Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [688,4,Mod(1,688)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(688, 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("688.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 688 = 2^{4} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 688.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: | \(40.5933140839\) |
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: | \( x^{6} - 32x^{4} - 16x^{3} + 251x^{2} + 276x + 60 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.299707\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 688.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.43046 | −0.275293 | −0.137646 | − | 0.990481i | \(-0.543954\pi\) | ||||
−0.137646 | + | 0.990481i | \(0.543954\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 20.4116 | 1.82567 | 0.912835 | − | 0.408329i | \(-0.133888\pi\) | ||||
0.912835 | + | 0.408329i | \(0.133888\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −29.9522 | −1.61727 | −0.808635 | − | 0.588311i | \(-0.799793\pi\) | ||||
−0.808635 | + | 0.588311i | \(0.799793\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −24.9538 | −0.924214 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 22.8719 | 0.626922 | 0.313461 | − | 0.949601i | \(-0.398512\pi\) | ||||
0.313461 | + | 0.949601i | \(0.398512\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −44.4397 | −0.948104 | −0.474052 | − | 0.880497i | \(-0.657209\pi\) | ||||
−0.474052 | + | 0.880497i | \(0.657209\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −29.1981 | −0.502594 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −13.0970 | −0.186852 | −0.0934260 | − | 0.995626i | \(-0.529782\pi\) | ||||
−0.0934260 | + | 0.995626i | \(0.529782\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.41527 | −0.0653868 | −0.0326934 | − | 0.999465i | \(-0.510408\pi\) | ||||
−0.0326934 | + | 0.999465i | \(0.510408\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 42.8456 | 0.445223 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 175.226 | 1.58857 | 0.794287 | − | 0.607542i | \(-0.207845\pi\) | ||||
0.794287 | + | 0.607542i | \(0.207845\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 291.634 | 2.33307 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 74.3180 | 0.529722 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 165.972 | 1.06277 | 0.531383 | − | 0.847132i | \(-0.321672\pi\) | ||||
0.531383 | + | 0.847132i | \(0.321672\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 155.581 | 0.901395 | 0.450697 | − | 0.892677i | \(-0.351175\pi\) | ||||
0.450697 | + | 0.892677i | \(0.351175\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −32.7174 | −0.172587 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −611.374 | −2.95260 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −95.3991 | −0.423879 | −0.211939 | − | 0.977283i | \(-0.567978\pi\) | ||||
−0.211939 | + | 0.977283i | \(0.567978\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 63.5693 | 0.261006 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 189.928 | 0.723457 | 0.361728 | − | 0.932284i | \(-0.382187\pi\) | ||||
0.361728 | + | 0.932284i | \(0.382187\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 43.0000 | 0.152499 | ||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −509.347 | −1.68731 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 37.2349 | 0.115559 | 0.0577794 | − | 0.998329i | \(-0.481598\pi\) | ||||
0.0577794 | + | 0.998329i | \(0.481598\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 554.137 | 1.61556 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18.7348 | 0.0514390 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 559.862 | 1.45100 | 0.725500 | − | 0.688223i | \(-0.241609\pi\) | ||||
0.725500 | + | 0.688223i | \(0.241609\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 466.852 | 1.14455 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.74635 | 0.0180005 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 82.3042 | 0.181612 | 0.0908059 | − | 0.995869i | \(-0.471056\pi\) | ||||
0.0908059 | + | 0.995869i | \(0.471056\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −640.304 | −1.34398 | −0.671988 | − | 0.740562i | \(-0.734559\pi\) | ||||
−0.671988 | + | 0.740562i | \(0.734559\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 747.422 | 1.49470 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −907.085 | −1.73092 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 509.592 | 0.929203 | 0.464602 | − | 0.885520i | \(-0.346198\pi\) | ||||
0.464602 | + | 0.885520i | \(0.346198\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −250.655 | −0.437323 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −792.932 | −1.32540 | −0.662702 | − | 0.748883i | \(-0.730590\pi\) | ||||
−0.662702 | + | 0.748883i | \(0.730590\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 612.727 | 0.982387 | 0.491194 | − | 0.871050i | \(-0.336561\pi\) | ||||
0.491194 | + | 0.871050i | \(0.336561\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −417.171 | −0.642277 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −685.065 | −1.01390 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −237.047 | −0.337594 | −0.168797 | − | 0.985651i | \(-0.553988\pi\) | ||||
−0.168797 | + | 0.985651i | \(0.553988\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 567.443 | 0.778385 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −418.683 | −0.553691 | −0.276846 | − | 0.960914i | \(-0.589289\pi\) | ||||
−0.276846 | + | 0.960914i | \(0.589289\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −267.330 | −0.341130 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −237.417 | −0.292572 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 113.788 | 0.135523 | 0.0677615 | − | 0.997702i | \(-0.478414\pi\) | ||||
0.0677615 | + | 0.997702i | \(0.478414\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1331.07 | 1.53334 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −222.553 | −0.248147 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −110.534 | −0.119375 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1649.00 | 1.72609 | 0.863045 | − | 0.505127i | \(-0.168554\pi\) | ||||
0.863045 | + | 0.505127i | \(0.168554\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −570.740 | −0.579410 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −165.065 | −0.162619 | −0.0813097 | − | 0.996689i | \(-0.525910\pi\) | ||||
−0.0813097 | + | 0.996689i | \(0.525910\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1665.32 | 1.59309 | 0.796547 | − | 0.604576i | \(-0.206658\pi\) | ||||
