Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(1,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, 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("105.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.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: | \(6.19520055060\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.236068 | 0.0834626 | 0.0417313 | − | 0.999129i | \(-0.486713\pi\) | ||||
0.0417313 | + | 0.999129i | \(0.486713\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −7.94427 | −0.993034 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0.708204 | 0.0481872 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | −3.76393 | −0.166344 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −1.18034 | −0.0373256 | ||||||||
\(11\) | −50.4721 | −1.38345 | −0.691724 | − | 0.722162i | \(-0.743148\pi\) | ||||
−0.691724 | + | 0.722162i | \(0.743148\pi\) | |||||||
\(12\) | −23.8328 | −0.573328 | ||||||||
\(13\) | −80.9706 | −1.72748 | −0.863738 | − | 0.503940i | \(-0.831883\pi\) | ||||
−0.863738 | + | 0.503940i | \(0.831883\pi\) | |||||||
\(14\) | −1.65248 | −0.0315459 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | 62.6656 | 0.979150 | ||||||||
\(17\) | 76.3870 | 1.08980 | 0.544899 | − | 0.838502i | \(-0.316568\pi\) | ||||
0.544899 | + | 0.838502i | \(0.316568\pi\) | |||||||
\(18\) | 2.12461 | 0.0278209 | ||||||||
\(19\) | 4.13777 | 0.0499615 | 0.0249808 | − | 0.999688i | \(-0.492048\pi\) | ||||
0.0249808 | + | 0.999688i | \(0.492048\pi\) | |||||||
\(20\) | 39.7214 | 0.444098 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | −11.9149 | −0.115466 | ||||||||
\(23\) | −204.721 | −1.85597 | −0.927986 | − | 0.372615i | \(-0.878461\pi\) | ||||
−0.927986 | + | 0.372615i | \(0.878461\pi\) | |||||||
\(24\) | −11.2918 | −0.0960387 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −19.1146 | −0.144180 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 55.6099 | 0.375332 | ||||||||
\(29\) | −91.1672 | −0.583770 | −0.291885 | − | 0.956453i | \(-0.594282\pi\) | ||||
−0.291885 | + | 0.956453i | \(0.594282\pi\) | |||||||
\(30\) | −3.54102 | −0.0215500 | ||||||||
\(31\) | 198.079 | 1.14761 | 0.573807 | − | 0.818991i | \(-0.305466\pi\) | ||||
0.573807 | + | 0.818991i | \(0.305466\pi\) | |||||||
\(32\) | 44.9048 | 0.248066 | ||||||||
\(33\) | −151.416 | −0.798734 | ||||||||
\(34\) | 18.0325 | 0.0909574 | ||||||||
\(35\) | 35.0000 | 0.169031 | ||||||||
\(36\) | −71.4984 | −0.331011 | ||||||||
\(37\) | 155.666 | 0.691656 | 0.345828 | − | 0.938298i | \(-0.387598\pi\) | ||||
0.345828 | + | 0.938298i | \(0.387598\pi\) | |||||||
\(38\) | 0.976794 | 0.00416992 | ||||||||
\(39\) | −242.912 | −0.997359 | ||||||||
\(40\) | 18.8197 | 0.0743912 | ||||||||
\(41\) | −156.885 | −0.597595 | −0.298797 | − | 0.954317i | \(-0.596585\pi\) | ||||
−0.298797 | + | 0.954317i | \(0.596585\pi\) | |||||||
