | \(-0.384955\pi\) | ||||
0.353607 | + | 0.935394i | \(0.384955\pi\) | |||||||
\(20\) | −12.6289 | −2.82392 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.39664 | 0.510966 | ||||||||
\(23\) | 2.97074 | 0.619443 | 0.309722 | − | 0.950827i | \(-0.399764\pi\) | ||||
0.309722 | + | 0.950827i | \(0.399764\pi\) | |||||||
\(24\) | 3.87933 | 0.791866 | ||||||||
\(25\) | 7.07502 | 1.41500 | ||||||||
\(26\) | −8.77089 | −1.72011 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.10211 | 1.13313 | 0.566567 | − | 0.824016i | \(-0.308271\pi\) | ||||
0.566567 | + | 0.824016i | \(0.308271\pi\) | |||||||
\(30\) | −8.24830 | −1.50593 | ||||||||
\(31\) | 1.10018 | 0.197598 | 0.0987988 | − | 0.995107i | \(-0.468500\pi\) | ||||
0.0987988 | + | 0.995107i | \(0.468500\pi\) | |||||||
\(32\) | −3.15463 | −0.557664 | ||||||||
\(33\) | 1.00968 | 0.175762 | ||||||||
\(34\) | 5.37501 | 0.921807 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.63432 | 0.605720 | ||||||||
\(37\) | 7.80010 | 1.28233 | 0.641164 | − | 0.767404i | \(-0.278452\pi\) | ||||
0.641164 | + | 0.767404i | \(0.278452\pi\) | |||||||
\(38\) | 7.31725 | 1.18702 | ||||||||
\(39\) | −3.69507 | −0.591685 | ||||||||
\(40\) | −13.4803 | −2.13143 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.3610 | 1.73254 | 0.866271 | − | 0.499574i | \(-0.166510\pi\) | ||||
0.866271 | + | 0.499574i | \(0.166510\pi\) | |||||||
\(44\) | 3.66949 | 0.553196 | ||||||||
\(45\) | −3.47491 | −0.518009 | ||||||||
\(46\) | 7.05157 | 1.03970 | ||||||||
\(47\) | 10.8405 | 1.58125 | 0.790623 | − | 0.612303i | \(-0.209757\pi\) | ||||
0.790623 | + | 0.612303i | \(0.209757\pi\) | |||||||
\(48\) | 1.93963 | 0.279961 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 16.7938 | 2.37500 | ||||||||
\(51\) | 2.26443 | 0.317084 | ||||||||
\(52\) | −13.4291 | −1.86228 | ||||||||
\(53\) | −3.15739 | −0.433701 | −0.216850 | − | 0.976205i | \(-0.569578\pi\) | ||||
−0.216850 | + | 0.976205i | \(0.569578\pi\) | |||||||
\(54\) | 2.37367 | 0.323016 | ||||||||
\(55\) | −3.50854 | −0.473092 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.08267 | 0.408310 | ||||||||
\(58\) | 14.4844 | 1.90190 | ||||||||
\(59\) | 10.4467 | 1.36005 | 0.680024 | − | 0.733190i | \(-0.261969\pi\) | ||||
0.680024 | + | 0.733190i | \(0.261969\pi\) | |||||||
\(60\) | −12.6289 | −1.63039 | ||||||||
\(61\) | 2.86665 | 0.367037 | 0.183518 | − | 0.983016i | \(-0.441251\pi\) | ||||
0.183518 | + | 0.983016i | \(0.441251\pi\) | |||||||
\(62\) | 2.61146 | 0.331656 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.3673 | −1.42091 | ||||||||
\(65\) | 12.8401 | 1.59261 | ||||||||
\(66\) | 2.39664 | 0.295006 | ||||||||
\(67\) | −7.54599 | −0.921889 | −0.460944 | − | 0.887429i | \(-0.652489\pi\) | ||||
−0.460944 | + | 0.887429i | \(0.652489\pi\) | |||||||
\(68\) | 8.22965 | 0.997992 | ||||||||
\(69\) | 2.97074 | 0.357636 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.56311 | 0.897576 | 0.448788 | − | 0.893638i | \(-0.351856\pi\) | ||||
0.448788 | + | 0.893638i | \(0.351856\pi\) | |||||||
\(72\) | 3.87933 | 0.457184 | ||||||||
\(73\) | −8.49635 | −0.994422 | −0.497211 | − | 0.867630i | \(-0.665643\pi\) | ||||
−0.497211 | + | 0.867630i | \(0.665643\pi\) | |||||||
\(74\) | 18.5149 | 2.15231 | ||||||||
\(75\) | 7.07502 | 0.816953 | ||||||||
\(76\) | 11.2034 | 1.28512 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −8.77089 | −0.993107 | ||||||||
\(79\) | 8.24616 | 0.927766 | 0.463883 | − | 0.885897i | \(-0.346456\pi\) | ||||
0.463883 | + | 0.885897i | \(0.346456\pi\) | |||||||
\(80\) | −6.74004 | −0.753559 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.37367 | −0.262128 | ||||||||
\(83\) | −12.4677 | −1.36851 | −0.684255 | − | 0.729243i | \(-0.739872\pi\) | ||||
−0.684255 | + | 0.729243i | \(0.739872\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.86870 | −0.853480 | ||||||||
\(86\) | 26.9674 | 2.90797 | ||||||||
\(87\) | 6.10211 | 0.654215 | ||||||||
\(88\) | 3.91688 | 0.417540 | ||||||||
\(89\) | −7.10936 | −0.753591 | −0.376795 | − | 0.926296i | \(-0.622974\pi\) | ||||
−0.376795 | + | 0.926296i | \(0.622974\pi\) | |||||||
\(90\) | −8.24830 | −0.869448 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 10.7966 | 1.12563 | ||||||||
\(93\) | 1.10018 | 0.114083 | ||||||||
\(94\) | 25.7317 | 2.65403 | ||||||||
\(95\) | −10.7120 | −1.09903 | ||||||||
\(96\) | −3.15463 | −0.321968 | ||||||||
\(97\) | 1.37040 | 0.139143 | 0.0695717 | − | 0.997577i | \(-0.477837\pi\) | ||||
0.0695717 | + | 0.997577i | \(0.477837\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00968 | 0.101476 | ||||||||
\(100\) | 25.7129 | 2.57129 | ||||||||
\(101\) | 3.16096 | 0.314528 | 0.157264 | − | 0.987557i | \(-0.449733\pi\) | ||||
0.157264 | + | 0.987557i | \(0.449733\pi\) | |||||||
\(102\) | 5.37501 | 0.532205 | ||||||||
\(103\) | 5.03265 | 0.495881 | 0.247941 | − | 0.968775i | \(-0.420246\pi\) | ||||
0.247941 | + | 0.968775i | \(0.420246\pi\) | |||||||
\(104\) | −14.3344 | −1.40560 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.49461 | −0.727941 | ||||||||
\(107\) | 8.80363 | 0.851079 | 0.425540 | − | 0.904940i | \(-0.360084\pi\) | ||||
0.425540 | + | 0.904940i | \(0.360084\pi\) | |||||||
\(108\) | 3.63432 | 0.349712 | ||||||||
\(109\) | −0.819402 | −0.0784845 | −0.0392422 | − | 0.999230i | \(-0.512494\pi\) | ||||
−0.0392422 | + | 0.999230i | \(0.512494\pi\) | |||||||
\(110\) | −8.32813 | −0.794056 | ||||||||
\(111\) | 7.80010 | 0.740353 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.73111 | −0.350994 | −0.175497 | − | 0.984480i | \(-0.556153\pi\) | ||||
−0.175497 | + | 0.984480i | \(0.556153\pi\) | |||||||
\(114\) | 7.31725 | 0.685324 | ||||||||
\(115\) | −10.3231 | −0.962632 | ||||||||
\(116\) | 22.1770 | 2.05908 | ||||||||
\(117\) | −3.69507 | −0.341610 | ||||||||
\(118\) | 24.7971 | 2.28276 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −13.4803 | −1.23058 | ||||||||
\(121\) | −9.98055 | −0.907323 | ||||||||
\(122\) | 6.80449 | 0.616049 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | 3.99839 | 0.359066 | ||||||||
\(125\) | −7.21052 | −0.644929 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.70586 | −0.417578 | −0.208789 | − | 0.977961i | \(-0.566952\pi\) | ||||
−0.208789 | + | 0.977961i | \(0.566952\pi\) | |||||||
\(128\) | −20.6730 | −1.82725 | ||||||||
\(129\) | 11.3610 | 1.00028 | ||||||||
\(130\) | 30.4781 | 2.67310 | ||||||||
\(131\) | −5.84671 | −0.510829 | −0.255415 | − | 0.966832i | \(-0.582212\pi\) | ||||
−0.255415 | + | 0.966832i | \(0.582212\pi\) | |||||||
\(132\) | 3.66949 | 0.319388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −17.9117 | −1.54733 | ||||||||
\(135\) | −3.47491 | −0.299073 | ||||||||
\(136\) | 8.78448 | 0.753263 | ||||||||
