Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3762,2,Mod(1,3762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3762, 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("3762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3762 = 2 \cdot 3^{2} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3762.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: | \(30.0397212404\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.7578576.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 12x^{3} + 14x^{2} + 35x - 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.314438\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3762.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.685562 | −0.306592 | −0.153296 | − | 0.988180i | \(-0.548989\pi\) | ||||
−0.153296 | + | 0.988180i | \(0.548989\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.816139 | −0.308471 | −0.154236 | − | 0.988034i | \(-0.549292\pi\) | ||||
−0.154236 | + | 0.988034i | \(0.549292\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.685562 | 0.216794 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.21557 | −1.16919 | −0.584594 | − | 0.811326i | \(-0.698746\pi\) | ||||
−0.584594 | + | 0.811326i | \(0.698746\pi\) | |||||||
\(14\) | 0.816139 | 0.218122 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.97049 | 1.20552 | 0.602761 | − | 0.797922i | \(-0.294067\pi\) | ||||
0.602761 | + | 0.797922i | \(0.294067\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −0.685562 | −0.153296 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −6.21557 | −1.29604 | −0.648018 | − | 0.761625i | \(-0.724402\pi\) | ||||
−0.648018 | + | 0.761625i | \(0.724402\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.53001 | −0.906001 | ||||||||
\(26\) | 4.21557 | 0.826741 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.816139 | −0.154236 | ||||||||
\(29\) | −6.90113 | −1.28151 | −0.640754 | − | 0.767747i | \(-0.721378\pi\) | ||||
−0.640754 | + | 0.767747i | \(0.721378\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.10107 | 1.63460 | 0.817300 | − | 0.576212i | \(-0.195470\pi\) | ||||
0.817300 | + | 0.576212i | \(0.195470\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.97049 | −0.852432 | ||||||||
\(35\) | 0.559513 | 0.0945750 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.9294 | 1.79679 | 0.898394 | − | 0.439191i | \(-0.144735\pi\) | ||||
0.898394 | + | 0.439191i | \(0.144735\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.685562 | 0.108397 | ||||||||
\(41\) | −3.70164 | −0.578099 | −0.289050 | − | 0.957314i | \(-0.593339\pi\) | ||||
−0.289050 | + | 0.957314i | \(0.593339\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.53001 | 1.14832 | 0.574158 | − | 0.818745i | \(-0.305330\pi\) | ||||
0.574158 | + | 0.818745i | \(0.305330\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.21557 | 0.916435 | ||||||||
\(47\) | −6.21557 | −0.906634 | −0.453317 | − | 0.891349i | \(-0.649759\pi\) | ||||
−0.453317 | + | 0.891349i | \(0.649759\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.33392 | −0.904845 | ||||||||
\(50\) | 4.53001 | 0.640639 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.21557 | −0.584594 | ||||||||
\(53\) | −0.885502 | −0.121633 | −0.0608165 | − | 0.998149i | \(-0.519370\pi\) | ||||
−0.0608165 | + | 0.998149i | \(0.519370\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.685562 | 0.0924411 | ||||||||
\(56\) | 0.816139 | 0.109061 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.90113 | 0.906163 | ||||||||
\(59\) | −1.93064 | −0.251347 | −0.125674 | − | 0.992072i | \(-0.540109\pi\) | ||||
−0.125674 | + | 0.992072i | \(0.540109\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.0478 | 1.79863 | 0.899317 | − | 0.437297i | \(-0.144064\pi\) | ||||
0.899317 | + | 0.437297i | \(0.144064\pi\) | |||||||
\(62\) | −9.10107 | −1.15584 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.89003 | 0.358464 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.34162 | −0.530413 | −0.265206 | − | 0.964192i | \(-0.585440\pi\) | ||||
−0.265206 | + | 0.964192i | \(0.585440\pi\) | |||||||
\(68\) | 4.97049 | 0.602761 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.559513 | −0.0668746 | ||||||||
\(71\) | −2.44842 | −0.290573 | −0.145287 | − | 0.989390i | \(-0.546410\pi\) | ||||
−0.145287 | + | 0.989390i | \(0.546410\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.96279 | 1.16606 | 0.583028 | − | 0.812452i | \(-0.301868\pi\) | ||||
0.583028 | + | 0.812452i | \(0.301868\pi\) | |||||||
\(74\) | −10.9294 | −1.27052 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0.816139 | 0.0930076 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.21897 | −0.587180 | −0.293590 | − | 0.955931i | \(-0.594850\pi\) | ||||
−0.293590 | + | 0.955931i | \(0.594850\pi\) | |||||||
\(80\) | −0.685562 | −0.0766481 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.70164 | 0.408778 | ||||||||
\(83\) | −3.70164 | −0.406308 | −0.203154 | − | 0.979147i | \(-0.565119\pi\) | ||||
−0.203154 | + | 0.979147i | \(0.565119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.40758 | −0.369604 | ||||||||
\(86\) | −7.53001 | −0.811981 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 4.41098 | 0.467563 | 0.233781 | − | 0.972289i | \(-0.424890\pi\) | ||||
0.233781 | + | 0.972289i | \(0.424890\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.44049 | 0.360661 | ||||||||
\(92\) | −6.21557 | −0.648018 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.21557 | 0.641087 | ||||||||
\(95\) | −0.685562 | −0.0703371 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.12937 | −0.723878 | −0.361939 | − | 0.932202i | \(-0.617885\pi\) | ||||
−0.361939 | + | 0.932202i | \(0.617885\pi\) | |||||||
\(98\) | 6.33392 | 0.639822 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.53001 | −0.453001 | ||||||||
\(101\) | 15.8306 | 1.57520 | 0.787600 | − | 0.616187i | \(-0.211323\pi\) | ||||
0.787600 | + | 0.616187i | \(0.211323\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.8999 | 1.56667 | 0.783333 | − | 0.621602i | \(-0.213518\pi\) | ||||
0.783333 | + | 0.621602i | \(0.213518\pi\) | |||||||
\(104\) | 4.21557 | 0.413370 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.885502 | 0.0860076 | ||||||||
\(107\) | 16.2350 | 1.56950 | 0.784751 | − | 0.619812i | \(-0.212791\pi\) | ||||
0.784751 | + | 0.619812i | \(0.212791\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.98657 | −0.573410 | −0.286705 | − | 0.958019i | \(-0.592560\pi\) | ||||
−0.286705 | + | 0.958019i | \(0.592560\pi\) | |||||||
