Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(109.507544971\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 245x^{10} + 21294x^{8} - 755514x^{6} + 8955005x^{4} - 27099393x^{2} + 23710340 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{19} \) |
Twist minimal: | no (minimal twist has level 928) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.50033\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | ||||||||
\(3\) | 1.50033 | 0.288738 | 0.144369 | − | 0.989524i | \(-0.453885\pi\) | ||||
0.144369 | + | 0.989524i | \(0.453885\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.787262 | −0.0704148 | −0.0352074 | − | 0.999380i | \(-0.511209\pi\) | ||||
−0.0352074 | + | 0.999380i | \(0.511209\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 27.3506 | 1.47679 | 0.738396 | − | 0.674367i | \(-0.235583\pi\) | ||||
0.738396 | + | 0.674367i | \(0.235583\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −24.7490 | −0.916630 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 62.2529 | 1.70636 | 0.853180 | − | 0.521616i | \(-0.174671\pi\) | ||||
0.853180 | + | 0.521616i | \(0.174671\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 27.7949 | 0.592993 | 0.296497 | − | 0.955034i | \(-0.404182\pi\) | ||||
0.296497 | + | 0.955034i | \(0.404182\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.18115 | −0.0203314 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 102.604 | 1.46383 | 0.731913 | − | 0.681398i | \(-0.238628\pi\) | ||||
0.731913 | + | 0.681398i | \(0.238628\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 55.9390 | 0.675436 | 0.337718 | − | 0.941247i | \(-0.390345\pi\) | ||||
0.337718 | + | 0.941247i | \(0.390345\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 41.0348 | 0.426406 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 175.715 | 1.59300 | 0.796502 | − | 0.604636i | \(-0.206681\pi\) | ||||
0.796502 | + | 0.604636i | \(0.206681\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.380 | −0.995042 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −77.6404 | −0.553404 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 199.792 | 1.15754 | 0.578769 | − | 0.815492i | \(-0.303533\pi\) | ||||
0.578769 | + | 0.815492i | \(0.303533\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 93.3997 | 0.492691 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −21.5321 | −0.103988 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −403.647 | −1.79349 | −0.896746 | − | 0.442546i | \(-0.854075\pi\) | ||||
−0.896746 | + | 0.442546i | \(0.854075\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 41.7014 | 0.171220 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −118.286 | −0.450565 | −0.225282 | − | 0.974294i | \(-0.572330\pi\) | ||||
−0.225282 | + | 0.974294i | \(0.572330\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 354.315 | 1.25657 | 0.628286 | − | 0.777982i | \(-0.283757\pi\) | ||||
0.628286 | + | 0.777982i | \(0.283757\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 19.4840 | 0.0645444 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −148.783 | −0.461750 | −0.230875 | − | 0.972983i | \(-0.574159\pi\) | ||||
−0.230875 | + | 0.972983i | \(0.574159\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 405.055 | 1.18092 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 153.939 | 0.422662 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −376.090 | −0.974716 | −0.487358 | − | 0.873202i | \(-0.662039\pi\) | ||||
−0.487358 | + | 0.873202i | \(0.662039\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −49.0093 | −0.120153 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 83.9268 | 0.195024 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 329.095 | 0.726178 | 0.363089 | − | 0.931754i | \(-0.381722\pi\) | ||||
0.363089 | + | 0.931754i | \(0.381722\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −789.113 | −1.65632 | −0.828160 | − | 0.560492i | \(-0.810612\pi\) | ||||
−0.828160 | + | 0.560492i | \(0.810612\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −676.900 | −1.35367 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −21.8818 | −0.0417555 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 147.681 | 0.269286 | 0.134643 | − | 0.990894i | \(-0.457011\pi\) | ||||
0.134643 | + | 0.990894i | \(0.457011\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 263.630 | 0.459961 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 254.191 | 0.424887 | 0.212443 | − | 0.977173i | \(-0.431858\pi\) | ||||
0.212443 | + | 0.977173i | \(0.431858\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −402.746 | −0.645725 | −0.322862 | − | 0.946446i | \(-0.604645\pi\) | ||||
−0.322862 | + | 0.946446i | \(0.604645\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −186.611 | −0.287306 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1702.65 | 2.51994 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −429.232 | −0.611295 | −0.305648 | − | 0.952145i | \(-0.598873\pi\) | ||||
−0.305648 | + | 0.952145i | \(0.598873\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 551.738 | 0.756842 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 78.8317 | 0.104252 | 0.0521259 | − | 0.998641i | \(-0.483400\pi\) | ||||
0.0521259 | + | 0.998641i | \(0.483400\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −80.7759 | −0.103075 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 43.5095 | 0.0536173 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1034.55 | 1.23216 | 0.616081 | − | 0.787683i | \(-0.288720\pi\) | ||||
0.616081 | + | 0.787683i | \(0.288720\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 760.207 | 0.875729 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 299.753 | 0.334225 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −44.0386 | −0.0475607 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1790.86 | 1.87458 | 0.937289 | − | 0.348552i | \(-0.113327\pi\) | ||||
0.937289 | + | 0.348552i | \(0.113327\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1540.70 | −1.56410 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −724.751 | −0.714014 | −0.357007 | − | 0.934102i | \(-0.616203\pi\) | ||||
−0.357007 | + | 0.934102i | \(0.616203\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 178.280 | 0.170548 | 0.0852739 | − | 0.996358i | \(-0.472823\pi\) | ||||
0.0852739 | + | 0.996358i | \(0.472823\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −32.3051 | −0.0300253 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1815.82 | −1.64058 | −0.820290 | − | 0.571948i | \(-0.806188\pi\) | ||||
