Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,4,Mod(1,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.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: | \(108.563514411\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 80x^{3} + 121x^{2} + 1212x + 1044 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 460) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-7.88744\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1 |
$q$-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 | ||||||||
\(3\) | 8.88744 | 1.71039 | 0.855194 | − | 0.518307i | \(-0.173438\pi\) | ||||
0.855194 | + | 0.518307i | \(0.173438\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 15.9808 | 0.862884 | 0.431442 | − | 0.902141i | \(-0.358005\pi\) | ||||
0.431442 | + | 0.902141i | \(0.358005\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 51.9866 | 1.92543 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9.63486 | −0.264093 | −0.132046 | − | 0.991244i | \(-0.542155\pi\) | ||||
−0.132046 | + | 0.991244i | \(0.542155\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 42.2114 | 0.900565 | 0.450282 | − | 0.892886i | \(-0.351323\pi\) | ||||
0.450282 | + | 0.892886i | \(0.351323\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −44.4372 | −0.764909 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 40.5247 | 0.578158 | 0.289079 | − | 0.957305i | \(-0.406651\pi\) | ||||
0.289079 | + | 0.957305i | \(0.406651\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −18.3222 | −0.221232 | −0.110616 | − | 0.993863i | \(-0.535282\pi\) | ||||
−0.110616 | + | 0.993863i | \(0.535282\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 142.029 | 1.47587 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 222.067 | 1.58284 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 31.6437 | 0.202624 | 0.101312 | − | 0.994855i | \(-0.467696\pi\) | ||||
0.101312 | + | 0.994855i | \(0.467696\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −63.3450 | −0.367003 | −0.183502 | − | 0.983019i | \(-0.558743\pi\) | ||||
−0.183502 | + | 0.983019i | \(0.558743\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −85.6293 | −0.451701 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −79.9042 | −0.385894 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −30.9604 | −0.137564 | −0.0687819 | − | 0.997632i | \(-0.521911\pi\) | ||||
−0.0687819 | + | 0.997632i | \(0.521911\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 375.151 | 1.54032 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 203.566 | 0.775407 | 0.387704 | − | 0.921784i | \(-0.373268\pi\) | ||||
0.387704 | + | 0.921784i | \(0.373268\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 170.854 | 0.605929 | 0.302964 | − | 0.953002i | \(-0.402024\pi\) | ||||
0.302964 | + | 0.953002i | \(0.402024\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −259.933 | −0.861078 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 505.645 | 1.56927 | 0.784637 | − | 0.619955i | \(-0.212849\pi\) | ||||
0.784637 | + | 0.619955i | \(0.212849\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −87.6127 | −0.255431 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 360.161 | 0.988875 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −224.035 | −0.580632 | −0.290316 | − | 0.956931i | \(-0.593760\pi\) | ||||
−0.290316 | + | 0.956931i | \(0.593760\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 48.1743 | 0.118106 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −162.838 | −0.378393 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −263.713 | −0.581906 | −0.290953 | − | 0.956737i | \(-0.593972\pi\) | ||||
−0.290953 | + | 0.956737i | \(0.593972\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 501.998 | 1.05368 | 0.526838 | − | 0.849966i | \(-0.323377\pi\) | ||||
0.526838 | + | 0.849966i | \(0.323377\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 830.789 | 1.66142 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −211.057 | −0.402745 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 184.030 | 0.335565 | 0.167783 | − | 0.985824i | \(-0.446339\pi\) | ||||
0.167783 | + | 0.985824i | \(0.446339\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 204.411 | 0.356641 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −109.717 | −0.183395 | −0.0916976 | − | 0.995787i | \(-0.529229\pi\) | ||||
−0.0916976 | + | 0.995787i | \(0.529229\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −679.979 | −1.09021 | −0.545107 | − | 0.838367i | \(-0.683511\pi\) | ||||
−0.545107 | + | 0.838367i | \(0.683511\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 222.186 | 0.342078 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −153.973 | −0.227882 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 331.528 | 0.472150 | 0.236075 | − | 0.971735i | \(-0.424139\pi\) | ||||
0.236075 | + | 0.971735i | \(0.424139\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 569.968 | 0.781849 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1305.31 | 1.72622 | 0.863108 | − | 0.505019i | \(-0.168515\pi\) | ||||
0.863108 | + | 0.505019i | \(0.168515\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −202.624 | −0.258560 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 281.231 | 0.346565 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 122.494 | 0.145891 | 0.0729456 | − | 0.997336i | \(-0.476760\pi\) | ||||
0.0729456 | + | 0.997336i | \(0.476760\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 674.574 | 0.777083 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −562.975 | −0.627718 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 91.6111 | 0.0989379 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −220.692 | −0.231009 | −0.115504 | − | 0.993307i | \(-0.536848\pi\) | ||||
−0.115504 | + | 0.993307i | \(0.536848\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −500.884 | −0.508492 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −258.949 | −0.255113 | −0.127557 | − | 0.991831i | \(-0.540713\pi\) | ||||
−0.127557 | + | 0.991831i | \(0.540713\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1028.64 | 0.984032 | 0.492016 | − | 0.870586i | \(-0.336260\pi\) | ||||
0.492016 | + | 0.870586i | \(0.336260\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −710.144 | −0.660028 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1855.11 | −1.67608 | −0.838038 | − | 0.545612i | \(-0.816297\pi\) | ||||
−0.838038 | + | 0.545612i | \(0.816297\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 628.684 | 0.552450 | 0.276225 | − | 0.961093i | \(-0.410917\pi\) | ||||
