Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [208,4,Mod(129,208)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(208, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("208.129");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 208 = 2^{4} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 208.f (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(12.2723972812\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 208.129 |
Dual form | 208.4.f.b.129.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/208\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(79\) | \(145\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.192450 | 0.0962250 | − | 0.995360i | \(-0.469323\pi\) | ||||
0.0962250 | + | 0.995360i | \(0.469323\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 9.00000i | − | 0.804984i | −0.915423 | − | 0.402492i | \(-0.868144\pi\) | ||
0.915423 | − | 0.402492i | \(-0.131856\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 15.0000i | 0.809924i | 0.914334 | + | 0.404962i | \(0.132715\pi\) | ||||
−0.914334 | + | 0.404962i | \(0.867285\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.0000 | −0.962963 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 48.0000i | − | 1.31569i | −0.753155 | − | 0.657843i | \(-0.771469\pi\) | ||
0.753155 | − | 0.657843i | \(-0.228531\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 26.0000 | − | 39.0000i | 0.554700 | − | 0.832050i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 9.00000i | − | 0.154919i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −45.0000 | −0.642006 | −0.321003 | − | 0.947078i | \(-0.604020\pi\) | ||||
−0.321003 | + | 0.947078i | \(0.604020\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.00000i | − | 0.0724471i | −0.999344 | − | 0.0362235i | \(-0.988467\pi\) | ||
0.999344 | − | 0.0362235i | \(-0.0115328\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 15.0000i | 0.155870i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −162.000 | −1.46867 | −0.734333 | − | 0.678789i | \(-0.762505\pi\) | ||||
−0.734333 | + | 0.678789i | \(0.762505\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 44.0000 | 0.352000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −53.0000 | −0.377772 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −144.000 | −0.922073 | −0.461037 | − | 0.887381i | \(-0.652522\pi\) | ||||
−0.461037 | + | 0.887381i | \(0.652522\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 264.000i | − | 1.52954i | −0.644302 | − | 0.764771i | \(-0.722852\pi\) | ||
0.644302 | − | 0.764771i | \(-0.277148\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 48.0000i | − | 0.253204i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 135.000 | 0.651976 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 303.000i | − | 1.34629i | −0.739509 | − | 0.673147i | \(-0.764942\pi\) | ||
0.739509 | − | 0.673147i | \(-0.235058\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 26.0000 | − | 39.0000i | 0.106752 | − | 0.160128i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 192.000i | − | 0.731350i | −0.930743 | − | 0.365675i | \(-0.880838\pi\) | ||
0.930743 | − | 0.365675i | \(-0.119162\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 97.0000 | 0.344008 | 0.172004 | − | 0.985096i | \(-0.444976\pi\) | ||||
0.172004 | + | 0.985096i | \(0.444976\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 234.000i | 0.775170i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 111.000i | 0.344490i | 0.985054 | + | 0.172245i | \(0.0551020\pi\) | ||||
−0.985054 | + | 0.172245i | \(0.944898\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 118.000 | 0.344023 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −45.0000 | −0.123554 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −414.000 | −1.07297 | −0.536484 | − | 0.843911i | \(-0.680248\pi\) | ||||
−0.536484 | + | 0.843911i | \(0.680248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −432.000 | −1.05911 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 6.00000i | − | 0.0139424i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 522.000i | 1.15184i | 0.817506 | + | 0.575920i | \(0.195356\pi\) | ||||
−0.817506 | + | 0.575920i | \(0.804644\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 376.000 | 0.789211 | 0.394605 | − | 0.918851i | \(-0.370881\pi\) | ||||
0.394605 | + | 0.918851i | \(0.370881\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 390.000i | − | 0.779927i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −351.000 | − | 234.000i | −0.669788 | − | 0.446525i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 36.0000i | 0.0656433i | 0.999461 | + | 0.0328216i | \(0.0104493\pi\) | ||||
−0.999461 | + | 0.0328216i | \(0.989551\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −162.000 | −0.282645 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 357.000i | − | 0.596734i | −0.954451 | − | 0.298367i | \(-0.903558\pi\) | ||
0.954451 | − | 0.298367i | \(-0.0964419\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1098.00i | 1.76043i | 0.474578 | + | 0.880214i | \(0.342601\pi\) | ||||
−0.474578 | + | 0.880214i | \(0.657399\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 44.0000 | 0.0677424 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 720.000 | 1.06561 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 830.000 | 1.18205 | 0.591027 | − | 0.806652i | \(-0.298723\pi\) | ||||
0.591027 | + | 0.806652i | \(0.298723\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 649.000 | 0.890261 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 438.000i | 0.579238i | 0.957142 | + | 0.289619i | \(0.0935286\pi\) | ||||
−0.957142 | + | 0.289619i | \(0.906471\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 405.000i | 0.516805i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −144.000 | −0.177453 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 438.000i | 0.521662i | 0.965384 | + | 0.260831i | \(0.0839965\pi\) | ||||
−0.965384 | + | 0.260831i | \(0.916003\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 585.000 | + | 390.000i | 0.673897 | + | 0.449265i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 264.000i | − | 0.294360i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −54.0000 | −0.0583188 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 852.000i | − | 0.891830i | −0.895075 | − | 0.445915i | \(-0.852878\pi\) | ||
0.895075 | − | 0.445915i | \(-0.147122\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1248.00i | 1.26696i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 396.000 | 0.390133 | 0.195067 | − | 0.980790i | \(-0.437508\pi\) | ||||
0.195067 | + | 0.980790i | \(0.437508\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −182.000 | −0.174107 | −0.0870534 | − | 0.996204i | \(-0.527745\pi\) | ||||
−0.0870534 | + | 0.996204i | \(0.527745\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 135.000 | 0.125473 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 612.000 | 0.552937 | 0.276469 | − | 0.961023i | \(-0.410836\pi\) | ||||
