Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(109.094531601\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 59x^{8} + 42x^{7} + 1187x^{6} - 541x^{5} - 9389x^{4} + 2180x^{3} + 22676x^{2} - 320x - 768 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.14781\) of defining polynomial | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.14781 | −0.759365 | −0.379682 | − | 0.925117i | \(-0.623967\pi\) | ||||
−0.379682 | + | 0.925117i | \(0.623967\pi\) | |||||||
\(3\) | 6.84883 | 1.31806 | 0.659029 | − | 0.752118i | \(-0.270968\pi\) | ||||
0.659029 | + | 0.752118i | \(0.270968\pi\) | |||||||
\(4\) | −3.38692 | −0.423365 | ||||||||
\(5\) | −17.1363 | −1.53272 | −0.766360 | − | 0.642411i | \(-0.777934\pi\) | ||||
−0.766360 | + | 0.642411i | \(0.777934\pi\) | |||||||
\(6\) | −14.7100 | −1.00089 | ||||||||
\(7\) | 22.9786 | 1.24073 | 0.620364 | − | 0.784314i | \(-0.286985\pi\) | ||||
0.620364 | + | 0.784314i | \(0.286985\pi\) | |||||||
\(8\) | 24.4569 | 1.08085 | ||||||||
\(9\) | 19.9064 | 0.737275 | ||||||||
\(10\) | 36.8056 | 1.16389 | ||||||||
\(11\) | −49.3031 | −1.35140 | −0.675702 | − | 0.737175i | \(-0.736159\pi\) | ||||
−0.675702 | + | 0.737175i | \(0.736159\pi\) | |||||||
\(12\) | −23.1964 | −0.558019 | ||||||||
\(13\) | 15.4223 | 0.329029 | 0.164514 | − | 0.986375i | \(-0.447394\pi\) | ||||
0.164514 | + | 0.986375i | \(0.447394\pi\) | |||||||
\(14\) | −49.3537 | −0.942166 | ||||||||
\(15\) | −117.364 | −2.02021 | ||||||||
\(16\) | −25.4334 | −0.397397 | ||||||||
\(17\) | 71.6119 | 1.02167 | 0.510837 | − | 0.859678i | \(-0.329336\pi\) | ||||
0.510837 | + | 0.859678i | \(0.329336\pi\) | |||||||
\(18\) | −42.7552 | −0.559861 | ||||||||
\(19\) | −59.6425 | −0.720154 | −0.360077 | − | 0.932923i | \(-0.617250\pi\) | ||||
−0.360077 | + | 0.932923i | \(0.617250\pi\) | |||||||
\(20\) | 58.0394 | 0.648900 | ||||||||
\(21\) | 157.377 | 1.63535 | ||||||||
\(22\) | 105.894 | 1.02621 | ||||||||
\(23\) | 161.135 | 1.46082 | 0.730412 | − | 0.683007i | \(-0.239328\pi\) | ||||
0.730412 | + | 0.683007i | \(0.239328\pi\) | |||||||
\(24\) | 167.501 | 1.42463 | ||||||||
\(25\) | 168.654 | 1.34923 | ||||||||
\(26\) | −33.1241 | −0.249853 | ||||||||
\(27\) | −48.5826 | −0.346286 | ||||||||
\(28\) | −77.8267 | −0.525281 | ||||||||
\(29\) | −7.84331 | −0.0502230 | −0.0251115 | − | 0.999685i | \(-0.507994\pi\) | ||||
−0.0251115 | + | 0.999685i | \(0.507994\pi\) | |||||||
\(30\) | 252.075 | 1.53408 | ||||||||
\(31\) | −208.323 | −1.20697 | −0.603484 | − | 0.797375i | \(-0.706221\pi\) | ||||
−0.603484 | + | 0.797375i | \(0.706221\pi\) | |||||||
\(32\) | −141.029 | −0.779084 | ||||||||
\(33\) | −337.668 | −1.78123 | ||||||||
\(34\) | −153.809 | −0.775823 | ||||||||
\(35\) | −393.769 | −1.90169 | ||||||||
\(36\) | −67.4215 | −0.312137 | ||||||||
\(37\) | −25.8568 | −0.114887 | −0.0574436 | − | 0.998349i | \(-0.518295\pi\) | ||||
−0.0574436 | + | 0.998349i | \(0.518295\pi\) | |||||||
\(38\) | 128.101 | 0.546859 | ||||||||
\(39\) | 105.625 | 0.433679 | ||||||||
\(40\) | −419.102 | −1.65665 | ||||||||
\(41\) | 383.496 | 1.46078 | 0.730391 | − | 0.683029i | \(-0.239338\pi\) | ||||
0.730391 | + | 0.683029i | \(0.239338\pi\) | |||||||
\(42\) | −338.015 | −1.24183 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 166.986 | 0.572137 | ||||||||
\(45\) | −341.123 | −1.13004 | ||||||||
\(46\) | −346.087 | −1.10930 | ||||||||
\(47\) | −577.020 | −1.79079 | −0.895394 | − | 0.445276i | \(-0.853106\pi\) | ||||
−0.895394 | + | 0.445276i | \(0.853106\pi\) | |||||||
\(48\) | −174.189 | −0.523792 | ||||||||
\(49\) | 185.017 | 0.539408 | ||||||||
\(50\) | −362.237 | −1.02456 | ||||||||
\(51\) | 490.458 | 1.34662 | ||||||||
\(52\) | −52.2341 | −0.139299 | ||||||||
\(53\) | 134.370 | 0.348247 | 0.174124 | − | 0.984724i | \(-0.444291\pi\) | ||||
0.174124 | + | 0.984724i | \(0.444291\pi\) | |||||||
\(54\) | 104.346 | 0.262958 | ||||||||
\(55\) | 844.874 | 2.07132 | ||||||||
\(56\) | 561.986 | 1.34105 | ||||||||
\(57\) | −408.481 | −0.949204 | ||||||||
\(58\) | 16.8459 | 0.0381375 | ||||||||
\(59\) | 532.562 | 1.17515 | 0.587573 | − | 0.809171i | \(-0.300084\pi\) | ||||
0.587573 | + | 0.809171i | \(0.300084\pi\) | |||||||
\(60\) | 397.502 | 0.855288 | ||||||||
\(61\) | 253.789 | 0.532694 | 0.266347 | − | 0.963877i | \(-0.414183\pi\) | ||||
0.266347 | + | 0.963877i | \(0.414183\pi\) | |||||||
\(62\) | 447.439 | 0.916529 | ||||||||
\(63\) | 457.422 | 0.914759 | ||||||||
\(64\) | 506.371 | 0.989006 | ||||||||
\(65\) | −264.282 | −0.504309 | ||||||||
\(66\) | 725.247 | 1.35260 | ||||||||
\(67\) | −690.488 | −1.25905 | −0.629527 | − | 0.776979i | \(-0.716751\pi\) | ||||
−0.629527 | + | 0.776979i | \(0.716751\pi\) | |||||||
\(68\) | −242.544 | −0.432541 | ||||||||
\(69\) | 1103.59 | 1.92545 | ||||||||
\(70\) | 845.741 | 1.44408 | ||||||||
\(71\) | −636.819 | −1.06446 | −0.532229 | − | 0.846600i | \(-0.678646\pi\) | ||||
−0.532229 | + | 0.846600i | \(0.678646\pi\) | |||||||
\(72\) | 486.850 | 0.796887 | ||||||||
\(73\) | 475.895 | 0.763004 | 0.381502 | − | 0.924368i | \(-0.375407\pi\) | ||||
0.381502 | + | 0.924368i | \(0.375407\pi\) | |||||||
\(74\) | 55.5354 | 0.0872413 | ||||||||
\(75\) | 1155.08 | 1.77837 | ||||||||
\(76\) | 202.004 | 0.304888 | ||||||||
\(77\) | −1132.92 | −1.67673 | ||||||||
\(78\) | −226.861 | −0.329321 | ||||||||
\(79\) | 146.424 | 0.208531 | 0.104266 | − | 0.994549i | \(-0.466751\pi\) | ||||
0.104266 | + | 0.994549i | \(0.466751\pi\) | |||||||
\(80\) | 435.836 | 0.609099 | ||||||||
\(81\) | −870.208 | −1.19370 | ||||||||
\(82\) | −823.677 | −1.10927 | ||||||||
\(83\) | −783.374 | −1.03598 | −0.517991 | − | 0.855386i | \(-0.673320\pi\) | ||||
−0.517991 | + | 0.855386i | \(0.673320\pi\) | |||||||
\(84\) | −533.022 | −0.692351 | ||||||||
\(85\) | −1227.17 | −1.56594 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −53.7175 | −0.0661967 | ||||||||
\(88\) | −1205.80 | −1.46067 | ||||||||
\(89\) | 1056.24 | 1.25799 | 0.628997 | − | 0.777407i | \(-0.283466\pi\) | ||||
0.628997 | + | 0.777407i | \(0.283466\pi\) | |||||||
\(90\) | 732.668 | 0.858111 | ||||||||
\(91\) | 354.383 | 0.408236 | ||||||||
\(92\) | −545.751 | −0.618462 | ||||||||
\(93\) | −1426.77 | −1.59085 | ||||||||
\(94\) | 1239.33 | 1.35986 | ||||||||
\(95\) | 1022.05 | 1.10379 | ||||||||
\(96\) | −965.885 | −1.02688 | ||||||||
\(97\) | −102.057 | −0.106828 | −0.0534140 | − | 0.998572i | \(-0.517010\pi\) | ||||
−0.0534140 | + | 0.998572i | \(0.517010\pi\) | |||||||
\(98\) | −397.381 | −0.409608 | ||||||||
\(99\) | −981.449 | −0.996357 | ||||||||
\(100\) | −571.218 | −0.571218 | ||||||||
\(101\) | 1135.10 | 1.11828 | 0.559140 | − | 0.829073i | \(-0.311131\pi\) | ||||
0.559140 | + | 0.829073i | \(0.311131\pi\) | |||||||
\(102\) | −1053.41 | −1.02258 | ||||||||
\(103\) | 759.720 | 0.726772 | 0.363386 | − | 0.931639i | \(-0.381621\pi\) | ||||
0.363386 | + | 0.931639i | \(0.381621\pi\) | |||||||
\(104\) | 377.182 | 0.355632 | ||||||||
\(105\) | −2696.86 | −2.50654 | ||||||||
\(106\) | −288.600 | −0.264447 | ||||||||
\(107\) | −587.456 | −0.530761 | −0.265381 | − | 0.964144i | \(-0.585498\pi\) | ||||
−0.265381 | + | 0.964144i | \(0.585498\pi\) | |||||||
\(108\) | 164.545 | 0.146605 | ||||||||
