Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [261,4,Mod(1,261)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(261, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("261.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 261 = 3^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 261.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: | \(15.3994985115\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.13458092.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 14x^{3} + 18x^{2} + 20x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 29) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.328194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 261.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.24125 | −0.792400 | −0.396200 | − | 0.918164i | \(-0.629671\pi\) | ||||
−0.396200 | + | 0.918164i | \(0.629671\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.97681 | −0.372101 | ||||||||
\(5\) | −18.3339 | −1.63984 | −0.819918 | − | 0.572481i | \(-0.805981\pi\) | ||||
−0.819918 | + | 0.572481i | \(0.805981\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.8583 | −0.910262 | −0.455131 | − | 0.890425i | \(-0.650408\pi\) | ||||
−0.455131 | + | 0.890425i | \(0.650408\pi\) | |||||||
\(8\) | 24.6017 | 1.08725 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 41.0908 | 1.29941 | ||||||||
\(11\) | −52.4385 | −1.43735 | −0.718673 | − | 0.695348i | \(-0.755250\pi\) | ||||
−0.718673 | + | 0.695348i | \(0.755250\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −87.5580 | −1.86802 | −0.934008 | − | 0.357252i | \(-0.883714\pi\) | ||||
−0.934008 | + | 0.357252i | \(0.883714\pi\) | |||||||
\(14\) | 37.7836 | 0.721292 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −31.3241 | −0.489439 | ||||||||
\(17\) | −15.4072 | −0.219812 | −0.109906 | − | 0.993942i | \(-0.535055\pi\) | ||||
−0.109906 | + | 0.993942i | \(0.535055\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 67.0156 | 0.809181 | 0.404591 | − | 0.914498i | \(-0.367414\pi\) | ||||
0.404591 | + | 0.914498i | \(0.367414\pi\) | |||||||
\(20\) | 54.5766 | 0.610185 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 117.528 | 1.13895 | ||||||||
\(23\) | −132.679 | −1.20285 | −0.601423 | − | 0.798931i | \(-0.705399\pi\) | ||||
−0.601423 | + | 0.798931i | \(0.705399\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 211.133 | 1.68906 | ||||||||
\(26\) | 196.239 | 1.48022 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 50.1839 | 0.338710 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 90.2221 | 0.522721 | 0.261361 | − | 0.965241i | \(-0.415829\pi\) | ||||
0.261361 | + | 0.965241i | \(0.415829\pi\) | |||||||
\(32\) | −126.609 | −0.699422 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 34.5314 | 0.174179 | ||||||||
\(35\) | 309.078 | 1.49268 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.1247 | 0.0494296 | 0.0247148 | − | 0.999695i | \(-0.492132\pi\) | ||||
0.0247148 | + | 0.999695i | \(0.492132\pi\) | |||||||
\(38\) | −150.199 | −0.641196 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −451.047 | −1.78292 | ||||||||
\(41\) | 18.8392 | 0.0717608 | 0.0358804 | − | 0.999356i | \(-0.488576\pi\) | ||||
0.0358804 | + | 0.999356i | \(0.488576\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −147.756 | −0.524013 | −0.262007 | − | 0.965066i | \(-0.584384\pi\) | ||||
−0.262007 | + | 0.965066i | \(0.584384\pi\) | |||||||
\(44\) | 156.100 | 0.534839 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 297.366 | 0.953136 | ||||||||
\(47\) | −21.0963 | −0.0654726 | −0.0327363 | − | 0.999464i | \(-0.510422\pi\) | ||||
−0.0327363 | + | 0.999464i | \(0.510422\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −58.7983 | −0.171424 | ||||||||
\(50\) | −473.201 | −1.33841 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 260.644 | 0.695092 | ||||||||
\(53\) | 290.454 | 0.752772 | 0.376386 | − | 0.926463i | \(-0.377167\pi\) | ||||
0.376386 | + | 0.926463i | \(0.377167\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 961.404 | 2.35701 | ||||||||
\(56\) | −414.743 | −0.989686 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −64.9962 | −0.147145 | ||||||||
\(59\) | 337.343 | 0.744379 | 0.372190 | − | 0.928157i | \(-0.378607\pi\) | ||||
0.372190 | + | 0.928157i | \(0.378607\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 84.0147 | 0.176344 | 0.0881720 | − | 0.996105i | \(-0.471897\pi\) | ||||
0.0881720 | + | 0.996105i | \(0.471897\pi\) | |||||||
\(62\) | −202.210 | −0.414205 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 534.355 | 1.04366 | ||||||||
\(65\) | 1605.28 | 3.06324 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 330.821 | 0.603228 | 0.301614 | − | 0.953430i | \(-0.402475\pi\) | ||||
0.301614 | + | 0.953430i | \(0.402475\pi\) | |||||||
\(68\) | 45.8644 | 0.0817922 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −692.721 | −1.18280 | ||||||||
\(71\) | −492.420 | −0.823092 | −0.411546 | − | 0.911389i | \(-0.635011\pi\) | ||||
−0.411546 | + | 0.911389i | \(0.635011\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −347.053 | −0.556431 | −0.278216 | − | 0.960519i | \(-0.589743\pi\) | ||||
−0.278216 | + | 0.960519i | \(0.589743\pi\) | |||||||
\(74\) | −24.9333 | −0.0391681 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −199.493 | −0.301098 | ||||||||
\(77\) | 884.023 | 1.30836 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −986.297 | −1.40465 | −0.702324 | − | 0.711858i | \(-0.747854\pi\) | ||||
−0.702324 | + | 0.711858i | \(0.747854\pi\) | |||||||
\(80\) | 574.294 | 0.802600 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −42.2234 | −0.0568633 | ||||||||
\(83\) | −594.382 | −0.786048 | −0.393024 | − | 0.919528i | \(-0.628571\pi\) | ||||
−0.393024 | + | 0.919528i | \(0.628571\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 282.475 | 0.360455 | ||||||||
\(86\) | 331.157 | 0.415228 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1290.08 | −1.56276 | ||||||||
\(89\) | −1387.04 | −1.65197 | −0.825987 | − | 0.563689i | \(-0.809382\pi\) | ||||
−0.825987 | + | 0.563689i | \(0.809382\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1476.08 | 1.70038 | ||||||||
\(92\) | 394.960 | 0.447581 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 47.2820 | 0.0518805 | ||||||||
\(95\) | −1228.66 | −1.32692 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −334.003 | −0.349617 | −0.174808 | − | 0.984602i | \(-0.555931\pi\) | ||||
−0.174808 | + | 0.984602i | \(0.555931\pi\) | |||||||
\(98\) | 131.781 | 0.135836 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −628.502 | −0.628502 | ||||||||
\(101\) | 245.919 | 0.242276 | 0.121138 | − | 0.992636i | \(-0.461346\pi\) | ||||
0.121138 | + | 0.992636i | \(0.461346\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −531.298 | −0.508255 | −0.254128 | − | 0.967171i | \(-0.581788\pi\) | ||||