0.796547 | + | 0.604576i | \(0.206658\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 874.547 | 0.812829 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 631.683 | 0.570721 | 0.285360 | − | 0.958420i | \(-0.407887\pi\) | ||||
0.285360 | + | 0.958420i | \(0.407887\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 839.368 | 0.737586 | 0.368793 | − | 0.929512i | \(-0.379771\pi\) | ||||
0.368793 | + | 0.929512i | \(0.379771\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 136.465 | 0.116691 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1080.84 | −0.899796 | −0.449898 | − | 0.893080i | \(-0.648540\pi\) | ||||
−0.449898 | + | 0.893080i | \(0.648540\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3576.65 | 2.90021 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1108.94 | 0.876251 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 392.284 | 0.302190 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −807.876 | −0.606969 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −271.685 | −0.199162 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3401.26 | 2.43375 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −594.837 | −0.415616 | −0.207808 | − | 0.978170i | \(-0.566633\pi\) | ||||
−0.207808 | + | 0.978170i | \(0.566633\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −61.5099 | −0.0419818 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1987.90 | −1.32583 | −0.662916 | − | 0.748694i | \(-0.730681\pi\) | ||||
−0.662916 | + | 0.748694i | \(0.730681\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 162.200 | 0.105748 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1516.95 | 0.967098 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1717.01 | 1.07076 | 0.535379 | − | 0.844612i | \(-0.320169\pi\) | ||||
0.535379 | + | 0.844612i | \(0.320169\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1735.09 | 1.05876 | 0.529381 | − | 0.848384i | \(-0.322424\pi\) | ||||
0.529381 | + | 0.848384i | \(0.322424\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −53.2631 | −0.0318125 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1016.42 | −0.594387 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3387.76 | 1.94026 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −792.673 | −0.444752 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 456.600 | 0.251048 | 0.125524 | − | 0.992091i | \(-0.459939\pi\) | ||||
0.125524 | + | 0.992091i | \(0.459939\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 483.618 | 0.260638 | 0.130319 | − | 0.991472i | \(-0.458400\pi\) | ||||
0.130319 | + | 0.991472i | \(0.458400\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 326.819 | 0.172691 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3175.67 | 1.64565 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2300.64 | 1.16950 | 0.584749 | − | 0.811214i | \(-0.301193\pi\) | ||||
0.584749 | + | 0.811214i | \(0.301193\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −800.862 | −0.399450 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5248.42 | −2.56915 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −314.362 | −0.151060 | −0.0755299 | − | 0.997144i | \(-0.524065\pi\) | ||||
−0.0755299 | + | 0.997144i | \(0.524065\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −667.815 | −0.315087 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 282.441 | 0.130874 | 0.0654369 | − | 0.997857i | \(-0.479156\pi\) | ||||
0.0654369 | + | 0.997857i | \(0.479156\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −222.114 | −0.101099 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 135.131 | 0.0604314 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1774.10 | 0.779667 | 0.389834 | − | 0.920885i | \(-0.372532\pi\) | ||||
0.389834 | + | 0.920885i | \(0.372532\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8735.09 | −3.77320 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −117.733 | −0.0499964 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −890.113 | −0.371677 | −0.185839 | − | 0.982580i | \(-0.559500\pi\) | ||||
−0.185839 | + | 0.982580i | \(0.559500\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2883.82 | −1.18427 | −0.592135 | − | 0.805838i | \(-0.701715\pi\) | ||||
−0.592135 | + | 0.805838i | \(0.701715\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 915.931 | 0.369987 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1947.25 | −0.773863 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −299.553 | −0.117142 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2225.99 | −0.856704 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1120.48 | −0.424478 | −0.212239 | − | 0.977218i | \(-0.568076\pi\) | ||||
−0.212239 | + | 0.977218i | \(0.568076\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2777.72 | −1.03598 | −0.517992 | − | 0.855385i | \(-0.673320\pi\) | ||||
−0.517992 | + | 0.855385i | \(0.673320\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1297.55 | 0.476511 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1266.30 | −0.457971 | −0.228985 | − | 0.973430i | \(-0.573541\pi\) | ||||
−0.228985 | + | 0.973430i | \(0.573541\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5113.40 | 1.82150 | 0.910752 | − | 0.412955i | \(-0.135503\pi\) | ||||
0.910752 | + | 0.412955i | \(0.135503\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −728.953 | −0.255803 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4971.23 | −1.71878 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3876.73 | 1.32079 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4372.56 | −1.46818 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −123.858 | −0.0409924 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1318.35 | 0.430138 | 0.215069 | − | 0.976599i | \(-0.431002\pi\) | ||||
0.215069 | + | 0.976599i | \(0.431002\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1134.26 | 0.364874 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 877.699 | 0.278412 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4660.01 | −1.45780 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −876.483 | −0.270444 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 582.026 | 0.177155 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 812.504 | 0.243988 | 0.121994 | − | 0.992531i | \(-0.461071\pi\) | ||||
0.121994 | + | 0.992531i | \(0.461071\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7277.36 | −2.15626 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1890.51 | −0.552763 | −0.276382 | − | 0.961048i | \(-0.589135\pi\) | ||||