\(110\) | −0.685562 | −0.0653657 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.816139 | −0.0771178 | ||||||||
\(113\) | 7.50819 | 0.706312 | 0.353156 | − | 0.935565i | \(-0.385109\pi\) | ||||
0.353156 | + | 0.935565i | \(0.385109\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.26115 | 0.397355 | ||||||||
\(116\) | −6.90113 | −0.640754 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.93064 | 0.177729 | ||||||||
\(119\) | −4.05661 | −0.371869 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −14.0478 | −1.27183 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.10107 | 0.817300 | ||||||||
\(125\) | 6.53341 | 0.584366 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.31784 | 0.738089 | 0.369044 | − | 0.929412i | \(-0.379685\pi\) | ||||
0.369044 | + | 0.929412i | \(0.379685\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.89003 | −0.253472 | ||||||||
\(131\) | 6.44389 | 0.563005 | 0.281503 | − | 0.959560i | \(-0.409167\pi\) | ||||
0.281503 | + | 0.959560i | \(0.409167\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.816139 | −0.0707682 | ||||||||
\(134\) | 4.34162 | 0.375058 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.97049 | −0.426216 | ||||||||
\(137\) | −10.9444 | −0.935042 | −0.467521 | − | 0.883982i | \(-0.654853\pi\) | ||||
−0.467521 | + | 0.883982i | \(0.654853\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.1439 | −1.53894 | −0.769472 | − | 0.638681i | \(-0.779480\pi\) | ||||
−0.769472 | + | 0.638681i | \(0.779480\pi\) | |||||||
\(140\) | 0.559513 | 0.0472875 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.44842 | 0.205466 | ||||||||
\(143\) | 4.21557 | 0.352523 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.73115 | 0.392901 | ||||||||
\(146\) | −9.96279 | −0.824527 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.9294 | 0.898394 | ||||||||
\(149\) | −7.66058 | −0.627579 | −0.313790 | − | 0.949493i | \(-0.601599\pi\) | ||||
−0.313790 | + | 0.949493i | \(0.601599\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.0033 | 0.895438 | 0.447719 | − | 0.894174i | \(-0.352237\pi\) | ||||
0.447719 | + | 0.894174i | \(0.352237\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.816139 | −0.0657663 | ||||||||
\(155\) | −6.23934 | −0.501156 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.74225 | 0.378472 | 0.189236 | − | 0.981932i | \(-0.439399\pi\) | ||||
0.189236 | + | 0.981932i | \(0.439399\pi\) | |||||||
\(158\) | 5.21897 | 0.415199 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.685562 | 0.0541984 | ||||||||
\(161\) | 5.07276 | 0.399790 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.07276 | 0.553982 | 0.276991 | − | 0.960873i | \(-0.410663\pi\) | ||||
0.276991 | + | 0.960873i | \(0.410663\pi\) | |||||||
\(164\) | −3.70164 | −0.289050 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.70164 | 0.287303 | ||||||||
\(167\) | 12.6357 | 0.977778 | 0.488889 | − | 0.872346i | \(-0.337402\pi\) | ||||
0.488889 | + | 0.872346i | \(0.337402\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.77100 | 0.367000 | ||||||||
\(170\) | 3.40758 | 0.261349 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.53001 | 0.574158 | ||||||||
\(173\) | 19.7321 | 1.50021 | 0.750104 | − | 0.661320i | \(-0.230004\pi\) | ||||
0.750104 | + | 0.661320i | \(0.230004\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.69711 | 0.279475 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.41098 | −0.330617 | ||||||||
\(179\) | 2.89003 | 0.216011 | 0.108006 | − | 0.994150i | \(-0.465554\pi\) | ||||
0.108006 | + | 0.994150i | \(0.465554\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.92943 | −0.515061 | −0.257530 | − | 0.966270i | \(-0.582909\pi\) | ||||
−0.257530 | + | 0.966270i | \(0.582909\pi\) | |||||||
\(182\) | −3.44049 | −0.255026 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.21557 | 0.458218 | ||||||||
\(185\) | −7.49280 | −0.550882 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.97049 | −0.363478 | ||||||||
\(188\) | −6.21557 | −0.453317 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.685562 | 0.0497359 | ||||||||
\(191\) | −7.35089 | −0.531892 | −0.265946 | − | 0.963988i | \(-0.585684\pi\) | ||||
−0.265946 | + | 0.963988i | \(0.585684\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.00770 | 0.360462 | 0.180231 | − | 0.983624i | \(-0.442315\pi\) | ||||
0.180231 | + | 0.983624i | \(0.442315\pi\) | |||||||
\(194\) | 7.12937 | 0.511859 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.33392 | −0.452423 | ||||||||
\(197\) | −17.6016 | −1.25406 | −0.627030 | − | 0.778995i | \(-0.715730\pi\) | ||||
−0.627030 | + | 0.778995i | \(0.715730\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.90453 | 0.276785 | 0.138392 | − | 0.990377i | \(-0.455807\pi\) | ||||
0.138392 | + | 0.990377i | \(0.455807\pi\) | |||||||
\(200\) | 4.53001 | 0.320320 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.8306 | −1.11383 | ||||||||
\(203\) | 5.63228 | 0.395308 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.53770 | 0.177241 | ||||||||
\(206\) | −15.8999 | −1.10780 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.21557 | −0.292297 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.69569 | −0.667479 | −0.333739 | − | 0.942665i | \(-0.608311\pi\) | ||||
−0.333739 | + | 0.942665i | \(0.608311\pi\) | |||||||
\(212\) | −0.885502 | −0.0608165 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −16.2350 | −1.10980 | ||||||||
\(215\) | −5.16228 | −0.352065 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.42773 | −0.504227 | ||||||||
\(218\) | 5.98657 | 0.405462 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.685562 | 0.0462206 | ||||||||
\(221\) | −20.9534 | −1.40948 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.4756 | 1.17025 | 0.585126 | − | 0.810942i | \(-0.301045\pi\) | ||||
0.585126 | + | 0.810942i | \(0.301045\pi\) | |||||||
\(224\) | 0.816139 | 0.0545306 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.50819 | −0.499438 | ||||||||
\(227\) | 17.5622 | 1.16564 | 0.582821 | − | 0.812601i | \(-0.301949\pi\) | ||||
0.582821 | + | 0.812601i | \(0.301949\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.1110 | 1.32897 | 0.664485 | − | 0.747302i | \(-0.268651\pi\) | ||||
0.664485 | + | 0.747302i | \(0.268651\pi\) | |||||||
\(230\) | −4.26115 | −0.280972 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.90113 | 0.453081 | ||||||||
\(233\) | −16.7244 | −1.09565 | −0.547827 | − | 0.836591i | \(-0.684545\pi\) | ||||
−0.547827 | + | 0.836591i | \(0.684545\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.26115 | 0.277967 | ||||||||
