Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} + 152 x^{17} - 274 x^{16} - 1061 x^{15} + 3125 x^{14} + 2977 x^{13} - 15474 x^{12} + \cdots + 31 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 889) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(-0.731838\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.731838 | 0.517488 | 0.258744 | − | 0.965946i | \(-0.416691\pi\) | ||||
0.258744 | + | 0.965946i | \(0.416691\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.46441 | −0.732207 | ||||||||
\(5\) | −3.93264 | −1.75873 | −0.879366 | − | 0.476146i | \(-0.842033\pi\) | ||||
−0.879366 | + | 0.476146i | \(0.842033\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.53539 | −0.896395 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.87806 | −0.910122 | ||||||||
\(11\) | −4.56737 | −1.37711 | −0.688557 | − | 0.725183i | \(-0.741755\pi\) | ||||
−0.688557 | + | 0.725183i | \(0.741755\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.89555 | −1.08043 | −0.540216 | − | 0.841527i | \(-0.681657\pi\) | ||||
−0.540216 | + | 0.841527i | \(0.681657\pi\) | |||||||
\(14\) | 0.731838 | 0.195592 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.07333 | 0.268333 | ||||||||
\(17\) | 6.78176 | 1.64482 | 0.822409 | − | 0.568896i | \(-0.192629\pi\) | ||||
0.822409 | + | 0.568896i | \(0.192629\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.75086 | 1.31934 | 0.659669 | − | 0.751556i | \(-0.270696\pi\) | ||||
0.659669 | + | 0.751556i | \(0.270696\pi\) | |||||||
\(20\) | 5.75902 | 1.28776 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.34257 | −0.712639 | ||||||||
\(23\) | −1.77247 | −0.369585 | −0.184793 | − | 0.982778i | \(-0.559161\pi\) | ||||
−0.184793 | + | 0.982778i | \(0.559161\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.4657 | 2.09314 | ||||||||
\(26\) | −2.85091 | −0.559110 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.46441 | −0.276748 | ||||||||
\(29\) | 2.04719 | 0.380153 | 0.190077 | − | 0.981769i | \(-0.439126\pi\) | ||||
0.190077 | + | 0.981769i | \(0.439126\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.75876 | −0.854698 | −0.427349 | − | 0.904087i | \(-0.640553\pi\) | ||||
−0.427349 | + | 0.904087i | \(0.640553\pi\) | |||||||
\(32\) | 5.85628 | 1.03525 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.96315 | 0.851173 | ||||||||
\(35\) | −3.93264 | −0.664738 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.62146 | −0.595365 | −0.297683 | − | 0.954665i | \(-0.596214\pi\) | ||||
−0.297683 | + | 0.954665i | \(0.596214\pi\) | |||||||
\(38\) | 4.20870 | 0.682741 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 9.97078 | 1.57652 | ||||||||
\(41\) | −3.27869 | −0.512045 | −0.256023 | − | 0.966671i | \(-0.582412\pi\) | ||||
−0.256023 | + | 0.966671i | \(0.582412\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.5020 | 1.90654 | 0.953268 | − | 0.302125i | \(-0.0976960\pi\) | ||||
0.953268 | + | 0.302125i | \(0.0976960\pi\) | |||||||
\(44\) | 6.68851 | 1.00833 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.29716 | −0.191256 | ||||||||
\(47\) | −0.353812 | −0.0516089 | −0.0258044 | − | 0.999667i | \(-0.508215\pi\) | ||||
−0.0258044 | + | 0.999667i | \(0.508215\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 7.65919 | 1.08317 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.70470 | 0.791099 | ||||||||
\(53\) | 8.18257 | 1.12396 | 0.561981 | − | 0.827150i | \(-0.310039\pi\) | ||||
0.561981 | + | 0.827150i | \(0.310039\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.9618 | 2.42197 | ||||||||
\(56\) | −2.53539 | −0.338806 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.49821 | 0.196725 | ||||||||
\(59\) | −10.8977 | −1.41876 | −0.709378 | − | 0.704828i | \(-0.751024\pi\) | ||||
−0.709378 | + | 0.704828i | \(0.751024\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.82338 | 1.25775 | 0.628877 | − | 0.777504i | \(-0.283515\pi\) | ||||
0.628877 | + | 0.777504i | \(0.283515\pi\) | |||||||
\(62\) | −3.48264 | −0.442296 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.13919 | 0.267398 | ||||||||
\(65\) | 15.3198 | 1.90019 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.08050 | 0.742851 | 0.371426 | − | 0.928463i | \(-0.378869\pi\) | ||||
0.371426 | + | 0.928463i | \(0.378869\pi\) | |||||||
\(68\) | −9.93130 | −1.20435 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.87806 | −0.343994 | ||||||||
\(71\) | −11.4162 | −1.35486 | −0.677428 | − | 0.735589i | \(-0.736905\pi\) | ||||
−0.677428 | + | 0.735589i | \(0.736905\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.83793 | 0.215113 | 0.107556 | − | 0.994199i | \(-0.465697\pi\) | ||||
0.107556 | + | 0.994199i | \(0.465697\pi\) | |||||||
\(74\) | −2.65032 | −0.308094 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.42164 | −0.966028 | ||||||||
\(77\) | −4.56737 | −0.520500 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.38973 | −0.831409 | −0.415705 | − | 0.909500i | \(-0.636465\pi\) | ||||
−0.415705 | + | 0.909500i | \(0.636465\pi\) | |||||||
\(80\) | −4.22104 | −0.471926 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.39947 | −0.264977 | ||||||||
\(83\) | 7.42793 | 0.815321 | 0.407660 | − | 0.913134i | \(-0.366345\pi\) | ||||
0.407660 | + | 0.913134i | \(0.366345\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −26.6703 | −2.89280 | ||||||||
\(86\) | 9.14944 | 0.986609 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 11.5801 | 1.23444 | ||||||||
\(89\) | 6.77417 | 0.718060 | 0.359030 | − | 0.933326i | \(-0.383108\pi\) | ||||
0.359030 | + | 0.933326i | \(0.383108\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.89555 | −0.408365 | ||||||||
\(92\) | 2.59563 | 0.270613 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.258933 | −0.0267069 | ||||||||
\(95\) | −22.6161 | −2.32036 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.9733 | 1.11417 | 0.557084 | − | 0.830456i | \(-0.311920\pi\) | ||||
0.557084 | + | 0.830456i | \(0.311920\pi\) | |||||||
\(98\) | 0.731838 | 0.0739268 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −15.3261 | −1.53261 | ||||||||
\(101\) | −3.77928 | −0.376053 | −0.188026 | − | 0.982164i | \(-0.560209\pi\) | ||||
−0.188026 | + | 0.982164i | \(0.560209\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.84662 | −0.871683 | −0.435842 | − | 0.900023i | \(-0.643549\pi\) | ||||
−0.435842 | + | 0.900023i | \(0.643549\pi\) | |||||||
\(104\) | 9.87674 | 0.968494 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.98832 | 0.581637 | ||||||||
\(107\) | −11.9793 | −1.15808 | −0.579040 | − | 0.815299i | \(-0.696573\pi\) | ||||
−0.579040 | + | 0.815299i | \(0.696573\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.50483 | 0.527267 | 0.263634 | − | 0.964623i | \(-0.415079\pi\) | ||||
