Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, 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("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.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: | \(72.4642398343\) |
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: | no (minimal twist has level 825) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-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 | \(0.174443\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.41421 | −0.985599 | ||||||||
\(7\) | 0.414214 | 0.156558 | 0.0782790 | − | 0.996931i | \(-0.475058\pi\) | ||||
0.0782790 | + | 0.996931i | \(0.475058\pi\) | |||||||
\(8\) | 4.41421 | 1.56066 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −3.82843 | −1.10517 | ||||||||
\(13\) | −2.82843 | −0.784465 | −0.392232 | − | 0.919866i | \(-0.628297\pi\) | ||||
−0.392232 | + | 0.919866i | \(0.628297\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 2.41421 | 0.585533 | 0.292766 | − | 0.956184i | \(-0.405424\pi\) | ||||
0.292766 | + | 0.956184i | \(0.405424\pi\) | |||||||
\(18\) | 2.41421 | 0.569036 | ||||||||
\(19\) | −6.41421 | −1.47152 | −0.735761 | − | 0.677242i | \(-0.763175\pi\) | ||||
−0.735761 | + | 0.677242i | \(0.763175\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.414214 | −0.0903888 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | −0.104257 | − | 0.994550i | \(-0.533247\pi\) | ||||
−0.104257 | + | 0.994550i | \(0.533247\pi\) | |||||||
\(24\) | −4.41421 | −0.901048 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.82843 | −1.33916 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.58579 | 0.299685 | ||||||||
\(29\) | −1.17157 | −0.217556 | −0.108778 | − | 0.994066i | \(-0.534694\pi\) | ||||
−0.108778 | + | 0.994066i | \(0.534694\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.48528 | −1.52400 | −0.762001 | − | 0.647576i | \(-0.775783\pi\) | ||||
−0.762001 | + | 0.647576i | \(0.775783\pi\) | |||||||
\(32\) | −1.58579 | −0.280330 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.82843 | 0.999567 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.82843 | 0.638071 | ||||||||
\(37\) | 0.171573 | 0.0282064 | 0.0141032 | − | 0.999901i | \(-0.495511\pi\) | ||||
0.0141032 | + | 0.999901i | \(0.495511\pi\) | |||||||
\(38\) | −15.4853 | −2.51204 | ||||||||
\(39\) | 2.82843 | 0.452911 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.8995 | 1.70222 | 0.851108 | − | 0.524991i | \(-0.175931\pi\) | ||||
0.851108 | + | 0.524991i | \(0.175931\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | −11.6569 | −1.77765 | −0.888827 | − | 0.458243i | \(-0.848479\pi\) | ||||
−0.888827 | + | 0.458243i | \(0.848479\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.41421 | −0.355956 | ||||||||
\(47\) | 7.48528 | 1.09184 | 0.545920 | − | 0.837837i | \(-0.316180\pi\) | ||||
0.545920 | + | 0.837837i | \(0.316180\pi\) | |||||||
\(48\) | −3.00000 | −0.433013 | ||||||||
\(49\) | −6.82843 | −0.975490 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.41421 | −0.338058 | ||||||||
\(52\) | −10.8284 | −1.50163 | ||||||||
\(53\) | −7.65685 | −1.05175 | −0.525875 | − | 0.850562i | \(-0.676262\pi\) | ||||
−0.525875 | + | 0.850562i | \(0.676262\pi\) | |||||||
\(54\) | −2.41421 | −0.328533 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.82843 | 0.244334 | ||||||||
\(57\) | 6.41421 | 0.849583 | ||||||||
\(58\) | −2.82843 | −0.371391 | ||||||||
\(59\) | 11.0000 | 1.43208 | 0.716039 | − | 0.698060i | \(-0.245953\pi\) | ||||
0.716039 | + | 0.698060i | \(0.245953\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.82843 | −1.13036 | −0.565182 | − | 0.824966i | \(-0.691194\pi\) | ||||
−0.565182 | + | 0.824966i | \(0.691194\pi\) | |||||||
\(62\) | −20.4853 | −2.60163 | ||||||||
\(63\) | 0.414214 | 0.0521860 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.343146 | 0.0419219 | 0.0209610 | − | 0.999780i | \(-0.493327\pi\) | ||||
0.0209610 | + | 0.999780i | \(0.493327\pi\) | |||||||
\(68\) | 9.24264 | 1.12083 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.82843 | 0.929063 | 0.464532 | − | 0.885556i | \(-0.346223\pi\) | ||||
0.464532 | + | 0.885556i | \(0.346223\pi\) | |||||||
\(72\) | 4.41421 | 0.520220 | ||||||||
\(73\) | −8.82843 | −1.03329 | −0.516645 | − | 0.856200i | \(-0.672819\pi\) | ||||
−0.516645 | + | 0.856200i | \(0.672819\pi\) | |||||||
\(74\) | 0.414214 | 0.0481513 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −24.5563 | −2.81681 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.82843 | 0.773167 | ||||||||
\(79\) | −13.2426 | −1.48991 | −0.744957 | − | 0.667113i | \(-0.767530\pi\) | ||||
−0.744957 | + | 0.667113i | \(0.767530\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 26.3137 | 2.90586 | ||||||||
\(83\) | −4.48528 | −0.492324 | −0.246162 | − | 0.969229i | \(-0.579169\pi\) | ||||
−0.246162 | + | 0.969229i | \(0.579169\pi\) | |||||||
\(84\) | −1.58579 | −0.173023 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −28.1421 | −3.03464 | ||||||||
\(87\) | 1.17157 | 0.125606 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.65685 | 0.387626 | 0.193813 | − | 0.981039i | \(-0.437915\pi\) | ||||
0.193813 | + | 0.981039i | \(0.437915\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.17157 | −0.122814 | ||||||||
\(92\) | −3.82843 | −0.399141 | ||||||||
\(93\) | 8.48528 | 0.879883 | ||||||||
\(94\) | 18.0711 | 1.86389 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.58579 | 0.161849 | ||||||||
\(97\) | −5.82843 | −0.591787 | −0.295894 | − | 0.955221i | \(-0.595617\pi\) | ||||
−0.295894 | + | 0.955221i | \(0.595617\pi\) | |||||||
\(98\) | −16.4853 | −1.66526 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.8995 | −1.48256 | −0.741278 | − | 0.671199i | \(-0.765780\pi\) | ||||
−0.741278 | + | 0.671199i | \(0.765780\pi\) | |||||||
\(102\) | −5.82843 | −0.577100 | ||||||||
\(103\) | 13.6569 | 1.34565 | 0.672825 | − | 0.739802i | \(-0.265081\pi\) | ||||
0.672825 | + | 0.739802i | \(0.265081\pi\) | |||||||
\(104\) | −12.4853 | −1.22428 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −18.4853 | −1.79545 | ||||||||
\(107\) | −5.31371 | −0.513696 | −0.256848 | − | 0.966452i | \(-0.582684\pi\) | ||||
−0.256848 | + | 0.966452i | \(0.582684\pi\) | |||||||
\(108\) | −3.82843 | −0.368391 | ||||||||
\(109\) | −5.31371 | −0.508961 | −0.254480 | − | 0.967078i | \(-0.581904\pi\) | ||||
−0.254480 | + | 0.967078i | \(0.581904\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.171573 | −0.0162850 | ||||||||
\(112\) | 1.24264 | 0.117419 | ||||||||
\(113\) | 10.0000 | 0.940721 | 0.470360 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(114\) | 15.4853 | 1.45033 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.48528 | −0.416448 | ||||||||
