Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [145,2,Mod(1,145)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(145, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("145.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 145 = 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 145.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: | \(1.15783082931\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 145.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41421 | −1.70711 | −0.853553 | − | 0.521005i | \(-0.825557\pi\) | ||||
−0.853553 | + | 0.521005i | \(0.825557\pi\) | |||||||
\(3\) | −2.00000 | −1.15470 | −0.577350 | − | 0.816497i | \(-0.695913\pi\) | ||||
−0.577350 | + | 0.816497i | \(0.695913\pi\) | |||||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 4.82843 | 1.97120 | ||||||||
\(7\) | 0.828427 | 0.313116 | 0.156558 | − | 0.987669i | \(-0.449960\pi\) | ||||
0.156558 | + | 0.987669i | \(0.449960\pi\) | |||||||
\(8\) | −4.41421 | −1.56066 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.41421 | −0.763441 | ||||||||
\(11\) | −4.82843 | −1.45583 | −0.727913 | − | 0.685670i | \(-0.759509\pi\) | ||||
−0.727913 | + | 0.685670i | \(0.759509\pi\) | |||||||
\(12\) | −7.65685 | −2.21034 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | −2.00000 | −0.516398 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | −2.82843 | −0.685994 | −0.342997 | − | 0.939336i | \(-0.611442\pi\) | ||||
−0.342997 | + | 0.939336i | \(0.611442\pi\) | |||||||
\(18\) | −2.41421 | −0.569036 | ||||||||
\(19\) | 0.828427 | 0.190054 | 0.0950271 | − | 0.995475i | \(-0.469706\pi\) | ||||
0.0950271 | + | 0.995475i | \(0.469706\pi\) | |||||||
\(20\) | 3.82843 | 0.856062 | ||||||||
\(21\) | −1.65685 | −0.361555 | ||||||||
\(22\) | 11.6569 | 2.48525 | ||||||||
\(23\) | −8.82843 | −1.84085 | −0.920427 | − | 0.390914i | \(-0.872159\pi\) | ||||
−0.920427 | + | 0.390914i | \(0.872159\pi\) | |||||||
\(24\) | 8.82843 | 1.80210 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.82843 | 0.946932 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 3.17157 | 0.599371 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 4.82843 | 0.881546 | ||||||||
\(31\) | −10.4853 | −1.88321 | −0.941606 | − | 0.336717i | \(-0.890684\pi\) | ||||
−0.941606 | + | 0.336717i | \(0.890684\pi\) | |||||||
\(32\) | 1.58579 | 0.280330 | ||||||||
\(33\) | 9.65685 | 1.68104 | ||||||||
\(34\) | 6.82843 | 1.17107 | ||||||||
\(35\) | 0.828427 | 0.140030 | ||||||||
\(36\) | 3.82843 | 0.638071 | ||||||||
\(37\) | 8.48528 | 1.39497 | 0.697486 | − | 0.716599i | \(-0.254302\pi\) | ||||
0.697486 | + | 0.716599i | \(0.254302\pi\) | |||||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | −4.41421 | −0.697948 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 4.00000 | 0.617213 | ||||||||
\(43\) | −6.00000 | −0.914991 | −0.457496 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457496 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(44\) | −18.4853 | −2.78676 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 21.3137 | 3.14253 | ||||||||
\(47\) | −0.343146 | −0.0500530 | −0.0250265 | − | 0.999687i | \(-0.507967\pi\) | ||||
−0.0250265 | + | 0.999687i | \(0.507967\pi\) | |||||||
\(48\) | −6.00000 | −0.866025 | ||||||||
\(49\) | −6.31371 | −0.901958 | ||||||||
\(50\) | −2.41421 | −0.341421 | ||||||||
\(51\) | 5.65685 | 0.792118 | ||||||||
\(52\) | −7.65685 | −1.06181 | ||||||||
\(53\) | 7.65685 | 1.05175 | 0.525875 | − | 0.850562i | \(-0.323738\pi\) | ||||
0.525875 | + | 0.850562i | \(0.323738\pi\) | |||||||
\(54\) | −9.65685 | −1.31413 | ||||||||
\(55\) | −4.82843 | −0.651065 | ||||||||
\(56\) | −3.65685 | −0.488668 | ||||||||
\(57\) | −1.65685 | −0.219456 | ||||||||
\(58\) | −2.41421 | −0.317002 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | −7.65685 | −0.988496 | ||||||||
\(61\) | 7.65685 | 0.980360 | 0.490180 | − | 0.871621i | \(-0.336931\pi\) | ||||
0.490180 | + | 0.871621i | \(0.336931\pi\) | |||||||
\(62\) | 25.3137 | 3.21484 | ||||||||
\(63\) | 0.828427 | 0.104372 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | −2.00000 | −0.248069 | ||||||||
\(66\) | −23.3137 | −2.86972 | ||||||||
\(67\) | −10.4853 | −1.28098 | −0.640490 | − | 0.767966i | \(-0.721269\pi\) | ||||
−0.640490 | + | 0.767966i | \(0.721269\pi\) | |||||||
\(68\) | −10.8284 | −1.31314 | ||||||||
\(69\) | 17.6569 | 2.12564 | ||||||||
\(70\) | −2.00000 | −0.239046 | ||||||||
\(71\) | 7.31371 | 0.867978 | 0.433989 | − | 0.900918i | \(-0.357106\pi\) | ||||
0.433989 | + | 0.900918i | \(0.357106\pi\) | |||||||
\(72\) | −4.41421 | −0.520220 | ||||||||
\(73\) | −8.48528 | −0.993127 | −0.496564 | − | 0.868000i | \(-0.665405\pi\) | ||||
−0.496564 | + | 0.868000i | \(0.665405\pi\) | |||||||
\(74\) | −20.4853 | −2.38137 | ||||||||
\(75\) | −2.00000 | −0.230940 | ||||||||
\(76\) | 3.17157 | 0.363804 | ||||||||
\(77\) | −4.00000 | −0.455842 | ||||||||
\(78\) | −9.65685 | −1.09342 | ||||||||
\(79\) | 14.4853 | 1.62972 | 0.814861 | − | 0.579657i | \(-0.196813\pi\) | ||||
0.814861 | + | 0.579657i | \(0.196813\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 14.4853 | 1.59963 | ||||||||
\(83\) | 12.8284 | 1.40810 | 0.704051 | − | 0.710149i | \(-0.251372\pi\) | ||||
0.704051 | + | 0.710149i | \(0.251372\pi\) | |||||||
\(84\) | −6.34315 | −0.692094 | ||||||||
\(85\) | −2.82843 | −0.306786 | ||||||||
\(86\) | 14.4853 | 1.56199 | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | 21.3137 | 2.27205 | ||||||||
\(89\) | 3.65685 | 0.387626 | 0.193813 | − | 0.981039i | \(-0.437915\pi\) | ||||
0.193813 | + | 0.981039i | \(0.437915\pi\) | |||||||
\(90\) | −2.41421 | −0.254480 | ||||||||
\(91\) | −1.65685 | −0.173686 | ||||||||
\(92\) | −33.7990 | −3.52379 | ||||||||
\(93\) | 20.9706 | 2.17455 | ||||||||
\(94\) | 0.828427 | 0.0854457 | ||||||||
\(95\) | 0.828427 | 0.0849948 | ||||||||
\(96\) | −3.17157 | −0.323697 | ||||||||
\(97\) | 4.48528 | 0.455411 | 0.227706 | − | 0.973730i | \(-0.426878\pi\) | ||||
0.227706 | + | 0.973730i | \(0.426878\pi\) | |||||||
\(98\) | 15.2426 | 1.53974 | ||||||||
\(99\) | −4.82843 | −0.485275 | ||||||||
\(100\) | 3.82843 | 0.382843 | ||||||||
\(101\) | 4.34315 | 0.432159 | 0.216080 | − | 0.976376i | \(-0.430673\pi\) | ||||
0.216080 | + | 0.976376i | \(0.430673\pi\) | |||||||
\(102\) | −13.6569 | −1.35223 | ||||||||
\(103\) | −12.1421 | −1.19640 | −0.598200 | − | 0.801347i | \(-0.704117\pi\) | ||||
−0.598200 | + | 0.801347i | \(0.704117\pi\) | |||||||
\(104\) | 8.82843 | 0.865699 | ||||||||
\(105\) | −1.65685 | −0.161692 | ||||||||
\(106\) | −18.4853 | −1.79545 | ||||||||
\(107\) | −8.14214 | −0.787130 | −0.393565 | − | 0.919297i | \(-0.628758\pi\) | ||||
−0.393565 | + | 0.919297i | \(0.628758\pi\) | |||||||
\(108\) | 15.3137 | 1.47356 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 11.6569 | 1.11144 | ||||||||
\(111\) | −16.9706 | −1.61077 | ||||||||
\(112\) | 2.48528 | 0.234837 | ||||||||
\(113\) | 2.82843 | 0.266076 | 0.133038 | − | 0.991111i | \(-0.457527\pi\) | ||||
0.133038 | + | 0.991111i | \(0.457527\pi\) | |||||||
\(114\) | 4.00000 | 0.374634 | ||||||||
\(115\) | −8.82843 | −0.823255 | ||||||||
