Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(143,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.l (of order \(4\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(4.59938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 431.2 | ||
Root | \(0.944649 + 1.05244i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.431 |
Dual form | 576.2.l.a.143.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.10489 | − | 2.10489i | −0.941334 | − | 0.941334i | 0.0570377 | − | 0.998372i | \(-0.481834\pi\) |
−0.998372 | + | 0.0570377i | \(0.981834\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.40731 | 1.66581 | 0.832904 | − | 0.553418i | \(-0.186677\pi\) | ||||
0.832904 | + | 0.553418i | \(0.186677\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.215589 | + | 0.215589i | −0.0650026 | + | 0.0650026i | −0.738861 | − | 0.673858i | \(-0.764636\pi\) |
0.673858 | + | 0.738861i | \(0.264636\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.73544 | − | 2.73544i | −0.758675 | − | 0.758675i | 0.217406 | − | 0.976081i | \(-0.430240\pi\) |
−0.976081 | + | 0.217406i | \(0.930240\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.36438i | − | 0.573447i | −0.958013 | − | 0.286724i | \(-0.907434\pi\) | ||
0.958013 | − | 0.286724i | \(-0.0925661\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.758681 | + | 0.758681i | −0.174053 | + | 0.174053i | −0.788758 | − | 0.614704i | \(-0.789275\pi\) |
0.614704 | + | 0.788758i | \(0.289275\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.75549i | − | 0.366045i | −0.983109 | − | 0.183023i | \(-0.941412\pi\) | ||
0.983109 | − | 0.183023i | \(-0.0585881\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.86110i | 0.772221i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.54221 | − | 5.54221i | 1.02916 | − | 1.02916i | 0.0296002 | − | 0.999562i | \(-0.490577\pi\) |
0.999562 | − | 0.0296002i | \(-0.00942341\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.01709i | − | 1.61952i | −0.586763 | − | 0.809759i | \(-0.699598\pi\) | ||
0.586763 | − | 0.809759i | \(-0.300402\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.27690 | − | 9.27690i | −1.56808 | − | 1.56808i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.10242 | − | 3.10242i | 0.510035 | − | 0.510035i | −0.404502 | − | 0.914537i | \(-0.632555\pi\) |
0.914537 | + | 0.404502i | \(0.132555\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.1014 | −1.57757 | −0.788785 | − | 0.614669i | \(-0.789290\pi\) | ||||
−0.788785 | + | 0.614669i | \(0.789290\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.54621 | + | 3.54621i | 0.540792 | + | 0.540792i | 0.923761 | − | 0.382969i | \(-0.125099\pi\) |
−0.382969 | + | 0.923761i | \(0.625099\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.90136 | 0.569072 | 0.284536 | − | 0.958665i | \(-0.408160\pi\) | ||||
0.284536 | + | 0.958665i | \(0.408160\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.4244 | 1.77491 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.71378 | + | 2.71378i | 0.372766 | + | 0.372766i | 0.868484 | − | 0.495717i | \(-0.165095\pi\) |
−0.495717 | + | 0.868484i | \(0.665095\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.907583 | 0.122378 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.40445 | − | 3.40445i | 0.443222 | − | 0.443222i | −0.449871 | − | 0.893093i | \(-0.648530\pi\) |
0.893093 | + | 0.449871i | \(0.148530\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.75868 | − | 1.75868i | −0.225176 | − | 0.225176i | 0.585498 | − | 0.810674i | \(-0.300899\pi\) |
−0.810674 | + | 0.585498i | \(0.800899\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.5156i | 1.42833i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.11951 | + | 9.11951i | −1.11413 | + | 1.11413i | −0.121539 | + | 0.992587i | \(0.538783\pi\) |
−0.992587 | + | 0.121539i | \(0.961217\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.8897i | 1.41105i | 0.708684 | + | 0.705526i | \(0.249289\pi\) | ||||
−0.708684 | + | 0.705526i | \(0.750711\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.482639i | − | 0.0564886i | −0.999601 | − | 0.0282443i | \(-0.991008\pi\) | ||
0.999601 | − | 0.0282443i | \(-0.00899163\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.950169 | + | 0.950169i | −0.108282 | + | 0.108282i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.88995i | 0.775180i | 0.921832 | + | 0.387590i | \(0.126692\pi\) | ||||
−0.921832 | + | 0.387590i | \(0.873308\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.79951 | + | 4.79951i | 0.526814 | + | 0.526814i | 0.919621 | − | 0.392807i | \(-0.128496\pi\) |
−0.392807 | + | 0.919621i | \(0.628496\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.97676 | + | 4.97676i | −0.539805 | + | 0.539805i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.00534 | 0.742564 | 0.371282 | − | 0.928520i | \(-0.378918\pi\) | ||||
0.371282 | + | 0.928520i | \(0.378918\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.0559 | − | 12.0559i | −1.26381 | − | 1.26381i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.19387 | 0.327685 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.34374 | −0.339506 | −0.169753 | − | 0.985487i | \(-0.554297\pi\) | ||||
−0.169753 | + | 0.985487i | \(0.554297\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.76361 | − | 1.76361i | −0.175486 | − | 0.175486i | 0.613899 | − | 0.789385i | \(-0.289600\pi\) |
−0.789385 | + | 0.613899i | \(0.789600\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.01709 | 0.100217 | 0.0501085 | − | 0.998744i | \(-0.484043\pi\) | ||||
0.0501085 | + | 0.998744i | \(0.484043\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.33152 | + | 2.33152i | −0.225396 | + | 0.225396i | −0.810766 | − | 0.585370i | \(-0.800949\pi\) |