−0.820290 | + | 0.571948i | \(0.806188\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1002.06 | −0.880548 | −0.440274 | − | 0.897863i | \(-0.645119\pi\) | ||||
−0.440274 | + | 0.897863i | \(0.645119\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −605.603 | −0.517849 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 85.9758 | 0.0715745 | 0.0357873 | − | 0.999359i | \(-0.488606\pi\) | ||||
0.0357873 | + | 0.999359i | \(0.488606\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −138.334 | −0.112171 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −687.896 | −0.543556 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2806.27 | 2.16177 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2544.43 | 1.91167 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −177.468 | −0.130095 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 196.327 | 0.140480 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1766.02 | −1.23393 | −0.616965 | − | 0.786991i | \(-0.711638\pi\) | ||||
−0.616965 | + | 0.786991i | \(0.711638\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 531.589 | 0.362820 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1040.00 | −0.693628 | −0.346814 | − | 0.937934i | \(-0.612737\pi\) | ||||
−0.346814 | + | 0.937934i | \(0.612737\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1529.97 | 0.997480 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 61.1233 | 0.0389678 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1620.70 | 1.01070 | 0.505351 | − | 0.862914i | \(-0.331363\pi\) | ||||
0.505351 | + | 0.862914i | \(0.331363\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −606.981 | −0.370385 | −0.185192 | − | 0.982702i | \(-0.559291\pi\) | ||||
−0.185192 | + | 0.982702i | \(0.559291\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −223.223 | −0.133325 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1730.31 | 1.01186 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22.8306 | −0.0130757 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 607.714 | 0.340976 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1203.11 | −0.661494 | −0.330747 | − | 0.943719i | \(-0.607301\pi\) | ||||
−0.330747 | + | 0.943719i | \(0.607301\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1644.41 | 0.886227 | 0.443114 | − | 0.896465i | \(-0.353874\pi\) | ||||
0.443114 | + | 0.896465i | \(0.353874\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2539.34 | −1.34179 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −157.288 | −0.0815078 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1262.40 | −0.641725 | −0.320862 | − | 0.947126i | \(-0.603973\pi\) | ||||
−0.320862 | + | 0.947126i | \(0.603973\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −564.258 | −0.281437 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4805.91 | 2.35254 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2456.18 | 1.18026 | 0.590131 | − | 0.807307i | \(-0.299076\pi\) | ||||
0.590131 | + | 0.807307i | \(0.299076\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −73.5300 | −0.0346928 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −775.298 | −0.359248 | −0.179624 | − | 0.983735i | \(-0.557488\pi\) | ||||
−0.179624 | + | 0.983735i | \(0.557488\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1424.44 | −0.648359 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1384.44 | −0.619125 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −823.000 | −0.361685 | −0.180842 | − | 0.983512i | \(-0.557882\pi\) | ||||
−0.180842 | + | 0.983512i | \(0.557882\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3401.87 | −1.46947 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 493.750 | 0.209675 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3570.45 | 1.49088 | 0.745441 | − | 0.666571i | \(-0.232239\pi\) | ||||
0.745441 | + | 0.666571i | \(0.232239\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −671.175 | −0.275624 | −0.137812 | − | 0.990458i | \(-0.544007\pi\) | ||||
−0.137812 | + | 0.990458i | \(0.544007\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1183.93 | −0.478242 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 317.776 | 0.126288 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6387.38 | 2.49782 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2123.51 | −0.817263 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5081.79 | 1.92516 | 0.962579 | − | 0.271002i | \(-0.0873550\pi\) | ||||
0.962579 | + | 0.271002i | \(0.0873550\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2000.69 | −0.746179 | −0.373089 | − | 0.927795i | \(-0.621702\pi\) | ||||
−0.373089 | + | 0.927795i | \(0.621702\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −32.8299 | −0.0120564 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1144.50 | 0.413919 | 0.206960 | − | 0.978349i | \(-0.433643\pi\) | ||||
0.206960 | + | 0.978349i | \(0.433643\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1651.91 | −0.588445 | −0.294222 | − | 0.955737i | \(-0.595061\pi\) | ||||
−0.294222 | + | 0.955737i | \(0.595061\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 221.570 | 0.0777530 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 793.167 | 0.274234 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 93.1220 | 0.0317264 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4348.77 | −1.46020 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3482.37 | 1.15254 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2761.98 | −0.901149 | −0.450574 | − | 0.892739i | \(-0.648781\pi\) | ||||
−0.450574 | + | 0.892739i | \(0.648781\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 381.370 | 0.122681 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −278.939 | −0.0884813 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5464.42 | 1.70944 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −604.251 | −0.186445 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2851.86 | 0.868039 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −701.622 | −0.210691 | −0.105345 | − | 0.994436i | \(-0.533595\pi\) | ||||
−0.105345 | + | 0.994436i | \(0.533595\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3078.29 | 0.912085 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5281.91 | −1.54437 | −0.772187 | − | 0.635395i | \(-0.780837\pi\) | ||||
−0.772187 | + | 0.635395i | \(0.780837\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5162.80 | 1.48982 | 0.744908 | − | 0.667168i | \(-0.232493\pi\) | ||||
