Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5445,2,Mod(1,5445)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5445, 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("5445.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5445.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: | \(43.4785439006\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 3x^{6} + 22x^{5} - 3x^{4} - 32x^{3} + 9x^{2} + 8x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 495) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.48523\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5445.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.485227 | 0.343107 | 0.171554 | − | 0.985175i | \(-0.445121\pi\) | ||||
0.171554 | + | 0.985175i | \(0.445121\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.76455 | −0.882277 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.61947 | −0.612103 | −0.306052 | − | 0.952015i | \(-0.599008\pi\) | ||||
−0.306052 | + | 0.952015i | \(0.599008\pi\) | |||||||
\(8\) | −1.82666 | −0.645823 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.485227 | −0.153442 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.95793 | 1.37508 | 0.687542 | − | 0.726145i | \(-0.258690\pi\) | ||||
0.687542 | + | 0.726145i | \(0.258690\pi\) | |||||||
\(14\) | −0.785812 | −0.210017 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.64276 | 0.660691 | ||||||||
\(17\) | −3.13866 | −0.761238 | −0.380619 | − | 0.924732i | \(-0.624289\pi\) | ||||
−0.380619 | + | 0.924732i | \(0.624289\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.09825 | 0.251956 | 0.125978 | − | 0.992033i | \(-0.459793\pi\) | ||||
0.125978 | + | 0.992033i | \(0.459793\pi\) | |||||||
\(20\) | 1.76455 | 0.394566 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.75778 | −1.40909 | −0.704547 | − | 0.709657i | \(-0.748850\pi\) | ||||
−0.704547 | + | 0.709657i | \(0.748850\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.40572 | 0.471801 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.85765 | 0.540045 | ||||||||
\(29\) | 3.55099 | 0.659402 | 0.329701 | − | 0.944085i | \(-0.393052\pi\) | ||||
0.329701 | + | 0.944085i | \(0.393052\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.53688 | 1.53327 | 0.766634 | − | 0.642084i | \(-0.221930\pi\) | ||||
0.766634 | + | 0.642084i | \(0.221930\pi\) | |||||||
\(32\) | 4.93567 | 0.872511 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.52296 | −0.261186 | ||||||||
\(35\) | 1.61947 | 0.273741 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.35976 | −0.881139 | −0.440570 | − | 0.897718i | \(-0.645223\pi\) | ||||
−0.440570 | + | 0.897718i | \(0.645223\pi\) | |||||||
\(38\) | 0.532901 | 0.0864479 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.82666 | 0.288821 | ||||||||
\(41\) | −5.32036 | −0.830901 | −0.415451 | − | 0.909616i | \(-0.636376\pi\) | ||||
−0.415451 | + | 0.909616i | \(0.636376\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.41085 | 0.520150 | 0.260075 | − | 0.965588i | \(-0.416253\pi\) | ||||
0.260075 | + | 0.965588i | \(0.416253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.27906 | −0.483471 | ||||||||
\(47\) | 6.60156 | 0.962937 | 0.481469 | − | 0.876463i | \(-0.340104\pi\) | ||||
0.481469 | + | 0.876463i | \(0.340104\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.37731 | −0.625330 | ||||||||
\(50\) | 0.485227 | 0.0686215 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.74854 | −1.21320 | ||||||||
\(53\) | 9.71622 | 1.33463 | 0.667313 | − | 0.744778i | \(-0.267444\pi\) | ||||
0.667313 | + | 0.744778i | \(0.267444\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.95823 | 0.395310 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.72304 | 0.226246 | ||||||||
\(59\) | 7.18545 | 0.935466 | 0.467733 | − | 0.883870i | \(-0.345071\pi\) | ||||
0.467733 | + | 0.883870i | \(0.345071\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.63497 | −0.849521 | −0.424760 | − | 0.905306i | \(-0.639642\pi\) | ||||
−0.424760 | + | 0.905306i | \(0.639642\pi\) | |||||||
\(62\) | 4.14232 | 0.526076 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.89061 | −0.361326 | ||||||||
\(65\) | −4.95793 | −0.614956 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.36043 | 0.288373 | 0.144186 | − | 0.989551i | \(-0.453944\pi\) | ||||
0.144186 | + | 0.989551i | \(0.453944\pi\) | |||||||
\(68\) | 5.53834 | 0.671623 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.785812 | 0.0939225 | ||||||||
\(71\) | −16.6559 | −1.97670 | −0.988348 | − | 0.152212i | \(-0.951360\pi\) | ||||
−0.988348 | + | 0.152212i | \(0.951360\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.49548 | 0.994320 | 0.497160 | − | 0.867659i | \(-0.334376\pi\) | ||||
0.497160 | + | 0.867659i | \(0.334376\pi\) | |||||||
\(74\) | −2.60070 | −0.302325 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.93792 | −0.222295 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.99189 | −0.224105 | −0.112053 | − | 0.993702i | \(-0.535742\pi\) | ||||
−0.112053 | + | 0.993702i | \(0.535742\pi\) | |||||||
\(80\) | −2.64276 | −0.295470 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.58158 | −0.285088 | ||||||||
\(83\) | 9.54929 | 1.04817 | 0.524085 | − | 0.851666i | \(-0.324407\pi\) | ||||
0.524085 | + | 0.851666i | \(0.324407\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.13866 | 0.340436 | ||||||||
\(86\) | 1.65504 | 0.178467 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.65371 | −0.281293 | −0.140647 | − | 0.990060i | \(-0.544918\pi\) | ||||
−0.140647 | + | 0.990060i | \(0.544918\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.02924 | −0.841693 | ||||||||
\(92\) | 11.9245 | 1.24321 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.20326 | 0.330391 | ||||||||
\(95\) | −1.09825 | −0.112678 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.5239 | −1.47468 | −0.737338 | − | 0.675524i | \(-0.763918\pi\) | ||||
−0.737338 | + | 0.675524i | \(0.763918\pi\) | |||||||
\(98\) | −2.12399 | −0.214555 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.76455 | −0.176455 | ||||||||
\(101\) | −17.6927 | −1.76049 | −0.880247 | − | 0.474517i | \(-0.842623\pi\) | ||||
−0.880247 | + | 0.474517i | \(0.842623\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.93631 | −0.486389 | −0.243195 | − | 0.969978i | \(-0.578195\pi\) | ||||
−0.243195 | + | 0.969978i | \(0.578195\pi\) | |||||||
\(104\) | −9.05648 | −0.888061 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.71457 | 0.457920 | ||||||||