−0.276382 | + | 0.961048i | \(0.589135\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1368.43 | 0.394884 | 0.197442 | − | 0.980315i | \(-0.436737\pi\) | ||||
0.197442 | + | 0.980315i | \(0.436737\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 979.960 | 0.279120 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3535.33 | −0.994023 | −0.497012 | − | 0.867744i | \(-0.665569\pi\) | ||||
−0.497012 | + | 0.867744i | \(0.665569\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 760.023 | 0.210972 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 339.088 | 0.0929371 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1515.24 | −0.410095 | −0.205047 | − | 0.978752i | \(-0.565735\pi\) | ||||
−0.205047 | + | 0.978752i | \(0.565735\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6717.46 | −1.79548 | −0.897738 | − | 0.440530i | \(-0.854791\pi\) | ||||
−0.897738 | + | 0.440530i | \(0.854791\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2818.29 | −0.744006 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11310.8 | 2.94948 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 240.653 | 0.0619934 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 598.910 | 0.152427 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2291.38 | 0.576217 | 0.288109 | − | 0.957598i | \(-0.406974\pi\) | ||||
0.288109 | + | 0.957598i | \(0.406974\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4007.76 | 0.995912 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 382.406 | 0.0939107 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2236.18 | −0.542760 | −0.271380 | − | 0.962472i | \(-0.587480\pi\) | ||||
−0.271380 | + | 0.962472i | \(0.587480\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2857.42 | 0.685526 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4141.63 | −0.982224 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6393.87 | 1.49910 | 0.749550 | − | 0.661948i | \(-0.230270\pi\) | ||||
0.749550 | + | 0.661948i | \(0.230270\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11427.7 | 2.64905 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −162.770 | −0.0373085 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2688.95 | −0.609473 | −0.304736 | − | 0.952437i | \(-0.598568\pi\) | ||||
−0.304736 | + | 0.952437i | \(0.598568\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1057.95 | 0.237143 | 0.118572 | − | 0.992945i | \(-0.462168\pi\) | ||||
0.118572 | + | 0.992945i | \(0.462168\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1904.04 | −0.422117 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6670.22 | 1.46265 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1904.17 | 0.413035 | 0.206518 | − | 0.978443i | \(-0.433787\pi\) | ||||
0.206518 | + | 0.978443i | \(0.433787\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3882.34 | −0.833081 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6520.37 | 1.38424 | 0.692122 | − | 0.721781i | \(-0.256676\pi\) | ||||
0.692122 | + | 0.721781i | \(0.256676\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −130.376 | −0.0273854 | −0.0136927 | − | 0.999906i | \(-0.504359\pi\) | ||||
−0.0136927 | + | 0.999906i | \(0.504359\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 158.115 | 0.0328630 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5688.76 | −1.17002 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4741.47 | −0.965086 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2358.84 | −0.475180 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −321.150 | −0.0640333 | −0.0320166 | − | 0.999487i | \(-0.510193\pi\) | ||||
−0.0320166 | + | 0.999487i | \(0.510193\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1679.96 | 0.331563 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1699.79 | 0.332094 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7787.00 | −1.50613 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1287.95 | −0.246631 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 236.119 | 0.0447679 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13069.6 | −2.45366 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3944.87 | −0.733374 | −0.366687 | − | 0.930344i | \(-0.619508\pi\) | ||||
−0.366687 | + | 0.930344i | \(0.619508\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2382.18 | −0.438567 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7046.04 | −1.28471 | −0.642354 | − | 0.766408i | \(-0.722042\pi\) | ||||
−0.642354 | + | 0.766408i | \(0.722042\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −230.283 | −0.0415858 | −0.0207929 | − | 0.999784i | \(-0.506619\pi\) | ||||
−0.0207929 | + | 0.999784i | \(0.506619\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 15256.1 | 2.72883 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6574.02 | 1.16477 | 0.582387 | − | 0.812911i | \(-0.302119\pi\) | ||||
0.582387 | + | 0.812911i | \(0.302119\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3796.10 | 0.666271 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −903.600 | −0.157115 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 70.9237 | 0.0122177 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12960.1 | −2.21199 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1200.68 | −0.203052 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1115.27 | −0.186890 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8326.42 | −1.38266 | −0.691331 | − | 0.722538i | \(-0.742975\pi\) | ||||
−0.691331 | + | 0.722538i | \(0.742975\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2380.57 | 0.391755 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10401.6 | 1.69642 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9021.52 | 1.45826 | 0.729130 | − | 0.684375i | \(-0.239925\pi\) | ||||
0.729130 | + | 0.684375i | \(0.239925\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1546.10 | 0.247707 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3558.44 | 0.565104 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6324.03 | −0.995526 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5116.27 | −0.798408 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −133.107 | −0.0205925 | −0.0102962 | − | 0.999947i | \(-0.503277\pi\) | ||||
−0.0102962 | + | 0.999947i | \(0.503277\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1322.67 | −0.202868 | −0.101434 | − | 0.994842i | \(-0.532343\pi\) | ||||
−0.101434 | + | 0.994842i | \(0.532343\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3302.67 | −0.502232 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12515.7 | 1.88709 | 0.943543 | − | 0.331251i | \(-0.107471\pi\) | ||||