0.263634 | + | 0.964623i | \(0.415079\pi\) | |||||||
\(110\) | 13.1452 | 1.25334 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.07333 | 0.101420 | ||||||||
\(113\) | 1.11071 | 0.104487 | 0.0522435 | − | 0.998634i | \(-0.483363\pi\) | ||||
0.0522435 | + | 0.998634i | \(0.483363\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.97049 | 0.650002 | ||||||||
\(116\) | −2.99793 | −0.278351 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.97533 | −0.734189 | ||||||||
\(119\) | 6.78176 | 0.621683 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.86085 | 0.896441 | ||||||||
\(122\) | 7.18912 | 0.650873 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.96879 | 0.625816 | ||||||||
\(125\) | −21.4946 | −1.92254 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −10.1470 | −0.896879 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 11.2116 | 0.983324 | ||||||||
\(131\) | 11.6742 | 1.01998 | 0.509989 | − | 0.860181i | \(-0.329649\pi\) | ||||
0.509989 | + | 0.860181i | \(0.329649\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.75086 | 0.498663 | ||||||||
\(134\) | 4.44994 | 0.384416 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −17.1944 | −1.47441 | ||||||||
\(137\) | −21.9031 | −1.87131 | −0.935654 | − | 0.352919i | \(-0.885189\pi\) | ||||
−0.935654 | + | 0.352919i | \(0.885189\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.0623 | −1.61684 | −0.808421 | − | 0.588604i | \(-0.799678\pi\) | ||||
−0.808421 | + | 0.588604i | \(0.799678\pi\) | |||||||
\(140\) | 5.75902 | 0.486726 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.35482 | −0.701121 | ||||||||
\(143\) | 17.7924 | 1.48788 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.05086 | −0.668587 | ||||||||
\(146\) | 1.34506 | 0.111318 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.30332 | 0.435930 | ||||||||
\(149\) | 1.94463 | 0.159311 | 0.0796553 | − | 0.996822i | \(-0.474618\pi\) | ||||
0.0796553 | + | 0.996822i | \(0.474618\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.3431 | 1.00447 | 0.502234 | − | 0.864732i | \(-0.332512\pi\) | ||||
0.502234 | + | 0.864732i | \(0.332512\pi\) | |||||||
\(152\) | −14.5807 | −1.18265 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.34257 | −0.269352 | ||||||||
\(155\) | 18.7145 | 1.50319 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.61611 | 0.288597 | 0.144298 | − | 0.989534i | \(-0.453907\pi\) | ||||
0.144298 | + | 0.989534i | \(0.453907\pi\) | |||||||
\(158\) | −5.40808 | −0.430244 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −23.0307 | −1.82074 | ||||||||
\(161\) | −1.77247 | −0.139690 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0075 | 0.783847 | 0.391923 | − | 0.919998i | \(-0.371810\pi\) | ||||
0.391923 | + | 0.919998i | \(0.371810\pi\) | |||||||
\(164\) | 4.80136 | 0.374923 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.43604 | 0.421918 | ||||||||
\(167\) | −15.9926 | −1.23754 | −0.618771 | − | 0.785572i | \(-0.712369\pi\) | ||||
−0.618771 | + | 0.785572i | \(0.712369\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.17531 | 0.167332 | ||||||||
\(170\) | −19.5183 | −1.49699 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −18.3081 | −1.39598 | ||||||||
\(173\) | −7.76734 | −0.590540 | −0.295270 | − | 0.955414i | \(-0.595410\pi\) | ||||
−0.295270 | + | 0.955414i | \(0.595410\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.4657 | 0.791132 | ||||||||
\(176\) | −4.90231 | −0.369525 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.95759 | 0.371587 | ||||||||
\(179\) | 23.6261 | 1.76590 | 0.882951 | − | 0.469466i | \(-0.155554\pi\) | ||||
0.882951 | + | 0.469466i | \(0.155554\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.0001 | 1.63525 | 0.817626 | − | 0.575750i | \(-0.195290\pi\) | ||||
0.817626 | + | 0.575750i | \(0.195290\pi\) | |||||||
\(182\) | −2.85091 | −0.211324 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.49390 | 0.331295 | ||||||||
\(185\) | 14.2419 | 1.04709 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −30.9748 | −2.26510 | ||||||||
\(188\) | 0.518128 | 0.0377883 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −16.5513 | −1.20076 | ||||||||
\(191\) | −23.6532 | −1.71148 | −0.855742 | − | 0.517403i | \(-0.826899\pi\) | ||||
−0.855742 | + | 0.517403i | \(0.826899\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.5476 | −1.04716 | −0.523581 | − | 0.851976i | \(-0.675404\pi\) | ||||
−0.523581 | + | 0.851976i | \(0.675404\pi\) | |||||||
\(194\) | 8.03066 | 0.576568 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.46441 | −0.104601 | ||||||||
\(197\) | −8.86925 | −0.631908 | −0.315954 | − | 0.948775i | \(-0.602325\pi\) | ||||
−0.315954 | + | 0.948775i | \(0.602325\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.8851 | −0.984291 | −0.492146 | − | 0.870513i | \(-0.663787\pi\) | ||||
−0.492146 | + | 0.870513i | \(0.663787\pi\) | |||||||
\(200\) | −26.5346 | −1.87628 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.76582 | −0.194603 | ||||||||
\(203\) | 2.04719 | 0.143684 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.8939 | 0.900550 | ||||||||
\(206\) | −6.47429 | −0.451085 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.18122 | −0.289916 | ||||||||
\(209\) | −26.2663 | −1.81688 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.6380 | 0.938880 | 0.469440 | − | 0.882964i | \(-0.344456\pi\) | ||||
0.469440 | + | 0.882964i | \(0.344456\pi\) | |||||||
\(212\) | −11.9827 | −0.822973 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.76689 | −0.599292 | ||||||||
\(215\) | −49.1659 | −3.35309 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.75876 | −0.323046 | ||||||||
\(218\) | 4.02864 | 0.272854 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −26.3035 | −1.77338 | ||||||||
\(221\) | −26.4187 | −1.77711 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.12924 | −0.611339 | −0.305670 | − | 0.952138i | \(-0.598880\pi\) | ||||
−0.305670 | + | 0.952138i | \(0.598880\pi\) | |||||||
\(224\) | 5.85628 | 0.391289 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.812862 | 0.0540708 | ||||||||
\(227\) | −25.9253 | −1.72072 | −0.860362 | − | 0.509683i | \(-0.829763\pi\) | ||||
−0.860362 | + | 0.509683i | \(0.829763\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.02046 | 0.397843 | 0.198922 | − | 0.980015i | \(-0.436256\pi\) | ||||
0.198922 | + | 0.980015i | \(0.436256\pi\) | |||||||
\(230\) | 5.10127 | 0.336368 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.19042 | −0.340767 | ||||||||
\(233\) | 2.47265 | 0.161989 | 0.0809943 | − | 0.996715i | \(-0.474190\pi\) | ||||