\(137\) | −18.0997 | −1.54636 | −0.773181 | − | 0.634185i | \(-0.781336\pi\) | ||||
−0.773181 | + | 0.634185i | \(0.781336\pi\) | |||||||
\(138\) | 7.05157 | 0.600270 | ||||||||
\(139\) | 5.95439 | 0.505045 | 0.252522 | − | 0.967591i | \(-0.418740\pi\) | ||||
0.252522 | + | 0.967591i | \(0.418740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.8405 | 0.912933 | ||||||||
\(142\) | 17.9523 | 1.50653 | ||||||||
\(143\) | −3.73083 | −0.311988 | ||||||||
\(144\) | 1.93963 | 0.161636 | ||||||||
\(145\) | −21.2043 | −1.76092 | ||||||||
\(146\) | −20.1675 | −1.66908 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 28.3480 | 2.33019 | ||||||||
\(149\) | 2.81919 | 0.230957 | 0.115479 | − | 0.993310i | \(-0.463160\pi\) | ||||
0.115479 | + | 0.993310i | \(0.463160\pi\) | |||||||
\(150\) | 16.7938 | 1.37121 | ||||||||
\(151\) | 2.17246 | 0.176793 | 0.0883963 | − | 0.996085i | \(-0.471826\pi\) | ||||
0.0883963 | + | 0.996085i | \(0.471826\pi\) | |||||||
\(152\) | 11.9587 | 0.969980 | ||||||||
\(153\) | 2.26443 | 0.183068 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.82302 | −0.307072 | ||||||||
\(156\) | −13.4291 | −1.07519 | ||||||||
\(157\) | 9.90769 | 0.790719 | 0.395360 | − | 0.918526i | \(-0.370620\pi\) | ||||
0.395360 | + | 0.918526i | \(0.370620\pi\) | |||||||
\(158\) | 19.5737 | 1.55720 | ||||||||
\(159\) | −3.15739 | −0.250397 | ||||||||
\(160\) | 10.9621 | 0.866626 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.37367 | 0.186493 | ||||||||
\(163\) | −10.6771 | −0.836299 | −0.418149 | − | 0.908378i | \(-0.637321\pi\) | ||||
−0.418149 | + | 0.908378i | \(0.637321\pi\) | |||||||
\(164\) | −3.63432 | −0.283793 | ||||||||
\(165\) | −3.50854 | −0.273140 | ||||||||
\(166\) | −29.5943 | −2.29696 | ||||||||
\(167\) | 22.2093 | 1.71861 | 0.859305 | − | 0.511463i | \(-0.170896\pi\) | ||||
0.859305 | + | 0.511463i | \(0.170896\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.653556 | 0.0502735 | ||||||||
\(170\) | −18.6777 | −1.43251 | ||||||||
\(171\) | 3.08267 | 0.235738 | ||||||||
\(172\) | 41.2896 | 3.14830 | ||||||||
\(173\) | −2.71224 | −0.206208 | −0.103104 | − | 0.994671i | \(-0.532877\pi\) | ||||
−0.103104 | + | 0.994671i | \(0.532877\pi\) | |||||||
\(174\) | 14.4844 | 1.09806 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.95840 | 0.147620 | ||||||||
\(177\) | 10.4467 | 0.785224 | ||||||||
\(178\) | −16.8753 | −1.26486 | ||||||||
\(179\) | −25.9226 | −1.93755 | −0.968774 | − | 0.247944i | \(-0.920245\pi\) | ||||
−0.968774 | + | 0.247944i | \(0.920245\pi\) | |||||||
\(180\) | −12.6289 | −0.941305 | ||||||||
\(181\) | −14.9349 | −1.11011 | −0.555053 | − | 0.831815i | \(-0.687302\pi\) | ||||
−0.555053 | + | 0.831815i | \(0.687302\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.86665 | 0.211909 | ||||||||
\(184\) | 11.5245 | 0.849598 | ||||||||
\(185\) | −27.1047 | −1.99277 | ||||||||
\(186\) | 2.61146 | 0.191482 | ||||||||
\(187\) | 2.28634 | 0.167194 | ||||||||
\(188\) | 39.3977 | 2.87338 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −25.4268 | −1.84466 | ||||||||
\(191\) | −3.25643 | −0.235627 | −0.117813 | − | 0.993036i | \(-0.537588\pi\) | ||||
−0.117813 | + | 0.993036i | \(0.537588\pi\) | |||||||
\(192\) | −11.3673 | −0.820364 | ||||||||
\(193\) | 21.7417 | 1.56500 | 0.782499 | − | 0.622651i | \(-0.213944\pi\) | ||||
0.782499 | + | 0.622651i | \(0.213944\pi\) | |||||||
\(194\) | 3.25289 | 0.233544 | ||||||||
\(195\) | 12.8401 | 0.919495 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.4747 | 1.60125 | 0.800626 | − | 0.599164i | \(-0.204500\pi\) | ||||
0.800626 | + | 0.599164i | \(0.204500\pi\) | |||||||
\(198\) | 2.39664 | 0.170322 | ||||||||
\(199\) | −0.769084 | −0.0545189 | −0.0272595 | − | 0.999628i | \(-0.508678\pi\) | ||||
−0.0272595 | + | 0.999628i | \(0.508678\pi\) | |||||||
\(200\) | 27.4464 | 1.94075 | ||||||||
\(201\) | −7.54599 | −0.532253 | ||||||||
\(202\) | 7.50309 | 0.527916 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 8.22965 | 0.576191 | ||||||||
\(205\) | 3.47491 | 0.242698 | ||||||||
\(206\) | 11.9459 | 0.832307 | ||||||||
\(207\) | 2.97074 | 0.206481 | ||||||||
\(208\) | −7.16706 | −0.496947 | ||||||||
\(209\) | 3.11251 | 0.215297 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.39650 | −0.440354 | −0.220177 | − | 0.975460i | \(-0.570663\pi\) | ||||
−0.220177 | + | 0.975460i | \(0.570663\pi\) | |||||||
\(212\) | −11.4750 | −0.788104 | ||||||||
\(213\) | 7.56311 | 0.518216 | ||||||||
\(214\) | 20.8969 | 1.42848 | ||||||||
\(215\) | −39.4786 | −2.69242 | ||||||||
\(216\) | 3.87933 | 0.263955 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.94499 | −0.131731 | ||||||||
\(219\) | −8.49635 | −0.574130 | ||||||||
\(220\) | −12.7512 | −0.859683 | ||||||||
\(221\) | −8.36723 | −0.562841 | ||||||||
\(222\) | 18.5149 | 1.24264 | ||||||||
\(223\) | −13.5518 | −0.907499 | −0.453749 | − | 0.891129i | \(-0.649914\pi\) | ||||
−0.453749 | + | 0.891129i | \(0.649914\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.07502 | 0.471668 | ||||||||
\(226\) | −8.85644 | −0.589121 | ||||||||
\(227\) | 11.0791 | 0.735344 | 0.367672 | − | 0.929955i | \(-0.380155\pi\) | ||||
0.367672 | + | 0.929955i | \(0.380155\pi\) | |||||||
\(228\) | 11.2034 | 0.741964 | ||||||||
\(229\) | −4.05671 | −0.268075 | −0.134038 | − | 0.990976i | \(-0.542794\pi\) | ||||
−0.134038 | + | 0.990976i | \(0.542794\pi\) | |||||||
\(230\) | −24.5036 | −1.61572 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 23.6721 | 1.55415 | ||||||||
\(233\) | −5.83354 | −0.382168 | −0.191084 | − | 0.981574i | \(-0.561200\pi\) | ||||
−0.191084 | + | 0.981574i | \(0.561200\pi\) | |||||||
\(234\) | −8.77089 | −0.573371 | ||||||||
\(235\) | −37.6697 | −2.45730 | ||||||||
\(236\) | 37.9667 | 2.47142 | ||||||||
\(237\) | 8.24616 | 0.535646 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.8223 | 0.829407 | 0.414703 | − | 0.909957i | \(-0.363885\pi\) | ||||
0.414703 | + | 0.909957i | \(0.363885\pi\) | |||||||
\(240\) | −6.74004 | −0.435068 | ||||||||
\(241\) | −3.16368 | −0.203790 | −0.101895 | − | 0.994795i | \(-0.532491\pi\) | ||||
−0.101895 | + | 0.994795i | \(0.532491\pi\) | |||||||
\(242\) | −23.6906 | −1.52289 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 10.4183 | 0.666964 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.37367 | −0.151340 | ||||||||
\(247\) | −11.3907 | −0.724773 | ||||||||
\(248\) | 4.26795 | 0.271015 | ||||||||
\(249\) | −12.4677 | −0.790109 | ||||||||
\(250\) | −17.1154 | −1.08247 | ||||||||
\(251\) | 13.8603 | 0.874851 | 0.437426 | − | 0.899255i | \(-0.355890\pi\) | ||||
0.437426 | + | 0.899255i | \(0.355890\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.99949 | 0.188577 | ||||||||
\(254\) | −11.1702 | −0.700879 | ||||||||
\(255\) | −7.86870 | −0.492757 | ||||||||
