Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6160,2,Mod(1,6160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6160.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6160 = 2^{4} \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6160.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: | \(49.1878476451\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.892.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 8x + 10 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.59774\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6160.1 |
$q$-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 | ||||||||
\(3\) | −3.34596 | −1.93179 | −0.965896 | − | 0.258929i | \(-0.916630\pi\) | ||||
−0.965896 | + | 0.258929i | \(0.916630\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.19547 | 2.73182 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.69193 | 1.85601 | 0.928003 | − | 0.372572i | \(-0.121524\pi\) | ||||
0.928003 | + | 0.372572i | \(0.121524\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.34596 | 0.863924 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.19547 | −1.74516 | −0.872579 | − | 0.488473i | \(-0.837554\pi\) | ||||
−0.872579 | + | 0.488473i | \(0.837554\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.84951 | 0.424306 | 0.212153 | − | 0.977236i | \(-0.431952\pi\) | ||||
0.212153 | + | 0.977236i | \(0.431952\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.34596 | −0.730149 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.84951 | −0.385649 | −0.192824 | − | 0.981233i | \(-0.561765\pi\) | ||||
−0.192824 | + | 0.981233i | \(0.561765\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −17.3839 | −3.34552 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.84242 | 1.27061 | 0.635303 | − | 0.772263i | \(-0.280875\pi\) | ||||
0.635303 | + | 0.772263i | \(0.280875\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.34596 | 0.582457 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.54143 | −1.07541 | −0.537703 | − | 0.843135i | \(-0.680708\pi\) | ||||
−0.537703 | + | 0.843135i | \(0.680708\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −22.3909 | −3.58542 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.34596 | −1.45959 | −0.729797 | − | 0.683664i | \(-0.760385\pi\) | ||||
−0.729797 | + | 0.683664i | \(0.760385\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.503544 | −0.0767897 | −0.0383949 | − | 0.999263i | \(-0.512224\pi\) | ||||
−0.0383949 | + | 0.999263i | \(0.512224\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.19547 | −1.22171 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.49646 | 0.218281 | 0.109140 | − | 0.994026i | \(-0.465190\pi\) | ||||
0.109140 | + | 0.994026i | \(0.465190\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 24.0758 | 3.37128 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.84242 | 0.939879 | 0.469939 | − | 0.882699i | \(-0.344276\pi\) | ||||
0.469939 | + | 0.882699i | \(0.344276\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.18838 | −0.819671 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.88740 | 1.02685 | 0.513426 | − | 0.858134i | \(-0.328376\pi\) | ||||
0.513426 | + | 0.858134i | \(0.328376\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.50354 | 0.576620 | 0.288310 | − | 0.957537i | \(-0.406907\pi\) | ||||
0.288310 | + | 0.957537i | \(0.406907\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.19547 | 1.03253 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.69193 | −0.830031 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.00000 | −0.977356 | −0.488678 | − | 0.872464i | \(-0.662521\pi\) | ||||
−0.488678 | + | 0.872464i | \(0.662521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.18838 | 0.744994 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.300986 | −0.0357204 | −0.0178602 | − | 0.999840i | \(-0.505685\pi\) | ||||
−0.0178602 | + | 0.999840i | \(0.505685\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.1884 | −1.19246 | −0.596230 | − | 0.802814i | \(-0.703335\pi\) | ||||
−0.596230 | + | 0.802814i | \(0.703335\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.34596 | −0.386359 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.2404 | 1.37716 | 0.688579 | − | 0.725161i | \(-0.258235\pi\) | ||||
0.688579 | + | 0.725161i | \(0.258235\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 33.5793 | 3.73104 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.30807 | 0.143580 | 0.0717899 | − | 0.997420i | \(-0.477129\pi\) | ||||
0.0717899 | + | 0.997420i | \(0.477129\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.19547 | 0.780458 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −22.8945 | −2.45455 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.69193 | −0.921342 | −0.460671 | − | 0.887571i | \(-0.652391\pi\) | ||||
−0.460671 | + | 0.887571i | \(0.652391\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.69193 | 0.701505 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 20.0758 | 2.08176 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.84951 | −0.189755 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.84951 | 0.390858 | 0.195429 | − | 0.980718i | \(-0.437390\pi\) | ||||
0.195429 | + | 0.980718i | \(0.437390\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.19547 | −0.823676 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.89448 | 0.686027 | 0.343013 | − | 0.939331i | \(-0.388552\pi\) | ||||
0.343013 | + | 0.939331i | \(0.388552\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.5793 | 1.04241 | 0.521206 | − | 0.853431i | \(-0.325482\pi\) | ||||
0.521206 | + | 0.853431i | \(0.325482\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.34596 | 0.326533 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.49646 | 0.724710 | 0.362355 | − | 0.932040i | \(-0.381973\pi\) | ||||
0.362355 | + | 0.932040i | \(0.381973\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.45857 | 0.139705 | 0.0698527 | − | 0.997557i | \(-0.477747\pi\) | ||||
0.0698527 | + | 0.997557i | \(0.477747\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21.8874 | 2.07746 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.0000 | −1.31701 | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.84951 | 0.172467 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 54.8435 | 5.07028 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.19547 | −0.659608 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 31.2713 | 2.81963 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.7748 | 1.75473 | 0.877365 | − | 0.479824i | \(-0.159300\pi\) | ||||
