Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,4,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("177.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(10.4433380710\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 41x^{5} - 7x^{4} + 484x^{3} + 63x^{2} - 1736x - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-4.58037\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.58037 | 1.61941 | 0.809703 | − | 0.586840i | \(-0.199628\pi\) | ||||
0.809703 | + | 0.586840i | \(0.199628\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 12.9798 | 1.62247 | ||||||||
\(5\) | −17.0129 | −1.52168 | −0.760840 | − | 0.648939i | \(-0.775213\pi\) | ||||
−0.760840 | + | 0.648939i | \(0.775213\pi\) | |||||||
\(6\) | −13.7411 | −0.934964 | ||||||||
\(7\) | −20.9898 | −1.13334 | −0.566671 | − | 0.823944i | \(-0.691769\pi\) | ||||
−0.566671 | + | 0.823944i | \(0.691769\pi\) | |||||||
\(8\) | 22.8093 | 1.00804 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −77.9254 | −2.46422 | ||||||||
\(11\) | −48.1602 | −1.32008 | −0.660038 | − | 0.751232i | \(-0.729460\pi\) | ||||
−0.660038 | + | 0.751232i | \(0.729460\pi\) | |||||||
\(12\) | −38.9394 | −0.936735 | ||||||||
\(13\) | 29.4612 | 0.628544 | 0.314272 | − | 0.949333i | \(-0.398240\pi\) | ||||
0.314272 | + | 0.949333i | \(0.398240\pi\) | |||||||
\(14\) | −96.1410 | −1.83534 | ||||||||
\(15\) | 51.0387 | 0.878543 | ||||||||
\(16\) | 0.636565 | 0.00994633 | ||||||||
\(17\) | 108.283 | 1.54486 | 0.772429 | − | 0.635101i | \(-0.219042\pi\) | ||||
0.772429 | + | 0.635101i | \(0.219042\pi\) | |||||||
\(18\) | 41.2233 | 0.539802 | ||||||||
\(19\) | −111.228 | −1.34302 | −0.671510 | − | 0.740995i | \(-0.734354\pi\) | ||||
−0.671510 | + | 0.740995i | \(0.734354\pi\) | |||||||
\(20\) | −220.824 | −2.46889 | ||||||||
\(21\) | 62.9694 | 0.654335 | ||||||||
\(22\) | −220.591 | −2.13774 | ||||||||
\(23\) | −14.3946 | −0.130499 | −0.0652495 | − | 0.997869i | \(-0.520784\pi\) | ||||
−0.0652495 | + | 0.997869i | \(0.520784\pi\) | |||||||
\(24\) | −68.4278 | −0.581990 | ||||||||
\(25\) | 164.439 | 1.31551 | ||||||||
\(26\) | 134.943 | 1.01787 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −272.443 | −1.83882 | ||||||||
\(29\) | 292.789 | 1.87481 | 0.937406 | − | 0.348238i | \(-0.113220\pi\) | ||||
0.937406 | + | 0.348238i | \(0.113220\pi\) | |||||||
\(30\) | 233.776 | 1.42272 | ||||||||
\(31\) | −216.676 | −1.25536 | −0.627680 | − | 0.778471i | \(-0.715995\pi\) | ||||
−0.627680 | + | 0.778471i | \(0.715995\pi\) | |||||||
\(32\) | −179.558 | −0.991929 | ||||||||
\(33\) | 144.480 | 0.762146 | ||||||||
\(34\) | 495.978 | 2.50175 | ||||||||
\(35\) | 357.097 | 1.72458 | ||||||||
\(36\) | 116.818 | 0.540824 | ||||||||
\(37\) | −168.516 | −0.748755 | −0.374378 | − | 0.927276i | \(-0.622144\pi\) | ||||
−0.374378 | + | 0.927276i | \(0.622144\pi\) | |||||||
\(38\) | −509.464 | −2.17489 | ||||||||
\(39\) | −88.3836 | −0.362890 | ||||||||
\(40\) | −388.052 | −1.53391 | ||||||||
\(41\) | −342.050 | −1.30291 | −0.651453 | − | 0.758689i | \(-0.725840\pi\) | ||||
−0.651453 | + | 0.758689i | \(0.725840\pi\) | |||||||
\(42\) | 288.423 | 1.05963 | ||||||||
\(43\) | 325.352 | 1.15385 | 0.576927 | − | 0.816795i | \(-0.304252\pi\) | ||||
0.576927 | + | 0.816795i | \(0.304252\pi\) | |||||||
\(44\) | −625.109 | −2.14179 | ||||||||
\(45\) | −153.116 | −0.507227 | ||||||||
\(46\) | −65.9325 | −0.211331 | ||||||||
\(47\) | −315.587 | −0.979426 | −0.489713 | − | 0.871884i | \(-0.662898\pi\) | ||||
−0.489713 | + | 0.871884i | \(0.662898\pi\) | |||||||
\(48\) | −1.90970 | −0.00574252 | ||||||||
\(49\) | 97.5712 | 0.284464 | ||||||||
\(50\) | 753.191 | 2.13035 | ||||||||
\(51\) | −324.850 | −0.891924 | ||||||||
\(52\) | 382.400 | 1.01980 | ||||||||
\(53\) | 256.246 | 0.664115 | 0.332058 | − | 0.943259i | \(-0.392257\pi\) | ||||
0.332058 | + | 0.943259i | \(0.392257\pi\) | |||||||
\(54\) | −123.670 | −0.311655 | ||||||||
\(55\) | 819.344 | 2.00873 | ||||||||
\(56\) | −478.762 | −1.14245 | ||||||||
\(57\) | 333.683 | 0.775393 | ||||||||
\(58\) | 1341.08 | 3.03608 | ||||||||
\(59\) | 59.0000 | 0.130189 | ||||||||
\(60\) | 662.472 | 1.42541 | ||||||||
\(61\) | −749.020 | −1.57217 | −0.786083 | − | 0.618120i | \(-0.787894\pi\) | ||||
−0.786083 | + | 0.618120i | \(0.787894\pi\) | |||||||
\(62\) | −992.457 | −2.03294 | ||||||||
\(63\) | −188.908 | −0.377781 | ||||||||
\(64\) | −827.536 | −1.61628 | ||||||||
\(65\) | −501.221 | −0.956443 | ||||||||
\(66\) | 661.774 | 1.23422 | ||||||||
\(67\) | 664.622 | 1.21189 | 0.605944 | − | 0.795507i | \(-0.292796\pi\) | ||||
0.605944 | + | 0.795507i | \(0.292796\pi\) | |||||||
\(68\) | 1405.50 | 2.50649 | ||||||||
\(69\) | 43.1837 | 0.0753436 | ||||||||
\(70\) | 1635.64 | 2.79280 | ||||||||
\(71\) | 207.420 | 0.346708 | 0.173354 | − | 0.984860i | \(-0.444540\pi\) | ||||
0.173354 | + | 0.984860i | \(0.444540\pi\) | |||||||
\(72\) | 205.283 | 0.336012 | ||||||||
\(73\) | 45.3093 | 0.0726445 | 0.0363222 | − | 0.999340i | \(-0.488436\pi\) | ||||
0.0363222 | + | 0.999340i | \(0.488436\pi\) | |||||||
\(74\) | −771.868 | −1.21254 | ||||||||
\(75\) | −493.317 | −0.759511 | ||||||||
\(76\) | −1443.71 | −2.17901 | ||||||||
\(77\) | 1010.87 | 1.49610 | ||||||||
\(78\) | −404.830 | −0.587666 | ||||||||
\(79\) | −813.087 | −1.15797 | −0.578984 | − | 0.815339i | \(-0.696551\pi\) | ||||
−0.578984 | + | 0.815339i | \(0.696551\pi\) | |||||||
\(80\) | −10.8298 | −0.0151351 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −1566.71 | −2.10993 | ||||||||
\(83\) | 19.2056 | 0.0253986 | 0.0126993 | − | 0.999919i | \(-0.495958\pi\) | ||||
0.0126993 | + | 0.999919i | \(0.495958\pi\) | |||||||
\(84\) | 817.329 | 1.06164 | ||||||||
\(85\) | −1842.22 | −2.35078 | ||||||||
\(86\) | 1490.23 | 1.86856 | ||||||||
\(87\) | −878.367 | −1.08242 | ||||||||
\(88\) | −1098.50 | −1.33068 | ||||||||
\(89\) | −636.087 | −0.757585 | −0.378792 | − | 0.925482i | \(-0.623661\pi\) | ||||
−0.378792 | + | 0.925482i | \(0.623661\pi\) | |||||||
\(90\) | −701.328 | −0.821406 | ||||||||
\(91\) | −618.385 | −0.712355 | ||||||||
\(92\) | −186.838 | −0.211731 | ||||||||
\(93\) | 650.028 | 0.724783 | ||||||||
\(94\) | −1445.50 | −1.58609 | ||||||||
\(95\) | 1892.31 | 2.04365 | ||||||||
\(96\) | 538.675 | 0.572691 | ||||||||
\(97\) | −235.487 | −0.246495 | −0.123248 | − | 0.992376i | \(-0.539331\pi\) | ||||
−0.123248 | + | 0.992376i | \(0.539331\pi\) | |||||||
\(98\) | 446.912 | 0.460663 | ||||||||
\(99\) | −433.441 | −0.440025 | ||||||||
\(100\) | 2134.38 | 2.13438 | ||||||||
\(101\) | 1807.59 | 1.78081 | 0.890406 | − | 0.455167i | \(-0.150420\pi\) | ||||
0.890406 | + | 0.455167i | \(0.150420\pi\) | |||||||
\(102\) | −1487.93 | −1.44439 | ||||||||
\(103\) | −1437.56 | −1.37522 | −0.687609 | − | 0.726081i | \(-0.741340\pi\) | ||||
−0.687609 | + | 0.726081i | \(0.741340\pi\) | |||||||
\(104\) | 671.989 | 0.633595 | ||||||||
\(105\) | −1071.29 | −0.995689 | ||||||||
\(106\) | 1173.70 | 1.07547 | ||||||||
\(107\) | −430.727 | −0.389158 | −0.194579 | − | 0.980887i | \(-0.562334\pi\) | ||||
−0.194579 | + | 0.980887i | \(0.562334\pi\) | |||||||
\(108\) | −350.454 | −0.312245 | ||||||||
