Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.5225.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + x + 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.26498\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.04678 | −1.18171 | −0.590853 | − | 0.806779i | \(-0.701209\pi\) | ||||
−0.590853 | + | 0.806779i | \(0.701209\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.04678 | −0.835593 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.18929 | 0.396431 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.04678 | −0.590853 | ||||||||
\(13\) | 3.50105 | 0.971015 | 0.485508 | − | 0.874232i | \(-0.338635\pi\) | ||||
0.485508 | + | 0.874232i | \(0.338635\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 2.04678 | 0.528475 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.28284 | −1.03874 | −0.519371 | − | 0.854549i | \(-0.673834\pi\) | ||||
−0.519371 | + | 0.854549i | \(0.673834\pi\) | |||||||
\(18\) | 1.18929 | 0.280319 | ||||||||
\(19\) | 4.44661 | 1.02012 | 0.510061 | − | 0.860138i | \(-0.329623\pi\) | ||||
0.510061 | + | 0.860138i | \(0.329623\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −2.04678 | −0.446643 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | −0.417029 | −0.208514 | − | 0.978019i | \(-0.566863\pi\) | ||||
−0.208514 | + | 0.978019i | \(0.566863\pi\) | |||||||
\(24\) | −2.04678 | −0.417796 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.50105 | 0.686611 | ||||||||
\(27\) | 3.70611 | 0.713242 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 1.30628 | 0.242570 | 0.121285 | − | 0.992618i | \(-0.461298\pi\) | ||||
0.121285 | + | 0.992618i | \(0.461298\pi\) | |||||||
\(30\) | 2.04678 | 0.373688 | ||||||||
\(31\) | −5.70820 | −1.02522 | −0.512612 | − | 0.858620i | \(-0.671322\pi\) | ||||
−0.512612 | + | 0.858620i | \(0.671322\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.28284 | −0.734502 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 1.18929 | 0.198215 | ||||||||
\(37\) | −0.327530 | −0.0538456 | −0.0269228 | − | 0.999638i | \(-0.508571\pi\) | ||||
−0.0269228 | + | 0.999638i | \(0.508571\pi\) | |||||||
\(38\) | 4.44661 | 0.721335 | ||||||||
\(39\) | −7.16586 | −1.14746 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −3.87535 | −0.605228 | −0.302614 | − | 0.953113i | \(-0.597859\pi\) | ||||
−0.302614 | + | 0.953113i | \(0.597859\pi\) | |||||||
\(42\) | −2.04678 | −0.315824 | ||||||||
\(43\) | −2.63928 | −0.402487 | −0.201243 | − | 0.979541i | \(-0.564498\pi\) | ||||
−0.201243 | + | 0.979541i | \(0.564498\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.18929 | −0.177289 | ||||||||
\(46\) | −2.00000 | −0.294884 | ||||||||
\(47\) | 12.2258 | 1.78331 | 0.891655 | − | 0.452715i | \(-0.149544\pi\) | ||||
0.891655 | + | 0.452715i | \(0.149544\pi\) | |||||||
\(48\) | −2.04678 | −0.295427 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 8.76602 | 1.22749 | ||||||||
\(52\) | 3.50105 | 0.485508 | ||||||||
\(53\) | 1.09146 | 0.149924 | 0.0749619 | − | 0.997186i | \(-0.476116\pi\) | ||||
0.0749619 | + | 0.997186i | \(0.476116\pi\) | |||||||
\(54\) | 3.70611 | 0.504338 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −9.10121 | −1.20549 | ||||||||
\(58\) | 1.30628 | 0.171523 | ||||||||
\(59\) | 10.0613 | 1.30986 | 0.654932 | − | 0.755688i | \(-0.272697\pi\) | ||||
0.654932 | + | 0.755688i | \(0.272697\pi\) | |||||||
\(60\) | 2.04678 | 0.264238 | ||||||||
\(61\) | 13.0021 | 1.66475 | 0.832374 | − | 0.554215i | \(-0.186981\pi\) | ||||
0.832374 | + | 0.554215i | \(0.186981\pi\) | |||||||
\(62\) | −5.70820 | −0.724943 | ||||||||
\(63\) | 1.18929 | 0.149837 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.50105 | −0.434251 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.44661 | −1.03192 | −0.515959 | − | 0.856613i | \(-0.672564\pi\) | ||||
−0.515959 | + | 0.856613i | \(0.672564\pi\) | |||||||
\(68\) | −4.28284 | −0.519371 | ||||||||
\(69\) | 4.09355 | 0.492806 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −5.87963 | −0.697784 | −0.348892 | − | 0.937163i | \(-0.613442\pi\) | ||||
−0.348892 | + | 0.937163i | \(0.613442\pi\) | |||||||
\(72\) | 1.18929 | 0.140159 | ||||||||
\(73\) | −7.44187 | −0.871006 | −0.435503 | − | 0.900187i | \(-0.643429\pi\) | ||||
−0.435503 | + | 0.900187i | \(0.643429\pi\) | |||||||
\(74\) | −0.327530 | −0.0380746 | ||||||||
\(75\) | −2.04678 | −0.236341 | ||||||||
\(76\) | 4.44661 | 0.510061 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −7.16586 | −0.811373 | ||||||||
\(79\) | 0.498955 | 0.0561368 | 0.0280684 | − | 0.999606i | \(-0.491064\pi\) | ||||
0.0280684 | + | 0.999606i | \(0.491064\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −11.1535 | −1.23927 | ||||||||
\(82\) | −3.87535 | −0.427961 | ||||||||
\(83\) | −12.6125 | −1.38440 | −0.692199 | − | 0.721707i | \(-0.743358\pi\) | ||||
−0.692199 | + | 0.721707i | \(0.743358\pi\) | |||||||
\(84\) | −2.04678 | −0.223322 | ||||||||
\(85\) | 4.28284 | 0.464540 | ||||||||
\(86\) | −2.63928 | −0.284601 | ||||||||
\(87\) | −2.67366 | −0.286647 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.39645 | 0.148023 | 0.0740117 | − | 0.997257i | \(-0.476420\pi\) | ||||
0.0740117 | + | 0.997257i | \(0.476420\pi\) | |||||||
\(90\) | −1.18929 | −0.125362 | ||||||||
\(91\) | 3.50105 | 0.367009 | ||||||||
\(92\) | −2.00000 | −0.208514 | ||||||||
\(93\) | 11.6834 | 1.21151 | ||||||||
\(94\) | 12.2258 | 1.26099 | ||||||||
\(95\) | −4.44661 | −0.456212 | ||||||||
\(96\) | −2.04678 | −0.208898 | ||||||||
\(97\) | −9.79837 | −0.994874 | −0.497437 | − | 0.867500i | \(-0.665725\pi\) | ||||
−0.497437 | + | 0.867500i | \(0.665725\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 17.3874 | 1.73011 | 0.865057 | − | 0.501673i | \(-0.167282\pi\) | ||||
0.865057 | + | 0.501673i | \(0.167282\pi\) | |||||||
\(102\) | 8.76602 | 0.867966 | ||||||||
\(103\) | 6.86988 | 0.676909 | 0.338455 | − | 0.940983i | \(-0.390096\pi\) | ||||
0.338455 | + | 0.940983i | \(0.390096\pi\) | |||||||
\(104\) | 3.50105 | 0.343306 | ||||||||
\(105\) | 2.04678 | 0.199745 | ||||||||
\(106\) | 1.09146 | 0.106012 | ||||||||
\(107\) | 1.75025 | 0.169203 | 0.0846013 | − | 0.996415i | \(-0.473038\pi\) | ||||
0.0846013 | + | 0.996415i | \(0.473038\pi\) | |||||||
\(108\) | 3.70611 | 0.356621 | ||||||||
\(109\) | −5.88436 | −0.563620 | −0.281810 | − | 0.959470i | \(-0.590935\pi\) | ||||
−0.281810 | + | 0.959470i | \(0.590935\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.670380 | 0.0636297 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 17.1279 | 1.61126 | 0.805630 | − | 0.592419i | \(-0.201827\pi\) | ||||
0.805630 | + | 0.592419i | \(0.201827\pi\) | |||||||
\(114\) | −9.10121 | −0.852407 | ||||||||
\(115\) | 2.00000 | 0.186501 | ||||||||
\(116\) | 1.30628 | 0.121285 | ||||||||
\(117\) | 4.16376 | 0.384940 | ||||||||
\(118\) | 10.0613 | 0.926214 | ||||||||
\(119\) | −4.28284 | −0.392608 | ||||||||