0.744908 | + | 0.667168i | \(0.232493\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2554.54 | 0.727603 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5656.98 | 1.59056 | 0.795281 | − | 0.606241i | \(-0.207323\pi\) | ||||
0.795281 | + | 0.606241i | \(0.207323\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 117.131 | 0.0325140 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −643.988 | −0.176504 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4688.50 | 1.26893 | 0.634464 | − | 0.772953i | \(-0.281221\pi\) | ||||
0.634464 | + | 0.772953i | \(0.281221\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2254.32 | −0.602545 | −0.301273 | − | 0.953538i | \(-0.597411\pi\) | ||||
−0.301273 | + | 0.953538i | \(0.597411\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2924.08 | 0.771933 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −318.884 | −0.0831541 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1554.82 | 0.400529 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 118.273 | 0.0301015 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 906.394 | 0.227933 | 0.113966 | − | 0.993485i | \(-0.463644\pi\) | ||||
0.113966 | + | 0.993485i | \(0.463644\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10938.8 | 2.71824 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −121.190 | −0.0297617 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5953.47 | −1.44501 | −0.722504 | − | 0.691367i | \(-0.757009\pi\) | ||||
−0.722504 | + | 0.691367i | \(0.757009\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11040.0 | −2.64862 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −717.722 | −0.170214 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2339.06 | −0.548414 | −0.274207 | − | 0.961671i | \(-0.588415\pi\) | ||||
−0.274207 | + | 0.961671i | \(0.588415\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 296.081 | 0.0686344 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1552.17 | 0.355772 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 574.684 | 0.130257 | 0.0651285 | − | 0.997877i | \(-0.479254\pi\) | ||||
0.0651285 | + | 0.997877i | \(0.479254\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4985.61 | 1.11754 | 0.558772 | − | 0.829321i | \(-0.311273\pi\) | ||||
0.558772 | + | 0.829321i | \(0.311273\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1140.56 | 0.252856 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7743.03 | −1.69790 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2383.28 | −0.516959 | −0.258480 | − | 0.966017i | \(-0.583221\pi\) | ||||
−0.258480 | + | 0.966017i | \(0.583221\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4944.65 | −1.06103 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1020.93 | −0.216739 | −0.108370 | − | 0.994111i | \(-0.534563\pi\) | ||||
−0.108370 | + | 0.994111i | \(0.534563\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2873.16 | 0.603504 | 0.301752 | − | 0.953387i | \(-0.402429\pi\) | ||||
0.301752 | + | 0.953387i | \(0.402429\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −66.0723 | −0.0137326 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3235.19 | −0.665391 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5614.51 | 1.14279 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2686.87 | 0.541262 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2250.38 | −0.448698 | −0.224349 | − | 0.974509i | \(-0.572026\pi\) | ||||
−0.224349 | + | 0.974509i | \(0.572026\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −259.084 | −0.0511337 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4833.35 | −0.944307 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4883.98 | 0.944641 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9690.74 | 1.85570 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1087.36 | −0.206163 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 621.238 | 0.116629 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4353.67 | 0.809372 | 0.404686 | − | 0.914456i | \(-0.367381\pi\) | ||||
0.404686 | + | 0.914456i | \(0.367381\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 267.478 | 0.0492436 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 995.466 | 0.181504 | 0.0907519 | − | 0.995874i | \(-0.471073\pi\) | ||||
0.0907519 | + | 0.995874i | \(0.471073\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10687.1 | 1.92993 | 0.964966 | − | 0.262375i | \(-0.0845059\pi\) | ||||
0.964966 | + | 0.262375i | \(0.0845059\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 532.898 | 0.0953187 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8547.86 | −1.51450 | −0.757249 | − | 0.653127i | \(-0.773457\pi\) | ||||
−0.757249 | + | 0.653127i | \(0.773457\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1805.34 | 0.316863 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2724.32 | −0.473698 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5739.55 | 0.988721 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3457.13 | −0.590053 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1503.41 | −0.254248 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4069.30 | −0.681908 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4474.69 | −0.743055 | −0.371528 | − | 0.928422i | \(-0.621166\pi\) | ||||
−0.371528 | + | 0.928422i | \(0.621166\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9989.87 | 1.64397 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −116.264 | −0.0189617 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7158.57 | 1.15713 | 0.578564 | − | 0.815637i | \(-0.303613\pi\) | ||||
0.578564 | + | 0.815637i | \(0.303613\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 128.992 | 0.0206663 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12437.6 | 1.97518 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1697.23 | 0.267178 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −207.546 | −0.0323881 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1529.77 | 0.236663 | 0.118332 | − | 0.992974i | \(-0.462245\pi\) | ||||
0.118332 | + | 0.992974i | \(0.462245\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1291.38 | −0.198068 | −0.0990340 | − | 0.995084i | \(-0.531575\pi\) | ||||
−0.0990340 | + | 0.995084i | \(0.531575\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2158.01 | −0.328165 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1268.27 | −0.191228 | −0.0956139 | − | 0.995418i | \(-0.530481\pi\) | ||||
