Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1305,2,Mod(1,1305)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1305, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1305.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1305 = 3^{2} \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1305.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: | \(10.4204774638\) |
Analytic rank: | \(0\) |
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: | no (minimal twist has level 145) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1305.1 |
$q$-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 | \(-0.174443\pi\) | ||||
0.853553 | + | 0.521005i | \(0.174443\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.828427 | 0.313116 | 0.156558 | − | 0.987669i | \(-0.449960\pi\) | ||||
0.156558 | + | 0.987669i | \(0.449960\pi\) | |||||||
\(8\) | 4.41421 | 1.56066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.41421 | −0.763441 | ||||||||
\(11\) | 4.82843 | 1.45583 | 0.727913 | − | 0.685670i | \(-0.240491\pi\) | ||||
0.727913 | + | 0.685670i | \(0.240491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 2.82843 | 0.685994 | 0.342997 | − | 0.939336i | \(-0.388558\pi\) | ||||
0.342997 | + | 0.939336i | \(0.388558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.828427 | 0.190054 | 0.0950271 | − | 0.995475i | \(-0.469706\pi\) | ||||
0.0950271 | + | 0.995475i | \(0.469706\pi\) | |||||||
\(20\) | −3.82843 | −0.856062 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 11.6569 | 2.48525 | ||||||||
\(23\) | 8.82843 | 1.84085 | 0.920427 | − | 0.390914i | \(-0.127841\pi\) | ||||
0.920427 | + | 0.390914i | \(0.127841\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.82843 | −0.946932 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.17157 | 0.599371 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.4853 | −1.88321 | −0.941606 | − | 0.336717i | \(-0.890684\pi\) | ||||
−0.941606 | + | 0.336717i | \(0.890684\pi\) | |||||||
\(32\) | −1.58579 | −0.280330 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.82843 | 1.17107 | ||||||||
\(35\) | −0.828427 | −0.140030 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.48528 | 1.39497 | 0.697486 | − | 0.716599i | \(-0.254302\pi\) | ||||
0.697486 | + | 0.716599i | \(0.254302\pi\) | |||||||
\(38\) | 2.00000 | 0.324443 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.41421 | −0.697948 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.00000 | −0.914991 | −0.457496 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457496 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(44\) | 18.4853 | 2.78676 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 21.3137 | 3.14253 | ||||||||
\(47\) | 0.343146 | 0.0500530 | 0.0250265 | − | 0.999687i | \(-0.492033\pi\) | ||||
0.0250265 | + | 0.999687i | \(0.492033\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.31371 | −0.901958 | ||||||||
\(50\) | 2.41421 | 0.341421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.65685 | −1.06181 | ||||||||
\(53\) | −7.65685 | −1.05175 | −0.525875 | − | 0.850562i | \(-0.676262\pi\) | ||||
−0.525875 | + | 0.850562i | \(0.676262\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.82843 | −0.651065 | ||||||||
\(56\) | 3.65685 | 0.488668 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.41421 | −0.317002 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 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 | 0 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.4853 | −1.28098 | −0.640490 | − | 0.767966i | \(-0.721269\pi\) | ||||
−0.640490 | + | 0.767966i | \(0.721269\pi\) | |||||||
\(68\) | 10.8284 | 1.31314 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.00000 | −0.239046 | ||||||||
\(71\) | −7.31371 | −0.867978 | −0.433989 | − | 0.900918i | \(-0.642894\pi\) | ||||
−0.433989 | + | 0.900918i | \(0.642894\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.48528 | −0.993127 | −0.496564 | − | 0.868000i | \(-0.665405\pi\) | ||||
−0.496564 | + | 0.868000i | \(0.665405\pi\) | |||||||
\(74\) | 20.4853 | 2.38137 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.17157 | 0.363804 | ||||||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.4853 | 1.62972 | 0.814861 | − | 0.579657i | \(-0.196813\pi\) | ||||
0.814861 | + | 0.579657i | \(0.196813\pi\) | |||||||
\(80\) | −3.00000 | −0.335410 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 14.4853 | 1.59963 | ||||||||
\(83\) | −12.8284 | −1.40810 | −0.704051 | − | 0.710149i | \(-0.748628\pi\) | ||||
−0.704051 | + | 0.710149i | \(0.748628\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.82843 | −0.306786 | ||||||||
\(86\) | −14.4853 | −1.56199 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 21.3137 | 2.27205 | ||||||||
\(89\) | −3.65685 | −0.387626 | −0.193813 | − | 0.981039i | \(-0.562085\pi\) | ||||
−0.193813 | + | 0.981039i | \(0.562085\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.65685 | −0.173686 | ||||||||
\(92\) | 33.7990 | 3.52379 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.828427 | 0.0854457 | ||||||||
\(95\) | −0.828427 | −0.0849948 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.48528 | 0.455411 | 0.227706 | − | 0.973730i | \(-0.426878\pi\) | ||||
0.227706 | + | 0.973730i | \(0.426878\pi\) | |||||||
\(98\) | −15.2426 | −1.53974 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.82843 | 0.382843 | ||||||||
\(101\) | −4.34315 | −0.432159 | −0.216080 | − | 0.976376i | \(-0.569327\pi\) | ||||
−0.216080 | + | 0.976376i | \(0.569327\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.1421 | −1.19640 | −0.598200 | − | 0.801347i | \(-0.704117\pi\) | ||||
−0.598200 | + | 0.801347i | \(0.704117\pi\) | |||||||
\(104\) | −8.82843 | −0.865699 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −18.4853 | −1.79545 | ||||||||
\(107\) | 8.14214 | 0.787130 | 0.393565 | − | 0.919297i | \(-0.371242\pi\) | ||||
0.393565 | + | 0.919297i | \(0.371242\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | −11.6569 | −1.11144 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.48528 | 0.234837 | ||||||||
\(113\) | −2.82843 | −0.266076 | −0.133038 | − | 0.991111i | \(-0.542473\pi\) | ||||
−0.133038 | + | 0.991111i | \(0.542473\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.82843 | −0.823255 | ||||||||