\(117\) | −2.82843 | −0.261488 | ||||||||
\(118\) | 26.5563 | 2.44471 | ||||||||
\(119\) | 1.00000 | 0.0916698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −21.3137 | −1.92965 | ||||||||
\(123\) | −10.8995 | −0.982774 | ||||||||
\(124\) | −32.4853 | −2.91726 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 7.24264 | 0.642680 | 0.321340 | − | 0.946964i | \(-0.395867\pi\) | ||||
0.321340 | + | 0.946964i | \(0.395867\pi\) | |||||||
\(128\) | −20.5563 | −1.81694 | ||||||||
\(129\) | 11.6569 | 1.02633 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.82843 | −0.596602 | −0.298301 | − | 0.954472i | \(-0.596420\pi\) | ||||
−0.298301 | + | 0.954472i | \(0.596420\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.65685 | −0.230378 | ||||||||
\(134\) | 0.828427 | 0.0715652 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.6569 | 0.913818 | ||||||||
\(137\) | 12.1421 | 1.03737 | 0.518686 | − | 0.854965i | \(-0.326421\pi\) | ||||
0.518686 | + | 0.854965i | \(0.326421\pi\) | |||||||
\(138\) | 2.41421 | 0.205512 | ||||||||
\(139\) | 18.9706 | 1.60906 | 0.804531 | − | 0.593911i | \(-0.202417\pi\) | ||||
0.804531 | + | 0.593911i | \(0.202417\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.48528 | −0.630374 | ||||||||
\(142\) | 18.8995 | 1.58601 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −21.3137 | −1.76394 | ||||||||
\(147\) | 6.82843 | 0.563199 | ||||||||
\(148\) | 0.656854 | 0.0539931 | ||||||||
\(149\) | −7.72792 | −0.633096 | −0.316548 | − | 0.948576i | \(-0.602524\pi\) | ||||
−0.316548 | + | 0.948576i | \(0.602524\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.0000 | −1.13930 | −0.569652 | − | 0.821886i | \(-0.692922\pi\) | ||||
−0.569652 | + | 0.821886i | \(0.692922\pi\) | |||||||
\(152\) | −28.3137 | −2.29655 | ||||||||
\(153\) | 2.41421 | 0.195178 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.8284 | 0.866968 | ||||||||
\(157\) | −6.00000 | −0.478852 | −0.239426 | − | 0.970915i | \(-0.576959\pi\) | ||||
−0.239426 | + | 0.970915i | \(0.576959\pi\) | |||||||
\(158\) | −31.9706 | −2.54344 | ||||||||
\(159\) | 7.65685 | 0.607228 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.414214 | −0.0326446 | ||||||||
\(162\) | 2.41421 | 0.189679 | ||||||||
\(163\) | −15.7990 | −1.23747 | −0.618736 | − | 0.785599i | \(-0.712355\pi\) | ||||
−0.618736 | + | 0.785599i | \(0.712355\pi\) | |||||||
\(164\) | 41.7279 | 3.25840 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.8284 | −0.840449 | ||||||||
\(167\) | 21.7990 | 1.68686 | 0.843428 | − | 0.537242i | \(-0.180534\pi\) | ||||
0.843428 | + | 0.537242i | \(0.180534\pi\) | |||||||
\(168\) | −1.82843 | −0.141066 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.41421 | −0.490507 | ||||||||
\(172\) | −44.6274 | −3.40281 | ||||||||
\(173\) | −12.5563 | −0.954642 | −0.477321 | − | 0.878729i | \(-0.658392\pi\) | ||||
−0.477321 | + | 0.878729i | \(0.658392\pi\) | |||||||
\(174\) | 2.82843 | 0.214423 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.0000 | −0.826811 | ||||||||
\(178\) | 8.82843 | 0.661719 | ||||||||
\(179\) | 16.7990 | 1.25562 | 0.627808 | − | 0.778368i | \(-0.283952\pi\) | ||||
0.627808 | + | 0.778368i | \(0.283952\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.9706 | −1.63306 | −0.816530 | − | 0.577304i | \(-0.804105\pi\) | ||||
−0.816530 | + | 0.577304i | \(0.804105\pi\) | |||||||
\(182\) | −2.82843 | −0.209657 | ||||||||
\(183\) | 8.82843 | 0.652616 | ||||||||
\(184\) | −4.41421 | −0.325420 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 20.4853 | 1.50205 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 28.6569 | 2.09002 | ||||||||
\(189\) | −0.414214 | −0.0301296 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.17157 | 0.446559 | 0.223280 | − | 0.974754i | \(-0.428324\pi\) | ||||
0.223280 | + | 0.974754i | \(0.428324\pi\) | |||||||
\(192\) | 9.82843 | 0.709306 | ||||||||
\(193\) | 3.31371 | 0.238526 | 0.119263 | − | 0.992863i | \(-0.461947\pi\) | ||||
0.119263 | + | 0.992863i | \(0.461947\pi\) | |||||||
\(194\) | −14.0711 | −1.01024 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −26.1421 | −1.86730 | ||||||||
\(197\) | 4.75736 | 0.338948 | 0.169474 | − | 0.985535i | \(-0.445793\pi\) | ||||
0.169474 | + | 0.985535i | \(0.445793\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.8284 | 0.767607 | 0.383803 | − | 0.923415i | \(-0.374614\pi\) | ||||
0.383803 | + | 0.923415i | \(0.374614\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.343146 | −0.0242036 | ||||||||
\(202\) | −35.9706 | −2.53088 | ||||||||
\(203\) | −0.485281 | −0.0340601 | ||||||||
\(204\) | −9.24264 | −0.647114 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 32.9706 | 2.29717 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −8.48528 | −0.588348 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.3137 | 0.916553 | 0.458277 | − | 0.888810i | \(-0.348467\pi\) | ||||
0.458277 | + | 0.888810i | \(0.348467\pi\) | |||||||
\(212\) | −29.3137 | −2.01327 | ||||||||
\(213\) | −7.82843 | −0.536395 | ||||||||
\(214\) | −12.8284 | −0.876933 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.41421 | −0.300349 | ||||||||
\(217\) | −3.51472 | −0.238595 | ||||||||
\(218\) | −12.8284 | −0.868851 | ||||||||
\(219\) | 8.82843 | 0.596570 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.82843 | −0.459330 | ||||||||
\(222\) | −0.414214 | −0.0278002 | ||||||||
\(223\) | 21.1716 | 1.41775 | 0.708877 | − | 0.705332i | \(-0.249202\pi\) | ||||
0.708877 | + | 0.705332i | \(0.249202\pi\) | |||||||
\(224\) | −0.656854 | −0.0438879 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 24.1421 | 1.60591 | ||||||||
\(227\) | −18.4853 | −1.22691 | −0.613456 | − | 0.789729i | \(-0.710221\pi\) | ||||
−0.613456 | + | 0.789729i | \(0.710221\pi\) | |||||||
\(228\) | 24.5563 | 1.62628 | ||||||||
\(229\) | −2.51472 | −0.166177 | −0.0830886 | − | 0.996542i | \(-0.526478\pi\) | ||||
−0.0830886 | + | 0.996542i | \(0.526478\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.17157 | −0.339530 | ||||||||
\(233\) | 16.5563 | 1.08464 | 0.542321 | − | 0.840171i | \(-0.317546\pi\) | ||||
0.542321 | + | 0.840171i | \(0.317546\pi\) | |||||||
\(234\) | −6.82843 | −0.446388 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 42.1127 | 2.74130 | ||||||||
\(237\) | 13.2426 | 0.860202 | ||||||||
\(238\) | 2.41421 | 0.156490 | ||||||||
\(239\) | −23.6569 | −1.53023 | −0.765117 | − | 0.643891i | \(-0.777319\pi\) | ||||
−0.765117 | + | 0.643891i | \(0.777319\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.1421 | −0.910975 | −0.455488 | − | 0.890242i | \(-0.650535\pi\) | ||||
