Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1225,2,Mod(1,1225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1225 = 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1225.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: | \(9.78167424761\) |
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 35) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1225.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41421 | −1.70711 | −0.853553 | − | 0.521005i | \(-0.825557\pi\) | ||||
−0.853553 | + | 0.521005i | \(0.825557\pi\) | |||||||
\(3\) | −0.414214 | −0.239146 | −0.119573 | − | 0.992825i | \(-0.538153\pi\) | ||||
−0.119573 | + | 0.992825i | \(0.538153\pi\) | |||||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4.41421 | −1.56066 | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.828427 | −0.249780 | −0.124890 | − | 0.992171i | \(-0.539858\pi\) | ||||
−0.124890 | + | 0.992171i | \(0.539858\pi\) | |||||||
\(12\) | −1.58579 | −0.457777 | ||||||||
\(13\) | −4.82843 | −1.33916 | −0.669582 | − | 0.742738i | \(-0.733527\pi\) | ||||
−0.669582 | + | 0.742738i | \(0.733527\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 4.82843 | 1.17107 | 0.585533 | − | 0.810649i | \(-0.300885\pi\) | ||||
0.585533 | + | 0.810649i | \(0.300885\pi\) | |||||||
\(18\) | 6.82843 | 1.60948 | ||||||||
\(19\) | −2.82843 | −0.648886 | −0.324443 | − | 0.945905i | \(-0.605177\pi\) | ||||
−0.324443 | + | 0.945905i | \(0.605177\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | 0.426401 | ||||||||
\(23\) | −0.414214 | −0.0863695 | −0.0431847 | − | 0.999067i | \(-0.513750\pi\) | ||||
−0.0431847 | + | 0.999067i | \(0.513750\pi\) | |||||||
\(24\) | 1.82843 | 0.373226 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 11.6569 | 2.28610 | ||||||||
\(27\) | 2.41421 | 0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | −0.0928477 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928477 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 1.58579 | 0.280330 | ||||||||
\(33\) | 0.343146 | 0.0597340 | ||||||||
\(34\) | −11.6569 | −1.99913 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −10.8284 | −1.80474 | ||||||||
\(37\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(38\) | 6.82843 | 1.10772 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.82843 | 1.22259 | 0.611297 | − | 0.791401i | \(-0.290648\pi\) | ||||
0.611297 | + | 0.791401i | \(0.290648\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.58579 | −0.546827 | −0.273414 | − | 0.961897i | \(-0.588153\pi\) | ||||
−0.273414 | + | 0.961897i | \(0.588153\pi\) | |||||||
\(44\) | −3.17157 | −0.478133 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 2.00000 | 0.291730 | 0.145865 | − | 0.989305i | \(-0.453403\pi\) | ||||
0.145865 | + | 0.989305i | \(0.453403\pi\) | |||||||
\(48\) | −1.24264 | −0.179360 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | −18.4853 | −2.56345 | ||||||||
\(53\) | 1.17157 | 0.160928 | 0.0804640 | − | 0.996758i | \(-0.474360\pi\) | ||||
0.0804640 | + | 0.996758i | \(0.474360\pi\) | |||||||
\(54\) | −5.82843 | −0.793148 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.17157 | 0.155179 | ||||||||
\(58\) | 2.41421 | 0.317002 | ||||||||
\(59\) | −4.48528 | −0.583934 | −0.291967 | − | 0.956428i | \(-0.594310\pi\) | ||||
−0.291967 | + | 0.956428i | \(0.594310\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.48528 | −0.702318 | −0.351159 | − | 0.936316i | \(-0.614212\pi\) | ||||
−0.351159 | + | 0.936316i | \(0.614212\pi\) | |||||||
\(62\) | −14.4853 | −1.83963 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.828427 | −0.101972 | ||||||||
\(67\) | −9.58579 | −1.17109 | −0.585545 | − | 0.810640i | \(-0.699119\pi\) | ||||
−0.585545 | + | 0.810640i | \(0.699119\pi\) | |||||||
\(68\) | 18.4853 | 2.24167 | ||||||||
\(69\) | 0.171573 | 0.0206549 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.48528 | 0.532305 | 0.266152 | − | 0.963931i | \(-0.414248\pi\) | ||||
0.266152 | + | 0.963931i | \(0.414248\pi\) | |||||||
\(72\) | 12.4853 | 1.47140 | ||||||||
\(73\) | −0.828427 | −0.0969601 | −0.0484800 | − | 0.998824i | \(-0.515438\pi\) | ||||
−0.0484800 | + | 0.998824i | \(0.515438\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.8284 | −1.24211 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.82843 | −0.546712 | ||||||||
\(79\) | 14.8284 | 1.66833 | 0.834164 | − | 0.551516i | \(-0.185951\pi\) | ||||
0.834164 | + | 0.551516i | \(0.185951\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | −18.8995 | −2.08710 | ||||||||
\(83\) | 13.7279 | 1.50684 | 0.753418 | − | 0.657542i | \(-0.228404\pi\) | ||||
0.753418 | + | 0.657542i | \(0.228404\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.65685 | 0.933493 | ||||||||
\(87\) | 0.414214 | 0.0444084 | ||||||||
\(88\) | 3.65685 | 0.389822 | ||||||||
\(89\) | 8.65685 | 0.917625 | 0.458812 | − | 0.888533i | \(-0.348275\pi\) | ||||
0.458812 | + | 0.888533i | \(0.348275\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.58579 | −0.165330 | ||||||||
\(93\) | −2.48528 | −0.257712 | ||||||||
\(94\) | −4.82843 | −0.498014 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.656854 | −0.0670399 | ||||||||
\(97\) | 11.6569 | 1.18357 | 0.591787 | − | 0.806094i | \(-0.298423\pi\) | ||||
0.591787 | + | 0.806094i | \(0.298423\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.34315 | 0.235495 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3137 | 1.02625 | 0.513126 | − | 0.858313i | \(-0.328487\pi\) | ||||
0.513126 | + | 0.858313i | \(0.328487\pi\) | |||||||
\(102\) | 4.82843 | 0.478086 | ||||||||
\(103\) | −2.41421 | −0.237880 | −0.118940 | − | 0.992901i | \(-0.537950\pi\) | ||||
−0.118940 | + | 0.992901i | \(0.537950\pi\) | |||||||
\(104\) | 21.3137 | 2.08998 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.82843 | −0.274721 | ||||||||
\(107\) | −11.2426 | −1.08687 | −0.543434 | − | 0.839452i | \(-0.682876\pi\) | ||||
−0.543434 | + | 0.839452i | \(0.682876\pi\) | |||||||
\(108\) | 9.24264 | 0.889374 | ||||||||
\(109\) | −13.4853 | −1.29166 | −0.645828 | − | 0.763483i | \(-0.723488\pi\) | ||||
−0.645828 | + | 0.763483i | \(0.723488\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.48528 | 0.421940 | 0.210970 | − | 0.977493i | \(-0.432338\pi\) | ||||
0.210970 | + | 0.977493i | \(0.432338\pi\) | |||||||
\(114\) | −2.82843 | −0.264906 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.82843 | −0.355461 | ||||||||
\(117\) | 13.6569 | 1.26258 | ||||||||
\(118\) | 10.8284 | 0.996838 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3137 | −0.937610 | ||||||||
\(122\) | 13.2426 | 1.19893 | ||||||||