−0.0956139 | + | 0.995418i | \(0.530481\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −200.115 | −0.0299183 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4210.32 | 0.624185 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11996.6 | −1.76366 | −0.881832 | − | 0.471564i | \(-0.843690\pi\) | ||||
−0.881832 | + | 0.471564i | \(0.843690\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3729.83 | −0.543786 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3817.47 | 0.551971 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 317.067 | 0.0454686 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11662.6 | 1.65881 | 0.829406 | − | 0.558646i | \(-0.188679\pi\) | ||||
0.829406 | + | 0.558646i | \(0.188679\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2927.46 | 0.413001 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10286.3 | −1.43945 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9970.91 | 1.38411 | 0.692057 | − | 0.721843i | \(-0.256705\pi\) | ||||
0.692057 | + | 0.721843i | \(0.256705\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 294.555 | 0.0405621 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 806.052 | 0.110116 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7518.92 | 1.01905 | 0.509526 | − | 0.860455i | \(-0.329821\pi\) | ||||
0.509526 | + | 0.860455i | \(0.329821\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2649.61 | −0.356282 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6929.25 | −0.924460 | −0.462230 | − | 0.886760i | \(-0.652951\pi\) | ||||
−0.462230 | + | 0.886760i | \(0.652951\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1340.43 | −0.177441 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8768.96 | −1.15181 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 296.982 | 0.0387084 | 0.0193542 | − | 0.999813i | \(-0.493839\pi\) | ||||
0.0193542 | + | 0.999813i | \(0.493839\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18029.0 | 2.33188 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1560.34 | −0.200277 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 337.918 | 0.0430442 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14349.1 | 1.81401 | 0.907004 | − | 0.421123i | \(-0.138364\pi\) | ||||
0.907004 | + | 0.421123i | \(0.138364\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2295.45 | 0.288010 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −250.164 | −0.0311536 | −0.0155768 | − | 0.999879i | \(-0.504958\pi\) | ||||
−0.0155768 | + | 0.999879i | \(0.504958\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5553.19 | 0.686412 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −434.362 | −0.0532929 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25128.2 | −3.06034 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13128.8 | −1.58723 | −0.793616 | − | 0.608419i | \(-0.791804\pi\) | ||||
−0.793616 | + | 0.608419i | \(0.791804\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2431.59 | 0.291828 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9000.94 | 1.07241 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −62.0612 | −0.00734088 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −910.670 | −0.106944 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11430.9 | 1.33278 | 0.666389 | − | 0.745604i | \(-0.267839\pi\) | ||||
0.666389 | + | 0.745604i | \(0.267839\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13092.7 | −1.51567 | −0.757835 | − | 0.652446i | \(-0.773743\pi\) | ||||
−0.757835 | + | 0.652446i | \(0.773743\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3682.23 | 0.423254 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12761.9 | −1.45657 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21582.7 | −2.44604 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2596.04 | 0.292163 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2761.82 | 0.308660 | 0.154330 | − | 0.988019i | \(-0.450678\pi\) | ||||
0.154330 | + | 0.988019i | \(0.450678\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12593.9 | −1.39774 | −0.698872 | − | 0.715247i | \(-0.746314\pi\) | ||||
−0.698872 | + | 0.715247i | \(0.746314\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −34.2533 | −0.00377545 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9829.32 | 1.07597 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15492.1 | −1.68428 | −0.842138 | − | 0.539261i | \(-0.818703\pi\) | ||||
−0.842138 | + | 0.539261i | \(0.818703\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10024.7 | −1.08246 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8097.69 | −0.868472 | −0.434236 | − | 0.900799i | \(-0.642982\pi\) | ||||
−0.434236 | + | 0.900799i | \(0.642982\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −814.463 | −0.0867624 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1805.06 | −0.190998 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7625.66 | 0.801508 | 0.400754 | − | 0.916186i | \(-0.368748\pi\) | ||||
0.400754 | + | 0.916186i | \(0.368748\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7363.65 | −0.768826 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2467.15 | 0.255887 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −598.481 | −0.0616643 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3035.58 | 0.310719 | 0.155360 | − | 0.987858i | \(-0.450346\pi\) | ||||
0.155360 | + | 0.987858i | \(0.450346\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7966.19 | −0.810087 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18036.1 | −1.82218 | −0.911088 | − | 0.412213i | \(-0.864756\pi\) | ||||
−0.911088 | + | 0.412213i | \(0.864756\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2284.08 | 0.229266 | 0.114633 | − | 0.993408i | \(-0.463431\pi\) | ||||
0.114633 | + | 0.993408i | \(0.463431\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −235.984 | −0.0235344 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8813.46 | 0.873316 | 0.436658 | − | 0.899628i | \(-0.356162\pi\) | ||||
0.436658 | + | 0.899628i | \(0.356162\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4039.17 | 0.397679 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1894.02 | −0.185290 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22057.2 | 2.14417 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6957.71 | −0.672087 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9307.86 | 0.893454 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18983.6 | 1.81082 | 0.905411 | − | 0.424537i | \(-0.139563\pi\) | ||||
