Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1088,4,Mod(1,1088)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1088, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1088.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1088 = 2^{6} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1088.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: | \(64.1940780862\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1524.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 68) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.13264\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1088.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 5.36156 | 1.03183 | 0.515916 | − | 0.856639i | \(-0.327452\pi\) | ||||
0.515916 | + | 0.856639i | \(0.327452\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.53055 | 0.226339 | 0.113170 | − | 0.993576i | \(-0.463900\pi\) | ||||
0.113170 | + | 0.993576i | \(0.463900\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −32.2301 | −1.74026 | −0.870131 | − | 0.492821i | \(-0.835966\pi\) | ||||
−0.870131 | + | 0.492821i | \(0.835966\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.74633 | 0.0646789 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.42266 | −0.176046 | −0.0880230 | − | 0.996118i | \(-0.528055\pi\) | ||||
−0.0880230 | + | 0.996118i | \(0.528055\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −14.3612 | −0.306391 | −0.153195 | − | 0.988196i | \(-0.548956\pi\) | ||||
−0.153195 | + | 0.988196i | \(0.548956\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 13.5677 | 0.233544 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 17.0000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 72.4138 | 0.874361 | 0.437180 | − | 0.899374i | \(-0.355977\pi\) | ||||
0.437180 | + | 0.899374i | \(0.355977\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −172.804 | −1.79566 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 167.198 | 1.51579 | 0.757894 | − | 0.652378i | \(-0.226229\pi\) | ||||
0.757894 | + | 0.652378i | \(0.226229\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −118.596 | −0.948771 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −135.399 | −0.965095 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 113.377 | 0.725983 | 0.362992 | − | 0.931792i | \(-0.381755\pi\) | ||||
0.362992 | + | 0.931792i | \(0.381755\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 159.556 | 0.924420 | 0.462210 | − | 0.886770i | \(-0.347057\pi\) | ||||
0.462210 | + | 0.886770i | \(0.347057\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −34.4355 | −0.181650 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −81.5599 | −0.393889 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 39.5931 | 0.175921 | 0.0879604 | − | 0.996124i | \(-0.471965\pi\) | ||||
0.0879604 | + | 0.996124i | \(0.471965\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −76.9984 | −0.316144 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 380.135 | 1.44798 | 0.723988 | − | 0.689812i | \(-0.242307\pi\) | ||||
0.723988 | + | 0.689812i | \(0.242307\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −192.903 | −0.684125 | −0.342062 | − | 0.939677i | \(-0.611125\pi\) | ||||
−0.342062 | + | 0.939677i | \(0.611125\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.41917 | 0.0146394 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 309.261 | 0.959793 | 0.479897 | − | 0.877325i | \(-0.340674\pi\) | ||||
0.479897 | + | 0.877325i | \(0.340674\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 695.779 | 2.02851 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 91.1465 | 0.250256 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −26.9125 | −0.0697494 | −0.0348747 | − | 0.999392i | \(-0.511103\pi\) | ||||
−0.0348747 | + | 0.999392i | \(0.511103\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.2529 | −0.0398461 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 388.251 | 0.902194 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 214.256 | 0.472775 | 0.236388 | − | 0.971659i | \(-0.424036\pi\) | ||||
0.236388 | + | 0.971659i | \(0.424036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −140.744 | −0.295417 | −0.147708 | − | 0.989031i | \(-0.547190\pi\) | ||||
−0.147708 | + | 0.989031i | \(0.547190\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −56.2844 | −0.112558 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −36.3417 | −0.0693482 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 676.207 | 1.23301 | 0.616507 | − | 0.787350i | \(-0.288547\pi\) | ||||
0.616507 | + | 0.787350i | \(0.288547\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 896.440 | 1.56404 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 966.999 | 1.61636 | 0.808181 | − | 0.588935i | \(-0.200452\pi\) | ||||
0.808181 | + | 0.588935i | \(0.200452\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 639.471 | 1.02527 | 0.512633 | − | 0.858608i | \(-0.328670\pi\) | ||||
0.512633 | + | 0.858608i | \(0.328670\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −635.861 | −0.978973 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 207.003 | 0.306366 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1319.92 | −1.87978 | −0.939892 | − | 0.341473i | \(-0.889074\pi\) | ||||
−0.939892 | + | 0.341473i | \(0.889074\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −773.101 | −1.06050 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1418.37 | 1.87575 | 0.937873 | − | 0.346979i | \(-0.112793\pi\) | ||||
0.937873 | + | 0.346979i | \(0.112793\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 43.0193 | 0.0548953 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 607.876 | 0.749093 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −387.832 | −0.461912 | −0.230956 | − | 0.972964i | \(-0.574185\pi\) | ||||
−0.230956 | + | 0.972964i | \(0.574185\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 462.862 | 0.533200 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 855.467 | 0.953847 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 183.247 | 0.197902 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −359.767 | −0.376585 | −0.188293 | − | 0.982113i | \(-0.560295\pi\) | ||||
−0.188293 | + | 0.982113i | \(0.560295\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.2161 | −0.0113864 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1266.61 | 1.24785 | 0.623924 | − | 0.781485i | \(-0.285537\pi\) | ||||
0.623924 | + | 0.781485i | \(0.285537\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 600.773 | 0.574718 | 0.287359 | − | 0.957823i | \(-0.407223\pi\) | ||||