\(256\) | −26.3363 | −1.64602 | ||||||||
\(257\) | 26.8020 | 1.67186 | 0.835931 | − | 0.548835i | \(-0.184928\pi\) | ||||
0.835931 | + | 0.548835i | \(0.184928\pi\) | |||||||
\(258\) | 26.9674 | 1.67892 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 46.6648 | 2.89403 | ||||||||
\(261\) | 6.10211 | 0.377711 | ||||||||
\(262\) | −13.8782 | −0.857396 | ||||||||
\(263\) | −24.5257 | −1.51232 | −0.756161 | − | 0.654386i | \(-0.772927\pi\) | ||||
−0.756161 | + | 0.654386i | \(0.772927\pi\) | |||||||
\(264\) | 3.91688 | 0.241067 | ||||||||
\(265\) | 10.9717 | 0.673984 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.10936 | −0.435086 | ||||||||
\(268\) | −27.4245 | −1.67522 | ||||||||
\(269\) | −20.3063 | −1.23810 | −0.619049 | − | 0.785353i | \(-0.712482\pi\) | ||||
−0.619049 | + | 0.785353i | \(0.712482\pi\) | |||||||
\(270\) | −8.24830 | −0.501976 | ||||||||
\(271\) | 10.3354 | 0.627829 | 0.313915 | − | 0.949451i | \(-0.398359\pi\) | ||||
0.313915 | + | 0.949451i | \(0.398359\pi\) | |||||||
\(272\) | 4.39215 | 0.266313 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −42.9627 | −2.59547 | ||||||||
\(275\) | 7.14349 | 0.430769 | ||||||||
\(276\) | 10.7966 | 0.649881 | ||||||||
\(277\) | 4.41311 | 0.265158 | 0.132579 | − | 0.991172i | \(-0.457674\pi\) | ||||
0.132579 | + | 0.991172i | \(0.457674\pi\) | |||||||
\(278\) | 14.1338 | 0.847687 | ||||||||
\(279\) | 1.10018 | 0.0658659 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.2364 | 1.26686 | 0.633429 | − | 0.773801i | \(-0.281647\pi\) | ||||
0.633429 | + | 0.773801i | \(0.281647\pi\) | |||||||
\(282\) | 25.7317 | 1.53230 | ||||||||
\(283\) | 14.7031 | 0.874010 | 0.437005 | − | 0.899459i | \(-0.356039\pi\) | ||||
0.437005 | + | 0.899459i | \(0.356039\pi\) | |||||||
\(284\) | 27.4867 | 1.63104 | ||||||||
\(285\) | −10.7120 | −0.634525 | ||||||||
\(286\) | −8.85577 | −0.523653 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.15463 | −0.185888 | ||||||||
\(289\) | −11.8724 | −0.698374 | ||||||||
\(290\) | −50.3321 | −2.95560 | ||||||||
\(291\) | 1.37040 | 0.0803344 | ||||||||
\(292\) | −30.8784 | −1.80702 | ||||||||
\(293\) | −3.42974 | −0.200367 | −0.100184 | − | 0.994969i | \(-0.531943\pi\) | ||||
−0.100184 | + | 0.994969i | \(0.531943\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −36.3015 | −2.11355 | ||||||||
\(296\) | 30.2592 | 1.75878 | ||||||||
\(297\) | 1.00968 | 0.0585874 | ||||||||
\(298\) | 6.69183 | 0.387648 | ||||||||
\(299\) | −10.9771 | −0.634823 | ||||||||
\(300\) | 25.7129 | 1.48453 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.15671 | 0.296736 | ||||||||
\(303\) | 3.16096 | 0.181593 | ||||||||
\(304\) | 5.97924 | 0.342933 | ||||||||
\(305\) | −9.96136 | −0.570386 | ||||||||
\(306\) | 5.37501 | 0.307269 | ||||||||
\(307\) | 19.0304 | 1.08612 | 0.543062 | − | 0.839693i | \(-0.317265\pi\) | ||||
0.543062 | + | 0.839693i | \(0.317265\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.03265 | 0.286297 | ||||||||
\(310\) | −9.07460 | −0.515402 | ||||||||
\(311\) | −22.3897 | −1.26961 | −0.634803 | − | 0.772674i | \(-0.718919\pi\) | ||||
−0.634803 | + | 0.772674i | \(0.718919\pi\) | |||||||
\(312\) | −14.3344 | −0.811526 | ||||||||
\(313\) | −29.2085 | −1.65096 | −0.825482 | − | 0.564429i | \(-0.809097\pi\) | ||||
−0.825482 | + | 0.564429i | \(0.809097\pi\) | |||||||
\(314\) | 23.5176 | 1.32717 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 29.9692 | 1.68590 | ||||||||
\(317\) | −14.5913 | −0.819527 | −0.409764 | − | 0.912192i | \(-0.634389\pi\) | ||||
−0.409764 | + | 0.912192i | \(0.634389\pi\) | |||||||
\(318\) | −7.49461 | −0.420277 | ||||||||
\(319\) | 6.16117 | 0.344959 | ||||||||
\(320\) | 39.5004 | 2.20814 | ||||||||
\(321\) | 8.80363 | 0.491371 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.98050 | 0.388405 | ||||||||
\(324\) | 3.63432 | 0.201907 | ||||||||
\(325\) | −26.1427 | −1.45014 | ||||||||
\(326\) | −25.3440 | −1.40368 | ||||||||
\(327\) | −0.819402 | −0.0453130 | ||||||||
\(328\) | −3.87933 | −0.214200 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −8.32813 | −0.458448 | ||||||||
\(331\) | 11.5685 | 0.635862 | 0.317931 | − | 0.948114i | \(-0.397012\pi\) | ||||
0.317931 | + | 0.948114i | \(0.397012\pi\) | |||||||
\(332\) | −45.3116 | −2.48680 | ||||||||
\(333\) | 7.80010 | 0.427443 | ||||||||
\(334\) | 52.7177 | 2.88458 | ||||||||
\(335\) | 26.2216 | 1.43264 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.96558 | 0.542860 | 0.271430 | − | 0.962458i | \(-0.412504\pi\) | ||||
0.271430 | + | 0.962458i | \(0.412504\pi\) | |||||||
\(338\) | 1.55133 | 0.0843811 | ||||||||
\(339\) | −3.73111 | −0.202646 | ||||||||
\(340\) | −28.5973 | −1.55091 | ||||||||
\(341\) | 1.11082 | 0.0601545 | ||||||||
\(342\) | 7.31725 | 0.395672 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 44.0732 | 2.37627 | ||||||||
\(345\) | −10.3231 | −0.555776 | ||||||||
\(346\) | −6.43797 | −0.346108 | ||||||||
\(347\) | 14.1125 | 0.757598 | 0.378799 | − | 0.925479i | \(-0.376337\pi\) | ||||
0.378799 | + | 0.925479i | \(0.376337\pi\) | |||||||
\(348\) | 22.1770 | 1.18881 | ||||||||
\(349\) | −8.09565 | −0.433350 | −0.216675 | − | 0.976244i | \(-0.569521\pi\) | ||||
−0.216675 | + | 0.976244i | \(0.569521\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.69507 | −0.197228 | ||||||||
\(352\) | −3.18516 | −0.169769 | ||||||||
\(353\) | −26.0876 | −1.38850 | −0.694252 | − | 0.719732i | \(-0.744265\pi\) | ||||
−0.694252 | + | 0.719732i | \(0.744265\pi\) | |||||||
\(354\) | 24.7971 | 1.31795 | ||||||||
\(355\) | −26.2811 | −1.39486 | ||||||||
\(356\) | −25.8377 | −1.36939 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −61.5318 | −3.25206 | ||||||||
\(359\) | 34.2480 | 1.80754 | 0.903770 | − | 0.428019i | \(-0.140788\pi\) | ||||
0.903770 | + | 0.428019i | \(0.140788\pi\) | |||||||
\(360\) | −13.4803 | −0.710477 | ||||||||
\(361\) | −9.49713 | −0.499849 | ||||||||
\(362\) | −35.4507 | −1.86325 | ||||||||
\(363\) | −9.98055 | −0.523843 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 29.5241 | 1.54536 | ||||||||
\(366\) | 6.80449 | 0.355676 | ||||||||
\(367\) | −18.9226 | −0.987751 | −0.493876 | − | 0.869532i | \(-0.664420\pi\) | ||||
−0.493876 | + | 0.869532i | \(0.664420\pi\) | |||||||
\(368\) | 5.76214 | 0.300372 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | −64.3376 | −3.34475 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.99839 | 0.207307 | ||||||||
\(373\) | −30.9953 | −1.60487 | −0.802437 | − | 0.596736i | \(-0.796464\pi\) | ||||
−0.802437 | + | 0.596736i | \(0.796464\pi\) | |||||||
\(374\) | 5.42703 | 0.280625 | ||||||||
\(375\) | −7.21052 | −0.372350 | ||||||||
\(376\) | 42.0538 | 2.16876 | ||||||||