\(109\) | 591.336 | 0.519630 | 0.259815 | − | 0.965658i | \(-0.416338\pi\) | ||||
0.259815 | + | 0.965658i | \(0.416338\pi\) | |||||||
\(110\) | −1814.63 | −1.57289 | ||||||||
\(111\) | −177.089 | −0.151428 | ||||||||
\(112\) | −584.425 | −0.493062 | ||||||||
\(113\) | −904.939 | −0.753359 | −0.376679 | − | 0.926344i | \(-0.622934\pi\) | ||||
−0.376679 | + | 0.926344i | \(0.622934\pi\) | |||||||
\(114\) | 877.339 | 0.720792 | ||||||||
\(115\) | −2761.26 | −2.23903 | ||||||||
\(116\) | 26.5647 | 0.0212626 | ||||||||
\(117\) | 307.003 | 0.242585 | ||||||||
\(118\) | −1143.84 | −0.892365 | ||||||||
\(119\) | 1645.54 | 1.26762 | ||||||||
\(120\) | −2870.36 | −2.18355 | ||||||||
\(121\) | 1099.79 | 0.826292 | ||||||||
\(122\) | −545.090 | −0.404509 | ||||||||
\(123\) | 2626.50 | 1.92539 | ||||||||
\(124\) | 705.575 | 0.510988 | ||||||||
\(125\) | −748.071 | −0.535276 | ||||||||
\(126\) | −982.456 | −0.694636 | ||||||||
\(127\) | 1437.81 | 1.00461 | 0.502303 | − | 0.864692i | \(-0.332486\pi\) | ||||
0.502303 | + | 0.864692i | \(0.332486\pi\) | |||||||
\(128\) | 40.6460 | 0.0280674 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 567.626 | 0.382955 | ||||||||
\(131\) | 839.267 | 0.559749 | 0.279874 | − | 0.960037i | \(-0.409707\pi\) | ||||
0.279874 | + | 0.960037i | \(0.409707\pi\) | |||||||
\(132\) | 1143.66 | 0.754109 | ||||||||
\(133\) | −1370.50 | −0.893516 | ||||||||
\(134\) | 1483.04 | 0.956081 | ||||||||
\(135\) | 832.528 | 0.530760 | ||||||||
\(136\) | 1751.41 | 1.10428 | ||||||||
\(137\) | 1329.77 | 0.829272 | 0.414636 | − | 0.909987i | \(-0.363909\pi\) | ||||
0.414636 | + | 0.909987i | \(0.363909\pi\) | |||||||
\(138\) | −2370.29 | −1.46212 | ||||||||
\(139\) | −2130.67 | −1.30015 | −0.650075 | − | 0.759870i | \(-0.725263\pi\) | ||||
−0.650075 | + | 0.759870i | \(0.725263\pi\) | |||||||
\(140\) | 1333.67 | 0.805109 | ||||||||
\(141\) | −3951.91 | −2.36036 | ||||||||
\(142\) | 1367.77 | 0.808312 | ||||||||
\(143\) | −760.367 | −0.444651 | ||||||||
\(144\) | −506.289 | −0.292991 | ||||||||
\(145\) | 134.406 | 0.0769778 | ||||||||
\(146\) | −1022.13 | −0.579398 | ||||||||
\(147\) | 1267.15 | 0.710971 | ||||||||
\(148\) | 87.5748 | 0.0486392 | ||||||||
\(149\) | −336.440 | −0.184981 | −0.0924906 | − | 0.995714i | \(-0.529483\pi\) | ||||
−0.0924906 | + | 0.995714i | \(0.529483\pi\) | |||||||
\(150\) | −2480.90 | −1.35043 | ||||||||
\(151\) | 1200.49 | 0.646982 | 0.323491 | − | 0.946231i | \(-0.395143\pi\) | ||||
0.323491 | + | 0.946231i | \(0.395143\pi\) | |||||||
\(152\) | −1458.67 | −0.778381 | ||||||||
\(153\) | 1425.54 | 0.753255 | ||||||||
\(154\) | 2433.29 | 1.27325 | ||||||||
\(155\) | 3569.90 | 1.84994 | ||||||||
\(156\) | −357.742 | −0.183604 | ||||||||
\(157\) | −1592.21 | −0.809378 | −0.404689 | − | 0.914454i | \(-0.632620\pi\) | ||||
−0.404689 | + | 0.914454i | \(0.632620\pi\) | |||||||
\(158\) | −314.490 | −0.158351 | ||||||||
\(159\) | 920.275 | 0.459010 | ||||||||
\(160\) | 2416.73 | 1.19412 | ||||||||
\(161\) | 3702.66 | 1.81249 | ||||||||
\(162\) | 1869.04 | 0.906454 | ||||||||
\(163\) | 3945.38 | 1.89587 | 0.947933 | − | 0.318469i | \(-0.103169\pi\) | ||||
0.947933 | + | 0.318469i | \(0.103169\pi\) | |||||||
\(164\) | −1298.87 | −0.618444 | ||||||||
\(165\) | 5786.40 | 2.73012 | ||||||||
\(166\) | 1682.54 | 0.786688 | ||||||||
\(167\) | 2058.29 | 0.953746 | 0.476873 | − | 0.878972i | \(-0.341770\pi\) | ||||
0.476873 | + | 0.878972i | \(0.341770\pi\) | |||||||
\(168\) | 3848.95 | 1.76758 | ||||||||
\(169\) | −1959.15 | −0.891740 | ||||||||
\(170\) | 2635.72 | 1.18912 | ||||||||
\(171\) | −1187.27 | −0.530952 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1201.75 | 0.528134 | 0.264067 | − | 0.964504i | \(-0.414936\pi\) | ||||
0.264067 | + | 0.964504i | \(0.414936\pi\) | |||||||
\(174\) | 115.375 | 0.0502675 | ||||||||
\(175\) | 3875.44 | 1.67403 | ||||||||
\(176\) | 1253.95 | 0.537044 | ||||||||
\(177\) | 3647.42 | 1.54891 | ||||||||
\(178\) | −2268.61 | −0.955277 | ||||||||
\(179\) | 3664.67 | 1.53023 | 0.765113 | − | 0.643896i | \(-0.222683\pi\) | ||||
0.765113 | + | 0.643896i | \(0.222683\pi\) | |||||||
\(180\) | 1155.36 | 0.478418 | ||||||||
\(181\) | 185.832 | 0.0763138 | 0.0381569 | − | 0.999272i | \(-0.487851\pi\) | ||||
0.0381569 | + | 0.999272i | \(0.487851\pi\) | |||||||
\(182\) | −761.147 | −0.310000 | ||||||||
\(183\) | 1738.16 | 0.702121 | ||||||||
\(184\) | 3940.86 | 1.57894 | ||||||||
\(185\) | 443.090 | 0.176090 | ||||||||
\(186\) | 3064.43 | 1.20804 | ||||||||
\(187\) | −3530.69 | −1.38069 | ||||||||
\(188\) | 1954.32 | 0.758157 | ||||||||
\(189\) | −1116.36 | −0.429647 | ||||||||
\(190\) | −2195.17 | −0.838183 | ||||||||
\(191\) | 1326.38 | 0.502478 | 0.251239 | − | 0.967925i | \(-0.419162\pi\) | ||||
0.251239 | + | 0.967925i | \(0.419162\pi\) | |||||||
\(192\) | 3468.05 | 1.30357 | ||||||||
\(193\) | −1507.87 | −0.562378 | −0.281189 | − | 0.959652i | \(-0.590729\pi\) | ||||
−0.281189 | + | 0.959652i | \(0.590729\pi\) | |||||||
\(194\) | 219.199 | 0.0811214 | ||||||||
\(195\) | −1810.02 | −0.664709 | ||||||||
\(196\) | −626.638 | −0.228367 | ||||||||
\(197\) | 407.216 | 0.147274 | 0.0736369 | − | 0.997285i | \(-0.476539\pi\) | ||||
0.0736369 | + | 0.997285i | \(0.476539\pi\) | |||||||
\(198\) | 2107.96 | 0.756598 | ||||||||
\(199\) | 394.575 | 0.140556 | 0.0702782 | − | 0.997527i | \(-0.477611\pi\) | ||||
0.0702782 | + | 0.997527i | \(0.477611\pi\) | |||||||
\(200\) | 4124.76 | 1.45832 | ||||||||
\(201\) | −4729.03 | −1.65950 | ||||||||
\(202\) | −2437.97 | −0.849183 | ||||||||
\(203\) | −180.228 | −0.0623131 | ||||||||
\(204\) | −1661.14 | −0.570113 | ||||||||
\(205\) | −6571.72 | −2.23897 | ||||||||
\(206\) | −1631.73 | −0.551885 | ||||||||
\(207\) | 3207.62 | 1.07703 | ||||||||
\(208\) | −392.242 | −0.130755 | ||||||||
\(209\) | 2940.56 | 0.973218 | ||||||||
\(210\) | 5792.34 | 1.90338 | ||||||||
\(211\) | 3347.80 | 1.09229 | 0.546143 | − | 0.837692i | \(-0.316096\pi\) | ||||
0.546143 | + | 0.837692i | \(0.316096\pi\) | |||||||
\(212\) | −455.099 | −0.147436 | ||||||||
\(213\) | −4361.47 | −1.40302 | ||||||||
\(214\) | 1261.74 | 0.403042 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1188.18 | −0.374285 | ||||||||
\(217\) | −4786.99 | −1.49752 | ||||||||
\(218\) | −1270.08 | −0.394589 | ||||||||
\(219\) | 3259.32 | 1.00568 | ||||||||
\(220\) | −2861.52 | −0.876926 | ||||||||
\(221\) | 1104.42 | 0.336160 | ||||||||
\(222\) | 380.352 | 0.114989 | ||||||||
\(223\) | −820.804 | −0.246480 | −0.123240 | − | 0.992377i | \(-0.539329\pi\) | ||||
−0.123240 | + | 0.992377i | \(0.539329\pi\) | |||||||
\(224\) | −3240.66 | −0.966632 | ||||||||
\(225\) | 3357.30 | 0.994756 | ||||||||
\(226\) | 1943.64 | 0.572074 | ||||||||
\(227\) | −2225.27 | −0.650646 | −0.325323 | − | 0.945603i | \(-0.605473\pi\) | ||||
−0.325323 | + | 0.945603i | \(0.605473\pi\) | |||||||
\(228\) | 1383.49 | 0.401860 | ||||||||
\(229\) | −2109.88 | −0.608842 | −0.304421 | − | 0.952538i | \(-0.598463\pi\) | ||||
−0.304421 | + | 0.952538i | \(0.598463\pi\) | |||||||
\(230\) | 5930.66 | 1.70024 | ||||||||
\(231\) | −7759.15 | −2.21002 | ||||||||
\(232\) | −191.823 | −0.0542837 | ||||||||
