Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.40131 | −0.495437 | −0.247719 | − | 0.968832i | \(-0.579681\pi\) | ||||
−0.247719 | + | 0.968832i | \(0.579681\pi\) | |||||||
\(3\) | 7.71122 | 1.48403 | 0.742013 | − | 0.670386i | \(-0.233871\pi\) | ||||
0.742013 | + | 0.670386i | \(0.233871\pi\) | |||||||
\(4\) | −6.03633 | −0.754542 | ||||||||
\(5\) | 16.2919 | 1.45720 | 0.728598 | − | 0.684942i | \(-0.240172\pi\) | ||||
0.728598 | + | 0.684942i | \(0.240172\pi\) | |||||||
\(6\) | −10.8058 | −0.735242 | ||||||||
\(7\) | 16.8292 | 0.908691 | 0.454346 | − | 0.890825i | \(-0.349873\pi\) | ||||
0.454346 | + | 0.890825i | \(0.349873\pi\) | |||||||
\(8\) | 19.6692 | 0.869266 | ||||||||
\(9\) | 32.4629 | 1.20233 | ||||||||
\(10\) | −22.8300 | −0.721949 | ||||||||
\(11\) | 16.6284 | 0.455787 | 0.227894 | − | 0.973686i | \(-0.426816\pi\) | ||||
0.227894 | + | 0.973686i | \(0.426816\pi\) | |||||||
\(12\) | −46.5475 | −1.11976 | ||||||||
\(13\) | −80.3768 | −1.71481 | −0.857404 | − | 0.514643i | \(-0.827924\pi\) | ||||
−0.857404 | + | 0.514643i | \(0.827924\pi\) | |||||||
\(14\) | −23.5829 | −0.450200 | ||||||||
\(15\) | 125.631 | 2.16252 | ||||||||
\(16\) | 20.7280 | 0.323875 | ||||||||
\(17\) | −86.4572 | −1.23347 | −0.616734 | − | 0.787171i | \(-0.711545\pi\) | ||||
−0.616734 | + | 0.787171i | \(0.711545\pi\) | |||||||
\(18\) | −45.4906 | −0.595680 | ||||||||
\(19\) | 134.427 | 1.62314 | 0.811568 | − | 0.584258i | \(-0.198614\pi\) | ||||
0.811568 | + | 0.584258i | \(0.198614\pi\) | |||||||
\(20\) | −98.3436 | −1.09952 | ||||||||
\(21\) | 129.774 | 1.34852 | ||||||||
\(22\) | −23.3016 | −0.225814 | ||||||||
\(23\) | 92.8088 | 0.841391 | 0.420695 | − | 0.907202i | \(-0.361786\pi\) | ||||
0.420695 | + | 0.907202i | \(0.361786\pi\) | |||||||
\(24\) | 151.674 | 1.29001 | ||||||||
\(25\) | 140.427 | 1.12342 | ||||||||
\(26\) | 112.633 | 0.849580 | ||||||||
\(27\) | 42.1260 | 0.300265 | ||||||||
\(28\) | −101.587 | −0.685646 | ||||||||
\(29\) | 49.5793 | 0.317471 | 0.158735 | − | 0.987321i | \(-0.449258\pi\) | ||||
0.158735 | + | 0.987321i | \(0.449258\pi\) | |||||||
\(30\) | −176.048 | −1.07139 | ||||||||
\(31\) | −59.7856 | −0.346381 | −0.173191 | − | 0.984888i | \(-0.555408\pi\) | ||||
−0.173191 | + | 0.984888i | \(0.555408\pi\) | |||||||
\(32\) | −186.400 | −1.02973 | ||||||||
\(33\) | 128.226 | 0.676400 | ||||||||
\(34\) | 121.153 | 0.611106 | ||||||||
\(35\) | 274.180 | 1.32414 | ||||||||
\(36\) | −195.957 | −0.907209 | ||||||||
\(37\) | −128.973 | −0.573053 | −0.286526 | − | 0.958072i | \(-0.592501\pi\) | ||||
−0.286526 | + | 0.958072i | \(0.592501\pi\) | |||||||
\(38\) | −188.373 | −0.804162 | ||||||||
\(39\) | −619.803 | −2.54482 | ||||||||
\(40\) | 320.450 | 1.26669 | ||||||||
\(41\) | 244.655 | 0.931920 | 0.465960 | − | 0.884806i | \(-0.345709\pi\) | ||||
0.465960 | + | 0.884806i | \(0.345709\pi\) | |||||||
\(42\) | −181.853 | −0.668108 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −100.375 | −0.343911 | ||||||||
\(45\) | 528.885 | 1.75203 | ||||||||
\(46\) | −130.054 | −0.416856 | ||||||||
\(47\) | 77.7808 | 0.241394 | 0.120697 | − | 0.992689i | \(-0.461487\pi\) | ||||
0.120697 | + | 0.992689i | \(0.461487\pi\) | |||||||
\(48\) | 159.838 | 0.480639 | ||||||||
\(49\) | −59.7780 | −0.174280 | ||||||||
\(50\) | −196.782 | −0.556584 | ||||||||
\(51\) | −666.691 | −1.83050 | ||||||||
\(52\) | 485.181 | 1.29390 | ||||||||
\(53\) | 444.048 | 1.15084 | 0.575422 | − | 0.817857i | \(-0.304838\pi\) | ||||
0.575422 | + | 0.817857i | \(0.304838\pi\) | |||||||
\(54\) | −59.0315 | −0.148762 | ||||||||
\(55\) | 270.910 | 0.664172 | ||||||||
\(56\) | 331.017 | 0.789894 | ||||||||
\(57\) | 1036.59 | 2.40878 | ||||||||
\(58\) | −69.4759 | −0.157287 | ||||||||
\(59\) | 539.288 | 1.18999 | 0.594995 | − | 0.803730i | \(-0.297154\pi\) | ||||
0.594995 | + | 0.803730i | \(0.297154\pi\) | |||||||
\(60\) | −758.350 | −1.63171 | ||||||||
\(61\) | 627.205 | 1.31648 | 0.658241 | − | 0.752807i | \(-0.271301\pi\) | ||||
0.658241 | + | 0.752807i | \(0.271301\pi\) | |||||||
\(62\) | 83.7781 | 0.171610 | ||||||||
\(63\) | 546.325 | 1.09255 | ||||||||
\(64\) | 95.3801 | 0.186289 | ||||||||
\(65\) | −1309.49 | −2.49881 | ||||||||
\(66\) | −179.684 | −0.335114 | ||||||||
\(67\) | 546.765 | 0.996985 | 0.498493 | − | 0.866894i | \(-0.333887\pi\) | ||||
0.498493 | + | 0.866894i | \(0.333887\pi\) | |||||||
\(68\) | 521.885 | 0.930703 | ||||||||
\(69\) | 715.670 | 1.24864 | ||||||||
\(70\) | −384.211 | −0.656029 | ||||||||
\(71\) | 226.963 | 0.379374 | 0.189687 | − | 0.981845i | \(-0.439253\pi\) | ||||
0.189687 | + | 0.981845i | \(0.439253\pi\) | |||||||
\(72\) | 638.521 | 1.04515 | ||||||||
\(73\) | 736.342 | 1.18058 | 0.590290 | − | 0.807191i | \(-0.299013\pi\) | ||||
0.590290 | + | 0.807191i | \(0.299013\pi\) | |||||||
\(74\) | 180.730 | 0.283912 | ||||||||
\(75\) | 1082.87 | 1.66718 | ||||||||
\(76\) | −811.444 | −1.22472 | ||||||||
\(77\) | 279.843 | 0.414170 | ||||||||
\(78\) | 868.536 | 1.26080 | ||||||||
\(79\) | 440.716 | 0.627651 | 0.313826 | − | 0.949481i | \(-0.398389\pi\) | ||||
0.313826 | + | 0.949481i | \(0.398389\pi\) | |||||||
\(80\) | 337.700 | 0.471950 | ||||||||
\(81\) | −551.657 | −0.756731 | ||||||||
\(82\) | −342.838 | −0.461708 | ||||||||
\(83\) | −85.4566 | −0.113013 | −0.0565065 | − | 0.998402i | \(-0.517996\pi\) | ||||
−0.0565065 | + | 0.998402i | \(0.517996\pi\) | |||||||
\(84\) | −783.357 | −1.01752 | ||||||||
\(85\) | −1408.56 | −1.79740 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 382.317 | 0.471134 | ||||||||
\(88\) | 327.069 | 0.396200 | ||||||||
\(89\) | 882.327 | 1.05086 | 0.525429 | − | 0.850837i | \(-0.323905\pi\) | ||||
0.525429 | + | 0.850837i | \(0.323905\pi\) | |||||||
\(90\) | −741.130 | −0.868022 | ||||||||
\(91\) | −1352.68 | −1.55823 | ||||||||
\(92\) | −560.225 | −0.634864 | ||||||||
\(93\) | −461.020 | −0.514038 | ||||||||
\(94\) | −108.995 | −0.119595 | ||||||||
\(95\) | 2190.07 | 2.36523 | ||||||||
\(96\) | −1437.37 | −1.52814 | ||||||||
\(97\) | −6.99165 | −0.00731850 | −0.00365925 | − | 0.999993i | \(-0.501165\pi\) | ||||
−0.00365925 | + | 0.999993i | \(0.501165\pi\) | |||||||
\(98\) | 83.7674 | 0.0863448 | ||||||||
\(99\) | 539.808 | 0.548008 | ||||||||
\(100\) | −847.667 | −0.847667 | ||||||||
\(101\) | 757.748 | 0.746522 | 0.373261 | − | 0.927726i | \(-0.378240\pi\) | ||||
0.373261 | + | 0.927726i | \(0.378240\pi\) | |||||||
\(102\) | 934.240 | 0.906897 | ||||||||
\(103\) | 717.838 | 0.686705 | 0.343353 | − | 0.939207i | \(-0.388437\pi\) | ||||
0.343353 | + | 0.939207i | \(0.388437\pi\) | |||||||
\(104\) | −1580.95 | −1.49062 | ||||||||
\(105\) | 2114.27 | 1.96506 | ||||||||
\(106\) | −622.248 | −0.570171 | ||||||||
\(107\) | 0.557731 | 0.000503905 0 | 0.000251953 | − | 1.00000i | \(-0.499920\pi\) | ||||
0.000251953 | 1.00000i | \(0.499920\pi\) | ||||||||
\(108\) | −254.287 | −0.226562 | ||||||||
\(109\) | −1205.08 | −1.05895 | −0.529477 | − | 0.848324i | \(-0.677612\pi\) | ||||
−0.529477 | + | 0.848324i | \(0.677612\pi\) | |||||||
\(110\) | −379.628 | −0.329055 | ||||||||
\(111\) | −994.536 | −0.850425 | ||||||||
\(112\) | 348.836 | 0.294303 | ||||||||