−0.455488 | + | 0.890242i | \(0.650535\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −33.7990 | −2.16376 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −26.3137 | −1.67770 | ||||||||
\(247\) | 18.1421 | 1.15436 | ||||||||
\(248\) | −37.4558 | −2.37845 | ||||||||
\(249\) | 4.48528 | 0.284243 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.97056 | 0.566217 | 0.283108 | − | 0.959088i | \(-0.408634\pi\) | ||||
0.283108 | + | 0.959088i | \(0.408634\pi\) | |||||||
\(252\) | 1.58579 | 0.0998952 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 17.4853 | 1.09712 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | −9.31371 | −0.580973 | −0.290487 | − | 0.956879i | \(-0.593817\pi\) | ||||
−0.290487 | + | 0.956879i | \(0.593817\pi\) | |||||||
\(258\) | 28.1421 | 1.75205 | ||||||||
\(259\) | 0.0710678 | 0.00441594 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.17157 | −0.0725185 | ||||||||
\(262\) | −16.4853 | −1.01846 | ||||||||
\(263\) | 22.9706 | 1.41643 | 0.708213 | − | 0.705999i | \(-0.249502\pi\) | ||||
0.708213 | + | 0.705999i | \(0.249502\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.41421 | −0.393281 | ||||||||
\(267\) | −3.65685 | −0.223796 | ||||||||
\(268\) | 1.31371 | 0.0802475 | ||||||||
\(269\) | −15.7990 | −0.963281 | −0.481641 | − | 0.876369i | \(-0.659959\pi\) | ||||
−0.481641 | + | 0.876369i | \(0.659959\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.89949 | −0.540606 | −0.270303 | − | 0.962775i | \(-0.587124\pi\) | ||||
−0.270303 | + | 0.962775i | \(0.587124\pi\) | |||||||
\(272\) | 7.24264 | 0.439150 | ||||||||
\(273\) | 1.17157 | 0.0709068 | ||||||||
\(274\) | 29.3137 | 1.77091 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.82843 | 0.230444 | ||||||||
\(277\) | 4.82843 | 0.290112 | 0.145056 | − | 0.989423i | \(-0.453664\pi\) | ||||
0.145056 | + | 0.989423i | \(0.453664\pi\) | |||||||
\(278\) | 45.7990 | 2.74684 | ||||||||
\(279\) | −8.48528 | −0.508001 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.0711 | −1.91320 | −0.956600 | − | 0.291405i | \(-0.905877\pi\) | ||||
−0.956600 | + | 0.291405i | \(0.905877\pi\) | |||||||
\(282\) | −18.0711 | −1.07612 | ||||||||
\(283\) | −0.899495 | −0.0534694 | −0.0267347 | − | 0.999643i | \(-0.508511\pi\) | ||||
−0.0267347 | + | 0.999643i | \(0.508511\pi\) | |||||||
\(284\) | 29.9706 | 1.77843 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.51472 | 0.266495 | ||||||||
\(288\) | −1.58579 | −0.0934434 | ||||||||
\(289\) | −11.1716 | −0.657151 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.82843 | 0.341668 | ||||||||
\(292\) | −33.7990 | −1.97794 | ||||||||
\(293\) | 17.5858 | 1.02737 | 0.513686 | − | 0.857978i | \(-0.328280\pi\) | ||||
0.513686 | + | 0.857978i | \(0.328280\pi\) | |||||||
\(294\) | 16.4853 | 0.961441 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.757359 | 0.0440206 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.6569 | −1.08076 | ||||||||
\(299\) | 2.82843 | 0.163572 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.82843 | −0.278306 | ||||||||
\(302\) | −33.7990 | −1.94491 | ||||||||
\(303\) | 14.8995 | 0.855954 | ||||||||
\(304\) | −19.2426 | −1.10364 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.82843 | 0.333189 | ||||||||
\(307\) | 6.68629 | 0.381607 | 0.190803 | − | 0.981628i | \(-0.438891\pi\) | ||||
0.190803 | + | 0.981628i | \(0.438891\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.6569 | −0.776911 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.6569 | 0.774409 | 0.387205 | − | 0.921994i | \(-0.373441\pi\) | ||||
0.387205 | + | 0.921994i | \(0.373441\pi\) | |||||||
\(312\) | 12.4853 | 0.706840 | ||||||||
\(313\) | 27.1421 | 1.53416 | 0.767082 | − | 0.641549i | \(-0.221708\pi\) | ||||
0.767082 | + | 0.641549i | \(0.221708\pi\) | |||||||
\(314\) | −14.4853 | −0.817452 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −50.6985 | −2.85201 | ||||||||
\(317\) | −30.8284 | −1.73150 | −0.865748 | − | 0.500479i | \(-0.833157\pi\) | ||||
−0.865748 | + | 0.500479i | \(0.833157\pi\) | |||||||
\(318\) | 18.4853 | 1.03660 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.31371 | 0.296582 | ||||||||
\(322\) | −1.00000 | −0.0557278 | ||||||||
\(323\) | −15.4853 | −0.861624 | ||||||||
\(324\) | 3.82843 | 0.212690 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −38.1421 | −2.11250 | ||||||||
\(327\) | 5.31371 | 0.293849 | ||||||||
\(328\) | 48.1127 | 2.65658 | ||||||||
\(329\) | 3.10051 | 0.170936 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.1421 | −1.76669 | −0.883346 | − | 0.468722i | \(-0.844715\pi\) | ||||
−0.883346 | + | 0.468722i | \(0.844715\pi\) | |||||||
\(332\) | −17.1716 | −0.942412 | ||||||||
\(333\) | 0.171573 | 0.00940214 | ||||||||
\(334\) | 52.6274 | 2.87964 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.24264 | −0.0677916 | ||||||||
\(337\) | 4.14214 | 0.225637 | 0.112818 | − | 0.993616i | \(-0.464012\pi\) | ||||
0.112818 | + | 0.993616i | \(0.464012\pi\) | |||||||
\(338\) | −12.0711 | −0.656580 | ||||||||
\(339\) | −10.0000 | −0.543125 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −15.4853 | −0.837348 | ||||||||
\(343\) | −5.72792 | −0.309279 | ||||||||
\(344\) | −51.4558 | −2.77431 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −30.3137 | −1.62968 | ||||||||
\(347\) | −21.1716 | −1.13655 | −0.568275 | − | 0.822839i | \(-0.692389\pi\) | ||||
−0.568275 | + | 0.822839i | \(0.692389\pi\) | |||||||
\(348\) | 4.48528 | 0.240436 | ||||||||
\(349\) | 2.48528 | 0.133034 | 0.0665170 | − | 0.997785i | \(-0.478811\pi\) | ||||
0.0665170 | + | 0.997785i | \(0.478811\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.82843 | 0.150970 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.48528 | 0.238727 | 0.119364 | − | 0.992851i | \(-0.461915\pi\) | ||||
0.119364 | + | 0.992851i | \(0.461915\pi\) | |||||||
\(354\) | −26.5563 | −1.41145 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.0000 | 0.741999 | ||||||||
\(357\) | −1.00000 | −0.0529256 | ||||||||
\(358\) | 40.5563 | 2.14347 | ||||||||
\(359\) | −15.5147 | −0.818836 | −0.409418 | − | 0.912347i | \(-0.634268\pi\) | ||||
−0.409418 | + | 0.912347i | \(0.634268\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.1421 | 1.16538 | ||||||||
\(362\) | −53.0416 | −2.78781 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.48528 | −0.235093 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 21.3137 | 1.11409 | ||||||||
\(367\) | −1.31371 | −0.0685750 | −0.0342875 | − | 0.999412i | \(-0.510916\pi\) | ||||
−0.0342875 | + | 0.999412i | \(0.510916\pi\) | |||||||
\(368\) | −3.00000 | −0.156386 | ||||||||
