Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4830,2,Mod(1,4830)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4830, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4830.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4830.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: | \(38.5677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.86081\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4830.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −0.925197 | −0.278957 | −0.139479 | − | 0.990225i | \(-0.544543\pi\) | ||||
−0.139479 | + | 0.990225i | \(0.544543\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −4.64681 | −1.28879 | −0.644396 | − | 0.764692i | \(-0.722891\pi\) | ||||
−0.644396 | + | 0.764692i | \(0.722891\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.72161 | −0.902623 | −0.451312 | − | 0.892366i | \(-0.649044\pi\) | ||||
−0.451312 | + | 0.892366i | \(0.649044\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.72161 | −0.394965 | −0.197482 | − | 0.980306i | \(-0.563277\pi\) | ||||
−0.197482 | + | 0.980306i | \(0.563277\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −0.925197 | −0.197253 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.64681 | −0.911314 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 2.92520 | 0.543195 | 0.271598 | − | 0.962411i | \(-0.412448\pi\) | ||||
0.271598 | + | 0.962411i | \(0.412448\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 5.72161 | 1.02763 | 0.513816 | − | 0.857900i | \(-0.328231\pi\) | ||||
0.513816 | + | 0.857900i | \(0.328231\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.925197 | 0.161056 | ||||||||
\(34\) | −3.72161 | −0.638251 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 9.44322 | 1.55246 | 0.776228 | − | 0.630452i | \(-0.217130\pi\) | ||||
0.776228 | + | 0.630452i | \(0.217130\pi\) | |||||||
\(38\) | −1.72161 | −0.279282 | ||||||||
\(39\) | 4.64681 | 0.744085 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 5.44322 | 0.850089 | 0.425044 | − | 0.905173i | \(-0.360259\pi\) | ||||
0.425044 | + | 0.905173i | \(0.360259\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | 8.92520 | 1.36108 | 0.680540 | − | 0.732711i | \(-0.261745\pi\) | ||||
0.680540 | + | 0.732711i | \(0.261745\pi\) | |||||||
\(44\) | −0.925197 | −0.139479 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 5.72161 | 0.834583 | 0.417291 | − | 0.908773i | \(-0.362979\pi\) | ||||
0.417291 | + | 0.908773i | \(0.362979\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 3.72161 | 0.521130 | ||||||||
\(52\) | −4.64681 | −0.644396 | ||||||||
\(53\) | 9.44322 | 1.29713 | 0.648563 | − | 0.761161i | \(-0.275370\pi\) | ||||
0.648563 | + | 0.761161i | \(0.275370\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −0.925197 | −0.124754 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 1.72161 | 0.228033 | ||||||||
\(58\) | 2.92520 | 0.384097 | ||||||||
\(59\) | −7.44322 | −0.969025 | −0.484513 | − | 0.874784i | \(-0.661003\pi\) | ||||
−0.484513 | + | 0.874784i | \(0.661003\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 5.72161 | 0.726645 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.64681 | −0.576366 | ||||||||
\(66\) | 0.925197 | 0.113884 | ||||||||
\(67\) | 0.925197 | 0.113031 | 0.0565154 | − | 0.998402i | \(-0.482001\pi\) | ||||
0.0565154 | + | 0.998402i | \(0.482001\pi\) | |||||||
\(68\) | −3.72161 | −0.451312 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | 6.77559 | 0.804115 | 0.402057 | − | 0.915614i | \(-0.368295\pi\) | ||||
0.402057 | + | 0.915614i | \(0.368295\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 15.2936 | 1.78998 | 0.894991 | − | 0.446084i | \(-0.147182\pi\) | ||||
0.894991 | + | 0.446084i | \(0.147182\pi\) | |||||||
\(74\) | 9.44322 | 1.09775 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −1.72161 | −0.197482 | ||||||||
\(77\) | −0.925197 | −0.105436 | ||||||||
\(78\) | 4.64681 | 0.526147 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.44322 | 0.601103 | ||||||||
\(83\) | 15.0152 | 1.64814 | 0.824068 | − | 0.566491i | \(-0.191700\pi\) | ||||
0.824068 | + | 0.566491i | \(0.191700\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | −3.72161 | −0.403665 | ||||||||
\(86\) | 8.92520 | 0.962429 | ||||||||
\(87\) | −2.92520 | −0.313614 | ||||||||
\(88\) | −0.925197 | −0.0986263 | ||||||||
\(89\) | −6.79641 | −0.720419 | −0.360209 | − | 0.932872i | \(-0.617295\pi\) | ||||
−0.360209 | + | 0.932872i | \(0.617295\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | −4.64681 | −0.487118 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −5.72161 | −0.593303 | ||||||||
\(94\) | 5.72161 | 0.590139 | ||||||||
\(95\) | −1.72161 | −0.176634 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −10.2396 | −1.03968 | −0.519839 | − | 0.854264i | \(-0.674008\pi\) | ||||
−0.519839 | + | 0.854264i | \(0.674008\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −0.925197 | −0.0929858 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −2.79641 | −0.278254 | −0.139127 | − | 0.990275i | \(-0.544430\pi\) | ||||
−0.139127 | + | 0.990275i | \(0.544430\pi\) | |||||||
\(102\) | 3.72161 | 0.368494 | ||||||||
\(103\) | 1.85039 | 0.182325 | 0.0911624 | − | 0.995836i | \(-0.470942\pi\) | ||||
0.0911624 | + | 0.995836i | \(0.470942\pi\) | |||||||
\(104\) | −4.64681 | −0.455657 | ||||||||
\(105\) | −1.00000 | −0.0975900 | ||||||||
\(106\) | 9.44322 | 0.917207 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −0.149606 | −0.0143297 | −0.00716484 | − | 0.999974i | \(-0.502281\pi\) | ||||
−0.00716484 | + | 0.999974i | \(0.502281\pi\) | |||||||
\(110\) | −0.925197 | −0.0882141 | ||||||||
\(111\) | −9.44322 | −0.896311 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 13.4432 | 1.26463 | 0.632316 | − | 0.774711i | \(-0.282104\pi\) | ||||
0.632316 | + | 0.774711i | \(0.282104\pi\) | |||||||
\(114\) | 1.72161 | 0.161244 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 2.92520 | 0.271598 | ||||||||
\(117\) | −4.64681 | −0.429598 | ||||||||
\(118\) | −7.44322 | −0.685204 | ||||||||
\(119\) | −3.72161 | −0.341160 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −10.1440 | −0.922183 | ||||||||
\(122\) | −2.00000 | −0.181071 | ||||||||
\(123\) | −5.44322 | −0.490799 | ||||||||
\(124\) | 5.72161 | 0.513816 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | −0.368420 | −0.0326920 | −0.0163460 | − | 0.999866i | \(-0.505203\pi\) | ||||
−0.0163460 | + | 0.999866i | \(0.505203\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −8.92520 | −0.785820 | ||||||||
\(130\) | −4.64681 | −0.407552 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 0.925197 | 0.0805280 | ||||||||
\(133\) | −1.72161 | −0.149283 | ||||||||
\(134\) | 0.925197 | 0.0799248 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −3.72161 | −0.319126 | ||||||||
