Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,4,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(61.6569959560\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.35702 | −1.89399 | −0.946997 | − | 0.321243i | \(-0.895899\pi\) | ||||
−0.946997 | + | 0.321243i | \(0.895899\pi\) | |||||||
\(3\) | −10.2482 | −1.97227 | −0.986137 | − | 0.165935i | \(-0.946936\pi\) | ||||
−0.986137 | + | 0.165935i | \(0.946936\pi\) | |||||||
\(4\) | 20.6977 | 2.58721 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 54.9000 | 3.73547 | ||||||||
\(7\) | −17.5818 | −0.949328 | −0.474664 | − | 0.880167i | \(-0.657430\pi\) | ||||
−0.474664 | + | 0.880167i | \(0.657430\pi\) | |||||||
\(8\) | −68.0218 | −3.00617 | ||||||||
\(9\) | 78.0263 | 2.88986 | ||||||||
\(10\) | −26.7851 | −0.847020 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | −212.115 | −5.10269 | ||||||||
\(13\) | 22.3565 | 0.476968 | 0.238484 | − | 0.971146i | \(-0.423350\pi\) | ||||
0.238484 | + | 0.971146i | \(0.423350\pi\) | |||||||
\(14\) | 94.1861 | 1.79802 | ||||||||
\(15\) | −51.2412 | −0.882027 | ||||||||
\(16\) | 198.813 | 3.10645 | ||||||||
\(17\) | 122.147 | 1.74265 | 0.871324 | − | 0.490707i | \(-0.163262\pi\) | ||||
0.871324 | + | 0.490707i | \(0.163262\pi\) | |||||||
\(18\) | −417.989 | −5.47338 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | 103.488 | 1.15704 | ||||||||
\(21\) | 180.182 | 1.87233 | ||||||||
\(22\) | 58.9273 | 0.571061 | ||||||||
\(23\) | −136.576 | −1.23818 | −0.619088 | − | 0.785322i | \(-0.712497\pi\) | ||||
−0.619088 | + | 0.785322i | \(0.712497\pi\) | |||||||
\(24\) | 697.104 | 5.92899 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −119.764 | −0.903374 | ||||||||
\(27\) | −522.929 | −3.72732 | ||||||||
\(28\) | −363.903 | −2.45611 | ||||||||
\(29\) | −107.494 | −0.688314 | −0.344157 | − | 0.938912i | \(-0.611835\pi\) | ||||
−0.344157 | + | 0.938912i | \(0.611835\pi\) | |||||||
\(30\) | 274.500 | 1.67055 | ||||||||
\(31\) | 66.8030 | 0.387038 | 0.193519 | − | 0.981097i | \(-0.438010\pi\) | ||||
0.193519 | + | 0.981097i | \(0.438010\pi\) | |||||||
\(32\) | −520.871 | −2.87743 | ||||||||
\(33\) | 112.731 | 0.594663 | ||||||||
\(34\) | −654.345 | −3.30057 | ||||||||
\(35\) | −87.9090 | −0.424552 | ||||||||
\(36\) | 1614.96 | 7.47669 | ||||||||
\(37\) | −152.006 | −0.675396 | −0.337698 | − | 0.941255i | \(-0.609648\pi\) | ||||
−0.337698 | + | 0.941255i | \(0.609648\pi\) | |||||||
\(38\) | 101.783 | 0.434512 | ||||||||
\(39\) | −229.115 | −0.940711 | ||||||||
\(40\) | −340.109 | −1.34440 | ||||||||
\(41\) | −228.172 | −0.869136 | −0.434568 | − | 0.900639i | \(-0.643099\pi\) | ||||
−0.434568 | + | 0.900639i | \(0.643099\pi\) | |||||||
\(42\) | −965.241 | −3.54619 | ||||||||
\(43\) | −282.305 | −1.00119 | −0.500595 | − | 0.865682i | \(-0.666885\pi\) | ||||
−0.500595 | + | 0.865682i | \(0.666885\pi\) | |||||||
\(44\) | −227.675 | −0.780074 | ||||||||
\(45\) | 390.131 | 1.29239 | ||||||||
\(46\) | 731.640 | 2.34510 | ||||||||
\(47\) | 133.238 | 0.413504 | 0.206752 | − | 0.978393i | \(-0.433711\pi\) | ||||
0.206752 | + | 0.978393i | \(0.433711\pi\) | |||||||
\(48\) | −2037.48 | −6.12678 | ||||||||
\(49\) | −33.8802 | −0.0987760 | ||||||||
\(50\) | −133.926 | −0.378799 | ||||||||
\(51\) | −1251.79 | −3.43698 | ||||||||
\(52\) | 462.728 | 1.23402 | ||||||||
\(53\) | 402.016 | 1.04191 | 0.520954 | − | 0.853585i | \(-0.325576\pi\) | ||||
0.520954 | + | 0.853585i | \(0.325576\pi\) | |||||||
\(54\) | 2801.34 | 7.05953 | ||||||||
\(55\) | −55.0000 | −0.134840 | ||||||||
\(56\) | 1195.95 | 2.85384 | ||||||||
\(57\) | 194.716 | 0.452471 | ||||||||
\(58\) | 575.847 | 1.30366 | ||||||||
\(59\) | 78.0966 | 0.172327 | 0.0861637 | − | 0.996281i | \(-0.472539\pi\) | ||||
0.0861637 | + | 0.996281i | \(0.472539\pi\) | |||||||
\(60\) | −1060.57 | −2.28199 | ||||||||
\(61\) | 665.770 | 1.39743 | 0.698714 | − | 0.715401i | \(-0.253756\pi\) | ||||
0.698714 | + | 0.715401i | \(0.253756\pi\) | |||||||
\(62\) | −357.865 | −0.733047 | ||||||||
\(63\) | −1371.84 | −2.74343 | ||||||||
\(64\) | 1199.81 | 2.34339 | ||||||||
\(65\) | 111.783 | 0.213307 | ||||||||
\(66\) | −603.900 | −1.12629 | ||||||||
\(67\) | −431.056 | −0.785998 | −0.392999 | − | 0.919539i | \(-0.628562\pi\) | ||||
−0.392999 | + | 0.919539i | \(0.628562\pi\) | |||||||
\(68\) | 2528.16 | 4.50860 | ||||||||
\(69\) | 1399.66 | 2.44202 | ||||||||
\(70\) | 470.931 | 0.804100 | ||||||||
\(71\) | −388.228 | −0.648932 | −0.324466 | − | 0.945897i | \(-0.605185\pi\) | ||||
−0.324466 | + | 0.945897i | \(0.605185\pi\) | |||||||
\(72\) | −5307.49 | −8.68741 | ||||||||
\(73\) | 1225.28 | 1.96450 | 0.982251 | − | 0.187570i | \(-0.0600611\pi\) | ||||
0.982251 | + | 0.187570i | \(0.0600611\pi\) | |||||||
\(74\) | 814.300 | 1.27920 | ||||||||
\(75\) | −256.206 | −0.394455 | ||||||||
\(76\) | −393.256 | −0.593547 | ||||||||
\(77\) | 193.400 | 0.286233 | ||||||||
\(78\) | 1227.37 | 1.78170 | ||||||||
\(79\) | 935.437 | 1.33221 | 0.666107 | − | 0.745856i | \(-0.267960\pi\) | ||||
0.666107 | + | 0.745856i | \(0.267960\pi\) | |||||||
\(80\) | 994.065 | 1.38925 | ||||||||
\(81\) | 3252.39 | 4.46144 | ||||||||
\(82\) | 1222.33 | 1.64614 | ||||||||
\(83\) | −475.989 | −0.629477 | −0.314738 | − | 0.949178i | \(-0.601917\pi\) | ||||
−0.314738 | + | 0.949178i | \(0.601917\pi\) | |||||||
\(84\) | 3729.36 | 4.84413 | ||||||||
\(85\) | 610.736 | 0.779336 | ||||||||
\(86\) | 1512.32 | 1.89625 | ||||||||
\(87\) | 1101.62 | 1.35754 | ||||||||
\(88\) | 748.240 | 0.906394 | ||||||||
\(89\) | −1267.32 | −1.50939 | −0.754693 | − | 0.656078i | \(-0.772214\pi\) | ||||
−0.754693 | + | 0.656078i | \(0.772214\pi\) | |||||||
\(90\) | −2089.94 | −2.44777 | ||||||||
\(91\) | −393.068 | −0.452799 | ||||||||
\(92\) | −2826.80 | −3.20342 | ||||||||
\(93\) | −684.613 | −0.763344 | ||||||||
\(94\) | −713.757 | −0.783175 | ||||||||
\(95\) | −95.0000 | −0.102598 | ||||||||
\(96\) | 5338.01 | 5.67509 | ||||||||
\(97\) | 476.201 | 0.498463 | 0.249232 | − | 0.968444i | \(-0.419822\pi\) | ||||
0.249232 | + | 0.968444i | \(0.419822\pi\) | |||||||
\(98\) | 181.497 | 0.187081 | ||||||||
\(99\) | −858.289 | −0.871326 | ||||||||
\(100\) | 517.442 | 0.517442 | ||||||||
\(101\) | −64.5129 | −0.0635571 | −0.0317786 | − | 0.999495i | \(-0.510117\pi\) | ||||
−0.0317786 | + | 0.999495i | \(0.510117\pi\) | |||||||
\(102\) | 6705.88 | 6.50962 | ||||||||
\(103\) | 1946.30 | 1.86189 | 0.930945 | − | 0.365160i | \(-0.118986\pi\) | ||||
0.930945 | + | 0.365160i | \(0.118986\pi\) | |||||||
\(104\) | −1520.73 | −1.43385 | ||||||||
\(105\) | 900.912 | 0.837334 | ||||||||
\(106\) | −2153.61 | −1.97337 | ||||||||
\(107\) | 581.019 | 0.524946 | 0.262473 | − | 0.964939i | \(-0.415462\pi\) | ||||
0.262473 | + | 0.964939i | \(0.415462\pi\) | |||||||
\(108\) | −10823.4 | −9.64338 | ||||||||
\(109\) | −974.937 | −0.856715 | −0.428358 | − | 0.903609i | \(-0.640908\pi\) | ||||
−0.428358 | + | 0.903609i | \(0.640908\pi\) | |||||||
\(110\) | 294.636 | 0.255386 | ||||||||
\(111\) | 1557.79 | 1.33206 | ||||||||
\(112\) | −3495.49 | −2.94904 | ||||||||
