Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [861,2,Mod(1,861)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(861, 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("861.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 861 = 3 \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 861.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: | \(6.87511961403\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.626512.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 6x^{3} + 4x^{2} + 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.56695\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 861.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.56695 | 1.81511 | 0.907554 | − | 0.419935i | \(-0.137947\pi\) | ||||
0.907554 | + | 0.419935i | \(0.137947\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.58924 | 2.29462 | ||||||||
\(5\) | 1.31287 | 0.587135 | 0.293567 | − | 0.955938i | \(-0.405158\pi\) | ||||
0.293567 | + | 0.955938i | \(0.405158\pi\) | |||||||
\(6\) | 2.56695 | 1.04795 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 6.64645 | 2.34987 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.37008 | 1.06571 | ||||||||
\(11\) | −4.88262 | −1.47217 | −0.736083 | − | 0.676891i | \(-0.763327\pi\) | ||||
−0.736083 | + | 0.676891i | \(0.763327\pi\) | |||||||
\(12\) | 4.58924 | 1.32480 | ||||||||
\(13\) | −1.82542 | −0.506279 | −0.253140 | − | 0.967430i | \(-0.581463\pi\) | ||||
−0.253140 | + | 0.967430i | \(0.581463\pi\) | |||||||
\(14\) | −2.56695 | −0.686047 | ||||||||
\(15\) | 1.31287 | 0.338982 | ||||||||
\(16\) | 7.88262 | 1.97066 | ||||||||
\(17\) | 1.68713 | 0.409188 | 0.204594 | − | 0.978847i | \(-0.434413\pi\) | ||||
0.204594 | + | 0.978847i | \(0.434413\pi\) | |||||||
\(18\) | 2.56695 | 0.605036 | ||||||||
\(19\) | 1.82262 | 0.418137 | 0.209068 | − | 0.977901i | \(-0.432957\pi\) | ||||
0.209068 | + | 0.977901i | \(0.432957\pi\) | |||||||
\(20\) | 6.02509 | 1.34725 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −12.5335 | −2.67214 | ||||||||
\(23\) | 3.03931 | 0.633740 | 0.316870 | − | 0.948469i | \(-0.397368\pi\) | ||||
0.316870 | + | 0.948469i | \(0.397368\pi\) | |||||||
\(24\) | 6.64645 | 1.35670 | ||||||||
\(25\) | −3.27636 | −0.655273 | ||||||||
\(26\) | −4.68575 | −0.918952 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.58924 | −0.867284 | ||||||||
\(29\) | −2.73736 | −0.508315 | −0.254158 | − | 0.967163i | \(-0.581798\pi\) | ||||
−0.254158 | + | 0.967163i | \(0.581798\pi\) | |||||||
\(30\) | 3.37008 | 0.615290 | ||||||||
\(31\) | 2.17738 | 0.391070 | 0.195535 | − | 0.980697i | \(-0.437356\pi\) | ||||
0.195535 | + | 0.980697i | \(0.437356\pi\) | |||||||
\(32\) | 6.94142 | 1.22708 | ||||||||
\(33\) | −4.88262 | −0.849956 | ||||||||
\(34\) | 4.33077 | 0.742721 | ||||||||
\(35\) | −1.31287 | −0.221916 | ||||||||
\(36\) | 4.58924 | 0.764873 | ||||||||
\(37\) | −3.96349 | −0.651594 | −0.325797 | − | 0.945440i | \(-0.605633\pi\) | ||||
−0.325797 | + | 0.945440i | \(0.605633\pi\) | |||||||
\(38\) | 4.67857 | 0.758964 | ||||||||
\(39\) | −1.82542 | −0.292301 | ||||||||
\(40\) | 8.72594 | 1.37969 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | −2.56695 | −0.396089 | ||||||||
\(43\) | −7.49135 | −1.14242 | −0.571210 | − | 0.820804i | \(-0.693526\pi\) | ||||
−0.571210 | + | 0.820804i | \(0.693526\pi\) | |||||||
\(44\) | −22.4075 | −3.37806 | ||||||||
\(45\) | 1.31287 | 0.195712 | ||||||||
\(46\) | 7.80176 | 1.15031 | ||||||||
\(47\) | −2.68015 | −0.390941 | −0.195470 | − | 0.980710i | \(-0.562623\pi\) | ||||
−0.195470 | + | 0.980710i | \(0.562623\pi\) | |||||||
\(48\) | 7.88262 | 1.13776 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −8.41027 | −1.18939 | ||||||||
\(51\) | 1.68713 | 0.236245 | ||||||||
\(52\) | −8.37727 | −1.16172 | ||||||||
\(53\) | −5.35306 | −0.735299 | −0.367650 | − | 0.929964i | \(-0.619837\pi\) | ||||
−0.367650 | + | 0.929964i | \(0.619837\pi\) | |||||||
\(54\) | 2.56695 | 0.349318 | ||||||||
\(55\) | −6.41027 | −0.864360 | ||||||||
\(56\) | −6.64645 | −0.888169 | ||||||||
\(57\) | 1.82262 | 0.241411 | ||||||||
\(58\) | −7.02667 | −0.922647 | ||||||||
\(59\) | 4.82103 | 0.627644 | 0.313822 | − | 0.949482i | \(-0.398390\pi\) | ||||
0.313822 | + | 0.949482i | \(0.398390\pi\) | |||||||
\(60\) | 6.02509 | 0.777835 | ||||||||
\(61\) | 12.7554 | 1.63316 | 0.816582 | − | 0.577230i | \(-0.195866\pi\) | ||||
0.816582 | + | 0.577230i | \(0.195866\pi\) | |||||||
\(62\) | 5.58924 | 0.709834 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 2.05304 | 0.256629 | ||||||||
\(65\) | −2.39654 | −0.297254 | ||||||||
\(66\) | −12.5335 | −1.54276 | ||||||||
\(67\) | 4.06001 | 0.496009 | 0.248004 | − | 0.968759i | \(-0.420225\pi\) | ||||
0.248004 | + | 0.968759i | \(0.420225\pi\) | |||||||
\(68\) | 7.74263 | 0.938931 | ||||||||
\(69\) | 3.03931 | 0.365890 | ||||||||
\(70\) | −3.37008 | −0.402802 | ||||||||
\(71\) | 11.2580 | 1.33608 | 0.668038 | − | 0.744128i | \(-0.267135\pi\) | ||||
0.668038 | + | 0.744128i | \(0.267135\pi\) | |||||||
\(72\) | 6.64645 | 0.783291 | ||||||||
\(73\) | −4.33077 | −0.506879 | −0.253439 | − | 0.967351i | \(-0.581562\pi\) | ||||
−0.253439 | + | 0.967351i | \(0.581562\pi\) | |||||||
\(74\) | −10.1741 | −1.18271 | ||||||||
\(75\) | −3.27636 | −0.378322 | ||||||||
\(76\) | 8.36442 | 0.959465 | ||||||||
\(77\) | 4.88262 | 0.556427 | ||||||||
\(78\) | −4.68575 | −0.530557 | ||||||||
\(79\) | 6.58226 | 0.740563 | 0.370281 | − | 0.928920i | \(-0.379261\pi\) | ||||
0.370281 | + | 0.928920i | \(0.379261\pi\) | |||||||
\(80\) | 10.3489 | 1.15704 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.56695 | −0.283472 | ||||||||
\(83\) | 13.4974 | 1.48154 | 0.740768 | − | 0.671760i | \(-0.234462\pi\) | ||||
0.740768 | + | 0.671760i | \(0.234462\pi\) | |||||||
\(84\) | −4.58924 | −0.500727 | ||||||||
\(85\) | 2.21498 | 0.240249 | ||||||||
\(86\) | −19.2299 | −2.07362 | ||||||||
\(87\) | −2.73736 | −0.293476 | ||||||||
\(88\) | −32.4521 | −3.45940 | ||||||||
\(89\) | −8.01653 | −0.849750 | −0.424875 | − | 0.905252i | \(-0.639682\pi\) | ||||
−0.424875 | + | 0.905252i | \(0.639682\pi\) | |||||||
\(90\) | 3.37008 | 0.355238 | ||||||||
\(91\) | 1.82542 | 0.191356 | ||||||||
\(92\) | 13.9481 | 1.45419 | ||||||||
\(93\) | 2.17738 | 0.225784 | ||||||||
\(94\) | −6.87982 | −0.709600 | ||||||||
\(95\) | 2.39286 | 0.245503 | ||||||||
\(96\) | 6.94142 | 0.708456 | ||||||||
\(97\) | −11.3241 | −1.14979 | −0.574896 | − | 0.818227i | \(-0.694957\pi\) | ||||
−0.574896 | + | 0.818227i | \(0.694957\pi\) | |||||||
\(98\) | 2.56695 | 0.259301 | ||||||||
\(99\) | −4.88262 | −0.490722 | ||||||||
\(100\) | −15.0360 | −1.50360 | ||||||||
\(101\) | 4.01093 | 0.399102 | 0.199551 | − | 0.979887i | \(-0.436052\pi\) | ||||
0.199551 | + | 0.979887i | \(0.436052\pi\) | |||||||
\(102\) | 4.33077 | 0.428810 | ||||||||
\(103\) | 10.5595 | 1.04046 | 0.520228 | − | 0.854027i | \(-0.325847\pi\) | ||||
0.520228 | + | 0.854027i | \(0.325847\pi\) | |||||||
\(104\) | −12.1325 | −1.18969 | ||||||||
\(105\) | −1.31287 | −0.128123 | ||||||||
\(106\) | −13.7410 | −1.33465 | ||||||||
\(107\) | 4.86193 | 0.470020 | 0.235010 | − | 0.971993i | \(-0.424488\pi\) | ||||
