Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,2,Mod(1,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, 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("2205.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.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: | \(17.6070136457\) |
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 | \(\chi\) | \(=\) | 2205.1 |
$q$-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 | 0 | ||||||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4.41421 | −1.56066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.41421 | −0.763441 | ||||||||
\(11\) | 0.828427 | 0.249780 | 0.124890 | − | 0.992171i | \(-0.460142\pi\) | ||||
0.124890 | + | 0.992171i | \(0.460142\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.82843 | 1.33916 | 0.669582 | − | 0.742738i | \(-0.266473\pi\) | ||||
0.669582 | + | 0.742738i | \(0.266473\pi\) | |||||||
\(14\) | 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 | \(0.300885\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.82843 | −0.648886 | −0.324443 | − | 0.945905i | \(-0.605177\pi\) | ||||
−0.324443 | + | 0.945905i | \(0.605177\pi\) | |||||||
\(20\) | 3.82843 | 0.856062 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | −0.414214 | −0.0863695 | −0.0431847 | − | 0.999067i | \(-0.513750\pi\) | ||||
−0.0431847 | + | 0.999067i | \(0.513750\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −11.6569 | −2.28610 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 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 | 0 | ||||||||
\(34\) | −11.6569 | −1.99913 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(38\) | 6.82843 | 1.10772 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.41421 | −0.697948 | ||||||||
\(41\) | −7.82843 | −1.22259 | −0.611297 | − | 0.791401i | \(-0.709352\pi\) | ||||
−0.611297 | + | 0.791401i | \(0.709352\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.58579 | 0.546827 | 0.273414 | − | 0.961897i | \(-0.411847\pi\) | ||||
0.273414 | + | 0.961897i | \(0.411847\pi\) | |||||||
\(44\) | 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 | \(0.453403\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.41421 | −0.341421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 18.4853 | 2.56345 | ||||||||
\(53\) | 1.17157 | 0.160928 | 0.0804640 | − | 0.996758i | \(-0.474360\pi\) | ||||
0.0804640 | + | 0.996758i | \(0.474360\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.828427 | 0.111705 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.41421 | −0.317002 | ||||||||
\(59\) | 4.48528 | 0.583934 | 0.291967 | − | 0.956428i | \(-0.405690\pi\) | ||||
0.291967 | + | 0.956428i | \(0.405690\pi\) | |||||||
\(60\) | 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 | ||||||||
\(65\) | 4.82843 | 0.598893 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.58579 | 1.17109 | 0.585545 | − | 0.810640i | \(-0.300881\pi\) | ||||
0.585545 | + | 0.810640i | \(0.300881\pi\) | |||||||
\(68\) | 18.4853 | 2.24167 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.48528 | −0.532305 | −0.266152 | − | 0.963931i | \(-0.585752\pi\) | ||||
−0.266152 | + | 0.963931i | \(0.585752\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.828427 | 0.0969601 | 0.0484800 | − | 0.998824i | \(-0.484562\pi\) | ||||
0.0484800 | + | 0.998824i | \(0.484562\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.8284 | −1.24211 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.8284 | 1.66833 | 0.834164 | − | 0.551516i | \(-0.185951\pi\) | ||||
0.834164 | + | 0.551516i | \(0.185951\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 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 | ||||||||
\(85\) | 4.82843 | 0.523716 | ||||||||
\(86\) | −8.65685 | −0.933493 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.65685 | −0.389822 | ||||||||
\(89\) | −8.65685 | −0.917625 | −0.458812 | − | 0.888533i | \(-0.651725\pi\) | ||||
−0.458812 | + | 0.888533i | \(0.651725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.58579 | −0.165330 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.82843 | −0.498014 | ||||||||
\(95\) | −2.82843 | −0.290191 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.6569 | −1.18357 | −0.591787 | − | 0.806094i | \(-0.701577\pi\) | ||||
−0.591787 | + | 0.806094i | \(0.701577\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.82843 | 0.382843 | ||||||||
\(101\) | −10.3137 | −1.02625 | −0.513126 | − | 0.858313i | \(-0.671513\pi\) | ||||
−0.513126 | + | 0.858313i | \(0.671513\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.41421 | 0.237880 | 0.118940 | − | 0.992901i | \(-0.462050\pi\) | ||||
0.118940 | + | 0.992901i | \(0.462050\pi\) | |||||||
\(104\) | −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 | \(0.682876\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.4853 | −1.29166 | −0.645828 | − | 0.763483i | \(-0.723488\pi\) | ||||
−0.645828 | + | 0.763483i | \(0.723488\pi\) | |||||||
\(110\) | −2.00000 | −0.190693 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.48528 | 0.421940 | 0.210970 | − | 0.977493i | \(-0.432338\pi\) | ||||
0.210970 | + | 0.977493i | \(0.432338\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.414214 | −0.0386256 | ||||||||
