Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6042,2,Mod(1,6042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6042, 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("6042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6042.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2456129013\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 16x^{7} + 76x^{6} + 30x^{5} - 366x^{4} + 300x^{3} + 101x^{2} - 106x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.25110\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6042.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.51610 | −1.12523 | −0.562617 | − | 0.826718i | \(-0.690205\pi\) | ||||
−0.562617 | + | 0.826718i | \(0.690205\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −4.25110 | −1.60677 | −0.803383 | − | 0.595462i | \(-0.796969\pi\) | ||||
−0.803383 | + | 0.595462i | \(0.796969\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.51610 | −0.795661 | ||||||||
\(11\) | 1.96359 | 0.592046 | 0.296023 | − | 0.955181i | \(-0.404339\pi\) | ||||
0.296023 | + | 0.955181i | \(0.404339\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −2.77674 | −0.770129 | −0.385064 | − | 0.922890i | \(-0.625821\pi\) | ||||
−0.385064 | + | 0.922890i | \(0.625821\pi\) | |||||||
\(14\) | −4.25110 | −1.13616 | ||||||||
\(15\) | 2.51610 | 0.649654 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.83822 | 1.65851 | 0.829256 | − | 0.558870i | \(-0.188765\pi\) | ||||
0.829256 | + | 0.558870i | \(0.188765\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −2.51610 | −0.562617 | ||||||||
\(21\) | 4.25110 | 0.927667 | ||||||||
\(22\) | 1.96359 | 0.418640 | ||||||||
\(23\) | 6.37856 | 1.33002 | 0.665011 | − | 0.746833i | \(-0.268427\pi\) | ||||
0.665011 | + | 0.746833i | \(0.268427\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.33076 | 0.266152 | ||||||||
\(26\) | −2.77674 | −0.544563 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.25110 | −0.803383 | ||||||||
\(29\) | 5.73064 | 1.06415 | 0.532076 | − | 0.846696i | \(-0.321412\pi\) | ||||
0.532076 | + | 0.846696i | \(0.321412\pi\) | |||||||
\(30\) | 2.51610 | 0.459375 | ||||||||
\(31\) | −0.117223 | −0.0210539 | −0.0105269 | − | 0.999945i | \(-0.503351\pi\) | ||||
−0.0105269 | + | 0.999945i | \(0.503351\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.96359 | −0.341818 | ||||||||
\(34\) | 6.83822 | 1.17274 | ||||||||
\(35\) | 10.6962 | 1.80799 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.48789 | −0.902204 | −0.451102 | − | 0.892472i | \(-0.648969\pi\) | ||||
−0.451102 | + | 0.892472i | \(0.648969\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 2.77674 | 0.444634 | ||||||||
\(40\) | −2.51610 | −0.397830 | ||||||||
\(41\) | −9.92819 | −1.55052 | −0.775261 | − | 0.631640i | \(-0.782382\pi\) | ||||
−0.775261 | + | 0.631640i | \(0.782382\pi\) | |||||||
\(42\) | 4.25110 | 0.655960 | ||||||||
\(43\) | −1.57694 | −0.240481 | −0.120241 | − | 0.992745i | \(-0.538367\pi\) | ||||
−0.120241 | + | 0.992745i | \(0.538367\pi\) | |||||||
\(44\) | 1.96359 | 0.296023 | ||||||||
\(45\) | −2.51610 | −0.375078 | ||||||||
\(46\) | 6.37856 | 0.940468 | ||||||||
\(47\) | 0.666390 | 0.0972030 | 0.0486015 | − | 0.998818i | \(-0.484524\pi\) | ||||
0.0486015 | + | 0.998818i | \(0.484524\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 11.0719 | 1.58170 | ||||||||
\(50\) | 1.33076 | 0.188198 | ||||||||
\(51\) | −6.83822 | −0.957542 | ||||||||
\(52\) | −2.77674 | −0.385064 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −4.94060 | −0.666191 | ||||||||
\(56\) | −4.25110 | −0.568078 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 5.73064 | 0.752470 | ||||||||
\(59\) | 3.13796 | 0.408528 | 0.204264 | − | 0.978916i | \(-0.434520\pi\) | ||||
0.204264 | + | 0.978916i | \(0.434520\pi\) | |||||||
\(60\) | 2.51610 | 0.324827 | ||||||||
\(61\) | −0.415900 | −0.0532505 | −0.0266252 | − | 0.999645i | \(-0.508476\pi\) | ||||
−0.0266252 | + | 0.999645i | \(0.508476\pi\) | |||||||
\(62\) | −0.117223 | −0.0148873 | ||||||||
\(63\) | −4.25110 | −0.535589 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.98655 | 0.866575 | ||||||||
\(66\) | −1.96359 | −0.241702 | ||||||||
\(67\) | 7.65377 | 0.935057 | 0.467529 | − | 0.883978i | \(-0.345144\pi\) | ||||
0.467529 | + | 0.883978i | \(0.345144\pi\) | |||||||
\(68\) | 6.83822 | 0.829256 | ||||||||
\(69\) | −6.37856 | −0.767889 | ||||||||
\(70\) | 10.6962 | 1.27844 | ||||||||
\(71\) | 9.28244 | 1.10162 | 0.550811 | − | 0.834630i | \(-0.314318\pi\) | ||||
0.550811 | + | 0.834630i | \(0.314318\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −0.563587 | −0.0659628 | −0.0329814 | − | 0.999456i | \(-0.510500\pi\) | ||||
−0.0329814 | + | 0.999456i | \(0.510500\pi\) | |||||||
\(74\) | −5.48789 | −0.637954 | ||||||||
\(75\) | −1.33076 | −0.153663 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −8.34745 | −0.951280 | ||||||||
\(78\) | 2.77674 | 0.314404 | ||||||||
\(79\) | −16.0290 | −1.80340 | −0.901700 | − | 0.432363i | \(-0.857680\pi\) | ||||
−0.901700 | + | 0.432363i | \(0.857680\pi\) | |||||||
\(80\) | −2.51610 | −0.281309 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.92819 | −1.09639 | ||||||||
\(83\) | 0.307939 | 0.0338007 | 0.0169003 | − | 0.999857i | \(-0.494620\pi\) | ||||
0.0169003 | + | 0.999857i | \(0.494620\pi\) | |||||||
\(84\) | 4.25110 | 0.463834 | ||||||||
\(85\) | −17.2056 | −1.86621 | ||||||||
\(86\) | −1.57694 | −0.170046 | ||||||||
\(87\) | −5.73064 | −0.614389 | ||||||||
\(88\) | 1.96359 | 0.209320 | ||||||||
\(89\) | 10.6809 | 1.13217 | 0.566086 | − | 0.824346i | \(-0.308457\pi\) | ||||
0.566086 | + | 0.824346i | \(0.308457\pi\) | |||||||
\(90\) | −2.51610 | −0.265220 | ||||||||
\(91\) | 11.8042 | 1.23742 | ||||||||
\(92\) | 6.37856 | 0.665011 | ||||||||
\(93\) | 0.117223 | 0.0121555 | ||||||||
\(94\) | 0.666390 | 0.0687329 | ||||||||
\(95\) | 2.51610 | 0.258146 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −8.44389 | −0.857348 | −0.428674 | − | 0.903459i | \(-0.641019\pi\) | ||||
−0.428674 | + | 0.903459i | \(0.641019\pi\) | |||||||
\(98\) | 11.0719 | 1.11843 | ||||||||
\(99\) | 1.96359 | 0.197349 | ||||||||
\(100\) | 1.33076 | 0.133076 | ||||||||
\(101\) | 4.79119 | 0.476741 | 0.238371 | − | 0.971174i | \(-0.423387\pi\) | ||||
0.238371 | + | 0.971174i | \(0.423387\pi\) | |||||||
\(102\) | −6.83822 | −0.677084 | ||||||||
\(103\) | −9.79253 | −0.964887 | −0.482443 | − | 0.875927i | \(-0.660251\pi\) | ||||
−0.482443 | + | 0.875927i | \(0.660251\pi\) | |||||||
\(104\) | −2.77674 | −0.272282 | ||||||||
\(105\) | −10.6962 | −1.04384 | ||||||||
\(106\) | 1.00000 | 0.0971286 | ||||||||
\(107\) | −15.2769 | −1.47688 | −0.738438 | − | 0.674322i | \(-0.764436\pi\) | ||||
−0.738438 | + | 0.674322i | \(0.764436\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 7.91690 | 0.758302 | 0.379151 | − | 0.925335i | \(-0.376216\pi\) | ||||
0.379151 | + | 0.925335i | \(0.376216\pi\) | |||||||
\(110\) | −4.94060 | −0.471068 | ||||||||
\(111\) | 5.48789 | 0.520888 | ||||||||
\(112\) | −4.25110 | −0.401692 | ||||||||
