Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,4,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, 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("1575.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(92.9280082590\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.26729725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 18x^{2} + 19x + 44 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 525) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.56826\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.56826 | −0.908017 | −0.454008 | − | 0.890997i | \(-0.650006\pi\) | ||||
−0.454008 | + | 0.890997i | \(0.650006\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.40404 | −0.175505 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 24.1520 | 1.06738 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −66.4181 | −1.82053 | −0.910264 | − | 0.414029i | \(-0.864121\pi\) | ||||
−0.910264 | + | 0.414029i | \(0.864121\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −34.0329 | −0.726079 | −0.363040 | − | 0.931774i | \(-0.618261\pi\) | ||||
−0.363040 | + | 0.931774i | \(0.618261\pi\) | |||||||
\(14\) | −17.9778 | −0.343198 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −50.7963 | −0.793692 | ||||||||
\(17\) | −6.12934 | −0.0874461 | −0.0437231 | − | 0.999044i | \(-0.513922\pi\) | ||||
−0.0437231 | + | 0.999044i | \(0.513922\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −163.424 | −1.97327 | −0.986634 | − | 0.162951i | \(-0.947899\pi\) | ||||
−0.986634 | + | 0.162951i | \(0.947899\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 170.579 | 1.65307 | ||||||||
\(23\) | −35.8799 | −0.325282 | −0.162641 | − | 0.986685i | \(-0.552001\pi\) | ||||
−0.162641 | + | 0.986685i | \(0.552001\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 87.4053 | 0.659292 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −9.82830 | −0.0663348 | ||||||||
\(29\) | −27.7256 | −0.177535 | −0.0887676 | − | 0.996052i | \(-0.528293\pi\) | ||||
−0.0887676 | + | 0.996052i | \(0.528293\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 74.3417 | 0.430715 | 0.215358 | − | 0.976535i | \(-0.430908\pi\) | ||||
0.215358 | + | 0.976535i | \(0.430908\pi\) | |||||||
\(32\) | −62.7581 | −0.346693 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 15.7417 | 0.0794026 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −260.966 | −1.15953 | −0.579763 | − | 0.814785i | \(-0.696855\pi\) | ||||
−0.579763 | + | 0.814785i | \(0.696855\pi\) | |||||||
\(38\) | 419.716 | 1.79176 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 445.485 | 1.69690 | 0.848452 | − | 0.529272i | \(-0.177535\pi\) | ||||
0.848452 | + | 0.529272i | \(0.177535\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −474.985 | −1.68452 | −0.842261 | − | 0.539070i | \(-0.818776\pi\) | ||||
−0.842261 | + | 0.539070i | \(0.818776\pi\) | |||||||
\(44\) | 93.2538 | 0.319512 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 92.1489 | 0.295361 | ||||||||
\(47\) | 51.0436 | 0.158414 | 0.0792072 | − | 0.996858i | \(-0.474761\pi\) | ||||
0.0792072 | + | 0.996858i | \(0.474761\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 47.7837 | 0.127431 | ||||||||
\(53\) | 676.667 | 1.75372 | 0.876862 | − | 0.480742i | \(-0.159633\pi\) | ||||
0.876862 | + | 0.480742i | \(0.159633\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 169.064 | 0.403431 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 71.2066 | 0.161205 | ||||||||
\(59\) | 115.979 | 0.255917 | 0.127959 | − | 0.991779i | \(-0.459158\pi\) | ||||
0.127959 | + | 0.991779i | \(0.459158\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −390.356 | −0.819344 | −0.409672 | − | 0.912233i | \(-0.634357\pi\) | ||||
−0.409672 | + | 0.912233i | \(0.634357\pi\) | |||||||
\(62\) | −190.929 | −0.391097 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 567.550 | 1.10850 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −713.721 | −1.30142 | −0.650708 | − | 0.759328i | \(-0.725528\pi\) | ||||
−0.650708 | + | 0.759328i | \(0.725528\pi\) | |||||||
\(68\) | 8.60586 | 0.0153473 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −810.524 | −1.35481 | −0.677405 | − | 0.735610i | \(-0.736896\pi\) | ||||
−0.677405 | + | 0.735610i | \(0.736896\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 350.196 | 0.561470 | 0.280735 | − | 0.959785i | \(-0.409422\pi\) | ||||
0.280735 | + | 0.959785i | \(0.409422\pi\) | |||||||
\(74\) | 670.227 | 1.05287 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 229.455 | 0.346319 | ||||||||
\(77\) | −464.927 | −0.688095 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −50.9307 | −0.0725336 | −0.0362668 | − | 0.999342i | \(-0.511547\pi\) | ||||
−0.0362668 | + | 0.999342i | \(0.511547\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1144.12 | −1.54082 | ||||||||
\(83\) | 84.8904 | 0.112264 | 0.0561321 | − | 0.998423i | \(-0.482123\pi\) | ||||
0.0561321 | + | 0.998423i | \(0.482123\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1219.88 | 1.52957 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1604.13 | −1.94319 | ||||||||
\(89\) | −1521.82 | −1.81251 | −0.906253 | − | 0.422735i | \(-0.861070\pi\) | ||||
−0.906253 | + | 0.422735i | \(0.861070\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −238.230 | −0.274432 | ||||||||
\(92\) | 50.3769 | 0.0570887 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −131.093 | −0.143843 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1232.08 | −1.28968 | −0.644840 | − | 0.764317i | \(-0.723076\pi\) | ||||
−0.644840 | + | 0.764317i | \(0.723076\pi\) | |||||||
\(98\) | −125.845 | −0.129717 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1661.64 | 1.63702 | 0.818510 | − | 0.574492i | \(-0.194800\pi\) | ||||
0.818510 | + | 0.574492i | \(0.194800\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −193.631 | −0.185233 | −0.0926167 | − | 0.995702i | \(-0.529523\pi\) | ||||
−0.0926167 | + | 0.995702i | \(0.529523\pi\) | |||||||
\(104\) | −821.963 | −0.775001 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1737.86 | −1.59241 | ||||||||
