Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1351,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.1 | ||
Root | \(-1.24698i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.x.1351.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5070\mathbb{Z}\right)^\times\).
\(n\) | \(1691\) | \(1861\) | \(4057\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | − 1.00000i | − 0.408248i | ||||||||
\(7\) | − 0.801938i | − 0.303104i | −0.988449 | − | 0.151552i | \(-0.951573\pi\) | ||||
0.988449 | − | 0.151552i | \(-0.0484271\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | − 3.04892i | − 0.919283i | −0.888105 | − | 0.459642i | \(-0.847978\pi\) | ||||
0.888105 | − | 0.459642i | \(-0.152022\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.801938 | −0.214327 | ||||||||
\(15\) | − 1.00000i | − 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.24698 | 0.302437 | 0.151218 | − | 0.988500i | \(-0.451680\pi\) | ||||
0.151218 | + | 0.988500i | \(0.451680\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | − 7.40581i | − 1.69901i | −0.527581 | − | 0.849505i | \(-0.676901\pi\) | ||||
0.527581 | − | 0.849505i | \(-0.323099\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | − 0.801938i | − 0.174997i | ||||||||
\(22\) | −3.04892 | −0.650031 | ||||||||
\(23\) | 0.356896 | 0.0744179 | 0.0372090 | − | 0.999308i | \(-0.488153\pi\) | ||||
0.0372090 | + | 0.999308i | \(0.488153\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.801938i | 0.151552i | ||||||||
\(29\) | 0.307979 | 0.0571902 | 0.0285951 | − | 0.999591i | \(-0.490897\pi\) | ||||
0.0285951 | + | 0.999591i | \(0.490897\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | − 3.44504i | − 0.618748i | −0.950940 | − | 0.309374i | \(-0.899881\pi\) | ||||
0.950940 | − | 0.309374i | \(-0.100119\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | − 3.04892i | − 0.530748i | ||||||||
\(34\) | − 1.24698i | − 0.213855i | ||||||||
\(35\) | −0.801938 | −0.135552 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 7.29590i | 1.19944i | 0.800211 | + | 0.599719i | \(0.204721\pi\) | ||||
−0.800211 | + | 0.599719i | \(0.795279\pi\) | |||||||
\(38\) | −7.40581 | −1.20138 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | − 3.40581i | − 0.531899i | −0.963987 | − | 0.265949i | \(-0.914315\pi\) | ||||
0.963987 | − | 0.265949i | \(-0.0856854\pi\) | |||||||
\(42\) | −0.801938 | −0.123742 | ||||||||
\(43\) | −6.54288 | −0.997779 | −0.498890 | − | 0.866666i | \(-0.666259\pi\) | ||||
−0.498890 | + | 0.866666i | \(0.666259\pi\) | |||||||
\(44\) | 3.04892i | 0.459642i | ||||||||
\(45\) | − 1.00000i | − 0.149071i | ||||||||
\(46\) | − 0.356896i | − 0.0526214i | ||||||||
\(47\) | 0.603875i | 0.0880843i | 0.999030 | + | 0.0440421i | \(0.0140236\pi\) | ||||
−0.999030 | + | 0.0440421i | \(0.985976\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 6.35690 | 0.908128 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | 1.24698 | 0.174612 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.29590 | −0.864808 | −0.432404 | − | 0.901680i | \(-0.642335\pi\) | ||||
−0.432404 | + | 0.901680i | \(0.642335\pi\) | |||||||
\(54\) | − 1.00000i | − 0.136083i | ||||||||
\(55\) | −3.04892 | −0.411116 | ||||||||
\(56\) | 0.801938 | 0.107163 | ||||||||
\(57\) | − 7.40581i | − 0.980924i | ||||||||
\(58\) | − 0.307979i | − 0.0404396i | ||||||||
\(59\) | 3.11529i | 0.405577i | 0.979223 | + | 0.202788i | \(0.0650003\pi\) | ||||
−0.979223 | + | 0.202788i | \(0.935000\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | 11.0368 | 1.41312 | 0.706561 | − | 0.707652i | \(-0.250246\pi\) | ||||
0.706561 | + | 0.707652i | \(0.250246\pi\) | |||||||
\(62\) | −3.44504 | −0.437521 | ||||||||
\(63\) | − 0.801938i | − 0.101035i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.04892 | −0.375296 | ||||||||
\(67\) | − 5.96077i | − 0.728224i | −0.931355 | − | 0.364112i | \(-0.881373\pi\) | ||||
0.931355 | − | 0.364112i | \(-0.118627\pi\) | |||||||
\(68\) | −1.24698 | −0.151218 | ||||||||
\(69\) | 0.356896 | 0.0429652 | ||||||||
\(70\) | 0.801938i | 0.0958499i | ||||||||
\(71\) | − 6.67456i | − 0.792125i | −0.918224 | − | 0.396062i | \(-0.870376\pi\) | ||||
0.918224 | − | 0.396062i | \(-0.129624\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 10.1371i | 1.18645i | 0.805035 | + | 0.593227i | \(0.202146\pi\) | ||||
−0.805035 | + | 0.593227i | \(0.797854\pi\) | |||||||
\(74\) | 7.29590 | 0.848131 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 7.40581i | 0.849505i | ||||||||
\(77\) | −2.44504 | −0.278638 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.6799 | −1.53911 | −0.769557 | − | 0.638578i | \(-0.779523\pi\) | ||||
−0.769557 | + | 0.638578i | \(0.779523\pi\) | |||||||
\(80\) | − 1.00000i | − 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.40581 | −0.376109 | ||||||||
\(83\) | 3.93900i | 0.432362i | 0.976353 | + | 0.216181i | \(0.0693601\pi\) | ||||
−0.976353 | + | 0.216181i | \(0.930640\pi\) | |||||||
\(84\) | 0.801938i | 0.0874986i | ||||||||
\(85\) | − 1.24698i | − 0.135254i | ||||||||
\(86\) | 6.54288i | 0.705537i | ||||||||
\(87\) | 0.307979 | 0.0330188 | ||||||||
\(88\) | 3.04892 | 0.325016 | ||||||||
\(89\) | − 8.05861i | − 0.854211i | −0.904202 | − | 0.427105i | \(-0.859533\pi\) | ||||
0.904202 | − | 0.427105i | \(-0.140467\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.356896 | −0.0372090 | ||||||||
\(93\) | − 3.44504i | − 0.357234i | ||||||||
\(94\) | 0.603875 | 0.0622850 | ||||||||
\(95\) | −7.40581 | −0.759820 | ||||||||
\(96\) | − 1.00000i | − 0.102062i | ||||||||
\(97\) | − 9.73556i | − 0.988497i | −0.869321 | − | 0.494248i | \(-0.835443\pi\) | ||||
0.869321 | − | 0.494248i | \(-0.164557\pi\) | |||||||
\(98\) | − 6.35690i | − 0.642143i | ||||||||
\(99\) | − 3.04892i | − 0.306428i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −7.65817 | −0.762016 | −0.381008 | − | 0.924572i | \(-0.624423\pi\) | ||||
−0.381008 | + | 0.924572i | \(0.624423\pi\) | |||||||
\(102\) | − 1.24698i | − 0.123469i | ||||||||
\(103\) | −2.32975 | −0.229557 | −0.114778 | − | 0.993391i | \(-0.536616\pi\) | ||||
−0.114778 | + | 0.993391i | \(0.536616\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.801938 | −0.0782611 | ||||||||
\(106\) | 6.29590i | 0.611512i | ||||||||
\(107\) | 3.77479 | 0.364923 | 0.182461 | − | 0.983213i | \(-0.441594\pi\) | ||||
0.182461 | + | 0.983213i | \(0.441594\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 1.05861i | 0.101396i | 0.998714 | + | 0.0506980i | \(0.0161446\pi\) | ||||
−0.998714 | + | 0.0506980i | \(0.983855\pi\) | |||||||
\(110\) | 3.04892i | 0.290703i | ||||||||
\(111\) | 7.29590i | 0.692496i | ||||||||
\(112\) | − 0.801938i | − 0.0757760i | ||||||||
\(113\) | 11.0368 | 1.03826 | 0.519129 | − | 0.854696i | \(-0.326256\pi\) | ||||
0.519129 | + | 0.854696i | \(0.326256\pi\) | |||||||
\(114\) | −7.40581 | −0.693618 | ||||||||
\(115\) | − 0.356896i | − 0.0332807i | ||||||||
\(116\) | −0.307979 | −0.0285951 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.11529 | 0.286786 | ||||||||
\(119\) | − 1.00000i | − 0.0916698i | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 1.70410 | 0.154918 | ||||||||