\(116\) | 3.82843 | 0.355461 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.8284 | −0.996838 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3137 | −0.937610 | ||||||||
\(122\) | 13.2426 | 1.19893 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 22.9706 | 2.06282 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.31371 | −0.826458 | −0.413229 | − | 0.910627i | \(-0.635599\pi\) | ||||
−0.413229 | + | 0.910627i | \(0.635599\pi\) | |||||||
\(128\) | 20.5563 | 1.81694 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −11.6569 | −1.02237 | ||||||||
\(131\) | −19.3137 | −1.68745 | −0.843723 | − | 0.536778i | \(-0.819641\pi\) | ||||
−0.843723 | + | 0.536778i | \(0.819641\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 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 | 0 | ||||||||
\(139\) | 16.1421 | 1.36916 | 0.684579 | − | 0.728939i | \(-0.259986\pi\) | ||||
0.684579 | + | 0.728939i | \(0.259986\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.8284 | 0.908701 | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.00000 | 0.0830455 | ||||||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.17157 | 0.177902 | 0.0889511 | − | 0.996036i | \(-0.471649\pi\) | ||||
0.0889511 | + | 0.996036i | \(0.471649\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.00000 | 0.481932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.3137 | −1.38178 | −0.690892 | − | 0.722958i | \(-0.742782\pi\) | ||||
−0.690892 | + | 0.722958i | \(0.742782\pi\) | |||||||
\(158\) | −35.7990 | −2.84801 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.58579 | 0.125367 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.3431 | 0.966790 | 0.483395 | − | 0.875402i | \(-0.339404\pi\) | ||||
0.483395 | + | 0.875402i | \(0.339404\pi\) | |||||||
\(164\) | −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 | ||||||||
\(170\) | −11.6569 | −0.894040 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.7279 | 1.04674 | ||||||||
\(173\) | 3.31371 | 0.251937 | 0.125968 | − | 0.992034i | \(-0.459796\pi\) | ||||
0.125968 | + | 0.992034i | \(0.459796\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.48528 | 0.187335 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 20.8995 | 1.56648 | ||||||||
\(179\) | 10.0000 | 0.747435 | 0.373718 | − | 0.927543i | \(-0.378083\pi\) | ||||
0.373718 | + | 0.927543i | \(0.378083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.65685 | −0.197482 | −0.0987412 | − | 0.995113i | \(-0.531482\pi\) | ||||
−0.0987412 | + | 0.995113i | \(0.531482\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.82843 | 0.134793 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | 0.292509 | ||||||||
\(188\) | 7.65685 | 0.558433 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.82843 | 0.495386 | ||||||||
\(191\) | 12.8284 | 0.928232 | 0.464116 | − | 0.885774i | \(-0.346372\pi\) | ||||
0.464116 | + | 0.885774i | \(0.346372\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.00000 | −0.143963 | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | 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 | \(0.355083\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.65685 | 0.684556 | 0.342278 | − | 0.939599i | \(-0.388801\pi\) | ||||
0.342278 | + | 0.939599i | \(0.388801\pi\) | |||||||
\(200\) | −4.41421 | −0.312132 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 24.8995 | 1.75192 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.82843 | −0.546761 | ||||||||
\(206\) | −5.82843 | −0.406086 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 27.1421 | 1.85540 | ||||||||
\(215\) | 3.58579 | 0.244549 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 32.5563 | 2.20499 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.17157 | 0.213827 | ||||||||
\(221\) | 23.3137 | 1.56825 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.343146 | −0.0229787 | −0.0114894 | − | 0.999934i | \(-0.503657\pi\) | ||||
−0.0114894 | + | 0.999934i | \(0.503657\pi\) | |||||||
\(224\) | 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 | \(0.574306\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.6569 | 0.770307 | 0.385153 | − | 0.922853i | \(-0.374149\pi\) | ||||
0.385153 | + | 0.922853i | \(0.374149\pi\) | |||||||
\(230\) | 1.00000 | 0.0659380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.41421 | −0.289807 | ||||||||
\(233\) | 16.8284 | 1.10247 | 0.551233 | − | 0.834351i | \(-0.314157\pi\) | ||||
0.551233 | + | 0.834351i | \(0.314157\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.00000 | 0.130466 | ||||||||
\(236\) | 17.1716 | 1.11777 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.3137 | 1.37867 | 0.689335 | − | 0.724443i | \(-0.257903\pi\) | ||||
0.689335 | + | 0.724443i | \(0.257903\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −21.0000 | −1.34439 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.6569 | −0.868965 | ||||||||
\(248\) | −26.4853 | −1.68182 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.41421 | −0.152688 | ||||||||
\(251\) | −9.31371 | −0.587876 | −0.293938 | − | 0.955824i | \(-0.594966\pi\) | ||||
−0.293938 | + | 0.955824i | \(0.594966\pi\) | |||||||