0.276469 | + | 0.961023i | \(0.410836\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1083.00i | 0.951675i | 0.879533 | + | 0.475838i | \(0.157855\pi\) | ||||
−0.879533 | + | 0.475838i | \(0.842145\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 303.000i | − | 0.259094i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 90.0000 | 0.0749247 | 0.0374623 | − | 0.999298i | \(-0.488073\pi\) | ||||
0.0374623 | + | 0.999298i | \(0.488073\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1458.00i | 1.18225i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −676.000 | + | 1014.00i | −0.534156 | + | 0.801234i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 675.000i | − | 0.519976i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −973.000 | −0.731029 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 192.000i | − | 0.140748i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1521.00i | − | 1.08834i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2086.00 | −1.45750 | −0.728750 | − | 0.684780i | \(-0.759898\pi\) | ||||
−0.728750 | + | 0.684780i | \(0.759898\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 97.0000 | 0.0662044 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1467.00 | 0.978415 | 0.489208 | − | 0.872167i | \(-0.337286\pi\) | ||||
0.489208 | + | 0.872167i | \(0.337286\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 90.0000 | 0.0586766 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 477.000i | 0.304101i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 414.000i | 0.258178i | 0.991633 | + | 0.129089i | \(0.0412053\pi\) | ||||
−0.991633 | + | 0.129089i | \(0.958795\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2419.00 | 1.47609 | 0.738046 | − | 0.674750i | \(-0.235749\pi\) | ||||
0.738046 | + | 0.674750i | \(0.235749\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 111.000i | 0.0662971i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1872.00 | − | 1248.00i | −1.09472 | − | 0.729811i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1296.00i | 0.742255i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 118.000 | 0.0662073 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 930.000i | − | 0.511333i | −0.966765 | − | 0.255666i | \(-0.917705\pi\) | ||
0.966765 | − | 0.255666i | \(-0.0822948\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1683.00i | − | 0.907024i | −0.891250 | − | 0.453512i | \(-0.850171\pi\) | ||
0.891250 | − | 0.453512i | \(-0.149829\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1170.00 | 0.618228 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2376.00 | −1.23126 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1874.00 | 0.952621 | 0.476310 | − | 0.879277i | \(-0.341974\pi\) | ||||
0.476310 | + | 0.879277i | \(0.341974\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −414.000 | −0.206493 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2430.00i | − | 1.18951i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1194.00i | − | 0.573750i | −0.957968 | − | 0.286875i | \(-0.907384\pi\) | ||
0.957968 | − | 0.286875i | \(-0.0926165\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −432.000 | −0.203825 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2388.00i | − | 1.10652i | −0.833008 | − | 0.553260i | \(-0.813383\pi\) | ||
0.833008 | − | 0.553260i | \(-0.186617\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −845.000 | − | 2028.00i | −0.384615 | − | 0.923077i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 156.000i | 0.0697638i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1566.00 | −0.688213 | −0.344106 | − | 0.938931i | \(-0.611818\pi\) | ||||
−0.344106 | + | 0.938931i | \(0.611818\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 660.000i | 0.285093i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 522.000i | 0.221672i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 657.000 | 0.274338 | 0.137169 | − | 0.990548i | \(-0.456200\pi\) | ||||
0.137169 | + | 0.990548i | \(0.456200\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1222.00 | −0.501826 | −0.250913 | − | 0.968010i | \(-0.580731\pi\) | ||||
−0.250913 | + | 0.968010i | \(0.580731\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 376.000 | 0.151884 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2727.00 | −1.08375 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2160.00i | 0.844678i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 795.000i | − | 0.305967i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1260.00 | −0.477332 | −0.238666 | − | 0.971102i | \(-0.576710\pi\) | ||||
−0.238666 | + | 0.971102i | \(0.576710\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 342.000i | − | 0.127553i | −0.997964 | − | 0.0637764i | \(-0.979686\pi\) | ||
0.997964 | − | 0.0637764i | \(-0.0203145\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −351.000 | − | 234.000i | −0.128901 | − | 0.0859338i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 81.0000i | 0.0292945i | 0.999893 | + | 0.0146472i | \(0.00466253\pi\) | ||||
−0.999893 | + | 0.0146472i | \(0.995337\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1996.00 | −0.711019 | −0.355509 | − | 0.934673i | \(-0.615693\pi\) | ||||
−0.355509 | + | 0.934673i | \(0.615693\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 36.0000i | 0.0126331i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 2160.00i | − | 0.746809i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1728.00 | −0.588726 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4212.00 | 1.41427 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −288.000 | −0.0953176 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2833.00 | −0.924321 | −0.462161 | − | 0.886796i | \(-0.652926\pi\) | ||||
−0.462161 | + | 0.886796i | \(0.652926\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 357.000i | − | 0.114841i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 873.000i | − | 0.276921i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3960.00 | 1.23881 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1098.00i | 0.338794i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1170.00 | + | 1755.00i | −0.356121 | + | 0.534181i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3507.00i | 1.05312i | 0.850138 | + | 0.526561i | \(0.176519\pi\) | ||||
−0.850138 | + | 0.526561i | \(0.823481\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1144.00 | −0.338963 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 228.000i | 0.0666647i | 0.999444 | + | 0.0333324i | \(0.0106120\pi\) | ||||
−0.999444 | + | 0.0333324i | \(0.989388\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5493.00i | − | 1.58510i | −0.609808 | − | 0.792549i | \(-0.708753\pi\) | ||
0.609808 | − | 0.792549i | \(-0.291247\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 720.000 | 0.205076 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3627.00 | 1.01980 | 0.509898 | − | 0.860235i | \(-0.329683\pi\) | ||||
0.509898 | + | 0.860235i | \(0.329683\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 999.000 | 0.277309 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 830.000 | 0.227486 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6075.00i | − | 1.64418i | −0.569357 | − | 0.822090i | \(-0.692808\pi\) | ||