\(113\) | −1475.54 | −1.22838 | −0.614190 | − | 0.789158i | \(-0.710517\pi\) | ||||
−0.614190 | + | 0.789158i | \(0.710517\pi\) | |||||||
\(114\) | −1043.10 | −0.856976 | ||||||||
\(115\) | −682.879 | −0.553729 | ||||||||
\(116\) | −2224.87 | −1.78081 | ||||||||
\(117\) | 1744.40 | 1.37837 | ||||||||
\(118\) | −418.365 | −0.326387 | ||||||||
\(119\) | −2147.57 | −1.65435 | ||||||||
\(120\) | 3485.52 | 2.65152 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −3566.54 | −2.64672 | ||||||||
\(123\) | 2338.36 | 1.71417 | ||||||||
\(124\) | 1382.67 | 1.00135 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 7348.99 | 5.19603 | ||||||||
\(127\) | 300.551 | 0.209997 | 0.104998 | − | 0.994472i | \(-0.466516\pi\) | ||||
0.104998 | + | 0.994472i | \(0.466516\pi\) | |||||||
\(128\) | −2260.47 | −1.56093 | ||||||||
\(129\) | 2893.13 | 1.97462 | ||||||||
\(130\) | −598.822 | −0.404001 | ||||||||
\(131\) | 2328.92 | 1.55327 | 0.776636 | − | 0.629949i | \(-0.216924\pi\) | ||||
0.776636 | + | 0.629949i | \(0.216924\pi\) | |||||||
\(132\) | 2333.26 | 1.53852 | ||||||||
\(133\) | 334.054 | 0.217791 | ||||||||
\(134\) | 2309.18 | 1.48868 | ||||||||
\(135\) | −2614.65 | −1.66691 | ||||||||
\(136\) | −8308.67 | −5.23870 | ||||||||
\(137\) | 1875.98 | 1.16990 | 0.584948 | − | 0.811071i | \(-0.301115\pi\) | ||||
0.584948 | + | 0.811071i | \(0.301115\pi\) | |||||||
\(138\) | −7498.02 | −4.62517 | ||||||||
\(139\) | 3061.96 | 1.86843 | 0.934216 | − | 0.356709i | \(-0.116101\pi\) | ||||
0.934216 | + | 0.356709i | \(0.116101\pi\) | |||||||
\(140\) | −1819.51 | −1.09841 | ||||||||
\(141\) | −1365.45 | −0.815544 | ||||||||
\(142\) | 2079.75 | 1.22907 | ||||||||
\(143\) | −245.922 | −0.143811 | ||||||||
\(144\) | 15512.6 | 8.97722 | ||||||||
\(145\) | −537.469 | −0.307823 | ||||||||
\(146\) | −6563.88 | −3.72076 | ||||||||
\(147\) | 347.212 | 0.194813 | ||||||||
\(148\) | −3146.18 | −1.74739 | ||||||||
\(149\) | −2524.81 | −1.38819 | −0.694094 | − | 0.719884i | \(-0.744195\pi\) | ||||
−0.694094 | + | 0.719884i | \(0.744195\pi\) | |||||||
\(150\) | 1372.50 | 0.747095 | ||||||||
\(151\) | 599.046 | 0.322845 | 0.161423 | − | 0.986885i | \(-0.448392\pi\) | ||||
0.161423 | + | 0.986885i | \(0.448392\pi\) | |||||||
\(152\) | 1292.42 | 0.689663 | ||||||||
\(153\) | 9530.69 | 5.03601 | ||||||||
\(154\) | −1036.05 | −0.542124 | ||||||||
\(155\) | 334.015 | 0.173089 | ||||||||
\(156\) | −4742.15 | −2.43382 | ||||||||
\(157\) | −2324.10 | −1.18142 | −0.590711 | − | 0.806883i | \(-0.701153\pi\) | ||||
−0.590711 | + | 0.806883i | \(0.701153\pi\) | |||||||
\(158\) | −5011.16 | −2.52320 | ||||||||
\(159\) | −4119.95 | −2.05493 | ||||||||
\(160\) | −2604.36 | −1.28683 | ||||||||
\(161\) | 2401.25 | 1.17543 | ||||||||
\(162\) | −17423.1 | −8.44994 | ||||||||
\(163\) | −2448.46 | −1.17655 | −0.588276 | − | 0.808660i | \(-0.700193\pi\) | ||||
−0.588276 | + | 0.808660i | \(0.700193\pi\) | |||||||
\(164\) | −4722.64 | −2.24864 | ||||||||
\(165\) | 563.653 | 0.265941 | ||||||||
\(166\) | 2549.88 | 1.19222 | ||||||||
\(167\) | 416.578 | 0.193029 | 0.0965144 | − | 0.995332i | \(-0.469231\pi\) | ||||
0.0965144 | + | 0.995332i | \(0.469231\pi\) | |||||||
\(168\) | −12256.3 | −5.62856 | ||||||||
\(169\) | −1697.19 | −0.772502 | ||||||||
\(170\) | −3271.72 | −1.47606 | ||||||||
\(171\) | −1482.50 | −0.662980 | ||||||||
\(172\) | −5843.07 | −2.59029 | ||||||||
\(173\) | 1241.65 | 0.545668 | 0.272834 | − | 0.962061i | \(-0.412039\pi\) | ||||
0.272834 | + | 0.962061i | \(0.412039\pi\) | |||||||
\(174\) | −5901.41 | −2.57118 | ||||||||
\(175\) | −439.545 | −0.189866 | ||||||||
\(176\) | −2186.94 | −0.936631 | ||||||||
\(177\) | −800.352 | −0.339877 | ||||||||
\(178\) | 6789.05 | 2.85877 | ||||||||
\(179\) | −3277.94 | −1.36874 | −0.684370 | − | 0.729135i | \(-0.739923\pi\) | ||||
−0.684370 | + | 0.729135i | \(0.739923\pi\) | |||||||
\(180\) | 8074.82 | 3.34368 | ||||||||
\(181\) | −368.648 | −0.151389 | −0.0756945 | − | 0.997131i | \(-0.524117\pi\) | ||||
−0.0756945 | + | 0.997131i | \(0.524117\pi\) | |||||||
\(182\) | 2105.67 | 0.857599 | ||||||||
\(183\) | −6822.97 | −2.75611 | ||||||||
\(184\) | 9290.14 | 3.72216 | ||||||||
\(185\) | −760.030 | −0.302046 | ||||||||
\(186\) | 3667.49 | 1.44577 | ||||||||
\(187\) | −1343.62 | −0.525428 | ||||||||
\(188\) | 2757.71 | 1.06982 | ||||||||
\(189\) | 9194.04 | 3.53845 | ||||||||
\(190\) | 508.917 | 0.194320 | ||||||||
\(191\) | 3566.75 | 1.35121 | 0.675605 | − | 0.737264i | \(-0.263883\pi\) | ||||
0.675605 | + | 0.737264i | \(0.263883\pi\) | |||||||
\(192\) | −12296.0 | −4.62180 | ||||||||
\(193\) | 2635.17 | 0.982818 | 0.491409 | − | 0.870929i | \(-0.336482\pi\) | ||||
0.491409 | + | 0.870929i | \(0.336482\pi\) | |||||||
\(194\) | −2551.02 | −0.944086 | ||||||||
\(195\) | −1145.57 | −0.420699 | ||||||||
\(196\) | −701.241 | −0.255554 | ||||||||
\(197\) | −3188.41 | −1.15312 | −0.576561 | − | 0.817054i | \(-0.695606\pi\) | ||||
−0.576561 | + | 0.817054i | \(0.695606\pi\) | |||||||
\(198\) | 4597.87 | 1.65029 | ||||||||
\(199\) | 1975.30 | 0.703644 | 0.351822 | − | 0.936067i | \(-0.385562\pi\) | ||||
0.351822 | + | 0.936067i | \(0.385562\pi\) | |||||||
\(200\) | −1700.55 | −0.601234 | ||||||||
\(201\) | 4417.56 | 1.55020 | ||||||||
\(202\) | 345.597 | 0.120377 | ||||||||
\(203\) | 1889.94 | 0.653436 | ||||||||
\(204\) | −25909.2 | −8.89220 | ||||||||
\(205\) | −1140.86 | −0.388689 | ||||||||
\(206\) | −10426.4 | −3.52641 | ||||||||
\(207\) | −10656.5 | −3.57816 | ||||||||
\(208\) | 4444.77 | 1.48168 | ||||||||
\(209\) | 209.000 | 0.0691714 | ||||||||
\(210\) | −4826.21 | −1.58590 | ||||||||
\(211\) | 1868.49 | 0.609631 | 0.304816 | − | 0.952411i | \(-0.401405\pi\) | ||||
0.304816 | + | 0.952411i | \(0.401405\pi\) | |||||||
\(212\) | 8320.80 | 2.69564 | ||||||||
\(213\) | 3978.65 | 1.27987 | ||||||||
\(214\) | −3112.53 | −0.994244 | ||||||||
\(215\) | −1411.53 | −0.447745 | ||||||||
\(216\) | 35570.6 | 11.2050 | ||||||||
\(217\) | −1174.52 | −0.367426 | ||||||||
\(218\) | 5222.76 | 1.62261 | ||||||||
\(219\) | −12557.0 | −3.87454 | ||||||||
\(220\) | −1138.37 | −0.348860 | ||||||||
\(221\) | 2730.78 | 0.831188 | ||||||||
\(222\) | −8345.14 | −2.52292 | ||||||||
\(223\) | 720.605 | 0.216391 | 0.108196 | − | 0.994130i | \(-0.465493\pi\) | ||||
0.108196 | + | 0.994130i | \(0.465493\pi\) | |||||||
\(224\) | 9157.86 | 2.73163 | ||||||||
\(225\) | 1950.66 | 0.577972 | ||||||||
\(226\) | 7904.49 | 2.32654 | ||||||||
\(227\) | 933.659 | 0.272992 | 0.136496 | − | 0.990641i | \(-0.456416\pi\) | ||||
0.136496 | + | 0.990641i | \(0.456416\pi\) | |||||||
\(228\) | 4030.18 | 1.17064 | ||||||||
\(229\) | 3861.15 | 1.11420 | 0.557100 | − | 0.830445i | \(-0.311914\pi\) | ||||
0.557100 | + | 0.830445i | \(0.311914\pi\) | |||||||
\(230\) | 3658.20 | 1.04876 | ||||||||
\(231\) | −1982.01 | −0.564530 | ||||||||
\(232\) | 7311.93 | 2.06919 | ||||||||
\(233\) | −2597.68 | −0.730386 | −0.365193 | − | 0.930932i | \(-0.618997\pi\) | ||||
−0.365193 | + | 0.930932i | \(0.618997\pi\) | |||||||
\(234\) | −9344.77 | −2.61063 | ||||||||
\(235\) | 666.188 | 0.184925 | ||||||||
\(236\) | 1616.42 | 0.445847 | ||||||||