−0.254128 | + | 0.967171i | \(0.581788\pi\) | |||||||
\(104\) | −2154.08 | −2.03101 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −650.979 | −0.596497 | ||||||||
\(107\) | 429.030 | 0.387625 | 0.193812 | − | 0.981039i | \(-0.437915\pi\) | ||||
0.193812 | + | 0.981039i | \(0.437915\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −967.263 | −0.849972 | −0.424986 | − | 0.905200i | \(-0.639721\pi\) | ||||
−0.424986 | + | 0.905200i | \(0.639721\pi\) | |||||||
\(110\) | −2154.74 | −1.86770 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 528.070 | 0.445518 | ||||||||
\(113\) | 1705.23 | 1.41960 | 0.709798 | − | 0.704405i | \(-0.248786\pi\) | ||||
0.709798 | + | 0.704405i | \(0.248786\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2432.52 | 1.97247 | ||||||||
\(116\) | −86.3275 | −0.0690975 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −756.070 | −0.589846 | ||||||||
\(119\) | 259.739 | 0.200086 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1418.80 | 1.06596 | ||||||||
\(122\) | −188.298 | −0.139735 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −268.574 | −0.194505 | ||||||||
\(125\) | −1579.15 | −1.12995 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2670.28 | −1.86574 | −0.932870 | − | 0.360213i | \(-0.882704\pi\) | ||||
−0.932870 | + | 0.360213i | \(0.882704\pi\) | |||||||
\(128\) | −184.749 | −0.127576 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3597.83 | −2.42731 | ||||||||
\(131\) | −879.993 | −0.586911 | −0.293455 | − | 0.955973i | \(-0.594805\pi\) | ||||
−0.293455 | + | 0.955973i | \(0.594805\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1129.77 | −0.736567 | ||||||||
\(134\) | −741.452 | −0.477998 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −379.044 | −0.238991 | ||||||||
\(137\) | −2064.15 | −1.28724 | −0.643620 | − | 0.765345i | \(-0.722568\pi\) | ||||
−0.643620 | + | 0.765345i | \(0.722568\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 605.130 | 0.369255 | 0.184628 | − | 0.982809i | \(-0.440892\pi\) | ||||
0.184628 | + | 0.982809i | \(0.440892\pi\) | |||||||
\(140\) | −920.068 | −0.555428 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1103.63 | 0.652218 | ||||||||
\(143\) | 4591.41 | 2.68499 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −531.684 | −0.304510 | ||||||||
\(146\) | 777.832 | 0.440917 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −33.1163 | −0.0183928 | ||||||||
\(149\) | 775.322 | 0.426287 | 0.213144 | − | 0.977021i | \(-0.431630\pi\) | ||||
0.213144 | + | 0.977021i | \(0.431630\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 427.925 | 0.230623 | 0.115311 | − | 0.993329i | \(-0.463213\pi\) | ||||
0.115311 | + | 0.993329i | \(0.463213\pi\) | |||||||
\(152\) | 1648.70 | 0.879785 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1981.31 | −1.03675 | ||||||||
\(155\) | −1654.12 | −0.857177 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1680.93 | −0.854474 | −0.427237 | − | 0.904140i | \(-0.640513\pi\) | ||||
−0.427237 | + | 0.904140i | \(0.640513\pi\) | |||||||
\(158\) | 2210.54 | 1.11304 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2321.24 | 1.14694 | ||||||||
\(161\) | 2236.74 | 1.09490 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2038.68 | 0.979645 | 0.489822 | − | 0.871822i | \(-0.337062\pi\) | ||||
0.489822 | + | 0.871822i | \(0.337062\pi\) | |||||||
\(164\) | −56.0808 | −0.0267023 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1332.16 | 0.622865 | ||||||||
\(167\) | −2543.12 | −1.17840 | −0.589199 | − | 0.807988i | \(-0.700557\pi\) | ||||
−0.589199 | + | 0.807988i | \(0.700557\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5469.40 | 2.48949 | ||||||||
\(170\) | −633.095 | −0.285625 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 439.842 | 0.194986 | ||||||||
\(173\) | 306.031 | 0.134492 | 0.0672460 | − | 0.997736i | \(-0.478579\pi\) | ||||
0.0672460 | + | 0.997736i | \(0.478579\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3559.34 | −1.53749 | ||||||||
\(176\) | 1642.59 | 0.703493 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3108.69 | 1.30903 | ||||||||
\(179\) | 478.797 | 0.199927 | 0.0999635 | − | 0.994991i | \(-0.468127\pi\) | ||||
0.0999635 | + | 0.994991i | \(0.468127\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −478.433 | −0.196473 | −0.0982367 | − | 0.995163i | \(-0.531320\pi\) | ||||
−0.0982367 | + | 0.995163i | \(0.531320\pi\) | |||||||
\(182\) | −3308.25 | −1.34739 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3264.13 | −1.30780 | ||||||||
\(185\) | −203.960 | −0.0810565 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 807.931 | 0.315945 | ||||||||
\(188\) | 62.7998 | 0.0243625 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2753.73 | 1.05146 | ||||||||
\(191\) | −833.106 | −0.315610 | −0.157805 | − | 0.987470i | \(-0.550442\pi\) | ||||
−0.157805 | + | 0.987470i | \(0.550442\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1449.88 | −0.540751 | −0.270376 | − | 0.962755i | \(-0.587148\pi\) | ||||
−0.270376 | + | 0.962755i | \(0.587148\pi\) | |||||||
\(194\) | 748.582 | 0.277037 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 175.031 | 0.0637870 | ||||||||
\(197\) | 1993.27 | 0.720886 | 0.360443 | − | 0.932781i | \(-0.382626\pi\) | ||||
0.360443 | + | 0.932781i | \(0.382626\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −356.359 | −0.126943 | −0.0634714 | − | 0.997984i | \(-0.520217\pi\) | ||||
−0.0634714 | + | 0.997984i | \(0.520217\pi\) | |||||||
\(200\) | 5194.23 | 1.83644 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −551.165 | −0.191979 | ||||||||
\(203\) | −488.890 | −0.169031 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −345.397 | −0.117676 | ||||||||
\(206\) | 1190.77 | 0.402742 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2742.67 | 0.914280 | ||||||||
\(209\) | −3514.20 | −1.16307 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4131.66 | 1.34803 | 0.674017 | − | 0.738716i | \(-0.264567\pi\) | ||||
0.674017 | + | 0.738716i | \(0.264567\pi\) | |||||||
\(212\) | −864.626 | −0.280107 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −961.562 | −0.307154 | ||||||||
\(215\) | 2708.95 | 0.859296 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1520.99 | −0.475813 | ||||||||
\(218\) | 2167.87 | 0.673518 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2861.92 | −0.877048 | ||||||||
\(221\) | 1349.02 | 0.410612 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1332.32 | 0.400086 | 0.200043 | − | 0.979787i | \(-0.435892\pi\) | ||||
0.200043 | + | 0.979787i | \(0.435892\pi\) | |||||||
\(224\) | 2134.41 | 0.636657 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3821.84 | −1.12489 | ||||||||
\(227\) | 1329.33 | 0.388681 | 0.194340 | − | 0.980934i | \(-0.437743\pi\) | ||||
