Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,4,Mod(1,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("975.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.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: | \(57.5268622556\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3144.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 16x - 8 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.526440\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 975.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.52644 | −0.539678 | −0.269839 | − | 0.962905i | \(-0.586970\pi\) | ||||
−0.269839 | + | 0.962905i | \(0.586970\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −5.66998 | −0.708748 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.57932 | 0.311583 | ||||||||
\(7\) | −4.84136 | −0.261409 | −0.130704 | − | 0.991421i | \(-0.541724\pi\) | ||||
−0.130704 | + | 0.991421i | \(0.541724\pi\) | |||||||
\(8\) | 20.8664 | 0.922173 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −61.0728 | −1.67401 | −0.837006 | − | 0.547194i | \(-0.815696\pi\) | ||||
−0.837006 | + | 0.547194i | \(0.815696\pi\) | |||||||
\(12\) | 17.0099 | 0.409196 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 7.39005 | 0.141077 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.5085 | 0.211071 | ||||||||
\(17\) | 41.7885 | 0.596188 | 0.298094 | − | 0.954537i | \(-0.403649\pi\) | ||||
0.298094 | + | 0.954537i | \(0.403649\pi\) | |||||||
\(18\) | −13.7380 | −0.179893 | ||||||||
\(19\) | −107.561 | −1.29875 | −0.649374 | − | 0.760469i | \(-0.724969\pi\) | ||||
−0.649374 | + | 0.760469i | \(0.724969\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14.5241 | 0.150925 | ||||||||
\(22\) | 93.2239 | 0.903427 | ||||||||
\(23\) | −28.5138 | −0.258502 | −0.129251 | − | 0.991612i | \(-0.541257\pi\) | ||||
−0.129251 | + | 0.991612i | \(0.541257\pi\) | |||||||
\(24\) | −62.5992 | −0.532417 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 19.8437 | 0.149680 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 27.4504 | 0.185273 | ||||||||
\(29\) | −89.8886 | −0.575583 | −0.287791 | − | 0.957693i | \(-0.592921\pi\) | ||||
−0.287791 | + | 0.957693i | \(0.592921\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 183.108 | 1.06087 | 0.530437 | − | 0.847724i | \(-0.322028\pi\) | ||||
0.530437 | + | 0.847724i | \(0.322028\pi\) | |||||||
\(32\) | −187.551 | −1.03608 | ||||||||
\(33\) | 183.218 | 0.966491 | ||||||||
\(34\) | −63.7876 | −0.321750 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −51.0298 | −0.236249 | ||||||||
\(37\) | −418.029 | −1.85739 | −0.928696 | − | 0.370843i | \(-0.879069\pi\) | ||||
−0.928696 | + | 0.370843i | \(0.879069\pi\) | |||||||
\(38\) | 164.185 | 0.700905 | ||||||||
\(39\) | 39.0000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −142.674 | −0.543460 | −0.271730 | − | 0.962373i | \(-0.587596\pi\) | ||||
−0.271730 | + | 0.962373i | \(0.587596\pi\) | |||||||
\(42\) | −22.1701 | −0.0814506 | ||||||||
\(43\) | 71.0935 | 0.252132 | 0.126066 | − | 0.992022i | \(-0.459765\pi\) | ||||
0.126066 | + | 0.992022i | \(0.459765\pi\) | |||||||
\(44\) | 346.281 | 1.18645 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 43.5246 | 0.139508 | ||||||||
\(47\) | −323.711 | −1.00464 | −0.502321 | − | 0.864681i | \(-0.667520\pi\) | ||||
−0.502321 | + | 0.864681i | \(0.667520\pi\) | |||||||
\(48\) | −40.5256 | −0.121862 | ||||||||
\(49\) | −319.561 | −0.931665 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −125.365 | −0.344209 | ||||||||
\(52\) | 73.7098 | 0.196571 | ||||||||
\(53\) | 25.1047 | 0.0650641 | 0.0325321 | − | 0.999471i | \(-0.489643\pi\) | ||||
0.0325321 | + | 0.999471i | \(0.489643\pi\) | |||||||
\(54\) | 41.2139 | 0.103861 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −101.022 | −0.241064 | ||||||||
\(57\) | 322.683 | 0.749832 | ||||||||
\(58\) | 137.210 | 0.310629 | ||||||||
\(59\) | −684.508 | −1.51043 | −0.755215 | − | 0.655477i | \(-0.772467\pi\) | ||||
−0.755215 | + | 0.655477i | \(0.772467\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 308.125 | 0.646744 | 0.323372 | − | 0.946272i | \(-0.395184\pi\) | ||||
0.323372 | + | 0.946272i | \(0.395184\pi\) | |||||||
\(62\) | −279.503 | −0.572531 | ||||||||
\(63\) | −43.5723 | −0.0871363 | ||||||||
\(64\) | 178.217 | 0.348081 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −279.672 | −0.521594 | ||||||||
\(67\) | −672.808 | −1.22681 | −0.613407 | − | 0.789767i | \(-0.710202\pi\) | ||||
−0.613407 | + | 0.789767i | \(0.710202\pi\) | |||||||
\(68\) | −236.940 | −0.422547 | ||||||||
\(69\) | 85.5413 | 0.149246 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −326.837 | −0.546315 | −0.273158 | − | 0.961969i | \(-0.588068\pi\) | ||||
−0.273158 | + | 0.961969i | \(0.588068\pi\) | |||||||
\(72\) | 187.798 | 0.307391 | ||||||||
\(73\) | −24.3058 | −0.0389695 | −0.0194847 | − | 0.999810i | \(-0.506203\pi\) | ||||
−0.0194847 | + | 0.999810i | \(0.506203\pi\) | |||||||
\(74\) | 638.095 | 1.00239 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 609.869 | 0.920484 | ||||||||
\(77\) | 295.675 | 0.437602 | ||||||||
\(78\) | −59.5311 | −0.0864176 | ||||||||
\(79\) | 166.810 | 0.237565 | 0.118783 | − | 0.992920i | \(-0.462101\pi\) | ||||
0.118783 | + | 0.992920i | \(0.462101\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 217.783 | 0.293294 | ||||||||
\(83\) | 201.093 | 0.265938 | 0.132969 | − | 0.991120i | \(-0.457549\pi\) | ||||
0.132969 | + | 0.991120i | \(0.457549\pi\) | |||||||
\(84\) | −82.3513 | −0.106967 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −108.520 | −0.136070 | ||||||||
\(87\) | 269.666 | 0.332313 | ||||||||
\(88\) | −1274.37 | −1.54373 | ||||||||
\(89\) | 108.834 | 0.129622 | 0.0648109 | − | 0.997898i | \(-0.479356\pi\) | ||||
0.0648109 | + | 0.997898i | \(0.479356\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 62.9377 | 0.0725018 | ||||||||
\(92\) | 161.673 | 0.183212 | ||||||||
\(93\) | −549.323 | −0.612496 | ||||||||
\(94\) | 494.126 | 0.542183 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 562.654 | 0.598183 | ||||||||
\(97\) | −1157.95 | −1.21208 | −0.606041 | − | 0.795434i | \(-0.707243\pi\) | ||||
−0.606041 | + | 0.795434i | \(0.707243\pi\) | |||||||
\(98\) | 487.791 | 0.502799 | ||||||||
\(99\) | −549.655 | −0.558004 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1702.75 | 1.67752 | 0.838761 | − | 0.544500i | \(-0.183281\pi\) | ||||
0.838761 | + | 0.544500i | \(0.183281\pi\) | |||||||
\(102\) | 191.363 | 0.185762 | ||||||||
\(103\) | 1455.14 | 1.39203 | 0.696015 | − | 0.718027i | \(-0.254955\pi\) | ||||
0.696015 | + | 0.718027i | \(0.254955\pi\) | |||||||
\(104\) | −271.263 | −0.255765 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −38.3209 | −0.0351137 | ||||||||
\(107\) | 822.762 | 0.743359 | 0.371679 | − | 0.928361i | \(-0.378782\pi\) | ||||
0.371679 | + | 0.928361i | \(0.378782\pi\) | |||||||
\(108\) | 153.090 | 0.136399 | ||||||||
\(109\) | 457.264 | 0.401816 | 0.200908 | − | 0.979610i | \(-0.435611\pi\) | ||||
