Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(1\) |
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 | 1.2 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-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 | \(-0.350417\pi\) | ||||
0.452823 | + | 0.891601i | \(0.350417\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.43845 | −0.179806 | ||||||||
\(5\) | 0.561553 | 0.0502268 | 0.0251134 | − | 0.999685i | \(-0.492005\pi\) | ||||
0.0251134 | + | 0.999685i | \(0.492005\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.1771 | −0.981470 | −0.490735 | − | 0.871309i | \(-0.663272\pi\) | ||||
−0.490735 | + | 0.871309i | \(0.663272\pi\) | |||||||
\(8\) | −24.1771 | −1.06849 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.43845 | 0.0454877 | ||||||||
\(11\) | 64.7386 | 1.77449 | 0.887247 | − | 0.461295i | \(-0.152615\pi\) | ||||
0.887247 | + | 0.461295i | \(0.152615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −46.5616 | −0.888864 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −50.4233 | −0.787864 | ||||||||
\(17\) | 25.5464 | 0.364465 | 0.182233 | − | 0.983255i | \(-0.441668\pi\) | ||||
0.182233 | + | 0.983255i | \(0.441668\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 107.970 | 1.30368 | 0.651841 | − | 0.758356i | \(-0.273997\pi\) | ||||
0.651841 | + | 0.758356i | \(0.273997\pi\) | |||||||
\(20\) | −0.807764 | −0.00903108 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 165.831 | 1.60706 | ||||||||
\(23\) | −73.2614 | −0.664176 | −0.332088 | − | 0.943248i | \(-0.607753\pi\) | ||||
−0.332088 | + | 0.943248i | \(0.607753\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.685 | −0.997477 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 26.1468 | 0.176474 | ||||||||
\(29\) | −175.909 | −1.12640 | −0.563198 | − | 0.826322i | \(-0.690429\pi\) | ||||
−0.563198 | + | 0.826322i | \(0.690429\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 113.093 | 0.655228 | 0.327614 | − | 0.944812i | \(-0.393755\pi\) | ||||
0.327614 | + | 0.944812i | \(0.393755\pi\) | |||||||
\(32\) | 64.2547 | 0.354961 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 65.4384 | 0.330077 | ||||||||
\(35\) | −10.2074 | −0.0492961 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −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 | \(-0.542347\pi\) | ||||
−0.132645 | + | 0.991164i | \(0.542347\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 438.302 | 1.55443 | 0.777214 | − | 0.629236i | \(-0.216632\pi\) | ||||
0.777214 | + | 0.629236i | \(0.216632\pi\) | |||||||
\(44\) | −93.1231 | −0.319064 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −187.663 | −0.601508 | ||||||||
\(47\) | −31.9479 | −0.0991506 | −0.0495753 | − | 0.998770i | \(-0.515787\pi\) | ||||
−0.0495753 | + | 0.998770i | \(0.515787\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12.5937 | −0.0367164 | ||||||||
\(50\) | −319.386 | −0.903361 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.84658 | −0.00737752 | −0.00368876 | − | 0.999993i | \(-0.501174\pi\) | ||||
−0.00368876 | + | 0.999993i | \(0.501174\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 36.3542 | 0.0891272 | ||||||||
\(56\) | 439.469 | 1.04869 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −450.600 | −1.02012 | ||||||||
\(59\) | 71.6325 | 0.158064 | 0.0790319 | − | 0.996872i | \(-0.474817\pi\) | ||||
0.0790319 | + | 0.996872i | \(0.474817\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −920.695 | −1.93251 | −0.966253 | − | 0.257593i | \(-0.917071\pi\) | ||||
−0.966253 | + | 0.257593i | \(0.917071\pi\) | |||||||
\(62\) | 289.693 | 0.593404 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 567.978 | 1.10933 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 444.280 | 0.810112 | 0.405056 | − | 0.914292i | \(-0.367252\pi\) | ||||
0.405056 | + | 0.914292i | \(0.367252\pi\) | |||||||
\(68\) | −36.7471 | −0.0655330 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −26.1468 | −0.0446448 | ||||||||
\(71\) | −541.719 | −0.905496 | −0.452748 | − | 0.891639i | \(-0.649556\pi\) | ||||
−0.452748 | + | 0.891639i | \(0.649556\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −764.004 | −1.22493 | −0.612465 | − | 0.790498i | \(-0.709822\pi\) | ||||
−0.612465 | + | 0.790498i | \(0.709822\pi\) | |||||||
\(74\) | −294.086 | −0.461984 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −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 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −178.401 | −0.240258 | ||||||||
\(83\) | 603.797 | 0.798498 | 0.399249 | − | 0.916842i | \(-0.369271\pi\) | ||||
0.399249 | + | 0.916842i | \(0.369271\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.3457 | 0.0183059 | ||||||||
\(86\) | 1122.73 | 1.40776 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1565.19 | −1.89602 | ||||||||
\(89\) | −1159.88 | −1.38143 | −0.690715 | − | 0.723127i | \(-0.742704\pi\) | ||||
−0.690715 | + | 0.723127i | \(0.742704\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 105.383 | 0.119423 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −81.8362 | −0.0897953 | ||||||||
\(95\) | 60.6307 | 0.0654798 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −583.269 | −0.610536 | −0.305268 | − | 0.952267i | \(-0.598746\pi\) | ||||
−0.305268 | + | 0.952267i | \(0.598746\pi\) | |||||||
\(98\) | −32.2595 | −0.0332521 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 179.352 | 0.179352 | ||||||||
\(101\) | −921.740 | −0.908085 | −0.454043 | − | 0.890980i | \(-0.650019\pi\) | ||||
−0.454043 | + | 0.890980i | \(0.650019\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −930.712 | −0.890347 | −0.445174 | − | 0.895444i | \(-0.646858\pi\) | ||||
−0.445174 | + | 0.895444i | \(0.646858\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.29168 | −0.00668142 | ||||||||
\(107\) | −857.383 | −0.774638 | −0.387319 | − | 0.921946i | \(-0.626599\pi\) | ||||
−0.387319 | + | 0.921946i | \(0.626599\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −671.853 | −0.590384 | −0.295192 | − | 0.955438i | \(-0.595384\pi\) | ||||
−0.295192 | + | 0.955438i | \(0.595384\pi\) | |||||||
\(110\) | 93.1231 | 0.0807176 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 916.548 | 0.773265 | ||||||||
\(113\) | −641.474 | −0.534024 | −0.267012 | − | 0.963693i | \(-0.586036\pi\) | ||||