\(109\) | 459.238 | 0.403551 | 0.201775 | − | 0.979432i | \(-0.435329\pi\) | ||||
0.201775 | + | 0.979432i | \(0.435329\pi\) | |||||||
\(110\) | 3752.90 | 3.25295 | ||||||||
\(111\) | 505.549 | 0.432294 | ||||||||
\(112\) | −13.3614 | −0.0112726 | ||||||||
\(113\) | −1009.57 | −0.840460 | −0.420230 | − | 0.907418i | \(-0.638051\pi\) | ||||
−0.420230 | + | 0.907418i | \(0.638051\pi\) | |||||||
\(114\) | 1528.39 | 1.25568 | ||||||||
\(115\) | 244.893 | 0.198578 | ||||||||
\(116\) | 3800.34 | 3.04183 | ||||||||
\(117\) | 265.151 | 0.209515 | ||||||||
\(118\) | 270.242 | 0.210829 | ||||||||
\(119\) | −2272.85 | −1.75085 | ||||||||
\(120\) | 1164.16 | 0.885603 | ||||||||
\(121\) | 988.402 | 0.742601 | ||||||||
\(122\) | −3430.79 | −2.54598 | ||||||||
\(123\) | 1026.15 | 0.752233 | ||||||||
\(124\) | −2812.41 | −2.03679 | ||||||||
\(125\) | −670.969 | −0.480107 | ||||||||
\(126\) | −865.269 | −0.611780 | ||||||||
\(127\) | 392.027 | 0.273912 | 0.136956 | − | 0.990577i | \(-0.456268\pi\) | ||||
0.136956 | + | 0.990577i | \(0.456268\pi\) | |||||||
\(128\) | −2353.96 | −1.62549 | ||||||||
\(129\) | −976.057 | −0.666178 | ||||||||
\(130\) | −2295.78 | −1.54887 | ||||||||
\(131\) | 1782.88 | 1.18909 | 0.594546 | − | 0.804062i | \(-0.297332\pi\) | ||||
0.594546 | + | 0.804062i | \(0.297332\pi\) | |||||||
\(132\) | 1875.33 | 1.23656 | ||||||||
\(133\) | 2334.65 | 1.52210 | ||||||||
\(134\) | 3044.21 | 1.96254 | ||||||||
\(135\) | 459.348 | 0.292848 | ||||||||
\(136\) | 2469.86 | 1.55727 | ||||||||
\(137\) | −776.765 | −0.484405 | −0.242203 | − | 0.970226i | \(-0.577870\pi\) | ||||
−0.242203 | + | 0.970226i | \(0.577870\pi\) | |||||||
\(138\) | 197.797 | 0.122012 | ||||||||
\(139\) | −555.020 | −0.338678 | −0.169339 | − | 0.985558i | \(-0.554163\pi\) | ||||
−0.169339 | + | 0.985558i | \(0.554163\pi\) | |||||||
\(140\) | 4635.05 | 2.79809 | ||||||||
\(141\) | 946.760 | 0.565472 | ||||||||
\(142\) | 950.062 | 0.561461 | ||||||||
\(143\) | −1418.86 | −0.829726 | ||||||||
\(144\) | 5.72909 | 0.00331544 | ||||||||
\(145\) | −4981.19 | −2.85287 | ||||||||
\(146\) | 207.533 | 0.117641 | ||||||||
\(147\) | −292.713 | −0.164235 | ||||||||
\(148\) | −2187.31 | −1.21484 | ||||||||
\(149\) | 2066.64 | 1.13628 | 0.568141 | − | 0.822932i | \(-0.307663\pi\) | ||||
0.568141 | + | 0.822932i | \(0.307663\pi\) | |||||||
\(150\) | −2259.57 | −1.22996 | ||||||||
\(151\) | −922.182 | −0.496994 | −0.248497 | − | 0.968633i | \(-0.579937\pi\) | ||||
−0.248497 | + | 0.968633i | \(0.579937\pi\) | |||||||
\(152\) | −2537.02 | −1.35381 | ||||||||
\(153\) | 974.551 | 0.514953 | ||||||||
\(154\) | 4630.17 | 2.42279 | ||||||||
\(155\) | 3686.29 | 1.91026 | ||||||||
\(156\) | −1147.20 | −0.588779 | ||||||||
\(157\) | −2147.92 | −1.09187 | −0.545933 | − | 0.837829i | \(-0.683825\pi\) | ||||
−0.545933 | + | 0.837829i | \(0.683825\pi\) | |||||||
\(158\) | −3724.24 | −1.87522 | ||||||||
\(159\) | −768.739 | −0.383427 | ||||||||
\(160\) | 3054.81 | 1.50940 | ||||||||
\(161\) | 302.139 | 0.147900 | ||||||||
\(162\) | 371.010 | 0.179934 | ||||||||
\(163\) | 202.941 | 0.0975188 | 0.0487594 | − | 0.998811i | \(-0.484473\pi\) | ||||
0.0487594 | + | 0.998811i | \(0.484473\pi\) | |||||||
\(164\) | −4439.73 | −2.11393 | ||||||||
\(165\) | −2458.03 | −1.15974 | ||||||||
\(166\) | 87.9686 | 0.0411307 | ||||||||
\(167\) | −1984.16 | −0.919395 | −0.459697 | − | 0.888076i | \(-0.652042\pi\) | ||||
−0.459697 | + | 0.888076i | \(0.652042\pi\) | |||||||
\(168\) | 1436.28 | 0.659594 | ||||||||
\(169\) | −1329.04 | −0.604933 | ||||||||
\(170\) | −8438.03 | −3.80687 | ||||||||
\(171\) | −1001.05 | −0.447673 | ||||||||
\(172\) | 4223.00 | 1.87210 | ||||||||
\(173\) | −1484.23 | −0.652279 | −0.326139 | − | 0.945322i | \(-0.605748\pi\) | ||||
−0.326139 | + | 0.945322i | \(0.605748\pi\) | |||||||
\(174\) | −4023.25 | −1.75288 | ||||||||
\(175\) | −3451.54 | −1.49092 | ||||||||
\(176\) | −30.6571 | −0.0131299 | ||||||||
\(177\) | −177.000 | −0.0751646 | ||||||||
\(178\) | −2913.51 | −1.22684 | ||||||||
\(179\) | −546.514 | −0.228203 | −0.114102 | − | 0.993469i | \(-0.536399\pi\) | ||||
−0.114102 | + | 0.993469i | \(0.536399\pi\) | |||||||
\(180\) | −1987.41 | −0.822962 | ||||||||
\(181\) | −4561.98 | −1.87342 | −0.936710 | − | 0.350106i | \(-0.886145\pi\) | ||||
−0.936710 | + | 0.350106i | \(0.886145\pi\) | |||||||
\(182\) | −2832.43 | −1.15359 | ||||||||
\(183\) | 2247.06 | 0.907691 | ||||||||
\(184\) | −328.330 | −0.131548 | ||||||||
\(185\) | 2866.95 | 1.13937 | ||||||||
\(186\) | 2977.37 | 1.17372 | ||||||||
\(187\) | −5214.95 | −2.03933 | ||||||||
\(188\) | −4096.25 | −1.58909 | ||||||||
\(189\) | 566.724 | 0.218112 | ||||||||
\(190\) | 8667.46 | 3.30949 | ||||||||
\(191\) | −837.383 | −0.317230 | −0.158615 | − | 0.987341i | \(-0.550703\pi\) | ||||
−0.158615 | + | 0.987341i | \(0.550703\pi\) | |||||||
\(192\) | 2482.61 | 0.933161 | ||||||||
\(193\) | −3423.57 | −1.27686 | −0.638430 | − | 0.769680i | \(-0.720416\pi\) | ||||
−0.638430 | + | 0.769680i | \(0.720416\pi\) | |||||||
\(194\) | −1078.62 | −0.399176 | ||||||||
\(195\) | 1503.66 | 0.552203 | ||||||||
\(196\) | 1266.45 | 0.461535 | ||||||||
\(197\) | 3978.23 | 1.43877 | 0.719383 | − | 0.694613i | \(-0.244425\pi\) | ||||
0.719383 | + | 0.694613i | \(0.244425\pi\) | |||||||
\(198\) | −1985.32 | −0.712579 | ||||||||
\(199\) | 2224.15 | 0.792290 | 0.396145 | − | 0.918188i | \(-0.370348\pi\) | ||||
0.396145 | + | 0.918188i | \(0.370348\pi\) | |||||||
\(200\) | 3750.73 | 1.32608 | ||||||||
\(201\) | −1993.87 | −0.699684 | ||||||||
\(202\) | 8279.44 | 2.88386 | ||||||||
\(203\) | −6145.58 | −2.12480 | ||||||||
\(204\) | −4216.49 | −1.44712 | ||||||||
\(205\) | 5819.26 | 1.98261 | ||||||||
\(206\) | −6584.58 | −2.22703 | ||||||||
\(207\) | −129.551 | −0.0434997 | ||||||||
\(208\) | 18.7540 | 0.00625171 | ||||||||
\(209\) | 5356.74 | 1.77289 | ||||||||
\(210\) | −4906.91 | −1.61242 | ||||||||
\(211\) | 1783.56 | 0.581921 | 0.290961 | − | 0.956735i | \(-0.406025\pi\) | ||||
0.290961 | + | 0.956735i | \(0.406025\pi\) | |||||||
\(212\) | 3326.02 | 1.07751 | ||||||||
\(213\) | −622.261 | −0.200172 | ||||||||
\(214\) | −1972.89 | −0.630205 | ||||||||
\(215\) | −5535.19 | −1.75580 | ||||||||
\(216\) | −615.850 | −0.193997 | ||||||||
\(217\) | 4547.98 | 1.42275 | ||||||||
\(218\) | 2103.48 | 0.653513 | ||||||||
\(219\) | −135.928 | −0.0419413 | ||||||||
\(220\) | 10634.9 | 3.25912 | ||||||||
\(221\) | 3190.16 | 0.971011 | ||||||||
\(222\) | 2315.60 | 0.700059 | ||||||||
\(223\) | 477.801 | 0.143479 | 0.0717397 | − | 0.997423i | \(-0.477145\pi\) | ||||
0.0717397 | + | 0.997423i | \(0.477145\pi\) | |||||||
\(224\) | 3768.89 | 1.12420 | ||||||||
\(225\) | 1479.95 | 0.438504 | ||||||||
\(226\) | −4624.18 | −1.36105 | ||||||||
\(227\) | 2763.61 | 0.808050 | 0.404025 | − | 0.914748i | \(-0.367611\pi\) | ||||
0.404025 | + | 0.914748i | \(0.367611\pi\) | |||||||
\(228\) | 4331.14 | 1.25805 | ||||||||
\(229\) | 2794.53 | 0.806408 | 0.403204 | − | 0.915110i | \(-0.367896\pi\) | ||||
0.403204 | + | 0.915110i | \(0.367896\pi\) | |||||||
\(230\) | 1121.70 | 0.321578 | ||||||||
\(231\) | −3032.61 | −0.863772 | ||||||||
\(232\) | 6678.30 | 1.88988 | ||||||||
