Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,4,Mod(1,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, 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("2352.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.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: | \(138.772492334\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 294) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1 |
$q$-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 | ||||||||
\(5\) | −7.41421 | −0.663147 | −0.331574 | − | 0.943429i | \(-0.607580\pi\) | ||||
−0.331574 | + | 0.943429i | \(0.607580\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −10.4853 | −0.287403 | −0.143701 | − | 0.989621i | \(-0.545900\pi\) | ||||
−0.143701 | + | 0.989621i | \(0.545900\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.78680 | −0.0594553 | −0.0297276 | − | 0.999558i | \(-0.509464\pi\) | ||||
−0.0297276 | + | 0.999558i | \(0.509464\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −22.2426 | −0.382868 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −50.4437 | −0.719670 | −0.359835 | − | 0.933016i | \(-0.617167\pi\) | ||||
−0.359835 | + | 0.933016i | \(0.617167\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 125.054 | 1.50996 | 0.754982 | − | 0.655746i | \(-0.227646\pi\) | ||||
0.754982 | + | 0.655746i | \(0.227646\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 182.250 | 1.65225 | 0.826124 | − | 0.563488i | \(-0.190541\pi\) | ||||
0.826124 | + | 0.563488i | \(0.190541\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −70.0294 | −0.560235 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 156.132 | 0.999758 | 0.499879 | − | 0.866095i | \(-0.333378\pi\) | ||||
0.499879 | + | 0.866095i | \(0.333378\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 139.632 | 0.808991 | 0.404496 | − | 0.914540i | \(-0.367447\pi\) | ||||
0.404496 | + | 0.914540i | \(0.367447\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −31.4558 | −0.165932 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −394.558 | −1.75311 | −0.876554 | − | 0.481303i | \(-0.840164\pi\) | ||||
−0.876554 | + | 0.481303i | \(0.840164\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.36039 | −0.0343265 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −197.605 | −0.752701 | −0.376350 | − | 0.926477i | \(-0.622821\pi\) | ||||
−0.376350 | + | 0.926477i | \(0.622821\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −343.294 | −1.21748 | −0.608741 | − | 0.793369i | \(-0.708325\pi\) | ||||
−0.608741 | + | 0.793369i | \(0.708325\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −66.7279 | −0.221049 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −610.004 | −1.89315 | −0.946577 | − | 0.322477i | \(-0.895484\pi\) | ||||
−0.946577 | + | 0.322477i | \(0.895484\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −151.331 | −0.415501 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −137.529 | −0.356435 | −0.178218 | − | 0.983991i | \(-0.557033\pi\) | ||||
−0.178218 | + | 0.983991i | \(0.557033\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 77.7401 | 0.190590 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 375.161 | 0.871778 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 589.436 | 1.30064 | 0.650322 | − | 0.759659i | \(-0.274634\pi\) | ||||
0.650322 | + | 0.759659i | \(0.274634\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −247.217 | −0.518901 | −0.259450 | − | 0.965756i | \(-0.583541\pi\) | ||||
−0.259450 | + | 0.965756i | \(0.583541\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 20.6619 | 0.0394276 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 395.647 | 0.721432 | 0.360716 | − | 0.932676i | \(-0.382532\pi\) | ||||
0.360716 | + | 0.932676i | \(0.382532\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 546.749 | 0.953926 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −285.661 | −0.477489 | −0.238745 | − | 0.971082i | \(-0.576736\pi\) | ||||
−0.238745 | + | 0.971082i | \(0.576736\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 997.457 | 1.59923 | 0.799613 | − | 0.600515i | \(-0.205038\pi\) | ||||
0.799613 | + | 0.600515i | \(0.205038\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −210.088 | −0.323452 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 848.264 | 1.20807 | 0.604033 | − | 0.796960i | \(-0.293560\pi\) | ||||
0.604033 | + | 0.796960i | \(0.293560\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −210.863 | −0.278858 | −0.139429 | − | 0.990232i | \(-0.544527\pi\) | ||||
−0.139429 | + | 0.990232i | \(0.544527\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 374.000 | 0.477247 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 468.396 | 0.577211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 553.487 | 0.659208 | 0.329604 | − | 0.944119i | \(-0.393085\pi\) | ||||
0.329604 | + | 0.944119i | \(0.393085\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 418.897 | 0.467071 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −927.176 | −1.00133 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 903.910 | 0.946166 | 0.473083 | − | 0.881018i | \(-0.343141\pi\) | ||||
0.473083 | + | 0.881018i | \(0.343141\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −94.3675 | −0.0958009 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 313.611 | 0.308965 | 0.154482 | − | 0.987996i | \(-0.450629\pi\) | ||||
0.154482 | + | 0.987996i | \(0.450629\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 230.975 | 0.220957 | 0.110479 | − | 0.993878i | \(-0.464762\pi\) | ||||
0.110479 | + | 0.993878i | \(0.464762\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −125.486 | −0.113376 | −0.0566879 | − | 0.998392i | \(-0.518054\pi\) | ||||
−0.0566879 | + | 0.998392i | \(0.518054\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 745.527 | 0.655124 | 0.327562 | − | 0.944830i | \(-0.393773\pi\) | ||||