0.569357 | − | 0.822090i | \(-0.307192\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 210.000i | − | 0.0561298i | −0.999606 | − | 0.0280649i | \(-0.991065\pi\) | ||
0.999606 | − | 0.0280649i | \(-0.00893451\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2080.00 | 0.549103 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 1062.00i | − | 0.276933i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −234.000 | − | 156.000i | −0.0602796 | − | 0.0401864i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 438.000i | 0.111474i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7092.00 | −1.78344 | −0.891719 | − | 0.452589i | \(-0.850501\pi\) | ||||
−0.891719 | + | 0.452589i | \(0.850501\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7776.00i | 1.93230i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 405.000i | 0.0994592i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5805.00 | −1.40897 | −0.704486 | − | 0.709718i | \(-0.748823\pi\) | ||||
−0.704486 | + | 0.709718i | \(0.748823\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4545.00 | 1.09040 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3744.00 | 0.887923 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −792.000 | −0.185691 | −0.0928457 | − | 0.995681i | \(-0.529596\pi\) | ||||
−0.0928457 | + | 0.995681i | \(0.529596\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3726.00i | 0.863722i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 438.000i | 0.100394i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5472.00 | 1.24027 | 0.620137 | − | 0.784493i | \(-0.287077\pi\) | ||||
0.620137 | + | 0.784493i | \(0.287077\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2331.00i | 0.522502i | 0.965271 | + | 0.261251i | \(0.0841351\pi\) | ||||
−0.965271 | + | 0.261251i | \(0.915865\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 585.000 | + | 390.000i | 0.129692 | + | 0.0864611i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 2112.00i | − | 0.463121i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1384.00 | −0.300204 | −0.150102 | − | 0.988671i | \(-0.547960\pi\) | ||||
−0.150102 | + | 0.988671i | \(0.547960\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6864.00i | 1.47289i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4062.00i | 0.862344i | 0.902270 | + | 0.431172i | \(0.141900\pi\) | ||||
−0.902270 | + | 0.431172i | \(0.858100\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3764.00 | 0.790624 | 0.395312 | − | 0.918547i | \(-0.370636\pi\) | ||||
0.395312 | + | 0.918547i | \(0.370636\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −54.0000 | −0.0112235 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2880.00 | 0.592338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2888.00 | −0.587828 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 852.000i | − | 0.171633i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 4227.00i | − | 0.842812i | −0.906872 | − | 0.421406i | \(-0.861537\pi\) | ||
0.906872 | − | 0.421406i | \(-0.138463\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4698.00 | 0.927214 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2544.00i | 0.497030i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4212.00 | + | 6318.00i | −0.814670 | + | 1.22200i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1455.00i | 0.278621i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 396.000 | 0.0750812 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3384.00i | − | 0.635303i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 306.000i | 0.0568871i | 0.999595 | + | 0.0284436i | \(0.00905509\pi\) | ||||
−0.999595 | + | 0.0284436i | \(0.990945\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −182.000 | −0.0335069 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2106.00 | 0.383988 | 0.191994 | − | 0.981396i | \(-0.438505\pi\) | ||||
0.191994 | + | 0.981396i | \(0.438505\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10051.0 | 1.81507 | 0.907534 | − | 0.419979i | \(-0.137963\pi\) | ||||
0.907534 | + | 0.419979i | \(0.137963\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3510.00 | −0.627829 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 2154.00i | − | 0.381643i | −0.981625 | − | 0.190821i | \(-0.938885\pi\) | ||
0.981625 | − | 0.190821i | \(-0.0611151\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6912.00i | 1.21316i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 612.000 | 0.106413 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 270.000i | 0.0465115i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1144.00 | − | 1716.00i | 0.195254 | − | 0.292882i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1083.00i | 0.183150i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1665.00 | −0.279010 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 10770.0i | − | 1.78844i | −0.447630 | − | 0.894219i | \(-0.647732\pi\) | ||
0.447630 | − | 0.894219i | \(-0.352268\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7878.00i | 1.29643i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 324.000 | 0.0528418 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2171.00 | −0.350926 | −0.175463 | − | 0.984486i | \(-0.556142\pi\) | ||||
−0.175463 | + | 0.984486i | \(0.556142\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 90.0000 | 0.0144193 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12672.0 | −2.01240 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6915.00i | 1.08856i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1458.00i | 0.227525i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7047.00 | 1.09021 | 0.545105 | − | 0.838368i | \(-0.316490\pi\) | ||||
0.545105 | + | 0.838368i | \(0.316490\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6873.00i | 1.05416i | 0.849814 | + | 0.527082i | \(0.176714\pi\) | ||||
−0.849814 | + | 0.527082i | \(0.823286\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1378.00 | + | 2067.00i | −0.209550 | + | 0.314326i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 9318.00i | − | 1.40495i | −0.711709 | − | 0.702475i | \(-0.752078\pi\) | ||
0.711709 | − | 0.702475i | \(-0.247922\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3213.00 | −0.480362 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 675.000i | − | 0.100069i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4128.00i | 0.606873i | 0.952852 | + | 0.303437i | \(0.0981341\pi\) | ||||
−0.952852 | + | 0.303437i | \(0.901866\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6823.00 | 0.994751 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −973.000 | −0.140687 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9882.00 | 1.41712 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2536.00 | 0.360703 | 0.180352 | − | 0.983602i | \(-0.442276\pi\) | ||||