\(116\) | −3.82843 | −0.355461 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.34315 | 0.214796 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.3137 | 1.11943 | ||||||||
\(122\) | 18.4853 | 1.67358 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −40.1421 | −3.60487 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.00000 | 0.532414 | 0.266207 | − | 0.963916i | \(-0.414230\pi\) | ||||
0.266207 | + | 0.963916i | \(0.414230\pi\) | |||||||
\(128\) | −20.5563 | −1.81694 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.82843 | 0.423481 | ||||||||
\(131\) | −16.1421 | −1.41034 | −0.705172 | − | 0.709036i | \(-0.749130\pi\) | ||||
−0.705172 | + | 0.709036i | \(0.749130\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.686292 | 0.0595090 | ||||||||
\(134\) | −25.3137 | −2.18677 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.4853 | 1.07060 | ||||||||
\(137\) | 10.8284 | 0.925135 | 0.462567 | − | 0.886584i | \(-0.346928\pi\) | ||||
0.462567 | + | 0.886584i | \(0.346928\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 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 | 0 | ||||||||
\(142\) | −17.6569 | −1.48173 | ||||||||
\(143\) | −9.65685 | −0.807547 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.00000 | 0.0830455 | ||||||||
\(146\) | −20.4853 | −1.69537 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 32.4853 | 2.67027 | ||||||||
\(149\) | 13.3137 | 1.09070 | 0.545351 | − | 0.838208i | \(-0.316396\pi\) | ||||
0.545351 | + | 0.838208i | \(0.316396\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 3.65685 | 0.296610 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 9.65685 | 0.778171 | ||||||||
\(155\) | 10.4853 | 0.842198 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.4853 | −1.31567 | −0.657834 | − | 0.753163i | \(-0.728527\pi\) | ||||
−0.657834 | + | 0.753163i | \(0.728527\pi\) | |||||||
\(158\) | 34.9706 | 2.78211 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.58579 | 0.125367 | ||||||||
\(161\) | 7.31371 | 0.576401 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.6569 | −1.53964 | −0.769822 | − | 0.638259i | \(-0.779655\pi\) | ||||
−0.769822 | + | 0.638259i | \(0.779655\pi\) | |||||||
\(164\) | 22.9706 | 1.79370 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −30.9706 | −2.40378 | ||||||||
\(167\) | −14.4853 | −1.12090 | −0.560452 | − | 0.828187i | \(-0.689373\pi\) | ||||
−0.560452 | + | 0.828187i | \(0.689373\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −6.82843 | −0.523716 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −22.9706 | −1.75149 | ||||||||
\(173\) | 5.31371 | 0.403994 | 0.201997 | − | 0.979386i | \(-0.435257\pi\) | ||||
0.201997 | + | 0.979386i | \(0.435257\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 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 | \(-0.491835\pi\) | ||||
0.0256479 | + | 0.999671i | \(0.491835\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | −4.00000 | −0.296500 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 38.9706 | 2.87295 | ||||||||
\(185\) | −8.48528 | −0.623850 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.6569 | 0.998688 | ||||||||
\(188\) | 1.31371 | 0.0958120 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.00000 | −0.145095 | ||||||||
\(191\) | 15.1716 | 1.09778 | 0.548888 | − | 0.835896i | \(-0.315051\pi\) | ||||
0.548888 | + | 0.835896i | \(0.315051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.4853 | −0.898710 | −0.449355 | − | 0.893353i | \(-0.648346\pi\) | ||||
−0.449355 | + | 0.893353i | \(0.648346\pi\) | |||||||
\(194\) | 10.8284 | 0.777436 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24.1716 | −1.72654 | ||||||||
\(197\) | 8.34315 | 0.594425 | 0.297212 | − | 0.954811i | \(-0.403943\pi\) | ||||
0.297212 | + | 0.954811i | \(0.403943\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.0000 | 0.850657 | 0.425329 | − | 0.905039i | \(-0.360158\pi\) | ||||
0.425329 | + | 0.905039i | \(0.360158\pi\) | |||||||
\(200\) | 4.41421 | 0.312132 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.4853 | −0.737742 | ||||||||
\(203\) | −0.828427 | −0.0581442 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | −0.419058 | ||||||||
\(206\) | −29.3137 | −2.04238 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.00000 | −0.416025 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.82843 | 0.332403 | 0.166201 | − | 0.986092i | \(-0.446850\pi\) | ||||
0.166201 | + | 0.986092i | \(0.446850\pi\) | |||||||
\(212\) | −29.3137 | −2.01327 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 19.6569 | 1.34371 | ||||||||
\(215\) | 6.00000 | 0.409197 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.68629 | −0.589664 | ||||||||
\(218\) | 4.82843 | 0.327022 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −18.4853 | −1.24628 | ||||||||
\(221\) | −5.65685 | −0.380521 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.7990 | 1.45977 | 0.729884 | − | 0.683571i | \(-0.239574\pi\) | ||||
0.729884 | + | 0.683571i | \(0.239574\pi\) | |||||||
\(224\) | −1.31371 | −0.0877758 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.82843 | −0.454220 | ||||||||
\(227\) | 8.14214 | 0.540413 | 0.270206 | − | 0.962802i | \(-0.412908\pi\) | ||||
0.270206 | + | 0.962802i | \(0.412908\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.00000 | −0.132164 | −0.0660819 | − | 0.997814i | \(-0.521050\pi\) | ||||
−0.0660819 | + | 0.997814i | \(0.521050\pi\) | |||||||
\(230\) | −21.3137 | −1.40538 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.41421 | −0.289807 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.343146 | −0.0223844 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.65685 | 0.366679 | ||||||||
\(239\) | 23.3137 | 1.50804 | 0.754019 | − | 0.656852i | \(-0.228113\pi\) | ||||
0.754019 | + | 0.656852i | \(0.228113\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | 29.7279 | 1.91098 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 29.3137 | 1.87662 | ||||||||
\(245\) | 6.31371 | 0.403368 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.65685 | −0.105423 | ||||||||
\(248\) | −46.2843 | −2.93905 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.41421 | −0.152688 | ||||||||
\(251\) | −3.17157 | −0.200188 | −0.100094 | − | 0.994978i | \(-0.531914\pi\) | ||||
−0.100094 | + | 0.994978i | \(0.531914\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 42.6274 | 2.67996 | ||||||||