\(116\) | 3.82843 | 0.355461 | ||||||||
\(117\) | −2.00000 | −0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.34315 | −0.214796 | ||||||||
\(120\) | 8.82843 | 0.805921 | ||||||||
\(121\) | 12.3137 | 1.11943 | ||||||||
\(122\) | −18.4853 | −1.67358 | ||||||||
\(123\) | 12.0000 | 1.08200 | ||||||||
\(124\) | −40.1421 | −3.60487 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −2.00000 | −0.178174 | ||||||||
\(127\) | 6.00000 | 0.532414 | 0.266207 | − | 0.963916i | \(-0.414230\pi\) | ||||
0.266207 | + | 0.963916i | \(0.414230\pi\) | |||||||
\(128\) | 20.5563 | 1.81694 | ||||||||
\(129\) | 12.0000 | 1.05654 | ||||||||
\(130\) | 4.82843 | 0.423481 | ||||||||
\(131\) | 16.1421 | 1.41034 | 0.705172 | − | 0.709036i | \(-0.250870\pi\) | ||||
0.705172 | + | 0.709036i | \(0.250870\pi\) | |||||||
\(132\) | 36.9706 | 3.21787 | ||||||||
\(133\) | 0.686292 | 0.0595090 | ||||||||
\(134\) | 25.3137 | 2.18677 | ||||||||
\(135\) | 4.00000 | 0.344265 | ||||||||
\(136\) | 12.4853 | 1.07060 | ||||||||
\(137\) | −10.8284 | −0.925135 | −0.462567 | − | 0.886584i | \(-0.653072\pi\) | ||||
−0.462567 | + | 0.886584i | \(0.653072\pi\) | |||||||
\(138\) | −42.6274 | −3.62869 | ||||||||
\(139\) | 10.3431 | 0.877294 | 0.438647 | − | 0.898659i | \(-0.355458\pi\) | ||||
0.438647 | + | 0.898659i | \(0.355458\pi\) | |||||||
\(140\) | 3.17157 | 0.268047 | ||||||||
\(141\) | 0.686292 | 0.0577962 | ||||||||
\(142\) | −17.6569 | −1.48173 | ||||||||
\(143\) | 9.65685 | 0.807547 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 1.00000 | 0.0830455 | ||||||||
\(146\) | 20.4853 | 1.69537 | ||||||||
\(147\) | 12.6274 | 1.04149 | ||||||||
\(148\) | 32.4853 | 2.67027 | ||||||||
\(149\) | −13.3137 | −1.09070 | −0.545351 | − | 0.838208i | \(-0.683604\pi\) | ||||
−0.545351 | + | 0.838208i | \(0.683604\pi\) | |||||||
\(150\) | 4.82843 | 0.394239 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | −3.65685 | −0.296610 | ||||||||
\(153\) | −2.82843 | −0.228665 | ||||||||
\(154\) | 9.65685 | 0.778171 | ||||||||
\(155\) | −10.4853 | −0.842198 | ||||||||
\(156\) | 15.3137 | 1.22608 | ||||||||
\(157\) | −16.4853 | −1.31567 | −0.657834 | − | 0.753163i | \(-0.728527\pi\) | ||||
−0.657834 | + | 0.753163i | \(0.728527\pi\) | |||||||
\(158\) | −34.9706 | −2.78211 | ||||||||
\(159\) | −15.3137 | −1.21446 | ||||||||
\(160\) | 1.58579 | 0.125367 | ||||||||
\(161\) | −7.31371 | −0.576401 | ||||||||
\(162\) | 26.5563 | 2.08646 | ||||||||
\(163\) | −19.6569 | −1.53964 | −0.769822 | − | 0.638259i | \(-0.779655\pi\) | ||||
−0.769822 | + | 0.638259i | \(0.779655\pi\) | |||||||
\(164\) | −22.9706 | −1.79370 | ||||||||
\(165\) | 9.65685 | 0.751785 | ||||||||
\(166\) | −30.9706 | −2.40378 | ||||||||
\(167\) | 14.4853 | 1.12090 | 0.560452 | − | 0.828187i | \(-0.310627\pi\) | ||||
0.560452 | + | 0.828187i | \(0.310627\pi\) | |||||||
\(168\) | 7.31371 | 0.564265 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 6.82843 | 0.523716 | ||||||||
\(171\) | 0.828427 | 0.0633514 | ||||||||
\(172\) | −22.9706 | −1.75149 | ||||||||
\(173\) | −5.31371 | −0.403994 | −0.201997 | − | 0.979386i | \(-0.564743\pi\) | ||||
−0.201997 | + | 0.979386i | \(0.564743\pi\) | |||||||
\(174\) | 4.82843 | 0.366042 | ||||||||
\(175\) | 0.828427 | 0.0626232 | ||||||||
\(176\) | −14.4853 | −1.09187 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.82843 | −0.661719 | ||||||||
\(179\) | −0.686292 | −0.0512958 | −0.0256479 | − | 0.999671i | \(-0.508165\pi\) | ||||
−0.0256479 | + | 0.999671i | \(0.508165\pi\) | |||||||
\(180\) | 3.82843 | 0.285354 | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | 4.00000 | 0.296500 | ||||||||
\(183\) | −15.3137 | −1.13202 | ||||||||
\(184\) | 38.9706 | 2.87295 | ||||||||
\(185\) | 8.48528 | 0.623850 | ||||||||
\(186\) | −50.6274 | −3.71218 | ||||||||
\(187\) | 13.6569 | 0.998688 | ||||||||
\(188\) | −1.31371 | −0.0958120 | ||||||||
\(189\) | 3.31371 | 0.241037 | ||||||||
\(190\) | −2.00000 | −0.145095 | ||||||||
\(191\) | −15.1716 | −1.09778 | −0.548888 | − | 0.835896i | \(-0.684949\pi\) | ||||
−0.548888 | + | 0.835896i | \(0.684949\pi\) | |||||||
\(192\) | 19.6569 | 1.41861 | ||||||||
\(193\) | −12.4853 | −0.898710 | −0.449355 | − | 0.893353i | \(-0.648346\pi\) | ||||
−0.449355 | + | 0.893353i | \(0.648346\pi\) | |||||||
\(194\) | −10.8284 | −0.777436 | ||||||||
\(195\) | 4.00000 | 0.286446 | ||||||||
\(196\) | −24.1716 | −1.72654 | ||||||||
\(197\) | −8.34315 | −0.594425 | −0.297212 | − | 0.954811i | \(-0.596057\pi\) | ||||
−0.297212 | + | 0.954811i | \(0.596057\pi\) | |||||||
\(198\) | 11.6569 | 0.828417 | ||||||||
\(199\) | 12.0000 | 0.850657 | 0.425329 | − | 0.905039i | \(-0.360158\pi\) | ||||
0.425329 | + | 0.905039i | \(0.360158\pi\) | |||||||
\(200\) | −4.41421 | −0.312132 | ||||||||
\(201\) | 20.9706 | 1.47915 | ||||||||
\(202\) | −10.4853 | −0.737742 | ||||||||
\(203\) | 0.828427 | 0.0581442 | ||||||||
\(204\) | 21.6569 | 1.51628 | ||||||||
\(205\) | −6.00000 | −0.419058 | ||||||||
\(206\) | 29.3137 | 2.04238 | ||||||||
\(207\) | −8.82843 | −0.613618 | ||||||||
\(208\) | −6.00000 | −0.416025 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 4.00000 | 0.276026 | ||||||||
\(211\) | 4.82843 | 0.332403 | 0.166201 | − | 0.986092i | \(-0.446850\pi\) | ||||
0.166201 | + | 0.986092i | \(0.446850\pi\) | |||||||
\(212\) | 29.3137 | 2.01327 | ||||||||
\(213\) | −14.6274 | −1.00225 | ||||||||
\(214\) | 19.6569 | 1.34371 | ||||||||
\(215\) | −6.00000 | −0.409197 | ||||||||
\(216\) | −17.6569 | −1.20140 | ||||||||
\(217\) | −8.68629 | −0.589664 | ||||||||
\(218\) | −4.82843 | −0.327022 | ||||||||
\(219\) | 16.9706 | 1.14676 | ||||||||
\(220\) | −18.4853 | −1.24628 | ||||||||
\(221\) | 5.65685 | 0.380521 | ||||||||
\(222\) | 40.9706 | 2.74976 | ||||||||
\(223\) | 21.7990 | 1.45977 | 0.729884 | − | 0.683571i | \(-0.239574\pi\) | ||||
0.729884 | + | 0.683571i | \(0.239574\pi\) | |||||||
\(224\) | 1.31371 | 0.0877758 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −6.82843 | −0.454220 | ||||||||
\(227\) | −8.14214 | −0.540413 | −0.270206 | − | 0.962802i | \(-0.587092\pi\) | ||||
−0.270206 | + | 0.962802i | \(0.587092\pi\) | |||||||
\(228\) | −6.34315 | −0.420085 | ||||||||
\(229\) | −2.00000 | −0.132164 | −0.0660819 | − | 0.997814i | \(-0.521050\pi\) | ||||
−0.0660819 | + | 0.997814i | \(0.521050\pi\) | |||||||
\(230\) | 21.3137 | 1.40538 | ||||||||
\(231\) | 8.00000 | 0.526361 | ||||||||
\(232\) | −4.41421 | −0.289807 | ||||||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | 4.82843 | 0.315644 | ||||||||
\(235\) | −0.343146 | −0.0223844 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −28.9706 | −1.88184 | ||||||||
\(238\) | 5.65685 | 0.366679 | ||||||||
\(239\) | −23.3137 | −1.50804 | −0.754019 | − | 0.656852i | \(-0.771887\pi\) | ||||
−0.754019 | + | 0.656852i | \(0.771887\pi\) | |||||||
\(240\) | −6.00000 | −0.387298 | ||||||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | −29.7279 | −1.91098 | ||||||||
\(243\) | 10.0000 | 0.641500 | ||||||||
\(244\) | 29.3137 | 1.87662 | ||||||||
\(245\) | −6.31371 | −0.403368 | ||||||||
\(246\) | −28.9706 | −1.84710 | ||||||||
\(247\) | −1.65685 | −0.105423 | ||||||||