\(107\) | −12.7475 | −1.23235 | −0.616173 | − | 0.787611i | \(-0.711318\pi\) | ||||
−0.616173 | + | 0.787611i | \(0.711318\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.5953 | 1.49376 | 0.746879 | − | 0.664960i | \(-0.231551\pi\) | ||||
0.746879 | + | 0.664960i | \(0.231551\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.27988 | −0.404411 | ||||||||
\(113\) | 5.63373 | 0.529977 | 0.264988 | − | 0.964252i | \(-0.414632\pi\) | ||||
0.264988 | + | 0.964252i | \(0.414632\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.75778 | 0.630166 | ||||||||
\(116\) | −6.26592 | −0.581776 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.48658 | 0.320965 | ||||||||
\(119\) | 5.08298 | 0.465956 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −3.21947 | −0.291477 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −15.0638 | −1.35277 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.36289 | 0.653351 | 0.326676 | − | 0.945137i | \(-0.394072\pi\) | ||||
0.326676 | + | 0.945137i | \(0.394072\pi\) | |||||||
\(128\) | −11.2739 | −0.996485 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.40572 | −0.210996 | ||||||||
\(131\) | 6.74024 | 0.588897 | 0.294449 | − | 0.955667i | \(-0.404864\pi\) | ||||
0.294449 | + | 0.955667i | \(0.404864\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.77859 | −0.154223 | ||||||||
\(134\) | 1.14535 | 0.0989428 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.73328 | 0.491625 | ||||||||
\(137\) | −6.32003 | −0.539957 | −0.269978 | − | 0.962866i | \(-0.587017\pi\) | ||||
−0.269978 | + | 0.962866i | \(0.587017\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.0838 | −1.19457 | −0.597285 | − | 0.802029i | \(-0.703754\pi\) | ||||
−0.597285 | + | 0.802029i | \(0.703754\pi\) | |||||||
\(140\) | −2.85765 | −0.241515 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.08191 | −0.678219 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.55099 | −0.294894 | ||||||||
\(146\) | 4.12224 | 0.341159 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.45759 | 0.777409 | ||||||||
\(149\) | −17.3475 | −1.42116 | −0.710582 | − | 0.703614i | \(-0.751568\pi\) | ||||
−0.710582 | + | 0.703614i | \(0.751568\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.01455 | −0.733593 | −0.366797 | − | 0.930301i | \(-0.619546\pi\) | ||||
−0.366797 | + | 0.930301i | \(0.619546\pi\) | |||||||
\(152\) | −2.00613 | −0.162719 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.53688 | −0.685698 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.9364 | 0.952628 | 0.476314 | − | 0.879275i | \(-0.341972\pi\) | ||||
0.476314 | + | 0.879275i | \(0.341972\pi\) | |||||||
\(158\) | −0.966519 | −0.0768921 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.93567 | −0.390199 | ||||||||
\(161\) | 10.9440 | 0.862511 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.32743 | −0.182298 | −0.0911491 | − | 0.995837i | \(-0.529054\pi\) | ||||
−0.0911491 | + | 0.995837i | \(0.529054\pi\) | |||||||
\(164\) | 9.38807 | 0.733085 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.63357 | 0.359635 | ||||||||
\(167\) | −9.82442 | −0.760237 | −0.380118 | − | 0.924938i | \(-0.624117\pi\) | ||||
−0.380118 | + | 0.924938i | \(0.624117\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5811 | 0.890854 | ||||||||
\(170\) | 1.52296 | 0.116806 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.01864 | −0.458917 | ||||||||
\(173\) | −23.2400 | −1.76690 | −0.883452 | − | 0.468521i | \(-0.844787\pi\) | ||||
−0.883452 | + | 0.468521i | \(0.844787\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.61947 | −0.122421 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.28765 | −0.0965137 | ||||||||
\(179\) | 0.376550 | 0.0281447 | 0.0140724 | − | 0.999901i | \(-0.495520\pi\) | ||||
0.0140724 | + | 0.999901i | \(0.495520\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.58158 | −0.563534 | −0.281767 | − | 0.959483i | \(-0.590921\pi\) | ||||
−0.281767 | + | 0.959483i | \(0.590921\pi\) | |||||||
\(182\) | −3.89600 | −0.288791 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.3442 | 0.910026 | ||||||||
\(185\) | 5.35976 | 0.394057 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −11.6488 | −0.849578 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.532901 | −0.0386607 | ||||||||
\(191\) | −2.16401 | −0.156583 | −0.0782913 | − | 0.996931i | \(-0.524946\pi\) | ||||
−0.0782913 | + | 0.996931i | \(0.524946\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.5881 | −1.33800 | −0.668999 | − | 0.743263i | \(-0.733277\pi\) | ||||
−0.668999 | + | 0.743263i | \(0.733277\pi\) | |||||||
\(194\) | −7.04738 | −0.505972 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.72400 | 0.551714 | ||||||||
\(197\) | 8.70640 | 0.620306 | 0.310153 | − | 0.950687i | \(-0.399620\pi\) | ||||
0.310153 | + | 0.950687i | \(0.399620\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.9231 | −1.34142 | −0.670712 | − | 0.741718i | \(-0.734011\pi\) | ||||
−0.670712 | + | 0.741718i | \(0.734011\pi\) | |||||||
\(200\) | −1.82666 | −0.129165 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.58499 | −0.604038 | ||||||||
\(203\) | −5.75073 | −0.403622 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.32036 | 0.371590 | ||||||||
\(206\) | −2.39523 | −0.166884 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 13.1026 | 0.908505 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.3522 | 1.19457 | 0.597287 | − | 0.802027i | \(-0.296245\pi\) | ||||
0.597287 | + | 0.802027i | \(0.296245\pi\) | |||||||
\(212\) | −17.1448 | −1.17751 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.18542 | −0.422827 | ||||||||
\(215\) | −3.41085 | −0.232618 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.8252 | −0.938519 | ||||||||
\(218\) | 7.56726 | 0.512519 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.5613 | −1.04677 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.19082 | 0.481533 | 0.240767 | − | 0.970583i | \(-0.422601\pi\) | ||||
0.240767 | + | 0.970583i | \(0.422601\pi\) | |||||||
\(224\) | −7.99318 | −0.534067 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.73364 | 0.181839 | ||||||||
\(227\) | −27.3012 | −1.81205 | −0.906023 | − | 0.423229i | \(-0.860897\pi\) | ||||
−0.906023 | + | 0.423229i | \(0.860897\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.3763 | 0.817848 | 0.408924 | − | 0.912568i | \(-0.365904\pi\) | ||||
0.408924 | + | 0.912568i | \(0.365904\pi\) | |||||||