\(237\) | −9586.57 | −2.62749 | ||||||||
\(238\) | 11504.6 | 3.13332 | ||||||||
\(239\) | −4138.45 | −1.12006 | −0.560030 | − | 0.828473i | \(-0.689210\pi\) | ||||
−0.560030 | + | 0.828473i | \(0.689210\pi\) | |||||||
\(240\) | −10187.4 | −2.73998 | ||||||||
\(241\) | −4421.41 | −1.18178 | −0.590888 | − | 0.806753i | \(-0.701223\pi\) | ||||
−0.590888 | + | 0.806753i | \(0.701223\pi\) | |||||||
\(242\) | −648.200 | −0.172181 | ||||||||
\(243\) | −19212.2 | −5.07186 | ||||||||
\(244\) | 13779.9 | 3.61544 | ||||||||
\(245\) | −169.401 | −0.0441740 | ||||||||
\(246\) | −12526.7 | −3.24663 | ||||||||
\(247\) | −424.774 | −0.109424 | ||||||||
\(248\) | −4544.06 | −1.16350 | ||||||||
\(249\) | 4878.04 | 1.24150 | ||||||||
\(250\) | −669.628 | −0.169404 | ||||||||
\(251\) | −1157.13 | −0.290986 | −0.145493 | − | 0.989359i | \(-0.546477\pi\) | ||||
−0.145493 | + | 0.989359i | \(0.546477\pi\) | |||||||
\(252\) | −28394.0 | −7.09783 | ||||||||
\(253\) | 1502.33 | 0.373324 | ||||||||
\(254\) | −1610.06 | −0.397732 | ||||||||
\(255\) | −6258.96 | −1.53706 | ||||||||
\(256\) | 2510.85 | 0.613000 | ||||||||
\(257\) | 2158.82 | 0.523982 | 0.261991 | − | 0.965070i | \(-0.415621\pi\) | ||||
0.261991 | + | 0.965070i | \(0.415621\pi\) | |||||||
\(258\) | −15498.6 | −3.73992 | ||||||||
\(259\) | 2672.54 | 0.641172 | ||||||||
\(260\) | 2313.64 | 0.551869 | ||||||||
\(261\) | −8387.34 | −1.98913 | ||||||||
\(262\) | −12476.1 | −2.94189 | ||||||||
\(263\) | 3522.37 | 0.825851 | 0.412926 | − | 0.910765i | \(-0.364507\pi\) | ||||
0.412926 | + | 0.910765i | \(0.364507\pi\) | |||||||
\(264\) | −7668.14 | −1.78766 | ||||||||
\(265\) | 2010.08 | 0.465955 | ||||||||
\(266\) | −1789.54 | −0.412494 | ||||||||
\(267\) | 12987.8 | 2.97692 | ||||||||
\(268\) | −8921.87 | −2.03354 | ||||||||
\(269\) | −3275.36 | −0.742388 | −0.371194 | − | 0.928555i | \(-0.621051\pi\) | ||||
−0.371194 | + | 0.928555i | \(0.621051\pi\) | |||||||
\(270\) | 14006.7 | 3.15712 | ||||||||
\(271\) | −8668.59 | −1.94310 | −0.971549 | − | 0.236838i | \(-0.923889\pi\) | ||||
−0.971549 | + | 0.236838i | \(0.923889\pi\) | |||||||
\(272\) | 24284.4 | 5.41346 | ||||||||
\(273\) | 4028.25 | 0.893043 | ||||||||
\(274\) | −10049.7 | −2.21578 | ||||||||
\(275\) | −275.000 | −0.0603023 | ||||||||
\(276\) | 28969.8 | 6.31802 | ||||||||
\(277\) | 5182.43 | 1.12412 | 0.562061 | − | 0.827096i | \(-0.310009\pi\) | ||||
0.562061 | + | 0.827096i | \(0.310009\pi\) | |||||||
\(278\) | −16403.0 | −3.53880 | ||||||||
\(279\) | 5212.39 | 1.11849 | ||||||||
\(280\) | 5979.73 | 1.27628 | ||||||||
\(281\) | 236.777 | 0.0502666 | 0.0251333 | − | 0.999684i | \(-0.491999\pi\) | ||||
0.0251333 | + | 0.999684i | \(0.491999\pi\) | |||||||
\(282\) | 7314.75 | 1.54463 | ||||||||
\(283\) | 3240.59 | 0.680683 | 0.340341 | − | 0.940302i | \(-0.389457\pi\) | ||||
0.340341 | + | 0.940302i | \(0.389457\pi\) | |||||||
\(284\) | −8035.42 | −1.67892 | ||||||||
\(285\) | 973.582 | 0.202351 | ||||||||
\(286\) | 1317.41 | 0.272378 | ||||||||
\(287\) | 4011.68 | 0.825095 | ||||||||
\(288\) | −40641.6 | −8.31539 | ||||||||
\(289\) | 10006.9 | 2.03683 | ||||||||
\(290\) | 2879.23 | 0.583015 | ||||||||
\(291\) | −4880.22 | −0.983105 | ||||||||
\(292\) | 25360.6 | 5.08258 | ||||||||
\(293\) | 745.107 | 0.148565 | 0.0742826 | − | 0.997237i | \(-0.476333\pi\) | ||||
0.0742826 | + | 0.997237i | \(0.476333\pi\) | |||||||
\(294\) | −1860.02 | −0.368975 | ||||||||
\(295\) | 390.483 | 0.0770671 | ||||||||
\(296\) | 10339.7 | 2.03035 | ||||||||
\(297\) | 5752.22 | 1.12383 | ||||||||
\(298\) | 13525.4 | 2.62922 | ||||||||
\(299\) | −3053.36 | −0.590570 | ||||||||
\(300\) | −5302.87 | −1.02054 | ||||||||
\(301\) | 4963.43 | 0.950457 | ||||||||
\(302\) | −3209.10 | −0.611467 | ||||||||
\(303\) | 661.143 | 0.125352 | ||||||||
\(304\) | −3777.45 | −0.712669 | ||||||||
\(305\) | 3328.85 | 0.624949 | ||||||||
\(306\) | −51056.1 | −9.53818 | ||||||||
\(307\) | 6652.85 | 1.23680 | 0.618401 | − | 0.785863i | \(-0.287781\pi\) | ||||
0.618401 | + | 0.785863i | \(0.287781\pi\) | |||||||
\(308\) | 4002.93 | 0.740546 | ||||||||
\(309\) | −19946.1 | −3.67216 | ||||||||
\(310\) | −1789.33 | −0.327829 | ||||||||
\(311\) | −9396.95 | −1.71335 | −0.856675 | − | 0.515856i | \(-0.827474\pi\) | ||||
−0.856675 | + | 0.515856i | \(0.827474\pi\) | |||||||
\(312\) | 15584.8 | 2.82794 | ||||||||
\(313\) | −3328.41 | −0.601063 | −0.300532 | − | 0.953772i | \(-0.597164\pi\) | ||||
−0.300532 | + | 0.953772i | \(0.597164\pi\) | |||||||
\(314\) | 12450.3 | 2.23761 | ||||||||
\(315\) | −6859.21 | −1.22690 | ||||||||
\(316\) | 19361.4 | 3.44672 | ||||||||
\(317\) | 1827.59 | 0.323810 | 0.161905 | − | 0.986806i | \(-0.448236\pi\) | ||||
0.161905 | + | 0.986806i | \(0.448236\pi\) | |||||||
\(318\) | 22070.7 | 3.89202 | ||||||||
\(319\) | 1182.43 | 0.207534 | ||||||||
\(320\) | 5999.07 | 1.04800 | ||||||||
\(321\) | −5954.42 | −1.03534 | ||||||||
\(322\) | −12863.5 | −2.22627 | ||||||||
\(323\) | −2320.80 | −0.399791 | ||||||||
\(324\) | 67317.0 | 11.5427 | ||||||||
\(325\) | 558.913 | 0.0953936 | ||||||||
\(326\) | 13116.4 | 2.22838 | ||||||||
\(327\) | 9991.38 | 1.68968 | ||||||||
\(328\) | 15520.7 | 2.61277 | ||||||||
\(329\) | −2342.56 | −0.392551 | ||||||||
\(330\) | −3019.50 | −0.503691 | ||||||||
\(331\) | 4218.31 | 0.700482 | 0.350241 | − | 0.936660i | \(-0.386100\pi\) | ||||
0.350241 | + | 0.936660i | \(0.386100\pi\) | |||||||
\(332\) | −9851.87 | −1.62859 | ||||||||
\(333\) | −11860.5 | −1.95180 | ||||||||
\(334\) | −2231.62 | −0.365595 | ||||||||
\(335\) | −2155.28 | −0.351509 | ||||||||
\(336\) | 35822.6 | 5.81632 | ||||||||
\(337\) | 1969.47 | 0.318350 | 0.159175 | − | 0.987250i | \(-0.449117\pi\) | ||||
0.159175 | + | 0.987250i | \(0.449117\pi\) | |||||||
\(338\) | 9091.87 | 1.46311 | ||||||||
\(339\) | 15121.7 | 2.42270 | ||||||||
\(340\) | 12640.8 | 2.01631 | ||||||||
\(341\) | −734.833 | −0.116696 | ||||||||
\(342\) | 7941.78 | 1.25568 | ||||||||
\(343\) | 6626.23 | 1.04310 | ||||||||
\(344\) | 19202.9 | 3.00974 | ||||||||
\(345\) | 6998.30 | 1.09210 | ||||||||
\(346\) | −6651.53 | −1.03349 | ||||||||
\(347\) | 3326.07 | 0.514561 | 0.257280 | − | 0.966337i | \(-0.417174\pi\) | ||||
0.257280 | + | 0.966337i | \(0.417174\pi\) | |||||||
\(348\) | 22801.0 | 3.51225 | ||||||||
\(349\) | −5500.77 | −0.843694 | −0.421847 | − | 0.906667i | \(-0.638618\pi\) | ||||
−0.421847 | + | 0.906667i | \(0.638618\pi\) | |||||||
\(350\) | 2354.65 | 0.359604 | ||||||||
\(351\) | −11690.9 | −1.77781 | ||||||||
\(352\) | 5729.58 | 0.867579 | ||||||||
\(353\) | −4985.29 | −0.751672 | −0.375836 | − | 0.926686i | \(-0.622644\pi\) | ||||
−0.375836 | + | 0.926686i | \(0.622644\pi\) | |||||||
\(354\) | 4287.51 | 0.643724 | ||||||||
\(355\) | −1941.14 | −0.290211 | ||||||||
\(356\) | −26230.5 | −3.90510 | ||||||||
\(357\) | 22008.8 | 3.26282 | ||||||||
\(358\) | 17560.0 | 2.59238 | ||||||||
\(359\) | −4940.66 | −0.726346 | −0.363173 | − | 0.931722i | \(-0.618307\pi\) | ||||
−0.363173 | + | 0.931722i | \(0.618307\pi\) | |||||||
\(360\) | −26537.5 | −3.88513 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 1974.86 | 0.286730 | ||||||||