\(113\) | 2.86186 | 0.269221 | 0.134611 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134611 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | −16.0491 | −1.49659 | ||||||||
\(116\) | 5.73064 | 0.532076 | ||||||||
\(117\) | −2.77674 | −0.256710 | ||||||||
\(118\) | 3.13796 | 0.288873 | ||||||||
\(119\) | −29.0700 | −2.66484 | ||||||||
\(120\) | 2.51610 | 0.229688 | ||||||||
\(121\) | −7.14429 | −0.649481 | ||||||||
\(122\) | −0.415900 | −0.0376538 | ||||||||
\(123\) | 9.92819 | 0.895195 | ||||||||
\(124\) | −0.117223 | −0.0105269 | ||||||||
\(125\) | 9.23217 | 0.825751 | ||||||||
\(126\) | −4.25110 | −0.378719 | ||||||||
\(127\) | −18.0636 | −1.60289 | −0.801444 | − | 0.598069i | \(-0.795935\pi\) | ||||
−0.801444 | + | 0.598069i | \(0.795935\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.57694 | 0.138842 | ||||||||
\(130\) | 6.98655 | 0.612761 | ||||||||
\(131\) | −18.2116 | −1.59115 | −0.795576 | − | 0.605854i | \(-0.792832\pi\) | ||||
−0.795576 | + | 0.605854i | \(0.792832\pi\) | |||||||
\(132\) | −1.96359 | −0.170909 | ||||||||
\(133\) | 4.25110 | 0.368618 | ||||||||
\(134\) | 7.65377 | 0.661185 | ||||||||
\(135\) | 2.51610 | 0.216551 | ||||||||
\(136\) | 6.83822 | 0.586372 | ||||||||
\(137\) | −18.2145 | −1.55617 | −0.778084 | − | 0.628160i | \(-0.783808\pi\) | ||||
−0.778084 | + | 0.628160i | \(0.783808\pi\) | |||||||
\(138\) | −6.37856 | −0.542979 | ||||||||
\(139\) | 7.07490 | 0.600085 | 0.300042 | − | 0.953926i | \(-0.402999\pi\) | ||||
0.300042 | + | 0.953926i | \(0.402999\pi\) | |||||||
\(140\) | 10.6962 | 0.903994 | ||||||||
\(141\) | −0.666390 | −0.0561202 | ||||||||
\(142\) | 9.28244 | 0.778965 | ||||||||
\(143\) | −5.45239 | −0.455952 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −14.4189 | −1.19742 | ||||||||
\(146\) | −0.563587 | −0.0466428 | ||||||||
\(147\) | −11.0719 | −0.913194 | ||||||||
\(148\) | −5.48789 | −0.451102 | ||||||||
\(149\) | −16.8298 | −1.37875 | −0.689375 | − | 0.724405i | \(-0.742115\pi\) | ||||
−0.689375 | + | 0.724405i | \(0.742115\pi\) | |||||||
\(150\) | −1.33076 | −0.108656 | ||||||||
\(151\) | 9.22370 | 0.750614 | 0.375307 | − | 0.926901i | \(-0.377537\pi\) | ||||
0.375307 | + | 0.926901i | \(0.377537\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 6.83822 | 0.552837 | ||||||||
\(154\) | −8.34745 | −0.672657 | ||||||||
\(155\) | 0.294945 | 0.0236906 | ||||||||
\(156\) | 2.77674 | 0.222317 | ||||||||
\(157\) | −18.0398 | −1.43973 | −0.719865 | − | 0.694114i | \(-0.755796\pi\) | ||||
−0.719865 | + | 0.694114i | \(0.755796\pi\) | |||||||
\(158\) | −16.0290 | −1.27520 | ||||||||
\(159\) | −1.00000 | −0.0793052 | ||||||||
\(160\) | −2.51610 | −0.198915 | ||||||||
\(161\) | −27.1159 | −2.13704 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −0.0245472 | −0.00192269 | −0.000961343 | − | 1.00000i | \(-0.500306\pi\) | ||||
−0.000961343 | 1.00000i | \(0.500306\pi\) | ||||||||
\(164\) | −9.92819 | −0.775261 | ||||||||
\(165\) | 4.94060 | 0.384625 | ||||||||
\(166\) | 0.307939 | 0.0239007 | ||||||||
\(167\) | 14.1169 | 1.09239 | 0.546197 | − | 0.837657i | \(-0.316075\pi\) | ||||
0.546197 | + | 0.837657i | \(0.316075\pi\) | |||||||
\(168\) | 4.25110 | 0.327980 | ||||||||
\(169\) | −5.28972 | −0.406902 | ||||||||
\(170\) | −17.2056 | −1.31961 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | −1.57694 | −0.120241 | ||||||||
\(173\) | −22.0740 | −1.67826 | −0.839129 | − | 0.543933i | \(-0.816935\pi\) | ||||
−0.839129 | + | 0.543933i | \(0.816935\pi\) | |||||||
\(174\) | −5.73064 | −0.434439 | ||||||||
\(175\) | −5.65721 | −0.427645 | ||||||||
\(176\) | 1.96359 | 0.148012 | ||||||||
\(177\) | −3.13796 | −0.235864 | ||||||||
\(178\) | 10.6809 | 0.800567 | ||||||||
\(179\) | 18.7893 | 1.40438 | 0.702189 | − | 0.711991i | \(-0.252206\pi\) | ||||
0.702189 | + | 0.711991i | \(0.252206\pi\) | |||||||
\(180\) | −2.51610 | −0.187539 | ||||||||
\(181\) | −11.4778 | −0.853136 | −0.426568 | − | 0.904455i | \(-0.640278\pi\) | ||||
−0.426568 | + | 0.904455i | \(0.640278\pi\) | |||||||
\(182\) | 11.8042 | 0.874986 | ||||||||
\(183\) | 0.415900 | 0.0307442 | ||||||||
\(184\) | 6.37856 | 0.470234 | ||||||||
\(185\) | 13.8081 | 1.01519 | ||||||||
\(186\) | 0.117223 | 0.00859521 | ||||||||
\(187\) | 13.4275 | 0.981915 | ||||||||
\(188\) | 0.666390 | 0.0486015 | ||||||||
\(189\) | 4.25110 | 0.309222 | ||||||||
\(190\) | 2.51610 | 0.182537 | ||||||||
\(191\) | −1.50328 | −0.108774 | −0.0543869 | − | 0.998520i | \(-0.517320\pi\) | ||||
−0.0543869 | + | 0.998520i | \(0.517320\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 10.5502 | 0.759417 | 0.379709 | − | 0.925106i | \(-0.376024\pi\) | ||||
0.379709 | + | 0.925106i | \(0.376024\pi\) | |||||||
\(194\) | −8.44389 | −0.606236 | ||||||||
\(195\) | −6.98655 | −0.500318 | ||||||||
\(196\) | 11.0719 | 0.790849 | ||||||||
\(197\) | −5.16113 | −0.367715 | −0.183858 | − | 0.982953i | \(-0.558859\pi\) | ||||
−0.183858 | + | 0.982953i | \(0.558859\pi\) | |||||||
\(198\) | 1.96359 | 0.139547 | ||||||||
\(199\) | −21.8391 | −1.54814 | −0.774068 | − | 0.633103i | \(-0.781781\pi\) | ||||
−0.774068 | + | 0.633103i | \(0.781781\pi\) | |||||||
\(200\) | 1.33076 | 0.0940991 | ||||||||
\(201\) | −7.65377 | −0.539856 | ||||||||
\(202\) | 4.79119 | 0.337107 | ||||||||
\(203\) | −24.3615 | −1.70985 | ||||||||
\(204\) | −6.83822 | −0.478771 | ||||||||
\(205\) | 24.9803 | 1.74470 | ||||||||
\(206\) | −9.79253 | −0.682278 | ||||||||
\(207\) | 6.37856 | 0.443341 | ||||||||
\(208\) | −2.77674 | −0.192532 | ||||||||
\(209\) | −1.96359 | −0.135825 | ||||||||
\(210\) | −10.6962 | −0.738108 | ||||||||
\(211\) | 18.8235 | 1.29586 | 0.647932 | − | 0.761699i | \(-0.275634\pi\) | ||||
0.647932 | + | 0.761699i | \(0.275634\pi\) | |||||||
\(212\) | 1.00000 | 0.0686803 | ||||||||
\(213\) | −9.28244 | −0.636022 | ||||||||
\(214\) | −15.2769 | −1.04431 | ||||||||
\(215\) | 3.96774 | 0.270598 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0.498327 | 0.0338287 | ||||||||
\(218\) | 7.91690 | 0.536200 | ||||||||
\(219\) | 0.563587 | 0.0380837 | ||||||||
\(220\) | −4.94060 | −0.333095 | ||||||||
\(221\) | −18.9879 | −1.27727 | ||||||||
\(222\) | 5.48789 | 0.368323 | ||||||||
\(223\) | −22.7495 | −1.52342 | −0.761711 | − | 0.647917i | \(-0.775640\pi\) | ||||
−0.761711 | + | 0.647917i | \(0.775640\pi\) | |||||||
\(224\) | −4.25110 | −0.284039 | ||||||||
\(225\) | 1.33076 | 0.0887175 | ||||||||
\(226\) | 2.86186 | 0.190368 | ||||||||
\(227\) | 7.21237 | 0.478701 | 0.239351 | − | 0.970933i | \(-0.423065\pi\) | ||||
0.239351 | + | 0.970933i | \(0.423065\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | 3.30012 | 0.218078 | 0.109039 | − | 0.994037i | \(-0.465223\pi\) | ||||
0.109039 | + | 0.994037i | \(0.465223\pi\) | |||||||
\(230\) | −16.0491 | −1.05825 | ||||||||
\(231\) | 8.34745 | 0.549222 | ||||||||
\(232\) | 5.73064 | 0.376235 | ||||||||
\(233\) | −7.84552 | −0.513977 | −0.256989 | − | 0.966414i | \(-0.582730\pi\) | ||||
−0.256989 | + | 0.966414i | \(0.582730\pi\) | |||||||
\(234\) | −2.77674 | −0.181521 | ||||||||
\(235\) | −1.67671 | −0.109376 | ||||||||
\(236\) | 3.13796 | 0.204264 | ||||||||
\(237\) | 16.0290 | 1.04119 | ||||||||
