Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,4,Mod(1,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1200.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.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: | \(70.8022920069\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{19}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 19 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 75) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.35890\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −30.4356 | −1.64337 | −0.821684 | − | 0.569944i | \(-0.806965\pi\) | ||||
−0.821684 | + | 0.569944i | \(0.806965\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −31.4356 | −0.861654 | −0.430827 | − | 0.902435i | \(-0.641778\pi\) | ||||
−0.430827 | + | 0.902435i | \(0.641778\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −60.7424 | −1.29592 | −0.647958 | − | 0.761676i | \(-0.724377\pi\) | ||||
−0.647958 | + | 0.761676i | \(0.724377\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −121.178 | −1.72882 | −0.864411 | − | 0.502786i | \(-0.832308\pi\) | ||||
−0.864411 | + | 0.502786i | \(0.832308\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.4356 | 0.174303 | 0.0871514 | − | 0.996195i | \(-0.472224\pi\) | ||||
0.0871514 | + | 0.996195i | \(0.472224\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 91.3068 | 0.948799 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −13.6932 | −0.124141 | −0.0620703 | − | 0.998072i | \(-0.519770\pi\) | ||||
−0.0620703 | + | 0.998072i | \(0.519770\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −76.0492 | −0.486965 | −0.243482 | − | 0.969905i | \(-0.578290\pi\) | ||||
−0.243482 | + | 0.969905i | \(0.578290\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −183.049 | −1.06054 | −0.530268 | − | 0.847830i | \(-0.677909\pi\) | ||||
−0.530268 | + | 0.847830i | \(0.677909\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 94.3068 | 0.497476 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −37.3864 | −0.166116 | −0.0830580 | − | 0.996545i | \(-0.526469\pi\) | ||||
−0.0830580 | + | 0.996545i | \(0.526469\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 182.227 | 0.748197 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −30.6627 | −0.116798 | −0.0583990 | − | 0.998293i | \(-0.518600\pi\) | ||||
−0.0583990 | + | 0.998293i | \(0.518600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −327.564 | −1.16170 | −0.580850 | − | 0.814011i | \(-0.697280\pi\) | ||||
−0.580850 | + | 0.814011i | \(0.697280\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 449.485 | 1.39498 | 0.697490 | − | 0.716594i | \(-0.254300\pi\) | ||||
0.697490 | + | 0.716594i | \(0.254300\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 583.325 | 1.70066 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 363.534 | 0.998136 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −301.951 | −0.782569 | −0.391284 | − | 0.920270i | \(-0.627969\pi\) | ||||
−0.391284 | + | 0.920270i | \(0.627969\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −43.3068 | −0.100634 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −340.970 | −0.752381 | −0.376190 | − | 0.926542i | \(-0.622766\pi\) | ||||
−0.376190 | + | 0.926542i | \(0.622766\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 619.098 | 1.29947 | 0.649733 | − | 0.760163i | \(-0.274881\pi\) | ||||
0.649733 | + | 0.760163i | \(0.274881\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −273.920 | −0.547789 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −256.890 | −0.468419 | −0.234210 | − | 0.972186i | \(-0.575250\pi\) | ||||
−0.234210 | + | 0.972186i | \(0.575250\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 41.0796 | 0.0716726 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −499.178 | −0.834388 | −0.417194 | − | 0.908818i | \(-0.636986\pi\) | ||||
−0.417194 | + | 0.908818i | \(0.636986\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −19.1288 | −0.0306693 | −0.0153346 | − | 0.999882i | \(-0.504881\pi\) | ||||
−0.0153346 | + | 0.999882i | \(0.504881\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 956.761 | 1.41601 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −257.424 | −0.366613 | −0.183307 | − | 0.983056i | \(-0.558680\pi\) | ||||
−0.183307 | + | 0.983056i | \(0.558680\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −914.909 | −1.20993 | −0.604965 | − | 0.796252i | \(-0.706813\pi\) | ||||
−0.604965 | + | 0.796252i | \(0.706813\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 228.148 | 0.281149 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1059.68 | −1.26209 | −0.631045 | − | 0.775746i | \(-0.717374\pi\) | ||||
−0.631045 | + | 0.775746i | \(0.717374\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1848.73 | 2.12967 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 549.148 | 0.612300 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 521.000 | 0.545356 | 0.272678 | − | 0.962105i | \(-0.412091\pi\) | ||||
0.272678 | + | 0.962105i | \(0.412091\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −282.920 | −0.287218 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 347.080 | 0.341938 | 0.170969 | − | 0.985276i | \(-0.445310\pi\) | ||||
0.170969 | + | 0.985276i | \(0.445310\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 770.749 | 0.737322 | 0.368661 | − | 0.929564i | \(-0.379816\pi\) | ||||
0.368661 | + | 0.929564i | \(0.379816\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1415.37 | 1.27878 | 0.639390 | − | 0.768883i | \(-0.279187\pi\) | ||||
0.639390 | + | 0.768883i | \(0.279187\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 908.386 | 0.798235 | 0.399118 | − | 0.916900i | \(-0.369317\pi\) | ||||