\(233\) | 2118.94 | 0.595779 | 0.297890 | − | 0.954600i | \(-0.403717\pi\) | ||||
0.297890 | + | 0.954600i | \(0.403717\pi\) | |||||||
\(234\) | −659.383 | −0.184210 | ||||||||
\(235\) | 9888.01 | 2.74478 | ||||||||
\(236\) | −1803.74 | −0.497516 | ||||||||
\(237\) | 1002.83 | 0.274856 | ||||||||
\(238\) | −3534.31 | −0.962586 | ||||||||
\(239\) | 2706.53 | 0.732513 | 0.366257 | − | 0.930514i | \(-0.380639\pi\) | ||||
0.366257 | + | 0.930514i | \(0.380639\pi\) | |||||||
\(240\) | 2984.96 | 0.802827 | ||||||||
\(241\) | −965.679 | −0.258111 | −0.129056 | − | 0.991637i | \(-0.541195\pi\) | ||||
−0.129056 | + | 0.991637i | \(0.541195\pi\) | |||||||
\(242\) | −2362.15 | −0.627457 | ||||||||
\(243\) | −4648.17 | −1.22708 | ||||||||
\(244\) | −859.562 | −0.225524 | ||||||||
\(245\) | −3170.51 | −0.826762 | ||||||||
\(246\) | −5641.22 | −1.46208 | ||||||||
\(247\) | −919.824 | −0.236951 | ||||||||
\(248\) | −5094.95 | −1.30455 | ||||||||
\(249\) | −5365.19 | −1.36548 | ||||||||
\(250\) | 1606.71 | 0.406470 | ||||||||
\(251\) | 6103.02 | 1.53474 | 0.767369 | − | 0.641205i | \(-0.221565\pi\) | ||||
0.767369 | + | 0.641205i | \(0.221565\pi\) | |||||||
\(252\) | −1549.25 | −0.387277 | ||||||||
\(253\) | −7944.45 | −1.97416 | ||||||||
\(254\) | −3088.14 | −0.762862 | ||||||||
\(255\) | −8404.65 | −2.06400 | ||||||||
\(256\) | −4138.27 | −1.01032 | ||||||||
\(257\) | 6760.71 | 1.64094 | 0.820469 | − | 0.571691i | \(-0.193712\pi\) | ||||
0.820469 | + | 0.571691i | \(0.193712\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −594.153 | −0.142544 | ||||||||
\(260\) | 895.101 | 0.213507 | ||||||||
\(261\) | −156.132 | −0.0370281 | ||||||||
\(262\) | −1802.59 | −0.425054 | ||||||||
\(263\) | 7838.17 | 1.83773 | 0.918864 | − | 0.394574i | \(-0.129108\pi\) | ||||
0.918864 | + | 0.394574i | \(0.129108\pi\) | |||||||
\(264\) | −8258.33 | −1.92525 | ||||||||
\(265\) | −2302.60 | −0.533766 | ||||||||
\(266\) | 2943.57 | 0.678504 | ||||||||
\(267\) | 7234.02 | 1.65811 | ||||||||
\(268\) | 2338.63 | 0.533039 | ||||||||
\(269\) | −3952.54 | −0.895876 | −0.447938 | − | 0.894065i | \(-0.647842\pi\) | ||||
−0.447938 | + | 0.894065i | \(0.647842\pi\) | |||||||
\(270\) | −1788.11 | −0.403040 | ||||||||
\(271\) | −583.263 | −0.130741 | −0.0653703 | − | 0.997861i | \(-0.520823\pi\) | ||||
−0.0653703 | + | 0.997861i | \(0.520823\pi\) | |||||||
\(272\) | −1821.34 | −0.406010 | ||||||||
\(273\) | 2427.11 | 0.538078 | ||||||||
\(274\) | −2856.10 | −0.629720 | ||||||||
\(275\) | −8315.17 | −1.82336 | ||||||||
\(276\) | −3737.75 | −0.815168 | ||||||||
\(277\) | 3050.70 | 0.661729 | 0.330864 | − | 0.943678i | \(-0.392660\pi\) | ||||
0.330864 | + | 0.943678i | \(0.392660\pi\) | |||||||
\(278\) | 4576.27 | 0.987288 | ||||||||
\(279\) | −4146.98 | −0.889867 | ||||||||
\(280\) | −9630.39 | −2.05545 | ||||||||
\(281\) | 6333.07 | 1.34448 | 0.672241 | − | 0.740332i | \(-0.265332\pi\) | ||||
0.672241 | + | 0.740332i | \(0.265332\pi\) | |||||||
\(282\) | 8487.94 | 1.79237 | ||||||||
\(283\) | 7840.90 | 1.64697 | 0.823486 | − | 0.567337i | \(-0.192026\pi\) | ||||
0.823486 | + | 0.567337i | \(0.192026\pi\) | |||||||
\(284\) | 2156.86 | 0.450654 | ||||||||
\(285\) | 6999.87 | 1.45486 | ||||||||
\(286\) | 1633.12 | 0.337652 | ||||||||
\(287\) | 8812.22 | 1.81243 | ||||||||
\(288\) | −2807.39 | −0.574399 | ||||||||
\(289\) | 215.269 | 0.0438163 | ||||||||
\(290\) | −288.677 | −0.0584542 | ||||||||
\(291\) | −698.971 | −0.140805 | ||||||||
\(292\) | −1611.82 | −0.323029 | ||||||||
\(293\) | 7168.90 | 1.42939 | 0.714696 | − | 0.699435i | \(-0.246565\pi\) | ||||
0.714696 | + | 0.699435i | \(0.246565\pi\) | |||||||
\(294\) | −2721.59 | −0.539886 | ||||||||
\(295\) | −9126.16 | −1.80117 | ||||||||
\(296\) | −632.377 | −0.124176 | ||||||||
\(297\) | 2395.27 | 0.467972 | ||||||||
\(298\) | 722.608 | 0.140468 | ||||||||
\(299\) | 2485.07 | 0.480653 | ||||||||
\(300\) | −3912.17 | −0.752898 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2578.42 | −0.491295 | ||||||||
\(303\) | 7774.08 | 1.47396 | ||||||||
\(304\) | 1516.91 | 0.286187 | ||||||||
\(305\) | −4349.01 | −0.816471 | ||||||||
\(306\) | −3061.78 | −0.571995 | ||||||||
\(307\) | 697.459 | 0.129662 | 0.0648308 | − | 0.997896i | \(-0.479349\pi\) | ||||
0.0648308 | + | 0.997896i | \(0.479349\pi\) | |||||||
\(308\) | 3837.10 | 0.709867 | ||||||||
\(309\) | 5203.19 | 0.957927 | ||||||||
\(310\) | −7667.46 | −1.40478 | ||||||||
\(311\) | 2348.86 | 0.428269 | 0.214135 | − | 0.976804i | \(-0.431307\pi\) | ||||
0.214135 | + | 0.976804i | \(0.431307\pi\) | |||||||
\(312\) | 2583.25 | 0.468743 | ||||||||
\(313\) | 9405.55 | 1.69851 | 0.849254 | − | 0.527985i | \(-0.177052\pi\) | ||||
0.849254 | + | 0.527985i | \(0.177052\pi\) | |||||||
\(314\) | 3419.77 | 0.614613 | ||||||||
\(315\) | −7838.54 | −1.40207 | ||||||||
\(316\) | −495.926 | −0.0882848 | ||||||||
\(317\) | −6357.40 | −1.12640 | −0.563198 | − | 0.826322i | \(-0.690429\pi\) | ||||
−0.563198 | + | 0.826322i | \(0.690429\pi\) | |||||||
\(318\) | −1976.57 | −0.348556 | ||||||||
\(319\) | 386.699 | 0.0678715 | ||||||||
\(320\) | −8677.35 | −1.51587 | ||||||||
\(321\) | −4023.38 | −0.699574 | ||||||||
\(322\) | −7952.60 | −1.37634 | ||||||||
\(323\) | −4271.11 | −0.735762 | ||||||||
\(324\) | 2947.32 | 0.505371 | ||||||||
\(325\) | 2601.03 | 0.443936 | ||||||||
\(326\) | −8473.93 | −1.43965 | ||||||||
\(327\) | 4049.96 | 0.684902 | ||||||||
\(328\) | 9379.14 | 1.57889 | ||||||||
\(329\) | −13259.1 | −2.22188 | ||||||||
\(330\) | −12428.1 | −2.07316 | ||||||||
\(331\) | 6083.41 | 1.01019 | 0.505097 | − | 0.863062i | \(-0.331457\pi\) | ||||
0.505097 | + | 0.863062i | \(0.331457\pi\) | |||||||
\(332\) | 2653.22 | 0.438598 | ||||||||
\(333\) | −514.716 | −0.0847035 | ||||||||
\(334\) | −4420.82 | −0.724241 | ||||||||
\(335\) | 11832.4 | 1.92978 | ||||||||
\(336\) | −4002.62 | −0.649884 | ||||||||
\(337\) | −3365.71 | −0.544041 | −0.272020 | − | 0.962291i | \(-0.587692\pi\) | ||||
−0.272020 | + | 0.962291i | \(0.587692\pi\) | |||||||
\(338\) | 4207.88 | 0.677156 | ||||||||
\(339\) | −6197.77 | −0.992970 | ||||||||
\(340\) | 4156.31 | 0.662964 | ||||||||
\(341\) | 10271.0 | 1.63110 | ||||||||
\(342\) | 2550.03 | 0.403186 | ||||||||
\(343\) | −3630.23 | −0.571470 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −18911.4 | −2.95118 | ||||||||
\(346\) | −2581.12 | −0.401046 | ||||||||
\(347\) | 2220.51 | 0.343524 | 0.171762 | − | 0.985138i | \(-0.445054\pi\) | ||||
0.171762 | + | 0.985138i | \(0.445054\pi\) | |||||||
\(348\) | 181.937 | 0.0280254 | ||||||||
\(349\) | −3836.59 | −0.588447 | −0.294223 | − | 0.955737i | \(-0.595061\pi\) | ||||
−0.294223 | + | 0.955737i | \(0.595061\pi\) | |||||||
\(350\) | −8323.70 | −1.27120 | ||||||||
\(351\) | −749.255 | −0.113938 | ||||||||
\(352\) | 6953.18 | 1.05286 | ||||||||
\(353\) | −3271.92 | −0.493334 | −0.246667 | − | 0.969100i | \(-0.579335\pi\) | ||||
−0.246667 | + | 0.969100i | \(0.579335\pi\) | |||||||
\(354\) | −7833.96 | −1.17619 | ||||||||
\(355\) | 10912.8 | 1.63152 | ||||||||
\(356\) | −3577.41 | −0.532591 | ||||||||
\(357\) | 11270.0 | 1.67080 | ||||||||
\(358\) | −7871.02 | −1.16200 | ||||||||