\(120\) | 2.04678 | 0.186844 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 13.0021 | 1.17715 | ||||||||
\(123\) | 7.93198 | 0.715202 | ||||||||
\(124\) | −5.70820 | −0.512612 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 1.18929 | 0.105951 | ||||||||
\(127\) | −9.94218 | −0.882226 | −0.441113 | − | 0.897452i | \(-0.645416\pi\) | ||||
−0.441113 | + | 0.897452i | \(0.645416\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 5.40202 | 0.475621 | ||||||||
\(130\) | −3.50105 | −0.307062 | ||||||||
\(131\) | −7.65112 | −0.668482 | −0.334241 | − | 0.942488i | \(-0.608480\pi\) | ||||
−0.334241 | + | 0.942488i | \(0.608480\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.44661 | 0.385570 | ||||||||
\(134\) | −8.44661 | −0.729676 | ||||||||
\(135\) | −3.70611 | −0.318971 | ||||||||
\(136\) | −4.28284 | −0.367251 | ||||||||
\(137\) | 2.16038 | 0.184574 | 0.0922870 | − | 0.995732i | \(-0.470582\pi\) | ||||
0.0922870 | + | 0.995732i | \(0.470582\pi\) | |||||||
\(138\) | 4.09355 | 0.348466 | ||||||||
\(139\) | −21.1314 | −1.79234 | −0.896170 | − | 0.443711i | \(-0.853662\pi\) | ||||
−0.896170 | + | 0.443711i | \(0.853662\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −25.0234 | −2.10735 | ||||||||
\(142\) | −5.87963 | −0.493408 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.18929 | 0.0991077 | ||||||||
\(145\) | −1.30628 | −0.108481 | ||||||||
\(146\) | −7.44187 | −0.615894 | ||||||||
\(147\) | −2.04678 | −0.168815 | ||||||||
\(148\) | −0.327530 | −0.0269228 | ||||||||
\(149\) | 16.0089 | 1.31150 | 0.655751 | − | 0.754977i | \(-0.272352\pi\) | ||||
0.655751 | + | 0.754977i | \(0.272352\pi\) | |||||||
\(150\) | −2.04678 | −0.167119 | ||||||||
\(151\) | −12.9386 | −1.05293 | −0.526466 | − | 0.850196i | \(-0.676483\pi\) | ||||
−0.526466 | + | 0.850196i | \(0.676483\pi\) | |||||||
\(152\) | 4.44661 | 0.360668 | ||||||||
\(153\) | −5.09355 | −0.411789 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.70820 | 0.458494 | ||||||||
\(156\) | −7.16586 | −0.573728 | ||||||||
\(157\) | 18.4955 | 1.47610 | 0.738050 | − | 0.674746i | \(-0.235747\pi\) | ||||
0.738050 | + | 0.674746i | \(0.235747\pi\) | |||||||
\(158\) | 0.498955 | 0.0396947 | ||||||||
\(159\) | −2.23398 | −0.177166 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −2.00000 | −0.157622 | ||||||||
\(162\) | −11.1535 | −0.876299 | ||||||||
\(163\) | 6.52922 | 0.511408 | 0.255704 | − | 0.966755i | \(-0.417693\pi\) | ||||
0.255704 | + | 0.966755i | \(0.417693\pi\) | |||||||
\(164\) | −3.87535 | −0.302614 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.6125 | −0.978917 | ||||||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | −2.04678 | −0.157912 | ||||||||
\(169\) | −0.742683 | −0.0571295 | ||||||||
\(170\) | 4.28284 | 0.328479 | ||||||||
\(171\) | 5.28832 | 0.404408 | ||||||||
\(172\) | −2.63928 | −0.201243 | ||||||||
\(173\) | 7.54354 | 0.573525 | 0.286762 | − | 0.958002i | \(-0.407421\pi\) | ||||
0.286762 | + | 0.958002i | \(0.407421\pi\) | |||||||
\(174\) | −2.67366 | −0.202690 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −20.5931 | −1.54788 | ||||||||
\(178\) | 1.39645 | 0.104668 | ||||||||
\(179\) | 6.66819 | 0.498404 | 0.249202 | − | 0.968452i | \(-0.419832\pi\) | ||||
0.249202 | + | 0.968452i | \(0.419832\pi\) | |||||||
\(180\) | −1.18929 | −0.0886446 | ||||||||
\(181\) | −3.26233 | −0.242487 | −0.121244 | − | 0.992623i | \(-0.538688\pi\) | ||||
−0.121244 | + | 0.992623i | \(0.538688\pi\) | |||||||
\(182\) | 3.50105 | 0.259515 | ||||||||
\(183\) | −26.6124 | −1.96724 | ||||||||
\(184\) | −2.00000 | −0.147442 | ||||||||
\(185\) | 0.327530 | 0.0240805 | ||||||||
\(186\) | 11.6834 | 0.856670 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12.2258 | 0.891655 | ||||||||
\(189\) | 3.70611 | 0.269580 | ||||||||
\(190\) | −4.44661 | −0.322591 | ||||||||
\(191\) | −13.7035 | −0.991548 | −0.495774 | − | 0.868452i | \(-0.665116\pi\) | ||||
−0.495774 | + | 0.868452i | \(0.665116\pi\) | |||||||
\(192\) | −2.04678 | −0.147713 | ||||||||
\(193\) | −11.1467 | −0.802357 | −0.401178 | − | 0.916000i | \(-0.631399\pi\) | ||||
−0.401178 | + | 0.916000i | \(0.631399\pi\) | |||||||
\(194\) | −9.79837 | −0.703482 | ||||||||
\(195\) | 7.16586 | 0.513158 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 3.51254 | 0.250258 | 0.125129 | − | 0.992140i | \(-0.460065\pi\) | ||||
0.125129 | + | 0.992140i | \(0.460065\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.5167 | 1.38350 | 0.691752 | − | 0.722135i | \(-0.256839\pi\) | ||||
0.691752 | + | 0.722135i | \(0.256839\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 17.2883 | 1.21942 | ||||||||
\(202\) | 17.3874 | 1.22338 | ||||||||
\(203\) | 1.30628 | 0.0916829 | ||||||||
\(204\) | 8.76602 | 0.613744 | ||||||||
\(205\) | 3.87535 | 0.270666 | ||||||||
\(206\) | 6.86988 | 0.478647 | ||||||||
\(207\) | −2.37858 | −0.165323 | ||||||||
\(208\) | 3.50105 | 0.242754 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.04678 | 0.141241 | ||||||||
\(211\) | 14.3495 | 0.987861 | 0.493931 | − | 0.869501i | \(-0.335560\pi\) | ||||
0.493931 | + | 0.869501i | \(0.335560\pi\) | |||||||
\(212\) | 1.09146 | 0.0749619 | ||||||||
\(213\) | 12.0343 | 0.824576 | ||||||||
\(214\) | 1.75025 | 0.119644 | ||||||||
\(215\) | 2.63928 | 0.179998 | ||||||||
\(216\) | 3.70611 | 0.252169 | ||||||||
\(217\) | −5.70820 | −0.387498 | ||||||||
\(218\) | −5.88436 | −0.398539 | ||||||||
\(219\) | 15.2319 | 1.02927 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.9944 | −1.00863 | ||||||||
\(222\) | 0.670380 | 0.0449930 | ||||||||
\(223\) | 13.2981 | 0.890504 | 0.445252 | − | 0.895405i | \(-0.353114\pi\) | ||||
0.445252 | + | 0.895405i | \(0.353114\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 1.18929 | 0.0792861 | ||||||||
\(226\) | 17.1279 | 1.13933 | ||||||||
\(227\) | 18.9140 | 1.25537 | 0.627683 | − | 0.778469i | \(-0.284003\pi\) | ||||
0.627683 | + | 0.778469i | \(0.284003\pi\) | |||||||
\(228\) | −9.10121 | −0.602743 | ||||||||
\(229\) | 3.89113 | 0.257133 | 0.128566 | − | 0.991701i | \(-0.458962\pi\) | ||||
0.128566 | + | 0.991701i | \(0.458962\pi\) | |||||||
\(230\) | 2.00000 | 0.131876 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.30628 | 0.0857615 | ||||||||
\(233\) | −6.92431 | −0.453627 | −0.226813 | − | 0.973938i | \(-0.572831\pi\) | ||||
−0.226813 | + | 0.973938i | \(0.572831\pi\) | |||||||
\(234\) | 4.16376 | 0.272194 | ||||||||
\(235\) | −12.2258 | −0.797521 | ||||||||
\(236\) | 10.0613 | 0.654932 | ||||||||
\(237\) | −1.02125 | −0.0663372 | ||||||||
\(238\) | −4.28284 | −0.277616 | ||||||||
\(239\) | 26.6477 | 1.72370 | 0.861850 | − | 0.507164i | \(-0.169306\pi\) | ||||
0.861850 | + | 0.507164i | \(0.169306\pi\) | |||||||
\(240\) | 2.04678 | 0.132119 | ||||||||
\(241\) | 0.0928140 | 0.00597868 | 0.00298934 | − | 0.999996i | \(-0.499048\pi\) | ||||
0.00298934 | + | 0.999996i | \(0.499048\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.7103 | 0.751216 | ||||||||