\(254\) | 14.4853 | 0.908887 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | −29.3137 | −1.82854 | −0.914269 | − | 0.405107i | \(-0.867234\pi\) | ||||
−0.914269 | + | 0.405107i | \(0.867234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.02944 | 0.436788 | ||||||||
\(260\) | 7.65685 | 0.474858 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −38.9706 | −2.40761 | ||||||||
\(263\) | 8.34315 | 0.514460 | 0.257230 | − | 0.966350i | \(-0.417190\pi\) | ||||
0.257230 | + | 0.966350i | \(0.417190\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.65685 | 0.470357 | ||||||||
\(266\) | 1.65685 | 0.101588 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −40.1421 | −2.45207 | ||||||||
\(269\) | −1.31371 | −0.0800982 | −0.0400491 | − | 0.999198i | \(-0.512751\pi\) | ||||
−0.0400491 | + | 0.999198i | \(0.512751\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.7990 | 1.81016 | 0.905080 | − | 0.425242i | \(-0.139811\pi\) | ||||
0.905080 | + | 0.425242i | \(0.139811\pi\) | |||||||
\(272\) | 8.48528 | 0.514496 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 26.1421 | 1.57930 | ||||||||
\(275\) | 4.82843 | 0.291165 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.65685 | 0.460056 | 0.230028 | − | 0.973184i | \(-0.426118\pi\) | ||||
0.230028 | + | 0.973184i | \(0.426118\pi\) | |||||||
\(278\) | 24.9706 | 1.49763 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.65685 | −0.218539 | ||||||||
\(281\) | 6.68629 | 0.398871 | 0.199435 | − | 0.979911i | \(-0.436089\pi\) | ||||
0.199435 | + | 0.979911i | \(0.436089\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.828427 | −0.0492449 | −0.0246224 | − | 0.999697i | \(-0.507838\pi\) | ||||
−0.0246224 | + | 0.999697i | \(0.507838\pi\) | |||||||
\(284\) | −28.0000 | −1.66149 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −23.3137 | −1.37857 | ||||||||
\(287\) | 4.97056 | 0.293403 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.00000 | −0.529412 | ||||||||
\(290\) | 2.41421 | 0.141768 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −32.4853 | −1.90106 | ||||||||
\(293\) | 8.48528 | 0.495715 | 0.247858 | − | 0.968796i | \(-0.420273\pi\) | ||||
0.247858 | + | 0.968796i | \(0.420273\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 37.4558 | 2.17708 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 32.1421 | 1.86194 | ||||||||
\(299\) | −17.6569 | −1.02112 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.97056 | −0.286498 | ||||||||
\(302\) | −28.9706 | −1.66707 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.48528 | 0.142541 | ||||||||
\(305\) | −7.65685 | −0.438430 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.9706 | 0.626123 | 0.313062 | − | 0.949733i | \(-0.398645\pi\) | ||||
0.313062 | + | 0.949733i | \(0.398645\pi\) | |||||||
\(308\) | 15.3137 | 0.872580 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 25.3137 | 1.43772 | ||||||||
\(311\) | 2.48528 | 0.140927 | 0.0704637 | − | 0.997514i | \(-0.477552\pi\) | ||||
0.0704637 | + | 0.997514i | \(0.477552\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −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 | 0 | ||||||||
\(316\) | 55.4558 | 3.11963 | ||||||||
\(317\) | 2.82843 | 0.158860 | 0.0794301 | − | 0.996840i | \(-0.474690\pi\) | ||||
0.0794301 | + | 0.996840i | \(0.474690\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.82843 | −0.270340 | ||||||||
\(320\) | 9.82843 | 0.549426 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 17.6569 | 0.983978 | ||||||||
\(323\) | 2.34315 | 0.130376 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.00000 | −0.110940 | ||||||||
\(326\) | −47.4558 | −2.62834 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 26.4853 | 1.46241 | ||||||||
\(329\) | 0.284271 | 0.0156724 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.7990 | −0.978321 | −0.489160 | − | 0.872194i | \(-0.662697\pi\) | ||||
−0.489160 | + | 0.872194i | \(0.662697\pi\) | |||||||
\(332\) | −49.1127 | −2.69541 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −34.9706 | −1.91350 | ||||||||
\(335\) | 10.4853 | 0.572872 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.82843 | −0.371968 | −0.185984 | − | 0.982553i | \(-0.559547\pi\) | ||||
−0.185984 | + | 0.982553i | \(0.559547\pi\) | |||||||
\(338\) | −21.7279 | −1.18184 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10.8284 | −0.587254 | ||||||||
\(341\) | −50.6274 | −2.74163 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.0294 | −0.595534 | ||||||||
\(344\) | −26.4853 | −1.42799 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.8284 | 0.689661 | ||||||||
\(347\) | −20.1421 | −1.08129 | −0.540643 | − | 0.841252i | \(-0.681819\pi\) | ||||
−0.540643 | + | 0.841252i | \(0.681819\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.6274 | −1.31828 | −0.659138 | − | 0.752022i | \(-0.729079\pi\) | ||||
−0.659138 | + | 0.752022i | \(0.729079\pi\) | |||||||
\(350\) | 2.00000 | 0.106904 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.65685 | −0.408112 | ||||||||
\(353\) | 15.6569 | 0.833330 | 0.416665 | − | 0.909060i | \(-0.363199\pi\) | ||||
0.416665 | + | 0.909060i | \(0.363199\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.31371 | 0.388171 | ||||||||
\(356\) | −14.0000 | −0.741999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.65685 | 0.0875675 | ||||||||
\(359\) | 32.1421 | 1.69640 | 0.848199 | − | 0.529678i | \(-0.177687\pi\) | ||||
0.848199 | + | 0.529678i | \(0.177687\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3137 | −0.963879 | ||||||||
\(362\) | −14.4853 | −0.761329 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.34315 | −0.332471 | ||||||||
\(365\) | 8.48528 | 0.444140 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.0000 | 0.939592 | 0.469796 | − | 0.882775i | \(-0.344327\pi\) | ||||
0.469796 | + | 0.882775i | \(0.344327\pi\) | |||||||
\(368\) | 26.4853 | 1.38064 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −20.4853 | −1.06498 | ||||||||
\(371\) | −6.34315 | −0.329320 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.9706 | 1.39648 | 0.698241 | − | 0.715862i | \(-0.253966\pi\) | ||||
0.698241 | + | 0.715862i | \(0.253966\pi\) | |||||||
\(374\) | 32.9706 | 1.70487 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.51472 | 0.0781156 | ||||||||
\(377\) | 2.00000 | 0.103005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.51472 | 0.283272 | 0.141636 | − | 0.989919i | \(-0.454764\pi\) | ||||
