Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,4,Mod(1,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, 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("2205.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.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: | \(130.099211563\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 34x^{4} + 241x^{2} - 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.525584\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2205.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.525584 | 0.185822 | 0.0929109 | − | 0.995674i | \(-0.470383\pi\) | ||||
0.0929109 | + | 0.995674i | \(0.470383\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.72376 | −0.965470 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.26415 | −0.365227 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.62792 | 0.0831021 | ||||||||
\(11\) | 48.9415 | 1.34149 | 0.670746 | − | 0.741687i | \(-0.265974\pi\) | ||||
0.670746 | + | 0.741687i | \(0.265974\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 40.1517 | 0.856622 | 0.428311 | − | 0.903631i | \(-0.359109\pi\) | ||||
0.428311 | + | 0.903631i | \(0.359109\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 57.4466 | 0.897603 | ||||||||
\(17\) | 59.1704 | 0.844172 | 0.422086 | − | 0.906556i | \(-0.361298\pi\) | ||||
0.422086 | + | 0.906556i | \(0.361298\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 129.508 | 1.56375 | 0.781873 | − | 0.623438i | \(-0.214265\pi\) | ||||
0.781873 | + | 0.623438i | \(0.214265\pi\) | |||||||
\(20\) | −38.6188 | −0.431771 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 25.7228 | 0.249278 | ||||||||
\(23\) | 93.5609 | 0.848209 | 0.424104 | − | 0.905613i | \(-0.360589\pi\) | ||||
0.424104 | + | 0.905613i | \(0.360589\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 21.1031 | 0.159179 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 117.184 | 0.750365 | 0.375183 | − | 0.926951i | \(-0.377580\pi\) | ||||
0.375183 | + | 0.926951i | \(0.377580\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −162.945 | −0.944057 | −0.472029 | − | 0.881583i | \(-0.656478\pi\) | ||||
−0.472029 | + | 0.881583i | \(0.656478\pi\) | |||||||
\(32\) | 96.3062 | 0.532022 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 31.0990 | 0.156866 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.72097 | −0.0165331 | −0.00826654 | − | 0.999966i | \(-0.502631\pi\) | ||||
−0.00826654 | + | 0.999966i | \(0.502631\pi\) | |||||||
\(38\) | 68.0673 | 0.290578 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −41.3208 | −0.163335 | ||||||||
\(41\) | −222.816 | −0.848732 | −0.424366 | − | 0.905491i | \(-0.639503\pi\) | ||||
−0.424366 | + | 0.905491i | \(0.639503\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −62.2753 | −0.220858 | −0.110429 | − | 0.993884i | \(-0.535222\pi\) | ||||
−0.110429 | + | 0.993884i | \(0.535222\pi\) | |||||||
\(44\) | −378.012 | −1.29517 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 49.1741 | 0.157616 | ||||||||
\(47\) | −460.327 | −1.42863 | −0.714315 | − | 0.699824i | \(-0.753262\pi\) | ||||
−0.714315 | + | 0.699824i | \(0.753262\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 13.1396 | 0.0371644 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −310.122 | −0.827043 | ||||||||
\(53\) | −492.977 | −1.27765 | −0.638826 | − | 0.769351i | \(-0.720580\pi\) | ||||
−0.638826 | + | 0.769351i | \(0.720580\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 244.707 | 0.599933 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 61.5902 | 0.139434 | ||||||||
\(59\) | 153.928 | 0.339657 | 0.169829 | − | 0.985474i | \(-0.445679\pi\) | ||||
0.169829 | + | 0.985474i | \(0.445679\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 194.916 | 0.409122 | 0.204561 | − | 0.978854i | \(-0.434423\pi\) | ||||
0.204561 | + | 0.978854i | \(0.434423\pi\) | |||||||
\(62\) | −85.6412 | −0.175427 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −408.956 | −0.798742 | ||||||||
\(65\) | 200.759 | 0.383093 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 667.084 | 1.21638 | 0.608189 | − | 0.793793i | \(-0.291896\pi\) | ||||
0.608189 | + | 0.793793i | \(0.291896\pi\) | |||||||
\(68\) | −457.018 | −0.815023 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −256.941 | −0.429483 | −0.214741 | − | 0.976671i | \(-0.568891\pi\) | ||||
−0.214741 | + | 0.976671i | \(0.568891\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1219.59 | 1.95537 | 0.977686 | − | 0.210073i | \(-0.0673703\pi\) | ||||
0.977686 | + | 0.210073i | \(0.0673703\pi\) | |||||||
\(74\) | −1.95568 | −0.00307221 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1000.29 | −1.50975 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 381.236 | 0.542941 | 0.271471 | − | 0.962447i | \(-0.412490\pi\) | ||||
0.271471 | + | 0.962447i | \(0.412490\pi\) | |||||||
\(80\) | 287.233 | 0.401420 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −117.108 | −0.157713 | ||||||||
\(83\) | −281.766 | −0.372625 | −0.186313 | − | 0.982491i | \(-0.559654\pi\) | ||||
−0.186313 | + | 0.982491i | \(0.559654\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 295.852 | 0.377525 | ||||||||
\(86\) | −32.7309 | −0.0410402 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −404.460 | −0.489949 | ||||||||
\(89\) | −926.242 | −1.10316 | −0.551581 | − | 0.834121i | \(-0.685975\pi\) | ||||
−0.551581 | + | 0.834121i | \(0.685975\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −722.642 | −0.818920 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −241.940 | −0.265471 | ||||||||
\(95\) | 647.540 | 0.699328 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −634.683 | −0.664354 | −0.332177 | − | 0.943217i | \(-0.607783\pi\) | ||||
−0.332177 | + | 0.943217i | \(0.607783\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −193.094 | −0.193094 | ||||||||
\(101\) | 1921.81 | 1.89334 | 0.946670 | − | 0.322205i | \(-0.104424\pi\) | ||||
0.946670 | + | 0.322205i | \(0.104424\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1310.57 | −1.25373 | −0.626865 | − | 0.779128i | \(-0.715662\pi\) | ||||
−0.626865 | + | 0.779128i | \(0.715662\pi\) | |||||||
\(104\) | −331.820 | −0.312862 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −259.101 | −0.237416 | ||||||||