\(244\) | 13.0021 | 0.832374 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 7.93198 | 0.505724 | ||||||||
\(247\) | 15.5678 | 0.990554 | ||||||||
\(248\) | −5.70820 | −0.362471 | ||||||||
\(249\) | 25.8149 | 1.63595 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 21.0063 | 1.32590 | 0.662952 | − | 0.748662i | \(-0.269303\pi\) | ||||
0.662952 | + | 0.748662i | \(0.269303\pi\) | |||||||
\(252\) | 1.18929 | 0.0749184 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −9.94218 | −0.623828 | ||||||||
\(255\) | −8.76602 | −0.548950 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.23060 | −0.263897 | −0.131949 | − | 0.991257i | \(-0.542123\pi\) | ||||
−0.131949 | + | 0.991257i | \(0.542123\pi\) | |||||||
\(258\) | 5.40202 | 0.336315 | ||||||||
\(259\) | −0.327530 | −0.0203517 | ||||||||
\(260\) | −3.50105 | −0.217126 | ||||||||
\(261\) | 1.55355 | 0.0961623 | ||||||||
\(262\) | −7.65112 | −0.472688 | ||||||||
\(263\) | 16.4789 | 1.01613 | 0.508066 | − | 0.861318i | \(-0.330361\pi\) | ||||
0.508066 | + | 0.861318i | \(0.330361\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.09146 | −0.0670480 | ||||||||
\(266\) | 4.44661 | 0.272639 | ||||||||
\(267\) | −2.85822 | −0.174920 | ||||||||
\(268\) | −8.44661 | −0.515959 | ||||||||
\(269\) | 20.2848 | 1.23679 | 0.618394 | − | 0.785868i | \(-0.287784\pi\) | ||||
0.618394 | + | 0.785868i | \(0.287784\pi\) | |||||||
\(270\) | −3.70611 | −0.225547 | ||||||||
\(271\) | 13.8443 | 0.840979 | 0.420489 | − | 0.907298i | \(-0.361858\pi\) | ||||
0.420489 | + | 0.907298i | \(0.361858\pi\) | |||||||
\(272\) | −4.28284 | −0.259686 | ||||||||
\(273\) | −7.16586 | −0.433697 | ||||||||
\(274\) | 2.16038 | 0.130513 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.09355 | 0.246403 | ||||||||
\(277\) | −8.50369 | −0.510937 | −0.255469 | − | 0.966817i | \(-0.582230\pi\) | ||||
−0.255469 | + | 0.966817i | \(0.582230\pi\) | |||||||
\(278\) | −21.1314 | −1.26738 | ||||||||
\(279\) | −6.78872 | −0.406430 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 2.06245 | 0.123036 | 0.0615179 | − | 0.998106i | \(-0.480406\pi\) | ||||
0.0615179 | + | 0.998106i | \(0.480406\pi\) | |||||||
\(282\) | −25.0234 | −1.49012 | ||||||||
\(283\) | 27.3214 | 1.62409 | 0.812044 | − | 0.583596i | \(-0.198355\pi\) | ||||
0.812044 | + | 0.583596i | \(0.198355\pi\) | |||||||
\(284\) | −5.87963 | −0.348892 | ||||||||
\(285\) | 9.10121 | 0.539109 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.87535 | −0.228755 | ||||||||
\(288\) | 1.18929 | 0.0700797 | ||||||||
\(289\) | 1.34275 | 0.0789854 | ||||||||
\(290\) | −1.30628 | −0.0767075 | ||||||||
\(291\) | 20.0551 | 1.17565 | ||||||||
\(292\) | −7.44187 | −0.435503 | ||||||||
\(293\) | 19.0599 | 1.11349 | 0.556746 | − | 0.830683i | \(-0.312050\pi\) | ||||
0.556746 | + | 0.830683i | \(0.312050\pi\) | |||||||
\(294\) | −2.04678 | −0.119370 | ||||||||
\(295\) | −10.0613 | −0.585789 | ||||||||
\(296\) | −0.327530 | −0.0190373 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.0089 | 0.927372 | ||||||||
\(299\) | −7.00209 | −0.404941 | ||||||||
\(300\) | −2.04678 | −0.118171 | ||||||||
\(301\) | −2.63928 | −0.152126 | ||||||||
\(302\) | −12.9386 | −0.744535 | ||||||||
\(303\) | −35.5882 | −2.04449 | ||||||||
\(304\) | 4.44661 | 0.255031 | ||||||||
\(305\) | −13.0021 | −0.744498 | ||||||||
\(306\) | −5.09355 | −0.291179 | ||||||||
\(307\) | −27.8834 | −1.59139 | −0.795694 | − | 0.605699i | \(-0.792894\pi\) | ||||
−0.795694 | + | 0.605699i | \(0.792894\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.0611 | −0.799908 | ||||||||
\(310\) | 5.70820 | 0.324204 | ||||||||
\(311\) | 21.0336 | 1.19271 | 0.596354 | − | 0.802721i | \(-0.296615\pi\) | ||||
0.596354 | + | 0.802721i | \(0.296615\pi\) | |||||||
\(312\) | −7.16586 | −0.405687 | ||||||||
\(313\) | 3.94821 | 0.223166 | 0.111583 | − | 0.993755i | \(-0.464408\pi\) | ||||
0.111583 | + | 0.993755i | \(0.464408\pi\) | |||||||
\(314\) | 18.4955 | 1.04376 | ||||||||
\(315\) | −1.18929 | −0.0670090 | ||||||||
\(316\) | 0.498955 | 0.0280684 | ||||||||
\(317\) | −28.1225 | −1.57952 | −0.789759 | − | 0.613417i | \(-0.789794\pi\) | ||||
−0.789759 | + | 0.613417i | \(0.789794\pi\) | |||||||
\(318\) | −2.23398 | −0.125275 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −3.58236 | −0.199948 | ||||||||
\(322\) | −2.00000 | −0.111456 | ||||||||
\(323\) | −19.0441 | −1.05964 | ||||||||
\(324\) | −11.1535 | −0.619637 | ||||||||
\(325\) | 3.50105 | 0.194203 | ||||||||
\(326\) | 6.52922 | 0.361620 | ||||||||
\(327\) | 12.0440 | 0.666033 | ||||||||
\(328\) | −3.87535 | −0.213980 | ||||||||
\(329\) | 12.2258 | 0.674028 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.2738 | 1.66400 | 0.831999 | − | 0.554777i | \(-0.187196\pi\) | ||||
0.831999 | + | 0.554777i | \(0.187196\pi\) | |||||||
\(332\) | −12.6125 | −0.692199 | ||||||||
\(333\) | −0.389529 | −0.0213460 | ||||||||
\(334\) | 12.0000 | 0.656611 | ||||||||
\(335\) | 8.44661 | 0.461488 | ||||||||
\(336\) | −2.04678 | −0.111661 | ||||||||
\(337\) | −32.0764 | −1.74731 | −0.873656 | − | 0.486544i | \(-0.838257\pi\) | ||||
−0.873656 | + | 0.486544i | \(0.838257\pi\) | |||||||
\(338\) | −0.742683 | −0.0403966 | ||||||||
\(339\) | −35.0570 | −1.90404 | ||||||||
\(340\) | 4.28284 | 0.232270 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 5.28832 | 0.285959 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −2.63928 | −0.142301 | ||||||||
\(345\) | −4.09355 | −0.220389 | ||||||||
\(346\) | 7.54354 | 0.405543 | ||||||||
\(347\) | 16.6585 | 0.894275 | 0.447138 | − | 0.894465i | \(-0.352443\pi\) | ||||
0.447138 | + | 0.894465i | \(0.352443\pi\) | |||||||
\(348\) | −2.67366 | −0.143323 | ||||||||
\(349\) | −5.44944 | −0.291702 | −0.145851 | − | 0.989307i | \(-0.546592\pi\) | ||||
−0.145851 | + | 0.989307i | \(0.546592\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 12.9753 | 0.692569 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.9302 | 0.688207 | 0.344104 | − | 0.938932i | \(-0.388183\pi\) | ||||
0.344104 | + | 0.938932i | \(0.388183\pi\) | |||||||
\(354\) | −20.5931 | −1.09451 | ||||||||
\(355\) | 5.87963 | 0.312058 | ||||||||
\(356\) | 1.39645 | 0.0740117 | ||||||||
\(357\) | 8.76602 | 0.463947 | ||||||||
\(358\) | 6.66819 | 0.352425 | ||||||||
\(359\) | 30.5347 | 1.61156 | 0.805780 | − | 0.592216i | \(-0.201747\pi\) | ||||
0.805780 | + | 0.592216i | \(0.201747\pi\) | |||||||
\(360\) | −1.18929 | −0.0626812 | ||||||||
\(361\) | 0.772330 | 0.0406490 | ||||||||
\(362\) | −3.26233 | −0.171464 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.50105 | 0.183505 | ||||||||
\(365\) | 7.44187 | 0.389526 | ||||||||
\(366\) | −26.6124 | −1.39105 | ||||||||
\(367\) | 27.8437 | 1.45343 | 0.726715 | − | 0.686939i | \(-0.241046\pi\) | ||||
0.726715 | + | 0.686939i | \(0.241046\pi\) | |||||||
\(368\) | −2.00000 | −0.104257 | ||||||||
\(369\) | −4.60892 | −0.239931 | ||||||||
\(370\) | 0.327530 | 0.0170275 | ||||||||