\(122\) | − 11.0368i | − 0.999228i | ||||||||
\(123\) | − 3.40581i | − 0.307092i | ||||||||
\(124\) | 3.44504i | 0.309374i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −0.801938 | −0.0714423 | ||||||||
\(127\) | −15.9541 | −1.41569 | −0.707847 | − | 0.706366i | \(-0.750333\pi\) | ||||
−0.707847 | + | 0.706366i | \(0.750333\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −6.54288 | −0.576068 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.0911 | −1.49326 | −0.746629 | − | 0.665240i | \(-0.768329\pi\) | ||||
−0.746629 | + | 0.665240i | \(0.768329\pi\) | |||||||
\(132\) | 3.04892i | 0.265374i | ||||||||
\(133\) | −5.93900 | −0.514977 | ||||||||
\(134\) | −5.96077 | −0.514932 | ||||||||
\(135\) | − 1.00000i | − 0.0860663i | ||||||||
\(136\) | 1.24698i | 0.106928i | ||||||||
\(137\) | − 16.4373i | − 1.40433i | −0.712014 | − | 0.702165i | \(-0.752217\pi\) | ||||
0.712014 | − | 0.702165i | \(-0.247783\pi\) | |||||||
\(138\) | − 0.356896i | − 0.0303810i | ||||||||
\(139\) | −8.10992 | −0.687874 | −0.343937 | − | 0.938993i | \(-0.611761\pi\) | ||||
−0.343937 | + | 0.938993i | \(0.611761\pi\) | |||||||
\(140\) | 0.801938 | 0.0677761 | ||||||||
\(141\) | 0.603875i | 0.0508555i | ||||||||
\(142\) | −6.67456 | −0.560117 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | − 0.307979i | − 0.0255762i | ||||||||
\(146\) | 10.1371 | 0.838949 | ||||||||
\(147\) | 6.35690 | 0.524308 | ||||||||
\(148\) | − 7.29590i | − 0.599719i | ||||||||
\(149\) | − 11.0532i | − 0.905516i | −0.891633 | − | 0.452758i | \(-0.850440\pi\) | ||||
0.891633 | − | 0.452758i | \(-0.149560\pi\) | |||||||
\(150\) | 1.00000i | 0.0816497i | ||||||||
\(151\) | 6.89546i | 0.561145i | 0.959833 | + | 0.280572i | \(0.0905242\pi\) | ||||
−0.959833 | + | 0.280572i | \(0.909476\pi\) | |||||||
\(152\) | 7.40581 | 0.600691 | ||||||||
\(153\) | 1.24698 | 0.100812 | ||||||||
\(154\) | 2.44504i | 0.197027i | ||||||||
\(155\) | −3.44504 | −0.276712 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.8388 | −1.66312 | −0.831558 | − | 0.555439i | \(-0.812550\pi\) | ||||
−0.831558 | + | 0.555439i | \(0.812550\pi\) | |||||||
\(158\) | 13.6799i | 1.08832i | ||||||||
\(159\) | −6.29590 | −0.499297 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | − 0.286208i | − 0.0225564i | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | − 4.71917i | − 0.369634i | −0.982773 | − | 0.184817i | \(-0.940831\pi\) | ||||
0.982773 | − | 0.184817i | \(-0.0591692\pi\) | |||||||
\(164\) | 3.40581i | 0.265949i | ||||||||
\(165\) | −3.04892 | −0.237358 | ||||||||
\(166\) | 3.93900 | 0.305726 | ||||||||
\(167\) | − 14.5308i | − 1.12443i | −0.826992 | − | 0.562213i | \(-0.809950\pi\) | ||||
0.826992 | − | 0.562213i | \(-0.190050\pi\) | |||||||
\(168\) | 0.801938 | 0.0618708 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1.24698 | −0.0956390 | ||||||||
\(171\) | − 7.40581i | − 0.566337i | ||||||||
\(172\) | 6.54288 | 0.498890 | ||||||||
\(173\) | −11.4523 | −0.870705 | −0.435353 | − | 0.900260i | \(-0.643376\pi\) | ||||
−0.435353 | + | 0.900260i | \(0.643376\pi\) | |||||||
\(174\) | − 0.307979i | − 0.0233478i | ||||||||
\(175\) | 0.801938i | 0.0606208i | ||||||||
\(176\) | − 3.04892i | − 0.229821i | ||||||||
\(177\) | 3.11529i | 0.234160i | ||||||||
\(178\) | −8.05861 | −0.604018 | ||||||||
\(179\) | 4.32975 | 0.323621 | 0.161810 | − | 0.986822i | \(-0.448267\pi\) | ||||
0.161810 | + | 0.986822i | \(0.448267\pi\) | |||||||
\(180\) | 1.00000i | 0.0745356i | ||||||||
\(181\) | 24.8321 | 1.84575 | 0.922877 | − | 0.385096i | \(-0.125832\pi\) | ||||
0.922877 | + | 0.385096i | \(0.125832\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.0368 | 0.815866 | ||||||||
\(184\) | 0.356896i | 0.0263107i | ||||||||
\(185\) | 7.29590 | 0.536405 | ||||||||
\(186\) | −3.44504 | −0.252603 | ||||||||
\(187\) | − 3.80194i | − 0.278025i | ||||||||
\(188\) | − 0.603875i | − 0.0440421i | ||||||||
\(189\) | − 0.801938i | − 0.0583324i | ||||||||
\(190\) | 7.40581i | 0.537274i | ||||||||
\(191\) | 22.1933 | 1.60585 | 0.802925 | − | 0.596081i | \(-0.203276\pi\) | ||||
0.802925 | + | 0.596081i | \(0.203276\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 25.4306i | 1.83053i | 0.402850 | + | 0.915266i | \(0.368020\pi\) | ||||
−0.402850 | + | 0.915266i | \(0.631980\pi\) | |||||||
\(194\) | −9.73556 | −0.698973 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.35690 | −0.454064 | ||||||||
\(197\) | 10.6310i | 0.757429i | 0.925514 | + | 0.378714i | \(0.123634\pi\) | ||||
−0.925514 | + | 0.378714i | \(0.876366\pi\) | |||||||
\(198\) | −3.04892 | −0.216677 | ||||||||
\(199\) | −11.0465 | −0.783067 | −0.391534 | − | 0.920164i | \(-0.628055\pi\) | ||||
−0.391534 | + | 0.920164i | \(0.628055\pi\) | |||||||
\(200\) | − 1.00000i | − 0.0707107i | ||||||||
\(201\) | − 5.96077i | − 0.420440i | ||||||||
\(202\) | 7.65817i | 0.538827i | ||||||||
\(203\) | − 0.246980i | − 0.0173346i | ||||||||
\(204\) | −1.24698 | −0.0873060 | ||||||||
\(205\) | −3.40581 | −0.237872 | ||||||||
\(206\) | 2.32975i | 0.162321i | ||||||||
\(207\) | 0.356896 | 0.0248060 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.5797 | −1.56187 | ||||||||
\(210\) | 0.801938i | 0.0553390i | ||||||||
\(211\) | −21.3491 | −1.46973 | −0.734867 | − | 0.678211i | \(-0.762756\pi\) | ||||
−0.734867 | + | 0.678211i | \(0.762756\pi\) | |||||||
\(212\) | 6.29590 | 0.432404 | ||||||||
\(213\) | − 6.67456i | − 0.457334i | ||||||||
\(214\) | − 3.77479i | − 0.258039i | ||||||||
\(215\) | 6.54288i | 0.446220i | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −2.76271 | −0.187545 | ||||||||
\(218\) | 1.05861 | 0.0716978 | ||||||||
\(219\) | 10.1371i | 0.684999i | ||||||||
\(220\) | 3.04892 | 0.205558 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 7.29590 | 0.489669 | ||||||||
\(223\) | 12.7603i | 0.854494i | 0.904135 | + | 0.427247i | \(0.140517\pi\) | ||||
−0.904135 | + | 0.427247i | \(0.859483\pi\) | |||||||
\(224\) | −0.801938 | −0.0535817 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | − 11.0368i | − 0.734159i | ||||||||
\(227\) | − 14.1836i | − 0.941398i | −0.882294 | − | 0.470699i | \(-0.844002\pi\) | ||||
0.882294 | − | 0.470699i | \(-0.155998\pi\) | |||||||
\(228\) | 7.40581i | 0.490462i | ||||||||
\(229\) | − 4.71140i | − 0.311338i | −0.987809 | − | 0.155669i | \(-0.950247\pi\) | ||||
0.987809 | − | 0.155669i | \(-0.0497533\pi\) | |||||||
\(230\) | −0.356896 | −0.0235330 | ||||||||
\(231\) | −2.44504 | −0.160872 | ||||||||
\(232\) | 0.307979i | 0.0202198i | ||||||||
\(233\) | −0.0556221 | −0.00364393 | −0.00182196 | − | 0.999998i | \(-0.500580\pi\) | ||||
−0.00182196 | + | 0.999998i | \(0.500580\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.603875 | 0.0393925 | ||||||||
\(236\) | − 3.11529i | − 0.202788i | ||||||||
\(237\) | −13.6799 | −0.888608 | ||||||||
\(238\) | −1.00000 | −0.0648204 | ||||||||
\(239\) | − 21.0489i | − 1.36154i | −0.732497 | − | 0.680771i | \(-0.761645\pi\) | ||||
0.732497 | − | 0.680771i | \(-0.238355\pi\) | |||||||
\(240\) | − 1.00000i | − 0.0645497i | ||||||||
\(241\) | − 12.0030i | − 0.773180i | −0.922252 | − | 0.386590i | \(-0.873653\pi\) | ||||
