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 | 1.3 | ||
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 | \(-0.661998\pi\) | ||||
−0.487246 | + | 0.873265i | \(0.661998\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.402937 | −0.0503671 | ||||||||
\(5\) | −0.313209 | −0.0280143 | −0.0140071 | − | 0.999902i | \(-0.504459\pi\) | ||||
−0.0140071 | + | 0.999902i | \(0.504459\pi\) | |||||||
\(6\) | 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 | \(-0.833570\pi\) | ||||
−0.866397 | + | 0.499356i | \(0.833570\pi\) | |||||||
\(12\) | 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 | \(-0.250959\pi\) | ||||
0.704973 | + | 0.709234i | \(0.250959\pi\) | |||||||
\(18\) | 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 | \(-0.520778\pi\) | ||||
−0.0652286 | + | 0.997870i | \(0.520778\pi\) | |||||||
\(24\) | 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 | \(-0.716301\pi\) | ||||
−0.628428 | + | 0.777868i | \(0.716301\pi\) | |||||||
\(30\) | 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 | \(-0.729096\pi\) | ||||
−0.659180 | + | 0.751986i | \(0.729096\pi\) | |||||||
\(42\) | 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 | \(-0.449468\pi\) | ||||
0.158085 | + | 0.987426i | \(0.449468\pi\) | |||||||
\(48\) | 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 | \(-0.780145\pi\) | ||||
−0.770804 | + | 0.637072i | \(0.780145\pi\) | |||||||
\(54\) | 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 | \(-0.427568\pi\) | ||||
0.225595 | + | 0.974221i | \(0.427568\pi\) | |||||||
\(60\) | 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 | \(-0.790352\pi\) | ||||
−0.790832 | + | 0.612033i | \(0.790352\pi\) | |||||||
\(72\) | 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 | \(-0.691407\pi\) | ||||
−0.565733 | + | 0.824588i | \(0.691407\pi\) | |||||||
\(84\) | 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 | \(-0.771274\pi\) | ||||
−0.752753 | + | 0.658303i | \(0.771274\pi\) | |||||||
\(90\) | 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 | \(-0.627839\pi\) | ||||
−0.390907 | + | 0.920430i | \(0.627839\pi\) | |||||||
\(102\) | 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 | \(-0.618617\pi\) | ||||
−0.364082 | + | 0.931367i | \(0.618617\pi\) | |||||||
\(108\) | 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 | \(-0.492530\pi\) | ||||
0.0234670 | + | 0.999725i | \(0.492530\pi\) | |||||||
\(114\) | 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 | \(-0.564407\pi\) | ||||
−0.200962 | + | 0.979599i | \(0.564407\pi\) | |||||||
\(132\) | 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 | \(-0.541971\pi\) | ||||
−0.131476 | + | 0.991319i | \(0.541971\pi\) | |||||||
\(138\) | 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 | \(-0.700400\pi\) | ||||
−0.588802 | + | 0.808278i | \(0.700400\pi\) | |||||||
\(150\) | 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 | \(-0.129752\pi\) | ||||
0.918064 | + | 0.396432i | \(0.129752\pi\) | |||||||
\(168\) | 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 | \(-0.624091\pi\) | ||||
−0.380042 | + | 0.924969i | \(0.624091\pi\) | |||||||
\(174\) | 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 | \(-0.401898\pi\) | ||||
0.303340 | + | 0.952882i | \(0.401898\pi\) | |||||||
\(180\) | 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 | \(-0.384835\pi\) | ||||
0.353960 | + | 0.935260i | \(0.384835\pi\) | |||||||
\(192\) | 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 | \(-0.411237\pi\) | ||||
0.275257 | + | 0.961371i | \(0.411237\pi\) | |||||||
\(198\) | 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 | \(-0.325730\pi\) | ||||
0.520542 | + | 0.853836i | \(0.325730\pi\) | |||||||
\(228\) | 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 | \(-0.461757\pi\) | ||||
0.119854 | + | 0.992792i | \(0.461757\pi\) | |||||||
\(234\) | 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 | \(-0.404258\pi\) | ||||
0.296267 | + | 0.955105i | \(0.404258\pi\) | |||||||
\(240\) | 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 | \(-0.350346\pi\) | ||||
0.453023 | + | 0.891499i | \(0.350346\pi\) | |||||||
\(252\) | 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 | \(-0.621633\pi\) | ||||
−0.372891 | + | 0.927875i | \(0.621633\pi\) | |||||||
\(258\) | 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 | \(-0.363653\pi\) | ||||
0.415367 | + | 0.909654i | \(0.363653\pi\) | |||||||
\(264\) | 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 | \(-0.733122\pi\) | ||||