\(248\) | 46.2843 | 2.93905 | ||||||||
\(249\) | −25.6569 | −1.62594 | ||||||||
\(250\) | −2.41421 | −0.152688 | ||||||||
\(251\) | 3.17157 | 0.200188 | 0.100094 | − | 0.994978i | \(-0.468086\pi\) | ||||
0.100094 | + | 0.994978i | \(0.468086\pi\) | |||||||
\(252\) | 3.17157 | 0.199790 | ||||||||
\(253\) | 42.6274 | 2.67996 | ||||||||
\(254\) | −14.4853 | −0.908887 | ||||||||
\(255\) | 5.65685 | 0.354246 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 29.3137 | 1.82854 | 0.914269 | − | 0.405107i | \(-0.132766\pi\) | ||||
0.914269 | + | 0.405107i | \(0.132766\pi\) | |||||||
\(258\) | −28.9706 | −1.80363 | ||||||||
\(259\) | 7.02944 | 0.436788 | ||||||||
\(260\) | −7.65685 | −0.474858 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | −38.9706 | −2.40761 | ||||||||
\(263\) | −8.34315 | −0.514460 | −0.257230 | − | 0.966350i | \(-0.582810\pi\) | ||||
−0.257230 | + | 0.966350i | \(0.582810\pi\) | |||||||
\(264\) | −42.6274 | −2.62354 | ||||||||
\(265\) | 7.65685 | 0.470357 | ||||||||
\(266\) | −1.65685 | −0.101588 | ||||||||
\(267\) | −7.31371 | −0.447592 | ||||||||
\(268\) | −40.1421 | −2.45207 | ||||||||
\(269\) | 1.31371 | 0.0800982 | 0.0400491 | − | 0.999198i | \(-0.487249\pi\) | ||||
0.0400491 | + | 0.999198i | \(0.487249\pi\) | |||||||
\(270\) | −9.65685 | −0.587697 | ||||||||
\(271\) | 29.7990 | 1.81016 | 0.905080 | − | 0.425242i | \(-0.139811\pi\) | ||||
0.905080 | + | 0.425242i | \(0.139811\pi\) | |||||||
\(272\) | −8.48528 | −0.514496 | ||||||||
\(273\) | 3.31371 | 0.200555 | ||||||||
\(274\) | 26.1421 | 1.57930 | ||||||||
\(275\) | −4.82843 | −0.291165 | ||||||||
\(276\) | 67.5980 | 4.06892 | ||||||||
\(277\) | 7.65685 | 0.460056 | 0.230028 | − | 0.973184i | \(-0.426118\pi\) | ||||
0.230028 | + | 0.973184i | \(0.426118\pi\) | |||||||
\(278\) | −24.9706 | −1.49763 | ||||||||
\(279\) | −10.4853 | −0.627737 | ||||||||
\(280\) | −3.65685 | −0.218539 | ||||||||
\(281\) | −6.68629 | −0.398871 | −0.199435 | − | 0.979911i | \(-0.563911\pi\) | ||||
−0.199435 | + | 0.979911i | \(0.563911\pi\) | |||||||
\(282\) | −1.65685 | −0.0986642 | ||||||||
\(283\) | −0.828427 | −0.0492449 | −0.0246224 | − | 0.999697i | \(-0.507838\pi\) | ||||
−0.0246224 | + | 0.999697i | \(0.507838\pi\) | |||||||
\(284\) | 28.0000 | 1.66149 | ||||||||
\(285\) | −1.65685 | −0.0981436 | ||||||||
\(286\) | −23.3137 | −1.37857 | ||||||||
\(287\) | −4.97056 | −0.293403 | ||||||||
\(288\) | 1.58579 | 0.0934434 | ||||||||
\(289\) | −9.00000 | −0.529412 | ||||||||
\(290\) | −2.41421 | −0.141768 | ||||||||
\(291\) | −8.97056 | −0.525864 | ||||||||
\(292\) | −32.4853 | −1.90106 | ||||||||
\(293\) | −8.48528 | −0.495715 | −0.247858 | − | 0.968796i | \(-0.579727\pi\) | ||||
−0.247858 | + | 0.968796i | \(0.579727\pi\) | |||||||
\(294\) | −30.4853 | −1.77794 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −37.4558 | −2.17708 | ||||||||
\(297\) | −19.3137 | −1.12070 | ||||||||
\(298\) | 32.1421 | 1.86194 | ||||||||
\(299\) | 17.6569 | 1.02112 | ||||||||
\(300\) | −7.65685 | −0.442069 | ||||||||
\(301\) | −4.97056 | −0.286498 | ||||||||
\(302\) | 28.9706 | 1.66707 | ||||||||
\(303\) | −8.68629 | −0.499014 | ||||||||
\(304\) | 2.48528 | 0.142541 | ||||||||
\(305\) | 7.65685 | 0.438430 | ||||||||
\(306\) | 6.82843 | 0.390355 | ||||||||
\(307\) | 10.9706 | 0.626123 | 0.313062 | − | 0.949733i | \(-0.398645\pi\) | ||||
0.313062 | + | 0.949733i | \(0.398645\pi\) | |||||||
\(308\) | −15.3137 | −0.872580 | ||||||||
\(309\) | 24.2843 | 1.38148 | ||||||||
\(310\) | 25.3137 | 1.43772 | ||||||||
\(311\) | −2.48528 | −0.140927 | −0.0704637 | − | 0.997514i | \(-0.522448\pi\) | ||||
−0.0704637 | + | 0.997514i | \(0.522448\pi\) | |||||||
\(312\) | −17.6569 | −0.999623 | ||||||||
\(313\) | −6.00000 | −0.339140 | −0.169570 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169570 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(314\) | 39.7990 | 2.24599 | ||||||||
\(315\) | 0.828427 | 0.0466766 | ||||||||
\(316\) | 55.4558 | 3.11963 | ||||||||
\(317\) | −2.82843 | −0.158860 | −0.0794301 | − | 0.996840i | \(-0.525310\pi\) | ||||
−0.0794301 | + | 0.996840i | \(0.525310\pi\) | |||||||
\(318\) | 36.9706 | 2.07321 | ||||||||
\(319\) | −4.82843 | −0.270340 | ||||||||
\(320\) | −9.82843 | −0.549426 | ||||||||
\(321\) | 16.2843 | 0.908899 | ||||||||
\(322\) | 17.6569 | 0.983978 | ||||||||
\(323\) | −2.34315 | −0.130376 | ||||||||
\(324\) | −42.1127 | −2.33959 | ||||||||
\(325\) | −2.00000 | −0.110940 | ||||||||
\(326\) | 47.4558 | 2.62834 | ||||||||
\(327\) | −4.00000 | −0.221201 | ||||||||
\(328\) | 26.4853 | 1.46241 | ||||||||
\(329\) | −0.284271 | −0.0156724 | ||||||||
\(330\) | −23.3137 | −1.28338 | ||||||||
\(331\) | −17.7990 | −0.978321 | −0.489160 | − | 0.872194i | \(-0.662697\pi\) | ||||
−0.489160 | + | 0.872194i | \(0.662697\pi\) | |||||||
\(332\) | 49.1127 | 2.69541 | ||||||||
\(333\) | 8.48528 | 0.464991 | ||||||||
\(334\) | −34.9706 | −1.91350 | ||||||||
\(335\) | −10.4853 | −0.572872 | ||||||||
\(336\) | −4.97056 | −0.271166 | ||||||||
\(337\) | −6.82843 | −0.371968 | −0.185984 | − | 0.982553i | \(-0.559547\pi\) | ||||
−0.185984 | + | 0.982553i | \(0.559547\pi\) | |||||||
\(338\) | 21.7279 | 1.18184 | ||||||||
\(339\) | −5.65685 | −0.307238 | ||||||||
\(340\) | −10.8284 | −0.587254 | ||||||||
\(341\) | 50.6274 | 2.74163 | ||||||||
\(342\) | −2.00000 | −0.108148 | ||||||||
\(343\) | −11.0294 | −0.595534 | ||||||||
\(344\) | 26.4853 | 1.42799 | ||||||||
\(345\) | 17.6569 | 0.950613 | ||||||||
\(346\) | 12.8284 | 0.689661 | ||||||||
\(347\) | 20.1421 | 1.08129 | 0.540643 | − | 0.841252i | \(-0.318181\pi\) | ||||
0.540643 | + | 0.841252i | \(0.318181\pi\) | |||||||
\(348\) | −7.65685 | −0.410450 | ||||||||
\(349\) | −24.6274 | −1.31828 | −0.659138 | − | 0.752022i | \(-0.729079\pi\) | ||||
−0.659138 | + | 0.752022i | \(0.729079\pi\) | |||||||
\(350\) | −2.00000 | −0.106904 | ||||||||
\(351\) | −8.00000 | −0.427008 | ||||||||
\(352\) | −7.65685 | −0.408112 | ||||||||
\(353\) | −15.6569 | −0.833330 | −0.416665 | − | 0.909060i | \(-0.636801\pi\) | ||||
−0.416665 | + | 0.909060i | \(0.636801\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.31371 | 0.388171 | ||||||||
\(356\) | 14.0000 | 0.741999 | ||||||||
\(357\) | 4.68629 | 0.248025 | ||||||||
\(358\) | 1.65685 | 0.0875675 | ||||||||
\(359\) | −32.1421 | −1.69640 | −0.848199 | − | 0.529678i | \(-0.822313\pi\) | ||||
−0.848199 | + | 0.529678i | \(0.822313\pi\) | |||||||
\(360\) | −4.41421 | −0.232649 | ||||||||
\(361\) | −18.3137 | −0.963879 | ||||||||
\(362\) | 14.4853 | 0.761329 | ||||||||
\(363\) | −24.6274 | −1.29260 | ||||||||
\(364\) | −6.34315 | −0.332471 | ||||||||
\(365\) | −8.48528 | −0.444140 | ||||||||
\(366\) | 36.9706 | 1.93248 | ||||||||
\(367\) | 18.0000 | 0.939592 | 0.469796 | − | 0.882775i | \(-0.344327\pi\) | ||||
0.469796 | + | 0.882775i | \(0.344327\pi\) | |||||||
\(368\) | −26.4853 | −1.38064 | ||||||||
\(369\) | −6.00000 | −0.312348 | ||||||||
\(370\) | −20.4853 | −1.06498 | ||||||||
\(371\) | 6.34315 | 0.329320 | ||||||||
\(372\) | 80.2843 | 4.16255 | ||||||||
\(373\) | 26.9706 | 1.39648 | 0.698241 | − | 0.715862i | \(-0.253966\pi\) | ||||