\(113\) | −1863.95 | −1.55173 | −0.775864 | − | 0.630900i | \(-0.782686\pi\) | ||||
−0.775864 | + | 0.630900i | \(0.782686\pi\) | |||||||
\(114\) | −1452.59 | −1.19340 | ||||||||
\(115\) | 1512.04 | 1.22607 | ||||||||
\(116\) | −299.277 | −0.239545 | ||||||||
\(117\) | −2609.27 | −2.06177 | ||||||||
\(118\) | −755.709 | −0.589565 | ||||||||
\(119\) | −1455.01 | −1.12084 | ||||||||
\(120\) | 2471.06 | 1.87980 | ||||||||
\(121\) | −1054.50 | −0.792258 | ||||||||
\(122\) | −878.908 | −0.652235 | ||||||||
\(123\) | 1886.59 | 1.38299 | ||||||||
\(124\) | 360.886 | 0.261359 | ||||||||
\(125\) | 251.344 | 0.179847 | ||||||||
\(126\) | −765.570 | −0.541289 | ||||||||
\(127\) | −2481.26 | −1.73367 | −0.866834 | − | 0.498597i | \(-0.833849\pi\) | ||||
−0.866834 | + | 0.498597i | \(0.833849\pi\) | |||||||
\(128\) | 1357.54 | 0.937431 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1835.01 | 1.23801 | ||||||||
\(131\) | 962.683 | 0.642061 | 0.321031 | − | 0.947069i | \(-0.395971\pi\) | ||||
0.321031 | + | 0.947069i | \(0.395971\pi\) | |||||||
\(132\) | −774.012 | −0.510372 | ||||||||
\(133\) | 2262.29 | 1.47493 | ||||||||
\(134\) | −766.187 | −0.493944 | ||||||||
\(135\) | 686.314 | 0.437545 | ||||||||
\(136\) | −1700.55 | −1.07221 | ||||||||
\(137\) | −78.1818 | −0.0487556 | −0.0243778 | − | 0.999703i | \(-0.507760\pi\) | ||||
−0.0243778 | + | 0.999703i | \(0.507760\pi\) | |||||||
\(138\) | −1002.87 | −0.618625 | ||||||||
\(139\) | 2040.84 | 1.24534 | 0.622668 | − | 0.782486i | \(-0.286049\pi\) | ||||
0.622668 | + | 0.782486i | \(0.286049\pi\) | |||||||
\(140\) | −1655.04 | −0.999120 | ||||||||
\(141\) | 599.785 | 0.358234 | ||||||||
\(142\) | −318.045 | −0.187956 | ||||||||
\(143\) | −1336.54 | −0.781588 | ||||||||
\(144\) | 672.892 | 0.389405 | ||||||||
\(145\) | 807.743 | 0.462617 | ||||||||
\(146\) | −1031.84 | −0.584904 | ||||||||
\(147\) | −460.962 | −0.258636 | ||||||||
\(148\) | 778.521 | 0.432392 | ||||||||
\(149\) | 336.571 | 0.185053 | 0.0925267 | − | 0.995710i | \(-0.470506\pi\) | ||||
0.0925267 | + | 0.995710i | \(0.470506\pi\) | |||||||
\(150\) | −1517.43 | −0.825985 | ||||||||
\(151\) | 1352.41 | 0.728856 | 0.364428 | − | 0.931232i | \(-0.381265\pi\) | ||||
0.364428 | + | 0.931232i | \(0.381265\pi\) | |||||||
\(152\) | 2644.07 | 1.41094 | ||||||||
\(153\) | −2806.66 | −1.48304 | ||||||||
\(154\) | −392.147 | −0.205195 | ||||||||
\(155\) | −974.024 | −0.504745 | ||||||||
\(156\) | 3741.34 | 1.92017 | ||||||||
\(157\) | 886.998 | 0.450893 | 0.225446 | − | 0.974256i | \(-0.427616\pi\) | ||||
0.225446 | + | 0.974256i | \(0.427616\pi\) | |||||||
\(158\) | −617.579 | −0.310962 | ||||||||
\(159\) | 3424.15 | 1.70788 | ||||||||
\(160\) | −3036.82 | −1.50051 | ||||||||
\(161\) | 1561.90 | 0.764564 | ||||||||
\(162\) | 773.041 | 0.374913 | ||||||||
\(163\) | −218.070 | −0.104789 | −0.0523944 | − | 0.998626i | \(-0.516685\pi\) | ||||
−0.0523944 | + | 0.998626i | \(0.516685\pi\) | |||||||
\(164\) | −1476.82 | −0.703173 | ||||||||
\(165\) | 2089.04 | 0.985647 | ||||||||
\(166\) | 119.751 | 0.0559908 | ||||||||
\(167\) | −2766.96 | −1.28212 | −0.641058 | − | 0.767492i | \(-0.721504\pi\) | ||||
−0.641058 | + | 0.767492i | \(0.721504\pi\) | |||||||
\(168\) | 2552.55 | 1.17222 | ||||||||
\(169\) | 4263.43 | 1.94057 | ||||||||
\(170\) | 1973.82 | 0.890502 | ||||||||
\(171\) | 4363.89 | 1.95155 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2722.10 | −1.19628 | −0.598142 | − | 0.801390i | \(-0.704094\pi\) | ||||
−0.598142 | + | 0.801390i | \(0.704094\pi\) | |||||||
\(174\) | −535.744 | −0.233418 | ||||||||
\(175\) | 2363.28 | 1.02084 | ||||||||
\(176\) | 344.674 | 0.147618 | ||||||||
\(177\) | 4158.57 | 1.76597 | ||||||||
\(178\) | −1236.41 | −0.520635 | ||||||||
\(179\) | −4376.37 | −1.82741 | −0.913703 | − | 0.406383i | \(-0.866790\pi\) | ||||
−0.913703 | + | 0.406383i | \(0.866790\pi\) | |||||||
\(180\) | −3192.52 | −1.32198 | ||||||||
\(181\) | −1853.95 | −0.761342 | −0.380671 | − | 0.924710i | \(-0.624307\pi\) | ||||
−0.380671 | + | 0.924710i | \(0.624307\pi\) | |||||||
\(182\) | 1895.52 | 0.772006 | ||||||||
\(183\) | 4836.52 | 1.95369 | ||||||||
\(184\) | 1825.48 | 0.731392 | ||||||||
\(185\) | −2101.21 | −0.835050 | ||||||||
\(186\) | 646.032 | 0.254674 | ||||||||
\(187\) | −1437.65 | −0.562199 | ||||||||
\(188\) | −469.511 | −0.182142 | ||||||||
\(189\) | 708.947 | 0.272848 | ||||||||
\(190\) | −3068.97 | −1.17182 | ||||||||
\(191\) | −1136.38 | −0.430499 | −0.215249 | − | 0.976559i | \(-0.569056\pi\) | ||||
−0.215249 | + | 0.976559i | \(0.569056\pi\) | |||||||
\(192\) | 735.497 | 0.276458 | ||||||||
\(193\) | −2739.66 | −1.02179 | −0.510895 | − | 0.859643i | \(-0.670686\pi\) | ||||
−0.510895 | + | 0.859643i | \(0.670686\pi\) | |||||||
\(194\) | 9.79745 | 0.00362586 | ||||||||
\(195\) | −10097.8 | −3.70830 | ||||||||
\(196\) | 360.840 | 0.131502 | ||||||||
\(197\) | 2862.90 | 1.03540 | 0.517699 | − | 0.855563i | \(-0.326789\pi\) | ||||
0.517699 | + | 0.855563i | \(0.326789\pi\) | |||||||
\(198\) | −756.438 | −0.271503 | ||||||||
\(199\) | −15.5940 | −0.00555491 | −0.00277745 | − | 0.999996i | \(-0.500884\pi\) | ||||
−0.00277745 | + | 0.999996i | \(0.500884\pi\) | |||||||
\(200\) | 2762.10 | 0.976550 | ||||||||
\(201\) | 4216.23 | 1.47955 | ||||||||
\(202\) | −1061.84 | −0.369855 | ||||||||
\(203\) | 834.380 | 0.288483 | ||||||||
\(204\) | 4024.37 | 1.38119 | ||||||||
\(205\) | 3985.91 | 1.35799 | ||||||||
\(206\) | −1005.91 | −0.340219 | ||||||||
\(207\) | 3012.85 | 1.01163 | ||||||||
\(208\) | −1666.05 | −0.555384 | ||||||||
\(209\) | 2235.31 | 0.739805 | ||||||||
\(210\) | −2962.74 | −0.973564 | ||||||||
\(211\) | 4255.88 | 1.38856 | 0.694281 | − | 0.719704i | \(-0.255722\pi\) | ||||
0.694281 | + | 0.719704i | \(0.255722\pi\) | |||||||
\(212\) | −2680.42 | −0.868359 | ||||||||
\(213\) | 1750.16 | 0.563000 | ||||||||
\(214\) | −0.781553 | −0.000249653 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 828.586 | 0.261010 | ||||||||
\(217\) | −1006.14 | −0.314754 | ||||||||
\(218\) | 1688.69 | 0.524646 | ||||||||
\(219\) | 5678.10 | 1.75201 | ||||||||
\(220\) | −1635.30 | −0.501145 | ||||||||
\(221\) | 6949.16 | 2.11516 | ||||||||
\(222\) | 1393.65 | 0.421332 | ||||||||
\(223\) | 539.062 | 0.161876 | 0.0809378 | − | 0.996719i | \(-0.474208\pi\) | ||||
0.0809378 | + | 0.996719i | \(0.474208\pi\) | |||||||
\(224\) | −3136.97 | −0.935703 | ||||||||
\(225\) | 4558.69 | 1.35072 | ||||||||
\(226\) | 2611.96 | 0.768784 | ||||||||
\(227\) | −5992.14 | −1.75204 | −0.876018 | − | 0.482278i | \(-0.839810\pi\) | ||||
−0.876018 | + | 0.482278i | \(0.839810\pi\) | |||||||
\(228\) | −6257.23 | −1.81752 | ||||||||
\(229\) | 1856.30 | 0.535668 | 0.267834 | − | 0.963465i | \(-0.413692\pi\) | ||||
0.267834 | + | 0.963465i | \(0.413692\pi\) | |||||||
\(230\) | −2118.83 | −0.607441 | ||||||||
\(231\) | 2157.93 | 0.614639 | ||||||||
\(232\) | 975.187 | 0.275966 | ||||||||
\(233\) | −2328.11 | −0.654590 | −0.327295 | − | 0.944922i | \(-0.606137\pi\) | ||||
−0.327295 | + | 0.944922i | \(0.606137\pi\) | |||||||
\(234\) | 3656.39 | 1.02148 | ||||||||
\(235\) | 1267.20 | 0.351758 | ||||||||