0.200908 | + | 0.979610i | \(0.435611\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1254.09 | 1.07237 | ||||||||
\(112\) | −65.3998 | −0.0551759 | ||||||||
\(113\) | 381.693 | 0.317758 | 0.158879 | − | 0.987298i | \(-0.449212\pi\) | ||||
0.158879 | + | 0.987298i | \(0.449212\pi\) | |||||||
\(114\) | −492.556 | −0.404668 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 509.667 | 0.407943 | ||||||||
\(117\) | −117.000 | −0.0924500 | ||||||||
\(118\) | 1044.86 | 0.815146 | ||||||||
\(119\) | −202.313 | −0.155849 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2398.88 | 1.80232 | ||||||||
\(122\) | −470.334 | −0.349033 | ||||||||
\(123\) | 428.021 | 0.313767 | ||||||||
\(124\) | −1038.22 | −0.751892 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 66.5104 | 0.0470255 | ||||||||
\(127\) | 1129.09 | 0.788905 | 0.394452 | − | 0.918916i | \(-0.370934\pi\) | ||||
0.394452 | + | 0.918916i | \(0.370934\pi\) | |||||||
\(128\) | 1228.37 | 0.848232 | ||||||||
\(129\) | −213.281 | −0.145568 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −852.761 | −0.568749 | −0.284374 | − | 0.958713i | \(-0.591786\pi\) | ||||
−0.284374 | + | 0.958713i | \(0.591786\pi\) | |||||||
\(132\) | −1038.84 | −0.684999 | ||||||||
\(133\) | 520.742 | 0.339504 | ||||||||
\(134\) | 1027.00 | 0.662085 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 871.975 | 0.549789 | ||||||||
\(137\) | 488.903 | 0.304889 | 0.152445 | − | 0.988312i | \(-0.451285\pi\) | ||||
0.152445 | + | 0.988312i | \(0.451285\pi\) | |||||||
\(138\) | −130.574 | −0.0805447 | ||||||||
\(139\) | 407.123 | 0.248430 | 0.124215 | − | 0.992255i | \(-0.460359\pi\) | ||||
0.124215 | + | 0.992255i | \(0.460359\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 971.134 | 0.580030 | ||||||||
\(142\) | 498.897 | 0.294834 | ||||||||
\(143\) | 793.946 | 0.464287 | ||||||||
\(144\) | 121.577 | 0.0703570 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 37.1013 | 0.0210310 | ||||||||
\(147\) | 958.684 | 0.537897 | ||||||||
\(148\) | 2370.21 | 1.31642 | ||||||||
\(149\) | 1717.63 | 0.944388 | 0.472194 | − | 0.881495i | \(-0.343462\pi\) | ||||
0.472194 | + | 0.881495i | \(0.343462\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1341.79 | 0.723133 | 0.361567 | − | 0.932346i | \(-0.382242\pi\) | ||||
0.361567 | + | 0.932346i | \(0.382242\pi\) | |||||||
\(152\) | −2244.41 | −1.19767 | ||||||||
\(153\) | 376.096 | 0.198729 | ||||||||
\(154\) | −451.331 | −0.236164 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −221.129 | −0.113490 | ||||||||
\(157\) | 760.546 | 0.386612 | 0.193306 | − | 0.981138i | \(-0.438079\pi\) | ||||
0.193306 | + | 0.981138i | \(0.438079\pi\) | |||||||
\(158\) | −254.626 | −0.128209 | ||||||||
\(159\) | −75.3142 | −0.0375648 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 138.046 | 0.0675746 | ||||||||
\(162\) | −123.642 | −0.0599642 | ||||||||
\(163\) | −2712.09 | −1.30323 | −0.651616 | − | 0.758549i | \(-0.725909\pi\) | ||||
−0.651616 | + | 0.758549i | \(0.725909\pi\) | |||||||
\(164\) | 808.957 | 0.385176 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −306.957 | −0.143521 | ||||||||
\(167\) | −1551.69 | −0.719004 | −0.359502 | − | 0.933144i | \(-0.617053\pi\) | ||||
−0.359502 | + | 0.933144i | \(0.617053\pi\) | |||||||
\(168\) | 303.065 | 0.139179 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −968.050 | −0.432916 | ||||||||
\(172\) | −403.099 | −0.178698 | ||||||||
\(173\) | 3970.26 | 1.74482 | 0.872409 | − | 0.488777i | \(-0.162557\pi\) | ||||
0.872409 | + | 0.488777i | \(0.162557\pi\) | |||||||
\(174\) | −411.629 | −0.179342 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −825.004 | −0.353335 | ||||||||
\(177\) | 2053.52 | 0.872047 | ||||||||
\(178\) | −166.128 | −0.0699540 | ||||||||
\(179\) | −2690.95 | −1.12364 | −0.561818 | − | 0.827261i | \(-0.689898\pi\) | ||||
−0.561818 | + | 0.827261i | \(0.689898\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4371.10 | −1.79503 | −0.897517 | − | 0.440980i | \(-0.854631\pi\) | ||||
−0.897517 | + | 0.440980i | \(0.854631\pi\) | |||||||
\(182\) | −96.0706 | −0.0391276 | ||||||||
\(183\) | −924.375 | −0.373398 | ||||||||
\(184\) | −594.980 | −0.238383 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 838.508 | 0.330551 | ||||||||
\(187\) | −2552.14 | −0.998026 | ||||||||
\(188\) | 1835.44 | 0.712038 | ||||||||
\(189\) | 130.717 | 0.0503082 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1408.47 | 0.533578 | 0.266789 | − | 0.963755i | \(-0.414037\pi\) | ||||
0.266789 | + | 0.963755i | \(0.414037\pi\) | |||||||
\(192\) | −534.652 | −0.200964 | ||||||||
\(193\) | 4131.69 | 1.54096 | 0.770481 | − | 0.637463i | \(-0.220016\pi\) | ||||
0.770481 | + | 0.637463i | \(0.220016\pi\) | |||||||
\(194\) | 1767.54 | 0.654134 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1811.91 | 0.660316 | ||||||||
\(197\) | 3401.23 | 1.23009 | 0.615045 | − | 0.788492i | \(-0.289138\pi\) | ||||
0.615045 | + | 0.788492i | \(0.289138\pi\) | |||||||
\(198\) | 839.015 | 0.301142 | ||||||||
\(199\) | −3520.74 | −1.25416 | −0.627081 | − | 0.778954i | \(-0.715751\pi\) | ||||
−0.627081 | + | 0.778954i | \(0.715751\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2018.42 | 0.708302 | ||||||||
\(202\) | −2599.14 | −0.905321 | ||||||||
\(203\) | 435.183 | 0.150463 | ||||||||
\(204\) | 710.820 | 0.243958 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2221.18 | −0.751248 | ||||||||
\(207\) | −256.624 | −0.0861672 | ||||||||
\(208\) | −175.611 | −0.0585406 | ||||||||
\(209\) | 6569.05 | 2.17412 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2245.22 | −0.732545 | −0.366272 | − | 0.930508i | \(-0.619366\pi\) | ||||
−0.366272 | + | 0.930508i | \(0.619366\pi\) | |||||||
\(212\) | −142.343 | −0.0461141 | ||||||||
\(213\) | 980.510 | 0.315415 | ||||||||
\(214\) | −1255.90 | −0.401174 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −563.393 | −0.177472 | ||||||||
\(217\) | −886.490 | −0.277322 | ||||||||
\(218\) | −697.986 | −0.216851 | ||||||||
\(219\) | 72.9173 | 0.0224990 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −543.250 | −0.165353 | ||||||||
\(222\) | −1914.29 | −0.578732 | ||||||||
\(223\) | −3431.26 | −1.03038 | −0.515188 | − | 0.857077i | \(-0.672278\pi\) | ||||
−0.515188 | + | 0.857077i | \(0.672278\pi\) | |||||||
\(224\) | 908.003 | 0.270842 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −582.631 | −0.171487 | ||||||||
\(227\) | 4757.91 | 1.39116 | 0.695581 | − | 0.718448i | \(-0.255147\pi\) | ||||
0.695581 | + | 0.718448i | \(0.255147\pi\) | |||||||
\(228\) | −1829.61 | −0.531442 | ||||||||
\(229\) | −4368.93 | −1.26073 | −0.630364 | − | 0.776300i | \(-0.717094\pi\) | ||||
−0.630364 | + | 0.776300i | \(0.717094\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −887.026 | −0.252649 | ||||||||
\(232\) | −1875.65 | −0.530787 | ||||||||
\(233\) | 3642.00 | 1.02401 | 0.512007 | − | 0.858981i | \(-0.328902\pi\) | ||||
0.512007 | + | 0.858981i | \(0.328902\pi\) | |||||||
\(234\) | 178.593 | 0.0498932 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3881.15 | 1.07051 | ||||||||