\(233\) | 6224.12 | 1.75002 | 0.875012 | − | 0.484102i | \(-0.160854\pi\) | ||||
0.875012 | + | 0.484102i | \(0.160854\pi\) | |||||||
\(234\) | 1214.49 | 0.339289 | ||||||||
\(235\) | 5369.04 | 1.49037 | ||||||||
\(236\) | 765.807 | 0.211228 | ||||||||
\(237\) | 2439.26 | 0.668553 | ||||||||
\(238\) | −10410.5 | −2.83534 | ||||||||
\(239\) | −2721.14 | −0.736468 | −0.368234 | − | 0.929733i | \(-0.620037\pi\) | ||||
−0.368234 | + | 0.929733i | \(0.620037\pi\) | |||||||
\(240\) | 32.4895 | 0.00873828 | ||||||||
\(241\) | 2695.03 | 0.720340 | 0.360170 | − | 0.932887i | \(-0.382719\pi\) | ||||
0.360170 | + | 0.932887i | \(0.382719\pi\) | |||||||
\(242\) | 4527.24 | 1.20257 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −9722.12 | −2.55080 | ||||||||
\(245\) | −1659.97 | −0.432863 | ||||||||
\(246\) | 4700.14 | 1.21817 | ||||||||
\(247\) | −3276.90 | −0.844147 | ||||||||
\(248\) | −4942.22 | −1.26545 | ||||||||
\(249\) | −57.6167 | −0.0146639 | ||||||||
\(250\) | −3073.29 | −0.777487 | ||||||||
\(251\) | −1146.02 | −0.288191 | −0.144096 | − | 0.989564i | \(-0.546027\pi\) | ||||
−0.144096 | + | 0.989564i | \(0.546027\pi\) | |||||||
\(252\) | −2451.99 | −0.612939 | ||||||||
\(253\) | 693.245 | 0.172269 | ||||||||
\(254\) | 1795.63 | 0.443574 | ||||||||
\(255\) | 5526.65 | 1.35722 | ||||||||
\(256\) | −4161.69 | −1.01604 | ||||||||
\(257\) | −964.525 | −0.234107 | −0.117053 | − | 0.993126i | \(-0.537345\pi\) | ||||
−0.117053 | + | 0.993126i | \(0.537345\pi\) | |||||||
\(258\) | −4470.70 | −1.07881 | ||||||||
\(259\) | 3537.12 | 0.848596 | ||||||||
\(260\) | −6505.74 | −1.55180 | ||||||||
\(261\) | 2635.10 | 0.624938 | ||||||||
\(262\) | 8166.26 | 1.92562 | ||||||||
\(263\) | −5111.64 | −1.19847 | −0.599234 | − | 0.800574i | \(-0.704528\pi\) | ||||
−0.599234 | + | 0.800574i | \(0.704528\pi\) | |||||||
\(264\) | 3295.49 | 0.768271 | ||||||||
\(265\) | −4359.49 | −1.01057 | ||||||||
\(266\) | 10693.5 | 2.46490 | ||||||||
\(267\) | 1908.26 | 0.437392 | ||||||||
\(268\) | 8626.65 | 1.96626 | ||||||||
\(269\) | −4488.46 | −1.01735 | −0.508673 | − | 0.860960i | \(-0.669864\pi\) | ||||
−0.508673 | + | 0.860960i | \(0.669864\pi\) | |||||||
\(270\) | 2103.99 | 0.474239 | ||||||||
\(271\) | 4399.29 | 0.986118 | 0.493059 | − | 0.869996i | \(-0.335879\pi\) | ||||
0.493059 | + | 0.869996i | \(0.335879\pi\) | |||||||
\(272\) | 68.9295 | 0.0153657 | ||||||||
\(273\) | 1855.15 | 0.411278 | ||||||||
\(274\) | −3557.87 | −0.784448 | ||||||||
\(275\) | −7919.40 | −1.73657 | ||||||||
\(276\) | 560.515 | 0.122243 | ||||||||
\(277\) | −4750.92 | −1.03052 | −0.515262 | − | 0.857033i | \(-0.672305\pi\) | ||||
−0.515262 | + | 0.857033i | \(0.672305\pi\) | |||||||
\(278\) | −2542.20 | −0.548456 | ||||||||
\(279\) | −1950.08 | −0.418453 | ||||||||
\(280\) | 8145.12 | 1.73844 | ||||||||
\(281\) | 8074.21 | 1.71412 | 0.857058 | − | 0.515219i | \(-0.172289\pi\) | ||||
0.857058 | + | 0.515219i | \(0.172289\pi\) | |||||||
\(282\) | 4336.51 | 0.915728 | ||||||||
\(283\) | 1950.54 | 0.409708 | 0.204854 | − | 0.978793i | \(-0.434328\pi\) | ||||
0.204854 | + | 0.978793i | \(0.434328\pi\) | |||||||
\(284\) | 2692.27 | 0.562525 | ||||||||
\(285\) | −5676.92 | −1.17990 | ||||||||
\(286\) | −6498.89 | −1.34366 | ||||||||
\(287\) | 7179.55 | 1.47664 | ||||||||
\(288\) | −1616.03 | −0.330643 | ||||||||
\(289\) | 6812.30 | 1.38659 | ||||||||
\(290\) | −22815.7 | −4.61995 | ||||||||
\(291\) | 706.460 | 0.142314 | ||||||||
\(292\) | 588.105 | 0.117864 | ||||||||
\(293\) | −7662.67 | −1.52784 | −0.763921 | − | 0.645309i | \(-0.776728\pi\) | ||||
−0.763921 | + | 0.645309i | \(0.776728\pi\) | |||||||
\(294\) | −1340.74 | −0.265964 | ||||||||
\(295\) | −1003.76 | −0.198106 | ||||||||
\(296\) | −3843.74 | −0.754772 | ||||||||
\(297\) | 1300.32 | 0.254049 | ||||||||
\(298\) | 9465.98 | 1.84010 | ||||||||
\(299\) | −424.082 | −0.0820243 | ||||||||
\(300\) | −6403.14 | −1.23229 | ||||||||
\(301\) | −6829.07 | −1.30771 | ||||||||
\(302\) | −4223.93 | −0.804835 | ||||||||
\(303\) | −5422.77 | −1.02815 | ||||||||
\(304\) | −70.8037 | −0.0133581 | ||||||||
\(305\) | 12743.0 | 2.39234 | ||||||||
\(306\) | 4463.80 | 0.833917 | ||||||||
\(307\) | −1433.79 | −0.266550 | −0.133275 | − | 0.991079i | \(-0.542549\pi\) | ||||
−0.133275 | + | 0.991079i | \(0.542549\pi\) | |||||||
\(308\) | 13120.9 | 2.42738 | ||||||||
\(309\) | 4312.69 | 0.793982 | ||||||||
\(310\) | 16884.6 | 3.09348 | ||||||||
\(311\) | 8645.17 | 1.57628 | 0.788140 | − | 0.615497i | \(-0.211045\pi\) | ||||
0.788140 | + | 0.615497i | \(0.211045\pi\) | |||||||
\(312\) | −2015.97 | −0.365806 | ||||||||
\(313\) | 6474.17 | 1.16914 | 0.584571 | − | 0.811342i | \(-0.301263\pi\) | ||||
0.584571 | + | 0.811342i | \(0.301263\pi\) | |||||||
\(314\) | −9838.29 | −1.76817 | ||||||||
\(315\) | 3213.87 | 0.574861 | ||||||||
\(316\) | −10553.7 | −1.87877 | ||||||||
\(317\) | 5278.69 | 0.935270 | 0.467635 | − | 0.883922i | \(-0.345106\pi\) | ||||
0.467635 | + | 0.883922i | \(0.345106\pi\) | |||||||
\(318\) | −3521.11 | −0.620924 | ||||||||
\(319\) | −14100.8 | −2.47490 | ||||||||
\(320\) | 14078.8 | 2.45946 | ||||||||
\(321\) | 1292.18 | 0.224681 | ||||||||
\(322\) | 1383.91 | 0.239510 | ||||||||
\(323\) | −12044.1 | −2.07478 | ||||||||
\(324\) | 1051.36 | 0.180275 | ||||||||
\(325\) | 4844.57 | 0.826856 | ||||||||
\(326\) | 929.545 | 0.157923 | ||||||||
\(327\) | −1377.72 | −0.232990 | ||||||||
\(328\) | −7801.90 | −1.31338 | ||||||||
\(329\) | 6624.09 | 1.11002 | ||||||||
\(330\) | −11258.7 | −1.87809 | ||||||||
\(331\) | 7562.70 | 1.25584 | 0.627921 | − | 0.778277i | \(-0.283906\pi\) | ||||
0.627921 | + | 0.778277i | \(0.283906\pi\) | |||||||
\(332\) | 249.284 | 0.0412086 | ||||||||
\(333\) | −1516.65 | −0.249585 | ||||||||
\(334\) | −9088.19 | −1.48887 | ||||||||
\(335\) | −11307.2 | −1.84411 | ||||||||
\(336\) | 40.0841 | 0.00650824 | ||||||||
\(337\) | 1241.33 | 0.200652 | 0.100326 | − | 0.994955i | \(-0.468011\pi\) | ||||
0.100326 | + | 0.994955i | \(0.468011\pi\) | |||||||
\(338\) | −6087.48 | −0.979631 | ||||||||
\(339\) | 3028.70 | 0.485240 | ||||||||
\(340\) | −23911.6 | −3.81408 | ||||||||
\(341\) | 10435.2 | 1.65717 | ||||||||
\(342\) | −4585.18 | −0.724965 | ||||||||
\(343\) | 5151.50 | 0.810947 | ||||||||
\(344\) | 7421.05 | 1.16313 | ||||||||
\(345\) | −734.680 | −0.114649 | ||||||||
\(346\) | −6798.34 | −1.05630 | ||||||||
\(347\) | 10314.8 | 1.59576 | 0.797879 | − | 0.602818i | \(-0.205956\pi\) | ||||
0.797879 | + | 0.602818i | \(0.205956\pi\) | |||||||
\(348\) | −11401.0 | −1.75620 | ||||||||
\(349\) | 6190.01 | 0.949409 | 0.474704 | − | 0.880145i | \(-0.342555\pi\) | ||||
0.474704 | + | 0.880145i | \(0.342555\pi\) | |||||||
\(350\) | −15809.3 | −2.41441 | ||||||||
\(351\) | −795.453 | −0.120963 | ||||||||
\(352\) | 8647.56 | 1.30942 | ||||||||
\(353\) | 2309.30 | 0.348191 | 0.174096 | − | 0.984729i | \(-0.444300\pi\) | ||||
0.174096 | + | 0.984729i | \(0.444300\pi\) | |||||||
\(354\) | −810.725 | −0.121722 | ||||||||
\(355\) | −3528.82 | −0.527579 | ||||||||
\(356\) | −8256.27 | −1.22916 | ||||||||
\(357\) | 6818.54 | 1.01086 | ||||||||
\(358\) | −2503.24 | −0.369554 | ||||||||