0.585370 | + | 0.810766i | \(0.300949\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.07918 | − | 8.07918i | −0.773845 | − | 0.773845i | 0.204931 | − | 0.978776i | \(-0.434303\pi\) |
−0.978776 | + | 0.204931i | \(0.934303\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.09677i | 0.197247i | 0.995125 | + | 0.0986237i | \(0.0314440\pi\) | ||||
−0.995125 | + | 0.0986237i | \(0.968556\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.69511 | + | 3.69511i | −0.344571 | + | 0.344571i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 10.4206i | − | 0.955253i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9070i | 0.991549i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.39725 | + | 2.39725i | −0.214416 | + | 0.214416i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.2802i | − | 0.912218i | −0.889924 | − | 0.456109i | \(-0.849243\pi\) | ||
0.889924 | − | 0.456109i | \(-0.150757\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.80891 | + | 6.80891i | 0.594897 | + | 0.594897i | 0.938950 | − | 0.344053i | \(-0.111800\pi\) |
−0.344053 | + | 0.938950i | \(0.611800\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.34374 | + | 3.34374i | −0.289939 | + | 0.289939i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.7922 | 1.17834 | 0.589172 | − | 0.808008i | \(-0.299454\pi\) | ||||
0.589172 | + | 0.808008i | \(0.299454\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.1195 | + | 13.1195i | 1.11278 | + | 1.11278i | 0.992773 | + | 0.120010i | \(0.0382927\pi\) |
0.120010 | + | 0.992773i | \(0.461707\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.17946 | 0.0986317 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −23.3314 | −1.93757 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.76174 | + | 7.76174i | 0.635867 | + | 0.635867i | 0.949533 | − | 0.313667i | \(-0.101557\pi\) |
−0.313667 | + | 0.949533i | \(0.601557\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.202466 | 0.0164765 | 0.00823823 | − | 0.999966i | \(-0.497378\pi\) | ||||
0.00823823 | + | 0.999966i | \(0.497378\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.9800 | + | 18.9800i | −1.52451 | + | 1.52451i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.75868 | + | 3.75868i | 0.299975 | + | 0.299975i | 0.841004 | − | 0.541029i | \(-0.181965\pi\) |
−0.541029 | + | 0.841004i | \(0.681965\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 7.73700i | − | 0.609761i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.2684 | − | 13.2684i | 1.03926 | − | 1.03926i | 0.0400655 | − | 0.999197i | \(-0.487243\pi\) |
0.999197 | − | 0.0400655i | \(-0.0127567\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.1644i | 1.56037i | 0.625548 | + | 0.780186i | \(0.284875\pi\) | ||||
−0.625548 | + | 0.780186i | \(0.715125\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.96528i | 0.151175i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.98315 | + | 3.98315i | −0.302833 | + | 0.302833i | −0.842121 | − | 0.539288i | \(-0.818693\pi\) |
0.539288 | + | 0.842121i | \(0.318693\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.0171i | 1.28637i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.7182 | + | 14.7182i | 1.10009 | + | 1.10009i | 0.994399 | + | 0.105688i | \(0.0337044\pi\) |
0.105688 | + | 0.994399i | \(0.466296\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.26456 | − | 3.26456i | 0.242653 | − | 0.242653i | −0.575294 | − | 0.817947i | \(-0.695112\pi\) |
0.817947 | + | 0.575294i | \(0.195112\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.0605 | −0.960227 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.509736 | + | 0.509736i | 0.0372756 | + | 0.0372756i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.69868 | −0.557057 | −0.278528 | − | 0.960428i | \(-0.589847\pi\) | ||||
−0.278528 | + | 0.960428i | \(0.589847\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.51736 | −0.253185 | −0.126593 | − | 0.991955i | \(-0.540404\pi\) | ||||
−0.126593 | + | 0.991955i | \(0.540404\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.40456 | + | 6.40456i | 0.456306 | + | 0.456306i | 0.897441 | − | 0.441135i | \(-0.145424\pi\) |
−0.441135 | + | 0.897441i | \(0.645424\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.3491 | −1.65517 | −0.827586 | − | 0.561339i | \(-0.810286\pi\) | ||||
−0.827586 | + | 0.561339i | \(0.810286\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24.4262 | − | 24.4262i | 1.71439 | − | 1.71439i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.2623 | + | 21.2623i | 1.48502 | + | 1.48502i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 0.327127i | − | 0.0226278i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.63688 | − | 6.63688i | 0.456901 | − | 0.456901i | −0.440736 | − | 0.897637i | \(-0.645282\pi\) |
0.897637 | + | 0.440736i | \(0.145282\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 14.9287i | − | 1.01813i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 39.7411i | − | 2.69780i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.46763 | + | 6.46763i | −0.435060 | + | 0.435060i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.2219i | 0.885406i | 0.896668 | + | 0.442703i | \(0.145980\pi\) | ||||
−0.896668 | + | 0.442703i | \(0.854020\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.4029 | − | 16.4029i | −1.08870 | − | 1.08870i | −0.995663 | − | 0.0930369i | \(-0.970343\pi\) |
−0.0930369 | − | 0.995663i | \(-0.529657\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.98677 | + | 4.98677i | −0.329535 | + | 0.329535i | −0.852410 | − | 0.522875i | \(-0.824860\pi\) |
0.522875 | + | 0.852410i | \(0.324860\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.05879 | −0.0693634 | −0.0346817 | − | 0.999398i | \(-0.511042\pi\) | ||||
