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 | 1.44 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.78088 | 1.69030 | 0.845148 | − | 0.534533i | \(-0.179513\pi\) | ||||
0.845148 | + | 0.534533i | \(0.179513\pi\) | |||||||
\(3\) | −1.15757 | −0.222774 | −0.111387 | − | 0.993777i | \(-0.535529\pi\) | ||||
−0.111387 | + | 0.993777i | \(0.535529\pi\) | |||||||
\(4\) | 14.8568 | 1.85710 | ||||||||
\(5\) | 21.3015 | 1.90527 | 0.952633 | − | 0.304122i | \(-0.0983630\pi\) | ||||
0.952633 | + | 0.304122i | \(0.0983630\pi\) | |||||||
\(6\) | −5.53419 | −0.376554 | ||||||||
\(7\) | −24.0536 | −1.29877 | −0.649386 | − | 0.760459i | \(-0.724974\pi\) | ||||
−0.649386 | + | 0.760459i | \(0.724974\pi\) | |||||||
\(8\) | 32.7814 | 1.44875 | ||||||||
\(9\) | −25.6600 | −0.950372 | ||||||||
\(10\) | 101.840 | 3.22046 | ||||||||
\(11\) | 17.5943 | 0.482262 | 0.241131 | − | 0.970493i | \(-0.422482\pi\) | ||||
0.241131 | + | 0.970493i | \(0.422482\pi\) | |||||||
\(12\) | −17.1977 | −0.413713 | ||||||||
\(13\) | −56.9423 | −1.21484 | −0.607422 | − | 0.794380i | \(-0.707796\pi\) | ||||
−0.607422 | + | 0.794380i | \(0.707796\pi\) | |||||||
\(14\) | −114.997 | −2.19531 | ||||||||
\(15\) | −24.6580 | −0.424444 | ||||||||
\(16\) | 37.8697 | 0.591714 | ||||||||
\(17\) | −74.3144 | −1.06023 | −0.530114 | − | 0.847926i | \(-0.677851\pi\) | ||||
−0.530114 | + | 0.847926i | \(0.677851\pi\) | |||||||
\(18\) | −122.677 | −1.60641 | ||||||||
\(19\) | −100.891 | −1.21821 | −0.609104 | − | 0.793090i | \(-0.708471\pi\) | ||||
−0.609104 | + | 0.793090i | \(0.708471\pi\) | |||||||
\(20\) | 316.472 | 3.53827 | ||||||||
\(21\) | 27.8436 | 0.289332 | ||||||||
\(22\) | 84.1161 | 0.815164 | ||||||||
\(23\) | −13.9922 | −0.126851 | −0.0634254 | − | 0.997987i | \(-0.520202\pi\) | ||||
−0.0634254 | + | 0.997987i | \(0.520202\pi\) | |||||||
\(24\) | −37.9467 | −0.322743 | ||||||||
\(25\) | 328.755 | 2.63004 | ||||||||
\(26\) | −272.234 | −2.05344 | ||||||||
\(27\) | 60.9576 | 0.434492 | ||||||||
\(28\) | −357.359 | −2.41195 | ||||||||
\(29\) | −87.1198 | −0.557853 | −0.278927 | − | 0.960312i | \(-0.589979\pi\) | ||||
−0.278927 | + | 0.960312i | \(0.589979\pi\) | |||||||
\(30\) | −117.887 | −0.717435 | ||||||||
\(31\) | −127.229 | −0.737131 | −0.368566 | − | 0.929602i | \(-0.620151\pi\) | ||||
−0.368566 | + | 0.929602i | \(0.620151\pi\) | |||||||
\(32\) | −81.2011 | −0.448577 | ||||||||
\(33\) | −20.3666 | −0.107435 | ||||||||
\(34\) | −355.288 | −1.79210 | ||||||||
\(35\) | −512.378 | −2.47451 | ||||||||
\(36\) | −381.226 | −1.76493 | ||||||||
\(37\) | −125.930 | −0.559535 | −0.279767 | − | 0.960068i | \(-0.590257\pi\) | ||||
−0.279767 | + | 0.960068i | \(0.590257\pi\) | |||||||
\(38\) | −482.347 | −2.05913 | ||||||||
\(39\) | 65.9146 | 0.270635 | ||||||||
\(40\) | 698.294 | 2.76025 | ||||||||
\(41\) | −82.7414 | −0.315172 | −0.157586 | − | 0.987505i | \(-0.550371\pi\) | ||||
−0.157586 | + | 0.987505i | \(0.550371\pi\) | |||||||
\(42\) | 133.117 | 0.489057 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 261.394 | 0.895607 | ||||||||
\(45\) | −546.598 | −1.81071 | ||||||||
\(46\) | −66.8948 | −0.214415 | ||||||||
\(47\) | −71.5573 | −0.222079 | −0.111039 | − | 0.993816i | \(-0.535418\pi\) | ||||
−0.111039 | + | 0.993816i | \(0.535418\pi\) | |||||||
\(48\) | −43.8367 | −0.131818 | ||||||||
\(49\) | 235.575 | 0.686807 | ||||||||
\(50\) | 1571.74 | 4.44554 | ||||||||
\(51\) | 86.0239 | 0.236191 | ||||||||
\(52\) | −845.980 | −2.25608 | ||||||||
\(53\) | 152.062 | 0.394101 | 0.197050 | − | 0.980393i | \(-0.436864\pi\) | ||||
0.197050 | + | 0.980393i | \(0.436864\pi\) | |||||||
\(54\) | 291.431 | 0.734420 | ||||||||
\(55\) | 374.785 | 0.918837 | ||||||||
\(56\) | −788.511 | −1.88159 | ||||||||
\(57\) | 116.788 | 0.271385 | ||||||||
\(58\) | −416.509 | −0.942936 | ||||||||
\(59\) | 319.919 | 0.705931 | 0.352965 | − | 0.935636i | \(-0.385173\pi\) | ||||
0.352965 | + | 0.935636i | \(0.385173\pi\) | |||||||
\(60\) | −366.338 | −0.788234 | ||||||||
\(61\) | 353.020 | 0.740977 | 0.370488 | − | 0.928837i | \(-0.379190\pi\) | ||||
0.370488 | + | 0.928837i | \(0.379190\pi\) | |||||||
\(62\) | −608.268 | −1.24597 | ||||||||
\(63\) | 617.216 | 1.23432 | ||||||||
\(64\) | −691.170 | −1.34994 | ||||||||
\(65\) | −1212.96 | −2.31460 | ||||||||
\(66\) | −97.3701 | −0.181597 | ||||||||
\(67\) | 37.2004 | 0.0678320 | 0.0339160 | − | 0.999425i | \(-0.489202\pi\) | ||||
0.0339160 | + | 0.999425i | \(0.489202\pi\) | |||||||
\(68\) | −1104.07 | −1.96895 | ||||||||
\(69\) | 16.1969 | 0.0282591 | ||||||||
\(70\) | −2449.62 | −4.18264 | ||||||||
\(71\) | 781.921 | 1.30700 | 0.653500 | − | 0.756927i | \(-0.273300\pi\) | ||||
0.653500 | + | 0.756927i | \(0.273300\pi\) | |||||||
\(72\) | −841.173 | −1.37685 | ||||||||
\(73\) | −1171.74 | −1.87866 | −0.939331 | − | 0.343013i | \(-0.888552\pi\) | ||||
−0.939331 | + | 0.343013i | \(0.888552\pi\) | |||||||
\(74\) | −602.056 | −0.945779 | ||||||||
\(75\) | −380.556 | −0.585905 | ||||||||
\(76\) | −1498.91 | −2.26233 | ||||||||
\(77\) | −423.206 | −0.626347 | ||||||||
\(78\) | 315.130 | 0.457454 | ||||||||
\(79\) | 841.963 | 1.19909 | 0.599546 | − | 0.800340i | \(-0.295348\pi\) | ||||
0.599546 | + | 0.800340i | \(0.295348\pi\) | |||||||
\(80\) | 806.682 | 1.12737 | ||||||||
\(81\) | 622.259 | 0.853578 | ||||||||
\(82\) | −395.577 | −0.532733 | ||||||||
\(83\) | −1113.00 | −1.47190 | −0.735950 | − | 0.677036i | \(-0.763264\pi\) | ||||
−0.735950 | + | 0.677036i | \(0.763264\pi\) | |||||||
\(84\) | 413.667 | 0.537319 | ||||||||
\(85\) | −1583.01 | −2.02002 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 100.847 | 0.124275 | ||||||||
\(88\) | 576.766 | 0.698675 | ||||||||
\(89\) | −308.616 | −0.367564 | −0.183782 | − | 0.982967i | \(-0.558834\pi\) | ||||
−0.183782 | + | 0.982967i | \(0.558834\pi\) | |||||||
\(90\) | −2613.22 | −3.06064 | ||||||||
\(91\) | 1369.67 | 1.57780 | ||||||||
\(92\) | −207.879 | −0.235574 | ||||||||
\(93\) | 147.277 | 0.164214 | ||||||||
\(94\) | −342.106 | −0.375379 | ||||||||
\(95\) | −2149.13 | −2.32101 | ||||||||
\(96\) | 93.9957 | 0.0999312 | ||||||||
\(97\) | 1108.36 | 1.16017 | 0.580085 | − | 0.814556i | \(-0.303019\pi\) | ||||
0.580085 | + | 0.814556i | \(0.303019\pi\) | |||||||
\(98\) | 1126.25 | 1.16091 | ||||||||
\(99\) | −451.470 | −0.458328 | ||||||||
\(100\) | 4884.24 | 4.88424 | ||||||||
\(101\) | −774.120 | −0.762652 | −0.381326 | − | 0.924441i | \(-0.624532\pi\) | ||||
−0.381326 | + | 0.924441i | \(0.624532\pi\) | |||||||
\(102\) | 411.270 | 0.399233 | ||||||||
\(103\) | 317.377 | 0.303612 | 0.151806 | − | 0.988410i | \(-0.451491\pi\) | ||||
0.151806 | + | 0.988410i | \(0.451491\pi\) | |||||||
\(104\) | −1866.65 | −1.76000 | ||||||||
\(105\) | 593.112 | 0.551255 | ||||||||
\(106\) | 726.990 | 0.666146 | ||||||||
\(107\) | 648.591 | 0.585997 | 0.292998 | − | 0.956113i | \(-0.405347\pi\) | ||||
0.292998 | + | 0.956113i | \(0.405347\pi\) | |||||||
\(108\) | 905.633 | 0.806894 | ||||||||
\(109\) | 575.465 | 0.505684 | 0.252842 | − | 0.967508i | \(-0.418635\pi\) | ||||
0.252842 | + | 0.967508i | \(0.418635\pi\) | |||||||