0.905411 | + | 0.424537i | \(0.139563\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11219.3 | −1.06353 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7210.43 | 0.679267 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1409.87 | −0.131998 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17208.6 | 1.60122 | 0.800610 | − | 0.599186i | \(-0.204509\pi\) | ||||
0.800610 | + | 0.599186i | \(0.204509\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3685.07 | 0.340787 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20652.2 | −1.89821 | −0.949106 | − | 0.314957i | \(-0.898010\pi\) | ||||
−0.949106 | + | 0.314957i | \(0.898010\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2975.51 | 0.271826 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1212.93 | 0.110136 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6952.28 | 0.627469 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19866.7 | 1.78228 | 0.891139 | − | 0.453730i | \(-0.149907\pi\) | ||||
0.891139 | + | 0.453730i | \(0.149907\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1163.20 | −0.103729 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5377.97 | −0.476723 | −0.238362 | − | 0.971176i | \(-0.576610\pi\) | ||||
−0.238362 | + | 0.971176i | \(0.576610\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 570.568 | 0.0502771 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2137.13 | −0.187206 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 701.222 | 0.0610631 | 0.0305315 | − | 0.999534i | \(-0.490280\pi\) | ||||
0.0305315 | + | 0.999534i | \(0.490280\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11015.4 | −0.953602 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4343.13 | −0.373789 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −140.353 | −0.0120091 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9262.18 | −0.787911 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1234.77 | −0.104432 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21334.1 | −1.79398 | −0.896990 | − | 0.442051i | \(-0.854251\pi\) | ||||
−0.896990 | + | 0.442051i | \(0.854251\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12288.4 | 1.02741 | 0.513703 | − | 0.857968i | \(-0.328273\pi\) | ||||
0.513703 | + | 0.857968i | \(0.328273\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5103.92 | −0.424292 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20499.4 | 1.69443 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18708.7 | 1.53766 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8144.78 | −0.665637 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3287.74 | −0.267182 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1429.53 | 0.115521 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5356.84 | 0.430474 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25215.8 | 2.01507 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1517.00 | −0.120556 | −0.0602780 | − | 0.998182i | \(-0.519199\pi\) | ||||
−0.0602780 | + | 0.998182i | \(0.519199\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1006.98 | −0.0795832 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 788.882 | 0.0620036 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15366.1 | 1.20111 | 0.600554 | − | 0.799584i | \(-0.294947\pi\) | ||||
0.600554 | + | 0.799584i | \(0.294947\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 19529.8 | 1.51823 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1622.23 | 0.125425 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11739.7 | −0.902757 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 476.768 | 0.0364642 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7717.53 | 0.587078 | 0.293539 | − | 0.955947i | \(-0.405167\pi\) | ||||
0.293539 | + | 0.955947i | \(0.405167\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9848.16 | 0.745139 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9583.15 | 0.721214 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7026.17 | 0.525964 | 0.262982 | − | 0.964801i | \(-0.415294\pi\) | ||||
0.262982 | + | 0.964801i | \(0.415294\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −67.6854 | −0.00503991 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15090.3 | 1.11770 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10743.0 | −0.791510 | −0.395755 | − | 0.918356i | \(-0.629517\pi\) | ||||
−0.395755 | + | 0.918356i | \(0.629517\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9274.65 | −0.679741 | −0.339871 | − | 0.940472i | \(-0.610383\pi\) | ||||
−0.339871 | + | 0.940472i | \(0.610383\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7624.34 | 0.555866 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21855.5 | −1.58511 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14538.6 | −1.04896 | −0.524479 | − | 0.851423i | \(-0.675740\pi\) | ||||
−0.524479 | + | 0.851423i | \(0.675740\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3001.68 | −0.215450 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2156.09 | 0.153958 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23412.7 | −1.66322 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 541.554 | 0.0382744 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15075.6 | −1.06003 | −0.530014 | − | 0.847989i | \(-0.677813\pi\) | ||||
−0.530014 | + | 0.847989i | \(0.677813\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11176.2 | 0.781843 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1717.12 | 0.119514 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10204.6 | 0.706668 | 0.353334 | − | 0.935497i | \(-0.385048\pi\) | ||||
0.353334 | + | 0.935497i | \(0.385048\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2209.27 | −0.152220 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2478.40 | −0.169906 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12544.9 | 0.855713 | 0.427856 | − | 0.903847i | \(-0.359269\pi\) | ||||
0.427856 | + | 0.903847i | \(0.359269\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18702.6 | −1.26937 | −0.634687 | − | 0.772770i | \(-0.718871\pi\) | ||||
−0.634687 | + | 0.772770i | \(0.718871\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3654.97 | −0.246835 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2003.13 | −0.134610 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5121.68 | −0.342475 | −0.171238 | − | 0.985230i | \(-0.554777\pi\) | ||||
−0.171238 | + | 0.985230i | \(0.554777\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1190.01 | 0.0791817 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4135.41 | −0.273814 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3382.24 | −0.222850 | −0.111425 | − | 0.993773i | \(-0.535542\pi\) | ||||