0.194340 | + | 0.980934i | \(0.437743\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5455.47 | 1.57427 | 0.787135 | − | 0.616780i | \(-0.211563\pi\) | ||||
0.787135 | + | 0.616780i | \(0.211563\pi\) | |||||||
\(230\) | −5451.89 | −1.56299 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 713.451 | 0.201898 | ||||||||
\(233\) | 591.158 | 0.166215 | 0.0831075 | − | 0.996541i | \(-0.473516\pi\) | ||||
0.0831075 | + | 0.996541i | \(0.473516\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 386.778 | 0.107364 | ||||||||
\(236\) | −1004.21 | −0.276985 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −582.139 | −0.158548 | ||||||||
\(239\) | −6946.01 | −1.87992 | −0.939959 | − | 0.341289i | \(-0.889137\pi\) | ||||
−0.939959 | + | 0.341289i | \(0.889137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7105.62 | 1.89923 | 0.949613 | − | 0.313426i | \(-0.101477\pi\) | ||||
0.949613 | + | 0.313426i | \(0.101477\pi\) | |||||||
\(242\) | −3179.88 | −0.844670 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −250.096 | −0.0656179 | ||||||||
\(245\) | 1078.00 | 0.281106 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5867.75 | −1.51156 | ||||||||
\(248\) | 2219.62 | 0.568331 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3539.27 | 0.895372 | ||||||||
\(251\) | 4874.53 | 1.22581 | 0.612904 | − | 0.790158i | \(-0.290001\pi\) | ||||
0.612904 | + | 0.790158i | \(0.290001\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6957.49 | 1.72891 | ||||||||
\(254\) | 5984.75 | 1.47841 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3860.77 | −0.942570 | ||||||||
\(257\) | −2488.22 | −0.603934 | −0.301967 | − | 0.953318i | \(-0.597643\pi\) | ||||
−0.301967 | + | 0.953318i | \(0.597643\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −187.544 | −0.0449939 | ||||||||
\(260\) | −4778.62 | −1.13984 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1972.28 | 0.465068 | ||||||||
\(263\) | 2812.52 | 0.659419 | 0.329709 | − | 0.944082i | \(-0.393049\pi\) | ||||
0.329709 | + | 0.944082i | \(0.393049\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5325.16 | −1.23442 | ||||||||
\(266\) | 2532.09 | 0.583656 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −984.793 | −0.224462 | ||||||||
\(269\) | 5554.63 | 1.25900 | 0.629501 | − | 0.777000i | \(-0.283259\pi\) | ||||
0.629501 | + | 0.777000i | \(0.283259\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3168.41 | −0.710211 | −0.355105 | − | 0.934826i | \(-0.615555\pi\) | ||||
−0.355105 | + | 0.934826i | \(0.615555\pi\) | |||||||
\(272\) | 482.617 | 0.107584 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4626.26 | 1.02001 | ||||||||
\(275\) | −11071.5 | −2.42777 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3965.64 | 0.860189 | 0.430095 | − | 0.902784i | \(-0.358480\pi\) | ||||
0.430095 | + | 0.902784i | \(0.358480\pi\) | |||||||
\(278\) | −1356.25 | −0.292598 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7603.87 | 1.62292 | ||||||||
\(281\) | −1655.16 | −0.351383 | −0.175692 | − | 0.984445i | \(-0.556216\pi\) | ||||
−0.175692 | + | 0.984445i | \(0.556216\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7786.09 | 1.63546 | 0.817730 | − | 0.575602i | \(-0.195232\pi\) | ||||
0.817730 | + | 0.575602i | \(0.195232\pi\) | |||||||
\(284\) | 1465.84 | 0.306274 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10290.5 | −2.12758 | ||||||||
\(287\) | −317.597 | −0.0653211 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4675.62 | −0.951683 | ||||||||
\(290\) | 1191.63 | 0.241294 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1033.11 | 0.207049 | ||||||||
\(293\) | −8090.80 | −1.61321 | −0.806603 | − | 0.591094i | \(-0.798696\pi\) | ||||
−0.806603 | + | 0.591094i | \(0.798696\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6184.83 | −1.22066 | ||||||||
\(296\) | 273.688 | 0.0537426 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1737.69 | −0.337790 | ||||||||
\(299\) | 11617.1 | 2.24694 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2490.91 | 0.476989 | ||||||||
\(302\) | −959.086 | −0.182746 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2099.20 | −0.396045 | ||||||||
\(305\) | −1540.32 | −0.289175 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6129.49 | −1.13951 | −0.569753 | − | 0.821816i | \(-0.692961\pi\) | ||||
−0.569753 | + | 0.821816i | \(0.692961\pi\) | |||||||
\(308\) | −2631.57 | −0.486843 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3707.30 | 0.679228 | ||||||||
\(311\) | 8167.93 | 1.48926 | 0.744632 | − | 0.667476i | \(-0.232625\pi\) | ||||
0.744632 | + | 0.667476i | \(0.232625\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1877.25 | 0.339005 | 0.169502 | − | 0.985530i | \(-0.445784\pi\) | ||||
0.169502 | + | 0.985530i | \(0.445784\pi\) | |||||||
\(314\) | 3767.37 | 0.677086 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2936.02 | 0.522671 | ||||||||
\(317\) | −1222.93 | −0.216677 | −0.108338 | − | 0.994114i | \(-0.534553\pi\) | ||||
−0.108338 | + | 0.994114i | \(0.534553\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1520.72 | −0.266908 | ||||||||
\(320\) | −9796.82 | −1.71143 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5013.08 | −0.867603 | ||||||||
\(323\) | −1032.52 | −0.177867 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18486.4 | −3.15520 | ||||||||
\(326\) | −4569.20 | −0.776271 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 463.478 | 0.0780222 | ||||||||
\(329\) | 355.648 | 0.0595972 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3769.03 | 0.625876 | 0.312938 | − | 0.949774i | \(-0.398687\pi\) | ||||
0.312938 | + | 0.949774i | \(0.398687\pi\) | |||||||
\(332\) | 1769.36 | 0.292489 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5699.76 | 0.933763 | ||||||||
\(335\) | −6065.25 | −0.989195 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10900.2 | −1.76193 | −0.880967 | − | 0.473179i | \(-0.843107\pi\) | ||||
−0.880967 | + | 0.473179i | \(0.843107\pi\) | |||||||
\(338\) | −12258.3 | −1.97267 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −840.874 | −0.134126 | ||||||||
\(341\) | −4731.11 | −0.751332 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6773.63 | 1.06630 | ||||||||
\(344\) | −3635.05 | −0.569735 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −685.892 | −0.106572 | ||||||||
\(347\) | 8542.30 | 1.32154 | 0.660771 | − | 0.750588i | \(-0.270230\pi\) | ||||
0.660771 | + | 0.750588i | \(0.270230\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −993.823 | −0.152430 | −0.0762151 | − | 0.997091i | \(-0.524284\pi\) | ||||
−0.0762151 | + | 0.997091i | \(0.524284\pi\) | |||||||
\(350\) | 7977.35 | 1.21831 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6639.19 | 1.00531 | ||||||||
\(353\) | −8191.10 | −1.23504 | −0.617519 | − | 0.786556i | \(-0.711862\pi\) | ||||
−0.617519 | + | 0.786556i | \(0.711862\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9027.99 | 1.34974 | ||||||||