0.327562 | + | 0.944830i | \(0.393773\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1183.68 | −1.01216 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1043.76 | −0.868929 | −0.434464 | − | 0.900689i | \(-0.643062\pi\) | ||||
−0.434464 | + | 0.900689i | \(0.643062\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1351.24 | −1.09568 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −25.0812 | −0.0198184 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1221.06 | −0.917400 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −592.815 | −0.434572 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1445.99 | 1.03467 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2080.17 | 1.45343 | 0.726715 | − | 0.686939i | \(-0.241046\pi\) | ||||
0.726715 | + | 0.686939i | \(0.241046\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1029.88 | −0.702914 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1269.53 | −0.846711 | −0.423355 | − | 0.905964i | \(-0.639148\pi\) | ||||
−0.423355 | + | 0.905964i | \(0.639148\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −200.184 | −0.127623 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3073.19 | 1.91650 | 0.958249 | − | 0.285935i | \(-0.0923043\pi\) | ||||
0.958249 | + | 0.285935i | \(0.0923043\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1013.60 | 0.618504 | 0.309252 | − | 0.950980i | \(-0.399921\pi\) | ||||
0.309252 | + | 0.950980i | \(0.399921\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1830.01 | −1.09301 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 29.2203 | 0.0170876 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1157.60 | −0.662987 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1231.47 | 0.677087 | 0.338544 | − | 0.940951i | \(-0.390066\pi\) | ||||
0.338544 | + | 0.940951i | \(0.390066\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2244.74 | 1.20976 | 0.604881 | − | 0.796316i | \(-0.293221\pi\) | ||||
0.604881 | + | 0.796316i | \(0.293221\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −453.993 | −0.239890 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1035.26 | −0.536481 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3787.16 | 1.92515 | 0.962573 | − | 0.271021i | \(-0.0873614\pi\) | ||||
0.962573 | + | 0.271021i | \(0.0873614\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −412.587 | −0.205788 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2108.56 | 1.01322 | 0.506611 | − | 0.862175i | \(-0.330898\pi\) | ||||
0.506611 | + | 0.862175i | \(0.330898\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 233.220 | 0.110037 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1502.41 | 0.696170 | 0.348085 | − | 0.937463i | \(-0.386832\pi\) | ||||
0.348085 | + | 0.937463i | \(0.386832\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2189.23 | −0.996465 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1125.48 | 0.503321 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −471.256 | −0.207104 | −0.103552 | − | 0.994624i | \(-0.533021\pi\) | ||||
−0.103552 | + | 0.994624i | \(0.533021\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1768.31 | 0.750927 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1332.49 | −0.556395 | −0.278198 | − | 0.960524i | \(-0.589737\pi\) | ||||
−0.278198 | + | 0.960524i | \(0.589737\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 997.727 | 0.409726 | 0.204863 | − | 0.978791i | \(-0.434325\pi\) | ||||
0.204863 | + | 0.978791i | \(0.434325\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −741.652 | −0.299587 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2925.34 | 1.16257 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 528.916 | 0.206835 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1226.72 | −0.464725 | −0.232362 | − | 0.972629i | \(-0.574646\pi\) | ||||
−0.232362 | + | 0.972629i | \(0.574646\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3479.29 | −1.29764 | −0.648821 | − | 0.760941i | \(-0.724738\pi\) | ||||
−0.648821 | + | 0.760941i | \(0.724738\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 61.9857 | 0.0227635 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3193.47 | 1.15495 | 0.577476 | − | 0.816408i | \(-0.304038\pi\) | ||||
0.577476 | + | 0.816408i | \(0.304038\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1065.15 | 0.379429 | 0.189715 | − | 0.981839i | \(-0.439244\pi\) | ||||
0.189715 | + | 0.981839i | \(0.439244\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1186.94 | 0.416519 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1465.09 | 0.499152 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1640.25 | 0.550749 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1311.22 | −0.433968 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2057.50 | −0.671298 | −0.335649 | − | 0.941987i | \(-0.608956\pi\) | ||||
−0.335649 | + | 0.941987i | \(0.608956\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −856.983 | −0.275678 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2545.25 | 0.807371 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2992.37 | 0.923314 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 140.576 | 0.0427881 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2028.27 | 0.609071 | 0.304536 | − | 0.952501i | \(-0.401499\pi\) | ||||
0.304536 | + | 0.952501i | \(0.401499\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −630.265 | −0.186745 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2423.96 | 0.708739 | 0.354369 | − | 0.935106i | \(-0.384696\pi\) | ||||
0.354369 | + | 0.935106i | \(0.384696\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1967.17 | 0.567660 | 0.283830 | − | 0.958875i | \(-0.408395\pi\) | ||||
0.283830 | + | 0.958875i | \(0.408395\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4478.33 | 1.25916 | 0.629582 | − | 0.776934i | \(-0.283226\pi\) | ||||
0.629582 | + | 0.776934i | \(0.283226\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4522.70 | 1.25544 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2544.79 | 0.697477 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6116.92 | −1.65553 | −0.827763 | − | 0.561078i | \(-0.810387\pi\) | ||||