\(236\) | −1.93064 | −0.125674 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.05661 | 0.262951 | ||||||||
\(239\) | 16.7444 | 1.08311 | 0.541554 | − | 0.840666i | \(-0.317836\pi\) | ||||
0.541554 | + | 0.840666i | \(0.317836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.6846 | −1.13916 | −0.569582 | − | 0.821934i | \(-0.692895\pi\) | ||||
−0.569582 | + | 0.821934i | \(0.692895\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.0478 | 0.899317 | ||||||||
\(245\) | 4.34229 | 0.277419 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.21557 | −0.268230 | ||||||||
\(248\) | −9.10107 | −0.577918 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.53341 | −0.413209 | ||||||||
\(251\) | 15.4076 | 0.972518 | 0.486259 | − | 0.873815i | \(-0.338361\pi\) | ||||
0.486259 | + | 0.873815i | \(0.338361\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.21557 | 0.390769 | ||||||||
\(254\) | −8.31784 | −0.521908 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −30.0087 | −1.87189 | −0.935945 | − | 0.352145i | \(-0.885452\pi\) | ||||
−0.935945 | + | 0.352145i | \(0.885452\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.91993 | −0.554258 | ||||||||
\(260\) | 2.89003 | 0.179232 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.44389 | −0.398105 | ||||||||
\(263\) | 7.42124 | 0.457613 | 0.228807 | − | 0.973472i | \(-0.426518\pi\) | ||||
0.228807 | + | 0.973472i | \(0.426518\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.607066 | 0.0372918 | ||||||||
\(266\) | 0.816139 | 0.0500407 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.34162 | −0.265206 | ||||||||
\(269\) | −5.43001 | −0.331073 | −0.165537 | − | 0.986204i | \(-0.552936\pi\) | ||||
−0.165537 | + | 0.986204i | \(0.552936\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.72496 | 0.530004 | 0.265002 | − | 0.964248i | \(-0.414627\pi\) | ||||
0.265002 | + | 0.964248i | \(0.414627\pi\) | |||||||
\(272\) | 4.97049 | 0.301380 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.9444 | 0.661174 | ||||||||
\(275\) | 4.53001 | 0.273170 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.1078 | 1.50858 | 0.754291 | − | 0.656541i | \(-0.227981\pi\) | ||||
0.754291 | + | 0.656541i | \(0.227981\pi\) | |||||||
\(278\) | 18.1439 | 1.08820 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.559513 | −0.0334373 | ||||||||
\(281\) | 28.7720 | 1.71639 | 0.858197 | − | 0.513321i | \(-0.171585\pi\) | ||||
0.858197 | + | 0.513321i | \(0.171585\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.6517 | 0.811508 | 0.405754 | − | 0.913982i | \(-0.367009\pi\) | ||||
0.405754 | + | 0.913982i | \(0.367009\pi\) | |||||||
\(284\) | −2.44842 | −0.145287 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.21557 | −0.249272 | ||||||||
\(287\) | 3.02105 | 0.178327 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.70579 | 0.453282 | ||||||||
\(290\) | −4.73115 | −0.277823 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.96279 | 0.583028 | ||||||||
\(293\) | −1.87328 | −0.109438 | −0.0547190 | − | 0.998502i | \(-0.517426\pi\) | ||||
−0.0547190 | + | 0.998502i | \(0.517426\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.32357 | 0.0770612 | ||||||||
\(296\) | −10.9294 | −0.635260 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.66058 | 0.443766 | ||||||||
\(299\) | 26.2021 | 1.51531 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.14553 | −0.354222 | ||||||||
\(302\) | −11.0033 | −0.633170 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −9.63062 | −0.551448 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.06001 | −0.517082 | −0.258541 | − | 0.966000i | \(-0.583242\pi\) | ||||
−0.258541 | + | 0.966000i | \(0.583242\pi\) | |||||||
\(308\) | 0.816139 | 0.0465038 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.23934 | 0.354371 | ||||||||
\(311\) | 15.1378 | 0.858383 | 0.429192 | − | 0.903213i | \(-0.358798\pi\) | ||||
0.429192 | + | 0.903213i | \(0.358798\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.0849 | 1.13526 | 0.567632 | − | 0.823283i | \(-0.307860\pi\) | ||||
0.567632 | + | 0.823283i | \(0.307860\pi\) | |||||||
\(314\) | −4.74225 | −0.267620 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.21897 | −0.293590 | ||||||||
\(317\) | 23.4146 | 1.31510 | 0.657548 | − | 0.753413i | \(-0.271594\pi\) | ||||
0.657548 | + | 0.753413i | \(0.271594\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.90113 | 0.386389 | ||||||||
\(320\) | −0.685562 | −0.0383241 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.07276 | −0.282694 | ||||||||
\(323\) | 4.97049 | 0.276566 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.0965 | 1.05929 | ||||||||
\(326\) | −7.07276 | −0.391724 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.70164 | 0.204389 | ||||||||
\(329\) | 5.07276 | 0.279671 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.84112 | −0.321057 | −0.160528 | − | 0.987031i | \(-0.551320\pi\) | ||||
−0.160528 | + | 0.987031i | \(0.551320\pi\) | |||||||
\(332\) | −3.70164 | −0.203154 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.6357 | −0.691394 | ||||||||
\(335\) | 2.97644 | 0.162621 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.3135 | 1.10655 | 0.553273 | − | 0.833000i | \(-0.313379\pi\) | ||||
0.553273 | + | 0.833000i | \(0.313379\pi\) | |||||||
\(338\) | −4.77100 | −0.259508 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.40758 | −0.184802 | ||||||||
\(341\) | −9.10107 | −0.492851 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.8823 | 0.587590 | ||||||||
\(344\) | −7.53001 | −0.405991 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.7321 | −1.06081 | ||||||||
\(347\) | −15.1615 | −0.813914 | −0.406957 | − | 0.913447i | \(-0.633410\pi\) | ||||
−0.406957 | + | 0.913447i | \(0.633410\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.1069 | −1.45100 | −0.725499 | − | 0.688223i | \(-0.758391\pi\) | ||||
−0.725499 | + | 0.688223i | \(0.758391\pi\) | |||||||
\(350\) | −3.69711 | −0.197619 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 21.7523 | 1.15776 | 0.578879 | − | 0.815413i | \(-0.303490\pi\) | ||||
0.578879 | + | 0.815413i | \(0.303490\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.67854 | 0.0890876 | ||||||||
\(356\) | 4.41098 | 0.233781 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.89003 | −0.152743 | ||||||||
\(359\) | 36.1923 | 1.91016 | 0.955079 | − | 0.296351i | \(-0.0957698\pi\) | ||||
0.955079 | + | 0.296351i | \(0.0957698\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 6.92943 | 0.364203 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.44049 | 0.180331 | ||||||||