0.922252 | − | 0.386590i | \(-0.126347\pi\) | |||||||
\(242\) | − 1.70410i | − 0.109544i | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −11.0368 | −0.706561 | ||||||||
\(245\) | − 6.35690i | − 0.406127i | ||||||||
\(246\) | −3.40581 | −0.217147 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.44504 | 0.218760 | ||||||||
\(249\) | 3.93900i | 0.249624i | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 2.25906 | 0.142591 | 0.0712953 | − | 0.997455i | \(-0.477287\pi\) | ||||
0.0712953 | + | 0.997455i | \(0.477287\pi\) | |||||||
\(252\) | 0.801938i | 0.0505173i | ||||||||
\(253\) | − 1.08815i | − 0.0684112i | ||||||||
\(254\) | 15.9541i | 1.00105i | ||||||||
\(255\) | − 1.24698i | − 0.0780889i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.0043 | 1.06070 | 0.530350 | − | 0.847779i | \(-0.322061\pi\) | ||||
0.530350 | + | 0.847779i | \(0.322061\pi\) | |||||||
\(258\) | 6.54288i | 0.407342i | ||||||||
\(259\) | 5.85086 | 0.363554 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.307979 | 0.0190634 | ||||||||
\(262\) | 17.0911i | 1.05589i | ||||||||
\(263\) | −28.5773 | −1.76215 | −0.881077 | − | 0.472974i | \(-0.843181\pi\) | ||||
−0.881077 | + | 0.472974i | \(0.843181\pi\) | |||||||
\(264\) | 3.04892 | 0.187648 | ||||||||
\(265\) | 6.29590i | 0.386754i | ||||||||
\(266\) | 5.93900i | 0.364144i | ||||||||
\(267\) | − 8.05861i | − 0.493179i | ||||||||
\(268\) | 5.96077i | 0.364112i | ||||||||
\(269\) | −3.28083 | −0.200036 | −0.100018 | − | 0.994986i | \(-0.531890\pi\) | ||||
−0.100018 | + | 0.994986i | \(0.531890\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | − 8.70948i | − 0.529063i | −0.964377 | − | 0.264532i | \(-0.914783\pi\) | ||||
0.964377 | − | 0.264532i | \(-0.0852173\pi\) | |||||||
\(272\) | 1.24698 | 0.0756092 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.4373 | −0.993012 | ||||||||
\(275\) | 3.04892i | 0.183857i | ||||||||
\(276\) | −0.356896 | −0.0214826 | ||||||||
\(277\) | 8.91185 | 0.535461 | 0.267731 | − | 0.963494i | \(-0.413726\pi\) | ||||
0.267731 | + | 0.963494i | \(0.413726\pi\) | |||||||
\(278\) | 8.10992i | 0.486400i | ||||||||
\(279\) | − 3.44504i | − 0.206249i | ||||||||
\(280\) | − 0.801938i | − 0.0479249i | ||||||||
\(281\) | − 1.90648i | − 0.113731i | −0.998382 | − | 0.0568654i | \(-0.981889\pi\) | ||||
0.998382 | − | 0.0568654i | \(-0.0181106\pi\) | |||||||
\(282\) | 0.603875 | 0.0359603 | ||||||||
\(283\) | 14.9245 | 0.887171 | 0.443586 | − | 0.896232i | \(-0.353706\pi\) | ||||
0.443586 | + | 0.896232i | \(0.353706\pi\) | |||||||
\(284\) | 6.67456i | 0.396062i | ||||||||
\(285\) | −7.40581 | −0.438683 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.73125 | −0.161221 | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | −15.4450 | −0.908532 | ||||||||
\(290\) | −0.307979 | −0.0180851 | ||||||||
\(291\) | − 9.73556i | − 0.570709i | ||||||||
\(292\) | − 10.1371i | − 0.593227i | ||||||||
\(293\) | − 12.8901i | − 0.753047i | −0.926407 | − | 0.376523i | \(-0.877119\pi\) | ||||
0.926407 | − | 0.376523i | \(-0.122881\pi\) | |||||||
\(294\) | − 6.35690i | − 0.370742i | ||||||||
\(295\) | 3.11529 | 0.181379 | ||||||||
\(296\) | −7.29590 | −0.424065 | ||||||||
\(297\) | − 3.04892i | − 0.176916i | ||||||||
\(298\) | −11.0532 | −0.640296 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 5.24698i | 0.302431i | ||||||||
\(302\) | 6.89546 | 0.396789 | ||||||||
\(303\) | −7.65817 | −0.439950 | ||||||||
\(304\) | − 7.40581i | − 0.424753i | ||||||||
\(305\) | − 11.0368i | − 0.631967i | ||||||||
\(306\) | − 1.24698i | − 0.0712851i | ||||||||
\(307\) | 19.2892i | 1.10089i | 0.834871 | + | 0.550446i | \(0.185542\pi\) | ||||
−0.834871 | + | 0.550446i | \(0.814458\pi\) | |||||||
\(308\) | 2.44504 | 0.139319 | ||||||||
\(309\) | −2.32975 | −0.132535 | ||||||||
\(310\) | 3.44504i | 0.195665i | ||||||||
\(311\) | −1.23729 | −0.0701603 | −0.0350802 | − | 0.999385i | \(-0.511169\pi\) | ||||
−0.0350802 | + | 0.999385i | \(0.511169\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.09113 | 0.457338 | 0.228669 | − | 0.973504i | \(-0.426563\pi\) | ||||
0.228669 | + | 0.973504i | \(0.426563\pi\) | |||||||
\(314\) | 20.8388i | 1.17600i | ||||||||
\(315\) | −0.801938 | −0.0451841 | ||||||||
\(316\) | 13.6799 | 0.769557 | ||||||||
\(317\) | 21.0368i | 1.18155i | 0.806838 | + | 0.590773i | \(0.201177\pi\) | ||||
−0.806838 | + | 0.590773i | \(0.798823\pi\) | |||||||
\(318\) | 6.29590i | 0.353056i | ||||||||
\(319\) | − 0.939001i | − 0.0525740i | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | 3.77479 | 0.210688 | ||||||||
\(322\) | −0.286208 | −0.0159498 | ||||||||
\(323\) | − 9.23490i | − 0.513843i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.71917 | −0.261371 | ||||||||
\(327\) | 1.05861i | 0.0585410i | ||||||||
\(328\) | 3.40581 | 0.188055 | ||||||||
\(329\) | 0.484271 | 0.0266987 | ||||||||
\(330\) | 3.04892i | 0.167837i | ||||||||
\(331\) | 29.4252i | 1.61735i | 0.588252 | + | 0.808677i | \(0.299816\pi\) | ||||
−0.588252 | + | 0.808677i | \(0.700184\pi\) | |||||||
\(332\) | − 3.93900i | − 0.216181i | ||||||||
\(333\) | 7.29590i | 0.399813i | ||||||||
\(334\) | −14.5308 | −0.795090 | ||||||||
\(335\) | −5.96077 | −0.325672 | ||||||||
\(336\) | − 0.801938i | − 0.0437493i | ||||||||
\(337\) | 17.5483 | 0.955914 | 0.477957 | − | 0.878383i | \(-0.341377\pi\) | ||||
0.477957 | + | 0.878383i | \(0.341377\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.0368 | 0.599439 | ||||||||
\(340\) | 1.24698i | 0.0676270i | ||||||||
\(341\) | −10.5036 | −0.568804 | ||||||||
\(342\) | −7.40581 | −0.400461 | ||||||||
\(343\) | − 10.7114i | − 0.578361i | ||||||||
\(344\) | − 6.54288i | − 0.352768i | ||||||||
\(345\) | − 0.356896i | − 0.0192146i | ||||||||
\(346\) | 11.4523i | 0.615681i | ||||||||
\(347\) | 1.27844 | 0.0686302 | 0.0343151 | − | 0.999411i | \(-0.489075\pi\) | ||||
0.0343151 | + | 0.999411i | \(0.489075\pi\) | |||||||
\(348\) | −0.307979 | −0.0165094 | ||||||||
\(349\) | 18.0911i | 0.968396i | 0.874958 | + | 0.484198i | \(0.160889\pi\) | ||||
−0.874958 | + | 0.484198i | \(0.839111\pi\) | |||||||
\(350\) | 0.801938 | 0.0428654 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.04892 | −0.162508 | ||||||||
\(353\) | 18.9071i | 1.00632i | 0.864193 | + | 0.503161i | \(0.167830\pi\) | ||||
−0.864193 | + | 0.503161i | \(0.832170\pi\) | |||||||
\(354\) | 3.11529 | 0.165576 | ||||||||
\(355\) | −6.67456 | −0.354249 | ||||||||
\(356\) | 8.05861i | 0.427105i | ||||||||
\(357\) | − 1.00000i | − 0.0529256i | ||||||||
\(358\) | − 4.32975i | − 0.228834i | ||||||||
\(359\) | 32.7308i | 1.72746i | 0.503951 | + | 0.863732i | \(0.331879\pi\) | ||||
−0.503951 | + | 0.863732i | \(0.668121\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −35.8461 | −1.88664 | ||||||||
\(362\) | − 24.8321i | − 1.30514i | ||||||||
\(363\) | 1.70410 | 0.0894422 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.1371 | 0.530598 | ||||||||
\(366\) | − 11.0368i | − 0.576905i | ||||||||
\(367\) | −3.10321 | −0.161986 | −0.0809932 | − | 0.996715i | \(-0.525809\pi\) | ||||
−0.0809932 | + | 0.996715i | \(0.525809\pi\) | |||||||
\(368\) | 0.356896 | 0.0186045 | ||||||||