−0.827763 | + | 0.561078i | \(0.810387\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6228.38 | −1.66475 | −0.832376 | − | 0.554211i | \(-0.813020\pi\) | ||||
−0.832376 | + | 0.554211i | \(0.813020\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −348.500 | −0.0897753 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −632.589 | −0.160999 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5904.42 | 1.48479 | 0.742397 | − | 0.669960i | \(-0.233689\pi\) | ||||
0.742397 | + | 0.669960i | \(0.233689\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1910.94 | −0.474861 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1122.00 | 0.275539 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 408.223 | 0.0990827 | 0.0495414 | − | 0.998772i | \(-0.484224\pi\) | ||||
0.0495414 | + | 0.998772i | \(0.484224\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1405.19 | 0.333253 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4626.01 | 1.08461 | 0.542304 | − | 0.840182i | \(-0.317552\pi\) | ||||
0.542304 | + | 0.840182i | \(0.317552\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1019.67 | 0.236369 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1660.46 | 0.380594 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 871.293 | 0.197486 | 0.0987429 | − | 0.995113i | \(-0.468518\pi\) | ||||
0.0987429 | + | 0.995113i | \(0.468518\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6472.35 | 1.45080 | 0.725401 | − | 0.688327i | \(-0.241655\pi\) | ||||
0.725401 | + | 0.688327i | \(0.241655\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 734.278 | 0.161013 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4711.88 | 1.02206 | 0.511028 | − | 0.859564i | \(-0.329265\pi\) | ||||
0.511028 | + | 0.859564i | \(0.329265\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1256.69 | 0.269664 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7165.66 | −1.52124 | −0.760618 | − | 0.649200i | \(-0.775104\pi\) | ||||
−0.760618 | + | 0.649200i | \(0.775104\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6347.00 | 1.33318 | 0.666590 | − | 0.745424i | \(-0.267753\pi\) | ||||
0.666590 | + | 0.745424i | \(0.267753\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2781.53 | −0.578117 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2368.44 | −0.482076 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2711.73 | 0.546269 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9233.78 | −1.84110 | −0.920552 | − | 0.390621i | \(-0.872260\pi\) | ||||
−0.920552 | + | 0.390621i | \(0.872260\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4370.20 | −0.862519 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −283.103 | −0.0553107 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −507.893 | −0.0982348 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 940.833 | 0.178381 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1832.92 | 0.344108 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6786.53 | 1.26165 | 0.630827 | − | 0.775923i | \(-0.282716\pi\) | ||||
0.630827 | + | 0.775923i | \(0.282716\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 692.924 | 0.127570 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5136.77 | 0.936590 | 0.468295 | − | 0.883572i | \(-0.344868\pi\) | ||||
0.468295 | + | 0.883572i | \(0.344868\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3763.56 | 0.679645 | 0.339822 | − | 0.940490i | \(-0.389633\pi\) | ||||
0.339822 | + | 0.940490i | \(0.389633\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1034.95 | −0.183370 | −0.0916851 | − | 0.995788i | \(-0.529225\pi\) | ||||
−0.0916851 | + | 0.995788i | \(0.529225\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1637.09 | −0.287333 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −376.458 | −0.0654575 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6308.17 | −1.08668 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 195.158 | 0.0333089 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2236.58 | 0.378236 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8800.06 | −1.46131 | −0.730657 | − | 0.682744i | \(-0.760786\pi\) | ||||
−0.730657 | + | 0.682744i | \(0.760786\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3551.03 | −0.584369 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2933.41 | −0.478416 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5859.78 | −0.947189 | −0.473595 | − | 0.880743i | \(-0.657044\pi\) | ||||
−0.473595 | + | 0.880743i | \(0.657044\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3131.29 | −0.501676 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1464.09 | −0.232506 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4053.72 | −0.632593 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7938.54 | −1.22814 | −0.614068 | − | 0.789253i | \(-0.710468\pi\) | ||||
−0.614068 | + | 0.789253i | \(0.710468\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9927.75 | 1.52269 | 0.761347 | − | 0.648344i | \(-0.224538\pi\) | ||||
0.761347 | + | 0.648344i | \(0.224538\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −75.2435 | −0.0114422 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10103.0 | 1.52332 | 0.761658 | − | 0.647979i | \(-0.224386\pi\) | ||||
0.761658 | + | 0.647979i | \(0.224386\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2117.95 | 0.316646 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4825.27 | 0.709382 | 0.354691 | − | 0.934984i | \(-0.384586\pi\) | ||||
0.354691 | + | 0.934984i | \(0.384586\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8779.46 | 1.27999 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3663.18 | −0.529661 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7395.36 | −1.06052 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6935.30 | 0.986430 | 0.493215 | − | 0.869907i | \(-0.335822\pi\) | ||||