\(123\) | −3.24264 | −0.292379 | ||||||||
\(124\) | 22.9706 | 2.06282 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.31371 | 0.826458 | 0.413229 | − | 0.910627i | \(-0.364401\pi\) | ||||
0.413229 | + | 0.910627i | \(0.364401\pi\) | |||||||
\(128\) | 20.5563 | 1.81694 | ||||||||
\(129\) | 1.48528 | 0.130772 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.3137 | 1.68745 | 0.843723 | − | 0.536778i | \(-0.180359\pi\) | ||||
0.843723 | + | 0.536778i | \(0.180359\pi\) | |||||||
\(132\) | 1.31371 | 0.114344 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 23.1421 | 1.99918 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −21.3137 | −1.82764 | ||||||||
\(137\) | 9.65685 | 0.825041 | 0.412520 | − | 0.910948i | \(-0.364649\pi\) | ||||
0.412520 | + | 0.910948i | \(0.364649\pi\) | |||||||
\(138\) | −0.414214 | −0.0352602 | ||||||||
\(139\) | 16.1421 | 1.36916 | 0.684579 | − | 0.728939i | \(-0.259986\pi\) | ||||
0.684579 | + | 0.728939i | \(0.259986\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.828427 | −0.0697661 | ||||||||
\(142\) | −10.8284 | −0.908701 | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | −8.48528 | −0.707107 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.00000 | 0.165521 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.17157 | −0.177902 | −0.0889511 | − | 0.996036i | \(-0.528351\pi\) | ||||
−0.0889511 | + | 0.996036i | \(0.528351\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.6569 | 0.948621 | 0.474311 | − | 0.880358i | \(-0.342697\pi\) | ||||
0.474311 | + | 0.880358i | \(0.342697\pi\) | |||||||
\(152\) | 12.4853 | 1.01269 | ||||||||
\(153\) | −13.6569 | −1.10409 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.65685 | 0.613039 | ||||||||
\(157\) | 17.3137 | 1.38178 | 0.690892 | − | 0.722958i | \(-0.257218\pi\) | ||||
0.690892 | + | 0.722958i | \(0.257218\pi\) | |||||||
\(158\) | −35.7990 | −2.84801 | ||||||||
\(159\) | −0.485281 | −0.0384853 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −18.0711 | −1.41980 | ||||||||
\(163\) | −12.3431 | −0.966790 | −0.483395 | − | 0.875402i | \(-0.660596\pi\) | ||||
−0.483395 | + | 0.875402i | \(0.660596\pi\) | |||||||
\(164\) | 29.9706 | 2.34031 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −33.1421 | −2.57233 | ||||||||
\(167\) | 22.4142 | 1.73446 | 0.867232 | − | 0.497904i | \(-0.165897\pi\) | ||||
0.867232 | + | 0.497904i | \(0.165897\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.3137 | 0.793362 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.00000 | 0.611775 | ||||||||
\(172\) | −13.7279 | −1.04674 | ||||||||
\(173\) | 3.31371 | 0.251937 | 0.125968 | − | 0.992034i | \(-0.459796\pi\) | ||||
0.125968 | + | 0.992034i | \(0.459796\pi\) | |||||||
\(174\) | −1.00000 | −0.0758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.48528 | −0.187335 | ||||||||
\(177\) | 1.85786 | 0.139646 | ||||||||
\(178\) | −20.8995 | −1.56648 | ||||||||
\(179\) | −10.0000 | −0.747435 | −0.373718 | − | 0.927543i | \(-0.621917\pi\) | ||||
−0.373718 | + | 0.927543i | \(0.621917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.65685 | −0.197482 | −0.0987412 | − | 0.995113i | \(-0.531482\pi\) | ||||
−0.0987412 | + | 0.995113i | \(0.531482\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.27208 | 0.167957 | ||||||||
\(184\) | 1.82843 | 0.134793 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | −4.00000 | −0.292509 | ||||||||
\(188\) | 7.65685 | 0.558433 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.8284 | −0.928232 | −0.464116 | − | 0.885774i | \(-0.653628\pi\) | ||||
−0.464116 | + | 0.885774i | \(0.653628\pi\) | |||||||
\(192\) | 4.07107 | 0.293804 | ||||||||
\(193\) | 2.00000 | 0.143963 | 0.0719816 | − | 0.997406i | \(-0.477068\pi\) | ||||
0.0719816 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(194\) | −28.1421 | −2.02049 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.3431 | 0.879413 | 0.439706 | − | 0.898142i | \(-0.355083\pi\) | ||||
0.439706 | + | 0.898142i | \(0.355083\pi\) | |||||||
\(198\) | −5.65685 | −0.402015 | ||||||||
\(199\) | 9.65685 | 0.684556 | 0.342278 | − | 0.939599i | \(-0.388801\pi\) | ||||
0.342278 | + | 0.939599i | \(0.388801\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.97056 | 0.280062 | ||||||||
\(202\) | −24.8995 | −1.75192 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7.65685 | −0.536087 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.82843 | 0.406086 | ||||||||
\(207\) | 1.17157 | 0.0814299 | ||||||||
\(208\) | −14.4853 | −1.00437 | ||||||||
\(209\) | 2.34315 | 0.162079 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.4853 | 1.41026 | 0.705132 | − | 0.709076i | \(-0.250888\pi\) | ||||
0.705132 | + | 0.709076i | \(0.250888\pi\) | |||||||
\(212\) | 4.48528 | 0.308050 | ||||||||
\(213\) | −1.85786 | −0.127299 | ||||||||
\(214\) | 27.1421 | 1.85540 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −10.6569 | −0.725107 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 32.5563 | 2.20499 | ||||||||
\(219\) | 0.343146 | 0.0231876 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.3137 | −1.56825 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.343146 | 0.0229787 | 0.0114894 | − | 0.999934i | \(-0.496343\pi\) | ||||
0.0114894 | + | 0.999934i | \(0.496343\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.8284 | −0.720296 | ||||||||
\(227\) | −6.97056 | −0.462652 | −0.231326 | − | 0.972876i | \(-0.574306\pi\) | ||||
−0.231326 | + | 0.972876i | \(0.574306\pi\) | |||||||
\(228\) | 4.48528 | 0.297045 | ||||||||
\(229\) | 11.6569 | 0.770307 | 0.385153 | − | 0.922853i | \(-0.374149\pi\) | ||||
0.385153 | + | 0.922853i | \(0.374149\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.41421 | 0.289807 | ||||||||
\(233\) | 16.8284 | 1.10247 | 0.551233 | − | 0.834351i | \(-0.314157\pi\) | ||||
0.551233 | + | 0.834351i | \(0.314157\pi\) | |||||||
\(234\) | −32.9706 | −2.15535 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −17.1716 | −1.11777 | ||||||||
\(237\) | −6.14214 | −0.398975 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.3137 | −1.37867 | −0.689335 | − | 0.724443i | \(-0.742097\pi\) | ||||
−0.689335 | + | 0.724443i | \(0.742097\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.6569 | −1.78153 | −0.890767 | − | 0.454460i | \(-0.849832\pi\) | ||||
−0.890767 | + | 0.454460i | \(0.849832\pi\) | |||||||
\(242\) | 24.8995 | 1.60060 | ||||||||
\(243\) | −10.3431 | −0.663513 | ||||||||
\(244\) | −21.0000 | −1.34439 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.82843 | 0.499122 | ||||||||
\(247\) | 13.6569 | 0.868965 | ||||||||