\(230\) | 3.27906 | 0.216215 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.48646 | −0.425857 | ||||||||
\(233\) | −14.5447 | −0.952857 | −0.476429 | − | 0.879213i | \(-0.658069\pi\) | ||||
−0.476429 | + | 0.879213i | \(0.658069\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.60156 | −0.430639 | ||||||||
\(236\) | −12.6791 | −0.825341 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.46640 | 0.159873 | ||||||||
\(239\) | −28.9267 | −1.87112 | −0.935558 | − | 0.353173i | \(-0.885103\pi\) | ||||
−0.935558 | + | 0.353173i | \(0.885103\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.40610 | −0.605900 | −0.302950 | − | 0.953006i | \(-0.597972\pi\) | ||||
−0.302950 | + | 0.953006i | \(0.597972\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.7078 | 0.749513 | ||||||||
\(245\) | 4.37731 | 0.279656 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.44505 | 0.346460 | ||||||||
\(248\) | −15.5940 | −0.990220 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.485227 | −0.0306885 | ||||||||
\(251\) | −0.0325382 | −0.00205379 | −0.00102690 | − | 0.999999i | \(-0.500327\pi\) | ||||
−0.00102690 | + | 0.999999i | \(0.500327\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 3.57267 | 0.224170 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.310793 | 0.0194246 | ||||||||
\(257\) | −6.61680 | −0.412745 | −0.206372 | − | 0.978474i | \(-0.566166\pi\) | ||||
−0.206372 | + | 0.978474i | \(0.566166\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.67999 | 0.539348 | ||||||||
\(260\) | 8.74854 | 0.542562 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.27055 | 0.202055 | ||||||||
\(263\) | −5.19057 | −0.320064 | −0.160032 | − | 0.987112i | \(-0.551160\pi\) | ||||
−0.160032 | + | 0.987112i | \(0.551160\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.71622 | −0.596863 | ||||||||
\(266\) | −0.863018 | −0.0529150 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.16511 | −0.254425 | ||||||||
\(269\) | 15.8774 | 0.968060 | 0.484030 | − | 0.875052i | \(-0.339173\pi\) | ||||
0.484030 | + | 0.875052i | \(0.339173\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.2337 | −1.59358 | −0.796791 | − | 0.604255i | \(-0.793471\pi\) | ||||
−0.796791 | + | 0.604255i | \(0.793471\pi\) | |||||||
\(272\) | −8.29474 | −0.502943 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.06665 | −0.185263 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.51114 | −0.391216 | −0.195608 | − | 0.980682i | \(-0.562668\pi\) | ||||
−0.195608 | + | 0.980682i | \(0.562668\pi\) | |||||||
\(278\) | −6.83383 | −0.409866 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.95823 | −0.176788 | ||||||||
\(281\) | −11.2188 | −0.669258 | −0.334629 | − | 0.942350i | \(-0.608611\pi\) | ||||
−0.334629 | + | 0.942350i | \(0.608611\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.27653 | 0.491989 | 0.245994 | − | 0.969271i | \(-0.420886\pi\) | ||||
0.245994 | + | 0.969271i | \(0.420886\pi\) | |||||||
\(284\) | 29.3903 | 1.74399 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.61619 | 0.508597 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.14879 | −0.420517 | ||||||||
\(290\) | −1.72304 | −0.101180 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.9907 | −0.877266 | ||||||||
\(293\) | 0.418459 | 0.0244466 | 0.0122233 | − | 0.999925i | \(-0.496109\pi\) | ||||
0.0122233 | + | 0.999925i | \(0.496109\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.18545 | −0.418353 | ||||||||
\(296\) | 9.79048 | 0.569060 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.41749 | −0.487612 | ||||||||
\(299\) | −33.5046 | −1.93762 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.52378 | −0.318386 | ||||||||
\(302\) | −4.37410 | −0.251701 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.90241 | 0.166465 | ||||||||
\(305\) | 6.63497 | 0.379917 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −32.7941 | −1.87166 | −0.935828 | − | 0.352457i | \(-0.885346\pi\) | ||||
−0.935828 | + | 0.352457i | \(0.885346\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.14232 | −0.235268 | ||||||||
\(311\) | 0.509602 | 0.0288969 | 0.0144484 | − | 0.999896i | \(-0.495401\pi\) | ||||
0.0144484 | + | 0.999896i | \(0.495401\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.83268 | 0.160113 | 0.0800563 | − | 0.996790i | \(-0.474490\pi\) | ||||
0.0800563 | + | 0.996790i | \(0.474490\pi\) | |||||||
\(314\) | 5.79186 | 0.326854 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.51480 | 0.197723 | ||||||||
\(317\) | 26.9913 | 1.51598 | 0.757992 | − | 0.652264i | \(-0.226181\pi\) | ||||
0.757992 | + | 0.652264i | \(0.226181\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 2.89061 | 0.161590 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.31034 | 0.295934 | ||||||||
\(323\) | −3.44704 | −0.191798 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.95793 | 0.275017 | ||||||||
\(326\) | −1.12933 | −0.0625479 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.71852 | 0.536615 | ||||||||
\(329\) | −10.6911 | −0.589417 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.5474 | 1.18435 | 0.592175 | − | 0.805809i | \(-0.298269\pi\) | ||||
0.592175 | + | 0.805809i | \(0.298269\pi\) | |||||||
\(332\) | −16.8502 | −0.924777 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.76708 | −0.260843 | ||||||||
\(335\) | −2.36043 | −0.128964 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.9766 | 0.597932 | 0.298966 | − | 0.954264i | \(-0.403358\pi\) | ||||
0.298966 | + | 0.954264i | \(0.403358\pi\) | |||||||
\(338\) | 5.61946 | 0.305658 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.53834 | −0.300359 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4252 | 0.994870 | ||||||||
\(344\) | −6.23048 | −0.335925 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.2767 | −0.606238 | ||||||||
\(347\) | −16.7192 | −0.897532 | −0.448766 | − | 0.893649i | \(-0.648136\pi\) | ||||
−0.448766 | + | 0.893649i | \(0.648136\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.59837 | 0.246145 | 0.123072 | − | 0.992398i | \(-0.460725\pi\) | ||||
0.123072 | + | 0.992398i | \(0.460725\pi\) | |||||||
\(350\) | −0.785812 | −0.0420034 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.4628 | 0.769775 | 0.384887 | − | 0.922964i | \(-0.374240\pi\) | ||||
0.384887 | + | 0.922964i | \(0.374240\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.6559 | 0.884005 | ||||||||
\(356\) | 4.68262 | 0.248179 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.182712 | 0.00965665 | ||||||||