0.0809943 | + | 0.996715i | \(0.474190\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.39142 | 0.0907661 | ||||||||
\(236\) | 15.9587 | 1.03882 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.96315 | 0.321713 | ||||||||
\(239\) | −21.8465 | −1.41313 | −0.706567 | − | 0.707646i | \(-0.749757\pi\) | ||||
−0.706567 | + | 0.707646i | \(0.749757\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.16053 | −0.461250 | −0.230625 | − | 0.973043i | \(-0.574077\pi\) | ||||
−0.230625 | + | 0.973043i | \(0.574077\pi\) | |||||||
\(242\) | 7.21654 | 0.463897 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.3855 | −0.920936 | ||||||||
\(245\) | −3.93264 | −0.251247 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.4028 | −1.42545 | ||||||||
\(248\) | 12.0653 | 0.766148 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −15.7306 | −0.994889 | ||||||||
\(251\) | 10.6859 | 0.674488 | 0.337244 | − | 0.941417i | \(-0.390505\pi\) | ||||
0.337244 | + | 0.941417i | \(0.390505\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.09552 | 0.508961 | ||||||||
\(254\) | −0.731838 | −0.0459196 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.7044 | −0.731522 | ||||||||
\(257\) | 16.4530 | 1.02631 | 0.513155 | − | 0.858296i | \(-0.328477\pi\) | ||||
0.513155 | + | 0.858296i | \(0.328477\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.62146 | −0.225027 | ||||||||
\(260\) | −22.4345 | −1.39133 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.54361 | 0.527826 | ||||||||
\(263\) | −5.82474 | −0.359169 | −0.179584 | − | 0.983743i | \(-0.557475\pi\) | ||||
−0.179584 | + | 0.983743i | \(0.557475\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −32.1792 | −1.97675 | ||||||||
\(266\) | 4.20870 | 0.258052 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.90437 | −0.543921 | ||||||||
\(269\) | 15.3418 | 0.935406 | 0.467703 | − | 0.883886i | \(-0.345082\pi\) | ||||
0.467703 | + | 0.883886i | \(0.345082\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.0137 | 1.45873 | 0.729365 | − | 0.684125i | \(-0.239816\pi\) | ||||
0.729365 | + | 0.684125i | \(0.239816\pi\) | |||||||
\(272\) | 7.27909 | 0.441359 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.0295 | −0.968378 | ||||||||
\(275\) | −47.8007 | −2.88249 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.16090 | −0.250004 | −0.125002 | − | 0.992156i | \(-0.539894\pi\) | ||||
−0.125002 | + | 0.992156i | \(0.539894\pi\) | |||||||
\(278\) | −13.9505 | −0.836696 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 9.97078 | 0.595868 | ||||||||
\(281\) | 14.1868 | 0.846312 | 0.423156 | − | 0.906057i | \(-0.360922\pi\) | ||||
0.423156 | + | 0.906057i | \(0.360922\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.9011 | −0.945225 | −0.472612 | − | 0.881270i | \(-0.656689\pi\) | ||||
−0.472612 | + | 0.881270i | \(0.656689\pi\) | |||||||
\(284\) | 16.7181 | 0.992034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.0212 | 0.769957 | ||||||||
\(287\) | −3.27869 | −0.193535 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.9923 | 1.70543 | ||||||||
\(290\) | −5.89192 | −0.345986 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.69148 | −0.157507 | ||||||||
\(293\) | −7.33737 | −0.428654 | −0.214327 | − | 0.976762i | \(-0.568756\pi\) | ||||
−0.214327 | + | 0.976762i | \(0.568756\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 42.8567 | 2.49521 | ||||||||
\(296\) | 9.18182 | 0.533682 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.42316 | 0.0824413 | ||||||||
\(299\) | 6.90474 | 0.399312 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.5020 | 0.720603 | ||||||||
\(302\) | 9.03315 | 0.519799 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.17259 | 0.354022 | ||||||||
\(305\) | −38.6319 | −2.21205 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.7027 | −1.46693 | −0.733465 | − | 0.679727i | \(-0.762098\pi\) | ||||
−0.733465 | + | 0.679727i | \(0.762098\pi\) | |||||||
\(308\) | 6.68851 | 0.381113 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.6960 | 0.777880 | ||||||||
\(311\) | −1.41386 | −0.0801724 | −0.0400862 | − | 0.999196i | \(-0.512763\pi\) | ||||
−0.0400862 | + | 0.999196i | \(0.512763\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.7255 | −0.662762 | −0.331381 | − | 0.943497i | \(-0.607514\pi\) | ||||
−0.331381 | + | 0.943497i | \(0.607514\pi\) | |||||||
\(314\) | 2.64641 | 0.149345 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.8216 | 0.608763 | ||||||||
\(317\) | 9.44210 | 0.530321 | 0.265161 | − | 0.964204i | \(-0.414575\pi\) | ||||
0.265161 | + | 0.964204i | \(0.414575\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.35026 | −0.523514 | ||||||||
\(320\) | −8.41265 | −0.470282 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.29716 | −0.0722879 | ||||||||
\(323\) | 39.0010 | 2.17007 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −40.7696 | −2.26149 | ||||||||
\(326\) | 7.32386 | 0.405631 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.31275 | 0.458995 | ||||||||
\(329\) | −0.353812 | −0.0195063 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.56053 | 0.0857743 | 0.0428871 | − | 0.999080i | \(-0.486344\pi\) | ||||
0.0428871 | + | 0.999080i | \(0.486344\pi\) | |||||||
\(332\) | −10.8776 | −0.596983 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.7040 | −0.640412 | ||||||||
\(335\) | −23.9124 | −1.30648 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.82064 | −0.262597 | −0.131298 | − | 0.991343i | \(-0.541915\pi\) | ||||
−0.131298 | + | 0.991343i | \(0.541915\pi\) | |||||||
\(338\) | 1.59198 | 0.0865922 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 39.0563 | 2.11812 | ||||||||
\(341\) | 21.7350 | 1.17702 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −31.6974 | −1.70901 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.68443 | −0.305597 | ||||||||
\(347\) | 7.89995 | 0.424092 | 0.212046 | − | 0.977260i | \(-0.431987\pi\) | ||||
0.212046 | + | 0.977260i | \(0.431987\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.0702 | −1.34198 | −0.670988 | − | 0.741468i | \(-0.734130\pi\) | ||||
−0.670988 | + | 0.741468i | \(0.734130\pi\) | |||||||
\(350\) | 7.65919 | 0.409401 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −26.7478 | −1.42566 | ||||||||
\(353\) | 3.30600 | 0.175961 | 0.0879804 | − | 0.996122i | \(-0.471959\pi\) | ||||
0.0879804 | + | 0.996122i | \(0.471959\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 44.8959 | 2.38283 | ||||||||
\(356\) | −9.92018 | −0.525768 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.2905 | 0.913832 | ||||||||
\(359\) | −25.7381 | −1.35840 | −0.679202 | − | 0.733952i | \(-0.737674\pi\) | ||||