−0.267012 | + | 0.963693i | \(0.586036\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −41.1401 | −0.0333594 | ||||||||
\(116\) | 253.036 | 0.202533 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 183.491 | 0.143150 | ||||||||
\(119\) | −464.359 | −0.357712 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2860.09 | 2.14883 | ||||||||
\(122\) | −2358.41 | −1.75017 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −162.678 | −0.117814 | ||||||||
\(125\) | −140.211 | −0.100327 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −553.174 | −0.386506 | −0.193253 | − | 0.981149i | \(-0.561904\pi\) | ||||
−0.193253 | + | 0.981149i | \(0.561904\pi\) | |||||||
\(128\) | 940.868 | 0.649702 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2056.40 | −1.37152 | −0.685758 | − | 0.727830i | \(-0.740529\pi\) | ||||
−0.685758 | + | 0.727830i | \(0.740529\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1962.57 | −1.27952 | ||||||||
\(134\) | 1138.05 | 0.733674 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −617.637 | −0.389426 | ||||||||
\(137\) | −1808.57 | −1.12786 | −0.563928 | − | 0.825824i | \(-0.690710\pi\) | ||||
−0.563928 | + | 0.825824i | \(0.690710\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1493.64 | 0.911428 | 0.455714 | − | 0.890126i | \(-0.349384\pi\) | ||||
0.455714 | + | 0.890126i | \(0.349384\pi\) | |||||||
\(140\) | 14.6828 | 0.00886373 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1387.64 | −0.820058 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −98.7822 | −0.0565753 | ||||||||
\(146\) | −1957.04 | −1.10935 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 165.145 | 0.0917218 | ||||||||
\(149\) | −2759.02 | −1.51696 | −0.758482 | − | 0.651694i | \(-0.774059\pi\) | ||||
−0.758482 | + | 0.651694i | \(0.774059\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 976.355 | 0.526190 | 0.263095 | − | 0.964770i | \(-0.415257\pi\) | ||||
0.263095 | + | 0.964770i | \(0.415257\pi\) | |||||||
\(152\) | −2610.39 | −1.39297 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −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 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 36.0824 | 0.0178285 | ||||||||
\(161\) | 1331.68 | 0.651869 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1508.53 | −0.724892 | −0.362446 | − | 0.932005i | \(-0.618058\pi\) | ||||
−0.362446 | + | 0.932005i | \(0.618058\pi\) | |||||||
\(164\) | 100.182 | 0.0477005 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1546.66 | 0.723157 | ||||||||
\(167\) | 592.521 | 0.274555 | 0.137277 | − | 0.990533i | \(-0.456165\pi\) | ||||
0.137277 | + | 0.990533i | \(0.456165\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 36.7471 | 0.0165787 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −630.474 | −0.279495 | ||||||||
\(173\) | 4495.57 | 1.97568 | 0.987838 | − | 0.155488i | \(-0.0496952\pi\) | ||||
0.987838 | + | 0.155488i | \(0.0496952\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2266.40 | 0.978994 | ||||||||
\(176\) | −3264.34 | −1.39806 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2971.10 | −1.25109 | ||||||||
\(179\) | 154.285 | 0.0644235 | 0.0322117 | − | 0.999481i | \(-0.489745\pi\) | ||||
0.0322117 | + | 0.999481i | \(0.489745\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1071.35 | 0.439959 | 0.219979 | − | 0.975505i | \(-0.429401\pi\) | ||||
0.219979 | + | 0.975505i | \(0.429401\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1771.25 | 0.709663 | ||||||||
\(185\) | −64.4706 | −0.0256215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1653.84 | 0.646742 | ||||||||
\(188\) | 45.9554 | 0.0178279 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 155.309 | 0.0593015 | ||||||||
\(191\) | −677.203 | −0.256548 | −0.128274 | − | 0.991739i | \(-0.540944\pi\) | ||||
−0.128274 | + | 0.991739i | \(0.540944\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −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 | \(-0.426396\pi\) | ||||
0.229178 | + | 0.973385i | \(0.426396\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2396.24 | 0.853593 | 0.426796 | − | 0.904348i | \(-0.359642\pi\) | ||||
0.426796 | + | 0.904348i | \(0.359642\pi\) | |||||||
\(200\) | 3014.51 | 1.06579 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2361.09 | −0.822403 | ||||||||
\(203\) | 3197.51 | 1.10552 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −39.1098 | −0.0133246 | ||||||||
\(206\) | −2384.07 | −0.806339 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6989.81 | 2.31337 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −91.5539 | −0.0298712 | −0.0149356 | − | 0.999888i | \(-0.504754\pi\) | ||||
−0.0149356 | + | 0.999888i | \(0.504754\pi\) | |||||||
\(212\) | 4.09466 | 0.00132652 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2196.23 | −0.701548 | ||||||||
\(215\) | 246.130 | 0.0780740 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2055.70 | −0.643087 | ||||||||
\(218\) | −1720.99 | −0.534679 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −52.2935 | −0.0160256 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1235.42 | −0.370985 | −0.185493 | − | 0.982646i | \(-0.559388\pi\) | ||||
−0.185493 | + | 0.982646i | \(0.559388\pi\) | |||||||
\(224\) | −1167.96 | −0.348383 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1643.17 | −0.483637 | ||||||||
\(227\) | 3301.66 | 0.965370 | 0.482685 | − | 0.875794i | \(-0.339662\pi\) | ||||
0.482685 | + | 0.875794i | \(0.339662\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −211.283 | −0.0609694 | −0.0304847 | − | 0.999535i | \(-0.509705\pi\) | ||||
−0.0304847 | + | 0.999535i | \(0.509705\pi\) | |||||||
\(230\) | −105.383 | −0.0302118 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4252.97 | 1.20354 | ||||||||
\(233\) | 256.724 | 0.0721827 | 0.0360913 | − | 0.999348i | \(-0.488509\pi\) | ||||
0.0360913 | + | 0.999348i | \(0.488509\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.9404 | −0.00498002 | ||||||||
\(236\) | −103.040 | −0.0284208 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1189.48 | −0.323960 | ||||||||
\(239\) | −3549.62 | −0.960694 | −0.480347 | − | 0.877078i | \(-0.659489\pi\) | ||||
−0.480347 | + | 0.877078i | \(0.659489\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5030.10 | 1.34447 | 0.672235 | − | 0.740338i | \(-0.265335\pi\) | ||||