0.180352 | + | 0.983602i | \(0.442276\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4992.00i | 0.704263i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 6210.00i | − | 0.869022i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −92.0000 | −0.0127710 | −0.00638550 | − | 0.999980i | \(-0.502033\pi\) | ||||
−0.00638550 | + | 0.999980i | \(0.502033\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1521.00i | − | 0.209451i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3744.00 | + | 5616.00i | −0.511474 | + | 0.767211i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 10182.0i | − | 1.37998i | −0.723817 | − | 0.689992i | \(-0.757614\pi\) | ||
0.723817 | − | 0.689992i | \(-0.242386\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2086.00 | −0.280496 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 579.000i | 0.0772468i | 0.999254 | + | 0.0386234i | \(0.0122973\pi\) | ||||
−0.999254 | + | 0.0386234i | \(0.987703\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 6480.00i | − | 0.857796i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2522.00 | −0.331267 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2106.00 | 0.274495 | 0.137247 | − | 0.990537i | \(-0.456174\pi\) | ||||
0.137247 | + | 0.990537i | \(0.456174\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7290.00 | 0.942893 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1467.00 | 0.188296 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 7470.00i | − | 0.951535i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1974.00i | 0.249552i | 0.992185 | + | 0.124776i | \(0.0398213\pi\) | ||||
−0.992185 | + | 0.124776i | \(0.960179\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 90.0000 | 0.0112923 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 11886.0i | − | 1.48020i | −0.672499 | − | 0.740098i | \(-0.734779\pi\) | ||
0.672499 | − | 0.740098i | \(-0.265221\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10296.0 | − | 6864.00i | −1.27266 | − | 0.848437i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 5841.00i | − | 0.716646i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14544.0 | −1.77130 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1254.00i | 0.151605i | 0.997123 | + | 0.0758023i | \(0.0241518\pi\) | ||||
−0.997123 | + | 0.0758023i | \(0.975848\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 414.000i | 0.0496864i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7830.00 | −0.932903 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3942.00 | 0.466278 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2419.00 | 0.284074 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5823.00 | −0.678931 | −0.339466 | − | 0.940618i | \(-0.610246\pi\) | ||||
−0.339466 | + | 0.940618i | \(0.610246\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 7341.00i | − | 0.849830i | −0.905233 | − | 0.424915i | \(-0.860304\pi\) | ||
0.905233 | − | 0.424915i | \(-0.139696\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 2886.00i | − | 0.331731i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1980.00 | −0.225986 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5640.00i | 0.639201i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1872.00 | − | 1248.00i | −0.210678 | − | 0.140452i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7485.00i | 0.836519i | 0.908328 | + | 0.418260i | \(0.137360\pi\) | ||||
−0.908328 | + | 0.418260i | \(0.862640\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15203.0 | −1.68732 | −0.843660 | − | 0.536878i | \(-0.819604\pi\) | ||||
−0.843660 | + | 0.536878i | \(0.819604\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1296.00i | 0.142847i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 972.000i | 0.106401i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1762.00 | 0.191562 | 0.0957809 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957809 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3068.00 | −0.331282 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7317.00 | 0.784743 | 0.392372 | − | 0.919807i | \(-0.371655\pi\) | ||||
0.392372 | + | 0.919807i | \(0.371655\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3942.00 | 0.419930 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 930.000i | − | 0.0984060i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5016.00i | 0.527215i | 0.964630 | + | 0.263608i | \(0.0849124\pi\) | ||||
−0.964630 | + | 0.263608i | \(0.915088\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9216.00 | −0.962227 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 1683.00i | − | 0.174557i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3510.00 | − | 5265.00i | 0.361651 | − | 0.542477i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9870.00i | 1.01028i | 0.863037 | + | 0.505141i | \(0.168560\pi\) | ||||
−0.863037 | + | 0.505141i | \(0.831440\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2385.00 | 0.242532 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 14541.0i | − | 1.46907i | −0.678570 | − | 0.734536i | \(-0.737400\pi\) | ||
0.678570 | − | 0.734536i | \(-0.262600\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2112.00i | − | 0.211993i | −0.994366 | − | 0.105997i | \(-0.966197\pi\) | ||
0.994366 | − | 0.105997i | \(-0.0338033\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2376.00 | −0.236956 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3276.00 | −0.324615 | −0.162307 | − | 0.986740i | \(-0.551894\pi\) | ||||
−0.162307 | + | 0.986740i | \(0.551894\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −540.000 | −0.0531661 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1874.00 | 0.183332 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 4656.00i | − | 0.452607i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 264.000i | − | 0.0255014i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10764.0 | 1.03323 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 15453.0i | − | 1.47404i | −0.675870 | − | 0.737020i | \(-0.736232\pi\) | ||
0.675870 | − | 0.737020i | \(-0.263768\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11817.0 | − | 7878.00i | −1.12018 | − | 0.746790i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 2430.00i | − | 0.228921i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7668.00 | −0.717909 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3660.00i | 0.340555i | 0.985396 | + | 0.170278i | \(0.0544665\pi\) | ||||
−0.985396 | + | 0.170278i | \(0.945534\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 1194.00i | − | 0.110418i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −747.000 | −0.0686591 | −0.0343296 | − | 0.999411i | \(-0.510930\pi\) | ||||
−0.0343296 | + | 0.999411i | \(0.510930\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6480.00 | 0.591977 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11232.0 | 1.01988 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5355.00 | 0.483309 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15804.0i | 1.41780i | 0.705307 | + | 0.708902i | \(0.250809\pi\) | ||||
−0.705307 | + | 0.708902i | \(0.749191\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 2388.00i | − | 0.212950i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12078.0 | 1.07064 | 0.535319 | − | 0.844650i | \(-0.320191\pi\) | ||||