0.877365 | + | 0.479824i | \(0.159300\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.68484 | 0.148342 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.15049 | −0.187889 | −0.0939447 | − | 0.995577i | \(-0.529948\pi\) | ||||
−0.0939447 | + | 0.995577i | \(0.529948\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.84951 | 0.160373 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 17.3839 | 1.49616 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.39094 | −0.716886 | −0.358443 | − | 0.933552i | \(-0.616692\pi\) | ||||
−0.358443 | + | 0.933552i | \(0.616692\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.9253 | −1.52040 | −0.760201 | − | 0.649687i | \(-0.774900\pi\) | ||||
−0.760201 | + | 0.649687i | \(0.774900\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.00709 | −0.421673 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.69193 | −0.559607 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.84242 | −0.568232 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.34596 | −0.275970 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.451479 | −0.0369866 | −0.0184933 | − | 0.999829i | \(-0.505887\pi\) | ||||
−0.0184933 | + | 0.999829i | \(0.505887\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.2334 | −1.56519 | −0.782594 | − | 0.622532i | \(-0.786104\pi\) | ||||
−0.782594 | + | 0.622532i | \(0.786104\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −58.9703 | −4.76746 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.00000 | 0.481932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.69901 | −0.774066 | −0.387033 | − | 0.922066i | \(-0.626500\pi\) | ||||
−0.387033 | + | 0.922066i | \(0.626500\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −22.8945 | −1.81565 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.84951 | −0.145762 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.00000 | 0.626608 | 0.313304 | − | 0.949653i | \(-0.398564\pi\) | ||||
0.313304 | + | 0.949653i | \(0.398564\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.34596 | −0.260483 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 31.7819 | 2.44476 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.1576 | 1.15913 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.4965 | −1.17817 | −0.589087 | − | 0.808070i | \(-0.700512\pi\) | ||||
−0.589087 | + | 0.808070i | \(0.700512\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −26.3909 | −1.98366 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.8874 | 1.03799 | 0.518996 | − | 0.854776i | \(-0.326306\pi\) | ||||
0.518996 | + | 0.854776i | \(0.326306\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.7819 | 1.39605 | 0.698023 | − | 0.716075i | \(-0.254063\pi\) | ||||
0.698023 | + | 0.716075i | \(0.254063\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.0687 | −1.11391 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.54143 | 0.480936 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.19547 | 0.526185 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −17.3839 | −1.26449 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.39094 | 0.462432 | 0.231216 | − | 0.972902i | \(-0.425730\pi\) | ||||
0.231216 | + | 0.972902i | \(0.425730\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.1955 | −0.949831 | −0.474915 | − | 0.880031i | \(-0.657521\pi\) | ||||
−0.474915 | + | 0.880031i | \(0.657521\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 22.3909 | 1.60345 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.69193 | −0.334286 | −0.167143 | − | 0.985933i | \(-0.553454\pi\) | ||||
−0.167143 | + | 0.985933i | \(0.553454\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.49646 | 0.673186 | 0.336593 | − | 0.941650i | \(-0.390725\pi\) | ||||
0.336593 | + | 0.941650i | \(0.390725\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 26.7677 | 1.88805 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.84242 | 0.480244 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.34596 | 0.652750 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.1576 | −1.05352 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.84951 | −0.127933 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.39094 | 0.164599 | 0.0822996 | − | 0.996608i | \(-0.473774\pi\) | ||||
0.0822996 | + | 0.996608i | \(0.473774\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.00709 | 0.0690045 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.503544 | 0.0343414 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | −0.407307 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 34.0900 | 2.30359 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −48.1516 | −3.23902 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.188383 | −0.0126150 | −0.00630752 | − | 0.999980i | \(-0.502008\pi\) | ||||
−0.00630752 | + | 0.999980i | \(0.502008\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.19547 | 0.546365 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.99291 | 0.464136 | 0.232068 | − | 0.972700i | \(-0.425451\pi\) | ||||
0.232068 | + | 0.972700i | \(0.425451\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.19547 | −0.607654 | −0.303827 | − | 0.952727i | \(-0.598264\pi\) | ||||
−0.303827 | + | 0.952727i | \(0.598264\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.34596 | 0.220148 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.992912 | −0.0650479 | −0.0325239 | − | 0.999471i | \(-0.510355\pi\) | ||||
−0.0325239 | + | 0.999471i | \(0.510355\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.49646 | −0.0976180 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −40.9561 | −2.66038 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.14341 | 0.0739607 | 0.0369804 | − | 0.999316i | \(-0.488226\pi\) | ||||
0.0369804 | + | 0.999316i | \(0.488226\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.33888 | 0.537154 | 0.268577 | − | 0.963258i | \(-0.413447\pi\) | ||||