\(377\) | −22.5477 | −1.16127 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.74457 | 0.0896124 | 0.0448062 | − | 0.998996i | \(-0.485733\pi\) | ||||
0.0448062 | + | 0.998996i | \(0.485733\pi\) | |||||||
\(380\) | −38.9309 | −1.99711 | ||||||||
\(381\) | −4.70586 | −0.241089 | ||||||||
\(382\) | −7.72969 | −0.395485 | ||||||||
\(383\) | 35.0490 | 1.79092 | 0.895461 | − | 0.445140i | \(-0.146846\pi\) | ||||
0.895461 | + | 0.445140i | \(0.146846\pi\) | |||||||
\(384\) | −20.6730 | −1.05496 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 51.6076 | 2.62676 | ||||||||
\(387\) | 11.3610 | 0.577514 | ||||||||
\(388\) | 4.98048 | 0.252845 | ||||||||
\(389\) | 28.5924 | 1.44969 | 0.724846 | − | 0.688911i | \(-0.241911\pi\) | ||||
0.724846 | + | 0.688911i | \(0.241911\pi\) | |||||||
\(390\) | 30.4781 | 1.54332 | ||||||||
\(391\) | 6.72704 | 0.340201 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.84671 | −0.294927 | ||||||||
\(394\) | 53.3475 | 2.68761 | ||||||||
\(395\) | −28.6547 | −1.44177 | ||||||||
\(396\) | 3.66949 | 0.184399 | ||||||||
\(397\) | −7.20191 | −0.361453 | −0.180727 | − | 0.983533i | \(-0.557845\pi\) | ||||
−0.180727 | + | 0.983533i | \(0.557845\pi\) | |||||||
\(398\) | −1.82555 | −0.0915067 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.7229 | 0.686146 | ||||||||
\(401\) | 2.25286 | 0.112502 | 0.0562512 | − | 0.998417i | \(-0.482085\pi\) | ||||
0.0562512 | + | 0.998417i | \(0.482085\pi\) | |||||||
\(402\) | −17.9117 | −0.893354 | ||||||||
\(403\) | −4.06523 | −0.202504 | ||||||||
\(404\) | 11.4879 | 0.571547 | ||||||||
\(405\) | −3.47491 | −0.172670 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.87559 | 0.390378 | ||||||||
\(408\) | 8.78448 | 0.434896 | ||||||||
\(409\) | 20.8350 | 1.03023 | 0.515113 | − | 0.857122i | \(-0.327750\pi\) | ||||
0.515113 | + | 0.857122i | \(0.327750\pi\) | |||||||
\(410\) | 8.24830 | 0.407355 | ||||||||
\(411\) | −18.0997 | −0.892792 | ||||||||
\(412\) | 18.2902 | 0.901095 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 7.05157 | 0.346566 | ||||||||
\(415\) | 43.3242 | 2.12670 | ||||||||
\(416\) | 11.6566 | 0.571510 | ||||||||
\(417\) | 5.95439 | 0.291588 | ||||||||
\(418\) | 7.38807 | 0.361362 | ||||||||
\(419\) | 36.6553 | 1.79073 | 0.895363 | − | 0.445336i | \(-0.146916\pi\) | ||||
0.895363 | + | 0.445336i | \(0.146916\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.8563 | −1.89374 | −0.946870 | − | 0.321616i | \(-0.895774\pi\) | ||||
−0.946870 | + | 0.321616i | \(0.895774\pi\) | |||||||
\(422\) | −15.1832 | −0.739107 | ||||||||
\(423\) | 10.8405 | 0.527082 | ||||||||
\(424\) | −12.2486 | −0.594843 | ||||||||
\(425\) | 16.0209 | 0.777127 | ||||||||
\(426\) | 17.9523 | 0.869793 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 31.9952 | 1.54655 | ||||||||
\(429\) | −3.73083 | −0.180126 | ||||||||
\(430\) | −93.7093 | −4.51906 | ||||||||
\(431\) | 5.46635 | 0.263305 | 0.131652 | − | 0.991296i | \(-0.457972\pi\) | ||||
0.131652 | + | 0.991296i | \(0.457972\pi\) | |||||||
\(432\) | 1.93963 | 0.0933204 | ||||||||
\(433\) | 13.4046 | 0.644184 | 0.322092 | − | 0.946708i | \(-0.395614\pi\) | ||||
0.322092 | + | 0.946708i | \(0.395614\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21.2043 | −1.01667 | ||||||||
\(436\) | −2.97797 | −0.142619 | ||||||||
\(437\) | 9.15783 | 0.438079 | ||||||||
\(438\) | −20.1675 | −0.963642 | ||||||||
\(439\) | −13.9165 | −0.664201 | −0.332100 | − | 0.943244i | \(-0.607757\pi\) | ||||
−0.332100 | + | 0.943244i | \(0.607757\pi\) | |||||||
\(440\) | −13.6108 | −0.648870 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −19.8611 | −0.944694 | ||||||||
\(443\) | 18.5861 | 0.883052 | 0.441526 | − | 0.897248i | \(-0.354437\pi\) | ||||
0.441526 | + | 0.897248i | \(0.354437\pi\) | |||||||
\(444\) | 28.3480 | 1.34534 | ||||||||
\(445\) | 24.7044 | 1.17110 | ||||||||
\(446\) | −32.1676 | −1.52318 | ||||||||
\(447\) | 2.81919 | 0.133343 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.8861 | −0.844095 | −0.422047 | − | 0.906574i | \(-0.638688\pi\) | ||||
−0.422047 | + | 0.906574i | \(0.638688\pi\) | |||||||
\(450\) | 16.7938 | 0.791666 | ||||||||
\(451\) | −1.00968 | −0.0475439 | ||||||||
\(452\) | −13.5600 | −0.637811 | ||||||||
\(453\) | 2.17246 | 0.102071 | ||||||||
\(454\) | 26.2981 | 1.23423 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 11.9587 | 0.560018 | ||||||||
\(457\) | −32.9497 | −1.54132 | −0.770662 | − | 0.637244i | \(-0.780074\pi\) | ||||
−0.770662 | + | 0.637244i | \(0.780074\pi\) | |||||||
\(458\) | −9.62930 | −0.449948 | ||||||||
\(459\) | 2.26443 | 0.105695 | ||||||||
\(460\) | −37.5173 | −1.74926 | ||||||||
\(461\) | 17.5230 | 0.816126 | 0.408063 | − | 0.912954i | \(-0.366204\pi\) | ||||
0.408063 | + | 0.912954i | \(0.366204\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.74652 | 0.0811677 | 0.0405839 | − | 0.999176i | \(-0.487078\pi\) | ||||
0.0405839 | + | 0.999176i | \(0.487078\pi\) | |||||||
\(464\) | 11.8358 | 0.549465 | ||||||||
\(465\) | −3.82302 | −0.177288 | ||||||||
\(466\) | −13.8469 | −0.641446 | ||||||||
\(467\) | −28.1306 | −1.30173 | −0.650865 | − | 0.759194i | \(-0.725593\pi\) | ||||
−0.650865 | + | 0.759194i | \(0.725593\pi\) | |||||||
\(468\) | −13.4291 | −0.620759 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −89.4156 | −4.12443 | ||||||||
\(471\) | 9.90769 | 0.456522 | ||||||||
\(472\) | 40.5263 | 1.86538 | ||||||||
\(473\) | 11.4710 | 0.527437 | ||||||||
\(474\) | 19.5737 | 0.899049 | ||||||||
\(475\) | 21.8100 | 1.00071 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.15739 | −0.144567 | ||||||||
\(478\) | 30.4360 | 1.39211 | ||||||||
\(479\) | 23.7456 | 1.08497 | 0.542483 | − | 0.840067i | \(-0.317484\pi\) | ||||
0.542483 | + | 0.840067i | \(0.317484\pi\) | |||||||
\(480\) | 10.9621 | 0.500347 | ||||||||
\(481\) | −28.8219 | −1.31417 | ||||||||
\(482\) | −7.50953 | −0.342050 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −36.2725 | −1.64875 | ||||||||
\(485\) | −4.76203 | −0.216233 | ||||||||
\(486\) | 2.37367 | 0.107672 | ||||||||
\(487\) | −9.71321 | −0.440147 | −0.220074 | − | 0.975483i | \(-0.570630\pi\) | ||||
−0.220074 | + | 0.975483i | \(0.570630\pi\) | |||||||
\(488\) | 11.1207 | 0.503410 | ||||||||
\(489\) | −10.6771 | −0.482837 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.4411 | 0.741977 | 0.370988 | − | 0.928638i | \(-0.379019\pi\) | ||||
0.370988 | + | 0.928638i | \(0.379019\pi\) | |||||||
\(492\) | −3.63432 | −0.163848 | ||||||||
\(493\) | 13.8178 | 0.622323 | ||||||||
\(494\) | −27.0378 | −1.21649 | ||||||||
\(495\) | −3.50854 | −0.157697 | ||||||||
\(496\) | 2.13393 | 0.0958165 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −29.5943 | −1.32615 | ||||||||
\(499\) | −41.1165 | −1.84063 | −0.920314 | − | 0.391180i | \(-0.872067\pi\) | ||||