\(248\) | −26.4853 | −1.68182 | ||||||||
\(249\) | −5.68629 | −0.360354 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.31371 | 0.587876 | 0.293938 | − | 0.955824i | \(-0.405034\pi\) | ||||
0.293938 | + | 0.955824i | \(0.405034\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.343146 | 0.0215734 | ||||||||
\(254\) | −22.4853 | −1.41085 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 6.34315 | 0.395675 | 0.197837 | − | 0.980235i | \(-0.436608\pi\) | ||||
0.197837 | + | 0.980235i | \(0.436608\pi\) | |||||||
\(258\) | −3.58579 | −0.223241 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.82843 | 0.175075 | ||||||||
\(262\) | −46.6274 | −2.88065 | ||||||||
\(263\) | 29.0416 | 1.79078 | 0.895392 | − | 0.445279i | \(-0.146896\pi\) | ||||
0.895392 | + | 0.445279i | \(0.146896\pi\) | |||||||
\(264\) | −1.51472 | −0.0932245 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.58579 | −0.219447 | ||||||||
\(268\) | −36.6985 | −2.24172 | ||||||||
\(269\) | −20.4558 | −1.24721 | −0.623607 | − | 0.781738i | \(-0.714334\pi\) | ||||
−0.623607 | + | 0.781738i | \(0.714334\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.4853 | −1.00141 | −0.500705 | − | 0.865618i | \(-0.666926\pi\) | ||||
−0.500705 | + | 0.865618i | \(0.666926\pi\) | |||||||
\(272\) | 14.4853 | 0.878299 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −23.3137 | −1.40843 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.656854 | 0.0395380 | ||||||||
\(277\) | −16.1421 | −0.969887 | −0.484943 | − | 0.874546i | \(-0.661160\pi\) | ||||
−0.484943 | + | 0.874546i | \(0.661160\pi\) | |||||||
\(278\) | −38.9706 | −2.33730 | ||||||||
\(279\) | −16.9706 | −1.01600 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.2843 | −1.80661 | −0.903304 | − | 0.429001i | \(-0.858866\pi\) | ||||
−0.903304 | + | 0.429001i | \(0.858866\pi\) | |||||||
\(282\) | 2.00000 | 0.119098 | ||||||||
\(283\) | 14.0000 | 0.832214 | 0.416107 | − | 0.909316i | \(-0.363394\pi\) | ||||
0.416107 | + | 0.909316i | \(0.363394\pi\) | |||||||
\(284\) | 17.1716 | 1.01895 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.65685 | −0.571022 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.48528 | −0.264298 | ||||||||
\(289\) | 6.31371 | 0.371395 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.82843 | −0.283047 | ||||||||
\(292\) | −3.17157 | −0.185602 | ||||||||
\(293\) | −16.0000 | −0.934730 | −0.467365 | − | 0.884064i | \(-0.654797\pi\) | ||||
−0.467365 | + | 0.884064i | \(0.654797\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.00000 | −0.116052 | ||||||||
\(298\) | 5.24264 | 0.303698 | ||||||||
\(299\) | 2.00000 | 0.115663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −28.1421 | −1.61940 | ||||||||
\(303\) | −4.27208 | −0.245424 | ||||||||
\(304\) | −8.48528 | −0.486664 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 32.9706 | 1.88480 | ||||||||
\(307\) | −4.75736 | −0.271517 | −0.135758 | − | 0.990742i | \(-0.543347\pi\) | ||||
−0.135758 | + | 0.990742i | \(0.543347\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.1716 | 0.746891 | 0.373446 | − | 0.927652i | \(-0.378176\pi\) | ||||
0.373446 | + | 0.927652i | \(0.378176\pi\) | |||||||
\(312\) | −8.82843 | −0.499811 | ||||||||
\(313\) | −6.34315 | −0.358536 | −0.179268 | − | 0.983800i | \(-0.557373\pi\) | ||||
−0.179268 | + | 0.983800i | \(0.557373\pi\) | |||||||
\(314\) | −41.7990 | −2.35885 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 56.7696 | 3.19354 | ||||||||
\(317\) | 13.7990 | 0.775028 | 0.387514 | − | 0.921864i | \(-0.373334\pi\) | ||||
0.387514 | + | 0.921864i | \(0.373334\pi\) | |||||||
\(318\) | 1.17157 | 0.0656985 | ||||||||
\(319\) | 0.828427 | 0.0463830 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.65685 | 0.259920 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.6569 | −0.759888 | ||||||||
\(324\) | 28.6569 | 1.59205 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 29.7990 | 1.65041 | ||||||||
\(327\) | 5.58579 | 0.308895 | ||||||||
\(328\) | −34.5563 | −1.90806 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.9706 | 1.26258 | 0.631288 | − | 0.775548i | \(-0.282527\pi\) | ||||
0.631288 | + | 0.775548i | \(0.282527\pi\) | |||||||
\(332\) | 52.5563 | 2.88440 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −54.1127 | −2.96092 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.17157 | −0.499607 | −0.249804 | − | 0.968296i | \(-0.580366\pi\) | ||||
−0.249804 | + | 0.968296i | \(0.580366\pi\) | |||||||
\(338\) | −24.8995 | −1.35435 | ||||||||
\(339\) | −1.85786 | −0.100905 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.97056 | −0.269171 | ||||||||
\(342\) | −19.3137 | −1.04437 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 15.8284 | 0.853412 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.00000 | −0.430083 | ||||||||
\(347\) | −7.92893 | −0.425647 | −0.212824 | − | 0.977091i | \(-0.568266\pi\) | ||||
−0.212824 | + | 0.977091i | \(0.568266\pi\) | |||||||
\(348\) | 1.58579 | 0.0850071 | ||||||||
\(349\) | 15.3431 | 0.821300 | 0.410650 | − | 0.911793i | \(-0.365302\pi\) | ||||
0.410650 | + | 0.911793i | \(0.365302\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.6569 | −0.622197 | ||||||||
\(352\) | −1.31371 | −0.0700209 | ||||||||
\(353\) | −26.8284 | −1.42793 | −0.713967 | − | 0.700180i | \(-0.753103\pi\) | ||||
−0.713967 | + | 0.700180i | \(0.753103\pi\) | |||||||
\(354\) | −4.48528 | −0.238390 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 33.1421 | 1.75653 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.1421 | 1.27595 | ||||||||
\(359\) | −10.0000 | −0.527780 | −0.263890 | − | 0.964553i | \(-0.585006\pi\) | ||||
−0.263890 | + | 0.964553i | \(0.585006\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 6.41421 | 0.337124 | ||||||||
\(363\) | 4.27208 | 0.224226 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.48528 | −0.286720 | ||||||||
\(367\) | −2.75736 | −0.143933 | −0.0719665 | − | 0.997407i | \(-0.522927\pi\) | ||||
−0.0719665 | + | 0.997407i | \(0.522927\pi\) | |||||||
\(368\) | −1.24264 | −0.0647771 | ||||||||
\(369\) | −22.1421 | −1.15267 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −9.51472 | −0.493315 | ||||||||
\(373\) | 20.9706 | 1.08581 | 0.542907 | − | 0.839793i | \(-0.317323\pi\) | ||||
0.542907 | + | 0.839793i | \(0.317323\pi\) | |||||||
\(374\) | 9.65685 | 0.499344 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.82843 | −0.455291 | ||||||||
\(377\) | 4.82843 | 0.248677 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.8284 | 1.37808 | 0.689042 | − | 0.724722i | \(-0.258032\pi\) | ||||