0.268577 | + | 0.963258i | \(0.413447\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −60.2036 | −3.86206 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.3768 | 0.787515 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.37677 | −0.277366 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.8874 | −1.50776 | −0.753880 | − | 0.657013i | \(-0.771820\pi\) | ||||
−0.753880 | + | 0.657013i | \(0.771820\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.84951 | 0.116278 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −24.0758 | −1.50768 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −31.6243 | −1.97267 | −0.986335 | − | 0.164753i | \(-0.947317\pi\) | ||||
−0.986335 | + | 0.164753i | \(0.947317\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.54143 | −0.406465 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 56.0768 | 3.47107 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.3839 | −0.825284 | −0.412642 | − | 0.910893i | \(-0.635394\pi\) | ||||
−0.412642 | + | 0.910893i | \(0.635394\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.84242 | −0.420326 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 29.0829 | 1.77984 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.79744 | 0.353476 | 0.176738 | − | 0.984258i | \(-0.443445\pi\) | ||||
0.176738 | + | 0.984258i | \(0.443445\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.0758 | 1.21952 | 0.609758 | − | 0.792587i | \(-0.291266\pi\) | ||||
0.609758 | + | 0.792587i | \(0.291266\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −22.3909 | −1.35516 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.0000 | 1.32185 | 0.660926 | − | 0.750451i | \(-0.270164\pi\) | ||||
0.660926 | + | 0.750451i | \(0.270164\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −49.1728 | −2.94390 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.30099 | −0.375885 | −0.187943 | − | 0.982180i | \(-0.560182\pi\) | ||||
−0.187943 | + | 0.982180i | \(0.560182\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.3909 | −1.33100 | −0.665502 | − | 0.746396i | \(-0.731782\pi\) | ||||
−0.665502 | + | 0.746396i | \(0.731782\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.18838 | 0.366568 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.34596 | −0.551675 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 34.7748 | 2.04558 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.8803 | −0.755057 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.6919 | −0.624629 | −0.312315 | − | 0.949979i | \(-0.601104\pi\) | ||||
−0.312315 | + | 0.949979i | \(0.601104\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.88740 | −0.459222 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.3839 | 1.00871 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.3768 | −0.715767 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.503544 | −0.0290238 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −23.0687 | −1.32526 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.50354 | −0.257872 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.08287 | 0.518387 | 0.259193 | − | 0.965825i | \(-0.416543\pi\) | ||||
0.259193 | + | 0.965825i | \(0.416543\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −35.3980 | −2.01372 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.3839 | 0.645519 | 0.322760 | − | 0.946481i | \(-0.395389\pi\) | ||||
0.322760 | + | 0.946481i | \(0.395389\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.6243 | −1.33532 | −0.667662 | − | 0.744464i | \(-0.732705\pi\) | ||||
−0.667662 | + | 0.744464i | \(0.732705\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.19547 | −0.461762 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.53435 | −0.535502 | −0.267751 | − | 0.963488i | \(-0.586280\pi\) | ||||
−0.267751 | + | 0.963488i | \(0.586280\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.84242 | −0.383102 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −25.0829 | −1.39999 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.3081 | −0.740481 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.69193 | 0.371201 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.88031 | −0.269882 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.49646 | 0.0825023 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.503544 | −0.0276773 | −0.0138386 | − | 0.999904i | \(-0.504405\pi\) | ||||
−0.0138386 | + | 0.999904i | \(0.504405\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −53.6101 | −2.93782 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.00000 | 0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.3909 | 0.674978 | 0.337489 | − | 0.941330i | \(-0.390422\pi\) | ||||
0.337489 | + | 0.941330i | \(0.390422\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 46.8435 | 2.54419 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | 0.324918 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.18838 | −0.333171 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.8803 | −1.12091 | −0.560457 | − | 0.828184i | \(-0.689374\pi\) | ||||
−0.560457 | + | 0.828184i | \(0.689374\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.1884 | −1.18772 | −0.593858 | − | 0.804570i | \(-0.702396\pi\) | ||||
−0.593858 | + | 0.804570i | \(0.702396\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −116.331 | −6.20931 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.6243 | −1.68319 | −0.841596 | − | 0.540108i | \(-0.818383\pi\) | ||||
−0.841596 | + | 0.540108i | \(0.818383\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.300986 | 0.0159747 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 24.0758 | 1.27423 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.5273 | −1.61117 | −0.805584 | − | 0.592482i | \(-0.798148\pi\) | ||||
−0.805584 | + | 0.592482i | \(0.798148\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.5793 | −0.819964 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.34596 | −0.175618 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.1884 | 0.533284 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.5793 | 0.552236 | 0.276118 | − | 0.961124i | \(-0.410952\pi\) | ||||
0.276118 | + | 0.961124i | \(0.410952\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −76.5946 | −3.98735 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.84242 | 0.355241 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 36.4667 | 1.88818 | 0.944088 | − | 0.329695i | \(-0.106946\pi\) | ||||