0.141636 | + | 0.989919i | \(0.454764\pi\) | |||||||
\(380\) | −3.17157 | −0.162698 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 36.6274 | 1.87402 | ||||||||
\(383\) | 14.4853 | 0.740163 | 0.370082 | − | 0.928999i | \(-0.379330\pi\) | ||||
0.370082 | + | 0.928999i | \(0.379330\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.00000 | −0.203859 | ||||||||
\(386\) | −30.1421 | −1.53419 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.1716 | 0.871755 | ||||||||
\(389\) | 6.68629 | 0.339008 | 0.169504 | − | 0.985529i | \(-0.445783\pi\) | ||||
0.169504 | + | 0.985529i | \(0.445783\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.9706 | 1.26282 | ||||||||
\(392\) | −27.8701 | −1.40765 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 20.1421 | 1.01475 | ||||||||
\(395\) | −14.4853 | −0.728834 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.34315 | −0.418730 | −0.209365 | − | 0.977838i | \(-0.567140\pi\) | ||||
−0.209365 | + | 0.977838i | \(0.567140\pi\) | |||||||
\(398\) | 28.9706 | 1.45216 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | 29.3137 | 1.46386 | 0.731928 | − | 0.681382i | \(-0.238621\pi\) | ||||
0.731928 | + | 0.681382i | \(0.238621\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.9706 | 1.04462 | ||||||||
\(404\) | −16.6274 | −0.827245 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.00000 | −0.0992583 | ||||||||
\(407\) | 40.9706 | 2.03084 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.9706 | 1.53140 | 0.765698 | − | 0.643200i | \(-0.222394\pi\) | ||||
0.765698 | + | 0.643200i | \(0.222394\pi\) | |||||||
\(410\) | −14.4853 | −0.715377 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −46.4853 | −2.29017 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.8284 | 0.629723 | ||||||||
\(416\) | 3.17157 | 0.155499 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.65685 | 0.472332 | ||||||||
\(419\) | 4.97056 | 0.242828 | 0.121414 | − | 0.992602i | \(-0.461257\pi\) | ||||
0.121414 | + | 0.992602i | \(0.461257\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −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 | 0 | ||||||||
\(424\) | −33.7990 | −1.64142 | ||||||||
\(425\) | 2.82843 | 0.137199 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.34315 | 0.306966 | ||||||||
\(428\) | 31.1716 | 1.50673 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.4853 | 0.698542 | ||||||||
\(431\) | 19.3137 | 0.930309 | 0.465154 | − | 0.885230i | \(-0.345999\pi\) | ||||
0.465154 | + | 0.885230i | \(0.345999\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.8284 | −1.67375 | −0.836874 | − | 0.547396i | \(-0.815619\pi\) | ||||
−0.836874 | + | 0.547396i | \(0.815619\pi\) | |||||||
\(434\) | −20.9706 | −1.00662 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.65685 | 0.366697 | ||||||||
\(437\) | 7.31371 | 0.349862 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.6569 | −1.03363 | −0.516813 | − | 0.856099i | \(-0.672882\pi\) | ||||
−0.516813 | + | 0.856099i | \(0.672882\pi\) | |||||||
\(440\) | −21.3137 | −1.01609 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.6569 | −0.649590 | ||||||||
\(443\) | −3.65685 | −0.173742 | −0.0868712 | − | 0.996220i | \(-0.527687\pi\) | ||||
−0.0868712 | + | 0.996220i | \(0.527687\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.65685 | 0.173352 | ||||||||
\(446\) | 52.6274 | 2.49198 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.14214 | −0.384680 | ||||||||
\(449\) | −0.343146 | −0.0161940 | −0.00809702 | − | 0.999967i | \(-0.502577\pi\) | ||||
−0.00809702 | + | 0.999967i | \(0.502577\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.9706 | 1.36417 | ||||||||
\(452\) | −10.8284 | −0.509326 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 19.6569 | 0.922542 | ||||||||
\(455\) | 1.65685 | 0.0776745 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.34315 | 0.390276 | 0.195138 | − | 0.980776i | \(-0.437485\pi\) | ||||
0.195138 | + | 0.980776i | \(0.437485\pi\) | |||||||
\(458\) | −4.82843 | −0.225618 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −33.7990 | −1.57589 | ||||||||
\(461\) | 24.3431 | 1.13377 | 0.566887 | − | 0.823796i | \(-0.308148\pi\) | ||||
0.566887 | + | 0.823796i | \(0.308148\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.7990 | −0.827189 | −0.413595 | − | 0.910461i | \(-0.635727\pi\) | ||||
−0.413595 | + | 0.910461i | \(0.635727\pi\) | |||||||
\(464\) | −3.00000 | −0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −43.4558 | −2.01305 | ||||||||
\(467\) | 22.9706 | 1.06295 | 0.531475 | − | 0.847074i | \(-0.321638\pi\) | ||||
0.531475 | + | 0.847074i | \(0.321638\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.68629 | −0.401096 | ||||||||
\(470\) | −0.828427 | −0.0382125 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −28.9706 | −1.33207 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.828427 | 0.0380108 | ||||||||
\(476\) | 8.97056 | 0.411165 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 56.2843 | 2.57438 | ||||||||
\(479\) | −12.8284 | −0.586146 | −0.293073 | − | 0.956090i | \(-0.594678\pi\) | ||||
−0.293073 | + | 0.956090i | \(0.594678\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.9706 | −0.773791 | ||||||||
\(482\) | 24.1421 | 1.09964 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 47.1421 | 2.14282 | ||||||||
\(485\) | −4.48528 | −0.203666 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.7990 | −1.35032 | −0.675161 | − | 0.737671i | \(-0.735926\pi\) | ||||
−0.675161 | + | 0.737671i | \(0.735926\pi\) | |||||||
\(488\) | 33.7990 | 1.53001 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 15.2426 | 0.688592 | ||||||||
\(491\) | −43.4558 | −1.96113 | −0.980567 | − | 0.196183i | \(-0.937145\pi\) | ||||
−0.980567 | + | 0.196183i | \(0.937145\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.82843 | −0.127386 | ||||||||
\(494\) | −4.00000 | −0.179969 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −31.4558 | −1.41241 | ||||||||
\(497\) | −6.05887 | −0.271778 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.0000 | 1.61158 | 0.805791 | − | 0.592200i | \(-0.201741\pi\) | ||||
0.805791 | + | 0.592200i | \(0.201741\pi\) | |||||||
\(500\) | −3.82843 | −0.171212 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.65685 | −0.341742 | ||||||||
