Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.78088 | −1.69030 | −0.845148 | − | 0.534533i | \(-0.820487\pi\) | ||||
−0.845148 | + | 0.534533i | \(0.820487\pi\) | |||||||
\(3\) | 1.15757 | 0.222774 | 0.111387 | − | 0.993777i | \(-0.464471\pi\) | ||||
0.111387 | + | 0.993777i | \(0.464471\pi\) | |||||||
\(4\) | 14.8568 | 1.85710 | ||||||||
\(5\) | −21.3015 | −1.90527 | −0.952633 | − | 0.304122i | \(-0.901637\pi\) | ||||
−0.952633 | + | 0.304122i | \(0.901637\pi\) | |||||||
\(6\) | −5.53419 | −0.376554 | ||||||||
\(7\) | 24.0536 | 1.29877 | 0.649386 | − | 0.760459i | \(-0.275026\pi\) | ||||
0.649386 | + | 0.760459i | \(0.275026\pi\) | |||||||
\(8\) | −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 | \(-0.291529\pi\) | ||||
0.609104 | + | 0.793090i | \(0.291529\pi\) | |||||||
\(20\) | −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 | \(-0.410021\pi\) | ||||
0.278927 | + | 0.960312i | \(0.410021\pi\) | |||||||
\(30\) | 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 | \(-0.409743\pi\) | ||||
0.279767 | + | 0.960068i | \(0.409743\pi\) | |||||||
\(38\) | −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 | \(-0.620810\pi\) | ||||
−0.370488 | + | 0.928837i | \(0.620810\pi\) | |||||||
\(62\) | 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 | \(-0.726700\pi\) | ||||
−0.653500 | + | 0.756927i | \(0.726700\pi\) | |||||||
\(72\) | 841.173 | 1.37685 | ||||||||
\(73\) | 1171.74 | 1.87866 | 0.939331 | − | 0.343013i | \(-0.111448\pi\) | ||||
0.939331 | + | 0.343013i | \(0.111448\pi\) | |||||||
\(74\) | −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 | \(-0.441166\pi\) | ||||
0.183782 | + | 0.982967i | \(0.441166\pi\) | |||||||
\(90\) | −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 | \(-0.431927\pi\) | ||||
0.212232 | + | 0.977219i | \(0.431927\pi\) | |||||||
\(114\) | −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 | \(-0.165056\pi\) | ||||
0.868544 | + | 0.495611i | \(0.165056\pi\) | |||||||
\(132\) | 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 | \(-0.566512\pi\) | ||||
−0.207437 | + | 0.978248i | \(0.566512\pi\) | |||||||
\(138\) | 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 | \(-0.603060\pi\) | ||||
−0.318144 | + | 0.948042i | \(0.603060\pi\) | |||||||
\(150\) | −1819.39 | −0.990352 | ||||||||
\(151\) | −1380.36 | −0.743922 | −0.371961 | − | 0.928248i | \(-0.621314\pi\) | ||||
−0.371961 | + | 0.928248i | \(0.621314\pi\) | |||||||
\(152\) | −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 | \(-0.758976\pi\) | ||||
−0.726762 | + | 0.686890i | \(0.758976\pi\) | |||||||
\(158\) | −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 | \(-0.658752\pi\) | ||||
−0.478314 | + | 0.878189i | \(0.658752\pi\) | |||||||
\(164\) | −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 | \(-0.195377\pi\) | ||||
0.817467 | + | 0.575975i | \(0.195377\pi\) | |||||||
\(180\) | 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 | \(-0.476264\pi\) | ||||
0.0744989 | + | 0.997221i | \(0.476264\pi\) | |||||||
\(192\) | −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 | \(-0.372654\pi\) | ||||
0.389482 | + | 0.921034i | \(0.372654\pi\) | |||||||
\(200\) | −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 | \(-0.190709\pi\) | ||||
0.825827 | + | 0.563923i | \(0.190709\pi\) | |||||||