0.944088 | + | 0.329695i | \(0.106946\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.34596 | 0.172785 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 45.7890 | 2.35825 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.9929 | −0.770134 | −0.385067 | − | 0.922889i | \(-0.625822\pi\) | ||||
−0.385067 | + | 0.922889i | \(0.625822\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −66.1657 | −3.38977 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −35.1813 | −1.79768 | −0.898840 | − | 0.438277i | \(-0.855589\pi\) | ||||
−0.898840 | + | 0.438277i | \(0.855589\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.00000 | 0.0509647 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.12678 | −0.209776 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.30099 | 0.116665 | 0.0583323 | − | 0.998297i | \(-0.481422\pi\) | ||||
0.0583323 | + | 0.998297i | \(0.481422\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.3081 | 0.673018 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.19547 | 0.362963 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.2404 | −0.615884 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.0758 | 0.907197 | 0.453599 | − | 0.891206i | \(-0.350140\pi\) | ||||
0.453599 | + | 0.891206i | \(0.350140\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.18838 | −0.309807 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.5793 | 1.12756 | 0.563779 | − | 0.825926i | \(-0.309347\pi\) | ||||
0.563779 | + | 0.825926i | \(0.309347\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −40.1516 | −2.00009 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −33.5793 | −1.66857 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.54143 | 0.324247 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.04498 | 0.0516708 | 0.0258354 | − | 0.999666i | \(-0.491775\pi\) | ||||
0.0258354 | + | 0.999666i | \(0.491775\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.0758 | 1.38488 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.88740 | 0.388113 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.30807 | −0.0642108 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 59.9774 | 2.93710 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.49646 | −0.268519 | −0.134260 | − | 0.990946i | \(-0.542866\pi\) | ||||
−0.134260 | + | 0.990946i | \(0.542866\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.60197 | 0.126812 | 0.0634062 | − | 0.997988i | \(-0.479804\pi\) | ||||
0.0634062 | + | 0.997988i | \(0.479804\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.2642 | 0.596304 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.19547 | −0.349032 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.50354 | 0.217942 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 22.3909 | 1.08104 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.2334 | −0.926438 | −0.463219 | − | 0.886244i | \(-0.653306\pi\) | ||||
−0.463219 | + | 0.886244i | \(0.653306\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.93237 | −0.429263 | −0.214631 | − | 0.976695i | \(-0.568855\pi\) | ||||
−0.214631 | + | 0.976695i | \(0.568855\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 22.8945 | 1.09771 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.42068 | −0.163633 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.300986 | 0.0143653 | 0.00718264 | − | 0.999974i | \(-0.497714\pi\) | ||||
0.00718264 | + | 0.999974i | \(0.497714\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.19547 | 0.390260 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.7677 | −1.46182 | −0.730909 | − | 0.682475i | \(-0.760904\pi\) | ||||
−0.730909 | + | 0.682475i | \(0.760904\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.69193 | 0.412037 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.51063 | 0.0714504 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.19547 | −0.0564177 | −0.0282089 | − | 0.999602i | \(-0.508980\pi\) | ||||
−0.0282089 | + | 0.999602i | \(0.508980\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.34596 | 0.440084 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 64.3541 | 3.02362 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.69193 | −0.313722 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.7748 | −1.20569 | −0.602847 | − | 0.797857i | \(-0.705967\pi\) | ||||
−0.602847 | + | 0.797857i | \(0.705967\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 125.085 | 5.83847 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.5722 | 0.538973 | 0.269486 | − | 0.963004i | \(-0.413146\pi\) | ||||
0.269486 | + | 0.963004i | \(0.413146\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.9182 | 1.52984 | 0.764919 | − | 0.644126i | \(-0.222779\pi\) | ||||
0.764919 | + | 0.644126i | \(0.222779\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20.0758 | −0.930992 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.6399 | 0.677452 | 0.338726 | − | 0.940885i | \(-0.390004\pi\) | ||||
0.338726 | + | 0.940885i | \(0.390004\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.00000 | −0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 32.4525 | 1.49533 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.503544 | 0.0231530 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.84951 | 0.0848612 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 56.0768 | 2.56758 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.3909 | −0.474774 | −0.237387 | − | 0.971415i | \(-0.576291\pi\) | ||||
−0.237387 | + | 0.971415i | \(0.576291\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −43.7748 | −1.99596 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.18838 | 0.281581 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.84951 | −0.174797 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.3091 | −1.78127 | −0.890634 | − | 0.454722i | \(-0.849739\pi\) | ||||
−0.890634 | + | 0.454722i | \(0.849739\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −26.7677 | −1.21048 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.7748 | −1.07294 | −0.536471 | − | 0.843919i | \(-0.680243\pi\) | ||||