\(137\) | −9.70079 | −0.828794 | −0.414397 | − | 0.910096i | \(-0.636008\pi\) | ||||
−0.414397 | + | 0.910096i | \(0.636008\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | 9.29362 | 0.788274 | 0.394137 | − | 0.919052i | \(-0.371043\pi\) | ||||
0.394137 | + | 0.919052i | \(0.371043\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | −5.72161 | −0.481847 | ||||||||
\(142\) | 6.77559 | 0.568595 | ||||||||
\(143\) | 4.29921 | 0.359518 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.92520 | 0.242924 | ||||||||
\(146\) | 15.2936 | 1.26571 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 9.44322 | 0.776228 | ||||||||
\(149\) | −17.1440 | −1.40449 | −0.702246 | − | 0.711934i | \(-0.747819\pi\) | ||||
−0.702246 | + | 0.711934i | \(0.747819\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | −13.2936 | −1.08182 | −0.540910 | − | 0.841081i | \(-0.681920\pi\) | ||||
−0.540910 | + | 0.841081i | \(0.681920\pi\) | |||||||
\(152\) | −1.72161 | −0.139641 | ||||||||
\(153\) | −3.72161 | −0.300874 | ||||||||
\(154\) | −0.925197 | −0.0745545 | ||||||||
\(155\) | 5.72161 | 0.459571 | ||||||||
\(156\) | 4.64681 | 0.372042 | ||||||||
\(157\) | 14.7368 | 1.17613 | 0.588064 | − | 0.808814i | \(-0.299890\pi\) | ||||
0.588064 | + | 0.808814i | \(0.299890\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.44322 | −0.748896 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −1.29362 | −0.101324 | −0.0506620 | − | 0.998716i | \(-0.516133\pi\) | ||||
−0.0506620 | + | 0.998716i | \(0.516133\pi\) | |||||||
\(164\) | 5.44322 | 0.425044 | ||||||||
\(165\) | 0.925197 | 0.0720265 | ||||||||
\(166\) | 15.0152 | 1.16541 | ||||||||
\(167\) | −14.4585 | −1.11883 | −0.559414 | − | 0.828888i | \(-0.688974\pi\) | ||||
−0.559414 | + | 0.828888i | \(0.688974\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 8.59283 | 0.660987 | ||||||||
\(170\) | −3.72161 | −0.285435 | ||||||||
\(171\) | −1.72161 | −0.131655 | ||||||||
\(172\) | 8.92520 | 0.680540 | ||||||||
\(173\) | 7.16484 | 0.544732 | 0.272366 | − | 0.962194i | \(-0.412194\pi\) | ||||
0.272366 | + | 0.962194i | \(0.412194\pi\) | |||||||
\(174\) | −2.92520 | −0.221759 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −0.925197 | −0.0697393 | ||||||||
\(177\) | 7.44322 | 0.559467 | ||||||||
\(178\) | −6.79641 | −0.509413 | ||||||||
\(179\) | 20.7368 | 1.54994 | 0.774972 | − | 0.631995i | \(-0.217764\pi\) | ||||
0.774972 | + | 0.631995i | \(0.217764\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | −4.64681 | −0.344444 | ||||||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 9.44322 | 0.694280 | ||||||||
\(186\) | −5.72161 | −0.419529 | ||||||||
\(187\) | 3.44322 | 0.251793 | ||||||||
\(188\) | 5.72161 | 0.417291 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −1.72161 | −0.124899 | ||||||||
\(191\) | 4.55678 | 0.329717 | 0.164858 | − | 0.986317i | \(-0.447283\pi\) | ||||
0.164858 | + | 0.986317i | \(0.447283\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 6.55678 | 0.471967 | 0.235984 | − | 0.971757i | \(-0.424169\pi\) | ||||
0.235984 | + | 0.971757i | \(0.424169\pi\) | |||||||
\(194\) | −10.2396 | −0.735163 | ||||||||
\(195\) | 4.64681 | 0.332765 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −1.74244 | −0.124143 | −0.0620717 | − | 0.998072i | \(-0.519771\pi\) | ||||
−0.0620717 | + | 0.998072i | \(0.519771\pi\) | |||||||
\(198\) | −0.925197 | −0.0657509 | ||||||||
\(199\) | −3.44322 | −0.244084 | −0.122042 | − | 0.992525i | \(-0.538944\pi\) | ||||
−0.122042 | + | 0.992525i | \(0.538944\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −0.925197 | −0.0652584 | ||||||||
\(202\) | −2.79641 | −0.196755 | ||||||||
\(203\) | 2.92520 | 0.205309 | ||||||||
\(204\) | 3.72161 | 0.260565 | ||||||||
\(205\) | 5.44322 | 0.380171 | ||||||||
\(206\) | 1.85039 | 0.128923 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −4.64681 | −0.322198 | ||||||||
\(209\) | 1.59283 | 0.110178 | ||||||||
\(210\) | −1.00000 | −0.0690066 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 9.44322 | 0.648563 | ||||||||
\(213\) | −6.77559 | −0.464256 | ||||||||
\(214\) | 4.00000 | 0.273434 | ||||||||
\(215\) | 8.92520 | 0.608693 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 5.72161 | 0.388408 | ||||||||
\(218\) | −0.149606 | −0.0101326 | ||||||||
\(219\) | −15.2936 | −1.03345 | ||||||||
\(220\) | −0.925197 | −0.0623768 | ||||||||
\(221\) | 17.2936 | 1.16329 | ||||||||
\(222\) | −9.44322 | −0.633788 | ||||||||
\(223\) | −4.49720 | −0.301155 | −0.150577 | − | 0.988598i | \(-0.548113\pi\) | ||||
−0.150577 | + | 0.988598i | \(0.548113\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 13.4432 | 0.894230 | ||||||||
\(227\) | −6.27839 | −0.416711 | −0.208356 | − | 0.978053i | \(-0.566811\pi\) | ||||
−0.208356 | + | 0.978053i | \(0.566811\pi\) | |||||||
\(228\) | 1.72161 | 0.114017 | ||||||||
\(229\) | −0.149606 | −0.00988626 | −0.00494313 | − | 0.999988i | \(-0.501573\pi\) | ||||
−0.00494313 | + | 0.999988i | \(0.501573\pi\) | |||||||
\(230\) | −1.00000 | −0.0659380 | ||||||||
\(231\) | 0.925197 | 0.0608735 | ||||||||
\(232\) | 2.92520 | 0.192049 | ||||||||
\(233\) | 5.44322 | 0.356597 | 0.178299 | − | 0.983976i | \(-0.442941\pi\) | ||||
0.178299 | + | 0.983976i | \(0.442941\pi\) | |||||||
\(234\) | −4.64681 | −0.303771 | ||||||||
\(235\) | 5.72161 | 0.373237 | ||||||||
\(236\) | −7.44322 | −0.484513 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.72161 | −0.241236 | ||||||||
\(239\) | 14.7756 | 0.955753 | 0.477877 | − | 0.878427i | \(-0.341407\pi\) | ||||
0.477877 | + | 0.878427i | \(0.341407\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 3.16484 | 0.203865 | 0.101932 | − | 0.994791i | \(-0.467497\pi\) | ||||
0.101932 | + | 0.994791i | \(0.467497\pi\) | |||||||
\(242\) | −10.1440 | −0.652082 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −5.44322 | −0.347047 | ||||||||
\(247\) | 8.00000 | 0.509028 | ||||||||
\(248\) | 5.72161 | 0.363323 | ||||||||
\(249\) | −15.0152 | −0.951551 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −4.79641 | −0.302747 | −0.151374 | − | 0.988477i | \(-0.548370\pi\) | ||||
−0.151374 | + | 0.988477i | \(0.548370\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 0.925197 | 0.0581666 | ||||||||
\(254\) | −0.368420 | −0.0231167 | ||||||||
\(255\) | 3.72161 | 0.233056 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −29.1440 | −1.81795 | −0.908977 | − | 0.416847i | \(-0.863135\pi\) | ||||
−0.908977 | + | 0.416847i | \(0.863135\pi\) | |||||||
\(258\) | −8.92520 | −0.555658 | ||||||||
\(259\) | 9.44322 | 0.586773 | ||||||||
\(260\) | −4.64681 | −0.288183 | ||||||||
\(261\) | 2.92520 | 0.181065 | ||||||||
\(262\) | −4.00000 | −0.247121 | ||||||||