\(110\) | 1791.80 | 1.55311 | ||||||||
\(111\) | 145.773 | 0.124650 | ||||||||
\(112\) | −910.902 | −0.768501 | ||||||||
\(113\) | −509.868 | −0.424463 | −0.212232 | − | 0.977219i | \(-0.568073\pi\) | ||||
−0.212232 | + | 0.977219i | \(0.568073\pi\) | |||||||
\(114\) | 558.349 | 0.458721 | ||||||||
\(115\) | −298.055 | −0.241685 | ||||||||
\(116\) | −1294.32 | −1.03599 | ||||||||
\(117\) | 1461.14 | 1.15455 | ||||||||
\(118\) | 1529.49 | 1.19323 | ||||||||
\(119\) | 1787.53 | 1.37699 | ||||||||
\(120\) | −808.323 | −0.614912 | ||||||||
\(121\) | −1021.44 | −0.767424 | ||||||||
\(122\) | 1687.75 | 1.25247 | ||||||||
\(123\) | 95.7788 | 0.0702121 | ||||||||
\(124\) | −1890.22 | −1.36892 | ||||||||
\(125\) | 4340.29 | 3.10566 | ||||||||
\(126\) | 2950.83 | 2.08636 | ||||||||
\(127\) | 2623.19 | 1.83284 | 0.916421 | − | 0.400217i | \(-0.131065\pi\) | ||||
0.916421 | + | 0.400217i | \(0.131065\pi\) | |||||||
\(128\) | −2654.79 | −1.83322 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5799.01 | −3.91236 | ||||||||
\(131\) | −2604.53 | −1.73709 | −0.868544 | − | 0.495611i | \(-0.834944\pi\) | ||||
−0.868544 | + | 0.495611i | \(0.834944\pi\) | |||||||
\(132\) | −302.582 | −0.199518 | ||||||||
\(133\) | 2426.79 | 1.58217 | ||||||||
\(134\) | 177.850 | 0.114656 | ||||||||
\(135\) | 1298.49 | 0.827823 | ||||||||
\(136\) | −2436.13 | −1.53600 | ||||||||
\(137\) | 665.268 | 0.414873 | 0.207437 | − | 0.978248i | \(-0.433488\pi\) | ||||
0.207437 | + | 0.978248i | \(0.433488\pi\) | |||||||
\(138\) | 77.4353 | 0.0477662 | ||||||||
\(139\) | −876.154 | −0.534636 | −0.267318 | − | 0.963608i | \(-0.586137\pi\) | ||||
−0.267318 | + | 0.963608i | \(0.586137\pi\) | |||||||
\(140\) | −7612.29 | −4.59540 | ||||||||
\(141\) | 82.8324 | 0.0494734 | ||||||||
\(142\) | 3738.27 | 2.20921 | ||||||||
\(143\) | −1001.86 | −0.585872 | ||||||||
\(144\) | −971.738 | −0.562348 | ||||||||
\(145\) | −1855.78 | −1.06286 | ||||||||
\(146\) | −5601.96 | −3.17549 | ||||||||
\(147\) | −272.694 | −0.153003 | ||||||||
\(148\) | −1870.92 | −1.03911 | ||||||||
\(149\) | 1157.27 | 0.636289 | 0.318144 | − | 0.948042i | \(-0.396940\pi\) | ||||
0.318144 | + | 0.948042i | \(0.396940\pi\) | |||||||
\(150\) | −1819.39 | −0.990352 | ||||||||
\(151\) | 1380.36 | 0.743922 | 0.371961 | − | 0.928248i | \(-0.378686\pi\) | ||||
0.371961 | + | 0.928248i | \(0.378686\pi\) | |||||||
\(152\) | −3307.35 | −1.76488 | ||||||||
\(153\) | 1906.91 | 1.00761 | ||||||||
\(154\) | −2023.29 | −1.05871 | ||||||||
\(155\) | −2710.18 | −1.40443 | ||||||||
\(156\) | 979.279 | 0.502596 | ||||||||
\(157\) | 2859.38 | 1.45352 | 0.726762 | − | 0.686890i | \(-0.241024\pi\) | ||||
0.726762 | + | 0.686890i | \(0.241024\pi\) | |||||||
\(158\) | 4025.32 | 2.02682 | ||||||||
\(159\) | −176.022 | −0.0877954 | ||||||||
\(160\) | −1729.71 | −0.854658 | ||||||||
\(161\) | 336.562 | 0.164750 | ||||||||
\(162\) | 2974.94 | 1.44280 | ||||||||
\(163\) | 1990.78 | 0.956627 | 0.478314 | − | 0.878189i | \(-0.341248\pi\) | ||||
0.478314 | + | 0.878189i | \(0.341248\pi\) | |||||||
\(164\) | −1229.27 | −0.585305 | ||||||||
\(165\) | −433.839 | −0.204693 | ||||||||
\(166\) | −5321.12 | −2.48794 | ||||||||
\(167\) | −1753.53 | −0.812527 | −0.406263 | − | 0.913756i | \(-0.633168\pi\) | ||||
−0.406263 | + | 0.913756i | \(0.633168\pi\) | |||||||
\(168\) | 912.754 | 0.419170 | ||||||||
\(169\) | 1045.43 | 0.475844 | ||||||||
\(170\) | −7568.17 | −3.41443 | ||||||||
\(171\) | 2588.86 | 1.15775 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1857.37 | 0.816263 | 0.408131 | − | 0.912923i | \(-0.366180\pi\) | ||||
0.408131 | + | 0.912923i | \(0.366180\pi\) | |||||||
\(174\) | 482.137 | 0.210062 | ||||||||
\(175\) | −7907.73 | −3.41582 | ||||||||
\(176\) | 666.290 | 0.285361 | ||||||||
\(177\) | −370.328 | −0.157263 | ||||||||
\(178\) | −1475.45 | −0.621291 | ||||||||
\(179\) | −3915.43 | −1.63493 | −0.817467 | − | 0.575975i | \(-0.804623\pi\) | ||||
−0.817467 | + | 0.575975i | \(0.804623\pi\) | |||||||
\(180\) | −8120.69 | −3.36267 | ||||||||
\(181\) | 3009.44 | 1.23586 | 0.617928 | − | 0.786234i | \(-0.287972\pi\) | ||||
0.617928 | + | 0.786234i | \(0.287972\pi\) | |||||||
\(182\) | 6548.21 | 2.66695 | ||||||||
\(183\) | −408.645 | −0.165070 | ||||||||
\(184\) | −458.683 | −0.183775 | ||||||||
\(185\) | −2682.50 | −1.06606 | ||||||||
\(186\) | 704.111 | 0.277570 | ||||||||
\(187\) | −1307.51 | −0.511308 | ||||||||
\(188\) | −1063.11 | −0.412422 | ||||||||
\(189\) | −1466.25 | −0.564306 | ||||||||
\(190\) | −10274.7 | −3.92319 | ||||||||
\(191\) | −393.305 | −0.148998 | −0.0744989 | − | 0.997221i | \(-0.523736\pi\) | ||||
−0.0744989 | + | 0.997221i | \(0.523736\pi\) | |||||||
\(192\) | 800.076 | 0.300732 | ||||||||
\(193\) | 1329.16 | 0.495725 | 0.247862 | − | 0.968795i | \(-0.420272\pi\) | ||||
0.247862 | + | 0.968795i | \(0.420272\pi\) | |||||||
\(194\) | 5298.91 | 1.96103 | ||||||||
\(195\) | 1404.08 | 0.515633 | ||||||||
\(196\) | 3499.88 | 1.27547 | ||||||||
\(197\) | −533.591 | −0.192978 | −0.0964892 | − | 0.995334i | \(-0.530761\pi\) | ||||
−0.0964892 | + | 0.995334i | \(0.530761\pi\) | |||||||
\(198\) | −2158.42 | −0.774709 | ||||||||
\(199\) | −2186.74 | −0.778964 | −0.389482 | − | 0.921034i | \(-0.627346\pi\) | ||||
−0.389482 | + | 0.921034i | \(0.627346\pi\) | |||||||
\(200\) | 10777.1 | 3.81026 | ||||||||
\(201\) | −43.0619 | −0.0151112 | ||||||||
\(202\) | −3700.97 | −1.28911 | ||||||||
\(203\) | 2095.54 | 0.724524 | ||||||||
\(204\) | 1278.04 | 0.438630 | ||||||||
\(205\) | −1762.52 | −0.600486 | ||||||||
\(206\) | 1517.34 | 0.513195 | ||||||||
\(207\) | 359.040 | 0.120555 | ||||||||
\(208\) | −2156.39 | −0.718840 | ||||||||
\(209\) | −1775.10 | −0.587495 | ||||||||
\(210\) | 2835.60 | 0.931784 | ||||||||
\(211\) | −5062.24 | −1.65165 | −0.825827 | − | 0.563923i | \(-0.809291\pi\) | ||||
−0.825827 | + | 0.563923i | \(0.809291\pi\) | |||||||
\(212\) | 2259.15 | 0.731883 | ||||||||
\(213\) | −905.127 | −0.291165 | ||||||||
\(214\) | 3100.83 | 0.990508 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1998.28 | 0.629470 | ||||||||
\(217\) | 3060.32 | 0.957365 | ||||||||
\(218\) | 2751.23 | 0.854755 | ||||||||
\(219\) | 1356.37 | 0.418517 | ||||||||
\(220\) | 5568.10 | 1.70637 | ||||||||
\(221\) | 4231.63 | 1.28801 | ||||||||
\(222\) | 696.921 | 0.210695 | ||||||||
\(223\) | −5423.05 | −1.62850 | −0.814248 | − | 0.580518i | \(-0.802850\pi\) | ||||
−0.814248 | + | 0.580518i | \(0.802850\pi\) | |||||||
\(224\) | 1953.18 | 0.582599 | ||||||||
\(225\) | −8435.87 | −2.49952 | ||||||||
\(226\) | −2437.62 | −0.717468 | ||||||||
\(227\) | −1368.39 | −0.400103 | −0.200052 | − | 0.979785i | \(-0.564111\pi\) | ||||
−0.200052 | + | 0.979785i | \(0.564111\pi\) | |||||||
\(228\) | 1735.09 | 0.503988 | ||||||||
\(229\) | 3079.65 | 0.888685 | 0.444342 | − | 0.895857i | \(-0.353437\pi\) | ||||
0.444342 | + | 0.895857i | \(0.353437\pi\) | |||||||
\(230\) | −1424.96 | −0.408518 | ||||||||
\(231\) | 489.889 | 0.139534 | ||||||||
\(232\) | −2855.91 | −0.808189 | ||||||||
\(233\) | −1874.11 | −0.526939 | −0.263469 | − | 0.964668i | \(-0.584867\pi\) | ||||