\(359\) | 8.56634 | 0.452114 | 0.226057 | − | 0.974114i | \(-0.427416\pi\) | ||||
0.226057 | + | 0.974114i | \(0.427416\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7938 | −0.936518 | ||||||||
\(362\) | −3.67879 | −0.193353 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 14.1680 | 0.742607 | ||||||||
\(365\) | −8.49548 | −0.444674 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.14927 | 0.0599913 | 0.0299956 | − | 0.999550i | \(-0.490451\pi\) | ||||
0.0299956 | + | 0.999550i | \(0.490451\pi\) | |||||||
\(368\) | −17.8592 | −0.930975 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.60070 | 0.135204 | ||||||||
\(371\) | −15.7352 | −0.816929 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.1348 | 1.66388 | 0.831939 | − | 0.554867i | \(-0.187231\pi\) | ||||
0.831939 | + | 0.554867i | \(0.187231\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.0588 | −0.621887 | ||||||||
\(377\) | 17.6056 | 0.906733 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.7386 | 0.757073 | 0.378537 | − | 0.925586i | \(-0.376427\pi\) | ||||
0.378537 | + | 0.925586i | \(0.376427\pi\) | |||||||
\(380\) | 1.93792 | 0.0994133 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.05004 | −0.0537246 | ||||||||
\(383\) | −30.0887 | −1.53746 | −0.768732 | − | 0.639572i | \(-0.779112\pi\) | ||||
−0.768732 | + | 0.639572i | \(0.779112\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.01943 | −0.459077 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 25.6282 | 1.30107 | ||||||||
\(389\) | 34.6757 | 1.75813 | 0.879064 | − | 0.476704i | \(-0.158169\pi\) | ||||
0.879064 | + | 0.476704i | \(0.158169\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.2104 | 1.07266 | ||||||||
\(392\) | 7.99587 | 0.403852 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.22458 | 0.212831 | ||||||||
\(395\) | 1.99189 | 0.100223 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 36.4341 | 1.82858 | 0.914288 | − | 0.405064i | \(-0.132751\pi\) | ||||
0.914288 | + | 0.405064i | \(0.132751\pi\) | |||||||
\(398\) | −9.18200 | −0.460252 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.64276 | 0.132138 | ||||||||
\(401\) | 21.5435 | 1.07583 | 0.537917 | − | 0.842998i | \(-0.319212\pi\) | ||||
0.537917 | + | 0.842998i | \(0.319212\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 42.3253 | 2.10837 | ||||||||
\(404\) | 31.2198 | 1.55324 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.79041 | −0.138486 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.77447 | −0.285529 | −0.142765 | − | 0.989757i | \(-0.545599\pi\) | ||||
−0.142765 | + | 0.989757i | \(0.545599\pi\) | |||||||
\(410\) | 2.58158 | 0.127495 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.71039 | 0.429130 | ||||||||
\(413\) | −11.6366 | −0.572602 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.54929 | −0.468756 | ||||||||
\(416\) | 24.4707 | 1.19978 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.4745 | −0.658273 | −0.329137 | − | 0.944282i | \(-0.606758\pi\) | ||||
−0.329137 | + | 0.944282i | \(0.606758\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.2366 | −1.18122 | −0.590610 | − | 0.806957i | \(-0.701113\pi\) | ||||
−0.590610 | + | 0.806957i | \(0.701113\pi\) | |||||||
\(422\) | 8.41976 | 0.409867 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −17.7483 | −0.861932 | ||||||||
\(425\) | −3.13866 | −0.152248 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.7452 | 0.519994 | ||||||||
\(428\) | 22.4936 | 1.08727 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.65504 | −0.0798130 | ||||||||
\(431\) | −0.775904 | −0.0373740 | −0.0186870 | − | 0.999825i | \(-0.505949\pi\) | ||||
−0.0186870 | + | 0.999825i | \(0.505949\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.5838 | 1.66199 | 0.830995 | − | 0.556280i | \(-0.187772\pi\) | ||||
0.830995 | + | 0.556280i | \(0.187772\pi\) | |||||||
\(434\) | −6.70838 | −0.322013 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −27.5187 | −1.31791 | ||||||||
\(437\) | −7.42173 | −0.355030 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.24100 | 0.345594 | 0.172797 | − | 0.984957i | \(-0.444720\pi\) | ||||
0.172797 | + | 0.984957i | \(0.444720\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.55076 | −0.359153 | ||||||||
\(443\) | −5.41215 | −0.257139 | −0.128570 | − | 0.991701i | \(-0.541039\pi\) | ||||
−0.128570 | + | 0.991701i | \(0.541039\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.65371 | 0.125798 | ||||||||
\(446\) | 3.48918 | 0.165218 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.68126 | 0.221169 | ||||||||
\(449\) | 12.8909 | 0.608359 | 0.304180 | − | 0.952615i | \(-0.401618\pi\) | ||||
0.304180 | + | 0.952615i | \(0.401618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −9.94102 | −0.467586 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.2473 | −0.621726 | ||||||||
\(455\) | 8.02924 | 0.376416 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.70545 | 0.0797777 | 0.0398888 | − | 0.999204i | \(-0.487300\pi\) | ||||
0.0398888 | + | 0.999204i | \(0.487300\pi\) | |||||||
\(458\) | 6.00531 | 0.280610 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −11.9245 | −0.555981 | ||||||||
\(461\) | −29.9226 | −1.39364 | −0.696818 | − | 0.717248i | \(-0.745401\pi\) | ||||
−0.696818 | + | 0.717248i | \(0.745401\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.9765 | −1.57902 | −0.789511 | − | 0.613736i | \(-0.789666\pi\) | ||||
−0.789511 | + | 0.613736i | \(0.789666\pi\) | |||||||
\(464\) | 9.38442 | 0.435661 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.05750 | −0.326932 | ||||||||
\(467\) | −0.169922 | −0.00786304 | −0.00393152 | − | 0.999992i | \(-0.501251\pi\) | ||||
−0.00393152 | + | 0.999992i | \(0.501251\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.82265 | −0.176514 | ||||||||
\(470\) | −3.20326 | −0.147755 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −13.1254 | −0.604146 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.09825 | 0.0503912 | ||||||||
\(476\) | −8.96920 | −0.411103 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14.0360 | −0.641994 | ||||||||
\(479\) | −14.6180 | −0.667912 | −0.333956 | − | 0.942589i | \(-0.608384\pi\) | ||||
−0.333956 | + | 0.942589i | \(0.608384\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.5733 | −1.21164 | ||||||||
\(482\) | −4.56410 | −0.207889 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.5239 | 0.659495 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.9520 | −1.08537 | −0.542684 | − | 0.839937i | \(-0.682592\pi\) | ||||