\(371\) | 1.09146 | 0.0566659 | ||||||||
\(372\) | 11.6834 | 0.605757 | ||||||||
\(373\) | −14.5146 | −0.751539 | −0.375770 | − | 0.926713i | \(-0.622622\pi\) | ||||
−0.375770 | + | 0.926713i | \(0.622622\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.04678 | 0.105695 | ||||||||
\(376\) | 12.2258 | 0.630496 | ||||||||
\(377\) | 4.57335 | 0.235539 | ||||||||
\(378\) | 3.70611 | 0.190622 | ||||||||
\(379\) | −11.9208 | −0.612329 | −0.306165 | − | 0.951979i | \(-0.599046\pi\) | ||||
−0.306165 | + | 0.951979i | \(0.599046\pi\) | |||||||
\(380\) | −4.44661 | −0.228106 | ||||||||
\(381\) | 20.3494 | 1.04253 | ||||||||
\(382\) | −13.7035 | −0.701131 | ||||||||
\(383\) | 31.7926 | 1.62453 | 0.812264 | − | 0.583290i | \(-0.198235\pi\) | ||||
0.812264 | + | 0.583290i | \(0.198235\pi\) | |||||||
\(384\) | −2.04678 | −0.104449 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.1467 | −0.567352 | ||||||||
\(387\) | −3.13888 | −0.159558 | ||||||||
\(388\) | −9.79837 | −0.497437 | ||||||||
\(389\) | 3.03309 | 0.153784 | 0.0768919 | − | 0.997039i | \(-0.475500\pi\) | ||||
0.0768919 | + | 0.997039i | \(0.475500\pi\) | |||||||
\(390\) | 7.16586 | 0.362857 | ||||||||
\(391\) | 8.56569 | 0.433185 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 15.6601 | 0.789949 | ||||||||
\(394\) | 3.51254 | 0.176959 | ||||||||
\(395\) | −0.498955 | −0.0251051 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.8927 | −1.45008 | −0.725041 | − | 0.688706i | \(-0.758179\pi\) | ||||
−0.725041 | + | 0.688706i | \(0.758179\pi\) | |||||||
\(398\) | 19.5167 | 0.978285 | ||||||||
\(399\) | −9.10121 | −0.455631 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 36.2856 | 1.81202 | 0.906009 | − | 0.423258i | \(-0.139114\pi\) | ||||
0.906009 | + | 0.423258i | \(0.139114\pi\) | |||||||
\(402\) | 17.2883 | 0.862263 | ||||||||
\(403\) | −19.9847 | −0.995508 | ||||||||
\(404\) | 17.3874 | 0.865057 | ||||||||
\(405\) | 11.1535 | 0.554220 | ||||||||
\(406\) | 1.30628 | 0.0648296 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 8.76602 | 0.433983 | ||||||||
\(409\) | −5.94636 | −0.294029 | −0.147014 | − | 0.989134i | \(-0.546966\pi\) | ||||
−0.147014 | + | 0.989134i | \(0.546966\pi\) | |||||||
\(410\) | 3.87535 | 0.191390 | ||||||||
\(411\) | −4.42182 | −0.218112 | ||||||||
\(412\) | 6.86988 | 0.338455 | ||||||||
\(413\) | 10.0613 | 0.495082 | ||||||||
\(414\) | −2.37858 | −0.116901 | ||||||||
\(415\) | 12.6125 | 0.619122 | ||||||||
\(416\) | 3.50105 | 0.171653 | ||||||||
\(417\) | 43.2512 | 2.11802 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.10047 | 0.346881 | 0.173440 | − | 0.984844i | \(-0.444512\pi\) | ||||
0.173440 | + | 0.984844i | \(0.444512\pi\) | |||||||
\(420\) | 2.04678 | 0.0998724 | ||||||||
\(421\) | −21.7460 | −1.05983 | −0.529917 | − | 0.848050i | \(-0.677777\pi\) | ||||
−0.529917 | + | 0.848050i | \(0.677777\pi\) | |||||||
\(422\) | 14.3495 | 0.698524 | ||||||||
\(423\) | 14.5400 | 0.706959 | ||||||||
\(424\) | 1.09146 | 0.0530061 | ||||||||
\(425\) | −4.28284 | −0.207748 | ||||||||
\(426\) | 12.0343 | 0.583063 | ||||||||
\(427\) | 13.0021 | 0.629215 | ||||||||
\(428\) | 1.75025 | 0.0846013 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.63928 | 0.127278 | ||||||||
\(431\) | 18.7940 | 0.905277 | 0.452638 | − | 0.891694i | \(-0.350483\pi\) | ||||
0.452638 | + | 0.891694i | \(0.350483\pi\) | |||||||
\(432\) | 3.70611 | 0.178310 | ||||||||
\(433\) | −32.4488 | −1.55939 | −0.779694 | − | 0.626161i | \(-0.784625\pi\) | ||||
−0.779694 | + | 0.626161i | \(0.784625\pi\) | |||||||
\(434\) | −5.70820 | −0.274003 | ||||||||
\(435\) | 2.67366 | 0.128192 | ||||||||
\(436\) | −5.88436 | −0.281810 | ||||||||
\(437\) | −8.89322 | −0.425420 | ||||||||
\(438\) | 15.2319 | 0.727806 | ||||||||
\(439\) | 17.1535 | 0.818690 | 0.409345 | − | 0.912380i | \(-0.365757\pi\) | ||||
0.409345 | + | 0.912380i | \(0.365757\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.18929 | 0.0566330 | ||||||||
\(442\) | −14.9944 | −0.713212 | ||||||||
\(443\) | 4.23861 | 0.201383 | 0.100691 | − | 0.994918i | \(-0.467895\pi\) | ||||
0.100691 | + | 0.994918i | \(0.467895\pi\) | |||||||
\(444\) | 0.670380 | 0.0318148 | ||||||||
\(445\) | −1.39645 | −0.0661981 | ||||||||
\(446\) | 13.2981 | 0.629682 | ||||||||
\(447\) | −32.7667 | −1.54981 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 13.1589 | 0.621008 | 0.310504 | − | 0.950572i | \(-0.399502\pi\) | ||||
0.310504 | + | 0.950572i | \(0.399502\pi\) | |||||||
\(450\) | 1.18929 | 0.0560638 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 17.1279 | 0.805630 | ||||||||
\(453\) | 26.4825 | 1.24426 | ||||||||
\(454\) | 18.9140 | 0.887678 | ||||||||
\(455\) | −3.50105 | −0.164132 | ||||||||
\(456\) | −9.10121 | −0.426203 | ||||||||
\(457\) | 0.679393 | 0.0317806 | 0.0158903 | − | 0.999874i | \(-0.494942\pi\) | ||||
0.0158903 | + | 0.999874i | \(0.494942\pi\) | |||||||
\(458\) | 3.89113 | 0.181820 | ||||||||
\(459\) | −15.8727 | −0.740875 | ||||||||
\(460\) | 2.00000 | 0.0932505 | ||||||||
\(461\) | 33.9310 | 1.58033 | 0.790163 | − | 0.612897i | \(-0.209996\pi\) | ||||
0.790163 | + | 0.612897i | \(0.209996\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.67985 | −0.403387 | −0.201693 | − | 0.979449i | \(-0.564644\pi\) | ||||
−0.201693 | + | 0.979449i | \(0.564644\pi\) | |||||||
\(464\) | 1.30628 | 0.0606426 | ||||||||
\(465\) | −11.6834 | −0.541805 | ||||||||
\(466\) | −6.92431 | −0.320763 | ||||||||
\(467\) | 4.58156 | 0.212009 | 0.106005 | − | 0.994366i | \(-0.466194\pi\) | ||||
0.106005 | + | 0.994366i | \(0.466194\pi\) | |||||||
\(468\) | 4.16376 | 0.192470 | ||||||||
\(469\) | −8.44661 | −0.390028 | ||||||||
\(470\) | −12.2258 | −0.563932 | ||||||||
\(471\) | −37.8561 | −1.74432 | ||||||||
\(472\) | 10.0613 | 0.463107 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −1.02125 | −0.0469075 | ||||||||
\(475\) | 4.44661 | 0.204024 | ||||||||
\(476\) | −4.28284 | −0.196304 | ||||||||
\(477\) | 1.29807 | 0.0594344 | ||||||||
\(478\) | 26.6477 | 1.21884 | ||||||||
\(479\) | −38.8930 | −1.77707 | −0.888534 | − | 0.458811i | \(-0.848275\pi\) | ||||
−0.888534 | + | 0.458811i | \(0.848275\pi\) | |||||||
\(480\) | 2.04678 | 0.0934221 | ||||||||
\(481\) | −1.14670 | −0.0522849 | ||||||||
\(482\) | 0.0928140 | 0.00422756 | ||||||||
\(483\) | 4.09355 | 0.186263 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.79837 | 0.444921 | ||||||||
\(486\) | 11.7103 | 0.531190 | ||||||||
\(487\) | 19.7593 | 0.895377 | 0.447689 | − | 0.894189i | \(-0.352247\pi\) | ||||
0.447689 | + | 0.894189i | \(0.352247\pi\) | |||||||
\(488\) | 13.0021 | 0.588577 | ||||||||
\(489\) | −13.3638 | −0.604334 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 30.7082 | 1.38584 | 0.692920 | − | 0.721014i | \(-0.256324\pi\) | ||||
0.692920 | + | 0.721014i | \(0.256324\pi\) | |||||||
\(492\) | 7.93198 | 0.357601 | ||||||||
\(493\) | −5.59460 | −0.251968 | ||||||||