−0.263469 | + | 0.964668i | \(0.584867\pi\) | |||||||
\(234\) | 6985.54 | 1.95153 | ||||||||
\(235\) | −1524.28 | −0.423119 | ||||||||
\(236\) | 4752.97 | 1.31098 | ||||||||
\(237\) | −974.629 | −0.267126 | ||||||||
\(238\) | 8545.95 | 2.32753 | ||||||||
\(239\) | −2112.85 | −0.571837 | −0.285919 | − | 0.958254i | \(-0.592299\pi\) | ||||
−0.285919 | + | 0.958254i | \(0.592299\pi\) | |||||||
\(240\) | −933.789 | −0.251149 | ||||||||
\(241\) | 242.170 | 0.0647285 | 0.0323642 | − | 0.999476i | \(-0.489696\pi\) | ||||
0.0323642 | + | 0.999476i | \(0.489696\pi\) | |||||||
\(242\) | −4883.38 | −1.29717 | ||||||||
\(243\) | −2366.16 | −0.624647 | ||||||||
\(244\) | 5244.74 | 1.37607 | ||||||||
\(245\) | 5018.10 | 1.30855 | ||||||||
\(246\) | 457.907 | 0.118679 | ||||||||
\(247\) | 5744.96 | 1.47993 | ||||||||
\(248\) | −4170.76 | −1.06792 | ||||||||
\(249\) | 1288.37 | 0.327901 | ||||||||
\(250\) | 20750.4 | 5.24948 | ||||||||
\(251\) | −2026.35 | −0.509569 | −0.254784 | − | 0.966998i | \(-0.582005\pi\) | ||||
−0.254784 | + | 0.966998i | \(0.582005\pi\) | |||||||
\(252\) | 9169.84 | 2.29224 | ||||||||
\(253\) | −246.182 | −0.0611753 | ||||||||
\(254\) | 12541.2 | 3.09804 | ||||||||
\(255\) | 1832.44 | 0.450007 | ||||||||
\(256\) | −7162.86 | −1.74875 | ||||||||
\(257\) | −2709.06 | −0.657534 | −0.328767 | − | 0.944411i | \(-0.606633\pi\) | ||||
−0.328767 | + | 0.944411i | \(0.606633\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3029.07 | 0.726707 | ||||||||
\(260\) | −18020.7 | −4.29844 | ||||||||
\(261\) | 2235.50 | 0.530168 | ||||||||
\(262\) | −12451.9 | −2.93619 | ||||||||
\(263\) | −1614.38 | −0.378507 | −0.189253 | − | 0.981928i | \(-0.560607\pi\) | ||||
−0.189253 | + | 0.981928i | \(0.560607\pi\) | |||||||
\(264\) | −667.645 | −0.155647 | ||||||||
\(265\) | 3239.15 | 0.750867 | ||||||||
\(266\) | 11602.2 | 2.67434 | ||||||||
\(267\) | 357.243 | 0.0818837 | ||||||||
\(268\) | 552.678 | 0.125971 | ||||||||
\(269\) | −3571.10 | −0.809420 | −0.404710 | − | 0.914445i | \(-0.632627\pi\) | ||||
−0.404710 | + | 0.914445i | \(0.632627\pi\) | |||||||
\(270\) | 6207.92 | 1.39927 | ||||||||
\(271\) | −7251.79 | −1.62552 | −0.812758 | − | 0.582602i | \(-0.802035\pi\) | ||||
−0.812758 | + | 0.582602i | \(0.802035\pi\) | |||||||
\(272\) | −2814.26 | −0.627352 | ||||||||
\(273\) | −1585.48 | −0.351494 | ||||||||
\(274\) | 3180.56 | 0.701258 | ||||||||
\(275\) | 5784.21 | 1.26837 | ||||||||
\(276\) | 240.634 | 0.0524799 | ||||||||
\(277\) | 4897.85 | 1.06239 | 0.531197 | − | 0.847248i | \(-0.321742\pi\) | ||||
0.531197 | + | 0.847248i | \(0.321742\pi\) | |||||||
\(278\) | −4188.78 | −0.903693 | ||||||||
\(279\) | 3264.71 | 0.700549 | ||||||||
\(280\) | −16796.5 | −3.58493 | ||||||||
\(281\) | −3332.97 | −0.707573 | −0.353787 | − | 0.935326i | \(-0.615106\pi\) | ||||
−0.353787 | + | 0.935326i | \(0.615106\pi\) | |||||||
\(282\) | 396.011 | 0.0836246 | ||||||||
\(283\) | −3141.03 | −0.659770 | −0.329885 | − | 0.944021i | \(-0.607010\pi\) | ||||
−0.329885 | + | 0.944021i | \(0.607010\pi\) | |||||||
\(284\) | 11616.8 | 2.42723 | ||||||||
\(285\) | 2487.76 | 0.517061 | ||||||||
\(286\) | −4789.77 | −0.990297 | ||||||||
\(287\) | 1990.23 | 0.409336 | ||||||||
\(288\) | 2083.62 | 0.426315 | ||||||||
\(289\) | 609.628 | 0.124085 | ||||||||
\(290\) | −8872.28 | −1.79654 | ||||||||
\(291\) | −1283.00 | −0.258456 | ||||||||
\(292\) | −17408.3 | −3.48886 | ||||||||
\(293\) | −4342.75 | −0.865891 | −0.432945 | − | 0.901420i | \(-0.642526\pi\) | ||||
−0.432945 | + | 0.901420i | \(0.642526\pi\) | |||||||
\(294\) | −1303.71 | −0.258620 | ||||||||
\(295\) | 6814.76 | 1.34499 | ||||||||
\(296\) | −4128.17 | −0.810625 | ||||||||
\(297\) | 1072.50 | 0.209539 | ||||||||
\(298\) | 5532.75 | 1.07552 | ||||||||
\(299\) | 796.747 | 0.154104 | ||||||||
\(300\) | −5653.84 | −1.08808 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6599.34 | 1.25745 | ||||||||
\(303\) | 896.096 | 0.169899 | ||||||||
\(304\) | −3820.70 | −0.720830 | ||||||||
\(305\) | 7519.87 | 1.41176 | ||||||||
\(306\) | 9116.70 | 1.70316 | ||||||||
\(307\) | −8180.43 | −1.52079 | −0.760394 | − | 0.649462i | \(-0.774994\pi\) | ||||
−0.760394 | + | 0.649462i | \(0.774994\pi\) | |||||||
\(308\) | −6287.47 | −1.16319 | ||||||||
\(309\) | −367.385 | −0.0676370 | ||||||||
\(310\) | −12957.0 | −2.37390 | ||||||||
\(311\) | −4932.66 | −0.899375 | −0.449687 | − | 0.893186i | \(-0.648465\pi\) | ||||
−0.449687 | + | 0.893186i | \(0.648465\pi\) | |||||||
\(312\) | 2160.77 | 0.392083 | ||||||||
\(313\) | 4008.91 | 0.723952 | 0.361976 | − | 0.932187i | \(-0.382102\pi\) | ||||
0.361976 | + | 0.932187i | \(0.382102\pi\) | |||||||
\(314\) | 13670.3 | 2.45688 | ||||||||
\(315\) | 13147.6 | 2.35170 | ||||||||
\(316\) | 12508.9 | 2.22683 | ||||||||
\(317\) | 1568.08 | 0.277831 | 0.138915 | − | 0.990304i | \(-0.455638\pi\) | ||||
0.138915 | + | 0.990304i | \(0.455638\pi\) | |||||||
\(318\) | −841.540 | −0.148400 | ||||||||
\(319\) | −1532.81 | −0.269031 | ||||||||
\(320\) | −14723.0 | −2.57200 | ||||||||
\(321\) | −750.788 | −0.130545 | ||||||||
\(322\) | 1609.06 | 0.278477 | ||||||||
\(323\) | 7497.64 | 1.29158 | ||||||||
\(324\) | 9244.76 | 1.58518 | ||||||||
\(325\) | −18720.1 | −3.19509 | ||||||||
\(326\) | 9517.69 | 1.61698 | ||||||||
\(327\) | −666.140 | −0.112653 | ||||||||
\(328\) | −2712.38 | −0.456604 | ||||||||
\(329\) | 1721.21 | 0.288429 | ||||||||
\(330\) | −2074.13 | −0.345991 | ||||||||
\(331\) | −2987.88 | −0.496160 | −0.248080 | − | 0.968740i | \(-0.579800\pi\) | ||||
−0.248080 | + | 0.968740i | \(0.579800\pi\) | |||||||
\(332\) | −16535.6 | −2.73346 | ||||||||
\(333\) | 3231.37 | 0.531766 | ||||||||
\(334\) | −8383.39 | −1.37341 | ||||||||
\(335\) | 792.424 | 0.129238 | ||||||||
\(336\) | 1054.43 | 0.171202 | ||||||||
\(337\) | −5177.88 | −0.836965 | −0.418483 | − | 0.908225i | \(-0.637438\pi\) | ||||
−0.418483 | + | 0.908225i | \(0.637438\pi\) | |||||||
\(338\) | 4998.07 | 0.804317 | ||||||||
\(339\) | 590.207 | 0.0945594 | ||||||||
\(340\) | −23518.4 | −3.75137 | ||||||||
\(341\) | −2238.51 | −0.355490 | ||||||||
\(342\) | 12377.0 | 1.95694 | ||||||||
\(343\) | 2583.96 | 0.406766 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 345.018 | 0.0538411 | ||||||||
\(346\) | 8879.87 | 1.37973 | ||||||||
\(347\) | 8237.38 | 1.27437 | 0.637184 | − | 0.770712i | \(-0.280099\pi\) | ||||
0.637184 | + | 0.770712i | \(0.280099\pi\) | |||||||
\(348\) | 1498.26 | 0.230791 | ||||||||
\(349\) | −2750.91 | −0.421928 | −0.210964 | − | 0.977494i | \(-0.567660\pi\) | ||||
−0.210964 | + | 0.977494i | \(0.567660\pi\) | |||||||
\(350\) | −37805.9 | −5.77374 | ||||||||
\(351\) | −3471.07 | −0.527840 | ||||||||
\(352\) | −1428.67 | −0.216331 | ||||||||
\(353\) | −109.272 | −0.0164758 | −0.00823789 | − | 0.999966i | \(-0.502622\pi\) | ||||
−0.00823789 | + | 0.999966i | \(0.502622\pi\) | |||||||
\(354\) | −1770.49 | −0.265821 | ||||||||
\(355\) | 16656.1 | 2.49018 | ||||||||
\(356\) | −4585.03 | −0.682602 | ||||||||
\(357\) | −2069.18 | −0.306759 | ||||||||
\(358\) | −18719.2 | −2.76352 | ||||||||
\(359\) | −11539.3 | −1.69643 | −0.848216 | − | 0.529650i | \(-0.822323\pi\) | ||||