0.672235 | + | 0.740338i | \(0.265335\pi\) | |||||||
\(242\) | 7326.27 | 1.94608 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1324.37 | 0.347476 | ||||||||
\(245\) | −7.07204 | −0.00184415 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −2734.25 | −0.700102 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −359.158 | −0.0908606 | ||||||||
\(251\) | 718.784 | 0.180754 | 0.0903770 | − | 0.995908i | \(-0.471193\pi\) | ||||
0.0903770 | + | 0.995908i | \(0.471193\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4742.84 | −1.17858 | ||||||||
\(254\) | −1416.98 | −0.350038 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2133.74 | −0.520933 | ||||||||
\(257\) | −1280.79 | −0.310871 | −0.155435 | − | 0.987846i | \(-0.549678\pi\) | ||||
−0.155435 | + | 0.987846i | \(0.549678\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2086.87 | 0.500663 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5267.58 | −1.24211 | ||||||||
\(263\) | −5225.55 | −1.22517 | −0.612587 | − | 0.790403i | \(-0.709871\pi\) | ||||
−0.612587 | + | 0.790403i | \(0.709871\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.59851 | −0.000370549 0 | ||||||||
\(266\) | −5027.24 | −1.15880 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −639.074 | −0.145663 | ||||||||
\(269\) | −6443.80 | −1.46054 | −0.730270 | − | 0.683158i | \(-0.760606\pi\) | ||||
−0.730270 | + | 0.683158i | \(0.760606\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 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 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5884.40 | −1.27639 | −0.638194 | − | 0.769876i | \(-0.720318\pi\) | ||||
−0.638194 | + | 0.769876i | \(0.720318\pi\) | |||||||
\(278\) | 3826.03 | 0.825431 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 246.785 | 0.0526722 | ||||||||
\(281\) | 3529.79 | 0.749358 | 0.374679 | − | 0.927155i | \(-0.377753\pi\) | ||||
0.374679 | + | 0.927155i | \(0.377753\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2611.00 | −0.548438 | −0.274219 | − | 0.961667i | \(-0.588419\pi\) | ||||
−0.274219 | + | 0.961667i | \(0.588419\pi\) | |||||||
\(284\) | 779.234 | 0.162813 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1265.96 | 0.260373 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4260.38 | −0.867165 | ||||||||
\(290\) | −253.036 | −0.0512372 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1098.98 | 0.220250 | ||||||||
\(293\) | −5491.03 | −1.09484 | −0.547422 | − | 0.836857i | \(-0.684391\pi\) | ||||
−0.547422 | + | 0.836857i | \(0.684391\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 40.2255 | 0.00793904 | ||||||||
\(296\) | 2775.72 | 0.545052 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7067.37 | −1.37383 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7967.05 | −1.52563 | ||||||||
\(302\) | 2500.99 | 0.476542 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5444.19 | −1.02712 | ||||||||
\(305\) | −517.019 | −0.0970637 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7307.59 | 1.35852 | 0.679261 | − | 0.733897i | \(-0.262300\pi\) | ||||
0.679261 | + | 0.733897i | \(0.262300\pi\) | |||||||
\(308\) | 1692.71 | 0.313152 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 162.678 | 0.0298048 | ||||||||
\(311\) | −7904.92 | −1.44131 | −0.720654 | − | 0.693295i | \(-0.756158\pi\) | ||||
−0.720654 | + | 0.693295i | \(0.756158\pi\) | |||||||
\(312\) | 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 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 606.360 | 0.107944 | ||||||||
\(317\) | −6230.81 | −1.10397 | −0.551983 | − | 0.833856i | \(-0.686129\pi\) | ||||
−0.551983 | + | 0.833856i | \(0.686129\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11388.1 | −1.99878 | ||||||||
\(320\) | 318.950 | 0.0557182 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3411.16 | 0.590362 | ||||||||
\(323\) | 2758.24 | 0.475147 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3864.19 | −0.656495 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1683.83 | 0.283458 | ||||||||
\(329\) | 580.719 | 0.0973134 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4634.51 | 0.769594 | 0.384797 | − | 0.923001i | \(-0.374271\pi\) | ||||
0.384797 | + | 0.923001i | \(0.374271\pi\) | |||||||
\(332\) | −868.531 | −0.143575 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1517.77 | 0.248649 | ||||||||
\(335\) | 249.487 | 0.0406893 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3029.82 | 0.489747 | 0.244874 | − | 0.969555i | \(-0.421254\pi\) | ||||
0.244874 | + | 0.969555i | \(0.421254\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −20.6355 | −0.00329151 | ||||||||
\(341\) | 7321.47 | 1.16270 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6463.66 | 1.01751 | ||||||||
\(344\) | −10596.9 | −1.66089 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11515.6 | 1.78926 | ||||||||
\(347\) | −2841.60 | −0.439611 | −0.219805 | − | 0.975544i | \(-0.570542\pi\) | ||||
−0.219805 | + | 0.975544i | \(0.570542\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −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 | \(-0.556435\pi\) | ||||
−0.176368 | + | 0.984324i | \(0.556435\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −304.204 | −0.0454802 | ||||||||
\(356\) | 1668.43 | 0.248389 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 395.209 | 0.0583449 | ||||||||
\(359\) | −2531.68 | −0.372192 | −0.186096 | − | 0.982532i | \(-0.559583\pi\) | ||||
−0.186096 | + | 0.982532i | \(0.559583\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4798.45 | 0.699585 | ||||||||
\(362\) | 2744.31 | 0.398447 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −429.028 | −0.0615243 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6577.81 | 0.935583 | 0.467792 | − | 0.883839i | \(-0.345050\pi\) | ||||
0.467792 | + | 0.883839i | \(0.345050\pi\) | |||||||
\(368\) | 3694.08 | 0.523280 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −165.145 | −0.0232040 | ||||||||
\(371\) | 51.7426 | 0.00724081 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2902.72 | 0.402942 | 0.201471 | − | 0.979495i | \(-0.435428\pi\) | ||||
0.201471 | + | 0.979495i | \(0.435428\pi\) | |||||||
\(374\) | 4236.40 | 0.585719 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 772.407 | 0.105941 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1865.73 | 0.252866 | 0.126433 | − | 0.991975i | \(-0.459647\pi\) | ||||