\(359\) | 12546.4 | 1.84449 | 0.922244 | − | 0.386608i | \(-0.126353\pi\) | ||||
0.922244 | + | 0.386608i | \(0.126353\pi\) | |||||||
\(360\) | −3492.47 | −0.511303 | ||||||||
\(361\) | 5512.60 | 0.803703 | ||||||||
\(362\) | −20895.5 | −3.03383 | ||||||||
\(363\) | −2965.20 | −0.428741 | ||||||||
\(364\) | −8026.50 | −1.15578 | ||||||||
\(365\) | −770.842 | −0.110542 | ||||||||
\(366\) | 10292.4 | 1.46992 | ||||||||
\(367\) | −9343.94 | −1.32902 | −0.664509 | − | 0.747280i | \(-0.731359\pi\) | ||||
−0.664509 | + | 0.747280i | \(0.731359\pi\) | |||||||
\(368\) | −9.16309 | −0.00129799 | ||||||||
\(369\) | −3078.45 | −0.434302 | ||||||||
\(370\) | 13131.7 | 1.84509 | ||||||||
\(371\) | −5378.55 | −0.752670 | ||||||||
\(372\) | 8437.23 | 1.17594 | ||||||||
\(373\) | −8906.58 | −1.23637 | −0.618184 | − | 0.786033i | \(-0.712131\pi\) | ||||
−0.618184 | + | 0.786033i | \(0.712131\pi\) | |||||||
\(374\) | −23886.4 | −3.30250 | ||||||||
\(375\) | 2012.91 | 0.277190 | ||||||||
\(376\) | −7198.30 | −0.987297 | ||||||||
\(377\) | 8625.92 | 1.17840 | ||||||||
\(378\) | 2595.81 | 0.353211 | ||||||||
\(379\) | 3568.77 | 0.483681 | 0.241841 | − | 0.970316i | \(-0.422249\pi\) | ||||
0.241841 | + | 0.970316i | \(0.422249\pi\) | |||||||
\(380\) | 24561.7 | 3.31576 | ||||||||
\(381\) | −1176.08 | −0.158143 | ||||||||
\(382\) | −3835.52 | −0.513724 | ||||||||
\(383\) | −9195.63 | −1.22683 | −0.613414 | − | 0.789762i | \(-0.710204\pi\) | ||||
−0.613414 | + | 0.789762i | \(0.710204\pi\) | |||||||
\(384\) | 7061.87 | 0.938475 | ||||||||
\(385\) | −17197.9 | −2.27658 | ||||||||
\(386\) | −15681.2 | −2.06775 | ||||||||
\(387\) | 2928.17 | 0.384618 | ||||||||
\(388\) | −3056.57 | −0.399932 | ||||||||
\(389\) | −7464.36 | −0.972900 | −0.486450 | − | 0.873708i | \(-0.661708\pi\) | ||||
−0.486450 | + | 0.873708i | \(0.661708\pi\) | |||||||
\(390\) | 6887.33 | 0.894240 | ||||||||
\(391\) | −1558.69 | −0.201602 | ||||||||
\(392\) | 2225.53 | 0.286750 | ||||||||
\(393\) | −5348.64 | −0.686523 | ||||||||
\(394\) | 18221.8 | 2.32995 | ||||||||
\(395\) | 13833.0 | 1.76206 | ||||||||
\(396\) | −5625.98 | −0.713929 | ||||||||
\(397\) | 9258.84 | 1.17050 | 0.585249 | − | 0.810853i | \(-0.300997\pi\) | ||||
0.585249 | + | 0.810853i | \(0.300997\pi\) | |||||||
\(398\) | 10187.4 | 1.28304 | ||||||||
\(399\) | −7003.94 | −0.878786 | ||||||||
\(400\) | 104.676 | 0.0130845 | ||||||||
\(401\) | −9944.75 | −1.23845 | −0.619224 | − | 0.785215i | \(-0.712553\pi\) | ||||
−0.619224 | + | 0.785215i | \(0.712553\pi\) | |||||||
\(402\) | −9132.64 | −1.13307 | ||||||||
\(403\) | −6383.54 | −0.789049 | ||||||||
\(404\) | 23462.1 | 2.88932 | ||||||||
\(405\) | −1378.05 | −0.169076 | ||||||||
\(406\) | −28149.0 | −3.44092 | ||||||||
\(407\) | 8115.78 | 0.988414 | ||||||||
\(408\) | −7409.59 | −0.899092 | ||||||||
\(409\) | −2770.27 | −0.334917 | −0.167459 | − | 0.985879i | \(-0.553556\pi\) | ||||
−0.167459 | + | 0.985879i | \(0.553556\pi\) | |||||||
\(410\) | 26654.3 | 3.21064 | ||||||||
\(411\) | 2330.29 | 0.279671 | ||||||||
\(412\) | −18659.3 | −2.23125 | ||||||||
\(413\) | −1238.40 | −0.147549 | ||||||||
\(414\) | −593.392 | −0.0704436 | ||||||||
\(415\) | −326.743 | −0.0386486 | ||||||||
\(416\) | −5290.01 | −0.623471 | ||||||||
\(417\) | 1665.06 | 0.195536 | ||||||||
\(418\) | 24535.9 | 2.87103 | ||||||||
\(419\) | −10519.7 | −1.22654 | −0.613272 | − | 0.789872i | \(-0.710147\pi\) | ||||
−0.613272 | + | 0.789872i | \(0.710147\pi\) | |||||||
\(420\) | −13905.1 | −1.61548 | ||||||||
\(421\) | −15029.7 | −1.73991 | −0.869957 | − | 0.493127i | \(-0.835854\pi\) | ||||
−0.869957 | + | 0.493127i | \(0.835854\pi\) | |||||||
\(422\) | 8169.37 | 0.942366 | ||||||||
\(423\) | −2840.28 | −0.326475 | ||||||||
\(424\) | 5844.79 | 0.669453 | ||||||||
\(425\) | 17806.0 | 2.03228 | ||||||||
\(426\) | −2850.19 | −0.324160 | ||||||||
\(427\) | 15721.8 | 1.78180 | ||||||||
\(428\) | −5590.74 | −0.631399 | ||||||||
\(429\) | 4256.57 | 0.479042 | ||||||||
\(430\) | −25353.2 | −2.84335 | ||||||||
\(431\) | −5056.76 | −0.565140 | −0.282570 | − | 0.959247i | \(-0.591187\pi\) | ||||
−0.282570 | + | 0.959247i | \(0.591187\pi\) | |||||||
\(432\) | −17.1873 | −0.00191417 | ||||||||
\(433\) | −10275.6 | −1.14045 | −0.570226 | − | 0.821488i | \(-0.693144\pi\) | ||||
−0.570226 | + | 0.821488i | \(0.693144\pi\) | |||||||
\(434\) | 20831.5 | 2.30401 | ||||||||
\(435\) | 14943.6 | 1.64710 | ||||||||
\(436\) | 5960.82 | 0.654751 | ||||||||
\(437\) | 1601.08 | 0.175263 | ||||||||
\(438\) | −622.600 | −0.0679200 | ||||||||
\(439\) | −1490.51 | −0.162046 | −0.0810232 | − | 0.996712i | \(-0.525819\pi\) | ||||
−0.0810232 | + | 0.996712i | \(0.525819\pi\) | |||||||
\(440\) | 18688.6 | 2.02488 | ||||||||
\(441\) | 878.140 | 0.0948213 | ||||||||
\(442\) | 14612.1 | 1.57246 | ||||||||
\(443\) | −1892.30 | −0.202948 | −0.101474 | − | 0.994838i | \(-0.532356\pi\) | ||||
−0.101474 | + | 0.994838i | \(0.532356\pi\) | |||||||
\(444\) | 6561.92 | 0.701385 | ||||||||
\(445\) | 10821.7 | 1.15280 | ||||||||
\(446\) | 2188.50 | 0.232351 | ||||||||
\(447\) | −6199.92 | −0.656032 | ||||||||
\(448\) | 17369.8 | 1.83180 | ||||||||
\(449\) | −6571.09 | −0.690665 | −0.345333 | − | 0.938480i | \(-0.612234\pi\) | ||||
−0.345333 | + | 0.938480i | \(0.612234\pi\) | |||||||
\(450\) | 6778.72 | 0.710115 | ||||||||
\(451\) | 16473.2 | 1.71994 | ||||||||
\(452\) | −13103.9 | −1.36362 | ||||||||
\(453\) | 2766.55 | 0.286940 | ||||||||
\(454\) | 12658.4 | 1.30856 | ||||||||
\(455\) | 10520.5 | 1.08398 | ||||||||
\(456\) | 7611.07 | 0.781625 | ||||||||
\(457\) | −5361.76 | −0.548824 | −0.274412 | − | 0.961612i | \(-0.588483\pi\) | ||||
−0.274412 | + | 0.961612i | \(0.588483\pi\) | |||||||
\(458\) | 12800.0 | 1.30590 | ||||||||
\(459\) | −2923.65 | −0.297308 | ||||||||
\(460\) | 3178.67 | 0.322187 | ||||||||
\(461\) | −1940.27 | −0.196025 | −0.0980125 | − | 0.995185i | \(-0.531249\pi\) | ||||
−0.0980125 | + | 0.995185i | \(0.531249\pi\) | |||||||
\(462\) | −13890.5 | −1.39880 | ||||||||
\(463\) | −9369.84 | −0.940504 | −0.470252 | − | 0.882532i | \(-0.655837\pi\) | ||||
−0.470252 | + | 0.882532i | \(0.655837\pi\) | |||||||
\(464\) | 186.379 | 0.0186475 | ||||||||
\(465\) | −11058.9 | −1.10289 | ||||||||
\(466\) | 28508.8 | 2.83400 | ||||||||
\(467\) | −10643.9 | −1.05469 | −0.527344 | − | 0.849652i | \(-0.676812\pi\) | ||||
−0.527344 | + | 0.849652i | \(0.676812\pi\) | |||||||
\(468\) | 3441.60 | 0.339932 | ||||||||
\(469\) | −13950.3 | −1.37348 | ||||||||
\(470\) | 24592.2 | 2.41352 | ||||||||
\(471\) | 6443.77 | 0.630389 | ||||||||
\(472\) | 1345.75 | 0.131235 | ||||||||
\(473\) | −15669.0 | −1.52318 | ||||||||
\(474\) | 11172.7 | 1.08266 | ||||||||
\(475\) | −18290.2 | −1.76676 | ||||||||
\(476\) | −29501.1 | −2.84071 | ||||||||
\(477\) | 2306.22 | 0.221372 | ||||||||
\(478\) | −12463.8 | −1.19264 | ||||||||
\(479\) | −787.956 | −0.0751620 | −0.0375810 | − | 0.999294i | \(-0.511965\pi\) | ||||
−0.0375810 | + | 0.999294i | \(0.511965\pi\) | |||||||
\(480\) | −9164.43 | −0.871452 | ||||||||
\(481\) | −4964.70 | −0.470625 | ||||||||
\(482\) | 12344.2 | 1.16652 | ||||||||
\(483\) | −906.417 | −0.0853901 | ||||||||
\(484\) | 12829.2 | 1.20485 | ||||||||