−0.920314 | + | 0.391180i | \(0.872067\pi\) | |||||||
\(500\) | −26.2053 | −1.17194 | ||||||||
\(501\) | 22.2093 | 0.992240 | ||||||||
\(502\) | 32.8997 | 1.46838 | ||||||||
\(503\) | 14.0518 | 0.626537 | 0.313269 | − | 0.949665i | \(-0.398576\pi\) | ||||
0.313269 | + | 0.949665i | \(0.398576\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.9841 | −0.488785 | ||||||||
\(506\) | 7.11981 | 0.316514 | ||||||||
\(507\) | 0.653556 | 0.0290254 | ||||||||
\(508\) | −17.1026 | −0.758805 | ||||||||
\(509\) | 6.46752 | 0.286668 | 0.143334 | − | 0.989674i | \(-0.454218\pi\) | ||||
0.143334 | + | 0.989674i | \(0.454218\pi\) | |||||||
\(510\) | −18.6777 | −0.827062 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −21.1677 | −0.935490 | ||||||||
\(513\) | 3.08267 | 0.136103 | ||||||||
\(514\) | 63.6191 | 2.80612 | ||||||||
\(515\) | −17.4880 | −0.770614 | ||||||||
\(516\) | 41.2896 | 1.81767 | ||||||||
\(517\) | 10.9454 | 0.481378 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.71224 | −0.119054 | ||||||||
\(520\) | 49.8108 | 2.18435 | ||||||||
\(521\) | −24.9703 | −1.09397 | −0.546984 | − | 0.837143i | \(-0.684224\pi\) | ||||
−0.546984 | + | 0.837143i | \(0.684224\pi\) | |||||||
\(522\) | 14.4844 | 0.633966 | ||||||||
\(523\) | 14.3767 | 0.628648 | 0.314324 | − | 0.949316i | \(-0.398222\pi\) | ||||
0.314324 | + | 0.949316i | \(0.398222\pi\) | |||||||
\(524\) | −21.2488 | −0.928257 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −58.2160 | −2.53834 | ||||||||
\(527\) | 2.49127 | 0.108522 | ||||||||
\(528\) | 1.95840 | 0.0852284 | ||||||||
\(529\) | −14.1747 | −0.616290 | ||||||||
\(530\) | 26.0431 | 1.13124 | ||||||||
\(531\) | 10.4467 | 0.453350 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.69507 | 0.160051 | ||||||||
\(534\) | −16.8753 | −0.730265 | ||||||||
\(535\) | −30.5919 | −1.32260 | ||||||||
\(536\) | −29.2734 | −1.26442 | ||||||||
\(537\) | −25.9226 | −1.11864 | ||||||||
\(538\) | −48.2005 | −2.07807 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −12.6289 | −0.543463 | ||||||||
\(541\) | 19.9925 | 0.859543 | 0.429771 | − | 0.902938i | \(-0.358594\pi\) | ||||
0.429771 | + | 0.902938i | \(0.358594\pi\) | |||||||
\(542\) | 24.5328 | 1.05377 | ||||||||
\(543\) | −14.9349 | −0.640920 | ||||||||
\(544\) | −7.14343 | −0.306272 | ||||||||
\(545\) | 2.84735 | 0.121967 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.3349 | 1.08324 | 0.541621 | − | 0.840623i | \(-0.317811\pi\) | ||||
0.541621 | + | 0.840623i | \(0.317811\pi\) | |||||||
\(548\) | −65.7801 | −2.80998 | ||||||||
\(549\) | 2.86665 | 0.122346 | ||||||||
\(550\) | 16.9563 | 0.723019 | ||||||||
\(551\) | 18.8108 | 0.801368 | ||||||||
\(552\) | 11.5245 | 0.490516 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 10.4753 | 0.445052 | ||||||||
\(555\) | −27.1047 | −1.15053 | ||||||||
\(556\) | 21.6401 | 0.917746 | ||||||||
\(557\) | −25.8533 | −1.09544 | −0.547719 | − | 0.836662i | \(-0.684504\pi\) | ||||
−0.547719 | + | 0.836662i | \(0.684504\pi\) | |||||||
\(558\) | 2.61146 | 0.110552 | ||||||||
\(559\) | −41.9798 | −1.77556 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.28634 | 0.0965295 | ||||||||
\(562\) | 50.4082 | 2.12634 | ||||||||
\(563\) | 13.7843 | 0.580938 | 0.290469 | − | 0.956884i | \(-0.406189\pi\) | ||||
0.290469 | + | 0.956884i | \(0.406189\pi\) | |||||||
\(564\) | 39.3977 | 1.65894 | ||||||||
\(565\) | 12.9653 | 0.545454 | ||||||||
\(566\) | 34.9004 | 1.46697 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 29.3398 | 1.23107 | ||||||||
\(569\) | 46.5561 | 1.95173 | 0.975867 | − | 0.218365i | \(-0.0700722\pi\) | ||||
0.975867 | + | 0.218365i | \(0.0700722\pi\) | |||||||
\(570\) | −25.4268 | −1.06501 | ||||||||
\(571\) | −31.0198 | −1.29814 | −0.649069 | − | 0.760729i | \(-0.724841\pi\) | ||||
−0.649069 | + | 0.760729i | \(0.724841\pi\) | |||||||
\(572\) | −13.5590 | −0.566931 | ||||||||
\(573\) | −3.25643 | −0.136039 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.0181 | 0.876515 | ||||||||
\(576\) | −11.3673 | −0.473638 | ||||||||
\(577\) | −16.4966 | −0.686761 | −0.343380 | − | 0.939196i | \(-0.611572\pi\) | ||||
−0.343380 | + | 0.939196i | \(0.611572\pi\) | |||||||
\(578\) | −28.1811 | −1.17218 | ||||||||
\(579\) | 21.7417 | 0.903553 | ||||||||
\(580\) | −77.0632 | −3.19988 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.25289 | 0.134836 | ||||||||
\(583\) | −3.18795 | −0.132031 | ||||||||
\(584\) | −32.9602 | −1.36390 | ||||||||
\(585\) | 12.8401 | 0.530871 | ||||||||
\(586\) | −8.14107 | −0.336305 | ||||||||
\(587\) | 42.7305 | 1.76368 | 0.881838 | − | 0.471552i | \(-0.156306\pi\) | ||||
0.881838 | + | 0.471552i | \(0.156306\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.39149 | 0.139744 | ||||||||
\(590\) | −86.1678 | −3.54747 | ||||||||
\(591\) | 22.4747 | 0.924484 | ||||||||
\(592\) | 15.1293 | 0.621810 | ||||||||
\(593\) | 2.65943 | 0.109210 | 0.0546049 | − | 0.998508i | \(-0.482610\pi\) | ||||
0.0546049 | + | 0.998508i | \(0.482610\pi\) | |||||||
\(594\) | 2.39664 | 0.0983355 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.2458 | 0.419686 | ||||||||
\(597\) | −0.769084 | −0.0314765 | ||||||||
\(598\) | −26.0561 | −1.06551 | ||||||||
\(599\) | 31.5643 | 1.28968 | 0.644842 | − | 0.764316i | \(-0.276923\pi\) | ||||
0.644842 | + | 0.764316i | \(0.276923\pi\) | |||||||
\(600\) | 27.4464 | 1.12049 | ||||||||
\(601\) | −15.8856 | −0.647988 | −0.323994 | − | 0.946059i | \(-0.605026\pi\) | ||||
−0.323994 | + | 0.946059i | \(0.605026\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.54599 | −0.307296 | ||||||||
\(604\) | 7.89542 | 0.321260 | ||||||||
\(605\) | 34.6815 | 1.41001 | ||||||||
\(606\) | 7.50309 | 0.304792 | ||||||||
\(607\) | 23.0792 | 0.936757 | 0.468378 | − | 0.883528i | \(-0.344838\pi\) | ||||
0.468378 | + | 0.883528i | \(0.344838\pi\) | |||||||
\(608\) | −9.72468 | −0.394388 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −23.6450 | −0.957358 | ||||||||
\(611\) | −40.0564 | −1.62051 | ||||||||
\(612\) | 8.22965 | 0.332664 | ||||||||
\(613\) | −13.4943 | −0.545028 | −0.272514 | − | 0.962152i | \(-0.587855\pi\) | ||||
−0.272514 | + | 0.962152i | \(0.587855\pi\) | |||||||
\(614\) | 45.1720 | 1.82299 | ||||||||
\(615\) | 3.47491 | 0.140122 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.7047 | −0.591991 | −0.295995 | − | 0.955189i | \(-0.595651\pi\) | ||||
−0.295995 | + | 0.955189i | \(0.595651\pi\) | |||||||
\(618\) | 11.9459 | 0.480533 | ||||||||
\(619\) | 12.1213 | 0.487196 | 0.243598 | − | 0.969876i | \(-0.421672\pi\) | ||||
0.243598 | + | 0.969876i | \(0.421672\pi\) | |||||||
\(620\) | −13.8941 | −0.557999 | ||||||||
\(621\) | 2.97074 | 0.119212 | ||||||||
\(622\) | −53.1459 | −2.13096 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −7.16706 | −0.286912 | ||||||||