−0.679202 | + | 0.733952i | \(0.737674\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.0724 | 0.740654 | ||||||||
\(362\) | 16.1005 | 0.846223 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.70470 | 0.299007 | ||||||||
\(365\) | −7.22791 | −0.378326 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.640561 | −0.0334370 | −0.0167185 | − | 0.999860i | \(-0.505322\pi\) | ||||
−0.0167185 | + | 0.999860i | \(0.505322\pi\) | |||||||
\(368\) | −1.90245 | −0.0991720 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.4228 | 0.541855 | ||||||||
\(371\) | 8.18257 | 0.424818 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.16876 | 0.267628 | 0.133814 | − | 0.991006i | \(-0.457277\pi\) | ||||
0.133814 | + | 0.991006i | \(0.457277\pi\) | |||||||
\(374\) | −22.6685 | −1.17216 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.897052 | 0.0462619 | ||||||||
\(377\) | −7.97492 | −0.410729 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.1015 | −1.70031 | −0.850156 | − | 0.526531i | \(-0.823493\pi\) | ||||
−0.850156 | + | 0.526531i | \(0.823493\pi\) | |||||||
\(380\) | 33.1193 | 1.69898 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −17.3103 | −0.885672 | ||||||||
\(383\) | 22.3539 | 1.14223 | 0.571116 | − | 0.820869i | \(-0.306510\pi\) | ||||
0.571116 | + | 0.820869i | \(0.306510\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.9618 | 0.915420 | ||||||||
\(386\) | −10.6465 | −0.541893 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.0694 | −0.815801 | ||||||||
\(389\) | 13.3831 | 0.678551 | 0.339275 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339275 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.0205 | −0.607901 | ||||||||
\(392\) | −2.53539 | −0.128056 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.49085 | −0.327005 | ||||||||
\(395\) | 29.0612 | 1.46223 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.3190 | 0.919404 | 0.459702 | − | 0.888073i | \(-0.347956\pi\) | ||||
0.459702 | + | 0.888073i | \(0.347956\pi\) | |||||||
\(398\) | −10.1617 | −0.509359 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.2332 | 0.561658 | ||||||||
\(401\) | −26.1476 | −1.30575 | −0.652873 | − | 0.757467i | \(-0.726437\pi\) | ||||
−0.652873 | + | 0.757467i | \(0.726437\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.5380 | 0.923443 | ||||||||
\(404\) | 5.53443 | 0.275348 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.49821 | 0.0743549 | ||||||||
\(407\) | 16.5406 | 0.819885 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.8085 | 1.02891 | 0.514457 | − | 0.857516i | \(-0.327994\pi\) | ||||
0.514457 | + | 0.857516i | \(0.327994\pi\) | |||||||
\(410\) | 9.43626 | 0.466024 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.9551 | 0.638252 | ||||||||
\(413\) | −10.8977 | −0.536240 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −29.2114 | −1.43393 | ||||||||
\(416\) | −22.8134 | −1.11852 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −19.2227 | −0.940212 | ||||||||
\(419\) | 37.7760 | 1.84548 | 0.922740 | − | 0.385423i | \(-0.125944\pi\) | ||||
0.922740 | + | 0.385423i | \(0.125944\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.29583 | −0.0631551 | −0.0315776 | − | 0.999501i | \(-0.510053\pi\) | ||||
−0.0315776 | + | 0.999501i | \(0.510053\pi\) | |||||||
\(422\) | 9.98082 | 0.485859 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −20.7460 | −1.00752 | ||||||||
\(425\) | 70.9758 | 3.44283 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.82338 | 0.475387 | ||||||||
\(428\) | 17.5426 | 0.847954 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −35.9815 | −1.73518 | ||||||||
\(431\) | 10.8722 | 0.523694 | 0.261847 | − | 0.965109i | \(-0.415668\pi\) | ||||
0.261847 | + | 0.965109i | \(0.415668\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.3839 | −0.547075 | −0.273538 | − | 0.961861i | \(-0.588194\pi\) | ||||
−0.273538 | + | 0.961861i | \(0.588194\pi\) | |||||||
\(434\) | −3.48264 | −0.167172 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.06135 | −0.386069 | ||||||||
\(437\) | −10.1932 | −0.487608 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.55817 | 0.408459 | 0.204230 | − | 0.978923i | \(-0.434531\pi\) | ||||
0.204230 | + | 0.978923i | \(0.434531\pi\) | |||||||
\(440\) | −45.5402 | −2.17105 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −19.3342 | −0.919634 | ||||||||
\(443\) | 20.8475 | 0.990493 | 0.495246 | − | 0.868753i | \(-0.335078\pi\) | ||||
0.495246 | + | 0.868753i | \(0.335078\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −26.6404 | −1.26288 | ||||||||
\(446\) | −6.68112 | −0.316360 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.13919 | 0.101067 | ||||||||
\(449\) | 24.0389 | 1.13447 | 0.567233 | − | 0.823558i | \(-0.308014\pi\) | ||||
0.567233 | + | 0.823558i | \(0.308014\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.9750 | 0.705144 | ||||||||
\(452\) | −1.62654 | −0.0765061 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −18.9731 | −0.890454 | ||||||||
\(455\) | 15.3198 | 0.718204 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.8458 | −0.788013 | −0.394007 | − | 0.919108i | \(-0.628911\pi\) | ||||
−0.394007 | + | 0.919108i | \(0.628911\pi\) | |||||||
\(458\) | 4.40600 | 0.205879 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.2077 | −0.475935 | ||||||||
\(461\) | 2.07046 | 0.0964310 | 0.0482155 | − | 0.998837i | \(-0.484647\pi\) | ||||
0.0482155 | + | 0.998837i | \(0.484647\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.79150 | −0.222680 | −0.111340 | − | 0.993782i | \(-0.535514\pi\) | ||||
−0.111340 | + | 0.993782i | \(0.535514\pi\) | |||||||
\(464\) | 2.19731 | 0.102008 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.80958 | 0.0838271 | ||||||||
\(467\) | 16.9848 | 0.785961 | 0.392980 | − | 0.919547i | \(-0.371444\pi\) | ||||
0.392980 | + | 0.919547i | \(0.371444\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.08050 | 0.280771 | ||||||||
\(470\) | 1.01829 | 0.0469704 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 27.6299 | 1.27177 | ||||||||
\(473\) | −57.1012 | −2.62552 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 60.1868 | 2.76156 | ||||||||
\(476\) | −9.93130 | −0.455200 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −15.9881 | −0.731279 | ||||||||
\(479\) | −19.0396 | −0.869942 | −0.434971 | − | 0.900444i | \(-0.643241\pi\) | ||||
−0.434971 | + | 0.900444i | \(0.643241\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.1076 | 0.643251 | ||||||||
\(482\) | −5.24035 | −0.238691 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −14.4404 | −0.656380 | ||||||||
\(485\) | −43.1540 | −1.95952 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.9169 | −1.08378 | −0.541890 | − | 0.840450i | \(-0.682291\pi\) | ||||