\(42\) | −4.95743 | −0.0182130 | ||||||||
\(43\) | 354.217 | 1.25622 | 0.628111 | − | 0.778124i | \(-0.283828\pi\) | ||||
0.628111 | + | 0.778124i | \(0.283828\pi\) | |||||||
\(44\) | 400.964 | 1.37381 | ||||||||
\(45\) | −45.0000 | −0.149071 | ||||||||
\(46\) | −48.3282 | −0.154904 | ||||||||
\(47\) | −175.659 | −0.545161 | −0.272580 | − | 0.962133i | \(-0.587877\pi\) | ||||
−0.272580 | + | 0.962133i | \(0.587877\pi\) | |||||||
\(48\) | 187.997 | 0.565313 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 5.90170 | 0.0166925 | ||||||||
\(51\) | 229.161 | 0.629195 | ||||||||
\(52\) | 643.252 | 1.71544 | ||||||||
\(53\) | 200.302 | 0.519124 | 0.259562 | − | 0.965726i | \(-0.416422\pi\) | ||||
0.259562 | + | 0.965726i | \(0.416422\pi\) | |||||||
\(54\) | 6.37384 | 0.0160624 | ||||||||
\(55\) | 252.361 | 0.618696 | ||||||||
\(56\) | 26.3475 | 0.0628721 | ||||||||
\(57\) | 12.4133 | 0.0288453 | ||||||||
\(58\) | −21.5217 | −0.0487230 | ||||||||
\(59\) | −312.498 | −0.689556 | −0.344778 | − | 0.938684i | \(-0.612046\pi\) | ||||
−0.344778 | + | 0.938684i | \(0.612046\pi\) | |||||||
\(60\) | 119.164 | 0.256400 | ||||||||
\(61\) | −154.170 | −0.323598 | −0.161799 | − | 0.986824i | \(-0.551730\pi\) | ||||
−0.161799 | + | 0.986824i | \(0.551730\pi\) | |||||||
\(62\) | 46.7601 | 0.0957829 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | −490.724 | −0.958446 | ||||||||
\(65\) | 404.853 | 0.772551 | ||||||||
\(66\) | −35.7446 | −0.0666644 | ||||||||
\(67\) | 734.715 | 1.33970 | 0.669849 | − | 0.742498i | \(-0.266359\pi\) | ||||
0.669849 | + | 0.742498i | \(0.266359\pi\) | |||||||
\(68\) | −606.839 | −1.08221 | ||||||||
\(69\) | −614.164 | −1.07155 | ||||||||
\(70\) | 8.26238 | 0.0141078 | ||||||||
\(71\) | −678.577 | −1.13426 | −0.567129 | − | 0.823629i | \(-0.691946\pi\) | ||||
−0.567129 | + | 0.823629i | \(0.691946\pi\) | |||||||
\(72\) | −33.8754 | −0.0554480 | ||||||||
\(73\) | −60.8003 | −0.0974813 | −0.0487407 | − | 0.998811i | \(-0.515521\pi\) | ||||
−0.0487407 | + | 0.998811i | \(0.515521\pi\) | |||||||
\(74\) | 36.7477 | 0.0577274 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | −32.8715 | −0.0496135 | ||||||||
\(77\) | 353.305 | 0.522894 | ||||||||
\(78\) | −57.3437 | −0.0832422 | ||||||||
\(79\) | −1286.26 | −1.83184 | −0.915919 | − | 0.401363i | \(-0.868537\pi\) | ||||
−0.915919 | + | 0.401363i | \(0.868537\pi\) | |||||||
\(80\) | −313.328 | −0.437889 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −37.0356 | −0.0498768 | ||||||||
\(83\) | 116.170 | 0.153631 | 0.0768153 | − | 0.997045i | \(-0.475525\pi\) | ||||
0.0768153 | + | 0.997045i | \(0.475525\pi\) | |||||||
\(84\) | 166.830 | 0.216698 | ||||||||
\(85\) | −381.935 | −0.487372 | ||||||||
\(86\) | 83.6192 | 0.104848 | ||||||||
\(87\) | −273.502 | −0.337040 | ||||||||
\(88\) | 189.974 | 0.230128 | ||||||||