0.943543 | + | 0.331251i | \(0.107471\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16185.0 | −2.41975 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −561.148 | −0.0831907 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12654.2 | 1.86035 | 0.930174 | − | 0.367118i | \(-0.119656\pi\) | ||||
0.930174 | + | 0.367118i | \(0.119656\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6829.67 | −0.995725 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1155.64 | 0.167094 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12506.7 | 1.79351 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13307.8 | 1.89281 | 0.946407 | − | 0.322976i | \(-0.104683\pi\) | ||||
0.946407 | + | 0.322976i | \(0.104683\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4739.41 | −0.668629 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16769.1 | −2.34666 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6552.61 | −0.909602 | −0.454801 | − | 0.890593i | \(-0.650290\pi\) | ||||
−0.454801 | + | 0.890593i | \(0.650290\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4865.38 | −0.669993 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7375.74 | −1.00761 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11236.0 | −1.52284 | −0.761418 | − | 0.648262i | \(-0.775496\pi\) | ||||
−0.761418 | + | 0.648262i | \(0.775496\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 850.893 | 0.114416 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6353.36 | −0.847628 | −0.423814 | − | 0.905749i | \(-0.639309\pi\) | ||||
−0.423814 | + | 0.905749i | \(0.639309\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13983.3 | −1.85105 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1073.01 | −0.140941 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3788.91 | 0.493844 | 0.246922 | − | 0.969035i | \(-0.420581\pi\) | ||||
0.246922 | + | 0.969035i | \(0.420581\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2294.94 | −0.296828 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2843.62 | 0.364992 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4838.52 | −0.616335 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2601.66 | −0.328901 | −0.164451 | − | 0.986385i | \(-0.552585\pi\) | ||||
−0.164451 | + | 0.986385i | \(0.552585\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −232.021 | −0.0291117 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1698.36 | −0.211501 | −0.105750 | − | 0.994393i | \(-0.533724\pi\) | ||||
−0.105750 | + | 0.994393i | \(0.533724\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6913.99 | −0.854616 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11582.4 | 1.42107 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2181.96 | −0.265739 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5511.51 | −0.666324 | −0.333162 | − | 0.942870i | \(-0.608116\pi\) | ||||
−0.333162 | + | 0.942870i | \(0.608116\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2456.12 | −0.294772 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2465.20 | −0.293715 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8545.99 | −1.01086 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2481.98 | −0.291470 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6137.26 | 0.715573 | 0.357786 | − | 0.933803i | \(-0.383532\pi\) | ||||
0.357786 | + | 0.933803i | \(0.383532\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9168.60 | 1.06140 | 0.530701 | − | 0.847559i | \(-0.321929\pi\) | ||||
0.530701 | + | 0.847559i | \(0.321929\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −929.150 | −0.106801 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3819.52 | −0.435939 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19178.5 | 2.17357 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1453.95 | 0.163630 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12535.8 | −1.40099 | −0.700494 | − | 0.713658i | \(-0.747037\pi\) | ||||
−0.700494 | + | 0.713658i | \(0.747037\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7163.93 | 0.795095 | 0.397548 | − | 0.917582i | \(-0.369861\pi\) | ||||
0.397548 | + | 0.917582i | \(0.369861\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4846.06 | −0.534140 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −948.898 | −0.103872 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2988.31 | 0.324884 | 0.162442 | − | 0.986718i | \(-0.448063\pi\) | ||||
0.162442 | + | 0.986718i | \(0.448063\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13827.8 | −1.49312 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11257.1 | 1.20732 | 0.603660 | − | 0.797242i | \(-0.293708\pi\) | ||||
0.603660 | + | 0.797242i | \(0.293708\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2322.60 | 0.247420 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −653.150 | −0.0691117 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4960.39 | −0.521371 | −0.260685 | − | 0.965424i | \(-0.583948\pi\) | ||||
−0.260685 | + | 0.965424i | \(0.583948\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4344.01 | 0.453551 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −691.798 | −0.0717517 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 27169.2 | 2.79937 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4911.00 | −0.502685 | −0.251343 | − | 0.967898i | \(-0.580872\pi\) | ||||
−0.251343 | + | 0.967898i | \(0.580872\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −973.341 | −0.0989797 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3089.54 | −0.312135 | −0.156068 | − | 0.987746i | \(-0.549882\pi\) | ||||
−0.156068 | + | 0.987746i | \(0.549882\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2821.14 | −0.283174 | −0.141587 | − | 0.989926i | \(-0.545221\pi\) | ||||
−0.141587 | + | 0.989926i | \(0.545221\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4542.67 | −0.453035 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −483.354 | −0.0478950 | −0.0239475 | − | 0.999713i | \(-0.507623\pi\) | ||||
−0.0239475 | + | 0.999713i | \(0.507623\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15263.4 | −1.50277 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3290.99 | −0.321955 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 983.492 | 0.0956047 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1579.28 | −0.152552 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13970.7 | −1.34103 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5570.85 | 0.531396 | 0.265698 | − | 0.964056i | \(-0.414398\pi\) | ||||