0.126433 | + | 0.991975i | \(0.459647\pi\) | |||||||
\(380\) | −87.2140 | −0.0117736 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1734.69 | −0.232342 | ||||||||
\(383\) | 10836.0 | 1.44567 | 0.722837 | − | 0.691019i | \(-0.242838\pi\) | ||||
0.722837 | + | 0.691019i | \(0.242838\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −660.813 | −0.0874757 | ||||||||
\(386\) | −3385.55 | −0.446425 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 839.001 | 0.109778 | ||||||||
\(389\) | 9520.34 | 1.24088 | 0.620438 | − | 0.784256i | \(-0.286955\pi\) | ||||
0.620438 | + | 0.784256i | \(0.286955\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1871.56 | −0.242069 | ||||||||
\(392\) | 304.480 | 0.0392310 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3246.43 | 0.415108 | ||||||||
\(395\) | −236.716 | −0.0301531 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10108.8 | 1.27796 | 0.638978 | − | 0.769225i | \(-0.279358\pi\) | ||||
0.638978 | + | 0.769225i | \(0.279358\pi\) | |||||||
\(398\) | 6138.10 | 0.773053 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6287.01 | 0.785876 | ||||||||
\(401\) | 2084.38 | 0.259573 | 0.129787 | − | 0.991542i | \(-0.458571\pi\) | ||||
0.129787 | + | 0.991542i | \(0.458571\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1325.88 | 0.163279 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8190.60 | 1.00121 | ||||||||
\(407\) | −7432.50 | −0.905197 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9716.53 | 1.17470 | 0.587349 | − | 0.809334i | \(-0.300172\pi\) | ||||
0.587349 | + | 0.809334i | \(0.300172\pi\) | |||||||
\(410\) | −100.182 | −0.0120674 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1338.78 | 0.160090 | ||||||||
\(413\) | −1302.07 | −0.155135 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 339.064 | 0.0401060 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 17904.8 | 2.09510 | ||||||||
\(419\) | −13381.9 | −1.56026 | −0.780129 | − | 0.625619i | \(-0.784847\pi\) | ||||
−0.780129 | + | 0.625619i | \(0.784847\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9463.37 | 1.09553 | 0.547763 | − | 0.836633i | \(-0.315479\pi\) | ||||
0.547763 | + | 0.836633i | \(0.315479\pi\) | |||||||
\(422\) | −234.520 | −0.0270527 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 68.8221 | 0.00788278 | ||||||||
\(425\) | −3185.24 | −0.363546 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 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 | \(-0.412598\pi\) | ||||
0.271144 | + | 0.962539i | \(0.412598\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8208.00 | −0.910973 | −0.455486 | − | 0.890243i | \(-0.650535\pi\) | ||||
−0.455486 | + | 0.890243i | \(0.650535\pi\) | |||||||
\(434\) | −5265.78 | −0.582409 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 966.425 | 0.106155 | ||||||||
\(437\) | −7910.01 | −0.865874 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2993.80 | −0.325481 | −0.162741 | − | 0.986669i | \(-0.552033\pi\) | ||||
−0.162741 | + | 0.986669i | \(0.552033\pi\) | |||||||
\(440\) | −878.938 | −0.0952311 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9743.67 | −1.04500 | −0.522501 | − | 0.852639i | \(-0.675001\pi\) | ||||
−0.522501 | + | 0.852639i | \(0.675001\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −651.335 | −0.0693848 | ||||||||
\(446\) | −3164.59 | −0.335981 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10324.2 | −1.08878 | ||||||||
\(449\) | −561.459 | −0.0590131 | −0.0295065 | − | 0.999565i | \(-0.509394\pi\) | ||||
−0.0295065 | + | 0.999565i | \(0.509394\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4508.78 | −0.470754 | ||||||||
\(452\) | 922.726 | 0.0960207 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8457.38 | 0.874283 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13758.4 | −1.40830 | −0.704148 | − | 0.710054i | \(-0.748671\pi\) | ||||
−0.704148 | + | 0.710054i | \(0.748671\pi\) | |||||||
\(458\) | −541.213 | −0.0552166 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 59.1779 | 0.00599823 | ||||||||
\(461\) | 12009.2 | 1.21329 | 0.606644 | − | 0.794974i | \(-0.292515\pi\) | ||||
0.606644 | + | 0.794974i | \(0.292515\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13635.7 | −1.36870 | −0.684348 | − | 0.729156i | \(-0.739913\pi\) | ||||
−0.684348 | + | 0.729156i | \(0.739913\pi\) | |||||||
\(464\) | 8869.91 | 0.887447 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 657.613 | 0.0653719 | ||||||||
\(467\) | −8821.95 | −0.874157 | −0.437079 | − | 0.899423i | \(-0.643987\pi\) | ||||
−0.437079 | + | 0.899423i | \(0.643987\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8075.72 | −0.795100 | ||||||||
\(470\) | −45.9554 | −0.00451013 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1731.87 | −0.168889 | ||||||||
\(473\) | 28375.1 | 2.75832 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13462.2 | −1.30039 | ||||||||
\(476\) | 667.956 | 0.0643187 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9092.54 | −0.870049 | ||||||||
\(479\) | −14620.0 | −1.39459 | −0.697293 | − | 0.716786i | \(-0.745612\pi\) | ||||
−0.697293 | + | 0.716786i | \(0.745612\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 12884.9 | 1.21761 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4114.09 | −0.386372 | ||||||||
\(485\) | −327.536 | −0.0306653 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9798.86 | 0.911763 | 0.455882 | − | 0.890040i | \(-0.349324\pi\) | ||||
0.455882 | + | 0.890040i | \(0.349324\pi\) | |||||||
\(488\) | 22259.7 | 2.06486 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −18.1154 | −0.00167014 | ||||||||
\(491\) | 10836.1 | 0.995977 | 0.497989 | − | 0.867184i | \(-0.334072\pi\) | ||||
0.497989 | + | 0.867184i | \(0.334072\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4493.84 | −0.410532 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5702.51 | −0.516230 | ||||||||
\(497\) | 9846.86 | 0.888717 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2589.96 | −0.232349 | −0.116175 | − | 0.993229i | \(-0.537063\pi\) | ||||
−0.116175 | + | 0.993229i | \(0.537063\pi\) | |||||||
\(500\) | 201.686 | 0.0180394 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1841.20 | 0.163699 | ||||||||