0.287359 | + | 0.957823i | \(0.407223\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −437.288 | −0.406428 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2133.76 | −1.92784 | −0.963918 | − | 0.266199i | \(-0.914232\pi\) | ||||
−0.963918 | + | 0.266199i | \(0.914232\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1558.38 | −1.36941 | −0.684703 | − | 0.728822i | \(-0.740068\pi\) | ||||
−0.684703 | + | 0.728822i | \(0.740068\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 212.281 | 0.181521 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 411.282 | 0.342391 | 0.171196 | − | 0.985237i | \(-0.445237\pi\) | ||||
0.171196 | + | 0.985237i | \(0.445237\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 423.102 | 0.343082 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −25.0794 | −0.0198170 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −547.912 | −0.422075 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1289.75 | −0.969008 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2038.11 | 1.49407 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −616.433 | −0.441083 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1538.23 | 1.07477 | 0.537385 | − | 0.843337i | \(-0.319412\pi\) | ||||
0.537385 | + | 0.843337i | \(0.319412\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1034.26 | −0.705902 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1967.91 | 1.31250 | 0.656248 | − | 0.754546i | \(-0.272143\pi\) | ||||
0.656248 | + | 0.754546i | \(0.272143\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2333.90 | −1.52162 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −342.634 | −0.218439 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 633.040 | 0.394776 | 0.197388 | − | 0.980325i | \(-0.436754\pi\) | ||||
0.197388 | + | 0.980325i | \(0.436754\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 984.854 | 0.600966 | 0.300483 | − | 0.953787i | \(-0.402852\pi\) | ||||
0.300483 | + | 0.953787i | \(0.402852\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1658.12 | 0.990346 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 92.2370 | 0.0539388 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 286.905 | 0.164318 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3730.46 | 2.09308 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1818.23 | −0.999701 | −0.499850 | − | 0.866112i | \(-0.666612\pi\) | ||||
−0.499850 | + | 0.866112i | \(0.666612\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 950.482 | 0.512246 | 0.256123 | − | 0.966644i | \(-0.417555\pi\) | ||||
0.256123 | + | 0.966644i | \(0.417555\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 29.6876 | 0.0156869 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 403.763 | 0.209233 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3661.42 | −1.86123 | −0.930616 | − | 0.365996i | \(-0.880728\pi\) | ||||
−0.930616 | + | 0.365996i | \(0.880728\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −144.293 | −0.0719697 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5388.79 | −2.63787 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2121.63 | −1.01950 | −0.509752 | − | 0.860322i | \(-0.670263\pi\) | ||||
−0.509752 | + | 0.860322i | \(0.670263\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −87.1407 | −0.0411145 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1235.39 | −0.572438 | −0.286219 | − | 0.958164i | \(-0.592398\pi\) | ||||
−0.286219 | + | 0.958164i | \(0.592398\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1990.76 | −0.906125 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 126.458 | 0.0565527 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3633.55 | 1.59684 | 0.798420 | − | 0.602100i | \(-0.205669\pi\) | ||||
0.798420 | + | 0.602100i | \(0.205669\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3822.37 | 1.65111 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1148.75 | 0.487825 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1419.17 | 0.592592 | 0.296296 | − | 0.955096i | \(-0.404248\pi\) | ||||
0.296296 | + | 0.955096i | \(0.404248\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2145.55 | −0.881092 | −0.440546 | − | 0.897730i | \(-0.645215\pi\) | ||||
−0.440546 | + | 0.897730i | \(0.645215\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −754.608 | −0.304821 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 100.192 | 0.0398178 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −109.185 | −0.0426974 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4363.92 | 1.67952 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2578.53 | 0.976837 | 0.488418 | − | 0.872610i | \(-0.337574\pi\) | ||||
0.488418 | + | 0.872610i | \(0.337574\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3786.54 | 1.41223 | 0.706116 | − | 0.708096i | \(-0.250446\pi\) | ||||
0.706116 | + | 0.708096i | \(0.250446\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −194.848 | −0.0715558 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3492.69 | −1.26317 | −0.631583 | − | 0.775308i | \(-0.717595\pi\) | ||||
−0.631583 | + | 0.775308i | \(0.717595\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −502.370 | −0.178955 | −0.0894775 | − | 0.995989i | \(-0.528520\pi\) | ||||
−0.0894775 | + | 0.995989i | \(0.528520\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3625.53 | 1.27226 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3654.14 | −1.26340 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 961.949 | 0.327734 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 291.982 | 0.0980394 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −465.089 | −0.153928 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1564.72 | −0.510522 | −0.255261 | − | 0.966872i | \(-0.582161\pi\) | ||||
−0.255261 | + | 0.966872i | \(0.582161\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5184.62 | 1.66781 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −488.150 | −0.154844 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5142.49 | −1.60873 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3428.56 | 1.05790 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −244.140 | −0.0743106 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5154.57 | 1.54787 | 0.773936 | − | 0.633264i | \(-0.218285\pi\) | ||||
0.773936 | + | 0.633264i | \(0.218285\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −207.108 | −0.0613654 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4590.10 | 1.34210 | 0.671048 | − | 0.741414i | \(-0.265844\pi\) | ||||
0.671048 | + | 0.741414i | \(0.265844\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 457.844 | 0.132119 | 0.0660593 | − | 0.997816i | \(-0.478957\pi\) | ||||