\(359\) | −1270.02 | −0.186711 | −0.0933555 | − | 0.995633i | \(-0.529759\pi\) | ||||
−0.0933555 | + | 0.995633i | \(0.529759\pi\) | |||||||
\(360\) | −8342.83 | −1.22140 | ||||||||
\(361\) | −3301.78 | −0.481379 | ||||||||
\(362\) | −399.132 | −0.0579500 | ||||||||
\(363\) | 7532.30 | 1.08910 | ||||||||
\(364\) | −1200.27 | −0.172833 | ||||||||
\(365\) | −8155.10 | −1.16947 | ||||||||
\(366\) | −3733.23 | −0.533166 | ||||||||
\(367\) | −7336.15 | −1.04344 | −0.521722 | − | 0.853115i | \(-0.674710\pi\) | ||||
−0.521722 | + | 0.853115i | \(0.674710\pi\) | |||||||
\(368\) | −4098.21 | −0.580527 | ||||||||
\(369\) | 7634.04 | 1.07700 | ||||||||
\(370\) | −951.673 | −0.133717 | ||||||||
\(371\) | 3087.63 | 0.432080 | ||||||||
\(372\) | 4832.36 | 0.673511 | ||||||||
\(373\) | 10341.7 | 1.43558 | 0.717791 | − | 0.696259i | \(-0.245154\pi\) | ||||
0.717791 | + | 0.696259i | \(0.245154\pi\) | |||||||
\(374\) | 7583.24 | 1.04845 | ||||||||
\(375\) | −5123.41 | −0.705525 | ||||||||
\(376\) | −14112.1 | −1.93558 | ||||||||
\(377\) | −120.962 | −0.0165248 | ||||||||
\(378\) | 2397.73 | 0.326259 | ||||||||
\(379\) | −2889.02 | −0.391555 | −0.195777 | − | 0.980648i | \(-0.562723\pi\) | ||||
−0.195777 | + | 0.980648i | \(0.562723\pi\) | |||||||
\(380\) | −3461.61 | −0.467308 | ||||||||
\(381\) | 9847.30 | 1.32413 | ||||||||
\(382\) | −2848.81 | −0.381564 | ||||||||
\(383\) | 1083.65 | 0.144575 | 0.0722874 | − | 0.997384i | \(-0.476970\pi\) | ||||
0.0722874 | + | 0.997384i | \(0.476970\pi\) | |||||||
\(384\) | 278.377 | 0.0369945 | ||||||||
\(385\) | 19414.0 | 2.56995 | ||||||||
\(386\) | 3238.62 | 0.427050 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 345.659 | 0.0452272 | ||||||||
\(389\) | 683.935 | 0.0891436 | 0.0445718 | − | 0.999006i | \(-0.485808\pi\) | ||||
0.0445718 | + | 0.999006i | \(0.485808\pi\) | |||||||
\(390\) | 3887.57 | 0.504756 | ||||||||
\(391\) | 11539.2 | 1.49248 | ||||||||
\(392\) | 4524.95 | 0.583021 | ||||||||
\(393\) | 5748.00 | 0.737781 | ||||||||
\(394\) | −874.622 | −0.111835 | ||||||||
\(395\) | −2509.17 | −0.319620 | ||||||||
\(396\) | 3324.09 | 0.421823 | ||||||||
\(397\) | −11007.5 | −1.39156 | −0.695779 | − | 0.718256i | \(-0.744941\pi\) | ||||
−0.695779 | + | 0.718256i | \(0.744941\pi\) | |||||||
\(398\) | −847.472 | −0.106734 | ||||||||
\(399\) | −9386.33 | −1.17770 | ||||||||
\(400\) | −4289.45 | −0.536181 | ||||||||
\(401\) | 6198.42 | 0.771906 | 0.385953 | − | 0.922519i | \(-0.373873\pi\) | ||||
0.385953 | + | 0.922519i | \(0.373873\pi\) | |||||||
\(402\) | 10157.1 | 1.26017 | ||||||||
\(403\) | −3212.83 | −0.397127 | ||||||||
\(404\) | −3844.48 | −0.473441 | ||||||||
\(405\) | 14912.2 | 1.82961 | ||||||||
\(406\) | 387.096 | 0.0473184 | ||||||||
\(407\) | 1274.82 | 0.155259 | ||||||||
\(408\) | 11995.1 | 1.45550 | ||||||||
\(409\) | 5803.79 | 0.701660 | 0.350830 | − | 0.936439i | \(-0.385899\pi\) | ||||
0.350830 | + | 0.936439i | \(0.385899\pi\) | |||||||
\(410\) | 14114.8 | 1.70020 | ||||||||
\(411\) | 9107.39 | 1.09303 | ||||||||
\(412\) | −2573.11 | −0.307690 | ||||||||
\(413\) | 12237.5 | 1.45804 | ||||||||
\(414\) | −6889.36 | −0.817858 | ||||||||
\(415\) | 13424.2 | 1.58787 | ||||||||
\(416\) | −2174.99 | −0.256341 | ||||||||
\(417\) | −14592.6 | −1.71367 | ||||||||
\(418\) | −6315.75 | −0.739028 | ||||||||
\(419\) | 6575.42 | 0.766660 | 0.383330 | − | 0.923612i | \(-0.374777\pi\) | ||||
0.383330 | + | 0.923612i | \(0.374777\pi\) | |||||||
\(420\) | 9134.04 | 1.06118 | ||||||||
\(421\) | −12514.9 | −1.44878 | −0.724391 | − | 0.689390i | \(-0.757879\pi\) | ||||
−0.724391 | + | 0.689390i | \(0.757879\pi\) | |||||||
\(422\) | −7190.44 | −0.829444 | ||||||||
\(423\) | −11486.4 | −1.32030 | ||||||||
\(424\) | 3286.27 | 0.376404 | ||||||||
\(425\) | 12077.6 | 1.37847 | ||||||||
\(426\) | 9367.59 | 1.06540 | ||||||||
\(427\) | 5831.72 | 0.660929 | ||||||||
\(428\) | 1989.66 | 0.224706 | ||||||||
\(429\) | −5207.62 | −0.586075 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8400.34 | 0.938818 | 0.469409 | − | 0.882981i | \(-0.344467\pi\) | ||||
0.469409 | + | 0.882981i | \(0.344467\pi\) | |||||||
\(432\) | 1235.62 | 0.137613 | ||||||||
\(433\) | 2423.78 | 0.269005 | 0.134503 | − | 0.990913i | \(-0.457056\pi\) | ||||
0.134503 | + | 0.990913i | \(0.457056\pi\) | |||||||
\(434\) | 10281.5 | 1.13716 | ||||||||
\(435\) | 920.521 | 0.101461 | ||||||||
\(436\) | −2002.81 | −0.219993 | ||||||||
\(437\) | −9610.48 | −1.05202 | ||||||||
\(438\) | −7000.40 | −0.763680 | ||||||||
\(439\) | 813.778 | 0.0884727 | 0.0442363 | − | 0.999021i | \(-0.485915\pi\) | ||||
0.0442363 | + | 0.999021i | \(0.485915\pi\) | |||||||
\(440\) | 20663.0 | 2.23880 | ||||||||
\(441\) | 3683.03 | 0.397692 | ||||||||
\(442\) | −2372.08 | −0.255268 | ||||||||
\(443\) | 6180.97 | 0.662904 | 0.331452 | − | 0.943472i | \(-0.392461\pi\) | ||||
0.331452 | + | 0.943472i | \(0.392461\pi\) | |||||||
\(444\) | 599.785 | 0.0641093 | ||||||||
\(445\) | −18100.1 | −1.92815 | ||||||||
\(446\) | 1762.93 | 0.187169 | ||||||||
\(447\) | −2304.22 | −0.243816 | ||||||||
\(448\) | 11635.7 | 1.22709 | ||||||||
\(449\) | −5792.95 | −0.608878 | −0.304439 | − | 0.952532i | \(-0.598469\pi\) | ||||
−0.304439 | + | 0.952532i | \(0.598469\pi\) | |||||||
\(450\) | −7210.84 | −0.755383 | ||||||||
\(451\) | −18907.6 | −1.97411 | ||||||||
\(452\) | 3064.96 | 0.318946 | ||||||||
\(453\) | 8221.93 | 0.852759 | ||||||||
\(454\) | 4779.46 | 0.494078 | ||||||||
\(455\) | −6072.83 | −0.625711 | ||||||||
\(456\) | −9990.19 | −1.02595 | ||||||||
\(457\) | 1579.20 | 0.161646 | 0.0808228 | − | 0.996728i | \(-0.474245\pi\) | ||||
0.0808228 | + | 0.996728i | \(0.474245\pi\) | |||||||
\(458\) | 4531.62 | 0.462333 | ||||||||
\(459\) | −3479.09 | −0.353791 | ||||||||
\(460\) | 9352.17 | 0.947929 | ||||||||
\(461\) | −3027.25 | −0.305842 | −0.152921 | − | 0.988238i | \(-0.548868\pi\) | ||||
−0.152921 | + | 0.988238i | \(0.548868\pi\) | |||||||
\(462\) | 16665.2 | 1.67821 | ||||||||
\(463\) | 1731.83 | 0.173834 | 0.0869168 | − | 0.996216i | \(-0.472299\pi\) | ||||
0.0869168 | + | 0.996216i | \(0.472299\pi\) | |||||||
\(464\) | 199.482 | 0.0199585 | ||||||||
\(465\) | 24449.6 | 2.43833 | ||||||||
\(466\) | −4551.08 | −0.452414 | ||||||||
\(467\) | −4012.33 | −0.397577 | −0.198788 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198788 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(468\) | −1039.79 | −0.102702 | ||||||||
\(469\) | −15866.5 | −1.56214 | ||||||||
\(470\) | −21237.5 | −2.08429 | ||||||||
\(471\) | −10904.8 | −1.06681 | ||||||||
\(472\) | 13024.8 | 1.27016 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −2153.89 | −0.208716 | ||||||||
\(475\) | −10058.9 | −0.971655 | ||||||||
\(476\) | −5573.32 | −0.536666 | ||||||||
\(477\) | 2674.82 | 0.256754 | ||||||||
\(478\) | −5813.10 | −0.556245 | ||||||||
\(479\) | 5871.47 | 0.560072 | 0.280036 | − | 0.959990i | \(-0.409654\pi\) | ||||
0.280036 | + | 0.959990i | \(0.409654\pi\) | |||||||
\(480\) | 16551.7 | 1.57392 | ||||||||
\(481\) | −398.771 | −0.0378012 | ||||||||
\(482\) | 2074.09 | 0.196001 | ||||||||
\(483\) | 25358.9 | 2.38896 | ||||||||
\(484\) | −3724.92 | −0.349823 | ||||||||
\(485\) | 1748.88 | 0.163737 | ||||||||