−0.0346817 | + | 0.999398i | \(0.511042\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.21193 | − | 8.21193i | −0.535687 | − | 0.535687i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.317107 | 0.0205119 | 0.0102560 | − | 0.999947i | \(-0.496735\pi\) | ||||
0.0102560 | + | 0.999947i | \(0.496735\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.7334 | 0.755816 | 0.377908 | − | 0.925843i | \(-0.376644\pi\) | ||||
0.377908 | + | 0.925843i | \(0.376644\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −26.1520 | − | 26.1520i | −1.67079 | − | 1.67079i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.15065 | 0.264100 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.02450 | − | 7.02450i | 0.443382 | − | 0.443382i | −0.449765 | − | 0.893147i | \(-0.648492\pi\) |
0.893147 | + | 0.449765i | \(0.148492\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.378465 | + | 0.378465i | 0.0237939 | + | 0.0237939i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 23.5830i | − | 1.47107i | −0.677487 | − | 0.735535i | \(-0.736931\pi\) | ||
0.677487 | − | 0.735535i | \(-0.263069\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.6733 | − | 13.6733i | 0.849621 | − | 0.849621i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 20.1370i | − | 1.24170i | −0.783928 | − | 0.620851i | \(-0.786787\pi\) | ||
0.783928 | − | 0.620851i | \(-0.213213\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 11.4244i | − | 0.701796i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.62201 | − | 8.62201i | 0.525693 | − | 0.525693i | −0.393592 | − | 0.919285i | \(-0.628768\pi\) |
0.919285 | + | 0.393592i | \(0.128768\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.18722i | − | 0.132864i | −0.997791 | − | 0.0664319i | \(-0.978838\pi\) | ||
0.997791 | − | 0.0664319i | \(-0.0211615\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.832413 | − | 0.832413i | −0.0501964 | − | 0.0501964i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.64248 | − | 8.64248i | 0.519277 | − | 0.519277i | −0.398076 | − | 0.917352i | \(-0.630322\pi\) |
0.917352 | + | 0.398076i | \(0.130322\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.8081 | 0.883375 | 0.441688 | − | 0.897169i | \(-0.354380\pi\) | ||||
0.441688 | + | 0.897169i | \(0.354380\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.12714 | − | 6.12714i | −0.364221 | − | 0.364221i | 0.501144 | − | 0.865364i | \(-0.332913\pi\) |
−0.865364 | + | 0.501144i | \(0.832913\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −44.5199 | −2.62793 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.4097 | 0.671158 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.8979 | + | 11.8979i | 0.695080 | + | 0.695080i | 0.963345 | − | 0.268265i | \(-0.0864503\pi\) |
−0.268265 | + | 0.963345i | \(0.586450\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.3320 | −0.834441 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.80204 | + | 4.80204i | −0.277709 | + | 0.277709i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.6293 | + | 15.6293i | 0.900855 | + | 0.900855i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.40365i | 0.423932i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.91467 | + | 4.91467i | −0.280495 | + | 0.280495i | −0.833306 | − | 0.552811i | \(-0.813555\pi\) |
0.552811 | + | 0.833306i | \(0.313555\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 20.7712i | − | 1.17783i | −0.808195 | − | 0.588915i | \(-0.799555\pi\) | ||
0.808195 | − | 0.588915i | \(-0.200445\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.3897i | 0.926400i | 0.886254 | + | 0.463200i | \(0.153299\pi\) | ||||
−0.886254 | + | 0.463200i | \(0.846701\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.3592 | + | 22.3592i | −1.25582 | + | 1.25582i | −0.302749 | + | 0.953070i | \(0.597904\pi\) |
−0.953070 | + | 0.302749i | \(0.902096\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.38968i | 0.133796i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.79381 | + | 1.79381i | 0.0998103 | + | 0.0998103i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.5618 | − | 10.5618i | 0.585865 | − | 0.585865i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.1945 | 0.947965 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.08533 | + | 7.08533i | 0.389445 | + | 0.389445i | 0.874490 | − | 0.485044i | \(-0.161197\pi\) |
−0.485044 | + | 0.874490i | \(0.661197\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 38.3911 | 2.09753 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.3314 | −1.27094 | −0.635472 | − | 0.772124i | \(-0.719195\pi\) | ||||
−0.635472 | + | 0.772124i | \(0.719195\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.94399 | + | 1.94399i | 0.105273 | + | 0.105273i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 23.9070 | 1.29086 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.2074 | + | 21.2074i | −1.13847 | + | 1.13847i | −0.149751 | + | 0.988724i | \(0.547847\pi\) |
−0.988724 | + | 0.149751i | \(0.952153\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.38022 | + | 5.38022i | 0.287996 | + | 0.287996i | 0.836288 | − | 0.548291i | \(-0.184721\pi\) |
−0.548291 | + | 0.836288i | \(0.684721\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 10.5163i | − | 0.559727i | −0.960040 | − | 0.279864i | \(-0.909711\pi\) | ||
0.960040 | − | 0.279864i | \(-0.0902892\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.0266 | − | 25.0266i | 1.32827 | − | 1.32827i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 11.7583i | − | 0.620578i | −0.950642 | − | 0.310289i | \(-0.899574\pi\) | ||
0.950642 | − | 0.310289i | \(-0.100426\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.8488i | 0.939411i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.01590 | + | 1.01590i | −0.0531747 | + | 0.0531747i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 3.49973i | − | 0.182684i | −0.995820 | − | 0.0913422i | \(-0.970884\pi\) | ||