\(252\) | 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 | \(0.436608\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 18.4853 | 1.14641 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 46.6274 | 2.88065 | ||||||||
\(263\) | 29.0416 | 1.79078 | 0.895392 | − | 0.445279i | \(-0.146896\pi\) | ||||
0.895392 | + | 0.445279i | \(0.146896\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.17157 | 0.0719691 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 36.6985 | 2.24172 | ||||||||
\(269\) | 20.4558 | 1.24721 | 0.623607 | − | 0.781738i | \(-0.285666\pi\) | ||||
0.623607 | + | 0.781738i | \(0.285666\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | 0.828427 | 0.0499560 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.1421 | 0.969887 | 0.484943 | − | 0.874546i | \(-0.338840\pi\) | ||||
0.484943 | + | 0.874546i | \(0.338840\pi\) | |||||||
\(278\) | −38.9706 | −2.33730 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.2843 | 1.80661 | 0.903304 | − | 0.429001i | \(-0.141134\pi\) | ||||
0.903304 | + | 0.429001i | \(0.141134\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.0000 | −0.832214 | −0.416107 | − | 0.909316i | \(-0.636606\pi\) | ||||
−0.416107 | + | 0.909316i | \(0.636606\pi\) | |||||||
\(284\) | −17.1716 | −1.01895 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.65685 | −0.571022 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.31371 | 0.371395 | ||||||||
\(290\) | −2.41421 | −0.141768 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 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 | ||||||||
\(295\) | 4.48528 | 0.261143 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.24264 | −0.303698 | ||||||||
\(299\) | −2.00000 | −0.115663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −28.1421 | −1.61940 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.48528 | −0.486664 | ||||||||
\(305\) | −5.48528 | −0.314086 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.75736 | 0.271517 | 0.135758 | − | 0.990742i | \(-0.456653\pi\) | ||||
0.135758 | + | 0.990742i | \(0.456653\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −14.4853 | −0.822709 | ||||||||
\(311\) | −13.1716 | −0.746891 | −0.373446 | − | 0.927652i | \(-0.621824\pi\) | ||||
−0.373446 | + | 0.927652i | \(0.621824\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.34315 | 0.358536 | 0.179268 | − | 0.983800i | \(-0.442627\pi\) | ||||
0.179268 | + | 0.983800i | \(0.442627\pi\) | |||||||
\(314\) | 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 | \(0.373334\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.828427 | 0.0463830 | ||||||||
\(320\) | −9.82843 | −0.549426 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.6569 | −0.759888 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.82843 | 0.267833 | ||||||||
\(326\) | −29.7990 | −1.65041 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | ||||||||
\(335\) | 9.58579 | 0.523727 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.17157 | 0.499607 | 0.249804 | − | 0.968296i | \(-0.419634\pi\) | ||||
0.249804 | + | 0.968296i | \(0.419634\pi\) | |||||||
\(338\) | −24.8995 | −1.35435 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 18.4853 | 1.00251 | ||||||||
\(341\) | 4.97056 | 0.269171 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 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 | \(0.568266\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.3431 | 0.821300 | 0.410650 | − | 0.911793i | \(-0.365302\pi\) | ||||
0.410650 | + | 0.911793i | \(0.365302\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.31371 | 0.0700209 | ||||||||
\(353\) | −26.8284 | −1.42793 | −0.713967 | − | 0.700180i | \(-0.753103\pi\) | ||||
−0.713967 | + | 0.700180i | \(0.753103\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.48528 | −0.238054 | ||||||||
\(356\) | −33.1421 | −1.75653 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −24.1421 | −1.27595 | ||||||||
\(359\) | 10.0000 | 0.527780 | 0.263890 | − | 0.964553i | \(-0.414994\pi\) | ||||
0.263890 | + | 0.964553i | \(0.414994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 6.41421 | 0.337124 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.828427 | 0.0433619 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.75736 | 0.143933 | 0.0719665 | − | 0.997407i | \(-0.477073\pi\) | ||||
0.0719665 | + | 0.997407i | \(0.477073\pi\) | |||||||
\(368\) | −1.24264 | −0.0647771 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.9706 | −1.08581 | −0.542907 | − | 0.839793i | \(-0.682677\pi\) | ||||
−0.542907 | + | 0.839793i | \(0.682677\pi\) | |||||||
\(374\) | −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 | \(0.258032\pi\) | |||||||
\(380\) | −10.8284 | −0.555487 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −30.9706 | −1.58459 | ||||||||
\(383\) | −2.89949 | −0.148157 | −0.0740786 | − | 0.997252i | \(-0.523602\pi\) | ||||
−0.0740786 | + | 0.997252i | \(0.523602\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.82843 | 0.245760 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −44.6274 | −2.26561 | ||||||||
\(389\) | −23.6569 | −1.19945 | −0.599725 | − | 0.800206i | \(-0.704723\pi\) | ||||