\(236\) | −3255.32 | −0.897897 | ||||||||
\(237\) | 3398.46 | 0.931450 | ||||||||
\(238\) | 2038.91 | 0.555307 | ||||||||
\(239\) | −61.5635 | −0.0166620 | −0.00833098 | − | 0.999965i | \(-0.502652\pi\) | ||||
−0.00833098 | + | 0.999965i | \(0.502652\pi\) | |||||||
\(240\) | 2604.08 | 0.700385 | ||||||||
\(241\) | 2036.64 | 0.544364 | 0.272182 | − | 0.962246i | \(-0.412255\pi\) | ||||
0.272182 | + | 0.962246i | \(0.412255\pi\) | |||||||
\(242\) | 1477.67 | 0.392514 | ||||||||
\(243\) | −5391.35 | −1.42327 | ||||||||
\(244\) | −3786.02 | −0.993341 | ||||||||
\(245\) | −973.900 | −0.253960 | ||||||||
\(246\) | −2643.70 | −0.685187 | ||||||||
\(247\) | −10804.8 | −2.78337 | ||||||||
\(248\) | −1175.94 | −0.301097 | ||||||||
\(249\) | −658.975 | −0.167714 | ||||||||
\(250\) | −352.210 | −0.0891028 | ||||||||
\(251\) | 3260.59 | 0.819946 | 0.409973 | − | 0.912098i | \(-0.365538\pi\) | ||||
0.409973 | + | 0.912098i | \(0.365538\pi\) | |||||||
\(252\) | −3297.80 | −0.824373 | ||||||||
\(253\) | 1543.27 | 0.383495 | ||||||||
\(254\) | 3477.00 | 0.858924 | ||||||||
\(255\) | −10861.7 | −2.66739 | ||||||||
\(256\) | −2665.38 | −0.650728 | ||||||||
\(257\) | −2352.03 | −0.570878 | −0.285439 | − | 0.958397i | \(-0.592139\pi\) | ||||
−0.285439 | + | 0.958397i | \(0.592139\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2170.50 | −0.520728 | ||||||||
\(260\) | 7904.55 | 1.88546 | ||||||||
\(261\) | 1609.49 | 0.381705 | ||||||||
\(262\) | −1349.02 | −0.318101 | ||||||||
\(263\) | 1854.77 | 0.434866 | 0.217433 | − | 0.976075i | \(-0.430232\pi\) | ||||
0.217433 | + | 0.976075i | \(0.430232\pi\) | |||||||
\(264\) | 2522.10 | 0.587971 | ||||||||
\(265\) | 7234.41 | 1.67700 | ||||||||
\(266\) | −3170.17 | −0.730735 | ||||||||
\(267\) | 6803.82 | 1.55950 | ||||||||
\(268\) | −3300.46 | −0.752267 | ||||||||
\(269\) | 7378.17 | 1.67232 | 0.836162 | − | 0.548483i | \(-0.184794\pi\) | ||||
0.836162 | + | 0.548483i | \(0.184794\pi\) | |||||||
\(270\) | −961.738 | −0.216776 | ||||||||
\(271\) | 239.453 | 0.0536743 | 0.0268371 | − | 0.999640i | \(-0.491456\pi\) | ||||
0.0268371 | + | 0.999640i | \(0.491456\pi\) | |||||||
\(272\) | −1792.09 | −0.399490 | ||||||||
\(273\) | −10430.8 | −2.31246 | ||||||||
\(274\) | 109.557 | 0.0241554 | ||||||||
\(275\) | 2335.09 | 0.512041 | ||||||||
\(276\) | −4320.02 | −0.942155 | ||||||||
\(277\) | 4600.42 | 0.997879 | 0.498940 | − | 0.866637i | \(-0.333723\pi\) | ||||
0.498940 | + | 0.866637i | \(0.333723\pi\) | |||||||
\(278\) | −2859.84 | −0.616986 | ||||||||
\(279\) | −1940.82 | −0.416465 | ||||||||
\(280\) | 5392.92 | 1.15103 | ||||||||
\(281\) | 3363.99 | 0.714160 | 0.357080 | − | 0.934074i | \(-0.383772\pi\) | ||||
0.357080 | + | 0.934074i | \(0.383772\pi\) | |||||||
\(282\) | −840.484 | −0.177483 | ||||||||
\(283\) | 2786.90 | 0.585385 | 0.292693 | − | 0.956207i | \(-0.405449\pi\) | ||||
0.292693 | + | 0.956207i | \(0.405449\pi\) | |||||||
\(284\) | −1370.02 | −0.286253 | ||||||||
\(285\) | 16888.1 | 3.51006 | ||||||||
\(286\) | 1872.91 | 0.387228 | ||||||||
\(287\) | 4117.35 | 0.846828 | ||||||||
\(288\) | −6051.10 | −1.23807 | ||||||||
\(289\) | 2561.86 | 0.521444 | ||||||||
\(290\) | −1131.90 | −0.229198 | ||||||||
\(291\) | −53.9141 | −0.0108608 | ||||||||
\(292\) | −4444.81 | −0.890797 | ||||||||
\(293\) | 1548.87 | 0.308826 | 0.154413 | − | 0.988006i | \(-0.450651\pi\) | ||||
0.154413 | + | 0.988006i | \(0.450651\pi\) | |||||||
\(294\) | 645.949 | 0.128138 | ||||||||
\(295\) | 8786.06 | 1.73405 | ||||||||
\(296\) | −2536.79 | −0.498135 | ||||||||
\(297\) | 700.489 | 0.136857 | ||||||||
\(298\) | −471.640 | −0.0916824 | ||||||||
\(299\) | −7459.68 | −1.44282 | ||||||||
\(300\) | −6536.55 | −1.25796 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1895.14 | −0.361102 | ||||||||
\(303\) | 5843.16 | 1.10786 | ||||||||
\(304\) | 2786.40 | 0.525694 | ||||||||
\(305\) | 10218.4 | 1.91837 | ||||||||
\(306\) | 3932.99 | 0.734752 | ||||||||
\(307\) | 702.537 | 0.130605 | 0.0653027 | − | 0.997865i | \(-0.479199\pi\) | ||||
0.0653027 | + | 0.997865i | \(0.479199\pi\) | |||||||
\(308\) | −1689.23 | −0.312509 | ||||||||
\(309\) | 5535.41 | 1.01909 | ||||||||
\(310\) | 1364.91 | 0.250070 | ||||||||
\(311\) | −5078.98 | −0.926054 | −0.463027 | − | 0.886344i | \(-0.653237\pi\) | ||||
−0.463027 | + | 0.886344i | \(0.653237\pi\) | |||||||
\(312\) | −12191.1 | −2.21212 | ||||||||
\(313\) | −5191.94 | −0.937590 | −0.468795 | − | 0.883307i | \(-0.655312\pi\) | ||||
−0.468795 | + | 0.883307i | \(0.655312\pi\) | |||||||
\(314\) | −1242.96 | −0.223389 | ||||||||
\(315\) | 8900.70 | 1.59206 | ||||||||
\(316\) | −2660.31 | −0.473589 | ||||||||
\(317\) | 369.900 | 0.0655384 | 0.0327692 | − | 0.999463i | \(-0.489567\pi\) | ||||
0.0327692 | + | 0.999463i | \(0.489567\pi\) | |||||||
\(318\) | −4798.29 | −0.846148 | ||||||||
\(319\) | 824.426 | 0.144699 | ||||||||
\(320\) | 1553.93 | 0.271460 | ||||||||
\(321\) | 4.30078 | 0.000747808 0 | ||||||||
\(322\) | −2188.70 | −0.378794 | ||||||||
\(323\) | −11622.2 | −2.00209 | ||||||||
\(324\) | 3329.98 | 0.570985 | ||||||||
\(325\) | −11287.1 | −1.92645 | ||||||||
\(326\) | 305.584 | 0.0519163 | ||||||||
\(327\) | −9292.67 | −1.57152 | ||||||||
\(328\) | 4812.18 | 0.810086 | ||||||||
\(329\) | 1308.99 | 0.219352 | ||||||||
\(330\) | −2927.39 | −0.488327 | ||||||||
\(331\) | −5643.44 | −0.937135 | −0.468567 | − | 0.883428i | \(-0.655230\pi\) | ||||
−0.468567 | + | 0.883428i | \(0.655230\pi\) | |||||||
\(332\) | 515.844 | 0.0852730 | ||||||||
\(333\) | −4186.83 | −0.688999 | ||||||||
\(334\) | 3877.36 | 0.635208 | ||||||||
\(335\) | 8907.87 | 1.45280 | ||||||||
\(336\) | 2689.95 | 0.436752 | ||||||||
\(337\) | 11132.1 | 1.79942 | 0.899711 | − | 0.436486i | \(-0.143777\pi\) | ||||
0.899711 | + | 0.436486i | \(0.143777\pi\) | |||||||
\(338\) | −5974.38 | −0.961431 | ||||||||
\(339\) | −14373.3 | −2.30280 | ||||||||
\(340\) | 8502.52 | 1.35622 | ||||||||
\(341\) | −994.141 | −0.157876 | ||||||||
\(342\) | −6115.15 | −0.966870 | ||||||||
\(343\) | −6778.43 | −1.06706 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11659.6 | 1.81952 | ||||||||
\(346\) | 3814.50 | 0.592684 | ||||||||
\(347\) | −11505.4 | −1.77995 | −0.889973 | − | 0.456014i | \(-0.849277\pi\) | ||||
−0.889973 | + | 0.456014i | \(0.849277\pi\) | |||||||
\(348\) | −2307.79 | −0.355491 | ||||||||
\(349\) | 2860.19 | 0.438689 | 0.219344 | − | 0.975648i | \(-0.429608\pi\) | ||||
0.219344 | + | 0.975648i | \(0.429608\pi\) | |||||||
\(350\) | −3311.69 | −0.505763 | ||||||||
\(351\) | −3385.95 | −0.514897 | ||||||||
\(352\) | −3099.54 | −0.469336 | ||||||||
\(353\) | −12054.9 | −1.81761 | −0.908805 | − | 0.417222i | \(-0.863004\pi\) | ||||
−0.908805 | + | 0.417222i | \(0.863004\pi\) | |||||||
\(354\) | −5827.44 | −0.874930 | ||||||||
\(355\) | 3697.67 | 0.552822 | ||||||||
\(356\) | −5326.02 | −0.792917 | ||||||||
\(357\) | −11219.9 | −1.66336 | ||||||||
\(358\) | 6132.65 | 0.905365 | ||||||||
\(359\) | −1496.02 | −0.219935 | −0.109968 | − | 0.993935i | \(-0.535075\pi\) | ||||
−0.109968 | + | 0.993935i | \(0.535075\pi\) | |||||||
\(360\) | 10402.8 | 1.52298 | ||||||||
\(361\) | 11211.5 | 1.63457 | ||||||||