\(486\) | 9983.38 | 0.931801 | ||||||||
\(487\) | 7302.93 | 0.679522 | 0.339761 | − | 0.940512i | \(-0.389654\pi\) | ||||
0.339761 | + | 0.940512i | \(0.389654\pi\) | |||||||
\(488\) | 6206.89 | 0.575764 | ||||||||
\(489\) | 27021.2 | 2.49886 | ||||||||
\(490\) | 6809.66 | 0.627814 | ||||||||
\(491\) | 41.1543 | 0.00378262 | 0.00189131 | − | 0.999998i | \(-0.499398\pi\) | ||||
0.00189131 | + | 0.999998i | \(0.499398\pi\) | |||||||
\(492\) | −8895.74 | −0.815145 | ||||||||
\(493\) | −561.674 | −0.0513115 | ||||||||
\(494\) | 1975.61 | 0.179933 | ||||||||
\(495\) | 16818.4 | 1.52714 | ||||||||
\(496\) | 5298.38 | 0.479645 | ||||||||
\(497\) | −14633.2 | −1.32070 | ||||||||
\(498\) | 11523.4 | 1.03690 | ||||||||
\(499\) | 6119.14 | 0.548959 | 0.274479 | − | 0.961593i | \(-0.411495\pi\) | ||||
0.274479 | + | 0.961593i | \(0.411495\pi\) | |||||||
\(500\) | 2533.66 | 0.226617 | ||||||||
\(501\) | 14096.9 | 1.25709 | ||||||||
\(502\) | −13108.1 | −1.16543 | ||||||||
\(503\) | −13276.4 | −1.17687 | −0.588435 | − | 0.808545i | \(-0.700256\pi\) | ||||
−0.588435 | + | 0.808545i | \(0.700256\pi\) | |||||||
\(504\) | 11187.1 | 0.988720 | ||||||||
\(505\) | −19451.4 | −1.71401 | ||||||||
\(506\) | 17063.2 | 1.49911 | ||||||||
\(507\) | −13417.9 | −1.17536 | ||||||||
\(508\) | −4869.74 | −0.425315 | ||||||||
\(509\) | 22154.6 | 1.92924 | 0.964622 | − | 0.263637i | \(-0.0849220\pi\) | ||||
0.964622 | + | 0.263637i | \(0.0849220\pi\) | |||||||
\(510\) | 18051.6 | 1.56733 | ||||||||
\(511\) | 10935.4 | 0.946681 | ||||||||
\(512\) | 8563.04 | 0.739134 | ||||||||
\(513\) | 2897.59 | 0.249379 | ||||||||
\(514\) | −14520.7 | −1.24607 | ||||||||
\(515\) | −13018.8 | −1.11394 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28448.9 | 2.42008 | ||||||||
\(518\) | 1276.13 | 0.108243 | ||||||||
\(519\) | 8230.56 | 0.696111 | ||||||||
\(520\) | −6463.52 | −0.545084 | ||||||||
\(521\) | 866.938 | 0.0729006 | 0.0364503 | − | 0.999335i | \(-0.488395\pi\) | ||||
0.0364503 | + | 0.999335i | \(0.488395\pi\) | |||||||
\(522\) | 335.342 | 0.0281179 | ||||||||
\(523\) | −19705.6 | −1.64755 | −0.823773 | − | 0.566920i | \(-0.808135\pi\) | ||||
−0.823773 | + | 0.566920i | \(0.808135\pi\) | |||||||
\(524\) | −2842.53 | −0.236978 | ||||||||
\(525\) | 26542.2 | 2.20647 | ||||||||
\(526\) | −16834.9 | −1.39551 | ||||||||
\(527\) | −14918.4 | −1.23313 | ||||||||
\(528\) | 8588.06 | 0.707855 | ||||||||
\(529\) | 13797.5 | 1.13401 | ||||||||
\(530\) | 4945.55 | 0.405323 | ||||||||
\(531\) | 10601.4 | 0.866406 | ||||||||
\(532\) | 4641.78 | 0.378283 | ||||||||
\(533\) | 5914.39 | 0.480639 | ||||||||
\(534\) | −15537.3 | −1.25911 | ||||||||
\(535\) | 10066.8 | 0.813509 | ||||||||
\(536\) | −16887.2 | −1.36085 | ||||||||
\(537\) | 25098.7 | 2.01693 | ||||||||
\(538\) | 8489.30 | 0.680297 | ||||||||
\(539\) | −9121.91 | −0.728958 | ||||||||
\(540\) | −2819.71 | −0.224705 | ||||||||
\(541\) | −8302.80 | −0.659825 | −0.329912 | − | 0.944012i | \(-0.607019\pi\) | ||||
−0.329912 | + | 0.944012i | \(0.607019\pi\) | |||||||
\(542\) | 1252.74 | 0.0992799 | ||||||||
\(543\) | 1272.73 | 0.100586 | ||||||||
\(544\) | −10099.4 | −0.795969 | ||||||||
\(545\) | −10133.3 | −0.796448 | ||||||||
\(546\) | −5212.96 | −0.408598 | ||||||||
\(547\) | −10861.2 | −0.848977 | −0.424489 | − | 0.905433i | \(-0.639546\pi\) | ||||
−0.424489 | + | 0.905433i | \(0.639546\pi\) | |||||||
\(548\) | −4503.84 | −0.351085 | ||||||||
\(549\) | 5052.03 | 0.392742 | ||||||||
\(550\) | 17859.4 | 1.38459 | ||||||||
\(551\) | 467.794 | 0.0361682 | ||||||||
\(552\) | 26990.3 | 2.08113 | ||||||||
\(553\) | 3364.62 | 0.258731 | ||||||||
\(554\) | −6552.32 | −0.502494 | ||||||||
\(555\) | 3034.65 | 0.232097 | ||||||||
\(556\) | 7216.40 | 0.550438 | ||||||||
\(557\) | 16029.1 | 1.21934 | 0.609670 | − | 0.792655i | \(-0.291302\pi\) | ||||
0.609670 | + | 0.792655i | \(0.291302\pi\) | |||||||
\(558\) | 8906.91 | 0.675734 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 10014.9 | 0.755726 | ||||||||
\(561\) | −24181.1 | −1.81983 | ||||||||
\(562\) | −13602.2 | −1.02095 | ||||||||
\(563\) | 23819.0 | 1.78304 | 0.891518 | − | 0.452985i | \(-0.149641\pi\) | ||||
0.891518 | + | 0.452985i | \(0.149641\pi\) | |||||||
\(564\) | 13384.8 | 0.999294 | ||||||||
\(565\) | 15507.3 | 1.15469 | ||||||||
\(566\) | −16840.7 | −1.25065 | ||||||||
\(567\) | −19996.2 | −1.48106 | ||||||||
\(568\) | −15574.6 | −1.15052 | ||||||||
\(569\) | −6026.59 | −0.444021 | −0.222010 | − | 0.975044i | \(-0.571262\pi\) | ||||
−0.222010 | + | 0.975044i | \(0.571262\pi\) | |||||||
\(570\) | −15034.4 | −1.10477 | ||||||||
\(571\) | 17370.8 | 1.27311 | 0.636554 | − | 0.771232i | \(-0.280359\pi\) | ||||
0.636554 | + | 0.771232i | \(0.280359\pi\) | |||||||
\(572\) | 2575.30 | 0.188250 | ||||||||
\(573\) | 9084.13 | 0.662295 | ||||||||
\(574\) | −18927.0 | −1.37630 | ||||||||
\(575\) | 27176.1 | 1.97099 | ||||||||
\(576\) | 10080.0 | 0.729170 | ||||||||
\(577\) | 4746.69 | 0.342474 | 0.171237 | − | 0.985230i | \(-0.445224\pi\) | ||||
0.171237 | + | 0.985230i | \(0.445224\pi\) | |||||||
\(578\) | −462.357 | −0.0332725 | ||||||||
\(579\) | −10327.1 | −0.741246 | ||||||||
\(580\) | −455.221 | −0.0325897 | ||||||||
\(581\) | −18000.9 | −1.28537 | ||||||||
\(582\) | 1501.25 | 0.106923 | ||||||||
\(583\) | −6624.84 | −0.470623 | ||||||||
\(584\) | 11638.9 | 0.824695 | ||||||||
\(585\) | −5260.91 | −0.371815 | ||||||||
\(586\) | −15397.4 | −1.08543 | ||||||||
\(587\) | 1574.61 | 0.110718 | 0.0553588 | − | 0.998467i | \(-0.482370\pi\) | ||||
0.0553588 | + | 0.998467i | \(0.482370\pi\) | |||||||
\(588\) | −4291.73 | −0.301000 | ||||||||
\(589\) | 12424.9 | 0.869202 | ||||||||
\(590\) | 19601.2 | 1.36775 | ||||||||
\(591\) | 2788.95 | 0.194115 | ||||||||
\(592\) | 657.626 | 0.0456559 | ||||||||
\(593\) | 6250.28 | 0.432830 | 0.216415 | − | 0.976301i | \(-0.430564\pi\) | ||||
0.216415 | + | 0.976301i | \(0.430564\pi\) | |||||||
\(594\) | −5144.59 | −0.355362 | ||||||||
\(595\) | −28198.6 | −1.94291 | ||||||||
\(596\) | 1139.49 | 0.0783146 | ||||||||
\(597\) | 2702.38 | 0.185261 | ||||||||
\(598\) | −5337.45 | −0.364991 | ||||||||
\(599\) | −566.197 | −0.0386213 | −0.0193107 | − | 0.999814i | \(-0.506147\pi\) | ||||
−0.0193107 | + | 0.999814i | \(0.506147\pi\) | |||||||
\(600\) | 28249.8 | 1.92215 | ||||||||
\(601\) | −6295.44 | −0.427282 | −0.213641 | − | 0.976912i | \(-0.568532\pi\) | ||||
−0.213641 | + | 0.976912i | \(0.568532\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13745.2 | −0.928269 | ||||||||
\(604\) | −4065.95 | −0.273909 | ||||||||
\(605\) | −18846.5 | −1.26648 | ||||||||
\(606\) | −16697.2 | −1.11927 | ||||||||
\(607\) | 22657.5 | 1.51506 | 0.757528 | − | 0.652803i | \(-0.226407\pi\) | ||||
0.757528 | + | 0.652803i | \(0.226407\pi\) | |||||||
\(608\) | 8411.33 | 0.561060 | ||||||||
\(609\) | −1234.35 | −0.0821322 | ||||||||
\(610\) | 9340.84 | 0.619999 | ||||||||
\(611\) | −8898.97 | −0.589221 | ||||||||
\(612\) | −4828.18 | −0.318902 | ||||||||
\(613\) | 3576.79 | 0.235669 | 0.117835 | − | 0.993033i | \(-0.462405\pi\) | ||||
0.117835 | + | 0.993033i | \(0.462405\pi\) | |||||||
\(614\) | −1498.01 | −0.0984605 | ||||||||