−0.848216 | + | 0.529650i | \(0.822323\pi\) | |||||||
\(360\) | −17918.3 | −2.62326 | ||||||||
\(361\) | 3319.96 | 0.484030 | ||||||||
\(362\) | 14387.8 | 2.08896 | ||||||||
\(363\) | 1182.39 | 0.170962 | ||||||||
\(364\) | 20348.8 | 2.93013 | ||||||||
\(365\) | −24959.9 | −3.57935 | ||||||||
\(366\) | −1953.68 | −0.279018 | ||||||||
\(367\) | −13092.1 | −1.86213 | −0.931064 | − | 0.364857i | \(-0.881118\pi\) | ||||
−0.931064 | + | 0.364857i | \(0.881118\pi\) | |||||||
\(368\) | −529.879 | −0.0750594 | ||||||||
\(369\) | 2123.15 | 0.299530 | ||||||||
\(370\) | −12824.7 | −1.80196 | ||||||||
\(371\) | −3657.64 | −0.511847 | ||||||||
\(372\) | 2188.06 | 0.304961 | ||||||||
\(373\) | 9972.25 | 1.38430 | 0.692150 | − | 0.721754i | \(-0.256664\pi\) | ||||
0.692150 | + | 0.721754i | \(0.256664\pi\) | |||||||
\(374\) | −6251.04 | −0.864261 | ||||||||
\(375\) | −5024.18 | −0.691860 | ||||||||
\(376\) | −2345.75 | −0.321736 | ||||||||
\(377\) | 4960.80 | 0.677704 | ||||||||
\(378\) | −7009.95 | −0.953843 | ||||||||
\(379\) | 1702.20 | 0.230702 | 0.115351 | − | 0.993325i | \(-0.463201\pi\) | ||||
0.115351 | + | 0.993325i | \(0.463201\pi\) | |||||||
\(380\) | −31929.1 | −4.31034 | ||||||||
\(381\) | −3036.52 | −0.408309 | ||||||||
\(382\) | −1880.34 | −0.251850 | ||||||||
\(383\) | −3035.45 | −0.404972 | −0.202486 | − | 0.979285i | \(-0.564902\pi\) | ||||
−0.202486 | + | 0.979285i | \(0.564902\pi\) | |||||||
\(384\) | 3073.10 | 0.408394 | ||||||||
\(385\) | −9014.92 | −1.19336 | ||||||||
\(386\) | 6354.54 | 0.837921 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16466.6 | 2.15455 | ||||||||
\(389\) | 9435.36 | 1.22980 | 0.614900 | − | 0.788605i | \(-0.289196\pi\) | ||||
0.614900 | + | 0.788605i | \(0.289196\pi\) | |||||||
\(390\) | 6712.74 | 0.871571 | ||||||||
\(391\) | 1039.82 | 0.134491 | ||||||||
\(392\) | 7722.47 | 0.995010 | ||||||||
\(393\) | 3014.92 | 0.386978 | ||||||||
\(394\) | −2551.03 | −0.326191 | ||||||||
\(395\) | 17935.1 | 2.28459 | ||||||||
\(396\) | −6707.39 | −0.851159 | ||||||||
\(397\) | 4943.82 | 0.624995 | 0.312498 | − | 0.949919i | \(-0.398834\pi\) | ||||
0.312498 | + | 0.949919i | \(0.398834\pi\) | |||||||
\(398\) | −10454.5 | −1.31668 | ||||||||
\(399\) | −2809.17 | −0.352467 | ||||||||
\(400\) | 12449.8 | 1.55623 | ||||||||
\(401\) | −10139.0 | −1.26264 | −0.631318 | − | 0.775524i | \(-0.717486\pi\) | ||||
−0.631318 | + | 0.775524i | \(0.717486\pi\) | |||||||
\(402\) | −205.874 | −0.0255424 | ||||||||
\(403\) | 7244.74 | 0.895499 | ||||||||
\(404\) | −11500.9 | −1.41632 | ||||||||
\(405\) | 13255.1 | 1.62629 | ||||||||
\(406\) | 10018.5 | 1.22466 | ||||||||
\(407\) | −2215.65 | −0.269842 | ||||||||
\(408\) | 2819.99 | 0.342182 | ||||||||
\(409\) | −740.411 | −0.0895134 | −0.0447567 | − | 0.998998i | \(-0.514251\pi\) | ||||
−0.0447567 | + | 0.998998i | \(0.514251\pi\) | |||||||
\(410\) | −8426.39 | −1.01500 | ||||||||
\(411\) | −770.092 | −0.0924230 | ||||||||
\(412\) | 4715.20 | 0.563838 | ||||||||
\(413\) | −7695.20 | −0.916843 | ||||||||
\(414\) | 1716.52 | 0.203774 | ||||||||
\(415\) | −23708.6 | −2.80436 | ||||||||
\(416\) | 4623.78 | 0.544950 | ||||||||
\(417\) | 1014.21 | 0.119103 | ||||||||
\(418\) | −8486.55 | −0.993040 | ||||||||
\(419\) | 12031.8 | 1.40284 | 0.701421 | − | 0.712747i | \(-0.252549\pi\) | ||||
0.701421 | + | 0.712747i | \(0.252549\pi\) | |||||||
\(420\) | 8811.74 | 1.02374 | ||||||||
\(421\) | −1281.44 | −0.148346 | −0.0741731 | − | 0.997245i | \(-0.523632\pi\) | ||||
−0.0741731 | + | 0.997245i | \(0.523632\pi\) | |||||||
\(422\) | −24202.0 | −2.79178 | ||||||||
\(423\) | 1836.16 | 0.211057 | ||||||||
\(424\) | 4984.81 | 0.570952 | ||||||||
\(425\) | −24431.2 | −2.78844 | ||||||||
\(426\) | −4327.30 | −0.492156 | ||||||||
\(427\) | −8491.40 | −0.962360 | ||||||||
\(428\) | 9635.98 | 1.08825 | ||||||||
\(429\) | 1159.72 | 0.130517 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5537.45 | −0.618862 | −0.309431 | − | 0.950922i | \(-0.600139\pi\) | ||||
−0.309431 | + | 0.950922i | \(0.600139\pi\) | |||||||
\(432\) | 2308.44 | 0.257095 | ||||||||
\(433\) | 10109.8 | 1.12205 | 0.561023 | − | 0.827800i | \(-0.310408\pi\) | ||||
0.561023 | + | 0.827800i | \(0.310408\pi\) | |||||||
\(434\) | 14631.0 | 1.61823 | ||||||||
\(435\) | 2148.20 | 0.236777 | ||||||||
\(436\) | 8549.56 | 0.939104 | ||||||||
\(437\) | 1411.68 | 0.154531 | ||||||||
\(438\) | 6484.65 | 0.707417 | ||||||||
\(439\) | 13005.7 | 1.41396 | 0.706981 | − | 0.707233i | \(-0.250057\pi\) | ||||
0.706981 | + | 0.707233i | \(0.250057\pi\) | |||||||
\(440\) | 12286.0 | 1.33116 | ||||||||
\(441\) | −6044.86 | −0.652722 | ||||||||
\(442\) | 20230.9 | 2.17712 | ||||||||
\(443\) | 12636.5 | 1.35526 | 0.677630 | − | 0.735403i | \(-0.263007\pi\) | ||||
0.677630 | + | 0.735403i | \(0.263007\pi\) | |||||||
\(444\) | 2165.71 | 0.231487 | ||||||||
\(445\) | −6573.98 | −0.700307 | ||||||||
\(446\) | −25926.9 | −2.75264 | ||||||||
\(447\) | −1339.61 | −0.141749 | ||||||||
\(448\) | 16625.1 | 1.75326 | ||||||||
\(449\) | 1602.63 | 0.168447 | 0.0842237 | − | 0.996447i | \(-0.473159\pi\) | ||||
0.0842237 | + | 0.996447i | \(0.473159\pi\) | |||||||
\(450\) | −40330.8 | −4.22492 | ||||||||
\(451\) | −1455.78 | −0.151995 | ||||||||
\(452\) | −7575.00 | −0.788269 | ||||||||
\(453\) | −1597.86 | −0.165726 | ||||||||
\(454\) | −6542.12 | −0.676292 | ||||||||
\(455\) | 29176.0 | 3.00614 | ||||||||
\(456\) | 3828.48 | 0.393168 | ||||||||
\(457\) | −12386.5 | −1.26786 | −0.633932 | − | 0.773389i | \(-0.718560\pi\) | ||||
−0.633932 | + | 0.773389i | \(0.718560\pi\) | |||||||
\(458\) | 14723.4 | 1.50214 | ||||||||
\(459\) | −4530.02 | −0.460661 | ||||||||
\(460\) | −4428.13 | −0.448832 | ||||||||
\(461\) | 7814.88 | 0.789534 | 0.394767 | − | 0.918781i | \(-0.370825\pi\) | ||||
0.394767 | + | 0.918781i | \(0.370825\pi\) | |||||||
\(462\) | 2342.10 | 0.235854 | ||||||||
\(463\) | −7828.20 | −0.785761 | −0.392881 | − | 0.919589i | \(-0.628521\pi\) | ||||
−0.392881 | + | 0.919589i | \(0.628521\pi\) | |||||||
\(464\) | −3299.20 | −0.330089 | ||||||||
\(465\) | 3137.22 | 0.312871 | ||||||||
\(466\) | −8959.87 | −0.890682 | ||||||||
\(467\) | −372.814 | −0.0369417 | −0.0184709 | − | 0.999829i | \(-0.505880\pi\) | ||||
−0.0184709 | + | 0.999829i | \(0.505880\pi\) | |||||||
\(468\) | 21707.9 | 2.14412 | ||||||||
\(469\) | −894.802 | −0.0880983 | ||||||||
\(470\) | −7287.39 | −0.715196 | ||||||||
\(471\) | −3309.92 | −0.323807 | ||||||||
\(472\) | 10487.4 | 1.02272 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −4659.58 | −0.451522 | ||||||||
\(475\) | −33168.4 | −3.20393 | ||||||||
\(476\) | 26556.9 | 2.55721 | ||||||||
\(477\) | −3901.92 | −0.374542 | ||||||||
\(478\) | −10101.3 | −0.966574 | ||||||||
\(479\) | 6085.36 | 0.580474 | 0.290237 | − | 0.956955i | \(-0.406266\pi\) | ||||
0.290237 | + | 0.956955i | \(0.406266\pi\) | |||||||
\(480\) | 2002.25 | 0.190396 | ||||||||
\(481\) | 7170.75 | 0.679747 | ||||||||
\(482\) | 1157.79 | 0.109410 | ||||||||
\(483\) | −389.593 | −0.0367021 | ||||||||
\(484\) | −15175.3 | −1.42518 | ||||||||
\(485\) | 23609.7 | 2.21043 | ||||||||