−0.599725 | + | 0.800206i | \(0.704723\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.00000 | −0.101144 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −29.7990 | −1.50125 | ||||||||
\(395\) | 14.8284 | 0.746099 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.6274 | 0.834506 | 0.417253 | − | 0.908790i | \(-0.362993\pi\) | ||||
0.417253 | + | 0.908790i | \(0.362993\pi\) | |||||||
\(398\) | −23.3137 | −1.16861 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | −30.3137 | −1.51379 | −0.756897 | − | 0.653534i | \(-0.773286\pi\) | ||||
−0.756897 | + | 0.653534i | \(0.773286\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.9706 | 1.44313 | ||||||||
\(404\) | −39.4853 | −1.96447 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.7990 | 0.731763 | 0.365881 | − | 0.930661i | \(-0.380768\pi\) | ||||
0.365881 | + | 0.930661i | \(0.380768\pi\) | |||||||
\(410\) | 18.8995 | 0.933380 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.24264 | 0.455352 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.7279 | 0.673877 | ||||||||
\(416\) | 7.65685 | 0.375408 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.65685 | 0.276686 | ||||||||
\(419\) | −0.686292 | −0.0335275 | −0.0167638 | − | 0.999859i | \(-0.505336\pi\) | ||||
−0.0167638 | + | 0.999859i | \(0.505336\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.17157 | −0.251154 | ||||||||
\(425\) | 4.82843 | 0.234213 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −43.0416 | −2.08050 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.65685 | −0.417471 | ||||||||
\(431\) | −17.7990 | −0.857347 | −0.428674 | − | 0.903459i | \(-0.641019\pi\) | ||||
−0.428674 | + | 0.903459i | \(0.641019\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.79899 | −0.374796 | −0.187398 | − | 0.982284i | \(-0.560005\pi\) | ||||
−0.187398 | + | 0.982284i | \(0.560005\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −51.6274 | −2.47250 | ||||||||
\(437\) | 1.17157 | 0.0560439 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.9411 | 1.61992 | 0.809961 | − | 0.586484i | \(-0.199488\pi\) | ||||
0.809961 | + | 0.586484i | \(0.199488\pi\) | |||||||
\(440\) | −3.65685 | −0.174334 | ||||||||
\(441\) | 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 | ||||||||
\(445\) | −8.65685 | −0.410374 | ||||||||
\(446\) | 0.828427 | 0.0392272 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.82843 | −0.180675 | −0.0903373 | − | 0.995911i | \(-0.528795\pi\) | ||||
−0.0903373 | + | 0.995911i | \(0.528795\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.48528 | −0.305380 | ||||||||
\(452\) | 17.1716 | 0.807683 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.8284 | 0.789797 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.2843 | 1.13597 | 0.567985 | − | 0.823039i | \(-0.307723\pi\) | ||||
0.567985 | + | 0.823039i | \(0.307723\pi\) | |||||||
\(458\) | −28.1421 | −1.31500 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.58579 | −0.0739377 | ||||||||
\(461\) | 41.3137 | 1.92417 | 0.962086 | − | 0.272748i | \(-0.0879324\pi\) | ||||
0.962086 | + | 0.272748i | \(0.0879324\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −37.0416 | −1.72147 | −0.860735 | − | 0.509053i | \(-0.829996\pi\) | ||||
−0.860735 | + | 0.509053i | \(0.829996\pi\) | |||||||
\(464\) | 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 | \(0.522854\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.82843 | −0.222719 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −19.7990 | −0.911322 | ||||||||
\(473\) | 2.97056 | 0.136587 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.82843 | −0.129777 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −51.4558 | −2.35354 | ||||||||
\(479\) | −35.6569 | −1.62920 | −0.814602 | − | 0.580021i | \(-0.803044\pi\) | ||||
−0.814602 | + | 0.580021i | \(0.803044\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 66.7696 | 3.04127 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −39.4853 | −1.79479 | ||||||||
\(485\) | −11.6569 | −0.529310 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.34315 | 0.196807 | 0.0984034 | − | 0.995147i | \(-0.468626\pi\) | ||||
0.0984034 | + | 0.995147i | \(0.468626\pi\) | |||||||
\(488\) | 24.2132 | 1.09608 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.31371 | −0.420322 | −0.210161 | − | 0.977667i | \(-0.567399\pi\) | ||||
−0.210161 | + | 0.977667i | \(0.567399\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.82843 | 0.217461 | ||||||||
\(494\) | 32.9706 | 1.48342 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.0000 | 0.808224 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.828427 | −0.0370855 | −0.0185427 | − | 0.999828i | \(-0.505903\pi\) | ||||
−0.0185427 | + | 0.999828i | \(0.505903\pi\) | |||||||
\(500\) | 3.82843 | 0.171212 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 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 | ||||||||
\(505\) | −10.3137 | −0.458954 | ||||||||
\(506\) | 0.828427 | 0.0368281 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −35.6569 | −1.58202 | ||||||||
\(509\) | 13.3431 | 0.591425 | 0.295712 | − | 0.955277i | \(-0.404443\pi\) | ||||
0.295712 | + | 0.955277i | \(0.404443\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 31.2426 | 1.38074 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −15.3137 | −0.675459 | ||||||||