−0.111425 | + | 0.993773i | \(0.535542\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 139.713 | 0.00916063 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −571.111 | −0.0372643 | −0.0186321 | − | 0.999826i | \(-0.505931\pi\) | ||||
−0.0186321 | + | 0.999826i | \(0.505931\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10978.5 | 0.712867 | 0.356433 | − | 0.934321i | \(-0.383993\pi\) | ||||
0.356433 | + | 0.934321i | \(0.383993\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13642.6 | −0.881575 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 28295.6 | 1.81965 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15393.0 | 0.985150 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5224.69 | 0.332782 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −41415.7 | −2.62536 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2688.48 | 0.169615 | 0.0848073 | − | 0.996397i | \(-0.472973\pi\) | ||||
0.0848073 | + | 0.996397i | \(0.472973\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4143.87 | −0.260196 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1390.32 | 0.0868869 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11258.4 | 0.700276 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6290.98 | −0.389464 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12783.8 | −0.787724 | −0.393862 | − | 0.919170i | \(-0.628861\pi\) | ||||
−0.393862 | + | 0.919170i | \(0.628861\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21418.6 | 1.31363 | 0.656816 | − | 0.754051i | \(-0.271903\pi\) | ||||
0.656816 | + | 0.754051i | \(0.271903\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −418.500 | −0.0255479 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1439.68 | 0.0874799 | 0.0437400 | − | 0.999043i | \(-0.486073\pi\) | ||||
0.0437400 | + | 0.999043i | \(0.486073\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20487.1 | 1.23912 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8198.42 | 0.493581 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11505.7 | 0.689515 | 0.344757 | − | 0.938692i | \(-0.387961\pi\) | ||||
0.344757 | + | 0.938692i | \(0.387961\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 818.753 | 0.0488417 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9967.58 | 0.591891 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3275.96 | −0.193647 | −0.0968234 | − | 0.995302i | \(-0.530868\pi\) | ||||
−0.0968234 | + | 0.995302i | \(0.530868\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5455.49 | 0.321019 | 0.160510 | − | 0.987034i | \(-0.448686\pi\) | ||||
0.160510 | + | 0.987034i | \(0.448686\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4278.72 | 0.250636 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1204.48 | −0.0702373 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5095.73 | 0.295813 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1052.66 | −0.0608345 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −49124.6 | −2.82628 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 535.453 | 0.0306689 | 0.0153345 | − | 0.999882i | \(-0.495119\pi\) | ||||
0.0153345 | + | 0.999882i | \(0.495119\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9656.93 | 0.550660 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16698.6 | −0.947976 | −0.473988 | − | 0.880531i | \(-0.657186\pi\) | ||||
−0.473988 | + | 0.880531i | \(0.657186\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 48981.0 | 2.76836 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7924.59 | −0.445919 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1082.40 | −0.0606396 | −0.0303198 | − | 0.999540i | \(-0.509653\pi\) | ||||
−0.0303198 | + | 0.999540i | \(0.509653\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1275.92 | −0.0711683 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7745.89 | 0.430166 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10453.4 | −0.578000 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9761.34 | 0.537393 | 0.268697 | − | 0.963225i | \(-0.413407\pi\) | ||||
0.268697 | + | 0.963225i | \(0.413407\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −42139.0 | −2.30985 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 477.853 | 0.0260806 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12136.6 | −0.659549 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8487.31 | 0.459256 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3032.05 | 0.163365 | 0.0816827 | − | 0.996658i | \(-0.473971\pi\) | ||||
0.0816827 | + | 0.996658i | \(0.473971\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22579.6 | −1.21139 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 175.735 | 0.00938803 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19822.4 | −1.05445 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4640.54 | 0.245810 | 0.122905 | − | 0.992418i | \(-0.460779\pi\) | ||||
0.122905 | + | 0.992418i | \(0.460779\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10623.1 | 0.560332 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 35106.4 | 1.84396 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1362.21 | −0.0712500 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7034.27 | 0.366387 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20575.7 | −1.06724 | −0.533619 | − | 0.845725i | \(-0.679168\pi\) | ||||
−0.533619 | + | 0.845725i | \(0.679168\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4876.06 | 0.251864 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3382.21 | −0.173978 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3607.03 | −0.184775 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13890.0 | −0.708600 | −0.354300 | − | 0.935132i | \(-0.615281\pi\) | ||||
−0.354300 | + | 0.935132i | \(0.615281\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10509.8 | −0.533955 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36354.1 | 1.83940 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6253.36 | −0.315107 | −0.157553 | − | 0.987510i | \(-0.550361\pi\) | ||||
−0.157553 | + | 0.987510i | \(0.550361\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −478.430 | −0.0240097 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9193.59 | 0.459498 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4938.33 | −0.245818 | −0.122909 | − | 0.992418i | \(-0.539222\pi\) | ||||
−0.122909 | + | 0.992418i | \(0.539222\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2332.74 | 0.115648 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17443.8 | −0.861307 | −0.430653 | − | 0.902517i | \(-0.641717\pi\) | ||||