0.698241 | + | 0.715862i | \(0.253966\pi\) | |||||||
\(374\) | −32.9706 | −1.70487 | ||||||||
\(375\) | −2.00000 | −0.103280 | ||||||||
\(376\) | 1.51472 | 0.0781156 | ||||||||
\(377\) | −2.00000 | −0.103005 | ||||||||
\(378\) | −8.00000 | −0.411476 | ||||||||
\(379\) | 5.51472 | 0.283272 | 0.141636 | − | 0.989919i | \(-0.454764\pi\) | ||||
0.141636 | + | 0.989919i | \(0.454764\pi\) | |||||||
\(380\) | 3.17157 | 0.162698 | ||||||||
\(381\) | −12.0000 | −0.614779 | ||||||||
\(382\) | 36.6274 | 1.87402 | ||||||||
\(383\) | −14.4853 | −0.740163 | −0.370082 | − | 0.928999i | \(-0.620670\pi\) | ||||
−0.370082 | + | 0.928999i | \(0.620670\pi\) | |||||||
\(384\) | −41.1127 | −2.09802 | ||||||||
\(385\) | −4.00000 | −0.203859 | ||||||||
\(386\) | 30.1421 | 1.53419 | ||||||||
\(387\) | −6.00000 | −0.304997 | ||||||||
\(388\) | 17.1716 | 0.871755 | ||||||||
\(389\) | −6.68629 | −0.339008 | −0.169504 | − | 0.985529i | \(-0.554217\pi\) | ||||
−0.169504 | + | 0.985529i | \(0.554217\pi\) | |||||||
\(390\) | −9.65685 | −0.488994 | ||||||||
\(391\) | 24.9706 | 1.26282 | ||||||||
\(392\) | 27.8701 | 1.40765 | ||||||||
\(393\) | −32.2843 | −1.62853 | ||||||||
\(394\) | 20.1421 | 1.01475 | ||||||||
\(395\) | 14.4853 | 0.728834 | ||||||||
\(396\) | −18.4853 | −0.928920 | ||||||||
\(397\) | −8.34315 | −0.418730 | −0.209365 | − | 0.977838i | \(-0.567140\pi\) | ||||
−0.209365 | + | 0.977838i | \(0.567140\pi\) | |||||||
\(398\) | −28.9706 | −1.45216 | ||||||||
\(399\) | −1.37258 | −0.0687151 | ||||||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | −29.3137 | −1.46386 | −0.731928 | − | 0.681382i | \(-0.761379\pi\) | ||||
−0.731928 | + | 0.681382i | \(0.761379\pi\) | |||||||
\(402\) | −50.6274 | −2.52507 | ||||||||
\(403\) | 20.9706 | 1.04462 | ||||||||
\(404\) | 16.6274 | 0.827245 | ||||||||
\(405\) | −11.0000 | −0.546594 | ||||||||
\(406\) | −2.00000 | −0.0992583 | ||||||||
\(407\) | −40.9706 | −2.03084 | ||||||||
\(408\) | −24.9706 | −1.23623 | ||||||||
\(409\) | 30.9706 | 1.53140 | 0.765698 | − | 0.643200i | \(-0.222394\pi\) | ||||
0.765698 | + | 0.643200i | \(0.222394\pi\) | |||||||
\(410\) | 14.4853 | 0.715377 | ||||||||
\(411\) | 21.6569 | 1.06825 | ||||||||
\(412\) | −46.4853 | −2.29017 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 21.3137 | 1.04751 | ||||||||
\(415\) | 12.8284 | 0.629723 | ||||||||
\(416\) | −3.17157 | −0.155499 | ||||||||
\(417\) | −20.6863 | −1.01301 | ||||||||
\(418\) | 9.65685 | 0.472332 | ||||||||
\(419\) | −4.97056 | −0.242828 | −0.121414 | − | 0.992602i | \(-0.538743\pi\) | ||||
−0.121414 | + | 0.992602i | \(0.538743\pi\) | |||||||
\(420\) | −6.34315 | −0.309514 | ||||||||
\(421\) | −14.9706 | −0.729621 | −0.364810 | − | 0.931082i | \(-0.618866\pi\) | ||||
−0.364810 | + | 0.931082i | \(0.618866\pi\) | |||||||
\(422\) | −11.6569 | −0.567447 | ||||||||
\(423\) | −0.343146 | −0.0166843 | ||||||||
\(424\) | −33.7990 | −1.64142 | ||||||||
\(425\) | −2.82843 | −0.137199 | ||||||||
\(426\) | 35.3137 | 1.71095 | ||||||||
\(427\) | 6.34315 | 0.306966 | ||||||||
\(428\) | −31.1716 | −1.50673 | ||||||||
\(429\) | −19.3137 | −0.932475 | ||||||||
\(430\) | 14.4853 | 0.698542 | ||||||||
\(431\) | −19.3137 | −0.930309 | −0.465154 | − | 0.885230i | \(-0.654001\pi\) | ||||
−0.465154 | + | 0.885230i | \(0.654001\pi\) | |||||||
\(432\) | 12.0000 | 0.577350 | ||||||||
\(433\) | −34.8284 | −1.67375 | −0.836874 | − | 0.547396i | \(-0.815619\pi\) | ||||
−0.836874 | + | 0.547396i | \(0.815619\pi\) | |||||||
\(434\) | 20.9706 | 1.00662 | ||||||||
\(435\) | −2.00000 | −0.0958927 | ||||||||
\(436\) | 7.65685 | 0.366697 | ||||||||
\(437\) | −7.31371 | −0.349862 | ||||||||
\(438\) | −40.9706 | −1.95765 | ||||||||
\(439\) | −21.6569 | −1.03363 | −0.516813 | − | 0.856099i | \(-0.672882\pi\) | ||||
−0.516813 | + | 0.856099i | \(0.672882\pi\) | |||||||
\(440\) | 21.3137 | 1.01609 | ||||||||
\(441\) | −6.31371 | −0.300653 | ||||||||
\(442\) | −13.6569 | −0.649590 | ||||||||
\(443\) | 3.65685 | 0.173742 | 0.0868712 | − | 0.996220i | \(-0.472313\pi\) | ||||
0.0868712 | + | 0.996220i | \(0.472313\pi\) | |||||||
\(444\) | −64.9706 | −3.08337 | ||||||||
\(445\) | 3.65685 | 0.173352 | ||||||||
\(446\) | −52.6274 | −2.49198 | ||||||||
\(447\) | 26.6274 | 1.25943 | ||||||||
\(448\) | −8.14214 | −0.384680 | ||||||||
\(449\) | 0.343146 | 0.0161940 | 0.00809702 | − | 0.999967i | \(-0.497423\pi\) | ||||
0.00809702 | + | 0.999967i | \(0.497423\pi\) | |||||||
\(450\) | −2.41421 | −0.113807 | ||||||||
\(451\) | 28.9706 | 1.36417 | ||||||||
\(452\) | 10.8284 | 0.509326 | ||||||||
\(453\) | 24.0000 | 1.12762 | ||||||||
\(454\) | 19.6569 | 0.922542 | ||||||||
\(455\) | −1.65685 | −0.0776745 | ||||||||
\(456\) | 7.31371 | 0.342496 | ||||||||
\(457\) | 8.34315 | 0.390276 | 0.195138 | − | 0.980776i | \(-0.437485\pi\) | ||||
0.195138 | + | 0.980776i | \(0.437485\pi\) | |||||||
\(458\) | 4.82843 | 0.225618 | ||||||||
\(459\) | −11.3137 | −0.528079 | ||||||||
\(460\) | −33.7990 | −1.57589 | ||||||||
\(461\) | −24.3431 | −1.13377 | −0.566887 | − | 0.823796i | \(-0.691852\pi\) | ||||
−0.566887 | + | 0.823796i | \(0.691852\pi\) | |||||||
\(462\) | −19.3137 | −0.898555 | ||||||||
\(463\) | −17.7990 | −0.827189 | −0.413595 | − | 0.910461i | \(-0.635727\pi\) | ||||
−0.413595 | + | 0.910461i | \(0.635727\pi\) | |||||||
\(464\) | 3.00000 | 0.139272 | ||||||||
\(465\) | 20.9706 | 0.972487 | ||||||||
\(466\) | −43.4558 | −2.01305 | ||||||||
\(467\) | −22.9706 | −1.06295 | −0.531475 | − | 0.847074i | \(-0.678362\pi\) | ||||
−0.531475 | + | 0.847074i | \(0.678362\pi\) | |||||||
\(468\) | −7.65685 | −0.353938 | ||||||||
\(469\) | −8.68629 | −0.401096 | ||||||||
\(470\) | 0.828427 | 0.0382125 | ||||||||
\(471\) | 32.9706 | 1.51920 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 28.9706 | 1.33207 | ||||||||
\(474\) | 69.9411 | 3.21250 | ||||||||
\(475\) | 0.828427 | 0.0380108 | ||||||||
\(476\) | −8.97056 | −0.411165 | ||||||||
\(477\) | 7.65685 | 0.350583 | ||||||||
\(478\) | 56.2843 | 2.57438 | ||||||||
\(479\) | 12.8284 | 0.586146 | 0.293073 | − | 0.956090i | \(-0.405322\pi\) | ||||
0.293073 | + | 0.956090i | \(0.405322\pi\) | |||||||
\(480\) | −3.17157 | −0.144762 | ||||||||
\(481\) | −16.9706 | −0.773791 | ||||||||
\(482\) | −24.1421 | −1.09964 | ||||||||
\(483\) | 14.6274 | 0.665571 | ||||||||
\(484\) | 47.1421 | 2.14282 | ||||||||
\(485\) | 4.48528 | 0.203666 | ||||||||
\(486\) | −24.1421 | −1.09511 | ||||||||
\(487\) | −29.7990 | −1.35032 | −0.675161 | − | 0.737671i | \(-0.735926\pi\) | ||||
−0.675161 | + | 0.737671i | \(0.735926\pi\) | |||||||
\(488\) | −33.7990 | −1.53001 | ||||||||
\(489\) | 39.3137 | 1.77783 | ||||||||
\(490\) | 15.2426 | 0.688592 | ||||||||
\(491\) | 43.4558 | 1.96113 | 0.980567 | − | 0.196183i | \(-0.0628545\pi\) | ||||
0.980567 | + | 0.196183i | \(0.0628545\pi\) | |||||||
\(492\) | 45.9411 | 2.07119 | ||||||||
\(493\) | −2.82843 | −0.127386 | ||||||||
\(494\) | 4.00000 | 0.179969 | ||||||||
\(495\) | −4.82843 | −0.217022 | ||||||||
\(496\) | −31.4558 | −1.41241 | ||||||||
\(497\) | 6.05887 | 0.271778 | ||||||||
\(498\) | 61.9411 | 2.77565 | ||||||||