\(362\) | 2597.95 | 0.377197 | ||||||||
\(363\) | −8131.45 | −1.17573 | ||||||||
\(364\) | 8165.21 | 1.17575 | ||||||||
\(365\) | 11996.5 | 1.72034 | ||||||||
\(366\) | −6777.46 | −0.967933 | ||||||||
\(367\) | −7457.74 | −1.06074 | −0.530369 | − | 0.847767i | \(-0.677947\pi\) | ||||
−0.530369 | + | 0.847767i | \(0.677947\pi\) | |||||||
\(368\) | 1923.74 | 0.272505 | ||||||||
\(369\) | 7942.23 | 1.12048 | ||||||||
\(370\) | 2944.45 | 0.413715 | ||||||||
\(371\) | 7472.97 | 1.04576 | ||||||||
\(372\) | 2782.87 | 0.387864 | ||||||||
\(373\) | 7188.19 | 0.997830 | 0.498915 | − | 0.866651i | \(-0.333732\pi\) | ||||
0.498915 | + | 0.866651i | \(0.333732\pi\) | |||||||
\(374\) | 2014.59 | 0.278535 | ||||||||
\(375\) | 1938.17 | 0.266897 | ||||||||
\(376\) | 1529.89 | 0.209835 | ||||||||
\(377\) | −3985.03 | −0.544401 | ||||||||
\(378\) | −993.453 | −0.135179 | ||||||||
\(379\) | 8220.25 | 1.11411 | 0.557053 | − | 0.830477i | \(-0.311932\pi\) | ||||
0.557053 | + | 0.830477i | \(0.311932\pi\) | |||||||
\(380\) | −13220.0 | −1.78466 | ||||||||
\(381\) | −19133.5 | −2.57281 | ||||||||
\(382\) | 1592.41 | 0.213285 | ||||||||
\(383\) | −6162.57 | −0.822174 | −0.411087 | − | 0.911596i | \(-0.634851\pi\) | ||||
−0.411087 | + | 0.911596i | \(0.634851\pi\) | |||||||
\(384\) | 10468.3 | 1.39117 | ||||||||
\(385\) | 4559.19 | 0.603527 | ||||||||
\(386\) | 3839.11 | 0.506233 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 42.2039 | 0.00552211 | ||||||||
\(389\) | −4726.05 | −0.615990 | −0.307995 | − | 0.951388i | \(-0.599658\pi\) | ||||
−0.307995 | + | 0.951388i | \(0.599658\pi\) | |||||||
\(390\) | 14150.1 | 1.83723 | ||||||||
\(391\) | −8024.00 | −1.03783 | ||||||||
\(392\) | −1175.79 | −0.151496 | ||||||||
\(393\) | 7423.46 | 0.952835 | ||||||||
\(394\) | −4011.81 | −0.512975 | ||||||||
\(395\) | 7180.12 | 0.914611 | ||||||||
\(396\) | −3258.46 | −0.413495 | ||||||||
\(397\) | 12143.2 | 1.53513 | 0.767567 | − | 0.640968i | \(-0.221467\pi\) | ||||
0.767567 | + | 0.640968i | \(0.221467\pi\) | |||||||
\(398\) | 21.8519 | 0.00275211 | ||||||||
\(399\) | 17445.0 | 2.18883 | ||||||||
\(400\) | 2910.78 | 0.363848 | ||||||||
\(401\) | −4215.81 | −0.525006 | −0.262503 | − | 0.964931i | \(-0.584548\pi\) | ||||
−0.262503 | + | 0.964931i | \(0.584548\pi\) | |||||||
\(402\) | −5908.24 | −0.733025 | ||||||||
\(403\) | 4805.38 | 0.593978 | ||||||||
\(404\) | −4574.02 | −0.563282 | ||||||||
\(405\) | −8987.56 | −1.10270 | ||||||||
\(406\) | −1169.22 | −0.142925 | ||||||||
\(407\) | −2144.61 | −0.261190 | ||||||||
\(408\) | −13113.3 | −1.59119 | ||||||||
\(409\) | 239.924 | 0.0290061 | 0.0145030 | − | 0.999895i | \(-0.495383\pi\) | ||||
0.0145030 | + | 0.999895i | \(0.495383\pi\) | |||||||
\(410\) | −5585.49 | −0.672799 | ||||||||
\(411\) | −602.877 | −0.0723546 | ||||||||
\(412\) | −4333.11 | −0.518148 | ||||||||
\(413\) | 9075.79 | 1.08133 | ||||||||
\(414\) | −4221.93 | −0.501199 | ||||||||
\(415\) | −1392.25 | −0.164682 | ||||||||
\(416\) | 14982.3 | 1.76578 | ||||||||
\(417\) | 15737.4 | 1.84811 | ||||||||
\(418\) | −3132.35 | −0.366527 | ||||||||
\(419\) | −31.4797 | −0.00367037 | −0.00183518 | − | 0.999998i | \(-0.500584\pi\) | ||||
−0.00183518 | + | 0.999998i | \(0.500584\pi\) | |||||||
\(420\) | −12762.4 | −1.48272 | ||||||||
\(421\) | 940.763 | 0.108907 | 0.0544537 | − | 0.998516i | \(-0.482658\pi\) | ||||
0.0544537 | + | 0.998516i | \(0.482658\pi\) | |||||||
\(422\) | −5963.80 | −0.687946 | ||||||||
\(423\) | 2524.99 | 0.290235 | ||||||||
\(424\) | 8734.08 | 1.00039 | ||||||||
\(425\) | −12141.0 | −1.38570 | ||||||||
\(426\) | −2452.52 | −0.278931 | ||||||||
\(427\) | 10555.4 | 1.19628 | ||||||||
\(428\) | −3.36665 | −0.000380217 0 | ||||||||
\(429\) | −10306.4 | −1.15990 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2818.53 | 0.314997 | 0.157499 | − | 0.987519i | \(-0.449657\pi\) | ||||
0.157499 | + | 0.987519i | \(0.449657\pi\) | |||||||
\(432\) | 873.188 | 0.0972483 | ||||||||
\(433\) | 14883.7 | 1.65188 | 0.825942 | − | 0.563756i | \(-0.190644\pi\) | ||||
0.825942 | + | 0.563756i | \(0.190644\pi\) | |||||||
\(434\) | 1409.92 | 0.155941 | ||||||||
\(435\) | 6228.69 | 0.686535 | ||||||||
\(436\) | 7274.29 | 0.799026 | ||||||||
\(437\) | 12476.0 | 1.36569 | ||||||||
\(438\) | −7956.77 | −0.868012 | ||||||||
\(439\) | 3638.21 | 0.395540 | 0.197770 | − | 0.980248i | \(-0.436630\pi\) | ||||
0.197770 | + | 0.980248i | \(0.436630\pi\) | |||||||
\(440\) | 5328.58 | 0.577341 | ||||||||
\(441\) | −1940.57 | −0.209542 | ||||||||
\(442\) | −9737.91 | −1.04793 | ||||||||
\(443\) | 5735.65 | 0.615144 | 0.307572 | − | 0.951525i | \(-0.400484\pi\) | ||||
0.307572 | + | 0.951525i | \(0.400484\pi\) | |||||||
\(444\) | 6003.35 | 0.641681 | ||||||||
\(445\) | 14374.8 | 1.53131 | ||||||||
\(446\) | −755.392 | −0.0801992 | ||||||||
\(447\) | 2595.37 | 0.274624 | ||||||||
\(448\) | 1605.17 | 0.169279 | ||||||||
\(449\) | 13651.3 | 1.43484 | 0.717421 | − | 0.696640i | \(-0.245322\pi\) | ||||
0.717421 | + | 0.696640i | \(0.245322\pi\) | |||||||
\(450\) | −6388.13 | −0.669199 | ||||||||
\(451\) | 4068.23 | 0.424758 | ||||||||
\(452\) | 11251.4 | 1.17084 | ||||||||
\(453\) | 10428.7 | 1.08164 | ||||||||
\(454\) | 8396.84 | 0.868025 | ||||||||
\(455\) | −22037.7 | −2.27065 | ||||||||
\(456\) | 20389.0 | 2.09387 | ||||||||
\(457\) | −18054.8 | −1.84807 | −0.924037 | − | 0.382303i | \(-0.875131\pi\) | ||||
−0.924037 | + | 0.382303i | \(0.875131\pi\) | |||||||
\(458\) | −2601.25 | −0.265390 | ||||||||
\(459\) | −3642.10 | −0.370367 | ||||||||
\(460\) | −9127.16 | −0.925122 | ||||||||
\(461\) | −7748.85 | −0.782863 | −0.391432 | − | 0.920207i | \(-0.628020\pi\) | ||||
−0.391432 | + | 0.920207i | \(0.628020\pi\) | |||||||
\(462\) | −3023.93 | −0.304515 | ||||||||
\(463\) | −5930.29 | −0.595257 | −0.297629 | − | 0.954682i | \(-0.596196\pi\) | ||||
−0.297629 | + | 0.954682i | \(0.596196\pi\) | |||||||
\(464\) | 1027.68 | 0.102821 | ||||||||
\(465\) | −7510.92 | −0.749055 | ||||||||
\(466\) | 3262.40 | 0.324308 | ||||||||
\(467\) | −3326.65 | −0.329634 | −0.164817 | − | 0.986324i | \(-0.552703\pi\) | ||||
−0.164817 | + | 0.986324i | \(0.552703\pi\) | |||||||
\(468\) | 15750.4 | 1.55569 | ||||||||
\(469\) | 9201.62 | 0.905952 | ||||||||
\(470\) | −1775.74 | −0.174274 | ||||||||
\(471\) | 6839.84 | 0.669136 | ||||||||
\(472\) | 10607.4 | 1.03442 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −4762.29 | −0.461475 | ||||||||
\(475\) | 18877.2 | 1.82346 | ||||||||
\(476\) | 8782.90 | 0.845722 | ||||||||
\(477\) | 14415.1 | 1.38369 | ||||||||
\(478\) | 86.2694 | 0.00825496 | ||||||||
\(479\) | −3999.59 | −0.381516 | −0.190758 | − | 0.981637i | \(-0.561094\pi\) | ||||
−0.190758 | + | 0.981637i | \(0.561094\pi\) | |||||||
\(480\) | −23417.6 | −2.22680 | ||||||||
\(481\) | 10366.4 | 0.982676 | ||||||||
\(482\) | −2853.96 | −0.269698 | ||||||||
\(483\) | 12044.1 | 1.13463 | ||||||||
\(484\) | 6365.29 | 0.597792 | ||||||||
\(485\) | −113.908 | −0.0106645 | ||||||||
\(486\) | 7554.94 | 0.705142 | ||||||||
\(487\) | −17715.0 | −1.64834 | −0.824170 | − | 0.566342i | \(-0.808358\pi\) | ||||
−0.824170 | + | 0.566342i | \(0.808358\pi\) | |||||||