\(363\) | −1240.04 | −0.179298 | ||||||||
\(364\) | −8135.60 | −1.17149 | ||||||||
\(365\) | 6126.42 | 0.878552 | ||||||||
\(366\) | 36550.8 | 5.22005 | ||||||||
\(367\) | 1863.31 | 0.265025 | 0.132512 | − | 0.991181i | \(-0.457696\pi\) | ||||
0.132512 | + | 0.991181i | \(0.457696\pi\) | |||||||
\(368\) | −27153.1 | −3.84633 | ||||||||
\(369\) | −17803.5 | −2.51168 | ||||||||
\(370\) | 4071.50 | 0.572073 | ||||||||
\(371\) | −7068.16 | −0.989112 | ||||||||
\(372\) | −14169.9 | −1.97493 | ||||||||
\(373\) | −11611.1 | −1.61180 | −0.805900 | − | 0.592051i | \(-0.798318\pi\) | ||||
−0.805900 | + | 0.592051i | \(0.798318\pi\) | |||||||
\(374\) | 7197.79 | 0.995158 | ||||||||
\(375\) | −1281.03 | −0.176405 | ||||||||
\(376\) | −9063.07 | −1.24306 | ||||||||
\(377\) | −2403.19 | −0.328304 | ||||||||
\(378\) | −49252.7 | −6.70181 | ||||||||
\(379\) | 10339.8 | 1.40137 | 0.700686 | − | 0.713470i | \(-0.252877\pi\) | ||||
0.700686 | + | 0.713470i | \(0.252877\pi\) | |||||||
\(380\) | −1966.28 | −0.265442 | ||||||||
\(381\) | −3080.11 | −0.414171 | ||||||||
\(382\) | −19107.2 | −2.55918 | ||||||||
\(383\) | −5035.18 | −0.671765 | −0.335882 | − | 0.941904i | \(-0.609034\pi\) | ||||
−0.335882 | + | 0.941904i | \(0.609034\pi\) | |||||||
\(384\) | 23165.8 | 3.07858 | ||||||||
\(385\) | 966.999 | 0.128007 | ||||||||
\(386\) | −14116.7 | −1.86145 | ||||||||
\(387\) | −22027.2 | −2.89330 | ||||||||
\(388\) | 9856.27 | 1.28963 | ||||||||
\(389\) | −10846.6 | −1.41374 | −0.706870 | − | 0.707343i | \(-0.749893\pi\) | ||||
−0.706870 | + | 0.707343i | \(0.749893\pi\) | |||||||
\(390\) | 6136.87 | 0.796801 | ||||||||
\(391\) | −16682.3 | −2.15770 | ||||||||
\(392\) | 2304.59 | 0.296937 | ||||||||
\(393\) | −23867.3 | −3.06348 | ||||||||
\(394\) | 17080.4 | 2.18401 | ||||||||
\(395\) | 4677.18 | 0.595784 | ||||||||
\(396\) | −17764.6 | −2.25431 | ||||||||
\(397\) | 3844.91 | 0.486072 | 0.243036 | − | 0.970017i | \(-0.421857\pi\) | ||||
0.243036 | + | 0.970017i | \(0.421857\pi\) | |||||||
\(398\) | −10581.7 | −1.33270 | ||||||||
\(399\) | −3423.47 | −0.429543 | ||||||||
\(400\) | 4970.33 | 0.621291 | ||||||||
\(401\) | −10086.3 | −1.25608 | −0.628039 | − | 0.778182i | \(-0.716142\pi\) | ||||
−0.628039 | + | 0.778182i | \(0.716142\pi\) | |||||||
\(402\) | −23665.0 | −2.93608 | ||||||||
\(403\) | 1493.48 | 0.184605 | ||||||||
\(404\) | −1335.27 | −0.164436 | ||||||||
\(405\) | 16262.0 | 1.99522 | ||||||||
\(406\) | −10124.4 | −1.23760 | ||||||||
\(407\) | 1672.07 | 0.203639 | ||||||||
\(408\) | 85149.2 | 10.3321 | ||||||||
\(409\) | 9080.10 | 1.09776 | 0.548878 | − | 0.835903i | \(-0.315055\pi\) | ||||
0.548878 | + | 0.835903i | \(0.315055\pi\) | |||||||
\(410\) | 6111.63 | 0.736175 | ||||||||
\(411\) | −19225.5 | −2.30736 | ||||||||
\(412\) | 40283.9 | 4.81710 | ||||||||
\(413\) | −1373.08 | −0.163595 | ||||||||
\(414\) | 57087.1 | 6.77700 | ||||||||
\(415\) | −2379.94 | −0.281510 | ||||||||
\(416\) | −11644.9 | −1.37244 | ||||||||
\(417\) | −31379.7 | −3.68506 | ||||||||
\(418\) | −1119.62 | −0.131010 | ||||||||
\(419\) | −689.620 | −0.0804060 | −0.0402030 | − | 0.999192i | \(-0.512800\pi\) | ||||
−0.0402030 | + | 0.999192i | \(0.512800\pi\) | |||||||
\(420\) | 18646.8 | 2.16636 | ||||||||
\(421\) | 4657.73 | 0.539202 | 0.269601 | − | 0.962972i | \(-0.413108\pi\) | ||||
0.269601 | + | 0.962972i | \(0.413108\pi\) | |||||||
\(422\) | −10009.6 | −1.15464 | ||||||||
\(423\) | 10396.0 | 1.19497 | ||||||||
\(424\) | −27345.8 | −3.13215 | ||||||||
\(425\) | 3053.68 | 0.348530 | ||||||||
\(426\) | −21313.7 | −2.42407 | ||||||||
\(427\) | −11705.4 | −1.32662 | ||||||||
\(428\) | 12025.8 | 1.35815 | ||||||||
\(429\) | 2520.26 | 0.283635 | ||||||||
\(430\) | 7561.58 | 0.848027 | ||||||||
\(431\) | −4942.88 | −0.552413 | −0.276207 | − | 0.961098i | \(-0.589077\pi\) | ||||
−0.276207 | + | 0.961098i | \(0.589077\pi\) | |||||||
\(432\) | −103965. | −11.5788 | ||||||||
\(433\) | −13852.0 | −1.53738 | −0.768691 | − | 0.639620i | \(-0.779092\pi\) | ||||
−0.768691 | + | 0.639620i | \(0.779092\pi\) | |||||||
\(434\) | 6291.92 | 0.695902 | ||||||||
\(435\) | 5508.11 | 0.607112 | ||||||||
\(436\) | −20178.9 | −2.21650 | ||||||||
\(437\) | 2594.94 | 0.284057 | ||||||||
\(438\) | 67268.1 | 7.33835 | ||||||||
\(439\) | 6315.04 | 0.686561 | 0.343281 | − | 0.939233i | \(-0.388462\pi\) | ||||
0.343281 | + | 0.939233i | \(0.388462\pi\) | |||||||
\(440\) | 3741.20 | 0.405352 | ||||||||
\(441\) | −2643.54 | −0.285449 | ||||||||
\(442\) | −14628.9 | −1.57426 | ||||||||
\(443\) | −15593.0 | −1.67234 | −0.836170 | − | 0.548471i | \(-0.815210\pi\) | ||||
−0.836170 | + | 0.548471i | \(0.815210\pi\) | |||||||
\(444\) | 32242.7 | 3.44633 | ||||||||
\(445\) | −6336.59 | −0.675018 | ||||||||
\(446\) | −3860.30 | −0.409844 | ||||||||
\(447\) | 25874.8 | 2.73789 | ||||||||
\(448\) | −21094.9 | −2.22464 | ||||||||
\(449\) | 14240.7 | 1.49680 | 0.748399 | − | 0.663249i | \(-0.230823\pi\) | ||||
0.748399 | + | 0.663249i | \(0.230823\pi\) | |||||||
\(450\) | −10449.7 | −1.09468 | ||||||||
\(451\) | 2509.90 | 0.262054 | ||||||||
\(452\) | −30540.2 | −3.17808 | ||||||||
\(453\) | −6139.16 | −0.636739 | ||||||||
\(454\) | −5001.63 | −0.517044 | ||||||||
\(455\) | −1965.34 | −0.202498 | ||||||||
\(456\) | −13245.0 | −1.36020 | ||||||||
\(457\) | −3433.25 | −0.351424 | −0.175712 | − | 0.984442i | \(-0.556223\pi\) | ||||
−0.175712 | + | 0.984442i | \(0.556223\pi\) | |||||||
\(458\) | −20684.3 | −2.11029 | ||||||||
\(459\) | −63874.3 | −6.49542 | ||||||||
\(460\) | −14134.0 | −1.43261 | ||||||||
\(461\) | −2067.32 | −0.208860 | −0.104430 | − | 0.994532i | \(-0.533302\pi\) | ||||
−0.104430 | + | 0.994532i | \(0.533302\pi\) | |||||||
\(462\) | 10617.7 | 1.06922 | ||||||||
\(463\) | 754.808 | 0.0757644 | 0.0378822 | − | 0.999282i | \(-0.487939\pi\) | ||||
0.0378822 | + | 0.999282i | \(0.487939\pi\) | |||||||
\(464\) | −21371.2 | −2.13822 | ||||||||
\(465\) | −3423.06 | −0.341378 | ||||||||
\(466\) | 13915.9 | 1.38335 | ||||||||
\(467\) | −2552.61 | −0.252935 | −0.126468 | − | 0.991971i | \(-0.540364\pi\) | ||||
−0.126468 | + | 0.991971i | \(0.540364\pi\) | |||||||
\(468\) | 36105.0 | 3.56614 | ||||||||
\(469\) | 7578.74 | 0.746170 | ||||||||
\(470\) | −3568.79 | −0.350246 | ||||||||
\(471\) | 23817.9 | 2.33009 | ||||||||
\(472\) | −5312.28 | −0.518045 | ||||||||
\(473\) | 3105.36 | 0.301870 | ||||||||
\(474\) | 51355.5 | 4.97645 | ||||||||
\(475\) | −475.000 | −0.0458831 | ||||||||
\(476\) | −44449.7 | −4.28014 | ||||||||
\(477\) | 31367.8 | 3.01097 | ||||||||
\(478\) | 22169.8 | 2.12138 | ||||||||
\(479\) | −4618.53 | −0.440555 | −0.220278 | − | 0.975437i | \(-0.570696\pi\) | ||||
−0.220278 | + | 0.975437i | \(0.570696\pi\) | |||||||
\(480\) | 26690.0 | 2.53798 | ||||||||
\(481\) | −3398.33 | −0.322142 | ||||||||
\(482\) | 23685.6 | 2.23828 | ||||||||
\(483\) | −24608.6 | −2.31828 | ||||||||
\(484\) | 2504.42 | 0.235201 | ||||||||
\(485\) | 2381.01 | 0.222919 | ||||||||
\(486\) | 102920. | 9.60606 | ||||||||
\(487\) | 10808.0 | 1.00567 | 0.502833 | − | 0.864384i | \(-0.332291\pi\) | ||||
