Newspace parameters
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.24 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-expansion
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.902811 | −0.319192 | −0.159596 | − | 0.987182i | \(-0.551019\pi\) | ||||
−0.159596 | + | 0.987182i | \(0.551019\pi\) | |||||||
\(3\) | −9.58399 | −1.84444 | −0.922220 | − | 0.386667i | \(-0.873626\pi\) | ||||
−0.922220 | + | 0.386667i | \(0.873626\pi\) | |||||||
\(4\) | −7.18493 | −0.898117 | ||||||||
\(5\) | −2.03345 | −0.181877 | −0.0909387 | − | 0.995856i | \(-0.528987\pi\) | ||||
−0.0909387 | + | 0.995856i | \(0.528987\pi\) | |||||||
\(6\) | 8.65253 | 0.588730 | ||||||||
\(7\) | 26.8278 | 1.44857 | 0.724284 | − | 0.689502i | \(-0.242171\pi\) | ||||
0.724284 | + | 0.689502i | \(0.242171\pi\) | |||||||
\(8\) | 13.7091 | 0.605863 | ||||||||
\(9\) | 64.8528 | 2.40196 | ||||||||
\(10\) | 1.83582 | 0.0580538 | ||||||||
\(11\) | 38.6799 | 1.06022 | 0.530110 | − | 0.847929i | \(-0.322151\pi\) | ||||
0.530110 | + | 0.847929i | \(0.322151\pi\) | |||||||
\(12\) | 68.8603 | 1.65652 | ||||||||
\(13\) | −37.4866 | −0.799762 | −0.399881 | − | 0.916567i | \(-0.630949\pi\) | ||||
−0.399881 | + | 0.916567i | \(0.630949\pi\) | |||||||
\(14\) | −24.2205 | −0.462371 | ||||||||
\(15\) | 19.4886 | 0.335462 | ||||||||
\(16\) | 45.1027 | 0.704730 | ||||||||
\(17\) | −12.0881 | −0.172459 | −0.0862294 | − | 0.996275i | \(-0.527482\pi\) | ||||
−0.0862294 | + | 0.996275i | \(0.527482\pi\) | |||||||
\(18\) | −58.5498 | −0.766685 | ||||||||
\(19\) | −64.0712 | −0.773628 | −0.386814 | − | 0.922158i | \(-0.626424\pi\) | ||||
−0.386814 | + | 0.922158i | \(0.626424\pi\) | |||||||
\(20\) | 14.6102 | 0.163347 | ||||||||
\(21\) | −257.118 | −2.67179 | ||||||||
\(22\) | −34.9206 | −0.338414 | ||||||||
\(23\) | −85.2739 | −0.773080 | −0.386540 | − | 0.922273i | \(-0.626330\pi\) | ||||
−0.386540 | + | 0.922273i | \(0.626330\pi\) | |||||||
\(24\) | −131.388 | −1.11748 | ||||||||
\(25\) | −120.865 | −0.966921 | ||||||||
\(26\) | 33.8433 | 0.255278 | ||||||||
\(27\) | −362.781 | −2.58582 | ||||||||
\(28\) | −192.756 | −1.30098 | ||||||||
\(29\) | 129.469 | 0.829029 | 0.414514 | − | 0.910043i | \(-0.363951\pi\) | ||||
0.414514 | + | 0.910043i | \(0.363951\pi\) | |||||||
\(30\) | −17.5945 | −0.107077 | ||||||||
\(31\) | 261.836 | 1.51700 | 0.758501 | − | 0.651671i | \(-0.225932\pi\) | ||||
0.758501 | + | 0.651671i | \(0.225932\pi\) | |||||||
\(32\) | −150.392 | −0.830808 | ||||||||
\(33\) | −370.707 | −1.95551 | ||||||||
\(34\) | 10.9133 | 0.0550474 | ||||||||
\(35\) | −54.5531 | −0.263462 | ||||||||
\(36\) | −465.963 | −2.15724 | ||||||||
\(37\) | 310.147 | 1.37805 | 0.689024 | − | 0.724739i | \(-0.258039\pi\) | ||||
0.689024 | + | 0.724739i | \(0.258039\pi\) | |||||||
\(38\) | 57.8442 | 0.246936 | ||||||||
\(39\) | 359.271 | 1.47511 | ||||||||
\(40\) | −27.8768 | −0.110193 | ||||||||
\(41\) | −333.686 | −1.27105 | −0.635524 | − | 0.772081i | \(-0.719216\pi\) | ||||
−0.635524 | + | 0.772081i | \(0.719216\pi\) | |||||||
\(42\) | 232.129 | 0.852815 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −277.912 | −0.952201 | ||||||||
\(45\) | −131.875 | −0.436861 | ||||||||
\(46\) | 76.9862 | 0.246761 | ||||||||
\(47\) | −475.663 | −1.47622 | −0.738112 | − | 0.674678i | \(-0.764282\pi\) | ||||
−0.738112 | + | 0.674678i | \(0.764282\pi\) | |||||||
\(48\) | −432.264 | −1.29983 | ||||||||
\(49\) | 376.733 | 1.09835 | ||||||||
\(50\) | 109.118 | 0.308633 | ||||||||
\(51\) | 115.852 | 0.318090 | ||||||||
\(52\) | 269.339 | 0.718280 | ||||||||
\(53\) | 14.1574 | 0.0366919 | 0.0183460 | − | 0.999832i | \(-0.494160\pi\) | ||||
0.0183460 | + | 0.999832i | \(0.494160\pi\) | |||||||
\(54\) | 327.523 | 0.825374 | ||||||||
\(55\) | −78.6536 | −0.192830 | ||||||||
\(56\) | 367.786 | 0.877634 | ||||||||
\(57\) | 614.057 | 1.42691 | ||||||||
\(58\) | −116.886 | −0.264619 | ||||||||
\(59\) | −652.202 | −1.43914 | −0.719571 | − | 0.694419i | \(-0.755662\pi\) | ||||
−0.719571 | + | 0.694419i | \(0.755662\pi\) | |||||||
\(60\) | −140.024 | −0.301284 | ||||||||
\(61\) | −233.602 | −0.490323 | −0.245162 | − | 0.969482i | \(-0.578841\pi\) | ||||
−0.245162 | + | 0.969482i | \(0.578841\pi\) | |||||||
\(62\) | −236.388 | −0.484215 | ||||||||
\(63\) | 1739.86 | 3.47939 | ||||||||
\(64\) | −225.046 | −0.439543 | ||||||||
\(65\) | 76.2271 | 0.145459 | ||||||||
\(66\) | 334.679 | 0.624183 | ||||||||
\(67\) | 963.472 | 1.75682 | 0.878409 | − | 0.477909i | \(-0.158605\pi\) | ||||
0.878409 | + | 0.477909i | \(0.158605\pi\) | |||||||
\(68\) | 86.8523 | 0.154888 | ||||||||
\(69\) | 817.264 | 1.42590 | ||||||||
\(70\) | 49.2511 | 0.0840948 | ||||||||
\(71\) | 887.185 | 1.48295 | 0.741475 | − | 0.670980i | \(-0.234126\pi\) | ||||
0.741475 | + | 0.670980i | \(0.234126\pi\) | |||||||
\(72\) | 889.075 | 1.45526 | ||||||||
\(73\) | −345.150 | −0.553380 | −0.276690 | − | 0.960959i | \(-0.589238\pi\) | ||||
−0.276690 | + | 0.960959i | \(0.589238\pi\) | |||||||
\(74\) | −280.004 | −0.439862 | ||||||||
\(75\) | 1158.37 | 1.78343 | ||||||||
\(76\) | 460.347 | 0.694808 | ||||||||
\(77\) | 1037.70 | 1.53580 | ||||||||
\(78\) | −324.354 | −0.470844 | ||||||||
\(79\) | −396.269 | −0.564351 | −0.282176 | − | 0.959363i | \(-0.591056\pi\) | ||||
−0.282176 | + | 0.959363i | \(0.591056\pi\) | |||||||
\(80\) | −91.7141 | −0.128174 | ||||||||
\(81\) | 1725.86 | 2.36744 | ||||||||
\(82\) | 301.255 | 0.405708 | ||||||||
\(83\) | 539.877 | 0.713966 | 0.356983 | − | 0.934111i | \(-0.383805\pi\) | ||||
0.356983 | + | 0.934111i | \(0.383805\pi\) | |||||||
\(84\) | 1847.37 | 2.39958 | ||||||||
\(85\) | 24.5806 | 0.0313663 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1240.83 | −1.52909 | ||||||||
\(88\) | 530.267 | 0.642349 | ||||||||
\(89\) | 295.412 | 0.351838 | 0.175919 | − | 0.984405i | \(-0.443710\pi\) | ||||
0.175919 | + | 0.984405i | \(0.443710\pi\) | |||||||
\(90\) | 119.058 | 0.139443 | ||||||||
\(91\) | −1005.68 | −1.15851 | ||||||||
\(92\) | 612.687 | 0.694316 | ||||||||
\(93\) | −2509.43 | −2.79802 | ||||||||
\(94\) | 429.433 | 0.471199 | ||||||||
\(95\) | 130.286 | 0.140705 | ||||||||
\(96\) | 1441.36 | 1.53237 | ||||||||
\(97\) | 191.963 | 0.200937 | 0.100469 | − | 0.994940i | \(-0.467966\pi\) | ||||
0.100469 | + | 0.994940i | \(0.467966\pi\) | |||||||
\(98\) | −340.119 | −0.350584 | ||||||||
\(99\) | 2508.50 | 2.54660 | ||||||||
\(100\) | 868.407 | 0.868407 | ||||||||
\(101\) | −1717.20 | −1.69176 | −0.845878 | − | 0.533377i | \(-0.820923\pi\) | ||||
−0.845878 | + | 0.533377i | \(0.820923\pi\) | |||||||
\(102\) | −104.593 | −0.101532 | ||||||||
\(103\) | −31.9437 | −0.0305583 | −0.0152792 | − | 0.999883i | \(-0.504864\pi\) | ||||
−0.0152792 | + | 0.999883i | \(0.504864\pi\) | |||||||
\(104\) | −513.908 | −0.484547 | ||||||||
\(105\) | 522.836 | 0.485939 | ||||||||
\(106\) | −12.7815 | −0.0117118 | ||||||||
\(107\) | 1275.01 | 1.15196 | 0.575980 | − | 0.817463i | \(-0.304620\pi\) | ||||
0.575980 | + | 0.817463i | \(0.304620\pi\) | |||||||
\(108\) | 2606.56 | 2.32237 | ||||||||
\(109\) | −1181.87 | −1.03856 | −0.519278 | − | 0.854606i | \(-0.673799\pi\) | ||||