\(494\) | 15.5678 | 0.700427 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.70820 | −0.256306 | ||||||||
\(497\) | −5.87963 | −0.263737 | ||||||||
\(498\) | 25.8149 | 1.15679 | ||||||||
\(499\) | −18.5980 | −0.832563 | −0.416281 | − | 0.909236i | \(-0.636667\pi\) | ||||
−0.416281 | + | 0.909236i | \(0.636667\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −24.5613 | −1.09732 | ||||||||
\(502\) | 21.0063 | 0.937556 | ||||||||
\(503\) | 1.53678 | 0.0685216 | 0.0342608 | − | 0.999413i | \(-0.489092\pi\) | ||||
0.0342608 | + | 0.999413i | \(0.489092\pi\) | |||||||
\(504\) | 1.18929 | 0.0529753 | ||||||||
\(505\) | −17.3874 | −0.773731 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.52011 | 0.0675103 | ||||||||
\(508\) | −9.94218 | −0.441113 | ||||||||
\(509\) | −19.0488 | −0.844322 | −0.422161 | − | 0.906521i | \(-0.638728\pi\) | ||||
−0.422161 | + | 0.906521i | \(0.638728\pi\) | |||||||
\(510\) | −8.76602 | −0.388166 | ||||||||
\(511\) | −7.44187 | −0.329209 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 16.4796 | 0.727594 | ||||||||
\(514\) | −4.23060 | −0.186604 | ||||||||
\(515\) | −6.86988 | −0.302723 | ||||||||
\(516\) | 5.40202 | 0.237811 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −0.327530 | −0.0143908 | ||||||||
\(519\) | −15.4399 | −0.677738 | ||||||||
\(520\) | −3.50105 | −0.153531 | ||||||||
\(521\) | 18.1769 | 0.796344 | 0.398172 | − | 0.917311i | \(-0.369645\pi\) | ||||
0.398172 | + | 0.917311i | \(0.369645\pi\) | |||||||
\(522\) | 1.55355 | 0.0679970 | ||||||||
\(523\) | −17.2935 | −0.756192 | −0.378096 | − | 0.925766i | \(-0.623421\pi\) | ||||
−0.378096 | + | 0.925766i | \(0.623421\pi\) | |||||||
\(524\) | −7.65112 | −0.334241 | ||||||||
\(525\) | −2.04678 | −0.0893286 | ||||||||
\(526\) | 16.4789 | 0.718514 | ||||||||
\(527\) | 24.4473 | 1.06494 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | −1.09146 | −0.0474101 | ||||||||
\(531\) | 11.9658 | 0.519270 | ||||||||
\(532\) | 4.44661 | 0.192785 | ||||||||
\(533\) | −13.5678 | −0.587686 | ||||||||
\(534\) | −2.85822 | −0.123687 | ||||||||
\(535\) | −1.75025 | −0.0756697 | ||||||||
\(536\) | −8.44661 | −0.364838 | ||||||||
\(537\) | −13.6483 | −0.588967 | ||||||||
\(538\) | 20.2848 | 0.874541 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.70611 | −0.159486 | ||||||||
\(541\) | 24.4783 | 1.05241 | 0.526203 | − | 0.850359i | \(-0.323615\pi\) | ||||
0.526203 | + | 0.850359i | \(0.323615\pi\) | |||||||
\(542\) | 13.8443 | 0.594662 | ||||||||
\(543\) | 6.67726 | 0.286549 | ||||||||
\(544\) | −4.28284 | −0.183625 | ||||||||
\(545\) | 5.88436 | 0.252058 | ||||||||
\(546\) | −7.16586 | −0.306670 | ||||||||
\(547\) | 39.8203 | 1.70259 | 0.851297 | − | 0.524684i | \(-0.175817\pi\) | ||||
0.851297 | + | 0.524684i | \(0.175817\pi\) | |||||||
\(548\) | 2.16038 | 0.0922870 | ||||||||
\(549\) | 15.4633 | 0.659957 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.80852 | 0.247451 | ||||||||
\(552\) | 4.09355 | 0.174233 | ||||||||
\(553\) | 0.498955 | 0.0212177 | ||||||||
\(554\) | −8.50369 | −0.361287 | ||||||||
\(555\) | −0.670380 | −0.0284560 | ||||||||
\(556\) | −21.1314 | −0.896170 | ||||||||
\(557\) | 22.9552 | 0.972644 | 0.486322 | − | 0.873780i | \(-0.338338\pi\) | ||||
0.486322 | + | 0.873780i | \(0.338338\pi\) | |||||||
\(558\) | −6.78872 | −0.287389 | ||||||||
\(559\) | −9.24025 | −0.390821 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.06245 | 0.0869994 | ||||||||
\(563\) | −15.9140 | −0.670696 | −0.335348 | − | 0.942094i | \(-0.608854\pi\) | ||||
−0.335348 | + | 0.942094i | \(0.608854\pi\) | |||||||
\(564\) | −25.0234 | −1.05368 | ||||||||
\(565\) | −17.1279 | −0.720578 | ||||||||
\(566\) | 27.3214 | 1.14840 | ||||||||
\(567\) | −11.1535 | −0.468401 | ||||||||
\(568\) | −5.87963 | −0.246704 | ||||||||
\(569\) | 17.7349 | 0.743484 | 0.371742 | − | 0.928336i | \(-0.378761\pi\) | ||||
0.371742 | + | 0.928336i | \(0.378761\pi\) | |||||||
\(570\) | 9.10121 | 0.381208 | ||||||||
\(571\) | 1.05280 | 0.0440584 | 0.0220292 | − | 0.999757i | \(-0.492987\pi\) | ||||
0.0220292 | + | 0.999757i | \(0.492987\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 28.0479 | 1.17172 | ||||||||
\(574\) | −3.87535 | −0.161754 | ||||||||
\(575\) | −2.00000 | −0.0834058 | ||||||||
\(576\) | 1.18929 | 0.0495538 | ||||||||
\(577\) | −12.8223 | −0.533798 | −0.266899 | − | 0.963725i | \(-0.585999\pi\) | ||||
−0.266899 | + | 0.963725i | \(0.585999\pi\) | |||||||
\(578\) | 1.34275 | 0.0558511 | ||||||||
\(579\) | 22.8148 | 0.948150 | ||||||||
\(580\) | −1.30628 | −0.0542404 | ||||||||
\(581\) | −12.6125 | −0.523253 | ||||||||
\(582\) | 20.0551 | 0.831310 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −7.44187 | −0.307947 | ||||||||
\(585\) | −4.16376 | −0.172150 | ||||||||
\(586\) | 19.0599 | 0.787358 | ||||||||
\(587\) | −9.76035 | −0.402853 | −0.201426 | − | 0.979504i | \(-0.564558\pi\) | ||||
−0.201426 | + | 0.979504i | \(0.564558\pi\) | |||||||
\(588\) | −2.04678 | −0.0844076 | ||||||||
\(589\) | −25.3822 | −1.04585 | ||||||||
\(590\) | −10.0613 | −0.414216 | ||||||||
\(591\) | −7.18939 | −0.295732 | ||||||||
\(592\) | −0.327530 | −0.0134614 | ||||||||
\(593\) | 25.4142 | 1.04364 | 0.521818 | − | 0.853057i | \(-0.325254\pi\) | ||||
0.521818 | + | 0.853057i | \(0.325254\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.28284 | 0.175579 | ||||||||
\(596\) | 16.0089 | 0.655751 | ||||||||
\(597\) | −39.9464 | −1.63490 | ||||||||
\(598\) | −7.00209 | −0.286337 | ||||||||
\(599\) | −41.3324 | −1.68879 | −0.844397 | − | 0.535718i | \(-0.820041\pi\) | ||||
−0.844397 | + | 0.535718i | \(0.820041\pi\) | |||||||
\(600\) | −2.04678 | −0.0835593 | ||||||||
\(601\) | 39.2422 | 1.60072 | 0.800361 | − | 0.599518i | \(-0.204641\pi\) | ||||
0.800361 | + | 0.599518i | \(0.204641\pi\) | |||||||
\(602\) | −2.63928 | −0.107569 | ||||||||
\(603\) | −10.0455 | −0.409084 | ||||||||
\(604\) | −12.9386 | −0.526466 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −35.5882 | −1.44567 | ||||||||
\(607\) | 7.82091 | 0.317441 | 0.158721 | − | 0.987324i | \(-0.449263\pi\) | ||||
0.158721 | + | 0.987324i | \(0.449263\pi\) | |||||||
\(608\) | 4.44661 | 0.180334 | ||||||||
\(609\) | −2.67366 | −0.108342 | ||||||||
\(610\) | −13.0021 | −0.526439 | ||||||||
\(611\) | 42.8029 | 1.73162 | ||||||||
\(612\) | −5.09355 | −0.205895 | ||||||||
\(613\) | 1.22930 | 0.0496511 | 0.0248256 | − | 0.999692i | \(-0.492097\pi\) | ||||
0.0248256 | + | 0.999692i | \(0.492097\pi\) | |||||||
\(614\) | −27.8834 | −1.12528 | ||||||||
\(615\) | −7.93198 | −0.319848 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.43129 | −0.339431 | −0.169715 | − | 0.985493i | \(-0.554285\pi\) | ||||
−0.169715 | + | 0.985493i | \(0.554285\pi\) | |||||||
\(618\) | −14.0611 | −0.565620 | ||||||||
\(619\) | 7.19522 | 0.289200 | 0.144600 | − | 0.989490i | \(-0.453810\pi\) | ||||
0.144600 | + | 0.989490i | \(0.453810\pi\) | |||||||
\(620\) | 5.70820 | 0.229247 | ||||||||