\(485\) | 4006.31 | 0.375087 | ||||||||
\(486\) | −1113.03 | −0.103885 | ||||||||
\(487\) | −11562.0 | −1.07582 | −0.537908 | − | 0.843004i | \(-0.680785\pi\) | ||||
−0.537908 | + | 0.843004i | \(0.680785\pi\) | |||||||
\(488\) | −17084.6 | −1.58480 | ||||||||
\(489\) | −608.823 | −0.0563025 | ||||||||
\(490\) | −7603.27 | −0.700981 | ||||||||
\(491\) | −784.077 | −0.0720670 | −0.0360335 | − | 0.999351i | \(-0.511472\pi\) | ||||
−0.0360335 | + | 0.999351i | \(0.511472\pi\) | |||||||
\(492\) | 13319.2 | 1.22048 | ||||||||
\(493\) | 31704.2 | 2.89632 | ||||||||
\(494\) | −15009.4 | −1.36702 | ||||||||
\(495\) | 7374.10 | 0.669578 | ||||||||
\(496\) | −137.928 | −0.0124862 | ||||||||
\(497\) | −4353.71 | −0.392939 | ||||||||
\(498\) | −263.906 | −0.0237468 | ||||||||
\(499\) | 1378.28 | 0.123648 | 0.0618238 | − | 0.998087i | \(-0.480308\pi\) | ||||
0.0618238 | + | 0.998087i | \(0.480308\pi\) | |||||||
\(500\) | −8709.04 | −0.778960 | ||||||||
\(501\) | 5952.48 | 0.530813 | ||||||||
\(502\) | −5249.18 | −0.466698 | ||||||||
\(503\) | −1919.94 | −0.170190 | −0.0850952 | − | 0.996373i | \(-0.527119\pi\) | ||||
−0.0850952 | + | 0.996373i | \(0.527119\pi\) | |||||||
\(504\) | −4308.85 | −0.380817 | ||||||||
\(505\) | −30752.4 | −2.70983 | ||||||||
\(506\) | 3175.32 | 0.278973 | ||||||||
\(507\) | 3987.11 | 0.349258 | ||||||||
\(508\) | 5088.43 | 0.444414 | ||||||||
\(509\) | −20478.5 | −1.78329 | −0.891646 | − | 0.452734i | \(-0.850449\pi\) | ||||
−0.891646 | + | 0.452734i | \(0.850449\pi\) | |||||||
\(510\) | 25314.1 | 2.19789 | ||||||||
\(511\) | −951.032 | −0.0823311 | ||||||||
\(512\) | −230.457 | −0.0198923 | ||||||||
\(513\) | 3003.15 | 0.258464 | ||||||||
\(514\) | −4417.88 | −0.379113 | ||||||||
\(515\) | 24457.1 | 2.09264 | ||||||||
\(516\) | −12669.0 | −1.08086 | ||||||||
\(517\) | 15198.7 | 1.29292 | ||||||||
\(518\) | 16201.3 | 1.37422 | ||||||||
\(519\) | 4452.70 | 0.376593 | ||||||||
\(520\) | −11432.5 | −0.964129 | ||||||||
\(521\) | 15109.6 | 1.27056 | 0.635280 | − | 0.772282i | \(-0.280885\pi\) | ||||
0.635280 | + | 0.772282i | \(0.280885\pi\) | |||||||
\(522\) | 12069.7 | 1.01203 | ||||||||
\(523\) | −1296.32 | −0.108383 | −0.0541914 | − | 0.998531i | \(-0.517258\pi\) | ||||
−0.0541914 | + | 0.998531i | \(0.517258\pi\) | |||||||
\(524\) | 23141.4 | 1.92927 | ||||||||
\(525\) | 10354.6 | 0.860785 | ||||||||
\(526\) | −23413.2 | −1.94081 | ||||||||
\(527\) | −23462.4 | −1.93935 | ||||||||
\(528\) | 91.9713 | 0.00758056 | ||||||||
\(529\) | −11959.8 | −0.982970 | ||||||||
\(530\) | −19968.1 | −1.63652 | ||||||||
\(531\) | 531.000 | 0.0433963 | ||||||||
\(532\) | 30303.2 | 2.46957 | ||||||||
\(533\) | −10077.2 | −0.818934 | ||||||||
\(534\) | 8740.54 | 0.708315 | ||||||||
\(535\) | 7327.92 | 0.592175 | ||||||||
\(536\) | 15159.5 | 1.22163 | ||||||||
\(537\) | 1639.54 | 0.131753 | ||||||||
\(538\) | −20558.8 | −1.64750 | ||||||||
\(539\) | −4699.04 | −0.375514 | ||||||||
\(540\) | 5962.24 | 0.475137 | ||||||||
\(541\) | −15541.1 | −1.23505 | −0.617525 | − | 0.786551i | \(-0.711865\pi\) | ||||
−0.617525 | + | 0.786551i | \(0.711865\pi\) | |||||||
\(542\) | 20150.4 | 1.59692 | ||||||||
\(543\) | 13685.9 | 1.08162 | ||||||||
\(544\) | −19443.2 | −1.53239 | ||||||||
\(545\) | −7812.98 | −0.614076 | ||||||||
\(546\) | 8497.29 | 0.666027 | ||||||||
\(547\) | −10003.4 | −0.781926 | −0.390963 | − | 0.920406i | \(-0.627858\pi\) | ||||
−0.390963 | + | 0.920406i | \(0.627858\pi\) | |||||||
\(548\) | −10082.2 | −0.785934 | ||||||||
\(549\) | −6741.18 | −0.524056 | ||||||||
\(550\) | −36273.8 | −2.81222 | ||||||||
\(551\) | −32566.3 | −2.51791 | ||||||||
\(552\) | 984.989 | 0.0759491 | ||||||||
\(553\) | 17066.5 | 1.31237 | ||||||||
\(554\) | −21761.0 | −1.66883 | ||||||||
\(555\) | −8600.86 | −0.657813 | ||||||||
\(556\) | −7204.04 | −0.549495 | ||||||||
\(557\) | −8031.77 | −0.610982 | −0.305491 | − | 0.952195i | \(-0.598821\pi\) | ||||
−0.305491 | + | 0.952195i | \(0.598821\pi\) | |||||||
\(558\) | −8932.11 | −0.677646 | ||||||||
\(559\) | 9585.27 | 0.725248 | ||||||||
\(560\) | 227.316 | 0.0171533 | ||||||||
\(561\) | 15644.8 | 1.17741 | ||||||||
\(562\) | 36982.9 | 2.77585 | ||||||||
\(563\) | −8865.46 | −0.663649 | −0.331825 | − | 0.943341i | \(-0.607664\pi\) | ||||
−0.331825 | + | 0.943341i | \(0.607664\pi\) | |||||||
\(564\) | 12288.7 | 0.917463 | ||||||||
\(565\) | 17175.6 | 1.27891 | ||||||||
\(566\) | 8934.18 | 0.663483 | ||||||||
\(567\) | −1700.17 | −0.125927 | ||||||||
\(568\) | 4731.11 | 0.349494 | ||||||||
\(569\) | 20450.1 | 1.50670 | 0.753351 | − | 0.657619i | \(-0.228436\pi\) | ||||
0.753351 | + | 0.657619i | \(0.228436\pi\) | |||||||
\(570\) | −26002.4 | −1.91074 | ||||||||
\(571\) | −10105.3 | −0.740618 | −0.370309 | − | 0.928909i | \(-0.620748\pi\) | ||||
−0.370309 | + | 0.928909i | \(0.620748\pi\) | |||||||
\(572\) | −18416.5 | −1.34621 | ||||||||
\(573\) | 2512.15 | 0.183153 | ||||||||
\(574\) | 32885.0 | 2.39128 | ||||||||
\(575\) | −2367.03 | −0.171673 | ||||||||
\(576\) | −7447.83 | −0.538761 | ||||||||
\(577\) | 17381.4 | 1.25407 | 0.627033 | − | 0.778993i | \(-0.284269\pi\) | ||||
0.627033 | + | 0.778993i | \(0.284269\pi\) | |||||||
\(578\) | 31202.8 | 2.24544 | ||||||||
\(579\) | 10270.7 | 0.737196 | ||||||||
\(580\) | −64654.8 | −4.62870 | ||||||||
\(581\) | −403.121 | −0.0287853 | ||||||||
\(582\) | 3235.85 | 0.230464 | ||||||||
\(583\) | −12340.9 | −0.876683 | ||||||||
\(584\) | 1033.47 | 0.0732283 | ||||||||
\(585\) | −4510.99 | −0.318814 | ||||||||
\(586\) | −35097.9 | −2.47420 | ||||||||
\(587\) | 19176.4 | 1.34837 | 0.674186 | − | 0.738561i | \(-0.264495\pi\) | ||||
0.674186 | + | 0.738561i | \(0.264495\pi\) | |||||||
\(588\) | −3799.36 | −0.266468 | ||||||||
\(589\) | 24100.4 | 1.68597 | ||||||||
\(590\) | −4597.60 | −0.320814 | ||||||||
\(591\) | −11934.7 | −0.830672 | ||||||||
\(592\) | −107.272 | −0.00744737 | ||||||||
\(593\) | −10703.5 | −0.741213 | −0.370606 | − | 0.928790i | \(-0.620850\pi\) | ||||
−0.370606 | + | 0.928790i | \(0.620850\pi\) | |||||||
\(594\) | 5955.97 | 0.411408 | ||||||||
\(595\) | 38667.7 | 2.66424 | ||||||||
\(596\) | 26824.6 | 1.84359 | ||||||||
\(597\) | −6672.45 | −0.457429 | ||||||||
\(598\) | −1942.45 | −0.132831 | ||||||||
\(599\) | −16229.7 | −1.10705 | −0.553527 | − | 0.832831i | \(-0.686719\pi\) | ||||
−0.553527 | + | 0.832831i | \(0.686719\pi\) | |||||||
\(600\) | −11252.2 | −0.765614 | ||||||||
\(601\) | 5481.06 | 0.372009 | 0.186004 | − | 0.982549i | \(-0.440446\pi\) | ||||
0.186004 | + | 0.982549i | \(0.440446\pi\) | |||||||
\(602\) | −31279.7 | −2.11772 | ||||||||
\(603\) | 5981.60 | 0.403963 | ||||||||
\(604\) | −11969.7 | −0.806359 | ||||||||
\(605\) | −16815.6 | −1.13000 | ||||||||
\(606\) | −24838.3 | −1.66500 | ||||||||
\(607\) | −17029.8 | −1.13874 | −0.569372 | − | 0.822080i | \(-0.692814\pi\) | ||||
−0.569372 | + | 0.822080i | \(0.692814\pi\) | |||||||
\(608\) | 19971.9 | 1.33218 | ||||||||
\(609\) | 18436.7 | 1.22676 | ||||||||
\(610\) | 58367.7 | 3.87416 | ||||||||
\(611\) | −9297.56 | −0.615612 | ||||||||
\(612\) | 12649.5 | 0.835497 | ||||||||
\(613\) | 7096.79 | 0.467597 | 0.233798 | − | 0.972285i | \(-0.424884\pi\) | ||||