−0.519278 | + | 0.854606i | \(0.673799\pi\) | |||||||
\(110\) | 71.0094 | 0.0615498 | ||||||||
\(111\) | −2972.44 | −2.54173 | ||||||||
\(112\) | 1210.01 | 1.02085 | ||||||||
\(113\) | 1007.21 | 0.838495 | 0.419248 | − | 0.907872i | \(-0.362294\pi\) | ||||
0.419248 | + | 0.907872i | \(0.362294\pi\) | |||||||
\(114\) | −554.378 | −0.455458 | ||||||||
\(115\) | 173.400 | 0.140606 | ||||||||
\(116\) | −930.228 | −0.744564 | ||||||||
\(117\) | −2431.11 | −1.92099 | ||||||||
\(118\) | 588.815 | 0.459363 | ||||||||
\(119\) | −324.298 | −0.249818 | ||||||||
\(120\) | 267.171 | 0.203244 | ||||||||
\(121\) | 165.132 | 0.124066 | ||||||||
\(122\) | 210.899 | 0.156507 | ||||||||
\(123\) | 3198.04 | 2.34437 | ||||||||
\(124\) | −1881.27 | −1.36245 | ||||||||
\(125\) | 499.955 | 0.357738 | ||||||||
\(126\) | −1570.77 | −1.11059 | ||||||||
\(127\) | −694.035 | −0.484926 | −0.242463 | − | 0.970161i | \(-0.577955\pi\) | ||||
−0.242463 | + | 0.970161i | \(0.577955\pi\) | |||||||
\(128\) | 1406.31 | 0.971106 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −68.8187 | −0.0464292 | ||||||||
\(131\) | −1014.00 | −0.676286 | −0.338143 | − | 0.941095i | \(-0.609799\pi\) | ||||
−0.338143 | + | 0.941095i | \(0.609799\pi\) | |||||||
\(132\) | 2663.51 | 1.75628 | ||||||||
\(133\) | −1718.89 | −1.12065 | ||||||||
\(134\) | −869.833 | −0.560762 | ||||||||
\(135\) | 737.697 | 0.470303 | ||||||||
\(136\) | −165.717 | −0.104486 | ||||||||
\(137\) | 633.186 | 0.394867 | 0.197433 | − | 0.980316i | \(-0.436739\pi\) | ||||
0.197433 | + | 0.980316i | \(0.436739\pi\) | |||||||
\(138\) | −737.835 | −0.455135 | ||||||||
\(139\) | −437.269 | −0.266825 | −0.133412 | − | 0.991061i | \(-0.542594\pi\) | ||||
−0.133412 | + | 0.991061i | \(0.542594\pi\) | |||||||
\(140\) | 391.960 | 0.236619 | ||||||||
\(141\) | 4558.74 | 2.72280 | ||||||||
\(142\) | −800.961 | −0.473346 | ||||||||
\(143\) | −1449.98 | −0.847924 | ||||||||
\(144\) | 2925.04 | 1.69273 | ||||||||
\(145\) | −263.269 | −0.150782 | ||||||||
\(146\) | 311.605 | 0.176635 | ||||||||
\(147\) | −3610.60 | −2.02583 | ||||||||
\(148\) | −2228.38 | −1.23765 | ||||||||
\(149\) | 2052.33 | 1.12841 | 0.564205 | − | 0.825635i | \(-0.309183\pi\) | ||||
0.564205 | + | 0.825635i | \(0.309183\pi\) | |||||||
\(150\) | −1045.79 | −0.569255 | ||||||||
\(151\) | 1021.62 | 0.550583 | 0.275292 | − | 0.961361i | \(-0.411226\pi\) | ||||
0.275292 | + | 0.961361i | \(0.411226\pi\) | |||||||
\(152\) | −878.360 | −0.468713 | ||||||||
\(153\) | −783.948 | −0.414238 | ||||||||
\(154\) | −936.845 | −0.490215 | ||||||||
\(155\) | −532.430 | −0.275909 | ||||||||
\(156\) | −2581.34 | −1.32482 | ||||||||
\(157\) | 183.529 | 0.0932942 | 0.0466471 | − | 0.998911i | \(-0.485146\pi\) | ||||
0.0466471 | + | 0.998911i | \(0.485146\pi\) | |||||||
\(158\) | 357.756 | 0.180136 | ||||||||
\(159\) | −135.685 | −0.0676760 | ||||||||
\(160\) | 305.815 | 0.151105 | ||||||||
\(161\) | −2287.71 | −1.11986 | ||||||||
\(162\) | −1558.13 | −0.755666 | ||||||||
\(163\) | 832.248 | 0.399918 | 0.199959 | − | 0.979804i | \(-0.435919\pi\) | ||||
0.199959 | + | 0.979804i | \(0.435919\pi\) | |||||||
\(164\) | 2397.51 | 1.14155 | ||||||||
\(165\) | 753.815 | 0.355663 | ||||||||
\(166\) | −487.407 | −0.227892 | ||||||||
\(167\) | −319.899 | −0.148231 | −0.0741153 | − | 0.997250i | \(-0.523613\pi\) | ||||
−0.0741153 | + | 0.997250i | \(0.523613\pi\) | |||||||
\(168\) | −3524.86 | −1.61874 | ||||||||
\(169\) | −791.756 | −0.360380 | ||||||||
\(170\) | −22.1916 | −0.0100119 | ||||||||
\(171\) | −4155.20 | −1.85822 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3014.11 | −1.32462 | −0.662309 | − | 0.749231i | \(-0.730423\pi\) | ||||
−0.662309 | + | 0.749231i | \(0.730423\pi\) | |||||||
\(174\) | 1120.24 | 0.488074 | ||||||||
\(175\) | −3242.55 | −1.40065 | ||||||||
\(176\) | 1744.57 | 0.747169 | ||||||||
\(177\) | 6250.69 | 2.65441 | ||||||||
\(178\) | −266.701 | −0.112304 | ||||||||
\(179\) | 3477.58 | 1.45211 | 0.726053 | − | 0.687639i | \(-0.241353\pi\) | ||||
0.726053 | + | 0.687639i | \(0.241353\pi\) | |||||||
\(180\) | 947.513 | 0.392352 | ||||||||
\(181\) | 7.73635 | 0.00317701 | 0.00158850 | − | 0.999999i | \(-0.499494\pi\) | ||||
0.00158850 | + | 0.999999i | \(0.499494\pi\) | |||||||
\(182\) | 907.943 | 0.369787 | ||||||||
\(183\) | 2238.84 | 0.904372 | ||||||||
\(184\) | −1169.03 | −0.468381 | ||||||||
\(185\) | −630.668 | −0.250636 | ||||||||
\(186\) | 2265.54 | 0.893105 | ||||||||
\(187\) | −467.567 | −0.182844 | ||||||||
\(188\) | 3417.60 | 1.32582 | ||||||||
\(189\) | −9732.63 | −3.74574 | ||||||||
\(190\) | −117.623 | −0.0449121 | ||||||||
\(191\) | −1301.75 | −0.493147 | −0.246574 | − | 0.969124i | \(-0.579305\pi\) | ||||
−0.246574 | + | 0.969124i | \(0.579305\pi\) | |||||||
\(192\) | 2156.84 | 0.810710 | ||||||||
\(193\) | −760.523 | −0.283646 | −0.141823 | − | 0.989892i | \(-0.545296\pi\) | ||||
−0.141823 | + | 0.989892i | \(0.545296\pi\) | |||||||
\(194\) | −173.306 | −0.0641375 | ||||||||
\(195\) | −730.560 | −0.268290 | ||||||||
\(196\) | −2706.80 | −0.986444 | ||||||||
\(197\) | −200.537 | −0.0725263 | −0.0362632 | − | 0.999342i | \(-0.511545\pi\) | ||||
−0.0362632 | + | 0.999342i | \(0.511545\pi\) | |||||||
\(198\) | −2264.70 | −0.812855 | ||||||||
\(199\) | −1878.65 | −0.669217 | −0.334608 | − | 0.942357i | \(-0.608604\pi\) | ||||
−0.334608 | + | 0.942357i | \(0.608604\pi\) | |||||||
\(200\) | −1656.95 | −0.585822 | ||||||||
\(201\) | −9233.90 | −3.24034 | ||||||||
\(202\) | 1550.30 | 0.539995 | ||||||||
\(203\) | 3473.38 | 1.20090 | ||||||||
\(204\) | −832.391 | −0.285682 | ||||||||
\(205\) | 678.534 | 0.231175 | ||||||||
\(206\) | 28.8391 | 0.00975397 | ||||||||
\(207\) | −5530.25 | −1.85690 | ||||||||
\(208\) | −1690.75 | −0.563616 | ||||||||
\(209\) | −2478.26 | −0.820216 | ||||||||
\(210\) | −472.022 | −0.155108 | ||||||||
\(211\) | −907.815 | −0.296192 | −0.148096 | − | 0.988973i | \(-0.547315\pi\) | ||||
−0.148096 | + | 0.988973i | \(0.547315\pi\) | |||||||
\(212\) | −101.720 | −0.0329536 | ||||||||
\(213\) | −8502.77 | −2.73521 | ||||||||
\(214\) | −1151.09 | −0.367697 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4973.41 | −1.56666 | ||||||||
\(217\) | 7024.49 | 2.19748 | ||||||||
\(218\) | 1067.00 | 0.331498 | ||||||||
\(219\) | 3307.91 | 1.02068 | ||||||||
\(220\) | 565.121 | 0.173184 | ||||||||
\(221\) | 453.142 | 0.137926 | ||||||||
\(222\) | 2683.55 | 0.811298 | ||||||||
\(223\) | −2724.67 | −0.818193 | −0.409097 | − | 0.912491i | \(-0.634156\pi\) | ||||
−0.409097 | + | 0.912491i | \(0.634156\pi\) | |||||||
\(224\) | −4034.70 | −1.20348 | ||||||||
\(225\) | −7838.44 | −2.32250 | ||||||||
\(226\) | −909.317 | −0.267641 | ||||||||
\(227\) | 2297.13 | 0.671655 | 0.335828 | − | 0.941923i | \(-0.390984\pi\) | ||||
0.335828 | + | 0.941923i | \(0.390984\pi\) | |||||||
\(228\) | −4411.96 | −1.28153 | ||||||||
\(229\) | 3034.87 | 0.875763 | 0.437882 | − | 0.899033i | \(-0.355729\pi\) | ||||
0.437882 | + | 0.899033i | \(0.355729\pi\) | |||||||
\(230\) | −156.548 | −0.0448802 | ||||||||
\(231\) | −9945.28 | −2.83269 | ||||||||
\(232\) | 1774.91 | 0.502278 | ||||||||
\(233\) | 4994.74 | 1.40436 | 0.702180 | − | 0.711999i | \(-0.252210\pi\) | ||||