0.276225 | + | 0.961093i | \(0.410917\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −275.159 | −0.235288 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −816.227 | −0.679506 | −0.339753 | − | 0.940515i | \(-0.610344\pi\) | ||||
−0.339753 | + | 0.940515i | \(0.610344\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −115.000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2194.43 | 1.73397 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 647.619 | 0.498884 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1238.17 | −0.930255 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1809.18 | 1.32625 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2264.62 | −1.58230 | −0.791150 | − | 0.611622i | \(-0.790518\pi\) | ||||
−0.791150 | + | 0.611622i | \(0.790518\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1518.45 | 1.03637 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1411.42 | 0.941347 | 0.470674 | − | 0.882307i | \(-0.344011\pi\) | ||||
0.470674 | + | 0.882307i | \(0.344011\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −292.805 | −0.190898 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1110.33 | −0.707869 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 835.349 | 0.520939 | 0.260470 | − | 0.965482i | \(-0.416123\pi\) | ||||
0.260470 | + | 0.965482i | \(0.416123\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −277.196 | −0.169147 | −0.0845735 | − | 0.996417i | \(-0.526953\pi\) | ||||
−0.0845735 | + | 0.996417i | \(0.526953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4493.89 | 2.68407 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −406.701 | −0.237833 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −158.218 | −0.0906161 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −778.653 | −0.436886 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1137.79 | 0.625582 | 0.312791 | − | 0.949822i | \(-0.398736\pi\) | ||||
0.312791 | + | 0.949822i | \(0.398736\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −414.752 | −0.223524 | −0.111762 | − | 0.993735i | \(-0.535649\pi\) | ||||
−0.111762 | + | 0.993735i | \(0.535649\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2106.74 | 1.11320 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 316.725 | 0.164129 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3545.22 | 1.80216 | 0.901080 | − | 0.433653i | \(-0.142776\pi\) | ||||
0.901080 | + | 0.433653i | \(0.142776\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1991.09 | −0.993107 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 367.559 | 0.179924 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1942.88 | 0.933609 | 0.466805 | − | 0.884360i | \(-0.345405\pi\) | ||||
0.466805 | + | 0.884360i | \(0.345405\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 428.146 | 0.202007 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2696.57 | 1.24950 | 0.624750 | − | 0.780825i | \(-0.285201\pi\) | ||||
0.624750 | + | 0.780825i | \(0.285201\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −415.196 | −0.188983 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −952.510 | −0.425967 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3656.58 | 1.60697 | 0.803483 | − | 0.595328i | \(-0.202978\pi\) | ||||
0.803483 | + | 0.595328i | \(0.202978\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 399.521 | 0.172577 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2343.73 | −0.995285 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1984.62 | 0.828701 | 0.414351 | − | 0.910117i | \(-0.364009\pi\) | ||||
0.414351 | + | 0.910117i | \(0.364009\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2426.26 | 0.996365 | 0.498183 | − | 0.867072i | \(-0.334001\pi\) | ||||
0.498183 | + | 0.867072i | \(0.334001\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4461.48 | 1.80220 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 154.802 | 0.0615204 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −390.450 | −0.152687 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3548.82 | 1.36581 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4350.91 | 1.64828 | 0.824139 | − | 0.566387i | \(-0.191659\pi\) | ||||
0.824139 | + | 0.566387i | \(0.191659\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2425.67 | −0.904680 | −0.452340 | − | 0.891846i | \(-0.649411\pi\) | ||||
−0.452340 | + | 0.891846i | \(0.649411\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1875.76 | −0.688850 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4818.67 | −1.74272 | −0.871360 | − | 0.490644i | \(-0.836761\pi\) | ||||
−0.871360 | + | 0.490644i | \(0.836761\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1679.82 | −0.598390 | −0.299195 | − | 0.954192i | \(-0.596718\pi\) | ||||
−0.299195 | + | 0.954192i | \(0.596718\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1635.56 | 0.573947 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 505.693 | 0.174841 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1017.83 | −0.346773 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1195.69 | 0.401480 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 176.532 | 0.0584258 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 583.138 | 0.190260 | 0.0951301 | − | 0.995465i | \(-0.469673\pi\) | ||||
0.0951301 | + | 0.995465i | \(0.469673\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −975.107 | −0.313677 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −854.268 | −0.270980 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1012.31 | −0.316681 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6043.28 | −1.86469 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1710.61 | 0.520669 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3083.05 | 0.925814 | 0.462907 | − | 0.886407i | \(-0.346806\pi\) | ||||
0.462907 | + | 0.886407i | \(0.346806\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1299.66 | 0.385086 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −682.335 | −0.199507 | −0.0997537 | − | 0.995012i | \(-0.531805\pi\) | ||||
−0.0997537 | + | 0.995012i | \(0.531805\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4400.81 | −1.26993 | −0.634964 | − | 0.772541i | \(-0.718985\pi\) | ||||
−0.634964 | + | 0.772541i | \(0.718985\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1368.43 | −0.389766 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3391.37 | −0.953545 | −0.476772 | − | 0.879027i | \(-0.658193\pi\) | ||||