0.0660593 | + | 0.997816i | \(0.478957\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1109.86 | 0.316118 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5051.77 | 1.42040 | 0.710199 | − | 0.704001i | \(-0.248605\pi\) | ||||
0.710199 | + | 0.704001i | \(0.248605\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 782.599 | 0.217239 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7076.84 | −1.93962 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3812.18 | 1.03175 | 0.515877 | − | 0.856663i | \(-0.327466\pi\) | ||||
0.515877 | + | 0.856663i | \(0.327466\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4221.39 | −1.12831 | −0.564157 | − | 0.825667i | \(-0.690799\pi\) | ||||
−0.564157 | + | 0.825667i | \(0.690799\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −489.254 | −0.129159 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1760.70 | 0.459131 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1039.95 | −0.267896 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7604.70 | 1.93546 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1487.11 | 0.373966 | 0.186983 | − | 0.982363i | \(-0.440129\pi\) | ||||
0.186983 | + | 0.982363i | \(0.440129\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1073.85 | −0.266848 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 230.651 | 0.0566428 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6590.66 | 1.59966 | 0.799832 | − | 0.600223i | \(-0.204922\pi\) | ||||
0.799832 | + | 0.600223i | \(0.204922\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1276.09 | −0.306148 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 197.993 | 0.0469558 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 171.136 | 0.0401244 | 0.0200622 | − | 0.999799i | \(-0.493614\pi\) | ||||
0.0200622 | + | 0.999799i | \(0.493614\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −68.1035 | −0.0157870 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2079.39 | −0.476616 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1676.61 | −0.380018 | −0.190009 | − | 0.981782i | \(-0.560852\pi\) | ||||
−0.190009 | + | 0.981782i | \(0.560852\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3667.65 | 0.822118 | 0.411059 | − | 0.911609i | \(-0.365159\pi\) | ||||
0.411059 | + | 0.911609i | \(0.365159\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2481.66 | 0.550173 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 761.704 | 0.167027 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6145.42 | −1.33301 | −0.666503 | − | 0.745502i | \(-0.732210\pi\) | ||||
−0.666503 | + | 0.745502i | \(0.732210\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 278.637 | 0.0597905 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1380.54 | 0.293082 | 0.146541 | − | 0.989205i | \(-0.453186\pi\) | ||||
0.146541 | + | 0.989205i | \(0.453186\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1028.78 | −0.216095 | −0.108047 | − | 0.994146i | \(-0.534460\pi\) | ||||
−0.108047 | + | 0.994146i | \(0.534460\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 982.488 | 0.204202 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12251.8 | −2.51986 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 289.000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1928.91 | −0.388573 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1889.19 | −0.376682 | −0.188341 | − | 0.982104i | \(-0.560311\pi\) | ||||
−0.188341 | + | 0.982104i | \(0.560311\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 542.185 | 0.107008 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 869.622 | 0.169901 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2401.16 | −0.464423 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6217.27 | 1.19056 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6791.02 | 1.28757 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −356.160 | −0.0668645 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6219.66 | −1.15627 | −0.578135 | − | 0.815941i | \(-0.696219\pi\) | ||||
−0.578135 | + | 0.815941i | \(0.696219\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3221.08 | 0.593013 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5349.83 | 0.975437 | 0.487718 | − | 0.873001i | \(-0.337829\pi\) | ||||
0.487718 | + | 0.873001i | \(0.337829\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7696.97 | 1.38996 | 0.694982 | − | 0.719027i | \(-0.255412\pi\) | ||||
0.694982 | + | 0.719027i | \(0.255412\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −142.430 | −0.0254763 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7760.26 | 1.37495 | 0.687475 | − | 0.726208i | \(-0.258719\pi\) | ||||
0.687475 | + | 0.726208i | \(0.258719\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −728.179 | −0.127806 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11440.3 | −1.98920 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1231.03 | 0.212064 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1703.18 | 0.290694 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8355.33 | −1.41300 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9967.50 | −1.67029 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1005.22 | −0.166923 | −0.0834617 | − | 0.996511i | \(-0.526598\pi\) | ||||
−0.0834617 | + | 0.996511i | \(0.526598\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 69.1427 | 0.0113784 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1711.18 | 0.279079 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10322.2 | −1.66851 | −0.834255 | − | 0.551379i | \(-0.814102\pi\) | ||||
−0.834255 | + | 0.551379i | \(0.814102\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2205.12 | 0.353290 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1024.77 | −0.162740 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11370.1 | −1.78987 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2268.49 | 0.354003 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8743.53 | 1.35267 | 0.676337 | − | 0.736593i | \(-0.263567\pi\) | ||||
0.676337 | + | 0.736593i | \(0.263567\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1613.43 | 0.247464 | 0.123732 | − | 0.992316i | \(-0.460514\pi\) | ||||
0.123732 | + | 0.992316i | \(0.460514\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1944.49 | 0.295696 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3318.12 | −0.500299 | −0.250150 | − | 0.968207i | \(-0.580480\pi\) | ||||
−0.250150 | + | 0.968207i | \(0.580480\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2447.04 | 0.365846 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2937.66 | −0.435511 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9734.63 | −1.43113 | −0.715563 | − | 0.698549i | \(-0.753830\pi\) | ||||