0.702180 | + | 0.711999i | \(0.252210\pi\) | |||||||
\(234\) | 2194.83 | 0.613166 | ||||||||
\(235\) | 967.237 | 0.268492 | ||||||||
\(236\) | 4686.02 | 1.29252 | ||||||||
\(237\) | 3797.84 | 1.04091 | ||||||||
\(238\) | 292.780 | 0.0797399 | ||||||||
\(239\) | −2939.14 | −0.795470 | −0.397735 | − | 0.917500i | \(-0.630204\pi\) | ||||
−0.397735 | + | 0.917500i | \(0.630204\pi\) | |||||||
\(240\) | 878.987 | 0.236410 | ||||||||
\(241\) | −4981.47 | −1.33147 | −0.665736 | − | 0.746187i | \(-0.731882\pi\) | ||||
−0.665736 | + | 0.746187i | \(0.731882\pi\) | |||||||
\(242\) | −149.083 | −0.0396010 | ||||||||
\(243\) | −6745.54 | −1.78077 | ||||||||
\(244\) | 1678.42 | 0.440368 | ||||||||
\(245\) | −766.068 | −0.199765 | ||||||||
\(246\) | −2887.23 | −0.748304 | ||||||||
\(247\) | 2401.81 | 0.618719 | ||||||||
\(248\) | 3589.54 | 0.919097 | ||||||||
\(249\) | −5174.17 | −1.31687 | ||||||||
\(250\) | −451.365 | −0.114187 | ||||||||
\(251\) | 5028.93 | 1.26463 | 0.632317 | − | 0.774709i | \(-0.282104\pi\) | ||||
0.632317 | + | 0.774709i | \(0.282104\pi\) | |||||||
\(252\) | −12500.8 | −3.12490 | ||||||||
\(253\) | −3298.38 | −0.819634 | ||||||||
\(254\) | 626.583 | 0.154785 | ||||||||
\(255\) | −235.580 | −0.0578533 | ||||||||
\(256\) | 530.733 | 0.129573 | ||||||||
\(257\) | −846.260 | −0.205402 | −0.102701 | − | 0.994712i | \(-0.532748\pi\) | ||||
−0.102701 | + | 0.994712i | \(0.532748\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8320.56 | 1.99620 | ||||||||
\(260\) | −547.687 | −0.130639 | ||||||||
\(261\) | 8396.44 | 1.99129 | ||||||||
\(262\) | 915.449 | 0.215865 | ||||||||
\(263\) | −7725.74 | −1.81137 | −0.905684 | − | 0.423954i | \(-0.860642\pi\) | ||||
−0.905684 | + | 0.423954i | \(0.860642\pi\) | |||||||
\(264\) | −5082.07 | −1.18477 | ||||||||
\(265\) | −28.7884 | −0.00667343 | ||||||||
\(266\) | 1551.83 | 0.357703 | ||||||||
\(267\) | −2831.23 | −0.648944 | ||||||||
\(268\) | −6922.48 | −1.57783 | ||||||||
\(269\) | −1281.93 | −0.290559 | −0.145279 | − | 0.989391i | \(-0.546408\pi\) | ||||
−0.145279 | + | 0.989391i | \(0.546408\pi\) | |||||||
\(270\) | −666.001 | −0.150117 | ||||||||
\(271\) | 1156.22 | 0.259171 | 0.129585 | − | 0.991568i | \(-0.458635\pi\) | ||||
0.129585 | + | 0.991568i | \(0.458635\pi\) | |||||||
\(272\) | −545.207 | −0.121537 | ||||||||
\(273\) | 9638.46 | 2.13680 | ||||||||
\(274\) | −571.648 | −0.126038 | ||||||||
\(275\) | −4675.05 | −1.02515 | ||||||||
\(276\) | −5871.98 | −1.28062 | ||||||||
\(277\) | 2086.27 | 0.452533 | 0.226266 | − | 0.974065i | \(-0.427348\pi\) | ||||
0.226266 | + | 0.974065i | \(0.427348\pi\) | |||||||
\(278\) | 394.771 | 0.0851684 | ||||||||
\(279\) | 16980.8 | 3.64377 | ||||||||
\(280\) | −747.875 | −0.159622 | ||||||||
\(281\) | 1154.08 | 0.245006 | 0.122503 | − | 0.992468i | \(-0.460908\pi\) | ||||
0.122503 | + | 0.992468i | \(0.460908\pi\) | |||||||
\(282\) | −4115.68 | −0.869097 | ||||||||
\(283\) | 5288.51 | 1.11085 | 0.555423 | − | 0.831568i | \(-0.312556\pi\) | ||||
0.555423 | + | 0.831568i | \(0.312556\pi\) | |||||||
\(284\) | −6374.37 | −1.33186 | ||||||||
\(285\) | −1248.66 | −0.259523 | ||||||||
\(286\) | 1309.05 | 0.270650 | ||||||||
\(287\) | −8952.07 | −1.84120 | ||||||||
\(288\) | −9753.36 | −1.99556 | ||||||||
\(289\) | −4766.88 | −0.970258 | ||||||||
\(290\) | 237.683 | 0.0481283 | ||||||||
\(291\) | −1839.77 | −0.370616 | ||||||||
\(292\) | 2479.88 | 0.497000 | ||||||||
\(293\) | −3079.73 | −0.614060 | −0.307030 | − | 0.951700i | \(-0.599335\pi\) | ||||
−0.307030 | + | 0.951700i | \(0.599335\pi\) | |||||||
\(294\) | 3259.69 | 0.646630 | ||||||||
\(295\) | 1326.22 | 0.261747 | ||||||||
\(296\) | 4251.84 | 0.834909 | ||||||||
\(297\) | −14032.3 | −2.74154 | ||||||||
\(298\) | −1852.86 | −0.360179 | ||||||||
\(299\) | 3196.63 | 0.618280 | ||||||||
\(300\) | −8322.80 | −1.60172 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −922.328 | −0.175742 | ||||||||
\(303\) | 16457.6 | 3.12034 | ||||||||
\(304\) | −2889.78 | −0.545199 | ||||||||
\(305\) | 475.019 | 0.0891787 | ||||||||
\(306\) | 707.757 | 0.132222 | ||||||||
\(307\) | −639.484 | −0.118884 | −0.0594419 | − | 0.998232i | \(-0.518932\pi\) | ||||
−0.0594419 | + | 0.998232i | \(0.518932\pi\) | |||||||
\(308\) | −7455.79 | −1.37933 | ||||||||
\(309\) | 306.148 | 0.0563630 | ||||||||
\(310\) | 480.684 | 0.0880678 | ||||||||
\(311\) | 7068.39 | 1.28878 | 0.644391 | − | 0.764696i | \(-0.277111\pi\) | ||||
0.644391 | + | 0.764696i | \(0.277111\pi\) | |||||||
\(312\) | 4925.29 | 0.893717 | ||||||||
\(313\) | 5479.55 | 0.989528 | 0.494764 | − | 0.869027i | \(-0.335254\pi\) | ||||
0.494764 | + | 0.869027i | \(0.335254\pi\) | |||||||
\(314\) | −165.692 | −0.0297787 | ||||||||
\(315\) | −3537.92 | −0.632823 | ||||||||
\(316\) | 2847.17 | 0.506853 | ||||||||
\(317\) | 6514.68 | 1.15426 | 0.577131 | − | 0.816652i | \(-0.304172\pi\) | ||||
0.577131 | + | 0.816652i | \(0.304172\pi\) | |||||||
\(318\) | 122.498 | 0.0216016 | ||||||||
\(319\) | 5007.85 | 0.878953 | ||||||||
\(320\) | 457.620 | 0.0799429 | ||||||||
\(321\) | −12219.7 | −2.12472 | ||||||||
\(322\) | 2065.37 | 0.357450 | ||||||||
\(323\) | 774.500 | 0.133419 | ||||||||
\(324\) | −12400.2 | −2.12623 | ||||||||
\(325\) | 4530.82 | 0.773307 | ||||||||
\(326\) | −751.363 | −0.127651 | ||||||||
\(327\) | 11327.0 | 1.91555 | ||||||||
\(328\) | −4574.54 | −0.770081 | ||||||||
\(329\) | −12761.0 | −2.13841 | ||||||||
\(330\) | −680.553 | −0.113525 | ||||||||
\(331\) | −3774.59 | −0.626799 | −0.313399 | − | 0.949621i | \(-0.601468\pi\) | ||||
−0.313399 | + | 0.949621i | \(0.601468\pi\) | |||||||
\(332\) | −3878.98 | −0.641225 | ||||||||
\(333\) | 20113.9 | 3.31001 | ||||||||
\(334\) | 288.808 | 0.0473140 | ||||||||
\(335\) | −1959.17 | −0.319526 | ||||||||
\(336\) | −11596.7 | −1.88289 | ||||||||
\(337\) | 11690.7 | 1.88972 | 0.944859 | − | 0.327478i | \(-0.106199\pi\) | ||||
0.944859 | + | 0.327478i | \(0.106199\pi\) | |||||||
\(338\) | 714.806 | 0.115031 | ||||||||
\(339\) | −9653.05 | −1.54655 | ||||||||
\(340\) | −176.610 | −0.0281706 | ||||||||
\(341\) | 10127.8 | 1.60836 | ||||||||
\(342\) | 3751.36 | 0.593129 | ||||||||
\(343\) | 904.985 | 0.142462 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1661.87 | −0.259339 | ||||||||
\(346\) | 2721.18 | 0.422807 | ||||||||
\(347\) | −11140.5 | −1.72349 | −0.861746 | − | 0.507340i | \(-0.830629\pi\) | ||||
−0.861746 | + | 0.507340i | \(0.830629\pi\) | |||||||
\(348\) | 8915.29 | 1.37330 | ||||||||
\(349\) | 1226.84 | 0.188170 | 0.0940852 | − | 0.995564i | \(-0.470007\pi\) | ||||
0.0940852 | + | 0.995564i | \(0.470007\pi\) | |||||||
\(350\) | 2927.41 | 0.447076 | ||||||||
\(351\) | 13599.4 | 2.06804 | ||||||||
\(352\) | −5817.15 | −0.880839 | ||||||||
\(353\) | −1582.18 | −0.238558 | −0.119279 | − | 0.992861i | \(-0.538058\pi\) | ||||
−0.119279 | + | 0.992861i | \(0.538058\pi\) | |||||||
\(354\) | −5643.19 | −0.847267 | ||||||||
\(355\) | −1804.05 | −0.269715 | ||||||||
\(356\) | −2122.52 | −0.315992 | ||||||||
\(357\) | 3108.07 | 0.460774 | ||||||||
\(358\) | −3139.60 | −0.463500 | ||||||||