\(263\) | −20.1801 | −1.24436 | −0.622178 | − | 0.782876i | \(-0.713752\pi\) | ||||
−0.622178 | + | 0.782876i | \(0.713752\pi\) | |||||||
\(264\) | 0.925197 | 0.0569419 | ||||||||
\(265\) | 9.44322 | 0.580093 | ||||||||
\(266\) | −1.72161 | −0.105559 | ||||||||
\(267\) | 6.79641 | 0.415934 | ||||||||
\(268\) | 0.925197 | 0.0565154 | ||||||||
\(269\) | −27.5333 | −1.67873 | −0.839366 | − | 0.543567i | \(-0.817074\pi\) | ||||
−0.839366 | + | 0.543567i | \(0.817074\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 2.02082 | 0.122756 | 0.0613782 | − | 0.998115i | \(-0.480450\pi\) | ||||
0.0613782 | + | 0.998115i | \(0.480450\pi\) | |||||||
\(272\) | −3.72161 | −0.225656 | ||||||||
\(273\) | 4.64681 | 0.281238 | ||||||||
\(274\) | −9.70079 | −0.586046 | ||||||||
\(275\) | −0.925197 | −0.0557915 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | 6.36842 | 0.382641 | 0.191321 | − | 0.981528i | \(-0.438723\pi\) | ||||
0.191321 | + | 0.981528i | \(0.438723\pi\) | |||||||
\(278\) | 9.29362 | 0.557394 | ||||||||
\(279\) | 5.72161 | 0.342544 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 16.5180 | 0.985383 | 0.492691 | − | 0.870204i | \(-0.336013\pi\) | ||||
0.492691 | + | 0.870204i | \(0.336013\pi\) | |||||||
\(282\) | −5.72161 | −0.340717 | ||||||||
\(283\) | 29.5333 | 1.75557 | 0.877785 | − | 0.479055i | \(-0.159021\pi\) | ||||
0.877785 | + | 0.479055i | \(0.159021\pi\) | |||||||
\(284\) | 6.77559 | 0.402057 | ||||||||
\(285\) | 1.72161 | 0.101979 | ||||||||
\(286\) | 4.29921 | 0.254218 | ||||||||
\(287\) | 5.44322 | 0.321303 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −3.14961 | −0.185271 | ||||||||
\(290\) | 2.92520 | 0.171773 | ||||||||
\(291\) | 10.2396 | 0.600258 | ||||||||
\(292\) | 15.2936 | 0.894991 | ||||||||
\(293\) | −3.85039 | −0.224942 | −0.112471 | − | 0.993655i | \(-0.535877\pi\) | ||||
−0.112471 | + | 0.993655i | \(0.535877\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −7.44322 | −0.433361 | ||||||||
\(296\) | 9.44322 | 0.548876 | ||||||||
\(297\) | 0.925197 | 0.0536854 | ||||||||
\(298\) | −17.1440 | −0.993126 | ||||||||
\(299\) | 4.64681 | 0.268732 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 8.92520 | 0.514440 | ||||||||
\(302\) | −13.2936 | −0.764962 | ||||||||
\(303\) | 2.79641 | 0.160650 | ||||||||
\(304\) | −1.72161 | −0.0987412 | ||||||||
\(305\) | −2.00000 | −0.114520 | ||||||||
\(306\) | −3.72161 | −0.212750 | ||||||||
\(307\) | 25.0361 | 1.42888 | 0.714442 | − | 0.699695i | \(-0.246681\pi\) | ||||
0.714442 | + | 0.699695i | \(0.246681\pi\) | |||||||
\(308\) | −0.925197 | −0.0527180 | ||||||||
\(309\) | −1.85039 | −0.105265 | ||||||||
\(310\) | 5.72161 | 0.324966 | ||||||||
\(311\) | 14.0900 | 0.798972 | 0.399486 | − | 0.916739i | \(-0.369189\pi\) | ||||
0.399486 | + | 0.916739i | \(0.369189\pi\) | |||||||
\(312\) | 4.64681 | 0.263074 | ||||||||
\(313\) | 3.05398 | 0.172621 | 0.0863105 | − | 0.996268i | \(-0.472492\pi\) | ||||
0.0863105 | + | 0.996268i | \(0.472492\pi\) | |||||||
\(314\) | 14.7368 | 0.831648 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.29362 | 0.184988 | 0.0924940 | − | 0.995713i | \(-0.470516\pi\) | ||||
0.0924940 | + | 0.995713i | \(0.470516\pi\) | |||||||
\(318\) | −9.44322 | −0.529550 | ||||||||
\(319\) | −2.70638 | −0.151528 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | −1.00000 | −0.0557278 | ||||||||
\(323\) | 6.40717 | 0.356504 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.64681 | −0.257759 | ||||||||
\(326\) | −1.29362 | −0.0716468 | ||||||||
\(327\) | 0.149606 | 0.00827325 | ||||||||
\(328\) | 5.44322 | 0.300552 | ||||||||
\(329\) | 5.72161 | 0.315443 | ||||||||
\(330\) | 0.925197 | 0.0509304 | ||||||||
\(331\) | 10.4072 | 0.572030 | 0.286015 | − | 0.958225i | \(-0.407669\pi\) | ||||
0.286015 | + | 0.958225i | \(0.407669\pi\) | |||||||
\(332\) | 15.0152 | 0.824068 | ||||||||
\(333\) | 9.44322 | 0.517485 | ||||||||
\(334\) | −14.4585 | −0.791131 | ||||||||
\(335\) | 0.925197 | 0.0505489 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 5.33237 | 0.290473 | 0.145236 | − | 0.989397i | \(-0.453606\pi\) | ||||
0.145236 | + | 0.989397i | \(0.453606\pi\) | |||||||
\(338\) | 8.59283 | 0.467388 | ||||||||
\(339\) | −13.4432 | −0.730136 | ||||||||
\(340\) | −3.72161 | −0.201833 | ||||||||
\(341\) | −5.29362 | −0.286665 | ||||||||
\(342\) | −1.72161 | −0.0930941 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 8.92520 | 0.481214 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | 7.16484 | 0.385184 | ||||||||
\(347\) | −5.59283 | −0.300239 | −0.150119 | − | 0.988668i | \(-0.547966\pi\) | ||||
−0.150119 | + | 0.988668i | \(0.547966\pi\) | |||||||
\(348\) | −2.92520 | −0.156807 | ||||||||
\(349\) | −12.0208 | −0.643460 | −0.321730 | − | 0.946831i | \(-0.604264\pi\) | ||||
−0.321730 | + | 0.946831i | \(0.604264\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 4.64681 | 0.248028 | ||||||||
\(352\) | −0.925197 | −0.0493132 | ||||||||
\(353\) | −11.0361 | −0.587390 | −0.293695 | − | 0.955899i | \(-0.594885\pi\) | ||||
−0.293695 | + | 0.955899i | \(0.594885\pi\) | |||||||
\(354\) | 7.44322 | 0.395603 | ||||||||
\(355\) | 6.77559 | 0.359611 | ||||||||
\(356\) | −6.79641 | −0.360209 | ||||||||
\(357\) | 3.72161 | 0.196969 | ||||||||
\(358\) | 20.7368 | 1.09598 | ||||||||
\(359\) | 7.14401 | 0.377046 | 0.188523 | − | 0.982069i | \(-0.439630\pi\) | ||||
0.188523 | + | 0.982069i | \(0.439630\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −16.0361 | −0.844003 | ||||||||
\(362\) | 6.00000 | 0.315353 | ||||||||
\(363\) | 10.1440 | 0.532422 | ||||||||
\(364\) | −4.64681 | −0.243559 | ||||||||
\(365\) | 15.2936 | 0.800505 | ||||||||
\(366\) | 2.00000 | 0.104542 | ||||||||
\(367\) | −20.4376 | −1.06684 | −0.533418 | − | 0.845852i | \(-0.679093\pi\) | ||||
−0.533418 | + | 0.845852i | \(0.679093\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 5.44322 | 0.283363 | ||||||||
\(370\) | 9.44322 | 0.490930 | ||||||||
\(371\) | 9.44322 | 0.490268 | ||||||||
\(372\) | −5.72161 | −0.296652 | ||||||||
\(373\) | −1.14401 | −0.0592346 | −0.0296173 | − | 0.999561i | \(-0.509429\pi\) | ||||
−0.0296173 | + | 0.999561i | \(0.509429\pi\) | |||||||
\(374\) | 3.44322 | 0.178045 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 5.72161 | 0.295070 | ||||||||
\(377\) | −13.5928 | −0.700066 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 0.299213 | 0.0153695 | 0.00768476 | − | 0.999970i | \(-0.497554\pi\) | ||||
0.00768476 | + | 0.999970i | \(0.497554\pi\) | |||||||
\(380\) | −1.72161 | −0.0883168 | ||||||||
\(381\) | 0.368420 | 0.0188747 | ||||||||
\(382\) | 4.55678 | 0.233145 | ||||||||
\(383\) | 0.736841 | 0.0376508 | 0.0188254 | − | 0.999823i | \(-0.494007\pi\) | ||||
0.0188254 | + | 0.999823i | \(0.494007\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −0.925197 | −0.0471524 | ||||||||