−0.476772 | + | 0.879027i | \(0.658193\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2528.22 | −0.701801 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2946.44 | 0.807560 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 750.785 | 0.203198 | 0.101599 | − | 0.994825i | \(-0.467604\pi\) | ||||
0.101599 | + | 0.994825i | \(0.467604\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −349.695 | −0.0934682 | −0.0467341 | − | 0.998907i | \(-0.514881\pi\) | ||||
−0.0467341 | + | 0.998907i | \(0.514881\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −930.249 | −0.245578 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 438.064 | 0.114232 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −773.407 | −0.199234 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11600.8 | 2.95250 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2597.01 | 0.653074 | 0.326537 | − | 0.945184i | \(-0.394118\pi\) | ||||
0.326537 | + | 0.945184i | \(0.394118\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −221.602 | −0.0550672 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1800.81 | −0.442238 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −221.689 | −0.0538077 | −0.0269039 | − | 0.999638i | \(-0.508565\pi\) | ||||
−0.0269039 | + | 0.999638i | \(0.508565\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −494.773 | −0.118702 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1645.05 | 0.390138 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2779.66 | 0.651716 | 0.325858 | − | 0.945419i | \(-0.394347\pi\) | ||||
0.325858 | + | 0.945419i | \(0.394347\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1120.17 | 0.259667 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1088.66 | 0.249531 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4836.46 | −1.09622 | −0.548112 | − | 0.836405i | \(-0.684653\pi\) | ||||
−0.548112 | + | 0.836405i | \(0.684653\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2166.54 | −0.485637 | −0.242819 | − | 0.970072i | \(-0.578072\pi\) | ||||
−0.242819 | + | 0.970072i | \(0.578072\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5995.24 | 1.32911 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −240.872 | −0.0528186 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5271.29 | −1.14340 | −0.571699 | − | 0.820463i | \(-0.693716\pi\) | ||||
−0.571699 | + | 0.820463i | \(0.693716\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3293.09 | −0.706639 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4213.36 | −0.894476 | −0.447238 | − | 0.894415i | \(-0.647592\pi\) | ||||
−0.447238 | + | 0.894415i | \(0.647592\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6015.10 | −1.26346 | −0.631732 | − | 0.775187i | \(-0.717656\pi\) | ||||
−0.631732 | + | 0.775187i | \(0.717656\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 814.189 | 0.169222 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3253.16 | 0.669087 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3270.75 | −0.665733 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1961.39 | −0.395115 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1705.88 | 0.340131 | 0.170065 | − | 0.985433i | \(-0.445602\pi\) | ||||
0.170065 | + | 0.985433i | \(0.445602\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1318.56 | 0.260236 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2139.58 | −0.418018 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 970.863 | 0.187781 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2730.38 | 0.522846 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2301.40 | −0.436342 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2509.99 | −0.471218 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7171.22 | −1.33317 | −0.666585 | − | 0.745429i | \(-0.732245\pi\) | ||||
−0.666585 | + | 0.745429i | \(0.732245\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9142.01 | 1.68308 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6909.11 | 1.25974 | 0.629871 | − | 0.776700i | \(-0.283108\pi\) | ||||
0.629871 | + | 0.776700i | \(0.283108\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2726.24 | −0.492320 | −0.246160 | − | 0.969229i | \(-0.579169\pi\) | ||||
−0.246160 | + | 0.969229i | \(0.579169\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4153.95 | −0.743011 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10048.4 | −1.78036 | −0.890181 | − | 0.455607i | \(-0.849422\pi\) | ||||
−0.890181 | + | 0.455607i | \(0.849422\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −304.883 | −0.0535115 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16487.2 | −2.86674 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −742.503 | −0.127907 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1055.29 | 0.180113 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5587.39 | 0.944904 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8080.63 | 1.35410 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2907.79 | 0.482859 | 0.241430 | − | 0.970418i | \(-0.422384\pi\) | ||||
0.241430 | + | 0.970418i | \(0.422384\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1609.53 | −0.264869 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −920.151 | −0.150069 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1439.69 | 0.232715 | 0.116358 | − | 0.993207i | \(-0.462878\pi\) | ||||
0.116358 | + | 0.993207i | \(0.462878\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7254.17 | −1.16222 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 610.321 | 0.0969229 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6881.55 | −1.08329 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1022.06 | −0.159495 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5642.54 | −0.872933 | −0.436466 | − | 0.899721i | \(-0.643770\pi\) | ||||
−0.436466 | + | 0.899721i | \(0.643770\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8114.51 | 1.24458 | 0.622292 | − | 0.782785i | \(-0.286202\pi\) | ||||
0.622292 | + | 0.782785i | \(0.286202\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9373.76 | 1.42545 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2256.43 | 0.340220 | 0.170110 | − | 0.985425i | \(-0.445588\pi\) | ||||
0.170110 | + | 0.985425i | \(0.445588\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 548.587 | 0.0820168 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5755.68 | 0.853285 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12942.1 | 1.90266 | 0.951332 | − | 0.308169i | \(-0.0997162\pi\) | ||||