\(369\) | 10.8995 | 0.567405 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.17157 | −0.164660 | ||||||||
\(372\) | 32.4853 | 1.68428 | ||||||||
\(373\) | −23.6569 | −1.22491 | −0.612453 | − | 0.790507i | \(-0.709817\pi\) | ||||
−0.612453 | + | 0.790507i | \(0.709817\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 33.0416 | 1.70399 | ||||||||
\(377\) | 3.31371 | 0.170665 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 9.17157 | 0.471112 | 0.235556 | − | 0.971861i | \(-0.424309\pi\) | ||||
0.235556 | + | 0.971861i | \(0.424309\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.24264 | −0.371052 | ||||||||
\(382\) | 14.8995 | 0.762324 | ||||||||
\(383\) | −20.0000 | −1.02195 | −0.510976 | − | 0.859595i | \(-0.670716\pi\) | ||||
−0.510976 | + | 0.859595i | \(0.670716\pi\) | |||||||
\(384\) | 20.5563 | 1.04901 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.00000 | 0.407189 | ||||||||
\(387\) | −11.6569 | −0.592551 | ||||||||
\(388\) | −22.3137 | −1.13281 | ||||||||
\(389\) | −17.6569 | −0.895238 | −0.447619 | − | 0.894224i | \(-0.647728\pi\) | ||||
−0.447619 | + | 0.894224i | \(0.647728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.41421 | −0.122092 | ||||||||
\(392\) | −30.1421 | −1.52241 | ||||||||
\(393\) | 6.82843 | 0.344449 | ||||||||
\(394\) | 11.4853 | 0.578620 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.9411 | 1.80383 | 0.901917 | − | 0.431910i | \(-0.142160\pi\) | ||||
0.901917 | + | 0.431910i | \(0.142160\pi\) | |||||||
\(398\) | 26.1421 | 1.31039 | ||||||||
\(399\) | 2.65685 | 0.133009 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.7990 | 1.58797 | 0.793983 | − | 0.607940i | \(-0.208004\pi\) | ||||
0.793983 | + | 0.607940i | \(0.208004\pi\) | |||||||
\(402\) | −0.828427 | −0.0413182 | ||||||||
\(403\) | 24.0000 | 1.19553 | ||||||||
\(404\) | −57.0416 | −2.83793 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.17157 | −0.0581442 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −10.6569 | −0.527593 | ||||||||
\(409\) | 4.14214 | 0.204815 | 0.102408 | − | 0.994743i | \(-0.467345\pi\) | ||||
0.102408 | + | 0.994743i | \(0.467345\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.1421 | −0.598927 | ||||||||
\(412\) | 52.2843 | 2.57586 | ||||||||
\(413\) | 4.55635 | 0.224203 | ||||||||
\(414\) | −2.41421 | −0.118652 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.48528 | 0.219909 | ||||||||
\(417\) | −18.9706 | −0.928992 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.4853 | −1.24504 | −0.622519 | − | 0.782605i | \(-0.713891\pi\) | ||||
−0.622519 | + | 0.782605i | \(0.713891\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.0000 | −1.31590 | −0.657950 | − | 0.753062i | \(-0.728576\pi\) | ||||
−0.657950 | + | 0.753062i | \(0.728576\pi\) | |||||||
\(422\) | 32.1421 | 1.56465 | ||||||||
\(423\) | 7.48528 | 0.363947 | ||||||||
\(424\) | −33.7990 | −1.64142 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −18.8995 | −0.915684 | ||||||||
\(427\) | −3.65685 | −0.176968 | ||||||||
\(428\) | −20.3431 | −0.983323 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.17157 | −0.0564327 | −0.0282163 | − | 0.999602i | \(-0.508983\pi\) | ||||
−0.0282163 | + | 0.999602i | \(0.508983\pi\) | |||||||
\(432\) | −3.00000 | −0.144338 | ||||||||
\(433\) | 13.3137 | 0.639816 | 0.319908 | − | 0.947449i | \(-0.396348\pi\) | ||||
0.319908 | + | 0.947449i | \(0.396348\pi\) | |||||||
\(434\) | −8.48528 | −0.407307 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −20.3431 | −0.974260 | ||||||||
\(437\) | 6.41421 | 0.306833 | ||||||||
\(438\) | 21.3137 | 1.01841 | ||||||||
\(439\) | −2.27208 | −0.108440 | −0.0542202 | − | 0.998529i | \(-0.517267\pi\) | ||||
−0.0542202 | + | 0.998529i | \(0.517267\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.82843 | −0.325163 | ||||||||
\(442\) | −16.4853 | −0.784125 | ||||||||
\(443\) | 7.97056 | 0.378693 | 0.189346 | − | 0.981910i | \(-0.439363\pi\) | ||||
0.189346 | + | 0.981910i | \(0.439363\pi\) | |||||||
\(444\) | −0.656854 | −0.0311729 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 51.1127 | 2.42026 | ||||||||
\(447\) | 7.72792 | 0.365518 | ||||||||
\(448\) | −4.07107 | −0.192340 | ||||||||
\(449\) | −6.48528 | −0.306059 | −0.153030 | − | 0.988222i | \(-0.548903\pi\) | ||||
−0.153030 | + | 0.988222i | \(0.548903\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 38.2843 | 1.80074 | ||||||||
\(453\) | 14.0000 | 0.657777 | ||||||||
\(454\) | −44.6274 | −2.09447 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 28.3137 | 1.32591 | ||||||||
\(457\) | 3.85786 | 0.180463 | 0.0902316 | − | 0.995921i | \(-0.471239\pi\) | ||||
0.0902316 | + | 0.995921i | \(0.471239\pi\) | |||||||
\(458\) | −6.07107 | −0.283682 | ||||||||
\(459\) | −2.41421 | −0.112686 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.7696 | 1.52623 | 0.763115 | − | 0.646263i | \(-0.223669\pi\) | ||||
0.763115 | + | 0.646263i | \(0.223669\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.9706 | −1.62522 | −0.812610 | − | 0.582808i | \(-0.801954\pi\) | ||||
−0.812610 | + | 0.582808i | \(0.801954\pi\) | |||||||
\(464\) | −3.51472 | −0.163167 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 39.9706 | 1.85160 | ||||||||
\(467\) | −10.6274 | −0.491778 | −0.245889 | − | 0.969298i | \(-0.579080\pi\) | ||||
−0.245889 | + | 0.969298i | \(0.579080\pi\) | |||||||
\(468\) | −10.8284 | −0.500544 | ||||||||
\(469\) | 0.142136 | 0.00656321 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.00000 | 0.276465 | ||||||||
\(472\) | 48.5563 | 2.23499 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 31.9706 | 1.46846 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.82843 | 0.175476 | ||||||||
\(477\) | −7.65685 | −0.350583 | ||||||||
\(478\) | −57.1127 | −2.61227 | ||||||||
\(479\) | 24.4853 | 1.11876 | 0.559381 | − | 0.828911i | \(-0.311039\pi\) | ||||
0.559381 | + | 0.828911i | \(0.311039\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.485281 | −0.0221269 | ||||||||
\(482\) | −34.1421 | −1.55513 | ||||||||
\(483\) | 0.414214 | 0.0188474 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.41421 | −0.109511 | ||||||||
\(487\) | 6.48528 | 0.293876 | 0.146938 | − | 0.989146i | \(-0.453058\pi\) | ||||
0.146938 | + | 0.989146i | \(0.453058\pi\) | |||||||
\(488\) | −38.9706 | −1.76411 | ||||||||
\(489\) | 15.7990 | 0.714455 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.1421 | 1.08952 | 0.544760 | − | 0.838592i | \(-0.316621\pi\) | ||||
0.544760 | + | 0.838592i | \(0.316621\pi\) | |||||||
\(492\) | −41.7279 | −1.88124 | ||||||||
\(493\) | −2.82843 | −0.127386 | ||||||||
\(494\) | 43.7990 | 1.97061 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −25.4558 | −1.14300 | ||||||||