\(503\) | 17067.5 | 1.51292 | 0.756462 | − | 0.654038i | \(-0.226926\pi\) | ||||
0.756462 | + | 0.654038i | \(0.226926\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −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 | \(-0.514043\pi\) | ||||
−0.0441019 | + | 0.999027i | \(0.514043\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13887.4 | 1.20223 | ||||||||
\(512\) | −12992.6 | −1.12148 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3280.82 | −0.281539 | ||||||||
\(515\) | −522.644 | −0.0447193 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2068.26 | −0.175942 | ||||||||
\(518\) | 5345.63 | 0.453424 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14367.7 | 1.20818 | 0.604089 | − | 0.796917i | \(-0.293537\pi\) | ||||
0.604089 | + | 0.796917i | \(0.293537\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16219.9 | −1.35611 | −0.678057 | − | 0.735010i | \(-0.737178\pi\) | ||||
−0.678057 | + | 0.735010i | \(0.737178\pi\) | |||||||
\(524\) | 2958.02 | 0.246607 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13385.5 | −1.10957 | ||||||||
\(527\) | 2889.11 | 0.238808 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6799.77 | −0.558870 | ||||||||
\(530\) | −4.09466 | −0.000335586 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2823.06 | 0.230066 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −481.466 | −0.0389076 | ||||||||
\(536\) | −10741.4 | −0.865593 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16506.1 | −1.32273 | ||||||||
\(539\) | −815.301 | −0.0651530 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17592.2 | −1.39806 | −0.699029 | − | 0.715094i | \(-0.746384\pi\) | ||||
−0.699029 | + | 0.715094i | \(0.746384\pi\) | |||||||
\(542\) | 10066.7 | 0.797792 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 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 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −20676.6 | −1.60301 | ||||||||
\(551\) | −18992.8 | −1.46846 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7662.33 | 0.589214 | ||||||||
\(554\) | −15073.2 | −1.15596 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2148.52 | −0.163880 | ||||||||
\(557\) | −507.558 | −0.0386102 | −0.0193051 | − | 0.999814i | \(-0.506145\pi\) | ||||
−0.0193051 | + | 0.999814i | \(0.506145\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 514.690 | 0.0388386 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9041.75 | 0.678653 | ||||||||
\(563\) | 3443.14 | 0.257746 | 0.128873 | − | 0.991661i | \(-0.458864\pi\) | ||||
0.128873 | + | 0.991661i | \(0.458864\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −360.221 | −0.0268223 | ||||||||
\(566\) | −6688.21 | −0.496690 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13097.2 | 0.967509 | ||||||||
\(569\) | −23972.2 | −1.76620 | −0.883098 | − | 0.469189i | \(-0.844546\pi\) | ||||
−0.883098 | + | 0.469189i | \(0.844546\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7458.32 | −0.546622 | −0.273311 | − | 0.961926i | \(-0.588119\pi\) | ||||
−0.273311 | + | 0.961926i | \(0.588119\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3242.82 | 0.235806 | ||||||||
\(575\) | 9134.57 | 0.662501 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5669.57 | −0.409059 | −0.204530 | − | 0.978860i | \(-0.565566\pi\) | ||||
−0.204530 | + | 0.978860i | \(0.565566\pi\) | |||||||
\(578\) | −10913.2 | −0.785344 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 142.093 | 0.0101726 | ||||||||
\(581\) | −10975.3 | −0.783702 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −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 | \(-0.488612\pi\) | ||||
0.0357685 | + | 0.999360i | \(0.488612\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12210.6 | 0.854208 | ||||||||
\(590\) | 103.040 | 0.00718996 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5788.99 | 0.401902 | ||||||||
\(593\) | −10198.2 | −0.706221 | −0.353111 | − | 0.935582i | \(-0.614876\pi\) | ||||
−0.353111 | + | 0.935582i | \(0.614876\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −260.762 | −0.0179667 | ||||||||
\(596\) | 3968.70 | 0.272759 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12516.3 | −0.853763 | −0.426881 | − | 0.904308i | \(-0.640388\pi\) | ||||
−0.426881 | + | 0.904308i | \(0.640388\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9627.46 | 0.653431 | 0.326716 | − | 0.945123i | \(-0.394058\pi\) | ||||
0.326716 | + | 0.945123i | \(0.394058\pi\) | |||||||
\(602\) | −20408.0 | −1.38168 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1404.44 | −0.0946120 | ||||||||
\(605\) | 1606.09 | 0.107929 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6667.20 | 0.445821 | 0.222910 | − | 0.974839i | \(-0.428444\pi\) | ||||
0.222910 | + | 0.974839i | \(0.428444\pi\) | |||||||
\(608\) | 6937.56 | 0.462755 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1324.37 | −0.0879053 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23085.4 | 1.52106 | 0.760530 | − | 0.649302i | \(-0.224939\pi\) | ||||
0.760530 | + | 0.649302i | \(0.224939\pi\) | |||||||
\(614\) | 18718.8 | 1.23034 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 28450.6 | 1.86089 | ||||||||
\(617\) | 3049.24 | 0.198959 | 0.0994796 | − | 0.995040i | \(-0.468282\pi\) | ||||
0.0994796 | + | 0.995040i | \(0.468282\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7296.58 | −0.473787 | −0.236894 | − | 0.971536i | \(-0.576129\pi\) | ||||
−0.236894 | + | 0.971536i | \(0.576129\pi\) | |||||||
\(620\) | −91.3523 | −0.00591741 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −20248.9 | −1.30531 | ||||||||
\(623\) | 21083.3 | 1.35583 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15506.8 | 0.992438 | ||||||||
\(626\) | 25621.7 | 1.63586 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 812.543 | 0.0516305 | ||||||||
\(629\) | −2932.92 | −0.185920 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23829.5 | 1.50339 | 0.751694 | − | 0.659512i | \(-0.229237\pi\) | ||||
0.751694 | + | 0.659512i | \(0.229237\pi\) | |||||||
\(632\) | 10191.6 | 0.641453 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15960.5 | −0.999801 | ||||||||
\(635\) | −310.637 | −0.0194130 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −29171.3 | −1.81019 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 528.347 | 0.0326324 | ||||||||