0.265698 | + | 0.964056i | \(0.414398\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4239.51 | 0.401881 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7507.68 | 0.707269 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 33658.8 | 3.15127 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −453.859 | −0.0422306 | −0.0211153 | − | 0.999777i | \(-0.506722\pi\) | ||||
−0.0211153 | + | 0.999777i | \(0.506722\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 449.684 | 0.0415857 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2787.17 | −0.256178 | −0.128089 | − | 0.991763i | \(-0.540884\pi\) | ||||
−0.128089 | + | 0.991763i | \(0.540884\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2173.73 | −0.198580 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11649.7 | −1.05781 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23750.1 | 2.14354 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 325.118 | 0.0291669 | 0.0145834 | − | 0.999894i | \(-0.495358\pi\) | ||||
0.0145834 | + | 0.999894i | \(0.495358\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −404.022 | −0.0360286 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11441.8 | 1.01424 | 0.507120 | − | 0.861875i | \(-0.330710\pi\) | ||||
0.507120 | + | 0.861875i | \(0.330710\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3369.24 | −0.296889 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 317.727 | 0.0278318 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8398.29 | −0.731332 | −0.365666 | − | 0.930746i | \(-0.619159\pi\) | ||||
−0.365666 | + | 0.930746i | \(0.619159\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18352.5 | −1.58878 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −402.452 | −0.0346368 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 33991.8 | 2.90846 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 851.632 | 0.0724463 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2537.79 | −0.214637 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9762.74 | 0.820947 | 0.410474 | − | 0.911873i | \(-0.365363\pi\) | ||||
0.410474 | + | 0.911873i | \(0.365363\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14406.0 | 1.20445 | 0.602227 | − | 0.798325i | \(-0.294280\pi\) | ||||
0.602227 | + | 0.798325i | \(0.294280\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12495.2 | 1.03874 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2037.65 | −0.168427 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18537.3 | 1.52357 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2053.80 | −0.167848 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8440.33 | −0.685912 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12893.7 | 1.04195 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1273.27 | 0.102320 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12674.2 | 1.01283 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22048.2 | 1.75217 | 0.876087 | − | 0.482153i | \(-0.160145\pi\) | ||||
0.876087 | + | 0.482153i | \(0.160145\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4125.21 | 0.326021 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17132.8 | 1.34659 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6165.00 | −0.481895 | −0.240947 | − | 0.970538i | \(-0.577458\pi\) | ||||
−0.240947 | + | 0.970538i | \(0.577458\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15978.0 | 1.24212 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −898.784 | −0.0694909 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7100.10 | 0.545980 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2785.47 | 0.213039 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12519.9 | −0.952400 | −0.476200 | − | 0.879337i | \(-0.657986\pi\) | ||||
−0.476200 | + | 0.879337i | \(0.657986\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1910.91 | −0.144584 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 428.499 | 0.0322482 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21124.7 | −1.58135 | −0.790674 | − | 0.612237i | \(-0.790270\pi\) | ||||
−0.790674 | + | 0.612237i | \(0.790270\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22061.7 | −1.64273 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16996.2 | −1.25886 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22782.7 | −1.67856 | −0.839279 | − | 0.543700i | \(-0.817023\pi\) | ||||
−0.839279 | + | 0.543700i | \(0.817023\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12990.7 | 0.952092 | 0.476046 | − | 0.879420i | \(-0.342070\pi\) | ||||
0.476046 | + | 0.879420i | \(0.342070\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1602.81 | 0.116856 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 51101.9 | 3.70626 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25759.9 | −1.85858 | −0.929289 | − | 0.369353i | \(-0.879579\pi\) | ||||
−0.929289 | + | 0.369353i | \(0.879579\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3973.43 | 0.285199 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12540.5 | 0.895468 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12805.1 | 0.909663 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 22635.2 | 1.59974 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4369.06 | 0.307207 | 0.153604 | − | 0.988133i | \(-0.450912\pi\) | ||||
0.153604 | + | 0.988133i | \(0.450912\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −842.515 | −0.0589393 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1811.40 | 0.126076 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3241.12 | 0.224447 | 0.112223 | − | 0.993683i | \(-0.464203\pi\) | ||||
0.112223 | + | 0.993683i | \(0.464203\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8007.15 | 0.551699 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7314.53 | −0.501447 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4294.37 | 0.292927 | 0.146463 | − | 0.989216i | \(-0.453211\pi\) | ||||
0.146463 | + | 0.989216i | \(0.453211\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1277.55 | 0.0867093 | 0.0433546 | − | 0.999060i | \(-0.486195\pi\) | ||||
0.0433546 | + | 0.999060i | \(0.486195\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12716.3 | −0.858782 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16490.0 | −1.10813 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17305.3 | −1.15717 | −0.578584 | − | 0.815623i | \(-0.696394\pi\) | ||||
−0.578584 | + | 0.815623i | \(0.696394\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7111.17 | 0.473168 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1654.71 | −0.109562 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12812.9 | −0.844225 | −0.422112 | − | 0.906544i | \(-0.638711\pi\) | ||||