\(499\) | 36.0000 | 1.61158 | 0.805791 | − | 0.592200i | \(-0.201741\pi\) | ||||
0.805791 | + | 0.592200i | \(0.201741\pi\) | |||||||
\(500\) | 3.82843 | 0.171212 | ||||||||
\(501\) | −28.9706 | −1.29431 | ||||||||
\(502\) | −7.65685 | −0.341742 | ||||||||
\(503\) | −30.0000 | −1.33763 | −0.668817 | − | 0.743427i | \(-0.733199\pi\) | ||||
−0.668817 | + | 0.743427i | \(0.733199\pi\) | |||||||
\(504\) | −3.65685 | −0.162889 | ||||||||
\(505\) | 4.34315 | 0.193267 | ||||||||
\(506\) | −102.912 | −4.57498 | ||||||||
\(507\) | 18.0000 | 0.799408 | ||||||||
\(508\) | 22.9706 | 1.01915 | ||||||||
\(509\) | −44.6274 | −1.97808 | −0.989038 | − | 0.147663i | \(-0.952825\pi\) | ||||
−0.989038 | + | 0.147663i | \(0.952825\pi\) | |||||||
\(510\) | −13.6569 | −0.604736 | ||||||||
\(511\) | −7.02944 | −0.310964 | ||||||||
\(512\) | 31.2426 | 1.38074 | ||||||||
\(513\) | 3.31371 | 0.146304 | ||||||||
\(514\) | −70.7696 | −3.12151 | ||||||||
\(515\) | −12.1421 | −0.535046 | ||||||||
\(516\) | 45.9411 | 2.02245 | ||||||||
\(517\) | 1.65685 | 0.0728684 | ||||||||
\(518\) | −16.9706 | −0.745644 | ||||||||
\(519\) | 10.6274 | 0.466492 | ||||||||
\(520\) | 8.82843 | 0.387152 | ||||||||
\(521\) | 1.31371 | 0.0575546 | 0.0287773 | − | 0.999586i | \(-0.490839\pi\) | ||||
0.0287773 | + | 0.999586i | \(0.490839\pi\) | |||||||
\(522\) | −2.41421 | −0.105667 | ||||||||
\(523\) | −14.4853 | −0.633397 | −0.316699 | − | 0.948526i | \(-0.602574\pi\) | ||||
−0.316699 | + | 0.948526i | \(0.602574\pi\) | |||||||
\(524\) | 61.7990 | 2.69970 | ||||||||
\(525\) | −1.65685 | −0.0723110 | ||||||||
\(526\) | 20.1421 | 0.878239 | ||||||||
\(527\) | 29.6569 | 1.29187 | ||||||||
\(528\) | 28.9706 | 1.26078 | ||||||||
\(529\) | 54.9411 | 2.38874 | ||||||||
\(530\) | −18.4853 | −0.802949 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.62742 | 0.113913 | ||||||||
\(533\) | 12.0000 | 0.519778 | ||||||||
\(534\) | 17.6569 | 0.764087 | ||||||||
\(535\) | −8.14214 | −0.352015 | ||||||||
\(536\) | 46.2843 | 1.99918 | ||||||||
\(537\) | 1.37258 | 0.0592313 | ||||||||
\(538\) | −3.17157 | −0.136736 | ||||||||
\(539\) | 30.4853 | 1.31309 | ||||||||
\(540\) | 15.3137 | 0.658997 | ||||||||
\(541\) | −38.9706 | −1.67548 | −0.837738 | − | 0.546073i | \(-0.816122\pi\) | ||||
−0.837738 | + | 0.546073i | \(0.816122\pi\) | |||||||
\(542\) | −71.9411 | −3.09014 | ||||||||
\(543\) | 12.0000 | 0.514969 | ||||||||
\(544\) | −4.48528 | −0.192305 | ||||||||
\(545\) | 2.00000 | 0.0856706 | ||||||||
\(546\) | −8.00000 | −0.342368 | ||||||||
\(547\) | 14.4853 | 0.619346 | 0.309673 | − | 0.950843i | \(-0.399780\pi\) | ||||
0.309673 | + | 0.950843i | \(0.399780\pi\) | |||||||
\(548\) | −41.4558 | −1.77091 | ||||||||
\(549\) | 7.65685 | 0.326787 | ||||||||
\(550\) | 11.6569 | 0.497050 | ||||||||
\(551\) | 0.828427 | 0.0352922 | ||||||||
\(552\) | −77.9411 | −3.31739 | ||||||||
\(553\) | 12.0000 | 0.510292 | ||||||||
\(554\) | −18.4853 | −0.785364 | ||||||||
\(555\) | −16.9706 | −0.720360 | ||||||||
\(556\) | 39.5980 | 1.67933 | ||||||||
\(557\) | 39.9411 | 1.69236 | 0.846180 | − | 0.532897i | \(-0.178897\pi\) | ||||
0.846180 | + | 0.532897i | \(0.178897\pi\) | |||||||
\(558\) | 25.3137 | 1.07161 | ||||||||
\(559\) | 12.0000 | 0.507546 | ||||||||
\(560\) | 2.48528 | 0.105022 | ||||||||
\(561\) | −27.3137 | −1.15319 | ||||||||
\(562\) | 16.1421 | 0.680915 | ||||||||
\(563\) | −3.65685 | −0.154118 | −0.0770590 | − | 0.997027i | \(-0.524553\pi\) | ||||
−0.0770590 | + | 0.997027i | \(0.524553\pi\) | |||||||
\(564\) | 2.62742 | 0.110634 | ||||||||
\(565\) | 2.82843 | 0.118993 | ||||||||
\(566\) | 2.00000 | 0.0840663 | ||||||||
\(567\) | −9.11270 | −0.382697 | ||||||||
\(568\) | −32.2843 | −1.35462 | ||||||||
\(569\) | 16.3431 | 0.685140 | 0.342570 | − | 0.939492i | \(-0.388703\pi\) | ||||
0.342570 | + | 0.939492i | \(0.388703\pi\) | |||||||
\(570\) | 4.00000 | 0.167542 | ||||||||
\(571\) | 28.0000 | 1.17176 | 0.585882 | − | 0.810397i | \(-0.300748\pi\) | ||||
0.585882 | + | 0.810397i | \(0.300748\pi\) | |||||||
\(572\) | 36.9706 | 1.54582 | ||||||||
\(573\) | 30.3431 | 1.26760 | ||||||||
\(574\) | 12.0000 | 0.500870 | ||||||||
\(575\) | −8.82843 | −0.368171 | ||||||||
\(576\) | −9.82843 | −0.409518 | ||||||||
\(577\) | −15.7990 | −0.657721 | −0.328860 | − | 0.944379i | \(-0.606665\pi\) | ||||
−0.328860 | + | 0.944379i | \(0.606665\pi\) | |||||||
\(578\) | 21.7279 | 0.903762 | ||||||||
\(579\) | 24.9706 | 1.03774 | ||||||||
\(580\) | 3.82843 | 0.158967 | ||||||||
\(581\) | 10.6274 | 0.440900 | ||||||||
\(582\) | 21.6569 | 0.897705 | ||||||||
\(583\) | −36.9706 | −1.53116 | ||||||||
\(584\) | 37.4558 | 1.54993 | ||||||||
\(585\) | −2.00000 | −0.0826898 | ||||||||
\(586\) | 20.4853 | 0.846239 | ||||||||
\(587\) | 9.79899 | 0.404448 | 0.202224 | − | 0.979339i | \(-0.435183\pi\) | ||||
0.202224 | + | 0.979339i | \(0.435183\pi\) | |||||||
\(588\) | 48.3431 | 1.99364 | ||||||||
\(589\) | −8.68629 | −0.357912 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.6863 | 0.686382 | ||||||||
\(592\) | 25.4558 | 1.04623 | ||||||||
\(593\) | 3.65685 | 0.150169 | 0.0750845 | − | 0.997177i | \(-0.476077\pi\) | ||||
0.0750845 | + | 0.997177i | \(0.476077\pi\) | |||||||
\(594\) | 46.6274 | 1.91315 | ||||||||
\(595\) | −2.34315 | −0.0960596 | ||||||||
\(596\) | −50.9706 | −2.08784 | ||||||||
\(597\) | −24.0000 | −0.982255 | ||||||||
\(598\) | −42.6274 | −1.74316 | ||||||||
\(599\) | 1.79899 | 0.0735047 | 0.0367524 | − | 0.999324i | \(-0.488299\pi\) | ||||
0.0367524 | + | 0.999324i | \(0.488299\pi\) | |||||||
\(600\) | 8.82843 | 0.360419 | ||||||||
\(601\) | 2.00000 | 0.0815817 | 0.0407909 | − | 0.999168i | \(-0.487012\pi\) | ||||
0.0407909 | + | 0.999168i | \(0.487012\pi\) | |||||||
\(602\) | 12.0000 | 0.489083 | ||||||||
\(603\) | −10.4853 | −0.426994 | ||||||||
\(604\) | −45.9411 | −1.86932 | ||||||||
\(605\) | 12.3137 | 0.500623 | ||||||||
\(606\) | 20.9706 | 0.851871 | ||||||||
\(607\) | 42.9706 | 1.74412 | 0.872061 | − | 0.489398i | \(-0.162783\pi\) | ||||
0.872061 | + | 0.489398i | \(0.162783\pi\) | |||||||
\(608\) | 1.31371 | 0.0532779 | ||||||||
\(609\) | −1.65685 | −0.0671391 | ||||||||
\(610\) | −18.4853 | −0.748447 | ||||||||
\(611\) | 0.686292 | 0.0277644 | ||||||||
\(612\) | −10.8284 | −0.437713 | ||||||||
\(613\) | −2.00000 | −0.0807792 | −0.0403896 | − | 0.999184i | \(-0.512860\pi\) | ||||
−0.0403896 | + | 0.999184i | \(0.512860\pi\) | |||||||
\(614\) | −26.4853 | −1.06886 | ||||||||
\(615\) | 12.0000 | 0.483887 | ||||||||
\(616\) | 17.6569 | 0.711415 | ||||||||
\(617\) | −14.8284 | −0.596970 | −0.298485 | − | 0.954414i | \(-0.596481\pi\) | ||||
−0.298485 | + | 0.954414i | \(0.596481\pi\) | |||||||
\(618\) | −58.6274 | −2.35834 | ||||||||
\(619\) | 29.7990 | 1.19772 | 0.598861 | − | 0.800853i | \(-0.295620\pi\) | ||||
0.598861 | + | 0.800853i | \(0.295620\pi\) | |||||||
\(620\) | −40.1421 | −1.61215 | ||||||||
\(621\) | −35.3137 | −1.41709 | ||||||||
\(622\) | 6.00000 | 0.240578 | ||||||||
\(623\) | 3.02944 | 0.121372 | ||||||||
\(624\) | 12.0000 | 0.480384 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 14.4853 | 0.578948 | ||||||||
\(627\) | 8.00000 | 0.319489 | ||||||||