\(503\) | 30.0000 | 1.33763 | 0.668817 | − | 0.743427i | \(-0.266801\pi\) | ||||
0.668817 | + | 0.743427i | \(0.266801\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.34315 | 0.193267 | ||||||||
\(506\) | 102.912 | 4.57498 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 22.9706 | 1.01915 | ||||||||
\(509\) | 44.6274 | 1.97808 | 0.989038 | − | 0.147663i | \(-0.0471751\pi\) | ||||
0.989038 | + | 0.147663i | \(0.0471751\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.02944 | −0.310964 | ||||||||
\(512\) | −31.2426 | −1.38074 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −70.7696 | −3.12151 | ||||||||
\(515\) | 12.1421 | 0.535046 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.65685 | 0.0728684 | ||||||||
\(518\) | 16.9706 | 0.745644 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.82843 | 0.387152 | ||||||||
\(521\) | −1.31371 | −0.0575546 | −0.0287773 | − | 0.999586i | \(-0.509161\pi\) | ||||
−0.0287773 | + | 0.999586i | \(0.509161\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.4853 | −0.633397 | −0.316699 | − | 0.948526i | \(-0.602574\pi\) | ||||
−0.316699 | + | 0.948526i | \(0.602574\pi\) | |||||||
\(524\) | −61.7990 | −2.69970 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.1421 | 0.878239 | ||||||||
\(527\) | −29.6569 | −1.29187 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 54.9411 | 2.38874 | ||||||||
\(530\) | 18.4853 | 0.802949 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.62742 | 0.113913 | ||||||||
\(533\) | −12.0000 | −0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.14214 | −0.352015 | ||||||||
\(536\) | −46.2843 | −1.99918 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.17157 | −0.136736 | ||||||||
\(539\) | −30.4853 | −1.31309 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.9706 | −1.67548 | −0.837738 | − | 0.546073i | \(-0.816122\pi\) | ||||
−0.837738 | + | 0.546073i | \(0.816122\pi\) | |||||||
\(542\) | 71.9411 | 3.09014 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.48528 | −0.192305 | ||||||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.4853 | 0.619346 | 0.309673 | − | 0.950843i | \(-0.399780\pi\) | ||||
0.309673 | + | 0.950843i | \(0.399780\pi\) | |||||||
\(548\) | 41.4558 | 1.77091 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.6569 | 0.497050 | ||||||||
\(551\) | −0.828427 | −0.0352922 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.0000 | 0.510292 | ||||||||
\(554\) | 18.4853 | 0.785364 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 39.5980 | 1.67933 | ||||||||
\(557\) | −39.9411 | −1.69236 | −0.846180 | − | 0.532897i | \(-0.821103\pi\) | ||||
−0.846180 | + | 0.532897i | \(0.821103\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.0000 | 0.507546 | ||||||||
\(560\) | −2.48528 | −0.105022 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.1421 | 0.680915 | ||||||||
\(563\) | 3.65685 | 0.154118 | 0.0770590 | − | 0.997027i | \(-0.475447\pi\) | ||||
0.0770590 | + | 0.997027i | \(0.475447\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.82843 | 0.118993 | ||||||||
\(566\) | −2.00000 | −0.0840663 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −32.2843 | −1.35462 | ||||||||
\(569\) | −16.3431 | −0.685140 | −0.342570 | − | 0.939492i | \(-0.611297\pi\) | ||||
−0.342570 | + | 0.939492i | \(0.611297\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.0000 | 1.17176 | 0.585882 | − | 0.810397i | \(-0.300748\pi\) | ||||
0.585882 | + | 0.810397i | \(0.300748\pi\) | |||||||
\(572\) | −36.9706 | −1.54582 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.0000 | 0.500870 | ||||||||
\(575\) | 8.82843 | 0.368171 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.7990 | −0.657721 | −0.328860 | − | 0.944379i | \(-0.606665\pi\) | ||||
−0.328860 | + | 0.944379i | \(0.606665\pi\) | |||||||
\(578\) | −21.7279 | −0.903762 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.82843 | 0.158967 | ||||||||
\(581\) | −10.6274 | −0.440900 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −36.9706 | −1.53116 | ||||||||
\(584\) | −37.4558 | −1.54993 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.4853 | 0.846239 | ||||||||
\(587\) | −9.79899 | −0.404448 | −0.202224 | − | 0.979339i | \(-0.564817\pi\) | ||||
−0.202224 | + | 0.979339i | \(0.564817\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.68629 | −0.357912 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 25.4558 | 1.04623 | ||||||||
\(593\) | −3.65685 | −0.150169 | −0.0750845 | − | 0.997177i | \(-0.523923\pi\) | ||||
−0.0750845 | + | 0.997177i | \(0.523923\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.34315 | −0.0960596 | ||||||||
\(596\) | 50.9706 | 2.08784 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −42.6274 | −1.74316 | ||||||||
\(599\) | −1.79899 | −0.0735047 | −0.0367524 | − | 0.999324i | \(-0.511701\pi\) | ||||
−0.0367524 | + | 0.999324i | \(0.511701\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.00000 | 0.0815817 | 0.0407909 | − | 0.999168i | \(-0.487012\pi\) | ||||
0.0407909 | + | 0.999168i | \(0.487012\pi\) | |||||||
\(602\) | −12.0000 | −0.489083 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −45.9411 | −1.86932 | ||||||||
\(605\) | −12.3137 | −0.500623 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.9706 | 1.74412 | 0.872061 | − | 0.489398i | \(-0.162783\pi\) | ||||
0.872061 | + | 0.489398i | \(0.162783\pi\) | |||||||
\(608\) | −1.31371 | −0.0532779 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18.4853 | −0.748447 | ||||||||
\(611\) | −0.686292 | −0.0277644 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.00000 | −0.0807792 | −0.0403896 | − | 0.999184i | \(-0.512860\pi\) | ||||
−0.0403896 | + | 0.999184i | \(0.512860\pi\) | |||||||
\(614\) | 26.4853 | 1.06886 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 17.6569 | 0.711415 | ||||||||
\(617\) | 14.8284 | 0.596970 | 0.298485 | − | 0.954414i | \(-0.403519\pi\) | ||||
0.298485 | + | 0.954414i | \(0.403519\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.7990 | 1.19772 | 0.598861 | − | 0.800853i | \(-0.295620\pi\) | ||||
0.598861 | + | 0.800853i | \(0.295620\pi\) | |||||||
\(620\) | 40.1421 | 1.61215 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.00000 | 0.240578 | ||||||||
\(623\) | −3.02944 | −0.121372 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −14.4853 | −0.578948 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −63.1127 | −2.51847 | ||||||||