0.689042 | + | 0.724722i | \(0.258032\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.85786 | −0.197644 | ||||||||
\(382\) | 30.9706 | 1.58459 | ||||||||
\(383\) | −2.89949 | −0.148157 | −0.0740786 | − | 0.997252i | \(-0.523602\pi\) | ||||
−0.0740786 | + | 0.997252i | \(0.523602\pi\) | |||||||
\(384\) | −8.51472 | −0.434515 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.82843 | −0.245760 | ||||||||
\(387\) | 10.1421 | 0.515554 | ||||||||
\(388\) | 44.6274 | 2.26561 | ||||||||
\(389\) | 23.6569 | 1.19945 | 0.599725 | − | 0.800206i | \(-0.295277\pi\) | ||||
0.599725 | + | 0.800206i | \(0.295277\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.00000 | −0.101144 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.00000 | −0.403547 | ||||||||
\(394\) | −29.7990 | −1.50125 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.97056 | 0.450788 | ||||||||
\(397\) | −16.6274 | −0.834506 | −0.417253 | − | 0.908790i | \(-0.637007\pi\) | ||||
−0.417253 | + | 0.908790i | \(0.637007\pi\) | |||||||
\(398\) | −23.3137 | −1.16861 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.3137 | 1.51379 | 0.756897 | − | 0.653534i | \(-0.226714\pi\) | ||||
0.756897 | + | 0.653534i | \(0.226714\pi\) | |||||||
\(402\) | −9.58579 | −0.478096 | ||||||||
\(403\) | −28.9706 | −1.44313 | ||||||||
\(404\) | 39.4853 | 1.96447 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 8.82843 | 0.437072 | ||||||||
\(409\) | 14.7990 | 0.731763 | 0.365881 | − | 0.930661i | \(-0.380768\pi\) | ||||
0.365881 | + | 0.930661i | \(0.380768\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.00000 | −0.197305 | ||||||||
\(412\) | −9.24264 | −0.455352 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.82843 | −0.139010 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.65685 | −0.375408 | ||||||||
\(417\) | −6.68629 | −0.327429 | ||||||||
\(418\) | −5.65685 | −0.276686 | ||||||||
\(419\) | 0.686292 | 0.0335275 | 0.0167638 | − | 0.999859i | \(-0.494664\pi\) | ||||
0.0167638 | + | 0.999859i | \(0.494664\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.4853 | 0.657232 | 0.328616 | − | 0.944464i | \(-0.393418\pi\) | ||||
0.328616 | + | 0.944464i | \(0.393418\pi\) | |||||||
\(422\) | −49.4558 | −2.40747 | ||||||||
\(423\) | −5.65685 | −0.275046 | ||||||||
\(424\) | −5.17157 | −0.251154 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.48528 | 0.217313 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −43.0416 | −2.08050 | ||||||||
\(429\) | −1.65685 | −0.0799937 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.7990 | 0.857347 | 0.428674 | − | 0.903459i | \(-0.358981\pi\) | ||||
0.428674 | + | 0.903459i | \(0.358981\pi\) | |||||||
\(432\) | 7.24264 | 0.348462 | ||||||||
\(433\) | 7.79899 | 0.374796 | 0.187398 | − | 0.982284i | \(-0.439995\pi\) | ||||
0.187398 | + | 0.982284i | \(0.439995\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −51.6274 | −2.47250 | ||||||||
\(437\) | 1.17157 | 0.0560439 | ||||||||
\(438\) | −0.828427 | −0.0395838 | ||||||||
\(439\) | 33.9411 | 1.61992 | 0.809961 | − | 0.586484i | \(-0.199488\pi\) | ||||
0.809961 | + | 0.586484i | \(0.199488\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 56.2843 | 2.67717 | ||||||||
\(443\) | −30.2132 | −1.43547 | −0.717736 | − | 0.696315i | \(-0.754822\pi\) | ||||
−0.717736 | + | 0.696315i | \(0.754822\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.828427 | −0.0392272 | ||||||||
\(447\) | 0.899495 | 0.0425447 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.82843 | 0.180675 | 0.0903373 | − | 0.995911i | \(-0.471205\pi\) | ||||
0.0903373 | + | 0.995911i | \(0.471205\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.48528 | −0.305380 | ||||||||
\(452\) | 17.1716 | 0.807683 | ||||||||
\(453\) | −4.82843 | −0.226859 | ||||||||
\(454\) | 16.8284 | 0.789797 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.17157 | −0.242181 | ||||||||
\(457\) | −24.2843 | −1.13597 | −0.567985 | − | 0.823039i | \(-0.692277\pi\) | ||||
−0.567985 | + | 0.823039i | \(0.692277\pi\) | |||||||
\(458\) | −28.1421 | −1.31500 | ||||||||
\(459\) | 11.6569 | 0.544095 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −41.3137 | −1.92417 | −0.962086 | − | 0.272748i | \(-0.912068\pi\) | ||||
−0.962086 | + | 0.272748i | \(0.912068\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.0416 | 1.72147 | 0.860735 | − | 0.509053i | \(-0.170004\pi\) | ||||
0.860735 | + | 0.509053i | \(0.170004\pi\) | |||||||
\(464\) | −3.00000 | −0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −40.6274 | −1.88203 | ||||||||
\(467\) | −3.10051 | −0.143474 | −0.0717371 | − | 0.997424i | \(-0.522854\pi\) | ||||
−0.0717371 | + | 0.997424i | \(0.522854\pi\) | |||||||
\(468\) | 52.2843 | 2.41684 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.17157 | −0.330449 | ||||||||
\(472\) | 19.7990 | 0.911322 | ||||||||
\(473\) | 2.97056 | 0.136587 | ||||||||
\(474\) | 14.8284 | 0.681092 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.31371 | −0.151724 | ||||||||
\(478\) | 51.4558 | 2.35354 | ||||||||
\(479\) | 35.6569 | 1.62920 | 0.814602 | − | 0.580021i | \(-0.196956\pi\) | ||||
0.814602 | + | 0.580021i | \(0.196956\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 66.7696 | 3.04127 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −39.4853 | −1.79479 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 24.9706 | 1.13269 | ||||||||
\(487\) | −4.34315 | −0.196807 | −0.0984034 | − | 0.995147i | \(-0.531374\pi\) | ||||
−0.0984034 | + | 0.995147i | \(0.531374\pi\) | |||||||
\(488\) | 24.2132 | 1.09608 | ||||||||
\(489\) | 5.11270 | 0.231204 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.31371 | 0.420322 | 0.210161 | − | 0.977667i | \(-0.432601\pi\) | ||||
0.210161 | + | 0.977667i | \(0.432601\pi\) | |||||||
\(492\) | −12.4142 | −0.559676 | ||||||||
\(493\) | −4.82843 | −0.217461 | ||||||||
\(494\) | −32.9706 | −1.48342 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.0000 | 0.808224 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 13.7279 | 0.615163 | ||||||||
\(499\) | −0.828427 | −0.0370855 | −0.0185427 | − | 0.999828i | \(-0.505903\pi\) | ||||
−0.0185427 | + | 0.999828i | \(0.505903\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.28427 | −0.414791 | ||||||||
\(502\) | −22.4853 | −1.00357 | ||||||||
\(503\) | −15.8701 | −0.707611 | −0.353805 | − | 0.935319i | \(-0.615113\pi\) | ||||
−0.353805 | + | 0.935319i | \(0.615113\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.828427 | −0.0368281 | ||||||||
\(507\) | −4.27208 | −0.189730 | ||||||||
\(508\) | 35.6569 | 1.58202 | ||||||||
\(509\) | −13.3431 | −0.591425 | −0.295712 | − | 0.955277i | \(-0.595557\pi\) | ||||