\(237\) | −500.431 | −0.137158 | ||||||||
\(238\) | 308.819 | 0.0841082 | ||||||||
\(239\) | 2236.17 | 0.605213 | 0.302606 | − | 0.953116i | \(-0.402143\pi\) | ||||
0.302606 | + | 0.953116i | \(0.402143\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6538.78 | 1.74772 | 0.873858 | − | 0.486181i | \(-0.161610\pi\) | ||||
0.873858 | + | 0.486181i | \(0.161610\pi\) | |||||||
\(242\) | −3661.75 | −0.972670 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −1747.06 | −0.458378 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −653.348 | −0.169333 | ||||||||
\(247\) | 1398.29 | 0.360208 | ||||||||
\(248\) | 3820.80 | 0.978310 | ||||||||
\(249\) | −603.280 | −0.153539 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2507.12 | 0.630470 | 0.315235 | − | 0.949014i | \(-0.397917\pi\) | ||||
0.315235 | + | 0.949014i | \(0.397917\pi\) | |||||||
\(252\) | 247.054 | 0.0617577 | ||||||||
\(253\) | 1741.42 | 0.432735 | ||||||||
\(254\) | −1723.49 | −0.425755 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3300.77 | −0.805853 | ||||||||
\(257\) | 808.131 | 0.196147 | 0.0980735 | − | 0.995179i | \(-0.468732\pi\) | ||||
0.0980735 | + | 0.995179i | \(0.468732\pi\) | |||||||
\(258\) | 325.560 | 0.0785600 | ||||||||
\(259\) | 2023.83 | 0.485539 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −808.998 | −0.191861 | ||||||||
\(262\) | 1301.69 | 0.306941 | ||||||||
\(263\) | −2940.70 | −0.689472 | −0.344736 | − | 0.938700i | \(-0.612032\pi\) | ||||
−0.344736 | + | 0.938700i | \(0.612032\pi\) | |||||||
\(264\) | 3823.11 | 0.891273 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −794.881 | −0.183223 | ||||||||
\(267\) | −326.501 | −0.0748371 | ||||||||
\(268\) | 3814.81 | 0.869502 | ||||||||
\(269\) | 7111.50 | 1.61188 | 0.805940 | − | 0.591997i | \(-0.201660\pi\) | ||||
0.805940 | + | 0.591997i | \(0.201660\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2034.96 | 0.456145 | 0.228072 | − | 0.973644i | \(-0.426758\pi\) | ||||
0.228072 | + | 0.973644i | \(0.426758\pi\) | |||||||
\(272\) | 564.502 | 0.125838 | ||||||||
\(273\) | −188.813 | −0.0418589 | ||||||||
\(274\) | −746.281 | −0.164542 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −485.018 | −0.105778 | ||||||||
\(277\) | −2723.20 | −0.590689 | −0.295345 | − | 0.955391i | \(-0.595434\pi\) | ||||
−0.295345 | + | 0.955391i | \(0.595434\pi\) | |||||||
\(278\) | −621.449 | −0.134072 | ||||||||
\(279\) | 1647.97 | 0.353625 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3265.56 | 0.693263 | 0.346632 | − | 0.938001i | \(-0.387325\pi\) | ||||
0.346632 | + | 0.938001i | \(0.387325\pi\) | |||||||
\(282\) | −1482.38 | −0.313030 | ||||||||
\(283\) | −1144.02 | −0.240299 | −0.120150 | − | 0.992756i | \(-0.538337\pi\) | ||||
−0.120150 | + | 0.992756i | \(0.538337\pi\) | |||||||
\(284\) | 1853.16 | 0.387200 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1211.91 | −0.250566 | ||||||||
\(287\) | 690.735 | 0.142065 | ||||||||
\(288\) | −1687.96 | −0.345361 | ||||||||
\(289\) | −3166.72 | −0.644560 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3473.85 | 0.699796 | ||||||||
\(292\) | 137.813 | 0.0276195 | ||||||||
\(293\) | 1677.35 | 0.334444 | 0.167222 | − | 0.985919i | \(-0.446520\pi\) | ||||
0.167222 | + | 0.985919i | \(0.446520\pi\) | |||||||
\(294\) | −1463.37 | −0.290291 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8722.75 | −1.71284 | ||||||||
\(297\) | 1648.96 | 0.322164 | ||||||||
\(298\) | −2621.86 | −0.509666 | ||||||||
\(299\) | 370.679 | 0.0716954 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −344.190 | −0.0659095 | ||||||||
\(302\) | −2048.16 | −0.390259 | ||||||||
\(303\) | −5108.24 | −0.968518 | ||||||||
\(304\) | −1452.99 | −0.274128 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −574.088 | −0.107250 | ||||||||
\(307\) | −7207.70 | −1.33995 | −0.669975 | − | 0.742383i | \(-0.733695\pi\) | ||||
−0.669975 | + | 0.742383i | \(0.733695\pi\) | |||||||
\(308\) | −1676.47 | −0.310149 | ||||||||
\(309\) | −4365.42 | −0.803689 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 412.963 | 0.0752958 | 0.0376479 | − | 0.999291i | \(-0.488013\pi\) | ||||
0.0376479 | + | 0.999291i | \(0.488013\pi\) | |||||||
\(312\) | 813.790 | 0.147666 | ||||||||
\(313\) | −2936.39 | −0.530270 | −0.265135 | − | 0.964211i | \(-0.585417\pi\) | ||||
−0.265135 | + | 0.964211i | \(0.585417\pi\) | |||||||
\(314\) | −1160.93 | −0.208646 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −945.812 | −0.168374 | ||||||||
\(317\) | −377.956 | −0.0669657 | −0.0334828 | − | 0.999439i | \(-0.510660\pi\) | ||||
−0.0334828 | + | 0.999439i | \(0.510660\pi\) | |||||||
\(318\) | 114.963 | 0.0202729 | ||||||||
\(319\) | 5489.75 | 0.963533 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2468.28 | −0.429178 | ||||||||
\(322\) | −210.718 | −0.0364685 | ||||||||
\(323\) | −4494.81 | −0.774298 | ||||||||
\(324\) | −459.269 | −0.0787497 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4139.83 | 0.703326 | ||||||||
\(327\) | −1371.79 | −0.231989 | ||||||||
\(328\) | −2977.09 | −0.501165 | ||||||||
\(329\) | 1567.20 | 0.262622 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4428.17 | −0.735330 | −0.367665 | − | 0.929958i | \(-0.619843\pi\) | ||||
−0.367665 | + | 0.929958i | \(0.619843\pi\) | |||||||
\(332\) | −1140.20 | −0.188483 | ||||||||
\(333\) | −3762.26 | −0.619130 | ||||||||
\(334\) | 2368.57 | 0.388031 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 196.199 | 0.0318558 | ||||||||
\(337\) | 1768.76 | 0.285907 | 0.142953 | − | 0.989729i | \(-0.454340\pi\) | ||||
0.142953 | + | 0.989729i | \(0.454340\pi\) | |||||||
\(338\) | −257.968 | −0.0415137 | ||||||||
\(339\) | −1145.08 | −0.183458 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11182.9 | −1.77592 | ||||||||
\(342\) | 1477.67 | 0.233635 | ||||||||
\(343\) | 3207.70 | 0.504955 | ||||||||
\(344\) | 1483.47 | 0.232509 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6060.36 | −0.941639 | ||||||||
\(347\) | −2412.97 | −0.373300 | −0.186650 | − | 0.982426i | \(-0.559763\pi\) | ||||
−0.186650 | + | 0.982426i | \(0.559763\pi\) | |||||||
\(348\) | −1529.00 | −0.235526 | ||||||||
\(349\) | −9967.45 | −1.52878 | −0.764392 | − | 0.644752i | \(-0.776961\pi\) | ||||
−0.764392 | + | 0.644752i | \(0.776961\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 351.000 | 0.0533761 | ||||||||
\(352\) | 11454.3 | 1.73442 | ||||||||
\(353\) | −4516.30 | −0.680959 | −0.340479 | − | 0.940252i | \(-0.610589\pi\) | ||||
−0.340479 | + | 0.940252i | \(0.610589\pi\) | |||||||
\(354\) | −3134.58 | −0.470625 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −617.084 | −0.0918691 | ||||||||
\(357\) | 606.939 | 0.0899794 | ||||||||
\(358\) | 4107.57 | 0.606401 | ||||||||
\(359\) | 12159.8 | 1.78767 | 0.893833 | − | 0.448400i | \(-0.148006\pi\) | ||||
0.893833 | + | 0.448400i | \(0.148006\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4710.38 | 0.686745 | ||||||||
\(362\) | 6672.22 | 0.968740 | ||||||||
\(363\) | −7196.65 | −1.04057 | ||||||||