0.502833 | + | 0.864384i | \(0.332291\pi\) | |||||||
\(488\) | −45286.9 | −4.20091 | ||||||||
\(489\) | 25092.4 | 2.32048 | ||||||||
\(490\) | 907.484 | 0.0836652 | ||||||||
\(491\) | 382.870 | 0.0351908 | 0.0175954 | − | 0.999845i | \(-0.494399\pi\) | ||||
0.0175954 | + | 0.999845i | \(0.494399\pi\) | |||||||
\(492\) | 48398.8 | 4.43493 | ||||||||
\(493\) | −13130.1 | −1.19949 | ||||||||
\(494\) | 2275.52 | 0.207248 | ||||||||
\(495\) | −4291.45 | −0.389669 | ||||||||
\(496\) | 13281.3 | 1.20232 | ||||||||
\(497\) | 6825.74 | 0.616049 | ||||||||
\(498\) | −26131.8 | −2.35139 | ||||||||
\(499\) | −8075.28 | −0.724447 | −0.362224 | − | 0.932091i | \(-0.617982\pi\) | ||||
−0.362224 | + | 0.932091i | \(0.617982\pi\) | |||||||
\(500\) | 2587.21 | 0.231407 | ||||||||
\(501\) | −4269.19 | −0.380705 | ||||||||
\(502\) | 6198.77 | 0.551125 | ||||||||
\(503\) | 11916.7 | 1.05634 | 0.528171 | − | 0.849138i | \(-0.322878\pi\) | ||||
0.528171 | + | 0.849138i | \(0.322878\pi\) | |||||||
\(504\) | 93315.3 | 8.24721 | ||||||||
\(505\) | −322.564 | −0.0284236 | ||||||||
\(506\) | −8048.04 | −0.707073 | ||||||||
\(507\) | 17393.2 | 1.52358 | ||||||||
\(508\) | 6220.71 | 0.543306 | ||||||||
\(509\) | −16121.3 | −1.40386 | −0.701931 | − | 0.712245i | \(-0.747679\pi\) | ||||
−0.701931 | + | 0.712245i | \(0.747679\pi\) | |||||||
\(510\) | 33529.4 | 2.91119 | ||||||||
\(511\) | −21542.7 | −1.86496 | ||||||||
\(512\) | 4633.05 | 0.399910 | ||||||||
\(513\) | 9935.65 | 0.855107 | ||||||||
\(514\) | −11564.8 | −0.992419 | ||||||||
\(515\) | 9731.50 | 0.832662 | ||||||||
\(516\) | 59881.1 | 5.10876 | ||||||||
\(517\) | −1465.61 | −0.124676 | ||||||||
\(518\) | −14316.9 | −1.21438 | ||||||||
\(519\) | −12724.7 | −1.07621 | ||||||||
\(520\) | −7603.66 | −0.641236 | ||||||||
\(521\) | −4625.91 | −0.388992 | −0.194496 | − | 0.980903i | \(-0.562307\pi\) | ||||
−0.194496 | + | 0.980903i | \(0.562307\pi\) | |||||||
\(522\) | 44931.2 | 3.76740 | ||||||||
\(523\) | −12487.1 | −1.04402 | −0.522010 | − | 0.852940i | \(-0.674817\pi\) | ||||
−0.522010 | + | 0.852940i | \(0.674817\pi\) | |||||||
\(524\) | 48203.3 | 4.01865 | ||||||||
\(525\) | 4504.56 | 0.374467 | ||||||||
\(526\) | −18869.4 | −1.56416 | ||||||||
\(527\) | 8159.80 | 0.674471 | ||||||||
\(528\) | 22412.3 | 1.84729 | ||||||||
\(529\) | 6485.96 | 0.533078 | ||||||||
\(530\) | −10768.0 | −0.882516 | ||||||||
\(531\) | 6093.59 | 0.498002 | ||||||||
\(532\) | 6914.15 | 0.563471 | ||||||||
\(533\) | −5101.14 | −0.414550 | ||||||||
\(534\) | −69575.7 | −5.63827 | ||||||||
\(535\) | 2905.09 | 0.234763 | ||||||||
\(536\) | 29321.2 | 2.36284 | ||||||||
\(537\) | 33593.0 | 2.69953 | ||||||||
\(538\) | 17546.2 | 1.40608 | ||||||||
\(539\) | 372.682 | 0.0297821 | ||||||||
\(540\) | −54117.1 | −4.31265 | ||||||||
\(541\) | −137.057 | −0.0108920 | −0.00544598 | − | 0.999985i | \(-0.501734\pi\) | ||||
−0.00544598 | + | 0.999985i | \(0.501734\pi\) | |||||||
\(542\) | 46437.9 | 3.68022 | ||||||||
\(543\) | 3777.99 | 0.298580 | ||||||||
\(544\) | −63622.9 | −5.01436 | ||||||||
\(545\) | −4874.68 | −0.383135 | ||||||||
\(546\) | −21579.4 | −1.69142 | ||||||||
\(547\) | −10320.1 | −0.806681 | −0.403341 | − | 0.915050i | \(-0.632151\pi\) | ||||
−0.403341 | + | 0.915050i | \(0.632151\pi\) | |||||||
\(548\) | 38828.5 | 3.02677 | ||||||||
\(549\) | 51947.6 | 4.03837 | ||||||||
\(550\) | 1473.18 | 0.114212 | ||||||||
\(551\) | 2042.38 | 0.157910 | ||||||||
\(552\) | −95207.5 | −7.34113 | ||||||||
\(553\) | −16446.7 | −1.26471 | ||||||||
\(554\) | −27762.4 | −2.12908 | ||||||||
\(555\) | 7788.97 | 0.595718 | ||||||||
\(556\) | 63375.5 | 4.83403 | ||||||||
\(557\) | −13798.5 | −1.04966 | −0.524830 | − | 0.851207i | \(-0.675871\pi\) | ||||
−0.524830 | + | 0.851207i | \(0.675871\pi\) | |||||||
\(558\) | −27922.9 | −2.11841 | ||||||||
\(559\) | −6311.36 | −0.477535 | ||||||||
\(560\) | −17477.5 | −1.31885 | ||||||||
\(561\) | 13769.7 | 1.03629 | ||||||||
\(562\) | −1268.42 | −0.0952046 | ||||||||
\(563\) | −8764.57 | −0.656097 | −0.328048 | − | 0.944661i | \(-0.606391\pi\) | ||||
−0.328048 | + | 0.944661i | \(0.606391\pi\) | |||||||
\(564\) | −28261.7 | −2.10998 | ||||||||
\(565\) | −7377.69 | −0.549348 | ||||||||
\(566\) | −17359.9 | −1.28921 | ||||||||
\(567\) | −57182.9 | −4.23537 | ||||||||
\(568\) | 26408.0 | 1.95080 | ||||||||
\(569\) | 22241.5 | 1.63869 | 0.819344 | − | 0.573302i | \(-0.194338\pi\) | ||||
0.819344 | + | 0.573302i | \(0.194338\pi\) | |||||||
\(570\) | −5215.50 | −0.383251 | ||||||||
\(571\) | 1963.65 | 0.143916 | 0.0719581 | − | 0.997408i | \(-0.477075\pi\) | ||||
0.0719581 | + | 0.997408i | \(0.477075\pi\) | |||||||
\(572\) | −5090.01 | −0.372070 | ||||||||
\(573\) | −36552.9 | −2.66495 | ||||||||
\(574\) | −21490.7 | −1.56272 | ||||||||
\(575\) | −3414.40 | −0.247635 | ||||||||
\(576\) | 93617.1 | 6.77207 | ||||||||
\(577\) | −18689.9 | −1.34848 | −0.674238 | − | 0.738514i | \(-0.735528\pi\) | ||||
−0.674238 | + | 0.738514i | \(0.735528\pi\) | |||||||
\(578\) | −53607.3 | −3.85773 | ||||||||
\(579\) | −27005.9 | −1.93839 | ||||||||
\(580\) | −11124.4 | −0.796404 | ||||||||
\(581\) | 8368.74 | 0.597580 | ||||||||
\(582\) | 26143.5 | 1.86200 | ||||||||
\(583\) | −4422.17 | −0.314147 | ||||||||
\(584\) | −83346.1 | −5.90563 | ||||||||
\(585\) | 8721.98 | 0.616426 | ||||||||
\(586\) | −3991.55 | −0.281381 | ||||||||
\(587\) | 12745.7 | 0.896206 | 0.448103 | − | 0.893982i | \(-0.352100\pi\) | ||||
0.448103 | + | 0.893982i | \(0.352100\pi\) | |||||||
\(588\) | 7186.48 | 0.504023 | ||||||||
\(589\) | −1269.26 | −0.0887926 | ||||||||
\(590\) | −2091.83 | −0.145965 | ||||||||
\(591\) | 32675.6 | 2.27427 | ||||||||
\(592\) | −30220.8 | −2.09809 | ||||||||
\(593\) | 8483.09 | 0.587451 | 0.293726 | − | 0.955890i | \(-0.405105\pi\) | ||||
0.293726 | + | 0.955890i | \(0.405105\pi\) | |||||||
\(594\) | −30814.8 | −2.12853 | ||||||||
\(595\) | −10737.8 | −0.739846 | ||||||||
\(596\) | −52257.6 | −3.59154 | ||||||||
\(597\) | −20243.3 | −1.38778 | ||||||||
\(598\) | 16356.9 | 1.11854 | ||||||||
\(599\) | 11916.3 | 0.812831 | 0.406416 | − | 0.913688i | \(-0.366778\pi\) | ||||
0.406416 | + | 0.913688i | \(0.366778\pi\) | |||||||
\(600\) | 17427.6 | 1.18580 | ||||||||
\(601\) | 15408.8 | 1.04582 | 0.522910 | − | 0.852388i | \(-0.324847\pi\) | ||||
0.522910 | + | 0.852388i | \(0.324847\pi\) | |||||||
\(602\) | −26589.2 | −1.80016 | ||||||||
\(603\) | −33633.7 | −2.27143 | ||||||||
\(604\) | 12398.9 | 0.835269 | ||||||||
\(605\) | 605.000 | 0.0406558 | ||||||||
\(606\) | −3541.76 | −0.237416 | ||||||||
\(607\) | 9832.07 | 0.657449 | 0.328724 | − | 0.944426i | \(-0.393381\pi\) | ||||
0.328724 | + | 0.944426i | \(0.393381\pi\) | |||||||
\(608\) | 9896.55 | 0.660129 | ||||||||
\(609\) | −19368.5 | −1.28875 | ||||||||
\(610\) | −17832.7 | −1.18365 | ||||||||
\(611\) | 2978.73 | 0.197228 | ||||||||
\(612\) | 197263. | 13.0292 | ||||||||
\(613\) | −9526.36 | −0.627677 | −0.313838 | − | 0.949476i | \(-0.601615\pi\) | ||||
−0.313838 | + | 0.949476i | \(0.601615\pi\) | |||||||
\(614\) | −35639.5 | −2.34249 | ||||||||