\(107\) | 1866.73 | 1.68657 | 0.843286 | − | 0.537465i | \(-0.180618\pi\) | ||||
0.843286 | + | 0.537465i | \(0.180618\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −649.011 | −0.570312 | −0.285156 | − | 0.958481i | \(-0.592045\pi\) | ||||
−0.285156 | + | 0.958481i | \(0.592045\pi\) | |||||||
\(110\) | 128.614 | 0.111481 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 857.830 | 0.714140 | 0.357070 | − | 0.934078i | \(-0.383776\pi\) | ||||
0.357070 | + | 0.934078i | \(0.383776\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 467.805 | 0.379330 | ||||||||
\(116\) | −905.104 | −0.724455 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 80.9022 | 0.0631157 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1064.27 | 0.799600 | ||||||||
\(122\) | 102.445 | 0.0760238 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1258.55 | 0.911459 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 972.678 | 0.679616 | 0.339808 | − | 0.940495i | \(-0.389638\pi\) | ||||
0.339808 | + | 0.940495i | \(0.389638\pi\) | |||||||
\(128\) | −985.390 | −0.680445 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 105.515 | 0.0711871 | ||||||||
\(131\) | −131.175 | −0.0874873 | −0.0437436 | − | 0.999043i | \(-0.513928\pi\) | ||||
−0.0437436 | + | 0.999043i | \(0.513928\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 350.608 | 0.226029 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −488.993 | −0.308315 | ||||||||
\(137\) | 2160.79 | 1.34751 | 0.673754 | − | 0.738956i | \(-0.264681\pi\) | ||||
0.673754 | + | 0.738956i | \(0.264681\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1791.95 | 1.09346 | 0.546732 | − | 0.837308i | \(-0.315872\pi\) | ||||
0.546732 | + | 0.837308i | \(0.315872\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −135.044 | −0.0798073 | ||||||||
\(143\) | 1965.09 | 1.14915 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 585.922 | 0.335573 | ||||||||
\(146\) | 640.996 | 0.363351 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 28.7399 | 0.0159622 | ||||||||
\(149\) | −3022.74 | −1.66196 | −0.830981 | − | 0.556301i | \(-0.812220\pi\) | ||||
−0.830981 | + | 0.556301i | \(0.812220\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 908.211 | 0.489464 | 0.244732 | − | 0.969591i | \(-0.421300\pi\) | ||||
0.244732 | + | 0.969591i | \(0.421300\pi\) | |||||||
\(152\) | −1070.27 | −0.571123 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −814.725 | −0.422195 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1387.49 | 0.705310 | 0.352655 | − | 0.935753i | \(-0.385279\pi\) | ||||
0.352655 | + | 0.935753i | \(0.385279\pi\) | |||||||
\(158\) | 200.371 | 0.100890 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 481.531 | 0.237927 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2637.35 | −1.26732 | −0.633660 | − | 0.773612i | \(-0.718448\pi\) | ||||
−0.633660 | + | 0.773612i | \(0.718448\pi\) | |||||||
\(164\) | 1720.98 | 0.819425 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −148.092 | −0.0692419 | ||||||||
\(167\) | 2525.54 | 1.17025 | 0.585126 | − | 0.810943i | \(-0.301045\pi\) | ||||
0.585126 | + | 0.810943i | \(0.301045\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −584.838 | −0.266198 | ||||||||
\(170\) | 155.495 | 0.0701524 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 481.000 | 0.213232 | ||||||||
\(173\) | −649.874 | −0.285601 | −0.142801 | − | 0.989751i | \(-0.545611\pi\) | ||||
−0.142801 | + | 0.989751i | \(0.545611\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2811.52 | 1.20413 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −486.817 | −0.204992 | ||||||||
\(179\) | −3434.35 | −1.43405 | −0.717026 | − | 0.697047i | \(-0.754497\pi\) | ||||
−0.717026 | + | 0.697047i | \(0.754497\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1187.20 | 0.487537 | 0.243768 | − | 0.969834i | \(-0.421616\pi\) | ||||
0.243768 | + | 0.969834i | \(0.421616\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −773.201 | −0.309789 | ||||||||
\(185\) | −18.6049 | −0.00739382 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2895.88 | 1.13245 | ||||||||
\(188\) | 3555.46 | 1.37930 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 340.336 | 0.129950 | ||||||||
\(191\) | −180.895 | −0.0685293 | −0.0342646 | − | 0.999413i | \(-0.510909\pi\) | ||||
−0.0342646 | + | 0.999413i | \(0.510909\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3100.23 | −1.15627 | −0.578134 | − | 0.815942i | \(-0.696219\pi\) | ||||
−0.578134 | + | 0.815942i | \(0.696219\pi\) | |||||||
\(194\) | −333.579 | −0.123451 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −611.701 | −0.221228 | −0.110614 | − | 0.993863i | \(-0.535282\pi\) | ||||
−0.110614 | + | 0.993863i | \(0.535282\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1387.39 | −0.494218 | −0.247109 | − | 0.968988i | \(-0.579481\pi\) | ||||
−0.247109 | + | 0.968988i | \(0.579481\pi\) | |||||||
\(200\) | −206.604 | −0.0730455 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1010.07 | 0.351824 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1114.08 | −0.379564 | ||||||||
\(206\) | −688.814 | −0.232970 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2306.58 | 0.768907 | ||||||||
\(209\) | 6338.31 | 2.09775 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1415.49 | −0.461830 | −0.230915 | − | 0.972974i | \(-0.574172\pi\) | ||||
−0.230915 | + | 0.972974i | \(0.574172\pi\) | |||||||
\(212\) | 3807.64 | 1.23354 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 981.121 | 0.313402 | ||||||||
\(215\) | −311.377 | −0.0987707 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −341.109 | −0.105976 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1890.06 | −0.579218 | ||||||||
\(221\) | 2375.79 | 0.723136 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4213.75 | −1.26535 | −0.632676 | − | 0.774417i | \(-0.718043\pi\) | ||||
−0.632676 | + | 0.774417i | \(0.718043\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 450.861 | 0.132703 | ||||||||
\(227\) | 6180.32 | 1.80706 | 0.903529 | − | 0.428526i | \(-0.140967\pi\) | ||||
0.903529 | + | 0.428526i | \(0.140967\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1196.83 | −0.345365 | −0.172683 | − | 0.984978i | \(-0.555244\pi\) | ||||
−0.172683 | + | 0.984978i | \(0.555244\pi\) | |||||||