\(107\) | −921.040 | −0.832153 | −0.416076 | − | 0.909330i | \(-0.636595\pi\) | ||||
−0.416076 | + | 0.909330i | \(0.636595\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1304.73 | 1.14652 | 0.573260 | − | 0.819373i | \(-0.305678\pi\) | ||||
0.573260 | + | 0.819373i | \(0.305678\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −355.574 | −0.299988 | ||||||||
\(113\) | −237.585 | −0.197789 | −0.0988945 | − | 0.995098i | \(-0.531531\pi\) | ||||
−0.0988945 | + | 0.995098i | \(0.531531\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 38.9280 | 0.0311584 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −297.863 | −0.232377 | ||||||||
\(119\) | −42.9054 | −0.0330515 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3080.36 | 2.31432 | ||||||||
\(122\) | 1002.54 | 0.743978 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −104.379 | −0.0755928 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1442.31 | −1.00775 | −0.503876 | − | 0.863776i | \(-0.668093\pi\) | ||||
−0.503876 | + | 0.863776i | \(0.668093\pi\) | |||||||
\(128\) | −955.550 | −0.659840 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −644.035 | −0.429539 | −0.214770 | − | 0.976665i | \(-0.568900\pi\) | ||||
−0.214770 | + | 0.976665i | \(0.568900\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1143.97 | −0.745825 | ||||||||
\(134\) | 1833.02 | 1.18171 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −148.036 | −0.0933381 | ||||||||
\(137\) | 355.576 | 0.221744 | 0.110872 | − | 0.993835i | \(-0.464636\pi\) | ||||
0.110872 | + | 0.993835i | \(0.464636\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −472.016 | −0.288028 | −0.144014 | − | 0.989576i | \(-0.546001\pi\) | ||||
−0.144014 | + | 0.989576i | \(0.546001\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2081.64 | 1.23019 | ||||||||
\(143\) | 2260.40 | 1.32185 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −899.393 | −0.509824 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 366.407 | 0.203503 | ||||||||
\(149\) | 1091.53 | 0.600143 | 0.300072 | − | 0.953917i | \(-0.402989\pi\) | ||||
0.300072 | + | 0.953917i | \(0.402989\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2914.48 | 1.57071 | 0.785354 | − | 0.619047i | \(-0.212481\pi\) | ||||
0.785354 | + | 0.619047i | \(0.212481\pi\) | |||||||
\(152\) | −3947.03 | −2.10622 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1194.05 | 0.624802 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1476.94 | −0.750780 | −0.375390 | − | 0.926867i | \(-0.622491\pi\) | ||||
−0.375390 | + | 0.926867i | \(0.622491\pi\) | |||||||
\(158\) | 130.803 | 0.0658617 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −251.159 | −0.122945 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2764.56 | 1.32845 | 0.664224 | − | 0.747534i | \(-0.268762\pi\) | ||||
0.664224 | + | 0.747534i | \(0.268762\pi\) | |||||||
\(164\) | −625.480 | −0.297816 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −218.020 | −0.101938 | ||||||||
\(167\) | 255.508 | 0.118394 | 0.0591970 | − | 0.998246i | \(-0.481146\pi\) | ||||
0.0591970 | + | 0.998246i | \(0.481146\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1038.76 | −0.472809 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 666.899 | 0.295643 | ||||||||
\(173\) | 3850.56 | 1.69221 | 0.846105 | − | 0.533016i | \(-0.178941\pi\) | ||||
0.846105 | + | 0.533016i | \(0.178941\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3373.79 | 1.44494 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3908.44 | 1.64579 | ||||||||
\(179\) | −952.804 | −0.397854 | −0.198927 | − | 0.980014i | \(-0.563746\pi\) | ||||
−0.198927 | + | 0.980014i | \(0.563746\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1648.83 | 0.677109 | 0.338554 | − | 0.940947i | \(-0.390062\pi\) | ||||
0.338554 | + | 0.940947i | \(0.390062\pi\) | |||||||
\(182\) | 611.837 | 0.249189 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −866.572 | −0.347199 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 407.099 | 0.159198 | ||||||||
\(188\) | −71.6675 | −0.0278026 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −767.536 | −0.290769 | −0.145385 | − | 0.989375i | \(-0.546442\pi\) | ||||
−0.145385 | + | 0.989375i | \(0.546442\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1186.61 | −0.442561 | −0.221280 | − | 0.975210i | \(-0.571024\pi\) | ||||
−0.221280 | + | 0.975210i | \(0.571024\pi\) | |||||||
\(194\) | 3164.31 | 1.17105 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −68.7981 | −0.0250722 | ||||||||
\(197\) | −3614.72 | −1.30730 | −0.653650 | − | 0.756797i | \(-0.726763\pi\) | ||||
−0.653650 | + | 0.756797i | \(0.726763\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3077.54 | −1.09629 | −0.548144 | − | 0.836384i | \(-0.684665\pi\) | ||||
−0.548144 | + | 0.836384i | \(0.684665\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4267.52 | −1.48644 | ||||||||
\(203\) | −194.079 | −0.0671020 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 497.295 | 0.168195 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1728.75 | 0.576284 | ||||||||
\(209\) | 10854.3 | 3.59239 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 145.901 | 0.0476031 | 0.0238016 | − | 0.999717i | \(-0.492423\pi\) | ||||
0.0238016 | + | 0.999717i | \(0.492423\pi\) | |||||||
\(212\) | −950.070 | −0.307788 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2365.47 | 0.755609 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 520.392 | 0.162795 | ||||||||
\(218\) | −3350.89 | −1.04106 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 208.599 | 0.0634928 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3357.30 | 1.00817 | 0.504084 | − | 0.863655i | \(-0.331830\pi\) | ||||
0.504084 | + | 0.863655i | \(0.331830\pi\) | |||||||
\(224\) | −439.306 | −0.131037 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 610.181 | 0.179596 | ||||||||
\(227\) | 636.529 | 0.186114 | 0.0930570 | − | 0.995661i | \(-0.470336\pi\) | ||||
0.0930570 | + | 0.995661i | \(0.470336\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3652.17 | 1.05389 | 0.526947 | − | 0.849898i | \(-0.323337\pi\) | ||||