\(486\) | −11312.3 | −1.05584 | ||||||||
\(487\) | −1655.22 | −0.154015 | −0.0770075 | − | 0.997031i | \(-0.524537\pi\) | ||||
−0.0770075 | + | 0.997031i | \(0.524537\pi\) | |||||||
\(488\) | 11572.5 | 1.07349 | ||||||||
\(489\) | −2304.47 | −0.213112 | ||||||||
\(490\) | 23990.9 | 2.21184 | ||||||||
\(491\) | −14763.9 | −1.35700 | −0.678498 | − | 0.734602i | \(-0.737369\pi\) | ||||
−0.678498 | + | 0.734602i | \(0.737369\pi\) | |||||||
\(492\) | 1422.97 | 0.130391 | ||||||||
\(493\) | 6474.25 | 0.591452 | ||||||||
\(494\) | 27465.9 | 2.50152 | ||||||||
\(495\) | −9617.00 | −0.873236 | ||||||||
\(496\) | −4818.14 | −0.436171 | ||||||||
\(497\) | −18808.0 | −1.69749 | ||||||||
\(498\) | 6159.55 | 0.554249 | ||||||||
\(499\) | 5889.43 | 0.528350 | 0.264175 | − | 0.964475i | \(-0.414900\pi\) | ||||
0.264175 | + | 0.964475i | \(0.414900\pi\) | |||||||
\(500\) | 64482.8 | 5.76751 | ||||||||
\(501\) | 2029.83 | 0.181010 | ||||||||
\(502\) | −9687.71 | −0.861322 | ||||||||
\(503\) | 18376.1 | 1.62893 | 0.814463 | − | 0.580215i | \(-0.197032\pi\) | ||||
0.814463 | + | 0.580215i | \(0.197032\pi\) | |||||||
\(504\) | 20233.2 | 1.78821 | ||||||||
\(505\) | −16489.9 | −1.45305 | ||||||||
\(506\) | −1176.97 | −0.103404 | ||||||||
\(507\) | −1210.16 | −0.106006 | ||||||||
\(508\) | 38972.2 | 3.40376 | ||||||||
\(509\) | 8355.89 | 0.727639 | 0.363820 | − | 0.931469i | \(-0.381472\pi\) | ||||
0.363820 | + | 0.931469i | \(0.381472\pi\) | |||||||
\(510\) | 8760.67 | 0.760645 | ||||||||
\(511\) | 28184.6 | 2.43995 | ||||||||
\(512\) | −13006.4 | −1.12267 | ||||||||
\(513\) | −6150.06 | −0.529302 | ||||||||
\(514\) | −12951.7 | −1.11143 | ||||||||
\(515\) | 6760.61 | 0.578463 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1259.00 | −0.107100 | ||||||||
\(518\) | 14481.6 | 1.22835 | ||||||||
\(519\) | −2150.04 | −0.181842 | ||||||||
\(520\) | −39762.5 | −3.35327 | ||||||||
\(521\) | 19044.7 | 1.60146 | 0.800732 | − | 0.599022i | \(-0.204444\pi\) | ||||
0.800732 | + | 0.599022i | \(0.204444\pi\) | |||||||
\(522\) | 10687.6 | 0.896140 | ||||||||
\(523\) | −5907.61 | −0.493923 | −0.246961 | − | 0.969025i | \(-0.579432\pi\) | ||||
−0.246961 | + | 0.969025i | \(0.579432\pi\) | |||||||
\(524\) | −38694.9 | −3.22594 | ||||||||
\(525\) | 9153.74 | 0.760956 | ||||||||
\(526\) | −7718.18 | −0.639788 | ||||||||
\(527\) | 9454.97 | 0.781528 | ||||||||
\(528\) | −771.276 | −0.0635710 | ||||||||
\(529\) | −11971.2 | −0.983909 | ||||||||
\(530\) | 15486.0 | 1.26919 | ||||||||
\(531\) | −8209.14 | −0.670897 | ||||||||
\(532\) | 36054.2 | 2.93825 | ||||||||
\(533\) | 4711.49 | 0.382884 | ||||||||
\(534\) | 1707.94 | 0.138408 | ||||||||
\(535\) | 13816.0 | 1.11648 | ||||||||
\(536\) | 1219.48 | 0.0982715 | ||||||||
\(537\) | 4532.38 | 0.364221 | ||||||||
\(538\) | −17073.0 | −1.36816 | ||||||||
\(539\) | 4144.77 | 0.331221 | ||||||||
\(540\) | 19291.4 | 1.53735 | ||||||||
\(541\) | −22011.7 | −1.74927 | −0.874636 | − | 0.484780i | \(-0.838900\pi\) | ||||
−0.874636 | + | 0.484780i | \(0.838900\pi\) | |||||||
\(542\) | −34669.9 | −2.74760 | ||||||||
\(543\) | −3483.63 | −0.275317 | ||||||||
\(544\) | 6034.41 | 0.475594 | ||||||||
\(545\) | 12258.3 | 0.963463 | ||||||||
\(546\) | −7579.99 | −0.594128 | ||||||||
\(547\) | −19182.2 | −1.49940 | −0.749700 | − | 0.661777i | \(-0.769802\pi\) | ||||
−0.749700 | + | 0.661777i | \(0.769802\pi\) | |||||||
\(548\) | 9883.74 | 0.770460 | ||||||||
\(549\) | −9058.51 | −0.704204 | ||||||||
\(550\) | 27653.6 | 2.14391 | ||||||||
\(551\) | 8789.59 | 0.679581 | ||||||||
\(552\) | 530.957 | 0.0409403 | ||||||||
\(553\) | −20252.2 | −1.55735 | ||||||||
\(554\) | 23416.0 | 1.79576 | ||||||||
\(555\) | 3105.18 | 0.237491 | ||||||||
\(556\) | −13016.8 | −0.992872 | ||||||||
\(557\) | 12163.8 | 0.925306 | 0.462653 | − | 0.886539i | \(-0.346898\pi\) | ||||
0.462653 | + | 0.886539i | \(0.346898\pi\) | |||||||
\(558\) | 15608.2 | 1.18413 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −19403.6 | −1.46420 | ||||||||
\(561\) | 1513.53 | 0.113906 | ||||||||
\(562\) | −15934.5 | −1.19601 | ||||||||
\(563\) | 9583.99 | 0.717437 | 0.358718 | − | 0.933446i | \(-0.383214\pi\) | ||||
0.358718 | + | 0.933446i | \(0.383214\pi\) | |||||||
\(564\) | 1230.62 | 0.0918769 | ||||||||
\(565\) | −10861.0 | −0.808715 | ||||||||
\(566\) | −15016.9 | −1.11521 | ||||||||
\(567\) | −14967.5 | −1.10860 | ||||||||
\(568\) | 25632.5 | 1.89351 | ||||||||
\(569\) | 7956.37 | 0.586201 | 0.293100 | − | 0.956082i | \(-0.405313\pi\) | ||||
0.293100 | + | 0.956082i | \(0.405313\pi\) | |||||||
\(570\) | 11893.7 | 0.873985 | ||||||||
\(571\) | 4971.46 | 0.364360 | 0.182180 | − | 0.983265i | \(-0.441685\pi\) | ||||
0.182180 | + | 0.983265i | \(0.441685\pi\) | |||||||
\(572\) | −14884.4 | −1.08802 | ||||||||
\(573\) | 455.277 | 0.0331928 | ||||||||
\(574\) | 9515.03 | 0.691899 | ||||||||
\(575\) | −4600.00 | −0.333623 | ||||||||
\(576\) | 17735.4 | 1.28295 | ||||||||
\(577\) | 23376.7 | 1.68663 | 0.843315 | − | 0.537420i | \(-0.180601\pi\) | ||||
0.843315 | + | 0.537420i | \(0.180601\pi\) | |||||||
\(578\) | 2914.56 | 0.209740 | ||||||||
\(579\) | −1538.59 | −0.110435 | ||||||||
\(580\) | −27571.0 | −1.97383 | ||||||||
\(581\) | 26771.6 | 1.91166 | ||||||||
\(582\) | −6133.85 | −0.436866 | ||||||||
\(583\) | 2675.42 | 0.190060 | ||||||||
\(584\) | −38411.4 | −2.72171 | ||||||||
\(585\) | 31124.6 | 2.19973 | ||||||||
\(586\) | −20762.1 | −1.46361 | ||||||||
\(587\) | −13790.5 | −0.969670 | −0.484835 | − | 0.874606i | \(-0.661120\pi\) | ||||
−0.484835 | + | 0.874606i | \(0.661120\pi\) | |||||||
\(588\) | −4051.35 | −0.284141 | ||||||||
\(589\) | 12836.3 | 0.897979 | ||||||||
\(590\) | 32580.5 | 2.27342 | ||||||||
\(591\) | 617.667 | 0.0429906 | ||||||||
\(592\) | −4768.93 | −0.331084 | ||||||||
\(593\) | 22432.3 | 1.55343 | 0.776716 | − | 0.629851i | \(-0.216884\pi\) | ||||
0.776716 | + | 0.629851i | \(0.216884\pi\) | |||||||
\(594\) | 5127.51 | 0.354182 | ||||||||
\(595\) | 38077.1 | 2.62354 | ||||||||
\(596\) | 17193.3 | 1.18165 | ||||||||
\(597\) | 2531.30 | 0.173533 | ||||||||
\(598\) | 3809.15 | 0.260481 | ||||||||
\(599\) | 2181.92 | 0.148833 | 0.0744165 | − | 0.997227i | \(-0.476291\pi\) | ||||
0.0744165 | + | 0.997227i | \(0.476291\pi\) | |||||||
\(600\) | −12475.2 | −0.848828 | ||||||||
\(601\) | −10415.4 | −0.706907 | −0.353453 | − | 0.935452i | \(-0.614993\pi\) | ||||
−0.353453 | + | 0.935452i | \(0.614993\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −954.562 | −0.0644657 | ||||||||
\(604\) | 20507.7 | 1.38154 | ||||||||
\(605\) | −21758.3 | −1.46215 | ||||||||
\(606\) | 4284.12 | 0.287179 | ||||||||
\(607\) | 6163.42 | 0.412134 | 0.206067 | − | 0.978538i | \(-0.433933\pi\) | ||||
0.206067 | + | 0.978538i | \(0.433933\pi\) | |||||||
\(608\) | 8192.44 | 0.546460 | ||||||||
\(609\) | −2425.73 | −0.161405 | ||||||||
\(610\) | 35951.6 | 2.38629 | ||||||||
\(611\) | 4074.64 | 0.269791 | ||||||||
\(612\) | 28330.5 | 1.87123 | ||||||||
\(613\) | 6705.56 | 0.441819 | 0.220910 | − | 0.975294i | \(-0.429097\pi\) | ||||
0.220910 | + | 0.975294i | \(0.429097\pi\) | |||||||