\(365\) | −6.83011 | −0.357504 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.9679 | −1.56431 | −0.782157 | − | 0.623082i | \(-0.785880\pi\) | ||||
−0.782157 | + | 0.623082i | \(0.785880\pi\) | |||||||
\(368\) | −6.21557 | −0.324009 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.49280 | 0.389532 | ||||||||
\(371\) | 0.722692 | 0.0375203 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.2477 | 0.737719 | 0.368860 | − | 0.929485i | \(-0.379748\pi\) | ||||
0.368860 | + | 0.929485i | \(0.379748\pi\) | |||||||
\(374\) | 4.97049 | 0.257018 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.21557 | 0.320543 | ||||||||
\(377\) | 29.0922 | 1.49832 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.76240 | −0.450094 | −0.225047 | − | 0.974348i | \(-0.572254\pi\) | ||||
−0.225047 | + | 0.974348i | \(0.572254\pi\) | |||||||
\(380\) | −0.685562 | −0.0351686 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.35089 | 0.376104 | ||||||||
\(383\) | 39.0615 | 1.99595 | 0.997976 | − | 0.0635990i | \(-0.0202579\pi\) | ||||
0.997976 | + | 0.0635990i | \(0.0202579\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.559513 | −0.0285154 | ||||||||
\(386\) | −5.00770 | −0.254885 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.12937 | −0.361939 | ||||||||
\(389\) | −9.07344 | −0.460042 | −0.230021 | − | 0.973186i | \(-0.573879\pi\) | ||||
−0.230021 | + | 0.973186i | \(0.573879\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.8944 | −1.56240 | ||||||||
\(392\) | 6.33392 | 0.319911 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 17.6016 | 0.886754 | ||||||||
\(395\) | 3.57792 | 0.180025 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.5165 | −1.28064 | −0.640318 | − | 0.768110i | \(-0.721198\pi\) | ||||
−0.640318 | + | 0.768110i | \(0.721198\pi\) | |||||||
\(398\) | −3.90453 | −0.195716 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.53001 | −0.226500 | ||||||||
\(401\) | 0.457241 | 0.0228335 | 0.0114168 | − | 0.999935i | \(-0.496366\pi\) | ||||
0.0114168 | + | 0.999935i | \(0.496366\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −38.3662 | −1.91115 | ||||||||
\(404\) | 15.8306 | 0.787600 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.63228 | −0.279525 | ||||||||
\(407\) | −10.9294 | −0.541752 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.46230 | 0.270093 | 0.135047 | − | 0.990839i | \(-0.456882\pi\) | ||||
0.135047 | + | 0.990839i | \(0.456882\pi\) | |||||||
\(410\) | −2.53770 | −0.125328 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.8999 | 0.783333 | ||||||||
\(413\) | 1.57567 | 0.0775335 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.53770 | 0.124571 | ||||||||
\(416\) | 4.21557 | 0.206685 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.00000 | 0.0489116 | ||||||||
\(419\) | −26.2477 | −1.28228 | −0.641141 | − | 0.767423i | \(-0.721539\pi\) | ||||
−0.641141 | + | 0.767423i | \(0.721539\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.4504 | 0.899217 | 0.449608 | − | 0.893226i | \(-0.351564\pi\) | ||||
0.449608 | + | 0.893226i | \(0.351564\pi\) | |||||||
\(422\) | 9.69569 | 0.471979 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.885502 | 0.0430038 | ||||||||
\(425\) | −22.5164 | −1.09220 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.4649 | −0.554827 | ||||||||
\(428\) | 16.2350 | 0.784751 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.16228 | 0.248947 | ||||||||
\(431\) | −12.0956 | −0.582623 | −0.291312 | − | 0.956628i | \(-0.594092\pi\) | ||||
−0.291312 | + | 0.956628i | \(0.594092\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.5257 | 0.842232 | 0.421116 | − | 0.907007i | \(-0.361639\pi\) | ||||
0.421116 | + | 0.907007i | \(0.361639\pi\) | |||||||
\(434\) | 7.42773 | 0.356543 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.98657 | −0.286705 | ||||||||
\(437\) | −6.21557 | −0.297331 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.8623 | 0.613886 | 0.306943 | − | 0.951728i | \(-0.400694\pi\) | ||||
0.306943 | + | 0.951728i | \(0.400694\pi\) | |||||||
\(440\) | −0.685562 | −0.0326829 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.9534 | 0.996654 | ||||||||
\(443\) | −36.8648 | −1.75150 | −0.875749 | − | 0.482767i | \(-0.839632\pi\) | ||||
−0.875749 | + | 0.482767i | \(0.839632\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.02400 | −0.143351 | ||||||||
\(446\) | −17.4756 | −0.827493 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.816139 | −0.0385589 | ||||||||
\(449\) | 9.86127 | 0.465382 | 0.232691 | − | 0.972551i | \(-0.425247\pi\) | ||||
0.232691 | + | 0.972551i | \(0.425247\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.70164 | 0.174303 | ||||||||
\(452\) | 7.50819 | 0.353156 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −17.5622 | −0.824233 | ||||||||
\(455\) | −2.35867 | −0.110576 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.97555 | 0.185968 | 0.0929841 | − | 0.995668i | \(-0.470359\pi\) | ||||
0.0929841 | + | 0.995668i | \(0.470359\pi\) | |||||||
\(458\) | −20.1110 | −0.939724 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.26115 | 0.198677 | ||||||||
\(461\) | 37.6405 | 1.75309 | 0.876547 | − | 0.481316i | \(-0.159841\pi\) | ||||
0.876547 | + | 0.481316i | \(0.159841\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.74361 | −0.359876 | −0.179938 | − | 0.983678i | \(-0.557590\pi\) | ||||
−0.179938 | + | 0.983678i | \(0.557590\pi\) | |||||||
\(464\) | −6.90113 | −0.320377 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.7244 | 0.774745 | ||||||||
\(467\) | −25.3256 | −1.17193 | −0.585964 | − | 0.810337i | \(-0.699284\pi\) | ||||
−0.585964 | + | 0.810337i | \(0.699284\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.54336 | 0.163617 | ||||||||
\(470\) | −4.26115 | −0.196552 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.93064 | 0.0888647 | ||||||||
\(473\) | −7.53001 | −0.346230 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.53001 | −0.207851 | ||||||||
\(476\) | −4.05661 | −0.185934 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −16.7444 | −0.765873 | ||||||||
\(479\) | 17.6114 | 0.804684 | 0.402342 | − | 0.915489i | \(-0.368196\pi\) | ||||
0.402342 | + | 0.915489i | \(0.368196\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −46.0738 | −2.10078 | ||||||||
\(482\) | 17.6846 | 0.805511 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 4.88763 | 0.221936 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.6177 | 1.47805 | 0.739025 | − | 0.673678i | \(-0.235287\pi\) | ||||
0.739025 | + | 0.673678i | \(0.235287\pi\) | |||||||