0.399118 | + | 0.916900i | \(0.369317\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 112.159 | 0.0959071 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2049.94 | −1.70657 | −0.853283 | − | 0.521447i | \(-0.825392\pi\) | ||||
−0.853283 | + | 0.521447i | \(0.825392\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −546.681 | −0.431972 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3688.12 | 2.84109 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −342.803 | −0.257553 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 91.9882 | 0.0674333 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −281.644 | −0.196786 | −0.0983932 | − | 0.995148i | \(-0.531370\pi\) | ||||
−0.0983932 | + | 0.995148i | \(0.531370\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 982.693 | 0.670708 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −243.056 | −0.162106 | −0.0810531 | − | 0.996710i | \(-0.525828\pi\) | ||||
−0.0810531 | + | 0.996710i | \(0.525828\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −439.356 | −0.286444 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 909.386 | 0.567110 | 0.283555 | − | 0.958956i | \(-0.408486\pi\) | ||||
0.283555 | + | 0.958956i | \(0.408486\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2049.52 | 1.25063 | 0.625317 | − | 0.780371i | \(-0.284970\pi\) | ||||
0.625317 | + | 0.780371i | \(0.284970\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1348.45 | −0.805392 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1909.47 | 1.11663 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1749.98 | −0.981875 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3601.14 | 1.97998 | 0.989990 | − | 0.141136i | \(-0.0450753\pi\) | ||||
0.989990 | + | 0.141136i | \(0.0450753\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1383.38 | −0.745550 | −0.372775 | − | 0.927922i | \(-0.621594\pi\) | ||||
−0.372775 | + | 0.927922i | \(0.621594\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1090.60 | −0.576274 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −131.749 | −0.0669729 | −0.0334864 | − | 0.999439i | \(-0.510661\pi\) | ||||
−0.0334864 | + | 0.999439i | \(0.510661\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 905.852 | 0.451816 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 416.761 | 0.204009 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2897.74 | −1.39244 | −0.696222 | − | 0.717827i | \(-0.745137\pi\) | ||||
−0.696222 | + | 0.717827i | \(0.745137\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −260.283 | −0.120607 | −0.0603034 | − | 0.998180i | \(-0.519207\pi\) | ||||
−0.0603034 | + | 0.998180i | \(0.519207\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1492.64 | 0.679398 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 129.920 | 0.0581009 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1935.83 | −0.850742 | −0.425371 | − | 0.905019i | \(-0.639856\pi\) | ||||
−0.425371 | + | 0.905019i | \(0.639856\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1022.91 | 0.434387 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −576.627 | −0.240777 | −0.120389 | − | 0.992727i | \(-0.538414\pi\) | ||||
−0.120389 | + | 0.992727i | \(0.538414\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1962.04 | −0.805733 | −0.402866 | − | 0.915259i | \(-0.631986\pi\) | ||||
−0.402866 | + | 0.915259i | \(0.631986\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1857.30 | −0.750247 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3809.30 | 1.48965 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 821.761 | 0.316266 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4318.75 | 1.63609 | 0.818047 | − | 0.575152i | \(-0.195057\pi\) | ||||
0.818047 | + | 0.575152i | \(0.195057\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.97647 | 0.00111011 | 0.000555054 | − | 1.00000i | \(-0.499823\pi\) | ||||
0.000555054 | 1.00000i | \(0.499823\pi\) | ||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 569.705 | 0.206040 | 0.103020 | − | 0.994679i | \(-0.467149\pi\) | ||||
0.103020 | + | 0.994679i | \(0.467149\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3050.73 | 1.08674 | 0.543368 | − | 0.839494i | \(-0.317149\pi\) | ||||
0.543368 | + | 0.839494i | \(0.317149\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 770.670 | 0.270442 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2314.60 | 0.800262 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −123.239 | −0.0413802 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −453.792 | −0.150189 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 50.5104 | 0.0164800 | 0.00824000 | − | 0.999966i | \(-0.497377\pi\) | ||||
0.00824000 | + | 0.999966i | \(0.497377\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1497.53 | 0.481734 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5571.21 | 1.74285 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 57.3864 | 0.0177069 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7360.64 | 2.24041 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5453.55 | −1.63765 | −0.818827 | − | 0.574040i | \(-0.805375\pi\) | ||||
−0.818827 | + | 0.574040i | \(0.805375\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4777.14 | 1.39678 | 0.698392 | − | 0.715715i | \(-0.253899\pi\) | ||||
0.698392 | + | 0.715715i | \(0.253899\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2085.51 | −0.601808 | −0.300904 | − | 0.953654i | \(-0.597288\pi\) | ||||
−0.300904 | + | 0.953654i | \(0.597288\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2870.28 | −0.817536 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6484.53 | 1.82324 | 0.911622 | − | 0.411030i | \(-0.134831\pi\) | ||||