\(359\) | −613.266 | −0.0901586 | −0.0450793 | − | 0.998983i | \(-0.514354\pi\) | ||||
−0.0450793 | + | 0.998983i | \(0.514354\pi\) | |||||||
\(360\) | −1807.89 | −0.264678 | ||||||||
\(361\) | −2753.88 | −0.401499 | ||||||||
\(362\) | −6.98446 | −0.00101407 | ||||||||
\(363\) | −1582.63 | −0.228833 | ||||||||
\(364\) | 7225.77 | 1.04048 | ||||||||
\(365\) | 701.846 | 0.100647 | ||||||||
\(366\) | −2021.25 | −0.288668 | ||||||||
\(367\) | 2202.45 | 0.313261 | 0.156631 | − | 0.987657i | \(-0.449937\pi\) | ||||
0.156631 | + | 0.987657i | \(0.449937\pi\) | |||||||
\(368\) | −3846.08 | −0.544812 | ||||||||
\(369\) | −21640.5 | −3.05300 | ||||||||
\(370\) | 569.374 | 0.0800009 | ||||||||
\(371\) | 379.813 | 0.0531507 | ||||||||
\(372\) | 18030.1 | 2.51295 | ||||||||
\(373\) | 6268.78 | 0.870201 | 0.435101 | − | 0.900382i | \(-0.356713\pi\) | ||||
0.435101 | + | 0.900382i | \(0.356713\pi\) | |||||||
\(374\) | 422.124 | 0.0583624 | ||||||||
\(375\) | −4791.56 | −0.659827 | ||||||||
\(376\) | −6520.92 | −0.894390 | ||||||||
\(377\) | −4853.36 | −0.663026 | ||||||||
\(378\) | 8786.72 | 1.19561 | ||||||||
\(379\) | 3247.19 | 0.440097 | 0.220049 | − | 0.975489i | \(-0.429378\pi\) | ||||
0.220049 | + | 0.975489i | \(0.429378\pi\) | |||||||
\(380\) | −936.093 | −0.126370 | ||||||||
\(381\) | 6651.62 | 0.894417 | ||||||||
\(382\) | 1175.23 | 0.157409 | ||||||||
\(383\) | −8938.80 | −1.19256 | −0.596281 | − | 0.802776i | \(-0.703356\pi\) | ||||
−0.596281 | + | 0.802776i | \(0.703356\pi\) | |||||||
\(384\) | −13478.1 | −1.79115 | ||||||||
\(385\) | −2110.11 | −0.279327 | ||||||||
\(386\) | 686.609 | 0.0905375 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1379.24 | −0.180465 | ||||||||
\(389\) | −4626.84 | −0.603060 | −0.301530 | − | 0.953457i | \(-0.597497\pi\) | ||||
−0.301530 | + | 0.953457i | \(0.597497\pi\) | |||||||
\(390\) | 659.558 | 0.0856359 | ||||||||
\(391\) | 1030.80 | 0.133324 | ||||||||
\(392\) | 5164.68 | 0.665448 | ||||||||
\(393\) | 9718.15 | 1.24737 | ||||||||
\(394\) | 181.047 | 0.0231498 | ||||||||
\(395\) | 805.794 | 0.102643 | ||||||||
\(396\) | −18023.4 | −2.28714 | ||||||||
\(397\) | 10840.9 | 1.37051 | 0.685253 | − | 0.728305i | \(-0.259692\pi\) | ||||
0.685253 | + | 0.728305i | \(0.259692\pi\) | |||||||
\(398\) | 1696.07 | 0.213609 | ||||||||
\(399\) | 16473.8 | 2.06698 | ||||||||
\(400\) | −5451.34 | −0.681418 | ||||||||
\(401\) | −12391.8 | −1.54319 | −0.771594 | − | 0.636116i | \(-0.780540\pi\) | ||||
−0.771594 | + | 0.636116i | \(0.780540\pi\) | |||||||
\(402\) | 8336.47 | 1.03429 | ||||||||
\(403\) | −9815.33 | −1.21324 | ||||||||
\(404\) | 12337.9 | 1.51939 | ||||||||
\(405\) | −3509.45 | −0.430583 | ||||||||
\(406\) | −3135.81 | −0.383319 | ||||||||
\(407\) | 11996.4 | 1.46103 | ||||||||
\(408\) | 1588.23 | 0.192719 | ||||||||
\(409\) | 7910.71 | 0.956380 | 0.478190 | − | 0.878256i | \(-0.341293\pi\) | ||||
0.478190 | + | 0.878256i | \(0.341293\pi\) | |||||||
\(410\) | −612.588 | −0.0737891 | ||||||||
\(411\) | −6068.45 | −0.728308 | ||||||||
\(412\) | 229.513 | 0.0274449 | ||||||||
\(413\) | −17497.2 | −2.08469 | ||||||||
\(414\) | 4992.77 | 0.592708 | ||||||||
\(415\) | −1097.81 | −0.129854 | ||||||||
\(416\) | 5637.69 | 0.664448 | ||||||||
\(417\) | 4190.78 | 0.492142 | ||||||||
\(418\) | 2237.41 | 0.261806 | ||||||||
\(419\) | −12901.8 | −1.50428 | −0.752142 | − | 0.659001i | \(-0.770979\pi\) | ||||
−0.752142 | + | 0.659001i | \(0.770979\pi\) | |||||||
\(420\) | −3756.54 | −0.436430 | ||||||||
\(421\) | −16075.1 | −1.86093 | −0.930464 | − | 0.366382i | \(-0.880596\pi\) | ||||
−0.930464 | + | 0.366382i | \(0.880596\pi\) | |||||||
\(422\) | 819.586 | 0.0945422 | ||||||||
\(423\) | −30848.1 | −3.54582 | ||||||||
\(424\) | 194.086 | 0.0222303 | ||||||||
\(425\) | 1461.03 | 0.166754 | ||||||||
\(426\) | 7676.40 | 0.873058 | ||||||||
\(427\) | −6267.05 | −0.710266 | ||||||||
\(428\) | −9160.86 | −1.03460 | ||||||||
\(429\) | 13896.6 | 1.56394 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9277.47 | −1.03684 | −0.518422 | − | 0.855125i | \(-0.673480\pi\) | ||||
−0.518422 | + | 0.855125i | \(0.673480\pi\) | |||||||
\(432\) | −16362.4 | −1.82231 | ||||||||
\(433\) | −182.499 | −0.0202548 | −0.0101274 | − | 0.999949i | \(-0.503224\pi\) | ||||
−0.0101274 | + | 0.999949i | \(0.503224\pi\) | |||||||
\(434\) | −6341.79 | −0.701418 | ||||||||
\(435\) | 2523.17 | 0.278107 | ||||||||
\(436\) | 8491.65 | 0.932744 | ||||||||
\(437\) | 5463.60 | 0.598076 | ||||||||
\(438\) | −2986.42 | −0.325792 | ||||||||
\(439\) | −5806.09 | −0.631229 | −0.315614 | − | 0.948888i | \(-0.602211\pi\) | ||||
−0.315614 | + | 0.948888i | \(0.602211\pi\) | |||||||
\(440\) | −1078.27 | −0.116829 | ||||||||
\(441\) | 24432.2 | 2.63818 | ||||||||
\(442\) | −409.102 | −0.0440249 | ||||||||
\(443\) | 13300.1 | 1.42643 | 0.713214 | − | 0.700946i | \(-0.247239\pi\) | ||||
0.713214 | + | 0.700946i | \(0.247239\pi\) | |||||||
\(444\) | 21356.8 | 2.28277 | ||||||||
\(445\) | −600.706 | −0.0639914 | ||||||||
\(446\) | 2459.86 | 0.261161 | ||||||||
\(447\) | −19669.5 | −2.08128 | ||||||||
\(448\) | −6037.49 | −0.636707 | ||||||||
\(449\) | 7189.18 | 0.755631 | 0.377815 | − | 0.925881i | \(-0.376675\pi\) | ||||
0.377815 | + | 0.925881i | \(0.376675\pi\) | |||||||
\(450\) | 7076.63 | 0.741323 | ||||||||
\(451\) | −12906.9 | −1.34759 | ||||||||
\(452\) | −7236.71 | −0.753066 | ||||||||
\(453\) | −9791.17 | −1.01552 | ||||||||
\(454\) | −2073.87 | −0.214387 | ||||||||
\(455\) | 2045.01 | 0.210707 | ||||||||
\(456\) | 8418.19 | 0.864513 | ||||||||
\(457\) | −4199.15 | −0.429820 | −0.214910 | − | 0.976634i | \(-0.568946\pi\) | ||||
−0.214910 | + | 0.976634i | \(0.568946\pi\) | |||||||
\(458\) | −2739.91 | −0.279537 | ||||||||
\(459\) | 4385.34 | 0.445948 | ||||||||
\(460\) | −1245.87 | −0.126280 | ||||||||
\(461\) | −1185.60 | −0.119781 | −0.0598905 | − | 0.998205i | \(-0.519075\pi\) | ||||
−0.0598905 | + | 0.998205i | \(0.519075\pi\) | |||||||
\(462\) | 8978.71 | 0.904172 | ||||||||
\(463\) | −2522.44 | −0.253192 | −0.126596 | − | 0.991954i | \(-0.540405\pi\) | ||||
−0.126596 | + | 0.991954i | \(0.540405\pi\) | |||||||
\(464\) | 5839.41 | 0.584241 | ||||||||
\(465\) | 5102.80 | 0.508897 | ||||||||
\(466\) | −4509.30 | −0.448261 | ||||||||
\(467\) | 9629.56 | 0.954182 | 0.477091 | − | 0.878854i | \(-0.341691\pi\) | ||||
0.477091 | + | 0.878854i | \(0.341691\pi\) | |||||||
\(468\) | 17467.4 | 1.72528 | ||||||||
\(469\) | 25847.9 | 2.54487 | ||||||||
\(470\) | −873.232 | −0.0857004 | ||||||||
\(471\) | −1758.94 | −0.172075 | ||||||||
\(472\) | −8941.11 | −0.871924 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −3428.73 | −0.332251 | ||||||||
\(475\) | 7743.97 | 0.748037 | ||||||||
\(476\) | 2330.06 | 0.224366 | ||||||||
\(477\) | 918.149 | 0.0881324 | ||||||||
\(478\) | 2653.49 | 0.253908 | ||||||||
\(479\) | 12358.5 | 1.17886 | 0.589431 | − | 0.807819i | \(-0.299352\pi\) | ||||
0.589431 | + | 0.807819i | \(0.299352\pi\) | |||||||
\(480\) | −2930.93 | −0.278704 | ||||||||
\(481\) | −11626.3 | −1.10211 | ||||||||
\(482\) | 4497.33 | 0.424995 | ||||||||
\(483\) | 21925.4 | 2.06551 | ||||||||
\(484\) | −1186.47 | −0.111426 | ||||||||