0.235010 | + | 0.971993i | \(0.424488\pi\) | |||||||
\(108\) | 4.58924 | 0.441600 | ||||||||
\(109\) | −17.5419 | −1.68021 | −0.840106 | − | 0.542423i | \(-0.817507\pi\) | ||||
−0.840106 | + | 0.542423i | \(0.817507\pi\) | |||||||
\(110\) | −16.4548 | −1.56891 | ||||||||
\(111\) | −3.96349 | −0.376198 | ||||||||
\(112\) | −7.88262 | −0.744838 | ||||||||
\(113\) | 0.890970 | 0.0838154 | 0.0419077 | − | 0.999121i | \(-0.486656\pi\) | ||||
0.0419077 | + | 0.999121i | \(0.486656\pi\) | |||||||
\(114\) | 4.67857 | 0.438188 | ||||||||
\(115\) | 3.99023 | 0.372091 | ||||||||
\(116\) | −12.5624 | −1.16639 | ||||||||
\(117\) | −1.82542 | −0.168760 | ||||||||
\(118\) | 12.3753 | 1.13924 | ||||||||
\(119\) | −1.68713 | −0.154659 | ||||||||
\(120\) | 8.72594 | 0.796566 | ||||||||
\(121\) | 12.8400 | 1.16727 | ||||||||
\(122\) | 32.7425 | 2.96437 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | 9.99253 | 0.897356 | ||||||||
\(125\) | −10.8658 | −0.971868 | ||||||||
\(126\) | −2.56695 | −0.228682 | ||||||||
\(127\) | −1.34061 | −0.118960 | −0.0594798 | − | 0.998230i | \(-0.518944\pi\) | ||||
−0.0594798 | + | 0.998230i | \(0.518944\pi\) | |||||||
\(128\) | −8.61280 | −0.761271 | ||||||||
\(129\) | −7.49135 | −0.659576 | ||||||||
\(130\) | −6.15180 | −0.539549 | ||||||||
\(131\) | 9.55026 | 0.834411 | 0.417205 | − | 0.908812i | \(-0.363010\pi\) | ||||
0.417205 | + | 0.908812i | \(0.363010\pi\) | |||||||
\(132\) | −22.4075 | −1.95032 | ||||||||
\(133\) | −1.82262 | −0.158041 | ||||||||
\(134\) | 10.4218 | 0.900310 | ||||||||
\(135\) | 1.31287 | 0.112994 | ||||||||
\(136\) | 11.2134 | 0.961541 | ||||||||
\(137\) | −16.5363 | −1.41279 | −0.706394 | − | 0.707819i | \(-0.749679\pi\) | ||||
−0.706394 | + | 0.707819i | \(0.749679\pi\) | |||||||
\(138\) | 7.80176 | 0.664130 | ||||||||
\(139\) | 17.4941 | 1.48383 | 0.741917 | − | 0.670492i | \(-0.233917\pi\) | ||||
0.741917 | + | 0.670492i | \(0.233917\pi\) | |||||||
\(140\) | −6.02509 | −0.509213 | ||||||||
\(141\) | −2.68015 | −0.225710 | ||||||||
\(142\) | 28.8987 | 2.42512 | ||||||||
\(143\) | 8.91282 | 0.745328 | ||||||||
\(144\) | 7.88262 | 0.656885 | ||||||||
\(145\) | −3.59381 | −0.298450 | ||||||||
\(146\) | −11.1169 | −0.920039 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −18.1894 | −1.49516 | ||||||||
\(149\) | −0.260929 | −0.0213761 | −0.0106881 | − | 0.999943i | \(-0.503402\pi\) | ||||
−0.0106881 | + | 0.999943i | \(0.503402\pi\) | |||||||
\(150\) | −8.41027 | −0.686695 | ||||||||
\(151\) | −17.9296 | −1.45909 | −0.729544 | − | 0.683934i | \(-0.760267\pi\) | ||||
−0.729544 | + | 0.683934i | \(0.760267\pi\) | |||||||
\(152\) | 12.1139 | 0.982569 | ||||||||
\(153\) | 1.68713 | 0.136396 | ||||||||
\(154\) | 12.5335 | 1.00997 | ||||||||
\(155\) | 2.85863 | 0.229611 | ||||||||
\(156\) | −8.37727 | −0.670718 | ||||||||
\(157\) | 22.1072 | 1.76435 | 0.882174 | − | 0.470923i | \(-0.156079\pi\) | ||||
0.882174 | + | 0.470923i | \(0.156079\pi\) | |||||||
\(158\) | 16.8964 | 1.34420 | ||||||||
\(159\) | −5.35306 | −0.424525 | ||||||||
\(160\) | 9.11320 | 0.720462 | ||||||||
\(161\) | −3.03931 | −0.239531 | ||||||||
\(162\) | 2.56695 | 0.201679 | ||||||||
\(163\) | −3.11513 | −0.243996 | −0.121998 | − | 0.992530i | \(-0.538930\pi\) | ||||
−0.121998 | + | 0.992530i | \(0.538930\pi\) | |||||||
\(164\) | −4.58924 | −0.358359 | ||||||||
\(165\) | −6.41027 | −0.499039 | ||||||||
\(166\) | 34.6473 | 2.68915 | ||||||||
\(167\) | −19.6015 | −1.51681 | −0.758406 | − | 0.651783i | \(-0.774021\pi\) | ||||
−0.758406 | + | 0.651783i | \(0.774021\pi\) | |||||||
\(168\) | −6.64645 | −0.512784 | ||||||||
\(169\) | −9.66786 | −0.743681 | ||||||||
\(170\) | 5.68575 | 0.436077 | ||||||||
\(171\) | 1.82262 | 0.139379 | ||||||||
\(172\) | −34.3796 | −2.62142 | ||||||||
\(173\) | −3.01970 | −0.229584 | −0.114792 | − | 0.993390i | \(-0.536620\pi\) | ||||
−0.114792 | + | 0.993390i | \(0.536620\pi\) | |||||||
\(174\) | −7.02667 | −0.532691 | ||||||||
\(175\) | 3.27636 | 0.247670 | ||||||||
\(176\) | −38.4879 | −2.90113 | ||||||||
\(177\) | 4.82103 | 0.362371 | ||||||||
\(178\) | −20.5780 | −1.54239 | ||||||||
\(179\) | 22.2192 | 1.66074 | 0.830371 | − | 0.557211i | \(-0.188129\pi\) | ||||
0.830371 | + | 0.557211i | \(0.188129\pi\) | |||||||
\(180\) | 6.02509 | 0.449083 | ||||||||
\(181\) | −6.88350 | −0.511647 | −0.255823 | − | 0.966724i | \(-0.582347\pi\) | ||||
−0.255823 | + | 0.966724i | \(0.582347\pi\) | |||||||
\(182\) | 4.68575 | 0.347331 | ||||||||
\(183\) | 12.7554 | 0.942907 | ||||||||
\(184\) | 20.2006 | 1.48921 | ||||||||
\(185\) | −5.20356 | −0.382573 | ||||||||
\(186\) | 5.58924 | 0.409823 | ||||||||
\(187\) | −8.23761 | −0.602393 | ||||||||
\(188\) | −12.2999 | −0.897060 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 6.14236 | 0.445614 | ||||||||
\(191\) | 2.81366 | 0.203589 | 0.101795 | − | 0.994805i | \(-0.467542\pi\) | ||||
0.101795 | + | 0.994805i | \(0.467542\pi\) | |||||||
\(192\) | 2.05304 | 0.148165 | ||||||||
\(193\) | 19.3710 | 1.39436 | 0.697178 | − | 0.716898i | \(-0.254439\pi\) | ||||
0.697178 | + | 0.716898i | \(0.254439\pi\) | |||||||
\(194\) | −29.0685 | −2.08700 | ||||||||
\(195\) | −2.39654 | −0.171620 | ||||||||
\(196\) | 4.58924 | 0.327803 | ||||||||
\(197\) | 11.2985 | 0.804984 | 0.402492 | − | 0.915423i | \(-0.368144\pi\) | ||||
0.402492 | + | 0.915423i | \(0.368144\pi\) | |||||||
\(198\) | −12.5335 | −0.890714 | ||||||||
\(199\) | −15.4956 | −1.09845 | −0.549226 | − | 0.835674i | \(-0.685077\pi\) | ||||
−0.549226 | + | 0.835674i | \(0.685077\pi\) | |||||||
\(200\) | −21.7762 | −1.53981 | ||||||||
\(201\) | 4.06001 | 0.286371 | ||||||||
\(202\) | 10.2959 | 0.724414 | ||||||||
\(203\) | 2.73736 | 0.192125 | ||||||||
\(204\) | 7.74263 | 0.542092 | ||||||||
\(205\) | −1.31287 | −0.0916950 | ||||||||
\(206\) | 27.1057 | 1.88854 | ||||||||
\(207\) | 3.03931 | 0.211247 | ||||||||
\(208\) | −14.3891 | −0.997703 | ||||||||
\(209\) | −8.89915 | −0.615567 | ||||||||
\(210\) | −3.37008 | −0.232558 | ||||||||
\(211\) | −22.5367 | −1.55149 | −0.775745 | − | 0.631046i | \(-0.782626\pi\) | ||||
−0.775745 | + | 0.631046i | \(0.782626\pi\) | |||||||
\(212\) | −24.5665 | −1.68723 | ||||||||
\(213\) | 11.2580 | 0.771383 | ||||||||
\(214\) | 12.4803 | 0.853137 | ||||||||
\(215\) | −9.83519 | −0.670754 | ||||||||
\(216\) | 6.64645 | 0.452233 | ||||||||
\(217\) | −2.17738 | −0.147810 | ||||||||
\(218\) | −45.0292 | −3.04977 | ||||||||
\(219\) | −4.33077 | −0.292646 | ||||||||
\(220\) | −29.4182 | −1.98338 | ||||||||
\(221\) | −3.07971 | −0.207164 | ||||||||
\(222\) | −10.1741 | −0.682840 | ||||||||
\(223\) | 4.61752 | 0.309212 | 0.154606 | − | 0.987976i | \(-0.450589\pi\) | ||||
0.154606 | + | 0.987976i | \(0.450589\pi\) | |||||||
\(224\) | −6.94142 | −0.463793 | ||||||||
\(225\) | −3.27636 | −0.218424 | ||||||||
\(226\) | 2.28708 | 0.152134 | ||||||||
\(227\) | 17.9390 | 1.19065 | 0.595327 | − | 0.803484i | \(-0.297023\pi\) | ||||
0.595327 | + | 0.803484i | \(0.297023\pi\) | |||||||
\(228\) | 8.36442 | 0.553947 | ||||||||
\(229\) | −18.1453 | −1.19907 | −0.599536 | − | 0.800348i | \(-0.704648\pi\) | ||||
−0.599536 | + | 0.800348i | \(0.704648\pi\) | |||||||
\(230\) | 10.2427 | 0.675385 | ||||||||
\(231\) | 4.88262 | 0.321253 | ||||||||
