Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 52x^{6} + 805x^{4} - 4210x^{2} + 4992 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 117) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(2.75628\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.75628 | 0.974491 | 0.487246 | − | 0.873265i | \(-0.338002\pi\) | ||||
0.487246 | + | 0.873265i | \(0.338002\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.402937 | −0.0503671 | ||||||||
\(5\) | 0.313209 | 0.0280143 | 0.0140071 | − | 0.999902i | \(-0.495541\pi\) | ||||
0.0140071 | + | 0.999902i | \(0.495541\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −28.5660 | −1.54242 | −0.771208 | − | 0.636583i | \(-0.780347\pi\) | ||||
−0.771208 | + | 0.636583i | \(0.780347\pi\) | |||||||
\(8\) | −23.1608 | −1.02357 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.863291 | 0.0272997 | ||||||||
\(11\) | 63.2173 | 1.73279 | 0.866397 | − | 0.499356i | \(-0.166430\pi\) | ||||
0.866397 | + | 0.499356i | \(0.166430\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −78.7357 | −1.50307 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −60.6141 | −0.947096 | ||||||||
\(17\) | −98.8270 | −1.40995 | −0.704973 | − | 0.709234i | \(-0.749041\pi\) | ||||
−0.704973 | + | 0.709234i | \(0.749041\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.4897 | 0.174956 | 0.0874782 | − | 0.996166i | \(-0.472119\pi\) | ||||
0.0874782 | + | 0.996166i | \(0.472119\pi\) | |||||||
\(20\) | −0.126204 | −0.00141100 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 174.244 | 1.68859 | ||||||||
\(23\) | 14.3900 | 0.130457 | 0.0652286 | − | 0.997870i | \(-0.479222\pi\) | ||||
0.0652286 | + | 0.997870i | \(0.479222\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.902 | −0.999215 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 11.5103 | 0.0776871 | ||||||||
\(29\) | 196.283 | 1.25686 | 0.628428 | − | 0.777868i | \(-0.283699\pi\) | ||||
0.628428 | + | 0.777868i | \(0.283699\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −118.691 | −0.687661 | −0.343830 | − | 0.939032i | \(-0.611724\pi\) | ||||
−0.343830 | + | 0.939032i | \(0.611724\pi\) | |||||||
\(32\) | 18.2172 | 0.100637 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −272.395 | −1.37398 | ||||||||
\(35\) | −8.94712 | −0.0432097 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −319.114 | −1.41789 | −0.708947 | − | 0.705262i | \(-0.750829\pi\) | ||||
−0.708947 | + | 0.705262i | \(0.750829\pi\) | |||||||
\(38\) | 39.9377 | 0.170493 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.25418 | −0.0286747 | ||||||||
\(41\) | 346.106 | 1.31836 | 0.659180 | − | 0.751986i | \(-0.270904\pi\) | ||||
0.659180 | + | 0.751986i | \(0.270904\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −69.4854 | −0.246428 | −0.123214 | − | 0.992380i | \(-0.539320\pi\) | ||||
−0.123214 | + | 0.992380i | \(0.539320\pi\) | |||||||
\(44\) | −25.4726 | −0.0872758 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 39.6628 | 0.127129 | ||||||||
\(47\) | −101.875 | −0.316170 | −0.158085 | − | 0.987426i | \(-0.550532\pi\) | ||||
−0.158085 | + | 0.987426i | \(0.550532\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 473.014 | 1.37905 | ||||||||
\(50\) | −344.264 | −0.973726 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 594.823 | 1.54161 | 0.770804 | − | 0.637072i | \(-0.219855\pi\) | ||||
0.770804 | + | 0.637072i | \(0.219855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.8002 | 0.0485430 | ||||||||
\(56\) | 661.611 | 1.57878 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 541.010 | 1.22480 | ||||||||
\(59\) | −204.473 | −0.451189 | −0.225595 | − | 0.974221i | \(-0.572432\pi\) | ||||
−0.225595 | + | 0.974221i | \(0.572432\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −215.978 | −0.453331 | −0.226666 | − | 0.973973i | \(-0.572782\pi\) | ||||
−0.226666 | + | 0.973973i | \(0.572782\pi\) | |||||||
\(62\) | −327.144 | −0.670119 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 535.125 | 1.04517 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −68.6049 | −0.125096 | −0.0625480 | − | 0.998042i | \(-0.519923\pi\) | ||||
−0.0625480 | + | 0.998042i | \(0.519923\pi\) | |||||||
\(68\) | 39.8211 | 0.0710149 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −24.6607 | −0.0421075 | ||||||||
\(71\) | 946.241 | 1.58166 | 0.790832 | − | 0.612033i | \(-0.209648\pi\) | ||||
0.790832 | + | 0.612033i | \(0.209648\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 779.872 | 1.25037 | 0.625185 | − | 0.780476i | \(-0.285023\pi\) | ||||
0.625185 | + | 0.780476i | \(0.285023\pi\) | |||||||
\(74\) | −879.567 | −1.38172 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.83844 | −0.00881204 | ||||||||
\(77\) | −1805.86 | −2.67269 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 240.022 | 0.341831 | 0.170915 | − | 0.985286i | \(-0.445328\pi\) | ||||
0.170915 | + | 0.985286i | \(0.445328\pi\) | |||||||
\(80\) | −18.9849 | −0.0265322 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 953.965 | 1.28473 | ||||||||
\(83\) | 855.576 | 1.13147 | 0.565733 | − | 0.824588i | \(-0.308593\pi\) | ||||
0.565733 | + | 0.824588i | \(0.308593\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −30.9535 | −0.0394986 | ||||||||
\(86\) | −191.521 | −0.240142 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1464.16 | −1.77364 | ||||||||
\(89\) | 1264.06 | 1.50551 | 0.752753 | − | 0.658303i | \(-0.228726\pi\) | ||||
0.752753 | + | 0.658303i | \(0.228726\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.79825 | −0.00657075 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −280.795 | −0.308105 | ||||||||
\(95\) | 4.53831 | 0.00490128 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −662.290 | −0.693251 | −0.346625 | − | 0.938004i | \(-0.612672\pi\) | ||||
−0.346625 | + | 0.938004i | \(0.612672\pi\) | |||||||
\(98\) | 1303.76 | 1.34387 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 50.3276 | 0.0503276 | ||||||||
\(101\) | 793.571 | 0.781814 | 0.390907 | − | 0.920430i | \(-0.372161\pi\) | ||||
0.390907 | + | 0.920430i | \(0.372161\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 980.791 | 0.938254 | 0.469127 | − | 0.883131i | \(-0.344569\pi\) | ||||
0.469127 | + | 0.883131i | \(0.344569\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1639.50 | 1.50228 | ||||||||
\(107\) | 805.944 | 0.728164 | 0.364082 | − | 0.931367i | \(-0.381383\pi\) | ||||
0.364082 | + | 0.931367i | \(0.381383\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −845.184 | −0.742697 | −0.371348 | − | 0.928494i | \(-0.621104\pi\) | ||||