\(615\) | −45008.6 | −2.95109 | ||||||||
\(616\) | −27707.7 | −1.81229 | ||||||||
\(617\) | 5025.02 | 0.327877 | 0.163938 | − | 0.986471i | \(-0.447580\pi\) | ||||
0.163938 | + | 0.986471i | \(0.447580\pi\) | |||||||
\(618\) | −11175.5 | −0.727416 | ||||||||
\(619\) | −4767.52 | −0.309569 | −0.154784 | − | 0.987948i | \(-0.549468\pi\) | ||||
−0.154784 | + | 0.987948i | \(0.549468\pi\) | |||||||
\(620\) | −12091.0 | −0.783202 | ||||||||
\(621\) | −7828.35 | −0.505863 | ||||||||
\(622\) | −5044.91 | −0.325213 | ||||||||
\(623\) | 24271.0 | 1.56083 | ||||||||
\(624\) | −2686.40 | −0.172343 | ||||||||
\(625\) | −8262.56 | −0.528804 | ||||||||
\(626\) | −20201.3 | −1.28979 | ||||||||
\(627\) | 20139.4 | 1.28276 | ||||||||
\(628\) | 5392.69 | 0.342662 | ||||||||
\(629\) | −1851.65 | −0.117377 | ||||||||
\(630\) | 16835.7 | 1.06468 | ||||||||
\(631\) | 26994.4 | 1.70306 | 0.851531 | − | 0.524305i | \(-0.175675\pi\) | ||||
0.851531 | + | 0.524305i | \(0.175675\pi\) | |||||||
\(632\) | 3581.07 | 0.225392 | ||||||||
\(633\) | 22928.5 | 1.43970 | ||||||||
\(634\) | 13654.5 | 0.855345 | ||||||||
\(635\) | −24638.8 | −1.53978 | ||||||||
\(636\) | −3116.90 | −0.194329 | ||||||||
\(637\) | 2853.39 | 0.177481 | ||||||||
\(638\) | −830.556 | −0.0515392 | ||||||||
\(639\) | −12676.8 | −0.784799 | ||||||||
\(640\) | −696.523 | −0.0430195 | ||||||||
\(641\) | 2266.00 | 0.139628 | 0.0698141 | − | 0.997560i | \(-0.477759\pi\) | ||||
0.0698141 | + | 0.997560i | \(0.477759\pi\) | |||||||
\(642\) | 8641.45 | 0.531232 | ||||||||
\(643\) | −32171.8 | −1.97314 | −0.986572 | − | 0.163329i | \(-0.947777\pi\) | ||||
−0.986572 | + | 0.163329i | \(0.947777\pi\) | |||||||
\(644\) | −12540.6 | −0.767343 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9173.53 | 0.558712 | ||||||||
\(647\) | 18687.3 | 1.13551 | 0.567753 | − | 0.823199i | \(-0.307813\pi\) | ||||
0.567753 | + | 0.823199i | \(0.307813\pi\) | |||||||
\(648\) | −21282.6 | −1.29022 | ||||||||
\(649\) | −26256.9 | −1.58810 | ||||||||
\(650\) | −5586.52 | −0.337110 | ||||||||
\(651\) | −32785.2 | −1.97382 | ||||||||
\(652\) | −13362.7 | −0.802644 | ||||||||
\(653\) | 11503.4 | 0.689376 | 0.344688 | − | 0.938717i | \(-0.387985\pi\) | ||||
0.344688 | + | 0.938717i | \(0.387985\pi\) | |||||||
\(654\) | −8698.53 | −0.520091 | ||||||||
\(655\) | −14382.0 | −0.857939 | ||||||||
\(656\) | −9753.62 | −0.580511 | ||||||||
\(657\) | 9473.37 | 0.562544 | ||||||||
\(658\) | 28478.0 | 1.68722 | ||||||||
\(659\) | 14603.7 | 0.863245 | 0.431623 | − | 0.902054i | \(-0.357941\pi\) | ||||
0.431623 | + | 0.902054i | \(0.357941\pi\) | |||||||
\(660\) | −19598.1 | −1.15584 | ||||||||
\(661\) | 5556.15 | 0.326943 | 0.163471 | − | 0.986548i | \(-0.447731\pi\) | ||||
0.163471 | + | 0.986548i | \(0.447731\pi\) | |||||||
\(662\) | −13066.0 | −0.767106 | ||||||||
\(663\) | 7563.98 | 0.443078 | ||||||||
\(664\) | −19158.9 | −1.11974 | ||||||||
\(665\) | 23485.4 | 1.36951 | ||||||||
\(666\) | 1105.51 | 0.0643209 | ||||||||
\(667\) | −1263.83 | −0.0733669 | ||||||||
\(668\) | −6971.28 | −0.403783 | ||||||||
\(669\) | −5621.55 | −0.324875 | ||||||||
\(670\) | −25413.8 | −1.46540 | ||||||||
\(671\) | −12512.6 | −0.719885 | ||||||||
\(672\) | −22194.7 | −1.27408 | ||||||||
\(673\) | −3729.99 | −0.213641 | −0.106821 | − | 0.994278i | \(-0.534067\pi\) | ||||
−0.106821 | + | 0.994278i | \(0.534067\pi\) | |||||||
\(674\) | 7228.89 | 0.413125 | ||||||||
\(675\) | −8193.65 | −0.467221 | ||||||||
\(676\) | 6635.49 | 0.377531 | ||||||||
\(677\) | −30830.0 | −1.75021 | −0.875105 | − | 0.483933i | \(-0.839208\pi\) | ||||
−0.875105 | + | 0.483933i | \(0.839208\pi\) | |||||||
\(678\) | 13311.6 | 0.754027 | ||||||||
\(679\) | −2345.13 | −0.132545 | ||||||||
\(680\) | −30012.7 | −1.69255 | ||||||||
\(681\) | −15240.5 | −0.857589 | ||||||||
\(682\) | −22060.1 | −1.23860 | ||||||||
\(683\) | −18270.9 | −1.02360 | −0.511798 | − | 0.859106i | \(-0.671020\pi\) | ||||
−0.511798 | + | 0.859106i | \(0.671020\pi\) | |||||||
\(684\) | 4021.18 | 0.224786 | ||||||||
\(685\) | −22787.5 | −1.27104 | ||||||||
\(686\) | 7797.04 | 0.433954 | ||||||||
\(687\) | −14450.2 | −0.802489 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2072.29 | 0.114583 | ||||||||
\(690\) | 40618.1 | 2.24102 | ||||||||
\(691\) | 20487.0 | 1.12788 | 0.563939 | − | 0.825817i | \(-0.309285\pi\) | ||||
0.563939 | + | 0.825817i | \(0.309285\pi\) | |||||||
\(692\) | −4070.22 | −0.223593 | ||||||||
\(693\) | −22552.3 | −1.23621 | ||||||||
\(694\) | −4769.22 | −0.260860 | ||||||||
\(695\) | 36511.8 | 1.99277 | ||||||||
\(696\) | −1313.76 | −0.0715490 | ||||||||
\(697\) | 27462.9 | 1.49244 | ||||||||
\(698\) | 8240.26 | 0.446846 | ||||||||
\(699\) | 14512.3 | 0.785271 | ||||||||
\(700\) | −13125.8 | −0.708726 | ||||||||
\(701\) | −22050.4 | −1.18806 | −0.594030 | − | 0.804443i | \(-0.702464\pi\) | ||||
−0.594030 | + | 0.804443i | \(0.702464\pi\) | |||||||
\(702\) | 1609.26 | 0.0865206 | ||||||||
\(703\) | 1542.16 | 0.0827365 | ||||||||
\(704\) | −24965.7 | −1.33655 | ||||||||
\(705\) | 67721.3 | 3.61777 | ||||||||
\(706\) | 7027.46 | 0.374620 | ||||||||
\(707\) | 26082.9 | 1.38748 | ||||||||
\(708\) | −12353.5 | −0.655754 | ||||||||
\(709\) | 24913.2 | 1.31966 | 0.659828 | − | 0.751417i | \(-0.270629\pi\) | ||||
0.659828 | + | 0.751417i | \(0.270629\pi\) | |||||||
\(710\) | −23438.5 | −1.23892 | ||||||||
\(711\) | 2914.77 | 0.153745 | ||||||||
\(712\) | 25832.4 | 1.35971 | ||||||||
\(713\) | −33568.2 | −1.76317 | ||||||||
\(714\) | −24205.9 | −1.26874 | ||||||||
\(715\) | 13029.9 | 0.681526 | ||||||||
\(716\) | −12412.0 | −0.647844 | ||||||||
\(717\) | 18536.5 | 0.965495 | ||||||||
\(718\) | 2727.77 | 0.141782 | ||||||||
\(719\) | −3253.23 | −0.168741 | −0.0843706 | − | 0.996434i | \(-0.526888\pi\) | ||||
−0.0843706 | + | 0.996434i | \(0.526888\pi\) | |||||||
\(720\) | 8675.93 | 0.449074 | ||||||||
\(721\) | 17457.3 | 0.901726 | ||||||||
\(722\) | 7091.58 | 0.365542 | ||||||||
\(723\) | −6613.77 | −0.340206 | ||||||||
\(724\) | −629.399 | −0.0323086 | ||||||||
\(725\) | −1322.81 | −0.0677625 | ||||||||
\(726\) | −16177.9 | −0.827025 | ||||||||
\(727\) | −17101.1 | −0.872412 | −0.436206 | − | 0.899847i | \(-0.643678\pi\) | ||||
−0.436206 | + | 0.899847i | \(0.643678\pi\) | |||||||
\(728\) | 8667.12 | 0.441243 | ||||||||
\(729\) | −8338.92 | −0.423661 | ||||||||
\(730\) | 17515.6 | 0.888056 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −5886.99 | −0.297253 | ||||||||
\(733\) | 3820.21 | 0.192500 | 0.0962501 | − | 0.995357i | \(-0.469315\pi\) | ||||
0.0962501 | + | 0.995357i | \(0.469315\pi\) | |||||||
\(734\) | 15756.6 | 0.792355 | ||||||||
\(735\) | −21714.3 | −1.08972 | ||||||||
\(736\) | −22724.7 | −1.13810 | ||||||||
\(737\) | 34043.2 | 1.70149 | ||||||||
\(738\) | −16396.5 | −0.817835 | ||||||||
\(739\) | 22213.3 | 1.10572 | 0.552861 | − | 0.833274i | \(-0.313536\pi\) | ||||
0.552861 | + | 0.833274i | \(0.313536\pi\) | |||||||
\(740\) | −1500.71 | −0.0745504 | ||||||||
\(741\) | −6299.71 | −0.312315 | ||||||||
\(742\) | −6631.64 | −0.328107 | ||||||||
\(743\) | −12549.4 | −0.619642 | −0.309821 | − | 0.950795i | \(-0.600269\pi\) | ||||
−0.309821 | + | 0.950795i | \(0.600269\pi\) | |||||||