−0.541890 | + | 0.840450i | \(0.682291\pi\) | |||||||
\(488\) | −24.9061 | −1.12745 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.87806 | −0.130017 | ||||||||
\(491\) | −38.6421 | −1.74390 | −0.871948 | − | 0.489599i | \(-0.837143\pi\) | ||||
−0.871948 | + | 0.489599i | \(0.837143\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.8835 | 0.625283 | ||||||||
\(494\) | −16.3952 | −0.737655 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.10773 | −0.229344 | ||||||||
\(497\) | −11.4162 | −0.512087 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.3037 | 1.26705 | 0.633523 | − | 0.773724i | \(-0.281608\pi\) | ||||
0.633523 | + | 0.773724i | \(0.281608\pi\) | |||||||
\(500\) | 31.4770 | 1.40769 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.82034 | 0.349039 | ||||||||
\(503\) | −17.3592 | −0.774010 | −0.387005 | − | 0.922078i | \(-0.626490\pi\) | ||||
−0.387005 | + | 0.922078i | \(0.626490\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.8626 | 0.661376 | ||||||||
\(506\) | 5.92461 | 0.263381 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.46441 | 0.0649728 | ||||||||
\(509\) | 30.8979 | 1.36952 | 0.684762 | − | 0.728767i | \(-0.259906\pi\) | ||||
0.684762 | + | 0.728767i | \(0.259906\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.83793 | 0.0813051 | ||||||||
\(512\) | 11.7284 | 0.518326 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12.0409 | 0.531103 | ||||||||
\(515\) | 34.7906 | 1.53306 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.61599 | 0.0710712 | ||||||||
\(518\) | −2.65032 | −0.116449 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −38.8417 | −1.70332 | ||||||||
\(521\) | −8.47859 | −0.371454 | −0.185727 | − | 0.982601i | \(-0.559464\pi\) | ||||
−0.185727 | + | 0.982601i | \(0.559464\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.9260 | 1.30857 | 0.654286 | − | 0.756247i | \(-0.272969\pi\) | ||||
0.654286 | + | 0.756247i | \(0.272969\pi\) | |||||||
\(524\) | −17.0958 | −0.746835 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.26276 | −0.185865 | ||||||||
\(527\) | −32.2728 | −1.40582 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.8584 | −0.863407 | ||||||||
\(530\) | −23.5499 | −1.02294 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.42164 | −0.365124 | ||||||||
\(533\) | 12.7723 | 0.553230 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 47.1102 | 2.03675 | ||||||||
\(536\) | −15.4164 | −0.665889 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11.2277 | 0.484061 | ||||||||
\(539\) | −4.56737 | −0.196730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.1813 | −0.437728 | −0.218864 | − | 0.975755i | \(-0.570235\pi\) | ||||
−0.218864 | + | 0.975755i | \(0.570235\pi\) | |||||||
\(542\) | 17.5742 | 0.754875 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 39.7159 | 1.70281 | ||||||||
\(545\) | −21.6485 | −0.927322 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.5473 | −1.26335 | −0.631675 | − | 0.775233i | \(-0.717632\pi\) | ||||
−0.631675 | + | 0.775233i | \(0.717632\pi\) | |||||||
\(548\) | 32.0752 | 1.37018 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −34.9823 | −1.49165 | ||||||||
\(551\) | 11.7731 | 0.501551 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.38973 | −0.314243 | ||||||||
\(554\) | −3.04510 | −0.129374 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 27.9151 | 1.18386 | ||||||||
\(557\) | −15.4341 | −0.653963 | −0.326981 | − | 0.945031i | \(-0.606031\pi\) | ||||
−0.326981 | + | 0.945031i | \(0.606031\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −48.7022 | −2.05988 | ||||||||
\(560\) | −4.22104 | −0.178371 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.3824 | 0.437956 | ||||||||
\(563\) | 41.3758 | 1.74378 | 0.871890 | − | 0.489702i | \(-0.162894\pi\) | ||||
0.871890 | + | 0.489702i | \(0.162894\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.36804 | −0.183765 | ||||||||
\(566\) | −11.6371 | −0.489142 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 28.9445 | 1.21449 | ||||||||
\(569\) | 13.4486 | 0.563796 | 0.281898 | − | 0.959444i | \(-0.409036\pi\) | ||||
0.281898 | + | 0.959444i | \(0.409036\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.6397 | −0.445258 | −0.222629 | − | 0.974903i | \(-0.571464\pi\) | ||||
−0.222629 | + | 0.974903i | \(0.571464\pi\) | |||||||
\(572\) | −26.0554 | −1.08943 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.39947 | −0.100152 | ||||||||
\(575\) | −18.5501 | −0.773593 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.16461 | 0.381528 | 0.190764 | − | 0.981636i | \(-0.438904\pi\) | ||||
0.190764 | + | 0.981636i | \(0.438904\pi\) | |||||||
\(578\) | 21.2177 | 0.882538 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 11.7898 | 0.489544 | ||||||||
\(581\) | 7.42793 | 0.308162 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −37.3728 | −1.54782 | ||||||||
\(584\) | −4.65986 | −0.192826 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.36977 | −0.221823 | ||||||||
\(587\) | −8.98235 | −0.370741 | −0.185371 | − | 0.982669i | \(-0.559349\pi\) | ||||
−0.185371 | + | 0.982669i | \(0.559349\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.3670 | −1.12764 | ||||||||
\(590\) | 31.3642 | 1.29124 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.88704 | −0.159756 | ||||||||
\(593\) | 10.5609 | 0.433683 | 0.216842 | − | 0.976207i | \(-0.430425\pi\) | ||||
0.216842 | + | 0.976207i | \(0.430425\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −26.6703 | −1.09337 | ||||||||
\(596\) | −2.84775 | −0.116648 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.05315 | 0.206639 | ||||||||
\(599\) | −12.1190 | −0.495169 | −0.247585 | − | 0.968866i | \(-0.579637\pi\) | ||||
−0.247585 | + | 0.968866i | \(0.579637\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.2199 | −1.19190 | −0.595952 | − | 0.803020i | \(-0.703225\pi\) | ||||
−0.595952 | + | 0.803020i | \(0.703225\pi\) | |||||||
\(602\) | 9.14944 | 0.372903 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −18.0754 | −0.735477 | ||||||||
\(605\) | −38.7792 | −1.57660 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.3541 | −0.947916 | −0.473958 | − | 0.880548i | \(-0.657175\pi\) | ||||
−0.473958 | + | 0.880548i | \(0.657175\pi\) | |||||||
\(608\) | 33.6787 | 1.36585 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −28.2723 | −1.14471 | ||||||||
\(611\) | 1.37829 | 0.0557598 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.913187 | 0.0368833 | 0.0184416 | − | 0.999830i | \(-0.494130\pi\) | ||||
0.0184416 | + | 0.999830i | \(0.494130\pi\) | |||||||