0.951332 | + | 0.308169i | \(0.0997162\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6523.30 | −0.951056 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11004.2 | −1.59110 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3399.90 | 0.487558 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3183.88 | −0.452854 | −0.226427 | − | 0.974028i | \(-0.572704\pi\) | ||||
−0.226427 | + | 0.974028i | \(0.572704\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10582.7 | 1.49299 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3580.26 | −0.501019 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9005.13 | −1.25005 | −0.625024 | − | 0.780606i | \(-0.714911\pi\) | ||||
−0.625024 | + | 0.780606i | \(0.714911\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1110.93 | −0.152982 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1335.73 | 0.182476 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8772.11 | 1.18890 | 0.594450 | − | 0.804133i | \(-0.297370\pi\) | ||||
0.594450 | + | 0.804133i | \(0.297370\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20126.6 | −2.70635 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 746.557 | 0.0996013 | 0.0498006 | − | 0.998759i | \(-0.484141\pi\) | ||||
0.0498006 | + | 0.998759i | \(0.484141\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 769.866 | 0.101912 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8882.10 | 1.16667 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6657.68 | 0.867757 | 0.433879 | − | 0.900971i | \(-0.357145\pi\) | ||||
0.433879 | + | 0.900971i | \(0.357145\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 932.069 | 0.120554 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12543.9 | 1.61007 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1657.64 | −0.211152 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3734.41 | 0.472102 | 0.236051 | − | 0.971741i | \(-0.424147\pi\) | ||||
0.236051 | + | 0.971741i | \(0.424147\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2602.28 | −0.326509 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11824.3 | −1.47251 | −0.736253 | − | 0.676706i | \(-0.763407\pi\) | ||||
−0.736253 | + | 0.676706i | \(0.763407\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2673.88 | −0.330510 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2849.84 | −0.349654 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 298.299 | 0.0363296 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9697.52 | 1.17240 | 0.586200 | − | 0.810166i | \(-0.300623\pi\) | ||||
0.586200 | + | 0.810166i | \(0.300623\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7424.11 | 0.891008 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4214.35 | −0.502118 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6526.53 | −0.771987 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2463.56 | −0.289307 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9358.00 | 1.09109 | 0.545547 | − | 0.838080i | \(-0.316322\pi\) | ||||
0.545547 | + | 0.838080i | \(0.316322\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1372.14 | 0.158846 | 0.0794228 | − | 0.996841i | \(-0.474692\pi\) | ||||
0.0794228 | + | 0.996841i | \(0.474692\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 26286.8 | 3.02153 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1013.12 | 0.115632 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8022.35 | 0.909201 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3614.53 | −0.406786 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1101.08 | −0.123056 | −0.0615279 | − | 0.998105i | \(-0.519597\pi\) | ||||
−0.0615279 | + | 0.998105i | \(0.519597\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7940.12 | −0.881242 | −0.440621 | − | 0.897693i | \(-0.645242\pi\) | ||||
−0.440621 | + | 0.897693i | \(0.645242\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1406.16 | −0.154989 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −421.411 | −0.0461301 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9759.66 | 1.06106 | 0.530528 | − | 0.847668i | \(-0.321994\pi\) | ||||
0.530528 | + | 0.847668i | \(0.321994\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4554.69 | −0.491814 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13742.3 | 1.47385 | 0.736927 | − | 0.675972i | \(-0.236276\pi\) | ||||
0.736927 | + | 0.675972i | \(0.236276\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −612.469 | −0.0652446 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10112.1 | 1.06999 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 930.841 | 0.0978377 | 0.0489188 | − | 0.998803i | \(-0.484422\pi\) | ||||
0.0489188 | + | 0.998803i | \(0.484422\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1961.33 | −0.204779 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3686.09 | −0.382312 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3372.87 | −0.347522 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11416.7 | −1.16861 | −0.584303 | − | 0.811536i | \(-0.698632\pi\) | ||||
−0.584303 | + | 0.811536i | \(0.698632\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8999.20 | 0.915134 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1852.77 | −0.187184 | −0.0935922 | − | 0.995611i | \(-0.529835\pi\) | ||||
−0.0935922 | + | 0.995611i | \(0.529835\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17102.8 | 1.71671 | 0.858353 | − | 0.513060i | \(-0.171488\pi\) | ||||
0.858353 | + | 0.513060i | \(0.171488\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2814.87 | 0.280724 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1986.47 | 0.196837 | 0.0984184 | − | 0.995145i | \(-0.468622\pi\) | ||||
0.0984184 | + | 0.995145i | \(0.468622\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2940.96 | 0.289554 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 31507.9 | 3.08239 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1646.15 | −0.160021 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −458.056 | −0.0442464 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11646.8 | −1.11797 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 333.523 | 0.0318143 | 0.0159072 | − | 0.999873i | \(-0.494936\pi\) | ||||
0.0159072 | + | 0.999873i | \(0.494936\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1306.88 | −0.123885 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3266.66 | 0.307740 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1103.46 | 0.103310 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19465.1 | −1.81118 | −0.905592 | − | 0.424150i | \(-0.860573\pi\) | ||||