0.493215 | + | 0.869907i | \(0.335822\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1778.45 | −0.250900 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14093.1 | 1.95634 | 0.978168 | − | 0.207816i | \(-0.0666355\pi\) | ||||
0.978168 | + | 0.207816i | \(0.0666355\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4337.97 | 0.597365 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −435.108 | −0.0594409 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5354.17 | −0.725661 | −0.362830 | − | 0.931855i | \(-0.618190\pi\) | ||||
−0.362830 | + | 0.931855i | \(0.618190\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6240.52 | 0.839138 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8970.47 | −1.19679 | −0.598394 | − | 0.801202i | \(-0.704194\pi\) | ||||
−0.598394 | + | 0.801202i | \(0.704194\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3089.64 | −0.405828 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3702.58 | −0.482592 | −0.241296 | − | 0.970452i | \(-0.577572\pi\) | ||||
−0.241296 | + | 0.970452i | \(0.577572\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9193.34 | −1.18907 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3808.58 | −0.488849 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6289.21 | −0.801125 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2083.24 | 0.263362 | 0.131681 | − | 0.991292i | \(-0.457963\pi\) | ||||
0.131681 | + | 0.991292i | \(0.457963\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10634.0 | −1.32428 | −0.662141 | − | 0.749379i | \(-0.730352\pi\) | ||||
−0.662141 | + | 0.749379i | \(0.730352\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −389.127 | −0.0480988 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −600.551 | −0.0736830 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4137.06 | 0.503848 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6516.37 | 0.787808 | 0.393904 | − | 0.919152i | \(-0.371124\pi\) | ||||
0.393904 | + | 0.919152i | \(0.371124\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9219.56 | 1.10649 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1563.38 | 0.184924 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3040.79 | 0.357094 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6079.92 | 0.708887 | 0.354443 | − | 0.935077i | \(-0.384670\pi\) | ||||
0.354443 | + | 0.935077i | \(0.384670\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5631.58 | −0.651939 | −0.325969 | − | 0.945380i | \(-0.605691\pi\) | ||||
−0.325969 | + | 0.945380i | \(0.605691\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5490.04 | −0.631051 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3532.54 | 0.403184 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 87.6610 | 0.00986554 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3736.90 | 0.417633 | 0.208817 | − | 0.977955i | \(-0.433039\pi\) | ||||
0.208817 | + | 0.977955i | \(0.433039\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5757.46 | 0.638998 | 0.319499 | − | 0.947587i | \(-0.396485\pi\) | ||||
0.319499 | + | 0.947587i | \(0.396485\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3472.79 | −0.382776 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22791.0 | 2.49484 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9812.76 | −1.06683 | −0.533414 | − | 0.845854i | \(-0.679091\pi\) | ||||
−0.533414 | + | 0.845854i | \(0.679091\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5830.30 | −0.625296 | −0.312648 | − | 0.949869i | \(-0.601216\pi\) | ||||
−0.312648 | + | 0.949869i | \(0.601216\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4103.67 | −0.437152 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3694.41 | 0.390916 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8674.94 | −0.911794 | −0.455897 | − | 0.890033i | \(-0.650681\pi\) | ||||
−0.455897 | + | 0.890033i | \(0.650681\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2071.95 | 0.216328 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6734.21 | 0.698456 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9106.82 | 0.932165 | 0.466082 | − | 0.884741i | \(-0.345665\pi\) | ||||
0.466082 | + | 0.884741i | \(0.345665\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1361.98 | −0.138500 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8729.69 | 0.881957 | 0.440979 | − | 0.897518i | \(-0.354631\pi\) | ||||
0.440979 | + | 0.897518i | \(0.354631\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1795.62 | 0.180237 | 0.0901184 | − | 0.995931i | \(-0.471275\pi\) | ||||
0.0901184 | + | 0.995931i | \(0.471275\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3105.79 | −0.309737 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 130.559 | 0.0129370 | 0.00646849 | − | 0.999979i | \(-0.497941\pi\) | ||||
0.00646849 | + | 0.999979i | \(0.497941\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11361.5 | 1.11148 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3599.53 | 0.349908 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8757.45 | −0.845935 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1237.76 | −0.118812 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11845.8 | 1.12996 | 0.564978 | − | 0.825106i | \(-0.308885\pi\) | ||||
0.564978 | + | 0.825106i | \(0.308885\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1099.55 | 0.104232 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6701.78 | −0.627448 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4807.21 | 0.447301 | 0.223650 | − | 0.974669i | \(-0.428203\pi\) | ||||
0.223650 | + | 0.974669i | \(0.428203\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6325.68 | 0.584984 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6068.04 | −0.557733 | −0.278866 | − | 0.960330i | \(-0.589959\pi\) | ||||