\(488\) | −14.0478 | −0.635913 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.34229 | −0.196165 | ||||||||
\(491\) | 10.6601 | 0.481085 | 0.240542 | − | 0.970639i | \(-0.422675\pi\) | ||||
0.240542 | + | 0.970639i | \(0.422675\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.3020 | −1.54488 | ||||||||
\(494\) | 4.21557 | 0.189667 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.10107 | 0.408650 | ||||||||
\(497\) | 1.99825 | 0.0896336 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.7398 | −0.928443 | −0.464221 | − | 0.885719i | \(-0.653666\pi\) | ||||
−0.464221 | + | 0.885719i | \(0.653666\pi\) | |||||||
\(500\) | 6.53341 | 0.292183 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15.4076 | −0.687674 | ||||||||
\(503\) | 41.5413 | 1.85223 | 0.926117 | − | 0.377237i | \(-0.123126\pi\) | ||||
0.926117 | + | 0.377237i | \(0.123126\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.8528 | −0.482944 | ||||||||
\(506\) | −6.21557 | −0.276316 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.31784 | 0.369044 | ||||||||
\(509\) | −34.0655 | −1.50993 | −0.754964 | − | 0.655766i | \(-0.772346\pi\) | ||||
−0.754964 | + | 0.655766i | \(0.772346\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.13102 | −0.359695 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 30.0087 | 1.32363 | ||||||||
\(515\) | −10.9004 | −0.480328 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.21557 | 0.273360 | ||||||||
\(518\) | 8.91993 | 0.391919 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.89003 | −0.126736 | ||||||||
\(521\) | −5.58676 | −0.244761 | −0.122380 | − | 0.992483i | \(-0.539053\pi\) | ||||
−0.122380 | + | 0.992483i | \(0.539053\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.3721 | 1.32808 | 0.664040 | − | 0.747697i | \(-0.268840\pi\) | ||||
0.664040 | + | 0.747697i | \(0.268840\pi\) | |||||||
\(524\) | 6.44389 | 0.281503 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.42124 | −0.323581 | ||||||||
\(527\) | 45.2368 | 1.97055 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.6333 | 0.679707 | ||||||||
\(530\) | −0.607066 | −0.0263693 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.816139 | −0.0353841 | ||||||||
\(533\) | 15.6045 | 0.675907 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.1301 | −0.481197 | ||||||||
\(536\) | 4.34162 | 0.187529 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.43001 | 0.234104 | ||||||||
\(539\) | 6.33392 | 0.272821 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.2010 | 0.653542 | 0.326771 | − | 0.945103i | \(-0.394039\pi\) | ||||
0.326771 | + | 0.945103i | \(0.394039\pi\) | |||||||
\(542\) | −8.72496 | −0.374769 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.97049 | −0.213108 | ||||||||
\(545\) | 4.10416 | 0.175803 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.7245 | 1.69850 | 0.849249 | − | 0.527992i | \(-0.177055\pi\) | ||||
0.849249 | + | 0.527992i | \(0.177055\pi\) | |||||||
\(548\) | −10.9444 | −0.467521 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.53001 | −0.193160 | ||||||||
\(551\) | −6.90113 | −0.293998 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.25940 | 0.181128 | ||||||||
\(554\) | −25.1078 | −1.06673 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.1439 | −0.769472 | ||||||||
\(557\) | −35.0606 | −1.48556 | −0.742782 | − | 0.669534i | \(-0.766494\pi\) | ||||
−0.742782 | + | 0.669534i | \(0.766494\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.7432 | −1.34260 | ||||||||
\(560\) | 0.559513 | 0.0236438 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −28.7720 | −1.21367 | ||||||||
\(563\) | −10.4295 | −0.439550 | −0.219775 | − | 0.975551i | \(-0.570532\pi\) | ||||
−0.219775 | + | 0.975551i | \(0.570532\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.14733 | −0.216550 | ||||||||
\(566\) | −13.6517 | −0.573823 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.44842 | 0.102733 | ||||||||
\(569\) | −38.3571 | −1.60801 | −0.804007 | − | 0.594620i | \(-0.797302\pi\) | ||||
−0.804007 | + | 0.594620i | \(0.797302\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.8465 | −1.79307 | −0.896535 | − | 0.442972i | \(-0.853924\pi\) | ||||
−0.896535 | + | 0.442972i | \(0.853924\pi\) | |||||||
\(572\) | 4.21557 | 0.176262 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.02105 | −0.126096 | ||||||||
\(575\) | 28.1566 | 1.17421 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.2061 | 0.966084 | 0.483042 | − | 0.875597i | \(-0.339532\pi\) | ||||
0.483042 | + | 0.875597i | \(0.339532\pi\) | |||||||
\(578\) | −7.70579 | −0.320519 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.73115 | 0.196450 | ||||||||
\(581\) | 3.02105 | 0.125334 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.885502 | 0.0366738 | ||||||||
\(584\) | −9.96279 | −0.412263 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.87328 | 0.0773843 | ||||||||
\(587\) | 0.149825 | 0.00618393 | 0.00309197 | − | 0.999995i | \(-0.499016\pi\) | ||||
0.00309197 | + | 0.999995i | \(0.499016\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.10107 | 0.375003 | ||||||||
\(590\) | −1.32357 | −0.0544905 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.9294 | 0.449197 | ||||||||
\(593\) | 31.0858 | 1.27654 | 0.638269 | − | 0.769813i | \(-0.279651\pi\) | ||||
0.638269 | + | 0.769813i | \(0.279651\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.78106 | 0.114012 | ||||||||
\(596\) | −7.66058 | −0.313790 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −26.2021 | −1.07149 | ||||||||
\(599\) | 35.4581 | 1.44878 | 0.724389 | − | 0.689391i | \(-0.242122\pi\) | ||||
0.724389 | + | 0.689391i | \(0.242122\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.15118 | 0.128540 | 0.0642698 | − | 0.997933i | \(-0.479528\pi\) | ||||
0.0642698 | + | 0.997933i | \(0.479528\pi\) | |||||||
\(602\) | 6.14553 | 0.250473 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.0033 | 0.447719 | ||||||||
\(605\) | −0.685562 | −0.0278720 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.2397 | 1.02445 | 0.512223 | − | 0.858852i | \(-0.328822\pi\) | ||||
0.512223 | + | 0.858852i | \(0.328822\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.63062 | 0.389932 | ||||||||
\(611\) | 26.2021 | 1.06003 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.70746 | 0.230522 | 0.115261 | − | 0.993335i | \(-0.463230\pi\) | ||||
0.115261 | + | 0.993335i | \(0.463230\pi\) | |||||||
\(614\) | 9.06001 | 0.365632 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.816139 | −0.0328832 | ||||||||
\(617\) | −7.77100 | −0.312849 | −0.156424 | − | 0.987690i | \(-0.549997\pi\) | ||||