\(230\) | 245.870 | 0.0704879 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −968.429 | −0.274054 | ||||||||
\(233\) | 927.278 | 0.260721 | 0.130360 | − | 0.991467i | \(-0.458387\pi\) | ||||
0.130360 | + | 0.991467i | \(0.458387\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2301.64 | −0.638903 | ||||||||
\(236\) | −1188.91 | −0.327929 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3429.57 | −0.928202 | −0.464101 | − | 0.885782i | \(-0.653622\pi\) | ||||
−0.464101 | + | 0.885782i | \(0.653622\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4748.69 | 1.26925 | 0.634626 | − | 0.772819i | \(-0.281154\pi\) | ||||
0.634626 | + | 0.772819i | \(0.281154\pi\) | |||||||
\(242\) | 559.362 | 0.148583 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1505.49 | −0.394995 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5199.97 | 1.33954 | ||||||||
\(248\) | 1346.60 | 0.344796 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 65.6979 | 0.0166204 | ||||||||
\(251\) | 7273.04 | 1.82896 | 0.914482 | − | 0.404626i | \(-0.132598\pi\) | ||||
0.914482 | + | 0.404626i | \(0.132598\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4579.01 | 1.13786 | ||||||||
\(254\) | 511.223 | 0.126287 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2753.74 | 0.672300 | ||||||||
\(257\) | 1613.28 | 0.391570 | 0.195785 | − | 0.980647i | \(-0.437275\pi\) | ||||
0.195785 | + | 0.980647i | \(0.437275\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1550.61 | −0.369865 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −68.9436 | −0.0162571 | ||||||||
\(263\) | −2593.26 | −0.608013 | −0.304007 | − | 0.952670i | \(-0.598324\pi\) | ||||
−0.304007 | + | 0.952670i | \(0.598324\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2464.88 | −0.571384 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5152.40 | −1.17438 | ||||||||
\(269\) | 5922.82 | 1.34246 | 0.671228 | − | 0.741251i | \(-0.265767\pi\) | ||||
0.671228 | + | 0.741251i | \(0.265767\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1783.59 | −0.399798 | −0.199899 | − | 0.979816i | \(-0.564061\pi\) | ||||
−0.199899 | + | 0.979816i | \(0.564061\pi\) | |||||||
\(272\) | 3399.14 | 0.757731 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1135.68 | 0.250397 | ||||||||
\(275\) | 1223.54 | 0.268298 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3042.89 | −0.660035 | −0.330017 | − | 0.943975i | \(-0.607055\pi\) | ||||
−0.330017 | + | 0.943975i | \(0.607055\pi\) | |||||||
\(278\) | 941.821 | 0.203190 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1812.14 | −0.384708 | −0.192354 | − | 0.981326i | \(-0.561612\pi\) | ||||
−0.192354 | + | 0.981326i | \(0.561612\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7062.64 | −1.48350 | −0.741750 | − | 0.670677i | \(-0.766004\pi\) | ||||
−0.741750 | + | 0.670677i | \(0.766004\pi\) | |||||||
\(284\) | 1984.55 | 0.414653 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1032.82 | 0.213537 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1411.87 | −0.287374 | ||||||||
\(290\) | 307.951 | 0.0623569 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9419.82 | −1.88785 | ||||||||
\(293\) | 6252.90 | 1.24675 | 0.623376 | − | 0.781922i | \(-0.285760\pi\) | ||||
0.623376 | + | 0.781922i | \(0.285760\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 769.642 | 0.151899 | ||||||||
\(296\) | 30.7507 | 0.00603833 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1588.70 | −0.308829 | ||||||||
\(299\) | 3756.63 | 0.726594 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 477.341 | 0.0909532 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7439.79 | 1.40362 | ||||||||
\(305\) | 974.580 | 0.182965 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −946.955 | −0.176044 | −0.0880221 | − | 0.996119i | \(-0.528055\pi\) | ||||
−0.0880221 | + | 0.996119i | \(0.528055\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −428.206 | −0.0784531 | ||||||||
\(311\) | 7114.71 | 1.29723 | 0.648614 | − | 0.761117i | \(-0.275349\pi\) | ||||
0.648614 | + | 0.761117i | \(0.275349\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2357.90 | 0.425803 | 0.212901 | − | 0.977074i | \(-0.431709\pi\) | ||||
0.212901 | + | 0.977074i | \(0.431709\pi\) | |||||||
\(314\) | 729.241 | 0.131062 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2944.57 | −0.524194 | ||||||||
\(317\) | −9260.69 | −1.64079 | −0.820397 | − | 0.571794i | \(-0.806248\pi\) | ||||
−0.820397 | + | 0.571794i | \(0.806248\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5735.17 | 1.00661 | ||||||||
\(320\) | −2044.78 | −0.357208 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7663.03 | 1.32007 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1003.79 | 0.171324 | ||||||||
\(326\) | −1386.15 | −0.235496 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1841.38 | 0.309980 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10664.3 | 1.77089 | 0.885443 | − | 0.464748i | \(-0.153855\pi\) | ||||
0.885443 | + | 0.464748i | \(0.153855\pi\) | |||||||
\(332\) | 2176.30 | 0.359758 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1327.38 | 0.217458 | ||||||||
\(335\) | 3335.42 | 0.543980 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −865.728 | −0.139938 | −0.0699691 | − | 0.997549i | \(-0.522290\pi\) | ||||
−0.0699691 | + | 0.997549i | \(0.522290\pi\) | |||||||
\(338\) | −307.381 | −0.0494655 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2285.09 | −0.364489 | ||||||||
\(341\) | −7974.77 | −1.26645 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 514.653 | 0.0806634 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −341.563 | −0.0530710 | ||||||||
\(347\) | −8164.72 | −1.26313 | −0.631563 | − | 0.775324i | \(-0.717586\pi\) | ||||
−0.631563 | + | 0.775324i | \(0.717586\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6227.30 | −0.955128 | −0.477564 | − | 0.878597i | \(-0.658480\pi\) | ||||
−0.477564 | + | 0.878597i | \(0.658480\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4713.37 | 0.713703 | ||||||||
\(353\) | 11121.3 | 1.67685 | 0.838425 | − | 0.545017i | \(-0.183477\pi\) | ||||
0.838425 | + | 0.545017i | \(0.183477\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1284.70 | −0.192071 | ||||||||