−0.536471 | + | 0.843919i | \(0.680243\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −49.2344 | −2.21741 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.19547 | 0.368359 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.300986 | −0.0135011 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.11260 | 0.273638 | 0.136819 | − | 0.990596i | \(-0.456312\pi\) | ||||
0.136819 | + | 0.990596i | \(0.456312\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 26.7677 | 1.19589 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.1586 | 0.586715 | 0.293358 | − | 0.956003i | \(-0.405227\pi\) | ||||
0.293358 | + | 0.956003i | \(0.405227\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.89448 | −0.306801 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −106.341 | −4.72277 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.1799 | 1.51500 | 0.757499 | − | 0.652836i | \(-0.226421\pi\) | ||||
0.757499 | + | 0.652836i | \(0.226421\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.1884 | −0.450708 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −32.1516 | −1.41953 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.5793 | −0.466181 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.49646 | −0.0658141 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 51.8506 | 2.27599 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.6778 | −1.16877 | −0.584387 | − | 0.811475i | \(-0.698665\pi\) | ||||
−0.584387 | + | 0.811475i | \(0.698665\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.4880 | −1.11451 | −0.557256 | − | 0.830341i | \(-0.688146\pi\) | ||||
−0.557256 | + | 0.830341i | \(0.688146\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.34596 | −0.146030 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 43.1728 | 1.88064 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.5793 | −0.851275 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 64.6409 | 2.80518 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −62.5425 | −2.70902 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.49646 | −0.324100 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −46.4667 | −2.00519 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.45148 | 0.191384 | 0.0956920 | − | 0.995411i | \(-0.469494\pi\) | ||||
0.0956920 | + | 0.995411i | \(0.469494\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −62.8435 | −2.69687 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.45857 | −0.0624781 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.38385 | 0.0591693 | 0.0295846 | − | 0.999562i | \(-0.490582\pi\) | ||||
0.0295846 | + | 0.999562i | \(0.490582\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.9087 | 1.57522 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.6551 | 0.539126 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.2404 | 0.520517 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −21.8874 | −0.929068 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.70610 | −0.284147 | −0.142073 | − | 0.989856i | \(-0.545377\pi\) | ||||
−0.142073 | + | 0.989856i | \(0.545377\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.36968 | −0.142522 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.0758 | −1.01648 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.59488 | −0.151506 | −0.0757532 | − | 0.997127i | \(-0.524136\pi\) | ||||
−0.0757532 | + | 0.997127i | \(0.524136\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.0000 | 0.588984 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 33.5793 | 1.41020 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.7606 | 1.33147 | 0.665737 | − | 0.746186i | \(-0.268117\pi\) | ||||
0.665737 | + | 0.746186i | \(0.268117\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.68484 | 0.237903 | 0.118952 | − | 0.992900i | \(-0.462047\pi\) | ||||
0.118952 | + | 0.992900i | \(0.462047\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.3839 | −0.893323 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.84951 | −0.0771298 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.5343 | 0.563442 | 0.281721 | − | 0.959496i | \(-0.409095\pi\) | ||||
0.281721 | + | 0.959496i | \(0.409095\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 44.1516 | 1.83488 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.30807 | 0.0542680 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.84242 | −0.283384 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −54.8435 | −2.26750 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.0520650 | 0.00214895 | 0.00107448 | − | 0.999999i | \(-0.499658\pi\) | ||||
0.00107448 | + | 0.999999i | \(0.499658\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.0970 | −0.457246 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.6990 | 0.645771 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.9774 | 1.31315 | 0.656576 | − | 0.754260i | \(-0.272004\pi\) | ||||
0.656576 | + | 0.754260i | \(0.272004\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.19547 | 0.294986 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −31.7748 | −1.30046 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.0829 | −0.861423 | −0.430711 | − | 0.902490i | \(-0.641737\pi\) | ||||
−0.430711 | + | 0.902490i | \(0.641737\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.6469 | −0.882997 | −0.441499 | − | 0.897262i | \(-0.645553\pi\) | ||||
−0.441499 | + | 0.897262i | \(0.645553\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −65.5638 | −2.66996 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.6622 | −0.879241 | −0.439621 | − | 0.898184i | \(-0.644887\pi\) | ||||
−0.439621 | + | 0.898184i | \(0.644887\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −22.8945 | −0.927731 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.0142 | 0.405130 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.31516 | 0.335846 | 0.167923 | − | 0.985800i | \(-0.446294\pi\) | ||||
0.167923 | + | 0.985800i | \(0.446294\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −31.2713 | −1.26098 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.4667 | 0.501891 | 0.250946 | − | 0.968001i | \(-0.419258\pi\) | ||||
0.250946 | + | 0.968001i | \(0.419258\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.27125 | −0.211869 | −0.105935 | − | 0.994373i | \(-0.533783\pi\) | ||||