−0.278866 | + | 0.960330i | \(0.589959\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7875.87 | −0.719496 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 699.661 | 0.0635302 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15506.4 | 1.39111 | 0.695554 | − | 0.718474i | \(-0.255159\pi\) | ||||
0.695554 | + | 0.718474i | \(0.255159\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4507.24 | 0.401934 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1496.79 | −0.132681 | −0.0663405 | − | 0.997797i | \(-0.521132\pi\) | ||||
−0.0663405 | + | 0.997797i | \(0.521132\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2325.18 | −0.204889 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6567.70 | −0.575309 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5053.74 | 0.440084 | 0.220042 | − | 0.975490i | \(-0.429380\pi\) | ||||
0.220042 | + | 0.975490i | \(0.429380\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3376.45 | 0.290593 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1712.50 | −0.146527 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6396.07 | 0.544098 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1413.77 | −0.119571 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9736.73 | −0.818760 | −0.409380 | − | 0.912364i | \(-0.634255\pi\) | ||||
−0.409380 | + | 0.912364i | \(0.634255\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11796.7 | −0.986295 | −0.493148 | − | 0.869946i | \(-0.664154\pi\) | ||||
−0.493148 | + | 0.869946i | \(0.664154\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7043.57 | −0.582206 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21048.0 | 1.72992 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5304.92 | 0.433548 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 550.685 | 0.0447520 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 930.381 | 0.0751848 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3997.46 | −0.321235 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4310.82 | −0.342581 | −0.171291 | − | 0.985221i | \(-0.554794\pi\) | ||||
−0.171291 | + | 0.985221i | \(0.554794\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2993.18 | 0.236556 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5527.50 | −0.434444 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17015.9 | −1.33007 | −0.665034 | − | 0.746813i | \(-0.731583\pi\) | ||||
−0.665034 | + | 0.746813i | \(0.731583\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2224.96 | −0.172967 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19524.9 | 1.50960 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8776.02 | 0.671210 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1741.18 | 0.132452 | 0.0662262 | − | 0.997805i | \(-0.478904\pi\) | ||||
0.0662262 | + | 0.997805i | \(0.478904\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 956.689 | 0.0723858 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1586.75 | 0.119416 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11346.8 | 0.849401 | 0.424700 | − | 0.905334i | \(-0.360379\pi\) | ||||
0.424700 | + | 0.905334i | \(0.360379\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7738.68 | 0.576228 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18417.4 | −1.35694 | −0.678470 | − | 0.734628i | \(-0.737357\pi\) | ||||
−0.678470 | + | 0.734628i | \(0.737357\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9998.49 | −0.732791 | −0.366396 | − | 0.930459i | \(-0.619408\pi\) | ||||
−0.366396 | + | 0.930459i | \(0.619408\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3680.16 | −0.268309 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12762.8 | −0.925648 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1401.71 | 0.101133 | 0.0505667 | − | 0.998721i | \(-0.483897\pi\) | ||||
0.0505667 | + | 0.998721i | \(0.483897\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10437.9 | −0.749194 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1442.03 | 0.102440 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 185.957 | 0.0131425 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10851.3 | −0.763001 | −0.381500 | − | 0.924369i | \(-0.624593\pi\) | ||||
−0.381500 | + | 0.924369i | \(0.624593\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17461.6 | 1.22155 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9580.42 | 0.666812 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20462.0 | −1.41699 | −0.708493 | − | 0.705717i | \(-0.750625\pi\) | ||||
−0.708493 | + | 0.705717i | \(0.750625\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3195.45 | 0.219064 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9990.42 | −0.681465 | −0.340733 | − | 0.940160i | \(-0.610675\pi\) | ||||
−0.340733 | + | 0.940160i | \(0.610675\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17435.9 | −1.18341 | −0.591703 | − | 0.806156i | \(-0.701544\pi\) | ||||
−0.591703 | + | 0.806156i | \(0.701544\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3560.82 | 0.240477 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9053.19 | 0.608371 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16700.3 | 1.11671 | 0.558356 | − | 0.829601i | \(-0.311432\pi\) | ||||
0.558356 | + | 0.829601i | \(0.311432\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1699.96 | 0.112558 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26702.9 | −1.75941 | −0.879707 | − | 0.475515i | \(-0.842262\pi\) | ||||
−0.879707 | + | 0.475515i | \(0.842262\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4395.26 | 0.288185 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27790.4 | 1.81329 | 0.906645 | − | 0.421894i | \(-0.138635\pi\) | ||||
0.906645 | + | 0.421894i | \(0.138635\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1736.08 | 0.112728 | 0.0563642 | − | 0.998410i | \(-0.482049\pi\) | ||||
0.0563642 | + | 0.998410i | \(0.482049\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4920.74 | 0.317975 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1967.20 | −0.125901 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3933.67 | −0.250552 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19903.0 | 1.26166 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8990.27 | 0.567190 | 0.283595 | − | 0.958944i | \(-0.408473\pi\) | ||||