\(356\) | 4128.95 | 0.614702 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1073.10 | −0.158422 | ||||||||
\(359\) | 4703.71 | 0.691510 | 0.345755 | − | 0.938325i | \(-0.387623\pi\) | ||||
0.345755 | + | 0.938325i | \(0.387623\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2367.90 | −0.345226 | ||||||||
\(362\) | 1072.29 | 0.155686 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4394.00 | −0.632715 | ||||||||
\(365\) | 6362.85 | 0.912456 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9431.88 | 1.34153 | 0.670763 | − | 0.741672i | \(-0.265967\pi\) | ||||
0.670763 | + | 0.741672i | \(0.265967\pi\) | |||||||
\(368\) | 4156.05 | 0.588720 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 457.125 | 0.0642292 | ||||||||
\(371\) | −4896.55 | −0.685219 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8281.46 | −1.14959 | −0.574796 | − | 0.818297i | \(-0.694919\pi\) | ||||
−0.574796 | + | 0.818297i | \(0.694919\pi\) | |||||||
\(374\) | −1810.77 | −0.250355 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −519.006 | −0.0711854 | ||||||||
\(377\) | −2539.18 | −0.346882 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6875.50 | 0.931848 | 0.465924 | − | 0.884825i | \(-0.345722\pi\) | ||||
0.465924 | + | 0.884825i | \(0.345722\pi\) | |||||||
\(380\) | 3657.49 | 0.493750 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1867.20 | 0.250089 | ||||||||
\(383\) | 4826.61 | 0.643938 | 0.321969 | − | 0.946750i | \(-0.395655\pi\) | ||||
0.321969 | + | 0.946750i | \(0.395655\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16207.6 | −2.14550 | ||||||||
\(386\) | 3249.55 | 0.428492 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 994.263 | 0.130093 | ||||||||
\(389\) | −4970.57 | −0.647861 | −0.323930 | − | 0.946081i | \(-0.605004\pi\) | ||||
−0.323930 | + | 0.946081i | \(0.605004\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2044.21 | 0.264400 | ||||||||
\(392\) | −1446.54 | −0.186381 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4467.41 | −0.571230 | ||||||||
\(395\) | 18082.7 | 2.30339 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12288.8 | −1.55355 | −0.776774 | − | 0.629779i | \(-0.783145\pi\) | ||||
−0.776774 | + | 0.629779i | \(0.783145\pi\) | |||||||
\(398\) | 798.689 | 0.100590 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6613.54 | −0.826693 | ||||||||
\(401\) | 11971.7 | 1.49086 | 0.745432 | − | 0.666581i | \(-0.232243\pi\) | ||||
0.745432 | + | 0.666581i | \(0.232243\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7899.66 | −0.976452 | ||||||||
\(404\) | −732.055 | −0.0901512 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1095.72 | 0.133941 | ||||||||
\(407\) | −583.365 | −0.0710475 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11147.7 | 1.34772 | 0.673861 | − | 0.738858i | \(-0.264635\pi\) | ||||
0.673861 | + | 0.738858i | \(0.264635\pi\) | |||||||
\(410\) | 774.120 | 0.0932465 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1581.57 | 0.189123 | ||||||||
\(413\) | −5687.03 | −0.677580 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10897.4 | 1.28899 | ||||||||
\(416\) | 11085.6 | 1.30653 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7876.19 | 0.921620 | ||||||||
\(419\) | −11557.3 | −1.34752 | −0.673762 | − | 0.738949i | \(-0.735323\pi\) | ||||
−0.673762 | + | 0.738949i | \(0.735323\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12874.4 | −1.49040 | −0.745201 | − | 0.666840i | \(-0.767647\pi\) | ||||
−0.745201 | + | 0.666840i | \(0.767647\pi\) | |||||||
\(422\) | −9260.07 | −1.06818 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7145.67 | 0.818454 | ||||||||
\(425\) | −3252.97 | −0.371275 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1416.34 | −0.160519 | ||||||||
\(428\) | −1277.14 | −0.144236 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6071.42 | −0.680906 | ||||||||
\(431\) | 4088.31 | 0.456907 | 0.228454 | − | 0.973555i | \(-0.426633\pi\) | ||||
0.228454 | + | 0.973555i | \(0.426633\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3865.90 | −0.429060 | −0.214530 | − | 0.976717i | \(-0.568822\pi\) | ||||
−0.214530 | + | 0.976717i | \(0.568822\pi\) | |||||||
\(434\) | 3408.91 | 0.377035 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2879.36 | 0.316276 | ||||||||
\(437\) | −8891.56 | −0.973320 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10662.4 | 1.15920 | 0.579600 | − | 0.814901i | \(-0.303209\pi\) | ||||
0.579600 | + | 0.814901i | \(0.303209\pi\) | |||||||
\(440\) | 23652.2 | 2.56267 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3023.50 | −0.325369 | ||||||||
\(443\) | −10288.9 | −1.10347 | −0.551736 | − | 0.834019i | \(-0.686034\pi\) | ||||
−0.551736 | + | 0.834019i | \(0.686034\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25429.8 | 2.70897 | ||||||||
\(446\) | −2986.07 | −0.317028 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9008.30 | −0.950005 | ||||||||
\(449\) | −12426.2 | −1.30608 | −0.653041 | − | 0.757323i | \(-0.726507\pi\) | ||||
−0.653041 | + | 0.757323i | \(0.726507\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −987.901 | −0.103145 | ||||||||
\(452\) | −5076.14 | −0.528234 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2979.35 | −0.307991 | ||||||||
\(455\) | −27062.3 | −2.78835 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10657.8 | −1.09092 | −0.545462 | − | 0.838136i | \(-0.683646\pi\) | ||||
−0.545462 | + | 0.838136i | \(0.683646\pi\) | |||||||
\(458\) | −12227.1 | −1.24745 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7241.17 | −0.733959 | ||||||||
\(461\) | −9819.21 | −0.992031 | −0.496016 | − | 0.868314i | \(-0.665204\pi\) | ||||
−0.496016 | + | 0.868314i | \(0.665204\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19210.5 | −1.92827 | −0.964135 | − | 0.265412i | \(-0.914492\pi\) | ||||
−0.964135 | + | 0.265412i | \(0.914492\pi\) | |||||||
\(464\) | −908.399 | −0.0908865 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1324.93 | −0.131709 | ||||||||
\(467\) | 345.566 | 0.0342417 | 0.0171208 | − | 0.999853i | \(-0.494550\pi\) | ||||
0.0171208 | + | 0.999853i | \(0.494550\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5577.08 | −0.549095 | ||||||||
\(470\) | −866.865 | −0.0850756 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8299.24 | 0.809329 | ||||||||
\(473\) | 7748.10 | 0.753188 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14149.2 | 1.36676 | ||||||||
\(476\) | −773.194 | −0.0744523 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15567.7 | 1.48965 | ||||||||
\(479\) | 253.709 | 0.0242009 | 0.0121005 | − | 0.999927i | \(-0.496148\pi\) | ||||
0.0121005 | + | 0.999927i | \(0.496148\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −974.060 | −0.0923354 | ||||||||