\(625\) | −10.3192 | −0.412767 | ||||||||
\(626\) | −69.3315 | −2.77104 | ||||||||
\(627\) | 3.11251 | 0.124302 | ||||||||
\(628\) | 36.0077 | 1.43686 | ||||||||
\(629\) | 17.6628 | 0.704261 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.11700 | −0.323132 | −0.161566 | − | 0.986862i | \(-0.551655\pi\) | ||||
−0.161566 | + | 0.986862i | \(0.551655\pi\) | |||||||
\(632\) | 31.9896 | 1.27248 | ||||||||
\(633\) | −6.39650 | −0.254238 | ||||||||
\(634\) | −34.6349 | −1.37553 | ||||||||
\(635\) | 16.3525 | 0.648927 | ||||||||
\(636\) | −11.4750 | −0.455012 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 14.6246 | 0.578993 | ||||||||
\(639\) | 7.56311 | 0.299192 | ||||||||
\(640\) | 71.8369 | 2.83960 | ||||||||
\(641\) | −17.4968 | −0.691083 | −0.345541 | − | 0.938403i | \(-0.612305\pi\) | ||||
−0.345541 | + | 0.938403i | \(0.612305\pi\) | |||||||
\(642\) | 20.8969 | 0.824736 | ||||||||
\(643\) | −43.4568 | −1.71377 | −0.856884 | − | 0.515510i | \(-0.827603\pi\) | ||||
−0.856884 | + | 0.515510i | \(0.827603\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −39.4786 | −1.55447 | ||||||||
\(646\) | 16.5694 | 0.651914 | ||||||||
\(647\) | −30.3127 | −1.19171 | −0.595857 | − | 0.803091i | \(-0.703187\pi\) | ||||
−0.595857 | + | 0.803091i | \(0.703187\pi\) | |||||||
\(648\) | 3.87933 | 0.152395 | ||||||||
\(649\) | 10.5478 | 0.414039 | ||||||||
\(650\) | −62.0542 | −2.43397 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −38.8042 | −1.51969 | ||||||||
\(653\) | 7.99710 | 0.312951 | 0.156475 | − | 0.987682i | \(-0.449987\pi\) | ||||
0.156475 | + | 0.987682i | \(0.449987\pi\) | |||||||
\(654\) | −1.94499 | −0.0760552 | ||||||||
\(655\) | 20.3168 | 0.793843 | ||||||||
\(656\) | −1.93963 | −0.0757298 | ||||||||
\(657\) | −8.49635 | −0.331474 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.9761 | −1.59620 | −0.798102 | − | 0.602523i | \(-0.794162\pi\) | ||||
−0.798102 | + | 0.602523i | \(0.794162\pi\) | |||||||
\(660\) | −12.7512 | −0.496338 | ||||||||
\(661\) | 44.8953 | 1.74622 | 0.873112 | − | 0.487519i | \(-0.162098\pi\) | ||||
0.873112 | + | 0.487519i | \(0.162098\pi\) | |||||||
\(662\) | 27.4598 | 1.06726 | ||||||||
\(663\) | −8.36723 | −0.324956 | ||||||||
\(664\) | −48.3664 | −1.87698 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 18.5149 | 0.717437 | ||||||||
\(667\) | 18.1278 | 0.701912 | ||||||||
\(668\) | 80.7158 | 3.12299 | ||||||||
\(669\) | −13.5518 | −0.523945 | ||||||||
\(670\) | 62.2416 | 2.40460 | ||||||||
\(671\) | 2.89439 | 0.111737 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.5146 | −0.752232 | −0.376116 | − | 0.926573i | \(-0.622741\pi\) | ||||
−0.376116 | + | 0.926573i | \(0.622741\pi\) | |||||||
\(674\) | 23.6550 | 0.911157 | ||||||||
\(675\) | 7.07502 | 0.272318 | ||||||||
\(676\) | 2.37523 | 0.0913550 | ||||||||
\(677\) | 0.111472 | 0.00428421 | 0.00214210 | − | 0.999998i | \(-0.499318\pi\) | ||||
0.00214210 | + | 0.999998i | \(0.499318\pi\) | |||||||
\(678\) | −8.85644 | −0.340129 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −30.5253 | −1.17059 | ||||||||
\(681\) | 11.0791 | 0.424551 | ||||||||
\(682\) | 2.63673 | 0.100966 | ||||||||
\(683\) | 7.36917 | 0.281973 | 0.140987 | − | 0.990011i | \(-0.454973\pi\) | ||||
0.140987 | + | 0.990011i | \(0.454973\pi\) | |||||||
\(684\) | 11.2034 | 0.428373 | ||||||||
\(685\) | 62.8949 | 2.40309 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.05671 | −0.154773 | ||||||||
\(688\) | 22.0362 | 0.840122 | ||||||||
\(689\) | 11.6668 | 0.444469 | ||||||||
\(690\) | −24.5036 | −0.932836 | ||||||||
\(691\) | −7.90027 | −0.300540 | −0.150270 | − | 0.988645i | \(-0.548014\pi\) | ||||
−0.150270 | + | 0.988645i | \(0.548014\pi\) | |||||||
\(692\) | −9.85715 | −0.374713 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 33.4984 | 1.27158 | ||||||||
\(695\) | −20.6910 | −0.784854 | ||||||||
\(696\) | 23.6721 | 0.897290 | ||||||||
\(697\) | −2.26443 | −0.0857714 | ||||||||
\(698\) | −19.2164 | −0.727352 | ||||||||
\(699\) | −5.83354 | −0.220645 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.7000 | −0.819596 | −0.409798 | − | 0.912176i | \(-0.634401\pi\) | ||||
−0.409798 | + | 0.912176i | \(0.634401\pi\) | |||||||
\(702\) | −8.77089 | −0.331036 | ||||||||
\(703\) | 24.0452 | 0.906880 | ||||||||
\(704\) | −11.4773 | −0.432567 | ||||||||
\(705\) | −37.6697 | −1.41872 | ||||||||
\(706\) | −61.9234 | −2.33052 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 37.9667 | 1.42688 | ||||||||
\(709\) | −1.67315 | −0.0628365 | −0.0314182 | − | 0.999506i | \(-0.510002\pi\) | ||||
−0.0314182 | + | 0.999506i | \(0.510002\pi\) | |||||||
\(710\) | −62.3828 | −2.34118 | ||||||||
\(711\) | 8.24616 | 0.309255 | ||||||||
\(712\) | −27.5796 | −1.03359 | ||||||||
\(713\) | 3.26835 | 0.122401 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.9643 | 0.484838 | ||||||||
\(716\) | −94.2111 | −3.52083 | ||||||||
\(717\) | 12.8223 | 0.478858 | ||||||||
\(718\) | 81.2935 | 3.03385 | ||||||||
\(719\) | 34.7636 | 1.29646 | 0.648232 | − | 0.761443i | \(-0.275509\pi\) | ||||
0.648232 | + | 0.761443i | \(0.275509\pi\) | |||||||
\(720\) | −6.74004 | −0.251186 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −22.5431 | −0.838966 | ||||||||
\(723\) | −3.16368 | −0.117658 | ||||||||
\(724\) | −54.2783 | −2.01724 | ||||||||
\(725\) | 43.1726 | 1.60339 | ||||||||
\(726\) | −23.6906 | −0.879239 | ||||||||
\(727\) | 48.8728 | 1.81259 | 0.906297 | − | 0.422642i | \(-0.138897\pi\) | ||||
0.906297 | + | 0.422642i | \(0.138897\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 70.0804 | 2.59379 | ||||||||
\(731\) | 25.7263 | 0.951520 | ||||||||
\(732\) | 10.4183 | 0.385072 | ||||||||
\(733\) | 43.0612 | 1.59050 | 0.795250 | − | 0.606281i | \(-0.207339\pi\) | ||||
0.795250 | + | 0.606281i | \(0.207339\pi\) | |||||||
\(734\) | −44.9160 | −1.65788 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.37159 | −0.345441 | ||||||||
\(737\) | −7.61901 | −0.280650 | ||||||||
\(738\) | −2.37367 | −0.0873761 | ||||||||
\(739\) | −46.9948 | −1.72873 | −0.864366 | − | 0.502862i | \(-0.832280\pi\) | ||||
−0.864366 | + | 0.502862i | \(0.832280\pi\) | |||||||
\(740\) | −98.5070 | −3.62119 | ||||||||
\(741\) | −11.3907 | −0.418448 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.9341 | −0.914745 | −0.457372 | − | 0.889275i | \(-0.651209\pi\) | ||||
−0.457372 | + | 0.889275i | \(0.651209\pi\) | |||||||
\(744\) | 4.26795 | 0.156471 | ||||||||
\(745\) | −9.79644 | −0.358914 | ||||||||
\(746\) | −73.5726 | −2.69368 | ||||||||
\(747\) | −12.4677 | −0.456170 | ||||||||
\(748\) | 8.30930 | 0.303818 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −17.1154 | −0.624967 | ||||||||