\(89\) | −916.440 | −1.09149 | −0.545744 | − | 0.837952i | \(-0.683753\pi\) | ||||
−0.545744 | + | 0.837952i | \(0.683753\pi\) | |||||||
\(90\) | −10.6231 | −0.0124419 | ||||||||
\(91\) | 566.794 | 0.652925 | ||||||||
\(92\) | 1626.36 | 1.84304 | ||||||||
\(93\) | 594.237 | 0.662575 | ||||||||
\(94\) | −41.4676 | −0.0455006 | ||||||||
\(95\) | −20.6888 | −0.0223435 | ||||||||
\(96\) | 134.714 | 0.143221 | ||||||||
\(97\) | −1416.30 | −1.48251 | −0.741256 | − | 0.671222i | \(-0.765770\pi\) | ||||
−0.741256 | + | 0.671222i | \(0.765770\pi\) | |||||||
\(98\) | 11.5673 | 0.0119232 | ||||||||
\(99\) | −454.249 | −0.461149 | ||||||||
\(100\) | −198.607 | −0.198607 | ||||||||
\(101\) | −1379.19 | −1.35876 | −0.679381 | − | 0.733785i | \(-0.737752\pi\) | ||||
−0.679381 | + | 0.733785i | \(0.737752\pi\) | |||||||
\(102\) | 54.0976 | 0.0525143 | ||||||||
\(103\) | −1308.43 | −1.25169 | −0.625844 | − | 0.779949i | \(-0.715245\pi\) | ||||
−0.625844 | + | 0.779949i | \(0.715245\pi\) | |||||||
\(104\) | 304.768 | 0.287355 | ||||||||
\(105\) | 105.000 | 0.0975900 | ||||||||
\(106\) | 47.2849 | 0.0433275 | ||||||||
\(107\) | 1265.65 | 1.14351 | 0.571754 | − | 0.820425i | \(-0.306263\pi\) | ||||
0.571754 | + | 0.820425i | \(0.306263\pi\) | |||||||
\(108\) | −214.495 | −0.191109 | ||||||||
\(109\) | 2069.32 | 1.81839 | 0.909196 | − | 0.416368i | \(-0.136697\pi\) | ||||
0.909196 | + | 0.416368i | \(0.136697\pi\) | |||||||
\(110\) | 59.5743 | 0.0516380 | ||||||||
\(111\) | 466.997 | 0.399328 | ||||||||
\(112\) | −438.659 | −0.370084 | ||||||||
\(113\) | −1953.89 | −1.62661 | −0.813303 | − | 0.581840i | \(-0.802333\pi\) | ||||
−0.813303 | + | 0.581840i | \(0.802333\pi\) | |||||||
\(114\) | 2.93038 | 0.00240750 | ||||||||
\(115\) | 1023.61 | 0.830016 | ||||||||
\(116\) | 724.257 | 0.579703 | ||||||||
\(117\) | −728.735 | −0.575826 | ||||||||
\(118\) | −73.7709 | −0.0575522 | ||||||||
\(119\) | −534.709 | −0.411905 | ||||||||
\(120\) | 56.4590 | 0.0429498 | ||||||||
\(121\) | 1216.44 | 0.913927 | ||||||||
\(122\) | −36.3947 | −0.0270083 | ||||||||
\(123\) | −470.656 | −0.345022 | ||||||||
\(124\) | −1573.59 | −1.13962 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | −14.8723 | −0.0105153 | ||||||||
\(127\) | 224.251 | 0.156685 | 0.0783426 | − | 0.996926i | \(-0.475037\pi\) | ||||
0.0783426 | + | 0.996926i | \(0.475037\pi\) | |||||||
\(128\) | −475.083 | −0.328061 | ||||||||
\(129\) | 1062.65 | 0.725280 | ||||||||
\(130\) | 95.5728 | 0.0644792 | ||||||||
\(131\) | −490.898 | −0.327404 | −0.163702 | − | 0.986510i | \(-0.552344\pi\) | ||||
−0.163702 | + | 0.986510i | \(0.552344\pi\) | |||||||
\(132\) | 1202.89 | 0.793170 | ||||||||
\(133\) | −28.9644 | −0.0188837 | ||||||||
\(134\) | 173.443 | 0.111815 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | −287.515 | −0.181281 | ||||||||