\(485\) | −390.348 | −0.0365459 | ||||||||
\(486\) | 6089.95 | 0.568407 | ||||||||
\(487\) | 2723.31 | 0.253398 | 0.126699 | − | 0.991941i | \(-0.459562\pi\) | ||||
0.126699 | + | 0.991941i | \(0.459562\pi\) | |||||||
\(488\) | −3202.49 | −0.297069 | ||||||||
\(489\) | −7976.25 | −0.737625 | ||||||||
\(490\) | 691.615 | 0.0637632 | ||||||||
\(491\) | −4199.46 | −0.385986 | −0.192993 | − | 0.981200i | \(-0.561819\pi\) | ||||
−0.192993 | + | 0.981200i | \(0.561819\pi\) | |||||||
\(492\) | −22977.7 | −2.10552 | ||||||||
\(493\) | −1565.04 | −0.142973 | ||||||||
\(494\) | −2168.38 | −0.197490 | ||||||||
\(495\) | −5100.91 | −0.463169 | ||||||||
\(496\) | 11809.5 | 1.06908 | ||||||||
\(497\) | 23801.3 | 2.14815 | ||||||||
\(498\) | 4671.30 | 0.420333 | ||||||||
\(499\) | 19985.3 | 1.79292 | 0.896458 | − | 0.443129i | \(-0.146132\pi\) | ||||
0.896458 | + | 0.443129i | \(0.146132\pi\) | |||||||
\(500\) | −3592.14 | −0.321291 | ||||||||
\(501\) | 3065.90 | 0.273402 | ||||||||
\(502\) | −4540.18 | −0.403661 | ||||||||
\(503\) | 520.717 | 0.0461583 | 0.0230792 | − | 0.999734i | \(-0.492653\pi\) | ||||
0.0230792 | + | 0.999734i | \(0.492653\pi\) | |||||||
\(504\) | 23852.0 | 2.10804 | ||||||||
\(505\) | 3491.83 | 0.307692 | ||||||||
\(506\) | 2977.82 | 0.261621 | ||||||||
\(507\) | 7588.18 | 0.664700 | ||||||||
\(508\) | 4986.60 | 0.435520 | ||||||||
\(509\) | 1746.69 | 0.152103 | 0.0760517 | − | 0.997104i | \(-0.475769\pi\) | ||||
0.0760517 | + | 0.997104i | \(0.475769\pi\) | |||||||
\(510\) | 212.684 | 0.0184663 | ||||||||
\(511\) | −9259.63 | −0.801609 | ||||||||
\(512\) | −11729.6 | −1.01246 | ||||||||
\(513\) | 23243.8 | 2.00046 | ||||||||
\(514\) | 764.013 | 0.0655626 | ||||||||
\(515\) | 64.9560 | 0.00555787 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18398.6 | −1.56512 | ||||||||
\(518\) | −7511.90 | −0.637169 | ||||||||
\(519\) | 28887.2 | 2.44318 | ||||||||
\(520\) | 1045.01 | 0.0881281 | ||||||||
\(521\) | −12223.8 | −1.02790 | −0.513948 | − | 0.857821i | \(-0.671818\pi\) | ||||
−0.513948 | + | 0.857821i | \(0.671818\pi\) | |||||||
\(522\) | −7580.40 | −0.635604 | ||||||||
\(523\) | −12923.8 | −1.08053 | −0.540265 | − | 0.841495i | \(-0.681676\pi\) | ||||
−0.540265 | + | 0.841495i | \(0.681676\pi\) | |||||||
\(524\) | 7285.51 | 0.607383 | ||||||||
\(525\) | 31076.5 | 2.58341 | ||||||||
\(526\) | 6974.88 | 0.578174 | ||||||||
\(527\) | −3165.10 | −0.261620 | ||||||||
\(528\) | −16719.9 | −1.37811 | ||||||||
\(529\) | −4895.37 | −0.402348 | ||||||||
\(530\) | 25.9905 | 0.00213011 | ||||||||
\(531\) | −42297.1 | −3.45676 | ||||||||
\(532\) | 12350.1 | 1.00648 | ||||||||
\(533\) | 12508.7 | 1.01654 | ||||||||
\(534\) | 2556.06 | 0.207138 | ||||||||
\(535\) | −2592.67 | −0.209516 | ||||||||
\(536\) | 13208.4 | 1.06439 | ||||||||
\(537\) | −33329.1 | −2.67832 | ||||||||
\(538\) | 1157.34 | 0.0927441 | ||||||||
\(539\) | 14572.0 | 1.16449 | ||||||||
\(540\) | −5300.30 | −0.422387 | ||||||||
\(541\) | −10061.3 | −0.799574 | −0.399787 | − | 0.916608i | \(-0.630916\pi\) | ||||
−0.399787 | + | 0.916608i | \(0.630916\pi\) | |||||||
\(542\) | −1043.85 | −0.0827252 | ||||||||
\(543\) | −74.1451 | −0.00585980 | ||||||||
\(544\) | 1817.96 | 0.143280 | ||||||||
\(545\) | 2403.27 | 0.188890 | ||||||||
\(546\) | −8701.71 | −0.682049 | ||||||||
\(547\) | −23951.3 | −1.87218 | −0.936090 | − | 0.351761i | \(-0.885583\pi\) | ||||
−0.936090 | + | 0.351761i | \(0.885583\pi\) | |||||||
\(548\) | −4549.40 | −0.354636 | ||||||||
\(549\) | −15149.8 | −1.17774 | ||||||||
\(550\) | 4220.68 | 0.327219 | ||||||||
\(551\) | −8295.25 | −0.641360 | ||||||||
\(552\) | 11204.0 | 0.863900 | ||||||||
\(553\) | −10631.0 | −0.817501 | ||||||||
\(554\) | −1883.50 | −0.144445 | ||||||||
\(555\) | 6044.31 | 0.462282 | ||||||||
\(556\) | 3141.75 | 0.239640 | ||||||||
\(557\) | 8803.19 | 0.669665 | 0.334832 | − | 0.942278i | \(-0.391320\pi\) | ||||
0.334832 | + | 0.942278i | \(0.391320\pi\) | |||||||
\(558\) | −15330.4 | −1.16306 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2460.49 | −0.185669 | ||||||||
\(561\) | 4481.15 | 0.337245 | ||||||||
\(562\) | −1041.92 | −0.0782038 | ||||||||
\(563\) | −21876.5 | −1.63762 | −0.818812 | − | 0.574061i | \(-0.805367\pi\) | ||||
−0.818812 | + | 0.574061i | \(0.805367\pi\) | |||||||
\(564\) | −32754.3 | −2.44540 | ||||||||
\(565\) | −2048.10 | −0.152503 | ||||||||
\(566\) | −4774.53 | −0.354573 | ||||||||
\(567\) | 46301.1 | 3.42939 | ||||||||
\(568\) | 12162.5 | 0.898466 | ||||||||
\(569\) | −22198.4 | −1.63551 | −0.817756 | − | 0.575565i | \(-0.804782\pi\) | ||||
−0.817756 | + | 0.575565i | \(0.804782\pi\) | |||||||
\(570\) | 1127.30 | 0.0828376 | ||||||||
\(571\) | −13270.8 | −0.972619 | −0.486310 | − | 0.873787i | \(-0.661657\pi\) | ||||
−0.486310 | + | 0.873787i | \(0.661657\pi\) | |||||||
\(572\) | 10418.0 | 0.761534 | ||||||||
\(573\) | 12475.9 | 0.909580 | ||||||||
\(574\) | 8082.03 | 0.587696 | ||||||||
\(575\) | 10306.6 | 0.747507 | ||||||||
\(576\) | −14594.9 | −1.05576 | ||||||||
\(577\) | −15373.6 | −1.10921 | −0.554603 | − | 0.832115i | \(-0.687130\pi\) | ||||
−0.554603 | + | 0.832115i | \(0.687130\pi\) | |||||||
\(578\) | 4303.59 | 0.309699 | ||||||||
\(579\) | 7288.85 | 0.523168 | ||||||||
\(580\) | 1891.57 | 0.135419 | ||||||||
\(581\) | 14483.7 | 1.03423 | ||||||||
\(582\) | 1660.97 | 0.118298 | ||||||||
\(583\) | 547.607 | 0.0389015 | ||||||||
\(584\) | −4731.71 | −0.335273 | ||||||||
\(585\) | 4943.54 | 0.349385 | ||||||||
\(586\) | 2780.41 | 0.196003 | ||||||||
\(587\) | 863.918 | 0.0607457 | 0.0303728 | − | 0.999539i | \(-0.490331\pi\) | ||||
0.0303728 | + | 0.999539i | \(0.490331\pi\) | |||||||
\(588\) | 25942.0 | 1.81944 | ||||||||
\(589\) | −16776.1 | −1.17360 | ||||||||
\(590\) | −1197.33 | −0.0835477 | ||||||||
\(591\) | 1921.95 | 0.133770 | ||||||||
\(592\) | 13988.4 | 0.971151 | ||||||||
\(593\) | −1387.83 | −0.0961071 | −0.0480536 | − | 0.998845i | \(-0.515302\pi\) | ||||
−0.0480536 | + | 0.998845i | \(0.515302\pi\) | |||||||
\(594\) | 12668.5 | 0.875078 | ||||||||
\(595\) | 659.444 | 0.0454363 | ||||||||
\(596\) | −14745.8 | −1.01344 | ||||||||
\(597\) | 18005.0 | 1.23433 | ||||||||
\(598\) | −2885.95 | −0.197350 | ||||||||
\(599\) | −23119.8 | −1.57704 | −0.788521 | − | 0.615008i | \(-0.789153\pi\) | ||||
−0.788521 | + | 0.615008i | \(0.789153\pi\) | |||||||
\(600\) | 15880.2 | 1.08051 | ||||||||
\(601\) | 29375.9 | 1.99379 | 0.996897 | − | 0.0787233i | \(-0.0250844\pi\) | ||||
0.996897 | + | 0.0787233i | \(0.0250844\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 62483.9 | 4.21980 | ||||||||
\(604\) | −7340.26 | −0.494488 | ||||||||
\(605\) | −335.789 | −0.0225649 | ||||||||
\(606\) | −14858.1 | −0.995987 | ||||||||
\(607\) | −10354.5 | −0.692383 | −0.346191 | − | 0.938164i | \(-0.612525\pi\) | ||||
−0.346191 | + | 0.938164i | \(0.612525\pi\) | |||||||
\(608\) | 9635.81 | 0.642736 | ||||||||
\(609\) | −33288.8 | −2.21499 | ||||||||
\(610\) | −428.853 | −0.0284651 | ||||||||
\(611\) | 17831.0 | 1.18063 | ||||||||
\(612\) | 5632.61 | 0.372034 | ||||||||
\(613\) | −9960.96 | −0.656312 | −0.328156 | − | 0.944624i | \(-0.606427\pi\) | ||||