0.995820 | − | 0.0913422i | \(-0.0291157\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.9605 | + | 11.9605i | 0.620957 | + | 0.620957i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.1831 | − | 19.1831i | 0.993262 | − | 0.993262i | −0.00671500 | − | 0.999977i | \(-0.502137\pi\) |
0.999977 | + | 0.00671500i | \(0.00213747\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −30.3208 | −1.56160 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.9977 | + | 14.9977i | 0.770381 | + | 0.770381i | 0.978173 | − | 0.207792i | \(-0.0666278\pi\) |
−0.207792 | + | 0.978173i | \(0.566628\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.4027 | −1.55351 | −0.776754 | − | 0.629805i | \(-0.783135\pi\) | ||||
−0.776754 | + | 0.629805i | \(0.783135\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | 0.203859 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.4571 | − | 19.4571i | −0.986516 | − | 0.986516i | 0.0133943 | − | 0.999910i | \(-0.495736\pi\) |
−0.999910 | + | 0.0133943i | \(0.995736\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.15065 | −0.209908 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.5026 | − | 14.5026i | 0.729704 | − | 0.729704i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.4339 | − | 20.4339i | −1.02555 | − | 1.02555i | −0.999665 | − | 0.0258815i | \(-0.991761\pi\) |
−0.0258815 | − | 0.999665i | \(-0.508239\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 22.5671i | − | 1.12695i | −0.826133 | − | 0.563475i | \(-0.809464\pi\) | ||
0.826133 | − | 0.563475i | \(-0.190536\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.6657 | + | 24.6657i | −1.22869 | + | 1.22869i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.33770i | 0.0663073i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 9.78286i | − | 0.483731i | −0.970310 | − | 0.241866i | \(-0.922241\pi\) | ||
0.970310 | − | 0.241866i | \(-0.0777593\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.0045 | − | 15.0045i | 0.738323 | − | 0.738323i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 20.2048i | − | 0.991817i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.09125 | − | 9.09125i | −0.444137 | − | 0.444137i | 0.449263 | − | 0.893400i | \(-0.351687\pi\) |
−0.893400 | + | 0.449263i | \(0.851687\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.9862 | + | 17.9862i | −0.876595 | + | 0.876595i | −0.993181 | − | 0.116586i | \(-0.962805\pi\) |
0.116586 | + | 0.993181i | \(0.462805\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.12913 | 0.442828 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.75106 | − | 7.75106i | −0.375100 | − | 0.375100i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.7707 | 1.48217 | 0.741085 | − | 0.671411i | \(-0.234311\pi\) | ||||
0.741085 | + | 0.671411i | \(0.234311\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.49735 | 0.168072 | 0.0840360 | − | 0.996463i | \(-0.473219\pi\) | ||||
0.0840360 | + | 0.996463i | \(0.473219\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.33186 | + | 1.33186i | 0.0637113 | + | 0.0637113i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.1290 | 1.00843 | 0.504216 | − | 0.863578i | \(-0.331782\pi\) | ||||
0.504216 | + | 0.863578i | \(0.331782\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.6022 | + | 12.6022i | −0.598750 | + | 0.598750i | −0.939980 | − | 0.341230i | \(-0.889157\pi\) |
0.341230 | + | 0.939980i | \(0.389157\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.7454 | − | 14.7454i | −0.699001 | − | 0.699001i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.98731i | 0.471330i | 0.971834 | + | 0.235665i | \(0.0757268\pi\) | ||||
−0.971834 | + | 0.235665i | \(0.924273\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.17775 | − | 2.17775i | 0.102546 | − | 0.102546i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 50.7528i | 2.37933i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 15.2508i | − | 0.713402i | −0.934219 | − | 0.356701i | \(-0.883902\pi\) | ||
0.934219 | − | 0.356701i | \(-0.116098\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.3850 | − | 14.3850i | 0.669976 | − | 0.669976i | −0.287734 | − | 0.957710i | \(-0.592902\pi\) |
0.957710 | + | 0.287734i | \(0.0929019\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.1295i | 1.02845i | 0.857657 | + | 0.514223i | \(0.171920\pi\) | ||||
−0.857657 | + | 0.514223i | \(0.828080\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.79951 | + | 4.79951i | 0.222095 | + | 0.222095i | 0.809380 | − | 0.587285i | \(-0.199803\pi\) |
−0.587285 | + | 0.809380i | \(0.699803\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.1926 | + | 40.1926i | −1.85592 | + | 1.85592i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.52905 | −0.0703058 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.92934 | − | 2.92934i | −0.134408 | − | 0.134408i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.2801 | 1.06369 | 0.531847 | − | 0.846840i | \(-0.321498\pi\) | ||||
0.531847 | + | 0.846840i | \(0.321498\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.9730 | −0.773902 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.03820 | + | 7.03820i | 0.319588 | + | 0.319588i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.0748 | −0.954990 | −0.477495 | − | 0.878635i | \(-0.658455\pi\) | ||||
−0.477495 | + | 0.878635i | \(0.658455\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.1459 | − | 26.1459i | 1.17995 | − | 1.17995i | 0.200194 | − | 0.979756i | \(-0.435843\pi\) |