\(386\) | 6.55678 | 0.333731 | ||||||||
\(387\) | 8.92520 | 0.453693 | ||||||||
\(388\) | −10.2396 | −0.519839 | ||||||||
\(389\) | −31.0361 | −1.57359 | −0.786795 | − | 0.617214i | \(-0.788261\pi\) | ||||
−0.786795 | + | 0.617214i | \(0.788261\pi\) | |||||||
\(390\) | 4.64681 | 0.235300 | ||||||||
\(391\) | 3.72161 | 0.188210 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 4.00000 | 0.201773 | ||||||||
\(394\) | −1.74244 | −0.0877827 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.925197 | −0.0464929 | ||||||||
\(397\) | −4.64681 | −0.233217 | −0.116608 | − | 0.993178i | \(-0.537202\pi\) | ||||
−0.116608 | + | 0.993178i | \(0.537202\pi\) | |||||||
\(398\) | −3.44322 | −0.172593 | ||||||||
\(399\) | 1.72161 | 0.0861884 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −8.21881 | −0.410428 | −0.205214 | − | 0.978717i | \(-0.565789\pi\) | ||||
−0.205214 | + | 0.978717i | \(0.565789\pi\) | |||||||
\(402\) | −0.925197 | −0.0461446 | ||||||||
\(403\) | −26.5872 | −1.32440 | ||||||||
\(404\) | −2.79641 | −0.139127 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 2.92520 | 0.145175 | ||||||||
\(407\) | −8.73684 | −0.433069 | ||||||||
\(408\) | 3.72161 | 0.184247 | ||||||||
\(409\) | −12.1496 | −0.600759 | −0.300380 | − | 0.953820i | \(-0.597113\pi\) | ||||
−0.300380 | + | 0.953820i | \(0.597113\pi\) | |||||||
\(410\) | 5.44322 | 0.268822 | ||||||||
\(411\) | 9.70079 | 0.478505 | ||||||||
\(412\) | 1.85039 | 0.0911624 | ||||||||
\(413\) | −7.44322 | −0.366257 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 15.0152 | 0.737069 | ||||||||
\(416\) | −4.64681 | −0.227829 | ||||||||
\(417\) | −9.29362 | −0.455110 | ||||||||
\(418\) | 1.59283 | 0.0779078 | ||||||||
\(419\) | −26.3476 | −1.28716 | −0.643582 | − | 0.765377i | \(-0.722553\pi\) | ||||
−0.643582 | + | 0.765377i | \(0.722553\pi\) | |||||||
\(420\) | −1.00000 | −0.0487950 | ||||||||
\(421\) | 8.70638 | 0.424323 | 0.212162 | − | 0.977235i | \(-0.431950\pi\) | ||||
0.212162 | + | 0.977235i | \(0.431950\pi\) | |||||||
\(422\) | 4.00000 | 0.194717 | ||||||||
\(423\) | 5.72161 | 0.278194 | ||||||||
\(424\) | 9.44322 | 0.458603 | ||||||||
\(425\) | −3.72161 | −0.180525 | ||||||||
\(426\) | −6.77559 | −0.328278 | ||||||||
\(427\) | −2.00000 | −0.0967868 | ||||||||
\(428\) | 4.00000 | 0.193347 | ||||||||
\(429\) | −4.29921 | −0.207568 | ||||||||
\(430\) | 8.92520 | 0.430411 | ||||||||
\(431\) | 22.0305 | 1.06117 | 0.530585 | − | 0.847632i | \(-0.321972\pi\) | ||||
0.530585 | + | 0.847632i | \(0.321972\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −3.35319 | −0.161144 | −0.0805720 | − | 0.996749i | \(-0.525675\pi\) | ||||
−0.0805720 | + | 0.996749i | \(0.525675\pi\) | |||||||
\(434\) | 5.72161 | 0.274646 | ||||||||
\(435\) | −2.92520 | −0.140252 | ||||||||
\(436\) | −0.149606 | −0.00716484 | ||||||||
\(437\) | 1.72161 | 0.0823559 | ||||||||
\(438\) | −15.2936 | −0.730757 | ||||||||
\(439\) | −23.5720 | −1.12503 | −0.562515 | − | 0.826787i | \(-0.690166\pi\) | ||||
−0.562515 | + | 0.826787i | \(0.690166\pi\) | |||||||
\(440\) | −0.925197 | −0.0441070 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 17.2936 | 0.822573 | ||||||||
\(443\) | −12.4793 | −0.592908 | −0.296454 | − | 0.955047i | \(-0.595804\pi\) | ||||
−0.296454 | + | 0.955047i | \(0.595804\pi\) | |||||||
\(444\) | −9.44322 | −0.448156 | ||||||||
\(445\) | −6.79641 | −0.322181 | ||||||||
\(446\) | −4.49720 | −0.212949 | ||||||||
\(447\) | 17.1440 | 0.810884 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 30.1801 | 1.42429 | 0.712143 | − | 0.702035i | \(-0.247725\pi\) | ||||
0.712143 | + | 0.702035i | \(0.247725\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −5.03605 | −0.237138 | ||||||||
\(452\) | 13.4432 | 0.632316 | ||||||||
\(453\) | 13.2936 | 0.624589 | ||||||||
\(454\) | −6.27839 | −0.294659 | ||||||||
\(455\) | −4.64681 | −0.217846 | ||||||||
\(456\) | 1.72161 | 0.0806219 | ||||||||
\(457\) | 22.3268 | 1.04440 | 0.522201 | − | 0.852822i | \(-0.325111\pi\) | ||||
0.522201 | + | 0.852822i | \(0.325111\pi\) | |||||||
\(458\) | −0.149606 | −0.00699064 | ||||||||
\(459\) | 3.72161 | 0.173710 | ||||||||
\(460\) | −1.00000 | −0.0466252 | ||||||||
\(461\) | 8.38924 | 0.390726 | 0.195363 | − | 0.980731i | \(-0.437411\pi\) | ||||
0.195363 | + | 0.980731i | \(0.437411\pi\) | |||||||
\(462\) | 0.925197 | 0.0430441 | ||||||||
\(463\) | 24.1109 | 1.12053 | 0.560263 | − | 0.828315i | \(-0.310700\pi\) | ||||
0.560263 | + | 0.828315i | \(0.310700\pi\) | |||||||
\(464\) | 2.92520 | 0.135799 | ||||||||
\(465\) | −5.72161 | −0.265333 | ||||||||
\(466\) | 5.44322 | 0.252152 | ||||||||
\(467\) | 3.57201 | 0.165293 | 0.0826463 | − | 0.996579i | \(-0.473663\pi\) | ||||
0.0826463 | + | 0.996579i | \(0.473663\pi\) | |||||||
\(468\) | −4.64681 | −0.214799 | ||||||||
\(469\) | 0.925197 | 0.0427216 | ||||||||
\(470\) | 5.72161 | 0.263918 | ||||||||
\(471\) | −14.7368 | −0.679038 | ||||||||
\(472\) | −7.44322 | −0.342602 | ||||||||
\(473\) | −8.25756 | −0.379683 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.72161 | −0.0789930 | ||||||||
\(476\) | −3.72161 | −0.170580 | ||||||||
\(477\) | 9.44322 | 0.432375 | ||||||||
\(478\) | 14.7756 | 0.675820 | ||||||||
\(479\) | 23.6233 | 1.07938 | 0.539688 | − | 0.841865i | \(-0.318542\pi\) | ||||
0.539688 | + | 0.841865i | \(0.318542\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | −43.8809 | −2.00079 | ||||||||
\(482\) | 3.16484 | 0.144154 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | −10.1440 | −0.461091 | ||||||||
\(485\) | −10.2396 | −0.464958 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −3.07480 | −0.139333 | −0.0696663 | − | 0.997570i | \(-0.522193\pi\) | ||||
−0.0696663 | + | 0.997570i | \(0.522193\pi\) | |||||||
\(488\) | −2.00000 | −0.0905357 | ||||||||
\(489\) | 1.29362 | 0.0584994 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 18.8864 | 0.852333 | 0.426167 | − | 0.904645i | \(-0.359864\pi\) | ||||
0.426167 | + | 0.904645i | \(0.359864\pi\) | |||||||
\(492\) | −5.44322 | −0.245399 | ||||||||
\(493\) | −10.8864 | −0.490301 | ||||||||
\(494\) | 8.00000 | 0.359937 | ||||||||
\(495\) | −0.925197 | −0.0415845 | ||||||||
\(496\) | 5.72161 | 0.256908 | ||||||||
\(497\) | 6.77559 | 0.303927 | ||||||||
\(498\) | −15.0152 | −0.672848 | ||||||||
\(499\) | 33.7729 | 1.51188 | 0.755941 | − | 0.654640i | \(-0.227180\pi\) | ||||
0.755941 | + | 0.654640i | \(0.227180\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 14.4585 | 0.645956 | ||||||||
\(502\) | −4.79641 | −0.214074 | ||||||||
\(503\) | −21.0361 | −0.937951 | −0.468976 | − | 0.883211i | \(-0.655377\pi\) | ||||
−0.468976 | + | 0.883211i | \(0.655377\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | −2.79641 | −0.124439 | ||||||||