−0.295712 | + | 0.955277i | \(0.595557\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 31.2426 | 1.38074 | ||||||||
\(513\) | −6.82843 | −0.301482 | ||||||||
\(514\) | −15.3137 | −0.675459 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.68629 | 0.250325 | ||||||||
\(517\) | −1.65685 | −0.0728684 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.37258 | −0.0602497 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.9706 | −0.655872 | −0.327936 | − | 0.944700i | \(-0.606353\pi\) | ||||
−0.327936 | + | 0.944700i | \(0.606353\pi\) | |||||||
\(522\) | −6.82843 | −0.298872 | ||||||||
\(523\) | 35.6569 | 1.55917 | 0.779583 | − | 0.626299i | \(-0.215431\pi\) | ||||
0.779583 | + | 0.626299i | \(0.215431\pi\) | |||||||
\(524\) | 73.9411 | 3.23013 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −70.1127 | −3.05706 | ||||||||
\(527\) | 28.9706 | 1.26198 | ||||||||
\(528\) | 1.02944 | 0.0448005 | ||||||||
\(529\) | −22.8284 | −0.992540 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.6863 | 0.550538 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −37.7990 | −1.63726 | ||||||||
\(534\) | 8.65685 | 0.374619 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 42.3137 | 1.82767 | ||||||||
\(537\) | 4.14214 | 0.178746 | ||||||||
\(538\) | 49.3848 | 2.12913 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.34315 | 0.315706 | 0.157853 | − | 0.987463i | \(-0.449543\pi\) | ||||
0.157853 | + | 0.987463i | \(0.449543\pi\) | |||||||
\(542\) | 39.7990 | 1.70951 | ||||||||
\(543\) | 1.10051 | 0.0472272 | ||||||||
\(544\) | 7.65685 | 0.328285 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.8995 | −1.06463 | −0.532313 | − | 0.846548i | \(-0.678677\pi\) | ||||
−0.532313 | + | 0.846548i | \(0.678677\pi\) | |||||||
\(548\) | 36.9706 | 1.57930 | ||||||||
\(549\) | 15.5147 | 0.662152 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.82843 | 0.120495 | ||||||||
\(552\) | −0.757359 | −0.0322354 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 38.9706 | 1.65570 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 61.7990 | 2.62086 | ||||||||
\(557\) | −22.2843 | −0.944215 | −0.472107 | − | 0.881541i | \(-0.656507\pi\) | ||||
−0.472107 | + | 0.881541i | \(0.656507\pi\) | |||||||
\(558\) | 40.9706 | 1.73442 | ||||||||
\(559\) | 17.3137 | 0.732292 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.65685 | 0.0699524 | ||||||||
\(562\) | 73.1127 | 3.08407 | ||||||||
\(563\) | 41.7279 | 1.75862 | 0.879311 | − | 0.476248i | \(-0.158003\pi\) | ||||
0.879311 | + | 0.476248i | \(0.158003\pi\) | |||||||
\(564\) | −3.17157 | −0.133547 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −33.7990 | −1.42068 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −19.7990 | −0.830747 | ||||||||
\(569\) | 7.65685 | 0.320992 | 0.160496 | − | 0.987036i | \(-0.448691\pi\) | ||||
0.160496 | + | 0.987036i | \(0.448691\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.17157 | 0.383818 | 0.191909 | − | 0.981413i | \(-0.438532\pi\) | ||||
0.191909 | + | 0.981413i | \(0.438532\pi\) | |||||||
\(572\) | 15.3137 | 0.640298 | ||||||||
\(573\) | 5.31371 | 0.221983 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 27.7990 | 1.15829 | ||||||||
\(577\) | −43.9411 | −1.82929 | −0.914646 | − | 0.404255i | \(-0.867531\pi\) | ||||
−0.914646 | + | 0.404255i | \(0.867531\pi\) | |||||||
\(578\) | −15.2426 | −0.634010 | ||||||||
\(579\) | −0.828427 | −0.0344283 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 11.6569 | 0.483192 | ||||||||
\(583\) | −0.970563 | −0.0401966 | ||||||||
\(584\) | 3.65685 | 0.151322 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 38.6274 | 1.59568 | ||||||||
\(587\) | −34.2843 | −1.41506 | −0.707532 | − | 0.706682i | \(-0.750191\pi\) | ||||
−0.707532 | + | 0.706682i | \(0.750191\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.9706 | −0.699260 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.11270 | −0.210308 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.20101 | 0.172515 | 0.0862574 | − | 0.996273i | \(-0.472509\pi\) | ||||
0.0862574 | + | 0.996273i | \(0.472509\pi\) | |||||||
\(594\) | 4.82843 | 0.198113 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.31371 | −0.340543 | ||||||||
\(597\) | −4.00000 | −0.163709 | ||||||||
\(598\) | −4.82843 | −0.197449 | ||||||||
\(599\) | 6.34315 | 0.259174 | 0.129587 | − | 0.991568i | \(-0.458635\pi\) | ||||
0.129587 | + | 0.991568i | \(0.458635\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.6569 | −0.801820 | −0.400910 | − | 0.916117i | \(-0.631306\pi\) | ||||
−0.400910 | + | 0.916117i | \(0.631306\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 27.1127 | 1.10411 | ||||||||
\(604\) | 44.6274 | 1.81586 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.3137 | 0.418966 | ||||||||
\(607\) | 38.2132 | 1.55103 | 0.775513 | − | 0.631332i | \(-0.217491\pi\) | ||||
0.775513 | + | 0.631332i | \(0.217491\pi\) | |||||||
\(608\) | −4.48528 | −0.181902 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.65685 | −0.390675 | ||||||||
\(612\) | −52.2843 | −2.11347 | ||||||||
\(613\) | −35.4558 | −1.43205 | −0.716024 | − | 0.698076i | \(-0.754040\pi\) | ||||
−0.716024 | + | 0.698076i | \(0.754040\pi\) | |||||||
\(614\) | 11.4853 | 0.463508 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.3137 | −0.455473 | −0.227736 | − | 0.973723i | \(-0.573132\pi\) | ||||
−0.227736 | + | 0.973723i | \(0.573132\pi\) | |||||||
\(618\) | −2.41421 | −0.0971139 | ||||||||
\(619\) | −25.5147 | −1.02552 | −0.512762 | − | 0.858531i | \(-0.671378\pi\) | ||||
−0.512762 | + | 0.858531i | \(0.671378\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −31.7990 | −1.27502 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.00000 | 0.240192 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 15.3137 | 0.612059 | ||||||||
\(627\) | −0.970563 | −0.0387605 | ||||||||
\(628\) | 66.2843 | 2.64503 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.1421 | −0.801846 | −0.400923 | − | 0.916112i | \(-0.631310\pi\) | ||||
−0.400923 | + | 0.916112i | \(0.631310\pi\) | |||||||
\(632\) | −65.4558 | −2.60369 | ||||||||
\(633\) | −8.48528 | −0.337260 | ||||||||
\(634\) | −33.3137 | −1.32306 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.85786 | −0.0736691 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.00000 | −0.0791808 | ||||||||
\(639\) | −12.6863 | −0.501862 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.4853 | 1.24359 | 0.621797 | − | 0.783179i | \(-0.286403\pi\) | ||||
0.621797 | + | 0.783179i | \(0.286403\pi\) | |||||||
\(642\) | −11.2426 | −0.443712 | ||||||||