\(356\) | 7154.07 | 1.06507 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1805.04 | −0.266478 | ||||||||
\(359\) | 3362.46 | 0.494328 | 0.247164 | − | 0.968974i | \(-0.420501\pi\) | ||||
0.247164 | + | 0.968974i | \(0.420501\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9913.32 | 1.44530 | ||||||||
\(362\) | 623.974 | 0.0905949 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6097.95 | 0.874469 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1447.20 | −0.205839 | −0.102920 | − | 0.994690i | \(-0.532818\pi\) | ||||
−0.102920 | + | 0.994690i | \(0.532818\pi\) | |||||||
\(368\) | 5374.76 | 0.761355 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.77841 | −0.00137393 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13117.6 | −1.82092 | −0.910460 | − | 0.413597i | \(-0.864272\pi\) | ||||
−0.910460 | + | 0.413597i | \(0.864272\pi\) | |||||||
\(374\) | 1522.03 | 0.210434 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3804.21 | 0.521775 | ||||||||
\(377\) | 4705.15 | 0.642779 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4102.23 | −0.555983 | −0.277991 | − | 0.960584i | \(-0.589669\pi\) | ||||
−0.277991 | + | 0.960584i | \(0.589669\pi\) | |||||||
\(380\) | −5001.44 | −0.675181 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −95.0754 | −0.0127342 | ||||||||
\(383\) | −7371.61 | −0.983477 | −0.491739 | − | 0.870743i | \(-0.663638\pi\) | ||||
−0.491739 | + | 0.870743i | \(0.663638\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1629.43 | −0.214860 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4902.14 | 0.641414 | ||||||||
\(389\) | 8529.66 | 1.11175 | 0.555875 | − | 0.831266i | \(-0.312383\pi\) | ||||
0.555875 | + | 0.831266i | \(0.312383\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5536.03 | 0.716034 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −321.500 | −0.0411090 | ||||||||
\(395\) | 1906.18 | 0.242811 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10274.2 | 1.29886 | 0.649428 | − | 0.760423i | \(-0.275008\pi\) | ||||
0.649428 | + | 0.760423i | \(0.275008\pi\) | |||||||
\(398\) | −729.189 | −0.0918365 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1436.16 | 0.179521 | ||||||||
\(401\) | 254.845 | 0.0317366 | 0.0158683 | − | 0.999874i | \(-0.494949\pi\) | ||||
0.0158683 | + | 0.999874i | \(0.494949\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6542.52 | −0.808701 | ||||||||
\(404\) | −14843.6 | −1.82796 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −182.110 | −0.0221790 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6790.11 | −0.820903 | −0.410451 | − | 0.911882i | \(-0.634629\pi\) | ||||
−0.410451 | + | 0.911882i | \(0.634629\pi\) | |||||||
\(410\) | −585.542 | −0.0705314 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10122.5 | 1.21044 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1408.83 | −0.166643 | ||||||||
\(416\) | 3866.86 | 0.455741 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3331.31 | 0.389808 | ||||||||
\(419\) | 2717.47 | 0.316843 | 0.158421 | − | 0.987372i | \(-0.449360\pi\) | ||||
0.158421 | + | 0.987372i | \(0.449360\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3455.49 | −0.400024 | −0.200012 | − | 0.979793i | \(-0.564098\pi\) | ||||
−0.200012 | + | 0.979793i | \(0.564098\pi\) | |||||||
\(422\) | −743.957 | −0.0858181 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4074.04 | 0.466634 | ||||||||
\(425\) | 1479.26 | 0.168834 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −14418.1 | −1.62834 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −163.654 | −0.0183538 | ||||||||
\(431\) | 5333.95 | 0.596119 | 0.298060 | − | 0.954547i | \(-0.403661\pi\) | ||||
0.298060 | + | 0.954547i | \(0.403661\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14032.3 | 1.55739 | 0.778696 | − | 0.627401i | \(-0.215881\pi\) | ||||
0.778696 | + | 0.627401i | \(0.215881\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5012.81 | 0.550619 | ||||||||
\(437\) | 12116.9 | 1.32638 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13158.0 | −1.43052 | −0.715258 | − | 0.698860i | \(-0.753691\pi\) | ||||
−0.715258 | + | 0.698860i | \(0.753691\pi\) | |||||||
\(440\) | −2022.30 | −0.219112 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1248.68 | 0.134375 | ||||||||
\(443\) | 14922.9 | 1.60047 | 0.800237 | − | 0.599683i | \(-0.204707\pi\) | ||||
0.800237 | + | 0.599683i | \(0.204707\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4631.21 | −0.493349 | ||||||||
\(446\) | −2214.68 | −0.235130 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 640.776 | 0.0673498 | 0.0336749 | − | 0.999433i | \(-0.489279\pi\) | ||||
0.0336749 | + | 0.999433i | \(0.489279\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10904.9 | −1.13857 | ||||||||
\(452\) | −6625.67 | −0.689481 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3248.28 | 0.335791 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14469.0 | 1.48103 | 0.740515 | − | 0.672039i | \(-0.234581\pi\) | ||||
0.740515 | + | 0.672039i | \(0.234581\pi\) | |||||||
\(458\) | −629.033 | −0.0641764 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3613.21 | −0.366232 | ||||||||
\(461\) | −10275.8 | −1.03816 | −0.519082 | − | 0.854725i | \(-0.673726\pi\) | ||||
−0.519082 | + | 0.854725i | \(0.673726\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4435.77 | 0.445244 | 0.222622 | − | 0.974905i | \(-0.428538\pi\) | ||||
0.222622 | + | 0.974905i | \(0.428538\pi\) | |||||||
\(464\) | 6731.84 | 0.673530 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 487.362 | 0.0484476 | ||||||||
\(467\) | −12909.3 | −1.27917 | −0.639585 | − | 0.768720i | \(-0.720894\pi\) | ||||
−0.639585 | + | 0.768720i | \(0.720894\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1209.70 | −0.118722 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1272.09 | −0.124052 | ||||||||
\(473\) | −3047.85 | −0.296279 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3237.70 | 0.312749 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1802.52 | −0.172480 | ||||||||
\(479\) | 15622.8 | 1.49023 | 0.745117 | − | 0.666934i | \(-0.232394\pi\) | ||||
0.745117 | + | 0.666934i | \(0.232394\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −149.403 | −0.0141626 | ||||||||