0.911622 | + | 0.411030i | \(0.134831\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 772.271 | 0.211664 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2234.62 | −0.604792 | −0.302396 | − | 0.953182i | \(-0.597786\pi\) | ||||
−0.302396 | + | 0.953182i | \(0.597786\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2393.01 | −0.639616 | −0.319808 | − | 0.947482i | \(-0.603618\pi\) | ||||
−0.319808 | + | 0.947482i | \(0.603618\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −876.852 | −0.225882 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2744.73 | 0.698554 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 612.661 | 0.154067 | 0.0770335 | − | 0.997029i | \(-0.475455\pi\) | ||||
0.0770335 | + | 0.997029i | \(0.475455\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 430.454 | 0.106966 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −306.112 | −0.0742987 | −0.0371493 | − | 0.999310i | \(-0.511828\pi\) | ||||
−0.0371493 | + | 0.999310i | \(0.511828\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1137.88 | 0.272990 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −684.443 | −0.162322 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −283.839 | −0.0665484 | −0.0332742 | − | 0.999446i | \(-0.510593\pi\) | ||||
−0.0332742 | + | 0.999446i | \(0.510593\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3179.04 | 0.728668 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2426.21 | 0.549920 | 0.274960 | − | 0.961456i | \(-0.411335\pi\) | ||||
0.274960 | + | 0.961456i | \(0.411335\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 174.946 | 0.0392148 | 0.0196074 | − | 0.999808i | \(-0.493758\pi\) | ||||
0.0196074 | + | 0.999808i | \(0.493758\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5546.19 | −1.22956 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7807.07 | −1.69344 | −0.846718 | − | 0.532042i | \(-0.821425\pi\) | ||||
−0.846718 | + | 0.532042i | \(0.821425\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1647.44 | −0.353512 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 584.171 | 0.124017 | 0.0620084 | − | 0.998076i | \(-0.480249\pi\) | ||||
0.0620084 | + | 0.998076i | \(0.480249\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5897.31 | 1.23872 | 0.619362 | − | 0.785106i | \(-0.287391\pi\) | ||||
0.619362 | + | 0.785106i | \(0.287391\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 933.239 | 0.191942 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9771.10 | 1.98883 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1563.00 | −0.314861 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1609.73 | 0.320960 | 0.160480 | − | 0.987039i | \(-0.448696\pi\) | ||||
0.160480 | + | 0.987039i | \(0.448696\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 848.761 | 0.165825 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 831.758 | 0.160876 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9969.62 | 1.90910 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1041.24 | −0.197418 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −234.473 | −0.0435898 | −0.0217949 | − | 0.999762i | \(-0.506938\pi\) | ||||
−0.0217949 | + | 0.999762i | \(0.506938\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2312.25 | −0.425693 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1795.25 | 0.327329 | 0.163665 | − | 0.986516i | \(-0.447669\pi\) | ||||
0.163665 | + | 0.986516i | \(0.447669\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8440.61 | −1.52425 | −0.762127 | − | 0.647427i | \(-0.775845\pi\) | ||||
−0.762127 | + | 0.647427i | \(0.775845\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10551.7 | 1.86953 | 0.934766 | − | 0.355264i | \(-0.115609\pi\) | ||||
0.934766 | + | 0.355264i | \(0.115609\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2390.65 | 0.419595 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4246.12 | −0.738304 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1749.28 | −0.301339 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2725.16 | −0.460861 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13680.3 | −2.29247 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6743.17 | −1.11975 | −0.559876 | − | 0.828576i | \(-0.689151\pi\) | ||||
−0.559876 | + | 0.828576i | \(0.689151\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −336.478 | −0.0553720 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8437.26 | −1.36382 | −0.681909 | − | 0.731437i | \(-0.738850\pi\) | ||||
−0.681909 | + | 0.731437i | \(0.738850\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6149.82 | 0.985287 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5754.26 | 0.913814 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7314.45 | −1.15144 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1848.85 | 0.286027 | 0.143013 | − | 0.989721i | \(-0.454321\pi\) | ||||
0.143013 | + | 0.989721i | \(0.454321\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1148.38 | −0.176136 | −0.0880678 | − | 0.996114i | \(-0.528069\pi\) | ||||
−0.0880678 | + | 0.996114i | \(0.528069\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1640.04 | 0.249399 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5753.60 | −0.867516 | −0.433758 | − | 0.901029i | \(-0.642813\pi\) | ||||
−0.433758 | + | 0.901029i | \(0.642813\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11064.4 | −1.64030 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5452.01 | −0.801521 | −0.400761 | − | 0.916183i | \(-0.631254\pi\) | ||||