\(643\) | 26.2843 | 1.03655 | 0.518275 | − | 0.855214i | \(-0.326574\pi\) | ||||
0.518275 | + | 0.855214i | \(0.326574\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 32.9706 | 1.29721 | ||||||||
\(647\) | −31.0416 | −1.22037 | −0.610186 | − | 0.792258i | \(-0.708905\pi\) | ||||
−0.610186 | + | 0.792258i | \(0.708905\pi\) | |||||||
\(648\) | −33.0416 | −1.29800 | ||||||||
\(649\) | 3.71573 | 0.145855 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −47.2548 | −1.85064 | ||||||||
\(653\) | 19.1716 | 0.750242 | 0.375121 | − | 0.926976i | \(-0.377601\pi\) | ||||
0.375121 | + | 0.926976i | \(0.377601\pi\) | |||||||
\(654\) | −13.4853 | −0.527316 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 23.4853 | 0.916946 | ||||||||
\(657\) | 2.34315 | 0.0914148 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.1716 | 0.824727 | 0.412364 | − | 0.911019i | \(-0.364703\pi\) | ||||
0.412364 | + | 0.911019i | \(0.364703\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.8284 | −1.23798 | −0.618991 | − | 0.785398i | \(-0.712458\pi\) | ||||
−0.618991 | + | 0.785398i | \(0.712458\pi\) | |||||||
\(662\) | −55.4558 | −2.15535 | ||||||||
\(663\) | 9.65685 | 0.375041 | ||||||||
\(664\) | −60.5980 | −2.35166 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.414214 | 0.0160384 | ||||||||
\(668\) | 85.8112 | 3.32013 | ||||||||
\(669\) | −0.142136 | −0.00549528 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.54416 | 0.175425 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.6569 | −1.14319 | −0.571594 | − | 0.820537i | \(-0.693675\pi\) | ||||
−0.571594 | + | 0.820537i | \(0.693675\pi\) | |||||||
\(674\) | 22.1421 | 0.852883 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 39.4853 | 1.51866 | ||||||||
\(677\) | −28.1421 | −1.08159 | −0.540795 | − | 0.841154i | \(-0.681877\pi\) | ||||
−0.540795 | + | 0.841154i | \(0.681877\pi\) | |||||||
\(678\) | 4.48528 | 0.172256 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.88730 | 0.110642 | ||||||||
\(682\) | 12.0000 | 0.459504 | ||||||||
\(683\) | 34.7574 | 1.32995 | 0.664977 | − | 0.746864i | \(-0.268441\pi\) | ||||
0.664977 | + | 0.746864i | \(0.268441\pi\) | |||||||
\(684\) | 30.6274 | 1.17107 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.82843 | −0.184216 | ||||||||
\(688\) | −10.7574 | −0.410120 | ||||||||
\(689\) | −5.65685 | −0.215509 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.828427 | −0.0315149 | −0.0157574 | − | 0.999876i | \(-0.505016\pi\) | ||||
−0.0157574 | + | 0.999876i | \(0.505016\pi\) | |||||||
\(692\) | 12.6863 | 0.482260 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.1421 | 0.726626 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.82843 | −0.0693064 | ||||||||
\(697\) | 37.7990 | 1.43174 | ||||||||
\(698\) | −37.0416 | −1.40205 | ||||||||
\(699\) | −6.97056 | −0.263651 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.20101 | −0.120900 | −0.0604502 | − | 0.998171i | \(-0.519254\pi\) | ||||
−0.0604502 | + | 0.998171i | \(0.519254\pi\) | |||||||
\(702\) | 28.1421 | 1.06216 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 8.14214 | 0.306868 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 64.7696 | 2.43763 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 7.11270 | 0.267312 | ||||||||
\(709\) | 15.6863 | 0.589111 | 0.294556 | − | 0.955634i | \(-0.404828\pi\) | ||||
0.294556 | + | 0.955634i | \(0.404828\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −41.9411 | −1.57292 | ||||||||
\(712\) | −38.2132 | −1.43210 | ||||||||
\(713\) | −2.48528 | −0.0930745 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −38.2843 | −1.43075 | ||||||||
\(717\) | 8.82843 | 0.329704 | ||||||||
\(718\) | 24.1421 | 0.900976 | ||||||||
\(719\) | −21.1127 | −0.787371 | −0.393685 | − | 0.919245i | \(-0.628800\pi\) | ||||
−0.393685 | + | 0.919245i | \(0.628800\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 26.5563 | 0.988325 | ||||||||
\(723\) | 11.4558 | 0.426047 | ||||||||
\(724\) | −10.1716 | −0.378024 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −10.3137 | −0.382778 | ||||||||
\(727\) | −37.5858 | −1.39398 | −0.696990 | − | 0.717081i | \(-0.745478\pi\) | ||||
−0.696990 | + | 0.717081i | \(0.745478\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.3137 | −0.640371 | ||||||||
\(732\) | 8.69848 | 0.321505 | ||||||||
\(733\) | −22.0000 | −0.812589 | −0.406294 | − | 0.913742i | \(-0.633179\pi\) | ||||
−0.406294 | + | 0.913742i | \(0.633179\pi\) | |||||||
\(734\) | 6.65685 | 0.245709 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.656854 | −0.0242120 | ||||||||
\(737\) | 7.94113 | 0.292515 | ||||||||
\(738\) | 53.4558 | 1.96774 | ||||||||
\(739\) | −21.1127 | −0.776643 | −0.388322 | − | 0.921524i | \(-0.626945\pi\) | ||||
−0.388322 | + | 0.921524i | \(0.626945\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.65685 | −0.207810 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.0711 | 0.589590 | 0.294795 | − | 0.955560i | \(-0.404749\pi\) | ||||
0.294795 | + | 0.955560i | \(0.404749\pi\) | |||||||
\(744\) | 10.9706 | 0.402200 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −50.6274 | −1.85360 | ||||||||
\(747\) | −38.8284 | −1.42066 | ||||||||
\(748\) | −15.3137 | −0.559925 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.3431 | −1.10724 | −0.553619 | − | 0.832770i | \(-0.686753\pi\) | ||||
−0.553619 | + | 0.832770i | \(0.686753\pi\) | |||||||
\(752\) | 6.00000 | 0.218797 | ||||||||
\(753\) | −3.85786 | −0.140588 | ||||||||
\(754\) | −11.6569 | −0.424518 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.4558 | 1.14328 | 0.571641 | − | 0.820504i | \(-0.306307\pi\) | ||||
0.571641 | + | 0.820504i | \(0.306307\pi\) | |||||||
\(758\) | −64.7696 | −2.35254 | ||||||||
\(759\) | −0.142136 | −0.00515920 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.31371 | −0.337622 | −0.168811 | − | 0.985648i | \(-0.553993\pi\) | ||||
−0.168811 | + | 0.985648i | \(0.553993\pi\) | |||||||
\(762\) | 9.31371 | 0.337400 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −49.1127 | −1.77684 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.00000 | 0.252920 | ||||||||
\(767\) | 21.6569 | 0.781984 | ||||||||
\(768\) | 12.4142 | 0.447959 | ||||||||
\(769\) | 0.627417 | 0.0226252 | 0.0113126 | − | 0.999936i | \(-0.496399\pi\) | ||||
0.0113126 | + | 0.999936i | \(0.496399\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.62742 | −0.0946241 | ||||||||
\(772\) | 7.65685 | 0.275576 | ||||||||
\(773\) | −37.1127 | −1.33485 | −0.667425 | − | 0.744677i | \(-0.732604\pi\) | ||||
−0.667425 | + | 0.744677i | \(0.732604\pi\) | |||||||