\(364\) | −356.856 | −0.0513855 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1411.00 | 0.201514 | ||||||||
\(367\) | 2674.25 | 0.380367 | 0.190183 | − | 0.981749i | \(-0.439092\pi\) | ||||
0.190183 | + | 0.981749i | \(0.439092\pi\) | |||||||
\(368\) | −385.180 | −0.0545622 | ||||||||
\(369\) | −1284.06 | −0.181153 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −121.541 | −0.0170083 | ||||||||
\(372\) | 3114.65 | 0.434105 | ||||||||
\(373\) | −9601.74 | −1.33287 | −0.666433 | − | 0.745564i | \(-0.732180\pi\) | ||||
−0.666433 | + | 0.745564i | \(0.732180\pi\) | |||||||
\(374\) | 3895.69 | 0.538613 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6754.69 | −0.926454 | ||||||||
\(377\) | 1168.55 | 0.159638 | ||||||||
\(378\) | −199.531 | −0.0271502 | ||||||||
\(379\) | 9019.65 | 1.22245 | 0.611225 | − | 0.791457i | \(-0.290677\pi\) | ||||
0.611225 | + | 0.791457i | \(0.290677\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3387.28 | −0.455474 | ||||||||
\(382\) | −2149.95 | −0.287960 | ||||||||
\(383\) | 4015.34 | 0.535703 | 0.267852 | − | 0.963460i | \(-0.413686\pi\) | ||||
0.267852 | + | 0.963460i | \(0.413686\pi\) | |||||||
\(384\) | −3685.12 | −0.489727 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6306.78 | −0.831623 | ||||||||
\(387\) | 639.842 | 0.0840439 | ||||||||
\(388\) | 6565.55 | 0.859060 | ||||||||
\(389\) | −2725.35 | −0.355221 | −0.177610 | − | 0.984101i | \(-0.556837\pi\) | ||||
−0.177610 | + | 0.984101i | \(0.556837\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1191.55 | −0.154115 | ||||||||
\(392\) | −6668.09 | −0.859157 | ||||||||
\(393\) | 2558.28 | 0.328367 | ||||||||
\(394\) | −5191.78 | −0.663853 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3116.53 | 0.395484 | ||||||||
\(397\) | 4391.59 | 0.555182 | 0.277591 | − | 0.960699i | \(-0.410464\pi\) | ||||
0.277591 | + | 0.960699i | \(0.410464\pi\) | |||||||
\(398\) | 5374.19 | 0.676844 | ||||||||
\(399\) | −1562.23 | −0.196013 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3762.48 | 0.468552 | 0.234276 | − | 0.972170i | \(-0.424728\pi\) | ||||
0.234276 | + | 0.972170i | \(0.424728\pi\) | |||||||
\(402\) | −3081.00 | −0.382255 | ||||||||
\(403\) | −2380.40 | −0.294234 | ||||||||
\(404\) | −9654.55 | −1.18894 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −664.281 | −0.0812013 | ||||||||
\(407\) | 25530.2 | 3.10930 | ||||||||
\(408\) | −2615.93 | −0.317421 | ||||||||
\(409\) | −6797.81 | −0.821833 | −0.410917 | − | 0.911673i | \(-0.634791\pi\) | ||||
−0.410917 | + | 0.911673i | \(0.634791\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1466.71 | −0.176028 | ||||||||
\(412\) | −8250.61 | −0.986599 | ||||||||
\(413\) | 3313.95 | 0.394840 | ||||||||
\(414\) | 391.721 | 0.0465025 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2438.17 | 0.287358 | ||||||||
\(417\) | −1221.37 | −0.143431 | ||||||||
\(418\) | −10027.3 | −1.17332 | ||||||||
\(419\) | −12594.2 | −1.46841 | −0.734207 | − | 0.678925i | \(-0.762446\pi\) | ||||
−0.734207 | + | 0.678925i | \(0.762446\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6888.04 | 0.797393 | 0.398697 | − | 0.917083i | \(-0.369463\pi\) | ||||
0.398697 | + | 0.917083i | \(0.369463\pi\) | |||||||
\(422\) | 3427.19 | 0.395338 | ||||||||
\(423\) | −2913.40 | −0.334881 | ||||||||
\(424\) | 523.845 | 0.0600004 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1496.69 | −0.170223 | ||||||||
\(427\) | −1491.74 | −0.169065 | ||||||||
\(428\) | −4665.04 | −0.526854 | ||||||||
\(429\) | −2381.84 | −0.268056 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7384.53 | −0.825291 | −0.412645 | − | 0.910892i | \(-0.635395\pi\) | ||||
−0.412645 | + | 0.910892i | \(0.635395\pi\) | |||||||
\(432\) | −364.731 | −0.0406206 | ||||||||
\(433\) | −9068.33 | −1.00646 | −0.503229 | − | 0.864153i | \(-0.667855\pi\) | ||||
−0.503229 | + | 0.864153i | \(0.667855\pi\) | |||||||
\(434\) | 1353.17 | 0.149665 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2592.68 | −0.284786 | ||||||||
\(437\) | 3066.97 | 0.335728 | ||||||||
\(438\) | −111.304 | −0.0121422 | ||||||||
\(439\) | 16875.4 | 1.83466 | 0.917331 | − | 0.398125i | \(-0.130339\pi\) | ||||
0.917331 | + | 0.398125i | \(0.130339\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2876.05 | −0.310555 | ||||||||
\(442\) | 829.239 | 0.0892373 | ||||||||
\(443\) | 6766.18 | 0.725668 | 0.362834 | − | 0.931854i | \(-0.381809\pi\) | ||||
0.362834 | + | 0.931854i | \(0.381809\pi\) | |||||||
\(444\) | −7110.64 | −0.760037 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5237.61 | 0.556072 | ||||||||
\(447\) | −5152.90 | −0.545243 | ||||||||
\(448\) | −862.814 | −0.0909914 | ||||||||
\(449\) | 140.944 | 0.0148141 | 0.00740706 | − | 0.999973i | \(-0.497642\pi\) | ||||
0.00740706 | + | 0.999973i | \(0.497642\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8713.47 | 0.909759 | ||||||||
\(452\) | −2164.19 | −0.225210 | ||||||||
\(453\) | −4025.36 | −0.417501 | ||||||||
\(454\) | −7262.67 | −0.750779 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6733.24 | 0.691475 | ||||||||
\(457\) | 17733.1 | 1.81514 | 0.907571 | − | 0.419898i | \(-0.137934\pi\) | ||||
0.907571 | + | 0.419898i | \(0.137934\pi\) | |||||||
\(458\) | 6668.90 | 0.680387 | ||||||||
\(459\) | −1128.29 | −0.114736 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2293.37 | 0.231699 | 0.115849 | − | 0.993267i | \(-0.463041\pi\) | ||||
0.115849 | + | 0.993267i | \(0.463041\pi\) | |||||||
\(462\) | 1353.99 | 0.136349 | ||||||||
\(463\) | −13770.9 | −1.38226 | −0.691129 | − | 0.722731i | \(-0.742887\pi\) | ||||
−0.691129 | + | 0.722731i | \(0.742887\pi\) | |||||||
\(464\) | −1214.27 | −0.121489 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5559.29 | −0.552638 | ||||||||
\(467\) | 3477.37 | 0.344568 | 0.172284 | − | 0.985047i | \(-0.444885\pi\) | ||||
0.172284 | + | 0.985047i | \(0.444885\pi\) | |||||||
\(468\) | 663.388 | 0.0655237 | ||||||||
\(469\) | 3257.31 | 0.320700 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2281.64 | −0.223211 | ||||||||
\(472\) | −14283.2 | −1.39288 | ||||||||
\(473\) | −4341.88 | −0.422072 | ||||||||
\(474\) | 763.878 | 0.0740213 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1147.11 | 0.110458 | ||||||||
\(477\) | 225.943 | 0.0216880 | ||||||||
\(478\) | −3413.38 | −0.326620 | ||||||||
\(479\) | −3137.39 | −0.299271 | −0.149636 | − | 0.988741i | \(-0.547810\pi\) | ||||
−0.149636 | + | 0.988741i | \(0.547810\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5434.37 | 0.515148 | ||||||||
\(482\) | −9981.05 | −0.943204 | ||||||||
\(483\) | −414.137 | −0.0390142 | ||||||||
\(484\) | −13601.6 | −1.27739 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 370.925 | 0.0346204 | ||||||||
\(487\) | −5996.52 | −0.557964 | −0.278982 | − | 0.960296i | \(-0.589997\pi\) | ||||
−0.278982 | + | 0.960296i | \(0.589997\pi\) | |||||||
\(488\) | 6429.46 | 0.596410 | ||||||||
\(489\) | 8136.26 | 0.752422 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9401.49 | −0.864121 | −0.432060 | − | 0.901845i | \(-0.642213\pi\) | ||||