\(641\) | −13405.3 | −0.826016 | −0.413008 | − | 0.910727i | \(-0.635522\pi\) | ||||
−0.413008 | + | 0.910727i | \(0.635522\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5251.51 | −0.322083 | −0.161042 | − | 0.986948i | \(-0.551485\pi\) | ||||
−0.161042 | + | 0.986948i | \(0.551485\pi\) | |||||||
\(644\) | −1915.55 | −0.117210 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7065.37 | 0.430315 | ||||||||
\(647\) | −21611.4 | −1.31319 | −0.656595 | − | 0.754244i | \(-0.728004\pi\) | ||||
−0.656595 | + | 0.754244i | \(0.728004\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4637.39 | 0.280483 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2169.94 | 0.130340 | ||||||||
\(653\) | 21595.8 | 1.29420 | 0.647099 | − | 0.762406i | \(-0.275982\pi\) | ||||
0.647099 | + | 0.762406i | \(0.275982\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1154.78 | −0.0688869 | ||||||||
\(656\) | 3511.77 | 0.209012 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1487.54 | 0.0881314 | ||||||||
\(659\) | 16642.6 | 0.983768 | 0.491884 | − | 0.870661i | \(-0.336308\pi\) | ||||
0.491884 | + | 0.870661i | \(0.336308\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −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 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12887.3 | 0.748126 | ||||||||
\(668\) | −852.310 | −0.0493665 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 639.074 | 0.0368501 | ||||||||
\(671\) | −59604.5 | −3.42922 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11149.2 | 0.638591 | 0.319296 | − | 0.947655i | \(-0.396554\pi\) | ||||
0.319296 | + | 0.947655i | \(0.396554\pi\) | |||||||
\(674\) | 7761.04 | 0.443537 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3314.33 | −0.188154 | −0.0940769 | − | 0.995565i | \(-0.529990\pi\) | ||||
−0.0940769 | + | 0.995565i | \(0.529990\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10602.1 | 0.599223 | ||||||||
\(680\) | −346.836 | −0.0195596 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 18754.3 | 1.05299 | ||||||||
\(683\) | 24505.2 | 1.37287 | 0.686433 | − | 0.727193i | \(-0.259176\pi\) | ||||
0.686433 | + | 0.727193i | \(0.259176\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1015.61 | −0.0566486 | ||||||||
\(686\) | 16557.0 | 0.921500 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −22100.6 | −1.22468 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21752.8 | 1.19756 | 0.598782 | − | 0.800912i | \(-0.295652\pi\) | ||||
0.598782 | + | 0.800912i | \(0.295652\pi\) | |||||||
\(692\) | −6466.64 | −0.355238 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7278.90 | −0.398132 | ||||||||
\(695\) | 838.755 | 0.0457781 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1779.20 | −0.0966887 | ||||||||
\(698\) | −19379.9 | −1.05092 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3260.10 | −0.176029 | ||||||||
\(701\) | −34250.9 | −1.84542 | −0.922709 | − | 0.385496i | \(-0.874030\pi\) | ||||
−0.922709 | + | 0.385496i | \(0.874030\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12395.8 | −0.665028 | ||||||||
\(704\) | 36770.1 | 1.96850 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5992.59 | −0.319454 | ||||||||
\(707\) | 16754.6 | 0.891259 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5527.11 | 0.292771 | 0.146386 | − | 0.989228i | \(-0.453236\pi\) | ||||
0.146386 | + | 0.989228i | \(0.453236\pi\) | |||||||
\(710\) | −779.234 | −0.0411889 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 28042.6 | 1.47604 | ||||||||
\(713\) | −8285.33 | −0.435187 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −221.931 | −0.0115837 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6485.02 | −0.337074 | ||||||||
\(719\) | 3777.78 | 0.195949 | 0.0979745 | − | 0.995189i | \(-0.468764\pi\) | ||||
0.0979745 | + | 0.995189i | \(0.468764\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16917.6 | 0.873849 | ||||||||
\(722\) | 12291.5 | 0.633576 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1541.08 | −0.0791072 | ||||||||
\(725\) | 21933.2 | 1.12355 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19076.8 | 0.973204 | 0.486602 | − | 0.873624i | \(-0.338236\pi\) | ||||
0.486602 | + | 0.873624i | \(0.338236\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1098.98 | −0.0557192 | ||||||||
\(731\) | 11197.0 | 0.566535 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7997.30 | −0.402984 | −0.201492 | − | 0.979490i | \(-0.564579\pi\) | ||||
−0.201492 | + | 0.979490i | \(0.564579\pi\) | |||||||
\(734\) | 16849.4 | 0.847307 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4707.39 | −0.235756 | ||||||||
\(737\) | 28762.1 | 1.43754 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −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 | \(-0.656707\pi\) | ||||
−0.472662 | + | 0.881244i | \(0.656707\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1549.33 | −0.0761923 | ||||||||
\(746\) | 7435.47 | 0.364922 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2378.96 | −0.116288 | ||||||||
\(749\) | 15584.7 | 0.760284 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25516.9 | −1.23985 | −0.619923 | − | 0.784663i | \(-0.712836\pi\) | ||||
−0.619923 | + | 0.784663i | \(0.712836\pi\) | |||||||
\(752\) | 1610.92 | 0.0781172 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 548.275 | 0.0264288 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17230.6 | −0.827289 | −0.413645 | − | 0.910438i | \(-0.635744\pi\) | ||||
−0.413645 | + | 0.910438i | \(0.635744\pi\) | |||||||
\(758\) | 4779.17 | 0.229007 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1465.87 | −0.0699642 | ||||||||
\(761\) | −2343.06 | −0.111611 | −0.0558053 | − | 0.998442i | \(-0.517773\pi\) | ||||
−0.0558053 | + | 0.998442i | \(0.517773\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12212.3 | 0.579444 | ||||||||
\(764\) | 974.121 | 0.0461289 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27756.9 | 1.30927 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7100.18 | 0.332950 | 0.166475 | − | 0.986046i | \(-0.446761\pi\) | ||||
0.166475 | + | 0.986046i | \(0.446761\pi\) | |||||||
\(770\) | −1692.71 | −0.0792219 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1901.17 | 0.0886328 | ||||||||
\(773\) | 12270.4 | 0.570940 | 0.285470 | − | 0.958388i | \(-0.407850\pi\) | ||||