−0.422112 | + | 0.906544i | \(0.638711\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5545.52 | −0.363605 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3963.52 | −0.258615 | −0.129307 | − | 0.991605i | \(-0.541275\pi\) | ||||
−0.129307 | + | 0.991605i | \(0.541275\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26937.7 | −1.74914 | −0.874570 | − | 0.484899i | \(-0.838856\pi\) | ||||
−0.874570 | + | 0.484899i | \(0.838856\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13022.5 | 0.841503 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3408.22 | −0.219177 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 32971.0 | 2.11015 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 177.174 | 0.0112849 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1249.44 | 0.0792026 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2401.37 | 0.151501 | 0.0757504 | − | 0.997127i | \(-0.475865\pi\) | ||||
0.0757504 | + | 0.997127i | \(0.475865\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1885.85 | −0.118414 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12141.6 | −0.758778 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24625.7 | −1.53172 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19786.6 | 1.22496 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22872.8 | −1.40940 | −0.704698 | − | 0.709508i | \(-0.748917\pi\) | ||||
−0.704698 | + | 0.709508i | \(0.748917\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27051.9 | −1.65913 | −0.829566 | − | 0.558409i | \(-0.811412\pi\) | ||||
−0.829566 | + | 0.558409i | \(0.811412\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1255.52 | −0.0766448 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12947.9 | −0.786760 | −0.393380 | − | 0.919376i | \(-0.628694\pi\) | ||||
−0.393380 | + | 0.919376i | \(0.628694\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1882.45 | 0.113856 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6665.97 | 0.401321 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16218.4 | 0.971934 | 0.485967 | − | 0.873977i | \(-0.338467\pi\) | ||||
0.485967 | + | 0.873977i | \(0.338467\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −40576.3 | −2.42053 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15289.8 | −0.907936 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26252.1 | 1.55180 | 0.775901 | − | 0.630855i | \(-0.217296\pi\) | ||||
0.775901 | + | 0.630855i | \(0.217296\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24649.9 | 1.45049 | 0.725243 | − | 0.688493i | \(-0.241727\pi\) | ||||
0.725243 | + | 0.688493i | \(0.241727\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −832.566 | −0.0487695 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3310.75 | 0.193061 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29082.7 | 1.68828 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1162.26 | −0.0671681 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14645.0 | −0.842567 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4424.70 | 0.253432 | 0.126716 | − | 0.991939i | \(-0.459556\pi\) | ||||
0.126716 | + | 0.991939i | \(0.459556\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 21673.6 | 1.23588 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18153.6 | 1.03057 | 0.515287 | − | 0.857018i | \(-0.327685\pi\) | ||||
0.515287 | + | 0.857018i | \(0.327685\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −49391.3 | −2.79155 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2704.30 | 0.152172 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19887.7 | −1.11417 | −0.557087 | − | 0.830454i | \(-0.688081\pi\) | ||||
−0.557087 | + | 0.830454i | \(0.688081\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 35046.9 | 1.95485 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1957.49 | −0.108709 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24880.1 | −1.37570 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8550.10 | −0.470711 | −0.235355 | − | 0.971909i | \(-0.575625\pi\) | ||||
−0.235355 | + | 0.971909i | \(0.575625\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17095.0 | 0.937062 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 35415.9 | 1.93295 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2487.48 | −0.135179 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5057.17 | 0.273648 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19280.9 | −1.03884 | −0.519421 | − | 0.854518i | \(-0.673852\pi\) | ||||
−0.519421 | + | 0.854518i | \(0.673852\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 516.612 | 0.0277161 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1087.19 | −0.0580791 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4944.06 | 0.262999 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19384.3 | 1.02679 | 0.513394 | − | 0.858153i | \(-0.328388\pi\) | ||||
0.513394 | + | 0.858153i | \(0.328388\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5915.23 | 0.312009 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27261.9 | 1.43193 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20746.8 | −1.08515 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2167.49 | 0.112896 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11746.0 | 0.609253 | 0.304627 | − | 0.952472i | \(-0.401468\pi\) | ||||
0.304627 | + | 0.952472i | \(0.401468\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −49880.0 | −2.57646 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9609.08 | 0.494282 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 48403.0 | 2.47951 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10042.8 | −0.512333 | −0.256167 | − | 0.966633i | \(-0.582460\pi\) | ||||
−0.256167 | + | 0.966633i | \(0.582460\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11289.5 | −0.573566 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −563.170 | −0.0284947 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23541.9 | −1.18627 | −0.593136 | − | 0.805102i | \(-0.702111\pi\) | ||||
−0.593136 | + | 0.805102i | \(0.702111\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16179.7 | −0.811970 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11655.3 | 0.582538 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39871.6 | 1.98471 | 0.992354 | − | 0.123422i | \(-0.0393868\pi\) | ||||
0.992354 | + | 0.123422i | \(0.0393868\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −344.245 | −0.0170664 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11387.7 | 0.562281 | 0.281141 | − | 0.959667i | \(-0.409287\pi\) | ||||