−0.400761 | + | 0.916183i | \(0.631254\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6650.61 | −0.969619 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1028.41 | 0.148698 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8385.93 | −1.19276 | −0.596379 | − | 0.802703i | \(-0.703394\pi\) | ||||
−0.596379 | + | 0.802703i | \(0.703394\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −275.965 | −0.0389327 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9190.05 | 1.28605 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2728.30 | 0.378730 | 0.189365 | − | 0.981907i | \(-0.439357\pi\) | ||||
0.189365 | + | 0.981907i | \(0.439357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4619.41 | 0.631065 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3348.99 | −0.453895 | −0.226947 | − | 0.973907i | \(-0.572875\pi\) | ||||
−0.226947 | + | 0.973907i | \(0.572875\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 844.932 | 0.113615 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10430.3 | −1.39155 | −0.695774 | − | 0.718261i | \(-0.744938\pi\) | ||||
−0.695774 | + | 0.718261i | \(0.744938\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2948.08 | −0.387233 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9827.23 | 1.28088 | 0.640438 | − | 0.768010i | \(-0.278753\pi\) | ||||
0.640438 | + | 0.768010i | \(0.278753\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1659.32 | 0.214617 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 729.168 | 0.0935921 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −436.382 | −0.0551672 | −0.0275836 | − | 0.999619i | \(-0.508781\pi\) | ||||
−0.0275836 | + | 0.999619i | \(0.508781\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1318.07 | 0.165378 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14501.5 | −1.80591 | −0.902955 | − | 0.429736i | \(-0.858607\pi\) | ||||
−0.902955 | + | 0.429736i | \(0.858607\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11118.8 | 1.37436 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1175.26 | 0.143134 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12058.4 | −1.45782 | −0.728911 | − | 0.684609i | \(-0.759973\pi\) | ||||
−0.728911 | + | 0.684609i | \(0.759973\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2728.16 | −0.327421 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10377.6 | 1.23644 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6148.57 | −0.722054 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6042.95 | −0.704577 | −0.352288 | − | 0.935892i | \(-0.614596\pi\) | ||||
−0.352288 | + | 0.935892i | \(0.614596\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9994.67 | −1.15703 | −0.578516 | − | 0.815671i | \(-0.696368\pi\) | ||||
−0.578516 | + | 0.815671i | \(0.696368\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4045.36 | 0.464994 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18842.6 | −2.13550 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5728.42 | −0.644687 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9327.32 | −1.04242 | −0.521208 | − | 0.853430i | \(-0.674518\pi\) | ||||
−0.521208 | + | 0.853430i | \(0.674518\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7861.22 | −0.872485 | −0.436243 | − | 0.899829i | \(-0.643691\pi\) | ||||
−0.436243 | + | 0.899829i | \(0.643691\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −197.670 | −0.0216380 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7412.06 | −0.805828 | −0.402914 | − | 0.915238i | \(-0.632003\pi\) | ||||
−0.402914 | + | 0.915238i | \(0.632003\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5249.93 | 0.566886 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3043.66 | 0.326430 | 0.163215 | − | 0.986591i | \(-0.447814\pi\) | ||||
0.163215 | + | 0.986591i | \(0.447814\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10803.4 | −1.14314 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9547.87 | −1.00355 | −0.501773 | − | 0.864999i | \(-0.667319\pi\) | ||||
−0.501773 | + | 0.864999i | \(0.667319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 963.902 | 0.100639 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4150.14 | 0.430443 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13401.9 | 1.37180 | 0.685901 | − | 0.727695i | \(-0.259408\pi\) | ||||
0.685901 | + | 0.727695i | \(0.259408\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3271.81 | 0.332712 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4137.03 | −0.417962 | −0.208981 | − | 0.977920i | \(-0.567015\pi\) | ||||
−0.208981 | + | 0.977920i | \(0.567015\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13976.3 | 1.40288 | 0.701439 | − | 0.712729i | \(-0.252541\pi\) | ||||
0.701439 | + | 0.712729i | \(0.252541\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10796.5 | 1.06982 | 0.534908 | − | 0.844910i | \(-0.320346\pi\) | ||||
0.534908 | + | 0.844910i | \(0.320346\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7818.60 | 0.769785 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 395.248 | 0.0386668 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10297.2 | 1.00098 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2717.56 | −0.260856 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14568.4 | −1.38966 | −0.694830 | − | 0.719174i | \(-0.744521\pi\) | ||||
−0.694830 | + | 0.719174i | \(0.744521\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2270.94 | 0.215272 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1250.28 | −0.117784 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11456.6 | 1.06601 | 0.533004 | − | 0.846113i | \(-0.321063\pi\) | ||||
0.533004 | + | 0.846113i | \(0.321063\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8693.21 | 0.803928 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19666.5 | 1.80761 | 0.903804 | − | 0.427948i | \(-0.140763\pi\) | ||||