\(629\) | 24.0000 | 0.956943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.02944 | 0.120600 | 0.0603000 | − | 0.998180i | \(-0.480794\pi\) | ||||
0.0603000 | + | 0.998180i | \(0.480794\pi\) | |||||||
\(632\) | 63.9411 | 2.54344 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.82843 | 0.271191 | ||||||||
\(635\) | −6.00000 | −0.238103 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.6274 | 0.500316 | ||||||||
\(638\) | −11.6569 | −0.461499 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 20.5563 | 0.812561 | ||||||||
\(641\) | 44.6274 | 1.76268 | 0.881338 | − | 0.472485i | \(-0.156643\pi\) | ||||
0.881338 | + | 0.472485i | \(0.156643\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.4558 | −1.24050 | −0.620249 | − | 0.784405i | \(-0.712968\pi\) | ||||
−0.620249 | + | 0.784405i | \(0.712968\pi\) | |||||||
\(644\) | 28.0000 | 1.10335 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.65685 | 0.222566 | ||||||||
\(647\) | −21.1127 | −0.830026 | −0.415013 | − | 0.909816i | \(-0.636223\pi\) | ||||
−0.415013 | + | 0.909816i | \(0.636223\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.82843 | −0.189386 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −75.2548 | −2.94721 | ||||||||
\(653\) | 22.8284 | 0.893345 | 0.446673 | − | 0.894697i | \(-0.352609\pi\) | ||||
0.446673 | + | 0.894697i | \(0.352609\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.1421 | 0.630725 | ||||||||
\(656\) | 18.0000 | 0.702782 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.686292 | 0.0267544 | ||||||||
\(659\) | 37.7990 | 1.47244 | 0.736220 | − | 0.676743i | \(-0.236609\pi\) | ||||
0.736220 | + | 0.676743i | \(0.236609\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.0000 | 1.01128 | 0.505641 | − | 0.862744i | \(-0.331256\pi\) | ||||
0.505641 | + | 0.862744i | \(0.331256\pi\) | |||||||
\(662\) | −42.9706 | −1.67010 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −56.6274 | −2.19757 | ||||||||
\(665\) | −0.686292 | −0.0266132 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.82843 | −0.341838 | ||||||||
\(668\) | −55.4558 | −2.14565 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 25.3137 | 0.977954 | ||||||||
\(671\) | 36.9706 | 1.42723 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.9706 | −0.422884 | −0.211442 | − | 0.977391i | \(-0.567816\pi\) | ||||
−0.211442 | + | 0.977391i | \(0.567816\pi\) | |||||||
\(674\) | −16.4853 | −0.634989 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −34.4558 | −1.32522 | ||||||||
\(677\) | −36.7696 | −1.41317 | −0.706584 | − | 0.707629i | \(-0.749765\pi\) | ||||
−0.706584 | + | 0.707629i | \(0.749765\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.71573 | 0.142597 | ||||||||
\(680\) | −12.4853 | −0.478789 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −122.225 | −4.68025 | ||||||||
\(683\) | −40.1421 | −1.53600 | −0.767998 | − | 0.640452i | \(-0.778747\pi\) | ||||
−0.767998 | + | 0.640452i | \(0.778747\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.8284 | −0.413733 | ||||||||
\(686\) | −26.6274 | −1.01664 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18.0000 | −0.686244 | ||||||||
\(689\) | 15.3137 | 0.583406 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.0294 | −0.419580 | −0.209790 | − | 0.977747i | \(-0.567278\pi\) | ||||
−0.209790 | + | 0.977747i | \(0.567278\pi\) | |||||||
\(692\) | 20.3431 | 0.773330 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −48.6274 | −1.84587 | ||||||||
\(695\) | −10.3431 | −0.392338 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.9706 | 0.642806 | ||||||||
\(698\) | −59.4558 | −2.25044 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.17157 | 0.119874 | ||||||||
\(701\) | −29.3137 | −1.10716 | −0.553582 | − | 0.832795i | \(-0.686739\pi\) | ||||
−0.553582 | + | 0.832795i | \(0.686739\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.02944 | 0.265120 | ||||||||
\(704\) | −47.4558 | −1.78856 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −16.1421 | −0.604952 | ||||||||
\(713\) | −92.5685 | −3.46672 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.65685 | 0.361146 | ||||||||
\(716\) | 2.62742 | 0.0981912 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 77.5980 | 2.89593 | ||||||||
\(719\) | −10.6274 | −0.396336 | −0.198168 | − | 0.980168i | \(-0.563499\pi\) | ||||
−0.198168 | + | 0.980168i | \(0.563499\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.0589 | −0.374612 | ||||||||
\(722\) | −44.2132 | −1.64545 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −22.9706 | −0.853694 | ||||||||
\(725\) | −1.00000 | −0.0371391 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 43.9411 | 1.62969 | 0.814843 | − | 0.579682i | \(-0.196823\pi\) | ||||
0.814843 | + | 0.579682i | \(0.196823\pi\) | |||||||
\(728\) | −7.31371 | −0.271064 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 20.4853 | 0.758194 | ||||||||
\(731\) | −16.9706 | −0.627679 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.1716 | −0.634247 | −0.317123 | − | 0.948384i | \(-0.602717\pi\) | ||||
−0.317123 | + | 0.948384i | \(0.602717\pi\) | |||||||
\(734\) | 43.4558 | 1.60398 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.0000 | −0.516047 | ||||||||
\(737\) | −50.6274 | −1.86488 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.48528 | −0.0914226 | −0.0457113 | − | 0.998955i | \(-0.514555\pi\) | ||||
−0.0457113 | + | 0.998955i | \(0.514555\pi\) | |||||||
\(740\) | −32.4853 | −1.19418 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.3137 | −0.562184 | ||||||||
\(743\) | 7.37258 | 0.270474 | 0.135237 | − | 0.990813i | \(-0.456820\pi\) | ||||
0.135237 | + | 0.990813i | \(0.456820\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.3137 | −0.487777 | ||||||||
\(746\) | 65.1127 | 2.38395 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 52.2843 | 1.91170 | ||||||||
\(749\) | 6.74517 | 0.246463 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.1421 | −0.443073 | −0.221536 | − | 0.975152i | \(-0.571107\pi\) | ||||
−0.221536 | + | 0.975152i | \(0.571107\pi\) | |||||||
\(752\) | 1.02944 | 0.0375397 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.82843 | 0.175841 | ||||||||
\(755\) | 12.0000 | 0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.4853 | 1.32608 | 0.663040 | − | 0.748584i | \(-0.269266\pi\) | ||||
0.663040 | + | 0.748584i | \(0.269266\pi\) | |||||||