0.283595 | + | 0.958944i | \(0.408473\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6172.49 | −0.387574 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15422.9 | −0.963839 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2570.95 | −0.159163 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13769.6 | −0.848467 | −0.424233 | − | 0.905553i | \(-0.639456\pi\) | ||||
−0.424233 | + | 0.905553i | \(0.639456\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26969.9 | 1.65411 | 0.827053 | − | 0.562124i | \(-0.190015\pi\) | ||||
0.827053 | + | 0.562124i | \(0.190015\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7635.75 | 0.466136 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24401.7 | 1.48274 | 0.741368 | − | 0.671098i | \(-0.234177\pi\) | ||||
0.741368 | + | 0.671098i | \(0.234177\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6180.40 | −0.373809 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15969.6 | 0.957026 | 0.478513 | − | 0.878080i | \(-0.341176\pi\) | ||||
0.478513 | + | 0.878080i | \(0.341176\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9412.55 | 0.561494 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8977.11 | 0.533075 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11596.2 | 0.685467 | 0.342733 | − | 0.939433i | \(-0.388647\pi\) | ||||
0.342733 | + | 0.939433i | \(0.388647\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12602.2 | −0.741558 | −0.370779 | − | 0.928721i | \(-0.620909\pi\) | ||||
−0.370779 | + | 0.928721i | \(0.620909\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 421.729 | 0.0247037 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28455.0 | 1.65185 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6084.80 | 0.351647 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2592.14 | 0.149134 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2126.29 | 0.121787 | 0.0608934 | − | 0.998144i | \(-0.480605\pi\) | ||||
0.0608934 | + | 0.998144i | \(0.480605\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1890.79 | −0.107817 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2619.38 | −0.148702 | −0.0743508 | − | 0.997232i | \(-0.523688\pi\) | ||||
−0.0743508 | + | 0.997232i | \(0.523688\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7271.87 | 0.409190 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29929.8 | 1.67677 | 0.838383 | − | 0.545082i | \(-0.183501\pi\) | ||||
0.838383 | + | 0.545082i | \(0.183501\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22785.3 | −1.27092 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5901.51 | 0.327739 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 383.265 | 0.0211919 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6760.90 | 0.372209 | 0.186105 | − | 0.982530i | \(-0.440414\pi\) | ||||
0.186105 | + | 0.982530i | \(0.440414\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7515.02 | −0.410160 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9967.92 | 0.541696 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13435.0 | 0.726979 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 467.205 | 0.0251727 | 0.0125864 | − | 0.999921i | \(-0.495994\pi\) | ||||
0.0125864 | + | 0.999921i | \(0.495994\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −49341.0 | −2.64713 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13568.1 | 0.724829 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8824.64 | 0.467442 | 0.233721 | − | 0.972304i | \(-0.424910\pi\) | ||||
0.233721 | + | 0.972304i | \(0.424910\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7634.38 | 0.402688 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25448.0 | 1.33665 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −216.646 | −0.0113316 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18350.8 | −0.955818 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21098.9 | −1.09438 | −0.547188 | − | 0.837010i | \(-0.684302\pi\) | ||||
−0.547188 | + | 0.837010i | \(0.684302\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18685.1 | −0.961145 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10933.8 | −0.560100 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4616.48 | −0.235510 | −0.117755 | − | 0.993043i | \(-0.537570\pi\) | ||||
−0.117755 | + | 0.993043i | \(0.537570\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17317.0 | 0.876185 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10688.1 | 0.538571 | 0.269285 | − | 0.963060i | \(-0.413212\pi\) | ||||
0.269285 | + | 0.963060i | \(0.413212\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4148.47 | −0.207342 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15367.6 | 0.764959 | 0.382480 | − | 0.923964i | \(-0.375070\pi\) | ||||
0.382480 | + | 0.923964i | \(0.375070\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1045.50 | −0.0518318 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6502.58 | −0.321072 | −0.160536 | − | 0.987030i | \(-0.551322\pi\) | ||||
−0.160536 | + | 0.987030i | \(0.551322\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9130.38 | −0.449009 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1897.77 | −0.0929527 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19874.1 | 0.965670 | 0.482835 | − | 0.875711i | \(-0.339607\pi\) | ||||
0.482835 | + | 0.875711i | \(0.339607\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17713.2 | 0.857247 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16642.9 | −0.802250 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15157.8 | −0.727765 | −0.363883 | − | 0.931445i | \(-0.618549\pi\) | ||||
−0.363883 | + | 0.931445i | \(0.618549\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5732.82 | −0.274161 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35219.8 | −1.67768 | −0.838842 | − | 0.544375i | \(-0.816767\pi\) | ||||