−0.668638 | + | 0.743588i | \(0.733122\pi\) | |||||||
\(270\) | 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 | \(-0.669049\pi\) | ||||
−0.506469 | + | 0.862258i | \(0.669049\pi\) | |||||||
\(282\) | 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 | \(-0.620904\pi\) | ||||
−0.370764 | + | 0.928727i | \(0.620904\pi\) | |||||||
\(294\) | 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 | \(-0.636764\pi\) | ||||
−0.416560 | + | 0.909108i | \(0.636764\pi\) | |||||||
\(312\) | 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 | \(-0.348907\pi\) | ||||
0.457047 | + | 0.889442i | \(0.348907\pi\) | |||||||
\(318\) | 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 | \(-0.715786\pi\) | ||||
−0.627169 | + | 0.778883i | \(0.715786\pi\) | |||||||
\(348\) | 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 | \(-0.260985\pi\) | ||||
0.682288 | + | 0.731083i | \(0.260985\pi\) | |||||||
\(354\) | 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 | \(-0.326763\pi\) | ||||
0.517768 | + | 0.855521i | \(0.326763\pi\) | |||||||
\(360\) | 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 | \(-0.242993\pi\) | ||||
0.722500 | + | 0.691371i | \(0.242993\pi\) | |||||||
\(384\) | 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 | \(-0.394831\pi\) | ||||
0.324419 | + | 0.945914i | \(0.394831\pi\) | |||||||
\(390\) | 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 | \(-0.315961\pi\) | ||||
0.546498 | + | 0.837461i | \(0.315961\pi\) | |||||||
\(402\) | 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 | \(-0.746792\pi\) | ||||
−0.699944 | + | 0.714198i | \(0.746792\pi\) | |||||||
\(420\) | 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 | \(-0.573782\pi\) | ||||
−0.229723 | + | 0.973256i | \(0.573782\pi\) | |||||||
\(432\) | 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 | \(-0.737085\pi\) | ||||
−0.677843 | + | 0.735207i | \(0.737085\pi\) | |||||||
\(444\) | 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 | \(-0.529724\pi\) | ||||
−0.0932451 | + | 0.995643i | \(0.529724\pi\) | |||||||
\(450\) | 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 | \(-0.622909\pi\) | ||||
−0.376607 | + | 0.926373i | \(0.622909\pi\) | |||||||
\(462\) | 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 | \(-0.563374\pi\) | ||||
−0.197782 | + | 0.980246i | \(0.563374\pi\) | |||||||
\(468\) | 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 | \(-0.451971\pi\) | ||||
0.150315 | + | 0.988638i | \(0.451971\pi\) | |||||||
\(480\) | 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 | \(-0.598786\pi\) | ||||
−0.305388 | + | 0.952228i | \(0.598786\pi\) | |||||||
\(492\) | 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 | \(-0.661364\pi\) | ||||
−0.485505 | + | 0.874234i | \(0.661364\pi\) | |||||||
\(504\) | 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 | \(-0.660896\pi\) | ||||
−0.484220 | + | 0.874947i | \(0.660896\pi\) | |||||||
\(510\) | 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 | \(-0.532220\pi\) | ||||
−0.101048 | + | 0.994882i | \(0.532220\pi\) | |||||||
\(522\) | 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 | \(-0.470124\pi\) | ||||
0.0937202 | + | 0.995599i | \(0.470124\pi\) | |||||||
\(558\) | 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 | \(-0.735776\pi\) | ||||
−0.674815 | + | 0.737987i | \(0.735776\pi\) | |||||||
\(564\) | 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 | \(-0.644768\pi\) | ||||
−0.439286 | + | 0.898347i | \(0.644768\pi\) | |||||||
\(570\) | 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 | \(-0.657556\pi\) | ||||
−0.475011 | + | 0.879980i | \(0.657556\pi\) | |||||||
\(588\) | 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 | \(-0.315341\pi\) | ||||
0.548126 | + | 0.836396i | \(0.315341\pi\) | |||||||
\(594\) | 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 | \(-0.435351\pi\) | ||||
0.201706 | + | 0.979446i | \(0.435351\pi\) | |||||||
\(600\) | 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 | \(-0.393736\pi\) | ||||
0.327670 | + | 0.944792i | \(0.393736\pi\) | |||||||
\(618\) | 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 | \(-0.361757\pi\) | ||||
0.420777 | + | 0.907164i | \(0.361757\pi\) | |||||||
\(642\) | 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 | \(-0.332718\pi\) | ||||
0.501672 | + | 0.865058i | \(0.332718\pi\) | |||||||
\(648\) | 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 | \(-0.869191\pi\) | ||||