−0.371348 | + | 0.928494i | \(0.621104\pi\) | |||||||
\(110\) | 54.5749 | 0.0473047 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1731.50 | 1.46082 | ||||||||
\(113\) | −56.3774 | −0.0469340 | −0.0234670 | − | 0.999725i | \(-0.507470\pi\) | ||||
−0.0234670 | + | 0.999725i | \(0.507470\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.50707 | 0.00365467 | ||||||||
\(116\) | −79.0896 | −0.0633042 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −563.585 | −0.439680 | ||||||||
\(119\) | 2823.09 | 2.17472 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2665.43 | 2.00257 | ||||||||
\(122\) | −595.296 | −0.441767 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 47.8249 | 0.0346355 | ||||||||
\(125\) | −78.2716 | −0.0560066 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1666.65 | 1.16450 | 0.582248 | − | 0.813011i | \(-0.302173\pi\) | ||||
0.582248 | + | 0.813011i | \(0.302173\pi\) | |||||||
\(128\) | 1329.21 | 0.917868 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 602.630 | 0.401924 | 0.200962 | − | 0.979599i | \(-0.435593\pi\) | ||||
0.200962 | + | 0.979599i | \(0.435593\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −413.913 | −0.269856 | ||||||||
\(134\) | −189.094 | −0.121905 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2288.92 | 1.44318 | ||||||||
\(137\) | 421.654 | 0.262951 | 0.131476 | − | 0.991319i | \(-0.458029\pi\) | ||||
0.131476 | + | 0.991319i | \(0.458029\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 29.1702 | 0.0177999 | 0.00889995 | − | 0.999960i | \(-0.497167\pi\) | ||||
0.00889995 | + | 0.999960i | \(0.497167\pi\) | |||||||
\(140\) | 3.60512 | 0.00217635 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2608.10 | 1.54132 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 61.4776 | 0.0352099 | ||||||||
\(146\) | 2149.54 | 1.21848 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 128.583 | 0.0714152 | ||||||||
\(149\) | 2141.80 | 1.17760 | 0.588802 | − | 0.808278i | \(-0.299600\pi\) | ||||
0.588802 | + | 0.808278i | \(0.299600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1459.30 | −0.786462 | −0.393231 | − | 0.919440i | \(-0.628643\pi\) | ||||
−0.393231 | + | 0.919440i | \(0.628643\pi\) | |||||||
\(152\) | −335.594 | −0.179081 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4977.46 | −2.60451 | ||||||||
\(155\) | −37.1750 | −0.0192643 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2008.20 | 1.02084 | 0.510419 | − | 0.859926i | \(-0.329490\pi\) | ||||
0.510419 | + | 0.859926i | \(0.329490\pi\) | |||||||
\(158\) | 661.568 | 0.333111 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.70579 | 0.00281927 | ||||||||
\(161\) | −411.063 | −0.201219 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −548.495 | −0.263567 | −0.131784 | − | 0.991279i | \(-0.542070\pi\) | ||||
−0.131784 | + | 0.991279i | \(0.542070\pi\) | |||||||
\(164\) | −139.459 | −0.0664019 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2358.21 | 1.10260 | ||||||||
\(167\) | −3962.58 | −1.83613 | −0.918064 | − | 0.396432i | \(-0.870248\pi\) | ||||
−0.918064 | + | 0.396432i | \(0.870248\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −85.3165 | −0.0384910 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 27.9982 | 0.0124119 | ||||||||
\(173\) | 1729.54 | 0.760084 | 0.380042 | − | 0.924969i | \(-0.375909\pi\) | ||||
0.380042 | + | 0.924969i | \(0.375909\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3567.94 | 1.54121 | ||||||||
\(176\) | −3831.86 | −1.64112 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3484.10 | 1.46710 | ||||||||
\(179\) | −1452.91 | −0.606680 | −0.303340 | − | 0.952882i | \(-0.598102\pi\) | ||||
−0.303340 | + | 0.952882i | \(0.598102\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −550.329 | −0.225998 | −0.112999 | − | 0.993595i | \(-0.536046\pi\) | ||||
−0.112999 | + | 0.993595i | \(0.536046\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −333.284 | −0.133533 | ||||||||
\(185\) | −99.9495 | −0.0397213 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6247.58 | −2.44314 | ||||||||
\(188\) | 41.0491 | 0.0159246 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.5089 | 0.00477625 | ||||||||
\(191\) | −1868.68 | −0.707921 | −0.353960 | − | 0.935260i | \(-0.615165\pi\) | ||||
−0.353960 | + | 0.935260i | \(0.615165\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4156.52 | −1.55022 | −0.775112 | − | 0.631824i | \(-0.782306\pi\) | ||||
−0.775112 | + | 0.631824i | \(0.782306\pi\) | |||||||
\(194\) | −1825.45 | −0.675567 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −190.595 | −0.0694587 | ||||||||
\(197\) | −1522.18 | −0.550513 | −0.275257 | − | 0.961371i | \(-0.588763\pi\) | ||||
−0.275257 | + | 0.961371i | \(0.588763\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 808.130 | 0.287873 | 0.143937 | − | 0.989587i | \(-0.454024\pi\) | ||||
0.143937 | + | 0.989587i | \(0.454024\pi\) | |||||||
\(200\) | 2892.83 | 1.02277 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2187.30 | 0.761871 | ||||||||
\(203\) | −5607.01 | −1.93860 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 108.404 | 0.0369329 | ||||||||
\(206\) | 2703.33 | 0.914320 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 916.001 | 0.303163 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5260.03 | −1.71619 | −0.858094 | − | 0.513493i | \(-0.828351\pi\) | ||||
−0.858094 | + | 0.513493i | \(0.828351\pi\) | |||||||
\(212\) | −239.676 | −0.0776464 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2221.41 | 0.709590 | ||||||||
\(215\) | −21.7635 | −0.00690351 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3390.51 | 1.06066 | ||||||||
\(218\) | −2329.56 | −0.723751 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.97824 | −0.00244497 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4690.71 | 1.40858 | 0.704290 | − | 0.709912i | \(-0.251266\pi\) | ||||
0.704290 | + | 0.709912i | \(0.251266\pi\) | |||||||
\(224\) | −520.392 | −0.155224 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −155.392 | −0.0457368 | ||||||||
\(227\) | −3560.61 | −1.04108 | −0.520542 | − | 0.853836i | \(-0.674270\pi\) | ||||
−0.520542 | + | 0.853836i | \(0.674270\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3144.82 | 0.907490 | 0.453745 | − | 0.891131i | \(-0.350088\pi\) | ||||
0.453745 | + | 0.891131i | \(0.350088\pi\) | |||||||
\(230\) | 12.4227 | 0.00356144 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4546.07 | −1.28648 | ||||||||
\(233\) | −852.543 | −0.239708 | −0.119854 | − | 0.992792i | \(-0.538243\pi\) | ||||