\(137\) | 1831.12 | 1.14192 | 0.570961 | − | 0.820977i | \(-0.306571\pi\) | ||||
0.570961 | + | 0.820977i | \(0.306571\pi\) | |||||||
\(138\) | −144.984 | −0.0894340 | ||||||||
\(139\) | −3050.84 | −1.86165 | −0.930823 | − | 0.365469i | \(-0.880909\pi\) | ||||
−0.930823 | + | 0.365469i | \(0.880909\pi\) | |||||||
\(140\) | −278.050 | −0.167853 | ||||||||
\(141\) | −526.978 | −0.314749 | ||||||||
\(142\) | −160.190 | −0.0946682 | ||||||||
\(143\) | 4086.76 | 2.38987 | ||||||||
\(144\) | 563.991 | 0.326383 | ||||||||
\(145\) | 455.836 | 0.261070 | ||||||||
\(146\) | −14.3530 | −0.00813605 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | −1236.65 | −0.686838 | ||||||||
\(149\) | 2246.55 | 1.23520 | 0.617599 | − | 0.786493i | \(-0.288105\pi\) | ||||
0.617599 | + | 0.786493i | \(0.288105\pi\) | |||||||
\(150\) | 17.7051 | 0.00963743 | ||||||||
\(151\) | −1311.53 | −0.706826 | −0.353413 | − | 0.935467i | \(-0.614979\pi\) | ||||
−0.353413 | + | 0.935467i | \(0.614979\pi\) | |||||||
\(152\) | −15.5743 | −0.00831079 | ||||||||
\(153\) | 687.483 | 0.363266 | ||||||||
\(154\) | 83.4040 | 0.0436421 | ||||||||
\(155\) | −990.395 | −0.513228 | ||||||||
\(156\) | 1929.76 | 0.990412 | ||||||||
\(157\) | 1790.94 | 0.910398 | 0.455199 | − | 0.890390i | \(-0.349568\pi\) | ||||
0.455199 | + | 0.890390i | \(0.349568\pi\) | |||||||
\(158\) | −303.644 | −0.152890 | ||||||||
\(159\) | 600.906 | 0.299716 | ||||||||
\(160\) | −224.524 | −0.110939 | ||||||||
\(161\) | 1433.05 | 0.701491 | ||||||||
\(162\) | 19.1215 | 0.00927363 | ||||||||
\(163\) | −491.108 | −0.235991 | −0.117996 | − | 0.993014i | \(-0.537647\pi\) | ||||
−0.117996 | + | 0.993014i | \(0.537647\pi\) | |||||||
\(164\) | 1246.34 | 0.593432 | ||||||||
\(165\) | 757.082 | 0.357205 | ||||||||
\(166\) | 27.4241 | 0.0128224 | ||||||||
\(167\) | −826.059 | −0.382769 | −0.191384 | − | 0.981515i | \(-0.561298\pi\) | ||||
−0.191384 | + | 0.981515i | \(0.561298\pi\) | |||||||
\(168\) | 79.0426 | 0.0362992 | ||||||||
\(169\) | 4359.24 | 1.98418 | ||||||||
\(170\) | −90.1626 | −0.0406774 | ||||||||
\(171\) | 37.2399 | 0.0166538 | ||||||||
\(172\) | −2813.99 | −1.24747 | ||||||||
\(173\) | 2918.00 | 1.28238 | 0.641190 | − | 0.767382i | \(-0.278441\pi\) | ||||
0.641190 | + | 0.767382i | \(0.278441\pi\) | |||||||
\(174\) | −64.5650 | −0.0281302 | ||||||||
\(175\) | −175.000 | −0.0755929 | ||||||||
\(176\) | −3162.87 | −1.35460 | ||||||||
\(177\) | −937.495 | −0.398116 | ||||||||
\(178\) | −216.342 | −0.0910984 | ||||||||
\(179\) | 955.745 | 0.399082 | 0.199541 | − | 0.979889i | \(-0.436055\pi\) | ||||
0.199541 | + | 0.979889i | \(0.436055\pi\) | |||||||
\(180\) | 357.492 | 0.148033 | ||||||||
\(181\) | 206.080 | 0.0846289 | 0.0423145 | − | 0.999104i | \(-0.486527\pi\) | ||||
0.0423145 | + | 0.999104i | \(0.486527\pi\) | |||||||
\(182\) | 133.802 | 0.0544948 | ||||||||