\(506\) | 0.925197 | 0.0411300 | ||||||||
\(507\) | −8.59283 | −0.381621 | ||||||||
\(508\) | −0.368420 | −0.0163460 | ||||||||
\(509\) | −30.4972 | −1.35176 | −0.675882 | − | 0.737010i | \(-0.736237\pi\) | ||||
−0.675882 | + | 0.737010i | \(0.736237\pi\) | |||||||
\(510\) | 3.72161 | 0.164796 | ||||||||
\(511\) | 15.2936 | 0.676550 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.72161 | 0.0760110 | ||||||||
\(514\) | −29.1440 | −1.28549 | ||||||||
\(515\) | 1.85039 | 0.0815381 | ||||||||
\(516\) | −8.92520 | −0.392910 | ||||||||
\(517\) | −5.29362 | −0.232813 | ||||||||
\(518\) | 9.44322 | 0.414911 | ||||||||
\(519\) | −7.16484 | −0.314501 | ||||||||
\(520\) | −4.64681 | −0.203776 | ||||||||
\(521\) | −33.3836 | −1.46256 | −0.731282 | − | 0.682075i | \(-0.761078\pi\) | ||||
−0.731282 | + | 0.682075i | \(0.761078\pi\) | |||||||
\(522\) | 2.92520 | 0.128032 | ||||||||
\(523\) | 29.5333 | 1.29140 | 0.645700 | − | 0.763592i | \(-0.276566\pi\) | ||||
0.645700 | + | 0.763592i | \(0.276566\pi\) | |||||||
\(524\) | −4.00000 | −0.174741 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | −20.1801 | −0.879893 | ||||||||
\(527\) | −21.2936 | −0.927565 | ||||||||
\(528\) | 0.925197 | 0.0402640 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 9.44322 | 0.410187 | ||||||||
\(531\) | −7.44322 | −0.323008 | ||||||||
\(532\) | −1.72161 | −0.0746413 | ||||||||
\(533\) | −25.2936 | −1.09559 | ||||||||
\(534\) | 6.79641 | 0.294110 | ||||||||
\(535\) | 4.00000 | 0.172935 | ||||||||
\(536\) | 0.925197 | 0.0399624 | ||||||||
\(537\) | −20.7368 | −0.894861 | ||||||||
\(538\) | −27.5333 | −1.18704 | ||||||||
\(539\) | −0.925197 | −0.0398510 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 4.14961 | 0.178406 | 0.0892028 | − | 0.996013i | \(-0.471568\pi\) | ||||
0.0892028 | + | 0.996013i | \(0.471568\pi\) | |||||||
\(542\) | 2.02082 | 0.0868018 | ||||||||
\(543\) | −6.00000 | −0.257485 | ||||||||
\(544\) | −3.72161 | −0.159563 | ||||||||
\(545\) | −0.149606 | −0.00640843 | ||||||||
\(546\) | 4.64681 | 0.198865 | ||||||||
\(547\) | −34.0305 | −1.45504 | −0.727519 | − | 0.686088i | \(-0.759327\pi\) | ||||
−0.727519 | + | 0.686088i | \(0.759327\pi\) | |||||||
\(548\) | −9.70079 | −0.414397 | ||||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | −0.925197 | −0.0394505 | ||||||||
\(551\) | −5.03605 | −0.214543 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6.36842 | 0.270568 | ||||||||
\(555\) | −9.44322 | −0.400843 | ||||||||
\(556\) | 9.29362 | 0.394137 | ||||||||
\(557\) | −3.33527 | −0.141320 | −0.0706599 | − | 0.997500i | \(-0.522510\pi\) | ||||
−0.0706599 | + | 0.997500i | \(0.522510\pi\) | |||||||
\(558\) | 5.72161 | 0.242215 | ||||||||
\(559\) | −41.4737 | −1.75415 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | −3.44322 | −0.145373 | ||||||||
\(562\) | 16.5180 | 0.696771 | ||||||||
\(563\) | 15.0152 | 0.632816 | 0.316408 | − | 0.948623i | \(-0.397523\pi\) | ||||
0.316408 | + | 0.948623i | \(0.397523\pi\) | |||||||
\(564\) | −5.72161 | −0.240923 | ||||||||
\(565\) | 13.4432 | 0.565561 | ||||||||
\(566\) | 29.5333 | 1.24138 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 6.77559 | 0.284297 | ||||||||
\(569\) | −32.2188 | −1.35068 | −0.675341 | − | 0.737505i | \(-0.736004\pi\) | ||||
−0.675341 | + | 0.737505i | \(0.736004\pi\) | |||||||
\(570\) | 1.72161 | 0.0721104 | ||||||||
\(571\) | −0.556777 | −0.0233004 | −0.0116502 | − | 0.999932i | \(-0.503708\pi\) | ||||
−0.0116502 | + | 0.999932i | \(0.503708\pi\) | |||||||
\(572\) | 4.29921 | 0.179759 | ||||||||
\(573\) | −4.55678 | −0.190362 | ||||||||
\(574\) | 5.44322 | 0.227196 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −7.11355 | −0.296141 | −0.148071 | − | 0.988977i | \(-0.547306\pi\) | ||||
−0.148071 | + | 0.988977i | \(0.547306\pi\) | |||||||
\(578\) | −3.14961 | −0.131006 | ||||||||
\(579\) | −6.55678 | −0.272490 | ||||||||
\(580\) | 2.92520 | 0.121462 | ||||||||
\(581\) | 15.0152 | 0.622937 | ||||||||
\(582\) | 10.2396 | 0.424447 | ||||||||
\(583\) | −8.73684 | −0.361843 | ||||||||
\(584\) | 15.2936 | 0.632854 | ||||||||
\(585\) | −4.64681 | −0.192122 | ||||||||
\(586\) | −3.85039 | −0.159058 | ||||||||
\(587\) | −11.1440 | −0.459963 | −0.229981 | − | 0.973195i | \(-0.573866\pi\) | ||||
−0.229981 | + | 0.973195i | \(0.573866\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | −9.85039 | −0.405878 | ||||||||
\(590\) | −7.44322 | −0.306433 | ||||||||
\(591\) | 1.74244 | 0.0716742 | ||||||||
\(592\) | 9.44322 | 0.388114 | ||||||||
\(593\) | −22.2576 | −0.914009 | −0.457004 | − | 0.889464i | \(-0.651078\pi\) | ||||
−0.457004 | + | 0.889464i | \(0.651078\pi\) | |||||||
\(594\) | 0.925197 | 0.0379613 | ||||||||
\(595\) | −3.72161 | −0.152571 | ||||||||
\(596\) | −17.1440 | −0.702246 | ||||||||
\(597\) | 3.44322 | 0.140922 | ||||||||
\(598\) | 4.64681 | 0.190022 | ||||||||
\(599\) | −11.3324 | −0.463028 | −0.231514 | − | 0.972832i | \(-0.574368\pi\) | ||||
−0.231514 | + | 0.972832i | \(0.574368\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | 6.18006 | 0.252090 | 0.126045 | − | 0.992025i | \(-0.459772\pi\) | ||||
0.126045 | + | 0.992025i | \(0.459772\pi\) | |||||||
\(602\) | 8.92520 | 0.363764 | ||||||||
\(603\) | 0.925197 | 0.0376769 | ||||||||
\(604\) | −13.2936 | −0.540910 | ||||||||
\(605\) | −10.1440 | −0.412413 | ||||||||
\(606\) | 2.79641 | 0.113597 | ||||||||
\(607\) | 37.2340 | 1.51128 | 0.755642 | − | 0.654985i | \(-0.227325\pi\) | ||||
0.755642 | + | 0.654985i | \(0.227325\pi\) | |||||||
\(608\) | −1.72161 | −0.0698206 | ||||||||
\(609\) | −2.92520 | −0.118535 | ||||||||
\(610\) | −2.00000 | −0.0809776 | ||||||||
\(611\) | −26.5872 | −1.07560 | ||||||||
\(612\) | −3.72161 | −0.150437 | ||||||||
\(613\) | −22.4376 | −0.906247 | −0.453124 | − | 0.891448i | \(-0.649690\pi\) | ||||
−0.453124 | + | 0.891448i | \(0.649690\pi\) | |||||||
\(614\) | 25.0361 | 1.01037 | ||||||||
\(615\) | −5.44322 | −0.219492 | ||||||||
\(616\) | −0.925197 | −0.0372772 | ||||||||
\(617\) | 7.03605 | 0.283261 | 0.141630 | − | 0.989920i | \(-0.454766\pi\) | ||||
0.141630 | + | 0.989920i | \(0.454766\pi\) | |||||||
\(618\) | −1.85039 | −0.0744338 | ||||||||
\(619\) | 19.1953 | 0.771524 | 0.385762 | − | 0.922598i | \(-0.373939\pi\) | ||||
0.385762 | + | 0.922598i | \(0.373939\pi\) | |||||||
\(620\) | 5.72161 | 0.229785 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 14.0900 | 0.564959 | ||||||||
\(623\) | −6.79641 | −0.272293 | ||||||||
\(624\) | 4.64681 | 0.186021 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 3.05398 | 0.122062 | ||||||||
\(627\) | −1.59283 | −0.0636115 | ||||||||
\(628\) | 14.7368 | 0.588064 | ||||||||
\(629\) | −35.1440 | −1.40128 | ||||||||
\(630\) | 1.00000 | 0.0398410 | ||||||||
\(631\) | 4.29921 | 0.171149 | 0.0855745 | − | 0.996332i | \(-0.472727\pi\) | ||||