\(369\) | − 3.40581i | − 0.177300i | ||||||||
\(370\) | − 7.29590i | − 0.379296i | ||||||||
\(371\) | 5.04892i | 0.262127i | ||||||||
\(372\) | 3.44504i | 0.178617i | ||||||||
\(373\) | 13.7366 | 0.711256 | 0.355628 | − | 0.934628i | \(-0.384267\pi\) | ||||
0.355628 | + | 0.934628i | \(0.384267\pi\) | |||||||
\(374\) | −3.80194 | −0.196594 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | −0.603875 | −0.0311425 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.801938 | −0.0412472 | ||||||||
\(379\) | − 34.0097i | − 1.74696i | −0.486860 | − | 0.873480i | \(-0.661858\pi\) | ||||
0.486860 | − | 0.873480i | \(-0.338142\pi\) | |||||||
\(380\) | 7.40581 | 0.379910 | ||||||||
\(381\) | −15.9541 | −0.817352 | ||||||||
\(382\) | − 22.1933i | − 1.13551i | ||||||||
\(383\) | − 38.6902i | − 1.97698i | −0.151293 | − | 0.988489i | \(-0.548344\pi\) | ||||
0.151293 | − | 0.988489i | \(-0.451656\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 2.44504i | 0.124611i | ||||||||
\(386\) | 25.4306 | 1.29438 | ||||||||
\(387\) | −6.54288 | −0.332593 | ||||||||
\(388\) | 9.73556i | 0.494248i | ||||||||
\(389\) | 11.2567 | 0.570736 | 0.285368 | − | 0.958418i | \(-0.407884\pi\) | ||||
0.285368 | + | 0.958418i | \(0.407884\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.445042 | 0.0225067 | ||||||||
\(392\) | 6.35690i | 0.321072i | ||||||||
\(393\) | −17.0911 | −0.862133 | ||||||||
\(394\) | 10.6310 | 0.535583 | ||||||||
\(395\) | 13.6799i | 0.688312i | ||||||||
\(396\) | 3.04892i | 0.153214i | ||||||||
\(397\) | − 23.4403i | − 1.17643i | −0.808704 | − | 0.588216i | \(-0.799830\pi\) | ||||
0.808704 | − | 0.588216i | \(-0.200170\pi\) | |||||||
\(398\) | 11.0465i | 0.553712i | ||||||||
\(399\) | −5.93900 | −0.297322 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | − 37.6950i | − 1.88240i | −0.337852 | − | 0.941199i | \(-0.609700\pi\) | ||||
0.337852 | − | 0.941199i | \(-0.390300\pi\) | |||||||
\(402\) | −5.96077 | −0.297296 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 7.65817 | 0.381008 | ||||||||
\(405\) | − 1.00000i | − 0.0496904i | ||||||||
\(406\) | −0.246980 | −0.0122574 | ||||||||
\(407\) | 22.2446 | 1.10262 | ||||||||
\(408\) | 1.24698i | 0.0617347i | ||||||||
\(409\) | 1.19567i | 0.0591220i | 0.999563 | + | 0.0295610i | \(0.00941094\pi\) | ||||
−0.999563 | + | 0.0295610i | \(0.990589\pi\) | |||||||
\(410\) | 3.40581i | 0.168201i | ||||||||
\(411\) | − 16.4373i | − 0.810791i | ||||||||
\(412\) | 2.32975 | 0.114778 | ||||||||
\(413\) | 2.49827 | 0.122932 | ||||||||
\(414\) | − 0.356896i | − 0.0175405i | ||||||||
\(415\) | 3.93900 | 0.193358 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.10992 | −0.397144 | ||||||||
\(418\) | 22.5797i | 1.10441i | ||||||||
\(419\) | 1.77048 | 0.0864935 | 0.0432468 | − | 0.999064i | \(-0.486230\pi\) | ||||
0.0432468 | + | 0.999064i | \(0.486230\pi\) | |||||||
\(420\) | 0.801938 | 0.0391306 | ||||||||
\(421\) | − 1.80194i | − 0.0878211i | −0.999035 | − | 0.0439105i | \(-0.986018\pi\) | ||||
0.999035 | − | 0.0439105i | \(-0.0139817\pi\) | |||||||
\(422\) | 21.3491i | 1.03926i | ||||||||
\(423\) | 0.603875i | 0.0293614i | ||||||||
\(424\) | − 6.29590i | − 0.305756i | ||||||||
\(425\) | −1.24698 | −0.0604874 | ||||||||
\(426\) | −6.67456 | −0.323384 | ||||||||
\(427\) | − 8.85086i | − 0.428323i | ||||||||
\(428\) | −3.77479 | −0.182461 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.54288 | 0.315526 | ||||||||
\(431\) | 0.567040i | 0.0273133i | 0.999907 | + | 0.0136567i | \(0.00434719\pi\) | ||||
−0.999907 | + | 0.0136567i | \(0.995653\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −17.5743 | −0.844569 | −0.422284 | − | 0.906463i | \(-0.638772\pi\) | ||||
−0.422284 | + | 0.906463i | \(0.638772\pi\) | |||||||
\(434\) | 2.76271i | 0.132614i | ||||||||
\(435\) | − 0.307979i | − 0.0147664i | ||||||||
\(436\) | − 1.05861i | − 0.0506980i | ||||||||
\(437\) | − 2.64310i | − 0.126437i | ||||||||
\(438\) | 10.1371 | 0.484368 | ||||||||
\(439\) | −3.00969 | −0.143645 | −0.0718223 | − | 0.997417i | \(-0.522881\pi\) | ||||
−0.0718223 | + | 0.997417i | \(0.522881\pi\) | |||||||
\(440\) | − 3.04892i | − 0.145351i | ||||||||
\(441\) | 6.35690 | 0.302709 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.4499 | 1.82681 | 0.913406 | − | 0.407050i | \(-0.133442\pi\) | ||||
0.913406 | + | 0.407050i | \(0.133442\pi\) | |||||||
\(444\) | − 7.29590i | − 0.346248i | ||||||||
\(445\) | −8.05861 | −0.382015 | ||||||||
\(446\) | 12.7603 | 0.604218 | ||||||||
\(447\) | − 11.0532i | − 0.522800i | ||||||||
\(448\) | 0.801938i | 0.0378880i | ||||||||
\(449\) | 26.9909i | 1.27378i | 0.770955 | + | 0.636890i | \(0.219779\pi\) | ||||
−0.770955 | + | 0.636890i | \(0.780221\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | −10.3840 | −0.488965 | ||||||||
\(452\) | −11.0368 | −0.519129 | ||||||||
\(453\) | 6.89546i | 0.323977i | ||||||||
\(454\) | −14.1836 | −0.665669 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.40581 | 0.346809 | ||||||||
\(457\) | − 19.2664i | − 0.901242i | −0.892715 | − | 0.450621i | \(-0.851203\pi\) | ||||
0.892715 | − | 0.450621i | \(-0.148797\pi\) | |||||||
\(458\) | −4.71140 | −0.220149 | ||||||||
\(459\) | 1.24698 | 0.0582040 | ||||||||
\(460\) | 0.356896i | 0.0166404i | ||||||||
\(461\) | 18.5942i | 0.866018i | 0.901390 | + | 0.433009i | \(0.142548\pi\) | ||||
−0.901390 | + | 0.433009i | \(0.857452\pi\) | |||||||
\(462\) | 2.44504i | 0.113754i | ||||||||
\(463\) | 5.79417i | 0.269278i | 0.990895 | + | 0.134639i | \(0.0429874\pi\) | ||||
−0.990895 | + | 0.134639i | \(0.957013\pi\) | |||||||
\(464\) | 0.307979 | 0.0142975 | ||||||||
\(465\) | −3.44504 | −0.159760 | ||||||||
\(466\) | 0.0556221i | 0.00257664i | ||||||||
\(467\) | −11.2457 | −0.520387 | −0.260193 | − | 0.965557i | \(-0.583786\pi\) | ||||
−0.260193 | + | 0.965557i | \(0.583786\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.78017 | −0.220728 | ||||||||
\(470\) | − 0.603875i | − 0.0278547i | ||||||||
\(471\) | −20.8388 | −0.960200 | ||||||||
\(472\) | −3.11529 | −0.143393 | ||||||||
\(473\) | 19.9487i | 0.917242i | ||||||||
\(474\) | 13.6799i | 0.628340i | ||||||||
\(475\) | 7.40581i | 0.339802i | ||||||||
\(476\) | 1.00000i | 0.0458349i | ||||||||
\(477\) | −6.29590 | −0.288269 | ||||||||
\(478\) | −21.0489 | −0.962755 | ||||||||
\(479\) | − 35.2452i | − 1.61039i | −0.593008 | − | 0.805197i | \(-0.702060\pi\) | ||||
0.593008 | − | 0.805197i | \(-0.297940\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −12.0030 | −0.546721 | ||||||||
\(483\) | − 0.286208i | − 0.0130229i | ||||||||
\(484\) | −1.70410 | −0.0774592 | ||||||||
\(485\) | −9.73556 | −0.442069 | ||||||||
\(486\) | − 1.00000i | − 0.0453609i | ||||||||
\(487\) | − 8.49827i | − 0.385093i | −0.981288 | − | 0.192547i | \(-0.938325\pi\) | ||||
0.981288 | − | 0.192547i | \(-0.0616747\pi\) | |||||||
\(488\) | 11.0368i | 0.499614i | ||||||||
\(489\) | − 4.71917i | − 0.213408i | ||||||||
\(490\) | −6.35690 | −0.287175 | ||||||||
\(491\) | 25.5254 | 1.15195 | 0.575973 | − | 0.817469i | \(-0.304623\pi\) | ||||
0.575973 | + | 0.817469i | \(0.304623\pi\) | |||||||
\(492\) | 3.40581i | 0.153546i | ||||||||
