Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7600,2,Mod(1,7600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7600.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: | \(60.6863055362\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 190) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7600.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.41421 | −1.39385 | −0.696923 | − | 0.717146i | \(-0.745448\pi\) | ||||
−0.696923 | + | 0.717146i | \(0.745448\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.58579 | −0.599371 | −0.299685 | − | 0.954038i | \(-0.596882\pi\) | ||||
−0.299685 | + | 0.954038i | \(0.596882\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.41421 | −0.426401 | −0.213201 | − | 0.977008i | \(-0.568389\pi\) | ||||
−0.213201 | + | 0.977008i | \(0.568389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.171573 | 0.0475858 | 0.0237929 | − | 0.999717i | \(-0.492426\pi\) | ||||
0.0237929 | + | 0.999717i | \(0.492426\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | 0.121268 | − | 0.992620i | \(-0.461304\pi\) | ||||
0.121268 | + | 0.992620i | \(0.461304\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.82843 | 0.835431 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.24264 | −1.92722 | −0.963612 | − | 0.267305i | \(-0.913867\pi\) | ||||
−0.963612 | + | 0.267305i | \(0.913867\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.414214 | 0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.82843 | −1.08231 | −0.541156 | − | 0.840922i | \(-0.682013\pi\) | ||||
−0.541156 | + | 0.840922i | \(0.682013\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.24264 | 0.402790 | 0.201395 | − | 0.979510i | \(-0.435452\pi\) | ||||
0.201395 | + | 0.979510i | \(0.435452\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.41421 | 0.594338 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.48528 | 1.39497 | 0.697486 | − | 0.716599i | \(-0.254302\pi\) | ||||
0.697486 | + | 0.716599i | \(0.254302\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.414214 | −0.0663273 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.24264 | 0.662589 | 0.331295 | − | 0.943527i | \(-0.392515\pi\) | ||||
0.331295 | + | 0.943527i | \(0.392515\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.2426 | −1.56199 | −0.780994 | − | 0.624538i | \(-0.785287\pi\) | ||||
−0.780994 | + | 0.624538i | \(0.785287\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.48528 | −0.640754 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.41421 | −0.338058 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.4853 | −1.57762 | −0.788812 | − | 0.614634i | \(-0.789304\pi\) | ||||
−0.788812 | + | 0.614634i | \(0.789304\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.41421 | −0.319770 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.8995 | 1.67937 | 0.839686 | − | 0.543073i | \(-0.182739\pi\) | ||||
0.839686 | + | 0.543073i | \(0.182739\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.75736 | 0.737154 | 0.368577 | − | 0.929597i | \(-0.379845\pi\) | ||||
0.368577 | + | 0.929597i | \(0.379845\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.48528 | −0.565092 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.2426 | −1.61785 | −0.808923 | − | 0.587915i | \(-0.799949\pi\) | ||||
−0.808923 | + | 0.587915i | \(0.799949\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 22.3137 | 2.68625 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.5858 | 1.25630 | 0.628151 | − | 0.778092i | \(-0.283812\pi\) | ||||
0.628151 | + | 0.778092i | \(0.283812\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.48528 | −0.642004 | −0.321002 | − | 0.947079i | \(-0.604020\pi\) | ||||
−0.321002 | + | 0.947079i | \(0.604020\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.24264 | 0.255573 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.4853 | −1.17969 | −0.589843 | − | 0.807518i | \(-0.700810\pi\) | ||||
−0.589843 | + | 0.807518i | \(0.700810\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.48528 | 0.272795 | 0.136398 | − | 0.990654i | \(-0.456448\pi\) | ||||
0.136398 | + | 0.990654i | \(0.456448\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.0711 | 1.50858 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.07107 | −0.749532 | −0.374766 | − | 0.927119i | \(-0.622277\pi\) | ||||
−0.374766 | + | 0.927119i | \(0.622277\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.272078 | −0.0285215 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.41421 | −0.561428 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.6569 | −1.18357 | −0.591787 | − | 0.806094i | \(-0.701577\pi\) | ||||
−0.591787 | + | 0.806094i | \(0.701577\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.07107 | −0.106575 | −0.0532876 | − | 0.998579i | \(-0.516970\pi\) | ||||
−0.0532876 | + | 0.998579i | \(0.516970\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.24264 | 0.418040 | 0.209020 | − | 0.977911i | \(-0.432973\pi\) | ||||
0.209020 | + | 0.977911i | \(0.432973\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.72792 | 0.553739 | 0.276870 | − | 0.960908i | \(-0.410703\pi\) | ||||
0.276870 | + | 0.960908i | \(0.410703\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.9706 | 1.52970 | 0.764851 | − | 0.644207i | \(-0.222812\pi\) | ||||
0.764851 | + | 0.644207i | \(0.222812\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.4853 | −1.94438 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.75736 | −0.165318 | −0.0826592 | − | 0.996578i | \(-0.526341\pi\) | ||||