\(621\) | −7.41223 | −0.297442 | ||||||||
\(622\) | 21.0336 | 0.843372 | ||||||||
\(623\) | 1.39645 | 0.0559476 | ||||||||
\(624\) | −7.16586 | −0.286864 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 3.94821 | 0.157802 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.4955 | 0.738050 | ||||||||
\(629\) | 1.40276 | 0.0559317 | ||||||||
\(630\) | −1.18929 | −0.0473825 | ||||||||
\(631\) | 9.16167 | 0.364721 | 0.182360 | − | 0.983232i | \(-0.441626\pi\) | ||||
0.182360 | + | 0.983232i | \(0.441626\pi\) | |||||||
\(632\) | 0.498955 | 0.0198474 | ||||||||
\(633\) | −29.3702 | −1.16736 | ||||||||
\(634\) | −28.1225 | −1.11689 | ||||||||
\(635\) | 9.94218 | 0.394543 | ||||||||
\(636\) | −2.23398 | −0.0885830 | ||||||||
\(637\) | 3.50105 | 0.138716 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.99260 | −0.276623 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −7.82633 | −0.309121 | −0.154561 | − | 0.987983i | \(-0.549396\pi\) | ||||
−0.154561 | + | 0.987983i | \(0.549396\pi\) | |||||||
\(642\) | −3.58236 | −0.141385 | ||||||||
\(643\) | −42.1180 | −1.66097 | −0.830487 | − | 0.557038i | \(-0.811938\pi\) | ||||
−0.830487 | + | 0.557038i | \(0.811938\pi\) | |||||||
\(644\) | −2.00000 | −0.0788110 | ||||||||
\(645\) | −5.40202 | −0.212704 | ||||||||
\(646\) | −19.0441 | −0.749281 | ||||||||
\(647\) | −20.5480 | −0.807825 | −0.403913 | − | 0.914798i | \(-0.632350\pi\) | ||||
−0.403913 | + | 0.914798i | \(0.632350\pi\) | |||||||
\(648\) | −11.1535 | −0.438149 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 3.50105 | 0.137322 | ||||||||
\(651\) | 11.6834 | 0.457909 | ||||||||
\(652\) | 6.52922 | 0.255704 | ||||||||
\(653\) | −29.0694 | −1.13757 | −0.568786 | − | 0.822485i | \(-0.692587\pi\) | ||||
−0.568786 | + | 0.822485i | \(0.692587\pi\) | |||||||
\(654\) | 12.0440 | 0.470957 | ||||||||
\(655\) | 7.65112 | 0.298954 | ||||||||
\(656\) | −3.87535 | −0.151307 | ||||||||
\(657\) | −8.85056 | −0.345293 | ||||||||
\(658\) | 12.2258 | 0.476610 | ||||||||
\(659\) | 16.3882 | 0.638395 | 0.319198 | − | 0.947688i | \(-0.396587\pi\) | ||||
0.319198 | + | 0.947688i | \(0.396587\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.7386 | 1.46786 | 0.733932 | − | 0.679223i | \(-0.237683\pi\) | ||||
0.733932 | + | 0.679223i | \(0.237683\pi\) | |||||||
\(662\) | 30.2738 | 1.17662 | ||||||||
\(663\) | 30.6902 | 1.19191 | ||||||||
\(664\) | −12.6125 | −0.489459 | ||||||||
\(665\) | −4.44661 | −0.172432 | ||||||||
\(666\) | −0.389529 | −0.0150939 | ||||||||
\(667\) | −2.61256 | −0.101159 | ||||||||
\(668\) | 12.0000 | 0.464294 | ||||||||
\(669\) | −27.2182 | −1.05232 | ||||||||
\(670\) | 8.44661 | 0.326321 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −2.04678 | −0.0789561 | ||||||||
\(673\) | 21.0258 | 0.810486 | 0.405243 | − | 0.914209i | \(-0.367187\pi\) | ||||
0.405243 | + | 0.914209i | \(0.367187\pi\) | |||||||
\(674\) | −32.0764 | −1.23554 | ||||||||
\(675\) | 3.70611 | 0.142648 | ||||||||
\(676\) | −0.742683 | −0.0285647 | ||||||||
\(677\) | −6.89196 | −0.264880 | −0.132440 | − | 0.991191i | \(-0.542281\pi\) | ||||
−0.132440 | + | 0.991191i | \(0.542281\pi\) | |||||||
\(678\) | −35.0570 | −1.34636 | ||||||||
\(679\) | −9.79837 | −0.376027 | ||||||||
\(680\) | 4.28284 | 0.164240 | ||||||||
\(681\) | −38.7127 | −1.48348 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.37212 | −0.0525026 | −0.0262513 | − | 0.999655i | \(-0.508357\pi\) | ||||
−0.0262513 | + | 0.999655i | \(0.508357\pi\) | |||||||
\(684\) | 5.28832 | 0.202204 | ||||||||
\(685\) | −2.16038 | −0.0825440 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −7.96427 | −0.303856 | ||||||||
\(688\) | −2.63928 | −0.100622 | ||||||||
\(689\) | 3.82126 | 0.145578 | ||||||||
\(690\) | −4.09355 | −0.155839 | ||||||||
\(691\) | −9.39673 | −0.357469 | −0.178734 | − | 0.983897i | \(-0.557200\pi\) | ||||
−0.178734 | + | 0.983897i | \(0.557200\pi\) | |||||||
\(692\) | 7.54354 | 0.286762 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.6585 | 0.632348 | ||||||||
\(695\) | 21.1314 | 0.801559 | ||||||||
\(696\) | −2.67366 | −0.101345 | ||||||||
\(697\) | 16.5975 | 0.628676 | ||||||||
\(698\) | −5.44944 | −0.206264 | ||||||||
\(699\) | 14.1725 | 0.536054 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 13.5330 | 0.511133 | 0.255566 | − | 0.966792i | \(-0.417738\pi\) | ||||
0.255566 | + | 0.966792i | \(0.417738\pi\) | |||||||
\(702\) | 12.9753 | 0.489720 | ||||||||
\(703\) | −1.45640 | −0.0549290 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 25.0234 | 0.942436 | ||||||||
\(706\) | 12.9302 | 0.486636 | ||||||||
\(707\) | 17.3874 | 0.653922 | ||||||||
\(708\) | −20.5931 | −0.773938 | ||||||||
\(709\) | −40.1756 | −1.50883 | −0.754413 | − | 0.656400i | \(-0.772078\pi\) | ||||
−0.754413 | + | 0.656400i | \(0.772078\pi\) | |||||||
\(710\) | 5.87963 | 0.220659 | ||||||||
\(711\) | 0.593403 | 0.0222544 | ||||||||
\(712\) | 1.39645 | 0.0523342 | ||||||||
\(713\) | 11.4164 | 0.427548 | ||||||||
\(714\) | 8.76602 | 0.328060 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.66819 | 0.249202 | ||||||||
\(717\) | −54.5420 | −2.03691 | ||||||||
\(718\) | 30.5347 | 1.13954 | ||||||||
\(719\) | 13.1839 | 0.491677 | 0.245838 | − | 0.969311i | \(-0.420937\pi\) | ||||
0.245838 | + | 0.969311i | \(0.420937\pi\) | |||||||
\(720\) | −1.18929 | −0.0443223 | ||||||||
\(721\) | 6.86988 | 0.255848 | ||||||||
\(722\) | 0.772330 | 0.0287432 | ||||||||
\(723\) | −0.189970 | −0.00706504 | ||||||||
\(724\) | −3.26233 | −0.121244 | ||||||||
\(725\) | 1.30628 | 0.0485141 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.5403 | −1.50356 | −0.751779 | − | 0.659415i | \(-0.770804\pi\) | ||||
−0.751779 | + | 0.659415i | \(0.770804\pi\) | |||||||
\(728\) | 3.50105 | 0.129757 | ||||||||
\(729\) | 9.49203 | 0.351557 | ||||||||
\(730\) | 7.44187 | 0.275436 | ||||||||
\(731\) | 11.3036 | 0.418080 | ||||||||
\(732\) | −26.6124 | −0.983621 | ||||||||
\(733\) | 22.8799 | 0.845089 | 0.422545 | − | 0.906342i | \(-0.361137\pi\) | ||||
0.422545 | + | 0.906342i | \(0.361137\pi\) | |||||||
\(734\) | 27.8437 | 1.02773 | ||||||||
\(735\) | 2.04678 | 0.0754965 | ||||||||
\(736\) | −2.00000 | −0.0737210 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −4.60892 | −0.169657 | ||||||||
\(739\) | 30.1038 | 1.10738 | 0.553692 | − | 0.832721i | \(-0.313218\pi\) | ||||
0.553692 | + | 0.832721i | \(0.313218\pi\) | |||||||
\(740\) | 0.327530 | 0.0120402 | ||||||||
\(741\) | −31.8638 | −1.17054 | ||||||||
\(742\) | 1.09146 | 0.0400688 | ||||||||
\(743\) | −29.6655 | −1.08832 | −0.544161 | − | 0.838981i | \(-0.683152\pi\) | ||||
−0.544161 | + | 0.838981i | \(0.683152\pi\) | |||||||
\(744\) | 11.6834 | 0.428335 | ||||||||
\(745\) | −16.0089 | −0.586521 | ||||||||
\(746\) | −14.5146 | −0.531418 | ||||||||
\(747\) | −14.9999 | −0.548818 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.75025 | 0.0639526 | ||||||||