−0.119854 | + | 0.992792i | \(0.538243\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −31.9081 | −0.00885727 | ||||||||
\(236\) | 82.3898 | 0.0227251 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7781.22 | 2.11925 | ||||||||
\(239\) | −2189.33 | −0.592534 | −0.296267 | − | 0.955105i | \(-0.595742\pi\) | ||||
−0.296267 | + | 0.955105i | \(0.595742\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6329.98 | −1.69191 | −0.845954 | − | 0.533257i | \(-0.820968\pi\) | ||||
−0.845954 | + | 0.533257i | \(0.820968\pi\) | |||||||
\(242\) | 7346.65 | 1.95149 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 87.0257 | 0.0228330 | ||||||||
\(245\) | 148.152 | 0.0386331 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2748.97 | 0.703871 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −215.738 | −0.0545779 | ||||||||
\(251\) | −3602.97 | −0.906046 | −0.453023 | − | 0.891499i | \(-0.649654\pi\) | ||||
−0.453023 | + | 0.891499i | \(0.649654\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 909.695 | 0.226055 | ||||||||
\(254\) | 4593.74 | 1.13479 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −617.315 | −0.150712 | ||||||||
\(257\) | 3072.64 | 0.745781 | 0.372891 | − | 0.927875i | \(-0.378367\pi\) | ||||
0.372891 | + | 0.927875i | \(0.378367\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9115.80 | 2.18698 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1661.01 | 0.391671 | ||||||||
\(263\) | −3543.20 | −0.830734 | −0.415367 | − | 0.909654i | \(-0.636347\pi\) | ||||
−0.415367 | + | 0.909654i | \(0.636347\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 186.304 | 0.0431871 | ||||||||
\(266\) | −1140.86 | −0.262972 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 27.6435 | 0.00630072 | ||||||||
\(269\) | 5899.97 | 1.33728 | 0.668638 | − | 0.743588i | \(-0.266878\pi\) | ||||
0.668638 | + | 0.743588i | \(0.266878\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2109.52 | 0.472858 | 0.236429 | − | 0.971649i | \(-0.424023\pi\) | ||||
0.236429 | + | 0.971649i | \(0.424023\pi\) | |||||||
\(272\) | 5990.32 | 1.33535 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1162.19 | 0.256244 | ||||||||
\(275\) | −7895.96 | −1.73143 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7265.00 | 1.57585 | 0.787927 | − | 0.615769i | \(-0.211155\pi\) | ||||
0.787927 | + | 0.615769i | \(0.211155\pi\) | |||||||
\(278\) | 80.4012 | 0.0173458 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 207.223 | 0.0442283 | ||||||||
\(281\) | 4771.36 | 1.01294 | 0.506469 | − | 0.862258i | \(-0.330951\pi\) | ||||
0.506469 | + | 0.862258i | \(0.330951\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2036.26 | 0.427714 | 0.213857 | − | 0.976865i | \(-0.431397\pi\) | ||||
0.213857 | + | 0.976865i | \(0.431397\pi\) | |||||||
\(284\) | −381.275 | −0.0796639 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9886.86 | −2.03346 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4853.78 | 0.987947 | ||||||||
\(290\) | 169.449 | 0.0343118 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −314.239 | −0.0629776 | ||||||||
\(293\) | 3719.02 | 0.741527 | 0.370764 | − | 0.928727i | \(-0.379096\pi\) | ||||
0.370764 | + | 0.928727i | \(0.379096\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −64.0429 | −0.0126397 | ||||||||
\(296\) | 7390.95 | 1.45132 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5903.39 | 1.14756 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1984.92 | 0.380095 | ||||||||
\(302\) | −4022.22 | −0.766400 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −878.282 | −0.165700 | ||||||||
\(305\) | −67.6464 | −0.0126997 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7282.24 | 1.35381 | 0.676905 | − | 0.736070i | \(-0.263321\pi\) | ||||
0.676905 | + | 0.736070i | \(0.263321\pi\) | |||||||
\(308\) | 727.649 | 0.134616 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −102.465 | −0.0187729 | ||||||||
\(311\) | 4569.28 | 0.833120 | 0.416560 | − | 0.909108i | \(-0.363236\pi\) | ||||
0.416560 | + | 0.909108i | \(0.363236\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.0294 | 0.00379761 | 0.00189880 | − | 0.999998i | \(-0.499396\pi\) | ||||
0.00189880 | + | 0.999998i | \(0.499396\pi\) | |||||||
\(314\) | 5535.15 | 0.994797 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −96.7138 | −0.0172170 | ||||||||
\(317\) | −5159.17 | −0.914095 | −0.457047 | − | 0.889442i | \(-0.651093\pi\) | ||||
−0.457047 | + | 0.889442i | \(0.651093\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12408.5 | 2.17787 | ||||||||
\(320\) | 167.606 | 0.0292796 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1133.00 | −0.196087 | ||||||||
\(323\) | −1431.98 | −0.246679 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1511.80 | −0.256844 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8016.11 | −1.34944 | ||||||||
\(329\) | 2910.15 | 0.487666 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7577.53 | 1.25830 | 0.629152 | − | 0.777282i | \(-0.283402\pi\) | ||||
0.629152 | + | 0.777282i | \(0.283402\pi\) | |||||||
\(332\) | −344.743 | −0.0569887 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10922.0 | −1.78929 | ||||||||
\(335\) | −21.4877 | −0.00350447 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2109.79 | −0.341032 | −0.170516 | − | 0.985355i | \(-0.554543\pi\) | ||||
−0.170516 | + | 0.985355i | \(0.554543\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.4723 | 0.00198943 | ||||||||
\(341\) | −7503.30 | −1.19157 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3713.98 | −0.584653 | ||||||||
\(344\) | 1609.34 | 0.252237 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4767.09 | 0.740695 | ||||||||
\(347\) | 8107.91 | 1.25434 | 0.627169 | − | 0.778883i | \(-0.284214\pi\) | ||||
0.627169 | + | 0.778883i | \(0.284214\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8686.38 | −1.33230 | −0.666148 | − | 0.745820i | \(-0.732058\pi\) | ||||
−0.666148 | + | 0.745820i | \(0.732058\pi\) | |||||||
\(350\) | 9834.24 | 1.50189 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1151.64 | 0.174383 | ||||||||
\(353\) | −9050.23 | −1.36458 | −0.682288 | − | 0.731083i | \(-0.739015\pi\) | ||||
−0.682288 | + | 0.731083i | \(0.739015\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 296.371 | 0.0443092 | ||||||||
\(356\) | −509.336 | −0.0758279 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4004.63 | −0.591204 | ||||||||
\(359\) | −7043.80 | −1.03554 | −0.517768 | − | 0.855521i | \(-0.673237\pi\) | ||||
−0.517768 | + | 0.855521i | \(0.673237\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6649.05 | −0.969390 | ||||||||