−0.0826592 | + | 0.996578i | \(0.526341\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.485281 | 0.0448643 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.58579 | −0.145369 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.2426 | −0.923548 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.4853 | −1.28536 | −0.642680 | − | 0.766134i | \(-0.722178\pi\) | ||||
−0.642680 | + | 0.766134i | \(0.722178\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 24.7279 | 2.17717 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.9706 | −1.48272 | −0.741362 | − | 0.671105i | \(-0.765820\pi\) | ||||
−0.741362 | + | 0.671105i | \(0.765820\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.58579 | −0.137505 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.0000 | 1.11066 | 0.555332 | − | 0.831628i | \(-0.312591\pi\) | ||||
0.555332 | + | 0.831628i | \(0.312591\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000 | 1.01783 | 0.508913 | − | 0.860818i | \(-0.330047\pi\) | ||||
0.508913 | + | 0.860818i | \(0.330047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.242641 | −0.0202906 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.8284 | 0.893114 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.34315 | 0.519651 | 0.259825 | − | 0.965656i | \(-0.416335\pi\) | ||||
0.259825 | + | 0.965656i | \(0.416335\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.48528 | −0.527765 | −0.263882 | − | 0.964555i | \(-0.585003\pi\) | ||||
−0.263882 | + | 0.964555i | \(0.585003\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.82843 | 0.228665 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.343146 | 0.0273860 | 0.0136930 | − | 0.999906i | \(-0.495641\pi\) | ||||
0.0136930 | + | 0.999906i | \(0.495641\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 27.7279 | 2.19897 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.6569 | 1.15512 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.75736 | 0.137647 | 0.0688235 | − | 0.997629i | \(-0.478075\pi\) | ||||
0.0688235 | + | 0.997629i | \(0.478075\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.75736 | 0.755047 | 0.377524 | − | 0.926000i | \(-0.376776\pi\) | ||||
0.377524 | + | 0.926000i | \(0.376776\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9706 | −0.997736 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.82843 | 0.216295 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.4853 | −1.25335 | −0.626676 | − | 0.779280i | \(-0.715585\pi\) | ||||
−0.626676 | + | 0.779280i | \(0.715585\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −31.1421 | −2.34079 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.343146 | 0.0256479 | 0.0128240 | − | 0.999918i | \(-0.495918\pi\) | ||||
0.0128240 | + | 0.999918i | \(0.495918\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.48528 | 0.630706 | 0.315353 | − | 0.948974i | \(-0.397877\pi\) | ||||
0.315353 | + | 0.948974i | \(0.397877\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.8995 | −1.02748 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.41421 | −0.103418 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.656854 | −0.0477791 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.5563 | 1.34269 | 0.671345 | − | 0.741145i | \(-0.265717\pi\) | ||||
0.671345 | + | 0.741145i | \(0.265717\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.6569 | −0.839079 | −0.419539 | − | 0.907737i | \(-0.637808\pi\) | ||||
−0.419539 | + | 0.907737i | \(0.637808\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.2426 | −1.44223 | −0.721114 | − | 0.692816i | \(-0.756370\pi\) | ||||
−0.721114 | + | 0.692816i | \(0.756370\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.757359 | −0.0536878 | −0.0268439 | − | 0.999640i | \(-0.508546\pi\) | ||||
−0.0268439 | + | 0.999640i | \(0.508546\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 31.9706 | 2.25503 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.24264 | 0.648706 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −26.1421 | −1.81700 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.41421 | −0.0978232 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.72792 | −0.394326 | −0.197163 | − | 0.980371i | \(-0.563173\pi\) | ||||
−0.197163 | + | 0.980371i | \(0.563173\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −25.5563 | −1.75109 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.55635 | −0.241421 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.2426 | 0.894855 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.171573 | 0.0115412 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.8284 | 1.39477 | 0.697387 | − | 0.716694i | \(-0.254346\pi\) | ||||
0.697387 | + | 0.716694i | \(0.254346\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.2426 | 1.67541 | 0.837706 | − | 0.546121i | \(-0.183896\pi\) | ||||
0.837706 | + | 0.546121i | \(0.183896\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.9706 | −1.25361 | −0.626805 | − | 0.779176i | \(-0.715638\pi\) | ||||
−0.626805 | + | 0.779176i | \(0.715638\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.41421 | −0.356229 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.97056 | 0.587681 | 0.293841 | − | 0.955854i | \(-0.405067\pi\) | ||||