−0.905592 | + | 0.424150i | \(0.860573\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17267.3 | 1.59683 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18882.3 | −1.73553 | −0.867764 | − | 0.496976i | \(-0.834444\pi\) | ||||
−0.867764 | + | 0.496976i | \(0.834444\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1282.35 | 0.117149 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2504.42 | 0.227405 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1753.38 | −0.158249 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6415.92 | −0.575583 | −0.287792 | − | 0.957693i | \(-0.592921\pi\) | ||||
−0.287792 | + | 0.957693i | \(0.592921\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23965.6 | 2.13713 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3760.79 | −0.333371 | −0.166685 | − | 0.986010i | \(-0.553306\pi\) | ||||
−0.166685 | + | 0.986010i | \(0.553306\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1294.75 | 0.114090 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3690.03 | −0.323235 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7206.18 | −0.627521 | −0.313760 | − | 0.949502i | \(-0.601589\pi\) | ||||
−0.313760 | + | 0.949502i | \(0.601589\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10866.6 | −0.940728 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4068.76 | −0.350176 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5143.22 | −0.440073 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4871.82 | −0.414434 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 32497.7 | 2.74853 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1295.94 | −0.108976 | −0.0544879 | − | 0.998514i | \(-0.517353\pi\) | ||||
−0.0544879 | + | 0.998514i | \(0.517353\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19924.3 | −1.66583 | −0.832913 | − | 0.553404i | \(-0.813329\pi\) | ||||
−0.832913 | + | 0.553404i | \(0.813329\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3550.72 | 0.295174 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2567.04 | −0.212186 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13709.5 | −1.12042 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8592.81 | 0.698304 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9275.54 | 0.749564 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17638.2 | 1.41740 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 844.137 | 0.0674574 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10543.1 | 0.837866 | 0.418933 | − | 0.908017i | \(-0.362404\pi\) | ||||
0.418933 | + | 0.908017i | \(0.362404\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21563.2 | 1.70417 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3143.42 | −0.247063 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7341.41 | −0.573850 | −0.286925 | − | 0.957953i | \(-0.592633\pi\) | ||||
−0.286925 | + | 0.957953i | \(0.592633\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 26097.2 | 2.02878 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −579.783 | −0.0448268 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5298.10 | 0.407411 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1375.79 | 0.105224 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3231.59 | −0.245829 | −0.122915 | − | 0.992417i | \(-0.539224\pi\) | ||||
−0.122915 | + | 0.992417i | \(0.539224\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7211.97 | 0.545678 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3470.10 | −0.261155 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22615.7 | 1.69296 | 0.846481 | − | 0.532419i | \(-0.178717\pi\) | ||||
0.846481 | + | 0.532419i | \(0.178717\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4081.14 | 0.303884 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9108.57 | 0.674645 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11686.8 | 0.861046 | 0.430523 | − | 0.902580i | \(-0.358329\pi\) | ||||
0.430523 | + | 0.902580i | \(0.358329\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19619.6 | −1.43793 | −0.718963 | − | 0.695048i | \(-0.755383\pi\) | ||||
−0.718963 | + | 0.695048i | \(0.755383\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 38668.5 | 2.81920 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 575.000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11451.6 | 0.826230 | 0.413115 | − | 0.910679i | \(-0.364441\pi\) | ||||
0.413115 | + | 0.910679i | \(0.364441\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21558.0 | −1.54735 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20859.9 | 1.48952 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2158.54 | 0.153341 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10972.1 | −0.775457 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14547.0 | −1.02286 | −0.511430 | − | 0.859325i | \(-0.670884\pi\) | ||||
−0.511430 | + | 0.859325i | \(0.670884\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1160.62 | 0.0811928 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −42825.6 | −2.98073 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −202.333 | −0.0140115 | −0.00700575 | − | 0.999975i | \(-0.502230\pi\) | ||||
−0.00700575 | + | 0.999975i | \(0.502230\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3238.10 | −0.223108 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14929.3 | −1.02348 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4251.93 | 0.290032 | 0.145016 | − | 0.989429i | \(-0.453677\pi\) | ||||
0.145016 | + | 0.989429i | \(0.453677\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4098.39 | 0.278165 | 0.139082 | − | 0.990281i | \(-0.455585\pi\) | ||||
0.139082 | + | 0.990281i | \(0.455585\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9567.11 | 0.646107 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6190.85 | 0.416023 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11481.8 | −0.767765 | −0.383882 | − | 0.923382i | \(-0.625413\pi\) | ||||
−0.383882 | + | 0.923382i | \(0.625413\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4494.32 | 0.299046 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21344.0 | 1.41323 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26833.5 | −1.76802 | −0.884008 | − | 0.467471i | \(-0.845165\pi\) | ||||
−0.884008 | + | 0.467471i | \(0.845165\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9045.91 | −0.593116 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9603.82 | 0.626637 | 0.313319 | − | 0.949648i | \(-0.398559\pi\) | ||||