0.979756 | − | 0.200194i | \(-0.0641571\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.1039 | − | 13.1039i | −0.590170 | − | 0.590170i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 52.4018i | 2.35054i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.0195 | + | 21.0195i | −0.940961 | + | 0.940961i | −0.998352 | − | 0.0573910i | \(-0.981722\pi\) |
0.0573910 | + | 0.998352i | \(0.481722\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 44.4925i | 1.98382i | 0.126929 | + | 0.991912i | \(0.459488\pi\) | ||||
−0.126929 | + | 0.991912i | \(0.540512\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.42440i | 0.330382i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.7664 | − | 11.7664i | 0.521536 | − | 0.521536i | −0.396499 | − | 0.918035i | \(-0.629775\pi\) |
0.918035 | + | 0.396499i | \(0.129775\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 2.12714i | − | 0.0940991i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.14086 | − | 2.14086i | −0.0943377 | − | 0.0943377i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.841092 | + | 0.841092i | −0.0369912 | + | 0.0369912i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.6216 | −1.29775 | −0.648873 | − | 0.760897i | \(-0.724759\pi\) | ||||
−0.648873 | + | 0.760897i | \(0.724759\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.96353 | − | 4.96353i | −0.217040 | − | 0.217040i | 0.590210 | − | 0.807250i | \(-0.299045\pi\) |
−0.807250 | + | 0.590210i | \(0.799045\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.3199 | −0.928708 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.9183 | 0.866011 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.6317 | + | 27.6317i | 1.19686 | + | 1.19686i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.81517 | 0.424347 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.67857 | + | 2.67857i | −0.115374 | + | 0.115374i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.0792 | + | 10.0792i | 0.433338 | + | 0.433338i | 0.889762 | − | 0.456424i | \(-0.150870\pi\) |
−0.456424 | + | 0.889762i | \(0.650870\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 34.0115i | 1.45689i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.48797 | + | 2.48797i | −0.106378 | + | 0.106378i | −0.758293 | − | 0.651914i | \(-0.773966\pi\) |
0.651914 | + | 0.758293i | \(0.273966\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.40953i | 0.358258i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.3662i | 1.29130i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.2575 | + | 24.2575i | −1.02782 | + | 1.02782i | −0.0282205 | + | 0.999602i | \(0.508984\pi\) |
−0.999602 | + | 0.0282205i | \(0.991016\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 19.4009i | − | 0.820570i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.4061 | − | 14.4061i | −0.607143 | − | 0.607143i | 0.335055 | − | 0.942198i | \(-0.391245\pi\) |
−0.942198 | + | 0.335055i | \(0.891245\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.41346 | − | 4.41346i | 0.185676 | − | 0.185676i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.5254 | 1.40546 | 0.702729 | − | 0.711457i | \(-0.251964\pi\) | ||||
0.702729 | + | 0.711457i | \(0.251964\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.5368 | − | 14.5368i | −0.608348 | − | 0.608348i | 0.334167 | − | 0.942514i | \(-0.391545\pi\) |
−0.942514 | + | 0.334167i | \(0.891545\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.77813 | 0.282668 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.3662 | 0.847855 | 0.423927 | − | 0.905696i | \(-0.360651\pi\) | ||||
0.423927 | + | 0.905696i | \(0.360651\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.1529 | + | 21.1529i | 0.877571 | + | 0.877571i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.17012 | −0.0484616 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.4809 | + | 17.4809i | −0.721512 | + | 0.721512i | −0.968913 | − | 0.247401i | \(-0.920424\pi\) |
0.247401 | + | 0.968913i | \(0.420424\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.84109 | + | 6.84109i | 0.281882 | + | 0.281882i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 25.6632i | − | 1.05386i | −0.849908 | − | 0.526930i | \(-0.823343\pi\) | ||
0.849908 | − | 0.526930i | \(-0.176657\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.9341 | + | 21.9341i | −0.899212 | + | 0.899212i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 22.4652i | − | 0.917902i | −0.888461 | − | 0.458951i | \(-0.848225\pi\) | ||
0.888461 | − | 0.458951i | \(-0.151775\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.8106i | 1.29758i | 0.760967 | + | 0.648790i | \(0.224725\pi\) | ||||
−0.760967 | + | 0.648790i | \(0.775275\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.9581 | − | 22.9581i | 0.933379 | − | 0.933379i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 14.9829i | − | 0.608138i | −0.952650 | − | 0.304069i | \(-0.901655\pi\) | ||
0.952650 | − | 0.304069i | \(-0.0983453\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.6720 | − | 10.6720i | −0.431741 | − | 0.431741i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.6734 | − | 25.6734i | 1.03694 | − | 1.03694i | 0.0376494 | − | 0.999291i | \(-0.488013\pi\) |
0.999291 | − | 0.0376494i | \(-0.0119870\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.1598 | −1.09341 | −0.546705 | − | 0.837325i | \(-0.684118\pi\) | ||||
−0.546705 | + | 0.837325i | \(0.684118\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.4244 | + | 29.4244i | 1.18267 | + | 1.18267i | 0.979051 | + | 0.203616i | \(0.0652693\pi\) |
0.203616 | + | 0.979051i | \(0.434731\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 30.8747 | 1.23697 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 29.3974 | 1.17590 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.33532 | − | 7.33532i | −0.292478 | − | 0.292478i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.84697 | 0.312383 | 0.156191 | − | 0.987727i | \(-0.450078\pi\) | ||||