0.285470 | + | 0.958388i | \(0.407850\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14100.9 | −0.653575 | ||||||||
\(776\) | 14101.7 | 0.652349 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24386.9 | 1.12379 | ||||||||
\(779\) | −7519.64 | −0.345852 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35070.1 | −1.60680 | ||||||||
\(782\) | −4794.11 | −0.219229 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 635.017 | 0.0289275 | ||||||||
\(785\) | −317.207 | −0.0144224 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3425.04 | −0.155133 | −0.0775663 | − | 0.996987i | \(-0.524715\pi\) | ||||
−0.0775663 | + | 0.996987i | \(0.524715\pi\) | |||||||
\(788\) | −1823.04 | −0.0824151 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −606.360 | −0.0273080 | ||||||||
\(791\) | 11660.1 | 0.524129 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 25894.3 | 1.15737 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3446.87 | −0.153481 | ||||||||
\(797\) | 11781.1 | 0.523600 | 0.261800 | − | 0.965122i | \(-0.415684\pi\) | ||||
0.261800 | + | 0.965122i | \(0.415684\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −816.154 | −0.0361370 | ||||||||
\(800\) | −8011.58 | −0.354065 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5339.24 | 0.235081 | ||||||||
\(803\) | −49460.6 | −2.17363 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 747.807 | 0.0327413 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 22285.0 | 0.970276 | ||||||||
\(809\) | −18910.1 | −0.821810 | −0.410905 | − | 0.911678i | \(-0.634787\pi\) | ||||
−0.410905 | + | 0.911678i | \(0.634787\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12803.3 | −0.554359 | −0.277180 | − | 0.960818i | \(-0.589400\pi\) | ||||
−0.277180 | + | 0.960818i | \(0.589400\pi\) | |||||||
\(812\) | −4599.45 | −0.198780 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −19038.7 | −0.819788 | ||||||||
\(815\) | −847.121 | −0.0364090 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 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 | \(-0.365193\pi\) | ||||
0.410962 | + | 0.911653i | \(0.365193\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2125.90 | −0.0900417 | −0.0450209 | − | 0.998986i | \(-0.514335\pi\) | ||||
−0.0450209 | + | 0.998986i | \(0.514335\pi\) | |||||||
\(824\) | 22501.9 | 0.951324 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3335.32 | −0.140497 | ||||||||
\(827\) | −6989.24 | −0.293881 | −0.146941 | − | 0.989145i | \(-0.546943\pi\) | ||||
−0.146941 | + | 0.989145i | \(0.546943\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32649.7 | −1.36788 | −0.683938 | − | 0.729540i | \(-0.739734\pi\) | ||||
−0.683938 | + | 0.729540i | \(0.739734\pi\) | |||||||
\(830\) | 868.531 | 0.0363219 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −321.724 | −0.0133819 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 332.732 | 0.0137900 | ||||||||
\(836\) | −10054.5 | −0.415958 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −34278.4 | −1.41304 | ||||||||
\(839\) | −4038.23 | −0.166168 | −0.0830841 | − | 0.996543i | \(-0.526477\pi\) | ||||
−0.0830841 | + | 0.996543i | \(0.526477\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6555.00 | 0.268769 | ||||||||
\(842\) | 24240.9 | 0.992159 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 131.695 | 0.00537102 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −51988.1 | −2.10901 | ||||||||
\(848\) | 143.534 | 0.00581248 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8159.17 | −0.329244 | ||||||||
\(851\) | 8410.97 | 0.338807 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8114.12 | −0.325700 | −0.162850 | − | 0.986651i | \(-0.552069\pi\) | ||||
−0.162850 | + | 0.986651i | \(0.552069\pi\) | |||||||
\(854\) | 42869.0 | 1.71774 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20729.0 | 0.827690 | ||||||||
\(857\) | 22298.1 | 0.888786 | 0.444393 | − | 0.895832i | \(-0.353419\pi\) | ||||
0.444393 | + | 0.895832i | \(0.353419\pi\) | |||||||
\(858\) | 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 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12429.4 | 0.491121 | ||||||||
\(863\) | −14120.5 | −0.556972 | −0.278486 | − | 0.960440i | \(-0.589833\pi\) | ||||
−0.278486 | + | 0.960440i | \(0.589833\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2524.50 | 0.0992319 | ||||||||
\(866\) | −21025.2 | −0.825018 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2957.01 | 0.115631 | ||||||||
\(869\) | −27289.8 | −1.06530 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 16243.4 | 0.630817 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −20261.9 | −0.784175 | ||||||||
\(875\) | 2548.63 | 0.0984679 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1941.69 | 0.0747619 | 0.0373809 | − | 0.999301i | \(-0.488099\pi\) | ||||
0.0373809 | + | 0.999301i | \(0.488099\pi\) | |||||||
\(878\) | −7668.78 | −0.294771 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1833.10 | −0.0702201 | ||||||||
\(881\) | 790.231 | 0.0302197 | 0.0151099 | − | 0.999886i | \(-0.495190\pi\) | ||||
0.0151099 | + | 0.999886i | \(0.495190\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36638.6 | −1.39636 | −0.698180 | − | 0.715922i | \(-0.746007\pi\) | ||||
−0.698180 | + | 0.715922i | \(0.746007\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24958.9 | −0.946401 | ||||||||
\(887\) | 40686.3 | 1.54015 | 0.770075 | − | 0.637954i | \(-0.220219\pi\) | ||||
0.770075 | + | 0.637954i | \(0.220219\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10055.1 | 0.379344 | ||||||||
\(890\) | −1668.43 | −0.0628381 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1777.08 | 0.0667053 | ||||||||
\(893\) | −3449.40 | −0.129261 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 86.6392 | 0.00323579 | ||||||||
\(896\) | −17102.2 | −0.637663 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1438.21 | −0.0534449 | ||||||||
\(899\) | −19894.0 | −0.738046 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −72.7200 | −0.00268885 | ||||||||
\(902\) | −11549.5 | −0.426336 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15509.0 | 0.570598 | ||||||||
\(905\) | 601.618 | 0.0220977 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10464.4 | −0.383093 | −0.191547 | − | 0.981484i | \(-0.561350\pi\) | ||||