\(482\) | −15925.5 | −1.50495 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4223.50 | −0.396647 | ||||||||
\(485\) | 6123.58 | 0.573314 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13255.1 | −1.23336 | −0.616680 | − | 0.787214i | \(-0.711523\pi\) | ||||
−0.616680 | + | 0.787214i | \(0.711523\pi\) | |||||||
\(488\) | 2066.91 | 0.191731 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2416.07 | −0.222749 | ||||||||
\(491\) | 6454.57 | 0.593260 | 0.296630 | − | 0.954993i | \(-0.404137\pi\) | ||||
0.296630 | + | 0.954993i | \(0.404137\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −446.809 | −0.0408180 | ||||||||
\(494\) | 13151.1 | 1.19776 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2826.12 | −0.255840 | ||||||||
\(497\) | 8301.36 | 0.749229 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8090.41 | 0.725805 | 0.362902 | − | 0.931827i | \(-0.381786\pi\) | ||||
0.362902 | + | 0.931827i | \(0.381786\pi\) | |||||||
\(500\) | 4700.84 | 0.420455 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10925.0 | −0.971330 | ||||||||
\(503\) | 18897.4 | 1.67513 | 0.837567 | − | 0.546334i | \(-0.183977\pi\) | ||||
0.837567 | + | 0.546334i | \(0.183977\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4508.66 | −0.397293 | ||||||||
\(506\) | −15593.4 | −1.36999 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7948.92 | 0.694245 | ||||||||
\(509\) | −4265.15 | −0.371413 | −0.185707 | − | 0.982605i | \(-0.559457\pi\) | ||||
−0.185707 | + | 0.982605i | \(0.559457\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5850.72 | 0.506498 | ||||||||
\(512\) | 10130.9 | 0.874469 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5576.72 | 0.478558 | ||||||||
\(515\) | 9740.77 | 0.833455 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1106.26 | 0.0941068 | ||||||||
\(518\) | 420.333 | 0.0356532 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 39492.7 | 3.33052 | ||||||||
\(521\) | 3324.96 | 0.279595 | 0.139798 | − | 0.990180i | \(-0.455355\pi\) | ||||
0.139798 | + | 0.990180i | \(0.455355\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13017.6 | 1.08838 | 0.544188 | − | 0.838964i | \(-0.316838\pi\) | ||||
0.544188 | + | 0.838964i | \(0.316838\pi\) | |||||||
\(524\) | 2619.57 | 0.218390 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6303.54 | −0.522524 | ||||||||
\(527\) | −1390.07 | −0.114900 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5436.69 | 0.446839 | ||||||||
\(530\) | 11935.0 | 0.978156 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3363.11 | 0.274078 | ||||||||
\(533\) | −1649.52 | −0.134050 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7865.80 | −0.635641 | ||||||||
\(536\) | 8138.78 | 0.655862 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12449.3 | −0.997634 | ||||||||
\(539\) | 3083.29 | 0.246395 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17906.8 | −1.42305 | −0.711527 | − | 0.702658i | \(-0.751996\pi\) | ||||
−0.711527 | + | 0.702658i | \(0.751996\pi\) | |||||||
\(542\) | 7101.19 | 0.562771 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1950.69 | 0.153741 | ||||||||
\(545\) | 17733.7 | 1.39382 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1612.94 | 0.126078 | 0.0630389 | − | 0.998011i | \(-0.479921\pi\) | ||||
0.0630389 | + | 0.998011i | \(0.479921\pi\) | |||||||
\(548\) | 6144.58 | 0.478984 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 24813.9 | 1.92376 | ||||||||
\(551\) | 1943.45 | 0.150261 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16627.3 | 1.27860 | ||||||||
\(554\) | −8887.99 | −0.681614 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1801.36 | −0.137400 | ||||||||
\(557\) | 7803.94 | 0.593651 | 0.296826 | − | 0.954932i | \(-0.404072\pi\) | ||||
0.296826 | + | 0.954932i | \(0.404072\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12937.2 | 0.978865 | ||||||||
\(560\) | −9681.60 | −0.730576 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3709.63 | 0.278436 | ||||||||
\(563\) | 12329.5 | 0.922958 | 0.461479 | − | 0.887151i | \(-0.347319\pi\) | ||||
0.461479 | + | 0.887151i | \(0.347319\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −31263.5 | −2.32790 | ||||||||
\(566\) | −17450.6 | −1.29594 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12114.4 | −0.894910 | ||||||||
\(569\) | −1554.46 | −0.114528 | −0.0572640 | − | 0.998359i | \(-0.518238\pi\) | ||||
−0.0572640 | + | 0.998359i | \(0.518238\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15951.8 | 1.16911 | 0.584556 | − | 0.811353i | \(-0.301269\pi\) | ||||
0.584556 | + | 0.811353i | \(0.301269\pi\) | |||||||
\(572\) | −13667.8 | −0.999087 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 711.813 | 0.0517605 | ||||||||
\(575\) | −28012.9 | −2.03168 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10491.7 | 0.756975 | 0.378488 | − | 0.925606i | \(-0.376444\pi\) | ||||
0.378488 | + | 0.925606i | \(0.376444\pi\) | |||||||
\(578\) | 10479.2 | 0.754114 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1582.72 | 0.113309 | ||||||||
\(581\) | 10020.3 | 0.715509 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15231.0 | −1.08199 | ||||||||
\(584\) | −8538.11 | −0.604982 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18133.5 | 1.27831 | ||||||||
\(587\) | −6437.47 | −0.452645 | −0.226323 | − | 0.974052i | \(-0.572670\pi\) | ||||
−0.226323 | + | 0.974052i | \(0.572670\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6046.29 | 0.422976 | ||||||||
\(590\) | 13861.7 | 0.967251 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −348.473 | −0.0241928 | ||||||||
\(593\) | −11240.6 | −0.778411 | −0.389205 | − | 0.921151i | \(-0.627250\pi\) | ||||
−0.389205 | + | 0.921151i | \(0.627250\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4762.04 | −0.328108 | ||||||||
\(596\) | −2307.99 | −0.158622 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −26036.8 | −1.78047 | ||||||||
\(599\) | −15903.5 | −1.08481 | −0.542405 | − | 0.840117i | \(-0.682486\pi\) | ||||
−0.542405 | + | 0.840117i | \(0.682486\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 117.190 | 0.00795385 | 0.00397692 | − | 0.999992i | \(-0.498734\pi\) | ||||
0.00397692 | + | 0.999992i | \(0.498734\pi\) | |||||||
\(602\) | −5582.75 | −0.377966 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1273.85 | −0.0858151 | ||||||||
\(605\) | −26012.1 | −1.74801 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22047.8 | −1.47429 | −0.737143 | − | 0.675737i | \(-0.763825\pi\) | ||||
−0.737143 | + | 0.675737i | \(0.763825\pi\) | |||||||
\(608\) | −8484.78 | −0.565959 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3452.24 | 0.229143 | ||||||||
\(611\) | 1847.15 | 0.122304 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12719.2 | −0.838050 | −0.419025 | − | 0.907975i | \(-0.637628\pi\) | ||||
−0.419025 | + | 0.907975i | \(0.637628\pi\) | |||||||