\(238\) | −29.0700 | −1.88433 | ||||||||
\(239\) | 1.41077 | 0.0912550 | 0.0456275 | − | 0.998959i | \(-0.485471\pi\) | ||||
0.0456275 | + | 0.998959i | \(0.485471\pi\) | |||||||
\(240\) | 2.51610 | 0.162414 | ||||||||
\(241\) | 3.80810 | 0.245301 | 0.122651 | − | 0.992450i | \(-0.460861\pi\) | ||||
0.122651 | + | 0.992450i | \(0.460861\pi\) | |||||||
\(242\) | −7.14429 | −0.459253 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.415900 | −0.0266252 | ||||||||
\(245\) | −27.8580 | −1.77978 | ||||||||
\(246\) | 9.92819 | 0.632998 | ||||||||
\(247\) | 2.77674 | 0.176680 | ||||||||
\(248\) | −0.117223 | −0.00744367 | ||||||||
\(249\) | −0.307939 | −0.0195148 | ||||||||
\(250\) | 9.23217 | 0.583894 | ||||||||
\(251\) | 28.9995 | 1.83043 | 0.915215 | − | 0.402965i | \(-0.132020\pi\) | ||||
0.915215 | + | 0.402965i | \(0.132020\pi\) | |||||||
\(252\) | −4.25110 | −0.267794 | ||||||||
\(253\) | 12.5249 | 0.787435 | ||||||||
\(254\) | −18.0636 | −1.13341 | ||||||||
\(255\) | 17.2056 | 1.07746 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.4357 | −1.39950 | −0.699751 | − | 0.714387i | \(-0.746706\pi\) | ||||
−0.699751 | + | 0.714387i | \(0.746706\pi\) | |||||||
\(258\) | 1.57694 | 0.0981761 | ||||||||
\(259\) | 23.3296 | 1.44963 | ||||||||
\(260\) | 6.98655 | 0.433288 | ||||||||
\(261\) | 5.73064 | 0.354718 | ||||||||
\(262\) | −18.2116 | −1.12511 | ||||||||
\(263\) | 2.03837 | 0.125691 | 0.0628456 | − | 0.998023i | \(-0.479982\pi\) | ||||
0.0628456 | + | 0.998023i | \(0.479982\pi\) | |||||||
\(264\) | −1.96359 | −0.120851 | ||||||||
\(265\) | −2.51610 | −0.154563 | ||||||||
\(266\) | 4.25110 | 0.260652 | ||||||||
\(267\) | −10.6809 | −0.653660 | ||||||||
\(268\) | 7.65377 | 0.467529 | ||||||||
\(269\) | −24.6140 | −1.50074 | −0.750370 | − | 0.661018i | \(-0.770125\pi\) | ||||
−0.750370 | + | 0.661018i | \(0.770125\pi\) | |||||||
\(270\) | 2.51610 | 0.153125 | ||||||||
\(271\) | −26.9494 | −1.63706 | −0.818531 | − | 0.574462i | \(-0.805211\pi\) | ||||
−0.818531 | + | 0.574462i | \(0.805211\pi\) | |||||||
\(272\) | 6.83822 | 0.414628 | ||||||||
\(273\) | −11.8042 | −0.714423 | ||||||||
\(274\) | −18.2145 | −1.10038 | ||||||||
\(275\) | 2.61308 | 0.157574 | ||||||||
\(276\) | −6.37856 | −0.383944 | ||||||||
\(277\) | −22.7108 | −1.36456 | −0.682281 | − | 0.731090i | \(-0.739012\pi\) | ||||
−0.682281 | + | 0.731090i | \(0.739012\pi\) | |||||||
\(278\) | 7.07490 | 0.424324 | ||||||||
\(279\) | −0.117223 | −0.00701796 | ||||||||
\(280\) | 10.6962 | 0.639221 | ||||||||
\(281\) | 3.42468 | 0.204299 | 0.102150 | − | 0.994769i | \(-0.467428\pi\) | ||||
0.102150 | + | 0.994769i | \(0.467428\pi\) | |||||||
\(282\) | −0.666390 | −0.0396830 | ||||||||
\(283\) | −9.90360 | −0.588708 | −0.294354 | − | 0.955696i | \(-0.595104\pi\) | ||||
−0.294354 | + | 0.955696i | \(0.595104\pi\) | |||||||
\(284\) | 9.28244 | 0.550811 | ||||||||
\(285\) | −2.51610 | −0.149041 | ||||||||
\(286\) | −5.45239 | −0.322407 | ||||||||
\(287\) | 42.2058 | 2.49133 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 29.7612 | 1.75066 | ||||||||
\(290\) | −14.4189 | −0.846705 | ||||||||
\(291\) | 8.44389 | 0.494990 | ||||||||
\(292\) | −0.563587 | −0.0329814 | ||||||||
\(293\) | 3.52895 | 0.206163 | 0.103082 | − | 0.994673i | \(-0.467130\pi\) | ||||
0.103082 | + | 0.994673i | \(0.467130\pi\) | |||||||
\(294\) | −11.0719 | −0.645726 | ||||||||
\(295\) | −7.89544 | −0.459690 | ||||||||
\(296\) | −5.48789 | −0.318977 | ||||||||
\(297\) | −1.96359 | −0.113939 | ||||||||
\(298\) | −16.8298 | −0.974924 | ||||||||
\(299\) | −17.7116 | −1.02429 | ||||||||
\(300\) | −1.33076 | −0.0768316 | ||||||||
\(301\) | 6.70374 | 0.386397 | ||||||||
\(302\) | 9.22370 | 0.530764 | ||||||||
\(303\) | −4.79119 | −0.275247 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 1.04645 | 0.0599193 | ||||||||
\(306\) | 6.83822 | 0.390915 | ||||||||
\(307\) | 28.6666 | 1.63609 | 0.818046 | − | 0.575153i | \(-0.195058\pi\) | ||||
0.818046 | + | 0.575153i | \(0.195058\pi\) | |||||||
\(308\) | −8.34745 | −0.475640 | ||||||||
\(309\) | 9.79253 | 0.557078 | ||||||||
\(310\) | 0.294945 | 0.0167517 | ||||||||
\(311\) | −0.461697 | −0.0261804 | −0.0130902 | − | 0.999914i | \(-0.504167\pi\) | ||||
−0.0130902 | + | 0.999914i | \(0.504167\pi\) | |||||||
\(312\) | 2.77674 | 0.157202 | ||||||||
\(313\) | −22.6577 | −1.28069 | −0.640343 | − | 0.768089i | \(-0.721208\pi\) | ||||
−0.640343 | + | 0.768089i | \(0.721208\pi\) | |||||||
\(314\) | −18.0398 | −1.01804 | ||||||||
\(315\) | 10.6962 | 0.602663 | ||||||||
\(316\) | −16.0290 | −0.901700 | ||||||||
\(317\) | 23.2735 | 1.30717 | 0.653586 | − | 0.756852i | \(-0.273264\pi\) | ||||
0.653586 | + | 0.756852i | \(0.273264\pi\) | |||||||
\(318\) | −1.00000 | −0.0560772 | ||||||||
\(319\) | 11.2527 | 0.630028 | ||||||||
\(320\) | −2.51610 | −0.140654 | ||||||||
\(321\) | 15.2769 | 0.852674 | ||||||||
\(322\) | −27.1159 | −1.51111 | ||||||||
\(323\) | −6.83822 | −0.380489 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −3.69518 | −0.204972 | ||||||||
\(326\) | −0.0245472 | −0.00135954 | ||||||||
\(327\) | −7.91690 | −0.437806 | ||||||||
\(328\) | −9.92819 | −0.548193 | ||||||||
\(329\) | −2.83290 | −0.156183 | ||||||||
\(330\) | 4.94060 | 0.271971 | ||||||||
\(331\) | 5.39248 | 0.296397 | 0.148199 | − | 0.988958i | \(-0.452652\pi\) | ||||
0.148199 | + | 0.988958i | \(0.452652\pi\) | |||||||
\(332\) | 0.307939 | 0.0169003 | ||||||||
\(333\) | −5.48789 | −0.300735 | ||||||||
\(334\) | 14.1169 | 0.772440 | ||||||||
\(335\) | −19.2577 | −1.05216 | ||||||||
\(336\) | 4.25110 | 0.231917 | ||||||||
\(337\) | 5.36502 | 0.292251 | 0.146126 | − | 0.989266i | \(-0.453320\pi\) | ||||
0.146126 | + | 0.989266i | \(0.453320\pi\) | |||||||
\(338\) | −5.28972 | −0.287723 | ||||||||
\(339\) | −2.86186 | −0.155435 | ||||||||
\(340\) | −17.2056 | −0.933107 | ||||||||
\(341\) | −0.230179 | −0.0124649 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | −17.3100 | −0.934654 | ||||||||
\(344\) | −1.57694 | −0.0850230 | ||||||||
\(345\) | 16.0491 | 0.864055 | ||||||||
\(346\) | −22.0740 | −1.18671 | ||||||||
\(347\) | 11.7607 | 0.631349 | 0.315675 | − | 0.948867i | \(-0.397769\pi\) | ||||
0.315675 | + | 0.948867i | \(0.397769\pi\) | |||||||
\(348\) | −5.73064 | −0.307195 | ||||||||
\(349\) | 2.82073 | 0.150990 | 0.0754950 | − | 0.997146i | \(-0.475946\pi\) | ||||
0.0754950 | + | 0.997146i | \(0.475946\pi\) | |||||||
\(350\) | −5.65721 | −0.302390 | ||||||||
\(351\) | 2.77674 | 0.148211 | ||||||||
\(352\) | 1.96359 | 0.104660 | ||||||||
\(353\) | −19.2115 | −1.02253 | −0.511264 | − | 0.859424i | \(-0.670822\pi\) | ||||
−0.511264 | + | 0.859424i | \(0.670822\pi\) | |||||||
\(354\) | −3.13796 | −0.166781 | ||||||||
\(355\) | −23.3555 | −1.23958 | ||||||||
\(356\) | 10.6809 | 0.566086 | ||||||||
\(357\) | 29.0700 | 1.53855 | ||||||||
\(358\) | 18.7893 | 0.993045 | ||||||||
\(359\) | −16.7903 | −0.886156 | −0.443078 | − | 0.896483i | \(-0.646114\pi\) | ||||
−0.443078 | + | 0.896483i | \(0.646114\pi\) | |||||||
\(360\) | −2.51610 | −0.132610 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −11.4778 | −0.603258 | ||||||||