0.535319 | + | 0.844650i | \(0.320191\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 3564.00i | − | 0.314051i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −845.000 | − | 2028.00i | −0.0740193 | − | 0.177646i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16110.0i | 1.40287i | 0.712731 | + | 0.701437i | \(0.247458\pi\) | ||||
−0.712731 | + | 0.701437i | \(0.752542\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16470.0 | −1.42581 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 318.000i | 0.0273685i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1638.00i | 0.140153i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5328.00 | 0.453240 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1566.00 | −0.132447 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3915.00 | 0.329212 | 0.164606 | − | 0.986359i | \(-0.447365\pi\) | ||||
0.164606 | + | 0.986359i | \(0.447365\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16184.0 | −1.35311 | −0.676555 | − | 0.736392i | \(-0.736528\pi\) | ||||
−0.676555 | + | 0.736392i | \(0.736528\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 660.000i | 0.0548662i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11880.0i | 0.981975i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14077.0 | 1.15698 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 13572.0i | − | 1.10918i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7488.00 | − | 4992.00i | −0.608520 | − | 0.405680i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 5508.00i | − | 0.445106i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 657.000 | 0.0527964 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 5664.00i | − | 0.452627i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7923.00i | 0.629642i | 0.949151 | + | 0.314821i | \(0.101945\pi\) | ||||
−0.949151 | + | 0.314821i | \(0.898055\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1222.00 | −0.0965765 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9747.00 | 0.766084 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14389.0 | 1.12473 | 0.562367 | − | 0.826888i | \(-0.309891\pi\) | ||||
0.562367 | + | 0.826888i | \(0.309891\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9776.00 | −0.759981 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 864.000i | 0.0668015i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12450.0i | 0.957374i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2727.00 | −0.208567 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10383.0i | 0.789842i | 0.918715 | + | 0.394921i | \(0.129228\pi\) | ||||
−0.918715 | + | 0.394921i | \(0.870772\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2522.00 | − | 3783.00i | 0.190822 | − | 0.286232i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2160.00i | 0.162558i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16425.0 | 1.22954 | 0.614770 | − | 0.788706i | \(-0.289249\pi\) | ||||
0.614770 | + | 0.788706i | \(0.289249\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 810.000i | − | 0.0603132i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9735.00i | 0.721043i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12213.0 | 0.899817 | 0.449908 | − | 0.893075i | \(-0.351457\pi\) | ||||
0.449908 | + | 0.893075i | \(0.351457\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6383.00 | 0.467811 | 0.233906 | − | 0.972259i | \(-0.424849\pi\) | ||||
0.233906 | + | 0.972259i | \(0.424849\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1260.00 | −0.0918626 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7128.00 | −0.516971 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6426.00i | 0.463636i | 0.972759 | + | 0.231818i | \(0.0744674\pi\) | ||||
−0.972759 | + | 0.231818i | \(0.925533\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 342.000i | − | 0.0245476i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6570.00 | −0.469139 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19872.0i | 1.41169i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9126.00 | + | 6084.00i | 0.644981 | + | 0.429987i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21330.0i | 1.49980i | 0.661551 | + | 0.749901i | \(0.269899\pi\) | ||||
−0.661551 | + | 0.749901i | \(0.730101\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1584.00 | −0.110811 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 81.0000i | 0.00563772i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 12084.0i | − | 0.836813i | −0.908260 | − | 0.418407i | \(-0.862589\pi\) | ||
0.908260 | − | 0.418407i | \(-0.137411\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6075.00 | −0.418573 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1996.00 | −0.136836 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2394.00 | −0.163299 | −0.0816496 | − | 0.996661i | \(-0.526019\pi\) | ||||
−0.0816496 | + | 0.996661i | \(0.526019\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21971.0 | −1.49121 | −0.745604 | − | 0.666389i | \(-0.767839\pi\) | ||||
−0.745604 | + | 0.666389i | \(0.767839\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 936.000i | − | 0.0632121i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8757.00i | 0.588467i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15406.0 | 1.03017 | 0.515083 | − | 0.857141i | \(-0.327761\pi\) | ||||
0.515083 | + | 0.857141i | \(0.327761\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 2160.00i | − | 0.143724i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4329.00 | + | 2886.00i | 0.286633 | + | 0.191088i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 9630.00i | − | 0.634506i | −0.948341 | − | 0.317253i | \(-0.897240\pi\) | ||
0.948341 | − | 0.317253i | \(-0.102760\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1728.00 | −0.113300 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14748.0i | 0.962289i | 0.876641 | + | 0.481144i | \(0.159779\pi\) | ||||
−0.876641 | + | 0.481144i | \(0.840221\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 3672.00i | − | 0.238433i | −0.992868 | − | 0.119217i | \(-0.961962\pi\) | ||
0.992868 | − | 0.119217i | \(-0.0380383\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8586.00 | 0.554822 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6570.00 | −0.422506 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8189.00 | −0.524096 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −288.000 | −0.0183439 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13635.0i | 0.864329i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 19875.0i | − | 1.25390i | −0.779059 | − | 0.626950i | \(-0.784303\pi\) | ||
0.779059 | − | 0.626950i | \(-0.215697\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2833.00 | −0.177886 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18774.0i | 1.17327i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3068.00 | − | 4602.00i | 0.190830 | − | 0.286245i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9282.00i | 0.574633i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1710.00 | 0.105368 | 0.0526840 | − | 0.998611i | \(-0.483222\pi\) | ||||