0.0855745 | + | 0.996332i | \(0.472727\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.00000 | −0.158986 | ||||||||
\(634\) | 3.29362 | 0.130806 | ||||||||
\(635\) | −0.368420 | −0.0146203 | ||||||||
\(636\) | −9.44322 | −0.374448 | ||||||||
\(637\) | −4.64681 | −0.184113 | ||||||||
\(638\) | −2.70638 | −0.107147 | ||||||||
\(639\) | 6.77559 | 0.268038 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −14.3684 | −0.567518 | −0.283759 | − | 0.958896i | \(-0.591582\pi\) | ||||
−0.283759 | + | 0.958896i | \(0.591582\pi\) | |||||||
\(642\) | −4.00000 | −0.157867 | ||||||||
\(643\) | 29.7908 | 1.17484 | 0.587418 | − | 0.809284i | \(-0.300145\pi\) | ||||
0.587418 | + | 0.809284i | \(0.300145\pi\) | |||||||
\(644\) | −1.00000 | −0.0394055 | ||||||||
\(645\) | −8.92520 | −0.351429 | ||||||||
\(646\) | 6.40717 | 0.252087 | ||||||||
\(647\) | 16.0513 | 0.631041 | 0.315521 | − | 0.948919i | \(-0.397821\pi\) | ||||
0.315521 | + | 0.948919i | \(0.397821\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 6.88645 | 0.270317 | ||||||||
\(650\) | −4.64681 | −0.182263 | ||||||||
\(651\) | −5.72161 | −0.224248 | ||||||||
\(652\) | −1.29362 | −0.0506620 | ||||||||
\(653\) | 7.85039 | 0.307210 | 0.153605 | − | 0.988132i | \(-0.450912\pi\) | ||||
0.153605 | + | 0.988132i | \(0.450912\pi\) | |||||||
\(654\) | 0.149606 | 0.00585007 | ||||||||
\(655\) | −4.00000 | −0.156293 | ||||||||
\(656\) | 5.44322 | 0.212522 | ||||||||
\(657\) | 15.2936 | 0.596661 | ||||||||
\(658\) | 5.72161 | 0.223052 | ||||||||
\(659\) | −20.3684 | −0.793441 | −0.396721 | − | 0.917939i | \(-0.629852\pi\) | ||||
−0.396721 | + | 0.917939i | \(0.629852\pi\) | |||||||
\(660\) | 0.925197 | 0.0360132 | ||||||||
\(661\) | −19.8504 | −0.772091 | −0.386045 | − | 0.922480i | \(-0.626159\pi\) | ||||
−0.386045 | + | 0.922480i | \(0.626159\pi\) | |||||||
\(662\) | 10.4072 | 0.404486 | ||||||||
\(663\) | −17.2936 | −0.671628 | ||||||||
\(664\) | 15.0152 | 0.582704 | ||||||||
\(665\) | −1.72161 | −0.0667612 | ||||||||
\(666\) | 9.44322 | 0.365917 | ||||||||
\(667\) | −2.92520 | −0.113264 | ||||||||
\(668\) | −14.4585 | −0.559414 | ||||||||
\(669\) | 4.49720 | 0.173872 | ||||||||
\(670\) | 0.925197 | 0.0357435 | ||||||||
\(671\) | 1.85039 | 0.0714337 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | −3.29362 | −0.126960 | −0.0634798 | − | 0.997983i | \(-0.520220\pi\) | ||||
−0.0634798 | + | 0.997983i | \(0.520220\pi\) | |||||||
\(674\) | 5.33237 | 0.205395 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 8.59283 | 0.330493 | ||||||||
\(677\) | 12.8864 | 0.495266 | 0.247633 | − | 0.968854i | \(-0.420347\pi\) | ||||
0.247633 | + | 0.968854i | \(0.420347\pi\) | |||||||
\(678\) | −13.4432 | −0.516284 | ||||||||
\(679\) | −10.2396 | −0.392961 | ||||||||
\(680\) | −3.72161 | −0.142717 | ||||||||
\(681\) | 6.27839 | 0.240588 | ||||||||
\(682\) | −5.29362 | −0.202703 | ||||||||
\(683\) | 16.7785 | 0.642011 | 0.321006 | − | 0.947077i | \(-0.395979\pi\) | ||||
0.321006 | + | 0.947077i | \(0.395979\pi\) | |||||||
\(684\) | −1.72161 | −0.0658275 | ||||||||
\(685\) | −9.70079 | −0.370648 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0.149606 | 0.00570784 | ||||||||
\(688\) | 8.92520 | 0.340270 | ||||||||
\(689\) | −43.8809 | −1.67173 | ||||||||
\(690\) | 1.00000 | 0.0380693 | ||||||||
\(691\) | −1.89204 | −0.0719767 | −0.0359883 | − | 0.999352i | \(-0.511458\pi\) | ||||
−0.0359883 | + | 0.999352i | \(0.511458\pi\) | |||||||
\(692\) | 7.16484 | 0.272366 | ||||||||
\(693\) | −0.925197 | −0.0351453 | ||||||||
\(694\) | −5.59283 | −0.212301 | ||||||||
\(695\) | 9.29362 | 0.352527 | ||||||||
\(696\) | −2.92520 | −0.110879 | ||||||||
\(697\) | −20.2576 | −0.767310 | ||||||||
\(698\) | −12.0208 | −0.454995 | ||||||||
\(699\) | −5.44322 | −0.205882 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −22.1801 | −0.837729 | −0.418865 | − | 0.908049i | \(-0.637572\pi\) | ||||
−0.418865 | + | 0.908049i | \(0.637572\pi\) | |||||||
\(702\) | 4.64681 | 0.175382 | ||||||||
\(703\) | −16.2576 | −0.613166 | ||||||||
\(704\) | −0.925197 | −0.0348697 | ||||||||
\(705\) | −5.72161 | −0.215488 | ||||||||
\(706\) | −11.0361 | −0.415347 | ||||||||
\(707\) | −2.79641 | −0.105170 | ||||||||
\(708\) | 7.44322 | 0.279733 | ||||||||
\(709\) | −2.00000 | −0.0751116 | −0.0375558 | − | 0.999295i | \(-0.511957\pi\) | ||||
−0.0375558 | + | 0.999295i | \(0.511957\pi\) | |||||||
\(710\) | 6.77559 | 0.254283 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.79641 | −0.254706 | ||||||||
\(713\) | −5.72161 | −0.214276 | ||||||||
\(714\) | 3.72161 | 0.139278 | ||||||||
\(715\) | 4.29921 | 0.160781 | ||||||||
\(716\) | 20.7368 | 0.774972 | ||||||||
\(717\) | −14.7756 | −0.551805 | ||||||||
\(718\) | 7.14401 | 0.266612 | ||||||||
\(719\) | 34.2701 | 1.27806 | 0.639029 | − | 0.769182i | \(-0.279336\pi\) | ||||
0.639029 | + | 0.769182i | \(0.279336\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 1.85039 | 0.0689123 | ||||||||
\(722\) | −16.0361 | −0.596800 | ||||||||
\(723\) | −3.16484 | −0.117701 | ||||||||
\(724\) | 6.00000 | 0.222988 | ||||||||
\(725\) | 2.92520 | 0.108639 | ||||||||
\(726\) | 10.1440 | 0.376480 | ||||||||
\(727\) | −4.18006 | −0.155030 | −0.0775150 | − | 0.996991i | \(-0.524699\pi\) | ||||
−0.0775150 | + | 0.996991i | \(0.524699\pi\) | |||||||
\(728\) | −4.64681 | −0.172222 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 15.2936 | 0.566042 | ||||||||
\(731\) | −33.2161 | −1.22854 | ||||||||
\(732\) | 2.00000 | 0.0739221 | ||||||||
\(733\) | 25.4432 | 0.939767 | 0.469883 | − | 0.882728i | \(-0.344296\pi\) | ||||
0.469883 | + | 0.882728i | \(0.344296\pi\) | |||||||
\(734\) | −20.4376 | −0.754367 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −0.855989 | −0.0315308 | ||||||||
\(738\) | 5.44322 | 0.200368 | ||||||||
\(739\) | −29.5928 | −1.08859 | −0.544295 | − | 0.838894i | \(-0.683203\pi\) | ||||
−0.544295 | + | 0.838894i | \(0.683203\pi\) | |||||||
\(740\) | 9.44322 | 0.347140 | ||||||||
\(741\) | −8.00000 | −0.293887 | ||||||||
\(742\) | 9.44322 | 0.346672 | ||||||||
\(743\) | −48.3601 | −1.77416 | −0.887081 | − | 0.461615i | \(-0.847270\pi\) | ||||
−0.887081 | + | 0.461615i | \(0.847270\pi\) | |||||||
\(744\) | −5.72161 | −0.209764 | ||||||||
\(745\) | −17.1440 | −0.628108 | ||||||||
\(746\) | −1.14401 | −0.0418852 | ||||||||
\(747\) | 15.0152 | 0.549378 | ||||||||
\(748\) | 3.44322 | 0.125897 | ||||||||
\(749\) | 4.00000 | 0.146157 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 29.7729 | 1.08643 | 0.543214 | − | 0.839594i | \(-0.317207\pi\) | ||||
0.543214 | + | 0.839594i | \(0.317207\pi\) | |||||||
\(752\) | 5.72161 | 0.208646 | ||||||||
\(753\) | 4.79641 | 0.174791 | ||||||||
\(754\) | −13.5928 | −0.495022 | ||||||||