\(488\) | 12336.7 | 1.14437 | ||||||||
\(489\) | −1681.59 | −0.155509 | ||||||||
\(490\) | 1364.73 | 0.125821 | ||||||||
\(491\) | 6351.58 | 0.583794 | 0.291897 | − | 0.956450i | \(-0.405714\pi\) | ||||
0.291897 | + | 0.956450i | \(0.405714\pi\) | |||||||
\(492\) | −11388.1 | −1.04353 | ||||||||
\(493\) | −4286.49 | −0.391590 | ||||||||
\(494\) | 15140.8 | 1.37898 | ||||||||
\(495\) | 8794.52 | 0.798554 | ||||||||
\(496\) | −1239.24 | −0.112184 | ||||||||
\(497\) | 3819.60 | 0.344734 | ||||||||
\(498\) | 923.427 | 0.0830918 | ||||||||
\(499\) | 5595.78 | 0.502007 | 0.251003 | − | 0.967986i | \(-0.419239\pi\) | ||||
0.251003 | + | 0.967986i | \(0.419239\pi\) | |||||||
\(500\) | −1517.19 | −0.135702 | ||||||||
\(501\) | −21336.6 | −1.90269 | ||||||||
\(502\) | −4569.09 | −0.406232 | ||||||||
\(503\) | 6219.18 | 0.551291 | 0.275646 | − | 0.961259i | \(-0.411108\pi\) | ||||
0.275646 | + | 0.961259i | \(0.411108\pi\) | |||||||
\(504\) | 10745.8 | 0.949715 | ||||||||
\(505\) | 12345.2 | 1.08783 | ||||||||
\(506\) | −2162.59 | −0.189998 | ||||||||
\(507\) | 32876.3 | 2.87985 | ||||||||
\(508\) | 14977.7 | 1.30813 | ||||||||
\(509\) | 18178.1 | 1.58297 | 0.791485 | − | 0.611188i | \(-0.209308\pi\) | ||||
0.791485 | + | 0.611188i | \(0.209308\pi\) | |||||||
\(510\) | 15220.6 | 1.32153 | ||||||||
\(511\) | 12392.1 | 1.07278 | ||||||||
\(512\) | −7125.34 | −0.615036 | ||||||||
\(513\) | 5662.86 | 0.487371 | ||||||||
\(514\) | 3295.92 | 0.282834 | ||||||||
\(515\) | 11695.0 | 1.00066 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1293.37 | 0.110024 | ||||||||
\(518\) | 3041.55 | 0.257988 | ||||||||
\(519\) | −20990.7 | −1.77532 | ||||||||
\(520\) | −25756.8 | −2.17213 | ||||||||
\(521\) | −14404.1 | −1.21124 | −0.605620 | − | 0.795754i | \(-0.707075\pi\) | ||||
−0.605620 | + | 0.795754i | \(0.707075\pi\) | |||||||
\(522\) | −2255.39 | −0.189111 | ||||||||
\(523\) | −4841.59 | −0.404796 | −0.202398 | − | 0.979303i | \(-0.564873\pi\) | ||||
−0.202398 | + | 0.979303i | \(0.564873\pi\) | |||||||
\(524\) | −5811.08 | −0.484462 | ||||||||
\(525\) | 18223.8 | 1.51496 | ||||||||
\(526\) | −2599.10 | −0.215449 | ||||||||
\(527\) | 5168.90 | 0.427250 | ||||||||
\(528\) | 2657.86 | 0.219069 | ||||||||
\(529\) | −3553.52 | −0.292062 | ||||||||
\(530\) | −10137.6 | −0.830850 | ||||||||
\(531\) | 17506.9 | 1.43076 | ||||||||
\(532\) | −13656.0 | −1.11290 | ||||||||
\(533\) | −19664.6 | −1.59807 | ||||||||
\(534\) | −9534.25 | −0.772635 | ||||||||
\(535\) | 9.08652 | 0.000734288 0 | ||||||||
\(536\) | 10754.5 | 0.866645 | ||||||||
\(537\) | −33747.2 | −2.71192 | ||||||||
\(538\) | −10339.1 | −0.828532 | ||||||||
\(539\) | −994.015 | −0.0794346 | ||||||||
\(540\) | −4142.82 | −0.330146 | ||||||||
\(541\) | −8621.04 | −0.685116 | −0.342558 | − | 0.939497i | \(-0.611293\pi\) | ||||
−0.342558 | + | 0.939497i | \(0.611293\pi\) | |||||||
\(542\) | −335.547 | −0.0265922 | ||||||||
\(543\) | −14296.2 | −1.12985 | ||||||||
\(544\) | 16115.6 | 1.27013 | ||||||||
\(545\) | −19633.2 | −1.54310 | ||||||||
\(546\) | 14616.8 | 1.14568 | ||||||||
\(547\) | −8074.92 | −0.631186 | −0.315593 | − | 0.948895i | \(-0.602203\pi\) | ||||
−0.315593 | + | 0.948895i | \(0.602203\pi\) | |||||||
\(548\) | 471.931 | 0.0367882 | ||||||||
\(549\) | 20360.9 | 1.58285 | ||||||||
\(550\) | −3272.18 | −0.253684 | ||||||||
\(551\) | 6664.78 | 0.515298 | ||||||||
\(552\) | 14076.7 | 1.08540 | ||||||||
\(553\) | 7416.90 | 0.570341 | ||||||||
\(554\) | −6446.61 | −0.494387 | ||||||||
\(555\) | −16202.9 | −1.23924 | ||||||||
\(556\) | −12319.2 | −0.939658 | ||||||||
\(557\) | 5115.39 | 0.389131 | 0.194566 | − | 0.980890i | \(-0.437670\pi\) | ||||
0.194566 | + | 0.980890i | \(0.437670\pi\) | |||||||
\(558\) | 2719.68 | 0.206332 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 5683.21 | 0.428856 | ||||||||
\(561\) | −11086.0 | −0.834318 | ||||||||
\(562\) | −4713.99 | −0.353822 | ||||||||
\(563\) | −4303.04 | −0.322117 | −0.161058 | − | 0.986945i | \(-0.551491\pi\) | ||||
−0.161058 | + | 0.986945i | \(0.551491\pi\) | |||||||
\(564\) | −3620.50 | −0.270303 | ||||||||
\(565\) | −30367.3 | −2.26117 | ||||||||
\(566\) | −3905.31 | −0.290022 | ||||||||
\(567\) | −9283.94 | −0.687635 | ||||||||
\(568\) | 4464.19 | 0.329777 | ||||||||
\(569\) | −22456.6 | −1.65453 | −0.827266 | − | 0.561810i | \(-0.810105\pi\) | ||||
−0.827266 | + | 0.561810i | \(0.810105\pi\) | |||||||
\(570\) | −23665.5 | −1.73901 | ||||||||
\(571\) | 2012.73 | 0.147513 | 0.0737566 | − | 0.997276i | \(-0.476501\pi\) | ||||
0.0737566 | + | 0.997276i | \(0.476501\pi\) | |||||||
\(572\) | 8067.81 | 0.589741 | ||||||||
\(573\) | −8762.85 | −0.638871 | ||||||||
\(574\) | −5769.68 | −0.419550 | ||||||||
\(575\) | 13032.9 | 0.945235 | ||||||||
\(576\) | 3096.32 | 0.223981 | ||||||||
\(577\) | −6863.89 | −0.495229 | −0.247615 | − | 0.968859i | \(-0.579647\pi\) | ||||
−0.247615 | + | 0.968859i | \(0.579647\pi\) | |||||||
\(578\) | −3589.95 | −0.258343 | ||||||||
\(579\) | −21126.2 | −1.51636 | ||||||||
\(580\) | −4875.81 | −0.349064 | ||||||||
\(581\) | −1438.17 | −0.102694 | ||||||||
\(582\) | 75.5503 | 0.00538086 | ||||||||
\(583\) | 7383.82 | 0.524540 | ||||||||
\(584\) | 14483.3 | 1.02624 | ||||||||
\(585\) | −42510.1 | −3.00440 | ||||||||
\(586\) | −2170.44 | −0.153004 | ||||||||
\(587\) | −17290.7 | −1.21578 | −0.607891 | − | 0.794021i | \(-0.707984\pi\) | ||||
−0.607891 | + | 0.794021i | \(0.707984\pi\) | |||||||
\(588\) | 2782.52 | 0.195152 | ||||||||
\(589\) | −8036.78 | −0.562224 | ||||||||
\(590\) | −12312.0 | −0.859112 | ||||||||
\(591\) | 22076.5 | 1.53656 | ||||||||
\(592\) | −2673.34 | −0.185598 | ||||||||
\(593\) | −4413.61 | −0.305642 | −0.152821 | − | 0.988254i | \(-0.548836\pi\) | ||||
−0.152821 | + | 0.988254i | \(0.548836\pi\) | |||||||
\(594\) | −981.602 | −0.0678040 | ||||||||
\(595\) | −23704.9 | −1.63329 | ||||||||
\(596\) | −2031.65 | −0.139631 | ||||||||
\(597\) | −120.248 | −0.00824362 | ||||||||
\(598\) | 10453.3 | 0.714829 | ||||||||
\(599\) | 14099.4 | 0.961743 | 0.480871 | − | 0.876791i | \(-0.340320\pi\) | ||||
0.480871 | + | 0.876791i | \(0.340320\pi\) | |||||||
\(600\) | 21299.2 | 1.44923 | ||||||||
\(601\) | 3049.05 | 0.206944 | 0.103472 | − | 0.994632i | \(-0.467005\pi\) | ||||
0.103472 | + | 0.994632i | \(0.467005\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17749.6 | 1.19871 | ||||||||
\(604\) | −8163.57 | −0.549952 | ||||||||
\(605\) | −17179.8 | −1.15447 | ||||||||
\(606\) | −8188.07 | −0.548874 | ||||||||
\(607\) | −24259.5 | −1.62218 | −0.811091 | − | 0.584920i | \(-0.801126\pi\) | ||||
−0.811091 | + | 0.584920i | \(0.801126\pi\) | |||||||
\(608\) | −25057.2 | −1.67138 | ||||||||
\(609\) | 6434.09 | 0.428116 | ||||||||
\(610\) | −14319.1 | −0.950434 | ||||||||
\(611\) | −6251.78 | −0.413944 | ||||||||
\(612\) | 16941.9 | 1.11901 | ||||||||
\(613\) | 17207.8 | 1.13380 | 0.566898 | − | 0.823788i | \(-0.308144\pi\) | ||||
0.566898 | + | 0.823788i | \(0.308144\pi\) | |||||||
\(614\) | −984.470 | −0.0647068 | ||||||||
\(615\) | 30736.2 | 2.01529 | ||||||||
\(616\) | 5504.30 | 0.360024 | ||||||||
\(617\) | 18149.7 | 1.18425 | 0.592123 | − | 0.805848i | \(-0.298290\pi\) | ||||