\(515\) | 2.41421 | 0.106383 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.65685 | 0.0728684 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −21.3137 | −0.934668 | ||||||||
\(521\) | 14.9706 | 0.655872 | 0.327936 | − | 0.944700i | \(-0.393647\pi\) | ||||
0.327936 | + | 0.944700i | \(0.393647\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.6569 | −1.55917 | −0.779583 | − | 0.626299i | \(-0.784569\pi\) | ||||
−0.779583 | + | 0.626299i | \(0.784569\pi\) | |||||||
\(524\) | −73.9411 | −3.23013 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −70.1127 | −3.05706 | ||||||||
\(527\) | 28.9706 | 1.26198 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8284 | −0.992540 | ||||||||
\(530\) | −2.82843 | −0.122859 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −37.7990 | −1.63726 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.2426 | −0.486062 | ||||||||
\(536\) | −42.3137 | −1.82767 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.65685 | 0.328285 | ||||||||
\(545\) | −13.4853 | −0.577646 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.8995 | 1.06463 | 0.532313 | − | 0.846548i | \(-0.321323\pi\) | ||||
0.532313 | + | 0.846548i | \(0.321323\pi\) | |||||||
\(548\) | 36.9706 | 1.57930 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.00000 | −0.0852803 | ||||||||
\(551\) | −2.82843 | −0.120495 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 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 | \(0.656507\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.3137 | 0.732292 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −73.1127 | −3.08407 | ||||||||
\(563\) | 41.7279 | 1.75862 | 0.879311 | − | 0.476248i | \(-0.158003\pi\) | ||||
0.879311 | + | 0.476248i | \(0.158003\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.48528 | 0.188697 | ||||||||
\(566\) | 33.7990 | 1.42068 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 19.7990 | 0.830747 | ||||||||
\(569\) | −7.65685 | −0.320992 | −0.160496 | − | 0.987036i | \(-0.551309\pi\) | ||||
−0.160496 | + | 0.987036i | \(0.551309\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.414214 | −0.0172739 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.9411 | 1.82929 | 0.914646 | − | 0.404255i | \(-0.132469\pi\) | ||||
0.914646 | + | 0.404255i | \(0.132469\pi\) | |||||||
\(578\) | −15.2426 | −0.634010 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.82843 | 0.158967 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 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 | ||||||||
\(590\) | −10.8284 | −0.445799 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.20101 | 0.172515 | 0.0862574 | − | 0.996273i | \(-0.472509\pi\) | ||||
0.0862574 | + | 0.996273i | \(0.472509\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.31371 | 0.340543 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.82843 | 0.197449 | ||||||||
\(599\) | −6.34315 | −0.259174 | −0.129587 | − | 0.991568i | \(-0.541365\pi\) | ||||
−0.129587 | + | 0.991568i | \(0.541365\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.6569 | −0.801820 | −0.400910 | − | 0.916117i | \(-0.631306\pi\) | ||||
−0.400910 | + | 0.916117i | \(0.631306\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 44.6274 | 1.81586 | ||||||||
\(605\) | −10.3137 | −0.419312 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.2132 | −1.55103 | −0.775513 | − | 0.631332i | \(-0.782509\pi\) | ||||
−0.775513 | + | 0.631332i | \(0.782509\pi\) | |||||||
\(608\) | −4.48528 | −0.181902 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 13.2426 | 0.536179 | ||||||||
\(611\) | 9.65685 | 0.390675 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.4558 | 1.43205 | 0.716024 | − | 0.698076i | \(-0.245960\pi\) | ||||
0.716024 | + | 0.698076i | \(0.245960\pi\) | |||||||
\(614\) | −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 | \(0.573132\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.5147 | −1.02552 | −0.512762 | − | 0.858531i | \(-0.671378\pi\) | ||||
−0.512762 | + | 0.858531i | \(0.671378\pi\) | |||||||
\(620\) | 22.9706 | 0.922520 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 31.7990 | 1.27502 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −15.3137 | −0.612059 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −33.3137 | −1.32306 | ||||||||
\(635\) | −9.31371 | −0.369603 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.00000 | −0.0791808 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 20.5563 | 0.812561 | ||||||||
\(641\) | −31.4853 | −1.24359 | −0.621797 | − | 0.783179i | \(-0.713597\pi\) | ||||
−0.621797 | + | 0.783179i | \(0.713597\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.2843 | −1.03655 | −0.518275 | − | 0.855214i | \(-0.673426\pi\) | ||||
−0.518275 | + | 0.855214i | \(0.673426\pi\) | |||||||
\(644\) | 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 | \(0.708905\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.71573 | 0.145855 | ||||||||
\(650\) | −11.6569 | −0.457219 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 47.2548 | 1.85064 | ||||||||
\(653\) | 19.1716 | 0.750242 | 0.375121 | − | 0.926976i | \(-0.377601\pi\) | ||||