−0.156424 | + | 0.987690i | \(0.549997\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.8716 | −0.879095 | −0.439547 | − | 0.898219i | \(-0.644861\pi\) | ||||
−0.439547 | + | 0.898219i | \(0.644861\pi\) | |||||||
\(620\) | −6.23934 | −0.250578 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.1378 | −0.606969 | ||||||||
\(623\) | −3.59997 | −0.144230 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.1710 | 0.726839 | ||||||||
\(626\) | −20.0849 | −0.802752 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.74225 | 0.189236 | ||||||||
\(629\) | 54.3247 | 2.16607 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.7379 | 0.586708 | 0.293354 | − | 0.956004i | \(-0.405228\pi\) | ||||
0.293354 | + | 0.956004i | \(0.405228\pi\) | |||||||
\(632\) | 5.21897 | 0.207599 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −23.4146 | −0.929913 | ||||||||
\(635\) | −5.70239 | −0.226292 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.7011 | 1.05793 | ||||||||
\(638\) | −6.90113 | −0.273218 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.685562 | 0.0270992 | ||||||||
\(641\) | −14.1132 | −0.557439 | −0.278719 | − | 0.960373i | \(-0.589910\pi\) | ||||
−0.278719 | + | 0.960373i | \(0.589910\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.980299 | 0.0386592 | 0.0193296 | − | 0.999813i | \(-0.493847\pi\) | ||||
0.0193296 | + | 0.999813i | \(0.493847\pi\) | |||||||
\(644\) | 5.07276 | 0.199895 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.97049 | −0.195561 | ||||||||
\(647\) | 42.0064 | 1.65144 | 0.825720 | − | 0.564080i | \(-0.190769\pi\) | ||||
0.825720 | + | 0.564080i | \(0.190769\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.93064 | 0.0757841 | ||||||||
\(650\) | −19.0965 | −0.749028 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.07276 | 0.276991 | ||||||||
\(653\) | −38.1911 | −1.49453 | −0.747267 | − | 0.664524i | \(-0.768634\pi\) | ||||
−0.747267 | + | 0.664524i | \(0.768634\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.41768 | −0.172613 | ||||||||
\(656\) | −3.70164 | −0.144525 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.07276 | −0.197757 | ||||||||
\(659\) | −14.2021 | −0.553237 | −0.276618 | − | 0.960980i | \(-0.589214\pi\) | ||||
−0.276618 | + | 0.960980i | \(0.589214\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.5219 | −0.603730 | −0.301865 | − | 0.953351i | \(-0.597609\pi\) | ||||
−0.301865 | + | 0.953351i | \(0.597609\pi\) | |||||||
\(662\) | 5.84112 | 0.227021 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.70164 | 0.143652 | ||||||||
\(665\) | 0.559513 | 0.0216970 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 42.8944 | 1.66088 | ||||||||
\(668\) | 12.6357 | 0.488889 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.97644 | −0.114990 | ||||||||
\(671\) | −14.0478 | −0.542309 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.3169 | −0.667516 | −0.333758 | − | 0.942659i | \(-0.608317\pi\) | ||||
−0.333758 | + | 0.942659i | \(0.608317\pi\) | |||||||
\(674\) | −20.3135 | −0.782446 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.77100 | 0.183500 | ||||||||
\(677\) | 6.28335 | 0.241489 | 0.120744 | − | 0.992684i | \(-0.461472\pi\) | ||||
0.120744 | + | 0.992684i | \(0.461472\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.81856 | 0.223296 | ||||||||
\(680\) | 3.40758 | 0.130675 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.10107 | 0.348498 | ||||||||
\(683\) | 17.5801 | 0.672682 | 0.336341 | − | 0.941740i | \(-0.390810\pi\) | ||||
0.336341 | + | 0.941740i | \(0.390810\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.50305 | 0.286677 | ||||||||
\(686\) | −10.8823 | −0.415489 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.53001 | 0.287079 | ||||||||
\(689\) | 3.73289 | 0.142212 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.3468 | −0.469695 | −0.234848 | − | 0.972032i | \(-0.575459\pi\) | ||||
−0.234848 | + | 0.972032i | \(0.575459\pi\) | |||||||
\(692\) | 19.7321 | 0.750104 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.1615 | 0.575524 | ||||||||
\(695\) | 12.4387 | 0.471828 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.3990 | −0.696911 | ||||||||
\(698\) | 27.1069 | 1.02601 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.69711 | 0.139738 | ||||||||
\(701\) | −28.3782 | −1.07183 | −0.535915 | − | 0.844272i | \(-0.680033\pi\) | ||||
−0.535915 | + | 0.844272i | \(0.680033\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.9294 | 0.412211 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.7523 | −0.818659 | ||||||||
\(707\) | −12.9199 | −0.485904 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.3802 | −1.47895 | −0.739477 | − | 0.673182i | \(-0.764927\pi\) | ||||
−0.739477 | + | 0.673182i | \(0.764927\pi\) | |||||||
\(710\) | −1.67854 | −0.0629945 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.41098 | −0.165308 | ||||||||
\(713\) | −56.5683 | −2.11850 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.89003 | −0.108081 | ||||||||
\(716\) | 2.89003 | 0.108006 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −36.1923 | −1.35069 | ||||||||
\(719\) | 47.6131 | 1.77567 | 0.887835 | − | 0.460162i | \(-0.152209\pi\) | ||||
0.887835 | + | 0.460162i | \(0.152209\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.9765 | −0.483272 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.92943 | −0.257530 | ||||||||
\(725\) | 31.2621 | 1.16105 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.3044 | −1.34646 | −0.673228 | − | 0.739435i | \(-0.735093\pi\) | ||||
−0.673228 | + | 0.739435i | \(0.735093\pi\) | |||||||
\(728\) | −3.44049 | −0.127513 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.83011 | 0.252794 | ||||||||
\(731\) | 37.4278 | 1.38432 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.7703 | −0.656362 | −0.328181 | − | 0.944615i | \(-0.606436\pi\) | ||||
−0.328181 | + | 0.944615i | \(0.606436\pi\) | |||||||
\(734\) | 29.9679 | 1.10614 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.21557 | 0.229109 | ||||||||
\(737\) | 4.34162 | 0.159925 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.6207 | −0.758544 | −0.379272 | − | 0.925285i | \(-0.623825\pi\) | ||||
−0.379272 | + | 0.925285i | \(0.623825\pi\) | |||||||
\(740\) | −7.49280 | −0.275441 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.722692 | −0.0265309 | ||||||||
\(743\) | −46.9823 | −1.72361 | −0.861807 | − | 0.507237i | \(-0.830667\pi\) | ||||
−0.861807 | + | 0.507237i | \(0.830667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.25180 | 0.192411 | ||||||||