\(497\) | 3.24264 | 0.145452 | ||||||||
\(498\) | 10.8284 | 0.485233 | ||||||||
\(499\) | 35.1716 | 1.57450 | 0.787248 | − | 0.616637i | \(-0.211505\pi\) | ||||
0.787248 | + | 0.616637i | \(0.211505\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.7990 | −0.973907 | ||||||||
\(502\) | 21.6569 | 0.966593 | ||||||||
\(503\) | −34.2843 | −1.52866 | −0.764330 | − | 0.644825i | \(-0.776930\pi\) | ||||
−0.764330 | + | 0.644825i | \(0.776930\pi\) | |||||||
\(504\) | 1.82843 | 0.0814446 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.00000 | 0.222058 | ||||||||
\(508\) | 27.7279 | 1.23023 | ||||||||
\(509\) | 4.62742 | 0.205107 | 0.102553 | − | 0.994728i | \(-0.467299\pi\) | ||||
0.102553 | + | 0.994728i | \(0.467299\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.65685 | −0.161770 | ||||||||
\(512\) | −31.2426 | −1.38074 | ||||||||
\(513\) | 6.41421 | 0.283194 | ||||||||
\(514\) | −22.4853 | −0.991783 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 44.6274 | 1.96461 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.171573 | 0.00753848 | ||||||||
\(519\) | 12.5563 | 0.551163 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.1421 | −1.58342 | −0.791708 | − | 0.610900i | \(-0.790808\pi\) | ||||
−0.791708 | + | 0.610900i | \(0.790808\pi\) | |||||||
\(522\) | −2.82843 | −0.123797 | ||||||||
\(523\) | 42.2132 | 1.84585 | 0.922927 | − | 0.384974i | \(-0.125790\pi\) | ||||
0.922927 | + | 0.384974i | \(0.125790\pi\) | |||||||
\(524\) | −26.1421 | −1.14202 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 55.4558 | 2.41799 | ||||||||
\(527\) | −20.4853 | −0.892353 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0000 | −0.956522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.0000 | 0.477359 | ||||||||
\(532\) | −10.1716 | −0.440994 | ||||||||
\(533\) | −30.8284 | −1.33533 | ||||||||
\(534\) | −8.82843 | −0.382043 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.51472 | 0.0654259 | ||||||||
\(537\) | −16.7990 | −0.724930 | ||||||||
\(538\) | −38.1421 | −1.64442 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.3137 | −0.486414 | −0.243207 | − | 0.969974i | \(-0.578199\pi\) | ||||
−0.243207 | + | 0.969974i | \(0.578199\pi\) | |||||||
\(542\) | −21.4853 | −0.922872 | ||||||||
\(543\) | 21.9706 | 0.942847 | ||||||||
\(544\) | −3.82843 | −0.164142 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.82843 | 0.121046 | ||||||||
\(547\) | 35.8701 | 1.53369 | 0.766846 | − | 0.641831i | \(-0.221825\pi\) | ||||
0.766846 | + | 0.641831i | \(0.221825\pi\) | |||||||
\(548\) | 46.4853 | 1.98575 | ||||||||
\(549\) | −8.82843 | −0.376788 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.51472 | 0.320138 | ||||||||
\(552\) | 4.41421 | 0.187881 | ||||||||
\(553\) | −5.48528 | −0.233258 | ||||||||
\(554\) | 11.6569 | 0.495252 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 72.6274 | 3.08009 | ||||||||
\(557\) | −5.17157 | −0.219127 | −0.109563 | − | 0.993980i | \(-0.534945\pi\) | ||||
−0.109563 | + | 0.993980i | \(0.534945\pi\) | |||||||
\(558\) | −20.4853 | −0.867211 | ||||||||
\(559\) | 32.9706 | 1.39451 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −77.4264 | −3.26604 | ||||||||
\(563\) | 15.3137 | 0.645396 | 0.322698 | − | 0.946502i | \(-0.395410\pi\) | ||||
0.322698 | + | 0.946502i | \(0.395410\pi\) | |||||||
\(564\) | −28.6569 | −1.20667 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.17157 | −0.0912780 | ||||||||
\(567\) | 0.414214 | 0.0173953 | ||||||||
\(568\) | 34.5563 | 1.44995 | ||||||||
\(569\) | −15.2426 | −0.639005 | −0.319502 | − | 0.947585i | \(-0.603516\pi\) | ||||
−0.319502 | + | 0.947585i | \(0.603516\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.02944 | 0.377870 | 0.188935 | − | 0.981990i | \(-0.439496\pi\) | ||||
0.188935 | + | 0.981990i | \(0.439496\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.17157 | −0.257821 | ||||||||
\(574\) | 10.8995 | 0.454936 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −9.82843 | −0.409518 | ||||||||
\(577\) | −23.9706 | −0.997908 | −0.498954 | − | 0.866629i | \(-0.666282\pi\) | ||||
−0.498954 | + | 0.866629i | \(0.666282\pi\) | |||||||
\(578\) | −26.9706 | −1.12183 | ||||||||
\(579\) | −3.31371 | −0.137713 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.85786 | −0.0770772 | ||||||||
\(582\) | 14.0711 | 0.583265 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −38.9706 | −1.61261 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 42.4558 | 1.75383 | ||||||||
\(587\) | 36.6569 | 1.51299 | 0.756495 | − | 0.653999i | \(-0.226910\pi\) | ||||
0.756495 | + | 0.653999i | \(0.226910\pi\) | |||||||
\(588\) | 26.1421 | 1.07808 | ||||||||
\(589\) | 54.4264 | 2.24260 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.75736 | −0.195692 | ||||||||
\(592\) | 0.514719 | 0.0211548 | ||||||||
\(593\) | 3.79899 | 0.156006 | 0.0780029 | − | 0.996953i | \(-0.475146\pi\) | ||||
0.0780029 | + | 0.996953i | \(0.475146\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −29.5858 | −1.21188 | ||||||||
\(597\) | −10.8284 | −0.443178 | ||||||||
\(598\) | 6.82843 | 0.279235 | ||||||||
\(599\) | 36.3137 | 1.48374 | 0.741869 | − | 0.670545i | \(-0.233940\pi\) | ||||
0.741869 | + | 0.670545i | \(0.233940\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.8284 | 0.604864 | 0.302432 | − | 0.953171i | \(-0.402201\pi\) | ||||
0.302432 | + | 0.953171i | \(0.402201\pi\) | |||||||
\(602\) | −11.6569 | −0.475098 | ||||||||
\(603\) | 0.343146 | 0.0139740 | ||||||||
\(604\) | −53.5980 | −2.18087 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 35.9706 | 1.46120 | ||||||||
\(607\) | −2.97056 | −0.120571 | −0.0602857 | − | 0.998181i | \(-0.519201\pi\) | ||||
−0.0602857 | + | 0.998181i | \(0.519201\pi\) | |||||||
\(608\) | 10.1716 | 0.412512 | ||||||||
\(609\) | 0.485281 | 0.0196646 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.1716 | −0.856510 | ||||||||
\(612\) | 9.24264 | 0.373612 | ||||||||
\(613\) | −42.0000 | −1.69636 | −0.848182 | − | 0.529705i | \(-0.822303\pi\) | ||||
−0.848182 | + | 0.529705i | \(0.822303\pi\) | |||||||
\(614\) | 16.1421 | 0.651444 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.85786 | 0.396863 | 0.198431 | − | 0.980115i | \(-0.436415\pi\) | ||||
0.198431 | + | 0.980115i | \(0.436415\pi\) | |||||||
\(618\) | −32.9706 | −1.32627 | ||||||||
\(619\) | 38.6274 | 1.55257 | 0.776283 | − | 0.630384i | \(-0.217103\pi\) | ||||
0.776283 | + | 0.630384i | \(0.217103\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 32.9706 | 1.32200 | ||||||||
\(623\) | 1.51472 | 0.0606859 | ||||||||
\(624\) | 8.48528 | 0.339683 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 65.5269 | 2.61898 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −22.9706 | −0.916625 | ||||||||