\(482\) | 2495.83 | 0.235855 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8220.15 | −0.771990 | ||||||||
\(485\) | −3173.42 | −0.297108 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7817.06 | 0.727361 | 0.363680 | − | 0.931524i | \(-0.381520\pi\) | ||||
0.363680 | + | 0.931524i | \(0.381520\pi\) | |||||||
\(488\) | −1610.82 | −0.149423 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1057.33 | 0.0971822 | 0.0485911 | − | 0.998819i | \(-0.484527\pi\) | ||||
0.0485911 | + | 0.998819i | \(0.484527\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6933.84 | 0.633437 | ||||||||
\(494\) | 2733.02 | 0.248916 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9360.63 | −0.847389 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4434.30 | −0.397809 | −0.198904 | − | 0.980019i | \(-0.563738\pi\) | ||||
−0.198904 | + | 0.980019i | \(0.563738\pi\) | |||||||
\(500\) | −965.470 | −0.0863543 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3822.59 | 0.339862 | ||||||||
\(503\) | −3705.19 | −0.328442 | −0.164221 | − | 0.986424i | \(-0.552511\pi\) | ||||
−0.164221 | + | 0.986424i | \(0.552511\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9609.05 | 0.846727 | ||||||||
\(506\) | 2406.65 | 0.211440 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7512.73 | −0.656149 | ||||||||
\(509\) | 1670.83 | 0.145498 | 0.0727490 | − | 0.997350i | \(-0.476823\pi\) | ||||
0.0727490 | + | 0.997350i | \(0.476823\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 9330.44 | 0.805373 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 847.911 | 0.0727622 | ||||||||
\(515\) | −6552.85 | −0.560685 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22529.1 | −1.91649 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1659.10 | −0.139916 | ||||||||
\(521\) | 9521.12 | 0.800629 | 0.400315 | − | 0.916378i | \(-0.368901\pi\) | ||||
0.400315 | + | 0.916378i | \(0.368901\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14460.0 | −1.20897 | −0.604487 | − | 0.796615i | \(-0.706622\pi\) | ||||
−0.604487 | + | 0.796615i | \(0.706622\pi\) | |||||||
\(524\) | 1013.17 | 0.0844664 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1362.98 | −0.112982 | ||||||||
\(527\) | −9641.51 | −0.796947 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3413.36 | −0.280542 | ||||||||
\(530\) | −1295.50 | −0.106176 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8946.45 | −0.727042 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9333.63 | 0.754258 | ||||||||
\(536\) | −5512.88 | −0.444254 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3112.93 | 0.249458 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5461.17 | 0.434000 | 0.217000 | − | 0.976172i | \(-0.430373\pi\) | ||||
0.217000 | + | 0.976172i | \(0.430373\pi\) | |||||||
\(542\) | −937.425 | −0.0742913 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5698.47 | 0.449118 | ||||||||
\(545\) | −3245.05 | −0.255051 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20483.5 | 1.60112 | 0.800559 | − | 0.599254i | \(-0.204536\pi\) | ||||
0.800559 | + | 0.599254i | \(0.204536\pi\) | |||||||
\(548\) | −16689.4 | −1.30098 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 643.071 | 0.0498557 | ||||||||
\(551\) | 15176.3 | 1.17338 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1599.29 | −0.122649 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13840.6 | −1.05571 | ||||||||
\(557\) | −8382.62 | −0.637671 | −0.318836 | − | 0.947810i | \(-0.603292\pi\) | ||||
−0.318836 | + | 0.947810i | \(0.603292\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2500.46 | −0.189192 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −952.429 | −0.0714872 | ||||||||
\(563\) | 10678.5 | 0.799369 | 0.399685 | − | 0.916653i | \(-0.369120\pi\) | ||||
0.399685 | + | 0.916653i | \(0.369120\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4289.15 | 0.319373 | ||||||||
\(566\) | −3712.01 | −0.275667 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2123.40 | 0.156859 | ||||||||
\(569\) | 17416.3 | 1.28318 | 0.641590 | − | 0.767048i | \(-0.278275\pi\) | ||||
0.641590 | + | 0.767048i | \(0.278275\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7072.55 | 0.518348 | 0.259174 | − | 0.965831i | \(-0.416550\pi\) | ||||
0.259174 | + | 0.965831i | \(0.416550\pi\) | |||||||
\(572\) | −15177.8 | −1.10947 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2339.02 | 0.169642 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2399.09 | −0.173094 | −0.0865471 | − | 0.996248i | \(-0.527583\pi\) | ||||
−0.0865471 | + | 0.996248i | \(0.527583\pi\) | |||||||
\(578\) | −742.055 | −0.0534004 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4525.52 | −0.323986 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24127.0 | −1.71396 | ||||||||
\(584\) | −10078.9 | −0.714155 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3286.42 | 0.231674 | ||||||||
\(587\) | −10345.7 | −0.727451 | −0.363725 | − | 0.931506i | \(-0.618495\pi\) | ||||
−0.363725 | + | 0.931506i | \(0.618495\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21102.7 | −1.47627 | ||||||||
\(590\) | 404.511 | 0.0282262 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −213.757 | −0.0148401 | ||||||||
\(593\) | −3622.84 | −0.250881 | −0.125440 | − | 0.992101i | \(-0.540034\pi\) | ||||
−0.125440 | + | 0.992101i | \(0.540034\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 23346.9 | 1.60457 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1974.42 | 0.135017 | ||||||||
\(599\) | −1509.74 | −0.102982 | −0.0514910 | − | 0.998673i | \(-0.516397\pi\) | ||||
−0.0514910 | + | 0.998673i | \(0.516397\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10522.7 | −0.714194 | −0.357097 | − | 0.934067i | \(-0.616233\pi\) | ||||
−0.357097 | + | 0.934067i | \(0.616233\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7014.80 | −0.472563 | ||||||||
\(605\) | 5321.34 | 0.357592 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15525.1 | −1.03813 | −0.519065 | − | 0.854735i | \(-0.673720\pi\) | ||||
−0.519065 | + | 0.854735i | \(0.673720\pi\) | |||||||
\(608\) | 12472.4 | 0.831946 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 512.223 | 0.0339989 | ||||||||
\(611\) | −18482.9 | −1.22380 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10339.1 | −0.681227 | −0.340614 | − | 0.940203i | \(-0.610635\pi\) | ||||