\(746\) | −14.2477 | −0.521646 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.97049 | −0.181739 | ||||||||
\(749\) | −13.2500 | −0.484146 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.27345 | 0.119450 | 0.0597250 | − | 0.998215i | \(-0.480978\pi\) | ||||
0.0597250 | + | 0.998215i | \(0.480978\pi\) | |||||||
\(752\) | −6.21557 | −0.226658 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −29.0922 | −1.05947 | ||||||||
\(755\) | −7.54346 | −0.274535 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.0798 | −1.12961 | −0.564807 | − | 0.825223i | \(-0.691049\pi\) | ||||
−0.564807 | + | 0.825223i | \(0.691049\pi\) | |||||||
\(758\) | 8.76240 | 0.318265 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.685562 | 0.0248679 | ||||||||
\(761\) | 18.2418 | 0.661266 | 0.330633 | − | 0.943759i | \(-0.392738\pi\) | ||||
0.330633 | + | 0.943759i | \(0.392738\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.88587 | 0.176880 | ||||||||
\(764\) | −7.35089 | −0.265946 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −39.0615 | −1.41135 | ||||||||
\(767\) | 8.13873 | 0.293872 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −51.9350 | −1.87283 | −0.936413 | − | 0.350901i | \(-0.885875\pi\) | ||||
−0.936413 | + | 0.350901i | \(0.885875\pi\) | |||||||
\(770\) | 0.559513 | 0.0201635 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.00770 | 0.180231 | ||||||||
\(773\) | −25.9686 | −0.934026 | −0.467013 | − | 0.884250i | \(-0.654670\pi\) | ||||
−0.467013 | + | 0.884250i | \(0.654670\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −41.2279 | −1.48095 | ||||||||
\(776\) | 7.12937 | 0.255930 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.07344 | 0.325299 | ||||||||
\(779\) | −3.70164 | −0.132625 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.44842 | 0.0876112 | ||||||||
\(782\) | 30.8944 | 1.10478 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.33392 | −0.226211 | ||||||||
\(785\) | −3.25110 | −0.116037 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.7686 | 0.633382 | 0.316691 | − | 0.948529i | \(-0.397428\pi\) | ||||
0.316691 | + | 0.948529i | \(0.397428\pi\) | |||||||
\(788\) | −17.6016 | −0.627030 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.57792 | −0.127297 | ||||||||
\(791\) | −6.12773 | −0.217877 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −59.2194 | −2.10294 | ||||||||
\(794\) | 25.5165 | 0.905547 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.90453 | 0.138392 | ||||||||
\(797\) | 14.1001 | 0.499451 | 0.249726 | − | 0.968317i | \(-0.419660\pi\) | ||||
0.249726 | + | 0.968317i | \(0.419660\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.8944 | −1.09297 | ||||||||
\(800\) | 4.53001 | 0.160160 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.457241 | −0.0161458 | ||||||||
\(803\) | −9.96279 | −0.351579 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.47769 | −0.122573 | ||||||||
\(806\) | 38.3662 | 1.35139 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.8306 | −0.556917 | ||||||||
\(809\) | −34.2519 | −1.20423 | −0.602117 | − | 0.798408i | \(-0.705676\pi\) | ||||
−0.602117 | + | 0.798408i | \(0.705676\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.71439 | −0.0602005 | −0.0301003 | − | 0.999547i | \(-0.509583\pi\) | ||||
−0.0301003 | + | 0.999547i | \(0.509583\pi\) | |||||||
\(812\) | 5.63228 | 0.197654 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.9294 | 0.383076 | ||||||||
\(815\) | −4.84882 | −0.169847 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.53001 | 0.263442 | ||||||||
\(818\) | −5.46230 | −0.190985 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.53770 | 0.0886204 | ||||||||
\(821\) | 41.2497 | 1.43962 | 0.719812 | − | 0.694169i | \(-0.244228\pi\) | ||||
0.719812 | + | 0.694169i | \(0.244228\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.96454 | 0.103337 | 0.0516687 | − | 0.998664i | \(-0.483546\pi\) | ||||
0.0516687 | + | 0.998664i | \(0.483546\pi\) | |||||||
\(824\) | −15.8999 | −0.553900 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.57567 | −0.0548245 | ||||||||
\(827\) | 4.06936 | 0.141506 | 0.0707528 | − | 0.997494i | \(-0.477460\pi\) | ||||
0.0707528 | + | 0.997494i | \(0.477460\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.9218 | −1.24762 | −0.623808 | − | 0.781577i | \(-0.714415\pi\) | ||||
−0.623808 | + | 0.781577i | \(0.714415\pi\) | |||||||
\(830\) | −2.53770 | −0.0880849 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.21557 | −0.146148 | ||||||||
\(833\) | −31.4827 | −1.09081 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.66254 | −0.299779 | ||||||||
\(836\) | −1.00000 | −0.0345857 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 26.2477 | 0.906710 | ||||||||
\(839\) | −23.9982 | −0.828510 | −0.414255 | − | 0.910161i | \(-0.635958\pi\) | ||||
−0.414255 | + | 0.910161i | \(0.635958\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.6256 | 0.642261 | ||||||||
\(842\) | −18.4504 | −0.635842 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.69569 | −0.333739 | ||||||||
\(845\) | −3.27082 | −0.112520 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.816139 | −0.0280429 | ||||||||
\(848\) | −0.885502 | −0.0304083 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 22.5164 | 0.772305 | ||||||||
\(851\) | −67.9326 | −2.32870 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.38109 | −0.286963 | −0.143482 | − | 0.989653i | \(-0.545830\pi\) | ||||
−0.143482 | + | 0.989653i | \(0.545830\pi\) | |||||||
\(854\) | 11.4649 | 0.392322 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.2350 | −0.554902 | ||||||||
\(857\) | −11.2492 | −0.384264 | −0.192132 | − | 0.981369i | \(-0.561540\pi\) | ||||
−0.192132 | + | 0.981369i | \(0.561540\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.9454 | 0.748767 | 0.374383 | − | 0.927274i | \(-0.377854\pi\) | ||||
0.374383 | + | 0.927274i | \(0.377854\pi\) | |||||||
\(860\) | −5.16228 | −0.176032 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.0956 | 0.411977 | ||||||||
\(863\) | −52.2205 | −1.77761 | −0.888803 | − | 0.458289i | \(-0.848463\pi\) | ||||
−0.888803 | + | 0.458289i | \(0.848463\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.5276 | −0.459952 | ||||||||
\(866\) | −17.5257 | −0.595548 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.42773 | −0.252114 | ||||||||
\(869\) | 5.21897 | 0.177041 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.3024 | 0.620152 | ||||||||
\(872\) | 5.98657 | 0.202731 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.21557 | 0.210245 | ||||||||