0.293841 | + | 0.955854i | \(0.405067\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 25.3137 | 1.64430 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.8995 | −0.834399 | −0.417199 | − | 0.908815i | \(-0.636988\pi\) | ||||
−0.417199 | + | 0.908815i | \(0.636988\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.9706 | −1.60850 | −0.804248 | − | 0.594294i | \(-0.797431\pi\) | ||||
−0.804248 | + | 0.594294i | \(0.797431\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.6569 | 1.38929 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.171573 | 0.0109169 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.5563 | 1.73934 | 0.869671 | − | 0.493632i | \(-0.164331\pi\) | ||||
0.869671 | + | 0.493632i | \(0.164331\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.0711 | 0.821771 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.72792 | −0.294920 | −0.147460 | − | 0.989068i | \(-0.547110\pi\) | ||||
−0.147460 | + | 0.989068i | \(0.547110\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.4558 | −0.836105 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.4853 | −1.02041 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.97056 | −0.429823 | −0.214912 | − | 0.976633i | \(-0.568946\pi\) | ||||
−0.214912 | + | 0.976633i | \(0.568946\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.0711 | 1.04473 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.6274 | 1.74544 | 0.872722 | − | 0.488217i | \(-0.162353\pi\) | ||||
0.872722 | + | 0.488217i | \(0.162353\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.7574 | 1.13943 | 0.569714 | − | 0.821843i | \(-0.307054\pi\) | ||||
0.569714 | + | 0.821843i | \(0.307054\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.656854 | 0.0397546 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.34315 | 0.379754 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.24264 | −0.253095 | −0.126547 | − | 0.991961i | \(-0.540390\pi\) | ||||
−0.126547 | + | 0.991961i | \(0.540390\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.85786 | −0.229326 | −0.114663 | − | 0.993404i | \(-0.536579\pi\) | ||||
−0.114663 | + | 0.993404i | \(0.536579\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.72792 | −0.397137 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 28.1421 | 1.64972 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.4853 | 0.670977 | 0.335489 | − | 0.942044i | \(-0.391099\pi\) | ||||
0.335489 | + | 0.942044i | \(0.391099\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.585786 | −0.0339908 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.58579 | −0.0917084 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.2426 | 0.936210 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.58579 | 0.148550 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.34315 | 0.362022 | 0.181011 | − | 0.983481i | \(-0.442063\pi\) | ||||
0.181011 | + | 0.983481i | \(0.442063\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.2426 | −0.582683 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.2426 | 0.750921 | 0.375461 | − | 0.926838i | \(-0.377485\pi\) | ||||
0.375461 | + | 0.926838i | \(0.377485\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.9706 | 1.46794 | 0.733971 | − | 0.679180i | \(-0.237665\pi\) | ||||
0.733971 | + | 0.679180i | \(0.237665\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.48528 | 0.420415 | 0.210208 | − | 0.977657i | \(-0.432586\pi\) | ||||
0.210208 | + | 0.977657i | \(0.432586\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.24264 | 0.461499 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.8284 | −0.771828 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.00000 | 0.0556415 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −38.5563 | −2.13217 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.7574 | 0.591278 | 0.295639 | − | 0.955300i | \(-0.404467\pi\) | ||||
0.295639 | + | 0.955300i | \(0.404467\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 24.0000 | 1.31519 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.8995 | 1.84662 | 0.923312 | − | 0.384052i | \(-0.125472\pi\) | ||||
0.923312 | + | 0.384052i | \(0.125472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.24264 | 0.230429 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.17157 | −0.171750 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.2132 | 0.983421 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.4853 | 1.20707 | 0.603537 | − | 0.797335i | \(-0.293758\pi\) | ||||
0.603537 | + | 0.797335i | \(0.293758\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.00000 | 0.321173 | 0.160586 | − | 0.987022i | \(-0.448662\pi\) | ||||
0.160586 | + | 0.987022i | \(0.448662\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.0710678 | 0.00379332 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.4853 | −1.03710 | −0.518548 | − | 0.855048i | \(-0.673527\pi\) | ||||
−0.518548 | + | 0.855048i | \(0.673527\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.82843 | 0.202622 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.2426 | 1.64892 | 0.824462 | − | 0.565918i | \(-0.191478\pi\) | ||||
0.824462 | + | 0.565918i | \(0.191478\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.7279 | 1.14042 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.4558 | −1.32878 | −0.664392 | − | 0.747384i | \(-0.731309\pi\) | ||||
−0.664392 | + | 0.747384i | \(0.731309\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.0000 | 0.624695 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.2132 | 0.945582 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.00000 | 0.466002 | 0.233001 | − | 0.972476i | \(-0.425145\pi\) | ||||