\(615\) | 11691.8 | 0.766601 | ||||||||
\(616\) | −13155.4 | −0.860466 | ||||||||
\(617\) | 16852.9 | 1.09963 | 0.549815 | − | 0.835286i | \(-0.314698\pi\) | ||||
0.549815 | + | 0.835286i | \(0.314698\pi\) | |||||||
\(618\) | 106852. | 6.95504 | ||||||||
\(619\) | 26515.7 | 1.72174 | 0.860869 | − | 0.508827i | \(-0.169921\pi\) | ||||
0.860869 | + | 0.508827i | \(0.169921\pi\) | |||||||
\(620\) | 6913.34 | 0.447817 | ||||||||
\(621\) | 71419.5 | 4.61508 | ||||||||
\(622\) | 50339.7 | 3.24507 | ||||||||
\(623\) | 22281.7 | 1.43290 | ||||||||
\(624\) | −45551.0 | −2.92228 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 17830.4 | 1.13841 | ||||||||
\(627\) | −2141.88 | −0.136425 | ||||||||
\(628\) | −48103.5 | −3.05659 | ||||||||
\(629\) | −18567.1 | −1.17698 | ||||||||
\(630\) | 36745.0 | 2.32374 | ||||||||
\(631\) | 13284.1 | 0.838083 | 0.419041 | − | 0.907967i | \(-0.362366\pi\) | ||||
0.419041 | + | 0.907967i | \(0.362366\pi\) | |||||||
\(632\) | −63630.1 | −4.00486 | ||||||||
\(633\) | −19148.7 | −1.20236 | ||||||||
\(634\) | −9790.45 | −0.613294 | ||||||||
\(635\) | 1502.75 | 0.0939133 | ||||||||
\(636\) | −85273.5 | −5.31653 | ||||||||
\(637\) | −757.442 | −0.0471130 | ||||||||
\(638\) | −6334.32 | −0.393069 | ||||||||
\(639\) | −30292.0 | −1.87532 | ||||||||
\(640\) | −11302.3 | −0.698068 | ||||||||
\(641\) | −2618.02 | −0.161319 | −0.0806595 | − | 0.996742i | \(-0.525703\pi\) | ||||
−0.0806595 | + | 0.996742i | \(0.525703\pi\) | |||||||
\(642\) | 31897.9 | 1.96092 | ||||||||
\(643\) | 18996.3 | 1.16507 | 0.582535 | − | 0.812805i | \(-0.302061\pi\) | ||||
0.582535 | + | 0.812805i | \(0.302061\pi\) | |||||||
\(644\) | 49700.3 | 3.04110 | ||||||||
\(645\) | 14465.6 | 0.883076 | ||||||||
\(646\) | 12432.6 | 0.757202 | ||||||||
\(647\) | −24160.5 | −1.46808 | −0.734039 | − | 0.679108i | \(-0.762367\pi\) | ||||
−0.734039 | + | 0.679108i | \(0.762367\pi\) | |||||||
\(648\) | −221234. | −13.4118 | ||||||||
\(649\) | −859.063 | −0.0519587 | ||||||||
\(650\) | −2994.11 | −0.180675 | ||||||||
\(651\) | 12036.7 | 0.724664 | ||||||||
\(652\) | −50677.4 | −3.04399 | ||||||||
\(653\) | −9656.17 | −0.578675 | −0.289338 | − | 0.957227i | \(-0.593435\pi\) | ||||
−0.289338 | + | 0.957227i | \(0.593435\pi\) | |||||||
\(654\) | −53524.0 | −3.20024 | ||||||||
\(655\) | 11644.6 | 0.694645 | ||||||||
\(656\) | −45363.7 | −2.69993 | ||||||||
\(657\) | 95604.4 | 5.67714 | ||||||||
\(658\) | 12549.1 | 0.743490 | ||||||||
\(659\) | 29035.7 | 1.71634 | 0.858171 | − | 0.513364i | \(-0.171601\pi\) | ||||
0.858171 | + | 0.513364i | \(0.171601\pi\) | |||||||
\(660\) | 11666.3 | 0.688046 | ||||||||
\(661\) | 12259.2 | 0.721375 | 0.360688 | − | 0.932687i | \(-0.382542\pi\) | ||||
0.360688 | + | 0.932687i | \(0.382542\pi\) | |||||||
\(662\) | −22597.6 | −1.32671 | ||||||||
\(663\) | −27985.7 | −1.63933 | ||||||||
\(664\) | 32377.6 | 1.89231 | ||||||||
\(665\) | 1670.27 | 0.0973990 | ||||||||
\(666\) | 63536.8 | 3.69670 | ||||||||
\(667\) | 14681.1 | 0.852253 | ||||||||
\(668\) | 8622.21 | 0.499406 | ||||||||
\(669\) | −7384.92 | −0.426783 | ||||||||
\(670\) | 11545.9 | 0.665756 | ||||||||
\(671\) | −7323.47 | −0.421340 | ||||||||
\(672\) | −93851.8 | −5.38752 | ||||||||
\(673\) | −13899.6 | −0.796123 | −0.398062 | − | 0.917359i | \(-0.630317\pi\) | ||||
−0.398062 | + | 0.917359i | \(0.630317\pi\) | |||||||
\(674\) | −10550.5 | −0.602952 | ||||||||
\(675\) | −13073.2 | −0.745465 | ||||||||
\(676\) | −35127.8 | −1.99863 | ||||||||
\(677\) | 14551.4 | 0.826078 | 0.413039 | − | 0.910713i | \(-0.364467\pi\) | ||||
0.413039 | + | 0.910713i | \(0.364467\pi\) | |||||||
\(678\) | −81007.1 | −4.58858 | ||||||||
\(679\) | −8372.48 | −0.473205 | ||||||||
\(680\) | −41543.4 | −2.34282 | ||||||||
\(681\) | −9568.35 | −0.538414 | ||||||||
\(682\) | 3936.52 | 0.221022 | ||||||||
\(683\) | −18376.3 | −1.02950 | −0.514750 | − | 0.857341i | \(-0.672115\pi\) | ||||
−0.514750 | + | 0.857341i | \(0.672115\pi\) | |||||||
\(684\) | −30684.3 | −1.71527 | ||||||||
\(685\) | 9379.90 | 0.523194 | ||||||||
\(686\) | −35496.9 | −1.97562 | ||||||||
\(687\) | −39570.0 | −2.19751 | ||||||||
\(688\) | −56126.0 | −3.11015 | ||||||||
\(689\) | 8987.67 | 0.496956 | ||||||||
\(690\) | −37490.1 | −2.06844 | ||||||||
\(691\) | 3707.73 | 0.204123 | 0.102061 | − | 0.994778i | \(-0.467456\pi\) | ||||
0.102061 | + | 0.994778i | \(0.467456\pi\) | |||||||
\(692\) | 25699.2 | 1.41176 | ||||||||
\(693\) | 15090.3 | 0.827175 | ||||||||
\(694\) | −17817.8 | −0.974575 | ||||||||
\(695\) | 15309.8 | 0.835588 | ||||||||
\(696\) | −74934.3 | −4.08100 | ||||||||
\(697\) | −27870.6 | −1.51460 | ||||||||
\(698\) | 29467.7 | 1.59795 | ||||||||
\(699\) | 26621.7 | 1.44052 | ||||||||
\(700\) | −9097.57 | −0.491223 | ||||||||
\(701\) | −11773.4 | −0.634342 | −0.317171 | − | 0.948368i | \(-0.602733\pi\) | ||||
−0.317171 | + | 0.948368i | \(0.602733\pi\) | |||||||
\(702\) | 62628.3 | 3.36717 | ||||||||
\(703\) | 2888.12 | 0.154946 | ||||||||
\(704\) | −13198.0 | −0.706558 | ||||||||
\(705\) | −6827.25 | −0.364722 | ||||||||
\(706\) | 26706.3 | 1.42366 | ||||||||
\(707\) | 1134.25 | 0.0603366 | ||||||||
\(708\) | −16565.5 | −0.879333 | ||||||||
\(709\) | −8345.33 | −0.442053 | −0.221026 | − | 0.975268i | \(-0.570941\pi\) | ||||
−0.221026 | + | 0.975268i | \(0.570941\pi\) | |||||||
\(710\) | 10398.7 | 0.549658 | ||||||||
\(711\) | 72988.7 | 3.84991 | ||||||||
\(712\) | 86205.3 | 4.53747 | ||||||||
\(713\) | −9123.68 | −0.479221 | ||||||||
\(714\) | −117901. | −6.17976 | ||||||||
\(715\) | −1229.61 | −0.0643143 | ||||||||
\(716\) | −67845.7 | −3.54122 | ||||||||
\(717\) | 42411.8 | 2.20906 | ||||||||
\(718\) | 26467.2 | 1.37569 | ||||||||
\(719\) | 15608.5 | 0.809595 | 0.404798 | − | 0.914406i | \(-0.367342\pi\) | ||||
0.404798 | + | 0.914406i | \(0.367342\pi\) | |||||||
\(720\) | 77563.2 | 4.01474 | ||||||||
\(721\) | −34219.5 | −1.76754 | ||||||||
\(722\) | −1933.89 | −0.0996839 | ||||||||
\(723\) | 45311.7 | 2.33079 | ||||||||
\(724\) | −7630.16 | −0.391675 | ||||||||
\(725\) | −2687.35 | −0.137663 | ||||||||
\(726\) | 6642.90 | 0.339588 | ||||||||
\(727\) | −32543.1 | −1.66019 | −0.830094 | − | 0.557624i | \(-0.811713\pi\) | ||||
−0.830094 | + | 0.557624i | \(0.811713\pi\) | |||||||
\(728\) | 26737.2 | 1.36119 | ||||||||
\(729\) | 109076. | 5.54165 | ||||||||
\(730\) | −32819.4 | −1.66397 | ||||||||
\(731\) | −34482.8 | −1.74472 | ||||||||
\(732\) | −141220. | −7.13064 | ||||||||
\(733\) | −15281.4 | −0.770027 | −0.385014 | − | 0.922911i | \(-0.625803\pi\) | ||||
−0.385014 | + | 0.922911i | \(0.625803\pi\) | |||||||
\(734\) | −9981.81 | −0.501955 | ||||||||
\(735\) | 1736.06 | 0.0871231 | ||||||||
\(736\) | 71138.4 | 3.56277 | ||||||||
\(737\) | 4741.62 | 0.236987 | ||||||||
\(738\) | 95373.5 | 4.75711 | ||||||||
\(739\) | −33491.3 | −1.66711 | −0.833556 | − | 0.552435i | \(-0.813699\pi\) | ||||
−0.833556 | + | 0.552435i | \(0.813699\pi\) | |||||||
\(740\) | −15730.9 | −0.781457 | ||||||||
\(741\) | 4353.18 | 0.215814 | ||||||||
\(742\) | 37864.3 | 1.87337 | ||||||||