\(628\) | −63.1127 | −2.51847 | ||||||||
\(629\) | −24.0000 | −0.956943 | ||||||||
\(630\) | −2.00000 | −0.0796819 | ||||||||
\(631\) | 3.02944 | 0.120600 | 0.0603000 | − | 0.998180i | \(-0.480794\pi\) | ||||
0.0603000 | + | 0.998180i | \(0.480794\pi\) | |||||||
\(632\) | −63.9411 | −2.54344 | ||||||||
\(633\) | −9.65685 | −0.383825 | ||||||||
\(634\) | 6.82843 | 0.271191 | ||||||||
\(635\) | 6.00000 | 0.238103 | ||||||||
\(636\) | −58.6274 | −2.32473 | ||||||||
\(637\) | 12.6274 | 0.500316 | ||||||||
\(638\) | 11.6569 | 0.461499 | ||||||||
\(639\) | 7.31371 | 0.289326 | ||||||||
\(640\) | 20.5563 | 0.812561 | ||||||||
\(641\) | −44.6274 | −1.76268 | −0.881338 | − | 0.472485i | \(-0.843357\pi\) | ||||
−0.881338 | + | 0.472485i | \(0.843357\pi\) | |||||||
\(642\) | −39.3137 | −1.55159 | ||||||||
\(643\) | −31.4558 | −1.24050 | −0.620249 | − | 0.784405i | \(-0.712968\pi\) | ||||
−0.620249 | + | 0.784405i | \(0.712968\pi\) | |||||||
\(644\) | −28.0000 | −1.10335 | ||||||||
\(645\) | 12.0000 | 0.472500 | ||||||||
\(646\) | 5.65685 | 0.222566 | ||||||||
\(647\) | 21.1127 | 0.830026 | 0.415013 | − | 0.909816i | \(-0.363777\pi\) | ||||
0.415013 | + | 0.909816i | \(0.363777\pi\) | |||||||
\(648\) | 48.5563 | 1.90747 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 4.82843 | 0.189386 | ||||||||
\(651\) | 17.3726 | 0.680885 | ||||||||
\(652\) | −75.2548 | −2.94721 | ||||||||
\(653\) | −22.8284 | −0.893345 | −0.446673 | − | 0.894697i | \(-0.647391\pi\) | ||||
−0.446673 | + | 0.894697i | \(0.647391\pi\) | |||||||
\(654\) | 9.65685 | 0.377613 | ||||||||
\(655\) | 16.1421 | 0.630725 | ||||||||
\(656\) | −18.0000 | −0.702782 | ||||||||
\(657\) | −8.48528 | −0.331042 | ||||||||
\(658\) | 0.686292 | 0.0267544 | ||||||||
\(659\) | −37.7990 | −1.47244 | −0.736220 | − | 0.676743i | \(-0.763391\pi\) | ||||
−0.736220 | + | 0.676743i | \(0.763391\pi\) | |||||||
\(660\) | 36.9706 | 1.43908 | ||||||||
\(661\) | 26.0000 | 1.01128 | 0.505641 | − | 0.862744i | \(-0.331256\pi\) | ||||
0.505641 | + | 0.862744i | \(0.331256\pi\) | |||||||
\(662\) | 42.9706 | 1.67010 | ||||||||
\(663\) | −11.3137 | −0.439388 | ||||||||
\(664\) | −56.6274 | −2.19757 | ||||||||
\(665\) | 0.686292 | 0.0266132 | ||||||||
\(666\) | −20.4853 | −0.793789 | ||||||||
\(667\) | −8.82843 | −0.341838 | ||||||||
\(668\) | 55.4558 | 2.14565 | ||||||||
\(669\) | −43.5980 | −1.68560 | ||||||||
\(670\) | 25.3137 | 0.977954 | ||||||||
\(671\) | −36.9706 | −1.42723 | ||||||||
\(672\) | −2.62742 | −0.101355 | ||||||||
\(673\) | −10.9706 | −0.422884 | −0.211442 | − | 0.977391i | \(-0.567816\pi\) | ||||
−0.211442 | + | 0.977391i | \(0.567816\pi\) | |||||||
\(674\) | 16.4853 | 0.634989 | ||||||||
\(675\) | 4.00000 | 0.153960 | ||||||||
\(676\) | −34.4558 | −1.32522 | ||||||||
\(677\) | 36.7696 | 1.41317 | 0.706584 | − | 0.707629i | \(-0.250235\pi\) | ||||
0.706584 | + | 0.707629i | \(0.250235\pi\) | |||||||
\(678\) | 13.6569 | 0.524488 | ||||||||
\(679\) | 3.71573 | 0.142597 | ||||||||
\(680\) | 12.4853 | 0.478789 | ||||||||
\(681\) | 16.2843 | 0.624015 | ||||||||
\(682\) | −122.225 | −4.68025 | ||||||||
\(683\) | 40.1421 | 1.53600 | 0.767998 | − | 0.640452i | \(-0.221253\pi\) | ||||
0.767998 | + | 0.640452i | \(0.221253\pi\) | |||||||
\(684\) | 3.17157 | 0.121268 | ||||||||
\(685\) | −10.8284 | −0.413733 | ||||||||
\(686\) | 26.6274 | 1.01664 | ||||||||
\(687\) | 4.00000 | 0.152610 | ||||||||
\(688\) | −18.0000 | −0.686244 | ||||||||
\(689\) | −15.3137 | −0.583406 | ||||||||
\(690\) | −42.6274 | −1.62280 | ||||||||
\(691\) | −11.0294 | −0.419580 | −0.209790 | − | 0.977747i | \(-0.567278\pi\) | ||||
−0.209790 | + | 0.977747i | \(0.567278\pi\) | |||||||
\(692\) | −20.3431 | −0.773330 | ||||||||
\(693\) | −4.00000 | −0.151947 | ||||||||
\(694\) | −48.6274 | −1.84587 | ||||||||
\(695\) | 10.3431 | 0.392338 | ||||||||
\(696\) | 8.82843 | 0.334641 | ||||||||
\(697\) | 16.9706 | 0.642806 | ||||||||
\(698\) | 59.4558 | 2.25044 | ||||||||
\(699\) | −36.0000 | −1.36165 | ||||||||
\(700\) | 3.17157 | 0.119874 | ||||||||
\(701\) | 29.3137 | 1.10716 | 0.553582 | − | 0.832795i | \(-0.313261\pi\) | ||||
0.553582 | + | 0.832795i | \(0.313261\pi\) | |||||||
\(702\) | 19.3137 | 0.728949 | ||||||||
\(703\) | 7.02944 | 0.265120 | ||||||||
\(704\) | 47.4558 | 1.78856 | ||||||||
\(705\) | 0.686292 | 0.0258472 | ||||||||
\(706\) | 37.7990 | 1.42258 | ||||||||
\(707\) | 3.59798 | 0.135316 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.0000 | −0.826227 | −0.413114 | − | 0.910679i | \(-0.635559\pi\) | ||||
−0.413114 | + | 0.910679i | \(0.635559\pi\) | |||||||
\(710\) | −17.6569 | −0.662650 | ||||||||
\(711\) | 14.4853 | 0.543240 | ||||||||
\(712\) | −16.1421 | −0.604952 | ||||||||
\(713\) | 92.5685 | 3.46672 | ||||||||
\(714\) | −11.3137 | −0.423405 | ||||||||
\(715\) | 9.65685 | 0.361146 | ||||||||
\(716\) | −2.62742 | −0.0981912 | ||||||||
\(717\) | 46.6274 | 1.74133 | ||||||||
\(718\) | 77.5980 | 2.89593 | ||||||||
\(719\) | 10.6274 | 0.396336 | 0.198168 | − | 0.980168i | \(-0.436501\pi\) | ||||
0.198168 | + | 0.980168i | \(0.436501\pi\) | |||||||
\(720\) | 3.00000 | 0.111803 | ||||||||
\(721\) | −10.0589 | −0.374612 | ||||||||
\(722\) | 44.2132 | 1.64545 | ||||||||
\(723\) | −20.0000 | −0.743808 | ||||||||
\(724\) | −22.9706 | −0.853694 | ||||||||
\(725\) | 1.00000 | 0.0371391 | ||||||||
\(726\) | 59.4558 | 2.20661 | ||||||||
\(727\) | 43.9411 | 1.62969 | 0.814843 | − | 0.579682i | \(-0.196823\pi\) | ||||
0.814843 | + | 0.579682i | \(0.196823\pi\) | |||||||
\(728\) | 7.31371 | 0.271064 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 20.4853 | 0.758194 | ||||||||
\(731\) | 16.9706 | 0.627679 | ||||||||
\(732\) | −58.6274 | −2.16693 | ||||||||
\(733\) | −17.1716 | −0.634247 | −0.317123 | − | 0.948384i | \(-0.602717\pi\) | ||||
−0.317123 | + | 0.948384i | \(0.602717\pi\) | |||||||
\(734\) | −43.4558 | −1.60398 | ||||||||
\(735\) | 12.6274 | 0.465769 | ||||||||
\(736\) | −14.0000 | −0.516047 | ||||||||
\(737\) | 50.6274 | 1.86488 | ||||||||
\(738\) | 14.4853 | 0.533211 | ||||||||
\(739\) | −2.48528 | −0.0914226 | −0.0457113 | − | 0.998955i | \(-0.514555\pi\) | ||||
−0.0457113 | + | 0.998955i | \(0.514555\pi\) | |||||||
\(740\) | 32.4853 | 1.19418 | ||||||||
\(741\) | 3.31371 | 0.121732 | ||||||||
\(742\) | −15.3137 | −0.562184 | ||||||||
\(743\) | −7.37258 | −0.270474 | −0.135237 | − | 0.990813i | \(-0.543180\pi\) | ||||
−0.135237 | + | 0.990813i | \(0.543180\pi\) | |||||||
\(744\) | −92.5685 | −3.39373 | ||||||||
\(745\) | −13.3137 | −0.487777 | ||||||||
\(746\) | −65.1127 | −2.38395 | ||||||||
\(747\) | 12.8284 | 0.469368 | ||||||||
\(748\) | 52.2843 | 1.91170 | ||||||||
\(749\) | −6.74517 | −0.246463 | ||||||||
\(750\) | 4.82843 | 0.176309 | ||||||||
\(751\) | −12.1421 | −0.443073 | −0.221536 | − | 0.975152i | \(-0.571107\pi\) | ||||
−0.221536 | + | 0.975152i | \(0.571107\pi\) | |||||||
\(752\) | −1.02944 | −0.0375397 | ||||||||
\(753\) | −6.34315 | −0.231157 | ||||||||
\(754\) | 4.82843 | 0.175841 | ||||||||
\(755\) | −12.0000 | −0.436725 | ||||||||
\(756\) | 12.6863 | 0.461396 | ||||||||
\(757\) | 36.4853 | 1.32608 | 0.663040 | − | 0.748584i | \(-0.269266\pi\) | ||||