\(362\) | −1516.86 | −0.220233 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 244.263 | 0.0350282 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13825.1 | 1.96639 | 0.983194 | − | 0.182565i | \(-0.0584401\pi\) | ||||
0.983194 | + | 0.182565i | \(0.0584401\pi\) | |||||||
\(368\) | −872.236 | −0.123556 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −275.488 | −0.0387080 | ||||||||
\(371\) | −16991.7 | −2.37780 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6368.19 | 0.884001 | 0.442000 | − | 0.897015i | \(-0.354269\pi\) | ||||
0.442000 | + | 0.897015i | \(0.354269\pi\) | |||||||
\(374\) | −17220.1 | −2.38082 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2359.51 | 0.323623 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2451.66 | −0.332278 | −0.166139 | − | 0.986102i | \(-0.553130\pi\) | ||||
−0.166139 | + | 0.986102i | \(0.553130\pi\) | |||||||
\(380\) | −1.82865 | −0.000246863 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5150.60 | −0.689863 | ||||||||
\(383\) | −10830.9 | −1.44500 | −0.722500 | − | 0.691371i | \(-0.757007\pi\) | ||||
−0.722500 | + | 0.691371i | \(0.757007\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −565.613 | −0.0748735 | ||||||||
\(386\) | −11456.5 | −1.51068 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 266.861 | 0.0349170 | ||||||||
\(389\) | −4978.07 | −0.648838 | −0.324419 | − | 0.945914i | \(-0.605169\pi\) | ||||
−0.324419 | + | 0.945914i | \(0.605169\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1422.12 | −0.183938 | ||||||||
\(392\) | −10955.4 | −1.41156 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4195.56 | −0.536470 | ||||||||
\(395\) | 75.1772 | 0.00957614 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9450.67 | −1.19475 | −0.597375 | − | 0.801962i | \(-0.703790\pi\) | ||||
−0.597375 | + | 0.801962i | \(0.703790\pi\) | |||||||
\(398\) | 2227.43 | 0.280530 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7570.82 | 0.946353 | ||||||||
\(401\) | −8776.77 | −1.09300 | −0.546498 | − | 0.837461i | \(-0.684039\pi\) | ||||
−0.546498 | + | 0.837461i | \(0.684039\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −319.759 | −0.0393777 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15454.5 | −1.88914 | ||||||||
\(407\) | −20173.5 | −2.45692 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4520.19 | 0.546477 | 0.273238 | − | 0.961946i | \(-0.411905\pi\) | ||||
0.273238 | + | 0.961946i | \(0.411905\pi\) | |||||||
\(410\) | 298.791 | 0.0359908 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −395.197 | −0.0472571 | ||||||||
\(413\) | 5840.98 | 0.695922 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 267.974 | 0.0316972 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2524.75 | 0.295430 | ||||||||
\(419\) | 12006.4 | 1.39989 | 0.699944 | − | 0.714198i | \(-0.253208\pi\) | ||||
0.699944 | + | 0.714198i | \(0.253208\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9731.52 | 1.12657 | 0.563284 | − | 0.826263i | \(-0.309538\pi\) | ||||
0.563284 | + | 0.826263i | \(0.309538\pi\) | |||||||
\(422\) | −14498.1 | −1.67241 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −13776.6 | −1.57795 | ||||||||
\(425\) | 12343.7 | 1.40884 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6169.63 | 0.699226 | ||||||||
\(428\) | −324.745 | −0.0366755 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −59.9861 | −0.00672741 | ||||||||
\(431\) | 4111.03 | 0.459446 | 0.229723 | − | 0.973256i | \(-0.426218\pi\) | ||||
0.229723 | + | 0.973256i | \(0.426218\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2906.06 | 0.322532 | 0.161266 | − | 0.986911i | \(-0.448442\pi\) | ||||
0.161266 | + | 0.986911i | \(0.448442\pi\) | |||||||
\(434\) | 9345.19 | 1.03360 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 340.556 | 0.0374075 | ||||||||
\(437\) | 208.507 | 0.0228243 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8874.72 | 0.964846 | 0.482423 | − | 0.875938i | \(-0.339757\pi\) | ||||
0.482423 | + | 0.875938i | \(0.339757\pi\) | |||||||
\(440\) | −458.590 | −0.0496873 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12640.5 | 1.35569 | 0.677843 | − | 0.735207i | \(-0.262915\pi\) | ||||
0.677843 | + | 0.735207i | \(0.262915\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 395.915 | 0.0421756 | ||||||||
\(446\) | 12928.9 | 1.37265 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −15286.4 | −1.61208 | ||||||||
\(449\) | 1774.29 | 0.186490 | 0.0932451 | − | 0.995643i | \(-0.470276\pi\) | ||||
0.0932451 | + | 0.995643i | \(0.470276\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21879.9 | 2.28444 | ||||||||
\(452\) | 22.7165 | 0.00236393 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9814.04 | −1.01453 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6168.82 | −0.631433 | −0.315717 | − | 0.948854i | \(-0.602245\pi\) | ||||
−0.315717 | + | 0.948854i | \(0.602245\pi\) | |||||||
\(458\) | 8667.98 | 0.884341 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.81607 | −0.000184075 0 | ||||||||
\(461\) | 7455.38 | 0.753214 | 0.376607 | − | 0.926373i | \(-0.377091\pi\) | ||||
0.376607 | + | 0.926373i | \(0.377091\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5399.78 | −0.542006 | −0.271003 | − | 0.962578i | \(-0.587355\pi\) | ||||
−0.271003 | + | 0.962578i | \(0.587355\pi\) | |||||||
\(464\) | −11897.5 | −1.19036 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2349.85 | −0.233593 | ||||||||
\(467\) | 3992.01 | 0.395564 | 0.197782 | − | 0.980246i | \(-0.436626\pi\) | ||||
0.197782 | + | 0.980246i | \(0.436626\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1959.77 | 0.192950 | ||||||||
\(470\) | −87.9477 | −0.00863133 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4735.77 | 0.461825 | ||||||||
\(473\) | −4392.68 | −0.427009 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1809.79 | −0.174819 | ||||||||
\(476\) | −1137.53 | −0.109535 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6034.39 | −0.577419 | ||||||||
\(479\) | −3151.62 | −0.300629 | −0.150315 | − | 0.988638i | \(-0.548029\pi\) | ||||
−0.150315 | + | 0.988638i | \(0.548029\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −17447.2 | −1.64875 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1074.00 | −0.100864 | ||||||||
\(485\) | −207.435 | −0.0194209 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3909.18 | 0.363741 | 0.181870 | − | 0.983323i | \(-0.441785\pi\) | ||||
0.181870 | + | 0.983323i | \(0.441785\pi\) | |||||||