−0.340614 | + | 0.940203i | \(0.610635\pi\) | |||||||
\(614\) | −497.704 | −0.0327129 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12652.5 | −0.825562 | −0.412781 | − | 0.910830i | \(-0.635442\pi\) | ||||
−0.412781 | + | 0.910830i | \(0.635442\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4188.31 | −0.271959 | −0.135979 | − | 0.990712i | \(-0.543418\pi\) | ||||
−0.135979 | + | 0.990712i | \(0.543418\pi\) | |||||||
\(620\) | 6292.74 | 0.407617 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3739.37 | 0.241053 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 1239.27 | 0.0791235 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10716.6 | −0.680956 | ||||||||
\(629\) | −220.171 | −0.0139568 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12886.7 | −0.813016 | −0.406508 | − | 0.913647i | \(-0.633254\pi\) | ||||
−0.406508 | + | 0.913647i | \(0.633254\pi\) | |||||||
\(632\) | −3150.59 | −0.198297 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4867.26 | −0.304896 | ||||||||
\(635\) | 4863.39 | 0.303933 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3014.31 | 0.187050 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4926.95 | −0.304304 | ||||||||
\(641\) | 23195.4 | 1.42927 | 0.714635 | − | 0.699498i | \(-0.246593\pi\) | ||||
0.714635 | + | 0.699498i | \(0.246593\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9691.46 | −0.594391 | −0.297196 | − | 0.954817i | \(-0.596051\pi\) | ||||
−0.297196 | + | 0.954817i | \(0.596051\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4027.56 | 0.245298 | ||||||||
\(647\) | −15711.6 | −0.954694 | −0.477347 | − | 0.878715i | \(-0.658401\pi\) | ||||
−0.477347 | + | 0.878715i | \(0.658401\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7533.48 | 0.455647 | ||||||||
\(650\) | 527.577 | 0.0318358 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20370.3 | 1.22356 | ||||||||
\(653\) | −5596.58 | −0.335392 | −0.167696 | − | 0.985839i | \(-0.553633\pi\) | ||||
−0.167696 | + | 0.985839i | \(0.553633\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −655.876 | −0.0391255 | ||||||||
\(656\) | −12800.0 | −0.761824 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −490.979 | −0.0290225 | −0.0145112 | − | 0.999895i | \(-0.504619\pi\) | ||||
−0.0145112 | + | 0.999895i | \(0.504619\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26400.3 | 1.55348 | 0.776741 | − | 0.629820i | \(-0.216872\pi\) | ||||
0.776741 | + | 0.629820i | \(0.216872\pi\) | |||||||
\(662\) | 5604.98 | 0.329069 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2328.56 | 0.136093 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10963.9 | 0.636466 | ||||||||
\(668\) | −19506.7 | −1.12984 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1753.04 | 0.101083 | ||||||||
\(671\) | 9539.48 | 0.548834 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22727.4 | −1.30175 | −0.650875 | − | 0.759185i | \(-0.725598\pi\) | ||||
−0.650875 | + | 0.759185i | \(0.725598\pi\) | |||||||
\(674\) | −455.012 | −0.0260036 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4517.15 | 0.257007 | ||||||||
\(677\) | 26717.2 | 1.51673 | 0.758365 | − | 0.651830i | \(-0.225999\pi\) | ||||
0.758365 | + | 0.651830i | \(0.225999\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2444.96 | −0.137882 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4191.41 | −0.235333 | ||||||||
\(683\) | 19578.8 | 1.09687 | 0.548433 | − | 0.836194i | \(-0.315224\pi\) | ||||
0.548433 | + | 0.836194i | \(0.315224\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10803.9 | 0.602624 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3577.50 | −0.198243 | ||||||||
\(689\) | −19793.9 | −1.09447 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13856.7 | −0.762854 | −0.381427 | − | 0.924399i | \(-0.624567\pi\) | ||||
−0.381427 | + | 0.924399i | \(0.624567\pi\) | |||||||
\(692\) | 5019.47 | 0.275740 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4291.24 | −0.234717 | ||||||||
\(695\) | 8959.77 | 0.489012 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13184.1 | −0.716475 | ||||||||
\(698\) | −3272.97 | −0.177484 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28106.3 | −1.51435 | −0.757176 | − | 0.653210i | \(-0.773422\pi\) | ||||
−0.757176 | + | 0.653210i | \(0.773422\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −481.896 | −0.0258535 | ||||||||
\(704\) | −20014.9 | −1.07151 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5845.18 | 0.311595 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15866.5 | −0.840449 | −0.420225 | − | 0.907420i | \(-0.638049\pi\) | ||||
−0.420225 | + | 0.907420i | \(0.638049\pi\) | |||||||
\(710\) | −675.220 | −0.0356909 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7654.60 | 0.402905 | ||||||||
\(713\) | −15245.3 | −0.800758 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9825.43 | 0.513916 | ||||||||
\(716\) | 26526.1 | 1.38453 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1767.25 | 0.0918569 | ||||||||
\(719\) | 9593.84 | 0.497621 | 0.248811 | − | 0.968552i | \(-0.419960\pi\) | ||||
0.248811 | + | 0.968552i | \(0.419960\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5210.28 | 0.268568 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9169.67 | −0.470702 | ||||||||
\(725\) | 2929.61 | 0.150073 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29844.5 | 1.52252 | 0.761259 | − | 0.648448i | \(-0.224581\pi\) | ||||
0.761259 | + | 0.648448i | \(0.224581\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3204.98 | 0.162495 | ||||||||
\(731\) | −3684.85 | −0.186442 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26065.3 | 1.31343 | 0.656714 | − | 0.754139i | \(-0.271946\pi\) | ||||
0.656714 | + | 0.754139i | \(0.271946\pi\) | |||||||
\(734\) | −760.623 | −0.0382495 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9010.49 | 0.451265 | ||||||||
\(737\) | 32648.1 | 1.63176 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11751.1 | 0.584941 | 0.292470 | − | 0.956275i | \(-0.405523\pi\) | ||||
0.292470 | + | 0.956275i | \(0.405523\pi\) | |||||||
\(740\) | 143.699 | 0.00713851 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31874.5 | 1.57384 | 0.786919 | − | 0.617057i | \(-0.211675\pi\) | ||||