0.526947 | + | 0.849898i | \(0.323337\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −669.630 | −0.189497 | ||||||||
\(233\) | −3387.30 | −0.952400 | −0.476200 | − | 0.879337i | \(-0.657986\pi\) | ||||
−0.476200 | + | 0.879337i | \(0.657986\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −162.839 | −0.0449149 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 110.192 | 0.0300113 | ||||||||
\(239\) | 3382.64 | 0.915502 | 0.457751 | − | 0.889080i | \(-0.348655\pi\) | ||||
0.457751 | + | 0.889080i | \(0.348655\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5809.63 | 1.55283 | 0.776413 | − | 0.630225i | \(-0.217037\pi\) | ||||
0.776413 | + | 0.630225i | \(0.217037\pi\) | |||||||
\(242\) | −7911.17 | −2.10144 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 548.077 | 0.143799 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5561.80 | 1.43275 | ||||||||
\(248\) | 1795.50 | 0.459736 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 345.006 | 0.0867593 | 0.0433796 | − | 0.999059i | \(-0.486187\pi\) | ||||
0.0433796 | + | 0.999059i | \(0.486187\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2383.07 | 0.592184 | ||||||||
\(254\) | 3704.23 | 0.915056 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2086.30 | −0.509350 | ||||||||
\(257\) | 3142.39 | 0.762712 | 0.381356 | − | 0.924428i | \(-0.375457\pi\) | ||||
0.381356 | + | 0.924428i | \(0.375457\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1826.76 | −0.438260 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1654.05 | 0.390029 | ||||||||
\(263\) | 4949.02 | 1.16034 | 0.580170 | − | 0.814495i | \(-0.302986\pi\) | ||||
0.580170 | + | 0.814495i | \(0.302986\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2938.01 | 0.677222 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1002.10 | 0.228406 | ||||||||
\(269\) | 4570.60 | 1.03596 | 0.517982 | − | 0.855391i | \(-0.326683\pi\) | ||||
0.517982 | + | 0.855391i | \(0.326683\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5338.43 | −1.19663 | −0.598315 | − | 0.801261i | \(-0.704163\pi\) | ||||
−0.598315 | + | 0.801261i | \(0.704163\pi\) | |||||||
\(272\) | 311.348 | 0.0694053 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −913.213 | −0.201347 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2225.98 | 0.482837 | 0.241419 | − | 0.970421i | \(-0.422387\pi\) | ||||
0.241419 | + | 0.970421i | \(0.422387\pi\) | |||||||
\(278\) | 1212.26 | 0.261534 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1991.15 | −0.422712 | −0.211356 | − | 0.977409i | \(-0.567788\pi\) | ||||
−0.211356 | + | 0.977409i | \(0.567788\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7350.20 | −1.54390 | −0.771951 | − | 0.635682i | \(-0.780719\pi\) | ||||
−0.771951 | + | 0.635682i | \(0.780719\pi\) | |||||||
\(284\) | 1138.01 | 0.237777 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5805.29 | −1.20026 | ||||||||
\(287\) | 3118.39 | 0.641369 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4875.43 | −0.992353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −491.690 | −0.0985410 | ||||||||
\(293\) | −6250.16 | −1.24621 | −0.623103 | − | 0.782140i | \(-0.714128\pi\) | ||||
−0.623103 | + | 0.782140i | \(0.714128\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6302.85 | −1.23765 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2803.32 | −0.544940 | ||||||||
\(299\) | 1221.10 | 0.236180 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3324.89 | −0.636690 | ||||||||
\(302\) | −7485.13 | −1.42623 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8301.35 | 1.56617 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1259.29 | −0.234109 | −0.117054 | − | 0.993126i | \(-0.537345\pi\) | ||||
−0.117054 | + | 0.993126i | \(0.537345\pi\) | |||||||
\(308\) | 652.777 | 0.120764 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6711.92 | 1.22379 | 0.611894 | − | 0.790940i | \(-0.290408\pi\) | ||||
0.611894 | + | 0.790940i | \(0.290408\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2436.27 | 0.439955 | 0.219978 | − | 0.975505i | \(-0.429402\pi\) | ||||
0.219978 | + | 0.975505i | \(0.429402\pi\) | |||||||
\(314\) | 3793.16 | 0.681721 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 71.5089 | 0.0127300 | ||||||||
\(317\) | −1191.81 | −0.211164 | −0.105582 | − | 0.994411i | \(-0.533670\pi\) | ||||
−0.105582 | + | 0.994411i | \(0.533670\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1841.48 | 0.323208 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 645.042 | 0.111636 | ||||||||
\(323\) | 1001.68 | 0.172555 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7100.11 | −1.20625 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10759.4 | 1.81124 | ||||||||
\(329\) | 357.305 | 0.0598750 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5885.63 | 0.977351 | 0.488676 | − | 0.872466i | \(-0.337480\pi\) | ||||
0.488676 | + | 0.872466i | \(0.337480\pi\) | |||||||
\(332\) | −119.190 | −0.0197030 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −656.210 | −0.107504 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1209.73 | 0.195544 | 0.0977720 | − | 0.995209i | \(-0.468828\pi\) | ||||
0.0977720 | + | 0.995209i | \(0.468828\pi\) | |||||||
\(338\) | 2667.81 | 0.429319 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4937.63 | −0.784129 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | −11471.8 | −1.79802 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9889.23 | −1.53656 | ||||||||
\(347\) | 5065.21 | 0.783617 | 0.391808 | − | 0.920047i | \(-0.371850\pi\) | ||||
0.391808 | + | 0.920047i | \(0.371850\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5481.35 | 0.840716 | 0.420358 | − | 0.907358i | \(-0.361904\pi\) | ||||
0.420358 | + | 0.907358i | \(0.361904\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4168.27 | 0.631163 | ||||||||
\(353\) | 602.190 | 0.0907970 | 0.0453985 | − | 0.998969i | \(-0.485544\pi\) | ||||
0.0453985 | + | 0.998969i | \(0.485544\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2136.71 | 0.318105 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2447.05 | 0.361259 | ||||||||