0.0526840 | + | 0.998611i | \(0.483222\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16452.0i | 1.00903i | 0.863404 | + | 0.504513i | \(0.168328\pi\) | ||||
−0.863404 | + | 0.504513i | \(0.831672\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 873.000i | − | 0.0532936i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25902.0 | −1.57390 | −0.786950 | − | 0.617017i | \(-0.788341\pi\) | ||||
−0.786950 | + | 0.617017i | \(0.788341\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25056.0 | 1.51546 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3960.00 | 0.238410 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18108.0 | 1.08518 | 0.542589 | − | 0.839999i | \(-0.317444\pi\) | ||||
0.542589 | + | 0.839999i | \(0.317444\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 13203.0i | − | 0.787609i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 28548.0i | − | 1.69523i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32904.0 | 1.94500 | 0.972502 | − | 0.232894i | \(-0.0748195\pi\) | ||||
0.972502 | + | 0.232894i | \(0.0748195\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 15318.0i | − | 0.901363i | −0.892685 | − | 0.450682i | \(-0.851181\pi\) | ||
0.892685 | − | 0.450682i | \(-0.148819\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1170.00 | + | 1755.00i | −0.0685355 | + | 0.102803i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 810.000i | − | 0.0472338i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23328.0 | 1.35422 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3507.00i | 0.202673i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 18048.0i | − | 1.03835i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7729.00 | −0.442691 | −0.221346 | − | 0.975195i | \(-0.571045\pi\) | ||||
−0.221346 | + | 0.975195i | \(0.571045\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2332.00 | −0.132976 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19242.0 | 1.09236 | 0.546182 | − | 0.837667i | \(-0.316081\pi\) | ||||
0.546182 | + | 0.837667i | \(0.316081\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12780.0 | 0.722314 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 228.000i | 0.0128296i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22518.0i | 1.26153i | 0.775973 | + | 0.630767i | \(0.217260\pi\) | ||||
−0.775973 | + | 0.630767i | \(0.782740\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3726.00 | 0.207829 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 5493.00i | − | 0.305052i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10764.0 | + | 16146.0i | −0.595175 | + | 0.892763i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 9168.00i | − | 0.504728i | −0.967632 | − | 0.252364i | \(-0.918792\pi\) | ||
0.967632 | − | 0.252364i | \(-0.0812081\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18720.0 | −1.02614 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 21771.0i | − | 1.18823i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8640.00i | 0.469531i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3627.00 | 0.196260 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1170.00 | 0.0630389 | 0.0315195 | − | 0.999503i | \(-0.489965\pi\) | ||||
0.0315195 | + | 0.999503i | \(0.489965\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1818.00 | −0.0975351 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 999.000 | 0.0533681 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5940.00i | 0.315978i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1662.00i | 0.0880363i | 0.999031 | + | 0.0440181i | \(0.0140159\pi\) | ||||
−0.999031 | + | 0.0440181i | \(0.985984\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21580.0 | −1.13827 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 42768.0i | 2.24639i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11232.0 | + | 16848.0i | −0.587487 | + | 0.881230i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 6075.00i | − | 0.316423i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30960.0 | −1.60586 | −0.802930 | − | 0.596073i | \(-0.796727\pi\) | ||||
−0.802930 | + | 0.596073i | \(0.796727\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 2730.00i | − | 0.141013i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 210.000i | − | 0.0108022i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6336.00 | −0.324570 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8372.00 | 0.427098 | 0.213549 | − | 0.976932i | \(-0.431498\pi\) | ||||
0.213549 | + | 0.976932i | \(0.431498\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15443.0 | −0.784586 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4365.00 | −0.220855 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 2739.00i | − | 0.138018i | −0.997616 | − | 0.0690091i | \(-0.978016\pi\) | ||
0.997616 | − | 0.0690091i | \(-0.0219837\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 1062.00i | − | 0.0532959i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1728.00 | 0.0863659 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 6756.00i | − | 0.336297i | −0.985762 | − | 0.168148i | \(-0.946221\pi\) | ||
0.985762 | − | 0.168148i | \(-0.0537788\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −234.000 | − | 156.000i | −0.0116008 | − | 0.00773388i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 29643.0i | − | 1.46366i | −0.681490 | − | 0.731828i | \(-0.738668\pi\) | ||
0.681490 | − | 0.731828i | \(-0.261332\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8370.00 | −0.411615 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 11388.0i | − | 0.557785i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9180.00i | 0.447837i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18128.0 | −0.880826 | −0.440413 | − | 0.897795i | \(-0.645168\pi\) | ||||
−0.440413 | + | 0.897795i | \(0.645168\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7092.00 | −0.343223 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15147.0 | −0.730140 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6410.00 | −0.307761 | −0.153881 | − | 0.988089i | \(-0.549177\pi\) | ||||
−0.153881 | + | 0.988089i | \(0.549177\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7776.00i | 0.371872i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 28290.0i | − | 1.34758i | −0.738921 | − | 0.673792i | \(-0.764664\pi\) | ||
0.738921 | − | 0.673792i | \(-0.235336\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16245.0 | −0.770784 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 10530.0i | − | 0.497664i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20358.0 | + | 13572.0i | 0.958390 | + | 0.638926i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 27960.0i | − | 1.31114i | −0.755136 | − | 0.655568i | \(-0.772429\pi\) | ||
0.755136 | − | 0.655568i | \(-0.227571\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5805.00 | −0.271157 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 5649.00i | − | 0.262847i | −0.991326 | − | 0.131423i | \(-0.958045\pi\) | ||