\(183\) | −462.511 | −0.186829 | ||||||||
\(184\) | 770.557 | 0.308730 | ||||||||
\(185\) | −778.328 | −0.309318 | ||||||||
\(186\) | 140.280 | 0.0553003 | ||||||||
\(187\) | −3855.41 | −1.50768 | ||||||||
\(188\) | 1395.49 | 0.541363 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | −4.88397 | −0.00186485 | ||||||||
\(191\) | −2018.63 | −0.764727 | −0.382364 | − | 0.924012i | \(-0.624890\pi\) | ||||
−0.382364 | + | 0.924012i | \(0.624890\pi\) | |||||||
\(192\) | −1472.17 | −0.553359 | ||||||||
\(193\) | 1031.69 | 0.384781 | 0.192390 | − | 0.981318i | \(-0.438376\pi\) | ||||
0.192390 | + | 0.981318i | \(0.438376\pi\) | |||||||
\(194\) | −334.344 | −0.123734 | ||||||||
\(195\) | 1214.56 | 0.446033 | ||||||||
\(196\) | −389.269 | −0.141862 | ||||||||
\(197\) | −205.955 | −0.0744857 | −0.0372429 | − | 0.999306i | \(-0.511858\pi\) | ||||
−0.0372429 | + | 0.999306i | \(0.511858\pi\) | |||||||
\(198\) | −107.234 | −0.0384887 | ||||||||
\(199\) | −1831.38 | −0.652376 | −0.326188 | − | 0.945305i | \(-0.605764\pi\) | ||||
−0.326188 | + | 0.945305i | \(0.605764\pi\) | |||||||
\(200\) | −94.0983 | −0.0332688 | ||||||||
\(201\) | 2204.15 | 0.773475 | ||||||||
\(202\) | −325.584 | −0.113406 | ||||||||
\(203\) | 638.170 | 0.220644 | ||||||||
\(204\) | −1820.52 | −0.624812 | ||||||||
\(205\) | 784.427 | 0.267253 | ||||||||
\(206\) | −308.879 | −0.104469 | ||||||||
\(207\) | −1842.49 | −0.618657 | ||||||||
\(208\) | −5074.07 | −1.69146 | ||||||||
\(209\) | −208.842 | −0.0691191 | ||||||||
\(210\) | 24.7871 | 0.00814512 | ||||||||
\(211\) | 1030.19 | 0.336119 | 0.168060 | − | 0.985777i | \(-0.446250\pi\) | ||||
0.168060 | + | 0.985777i | \(0.446250\pi\) | |||||||
\(212\) | −1591.25 | −0.515508 | ||||||||
\(213\) | −2035.73 | −0.654864 | ||||||||
\(214\) | 298.780 | 0.0954402 | ||||||||
\(215\) | −1771.08 | −0.561800 | ||||||||
\(216\) | −101.626 | −0.0320129 | ||||||||
\(217\) | −1386.55 | −0.433757 | ||||||||
\(218\) | 488.500 | 0.151768 | ||||||||
\(219\) | −182.401 | −0.0562809 | ||||||||
\(220\) | −2004.82 | −0.614387 | ||||||||
\(221\) | −6185.10 | −1.88260 | ||||||||
\(222\) | 110.243 | 0.0333289 | ||||||||
\(223\) | 5368.67 | 1.61217 | 0.806083 | − | 0.591803i | \(-0.201584\pi\) | ||||
0.806083 | + | 0.591803i | \(0.201584\pi\) | |||||||
\(224\) | −314.334 | −0.0937603 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | −461.251 | −0.135761 | ||||||||
\(227\) | −932.121 | −0.272542 | −0.136271 | − | 0.990672i | \(-0.543512\pi\) | ||||
−0.136271 | + | 0.990672i | \(0.543512\pi\) | |||||||
\(228\) | −98.6146 | −0.0286444 | ||||||||
\(229\) | 3163.05 | 0.912752 | 0.456376 | − | 0.889787i | \(-0.349147\pi\) | ||||
0.456376 | + | 0.889787i | \(0.349147\pi\) | |||||||
\(230\) | 241.641 | 0.0692753 | ||||||||
\(231\) | 1059.91 | 0.301893 | ||||||||
\(232\) | 343.147 | 0.0971065 | ||||||||