\(359\) | −2004.84 | −0.294740 | −0.147370 | − | 0.989081i | \(-0.547081\pi\) | ||||
−0.147370 | + | 0.989081i | \(0.547081\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19848.5 | 2.89379 | ||||||||
\(362\) | −4234.63 | −0.614826 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 334.486 | 0.0481643 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7770.37 | −1.10520 | −0.552602 | − | 0.833445i | \(-0.686365\pi\) | ||||
−0.552602 | + | 0.833445i | \(0.686365\pi\) | |||||||
\(368\) | 1822.57 | 0.258174 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4736.67 | 0.662846 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7485.06 | 1.03904 | 0.519520 | − | 0.854458i | \(-0.326111\pi\) | ||||
0.519520 | + | 0.854458i | \(0.326111\pi\) | |||||||
\(374\) | −1045.54 | −0.144555 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1232.81 | 0.169088 | ||||||||
\(377\) | 943.583 | 0.128905 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4053.61 | −0.549393 | −0.274697 | − | 0.961531i | \(-0.588577\pi\) | ||||
−0.274697 | + | 0.961531i | \(0.588577\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1971.23 | 0.264023 | ||||||||
\(383\) | 4531.33 | 0.604543 | 0.302272 | − | 0.953222i | \(-0.402255\pi\) | ||||
0.302272 | + | 0.953222i | \(0.402255\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3047.53 | 0.401853 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1729.90 | 0.226346 | ||||||||
\(389\) | 1160.19 | 0.151219 | 0.0756093 | − | 0.997138i | \(-0.475910\pi\) | ||||
0.0756093 | + | 0.997138i | \(0.475910\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 219.920 | 0.0284446 | ||||||||
\(392\) | 1183.45 | 0.152483 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9283.53 | 1.18705 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6720.74 | 0.849632 | 0.424816 | − | 0.905280i | \(-0.360339\pi\) | ||||
0.424816 | + | 0.905280i | \(0.360339\pi\) | |||||||
\(398\) | 7903.93 | 0.995448 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2769.06 | −0.344839 | −0.172419 | − | 0.985024i | \(-0.555158\pi\) | ||||
−0.172419 | + | 0.985024i | \(0.555158\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2530.07 | −0.312733 | ||||||||
\(404\) | −2333.01 | −0.287306 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 498.446 | 0.0609297 | ||||||||
\(407\) | 17332.8 | 2.11095 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14438.9 | 1.74561 | 0.872806 | − | 0.488067i | \(-0.162298\pi\) | ||||
0.872806 | + | 0.488067i | \(0.162298\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 271.866 | 0.0325095 | ||||||||
\(413\) | 811.850 | 0.0967277 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2135.84 | 0.251726 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −27876.7 | −3.26195 | ||||||||
\(419\) | −6396.35 | −0.745780 | −0.372890 | − | 0.927875i | \(-0.621633\pi\) | ||||
−0.372890 | + | 0.927875i | \(0.621633\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8231.07 | −0.952868 | −0.476434 | − | 0.879210i | \(-0.658071\pi\) | ||||
−0.476434 | + | 0.879210i | \(0.658071\pi\) | |||||||
\(422\) | −374.712 | −0.0432244 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 16342.9 | 1.87189 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2732.49 | −0.309683 | ||||||||
\(428\) | 1293.18 | 0.146047 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5975.72 | 0.667843 | 0.333922 | − | 0.942601i | \(-0.391628\pi\) | ||||
0.333922 | + | 0.942601i | \(0.391628\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10912.9 | 1.21118 | 0.605591 | − | 0.795776i | \(-0.292937\pi\) | ||||
0.605591 | + | 0.795776i | \(0.292937\pi\) | |||||||
\(434\) | −1336.50 | −0.147821 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1831.90 | −0.201221 | ||||||||
\(437\) | 5863.65 | 0.641868 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3784.05 | 0.411396 | 0.205698 | − | 0.978616i | \(-0.434054\pi\) | ||||
0.205698 | + | 0.978616i | \(0.434054\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −535.737 | −0.0576526 | ||||||||
\(443\) | 7869.34 | 0.843981 | 0.421991 | − | 0.906600i | \(-0.361331\pi\) | ||||
0.421991 | + | 0.906600i | \(0.361331\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8622.42 | −0.915434 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3972.85 | 0.418972 | ||||||||
\(449\) | 15601.8 | 1.63986 | 0.819929 | − | 0.572465i | \(-0.194013\pi\) | ||||
0.819929 | + | 0.572465i | \(0.194013\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29588.3 | −3.08926 | ||||||||
\(452\) | 333.580 | 0.0347130 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1634.77 | −0.168995 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8840.78 | −0.904933 | −0.452466 | − | 0.891781i | \(-0.649456\pi\) | ||||
−0.452466 | + | 0.891781i | \(0.649456\pi\) | |||||||
\(458\) | −9379.71 | −0.956954 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10523.7 | 1.06321 | 0.531605 | − | 0.846993i | \(-0.321589\pi\) | ||||
0.531605 | + | 0.846993i | \(0.321589\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10781.6 | 1.08221 | 0.541107 | − | 0.840954i | \(-0.318006\pi\) | ||||
0.541107 | + | 0.840954i | \(0.318006\pi\) | |||||||
\(464\) | 1408.36 | 0.140908 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8699.46 | 0.864795 | ||||||||
\(467\) | 5592.55 | 0.554160 | 0.277080 | − | 0.960847i | \(-0.410633\pi\) | ||||
0.277080 | + | 0.960847i | \(0.410633\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4996.05 | −0.491889 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2801.12 | 0.273161 | ||||||||
\(473\) | 31547.6 | 3.06672 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 60.2410 | 0.00580072 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8687.51 | −0.831292 | ||||||||
\(479\) | 7835.28 | 0.747397 | 0.373698 | − | 0.927550i | \(-0.378089\pi\) | ||||
0.373698 | + | 0.927550i | \(0.378089\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8881.42 | 0.841908 | ||||||||
\(482\) | −14920.6 | −1.40999 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4324.96 | −0.406176 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5979.24 | 0.556356 | 0.278178 | − | 0.960530i | \(-0.410269\pi\) | ||||