\(755\) | −13.2936 | −0.483804 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | 34.4376 | 1.25166 | 0.625828 | − | 0.779961i | \(-0.284761\pi\) | ||||
0.625828 | + | 0.779961i | \(0.284761\pi\) | |||||||
\(758\) | 0.299213 | 0.0108679 | ||||||||
\(759\) | −0.925197 | −0.0335825 | ||||||||
\(760\) | −1.72161 | −0.0624494 | ||||||||
\(761\) | −24.8448 | −0.900623 | −0.450312 | − | 0.892871i | \(-0.648687\pi\) | ||||
−0.450312 | + | 0.892871i | \(0.648687\pi\) | |||||||
\(762\) | 0.368420 | 0.0133465 | ||||||||
\(763\) | −0.149606 | −0.00541611 | ||||||||
\(764\) | 4.55678 | 0.164858 | ||||||||
\(765\) | −3.72161 | −0.134555 | ||||||||
\(766\) | 0.736841 | 0.0266231 | ||||||||
\(767\) | 34.5872 | 1.24887 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −1.27279 | −0.0458981 | −0.0229490 | − | 0.999737i | \(-0.507306\pi\) | ||||
−0.0229490 | + | 0.999737i | \(0.507306\pi\) | |||||||
\(770\) | −0.925197 | −0.0333418 | ||||||||
\(771\) | 29.1440 | 1.04960 | ||||||||
\(772\) | 6.55678 | 0.235984 | ||||||||
\(773\) | 8.10796 | 0.291623 | 0.145811 | − | 0.989312i | \(-0.453421\pi\) | ||||
0.145811 | + | 0.989312i | \(0.453421\pi\) | |||||||
\(774\) | 8.92520 | 0.320810 | ||||||||
\(775\) | 5.72161 | 0.205526 | ||||||||
\(776\) | −10.2396 | −0.367582 | ||||||||
\(777\) | −9.44322 | −0.338774 | ||||||||
\(778\) | −31.0361 | −1.11270 | ||||||||
\(779\) | −9.37112 | −0.335755 | ||||||||
\(780\) | 4.64681 | 0.166382 | ||||||||
\(781\) | −6.26875 | −0.224314 | ||||||||
\(782\) | 3.72161 | 0.133085 | ||||||||
\(783\) | −2.92520 | −0.104538 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 14.7368 | 0.525980 | ||||||||
\(786\) | 4.00000 | 0.142675 | ||||||||
\(787\) | 19.2036 | 0.684534 | 0.342267 | − | 0.939603i | \(-0.388805\pi\) | ||||
0.342267 | + | 0.939603i | \(0.388805\pi\) | |||||||
\(788\) | −1.74244 | −0.0620717 | ||||||||
\(789\) | 20.1801 | 0.718429 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.4432 | 0.477986 | ||||||||
\(792\) | −0.925197 | −0.0328754 | ||||||||
\(793\) | 9.29362 | 0.330026 | ||||||||
\(794\) | −4.64681 | −0.164909 | ||||||||
\(795\) | −9.44322 | −0.334917 | ||||||||
\(796\) | −3.44322 | −0.122042 | ||||||||
\(797\) | 20.0305 | 0.709515 | 0.354758 | − | 0.934958i | \(-0.384563\pi\) | ||||
0.354758 | + | 0.934958i | \(0.384563\pi\) | |||||||
\(798\) | 1.72161 | 0.0609444 | ||||||||
\(799\) | −21.2936 | −0.753314 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −6.79641 | −0.240140 | ||||||||
\(802\) | −8.21881 | −0.290216 | ||||||||
\(803\) | −14.1496 | −0.499329 | ||||||||
\(804\) | −0.925197 | −0.0326292 | ||||||||
\(805\) | −1.00000 | −0.0352454 | ||||||||
\(806\) | −26.5872 | −0.936495 | ||||||||
\(807\) | 27.5333 | 0.969216 | ||||||||
\(808\) | −2.79641 | −0.0983775 | ||||||||
\(809\) | −29.7424 | −1.04569 | −0.522844 | − | 0.852428i | \(-0.675129\pi\) | ||||
−0.522844 | + | 0.852428i | \(0.675129\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 33.5512 | 1.17814 | 0.589071 | − | 0.808082i | \(-0.299494\pi\) | ||||
0.589071 | + | 0.808082i | \(0.299494\pi\) | |||||||
\(812\) | 2.92520 | 0.102654 | ||||||||
\(813\) | −2.02082 | −0.0708734 | ||||||||
\(814\) | −8.73684 | −0.306226 | ||||||||
\(815\) | −1.29362 | −0.0453134 | ||||||||
\(816\) | 3.72161 | 0.130282 | ||||||||
\(817\) | −15.3657 | −0.537579 | ||||||||
\(818\) | −12.1496 | −0.424801 | ||||||||
\(819\) | −4.64681 | −0.162373 | ||||||||
\(820\) | 5.44322 | 0.190086 | ||||||||
\(821\) | 46.5068 | 1.62310 | 0.811550 | − | 0.584283i | \(-0.198624\pi\) | ||||
0.811550 | + | 0.584283i | \(0.198624\pi\) | |||||||
\(822\) | 9.70079 | 0.338354 | ||||||||
\(823\) | 5.40447 | 0.188388 | 0.0941940 | − | 0.995554i | \(-0.469973\pi\) | ||||
0.0941940 | + | 0.995554i | \(0.469973\pi\) | |||||||
\(824\) | 1.85039 | 0.0644615 | ||||||||
\(825\) | 0.925197 | 0.0322112 | ||||||||
\(826\) | −7.44322 | −0.258983 | ||||||||
\(827\) | 10.8864 | 0.378559 | 0.189279 | − | 0.981923i | \(-0.439385\pi\) | ||||
0.189279 | + | 0.981923i | \(0.439385\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | −30.3505 | −1.05412 | −0.527058 | − | 0.849829i | \(-0.676705\pi\) | ||||
−0.527058 | + | 0.849829i | \(0.676705\pi\) | |||||||
\(830\) | 15.0152 | 0.521186 | ||||||||
\(831\) | −6.36842 | −0.220918 | ||||||||
\(832\) | −4.64681 | −0.161099 | ||||||||
\(833\) | −3.72161 | −0.128946 | ||||||||
\(834\) | −9.29362 | −0.321812 | ||||||||
\(835\) | −14.4585 | −0.500355 | ||||||||
\(836\) | 1.59283 | 0.0550892 | ||||||||
\(837\) | −5.72161 | −0.197768 | ||||||||
\(838\) | −26.3476 | −0.910163 | ||||||||
\(839\) | −12.5568 | −0.433508 | −0.216754 | − | 0.976226i | \(-0.569547\pi\) | ||||
−0.216754 | + | 0.976226i | \(0.569547\pi\) | |||||||
\(840\) | −1.00000 | −0.0345033 | ||||||||
\(841\) | −20.4432 | −0.704939 | ||||||||
\(842\) | 8.70638 | 0.300042 | ||||||||
\(843\) | −16.5180 | −0.568911 | ||||||||
\(844\) | 4.00000 | 0.137686 | ||||||||
\(845\) | 8.59283 | 0.295602 | ||||||||
\(846\) | 5.72161 | 0.196713 | ||||||||
\(847\) | −10.1440 | −0.348552 | ||||||||
\(848\) | 9.44322 | 0.324282 | ||||||||
\(849\) | −29.5333 | −1.01358 | ||||||||
\(850\) | −3.72161 | −0.127650 | ||||||||
\(851\) | −9.44322 | −0.323710 | ||||||||
\(852\) | −6.77559 | −0.232128 | ||||||||
\(853\) | 6.53885 | 0.223886 | 0.111943 | − | 0.993715i | \(-0.464293\pi\) | ||||
0.111943 | + | 0.993715i | \(0.464293\pi\) | |||||||
\(854\) | −2.00000 | −0.0684386 | ||||||||
\(855\) | −1.72161 | −0.0588779 | ||||||||
\(856\) | 4.00000 | 0.136717 | ||||||||
\(857\) | 21.3241 | 0.728417 | 0.364208 | − | 0.931318i | \(-0.381340\pi\) | ||||
0.364208 | + | 0.931318i | \(0.381340\pi\) | |||||||
\(858\) | −4.29921 | −0.146773 | ||||||||
\(859\) | −11.8809 | −0.405369 | −0.202685 | − | 0.979244i | \(-0.564967\pi\) | ||||
−0.202685 | + | 0.979244i | \(0.564967\pi\) | |||||||
\(860\) | 8.92520 | 0.304347 | ||||||||
\(861\) | −5.44322 | −0.185505 | ||||||||
\(862\) | 22.0305 | 0.750360 | ||||||||
\(863\) | 35.0665 | 1.19368 | 0.596839 | − | 0.802361i | \(-0.296423\pi\) | ||||
0.596839 | + | 0.802361i | \(0.296423\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 7.16484 | 0.243612 | ||||||||
\(866\) | −3.35319 | −0.113946 | ||||||||
\(867\) | 3.14961 | 0.106966 | ||||||||
\(868\) | 5.72161 | 0.194204 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −2.92520 | −0.0991735 | ||||||||
\(871\) | −4.29921 | −0.145673 | ||||||||
\(872\) | −0.149606 | −0.00506631 | ||||||||
\(873\) | −10.2396 | −0.346559 | ||||||||
\(874\) | 1.72161 | 0.0582344 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −15.2936 | −0.516723 | ||||||||
\(877\) | −4.47638 | −0.151157 | −0.0755783 | − | 0.997140i | \(-0.524080\pi\) | ||||
−0.0755783 | + | 0.997140i | \(0.524080\pi\) | |||||||
\(878\) | −23.5720 | −0.795517 | ||||||||