\(488\) | 5002.24 | 0.464018 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 408.349 | 0.0376476 | ||||||||
\(491\) | 6645.13 | 0.610775 | 0.305388 | − | 0.952228i | \(-0.401214\pi\) | ||||
0.305388 | + | 0.952228i | \(0.401214\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19398.1 | −1.77210 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7194.33 | 0.651281 | ||||||||
\(497\) | −27030.3 | −2.43959 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6111.83 | −0.548303 | −0.274151 | − | 0.961687i | \(-0.588397\pi\) | ||||
−0.274151 | + | 0.961687i | \(0.588397\pi\) | |||||||
\(500\) | 31.5385 | 0.00282089 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9930.79 | −0.882934 | ||||||||
\(503\) | 10954.1 | 0.971010 | 0.485505 | − | 0.874234i | \(-0.338636\pi\) | ||||
0.485505 | + | 0.874234i | \(0.338636\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 248.554 | 0.0219020 | ||||||||
\(506\) | 2507.37 | 0.220289 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −671.553 | −0.0586523 | ||||||||
\(509\) | 11121.1 | 0.968439 | 0.484220 | − | 0.874947i | \(-0.339104\pi\) | ||||
0.484220 | + | 0.874947i | \(0.339104\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22277.8 | −1.92859 | ||||||||
\(512\) | −12335.2 | −1.06473 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8469.04 | 0.726757 | ||||||||
\(515\) | 307.193 | 0.0262845 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6440.25 | −0.547857 | ||||||||
\(518\) | 25125.7 | 2.13119 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2403.33 | 0.202096 | 0.101048 | − | 0.994882i | \(-0.467780\pi\) | ||||
0.101048 | + | 0.994882i | \(0.467780\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4251.72 | 0.355477 | 0.177739 | − | 0.984078i | \(-0.443122\pi\) | ||||
0.177739 | + | 0.984078i | \(0.443122\pi\) | |||||||
\(524\) | −242.822 | −0.0202437 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9766.04 | −0.809543 | ||||||||
\(527\) | 11729.8 | 0.969564 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11959.9 | −0.982981 | ||||||||
\(530\) | 513.506 | 0.0420854 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 166.781 | 0.0135918 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 252.429 | 0.0203990 | ||||||||
\(536\) | 1588.95 | 0.128045 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16261.9 | 1.30316 | ||||||||
\(539\) | 29902.7 | 2.38961 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8924.44 | 0.709227 | 0.354613 | − | 0.935013i | \(-0.384612\pi\) | ||||
0.354613 | + | 0.935013i | \(0.384612\pi\) | |||||||
\(542\) | 5814.43 | 0.460796 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1800.35 | −0.141892 | ||||||||
\(545\) | −264.719 | −0.0208061 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14696.0 | −1.14873 | −0.574367 | − | 0.818598i | \(-0.694752\pi\) | ||||
−0.574367 | + | 0.818598i | \(0.694752\pi\) | |||||||
\(548\) | −169.900 | −0.0132441 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −21763.5 | −1.68727 | ||||||||
\(551\) | 2844.09 | 0.219895 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6856.47 | −0.527245 | ||||||||
\(554\) | 20024.3 | 1.53566 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.7538 | −0.000896530 0 | ||||||||
\(557\) | −2464.03 | −0.187440 | −0.0937202 | − | 0.995599i | \(-0.529876\pi\) | ||||
−0.0937202 | + | 0.995599i | \(0.529876\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 542.322 | 0.0409237 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13151.2 | 0.987098 | ||||||||
\(563\) | 18029.2 | 1.34963 | 0.674815 | − | 0.737987i | \(-0.264224\pi\) | ||||
0.674815 | + | 0.737987i | \(0.264224\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.6579 | −0.00131482 | ||||||||
\(566\) | 5612.50 | 0.416804 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21915.7 | −1.61895 | ||||||||
\(569\) | 11924.6 | 0.878572 | 0.439286 | − | 0.898347i | \(-0.355232\pi\) | ||||
0.439286 | + | 0.898347i | \(0.355232\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5834.77 | 0.427632 | 0.213816 | − | 0.976874i | \(-0.431411\pi\) | ||||
0.213816 | + | 0.976874i | \(0.431411\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −27250.9 | −1.98159 | ||||||||
\(575\) | −1797.33 | −0.130355 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15927.5 | −1.14917 | −0.574586 | − | 0.818444i | \(-0.694837\pi\) | ||||
−0.574586 | + | 0.818444i | \(0.694837\pi\) | |||||||
\(578\) | 13378.4 | 0.962745 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −24.7716 | −0.00177342 | ||||||||
\(581\) | −24440.4 | −1.74519 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 37603.1 | 2.67129 | ||||||||
\(584\) | −18062.5 | −1.27985 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10250.7 | 0.722612 | ||||||||
\(587\) | 13511.1 | 0.950022 | 0.475011 | − | 0.879980i | \(-0.342444\pi\) | ||||
0.475011 | + | 0.879980i | \(0.342444\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1719.80 | −0.120311 | ||||||||
\(590\) | −176.520 | −0.0123173 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 19342.8 | 1.34288 | ||||||||
\(593\) | −15830.4 | −1.09625 | −0.548126 | − | 0.836396i | \(-0.684659\pi\) | ||||
−0.548126 | + | 0.836396i | \(0.684659\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 884.217 | 0.0609233 | ||||||||
\(596\) | −863.009 | −0.0593125 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5914.12 | −0.403413 | −0.201706 | − | 0.979446i | \(-0.564649\pi\) | ||||
−0.201706 | + | 0.979446i | \(0.564649\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9892.19 | 0.671399 | 0.335700 | − | 0.941969i | \(-0.391027\pi\) | ||||
0.335700 | + | 0.941969i | \(0.391027\pi\) | |||||||
\(602\) | 5470.98 | 0.370399 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 588.004 | 0.0396118 | ||||||||
\(605\) | 834.836 | 0.0561007 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16782.3 | −1.12220 | −0.561098 | − | 0.827749i | \(-0.689621\pi\) | ||||
−0.561098 | + | 0.827749i | \(0.689621\pi\) | |||||||
\(608\) | 263.962 | 0.0176070 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −186.452 | −0.0123758 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12245.7 | −0.806847 | −0.403424 | − | 0.915013i | \(-0.632180\pi\) | ||||
−0.403424 | + | 0.915013i | \(0.632180\pi\) | |||||||
\(614\) | 20071.9 | 1.31928 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 41825.3 | 2.73569 | ||||||||
\(617\) | −10043.7 | −0.655341 | −0.327670 | − | 0.944792i | \(-0.606264\pi\) | ||||
−0.327670 | + | 0.944792i | \(0.606264\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9942.69 | 0.645607 | 0.322803 | − | 0.946466i | \(-0.395375\pi\) | ||||