−0.838842 | + | 0.544375i | \(0.816767\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3366.00 | 0.159082 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1642.64 | −0.0773301 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2264.35 | 0.106183 | 0.0530915 | − | 0.998590i | \(-0.483093\pi\) | ||||
0.0530915 | + | 0.998590i | \(0.483093\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1224.67 | 0.0572054 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9532.79 | 0.443558 | 0.221779 | − | 0.975097i | \(-0.428814\pi\) | ||||
0.221779 | + | 0.975097i | \(0.428814\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9778.38 | −0.453226 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24711.3 | −1.13655 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2995.24 | 0.137232 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4215.56 | 0.192404 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −28078.8 | −1.27666 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33213.0 | −1.50434 | −0.752170 | − | 0.658969i | \(-0.770993\pi\) | ||||
−0.752170 | + | 0.658969i | \(0.770993\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13878.0 | 0.626199 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 688.945 | 0.0308514 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3059.01 | 0.136468 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42065.6 | −1.86956 | −0.934781 | − | 0.355223i | \(-0.884405\pi\) | ||||
−0.934781 | + | 0.355223i | \(0.884405\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30770.8 | 1.36245 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4981.39 | 0.219736 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10458.6 | −0.459622 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2613.88 | 0.114018 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −777.560 | −0.0337918 | −0.0168959 | − | 0.999857i | \(-0.505378\pi\) | ||||
−0.0168959 | + | 0.999857i | \(0.505378\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16559.4 | 0.716991 | 0.358496 | − | 0.933531i | \(-0.383290\pi\) | ||||
0.358496 | + | 0.933531i | \(0.383290\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19417.0 | 0.837620 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15633.3 | −0.671916 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −42930.2 | −1.83836 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 231.224 | 0.00982921 | 0.00491460 | − | 0.999988i | \(-0.498436\pi\) | ||||
0.00491460 | + | 0.999988i | \(0.498436\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5222.86 | 0.221212 | 0.110606 | − | 0.993864i | \(-0.464721\pi\) | ||||
0.110606 | + | 0.993864i | \(0.464721\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2202.84 | 0.0929611 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46225.5 | 1.94367 | 0.971836 | − | 0.235658i | \(-0.0757246\pi\) | ||||
0.971836 | + | 0.235658i | \(0.0757246\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39594.2 | 1.65882 | 0.829410 | − | 0.558640i | \(-0.188677\pi\) | ||||
0.829410 | + | 0.558640i | \(0.188677\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14135.6 | 0.590084 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11139.2 | −0.461663 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3770.08 | 0.155690 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45737.6 | −1.88205 | −0.941023 | − | 0.338344i | \(-0.890133\pi\) | ||||
−0.941023 | + | 0.338344i | \(0.890133\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.7878 | −0.000483326 0 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21497.0 | −0.878286 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16231.4 | 0.660803 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19041.0 | 0.769712 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −71908.2 | −2.89657 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8795.55 | 0.353053 | 0.176526 | − | 0.984296i | \(-0.443514\pi\) | ||||
0.176526 | + | 0.984296i | \(0.443514\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8344.58 | −0.333776 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30254.9 | −1.20594 | −0.602969 | − | 0.797764i | \(-0.706016\pi\) | ||||
−0.602969 | + | 0.797764i | \(0.706016\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44993.5 | 1.78715 | 0.893573 | − | 0.448918i | \(-0.148191\pi\) | ||||
0.893573 | + | 0.448918i | \(0.148191\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44667.9 | −1.76189 | −0.880946 | − | 0.473217i | \(-0.843093\pi\) | ||||
−0.880946 | + | 0.473217i | \(0.843093\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3493.99 | 0.137340 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7105.31 | −0.278327 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8894.29 | −0.347201 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1102.59 | −0.0428929 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8135.19 | 0.315389 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5986.84 | 0.230515 | 0.115257 | − | 0.993336i | \(-0.463231\pi\) | ||||
0.115257 | + | 0.993336i | \(0.463231\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27701.3 | −1.06296 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37911.8 | −1.44981 | −0.724904 | − | 0.688850i | \(-0.758116\pi\) | ||||
−0.724904 | + | 0.688850i | \(0.758116\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16293.6 | 0.620978 | 0.310489 | − | 0.950577i | \(-0.399507\pi\) | ||||
0.310489 | + | 0.950577i | \(0.399507\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13110.6 | −0.497975 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8853.41 | 0.335139 | 0.167570 | − | 0.985860i | \(-0.446408\pi\) | ||||