\(744\) | −34894.4 | −1.71948 | ||||||||
\(745\) | 5765.34 | 0.283525 | ||||||||
\(746\) | −22211.9 | −1.09013 | ||||||||
\(747\) | −15594.2 | −0.763804 | ||||||||
\(748\) | 11958.2 | 0.584537 | ||||||||
\(749\) | −13498.9 | −0.658531 | ||||||||
\(750\) | 11004.1 | 0.535751 | ||||||||
\(751\) | 4953.67 | 0.240695 | 0.120348 | − | 0.992732i | \(-0.461599\pi\) | ||||
0.120348 | + | 0.992732i | \(0.461599\pi\) | |||||||
\(752\) | 14675.6 | 0.711654 | ||||||||
\(753\) | 41798.6 | 2.02287 | ||||||||
\(754\) | 259.803 | 0.0125484 | ||||||||
\(755\) | −20572.0 | −0.991643 | ||||||||
\(756\) | 3781.03 | 0.181898 | ||||||||
\(757\) | −22003.1 | −1.05643 | −0.528215 | − | 0.849111i | \(-0.677138\pi\) | ||||
−0.528215 | + | 0.849111i | \(0.677138\pi\) | |||||||
\(758\) | 6205.07 | 0.297333 | ||||||||
\(759\) | −54410.2 | −2.60206 | ||||||||
\(760\) | 24996.3 | 1.19304 | ||||||||
\(761\) | −6198.26 | −0.295252 | −0.147626 | − | 0.989043i | \(-0.547163\pi\) | ||||
−0.147626 | + | 0.989043i | \(0.547163\pi\) | |||||||
\(762\) | −21150.1 | −1.00550 | ||||||||
\(763\) | 13588.1 | 0.644720 | ||||||||
\(764\) | −4492.34 | −0.212732 | ||||||||
\(765\) | −24428.5 | −1.15453 | ||||||||
\(766\) | −2327.48 | −0.109785 | ||||||||
\(767\) | 8213.32 | 0.386657 | ||||||||
\(768\) | −28342.3 | −1.33166 | ||||||||
\(769\) | 12952.5 | 0.607386 | 0.303693 | − | 0.952770i | \(-0.401780\pi\) | ||||
0.303693 | + | 0.952770i | \(0.401780\pi\) | |||||||
\(770\) | −41697.7 | −1.95153 | ||||||||
\(771\) | 46302.9 | 2.16285 | ||||||||
\(772\) | 5107.04 | 0.238091 | ||||||||
\(773\) | −4395.08 | −0.204502 | −0.102251 | − | 0.994759i | \(-0.532604\pi\) | ||||
−0.102251 | + | 0.994759i | \(0.532604\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −35134.6 | −1.62848 | ||||||||
\(776\) | −2496.00 | −0.115465 | ||||||||
\(777\) | −4069.25 | −0.187881 | ||||||||
\(778\) | −1468.96 | −0.0676925 | ||||||||
\(779\) | −22872.7 | −1.05199 | ||||||||
\(780\) | 6130.39 | 0.281414 | ||||||||
\(781\) | 31397.2 | 1.43851 | ||||||||
\(782\) | −24784.0 | −1.13334 | ||||||||
\(783\) | 381.048 | 0.0173915 | ||||||||
\(784\) | −4705.61 | −0.214359 | ||||||||
\(785\) | 27284.7 | 1.24055 | ||||||||
\(786\) | −12345.6 | −0.560245 | ||||||||
\(787\) | −34887.0 | −1.58016 | −0.790080 | − | 0.613003i | \(-0.789961\pi\) | ||||
−0.790080 | + | 0.613003i | \(0.789961\pi\) | |||||||
\(788\) | −1379.21 | −0.0623506 | ||||||||
\(789\) | 53682.3 | 2.42223 | ||||||||
\(790\) | 5389.21 | 0.242708 | ||||||||
\(791\) | −20794.3 | −0.934714 | ||||||||
\(792\) | −24003.2 | −1.07692 | ||||||||
\(793\) | 3914.01 | 0.175272 | ||||||||
\(794\) | 23641.9 | 1.05670 | ||||||||
\(795\) | −15770.1 | −0.703534 | ||||||||
\(796\) | −1336.39 | −0.0595066 | ||||||||
\(797\) | 30402.7 | 1.35122 | 0.675609 | − | 0.737260i | \(-0.263881\pi\) | ||||
0.675609 | + | 0.737260i | \(0.263881\pi\) | |||||||
\(798\) | 20160.0 | 0.894308 | ||||||||
\(799\) | −41321.5 | −1.82960 | ||||||||
\(800\) | −23785.2 | −1.05117 | ||||||||
\(801\) | 21026.0 | 0.927488 | ||||||||
\(802\) | −13313.0 | −0.586158 | ||||||||
\(803\) | −23463.1 | −1.03113 | ||||||||
\(804\) | 16016.9 | 0.702576 | ||||||||
\(805\) | −63450.0 | −2.77804 | ||||||||
\(806\) | 6900.53 | 0.301564 | ||||||||
\(807\) | −27070.3 | −1.18082 | ||||||||
\(808\) | 27761.0 | 1.20870 | ||||||||
\(809\) | −7885.52 | −0.342695 | −0.171347 | − | 0.985211i | \(-0.554812\pi\) | ||||
−0.171347 | + | 0.985211i | \(0.554812\pi\) | |||||||
\(810\) | −32028.5 | −1.38934 | ||||||||
\(811\) | −26413.9 | −1.14367 | −0.571836 | − | 0.820368i | \(-0.693769\pi\) | ||||
−0.571836 | + | 0.820368i | \(0.693769\pi\) | |||||||
\(812\) | 610.419 | 0.0263812 | ||||||||
\(813\) | −3994.67 | −0.172324 | ||||||||
\(814\) | −2738.07 | −0.117898 | ||||||||
\(815\) | −67609.4 | −2.90583 | ||||||||
\(816\) | −12474.0 | −0.535145 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −12465.4 | −0.532816 | ||||||||
\(819\) | 7054.50 | 0.300982 | ||||||||
\(820\) | 22257.9 | 0.947902 | ||||||||
\(821\) | −30441.2 | −1.29404 | −0.647019 | − | 0.762474i | \(-0.723985\pi\) | ||||
−0.647019 | + | 0.762474i | \(0.723985\pi\) | |||||||
\(822\) | −19560.9 | −0.830007 | ||||||||
\(823\) | 8533.72 | 0.361442 | 0.180721 | − | 0.983534i | \(-0.442157\pi\) | ||||
0.180721 | + | 0.983534i | \(0.442157\pi\) | |||||||
\(824\) | 18580.4 | 0.785534 | ||||||||
\(825\) | −56949.1 | −2.40329 | ||||||||
\(826\) | −26283.9 | −1.10718 | ||||||||
\(827\) | −23457.2 | −0.986321 | −0.493160 | − | 0.869938i | \(-0.664158\pi\) | ||||
−0.493160 | + | 0.869938i | \(0.664158\pi\) | |||||||
\(828\) | −10864.0 | −0.455977 | ||||||||
\(829\) | 12755.8 | 0.534413 | 0.267206 | − | 0.963639i | \(-0.413899\pi\) | ||||
0.267206 | + | 0.963639i | \(0.413899\pi\) | |||||||
\(830\) | −28832.5 | −1.20577 | ||||||||
\(831\) | 20893.7 | 0.872197 | ||||||||
\(832\) | 7809.41 | 0.325412 | ||||||||
\(833\) | 13249.4 | 0.551099 | ||||||||
\(834\) | 31342.1 | 1.30130 | ||||||||
\(835\) | −35271.6 | −1.46183 | ||||||||
\(836\) | −9959.43 | −0.412027 | ||||||||
\(837\) | 10120.9 | 0.417956 | ||||||||
\(838\) | −14122.7 | −0.582174 | ||||||||
\(839\) | −3046.67 | −0.125367 | −0.0626834 | − | 0.998033i | \(-0.519966\pi\) | ||||
−0.0626834 | + | 0.998033i | \(0.519966\pi\) | |||||||
\(840\) | −65956.9 | −2.70920 | ||||||||
\(841\) | −24327.5 | −0.997478 | ||||||||
\(842\) | 26879.5 | 1.10015 | ||||||||
\(843\) | 43374.1 | 1.77210 | ||||||||
\(844\) | −11338.7 | −0.462436 | ||||||||
\(845\) | 33572.7 | 1.36679 | ||||||||
\(846\) | 24670.6 | 1.00259 | ||||||||
\(847\) | 25271.8 | 1.02520 | ||||||||
\(848\) | −3417.48 | −0.138392 | ||||||||
\(849\) | 53700.9 | 2.17080 | ||||||||
\(850\) | −25940.5 | −1.04677 | ||||||||
\(851\) | −4166.43 | −0.167830 | ||||||||
\(852\) | 14771.9 | 0.593988 | ||||||||
\(853\) | −30583.2 | −1.22761 | −0.613804 | − | 0.789459i | \(-0.710361\pi\) | ||||
−0.613804 | + | 0.789459i | \(0.710361\pi\) | |||||||
\(854\) | −12525.4 | −0.501886 | ||||||||
\(855\) | 20345.4 | 0.813800 | ||||||||
\(856\) | −14367.4 | −0.573675 | ||||||||
\(857\) | −6042.11 | −0.240834 | −0.120417 | − | 0.992723i | \(-0.538423\pi\) | ||||
−0.120417 | + | 0.992723i | \(0.538423\pi\) | |||||||
\(858\) | 11185.0 | 0.445045 | ||||||||
\(859\) | 29736.6 | 1.18114 | 0.590570 | − | 0.806987i | \(-0.298903\pi\) | ||||
0.590570 | + | 0.806987i | \(0.298903\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 60353.3 | 2.38889 | ||||||||
\(862\) | −18042.3 | −0.712905 | ||||||||
\(863\) | −33937.7 | −1.33865 | −0.669324 | − | 0.742971i | \(-0.733416\pi\) | ||||
−0.669324 | + | 0.742971i | \(0.733416\pi\) | |||||||
\(864\) | 6851.57 | 0.269786 | ||||||||
\(865\) | −20593.6 | −0.809482 | ||||||||
\(866\) | −5205.81 | −0.204273 | ||||||||
\(867\) | 1474.34 | 0.0577524 | ||||||||
\(868\) | 16213.1 | 0.633997 | ||||||||
\(869\) | −7219.14 | −0.281810 | ||||||||
\(870\) | −1977.10 | −0.0770460 | ||||||||
\(871\) | −10648.9 | −0.414265 | ||||||||
\(872\) | 14462.2 | 0.561644 | ||||||||
\(873\) | −2031.59 | −0.0787617 | ||||||||
\(874\) | 20641.5 | 0.798865 | ||||||||
\(875\) | −17189.6 | −0.664132 | ||||||||
\(876\) | −11039.1 | −0.425771 | ||||||||