−0.328156 | + | 0.944624i | \(0.606427\pi\) | |||||||
\(614\) | 577.334 | 0.0379467 | ||||||||
\(615\) | −6503.06 | −0.426388 | ||||||||
\(616\) | 14225.9 | 0.930485 | ||||||||
\(617\) | −13796.7 | −0.900218 | −0.450109 | − | 0.892974i | \(-0.648615\pi\) | ||||
−0.450109 | + | 0.892974i | \(0.648615\pi\) | |||||||
\(618\) | −276.394 | −0.0179906 | ||||||||
\(619\) | 25631.5 | 1.66432 | 0.832162 | − | 0.554533i | \(-0.187103\pi\) | ||||
0.832162 | + | 0.554533i | \(0.187103\pi\) | |||||||
\(620\) | 3825.47 | 0.247798 | ||||||||
\(621\) | 30935.7 | 1.99905 | ||||||||
\(622\) | −6381.42 | −0.411369 | ||||||||
\(623\) | 7925.27 | 0.509662 | ||||||||
\(624\) | 16204.1 | 1.03956 | ||||||||
\(625\) | 14091.5 | 0.901856 | ||||||||
\(626\) | −4947.00 | −0.315849 | ||||||||
\(627\) | 23751.7 | 1.51284 | ||||||||
\(628\) | −1318.64 | −0.0837890 | ||||||||
\(629\) | −3749.09 | −0.237656 | ||||||||
\(630\) | 3194.08 | 0.201992 | ||||||||
\(631\) | −17655.1 | −1.11385 | −0.556925 | − | 0.830563i | \(-0.688019\pi\) | ||||
−0.556925 | + | 0.830563i | \(0.688019\pi\) | |||||||
\(632\) | −5432.50 | −0.341920 | ||||||||
\(633\) | 8700.49 | 0.546309 | ||||||||
\(634\) | −5881.53 | −0.368431 | ||||||||
\(635\) | 1411.29 | 0.0881972 | ||||||||
\(636\) | 974.884 | 0.0607809 | ||||||||
\(637\) | −14122.4 | −0.878417 | ||||||||
\(638\) | −4521.15 | −0.280555 | ||||||||
\(639\) | 57536.5 | 3.56198 | ||||||||
\(640\) | −2859.67 | −0.176622 | ||||||||
\(641\) | 374.249 | 0.0230608 | 0.0115304 | − | 0.999934i | \(-0.496330\pi\) | ||||
0.0115304 | + | 0.999934i | \(0.496330\pi\) | |||||||
\(642\) | 11032.1 | 0.678194 | ||||||||
\(643\) | −18264.0 | −1.12016 | −0.560080 | − | 0.828438i | \(-0.689230\pi\) | ||||
−0.560080 | + | 0.828438i | \(0.689230\pi\) | |||||||
\(644\) | 16437.1 | 1.00576 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −699.227 | −0.0425863 | ||||||||
\(647\) | −1121.95 | −0.0681735 | −0.0340868 | − | 0.999419i | \(-0.510852\pi\) | ||||
−0.0340868 | + | 0.999419i | \(0.510852\pi\) | |||||||
\(648\) | 23660.0 | 1.43434 | ||||||||
\(649\) | −25227.1 | −1.52581 | ||||||||
\(650\) | −4090.47 | −0.246833 | ||||||||
\(651\) | −67322.6 | −4.05312 | ||||||||
\(652\) | −5979.65 | −0.359173 | ||||||||
\(653\) | −14019.2 | −0.840142 | −0.420071 | − | 0.907491i | \(-0.637995\pi\) | ||||
−0.420071 | + | 0.907491i | \(0.637995\pi\) | |||||||
\(654\) | −10226.2 | −0.611429 | ||||||||
\(655\) | 2061.92 | 0.123001 | ||||||||
\(656\) | −15050.1 | −0.895745 | ||||||||
\(657\) | −22384.0 | −1.32920 | ||||||||
\(658\) | 11520.8 | 0.682563 | ||||||||
\(659\) | −26897.3 | −1.58994 | −0.794969 | − | 0.606650i | \(-0.792513\pi\) | ||||
−0.794969 | + | 0.606650i | \(0.792513\pi\) | |||||||
\(660\) | −5416.11 | −0.319427 | ||||||||
\(661\) | 4456.60 | 0.262241 | 0.131121 | − | 0.991366i | \(-0.458142\pi\) | ||||
0.131121 | + | 0.991366i | \(0.458142\pi\) | |||||||
\(662\) | 3407.74 | 0.200069 | ||||||||
\(663\) | −4342.91 | −0.254396 | ||||||||
\(664\) | 7401.24 | 0.432566 | ||||||||
\(665\) | 3495.28 | 0.203821 | ||||||||
\(666\) | −18159.0 | −1.05653 | ||||||||
\(667\) | −11040.3 | −0.640905 | ||||||||
\(668\) | 2298.45 | 0.133128 | ||||||||
\(669\) | 26113.2 | 1.50911 | ||||||||
\(670\) | 1768.76 | 0.101990 | ||||||||
\(671\) | −9035.71 | −0.519851 | ||||||||
\(672\) | 38668.5 | 2.21975 | ||||||||
\(673\) | 12270.1 | 0.702787 | 0.351394 | − | 0.936228i | \(-0.385708\pi\) | ||||
0.351394 | + | 0.936228i | \(0.385708\pi\) | |||||||
\(674\) | −10554.5 | −0.603183 | ||||||||
\(675\) | 43847.5 | 2.50028 | ||||||||
\(676\) | 5688.71 | 0.323664 | ||||||||
\(677\) | 5587.24 | 0.317186 | 0.158593 | − | 0.987344i | \(-0.449304\pi\) | ||||
0.158593 | + | 0.987344i | \(0.449304\pi\) | |||||||
\(678\) | 8714.88 | 0.493647 | ||||||||
\(679\) | 5149.96 | 0.291071 | ||||||||
\(680\) | 336.978 | 0.0190037 | ||||||||
\(681\) | −22015.7 | −1.23883 | ||||||||
\(682\) | −9143.47 | −0.513375 | ||||||||
\(683\) | −16419.2 | −0.919860 | −0.459930 | − | 0.887955i | \(-0.652126\pi\) | ||||
−0.459930 | + | 0.887955i | \(0.652126\pi\) | |||||||
\(684\) | 29854.8 | 1.66890 | ||||||||
\(685\) | −1287.55 | −0.0718173 | ||||||||
\(686\) | −817.031 | −0.0454729 | ||||||||
\(687\) | −29086.1 | −1.61529 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −530.714 | −0.0293448 | ||||||||
\(690\) | 1500.35 | 0.0827788 | ||||||||
\(691\) | −21390.2 | −1.17760 | −0.588801 | − | 0.808278i | \(-0.700400\pi\) | ||||
−0.588801 | + | 0.808278i | \(0.700400\pi\) | |||||||
\(692\) | 21656.2 | 1.18966 | ||||||||
\(693\) | 67297.6 | 3.68892 | ||||||||
\(694\) | 10057.7 | 0.550125 | ||||||||
\(695\) | 889.165 | 0.0485294 | ||||||||
\(696\) | −17010.7 | −0.926422 | ||||||||
\(697\) | 4033.63 | 0.219203 | ||||||||
\(698\) | −1107.61 | −0.0600625 | ||||||||
\(699\) | −47869.5 | −2.59026 | ||||||||
\(700\) | 23297.5 | 1.25795 | ||||||||
\(701\) | 2029.82 | 0.109365 | 0.0546827 | − | 0.998504i | \(-0.482585\pi\) | ||||
0.0546827 | + | 0.998504i | \(0.482585\pi\) | |||||||
\(702\) | −12277.7 | −0.660103 | ||||||||
\(703\) | −19871.5 | −1.06610 | ||||||||
\(704\) | −8704.74 | −0.466012 | ||||||||
\(705\) | −9269.98 | −0.495217 | ||||||||
\(706\) | 1428.41 | 0.0761459 | ||||||||
\(707\) | −46068.6 | −2.45062 | ||||||||
\(708\) | −44910.8 | −2.38397 | ||||||||
\(709\) | 17269.2 | 0.914751 | 0.457376 | − | 0.889274i | \(-0.348789\pi\) | ||||
0.457376 | + | 0.889274i | \(0.348789\pi\) | |||||||
\(710\) | 1628.71 | 0.0860909 | ||||||||
\(711\) | −25699.2 | −1.35555 | ||||||||
\(712\) | 4049.84 | 0.213166 | ||||||||
\(713\) | −22327.7 | −1.17276 | ||||||||
\(714\) | −2806.00 | −0.147075 | ||||||||
\(715\) | 2948.46 | 0.154218 | ||||||||
\(716\) | −24986.2 | −1.30416 | ||||||||
\(717\) | 28168.7 | 1.46720 | ||||||||
\(718\) | 553.663 | 0.0287779 | ||||||||
\(719\) | 13317.0 | 0.690739 | 0.345369 | − | 0.938467i | \(-0.387754\pi\) | ||||
0.345369 | + | 0.938467i | \(0.387754\pi\) | |||||||
\(720\) | −5947.92 | −0.307869 | ||||||||
\(721\) | −856.981 | −0.0442658 | ||||||||
\(722\) | 2486.24 | 0.128155 | ||||||||
\(723\) | 47742.4 | 2.45582 | ||||||||
\(724\) | −55.5851 | −0.00285332 | ||||||||
\(725\) | −15648.3 | −0.801605 | ||||||||
\(726\) | 1428.81 | 0.0730416 | ||||||||
\(727\) | −22136.1 | −1.12927 | −0.564636 | − | 0.825340i | \(-0.690983\pi\) | ||||
−0.564636 | + | 0.825340i | \(0.690983\pi\) | |||||||
\(728\) | −13787.1 | −0.701899 | ||||||||
\(729\) | 18051.0 | 0.917084 | ||||||||
\(730\) | −633.634 | −0.0321258 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −16085.9 | −0.812231 | ||||||||
\(733\) | −17545.9 | −0.884139 | −0.442069 | − | 0.896981i | \(-0.645756\pi\) | ||||
−0.442069 | + | 0.896981i | \(0.645756\pi\) | |||||||
\(734\) | −1988.39 | −0.0999904 | ||||||||
\(735\) | 7341.99 | 0.368453 | ||||||||
\(736\) | 12824.5 | 0.642280 | ||||||||
\(737\) | 37267.0 | 1.86261 | ||||||||
\(738\) | 19537.2 | 0.974493 | ||||||||
\(739\) | −13702.8 | −0.682094 | −0.341047 | − | 0.940046i | \(-0.610781\pi\) | ||||
−0.341047 | + | 0.940046i | \(0.610781\pi\) | |||||||
\(740\) | 4531.31 | 0.225100 | ||||||||
\(741\) | −23018.9 | −1.14119 | ||||||||
\(742\) | −342.900 | −0.0169653 | ||||||||