−0.430653 | + | 0.902517i | \(0.641717\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 947.162 | 0.0465790 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1951.01 | −0.0955605 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −49663.8 | −2.42280 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13989.1 | −0.679718 | −0.339859 | − | 0.940476i | \(-0.610379\pi\) | ||||
−0.339859 | + | 0.940476i | \(0.610379\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1359.89 | 0.0658128 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1294.58 | −0.0624035 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35278.7 | −1.69382 | −0.846912 | − | 0.531733i | \(-0.821541\pi\) | ||||
−0.846912 | + | 0.531733i | \(0.821541\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16411.7 | 0.784859 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15090.1 | −0.718814 | −0.359407 | − | 0.933181i | \(-0.617021\pi\) | ||||
−0.359407 | + | 0.933181i | \(0.617021\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27406.9 | −1.30039 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1999.12 | 0.0944817 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9147.16 | 0.430619 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4238.61 | −0.198762 | −0.0993812 | − | 0.995049i | \(-0.531686\pi\) | ||||
−0.0993812 | + | 0.995049i | \(0.531686\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8932.14 | −0.417229 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36539.4 | −1.70017 | −0.850084 | − | 0.526647i | \(-0.823449\pi\) | ||||
−0.850084 | + | 0.526647i | \(0.823449\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24850.1 | −1.15180 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16563.6 | −0.764756 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6616.80 | −0.304328 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15824.1 | 0.725010 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2251.57 | −0.102765 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 993.842 | 0.0451869 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25556.5 | −1.15755 | −0.578774 | − | 0.815488i | \(-0.696469\pi\) | ||||
−0.578774 | + | 0.815488i | \(0.696469\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3509.36 | −0.158348 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2351.49 | 0.105701 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21933.3 | −0.982187 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 444.218 | 0.0198174 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16208.1 | −0.720352 | −0.360176 | − | 0.932884i | \(-0.617283\pi\) | ||||
−0.360176 | + | 0.932884i | \(0.617283\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15265.7 | −0.675921 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −25604.2 | −1.12944 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25072.2 | −1.10184 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3783.51 | −0.165653 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 862.214 | 0.0376101 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24649.6 | 1.07124 | 0.535621 | − | 0.844459i | \(-0.320078\pi\) | ||||
0.535621 | + | 0.844459i | \(0.320078\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43969.2 | −1.90378 | −0.951892 | − | 0.306435i | \(-0.900864\pi\) | ||||
−0.951892 | + | 0.306435i | \(0.900864\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7480.05 | 0.322677 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1933.66 | −0.0831080 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19820.1 | 0.848735 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18814.4 | −0.802719 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14759.0 | −0.627398 | −0.313699 | − | 0.949523i | \(-0.601568\pi\) | ||||
−0.313699 | + | 0.949523i | \(0.601568\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36849.9 | −1.56076 | −0.780381 | − | 0.625304i | \(-0.784975\pi\) | ||||
−0.780381 | + | 0.625304i | \(0.784975\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11617.1 | −0.490248 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7780.68 | 0.327159 | 0.163580 | − | 0.986530i | \(-0.447696\pi\) | ||||
0.163580 | + | 0.986530i | \(0.447696\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40014.8 | −1.67644 | −0.838221 | − | 0.545330i | \(-0.816404\pi\) | ||||
−0.838221 | + | 0.545330i | \(0.816404\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3575.70 | −0.149266 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 41560.1 | 1.72866 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 610.363 | 0.0252964 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15511.9 | −0.640586 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2466.60 | −0.101498 | −0.0507488 | − | 0.998711i | \(-0.516161\pi\) | ||||
−0.0507488 | + | 0.998711i | \(0.516161\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1531.73 | −0.0625809 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1121.41 | 0.0456541 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 69591.6 | 2.82314 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4310.68 | 0.174254 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −70926.8 | −2.85704 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7269.34 | 0.291791 | 0.145895 | − | 0.989300i | \(-0.453394\pi\) | ||||
0.145895 | + | 0.989300i | \(0.453394\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1089.91 | 0.0435956 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13378.5 | −0.533256 | −0.266628 | − | 0.963800i | \(-0.585910\pi\) | ||||
−0.266628 | + | 0.963800i | \(0.585910\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35532.4 | −1.41135 | −0.705675 | − | 0.708536i | \(-0.749356\pi\) | ||||
−0.705675 | + | 0.708536i | \(0.749356\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4853.84 | −0.192124 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9556.27 | 0.376940 | 0.188470 | − | 0.982079i | \(-0.439647\pi\) | ||||
0.188470 | + | 0.982079i | \(0.439647\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 647.916 | 0.0254680 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8423.60 | 0.329966 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −26720.9 | −1.04309 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4104.78 | 0.159685 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −44322.0 | −1.71830 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5369.67 | 0.207461 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18138.4 | 0.698394 | 0.349197 | − | 0.937049i | \(-0.386454\pi\) | ||||