−0.542684 | + | 0.839937i | \(0.682592\pi\) | |||||||
\(488\) | 12.1199 | 0.548640 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.12399 | 0.0959520 | ||||||||
\(491\) | −31.7288 | −1.43190 | −0.715950 | − | 0.698151i | \(-0.754006\pi\) | ||||
−0.715950 | + | 0.698151i | \(0.754006\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.1454 | −0.501962 | ||||||||
\(494\) | 2.64209 | 0.118873 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 22.5609 | 1.01302 | ||||||||
\(497\) | 26.9738 | 1.20994 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.1017 | 1.48183 | 0.740917 | − | 0.671596i | \(-0.234391\pi\) | ||||
0.740917 | + | 0.671596i | \(0.234391\pi\) | |||||||
\(500\) | 1.76455 | 0.0789133 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.0157884 | −0.000704672 0 | ||||||||
\(503\) | −18.1421 | −0.808917 | −0.404459 | − | 0.914556i | \(-0.632540\pi\) | ||||
−0.404459 | + | 0.914556i | \(0.632540\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.6927 | 0.787316 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.9922 | −0.576437 | ||||||||
\(509\) | 16.6736 | 0.739044 | 0.369522 | − | 0.929222i | \(-0.379522\pi\) | ||||
0.369522 | + | 0.929222i | \(0.379522\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.7582 | −0.608627 | ||||||||
\(512\) | 22.6987 | 1.00315 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.21065 | −0.141616 | ||||||||
\(515\) | 4.93631 | 0.217520 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 4.21176 | 0.185054 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.05648 | 0.397153 | ||||||||
\(521\) | −20.5225 | −0.899108 | −0.449554 | − | 0.893253i | \(-0.648417\pi\) | ||||
−0.449554 | + | 0.893253i | \(0.648417\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.404664 | 0.0176947 | 0.00884736 | − | 0.999961i | \(-0.497184\pi\) | ||||
0.00884736 | + | 0.999961i | \(0.497184\pi\) | |||||||
\(524\) | −11.8935 | −0.519571 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.51860 | −0.109816 | ||||||||
\(527\) | −26.7944 | −1.16718 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.6676 | 0.985546 | ||||||||
\(530\) | −4.71457 | −0.204788 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.13841 | 0.136067 | ||||||||
\(533\) | −26.3780 | −1.14256 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.7475 | 0.551122 | ||||||||
\(536\) | −4.31171 | −0.186238 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.70412 | 0.332148 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.7037 | −0.761142 | −0.380571 | − | 0.924752i | \(-0.624272\pi\) | ||||
−0.380571 | + | 0.924752i | \(0.624272\pi\) | |||||||
\(542\) | −12.7293 | −0.546769 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −15.4914 | −0.664188 | ||||||||
\(545\) | −15.5953 | −0.668029 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.79243 | 0.247666 | 0.123833 | − | 0.992303i | \(-0.460481\pi\) | ||||
0.123833 | + | 0.992303i | \(0.460481\pi\) | |||||||
\(548\) | 11.1520 | 0.476392 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.89987 | 0.166140 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.22581 | 0.137175 | ||||||||
\(554\) | −3.15938 | −0.134229 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 24.8516 | 1.05394 | ||||||||
\(557\) | 41.1689 | 1.74438 | 0.872191 | − | 0.489166i | \(-0.162699\pi\) | ||||
0.872191 | + | 0.489166i | \(0.162699\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.9108 | 0.715250 | ||||||||
\(560\) | 4.27988 | 0.180858 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.44367 | −0.229627 | ||||||||
\(563\) | −12.0373 | −0.507314 | −0.253657 | − | 0.967294i | \(-0.581633\pi\) | ||||
−0.253657 | + | 0.967294i | \(0.581633\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.63373 | −0.237013 | ||||||||
\(566\) | 4.01600 | 0.168805 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 30.4248 | 1.27660 | ||||||||
\(569\) | −3.69378 | −0.154851 | −0.0774256 | − | 0.996998i | \(-0.524670\pi\) | ||||
−0.0774256 | + | 0.996998i | \(0.524670\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.17733 | −0.216665 | −0.108332 | − | 0.994115i | \(-0.534551\pi\) | ||||
−0.108332 | + | 0.994115i | \(0.534551\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.18081 | 0.174503 | ||||||||
\(575\) | −6.75778 | −0.281819 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.984135 | 0.0409701 | 0.0204850 | − | 0.999790i | \(-0.493479\pi\) | ||||
0.0204850 | + | 0.999790i | \(0.493479\pi\) | |||||||
\(578\) | −3.46879 | −0.144282 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.26592 | 0.260178 | ||||||||
\(581\) | −15.4648 | −0.641589 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −15.5184 | −0.642155 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.203048 | 0.00838782 | ||||||||
\(587\) | −31.6510 | −1.30638 | −0.653188 | − | 0.757196i | \(-0.726569\pi\) | ||||
−0.653188 | + | 0.757196i | \(0.726569\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.37563 | 0.386316 | ||||||||
\(590\) | −3.48658 | −0.143540 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −14.1646 | −0.582160 | ||||||||
\(593\) | 38.9330 | 1.59879 | 0.799394 | − | 0.600808i | \(-0.205154\pi\) | ||||
0.799394 | + | 0.600808i | \(0.205154\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.08298 | −0.208382 | ||||||||
\(596\) | 30.6107 | 1.25386 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −16.2573 | −0.664812 | ||||||||
\(599\) | −1.69868 | −0.0694063 | −0.0347031 | − | 0.999398i | \(-0.511049\pi\) | ||||
−0.0347031 | + | 0.999398i | \(0.511049\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.0817 | −1.67576 | −0.837879 | − | 0.545856i | \(-0.816205\pi\) | ||||
−0.837879 | + | 0.545856i | \(0.816205\pi\) | |||||||
\(602\) | −2.68029 | −0.109240 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 15.9067 | 0.647233 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.8428 | −0.886573 | −0.443287 | − | 0.896380i | \(-0.646188\pi\) | ||||
−0.443287 | + | 0.896380i | \(0.646188\pi\) | |||||||
\(608\) | 5.42060 | 0.219834 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.21947 | 0.130352 | ||||||||
\(611\) | 32.7301 | 1.32412 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 45.7809 | 1.84907 | 0.924536 | − | 0.381096i | \(-0.124453\pi\) | ||||
0.924536 | + | 0.381096i | \(0.124453\pi\) | |||||||
\(614\) | −15.9126 | −0.642179 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −37.0763 | −1.49263 | −0.746317 | − | 0.665590i | \(-0.768180\pi\) | ||||