\(877\) | −42501.2 | −1.63645 | −0.818224 | − | 0.574900i | \(-0.805041\pi\) | ||||
−0.818224 | + | 0.574900i | \(0.805041\pi\) | |||||||
\(878\) | −1747.84 | −0.0671830 | ||||||||
\(879\) | 49098.6 | 1.88402 | ||||||||
\(880\) | −21488.0 | −0.823138 | ||||||||
\(881\) | −29766.2 | −1.13831 | −0.569154 | − | 0.822231i | \(-0.692729\pi\) | ||||
−0.569154 | + | 0.822231i | \(0.692729\pi\) | |||||||
\(882\) | −7910.44 | −0.301994 | ||||||||
\(883\) | −32939.0 | −1.25536 | −0.627682 | − | 0.778470i | \(-0.715996\pi\) | ||||
−0.627682 | + | 0.778470i | \(0.715996\pi\) | |||||||
\(884\) | −3740.58 | −0.142318 | ||||||||
\(885\) | −62503.5 | −2.37405 | ||||||||
\(886\) | −13275.5 | −0.503386 | ||||||||
\(887\) | −11353.9 | −0.429793 | −0.214896 | − | 0.976637i | \(-0.568941\pi\) | ||||
−0.214896 | + | 0.976637i | \(0.568941\pi\) | |||||||
\(888\) | −4331.04 | −0.163671 | ||||||||
\(889\) | 33038.9 | 1.24644 | ||||||||
\(890\) | 38875.6 | 1.46417 | ||||||||
\(891\) | 42903.9 | 1.61317 | ||||||||
\(892\) | 2780.00 | 0.104351 | ||||||||
\(893\) | 34414.9 | 1.28964 | ||||||||
\(894\) | 4949.02 | 0.185145 | ||||||||
\(895\) | −62799.1 | −2.34541 | ||||||||
\(896\) | 933.988 | 0.0348241 | ||||||||
\(897\) | 17019.8 | 0.633529 | ||||||||
\(898\) | 12442.2 | 0.462361 | ||||||||
\(899\) | 1633.94 | 0.0606175 | ||||||||
\(900\) | −11370.9 | −0.421145 | ||||||||
\(901\) | 9622.48 | 0.355795 | ||||||||
\(902\) | 40609.8 | 1.49907 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22132.0 | −0.814270 | ||||||||
\(905\) | −3184.48 | −0.116968 | ||||||||
\(906\) | −17659.1 | −0.647555 | ||||||||
\(907\) | −23589.4 | −0.863588 | −0.431794 | − | 0.901972i | \(-0.642119\pi\) | ||||
−0.431794 | + | 0.901972i | \(0.642119\pi\) | |||||||
\(908\) | 7536.82 | 0.275461 | ||||||||
\(909\) | 22595.7 | 0.824480 | ||||||||
\(910\) | 13043.3 | 0.475143 | ||||||||
\(911\) | −34818.1 | −1.26627 | −0.633137 | − | 0.774040i | \(-0.718233\pi\) | ||||
−0.633137 | + | 0.774040i | \(0.718233\pi\) | |||||||
\(912\) | 10389.1 | 0.377211 | ||||||||
\(913\) | 38622.8 | 1.40003 | ||||||||
\(914\) | −3391.83 | −0.122748 | ||||||||
\(915\) | −29785.6 | −1.07616 | ||||||||
\(916\) | 7146.00 | 0.257762 | ||||||||
\(917\) | 19285.2 | 0.694497 | ||||||||
\(918\) | 7472.43 | 0.268657 | ||||||||
\(919\) | 3187.72 | 0.114421 | 0.0572106 | − | 0.998362i | \(-0.481779\pi\) | ||||
0.0572106 | + | 0.998362i | \(0.481779\pi\) | |||||||
\(920\) | −67532.0 | −2.42007 | ||||||||
\(921\) | 4776.78 | 0.170901 | ||||||||
\(922\) | 6501.95 | 0.232246 | ||||||||
\(923\) | −9821.22 | −0.350238 | ||||||||
\(924\) | 26279.6 | 0.935645 | ||||||||
\(925\) | −4360.85 | −0.155010 | ||||||||
\(926\) | −3719.64 | −0.132003 | ||||||||
\(927\) | 15123.3 | 0.535831 | ||||||||
\(928\) | 1106.14 | 0.0391279 | ||||||||
\(929\) | −45524.5 | −1.60776 | −0.803881 | − | 0.594790i | \(-0.797235\pi\) | ||||
−0.803881 | + | 0.594790i | \(0.797235\pi\) | |||||||
\(930\) | −52513.1 | −1.85158 | ||||||||
\(931\) | −11034.9 | −0.388457 | ||||||||
\(932\) | −7176.69 | −0.252232 | ||||||||
\(933\) | 16087.0 | 0.564484 | ||||||||
\(934\) | 8617.71 | 0.301906 | ||||||||
\(935\) | 60503.1 | 2.11622 | ||||||||
\(936\) | 7508.35 | 0.262199 | ||||||||
\(937\) | 4059.73 | 0.141543 | 0.0707714 | − | 0.997493i | \(-0.477454\pi\) | ||||
0.0707714 | + | 0.997493i | \(0.477454\pi\) | |||||||
\(938\) | 34078.1 | 1.18624 | ||||||||
\(939\) | 64417.0 | 2.23873 | ||||||||
\(940\) | −33489.9 | −1.16204 | ||||||||
\(941\) | −54046.4 | −1.87233 | −0.936165 | − | 0.351562i | \(-0.885651\pi\) | ||||
−0.936165 | + | 0.351562i | \(0.885651\pi\) | |||||||
\(942\) | 23421.4 | 0.810095 | ||||||||
\(943\) | 61794.6 | 2.13395 | ||||||||
\(944\) | −13544.9 | −0.467000 | ||||||||
\(945\) | 19130.3 | 0.658529 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31268.1 | 1.07294 | 0.536472 | − | 0.843918i | \(-0.319757\pi\) | ||||
0.536472 | + | 0.843918i | \(0.319757\pi\) | |||||||
\(948\) | −3396.51 | −0.116364 | ||||||||
\(949\) | 7339.39 | 0.251050 | ||||||||
\(950\) | 21604.7 | 0.737841 | ||||||||
\(951\) | −43540.8 | −1.48465 | ||||||||
\(952\) | 40244.9 | 1.37011 | ||||||||
\(953\) | −11116.2 | −0.377849 | −0.188924 | − | 0.981992i | \(-0.560500\pi\) | ||||
−0.188924 | + | 0.981992i | \(0.560500\pi\) | |||||||
\(954\) | −5745.00 | −0.194970 | ||||||||
\(955\) | −22729.3 | −0.770159 | ||||||||
\(956\) | −9166.79 | −0.310120 | ||||||||
\(957\) | 2648.44 | 0.0894585 | ||||||||
\(958\) | −12610.8 | −0.425299 | ||||||||
\(959\) | 30556.4 | 1.02890 | ||||||||
\(960\) | −59429.6 | −1.99800 | ||||||||
\(961\) | 13607.7 | 0.456771 | ||||||||
\(962\) | 856.483 | 0.0287049 | ||||||||
\(963\) | −11694.1 | −0.391317 | ||||||||
\(964\) | 3270.68 | 0.109275 | ||||||||
\(965\) | 25839.4 | 0.861968 | ||||||||
\(966\) | −54466.0 | −1.81409 | ||||||||
\(967\) | 11030.9 | 0.366835 | 0.183417 | − | 0.983035i | \(-0.441284\pi\) | ||||
0.183417 | + | 0.983035i | \(0.441284\pi\) | |||||||
\(968\) | 26897.6 | 0.893101 | ||||||||
\(969\) | −29252.1 | −0.969776 | ||||||||
\(970\) | −3756.27 | −0.124336 | ||||||||
\(971\) | 856.625 | 0.0283114 | 0.0141557 | − | 0.999900i | \(-0.495494\pi\) | ||||
0.0141557 | + | 0.999900i | \(0.495494\pi\) | |||||||
\(972\) | 15743.0 | 0.519502 | ||||||||
\(973\) | −48959.8 | −1.61313 | ||||||||
\(974\) | −15685.3 | −0.516005 | ||||||||
\(975\) | 17814.0 | 0.585134 | ||||||||
\(976\) | −6454.72 | −0.211691 | ||||||||
\(977\) | 37169.2 | 1.21714 | 0.608572 | − | 0.793499i | \(-0.291743\pi\) | ||||
0.608572 | + | 0.793499i | \(0.291743\pi\) | |||||||
\(978\) | −58036.5 | −1.89755 | ||||||||
\(979\) | −52076.0 | −1.70006 | ||||||||
\(980\) | 10738.3 | 0.350022 | ||||||||
\(981\) | 11771.4 | 0.383110 | ||||||||
\(982\) | −88.3915 | −0.00287239 | ||||||||
\(983\) | −18476.9 | −0.599513 | −0.299757 | − | 0.954016i | \(-0.596905\pi\) | ||||
−0.299757 | + | 0.954016i | \(0.596905\pi\) | |||||||
\(984\) | 64236.1 | 2.08107 | ||||||||
\(985\) | −6978.19 | −0.225730 | ||||||||
\(986\) | 1206.37 | 0.0389641 | ||||||||
\(987\) | −90809.4 | −2.92857 | ||||||||
\(988\) | 3115.37 | 0.100317 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −36122.8 | −1.15965 | ||||||||
\(991\) | 38302.6 | 1.22777 | 0.613886 | − | 0.789395i | \(-0.289606\pi\) | ||||
0.613886 | + | 0.789395i | \(0.289606\pi\) | |||||||
\(992\) | 29379.7 | 0.940329 | ||||||||
\(993\) | 41664.2 | 1.33149 | ||||||||
\(994\) | 31429.4 | 1.00290 | ||||||||
\(995\) | −6761.58 | −0.215434 | ||||||||
\(996\) | 18171.5 | 0.578098 | ||||||||
\(997\) | 53758.0 | 1.70765 | 0.853827 | − | 0.520557i | \(-0.174276\pi\) | ||||
0.853827 | + | 0.520557i | \(0.174276\pi\) | |||||||
\(998\) | −13142.7 | −0.416860 | ||||||||
\(999\) | 1256.19 | 0.0397839 |
(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.d.1.4 | 10 | ||
43.6 | even | 3 | 43.4.c.a.36.4 | yes | 20 | ||
43.36 | even | 3 | 43.4.c.a.6.4 | ✓ | 20 | ||
43.42 | odd | 2 | 1849.4.a.f.1.7 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.c.a.6.4 | ✓ | 20 | 43.36 | even | 3 | ||
43.4.c.a.36.4 | yes | 20 | 43.6 | even | 3 | ||
1849.4.a.d.1.4 | 10 | 1.1 | even | 1 | trivial | ||
1849.4.a.f.1.7 | 10 | 43.42 | odd | 2 |