0.233798 | + | 0.972285i | \(0.424884\pi\) | |||||||
\(614\) | −6567.29 | −0.431652 | ||||||||
\(615\) | −17457.8 | −1.14466 | ||||||||
\(616\) | 23057.2 | 1.50812 | ||||||||
\(617\) | −9243.83 | −0.603148 | −0.301574 | − | 0.953443i | \(-0.597512\pi\) | ||||
−0.301574 | + | 0.953443i | \(0.597512\pi\) | |||||||
\(618\) | 19753.7 | 1.28578 | ||||||||
\(619\) | 24576.0 | 1.59579 | 0.797893 | − | 0.602799i | \(-0.205948\pi\) | ||||
0.797893 | + | 0.602799i | \(0.205948\pi\) | |||||||
\(620\) | 47847.2 | 3.09934 | ||||||||
\(621\) | 388.654 | 0.0251145 | ||||||||
\(622\) | 39598.1 | 2.55263 | ||||||||
\(623\) | 13351.3 | 0.858603 | ||||||||
\(624\) | −56.2620 | −0.00360943 | ||||||||
\(625\) | −9139.72 | −0.584942 | ||||||||
\(626\) | 29654.1 | 1.89332 | ||||||||
\(627\) | −16070.2 | −1.02358 | ||||||||
\(628\) | −27879.6 | −1.77152 | ||||||||
\(629\) | −18247.5 | −1.15672 | ||||||||
\(630\) | 14720.7 | 0.930934 | ||||||||
\(631\) | 16376.8 | 1.03320 | 0.516602 | − | 0.856226i | \(-0.327197\pi\) | ||||
0.516602 | + | 0.856226i | \(0.327197\pi\) | |||||||
\(632\) | −18545.9 | −1.16727 | ||||||||
\(633\) | −5350.68 | −0.335972 | ||||||||
\(634\) | 24178.3 | 1.51458 | ||||||||
\(635\) | −6669.52 | −0.416806 | ||||||||
\(636\) | −9978.06 | −0.622100 | ||||||||
\(637\) | 2874.56 | 0.178798 | ||||||||
\(638\) | −64586.7 | −4.00786 | ||||||||
\(639\) | 1866.78 | 0.115569 | ||||||||
\(640\) | 40047.6 | 2.47347 | ||||||||
\(641\) | −6614.72 | −0.407591 | −0.203795 | − | 0.979013i | \(-0.565328\pi\) | ||||
−0.203795 | + | 0.979013i | \(0.565328\pi\) | |||||||
\(642\) | 5918.67 | 0.363849 | ||||||||
\(643\) | −18544.9 | −1.13739 | −0.568693 | − | 0.822550i | \(-0.692551\pi\) | ||||
−0.568693 | + | 0.822550i | \(0.692551\pi\) | |||||||
\(644\) | 3921.70 | 0.239964 | ||||||||
\(645\) | 16605.6 | 1.01371 | ||||||||
\(646\) | −55166.5 | −3.35990 | ||||||||
\(647\) | 28164.5 | 1.71137 | 0.855687 | − | 0.517493i | \(-0.173135\pi\) | ||||
0.855687 | + | 0.517493i | \(0.173135\pi\) | |||||||
\(648\) | 1847.55 | 0.112004 | ||||||||
\(649\) | −2841.45 | −0.171859 | ||||||||
\(650\) | 22189.9 | 1.33902 | ||||||||
\(651\) | −13644.0 | −0.821427 | ||||||||
\(652\) | 2634.13 | 0.158222 | ||||||||
\(653\) | −11520.0 | −0.690370 | −0.345185 | − | 0.938535i | \(-0.612184\pi\) | ||||
−0.345185 | + | 0.938535i | \(0.612184\pi\) | |||||||
\(654\) | −6310.44 | −0.377306 | ||||||||
\(655\) | −30332.0 | −1.80942 | ||||||||
\(656\) | −217.737 | −0.0129591 | ||||||||
\(657\) | 407.783 | 0.0242148 | ||||||||
\(658\) | 30340.8 | 1.79758 | ||||||||
\(659\) | −16586.2 | −0.980434 | −0.490217 | − | 0.871600i | \(-0.663083\pi\) | ||||
−0.490217 | + | 0.871600i | \(0.663083\pi\) | |||||||
\(660\) | −31904.7 | −1.88165 | ||||||||
\(661\) | −15191.8 | −0.893935 | −0.446967 | − | 0.894550i | \(-0.647496\pi\) | ||||
−0.446967 | + | 0.894550i | \(0.647496\pi\) | |||||||
\(662\) | 34640.0 | 2.03372 | ||||||||
\(663\) | −9570.48 | −0.560614 | ||||||||
\(664\) | 438.065 | 0.0256027 | ||||||||
\(665\) | −39719.1 | −2.31615 | ||||||||
\(666\) | −6946.81 | −0.404179 | ||||||||
\(667\) | −4214.57 | −0.244661 | ||||||||
\(668\) | −25754.0 | −1.49169 | ||||||||
\(669\) | −1433.40 | −0.0828379 | ||||||||
\(670\) | −51790.9 | −2.98636 | ||||||||
\(671\) | 36072.9 | 2.07538 | ||||||||
\(672\) | −11306.7 | −0.649054 | ||||||||
\(673\) | 22990.5 | 1.31682 | 0.658410 | − | 0.752660i | \(-0.271229\pi\) | ||||
0.658410 | + | 0.752660i | \(0.271229\pi\) | |||||||
\(674\) | 5685.77 | 0.324937 | ||||||||
\(675\) | −4439.85 | −0.253170 | ||||||||
\(676\) | −17250.6 | −0.981487 | ||||||||
\(677\) | −18654.2 | −1.05899 | −0.529496 | − | 0.848313i | \(-0.677619\pi\) | ||||
−0.529496 | + | 0.848313i | \(0.677619\pi\) | |||||||
\(678\) | 13872.6 | 0.785800 | ||||||||
\(679\) | 4942.82 | 0.279364 | ||||||||
\(680\) | −42019.6 | −2.36967 | ||||||||
\(681\) | −8290.84 | −0.466528 | ||||||||
\(682\) | 47796.9 | 2.68363 | ||||||||
\(683\) | −13970.1 | −0.782649 | −0.391325 | − | 0.920253i | \(-0.627983\pi\) | ||||
−0.391325 | + | 0.920253i | \(0.627983\pi\) | |||||||
\(684\) | −12993.4 | −0.726338 | ||||||||
\(685\) | 13215.0 | 0.737110 | ||||||||
\(686\) | 23595.8 | 1.31325 | ||||||||
\(687\) | −8383.58 | −0.465580 | ||||||||
\(688\) | 207.108 | 0.0114766 | ||||||||
\(689\) | 7549.32 | 0.417426 | ||||||||
\(690\) | −3365.11 | −0.185663 | ||||||||
\(691\) | −4273.34 | −0.235261 | −0.117631 | − | 0.993057i | \(-0.537530\pi\) | ||||
−0.117631 | + | 0.993057i | \(0.537530\pi\) | |||||||
\(692\) | −19265.0 | −1.05830 | ||||||||
\(693\) | 9097.84 | 0.498699 | ||||||||
\(694\) | 47245.6 | 2.58418 | ||||||||
\(695\) | 9442.50 | 0.515359 | ||||||||
\(696\) | −20034.9 | −1.09112 | ||||||||
\(697\) | −37038.3 | −2.01281 | ||||||||
\(698\) | 28352.5 | 1.53748 | ||||||||
\(699\) | −18672.3 | −1.01038 | ||||||||
\(700\) | −44800.2 | −2.41898 | ||||||||
\(701\) | 13904.0 | 0.749141 | 0.374570 | − | 0.927199i | \(-0.377790\pi\) | ||||
0.374570 | + | 0.927199i | \(0.377790\pi\) | |||||||
\(702\) | −3643.47 | −0.195889 | ||||||||
\(703\) | 18743.7 | 1.00559 | ||||||||
\(704\) | 39854.3 | 2.13362 | ||||||||
\(705\) | −16107.1 | −0.860468 | ||||||||
\(706\) | 10577.4 | 0.563863 | ||||||||
\(707\) | −37941.0 | −2.01827 | ||||||||
\(708\) | −2297.42 | −0.121953 | ||||||||
\(709\) | 13659.3 | 0.723533 | 0.361766 | − | 0.932269i | \(-0.382174\pi\) | ||||
0.361766 | + | 0.932269i | \(0.382174\pi\) | |||||||
\(710\) | −16163.3 | −0.854364 | ||||||||
\(711\) | −7317.79 | −0.385989 | ||||||||
\(712\) | −14508.7 | −0.763673 | ||||||||
\(713\) | 3118.96 | 0.163823 | ||||||||
\(714\) | 31231.4 | 1.63698 | ||||||||
\(715\) | 24138.9 | 1.26258 | ||||||||
\(716\) | −7093.64 | −0.370254 | ||||||||
\(717\) | 8163.42 | 0.425200 | ||||||||
\(718\) | 57466.9 | 2.98697 | ||||||||
\(719\) | 10745.5 | 0.557358 | 0.278679 | − | 0.960384i | \(-0.410103\pi\) | ||||
0.278679 | + | 0.960384i | \(0.410103\pi\) | |||||||
\(720\) | −97.4684 | −0.00504505 | ||||||||
\(721\) | 30174.2 | 1.55859 | ||||||||
\(722\) | 25249.7 | 1.30152 | ||||||||
\(723\) | −8085.08 | −0.415889 | ||||||||
\(724\) | −59213.5 | −3.03957 | ||||||||
\(725\) | 48145.9 | 2.46634 | ||||||||
\(726\) | −13581.7 | −0.694305 | ||||||||
\(727\) | 23351.2 | 1.19126 | 0.595632 | − | 0.803257i | \(-0.296902\pi\) | ||||
0.595632 | + | 0.803257i | \(0.296902\pi\) | |||||||
\(728\) | −14104.9 | −0.718080 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −3530.74 | −0.179012 | ||||||||
\(731\) | 35230.3 | 1.78254 | ||||||||
\(732\) | 29166.4 | 1.47270 | ||||||||
\(733\) | 17996.9 | 0.906865 | 0.453432 | − | 0.891291i | \(-0.350199\pi\) | ||||
0.453432 | + | 0.891291i | \(0.350199\pi\) | |||||||
\(734\) | −42798.7 | −2.15222 | ||||||||
\(735\) | 4979.91 | 0.249914 | ||||||||
\(736\) | 2584.67 | 0.129446 | ||||||||
\(737\) | −32008.3 | −1.59978 | ||||||||
\(738\) | −14100.4 | −0.703311 | ||||||||
\(739\) | 13155.1 | 0.654829 | 0.327415 | − | 0.944881i | \(-0.393823\pi\) | ||||
0.327415 | + | 0.944881i | \(0.393823\pi\) | |||||||
\(740\) | 37212.5 | 1.84859 | ||||||||
\(741\) | 9830.71 | 0.487369 | ||||||||
\(742\) | −24635.8 | −1.21888 | ||||||||