−0.432060 | + | 0.901845i | \(0.642213\pi\) | |||||||
\(492\) | −2426.87 | −0.222382 | ||||||||
\(493\) | −3756.31 | −0.343156 | ||||||||
\(494\) | −2134.41 | −0.194396 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2473.52 | 0.223920 | ||||||||
\(497\) | 1582.34 | 0.142812 | ||||||||
\(498\) | 920.871 | 0.0828619 | ||||||||
\(499\) | −5052.33 | −0.453253 | −0.226626 | − | 0.973982i | \(-0.572770\pi\) | ||||
−0.226626 | + | 0.973982i | \(0.572770\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4655.08 | 0.415117 | ||||||||
\(502\) | −3826.96 | −0.340251 | ||||||||
\(503\) | −8184.02 | −0.725462 | −0.362731 | − | 0.931894i | \(-0.618156\pi\) | ||||
−0.362731 | + | 0.931894i | \(0.618156\pi\) | |||||||
\(504\) | −909.196 | −0.0803548 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2658.17 | −0.233537 | ||||||||
\(507\) | −507.000 | −0.0444116 | ||||||||
\(508\) | −6401.94 | −0.559134 | ||||||||
\(509\) | 6039.12 | 0.525892 | 0.262946 | − | 0.964811i | \(-0.415306\pi\) | ||||
0.262946 | + | 0.964811i | \(0.415306\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 117.673 | 0.0101870 | ||||||||
\(512\) | −4788.54 | −0.413331 | ||||||||
\(513\) | 2904.15 | 0.249944 | ||||||||
\(514\) | −1233.56 | −0.105856 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1209.30 | 0.103171 | ||||||||
\(517\) | 19770.0 | 1.68178 | ||||||||
\(518\) | −3089.25 | −0.262035 | ||||||||
\(519\) | −11910.8 | −1.00737 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14602.5 | −1.22792 | −0.613960 | − | 0.789337i | \(-0.710424\pi\) | ||||
−0.613960 | + | 0.789337i | \(0.710424\pi\) | |||||||
\(522\) | 1234.89 | 0.103543 | ||||||||
\(523\) | −8910.70 | −0.745005 | −0.372502 | − | 0.928031i | \(-0.621500\pi\) | ||||
−0.372502 | + | 0.928031i | \(0.621500\pi\) | |||||||
\(524\) | 4835.14 | 0.403099 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4488.80 | 0.372093 | ||||||||
\(527\) | 7651.79 | 0.632481 | ||||||||
\(528\) | 2475.01 | 0.203998 | ||||||||
\(529\) | −11354.0 | −0.933177 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6160.57 | −0.503477 | ||||||||
\(532\) | −2952.60 | −0.240623 | ||||||||
\(533\) | 1854.76 | 0.150729 | ||||||||
\(534\) | 498.384 | 0.0403879 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14039.1 | −1.13134 | ||||||||
\(537\) | 8072.84 | 0.648731 | ||||||||
\(538\) | −10855.3 | −0.869897 | ||||||||
\(539\) | 19516.5 | 1.55962 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13313.6 | −1.05803 | −0.529017 | − | 0.848611i | \(-0.677439\pi\) | ||||
−0.529017 | + | 0.848611i | \(0.677439\pi\) | |||||||
\(542\) | −3106.25 | −0.246171 | ||||||||
\(543\) | 13113.3 | 1.03636 | ||||||||
\(544\) | −7837.48 | −0.617701 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 288.212 | 0.0225903 | ||||||||
\(547\) | 4116.94 | 0.321806 | 0.160903 | − | 0.986970i | \(-0.448559\pi\) | ||||
0.160903 | + | 0.986970i | \(0.448559\pi\) | |||||||
\(548\) | −2772.07 | −0.216090 | ||||||||
\(549\) | 2773.12 | 0.215581 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9668.52 | 0.747537 | ||||||||
\(552\) | 1784.94 | 0.137631 | ||||||||
\(553\) | −807.590 | −0.0621016 | ||||||||
\(554\) | 4156.79 | 0.318782 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2308.38 | −0.176074 | ||||||||
\(557\) | 6888.37 | 0.524003 | 0.262002 | − | 0.965067i | \(-0.415617\pi\) | ||||
0.262002 | + | 0.965067i | \(0.415617\pi\) | |||||||
\(558\) | −2515.53 | −0.190844 | ||||||||
\(559\) | −924.216 | −0.0699288 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7656.42 | 0.576211 | ||||||||
\(562\) | −4984.68 | −0.374139 | ||||||||
\(563\) | −10537.1 | −0.788782 | −0.394391 | − | 0.918943i | \(-0.629045\pi\) | ||||
−0.394391 | + | 0.918943i | \(0.629045\pi\) | |||||||
\(564\) | −5506.31 | −0.411095 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1746.27 | 0.129684 | ||||||||
\(567\) | −392.150 | −0.0290454 | ||||||||
\(568\) | −6819.91 | −0.503798 | ||||||||
\(569\) | 26930.1 | 1.98413 | 0.992065 | − | 0.125722i | \(-0.0401248\pi\) | ||||
0.992065 | + | 0.125722i | \(0.0401248\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3125.60 | −0.229076 | −0.114538 | − | 0.993419i | \(-0.536539\pi\) | ||||
−0.114538 | + | 0.993419i | \(0.536539\pi\) | |||||||
\(572\) | −4501.66 | −0.329063 | ||||||||
\(573\) | −4225.42 | −0.308062 | ||||||||
\(574\) | −1054.36 | −0.0766696 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1603.96 | 0.116027 | ||||||||
\(577\) | −4787.13 | −0.345391 | −0.172696 | − | 0.984975i | \(-0.555248\pi\) | ||||
−0.172696 | + | 0.984975i | \(0.555248\pi\) | |||||||
\(578\) | 4833.81 | 0.347855 | ||||||||
\(579\) | −12395.1 | −0.889675 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −973.566 | −0.0695186 | ||||||||
\(582\) | −5302.62 | −0.377664 | ||||||||
\(583\) | −1533.22 | −0.108918 | ||||||||
\(584\) | −507.174 | −0.0359366 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2560.38 | −0.180492 | ||||||||
\(587\) | −18380.8 | −1.29243 | −0.646214 | − | 0.763156i | \(-0.723649\pi\) | ||||
−0.646214 | + | 0.763156i | \(0.723649\pi\) | |||||||
\(588\) | −5435.72 | −0.381233 | ||||||||
\(589\) | −19695.3 | −1.37781 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10203.7 | −0.710193 | ||||||||
\(592\) | −5646.96 | −0.392042 | ||||||||
\(593\) | 13831.7 | 0.957843 | 0.478922 | − | 0.877858i | \(-0.341028\pi\) | ||||
0.478922 | + | 0.877858i | \(0.341028\pi\) | |||||||
\(594\) | −2517.05 | −0.173865 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9738.94 | −0.669333 | ||||||||
\(597\) | 10562.2 | 0.724091 | ||||||||
\(598\) | −565.819 | −0.0386924 | ||||||||
\(599\) | 12248.6 | 0.835502 | 0.417751 | − | 0.908562i | \(-0.362818\pi\) | ||||
0.417751 | + | 0.908562i | \(0.362818\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9719.56 | 0.659682 | 0.329841 | − | 0.944036i | \(-0.393005\pi\) | ||||
0.329841 | + | 0.944036i | \(0.393005\pi\) | |||||||
\(602\) | 525.385 | 0.0355699 | ||||||||
\(603\) | −6055.27 | −0.408938 | ||||||||
\(604\) | −7607.91 | −0.512519 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7797.42 | 0.522688 | ||||||||
\(607\) | −1607.83 | −0.107512 | −0.0537560 | − | 0.998554i | \(-0.517119\pi\) | ||||
−0.0537560 | + | 0.998554i | \(0.517119\pi\) | |||||||
\(608\) | 20173.2 | 1.34561 | ||||||||
\(609\) | −1305.55 | −0.0868696 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4208.25 | 0.278638 | ||||||||
\(612\) | −2132.46 | −0.140849 | ||||||||
\(613\) | −14731.1 | −0.970610 | −0.485305 | − | 0.874345i | \(-0.661291\pi\) | ||||
−0.485305 | + | 0.874345i | \(0.661291\pi\) | |||||||
\(614\) | 11002.1 | 0.723142 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6169.68 | 0.403545 | ||||||||
\(617\) | −27951.8 | −1.82382 | −0.911909 | − | 0.410392i | \(-0.865392\pi\) | ||||
−0.911909 | + | 0.410392i | \(0.865392\pi\) | |||||||
\(618\) | 6663.55 | 0.433733 | ||||||||
\(619\) | 16200.2 | 1.05192 | 0.525961 | − | 0.850509i | \(-0.323706\pi\) | ||||
0.525961 | + | 0.850509i | \(0.323706\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 769.872 | 0.0497486 | ||||||||