\(751\) | −13.1644 | −0.480375 | −0.240187 | − | 0.970727i | \(-0.577209\pi\) | ||||
−0.240187 | + | 0.970727i | \(0.577209\pi\) | |||||||
\(752\) | 21.0265 | 0.766758 | ||||||||
\(753\) | 13.8603 | 0.505096 | ||||||||
\(754\) | −53.5209 | −1.94912 | ||||||||
\(755\) | −7.54912 | −0.274741 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.3243 | −0.702353 | −0.351177 | − | 0.936309i | \(-0.614218\pi\) | ||||
−0.351177 | + | 0.936309i | \(0.614218\pi\) | |||||||
\(758\) | 4.14103 | 0.150409 | ||||||||
\(759\) | 2.99949 | 0.108875 | ||||||||
\(760\) | −41.5555 | −1.50738 | ||||||||
\(761\) | −43.6803 | −1.58341 | −0.791705 | − | 0.610903i | \(-0.790807\pi\) | ||||
−0.791705 | + | 0.610903i | \(0.790807\pi\) | |||||||
\(762\) | −11.1702 | −0.404652 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −11.8349 | −0.428171 | ||||||||
\(765\) | −7.86870 | −0.284493 | ||||||||
\(766\) | 83.1949 | 3.00595 | ||||||||
\(767\) | −38.6014 | −1.39382 | ||||||||
\(768\) | −26.3363 | −0.950329 | ||||||||
\(769\) | −53.1969 | −1.91833 | −0.959165 | − | 0.282848i | \(-0.908721\pi\) | ||||
−0.959165 | + | 0.282848i | \(0.908721\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.8020 | 0.965250 | ||||||||
\(772\) | 79.0161 | 2.84385 | ||||||||
\(773\) | −26.0683 | −0.937613 | −0.468807 | − | 0.883301i | \(-0.655316\pi\) | ||||
−0.468807 | + | 0.883301i | \(0.655316\pi\) | |||||||
\(774\) | 26.9674 | 0.969322 | ||||||||
\(775\) | 7.78378 | 0.279602 | ||||||||
\(776\) | 5.31625 | 0.190842 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 67.8690 | 2.43322 | ||||||||
\(779\) | −3.08267 | −0.110448 | ||||||||
\(780\) | 46.6648 | 1.67087 | ||||||||
\(781\) | 7.63630 | 0.273248 | ||||||||
\(782\) | 15.9678 | 0.571007 | ||||||||
\(783\) | 6.10211 | 0.218072 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −34.4283 | −1.22880 | ||||||||
\(786\) | −13.8782 | −0.495018 | ||||||||
\(787\) | −39.5826 | −1.41097 | −0.705483 | − | 0.708727i | \(-0.749270\pi\) | ||||
−0.705483 | + | 0.708727i | \(0.749270\pi\) | |||||||
\(788\) | 81.6800 | 2.90973 | ||||||||
\(789\) | −24.5257 | −0.873139 | ||||||||
\(790\) | −68.0168 | −2.41993 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.91688 | 0.139180 | ||||||||
\(793\) | −10.5925 | −0.376150 | ||||||||
\(794\) | −17.0950 | −0.606677 | ||||||||
\(795\) | 10.9717 | 0.389125 | ||||||||
\(796\) | −2.79510 | −0.0990695 | ||||||||
\(797\) | −27.2314 | −0.964584 | −0.482292 | − | 0.876011i | \(-0.660196\pi\) | ||||
−0.482292 | + | 0.876011i | \(0.660196\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.5475 | 0.868428 | ||||||||
\(800\) | −22.3190 | −0.789098 | ||||||||
\(801\) | −7.10936 | −0.251197 | ||||||||
\(802\) | 5.34755 | 0.188828 | ||||||||
\(803\) | −8.57857 | −0.302731 | ||||||||
\(804\) | −27.4245 | −0.967188 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.64953 | −0.339890 | ||||||||
\(807\) | −20.3063 | −0.714816 | ||||||||
\(808\) | 12.2624 | 0.431391 | ||||||||
\(809\) | −53.5166 | −1.88154 | −0.940771 | − | 0.339042i | \(-0.889897\pi\) | ||||
−0.940771 | + | 0.339042i | \(0.889897\pi\) | |||||||
\(810\) | −8.24830 | −0.289816 | ||||||||
\(811\) | −14.5348 | −0.510387 | −0.255194 | − | 0.966890i | \(-0.582139\pi\) | ||||
−0.255194 | + | 0.966890i | \(0.582139\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.3354 | 0.362477 | ||||||||
\(814\) | 18.6941 | 0.655226 | ||||||||
\(815\) | 37.1022 | 1.29963 | ||||||||
\(816\) | 4.39215 | 0.153756 | ||||||||
\(817\) | 35.0224 | 1.22528 | ||||||||
\(818\) | 49.4555 | 1.72917 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.6289 | 0.441022 | ||||||||
\(821\) | −40.8286 | −1.42493 | −0.712463 | − | 0.701710i | \(-0.752420\pi\) | ||||
−0.712463 | + | 0.701710i | \(0.752420\pi\) | |||||||
\(822\) | −42.9627 | −1.49850 | ||||||||
\(823\) | 7.47635 | 0.260609 | 0.130305 | − | 0.991474i | \(-0.458405\pi\) | ||||
0.130305 | + | 0.991474i | \(0.458405\pi\) | |||||||
\(824\) | 19.5233 | 0.680127 | ||||||||
\(825\) | 7.14349 | 0.248705 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.331933 | 0.0115424 | 0.00577122 | − | 0.999983i | \(-0.498163\pi\) | ||||
0.00577122 | + | 0.999983i | \(0.498163\pi\) | |||||||
\(828\) | 10.7966 | 0.375209 | ||||||||
\(829\) | −46.9778 | −1.63161 | −0.815803 | − | 0.578330i | \(-0.803705\pi\) | ||||
−0.815803 | + | 0.578330i | \(0.803705\pi\) | |||||||
\(830\) | 102.837 | 3.56954 | ||||||||
\(831\) | 4.41311 | 0.153089 | ||||||||
\(832\) | 42.0030 | 1.45619 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 14.1338 | 0.489412 | ||||||||
\(835\) | −77.1755 | −2.67077 | ||||||||
\(836\) | 11.3118 | 0.391228 | ||||||||
\(837\) | 1.10018 | 0.0380277 | ||||||||
\(838\) | 87.0076 | 3.00563 | ||||||||
\(839\) | 34.8772 | 1.20409 | 0.602047 | − | 0.798461i | \(-0.294352\pi\) | ||||
0.602047 | + | 0.798461i | \(0.294352\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.23579 | 0.283993 | ||||||||
\(842\) | −92.2321 | −3.17853 | ||||||||
\(843\) | 21.2364 | 0.731421 | ||||||||
\(844\) | −23.2469 | −0.800192 | ||||||||
\(845\) | −2.27105 | −0.0781265 | ||||||||
\(846\) | 25.7317 | 0.884676 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.12416 | −0.210305 | ||||||||
\(849\) | 14.7031 | 0.504610 | ||||||||
\(850\) | 38.0283 | 1.30436 | ||||||||
\(851\) | 23.1721 | 0.794329 | ||||||||
\(852\) | 27.4867 | 0.941680 | ||||||||
\(853\) | −38.5842 | −1.32110 | −0.660549 | − | 0.750783i | \(-0.729677\pi\) | ||||
−0.660549 | + | 0.750783i | \(0.729677\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.7120 | −0.366343 | ||||||||
\(856\) | 34.1522 | 1.16730 | ||||||||
\(857\) | −49.3368 | −1.68531 | −0.842656 | − | 0.538452i | \(-0.819009\pi\) | ||||
−0.842656 | + | 0.538452i | \(0.819009\pi\) | |||||||
\(858\) | −8.85577 | −0.302331 | ||||||||
\(859\) | −14.0395 | −0.479021 | −0.239511 | − | 0.970894i | \(-0.576987\pi\) | ||||
−0.239511 | + | 0.970894i | \(0.576987\pi\) | |||||||
\(860\) | −143.478 | −4.89255 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.9753 | 0.441941 | ||||||||
\(863\) | −41.4234 | −1.41007 | −0.705034 | − | 0.709174i | \(-0.749068\pi\) | ||||
−0.705034 | + | 0.709174i | \(0.749068\pi\) | |||||||
\(864\) | −3.15463 | −0.107323 | ||||||||
\(865\) | 9.42481 | 0.320453 | ||||||||
\(866\) | 31.8181 | 1.08122 | ||||||||
\(867\) | −11.8724 | −0.403206 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.32597 | 0.282439 | ||||||||
\(870\) | −50.3321 | −1.70642 | ||||||||
\(871\) | 27.8830 | 0.944778 | ||||||||
\(872\) | −3.17873 | −0.107645 | ||||||||
\(873\) | 1.37040 | 0.0463811 | ||||||||
\(874\) | 21.7377 | 0.735288 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −30.8784 | −1.04329 | ||||||||
\(877\) | 11.2172 | 0.378779 | 0.189389 | − | 0.981902i | \(-0.439349\pi\) | ||||