\(363\) | 7.14429 | 0.374978 | ||||||||
\(364\) | 11.8042 | 0.618709 | ||||||||
\(365\) | 1.41804 | 0.0742236 | ||||||||
\(366\) | 0.415900 | 0.0217394 | ||||||||
\(367\) | 5.76787 | 0.301080 | 0.150540 | − | 0.988604i | \(-0.451899\pi\) | ||||
0.150540 | + | 0.988604i | \(0.451899\pi\) | |||||||
\(368\) | 6.37856 | 0.332506 | ||||||||
\(369\) | −9.92819 | −0.516841 | ||||||||
\(370\) | 13.8081 | 0.717848 | ||||||||
\(371\) | −4.25110 | −0.220706 | ||||||||
\(372\) | 0.117223 | 0.00607773 | ||||||||
\(373\) | 32.1422 | 1.66426 | 0.832130 | − | 0.554581i | \(-0.187122\pi\) | ||||
0.832130 | + | 0.554581i | \(0.187122\pi\) | |||||||
\(374\) | 13.4275 | 0.694319 | ||||||||
\(375\) | −9.23217 | −0.476747 | ||||||||
\(376\) | 0.666390 | 0.0343665 | ||||||||
\(377\) | −15.9125 | −0.819535 | ||||||||
\(378\) | 4.25110 | 0.218653 | ||||||||
\(379\) | 27.4613 | 1.41059 | 0.705296 | − | 0.708913i | \(-0.250814\pi\) | ||||
0.705296 | + | 0.708913i | \(0.250814\pi\) | |||||||
\(380\) | 2.51610 | 0.129073 | ||||||||
\(381\) | 18.0636 | 0.925428 | ||||||||
\(382\) | −1.50328 | −0.0769146 | ||||||||
\(383\) | 30.2728 | 1.54687 | 0.773435 | − | 0.633876i | \(-0.218537\pi\) | ||||
0.773435 | + | 0.633876i | \(0.218537\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 21.0030 | 1.07041 | ||||||||
\(386\) | 10.5502 | 0.536989 | ||||||||
\(387\) | −1.57694 | −0.0801604 | ||||||||
\(388\) | −8.44389 | −0.428674 | ||||||||
\(389\) | −17.8415 | −0.904597 | −0.452299 | − | 0.891867i | \(-0.649396\pi\) | ||||
−0.452299 | + | 0.891867i | \(0.649396\pi\) | |||||||
\(390\) | −6.98655 | −0.353778 | ||||||||
\(391\) | 43.6180 | 2.20586 | ||||||||
\(392\) | 11.0719 | 0.559215 | ||||||||
\(393\) | 18.2116 | 0.918652 | ||||||||
\(394\) | −5.16113 | −0.260014 | ||||||||
\(395\) | 40.3305 | 2.02925 | ||||||||
\(396\) | 1.96359 | 0.0986744 | ||||||||
\(397\) | 13.9044 | 0.697841 | 0.348920 | − | 0.937152i | \(-0.386548\pi\) | ||||
0.348920 | + | 0.937152i | \(0.386548\pi\) | |||||||
\(398\) | −21.8391 | −1.09470 | ||||||||
\(399\) | −4.25110 | −0.212821 | ||||||||
\(400\) | 1.33076 | 0.0665381 | ||||||||
\(401\) | −33.3661 | −1.66622 | −0.833112 | − | 0.553104i | \(-0.813443\pi\) | ||||
−0.833112 | + | 0.553104i | \(0.813443\pi\) | |||||||
\(402\) | −7.65377 | −0.381736 | ||||||||
\(403\) | 0.325498 | 0.0162142 | ||||||||
\(404\) | 4.79119 | 0.238371 | ||||||||
\(405\) | −2.51610 | −0.125026 | ||||||||
\(406\) | −24.3615 | −1.20904 | ||||||||
\(407\) | −10.7760 | −0.534146 | ||||||||
\(408\) | −6.83822 | −0.338542 | ||||||||
\(409\) | 18.2552 | 0.902660 | 0.451330 | − | 0.892357i | \(-0.350950\pi\) | ||||
0.451330 | + | 0.892357i | \(0.350950\pi\) | |||||||
\(410\) | 24.9803 | 1.23369 | ||||||||
\(411\) | 18.2145 | 0.898454 | ||||||||
\(412\) | −9.79253 | −0.482443 | ||||||||
\(413\) | −13.3398 | −0.656409 | ||||||||
\(414\) | 6.37856 | 0.313489 | ||||||||
\(415\) | −0.774805 | −0.0380337 | ||||||||
\(416\) | −2.77674 | −0.136141 | ||||||||
\(417\) | −7.07490 | −0.346459 | ||||||||
\(418\) | −1.96359 | −0.0960426 | ||||||||
\(419\) | −20.4441 | −0.998761 | −0.499381 | − | 0.866383i | \(-0.666439\pi\) | ||||
−0.499381 | + | 0.866383i | \(0.666439\pi\) | |||||||
\(420\) | −10.6962 | −0.521921 | ||||||||
\(421\) | −0.374365 | −0.0182454 | −0.00912272 | − | 0.999958i | \(-0.502904\pi\) | ||||
−0.00912272 | + | 0.999958i | \(0.502904\pi\) | |||||||
\(422\) | 18.8235 | 0.916314 | ||||||||
\(423\) | 0.666390 | 0.0324010 | ||||||||
\(424\) | 1.00000 | 0.0485643 | ||||||||
\(425\) | 9.10004 | 0.441417 | ||||||||
\(426\) | −9.28244 | −0.449736 | ||||||||
\(427\) | 1.76803 | 0.0855611 | ||||||||
\(428\) | −15.2769 | −0.738438 | ||||||||
\(429\) | 5.45239 | 0.263244 | ||||||||
\(430\) | 3.96774 | 0.191342 | ||||||||
\(431\) | −19.6831 | −0.948099 | −0.474050 | − | 0.880498i | \(-0.657208\pi\) | ||||
−0.474050 | + | 0.880498i | \(0.657208\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −16.9190 | −0.813073 | −0.406537 | − | 0.913634i | \(-0.633264\pi\) | ||||
−0.406537 | + | 0.913634i | \(0.633264\pi\) | |||||||
\(434\) | 0.498327 | 0.0239205 | ||||||||
\(435\) | 14.4189 | 0.691332 | ||||||||
\(436\) | 7.91690 | 0.379151 | ||||||||
\(437\) | −6.37856 | −0.305128 | ||||||||
\(438\) | 0.563587 | 0.0269292 | ||||||||
\(439\) | −22.5619 | −1.07682 | −0.538411 | − | 0.842682i | \(-0.680975\pi\) | ||||
−0.538411 | + | 0.842682i | \(0.680975\pi\) | |||||||
\(440\) | −4.94060 | −0.235534 | ||||||||
\(441\) | 11.0719 | 0.527233 | ||||||||
\(442\) | −18.9879 | −0.903164 | ||||||||
\(443\) | −13.7676 | −0.654120 | −0.327060 | − | 0.945004i | \(-0.606058\pi\) | ||||
−0.327060 | + | 0.945004i | \(0.606058\pi\) | |||||||
\(444\) | 5.48789 | 0.260444 | ||||||||
\(445\) | −26.8742 | −1.27396 | ||||||||
\(446\) | −22.7495 | −1.07722 | ||||||||
\(447\) | 16.8298 | 0.796022 | ||||||||
\(448\) | −4.25110 | −0.200846 | ||||||||
\(449\) | −6.70165 | −0.316270 | −0.158135 | − | 0.987417i | \(-0.550548\pi\) | ||||
−0.158135 | + | 0.987417i | \(0.550548\pi\) | |||||||
\(450\) | 1.33076 | 0.0627327 | ||||||||
\(451\) | −19.4949 | −0.917981 | ||||||||
\(452\) | 2.86186 | 0.134611 | ||||||||
\(453\) | −9.22370 | −0.433367 | ||||||||
\(454\) | 7.21237 | 0.338493 | ||||||||
\(455\) | −29.7006 | −1.39238 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | 23.6382 | 1.10575 | 0.552873 | − | 0.833265i | \(-0.313531\pi\) | ||||
0.552873 | + | 0.833265i | \(0.313531\pi\) | |||||||
\(458\) | 3.30012 | 0.154205 | ||||||||
\(459\) | −6.83822 | −0.319181 | ||||||||
\(460\) | −16.0491 | −0.748293 | ||||||||
\(461\) | −30.6242 | −1.42631 | −0.713155 | − | 0.701007i | \(-0.752734\pi\) | ||||
−0.713155 | + | 0.701007i | \(0.752734\pi\) | |||||||
\(462\) | 8.34745 | 0.388358 | ||||||||
\(463\) | 12.0260 | 0.558898 | 0.279449 | − | 0.960161i | \(-0.409848\pi\) | ||||
0.279449 | + | 0.960161i | \(0.409848\pi\) | |||||||
\(464\) | 5.73064 | 0.266038 | ||||||||
\(465\) | −0.294945 | −0.0136777 | ||||||||
\(466\) | −7.84552 | −0.363437 | ||||||||
\(467\) | −28.5051 | −1.31906 | −0.659528 | − | 0.751680i | \(-0.729244\pi\) | ||||
−0.659528 | + | 0.751680i | \(0.729244\pi\) | |||||||
\(468\) | −2.77674 | −0.128355 | ||||||||
\(469\) | −32.5370 | −1.50242 | ||||||||
\(470\) | −1.67671 | −0.0773406 | ||||||||
\(471\) | 18.0398 | 0.831228 | ||||||||
\(472\) | 3.13796 | 0.144437 | ||||||||
\(473\) | −3.09647 | −0.142376 | ||||||||
\(474\) | 16.0290 | 0.736235 | ||||||||
\(475\) | −1.33076 | −0.0610595 | ||||||||
\(476\) | −29.0700 | −1.33242 | ||||||||
\(477\) | 1.00000 | 0.0457869 | ||||||||
\(478\) | 1.41077 | 0.0645270 | ||||||||
\(479\) | −15.9510 | −0.728818 | −0.364409 | − | 0.931239i | \(-0.618729\pi\) | ||||
−0.364409 | + | 0.931239i | \(0.618729\pi\) | |||||||
\(480\) | 2.51610 | 0.114844 | ||||||||
\(481\) | 15.2384 | 0.694813 | ||||||||
\(482\) | 3.80810 | 0.173454 | ||||||||
\(483\) | 27.1159 | 1.23382 | ||||||||
\(484\) | −7.14429 | −0.324741 | ||||||||
\(485\) | 21.2457 | 0.964717 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 18.8436 | 0.853884 | 0.426942 | − | 0.904279i | \(-0.359591\pi\) | ||||