0.991326 | − | 0.131423i | \(-0.0419547\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 11616.0i | − | 0.538399i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4545.00 | 0.209847 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1152.00 | −0.0529842 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17136.0 | −0.785114 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7632.00 | 0.348334 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 16866.0i | − | 0.766845i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 756.000i | 0.0342420i | 0.999853 | + | 0.0171210i | \(0.00545006\pi\) | ||||
−0.999853 | + | 0.0171210i | \(0.994550\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −792.000 | −0.0357363 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1350.00i | 0.0606833i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9776.00 | − | 14664.0i | 0.437775 | − | 0.656663i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3726.00i | 0.166223i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31194.0 | 1.38638 | 0.693192 | − | 0.720753i | \(-0.256204\pi\) | ||||
0.693192 | + | 0.720753i | \(0.256204\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 4995.00i | − | 0.221164i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 11388.0i | − | 0.502341i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 52704.0 | 2.31617 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21870.0 | −0.957536 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5472.00 | 0.238691 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17055.0 | 0.741189 | 0.370594 | − | 0.928795i | \(-0.379154\pi\) | ||||
0.370594 | + | 0.928795i | \(0.379154\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 35520.0i | − | 1.53795i | −0.639280 | − | 0.768974i | \(-0.720768\pi\) | ||
0.639280 | − | 0.768974i | \(-0.279232\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2331.00i | 0.100556i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10746.0 | −0.461860 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 582.000i | − | 0.0249224i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15210.0 | − | 10140.0i | −0.648938 | − | 0.432625i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1095.00i | 0.0465478i | 0.999729 | + | 0.0232739i | \(0.00740899\pi\) | ||||
−0.999729 | + | 0.0232739i | \(0.992591\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2554.00 | 0.108174 | 0.0540868 | − | 0.998536i | \(-0.482775\pi\) | ||||
0.0540868 | + | 0.998536i | \(0.482775\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 2112.00i | − | 0.0891278i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21522.0i | 0.904950i | 0.891777 | + | 0.452475i | \(0.149459\pi\) | ||||
−0.891777 | + | 0.452475i | \(0.850541\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13124.0 | −0.549838 | −0.274919 | − | 0.961467i | \(-0.588651\pi\) | ||||
−0.274919 | + | 0.961467i | \(0.588651\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1384.00 | −0.0577743 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5310.00 | −0.220865 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21492.0 | −0.890732 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13992.0i | 0.577819i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 23424.0i | − | 0.963869i | −0.876207 | − | 0.481935i | \(-0.839934\pi\) | ||
0.876207 | − | 0.481935i | \(-0.160066\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3653.00 | −0.149781 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4062.00i | 0.165958i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18252.0 | + | 7605.00i | −0.743063 | + | 0.309609i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 14595.0i | − | 0.592078i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3764.00 | 0.152156 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 49086.0i | 1.97726i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 31077.0i | − | 1.24743i | −0.781653 | − | 0.623714i | \(-0.785623\pi\) | ||
0.781653 | − | 0.623714i | \(-0.214377\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1404.00 | 0.0561588 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19422.0 | −0.774146 | −0.387073 | − | 0.922049i | \(-0.626514\pi\) | ||||
−0.387073 | + | 0.922049i | \(0.626514\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1744.00 | −0.0692718 | −0.0346359 | − | 0.999400i | \(-0.511027\pi\) | ||||
−0.0346359 | + | 0.999400i | \(0.511027\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2880.00 | 0.113996 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 19179.0i | − | 0.756501i | −0.925703 | − | 0.378251i | \(-0.876526\pi\) | ||
0.925703 | − | 0.378251i | \(-0.123474\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14094.0i | 0.554000i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2888.00 | −0.113128 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 39840.0i | − | 1.55521i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1404.00 | + | 936.000i | 0.0546185 | + | 0.0364123i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22152.0i | 0.858799i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22815.0 | 0.881472 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29217.0i | 1.12496i | 0.826812 | + | 0.562479i | \(0.190152\pi\) | ||||
−0.826812 | + | 0.562479i | \(0.809848\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 4227.00i | − | 0.162199i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15633.0 | −0.597831 | −0.298916 | − | 0.954280i | \(-0.596625\pi\) | ||||
−0.298916 | + | 0.954280i | \(0.596625\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30589.0 | −1.16580 | −0.582900 | − | 0.812544i | \(-0.698082\pi\) | ||||
−0.582900 | + | 0.812544i | \(0.698082\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4698.00 | 0.178442 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25884.0 | 0.979819 | 0.489910 | − | 0.871773i | \(-0.337030\pi\) | ||||
0.489910 | + | 0.871773i | \(0.337030\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 31290.0i | − | 1.18046i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 31152.0i | − | 1.17130i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 666.000 | 0.0249573 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 5913.00i | − | 0.220838i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4212.00 | + | 6318.00i | −0.156783 | + | 0.235175i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38016.0i | 1.41035i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18630.0 | 0.688852 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1455.00i | 0.0536206i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10998.0i | 0.403962i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12305.0 | 0.450475 | 0.225237 | − | 0.974304i | \(-0.427684\pi\) | ||||
0.225237 | + | 0.974304i | \(0.427684\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10296.0 | −0.375684 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29772.0 | −1.08276 | −0.541378 | − | 0.840779i | \(-0.682097\pi\) | ||||