\(875\) | −5.33216 | −0.180260 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.9588 | −1.34931 | −0.674657 | − | 0.738132i | \(-0.735708\pi\) | ||||
−0.674657 | + | 0.738132i | \(0.735708\pi\) | |||||||
\(878\) | −12.8623 | −0.434083 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.685562 | 0.0231103 | ||||||||
\(881\) | 2.14447 | 0.0722491 | 0.0361246 | − | 0.999347i | \(-0.488499\pi\) | ||||
0.0361246 | + | 0.999347i | \(0.488499\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.5259 | −0.421529 | −0.210764 | − | 0.977537i | \(-0.567595\pi\) | ||||
−0.210764 | + | 0.977537i | \(0.567595\pi\) | |||||||
\(884\) | −20.9534 | −0.704741 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36.8648 | 1.23850 | ||||||||
\(887\) | 34.7557 | 1.16698 | 0.583491 | − | 0.812120i | \(-0.301686\pi\) | ||||
0.583491 | + | 0.812120i | \(0.301686\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.78851 | −0.227679 | ||||||||
\(890\) | 3.02400 | 0.101365 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 17.4756 | 0.585126 | ||||||||
\(893\) | −6.21557 | −0.207996 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.98129 | −0.0662274 | ||||||||
\(896\) | 0.816139 | 0.0272653 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.86127 | −0.329075 | ||||||||
\(899\) | −62.8076 | −2.09475 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.40138 | −0.146631 | ||||||||
\(902\) | −3.70164 | −0.123251 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.50819 | −0.249719 | ||||||||
\(905\) | 4.75055 | 0.157914 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.0430 | −1.22999 | −0.614996 | − | 0.788530i | \(-0.710842\pi\) | ||||
−0.614996 | + | 0.788530i | \(0.710842\pi\) | |||||||
\(908\) | 17.5622 | 0.582821 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.35867 | 0.0781890 | ||||||||
\(911\) | −10.5483 | −0.349480 | −0.174740 | − | 0.984615i | \(-0.555909\pi\) | ||||
−0.174740 | + | 0.984615i | \(0.555909\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.70164 | 0.122506 | ||||||||
\(914\) | −3.97555 | −0.131499 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.1110 | 0.664485 | ||||||||
\(917\) | −5.25910 | −0.173671 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.3261 | 0.967378 | 0.483689 | − | 0.875240i | \(-0.339297\pi\) | ||||
0.483689 | + | 0.875240i | \(0.339297\pi\) | |||||||
\(920\) | −4.26115 | −0.140486 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −37.6405 | −1.23962 | ||||||||
\(923\) | 10.3215 | 0.339735 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −49.5104 | −1.62789 | ||||||||
\(926\) | 7.74361 | 0.254471 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.90113 | 0.226541 | ||||||||
\(929\) | −32.2021 | −1.05652 | −0.528259 | − | 0.849083i | \(-0.677155\pi\) | ||||
−0.528259 | + | 0.849083i | \(0.677155\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.33392 | −0.207586 | ||||||||
\(932\) | −16.7244 | −0.547827 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 25.3256 | 0.828678 | ||||||||
\(935\) | 3.40758 | 0.111440 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.9628 | −0.586819 | −0.293409 | − | 0.955987i | \(-0.594790\pi\) | ||||
−0.293409 | + | 0.955987i | \(0.594790\pi\) | |||||||
\(938\) | −3.54336 | −0.115695 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.26115 | 0.138984 | ||||||||
\(941\) | −31.7844 | −1.03614 | −0.518070 | − | 0.855338i | \(-0.673349\pi\) | ||||
−0.518070 | + | 0.855338i | \(0.673349\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.0078 | 0.749237 | ||||||||
\(944\) | −1.93064 | −0.0628369 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.53001 | 0.244822 | ||||||||
\(947\) | −26.0836 | −0.847602 | −0.423801 | − | 0.905755i | \(-0.639304\pi\) | ||||
−0.423801 | + | 0.905755i | \(0.639304\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −41.9988 | −1.36334 | ||||||||
\(950\) | 4.53001 | 0.146973 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.05661 | 0.131475 | ||||||||
\(953\) | 33.5768 | 1.08766 | 0.543830 | − | 0.839196i | \(-0.316974\pi\) | ||||
0.543830 | + | 0.839196i | \(0.316974\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.03949 | 0.163074 | ||||||||
\(956\) | 16.7444 | 0.541554 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17.6114 | −0.568998 | ||||||||
\(959\) | 8.93213 | 0.288434 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 51.8295 | 1.67192 | ||||||||
\(962\) | 46.0738 | 1.48548 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −17.6846 | −0.569582 | ||||||||
\(965\) | −3.43309 | −0.110515 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.4044 | 0.656160 | 0.328080 | − | 0.944650i | \(-0.393598\pi\) | ||||
0.328080 | + | 0.944650i | \(0.393598\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.88763 | −0.156932 | ||||||||
\(971\) | −10.7077 | −0.343626 | −0.171813 | − | 0.985130i | \(-0.554962\pi\) | ||||
−0.171813 | + | 0.985130i | \(0.554962\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.8079 | 0.474720 | ||||||||
\(974\) | −32.6177 | −1.04514 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.0478 | 0.449659 | ||||||||
\(977\) | 24.0828 | 0.770478 | 0.385239 | − | 0.922817i | \(-0.374119\pi\) | ||||
0.385239 | + | 0.922817i | \(0.374119\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.41098 | −0.140975 | ||||||||
\(980\) | 4.34229 | 0.138709 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.6601 | −0.340178 | ||||||||
\(983\) | 27.5895 | 0.879968 | 0.439984 | − | 0.898006i | \(-0.354984\pi\) | ||||
0.439984 | + | 0.898006i | \(0.354984\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.0670 | 0.384485 | ||||||||
\(986\) | 34.3020 | 1.09240 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.21557 | −0.134115 | ||||||||
\(989\) | −46.8033 | −1.48826 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.1932 | −1.46738 | −0.733688 | − | 0.679486i | \(-0.762203\pi\) | ||||
−0.733688 | + | 0.679486i | \(0.762203\pi\) | |||||||
\(992\) | −9.10107 | −0.288959 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.99825 | −0.0633805 | ||||||||
\(995\) | −2.67680 | −0.0848601 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.2854 | −0.927477 | −0.463739 | − | 0.885972i | \(-0.653492\pi\) | ||||
−0.463739 | + | 0.885972i | \(0.653492\pi\) | |||||||
\(998\) | 20.7398 | 0.656508 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3762.2.a.bi.1.3 | ✓ | 5 | |
3.2 | odd | 2 | 3762.2.a.bl.1.3 | yes | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3762.2.a.bi.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
3762.2.a.bl.1.3 | yes | 5 | 3.2 | odd | 2 |