−0.191547 | + | 0.981484i | \(0.561350\pi\) | |||||||
\(908\) | −4749.26 | −0.173579 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35611.5 | 1.29513 | 0.647563 | − | 0.762011i | \(-0.275788\pi\) | ||||
0.647563 | + | 0.762011i | \(0.275788\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39089.0 | 1.41693 | ||||||||
\(914\) | −35242.9 | −1.27542 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 303.920 | 0.0109627 | ||||||||
\(917\) | 37379.4 | 1.34610 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1077.25 | 0.0386674 | 0.0193337 | − | 0.999813i | \(-0.493846\pi\) | ||||
0.0193337 | + | 0.999813i | \(0.493846\pi\) | |||||||
\(920\) | 994.648 | 0.0356441 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 30762.3 | 1.09881 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14314.8 | 0.508829 | ||||||||
\(926\) | −34928.6 | −1.23955 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −11303.0 | −0.399826 | ||||||||
\(929\) | 55733.8 | 1.96832 | 0.984159 | − | 0.177290i | \(-0.0567330\pi\) | ||||
0.984159 | + | 0.177290i | \(0.0567330\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1359.74 | −0.0478665 | ||||||||
\(932\) | −369.284 | −0.0129789 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −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 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 25.8064 | 0.000895437 0 | ||||||||
\(941\) | 8823.35 | 0.305667 | 0.152834 | − | 0.988252i | \(-0.451160\pi\) | ||||
0.152834 | + | 0.988252i | \(0.451160\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5102.35 | 0.176199 | ||||||||
\(944\) | −3611.95 | −0.124533 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 72684.3 | 2.49806 | ||||||||
\(947\) | 28290.4 | 0.970766 | 0.485383 | − | 0.874301i | \(-0.338680\pi\) | ||||
0.485383 | + | 0.874301i | \(0.338680\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −34484.0 | −1.17769 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11226.8 | 0.382210 | ||||||||
\(953\) | 12399.0 | 0.421452 | 0.210726 | − | 0.977545i | \(-0.432417\pi\) | ||||
0.210726 | + | 0.977545i | \(0.432417\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −380.285 | −0.0128856 | ||||||||
\(956\) | 5105.94 | 0.172739 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −37450.0 | −1.26300 | ||||||||
\(959\) | 32874.5 | 1.10696 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17001.0 | −0.570676 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7235.53 | −0.241744 | ||||||||
\(965\) | −742.193 | −0.0247586 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26667.1 | 0.886820 | 0.443410 | − | 0.896319i | \(-0.353769\pi\) | ||||
0.443410 | + | 0.896319i | \(0.353769\pi\) | |||||||
\(968\) | −69148.6 | −2.29599 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −839.001 | −0.0277719 | ||||||||
\(971\) | −49420.7 | −1.63335 | −0.816676 | − | 0.577096i | \(-0.804186\pi\) | ||||
−0.816676 | + | 0.577096i | \(0.804186\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −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 | \(-0.495941\pi\) | ||||
0.0127506 | + | 0.999919i | \(0.495941\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −75089.2 | −2.45134 | ||||||||
\(980\) | 10.1728 | 0.000331589 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 27757.2 | 0.902003 | ||||||||
\(983\) | 5997.90 | 0.194612 | 0.0973059 | − | 0.995255i | \(-0.468977\pi\) | ||||
0.0973059 | + | 0.995255i | \(0.468977\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 711.693 | 0.0230218 | ||||||||
\(986\) | −11511.2 | −0.371797 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −32110.6 | −1.03241 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8974.94 | 0.287688 | 0.143844 | − | 0.989600i | \(-0.454054\pi\) | ||||
0.143844 | + | 0.989600i | \(0.454054\pi\) | |||||||
\(992\) | 7266.75 | 0.232580 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 25223.3 | 0.804863 | ||||||||
\(995\) | 1345.62 | 0.0428732 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28530.2 | 0.906280 | 0.453140 | − | 0.891439i | \(-0.350304\pi\) | ||||
0.453140 | + | 0.891439i | \(0.350304\pi\) | |||||||
\(998\) | −6634.31 | −0.210426 | ||||||||
\(999\) | 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 | 1521.4.a.r.1.2 | 2 | ||
3.2 | odd | 2 | 169.4.a.g.1.1 | 2 | |||
13.12 | even | 2 | 117.4.a.d.1.1 | 2 | |||
39.2 | even | 12 | 169.4.e.f.147.1 | 8 | |||
39.5 | even | 4 | 169.4.b.f.168.4 | 4 | |||
39.8 | even | 4 | 169.4.b.f.168.1 | 4 | |||
39.11 | even | 12 | 169.4.e.f.147.4 | 8 | |||
39.17 | odd | 6 | 169.4.c.g.146.1 | 4 | |||
39.20 | even | 12 | 169.4.e.f.23.1 | 8 | |||
39.23 | odd | 6 | 169.4.c.g.22.1 | 4 | |||
39.29 | odd | 6 | 169.4.c.j.22.2 | 4 | |||
39.32 | even | 12 | 169.4.e.f.23.4 | 8 | |||
39.35 | odd | 6 | 169.4.c.j.146.2 | 4 | |||
39.38 | odd | 2 | 13.4.a.b.1.2 | ✓ | 2 | ||
52.51 | odd | 2 | 1872.4.a.bb.1.1 | 2 | |||
156.155 | even | 2 | 208.4.a.h.1.2 | 2 | |||
195.38 | even | 4 | 325.4.b.e.274.1 | 4 | |||
195.77 | even | 4 | 325.4.b.e.274.4 | 4 | |||
195.194 | odd | 2 | 325.4.a.f.1.1 | 2 | |||
273.272 | even | 2 | 637.4.a.b.1.2 | 2 | |||
312.77 | odd | 2 | 832.4.a.s.1.2 | 2 | |||
312.155 | even | 2 | 832.4.a.z.1.1 | 2 | |||
429.428 | even | 2 | 1573.4.a.b.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.a.b.1.2 | ✓ | 2 | 39.38 | odd | 2 | ||
117.4.a.d.1.1 | 2 | 13.12 | even | 2 | |||
169.4.a.g.1.1 | 2 | 3.2 | odd | 2 | |||
169.4.b.f.168.1 | 4 | 39.8 | even | 4 | |||
169.4.b.f.168.4 | 4 | 39.5 | even | 4 | |||
169.4.c.g.22.1 | 4 | 39.23 | odd | 6 | |||
169.4.c.g.146.1 | 4 | 39.17 | odd | 6 | |||
169.4.c.j.22.2 | 4 | 39.29 | odd | 6 | |||
169.4.c.j.146.2 | 4 | 39.35 | odd | 6 | |||
169.4.e.f.23.1 | 8 | 39.20 | even | 12 | |||
169.4.e.f.23.4 | 8 | 39.32 | even | 12 | |||
169.4.e.f.147.1 | 8 | 39.2 | even | 12 | |||
169.4.e.f.147.4 | 8 | 39.11 | even | 12 | |||
208.4.a.h.1.2 | 2 | 156.155 | even | 2 | |||
325.4.a.f.1.1 | 2 | 195.194 | odd | 2 | |||
325.4.b.e.274.1 | 4 | 195.38 | even | 4 | |||
325.4.b.e.274.4 | 4 | 195.77 | even | 4 | |||
637.4.a.b.1.2 | 2 | 273.272 | even | 2 | |||
832.4.a.s.1.2 | 2 | 312.77 | odd | 2 | |||
832.4.a.z.1.1 | 2 | 312.155 | even | 2 | |||
1521.4.a.r.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1573.4.a.b.1.1 | 2 | 429.428 | even | 2 | |||
1872.4.a.bb.1.1 | 2 | 52.51 | odd | 2 |