\(232\) | −18.1937 | −1.19448 | ||||||||
\(233\) | 25.5795 | 1.67577 | 0.837885 | − | 0.545847i | \(-0.183792\pi\) | ||||
0.837885 | + | 0.545847i | \(0.183792\pi\) | |||||||
\(234\) | −4.68575 | −0.306317 | ||||||||
\(235\) | −3.51870 | −0.229535 | ||||||||
\(236\) | 22.1248 | 1.44020 | ||||||||
\(237\) | 6.58226 | 0.427564 | ||||||||
\(238\) | −4.33077 | −0.280722 | ||||||||
\(239\) | 12.3963 | 0.801851 | 0.400926 | − | 0.916111i | \(-0.368689\pi\) | ||||
0.400926 | + | 0.916111i | \(0.368689\pi\) | |||||||
\(240\) | 10.3489 | 0.668018 | ||||||||
\(241\) | 13.1898 | 0.849630 | 0.424815 | − | 0.905280i | \(-0.360339\pi\) | ||||
0.424815 | + | 0.905280i | \(0.360339\pi\) | |||||||
\(242\) | 32.9597 | 2.11873 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 58.5376 | 3.74749 | ||||||||
\(245\) | 1.31287 | 0.0838764 | ||||||||
\(246\) | −2.56695 | −0.163663 | ||||||||
\(247\) | −3.32703 | −0.211694 | ||||||||
\(248\) | 14.4719 | 0.918964 | ||||||||
\(249\) | 13.4974 | 0.855366 | ||||||||
\(250\) | −27.8920 | −1.76405 | ||||||||
\(251\) | −2.11974 | −0.133797 | −0.0668985 | − | 0.997760i | \(-0.521310\pi\) | ||||
−0.0668985 | + | 0.997760i | \(0.521310\pi\) | |||||||
\(252\) | −4.58924 | −0.289095 | ||||||||
\(253\) | −14.8398 | −0.932970 | ||||||||
\(254\) | −3.44127 | −0.215925 | ||||||||
\(255\) | 2.21498 | 0.138708 | ||||||||
\(256\) | −26.2147 | −1.63842 | ||||||||
\(257\) | 20.9577 | 1.30730 | 0.653652 | − | 0.756796i | \(-0.273236\pi\) | ||||
0.653652 | + | 0.756796i | \(0.273236\pi\) | |||||||
\(258\) | −19.2299 | −1.19720 | ||||||||
\(259\) | 3.96349 | 0.246279 | ||||||||
\(260\) | −10.9983 | −0.682085 | ||||||||
\(261\) | −2.73736 | −0.169438 | ||||||||
\(262\) | 24.5151 | 1.51455 | ||||||||
\(263\) | 11.3323 | 0.698777 | 0.349389 | − | 0.936978i | \(-0.386389\pi\) | ||||
0.349389 | + | 0.936978i | \(0.386389\pi\) | |||||||
\(264\) | −32.4521 | −1.99729 | ||||||||
\(265\) | −7.02789 | −0.431720 | ||||||||
\(266\) | −4.67857 | −0.286861 | ||||||||
\(267\) | −8.01653 | −0.490603 | ||||||||
\(268\) | 18.6323 | 1.13815 | ||||||||
\(269\) | 15.6834 | 0.956234 | 0.478117 | − | 0.878296i | \(-0.341320\pi\) | ||||
0.478117 | + | 0.878296i | \(0.341320\pi\) | |||||||
\(270\) | 3.37008 | 0.205097 | ||||||||
\(271\) | −17.6977 | −1.07506 | −0.537529 | − | 0.843245i | \(-0.680642\pi\) | ||||
−0.537529 | + | 0.843245i | \(0.680642\pi\) | |||||||
\(272\) | 13.2990 | 0.806370 | ||||||||
\(273\) | 1.82542 | 0.110479 | ||||||||
\(274\) | −42.4478 | −2.56436 | ||||||||
\(275\) | 15.9973 | 0.964671 | ||||||||
\(276\) | 13.9481 | 0.839578 | ||||||||
\(277\) | 7.95465 | 0.477949 | 0.238974 | − | 0.971026i | \(-0.423189\pi\) | ||||
0.238974 | + | 0.971026i | \(0.423189\pi\) | |||||||
\(278\) | 44.9066 | 2.69332 | ||||||||
\(279\) | 2.17738 | 0.130357 | ||||||||
\(280\) | −8.72594 | −0.521475 | ||||||||
\(281\) | −1.53517 | −0.0915803 | −0.0457902 | − | 0.998951i | \(-0.514581\pi\) | ||||
−0.0457902 | + | 0.998951i | \(0.514581\pi\) | |||||||
\(282\) | −6.87982 | −0.409688 | ||||||||
\(283\) | −23.8827 | −1.41968 | −0.709840 | − | 0.704363i | \(-0.751233\pi\) | ||||
−0.709840 | + | 0.704363i | \(0.751233\pi\) | |||||||
\(284\) | 51.6655 | 3.06578 | ||||||||
\(285\) | 2.39286 | 0.141741 | ||||||||
\(286\) | 22.8788 | 1.35285 | ||||||||
\(287\) | 1.00000 | 0.0590281 | ||||||||
\(288\) | 6.94142 | 0.409027 | ||||||||
\(289\) | −14.1536 | −0.832565 | ||||||||
\(290\) | −9.22513 | −0.541718 | ||||||||
\(291\) | −11.3241 | −0.663833 | ||||||||
\(292\) | −19.8749 | −1.16309 | ||||||||
\(293\) | 21.4580 | 1.25359 | 0.626794 | − | 0.779185i | \(-0.284367\pi\) | ||||
0.626794 | + | 0.779185i | \(0.284367\pi\) | |||||||
\(294\) | 2.56695 | 0.149708 | ||||||||
\(295\) | 6.32940 | 0.368512 | ||||||||
\(296\) | −26.3431 | −1.53116 | ||||||||
\(297\) | −4.88262 | −0.283319 | ||||||||
\(298\) | −0.669792 | −0.0388000 | ||||||||
\(299\) | −5.54800 | −0.320849 | ||||||||
\(300\) | −15.0360 | −0.868105 | ||||||||
\(301\) | 7.49135 | 0.431794 | ||||||||
\(302\) | −46.0243 | −2.64840 | ||||||||
\(303\) | 4.01093 | 0.230422 | ||||||||
\(304\) | 14.3670 | 0.824004 | ||||||||
\(305\) | 16.7462 | 0.958887 | ||||||||
\(306\) | 4.33077 | 0.247574 | ||||||||
\(307\) | −5.76942 | −0.329278 | −0.164639 | − | 0.986354i | \(-0.552646\pi\) | ||||
−0.164639 | + | 0.986354i | \(0.552646\pi\) | |||||||
\(308\) | 22.4075 | 1.27679 | ||||||||
\(309\) | 10.5595 | 0.600708 | ||||||||
\(310\) | 7.33796 | 0.416768 | ||||||||
\(311\) | −4.30612 | −0.244177 | −0.122089 | − | 0.992519i | \(-0.538959\pi\) | ||||
−0.122089 | + | 0.992519i | \(0.538959\pi\) | |||||||
\(312\) | −12.1325 | −0.686869 | ||||||||
\(313\) | −17.7494 | −1.00325 | −0.501627 | − | 0.865084i | \(-0.667265\pi\) | ||||
−0.501627 | + | 0.865084i | \(0.667265\pi\) | |||||||
\(314\) | 56.7482 | 3.20248 | ||||||||
\(315\) | −1.31287 | −0.0739720 | ||||||||
\(316\) | 30.2076 | 1.69931 | ||||||||
\(317\) | 25.2987 | 1.42092 | 0.710460 | − | 0.703738i | \(-0.248487\pi\) | ||||
0.710460 | + | 0.703738i | \(0.248487\pi\) | |||||||
\(318\) | −13.7410 | −0.770559 | ||||||||
\(319\) | 13.3655 | 0.748325 | ||||||||
\(320\) | 2.69537 | 0.150676 | ||||||||
\(321\) | 4.86193 | 0.271366 | ||||||||
\(322\) | −7.80176 | −0.434775 | ||||||||
\(323\) | 3.07498 | 0.171097 | ||||||||
\(324\) | 4.58924 | 0.254958 | ||||||||
\(325\) | 5.98073 | 0.331751 | ||||||||
\(326\) | −7.99638 | −0.442878 | ||||||||
\(327\) | −17.5419 | −0.970070 | ||||||||
\(328\) | −6.64645 | −0.366989 | ||||||||
\(329\) | 2.68015 | 0.147762 | ||||||||
\(330\) | −16.4548 | −0.905809 | ||||||||
\(331\) | 24.3413 | 1.33792 | 0.668958 | − | 0.743300i | \(-0.266740\pi\) | ||||
0.668958 | + | 0.743300i | \(0.266740\pi\) | |||||||
\(332\) | 61.9430 | 3.39956 | ||||||||
\(333\) | −3.96349 | −0.217198 | ||||||||
\(334\) | −50.3162 | −2.75318 | ||||||||
\(335\) | 5.33028 | 0.291224 | ||||||||
\(336\) | −7.88262 | −0.430032 | ||||||||
\(337\) | −20.8089 | −1.13353 | −0.566766 | − | 0.823879i | \(-0.691806\pi\) | ||||
−0.566766 | + | 0.823879i | \(0.691806\pi\) | |||||||
\(338\) | −24.8169 | −1.34986 | ||||||||
\(339\) | 0.890970 | 0.0483908 | ||||||||
\(340\) | 10.1651 | 0.551279 | ||||||||
\(341\) | −10.6313 | −0.575720 | ||||||||
\(342\) | 4.67857 | 0.252988 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −49.7908 | −2.68454 | ||||||||
\(345\) | 3.99023 | 0.214827 | ||||||||
\(346\) | −7.75142 | −0.416719 | ||||||||
\(347\) | 22.2830 | 1.19622 | 0.598108 | − | 0.801416i | \(-0.295919\pi\) | ||||
0.598108 | + | 0.801416i | \(0.295919\pi\) | |||||||
\(348\) | −12.5624 | −0.673416 | ||||||||
\(349\) | 20.8218 | 1.11457 | 0.557283 | − | 0.830323i | \(-0.311844\pi\) | ||||
0.557283 | + | 0.830323i | \(0.311844\pi\) | |||||||
\(350\) | 8.41027 | 0.449548 | ||||||||
\(351\) | −1.82542 | −0.0974335 | ||||||||
\(352\) | −33.8923 | −1.80647 | ||||||||
\(353\) | −6.17551 | −0.328689 | −0.164345 | − | 0.986403i | \(-0.552551\pi\) | ||||
−0.164345 | + | 0.986403i | \(0.552551\pi\) | |||||||
\(354\) | 12.3753 | 0.657742 | ||||||||
\(355\) | 14.7803 | 0.784456 | ||||||||
\(356\) | −36.7897 | −1.94985 | ||||||||
\(357\) | −1.68713 | −0.0892922 | ||||||||