−0.746317 | + | 0.665590i | \(0.768180\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.2548 | 0.653334 | 0.326667 | − | 0.945139i | \(-0.394074\pi\) | ||||
0.326667 | + | 0.945139i | \(0.394074\pi\) | |||||||
\(620\) | 15.0638 | 0.604976 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.247273 | 0.00991474 | ||||||||
\(623\) | 4.29762 | 0.172180 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 1.37449 | 0.0549358 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −21.0624 | −0.840482 | ||||||||
\(629\) | 16.8225 | 0.670756 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.08331 | −0.361601 | −0.180800 | − | 0.983520i | \(-0.557869\pi\) | ||||
−0.180800 | + | 0.983520i | \(0.557869\pi\) | |||||||
\(632\) | 3.63851 | 0.144732 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.0969 | 0.520145 | ||||||||
\(635\) | −7.36289 | −0.292187 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.7024 | −0.859880 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11.2739 | 0.445641 | ||||||||
\(641\) | −7.45471 | −0.294443 | −0.147222 | − | 0.989104i | \(-0.547033\pi\) | ||||
−0.147222 | + | 0.989104i | \(0.547033\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.1591 | 1.74147 | 0.870733 | − | 0.491756i | \(-0.163645\pi\) | ||||
0.870733 | + | 0.491756i | \(0.163645\pi\) | |||||||
\(644\) | −19.3114 | −0.760974 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.67260 | −0.0658074 | ||||||||
\(647\) | −11.4388 | −0.449704 | −0.224852 | − | 0.974393i | \(-0.572190\pi\) | ||||
−0.224852 | + | 0.974393i | \(0.572190\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.40572 | 0.0943602 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.10687 | 0.160838 | ||||||||
\(653\) | 1.97887 | 0.0774393 | 0.0387196 | − | 0.999250i | \(-0.487672\pi\) | ||||
0.0387196 | + | 0.999250i | \(0.487672\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.74024 | −0.263363 | ||||||||
\(656\) | −14.0605 | −0.548969 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.18759 | −0.202233 | ||||||||
\(659\) | −18.3062 | −0.713107 | −0.356553 | − | 0.934275i | \(-0.616048\pi\) | ||||
−0.356553 | + | 0.934275i | \(0.616048\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.16189 | −0.0451922 | −0.0225961 | − | 0.999745i | \(-0.507193\pi\) | ||||
−0.0225961 | + | 0.999745i | \(0.507193\pi\) | |||||||
\(662\) | 10.4554 | 0.406359 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −17.4433 | −0.676933 | ||||||||
\(665\) | 1.77859 | 0.0689706 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.9968 | −0.929160 | ||||||||
\(668\) | 17.3357 | 0.670740 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.14535 | −0.0442485 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.31368 | 0.0506385 | 0.0253192 | − | 0.999679i | \(-0.491940\pi\) | ||||
0.0253192 | + | 0.999679i | \(0.491940\pi\) | |||||||
\(674\) | 5.32613 | 0.205155 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.4355 | −0.785980 | ||||||||
\(677\) | 19.2668 | 0.740484 | 0.370242 | − | 0.928935i | \(-0.379275\pi\) | ||||
0.370242 | + | 0.928935i | \(0.379275\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.5210 | 0.902654 | ||||||||
\(680\) | −5.73328 | −0.219861 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.15293 | 0.273699 | 0.136850 | − | 0.990592i | \(-0.456302\pi\) | ||||
0.136850 | + | 0.990592i | \(0.456302\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.32003 | 0.241476 | ||||||||
\(686\) | 8.94043 | 0.341347 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.01407 | 0.343658 | ||||||||
\(689\) | 48.1724 | 1.83522 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.8320 | 0.792485 | 0.396242 | − | 0.918146i | \(-0.370314\pi\) | ||||
0.396242 | + | 0.918146i | \(0.370314\pi\) | |||||||
\(692\) | 41.0083 | 1.55890 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.11259 | −0.307950 | ||||||||
\(695\) | 14.0838 | 0.534228 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.6988 | 0.632513 | ||||||||
\(698\) | 2.23125 | 0.0844541 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.85765 | 0.108009 | ||||||||
\(701\) | −18.7296 | −0.707408 | −0.353704 | − | 0.935357i | \(-0.615078\pi\) | ||||
−0.353704 | + | 0.935357i | \(0.615078\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.88636 | −0.222008 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.01772 | 0.264115 | ||||||||
\(707\) | 28.6529 | 1.07760 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.0328 | −0.677236 | −0.338618 | − | 0.940924i | \(-0.609959\pi\) | ||||
−0.338618 | + | 0.940924i | \(0.609959\pi\) | |||||||
\(710\) | 8.08191 | 0.303309 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.84744 | 0.181666 | ||||||||
\(713\) | −57.6903 | −2.16052 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.664444 | −0.0248314 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.15662 | 0.155124 | ||||||||
\(719\) | −39.4673 | −1.47188 | −0.735942 | − | 0.677045i | \(-0.763260\pi\) | ||||
−0.735942 | + | 0.677045i | \(0.763260\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.99423 | 0.297721 | ||||||||
\(722\) | −8.63406 | −0.321326 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.3781 | 0.497193 | ||||||||
\(725\) | 3.55099 | 0.131880 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.4002 | 0.459899 | 0.229950 | − | 0.973203i | \(-0.426144\pi\) | ||||
0.229950 | + | 0.973203i | \(0.426144\pi\) | |||||||
\(728\) | 14.6667 | 0.543585 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.12224 | −0.152571 | ||||||||
\(731\) | −10.7055 | −0.395958 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.9465 | 0.404320 | 0.202160 | − | 0.979353i | \(-0.435204\pi\) | ||||
0.202160 | + | 0.979353i | \(0.435204\pi\) | |||||||
\(734\) | 0.557656 | 0.0205834 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −33.3541 | −1.22945 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.7047 | 0.540920 | 0.270460 | − | 0.962731i | \(-0.412824\pi\) | ||||
0.270460 | + | 0.962731i | \(0.412824\pi\) | |||||||
\(740\) | −9.45759 | −0.347668 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.63512 | −0.280294 | ||||||||
\(743\) | 28.8578 | 1.05869 | 0.529345 | − | 0.848407i | \(-0.322438\pi\) | ||||
0.529345 | + | 0.848407i | \(0.322438\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.3475 | 0.635564 | ||||||||
\(746\) | 15.5927 | 0.570889 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.6442 | 0.754323 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.7450 | −0.939447 | −0.469723 | − | 0.882814i | \(-0.655646\pi\) | ||||