0.375121 | + | 0.926976i | \(0.377601\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.3137 | −0.754649 | ||||||||
\(656\) | −23.4853 | −0.916946 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.1716 | −0.824727 | −0.412364 | − | 0.911019i | \(-0.635297\pi\) | ||||
−0.412364 | + | 0.911019i | \(0.635297\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −60.5980 | −2.35166 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.414214 | −0.0160384 | ||||||||
\(668\) | 85.8112 | 3.32013 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −23.1421 | −0.894059 | ||||||||
\(671\) | −4.54416 | −0.175425 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.6569 | 1.14319 | 0.571594 | − | 0.820537i | \(-0.306325\pi\) | ||||
0.571594 | + | 0.820537i | \(0.306325\pi\) | |||||||
\(674\) | −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 | \(0.681877\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −21.3137 | −0.817343 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.0000 | −0.459504 | ||||||||
\(683\) | 34.7574 | 1.32995 | 0.664977 | − | 0.746864i | \(-0.268441\pi\) | ||||
0.664977 | + | 0.746864i | \(0.268441\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.65685 | 0.368969 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 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 | ||||||||
\(695\) | 16.1421 | 0.612306 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −37.7990 | −1.43174 | ||||||||
\(698\) | −37.0416 | −1.40205 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.20101 | 0.120900 | 0.0604502 | − | 0.998171i | \(-0.480746\pi\) | ||||
0.0604502 | + | 0.998171i | \(0.480746\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −8.14214 | −0.306868 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 64.7696 | 2.43763 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.6863 | 0.589111 | 0.294556 | − | 0.955634i | \(-0.404828\pi\) | ||||
0.294556 | + | 0.955634i | \(0.404828\pi\) | |||||||
\(710\) | 10.8284 | 0.406384 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 38.2132 | 1.43210 | ||||||||
\(713\) | −2.48528 | −0.0930745 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | 0.149592 | ||||||||
\(716\) | 38.2843 | 1.43075 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −24.1421 | −0.900976 | ||||||||
\(719\) | 21.1127 | 0.787371 | 0.393685 | − | 0.919245i | \(-0.371200\pi\) | ||||
0.393685 | + | 0.919245i | \(0.371200\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 26.5563 | 0.988325 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.1716 | −0.378024 | ||||||||
\(725\) | 1.00000 | 0.0371391 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.5858 | 1.39398 | 0.696990 | − | 0.717081i | \(-0.254522\pi\) | ||||
0.696990 | + | 0.717081i | \(0.254522\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.00000 | −0.0740233 | ||||||||
\(731\) | 17.3137 | 0.640371 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.0000 | 0.812589 | 0.406294 | − | 0.913742i | \(-0.366821\pi\) | ||||
0.406294 | + | 0.913742i | \(0.366821\pi\) | |||||||
\(734\) | −6.65685 | −0.245709 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.656854 | −0.0242120 | ||||||||
\(737\) | 7.94113 | 0.292515 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.1127 | −0.776643 | −0.388322 | − | 0.921524i | \(-0.626945\pi\) | ||||
−0.388322 | + | 0.921524i | \(0.626945\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.0711 | 0.589590 | 0.294795 | − | 0.955560i | \(-0.404749\pi\) | ||||
0.294795 | + | 0.955560i | \(0.404749\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.17157 | 0.0795603 | ||||||||
\(746\) | 50.6274 | 1.85360 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11.6569 | −0.424518 | ||||||||
\(755\) | 11.6569 | 0.424236 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.4558 | −1.14328 | −0.571641 | − | 0.820504i | \(-0.693693\pi\) | ||||
−0.571641 | + | 0.820504i | \(0.693693\pi\) | |||||||
\(758\) | −64.7696 | −2.35254 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.4853 | 0.452889 | ||||||||
\(761\) | 9.31371 | 0.337622 | 0.168811 | − | 0.985648i | \(-0.446007\pi\) | ||||
0.168811 | + | 0.985648i | \(0.446007\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 49.1127 | 1.77684 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.00000 | 0.252920 | ||||||||
\(767\) | 21.6569 | 0.781984 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.627417 | 0.0226252 | 0.0113126 | − | 0.999936i | \(-0.496399\pi\) | ||||
0.0113126 | + | 0.999936i | \(0.496399\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.65685 | −0.275576 | ||||||||
\(773\) | −37.1127 | −1.33485 | −0.667425 | − | 0.744677i | \(-0.732604\pi\) | ||||
−0.667425 | + | 0.744677i | \(0.732604\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.00000 | 0.215526 | ||||||||
\(776\) | 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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.3137 | −0.617953 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.55635 | −0.0911240 | −0.0455620 | − | 0.998962i | \(-0.514508\pi\) | ||||
−0.0455620 | + | 0.998962i | \(0.514508\pi\) | |||||||