\(358\) | 57.0356 | 3.01443 | ||||||||
\(359\) | −10.6861 | −0.563990 | −0.281995 | − | 0.959416i | \(-0.590996\pi\) | ||||
−0.281995 | + | 0.959416i | \(0.590996\pi\) | |||||||
\(360\) | 8.72594 | 0.459897 | ||||||||
\(361\) | −15.6781 | −0.825162 | ||||||||
\(362\) | −17.6696 | −0.928694 | ||||||||
\(363\) | 12.8400 | 0.673926 | ||||||||
\(364\) | 8.37727 | 0.439088 | ||||||||
\(365\) | −5.68575 | −0.297606 | ||||||||
\(366\) | 32.7425 | 1.71148 | ||||||||
\(367\) | 15.0205 | 0.784063 | 0.392031 | − | 0.919952i | \(-0.371772\pi\) | ||||
0.392031 | + | 0.919952i | \(0.371772\pi\) | |||||||
\(368\) | 23.9577 | 1.24888 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | −13.3573 | −0.694412 | ||||||||
\(371\) | 5.35306 | 0.277917 | ||||||||
\(372\) | 9.99253 | 0.518089 | ||||||||
\(373\) | −18.3738 | −0.951357 | −0.475679 | − | 0.879619i | \(-0.657797\pi\) | ||||
−0.475679 | + | 0.879619i | \(0.657797\pi\) | |||||||
\(374\) | −21.1455 | −1.09341 | ||||||||
\(375\) | −10.8658 | −0.561108 | ||||||||
\(376\) | −17.8135 | −0.918661 | ||||||||
\(377\) | 4.99683 | 0.257350 | ||||||||
\(378\) | −2.56695 | −0.132030 | ||||||||
\(379\) | 18.6617 | 0.958588 | 0.479294 | − | 0.877654i | \(-0.340893\pi\) | ||||
0.479294 | + | 0.877654i | \(0.340893\pi\) | |||||||
\(380\) | 10.9814 | 0.563335 | ||||||||
\(381\) | −1.34061 | −0.0686814 | ||||||||
\(382\) | 7.22252 | 0.369536 | ||||||||
\(383\) | −36.3994 | −1.85992 | −0.929962 | − | 0.367655i | \(-0.880161\pi\) | ||||
−0.929962 | + | 0.367655i | \(0.880161\pi\) | |||||||
\(384\) | −8.61280 | −0.439520 | ||||||||
\(385\) | 6.41027 | 0.326697 | ||||||||
\(386\) | 49.7244 | 2.53091 | ||||||||
\(387\) | −7.49135 | −0.380807 | ||||||||
\(388\) | −51.9691 | −2.63833 | ||||||||
\(389\) | 19.5262 | 0.990016 | 0.495008 | − | 0.868888i | \(-0.335165\pi\) | ||||
0.495008 | + | 0.868888i | \(0.335165\pi\) | |||||||
\(390\) | −6.15180 | −0.311509 | ||||||||
\(391\) | 5.12770 | 0.259319 | ||||||||
\(392\) | 6.64645 | 0.335696 | ||||||||
\(393\) | 9.55026 | 0.481747 | ||||||||
\(394\) | 29.0027 | 1.46113 | ||||||||
\(395\) | 8.64168 | 0.434810 | ||||||||
\(396\) | −22.4075 | −1.12602 | ||||||||
\(397\) | −17.0369 | −0.855057 | −0.427528 | − | 0.904002i | \(-0.640616\pi\) | ||||
−0.427528 | + | 0.904002i | \(0.640616\pi\) | |||||||
\(398\) | −39.7764 | −1.99381 | ||||||||
\(399\) | −1.82262 | −0.0912449 | ||||||||
\(400\) | −25.8263 | −1.29132 | ||||||||
\(401\) | −4.68642 | −0.234028 | −0.117014 | − | 0.993130i | \(-0.537332\pi\) | ||||
−0.117014 | + | 0.993130i | \(0.537332\pi\) | |||||||
\(402\) | 10.4218 | 0.519794 | ||||||||
\(403\) | −3.97463 | −0.197991 | ||||||||
\(404\) | 18.4071 | 0.915787 | ||||||||
\(405\) | 1.31287 | 0.0652372 | ||||||||
\(406\) | 7.02667 | 0.348728 | ||||||||
\(407\) | 19.3522 | 0.959255 | ||||||||
\(408\) | 11.2134 | 0.555146 | ||||||||
\(409\) | 26.3484 | 1.30285 | 0.651423 | − | 0.758714i | \(-0.274172\pi\) | ||||
0.651423 | + | 0.758714i | \(0.274172\pi\) | |||||||
\(410\) | −3.37008 | −0.166436 | ||||||||
\(411\) | −16.5363 | −0.815673 | ||||||||
\(412\) | 48.4600 | 2.38745 | ||||||||
\(413\) | −4.82103 | −0.237227 | ||||||||
\(414\) | 7.80176 | 0.383435 | ||||||||
\(415\) | 17.7204 | 0.869862 | ||||||||
\(416\) | −12.6710 | −0.621246 | ||||||||
\(417\) | 17.4941 | 0.856692 | ||||||||
\(418\) | −22.8437 | −1.11732 | ||||||||
\(419\) | −11.5944 | −0.566425 | −0.283213 | − | 0.959057i | \(-0.591400\pi\) | ||||
−0.283213 | + | 0.959057i | \(0.591400\pi\) | |||||||
\(420\) | −6.02509 | −0.293994 | ||||||||
\(421\) | −37.9490 | −1.84952 | −0.924761 | − | 0.380549i | \(-0.875735\pi\) | ||||
−0.924761 | + | 0.380549i | \(0.875735\pi\) | |||||||
\(422\) | −57.8506 | −2.81612 | ||||||||
\(423\) | −2.68015 | −0.130314 | ||||||||
\(424\) | −35.5788 | −1.72786 | ||||||||
\(425\) | −5.52764 | −0.268130 | ||||||||
\(426\) | 28.8987 | 1.40014 | ||||||||
\(427\) | −12.7554 | −0.617278 | ||||||||
\(428\) | 22.3125 | 1.07852 | ||||||||
\(429\) | 8.91282 | 0.430315 | ||||||||
\(430\) | −25.2464 | −1.21749 | ||||||||
\(431\) | 39.1044 | 1.88359 | 0.941797 | − | 0.336183i | \(-0.109136\pi\) | ||||
0.941797 | + | 0.336183i | \(0.109136\pi\) | |||||||
\(432\) | 7.88262 | 0.379253 | ||||||||
\(433\) | −24.7981 | −1.19172 | −0.595861 | − | 0.803088i | \(-0.703189\pi\) | ||||
−0.595861 | + | 0.803088i | \(0.703189\pi\) | |||||||
\(434\) | −5.58924 | −0.268292 | ||||||||
\(435\) | −3.59381 | −0.172310 | ||||||||
\(436\) | −80.5040 | −3.85544 | ||||||||
\(437\) | 5.53949 | 0.264990 | ||||||||
\(438\) | −11.1169 | −0.531185 | ||||||||
\(439\) | 8.41774 | 0.401757 | 0.200878 | − | 0.979616i | \(-0.435620\pi\) | ||||
0.200878 | + | 0.979616i | \(0.435620\pi\) | |||||||
\(440\) | −42.6055 | −2.03114 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −7.90546 | −0.376024 | ||||||||
\(443\) | −30.7906 | −1.46291 | −0.731453 | − | 0.681892i | \(-0.761158\pi\) | ||||
−0.731453 | + | 0.681892i | \(0.761158\pi\) | |||||||
\(444\) | −18.1894 | −0.863231 | ||||||||
\(445\) | −10.5247 | −0.498918 | ||||||||
\(446\) | 11.8530 | 0.561254 | ||||||||
\(447\) | −0.260929 | −0.0123415 | ||||||||
\(448\) | −2.05304 | −0.0969968 | ||||||||
\(449\) | −2.60695 | −0.123030 | −0.0615148 | − | 0.998106i | \(-0.519593\pi\) | ||||
−0.0615148 | + | 0.998106i | \(0.519593\pi\) | |||||||
\(450\) | −8.41027 | −0.396464 | ||||||||
\(451\) | 4.88262 | 0.229914 | ||||||||
\(452\) | 4.08887 | 0.192324 | ||||||||
\(453\) | −17.9296 | −0.842404 | ||||||||
\(454\) | 46.0485 | 2.16116 | ||||||||
\(455\) | 2.39654 | 0.112352 | ||||||||
\(456\) | 12.1139 | 0.567286 | ||||||||
\(457\) | −26.4155 | −1.23566 | −0.617832 | − | 0.786310i | \(-0.711989\pi\) | ||||
−0.617832 | + | 0.786310i | \(0.711989\pi\) | |||||||
\(458\) | −46.5780 | −2.17645 | ||||||||
\(459\) | 1.68713 | 0.0787483 | ||||||||
\(460\) | 18.3121 | 0.853806 | ||||||||
\(461\) | −13.7760 | −0.641610 | −0.320805 | − | 0.947145i | \(-0.603953\pi\) | ||||
−0.320805 | + | 0.947145i | \(0.603953\pi\) | |||||||
\(462\) | 12.5335 | 0.583109 | ||||||||
\(463\) | −24.7308 | −1.14934 | −0.574668 | − | 0.818387i | \(-0.694869\pi\) | ||||
−0.574668 | + | 0.818387i | \(0.694869\pi\) | |||||||
\(464\) | −21.5776 | −1.00171 | ||||||||
\(465\) | 2.85863 | 0.132566 | ||||||||
\(466\) | 65.6614 | 3.04170 | ||||||||
\(467\) | 9.06714 | 0.419577 | 0.209789 | − | 0.977747i | \(-0.432722\pi\) | ||||
0.209789 | + | 0.977747i | \(0.432722\pi\) | |||||||
\(468\) | −8.37727 | −0.387239 | ||||||||
\(469\) | −4.06001 | −0.187474 | ||||||||
\(470\) | −9.03234 | −0.416631 | ||||||||
\(471\) | 22.1072 | 1.01865 | ||||||||
\(472\) | 32.0427 | 1.47488 | ||||||||
\(473\) | 36.5774 | 1.68183 | ||||||||
\(474\) | 16.8964 | 0.776075 | ||||||||
\(475\) | −5.97155 | −0.273994 | ||||||||
\(476\) | −7.74263 | −0.354883 | ||||||||
\(477\) | −5.35306 | −0.245100 | ||||||||
\(478\) | 31.8207 | 1.45545 | ||||||||
\(479\) | 5.89718 | 0.269449 | 0.134725 | − | 0.990883i | \(-0.456985\pi\) | ||||
0.134725 | + | 0.990883i | \(0.456985\pi\) | |||||||
\(480\) | 9.11320 | 0.415959 | ||||||||
\(481\) | 7.23502 | 0.329889 | ||||||||
\(482\) | 33.8576 | 1.54217 | ||||||||
\(483\) | −3.03931 | −0.138293 | ||||||||
\(484\) | 58.9259 | 2.67845 | ||||||||