0.786919 | + | 0.617057i | \(0.211675\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15113.7 | −0.743252 | ||||||||
\(746\) | −6894.39 | −0.338367 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −22367.1 | −1.09335 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12981.1 | −0.630741 | −0.315370 | − | 0.948969i | \(-0.602129\pi\) | ||||
−0.315370 | + | 0.948969i | \(0.602129\pi\) | |||||||
\(752\) | −26444.2 | −1.28234 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2472.95 | 0.119442 | ||||||||
\(755\) | 4541.05 | 0.218895 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31766.3 | 1.52518 | 0.762592 | − | 0.646880i | \(-0.223927\pi\) | ||||
0.762592 | + | 0.646880i | \(0.223927\pi\) | |||||||
\(758\) | −2156.06 | −0.103314 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5351.37 | −0.255414 | ||||||||
\(761\) | 21164.7 | 1.00817 | 0.504087 | − | 0.863653i | \(-0.331829\pi\) | ||||
0.504087 | + | 0.863653i | \(0.331829\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1397.19 | 0.0661630 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3874.40 | −0.182752 | ||||||||
\(767\) | 6180.49 | 0.290958 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29643.8 | 1.39009 | 0.695047 | − | 0.718965i | \(-0.255384\pi\) | ||||
0.695047 | + | 0.718965i | \(0.255384\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 23945.5 | 1.11634 | ||||||||
\(773\) | −15627.2 | −0.727128 | −0.363564 | − | 0.931569i | \(-0.618440\pi\) | ||||
−0.363564 | + | 0.931569i | \(0.618440\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4073.62 | −0.188811 | ||||||||
\(776\) | 5245.12 | 0.242640 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4483.05 | 0.206587 | ||||||||
\(779\) | −28856.4 | −1.32720 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12575.1 | −0.576148 | ||||||||
\(782\) | 2909.65 | 0.133055 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6937.44 | 0.315424 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4641.64 | 0.210237 | 0.105118 | − | 0.994460i | \(-0.466478\pi\) | ||||
0.105118 | + | 0.994460i | \(0.466478\pi\) | |||||||
\(788\) | 4724.63 | 0.213589 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1001.86 | 0.0451196 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7826.22 | 0.350463 | ||||||||
\(794\) | 5399.93 | 0.241356 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10715.9 | 0.477153 | ||||||||
\(797\) | 4097.25 | 0.182098 | 0.0910489 | − | 0.995846i | \(-0.470978\pi\) | ||||
0.0910489 | + | 0.995846i | \(0.470978\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27237.7 | −1.20601 | ||||||||
\(800\) | 2407.65 | 0.106404 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 133.943 | 0.00589735 | ||||||||
\(803\) | 59688.5 | 2.62311 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3438.64 | −0.150274 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15882.1 | −0.691499 | ||||||||
\(809\) | −36787.7 | −1.59875 | −0.799374 | − | 0.600834i | \(-0.794835\pi\) | ||||
−0.799374 | + | 0.600834i | \(0.794835\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23507.4 | 1.01782 | 0.508912 | − | 0.860819i | \(-0.330048\pi\) | ||||
0.508912 | + | 0.860819i | \(0.330048\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −95.7139 | −0.00412134 | ||||||||
\(815\) | −13186.7 | −0.566762 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8065.15 | −0.345366 | ||||||||
\(818\) | −3568.77 | −0.152542 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8604.89 | 0.366458 | ||||||||
\(821\) | −34565.8 | −1.46937 | −0.734686 | − | 0.678407i | \(-0.762670\pi\) | ||||
−0.734686 | + | 0.678407i | \(0.762670\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26917.7 | 1.14009 | 0.570044 | − | 0.821614i | \(-0.306926\pi\) | ||||
0.570044 | + | 0.821614i | \(0.306926\pi\) | |||||||
\(824\) | 10830.7 | 0.457896 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35448.4 | −1.49052 | −0.745261 | − | 0.666773i | \(-0.767675\pi\) | ||||
−0.745261 | + | 0.666773i | \(0.767675\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24726.0 | 1.03591 | 0.517955 | − | 0.855408i | \(-0.326694\pi\) | ||||
0.517955 | + | 0.855408i | \(0.326694\pi\) | |||||||
\(830\) | −740.459 | −0.0309659 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −16420.3 | −0.684220 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12627.7 | 0.523352 | ||||||||
\(836\) | −48955.6 | −2.02532 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1428.26 | 0.0588764 | ||||||||
\(839\) | −21114.3 | −0.868829 | −0.434415 | − | 0.900713i | \(-0.643045\pi\) | ||||
−0.434415 | + | 0.900713i | \(0.643045\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10656.8 | −0.436952 | ||||||||
\(842\) | −1816.15 | −0.0743332 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10932.9 | 0.445883 | ||||||||
\(845\) | −2924.19 | −0.119048 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −28319.8 | −1.14682 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 777.474 | 0.0313731 | ||||||||
\(851\) | −348.138 | −0.0140235 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19801.4 | −0.794828 | −0.397414 | − | 0.917640i | \(-0.630092\pi\) | ||||
−0.397414 | + | 0.917640i | \(0.630092\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15426.9 | −0.615982 | ||||||||
\(857\) | 13201.0 | 0.526180 | 0.263090 | − | 0.964771i | \(-0.415258\pi\) | ||||
0.263090 | + | 0.964771i | \(0.415258\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43020.3 | 1.70877 | 0.854385 | − | 0.519641i | \(-0.173934\pi\) | ||||
0.854385 | + | 0.519641i | \(0.173934\pi\) | |||||||
\(860\) | 2405.00 | 0.0953602 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2803.44 | 0.110772 | ||||||||
\(863\) | 6633.09 | 0.261637 | 0.130819 | − | 0.991406i | \(-0.458239\pi\) | ||||
0.130819 | + | 0.991406i | \(0.458239\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3249.37 | −0.127725 | ||||||||
\(866\) | 7375.16 | 0.289397 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18658.2 | 0.728351 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26784.6 | 1.04198 | ||||||||
\(872\) | 5363.52 | 0.208293 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6368.44 | 0.246471 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41119.1 | 1.58323 | 0.791616 | − | 0.611019i | \(-0.209240\pi\) | ||||