−0.105935 | + | 0.994373i | \(0.533783\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 32.1516 | 1.29020 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.69193 | −0.348235 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.18838 | 0.247140 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 47.0687 | 1.87675 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.1586 | 0.683075 | 0.341537 | − | 0.939868i | \(-0.389052\pi\) | ||||
0.341537 | + | 0.939868i | \(0.389052\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.00000 | −0.317971 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.7748 | −0.784739 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.69193 | 0.265144 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.46672 | −0.0975820 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.7677 | 0.978266 | 0.489133 | − | 0.872209i | \(-0.337313\pi\) | ||||
0.489133 | + | 0.872209i | \(0.337313\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.03080 | −0.0406509 | −0.0203254 | − | 0.999793i | \(-0.506470\pi\) | ||||
−0.0203254 | + | 0.999793i | \(0.506470\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.68484 | −0.0663405 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.7904 | −0.502841 | −0.251420 | − | 0.967878i | \(-0.580898\pi\) | ||||
−0.251420 | + | 0.967878i | \(0.580898\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.88740 | −0.309607 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.0758 | 0.786832 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.3162 | −0.873301 | −0.436651 | − | 0.899631i | \(-0.643835\pi\) | ||||
−0.436651 | + | 0.899631i | \(0.643835\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.15049 | 0.0840267 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −83.4986 | −3.25759 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.6919 | −0.883952 | −0.441976 | − | 0.897027i | \(-0.645722\pi\) | ||||
−0.441976 | + | 0.897027i | \(0.645722\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.5638 | 1.69443 | 0.847217 | − | 0.531247i | \(-0.178276\pi\) | ||||
0.847217 | + | 0.531247i | \(0.178276\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 161.113 | 6.25712 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.84951 | −0.0717208 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.6551 | −0.490008 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.630322 | 0.0243697 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.50354 | −0.173857 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.0000 | 1.46479 | 0.732396 | − | 0.680879i | \(-0.238402\pi\) | ||||
0.732396 | + | 0.680879i | \(0.238402\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17.3839 | −0.669105 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.0984 | −0.618713 | −0.309356 | − | 0.950946i | \(-0.600114\pi\) | ||||
−0.309356 | + | 0.950946i | \(0.600114\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.84951 | 0.147731 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.3980 | −0.896614 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.0829 | −1.11282 | −0.556412 | − | 0.830906i | \(-0.687823\pi\) | ||||
−0.556412 | + | 0.830906i | \(0.687823\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.39094 | 0.320601 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 30.7677 | 1.17386 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 45.7890 | 1.74442 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.58641 | −0.288601 | −0.144300 | − | 0.989534i | \(-0.546093\pi\) | ||||
−0.144300 | + | 0.989534i | \(0.546093\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.19547 | −0.311320 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.9253 | 0.679945 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 67.2486 | 2.54722 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.32225 | 0.125659 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.07471 | 0.153900 | 0.0769499 | − | 0.997035i | \(-0.475482\pi\) | ||||
0.0769499 | + | 0.997035i | \(0.475482\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.0984 | −0.456301 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.00709 | 0.188578 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.89448 | 0.259294 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −46.4525 | −1.74456 | −0.872281 | − | 0.489005i | \(-0.837360\pi\) | ||||
−0.872281 | + | 0.489005i | \(0.837360\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 100.316 | 3.76215 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.0970 | 0.415588 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.69193 | 0.250264 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.82579 | −0.142877 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.8732 | 0.666559 | 0.333279 | − | 0.942828i | \(-0.391845\pi\) | ||||
0.333279 | + | 0.942828i | \(0.391845\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.5793 | 0.393995 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −27.9016 | −1.03767 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.84242 | 0.254121 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.8874 | 0.440879 | 0.220440 | − | 0.975401i | \(-0.429251\pi\) | ||||
0.220440 | + | 0.975401i | \(0.429251\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 100.701 | 3.72967 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.62323 | 0.134010 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.6764 | −1.16999 | −0.584997 | − | 0.811036i | \(-0.698904\pi\) | ||||
−0.584997 | + | 0.811036i | \(0.698904\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.34596 | 0.123418 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.00000 | 0.294684 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.5567 | −1.05047 | −0.525237 | − | 0.850956i | \(-0.676023\pi\) | ||||
−0.525237 | + | 0.850956i | \(0.676023\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −41.4122 | −1.52132 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.9858 | −0.513090 | −0.256545 | − | 0.966532i | \(-0.582584\pi\) | ||||
−0.256545 | + | 0.966532i | \(0.582584\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.451479 | 0.0165409 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.7203 | 0.392234 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.49646 | 0.273915 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.9171 | −0.690296 | −0.345148 | − | 0.938548i | \(-0.612171\pi\) | ||||