\(629\) | 0.414214 | 0.0165158 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.6274 | 1.06002 | 0.530010 | − | 0.847991i | \(-0.322188\pi\) | ||||
0.530010 | + | 0.847991i | \(0.322188\pi\) | |||||||
\(632\) | −58.4558 | −2.32525 | ||||||||
\(633\) | −13.3137 | −0.529172 | ||||||||
\(634\) | −74.4264 | −2.95585 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 29.3137 | 1.16236 | ||||||||
\(637\) | 19.3137 | 0.765237 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.82843 | 0.309688 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.4853 | −1.67807 | −0.839034 | − | 0.544079i | \(-0.816879\pi\) | ||||
−0.839034 | + | 0.544079i | \(0.816879\pi\) | |||||||
\(642\) | 12.8284 | 0.506298 | ||||||||
\(643\) | 32.9706 | 1.30023 | 0.650116 | − | 0.759835i | \(-0.274720\pi\) | ||||
0.650116 | + | 0.759835i | \(0.274720\pi\) | |||||||
\(644\) | −1.58579 | −0.0624887 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −37.3848 | −1.47088 | ||||||||
\(647\) | −17.3431 | −0.681829 | −0.340915 | − | 0.940094i | \(-0.610737\pi\) | ||||
−0.340915 | + | 0.940094i | \(0.610737\pi\) | |||||||
\(648\) | 4.41421 | 0.173407 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.51472 | 0.137753 | ||||||||
\(652\) | −60.4853 | −2.36879 | ||||||||
\(653\) | 40.4853 | 1.58431 | 0.792156 | − | 0.610319i | \(-0.208959\pi\) | ||||
0.792156 | + | 0.610319i | \(0.208959\pi\) | |||||||
\(654\) | 12.8284 | 0.501631 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 32.6985 | 1.27666 | ||||||||
\(657\) | −8.82843 | −0.344430 | ||||||||
\(658\) | 7.48528 | 0.291807 | ||||||||
\(659\) | −15.1127 | −0.588707 | −0.294354 | − | 0.955697i | \(-0.595104\pi\) | ||||
−0.294354 | + | 0.955697i | \(0.595104\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.6569 | −1.34800 | −0.673998 | − | 0.738733i | \(-0.735424\pi\) | ||||
−0.673998 | + | 0.738733i | \(0.735424\pi\) | |||||||
\(662\) | −77.5980 | −3.01593 | ||||||||
\(663\) | 6.82843 | 0.265194 | ||||||||
\(664\) | −19.7990 | −0.768350 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.414214 | 0.0160504 | ||||||||
\(667\) | 1.17157 | 0.0453635 | ||||||||
\(668\) | 83.4558 | 3.22900 | ||||||||
\(669\) | −21.1716 | −0.818540 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.656854 | 0.0253387 | ||||||||
\(673\) | 11.6569 | 0.449339 | 0.224669 | − | 0.974435i | \(-0.427870\pi\) | ||||
0.224669 | + | 0.974435i | \(0.427870\pi\) | |||||||
\(674\) | 10.0000 | 0.385186 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.1421 | −0.736236 | ||||||||
\(677\) | 40.4853 | 1.55598 | 0.777988 | − | 0.628279i | \(-0.216240\pi\) | ||||
0.777988 | + | 0.628279i | \(0.216240\pi\) | |||||||
\(678\) | −24.1421 | −0.927173 | ||||||||
\(679\) | −2.41421 | −0.0926490 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.4853 | 0.708358 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.4853 | −1.12822 | −0.564111 | − | 0.825699i | \(-0.690781\pi\) | ||||
−0.564111 | + | 0.825699i | \(0.690781\pi\) | |||||||
\(684\) | −24.5563 | −0.938935 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13.8284 | −0.527972 | ||||||||
\(687\) | 2.51472 | 0.0959425 | ||||||||
\(688\) | −34.9706 | −1.33324 | ||||||||
\(689\) | 21.6569 | 0.825060 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.4558 | 0.587968 | 0.293984 | − | 0.955810i | \(-0.405019\pi\) | ||||
0.293984 | + | 0.955810i | \(0.405019\pi\) | |||||||
\(692\) | −48.0711 | −1.82739 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −51.1127 | −1.94021 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.17157 | 0.196028 | ||||||||
\(697\) | 26.3137 | 0.996703 | ||||||||
\(698\) | 6.00000 | 0.227103 | ||||||||
\(699\) | −16.5563 | −0.626219 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.61522 | 0.174315 | 0.0871573 | − | 0.996195i | \(-0.472222\pi\) | ||||
0.0871573 | + | 0.996195i | \(0.472222\pi\) | |||||||
\(702\) | 6.82843 | 0.257722 | ||||||||
\(703\) | −1.10051 | −0.0415063 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.8284 | 0.407533 | ||||||||
\(707\) | −6.17157 | −0.232106 | ||||||||
\(708\) | −42.1127 | −1.58269 | ||||||||
\(709\) | −0.857864 | −0.0322178 | −0.0161089 | − | 0.999870i | \(-0.505128\pi\) | ||||
−0.0161089 | + | 0.999870i | \(0.505128\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.2426 | −0.496638 | ||||||||
\(712\) | 16.1421 | 0.604952 | ||||||||
\(713\) | 8.48528 | 0.317776 | ||||||||
\(714\) | −2.41421 | −0.0903497 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 64.3137 | 2.40352 | ||||||||
\(717\) | 23.6569 | 0.883481 | ||||||||
\(718\) | −37.4558 | −1.39784 | ||||||||
\(719\) | −1.65685 | −0.0617902 | −0.0308951 | − | 0.999523i | \(-0.509836\pi\) | ||||
−0.0308951 | + | 0.999523i | \(0.509836\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.65685 | 0.210672 | ||||||||
\(722\) | 53.4558 | 1.98942 | ||||||||
\(723\) | 14.1421 | 0.525952 | ||||||||
\(724\) | −84.1127 | −3.12602 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.9706 | 0.629403 | 0.314702 | − | 0.949191i | \(-0.398096\pi\) | ||||
0.314702 | + | 0.949191i | \(0.398096\pi\) | |||||||
\(728\) | −5.17157 | −0.191671 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.1421 | −1.04087 | ||||||||
\(732\) | 33.7990 | 1.24925 | ||||||||
\(733\) | 3.85786 | 0.142493 | 0.0712467 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712467 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(734\) | −3.17157 | −0.117065 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.58579 | 0.0584529 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 26.3137 | 0.968621 | ||||||||
\(739\) | −17.5858 | −0.646904 | −0.323452 | − | 0.946245i | \(-0.604843\pi\) | ||||
−0.323452 | + | 0.946245i | \(0.604843\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.1421 | −0.666468 | ||||||||
\(742\) | −7.65685 | −0.281092 | ||||||||
\(743\) | 31.1127 | 1.14141 | 0.570707 | − | 0.821154i | \(-0.306669\pi\) | ||||
0.570707 | + | 0.821154i | \(0.306669\pi\) | |||||||
\(744\) | 37.4558 | 1.37320 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −57.1127 | −2.09104 | ||||||||
\(747\) | −4.48528 | −0.164108 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.20101 | −0.0804232 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −47.5980 | −1.73687 | −0.868437 | − | 0.495799i | \(-0.834875\pi\) | ||||
−0.868437 | + | 0.495799i | \(0.834875\pi\) | |||||||
\(752\) | 22.4558 | 0.818880 | ||||||||
\(753\) | −8.97056 | −0.326905 | ||||||||
\(754\) | 8.00000 | 0.291343 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.58579 | −0.0576745 | ||||||||