0.903804 | + | 0.427948i | \(0.140763\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9215.48 | 0.841875 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15192.8 | 1.37121 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8379.31 | −0.751722 | −0.375861 | − | 0.926676i | \(-0.622653\pi\) | ||||
−0.375861 | + | 0.926676i | \(0.622653\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 780.850 | 0.0696323 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15678.1 | 1.38976 | 0.694881 | − | 0.719124i | \(-0.255457\pi\) | ||||
0.694881 | + | 0.719124i | \(0.255457\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4477.91 | −0.392251 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17037.3 | −1.48363 | −0.741813 | − | 0.670606i | \(-0.766034\pi\) | ||||
−0.741813 | + | 0.670606i | \(0.766034\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 582.197 | 0.0504009 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −389.761 | −0.0335446 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14129.8 | −1.20199 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5807.49 | 0.491176 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8776.12 | −0.737982 | −0.368991 | − | 0.929433i | \(-0.620297\pi\) | ||||
−0.368991 | + | 0.929433i | \(0.620297\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11120.4 | −0.929753 | −0.464877 | − | 0.885375i | \(-0.653901\pi\) | ||||
−0.464877 | + | 0.885375i | \(0.653901\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22181.5 | 1.83348 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11979.5 | −0.984589 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3068.73 | −0.250794 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1862.53 | 0.151360 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1729.88 | 0.139013 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18337.2 | −1.46538 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21730.6 | 1.72693 | 0.863467 | − | 0.504405i | \(-0.168288\pi\) | ||||
0.863467 | + | 0.504405i | \(0.168288\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5886.13 | 0.465190 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6926.17 | 0.541392 | 0.270696 | − | 0.962665i | \(-0.412746\pi\) | ||||
0.270696 | + | 0.962665i | \(0.412746\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5571.89 | 0.433155 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1097.82 | −0.0848793 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7834.85 | 0.602480 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6589.22 | −0.501246 | −0.250623 | − | 0.968085i | \(-0.580636\pi\) | ||||
−0.250623 | + | 0.968085i | \(0.580636\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19897.0 | 1.50547 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11427.9 | −0.860047 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3839.63 | −0.287426 | −0.143713 | − | 0.989619i | \(-0.545904\pi\) | ||||
−0.143713 | + | 0.989619i | \(0.545904\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2465.28 | −0.182596 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20874.0 | −1.53794 | −0.768968 | − | 0.639287i | \(-0.779229\pi\) | ||||
−0.768968 | + | 0.639287i | \(0.779229\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21175.9 | −1.55199 | −0.775994 | − | 0.630740i | \(-0.782752\pi\) | ||||
−0.775994 | + | 0.630740i | \(0.782752\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12956.3 | −0.944599 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14924.2 | −1.07678 | −0.538391 | − | 0.842695i | \(-0.680968\pi\) | ||||
−0.538391 | + | 0.842695i | \(0.680968\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.92941 | −0.000640922 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27845.8 | 1.98836 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9492.00 | 0.674303 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25218.0 | −1.77318 | −0.886592 | − | 0.462552i | \(-0.846934\pi\) | ||||
−0.886592 | + | 0.462552i | \(0.846934\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2642.42 | −0.184854 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1709.11 | −0.118957 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5011.77 | 0.347063 | 0.173532 | − | 0.984828i | \(-0.444482\pi\) | ||||
0.173532 | + | 0.984828i | \(0.444482\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9152.19 | −0.627428 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4943.41 | −0.337199 | −0.168600 | − | 0.985685i | \(-0.553925\pi\) | ||||
−0.168600 | + | 0.985685i | \(0.553925\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24334.8 | −1.65164 | −0.825821 | − | 0.563932i | \(-0.809288\pi\) | ||||
−0.825821 | + | 0.563932i | \(0.809288\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2312.01 | −0.156140 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28973.8 | −1.93741 | −0.968707 | − | 0.248207i | \(-0.920159\pi\) | ||||
−0.968707 | + | 0.248207i | \(0.920159\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6943.81 | −0.462032 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27302.8 | −1.80778 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15139.1 | 0.997490 | 0.498745 | − | 0.866749i | \(-0.333794\pi\) | ||||
0.498745 | + | 0.866749i | \(0.333794\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13894.8 | 0.906617 | 0.453309 | − | 0.891354i | \(-0.350244\pi\) | ||||
0.453309 | + | 0.891354i | \(0.350244\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4589.69 | 0.298021 | 0.149011 | − | 0.988836i | \(-0.452391\pi\) | ||||