\(614\) | −39109.6 | −2.57058 | ||||||||
\(615\) | 2040.24 | 0.133773 | ||||||||
\(616\) | −13873.3 | −0.907420 | ||||||||
\(617\) | −1560.14 | −0.101797 | −0.0508985 | − | 0.998704i | \(-0.516209\pi\) | ||||
−0.0508985 | + | 0.998704i | \(0.516209\pi\) | |||||||
\(618\) | −1756.42 | −0.114326 | ||||||||
\(619\) | −17652.2 | −1.14621 | −0.573104 | − | 0.819483i | \(-0.694261\pi\) | ||||
−0.573104 | + | 0.819483i | \(0.694261\pi\) | |||||||
\(620\) | −40264.5 | −2.60817 | ||||||||
\(621\) | −852.929 | −0.0551157 | ||||||||
\(622\) | −23582.4 | −1.52021 | ||||||||
\(623\) | 7423.31 | 0.477381 | ||||||||
\(624\) | 2496.17 | 0.160139 | ||||||||
\(625\) | 51360.5 | 3.28707 | ||||||||
\(626\) | 19166.1 | 1.22369 | ||||||||
\(627\) | 2054.80 | 0.130879 | ||||||||
\(628\) | 42481.1 | 2.69933 | ||||||||
\(629\) | 9358.42 | 0.593235 | ||||||||
\(630\) | 62857.2 | 3.97507 | ||||||||
\(631\) | 31138.2 | 1.96449 | 0.982245 | − | 0.187601i | \(-0.0600712\pi\) | ||||
0.982245 | + | 0.187601i | \(0.0600712\pi\) | |||||||
\(632\) | 27600.7 | 1.73718 | ||||||||
\(633\) | 5859.89 | 0.367946 | ||||||||
\(634\) | 7496.81 | 0.469616 | ||||||||
\(635\) | 55878.0 | 3.49205 | ||||||||
\(636\) | −2615.12 | −0.163045 | ||||||||
\(637\) | −13414.2 | −0.834363 | ||||||||
\(638\) | −7328.18 | −0.454742 | ||||||||
\(639\) | −20064.1 | −1.24214 | ||||||||
\(640\) | −56551.1 | −3.49278 | ||||||||
\(641\) | 17820.0 | 1.09805 | 0.549023 | − | 0.835807i | \(-0.315000\pi\) | ||||
0.549023 | + | 0.835807i | \(0.315000\pi\) | |||||||
\(642\) | −3589.43 | −0.220659 | ||||||||
\(643\) | −3961.12 | −0.242941 | −0.121471 | − | 0.992595i | \(-0.538761\pi\) | ||||
−0.121471 | + | 0.992595i | \(0.538761\pi\) | |||||||
\(644\) | 5000.23 | 0.305957 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 35845.3 | 2.18315 | ||||||||
\(647\) | 1807.07 | 0.109804 | 0.0549019 | − | 0.998492i | \(-0.482515\pi\) | ||||
0.0549019 | + | 0.998492i | \(0.482515\pi\) | |||||||
\(648\) | 20398.5 | 1.23662 | ||||||||
\(649\) | 5628.75 | 0.340443 | ||||||||
\(650\) | −89498.4 | −5.40064 | ||||||||
\(651\) | −3542.53 | −0.213276 | ||||||||
\(652\) | 29576.6 | 1.77655 | ||||||||
\(653\) | −20608.3 | −1.23502 | −0.617509 | − | 0.786564i | \(-0.711858\pi\) | ||||
−0.617509 | + | 0.786564i | \(0.711858\pi\) | |||||||
\(654\) | −3184.73 | −0.190417 | ||||||||
\(655\) | −55480.4 | −3.30962 | ||||||||
\(656\) | −3133.39 | −0.186492 | ||||||||
\(657\) | 30067.0 | 1.78543 | ||||||||
\(658\) | 8228.89 | 0.487531 | ||||||||
\(659\) | −5125.22 | −0.302959 | −0.151480 | − | 0.988460i | \(-0.548404\pi\) | ||||
−0.151480 | + | 0.988460i | \(0.548404\pi\) | |||||||
\(660\) | −6445.45 | −0.380135 | ||||||||
\(661\) | −19830.2 | −1.16688 | −0.583439 | − | 0.812157i | \(-0.698293\pi\) | ||||
−0.583439 | + | 0.812157i | \(0.698293\pi\) | |||||||
\(662\) | −14284.7 | −0.838656 | ||||||||
\(663\) | −4898.40 | −0.286935 | ||||||||
\(664\) | −36485.7 | −2.13241 | ||||||||
\(665\) | 51694.2 | 3.01446 | ||||||||
\(666\) | 15448.8 | 0.898841 | ||||||||
\(667\) | 1219.00 | 0.0707641 | ||||||||
\(668\) | −26051.8 | −1.50894 | ||||||||
\(669\) | 6277.55 | 0.362786 | ||||||||
\(670\) | 3788.48 | 0.218451 | ||||||||
\(671\) | 6211.14 | 0.357345 | ||||||||
\(672\) | −2260.93 | −0.129788 | ||||||||
\(673\) | −20904.7 | −1.19735 | −0.598675 | − | 0.800992i | \(-0.704306\pi\) | ||||
−0.598675 | + | 0.800992i | \(0.704306\pi\) | |||||||
\(674\) | −24754.8 | −1.41472 | ||||||||
\(675\) | 20040.1 | 1.14273 | ||||||||
\(676\) | 15531.7 | 0.883689 | ||||||||
\(677\) | −8266.41 | −0.469282 | −0.234641 | − | 0.972082i | \(-0.575392\pi\) | ||||
−0.234641 | + | 0.972082i | \(0.575392\pi\) | |||||||
\(678\) | 2821.70 | 0.159833 | ||||||||
\(679\) | −26659.9 | −1.50680 | ||||||||
\(680\) | −51893.3 | −2.92650 | ||||||||
\(681\) | 1584.01 | 0.0891326 | ||||||||
\(682\) | −10702.0 | −0.600883 | ||||||||
\(683\) | −27099.4 | −1.51820 | −0.759098 | − | 0.650976i | \(-0.774360\pi\) | ||||
−0.759098 | + | 0.650976i | \(0.774360\pi\) | |||||||
\(684\) | 38462.2 | 2.15006 | ||||||||
\(685\) | 14171.2 | 0.790444 | ||||||||
\(686\) | 12353.6 | 0.687555 | ||||||||
\(687\) | −3564.90 | −0.197976 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8658.77 | −0.478770 | ||||||||
\(690\) | 1649.49 | 0.0910073 | ||||||||
\(691\) | −18247.5 | −1.00458 | −0.502292 | − | 0.864698i | \(-0.667510\pi\) | ||||
−0.502292 | + | 0.864698i | \(0.667510\pi\) | |||||||
\(692\) | 27594.6 | 1.51588 | ||||||||
\(693\) | 10859.5 | 0.595263 | ||||||||
\(694\) | 39381.9 | 2.15406 | ||||||||
\(695\) | −18663.4 | −1.01862 | ||||||||
\(696\) | 3305.91 | 0.180043 | ||||||||
\(697\) | 6148.88 | 0.334154 | ||||||||
\(698\) | −13151.8 | −0.713183 | ||||||||
\(699\) | 2169.40 | 0.117388 | ||||||||
\(700\) | −117483. | −6.34351 | ||||||||
\(701\) | 27373.3 | 1.47486 | 0.737430 | − | 0.675424i | \(-0.236039\pi\) | ||||
0.737430 | + | 0.675424i | \(0.236039\pi\) | |||||||
\(702\) | −16594.7 | −0.892205 | ||||||||
\(703\) | 12705.2 | 0.681629 | ||||||||
\(704\) | −12160.6 | −0.651025 | ||||||||
\(705\) | 1764.46 | 0.0942599 | ||||||||
\(706\) | −522.415 | −0.0278489 | ||||||||
\(707\) | 18620.4 | 0.990510 | ||||||||
\(708\) | −5501.88 | −0.292053 | ||||||||
\(709\) | −12752.9 | −0.675524 | −0.337762 | − | 0.941232i | \(-0.609670\pi\) | ||||
−0.337762 | + | 0.941232i | \(0.609670\pi\) | |||||||
\(710\) | 79630.8 | 4.20914 | ||||||||
\(711\) | −21604.8 | −1.13958 | ||||||||
\(712\) | −10116.9 | −0.532507 | ||||||||
\(713\) | 1780.21 | 0.0935057 | ||||||||
\(714\) | −9892.51 | −0.518513 | ||||||||
\(715\) | −21341.1 | −1.11624 | ||||||||
\(716\) | −58170.7 | −3.03623 | ||||||||
\(717\) | 2445.77 | 0.127391 | ||||||||
\(718\) | −55167.8 | −2.86747 | ||||||||
\(719\) | −26662.5 | −1.38295 | −0.691477 | − | 0.722398i | \(-0.743040\pi\) | ||||
−0.691477 | + | 0.722398i | \(0.743040\pi\) | |||||||
\(720\) | −20699.5 | −1.07142 | ||||||||
\(721\) | −7634.05 | −0.394323 | ||||||||
\(722\) | 15872.3 | 0.818154 | ||||||||
\(723\) | −280.328 | −0.0144198 | ||||||||
\(724\) | 44710.6 | 2.29511 | ||||||||
\(725\) | −28641.1 | −1.46718 | ||||||||
\(726\) | 5652.85 | 0.288976 | ||||||||
\(727\) | 27767.2 | 1.41655 | 0.708273 | − | 0.705939i | \(-0.249475\pi\) | ||||
0.708273 | + | 0.705939i | \(0.249475\pi\) | |||||||
\(728\) | 44899.6 | 2.28584 | ||||||||
\(729\) | −14062.0 | −0.714423 | ||||||||
\(730\) | −119330. | −6.05016 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −6071.14 | −0.306552 | ||||||||
\(733\) | 5819.92 | 0.293265 | 0.146633 | − | 0.989191i | \(-0.453156\pi\) | ||||
0.146633 | + | 0.989191i | \(0.453156\pi\) | |||||||
\(734\) | −62591.6 | −3.14754 | ||||||||
\(735\) | −5808.79 | −0.291511 | ||||||||
\(736\) | 1136.18 | 0.0569023 | ||||||||
\(737\) | 654.514 | 0.0327128 | ||||||||
\(738\) | 10150.5 | 0.506295 | ||||||||
\(739\) | −4469.69 | −0.222490 | −0.111245 | − | 0.993793i | \(-0.535484\pi\) | ||||
−0.111245 | + | 0.993793i | \(0.535484\pi\) | |||||||
\(740\) | −39853.4 | −1.97978 | ||||||||
\(741\) | −6650.18 | −0.329690 | ||||||||
\(742\) | −17486.7 | −0.865172 | ||||||||