\(485\) | −14.8672 | −0.675083 | ||||||||
\(486\) | 2.56695 | 0.116439 | ||||||||
\(487\) | 24.7646 | 1.12219 | 0.561095 | − | 0.827751i | \(-0.310380\pi\) | ||||
0.561095 | + | 0.827751i | \(0.310380\pi\) | |||||||
\(488\) | 84.7782 | 3.83773 | ||||||||
\(489\) | −3.11513 | −0.140871 | ||||||||
\(490\) | 3.37008 | 0.152245 | ||||||||
\(491\) | 3.02036 | 0.136307 | 0.0681535 | − | 0.997675i | \(-0.478289\pi\) | ||||
0.0681535 | + | 0.997675i | \(0.478289\pi\) | |||||||
\(492\) | −4.58924 | −0.206899 | ||||||||
\(493\) | −4.61828 | −0.207997 | ||||||||
\(494\) | −8.54033 | −0.384248 | ||||||||
\(495\) | −6.41027 | −0.288120 | ||||||||
\(496\) | 17.1635 | 0.770664 | ||||||||
\(497\) | −11.2580 | −0.504989 | ||||||||
\(498\) | 34.6473 | 1.55258 | ||||||||
\(499\) | 31.7421 | 1.42097 | 0.710486 | − | 0.703711i | \(-0.248475\pi\) | ||||
0.710486 | + | 0.703711i | \(0.248475\pi\) | |||||||
\(500\) | −49.8658 | −2.23007 | ||||||||
\(501\) | −19.6015 | −0.875732 | ||||||||
\(502\) | −5.44127 | −0.242856 | ||||||||
\(503\) | −21.7388 | −0.969285 | −0.484642 | − | 0.874712i | \(-0.661050\pi\) | ||||
−0.484642 | + | 0.874712i | \(0.661050\pi\) | |||||||
\(504\) | −6.64645 | −0.296056 | ||||||||
\(505\) | 5.26584 | 0.234327 | ||||||||
\(506\) | −38.0930 | −1.69344 | ||||||||
\(507\) | −9.66786 | −0.429365 | ||||||||
\(508\) | −6.15236 | −0.272967 | ||||||||
\(509\) | −28.9296 | −1.28228 | −0.641140 | − | 0.767424i | \(-0.721538\pi\) | ||||
−0.641140 | + | 0.767424i | \(0.721538\pi\) | |||||||
\(510\) | 5.68575 | 0.251769 | ||||||||
\(511\) | 4.33077 | 0.191582 | ||||||||
\(512\) | −50.0663 | −2.21264 | ||||||||
\(513\) | 1.82262 | 0.0804705 | ||||||||
\(514\) | 53.7973 | 2.37290 | ||||||||
\(515\) | 13.8633 | 0.610888 | ||||||||
\(516\) | −34.3796 | −1.51348 | ||||||||
\(517\) | 13.0862 | 0.575530 | ||||||||
\(518\) | 10.1741 | 0.447024 | ||||||||
\(519\) | −3.01970 | −0.132550 | ||||||||
\(520\) | −15.9285 | −0.698510 | ||||||||
\(521\) | 34.9796 | 1.53248 | 0.766241 | − | 0.642553i | \(-0.222125\pi\) | ||||
0.766241 | + | 0.642553i | \(0.222125\pi\) | |||||||
\(522\) | −7.02667 | −0.307549 | ||||||||
\(523\) | −39.6515 | −1.73384 | −0.866920 | − | 0.498446i | \(-0.833904\pi\) | ||||
−0.866920 | + | 0.498446i | \(0.833904\pi\) | |||||||
\(524\) | 43.8284 | 1.91465 | ||||||||
\(525\) | 3.27636 | 0.142992 | ||||||||
\(526\) | 29.0894 | 1.26836 | ||||||||
\(527\) | 3.67352 | 0.160021 | ||||||||
\(528\) | −38.4879 | −1.67497 | ||||||||
\(529\) | −13.7626 | −0.598374 | ||||||||
\(530\) | −18.0402 | −0.783618 | ||||||||
\(531\) | 4.82103 | 0.209215 | ||||||||
\(532\) | −8.36442 | −0.362644 | ||||||||
\(533\) | 1.82542 | 0.0790676 | ||||||||
\(534\) | −20.5780 | −0.890498 | ||||||||
\(535\) | 6.38309 | 0.275965 | ||||||||
\(536\) | 26.9846 | 1.16556 | ||||||||
\(537\) | 22.2192 | 0.958830 | ||||||||
\(538\) | 40.2585 | 1.73567 | ||||||||
\(539\) | −4.88262 | −0.210310 | ||||||||
\(540\) | 6.02509 | 0.259278 | ||||||||
\(541\) | 8.54367 | 0.367321 | 0.183661 | − | 0.982990i | \(-0.441205\pi\) | ||||
0.183661 | + | 0.982990i | \(0.441205\pi\) | |||||||
\(542\) | −45.4291 | −1.95135 | ||||||||
\(543\) | −6.88350 | −0.295399 | ||||||||
\(544\) | 11.7111 | 0.502107 | ||||||||
\(545\) | −23.0303 | −0.986510 | ||||||||
\(546\) | 4.68575 | 0.200532 | ||||||||
\(547\) | 10.7543 | 0.459819 | 0.229910 | − | 0.973212i | \(-0.426157\pi\) | ||||
0.229910 | + | 0.973212i | \(0.426157\pi\) | |||||||
\(548\) | −75.8888 | −3.24181 | ||||||||
\(549\) | 12.7554 | 0.544388 | ||||||||
\(550\) | 41.0642 | 1.75098 | ||||||||
\(551\) | −4.98916 | −0.212545 | ||||||||
\(552\) | 20.2006 | 0.859795 | ||||||||
\(553\) | −6.58226 | −0.279906 | ||||||||
\(554\) | 20.4192 | 0.867528 | ||||||||
\(555\) | −5.20356 | −0.220879 | ||||||||
\(556\) | 80.2848 | 3.40483 | ||||||||
\(557\) | −26.1476 | −1.10791 | −0.553955 | − | 0.832547i | \(-0.686882\pi\) | ||||
−0.553955 | + | 0.832547i | \(0.686882\pi\) | |||||||
\(558\) | 5.58924 | 0.236611 | ||||||||
\(559\) | 13.6748 | 0.578384 | ||||||||
\(560\) | −10.3489 | −0.437320 | ||||||||
\(561\) | −8.23761 | −0.347792 | ||||||||
\(562\) | −3.94070 | −0.166228 | ||||||||
\(563\) | 12.8165 | 0.540152 | 0.270076 | − | 0.962839i | \(-0.412951\pi\) | ||||
0.270076 | + | 0.962839i | \(0.412951\pi\) | |||||||
\(564\) | −12.2999 | −0.517918 | ||||||||
\(565\) | 1.16973 | 0.0492109 | ||||||||
\(566\) | −61.3058 | −2.57687 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 74.8255 | 3.13961 | ||||||||
\(569\) | 22.9583 | 0.962462 | 0.481231 | − | 0.876594i | \(-0.340190\pi\) | ||||
0.481231 | + | 0.876594i | \(0.340190\pi\) | |||||||
\(570\) | 6.14236 | 0.257275 | ||||||||
\(571\) | −39.7733 | −1.66446 | −0.832230 | − | 0.554430i | \(-0.812936\pi\) | ||||
−0.832230 | + | 0.554430i | \(0.812936\pi\) | |||||||
\(572\) | 40.9031 | 1.71024 | ||||||||
\(573\) | 2.81366 | 0.117542 | ||||||||
\(574\) | 2.56695 | 0.107142 | ||||||||
\(575\) | −9.95788 | −0.415272 | ||||||||
\(576\) | 2.05304 | 0.0855431 | ||||||||
\(577\) | 19.2880 | 0.802970 | 0.401485 | − | 0.915866i | \(-0.368494\pi\) | ||||
0.401485 | + | 0.915866i | \(0.368494\pi\) | |||||||
\(578\) | −36.3316 | −1.51120 | ||||||||
\(579\) | 19.3710 | 0.805032 | ||||||||
\(580\) | −16.4928 | −0.684828 | ||||||||
\(581\) | −13.4974 | −0.559968 | ||||||||
\(582\) | −29.0685 | −1.20493 | ||||||||
\(583\) | 26.1370 | 1.08248 | ||||||||
\(584\) | −28.7842 | −1.19110 | ||||||||
\(585\) | −2.39654 | −0.0990847 | ||||||||
\(586\) | 55.0816 | 2.27540 | ||||||||
\(587\) | 21.7390 | 0.897264 | 0.448632 | − | 0.893717i | \(-0.351911\pi\) | ||||
0.448632 | + | 0.893717i | \(0.351911\pi\) | |||||||
\(588\) | 4.58924 | 0.189257 | ||||||||
\(589\) | 3.96854 | 0.163521 | ||||||||
\(590\) | 16.2473 | 0.668889 | ||||||||
\(591\) | 11.2985 | 0.464758 | ||||||||
\(592\) | −31.2427 | −1.28407 | ||||||||
\(593\) | 21.3404 | 0.876347 | 0.438173 | − | 0.898890i | \(-0.355626\pi\) | ||||
0.438173 | + | 0.898890i | \(0.355626\pi\) | |||||||
\(594\) | −12.5335 | −0.514254 | ||||||||
\(595\) | −2.21498 | −0.0908055 | ||||||||
\(596\) | −1.19746 | −0.0490501 | ||||||||
\(597\) | −15.4956 | −0.634192 | ||||||||
\(598\) | −14.2415 | −0.582376 | ||||||||
\(599\) | −13.7030 | −0.559891 | −0.279945 | − | 0.960016i | \(-0.590316\pi\) | ||||
−0.279945 | + | 0.960016i | \(0.590316\pi\) | |||||||
\(600\) | −21.7762 | −0.889009 | ||||||||
\(601\) | −15.6838 | −0.639757 | −0.319878 | − | 0.947459i | \(-0.603642\pi\) | ||||
−0.319878 | + | 0.947459i | \(0.603642\pi\) | |||||||
\(602\) | 19.2299 | 0.783753 | ||||||||
\(603\) | 4.06001 | 0.165336 | ||||||||
\(604\) | −82.2830 | −3.34805 | ||||||||
\(605\) | 16.8573 | 0.685347 | ||||||||
\(606\) | 10.2959 | 0.418240 | ||||||||
\(607\) | 30.8537 | 1.25231 | 0.626157 | − | 0.779697i | \(-0.284627\pi\) | ||||
0.626157 | + | 0.779697i | \(0.284627\pi\) | |||||||
\(608\) | 12.6515 | 0.513088 | ||||||||
\(609\) | 2.73736 | 0.110924 | ||||||||
\(610\) | 42.9868 | 1.74048 | ||||||||
\(611\) | 4.89240 | 0.197925 | ||||||||
\(612\) | 7.74263 | 0.312977 | ||||||||
\(613\) | 13.2957 | 0.537008 | 0.268504 | − | 0.963279i | \(-0.413471\pi\) | ||||
0.268504 | + | 0.963279i | \(0.413471\pi\) | |||||||