\(622\) | −630.364 | −0.0406355 | ||||||||
\(623\) | −526.903 | −0.0338843 | ||||||||
\(624\) | 526.833 | 0.0337984 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4482.22 | 0.286175 | ||||||||
\(627\) | −19707.2 | −1.25523 | ||||||||
\(628\) | −4312.28 | −0.274011 | ||||||||
\(629\) | −17468.8 | −1.10735 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12731.8 | 0.803239 | 0.401619 | − | 0.915807i | \(-0.368447\pi\) | ||||
0.401619 | + | 0.915807i | \(0.368447\pi\) | |||||||
\(632\) | 3480.73 | 0.219076 | ||||||||
\(633\) | 6735.65 | 0.422935 | ||||||||
\(634\) | 576.927 | 0.0361399 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 427.030 | 0.0266240 | ||||||||
\(637\) | 4154.30 | 0.258397 | ||||||||
\(638\) | −8379.77 | −0.519997 | ||||||||
\(639\) | −2941.53 | −0.182105 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11556.9 | −0.712119 | −0.356059 | − | 0.934463i | \(-0.615880\pi\) | ||||
−0.356059 | + | 0.934463i | \(0.615880\pi\) | |||||||
\(642\) | 3767.69 | 0.231618 | ||||||||
\(643\) | 9181.25 | 0.563100 | 0.281550 | − | 0.959547i | \(-0.409152\pi\) | ||||
0.281550 | + | 0.959547i | \(0.409152\pi\) | |||||||
\(644\) | −782.716 | −0.0478934 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6861.06 | 0.417871 | ||||||||
\(647\) | −5244.11 | −0.318651 | −0.159326 | − | 0.987226i | \(-0.550932\pi\) | ||||
−0.159326 | + | 0.987226i | \(0.550932\pi\) | |||||||
\(648\) | 1690.18 | 0.102464 | ||||||||
\(649\) | 41804.8 | 2.52848 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2659.47 | 0.160112 | ||||||||
\(652\) | 15377.5 | 0.923663 | ||||||||
\(653\) | 16421.4 | 0.984106 | 0.492053 | − | 0.870565i | \(-0.336247\pi\) | ||||
0.492053 | + | 0.870565i | \(0.336247\pi\) | |||||||
\(654\) | 2093.96 | 0.125199 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1927.31 | −0.114709 | ||||||||
\(657\) | −218.752 | −0.0129898 | ||||||||
\(658\) | −2392.24 | −0.141732 | ||||||||
\(659\) | 1838.11 | 0.108653 | 0.0543266 | − | 0.998523i | \(-0.482699\pi\) | ||||
0.0543266 | + | 0.998523i | \(0.482699\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5500.93 | −0.323694 | −0.161847 | − | 0.986816i | \(-0.551745\pi\) | ||||
−0.161847 | + | 0.986816i | \(0.551745\pi\) | |||||||
\(662\) | 6759.34 | 0.396841 | ||||||||
\(663\) | 1629.75 | 0.0954665 | ||||||||
\(664\) | 4196.10 | 0.245241 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5742.86 | 0.334131 | ||||||||
\(667\) | 2563.07 | 0.148789 | ||||||||
\(668\) | 8798.08 | 0.509593 | ||||||||
\(669\) | 10293.8 | 0.594888 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18818.0 | −1.08266 | ||||||||
\(672\) | −2724.01 | −0.156370 | ||||||||
\(673\) | 25986.7 | 1.48843 | 0.744216 | − | 0.667939i | \(-0.232823\pi\) | ||||
0.744216 | + | 0.667939i | \(0.232823\pi\) | |||||||
\(674\) | −2699.91 | −0.154298 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −958.227 | −0.0545191 | ||||||||
\(677\) | 11691.3 | 0.663714 | 0.331857 | − | 0.943330i | \(-0.392325\pi\) | ||||
0.331857 | + | 0.943330i | \(0.392325\pi\) | |||||||
\(678\) | 1747.89 | 0.0990080 | ||||||||
\(679\) | 5606.05 | 0.316849 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14273.7 | −0.803188 | ||||||||
\(682\) | 17070.0 | 0.958423 | ||||||||
\(683\) | 11111.5 | 0.622501 | 0.311251 | − | 0.950328i | \(-0.399252\pi\) | ||||
0.311251 | + | 0.950328i | \(0.399252\pi\) | |||||||
\(684\) | 5488.82 | 0.306828 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4896.36 | −0.272513 | ||||||||
\(687\) | 13106.8 | 0.727882 | ||||||||
\(688\) | 960.370 | 0.0532177 | ||||||||
\(689\) | −326.361 | −0.0180455 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7542.55 | −0.415242 | −0.207621 | − | 0.978209i | \(-0.566572\pi\) | ||||
−0.207621 | + | 0.978209i | \(0.566572\pi\) | |||||||
\(692\) | −22511.3 | −1.23664 | ||||||||
\(693\) | 2661.08 | 0.145867 | ||||||||
\(694\) | 3683.26 | 0.201462 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5626.96 | 0.306450 | ||||||||
\(697\) | −5962.11 | −0.324005 | ||||||||
\(698\) | 15214.7 | 0.825051 | ||||||||
\(699\) | −10926.0 | −0.591215 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8231.17 | −0.443491 | −0.221745 | − | 0.975105i | \(-0.571175\pi\) | ||||
−0.221745 | + | 0.975105i | \(0.571175\pi\) | |||||||
\(702\) | −535.780 | −0.0288059 | ||||||||
\(703\) | 44963.6 | 2.41228 | ||||||||
\(704\) | −10884.2 | −0.582691 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6893.86 | 0.367498 | ||||||||
\(707\) | −8243.61 | −0.438519 | ||||||||
\(708\) | −11643.4 | −0.618061 | ||||||||
\(709\) | 28044.6 | 1.48553 | 0.742764 | − | 0.669554i | \(-0.233515\pi\) | ||||
0.742764 | + | 0.669554i | \(0.233515\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1501.29 | 0.0791884 | ||||||||
\(712\) | 2270.96 | 0.119534 | ||||||||
\(713\) | −5221.09 | −0.274238 | ||||||||
\(714\) | −926.457 | −0.0485599 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15257.6 | 0.796374 | ||||||||
\(717\) | −6708.51 | −0.349420 | ||||||||
\(718\) | −18561.3 | −0.964764 | ||||||||
\(719\) | 29686.4 | 1.53980 | 0.769901 | − | 0.638163i | \(-0.220306\pi\) | ||||
0.769901 | + | 0.638163i | \(0.220306\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7044.86 | −0.363889 | ||||||||
\(722\) | −7190.12 | −0.370621 | ||||||||
\(723\) | −19616.3 | −1.00904 | ||||||||
\(724\) | 24784.0 | 1.27223 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 10985.3 | 0.561572 | ||||||||
\(727\) | 27654.5 | 1.41080 | 0.705398 | − | 0.708812i | \(-0.250768\pi\) | ||||
0.705398 | + | 0.708812i | \(0.250768\pi\) | |||||||
\(728\) | 1313.28 | 0.0668592 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2970.89 | 0.150318 | ||||||||
\(732\) | 5241.19 | 0.264645 | ||||||||
\(733\) | 13077.5 | 0.658975 | 0.329488 | − | 0.944160i | \(-0.393124\pi\) | ||||
0.329488 | + | 0.944160i | \(0.393124\pi\) | |||||||
\(734\) | −4082.08 | −0.205276 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5347.79 | 0.267829 | ||||||||
\(737\) | 41090.3 | 2.05370 | ||||||||
\(738\) | 1960.04 | 0.0977645 | ||||||||
\(739\) | −4218.33 | −0.209978 | −0.104989 | − | 0.994473i | \(-0.533481\pi\) | ||||
−0.104989 | + | 0.994473i | \(0.533481\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4194.88 | −0.207966 | ||||||||
\(742\) | 185.525 | 0.00917903 | ||||||||
\(743\) | −7725.54 | −0.381457 | −0.190728 | − | 0.981643i | \(-0.561085\pi\) | ||||
−0.190728 | + | 0.981643i | \(0.561085\pi\) | |||||||
\(744\) | −11462.4 | −0.564828 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 14656.5 | 0.719319 | ||||||||
\(747\) | 1809.84 | 0.0886460 | ||||||||
\(748\) | 14470.6 | 0.707349 | ||||||||
\(749\) | −3983.29 | −0.194321 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7506.12 | 0.364717 | 0.182358 | − | 0.983232i | \(-0.441627\pi\) | ||||
0.182358 | + | 0.983232i | \(0.441627\pi\) | |||||||
\(752\) | −4372.87 | −0.212051 | ||||||||
\(753\) | −7521.35 | −0.364002 | ||||||||