0.322803 | + | 0.946466i | \(0.395375\pi\) | |||||||
\(620\) | 14.9792 | 0.000970288 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12594.2 | 0.811868 | ||||||||
\(623\) | −36109.1 | −2.32212 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15588.2 | 0.997646 | ||||||||
\(626\) | 57.9628 | 0.00370074 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −809.176 | −0.0514166 | ||||||||
\(629\) | 31537.1 | 1.99915 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10268.6 | −0.647841 | −0.323920 | − | 0.946084i | \(-0.605001\pi\) | ||||
−0.323920 | + | 0.946084i | \(0.605001\pi\) | |||||||
\(632\) | −5559.11 | −0.349889 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14220.1 | −0.890777 | ||||||||
\(635\) | 522.009 | 0.0326225 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 34201.2 | 2.12232 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 416.322 | 0.0257134 | ||||||||
\(641\) | −13657.4 | −0.841555 | −0.420777 | − | 0.907164i | \(-0.638243\pi\) | ||||
−0.420777 | + | 0.907164i | \(0.638243\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24671.6 | −1.51314 | −0.756572 | − | 0.653910i | \(-0.773127\pi\) | ||||
−0.756572 | + | 0.653910i | \(0.773127\pi\) | |||||||
\(644\) | 165.633 | 0.0101348 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3946.92 | −0.240386 | ||||||||
\(647\) | −16512.3 | −1.00334 | −0.501672 | − | 0.865058i | \(-0.667282\pi\) | ||||
−0.501672 | + | 0.865058i | \(0.667282\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12926.3 | −0.781818 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 221.009 | 0.0132751 | ||||||||
\(653\) | 30594.8 | 1.83348 | 0.916742 | − | 0.399479i | \(-0.130809\pi\) | ||||
0.916742 | + | 0.399479i | \(0.130809\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 188.749 | 0.0112596 | ||||||||
\(656\) | −20978.9 | −1.24861 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8021.19 | 0.475226 | ||||||||
\(659\) | −2307.79 | −0.136417 | −0.0682084 | − | 0.997671i | \(-0.521728\pi\) | ||||
−0.0682084 | + | 0.997671i | \(0.521728\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27622.5 | 1.62540 | 0.812700 | − | 0.582683i | \(-0.197997\pi\) | ||||
0.812700 | + | 0.582683i | \(0.197997\pi\) | |||||||
\(662\) | 20885.8 | 1.22621 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −19815.9 | −1.15814 | ||||||||
\(665\) | −129.641 | −0.00755981 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2824.51 | 0.163966 | ||||||||
\(668\) | 1596.67 | 0.0924805 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −59.2260 | −0.00341508 | ||||||||
\(671\) | −13653.6 | −0.785530 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11305.9 | −0.647562 | −0.323781 | − | 0.946132i | \(-0.604954\pi\) | ||||
−0.323781 | + | 0.946132i | \(0.604954\pi\) | |||||||
\(674\) | −5815.17 | −0.332332 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15455.8 | 0.877419 | 0.438710 | − | 0.898629i | \(-0.355436\pi\) | ||||
0.438710 | + | 0.898629i | \(0.355436\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18918.9 | 1.06928 | ||||||||
\(680\) | 716.909 | 0.0404297 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −20681.2 | −1.16118 | ||||||||
\(683\) | −16841.9 | −0.943540 | −0.471770 | − | 0.881722i | \(-0.656385\pi\) | ||||
−0.471770 | + | 0.881722i | \(0.656385\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 132.066 | 0.00736639 | ||||||||
\(686\) | −10236.7 | −0.569739 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4211.80 | 0.233391 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25041.6 | 1.37862 | 0.689310 | − | 0.724467i | \(-0.257914\pi\) | ||||
0.689310 | + | 0.724467i | \(0.257914\pi\) | |||||||
\(692\) | −696.896 | −0.0382832 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22347.6 | 1.22234 | ||||||||
\(695\) | 9.13638 | 0.000498652 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −34204.7 | −1.85881 | ||||||||
\(698\) | −23942.1 | −1.29831 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1437.66 | −0.0776261 | ||||||||
\(701\) | −28309.0 | −1.52527 | −0.762635 | − | 0.646829i | \(-0.776095\pi\) | ||||
−0.762635 | + | 0.646829i | \(0.776095\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4623.88 | −0.248069 | ||||||||
\(704\) | 33829.1 | 1.81106 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24945.0 | −1.32977 | ||||||||
\(707\) | −22669.1 | −1.20588 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5041.17 | 0.267031 | 0.133516 | − | 0.991047i | \(-0.457373\pi\) | ||||
0.133516 | + | 0.991047i | \(0.457373\pi\) | |||||||
\(710\) | 816.882 | 0.0431789 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −29276.6 | −1.54100 | ||||||||
\(713\) | −1707.96 | −0.0897103 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 585.431 | 0.0305567 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19414.7 | −1.00912 | ||||||||
\(719\) | 11839.2 | 0.614088 | 0.307044 | − | 0.951695i | \(-0.400660\pi\) | ||||
0.307044 | + | 0.951695i | \(0.400660\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28017.2 | −1.44718 | ||||||||
\(722\) | −18326.6 | −0.944662 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 221.748 | 0.0113829 | ||||||||
\(725\) | −24516.1 | −1.25587 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31004.9 | −1.58172 | −0.790858 | − | 0.611999i | \(-0.790365\pi\) | ||||
−0.790858 | + | 0.611999i | \(0.790365\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 673.256 | 0.0341347 | ||||||||
\(731\) | 6867.03 | 0.347451 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15666.0 | −0.789411 | −0.394706 | − | 0.918808i | \(-0.629153\pi\) | ||||
−0.394706 | + | 0.918808i | \(0.629153\pi\) | |||||||
\(734\) | 38105.8 | 1.91623 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 262.145 | 0.0131288 | ||||||||
\(737\) | −4337.02 | −0.216765 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33339.4 | 1.65955 | 0.829777 | − | 0.558095i | \(-0.188467\pi\) | ||||
0.829777 | + | 0.558095i | \(0.188467\pi\) | |||||||
\(740\) | 40.2733 | 0.00200064 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −46833.8 | −2.31715 | ||||||||
\(743\) | −2026.14 | −0.100043 | −0.0500215 | − | 0.998748i | \(-0.515929\pi\) | ||||
−0.0500215 | + | 0.998748i | \(0.515929\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 670.831 | 0.0329897 | ||||||||
\(746\) | 17552.5 | 0.861451 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2517.38 | 0.123054 | ||||||||
\(749\) | −23022.6 | −1.12313 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35474.8 | 1.72369 | 0.861846 | − | 0.507170i | \(-0.169309\pi\) | ||||