0.233001 | + | 0.972476i | \(0.425145\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.00000 | −0.0515026 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.75736 | −0.141636 | −0.0708180 | − | 0.997489i | \(-0.522561\pi\) | ||||
−0.0708180 | + | 0.997489i | \(0.522561\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 34.9706 | 1.79160 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.75736 | −0.191992 | −0.0959960 | − | 0.995382i | \(-0.530604\pi\) | ||||
−0.0959960 | + | 0.995382i | \(0.530604\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −28.9706 | −1.47266 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 37.0711 | 1.87958 | 0.939789 | − | 0.341756i | \(-0.111021\pi\) | ||||
0.939789 | + | 0.341756i | \(0.111021\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.24264 | −0.467420 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 40.9706 | 2.06669 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.0000 | 1.20453 | 0.602263 | − | 0.798298i | \(-0.294266\pi\) | ||||
0.602263 | + | 0.798298i | \(0.294266\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.82843 | 0.191661 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.5858 | −1.12788 | −0.563940 | − | 0.825816i | \(-0.690715\pi\) | ||||
−0.563940 | + | 0.825816i | \(0.690715\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.384776 | 0.0191671 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.0000 | −0.594818 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.2132 | −0.851138 | −0.425569 | − | 0.904926i | \(-0.639926\pi\) | ||||
−0.425569 | + | 0.904926i | \(0.639926\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −31.3848 | −1.54810 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −20.4558 | −1.00657 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −28.9706 | −1.41869 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.5858 | −0.810269 | −0.405134 | − | 0.914257i | \(-0.632775\pi\) | ||||
−0.405134 | + | 0.914257i | \(0.632775\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.51472 | 0.122560 | 0.0612799 | − | 0.998121i | \(-0.480482\pi\) | ||||
0.0612799 | + | 0.998121i | \(0.480482\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.12994 | −0.441829 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.585786 | 0.0282820 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.3848 | −1.46358 | −0.731792 | − | 0.681528i | \(-0.761316\pi\) | ||||
−0.731792 | + | 0.681528i | \(0.761316\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.5563 | 1.03593 | 0.517966 | − | 0.855401i | \(-0.326689\pi\) | ||||
0.517966 | + | 0.855401i | \(0.326689\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.24264 | −0.442135 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.2426 | 0.679764 | 0.339882 | − | 0.940468i | \(-0.389613\pi\) | ||||
0.339882 | + | 0.940468i | \(0.389613\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.6863 | −0.604109 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.24264 | 0.201574 | 0.100787 | − | 0.994908i | \(-0.467864\pi\) | ||||
0.100787 | + | 0.994908i | \(0.467864\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.3137 | −0.724314 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.31371 | −0.250769 | −0.125385 | − | 0.992108i | \(-0.540017\pi\) | ||||
−0.125385 | + | 0.992108i | \(0.540017\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | −0.282529 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.6569 | 0.735623 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.00000 | −0.140334 | −0.0701670 | − | 0.997535i | \(-0.522353\pi\) | ||||
−0.0701670 | + | 0.997535i | \(0.522353\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.414214 | 0.0193338 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.5563 | 1.28343 | 0.641714 | − | 0.766944i | \(-0.278224\pi\) | ||||
0.641714 | + | 0.766944i | \(0.278224\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.1421 | 0.657241 | 0.328620 | − | 0.944462i | \(-0.393416\pi\) | ||||
0.328620 | + | 0.944462i | \(0.393416\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.7279 | 1.14427 | 0.572136 | − | 0.820159i | \(-0.306115\pi\) | ||||
0.572136 | + | 0.820159i | \(0.306115\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.0000 | 0.969690 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.828427 | −0.0381719 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.4853 | 0.666034 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −32.4853 | −1.48740 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.1127 | −1.42158 | −0.710788 | − | 0.703407i | \(-0.751661\pi\) | ||||
−0.710788 | + | 0.703407i | \(0.751661\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.45584 | 0.0663808 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −35.3848 | −1.61006 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.79899 | 0.0815200 | 0.0407600 | − | 0.999169i | \(-0.487022\pi\) | ||||
0.0407600 | + | 0.999169i | \(0.487022\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.24264 | −0.191859 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.44365 | 0.110280 | 0.0551402 | − | 0.998479i | \(-0.482439\pi\) | ||||