\(758\) | 13.3137 | 0.483576 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.65685 | −0.132648 | ||||||||
\(761\) | 36.6274 | 1.32774 | 0.663871 | − | 0.747847i | \(-0.268912\pi\) | ||||
0.663871 | + | 0.747847i | \(0.268912\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.65685 | 0.0599822 | ||||||||
\(764\) | 58.0833 | 2.10138 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34.9706 | 1.26354 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.34315 | −0.156618 | −0.0783089 | − | 0.996929i | \(-0.524952\pi\) | ||||
−0.0783089 | + | 0.996929i | \(0.524952\pi\) | |||||||
\(770\) | −9.65685 | −0.348009 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −47.7990 | −1.72032 | ||||||||
\(773\) | −8.48528 | −0.305194 | −0.152597 | − | 0.988288i | \(-0.548764\pi\) | ||||
−0.152597 | + | 0.988288i | \(0.548764\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.4853 | −0.376642 | ||||||||
\(776\) | 19.7990 | 0.710742 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.1421 | 0.578724 | ||||||||
\(779\) | 4.97056 | 0.178089 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35.3137 | −1.26362 | ||||||||
\(782\) | 60.2843 | 2.15576 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −18.9411 | −0.676469 | ||||||||
\(785\) | 16.4853 | 0.588385 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.7990 | −0.777050 | −0.388525 | − | 0.921438i | \(-0.627015\pi\) | ||||
−0.388525 | + | 0.921438i | \(0.627015\pi\) | |||||||
\(788\) | 31.9411 | 1.13786 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −34.9706 | −1.24420 | ||||||||
\(791\) | −2.34315 | −0.0833127 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.3137 | −0.543806 | ||||||||
\(794\) | −20.1421 | −0.714818 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 45.9411 | 1.62834 | ||||||||
\(797\) | 34.1421 | 1.20938 | 0.604688 | − | 0.796462i | \(-0.293298\pi\) | ||||
0.604688 | + | 0.796462i | \(0.293298\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.970563 | 0.0343360 | ||||||||
\(800\) | −1.58579 | −0.0560660 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 70.7696 | 2.49896 | ||||||||
\(803\) | −40.9706 | −1.44582 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.31371 | −0.257774 | ||||||||
\(806\) | 50.6274 | 1.78327 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −19.1716 | −0.674454 | ||||||||
\(809\) | 14.2843 | 0.502208 | 0.251104 | − | 0.967960i | \(-0.419206\pi\) | ||||
0.251104 | + | 0.967960i | \(0.419206\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.3431 | 0.925033 | 0.462516 | − | 0.886611i | \(-0.346947\pi\) | ||||
0.462516 | + | 0.886611i | \(0.346947\pi\) | |||||||
\(812\) | −3.17157 | −0.111300 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 98.9117 | 3.46685 | ||||||||
\(815\) | 19.6569 | 0.688550 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.97056 | −0.173898 | ||||||||
\(818\) | 74.7696 | 2.61426 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22.9706 | −0.802167 | ||||||||
\(821\) | 45.3137 | 1.58146 | 0.790730 | − | 0.612165i | \(-0.209701\pi\) | ||||
0.790730 | + | 0.612165i | \(0.209701\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.97056 | 0.103547 | 0.0517737 | − | 0.998659i | \(-0.483513\pi\) | ||||
0.0517737 | + | 0.998659i | \(0.483513\pi\) | |||||||
\(824\) | −53.5980 | −1.86717 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.31371 | 0.184776 | 0.0923879 | − | 0.995723i | \(-0.470550\pi\) | ||||
0.0923879 | + | 0.995723i | \(0.470550\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.6274 | −0.855346 | −0.427673 | − | 0.903934i | \(-0.640666\pi\) | ||||
−0.427673 | + | 0.903934i | \(0.640666\pi\) | |||||||
\(830\) | 30.9706 | 1.07500 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 19.6569 | 0.681479 | ||||||||
\(833\) | −17.8579 | −0.618738 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.4853 | 0.501284 | ||||||||
\(836\) | 15.3137 | 0.529636 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.0000 | 0.414533 | ||||||||
\(839\) | 14.4853 | 0.500087 | 0.250044 | − | 0.968235i | \(-0.419555\pi\) | ||||
0.250044 | + | 0.968235i | \(0.419555\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −36.1421 | −1.24554 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.4853 | 0.636290 | ||||||||
\(845\) | 9.00000 | 0.309609 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.2010 | 0.350511 | ||||||||
\(848\) | −22.9706 | −0.788812 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.82843 | 0.234213 | ||||||||
\(851\) | 74.9117 | 2.56794 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −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 | 0 | ||||||||
\(856\) | 35.9411 | 1.22844 | ||||||||
\(857\) | −48.6274 | −1.66108 | −0.830540 | − | 0.556958i | \(-0.811968\pi\) | ||||
−0.830540 | + | 0.556958i | \(0.811968\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.4264 | 0.969896 | 0.484948 | − | 0.874543i | \(-0.338838\pi\) | ||||
0.484948 | + | 0.874543i | \(0.338838\pi\) | |||||||
\(860\) | 22.9706 | 0.783290 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 46.6274 | 1.58814 | ||||||||
\(863\) | 7.85786 | 0.267485 | 0.133742 | − | 0.991016i | \(-0.457301\pi\) | ||||
0.133742 | + | 0.991016i | \(0.457301\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.31371 | −0.180672 | ||||||||
\(866\) | −84.0833 | −2.85727 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −33.2548 | −1.12874 | ||||||||
\(869\) | 69.9411 | 2.37259 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.9706 | 0.710560 | ||||||||
\(872\) | 8.82843 | 0.298968 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 17.6569 | 0.597252 | ||||||||
\(875\) | −0.828427 | −0.0280059 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.2843 | −0.617416 | −0.308708 | − | 0.951157i | \(-0.599897\pi\) | ||||
−0.308708 | + | 0.951157i | \(0.599897\pi\) | |||||||
\(878\) | −52.2843 | −1.76451 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −14.4853 | −0.488299 | ||||||||
\(881\) | −6.68629 | −0.225267 | −0.112633 | − | 0.993637i | \(-0.535929\pi\) | ||||
−0.112633 | + | 0.993637i | \(0.535929\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 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 | \(-0.336219\pi\) | ||||
0.492129 | + | 0.870522i | \(0.336219\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.97056 | 0.166707 | ||||||||