−0.916742 | + | 0.399479i | \(0.869191\pi\) | |||||||
\(654\) | 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 | \(-0.478272\pi\) | ||||
0.0682084 | + | 0.997671i | \(0.478272\pi\) | |||||||
\(660\) | 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 | \(-0.644564\pi\) | ||||
−0.438710 | + | 0.898629i | \(0.644564\pi\) | |||||||
\(678\) | 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 | \(-0.343615\pi\) | ||||
0.471770 | + | 0.881722i | \(0.343615\pi\) | |||||||
\(684\) | 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 | \(-0.223905\pi\) | ||||
0.762635 | + | 0.646829i | \(0.223905\pi\) | |||||||
\(702\) | 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 | \(-0.599340\pi\) | ||||
−0.307044 | + | 0.951695i | \(0.599340\pi\) | |||||||
\(720\) | 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 | \(-0.484071\pi\) | ||||
0.0500215 | + | 0.998748i | \(0.484071\pi\) | |||||||
\(744\) | 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 | \(-0.538035\pi\) | ||||
−0.119207 | + | 0.992869i | \(0.538035\pi\) | |||||||
\(762\) | 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 | \(-0.595735\pi\) | ||||
−0.296248 | + | 0.955111i | \(0.595735\pi\) | |||||||
\(774\) | 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 | \(-0.585384\pi\) | ||||
−0.265035 | + | 0.964239i | \(0.585384\pi\) | |||||||
\(798\) | 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 | \(-0.643149\pi\) | ||||
−0.434710 | + | 0.900570i | \(0.643149\pi\) | |||||||
\(810\) | 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 | \(-0.628320\pi\) | ||||
−0.392299 | + | 0.919838i | \(0.628320\pi\) | |||||||
\(822\) | 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 | \(-0.681414\pi\) | ||||
−0.539573 | + | 0.841939i | \(0.681414\pi\) | |||||||
\(828\) | 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 | \(-0.756097\pi\) | ||||
−0.720520 | + | 0.693435i | \(0.756097\pi\) | |||||||
\(840\) | 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 | \(-0.744239\pi\) | ||||
−0.694193 | + | 0.719789i | \(0.744239\pi\) | |||||||
\(858\) | 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 | \(-0.353829\pi\) | ||||
0.443240 | + | 0.896403i | \(0.353829\pi\) | |||||||
\(864\) | 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 | \(-0.307223\pi\) | ||||
0.569278 | + | 0.822145i | \(0.307223\pi\) | |||||||
\(882\) | 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 | \(-0.460558\pi\) | ||||
0.123594 | + | 0.992333i | \(0.460558\pi\) | |||||||
\(888\) | 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 | \(-0.866609\pi\) | ||||
−0.913472 | + | 0.406901i | \(0.866609\pi\) | |||||||
\(912\) | 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 | \(-0.350630\pi\) | ||||
0.452227 | + | 0.891903i | \(0.350630\pi\) | |||||||
\(930\) | 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 | \(-0.215839\pi\) | ||||
0.778780 | + | 0.627297i | \(0.215839\pi\) | |||||||
\(942\) | 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 | \(-0.695558\pi\) | ||||
−0.576439 | + | 0.817140i | \(0.695558\pi\) | |||||||
\(948\) | 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 | \(-0.355214\pi\) | ||||
0.439335 | + | 0.898323i | \(0.355214\pi\) | |||||||
\(954\) | 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 | \(-0.458823\pi\) | ||||
0.129001 | + | 0.991644i | \(0.458823\pi\) | |||||||
\(972\) | 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 | \(-0.134648\pi\) | ||||
0.911858 | + | 0.410507i | \(0.134648\pi\) | |||||||
\(978\) | 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 | \(-0.757761\pi\) | ||||
−0.724135 | + | 0.689658i | \(0.757761\pi\) | |||||||
\(984\) | 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.1.3 | 8 | ||
3.2 | odd | 2 | inner | 1521.4.a.bd.1.6 | 8 | ||
13.4 | even | 6 | 117.4.g.f.55.3 | ✓ | 16 | ||
13.10 | even | 6 | 117.4.g.f.100.3 | yes | 16 | ||
13.12 | even | 2 | 1521.4.a.bc.1.6 | 8 | |||
39.17 | odd | 6 | 117.4.g.f.55.6 | yes | 16 | ||
39.23 | odd | 6 | 117.4.g.f.100.6 | yes | 16 | ||
39.38 | odd | 2 | 1521.4.a.bc.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.4.g.f.55.3 | ✓ | 16 | 13.4 | even | 6 | ||
117.4.g.f.55.6 | yes | 16 | 39.17 | odd | 6 | ||
117.4.g.f.100.3 | yes | 16 | 13.10 | even | 6 | ||
117.4.g.f.100.6 | yes | 16 | 39.23 | odd | 6 | ||
1521.4.a.bc.1.3 | 8 | 39.38 | odd | 2 | |||
1521.4.a.bc.1.6 | 8 | 13.12 | even | 2 | |||
1521.4.a.bd.1.3 | 8 | 1.1 | even | 1 | trivial | ||
1521.4.a.bd.1.6 | 8 | 3.2 | odd | 2 | inner |