0.0551402 | + | 0.998479i | \(0.482439\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.82843 | −0.262499 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.7868 | −0.752991 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.2426 | 1.53291 | 0.766456 | − | 0.642297i | \(-0.222019\pi\) | ||||
0.766456 | + | 0.642297i | \(0.222019\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.5563 | −1.05242 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.7279 | −1.77138 | −0.885690 | − | 0.464277i | \(-0.846314\pi\) | ||||
−0.885690 | + | 0.464277i | \(0.846314\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 31.3137 | 1.39069 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.97056 | −0.220316 | −0.110158 | − | 0.993914i | \(-0.535136\pi\) | ||||
−0.110158 | + | 0.993914i | \(0.535136\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.69848 | 0.384798 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.414214 | 0.0182880 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 39.7990 | 1.74698 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.686292 | 0.0300670 | 0.0150335 | − | 0.999887i | \(-0.495215\pi\) | ||||
0.0150335 | + | 0.999887i | \(0.495215\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.7279 | 1.21246 | 0.606229 | − | 0.795290i | \(-0.292682\pi\) | ||||
0.606229 | + | 0.795290i | \(0.292682\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.24264 | 0.0976910 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 62.4264 | 2.71419 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 36.4853 | 1.58333 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.727922 | 0.0315298 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.828427 | −0.0357493 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.34315 | 0.273219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.2426 | 0.784312 | 0.392156 | − | 0.919899i | \(-0.371729\pi\) | ||||
0.392156 | + | 0.919899i | \(0.371729\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.4853 | −0.879108 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.31371 | −0.227198 | −0.113599 | − | 0.993527i | \(-0.536238\pi\) | ||||
−0.113599 | + | 0.993527i | \(0.536238\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.2843 | 0.694996 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.82843 | −0.248299 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.6274 | 0.707070 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.0000 | 0.677942 | 0.338971 | − | 0.940797i | \(-0.389921\pi\) | ||||
0.338971 | + | 0.940797i | \(0.389921\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.75736 | −0.0743284 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.41421 | 0.144148 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.9706 | 1.22096 | 0.610482 | − | 0.792030i | \(-0.290976\pi\) | ||||
0.610482 | + | 0.792030i | \(0.290976\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.0416 | 0.631689 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.2843 | 1.18574 | 0.592869 | − | 0.805299i | \(-0.297995\pi\) | ||||
0.592869 | + | 0.805299i | \(0.297995\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.24264 | −0.261246 | −0.130623 | − | 0.991432i | \(-0.541698\pi\) | ||||
−0.130623 | + | 0.991432i | \(0.541698\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −44.7990 | −1.87150 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.31371 | 0.0963209 | 0.0481605 | − | 0.998840i | \(-0.484664\pi\) | ||||
0.0481605 | + | 0.998840i | \(0.484664\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 28.1421 | 1.16955 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.94113 | −0.163505 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.2426 | 0.672701 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.7574 | −0.898022 | −0.449011 | − | 0.893526i | \(-0.648224\pi\) | ||||
−0.449011 | + | 0.893526i | \(0.648224\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.24264 | 0.0924064 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 48.8701 | 2.01025 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.0000 | 0.903432 | 0.451716 | − | 0.892162i | \(-0.350812\pi\) | ||||
0.451716 | + | 0.892162i | \(0.350812\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.82843 | 0.0748325 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.2132 | −1.11190 | −0.555951 | − | 0.831215i | \(-0.687646\pi\) | ||||
−0.555951 | + | 0.831215i | \(0.687646\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.7574 | −0.479593 | −0.239796 | − | 0.970823i | \(-0.577081\pi\) | ||||
−0.239796 | + | 0.970823i | \(0.577081\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −37.4558 | −1.52532 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.82843 | −0.358335 | −0.179167 | − | 0.983819i | \(-0.557340\pi\) | ||||
−0.179167 | + | 0.983819i | \(0.557340\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −22.3137 | −0.904197 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 47.6985 | 1.92652 | 0.963262 | − | 0.268564i | \(-0.0865491\pi\) | ||||
0.963262 | + | 0.268564i | \(0.0865491\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.4853 | 0.502639 | 0.251319 | − | 0.967904i | \(-0.419136\pi\) | ||||
0.251319 | + | 0.967904i | \(0.419136\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.2426 | −0.652847 | −0.326423 | − | 0.945224i | \(-0.605844\pi\) | ||||