0.426942 | + | 0.904279i | \(0.359591\pi\) | |||||||
\(488\) | −0.415900 | −0.0188269 | ||||||||
\(489\) | 0.0245472 | 0.00111006 | ||||||||
\(490\) | −27.8580 | −1.25850 | ||||||||
\(491\) | −12.6466 | −0.570732 | −0.285366 | − | 0.958419i | \(-0.592115\pi\) | ||||
−0.285366 | + | 0.958419i | \(0.592115\pi\) | |||||||
\(492\) | 9.92819 | 0.447597 | ||||||||
\(493\) | 39.1873 | 1.76491 | ||||||||
\(494\) | 2.77674 | 0.124931 | ||||||||
\(495\) | −4.94060 | −0.222064 | ||||||||
\(496\) | −0.117223 | −0.00526347 | ||||||||
\(497\) | −39.4606 | −1.77005 | ||||||||
\(498\) | −0.307939 | −0.0137991 | ||||||||
\(499\) | 22.4656 | 1.00570 | 0.502850 | − | 0.864374i | \(-0.332285\pi\) | ||||
0.502850 | + | 0.864374i | \(0.332285\pi\) | |||||||
\(500\) | 9.23217 | 0.412875 | ||||||||
\(501\) | −14.1169 | −0.630694 | ||||||||
\(502\) | 28.9995 | 1.29431 | ||||||||
\(503\) | −25.3832 | −1.13178 | −0.565891 | − | 0.824480i | \(-0.691468\pi\) | ||||
−0.565891 | + | 0.824480i | \(0.691468\pi\) | |||||||
\(504\) | −4.25110 | −0.189359 | ||||||||
\(505\) | −12.0551 | −0.536445 | ||||||||
\(506\) | 12.5249 | 0.556800 | ||||||||
\(507\) | 5.28972 | 0.234925 | ||||||||
\(508\) | −18.0636 | −0.801444 | ||||||||
\(509\) | 22.7504 | 1.00839 | 0.504197 | − | 0.863588i | \(-0.331788\pi\) | ||||
0.504197 | + | 0.863588i | \(0.331788\pi\) | |||||||
\(510\) | 17.2056 | 0.761879 | ||||||||
\(511\) | 2.39587 | 0.105987 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −22.4357 | −0.989598 | ||||||||
\(515\) | 24.6390 | 1.08572 | ||||||||
\(516\) | 1.57694 | 0.0694210 | ||||||||
\(517\) | 1.30852 | 0.0575487 | ||||||||
\(518\) | 23.3296 | 1.02504 | ||||||||
\(519\) | 22.0740 | 0.968943 | ||||||||
\(520\) | 6.98655 | 0.306381 | ||||||||
\(521\) | 29.1879 | 1.27874 | 0.639372 | − | 0.768898i | \(-0.279194\pi\) | ||||
0.639372 | + | 0.768898i | \(0.279194\pi\) | |||||||
\(522\) | 5.73064 | 0.250823 | ||||||||
\(523\) | −25.5569 | −1.11752 | −0.558762 | − | 0.829328i | \(-0.688724\pi\) | ||||
−0.558762 | + | 0.829328i | \(0.688724\pi\) | |||||||
\(524\) | −18.2116 | −0.795576 | ||||||||
\(525\) | 5.65721 | 0.246901 | ||||||||
\(526\) | 2.03837 | 0.0888771 | ||||||||
\(527\) | −0.801597 | −0.0349181 | ||||||||
\(528\) | −1.96359 | −0.0854545 | ||||||||
\(529\) | 17.6861 | 0.768959 | ||||||||
\(530\) | −2.51610 | −0.109292 | ||||||||
\(531\) | 3.13796 | 0.136176 | ||||||||
\(532\) | 4.25110 | 0.184309 | ||||||||
\(533\) | 27.5680 | 1.19410 | ||||||||
\(534\) | −10.6809 | −0.462207 | ||||||||
\(535\) | 38.4383 | 1.66183 | ||||||||
\(536\) | 7.65377 | 0.330593 | ||||||||
\(537\) | −18.7893 | −0.810818 | ||||||||
\(538\) | −24.6140 | −1.06118 | ||||||||
\(539\) | 21.7407 | 0.936439 | ||||||||
\(540\) | 2.51610 | 0.108276 | ||||||||
\(541\) | 13.0945 | 0.562978 | 0.281489 | − | 0.959565i | \(-0.409172\pi\) | ||||
0.281489 | + | 0.959565i | \(0.409172\pi\) | |||||||
\(542\) | −26.9494 | −1.15758 | ||||||||
\(543\) | 11.4778 | 0.492558 | ||||||||
\(544\) | 6.83822 | 0.293186 | ||||||||
\(545\) | −19.9197 | −0.853267 | ||||||||
\(546\) | −11.8042 | −0.505173 | ||||||||
\(547\) | −36.5701 | −1.56362 | −0.781812 | − | 0.623515i | \(-0.785704\pi\) | ||||
−0.781812 | + | 0.623515i | \(0.785704\pi\) | |||||||
\(548\) | −18.2145 | −0.778084 | ||||||||
\(549\) | −0.415900 | −0.0177502 | ||||||||
\(550\) | 2.61308 | 0.111422 | ||||||||
\(551\) | −5.73064 | −0.244133 | ||||||||
\(552\) | −6.37856 | −0.271490 | ||||||||
\(553\) | 68.1408 | 2.89764 | ||||||||
\(554\) | −22.7108 | −0.964891 | ||||||||
\(555\) | −13.8081 | −0.586121 | ||||||||
\(556\) | 7.07490 | 0.300042 | ||||||||
\(557\) | 29.6306 | 1.25549 | 0.627744 | − | 0.778420i | \(-0.283978\pi\) | ||||
0.627744 | + | 0.778420i | \(0.283978\pi\) | |||||||
\(558\) | −0.117223 | −0.00496245 | ||||||||
\(559\) | 4.37876 | 0.185202 | ||||||||
\(560\) | 10.6962 | 0.451997 | ||||||||
\(561\) | −13.4275 | −0.566909 | ||||||||
\(562\) | 3.42468 | 0.144461 | ||||||||
\(563\) | 3.50188 | 0.147586 | 0.0737932 | − | 0.997274i | \(-0.476490\pi\) | ||||
0.0737932 | + | 0.997274i | \(0.476490\pi\) | |||||||
\(564\) | −0.666390 | −0.0280601 | ||||||||
\(565\) | −7.20072 | −0.302937 | ||||||||
\(566\) | −9.90360 | −0.416279 | ||||||||
\(567\) | −4.25110 | −0.178530 | ||||||||
\(568\) | 9.28244 | 0.389482 | ||||||||
\(569\) | 9.14241 | 0.383270 | 0.191635 | − | 0.981466i | \(-0.438621\pi\) | ||||
0.191635 | + | 0.981466i | \(0.438621\pi\) | |||||||
\(570\) | −2.51610 | −0.105388 | ||||||||
\(571\) | 27.8557 | 1.16572 | 0.582862 | − | 0.812571i | \(-0.301933\pi\) | ||||
0.582862 | + | 0.812571i | \(0.301933\pi\) | |||||||
\(572\) | −5.45239 | −0.227976 | ||||||||
\(573\) | 1.50328 | 0.0628005 | ||||||||
\(574\) | 42.2058 | 1.76164 | ||||||||
\(575\) | 8.48835 | 0.353989 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −8.06279 | −0.335658 | −0.167829 | − | 0.985816i | \(-0.553676\pi\) | ||||
−0.167829 | + | 0.985816i | \(0.553676\pi\) | |||||||
\(578\) | 29.7612 | 1.23790 | ||||||||
\(579\) | −10.5502 | −0.438450 | ||||||||
\(580\) | −14.4189 | −0.598711 | ||||||||
\(581\) | −1.30908 | −0.0543098 | ||||||||
\(582\) | 8.44389 | 0.350011 | ||||||||
\(583\) | 1.96359 | 0.0813238 | ||||||||
\(584\) | −0.563587 | −0.0233214 | ||||||||
\(585\) | 6.98655 | 0.288858 | ||||||||
\(586\) | 3.52895 | 0.145779 | ||||||||
\(587\) | 15.4235 | 0.636596 | 0.318298 | − | 0.947991i | \(-0.396889\pi\) | ||||
0.318298 | + | 0.947991i | \(0.396889\pi\) | |||||||
\(588\) | −11.0719 | −0.456597 | ||||||||
\(589\) | 0.117223 | 0.00483009 | ||||||||
\(590\) | −7.89544 | −0.325050 | ||||||||
\(591\) | 5.16113 | 0.212301 | ||||||||
\(592\) | −5.48789 | −0.225551 | ||||||||
\(593\) | 0.610048 | 0.0250517 | 0.0125258 | − | 0.999922i | \(-0.496013\pi\) | ||||
0.0125258 | + | 0.999922i | \(0.496013\pi\) | |||||||
\(594\) | −1.96359 | −0.0805673 | ||||||||
\(595\) | 73.1430 | 2.99857 | ||||||||
\(596\) | −16.8298 | −0.689375 | ||||||||
\(597\) | 21.8391 | 0.893816 | ||||||||
\(598\) | −17.7116 | −0.724281 | ||||||||
\(599\) | −0.916684 | −0.0374547 | −0.0187273 | − | 0.999825i | \(-0.505961\pi\) | ||||
−0.0187273 | + | 0.999825i | \(0.505961\pi\) | |||||||
\(600\) | −1.33076 | −0.0543281 | ||||||||
\(601\) | 3.30078 | 0.134642 | 0.0673208 | − | 0.997731i | \(-0.478555\pi\) | ||||
0.0673208 | + | 0.997731i | \(0.478555\pi\) | |||||||
\(602\) | 6.70374 | 0.273224 | ||||||||
\(603\) | 7.65377 | 0.311686 | ||||||||
\(604\) | 9.22370 | 0.375307 | ||||||||
\(605\) | 17.9758 | 0.730819 | ||||||||
\(606\) | −4.79119 | −0.194629 | ||||||||
\(607\) | −37.2085 | −1.51025 | −0.755123 | − | 0.655583i | \(-0.772423\pi\) | ||||
−0.755123 | + | 0.655583i | \(0.772423\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 24.3615 | 0.987180 | ||||||||
\(610\) | 1.04645 | 0.0423693 | ||||||||
\(611\) | −1.85039 | −0.0748589 | ||||||||
\(612\) | 6.83822 | 0.276419 | ||||||||
\(613\) | −37.8515 | −1.52881 | −0.764403 | − | 0.644738i | \(-0.776966\pi\) | ||||
−0.764403 | + | 0.644738i | \(0.776966\pi\) | |||||||
\(614\) | 28.6666 | 1.15689 | ||||||||
\(615\) | −24.9803 | −1.00730 | ||||||||
\(616\) | −8.34745 | −0.336328 | ||||||||