\(614\) | 13737.7 | 0.902945 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 21748.5 | 1.42252 | ||||||||
\(617\) | −12736.9 | −0.831064 | −0.415532 | − | 0.909578i | \(-0.636405\pi\) | ||||
−0.415532 | + | 0.909578i | \(0.636405\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28083.4 | 1.82353 | 0.911767 | − | 0.410709i | \(-0.134719\pi\) | ||||
0.911767 | + | 0.410709i | \(0.134719\pi\) | |||||||
\(620\) | 4924.02 | 0.318957 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18306.4 | −1.18009 | ||||||||
\(623\) | 23383.1 | 1.50373 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2560.44 | 0.163868 | ||||||||
\(626\) | −4207.38 | −0.268628 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5003.80 | 0.317951 | ||||||||
\(629\) | −171.401 | −0.0108652 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 281.496 | 0.0177594 | 0.00887969 | − | 0.999961i | \(-0.497173\pi\) | ||||
0.00887969 | + | 0.999961i | \(0.497173\pi\) | |||||||
\(632\) | −24264.6 | −1.52721 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2740.89 | 0.171695 | ||||||||
\(635\) | 48956.7 | 3.05951 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5148.26 | 0.320222 | ||||||||
\(638\) | 3408.30 | 0.211498 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3387.18 | 0.209203 | ||||||||
\(641\) | 8440.98 | 0.520123 | 0.260061 | − | 0.965592i | \(-0.416257\pi\) | ||||
0.260061 | + | 0.965592i | \(0.416257\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1173.61 | −0.0719792 | −0.0359896 | − | 0.999352i | \(-0.511458\pi\) | ||||
−0.0359896 | + | 0.999352i | \(0.511458\pi\) | |||||||
\(644\) | −6658.35 | −0.407416 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2314.14 | 0.140942 | ||||||||
\(647\) | 10845.7 | 0.659025 | 0.329513 | − | 0.944151i | \(-0.393116\pi\) | ||||
0.329513 | + | 0.944151i | \(0.393116\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17689.8 | −1.06993 | ||||||||
\(650\) | 41432.5 | 2.50018 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6068.78 | −0.364527 | ||||||||
\(653\) | 5282.40 | 0.316564 | 0.158282 | − | 0.987394i | \(-0.449404\pi\) | ||||
0.158282 | + | 0.987394i | \(0.449404\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16133.7 | 0.962437 | ||||||||
\(656\) | −590.122 | −0.0351225 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −797.094 | −0.0472249 | ||||||||
\(659\) | 19243.7 | 1.13752 | 0.568761 | − | 0.822503i | \(-0.307423\pi\) | ||||
0.568761 | + | 0.822503i | \(0.307423\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29196.9 | 1.71804 | 0.859021 | − | 0.511940i | \(-0.171073\pi\) | ||||
0.859021 | + | 0.511940i | \(0.171073\pi\) | |||||||
\(662\) | −8447.34 | −0.495944 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14622.8 | −0.854633 | ||||||||
\(665\) | 20713.1 | 1.20785 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3847.69 | −0.223363 | ||||||||
\(668\) | 7570.39 | 0.438484 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13593.7 | 0.783838 | ||||||||
\(671\) | −4405.61 | −0.253467 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19924.5 | 1.14121 | 0.570605 | − | 0.821224i | \(-0.306709\pi\) | ||||
0.570605 | + | 0.821224i | \(0.306709\pi\) | |||||||
\(674\) | 24430.0 | 1.39616 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16281.4 | −0.926341 | ||||||||
\(677\) | 4980.43 | 0.282738 | 0.141369 | − | 0.989957i | \(-0.454850\pi\) | ||||
0.141369 | + | 0.989957i | \(0.454850\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5630.71 | 0.318243 | ||||||||
\(680\) | 6949.37 | 0.391906 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10603.6 | 0.595355 | ||||||||
\(683\) | −29295.8 | −1.64125 | −0.820624 | − | 0.571468i | \(-0.806374\pi\) | ||||
−0.820624 | + | 0.571468i | \(0.806374\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 37843.9 | 2.11086 | ||||||||
\(686\) | −15181.4 | −0.844938 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4628.32 | 0.256472 | ||||||||
\(689\) | −25431.5 | −1.40619 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32759.8 | −1.80353 | −0.901766 | − | 0.432225i | \(-0.857729\pi\) | ||||
−0.901766 | + | 0.432225i | \(0.857729\pi\) | |||||||
\(692\) | −910.998 | −0.0500447 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19145.4 | −1.04719 | ||||||||
\(695\) | −11094.4 | −0.605518 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −290.260 | −0.0157739 | ||||||||
\(698\) | 2227.40 | 0.120786 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10595.5 | 0.572102 | ||||||||
\(701\) | −27958.5 | −1.50639 | −0.753195 | − | 0.657797i | \(-0.771488\pi\) | ||||
−0.753195 | + | 0.657797i | \(0.771488\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 745.532 | 0.0399975 | ||||||||
\(704\) | −28020.8 | −1.50010 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18358.3 | 0.978644 | ||||||||
\(707\) | −4145.77 | −0.220534 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31863.5 | −1.68781 | −0.843906 | − | 0.536492i | \(-0.819749\pi\) | ||||
−0.843906 | + | 0.536492i | \(0.819749\pi\) | |||||||
\(710\) | −20234.0 | −1.06953 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −34123.6 | −1.79612 | ||||||||
\(713\) | −11970.6 | −0.628753 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −84178.6 | −4.40294 | ||||||||
\(716\) | −1425.29 | −0.0743931 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10542.2 | −0.547953 | ||||||||
\(719\) | −7944.76 | −0.412085 | −0.206043 | − | 0.978543i | \(-0.566059\pi\) | ||||
−0.206043 | + | 0.978543i | \(0.566059\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8956.76 | 0.462645 | ||||||||
\(722\) | 5307.06 | 0.273557 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1424.21 | 0.0731080 | ||||||||
\(725\) | 6122.85 | 0.313651 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28640.3 | 1.46109 | 0.730543 | − | 0.682866i | \(-0.239267\pi\) | ||||
0.730543 | + | 0.682866i | \(0.239267\pi\) | |||||||
\(728\) | 36314.1 | 1.84875 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −14260.7 | −0.723031 | ||||||||
\(731\) | 2276.51 | 0.115184 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11852.7 | 0.597258 | 0.298629 | − | 0.954369i | \(-0.403471\pi\) | ||||
0.298629 | + | 0.954369i | \(0.403471\pi\) | |||||||
\(734\) | −21139.2 | −1.06303 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16798.3 | 0.841297 | ||||||||
\(737\) | −17347.8 | −0.867047 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24052.5 | −1.19727 | −0.598636 | − | 0.801021i | \(-0.704290\pi\) | ||||
−0.598636 | + | 0.801021i | \(0.704290\pi\) | |||||||
\(740\) | 607.151 | 0.0301612 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10974.4 | 0.542968 | ||||||||
\(743\) | 12530.4 | 0.618704 | 0.309352 | − | 0.950948i | \(-0.399888\pi\) | ||||
0.309352 | + | 0.950948i | \(0.399888\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14214.7 | −0.699042 | ||||||||