−0.326423 | + | 0.945224i | \(0.605844\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.82843 | −0.153629 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.2132 | 0.449248 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.41421 | 0.136351 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.48528 | 0.338330 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.02944 | 0.200219 | 0.100109 | − | 0.994976i | \(-0.468081\pi\) | ||||
0.100109 | + | 0.994976i | \(0.468081\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.8284 | 0.549631 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.769553 | −0.0304908 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.9411 | 1.18445 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.0416 | 1.18657 | 0.593287 | − | 0.804991i | \(-0.297830\pi\) | ||||
0.593287 | + | 0.804991i | \(0.297830\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.48528 | −0.0980099 | −0.0490050 | − | 0.998799i | \(-0.515605\pi\) | ||||
−0.0490050 | + | 0.998799i | \(0.515605\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.2426 | 1.07102 | 0.535509 | − | 0.844529i | \(-0.320120\pi\) | ||||
0.535509 | + | 0.844529i | \(0.320120\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.2426 | −0.716086 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.58579 | 0.336504 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.97056 | 0.194513 | 0.0972566 | − | 0.995259i | \(-0.468993\pi\) | ||||
0.0972566 | + | 0.995259i | \(0.468993\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.5147 | −0.605287 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.899495 | 0.0350393 | 0.0175197 | − | 0.999847i | \(-0.494423\pi\) | ||||
0.0175197 | + | 0.999847i | \(0.494423\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.4558 | 1.26239 | 0.631193 | − | 0.775626i | \(-0.282566\pi\) | ||||
0.631193 | + | 0.775626i | \(0.282566\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.414214 | −0.0160867 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 53.8701 | 2.08586 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −50.2843 | −1.94410 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.14214 | −0.314324 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.0000 | −0.462566 | −0.231283 | − | 0.972887i | \(-0.574292\pi\) | ||||
−0.231283 | + | 0.972887i | \(0.574292\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.9411 | 1.03543 | 0.517716 | − | 0.855553i | \(-0.326782\pi\) | ||||
0.517716 | + | 0.855553i | \(0.326782\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.4853 | 0.709400 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −60.9411 | −2.33527 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.0000 | −0.459167 | −0.229584 | − | 0.973289i | \(-0.573736\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 45.7990 | 1.74734 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.97056 | −0.0750725 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.51472 | −0.209790 | −0.104895 | − | 0.994483i | \(-0.533451\pi\) | ||||
−0.104895 | + | 0.994483i | \(0.533451\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.34315 | 0.240956 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.24264 | 0.160701 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.6569 | −0.819137 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.9706 | −0.640969 | −0.320485 | − | 0.947254i | \(-0.603846\pi\) | ||||
−0.320485 | + | 0.947254i | \(0.603846\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.48528 | 0.320028 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.69848 | 0.0638781 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.0000 | −1.27690 | −0.638448 | − | 0.769665i | \(-0.720423\pi\) | ||||
−0.638448 | + | 0.769665i | \(0.720423\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29.6569 | −1.11222 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.7279 | −0.776267 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 31.1421 | 1.16302 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.8995 | 0.928594 | 0.464297 | − | 0.885679i | \(-0.346307\pi\) | ||||
0.464297 | + | 0.885679i | \(0.346307\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.72792 | −0.250561 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 60.2843 | 2.24200 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.7279 | 0.583316 | 0.291658 | − | 0.956523i | \(-0.405793\pi\) | ||||
0.291658 | + | 0.956523i | \(0.405793\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.2426 | −0.378838 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.0000 | 0.443230 | 0.221615 | − | 0.975134i | \(-0.428867\pi\) | ||||
0.221615 | + | 0.975134i | \(0.428867\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.7279 | 0.689852 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.7279 | −0.983203 | −0.491601 | − | 0.870820i | \(-0.663588\pi\) | ||||
−0.491601 | + | 0.870820i | \(0.663588\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.414214 | −0.0152165 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.7279 | 0.687061 | 0.343530 | − | 0.939142i | \(-0.388377\pi\) | ||||
0.343530 | + | 0.939142i | \(0.388377\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.02944 | 0.257194 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.08326 | −0.331895 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.27208 | 0.0464188 | 0.0232094 | − | 0.999731i | \(-0.492612\pi\) | ||||
0.0232094 | + | 0.999731i | \(0.492612\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −66.5269 | −2.42438 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.6569 | 0.859823 | 0.429911 | − | 0.902871i | \(-0.358545\pi\) | ||||