\(614\) | −14.8098 | −0.597676 | ||||||||
\(615\) | −1.31287 | −0.0529402 | ||||||||
\(616\) | 32.4521 | 1.30753 | ||||||||
\(617\) | −10.0553 | −0.404813 | −0.202406 | − | 0.979302i | \(-0.564876\pi\) | ||||
−0.202406 | + | 0.979302i | \(0.564876\pi\) | |||||||
\(618\) | 27.1057 | 1.09035 | ||||||||
\(619\) | 36.1745 | 1.45398 | 0.726988 | − | 0.686650i | \(-0.240919\pi\) | ||||
0.726988 | + | 0.686650i | \(0.240919\pi\) | |||||||
\(620\) | 13.1189 | 0.526869 | ||||||||
\(621\) | 3.03931 | 0.121963 | ||||||||
\(622\) | −11.0536 | −0.443208 | ||||||||
\(623\) | 8.01653 | 0.321175 | ||||||||
\(624\) | −14.3891 | −0.576024 | ||||||||
\(625\) | 2.11638 | 0.0846553 | ||||||||
\(626\) | −45.5618 | −1.82102 | ||||||||
\(627\) | −8.89915 | −0.355398 | ||||||||
\(628\) | 101.455 | 4.04851 | ||||||||
\(629\) | −6.68691 | −0.266625 | ||||||||
\(630\) | −3.37008 | −0.134267 | ||||||||
\(631\) | −40.8063 | −1.62447 | −0.812236 | − | 0.583329i | \(-0.801750\pi\) | ||||
−0.812236 | + | 0.583329i | \(0.801750\pi\) | |||||||
\(632\) | 43.7487 | 1.74023 | ||||||||
\(633\) | −22.5367 | −0.895753 | ||||||||
\(634\) | 64.9406 | 2.57912 | ||||||||
\(635\) | −1.76005 | −0.0698453 | ||||||||
\(636\) | −24.5665 | −0.974123 | ||||||||
\(637\) | −1.82542 | −0.0723256 | ||||||||
\(638\) | 34.3086 | 1.35829 | ||||||||
\(639\) | 11.2580 | 0.445358 | ||||||||
\(640\) | −11.3075 | −0.446969 | ||||||||
\(641\) | −34.5505 | −1.36466 | −0.682331 | − | 0.731044i | \(-0.739034\pi\) | ||||
−0.682331 | + | 0.731044i | \(0.739034\pi\) | |||||||
\(642\) | 12.4803 | 0.492559 | ||||||||
\(643\) | 19.8893 | 0.784358 | 0.392179 | − | 0.919889i | \(-0.371721\pi\) | ||||
0.392179 | + | 0.919889i | \(0.371721\pi\) | |||||||
\(644\) | −13.9481 | −0.549633 | ||||||||
\(645\) | −9.83519 | −0.387260 | ||||||||
\(646\) | 7.89334 | 0.310559 | ||||||||
\(647\) | −37.5903 | −1.47783 | −0.738914 | − | 0.673799i | \(-0.764661\pi\) | ||||
−0.738914 | + | 0.673799i | \(0.764661\pi\) | |||||||
\(648\) | 6.64645 | 0.261097 | ||||||||
\(649\) | −23.5393 | −0.923997 | ||||||||
\(650\) | 15.3522 | 0.602164 | ||||||||
\(651\) | −2.17738 | −0.0853384 | ||||||||
\(652\) | −14.2961 | −0.559877 | ||||||||
\(653\) | −27.9003 | −1.09182 | −0.545911 | − | 0.837843i | \(-0.683816\pi\) | ||||
−0.545911 | + | 0.837843i | \(0.683816\pi\) | |||||||
\(654\) | −45.0292 | −1.76078 | ||||||||
\(655\) | 12.5383 | 0.489911 | ||||||||
\(656\) | −7.88262 | −0.307765 | ||||||||
\(657\) | −4.33077 | −0.168960 | ||||||||
\(658\) | 6.87982 | 0.268203 | ||||||||
\(659\) | 41.4881 | 1.61615 | 0.808073 | − | 0.589082i | \(-0.200511\pi\) | ||||
0.808073 | + | 0.589082i | \(0.200511\pi\) | |||||||
\(660\) | −29.4182 | −1.14510 | ||||||||
\(661\) | −13.1749 | −0.512444 | −0.256222 | − | 0.966618i | \(-0.582478\pi\) | ||||
−0.256222 | + | 0.966618i | \(0.582478\pi\) | |||||||
\(662\) | 62.4828 | 2.42846 | ||||||||
\(663\) | −3.07971 | −0.119606 | ||||||||
\(664\) | 89.7100 | 3.48142 | ||||||||
\(665\) | −2.39286 | −0.0927913 | ||||||||
\(666\) | −10.1741 | −0.394238 | ||||||||
\(667\) | −8.31969 | −0.322140 | ||||||||
\(668\) | −89.9561 | −3.48050 | ||||||||
\(669\) | 4.61752 | 0.178524 | ||||||||
\(670\) | 13.6826 | 0.528603 | ||||||||
\(671\) | −62.2799 | −2.40429 | ||||||||
\(672\) | −6.94142 | −0.267771 | ||||||||
\(673\) | 29.2106 | 1.12599 | 0.562993 | − | 0.826462i | \(-0.309650\pi\) | ||||
0.562993 | + | 0.826462i | \(0.309650\pi\) | |||||||
\(674\) | −53.4154 | −2.05748 | ||||||||
\(675\) | −3.27636 | −0.126107 | ||||||||
\(676\) | −44.3681 | −1.70646 | ||||||||
\(677\) | −33.3295 | −1.28096 | −0.640479 | − | 0.767976i | \(-0.721264\pi\) | ||||
−0.640479 | + | 0.767976i | \(0.721264\pi\) | |||||||
\(678\) | 2.28708 | 0.0878346 | ||||||||
\(679\) | 11.3241 | 0.434580 | ||||||||
\(680\) | 14.7218 | 0.564554 | ||||||||
\(681\) | 17.9390 | 0.687424 | ||||||||
\(682\) | −27.2901 | −1.04499 | ||||||||
\(683\) | 30.6771 | 1.17383 | 0.586913 | − | 0.809650i | \(-0.300343\pi\) | ||||
0.586913 | + | 0.809650i | \(0.300343\pi\) | |||||||
\(684\) | 8.36442 | 0.319822 | ||||||||
\(685\) | −21.7100 | −0.829497 | ||||||||
\(686\) | −2.56695 | −0.0980066 | ||||||||
\(687\) | −18.1453 | −0.692285 | ||||||||
\(688\) | −59.0515 | −2.25132 | ||||||||
\(689\) | 9.77156 | 0.372267 | ||||||||
\(690\) | 10.2427 | 0.389934 | ||||||||
\(691\) | 1.87148 | 0.0711946 | 0.0355973 | − | 0.999366i | \(-0.488667\pi\) | ||||
0.0355973 | + | 0.999366i | \(0.488667\pi\) | |||||||
\(692\) | −13.8581 | −0.526807 | ||||||||
\(693\) | 4.88262 | 0.185476 | ||||||||
\(694\) | 57.1994 | 2.17126 | ||||||||
\(695\) | 22.9676 | 0.871211 | ||||||||
\(696\) | −18.1937 | −0.689631 | ||||||||
\(697\) | −1.68713 | −0.0639045 | ||||||||
\(698\) | 53.4486 | 2.02306 | ||||||||
\(699\) | 25.5795 | 0.967506 | ||||||||
\(700\) | 15.0360 | 0.568308 | ||||||||
\(701\) | 16.8636 | 0.636930 | 0.318465 | − | 0.947935i | \(-0.396833\pi\) | ||||
0.318465 | + | 0.947935i | \(0.396833\pi\) | |||||||
\(702\) | −4.68575 | −0.176852 | ||||||||
\(703\) | −7.22392 | −0.272455 | ||||||||
\(704\) | −10.0242 | −0.377801 | ||||||||
\(705\) | −3.51870 | −0.132522 | ||||||||
\(706\) | −15.8522 | −0.596607 | ||||||||
\(707\) | −4.01093 | −0.150846 | ||||||||
\(708\) | 22.1248 | 0.831503 | ||||||||
\(709\) | 24.6942 | 0.927410 | 0.463705 | − | 0.885990i | \(-0.346520\pi\) | ||||
0.463705 | + | 0.885990i | \(0.346520\pi\) | |||||||
\(710\) | 37.9403 | 1.42387 | ||||||||
\(711\) | 6.58226 | 0.246854 | ||||||||
\(712\) | −53.2814 | −1.99680 | ||||||||
\(713\) | 6.61774 | 0.247836 | ||||||||
\(714\) | −4.33077 | −0.162075 | ||||||||
\(715\) | 11.7014 | 0.437608 | ||||||||
\(716\) | 101.969 | 3.81077 | ||||||||
\(717\) | 12.3963 | 0.462949 | ||||||||
\(718\) | −27.4307 | −1.02370 | ||||||||
\(719\) | 15.1916 | 0.566550 | 0.283275 | − | 0.959039i | \(-0.408579\pi\) | ||||
0.283275 | + | 0.959039i | \(0.408579\pi\) | |||||||
\(720\) | 10.3489 | 0.385680 | ||||||||
\(721\) | −10.5595 | −0.393256 | ||||||||
\(722\) | −40.2448 | −1.49776 | ||||||||
\(723\) | 13.1898 | 0.490534 | ||||||||
\(724\) | −31.5900 | −1.17403 | ||||||||
\(725\) | 8.96859 | 0.333085 | ||||||||
\(726\) | 32.9597 | 1.22325 | ||||||||
\(727\) | −18.9276 | −0.701986 | −0.350993 | − | 0.936378i | \(-0.614156\pi\) | ||||
−0.350993 | + | 0.936378i | \(0.614156\pi\) | |||||||
\(728\) | 12.1325 | 0.449661 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −14.5951 | −0.540187 | ||||||||
\(731\) | −12.6389 | −0.467465 | ||||||||
\(732\) | 58.5376 | 2.16361 | ||||||||
\(733\) | −18.0703 | −0.667441 | −0.333720 | − | 0.942672i | \(-0.608304\pi\) | ||||
−0.333720 | + | 0.942672i | \(0.608304\pi\) | |||||||
\(734\) | 38.5568 | 1.42316 | ||||||||
\(735\) | 1.31287 | 0.0484261 | ||||||||
\(736\) | 21.0971 | 0.777650 | ||||||||
\(737\) | −19.8235 | −0.730208 | ||||||||
\(738\) | −2.56695 | −0.0944908 | ||||||||
\(739\) | 11.7429 | 0.431970 | 0.215985 | − | 0.976397i | \(-0.430704\pi\) | ||||
0.215985 | + | 0.976397i | \(0.430704\pi\) | |||||||
\(740\) | −23.8804 | −0.877860 | ||||||||
\(741\) | −3.32703 | −0.122222 | ||||||||
\(742\) | 13.7410 | 0.504449 | ||||||||
\(743\) | −1.00208 | −0.0367629 | −0.0183815 | − | 0.999831i | \(-0.505851\pi\) | ||||