\(493\) | 0.384043 | 0.0172964 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.04892 | −0.137039 | ||||||||
\(496\) | − 3.44504i | − 0.154687i | ||||||||
\(497\) | −5.35258 | −0.240096 | ||||||||
\(498\) | 3.93900 | 0.176511 | ||||||||
\(499\) | 29.4577i | 1.31871i | 0.751832 | + | 0.659354i | \(0.229170\pi\) | ||||
−0.751832 | + | 0.659354i | \(0.770830\pi\) | |||||||
\(500\) | − 1.00000i | − 0.0447214i | ||||||||
\(501\) | − 14.5308i | − 0.649188i | ||||||||
\(502\) | − 2.25906i | − 0.100827i | ||||||||
\(503\) | 14.4480 | 0.644206 | 0.322103 | − | 0.946705i | \(-0.395610\pi\) | ||||
0.322103 | + | 0.946705i | \(0.395610\pi\) | |||||||
\(504\) | 0.801938 | 0.0357211 | ||||||||
\(505\) | 7.65817i | 0.340784i | ||||||||
\(506\) | −1.08815 | −0.0483740 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15.9541 | 0.707847 | ||||||||
\(509\) | − 4.54288i | − 0.201359i | −0.994919 | − | 0.100680i | \(-0.967898\pi\) | ||||
0.994919 | − | 0.100680i | \(-0.0321017\pi\) | |||||||
\(510\) | −1.24698 | −0.0552172 | ||||||||
\(511\) | 8.12929 | 0.359619 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | − 7.40581i | − 0.326975i | ||||||||
\(514\) | − 17.0043i | − 0.750028i | ||||||||
\(515\) | 2.32975i | 0.102661i | ||||||||
\(516\) | 6.54288 | 0.288034 | ||||||||
\(517\) | 1.84117 | 0.0809744 | ||||||||
\(518\) | − 5.85086i | − 0.257072i | ||||||||
\(519\) | −11.4523 | −0.502702 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.0911 | −1.31832 | −0.659158 | − | 0.752004i | \(-0.729087\pi\) | ||||
−0.659158 | + | 0.752004i | \(0.729087\pi\) | |||||||
\(522\) | − 0.307979i | − 0.0134799i | ||||||||
\(523\) | −3.18359 | −0.139209 | −0.0696043 | − | 0.997575i | \(-0.522174\pi\) | ||||
−0.0696043 | + | 0.997575i | \(0.522174\pi\) | |||||||
\(524\) | 17.0911 | 0.746629 | ||||||||
\(525\) | 0.801938i | 0.0349994i | ||||||||
\(526\) | 28.5773i | 1.24603i | ||||||||
\(527\) | − 4.29590i | − 0.187132i | ||||||||
\(528\) | − 3.04892i | − 0.132687i | ||||||||
\(529\) | −22.8726 | −0.994462 | ||||||||
\(530\) | 6.29590 | 0.273476 | ||||||||
\(531\) | 3.11529i | 0.135192i | ||||||||
\(532\) | 5.93900 | 0.257488 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −8.05861 | −0.348730 | ||||||||
\(535\) | − 3.77479i | − 0.163198i | ||||||||
\(536\) | 5.96077 | 0.257466 | ||||||||
\(537\) | 4.32975 | 0.186842 | ||||||||
\(538\) | 3.28083i | 0.141447i | ||||||||
\(539\) | − 19.3817i | − 0.834827i | ||||||||
\(540\) | 1.00000i | 0.0430331i | ||||||||
\(541\) | 21.2825i | 0.915006i | 0.889208 | + | 0.457503i | \(0.151256\pi\) | ||||
−0.889208 | + | 0.457503i | \(0.848744\pi\) | |||||||
\(542\) | −8.70948 | −0.374104 | ||||||||
\(543\) | 24.8321 | 1.06565 | ||||||||
\(544\) | − 1.24698i | − 0.0534638i | ||||||||
\(545\) | 1.05861 | 0.0453457 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.5545 | 1.17814 | 0.589072 | − | 0.808080i | \(-0.299493\pi\) | ||||
0.589072 | + | 0.808080i | \(0.299493\pi\) | |||||||
\(548\) | 16.4373i | 0.702165i | ||||||||
\(549\) | 11.0368 | 0.471041 | ||||||||
\(550\) | 3.04892 | 0.130006 | ||||||||
\(551\) | − 2.28083i | − 0.0971667i | ||||||||
\(552\) | 0.356896i | 0.0151905i | ||||||||
\(553\) | 10.9705i | 0.466511i | ||||||||
\(554\) | − 8.91185i | − 0.378628i | ||||||||
\(555\) | 7.29590 | 0.309694 | ||||||||
\(556\) | 8.10992 | 0.343937 | ||||||||
\(557\) | − 3.88040i | − 0.164418i | −0.996615 | − | 0.0822088i | \(-0.973803\pi\) | ||||
0.996615 | − | 0.0822088i | \(-0.0261974\pi\) | |||||||
\(558\) | −3.44504 | −0.145840 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.801938 | −0.0338881 | ||||||||
\(561\) | − 3.80194i | − 0.160518i | ||||||||
\(562\) | −1.90648 | −0.0804199 | ||||||||
\(563\) | 38.6286 | 1.62800 | 0.814001 | − | 0.580863i | \(-0.197285\pi\) | ||||
0.814001 | + | 0.580863i | \(0.197285\pi\) | |||||||
\(564\) | − 0.603875i | − 0.0254277i | ||||||||
\(565\) | − 11.0368i | − 0.464323i | ||||||||
\(566\) | − 14.9245i | − 0.627325i | ||||||||
\(567\) | − 0.801938i | − 0.0336782i | ||||||||
\(568\) | 6.67456 | 0.280058 | ||||||||
\(569\) | 27.6746 | 1.16018 | 0.580089 | − | 0.814553i | \(-0.303018\pi\) | ||||
0.580089 | + | 0.814553i | \(0.303018\pi\) | |||||||
\(570\) | 7.40581i | 0.310195i | ||||||||
\(571\) | 10.9065 | 0.456422 | 0.228211 | − | 0.973612i | \(-0.426712\pi\) | ||||
0.228211 | + | 0.973612i | \(0.426712\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.1933 | 0.927137 | ||||||||
\(574\) | 2.73125i | 0.114000i | ||||||||
\(575\) | −0.356896 | −0.0148836 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − 29.9758i | − 1.24791i | −0.781460 | − | 0.623955i | \(-0.785525\pi\) | ||||
0.781460 | − | 0.623955i | \(-0.214475\pi\) | |||||||
\(578\) | 15.4450i | 0.642429i | ||||||||
\(579\) | 25.4306i | 1.05686i | ||||||||
\(580\) | 0.307979i | 0.0127881i | ||||||||
\(581\) | 3.15883 | 0.131051 | ||||||||
\(582\) | −9.73556 | −0.403552 | ||||||||
\(583\) | 19.1957i | 0.795003i | ||||||||
\(584\) | −10.1371 | −0.419475 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.8901 | −0.532484 | ||||||||
\(587\) | − 32.1551i | − 1.32718i | −0.748095 | − | 0.663592i | \(-0.769031\pi\) | ||||
0.748095 | − | 0.663592i | \(-0.230969\pi\) | |||||||
\(588\) | −6.35690 | −0.262154 | ||||||||
\(589\) | −25.5133 | −1.05126 | ||||||||
\(590\) | − 3.11529i | − 0.128255i | ||||||||
\(591\) | 10.6310i | 0.437302i | ||||||||
\(592\) | 7.29590i | 0.299860i | ||||||||
\(593\) | − 3.88876i | − 0.159692i | −0.996807 | − | 0.0798460i | \(-0.974557\pi\) | ||||
0.996807 | − | 0.0798460i | \(-0.0254429\pi\) | |||||||
\(594\) | −3.04892 | −0.125099 | ||||||||
\(595\) | −1.00000 | −0.0409960 | ||||||||
\(596\) | 11.0532i | 0.452758i | ||||||||
\(597\) | −11.0465 | −0.452104 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.2301 | −1.52118 | −0.760591 | − | 0.649232i | \(-0.775090\pi\) | ||||
−0.760591 | + | 0.649232i | \(0.775090\pi\) | |||||||
\(600\) | − 1.00000i | − 0.0408248i | ||||||||
\(601\) | −4.04593 | −0.165037 | −0.0825185 | − | 0.996590i | \(-0.526296\pi\) | ||||
−0.0825185 | + | 0.996590i | \(0.526296\pi\) | |||||||
\(602\) | 5.24698 | 0.213851 | ||||||||
\(603\) | − 5.96077i | − 0.242741i | ||||||||
\(604\) | − 6.89546i | − 0.280572i | ||||||||
\(605\) | − 1.70410i | − 0.0692816i | ||||||||
\(606\) | 7.65817i | 0.311092i | ||||||||
\(607\) | −6.36658 | −0.258412 | −0.129206 | − | 0.991618i | \(-0.541243\pi\) | ||||
−0.129206 | + | 0.991618i | \(0.541243\pi\) | |||||||
\(608\) | −7.40581 | −0.300345 | ||||||||
\(609\) | − 0.246980i | − 0.0100081i | ||||||||
\(610\) | −11.0368 | −0.446868 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.24698 | −0.0504062 | ||||||||
\(613\) | 42.2519i | 1.70654i | 0.521471 | + | 0.853269i | \(0.325383\pi\) | ||||
−0.521471 | + | 0.853269i | \(0.674617\pi\) | |||||||
\(614\) | 19.2892 | 0.778448 | ||||||||
\(615\) | −3.40581 | −0.137336 | ||||||||
\(616\) | − 2.44504i | − 0.0985135i | ||||||||
\(617\) | − 0.978230i | − 0.0393820i | −0.999806 | − | 0.0196910i | \(-0.993732\pi\) | ||||
0.999806 | − | 0.0196910i | \(-0.00626825\pi\) | |||||||
\(618\) | 2.32975i | 0.0937162i | ||||||||
\(619\) | 19.0392i | 0.765251i | 0.923903 | + | 0.382626i | \(0.124980\pi\) | ||||