0.429911 | + | 0.902871i | \(0.358545\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −31.5563 | −1.14542 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.0294 | 0.363567 | 0.181783 | − | 0.983339i | \(-0.441813\pi\) | ||||
0.181783 | + | 0.983339i | \(0.441813\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.3259 | −0.916859 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.21320 | 0.0799141 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.4558 | 0.521291 | 0.260646 | − | 0.965435i | \(-0.416065\pi\) | ||||
0.260646 | + | 0.965435i | \(0.416065\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.4142 | 0.411073 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.9706 | −0.718291 | −0.359146 | − | 0.933282i | \(-0.616932\pi\) | ||||
−0.359146 | + | 0.933282i | \(0.616932\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 32.4853 | 1.16540 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.24264 | 0.152008 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.9706 | −0.535689 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.41421 | −0.0862770 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.1838 | −1.25417 | −0.627083 | − | 0.778953i | \(-0.715751\pi\) | ||||
−0.627083 | + | 0.778953i | \(0.715751\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.8284 | 0.599108 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.78680 | 0.0990871 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.987807 | 0.0350780 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.5147 | −1.08089 | −0.540443 | − | 0.841380i | \(-0.681743\pi\) | ||||
−0.540443 | + | 0.841380i | \(0.681743\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.0000 | −0.706665 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.75736 | 0.273751 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −69.1127 | −2.43288 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.7990 | 0.379672 | 0.189836 | − | 0.981816i | \(-0.439204\pi\) | ||||
0.189836 | + | 0.981816i | \(0.439204\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.69848 | 0.235216 | 0.117608 | − | 0.993060i | \(-0.462477\pi\) | ||||
0.117608 | + | 0.993060i | \(0.462477\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −45.2843 | −1.58819 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.2426 | −0.358345 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.769553 | −0.0268903 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.6569 | 0.616228 | 0.308114 | − | 0.951349i | \(-0.400302\pi\) | ||||
0.308114 | + | 0.951349i | \(0.400302\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.72792 | −0.339094 | −0.169547 | − | 0.985522i | \(-0.554230\pi\) | ||||
−0.169547 | + | 0.985522i | \(0.554230\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.6985 | −1.34568 | −0.672839 | − | 0.739789i | \(-0.734925\pi\) | ||||
−0.672839 | + | 0.739789i | \(0.734925\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.4558 | −1.40509 | −0.702545 | − | 0.711640i | \(-0.747953\pi\) | ||||
−0.702545 | + | 0.711640i | \(0.747953\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.48528 | −0.155406 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.928932 | 0.0321086 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.6274 | 0.781185 | 0.390593 | − | 0.920564i | \(-0.372270\pi\) | ||||
0.390593 | + | 0.920564i | \(0.372270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.97056 | 0.171399 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.2426 | 0.352775 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.2721 | 0.490394 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.31371 | 0.319646 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −78.4264 | −2.68842 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.9411 | 1.36756 | 0.683779 | − | 0.729689i | \(-0.260335\pi\) | ||||
0.683779 | + | 0.729689i | \(0.260335\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.7279 | 0.707228 | 0.353614 | − | 0.935392i | \(-0.384953\pi\) | ||||
0.353614 | + | 0.935392i | \(0.384953\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16.2426 | 0.553548 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.7279 | 0.841748 | 0.420874 | − | 0.907119i | \(-0.361723\pi\) | ||||
0.420874 | + | 0.907119i | \(0.361723\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 38.6274 | 1.31186 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.8284 | 0.503020 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.27208 | −0.0769864 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −32.9706 | −1.11588 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.1421 | −1.59188 | −0.795938 | − | 0.605378i | \(-0.793022\pi\) | ||||
−0.795938 | + | 0.605378i | \(0.793022\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.7279 | −0.935240 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.5980 | 1.33409 | 0.667045 | − | 0.745018i | \(-0.267559\pi\) | ||||
0.667045 | + | 0.745018i | \(0.267559\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.48528 | 0.0836364 | 0.0418182 | − | 0.999125i | \(-0.486685\pi\) | ||||
0.0418182 | + | 0.999125i | \(0.486685\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.78680 | 0.0935715 | 0.0467857 | − | 0.998905i | \(-0.485102\pi\) | ||||