\(788\) | 47.2548 | 1.68338 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −35.7990 | −1.27367 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −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 | ||||||||
\(800\) | 1.58579 | 0.0560660 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 73.1838 | 2.58421 | ||||||||
\(803\) | 0.686292 | 0.0242187 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −69.9411 | −2.46357 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 45.5269 | 1.60163 | ||||||||
\(809\) | −35.6274 | −1.25259 | −0.626297 | − | 0.779585i | \(-0.715430\pi\) | ||||
−0.626297 | + | 0.779585i | \(0.715430\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.6274 | 0.724327 | 0.362163 | − | 0.932115i | \(-0.382038\pi\) | ||||
0.362163 | + | 0.932115i | \(0.382038\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.3431 | 0.432362 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.1421 | −0.354828 | ||||||||
\(818\) | −35.7279 | −1.24920 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −29.9706 | −1.04662 | ||||||||
\(821\) | −47.9411 | −1.67316 | −0.836578 | − | 0.547847i | \(-0.815448\pi\) | ||||
−0.836578 | + | 0.547847i | \(0.815448\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.07107 | 0.0721929 | 0.0360964 | − | 0.999348i | \(-0.488508\pi\) | ||||
0.0360964 | + | 0.999348i | \(0.488508\pi\) | |||||||
\(824\) | −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 | \(0.349367\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.3137 | −1.01811 | −0.509054 | − | 0.860735i | \(-0.670005\pi\) | ||||
−0.509054 | + | 0.860735i | \(0.670005\pi\) | |||||||
\(830\) | −33.1421 | −1.15038 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −47.4558 | −1.64524 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.4142 | 0.775676 | ||||||||
\(836\) | −8.97056 | −0.310253 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.65685 | 0.0572351 | ||||||||
\(839\) | 15.1716 | 0.523781 | 0.261890 | − | 0.965098i | \(-0.415654\pi\) | ||||
0.261890 | + | 0.965098i | \(0.415654\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | −32.5563 | −1.12197 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 78.4264 | 2.69955 | ||||||||
\(845\) | 10.3137 | 0.354802 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.51472 | 0.120696 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −11.6569 | −0.399827 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.54416 | −0.0871102 | −0.0435551 | − | 0.999051i | \(-0.513868\pi\) | ||||
−0.0435551 | + | 0.999051i | \(0.513868\pi\) | |||||||
\(854\) | 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 | \(0.300873\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.37258 | −0.0468319 | −0.0234160 | − | 0.999726i | \(-0.507454\pi\) | ||||
−0.0234160 | + | 0.999726i | \(0.507454\pi\) | |||||||
\(860\) | 13.7279 | 0.468118 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 42.9706 | 1.46358 | ||||||||
\(863\) | −14.5563 | −0.495504 | −0.247752 | − | 0.968823i | \(-0.579692\pi\) | ||||
−0.247752 | + | 0.968823i | \(0.579692\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.31371 | 0.112669 | ||||||||
\(866\) | 18.8284 | 0.639816 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.2843 | 0.416715 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.2843 | 1.56828 | ||||||||
\(872\) | 59.5269 | 2.01584 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.82843 | −0.0956730 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.1716 | 0.849984 | 0.424992 | − | 0.905197i | \(-0.360277\pi\) | ||||
0.424992 | + | 0.905197i | \(0.360277\pi\) | |||||||
\(878\) | −81.9411 | −2.76538 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.48528 | 0.0837788 | ||||||||
\(881\) | 1.82843 | 0.0616013 | 0.0308006 | − | 0.999526i | \(-0.490194\pi\) | ||||
0.0308006 | + | 0.999526i | \(0.490194\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.2843 | 0.615315 | 0.307657 | − | 0.951497i | \(-0.400455\pi\) | ||||
0.307657 | + | 0.951497i | \(0.400455\pi\) | |||||||
\(884\) | 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 | ||||||||
\(890\) | 20.8995 | 0.700553 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.31371 | −0.0439862 | ||||||||
\(893\) | −5.65685 | −0.189299 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.0000 | 0.334263 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 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 | ||||||||
\(905\) | −2.65685 | −0.0883168 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.2132 | −0.471942 | −0.235971 | − | 0.971760i | \(-0.575827\pi\) | ||||
−0.235971 | + | 0.971760i | \(0.575827\pi\) | |||||||
\(908\) | −26.6863 | −0.885616 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.2010 | 0.337975 | 0.168987 | − | 0.985618i | \(-0.445950\pi\) | ||||
0.168987 | + | 0.985618i | \(0.445950\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.3726 | 0.376378 | ||||||||
\(914\) | −58.6274 | −1.93922 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 44.6274 | 1.47453 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.1127 | −1.42216 | −0.711078 | − | 0.703113i | \(-0.751793\pi\) | ||||
−0.711078 | + | 0.703113i | \(0.751793\pi\) | |||||||