−0.715563 | + | 0.698549i | \(0.753830\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1615.25 | −0.235493 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6915.07 | −0.999854 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1618.21 | 0.232058 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6534.42 | 0.929411 | 0.464706 | − | 0.885465i | \(-0.346160\pi\) | ||||
0.464706 | + | 0.885465i | \(0.346160\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 663.840 | 0.0936535 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 867.393 | 0.121382 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4737.49 | −0.657635 | −0.328818 | − | 0.944393i | \(-0.606650\pi\) | ||||
−0.328818 | + | 0.944393i | \(0.606650\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3305.04 | −0.455124 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1628.22 | −0.222434 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3837.29 | 0.520074 | 0.260037 | − | 0.965599i | \(-0.416265\pi\) | ||||
0.260037 | + | 0.965599i | \(0.416265\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8247.31 | 1.10898 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1600.29 | −0.213501 | −0.106751 | − | 0.994286i | \(-0.534045\pi\) | ||||
−0.106751 | + | 0.994286i | \(0.534045\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 523.831 | 0.0693426 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −336.871 | −0.0442484 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1468.12 | 0.191353 | 0.0956767 | − | 0.995412i | \(-0.469498\pi\) | ||||
0.0956767 | + | 0.995412i | \(0.469498\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2842.36 | 0.367632 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10551.1 | 1.35428 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3340.13 | −0.425469 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6070.98 | 0.767490 | 0.383745 | − | 0.923439i | \(-0.374634\pi\) | ||||
0.383745 | + | 0.923439i | \(0.374634\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12513.4 | −1.57005 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4834.50 | 0.602054 | 0.301027 | − | 0.953616i | \(-0.402671\pi\) | ||||
0.301027 | + | 0.953616i | \(0.402671\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2291.41 | −0.283234 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1956.37 | −0.240032 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −254.293 | −0.0309701 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 880.103 | 0.106402 | 0.0532008 | − | 0.998584i | \(-0.483058\pi\) | ||||
0.0532008 | + | 0.998584i | \(0.483058\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3394.08 | 0.407342 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6905.49 | −0.822753 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3589.27 | 0.424555 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5280.35 | 0.620096 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11301.2 | −1.31766 | −0.658828 | − | 0.752293i | \(-0.728948\pi\) | ||||
−0.658828 | + | 0.752293i | \(0.728948\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8699.65 | −1.00711 | −0.503557 | − | 0.863962i | \(-0.667976\pi\) | ||||
−0.503557 | + | 0.863962i | \(0.667976\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 540.071 | 0.0620783 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2016.14 | −0.230111 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4536.19 | 0.514103 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 494.534 | 0.0556558 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9355.08 | −1.04552 | −0.522759 | − | 0.852481i | \(-0.675097\pi\) | ||||
−0.522759 | + | 0.852481i | \(0.675097\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1577.31 | 0.175060 | 0.0875298 | − | 0.996162i | \(-0.472103\pi\) | ||||
0.0875298 | + | 0.996162i | \(0.472103\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1538.26 | 0.169549 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12107.4 | 1.32535 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3598.01 | 0.391170 | 0.195585 | − | 0.980687i | \(-0.437339\pi\) | ||||
0.195585 | + | 0.980687i | \(0.437339\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1215.06 | 0.131202 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3503.46 | 0.375744 | 0.187872 | − | 0.982194i | \(-0.439841\pi\) | ||||
0.187872 | + | 0.982194i | \(0.439841\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −981.429 | −0.104549 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9748.56 | −1.03152 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5763.75 | 0.605809 | 0.302905 | − | 0.953021i | \(-0.402044\pi\) | ||||
0.302905 | + | 0.953021i | \(0.402044\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2441.47 | −0.254910 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5096.07 | 0.528552 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1171.30 | 0.120684 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 520.746 | 0.0533030 | 0.0266515 | − | 0.999645i | \(-0.491516\pi\) | ||||
0.0266515 | + | 0.999645i | \(0.491516\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2301.78 | −0.234070 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19646.7 | 1.98490 | 0.992451 | − | 0.122641i | \(-0.0391363\pi\) | ||||
0.992451 | + | 0.122641i | \(0.0391363\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9452.09 | 0.948760 | 0.474380 | − | 0.880320i | \(-0.342672\pi\) | ||||
0.474380 | + | 0.880320i | \(0.342672\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2164.80 | 0.215893 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16753.0 | 1.66004 | 0.830020 | − | 0.557734i | \(-0.188329\pi\) | ||||
0.830020 | + | 0.557734i | \(0.188329\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21794.2 | −2.14576 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19631.0 | −1.92048 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1238.95 | 0.120437 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8588.01 | −0.829568 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −46.9981 | −0.00451131 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8142.90 | −0.776740 | −0.388370 | − | 0.921503i | \(-0.626962\pi\) | ||||
−0.388370 | + | 0.921503i | \(0.626962\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −568.605 | −0.0539005 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −28892.3 | −2.72184 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −910.407 | −0.0852360 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10669.6 | 0.992780 | 0.496390 | − | 0.868100i | \(-0.334659\pi\) | ||||