\(212\) | 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 | \(-0.197150\pi\) | ||||
0.814248 | + | 0.580518i | \(0.197150\pi\) | |||||||
\(224\) | 1953.18 | 0.582599 | ||||||||
\(225\) | −8435.87 | −2.49952 | ||||||||
\(226\) | −2437.62 | −0.717468 | ||||||||
\(227\) | 1368.39 | 0.400103 | 0.200052 | − | 0.979785i | \(-0.435889\pi\) | ||||
0.200052 | + | 0.979785i | \(0.435889\pi\) | |||||||
\(228\) | 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 | \(-0.415133\pi\) | ||||
0.263469 | + | 0.964668i | \(0.415133\pi\) | |||||||
\(234\) | −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 | \(-0.510304\pi\) | ||||
−0.0323642 | + | 0.999476i | \(0.510304\pi\) | |||||||
\(242\) | 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 | \(-0.393367\pi\) | ||||
0.328767 | + | 0.944411i | \(0.393367\pi\) | |||||||
\(258\) | 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 | \(-0.439393\pi\) | ||||
0.189253 | + | 0.981928i | \(0.439393\pi\) | |||||||
\(264\) | −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 | \(-0.678258\pi\) | ||||
−0.531197 | + | 0.847248i | \(0.678258\pi\) | |||||||
\(278\) | 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 | \(-0.617898\pi\) | ||||
−0.361976 | + | 0.932187i | \(0.617898\pi\) | |||||||
\(314\) | 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 | \(-0.420200\pi\) | ||||
0.248080 | + | 0.968740i | \(0.420200\pi\) | |||||||
\(332\) | −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 | \(-0.719901\pi\) | ||||
−0.637184 | + | 0.770712i | \(0.719901\pi\) | |||||||
\(348\) | 1498.26 | 0.230791 | ||||||||
\(349\) | 2750.91 | 0.421928 | 0.210964 | − | 0.977494i | \(-0.432340\pi\) | ||||
0.210964 | + | 0.977494i | \(0.432340\pi\) | |||||||
\(350\) | −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 | \(-0.743336\pi\) | ||||
−0.692150 | + | 0.721754i | \(0.743336\pi\) | |||||||
\(374\) | 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 | \(-0.435098\pi\) | ||||
0.202486 | + | 0.979285i | \(0.435098\pi\) | |||||||
\(384\) | 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 | \(-0.710804\pi\) | ||||
−0.614900 | + | 0.788605i | \(0.710804\pi\) | |||||||
\(390\) | −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 | \(-0.485749\pi\) | ||||
0.0447567 | + | 0.998998i | \(0.485749\pi\) | |||||||
\(410\) | −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 | \(-0.747451\pi\) | ||||
−0.701421 | + | 0.712747i | \(0.747451\pi\) | |||||||
\(420\) | −8811.74 | −1.02374 | ||||||||
\(421\) | 1281.44 | 0.148346 | 0.0741731 | − | 0.997245i | \(-0.476368\pi\) | ||||
0.0741731 | + | 0.997245i | \(0.476368\pi\) | |||||||
\(422\) | −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 | \(-0.689592\pi\) | ||||
−0.561023 | + | 0.827800i | \(0.689592\pi\) | |||||||
\(434\) | 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 | \(-0.526841\pi\) | ||||
−0.0842237 | + | 0.996447i | \(0.526841\pi\) | |||||||
\(450\) | 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 | \(-0.281440\pi\) | ||||
0.633932 | + | 0.773389i | \(0.281440\pi\) | |||||||
\(458\) | −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 | \(-0.371479\pi\) | ||||
0.392881 | + | 0.919589i | \(0.371479\pi\) | |||||||
\(464\) | 3299.20 | 0.330089 | ||||||||
\(465\) | 3137.22 | 0.312871 | ||||||||
\(466\) | −8959.87 | −0.890682 | ||||||||