\(614\) | −18.8102 | −0.759118 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.5801 | 0.466574 | ||||||||
\(617\) | 5.60825 | 0.225780 | 0.112890 | − | 0.993608i | \(-0.463989\pi\) | ||||
0.112890 | + | 0.993608i | \(0.463989\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.38738 | −0.176344 | −0.0881718 | − | 0.996105i | \(-0.528102\pi\) | ||||
−0.0881718 | + | 0.996105i | \(0.528102\pi\) | |||||||
\(620\) | −27.4058 | −1.10064 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.03471 | −0.0414882 | ||||||||
\(623\) | 6.77417 | 0.271401 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 32.2022 | 1.28809 | ||||||||
\(626\) | −8.58113 | −0.342971 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.29548 | −0.211313 | ||||||||
\(629\) | −24.5599 | −0.979268 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.10432 | −0.243009 | −0.121505 | − | 0.992591i | \(-0.538772\pi\) | ||||
−0.121505 | + | 0.992591i | \(0.538772\pi\) | |||||||
\(632\) | 18.7358 | 0.745271 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.91009 | 0.274435 | ||||||||
\(635\) | 3.93264 | 0.156062 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.89555 | −0.154347 | ||||||||
\(638\) | −6.84287 | −0.270912 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 39.9047 | 1.57737 | ||||||||
\(641\) | −23.1532 | −0.914496 | −0.457248 | − | 0.889339i | \(-0.651165\pi\) | ||||
−0.457248 | + | 0.889339i | \(0.651165\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.44468 | 0.293589 | 0.146795 | − | 0.989167i | \(-0.453104\pi\) | ||||
0.146795 | + | 0.989167i | \(0.453104\pi\) | |||||||
\(644\) | 2.59563 | 0.102282 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 28.5424 | 1.12299 | ||||||||
\(647\) | 19.7448 | 0.776248 | 0.388124 | − | 0.921607i | \(-0.373123\pi\) | ||||
0.388124 | + | 0.921607i | \(0.373123\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 49.7737 | 1.95379 | ||||||||
\(650\) | −29.8368 | −1.17029 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.6551 | −0.573938 | ||||||||
\(653\) | −4.45874 | −0.174484 | −0.0872419 | − | 0.996187i | \(-0.527805\pi\) | ||||
−0.0872419 | + | 0.996187i | \(0.527805\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −45.9104 | −1.79387 | ||||||||
\(656\) | −3.51912 | −0.137399 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.258933 | −0.0100943 | ||||||||
\(659\) | −20.3543 | −0.792890 | −0.396445 | − | 0.918059i | \(-0.629756\pi\) | ||||
−0.396445 | + | 0.918059i | \(0.629756\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.8480 | −1.35543 | −0.677715 | − | 0.735325i | \(-0.737030\pi\) | ||||
−0.677715 | + | 0.735325i | \(0.737030\pi\) | |||||||
\(662\) | 1.14205 | 0.0443871 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −18.8327 | −0.730850 | ||||||||
\(665\) | −22.6161 | −0.877015 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.62858 | −0.140499 | ||||||||
\(668\) | 23.4197 | 0.906136 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −17.5000 | −0.676085 | ||||||||
\(671\) | −44.8670 | −1.73207 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.10381 | −0.158190 | −0.0790952 | − | 0.996867i | \(-0.525203\pi\) | ||||
−0.0790952 | + | 0.996867i | \(0.525203\pi\) | |||||||
\(674\) | −3.52793 | −0.135891 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.18556 | −0.122522 | ||||||||
\(677\) | −8.02022 | −0.308242 | −0.154121 | − | 0.988052i | \(-0.549255\pi\) | ||||
−0.154121 | + | 0.988052i | \(0.549255\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.9733 | 0.421116 | ||||||||
\(680\) | 67.6195 | 2.59309 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 15.9065 | 0.609091 | ||||||||
\(683\) | 3.56422 | 0.136381 | 0.0681906 | − | 0.997672i | \(-0.478277\pi\) | ||||
0.0681906 | + | 0.997672i | \(0.478277\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 86.1371 | 3.29113 | ||||||||
\(686\) | 0.731838 | 0.0279417 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 13.4188 | 0.511587 | ||||||||
\(689\) | −31.8756 | −1.21436 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.6852 | 1.16732 | 0.583660 | − | 0.811998i | \(-0.301620\pi\) | ||||
0.583660 | + | 0.811998i | \(0.301620\pi\) | |||||||
\(692\) | 11.3746 | 0.432397 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.78149 | 0.219462 | ||||||||
\(695\) | 74.9652 | 2.84359 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.2353 | −0.842222 | ||||||||
\(698\) | −18.3473 | −0.694456 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −15.3261 | −0.579272 | ||||||||
\(701\) | −34.2834 | −1.29487 | −0.647434 | − | 0.762122i | \(-0.724158\pi\) | ||||
−0.647434 | + | 0.762122i | \(0.724158\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.8265 | −0.785488 | ||||||||
\(704\) | −9.77045 | −0.368238 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.41946 | 0.0910575 | ||||||||
\(707\) | −3.77928 | −0.142135 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −50.8968 | −1.91147 | −0.955735 | − | 0.294229i | \(-0.904937\pi\) | ||||
−0.955735 | + | 0.294229i | \(0.904937\pi\) | |||||||
\(710\) | 32.8565 | 1.23308 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −17.1751 | −0.643666 | ||||||||
\(713\) | 8.43475 | 0.315884 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −69.9712 | −2.61678 | ||||||||
\(716\) | −34.5984 | −1.29300 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18.8361 | −0.702957 | ||||||||
\(719\) | −4.88651 | −0.182236 | −0.0911181 | − | 0.995840i | \(-0.529044\pi\) | ||||
−0.0911181 | + | 0.995840i | \(0.529044\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.84662 | −0.329465 | ||||||||
\(722\) | 10.2987 | 0.383279 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −32.2172 | −1.19734 | ||||||||
\(725\) | 21.4252 | 0.795713 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.8485 | −0.661963 | −0.330981 | − | 0.943637i | \(-0.607380\pi\) | ||||
−0.330981 | + | 0.943637i | \(0.607380\pi\) | |||||||
\(728\) | 9.87674 | 0.366056 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.28966 | −0.195779 | ||||||||
\(731\) | 84.7856 | 3.13591 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 50.4742 | 1.86431 | 0.932153 | − | 0.362065i | \(-0.117928\pi\) | ||||
0.932153 | + | 0.362065i | \(0.117928\pi\) | |||||||
\(734\) | −0.468787 | −0.0173032 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −10.3801 | −0.382615 | ||||||||
\(737\) | −27.7719 | −1.02299 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.4949 | −1.52642 | −0.763208 | − | 0.646153i | \(-0.776377\pi\) | ||||
−0.763208 | + | 0.646153i | \(0.776377\pi\) | |||||||
\(740\) | −20.8561 | −0.766684 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.98832 | 0.219838 | ||||||||