0.167570 | + | 0.985860i | \(0.446408\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −849.308 | −0.0319336 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −76283.4 | −2.85859 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9879.34 | 0.368972 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1523.68 | −0.0567159 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21801.1 | 0.808796 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6937.47 | 0.256516 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7397.36 | −0.271709 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16662.5 | −0.609998 | −0.304999 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304999 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2822.50 | 0.102988 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29071.2 | 1.05727 | 0.528635 | − | 0.848849i | \(-0.322704\pi\) | ||||
0.528635 | + | 0.848849i | \(0.322704\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2210.96 | 0.0801446 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5498.77 | 0.198671 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7973.39 | −0.286200 | −0.143100 | − | 0.989708i | \(-0.545707\pi\) | ||||
−0.143100 | + | 0.989708i | \(0.545707\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20359.6 | 0.728416 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 796.079 | 0.0283892 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27630.7 | 0.982154 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2078.77 | 0.0736525 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30141.5 | −1.06449 | −0.532244 | − | 0.846591i | \(-0.678651\pi\) | ||||
−0.532244 | + | 0.846591i | \(0.678651\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15410.3 | 0.540740 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3921.50 | −0.137162 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1126.37 | −0.0392709 | −0.0196354 | − | 0.999807i | \(-0.506251\pi\) | ||||
−0.0196354 | + | 0.999807i | \(0.506251\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11290.7 | 0.392393 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10333.3 | 0.357976 | 0.178988 | − | 0.983851i | \(-0.442718\pi\) | ||||
0.178988 | + | 0.983851i | \(0.442718\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36013.5 | −1.24365 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24810.3 | −0.851347 | −0.425673 | − | 0.904877i | \(-0.639963\pi\) | ||||
−0.425673 | + | 0.904877i | \(0.639963\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2779.71 | −0.0950824 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3104.84 | −0.105869 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15048.6 | −0.511513 | −0.255757 | − | 0.966741i | \(-0.582325\pi\) | ||||
−0.255757 | + | 0.966741i | \(0.582325\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9095.17 | 0.308181 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4911.26 | −0.165892 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10293.8 | −0.345533 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1129.38 | −0.0377919 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25796.2 | 0.860528 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15619.9 | 0.519442 | 0.259721 | − | 0.965684i | \(-0.416369\pi\) | ||||
0.259721 | + | 0.965684i | \(0.416369\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −18924.5 | −0.627392 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24833.0 | −0.820730 | −0.410365 | − | 0.911921i | \(-0.634599\pi\) | ||||
−0.410365 | + | 0.911921i | \(0.634599\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 585.473 | 0.0192309 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38656.8 | 1.26586 | 0.632928 | − | 0.774211i | \(-0.281853\pi\) | ||||
0.632928 | + | 0.774211i | \(0.281853\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5803.47 | −0.189458 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6709.75 | 0.218375 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26664.1 | 0.865162 | 0.432581 | − | 0.901595i | \(-0.357603\pi\) | ||||
0.432581 | + | 0.901595i | \(0.357603\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23677.1 | −0.765903 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −62565.2 | −2.01158 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27228.2 | −0.872786 | −0.436393 | − | 0.899756i | \(-0.643744\pi\) | ||||
−0.436393 | + | 0.899756i | \(0.643744\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26400.2 | −0.843690 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7897.24 | −0.251617 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5162.91 | −0.164003 | −0.0820016 | − | 0.996632i | \(-0.526131\pi\) | ||||
−0.0820016 | + | 0.996632i | \(0.526131\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10653.1 | −0.337386 |
(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 | 2352.4.a.bw.1.1 | 2 | ||
4.3 | odd | 2 | 294.4.a.l.1.1 | ✓ | 2 | ||
7.6 | odd | 2 | 2352.4.a.bu.1.2 | 2 | |||
12.11 | even | 2 | 882.4.a.bb.1.2 | 2 | |||
28.3 | even | 6 | 294.4.e.k.79.1 | 4 | |||
28.11 | odd | 6 | 294.4.e.m.79.2 | 4 | |||
28.19 | even | 6 | 294.4.e.k.67.1 | 4 | |||
28.23 | odd | 6 | 294.4.e.m.67.2 | 4 | |||
28.27 | even | 2 | 294.4.a.o.1.2 | yes | 2 | ||
84.11 | even | 6 | 882.4.g.be.667.1 | 4 | |||
84.23 | even | 6 | 882.4.g.be.361.1 | 4 | |||
84.47 | odd | 6 | 882.4.g.bk.361.2 | 4 | |||
84.59 | odd | 6 | 882.4.g.bk.667.2 | 4 | |||
84.83 | odd | 2 | 882.4.a.t.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
294.4.a.l.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
294.4.a.o.1.2 | yes | 2 | 28.27 | even | 2 | ||
294.4.e.k.67.1 | 4 | 28.19 | even | 6 | |||
294.4.e.k.79.1 | 4 | 28.3 | even | 6 | |||
294.4.e.m.67.2 | 4 | 28.23 | odd | 6 | |||
294.4.e.m.79.2 | 4 | 28.11 | odd | 6 | |||
882.4.a.t.1.1 | 2 | 84.83 | odd | 2 | |||
882.4.a.bb.1.2 | 2 | 12.11 | even | 2 | |||
882.4.g.be.361.1 | 4 | 84.23 | even | 6 | |||
882.4.g.be.667.1 | 4 | 84.11 | even | 6 | |||
882.4.g.bk.361.2 | 4 | 84.47 | odd | 6 | |||
882.4.g.bk.667.2 | 4 | 84.59 | odd | 6 | |||
2352.4.a.bu.1.2 | 2 | 7.6 | odd | 2 | |||
2352.4.a.bw.1.1 | 2 | 1.1 | even | 1 | trivial |