\(743\) | −11232.3 | −0.554608 | −0.277304 | − | 0.960782i | \(-0.589441\pi\) | ||||
−0.277304 | + | 0.960782i | \(0.589441\pi\) | |||||||
\(744\) | 46568.6 | 2.29474 | ||||||||
\(745\) | −12624.0 | −0.620817 | ||||||||
\(746\) | 62201.1 | 3.05274 | ||||||||
\(747\) | −37139.6 | −1.81910 | ||||||||
\(748\) | −27809.8 | −1.35939 | ||||||||
\(749\) | −10215.4 | −0.498346 | ||||||||
\(750\) | 6862.50 | 0.334111 | ||||||||
\(751\) | −12976.0 | −0.630493 | −0.315246 | − | 0.949010i | \(-0.602087\pi\) | ||||
−0.315246 | + | 0.949010i | \(0.602087\pi\) | |||||||
\(752\) | 26489.4 | 1.28453 | ||||||||
\(753\) | 11858.5 | 0.573903 | ||||||||
\(754\) | 12873.9 | 0.621805 | ||||||||
\(755\) | 2995.23 | 0.144381 | ||||||||
\(756\) | 190295. | 9.15473 | ||||||||
\(757\) | −8251.46 | −0.396175 | −0.198087 | − | 0.980184i | \(-0.563473\pi\) | ||||
−0.198087 | + | 0.980184i | \(0.563473\pi\) | |||||||
\(758\) | −55390.5 | −2.65419 | ||||||||
\(759\) | −15396.3 | −0.736297 | ||||||||
\(760\) | 6462.08 | 0.308426 | ||||||||
\(761\) | −20356.7 | −0.969684 | −0.484842 | − | 0.874602i | \(-0.661123\pi\) | ||||
−0.484842 | + | 0.874602i | \(0.661123\pi\) | |||||||
\(762\) | 16500.2 | 0.784437 | ||||||||
\(763\) | 17141.1 | 0.813304 | ||||||||
\(764\) | 73823.5 | 3.49587 | ||||||||
\(765\) | 47653.4 | 2.25217 | ||||||||
\(766\) | 26973.6 | 1.27232 | ||||||||
\(767\) | 1745.97 | 0.0821946 | ||||||||
\(768\) | −25731.8 | −1.20900 | ||||||||
\(769\) | −11065.1 | −0.518878 | −0.259439 | − | 0.965760i | \(-0.583538\pi\) | ||||
−0.259439 | + | 0.965760i | \(0.583538\pi\) | |||||||
\(770\) | −5180.24 | −0.242445 | ||||||||
\(771\) | −22124.1 | −1.03344 | ||||||||
\(772\) | 54542.0 | 2.54276 | ||||||||
\(773\) | −36895.8 | −1.71675 | −0.858376 | − | 0.513021i | \(-0.828526\pi\) | ||||
−0.858376 | + | 0.513021i | \(0.828526\pi\) | |||||||
\(774\) | 118000. | 5.47989 | ||||||||
\(775\) | 1670.08 | 0.0774076 | ||||||||
\(776\) | −32392.1 | −1.49846 | ||||||||
\(777\) | −27388.8 | −1.26457 | ||||||||
\(778\) | 58105.5 | 2.67761 | ||||||||
\(779\) | 4335.28 | 0.199393 | ||||||||
\(780\) | −23710.7 | −1.08844 | ||||||||
\(781\) | 4270.51 | 0.195660 | ||||||||
\(782\) | 89367.7 | 4.08668 | ||||||||
\(783\) | 56211.7 | 2.56557 | ||||||||
\(784\) | −6735.82 | −0.306843 | ||||||||
\(785\) | −11620.5 | −0.528348 | ||||||||
\(786\) | 127858. | 5.80221 | ||||||||
\(787\) | −36859.2 | −1.66949 | −0.834745 | − | 0.550637i | \(-0.814385\pi\) | ||||
−0.834745 | + | 0.550637i | \(0.814385\pi\) | |||||||
\(788\) | −65992.8 | −2.98337 | ||||||||
\(789\) | −36098.1 | −1.62880 | ||||||||
\(790\) | −25055.8 | −1.12841 | ||||||||
\(791\) | 25942.6 | 1.16614 | ||||||||
\(792\) | 58382.4 | 2.61935 | ||||||||
\(793\) | 14884.3 | 0.666528 | ||||||||
\(794\) | −20597.3 | −0.920617 | ||||||||
\(795\) | −20599.8 | −0.918991 | ||||||||
\(796\) | 40884.1 | 1.82048 | ||||||||
\(797\) | −35271.7 | −1.56761 | −0.783807 | − | 0.621005i | \(-0.786725\pi\) | ||||
−0.783807 | + | 0.621005i | \(0.786725\pi\) | |||||||
\(798\) | 18339.6 | 0.813552 | ||||||||
\(799\) | 16274.6 | 0.720593 | ||||||||
\(800\) | −13021.8 | −0.575487 | ||||||||
\(801\) | −98884.0 | −4.36192 | ||||||||
\(802\) | 54032.7 | 2.37900 | ||||||||
\(803\) | −13478.1 | −0.592320 | ||||||||
\(804\) | 91433.4 | 4.01071 | ||||||||
\(805\) | 12006.2 | 0.525670 | ||||||||
\(806\) | −8000.62 | −0.349640 | ||||||||
\(807\) | 33566.7 | 1.46419 | ||||||||
\(808\) | 4388.28 | 0.191063 | ||||||||
\(809\) | 24015.7 | 1.04369 | 0.521846 | − | 0.853040i | \(-0.325244\pi\) | ||||
0.521846 | + | 0.853040i | \(0.325244\pi\) | |||||||
\(810\) | −87115.7 | −3.77893 | ||||||||
\(811\) | −16204.2 | −0.701611 | −0.350806 | − | 0.936448i | \(-0.614092\pi\) | ||||
−0.350806 | + | 0.936448i | \(0.614092\pi\) | |||||||
\(812\) | 39117.3 | 1.69058 | ||||||||
\(813\) | 88837.8 | 3.83232 | ||||||||
\(814\) | −8957.30 | −0.385692 | ||||||||
\(815\) | −12242.3 | −0.526170 | ||||||||
\(816\) | −248873. | −10.6768 | ||||||||
\(817\) | 5363.80 | 0.229689 | ||||||||
\(818\) | −48642.3 | −2.07914 | ||||||||
\(819\) | −30669.6 | −1.30853 | ||||||||
\(820\) | −23613.2 | −1.00562 | ||||||||
\(821\) | 13747.4 | 0.584395 | 0.292197 | − | 0.956358i | \(-0.405614\pi\) | ||||
0.292197 | + | 0.956358i | \(0.405614\pi\) | |||||||
\(822\) | 102991. | 4.37012 | ||||||||
\(823\) | −23783.7 | −1.00735 | −0.503674 | − | 0.863894i | \(-0.668019\pi\) | ||||
−0.503674 | + | 0.863894i | \(0.668019\pi\) | |||||||
\(824\) | −132391. | −5.59716 | ||||||||
\(825\) | 2818.26 | 0.118933 | ||||||||
\(826\) | 7355.62 | 0.309848 | ||||||||
\(827\) | 33359.2 | 1.40268 | 0.701339 | − | 0.712828i | \(-0.252586\pi\) | ||||
0.701339 | + | 0.712828i | \(0.252586\pi\) | |||||||
\(828\) | −220565. | −9.25745 | ||||||||
\(829\) | 30807.7 | 1.29071 | 0.645353 | − | 0.763884i | \(-0.276710\pi\) | ||||
0.645353 | + | 0.763884i | \(0.276710\pi\) | |||||||
\(830\) | 12749.4 | 0.533179 | ||||||||
\(831\) | −53110.7 | −2.21708 | ||||||||
\(832\) | 26823.7 | 1.11772 | ||||||||
\(833\) | −4138.36 | −0.172132 | ||||||||
\(834\) | 168102. | 6.97948 | ||||||||
\(835\) | 2082.89 | 0.0863251 | ||||||||
\(836\) | 4325.82 | 0.178961 | ||||||||
\(837\) | −34933.2 | −1.44262 | ||||||||
\(838\) | 3694.31 | 0.152288 | ||||||||
\(839\) | 40537.6 | 1.66807 | 0.834036 | − | 0.551711i | \(-0.186025\pi\) | ||||
0.834036 | + | 0.551711i | \(0.186025\pi\) | |||||||
\(840\) | −61281.7 | −2.51717 | ||||||||
\(841\) | −12834.1 | −0.526224 | ||||||||
\(842\) | −24951.6 | −1.02124 | ||||||||
\(843\) | −2426.54 | −0.0991395 | ||||||||
\(844\) | 38673.5 | 1.57725 | ||||||||
\(845\) | −8485.93 | −0.345473 | ||||||||
\(846\) | −55691.8 | −2.26327 | ||||||||
\(847\) | −2127.40 | −0.0863026 | ||||||||
\(848\) | 79926.0 | 3.23664 | ||||||||
\(849\) | −33210.3 | −1.34249 | ||||||||
\(850\) | −16358.6 | −0.660113 | ||||||||
\(851\) | 20760.4 | 0.836258 | ||||||||
\(852\) | 82348.9 | 3.31130 | ||||||||
\(853\) | −10993.1 | −0.441262 | −0.220631 | − | 0.975357i | \(-0.570812\pi\) | ||||
−0.220631 | + | 0.975357i | \(0.570812\pi\) | |||||||
\(854\) | 62706.3 | 2.51261 | ||||||||
\(855\) | −7412.50 | −0.296494 | ||||||||
\(856\) | −39522.0 | −1.57808 | ||||||||
\(857\) | −5644.19 | −0.224973 | −0.112486 | − | 0.993653i | \(-0.535881\pi\) | ||||
−0.112486 | + | 0.993653i | \(0.535881\pi\) | |||||||
\(858\) | −13501.1 | −0.537203 | ||||||||
\(859\) | −46178.8 | −1.83422 | −0.917112 | − | 0.398629i | \(-0.869486\pi\) | ||||
−0.917112 | + | 0.398629i | \(0.869486\pi\) | |||||||
\(860\) | −29215.3 | −1.15841 | ||||||||
\(861\) | −41112.7 | −1.62731 | ||||||||
\(862\) | 26479.1 | 1.04627 | ||||||||
\(863\) | −15945.7 | −0.628966 | −0.314483 | − | 0.949263i | \(-0.601831\pi\) | ||||
−0.314483 | + | 0.949263i | \(0.601831\pi\) | |||||||
\(864\) | 272379. | 10.7251 | ||||||||
\(865\) | 6208.23 | 0.244030 | ||||||||
\(866\) | 74205.7 | 2.91179 | ||||||||
\(867\) | −102553. | −4.01718 | ||||||||
\(868\) | −24309.8 | −0.950609 | ||||||||
\(869\) | −10289.8 | −0.401677 | ||||||||
\(870\) | −29507.1 | −1.14987 | ||||||||
\(871\) | −9636.91 | −0.374896 | ||||||||
\(872\) | 66317.0 | 2.57543 | ||||||||