0.496390 | + | 0.868100i | \(0.334659\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11375.3 | −1.05196 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20917.7 | −1.92262 | −0.961308 | − | 0.275475i | \(-0.911165\pi\) | ||||
−0.961308 | + | 0.275475i | \(0.911165\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1927.40 | 0.176077 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −28.3829 | −0.00257720 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −31166.5 | −2.81289 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2264.43 | 0.203146 | 0.101573 | − | 0.994828i | \(-0.467612\pi\) | ||||
0.101573 | + | 0.994828i | \(0.467612\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6623.60 | −0.590660 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10397.1 | 0.921641 | 0.460820 | − | 0.887493i | \(-0.347555\pi\) | ||||
0.460820 | + | 0.887493i | \(0.347555\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3205.23 | 0.282437 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10673.6 | −0.934969 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8496.07 | −0.739846 | −0.369923 | − | 0.929062i | \(-0.620616\pi\) | ||||
−0.369923 | + | 0.929062i | \(0.620616\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20610.2 | −1.78423 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9804.76 | −0.843841 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1520.29 | 0.130081 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1986.28 | −0.168968 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19481.5 | 1.64767 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8994.22 | −0.756322 | −0.378161 | − | 0.925740i | \(-0.623443\pi\) | ||||
−0.378161 | + | 0.925740i | \(0.623443\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5072.24 | 0.424080 | 0.212040 | − | 0.977261i | \(-0.431989\pi\) | ||||
0.212040 | + | 0.977261i | \(0.431989\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20493.9 | 1.70367 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2712.45 | 0.224205 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15788.0 | 1.29761 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 374.161 | 0.0305786 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5459.18 | −0.443646 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5399.59 | −0.436345 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7608.99 | 0.611456 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4468.75 | −0.357111 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17722.4 | −1.40840 | −0.704202 | − | 0.710000i | \(-0.748695\pi\) | ||||
−0.704202 | + | 0.710000i | \(0.748695\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11503.5 | −0.909140 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3943.55 | −0.309951 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −282.133 | −0.0220533 | −0.0110266 | − | 0.999939i | \(-0.503510\pi\) | ||||
−0.0110266 | + | 0.999939i | \(0.503510\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −245.786 | −0.0191072 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8210.03 | 0.634771 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 42541.2 | 3.27131 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 537.188 | 0.0410853 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13294.8 | −1.01134 | −0.505672 | − | 0.862726i | \(-0.668755\pi\) | ||||
−0.505672 | + | 0.862726i | \(0.668755\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2770.31 | 0.209609 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −585.403 | −0.0440566 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1632.96 | 0.122240 | 0.0611198 | − | 0.998130i | \(-0.480533\pi\) | ||||
0.0611198 | + | 0.998130i | \(0.480533\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1040.77 | 0.0774965 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 24917.1 | 1.84554 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8267.89 | −0.609153 | −0.304577 | − | 0.952488i | \(-0.598515\pi\) | ||||
−0.304577 | + | 0.952488i | \(0.598515\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2750.70 | −0.201599 | −0.100800 | − | 0.994907i | \(-0.532140\pi\) | ||||
−0.100800 | + | 0.994907i | \(0.532140\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13824.9 | 1.00793 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19829.0 | −1.43813 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18366.0 | −1.32510 | −0.662552 | − | 0.749016i | \(-0.730527\pi\) | ||||
−0.662552 | + | 0.749016i | \(0.730527\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20301.7 | 1.45719 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −45714.4 | −3.26429 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 172.850 | 0.0122791 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −63.4646 | −0.00448536 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19167.2 | −1.34772 | −0.673862 | − | 0.738857i | \(-0.735366\pi\) | ||||
−0.673862 | + | 0.738857i | \(0.735366\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11554.0 | 0.808277 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18726.3 | −1.30338 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16857.3 | −1.16736 | −0.583680 | − | 0.811984i | \(-0.698388\pi\) | ||||
−0.583680 | + | 0.811984i | \(0.698388\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1386.52 | −0.0955322 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2693.49 | −0.184652 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23326.3 | −1.59113 | −0.795565 | − | 0.605869i | \(-0.792826\pi\) | ||||
−0.795565 | + | 0.605869i | \(0.792826\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1305.09 | 0.0885783 | 0.0442891 | − | 0.999019i | \(-0.485898\pi\) | ||||
0.0442891 | + | 0.999019i | \(0.485898\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1180.88 | 0.0797499 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3263.78 | −0.219325 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10225.7 | −0.683769 | −0.341884 | − | 0.939742i | \(-0.611065\pi\) | ||||
−0.341884 | + | 0.939742i | \(0.611065\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −19591.9 | −1.30362 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4441.35 | −0.294072 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2611.06 | −0.172039 | −0.0860194 | − | 0.996293i | \(-0.527415\pi\) | ||||
−0.0860194 | + | 0.996293i | \(0.527415\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5157.55 | 0.338167 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8225.49 | 0.536703 | 0.268351 | − | 0.963321i | \(-0.413521\pi\) | ||||
0.268351 | + | 0.963321i | \(0.413521\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2517.19 | 0.163448 | 0.0817242 | − | 0.996655i | \(-0.473957\pi\) | ||||