−0.0183815 | + | 0.999831i | \(0.505851\pi\) | |||||||
\(744\) | 14.4719 | 0.530564 | ||||||||
\(745\) | −0.342566 | −0.0125507 | ||||||||
\(746\) | −47.1645 | −1.72682 | ||||||||
\(747\) | 13.4974 | 0.493846 | ||||||||
\(748\) | −37.8043 | −1.38226 | ||||||||
\(749\) | −4.86193 | −0.177651 | ||||||||
\(750\) | −27.8920 | −1.01847 | ||||||||
\(751\) | −3.28392 | −0.119832 | −0.0599160 | − | 0.998203i | \(-0.519083\pi\) | ||||
−0.0599160 | + | 0.998203i | \(0.519083\pi\) | |||||||
\(752\) | −21.1266 | −0.770410 | ||||||||
\(753\) | −2.11974 | −0.0772477 | ||||||||
\(754\) | 12.8266 | 0.467117 | ||||||||
\(755\) | −23.5392 | −0.856681 | ||||||||
\(756\) | −4.58924 | −0.166909 | ||||||||
\(757\) | 31.3116 | 1.13804 | 0.569020 | − | 0.822324i | \(-0.307323\pi\) | ||||
0.569020 | + | 0.822324i | \(0.307323\pi\) | |||||||
\(758\) | 47.9037 | 1.73994 | ||||||||
\(759\) | −14.8398 | −0.538651 | ||||||||
\(760\) | 15.9040 | 0.576900 | ||||||||
\(761\) | 28.8300 | 1.04509 | 0.522544 | − | 0.852613i | \(-0.324983\pi\) | ||||
0.522544 | + | 0.852613i | \(0.324983\pi\) | |||||||
\(762\) | −3.44127 | −0.124664 | ||||||||
\(763\) | 17.5419 | 0.635060 | ||||||||
\(764\) | 12.9125 | 0.467159 | ||||||||
\(765\) | 2.21498 | 0.0800829 | ||||||||
\(766\) | −93.4356 | −3.37596 | ||||||||
\(767\) | −8.80038 | −0.317763 | ||||||||
\(768\) | −26.2147 | −0.945942 | ||||||||
\(769\) | −20.4272 | −0.736624 | −0.368312 | − | 0.929702i | \(-0.620064\pi\) | ||||
−0.368312 | + | 0.929702i | \(0.620064\pi\) | |||||||
\(770\) | 16.4548 | 0.592991 | ||||||||
\(771\) | 20.9577 | 0.754772 | ||||||||
\(772\) | 88.8982 | 3.19952 | ||||||||
\(773\) | 4.79951 | 0.172626 | 0.0863132 | − | 0.996268i | \(-0.472491\pi\) | ||||
0.0863132 | + | 0.996268i | \(0.472491\pi\) | |||||||
\(774\) | −19.2299 | −0.691205 | ||||||||
\(775\) | −7.13390 | −0.256257 | ||||||||
\(776\) | −75.2652 | −2.70186 | ||||||||
\(777\) | 3.96349 | 0.142189 | ||||||||
\(778\) | 50.1227 | 1.79699 | ||||||||
\(779\) | −1.82262 | −0.0653020 | ||||||||
\(780\) | −10.9983 | −0.393802 | ||||||||
\(781\) | −54.9684 | −1.96693 | ||||||||
\(782\) | 13.1626 | 0.470692 | ||||||||
\(783\) | −2.73736 | −0.0978253 | ||||||||
\(784\) | 7.88262 | 0.281522 | ||||||||
\(785\) | 29.0240 | 1.03591 | ||||||||
\(786\) | 24.5151 | 0.874423 | ||||||||
\(787\) | −16.2114 | −0.577875 | −0.288938 | − | 0.957348i | \(-0.593302\pi\) | ||||
−0.288938 | + | 0.957348i | \(0.593302\pi\) | |||||||
\(788\) | 51.8515 | 1.84713 | ||||||||
\(789\) | 11.3323 | 0.403439 | ||||||||
\(790\) | 22.1828 | 0.789227 | ||||||||
\(791\) | −0.890970 | −0.0316792 | ||||||||
\(792\) | −32.4521 | −1.15313 | ||||||||
\(793\) | −23.2839 | −0.826837 | ||||||||
\(794\) | −43.7329 | −1.55202 | ||||||||
\(795\) | −7.02789 | −0.249253 | ||||||||
\(796\) | −71.1129 | −2.52053 | ||||||||
\(797\) | −36.6223 | −1.29723 | −0.648613 | − | 0.761118i | \(-0.724651\pi\) | ||||
−0.648613 | + | 0.761118i | \(0.724651\pi\) | |||||||
\(798\) | −4.67857 | −0.165619 | ||||||||
\(799\) | −4.52176 | −0.159968 | ||||||||
\(800\) | −22.7426 | −0.804073 | ||||||||
\(801\) | −8.01653 | −0.283250 | ||||||||
\(802\) | −12.0298 | −0.424787 | ||||||||
\(803\) | 21.1455 | 0.746210 | ||||||||
\(804\) | 18.6323 | 0.657112 | ||||||||
\(805\) | −3.99023 | −0.140637 | ||||||||
\(806\) | −10.2027 | −0.359374 | ||||||||
\(807\) | 15.6834 | 0.552082 | ||||||||
\(808\) | 26.6584 | 0.937839 | ||||||||
\(809\) | 7.01611 | 0.246673 | 0.123337 | − | 0.992365i | \(-0.460640\pi\) | ||||
0.123337 | + | 0.992365i | \(0.460640\pi\) | |||||||
\(810\) | 3.37008 | 0.118413 | ||||||||
\(811\) | −34.8787 | −1.22476 | −0.612379 | − | 0.790564i | \(-0.709787\pi\) | ||||
−0.612379 | + | 0.790564i | \(0.709787\pi\) | |||||||
\(812\) | 12.5624 | 0.440854 | ||||||||
\(813\) | −17.6977 | −0.620685 | ||||||||
\(814\) | 49.6762 | 1.74115 | ||||||||
\(815\) | −4.08977 | −0.143258 | ||||||||
\(816\) | 13.2990 | 0.465558 | ||||||||
\(817\) | −13.6539 | −0.477688 | ||||||||
\(818\) | 67.6352 | 2.36481 | ||||||||
\(819\) | 1.82542 | 0.0637852 | ||||||||
\(820\) | −6.02509 | −0.210405 | ||||||||
\(821\) | 6.28647 | 0.219399 | 0.109700 | − | 0.993965i | \(-0.465011\pi\) | ||||
0.109700 | + | 0.993965i | \(0.465011\pi\) | |||||||
\(822\) | −42.4478 | −1.48054 | ||||||||
\(823\) | 16.6048 | 0.578806 | 0.289403 | − | 0.957207i | \(-0.406543\pi\) | ||||
0.289403 | + | 0.957207i | \(0.406543\pi\) | |||||||
\(824\) | 70.1830 | 2.44494 | ||||||||
\(825\) | 15.9973 | 0.556953 | ||||||||
\(826\) | −12.3753 | −0.430593 | ||||||||
\(827\) | −54.3533 | −1.89005 | −0.945025 | − | 0.326997i | \(-0.893963\pi\) | ||||
−0.945025 | + | 0.326997i | \(0.893963\pi\) | |||||||
\(828\) | 13.9481 | 0.484730 | ||||||||
\(829\) | −33.3938 | −1.15981 | −0.579907 | − | 0.814683i | \(-0.696911\pi\) | ||||
−0.579907 | + | 0.814683i | \(0.696911\pi\) | |||||||
\(830\) | 45.4875 | 1.57889 | ||||||||
\(831\) | 7.95465 | 0.275944 | ||||||||
\(832\) | −3.74764 | −0.129926 | ||||||||
\(833\) | 1.68713 | 0.0584555 | ||||||||
\(834\) | 44.9066 | 1.55499 | ||||||||
\(835\) | −25.7343 | −0.890573 | ||||||||
\(836\) | −40.8403 | −1.41249 | ||||||||
\(837\) | 2.17738 | 0.0752614 | ||||||||
\(838\) | −29.7624 | −1.02812 | ||||||||
\(839\) | 0.866263 | 0.0299067 | 0.0149534 | − | 0.999888i | \(-0.495240\pi\) | ||||
0.0149534 | + | 0.999888i | \(0.495240\pi\) | |||||||
\(840\) | −8.72594 | −0.301074 | ||||||||
\(841\) | −21.5068 | −0.741616 | ||||||||
\(842\) | −97.4132 | −3.35708 | ||||||||
\(843\) | −1.53517 | −0.0528739 | ||||||||
\(844\) | −103.426 | −3.56008 | ||||||||
\(845\) | −12.6927 | −0.436641 | ||||||||
\(846\) | −6.87982 | −0.236533 | ||||||||
\(847\) | −12.8400 | −0.441188 | ||||||||
\(848\) | −42.1961 | −1.44902 | ||||||||
\(849\) | −23.8827 | −0.819653 | ||||||||
\(850\) | −14.1892 | −0.486685 | ||||||||
\(851\) | −12.0463 | −0.412941 | ||||||||
\(852\) | 51.6655 | 1.77003 | ||||||||
\(853\) | −38.9886 | −1.33494 | −0.667472 | − | 0.744635i | \(-0.732623\pi\) | ||||
−0.667472 | + | 0.744635i | \(0.732623\pi\) | |||||||
\(854\) | −32.7425 | −1.12043 | ||||||||
\(855\) | 2.39286 | 0.0818342 | ||||||||
\(856\) | 32.3145 | 1.10449 | ||||||||
\(857\) | 3.55581 | 0.121464 | 0.0607320 | − | 0.998154i | \(-0.480657\pi\) | ||||
0.0607320 | + | 0.998154i | \(0.480657\pi\) | |||||||
\(858\) | 22.8788 | 0.781069 | ||||||||
\(859\) | 19.5753 | 0.667901 | 0.333951 | − | 0.942591i | \(-0.391618\pi\) | ||||
0.333951 | + | 0.942591i | \(0.391618\pi\) | |||||||
\(860\) | −45.1360 | −1.53913 | ||||||||
\(861\) | 1.00000 | 0.0340799 | ||||||||
\(862\) | 100.379 | 3.41893 | ||||||||
\(863\) | −30.9582 | −1.05383 | −0.526915 | − | 0.849918i | \(-0.676651\pi\) | ||||
−0.526915 | + | 0.849918i | \(0.676651\pi\) | |||||||
\(864\) | 6.94142 | 0.236152 | ||||||||
\(865\) | −3.96448 | −0.134797 | ||||||||
\(866\) | −63.6555 | −2.16310 | ||||||||
\(867\) | −14.1536 | −0.480682 | ||||||||
\(868\) | −9.99253 | −0.339169 | ||||||||
\(869\) | −32.1387 | −1.09023 | ||||||||
\(870\) | −9.22513 | −0.312761 | ||||||||
\(871\) | −7.41120 | −0.251119 | ||||||||
\(872\) | −116.591 | −3.94828 | ||||||||
\(873\) | −11.3241 | −0.383264 | ||||||||
\(874\) | 14.2196 | 0.480985 | ||||||||