\(617\) | −1.91601 | −0.0771357 | −0.0385678 | − | 0.999256i | \(-0.512280\pi\) | ||||
−0.0385678 | + | 0.999256i | \(0.512280\pi\) | |||||||
\(618\) | 9.79253 | 0.393913 | ||||||||
\(619\) | −20.0309 | −0.805109 | −0.402554 | − | 0.915396i | \(-0.631878\pi\) | ||||
−0.402554 | + | 0.915396i | \(0.631878\pi\) | |||||||
\(620\) | 0.294945 | 0.0118453 | ||||||||
\(621\) | −6.37856 | −0.255963 | ||||||||
\(622\) | −0.461697 | −0.0185124 | ||||||||
\(623\) | −45.4056 | −1.81914 | ||||||||
\(624\) | 2.77674 | 0.111159 | ||||||||
\(625\) | −29.8829 | −1.19532 | ||||||||
\(626\) | −22.6577 | −0.905582 | ||||||||
\(627\) | 1.96359 | 0.0784184 | ||||||||
\(628\) | −18.0398 | −0.719865 | ||||||||
\(629\) | −37.5274 | −1.49631 | ||||||||
\(630\) | 10.6962 | 0.426147 | ||||||||
\(631\) | 18.9725 | 0.755283 | 0.377642 | − | 0.925952i | \(-0.376735\pi\) | ||||
0.377642 | + | 0.925952i | \(0.376735\pi\) | |||||||
\(632\) | −16.0290 | −0.637598 | ||||||||
\(633\) | −18.8235 | −0.748167 | ||||||||
\(634\) | 23.2735 | 0.924310 | ||||||||
\(635\) | 45.4499 | 1.80363 | ||||||||
\(636\) | −1.00000 | −0.0396526 | ||||||||
\(637\) | −30.7438 | −1.21811 | ||||||||
\(638\) | 11.2527 | 0.445497 | ||||||||
\(639\) | 9.28244 | 0.367208 | ||||||||
\(640\) | −2.51610 | −0.0994576 | ||||||||
\(641\) | 6.94096 | 0.274152 | 0.137076 | − | 0.990561i | \(-0.456230\pi\) | ||||
0.137076 | + | 0.990561i | \(0.456230\pi\) | |||||||
\(642\) | 15.2769 | 0.602932 | ||||||||
\(643\) | 6.00715 | 0.236899 | 0.118449 | − | 0.992960i | \(-0.462208\pi\) | ||||
0.118449 | + | 0.992960i | \(0.462208\pi\) | |||||||
\(644\) | −27.1159 | −1.06852 | ||||||||
\(645\) | −3.96774 | −0.156230 | ||||||||
\(646\) | −6.83822 | −0.269046 | ||||||||
\(647\) | 23.6701 | 0.930569 | 0.465285 | − | 0.885161i | \(-0.345952\pi\) | ||||
0.465285 | + | 0.885161i | \(0.345952\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 6.16169 | 0.241868 | ||||||||
\(650\) | −3.69518 | −0.144937 | ||||||||
\(651\) | −0.498327 | −0.0195310 | ||||||||
\(652\) | −0.0245472 | −0.000961343 0 | ||||||||
\(653\) | 43.0932 | 1.68637 | 0.843183 | − | 0.537627i | \(-0.180679\pi\) | ||||
0.843183 | + | 0.537627i | \(0.180679\pi\) | |||||||
\(654\) | −7.91690 | −0.309575 | ||||||||
\(655\) | 45.8221 | 1.79042 | ||||||||
\(656\) | −9.92819 | −0.387631 | ||||||||
\(657\) | −0.563587 | −0.0219876 | ||||||||
\(658\) | −2.83290 | −0.110438 | ||||||||
\(659\) | 43.4810 | 1.69378 | 0.846890 | − | 0.531768i | \(-0.178472\pi\) | ||||
0.846890 | + | 0.531768i | \(0.178472\pi\) | |||||||
\(660\) | 4.94060 | 0.192313 | ||||||||
\(661\) | −24.1652 | −0.939919 | −0.469959 | − | 0.882688i | \(-0.655731\pi\) | ||||
−0.469959 | + | 0.882688i | \(0.655731\pi\) | |||||||
\(662\) | 5.39248 | 0.209585 | ||||||||
\(663\) | 18.9879 | 0.737431 | ||||||||
\(664\) | 0.307939 | 0.0119503 | ||||||||
\(665\) | −10.6962 | −0.414781 | ||||||||
\(666\) | −5.48789 | −0.212651 | ||||||||
\(667\) | 36.5532 | 1.41535 | ||||||||
\(668\) | 14.1169 | 0.546197 | ||||||||
\(669\) | 22.7495 | 0.879548 | ||||||||
\(670\) | −19.2577 | −0.743988 | ||||||||
\(671\) | −0.816658 | −0.0315267 | ||||||||
\(672\) | 4.25110 | 0.163990 | ||||||||
\(673\) | −6.57056 | −0.253276 | −0.126638 | − | 0.991949i | \(-0.540419\pi\) | ||||
−0.126638 | + | 0.991949i | \(0.540419\pi\) | |||||||
\(674\) | 5.36502 | 0.206653 | ||||||||
\(675\) | −1.33076 | −0.0512210 | ||||||||
\(676\) | −5.28972 | −0.203451 | ||||||||
\(677\) | −47.1841 | −1.81343 | −0.906717 | − | 0.421740i | \(-0.861420\pi\) | ||||
−0.906717 | + | 0.421740i | \(0.861420\pi\) | |||||||
\(678\) | −2.86186 | −0.109909 | ||||||||
\(679\) | 35.8959 | 1.37756 | ||||||||
\(680\) | −17.2056 | −0.659806 | ||||||||
\(681\) | −7.21237 | −0.276378 | ||||||||
\(682\) | −0.230179 | −0.00881399 | ||||||||
\(683\) | −4.37341 | −0.167344 | −0.0836719 | − | 0.996493i | \(-0.526665\pi\) | ||||
−0.0836719 | + | 0.996493i | \(0.526665\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | 45.8295 | 1.75105 | ||||||||
\(686\) | −17.3100 | −0.660900 | ||||||||
\(687\) | −3.30012 | −0.125908 | ||||||||
\(688\) | −1.57694 | −0.0601203 | ||||||||
\(689\) | −2.77674 | −0.105785 | ||||||||
\(690\) | 16.0491 | 0.610979 | ||||||||
\(691\) | −8.82808 | −0.335836 | −0.167918 | − | 0.985801i | \(-0.553704\pi\) | ||||
−0.167918 | + | 0.985801i | \(0.553704\pi\) | |||||||
\(692\) | −22.0740 | −0.839129 | ||||||||
\(693\) | −8.34745 | −0.317093 | ||||||||
\(694\) | 11.7607 | 0.446431 | ||||||||
\(695\) | −17.8012 | −0.675236 | ||||||||
\(696\) | −5.73064 | −0.217219 | ||||||||
\(697\) | −67.8911 | −2.57156 | ||||||||
\(698\) | 2.82073 | 0.106766 | ||||||||
\(699\) | 7.84552 | 0.296745 | ||||||||
\(700\) | −5.65721 | −0.213822 | ||||||||
\(701\) | 33.3377 | 1.25915 | 0.629574 | − | 0.776941i | \(-0.283230\pi\) | ||||
0.629574 | + | 0.776941i | \(0.283230\pi\) | |||||||
\(702\) | 2.77674 | 0.104801 | ||||||||
\(703\) | 5.48789 | 0.206980 | ||||||||
\(704\) | 1.96359 | 0.0740058 | ||||||||
\(705\) | 1.67671 | 0.0631484 | ||||||||
\(706\) | −19.2115 | −0.723036 | ||||||||
\(707\) | −20.3678 | −0.766012 | ||||||||
\(708\) | −3.13796 | −0.117932 | ||||||||
\(709\) | 22.1272 | 0.831004 | 0.415502 | − | 0.909592i | \(-0.363606\pi\) | ||||
0.415502 | + | 0.909592i | \(0.363606\pi\) | |||||||
\(710\) | −23.3555 | −0.876518 | ||||||||
\(711\) | −16.0290 | −0.601133 | ||||||||
\(712\) | 10.6809 | 0.400283 | ||||||||
\(713\) | −0.747715 | −0.0280021 | ||||||||
\(714\) | 29.0700 | 1.08792 | ||||||||
\(715\) | 13.7188 | 0.513053 | ||||||||
\(716\) | 18.7893 | 0.702189 | ||||||||
\(717\) | −1.41077 | −0.0526861 | ||||||||
\(718\) | −16.7903 | −0.626607 | ||||||||
\(719\) | 38.6599 | 1.44177 | 0.720886 | − | 0.693054i | \(-0.243735\pi\) | ||||
0.720886 | + | 0.693054i | \(0.243735\pi\) | |||||||
\(720\) | −2.51610 | −0.0937695 | ||||||||
\(721\) | 41.6291 | 1.55035 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −3.80810 | −0.141625 | ||||||||
\(724\) | −11.4778 | −0.426568 | ||||||||
\(725\) | 7.62612 | 0.283227 | ||||||||
\(726\) | 7.14429 | 0.265150 | ||||||||
\(727\) | 24.8890 | 0.923083 | 0.461542 | − | 0.887119i | \(-0.347296\pi\) | ||||
0.461542 | + | 0.887119i | \(0.347296\pi\) | |||||||
\(728\) | 11.8042 | 0.437493 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.41804 | 0.0524840 | ||||||||
\(731\) | −10.7835 | −0.398841 | ||||||||
\(732\) | 0.415900 | 0.0153721 | ||||||||
\(733\) | −25.7848 | −0.952383 | −0.476192 | − | 0.879342i | \(-0.657983\pi\) | ||||
−0.476192 | + | 0.879342i | \(0.657983\pi\) | |||||||
\(734\) | 5.76787 | 0.212896 | ||||||||
\(735\) | 27.8580 | 1.02756 | ||||||||
\(736\) | 6.37856 | 0.235117 | ||||||||
\(737\) | 15.0289 | 0.553597 | ||||||||
\(738\) | −9.92819 | −0.365462 | ||||||||
\(739\) | 15.8842 | 0.584311 | 0.292155 | − | 0.956371i | \(-0.405628\pi\) | ||||
0.292155 | + | 0.956371i | \(0.405628\pi\) | |||||||
\(740\) | 13.8081 | 0.507595 | ||||||||
\(741\) | −2.77674 | −0.102006 | ||||||||
\(742\) | −4.25110 | −0.156063 | ||||||||
\(743\) | 15.0640 | 0.552644 | 0.276322 | − | 0.961065i | \(-0.410884\pi\) | ||||
0.276322 | + | 0.961065i | \(0.410884\pi\) | |||||||