0.861846 | + | 0.507170i | \(0.169309\pi\) | |||||||
\(752\) | 6175.06 | 0.299443 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −457.065 | −0.0220322 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2398.58 | 0.115162 | 0.0575811 | − | 0.998341i | \(-0.481661\pi\) | ||||
0.0575811 | + | 0.998341i | \(0.481661\pi\) | |||||||
\(758\) | −6757.46 | −0.323802 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −105.111 | −0.00501682 | ||||||||
\(761\) | 5005.07 | 0.238415 | 0.119207 | − | 0.992869i | \(-0.461965\pi\) | ||||
0.119207 | + | 0.992869i | \(0.461965\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24143.5 | 1.14555 | ||||||||
\(764\) | 752.960 | 0.0356559 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −29853.1 | −1.40814 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14109.6 | −0.661644 | −0.330822 | − | 0.943693i | \(-0.607326\pi\) | ||||
−0.330822 | + | 0.943693i | \(0.607326\pi\) | |||||||
\(770\) | −1558.99 | −0.0729635 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1674.82 | 0.0780803 | ||||||||
\(773\) | 12733.7 | 0.592496 | 0.296248 | − | 0.955111i | \(-0.404265\pi\) | ||||
0.296248 | + | 0.955111i | \(0.404265\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14824.7 | 0.687121 | ||||||||
\(776\) | 15339.2 | 0.709593 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13720.9 | −0.632287 | ||||||||
\(779\) | 5014.98 | 0.230655 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 59818.8 | 2.74070 | ||||||||
\(782\) | −3919.75 | −0.179246 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −28671.3 | −1.30609 | ||||||||
\(785\) | 628.986 | 0.0285980 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28429.3 | −1.28767 | −0.643834 | − | 0.765165i | \(-0.722657\pi\) | ||||
−0.643834 | + | 0.765165i | \(0.722657\pi\) | |||||||
\(788\) | 613.344 | 0.0277278 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 207.209 | 0.00933186 | ||||||||
\(791\) | 1610.48 | 0.0723918 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −26048.7 | −1.16427 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −325.625 | −0.0144993 | ||||||||
\(797\) | 11926.7 | 0.530070 | 0.265035 | − | 0.964239i | \(-0.414616\pi\) | ||||
0.265035 | + | 0.964239i | \(0.414616\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10068.0 | 0.445782 | ||||||||
\(800\) | −2275.36 | −0.100558 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −24191.2 | −1.06511 | ||||||||
\(803\) | 49301.4 | 2.16663 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −128.749 | −0.00563702 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −18379.7 | −0.800244 | ||||||||
\(809\) | 20005.7 | 0.869421 | 0.434710 | − | 0.900570i | \(-0.356851\pi\) | ||||
0.434710 | + | 0.900570i | \(0.356851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5933.84 | 0.256924 | 0.128462 | − | 0.991714i | \(-0.458996\pi\) | ||||
0.128462 | + | 0.991714i | \(0.458996\pi\) | |||||||
\(812\) | 2259.27 | 0.0976415 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −55603.8 | −2.39424 | ||||||||
\(815\) | −171.794 | −0.00738364 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1006.82 | −0.0431142 | ||||||||
\(818\) | 12458.9 | 0.532537 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −43.6798 | −0.00186020 | ||||||||
\(821\) | 18457.0 | 0.784597 | 0.392299 | − | 0.919838i | \(-0.371680\pi\) | ||||
0.392299 | + | 0.919838i | \(0.371680\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26520.3 | −1.12325 | −0.561627 | − | 0.827390i | \(-0.689825\pi\) | ||||
−0.561627 | + | 0.827390i | \(0.689825\pi\) | |||||||
\(824\) | −22715.9 | −0.960372 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16099.4 | 0.678170 | ||||||||
\(827\) | 25664.8 | 1.07915 | 0.539573 | − | 0.841939i | \(-0.318586\pi\) | ||||
0.539573 | + | 0.841939i | \(0.318586\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4362.69 | 0.182777 | 0.0913887 | − | 0.995815i | \(-0.470869\pi\) | ||||
0.0913887 | + | 0.995815i | \(0.470869\pi\) | |||||||
\(830\) | 738.612 | 0.0308887 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −46746.6 | −1.94439 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1241.12 | −0.0514378 | ||||||||
\(836\) | −369.091 | −0.0152695 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 33093.1 | 1.36418 | ||||||||
\(839\) | 35020.2 | 1.44104 | 0.720520 | − | 0.693435i | \(-0.243903\pi\) | ||||
0.720520 | + | 0.693435i | \(0.243903\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14138.0 | 0.579687 | ||||||||
\(842\) | 26822.8 | 1.09783 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2119.46 | 0.0864394 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −76140.4 | −3.08880 | ||||||||
\(848\) | −36054.7 | −1.46005 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 34022.6 | 1.37290 | ||||||||
\(851\) | −4592.04 | −0.184974 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8318.36 | −0.333898 | −0.166949 | − | 0.985966i | \(-0.553392\pi\) | ||||
−0.166949 | + | 0.985966i | \(0.553392\pi\) | |||||||
\(854\) | 17005.2 | 0.681389 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18666.3 | −0.745330 | ||||||||
\(857\) | 34832.3 | 1.38839 | 0.694193 | − | 0.719789i | \(-0.255761\pi\) | ||||
0.694193 | + | 0.719789i | \(0.255761\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12571.8 | −0.499353 | −0.249676 | − | 0.968329i | \(-0.580324\pi\) | ||||
−0.249676 | + | 0.968329i | \(0.580324\pi\) | |||||||
\(860\) | 8.76930 | 0.000347710 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11331.1 | 0.447726 | ||||||||
\(863\) | −22474.2 | −0.886480 | −0.443240 | − | 0.896403i | \(-0.646171\pi\) | ||||
−0.443240 | + | 0.896403i | \(0.646171\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 541.708 | 0.0212932 | ||||||||
\(866\) | 8009.90 | 0.314304 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1366.16 | −0.0534223 | ||||||||
\(869\) | 15173.6 | 0.592322 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 19575.2 | 0.760205 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 574.702 | 0.0222421 | ||||||||
\(875\) | 2235.90 | 0.0863855 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5385.19 | −0.207349 | −0.103675 | − | 0.994611i | \(-0.533060\pi\) | ||||
−0.103675 | + | 0.994611i | \(0.533060\pi\) | |||||||
\(878\) | 24461.2 | 0.940233 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1200.17 | −0.0459749 | ||||||||
\(881\) | −29772.7 | −1.13856 | −0.569278 | − | 0.822145i | \(-0.692777\pi\) | ||||