\(743\) | −31260.1 | −1.54350 | −0.771752 | − | 0.635924i | \(-0.780619\pi\) | ||||
−0.771752 | + | 0.635924i | \(0.780619\pi\) | |||||||
\(744\) | 4827.94 | 0.237904 | ||||||||
\(745\) | 24651.6 | 1.21230 | ||||||||
\(746\) | 47676.1 | 2.33987 | ||||||||
\(747\) | 28559.6 | 1.39885 | ||||||||
\(748\) | −19425.4 | −0.949548 | ||||||||
\(749\) | −15600.9 | −0.761076 | ||||||||
\(750\) | −24020.0 | −1.16945 | ||||||||
\(751\) | 9943.65 | 0.483154 | 0.241577 | − | 0.970382i | \(-0.422335\pi\) | ||||
0.241577 | + | 0.970382i | \(0.422335\pi\) | |||||||
\(752\) | −2709.85 | −0.131407 | ||||||||
\(753\) | 2345.63 | 0.113519 | ||||||||
\(754\) | 23717.0 | 1.14552 | ||||||||
\(755\) | 29403.8 | 1.41737 | ||||||||
\(756\) | −21783.7 | −1.04797 | ||||||||
\(757\) | −11664.7 | −0.560056 | −0.280028 | − | 0.959992i | \(-0.590344\pi\) | ||||
−0.280028 | + | 0.959992i | \(0.590344\pi\) | |||||||
\(758\) | 8138.02 | 0.389955 | ||||||||
\(759\) | 284.973 | 0.0136283 | ||||||||
\(760\) | −70451.5 | −3.36256 | ||||||||
\(761\) | −23261.8 | −1.10807 | −0.554033 | − | 0.832495i | \(-0.686912\pi\) | ||||
−0.554033 | + | 0.832495i | \(0.686912\pi\) | |||||||
\(762\) | −14517.2 | −0.690163 | ||||||||
\(763\) | −13842.0 | −0.656768 | ||||||||
\(764\) | −5843.25 | −0.276703 | ||||||||
\(765\) | 40620.1 | 1.91977 | ||||||||
\(766\) | −14512.1 | −0.684522 | ||||||||
\(767\) | −18216.9 | −0.857595 | ||||||||
\(768\) | 8291.50 | 0.389575 | ||||||||
\(769\) | −12725.0 | −0.596717 | −0.298358 | − | 0.954454i | \(-0.596439\pi\) | ||||
−0.298358 | + | 0.954454i | \(0.596439\pi\) | |||||||
\(770\) | −43099.2 | −2.01713 | ||||||||
\(771\) | 3135.92 | 0.146482 | ||||||||
\(772\) | 19747.0 | 0.920609 | ||||||||
\(773\) | 31896.0 | 1.48411 | 0.742056 | − | 0.670337i | \(-0.233851\pi\) | ||||
0.742056 | + | 0.670337i | \(0.233851\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −41827.3 | −1.93868 | ||||||||
\(776\) | 36333.5 | 1.68079 | ||||||||
\(777\) | −3506.35 | −0.161892 | ||||||||
\(778\) | 45109.3 | 2.07872 | ||||||||
\(779\) | 8347.85 | 0.383945 | ||||||||
\(780\) | 20860.1 | 0.957580 | ||||||||
\(781\) | 13757.3 | 0.630316 | ||||||||
\(782\) | 4971.25 | 0.227329 | ||||||||
\(783\) | −5310.61 | −0.242383 | ||||||||
\(784\) | 8921.14 | 0.406393 | ||||||||
\(785\) | 60909.1 | 2.76935 | ||||||||
\(786\) | 14413.9 | 0.654107 | ||||||||
\(787\) | −3554.63 | −0.161003 | −0.0805013 | − | 0.996755i | \(-0.525652\pi\) | ||||
−0.0805013 | + | 0.996755i | \(0.525652\pi\) | |||||||
\(788\) | −7927.44 | −0.358380 | ||||||||
\(789\) | 1868.76 | 0.0843214 | ||||||||
\(790\) | 85745.5 | 3.86163 | ||||||||
\(791\) | 12264.1 | 0.551281 | ||||||||
\(792\) | −14799.8 | −0.664001 | ||||||||
\(793\) | −20101.8 | −0.900171 | ||||||||
\(794\) | 23635.8 | 1.05643 | ||||||||
\(795\) | −3749.54 | −0.167274 | ||||||||
\(796\) | −32487.9 | −1.44661 | ||||||||
\(797\) | 15944.6 | 0.708640 | 0.354320 | − | 0.935124i | \(-0.384712\pi\) | ||||
0.354320 | + | 0.935124i | \(0.384712\pi\) | |||||||
\(798\) | −13430.3 | −0.595773 | ||||||||
\(799\) | 5317.73 | 0.235454 | ||||||||
\(800\) | −26695.3 | −1.17977 | ||||||||
\(801\) | 7919.09 | 0.349322 | ||||||||
\(802\) | −48473.2 | −2.13423 | ||||||||
\(803\) | −20616.0 | −0.906006 | ||||||||
\(804\) | −639.762 | −0.0280630 | ||||||||
\(805\) | 7169.28 | 0.313893 | ||||||||
\(806\) | 34636.2 | 1.51366 | ||||||||
\(807\) | 4133.79 | 0.180318 | ||||||||
\(808\) | −25376.7 | −1.10489 | ||||||||
\(809\) | 12758.5 | 0.554467 | 0.277234 | − | 0.960803i | \(-0.410582\pi\) | ||||
0.277234 | + | 0.960803i | \(0.410582\pi\) | |||||||
\(810\) | 63370.8 | 2.74892 | ||||||||
\(811\) | 33232.7 | 1.43891 | 0.719457 | − | 0.694537i | \(-0.244391\pi\) | ||||
0.719457 | + | 0.694537i | \(0.244391\pi\) | |||||||
\(812\) | 31133.0 | 1.34551 | ||||||||
\(813\) | 8394.44 | 0.362123 | ||||||||
\(814\) | −10592.8 | −0.456113 | ||||||||
\(815\) | 42406.7 | 1.82263 | ||||||||
\(816\) | 3257.70 | 0.139758 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −3539.81 | −0.151304 | ||||||||
\(819\) | −35145.7 | −1.49950 | ||||||||
\(820\) | −26185.4 | −1.11516 | ||||||||
\(821\) | 1216.94 | 0.0517314 | 0.0258657 | − | 0.999665i | \(-0.491766\pi\) | ||||
0.0258657 | + | 0.999665i | \(0.491766\pi\) | |||||||
\(822\) | −3681.72 | −0.156222 | ||||||||
\(823\) | 4475.87 | 0.189574 | 0.0947869 | − | 0.995498i | \(-0.469783\pi\) | ||||
0.0947869 | + | 0.995498i | \(0.469783\pi\) | |||||||
\(824\) | 10404.1 | 0.439858 | ||||||||
\(825\) | −6695.61 | −0.282559 | ||||||||
\(826\) | −36789.8 | −1.54973 | ||||||||
\(827\) | 38299.6 | 1.61041 | 0.805205 | − | 0.592997i | \(-0.202055\pi\) | ||||
0.805205 | + | 0.592997i | \(0.202055\pi\) | |||||||
\(828\) | 5334.17 | 0.223883 | ||||||||
\(829\) | 14373.6 | 0.602192 | 0.301096 | − | 0.953594i | \(-0.402648\pi\) | ||||
0.301096 | + | 0.953594i | \(0.402648\pi\) | |||||||
\(830\) | −113348. | −4.74020 | ||||||||
\(831\) | −5669.59 | −0.236674 | ||||||||
\(832\) | 39356.8 | 1.63997 | ||||||||
\(833\) | −17506.6 | −0.728172 | ||||||||
\(834\) | 4848.80 | 0.201319 | ||||||||
\(835\) | −37352.8 | −1.54808 | ||||||||
\(836\) | −26372.3 | −1.09104 | ||||||||
\(837\) | −7755.59 | −0.320278 | ||||||||
\(838\) | 57522.5 | 2.37122 | ||||||||
\(839\) | 20770.8 | 0.854691 | 0.427346 | − | 0.904088i | \(-0.359449\pi\) | ||||
0.427346 | + | 0.904088i | \(0.359449\pi\) | |||||||
\(840\) | 19443.1 | 0.798630 | ||||||||
\(841\) | −16799.1 | −0.688800 | ||||||||
\(842\) | −6126.43 | −0.250749 | ||||||||
\(843\) | 3858.13 | 0.157629 | ||||||||
\(844\) | −75208.6 | −3.06728 | ||||||||
\(845\) | 22269.2 | 0.906609 | ||||||||
\(846\) | 8778.47 | 0.356749 | ||||||||
\(847\) | 24569.3 | 0.996708 | ||||||||
\(848\) | 5758.54 | 0.233195 | ||||||||
\(849\) | 3635.96 | 0.146980 | ||||||||
\(850\) | −116803. | −4.71329 | ||||||||
\(851\) | 1762.04 | 0.0709774 | ||||||||
\(852\) | −13447.3 | −0.540723 | ||||||||
\(853\) | 21536.0 | 0.864455 | 0.432228 | − | 0.901765i | \(-0.357728\pi\) | ||||
0.432228 | + | 0.901765i | \(0.357728\pi\) | |||||||
\(854\) | −40596.3 | −1.62667 | ||||||||
\(855\) | 55146.7 | 2.20582 | ||||||||
\(856\) | 21261.7 | 0.848962 | ||||||||
\(857\) | 34255.5 | 1.36540 | 0.682699 | − | 0.730700i | \(-0.260806\pi\) | ||||
0.682699 | + | 0.730700i | \(0.260806\pi\) | |||||||
\(858\) | 5544.48 | 0.220612 | ||||||||
\(859\) | 39691.7 | 1.57656 | 0.788279 | − | 0.615317i | \(-0.210972\pi\) | ||||
0.788279 | + | 0.615317i | \(0.210972\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2303.82 | −0.0911894 | ||||||||
\(862\) | −26473.9 | −1.04606 | ||||||||
\(863\) | 10554.4 | 0.416310 | 0.208155 | − | 0.978096i | \(-0.433254\pi\) | ||||
0.208155 | + | 0.978096i | \(0.433254\pi\) | |||||||
\(864\) | −4949.82 | −0.194903 | ||||||||
\(865\) | 39564.9 | 1.55520 | ||||||||
\(866\) | 48333.7 | 1.89659 | ||||||||
\(867\) | −705.686 | −0.0276429 | ||||||||
\(868\) | 45466.5 | 1.77792 | ||||||||
\(869\) | 14813.7 | 0.578276 | ||||||||
\(870\) | 10270.3 | 0.400224 | ||||||||
\(871\) | −2118.27 | −0.0824053 | ||||||||
\(872\) | 18864.6 | 0.732608 | ||||||||
\(873\) | −28440.5 | −1.10259 | ||||||||