\(233\) | 436.562 | 0.122747 | 0.0613737 | − | 0.998115i | \(-0.480452\pi\) | ||||
0.0613737 | + | 0.998115i | \(0.480452\pi\) | |||||||
\(234\) | −172.031 | −0.0480599 | ||||||||
\(235\) | 878.297 | 0.243803 | ||||||||
\(236\) | 2482.57 | 0.684753 | ||||||||
\(237\) | −3858.77 | −1.05761 | ||||||||
\(238\) | −126.228 | −0.0343787 | ||||||||
\(239\) | −1980.82 | −0.536103 | −0.268051 | − | 0.963405i | \(-0.586380\pi\) | ||||
−0.268051 | + | 0.963405i | \(0.586380\pi\) | |||||||
\(240\) | −939.984 | −0.252816 | ||||||||
\(241\) | 5303.55 | 1.41756 | 0.708780 | − | 0.705430i | \(-0.249246\pi\) | ||||
0.708780 | + | 0.705430i | \(0.249246\pi\) | |||||||
\(242\) | 287.162 | 0.0762787 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 1224.77 | 0.321344 | ||||||||
\(245\) | −245.000 | −0.0638877 | ||||||||
\(246\) | −111.107 | −0.0287964 | ||||||||
\(247\) | −335.037 | −0.0863074 | ||||||||
\(248\) | −745.556 | −0.190899 | ||||||||
\(249\) | 348.511 | 0.0886987 | ||||||||
\(250\) | −29.5085 | −0.00746512 | ||||||||
\(251\) | −2996.04 | −0.753420 | −0.376710 | − | 0.926331i | \(-0.622945\pi\) | ||||
−0.376710 | + | 0.926331i | \(0.622945\pi\) | |||||||
\(252\) | 500.489 | 0.125111 | ||||||||
\(253\) | 10332.7 | 2.56764 | ||||||||
\(254\) | 52.9384 | 0.0130774 | ||||||||
\(255\) | −1145.80 | −0.281385 | ||||||||
\(256\) | 3813.64 | 0.931065 | ||||||||
\(257\) | 968.861 | 0.235159 | 0.117580 | − | 0.993063i | \(-0.462487\pi\) | ||||
0.117580 | + | 0.993063i | \(0.462487\pi\) | |||||||
\(258\) | 250.858 | 0.0605338 | ||||||||
\(259\) | −1089.66 | −0.261421 | ||||||||
\(260\) | −3216.26 | −0.767170 | ||||||||
\(261\) | −820.505 | −0.194590 | ||||||||
\(262\) | −115.885 | −0.0273260 | ||||||||
\(263\) | −4830.18 | −1.13248 | −0.566239 | − | 0.824241i | \(-0.691602\pi\) | ||||
−0.566239 | + | 0.824241i | \(0.691602\pi\) | |||||||
\(264\) | 569.921 | 0.132864 | ||||||||
\(265\) | −1001.51 | −0.232159 | ||||||||
\(266\) | −6.83756 | −0.00157608 | ||||||||
\(267\) | −2749.32 | −0.630171 | ||||||||
\(268\) | −5836.78 | −1.33037 | ||||||||
\(269\) | −4774.97 | −1.08229 | −0.541143 | − | 0.840930i | \(-0.682008\pi\) | ||||
−0.541143 | + | 0.840930i | \(0.682008\pi\) | |||||||
\(270\) | −31.8692 | −0.00718332 | ||||||||
\(271\) | 141.909 | 0.0318094 | 0.0159047 | − | 0.999874i | \(-0.494937\pi\) | ||||
0.0159047 | + | 0.999874i | \(0.494937\pi\) | |||||||
\(272\) | 4786.84 | 1.06708 | ||||||||
\(273\) | 1700.38 | 0.376966 | ||||||||
\(274\) | 432.269 | 0.0953078 | ||||||||
\(275\) | −1261.80 | −0.276689 | ||||||||
\(276\) | 4879.09 | 1.06408 | ||||||||
\(277\) | −3621.13 | −0.785460 | −0.392730 | − | 0.919654i | \(-0.628469\pi\) | ||||
−0.392730 | + | 0.919654i | \(0.628469\pi\) | |||||||
\(278\) | −720.206 | −0.155378 | ||||||||
\(279\) | 1782.71 | 0.382538 | ||||||||
\(280\) | −131.738 | −0.0281172 | ||||||||