0.663040 | + | 0.748584i | \(0.269266\pi\) | |||||||
\(758\) | −13.3137 | −0.483576 | ||||||||
\(759\) | −85.2548 | −3.09455 | ||||||||
\(760\) | −3.65685 | −0.132648 | ||||||||
\(761\) | −36.6274 | −1.32774 | −0.663871 | − | 0.747847i | \(-0.731088\pi\) | ||||
−0.663871 | + | 0.747847i | \(0.731088\pi\) | |||||||
\(762\) | 28.9706 | 1.04949 | ||||||||
\(763\) | 1.65685 | 0.0599822 | ||||||||
\(764\) | −58.0833 | −2.10138 | ||||||||
\(765\) | −2.82843 | −0.102262 | ||||||||
\(766\) | 34.9706 | 1.26354 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 59.9411 | 2.16294 | ||||||||
\(769\) | −4.34315 | −0.156618 | −0.0783089 | − | 0.996929i | \(-0.524952\pi\) | ||||
−0.0783089 | + | 0.996929i | \(0.524952\pi\) | |||||||
\(770\) | 9.65685 | 0.348009 | ||||||||
\(771\) | −58.6274 | −2.11141 | ||||||||
\(772\) | −47.7990 | −1.72032 | ||||||||
\(773\) | 8.48528 | 0.305194 | 0.152597 | − | 0.988288i | \(-0.451236\pi\) | ||||
0.152597 | + | 0.988288i | \(0.451236\pi\) | |||||||
\(774\) | 14.4853 | 0.520663 | ||||||||
\(775\) | −10.4853 | −0.376642 | ||||||||
\(776\) | −19.7990 | −0.710742 | ||||||||
\(777\) | −14.0589 | −0.504359 | ||||||||
\(778\) | 16.1421 | 0.578724 | ||||||||
\(779\) | −4.97056 | −0.178089 | ||||||||
\(780\) | 15.3137 | 0.548319 | ||||||||
\(781\) | −35.3137 | −1.26362 | ||||||||
\(782\) | −60.2843 | −2.15576 | ||||||||
\(783\) | 4.00000 | 0.142948 | ||||||||
\(784\) | −18.9411 | −0.676469 | ||||||||
\(785\) | −16.4853 | −0.588385 | ||||||||
\(786\) | 77.9411 | 2.78007 | ||||||||
\(787\) | −21.7990 | −0.777050 | −0.388525 | − | 0.921438i | \(-0.627015\pi\) | ||||
−0.388525 | + | 0.921438i | \(0.627015\pi\) | |||||||
\(788\) | −31.9411 | −1.13786 | ||||||||
\(789\) | 16.6863 | 0.594048 | ||||||||
\(790\) | −34.9706 | −1.24420 | ||||||||
\(791\) | 2.34315 | 0.0833127 | ||||||||
\(792\) | 21.3137 | 0.757350 | ||||||||
\(793\) | −15.3137 | −0.543806 | ||||||||
\(794\) | 20.1421 | 0.714818 | ||||||||
\(795\) | −15.3137 | −0.543121 | ||||||||
\(796\) | 45.9411 | 1.62834 | ||||||||
\(797\) | −34.1421 | −1.20938 | −0.604688 | − | 0.796462i | \(-0.706702\pi\) | ||||
−0.604688 | + | 0.796462i | \(0.706702\pi\) | |||||||
\(798\) | 3.31371 | 0.117304 | ||||||||
\(799\) | 0.970563 | 0.0343360 | ||||||||
\(800\) | 1.58579 | 0.0560660 | ||||||||
\(801\) | 3.65685 | 0.129209 | ||||||||
\(802\) | 70.7696 | 2.49896 | ||||||||
\(803\) | 40.9706 | 1.44582 | ||||||||
\(804\) | 80.2843 | 2.83141 | ||||||||
\(805\) | −7.31371 | −0.257774 | ||||||||
\(806\) | −50.6274 | −1.78327 | ||||||||
\(807\) | −2.62742 | −0.0924895 | ||||||||
\(808\) | −19.1716 | −0.674454 | ||||||||
\(809\) | −14.2843 | −0.502208 | −0.251104 | − | 0.967960i | \(-0.580794\pi\) | ||||
−0.251104 | + | 0.967960i | \(0.580794\pi\) | |||||||
\(810\) | 26.5563 | 0.933095 | ||||||||
\(811\) | 26.3431 | 0.925033 | 0.462516 | − | 0.886611i | \(-0.346947\pi\) | ||||
0.462516 | + | 0.886611i | \(0.346947\pi\) | |||||||
\(812\) | 3.17157 | 0.111300 | ||||||||
\(813\) | −59.5980 | −2.09019 | ||||||||
\(814\) | 98.9117 | 3.46685 | ||||||||
\(815\) | −19.6569 | −0.688550 | ||||||||
\(816\) | 16.9706 | 0.594089 | ||||||||
\(817\) | −4.97056 | −0.173898 | ||||||||
\(818\) | −74.7696 | −2.61426 | ||||||||
\(819\) | −1.65685 | −0.0578952 | ||||||||
\(820\) | −22.9706 | −0.802167 | ||||||||
\(821\) | −45.3137 | −1.58146 | −0.790730 | − | 0.612165i | \(-0.790299\pi\) | ||||
−0.790730 | + | 0.612165i | \(0.790299\pi\) | |||||||
\(822\) | −52.2843 | −1.82362 | ||||||||
\(823\) | 2.97056 | 0.103547 | 0.0517737 | − | 0.998659i | \(-0.483513\pi\) | ||||
0.0517737 | + | 0.998659i | \(0.483513\pi\) | |||||||
\(824\) | 53.5980 | 1.86717 | ||||||||
\(825\) | 9.65685 | 0.336209 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.31371 | −0.184776 | −0.0923879 | − | 0.995723i | \(-0.529450\pi\) | ||||
−0.0923879 | + | 0.995723i | \(0.529450\pi\) | |||||||
\(828\) | −33.7990 | −1.17460 | ||||||||
\(829\) | −24.6274 | −0.855346 | −0.427673 | − | 0.903934i | \(-0.640666\pi\) | ||||
−0.427673 | + | 0.903934i | \(0.640666\pi\) | |||||||
\(830\) | −30.9706 | −1.07500 | ||||||||
\(831\) | −15.3137 | −0.531227 | ||||||||
\(832\) | 19.6569 | 0.681479 | ||||||||
\(833\) | 17.8579 | 0.618738 | ||||||||
\(834\) | 49.9411 | 1.72932 | ||||||||
\(835\) | 14.4853 | 0.501284 | ||||||||
\(836\) | −15.3137 | −0.529636 | ||||||||
\(837\) | −41.9411 | −1.44970 | ||||||||
\(838\) | 12.0000 | 0.414533 | ||||||||
\(839\) | −14.4853 | −0.500087 | −0.250044 | − | 0.968235i | \(-0.580445\pi\) | ||||
−0.250044 | + | 0.968235i | \(0.580445\pi\) | |||||||
\(840\) | 7.31371 | 0.252347 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 36.1421 | 1.24554 | ||||||||
\(843\) | 13.3726 | 0.460576 | ||||||||
\(844\) | 18.4853 | 0.636290 | ||||||||
\(845\) | −9.00000 | −0.309609 | ||||||||
\(846\) | 0.828427 | 0.0284819 | ||||||||
\(847\) | 10.2010 | 0.350511 | ||||||||
\(848\) | 22.9706 | 0.788812 | ||||||||
\(849\) | 1.65685 | 0.0568631 | ||||||||
\(850\) | 6.82843 | 0.234213 | ||||||||
\(851\) | −74.9117 | −2.56794 | ||||||||
\(852\) | −56.0000 | −1.91853 | ||||||||
\(853\) | −11.1127 | −0.380492 | −0.190246 | − | 0.981736i | \(-0.560928\pi\) | ||||
−0.190246 | + | 0.981736i | \(0.560928\pi\) | |||||||
\(854\) | −15.3137 | −0.524024 | ||||||||
\(855\) | 0.828427 | 0.0283316 | ||||||||
\(856\) | 35.9411 | 1.22844 | ||||||||
\(857\) | 48.6274 | 1.66108 | 0.830540 | − | 0.556958i | \(-0.188032\pi\) | ||||
0.830540 | + | 0.556958i | \(0.188032\pi\) | |||||||
\(858\) | 46.6274 | 1.59183 | ||||||||
\(859\) | 28.4264 | 0.969896 | 0.484948 | − | 0.874543i | \(-0.338838\pi\) | ||||
0.484948 | + | 0.874543i | \(0.338838\pi\) | |||||||
\(860\) | −22.9706 | −0.783290 | ||||||||
\(861\) | 9.94113 | 0.338793 | ||||||||
\(862\) | 46.6274 | 1.58814 | ||||||||
\(863\) | −7.85786 | −0.267485 | −0.133742 | − | 0.991016i | \(-0.542699\pi\) | ||||
−0.133742 | + | 0.991016i | \(0.542699\pi\) | |||||||
\(864\) | 6.34315 | 0.215798 | ||||||||
\(865\) | −5.31371 | −0.180672 | ||||||||
\(866\) | 84.0833 | 2.85727 | ||||||||
\(867\) | 18.0000 | 0.611312 | ||||||||
\(868\) | −33.2548 | −1.12874 | ||||||||
\(869\) | −69.9411 | −2.37259 | ||||||||
\(870\) | 4.82843 | 0.163699 | ||||||||
\(871\) | 20.9706 | 0.710560 | ||||||||
\(872\) | −8.82843 | −0.298968 | ||||||||
\(873\) | 4.48528 | 0.151804 | ||||||||
\(874\) | 17.6569 | 0.597252 | ||||||||
\(875\) | 0.828427 | 0.0280059 | ||||||||
\(876\) | 64.9706 | 2.19515 | ||||||||
\(877\) | −18.2843 | −0.617416 | −0.308708 | − | 0.951157i | \(-0.599897\pi\) | ||||
−0.308708 | + | 0.951157i | \(0.599897\pi\) | |||||||
\(878\) | 52.2843 | 1.76451 | ||||||||
\(879\) | 16.9706 | 0.572403 | ||||||||
\(880\) | −14.4853 | −0.488299 | ||||||||
\(881\) | 6.68629 | 0.225267 | 0.112633 | − | 0.993637i | \(-0.464071\pi\) | ||||
0.112633 | + | 0.993637i | \(0.464071\pi\) | |||||||
\(882\) | 15.2426 | 0.513246 | ||||||||
\(883\) | 2.48528 | 0.0836364 | 0.0418182 | − | 0.999125i | \(-0.486685\pi\) | ||||
0.0418182 | + | 0.999125i | \(0.486685\pi\) | |||||||
\(884\) | 21.6569 | 0.728399 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.82843 | −0.296597 | ||||||||