0.0467857 | + | 0.998905i | \(0.485102\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.9706 | 0.770408 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.4142 | 0.449393 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.82843 | 0.127827 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.0711 | −0.435945 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.4853 | −0.382630 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −39.2132 | −1.30493 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.6985 | 0.687282 | 0.343641 | − | 0.939101i | \(-0.388340\pi\) | ||||
0.343641 | + | 0.939101i | \(0.388340\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.02944 | −0.100480 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.2843 | 0.539522 | 0.269761 | − | 0.962927i | \(-0.413055\pi\) | ||||
0.269761 | + | 0.962927i | \(0.413055\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.51472 | −0.116320 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.9117 | 0.888702 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.2132 | −1.19456 | −0.597282 | − | 0.802032i | \(-0.703753\pi\) | ||||
−0.597282 | + | 0.802032i | \(0.703753\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.3137 | −0.504604 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.81623 | 0.0597821 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.0000 | 0.394132 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.8284 | −0.584932 | −0.292466 | − | 0.956276i | \(-0.594476\pi\) | ||||
−0.292466 | + | 0.956276i | \(0.594476\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.48528 | −0.146999 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31.9706 | −1.04667 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.0000 | 0.882052 | 0.441026 | − | 0.897494i | \(-0.354615\pi\) | ||||
0.441026 | + | 0.897494i | \(0.354615\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −62.6985 | −2.04609 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.8579 | 0.810343 | 0.405172 | − | 0.914241i | \(-0.367212\pi\) | ||||
0.405172 | + | 0.914241i | \(0.367212\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39.2132 | −1.27696 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.0000 | 0.389948 | 0.194974 | − | 0.980808i | \(-0.437538\pi\) | ||||
0.194974 | + | 0.980808i | \(0.437538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.941125 | −0.0305502 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0711 | −0.585995 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.72792 | −0.217939 | −0.108969 | − | 0.994045i | \(-0.534755\pi\) | ||||
−0.108969 | + | 0.994045i | \(0.534755\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.8995 | −0.643259 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.6152 | −0.665700 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.9706 | −0.837760 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.2010 | 0.522070 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.1127 | 0.614623 | 0.307311 | − | 0.951609i | \(-0.400571\pi\) | ||||
0.307311 | + | 0.951609i | \(0.400571\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.41421 | −0.0775557 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.3431 | −0.973758 | −0.486879 | − | 0.873469i | \(-0.661865\pi\) | ||||
−0.486879 | + | 0.873469i | \(0.661865\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.0294 | −0.610056 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.24264 | −0.263705 | −0.131853 | − | 0.991269i | \(-0.542093\pi\) | ||||
−0.131853 | + | 0.991269i | \(0.542093\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.0000 | 0.319601 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.1716 | 1.44222 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.544156 | 0.0173559 | 0.00867794 | − | 0.999962i | \(-0.497238\pi\) | ||||
0.00867794 | + | 0.999962i | \(0.497238\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 94.6690 | 3.01030 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.2426 | −0.706561 | −0.353280 | − | 0.935517i | \(-0.614934\pi\) | ||||
−0.353280 | + | 0.935517i | \(0.614934\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.9706 | −0.824151 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.2721 | 0.737034 | 0.368517 | − | 0.929621i | \(-0.379866\pi\) | ||||
0.368517 | + | 0.929621i | \(0.379866\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.51472 | 0.111201 |
(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 | 7600.2.a.v.1.1 | 2 | ||
4.3 | odd | 2 | 950.2.a.f.1.2 | 2 | |||
5.2 | odd | 4 | 1520.2.d.e.609.4 | 4 | |||
5.3 | odd | 4 | 1520.2.d.e.609.1 | 4 | |||
5.4 | even | 2 | 7600.2.a.bg.1.2 | 2 | |||
12.11 | even | 2 | 8550.2.a.cb.1.1 | 2 | |||
20.3 | even | 4 | 190.2.b.a.39.4 | yes | 4 | ||
20.7 | even | 4 | 190.2.b.a.39.1 | ✓ | 4 | ||
20.19 | odd | 2 | 950.2.a.g.1.1 | 2 | |||
60.23 | odd | 4 | 1710.2.d.c.1369.2 | 4 | |||
60.47 | odd | 4 | 1710.2.d.c.1369.4 | 4 | |||
60.59 | even | 2 | 8550.2.a.bn.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.b.a.39.1 | ✓ | 4 | 20.7 | even | 4 | ||
190.2.b.a.39.4 | yes | 4 | 20.3 | even | 4 | ||
950.2.a.f.1.2 | 2 | 4.3 | odd | 2 | |||
950.2.a.g.1.1 | 2 | 20.19 | odd | 2 | |||
1520.2.d.e.609.1 | 4 | 5.3 | odd | 4 | |||
1520.2.d.e.609.4 | 4 | 5.2 | odd | 4 | |||
1710.2.d.c.1369.2 | 4 | 60.23 | odd | 4 | |||
1710.2.d.c.1369.4 | 4 | 60.47 | odd | 4 | |||
7600.2.a.v.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7600.2.a.bg.1.2 | 2 | 5.4 | even | 2 | |||
8550.2.a.bn.1.2 | 2 | 60.59 | even | 2 | |||
8550.2.a.cb.1.1 | 2 | 12.11 | even | 2 |