\(281\) | 5790.87 | 1.22937 | 0.614687 | − | 0.788771i | \(-0.289282\pi\) | ||||
0.614687 | + | 0.788771i | \(0.289282\pi\) | |||||||
\(282\) | −124.403 | −0.0262698 | ||||||||
\(283\) | 526.043 | 0.110495 | 0.0552474 | − | 0.998473i | \(-0.482405\pi\) | ||||
0.0552474 | + | 0.998473i | \(0.482405\pi\) | |||||||
\(284\) | 5390.80 | 1.12636 | ||||||||
\(285\) | −62.0665 | −0.0129000 | ||||||||
\(286\) | 964.753 | 0.199465 | ||||||||
\(287\) | 1098.20 | 0.225870 | ||||||||
\(288\) | 404.143 | 0.0826888 | ||||||||
\(289\) | 921.972 | 0.187660 | ||||||||
\(290\) | 107.608 | 0.0217896 | ||||||||
\(291\) | −4248.91 | −0.855929 | ||||||||
\(292\) | 483.014 | 0.0968023 | ||||||||
\(293\) | 1914.88 | 0.381803 | 0.190901 | − | 0.981609i | \(-0.438859\pi\) | ||||
0.190901 | + | 0.981609i | \(0.438859\pi\) | |||||||
\(294\) | 34.7020 | 0.00688388 | ||||||||
\(295\) | 1562.49 | 0.308379 | ||||||||
\(296\) | −585.915 | −0.115053 | ||||||||
\(297\) | −1362.75 | −0.266245 | ||||||||
\(298\) | 530.339 | 0.103093 | ||||||||
\(299\) | 16576.4 | 3.20615 | ||||||||
\(300\) | −595.820 | −0.114666 | ||||||||
\(301\) | −2479.52 | −0.474807 | ||||||||
\(302\) | −309.610 | −0.0589936 | ||||||||
\(303\) | −4137.58 | −0.784482 | ||||||||
\(304\) | 259.296 | 0.0489199 | ||||||||
\(305\) | 770.851 | 0.144717 | ||||||||
\(306\) | 162.293 | 0.0303191 | ||||||||
\(307\) | −6244.17 | −1.16083 | −0.580413 | − | 0.814322i | \(-0.697109\pi\) | ||||
−0.580413 | + | 0.814322i | \(0.697109\pi\) | |||||||
\(308\) | −2806.75 | −0.519251 | ||||||||
\(309\) | −3925.30 | −0.722662 | ||||||||
\(310\) | −233.800 | −0.0428354 | ||||||||
\(311\) | −9658.78 | −1.76109 | −0.880545 | − | 0.473962i | \(-0.842823\pi\) | ||||
−0.880545 | + | 0.473962i | \(0.842823\pi\) | |||||||
\(312\) | 914.303 | 0.165905 | ||||||||
\(313\) | 2198.34 | 0.396988 | 0.198494 | − | 0.980102i | \(-0.436395\pi\) | ||||
0.198494 | + | 0.980102i | \(0.436395\pi\) | |||||||
\(314\) | 422.783 | 0.0759842 | ||||||||
\(315\) | 315.000 | 0.0563436 | ||||||||
\(316\) | 10218.4 | 1.81908 | ||||||||
\(317\) | 3030.78 | 0.536990 | 0.268495 | − | 0.963281i | \(-0.413474\pi\) | ||||
0.268495 | + | 0.963281i | \(0.413474\pi\) | |||||||
\(318\) | 141.855 | 0.0250151 | ||||||||
\(319\) | 4601.40 | 0.807615 | ||||||||
\(320\) | 2453.62 | 0.428630 | ||||||||
\(321\) | 3796.96 | 0.660204 | ||||||||
\(322\) | 338.297 | 0.0585483 | ||||||||
\(323\) | 316.072 | 0.0544480 | ||||||||
\(324\) | −643.486 | −0.110337 | ||||||||
\(325\) | −2024.26 | −0.345495 | ||||||||
\(326\) | −115.935 | −0.0196965 | ||||||||
\(327\) | 6207.96 | 1.04985 | ||||||||
\(328\) | 590.506 | 0.0994062 | ||||||||
\(329\) | 1229.62 | 0.206051 | ||||||||
\(330\) | 178.723 | 0.0298132 | ||||||||
\(331\) | 4753.74 | 0.789393 | 0.394696 | − | 0.918812i | \(-0.370850\pi\) | ||||