\(875\) | 10.8658 | 0.367332 | ||||||||
\(876\) | −19.8749 | −0.671512 | ||||||||
\(877\) | −9.25642 | −0.312567 | −0.156284 | − | 0.987712i | \(-0.549951\pi\) | ||||
−0.156284 | + | 0.987712i | \(0.549951\pi\) | |||||||
\(878\) | 21.6079 | 0.729232 | ||||||||
\(879\) | 21.4580 | 0.723760 | ||||||||
\(880\) | −50.5297 | −1.70336 | ||||||||
\(881\) | −23.6835 | −0.797917 | −0.398959 | − | 0.916969i | \(-0.630628\pi\) | ||||
−0.398959 | + | 0.916969i | \(0.630628\pi\) | |||||||
\(882\) | 2.56695 | 0.0864337 | ||||||||
\(883\) | −44.4147 | −1.49467 | −0.747337 | − | 0.664445i | \(-0.768668\pi\) | ||||
−0.747337 | + | 0.664445i | \(0.768668\pi\) | |||||||
\(884\) | −14.1335 | −0.475362 | ||||||||
\(885\) | 6.32940 | 0.212760 | ||||||||
\(886\) | −79.0380 | −2.65533 | ||||||||
\(887\) | 6.18660 | 0.207726 | 0.103863 | − | 0.994592i | \(-0.466880\pi\) | ||||
0.103863 | + | 0.994592i | \(0.466880\pi\) | |||||||
\(888\) | −26.3431 | −0.884017 | ||||||||
\(889\) | 1.34061 | 0.0449625 | ||||||||
\(890\) | −27.0163 | −0.905590 | ||||||||
\(891\) | −4.88262 | −0.163574 | ||||||||
\(892\) | 21.1909 | 0.709524 | ||||||||
\(893\) | −4.88489 | −0.163467 | ||||||||
\(894\) | −0.669792 | −0.0224012 | ||||||||
\(895\) | 29.1710 | 0.975079 | ||||||||
\(896\) | 8.61280 | 0.287733 | ||||||||
\(897\) | −5.54800 | −0.185242 | ||||||||
\(898\) | −6.69192 | −0.223312 | ||||||||
\(899\) | −5.96029 | −0.198787 | ||||||||
\(900\) | −15.0360 | −0.501200 | ||||||||
\(901\) | −9.03129 | −0.300876 | ||||||||
\(902\) | 12.5335 | 0.417318 | ||||||||
\(903\) | 7.49135 | 0.249296 | ||||||||
\(904\) | 5.92178 | 0.196956 | ||||||||
\(905\) | −9.03716 | −0.300405 | ||||||||
\(906\) | −46.0243 | −1.52906 | ||||||||
\(907\) | 32.1863 | 1.06873 | 0.534365 | − | 0.845254i | \(-0.320551\pi\) | ||||
0.534365 | + | 0.845254i | \(0.320551\pi\) | |||||||
\(908\) | 82.3263 | 2.73209 | ||||||||
\(909\) | 4.01093 | 0.133034 | ||||||||
\(910\) | 6.15180 | 0.203930 | ||||||||
\(911\) | −55.0672 | −1.82446 | −0.912228 | − | 0.409682i | \(-0.865640\pi\) | ||||
−0.912228 | + | 0.409682i | \(0.865640\pi\) | |||||||
\(912\) | 14.3670 | 0.475739 | ||||||||
\(913\) | −65.9029 | −2.18107 | ||||||||
\(914\) | −67.8072 | −2.24286 | ||||||||
\(915\) | 16.7462 | 0.553614 | ||||||||
\(916\) | −83.2729 | −2.75141 | ||||||||
\(917\) | −9.55026 | −0.315378 | ||||||||
\(918\) | 4.33077 | 0.142937 | ||||||||
\(919\) | 13.1533 | 0.433887 | 0.216943 | − | 0.976184i | \(-0.430391\pi\) | ||||
0.216943 | + | 0.976184i | \(0.430391\pi\) | |||||||
\(920\) | 26.5208 | 0.874366 | ||||||||
\(921\) | −5.76942 | −0.190109 | ||||||||
\(922\) | −35.3622 | −1.16459 | ||||||||
\(923\) | −20.5505 | −0.676427 | ||||||||
\(924\) | 22.4075 | 0.737153 | ||||||||
\(925\) | 12.9858 | 0.426972 | ||||||||
\(926\) | −63.4826 | −2.08617 | ||||||||
\(927\) | 10.5595 | 0.346819 | ||||||||
\(928\) | −19.0012 | −0.623744 | ||||||||
\(929\) | −57.3506 | −1.88161 | −0.940806 | − | 0.338946i | \(-0.889930\pi\) | ||||
−0.940806 | + | 0.338946i | \(0.889930\pi\) | |||||||
\(930\) | 7.33796 | 0.240621 | ||||||||
\(931\) | 1.82262 | 0.0597338 | ||||||||
\(932\) | 117.390 | 3.84525 | ||||||||
\(933\) | −4.30612 | −0.140976 | ||||||||
\(934\) | 23.2749 | 0.761578 | ||||||||
\(935\) | −10.8149 | −0.353686 | ||||||||
\(936\) | −12.1325 | −0.396564 | ||||||||
\(937\) | −5.23621 | −0.171060 | −0.0855298 | − | 0.996336i | \(-0.527258\pi\) | ||||
−0.0855298 | + | 0.996336i | \(0.527258\pi\) | |||||||
\(938\) | −10.4218 | −0.340285 | ||||||||
\(939\) | −17.7494 | −0.579229 | ||||||||
\(940\) | −16.1482 | −0.526695 | ||||||||
\(941\) | −10.0115 | −0.326367 | −0.163183 | − | 0.986596i | \(-0.552176\pi\) | ||||
−0.163183 | + | 0.986596i | \(0.552176\pi\) | |||||||
\(942\) | 56.7482 | 1.84895 | ||||||||
\(943\) | −3.03931 | −0.0989735 | ||||||||
\(944\) | 38.0024 | 1.23687 | ||||||||
\(945\) | −1.31287 | −0.0427078 | ||||||||
\(946\) | 93.8925 | 3.05271 | ||||||||
\(947\) | −27.3885 | −0.890006 | −0.445003 | − | 0.895529i | \(-0.646797\pi\) | ||||
−0.445003 | + | 0.895529i | \(0.646797\pi\) | |||||||
\(948\) | 30.2076 | 0.981096 | ||||||||
\(949\) | 7.90546 | 0.256622 | ||||||||
\(950\) | −15.3287 | −0.497328 | ||||||||
\(951\) | 25.2987 | 0.820368 | ||||||||
\(952\) | −11.2134 | −0.363428 | ||||||||
\(953\) | −2.54292 | −0.0823733 | −0.0411867 | − | 0.999151i | \(-0.513114\pi\) | ||||
−0.0411867 | + | 0.999151i | \(0.513114\pi\) | |||||||
\(954\) | −13.7410 | −0.444883 | ||||||||
\(955\) | 3.69397 | 0.119534 | ||||||||
\(956\) | 56.8897 | 1.83994 | ||||||||
\(957\) | 13.3655 | 0.432046 | ||||||||
\(958\) | 15.1378 | 0.489079 | ||||||||
\(959\) | 16.5363 | 0.533984 | ||||||||
\(960\) | 2.69537 | 0.0869928 | ||||||||
\(961\) | −26.2590 | −0.847065 | ||||||||
\(962\) | 18.5719 | 0.598784 | ||||||||
\(963\) | 4.86193 | 0.156673 | ||||||||
\(964\) | 60.5311 | 1.94958 | ||||||||
\(965\) | 25.4317 | 0.818675 | ||||||||
\(966\) | −7.80176 | −0.251017 | ||||||||
\(967\) | 9.44817 | 0.303833 | 0.151916 | − | 0.988393i | \(-0.451456\pi\) | ||||
0.151916 | + | 0.988393i | \(0.451456\pi\) | |||||||
\(968\) | 85.3405 | 2.74295 | ||||||||
\(969\) | 3.07498 | 0.0987827 | ||||||||
\(970\) | −38.1633 | −1.22535 | ||||||||
\(971\) | 0.540148 | 0.0173342 | 0.00866708 | − | 0.999962i | \(-0.497241\pi\) | ||||
0.00866708 | + | 0.999962i | \(0.497241\pi\) | |||||||
\(972\) | 4.58924 | 0.147200 | ||||||||
\(973\) | −17.4941 | −0.560837 | ||||||||
\(974\) | 63.5695 | 2.03690 | ||||||||
\(975\) | 5.98073 | 0.191537 | ||||||||
\(976\) | 100.546 | 3.21840 | ||||||||
\(977\) | −51.4138 | −1.64487 | −0.822437 | − | 0.568856i | \(-0.807386\pi\) | ||||
−0.822437 | + | 0.568856i | \(0.807386\pi\) | |||||||
\(978\) | −7.99638 | −0.255696 | ||||||||
\(979\) | 39.1417 | 1.25097 | ||||||||
\(980\) | 6.02509 | 0.192464 | ||||||||
\(981\) | −17.5419 | −0.560070 | ||||||||
\(982\) | 7.75312 | 0.247412 | ||||||||
\(983\) | −5.25359 | −0.167563 | −0.0837817 | − | 0.996484i | \(-0.526700\pi\) | ||||
−0.0837817 | + | 0.996484i | \(0.526700\pi\) | |||||||
\(984\) | −6.64645 | −0.211881 | ||||||||
\(985\) | 14.8335 | 0.472634 | ||||||||
\(986\) | −11.8549 | −0.377537 | ||||||||
\(987\) | 2.68015 | 0.0853102 | ||||||||
\(988\) | −15.2685 | −0.485757 | ||||||||
\(989\) | −22.7685 | −0.723997 | ||||||||
\(990\) | −16.4548 | −0.522969 | ||||||||
\(991\) | 23.1189 | 0.734397 | 0.367198 | − | 0.930143i | \(-0.380317\pi\) | ||||
0.367198 | + | 0.930143i | \(0.380317\pi\) | |||||||
\(992\) | 15.1141 | 0.479874 | ||||||||
\(993\) | 24.3413 | 0.772447 | ||||||||
\(994\) | −28.8987 | −0.916610 | ||||||||
\(995\) | −20.3437 | −0.644939 | ||||||||
\(996\) | 61.9430 | 1.96274 | ||||||||
\(997\) | 4.35145 | 0.137812 | 0.0689059 | − | 0.997623i | \(-0.478049\pi\) | ||||
0.0689059 | + | 0.997623i | \(0.478049\pi\) | |||||||
\(998\) | 81.4805 | 2.57922 | ||||||||
\(999\) | −3.96349 | −0.125399 |
(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 | 861.2.a.l.1.5 | ✓ | 5 | |
3.2 | odd | 2 | 2583.2.a.p.1.1 | 5 | |||
7.6 | odd | 2 | 6027.2.a.w.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.a.l.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial | |
2583.2.a.p.1.1 | 5 | 3.2 | odd | 2 | |||
6027.2.a.w.1.5 | 5 | 7.6 | odd | 2 |