0.156191 | + | 0.987727i | \(0.450078\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21.6386 | + | 21.6386i | −0.858702 | + | 0.858702i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.9862 | − | 33.9862i | −1.34658 | − | 1.34658i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.7956i | 1.49284i | 0.665477 | + | 0.746418i | \(0.268228\pi\) | ||||
−0.665477 | + | 0.746418i | \(0.731772\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.3026 | + | 27.3026i | −1.07671 | + | 1.07671i | −0.0799071 | + | 0.996802i | \(0.525462\pi\) |
−0.996802 | + | 0.0799071i | \(0.974538\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.100686i | 0.00395836i | 0.999998 | + | 0.00197918i | \(0.000629993\pi\) | ||||
−0.999998 | + | 0.00197918i | \(0.999370\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.46793i | 0.0576212i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.10477 | − | 9.10477i | 0.356297 | − | 0.356297i | −0.506149 | − | 0.862446i | \(-0.668931\pi\) |
0.862446 | + | 0.506149i | \(0.168931\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 28.6640i | − | 1.11999i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.6141 | + | 14.6141i | 0.569285 | + | 0.569285i | 0.931928 | − | 0.362643i | \(-0.118126\pi\) |
−0.362643 | + | 0.931928i | \(0.618126\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.87057 | − | 5.87057i | 0.228339 | − | 0.228339i | −0.583660 | − | 0.811998i | \(-0.698380\pi\) |
0.811998 | + | 0.583660i | \(0.198380\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.0764 | 0.545860 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.72929 | − | 9.72929i | −0.376720 | − | 0.376720i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.758305 | 0.0292741 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.3515 | −1.05432 | −0.527161 | − | 0.849766i | \(-0.676743\pi\) | ||||
−0.527161 | + | 0.849766i | \(0.676743\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.2462 | − | 31.2462i | −1.20089 | − | 1.20089i | −0.973897 | − | 0.226992i | \(-0.927111\pi\) |
−0.226992 | − | 0.973897i | \(-0.572889\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.7369 | −0.565551 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.0378 | − | 15.0378i | 0.575406 | − | 0.575406i | −0.358228 | − | 0.933634i | \(-0.616619\pi\) |
0.933634 | + | 0.358228i | \(0.116619\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.0310 | − | 29.0310i | −1.10922 | − | 1.10922i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 14.8468i | − | 0.565617i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.24894 | + | 4.24894i | −0.161637 | + | 0.161637i | −0.783292 | − | 0.621654i | \(-0.786461\pi\) |
0.621654 | + | 0.783292i | \(0.286461\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 55.2302i | − | 2.09500i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.8835i | 0.904653i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.4629 | + | 23.4629i | −0.886183 | + | 0.886183i | −0.994154 | − | 0.107971i | \(-0.965565\pi\) |
0.107971 | + | 0.994154i | \(0.465565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.70750i | 0.177547i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.77278 | − | 7.77278i | −0.292326 | − | 0.292326i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.79314 | − | 2.79314i | 0.104898 | − | 0.104898i | −0.652710 | − | 0.757608i | \(-0.726368\pi\) |
0.757608 | + | 0.652710i | \(0.226368\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.8294 | −0.592816 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.48264 | − | 2.48264i | −0.0928454 | − | 0.0928454i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.8130 | 1.26101 | 0.630507 | − | 0.776184i | \(-0.282847\pi\) | ||||
0.630507 | + | 0.776184i | \(0.282847\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.48264 | 0.166942 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.3990 | + | 21.3990i | 0.794740 | + | 0.794740i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.42732 | 0.0900245 | 0.0450122 | − | 0.998986i | \(-0.485667\pi\) | ||||
0.0450122 | + | 0.998986i | \(0.485667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.38460 | − | 8.38460i | 0.310115 | − | 0.310115i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.8596 | + | 16.8596i | 0.622725 | + | 0.622725i | 0.946227 | − | 0.323503i | \(-0.104860\pi\) |
−0.323503 | + | 0.946227i | \(0.604860\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 3.93214i | − | 0.144842i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.2243 | + | 25.2243i | −0.927892 | + | 0.927892i | −0.997570 | − | 0.0696780i | \(-0.977803\pi\) |
0.0696780 | + | 0.997570i | \(0.477803\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.4926i | 1.22872i | 0.789025 | + | 0.614361i | \(0.210586\pi\) | ||||
−0.789025 | + | 0.614361i | \(0.789414\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 32.6752i | − | 1.19713i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.2757 | + | 10.2757i | −0.375467 | + | 0.375467i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.9247i | 0.654081i | 0.945010 | + | 0.327040i | \(0.106051\pi\) | ||||
−0.945010 | + | 0.327040i | \(0.893949\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.426168 | − | 0.426168i | −0.0155099 | − | 0.0155099i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.10619 | − | 3.10619i | 0.112896 | − | 0.112896i | −0.648402 | − | 0.761298i | \(-0.724562\pi\) |
0.761298 | + | 0.648402i | \(0.224562\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.10917 | 0.0402073 | 0.0201037 | − | 0.999798i | \(-0.493600\pi\) | ||||