\(873\) | 37156.2 | 1.44049 | ||||||||
\(874\) | −13901.2 | −0.538002 | ||||||||
\(875\) | −2197.73 | −0.0849105 | ||||||||
\(876\) | −259901. | −10.0242 | ||||||||
\(877\) | −3561.97 | −0.137149 | −0.0685743 | − | 0.997646i | \(-0.521845\pi\) | ||||
−0.0685743 | + | 0.997646i | \(0.521845\pi\) | |||||||
\(878\) | −33829.8 | −1.30034 | ||||||||
\(879\) | −7636.03 | −0.293011 | ||||||||
\(880\) | −10934.7 | −0.418874 | ||||||||
\(881\) | −14389.6 | −0.550282 | −0.275141 | − | 0.961404i | \(-0.588725\pi\) | ||||
−0.275141 | + | 0.961404i | \(0.588725\pi\) | |||||||
\(882\) | 14161.5 | 0.540639 | ||||||||
\(883\) | 8926.08 | 0.340189 | 0.170094 | − | 0.985428i | \(-0.445593\pi\) | ||||
0.170094 | + | 0.985428i | \(0.445593\pi\) | |||||||
\(884\) | 56520.9 | 2.15046 | ||||||||
\(885\) | −4001.76 | −0.151997 | ||||||||
\(886\) | 83532.1 | 3.16740 | ||||||||
\(887\) | 16462.1 | 0.623160 | 0.311580 | − | 0.950220i | \(-0.399142\pi\) | ||||
0.311580 | + | 0.950220i | \(0.399142\pi\) | |||||||
\(888\) | −105964. | −4.00441 | ||||||||
\(889\) | −5284.23 | −0.199356 | ||||||||
\(890\) | 33945.2 | 1.27848 | ||||||||
\(891\) | −35776.3 | −1.34518 | ||||||||
\(892\) | 14914.9 | 0.559850 | ||||||||
\(893\) | −2531.51 | −0.0948644 | ||||||||
\(894\) | −138612. | −5.18554 | ||||||||
\(895\) | −16389.7 | −0.612119 | ||||||||
\(896\) | 39743.1 | 1.48183 | ||||||||
\(897\) | 31291.5 | 1.16477 | ||||||||
\(898\) | −76288.0 | −2.83493 | ||||||||
\(899\) | −7180.91 | −0.266404 | ||||||||
\(900\) | 40374.1 | 1.49534 | ||||||||
\(901\) | 49105.1 | 1.81568 | ||||||||
\(902\) | −13445.6 | −0.496329 | ||||||||
\(903\) | −50866.4 | −1.87456 | ||||||||
\(904\) | 100369. | 3.69272 | ||||||||
\(905\) | −1843.24 | −0.0677032 | ||||||||
\(906\) | 32887.6 | 1.20598 | ||||||||
\(907\) | −41412.3 | −1.51607 | −0.758033 | − | 0.652216i | \(-0.773840\pi\) | ||||
−0.758033 | + | 0.652216i | \(0.773840\pi\) | |||||||
\(908\) | 19324.6 | 0.706287 | ||||||||
\(909\) | −5033.70 | −0.183671 | ||||||||
\(910\) | 10528.4 | 0.383530 | ||||||||
\(911\) | 6059.30 | 0.220366 | 0.110183 | − | 0.993911i | \(-0.464856\pi\) | ||||
0.110183 | + | 0.993911i | \(0.464856\pi\) | |||||||
\(912\) | 38712.2 | 1.40558 | ||||||||
\(913\) | 5235.88 | 0.189794 | ||||||||
\(914\) | 18392.0 | 0.665594 | ||||||||
\(915\) | −34114.8 | −1.23257 | ||||||||
\(916\) | 79916.9 | 2.88267 | ||||||||
\(917\) | −40946.6 | −1.47457 | ||||||||
\(918\) | 342176. | 12.3023 | ||||||||
\(919\) | −14328.2 | −0.514301 | −0.257151 | − | 0.966371i | \(-0.582784\pi\) | ||||
−0.257151 | + | 0.966371i | \(0.582784\pi\) | |||||||
\(920\) | 46450.7 | 1.66460 | ||||||||
\(921\) | −68179.9 | −2.43931 | ||||||||
\(922\) | 11074.7 | 0.395580 | ||||||||
\(923\) | −8679.42 | −0.309520 | ||||||||
\(924\) | −41023.0 | −1.46056 | ||||||||
\(925\) | −3800.15 | −0.135079 | ||||||||
\(926\) | −4043.53 | −0.143497 | ||||||||
\(927\) | 151863. | 5.38060 | ||||||||
\(928\) | 55990.4 | 1.98058 | ||||||||
\(929\) | −26144.7 | −0.923336 | −0.461668 | − | 0.887053i | \(-0.652749\pi\) | ||||
−0.461668 | + | 0.887053i | \(0.652749\pi\) | |||||||
\(930\) | 18337.4 | 0.646568 | ||||||||
\(931\) | 643.723 | 0.0226608 | ||||||||
\(932\) | −53766.1 | −1.88966 | ||||||||
\(933\) | 96302.1 | 3.37919 | ||||||||
\(934\) | 13674.4 | 0.479057 | ||||||||
\(935\) | −6718.09 | −0.234979 | ||||||||
\(936\) | −118657. | −4.14362 | ||||||||
\(937\) | 25227.3 | 0.879551 | 0.439776 | − | 0.898108i | \(-0.355058\pi\) | ||||
0.439776 | + | 0.898108i | \(0.355058\pi\) | |||||||
\(938\) | −40599.5 | −1.41324 | ||||||||
\(939\) | 34110.3 | 1.18546 | ||||||||
\(940\) | 13788.6 | 0.478440 | ||||||||
\(941\) | −12630.8 | −0.437570 | −0.218785 | − | 0.975773i | \(-0.570209\pi\) | ||||
−0.218785 | + | 0.975773i | \(0.570209\pi\) | |||||||
\(942\) | −127593. | −4.41317 | ||||||||
\(943\) | 31162.8 | 1.07614 | ||||||||
\(944\) | 15526.6 | 0.535327 | ||||||||
\(945\) | 45970.2 | 1.58244 | ||||||||
\(946\) | −16635.5 | −0.571740 | ||||||||
\(947\) | 4795.83 | 0.164565 | 0.0822827 | − | 0.996609i | \(-0.473779\pi\) | ||||
0.0822827 | + | 0.996609i | \(0.473779\pi\) | |||||||
\(948\) | −198420. | −6.79787 | ||||||||
\(949\) | 27393.1 | 0.937005 | ||||||||
\(950\) | 2544.59 | 0.0869024 | ||||||||
\(951\) | −18729.6 | −0.638642 | ||||||||
\(952\) | 146081. | 4.97324 | ||||||||
\(953\) | −23179.9 | −0.787903 | −0.393951 | − | 0.919131i | \(-0.628892\pi\) | ||||
−0.393951 | + | 0.919131i | \(0.628892\pi\) | |||||||
\(954\) | −168038. | −5.70276 | ||||||||
\(955\) | 17833.8 | 0.604279 | ||||||||
\(956\) | −85656.4 | −2.89783 | ||||||||
\(957\) | −12117.8 | −0.409315 | ||||||||
\(958\) | 24741.6 | 0.834409 | ||||||||
\(959\) | −32983.1 | −1.11062 | ||||||||
\(960\) | −61479.9 | −2.06693 | ||||||||
\(961\) | −25328.4 | −0.850202 | ||||||||
\(962\) | 18204.9 | 0.610135 | ||||||||
\(963\) | 45334.7 | 1.51702 | ||||||||
\(964\) | −91513.0 | −3.05751 | ||||||||
\(965\) | 13175.9 | 0.439530 | ||||||||
\(966\) | 131829. | 4.39080 | ||||||||
\(967\) | −3000.93 | −0.0997967 | −0.0498983 | − | 0.998754i | \(-0.515890\pi\) | ||||
−0.0498983 | + | 0.998754i | \(0.515890\pi\) | |||||||
\(968\) | −8230.64 | −0.273288 | ||||||||
\(969\) | 23784.1 | 0.788497 | ||||||||
\(970\) | −12755.1 | −0.422208 | ||||||||
\(971\) | 75.1115 | 0.00248243 | 0.00124122 | − | 0.999999i | \(-0.499605\pi\) | ||||
0.00124122 | + | 0.999999i | \(0.499605\pi\) | |||||||
\(972\) | −397648. | −13.1220 | ||||||||
\(973\) | −53834.8 | −1.77375 | ||||||||
\(974\) | −57898.9 | −1.90472 | ||||||||
\(975\) | −5727.87 | −0.188142 | ||||||||
\(976\) | 132364. | 4.34105 | ||||||||
\(977\) | 21697.9 | 0.710520 | 0.355260 | − | 0.934767i | \(-0.384392\pi\) | ||||
0.355260 | + | 0.934767i | \(0.384392\pi\) | |||||||
\(978\) | −134420. | −4.39498 | ||||||||
\(979\) | 13940.5 | 0.455097 | ||||||||
\(980\) | −3506.21 | −0.114287 | ||||||||
\(981\) | −76070.7 | −2.47579 | ||||||||
\(982\) | −2051.04 | −0.0666511 | ||||||||
\(983\) | −16460.1 | −0.534075 | −0.267037 | − | 0.963686i | \(-0.586045\pi\) | ||||
−0.267037 | + | 0.963686i | \(0.586045\pi\) | |||||||
\(984\) | −159060. | −5.15309 | ||||||||
\(985\) | −15942.1 | −0.515692 | ||||||||
\(986\) | 70338.0 | 2.27183 | ||||||||
\(987\) | 24007.1 | 0.774219 | ||||||||
\(988\) | −8791.84 | −0.283103 | ||||||||
\(989\) | 38556.1 | 1.23965 | ||||||||
\(990\) | 22989.4 | 0.738030 | ||||||||
\(991\) | 1402.86 | 0.0449681 | 0.0224840 | − | 0.999747i | \(-0.492843\pi\) | ||||
0.0224840 | + | 0.999747i | \(0.492843\pi\) | |||||||
\(992\) | −34795.8 | −1.11368 | ||||||||
\(993\) | −43230.2 | −1.38154 | ||||||||
\(994\) | −36565.7 | −1.16679 | ||||||||
\(995\) | 9876.49 | 0.314679 | ||||||||
\(996\) | 100964. | 3.21202 | ||||||||
\(997\) | 58337.2 | 1.85312 | 0.926559 | − | 0.376149i | \(-0.122752\pi\) | ||||
0.926559 | + | 0.376149i | \(0.122752\pi\) | |||||||
\(998\) | 43259.5 | 1.37210 | ||||||||
\(999\) | 79488.4 | 2.51742 |
(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 | 1045.4.a.d.1.1 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.4.a.d.1.1 | ✓ | 22 | 1.1 | even | 1 | trivial |