\(743\) | −25720.3 | −1.26997 | −0.634984 | − | 0.772525i | \(-0.718993\pi\) | ||||
−0.634984 | + | 0.772525i | \(0.718993\pi\) | |||||||
\(744\) | 14826.7 | 0.730607 | ||||||||
\(745\) | −35159.6 | −1.72906 | ||||||||
\(746\) | −40795.4 | −2.00218 | ||||||||
\(747\) | 172.850 | 0.00846621 | ||||||||
\(748\) | −67688.9 | −3.30876 | ||||||||
\(749\) | 9040.87 | 0.441050 | ||||||||
\(750\) | 9219.86 | 0.448882 | ||||||||
\(751\) | −35919.3 | −1.74529 | −0.872645 | − | 0.488356i | \(-0.837597\pi\) | ||||
−0.872645 | + | 0.488356i | \(0.837597\pi\) | |||||||
\(752\) | −200.891 | −0.00974170 | ||||||||
\(753\) | 3438.05 | 0.166387 | ||||||||
\(754\) | 39509.9 | 1.90831 | ||||||||
\(755\) | 15689.0 | 0.756266 | ||||||||
\(756\) | 7355.96 | 0.353881 | ||||||||
\(757\) | −29818.5 | −1.43167 | −0.715834 | − | 0.698271i | \(-0.753953\pi\) | ||||
−0.715834 | + | 0.698271i | \(0.753953\pi\) | |||||||
\(758\) | 16346.3 | 0.783276 | ||||||||
\(759\) | −2079.74 | −0.0994593 | ||||||||
\(760\) | 43162.1 | 2.06007 | ||||||||
\(761\) | 35322.2 | 1.68256 | 0.841280 | − | 0.540600i | \(-0.181803\pi\) | ||||
0.841280 | + | 0.540600i | \(0.181803\pi\) | |||||||
\(762\) | −5386.89 | −0.256097 | ||||||||
\(763\) | −9639.32 | −0.457361 | ||||||||
\(764\) | −10869.1 | −0.514697 | ||||||||
\(765\) | −16579.9 | −0.783593 | ||||||||
\(766\) | −42119.4 | −1.98673 | ||||||||
\(767\) | 1738.21 | 0.0818294 | ||||||||
\(768\) | 12485.1 | 0.586610 | ||||||||
\(769\) | −6704.62 | −0.314402 | −0.157201 | − | 0.987567i | \(-0.550247\pi\) | ||||
−0.157201 | + | 0.987567i | \(0.550247\pi\) | |||||||
\(770\) | −78772.6 | −3.68671 | ||||||||
\(771\) | 2893.57 | 0.135161 | ||||||||
\(772\) | −44437.2 | −2.07167 | ||||||||
\(773\) | 10246.4 | 0.476762 | 0.238381 | − | 0.971172i | \(-0.423383\pi\) | ||||
0.238381 | + | 0.971172i | \(0.423383\pi\) | |||||||
\(774\) | 13412.1 | 0.622853 | ||||||||
\(775\) | −35630.0 | −1.65144 | ||||||||
\(776\) | −5371.28 | −0.248476 | ||||||||
\(777\) | −10611.4 | −0.489937 | ||||||||
\(778\) | −34189.5 | −1.57552 | ||||||||
\(779\) | 38045.4 | 1.74983 | ||||||||
\(780\) | 19517.2 | 0.895934 | ||||||||
\(781\) | −9989.40 | −0.457681 | ||||||||
\(782\) | −7139.39 | −0.326476 | ||||||||
\(783\) | −7905.30 | −0.360808 | ||||||||
\(784\) | 62.1104 | 0.00282937 | ||||||||
\(785\) | 36542.4 | 1.66147 | ||||||||
\(786\) | −24498.8 | −1.11176 | ||||||||
\(787\) | 25804.8 | 1.16880 | 0.584398 | − | 0.811467i | \(-0.301331\pi\) | ||||
0.584398 | + | 0.811467i | \(0.301331\pi\) | |||||||
\(788\) | 51636.5 | 2.33436 | ||||||||
\(789\) | 15334.9 | 0.691936 | ||||||||
\(790\) | 63360.1 | 2.85348 | ||||||||
\(791\) | 21190.6 | 0.952528 | ||||||||
\(792\) | −9886.48 | −0.443562 | ||||||||
\(793\) | −22067.0 | −0.988176 | ||||||||
\(794\) | 42408.9 | 1.89551 | ||||||||
\(795\) | 13078.5 | 0.583454 | ||||||||
\(796\) | 28869.0 | 1.28547 | ||||||||
\(797\) | 7971.15 | 0.354269 | 0.177135 | − | 0.984187i | \(-0.443317\pi\) | ||||
0.177135 | + | 0.984187i | \(0.443317\pi\) | |||||||
\(798\) | −32080.6 | −1.42311 | ||||||||
\(799\) | −34172.8 | −1.51307 | ||||||||
\(800\) | −29526.4 | −1.30489 | ||||||||
\(801\) | −5724.78 | −0.252528 | ||||||||
\(802\) | −45550.7 | −2.00555 | ||||||||
\(803\) | −2182.10 | −0.0958963 | ||||||||
\(804\) | −25880.0 | −1.13522 | ||||||||
\(805\) | −5140.26 | −0.225056 | ||||||||
\(806\) | −29239.0 | −1.27779 | ||||||||
\(807\) | 13465.4 | 0.587365 | ||||||||
\(808\) | 41229.8 | 1.79512 | ||||||||
\(809\) | −1869.81 | −0.0812595 | −0.0406297 | − | 0.999174i | \(-0.512936\pi\) | ||||
−0.0406297 | + | 0.999174i | \(0.512936\pi\) | |||||||
\(810\) | −6311.96 | −0.273802 | ||||||||
\(811\) | −4096.49 | −0.177370 | −0.0886851 | − | 0.996060i | \(-0.528266\pi\) | ||||
−0.0886851 | + | 0.996060i | \(0.528266\pi\) | |||||||
\(812\) | −79768.3 | −3.44744 | ||||||||
\(813\) | −13197.9 | −0.569336 | ||||||||
\(814\) | 37173.3 | 1.60064 | ||||||||
\(815\) | −3452.62 | −0.148393 | ||||||||
\(816\) | −206.788 | −0.00887138 | ||||||||
\(817\) | −36188.2 | −1.54965 | ||||||||
\(818\) | −12688.9 | −0.542367 | ||||||||
\(819\) | −5565.46 | −0.237452 | ||||||||
\(820\) | 75532.7 | 3.21673 | ||||||||
\(821\) | 32856.3 | 1.39670 | 0.698350 | − | 0.715756i | \(-0.253918\pi\) | ||||
0.698350 | + | 0.715756i | \(0.253918\pi\) | |||||||
\(822\) | 10673.6 | 0.452901 | ||||||||
\(823\) | −1727.41 | −0.0731638 | −0.0365819 | − | 0.999331i | \(-0.511647\pi\) | ||||
−0.0365819 | + | 0.999331i | \(0.511647\pi\) | |||||||
\(824\) | −32789.8 | −1.38627 | ||||||||
\(825\) | 23758.2 | 1.00261 | ||||||||
\(826\) | −5672.32 | −0.238941 | ||||||||
\(827\) | −38654.4 | −1.62533 | −0.812664 | − | 0.582733i | \(-0.801983\pi\) | ||||
−0.812664 | + | 0.582733i | \(0.801983\pi\) | |||||||
\(828\) | −1681.55 | −0.0705770 | ||||||||
\(829\) | −9211.90 | −0.385938 | −0.192969 | − | 0.981205i | \(-0.561812\pi\) | ||||
−0.192969 | + | 0.981205i | \(0.561812\pi\) | |||||||
\(830\) | −1496.60 | −0.0625877 | ||||||||
\(831\) | 14252.7 | 0.594973 | ||||||||
\(832\) | −24380.2 | −1.01590 | ||||||||
\(833\) | 10565.3 | 0.439457 | ||||||||
\(834\) | 7626.59 | 0.316651 | ||||||||
\(835\) | 33756.3 | 1.39902 | ||||||||
\(836\) | 69529.4 | 2.87646 | ||||||||
\(837\) | 5850.25 | 0.241594 | ||||||||
\(838\) | −48184.2 | −1.98627 | ||||||||
\(839\) | −44020.8 | −1.81140 | −0.905701 | − | 0.423917i | \(-0.860655\pi\) | ||||
−0.905701 | + | 0.423917i | \(0.860655\pi\) | |||||||
\(840\) | −24435.4 | −1.00369 | ||||||||
\(841\) | 61336.4 | 2.51492 | ||||||||
\(842\) | −68841.7 | −2.81763 | ||||||||
\(843\) | −24222.6 | −0.989646 | ||||||||
\(844\) | 23150.2 | 0.944152 | ||||||||
\(845\) | 22610.8 | 0.920514 | ||||||||
\(846\) | −13009.5 | −0.528696 | ||||||||
\(847\) | −20746.3 | −0.841621 | ||||||||
\(848\) | 163.117 | 0.00660551 | ||||||||
\(849\) | −5851.61 | −0.236545 | ||||||||
\(850\) | 81558.1 | 3.29108 | ||||||||
\(851\) | 2425.72 | 0.0977118 | ||||||||
\(852\) | −8076.82 | −0.324774 | ||||||||
\(853\) | 14157.1 | 0.568265 | 0.284133 | − | 0.958785i | \(-0.408294\pi\) | ||||
0.284133 | + | 0.958785i | \(0.408294\pi\) | |||||||
\(854\) | 72011.5 | 2.88546 | ||||||||
\(855\) | 17030.8 | 0.681216 | ||||||||
\(856\) | −9824.56 | −0.392286 | ||||||||
\(857\) | −21094.5 | −0.840810 | −0.420405 | − | 0.907337i | \(-0.638112\pi\) | ||||
−0.420405 | + | 0.907337i | \(0.638112\pi\) | |||||||
\(858\) | 19496.7 | 0.775764 | ||||||||
\(859\) | −37442.2 | −1.48721 | −0.743603 | − | 0.668622i | \(-0.766885\pi\) | ||||
−0.743603 | + | 0.668622i | \(0.766885\pi\) | |||||||
\(860\) | −71845.5 | −2.84874 | ||||||||
\(861\) | −21538.6 | −0.852538 | ||||||||
\(862\) | −23161.8 | −0.915191 | ||||||||
\(863\) | 15063.2 | 0.594156 | 0.297078 | − | 0.954853i | \(-0.403988\pi\) | ||||
0.297078 | + | 0.954853i | \(0.403988\pi\) | |||||||
\(864\) | 4848.08 | 0.190897 | ||||||||
\(865\) | 25251.1 | 0.992560 | ||||||||
\(866\) | −47066.2 | −1.84685 | ||||||||
\(867\) | −20436.9 | −0.800546 | ||||||||
\(868\) | 59031.9 | 2.30838 | ||||||||
\(869\) | 39158.4 | 1.52861 | ||||||||
\(870\) | 68447.1 | 2.66733 | ||||||||
\(871\) | 19580.6 | 0.761725 | ||||||||
\(872\) | 10474.9 | 0.406794 | ||||||||