\(467\) | 372.814 | 0.0369417 | 0.0184709 | − | 0.999829i | \(-0.494120\pi\) | ||||
0.0184709 | + | 0.999829i | \(0.494120\pi\) | |||||||
\(468\) | 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 | \(-0.262631\pi\) | ||||
0.678498 | + | 0.734602i | \(0.262631\pi\) | |||||||
\(492\) | −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 | \(-0.585100\pi\) | ||||
−0.264175 | + | 0.964475i | \(0.585100\pi\) | |||||||
\(500\) | −64482.8 | −5.76751 | ||||||||
\(501\) | −2029.83 | −0.181010 | ||||||||
\(502\) | 9687.71 | 0.861322 | ||||||||
\(503\) | −18376.1 | −1.62893 | −0.814463 | − | 0.580215i | \(-0.802968\pi\) | ||||
−0.814463 | + | 0.580215i | \(0.802968\pi\) | |||||||
\(504\) | 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 | \(-0.795556\pi\) | ||||
−0.800732 | + | 0.599022i | \(0.795556\pi\) | |||||||
\(522\) | 10687.6 | 0.896140 | ||||||||
\(523\) | 5907.61 | 0.493923 | 0.246961 | − | 0.969025i | \(-0.420568\pi\) | ||||
0.246961 | + | 0.969025i | \(0.420568\pi\) | |||||||
\(524\) | 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 | \(-0.558315\pi\) | ||||
−0.182180 | + | 0.983265i | \(0.558315\pi\) | |||||||
\(572\) | −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 | \(-0.819399\pi\) | ||||
−0.843315 | + | 0.537420i | \(0.819399\pi\) | |||||||
\(578\) | −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 | \(-0.338880\pi\) | ||||
0.484835 | + | 0.874606i | \(0.338880\pi\) | |||||||
\(588\) | 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 | \(-0.783116\pi\) | ||||
−0.776716 | + | 0.629851i | \(0.783116\pi\) | |||||||
\(594\) | 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 | \(-0.385007\pi\) | ||||
0.353453 | + | 0.935452i | \(0.385007\pi\) | |||||||
\(602\) | 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 | \(-0.566067\pi\) | ||||
−0.206067 | + | 0.978538i | \(0.566067\pi\) | |||||||
\(608\) | 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 | \(-0.939929\pi\) | ||||
−0.982245 | + | 0.187601i | \(0.939929\pi\) | |||||||
\(632\) | −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 | \(-0.685000\pi\) | ||||
−0.549023 | + | 0.835807i | \(0.685000\pi\) | |||||||
\(642\) | −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 | \(-0.517485\pi\) | ||||
−0.0549019 | + | 0.998492i | \(0.517485\pi\) | |||||||
\(648\) | −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 | \(-0.288142\pi\) | ||||
0.617509 | + | 0.786564i | \(0.288142\pi\) | |||||||
\(654\) | −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 | \(-0.295694\pi\) | ||||
0.598675 | + | 0.800992i | \(0.295694\pi\) | |||||||
\(674\) | 24754.8 | 1.41472 | ||||||||
\(675\) | −20040.1 | −1.14273 | ||||||||
\(676\) | 15531.7 | 0.883689 | ||||||||
\(677\) | 8266.41 | 0.469282 | 0.234641 | − | 0.972082i | \(-0.424608\pi\) | ||||
0.234641 | + | 0.972082i | \(0.424608\pi\) | |||||||
\(678\) | −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 | \(-0.332490\pi\) | ||||
0.502292 | + | 0.864698i | \(0.332490\pi\) | |||||||
\(692\) | 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 | \(-0.750525\pi\) | ||||
−0.708273 | + | 0.705939i | \(0.750525\pi\) | |||||||
\(728\) | 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 | \(-0.546844\pi\) | ||||
−0.146633 | + | 0.989191i | \(0.546844\pi\) | |||||||