\(920\) | 1.82843 | 0.0602815 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −99.7401 | −3.28477 | ||||||||
\(923\) | −21.6569 | −0.712844 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 89.4264 | 2.93873 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.58579 | 0.0520560 | ||||||||
\(929\) | 5.48528 | 0.179966 | 0.0899831 | − | 0.995943i | \(-0.471319\pi\) | ||||
0.0899831 | + | 0.995943i | \(0.471319\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 64.4264 | 2.11036 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.48528 | 0.244926 | ||||||||
\(935\) | 4.00000 | 0.130814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.6274 | −1.13123 | −0.565614 | − | 0.824670i | \(-0.691361\pi\) | ||||
−0.565614 | + | 0.824670i | \(0.691361\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.65685 | 0.249739 | ||||||||
\(941\) | −46.2843 | −1.50882 | −0.754412 | − | 0.656401i | \(-0.772078\pi\) | ||||
−0.754412 | + | 0.656401i | \(0.772078\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 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 | \(0.681260\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.00000 | 0.129845 | ||||||||
\(950\) | 6.82843 | 0.221543 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.6569 | 0.442389 | 0.221194 | − | 0.975230i | \(-0.429004\pi\) | ||||
0.221194 | + | 0.975230i | \(0.429004\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.8284 | 0.415118 | ||||||||
\(956\) | 81.5980 | 2.63907 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 86.0833 | 2.78122 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −105.882 | −3.41024 | ||||||||
\(965\) | −2.00000 | −0.0643823 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.5269 | 1.20678 | 0.603392 | − | 0.797445i | \(-0.293815\pi\) | ||||
0.603392 | + | 0.797445i | \(0.293815\pi\) | |||||||
\(968\) | 45.5269 | 1.46329 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 28.1421 | 0.903590 | ||||||||
\(971\) | −24.0000 | −0.770197 | −0.385098 | − | 0.922876i | \(-0.625832\pi\) | ||||
−0.385098 | + | 0.922876i | \(0.625832\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 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 | \(0.493310\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.17157 | −0.229204 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 22.4853 | 0.717534 | ||||||||
\(983\) | 28.2132 | 0.899861 | 0.449931 | − | 0.893063i | \(-0.351449\pi\) | ||||
0.449931 | + | 0.893063i | \(0.351449\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.3431 | 0.393285 | ||||||||
\(986\) | −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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.65685 | 0.306143 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.4558 | −1.05956 | −0.529779 | − | 0.848136i | \(-0.677725\pi\) | ||||
−0.529779 | + | 0.848136i | \(0.677725\pi\) | |||||||
\(998\) | 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 | 2205.2.a.q.1.1 | 2 | ||
3.2 | odd | 2 | 245.2.a.g.1.2 | 2 | |||
7.3 | odd | 6 | 315.2.j.e.226.2 | 4 | |||
7.5 | odd | 6 | 315.2.j.e.46.2 | 4 | |||
7.6 | odd | 2 | 2205.2.a.n.1.1 | 2 | |||
12.11 | even | 2 | 3920.2.a.bv.1.1 | 2 | |||
15.2 | even | 4 | 1225.2.b.h.99.4 | 4 | |||
15.8 | even | 4 | 1225.2.b.h.99.1 | 4 | |||
15.14 | odd | 2 | 1225.2.a.m.1.1 | 2 | |||
21.2 | odd | 6 | 245.2.e.e.116.1 | 4 | |||
21.5 | even | 6 | 35.2.e.a.11.1 | ✓ | 4 | ||
21.11 | odd | 6 | 245.2.e.e.226.1 | 4 | |||
21.17 | even | 6 | 35.2.e.a.16.1 | yes | 4 | ||
21.20 | even | 2 | 245.2.a.h.1.2 | 2 | |||
84.47 | odd | 6 | 560.2.q.k.81.1 | 4 | |||
84.59 | odd | 6 | 560.2.q.k.401.1 | 4 | |||
84.83 | odd | 2 | 3920.2.a.bq.1.2 | 2 | |||
105.17 | odd | 12 | 175.2.k.a.149.1 | 8 | |||
105.38 | odd | 12 | 175.2.k.a.149.4 | 8 | |||
105.47 | odd | 12 | 175.2.k.a.74.4 | 8 | |||
105.59 | even | 6 | 175.2.e.c.51.2 | 4 | |||
105.62 | odd | 4 | 1225.2.b.g.99.4 | 4 | |||
105.68 | odd | 12 | 175.2.k.a.74.1 | 8 | |||
105.83 | odd | 4 | 1225.2.b.g.99.1 | 4 | |||
105.89 | even | 6 | 175.2.e.c.151.2 | 4 | |||
105.104 | even | 2 | 1225.2.a.k.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.e.a.11.1 | ✓ | 4 | 21.5 | even | 6 | ||
35.2.e.a.16.1 | yes | 4 | 21.17 | even | 6 | ||
175.2.e.c.51.2 | 4 | 105.59 | even | 6 | |||
175.2.e.c.151.2 | 4 | 105.89 | even | 6 | |||
175.2.k.a.74.1 | 8 | 105.68 | odd | 12 | |||
175.2.k.a.74.4 | 8 | 105.47 | odd | 12 | |||
175.2.k.a.149.1 | 8 | 105.17 | odd | 12 | |||
175.2.k.a.149.4 | 8 | 105.38 | odd | 12 | |||
245.2.a.g.1.2 | 2 | 3.2 | odd | 2 | |||
245.2.a.h.1.2 | 2 | 21.20 | even | 2 | |||
245.2.e.e.116.1 | 4 | 21.2 | odd | 6 | |||
245.2.e.e.226.1 | 4 | 21.11 | odd | 6 | |||
315.2.j.e.46.2 | 4 | 7.5 | odd | 6 | |||
315.2.j.e.226.2 | 4 | 7.3 | odd | 6 | |||
560.2.q.k.81.1 | 4 | 84.47 | odd | 6 | |||
560.2.q.k.401.1 | 4 | 84.59 | odd | 6 | |||
1225.2.a.k.1.1 | 2 | 105.104 | even | 2 | |||
1225.2.a.m.1.1 | 2 | 15.14 | odd | 2 | |||
1225.2.b.g.99.1 | 4 | 105.83 | odd | 4 | |||
1225.2.b.g.99.4 | 4 | 105.62 | odd | 4 | |||
1225.2.b.h.99.1 | 4 | 15.8 | even | 4 | |||
1225.2.b.h.99.4 | 4 | 15.2 | even | 4 | |||
2205.2.a.n.1.1 | 2 | 7.6 | odd | 2 | |||
2205.2.a.q.1.1 | 2 | 1.1 | even | 1 | trivial | ||
3920.2.a.bq.1.2 | 2 | 84.83 | odd | 2 | |||
3920.2.a.bv.1.1 | 2 | 12.11 | even | 2 |