\(890\) | 8.82843 | 0.295930 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 83.4558 | 2.79431 | ||||||||
\(893\) | 0.284271 | 0.00951277 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.686292 | −0.0229402 | ||||||||
\(896\) | −17.0294 | −0.568914 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.828427 | −0.0276450 | ||||||||
\(899\) | 10.4853 | 0.349704 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.6569 | −0.721494 | ||||||||
\(902\) | 69.9411 | 2.32878 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.4853 | −0.415254 | ||||||||
\(905\) | 6.00000 | 0.199447 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.0000 | −0.332045 | −0.166022 | − | 0.986122i | \(-0.553092\pi\) | ||||
−0.166022 | + | 0.986122i | \(0.553092\pi\) | |||||||
\(908\) | 31.1716 | 1.03446 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.00000 | 0.132599 | ||||||||
\(911\) | −3.85786 | −0.127817 | −0.0639084 | − | 0.997956i | \(-0.520357\pi\) | ||||
−0.0639084 | + | 0.997956i | \(0.520357\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −61.9411 | −2.04995 | ||||||||
\(914\) | 20.1421 | 0.666243 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.65685 | −0.252990 | ||||||||
\(917\) | −13.3726 | −0.441602 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.0000 | −1.18753 | −0.593765 | − | 0.804638i | \(-0.702359\pi\) | ||||
−0.593765 | + | 0.804638i | \(0.702359\pi\) | |||||||
\(920\) | −38.9706 | −1.28482 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 58.7696 | 1.93547 | ||||||||
\(923\) | 14.6274 | 0.481467 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.48528 | 0.278994 | ||||||||
\(926\) | −42.9706 | −1.41210 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.58579 | 0.0520560 | ||||||||
\(929\) | −40.6274 | −1.33294 | −0.666471 | − | 0.745531i | \(-0.732196\pi\) | ||||
−0.666471 | + | 0.745531i | \(0.732196\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.23045 | −0.171421 | ||||||||
\(932\) | −68.9117 | −2.25728 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 55.4558 | 1.81457 | ||||||||
\(935\) | −13.6569 | −0.446627 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.34315 | 0.272559 | 0.136279 | − | 0.990670i | \(-0.456486\pi\) | ||||
0.136279 | + | 0.990670i | \(0.456486\pi\) | |||||||
\(938\) | −20.9706 | −0.684713 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.31371 | −0.0428484 | ||||||||
\(941\) | −39.9411 | −1.30204 | −0.651022 | − | 0.759059i | \(-0.725659\pi\) | ||||
−0.651022 | + | 0.759059i | \(0.725659\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52.9706 | 1.72496 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −69.9411 | −2.27398 | ||||||||
\(947\) | 56.9117 | 1.84938 | 0.924691 | − | 0.380719i | \(-0.124324\pi\) | ||||
0.924691 | + | 0.380719i | \(0.124324\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.9706 | 0.550888 | ||||||||
\(950\) | 2.00000 | 0.0648886 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.3431 | 0.335223 | ||||||||
\(953\) | −6.68629 | −0.216590 | −0.108295 | − | 0.994119i | \(-0.534539\pi\) | ||||
−0.108295 | + | 0.994119i | \(0.534539\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.1716 | −0.490941 | ||||||||
\(956\) | 89.2548 | 2.88671 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −30.9706 | −1.00061 | ||||||||
\(959\) | 8.97056 | 0.289675 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 78.9411 | 2.54649 | ||||||||
\(962\) | −40.9706 | −1.32094 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 38.2843 | 1.23305 | ||||||||
\(965\) | 12.4853 | 0.401915 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.9706 | −0.610052 | −0.305026 | − | 0.952344i | \(-0.598665\pi\) | ||||
−0.305026 | + | 0.952344i | \(0.598665\pi\) | |||||||
\(968\) | 54.3553 | 1.74705 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10.8284 | −0.347680 | ||||||||
\(971\) | 0.142136 | 0.00456135 | 0.00228067 | − | 0.999997i | \(-0.499274\pi\) | ||||
0.00228067 | + | 0.999997i | \(0.499274\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.56854 | 0.274695 | ||||||||
\(974\) | −71.9411 | −2.30514 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.9706 | 0.735270 | ||||||||
\(977\) | 25.3137 | 0.809857 | 0.404929 | − | 0.914348i | \(-0.367296\pi\) | ||||
0.404929 | + | 0.914348i | \(0.367296\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.6569 | −0.564316 | ||||||||
\(980\) | 24.1716 | 0.772133 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −104.912 | −3.34787 | ||||||||
\(983\) | −13.3137 | −0.424641 | −0.212321 | − | 0.977200i | \(-0.568102\pi\) | ||||
−0.212321 | + | 0.977200i | \(0.568102\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.34315 | −0.265835 | ||||||||
\(986\) | −6.82843 | −0.217461 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.34315 | −0.201802 | ||||||||
\(989\) | −52.9706 | −1.68437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.0000 | 1.65183 | 0.825917 | − | 0.563791i | \(-0.190658\pi\) | ||||
0.825917 | + | 0.563791i | \(0.190658\pi\) | |||||||
\(992\) | 16.6274 | 0.527921 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −14.6274 | −0.463953 | ||||||||
\(995\) | −12.0000 | −0.380426 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.17157 | 0.0371041 | 0.0185520 | − | 0.999828i | \(-0.494094\pi\) | ||||
0.0185520 | + | 0.999828i | \(0.494094\pi\) | |||||||
\(998\) | 86.9117 | 2.75114 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1305.2.a.n.1.2 | 2 | ||
3.2 | odd | 2 | 145.2.a.b.1.1 | ✓ | 2 | ||
5.4 | even | 2 | 6525.2.a.p.1.1 | 2 | |||
12.11 | even | 2 | 2320.2.a.k.1.1 | 2 | |||
15.2 | even | 4 | 725.2.b.c.349.1 | 4 | |||
15.8 | even | 4 | 725.2.b.c.349.4 | 4 | |||
15.14 | odd | 2 | 725.2.a.c.1.2 | 2 | |||
21.20 | even | 2 | 7105.2.a.e.1.1 | 2 | |||
24.5 | odd | 2 | 9280.2.a.be.1.2 | 2 | |||
24.11 | even | 2 | 9280.2.a.w.1.1 | 2 | |||
87.86 | odd | 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 | 3.2 | odd | 2 | ||
725.2.a.c.1.2 | 2 | 15.14 | odd | 2 | |||
725.2.b.c.349.1 | 4 | 15.2 | even | 4 | |||
725.2.b.c.349.4 | 4 | 15.8 | even | 4 | |||
1305.2.a.n.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2320.2.a.k.1.1 | 2 | 12.11 | even | 2 | |||
4205.2.a.d.1.2 | 2 | 87.86 | odd | 2 | |||
6525.2.a.p.1.1 | 2 | 5.4 | even | 2 | |||
7105.2.a.e.1.1 | 2 | 21.20 | even | 2 | |||
9280.2.a.w.1.1 | 2 | 24.11 | even | 2 | |||
9280.2.a.be.1.2 | 2 | 24.5 | odd | 2 |