\(744\) | 0.117223 | 0.00429761 | ||||||||
\(745\) | 42.3454 | 1.55142 | ||||||||
\(746\) | 32.1422 | 1.17681 | ||||||||
\(747\) | 0.307939 | 0.0112669 | ||||||||
\(748\) | 13.4275 | 0.490958 | ||||||||
\(749\) | 64.9438 | 2.37299 | ||||||||
\(750\) | −9.23217 | −0.337111 | ||||||||
\(751\) | −26.4659 | −0.965756 | −0.482878 | − | 0.875688i | \(-0.660409\pi\) | ||||
−0.482878 | + | 0.875688i | \(0.660409\pi\) | |||||||
\(752\) | 0.666390 | 0.0243008 | ||||||||
\(753\) | −28.9995 | −1.05680 | ||||||||
\(754\) | −15.9125 | −0.579499 | ||||||||
\(755\) | −23.2078 | −0.844617 | ||||||||
\(756\) | 4.25110 | 0.154611 | ||||||||
\(757\) | 1.72136 | 0.0625637 | 0.0312819 | − | 0.999511i | \(-0.490041\pi\) | ||||
0.0312819 | + | 0.999511i | \(0.490041\pi\) | |||||||
\(758\) | 27.4613 | 0.997439 | ||||||||
\(759\) | −12.5249 | −0.454626 | ||||||||
\(760\) | 2.51610 | 0.0912686 | ||||||||
\(761\) | −36.3698 | −1.31840 | −0.659201 | − | 0.751967i | \(-0.729105\pi\) | ||||
−0.659201 | + | 0.751967i | \(0.729105\pi\) | |||||||
\(762\) | 18.0636 | 0.654377 | ||||||||
\(763\) | −33.6556 | −1.21841 | ||||||||
\(764\) | −1.50328 | −0.0543869 | ||||||||
\(765\) | −17.2056 | −0.622071 | ||||||||
\(766\) | 30.2728 | 1.09380 | ||||||||
\(767\) | −8.71331 | −0.314619 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −1.13835 | −0.0410498 | −0.0205249 | − | 0.999789i | \(-0.506534\pi\) | ||||
−0.0205249 | + | 0.999789i | \(0.506534\pi\) | |||||||
\(770\) | 21.0030 | 0.756896 | ||||||||
\(771\) | 22.4357 | 0.808003 | ||||||||
\(772\) | 10.5502 | 0.379709 | ||||||||
\(773\) | 19.4447 | 0.699379 | 0.349689 | − | 0.936866i | \(-0.386287\pi\) | ||||
0.349689 | + | 0.936866i | \(0.386287\pi\) | |||||||
\(774\) | −1.57694 | −0.0566820 | ||||||||
\(775\) | −0.155996 | −0.00560354 | ||||||||
\(776\) | −8.44389 | −0.303118 | ||||||||
\(777\) | −23.3296 | −0.836945 | ||||||||
\(778\) | −17.8415 | −0.639647 | ||||||||
\(779\) | 9.92819 | 0.355714 | ||||||||
\(780\) | −6.98655 | −0.250159 | ||||||||
\(781\) | 18.2269 | 0.652212 | ||||||||
\(782\) | 43.6180 | 1.55978 | ||||||||
\(783\) | −5.73064 | −0.204796 | ||||||||
\(784\) | 11.0719 | 0.395425 | ||||||||
\(785\) | 45.3898 | 1.62003 | ||||||||
\(786\) | 18.2116 | 0.649585 | ||||||||
\(787\) | −42.4909 | −1.51464 | −0.757318 | − | 0.653046i | \(-0.773491\pi\) | ||||
−0.757318 | + | 0.653046i | \(0.773491\pi\) | |||||||
\(788\) | −5.16113 | −0.183858 | ||||||||
\(789\) | −2.03837 | −0.0725679 | ||||||||
\(790\) | 40.3305 | 1.43489 | ||||||||
\(791\) | −12.1661 | −0.432575 | ||||||||
\(792\) | 1.96359 | 0.0697733 | ||||||||
\(793\) | 1.15484 | 0.0410097 | ||||||||
\(794\) | 13.9044 | 0.493448 | ||||||||
\(795\) | 2.51610 | 0.0892369 | ||||||||
\(796\) | −21.8391 | −0.774068 | ||||||||
\(797\) | −35.5146 | −1.25799 | −0.628995 | − | 0.777409i | \(-0.716534\pi\) | ||||
−0.628995 | + | 0.777409i | \(0.716534\pi\) | |||||||
\(798\) | −4.25110 | −0.150487 | ||||||||
\(799\) | 4.55692 | 0.161212 | ||||||||
\(800\) | 1.33076 | 0.0470495 | ||||||||
\(801\) | 10.6809 | 0.377391 | ||||||||
\(802\) | −33.3661 | −1.17820 | ||||||||
\(803\) | −1.10666 | −0.0390530 | ||||||||
\(804\) | −7.65377 | −0.269928 | ||||||||
\(805\) | 68.2264 | 2.40467 | ||||||||
\(806\) | 0.325498 | 0.0114652 | ||||||||
\(807\) | 24.6140 | 0.866452 | ||||||||
\(808\) | 4.79119 | 0.168553 | ||||||||
\(809\) | −40.8919 | −1.43768 | −0.718841 | − | 0.695174i | \(-0.755327\pi\) | ||||
−0.718841 | + | 0.695174i | \(0.755327\pi\) | |||||||
\(810\) | −2.51610 | −0.0884068 | ||||||||
\(811\) | 15.7015 | 0.551355 | 0.275677 | − | 0.961250i | \(-0.411098\pi\) | ||||
0.275677 | + | 0.961250i | \(0.411098\pi\) | |||||||
\(812\) | −24.3615 | −0.854923 | ||||||||
\(813\) | 26.9494 | 0.945158 | ||||||||
\(814\) | −10.7760 | −0.377698 | ||||||||
\(815\) | 0.0617632 | 0.00216347 | ||||||||
\(816\) | −6.83822 | −0.239385 | ||||||||
\(817\) | 1.57694 | 0.0551702 | ||||||||
\(818\) | 18.2552 | 0.638277 | ||||||||
\(819\) | 11.8042 | 0.412472 | ||||||||
\(820\) | 24.9803 | 0.872351 | ||||||||
\(821\) | −25.1876 | −0.879054 | −0.439527 | − | 0.898229i | \(-0.644854\pi\) | ||||
−0.439527 | + | 0.898229i | \(0.644854\pi\) | |||||||
\(822\) | 18.2145 | 0.635303 | ||||||||
\(823\) | −27.0473 | −0.942808 | −0.471404 | − | 0.881917i | \(-0.656253\pi\) | ||||
−0.471404 | + | 0.881917i | \(0.656253\pi\) | |||||||
\(824\) | −9.79253 | −0.341139 | ||||||||
\(825\) | −2.61308 | −0.0909757 | ||||||||
\(826\) | −13.3398 | −0.464152 | ||||||||
\(827\) | 29.1801 | 1.01469 | 0.507346 | − | 0.861742i | \(-0.330627\pi\) | ||||
0.507346 | + | 0.861742i | \(0.330627\pi\) | |||||||
\(828\) | 6.37856 | 0.221670 | ||||||||
\(829\) | −15.8490 | −0.550458 | −0.275229 | − | 0.961379i | \(-0.588754\pi\) | ||||
−0.275229 | + | 0.961379i | \(0.588754\pi\) | |||||||
\(830\) | −0.774805 | −0.0268939 | ||||||||
\(831\) | 22.7108 | 0.787830 | ||||||||
\(832\) | −2.77674 | −0.0962661 | ||||||||
\(833\) | 75.7120 | 2.62326 | ||||||||
\(834\) | −7.07490 | −0.244984 | ||||||||
\(835\) | −35.5194 | −1.22920 | ||||||||
\(836\) | −1.96359 | −0.0679124 | ||||||||
\(837\) | 0.117223 | 0.00405182 | ||||||||
\(838\) | −20.4441 | −0.706231 | ||||||||
\(839\) | 6.86851 | 0.237127 | 0.118564 | − | 0.992946i | \(-0.462171\pi\) | ||||
0.118564 | + | 0.992946i | \(0.462171\pi\) | |||||||
\(840\) | −10.6962 | −0.369054 | ||||||||
\(841\) | 3.84023 | 0.132422 | ||||||||
\(842\) | −0.374365 | −0.0129015 | ||||||||
\(843\) | −3.42468 | −0.117952 | ||||||||
\(844\) | 18.8235 | 0.647932 | ||||||||
\(845\) | 13.3095 | 0.457860 | ||||||||
\(846\) | 0.666390 | 0.0229110 | ||||||||
\(847\) | 30.3711 | 1.04356 | ||||||||
\(848\) | 1.00000 | 0.0343401 | ||||||||
\(849\) | 9.90360 | 0.339891 | ||||||||
\(850\) | 9.10004 | 0.312129 | ||||||||
\(851\) | −35.0049 | −1.19995 | ||||||||
\(852\) | −9.28244 | −0.318011 | ||||||||
\(853\) | −22.6991 | −0.777203 | −0.388602 | − | 0.921406i | \(-0.627042\pi\) | ||||
−0.388602 | + | 0.921406i | \(0.627042\pi\) | |||||||
\(854\) | 1.76803 | 0.0605008 | ||||||||
\(855\) | 2.51610 | 0.0860488 | ||||||||
\(856\) | −15.2769 | −0.522154 | ||||||||
\(857\) | 16.4825 | 0.563033 | 0.281516 | − | 0.959556i | \(-0.409163\pi\) | ||||
0.281516 | + | 0.959556i | \(0.409163\pi\) | |||||||
\(858\) | 5.45239 | 0.186142 | ||||||||
\(859\) | −32.1978 | −1.09858 | −0.549288 | − | 0.835633i | \(-0.685101\pi\) | ||||
−0.549288 | + | 0.835633i | \(0.685101\pi\) | |||||||
\(860\) | 3.96774 | 0.135299 | ||||||||
\(861\) | −42.2058 | −1.43837 | ||||||||
\(862\) | −19.6831 | −0.670407 | ||||||||
\(863\) | −10.3252 | −0.351473 | −0.175737 | − | 0.984437i | \(-0.556231\pi\) | ||||
−0.175737 | + | 0.984437i | \(0.556231\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 55.5405 | 1.88843 | ||||||||
\(866\) | −16.9190 | −0.574930 | ||||||||
\(867\) | −29.7612 | −1.01074 | ||||||||
\(868\) | 0.498327 | 0.0169143 | ||||||||
\(869\) | −31.4744 | −1.06770 | ||||||||
\(870\) | 14.4189 | 0.488845 | ||||||||
\(871\) | −21.2525 | −0.720115 | ||||||||
\(872\) | 7.91690 | 0.268100 | ||||||||
\(873\) | −8.44389 | −0.285783 | ||||||||