0.349197 | + | 0.937049i | \(0.386454\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3376.30 | −0.129556 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38547.5 | 1.47412 | 0.737058 | − | 0.675829i | \(-0.236214\pi\) | ||||
0.737058 | + | 0.675829i | \(0.236214\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12228.3 | 0.466040 | 0.233020 | − | 0.972472i | \(-0.425139\pi\) | ||||
0.233020 | + | 0.972472i | \(0.425139\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −388.710 | −0.0147642 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35387.4 | −1.33956 | −0.669782 | − | 0.742558i | \(-0.733613\pi\) | ||||
−0.669782 | + | 0.742558i | \(0.733613\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −48301.7 | −1.82226 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 34347.3 | 1.29144 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8322.77 | −0.311882 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2810.88 | −0.104980 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7327.56 | 0.272754 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5793.96 | 0.214949 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38588.2 | −1.42681 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14539.3 | 0.535810 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 528.390 | 0.0194080 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25552.8 | 0.935465 | 0.467733 | − | 0.883870i | \(-0.345071\pi\) | ||||
0.467733 | + | 0.883870i | \(0.345071\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17936.9 | 0.654487 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11127.5 | 0.404688 | 0.202344 | − | 0.979314i | \(-0.435144\pi\) | ||||
0.202344 | + | 0.979314i | \(0.435144\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4907.51 | 0.177891 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 932.060 | 0.0336754 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −28444.6 | −1.02435 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34243.6 | 1.22915 | 0.614577 | − | 0.788857i | \(-0.289327\pi\) | ||||
0.614577 | + | 0.788857i | \(0.289327\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6531.93 | 0.233697 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7065.22 | 0.251955 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 50205.7 | 1.78460 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4412.25 | −0.156329 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5315.50 | 0.187724 | 0.0938621 | − | 0.995585i | \(-0.470079\pi\) | ||||
0.0938621 | + | 0.995585i | \(0.470079\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22658.4 | 0.797635 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1493.52 | 0.0524071 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5028.54 | −0.175883 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31475.4 | −1.09739 | −0.548697 | − | 0.836021i | \(-0.684876\pi\) | ||||
−0.548697 | + | 0.836021i | \(0.684876\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16034.1 | 0.557245 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16014.6 | 0.554794 | 0.277397 | − | 0.960755i | \(-0.410528\pi\) | ||||
0.277397 | + | 0.960755i | \(0.410528\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20784.6 | −0.717752 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1671.76 | 0.0575474 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28388.8 | −0.974140 | −0.487070 | − | 0.873363i | \(-0.661934\pi\) | ||||
−0.487070 | + | 0.873363i | \(0.661934\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11194.3 | −0.382911 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12824.6 | −0.437293 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32633.4 | 1.10924 | 0.554618 | − | 0.832105i | \(-0.312865\pi\) | ||||
0.554618 | + | 0.832105i | \(0.312865\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4000.69 | −0.135560 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2708.59 | 0.0914905 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 44327.2 | 1.49260 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10125.7 | 0.339893 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 44939.8 | 1.50380 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1575.06 | 0.0525421 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36126.7 | −1.20140 | −0.600702 | − | 0.799473i | \(-0.705112\pi\) | ||||
−0.600702 | + | 0.799473i | \(0.705112\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8611.20 | 0.285481 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45941.5 | 1.51836 | 0.759182 | − | 0.650878i | \(-0.225599\pi\) | ||||
0.759182 | + | 0.650878i | \(0.225599\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16601.3 | −0.546982 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5186.83 | −0.170371 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37251.1 | −1.21982 | −0.609911 | − | 0.792470i | \(-0.708795\pi\) | ||||
−0.609911 | + | 0.792470i | \(0.708795\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 64403.9 | 2.10251 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24800.0 | 0.807137 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 52551.7 | 1.70513 | 0.852563 | − | 0.522624i | \(-0.175047\pi\) | ||||
0.852563 | + | 0.522624i | \(0.175047\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −901.020 | −0.0291461 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6105.28 | −0.196893 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 62258.5 | 2.00172 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10063.1 | −0.322569 | −0.161284 | − | 0.986908i | \(-0.551564\pi\) | ||||
−0.161284 | + | 0.986908i | \(0.551564\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6713.50 | −0.214548 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1300.48 | 0.0414352 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2111.64 | −0.0670776 | −0.0335388 | − | 0.999437i | \(-0.510678\pi\) | ||||
−0.0335388 | + | 0.999437i | \(0.510678\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 31339.3 | 0.992525 |
(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 | 1856.4.a.bk.1.8 | 12 | ||
4.3 | odd | 2 | inner | 1856.4.a.bk.1.5 | 12 | ||
8.3 | odd | 2 | 928.4.a.i.1.8 | yes | 12 | ||
8.5 | even | 2 | 928.4.a.i.1.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
928.4.a.i.1.5 | ✓ | 12 | 8.5 | even | 2 | ||
928.4.a.i.1.8 | yes | 12 | 8.3 | odd | 2 | ||
1856.4.a.bk.1.5 | 12 | 4.3 | odd | 2 | inner | ||
1856.4.a.bk.1.8 | 12 | 1.1 | even | 1 | trivial |