0.278178 | + | 0.960530i | \(0.410269\pi\) | |||||||
\(488\) | −9427.89 | −0.874550 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1792.66 | 0.164769 | 0.0823846 | − | 0.996601i | \(-0.473746\pi\) | ||||
0.0823846 | + | 0.996601i | \(0.473746\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 169.940 | 0.0155248 | ||||||||
\(494\) | −14284.2 | −1.30096 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3776.29 | −0.341855 | ||||||||
\(497\) | −5673.67 | −0.512070 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20514.4 | −1.84038 | −0.920191 | − | 0.391470i | \(-0.871967\pi\) | ||||
−0.920191 | + | 0.391470i | \(0.871967\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −886.065 | −0.0787789 | ||||||||
\(503\) | −16294.5 | −1.44441 | −0.722205 | − | 0.691679i | \(-0.756871\pi\) | ||||
−0.722205 | + | 0.691679i | \(0.756871\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6120.35 | −0.537713 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2025.07 | 0.176866 | ||||||||
\(509\) | −12183.8 | −1.06097 | −0.530487 | − | 0.847693i | \(-0.677991\pi\) | ||||
−0.530487 | + | 0.847693i | \(0.677991\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2451.37 | 0.212216 | ||||||||
\(512\) | 13002.5 | 1.12234 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8070.48 | −0.692555 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3390.22 | −0.288398 | ||||||||
\(518\) | 4691.59 | 0.397947 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11251.3 | 0.946116 | 0.473058 | − | 0.881031i | \(-0.343150\pi\) | ||||
0.473058 | + | 0.881031i | \(0.343150\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13493.7 | −1.12818 | −0.564090 | − | 0.825713i | \(-0.690773\pi\) | ||||
−0.564090 | + | 0.825713i | \(0.690773\pi\) | |||||||
\(524\) | 904.254 | 0.0753865 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12710.4 | −1.05361 | ||||||||
\(527\) | −455.666 | −0.0376644 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10879.6 | −0.894192 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1606.18 | 0.130896 | ||||||||
\(533\) | −15161.1 | −1.23209 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −17237.8 | −1.38910 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11738.5 | −0.940673 | ||||||||
\(539\) | −3254.49 | −0.260075 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18810.8 | −1.49490 | −0.747449 | − | 0.664319i | \(-0.768722\pi\) | ||||
−0.747449 | + | 0.664319i | \(0.768722\pi\) | |||||||
\(542\) | 13710.5 | 1.08656 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 384.666 | 0.0303169 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9822.68 | 0.767801 | 0.383901 | − | 0.923374i | \(-0.374581\pi\) | ||||
0.383901 | + | 0.923374i | \(0.374581\pi\) | |||||||
\(548\) | −499.245 | −0.0389173 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4531.04 | 0.350324 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −356.515 | −0.0274151 | ||||||||
\(554\) | −5716.89 | −0.438424 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 662.731 | 0.0505504 | ||||||||
\(557\) | −23627.9 | −1.79739 | −0.898696 | − | 0.438571i | \(-0.855485\pi\) | ||||
−0.898696 | + | 0.438571i | \(0.855485\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16165.1 | 1.22310 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5113.79 | 0.383830 | ||||||||
\(563\) | 966.441 | 0.0723457 | 0.0361729 | − | 0.999346i | \(-0.488483\pi\) | ||||
0.0361729 | + | 0.999346i | \(0.488483\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 18877.2 | 1.40189 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −19575.8 | −1.44610 | ||||||||
\(569\) | −16451.2 | −1.21208 | −0.606038 | − | 0.795435i | \(-0.707242\pi\) | ||||
−0.606038 | + | 0.795435i | \(0.707242\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.8467 | 0.00277379 | 0.00138690 | − | 0.999999i | \(-0.499559\pi\) | ||||
0.00138690 | + | 0.999999i | \(0.499559\pi\) | |||||||
\(572\) | −3173.70 | −0.231991 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8008.85 | −0.582374 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23779.1 | −1.71566 | −0.857830 | − | 0.513933i | \(-0.828188\pi\) | ||||
−0.857830 | + | 0.513933i | \(0.828188\pi\) | |||||||
\(578\) | 12521.4 | 0.901073 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 594.233 | 0.0424319 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −44942.9 | −3.19270 | ||||||||
\(584\) | 8457.93 | 0.599301 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16052.0 | 1.13158 | ||||||||
\(587\) | 12556.0 | 0.882863 | 0.441432 | − | 0.897295i | \(-0.354471\pi\) | ||||
0.441432 | + | 0.897295i | \(0.354471\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12149.2 | −0.849917 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 13256.1 | 0.920307 | ||||||||
\(593\) | −26489.2 | −1.83437 | −0.917185 | − | 0.398461i | \(-0.869544\pi\) | ||||
−0.917185 | + | 0.398461i | \(0.869544\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1532.55 | −0.105328 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3136.09 | −0.214456 | ||||||||
\(599\) | −8910.78 | −0.607821 | −0.303910 | − | 0.952701i | \(-0.598292\pi\) | ||||
−0.303910 | + | 0.952701i | \(0.598292\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2943.50 | 0.199780 | 0.0998902 | − | 0.994998i | \(-0.468151\pi\) | ||||
0.0998902 | + | 0.994998i | \(0.468151\pi\) | |||||||
\(602\) | 8539.18 | 0.578125 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4092.05 | −0.275668 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20445.4 | 1.36714 | 0.683569 | − | 0.729886i | \(-0.260427\pi\) | ||||
0.683569 | + | 0.729886i | \(0.260427\pi\) | |||||||
\(608\) | 10256.2 | 0.684117 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1737.16 | −0.115021 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19174.7 | 1.26339 | 0.631697 | − | 0.775215i | \(-0.282359\pi\) | ||||
0.631697 | + | 0.775215i | \(0.282359\pi\) | |||||||
\(614\) | 3234.18 | 0.212575 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11228.9 | −0.734458 | ||||||||
\(617\) | 21445.6 | 1.39930 | 0.699650 | − | 0.714486i | \(-0.253339\pi\) | ||||
0.699650 | + | 0.714486i | \(0.253339\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17031.2 | −1.10588 | −0.552941 | − | 0.833220i | \(-0.686495\pi\) | ||||
−0.552941 | + | 0.833220i | \(0.686495\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17237.9 | −1.11122 | ||||||||
\(623\) | −10652.8 | −0.685063 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6256.97 | −0.399487 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2073.69 | 0.131766 | ||||||||
\(629\) | 1599.55 | 0.101396 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25190.1 | 1.58923 | 0.794614 | − | 0.607115i | \(-0.207673\pi\) | ||||
0.794614 | + | 0.607115i | \(0.207673\pi\) | |||||||
\(632\) | −1230.08 | −0.0774208 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3060.88 | 0.191740 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1667.61 | −0.103726 | ||||||||
\(638\) | −4729.40 | −0.293478 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11755.1 | −0.724335 | −0.362168 | − | 0.932113i | \(-0.617963\pi\) | ||||
−0.362168 | + | 0.932113i | \(0.617963\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24044.2 | 1.47467 | 0.737333 | − | 0.675530i | \(-0.236085\pi\) | ||||
0.737333 | + | 0.675530i | \(0.236085\pi\) | |||||||
\(644\) | 352.639 | 0.0215775 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2572.58 | −0.156683 | ||||||||
\(647\) | 5138.50 | 0.312234 | 0.156117 | − | 0.987739i | \(-0.450102\pi\) | ||||
0.156117 | + | 0.987739i | \(0.450102\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7703.07 | −0.465905 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3881.56 | −0.233150 | ||||||||
\(653\) | −6665.57 | −0.399455 | −0.199727 | − | 0.979851i | \(-0.564006\pi\) | ||||
−0.199727 | + | 0.979851i | \(0.564006\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −22629.0 | −1.34682 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −917.653 | −0.0543675 | ||||||||
\(659\) | −8996.31 | −0.531785 | −0.265893 | − | 0.964003i | \(-0.585667\pi\) | ||||
−0.265893 | + | 0.964003i | \(0.585667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24565.6 | 1.44553 | 0.722763 | − | 0.691096i | \(-0.242872\pi\) | ||||
0.722763 | + | 0.691096i | \(0.242872\pi\) | |||||||
\(662\) | −15115.8 | −0.887451 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2050.27 | 0.119828 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 994.793 | 0.0577489 | ||||||||
\(668\) | −358.744 | −0.0207788 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25926.7 | 1.49164 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22046.9 | −1.26277 | −0.631387 | − | 0.775468i | \(-0.717514\pi\) | ||||
−0.631387 | + | 0.775468i | \(0.717514\pi\) | |||||||
\(674\) | −3106.91 | −0.177557 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1458.47 | 0.0829805 | ||||||||
\(677\) | −25109.8 | −1.42548 | −0.712738 | − | 0.701430i | \(-0.752545\pi\) | ||||
−0.712738 | + | 0.701430i | \(0.752545\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8624.58 | −0.487453 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12681.1 | 0.712002 | ||||||||
\(683\) | −20540.1 | −1.15073 | −0.575363 | − | 0.817898i | \(-0.695139\pi\) | ||||
−0.575363 | + | 0.817898i | \(0.695139\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −880.913 | −0.0490283 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 24127.5 | 1.33699 | ||||||||
\(689\) | −23029.0 | −1.27334 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1635.59 | −0.0900446 | −0.0450223 | − | 0.998986i | \(-0.514336\pi\) | ||||
−0.0450223 | + | 0.998986i | \(0.514336\pi\) | |||||||
\(692\) | −5406.35 | −0.296992 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13008.8 | −0.711537 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2730.53 | −0.148388 | ||||||||
\(698\) | −14077.5 | −0.763385 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16895.6 | −0.910325 | −0.455163 | − | 0.890408i | \(-0.650419\pi\) | ||||
−0.455163 | + | 0.890408i | \(0.650419\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 42648.1 | 2.28806 | ||||||||
\(704\) | −37695.5 | −2.01805 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1546.58 | −0.0824452 | ||||||||
\(707\) | 11631.5 | 0.618736 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3527.13 | −0.186833 | −0.0934163 | − | 0.995627i | \(-0.529779\pi\) | ||||
−0.0934163 | + | 0.995627i | \(0.529779\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −36755.1 | −1.93463 | ||||||||
\(713\) | −2667.37 | −0.140104 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1337.78 | 0.0698256 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5148.95 | 0.267628 | ||||||||
\(719\) | 35693.3 | 1.85137 | 0.925687 | − | 0.378291i | \(-0.123488\pi\) | ||||
0.925687 | + | 0.378291i | \(0.123488\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1355.42 | −0.0700116 | ||||||||
\(722\) | −50976.1 | −2.62761 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2315.03 | −0.118836 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18829.9 | −0.960611 | −0.480305 | − | 0.877101i | \(-0.659474\pi\) | ||||
−0.480305 | + | 0.877101i | \(0.659474\pi\) | |||||||
\(728\) | −5753.74 | −0.292923 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2911.34 | 0.147305 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14895.4 | −0.750577 | −0.375288 | − | 0.926908i | \(-0.622456\pi\) | ||||
−0.375288 | + | 0.926908i | \(0.622456\pi\) | |||||||
\(734\) | 19956.3 | 1.00354 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2251.75 | 0.112773 | ||||||||
\(737\) | 47404.0 | 2.36926 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8866.34 | 0.441345 | 0.220672 | − | 0.975348i | \(-0.429175\pi\) | ||||
0.220672 | + | 0.975348i | \(0.429175\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12165.0 | −0.601875 | ||||||||
\(743\) | −14225.4 | −0.702394 | −0.351197 | − | 0.936302i | \(-0.614225\pi\) | ||||
−0.351197 | + | 0.936302i | \(0.614225\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −19223.6 | −0.943465 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −571.585 | −0.0279401 | ||||||||