−0.541378 | + | 0.840779i | \(0.682097\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21024.0 | 0.762095 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 3384.00i | − | 0.122264i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22005.0i | 0.792442i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47644.0 | −1.71015 | −0.855076 | − | 0.518502i | \(-0.826490\pi\) | ||||
−0.855076 | + | 0.518502i | \(0.826490\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 306.000i | 0.0109479i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13923.0 | − | 9282.00i | −0.496513 | − | 0.331008i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 13332.0i | − | 0.473896i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4732.00 | 0.167658 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21924.0i | 0.774277i | 0.922022 | + | 0.387138i | \(0.126536\pi\) | ||||
−0.922022 | + | 0.387138i | \(0.873464\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 708.000i | − | 0.0249235i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2106.00 | 0.0738985 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19440.0 | 0.679953 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32398.0 | 1.12956 | 0.564779 | − | 0.825242i | \(-0.308961\pi\) | ||||
0.564779 | + | 0.825242i | \(0.308961\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10051.0 | 0.349310 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2097.00i | 0.0726464i | 0.999340 | + | 0.0363232i | \(0.0115646\pi\) | ||||
−0.999340 | + | 0.0363232i | \(0.988435\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31104.0i | 1.07411i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7155.00 | −0.246299 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 20016.0i | − | 0.686835i | −0.939183 | − | 0.343417i | \(-0.888415\pi\) | ||
0.939183 | − | 0.343417i | \(-0.111585\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42822.0 | + | 28548.0i | 1.46476 | + | 0.976509i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 2154.00i | − | 0.0734471i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24993.0 | 0.849531 | 0.424765 | − | 0.905304i | \(-0.360357\pi\) | ||||
0.424765 | + | 0.905304i | \(0.360357\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11340.0i | 0.384245i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6912.00i | 0.233473i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6210.00 | −0.209105 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −39905.0 | −1.33950 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15912.0 | −0.532458 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3078.00 | −0.102678 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40959.0i | 1.36210i | 0.732236 | + | 0.681051i | \(0.238477\pi\) | ||||
−0.732236 | + | 0.681051i | \(0.761523\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 270.000i | 0.00895113i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48933.0 | 1.61723 | 0.808617 | − | 0.588335i | \(-0.200216\pi\) | ||||
0.808617 | + | 0.588335i | \(0.200216\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36285.0i | 1.19552i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1144.00 | − | 1716.00i | 0.0375767 | − | 0.0563651i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47388.0i | 1.55177i | 0.630876 | + | 0.775884i | \(0.282696\pi\) | ||||
−0.630876 | + | 0.775884i | \(0.717304\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21024.0 | 0.686343 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 28158.0i | − | 0.916428i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16803.0i | 0.545201i | 0.962127 | + | 0.272600i | \(0.0878837\pi\) | ||||
−0.962127 | + | 0.272600i | \(0.912116\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 729.000 | 0.0235816 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1665.00 | −0.0536956 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15714.0 | −0.505234 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57526.0 | 1.84397 | 0.921985 | − | 0.387226i | \(-0.126567\pi\) | ||||
0.921985 | + | 0.387226i | \(0.126567\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 10770.0i | − | 0.344185i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17964.0i | 0.572359i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25000.0 | −0.794140 | −0.397070 | − | 0.917788i | \(-0.629973\pi\) | ||||
−0.397070 | + | 0.917788i | \(0.629973\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16059.0i | 0.508593i |
(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 | 208.4.f.b.129.1 | 2 | ||
4.3 | odd | 2 | 13.4.b.a.12.2 | yes | 2 | ||
8.3 | odd | 2 | 832.4.f.e.129.2 | 2 | |||
8.5 | even | 2 | 832.4.f.c.129.2 | 2 | |||
12.11 | even | 2 | 117.4.b.a.64.1 | 2 | |||
13.12 | even | 2 | inner | 208.4.f.b.129.2 | 2 | ||
20.3 | even | 4 | 325.4.d.b.324.1 | 2 | |||
20.7 | even | 4 | 325.4.d.a.324.2 | 2 | |||
20.19 | odd | 2 | 325.4.c.b.51.1 | 2 | |||
52.3 | odd | 6 | 169.4.e.d.147.1 | 4 | |||
52.7 | even | 12 | 169.4.c.c.146.1 | 2 | |||
52.11 | even | 12 | 169.4.c.c.22.1 | 2 | |||
52.15 | even | 12 | 169.4.c.b.22.1 | 2 | |||
52.19 | even | 12 | 169.4.c.b.146.1 | 2 | |||
52.23 | odd | 6 | 169.4.e.d.147.2 | 4 | |||
52.31 | even | 4 | 169.4.a.c.1.1 | 1 | |||
52.35 | odd | 6 | 169.4.e.d.23.2 | 4 | |||
52.43 | odd | 6 | 169.4.e.d.23.1 | 4 | |||
52.47 | even | 4 | 169.4.a.b.1.1 | 1 | |||
52.51 | odd | 2 | 13.4.b.a.12.1 | ✓ | 2 | ||
104.51 | odd | 2 | 832.4.f.e.129.1 | 2 | |||
104.77 | even | 2 | 832.4.f.c.129.1 | 2 | |||
156.47 | odd | 4 | 1521.4.a.i.1.1 | 1 | |||
156.83 | odd | 4 | 1521.4.a.d.1.1 | 1 | |||
156.155 | even | 2 | 117.4.b.a.64.2 | 2 | |||
260.103 | even | 4 | 325.4.d.a.324.1 | 2 | |||
260.207 | even | 4 | 325.4.d.b.324.2 | 2 | |||
260.259 | odd | 2 | 325.4.c.b.51.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.b.a.12.1 | ✓ | 2 | 52.51 | odd | 2 | ||
13.4.b.a.12.2 | yes | 2 | 4.3 | odd | 2 | ||
117.4.b.a.64.1 | 2 | 12.11 | even | 2 | |||
117.4.b.a.64.2 | 2 | 156.155 | even | 2 | |||
169.4.a.b.1.1 | 1 | 52.47 | even | 4 | |||
169.4.a.c.1.1 | 1 | 52.31 | even | 4 | |||
169.4.c.b.22.1 | 2 | 52.15 | even | 12 | |||
169.4.c.b.146.1 | 2 | 52.19 | even | 12 | |||
169.4.c.c.22.1 | 2 | 52.11 | even | 12 | |||
169.4.c.c.146.1 | 2 | 52.7 | even | 12 | |||
169.4.e.d.23.1 | 4 | 52.43 | odd | 6 | |||
169.4.e.d.23.2 | 4 | 52.35 | odd | 6 | |||
169.4.e.d.147.1 | 4 | 52.3 | odd | 6 | |||
169.4.e.d.147.2 | 4 | 52.23 | odd | 6 | |||
208.4.f.b.129.1 | 2 | 1.1 | even | 1 | trivial | ||
208.4.f.b.129.2 | 2 | 13.12 | even | 2 | inner | ||
325.4.c.b.51.1 | 2 | 20.19 | odd | 2 | |||
325.4.c.b.51.2 | 2 | 260.259 | odd | 2 | |||
325.4.d.a.324.1 | 2 | 260.103 | even | 4 | |||
325.4.d.a.324.2 | 2 | 20.7 | even | 4 | |||
325.4.d.b.324.1 | 2 | 20.3 | even | 4 | |||
325.4.d.b.324.2 | 2 | 260.207 | even | 4 | |||
832.4.f.c.129.1 | 2 | 104.77 | even | 2 | |||
832.4.f.c.129.2 | 2 | 8.5 | even | 2 | |||
832.4.f.e.129.1 | 2 | 104.51 | odd | 2 | |||
832.4.f.e.129.2 | 2 | 8.3 | odd | 2 | |||
1521.4.a.d.1.1 | 1 | 156.83 | odd | 4 | |||
1521.4.a.i.1.1 | 1 | 156.47 | odd | 4 |