0.281141 | + | 0.959667i | \(0.409287\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9319.94 | 0.458331 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10447.7 | 0.511729 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18920.3 | −0.923009 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26156.9 | 1.27094 | 0.635471 | − | 0.772125i | \(-0.280806\pi\) | ||||
0.635471 | + | 0.772125i | \(0.280806\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3277.73 | −0.158629 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9871.43 | 0.475839 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9147.11 | 0.439178 | 0.219589 | − | 0.975593i | \(-0.429528\pi\) | ||||
0.219589 | + | 0.975593i | \(0.429528\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5732.95 | −0.274167 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41329.2 | −1.96870 | −0.984350 | − | 0.176225i | \(-0.943611\pi\) | ||||
−0.984350 | + | 0.176225i | \(0.943611\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25140.9 | −1.19287 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6670.90 | 0.315277 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3657.57 | −0.172187 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3722.69 | −0.174569 | −0.0872846 | − | 0.996183i | \(-0.527819\pi\) | ||||
−0.0872846 | + | 0.996183i | \(0.527819\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3198.78 | 0.149418 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34945.5 | 1.62600 | 0.813002 | − | 0.582261i | \(-0.197832\pi\) | ||||
0.813002 | + | 0.582261i | \(0.197832\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 45372.8 | 2.10302 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4087.43 | −0.188721 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1028.51 | −0.0473045 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18135.9 | −0.830925 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12334.7 | 0.562971 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46959.8 | 2.13512 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26135.3 | 1.18377 | 0.591883 | − | 0.806024i | \(-0.298385\pi\) | ||||
0.591883 | + | 0.806024i | \(0.298385\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9146.20 | −0.412691 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32373.6 | 1.45521 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28454.9 | 1.27423 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −16346.9 | −0.729263 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20345.9 | 0.904250 | 0.452125 | − | 0.891955i | \(-0.350666\pi\) | ||||
0.452125 | + | 0.891955i | \(0.350666\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −487.664 | −0.0215924 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2839.45 | −0.125252 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14014.2 | 0.615880 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −107129. | −4.69042 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3846.44 | 0.167783 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21515.4 | −0.935034 | −0.467517 | − | 0.883984i | \(-0.654851\pi\) | ||||
−0.467517 | + | 0.883984i | \(0.654851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19685.9 | 0.852363 | 0.426181 | − | 0.904638i | \(-0.359858\pi\) | ||||
0.426181 | + | 0.904638i | \(0.359858\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1513.36 | −0.0652838 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6416.64 | −0.275785 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −232.857 | −0.00997139 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −33215.2 | −1.41713 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23501.4 | 0.999029 | 0.499515 | − | 0.866305i | \(-0.333512\pi\) | ||||
0.499515 | + | 0.866305i | \(0.333512\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25153.6 | −1.06537 | −0.532684 | − | 0.846314i | \(-0.678817\pi\) | ||||
−0.532684 | + | 0.846314i | \(0.678817\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9541.51 | −0.402658 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31043.6 | −1.30531 | −0.652655 | − | 0.757655i | \(-0.726345\pi\) | ||||
−0.652655 | + | 0.757655i | \(0.726345\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16479.2 | 0.690404 | 0.345202 | − | 0.938528i | \(-0.387810\pi\) | ||||
0.345202 | + | 0.938528i | \(0.387810\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2723.85 | −0.113706 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7257.52 | −0.301871 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5765.08 | 0.238933 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11562.5 | 0.477489 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10409.3 | −0.428329 | −0.214164 | − | 0.976798i | \(-0.568703\pi\) | ||||
−0.214164 | + | 0.976798i | \(0.568703\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3157.71 | 0.129473 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9327.15 | −0.381072 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4533.71 | −0.184573 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24197.7 | 0.981633 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 186.499 | 0.00753901 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16716.4 | −0.673363 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1701.91 | 0.0683147 | 0.0341573 | − | 0.999416i | \(-0.489125\pi\) | ||||
0.0341573 | + | 0.999416i | \(0.489125\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2758.25 | 0.110328 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13987.3 | −0.557524 | −0.278762 | − | 0.960360i | \(-0.589924\pi\) | ||||
−0.278762 | + | 0.960360i | \(0.589924\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 845.375 | 0.0335784 | 0.0167892 | − | 0.999859i | \(-0.494656\pi\) | ||||
0.0167892 | + | 0.999859i | \(0.494656\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8137.56 | 0.322099 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16970.3 | 0.669381 | 0.334691 | − | 0.942328i | \(-0.391368\pi\) | ||||
0.334691 | + | 0.942328i | \(0.391368\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36212.3 | 1.42342 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6782.50 | 0.265681 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5421.72 | −0.211645 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22646.1 | −0.880981 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −41148.8 | −1.59528 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −101876. | −3.93602 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3402.23 | −0.130998 | −0.0654989 | − | 0.997853i | \(-0.520864\pi\) | ||||