0.313319 | + | 0.949648i | \(0.398559\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6805.10 | −0.441874 | −0.220937 | − | 0.975288i | \(-0.570912\pi\) | ||||
−0.220937 | + | 0.975288i | \(0.570912\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5107.54 | 0.330046 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1957.55 | 0.125887 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1568.92 | 0.0999308 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1254.66 | −0.0795336 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13205.5 | −0.833126 | −0.416563 | − | 0.909107i | \(-0.636765\pi\) | ||||
−0.416563 | + | 0.909107i | \(0.636765\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5182.61 | 0.325419 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11323.1 | 0.707626 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3698.26 | −0.230032 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5703.83 | −0.353114 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25910.3 | −1.59656 | −0.798280 | − | 0.602286i | \(-0.794257\pi\) | ||||
−0.798280 | + | 0.602286i | \(0.794257\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25201.9 | −1.54567 | −0.772834 | − | 0.634608i | \(-0.781162\pi\) | ||||
−0.772834 | + | 0.634608i | \(0.781162\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7592.26 | −0.463480 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20569.2 | −1.24986 | −0.624929 | − | 0.780681i | \(-0.714872\pi\) | ||||
−0.624929 | + | 0.780681i | \(0.714872\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2540.83 | 0.153677 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8996.81 | −0.541648 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15604.2 | −0.935126 | −0.467563 | − | 0.883960i | \(-0.654868\pi\) | ||||
−0.467563 | + | 0.883960i | \(0.654868\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7057.11 | −0.420983 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −35349.8 | −2.09913 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19937.8 | 1.17855 | 0.589277 | − | 0.807931i | \(-0.299413\pi\) | ||||
0.589277 | + | 0.807931i | \(0.299413\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22533.1 | 1.32592 | 0.662961 | − | 0.748654i | \(-0.269300\pi\) | ||||
0.662961 | + | 0.748654i | \(0.269300\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15202.9 | 0.890546 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1464.02 | 0.0853720 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 727.805 | 0.0422500 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 27400.5 | 1.58350 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4836.68 | −0.278268 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32433.5 | −1.85768 | −0.928842 | − | 0.370477i | \(-0.879194\pi\) | ||||
−0.928842 | + | 0.370477i | \(0.879194\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5551.67 | 0.316569 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3491.22 | 0.198196 | 0.0990979 | − | 0.995078i | \(-0.468404\pi\) | ||||
0.0990979 | + | 0.995078i | \(0.468404\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3526.84 | −0.199334 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6064.21 | −0.341235 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21137.5 | −1.18419 | −0.592096 | − | 0.805868i | \(-0.701699\pi\) | ||||
−0.592096 | + | 0.805868i | \(0.701699\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4176.74 | −0.232971 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −39111.9 | −2.17207 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9456.82 | −0.522897 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16463.1 | 0.906347 | 0.453174 | − | 0.891422i | \(-0.350292\pi\) | ||||
0.453174 | + | 0.891422i | \(0.350292\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8004.54 | −0.438770 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1385.98 | 0.0756448 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8249.46 | 0.448308 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −30140.6 | −1.63093 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13393.8 | −0.721648 | −0.360824 | − | 0.932634i | \(-0.617505\pi\) | ||||
−0.360824 | + | 0.932634i | \(0.617505\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 567.264 | 0.0304335 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −22469.4 | −1.20035 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4138.23 | −0.220133 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17609.5 | 0.932779 | 0.466390 | − | 0.884579i | \(-0.345555\pi\) | ||||
0.466390 | + | 0.884579i | \(0.345555\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17235.0 | 0.909091 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1456.94 | −0.0765255 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2033.51 | 0.106362 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6672.56 | 0.347547 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8610.73 | −0.446629 | −0.223314 | − | 0.974746i | \(-0.571688\pi\) | ||||
−0.223314 | + | 0.974746i | \(0.571688\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16438.6 | 0.849106 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3107.89 | −0.159867 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 791.092 | 0.0405247 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9153.66 | −0.466974 | −0.233487 | − | 0.972360i | \(-0.575014\pi\) | ||||
−0.233487 | + | 0.972360i | \(0.575014\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23656.7 | −1.20188 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6923.80 | 0.350323 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35745.4 | 1.80121 | 0.900604 | − | 0.434642i | \(-0.143125\pi\) | ||||
0.900604 | + | 0.434642i | \(0.143125\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3893.26 | 0.195381 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1773.11 | −0.0886204 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16842.9 | −0.838396 | −0.419198 | − | 0.907895i | \(-0.637689\pi\) | ||||
−0.419198 | + | 0.907895i | \(0.637689\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6873.61 | −0.340767 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6577.22 | −0.324758 | −0.162379 | − | 0.986729i | \(-0.551917\pi\) | ||||