\(746\) | 18560.8 | 0.910937 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2405.06 | −0.117564 | ||||||||
\(749\) | −7232.71 | −0.352840 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30921.6 | 1.50246 | 0.751229 | − | 0.660042i | \(-0.229461\pi\) | ||||
0.751229 | + | 0.660042i | \(0.229461\pi\) | |||||||
\(752\) | 660.823 | 0.0320449 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5690.93 | 0.274869 | ||||||||
\(755\) | −7845.54 | −0.378184 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6257.40 | −0.300435 | −0.150217 | − | 0.988653i | \(-0.547997\pi\) | ||||
−0.150217 | + | 0.988653i | \(0.547997\pi\) | |||||||
\(758\) | −15409.7 | −0.738397 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −30227.2 | −1.44270 | ||||||||
\(761\) | 20094.8 | 0.957211 | 0.478605 | − | 0.878030i | \(-0.341142\pi\) | ||||
0.478605 | + | 0.878030i | \(0.341142\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16306.4 | 0.773697 | ||||||||
\(764\) | 2480.00 | 0.117439 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10817.6 | −0.510257 | ||||||||
\(767\) | −29537.1 | −1.39051 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26647.8 | −1.24960 | −0.624801 | − | 0.780784i | \(-0.714820\pi\) | ||||
−0.624801 | + | 0.780784i | \(0.714820\pi\) | |||||||
\(770\) | 36325.3 | 1.70009 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4316.03 | 0.201214 | ||||||||
\(773\) | 18513.2 | 0.861414 | 0.430707 | − | 0.902492i | \(-0.358264\pi\) | ||||
0.430707 | + | 0.902492i | \(0.358264\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19048.8 | 0.882909 | ||||||||
\(776\) | −8217.05 | −0.380122 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11140.3 | 0.513365 | ||||||||
\(779\) | 1262.52 | 0.0580675 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25821.8 | 1.18307 | ||||||||
\(782\) | −4581.58 | −0.209510 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1841.80 | 0.0839014 | ||||||||
\(785\) | 30818.0 | 1.40120 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29524.5 | −1.33727 | −0.668636 | − | 0.743590i | \(-0.733122\pi\) | ||||
−0.668636 | + | 0.743590i | \(0.733122\pi\) | |||||||
\(788\) | −5933.59 | −0.268243 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −40527.8 | −1.82521 | ||||||||
\(791\) | −28747.2 | −1.29220 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7356.16 | −0.329413 | ||||||||
\(794\) | 27542.3 | 1.23103 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1060.81 | 0.0472356 | ||||||||
\(797\) | −38789.4 | −1.72395 | −0.861976 | − | 0.506949i | \(-0.830773\pi\) | ||||
−0.861976 | + | 0.506949i | \(0.830773\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 325.035 | 0.0143916 | ||||||||
\(800\) | −26731.3 | −1.18137 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −26831.5 | −1.18136 | ||||||||
\(803\) | 18199.0 | 0.799785 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −41008.2 | −1.79546 | ||||||||
\(806\) | 17705.1 | 0.773741 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6050.04 | 0.263415 | ||||||||
\(809\) | 11552.0 | 0.502037 | 0.251018 | − | 0.967982i | \(-0.419235\pi\) | ||||
0.251018 | + | 0.967982i | \(0.419235\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26939.1 | 1.16641 | 0.583205 | − | 0.812325i | \(-0.301798\pi\) | ||||
0.583205 | + | 0.812325i | \(0.301798\pi\) | |||||||
\(812\) | 1455.33 | 0.0628968 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1307.47 | 0.0562981 | ||||||||
\(815\) | −37377.1 | −1.60646 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9901.96 | −0.424022 | ||||||||
\(818\) | −24984.8 | −1.06794 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1028.18 | 0.0437874 | ||||||||
\(821\) | 7558.67 | 0.321315 | 0.160657 | − | 0.987010i | \(-0.448639\pi\) | ||||
0.160657 | + | 0.987010i | \(0.448639\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3201.90 | −0.135615 | −0.0678076 | − | 0.997698i | \(-0.521600\pi\) | ||||
−0.0678076 | + | 0.997698i | \(0.521600\pi\) | |||||||
\(824\) | −13070.8 | −0.552603 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12746.0 | 0.536915 | ||||||||
\(827\) | 11479.1 | 0.482670 | 0.241335 | − | 0.970442i | \(-0.422415\pi\) | ||||
0.241335 | + | 0.970442i | \(0.422415\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1667.94 | −0.0698794 | −0.0349397 | − | 0.999389i | \(-0.511124\pi\) | ||||
−0.0349397 | + | 0.999389i | \(0.511124\pi\) | |||||||
\(830\) | −24423.7 | −1.02140 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −46787.0 | −1.94958 | ||||||||
\(833\) | 905.917 | 0.0376809 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 46625.3 | 1.93238 | ||||||||
\(836\) | 10461.1 | 0.432781 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25902.8 | 1.06778 | ||||||||
\(839\) | −15210.3 | −0.625884 | −0.312942 | − | 0.949772i | \(-0.601315\pi\) | ||||
−0.312942 | + | 0.949772i | \(0.601315\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 28854.7 | 1.18100 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12299.2 | −0.501606 | ||||||||
\(845\) | −100276. | −4.08235 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23918.5 | −0.970306 | ||||||||
\(848\) | −9098.20 | −0.368436 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7290.70 | 0.294199 | ||||||||
\(851\) | −1476.02 | −0.0594563 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18281.2 | −0.733805 | −0.366902 | − | 0.930259i | \(-0.619582\pi\) | ||||
−0.366902 | + | 0.930259i | \(0.619582\pi\) | |||||||
\(854\) | 3174.38 | 0.127195 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10554.9 | 0.421447 | ||||||||
\(857\) | −585.415 | −0.0233342 | −0.0116671 | − | 0.999932i | \(-0.503714\pi\) | ||||
−0.0116671 | + | 0.999932i | \(0.503714\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −935.611 | −0.0371626 | −0.0185813 | − | 0.999827i | \(-0.505915\pi\) | ||||
−0.0185813 | + | 0.999827i | \(0.505915\pi\) | |||||||
\(860\) | −8064.02 | −0.319745 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9162.92 | −0.362054 | ||||||||
\(863\) | 12110.7 | 0.477696 | 0.238848 | − | 0.971057i | \(-0.423230\pi\) | ||||
0.238848 | + | 0.971057i | \(0.423230\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5610.75 | −0.220545 | ||||||||
\(866\) | 8664.43 | 0.339988 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4527.70 | 0.177051 | ||||||||
\(869\) | 51720.0 | 2.01896 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28966.1 | −1.12684 | ||||||||
\(872\) | −23796.4 | −0.924136 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19928.2 | 0.771260 | ||||||||
\(875\) | 26621.8 | 1.02855 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5841.41 | 0.224915 | 0.112458 | − | 0.993657i | \(-0.464128\pi\) | ||||
0.112458 | + | 0.993657i | \(0.464128\pi\) | |||||||
\(878\) | −23897.1 | −0.918551 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −30115.1 | −1.15361 | ||||||||