0.149011 | + | 0.988836i | \(0.452391\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 369.717 | 0.0238909 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 32252.0 | 2.07408 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1361.37 | 0.0867114 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4530.41 | 0.287185 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3005.77 | −0.189632 | −0.0948160 | − | 0.995495i | \(-0.530226\pi\) | ||||
−0.0948160 | + | 0.995495i | \(0.530226\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −151.531 | −0.00951473 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −35432.6 | −2.20391 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4492.60 | −0.278129 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5631.47 | −0.347004 | −0.173502 | − | 0.984834i | \(-0.555508\pi\) | ||||
−0.173502 | + | 0.984834i | \(0.555508\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11305.1 | −0.693358 | −0.346679 | − | 0.937984i | \(-0.612691\pi\) | ||||
−0.346679 | + | 0.937984i | \(0.612691\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8614.30 | 0.523436 | 0.261718 | − | 0.965144i | \(-0.415711\pi\) | ||||
0.261718 | + | 0.965144i | \(0.415711\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10718.6 | 0.648291 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16713.6 | −1.00623 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12639.8 | 0.757479 | 0.378739 | − | 0.925503i | \(-0.376358\pi\) | ||||
0.378739 | + | 0.925503i | \(0.376358\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −172.159 | −0.0102231 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13640.4 | −0.806306 | −0.403153 | − | 0.915133i | \(-0.632086\pi\) | ||||
−0.403153 | + | 0.915133i | \(0.632086\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17052.0 | −1.00340 | −0.501699 | − | 0.865042i | \(-0.667291\pi\) | ||||
−0.501699 | + | 0.865042i | \(0.667291\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22081.9 | −1.29350 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1041.36 | 0.0604521 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16360.7 | 0.945500 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19461.7 | −1.11969 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16419.7 | −0.940467 | −0.470234 | − | 0.882542i | \(-0.655830\pi\) | ||||
−0.470234 | + | 0.882542i | \(0.655830\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8670.47 | −0.492221 | −0.246110 | − | 0.969242i | \(-0.579153\pi\) | ||||
−0.246110 | + | 0.969242i | \(0.579153\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15856.9 | −0.896220 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14331.4 | −0.806434 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5973.36 | −0.334647 | −0.167324 | − | 0.985902i | \(-0.553512\pi\) | ||||
−0.167324 | + | 0.985902i | \(0.553512\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6256.52 | 0.347454 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18341.2 | 1.01414 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15316.3 | 0.843212 | 0.421606 | − | 0.906779i | \(-0.361467\pi\) | ||||
0.421606 | + | 0.906779i | \(0.361467\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8610.85 | 0.472005 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3715.65 | 0.201923 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19453.6 | −1.05265 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34583.1 | 1.86332 | 0.931660 | − | 0.363333i | \(-0.118361\pi\) | ||||
0.931660 | + | 0.363333i | \(0.118361\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −539.695 | −0.0289545 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10563.6 | −0.561929 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11194.1 | 0.592955 | 0.296477 | − | 0.955040i | \(-0.404188\pi\) | ||||
0.296477 | + | 0.955040i | \(0.404188\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2316.81 | −0.122204 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2506.53 | 0.131655 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6703.85 | 0.349177 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15491.9 | 0.803549 | 0.401774 | − | 0.915739i | \(-0.368394\pi\) | ||||
0.401774 | + | 0.915739i | \(0.368394\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23458.2 | −1.21169 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7179.04 | 0.369283 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6272.72 | 0.320003 | 0.160002 | − | 0.987117i | \(-0.448850\pi\) | ||||
0.160002 | + | 0.987117i | \(0.448850\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39693.6 | 2.00837 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24980.5 | 1.25877 | 0.629383 | − | 0.777095i | \(-0.283308\pi\) | ||||
0.629383 | + | 0.777095i | \(0.283308\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8075.49 | 0.403615 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30660.7 | 1.52621 | 0.763107 | − | 0.646272i | \(-0.223673\pi\) | ||||
0.763107 | + | 0.646272i | \(0.223673\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2630.56 | 0.130413 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17205.7 | 0.849551 | 0.424776 | − | 0.905299i | \(-0.360353\pi\) | ||||
0.424776 | + | 0.905299i | \(0.360353\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8234.18 | −0.403310 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −43077.8 | −2.10151 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18397.1 | −0.893901 | −0.446950 | − | 0.894559i | \(-0.647490\pi\) | ||||
−0.446950 | + | 0.894559i | \(0.647490\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1837.98 | −0.0889506 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22305.1 | 1.07093 | 0.535465 | − | 0.844557i | \(-0.320136\pi\) | ||||