\(750\) | 2.04678 | 0.0747377 | ||||||||
\(751\) | 47.4328 | 1.73085 | 0.865423 | − | 0.501041i | \(-0.167049\pi\) | ||||
0.865423 | + | 0.501041i | \(0.167049\pi\) | |||||||
\(752\) | 12.2258 | 0.445828 | ||||||||
\(753\) | −42.9951 | −1.56683 | ||||||||
\(754\) | 4.57335 | 0.166552 | ||||||||
\(755\) | 12.9386 | 0.470885 | ||||||||
\(756\) | 3.70611 | 0.134790 | ||||||||
\(757\) | −26.5518 | −0.965043 | −0.482522 | − | 0.875884i | \(-0.660279\pi\) | ||||
−0.482522 | + | 0.875884i | \(0.660279\pi\) | |||||||
\(758\) | −11.9208 | −0.432982 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.44661 | −0.161295 | ||||||||
\(761\) | 48.7468 | 1.76707 | 0.883534 | − | 0.468366i | \(-0.155157\pi\) | ||||
0.883534 | + | 0.468366i | \(0.155157\pi\) | |||||||
\(762\) | 20.3494 | 0.737182 | ||||||||
\(763\) | −5.88436 | −0.213028 | ||||||||
\(764\) | −13.7035 | −0.495774 | ||||||||
\(765\) | 5.09355 | 0.184158 | ||||||||
\(766\) | 31.7926 | 1.14871 | ||||||||
\(767\) | 35.2249 | 1.27190 | ||||||||
\(768\) | −2.04678 | −0.0738567 | ||||||||
\(769\) | 25.8289 | 0.931415 | 0.465708 | − | 0.884939i | \(-0.345800\pi\) | ||||
0.465708 | + | 0.884939i | \(0.345800\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.65908 | 0.311849 | ||||||||
\(772\) | −11.1467 | −0.401178 | ||||||||
\(773\) | 38.6257 | 1.38927 | 0.694634 | − | 0.719363i | \(-0.255566\pi\) | ||||
0.694634 | + | 0.719363i | \(0.255566\pi\) | |||||||
\(774\) | −3.13888 | −0.112825 | ||||||||
\(775\) | −5.70820 | −0.205045 | ||||||||
\(776\) | −9.79837 | −0.351741 | ||||||||
\(777\) | 0.670380 | 0.0240497 | ||||||||
\(778\) | 3.03309 | 0.108742 | ||||||||
\(779\) | −17.2322 | −0.617407 | ||||||||
\(780\) | 7.16586 | 0.256579 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 8.56569 | 0.306308 | ||||||||
\(783\) | 4.84123 | 0.173011 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −18.4955 | −0.660132 | ||||||||
\(786\) | 15.6601 | 0.558579 | ||||||||
\(787\) | −10.5712 | −0.376821 | −0.188411 | − | 0.982090i | \(-0.560334\pi\) | ||||
−0.188411 | + | 0.982090i | \(0.560334\pi\) | |||||||
\(788\) | 3.51254 | 0.125129 | ||||||||
\(789\) | −33.7286 | −1.20077 | ||||||||
\(790\) | −0.498955 | −0.0177520 | ||||||||
\(791\) | 17.1279 | 0.608999 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45.5209 | 1.61649 | ||||||||
\(794\) | −28.8927 | −1.02536 | ||||||||
\(795\) | 2.23398 | 0.0792310 | ||||||||
\(796\) | 19.5167 | 0.691752 | ||||||||
\(797\) | −40.3031 | −1.42761 | −0.713805 | − | 0.700345i | \(-0.753029\pi\) | ||||
−0.713805 | + | 0.700345i | \(0.753029\pi\) | |||||||
\(798\) | −9.10121 | −0.322179 | ||||||||
\(799\) | −52.3610 | −1.85240 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 1.66079 | 0.0586810 | ||||||||
\(802\) | 36.2856 | 1.28129 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 17.2883 | 0.609712 | ||||||||
\(805\) | 2.00000 | 0.0704907 | ||||||||
\(806\) | −19.9847 | −0.703930 | ||||||||
\(807\) | −41.5185 | −1.46152 | ||||||||
\(808\) | 17.3874 | 0.611688 | ||||||||
\(809\) | −14.7984 | −0.520283 | −0.260142 | − | 0.965570i | \(-0.583769\pi\) | ||||
−0.260142 | + | 0.965570i | \(0.583769\pi\) | |||||||
\(810\) | 11.1535 | 0.391893 | ||||||||
\(811\) | 30.8043 | 1.08169 | 0.540843 | − | 0.841124i | \(-0.318105\pi\) | ||||
0.540843 | + | 0.841124i | \(0.318105\pi\) | |||||||
\(812\) | 1.30628 | 0.0458415 | ||||||||
\(813\) | −28.3361 | −0.993790 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.52922 | −0.228708 | ||||||||
\(816\) | 8.76602 | 0.306872 | ||||||||
\(817\) | −11.7359 | −0.410586 | ||||||||
\(818\) | −5.94636 | −0.207910 | ||||||||
\(819\) | 4.16376 | 0.145494 | ||||||||
\(820\) | 3.87535 | 0.135333 | ||||||||
\(821\) | −26.5412 | −0.926296 | −0.463148 | − | 0.886281i | \(-0.653280\pi\) | ||||
−0.463148 | + | 0.886281i | \(0.653280\pi\) | |||||||
\(822\) | −4.42182 | −0.154229 | ||||||||
\(823\) | 39.8431 | 1.38884 | 0.694422 | − | 0.719568i | \(-0.255660\pi\) | ||||
0.694422 | + | 0.719568i | \(0.255660\pi\) | |||||||
\(824\) | 6.86988 | 0.239324 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.0613 | 0.350076 | ||||||||
\(827\) | −36.6888 | −1.27579 | −0.637896 | − | 0.770122i | \(-0.720195\pi\) | ||||
−0.637896 | + | 0.770122i | \(0.720195\pi\) | |||||||
\(828\) | −2.37858 | −0.0826615 | ||||||||
\(829\) | 16.8821 | 0.586339 | 0.293169 | − | 0.956061i | \(-0.405290\pi\) | ||||
0.293169 | + | 0.956061i | \(0.405290\pi\) | |||||||
\(830\) | 12.6125 | 0.437785 | ||||||||
\(831\) | 17.4051 | 0.603778 | ||||||||
\(832\) | 3.50105 | 0.121377 | ||||||||
\(833\) | −4.28284 | −0.148392 | ||||||||
\(834\) | 43.2512 | 1.49767 | ||||||||
\(835\) | −12.0000 | −0.415277 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21.1553 | −0.731233 | ||||||||
\(838\) | 7.10047 | 0.245282 | ||||||||
\(839\) | −40.8091 | −1.40889 | −0.704444 | − | 0.709760i | \(-0.748804\pi\) | ||||
−0.704444 | + | 0.709760i | \(0.748804\pi\) | |||||||
\(840\) | 2.04678 | 0.0706205 | ||||||||
\(841\) | −27.2936 | −0.941160 | ||||||||
\(842\) | −21.7460 | −0.749416 | ||||||||
\(843\) | −4.22138 | −0.145392 | ||||||||
\(844\) | 14.3495 | 0.493931 | ||||||||
\(845\) | 0.742683 | 0.0255491 | ||||||||
\(846\) | 14.5400 | 0.499896 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.09146 | 0.0374810 | ||||||||
\(849\) | −55.9208 | −1.91920 | ||||||||
\(850\) | −4.28284 | −0.146900 | ||||||||
\(851\) | 0.655059 | 0.0224552 | ||||||||
\(852\) | 12.0343 | 0.412288 | ||||||||
\(853\) | 0.0955818 | 0.00327266 | 0.00163633 | − | 0.999999i | \(-0.499479\pi\) | ||||
0.00163633 | + | 0.999999i | \(0.499479\pi\) | |||||||
\(854\) | 13.0021 | 0.444922 | ||||||||
\(855\) | −5.28832 | −0.180857 | ||||||||
\(856\) | 1.75025 | 0.0598222 | ||||||||
\(857\) | −51.9594 | −1.77490 | −0.887449 | − | 0.460906i | \(-0.847525\pi\) | ||||
−0.887449 | + | 0.460906i | \(0.847525\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.1186 | 1.19823 | 0.599115 | − | 0.800663i | \(-0.295519\pi\) | ||||
0.599115 | + | 0.800663i | \(0.295519\pi\) | |||||||
\(860\) | 2.63928 | 0.0899988 | ||||||||
\(861\) | 7.93198 | 0.270321 | ||||||||
\(862\) | 18.7940 | 0.640127 | ||||||||
\(863\) | −23.0325 | −0.784037 | −0.392018 | − | 0.919957i | \(-0.628223\pi\) | ||||
−0.392018 | + | 0.919957i | \(0.628223\pi\) | |||||||
\(864\) | 3.70611 | 0.126085 | ||||||||
\(865\) | −7.54354 | −0.256488 | ||||||||
\(866\) | −32.4488 | −1.10265 | ||||||||
\(867\) | −2.74831 | −0.0933376 | ||||||||
\(868\) | −5.70820 | −0.193749 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 2.67366 | 0.0906457 | ||||||||
\(871\) | −29.5720 | −1.00201 | ||||||||
\(872\) | −5.88436 | −0.199270 | ||||||||
\(873\) | −11.6531 | −0.394399 | ||||||||
\(874\) | −8.89322 | −0.300818 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 15.2319 | 0.514637 | ||||||||
\(877\) | 30.7254 | 1.03752 | 0.518762 | − | 0.854919i | \(-0.326393\pi\) | ||||
0.518762 | + | 0.854919i | \(0.326393\pi\) | |||||||