\(881\) | 47826.2 | 1.82895 | 0.914476 | − | 0.404641i | \(-0.132603\pi\) | ||||
0.914476 | + | 0.404641i | \(0.132603\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17337.5 | 0.660761 | 0.330381 | − | 0.943848i | \(-0.392823\pi\) | ||||
0.330381 | + | 0.943848i | \(0.392823\pi\) | |||||||
\(884\) | −4015.79 | −0.152789 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23059.9 | 0.874392 | ||||||||
\(887\) | −35181.5 | −1.33177 | −0.665885 | − | 0.746055i | \(-0.731946\pi\) | ||||
−0.665885 | + | 0.746055i | \(0.731946\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45016.3 | 1.69831 | ||||||||
\(890\) | −56994.6 | −2.14659 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3966.08 | −0.148872 | ||||||||
\(893\) | −1413.78 | −0.0529792 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8778.22 | −0.327848 | ||||||||
\(896\) | 3114.56 | 0.116127 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 27850.3 | 1.03494 | ||||||||
\(899\) | 2616.44 | 0.0970669 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4475.08 | −0.165468 | ||||||||
\(902\) | 2214.13 | 0.0817322 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 41951.6 | 1.54346 | ||||||||
\(905\) | 8771.56 | 0.322184 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28184.4 | −1.03180 | −0.515902 | − | 0.856648i | \(-0.672543\pi\) | ||||
−0.515902 | + | 0.856648i | \(0.672543\pi\) | |||||||
\(908\) | −3957.15 | −0.144629 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 60653.3 | 2.20949 | ||||||||
\(911\) | 34136.6 | 1.24149 | 0.620745 | − | 0.784013i | \(-0.286830\pi\) | ||||
0.620745 | + | 0.784013i | \(0.286830\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31168.5 | 1.12982 | ||||||||
\(914\) | 23886.8 | 0.864448 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16239.9 | −0.585788 | ||||||||
\(917\) | 14835.2 | 0.534242 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15512.0 | 0.556794 | 0.278397 | − | 0.960466i | \(-0.410197\pi\) | ||||
0.278397 | + | 0.960466i | \(0.410197\pi\) | |||||||
\(920\) | 59844.4 | 2.14458 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 22007.3 | 0.786086 | ||||||||
\(923\) | 43115.3 | 1.53755 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2348.80 | 0.0834897 | ||||||||
\(926\) | 43055.5 | 1.52796 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3671.66 | −0.129879 | ||||||||
\(929\) | 3100.72 | 0.109506 | 0.0547531 | − | 0.998500i | \(-0.482563\pi\) | ||||
0.0547531 | + | 0.998500i | \(0.482563\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3940.40 | −0.138713 | ||||||||
\(932\) | −1759.77 | −0.0618488 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −774.498 | −0.0271331 | ||||||||
\(935\) | −14812.5 | −0.518098 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19638.8 | −0.684708 | −0.342354 | − | 0.939571i | \(-0.611224\pi\) | ||||
−0.342354 | + | 0.939571i | \(0.611224\pi\) | |||||||
\(938\) | 12499.6 | 0.435103 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1151.37 | −0.0399504 | ||||||||
\(941\) | 50033.6 | 1.73332 | 0.866658 | − | 0.498903i | \(-0.166264\pi\) | ||||
0.866658 | + | 0.498903i | \(0.166264\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2499.57 | −0.0863172 | ||||||||
\(944\) | −10567.0 | −0.364328 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17365.4 | −0.596827 | ||||||||
\(947\) | −19758.4 | −0.677994 | −0.338997 | − | 0.940787i | \(-0.610088\pi\) | ||||
−0.338997 | + | 0.940787i | \(0.610088\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30387.3 | 1.03942 | ||||||||
\(950\) | −31711.8 | −1.08302 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6390.03 | 0.217544 | ||||||||
\(953\) | −33843.4 | −1.15036 | −0.575180 | − | 0.818027i | \(-0.695068\pi\) | ||||
−0.575180 | + | 0.818027i | \(0.695068\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15274.1 | 0.517548 | ||||||||
\(956\) | 20677.0 | 0.699520 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −568.624 | −0.0191768 | ||||||||
\(959\) | 34798.0 | 1.17173 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21651.0 | −0.726762 | ||||||||
\(962\) | 2183.11 | 0.0731666 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21152.1 | −0.706705 | ||||||||
\(965\) | 26582.1 | 0.886743 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35236.9 | 1.17181 | 0.585906 | − | 0.810379i | \(-0.300739\pi\) | ||||
0.585906 | + | 0.810379i | \(0.300739\pi\) | |||||||
\(968\) | 34904.9 | 1.15897 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13724.5 | −0.454294 | ||||||||
\(971\) | 4505.40 | 0.148903 | 0.0744517 | − | 0.997225i | \(-0.476279\pi\) | ||||
0.0744517 | + | 0.997225i | \(0.476279\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10201.5 | −0.336119 | ||||||||
\(974\) | 29708.0 | 0.977314 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2631.69 | −0.0863096 | ||||||||
\(977\) | 15167.4 | 0.496671 | 0.248336 | − | 0.968674i | \(-0.420116\pi\) | ||||
0.248336 | + | 0.968674i | \(0.420116\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 72734.2 | 2.37446 | ||||||||
\(980\) | −3209.01 | −0.104600 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −14466.3 | −0.470099 | ||||||||
\(983\) | −25342.5 | −0.822278 | −0.411139 | − | 0.911573i | \(-0.634869\pi\) | ||||
−0.411139 | + | 0.911573i | \(0.634869\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36544.4 | −1.18213 | ||||||||
\(986\) | 1001.41 | 0.0323442 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 17467.2 | 0.562455 | ||||||||
\(989\) | 19604.1 | 0.630307 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40576.1 | 1.30065 | 0.650324 | − | 0.759657i | \(-0.274633\pi\) | ||||
0.650324 | + | 0.759657i | \(0.274633\pi\) | |||||||
\(992\) | −11422.9 | −0.365603 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −18605.4 | −0.593689 | ||||||||
\(995\) | 6533.46 | 0.208166 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7442.49 | 0.236415 | 0.118208 | − | 0.992989i | \(-0.462285\pi\) | ||||
0.118208 | + | 0.992989i | \(0.462285\pi\) | |||||||
\(998\) | −18132.6 | −0.575128 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 261.4.a.f.1.2 | 5 | ||
3.2 | odd | 2 | 29.4.a.b.1.4 | ✓ | 5 | ||
12.11 | even | 2 | 464.4.a.l.1.3 | 5 | |||
15.14 | odd | 2 | 725.4.a.c.1.2 | 5 | |||
21.20 | even | 2 | 1421.4.a.e.1.4 | 5 | |||
24.5 | odd | 2 | 1856.4.a.y.1.3 | 5 | |||
24.11 | even | 2 | 1856.4.a.bb.1.3 | 5 | |||
87.86 | odd | 2 | 841.4.a.b.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.4.a.b.1.4 | ✓ | 5 | 3.2 | odd | 2 | ||
261.4.a.f.1.2 | 5 | 1.1 | even | 1 | trivial | ||
464.4.a.l.1.3 | 5 | 12.11 | even | 2 | |||
725.4.a.c.1.2 | 5 | 15.14 | odd | 2 | |||
841.4.a.b.1.2 | 5 | 87.86 | odd | 2 | |||
1421.4.a.e.1.4 | 5 | 21.20 | even | 2 | |||
1856.4.a.y.1.3 | 5 | 24.5 | odd | 2 | |||
1856.4.a.bb.1.3 | 5 | 24.11 | even | 2 |