\(754\) | −1783.72 | −0.0861531 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −741.162 | −0.0356558 | ||||||||
\(757\) | 2741.62 | 0.131632 | 0.0658162 | − | 0.997832i | \(-0.479035\pi\) | ||||
0.0658162 | + | 0.997832i | \(0.479035\pi\) | |||||||
\(758\) | −13768.0 | −0.659729 | ||||||||
\(759\) | −5224.25 | −0.249839 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29740.0 | 1.41666 | 0.708328 | − | 0.705883i | \(-0.249450\pi\) | ||||
0.708328 | + | 0.705883i | \(0.249450\pi\) | |||||||
\(762\) | 5170.48 | 0.245809 | ||||||||
\(763\) | −2213.78 | −0.105038 | ||||||||
\(764\) | −7986.01 | −0.378172 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6129.18 | −0.289107 | ||||||||
\(767\) | 8898.60 | 0.418918 | ||||||||
\(768\) | 9902.32 | 0.465259 | ||||||||
\(769\) | −19896.3 | −0.933004 | −0.466502 | − | 0.884520i | \(-0.654486\pi\) | ||||
−0.466502 | + | 0.884520i | \(0.654486\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2424.39 | −0.113246 | ||||||||
\(772\) | −23426.6 | −1.09215 | ||||||||
\(773\) | 13601.3 | 0.632866 | 0.316433 | − | 0.948615i | \(-0.397515\pi\) | ||||
0.316433 | + | 0.948615i | \(0.397515\pi\) | |||||||
\(774\) | −976.680 | −0.0453566 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −24162.2 | −1.11775 | ||||||||
\(777\) | −6071.48 | −0.280326 | ||||||||
\(778\) | 4160.09 | 0.191705 | ||||||||
\(779\) | 15346.1 | 0.705818 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19960.8 | 0.914539 | ||||||||
\(782\) | 1818.83 | 0.0831727 | ||||||||
\(783\) | 2426.99 | 0.110771 | ||||||||
\(784\) | −4316.81 | −0.196648 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3905.06 | −0.177212 | ||||||||
\(787\) | 1498.29 | 0.0678631 | 0.0339315 | − | 0.999424i | \(-0.489197\pi\) | ||||
0.0339315 | + | 0.999424i | \(0.489197\pi\) | |||||||
\(788\) | −19284.9 | −0.871824 | ||||||||
\(789\) | 8822.09 | 0.398067 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1847.91 | −0.0830647 | ||||||||
\(792\) | −11469.3 | −0.514577 | ||||||||
\(793\) | −4005.62 | −0.179374 | ||||||||
\(794\) | −6703.49 | −0.299620 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19962.5 | 0.888885 | ||||||||
\(797\) | 3713.30 | 0.165034 | 0.0825168 | − | 0.996590i | \(-0.473704\pi\) | ||||
0.0825168 | + | 0.996590i | \(0.473704\pi\) | |||||||
\(798\) | 2384.64 | 0.105784 | ||||||||
\(799\) | −13527.4 | −0.598955 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 979.502 | 0.0432072 | ||||||||
\(802\) | −5743.20 | −0.252867 | ||||||||
\(803\) | 1484.42 | 0.0652354 | ||||||||
\(804\) | −11444.4 | −0.502007 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3633.54 | 0.158791 | ||||||||
\(807\) | −21334.5 | −0.930620 | ||||||||
\(808\) | 35530.2 | 1.54697 | ||||||||
\(809\) | −34527.6 | −1.50053 | −0.750263 | − | 0.661139i | \(-0.770073\pi\) | ||||
−0.750263 | + | 0.661139i | \(0.770073\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37279.2 | −1.61412 | −0.807059 | − | 0.590471i | \(-0.798942\pi\) | ||||
−0.807059 | + | 0.590471i | \(0.798942\pi\) | |||||||
\(812\) | −2467.48 | −0.106640 | ||||||||
\(813\) | −6104.89 | −0.263355 | ||||||||
\(814\) | −38970.3 | −1.67802 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1693.51 | −0.0726526 | ||||||||
\(817\) | −7646.90 | −0.327455 | ||||||||
\(818\) | 10376.4 | 0.443525 | ||||||||
\(819\) | 566.439 | 0.0241673 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13877.9 | 0.589943 | 0.294972 | − | 0.955506i | \(-0.404690\pi\) | ||||
0.294972 | + | 0.955506i | \(0.404690\pi\) | |||||||
\(822\) | 2238.84 | 0.0949983 | ||||||||
\(823\) | −18945.1 | −0.802410 | −0.401205 | − | 0.915988i | \(-0.631408\pi\) | ||||
−0.401205 | + | 0.915988i | \(0.631408\pi\) | |||||||
\(824\) | 30363.5 | 1.28369 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5058.55 | −0.213086 | ||||||||
\(827\) | 7804.75 | 0.328171 | 0.164086 | − | 0.986446i | \(-0.447533\pi\) | ||||
0.164086 | + | 0.986446i | \(0.447533\pi\) | |||||||
\(828\) | 1455.05 | 0.0610708 | ||||||||
\(829\) | 5784.85 | 0.242360 | 0.121180 | − | 0.992631i | \(-0.461332\pi\) | ||||
0.121180 | + | 0.992631i | \(0.461332\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8169.59 | 0.341035 | ||||||||
\(832\) | −2316.82 | −0.0965402 | ||||||||
\(833\) | −13354.0 | −0.555448 | ||||||||
\(834\) | 1864.35 | 0.0774065 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −37246.4 | −1.54090 | ||||||||
\(837\) | −4943.91 | −0.204165 | ||||||||
\(838\) | 19224.3 | 0.792471 | ||||||||
\(839\) | −5011.42 | −0.206214 | −0.103107 | − | 0.994670i | \(-0.532878\pi\) | ||||
−0.103107 | + | 0.994670i | \(0.532878\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16309.0 | −0.668704 | ||||||||
\(842\) | −10514.2 | −0.430336 | ||||||||
\(843\) | −9796.68 | −0.400256 | ||||||||
\(844\) | 12730.3 | 0.519190 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4447.13 | 0.180728 | ||||||||
\(847\) | −11613.9 | −0.471142 | ||||||||
\(848\) | 339.128 | 0.0137332 | ||||||||
\(849\) | 3432.05 | 0.138737 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11919.6 | 0.480138 | ||||||||
\(852\) | −5559.48 | −0.223550 | ||||||||
\(853\) | 22059.0 | 0.885446 | 0.442723 | − | 0.896659i | \(-0.354013\pi\) | ||||
0.442723 | + | 0.896659i | \(0.354013\pi\) | |||||||
\(854\) | 2277.06 | 0.0912404 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17168.1 | 0.685506 | ||||||||
\(857\) | −13956.2 | −0.556283 | −0.278141 | − | 0.960540i | \(-0.589718\pi\) | ||||
−0.278141 | + | 0.960540i | \(0.589718\pi\) | |||||||
\(858\) | 3635.73 | 0.144664 | ||||||||
\(859\) | 12498.5 | 0.496442 | 0.248221 | − | 0.968703i | \(-0.420154\pi\) | ||||
0.248221 | + | 0.968703i | \(0.420154\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2072.20 | −0.0820215 | ||||||||
\(862\) | 11272.0 | 0.445391 | ||||||||
\(863\) | 38631.2 | 1.52378 | 0.761890 | − | 0.647707i | \(-0.224272\pi\) | ||||
0.761890 | + | 0.647707i | \(0.224272\pi\) | |||||||
\(864\) | 5063.88 | 0.199394 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 13842.3 | 0.543163 | ||||||||
\(867\) | 9500.17 | 0.372137 | ||||||||
\(868\) | 5026.38 | 0.196551 | ||||||||
\(869\) | −10187.6 | −0.397687 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8746.51 | 0.340257 | ||||||||
\(872\) | 9541.46 | 0.370544 | ||||||||
\(873\) | −10421.5 | −0.404027 | ||||||||
\(874\) | −4681.55 | −0.181185 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −413.440 | −0.0159462 | ||||||||
\(877\) | 856.756 | 0.0329881 | 0.0164941 | − | 0.999864i | \(-0.494750\pi\) | ||||
0.0164941 | + | 0.999864i | \(0.494750\pi\) | |||||||
\(878\) | −25759.2 | −0.990127 | ||||||||
\(879\) | −5032.06 | −0.193091 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33638.6 | 1.28640 | 0.643198 | − | 0.765700i | \(-0.277607\pi\) | ||||
0.643198 | + | 0.765700i | \(0.277607\pi\) | |||||||
\(882\) | 4390.12 | 0.167600 | ||||||||
\(883\) | 31109.1 | 1.18562 | 0.592811 | − | 0.805342i | \(-0.298018\pi\) | ||||
0.592811 | + | 0.805342i | \(0.298018\pi\) | |||||||
\(884\) | 3080.22 | 0.117193 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10328.2 | −0.391627 | ||||||||