0.791616 | + | 0.611019i | \(0.209240\pi\) | |||||||
\(878\) | −6915.62 | −0.265821 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 14057.6 | 0.538502 | ||||||||
\(881\) | −37501.8 | −1.43413 | −0.717064 | − | 0.697007i | \(-0.754515\pi\) | ||||
−0.717064 | + | 0.697007i | \(0.754515\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10396.0 | −0.396208 | −0.198104 | − | 0.980181i | \(-0.563478\pi\) | ||||
−0.198104 | + | 0.980181i | \(0.563478\pi\) | |||||||
\(884\) | −18350.1 | −0.698166 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7843.25 | 0.297403 | ||||||||
\(887\) | 42954.0 | 1.62599 | 0.812996 | − | 0.582270i | \(-0.197835\pi\) | ||||
0.812996 | + | 0.582270i | \(0.197835\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2434.09 | −0.0916750 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 32546.0 | 1.22166 | ||||||||
\(893\) | −59616.0 | −2.23401 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17171.7 | −0.641327 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 336.781 | 0.0125151 | ||||||||
\(899\) | −19094.6 | −0.708388 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29169.6 | −1.07856 | ||||||||
\(902\) | −5731.46 | −0.211571 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7089.23 | −0.260823 | ||||||||
\(905\) | 5936.02 | 0.218033 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45162.6 | −1.65336 | −0.826681 | − | 0.562670i | \(-0.809774\pi\) | ||||
−0.826681 | + | 0.562670i | \(0.809774\pi\) | |||||||
\(908\) | −47735.3 | −1.74466 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40669.4 | 1.47908 | 0.739538 | − | 0.673115i | \(-0.235044\pi\) | ||||
0.739538 | + | 0.673115i | \(0.235044\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13790.1 | −0.499873 | ||||||||
\(914\) | 7604.67 | 0.275208 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9244.02 | 0.333440 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50310.3 | −1.80586 | −0.902930 | − | 0.429788i | \(-0.858588\pi\) | ||||
−0.902930 | + | 0.429788i | \(0.858588\pi\) | |||||||
\(920\) | −3866.01 | −0.138542 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5400.81 | −0.192914 | ||||||||
\(923\) | −10316.6 | −0.367905 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −93.0243 | −0.00330662 | ||||||||
\(926\) | 2331.37 | 0.0827360 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 11285.6 | 0.399210 | ||||||||
\(929\) | 24058.7 | 0.849668 | 0.424834 | − | 0.905271i | \(-0.360332\pi\) | ||||
0.424834 | + | 0.905271i | \(0.360332\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7162.07 | −0.251718 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6784.93 | −0.237698 | ||||||||
\(935\) | 14479.4 | 0.506447 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11252.2 | −0.392310 | −0.196155 | − | 0.980573i | \(-0.562846\pi\) | ||||
−0.196155 | + | 0.980573i | \(0.562846\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 17777.3 | 0.616841 | ||||||||
\(941\) | −40002.5 | −1.38581 | −0.692903 | − | 0.721030i | \(-0.743669\pi\) | ||||
−0.692903 | + | 0.721030i | \(0.743669\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20846.9 | −0.719902 | ||||||||
\(944\) | 8842.66 | 0.304877 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1601.90 | −0.0550552 | ||||||||
\(947\) | 42875.0 | 1.47123 | 0.735613 | − | 0.677402i | \(-0.236894\pi\) | ||||
0.735613 | + | 0.677402i | \(0.236894\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 48968.6 | 1.67501 | ||||||||
\(950\) | 1701.68 | 0.0581156 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7241.41 | 0.246141 | 0.123070 | − | 0.992398i | \(-0.460726\pi\) | ||||
0.123070 | + | 0.992398i | \(0.460726\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −904.474 | −0.0306472 | ||||||||
\(956\) | 26489.2 | 0.896151 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8211.06 | 0.276918 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3239.93 | −0.108755 | ||||||||
\(962\) | −78.5240 | −0.00263172 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −36677.7 | −1.22543 | ||||||||
\(965\) | −15501.2 | −0.517099 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32573.3 | 1.08323 | 0.541617 | − | 0.840625i | \(-0.317812\pi\) | ||||
0.541617 | + | 0.840625i | \(0.317812\pi\) | |||||||
\(968\) | −8795.27 | −0.292036 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1667.90 | −0.0552092 | ||||||||
\(971\) | −1233.95 | −0.0407820 | −0.0203910 | − | 0.999792i | \(-0.506491\pi\) | ||||
−0.0203910 | + | 0.999792i | \(0.506491\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4108.52 | 0.135159 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11197.3 | 0.367229 | ||||||||
\(977\) | 35891.5 | 1.17530 | 0.587651 | − | 0.809115i | \(-0.300053\pi\) | ||||
0.587651 | + | 0.809115i | \(0.300053\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −45331.6 | −1.47988 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 555.713 | 0.0180586 | ||||||||
\(983\) | −26119.1 | −0.847476 | −0.423738 | − | 0.905785i | \(-0.639282\pi\) | ||||
−0.423738 | + | 0.905785i | \(0.639282\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3058.51 | −0.0989361 | ||||||||
\(986\) | 3644.31 | 0.117706 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −40163.3 | −1.29329 | ||||||||
\(989\) | −5826.53 | −0.187334 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7910.14 | −0.253556 | −0.126778 | − | 0.991931i | \(-0.540464\pi\) | ||||
−0.126778 | + | 0.991931i | \(0.540464\pi\) | |||||||
\(992\) | −15692.6 | −0.502259 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6936.95 | −0.221021 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22952.3 | −0.729094 | −0.364547 | − | 0.931185i | \(-0.618776\pi\) | ||||
−0.364547 | + | 0.931185i | \(0.618776\pi\) | |||||||
\(998\) | −2330.60 | −0.0739215 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2205.4.a.by.1.4 | yes | 6 | |
3.2 | odd | 2 | 2205.4.a.bx.1.3 | ✓ | 6 | ||
7.6 | odd | 2 | 2205.4.a.bx.1.4 | yes | 6 | ||
21.20 | even | 2 | inner | 2205.4.a.by.1.3 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2205.4.a.bx.1.3 | ✓ | 6 | 3.2 | odd | 2 | ||
2205.4.a.bx.1.4 | yes | 6 | 7.6 | odd | 2 | ||
2205.4.a.by.1.3 | yes | 6 | 21.20 | even | 2 | inner | |
2205.4.a.by.1.4 | yes | 6 | 1.1 | even | 1 | trivial |