\(874\) | −6.37856 | −0.215758 | ||||||||
\(875\) | −39.2469 | −1.32679 | ||||||||
\(876\) | 0.563587 | 0.0190418 | ||||||||
\(877\) | −55.9240 | −1.88842 | −0.944210 | − | 0.329345i | \(-0.893172\pi\) | ||||
−0.944210 | + | 0.329345i | \(0.893172\pi\) | |||||||
\(878\) | −22.5619 | −0.761429 | ||||||||
\(879\) | −3.52895 | −0.119028 | ||||||||
\(880\) | −4.94060 | −0.166548 | ||||||||
\(881\) | −40.3447 | −1.35925 | −0.679624 | − | 0.733561i | \(-0.737857\pi\) | ||||
−0.679624 | + | 0.733561i | \(0.737857\pi\) | |||||||
\(882\) | 11.0719 | 0.372810 | ||||||||
\(883\) | 18.6506 | 0.627643 | 0.313821 | − | 0.949482i | \(-0.398391\pi\) | ||||
0.313821 | + | 0.949482i | \(0.398391\pi\) | |||||||
\(884\) | −18.9879 | −0.638634 | ||||||||
\(885\) | 7.89544 | 0.265402 | ||||||||
\(886\) | −13.7676 | −0.462533 | ||||||||
\(887\) | 1.52230 | 0.0511140 | 0.0255570 | − | 0.999673i | \(-0.491864\pi\) | ||||
0.0255570 | + | 0.999673i | \(0.491864\pi\) | |||||||
\(888\) | 5.48789 | 0.184162 | ||||||||
\(889\) | 76.7904 | 2.57547 | ||||||||
\(890\) | −26.8742 | −0.900825 | ||||||||
\(891\) | 1.96359 | 0.0657829 | ||||||||
\(892\) | −22.7495 | −0.761711 | ||||||||
\(893\) | −0.666390 | −0.0222999 | ||||||||
\(894\) | 16.8298 | 0.562872 | ||||||||
\(895\) | −47.2757 | −1.58025 | ||||||||
\(896\) | −4.25110 | −0.142019 | ||||||||
\(897\) | 17.7116 | 0.591373 | ||||||||
\(898\) | −6.70165 | −0.223637 | ||||||||
\(899\) | −0.671763 | −0.0224046 | ||||||||
\(900\) | 1.33076 | 0.0443587 | ||||||||
\(901\) | 6.83822 | 0.227814 | ||||||||
\(902\) | −19.4949 | −0.649111 | ||||||||
\(903\) | −6.70374 | −0.223087 | ||||||||
\(904\) | 2.86186 | 0.0951840 | ||||||||
\(905\) | 28.8792 | 0.959978 | ||||||||
\(906\) | −9.22370 | −0.306437 | ||||||||
\(907\) | −9.52492 | −0.316270 | −0.158135 | − | 0.987418i | \(-0.550548\pi\) | ||||
−0.158135 | + | 0.987418i | \(0.550548\pi\) | |||||||
\(908\) | 7.21237 | 0.239351 | ||||||||
\(909\) | 4.79119 | 0.158914 | ||||||||
\(910\) | −29.7006 | −0.984564 | ||||||||
\(911\) | −29.2804 | −0.970104 | −0.485052 | − | 0.874485i | \(-0.661199\pi\) | ||||
−0.485052 | + | 0.874485i | \(0.661199\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | 0.604667 | 0.0200116 | ||||||||
\(914\) | 23.6382 | 0.781881 | ||||||||
\(915\) | −1.04645 | −0.0345944 | ||||||||
\(916\) | 3.30012 | 0.109039 | ||||||||
\(917\) | 77.4193 | 2.55661 | ||||||||
\(918\) | −6.83822 | −0.225695 | ||||||||
\(919\) | −40.2105 | −1.32642 | −0.663212 | − | 0.748432i | \(-0.730807\pi\) | ||||
−0.663212 | + | 0.748432i | \(0.730807\pi\) | |||||||
\(920\) | −16.0491 | −0.529123 | ||||||||
\(921\) | −28.6666 | −0.944598 | ||||||||
\(922\) | −30.6242 | −1.00855 | ||||||||
\(923\) | −25.7749 | −0.848391 | ||||||||
\(924\) | 8.34745 | 0.274611 | ||||||||
\(925\) | −7.30308 | −0.240124 | ||||||||
\(926\) | 12.0260 | 0.395200 | ||||||||
\(927\) | −9.79253 | −0.321629 | ||||||||
\(928\) | 5.73064 | 0.188117 | ||||||||
\(929\) | 1.71699 | 0.0563327 | 0.0281663 | − | 0.999603i | \(-0.491033\pi\) | ||||
0.0281663 | + | 0.999603i | \(0.491033\pi\) | |||||||
\(930\) | −0.294945 | −0.00967163 | ||||||||
\(931\) | −11.0719 | −0.362867 | ||||||||
\(932\) | −7.84552 | −0.256989 | ||||||||
\(933\) | 0.461697 | 0.0151153 | ||||||||
\(934\) | −28.5051 | −0.932714 | ||||||||
\(935\) | −33.7849 | −1.10488 | ||||||||
\(936\) | −2.77674 | −0.0907606 | ||||||||
\(937\) | 5.40914 | 0.176709 | 0.0883544 | − | 0.996089i | \(-0.471839\pi\) | ||||
0.0883544 | + | 0.996089i | \(0.471839\pi\) | |||||||
\(938\) | −32.5370 | −1.06237 | ||||||||
\(939\) | 22.6577 | 0.739405 | ||||||||
\(940\) | −1.67671 | −0.0546881 | ||||||||
\(941\) | −60.1847 | −1.96197 | −0.980983 | − | 0.194093i | \(-0.937824\pi\) | ||||
−0.980983 | + | 0.194093i | \(0.937824\pi\) | |||||||
\(942\) | 18.0398 | 0.587767 | ||||||||
\(943\) | −63.3276 | −2.06223 | ||||||||
\(944\) | 3.13796 | 0.102132 | ||||||||
\(945\) | −10.6962 | −0.347948 | ||||||||
\(946\) | −3.09647 | −0.100675 | ||||||||
\(947\) | −8.94861 | −0.290791 | −0.145395 | − | 0.989374i | \(-0.546445\pi\) | ||||
−0.145395 | + | 0.989374i | \(0.546445\pi\) | |||||||
\(948\) | 16.0290 | 0.520596 | ||||||||
\(949\) | 1.56493 | 0.0507999 | ||||||||
\(950\) | −1.33076 | −0.0431756 | ||||||||
\(951\) | −23.2735 | −0.754696 | ||||||||
\(952\) | −29.0700 | −0.942163 | ||||||||
\(953\) | −21.9082 | −0.709678 | −0.354839 | − | 0.934928i | \(-0.615464\pi\) | ||||
−0.354839 | + | 0.934928i | \(0.615464\pi\) | |||||||
\(954\) | 1.00000 | 0.0323762 | ||||||||
\(955\) | 3.78241 | 0.122396 | ||||||||
\(956\) | 1.41077 | 0.0456275 | ||||||||
\(957\) | −11.2527 | −0.363747 | ||||||||
\(958\) | −15.9510 | −0.515352 | ||||||||
\(959\) | 77.4317 | 2.50040 | ||||||||
\(960\) | 2.51610 | 0.0812068 | ||||||||
\(961\) | −30.9863 | −0.999557 | ||||||||
\(962\) | 15.2384 | 0.491307 | ||||||||
\(963\) | −15.2769 | −0.492292 | ||||||||
\(964\) | 3.80810 | 0.122651 | ||||||||
\(965\) | −26.5453 | −0.854522 | ||||||||
\(966\) | 27.1159 | 0.872441 | ||||||||
\(967\) | −20.1206 | −0.647034 | −0.323517 | − | 0.946222i | \(-0.604865\pi\) | ||||
−0.323517 | + | 0.946222i | \(0.604865\pi\) | |||||||
\(968\) | −7.14429 | −0.229626 | ||||||||
\(969\) | 6.83822 | 0.219675 | ||||||||
\(970\) | 21.2457 | 0.682158 | ||||||||
\(971\) | 15.5739 | 0.499789 | 0.249894 | − | 0.968273i | \(-0.419604\pi\) | ||||
0.249894 | + | 0.968273i | \(0.419604\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −30.0761 | −0.964196 | ||||||||
\(974\) | 18.8436 | 0.603787 | ||||||||
\(975\) | 3.69518 | 0.118340 | ||||||||
\(976\) | −0.415900 | −0.0133126 | ||||||||
\(977\) | 2.39326 | 0.0765671 | 0.0382836 | − | 0.999267i | \(-0.487811\pi\) | ||||
0.0382836 | + | 0.999267i | \(0.487811\pi\) | |||||||
\(978\) | 0.0245472 | 0.000784933 0 | ||||||||
\(979\) | 20.9729 | 0.670298 | ||||||||
\(980\) | −27.8580 | −0.889891 | ||||||||
\(981\) | 7.91690 | 0.252767 | ||||||||
\(982\) | −12.6466 | −0.403569 | ||||||||
\(983\) | 26.8992 | 0.857951 | 0.428976 | − | 0.903316i | \(-0.358875\pi\) | ||||
0.428976 | + | 0.903316i | \(0.358875\pi\) | |||||||
\(984\) | 9.92819 | 0.316499 | ||||||||
\(985\) | 12.9859 | 0.413766 | ||||||||
\(986\) | 39.1873 | 1.24798 | ||||||||
\(987\) | 2.83290 | 0.0901721 | ||||||||
\(988\) | 2.77674 | 0.0883398 | ||||||||
\(989\) | −10.0586 | −0.319846 | ||||||||
\(990\) | −4.94060 | −0.157023 | ||||||||
\(991\) | −33.1675 | −1.05360 | −0.526801 | − | 0.849989i | \(-0.676609\pi\) | ||||
−0.526801 | + | 0.849989i | \(0.676609\pi\) | |||||||
\(992\) | −0.117223 | −0.00372184 | ||||||||
\(993\) | −5.39248 | −0.171125 | ||||||||
\(994\) | −39.4606 | −1.25161 | ||||||||
\(995\) | 54.9495 | 1.74201 | ||||||||
\(996\) | −0.307939 | −0.00975741 | ||||||||
\(997\) | 47.5275 | 1.50521 | 0.752606 | − | 0.658472i | \(-0.228797\pi\) | ||||
0.752606 | + | 0.658472i | \(0.228797\pi\) | |||||||
\(998\) | 22.4656 | 0.711138 | ||||||||
\(999\) | 5.48789 | 0.173629 |
(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 | 6042.2.a.bb.1.3 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6042.2.a.bb.1.3 | ✓ | 9 | 1.1 | even | 1 | trivial |