−0.469723 | + | 0.882814i | \(0.655646\pi\) | |||||||
\(752\) | 17.4464 | 0.636204 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.54270 | 0.311107 | ||||||||
\(755\) | 9.01455 | 0.328073 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.6545 | 1.44127 | 0.720634 | − | 0.693316i | \(-0.243851\pi\) | ||||
0.720634 | + | 0.693316i | \(0.243851\pi\) | |||||||
\(758\) | 7.15159 | 0.259757 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.00613 | 0.0727701 | ||||||||
\(761\) | 31.1718 | 1.12998 | 0.564988 | − | 0.825099i | \(-0.308881\pi\) | ||||
0.564988 | + | 0.825099i | \(0.308881\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.2562 | −0.914334 | ||||||||
\(764\) | 3.81852 | 0.138149 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.5999 | −0.527515 | ||||||||
\(767\) | 35.6250 | 1.28634 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.5273 | −1.38933 | −0.694666 | − | 0.719333i | \(-0.744448\pi\) | ||||
−0.694666 | + | 0.719333i | \(0.744448\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 32.7997 | 1.18049 | ||||||||
\(773\) | 42.8510 | 1.54124 | 0.770621 | − | 0.637293i | \(-0.219946\pi\) | ||||
0.770621 | + | 0.637293i | \(0.219946\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.53688 | 0.306654 | ||||||||
\(776\) | 26.5302 | 0.952380 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.8256 | 0.603226 | ||||||||
\(779\) | −5.84309 | −0.209350 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 10.2919 | 0.368036 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −11.5682 | −0.413149 | ||||||||
\(785\) | −11.9364 | −0.426028 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.0485 | 0.964176 | 0.482088 | − | 0.876123i | \(-0.339879\pi\) | ||||
0.482088 | + | 0.876123i | \(0.339879\pi\) | |||||||
\(788\) | −15.3629 | −0.547282 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.966519 | 0.0343872 | ||||||||
\(791\) | −9.12367 | −0.324400 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.8957 | −1.16816 | ||||||||
\(794\) | 17.6788 | 0.627398 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 33.3909 | 1.18351 | ||||||||
\(797\) | −10.3959 | −0.368241 | −0.184121 | − | 0.982904i | \(-0.558944\pi\) | ||||
−0.184121 | + | 0.982904i | \(0.558944\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.7201 | −0.733024 | ||||||||
\(800\) | 4.93567 | 0.174502 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.4535 | 0.369126 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.9440 | −0.385727 | ||||||||
\(806\) | 20.5374 | 0.723398 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 32.3187 | 1.13697 | ||||||||
\(809\) | 39.9399 | 1.40421 | 0.702106 | − | 0.712073i | \(-0.252243\pi\) | ||||
0.702106 | + | 0.712073i | \(0.252243\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.5894 | −0.547417 | −0.273709 | − | 0.961813i | \(-0.588250\pi\) | ||||
−0.273709 | + | 0.961813i | \(0.588250\pi\) | |||||||
\(812\) | 10.1475 | 0.356107 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.32743 | 0.0815263 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.74597 | 0.131055 | ||||||||
\(818\) | −2.80193 | −0.0979671 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.38807 | −0.327846 | ||||||||
\(821\) | −2.46398 | −0.0859934 | −0.0429967 | − | 0.999075i | \(-0.513690\pi\) | ||||
−0.0429967 | + | 0.999075i | \(0.513690\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −55.1708 | −1.92313 | −0.961566 | − | 0.274573i | \(-0.911464\pi\) | ||||
−0.961566 | + | 0.274573i | \(0.911464\pi\) | |||||||
\(824\) | 9.01698 | 0.314122 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.64642 | −0.196464 | ||||||||
\(827\) | −30.7906 | −1.07069 | −0.535346 | − | 0.844633i | \(-0.679819\pi\) | ||||
−0.535346 | + | 0.844633i | \(0.679819\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.8676 | −0.898418 | −0.449209 | − | 0.893427i | \(-0.648294\pi\) | ||||
−0.449209 | + | 0.893427i | \(0.648294\pi\) | |||||||
\(830\) | −4.63357 | −0.160834 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −14.3314 | −0.496853 | ||||||||
\(833\) | 13.7389 | 0.476025 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.82442 | 0.339988 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.53820 | −0.225858 | ||||||||
\(839\) | −52.4369 | −1.81032 | −0.905161 | − | 0.425070i | \(-0.860250\pi\) | ||||
−0.905161 | + | 0.425070i | \(0.860250\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.3905 | −0.565189 | ||||||||
\(842\) | −11.7603 | −0.405285 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −30.6189 | −1.05395 | ||||||||
\(845\) | −11.5811 | −0.398402 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 25.6777 | 0.881775 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.52296 | −0.0522373 | ||||||||
\(851\) | 36.2201 | 1.24161 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.8759 | −1.02293 | −0.511465 | − | 0.859304i | \(-0.670897\pi\) | ||||
−0.511465 | + | 0.859304i | \(0.670897\pi\) | |||||||
\(854\) | 5.21384 | 0.178414 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 23.2854 | 0.795877 | ||||||||
\(857\) | −50.9131 | −1.73916 | −0.869579 | − | 0.493794i | \(-0.835610\pi\) | ||||
−0.869579 | + | 0.493794i | \(0.835610\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.2338 | 1.03156 | 0.515782 | − | 0.856720i | \(-0.327501\pi\) | ||||
0.515782 | + | 0.856720i | \(0.327501\pi\) | |||||||
\(860\) | 6.01864 | 0.205234 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.376490 | −0.0128233 | ||||||||
\(863\) | 18.8078 | 0.640225 | 0.320112 | − | 0.947380i | \(-0.396279\pi\) | ||||
0.320112 | + | 0.947380i | \(0.396279\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.2400 | 0.790184 | ||||||||
\(866\) | 16.7810 | 0.570241 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 24.3954 | 0.828034 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.7029 | 0.396536 | ||||||||
\(872\) | −28.4874 | −0.964703 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.60122 | −0.121813 | ||||||||
\(875\) | 1.61947 | 0.0547482 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.2915 | −1.52939 | −0.764693 | − | 0.644395i | \(-0.777109\pi\) | ||||
−0.764693 | + | 0.644395i | \(0.777109\pi\) | |||||||
\(878\) | 3.51353 | 0.118576 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.6233 | 0.829581 | 0.414791 | − | 0.909917i | \(-0.363855\pi\) | ||||