−0.345148 | + | 0.938548i | \(0.612171\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 79.9264 | 2.91268 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.2334 | 0.699974 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.9182 | 0.396829 | 0.198414 | − | 0.980118i | \(-0.436421\pi\) | ||||
0.198414 | + | 0.980118i | \(0.436421\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.18838 | −0.224624 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.3531 | −1.10030 | −0.550149 | − | 0.835067i | \(-0.685429\pi\) | ||||
−0.550149 | + | 0.835067i | \(0.685429\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.45857 | 0.0528036 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 58.9703 | 2.13207 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 52.7819 | 1.90584 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.7369 | −0.711731 | −0.355865 | − | 0.934537i | \(-0.615814\pi\) | ||||
−0.355865 | + | 0.934537i | \(0.615814\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 105.814 | 3.81079 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.3909 | −0.877281 | −0.438641 | − | 0.898663i | \(-0.644540\pi\) | ||||
−0.438641 | + | 0.898663i | \(0.644540\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.00000 | −0.215526 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21.8874 | 0.785206 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.2854 | −0.619315 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.300986 | 0.0107701 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −118.948 | −4.25084 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.69901 | 0.346173 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.7890 | −1.20445 | −0.602223 | − | 0.798328i | \(-0.705718\pi\) | ||||
−0.602223 | + | 0.798328i | \(0.705718\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 44.7819 | 1.59428 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.0000 | −0.497783 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.1374 | 1.07021 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 22.8945 | 0.811984 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.8435 | 1.30506 | 0.652532 | − | 0.757761i | \(-0.273707\pi\) | ||||
0.652532 | + | 0.757761i | \(0.273707\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.7677 | −0.380934 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −71.2344 | −2.51694 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.1884 | 0.359540 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.84951 | 0.0651866 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.3980 | −0.682843 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37.6990 | 1.32543 | 0.662713 | − | 0.748873i | \(-0.269405\pi\) | ||||
0.662713 | + | 0.748873i | \(0.269405\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.3304 | −1.34596 | −0.672981 | − | 0.739660i | \(-0.734987\pi\) | ||||
−0.672981 | + | 0.739660i | \(0.734987\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −67.1728 | −2.35585 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.00000 | −0.280228 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.931308 | −0.0325823 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 54.8435 | 1.91639 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.1363 | −0.632962 | −0.316481 | − | 0.948599i | \(-0.602501\pi\) | ||||
−0.316481 | + | 0.948599i | \(0.602501\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.86368 | 0.274111 | 0.137055 | − | 0.990563i | \(-0.456236\pi\) | ||||
0.137055 | + | 0.990563i | \(0.456236\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.34596 | 0.116491 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.80453 | 0.0974053 | 0.0487027 | − | 0.998813i | \(-0.484491\pi\) | ||||
0.0487027 | + | 0.998813i | \(0.484491\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −73.6112 | −2.55354 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.19547 | −0.249308 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.00000 | 0.276851 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 104.303 | 3.60524 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.9929 | −1.27714 | −0.638569 | − | 0.769565i | \(-0.720473\pi\) | ||||
−0.638569 | + | 0.769565i | \(0.720473\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.8187 | 0.614438 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.0829 | 0.726133 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −31.7819 | −1.09333 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 74.9193 | 2.57122 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.0984 | 0.414729 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −49.2571 | −1.68653 | −0.843265 | − | 0.537498i | \(-0.819370\pi\) | ||||
−0.843265 | + | 0.537498i | \(0.819370\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.1576 | −0.518378 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.3541 | −0.695283 | −0.347642 | − | 0.937627i | \(-0.613017\pi\) | ||||
−0.347642 | + | 0.937627i | \(0.613017\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.2783 | 1.16956 | 0.584781 | − | 0.811191i | \(-0.301180\pi\) | ||||
0.584781 | + | 0.811191i | \(0.301180\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31.2713 | 1.06572 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.4373 | 0.423371 | 0.211685 | − | 0.977338i | \(-0.432105\pi\) | ||||
0.211685 | + | 0.977338i | \(0.432105\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.4965 | 0.526895 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −116.355 | −3.95163 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.2404 | −0.415229 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −53.5354 | −1.81398 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 31.5485 | 1.06776 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.4809 | 1.16434 | 0.582169 | − | 0.813068i | \(-0.302204\pi\) | ||||
0.582169 | + | 0.813068i | \(0.302204\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 35.7748 | 1.20665 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.3839 | 0.922585 | 0.461293 | − | 0.887248i | \(-0.347386\pi\) | ||||
0.461293 | + | 0.887248i | \(0.347386\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.0900 | −0.743386 | −0.371693 | − | 0.928356i | \(-0.621223\pi\) | ||||