0.0817242 | + | 0.996655i | \(0.473957\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22638.4 | −1.46288 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12499.9 | 0.803847 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13264.6 | 0.848936 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2493.60 | −0.158828 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 673.083 | 0.0426671 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4769.93 | −0.300932 | −0.150466 | − | 0.988615i | \(-0.548077\pi\) | ||||
−0.150466 | + | 0.988615i | \(0.548077\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8389.36 | −0.526773 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3892.57 | 0.243263 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9992.21 | −0.621516 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1688.70 | 0.104544 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −276.323 | −0.0170267 | −0.00851335 | − | 0.999964i | \(-0.502710\pi\) | ||||
−0.00851335 | + | 0.999964i | \(0.502710\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19925.0 | −1.22203 | −0.611016 | − | 0.791618i | \(-0.709239\pi\) | ||||
−0.611016 | + | 0.791618i | \(0.709239\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2617.24 | −0.159773 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9664.69 | 0.587262 | 0.293631 | − | 0.955919i | \(-0.405136\pi\) | ||||
0.293631 | + | 0.955919i | \(0.405136\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1376.09 | −0.0832302 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −27571.8 | −1.65994 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23304.6 | −1.39660 | −0.698301 | − | 0.715805i | \(-0.746060\pi\) | ||||
−0.698301 | + | 0.715805i | \(0.746060\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4979.89 | 0.297069 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1116.73 | 0.0663130 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17048.8 | −1.00778 | −0.503890 | − | 0.863768i | \(-0.668098\pi\) | ||||
−0.503890 | + | 0.863768i | \(0.668098\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19310.8 | 1.13631 | 0.568157 | − | 0.822920i | \(-0.307657\pi\) | ||||
0.568157 | + | 0.822920i | \(0.307657\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1308.97 | −0.0766761 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5906.06 | −0.344402 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18956.3 | 1.10044 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 27636.5 | 1.59714 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 903.952 | 0.0520069 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11322.2 | 0.648496 | 0.324248 | − | 0.945972i | \(-0.394889\pi\) | ||||
0.324248 | + | 0.945972i | \(0.394889\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16057.8 | 0.915654 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5130.90 | 0.291280 | 0.145640 | − | 0.989338i | \(-0.453476\pi\) | ||||
0.145640 | + | 0.989338i | \(0.453476\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11595.3 | 0.655357 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24610.1 | 1.38482 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19250.8 | 1.07849 | 0.539247 | − | 0.842148i | \(-0.318709\pi\) | ||||
0.539247 | + | 0.842148i | \(0.318709\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1601.94 | 0.0893532 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2454.76 | 0.136324 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 386.496 | 0.0213706 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9816.53 | −0.540432 | −0.270216 | − | 0.962800i | \(-0.587095\pi\) | ||||
−0.270216 | + | 0.962800i | \(0.587095\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 361.495 | 0.0198154 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2492.22 | 0.136022 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6462.29 | 0.351186 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 27085.4 | 1.46561 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12994.6 | 0.700142 | 0.350071 | − | 0.936723i | \(-0.386158\pi\) | ||||
0.350071 | + | 0.936723i | \(0.386158\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2867.09 | 0.153818 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4195.95 | 0.224154 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −40823.1 | −2.17158 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29277.4 | 1.55083 | 0.775414 | − | 0.631454i | \(-0.217541\pi\) | ||||
0.775414 | + | 0.631454i | \(0.217541\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2305.02 | −0.121582 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26677.3 | 1.40123 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 233.410 | 0.0122085 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20439.2 | 1.06460 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14651.1 | −0.759934 | −0.379967 | − | 0.925000i | \(-0.624065\pi\) | ||||
−0.379967 | + | 0.925000i | \(0.624065\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19363.0 | −1.00016 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22633.2 | −1.16423 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13446.0 | −0.688791 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15552.0 | 0.793385 | 0.396692 | − | 0.917952i | \(-0.370158\pi\) | ||||
0.396692 | + | 0.917952i | \(0.370158\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18250.6 | 0.927225 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3279.34 | −0.165925 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21433.2 | 1.08002 | 0.540008 | − | 0.841660i | \(-0.318421\pi\) | ||||
0.540008 | + | 0.841660i | \(0.318421\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9440.11 | 0.473747 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4343.05 | −0.217067 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3561.65 | 0.177290 | 0.0886450 | − | 0.996063i | \(-0.471746\pi\) | ||||
0.0886450 | + | 0.996063i | \(0.471746\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5575.74 | −0.276424 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8804.42 | 0.434728 | 0.217364 | − | 0.976091i | \(-0.430254\pi\) | ||||
0.217364 | + | 0.976091i | \(0.430254\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4601.13 | −0.226271 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2476.95 | 0.121321 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 68771.3 | 3.35494 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16398.8 | 0.796806 | 0.398403 | − | 0.917210i | \(-0.369564\pi\) | ||||