0.189389 | + | 0.981902i | \(0.439349\pi\) | |||||||
\(878\) | −33.0333 | −1.11482 | ||||||||
\(879\) | −3.42974 | −0.115682 | ||||||||
\(880\) | −6.80527 | −0.229406 | ||||||||
\(881\) | 13.9187 | 0.468932 | 0.234466 | − | 0.972124i | \(-0.424666\pi\) | ||||
0.234466 | + | 0.972124i | \(0.424666\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.1531 | 1.65413 | 0.827066 | − | 0.562104i | \(-0.190008\pi\) | ||||
0.827066 | + | 0.562104i | \(0.190008\pi\) | |||||||
\(884\) | −30.4092 | −1.02277 | ||||||||
\(885\) | −36.3015 | −1.22026 | ||||||||
\(886\) | 44.1173 | 1.48215 | ||||||||
\(887\) | −14.7228 | −0.494343 | −0.247172 | − | 0.968972i | \(-0.579501\pi\) | ||||
−0.247172 | + | 0.968972i | \(0.579501\pi\) | |||||||
\(888\) | 30.2592 | 1.01543 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 58.6402 | 1.96562 | ||||||||
\(891\) | 1.00968 | 0.0338255 | ||||||||
\(892\) | −49.2517 | −1.64907 | ||||||||
\(893\) | 33.4177 | 1.11828 | ||||||||
\(894\) | 6.69183 | 0.223808 | ||||||||
\(895\) | 90.0789 | 3.01101 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.9771 | −0.366515 | ||||||||
\(898\) | −42.4556 | −1.41676 | ||||||||
\(899\) | 6.71341 | 0.223905 | ||||||||
\(900\) | 25.7129 | 0.857096 | ||||||||
\(901\) | −7.14969 | −0.238191 | ||||||||
\(902\) | −2.39664 | −0.0797995 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.4742 | −0.481406 | ||||||||
\(905\) | 51.8976 | 1.72514 | ||||||||
\(906\) | 5.15671 | 0.171320 | ||||||||
\(907\) | −26.6311 | −0.884271 | −0.442136 | − | 0.896948i | \(-0.645779\pi\) | ||||
−0.442136 | + | 0.896948i | \(0.645779\pi\) | |||||||
\(908\) | 40.2649 | 1.33624 | ||||||||
\(909\) | 3.16096 | 0.104843 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.5241 | 0.746257 | 0.373129 | − | 0.927780i | \(-0.378285\pi\) | ||||
0.373129 | + | 0.927780i | \(0.378285\pi\) | |||||||
\(912\) | 5.97924 | 0.197992 | ||||||||
\(913\) | −12.5884 | −0.416614 | ||||||||
\(914\) | −78.2119 | −2.58702 | ||||||||
\(915\) | −9.96136 | −0.329312 | ||||||||
\(916\) | −14.7434 | −0.487135 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.37501 | 0.177402 | ||||||||
\(919\) | 48.4583 | 1.59849 | 0.799247 | − | 0.601003i | \(-0.205232\pi\) | ||||
0.799247 | + | 0.601003i | \(0.205232\pi\) | |||||||
\(920\) | −40.0467 | −1.32030 | ||||||||
\(921\) | 19.0304 | 0.627074 | ||||||||
\(922\) | 41.5938 | 1.36982 | ||||||||
\(923\) | −27.9462 | −0.919861 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 55.1859 | 1.81450 | ||||||||
\(926\) | 4.14567 | 0.136235 | ||||||||
\(927\) | 5.03265 | 0.165294 | ||||||||
\(928\) | −19.2499 | −0.631908 | ||||||||
\(929\) | −28.9304 | −0.949177 | −0.474588 | − | 0.880208i | \(-0.657403\pi\) | ||||
−0.474588 | + | 0.880208i | \(0.657403\pi\) | |||||||
\(930\) | −9.07460 | −0.297568 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −21.2009 | −0.694460 | ||||||||
\(933\) | −22.3897 | −0.733007 | ||||||||
\(934\) | −66.7728 | −2.18487 | ||||||||
\(935\) | −7.94485 | −0.259824 | ||||||||
\(936\) | −14.3344 | −0.468535 | ||||||||
\(937\) | 16.6500 | 0.543933 | 0.271967 | − | 0.962307i | \(-0.412326\pi\) | ||||
0.271967 | + | 0.962307i | \(0.412326\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.2085 | −0.953184 | ||||||||
\(940\) | −136.904 | −4.46531 | ||||||||
\(941\) | 48.0871 | 1.56759 | 0.783797 | − | 0.621018i | \(-0.213281\pi\) | ||||
0.783797 | + | 0.621018i | \(0.213281\pi\) | |||||||
\(942\) | 23.5176 | 0.766245 | ||||||||
\(943\) | −2.97074 | −0.0967407 | ||||||||
\(944\) | 20.2628 | 0.659497 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27.2284 | 0.885270 | ||||||||
\(947\) | 57.4521 | 1.86694 | 0.933471 | − | 0.358653i | \(-0.116764\pi\) | ||||
0.933471 | + | 0.358653i | \(0.116764\pi\) | |||||||
\(948\) | 29.9692 | 0.973353 | ||||||||
\(949\) | 31.3946 | 1.01911 | ||||||||
\(950\) | 51.7697 | 1.67963 | ||||||||
\(951\) | −14.5913 | −0.473154 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.9002 | −1.45446 | −0.727230 | − | 0.686393i | \(-0.759193\pi\) | ||||
−0.727230 | + | 0.686393i | \(0.759193\pi\) | |||||||
\(954\) | −7.49461 | −0.242647 | ||||||||
\(955\) | 11.3158 | 0.366171 | ||||||||
\(956\) | 46.6004 | 1.50716 | ||||||||
\(957\) | 6.16117 | 0.199162 | ||||||||
\(958\) | 56.3643 | 1.82105 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 39.5004 | 1.27487 | ||||||||
\(961\) | −29.7896 | −0.960955 | ||||||||
\(962\) | −68.4138 | −2.20575 | ||||||||
\(963\) | 8.80363 | 0.283693 | ||||||||
\(964\) | −11.4978 | −0.370319 | ||||||||
\(965\) | −75.5504 | −2.43205 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.1975 | 0.938928 | 0.469464 | − | 0.882952i | \(-0.344447\pi\) | ||||
0.469464 | + | 0.882952i | \(0.344447\pi\) | |||||||
\(968\) | −38.7179 | −1.24444 | ||||||||
\(969\) | 6.98050 | 0.224246 | ||||||||
\(970\) | −11.3035 | −0.362933 | ||||||||
\(971\) | −13.4009 | −0.430057 | −0.215028 | − | 0.976608i | \(-0.568984\pi\) | ||||
−0.215028 | + | 0.976608i | \(0.568984\pi\) | |||||||
\(972\) | 3.63432 | 0.116571 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −23.0560 | −0.738761 | ||||||||
\(975\) | −26.1427 | −0.837237 | ||||||||
\(976\) | 5.56024 | 0.177979 | ||||||||
\(977\) | 23.3819 | 0.748052 | 0.374026 | − | 0.927418i | \(-0.377977\pi\) | ||||
0.374026 | + | 0.927418i | \(0.377977\pi\) | |||||||
\(978\) | −25.3440 | −0.810413 | ||||||||
\(979\) | −7.17817 | −0.229415 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.819402 | −0.0261615 | ||||||||
\(982\) | 39.0258 | 1.24536 | ||||||||
\(983\) | 48.9655 | 1.56176 | 0.780878 | − | 0.624683i | \(-0.214772\pi\) | ||||
0.780878 | + | 0.624683i | \(0.214772\pi\) | |||||||
\(984\) | −3.87933 | −0.123669 | ||||||||
\(985\) | −78.0975 | −2.48839 | ||||||||
\(986\) | 32.7989 | 1.04453 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −41.3974 | −1.31703 | ||||||||
\(989\) | 33.7507 | 1.07321 | ||||||||
\(990\) | −8.32813 | −0.264685 | ||||||||
\(991\) | −11.6616 | −0.370443 | −0.185221 | − | 0.982697i | \(-0.559300\pi\) | ||||
−0.185221 | + | 0.982697i | \(0.559300\pi\) | |||||||
\(992\) | −3.47065 | −0.110193 | ||||||||
\(993\) | 11.5685 | 0.367115 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.67250 | 0.0847240 | ||||||||
\(996\) | −45.3116 | −1.43575 | ||||||||
\(997\) | −0.480867 | −0.0152292 | −0.00761460 | − | 0.999971i | \(-0.502424\pi\) | ||||
−0.00761460 | + | 0.999971i | \(0.502424\pi\) | |||||||
\(998\) | −97.5971 | −3.08938 | ||||||||
\(999\) | 7.80010 | 0.246784 |
(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 | 6027.2.a.bo.1.20 | yes | 24 | |
7.6 | odd | 2 | 6027.2.a.bn.1.20 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bn.1.20 | ✓ | 24 | 7.6 | odd | 2 | ||
6027.2.a.bo.1.20 | yes | 24 | 1.1 | even | 1 | trivial |