0.535465 | + | 0.844557i | \(0.320136\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1291.36 | −0.0617569 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14458.5 | 0.688727 | 0.344364 | − | 0.938836i | \(-0.388095\pi\) | ||||
0.344364 | + | 0.938836i | \(0.388095\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27647.3 | −1.31179 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20711.3 | 0.975022 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39897.6 | −1.87093 | −0.935463 | − | 0.353424i | \(-0.885017\pi\) | ||||
−0.935463 | + | 0.353424i | \(0.885017\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 918.337 | 0.0428964 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20070.2 | 0.933863 | 0.466931 | − | 0.884294i | \(-0.345359\pi\) | ||||
0.466931 | + | 0.884294i | \(0.345359\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3413.63 | −0.157611 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −442.635 | −0.0203582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15692.0 | 0.718953 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2053.33 | 0.0937164 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10733.0 | −0.486137 | −0.243069 | − | 0.970009i | \(-0.578154\pi\) | ||||
−0.243069 | + | 0.970009i | \(0.578154\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 851.516 | 0.0384218 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 62391.1 | 2.80452 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −37605.5 | −1.68400 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14335.8 | −0.637140 | −0.318570 | − | 0.947899i | \(-0.603203\pi\) | ||||
−0.318570 | + | 0.947899i | \(0.603203\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −54467.7 | −2.41167 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9537.13 | −0.420697 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 601.325 | 0.0264263 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7278.63 | −0.317497 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20920.7 | 0.909187 | 0.454593 | − | 0.890699i | \(-0.349785\pi\) | ||||
0.454593 | + | 0.890699i | \(0.349785\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12816.5 | −0.554931 | −0.277465 | − | 0.960736i | \(-0.589494\pi\) | ||||
−0.277465 | + | 0.960736i | \(0.589494\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −524.838 | −0.0226407 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4728.59 | −0.202488 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16638.6 | 0.709889 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7253.55 | 0.308344 | 0.154172 | − | 0.988044i | \(-0.450729\pi\) | ||||
0.154172 | + | 0.988044i | \(0.450729\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35288.1 | −1.49461 | −0.747307 | − | 0.664479i | \(-0.768654\pi\) | ||||
−0.747307 | + | 0.664479i | \(0.768654\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32205.9 | 1.35418 | 0.677092 | − | 0.735899i | \(-0.263240\pi\) | ||||
0.677092 | + | 0.735899i | \(0.263240\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29993.3 | 1.25659 | 0.628294 | − | 0.777976i | \(-0.283754\pi\) | ||||
0.628294 | + | 0.777976i | \(0.283754\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23421.2 | 0.977706 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −70686.2 | −2.94013 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4942.33 | 0.204100 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35608.7 | 1.46526 | 0.732628 | − | 0.680629i | \(-0.238294\pi\) | ||||
0.732628 | + | 0.680629i | \(0.238294\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18605.5 | −0.762865 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1752.51 | −0.0716011 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10433.4 | 0.423255 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17691.9 | −0.715177 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 511.940 | 0.0206217 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11229.3 | −0.450744 | −0.225372 | − | 0.974273i | \(-0.572360\pi\) | ||||
−0.225372 | + | 0.974273i | \(0.572360\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22136.1 | 0.882327 | 0.441164 | − | 0.897427i | \(-0.354566\pi\) | ||||
0.441164 | + | 0.897427i | \(0.354566\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 820.727 | 0.0325994 | 0.0162997 | − | 0.999867i | \(-0.494811\pi\) | ||||
0.0162997 | + | 0.999867i | \(0.494811\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2799.72 | −0.110818 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 245.223 | 0.00967264 | 0.00483632 | − | 0.999988i | \(-0.498461\pi\) | ||||
0.00483632 | + | 0.999988i | \(0.498461\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −29313.3 | −1.14825 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8092.27 | 0.315894 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15604.1 | 0.607032 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4689.00 | 0.181785 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37727.8 | 1.45265 | 0.726326 | − | 0.687350i | \(-0.241226\pi\) | ||||
0.726326 | + | 0.687350i | \(0.241226\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4829.19 | −0.185306 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21738.8 | 0.831326 | 0.415663 | − | 0.909519i | \(-0.363550\pi\) | ||||
0.415663 | + | 0.909519i | \(0.363550\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44340.4 | 1.68989 | 0.844946 | − | 0.534852i | \(-0.179632\pi\) | ||||
0.844946 | + | 0.534852i | \(0.179632\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 681.008 | 0.0257790 | 0.0128895 | − | 0.999917i | \(-0.495897\pi\) | ||||