0.592123 | + | 0.805848i | \(0.298290\pi\) | |||||||
\(618\) | −7756.81 | −0.504894 | ||||||||
\(619\) | −1849.65 | −0.120103 | −0.0600514 | − | 0.998195i | \(-0.519126\pi\) | ||||
−0.0600514 | + | 0.998195i | \(0.519126\pi\) | |||||||
\(620\) | 5879.54 | 0.380851 | ||||||||
\(621\) | 3909.66 | 0.252640 | ||||||||
\(622\) | 7117.22 | 0.458802 | ||||||||
\(623\) | 14848.9 | 0.954906 | ||||||||
\(624\) | −12847.3 | −0.824204 | ||||||||
\(625\) | −13458.6 | −0.861348 | ||||||||
\(626\) | 7275.51 | 0.464517 | ||||||||
\(627\) | 17236.9 | 1.09789 | ||||||||
\(628\) | −5354.22 | −0.340217 | ||||||||
\(629\) | 11150.6 | 0.706842 | ||||||||
\(630\) | −12472.6 | −0.788764 | ||||||||
\(631\) | −13125.7 | −0.828090 | −0.414045 | − | 0.910256i | \(-0.635884\pi\) | ||||
−0.414045 | + | 0.910256i | \(0.635884\pi\) | |||||||
\(632\) | 8668.55 | 0.545596 | ||||||||
\(633\) | 32818.0 | 2.06066 | ||||||||
\(634\) | −518.345 | −0.0324702 | ||||||||
\(635\) | −40424.5 | −2.52629 | ||||||||
\(636\) | −20669.3 | −1.28867 | ||||||||
\(637\) | 4804.77 | 0.298857 | ||||||||
\(638\) | −1155.28 | −0.0716893 | ||||||||
\(639\) | 7367.89 | 0.456133 | ||||||||
\(640\) | 22117.0 | 1.36602 | ||||||||
\(641\) | 8940.53 | 0.550905 | 0.275452 | − | 0.961315i | \(-0.411172\pi\) | ||||
0.275452 | + | 0.961315i | \(0.411172\pi\) | |||||||
\(642\) | −6.02673 | −0.000370492 0 | ||||||||
\(643\) | −13835.3 | −0.848542 | −0.424271 | − | 0.905535i | \(-0.639470\pi\) | ||||
−0.424271 | + | 0.905535i | \(0.639470\pi\) | |||||||
\(644\) | −9428.14 | −0.576896 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16286.2 | 0.991909 | ||||||||
\(647\) | −2206.18 | −0.134055 | −0.0670277 | − | 0.997751i | \(-0.521352\pi\) | ||||
−0.0670277 | + | 0.997751i | \(0.521352\pi\) | |||||||
\(648\) | −10850.7 | −0.657800 | ||||||||
\(649\) | 8967.52 | 0.542382 | ||||||||
\(650\) | 15816.7 | 0.954435 | ||||||||
\(651\) | −7758.60 | −0.467102 | ||||||||
\(652\) | 1316.35 | 0.0790676 | ||||||||
\(653\) | 5668.15 | 0.339681 | 0.169841 | − | 0.985472i | \(-0.445675\pi\) | ||||
0.169841 | + | 0.985472i | \(0.445675\pi\) | |||||||
\(654\) | 13021.9 | 0.778588 | ||||||||
\(655\) | 15684.0 | 0.935609 | ||||||||
\(656\) | 5071.22 | 0.301826 | ||||||||
\(657\) | 23903.8 | 1.41945 | ||||||||
\(658\) | −1834.30 | −0.108675 | ||||||||
\(659\) | 6131.34 | 0.362432 | 0.181216 | − | 0.983443i | \(-0.441997\pi\) | ||||
0.181216 | + | 0.983443i | \(0.441997\pi\) | |||||||
\(660\) | −12610.2 | −0.743712 | ||||||||
\(661\) | −19986.7 | −1.17609 | −0.588044 | − | 0.808829i | \(-0.700102\pi\) | ||||
−0.588044 | + | 0.808829i | \(0.700102\pi\) | |||||||
\(662\) | 7908.20 | 0.464292 | ||||||||
\(663\) | 53586.5 | 3.13896 | ||||||||
\(664\) | −1680.87 | −0.0982383 | ||||||||
\(665\) | 36857.2 | 2.14926 | ||||||||
\(666\) | 5867.04 | 0.341356 | ||||||||
\(667\) | 4601.40 | 0.267117 | ||||||||
\(668\) | 16702.3 | 0.967410 | ||||||||
\(669\) | 4156.83 | 0.240227 | ||||||||
\(670\) | −12482.7 | −0.719773 | ||||||||
\(671\) | 10429.4 | 0.600036 | ||||||||
\(672\) | −24189.8 | −1.38861 | ||||||||
\(673\) | 8379.00 | 0.479921 | 0.239960 | − | 0.970783i | \(-0.422866\pi\) | ||||
0.239960 | + | 0.970783i | \(0.422866\pi\) | |||||||
\(674\) | −15599.5 | −0.891501 | ||||||||
\(675\) | 5915.65 | 0.337323 | ||||||||
\(676\) | −25735.5 | −1.46424 | ||||||||
\(677\) | −21124.8 | −1.19925 | −0.599626 | − | 0.800280i | \(-0.704684\pi\) | ||||
−0.599626 | + | 0.800280i | \(0.704684\pi\) | |||||||
\(678\) | 20141.4 | 1.14090 | ||||||||
\(679\) | −117.664 | −0.00665025 | ||||||||
\(680\) | −27705.2 | −1.56242 | ||||||||
\(681\) | −46206.7 | −2.60007 | ||||||||
\(682\) | 1393.10 | 0.0782178 | ||||||||
\(683\) | −22857.9 | −1.28058 | −0.640288 | − | 0.768135i | \(-0.721185\pi\) | ||||
−0.640288 | + | 0.768135i | \(0.721185\pi\) | |||||||
\(684\) | −26341.9 | −1.47252 | ||||||||
\(685\) | −1273.73 | −0.0710465 | ||||||||
\(686\) | 9498.67 | 0.528660 | ||||||||
\(687\) | 14314.4 | 0.794945 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −35691.2 | −1.97348 | ||||||||
\(690\) | −16338.8 | −0.901458 | ||||||||
\(691\) | 28371.8 | 1.56196 | 0.780979 | − | 0.624557i | \(-0.214720\pi\) | ||||
0.780979 | + | 0.624557i | \(0.214720\pi\) | |||||||
\(692\) | 16431.5 | 0.902646 | ||||||||
\(693\) | 9084.54 | 0.497970 | ||||||||
\(694\) | 16122.6 | 0.881851 | ||||||||
\(695\) | 33249.2 | 1.81470 | ||||||||
\(696\) | 7519.88 | 0.409541 | ||||||||
\(697\) | −21152.2 | −1.14949 | ||||||||
\(698\) | −4008.01 | −0.217343 | ||||||||
\(699\) | −17952.6 | −0.971428 | ||||||||
\(700\) | −14265.6 | −0.770268 | ||||||||
\(701\) | −2096.85 | −0.112977 | −0.0564885 | − | 0.998403i | \(-0.517990\pi\) | ||||
−0.0564885 | + | 0.998403i | \(0.517990\pi\) | |||||||
\(702\) | 4744.76 | 0.255099 | ||||||||
\(703\) | −17337.3 | −0.930143 | ||||||||
\(704\) | 1586.02 | 0.0849083 | ||||||||
\(705\) | 9771.67 | 0.522017 | ||||||||
\(706\) | 16892.6 | 0.900512 | ||||||||
\(707\) | 12752.3 | 0.678358 | ||||||||
\(708\) | −25102.5 | −1.33250 | ||||||||
\(709\) | 20456.2 | 1.08356 | 0.541782 | − | 0.840519i | \(-0.317750\pi\) | ||||
0.541782 | + | 0.840519i | \(0.317750\pi\) | |||||||
\(710\) | −5181.57 | −0.273889 | ||||||||
\(711\) | 14306.9 | 0.754645 | ||||||||
\(712\) | 17354.7 | 0.913475 | ||||||||
\(713\) | −5548.64 | −0.291442 | ||||||||
\(714\) | 15722.5 | 0.824090 | ||||||||
\(715\) | −21774.8 | −1.13893 | ||||||||
\(716\) | 26417.3 | 1.37885 | ||||||||
\(717\) | −474.730 | −0.0247268 | ||||||||
\(718\) | 2096.38 | 0.108964 | ||||||||
\(719\) | −15358.6 | −0.796631 | −0.398316 | − | 0.917248i | \(-0.630405\pi\) | ||||
−0.398316 | + | 0.917248i | \(0.630405\pi\) | |||||||
\(720\) | 10962.7 | 0.567440 | ||||||||
\(721\) | 12080.6 | 0.624003 | ||||||||
\(722\) | −15710.8 | −0.809828 | ||||||||
\(723\) | 15705.0 | 0.807850 | ||||||||
\(724\) | 11191.1 | 0.574465 | ||||||||
\(725\) | 6962.30 | 0.356653 | ||||||||
\(726\) | 11394.7 | 0.582501 | ||||||||
\(727\) | −23094.3 | −1.17816 | −0.589079 | − | 0.808075i | \(-0.700509\pi\) | ||||
−0.589079 | + | 0.808075i | \(0.700509\pi\) | |||||||
\(728\) | −26606.1 | −1.35452 | ||||||||
\(729\) | −26679.2 | −1.35544 | ||||||||
\(730\) | −16810.7 | −0.852319 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −29194.9 | −1.47414 | ||||||||
\(733\) | −24060.6 | −1.21241 | −0.606207 | − | 0.795307i | \(-0.707310\pi\) | ||||
−0.606207 | + | 0.795307i | \(0.707310\pi\) | |||||||
\(734\) | 10450.6 | 0.525529 | ||||||||
\(735\) | −7509.96 | −0.376883 | ||||||||
\(736\) | −17299.6 | −0.866401 | ||||||||
\(737\) | 9091.85 | 0.454413 | ||||||||
\(738\) | −11129.5 | −0.555126 | ||||||||
\(739\) | 15164.2 | 0.754836 | 0.377418 | − | 0.926043i | \(-0.376812\pi\) | ||||
0.377418 | + | 0.926043i | \(0.376812\pi\) | |||||||
\(740\) | 12683.6 | 0.630080 | ||||||||
\(741\) | −83318.1 | −4.13059 | ||||||||
\(742\) | −10471.9 | −0.518109 | ||||||||
\(743\) | 20690.1 | 1.02160 | 0.510799 | − | 0.859700i | \(-0.329349\pi\) | ||||
0.510799 | + | 0.859700i | \(0.329349\pi\) | |||||||
\(744\) | −9067.92 | −0.446836 | ||||||||
\(745\) | 5483.40 | 0.269659 | ||||||||