\(743\) | −12371.8 | −0.610871 | −0.305435 | − | 0.952213i | \(-0.598802\pi\) | ||||
−0.305435 | + | 0.952213i | \(0.598802\pi\) | |||||||
\(744\) | −34402.1 | −1.69522 | ||||||||
\(745\) | −4173.30 | −0.205232 | ||||||||
\(746\) | −5659.52 | −0.277761 | ||||||||
\(747\) | 35012.5 | 1.71492 | ||||||||
\(748\) | 3359.44 | 0.164215 | ||||||||
\(749\) | 34205.7 | 1.66869 | ||||||||
\(750\) | 4325.87 | 0.210611 | ||||||||
\(751\) | 9938.30 | 0.482895 | 0.241447 | − | 0.970414i | \(-0.422378\pi\) | ||||
0.241447 | + | 0.970414i | \(0.422378\pi\) | |||||||
\(752\) | −21453.7 | −1.04034 | ||||||||
\(753\) | −48197.2 | −2.33254 | ||||||||
\(754\) | 4381.67 | 0.211633 | ||||||||
\(755\) | −2077.41 | −0.100139 | ||||||||
\(756\) | 69928.3 | 3.36411 | ||||||||
\(757\) | −10311.6 | −0.495088 | −0.247544 | − | 0.968877i | \(-0.579623\pi\) | ||||
−0.247544 | + | 0.968877i | \(0.579623\pi\) | |||||||
\(758\) | −2931.60 | −0.140475 | ||||||||
\(759\) | 31611.7 | 1.51177 | ||||||||
\(760\) | 1786.10 | 0.0852483 | ||||||||
\(761\) | 19234.7 | 0.916238 | 0.458119 | − | 0.888891i | \(-0.348523\pi\) | ||||
0.458119 | + | 0.888891i | \(0.348523\pi\) | |||||||
\(762\) | −6005.16 | −0.285491 | ||||||||
\(763\) | −31707.0 | −1.50442 | ||||||||
\(764\) | 9352.97 | 0.442904 | ||||||||
\(765\) | 1594.12 | 0.0753406 | ||||||||
\(766\) | 8070.05 | 0.380656 | ||||||||
\(767\) | 24448.8 | 1.15097 | ||||||||
\(768\) | −5086.54 | −0.238990 | ||||||||
\(769\) | 13634.6 | 0.639370 | 0.319685 | − | 0.947524i | \(-0.396423\pi\) | ||||
0.319685 | + | 0.947524i | \(0.396423\pi\) | |||||||
\(770\) | 1905.03 | 0.0891590 | ||||||||
\(771\) | 8110.55 | 0.378851 | ||||||||
\(772\) | 5464.31 | 0.254747 | ||||||||
\(773\) | 11204.3 | 0.521335 | 0.260667 | − | 0.965429i | \(-0.416057\pi\) | ||||
0.260667 | + | 0.965429i | \(0.416057\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31646.8 | −1.46682 | ||||||||
\(776\) | 2631.65 | 0.121740 | ||||||||
\(777\) | −79744.2 | −3.68186 | ||||||||
\(778\) | 4177.17 | 0.192492 | ||||||||
\(779\) | 21379.6 | 0.983318 | ||||||||
\(780\) | 5249.02 | 0.240955 | ||||||||
\(781\) | 34316.2 | 1.57225 | ||||||||
\(782\) | −930.618 | −0.0425561 | ||||||||
\(783\) | −46969.0 | −2.14372 | ||||||||
\(784\) | 16991.7 | 0.774038 | ||||||||
\(785\) | −373.197 | −0.0169681 | ||||||||
\(786\) | −8773.65 | −0.398150 | ||||||||
\(787\) | −40995.2 | −1.85683 | −0.928413 | − | 0.371551i | \(-0.878826\pi\) | ||||
−0.928413 | + | 0.371551i | \(0.878826\pi\) | |||||||
\(788\) | 1440.85 | 0.0651371 | ||||||||
\(789\) | 74043.4 | 3.34096 | ||||||||
\(790\) | −727.480 | −0.0327627 | ||||||||
\(791\) | 27021.2 | 1.21462 | ||||||||
\(792\) | 34389.3 | 1.54289 | ||||||||
\(793\) | 8756.96 | 0.392142 | ||||||||
\(794\) | −9787.31 | −0.437454 | ||||||||
\(795\) | 275.908 | 0.0123087 | ||||||||
\(796\) | 13498.0 | 0.601034 | ||||||||
\(797\) | −1380.09 | −0.0613368 | −0.0306684 | − | 0.999530i | \(-0.509764\pi\) | ||||
−0.0306684 | + | 0.999530i | \(0.509764\pi\) | |||||||
\(798\) | −14872.8 | −0.659762 | ||||||||
\(799\) | 5749.86 | 0.254588 | ||||||||
\(800\) | 18177.2 | 0.803325 | ||||||||
\(801\) | 19158.3 | 0.845100 | ||||||||
\(802\) | 11187.5 | 0.492573 | ||||||||
\(803\) | −13350.4 | −0.586705 | ||||||||
\(804\) | 66345.0 | 2.91021 | ||||||||
\(805\) | 4651.95 | 0.203677 | ||||||||
\(806\) | 8861.39 | 0.387257 | ||||||||
\(807\) | 12286.0 | 0.535918 | ||||||||
\(808\) | −23541.2 | −1.02497 | ||||||||
\(809\) | −18158.2 | −0.789131 | −0.394566 | − | 0.918868i | \(-0.629105\pi\) | ||||
−0.394566 | + | 0.918868i | \(0.629105\pi\) | |||||||
\(810\) | 3168.37 | 0.137439 | ||||||||
\(811\) | −478.154 | −0.0207031 | −0.0103516 | − | 0.999946i | \(-0.503295\pi\) | ||||
−0.0103516 | + | 0.999946i | \(0.503295\pi\) | |||||||
\(812\) | −24956.0 | −1.07855 | ||||||||
\(813\) | −11081.2 | −0.478024 | ||||||||
\(814\) | −10830.5 | −0.466350 | ||||||||
\(815\) | −1692.34 | −0.0727361 | ||||||||
\(816\) | 5225.25 | 0.224167 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −7141.88 | −0.305269 | ||||||||
\(819\) | −65221.4 | −2.78269 | ||||||||
\(820\) | −4875.22 | −0.207622 | ||||||||
\(821\) | 7722.38 | 0.328274 | 0.164137 | − | 0.986438i | \(-0.447516\pi\) | ||||
0.164137 | + | 0.986438i | \(0.447516\pi\) | |||||||
\(822\) | 5478.66 | 0.232470 | ||||||||
\(823\) | −1765.67 | −0.0747842 | −0.0373921 | − | 0.999301i | \(-0.511905\pi\) | ||||
−0.0373921 | + | 0.999301i | \(0.511905\pi\) | |||||||
\(824\) | −437.920 | −0.0185142 | ||||||||
\(825\) | 44805.6 | 1.89082 | ||||||||
\(826\) | 15796.6 | 0.665418 | ||||||||
\(827\) | −19472.6 | −0.818776 | −0.409388 | − | 0.912360i | \(-0.634258\pi\) | ||||
−0.409388 | + | 0.912360i | \(0.634258\pi\) | |||||||
\(828\) | 39734.5 | 1.66772 | ||||||||
\(829\) | 26318.0 | 1.10261 | 0.551304 | − | 0.834304i | \(-0.314130\pi\) | ||||
0.551304 | + | 0.834304i | \(0.314130\pi\) | |||||||
\(830\) | 991.118 | 0.0414485 | ||||||||
\(831\) | −19994.7 | −0.834669 | ||||||||
\(832\) | 8436.20 | 0.351530 | ||||||||
\(833\) | −4553.99 | −0.189420 | ||||||||
\(834\) | −3783.48 | −0.157088 | ||||||||
\(835\) | 650.498 | 0.0269598 | ||||||||
\(836\) | 17806.2 | 0.736650 | ||||||||
\(837\) | −94989.0 | −3.92270 | ||||||||
\(838\) | 11647.9 | 0.480156 | ||||||||
\(839\) | 6566.60 | 0.270208 | 0.135104 | − | 0.990831i | \(-0.456863\pi\) | ||||
0.135104 | + | 0.990831i | \(0.456863\pi\) | |||||||
\(840\) | 7167.63 | 0.294413 | ||||||||
\(841\) | −7626.71 | −0.312711 | ||||||||
\(842\) | 14512.8 | 0.593994 | ||||||||
\(843\) | −11060.7 | −0.451898 | ||||||||
\(844\) | 6522.59 | 0.266015 | ||||||||
\(845\) | 1610.00 | 0.0655450 | ||||||||
\(846\) | 27850.0 | 1.13180 | ||||||||
\(847\) | 4430.15 | 0.179719 | ||||||||
\(848\) | 638.538 | 0.0258579 | ||||||||
\(849\) | −50685.0 | −2.04889 | ||||||||
\(850\) | −1319.04 | −0.0532265 | ||||||||
\(851\) | −26447.4 | −1.06534 | ||||||||
\(852\) | 61091.8 | 2.45654 | ||||||||
\(853\) | 39036.9 | 1.56694 | 0.783468 | − | 0.621432i | \(-0.213449\pi\) | ||||
0.783468 | + | 0.621432i | \(0.213449\pi\) | |||||||
\(854\) | 5657.96 | 0.226711 | ||||||||
\(855\) | 8449.39 | 0.337968 | ||||||||
\(856\) | 17479.3 | 0.697931 | ||||||||
\(857\) | −6060.17 | −0.241554 | −0.120777 | − | 0.992680i | \(-0.538539\pi\) | ||||
−0.120777 | + | 0.992680i | \(0.538539\pi\) | |||||||
\(858\) | −12546.0 | −0.499198 | ||||||||
\(859\) | 13664.8 | 0.542767 | 0.271383 | − | 0.962471i | \(-0.412519\pi\) | ||||
0.271383 | + | 0.962471i | \(0.412519\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 85796.5 | 3.39598 | ||||||||
\(862\) | 8375.80 | 0.330952 | ||||||||
\(863\) | −8805.11 | −0.347311 | −0.173655 | − | 0.984806i | \(-0.555558\pi\) | ||||
−0.173655 | + | 0.984806i | \(0.555558\pi\) | |||||||
\(864\) | 54559.4 | 2.14832 | ||||||||
\(865\) | 6129.05 | 0.240918 | ||||||||
\(866\) | 164.762 | 0.00646517 | ||||||||
\(867\) | 45685.7 | 1.78958 | ||||||||
\(868\) | −50470.5 | −1.97359 | ||||||||
\(869\) | −15327.6 | −0.598337 | ||||||||
\(870\) | −2277.95 | −0.0887697 | ||||||||
\(871\) | −36117.3 | −1.40504 | ||||||||
\(872\) | −16202.4 | −0.629223 | ||||||||
\(873\) | 12449.3 | 0.482642 | ||||||||