\(879\) | 3.85039 | 0.129871 | ||||||||
\(880\) | −0.925197 | −0.0311884 | ||||||||
\(881\) | −0.167532 | −0.00564430 | −0.00282215 | − | 0.999996i | \(-0.500898\pi\) | ||||
−0.00282215 | + | 0.999996i | \(0.500898\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | 48.1801 | 1.62139 | 0.810694 | − | 0.585470i | \(-0.199090\pi\) | ||||
0.810694 | + | 0.585470i | \(0.199090\pi\) | |||||||
\(884\) | 17.2936 | 0.581647 | ||||||||
\(885\) | 7.44322 | 0.250201 | ||||||||
\(886\) | −12.4793 | −0.419249 | ||||||||
\(887\) | −28.0096 | −0.940471 | −0.470236 | − | 0.882541i | \(-0.655831\pi\) | ||||
−0.470236 | + | 0.882541i | \(0.655831\pi\) | |||||||
\(888\) | −9.44322 | −0.316894 | ||||||||
\(889\) | −0.368420 | −0.0123564 | ||||||||
\(890\) | −6.79641 | −0.227816 | ||||||||
\(891\) | −0.925197 | −0.0309953 | ||||||||
\(892\) | −4.49720 | −0.150577 | ||||||||
\(893\) | −9.85039 | −0.329631 | ||||||||
\(894\) | 17.1440 | 0.573381 | ||||||||
\(895\) | 20.7368 | 0.693156 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −4.64681 | −0.155152 | ||||||||
\(898\) | 30.1801 | 1.00712 | ||||||||
\(899\) | 16.7368 | 0.558205 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −35.1440 | −1.17082 | ||||||||
\(902\) | −5.03605 | −0.167682 | ||||||||
\(903\) | −8.92520 | −0.297012 | ||||||||
\(904\) | 13.4432 | 0.447115 | ||||||||
\(905\) | 6.00000 | 0.199447 | ||||||||
\(906\) | 13.2936 | 0.441651 | ||||||||
\(907\) | 36.3684 | 1.20759 | 0.603797 | − | 0.797138i | \(-0.293654\pi\) | ||||
0.603797 | + | 0.797138i | \(0.293654\pi\) | |||||||
\(908\) | −6.27839 | −0.208356 | ||||||||
\(909\) | −2.79641 | −0.0927512 | ||||||||
\(910\) | −4.64681 | −0.154040 | ||||||||
\(911\) | 28.1801 | 0.933647 | 0.466824 | − | 0.884350i | \(-0.345398\pi\) | ||||
0.466824 | + | 0.884350i | \(0.345398\pi\) | |||||||
\(912\) | 1.72161 | 0.0570083 | ||||||||
\(913\) | −13.8920 | −0.459759 | ||||||||
\(914\) | 22.3268 | 0.738504 | ||||||||
\(915\) | 2.00000 | 0.0661180 | ||||||||
\(916\) | −0.149606 | −0.00494313 | ||||||||
\(917\) | −4.00000 | −0.132092 | ||||||||
\(918\) | 3.72161 | 0.122831 | ||||||||
\(919\) | −29.2936 | −0.966307 | −0.483154 | − | 0.875536i | \(-0.660509\pi\) | ||||
−0.483154 | + | 0.875536i | \(0.660509\pi\) | |||||||
\(920\) | −1.00000 | −0.0329690 | ||||||||
\(921\) | −25.0361 | −0.824966 | ||||||||
\(922\) | 8.38924 | 0.276285 | ||||||||
\(923\) | −31.4849 | −1.03634 | ||||||||
\(924\) | 0.925197 | 0.0304367 | ||||||||
\(925\) | 9.44322 | 0.310491 | ||||||||
\(926\) | 24.1109 | 0.792332 | ||||||||
\(927\) | 1.85039 | 0.0607749 | ||||||||
\(928\) | 2.92520 | 0.0960243 | ||||||||
\(929\) | −30.7368 | −1.00844 | −0.504222 | − | 0.863574i | \(-0.668220\pi\) | ||||
−0.504222 | + | 0.863574i | \(0.668220\pi\) | |||||||
\(930\) | −5.72161 | −0.187619 | ||||||||
\(931\) | −1.72161 | −0.0564235 | ||||||||
\(932\) | 5.44322 | 0.178299 | ||||||||
\(933\) | −14.0900 | −0.461287 | ||||||||
\(934\) | 3.57201 | 0.116880 | ||||||||
\(935\) | 3.44322 | 0.112605 | ||||||||
\(936\) | −4.64681 | −0.151886 | ||||||||
\(937\) | 6.01793 | 0.196597 | 0.0982985 | − | 0.995157i | \(-0.468660\pi\) | ||||
0.0982985 | + | 0.995157i | \(0.468660\pi\) | |||||||
\(938\) | 0.925197 | 0.0302087 | ||||||||
\(939\) | −3.05398 | −0.0996628 | ||||||||
\(940\) | 5.72161 | 0.186618 | ||||||||
\(941\) | −30.2992 | −0.987726 | −0.493863 | − | 0.869540i | \(-0.664416\pi\) | ||||
−0.493863 | + | 0.869540i | \(0.664416\pi\) | |||||||
\(942\) | −14.7368 | −0.480152 | ||||||||
\(943\) | −5.44322 | −0.177256 | ||||||||
\(944\) | −7.44322 | −0.242256 | ||||||||
\(945\) | −1.00000 | −0.0325300 | ||||||||
\(946\) | −8.25756 | −0.268477 | ||||||||
\(947\) | 4.00000 | 0.129983 | 0.0649913 | − | 0.997886i | \(-0.479298\pi\) | ||||
0.0649913 | + | 0.997886i | \(0.479298\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −71.0665 | −2.30692 | ||||||||
\(950\) | −1.72161 | −0.0558565 | ||||||||
\(951\) | −3.29362 | −0.106803 | ||||||||
\(952\) | −3.72161 | −0.120618 | ||||||||
\(953\) | 8.62888 | 0.279517 | 0.139758 | − | 0.990186i | \(-0.455367\pi\) | ||||
0.139758 | + | 0.990186i | \(0.455367\pi\) | |||||||
\(954\) | 9.44322 | 0.305736 | ||||||||
\(955\) | 4.55678 | 0.147454 | ||||||||
\(956\) | 14.7756 | 0.477877 | ||||||||
\(957\) | 2.70638 | 0.0874849 | ||||||||
\(958\) | 23.6233 | 0.763234 | ||||||||
\(959\) | −9.70079 | −0.313255 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 1.73684 | 0.0560271 | ||||||||
\(962\) | −43.8809 | −1.41478 | ||||||||
\(963\) | 4.00000 | 0.128898 | ||||||||
\(964\) | 3.16484 | 0.101932 | ||||||||
\(965\) | 6.55678 | 0.211070 | ||||||||
\(966\) | 1.00000 | 0.0321745 | ||||||||
\(967\) | −17.3628 | −0.558351 | −0.279175 | − | 0.960240i | \(-0.590061\pi\) | ||||
−0.279175 | + | 0.960240i | \(0.590061\pi\) | |||||||
\(968\) | −10.1440 | −0.326041 | ||||||||
\(969\) | −6.40717 | −0.205828 | ||||||||
\(970\) | −10.2396 | −0.328775 | ||||||||
\(971\) | 14.3892 | 0.461773 | 0.230886 | − | 0.972981i | \(-0.425837\pi\) | ||||
0.230886 | + | 0.972981i | \(0.425837\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 9.29362 | 0.297940 | ||||||||
\(974\) | −3.07480 | −0.0985230 | ||||||||
\(975\) | 4.64681 | 0.148817 | ||||||||
\(976\) | −2.00000 | −0.0640184 | ||||||||
\(977\) | −30.2217 | −0.966878 | −0.483439 | − | 0.875378i | \(-0.660613\pi\) | ||||
−0.483439 | + | 0.875378i | \(0.660613\pi\) | |||||||
\(978\) | 1.29362 | 0.0413653 | ||||||||
\(979\) | 6.28802 | 0.200966 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | −0.149606 | −0.00477656 | ||||||||
\(982\) | 18.8864 | 0.602691 | ||||||||
\(983\) | −55.0249 | −1.75502 | −0.877510 | − | 0.479558i | \(-0.840797\pi\) | ||||
−0.877510 | + | 0.479558i | \(0.840797\pi\) | |||||||
\(984\) | −5.44322 | −0.173524 | ||||||||
\(985\) | −1.74244 | −0.0555186 | ||||||||
\(986\) | −10.8864 | −0.346695 | ||||||||
\(987\) | −5.72161 | −0.182121 | ||||||||
\(988\) | 8.00000 | 0.254514 | ||||||||
\(989\) | −8.92520 | −0.283805 | ||||||||
\(990\) | −0.925197 | −0.0294047 | ||||||||
\(991\) | 24.4793 | 0.777610 | 0.388805 | − | 0.921320i | \(-0.372888\pi\) | ||||
0.388805 | + | 0.921320i | \(0.372888\pi\) | |||||||
\(992\) | 5.72161 | 0.181661 | ||||||||
\(993\) | −10.4072 | −0.330262 | ||||||||
\(994\) | 6.77559 | 0.214909 | ||||||||
\(995\) | −3.44322 | −0.109158 | ||||||||
\(996\) | −15.0152 | −0.475776 | ||||||||
\(997\) | 51.1149 | 1.61882 | 0.809412 | − | 0.587241i | \(-0.199786\pi\) | ||||
0.809412 | + | 0.587241i | \(0.199786\pi\) | |||||||
\(998\) | 33.7729 | 1.06906 | ||||||||
\(999\) | −9.44322 | −0.298770 |
(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 | 4830.2.a.cb.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4830.2.a.cb.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial |