Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(1,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.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: | \(9.97132279097\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 13) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.56155 | −0.905646 | −0.452823 | − | 0.891601i | \(-0.649583\pi\) | ||||
−0.452823 | + | 0.891601i | \(0.649583\pi\) | |||||||
\(3\) | −3.68466 | −0.709113 | −0.354556 | − | 0.935035i | \(-0.615368\pi\) | ||||
−0.354556 | + | 0.935035i | \(0.615368\pi\) | |||||||
\(4\) | −1.43845 | −0.179806 | ||||||||
\(5\) | −0.561553 | −0.0502268 | −0.0251134 | − | 0.999685i | \(-0.507995\pi\) | ||||
−0.0251134 | + | 0.999685i | \(0.507995\pi\) | |||||||
\(6\) | 9.43845 | 0.642205 | ||||||||
\(7\) | −18.1771 | −0.981470 | −0.490735 | − | 0.871309i | \(-0.663272\pi\) | ||||
−0.490735 | + | 0.871309i | \(0.663272\pi\) | |||||||
\(8\) | 24.1771 | 1.06849 | ||||||||
\(9\) | −13.4233 | −0.497159 | ||||||||
\(10\) | 1.43845 | 0.0454877 | ||||||||
\(11\) | −64.7386 | −1.77449 | −0.887247 | − | 0.461295i | \(-0.847385\pi\) | ||||
−0.887247 | + | 0.461295i | \(0.847385\pi\) | |||||||
\(12\) | 5.30019 | 0.127503 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 46.5616 | 0.888864 | ||||||||
\(15\) | 2.06913 | 0.0356165 | ||||||||
\(16\) | −50.4233 | −0.787864 | ||||||||
\(17\) | −25.5464 | −0.364465 | −0.182233 | − | 0.983255i | \(-0.558332\pi\) | ||||
−0.182233 | + | 0.983255i | \(0.558332\pi\) | |||||||
\(18\) | 34.3845 | 0.450250 | ||||||||
\(19\) | 107.970 | 1.30368 | 0.651841 | − | 0.758356i | \(-0.273997\pi\) | ||||
0.651841 | + | 0.758356i | \(0.273997\pi\) | |||||||
\(20\) | 0.807764 | 0.00903108 | ||||||||
\(21\) | 66.9763 | 0.695973 | ||||||||
\(22\) | 165.831 | 1.60706 | ||||||||
\(23\) | 73.2614 | 0.664176 | 0.332088 | − | 0.943248i | \(-0.392247\pi\) | ||||
0.332088 | + | 0.943248i | \(0.392247\pi\) | |||||||
\(24\) | −89.0843 | −0.757677 | ||||||||
\(25\) | −124.685 | −0.997477 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 148.946 | 1.06165 | ||||||||
\(28\) | 26.1468 | 0.176474 | ||||||||
\(29\) | 175.909 | 1.12640 | 0.563198 | − | 0.826322i | \(-0.309571\pi\) | ||||
0.563198 | + | 0.826322i | \(0.309571\pi\) | |||||||
\(30\) | −5.30019 | −0.0322559 | ||||||||
\(31\) | 113.093 | 0.655228 | 0.327614 | − | 0.944812i | \(-0.393755\pi\) | ||||
0.327614 | + | 0.944812i | \(0.393755\pi\) | |||||||
\(32\) | −64.2547 | −0.354961 | ||||||||
\(33\) | 238.540 | 1.25832 | ||||||||
\(34\) | 65.4384 | 0.330077 | ||||||||
\(35\) | 10.2074 | 0.0492961 | ||||||||
\(36\) | 19.3087 | 0.0893921 | ||||||||
\(37\) | −114.808 | −0.510116 | −0.255058 | − | 0.966926i | \(-0.582095\pi\) | ||||
−0.255058 | + | 0.966926i | \(0.582095\pi\) | |||||||
\(38\) | −276.570 | −1.18067 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −13.5767 | −0.0536666 | ||||||||
\(41\) | 69.6458 | 0.265289 | 0.132645 | − | 0.991164i | \(-0.457653\pi\) | ||||
0.132645 | + | 0.991164i | \(0.457653\pi\) | |||||||
\(42\) | −171.563 | −0.630305 | ||||||||
\(43\) | 438.302 | 1.55443 | 0.777214 | − | 0.629236i | \(-0.216632\pi\) | ||||
0.777214 | + | 0.629236i | \(0.216632\pi\) | |||||||
\(44\) | 93.1231 | 0.319064 | ||||||||
\(45\) | 7.53789 | 0.0249707 | ||||||||
\(46\) | −187.663 | −0.601508 | ||||||||
\(47\) | 31.9479 | 0.0991506 | 0.0495753 | − | 0.998770i | \(-0.484213\pi\) | ||||
0.0495753 | + | 0.998770i | \(0.484213\pi\) | |||||||
\(48\) | 185.793 | 0.558684 | ||||||||
\(49\) | −12.5937 | −0.0367164 | ||||||||
\(50\) | 319.386 | 0.903361 | ||||||||
\(51\) | 94.1298 | 0.258447 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.84658 | 0.00737752 | 0.00368876 | − | 0.999993i | \(-0.498826\pi\) | ||||
0.00368876 | + | 0.999993i | \(0.498826\pi\) | |||||||
\(54\) | −381.533 | −0.961483 | ||||||||
\(55\) | 36.3542 | 0.0891272 | ||||||||
\(56\) | −439.469 | −1.04869 | ||||||||
\(57\) | −397.831 | −0.924457 | ||||||||
\(58\) | −450.600 | −1.02012 | ||||||||
\(59\) | −71.6325 | −0.158064 | −0.0790319 | − | 0.996872i | \(-0.525183\pi\) | ||||
−0.0790319 | + | 0.996872i | \(0.525183\pi\) | |||||||
\(60\) | −2.97633 | −0.00640405 | ||||||||
\(61\) | −920.695 | −1.93251 | −0.966253 | − | 0.257593i | \(-0.917071\pi\) | ||||
−0.966253 | + | 0.257593i | \(0.917071\pi\) | |||||||
\(62\) | −289.693 | −0.593404 | ||||||||
\(63\) | 243.996 | 0.487947 | ||||||||
\(64\) | 567.978 | 1.10933 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −611.032 | −1.13959 | ||||||||
\(67\) | 444.280 | 0.810112 | 0.405056 | − | 0.914292i | \(-0.367252\pi\) | ||||
0.405056 | + | 0.914292i | \(0.367252\pi\) | |||||||
\(68\) | 36.7471 | 0.0655330 | ||||||||
\(69\) | −269.943 | −0.470976 | ||||||||
\(70\) | −26.1468 | −0.0446448 | ||||||||
\(71\) | 541.719 | 0.905496 | 0.452748 | − | 0.891639i | \(-0.350444\pi\) | ||||
0.452748 | + | 0.891639i | \(0.350444\pi\) | |||||||
\(72\) | −324.536 | −0.531207 | ||||||||
\(73\) | −764.004 | −1.22493 | −0.612465 | − | 0.790498i | \(-0.709822\pi\) | ||||
−0.612465 | + | 0.790498i | \(0.709822\pi\) | |||||||
\(74\) | 294.086 | 0.461984 | ||||||||
\(75\) | 459.420 | 0.707324 | ||||||||
\(76\) | −155.309 | −0.234410 | ||||||||
\(77\) | 1176.76 | 1.74161 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −421.538 | −0.600338 | −0.300169 | − | 0.953886i | \(-0.597043\pi\) | ||||
−0.300169 | + | 0.953886i | \(0.597043\pi\) | |||||||
\(80\) | 28.3153 | 0.0395719 | ||||||||
\(81\) | −186.386 | −0.255674 | ||||||||
\(82\) | −178.401 | −0.240258 | ||||||||
\(83\) | −603.797 | −0.798498 | −0.399249 | − | 0.916842i | \(-0.630729\pi\) | ||||
−0.399249 | + | 0.916842i | \(0.630729\pi\) | |||||||
\(84\) | −96.3419 | −0.125140 | ||||||||
\(85\) | 14.3457 | 0.0183059 | ||||||||
\(86\) | −1122.73 | −1.40776 | ||||||||
\(87\) | −648.165 | −0.798742 | ||||||||
\(88\) | −1565.19 | −1.89602 | ||||||||
\(89\) | 1159.88 | 1.38143 | 0.690715 | − | 0.723127i | \(-0.257296\pi\) | ||||
0.690715 | + | 0.723127i | \(0.257296\pi\) | |||||||
\(90\) | −19.3087 | −0.0226146 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −105.383 | −0.119423 | ||||||||
\(93\) | −416.708 | −0.464631 | ||||||||
\(94\) | −81.8362 | −0.0897953 | ||||||||
\(95\) | −60.6307 | −0.0654798 | ||||||||
\(96\) | 236.757 | 0.251707 | ||||||||
\(97\) | −583.269 | −0.610536 | −0.305268 | − | 0.952267i | \(-0.598746\pi\) | ||||
−0.305268 | + | 0.952267i | \(0.598746\pi\) | |||||||
\(98\) | 32.2595 | 0.0332521 | ||||||||
\(99\) | 869.006 | 0.882206 | ||||||||
\(100\) | 179.352 | 0.179352 | ||||||||
\(101\) | 921.740 | 0.908085 | 0.454043 | − | 0.890980i | \(-0.349981\pi\) | ||||
0.454043 | + | 0.890980i | \(0.349981\pi\) | |||||||
\(102\) | −241.118 | −0.234061 | ||||||||
\(103\) | −930.712 | −0.890347 | −0.445174 | − | 0.895444i | \(-0.646858\pi\) | ||||
−0.445174 | + | 0.895444i | \(0.646858\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −37.6107 | −0.0349565 | ||||||||
\(106\) | −7.29168 | −0.00668142 | ||||||||
\(107\) | 857.383 | 0.774638 | 0.387319 | − | 0.921946i | \(-0.373401\pi\) | ||||
0.387319 | + | 0.921946i | \(0.373401\pi\) | |||||||
\(108\) | −214.251 | −0.190892 | ||||||||
\(109\) | −671.853 | −0.590384 | −0.295192 | − | 0.955438i | \(-0.595384\pi\) | ||||
−0.295192 | + | 0.955438i | \(0.595384\pi\) | |||||||
\(110\) | −93.1231 | −0.0807176 | ||||||||
\(111\) | 423.027 | 0.361730 | ||||||||
\(112\) | 916.548 | 0.773265 | ||||||||
\(113\) | 641.474 | 0.534024 | 0.267012 | − | 0.963693i | \(-0.413964\pi\) | ||||
0.267012 | + | 0.963693i | \(0.413964\pi\) | |||||||
\(114\) | 1019.07 | 0.837231 | ||||||||
\(115\) | −41.1401 | −0.0333594 | ||||||||
\(116\) | −253.036 | −0.202533 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 183.491 | 0.143150 | ||||||||
\(119\) | 464.359 | 0.357712 | ||||||||
\(120\) | 50.0255 | 0.0380557 | ||||||||
\(121\) | 2860.09 | 2.14883 | ||||||||
\(122\) | 2358.41 | 1.75017 | ||||||||
\(123\) | −256.621 | −0.188120 | ||||||||
\(124\) | −162.678 | −0.117814 | ||||||||
\(125\) | 140.211 | 0.100327 | ||||||||
\(126\) | −625.009 | −0.441907 | ||||||||
\(127\) | −553.174 | −0.386506 | −0.193253 | − | 0.981149i | \(-0.561904\pi\) | ||||
−0.193253 | + | 0.981149i | \(0.561904\pi\) | |||||||
\(128\) | −940.868 | −0.649702 | ||||||||
\(129\) | −1614.99 | −1.10227 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2056.40 | 1.37152 | 0.685758 | − | 0.727830i | \(-0.259471\pi\) | ||||
0.685758 | + | 0.727830i | \(0.259471\pi\) | |||||||
\(132\) | −343.127 | −0.226253 | ||||||||
\(133\) | −1962.57 | −1.27952 | ||||||||
\(134\) | −1138.05 | −0.733674 | ||||||||
\(135\) | −83.6411 | −0.0533235 | ||||||||
\(136\) | −617.637 | −0.389426 | ||||||||
\(137\) | 1808.57 | 1.12786 | 0.563928 | − | 0.825824i | \(-0.309290\pi\) | ||||
0.563928 | + | 0.825824i | \(0.309290\pi\) | |||||||
\(138\) | 691.474 | 0.426537 | ||||||||
\(139\) | 1493.64 | 0.911428 | 0.455714 | − | 0.890126i | \(-0.349384\pi\) | ||||
0.455714 | + | 0.890126i | \(0.349384\pi\) | |||||||
\(140\) | −14.6828 | −0.00886373 | ||||||||
\(141\) | −117.717 | −0.0703090 | ||||||||
\(142\) | −1387.64 | −0.820058 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 676.847 | 0.391694 | ||||||||
\(145\) | −98.7822 | −0.0565753 | ||||||||
\(146\) | 1957.04 | 1.10935 | ||||||||
\(147\) | 46.4036 | 0.0260361 | ||||||||
\(148\) | 165.145 | 0.0917218 | ||||||||
\(149\) | 2759.02 | 1.51696 | 0.758482 | − | 0.651694i | \(-0.225941\pi\) | ||||
0.758482 | + | 0.651694i | \(0.225941\pi\) | |||||||
\(150\) | −1176.83 | −0.640585 | ||||||||
\(151\) | 976.355 | 0.526190 | 0.263095 | − | 0.964770i | \(-0.415257\pi\) | ||||
0.263095 | + | 0.964770i | \(0.415257\pi\) | |||||||
\(152\) | 2610.39 | 1.39297 | ||||||||
\(153\) | 342.917 | 0.181197 | ||||||||
\(154\) | −3014.33 | −1.57728 | ||||||||
\(155\) | −63.5076 | −0.0329100 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −564.875 | −0.287146 | −0.143573 | − | 0.989640i | \(-0.545859\pi\) | ||||
−0.143573 | + | 0.989640i | \(0.545859\pi\) | |||||||
\(158\) | 1079.79 | 0.543694 | ||||||||
\(159\) | −10.4887 | −0.00523149 | ||||||||
\(160\) | 36.0824 | 0.0178285 | ||||||||
\(161\) | −1331.68 | −0.651869 | ||||||||
\(162\) | 477.438 | 0.231550 | ||||||||
\(163\) | −1508.53 | −0.724892 | −0.362446 | − | 0.932005i | \(-0.618058\pi\) | ||||
−0.362446 | + | 0.932005i | \(0.618058\pi\) | |||||||
\(164\) | −100.182 | −0.0477005 | ||||||||
\(165\) | −133.953 | −0.0632012 | ||||||||
\(166\) | 1546.66 | 0.723157 | ||||||||
\(167\) | −592.521 | −0.274555 | −0.137277 | − | 0.990533i | \(-0.543835\pi\) | ||||
−0.137277 | + | 0.990533i | \(0.543835\pi\) | |||||||
\(168\) | 1619.29 | 0.743638 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −36.7471 | −0.0165787 | ||||||||
\(171\) | −1449.31 | −0.648137 | ||||||||
\(172\) | −630.474 | −0.279495 | ||||||||
\(173\) | −4495.57 | −1.97568 | −0.987838 | − | 0.155488i | \(-0.950305\pi\) | ||||
−0.987838 | + | 0.155488i | \(0.950305\pi\) | |||||||
\(174\) | 1660.31 | 0.723377 | ||||||||
\(175\) | 2266.40 | 0.978994 | ||||||||
\(176\) | 3264.34 | 1.39806 | ||||||||
\(177\) | 263.941 | 0.112085 | ||||||||
\(178\) | −2971.10 | −1.25109 | ||||||||
\(179\) | −154.285 | −0.0644235 | −0.0322117 | − | 0.999481i | \(-0.510255\pi\) | ||||
−0.0322117 | + | 0.999481i | \(0.510255\pi\) | |||||||
\(180\) | −10.8429 | −0.00448988 | ||||||||
\(181\) | 1071.35 | 0.439959 | 0.219979 | − | 0.975505i | \(-0.429401\pi\) | ||||
0.219979 | + | 0.975505i | \(0.429401\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3392.45 | 1.37037 | ||||||||
\(184\) | 1771.25 | 0.709663 | ||||||||
\(185\) | 64.4706 | 0.0256215 | ||||||||
\(186\) | 1067.42 | 0.420791 | ||||||||
\(187\) | 1653.84 | 0.646742 | ||||||||
\(188\) | −45.9554 | −0.0178279 | ||||||||
\(189\) | −2707.40 | −1.04198 | ||||||||
\(190\) | 155.309 | 0.0593015 | ||||||||
\(191\) | 677.203 | 0.256548 | 0.128274 | − | 0.991739i | \(-0.459056\pi\) | ||||
0.128274 | + | 0.991739i | \(0.459056\pi\) | |||||||
\(192\) | −2092.81 | −0.786642 | ||||||||
\(193\) | −1321.68 | −0.492936 | −0.246468 | − | 0.969151i | \(-0.579270\pi\) | ||||
−0.246468 | + | 0.969151i | \(0.579270\pi\) | |||||||
\(194\) | 1494.07 | 0.552929 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 18.1154 | 0.00660183 | ||||||||
\(197\) | −1267.37 | −0.458356 | −0.229178 | − | 0.973385i | \(-0.573604\pi\) | ||||
−0.229178 | + | 0.973385i | \(0.573604\pi\) | |||||||
\(198\) | −2226.00 | −0.798966 | ||||||||
\(199\) | 2396.24 | 0.853593 | 0.426796 | − | 0.904348i | \(-0.359642\pi\) | ||||
0.426796 | + | 0.904348i | \(0.359642\pi\) | |||||||
\(200\) | −3014.51 | −1.06579 | ||||||||
\(201\) | −1637.02 | −0.574460 | ||||||||
\(202\) | −2361.09 | −0.822403 | ||||||||
\(203\) | −3197.51 | −1.10552 | ||||||||
\(204\) | −135.401 | −0.0464703 | ||||||||
\(205\) | −39.1098 | −0.0133246 | ||||||||
\(206\) | 2384.07 | 0.806339 | ||||||||
\(207\) | −983.409 | −0.330201 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6989.81 | −2.31337 | ||||||||
\(210\) | 96.3419 | 0.0316582 | ||||||||
\(211\) | −91.5539 | −0.0298712 | −0.0149356 | − | 0.999888i | \(-0.504754\pi\) | ||||
−0.0149356 | + | 0.999888i | \(0.504754\pi\) | |||||||
\(212\) | −4.09466 | −0.00132652 | ||||||||
\(213\) | −1996.05 | −0.642099 | ||||||||
\(214\) | −2196.23 | −0.701548 | ||||||||
\(215\) | −246.130 | −0.0780740 | ||||||||
\(216\) | 3601.08 | 1.13436 | ||||||||
\(217\) | −2055.70 | −0.643087 | ||||||||
\(218\) | 1720.99 | 0.534679 | ||||||||
\(219\) | 2815.09 | 0.868613 | ||||||||
\(220\) | −52.2935 | −0.0160256 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1083.61 | −0.327599 | ||||||||
\(223\) | −1235.42 | −0.370985 | −0.185493 | − | 0.982646i | \(-0.559388\pi\) | ||||
−0.185493 | + | 0.982646i | \(0.559388\pi\) | |||||||
\(224\) | 1167.96 | 0.348383 | ||||||||
\(225\) | 1673.68 | 0.495905 | ||||||||
\(226\) | −1643.17 | −0.483637 | ||||||||
\(227\) | −3301.66 | −0.965370 | −0.482685 | − | 0.875794i | \(-0.660338\pi\) | ||||
−0.482685 | + | 0.875794i | \(0.660338\pi\) | |||||||
\(228\) | 572.260 | 0.166223 | ||||||||
\(229\) | −211.283 | −0.0609694 | −0.0304847 | − | 0.999535i | \(-0.509705\pi\) | ||||
−0.0304847 | + | 0.999535i | \(0.509705\pi\) | |||||||
\(230\) | 105.383 | 0.0302118 | ||||||||
\(231\) | −4335.96 | −1.23500 | ||||||||
\(232\) | 4252.97 | 1.20354 | ||||||||
\(233\) | −256.724 | −0.0721827 | −0.0360913 | − | 0.999348i | \(-0.511491\pi\) | ||||
−0.0360913 | + | 0.999348i | \(0.511491\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.9404 | −0.00498002 | ||||||||
\(236\) | 103.040 | 0.0284208 | ||||||||
\(237\) | 1553.22 | 0.425708 | ||||||||
\(238\) | −1189.48 | −0.323960 | ||||||||
\(239\) | 3549.62 | 0.960694 | 0.480347 | − | 0.877078i | \(-0.340511\pi\) | ||||
0.480347 | + | 0.877078i | \(0.340511\pi\) | |||||||
\(240\) | −104.332 | −0.0280609 | ||||||||
\(241\) | 5030.10 | 1.34447 | 0.672235 | − | 0.740338i | \(-0.265335\pi\) | ||||
0.672235 | + | 0.740338i | \(0.265335\pi\) | |||||||
\(242\) | −7326.27 | −1.94608 | ||||||||
\(243\) | −3334.77 | −0.880353 | ||||||||
\(244\) | 1324.37 | 0.347476 | ||||||||
\(245\) | 7.07204 | 0.00184415 | ||||||||
\(246\) | 657.349 | 0.170370 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2734.25 | 0.700102 | ||||||||
\(249\) | 2224.79 | 0.566226 | ||||||||
\(250\) | −359.158 | −0.0908606 | ||||||||
\(251\) | −718.784 | −0.180754 | −0.0903770 | − | 0.995908i | \(-0.528807\pi\) | ||||
−0.0903770 | + | 0.995908i | \(0.528807\pi\) | |||||||
\(252\) | −350.976 | −0.0877357 | ||||||||
\(253\) | −4742.84 | −1.17858 | ||||||||
\(254\) | 1416.98 | 0.350038 | ||||||||
\(255\) | −52.8588 | −0.0129810 | ||||||||
\(256\) | −2133.74 | −0.520933 | ||||||||
\(257\) | 1280.79 | 0.310871 | 0.155435 | − | 0.987846i | \(-0.450322\pi\) | ||||
0.155435 | + | 0.987846i | \(0.450322\pi\) | |||||||
\(258\) | 4136.89 | 0.998262 | ||||||||
\(259\) | 2086.87 | 0.500663 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2361.28 | −0.559998 | ||||||||
\(262\) | −5267.58 | −1.24211 | ||||||||
\(263\) | 5225.55 | 1.22517 | 0.612587 | − | 0.790403i | \(-0.290129\pi\) | ||||
0.612587 | + | 0.790403i | \(0.290129\pi\) | |||||||
\(264\) | 5767.19 | 1.34449 | ||||||||
\(265\) | −1.59851 | −0.000370549 0 | ||||||||
\(266\) | 5027.24 | 1.15880 | ||||||||
\(267\) | −4273.77 | −0.979590 | ||||||||
\(268\) | −639.074 | −0.145663 | ||||||||
\(269\) | 6443.80 | 1.46054 | 0.730270 | − | 0.683158i | \(-0.239394\pi\) | ||||
0.730270 | + | 0.683158i | \(0.239394\pi\) | |||||||
\(270\) | 214.251 | 0.0482922 | ||||||||
\(271\) | 3929.93 | 0.880909 | 0.440455 | − | 0.897775i | \(-0.354817\pi\) | ||||
0.440455 | + | 0.897775i | \(0.354817\pi\) | |||||||
\(272\) | 1288.13 | 0.287149 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4632.74 | −1.02144 | ||||||||
\(275\) | 8071.91 | 1.77002 | ||||||||
\(276\) | 388.299 | 0.0846842 | ||||||||
\(277\) | −5884.40 | −1.27639 | −0.638194 | − | 0.769876i | \(-0.720318\pi\) | ||||
−0.638194 | + | 0.769876i | \(0.720318\pi\) | |||||||
\(278\) | −3826.03 | −0.825431 | ||||||||
\(279\) | −1518.08 | −0.325752 | ||||||||
\(280\) | 246.785 | 0.0526722 | ||||||||
\(281\) | −3529.79 | −0.749358 | −0.374679 | − | 0.927155i | \(-0.622247\pi\) | ||||
−0.374679 | + | 0.927155i | \(0.622247\pi\) | |||||||
\(282\) | 301.538 | 0.0636750 | ||||||||
\(283\) | −2611.00 | −0.548438 | −0.274219 | − | 0.961667i | \(-0.588419\pi\) | ||||
−0.274219 | + | 0.961667i | \(0.588419\pi\) | |||||||
\(284\) | −779.234 | −0.162813 | ||||||||
\(285\) | 223.403 | 0.0464325 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1265.96 | −0.260373 | ||||||||
\(288\) | 862.510 | 0.176472 | ||||||||
\(289\) | −4260.38 | −0.867165 | ||||||||
\(290\) | 253.036 | 0.0512372 | ||||||||
\(291\) | 2149.15 | 0.432939 | ||||||||
\(292\) | 1098.98 | 0.220250 | ||||||||
\(293\) | 5491.03 | 1.09484 | 0.547422 | − | 0.836857i | \(-0.315609\pi\) | ||||
0.547422 | + | 0.836857i | \(0.315609\pi\) | |||||||
\(294\) | −118.865 | −0.0235795 | ||||||||
\(295\) | 40.2255 | 0.00793904 | ||||||||
\(296\) | −2775.72 | −0.545052 | ||||||||
\(297\) | −9642.56 | −1.88390 | ||||||||
\(298\) | −7067.37 | −1.37383 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −660.852 | −0.127181 | ||||||||
\(301\) | −7967.05 | −1.52563 | ||||||||
\(302\) | −2500.99 | −0.476542 | ||||||||
\(303\) | −3396.30 | −0.643935 | ||||||||
\(304\) | −5444.19 | −1.02712 | ||||||||
\(305\) | 517.019 | 0.0970637 | ||||||||
\(306\) | −878.399 | −0.164100 | ||||||||
\(307\) | 7307.59 | 1.35852 | 0.679261 | − | 0.733897i | \(-0.262300\pi\) | ||||
0.679261 | + | 0.733897i | \(0.262300\pi\) | |||||||
\(308\) | −1692.71 | −0.313152 | ||||||||
\(309\) | 3429.36 | 0.631357 | ||||||||
\(310\) | 162.678 | 0.0298048 | ||||||||
\(311\) | 7904.92 | 1.44131 | 0.720654 | − | 0.693295i | \(-0.243842\pi\) | ||||
0.720654 | + | 0.693295i | \(0.243842\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10002.4 | 1.80629 | 0.903145 | − | 0.429336i | \(-0.141252\pi\) | ||||
0.903145 | + | 0.429336i | \(0.141252\pi\) | |||||||
\(314\) | 1446.96 | 0.260053 | ||||||||
\(315\) | −137.017 | −0.0245080 | ||||||||
\(316\) | 606.360 | 0.107944 | ||||||||
\(317\) | 6230.81 | 1.10397 | 0.551983 | − | 0.833856i | \(-0.313871\pi\) | ||||
0.551983 | + | 0.833856i | \(0.313871\pi\) | |||||||
\(318\) | 26.8673 | 0.00473788 | ||||||||
\(319\) | −11388.1 | −1.99878 | ||||||||
\(320\) | −318.950 | −0.0557182 | ||||||||
\(321\) | −3159.16 | −0.549306 | ||||||||
\(322\) | 3411.16 | 0.590362 | ||||||||
\(323\) | −2758.24 | −0.475147 | ||||||||
\(324\) | 268.107 | 0.0459717 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3864.19 | 0.656495 | ||||||||
\(327\) | 2475.55 | 0.418649 | ||||||||
\(328\) | 1683.83 | 0.283458 | ||||||||
\(329\) | −580.719 | −0.0973134 | ||||||||
\(330\) | 343.127 | 0.0572379 | ||||||||
\(331\) | 4634.51 | 0.769594 | 0.384797 | − | 0.923001i | \(-0.374271\pi\) | ||||
0.384797 | + | 0.923001i | \(0.374271\pi\) | |||||||
\(332\) | 868.531 | 0.143575 | ||||||||
\(333\) | 1541.10 | 0.253609 | ||||||||
\(334\) | 1517.77 | 0.248649 | ||||||||
\(335\) | −249.487 | −0.0406893 | ||||||||
\(336\) | −3377.17 | −0.548332 | ||||||||
\(337\) | 3029.82 | 0.489747 | 0.244874 | − | 0.969555i | \(-0.421254\pi\) | ||||
0.244874 | + | 0.969555i | \(0.421254\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2363.61 | −0.378684 | ||||||||
\(340\) | −20.6355 | −0.00329151 | ||||||||
\(341\) | −7321.47 | −1.16270 | ||||||||
\(342\) | 3712.48 | 0.586982 | ||||||||
\(343\) | 6463.66 | 1.01751 | ||||||||
\(344\) | 10596.9 | 1.66089 | ||||||||
\(345\) | 151.587 | 0.0236556 | ||||||||
\(346\) | 11515.6 | 1.78926 | ||||||||
\(347\) | 2841.60 | 0.439611 | 0.219805 | − | 0.975544i | \(-0.429458\pi\) | ||||
0.219805 | + | 0.975544i | \(0.429458\pi\) | |||||||
\(348\) | 932.351 | 0.143619 | ||||||||
\(349\) | −7565.68 | −1.16040 | −0.580202 | − | 0.814472i | \(-0.697027\pi\) | ||||
−0.580202 | + | 0.814472i | \(0.697027\pi\) | |||||||
\(350\) | −5805.51 | −0.886622 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4159.76 | 0.629875 | ||||||||
\(353\) | 2339.44 | 0.352736 | 0.176368 | − | 0.984324i | \(-0.443565\pi\) | ||||
0.176368 | + | 0.984324i | \(0.443565\pi\) | |||||||
\(354\) | −676.100 | −0.101509 | ||||||||
\(355\) | −304.204 | −0.0454802 | ||||||||
\(356\) | −1668.43 | −0.248389 | ||||||||
\(357\) | −1711.00 | −0.253658 | ||||||||
\(358\) | 395.209 | 0.0583449 | ||||||||
\(359\) | 2531.68 | 0.372192 | 0.186096 | − | 0.982532i | \(-0.440417\pi\) | ||||
0.186096 | + | 0.982532i | \(0.440417\pi\) | |||||||
\(360\) | 182.244 | 0.0266809 | ||||||||
\(361\) | 4798.45 | 0.699585 | ||||||||
\(362\) | −2744.31 | −0.398447 | ||||||||
\(363\) | −10538.5 | −1.52376 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 429.028 | 0.0615243 | ||||||||
\(366\) | −8689.93 | −1.24107 | ||||||||
\(367\) | 6577.81 | 0.935583 | 0.467792 | − | 0.883839i | \(-0.345050\pi\) | ||||
0.467792 | + | 0.883839i | \(0.345050\pi\) | |||||||
\(368\) | −3694.08 | −0.523280 | ||||||||
\(369\) | −934.876 | −0.131891 | ||||||||
\(370\) | −165.145 | −0.0232040 | ||||||||
\(371\) | −51.7426 | −0.00724081 | ||||||||
\(372\) | 599.413 | 0.0835433 | ||||||||
\(373\) | 2902.72 | 0.402942 | 0.201471 | − | 0.979495i | \(-0.435428\pi\) | ||||
0.201471 | + | 0.979495i | \(0.435428\pi\) | |||||||
\(374\) | −4236.40 | −0.585719 | ||||||||
\(375\) | −516.630 | −0.0711431 | ||||||||
\(376\) | 772.407 | 0.105941 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 6935.16 | 0.943667 | ||||||||
\(379\) | 1865.73 | 0.252866 | 0.126433 | − | 0.991975i | \(-0.459647\pi\) | ||||
0.126433 | + | 0.991975i | \(0.459647\pi\) | |||||||
\(380\) | 87.2140 | 0.0117736 | ||||||||
\(381\) | 2038.26 | 0.274076 | ||||||||
\(382\) | −1734.69 | −0.232342 | ||||||||
\(383\) | −10836.0 | −1.44567 | −0.722837 | − | 0.691019i | \(-0.757162\pi\) | ||||
−0.722837 | + | 0.691019i | \(0.757162\pi\) | |||||||
\(384\) | 3466.78 | 0.460712 | ||||||||
\(385\) | −660.813 | −0.0874757 | ||||||||
\(386\) | 3385.55 | 0.446425 | ||||||||
\(387\) | −5883.46 | −0.772798 | ||||||||
\(388\) | 839.001 | 0.109778 | ||||||||
\(389\) | −9520.34 | −1.24088 | −0.620438 | − | 0.784256i | \(-0.713045\pi\) | ||||
−0.620438 | + | 0.784256i | \(0.713045\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1871.56 | −0.242069 | ||||||||
\(392\) | −304.480 | −0.0392310 | ||||||||
\(393\) | −7577.13 | −0.972559 | ||||||||
\(394\) | 3246.43 | 0.415108 | ||||||||
\(395\) | 236.716 | 0.0301531 | ||||||||
\(396\) | −1250.02 | −0.158626 | ||||||||
\(397\) | 10108.8 | 1.27796 | 0.638978 | − | 0.769225i | \(-0.279358\pi\) | ||||
0.638978 | + | 0.769225i | \(0.279358\pi\) | |||||||
\(398\) | −6138.10 | −0.773053 | ||||||||
\(399\) | 7231.41 | 0.907327 | ||||||||
\(400\) | 6287.01 | 0.785876 | ||||||||
\(401\) | −2084.38 | −0.259573 | −0.129787 | − | 0.991542i | \(-0.541429\pi\) | ||||
−0.129787 | + | 0.991542i | \(0.541429\pi\) | |||||||
\(402\) | 4193.32 | 0.520258 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1325.88 | −0.163279 | ||||||||
\(405\) | 104.666 | 0.0128417 | ||||||||
\(406\) | 8190.60 | 1.00121 | ||||||||
\(407\) | 7432.50 | 0.905197 | ||||||||
\(408\) | 2275.78 | 0.276147 | ||||||||
\(409\) | 9716.53 | 1.17470 | 0.587349 | − | 0.809334i | \(-0.300172\pi\) | ||||
0.587349 | + | 0.809334i | \(0.300172\pi\) | |||||||
\(410\) | 100.182 | 0.0120674 | ||||||||
\(411\) | −6663.95 | −0.799777 | ||||||||
\(412\) | 1338.78 | 0.160090 | ||||||||
\(413\) | 1302.07 | 0.155135 | ||||||||
\(414\) | 2519.05 | 0.299045 | ||||||||
\(415\) | 339.064 | 0.0401060 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5503.54 | −0.646305 | ||||||||
\(418\) | 17904.8 | 2.09510 | ||||||||
\(419\) | 13381.9 | 1.56026 | 0.780129 | − | 0.625619i | \(-0.215153\pi\) | ||||
0.780129 | + | 0.625619i | \(0.215153\pi\) | |||||||
\(420\) | 54.1011 | 0.00628539 | ||||||||
\(421\) | 9463.37 | 1.09553 | 0.547763 | − | 0.836633i | \(-0.315479\pi\) | ||||
0.547763 | + | 0.836633i | \(0.315479\pi\) | |||||||
\(422\) | 234.520 | 0.0270527 | ||||||||
\(423\) | −428.846 | −0.0492936 | ||||||||
\(424\) | 68.8221 | 0.00788278 | ||||||||
\(425\) | 3185.24 | 0.363546 | ||||||||
\(426\) | 5112.98 | 0.581514 | ||||||||
\(427\) | 16735.5 | 1.89670 | ||||||||
\(428\) | −1233.30 | −0.139285 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 630.474 | 0.0707074 | ||||||||
\(431\) | −4852.28 | −0.542288 | −0.271144 | − | 0.962539i | \(-0.587402\pi\) | ||||
−0.271144 | + | 0.962539i | \(0.587402\pi\) | |||||||
\(432\) | −7510.35 | −0.836439 | ||||||||
\(433\) | −8208.00 | −0.910973 | −0.455486 | − | 0.890243i | \(-0.650535\pi\) | ||||
−0.455486 | + | 0.890243i | \(0.650535\pi\) | |||||||
\(434\) | 5265.78 | 0.582409 | ||||||||
\(435\) | 363.979 | 0.0401183 | ||||||||
\(436\) | 966.425 | 0.106155 | ||||||||
\(437\) | 7910.01 | 0.865874 | ||||||||
\(438\) | −7211.01 | −0.786656 | ||||||||
\(439\) | −2993.80 | −0.325481 | −0.162741 | − | 0.986669i | \(-0.552033\pi\) | ||||
−0.162741 | + | 0.986669i | \(0.552033\pi\) | |||||||
\(440\) | 878.938 | 0.0952311 | ||||||||
\(441\) | 169.049 | 0.0182539 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9743.67 | 1.04500 | 0.522501 | − | 0.852639i | \(-0.324999\pi\) | ||||
0.522501 | + | 0.852639i | \(0.324999\pi\) | |||||||
\(444\) | −608.503 | −0.0650411 | ||||||||
\(445\) | −651.335 | −0.0693848 | ||||||||
\(446\) | 3164.59 | 0.335981 | ||||||||
\(447\) | −10166.0 | −1.07570 | ||||||||
\(448\) | −10324.2 | −1.08878 | ||||||||
\(449\) | 561.459 | 0.0590131 | 0.0295065 | − | 0.999565i | \(-0.490606\pi\) | ||||
0.0295065 | + | 0.999565i | \(0.490606\pi\) | |||||||
\(450\) | −4287.22 | −0.449114 | ||||||||
\(451\) | −4508.78 | −0.470754 | ||||||||
\(452\) | −922.726 | −0.0960207 | ||||||||
\(453\) | −3597.54 | −0.373128 | ||||||||
\(454\) | 8457.38 | 0.874283 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9618.40 | −0.987770 | ||||||||
\(457\) | −13758.4 | −1.40830 | −0.704148 | − | 0.710054i | \(-0.748671\pi\) | ||||
−0.704148 | + | 0.710054i | \(0.748671\pi\) | |||||||
\(458\) | 541.213 | 0.0552166 | ||||||||
\(459\) | −3805.03 | −0.386936 | ||||||||
\(460\) | 59.1779 | 0.00599823 | ||||||||
\(461\) | −12009.2 | −1.21329 | −0.606644 | − | 0.794974i | \(-0.707485\pi\) | ||||
−0.606644 | + | 0.794974i | \(0.707485\pi\) | |||||||
\(462\) | 11106.8 | 1.11847 | ||||||||
\(463\) | −13635.7 | −1.36870 | −0.684348 | − | 0.729156i | \(-0.739913\pi\) | ||||
−0.684348 | + | 0.729156i | \(0.739913\pi\) | |||||||
\(464\) | −8869.91 | −0.887447 | ||||||||
\(465\) | 234.004 | 0.0233369 | ||||||||
\(466\) | 657.613 | 0.0653719 | ||||||||
\(467\) | 8821.95 | 0.874157 | 0.437079 | − | 0.899423i | \(-0.356013\pi\) | ||||
0.437079 | + | 0.899423i | \(0.356013\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8075.72 | −0.795100 | ||||||||
\(470\) | 45.9554 | 0.00451013 | ||||||||
\(471\) | 2081.37 | 0.203619 | ||||||||
\(472\) | −1731.87 | −0.168889 | ||||||||
\(473\) | −28375.1 | −2.75832 | ||||||||
\(474\) | −3978.66 | −0.385540 | ||||||||
\(475\) | −13462.2 | −1.30039 | ||||||||
\(476\) | −667.956 | −0.0643187 | ||||||||
\(477\) | −38.2105 | −0.00366780 | ||||||||
\(478\) | −9092.54 | −0.870049 | ||||||||
\(479\) | 14620.0 | 1.39459 | 0.697293 | − | 0.716786i | \(-0.254388\pi\) | ||||
0.697293 | + | 0.716786i | \(0.254388\pi\) | |||||||
\(480\) | −132.951 | −0.0126424 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −12884.9 | −1.21761 | ||||||||
\(483\) | 4906.78 | 0.462249 | ||||||||
\(484\) | −4114.09 | −0.386372 | ||||||||
\(485\) | 327.536 | 0.0306653 | ||||||||
\(486\) | 8542.20 | 0.797288 | ||||||||
\(487\) | 9798.86 | 0.911763 | 0.455882 | − | 0.890040i | \(-0.349324\pi\) | ||||
0.455882 | + | 0.890040i | \(0.349324\pi\) | |||||||
\(488\) | −22259.7 | −2.06486 | ||||||||
\(489\) | 5558.43 | 0.514030 | ||||||||
\(490\) | −18.1154 | −0.00167014 | ||||||||
\(491\) | −10836.1 | −0.995977 | −0.497989 | − | 0.867184i | \(-0.665928\pi\) | ||||
−0.497989 | + | 0.867184i | \(0.665928\pi\) | |||||||
\(492\) | 369.136 | 0.0338251 | ||||||||
\(493\) | −4493.84 | −0.410532 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −487.993 | −0.0443104 | ||||||||
\(496\) | −5702.51 | −0.516230 | ||||||||
\(497\) | −9846.86 | −0.888717 | ||||||||
\(498\) | −5698.91 | −0.512800 | ||||||||
\(499\) | −2589.96 | −0.232349 | −0.116175 | − | 0.993229i | \(-0.537063\pi\) | ||||
−0.116175 | + | 0.993229i | \(0.537063\pi\) | |||||||
\(500\) | −201.686 | −0.0180394 | ||||||||
\(501\) | 2183.24 | 0.194690 | ||||||||
\(502\) | 1841.20 | 0.163699 | ||||||||
\(503\) | −17067.5 | −1.51292 | −0.756462 | − | 0.654038i | \(-0.773074\pi\) | ||||
−0.756462 | + | 0.654038i | \(0.773074\pi\) | |||||||
\(504\) | 5899.12 | 0.521364 | ||||||||
\(505\) | −517.606 | −0.0456102 | ||||||||
\(506\) | 12149.0 | 1.06737 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 795.712 | 0.0694961 | ||||||||
\(509\) | 1012.89 | 0.0882038 | 0.0441019 | − | 0.999027i | \(-0.485957\pi\) | ||||
0.0441019 | + | 0.999027i | \(0.485957\pi\) | |||||||
\(510\) | 135.401 | 0.0117562 | ||||||||
\(511\) | 13887.4 | 1.20223 | ||||||||
\(512\) | 12992.6 | 1.12148 | ||||||||
\(513\) | 16081.7 | 1.38406 | ||||||||
\(514\) | −3280.82 | −0.281539 | ||||||||
\(515\) | 522.644 | 0.0447193 | ||||||||
\(516\) | 2323.08 | 0.198194 | ||||||||
\(517\) | −2068.26 | −0.175942 | ||||||||
\(518\) | −5345.63 | −0.453424 | ||||||||
\(519\) | 16564.6 | 1.40098 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14367.7 | −1.20818 | −0.604089 | − | 0.796917i | \(-0.706463\pi\) | ||||
−0.604089 | + | 0.796917i | \(0.706463\pi\) | |||||||
\(522\) | 6048.54 | 0.507160 | ||||||||
\(523\) | −16219.9 | −1.35611 | −0.678057 | − | 0.735010i | \(-0.737178\pi\) | ||||
−0.678057 | + | 0.735010i | \(0.737178\pi\) | |||||||
\(524\) | −2958.02 | −0.246607 | ||||||||
\(525\) | −8350.92 | −0.694217 | ||||||||
\(526\) | −13385.5 | −1.10957 | ||||||||
\(527\) | −2889.11 | −0.238808 | ||||||||
\(528\) | −12028.0 | −0.991382 | ||||||||
\(529\) | −6799.77 | −0.558870 | ||||||||
\(530\) | 4.09466 | 0.000335586 0 | ||||||||
\(531\) | 961.545 | 0.0785828 | ||||||||
\(532\) | 2823.06 | 0.230066 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 10947.5 | 0.887161 | ||||||||
\(535\) | −481.466 | −0.0389076 | ||||||||
\(536\) | 10741.4 | 0.865593 | ||||||||
\(537\) | 568.488 | 0.0456835 | ||||||||
\(538\) | −16506.1 | −1.32273 | ||||||||
\(539\) | 815.301 | 0.0651530 | ||||||||
\(540\) | 120.313 | 0.00958788 | ||||||||
\(541\) | −17592.2 | −1.39806 | −0.699029 | − | 0.715094i | \(-0.746384\pi\) | ||||
−0.699029 | + | 0.715094i | \(0.746384\pi\) | |||||||
\(542\) | −10066.7 | −0.797792 | ||||||||
\(543\) | −3947.55 | −0.311980 | ||||||||
\(544\) | 1641.48 | 0.129371 | ||||||||
\(545\) | 377.281 | 0.0296531 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10504.6 | 0.821103 | 0.410552 | − | 0.911837i | \(-0.365336\pi\) | ||||
0.410552 | + | 0.911837i | \(0.365336\pi\) | |||||||
\(548\) | −2601.53 | −0.202795 | ||||||||
\(549\) | 12358.8 | 0.960763 | ||||||||
\(550\) | −20676.6 | −1.60301 | ||||||||
\(551\) | 18992.8 | 1.46846 | ||||||||
\(552\) | −6526.44 | −0.503231 | ||||||||
\(553\) | 7662.33 | 0.589214 | ||||||||
\(554\) | 15073.2 | 1.15596 | ||||||||
\(555\) | −237.552 | −0.0181685 | ||||||||
\(556\) | −2148.52 | −0.163880 | ||||||||
\(557\) | 507.558 | 0.0386102 | 0.0193051 | − | 0.999814i | \(-0.493855\pi\) | ||||
0.0193051 | + | 0.999814i | \(0.493855\pi\) | |||||||
\(558\) | 3888.64 | 0.295016 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −514.690 | −0.0388386 | ||||||||
\(561\) | −6093.83 | −0.458613 | ||||||||
\(562\) | 9041.75 | 0.678653 | ||||||||
\(563\) | −3443.14 | −0.257746 | −0.128873 | − | 0.991661i | \(-0.541136\pi\) | ||||
−0.128873 | + | 0.991661i | \(0.541136\pi\) | |||||||
\(564\) | 169.330 | 0.0126420 | ||||||||
\(565\) | −360.221 | −0.0268223 | ||||||||
\(566\) | 6688.21 | 0.496690 | ||||||||
\(567\) | 3387.96 | 0.250936 | ||||||||
\(568\) | 13097.2 | 0.967509 | ||||||||
\(569\) | 23972.2 | 1.76620 | 0.883098 | − | 0.469189i | \(-0.155454\pi\) | ||||
0.883098 | + | 0.469189i | \(0.155454\pi\) | |||||||
\(570\) | −572.260 | −0.0420514 | ||||||||
\(571\) | −7458.32 | −0.546622 | −0.273311 | − | 0.961926i | \(-0.588119\pi\) | ||||
−0.273311 | + | 0.961926i | \(0.588119\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2495.26 | −0.181922 | ||||||||
\(574\) | 3242.82 | 0.235806 | ||||||||
\(575\) | −9134.57 | −0.662501 | ||||||||
\(576\) | −7624.14 | −0.551515 | ||||||||
\(577\) | −5669.57 | −0.409059 | −0.204530 | − | 0.978860i | \(-0.565566\pi\) | ||||
−0.204530 | + | 0.978860i | \(0.565566\pi\) | |||||||
\(578\) | 10913.2 | 0.785344 | ||||||||
\(579\) | 4869.94 | 0.349547 | ||||||||
\(580\) | 142.093 | 0.0101726 | ||||||||
\(581\) | 10975.3 | 0.783702 | ||||||||
\(582\) | −5505.15 | −0.392089 | ||||||||
\(583\) | −184.284 | −0.0130914 | ||||||||
\(584\) | −18471.4 | −1.30882 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14065.6 | −0.991541 | ||||||||
\(587\) | −1017.39 | −0.0715371 | −0.0357685 | − | 0.999360i | \(-0.511388\pi\) | ||||
−0.0357685 | + | 0.999360i | \(0.511388\pi\) | |||||||
\(588\) | −66.7491 | −0.00468144 | ||||||||
\(589\) | 12210.6 | 0.854208 | ||||||||
\(590\) | −103.040 | −0.00718996 | ||||||||
\(591\) | 4669.81 | 0.325026 | ||||||||
\(592\) | 5788.99 | 0.401902 | ||||||||
\(593\) | 10198.2 | 0.706221 | 0.353111 | − | 0.935582i | \(-0.385124\pi\) | ||||
0.353111 | + | 0.935582i | \(0.385124\pi\) | |||||||
\(594\) | 24699.9 | 1.70615 | ||||||||
\(595\) | −260.762 | −0.0179667 | ||||||||
\(596\) | −3968.70 | −0.272759 | ||||||||
\(597\) | −8829.33 | −0.605294 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12516.3 | 0.853763 | 0.426881 | − | 0.904308i | \(-0.359612\pi\) | ||||
0.426881 | + | 0.904308i | \(0.359612\pi\) | |||||||
\(600\) | 11107.4 | 0.755766 | ||||||||
\(601\) | 9627.46 | 0.653431 | 0.326716 | − | 0.945123i | \(-0.394058\pi\) | ||||
0.326716 | + | 0.945123i | \(0.394058\pi\) | |||||||
\(602\) | 20408.0 | 1.38168 | ||||||||
\(603\) | −5963.70 | −0.402754 | ||||||||
\(604\) | −1404.44 | −0.0946120 | ||||||||
\(605\) | −1606.09 | −0.107929 | ||||||||
\(606\) | 8699.80 | 0.583177 | ||||||||
\(607\) | 6667.20 | 0.445821 | 0.222910 | − | 0.974839i | \(-0.428444\pi\) | ||||
0.222910 | + | 0.974839i | \(0.428444\pi\) | |||||||
\(608\) | −6937.56 | −0.462755 | ||||||||
\(609\) | 11781.7 | 0.783942 | ||||||||
\(610\) | −1324.37 | −0.0879053 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −493.268 | −0.0325803 | ||||||||
\(613\) | 23085.4 | 1.52106 | 0.760530 | − | 0.649302i | \(-0.224939\pi\) | ||||
0.760530 | + | 0.649302i | \(0.224939\pi\) | |||||||
\(614\) | −18718.8 | −1.23034 | ||||||||
\(615\) | 144.106 | 0.00944866 | ||||||||
\(616\) | 28450.6 | 1.86089 | ||||||||
\(617\) | −3049.24 | −0.198959 | −0.0994796 | − | 0.995040i | \(-0.531718\pi\) | ||||
−0.0994796 | + | 0.995040i | \(0.531718\pi\) | |||||||
\(618\) | −8784.48 | −0.571786 | ||||||||
\(619\) | −7296.58 | −0.473787 | −0.236894 | − | 0.971536i | \(-0.576129\pi\) | ||||
−0.236894 | + | 0.971536i | \(0.576129\pi\) | |||||||
\(620\) | 91.3523 | 0.00591741 | ||||||||
\(621\) | 10912.0 | 0.705126 | ||||||||
\(622\) | −20248.9 | −1.30531 | ||||||||
\(623\) | −21083.3 | −1.35583 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15506.8 | 0.992438 | ||||||||
\(626\) | −25621.7 | −1.63586 | ||||||||
\(627\) | 25755.1 | 1.64044 | ||||||||
\(628\) | 812.543 | 0.0516305 | ||||||||
\(629\) | 2932.92 | 0.185920 | ||||||||
\(630\) | 350.976 | 0.0221956 | ||||||||
\(631\) | 23829.5 | 1.50339 | 0.751694 | − | 0.659512i | \(-0.229237\pi\) | ||||
0.751694 | + | 0.659512i | \(0.229237\pi\) | |||||||
\(632\) | −10191.6 | −0.641453 | ||||||||
\(633\) | 337.345 | 0.0211821 | ||||||||
\(634\) | −15960.5 | −0.999801 | ||||||||
\(635\) | 310.637 | 0.0194130 | ||||||||
\(636\) | 15.0874 | 0.000940653 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 29171.3 | 1.81019 | ||||||||
\(639\) | −7271.65 | −0.450175 | ||||||||
\(640\) | 528.347 | 0.0326324 | ||||||||
\(641\) | 13405.3 | 0.826016 | 0.413008 | − | 0.910727i | \(-0.364478\pi\) | ||||
0.413008 | + | 0.910727i | \(0.364478\pi\) | |||||||
\(642\) | 8092.36 | 0.497477 | ||||||||
\(643\) | −5251.51 | −0.322083 | −0.161042 | − | 0.986948i | \(-0.551485\pi\) | ||||
−0.161042 | + | 0.986948i | \(0.551485\pi\) | |||||||
\(644\) | 1915.55 | 0.117210 | ||||||||
\(645\) | 906.904 | 0.0553633 | ||||||||
\(646\) | 7065.37 | 0.430315 | ||||||||
\(647\) | 21611.4 | 1.31319 | 0.656595 | − | 0.754244i | \(-0.271996\pi\) | ||||
0.656595 | + | 0.754244i | \(0.271996\pi\) | |||||||
\(648\) | −4506.28 | −0.273184 | ||||||||
\(649\) | 4637.39 | 0.280483 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7574.54 | 0.456021 | ||||||||
\(652\) | 2169.94 | 0.130340 | ||||||||
\(653\) | −21595.8 | −1.29420 | −0.647099 | − | 0.762406i | \(-0.724018\pi\) | ||||
−0.647099 | + | 0.762406i | \(0.724018\pi\) | |||||||
\(654\) | −6341.25 | −0.379148 | ||||||||
\(655\) | −1154.78 | −0.0688869 | ||||||||
\(656\) | −3511.77 | −0.209012 | ||||||||
\(657\) | 10255.4 | 0.608985 | ||||||||
\(658\) | 1487.54 | 0.0881314 | ||||||||
\(659\) | −16642.6 | −0.983768 | −0.491884 | − | 0.870661i | \(-0.663692\pi\) | ||||
−0.491884 | + | 0.870661i | \(0.663692\pi\) | |||||||
\(660\) | 192.684 | 0.0113640 | ||||||||
\(661\) | −26981.1 | −1.58766 | −0.793831 | − | 0.608139i | \(-0.791916\pi\) | ||||
−0.793831 | + | 0.608139i | \(0.791916\pi\) | |||||||
\(662\) | −11871.5 | −0.696980 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14598.1 | −0.853185 | ||||||||
\(665\) | 1102.09 | 0.0642664 | ||||||||
\(666\) | −3947.60 | −0.229680 | ||||||||
\(667\) | 12887.3 | 0.748126 | ||||||||
\(668\) | 852.310 | 0.0493665 | ||||||||
\(669\) | 4552.09 | 0.263070 | ||||||||
\(670\) | 639.074 | 0.0368501 | ||||||||
\(671\) | 59604.5 | 3.42922 | ||||||||
\(672\) | −4303.55 | −0.247043 | ||||||||
\(673\) | 11149.2 | 0.638591 | 0.319296 | − | 0.947655i | \(-0.396554\pi\) | ||||
0.319296 | + | 0.947655i | \(0.396554\pi\) | |||||||
\(674\) | −7761.04 | −0.443537 | ||||||||
\(675\) | −18571.3 | −1.05898 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3314.33 | 0.188154 | 0.0940769 | − | 0.995565i | \(-0.470010\pi\) | ||||
0.0940769 | + | 0.995565i | \(0.470010\pi\) | |||||||
\(678\) | 6054.51 | 0.342953 | ||||||||
\(679\) | 10602.1 | 0.599223 | ||||||||
\(680\) | 346.836 | 0.0195596 | ||||||||
\(681\) | 12165.5 | 0.684556 | ||||||||
\(682\) | 18754.3 | 1.05299 | ||||||||
\(683\) | −24505.2 | −1.37287 | −0.686433 | − | 0.727193i | \(-0.740824\pi\) | ||||
−0.686433 | + | 0.727193i | \(0.740824\pi\) | |||||||
\(684\) | 2084.75 | 0.116539 | ||||||||
\(685\) | −1015.61 | −0.0566486 | ||||||||
\(686\) | −16557.0 | −0.921500 | ||||||||
\(687\) | 778.506 | 0.0432342 | ||||||||
\(688\) | −22100.6 | −1.22468 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −388.299 | −0.0214236 | ||||||||
\(691\) | 21752.8 | 1.19756 | 0.598782 | − | 0.800912i | \(-0.295652\pi\) | ||||
0.598782 | + | 0.800912i | \(0.295652\pi\) | |||||||
\(692\) | 6466.64 | 0.355238 | ||||||||
\(693\) | −15796.0 | −0.865858 | ||||||||
\(694\) | −7278.90 | −0.398132 | ||||||||
\(695\) | −838.755 | −0.0457781 | ||||||||
\(696\) | −15670.7 | −0.853445 | ||||||||
\(697\) | −1779.20 | −0.0966887 | ||||||||
\(698\) | 19379.9 | 1.05092 | ||||||||
\(699\) | 945.941 | 0.0511857 | ||||||||
\(700\) | −3260.10 | −0.176029 | ||||||||
\(701\) | 34250.9 | 1.84542 | 0.922709 | − | 0.385496i | \(-0.125970\pi\) | ||||
0.922709 | + | 0.385496i | \(0.125970\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12395.8 | −0.665028 | ||||||||
\(704\) | −36770.1 | −1.96850 | ||||||||
\(705\) | 66.1043 | 0.00353140 | ||||||||
\(706\) | −5992.59 | −0.319454 | ||||||||
\(707\) | −16754.6 | −0.891259 | ||||||||
\(708\) | −379.666 | −0.0201536 | ||||||||
\(709\) | 5527.11 | 0.292771 | 0.146386 | − | 0.989228i | \(-0.453236\pi\) | ||||
0.146386 | + | 0.989228i | \(0.453236\pi\) | |||||||
\(710\) | 779.234 | 0.0411889 | ||||||||
\(711\) | 5658.43 | 0.298464 | ||||||||
\(712\) | 28042.6 | 1.47604 | ||||||||
\(713\) | 8285.33 | 0.435187 | ||||||||
\(714\) | 4382.83 | 0.229724 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 221.931 | 0.0115837 | ||||||||
\(717\) | −13079.1 | −0.681241 | ||||||||
\(718\) | −6485.02 | −0.337074 | ||||||||
\(719\) | −3777.78 | −0.195949 | −0.0979745 | − | 0.995189i | \(-0.531236\pi\) | ||||
−0.0979745 | + | 0.995189i | \(0.531236\pi\) | |||||||
\(720\) | −380.085 | −0.0196735 | ||||||||
\(721\) | 16917.6 | 0.873849 | ||||||||
\(722\) | −12291.5 | −0.633576 | ||||||||
\(723\) | −18534.2 | −0.953380 | ||||||||
\(724\) | −1541.08 | −0.0791072 | ||||||||
\(725\) | −21933.2 | −1.12355 | ||||||||
\(726\) | 26994.8 | 1.37999 | ||||||||
\(727\) | 19076.8 | 0.973204 | 0.486602 | − | 0.873624i | \(-0.338236\pi\) | ||||
0.486602 | + | 0.873624i | \(0.338236\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17319.9 | 0.879944 | ||||||||
\(730\) | −1098.98 | −0.0557192 | ||||||||
\(731\) | −11197.0 | −0.566535 | ||||||||
\(732\) | −4879.86 | −0.246400 | ||||||||
\(733\) | −7997.30 | −0.402984 | −0.201492 | − | 0.979490i | \(-0.564579\pi\) | ||||
−0.201492 | + | 0.979490i | \(0.564579\pi\) | |||||||
\(734\) | −16849.4 | −0.847307 | ||||||||
\(735\) | −26.0581 | −0.00130771 | ||||||||
\(736\) | −4707.39 | −0.235756 | ||||||||
\(737\) | −28762.1 | −1.43754 | ||||||||
\(738\) | 2394.74 | 0.119446 | ||||||||
\(739\) | −28983.6 | −1.44273 | −0.721367 | − | 0.692553i | \(-0.756486\pi\) | ||||
−0.721367 | + | 0.692553i | \(0.756486\pi\) | |||||||
\(740\) | −92.7376 | −0.00460689 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 132.541 | 0.00655761 | ||||||||
\(743\) | 19145.4 | 0.945324 | 0.472662 | − | 0.881244i | \(-0.343293\pi\) | ||||
0.472662 | + | 0.881244i | \(0.343293\pi\) | |||||||
\(744\) | −10074.8 | −0.496451 | ||||||||
\(745\) | −1549.33 | −0.0761923 | ||||||||
\(746\) | −7435.47 | −0.364922 | ||||||||
\(747\) | 8104.95 | 0.396981 | ||||||||
\(748\) | −2378.96 | −0.116288 | ||||||||
\(749\) | −15584.7 | −0.760284 | ||||||||
\(750\) | 1323.38 | 0.0644304 | ||||||||
\(751\) | −25516.9 | −1.23985 | −0.619923 | − | 0.784663i | \(-0.712836\pi\) | ||||
−0.619923 | + | 0.784663i | \(0.712836\pi\) | |||||||
\(752\) | −1610.92 | −0.0781172 | ||||||||
\(753\) | 2648.47 | 0.128175 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −548.275 | −0.0264288 | ||||||||
\(756\) | 3894.46 | 0.187355 | ||||||||
\(757\) | −17230.6 | −0.827289 | −0.413645 | − | 0.910438i | \(-0.635744\pi\) | ||||
−0.413645 | + | 0.910438i | \(0.635744\pi\) | |||||||
\(758\) | −4779.17 | −0.229007 | ||||||||
\(759\) | 17475.7 | 0.835744 | ||||||||
\(760\) | −1465.87 | −0.0699642 | ||||||||
\(761\) | 2343.06 | 0.111611 | 0.0558053 | − | 0.998442i | \(-0.482227\pi\) | ||||
0.0558053 | + | 0.998442i | \(0.482227\pi\) | |||||||
\(762\) | −5221.11 | −0.248216 | ||||||||
\(763\) | 12212.3 | 0.579444 | ||||||||
\(764\) | −974.121 | −0.0461289 | ||||||||
\(765\) | −192.566 | −0.00910096 | ||||||||
\(766\) | 27756.9 | 1.30927 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 7862.11 | 0.369400 | ||||||||
\(769\) | 7100.18 | 0.332950 | 0.166475 | − | 0.986046i | \(-0.446761\pi\) | ||||
0.166475 | + | 0.986046i | \(0.446761\pi\) | |||||||
\(770\) | 1692.71 | 0.0792219 | ||||||||
\(771\) | −4719.29 | −0.220442 | ||||||||
\(772\) | 1901.17 | 0.0886328 | ||||||||
\(773\) | −12270.4 | −0.570940 | −0.285470 | − | 0.958388i | \(-0.592150\pi\) | ||||
−0.285470 | + | 0.958388i | \(0.592150\pi\) | |||||||
\(774\) | 15070.8 | 0.699881 | ||||||||
\(775\) | −14100.9 | −0.653575 | ||||||||
\(776\) | −14101.7 | −0.652349 | ||||||||
\(777\) | −7689.40 | −0.355027 | ||||||||
\(778\) | 24386.9 | 1.12379 | ||||||||
\(779\) | 7519.64 | 0.345852 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35070.1 | −1.60680 | ||||||||
\(782\) | 4794.11 | 0.219229 | ||||||||
\(783\) | 26201.0 | 1.19584 | ||||||||
\(784\) | 635.017 | 0.0289275 | ||||||||
\(785\) | 317.207 | 0.0144224 | ||||||||
\(786\) | 19409.2 | 0.880794 | ||||||||
\(787\) | −3425.04 | −0.155133 | −0.0775663 | − | 0.996987i | \(-0.524715\pi\) | ||||
−0.0775663 | + | 0.996987i | \(0.524715\pi\) | |||||||
\(788\) | 1823.04 | 0.0824151 | ||||||||
\(789\) | −19254.3 | −0.868787 | ||||||||
\(790\) | −606.360 | −0.0273080 | ||||||||
\(791\) | −11660.1 | −0.524129 | ||||||||
\(792\) | 21010.0 | 0.942624 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −25894.3 | −1.15737 | ||||||||
\(795\) | 5.88995 | 0.000262761 0 | ||||||||
\(796\) | −3446.87 | −0.153481 | ||||||||
\(797\) | −11781.1 | −0.523600 | −0.261800 | − | 0.965122i | \(-0.584316\pi\) | ||||
−0.261800 | + | 0.965122i | \(0.584316\pi\) | |||||||
\(798\) | −18523.6 | −0.821717 | ||||||||
\(799\) | −816.154 | −0.0361370 | ||||||||
\(800\) | 8011.58 | 0.354065 | ||||||||
\(801\) | −15569.4 | −0.686790 | ||||||||
\(802\) | 5339.24 | 0.235081 | ||||||||
\(803\) | 49460.6 | 2.17363 | ||||||||
\(804\) | 2354.77 | 0.103291 | ||||||||
\(805\) | 747.807 | 0.0327413 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23743.2 | −1.03569 | ||||||||
\(808\) | 22285.0 | 0.970276 | ||||||||
\(809\) | 18910.1 | 0.821810 | 0.410905 | − | 0.911678i | \(-0.365213\pi\) | ||||
0.410905 | + | 0.911678i | \(0.365213\pi\) | |||||||
\(810\) | −268.107 | −0.0116300 | ||||||||
\(811\) | −12803.3 | −0.554359 | −0.277180 | − | 0.960818i | \(-0.589400\pi\) | ||||
−0.277180 | + | 0.960818i | \(0.589400\pi\) | |||||||
\(812\) | 4599.45 | 0.198780 | ||||||||
\(813\) | −14480.5 | −0.624664 | ||||||||
\(814\) | −19038.7 | −0.819788 | ||||||||
\(815\) | 847.121 | 0.0364090 | ||||||||
\(816\) | −4746.33 | −0.203621 | ||||||||
\(817\) | 47323.3 | 2.02648 | ||||||||
\(818\) | −24889.4 | −1.06386 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 56.2574 | 0.00239585 | ||||||||
\(821\) | −19335.1 | −0.821923 | −0.410962 | − | 0.911653i | \(-0.634807\pi\) | ||||
−0.410962 | + | 0.911653i | \(0.634807\pi\) | |||||||
\(822\) | 17070.1 | 0.724315 | ||||||||
\(823\) | −2125.90 | −0.0900417 | −0.0450209 | − | 0.998986i | \(-0.514335\pi\) | ||||
−0.0450209 | + | 0.998986i | \(0.514335\pi\) | |||||||
\(824\) | −22501.9 | −0.951324 | ||||||||
\(825\) | −29742.2 | −1.25514 | ||||||||
\(826\) | −3335.32 | −0.140497 | ||||||||
\(827\) | 6989.24 | 0.293881 | 0.146941 | − | 0.989145i | \(-0.453057\pi\) | ||||
0.146941 | + | 0.989145i | \(0.453057\pi\) | |||||||
\(828\) | 1414.58 | 0.0593721 | ||||||||
\(829\) | −32649.7 | −1.36788 | −0.683938 | − | 0.729540i | \(-0.739734\pi\) | ||||
−0.683938 | + | 0.729540i | \(0.739734\pi\) | |||||||
\(830\) | −868.531 | −0.0363219 | ||||||||
\(831\) | 21682.0 | 0.905103 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 321.724 | 0.0133819 | ||||||||
\(834\) | 14097.6 | 0.585324 | ||||||||
\(835\) | 332.732 | 0.0137900 | ||||||||
\(836\) | 10054.5 | 0.415958 | ||||||||
\(837\) | 16844.7 | 0.695626 | ||||||||
\(838\) | −34278.4 | −1.41304 | ||||||||
\(839\) | 4038.23 | 0.166168 | 0.0830841 | − | 0.996543i | \(-0.473523\pi\) | ||||
0.0830841 | + | 0.996543i | \(0.473523\pi\) | |||||||
\(840\) | −909.318 | −0.0373505 | ||||||||
\(841\) | 6555.00 | 0.268769 | ||||||||
\(842\) | −24240.9 | −0.992159 | ||||||||
\(843\) | 13006.1 | 0.531380 | ||||||||
\(844\) | 131.695 | 0.00537102 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1098.51 | 0.0446426 | ||||||||
\(847\) | −51988.1 | −2.10901 | ||||||||
\(848\) | −143.534 | −0.00581248 | ||||||||
\(849\) | 9620.64 | 0.388904 | ||||||||
\(850\) | −8159.17 | −0.329244 | ||||||||
\(851\) | −8410.97 | −0.338807 | ||||||||
\(852\) | 2871.21 | 0.115453 | ||||||||
\(853\) | −8114.12 | −0.325700 | −0.162850 | − | 0.986651i | \(-0.552069\pi\) | ||||
−0.162850 | + | 0.986651i | \(0.552069\pi\) | |||||||
\(854\) | −42869.0 | −1.71774 | ||||||||
\(855\) | 813.863 | 0.0325538 | ||||||||
\(856\) | 20729.0 | 0.827690 | ||||||||
\(857\) | −22298.1 | −0.888786 | −0.444393 | − | 0.895832i | \(-0.646581\pi\) | ||||
−0.444393 | + | 0.895832i | \(0.646581\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33550.5 | 1.33263 | 0.666315 | − | 0.745670i | \(-0.267870\pi\) | ||||
0.666315 | + | 0.745670i | \(0.267870\pi\) | |||||||
\(860\) | 354.045 | 0.0140382 | ||||||||
\(861\) | 4664.62 | 0.184634 | ||||||||
\(862\) | 12429.4 | 0.491121 | ||||||||
\(863\) | 14120.5 | 0.556972 | 0.278486 | − | 0.960440i | \(-0.410167\pi\) | ||||
0.278486 | + | 0.960440i | \(0.410167\pi\) | |||||||
\(864\) | −9570.49 | −0.376846 | ||||||||
\(865\) | 2524.50 | 0.0992319 | ||||||||
\(866\) | 21025.2 | 0.825018 | ||||||||
\(867\) | 15698.1 | 0.614918 | ||||||||
\(868\) | 2957.01 | 0.115631 | ||||||||
\(869\) | 27289.8 | 1.06530 | ||||||||
\(870\) | −932.351 | −0.0363329 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −16243.4 | −0.630817 | ||||||||
\(873\) | 7829.39 | 0.303533 | ||||||||
\(874\) | −20261.9 | −0.784175 | ||||||||
\(875\) | −2548.63 | −0.0984679 | ||||||||
\(876\) | −4049.36 | −0.156182 | ||||||||
\(877\) | 1941.69 | 0.0747619 | 0.0373809 | − | 0.999301i | \(-0.488099\pi\) | ||||
0.0373809 | + | 0.999301i | \(0.488099\pi\) | |||||||
\(878\) | 7668.78 | 0.294771 | ||||||||
\(879\) | −20232.6 | −0.776368 | ||||||||
\(880\) | −1833.10 | −0.0702201 | ||||||||
\(881\) | −790.231 | −0.0302197 | −0.0151099 | − | 0.999886i | \(-0.504810\pi\) | ||||
−0.0151099 | + | 0.999886i | \(0.504810\pi\) | |||||||
\(882\) | −433.029 | −0.0165316 | ||||||||
\(883\) | −36638.6 | −1.39636 | −0.698180 | − | 0.715922i | \(-0.746007\pi\) | ||||
−0.698180 | + | 0.715922i | \(0.746007\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −148.217 | −0.00562968 | ||||||||
\(886\) | −24958.9 | −0.946401 | ||||||||
\(887\) | −40686.3 | −1.54015 | −0.770075 | − | 0.637954i | \(-0.779781\pi\) | ||||
−0.770075 | + | 0.637954i | \(0.779781\pi\) | |||||||
\(888\) | 10227.6 | 0.386503 | ||||||||
\(889\) | 10055.1 | 0.379344 | ||||||||
\(890\) | 1668.43 | 0.0628381 | ||||||||
\(891\) | 12066.4 | 0.453692 | ||||||||
\(892\) | 1777.08 | 0.0667053 | ||||||||
\(893\) | 3449.40 | 0.129261 | ||||||||
\(894\) | 26040.9 | 0.974202 | ||||||||
\(895\) | 86.6392 | 0.00323579 | ||||||||
\(896\) | 17102.2 | 0.637663 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1438.21 | −0.0534449 | ||||||||
\(899\) | 19894.0 | 0.738046 | ||||||||
\(900\) | −2407.50 | −0.0891666 | ||||||||
\(901\) | −72.7200 | −0.00268885 | ||||||||
\(902\) | 11549.5 | 0.426336 | ||||||||