\(757\) | 33.3137 | 1.21081 | 0.605404 | − | 0.795919i | \(-0.293012\pi\) | ||||
0.605404 | + | 0.795919i | \(0.293012\pi\) | |||||||
\(758\) | 22.1421 | 0.804239 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.8284 | 0.392530 | 0.196265 | − | 0.980551i | \(-0.437119\pi\) | ||||
0.196265 | + | 0.980551i | \(0.437119\pi\) | |||||||
\(762\) | −17.4853 | −0.633425 | ||||||||
\(763\) | −2.20101 | −0.0796819 | ||||||||
\(764\) | 23.6274 | 0.854810 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −48.2843 | −1.74458 | ||||||||
\(767\) | −31.1127 | −1.12341 | ||||||||
\(768\) | 29.9706 | 1.08147 | ||||||||
\(769\) | −3.65685 | −0.131870 | −0.0659348 | − | 0.997824i | \(-0.521003\pi\) | ||||
−0.0659348 | + | 0.997824i | \(0.521003\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.31371 | 0.335425 | ||||||||
\(772\) | 12.6863 | 0.456590 | ||||||||
\(773\) | −4.82843 | −0.173666 | −0.0868332 | − | 0.996223i | \(-0.527675\pi\) | ||||
−0.0868332 | + | 0.996223i | \(0.527675\pi\) | |||||||
\(774\) | −28.1421 | −1.01155 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −25.7279 | −0.923579 | ||||||||
\(777\) | −0.0710678 | −0.00254954 | ||||||||
\(778\) | −42.6274 | −1.52827 | ||||||||
\(779\) | −69.9117 | −2.50485 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −5.82843 | −0.208424 | ||||||||
\(783\) | 1.17157 | 0.0418686 | ||||||||
\(784\) | −20.4853 | −0.731617 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 16.4853 | 0.588011 | ||||||||
\(787\) | −22.0711 | −0.786749 | −0.393374 | − | 0.919378i | \(-0.628692\pi\) | ||||
−0.393374 | + | 0.919378i | \(0.628692\pi\) | |||||||
\(788\) | 18.2132 | 0.648819 | ||||||||
\(789\) | −22.9706 | −0.817774 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.14214 | 0.147277 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.9706 | 0.886731 | ||||||||
\(794\) | 86.7696 | 3.07934 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 41.4558 | 1.46936 | ||||||||
\(797\) | −7.02944 | −0.248995 | −0.124498 | − | 0.992220i | \(-0.539732\pi\) | ||||
−0.124498 | + | 0.992220i | \(0.539732\pi\) | |||||||
\(798\) | 6.41421 | 0.227061 | ||||||||
\(799\) | 18.0711 | 0.639308 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.65685 | 0.129209 | ||||||||
\(802\) | 76.7696 | 2.71083 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.31371 | −0.0463309 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 57.9411 | 2.04089 | ||||||||
\(807\) | 15.7990 | 0.556151 | ||||||||
\(808\) | −65.7696 | −2.31376 | ||||||||
\(809\) | 17.7279 | 0.623281 | 0.311640 | − | 0.950200i | \(-0.399122\pi\) | ||||
0.311640 | + | 0.950200i | \(0.399122\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.2132 | 1.13116 | 0.565579 | − | 0.824694i | \(-0.308653\pi\) | ||||
0.565579 | + | 0.824694i | \(0.308653\pi\) | |||||||
\(812\) | −1.85786 | −0.0651983 | ||||||||
\(813\) | 8.89949 | 0.312119 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −7.24264 | −0.253543 | ||||||||
\(817\) | 74.7696 | 2.61586 | ||||||||
\(818\) | 10.0000 | 0.349642 | ||||||||
\(819\) | −1.17157 | −0.0409381 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.7990 | 0.830590 | 0.415295 | − | 0.909687i | \(-0.363678\pi\) | ||||
0.415295 | + | 0.909687i | \(0.363678\pi\) | |||||||
\(822\) | −29.3137 | −1.02243 | ||||||||
\(823\) | −18.9706 | −0.661272 | −0.330636 | − | 0.943758i | \(-0.607263\pi\) | ||||
−0.330636 | + | 0.943758i | \(0.607263\pi\) | |||||||
\(824\) | 60.2843 | 2.10010 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.0000 | 0.382739 | ||||||||
\(827\) | −35.3137 | −1.22798 | −0.613989 | − | 0.789315i | \(-0.710436\pi\) | ||||
−0.613989 | + | 0.789315i | \(0.710436\pi\) | |||||||
\(828\) | −3.82843 | −0.133047 | ||||||||
\(829\) | 19.9411 | 0.692584 | 0.346292 | − | 0.938127i | \(-0.387441\pi\) | ||||
0.346292 | + | 0.938127i | \(0.387441\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.82843 | −0.167496 | ||||||||
\(832\) | 27.7990 | 0.963757 | ||||||||
\(833\) | −16.4853 | −0.571181 | ||||||||
\(834\) | −45.7990 | −1.58589 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.48528 | 0.293294 | ||||||||
\(838\) | −61.5269 | −2.12541 | ||||||||
\(839\) | −24.6863 | −0.852265 | −0.426133 | − | 0.904661i | \(-0.640124\pi\) | ||||
−0.426133 | + | 0.904661i | \(0.640124\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.6274 | −0.952670 | ||||||||
\(842\) | −65.1838 | −2.24638 | ||||||||
\(843\) | 32.0711 | 1.10459 | ||||||||
\(844\) | 50.9706 | 1.75448 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 18.0711 | 0.621296 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −22.9706 | −0.788812 | ||||||||
\(849\) | 0.899495 | 0.0308706 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.171573 | −0.00588144 | ||||||||
\(852\) | −29.9706 | −1.02677 | ||||||||
\(853\) | −24.8284 | −0.850109 | −0.425055 | − | 0.905168i | \(-0.639745\pi\) | ||||
−0.425055 | + | 0.905168i | \(0.639745\pi\) | |||||||
\(854\) | −8.82843 | −0.302103 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −23.4558 | −0.801704 | ||||||||
\(857\) | 22.6985 | 0.775365 | 0.387683 | − | 0.921793i | \(-0.373276\pi\) | ||||
0.387683 | + | 0.921793i | \(0.373276\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.51472 | −0.119921 | −0.0599603 | − | 0.998201i | \(-0.519097\pi\) | ||||
−0.0599603 | + | 0.998201i | \(0.519097\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.51472 | −0.153861 | ||||||||
\(862\) | −2.82843 | −0.0963366 | ||||||||
\(863\) | 51.3137 | 1.74674 | 0.873369 | − | 0.487058i | \(-0.161930\pi\) | ||||
0.873369 | + | 0.487058i | \(0.161930\pi\) | |||||||
\(864\) | 1.58579 | 0.0539496 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 32.1421 | 1.09223 | ||||||||
\(867\) | 11.1716 | 0.379407 | ||||||||
\(868\) | −13.4558 | −0.456721 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.970563 | −0.0328863 | ||||||||
\(872\) | −23.4558 | −0.794315 | ||||||||
\(873\) | −5.82843 | −0.197262 | ||||||||
\(874\) | 15.4853 | 0.523797 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 33.7990 | 1.14196 | ||||||||
\(877\) | −47.1127 | −1.59088 | −0.795441 | − | 0.606031i | \(-0.792761\pi\) | ||||
−0.795441 | + | 0.606031i | \(0.792761\pi\) | |||||||
\(878\) | −5.48528 | −0.185119 | ||||||||
\(879\) | −17.5858 | −0.593154 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.0000 | −0.808581 | −0.404290 | − | 0.914631i | \(-0.632481\pi\) | ||||
−0.404290 | + | 0.914631i | \(0.632481\pi\) | |||||||
\(882\) | −16.4853 | −0.555088 | ||||||||
\(883\) | 6.62742 | 0.223030 | 0.111515 | − | 0.993763i | \(-0.464430\pi\) | ||||
0.111515 | + | 0.993763i | \(0.464430\pi\) | |||||||