−0.371693 | + | 0.928356i | \(0.621223\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 26.3909 | 0.887122 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.7890 | −0.865909 | −0.432954 | − | 0.901416i | \(-0.642529\pi\) | ||||
−0.432954 | + | 0.901416i | \(0.642529\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.7748 | 0.663225 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −33.5793 | −1.12495 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.76771 | 0.0926178 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.8874 | −0.464204 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 41.4122 | 1.38271 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41.0545 | −1.36924 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −49.2344 | −1.64024 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.68484 | 0.0560679 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.7819 | −0.624331 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.4596 | 1.50946 | 0.754731 | − | 0.656034i | \(-0.227767\pi\) | ||||
0.754731 | + | 0.656034i | \(0.227767\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 56.5035 | 1.87410 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.8506 | 0.525153 | 0.262576 | − | 0.964911i | \(-0.415428\pi\) | ||||
0.262576 | + | 0.964911i | \(0.415428\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.30807 | −0.0432909 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15.0687 | 0.498156 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.15049 | −0.0710155 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.6314 | −0.614593 | −0.307296 | − | 0.951614i | \(-0.599424\pi\) | ||||
−0.307296 | + | 0.951614i | \(0.599424\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.3909 | −1.00142 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.01418 | −0.0662974 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.54143 | −0.215081 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 86.7025 | 2.84768 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.2486 | −0.959616 | −0.479808 | − | 0.877374i | \(-0.659294\pi\) | ||||
−0.479808 | + | 0.877374i | \(0.659294\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.84951 | 0.0606151 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −38.0900 | −1.24701 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.19547 | −0.235317 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.4441 | −1.51726 | −0.758631 | − | 0.651521i | \(-0.774131\pi\) | ||||
−0.758631 | + | 0.651521i | \(0.774131\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 79.0460 | 2.57957 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.2713 | −1.28021 | −0.640103 | − | 0.768289i | \(-0.721108\pi\) | ||||
−0.640103 | + | 0.768289i | \(0.721108\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.2854 | 0.562891 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17.3839 | 0.565497 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −54.2415 | −1.76261 | −0.881306 | − | 0.472546i | \(-0.843335\pi\) | ||||
−0.881306 | + | 0.472546i | \(0.843335\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −68.1799 | −2.21321 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.9016 | 1.03448 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 59.3612 | 1.92290 | 0.961449 | − | 0.274983i | \(-0.0886723\pi\) | ||||
0.961449 | + | 0.274983i | \(0.0886723\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.39094 | −0.206806 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22.8945 | 0.740074 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.39094 | −0.270958 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 61.4370 | 1.97978 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.1955 | 0.424777 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.7677 | 0.603529 | 0.301764 | − | 0.953383i | \(-0.402424\pi\) | ||||
0.301764 | + | 0.953383i | \(0.402424\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 44.5283 | 1.43046 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 59.4370 | 1.90742 | 0.953712 | − | 0.300722i | \(-0.0972277\pi\) | ||||
0.953712 | + | 0.300722i | \(0.0972277\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.9253 | −0.574658 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −22.3909 | −0.717084 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32.7677 | −1.04833 | −0.524166 | − | 0.851616i | \(-0.675623\pi\) | ||||
−0.524166 | + | 0.851616i | \(0.675623\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.69193 | 0.277795 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.9536 | 0.381650 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.4207 | −0.428053 | −0.214027 | − | 0.976828i | \(-0.568658\pi\) | ||||
−0.214027 | + | 0.976828i | \(0.568658\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.69193 | 0.149497 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.00709 | −0.159377 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.931308 | 0.0296139 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.1657 | 1.21237 | 0.606187 | − | 0.795322i | \(-0.292698\pi\) | ||||
0.606187 | + | 0.795322i | \(0.292698\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.68484 | 0.0534668 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.49646 | −0.301058 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.6622 | −1.06609 | −0.533046 | − | 0.846086i | \(-0.678953\pi\) | ||||
−0.533046 | + | 0.846086i | \(0.678953\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 113.715 | 3.59779 |
(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 | 6160.2.a.bi.1.1 | 3 | ||
4.3 | odd | 2 | 770.2.a.l.1.3 | ✓ | 3 | ||
12.11 | even | 2 | 6930.2.a.cl.1.3 | 3 | |||
20.3 | even | 4 | 3850.2.c.z.1849.6 | 6 | |||
20.7 | even | 4 | 3850.2.c.z.1849.1 | 6 | |||
20.19 | odd | 2 | 3850.2.a.bu.1.1 | 3 | |||
28.27 | even | 2 | 5390.2.a.bz.1.1 | 3 | |||
44.43 | even | 2 | 8470.2.a.cl.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.a.l.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
3850.2.a.bu.1.1 | 3 | 20.19 | odd | 2 | |||
3850.2.c.z.1849.1 | 6 | 20.7 | even | 4 | |||
3850.2.c.z.1849.6 | 6 | 20.3 | even | 4 | |||
5390.2.a.bz.1.1 | 3 | 28.27 | even | 2 | |||
6160.2.a.bi.1.1 | 3 | 1.1 | even | 1 | trivial | ||
6930.2.a.cl.1.3 | 3 | 12.11 | even | 2 | |||
8470.2.a.cl.1.3 | 3 | 44.43 | even | 2 |