\(749\) | −6447.28 | −0.314524 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34300.2 | 1.66662 | 0.833311 | − | 0.552804i | \(-0.186442\pi\) | ||||
0.833311 | + | 0.552804i | \(0.186442\pi\) | |||||||
\(752\) | −2592.83 | −0.125732 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2423.37 | −0.117047 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2340.98 | −0.112397 | −0.0561984 | − | 0.998420i | \(-0.517898\pi\) | ||||
−0.0561984 | + | 0.998420i | \(0.517898\pi\) | |||||||
\(758\) | 10410.7 | 0.498858 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23894.9 | −1.13823 | −0.569113 | − | 0.822259i | \(-0.692713\pi\) | ||||
−0.569113 | + | 0.822259i | \(0.692713\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9133.13 | 0.433344 | ||||||||
\(764\) | 1077.65 | 0.0510316 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11637.6 | −0.548935 | ||||||||
\(767\) | −3947.09 | −0.185816 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22951.1 | 1.07625 | 0.538126 | − | 0.842864i | \(-0.319132\pi\) | ||||
0.538126 | + | 0.842864i | \(0.319132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1666.05 | 0.0776718 | ||||||||
\(773\) | −13526.7 | −0.629393 | −0.314696 | − | 0.949192i | \(-0.601903\pi\) | ||||
−0.314696 | + | 0.949192i | \(0.601903\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −29757.3 | −1.37658 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2979.67 | −0.137309 | ||||||||
\(779\) | −72803.1 | −3.34845 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 53833.5 | 2.46647 | ||||||||
\(782\) | −564.812 | −0.0258282 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2489.02 | −0.113385 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1611.55 | −0.0729929 | −0.0364965 | − | 0.999334i | \(-0.511620\pi\) | ||||
−0.0364965 | + | 0.999334i | \(0.511620\pi\) | |||||||
\(788\) | 5075.22 | 0.229438 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1663.10 | −0.0747572 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13285.0 | 0.594909 | ||||||||
\(794\) | −17260.6 | −0.771481 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4321.00 | 0.192404 | ||||||||
\(797\) | 7064.99 | 0.313996 | 0.156998 | − | 0.987599i | \(-0.449818\pi\) | ||||
0.156998 | + | 0.987599i | \(0.449818\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −312.864 | −0.0138527 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7111.67 | 0.313119 | ||||||||
\(803\) | −23259.3 | −1.02217 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6497.86 | 0.283967 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 40131.9 | 1.74732 | ||||||||
\(809\) | 6352.68 | 0.276079 | 0.138040 | − | 0.990427i | \(-0.455920\pi\) | ||||
0.138040 | + | 0.990427i | \(0.455920\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16809.3 | −0.727810 | −0.363905 | − | 0.931436i | \(-0.618557\pi\) | ||||
−0.363905 | + | 0.931436i | \(0.618557\pi\) | |||||||
\(812\) | 272.496 | 0.0117768 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −44515.2 | −1.91678 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 77624.0 | 3.32401 | ||||||||
\(818\) | −37082.7 | −1.58505 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41992.9 | 1.78510 | 0.892548 | − | 0.450952i | \(-0.148916\pi\) | ||||
0.892548 | + | 0.450952i | \(0.148916\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37046.2 | −1.56908 | −0.784538 | − | 0.620080i | \(-0.787100\pi\) | ||||
−0.784538 | + | 0.620080i | \(0.787100\pi\) | |||||||
\(824\) | −4676.58 | −0.197714 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2085.04 | −0.0878304 | ||||||||
\(827\) | 14371.8 | 0.604301 | 0.302151 | − | 0.953260i | \(-0.402295\pi\) | ||||
0.302151 | + | 0.953260i | \(0.402295\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43252.1 | −1.81207 | −0.906037 | − | 0.423199i | \(-0.860907\pi\) | ||||
−0.906037 | + | 0.423199i | \(0.860907\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −19315.4 | −0.804855 | ||||||||
\(833\) | −300.338 | −0.0124923 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −15239.9 | −0.630484 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16427.5 | 0.677181 | ||||||||
\(839\) | 6400.97 | 0.263392 | 0.131696 | − | 0.991290i | \(-0.457958\pi\) | ||||
0.131696 | + | 0.991290i | \(0.457958\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23620.3 | −0.968481 | ||||||||
\(842\) | 21139.5 | 0.865221 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −204.852 | −0.00835460 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21562.5 | 0.874731 | ||||||||
\(848\) | −34372.2 | −1.39192 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9363.42 | 0.377173 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17772.0 | 0.713368 | 0.356684 | − | 0.934225i | \(-0.383907\pi\) | ||||
0.356684 | + | 0.934225i | \(0.383907\pi\) | |||||||
\(854\) | 7017.75 | 0.281197 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −22245.0 | −0.888222 | ||||||||
\(857\) | −29094.3 | −1.15968 | −0.579839 | − | 0.814731i | \(-0.696885\pi\) | ||||
−0.579839 | + | 0.814731i | \(0.696885\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −599.045 | −0.0237941 | −0.0118971 | − | 0.999929i | \(-0.503787\pi\) | ||||
−0.0118971 | + | 0.999929i | \(0.503787\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15347.2 | −0.606413 | ||||||||
\(863\) | 19253.4 | 0.759435 | 0.379717 | − | 0.925103i | \(-0.376021\pi\) | ||||
0.379717 | + | 0.925103i | \(0.376021\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −28027.2 | −1.09977 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −730.653 | −0.0285714 | ||||||||
\(869\) | 3382.72 | 0.132049 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24290.0 | 0.944931 | ||||||||
\(872\) | 31511.9 | 1.22377 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15059.4 | −0.582827 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42907.7 | 1.65210 | 0.826049 | − | 0.563598i | \(-0.190583\pi\) | ||||
0.826049 | + | 0.563598i | \(0.190583\pi\) | |||||||