0.0128895 | + | 0.999917i | \(0.495897\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8572.00 | 0.323392 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2546.28 | −0.0957393 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6488.58 | 0.243149 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2495.28 | −0.0928816 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13920.7 | 0.516443 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36589.8 | 1.35292 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −29908.9 | −1.10222 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5348.01 | −0.195786 | −0.0978929 | − | 0.995197i | \(-0.531210\pi\) | ||||
−0.0978929 | + | 0.995197i | \(0.531210\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3123.72 | 0.113979 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14488.7 | −0.526930 | −0.263465 | − | 0.964669i | \(-0.584865\pi\) | ||||
−0.263465 | + | 0.964669i | \(0.584865\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28760.7 | 1.04254 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7397.56 | 0.266400 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22546.9 | 0.809308 | 0.404654 | − | 0.914470i | \(-0.367392\pi\) | ||||
0.404654 | + | 0.914470i | \(0.367392\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 703.419 | 0.0251666 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30321.3 | 1.08130 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6936.74 | 0.245774 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13980.7 | −0.493747 | −0.246874 | − | 0.969048i | \(-0.579403\pi\) | ||||
−0.246874 | + | 0.969048i | \(0.579403\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8420.65 | 0.296429 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5385.75 | −0.188984 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26362.6 | 0.919133 | 0.459567 | − | 0.888143i | \(-0.348005\pi\) | ||||
0.459567 | + | 0.888143i | \(0.348005\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25321.8 | 0.880029 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14715.6 | −0.509792 | −0.254896 | − | 0.966968i | \(-0.582041\pi\) | ||||
−0.254896 | + | 0.966968i | \(0.582041\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 419.871 | 0.0144994 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11818.2 | 0.405532 | 0.202766 | − | 0.979227i | \(-0.435007\pi\) | ||||
0.202766 | + | 0.979227i | \(0.435007\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1161.93 | 0.0397448 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31655.1 | −1.07937 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43832.3 | −1.48989 | −0.744945 | − | 0.667125i | \(-0.767524\pi\) | ||||
−0.744945 | + | 0.667125i | \(0.767524\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7171.95 | −0.242253 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27677.7 | −0.931971 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3716.00 | 0.124736 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12738.4 | 0.426260 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10696.2 | −0.355706 | −0.177853 | − | 0.984057i | \(-0.556915\pi\) | ||||
−0.177853 | + | 0.984057i | \(0.556915\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5247.83 | 0.173978 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27933.0 | −0.923187 | −0.461593 | − | 0.887092i | \(-0.652722\pi\) | ||||
−0.461593 | + | 0.887092i | \(0.652722\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −62378.4 | −2.05525 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24341.7 | 0.797094 | 0.398547 | − | 0.917148i | \(-0.369515\pi\) | ||||
0.398547 | + | 0.917148i | \(0.369515\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33311.7 | 1.08748 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8175.48 | 0.266078 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12553.0 | −0.407301 | −0.203651 | − | 0.979044i | \(-0.565281\pi\) | ||||
−0.203651 | + | 0.979044i | \(0.565281\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 41041.0 | 1.32356 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4485.41 | 0.144214 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45631.8 | 1.46271 | 0.731353 | − | 0.681999i | \(-0.238889\pi\) | ||||
0.731353 | + | 0.681999i | \(0.238889\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20229.5 | 0.646490 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34499.0 | −1.09588 | −0.547941 | − | 0.836517i | \(-0.684588\pi\) | ||||
−0.547941 | + | 0.836517i | \(0.684588\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1009.43 | 0.0319690 |
(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 | 1200.4.a.bl.1.1 | 2 | ||
4.3 | odd | 2 | 75.4.a.d.1.2 | ✓ | 2 | ||
5.2 | odd | 4 | 1200.4.f.v.49.3 | 4 | |||
5.3 | odd | 4 | 1200.4.f.v.49.2 | 4 | |||
5.4 | even | 2 | 1200.4.a.bu.1.2 | 2 | |||
12.11 | even | 2 | 225.4.a.n.1.1 | 2 | |||
20.3 | even | 4 | 75.4.b.c.49.2 | 4 | |||
20.7 | even | 4 | 75.4.b.c.49.3 | 4 | |||
20.19 | odd | 2 | 75.4.a.e.1.1 | yes | 2 | ||
60.23 | odd | 4 | 225.4.b.h.199.3 | 4 | |||
60.47 | odd | 4 | 225.4.b.h.199.2 | 4 | |||
60.59 | even | 2 | 225.4.a.j.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.4.a.d.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
75.4.a.e.1.1 | yes | 2 | 20.19 | odd | 2 | ||
75.4.b.c.49.2 | 4 | 20.3 | even | 4 | |||
75.4.b.c.49.3 | 4 | 20.7 | even | 4 | |||
225.4.a.j.1.2 | 2 | 60.59 | even | 2 | |||
225.4.a.n.1.1 | 2 | 12.11 | even | 2 | |||
225.4.b.h.199.2 | 4 | 60.47 | odd | 4 | |||
225.4.b.h.199.3 | 4 | 60.23 | odd | 4 | |||
1200.4.a.bl.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1200.4.a.bu.1.2 | 2 | 5.4 | even | 2 | |||
1200.4.f.v.49.2 | 4 | 5.3 | odd | 4 | |||
1200.4.f.v.49.3 | 4 | 5.2 | odd | 4 |