\(774\) | −24.4853 | −0.880105 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −51.4558 | −1.84716 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −57.1127 | −2.04759 | ||||||||
\(779\) | −22.1421 | −0.793324 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.71573 | −0.132959 | ||||||||
\(782\) | 4.82843 | 0.172664 | ||||||||
\(783\) | −2.41421 | −0.0862770 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 19.3137 | 0.688897 | ||||||||
\(787\) | 2.55635 | 0.0911240 | 0.0455620 | − | 0.998962i | \(-0.485492\pi\) | ||||
0.0455620 | + | 0.998962i | \(0.485492\pi\) | |||||||
\(788\) | 47.2548 | 1.68338 | ||||||||
\(789\) | −12.0294 | −0.428259 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −10.3431 | −0.367528 | ||||||||
\(793\) | 26.4853 | 0.940520 | ||||||||
\(794\) | 40.1421 | 1.42459 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 36.9706 | 1.31039 | ||||||||
\(797\) | −8.00000 | −0.283375 | −0.141687 | − | 0.989911i | \(-0.545253\pi\) | ||||
−0.141687 | + | 0.989911i | \(0.545253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.65685 | 0.341635 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.4853 | −0.865145 | ||||||||
\(802\) | −73.1838 | −2.58421 | ||||||||
\(803\) | 0.686292 | 0.0242187 | ||||||||
\(804\) | 15.2010 | 0.536098 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 69.9411 | 2.46357 | ||||||||
\(807\) | 8.47309 | 0.298267 | ||||||||
\(808\) | −45.5269 | −1.60163 | ||||||||
\(809\) | 35.6274 | 1.25259 | 0.626297 | − | 0.779585i | \(-0.284570\pi\) | ||||
0.626297 | + | 0.779585i | \(0.284570\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.6274 | 0.724327 | 0.362163 | − | 0.932115i | \(-0.382038\pi\) | ||||
0.362163 | + | 0.932115i | \(0.382038\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.82843 | 0.239483 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.00000 | −0.210042 | ||||||||
\(817\) | 10.1421 | 0.354828 | ||||||||
\(818\) | −35.7279 | −1.24920 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.9411 | 1.67316 | 0.836578 | − | 0.547847i | \(-0.184552\pi\) | ||||
0.836578 | + | 0.547847i | \(0.184552\pi\) | |||||||
\(822\) | 9.65685 | 0.336821 | ||||||||
\(823\) | −2.07107 | −0.0721929 | −0.0360964 | − | 0.999348i | \(-0.511492\pi\) | ||||
−0.0360964 | + | 0.999348i | \(0.511492\pi\) | |||||||
\(824\) | 10.6569 | 0.371249 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.2132 | 0.911522 | 0.455761 | − | 0.890102i | \(-0.349367\pi\) | ||||
0.455761 | + | 0.890102i | \(0.349367\pi\) | |||||||
\(828\) | 4.48528 | 0.155874 | ||||||||
\(829\) | −29.3137 | −1.01811 | −0.509054 | − | 0.860735i | \(-0.670005\pi\) | ||||
−0.509054 | + | 0.860735i | \(0.670005\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.68629 | 0.231945 | ||||||||
\(832\) | 47.4558 | 1.64524 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 16.1421 | 0.558956 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.97056 | 0.310253 | ||||||||
\(837\) | 14.4853 | 0.500685 | ||||||||
\(838\) | −1.65685 | −0.0572351 | ||||||||
\(839\) | −15.1716 | −0.523781 | −0.261890 | − | 0.965098i | \(-0.584346\pi\) | ||||
−0.261890 | + | 0.965098i | \(0.584346\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | −32.5563 | −1.12197 | ||||||||
\(843\) | 12.5442 | 0.432044 | ||||||||
\(844\) | 78.4264 | 2.69955 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 13.6569 | 0.469532 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.51472 | 0.120696 | ||||||||
\(849\) | −5.79899 | −0.199021 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −7.11270 | −0.243677 | ||||||||
\(853\) | 2.54416 | 0.0871102 | 0.0435551 | − | 0.999051i | \(-0.486132\pi\) | ||||
0.0435551 | + | 0.999051i | \(0.486132\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 49.6274 | 1.69623 | ||||||||
\(857\) | 34.2843 | 1.17113 | 0.585564 | − | 0.810626i | \(-0.300873\pi\) | ||||
0.585564 | + | 0.810626i | \(0.300873\pi\) | |||||||
\(858\) | 4.00000 | 0.136558 | ||||||||
\(859\) | −1.37258 | −0.0468319 | −0.0234160 | − | 0.999726i | \(-0.507454\pi\) | ||||
−0.0234160 | + | 0.999726i | \(0.507454\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −42.9706 | −1.46358 | ||||||||
\(863\) | −14.5563 | −0.495504 | −0.247752 | − | 0.968823i | \(-0.579692\pi\) | ||||
−0.247752 | + | 0.968823i | \(0.579692\pi\) | |||||||
\(864\) | 3.82843 | 0.130246 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −18.8284 | −0.639816 | ||||||||
\(867\) | −2.61522 | −0.0888177 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.2843 | −0.416715 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.2843 | 1.56828 | ||||||||
\(872\) | 59.5269 | 2.01584 | ||||||||
\(873\) | −32.9706 | −1.11588 | ||||||||
\(874\) | −2.82843 | −0.0956730 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.31371 | 0.0443861 | ||||||||
\(877\) | −25.1716 | −0.849984 | −0.424992 | − | 0.905197i | \(-0.639723\pi\) | ||||
−0.424992 | + | 0.905197i | \(0.639723\pi\) | |||||||
\(878\) | −81.9411 | −2.76538 | ||||||||
\(879\) | 6.62742 | 0.223537 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.82843 | −0.0616013 | −0.0308006 | − | 0.999526i | \(-0.509806\pi\) | ||||
−0.0308006 | + | 0.999526i | \(0.509806\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.2843 | −0.615315 | −0.307657 | − | 0.951497i | \(-0.599545\pi\) | ||||
−0.307657 | + | 0.951497i | \(0.599545\pi\) | |||||||
\(884\) | −89.2548 | −3.00196 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 72.9411 | 2.45051 | ||||||||
\(887\) | 29.9289 | 1.00492 | 0.502458 | − | 0.864602i | \(-0.332429\pi\) | ||||
0.502458 | + | 0.864602i | \(0.332429\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.20101 | −0.207742 | ||||||||
\(892\) | 1.31371 | 0.0439862 | ||||||||
\(893\) | −5.65685 | −0.189299 | ||||||||
\(894\) | −2.17157 | −0.0726283 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.828427 | −0.0276604 | ||||||||
\(898\) | −9.24264 | −0.308431 | ||||||||
\(899\) | −6.00000 | −0.200111 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.65685 | 0.188457 | ||||||||
\(902\) | 15.6569 | 0.521316 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.7990 | −0.658505 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 11.6569 | 0.387273 | ||||||||
\(907\) | 14.2132 | 0.471942 | 0.235971 | − | 0.971760i | \(-0.424173\pi\) | ||||
0.235971 | + | 0.971760i | \(0.424173\pi\) | |||||||
\(908\) | −26.6863 | −0.885616 | ||||||||
\(909\) | −29.1716 | −0.967560 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.2010 | −0.337975 | −0.168987 | − | 0.985618i | \(-0.554050\pi\) | ||||
−0.168987 | + | 0.985618i | \(0.554050\pi\) | |||||||