0.0201037 | + | 0.999798i | \(0.493600\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −35.6075 | − | 35.6075i | −1.28908 | − | 1.28908i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.6254 | −0.672523 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.4591 | 0.809897 | 0.404948 | − | 0.914340i | \(-0.367289\pi\) | ||||
0.404948 | + | 0.914340i | \(0.367289\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.6327 | − | 22.6327i | −0.814041 | − | 0.814041i | 0.171196 | − | 0.985237i | \(-0.445237\pi\) |
−0.985237 | + | 0.171196i | \(0.945237\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34.8159 | 1.25062 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.66372 | − | 7.66372i | 0.274581 | − | 0.274581i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.56330 | − | 2.56330i | −0.0917221 | − | 0.0917221i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 15.8232i | − | 0.564754i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.6505 | − | 38.6505i | 1.37774 | − | 1.37774i | 0.529315 | − | 0.848425i | \(-0.322449\pi\) |
0.848425 | − | 0.529315i | \(-0.177551\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.24111i | 0.328576i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.62153i | 0.341671i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.8969 | − | 37.8969i | 1.34238 | − | 1.34238i | 0.448686 | − | 0.893689i | \(-0.351892\pi\) |
0.893689 | − | 0.448686i | \(-0.148108\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 9.22432i | − | 0.326333i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.104052 | + | 0.104052i | 0.00367191 | + | 0.00367191i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.2855 | + | 16.2855i | −0.573989 | + | 0.573989i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.0719 | 0.951799 | 0.475899 | − | 0.879500i | \(-0.342123\pi\) | ||||
0.475899 | + | 0.879500i | \(0.342123\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.0554 | + | 19.0554i | 0.669126 | + | 0.669126i | 0.957514 | − | 0.288388i | \(-0.0931193\pi\) |
−0.288388 | + | 0.957514i | \(0.593119\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −55.8571 | −1.95659 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.38088 | −0.188253 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.5393 | − | 37.5393i | −1.31013 | − | 1.31013i | −0.921315 | − | 0.388817i | \(-0.872884\pi\) |
−0.388817 | − | 0.921315i | \(-0.627116\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.9589 | 0.974584 | 0.487292 | − | 0.873239i | \(-0.337985\pi\) | ||||
0.487292 | + | 0.873239i | \(0.337985\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.04182 | − | 2.04182i | 0.0710011 | − | 0.0710011i | −0.670715 | − | 0.741716i | \(-0.734012\pi\) |
0.741716 | + | 0.670715i | \(0.234012\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.5808 | + | 34.5808i | 1.20104 | + | 1.20104i | 0.973851 | + | 0.227188i | \(0.0729533\pi\) |
0.227188 | + | 0.973851i | \(0.427047\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 29.3760i | − | 1.01782i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 42.4439 | − | 42.4439i | 1.46883 | − | 1.46883i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.865723i | 0.0298881i | 0.999888 | + | 0.0149440i | \(0.00475701\pi\) | ||||
−0.999888 | + | 0.0149440i | \(0.995243\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 32.4321i | − | 1.11835i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.13669 | − | 4.13669i | 0.142306 | − | 0.142306i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48.0707i | 1.65173i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.44628 | − | 5.44628i | −0.186696 | − | 0.186696i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.4262 | + | 14.4262i | −0.493942 | + | 0.493942i | −0.909546 | − | 0.415604i | \(-0.863570\pi\) |
0.415604 | + | 0.909546i | \(0.363570\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −37.6532 | −1.28621 | −0.643105 | − | 0.765778i | \(-0.722354\pi\) | ||||
−0.643105 | + | 0.765778i | \(0.722354\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.7470 | + | 38.7470i | 1.32203 | + | 1.32203i | 0.912130 | + | 0.409901i | \(0.134437\pi\) |
0.409901 | + | 0.912130i | \(0.365563\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.8672 | −0.506085 | −0.253043 | − | 0.967455i | \(-0.581431\pi\) | ||||
−0.253043 | + | 0.967455i | \(0.581431\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.7681 | 0.570134 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.48540 | − | 1.48540i | −0.0503887 | − | 0.0503887i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49.8918 | 1.69052 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.5654 | + | 10.5654i | −0.357176 | + | 0.357176i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.7699 | − | 13.7699i | −0.464976 | − | 0.464976i | 0.435306 | − | 0.900283i | \(-0.356640\pi\) |
−0.900283 | + | 0.435306i | \(0.856640\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 20.6232i | − | 0.694812i | −0.937715 | − | 0.347406i | \(-0.887063\pi\) | ||
0.937715 | − | 0.347406i | \(-0.112937\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.5416 | − | 41.5416i | 1.39799 | − | 1.39799i | 0.592185 | − | 0.805802i | \(-0.298265\pi\) |
0.805802 | − | 0.592185i | \(-0.201735\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 7.44312i | − | 0.249916i | −0.992162 | − | 0.124958i | \(-0.960120\pi\) | ||
0.992162 | − | 0.124958i | \(-0.0398795\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 45.3079i | − | 1.51958i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.95989 | + | 2.95989i | −0.0990489 | + | 0.0990489i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 61.9602i | − | 2.07110i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −49.9746 | − | 49.9746i | −1.66675 | − | 1.66675i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.41642 | − | 6.41642i | 0.213762 | − | 0.213762i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.7431 | −0.456835 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.75106 | − | 3.75106i | −0.124552 | − | 0.124552i | 0.642083 | − | 0.766635i | \(-0.278070\pi\) |