−0.569278 | + | 0.822145i | \(0.692777\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27309.6 | −1.04082 | −0.520409 | − | 0.853917i | \(-0.674220\pi\) | ||||
−0.520409 | + | 0.853917i | \(0.674220\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 34840.7 | 1.32110 | ||||||||
\(887\) | −6529.97 | −0.247187 | −0.123594 | − | 0.992333i | \(-0.539442\pi\) | ||||
−0.123594 | + | 0.992333i | \(0.539442\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −47609.3 | −1.79614 | ||||||||
\(890\) | 1091.25 | 0.0410998 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1890.06 | −0.0709461 | ||||||||
\(893\) | −1476.14 | −0.0553159 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −455.065 | −0.0169957 | ||||||||
\(896\) | −37970.3 | −1.41573 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4890.45 | 0.181733 | ||||||||
\(899\) | −23297.0 | −0.864290 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −58784.6 | −2.17358 | ||||||||
\(902\) | 60307.1 | 2.22617 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1305.75 | 0.0480404 | ||||||||
\(905\) | −172.368 | −0.00633116 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19437.4 | 0.711586 | 0.355793 | − | 0.934565i | \(-0.384211\pi\) | ||||
0.355793 | + | 0.934565i | \(0.384211\pi\) | |||||||
\(908\) | 1434.70 | 0.0524364 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50234.6 | 1.82694 | 0.913472 | − | 0.406901i | \(-0.133391\pi\) | ||||
0.913472 | + | 0.406901i | \(0.133391\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 54087.2 | 1.96060 | ||||||||
\(914\) | −17003.0 | −0.615326 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1267.16 | −0.0457077 | ||||||||
\(917\) | −17214.7 | −0.619934 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12285.2 | 0.440971 | 0.220486 | − | 0.975390i | \(-0.429236\pi\) | ||||
0.220486 | + | 0.975390i | \(0.429236\pi\) | |||||||
\(920\) | −104.387 | −0.00374082 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20549.1 | 0.734000 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 39858.0 | 1.41678 | ||||||||
\(926\) | −14883.3 | −0.528180 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3575.72 | 0.126486 | ||||||||
\(929\) | −25610.0 | −0.904454 | −0.452227 | − | 0.891903i | \(-0.649370\pi\) | ||||
−0.452227 | + | 0.891903i | \(0.649370\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6853.84 | 0.241273 | ||||||||
\(932\) | 343.521 | 0.0120734 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11003.1 | 0.385474 | ||||||||
\(935\) | −1956.80 | −0.0684429 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29893.2 | −1.04223 | −0.521114 | − | 0.853487i | \(-0.674483\pi\) | ||||
−0.521114 | + | 0.853487i | \(0.674483\pi\) | |||||||
\(938\) | 5401.66 | 0.188028 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.8570 | 0.000446115 0 | ||||||||
\(941\) | −44960.3 | −1.55756 | −0.778780 | − | 0.627297i | \(-0.784161\pi\) | ||||
−0.778780 | + | 0.627297i | \(0.784161\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4980.46 | 0.171989 | ||||||||
\(944\) | 12394.0 | 0.427320 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12107.4 | −0.416117 | ||||||||
\(947\) | 33597.6 | 1.15288 | 0.576439 | − | 0.817140i | \(-0.304442\pi\) | ||||
0.576439 | + | 0.817140i | \(0.304442\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −4988.29 | −0.170360 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −65385.1 | −2.22599 | ||||||||
\(953\) | −25850.3 | −0.878670 | −0.439335 | − | 0.898323i | \(-0.644786\pi\) | ||||
−0.439335 | + | 0.898323i | \(0.644786\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −585.288 | −0.0198319 | ||||||||
\(956\) | 882.160 | 0.0298442 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8686.75 | −0.292960 | ||||||||
\(959\) | −12044.9 | −0.405580 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15703.5 | −0.527123 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2550.58 | 0.0852165 | ||||||||
\(965\) | −1301.86 | −0.0434284 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6296.49 | −0.209392 | −0.104696 | − | 0.994504i | \(-0.533387\pi\) | ||||
−0.104696 | + | 0.994504i | \(0.533387\pi\) | |||||||
\(968\) | −61733.5 | −2.04978 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −571.749 | −0.0189255 | ||||||||
\(971\) | −7806.43 | −0.258002 | −0.129001 | − | 0.991644i | \(-0.541177\pi\) | ||||
−0.129001 | + | 0.991644i | \(0.541177\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −833.276 | −0.0274549 | ||||||||
\(974\) | 10774.8 | 0.354462 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13091.3 | 0.429348 | ||||||||
\(977\) | −55692.8 | −1.82372 | −0.911858 | − | 0.410507i | \(-0.865352\pi\) | ||||
−0.911858 | + | 0.410507i | \(0.865352\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 79910.4 | 2.60873 | ||||||||
\(980\) | −59.6960 | −0.00194584 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18315.8 | 0.595195 | ||||||||
\(983\) | 44635.5 | 1.44827 | 0.724135 | − | 0.689658i | \(-0.242239\pi\) | ||||
0.724135 | + | 0.689658i | \(0.242239\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −476.762 | −0.0154222 | ||||||||
\(986\) | −53466.4 | −1.72689 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −999.892 | −0.0321484 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3884.32 | 0.124510 | 0.0622551 | − | 0.998060i | \(-0.480171\pi\) | ||||
0.0622551 | + | 0.998060i | \(0.480171\pi\) | |||||||
\(992\) | −2162.21 | −0.0692039 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −74503.0 | −2.37735 | ||||||||
\(995\) | 253.114 | 0.00806456 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18021.4 | −0.572462 | −0.286231 | − | 0.958161i | \(-0.592402\pi\) | ||||
−0.286231 | + | 0.958161i | \(0.592402\pi\) | |||||||
\(998\) | −16845.9 | −0.534316 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1521.4.a.bd.1.6 | 8 | ||
3.2 | odd | 2 | inner | 1521.4.a.bd.1.3 | 8 | ||
13.4 | even | 6 | 117.4.g.f.55.6 | yes | 16 | ||
13.10 | even | 6 | 117.4.g.f.100.6 | yes | 16 | ||
13.12 | even | 2 | 1521.4.a.bc.1.3 | 8 | |||
39.17 | odd | 6 | 117.4.g.f.55.3 | ✓ | 16 | ||
39.23 | odd | 6 | 117.4.g.f.100.3 | yes | 16 | ||
39.38 | odd | 2 | 1521.4.a.bc.1.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.4.g.f.55.3 | ✓ | 16 | 39.17 | odd | 6 | ||
117.4.g.f.55.6 | yes | 16 | 13.4 | even | 6 | ||
117.4.g.f.100.3 | yes | 16 | 39.23 | odd | 6 | ||
117.4.g.f.100.6 | yes | 16 | 13.10 | even | 6 | ||
1521.4.a.bc.1.3 | 8 | 13.12 | even | 2 | |||
1521.4.a.bc.1.6 | 8 | 39.38 | odd | 2 | |||
1521.4.a.bd.1.3 | 8 | 3.2 | odd | 2 | inner | ||
1521.4.a.bd.1.6 | 8 | 1.1 | even | 1 | trivial |