\(912\) | 3.51472 | 0.116384 | ||||||||
\(913\) | −11.3726 | −0.376378 | ||||||||
\(914\) | 58.6274 | 1.93922 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 44.6274 | 1.47453 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −28.1421 | −0.928829 | ||||||||
\(919\) | −43.1127 | −1.42216 | −0.711078 | − | 0.703113i | \(-0.751793\pi\) | ||||
−0.711078 | + | 0.703113i | \(0.751793\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.97056 | 0.0649323 | ||||||||
\(922\) | 99.7401 | 3.28477 | ||||||||
\(923\) | −21.6569 | −0.712844 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −89.4264 | −2.93873 | ||||||||
\(927\) | 6.82843 | 0.224275 | ||||||||
\(928\) | −1.58579 | −0.0520560 | ||||||||
\(929\) | −5.48528 | −0.179966 | −0.0899831 | − | 0.995943i | \(-0.528681\pi\) | ||||
−0.0899831 | + | 0.995943i | \(0.528681\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 64.4264 | 2.11036 | ||||||||
\(933\) | −5.45584 | −0.178616 | ||||||||
\(934\) | 7.48528 | 0.244926 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −60.2843 | −1.97045 | ||||||||
\(937\) | 34.6274 | 1.13123 | 0.565614 | − | 0.824670i | \(-0.308639\pi\) | ||||
0.565614 | + | 0.824670i | \(0.308639\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.62742 | 0.0857425 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.2843 | 1.50882 | 0.754412 | − | 0.656401i | \(-0.227922\pi\) | ||||
0.754412 | + | 0.656401i | \(0.227922\pi\) | |||||||
\(942\) | 17.3137 | 0.564111 | ||||||||
\(943\) | −3.24264 | −0.105595 | ||||||||
\(944\) | −13.4558 | −0.437950 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.17157 | −0.233168 | ||||||||
\(947\) | −33.1838 | −1.07833 | −0.539164 | − | 0.842201i | \(-0.681260\pi\) | ||||
−0.539164 | + | 0.842201i | \(0.681260\pi\) | |||||||
\(948\) | −23.5147 | −0.763723 | ||||||||
\(949\) | 4.00000 | 0.129845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.71573 | −0.185345 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.6569 | 0.442389 | 0.221194 | − | 0.975230i | \(-0.429004\pi\) | ||||
0.221194 | + | 0.975230i | \(0.429004\pi\) | |||||||
\(954\) | 8.00000 | 0.259010 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −81.5980 | −2.63907 | ||||||||
\(957\) | −0.343146 | −0.0110923 | ||||||||
\(958\) | −86.0833 | −2.78122 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 31.7990 | 1.02471 | ||||||||
\(964\) | −105.882 | −3.41024 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.5269 | −1.20678 | −0.603392 | − | 0.797445i | \(-0.706185\pi\) | ||||
−0.603392 | + | 0.797445i | \(0.706185\pi\) | |||||||
\(968\) | 45.5269 | 1.46329 | ||||||||
\(969\) | 5.65685 | 0.181724 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.0000 | 0.770197 | 0.385098 | − | 0.922876i | \(-0.374168\pi\) | ||||
0.385098 | + | 0.922876i | \(0.374168\pi\) | |||||||
\(972\) | −39.5980 | −1.27011 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 10.4853 | 0.335970 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.4558 | −0.526739 | ||||||||
\(977\) | 1.31371 | 0.0420293 | 0.0210146 | − | 0.999779i | \(-0.493310\pi\) | ||||
0.0210146 | + | 0.999779i | \(0.493310\pi\) | |||||||
\(978\) | −12.3431 | −0.394690 | ||||||||
\(979\) | −7.17157 | −0.229204 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 38.1421 | 1.21778 | ||||||||
\(982\) | −22.4853 | −0.717534 | ||||||||
\(983\) | 28.2132 | 0.899861 | 0.449931 | − | 0.893063i | \(-0.351449\pi\) | ||||
0.449931 | + | 0.893063i | \(0.351449\pi\) | |||||||
\(984\) | 14.3137 | 0.456304 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11.6569 | 0.371230 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 52.2843 | 1.66338 | ||||||||
\(989\) | 1.48528 | 0.0472292 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.34315 | −0.137965 | −0.0689823 | − | 0.997618i | \(-0.521975\pi\) | ||||
−0.0689823 | + | 0.997618i | \(0.521975\pi\) | |||||||
\(992\) | 9.51472 | 0.302093 | ||||||||
\(993\) | −9.51472 | −0.301940 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −21.7696 | −0.689795 | ||||||||
\(997\) | 33.4558 | 1.05956 | 0.529779 | − | 0.848136i | \(-0.322275\pi\) | ||||
0.529779 | + | 0.848136i | \(0.322275\pi\) | |||||||
\(998\) | 2.00000 | 0.0633089 | ||||||||
\(999\) | 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 | 1225.2.a.m.1.1 | 2 | ||
5.2 | odd | 4 | 1225.2.b.h.99.1 | 4 | |||
5.3 | odd | 4 | 1225.2.b.h.99.4 | 4 | |||
5.4 | even | 2 | 245.2.a.g.1.2 | 2 | |||
7.3 | odd | 6 | 175.2.e.c.51.2 | 4 | |||
7.5 | odd | 6 | 175.2.e.c.151.2 | 4 | |||
7.6 | odd | 2 | 1225.2.a.k.1.1 | 2 | |||
15.14 | odd | 2 | 2205.2.a.q.1.1 | 2 | |||
20.19 | odd | 2 | 3920.2.a.bv.1.1 | 2 | |||
35.3 | even | 12 | 175.2.k.a.149.1 | 8 | |||
35.4 | even | 6 | 245.2.e.e.226.1 | 4 | |||
35.9 | even | 6 | 245.2.e.e.116.1 | 4 | |||
35.12 | even | 12 | 175.2.k.a.74.1 | 8 | |||
35.13 | even | 4 | 1225.2.b.g.99.4 | 4 | |||
35.17 | even | 12 | 175.2.k.a.149.4 | 8 | |||
35.19 | odd | 6 | 35.2.e.a.11.1 | ✓ | 4 | ||
35.24 | odd | 6 | 35.2.e.a.16.1 | yes | 4 | ||
35.27 | even | 4 | 1225.2.b.g.99.1 | 4 | |||
35.33 | even | 12 | 175.2.k.a.74.4 | 8 | |||
35.34 | odd | 2 | 245.2.a.h.1.2 | 2 | |||
105.59 | even | 6 | 315.2.j.e.226.2 | 4 | |||
105.89 | even | 6 | 315.2.j.e.46.2 | 4 | |||
105.104 | even | 2 | 2205.2.a.n.1.1 | 2 | |||
140.19 | even | 6 | 560.2.q.k.81.1 | 4 | |||
140.59 | even | 6 | 560.2.q.k.401.1 | 4 | |||
140.139 | even | 2 | 3920.2.a.bq.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.e.a.11.1 | ✓ | 4 | 35.19 | odd | 6 | ||
35.2.e.a.16.1 | yes | 4 | 35.24 | odd | 6 | ||
175.2.e.c.51.2 | 4 | 7.3 | odd | 6 | |||
175.2.e.c.151.2 | 4 | 7.5 | odd | 6 | |||
175.2.k.a.74.1 | 8 | 35.12 | even | 12 | |||
175.2.k.a.74.4 | 8 | 35.33 | even | 12 | |||
175.2.k.a.149.1 | 8 | 35.3 | even | 12 | |||
175.2.k.a.149.4 | 8 | 35.17 | even | 12 | |||
245.2.a.g.1.2 | 2 | 5.4 | even | 2 | |||
245.2.a.h.1.2 | 2 | 35.34 | odd | 2 | |||
245.2.e.e.116.1 | 4 | 35.9 | even | 6 | |||
245.2.e.e.226.1 | 4 | 35.4 | even | 6 | |||
315.2.j.e.46.2 | 4 | 105.89 | even | 6 | |||
315.2.j.e.226.2 | 4 | 105.59 | even | 6 | |||
560.2.q.k.81.1 | 4 | 140.19 | even | 6 | |||
560.2.q.k.401.1 | 4 | 140.59 | even | 6 | |||
1225.2.a.k.1.1 | 2 | 7.6 | odd | 2 | |||
1225.2.a.m.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1225.2.b.g.99.1 | 4 | 35.27 | even | 4 | |||
1225.2.b.g.99.4 | 4 | 35.13 | even | 4 | |||
1225.2.b.h.99.1 | 4 | 5.2 | odd | 4 | |||
1225.2.b.h.99.4 | 4 | 5.3 | odd | 4 | |||
2205.2.a.n.1.1 | 2 | 105.104 | even | 2 | |||
2205.2.a.q.1.1 | 2 | 15.14 | odd | 2 | |||
3920.2.a.bq.1.2 | 2 | 140.139 | even | 2 | |||
3920.2.a.bv.1.1 | 2 | 20.19 | odd | 2 |