−0.162379 | + | 0.986729i | \(0.551917\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5688.97 | −0.279769 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 67858.4 | 3.32371 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29646.2 | −1.44626 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32188.7 | −1.56403 | −0.782013 | − | 0.623263i | \(-0.785807\pi\) | ||||
−0.782013 | + | 0.623263i | \(0.785807\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23080.8 | 1.11701 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2073.76 | 0.0999628 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16659.1 | 0.799848 | 0.399924 | − | 0.916548i | \(-0.369037\pi\) | ||||
0.399924 | + | 0.916548i | \(0.369037\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1969.47 | −0.0941862 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30186.6 | −1.43793 | −0.718965 | − | 0.695046i | \(-0.755384\pi\) | ||||
−0.718965 | + | 0.695046i | \(0.755384\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10046.9 | 0.476700 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10533.7 | −0.497839 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11131.7 | −0.524044 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27171.2 | −1.27415 | −0.637073 | − | 0.770803i | \(-0.719855\pi\) | ||||
−0.637073 | + | 0.770803i | \(0.719855\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1970.25 | −0.0920321 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36528.6 | −1.69967 | −0.849833 | − | 0.527052i | \(-0.823297\pi\) | ||||
−0.849833 | + | 0.527052i | \(0.823297\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1583.63 | −0.0734006 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4397.27 | −0.203026 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3729.79 | −0.171545 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1057.11 | 0.0484333 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7027.02 | 0.320722 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17726.1 | −0.805951 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3314.84 | 0.150141 | 0.0750706 | − | 0.997178i | \(-0.476082\pi\) | ||||
0.0750706 | + | 0.997178i | \(0.476082\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24704.1 | 1.11469 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13044.0 | −0.586335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21190.0 | 0.948903 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9955.47 | 0.444131 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 526.572 | 0.0234029 | 0.0117015 | − | 0.999932i | \(-0.496275\pi\) | ||||
0.0117015 | + | 0.999932i | \(0.496275\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20491.1 | 0.907289 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6368.04 | 0.280903 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6551.51 | 0.287917 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1837.80 | −0.0804644 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −42983.7 | −1.87497 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23931.8 | −1.04005 | −0.520023 | − | 0.854152i | \(-0.674077\pi\) | ||||
−0.520023 | + | 0.854152i | \(0.674077\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10319.3 | −0.446807 | −0.223404 | − | 0.974726i | \(-0.571717\pi\) | ||||
−0.223404 | + | 0.974726i | \(0.571717\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19255.0 | −0.830628 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9714.41 | −0.417523 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3130.42 | −0.134051 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 35068.8 | 1.49622 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22460.0 | −0.954760 | −0.477380 | − | 0.878697i | \(-0.658414\pi\) | ||||
−0.477380 | + | 0.878697i | \(0.658414\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10598.1 | 0.448880 | 0.224440 | − | 0.974488i | \(-0.427945\pi\) | ||||
0.224440 | + | 0.974488i | \(0.427945\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2140.73 | −0.0903403 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28688.4 | 1.20628 | 0.603139 | − | 0.797636i | \(-0.293916\pi\) | ||||
0.603139 | + | 0.797636i | \(0.293916\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15013.9 | 0.629018 | 0.314509 | − | 0.949255i | \(-0.398160\pi\) | ||||
0.314509 | + | 0.949255i | \(0.398160\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −46848.3 | −1.95566 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3550.48 | −0.147679 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13482.8 | −0.558793 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14066.8 | −0.580909 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18368.8 | −0.755853 | −0.377927 | − | 0.925836i | \(-0.623363\pi\) | ||||
−0.377927 | + | 0.925836i | \(0.623363\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23387.7 | −0.958944 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −37445.9 | −1.52990 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2075.98 | 0.0845159 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19787.0 | −0.802702 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −53458.8 | −2.16102 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −712.089 | −0.0286840 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27876.5 | 1.11896 | 0.559480 | − | 0.828844i | \(-0.311001\pi\) | ||||
0.559480 | + | 0.828844i | \(0.311001\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4762.55 | 0.190498 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41457.7 | 1.65247 | 0.826237 | − | 0.563323i | \(-0.190477\pi\) | ||||
0.826237 | + | 0.563323i | \(0.190477\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10862.0 | 0.431440 | 0.215720 | − | 0.976455i | \(-0.430790\pi\) | ||||
0.215720 | + | 0.976455i | \(0.430790\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 28912.2 | 1.14440 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5007.70 | 0.197525 | 0.0987624 | − | 0.995111i | \(-0.468512\pi\) | ||||
0.0987624 | + | 0.995111i | \(0.468512\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18282.9 | −0.718657 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −29068.6 | −1.13866 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3194.23 | −0.124691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7768.18 | 0.302198 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11473.0 | −0.444791 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1997.61 | −0.0771787 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11303.7 | −0.435231 | −0.217616 | − | 0.976035i | \(-0.569828\pi\) | ||||