−0.766635 | + | 0.642083i | \(0.778070\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.9816 | −0.993334 | −0.496667 | − | 0.867941i | \(-0.665443\pi\) | ||||
−0.496667 | + | 0.867941i | \(0.665443\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.06944 | −0.0684886 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 30.0090 | + | 30.0090i | 0.990984 | + | 0.990984i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.1402 | −1.25813 | −0.629064 | − | 0.777353i | \(-0.716562\pi\) | ||||
−0.629064 | + | 0.777353i | \(0.716562\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.5237 | − | 32.5237i | 1.07053 | − | 1.07053i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.9788 | + | 11.9788i | 0.393860 | + | 0.393860i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 13.8738i | − | 0.455183i | −0.973757 | − | 0.227592i | \(-0.926915\pi\) | ||
0.973757 | − | 0.227592i | \(-0.0730851\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.42615 | + | 9.42615i | −0.308930 | + | 0.308930i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 2.14587i | − | 0.0701775i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.4097i | 0.862767i | 0.902169 | + | 0.431384i | \(0.141974\pi\) | ||||
−0.902169 | + | 0.431384i | \(0.858026\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.91123 | + | 4.91123i | −0.160102 | + | 0.160102i | −0.782612 | − | 0.622510i | \(-0.786113\pi\) |
0.622510 | + | 0.782612i | \(0.286113\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.7329i | 0.577462i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.84386 | + | 6.84386i | 0.222396 | + | 0.222396i | 0.809507 | − | 0.587111i | \(-0.199735\pi\) |
−0.587111 | + | 0.809507i | \(0.699735\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.32023 | + | 1.32023i | −0.0428565 | + | 0.0428565i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.33045 | 0.140277 | 0.0701386 | − | 0.997537i | \(-0.477656\pi\) | ||||
0.0701386 | + | 0.997537i | \(0.477656\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.2048 | + | 16.2048i | 0.524377 | + | 0.524377i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 60.7864 | 1.96289 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −50.3079 | −1.62284 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.40365 | + | 7.40365i | 0.238332 | + | 0.238332i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.6664 | −1.30774 | −0.653871 | − | 0.756606i | \(-0.726856\pi\) | ||||
−0.653871 | + | 0.756606i | \(0.726856\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.0742 | + | 24.0742i | −0.772577 | + | 0.772577i | −0.978556 | − | 0.205979i | \(-0.933962\pi\) |
0.205979 | + | 0.978556i | \(0.433962\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 57.8218 | + | 57.8218i | 1.85368 | + | 1.85368i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.0381i | 0.673068i | 0.941671 | + | 0.336534i | \(0.109255\pi\) | ||||
−0.941671 | + | 0.336534i | \(0.890745\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.51028 | + | 1.51028i | −0.0482686 | + | 0.0482686i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 14.1206i | − | 0.450376i | −0.974315 | − | 0.225188i | \(-0.927700\pi\) | ||
0.974315 | − | 0.225188i | \(-0.0722997\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 26.9618i | − | 0.859074i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.22534 | − | 6.22534i | 0.197954 | − | 0.197954i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.3338i | 1.05888i | 0.848346 | + | 0.529442i | \(0.177599\pi\) | ||||
−0.848346 | + | 0.529442i | \(0.822401\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 49.1472 | + | 49.1472i | 1.55807 | + | 1.55807i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.8358 | − | 24.8358i | 0.786559 | − | 0.786559i | −0.194369 | − | 0.980928i | \(-0.562266\pi\) |
0.980928 | + | 0.194369i | \(0.0622660\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 576.2.l.a.431.2 | 16 | ||
3.2 | odd | 2 | inner | 576.2.l.a.431.7 | 16 | ||
4.3 | odd | 2 | 144.2.l.a.35.1 | ✓ | 16 | ||
8.3 | odd | 2 | 1152.2.l.a.863.7 | 16 | |||
8.5 | even | 2 | 1152.2.l.b.863.7 | 16 | |||
12.11 | even | 2 | 144.2.l.a.35.8 | yes | 16 | ||
16.3 | odd | 4 | 1152.2.l.b.287.2 | 16 | |||
16.5 | even | 4 | 144.2.l.a.107.8 | yes | 16 | ||
16.11 | odd | 4 | inner | 576.2.l.a.143.7 | 16 | ||
16.13 | even | 4 | 1152.2.l.a.287.2 | 16 | |||
24.5 | odd | 2 | 1152.2.l.b.863.2 | 16 | |||
24.11 | even | 2 | 1152.2.l.a.863.2 | 16 | |||
48.5 | odd | 4 | 144.2.l.a.107.1 | yes | 16 | ||
48.11 | even | 4 | inner | 576.2.l.a.143.2 | 16 | ||
48.29 | odd | 4 | 1152.2.l.a.287.7 | 16 | |||
48.35 | even | 4 | 1152.2.l.b.287.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.l.a.35.1 | ✓ | 16 | 4.3 | odd | 2 | ||
144.2.l.a.35.8 | yes | 16 | 12.11 | even | 2 | ||
144.2.l.a.107.1 | yes | 16 | 48.5 | odd | 4 | ||
144.2.l.a.107.8 | yes | 16 | 16.5 | even | 4 | ||
576.2.l.a.143.2 | 16 | 48.11 | even | 4 | inner | ||
576.2.l.a.143.7 | 16 | 16.11 | odd | 4 | inner | ||
576.2.l.a.431.2 | 16 | 1.1 | even | 1 | trivial | ||
576.2.l.a.431.7 | 16 | 3.2 | odd | 2 | inner | ||
1152.2.l.a.287.2 | 16 | 16.13 | even | 4 | |||
1152.2.l.a.287.7 | 16 | 48.29 | odd | 4 | |||
1152.2.l.a.863.2 | 16 | 24.11 | even | 2 | |||
1152.2.l.a.863.7 | 16 | 8.3 | odd | 2 | |||
1152.2.l.b.287.2 | 16 | 16.3 | odd | 4 | |||
1152.2.l.b.287.7 | 16 | 48.35 | even | 4 | |||
1152.2.l.b.863.2 | 16 | 24.5 | odd | 2 | |||
1152.2.l.b.863.7 | 16 | 8.5 | even | 2 |