−0.923903 | + | 0.382626i | \(0.875020\pi\) | |||||||
\(620\) | 3.44504 | 0.138356 | ||||||||
\(621\) | 0.356896 | 0.0143217 | ||||||||
\(622\) | 1.23729i | 0.0496108i | ||||||||
\(623\) | −6.46250 | −0.258915 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | − 8.09113i | − 0.323387i | ||||||||
\(627\) | −22.5797 | −0.901747 | ||||||||
\(628\) | 20.8388 | 0.831558 | ||||||||
\(629\) | 9.09783i | 0.362754i | ||||||||
\(630\) | 0.801938i | 0.0319500i | ||||||||
\(631\) | 37.2664i | 1.48355i | 0.670649 | + | 0.741775i | \(0.266016\pi\) | ||||
−0.670649 | + | 0.741775i | \(0.733984\pi\) | |||||||
\(632\) | − 13.6799i | − 0.544159i | ||||||||
\(633\) | −21.3491 | −0.848552 | ||||||||
\(634\) | 21.0368 | 0.835479 | ||||||||
\(635\) | 15.9541i | 0.633118i | ||||||||
\(636\) | 6.29590 | 0.249649 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.939001 | −0.0371754 | ||||||||
\(639\) | − 6.67456i | − 0.264042i | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 29.7017 | 1.17315 | 0.586574 | − | 0.809896i | \(-0.300477\pi\) | ||||
0.586574 | + | 0.809896i | \(0.300477\pi\) | |||||||
\(642\) | − 3.77479i | − 0.148979i | ||||||||
\(643\) | 21.5907i | 0.851455i | 0.904851 | + | 0.425728i | \(0.139982\pi\) | ||||
−0.904851 | + | 0.425728i | \(0.860018\pi\) | |||||||
\(644\) | 0.286208i | 0.0112782i | ||||||||
\(645\) | 6.54288i | 0.257626i | ||||||||
\(646\) | −9.23490 | −0.363342 | ||||||||
\(647\) | 29.3623 | 1.15435 | 0.577175 | − | 0.816620i | \(-0.304155\pi\) | ||||
0.577175 | + | 0.816620i | \(0.304155\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 9.49827 | 0.372840 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.76271 | −0.108279 | ||||||||
\(652\) | 4.71917i | 0.184817i | ||||||||
\(653\) | 33.4470 | 1.30888 | 0.654440 | − | 0.756114i | \(-0.272904\pi\) | ||||
0.654440 | + | 0.756114i | \(0.272904\pi\) | |||||||
\(654\) | 1.05861 | 0.0413948 | ||||||||
\(655\) | 17.0911i | 0.667806i | ||||||||
\(656\) | − 3.40581i | − 0.132975i | ||||||||
\(657\) | 10.1371i | 0.395485i | ||||||||
\(658\) | − 0.484271i | − 0.0188788i | ||||||||
\(659\) | 39.3715 | 1.53370 | 0.766848 | − | 0.641829i | \(-0.221824\pi\) | ||||
0.766848 | + | 0.641829i | \(0.221824\pi\) | |||||||
\(660\) | 3.04892 | 0.118679 | ||||||||
\(661\) | − 10.1274i | − 0.393909i | −0.980413 | − | 0.196955i | \(-0.936895\pi\) | ||||
0.980413 | − | 0.196955i | \(-0.0631052\pi\) | |||||||
\(662\) | 29.4252 | 1.14364 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.93900 | −0.152863 | ||||||||
\(665\) | 5.93900i | 0.230305i | ||||||||
\(666\) | 7.29590 | 0.282710 | ||||||||
\(667\) | 0.109916 | 0.00425597 | ||||||||
\(668\) | 14.5308i | 0.562213i | ||||||||
\(669\) | 12.7603i | 0.493342i | ||||||||
\(670\) | 5.96077i | 0.230285i | ||||||||
\(671\) | − 33.6504i | − 1.29906i | ||||||||
\(672\) | −0.801938 | −0.0309354 | ||||||||
\(673\) | 10.1400 | 0.390870 | 0.195435 | − | 0.980717i | \(-0.437388\pi\) | ||||
0.195435 | + | 0.980717i | \(0.437388\pi\) | |||||||
\(674\) | − 17.5483i | − 0.675933i | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.9952 | 0.883778 | 0.441889 | − | 0.897070i | \(-0.354309\pi\) | ||||
0.441889 | + | 0.897070i | \(0.354309\pi\) | |||||||
\(678\) | − 11.0368i | − 0.423867i | ||||||||
\(679\) | −7.80731 | −0.299617 | ||||||||
\(680\) | 1.24698 | 0.0478195 | ||||||||
\(681\) | − 14.1836i | − 0.543516i | ||||||||
\(682\) | 10.5036i | 0.402205i | ||||||||
\(683\) | − 4.10800i | − 0.157188i | −0.996907 | − | 0.0785941i | \(-0.974957\pi\) | ||||
0.996907 | − | 0.0785941i | \(-0.0250431\pi\) | |||||||
\(684\) | 7.40581i | 0.283168i | ||||||||
\(685\) | −16.4373 | −0.628036 | ||||||||
\(686\) | −10.7114 | −0.408963 | ||||||||
\(687\) | − 4.71140i | − 0.179751i | ||||||||
\(688\) | −6.54288 | −0.249445 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.356896 | −0.0135868 | ||||||||
\(691\) | − 30.1618i | − 1.14741i | −0.819062 | − | 0.573705i | \(-0.805506\pi\) | ||||
0.819062 | − | 0.573705i | \(-0.194494\pi\) | |||||||
\(692\) | 11.4523 | 0.435353 | ||||||||
\(693\) | −2.44504 | −0.0928795 | ||||||||
\(694\) | − 1.27844i | − 0.0485289i | ||||||||
\(695\) | 8.10992i | 0.307627i | ||||||||
\(696\) | 0.307979i | 0.0116739i | ||||||||
\(697\) | − 4.24698i | − 0.160866i | ||||||||
\(698\) | 18.0911 | 0.684759 | ||||||||
\(699\) | −0.0556221 | −0.00210382 | ||||||||
\(700\) | − 0.801938i | − 0.0303104i | ||||||||
\(701\) | 37.5066 | 1.41661 | 0.708303 | − | 0.705909i | \(-0.249461\pi\) | ||||
0.708303 | + | 0.705909i | \(0.249461\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 54.0320 | 2.03786 | ||||||||
\(704\) | 3.04892i | 0.114910i | ||||||||
\(705\) | 0.603875 | 0.0227433 | ||||||||
\(706\) | 18.9071 | 0.711577 | ||||||||
\(707\) | 6.14138i | 0.230970i | ||||||||
\(708\) | − 3.11529i | − 0.117080i | ||||||||
\(709\) | − 4.20211i | − 0.157814i | −0.996882 | − | 0.0789068i | \(-0.974857\pi\) | ||||
0.996882 | − | 0.0789068i | \(-0.0251430\pi\) | |||||||
\(710\) | 6.67456i | 0.250492i | ||||||||
\(711\) | −13.6799 | −0.513038 | ||||||||
\(712\) | 8.05861 | 0.302009 | ||||||||
\(713\) | − 1.22952i | − 0.0460459i | ||||||||
\(714\) | −1.00000 | −0.0374241 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.32975 | −0.161810 | ||||||||
\(717\) | − 21.0489i | − 0.786086i | ||||||||
\(718\) | 32.7308 | 1.22150 | ||||||||
\(719\) | 28.3532 | 1.05740 | 0.528698 | − | 0.848810i | \(-0.322681\pi\) | ||||
0.528698 | + | 0.848810i | \(0.322681\pi\) | |||||||
\(720\) | − 1.00000i | − 0.0372678i | ||||||||
\(721\) | 1.86831i | 0.0695796i | ||||||||
\(722\) | 35.8461i | 1.33405i | ||||||||
\(723\) | − 12.0030i | − 0.446396i | ||||||||
\(724\) | −24.8321 | −0.922877 | ||||||||
\(725\) | −0.307979 | −0.0114380 | ||||||||
\(726\) | − 1.70410i | − 0.0632452i | ||||||||
\(727\) | −10.2892 | −0.381605 | −0.190803 | − | 0.981628i | \(-0.561109\pi\) | ||||
−0.190803 | + | 0.981628i | \(0.561109\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − 10.1371i | − 0.375190i | ||||||||
\(731\) | −8.15883 | −0.301765 | ||||||||
\(732\) | −11.0368 | −0.407933 | ||||||||
\(733\) | 48.8963i | 1.80603i | 0.429613 | + | 0.903013i | \(0.358650\pi\) | ||||
−0.429613 | + | 0.903013i | \(0.641350\pi\) | |||||||
\(734\) | 3.10321i | 0.114542i | ||||||||
\(735\) | − 6.35690i | − 0.234478i | ||||||||
\(736\) | − 0.356896i | − 0.0131554i | ||||||||
\(737\) | −18.1739 | −0.669444 | ||||||||
\(738\) | −3.40581 | −0.125370 | ||||||||
\(739\) | − 23.7496i | − 0.873642i | −0.899549 | − | 0.436821i | \(-0.856104\pi\) | ||||
0.899549 | − | 0.436821i | \(-0.143896\pi\) | |||||||
\(740\) | −7.29590 | −0.268203 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.04892 | 0.185352 | ||||||||
\(743\) | 51.5153i | 1.88991i | 0.327198 | + | 0.944956i | \(0.393896\pi\) | ||||
−0.327198 | + | 0.944956i | \(0.606104\pi\) | |||||||
\(744\) | 3.44504 | 0.126301 | ||||||||
\(745\) | −11.0532 | −0.404959 | ||||||||
\(746\) | − 13.7366i | − 0.502934i | ||||||||
\(747\) | 3.93900i | 0.144121i | ||||||||
\(748\) | 3.80194i | 0.139013i | ||||||||