\(743\) | −48.8699 | −1.79286 | −0.896431 | − | 0.443183i | \(-0.853849\pi\) | ||||
−0.896431 | + | 0.443183i | \(0.853849\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.64755 | −0.280185 | ||||||||
\(746\) | 3.78269 | 0.138494 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 45.3599 | 1.65852 | ||||||||
\(749\) | −11.9793 | −0.437713 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.2391 | 1.03046 | 0.515230 | − | 0.857052i | \(-0.327706\pi\) | ||||
0.515230 | + | 0.857052i | \(0.327706\pi\) | |||||||
\(752\) | −0.379758 | −0.0138484 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.83635 | −0.212547 | ||||||||
\(755\) | −48.5410 | −1.76659 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.4750 | −0.962249 | −0.481124 | − | 0.876652i | \(-0.659771\pi\) | ||||
−0.481124 | + | 0.876652i | \(0.659771\pi\) | |||||||
\(758\) | −24.2250 | −0.879890 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 57.3406 | 2.07996 | ||||||||
\(761\) | 7.30535 | 0.264819 | 0.132409 | − | 0.991195i | \(-0.457729\pi\) | ||||
0.132409 | + | 0.991195i | \(0.457729\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.50483 | 0.199288 | ||||||||
\(764\) | 34.6380 | 1.25316 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.3595 | 0.591091 | ||||||||
\(767\) | 42.4525 | 1.53287 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.7720 | 1.18179 | 0.590894 | − | 0.806749i | \(-0.298775\pi\) | ||||
0.590894 | + | 0.806749i | \(0.298775\pi\) | |||||||
\(770\) | 13.1452 | 0.473718 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 21.3037 | 0.766739 | ||||||||
\(773\) | −16.5359 | −0.594754 | −0.297377 | − | 0.954760i | \(-0.596112\pi\) | ||||
−0.297377 | + | 0.954760i | \(0.596112\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −49.8037 | −1.78900 | ||||||||
\(776\) | −27.8215 | −0.998735 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.79427 | 0.351141 | ||||||||
\(779\) | −18.8553 | −0.675561 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 52.1420 | 1.86579 | ||||||||
\(782\) | −8.79703 | −0.314581 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.07333 | 0.0383333 | ||||||||
\(785\) | −14.2209 | −0.507565 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.9918 | −0.498753 | −0.249376 | − | 0.968407i | \(-0.580226\pi\) | ||||
−0.249376 | + | 0.968407i | \(0.580226\pi\) | |||||||
\(788\) | 12.9882 | 0.462687 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 21.2681 | 0.756684 | ||||||||
\(791\) | 1.11071 | 0.0394924 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.2675 | −1.35892 | ||||||||
\(794\) | 13.4065 | 0.475780 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.3336 | 0.720705 | ||||||||
\(797\) | −3.67638 | −0.130224 | −0.0651121 | − | 0.997878i | \(-0.520741\pi\) | ||||
−0.0651121 | + | 0.997878i | \(0.520741\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.39947 | −0.0848872 | ||||||||
\(800\) | 61.2901 | 2.16693 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.1358 | −0.675708 | ||||||||
\(803\) | −8.39449 | −0.296235 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.97049 | 0.245677 | ||||||||
\(806\) | 13.5668 | 0.477870 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.58195 | 0.337092 | ||||||||
\(809\) | 17.2258 | 0.605628 | 0.302814 | − | 0.953050i | \(-0.402074\pi\) | ||||
0.302814 | + | 0.953050i | \(0.402074\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.5686 | −0.792491 | −0.396245 | − | 0.918145i | \(-0.629687\pi\) | ||||
−0.396245 | + | 0.918145i | \(0.629687\pi\) | |||||||
\(812\) | −2.99793 | −0.105207 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.1050 | 0.424280 | ||||||||
\(815\) | −39.3559 | −1.37858 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 71.8973 | 2.51537 | ||||||||
\(818\) | 15.2284 | 0.532450 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −18.8820 | −0.659389 | ||||||||
\(821\) | 41.6913 | 1.45504 | 0.727518 | − | 0.686089i | \(-0.240674\pi\) | ||||
0.727518 | + | 0.686089i | \(0.240674\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.0148 | 1.49940 | 0.749701 | − | 0.661777i | \(-0.230197\pi\) | ||||
0.749701 | + | 0.661777i | \(0.230197\pi\) | |||||||
\(824\) | 22.4296 | 0.781373 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.97533 | −0.277497 | ||||||||
\(827\) | 37.9685 | 1.32029 | 0.660147 | − | 0.751136i | \(-0.270494\pi\) | ||||
0.660147 | + | 0.751136i | \(0.270494\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.20643 | 0.0766324 | 0.0383162 | − | 0.999266i | \(-0.487801\pi\) | ||||
0.0383162 | + | 0.999266i | \(0.487801\pi\) | |||||||
\(830\) | −21.3780 | −0.742041 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.33330 | −0.288905 | ||||||||
\(833\) | 6.78176 | 0.234974 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 62.8931 | 2.17650 | ||||||||
\(836\) | 38.4647 | 1.33033 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 27.6459 | 0.955013 | ||||||||
\(839\) | −45.0290 | −1.55457 | −0.777287 | − | 0.629147i | \(-0.783405\pi\) | ||||
−0.777287 | + | 0.629147i | \(0.783405\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.8090 | −0.855484 | ||||||||
\(842\) | −0.948341 | −0.0326820 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −19.9717 | −0.687454 | ||||||||
\(845\) | −8.55474 | −0.294292 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.86085 | 0.338823 | ||||||||
\(848\) | 8.78262 | 0.301597 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 51.9428 | 1.78162 | ||||||||
\(851\) | 6.41893 | 0.220038 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.0997 | −1.16755 | −0.583776 | − | 0.811915i | \(-0.698425\pi\) | ||||
−0.583776 | + | 0.811915i | \(0.698425\pi\) | |||||||
\(854\) | 7.18912 | 0.246007 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 30.3721 | 1.03810 | ||||||||
\(857\) | 40.1638 | 1.37197 | 0.685984 | − | 0.727617i | \(-0.259372\pi\) | ||||
0.685984 | + | 0.727617i | \(0.259372\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.9917 | −1.12566 | −0.562831 | − | 0.826572i | \(-0.690288\pi\) | ||||
−0.562831 | + | 0.826572i | \(0.690288\pi\) | |||||||
\(860\) | 71.9992 | 2.45515 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.95667 | 0.271005 | ||||||||
\(863\) | −17.4516 | −0.594060 | −0.297030 | − | 0.954868i | \(-0.595996\pi\) | ||||
−0.297030 | + | 0.954868i | \(0.595996\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.5462 | 1.03860 | ||||||||
\(866\) | −8.33117 | −0.283105 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.96879 | 0.236536 | ||||||||
\(869\) | 33.7516 | 1.14494 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.6869 | −0.802600 | ||||||||
\(872\) | −13.9569 | −0.472640 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.45979 | −0.252331 | ||||||||