\(746\) | −10072.9 | −0.494362 | ||||||||
\(747\) | −2774.17 | −0.135879 | ||||||||
\(748\) | 8678.13 | 0.424203 | ||||||||
\(749\) | 9.38616 | 0.000457894 0 | ||||||||
\(750\) | −2715.97 | −0.132231 | ||||||||
\(751\) | 9464.86 | 0.459890 | 0.229945 | − | 0.973204i | \(-0.426145\pi\) | ||||
0.229945 | + | 0.973204i | \(0.426145\pi\) | |||||||
\(752\) | 1612.24 | 0.0781814 | ||||||||
\(753\) | 25143.1 | 1.21682 | ||||||||
\(754\) | 5584.25 | 0.269717 | ||||||||
\(755\) | 22033.3 | 1.06209 | ||||||||
\(756\) | −4279.44 | −0.205875 | ||||||||
\(757\) | −10567.2 | −0.507361 | −0.253680 | − | 0.967288i | \(-0.581641\pi\) | ||||
−0.253680 | + | 0.967288i | \(0.581641\pi\) | |||||||
\(758\) | −11519.1 | −0.551969 | ||||||||
\(759\) | 11900.5 | 0.569117 | ||||||||
\(760\) | 43077.0 | 2.05601 | ||||||||
\(761\) | −11305.4 | −0.538531 | −0.269265 | − | 0.963066i | \(-0.586781\pi\) | ||||
−0.269265 | + | 0.963066i | \(0.586781\pi\) | |||||||
\(762\) | 26812.0 | 1.27467 | ||||||||
\(763\) | −20280.6 | −0.962263 | ||||||||
\(764\) | 6859.54 | 0.324829 | ||||||||
\(765\) | −45725.9 | −2.16108 | ||||||||
\(766\) | 8635.66 | 0.407335 | ||||||||
\(767\) | −43346.3 | −2.04060 | ||||||||
\(768\) | −20553.3 | −0.965696 | ||||||||
\(769\) | 7946.62 | 0.372643 | 0.186321 | − | 0.982489i | \(-0.440343\pi\) | ||||
0.186321 | + | 0.982489i | \(0.440343\pi\) | |||||||
\(770\) | −6388.83 | −0.299010 | ||||||||
\(771\) | −18137.0 | −0.847197 | ||||||||
\(772\) | 16537.5 | 0.770983 | ||||||||
\(773\) | 1530.93 | 0.0712340 | 0.0356170 | − | 0.999366i | \(-0.488660\pi\) | ||||
0.0356170 | + | 0.999366i | \(0.488660\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8395.54 | −0.389131 | ||||||||
\(776\) | −137.520 | −0.00636172 | ||||||||
\(777\) | −16737.2 | −0.772774 | ||||||||
\(778\) | 6622.66 | 0.305185 | ||||||||
\(779\) | 32888.2 | 1.51263 | ||||||||
\(780\) | 60953.7 | 2.79807 | ||||||||
\(781\) | 3774.04 | 0.172914 | ||||||||
\(782\) | 11244.1 | 0.514179 | ||||||||
\(783\) | 2088.58 | 0.0953253 | ||||||||
\(784\) | −1239.08 | −0.0564449 | ||||||||
\(785\) | 14450.9 | 0.657039 | ||||||||
\(786\) | −10402.6 | −0.472070 | ||||||||
\(787\) | −17765.6 | −0.804671 | −0.402335 | − | 0.915492i | \(-0.631801\pi\) | ||||
−0.402335 | + | 0.915492i | \(0.631801\pi\) | |||||||
\(788\) | −17281.4 | −0.781251 | ||||||||
\(789\) | 14302.5 | 0.645352 | ||||||||
\(790\) | −10061.6 | −0.453132 | ||||||||
\(791\) | −31368.7 | −1.41004 | ||||||||
\(792\) | 10617.6 | 0.476364 | ||||||||
\(793\) | −50412.8 | −2.25752 | ||||||||
\(794\) | −17016.3 | −0.760563 | ||||||||
\(795\) | 55786.1 | 2.48872 | ||||||||
\(796\) | 94.1304 | 0.00419141 | ||||||||
\(797\) | 12457.2 | 0.553645 | 0.276823 | − | 0.960921i | \(-0.410719\pi\) | ||||
0.276823 | + | 0.960921i | \(0.410719\pi\) | |||||||
\(798\) | −24445.9 | −1.08443 | ||||||||
\(799\) | −6724.72 | −0.297751 | ||||||||
\(800\) | −26175.7 | −1.15681 | ||||||||
\(801\) | 28642.9 | 1.26348 | ||||||||
\(802\) | 5907.65 | 0.260108 | ||||||||
\(803\) | 12244.2 | 0.538094 | ||||||||
\(804\) | −25450.6 | −1.11638 | ||||||||
\(805\) | 25446.4 | 1.11412 | ||||||||
\(806\) | −6733.82 | −0.294279 | ||||||||
\(807\) | 56894.7 | 2.48177 | ||||||||
\(808\) | 14904.3 | 0.648926 | ||||||||
\(809\) | −28363.3 | −1.23263 | −0.616316 | − | 0.787499i | \(-0.711376\pi\) | ||||
−0.616316 | + | 0.787499i | \(0.711376\pi\) | |||||||
\(810\) | 12594.3 | 0.546321 | ||||||||
\(811\) | −5605.49 | −0.242707 | −0.121354 | − | 0.992609i | \(-0.538723\pi\) | ||||
−0.121354 | + | 0.992609i | \(0.538723\pi\) | |||||||
\(812\) | −5036.60 | −0.217672 | ||||||||
\(813\) | 1846.48 | 0.0796540 | ||||||||
\(814\) | 3005.26 | 0.129403 | ||||||||
\(815\) | −3552.79 | −0.152698 | ||||||||
\(816\) | −13819.2 | −0.592853 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −336.208 | −0.0143707 | ||||||||
\(819\) | −43911.9 | −1.87351 | ||||||||
\(820\) | −24060.3 | −1.02466 | ||||||||
\(821\) | −17256.2 | −0.733549 | −0.366775 | − | 0.930310i | \(-0.619538\pi\) | ||||
−0.366775 | + | 0.930310i | \(0.619538\pi\) | |||||||
\(822\) | 844.817 | 0.0358472 | ||||||||
\(823\) | −23660.3 | −1.00212 | −0.501060 | − | 0.865413i | \(-0.667056\pi\) | ||||
−0.501060 | + | 0.865413i | \(0.667056\pi\) | |||||||
\(824\) | 14119.3 | 0.596929 | ||||||||
\(825\) | 18006.4 | 0.759881 | ||||||||
\(826\) | −12718.0 | −0.535733 | ||||||||
\(827\) | 30880.2 | 1.29844 | 0.649220 | − | 0.760601i | \(-0.275095\pi\) | ||||
0.649220 | + | 0.760601i | \(0.275095\pi\) | |||||||
\(828\) | −18186.6 | −0.763317 | ||||||||
\(829\) | −25312.2 | −1.06047 | −0.530235 | − | 0.847851i | \(-0.677896\pi\) | ||||
−0.530235 | + | 0.847851i | \(0.677896\pi\) | |||||||
\(830\) | 1950.98 | 0.0815896 | ||||||||
\(831\) | 35474.9 | 1.48088 | ||||||||
\(832\) | −7666.35 | −0.319451 | ||||||||
\(833\) | 5168.24 | 0.214969 | ||||||||
\(834\) | −22052.9 | −0.915623 | ||||||||
\(835\) | −45079.1 | −1.86829 | ||||||||
\(836\) | −13493.0 | −0.558214 | ||||||||
\(837\) | −2518.53 | −0.104006 | ||||||||
\(838\) | 44.1128 | 0.00181844 | ||||||||
\(839\) | 1329.25 | 0.0546971 | 0.0273485 | − | 0.999626i | \(-0.491294\pi\) | ||||
0.0273485 | + | 0.999626i | \(0.491294\pi\) | |||||||
\(840\) | 41586.0 | 1.70816 | ||||||||
\(841\) | −21930.9 | −0.899212 | ||||||||
\(842\) | −1318.30 | −0.0539568 | ||||||||
\(843\) | 25940.5 | 1.05983 | ||||||||
\(844\) | −25689.9 | −1.04773 | ||||||||
\(845\) | 69459.6 | 2.82779 | ||||||||
\(846\) | −3538.30 | −0.143793 | ||||||||
\(847\) | −17746.3 | −0.719918 | ||||||||
\(848\) | 9204.23 | 0.372729 | ||||||||
\(849\) | 21490.4 | 0.868727 | ||||||||
\(850\) | 17013.2 | 0.686529 | ||||||||
\(851\) | −11969.8 | −0.482161 | ||||||||
\(852\) | −10564.6 | −0.424807 | ||||||||
\(853\) | 26615.5 | 1.06834 | 0.534171 | − | 0.845376i | \(-0.320624\pi\) | ||||
0.534171 | + | 0.845376i | \(0.320624\pi\) | |||||||
\(854\) | −14791.3 | −0.592680 | ||||||||
\(855\) | 71096.2 | 2.84379 | ||||||||
\(856\) | 10.9701 | 0.000438027 0 | ||||||||
\(857\) | 39276.7 | 1.56554 | 0.782770 | − | 0.622311i | \(-0.213806\pi\) | ||||
0.782770 | + | 0.622311i | \(0.213806\pi\) | |||||||
\(858\) | 14442.4 | 0.574656 | ||||||||
\(859\) | 11705.3 | 0.464937 | 0.232468 | − | 0.972604i | \(-0.425320\pi\) | ||||
0.232468 | + | 0.972604i | \(0.425320\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31749.8 | 1.25671 | ||||||||
\(862\) | −3949.63 | −0.156061 | ||||||||
\(863\) | −38432.9 | −1.51596 | −0.757978 | − | 0.652280i | \(-0.773812\pi\) | ||||
−0.757978 | + | 0.652280i | \(0.773812\pi\) | |||||||
\(864\) | −7852.29 | −0.309190 | ||||||||
\(865\) | −44348.2 | −1.74322 | ||||||||
\(866\) | −20856.7 | −0.818405 | ||||||||
\(867\) | 19755.0 | 0.773836 | ||||||||
\(868\) | 6073.42 | 0.237495 | ||||||||
\(869\) | 7328.42 | 0.286076 | ||||||||
\(870\) | −8728.31 | −0.340135 | ||||||||
\(871\) | −43947.3 | −1.70964 | ||||||||
\(872\) | −23703.1 | −0.920513 | ||||||||
\(873\) | −226.969 | −0.00879926 | ||||||||
\(874\) | −17482.7 | −0.676615 | ||||||||
\(875\) | 4229.91 | 0.163425 | ||||||||
\(876\) | −34274.9 | −1.32197 | ||||||||
\(877\) | 17138.0 | 0.659873 | 0.329937 | − | 0.944003i | \(-0.392973\pi\) | ||||