\(874\) | 6749.08 | 0.261202 | ||||||||
\(875\) | −104400. | −4.03354 | ||||||||
\(876\) | 20151.3 | 0.777227 | ||||||||
\(877\) | −2628.97 | −0.101224 | −0.0506122 | − | 0.998718i | \(-0.516117\pi\) | ||||
−0.0506122 | + | 0.998718i | \(0.516117\pi\) | |||||||
\(878\) | 62178.7 | 2.39001 | ||||||||
\(879\) | 5027.02 | 0.192898 | ||||||||
\(880\) | 14193.0 | 0.543688 | ||||||||
\(881\) | −44531.4 | −1.70295 | −0.851476 | − | 0.524394i | \(-0.824292\pi\) | ||||
−0.851476 | + | 0.524394i | \(0.824292\pi\) | |||||||
\(882\) | −28899.7 | −1.10329 | ||||||||
\(883\) | 12638.0 | 0.481657 | 0.240828 | − | 0.970568i | \(-0.422581\pi\) | ||||
0.240828 | + | 0.970568i | \(0.422581\pi\) | |||||||
\(884\) | 62868.5 | 2.39196 | ||||||||
\(885\) | −7888.55 | −0.299628 | ||||||||
\(886\) | 60413.8 | 2.29079 | ||||||||
\(887\) | −47366.5 | −1.79302 | −0.896511 | − | 0.443022i | \(-0.853906\pi\) | ||||
−0.896511 | + | 0.443022i | \(0.853906\pi\) | |||||||
\(888\) | 4778.63 | 0.180586 | ||||||||
\(889\) | −63097.2 | −2.38044 | ||||||||
\(890\) | −31429.4 | −1.18373 | ||||||||
\(891\) | 10948.2 | 0.411648 | ||||||||
\(892\) | −80569.1 | −3.02427 | ||||||||
\(893\) | 7219.47 | 0.270538 | ||||||||
\(894\) | −6404.53 | −0.239597 | ||||||||
\(895\) | −83404.7 | −3.11499 | ||||||||
\(896\) | 63857.2 | 2.38094 | ||||||||
\(897\) | −922.288 | −0.0343303 | ||||||||
\(898\) | 7661.99 | 0.284726 | ||||||||
\(899\) | 11084.2 | 0.411211 | ||||||||
\(900\) | −125330. | −4.64184 | ||||||||
\(901\) | −11300.4 | −0.417837 | ||||||||
\(902\) | −6959.89 | −0.256917 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16714.2 | −0.614940 | ||||||||
\(905\) | 64105.7 | 2.35464 | ||||||||
\(906\) | −7639.18 | −0.280127 | ||||||||
\(907\) | 3162.85 | 0.115789 | 0.0578946 | − | 0.998323i | \(-0.481561\pi\) | ||||
0.0578946 | + | 0.998323i | \(0.481561\pi\) | |||||||
\(908\) | −20329.9 | −0.743031 | ||||||||
\(909\) | 19863.9 | 0.724802 | ||||||||
\(910\) | 139487. | 5.08126 | ||||||||
\(911\) | −13963.5 | −0.507829 | −0.253914 | − | 0.967227i | \(-0.581718\pi\) | ||||
−0.253914 | + | 0.967227i | \(0.581718\pi\) | |||||||
\(912\) | 4422.72 | 0.160582 | ||||||||
\(913\) | −19582.4 | −0.709840 | ||||||||
\(914\) | −59218.1 | −2.14306 | ||||||||
\(915\) | −8704.75 | −0.314503 | ||||||||
\(916\) | 45753.7 | 1.65037 | ||||||||
\(917\) | 62648.2 | 2.25608 | ||||||||
\(918\) | −21657.5 | −0.778653 | ||||||||
\(919\) | 5006.75 | 0.179714 | 0.0898572 | − | 0.995955i | \(-0.471359\pi\) | ||||
0.0898572 | + | 0.995955i | \(0.471359\pi\) | |||||||
\(920\) | −9770.65 | −0.350140 | ||||||||
\(921\) | 9469.40 | 0.338792 | ||||||||
\(922\) | 37362.0 | 1.33455 | ||||||||
\(923\) | −44524.4 | −1.58780 | ||||||||
\(924\) | 7278.18 | 0.259128 | ||||||||
\(925\) | −41400.1 | −1.47160 | ||||||||
\(926\) | −37425.7 | −1.32817 | ||||||||
\(927\) | −8143.91 | −0.288545 | ||||||||
\(928\) | 7074.22 | 0.250240 | ||||||||
\(929\) | −35356.7 | −1.24867 | −0.624336 | − | 0.781156i | \(-0.714630\pi\) | ||||
−0.624336 | + | 0.781156i | \(0.714630\pi\) | |||||||
\(930\) | 14998.6 | 0.528844 | ||||||||
\(931\) | −23767.3 | −0.836673 | ||||||||
\(932\) | −27843.2 | −0.978577 | ||||||||
\(933\) | 5709.89 | 0.200357 | ||||||||
\(934\) | −1782.38 | −0.0624425 | ||||||||
\(935\) | −27851.9 | −0.974177 | ||||||||
\(936\) | 47898.3 | 1.67266 | ||||||||
\(937\) | −42579.5 | −1.48454 | −0.742269 | − | 0.670103i | \(-0.766250\pi\) | ||||
−0.742269 | + | 0.670103i | \(0.766250\pi\) | |||||||
\(938\) | −4277.94 | −0.148912 | ||||||||
\(939\) | −4640.58 | −0.161278 | ||||||||
\(940\) | −22645.9 | −0.785774 | ||||||||
\(941\) | −24475.5 | −0.847905 | −0.423952 | − | 0.905685i | \(-0.639358\pi\) | ||||
−0.423952 | + | 0.905685i | \(0.639358\pi\) | |||||||
\(942\) | −15824.3 | −0.547330 | ||||||||
\(943\) | 1157.73 | 0.0399798 | ||||||||
\(944\) | 12115.2 | 0.417709 | ||||||||
\(945\) | −31233.3 | −1.07515 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5042.58 | 0.173032 | 0.0865162 | − | 0.996250i | \(-0.472427\pi\) | ||||
0.0865162 | + | 0.996250i | \(0.472427\pi\) | |||||||
\(948\) | −14479.9 | −0.496080 | ||||||||
\(949\) | 66721.8 | 2.28228 | ||||||||
\(950\) | −158574. | −5.41560 | ||||||||
\(951\) | −1815.16 | −0.0618934 | ||||||||
\(952\) | 58597.7 | 1.99492 | ||||||||
\(953\) | 22662.7 | 0.770323 | 0.385161 | − | 0.922849i | \(-0.374146\pi\) | ||||
0.385161 | + | 0.922849i | \(0.374146\pi\) | |||||||
\(954\) | −18654.6 | −0.633087 | ||||||||
\(955\) | −8378.00 | −0.283880 | ||||||||
\(956\) | −31390.2 | −1.06196 | ||||||||
\(957\) | 1774.33 | 0.0599331 | ||||||||
\(958\) | 29093.4 | 0.981173 | ||||||||
\(959\) | −16002.1 | −0.538826 | ||||||||
\(960\) | 17042.8 | 0.572974 | ||||||||
\(961\) | −13603.7 | −0.456638 | ||||||||
\(962\) | 34282.5 | 1.14897 | ||||||||
\(963\) | −16642.9 | −0.556915 | ||||||||
\(964\) | 3597.87 | 0.120207 | ||||||||
\(965\) | 28313.1 | 0.944488 | ||||||||
\(966\) | −1862.60 | −0.0620373 | ||||||||
\(967\) | 20319.2 | 0.675720 | 0.337860 | − | 0.941196i | \(-0.390297\pi\) | ||||
0.337860 | + | 0.941196i | \(0.390297\pi\) | |||||||
\(968\) | −33484.3 | −1.11180 | ||||||||
\(969\) | −8679.03 | −0.287730 | ||||||||
\(970\) | 112875. | 3.73628 | ||||||||
\(971\) | 2458.32 | 0.0812474 | 0.0406237 | − | 0.999175i | \(-0.487066\pi\) | ||||
0.0406237 | + | 0.999175i | \(0.487066\pi\) | |||||||
\(972\) | −35153.5 | −1.16003 | ||||||||
\(973\) | 21074.6 | 0.694370 | ||||||||
\(974\) | −7913.41 | −0.260331 | ||||||||
\(975\) | 21669.8 | 0.711782 | ||||||||
\(976\) | 13368.8 | 0.438446 | ||||||||
\(977\) | 56845.4 | 1.86146 | 0.930729 | − | 0.365709i | \(-0.119174\pi\) | ||||
0.930729 | + | 0.365709i | \(0.119174\pi\) | |||||||
\(978\) | −11017.4 | −0.360222 | ||||||||
\(979\) | −5429.87 | −0.177262 | ||||||||
\(980\) | 74552.8 | 2.43010 | ||||||||
\(981\) | −14766.5 | −0.480588 | ||||||||
\(982\) | −70584.4 | −2.29372 | ||||||||
\(983\) | 9749.84 | 0.316350 | 0.158175 | − | 0.987411i | \(-0.449439\pi\) | ||||
0.158175 | + | 0.987411i | \(0.449439\pi\) | |||||||
\(984\) | 3139.77 | 0.101720 | ||||||||
\(985\) | −11366.3 | −0.367675 | ||||||||
\(986\) | 30952.6 | 0.999728 | ||||||||
\(987\) | −1992.42 | −0.0642546 | ||||||||
\(988\) | 85351.6 | 2.74838 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −45977.7 | −1.47603 | ||||||||
\(991\) | −44926.5 | −1.44010 | −0.720050 | − | 0.693922i | \(-0.755881\pi\) | ||||
−0.720050 | + | 0.693922i | \(0.755881\pi\) | |||||||
\(992\) | 10331.2 | 0.330660 | ||||||||
\(993\) | 3458.68 | 0.110531 | ||||||||
\(994\) | −89918.7 | −2.86926 | ||||||||
\(995\) | −46580.9 | −1.48413 | ||||||||
\(996\) | 19141.1 | 0.608944 | ||||||||
\(997\) | −1536.04 | −0.0487934 | −0.0243967 | − | 0.999702i | \(-0.507766\pi\) | ||||
−0.0243967 | + | 0.999702i | \(0.507766\pi\) | |||||||
\(998\) | 28156.6 | 0.893068 | ||||||||
\(999\) | −7676.39 | −0.243113 |
(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.j.1.44 | yes | 50 | |
43.42 | odd | 2 | 1849.4.a.i.1.7 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.7 | ✓ | 50 | 43.42 | odd | 2 | ||
1849.4.a.j.1.44 | yes | 50 | 1.1 | even | 1 | trivial |