\(874\) | −4932.60 | −0.190901 | ||||||||
\(875\) | 13412.7 | 0.518208 | ||||||||
\(876\) | −23767.1 | −0.916686 | ||||||||
\(877\) | 24442.4 | 0.941120 | 0.470560 | − | 0.882368i | \(-0.344052\pi\) | ||||
0.470560 | + | 0.882368i | \(0.344052\pi\) | |||||||
\(878\) | 5241.80 | 0.201483 | ||||||||
\(879\) | 29516.1 | 1.13260 | ||||||||
\(880\) | −3547.49 | −0.135893 | ||||||||
\(881\) | −21839.8 | −0.835190 | −0.417595 | − | 0.908633i | \(-0.637127\pi\) | ||||
−0.417595 | + | 0.908633i | \(0.637127\pi\) | |||||||
\(882\) | −22057.7 | −0.842086 | ||||||||
\(883\) | 17757.9 | 0.676785 | 0.338393 | − | 0.941005i | \(-0.390117\pi\) | ||||
0.338393 | + | 0.941005i | \(0.390117\pi\) | |||||||
\(884\) | −3255.80 | −0.123874 | ||||||||
\(885\) | −12710.5 | −0.482777 | ||||||||
\(886\) | −12007.5 | −0.455304 | ||||||||
\(887\) | −42106.9 | −1.59392 | −0.796962 | − | 0.604030i | \(-0.793561\pi\) | ||||
−0.796962 | + | 0.604030i | \(0.793561\pi\) | |||||||
\(888\) | −40749.6 | −1.53994 | ||||||||
\(889\) | −18619.5 | −0.702449 | ||||||||
\(890\) | 542.324 | 0.0204256 | ||||||||
\(891\) | 66756.1 | 2.51000 | ||||||||
\(892\) | 19576.5 | 0.734833 | ||||||||
\(893\) | 30476.3 | 1.14205 | ||||||||
\(894\) | 17757.8 | 0.664329 | ||||||||
\(895\) | −7071.50 | −0.264105 | ||||||||
\(896\) | 37728.3 | 1.40671 | ||||||||
\(897\) | −30636.4 | −1.14038 | ||||||||
\(898\) | −6490.47 | −0.241191 | ||||||||
\(899\) | 33899.7 | 1.25764 | ||||||||
\(900\) | 56318.7 | 2.08588 | ||||||||
\(901\) | −171.137 | −0.00632784 | ||||||||
\(902\) | 11652.5 | 0.430140 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13807.9 | 0.508014 | ||||||||
\(905\) | −15.7315 | −0.000577826 0 | ||||||||
\(906\) | 8839.58 | 0.324145 | ||||||||
\(907\) | 1377.33 | 0.0504227 | 0.0252114 | − | 0.999682i | \(-0.491974\pi\) | ||||
0.0252114 | + | 0.999682i | \(0.491974\pi\) | |||||||
\(908\) | −16504.7 | −0.603225 | ||||||||
\(909\) | −111365. | −4.06352 | ||||||||
\(910\) | −1846.26 | −0.0672559 | ||||||||
\(911\) | −39864.1 | −1.44979 | −0.724895 | − | 0.688860i | \(-0.758112\pi\) | ||||
−0.724895 | + | 0.688860i | \(0.758112\pi\) | |||||||
\(912\) | 27695.6 | 1.00559 | ||||||||
\(913\) | 20882.4 | 0.756961 | ||||||||
\(914\) | 3791.04 | 0.137195 | ||||||||
\(915\) | −4552.58 | −0.164485 | ||||||||
\(916\) | −21805.3 | −0.786537 | ||||||||
\(917\) | −27203.4 | −0.979646 | ||||||||
\(918\) | −3959.13 | −0.142343 | ||||||||
\(919\) | 5830.88 | 0.209296 | 0.104648 | − | 0.994509i | \(-0.466628\pi\) | ||||
0.104648 | + | 0.994509i | \(0.466628\pi\) | |||||||
\(920\) | 2377.17 | 0.0851879 | ||||||||
\(921\) | 6128.81 | 0.219274 | ||||||||
\(922\) | 1070.38 | 0.0382331 | ||||||||
\(923\) | −33257.5 | −1.18601 | ||||||||
\(924\) | 71456.2 | 2.54409 | ||||||||
\(925\) | −37485.9 | −1.33246 | ||||||||
\(926\) | 2277.29 | 0.0808169 | ||||||||
\(927\) | −2071.64 | −0.0733998 | ||||||||
\(928\) | −19471.2 | −0.688763 | ||||||||
\(929\) | −4121.82 | −0.145568 | −0.0727840 | − | 0.997348i | \(-0.523188\pi\) | ||||
−0.0727840 | + | 0.997348i | \(0.523188\pi\) | |||||||
\(930\) | −4606.87 | −0.162436 | ||||||||
\(931\) | −24137.7 | −0.849712 | ||||||||
\(932\) | −35886.8 | −1.26128 | ||||||||
\(933\) | −67743.3 | −2.37708 | ||||||||
\(934\) | −8693.67 | −0.304567 | ||||||||
\(935\) | 950.774 | 0.0332552 | ||||||||
\(936\) | −33328.4 | −1.16386 | ||||||||
\(937\) | 33608.5 | 1.17176 | 0.585881 | − | 0.810397i | \(-0.300749\pi\) | ||||
0.585881 | + | 0.810397i | \(0.300749\pi\) | |||||||
\(938\) | −23335.7 | −0.812302 | ||||||||
\(939\) | −52515.9 | −1.82512 | ||||||||
\(940\) | −6949.53 | −0.241137 | ||||||||
\(941\) | −30075.8 | −1.04192 | −0.520958 | − | 0.853582i | \(-0.674425\pi\) | ||||
−0.520958 | + | 0.853582i | \(0.674425\pi\) | |||||||
\(942\) | 1587.99 | 0.0549251 | ||||||||
\(943\) | 28454.7 | 0.982621 | ||||||||
\(944\) | −29416.1 | −1.01421 | ||||||||
\(945\) | 19790.8 | 0.681265 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8945.08 | 0.306944 | 0.153472 | − | 0.988153i | \(-0.450955\pi\) | ||||
0.153472 | + | 0.988153i | \(0.450955\pi\) | |||||||
\(948\) | −27287.2 | −0.934860 | ||||||||
\(949\) | 12938.5 | 0.442573 | ||||||||
\(950\) | −6991.34 | −0.238767 | ||||||||
\(951\) | −62436.6 | −2.12897 | ||||||||
\(952\) | −4445.84 | −0.151356 | ||||||||
\(953\) | −51373.5 | −1.74622 | −0.873112 | − | 0.487519i | \(-0.837902\pi\) | ||||
−0.873112 | + | 0.487519i | \(0.837902\pi\) | |||||||
\(954\) | −828.915 | −0.0281311 | ||||||||
\(955\) | 2647.04 | 0.0896924 | ||||||||
\(956\) | 21117.5 | 0.714425 | ||||||||
\(957\) | −47995.2 | −1.62118 | ||||||||
\(958\) | −11157.4 | −0.376283 | ||||||||
\(959\) | 16987.0 | 0.571991 | ||||||||
\(960\) | −4385.82 | −0.147450 | ||||||||
\(961\) | 38767.0 | 1.30130 | ||||||||
\(962\) | 10496.4 | 0.351785 | ||||||||
\(963\) | 82687.9 | 2.76696 | ||||||||
\(964\) | 35791.5 | 1.19582 | ||||||||
\(965\) | 1546.49 | 0.0515888 | ||||||||
\(966\) | −19794.5 | −0.659294 | ||||||||
\(967\) | 22479.1 | 0.747549 | 0.373775 | − | 0.927520i | \(-0.378063\pi\) | ||||
0.373775 | + | 0.927520i | \(0.378063\pi\) | |||||||
\(968\) | 2263.82 | 0.0751673 | ||||||||
\(969\) | −7422.80 | −0.246083 | ||||||||
\(970\) | 352.410 | 0.0116652 | ||||||||
\(971\) | 45003.4 | 1.48736 | 0.743680 | − | 0.668536i | \(-0.233079\pi\) | ||||
0.743680 | + | 0.668536i | \(0.233079\pi\) | |||||||
\(972\) | 48466.3 | 1.59934 | ||||||||
\(973\) | −11731.0 | −0.386514 | ||||||||
\(974\) | −2458.63 | −0.0808826 | ||||||||
\(975\) | −43423.3 | −1.42632 | ||||||||
\(976\) | −10536.1 | −0.345545 | ||||||||
\(977\) | −21946.4 | −0.718657 | −0.359329 | − | 0.933211i | \(-0.616994\pi\) | ||||
−0.359329 | + | 0.933211i | \(0.616994\pi\) | |||||||
\(978\) | 7201.05 | 0.235444 | ||||||||
\(979\) | 11426.5 | 0.373026 | ||||||||
\(980\) | 5504.15 | 0.179412 | ||||||||
\(981\) | −76647.5 | −2.49456 | ||||||||
\(982\) | 3791.32 | 0.123204 | ||||||||
\(983\) | 950.865 | 0.0308524 | 0.0154262 | − | 0.999881i | \(-0.495089\pi\) | ||||
0.0154262 | + | 0.999881i | \(0.495089\pi\) | |||||||
\(984\) | 43842.3 | 1.42037 | ||||||||
\(985\) | 407.783 | 0.0131909 | ||||||||
\(986\) | 1412.93 | 0.0456359 | ||||||||
\(987\) | 122301. | 3.94417 | ||||||||
\(988\) | −17256.8 | −0.555681 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 4605.16 | 0.147840 | ||||||||
\(991\) | 51696.8 | 1.65712 | 0.828559 | − | 0.559901i | \(-0.189161\pi\) | ||||
0.828559 | + | 0.559901i | \(0.189161\pi\) | |||||||
\(992\) | −39378.1 | −1.26034 | ||||||||
\(993\) | 36175.6 | 1.15609 | ||||||||
\(994\) | −21488.0 | −0.685674 | ||||||||
\(995\) | 3820.15 | 0.121715 | ||||||||
\(996\) | 37176.1 | 1.18270 | ||||||||
\(997\) | 44474.6 | 1.41276 | 0.706381 | − | 0.707832i | \(-0.250326\pi\) | ||||
0.706381 | + | 0.707832i | \(0.250326\pi\) | |||||||
\(998\) | −18042.9 | −0.572284 | ||||||||
\(999\) | −112515. | −3.56339 |
(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.i.1.24 | ✓ | 50 | |
43.42 | odd | 2 | 1849.4.a.j.1.27 | yes | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.24 | ✓ | 50 | 1.1 | even | 1 | trivial | |
1849.4.a.j.1.27 | yes | 50 | 43.42 | odd | 2 |