−0.0654989 | + | 0.997853i | \(0.520864\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 459.393 | 0.0176279 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9753.40 | −0.372986 | −0.186493 | − | 0.982456i | \(-0.559712\pi\) | ||||
−0.186493 | + | 0.982456i | \(0.559712\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42672.3 | −1.62632 | −0.813159 | − | 0.582042i | \(-0.802254\pi\) | ||||
−0.813159 | + | 0.582042i | \(0.802254\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2403.12 | −0.0912769 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13027.3 | −0.493139 | −0.246570 | − | 0.969125i | \(-0.579303\pi\) | ||||
−0.246570 | + | 0.969125i | \(0.579303\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17816.7 | 0.672164 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12978.5 | 0.487987 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −201.637 | −0.00755601 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18168.6 | −0.678560 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11139.0 | 0.414628 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25822.1 | 0.957972 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7332.50 | −0.271122 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1842.36 | 0.0678958 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −58863.5 | −2.16209 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2184.13 | 0.0799591 | 0.0399796 | − | 0.999200i | \(-0.487271\pi\) | ||||
0.0399796 | + | 0.999200i | \(0.487271\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4118.99 | 0.150295 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15349.5 | −0.558236 | −0.279118 | − | 0.960257i | \(-0.590042\pi\) | ||||
−0.279118 | + | 0.960257i | \(0.590042\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9576.07 | −0.347121 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 18695.6 | 0.675474 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 59542.2 | 2.14423 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50672.7 | 1.81887 | 0.909433 | − | 0.415850i | \(-0.136516\pi\) | ||||
0.909433 | + | 0.415850i | \(0.136516\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5642.99 | 0.201892 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 35237.6 | 1.25662 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27821.6 | −0.988940 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −41556.0 | −1.47236 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −40538.7 | −1.43168 | −0.715841 | − | 0.698263i | \(-0.753957\pi\) | ||||
−0.715841 | + | 0.698263i | \(0.753957\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3000.80 | −0.105636 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10079.1 | 0.353671 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6114.36 | −0.213862 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13492.4 | 0.470413 | 0.235206 | − | 0.971945i | \(-0.424423\pi\) | ||||
0.235206 | + | 0.971945i | \(0.424423\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 329.411 | 0.0114483 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22597.2 | 0.782835 | 0.391417 | − | 0.920213i | \(-0.371985\pi\) | ||||
0.391417 | + | 0.920213i | \(0.371985\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33280.3 | 1.14926 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −45436.0 | −1.56406 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21796.6 | −0.747933 | −0.373967 | − | 0.927442i | \(-0.622003\pi\) | ||||
−0.373967 | + | 0.927442i | \(0.622003\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27229.4 | −0.931405 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9403.89 | −0.320654 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40073.5 | −1.36213 | −0.681064 | − | 0.732224i | \(-0.738482\pi\) | ||||
−0.681064 | + | 0.732224i | \(0.738482\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22870.9 | −0.774957 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5430.18 | −0.183420 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −51428.2 | −1.73170 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5585.45 | −0.187488 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15762.9 | −0.527468 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −56697.8 | −1.89137 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20836.9 | 0.692935 | 0.346468 | − | 0.938062i | \(-0.387381\pi\) | ||||
0.346468 | + | 0.938062i | \(0.387381\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −101.454 | −0.00336343 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5902.12 | 0.195065 | 0.0975325 | − | 0.995232i | \(-0.468905\pi\) | ||||
0.0975325 | + | 0.995232i | \(0.468905\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −51969.7 | −1.71230 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18539.0 | 0.608946 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17199.6 | 0.563218 | 0.281609 | − | 0.959529i | \(-0.409132\pi\) | ||||
0.281609 | + | 0.959529i | \(0.409132\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2602.56 | 0.0849623 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20945.4 | −0.681687 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8184.53 | −0.265561 | −0.132780 | − | 0.991145i | \(-0.542390\pi\) | ||||
−0.132780 | + | 0.991145i | \(0.542390\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25847.3 | −0.836104 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1595.35 | 0.0514494 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7534.73 | 0.242255 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43473.7 | 1.39353 | 0.696765 | − | 0.717300i | \(-0.254622\pi\) | ||||
0.696765 | + | 0.717300i | \(0.254622\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11910.6 | 0.380637 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 104373. | 3.32546 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42253.7 | 1.34221 | 0.671107 | − | 0.741361i | \(-0.265819\pi\) | ||||
0.671107 | + | 0.741361i | \(0.265819\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7089.87 | −0.224538 |
(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 | 688.4.a.i.1.4 | 6 | ||
4.3 | odd | 2 | 43.4.a.b.1.3 | ✓ | 6 | ||
12.11 | even | 2 | 387.4.a.h.1.4 | 6 | |||
20.19 | odd | 2 | 1075.4.a.b.1.4 | 6 | |||
28.27 | even | 2 | 2107.4.a.c.1.3 | 6 | |||
172.171 | even | 2 | 1849.4.a.c.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.a.b.1.3 | ✓ | 6 | 4.3 | odd | 2 | ||
387.4.a.h.1.4 | 6 | 12.11 | even | 2 | |||
688.4.a.i.1.4 | 6 | 1.1 | even | 1 | trivial | ||
1075.4.a.b.1.4 | 6 | 20.19 | odd | 2 | |||
1849.4.a.c.1.4 | 6 | 172.171 | even | 2 | |||
2107.4.a.c.1.3 | 6 | 28.27 | even | 2 |