0.414791 | + | 0.909917i | \(0.363855\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.9629 | 1.88330 | 0.941651 | − | 0.336591i | \(-0.109274\pi\) | ||||
0.941651 | + | 0.336591i | \(0.109274\pi\) | |||||||
\(884\) | 27.4587 | 0.923537 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.62612 | −0.0882263 | ||||||||
\(887\) | −23.5352 | −0.790234 | −0.395117 | − | 0.918631i | \(-0.629296\pi\) | ||||
−0.395117 | + | 0.918631i | \(0.629296\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.9240 | −0.399918 | ||||||||
\(890\) | 1.28765 | 0.0431623 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.6886 | −0.424846 | ||||||||
\(893\) | 7.25017 | 0.242618 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.376550 | −0.0125867 | ||||||||
\(896\) | 18.2578 | 0.609951 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.25501 | 0.208732 | ||||||||
\(899\) | 30.3144 | 1.01104 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.4959 | −1.01597 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.2909 | −0.342271 | ||||||||
\(905\) | 7.58158 | 0.252020 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.6222 | −1.51486 | −0.757430 | − | 0.652916i | \(-0.773545\pi\) | ||||
−0.757430 | + | 0.652916i | \(0.773545\pi\) | |||||||
\(908\) | 48.1745 | 1.59873 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.89600 | 0.129151 | ||||||||
\(911\) | −46.8905 | −1.55355 | −0.776776 | − | 0.629778i | \(-0.783146\pi\) | ||||
−0.776776 | + | 0.629778i | \(0.783146\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.827531 | 0.0273723 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21.8386 | −0.721569 | ||||||||
\(917\) | −10.9156 | −0.360466 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.8040 | −1.11509 | −0.557545 | − | 0.830146i | \(-0.688257\pi\) | ||||
−0.557545 | + | 0.830146i | \(0.688257\pi\) | |||||||
\(920\) | −12.3442 | −0.406976 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −14.5193 | −0.478167 | ||||||||
\(923\) | −82.5790 | −2.71812 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.35976 | −0.176228 | ||||||||
\(926\) | −16.4863 | −0.541774 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 17.5265 | 0.575336 | ||||||||
\(929\) | 15.5132 | 0.508971 | 0.254485 | − | 0.967077i | \(-0.418094\pi\) | ||||
0.254485 | + | 0.967077i | \(0.418094\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.80738 | −0.157555 | ||||||||
\(932\) | 25.6650 | 0.840684 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.0824506 | −0.00269787 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.34747 | −0.142026 | −0.0710128 | − | 0.997475i | \(-0.522623\pi\) | ||||
−0.0710128 | + | 0.997475i | \(0.522623\pi\) | |||||||
\(938\) | −1.85486 | −0.0605632 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.6488 | 0.379943 | ||||||||
\(941\) | −18.7131 | −0.610030 | −0.305015 | − | 0.952348i | \(-0.598662\pi\) | ||||
−0.305015 | + | 0.952348i | \(0.598662\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.9538 | 1.17082 | ||||||||
\(944\) | 18.9894 | 0.618054 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.6269 | 0.605294 | 0.302647 | − | 0.953103i | \(-0.402130\pi\) | ||||
0.302647 | + | 0.953103i | \(0.402130\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.1200 | 1.36727 | ||||||||
\(950\) | 0.532901 | 0.0172896 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.28490 | −0.300925 | ||||||||
\(953\) | 8.74307 | 0.283216 | 0.141608 | − | 0.989923i | \(-0.454773\pi\) | ||||
0.141608 | + | 0.989923i | \(0.454773\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.16401 | 0.0700259 | ||||||||
\(956\) | 51.0428 | 1.65084 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.09304 | −0.229166 | ||||||||
\(959\) | 10.2351 | 0.330509 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.8783 | 1.35091 | ||||||||
\(962\) | −12.8941 | −0.415722 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.5976 | 0.534572 | ||||||||
\(965\) | 18.5881 | 0.598371 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.6843 | 1.53342 | 0.766712 | − | 0.641992i | \(-0.221892\pi\) | ||||
0.766712 | + | 0.641992i | \(0.221892\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.04738 | 0.226278 | ||||||||
\(971\) | 32.8229 | 1.05334 | 0.526669 | − | 0.850070i | \(-0.323441\pi\) | ||||
0.526669 | + | 0.850070i | \(0.323441\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.8083 | 0.731200 | ||||||||
\(974\) | −11.6222 | −0.372398 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −17.5346 | −0.561270 | ||||||||
\(977\) | −46.1269 | −1.47573 | −0.737864 | − | 0.674949i | \(-0.764166\pi\) | ||||
−0.737864 | + | 0.674949i | \(0.764166\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −7.72400 | −0.246734 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15.3957 | −0.491296 | ||||||||
\(983\) | −16.1706 | −0.515761 | −0.257881 | − | 0.966177i | \(-0.583024\pi\) | ||||
−0.257881 | + | 0.966177i | \(0.583024\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.70640 | −0.277409 | ||||||||
\(986\) | −5.40803 | −0.172227 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.60809 | −0.305674 | ||||||||
\(989\) | −23.0498 | −0.732940 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 60.7308 | 1.92918 | 0.964589 | − | 0.263758i | \(-0.0849622\pi\) | ||||
0.964589 | + | 0.263758i | \(0.0849622\pi\) | |||||||
\(992\) | 42.1352 | 1.33779 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 13.0884 | 0.415140 | ||||||||
\(995\) | 18.9231 | 0.599903 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.9915 | −1.48824 | −0.744118 | − | 0.668048i | \(-0.767130\pi\) | ||||
−0.744118 | + | 0.668048i | \(0.767130\pi\) | |||||||
\(998\) | 16.0618 | 0.508428 | ||||||||
\(999\) | 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 | 5445.2.a.ca.1.6 | 8 | ||
3.2 | odd | 2 | 5445.2.a.cd.1.3 | 8 | |||
11.5 | even | 5 | 495.2.n.h.91.2 | yes | 16 | ||
11.9 | even | 5 | 495.2.n.h.136.2 | yes | 16 | ||
11.10 | odd | 2 | 5445.2.a.cc.1.3 | 8 | |||
33.5 | odd | 10 | 495.2.n.g.91.3 | ✓ | 16 | ||
33.20 | odd | 10 | 495.2.n.g.136.3 | yes | 16 | ||
33.32 | even | 2 | 5445.2.a.cb.1.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
495.2.n.g.91.3 | ✓ | 16 | 33.5 | odd | 10 | ||
495.2.n.g.136.3 | yes | 16 | 33.20 | odd | 10 | ||
495.2.n.h.91.2 | yes | 16 | 11.5 | even | 5 | ||
495.2.n.h.136.2 | yes | 16 | 11.9 | even | 5 | ||
5445.2.a.ca.1.6 | 8 | 1.1 | even | 1 | trivial | ||
5445.2.a.cb.1.6 | 8 | 33.32 | even | 2 | |||
5445.2.a.cc.1.3 | 8 | 11.10 | odd | 2 | |||
5445.2.a.cd.1.3 | 8 | 3.2 | odd | 2 |