\(878\) | −9718.41 | −0.373554 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5765.54 | 0.220484 | 0.110242 | − | 0.993905i | \(-0.464837\pi\) | ||||
0.110242 | + | 0.993905i | \(0.464837\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35426.8 | −1.35018 | −0.675089 | − | 0.737736i | \(-0.735895\pi\) | ||||
−0.675089 | + | 0.737736i | \(0.735895\pi\) | |||||||
\(884\) | −292.883 | −0.0111433 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20210.5 | −0.766349 | ||||||||
\(887\) | 24413.1 | 0.924138 | 0.462069 | − | 0.886844i | \(-0.347107\pi\) | ||||
0.462069 | + | 0.886844i | \(0.347107\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10096.2 | −0.380895 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4713.80 | −0.176939 | ||||||||
\(893\) | −8341.77 | −0.312594 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6688.85 | −0.249396 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −40069.6 | −1.48902 | ||||||||
\(899\) | −2061.17 | −0.0764671 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4147.53 | −0.153356 | ||||||||
\(902\) | 75990.3 | 2.80510 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5738.17 | −0.211116 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23459.2 | −0.858818 | −0.429409 | − | 0.903110i | \(-0.641278\pi\) | ||||
−0.429409 | + | 0.903110i | \(0.641278\pi\) | |||||||
\(908\) | −893.714 | −0.0326640 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45803.8 | 1.66580 | 0.832902 | − | 0.553421i | \(-0.186678\pi\) | ||||
0.832902 | + | 0.553421i | \(0.186678\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5638.25 | −0.204380 | ||||||||
\(914\) | 22705.4 | 0.821694 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5127.80 | −0.184964 | ||||||||
\(917\) | −4508.25 | −0.162351 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33360.4 | 1.19745 | 0.598725 | − | 0.800955i | \(-0.295674\pi\) | ||||
0.598725 | + | 0.800955i | \(0.295674\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −27027.7 | −0.965412 | ||||||||
\(923\) | 27584.5 | 0.983700 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −27690.0 | −0.982668 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1740.01 | 0.0615501 | ||||||||
\(929\) | −11194.3 | −0.395341 | −0.197670 | − | 0.980269i | \(-0.563338\pi\) | ||||
−0.197670 | + | 0.980269i | \(0.563338\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8007.79 | −0.281895 | ||||||||
\(932\) | 4755.91 | 0.167151 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14363.1 | −0.503186 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4383.20 | 0.152821 | 0.0764103 | − | 0.997076i | \(-0.475654\pi\) | ||||
0.0764103 | + | 0.997076i | \(0.475654\pi\) | |||||||
\(938\) | 12831.1 | 0.446644 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27642.7 | 0.957626 | 0.478813 | − | 0.877917i | \(-0.341067\pi\) | ||||
0.478813 | + | 0.877917i | \(0.341067\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15984.0 | −0.551972 | ||||||||
\(944\) | −5891.29 | −0.203120 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −81022.3 | −2.78463 | ||||||||
\(947\) | −25657.8 | −0.880428 | −0.440214 | − | 0.897893i | \(-0.645098\pi\) | ||||
−0.440214 | + | 0.897893i | \(0.645098\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11918.2 | −0.407672 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1036.25 | −0.0352785 | ||||||||
\(953\) | −48210.6 | −1.63871 | −0.819356 | − | 0.573285i | \(-0.805669\pi\) | ||||
−0.819356 | + | 0.573285i | \(0.805669\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4749.38 | −0.160676 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −20123.0 | −0.678649 | ||||||||
\(959\) | 2489.04 | 0.0838114 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24264.3 | −0.814484 | ||||||||
\(962\) | −22809.8 | −0.764467 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8156.97 | −0.272529 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17711.5 | −0.589002 | −0.294501 | − | 0.955651i | \(-0.595153\pi\) | ||||
−0.294501 | + | 0.955651i | \(0.595153\pi\) | |||||||
\(968\) | 74396.9 | 2.47026 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35777.8 | −1.18245 | −0.591227 | − | 0.806505i | \(-0.701356\pi\) | ||||
−0.591227 | + | 0.806505i | \(0.701356\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3304.11 | −0.108864 | ||||||||
\(974\) | −15356.2 | −0.505181 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 19828.7 | 0.650307 | ||||||||
\(977\) | −30436.2 | −0.996662 | −0.498331 | − | 0.866987i | \(-0.666054\pi\) | ||||
−0.498331 | + | 0.866987i | \(0.666054\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 101077. | 3.29972 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4604.02 | −0.149613 | ||||||||
\(983\) | 57841.2 | 1.87675 | 0.938376 | − | 0.345617i | \(-0.112330\pi\) | ||||
0.938376 | + | 0.345617i | \(0.112330\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −436.450 | −0.0140967 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7809.01 | −0.251455 | ||||||||
\(989\) | 17042.4 | 0.547944 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1521.84 | 0.0487819 | 0.0243909 | − | 0.999702i | \(-0.492235\pi\) | ||||
0.0243909 | + | 0.999702i | \(0.492235\pi\) | |||||||
\(992\) | −4665.54 | −0.149326 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 14571.5 | 0.464968 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46899.5 | 1.48979 | 0.744896 | − | 0.667181i | \(-0.232499\pi\) | ||||
0.744896 | + | 0.667181i | \(0.232499\pi\) | |||||||
\(998\) | 52686.3 | 1.67110 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1575.4.a.bm.1.1 | 4 | ||
3.2 | odd | 2 | 525.4.a.s.1.4 | ✓ | 4 | ||
5.4 | even | 2 | 1575.4.a.bf.1.4 | 4 | |||
15.2 | even | 4 | 525.4.d.o.274.6 | 8 | |||
15.8 | even | 4 | 525.4.d.o.274.3 | 8 | |||
15.14 | odd | 2 | 525.4.a.v.1.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.4.a.s.1.4 | ✓ | 4 | 3.2 | odd | 2 | ||
525.4.a.v.1.1 | yes | 4 | 15.14 | odd | 2 | ||
525.4.d.o.274.3 | 8 | 15.8 | even | 4 | |||
525.4.d.o.274.6 | 8 | 15.2 | even | 4 | |||
1575.4.a.bf.1.4 | 4 | 5.4 | even | 2 | |||
1575.4.a.bm.1.1 | 4 | 1.1 | even | 1 | trivial |