0.398403 | + | 0.917210i | \(0.369564\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7973.22 | 0.385870 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2405.24 | 0.115941 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1256.33 | −0.0603199 | −0.0301599 | − | 0.999545i | \(-0.509602\pi\) | ||||
−0.0301599 | + | 0.999545i | \(0.509602\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5757.53 | −0.275343 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3988.92 | 0.190011 | 0.0950053 | − | 0.995477i | \(-0.469713\pi\) | ||||
0.0950053 | + | 0.995477i | \(0.469713\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 50226.6 | 2.38313 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 75.1260 | 0.00355057 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3076.97 | −0.144854 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14908.0 | −0.699087 | −0.349543 | − | 0.936920i | \(-0.613663\pi\) | ||||
−0.349543 | + | 0.936920i | \(0.613663\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35336.2 | 1.65059 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10280.4 | 0.478343 | 0.239171 | − | 0.970977i | \(-0.423124\pi\) | ||||
0.239171 | + | 0.970977i | \(0.423124\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18922.7 | −0.877063 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6841.84 | −0.315894 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27527.0 | 1.26605 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6210.71 | −0.284554 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15351.1 | −0.700643 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9265.42 | −0.421270 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35038.6 | 1.58703 | 0.793514 | − | 0.608552i | \(-0.208249\pi\) | ||||
0.793514 | + | 0.608552i | \(0.208249\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 917.557 | 0.0414016 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13255.7 | −0.595850 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2021.25 | 0.0905130 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −365.141 | −0.0162896 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17732.3 | −0.788092 | −0.394046 | − | 0.919091i | \(-0.628925\pi\) | ||||
−0.394046 | + | 0.919091i | \(0.628925\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5257.43 | 0.232784 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −677.283 | −0.0298759 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4107.10 | −0.180494 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13636.6 | −0.597053 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8989.25 | −0.392115 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21264.4 | 0.924123 | 0.462062 | − | 0.886848i | \(-0.347110\pi\) | ||||
0.462062 | + | 0.886848i | \(0.347110\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18812.1 | 0.814527 | 0.407263 | − | 0.913311i | \(-0.366483\pi\) | ||||
0.407263 | + | 0.913311i | \(0.366483\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19664.3 | 0.848288 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5368.90 | −0.230754 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13968.8 | −0.598172 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 808.310 | 0.0344867 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15392.7 | −0.654336 | −0.327168 | − | 0.944966i | \(-0.606094\pi\) | ||||
−0.327168 | + | 0.944966i | \(0.606094\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10506.1 | −0.444981 | −0.222491 | − | 0.974935i | \(-0.571419\pi\) | ||||
−0.222491 | + | 0.974935i | \(0.571419\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4083.92 | 0.172344 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6255.99 | −0.263050 | −0.131525 | − | 0.991313i | \(-0.541987\pi\) | ||||
−0.131525 | + | 0.991313i | \(0.541987\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39592.2 | 1.65874 | 0.829370 | − | 0.558700i | \(-0.188700\pi\) | ||||
0.829370 | + | 0.558700i | \(0.188700\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −32949.1 | −1.37544 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11828.2 | 0.491986 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3126.21 | −0.129565 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21603.7 | −0.892154 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5161.09 | −0.212372 | −0.106186 | − | 0.994346i | \(-0.533864\pi\) | ||||
−0.106186 | + | 0.994346i | \(0.533864\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11534.7 | −0.472949 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7401.83 | 0.302411 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5037.71 | −0.205092 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 41568.7 | 1.68633 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5515.88 | −0.222974 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6619.88 | 0.266659 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29219.7 | 1.17288 | 0.586438 | − | 0.809994i | \(-0.300530\pi\) | ||||
0.586438 | + | 0.809994i | \(0.300530\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 320.009 | 0.0128001 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16277.5 | 0.648810 | 0.324405 | − | 0.945918i | \(-0.394836\pi\) | ||||
0.324405 | + | 0.945918i | \(0.394836\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33890.2 | −1.34612 | −0.673062 | − | 0.739586i | \(-0.735021\pi\) | ||||
−0.673062 | + | 0.739586i | \(0.735021\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −65688.6 | −2.60007 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24932.1 | 0.983429 | 0.491714 | − | 0.870757i | \(-0.336370\pi\) | ||||
0.491714 | + | 0.870757i | \(0.336370\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9194.87 | 0.361428 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1549.49 | 0.0606960 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8477.41 | 0.330928 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9711.14 | −0.377784 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −628.271 | −0.0243571 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19867.7 | 0.767600 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17205.0 | 0.662452 | 0.331226 | − | 0.943551i | \(-0.392538\pi\) | ||||
0.331226 | + | 0.943551i | \(0.392538\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10129.0 | −0.388673 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34861.7 | 1.33317 | 0.666583 | − | 0.745431i | \(-0.267756\pi\) | ||||
0.666583 | + | 0.745431i | \(0.267756\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30546.3 | −1.16417 | −0.582087 | − | 0.813126i | \(-0.697764\pi\) | ||||