\(887\) | −29.3137 | −0.984258 | −0.492129 | − | 0.870522i | \(-0.663781\pi\) | ||||
−0.492129 | + | 0.870522i | \(0.663781\pi\) | |||||||
\(888\) | 74.9117 | 2.51387 | ||||||||
\(889\) | 4.97056 | 0.166707 | ||||||||
\(890\) | −8.82843 | −0.295930 | ||||||||
\(891\) | 53.1127 | 1.77934 | ||||||||
\(892\) | 83.4558 | 2.79431 | ||||||||
\(893\) | −0.284271 | −0.00951277 | ||||||||
\(894\) | −64.2843 | −2.14999 | ||||||||
\(895\) | −0.686292 | −0.0229402 | ||||||||
\(896\) | 17.0294 | 0.568914 | ||||||||
\(897\) | −35.3137 | −1.17909 | ||||||||
\(898\) | −0.828427 | −0.0276450 | ||||||||
\(899\) | −10.4853 | −0.349704 | ||||||||
\(900\) | 3.82843 | 0.127614 | ||||||||
\(901\) | −21.6569 | −0.721494 | ||||||||
\(902\) | −69.9411 | −2.32878 | ||||||||
\(903\) | 9.94113 | 0.330820 | ||||||||
\(904\) | −12.4853 | −0.415254 | ||||||||
\(905\) | −6.00000 | −0.199447 | ||||||||
\(906\) | −57.9411 | −1.92496 | ||||||||
\(907\) | −10.0000 | −0.332045 | −0.166022 | − | 0.986122i | \(-0.553092\pi\) | ||||
−0.166022 | + | 0.986122i | \(0.553092\pi\) | |||||||
\(908\) | −31.1716 | −1.03446 | ||||||||
\(909\) | 4.34315 | 0.144053 | ||||||||
\(910\) | 4.00000 | 0.132599 | ||||||||
\(911\) | 3.85786 | 0.127817 | 0.0639084 | − | 0.997956i | \(-0.479643\pi\) | ||||
0.0639084 | + | 0.997956i | \(0.479643\pi\) | |||||||
\(912\) | −4.97056 | −0.164592 | ||||||||
\(913\) | −61.9411 | −2.04995 | ||||||||
\(914\) | −20.1421 | −0.666243 | ||||||||
\(915\) | −15.3137 | −0.506256 | ||||||||
\(916\) | −7.65685 | −0.252990 | ||||||||
\(917\) | 13.3726 | 0.441602 | ||||||||
\(918\) | 27.3137 | 0.901487 | ||||||||
\(919\) | −36.0000 | −1.18753 | −0.593765 | − | 0.804638i | \(-0.702359\pi\) | ||||
−0.593765 | + | 0.804638i | \(0.702359\pi\) | |||||||
\(920\) | 38.9706 | 1.28482 | ||||||||
\(921\) | −21.9411 | −0.722985 | ||||||||
\(922\) | 58.7696 | 1.93547 | ||||||||
\(923\) | −14.6274 | −0.481467 | ||||||||
\(924\) | 30.6274 | 1.00757 | ||||||||
\(925\) | 8.48528 | 0.278994 | ||||||||
\(926\) | 42.9706 | 1.41210 | ||||||||
\(927\) | −12.1421 | −0.398800 | ||||||||
\(928\) | 1.58579 | 0.0520560 | ||||||||
\(929\) | 40.6274 | 1.33294 | 0.666471 | − | 0.745531i | \(-0.267804\pi\) | ||||
0.666471 | + | 0.745531i | \(0.267804\pi\) | |||||||
\(930\) | −50.6274 | −1.66014 | ||||||||
\(931\) | −5.23045 | −0.171421 | ||||||||
\(932\) | 68.9117 | 2.25728 | ||||||||
\(933\) | 4.97056 | 0.162729 | ||||||||
\(934\) | 55.4558 | 1.81457 | ||||||||
\(935\) | 13.6569 | 0.446627 | ||||||||
\(936\) | 8.82843 | 0.288566 | ||||||||
\(937\) | 8.34315 | 0.272559 | 0.136279 | − | 0.990670i | \(-0.456486\pi\) | ||||
0.136279 | + | 0.990670i | \(0.456486\pi\) | |||||||
\(938\) | 20.9706 | 0.684713 | ||||||||
\(939\) | 12.0000 | 0.391605 | ||||||||
\(940\) | −1.31371 | −0.0428484 | ||||||||
\(941\) | 39.9411 | 1.30204 | 0.651022 | − | 0.759059i | \(-0.274341\pi\) | ||||
0.651022 | + | 0.759059i | \(0.274341\pi\) | |||||||
\(942\) | −79.5980 | −2.59344 | ||||||||
\(943\) | 52.9706 | 1.72496 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.31371 | 0.107795 | ||||||||
\(946\) | −69.9411 | −2.27398 | ||||||||
\(947\) | −56.9117 | −1.84938 | −0.924691 | − | 0.380719i | \(-0.875676\pi\) | ||||
−0.924691 | + | 0.380719i | \(0.875676\pi\) | |||||||
\(948\) | −110.912 | −3.60224 | ||||||||
\(949\) | 16.9706 | 0.550888 | ||||||||
\(950\) | −2.00000 | −0.0648886 | ||||||||
\(951\) | 5.65685 | 0.183436 | ||||||||
\(952\) | 10.3431 | 0.335223 | ||||||||
\(953\) | 6.68629 | 0.216590 | 0.108295 | − | 0.994119i | \(-0.465461\pi\) | ||||
0.108295 | + | 0.994119i | \(0.465461\pi\) | |||||||
\(954\) | −18.4853 | −0.598483 | ||||||||
\(955\) | −15.1716 | −0.490941 | ||||||||
\(956\) | −89.2548 | −2.88671 | ||||||||
\(957\) | 9.65685 | 0.312162 | ||||||||
\(958\) | −30.9706 | −1.00061 | ||||||||
\(959\) | −8.97056 | −0.289675 | ||||||||
\(960\) | 19.6569 | 0.634422 | ||||||||
\(961\) | 78.9411 | 2.54649 | ||||||||
\(962\) | 40.9706 | 1.32094 | ||||||||
\(963\) | −8.14214 | −0.262377 | ||||||||
\(964\) | 38.2843 | 1.23305 | ||||||||
\(965\) | −12.4853 | −0.401915 | ||||||||
\(966\) | −35.3137 | −1.13620 | ||||||||
\(967\) | −18.9706 | −0.610052 | −0.305026 | − | 0.952344i | \(-0.598665\pi\) | ||||
−0.305026 | + | 0.952344i | \(0.598665\pi\) | |||||||
\(968\) | −54.3553 | −1.74705 | ||||||||
\(969\) | 4.68629 | 0.150545 | ||||||||
\(970\) | −10.8284 | −0.347680 | ||||||||
\(971\) | −0.142136 | −0.00456135 | −0.00228067 | − | 0.999997i | \(-0.500726\pi\) | ||||
−0.00228067 | + | 0.999997i | \(0.500726\pi\) | |||||||
\(972\) | 38.2843 | 1.22797 | ||||||||
\(973\) | 8.56854 | 0.274695 | ||||||||
\(974\) | 71.9411 | 2.30514 | ||||||||
\(975\) | 4.00000 | 0.128103 | ||||||||
\(976\) | 22.9706 | 0.735270 | ||||||||
\(977\) | −25.3137 | −0.809857 | −0.404929 | − | 0.914348i | \(-0.632704\pi\) | ||||
−0.404929 | + | 0.914348i | \(0.632704\pi\) | |||||||
\(978\) | −94.9117 | −3.03494 | ||||||||
\(979\) | −17.6569 | −0.564316 | ||||||||
\(980\) | −24.1716 | −0.772133 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | −104.912 | −3.34787 | ||||||||
\(983\) | 13.3137 | 0.424641 | 0.212321 | − | 0.977200i | \(-0.431898\pi\) | ||||
0.212321 | + | 0.977200i | \(0.431898\pi\) | |||||||
\(984\) | −52.9706 | −1.68864 | ||||||||
\(985\) | −8.34315 | −0.265835 | ||||||||
\(986\) | 6.82843 | 0.217461 | ||||||||
\(987\) | 0.568542 | 0.0180969 | ||||||||
\(988\) | −6.34315 | −0.201802 | ||||||||
\(989\) | 52.9706 | 1.68437 | ||||||||
\(990\) | 11.6569 | 0.370479 | ||||||||
\(991\) | 52.0000 | 1.65183 | 0.825917 | − | 0.563791i | \(-0.190658\pi\) | ||||
0.825917 | + | 0.563791i | \(0.190658\pi\) | |||||||
\(992\) | −16.6274 | −0.527921 | ||||||||
\(993\) | 35.5980 | 1.12967 | ||||||||
\(994\) | −14.6274 | −0.463953 | ||||||||
\(995\) | 12.0000 | 0.380426 | ||||||||
\(996\) | −98.2254 | −3.11239 | ||||||||
\(997\) | 1.17157 | 0.0371041 | 0.0185520 | − | 0.999828i | \(-0.494094\pi\) | ||||
0.0185520 | + | 0.999828i | \(0.494094\pi\) | |||||||
\(998\) | −86.9117 | −2.75114 | ||||||||
\(999\) | 33.9411 | 1.07385 |
(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 | 145.2.a.b.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1305.2.a.n.1.2 | 2 | |||
4.3 | odd | 2 | 2320.2.a.k.1.1 | 2 | |||
5.2 | odd | 4 | 725.2.b.c.349.1 | 4 | |||
5.3 | odd | 4 | 725.2.b.c.349.4 | 4 | |||
5.4 | even | 2 | 725.2.a.c.1.2 | 2 | |||
7.6 | odd | 2 | 7105.2.a.e.1.1 | 2 | |||
8.3 | odd | 2 | 9280.2.a.w.1.1 | 2 | |||
8.5 | even | 2 | 9280.2.a.be.1.2 | 2 | |||
15.14 | odd | 2 | 6525.2.a.p.1.1 | 2 | |||
29.28 | even | 2 | 4205.2.a.d.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
145.2.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
725.2.a.c.1.2 | 2 | 5.4 | even | 2 | |||
725.2.b.c.349.1 | 4 | 5.2 | odd | 4 | |||
725.2.b.c.349.4 | 4 | 5.3 | odd | 4 | |||
1305.2.a.n.1.2 | 2 | 3.2 | odd | 2 | |||
2320.2.a.k.1.1 | 2 | 4.3 | odd | 2 | |||
4205.2.a.d.1.2 | 2 | 29.28 | even | 2 | |||
6525.2.a.p.1.1 | 2 | 15.14 | odd | 2 | |||
7105.2.a.e.1.1 | 2 | 7.6 | odd | 2 | |||
9280.2.a.w.1.1 | 2 | 8.3 | odd | 2 | |||
9280.2.a.be.1.2 | 2 | 8.5 | even | 2 |