0.329937 | + | 0.944003i | \(0.392973\pi\) | |||||||
\(878\) | −5098.25 | −0.195965 | ||||||||
\(879\) | 11943.7 | 0.458305 | ||||||||
\(880\) | 5615.42 | 0.215109 | ||||||||
\(881\) | −9092.54 | −0.347713 | −0.173857 | − | 0.984771i | \(-0.555623\pi\) | ||||
−0.173857 | + | 0.984771i | \(0.555623\pi\) | |||||||
\(882\) | 2719.34 | 0.103815 | ||||||||
\(883\) | −29537.5 | −1.12573 | −0.562864 | − | 0.826550i | \(-0.690300\pi\) | ||||
−0.562864 | + | 0.826550i | \(0.690300\pi\) | |||||||
\(884\) | −41947.4 | −1.59598 | ||||||||
\(885\) | 67751.2 | 2.57337 | ||||||||
\(886\) | −8037.41 | −0.304765 | ||||||||
\(887\) | 42029.3 | 1.59099 | 0.795494 | − | 0.605962i | \(-0.207212\pi\) | ||||
0.795494 | + | 0.605962i | \(0.207212\pi\) | |||||||
\(888\) | −19561.8 | −0.739245 | ||||||||
\(889\) | −41757.6 | −1.57537 | ||||||||
\(890\) | −20143.6 | −0.758667 | ||||||||
\(891\) | −9173.19 | −0.344908 | ||||||||
\(892\) | −3253.96 | −0.122142 | ||||||||
\(893\) | 10455.8 | 0.391815 | ||||||||
\(894\) | −3636.92 | −0.136059 | ||||||||
\(895\) | −71299.6 | −2.66289 | ||||||||
\(896\) | 22846.4 | 0.851835 | ||||||||
\(897\) | −57523.2 | −2.14119 | ||||||||
\(898\) | −19129.7 | −0.710875 | ||||||||
\(899\) | −2964.13 | −0.109966 | ||||||||
\(900\) | −27517.8 | −1.01918 | ||||||||
\(901\) | −38391.2 | −1.41953 | ||||||||
\(902\) | −5700.85 | −0.210441 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −36662.4 | −1.34886 | ||||||||
\(905\) | −30204.4 | −1.10942 | ||||||||
\(906\) | −14613.8 | −0.535885 | ||||||||
\(907\) | −4192.38 | −0.153479 | −0.0767397 | − | 0.997051i | \(-0.524451\pi\) | ||||
−0.0767397 | + | 0.997051i | \(0.524451\pi\) | |||||||
\(908\) | 36170.6 | 1.32199 | ||||||||
\(909\) | 24598.7 | 0.897567 | ||||||||
\(910\) | 30881.7 | 1.12496 | ||||||||
\(911\) | −7099.74 | −0.258205 | −0.129103 | − | 0.991631i | \(-0.541210\pi\) | ||||
−0.129103 | + | 0.991631i | \(0.541210\pi\) | |||||||
\(912\) | 21486.5 | 0.780143 | ||||||||
\(913\) | −1421.01 | −0.0515099 | ||||||||
\(914\) | 25300.4 | 0.915605 | ||||||||
\(915\) | 78796.3 | 2.84691 | ||||||||
\(916\) | −11205.3 | −0.404184 | ||||||||
\(917\) | 16201.2 | 0.583435 | ||||||||
\(918\) | 5103.70 | 0.183494 | ||||||||
\(919\) | −37186.6 | −1.33479 | −0.667396 | − | 0.744703i | \(-0.732591\pi\) | ||||
−0.667396 | + | 0.744703i | \(0.732591\pi\) | |||||||
\(920\) | 29740.6 | 1.06578 | ||||||||
\(921\) | 5417.42 | 0.193822 | ||||||||
\(922\) | 10858.5 | 0.387860 | ||||||||
\(923\) | −18242.6 | −0.650554 | ||||||||
\(924\) | −13026.0 | −0.463771 | ||||||||
\(925\) | −18111.3 | −0.643779 | ||||||||
\(926\) | 8310.17 | 0.294913 | ||||||||
\(927\) | 23303.1 | 0.825647 | ||||||||
\(928\) | −9241.59 | −0.326908 | ||||||||
\(929\) | −24894.6 | −0.879187 | −0.439593 | − | 0.898197i | \(-0.644877\pi\) | ||||
−0.439593 | + | 0.898197i | \(0.644877\pi\) | |||||||
\(930\) | 10525.1 | 0.371110 | ||||||||
\(931\) | −8035.76 | −0.282880 | ||||||||
\(932\) | 14053.2 | 0.493916 | ||||||||
\(933\) | −39165.2 | −1.37429 | ||||||||
\(934\) | 4661.66 | 0.163313 | ||||||||
\(935\) | −23422.1 | −0.819235 | ||||||||
\(936\) | −51322.3 | −1.79222 | ||||||||
\(937\) | −38380.7 | −1.33815 | −0.669073 | − | 0.743197i | \(-0.733308\pi\) | ||||
−0.669073 | + | 0.743197i | \(0.733308\pi\) | |||||||
\(938\) | −12894.3 | −0.448842 | ||||||||
\(939\) | −40036.2 | −1.39141 | ||||||||
\(940\) | −7649.25 | −0.265416 | ||||||||
\(941\) | 33578.2 | 1.16325 | 0.581625 | − | 0.813457i | \(-0.302417\pi\) | ||||
0.581625 | + | 0.813457i | \(0.302417\pi\) | |||||||
\(942\) | −9584.73 | −0.331515 | ||||||||
\(943\) | 22706.2 | 0.784109 | ||||||||
\(944\) | 11178.4 | 0.385408 | ||||||||
\(945\) | 11550.1 | 0.397593 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40210.2 | −1.37978 | −0.689892 | − | 0.723913i | \(-0.742342\pi\) | ||||
−0.689892 | + | 0.723913i | \(0.742342\pi\) | |||||||
\(948\) | −20514.2 | −0.702818 | ||||||||
\(949\) | −59184.9 | −2.02447 | ||||||||
\(950\) | −26452.8 | −0.903412 | ||||||||
\(951\) | 2852.38 | 0.0972607 | ||||||||
\(952\) | −28618.9 | −0.974309 | ||||||||
\(953\) | 18846.5 | 0.640607 | 0.320303 | − | 0.947315i | \(-0.396215\pi\) | ||||
0.320303 | + | 0.947315i | \(0.396215\pi\) | |||||||
\(954\) | −20200.0 | −0.685534 | ||||||||
\(955\) | −18513.8 | −0.627321 | ||||||||
\(956\) | 371.618 | 0.0125722 | ||||||||
\(957\) | 6357.33 | 0.214737 | ||||||||
\(958\) | 5604.66 | 0.189017 | ||||||||
\(959\) | −1315.74 | −0.0443038 | ||||||||
\(960\) | 11982.7 | 0.402854 | ||||||||
\(961\) | −26216.7 | −0.880020 | ||||||||
\(962\) | −14526.5 | −0.486854 | ||||||||
\(963\) | 18.1056 | 0.000605861 0 | ||||||||
\(964\) | −12293.9 | −0.410745 | ||||||||
\(965\) | −44634.5 | −1.48895 | ||||||||
\(966\) | −16877.6 | −0.562140 | ||||||||
\(967\) | 1189.70 | 0.0395637 | 0.0197819 | − | 0.999804i | \(-0.493703\pi\) | ||||
0.0197819 | + | 0.999804i | \(0.493703\pi\) | |||||||
\(968\) | −20741.1 | −0.688682 | ||||||||
\(969\) | −89621.0 | −2.97115 | ||||||||
\(970\) | 159.620 | 0.00528358 | ||||||||
\(971\) | −45974.0 | −1.51944 | −0.759720 | − | 0.650250i | \(-0.774664\pi\) | ||||
−0.759720 | + | 0.650250i | \(0.774664\pi\) | |||||||
\(972\) | 32544.0 | 1.07392 | ||||||||
\(973\) | 34345.7 | 1.13163 | ||||||||
\(974\) | 24824.1 | 0.816649 | ||||||||
\(975\) | −87037.4 | −2.85890 | ||||||||
\(976\) | 13000.7 | 0.426376 | ||||||||
\(977\) | 42690.2 | 1.39793 | 0.698967 | − | 0.715154i | \(-0.253644\pi\) | ||||
0.698967 | + | 0.715154i | \(0.253644\pi\) | |||||||
\(978\) | 2356.42 | 0.0770451 | ||||||||
\(979\) | 14671.7 | 0.478968 | ||||||||
\(980\) | 5878.79 | 0.191623 | ||||||||
\(981\) | −39120.6 | −1.27321 | ||||||||
\(982\) | −8900.52 | −0.289233 | ||||||||
\(983\) | 19065.0 | 0.618596 | 0.309298 | − | 0.950965i | \(-0.399906\pi\) | ||||
0.309298 | + | 0.950965i | \(0.399906\pi\) | |||||||
\(984\) | 37107.8 | 1.20219 | ||||||||
\(985\) | 46642.2 | 1.50878 | ||||||||
\(986\) | 6006.70 | 0.194008 | ||||||||
\(987\) | 10093.9 | 0.325524 | ||||||||
\(988\) | 65221.3 | 2.10017 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −12323.8 | −0.395634 | ||||||||
\(991\) | 51456.8 | 1.64942 | 0.824712 | − | 0.565553i | \(-0.191337\pi\) | ||||
0.824712 | + | 0.565553i | \(0.191337\pi\) | |||||||
\(992\) | 11144.1 | 0.356678 | ||||||||
\(993\) | −43517.8 | −1.39073 | ||||||||
\(994\) | −5352.44 | −0.170794 | ||||||||
\(995\) | −254.056 | −0.00809459 | ||||||||
\(996\) | 3977.79 | 0.126547 | ||||||||
\(997\) | 2972.68 | 0.0944291 | 0.0472146 | − | 0.998885i | \(-0.484966\pi\) | ||||
0.0472146 | + | 0.998885i | \(0.484966\pi\) | |||||||
\(998\) | −7841.41 | −0.248713 | ||||||||
\(999\) | −5433.10 | −0.172068 |
(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 | 1849.4.a.h.1.12 | 30 | ||
43.21 | even | 7 | 43.4.e.a.11.5 | yes | 60 | ||
43.41 | even | 7 | 43.4.e.a.4.5 | ✓ | 60 | ||
43.42 | odd | 2 | 1849.4.a.g.1.19 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.e.a.4.5 | ✓ | 60 | 43.41 | even | 7 | ||
43.4.e.a.11.5 | yes | 60 | 43.21 | even | 7 | ||
1849.4.a.g.1.19 | 30 | 43.42 | odd | 2 | |||
1849.4.a.h.1.12 | 30 | 1.1 | even | 1 | trivial |