\(875\) | −21.4946 | −0.726651 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −48.5747 | −1.64025 | −0.820125 | − | 0.572184i | \(-0.806096\pi\) | ||||
−0.820125 | + | 0.572184i | \(0.806096\pi\) | |||||||
\(878\) | 6.26320 | 0.211373 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 19.2790 | 0.649896 | ||||||||
\(881\) | 13.9540 | 0.470123 | 0.235062 | − | 0.971980i | \(-0.424471\pi\) | ||||
0.235062 | + | 0.971980i | \(0.424471\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.7927 | −0.430509 | −0.215255 | − | 0.976558i | \(-0.569058\pi\) | ||||
−0.215255 | + | 0.976558i | \(0.569058\pi\) | |||||||
\(884\) | 38.6879 | 1.30121 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.2570 | 0.512568 | ||||||||
\(887\) | 18.7133 | 0.628332 | 0.314166 | − | 0.949368i | \(-0.398275\pi\) | ||||
0.314166 | + | 0.949368i | \(0.398275\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | −19.4964 | −0.653522 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.3690 | 0.447627 | ||||||||
\(893\) | −2.03473 | −0.0680895 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −92.9132 | −3.10575 | ||||||||
\(896\) | −10.1470 | −0.338988 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.5926 | 0.587072 | ||||||||
\(899\) | −9.74207 | −0.324916 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 55.4923 | 1.84872 | ||||||||
\(902\) | 10.9593 | 0.364903 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.81609 | −0.0936617 | ||||||||
\(905\) | −86.5184 | −2.87597 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.2333 | −0.339791 | −0.169896 | − | 0.985462i | \(-0.554343\pi\) | ||||
−0.169896 | + | 0.985462i | \(0.554343\pi\) | |||||||
\(908\) | 37.9654 | 1.25993 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 11.2116 | 0.371662 | ||||||||
\(911\) | −6.73786 | −0.223235 | −0.111618 | − | 0.993751i | \(-0.535603\pi\) | ||||
−0.111618 | + | 0.993751i | \(0.535603\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.9261 | −1.12279 | ||||||||
\(914\) | −12.3284 | −0.407787 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.81645 | −0.291304 | ||||||||
\(917\) | 11.6742 | 0.385516 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.4499 | 0.476658 | 0.238329 | − | 0.971184i | \(-0.423400\pi\) | ||||
0.238329 | + | 0.971184i | \(0.423400\pi\) | |||||||
\(920\) | −17.6729 | −0.582658 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.51524 | 0.0499019 | ||||||||
\(923\) | 44.4724 | 1.46383 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −37.9011 | −1.24618 | ||||||||
\(926\) | −3.50660 | −0.115234 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 11.9889 | 0.393555 | ||||||||
\(929\) | 11.8627 | 0.389203 | 0.194601 | − | 0.980882i | \(-0.437659\pi\) | ||||
0.194601 | + | 0.980882i | \(0.437659\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.75086 | 0.188477 | ||||||||
\(932\) | −3.62098 | −0.118609 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 12.4301 | 0.406725 | ||||||||
\(935\) | 121.813 | 3.98371 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.41053 | −0.307429 | −0.153714 | − | 0.988115i | \(-0.549124\pi\) | ||||
−0.153714 | + | 0.988115i | \(0.549124\pi\) | |||||||
\(938\) | 4.44994 | 0.145296 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.03761 | −0.0664596 | ||||||||
\(941\) | 17.2696 | 0.562974 | 0.281487 | − | 0.959565i | \(-0.409172\pi\) | ||||
0.281487 | + | 0.959565i | \(0.409172\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.81138 | 0.189244 | ||||||||
\(944\) | −11.6968 | −0.380700 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −41.7888 | −1.35867 | ||||||||
\(947\) | −12.8026 | −0.416030 | −0.208015 | − | 0.978126i | \(-0.566700\pi\) | ||||
−0.208015 | + | 0.978126i | \(0.566700\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.15973 | −0.232415 | ||||||||
\(950\) | 44.0470 | 1.42907 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −17.1944 | −0.557274 | ||||||||
\(953\) | −33.1957 | −1.07531 | −0.537657 | − | 0.843164i | \(-0.680690\pi\) | ||||
−0.537657 | + | 0.843164i | \(0.680690\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 93.0195 | 3.01004 | ||||||||
\(956\) | 31.9923 | 1.03471 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13.9339 | −0.450184 | ||||||||
\(959\) | −21.9031 | −0.707288 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.35421 | −0.269490 | ||||||||
\(962\) | 10.3245 | 0.332874 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.4860 | 0.337731 | ||||||||
\(965\) | 57.2107 | 1.84168 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.4000 | 1.33133 | 0.665667 | − | 0.746249i | \(-0.268147\pi\) | ||||
0.665667 | + | 0.746249i | \(0.268147\pi\) | |||||||
\(968\) | −25.0011 | −0.803566 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −31.5817 | −1.01403 | ||||||||
\(971\) | −28.4833 | −0.914072 | −0.457036 | − | 0.889448i | \(-0.651089\pi\) | ||||
−0.457036 | + | 0.889448i | \(0.651089\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.0623 | −0.611109 | ||||||||
\(974\) | −17.5033 | −0.560842 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.5438 | 0.337497 | ||||||||
\(977\) | −43.3674 | −1.38745 | −0.693723 | − | 0.720242i | \(-0.744031\pi\) | ||||
−0.693723 | + | 0.720242i | \(0.744031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.9401 | −0.988850 | ||||||||
\(980\) | 5.75902 | 0.183965 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −28.2798 | −0.902444 | ||||||||
\(983\) | −18.7401 | −0.597715 | −0.298857 | − | 0.954298i | \(-0.596606\pi\) | ||||
−0.298857 | + | 0.954298i | \(0.596606\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.8796 | 1.11136 | ||||||||
\(986\) | 10.1605 | 0.323576 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 32.8069 | 1.04373 | ||||||||
\(989\) | −22.1594 | −0.704628 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.6186 | 1.44912 | 0.724561 | − | 0.689211i | \(-0.242043\pi\) | ||||
0.724561 | + | 0.689211i | \(0.242043\pi\) | |||||||
\(992\) | −27.8686 | −0.884830 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.35482 | −0.264999 | ||||||||
\(995\) | 54.6053 | 1.73110 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.1661 | 1.05038 | 0.525190 | − | 0.850985i | \(-0.323994\pi\) | ||||
0.525190 | + | 0.850985i | \(0.323994\pi\) | |||||||
\(998\) | 20.7137 | 0.655681 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.w.1.15 | 20 | ||
3.2 | odd | 2 | 889.2.a.d.1.6 | ✓ | 20 | ||
21.20 | even | 2 | 6223.2.a.l.1.6 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
889.2.a.d.1.6 | ✓ | 20 | 3.2 | odd | 2 | ||
6223.2.a.l.1.6 | 20 | 21.20 | even | 2 | |||
8001.2.a.w.1.15 | 20 | 1.1 | even | 1 | trivial |