\(749\) | − 3.02715i | − 0.110610i | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −43.8939 | −1.60171 | −0.800856 | − | 0.598857i | \(-0.795622\pi\) | ||||
−0.800856 | + | 0.598857i | \(0.795622\pi\) | |||||||
\(752\) | 0.603875i | 0.0220211i | ||||||||
\(753\) | 2.25906 | 0.0823248 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.89546 | 0.250952 | ||||||||
\(756\) | 0.801938i | 0.0291662i | ||||||||
\(757\) | −18.6136 | −0.676521 | −0.338261 | − | 0.941052i | \(-0.609839\pi\) | ||||
−0.338261 | + | 0.941052i | \(0.609839\pi\) | |||||||
\(758\) | −34.0097 | −1.23529 | ||||||||
\(759\) | − 1.08815i | − 0.0394972i | ||||||||
\(760\) | − 7.40581i | − 0.268637i | ||||||||
\(761\) | − 44.8364i | − 1.62532i | −0.582740 | − | 0.812659i | \(-0.698019\pi\) | ||||
0.582740 | − | 0.812659i | \(-0.301981\pi\) | |||||||
\(762\) | 15.9541i | 0.577955i | ||||||||
\(763\) | 0.848936 | 0.0307336 | ||||||||
\(764\) | −22.1933 | −0.802925 | ||||||||
\(765\) | − 1.24698i | − 0.0450846i | ||||||||
\(766\) | −38.6902 | −1.39793 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | − 39.5303i | − 1.42550i | −0.701418 | − | 0.712750i | \(-0.747449\pi\) | ||||
0.701418 | − | 0.712750i | \(-0.252551\pi\) | |||||||
\(770\) | 2.44504 | 0.0881132 | ||||||||
\(771\) | 17.0043 | 0.612395 | ||||||||
\(772\) | − 25.4306i | − 0.915266i | ||||||||
\(773\) | − 49.8665i | − 1.79357i | −0.442463 | − | 0.896787i | \(-0.645895\pi\) | ||||
0.442463 | − | 0.896787i | \(-0.354105\pi\) | |||||||
\(774\) | 6.54288i | 0.235179i | ||||||||
\(775\) | 3.44504i | 0.123750i | ||||||||
\(776\) | 9.73556 | 0.349486 | ||||||||
\(777\) | 5.85086 | 0.209898 | ||||||||
\(778\) | − 11.2567i | − 0.403571i | ||||||||
\(779\) | −25.2228 | −0.903701 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.3502 | −0.728187 | ||||||||
\(782\) | − 0.445042i | − 0.0159147i | ||||||||
\(783\) | 0.307979 | 0.0110063 | ||||||||
\(784\) | 6.35690 | 0.227032 | ||||||||
\(785\) | 20.8388i | 0.743768i | ||||||||
\(786\) | 17.0911i | 0.609620i | ||||||||
\(787\) | − 26.0398i | − 0.928219i | −0.885778 | − | 0.464110i | \(-0.846374\pi\) | ||||
0.885778 | − | 0.464110i | \(-0.153626\pi\) | |||||||
\(788\) | − 10.6310i | − 0.378714i | ||||||||
\(789\) | −28.5773 | −1.01738 | ||||||||
\(790\) | 13.6799 | 0.486710 | ||||||||
\(791\) | − 8.85086i | − 0.314700i | ||||||||
\(792\) | 3.04892 | 0.108339 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −23.4403 | −0.831864 | ||||||||
\(795\) | 6.29590i | 0.223292i | ||||||||
\(796\) | 11.0465 | 0.391534 | ||||||||
\(797\) | 23.9855 | 0.849611 | 0.424805 | − | 0.905285i | \(-0.360343\pi\) | ||||
0.424805 | + | 0.905285i | \(0.360343\pi\) | |||||||
\(798\) | 5.93900i | 0.210238i | ||||||||
\(799\) | 0.753020i | 0.0266399i | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | − 8.05861i | − 0.284737i | ||||||||
\(802\) | −37.6950 | −1.33106 | ||||||||
\(803\) | 30.9071 | 1.09069 | ||||||||
\(804\) | 5.96077i | 0.210220i | ||||||||
\(805\) | −0.286208 | −0.0100875 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.28083 | −0.115491 | ||||||||
\(808\) | − 7.65817i | − 0.269413i | ||||||||
\(809\) | 52.4825 | 1.84519 | 0.922593 | − | 0.385776i | \(-0.126066\pi\) | ||||
0.922593 | + | 0.385776i | \(0.126066\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | − 3.63666i | − 0.127700i | −0.997959 | − | 0.0638502i | \(-0.979662\pi\) | ||||
0.997959 | − | 0.0638502i | \(-0.0203380\pi\) | |||||||
\(812\) | 0.246980i | 0.00866728i | ||||||||
\(813\) | − 8.70948i | − 0.305455i | ||||||||
\(814\) | − 22.2446i | − 0.779672i | ||||||||
\(815\) | −4.71917 | −0.165305 | ||||||||
\(816\) | 1.24698 | 0.0436530 | ||||||||
\(817\) | 48.4553i | 1.69524i | ||||||||
\(818\) | 1.19567 | 0.0418056 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.40581 | 0.118936 | ||||||||
\(821\) | − 7.98984i | − 0.278847i | −0.990233 | − | 0.139424i | \(-0.955475\pi\) | ||||
0.990233 | − | 0.139424i | \(-0.0445250\pi\) | |||||||
\(822\) | −16.4373 | −0.573316 | ||||||||
\(823\) | −28.1395 | −0.980880 | −0.490440 | − | 0.871475i | \(-0.663164\pi\) | ||||
−0.490440 | + | 0.871475i | \(0.663164\pi\) | |||||||
\(824\) | − 2.32975i | − 0.0811606i | ||||||||
\(825\) | 3.04892i | 0.106150i | ||||||||
\(826\) | − 2.49827i | − 0.0869260i | ||||||||
\(827\) | − 30.9256i | − 1.07539i | −0.843140 | − | 0.537694i | \(-0.819296\pi\) | ||||
0.843140 | − | 0.537694i | \(-0.180704\pi\) | |||||||
\(828\) | −0.356896 | −0.0124030 | ||||||||
\(829\) | 31.9172 | 1.10853 | 0.554266 | − | 0.832340i | \(-0.312999\pi\) | ||||
0.554266 | + | 0.832340i | \(0.312999\pi\) | |||||||
\(830\) | − 3.93900i | − 0.136725i | ||||||||
\(831\) | 8.91185 | 0.309149 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.92692 | 0.274651 | ||||||||
\(834\) | 8.10992i | 0.280823i | ||||||||
\(835\) | −14.5308 | −0.502859 | ||||||||
\(836\) | 22.5797 | 0.780936 | ||||||||
\(837\) | − 3.44504i | − 0.119078i | ||||||||
\(838\) | − 1.77048i | − 0.0611602i | ||||||||
\(839\) | 24.9866i | 0.862633i | 0.902201 | + | 0.431316i | \(0.141951\pi\) | ||||
−0.902201 | + | 0.431316i | \(0.858049\pi\) | |||||||
\(840\) | − 0.801938i | − 0.0276695i | ||||||||
\(841\) | −28.9051 | −0.996729 | ||||||||
\(842\) | −1.80194 | −0.0620989 | ||||||||
\(843\) | − 1.90648i | − 0.0656626i | ||||||||
\(844\) | 21.3491 | 0.734867 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.603875 | 0.0207617 | ||||||||
\(847\) | − 1.36658i | − 0.0469564i | ||||||||
\(848\) | −6.29590 | −0.216202 | ||||||||
\(849\) | 14.9245 | 0.512208 | ||||||||
\(850\) | 1.24698i | 0.0427710i | ||||||||
\(851\) | 2.60388i | 0.0892597i | ||||||||
\(852\) | 6.67456i | 0.228667i | ||||||||
\(853\) | 35.4416i | 1.21350i | 0.794894 | + | 0.606748i | \(0.207526\pi\) | ||||
−0.794894 | + | 0.606748i | \(0.792474\pi\) | |||||||
\(854\) | −8.85086 | −0.302870 | ||||||||
\(855\) | −7.40581 | −0.253273 | ||||||||
\(856\) | 3.77479i | 0.129020i | ||||||||
\(857\) | 14.6541 | 0.500575 | 0.250288 | − | 0.968172i | \(-0.419475\pi\) | ||||
0.250288 | + | 0.968172i | \(0.419475\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.3153 | 1.58026 | 0.790128 | − | 0.612941i | \(-0.210014\pi\) | ||||
0.790128 | + | 0.612941i | \(0.210014\pi\) | |||||||
\(860\) | − 6.54288i | − 0.223110i | ||||||||
\(861\) | −2.73125 | −0.0930808 | ||||||||
\(862\) | 0.567040 | 0.0193134 | ||||||||
\(863\) | 40.3642i | 1.37401i | 0.726651 | + | 0.687007i | \(0.241076\pi\) | ||||
−0.726651 | + | 0.687007i | \(0.758924\pi\) | |||||||
\(864\) | − 1.00000i | − 0.0340207i | ||||||||
\(865\) | 11.4523i | 0.389391i | ||||||||
\(866\) | 17.5743i | 0.597200i | ||||||||
\(867\) | −15.4450 | −0.524541 | ||||||||
\(868\) | 2.76271 | 0.0937725 | ||||||||
\(869\) | 41.7090i | 1.41488i | ||||||||
\(870\) | −0.307979 | −0.0104414 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1.05861 | −0.0358489 | ||||||||
\(873\) | − 9.73556i | − 0.329499i | ||||||||
\(874\) | −2.64310 | −0.0894043 | ||||||||
\(875\) | 0.801938 | 0.0271104 | ||||||||
\(876\) | − 10.1371i | − 0.342500i | ||||||||
\(877\) | 35.0103i | 1.18221i | 0.806593 | + | 0.591107i | \(0.201309\pi\) | ||||
−0.806593 | + | 0.591107i | \(0.798691\pi\) | |||||||
\(878\) | 3.00969i | 0.101572i | ||||||||