\(873\) | −2119.38 | −0.0821652 | ||||||||
\(874\) | 7333.52 | 0.283821 | ||||||||
\(875\) | 14083.5 | 0.544125 | ||||||||
\(876\) | −1764.31 | −0.0680487 | ||||||||
\(877\) | 32525.7 | 1.25235 | 0.626177 | − | 0.779681i | \(-0.284619\pi\) | ||||
0.626177 | + | 0.779681i | \(0.284619\pi\) | |||||||
\(878\) | −6827.11 | −0.262419 | ||||||||
\(879\) | 22988.0 | 0.882100 | ||||||||
\(880\) | 521.566 | 0.0199795 | ||||||||
\(881\) | −17706.4 | −0.677123 | −0.338561 | − | 0.940944i | \(-0.609940\pi\) | ||||
−0.338561 | + | 0.940944i | \(0.609940\pi\) | |||||||
\(882\) | 4022.21 | 0.153554 | ||||||||
\(883\) | 24205.7 | 0.922522 | 0.461261 | − | 0.887264i | \(-0.347397\pi\) | ||||
0.461261 | + | 0.887264i | \(0.347397\pi\) | |||||||
\(884\) | 41407.6 | 1.57544 | ||||||||
\(885\) | 3011.28 | 0.114376 | ||||||||
\(886\) | −8667.43 | −0.328655 | ||||||||
\(887\) | 36290.4 | 1.37374 | 0.686872 | − | 0.726778i | \(-0.258983\pi\) | ||||
0.686872 | + | 0.726778i | \(0.258983\pi\) | |||||||
\(888\) | 11531.2 | 0.435768 | ||||||||
\(889\) | −8228.56 | −0.310435 | ||||||||
\(890\) | 49567.3 | 1.86685 | ||||||||
\(891\) | −3900.97 | −0.146675 | ||||||||
\(892\) | 6201.75 | 0.232791 | ||||||||
\(893\) | 35102.0 | 1.31539 | ||||||||
\(894\) | −28397.9 | −1.06238 | ||||||||
\(895\) | 9297.80 | 0.347253 | ||||||||
\(896\) | 49409.0 | 1.84223 | ||||||||
\(897\) | 1272.24 | 0.0473568 | ||||||||
\(898\) | −30098.0 | −1.11847 | ||||||||
\(899\) | −63440.4 | −2.35357 | ||||||||
\(900\) | 19209.4 | 0.711460 | ||||||||
\(901\) | 27747.2 | 1.02596 | ||||||||
\(902\) | 75453.2 | 2.78527 | ||||||||
\(903\) | 20487.2 | 0.755008 | ||||||||
\(904\) | −23027.5 | −0.847214 | ||||||||
\(905\) | 77612.5 | 2.85075 | ||||||||
\(906\) | 12671.8 | 0.464671 | ||||||||
\(907\) | −1572.57 | −0.0575705 | −0.0287852 | − | 0.999586i | \(-0.509164\pi\) | ||||
−0.0287852 | + | 0.999586i | \(0.509164\pi\) | |||||||
\(908\) | 35871.1 | 1.31104 | ||||||||
\(909\) | 16268.3 | 0.593604 | ||||||||
\(910\) | 48187.9 | 1.75540 | ||||||||
\(911\) | −23504.6 | −0.854820 | −0.427410 | − | 0.904058i | \(-0.640574\pi\) | ||||
−0.427410 | + | 0.904058i | \(0.640574\pi\) | |||||||
\(912\) | 212.411 | 0.00771232 | ||||||||
\(913\) | −924.944 | −0.0335281 | ||||||||
\(914\) | −24558.8 | −0.888768 | ||||||||
\(915\) | −38229.0 | −1.38122 | ||||||||
\(916\) | 36272.4 | 1.30838 | ||||||||
\(917\) | −37422.3 | −1.34765 | ||||||||
\(918\) | −13391.4 | −0.481462 | ||||||||
\(919\) | −28818.0 | −1.03440 | −0.517202 | − | 0.855863i | \(-0.673026\pi\) | ||||
−0.517202 | + | 0.855863i | \(0.673026\pi\) | |||||||
\(920\) | 5585.84 | 0.200174 | ||||||||
\(921\) | 4301.37 | 0.153892 | ||||||||
\(922\) | −8887.17 | −0.317444 | ||||||||
\(923\) | 6110.86 | 0.217921 | ||||||||
\(924\) | −39362.7 | −1.40145 | ||||||||
\(925\) | −27710.7 | −0.984995 | ||||||||
\(926\) | −42917.3 | −1.52306 | ||||||||
\(927\) | −12938.1 | −0.458406 | ||||||||
\(928\) | −52572.7 | −1.85968 | ||||||||
\(929\) | −40908.5 | −1.44474 | −0.722370 | − | 0.691506i | \(-0.756947\pi\) | ||||
−0.722370 | + | 0.691506i | \(0.756947\pi\) | |||||||
\(930\) | −50653.7 | −1.78602 | ||||||||
\(931\) | −10852.6 | −0.382041 | ||||||||
\(932\) | 80787.7 | 2.83937 | ||||||||
\(933\) | −25935.5 | −0.910065 | ||||||||
\(934\) | −48752.9 | −1.70797 | ||||||||
\(935\) | 88721.4 | 3.10321 | ||||||||
\(936\) | 6047.90 | 0.211198 | ||||||||
\(937\) | 42875.5 | 1.49486 | 0.747428 | − | 0.664343i | \(-0.231289\pi\) | ||||
0.747428 | + | 0.664343i | \(0.231289\pi\) | |||||||
\(938\) | −63897.4 | −2.22423 | ||||||||
\(939\) | −19422.5 | −0.675005 | ||||||||
\(940\) | 69689.0 | 2.41809 | ||||||||
\(941\) | 12952.0 | 0.448697 | 0.224348 | − | 0.974509i | \(-0.427975\pi\) | ||||
0.224348 | + | 0.974509i | \(0.427975\pi\) | |||||||
\(942\) | 29514.9 | 1.02086 | ||||||||
\(943\) | 4923.66 | 0.170028 | ||||||||
\(944\) | 37.5574 | 0.00129490 | ||||||||
\(945\) | −9641.62 | −0.331896 | ||||||||
\(946\) | −71769.9 | −2.46664 | ||||||||
\(947\) | −11075.5 | −0.380046 | −0.190023 | − | 0.981780i | \(-0.560856\pi\) | ||||
−0.190023 | + | 0.981780i | \(0.560856\pi\) | |||||||
\(948\) | 31661.1 | 1.08471 | ||||||||
\(949\) | 1334.87 | 0.0456603 | ||||||||
\(950\) | −83775.7 | −2.86110 | ||||||||
\(951\) | −15836.1 | −0.539978 | ||||||||
\(952\) | −51841.9 | −1.76492 | ||||||||
\(953\) | −16254.9 | −0.552515 | −0.276257 | − | 0.961084i | \(-0.589094\pi\) | ||||
−0.276257 | + | 0.961084i | \(0.589094\pi\) | |||||||
\(954\) | 10563.3 | 0.358491 | ||||||||
\(955\) | 14246.3 | 0.482722 | ||||||||
\(956\) | −35319.8 | −1.19490 | ||||||||
\(957\) | 42302.3 | 1.42888 | ||||||||
\(958\) | −3609.13 | −0.121718 | ||||||||
\(959\) | 16304.1 | 0.548997 | ||||||||
\(960\) | −42236.4 | −1.41997 | ||||||||
\(961\) | 17157.5 | 0.575930 | ||||||||
\(962\) | −22740.2 | −0.762133 | ||||||||
\(963\) | −3876.54 | −0.129719 | ||||||||
\(964\) | 34980.9 | 1.16873 | ||||||||
\(965\) | 58244.9 | 1.94297 | ||||||||
\(966\) | −4151.73 | −0.138281 | ||||||||
\(967\) | 17700.6 | 0.588637 | 0.294318 | − | 0.955707i | \(-0.404907\pi\) | ||||
0.294318 | + | 0.955707i | \(0.404907\pi\) | |||||||
\(968\) | 22544.7 | 0.748569 | ||||||||
\(969\) | 36132.3 | 1.19787 | ||||||||
\(970\) | 18350.4 | 0.607418 | ||||||||
\(971\) | 37930.1 | 1.25359 | 0.626794 | − | 0.779185i | \(-0.284367\pi\) | ||||
0.626794 | + | 0.779185i | \(0.284367\pi\) | |||||||
\(972\) | −3154.09 | −0.104082 | ||||||||
\(973\) | 11649.8 | 0.383837 | ||||||||
\(974\) | −52958.0 | −1.74218 | ||||||||
\(975\) | −14533.7 | −0.477386 | ||||||||
\(976\) | −476.800 | −0.0156373 | ||||||||
\(977\) | −14003.7 | −0.458565 | −0.229283 | − | 0.973360i | \(-0.573638\pi\) | ||||
−0.229283 | + | 0.973360i | \(0.573638\pi\) | |||||||
\(978\) | −2788.64 | −0.0911766 | ||||||||
\(979\) | 30634.0 | 1.00007 | ||||||||
\(980\) | −21546.0 | −0.702309 | ||||||||
\(981\) | 4133.15 | 0.134517 | ||||||||
\(982\) | −3591.36 | −0.116706 | ||||||||
\(983\) | −34728.6 | −1.12683 | −0.563413 | − | 0.826175i | \(-0.690512\pi\) | ||||
−0.563413 | + | 0.826175i | \(0.690512\pi\) | |||||||
\(984\) | 23405.7 | 0.758279 | ||||||||
\(985\) | −67681.2 | −2.18934 | ||||||||
\(986\) | 145217. | 4.69031 | ||||||||
\(987\) | −19872.3 | −0.640873 | ||||||||
\(988\) | −42533.5 | −1.36961 | ||||||||
\(989\) | −4683.31 | −0.150577 | ||||||||
\(990\) | 33776.1 | 1.08432 | ||||||||
\(991\) | 48169.3 | 1.54405 | 0.772023 | − | 0.635595i | \(-0.219245\pi\) | ||||
0.772023 | + | 0.635595i | \(0.219245\pi\) | |||||||
\(992\) | 38906.0 | 1.24523 | ||||||||
\(993\) | −22688.1 | −0.725060 | ||||||||
\(994\) | −19941.6 | −0.636327 | ||||||||
\(995\) | −37839.2 | −1.20561 | ||||||||
\(996\) | −747.853 | −0.0237918 | ||||||||
\(997\) | −15159.6 | −0.481553 | −0.240776 | − | 0.970581i | \(-0.577402\pi\) | ||||
−0.240776 | + | 0.970581i | \(0.577402\pi\) | |||||||
\(998\) | 6313.01 | 0.200235 | ||||||||
\(999\) | 4549.94 | 0.144098 |
(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 | 177.4.a.b.1.7 | ✓ | 7 | |
3.2 | odd | 2 | 531.4.a.c.1.1 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.a.b.1.7 | ✓ | 7 | 1.1 | even | 1 | trivial | |
531.4.a.c.1.1 | 7 | 3.2 | odd | 2 |