\(903\) | 29355.9 | 1.08184 | ||||||||
\(904\) | 15509.0 | 0.570598 | ||||||||
\(905\) | −601.618 | −0.0220977 | ||||||||
\(906\) | 9215.28 | 0.337922 | ||||||||
\(907\) | −10464.4 | −0.383093 | −0.191547 | − | 0.981484i | \(-0.561350\pi\) | ||||
−0.191547 | + | 0.981484i | \(0.561350\pi\) | |||||||
\(908\) | 4749.26 | 0.173579 | ||||||||
\(909\) | −12372.8 | −0.451463 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35611.5 | −1.29513 | −0.647563 | − | 0.762011i | \(-0.724212\pi\) | ||||
−0.647563 | + | 0.762011i | \(0.724212\pi\) | |||||||
\(912\) | 20060.0 | 0.728346 | ||||||||
\(913\) | 39089.0 | 1.41693 | ||||||||
\(914\) | 35242.9 | 1.27542 | ||||||||
\(915\) | −1905.04 | −0.0688291 | ||||||||
\(916\) | 303.920 | 0.0109627 | ||||||||
\(917\) | −37379.4 | −1.34610 | ||||||||
\(918\) | 9746.80 | 0.350427 | ||||||||
\(919\) | 1077.25 | 0.0386674 | 0.0193337 | − | 0.999813i | \(-0.493846\pi\) | ||||
0.0193337 | + | 0.999813i | \(0.493846\pi\) | |||||||
\(920\) | −994.648 | −0.0356441 | ||||||||
\(921\) | −26926.0 | −0.963346 | ||||||||
\(922\) | 30762.3 | 1.09881 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 6237.04 | 0.222060 | ||||||||
\(925\) | 14314.8 | 0.508829 | ||||||||
\(926\) | 34928.6 | 1.23955 | ||||||||
\(927\) | 12493.2 | 0.442644 | ||||||||
\(928\) | −11303.0 | −0.399826 | ||||||||
\(929\) | −55733.8 | −1.96832 | −0.984159 | − | 0.177290i | \(-0.943267\pi\) | ||||
−0.984159 | + | 0.177290i | \(0.943267\pi\) | |||||||
\(930\) | −599.413 | −0.0211350 | ||||||||
\(931\) | −1359.74 | −0.0478665 | ||||||||
\(932\) | 369.284 | 0.0129789 | ||||||||
\(933\) | −29126.9 | −1.02205 | ||||||||
\(934\) | −22597.9 | −0.791677 | ||||||||
\(935\) | −928.718 | −0.0324838 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3198.60 | −0.111519 | −0.0557596 | − | 0.998444i | \(-0.517758\pi\) | ||||
−0.0557596 | + | 0.998444i | \(0.517758\pi\) | |||||||
\(938\) | 20686.4 | 0.720079 | ||||||||
\(939\) | −36855.4 | −1.28086 | ||||||||
\(940\) | 25.8064 | 0.000895437 0 | ||||||||
\(941\) | −8823.35 | −0.305667 | −0.152834 | − | 0.988252i | \(-0.548840\pi\) | ||||
−0.152834 | + | 0.988252i | \(0.548840\pi\) | |||||||
\(942\) | −5331.54 | −0.184407 | ||||||||
\(943\) | 5102.35 | 0.176199 | ||||||||
\(944\) | 3611.95 | 0.124533 | ||||||||
\(945\) | 1520.35 | 0.0523354 | ||||||||
\(946\) | 72684.3 | 2.49806 | ||||||||
\(947\) | −28290.4 | −0.970766 | −0.485383 | − | 0.874301i | \(-0.661320\pi\) | ||||
−0.485383 | + | 0.874301i | \(0.661320\pi\) | |||||||
\(948\) | −2234.23 | −0.0765447 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 34484.0 | 1.17769 | ||||||||
\(951\) | −22958.4 | −0.782836 | ||||||||
\(952\) | 11226.8 | 0.382210 | ||||||||
\(953\) | −12399.0 | −0.421452 | −0.210726 | − | 0.977545i | \(-0.567583\pi\) | ||||
−0.210726 | + | 0.977545i | \(0.567583\pi\) | |||||||
\(954\) | 97.8783 | 0.00332173 | ||||||||
\(955\) | −380.285 | −0.0128856 | ||||||||
\(956\) | −5105.94 | −0.172739 | ||||||||
\(957\) | 41961.3 | 1.41736 | ||||||||
\(958\) | −37450.0 | −1.26300 | ||||||||
\(959\) | −32874.5 | −1.10696 | ||||||||
\(960\) | 1175.22 | 0.0395105 | ||||||||
\(961\) | −17001.0 | −0.570676 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11508.9 | −0.385118 | ||||||||
\(964\) | −7235.53 | −0.241744 | ||||||||
\(965\) | 742.193 | 0.0247586 | ||||||||
\(966\) | −12569.0 | −0.418634 | ||||||||
\(967\) | 26667.1 | 0.886820 | 0.443410 | − | 0.896319i | \(-0.353769\pi\) | ||||
0.443410 | + | 0.896319i | \(0.353769\pi\) | |||||||
\(968\) | 69148.6 | 2.29599 | ||||||||
\(969\) | 10163.2 | 0.336933 | ||||||||
\(970\) | −839.001 | −0.0277719 | ||||||||
\(971\) | 49420.7 | 1.63335 | 0.816676 | − | 0.577096i | \(-0.195814\pi\) | ||||
0.816676 | + | 0.577096i | \(0.195814\pi\) | |||||||
\(972\) | 4796.89 | 0.158293 | ||||||||
\(973\) | −27149.9 | −0.894539 | ||||||||
\(974\) | −25100.3 | −0.825735 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 46424.5 | 1.52255 | ||||||||
\(977\) | −778.759 | −0.0255012 | −0.0127506 | − | 0.999919i | \(-0.504059\pi\) | ||||
−0.0127506 | + | 0.999919i | \(0.504059\pi\) | |||||||
\(978\) | −14238.2 | −0.465529 | ||||||||
\(979\) | −75089.2 | −2.45134 | ||||||||
\(980\) | −10.1728 | −0.000331589 0 | ||||||||
\(981\) | 9018.48 | 0.293515 | ||||||||
\(982\) | 27757.2 | 0.902003 | ||||||||
\(983\) | −5997.90 | −0.194612 | −0.0973059 | − | 0.995255i | \(-0.531023\pi\) | ||||
−0.0973059 | + | 0.995255i | \(0.531023\pi\) | |||||||
\(984\) | −6204.35 | −0.201004 | ||||||||
\(985\) | 711.693 | 0.0230218 | ||||||||
\(986\) | 11511.2 | 0.371797 | ||||||||
\(987\) | 2139.75 | 0.0690062 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32110.6 | 1.03241 | ||||||||
\(990\) | 1250.02 | 0.0401295 | ||||||||
\(991\) | 8974.94 | 0.287688 | 0.143844 | − | 0.989600i | \(-0.454054\pi\) | ||||
0.143844 | + | 0.989600i | \(0.454054\pi\) | |||||||
\(992\) | −7266.75 | −0.232580 | ||||||||
\(993\) | −17076.6 | −0.545729 | ||||||||
\(994\) | 25223.3 | 0.804863 | ||||||||
\(995\) | −1345.62 | −0.0428732 | ||||||||
\(996\) | −3200.24 | −0.101811 | ||||||||
\(997\) | 28530.2 | 0.906280 | 0.453140 | − | 0.891439i | \(-0.350304\pi\) | ||||
0.453140 | + | 0.891439i | \(0.350304\pi\) | |||||||
\(998\) | 6634.31 | 0.210426 | ||||||||
\(999\) | −17100.2 | −0.541567 |
(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 | 169.4.a.g.1.1 | 2 | ||
3.2 | odd | 2 | 1521.4.a.r.1.2 | 2 | |||
13.2 | odd | 12 | 169.4.e.f.147.1 | 8 | |||
13.3 | even | 3 | 169.4.c.j.22.2 | 4 | |||
13.4 | even | 6 | 169.4.c.g.146.1 | 4 | |||
13.5 | odd | 4 | 169.4.b.f.168.4 | 4 | |||
13.6 | odd | 12 | 169.4.e.f.23.4 | 8 | |||
13.7 | odd | 12 | 169.4.e.f.23.1 | 8 | |||
13.8 | odd | 4 | 169.4.b.f.168.1 | 4 | |||
13.9 | even | 3 | 169.4.c.j.146.2 | 4 | |||
13.10 | even | 6 | 169.4.c.g.22.1 | 4 | |||
13.11 | odd | 12 | 169.4.e.f.147.4 | 8 | |||
13.12 | even | 2 | 13.4.a.b.1.2 | ✓ | 2 | ||
39.38 | odd | 2 | 117.4.a.d.1.1 | 2 | |||
52.51 | odd | 2 | 208.4.a.h.1.2 | 2 | |||
65.12 | odd | 4 | 325.4.b.e.274.4 | 4 | |||
65.38 | odd | 4 | 325.4.b.e.274.1 | 4 | |||
65.64 | even | 2 | 325.4.a.f.1.1 | 2 | |||
91.90 | odd | 2 | 637.4.a.b.1.2 | 2 | |||
104.51 | odd | 2 | 832.4.a.z.1.1 | 2 | |||
104.77 | even | 2 | 832.4.a.s.1.2 | 2 | |||
143.142 | odd | 2 | 1573.4.a.b.1.1 | 2 | |||
156.155 | even | 2 | 1872.4.a.bb.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.a.b.1.2 | ✓ | 2 | 13.12 | even | 2 | ||
117.4.a.d.1.1 | 2 | 39.38 | odd | 2 | |||
169.4.a.g.1.1 | 2 | 1.1 | even | 1 | trivial | ||
169.4.b.f.168.1 | 4 | 13.8 | odd | 4 | |||
169.4.b.f.168.4 | 4 | 13.5 | odd | 4 | |||
169.4.c.g.22.1 | 4 | 13.10 | even | 6 | |||
169.4.c.g.146.1 | 4 | 13.4 | even | 6 | |||
169.4.c.j.22.2 | 4 | 13.3 | even | 3 | |||
169.4.c.j.146.2 | 4 | 13.9 | even | 3 | |||
169.4.e.f.23.1 | 8 | 13.7 | odd | 12 | |||
169.4.e.f.23.4 | 8 | 13.6 | odd | 12 | |||
169.4.e.f.147.1 | 8 | 13.2 | odd | 12 | |||
169.4.e.f.147.4 | 8 | 13.11 | odd | 12 | |||
208.4.a.h.1.2 | 2 | 52.51 | odd | 2 | |||
325.4.a.f.1.1 | 2 | 65.64 | even | 2 | |||
325.4.b.e.274.1 | 4 | 65.38 | odd | 4 | |||
325.4.b.e.274.4 | 4 | 65.12 | odd | 4 | |||
637.4.a.b.1.2 | 2 | 91.90 | odd | 2 | |||
832.4.a.s.1.2 | 2 | 104.77 | even | 2 | |||
832.4.a.z.1.1 | 2 | 104.51 | odd | 2 | |||
1521.4.a.r.1.2 | 2 | 3.2 | odd | 2 | |||
1573.4.a.b.1.1 | 2 | 143.142 | odd | 2 | |||
1872.4.a.bb.1.1 | 2 | 156.155 | even | 2 |