\(879\) | − 12.8901i | − 0.434772i | ||||||||
\(880\) | −3.04892 | −0.102779 | ||||||||
\(881\) | −23.8689 | −0.804164 | −0.402082 | − | 0.915604i | \(-0.631713\pi\) | ||||
−0.402082 | + | 0.915604i | \(0.631713\pi\) | |||||||
\(882\) | − 6.35690i | − 0.214048i | ||||||||
\(883\) | −26.1806 | −0.881047 | −0.440524 | − | 0.897741i | \(-0.645207\pi\) | ||||
−0.440524 | + | 0.897741i | \(0.645207\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.11529 | 0.104719 | ||||||||
\(886\) | − 38.4499i | − 1.29175i | ||||||||
\(887\) | 25.8625 | 0.868377 | 0.434188 | − | 0.900822i | \(-0.357035\pi\) | ||||
0.434188 | + | 0.900822i | \(0.357035\pi\) | |||||||
\(888\) | −7.29590 | −0.244834 | ||||||||
\(889\) | 12.7942i | 0.429103i | ||||||||
\(890\) | 8.05861i | 0.270125i | ||||||||
\(891\) | − 3.04892i | − 0.102143i | ||||||||
\(892\) | − 12.7603i | − 0.427247i | ||||||||
\(893\) | 4.47219 | 0.149656 | ||||||||
\(894\) | −11.0532 | −0.369675 | ||||||||
\(895\) | − 4.32975i | − 0.144728i | ||||||||
\(896\) | 0.801938 | 0.0267909 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 26.9909 | 0.900698 | ||||||||
\(899\) | − 1.06100i | − 0.0353863i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −7.85086 | −0.261550 | ||||||||
\(902\) | 10.3840i | 0.345751i | ||||||||
\(903\) | 5.24698i | 0.174609i | ||||||||
\(904\) | 11.0368i | 0.367080i | ||||||||
\(905\) | − 24.8321i | − 0.825446i | ||||||||
\(906\) | 6.89546 | 0.229086 | ||||||||
\(907\) | −12.3980 | −0.411670 | −0.205835 | − | 0.978587i | \(-0.565991\pi\) | ||||
−0.205835 | + | 0.978587i | \(0.565991\pi\) | |||||||
\(908\) | 14.1836i | 0.470699i | ||||||||
\(909\) | −7.65817 | −0.254005 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.34183 | 0.176983 | 0.0884914 | − | 0.996077i | \(-0.471795\pi\) | ||||
0.0884914 | + | 0.996077i | \(0.471795\pi\) | |||||||
\(912\) | − 7.40581i | − 0.245231i | ||||||||
\(913\) | 12.0097 | 0.397463 | ||||||||
\(914\) | −19.2664 | −0.637274 | ||||||||
\(915\) | − 11.0368i | − 0.364867i | ||||||||
\(916\) | 4.71140i | 0.155669i | ||||||||
\(917\) | 13.7060i | 0.452613i | ||||||||
\(918\) | − 1.24698i | − 0.0411565i | ||||||||
\(919\) | 32.3327 | 1.06656 | 0.533279 | − | 0.845939i | \(-0.320960\pi\) | ||||
0.533279 | + | 0.845939i | \(0.320960\pi\) | |||||||
\(920\) | 0.356896 | 0.0117665 | ||||||||
\(921\) | 19.2892i | 0.635600i | ||||||||
\(922\) | 18.5942 | 0.612367 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.44504 | 0.0804360 | ||||||||
\(925\) | − 7.29590i | − 0.239888i | ||||||||
\(926\) | 5.79417 | 0.190408 | ||||||||
\(927\) | −2.32975 | −0.0765190 | ||||||||
\(928\) | − 0.307979i | − 0.0101099i | ||||||||
\(929\) | − 19.3381i | − 0.634463i | −0.948348 | − | 0.317231i | \(-0.897247\pi\) | ||||
0.948348 | − | 0.317231i | \(-0.102753\pi\) | |||||||
\(930\) | 3.44504i | 0.112967i | ||||||||
\(931\) | − 47.0780i | − 1.54292i | ||||||||
\(932\) | 0.0556221 | 0.00182196 | ||||||||
\(933\) | −1.23729 | −0.0405071 | ||||||||
\(934\) | 11.2457i | 0.367969i | ||||||||
\(935\) | −3.80194 | −0.124337 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.4271 | −1.32070 | −0.660348 | − | 0.750960i | \(-0.729591\pi\) | ||||
−0.660348 | + | 0.750960i | \(0.729591\pi\) | |||||||
\(938\) | 4.78017i | 0.156078i | ||||||||
\(939\) | 8.09113 | 0.264044 | ||||||||
\(940\) | −0.603875 | −0.0196962 | ||||||||
\(941\) | 9.38537i | 0.305954i | 0.988230 | + | 0.152977i | \(0.0488861\pi\) | ||||
−0.988230 | + | 0.152977i | \(0.951114\pi\) | |||||||
\(942\) | 20.8388i | 0.678964i | ||||||||
\(943\) | − 1.21552i | − 0.0395828i | ||||||||
\(944\) | 3.11529i | 0.101394i | ||||||||
\(945\) | −0.801938 | −0.0260870 | ||||||||
\(946\) | 19.9487 | 0.648588 | ||||||||
\(947\) | − 24.4252i | − 0.793712i | −0.917881 | − | 0.396856i | \(-0.870101\pi\) | ||||
0.917881 | − | 0.396856i | \(-0.129899\pi\) | |||||||
\(948\) | 13.6799 | 0.444304 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 7.40581 | 0.240276 | ||||||||
\(951\) | 21.0368i | 0.682166i | ||||||||
\(952\) | 1.00000 | 0.0324102 | ||||||||
\(953\) | −57.1657 | −1.85178 | −0.925889 | − | 0.377797i | \(-0.876682\pi\) | ||||
−0.925889 | + | 0.377797i | \(0.876682\pi\) | |||||||
\(954\) | 6.29590i | 0.203837i | ||||||||
\(955\) | − 22.1933i | − 0.718158i | ||||||||
\(956\) | 21.0489i | 0.680771i | ||||||||
\(957\) | − 0.939001i | − 0.0303536i | ||||||||
\(958\) | −35.2452 | −1.13872 | ||||||||
\(959\) | −13.1817 | −0.425658 | ||||||||
\(960\) | 1.00000i | 0.0322749i | ||||||||
\(961\) | 19.1317 | 0.617151 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.77479 | 0.121641 | ||||||||
\(964\) | 12.0030i | 0.386590i | ||||||||
\(965\) | 25.4306 | 0.818639 | ||||||||
\(966\) | −0.286208 | −0.00920860 | ||||||||
\(967\) | 5.76271i | 0.185316i | 0.995698 | + | 0.0926581i | \(0.0295364\pi\) | ||||
−0.995698 | + | 0.0926581i | \(0.970464\pi\) | |||||||
\(968\) | 1.70410i | 0.0547719i | ||||||||
\(969\) | − 9.23490i | − 0.296668i | ||||||||
\(970\) | 9.73556i | 0.312590i | ||||||||
\(971\) | −1.72694 | −0.0554201 | −0.0277100 | − | 0.999616i | \(-0.508822\pi\) | ||||
−0.0277100 | + | 0.999616i | \(0.508822\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 6.50365i | 0.208497i | ||||||||
\(974\) | −8.49827 | −0.272302 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.0368 | 0.353281 | ||||||||
\(977\) | − 26.4747i | − 0.847001i | −0.905896 | − | 0.423500i | \(-0.860801\pi\) | ||||
0.905896 | − | 0.423500i | \(-0.139199\pi\) | |||||||
\(978\) | −4.71917 | −0.150902 | ||||||||
\(979\) | −24.5700 | −0.785261 | ||||||||
\(980\) | 6.35690i | 0.203064i | ||||||||
\(981\) | 1.05861i | 0.0337987i | ||||||||
\(982\) | − 25.5254i | − 0.814549i | ||||||||
\(983\) | 6.81727i | 0.217437i | 0.994073 | + | 0.108719i | \(0.0346747\pi\) | ||||
−0.994073 | + | 0.108719i | \(0.965325\pi\) | |||||||
\(984\) | 3.40581 | 0.108573 | ||||||||
\(985\) | 10.6310 | 0.338733 | ||||||||
\(986\) | − 0.384043i | − 0.0122304i | ||||||||
\(987\) | 0.484271 | 0.0154145 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.33513 | −0.0742527 | ||||||||
\(990\) | 3.04892i | 0.0969010i | ||||||||
\(991\) | 8.31203 | 0.264040 | 0.132020 | − | 0.991247i | \(-0.457854\pi\) | ||||
0.132020 | + | 0.991247i | \(0.457854\pi\) | |||||||
\(992\) | −3.44504 | −0.109380 | ||||||||
\(993\) | 29.4252i | 0.933780i | ||||||||
\(994\) | 5.35258i | 0.169774i | ||||||||
\(995\) | 11.0465i | 0.350198i | ||||||||
\(996\) | − 3.93900i | − 0.124812i | ||||||||
\(997\) | 49.6002 | 1.57085 | 0.785426 | − | 0.618955i | \(-0.212444\pi\) | ||||
0.785426 | + | 0.618955i | \(0.212444\pi\) | |||||||
\(998\) | 29.4577 | 0.932468 | ||||||||
\(999\) | 7.29590i | 0.230832i |
(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 | 5070.2.b.x.1351.1 | 6 | ||
13.5 | odd | 4 | 5070.2.a.bn.1.3 | ✓ | 3 | ||
13.8 | odd | 4 | 5070.2.a.by.1.1 | yes | 3 | ||
13.12 | even | 2 | inner | 5070.2.b.x.1351.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bn.1.3 | ✓ | 3 | 13.5 | odd | 4 | ||
5070.2.a.by.1.1 | yes | 3 | 13.8 | odd | 4 | ||
5070.2.b.x.1351.1 | 6 | 1.1 | even | 1 | trivial | ||
5070.2.b.x.1351.6 | 6 | 13.12 | even | 2 | inner |