\(884\) | −26.1421 | −0.879255 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19.2426 | 0.646469 | ||||||||
\(887\) | 6.14214 | 0.206233 | 0.103116 | − | 0.994669i | \(-0.467119\pi\) | ||||
0.103116 | + | 0.994669i | \(0.467119\pi\) | |||||||
\(888\) | −0.757359 | −0.0254153 | ||||||||
\(889\) | 3.00000 | 0.100617 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 81.0538 | 2.71388 | ||||||||
\(893\) | −48.0122 | −1.60667 | ||||||||
\(894\) | 18.6569 | 0.623979 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.51472 | −0.284457 | ||||||||
\(897\) | −2.82843 | −0.0944384 | ||||||||
\(898\) | −15.6569 | −0.522476 | ||||||||
\(899\) | 9.94113 | 0.331555 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.4853 | −0.615834 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.82843 | 0.160680 | ||||||||
\(904\) | 44.1421 | 1.46815 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 33.7990 | 1.12290 | ||||||||
\(907\) | −14.4853 | −0.480976 | −0.240488 | − | 0.970652i | \(-0.577307\pi\) | ||||
−0.240488 | + | 0.970652i | \(0.577307\pi\) | |||||||
\(908\) | −70.7696 | −2.34857 | ||||||||
\(909\) | −14.8995 | −0.494185 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.4853 | 1.50699 | 0.753497 | − | 0.657451i | \(-0.228365\pi\) | ||||
0.753497 | + | 0.657451i | \(0.228365\pi\) | |||||||
\(912\) | 19.2426 | 0.637188 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 9.31371 | 0.308070 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.62742 | −0.318099 | ||||||||
\(917\) | −2.82843 | −0.0934029 | ||||||||
\(918\) | −5.82843 | −0.192367 | ||||||||
\(919\) | −44.2132 | −1.45846 | −0.729230 | − | 0.684269i | \(-0.760121\pi\) | ||||
−0.729230 | + | 0.684269i | \(0.760121\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.68629 | −0.220321 | ||||||||
\(922\) | 79.1127 | 2.60544 | ||||||||
\(923\) | −22.1421 | −0.728817 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −84.4264 | −2.77442 | ||||||||
\(927\) | 13.6569 | 0.448550 | ||||||||
\(928\) | 1.85786 | 0.0609874 | ||||||||
\(929\) | 25.7990 | 0.846437 | 0.423219 | − | 0.906028i | \(-0.360900\pi\) | ||||
0.423219 | + | 0.906028i | \(0.360900\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 43.7990 | 1.43545 | ||||||||
\(932\) | 63.3848 | 2.07624 | ||||||||
\(933\) | −13.6569 | −0.447105 | ||||||||
\(934\) | −25.6569 | −0.839518 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.4853 | −0.408094 | ||||||||
\(937\) | −16.0000 | −0.522697 | −0.261349 | − | 0.965244i | \(-0.584167\pi\) | ||||
−0.261349 | + | 0.965244i | \(0.584167\pi\) | |||||||
\(938\) | 0.343146 | 0.0112041 | ||||||||
\(939\) | −27.1421 | −0.885750 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.10051 | 0.101074 | 0.0505368 | − | 0.998722i | \(-0.483907\pi\) | ||||
0.0505368 | + | 0.998722i | \(0.483907\pi\) | |||||||
\(942\) | 14.4853 | 0.471956 | ||||||||
\(943\) | −10.8995 | −0.354936 | ||||||||
\(944\) | 33.0000 | 1.07406 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.79899 | −0.0909549 | −0.0454775 | − | 0.998965i | \(-0.514481\pi\) | ||||
−0.0454775 | + | 0.998965i | \(0.514481\pi\) | |||||||
\(948\) | 50.6985 | 1.64661 | ||||||||
\(949\) | 24.9706 | 0.810579 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.8284 | 0.999680 | ||||||||
\(952\) | 4.41421 | 0.143065 | ||||||||
\(953\) | 19.0416 | 0.616819 | 0.308409 | − | 0.951254i | \(-0.400203\pi\) | ||||
0.308409 | + | 0.951254i | \(0.400203\pi\) | |||||||
\(954\) | −18.4853 | −0.598483 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −90.5685 | −2.92920 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 59.1127 | 1.90984 | ||||||||
\(959\) | 5.02944 | 0.162409 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.0000 | 1.32258 | ||||||||
\(962\) | −1.17157 | −0.0377730 | ||||||||
\(963\) | −5.31371 | −0.171232 | ||||||||
\(964\) | −54.1421 | −1.74380 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.00000 | 0.0321745 | ||||||||
\(967\) | 38.0000 | 1.22200 | 0.610999 | − | 0.791632i | \(-0.290768\pi\) | ||||
0.610999 | + | 0.791632i | \(0.290768\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.4853 | 0.497459 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.6863 | −0.888495 | −0.444248 | − | 0.895904i | \(-0.646529\pi\) | ||||
−0.444248 | + | 0.895904i | \(0.646529\pi\) | |||||||
\(972\) | −3.82843 | −0.122797 | ||||||||
\(973\) | 7.85786 | 0.251912 | ||||||||
\(974\) | 15.6569 | 0.501678 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.4853 | −0.847773 | ||||||||
\(977\) | 52.5685 | 1.68182 | 0.840908 | − | 0.541178i | \(-0.182021\pi\) | ||||
0.840908 | + | 0.541178i | \(0.182021\pi\) | |||||||
\(978\) | 38.1421 | 1.21965 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.31371 | −0.169654 | ||||||||
\(982\) | 58.2843 | 1.85993 | ||||||||
\(983\) | 5.28427 | 0.168542 | 0.0842710 | − | 0.996443i | \(-0.473144\pi\) | ||||
0.0842710 | + | 0.996443i | \(0.473144\pi\) | |||||||
\(984\) | −48.1127 | −1.53378 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6.82843 | −0.217461 | ||||||||
\(987\) | −3.10051 | −0.0986902 | ||||||||
\(988\) | 69.4558 | 2.20968 | ||||||||
\(989\) | 11.6569 | 0.370666 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.2843 | 0.453755 | 0.226877 | − | 0.973923i | \(-0.427148\pi\) | ||||
0.226877 | + | 0.973923i | \(0.427148\pi\) | |||||||
\(992\) | 13.4558 | 0.427223 | ||||||||
\(993\) | 32.1421 | 1.02000 | ||||||||
\(994\) | 7.82843 | 0.248303 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 17.1716 | 0.544102 | ||||||||
\(997\) | 43.2548 | 1.36989 | 0.684947 | − | 0.728593i | \(-0.259825\pi\) | ||||
0.684947 | + | 0.728593i | \(0.259825\pi\) | |||||||
\(998\) | 84.9117 | 2.68783 | ||||||||
\(999\) | −0.171573 | −0.00542833 |
(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 | 9075.2.a.ca.1.2 | 2 | ||
5.4 | even | 2 | 9075.2.a.w.1.1 | 2 | |||
11.10 | odd | 2 | 825.2.a.d.1.1 | ✓ | 2 | ||
33.32 | even | 2 | 2475.2.a.w.1.2 | 2 | |||
55.32 | even | 4 | 825.2.c.d.199.1 | 4 | |||
55.43 | even | 4 | 825.2.c.d.199.4 | 4 | |||
55.54 | odd | 2 | 825.2.a.f.1.2 | yes | 2 | ||
165.32 | odd | 4 | 2475.2.c.o.199.4 | 4 | |||
165.98 | odd | 4 | 2475.2.c.o.199.1 | 4 | |||
165.164 | even | 2 | 2475.2.a.l.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.a.d.1.1 | ✓ | 2 | 11.10 | odd | 2 | ||
825.2.a.f.1.2 | yes | 2 | 55.54 | odd | 2 | ||
825.2.c.d.199.1 | 4 | 55.32 | even | 4 | |||
825.2.c.d.199.4 | 4 | 55.43 | even | 4 | |||
2475.2.a.l.1.1 | 2 | 165.164 | even | 2 | |||
2475.2.a.w.1.2 | 2 | 33.32 | even | 2 | |||
2475.2.c.o.199.1 | 4 | 165.98 | odd | 4 | |||
2475.2.c.o.199.4 | 4 | 165.32 | odd | 4 | |||
9075.2.a.w.1.1 | 2 | 5.4 | even | 2 | |||
9075.2.a.ca.1.2 | 2 | 1.1 | even | 1 | trivial |