\(878\) | 17.1535 | 0.578901 | ||||||||
\(879\) | −39.0114 | −1.31582 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.3788 | −1.42778 | −0.713890 | − | 0.700258i | \(-0.753068\pi\) | ||||
−0.713890 | + | 0.700258i | \(0.753068\pi\) | |||||||
\(882\) | 1.18929 | 0.0400455 | ||||||||
\(883\) | 38.3269 | 1.28980 | 0.644901 | − | 0.764266i | \(-0.276899\pi\) | ||||
0.644901 | + | 0.764266i | \(0.276899\pi\) | |||||||
\(884\) | −14.9944 | −0.504317 | ||||||||
\(885\) | 20.5931 | 0.692231 | ||||||||
\(886\) | 4.23861 | 0.142399 | ||||||||
\(887\) | 25.5816 | 0.858948 | 0.429474 | − | 0.903079i | \(-0.358699\pi\) | ||||
0.429474 | + | 0.903079i | \(0.358699\pi\) | |||||||
\(888\) | 0.670380 | 0.0224965 | ||||||||
\(889\) | −9.94218 | −0.333450 | ||||||||
\(890\) | −1.39645 | −0.0468091 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.2981 | 0.445252 | ||||||||
\(893\) | 54.3632 | 1.81919 | ||||||||
\(894\) | −32.7667 | −1.09588 | ||||||||
\(895\) | −6.66819 | −0.222893 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 14.3317 | 0.478522 | ||||||||
\(898\) | 13.1589 | 0.439119 | ||||||||
\(899\) | −7.45652 | −0.248689 | ||||||||
\(900\) | 1.18929 | 0.0396431 | ||||||||
\(901\) | −4.67456 | −0.155732 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.40202 | 0.179768 | ||||||||
\(904\) | 17.1279 | 0.569667 | ||||||||
\(905\) | 3.26233 | 0.108444 | ||||||||
\(906\) | 26.4825 | 0.879822 | ||||||||
\(907\) | −49.7760 | −1.65279 | −0.826393 | − | 0.563094i | \(-0.809611\pi\) | ||||
−0.826393 | + | 0.563094i | \(0.809611\pi\) | |||||||
\(908\) | 18.9140 | 0.627683 | ||||||||
\(909\) | 20.6787 | 0.685871 | ||||||||
\(910\) | −3.50105 | −0.116059 | ||||||||
\(911\) | 22.3261 | 0.739696 | 0.369848 | − | 0.929092i | \(-0.379410\pi\) | ||||
0.369848 | + | 0.929092i | \(0.379410\pi\) | |||||||
\(912\) | −9.10121 | −0.301371 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.679393 | 0.0224723 | ||||||||
\(915\) | 26.6124 | 0.879778 | ||||||||
\(916\) | 3.89113 | 0.128566 | ||||||||
\(917\) | −7.65112 | −0.252662 | ||||||||
\(918\) | −15.8727 | −0.523877 | ||||||||
\(919\) | 17.9670 | 0.592677 | 0.296338 | − | 0.955083i | \(-0.404234\pi\) | ||||
0.296338 | + | 0.955083i | \(0.404234\pi\) | |||||||
\(920\) | 2.00000 | 0.0659380 | ||||||||
\(921\) | 57.0710 | 1.88055 | ||||||||
\(922\) | 33.9310 | 1.11746 | ||||||||
\(923\) | −20.5848 | −0.677558 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.327530 | −0.0107691 | ||||||||
\(926\) | −8.67985 | −0.285238 | ||||||||
\(927\) | 8.17029 | 0.268348 | ||||||||
\(928\) | 1.30628 | 0.0428808 | ||||||||
\(929\) | 13.7491 | 0.451092 | 0.225546 | − | 0.974233i | \(-0.427583\pi\) | ||||
0.225546 | + | 0.974233i | \(0.427583\pi\) | |||||||
\(930\) | −11.6834 | −0.383114 | ||||||||
\(931\) | 4.44661 | 0.145732 | ||||||||
\(932\) | −6.92431 | −0.226813 | ||||||||
\(933\) | −43.0512 | −1.40943 | ||||||||
\(934\) | 4.58156 | 0.149913 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.16376 | 0.136097 | ||||||||
\(937\) | 8.38824 | 0.274032 | 0.137016 | − | 0.990569i | \(-0.456249\pi\) | ||||
0.137016 | + | 0.990569i | \(0.456249\pi\) | |||||||
\(938\) | −8.44661 | −0.275792 | ||||||||
\(939\) | −8.08110 | −0.263717 | ||||||||
\(940\) | −12.2258 | −0.398760 | ||||||||
\(941\) | 28.1650 | 0.918153 | 0.459077 | − | 0.888397i | \(-0.348180\pi\) | ||||
0.459077 | + | 0.888397i | \(0.348180\pi\) | |||||||
\(942\) | −37.8561 | −1.23342 | ||||||||
\(943\) | 7.75070 | 0.252398 | ||||||||
\(944\) | 10.0613 | 0.327466 | ||||||||
\(945\) | −3.70611 | −0.120560 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.901036 | −0.0292797 | −0.0146399 | − | 0.999893i | \(-0.504660\pi\) | ||||
−0.0146399 | + | 0.999893i | \(0.504660\pi\) | |||||||
\(948\) | −1.02125 | −0.0331686 | ||||||||
\(949\) | −26.0543 | −0.845760 | ||||||||
\(950\) | 4.44661 | 0.144267 | ||||||||
\(951\) | 57.5605 | 1.86653 | ||||||||
\(952\) | −4.28284 | −0.138808 | ||||||||
\(953\) | 5.45845 | 0.176817 | 0.0884083 | − | 0.996084i | \(-0.471822\pi\) | ||||
0.0884083 | + | 0.996084i | \(0.471822\pi\) | |||||||
\(954\) | 1.29807 | 0.0420265 | ||||||||
\(955\) | 13.7035 | 0.443434 | ||||||||
\(956\) | 26.6477 | 0.861850 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −38.8930 | −1.25658 | ||||||||
\(959\) | 2.16038 | 0.0697624 | ||||||||
\(960\) | 2.04678 | 0.0660594 | ||||||||
\(961\) | 1.58359 | 0.0510836 | ||||||||
\(962\) | −1.14670 | −0.0369710 | ||||||||
\(963\) | 2.08155 | 0.0670771 | ||||||||
\(964\) | 0.0928140 | 0.00298934 | ||||||||
\(965\) | 11.1467 | 0.358825 | ||||||||
\(966\) | 4.09355 | 0.131708 | ||||||||
\(967\) | 36.7612 | 1.18216 | 0.591079 | − | 0.806613i | \(-0.298702\pi\) | ||||
0.591079 | + | 0.806613i | \(0.298702\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 38.9791 | 1.25219 | ||||||||
\(970\) | 9.79837 | 0.314607 | ||||||||
\(971\) | −47.2855 | −1.51746 | −0.758731 | − | 0.651404i | \(-0.774180\pi\) | ||||
−0.758731 | + | 0.651404i | \(0.774180\pi\) | |||||||
\(972\) | 11.7103 | 0.375608 | ||||||||
\(973\) | −21.1314 | −0.677441 | ||||||||
\(974\) | 19.7593 | 0.633127 | ||||||||
\(975\) | −7.16586 | −0.229491 | ||||||||
\(976\) | 13.0021 | 0.416187 | ||||||||
\(977\) | −44.3011 | −1.41732 | −0.708658 | − | 0.705552i | \(-0.750699\pi\) | ||||
−0.708658 | + | 0.705552i | \(0.750699\pi\) | |||||||
\(978\) | −13.3638 | −0.427329 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −6.99823 | −0.223436 | ||||||||
\(982\) | 30.7082 | 0.979937 | ||||||||
\(983\) | −2.98404 | −0.0951761 | −0.0475880 | − | 0.998867i | \(-0.515153\pi\) | ||||
−0.0475880 | + | 0.998867i | \(0.515153\pi\) | |||||||
\(984\) | 7.93198 | 0.252862 | ||||||||
\(985\) | −3.51254 | −0.111919 | ||||||||
\(986\) | −5.59460 | −0.178168 | ||||||||
\(987\) | −25.0234 | −0.796504 | ||||||||
\(988\) | 15.5678 | 0.495277 | ||||||||
\(989\) | 5.27857 | 0.167849 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.4047 | −1.50586 | −0.752930 | − | 0.658100i | \(-0.771360\pi\) | ||||
−0.752930 | + | 0.658100i | \(0.771360\pi\) | |||||||
\(992\) | −5.70820 | −0.181236 | ||||||||
\(993\) | −61.9637 | −1.96636 | ||||||||
\(994\) | −5.87963 | −0.186491 | ||||||||
\(995\) | −19.5167 | −0.618722 | ||||||||
\(996\) | 25.8149 | 0.817976 | ||||||||
\(997\) | −16.7474 | −0.530394 | −0.265197 | − | 0.964194i | \(-0.585437\pi\) | ||||
−0.265197 | + | 0.964194i | \(0.585437\pi\) | |||||||
\(998\) | −18.5980 | −0.588711 | ||||||||
\(999\) | −1.21386 | −0.0384049 |
(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 | 8470.2.a.ct.1.1 | 4 | ||
11.2 | odd | 10 | 770.2.n.e.631.1 | yes | 8 | ||
11.6 | odd | 10 | 770.2.n.e.421.1 | ✓ | 8 | ||
11.10 | odd | 2 | 8470.2.a.cq.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.e.421.1 | ✓ | 8 | 11.6 | odd | 10 | ||
770.2.n.e.631.1 | yes | 8 | 11.2 | odd | 10 | ||
8470.2.a.cq.1.1 | 4 | 11.10 | odd | 2 | |||
8470.2.a.ct.1.1 | 4 | 1.1 | even | 1 | trivial |