\(887\) | −26080.3 | −0.987248 | −0.493624 | − | 0.869675i | \(-0.664328\pi\) | ||||
−0.493624 | + | 0.869675i | \(0.664328\pi\) | |||||||
\(888\) | 26168.3 | 0.988907 | ||||||||
\(889\) | −5466.35 | −0.206227 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4946.89 | −0.186001 | ||||||||
\(892\) | 19455.2 | 0.730277 | ||||||||
\(893\) | 34818.8 | 1.30478 | ||||||||
\(894\) | 7865.58 | 0.294256 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5946.99 | −0.221736 | ||||||||
\(897\) | −1112.04 | −0.0413934 | ||||||||
\(898\) | −215.142 | −0.00799486 | ||||||||
\(899\) | −16459.3 | −0.610621 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1049.09 | 0.0387905 | ||||||||
\(902\) | −13300.6 | −0.490977 | ||||||||
\(903\) | 1032.57 | 0.0380529 | ||||||||
\(904\) | 7964.56 | 0.293028 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6144.47 | 0.225316 | ||||||||
\(907\) | −20169.0 | −0.738369 | −0.369184 | − | 0.929356i | \(-0.620363\pi\) | ||||
−0.369184 | + | 0.929356i | \(0.620363\pi\) | |||||||
\(908\) | −26977.3 | −0.985983 | ||||||||
\(909\) | 15324.7 | 0.559174 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19982.2 | 0.726716 | 0.363358 | − | 0.931650i | \(-0.381630\pi\) | ||||
0.363358 | + | 0.931650i | \(0.381630\pi\) | |||||||
\(912\) | 4358.98 | 0.158268 | ||||||||
\(913\) | −12281.3 | −0.445184 | ||||||||
\(914\) | −27068.5 | −0.979593 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24771.7 | 0.893538 | ||||||||
\(917\) | 4128.52 | 0.148676 | ||||||||
\(918\) | 1722.27 | 0.0619207 | ||||||||
\(919\) | 38513.1 | 1.38241 | 0.691203 | − | 0.722661i | \(-0.257081\pi\) | ||||
0.691203 | + | 0.722661i | \(0.257081\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21623.1 | 0.773621 | ||||||||
\(922\) | −3500.70 | −0.125043 | ||||||||
\(923\) | 4248.88 | 0.151521 | ||||||||
\(924\) | 5029.42 | 0.179065 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 21020.4 | 0.745975 | ||||||||
\(927\) | 13096.3 | 0.464010 | ||||||||
\(928\) | 16858.7 | 0.596352 | ||||||||
\(929\) | 23218.9 | 0.820009 | 0.410005 | − | 0.912083i | \(-0.365527\pi\) | ||||
0.410005 | + | 0.912083i | \(0.365527\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34372.3 | 1.21000 | ||||||||
\(932\) | −20650.1 | −0.725768 | ||||||||
\(933\) | −1238.89 | −0.0434721 | ||||||||
\(934\) | −5307.99 | −0.185956 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2441.37 | −0.0852550 | ||||||||
\(937\) | 11112.9 | 0.387452 | 0.193726 | − | 0.981056i | \(-0.437943\pi\) | ||||
0.193726 | + | 0.981056i | \(0.437943\pi\) | |||||||
\(938\) | −4972.08 | −0.173075 | ||||||||
\(939\) | 8809.17 | 0.306152 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45570.4 | 1.57869 | 0.789347 | − | 0.613947i | \(-0.210419\pi\) | ||||
0.789347 | + | 0.613947i | \(0.210419\pi\) | |||||||
\(942\) | 3482.78 | 0.120462 | ||||||||
\(943\) | 4068.16 | 0.140485 | ||||||||
\(944\) | −9246.71 | −0.318808 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6627.62 | 0.227783 | ||||||||
\(947\) | −34903.9 | −1.19770 | −0.598852 | − | 0.800860i | \(-0.704376\pi\) | ||||
−0.598852 | + | 0.800860i | \(0.704376\pi\) | |||||||
\(948\) | 2837.44 | 0.0972106 | ||||||||
\(949\) | 315.975 | 0.0108082 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1133.87 | 0.0386626 | ||||||||
\(952\) | −4221.55 | −0.143720 | ||||||||
\(953\) | 2886.52 | 0.0981151 | 0.0490575 | − | 0.998796i | \(-0.484378\pi\) | ||||
0.0490575 | + | 0.998796i | \(0.484378\pi\) | |||||||
\(954\) | −344.888 | −0.0117046 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −12679.0 | −0.428943 | ||||||||
\(957\) | −16469.2 | −0.556296 | ||||||||
\(958\) | 4789.03 | 0.161510 | ||||||||
\(959\) | −2366.96 | −0.0797008 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3737.42 | 0.125455 | ||||||||
\(962\) | −8295.24 | −0.278014 | ||||||||
\(963\) | 7404.85 | 0.247786 | ||||||||
\(964\) | −37074.8 | −1.23869 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 632.155 | 0.0210551 | ||||||||
\(967\) | −11593.8 | −0.385556 | −0.192778 | − | 0.981242i | \(-0.561750\pi\) | ||||
−0.192778 | + | 0.981242i | \(0.561750\pi\) | |||||||
\(968\) | 50056.1 | 1.66205 | ||||||||
\(969\) | 13484.4 | 0.447041 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4952.12 | −0.163667 | −0.0818337 | − | 0.996646i | \(-0.526078\pi\) | ||||
−0.0818337 | + | 0.996646i | \(0.526078\pi\) | |||||||
\(972\) | 1377.81 | 0.0454662 | ||||||||
\(973\) | −1971.03 | −0.0649418 | ||||||||
\(974\) | 9153.33 | 0.301121 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4162.32 | 0.136509 | ||||||||
\(977\) | 19650.1 | 0.643462 | 0.321731 | − | 0.946831i | \(-0.395735\pi\) | ||||
0.321731 | + | 0.946831i | \(0.395735\pi\) | |||||||
\(978\) | −12419.5 | −0.406065 | ||||||||
\(979\) | −6646.77 | −0.216988 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4115.38 | 0.133939 | ||||||||
\(982\) | 14350.8 | 0.466347 | ||||||||
\(983\) | −56818.4 | −1.84357 | −0.921783 | − | 0.387707i | \(-0.873267\pi\) | ||||
−0.921783 | + | 0.387707i | \(0.873267\pi\) | |||||||
\(984\) | 8931.26 | 0.289348 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5733.78 | 0.185193 | ||||||||
\(987\) | −4701.61 | −0.151625 | ||||||||
\(988\) | −7928.30 | −0.255296 | ||||||||
\(989\) | −2027.15 | −0.0651764 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19120.4 | −0.612897 | −0.306448 | − | 0.951887i | \(-0.599141\pi\) | ||||
−0.306448 | + | 0.951887i | \(0.599141\pi\) | |||||||
\(992\) | −34342.1 | −1.09915 | ||||||||
\(993\) | 13284.5 | 0.424543 | ||||||||
\(994\) | −2415.34 | −0.0770723 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3420.59 | 0.108821 | ||||||||
\(997\) | −38887.9 | −1.23530 | −0.617650 | − | 0.786453i | \(-0.711915\pi\) | ||||
−0.617650 | + | 0.786453i | \(0.711915\pi\) | |||||||
\(998\) | 7712.07 | 0.244611 | ||||||||
\(999\) | 11286.8 | 0.357455 |
(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 | 975.4.a.l.1.2 | 3 | ||
5.4 | even | 2 | 39.4.a.c.1.2 | ✓ | 3 | ||
15.14 | odd | 2 | 117.4.a.f.1.2 | 3 | |||
20.19 | odd | 2 | 624.4.a.t.1.3 | 3 | |||
35.34 | odd | 2 | 1911.4.a.k.1.2 | 3 | |||
40.19 | odd | 2 | 2496.4.a.bp.1.1 | 3 | |||
40.29 | even | 2 | 2496.4.a.bl.1.1 | 3 | |||
60.59 | even | 2 | 1872.4.a.bk.1.1 | 3 | |||
65.34 | odd | 4 | 507.4.b.g.337.4 | 6 | |||
65.44 | odd | 4 | 507.4.b.g.337.3 | 6 | |||
65.64 | even | 2 | 507.4.a.h.1.2 | 3 | |||
195.194 | odd | 2 | 1521.4.a.u.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.a.c.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
117.4.a.f.1.2 | 3 | 15.14 | odd | 2 | |||
507.4.a.h.1.2 | 3 | 65.64 | even | 2 | |||
507.4.b.g.337.3 | 6 | 65.44 | odd | 4 | |||
507.4.b.g.337.4 | 6 | 65.34 | odd | 4 | |||
624.4.a.t.1.3 | 3 | 20.19 | odd | 2 | |||
975.4.a.l.1.2 | 3 | 1.1 | even | 1 | trivial | ||
1521.4.a.u.1.2 | 3 | 195.194 | odd | 2 | |||
1872.4.a.bk.1.1 | 3 | 60.59 | even | 2 | |||
1911.4.a.k.1.2 | 3 | 35.34 | odd | 2 | |||
2496.4.a.bl.1.1 | 3 | 40.29 | even | 2 | |||
2496.4.a.bp.1.1 | 3 | 40.19 | odd | 2 |