−0.217616 | + | 0.976035i | \(0.569828\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15160.9 | 0.581756 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16913.5 | 0.646801 | 0.323401 | − | 0.946262i | \(-0.395174\pi\) | ||||
0.323401 | + | 0.946262i | \(0.395174\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24529.2 | 0.934853 | 0.467426 | − | 0.884032i | \(-0.345181\pi\) | ||||
0.467426 | + | 0.884032i | \(0.345181\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11718.6 | 0.445105 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8626.24 | −0.326540 | −0.163270 | − | 0.986581i | \(-0.552204\pi\) | ||||
−0.163270 | + | 0.986581i | \(0.552204\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36190.5 | −1.36534 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5491.56 | −0.206481 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9264.54 | −0.347174 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9923.10 | −0.370606 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8628.48 | 0.321178 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2004.47 | −0.0743635 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9078.94 | −0.335697 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24266.1 | 0.894270 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12131.3 | −0.445588 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20552.6 | −0.752412 | −0.376206 | − | 0.926536i | \(-0.622771\pi\) | ||||
−0.376206 | + | 0.926536i | \(0.622771\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13461.9 | −0.491202 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20249.3 | −0.736431 | −0.368215 | − | 0.929741i | \(-0.620031\pi\) | ||||
−0.368215 | + | 0.929741i | \(0.620031\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12576.4 | −0.455881 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −22307.4 | −0.805966 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22555.7 | 0.812274 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17245.1 | −0.619003 | −0.309501 | − | 0.950899i | \(-0.600162\pi\) | ||||
−0.309501 | + | 0.950899i | \(0.600162\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −63733.8 | −2.28024 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4631.33 | −0.165159 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −774.010 | −0.0275128 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 53475.7 | 1.89468 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18564.9 | −0.655647 | −0.327823 | − | 0.944739i | \(-0.606315\pi\) | ||||
−0.327823 | + | 0.944739i | \(0.606315\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1605.26 | 0.0565094 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 61404.3 | 2.15465 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1952.25 | 0.0682839 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10059.7 | 0.350733 | 0.175367 | − | 0.984503i | \(-0.443889\pi\) | ||||
0.175367 | + | 0.984503i | \(0.443889\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24229.3 | −0.842059 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11428.2 | −0.395906 | −0.197953 | − | 0.980211i | \(-0.563429\pi\) | ||||
−0.197953 | + | 0.980211i | \(0.563429\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4682.02 | 0.161684 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −17744.1 | −0.610809 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33503.1 | 1.14964 | 0.574818 | − | 0.818281i | \(-0.305073\pi\) | ||||
0.574818 | + | 0.818281i | \(0.305073\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28702.9 | −0.981808 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −89304.6 | −3.04511 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18496.0 | 0.628694 | 0.314347 | − | 0.949308i | \(-0.398214\pi\) | ||||
0.314347 | + | 0.949308i | \(0.398214\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21754.6 | −0.737132 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2709.63 | −0.0915254 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13349.6 | 0.449510 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25778.4 | −0.865309 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −96440.8 | −3.22717 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12128.3 | 0.404585 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2658.65 | −0.0884140 | −0.0442070 | − | 0.999022i | \(-0.514076\pi\) | ||||
−0.0442070 | + | 0.999022i | \(0.514076\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6598.95 | −0.218771 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46521.0 | 1.53752 | 0.768760 | − | 0.639538i | \(-0.220874\pi\) | ||||
0.768760 | + | 0.639538i | \(0.220874\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4429.82 | −0.145954 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9378.79 | 0.308063 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5874.33 | −0.192361 | −0.0961803 | − | 0.995364i | \(-0.530663\pi\) | ||||
−0.0961803 | + | 0.995364i | \(0.530663\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1180.21 | −0.0385288 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 32683.1 | 1.06370 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9002.56 | −0.292103 | −0.146051 | − | 0.989277i | \(-0.546657\pi\) | ||||
−0.146051 | + | 0.989277i | \(0.546657\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24093.3 | 0.779368 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 71816.1 | 2.31604 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3929.63 | 0.126345 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26421.4 | −0.846926 | −0.423463 | − | 0.905913i | \(-0.639186\pi\) | ||||
−0.423463 | + | 0.905913i | \(0.639186\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25842.8 | 0.825877 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8399.12 | 0.267608 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47185.5 | −1.49888 | −0.749438 | − | 0.662074i | \(-0.769676\pi\) | ||||
−0.749438 | + | 0.662074i | \(0.769676\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6875.28 | −0.217742 |
(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 | 1840.4.a.o.1.5 | 5 | ||
4.3 | odd | 2 | 460.4.a.b.1.1 | ✓ | 5 | ||
20.3 | even | 4 | 2300.4.c.d.1749.1 | 10 | |||
20.7 | even | 4 | 2300.4.c.d.1749.10 | 10 | |||
20.19 | odd | 2 | 2300.4.a.c.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.4.a.b.1.1 | ✓ | 5 | 4.3 | odd | 2 | ||
1840.4.a.o.1.5 | 5 | 1.1 | even | 1 | trivial | ||
2300.4.a.c.1.5 | 5 | 20.19 | odd | 2 | |||
2300.4.c.d.1749.1 | 10 | 20.3 | even | 4 | |||
2300.4.c.d.1749.10 | 10 | 20.7 | even | 4 |