−0.582087 | + | 0.813126i | \(0.697764\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2906.96 | 0.110414 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8771.17 | 0.332026 | 0.166013 | − | 0.986124i | \(-0.446911\pi\) | ||||
0.166013 | + | 0.986124i | \(0.446911\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −49577.3 | −1.87038 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4965.37 | 0.186696 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22394.7 | 0.839206 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3591.29 | 0.134127 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12873.9 | −0.479207 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18089.9 | 0.671114 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −457.513 | −0.0169167 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 33334.3 | 1.22845 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5429.43 | −0.199426 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2257.34 | 0.0826393 | 0.0413196 | − | 0.999146i | \(-0.486844\pi\) | ||||
0.0413196 | + | 0.999146i | \(0.486844\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2211.92 | 0.0807095 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49374.3 | 1.79566 | 0.897829 | − | 0.440344i | \(-0.145143\pi\) | ||||
0.897829 | + | 0.440344i | \(0.145143\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9109.74 | −0.330217 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1909.57 | −0.0689929 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −63425.8 | −2.28408 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35777.0 | 1.28420 | 0.642098 | − | 0.766623i | \(-0.278064\pi\) | ||||
0.642098 | + | 0.766623i | \(0.278064\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33347.1 | −1.19308 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13887.3 | −0.495238 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4695.60 | −0.166909 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1049.15 | 0.0371721 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8342.11 | 0.294613 | 0.147307 | − | 0.989091i | \(-0.452940\pi\) | ||||
0.147307 | + | 0.989091i | \(0.452940\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 50384.0 | 1.77365 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 28683.4 | 1.00649 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −276.299 | −0.00966410 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11057.0 | 0.385502 | 0.192751 | − | 0.981248i | \(-0.438259\pi\) | ||||
0.192751 | + | 0.981248i | \(0.438259\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 41267.8 | 1.43421 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7354.58 | −0.254785 | −0.127392 | − | 0.991852i | \(-0.540661\pi\) | ||||
−0.127392 | + | 0.991852i | \(0.540661\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 63557.6 | 2.19482 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11043.1 | 0.380141 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18516.1 | −0.635368 | −0.317684 | − | 0.948197i | \(-0.602905\pi\) | ||||
−0.317684 | + | 0.948197i | \(0.602905\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9183.56 | −0.314132 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 41607.1 | 1.41872 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17617.6 | 0.598835 | 0.299418 | − | 0.954122i | \(-0.403208\pi\) | ||||
0.299418 | + | 0.954122i | \(0.403208\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6525.10 | 0.221096 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3904.18 | −0.131875 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20402.9 | −0.687013 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4333.00 | −0.145447 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3726.25 | −0.124690 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9582.02 | 0.319644 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24466.2 | −0.813629 | −0.406815 | − | 0.913511i | \(-0.633361\pi\) | ||||
−0.406815 | + | 0.913511i | \(0.633361\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6600.26 | 0.218814 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27002.9 | 0.892445 | 0.446222 | − | 0.894922i | \(-0.352769\pi\) | ||||
0.446222 | + | 0.894922i | \(0.352769\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31741.9 | −1.04584 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9131.72 | 0.299948 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −57325.0 | −1.87716 | −0.938582 | − | 0.345057i | \(-0.887860\pi\) | ||||
−0.938582 | + | 0.345057i | \(0.887860\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2490.92 | 0.0813177 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2721.44 | −0.0885717 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −50052.2 | −1.62403 | −0.812013 | − | 0.583640i | \(-0.801628\pi\) | ||||
−0.812013 | + | 0.583640i | \(0.801628\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8838.42 | −0.285904 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −53441.3 | −1.72346 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −32252.8 | −1.03699 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35053.6 | 1.12363 | 0.561813 | − | 0.827264i | \(-0.310104\pi\) | ||||
0.561813 | + | 0.827264i | \(0.310104\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5389.53 | −0.172237 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1271.27 | −0.0405046 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44154.7 | −1.40260 | −0.701300 | − | 0.712866i | \(-0.747397\pi\) | ||||
−0.701300 | + | 0.712866i | \(0.747397\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5360.87 | −0.169780 |
(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 | 1088.4.a.w.1.2 | 3 | ||
4.3 | odd | 2 | 1088.4.a.t.1.2 | 3 | |||
8.3 | odd | 2 | 68.4.a.b.1.2 | ✓ | 3 | ||
8.5 | even | 2 | 272.4.a.i.1.2 | 3 | |||
24.5 | odd | 2 | 2448.4.a.ba.1.3 | 3 | |||
24.11 | even | 2 | 612.4.a.g.1.3 | 3 | |||
40.3 | even | 4 | 1700.4.e.d.749.4 | 6 | |||
40.19 | odd | 2 | 1700.4.a.d.1.2 | 3 | |||
40.27 | even | 4 | 1700.4.e.d.749.3 | 6 | |||
136.67 | odd | 2 | 1156.4.a.g.1.2 | 3 | |||
136.115 | odd | 4 | 1156.4.b.e.577.4 | 6 | |||
136.123 | odd | 4 | 1156.4.b.e.577.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
68.4.a.b.1.2 | ✓ | 3 | 8.3 | odd | 2 | ||
272.4.a.i.1.2 | 3 | 8.5 | even | 2 | |||
612.4.a.g.1.3 | 3 | 24.11 | even | 2 | |||
1088.4.a.t.1.2 | 3 | 4.3 | odd | 2 | |||
1088.4.a.w.1.2 | 3 | 1.1 | even | 1 | trivial | ||
1156.4.a.g.1.2 | 3 | 136.67 | odd | 2 | |||
1156.4.b.e.577.3 | 6 | 136.123 | odd | 4 | |||
1156.4.b.e.577.4 | 6 | 136.115 | odd | 4 | |||
1700.4.a.d.1.2 | 3 | 40.19 | odd | 2 | |||
1700.4.e.d.749.3 | 6 | 40.27 | even | 4 | |||
1700.4.e.d.749.4 | 6 | 40.3 | even | 4 | |||
2448.4.a.ba.1.3 | 3 | 24.5 | odd | 2 |