\(734\) | 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 | \(-0.464516\pi\) | ||||
0.111245 | + | 0.993793i | \(0.464516\pi\) | |||||||
\(740\) | −39853.4 | −1.97978 | ||||||||
\(741\) | −6650.18 | −0.329690 | ||||||||
\(742\) | −17486.7 | −0.865172 | ||||||||
\(743\) | 31260.1 | 1.54350 | 0.771752 | − | 0.635924i | \(-0.219381\pi\) | ||||
0.771752 | + | 0.635924i | \(0.219381\pi\) | |||||||
\(744\) | 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 | \(-0.577665\pi\) | ||||
−0.241577 | + | 0.970382i | \(0.577665\pi\) | |||||||
\(752\) | −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 | \(-0.409656\pi\) | ||||
0.280028 | + | 0.959992i | \(0.409656\pi\) | |||||||
\(758\) | −8138.02 | −0.389955 | ||||||||
\(759\) | −284.973 | −0.0136283 | ||||||||
\(760\) | 70451.5 | 3.36256 | ||||||||
\(761\) | 23261.8 | 1.10807 | 0.554033 | − | 0.832495i | \(-0.313088\pi\) | ||||
0.554033 | + | 0.832495i | \(0.313088\pi\) | |||||||
\(762\) | −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 | \(-0.766149\pi\) | ||||
−0.742056 | + | 0.670337i | \(0.766149\pi\) | |||||||
\(774\) | 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 | \(-0.755609\pi\) | ||||
−0.719457 | + | 0.694537i | \(0.755609\pi\) | |||||||
\(812\) | 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 | \(-0.597352\pi\) | ||||
−0.301096 | + | 0.953594i | \(0.597352\pi\) | |||||||
\(830\) | −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 | \(-0.640551\pi\) | ||||
−0.427346 | + | 0.904088i | \(0.640551\pi\) | |||||||
\(840\) | 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 | \(-0.789028\pi\) | ||||
−0.788279 | + | 0.615317i | \(0.789028\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2303.82 | −0.0911894 | ||||||||
\(862\) | 26473.9 | 1.04606 | ||||||||
\(863\) | −10554.4 | −0.416310 | −0.208155 | − | 0.978096i | \(-0.566746\pi\) | ||||
−0.208155 | + | 0.978096i | \(0.566746\pi\) | |||||||
\(864\) | −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 | \(-0.146094\pi\) | ||||
0.896511 | + | 0.443022i | \(0.146094\pi\) | |||||||
\(888\) | −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 | \(-0.418282\pi\) | ||||
0.253914 | + | 0.967227i | \(0.418282\pi\) | |||||||
\(912\) | 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 | \(-0.285370\pi\) | ||||
0.624336 | + | 0.781156i | \(0.285370\pi\) | |||||||
\(930\) | −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 | \(-0.233750\pi\) | ||||
0.742269 | + | 0.670103i | \(0.233750\pi\) | |||||||
\(938\) | −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 | \(-0.625854\pi\) | ||||
−0.385161 | + | 0.922849i | \(0.625854\pi\) | |||||||
\(954\) | 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 | \(-0.550561\pi\) | ||||
−0.158175 | + | 0.987411i | \(0.550561\pi\) | |||||||
\(984\) | 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 | \(-0.244119\pi\) | ||||
0.720050 | + | 0.693922i | \(0.244119\pi\) | |||||||
\(992\) | −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 | \(-0.492234\pi\) | ||||
0.0243967 | + | 0.999702i | \(0.492234\pi\) | |||||||
\(998\) | 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.i.1.7 | ✓ | 50 | |
43.42 | odd | 2 | 1849.4.a.j.1.44 | yes | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.7 | ✓ | 50 | 1.1 | even | 1 | trivial | |
1849.4.a.j.1.44 | yes | 50 | 43.42 | odd | 2 |