0.394696 | + | 0.918812i | \(0.370850\pi\) | |||||||
\(332\) | −922.888 | −0.152560 | ||||||||
\(333\) | 1400.99 | 0.230552 | ||||||||
\(334\) | −195.006 | −0.0319469 | ||||||||
\(335\) | −3673.58 | −0.599131 | ||||||||
\(336\) | −1315.98 | −0.213668 | ||||||||
\(337\) | 8824.40 | 1.42640 | 0.713199 | − | 0.700962i | \(-0.247246\pi\) | ||||
0.713199 | + | 0.700962i | \(0.247246\pi\) | |||||||
\(338\) | 1029.08 | 0.165605 | ||||||||
\(339\) | −5861.67 | −0.939122 | ||||||||
\(340\) | 3034.20 | 0.483977 | ||||||||
\(341\) | −9997.47 | −1.58766 | ||||||||
\(342\) | 8.79115 | 0.00138997 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −1333.25 | −0.208965 | ||||||||
\(345\) | 3070.82 | 0.479210 | ||||||||
\(346\) | 688.847 | 0.107031 | ||||||||
\(347\) | −3413.97 | −0.528160 | −0.264080 | − | 0.964501i | \(-0.585068\pi\) | ||||
−0.264080 | + | 0.964501i | \(0.585068\pi\) | |||||||
\(348\) | 2172.77 | 0.334692 | ||||||||
\(349\) | −5676.32 | −0.870621 | −0.435310 | − | 0.900280i | \(-0.643361\pi\) | ||||
−0.435310 | + | 0.900280i | \(0.643361\pi\) | |||||||
\(350\) | −41.3119 | −0.00630918 | ||||||||
\(351\) | −2186.21 | −0.332453 | ||||||||
\(352\) | −2266.44 | −0.343187 | ||||||||
\(353\) | 6225.80 | 0.938713 | 0.469357 | − | 0.883009i | \(-0.344486\pi\) | ||||
0.469357 | + | 0.883009i | \(0.344486\pi\) | |||||||
\(354\) | −221.313 | −0.0332278 | ||||||||
\(355\) | 3392.89 | 0.507256 | ||||||||
\(356\) | 7280.45 | 1.08388 | ||||||||
\(357\) | −1604.13 | −0.237813 | ||||||||
\(358\) | 225.621 | 0.0333084 | ||||||||
\(359\) | −4907.73 | −0.721505 | −0.360752 | − | 0.932662i | \(-0.617480\pi\) | ||||
−0.360752 | + | 0.932662i | \(0.617480\pi\) | |||||||
\(360\) | 169.377 | 0.0247971 | ||||||||
\(361\) | −6841.88 | −0.997504 | ||||||||
\(362\) | 48.6490 | 0.00706335 | ||||||||
\(363\) | 3649.31 | 0.527656 | ||||||||
\(364\) | −4502.77 | −0.648377 | ||||||||
\(365\) | 304.001 | 0.0435950 | ||||||||
\(366\) | −109.184 | −0.0155933 | ||||||||
\(367\) | −3906.48 | −0.555631 | −0.277816 | − | 0.960634i | \(-0.589610\pi\) | ||||
−0.277816 | + | 0.960634i | \(0.589610\pi\) | |||||||
\(368\) | −12829.0 | −1.81728 | ||||||||
\(369\) | −1411.97 | −0.199198 | ||||||||
\(370\) | −183.738 | −0.0258165 | ||||||||
\(371\) | −1402.11 | −0.196210 | ||||||||
\(372\) | −4720.78 | −0.657960 | ||||||||
\(373\) | −2102.52 | −0.291862 | −0.145931 | − | 0.989295i | \(-0.546618\pi\) | ||||
−0.145931 | + | 0.989295i | \(0.546618\pi\) | |||||||
\(374\) | −910.140 | −0.125835 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | 661.170 | 0.0906842 | ||||||||
\(377\) | 7381.86 | 1.00845 | ||||||||
\(378\) | −44.6168 | −0.00607101 | ||||||||
\(379\) | −6612.76 | −0.896239 | −0.448120 | − | 0.893974i | \(-0.647906\pi\) | ||||
−0.448120 | + | 0.893974i | \(0.647906\pi\) | |||||||
\(380\) | 164.358 | 0.0221878 | ||||||||
\(381\) | 672.752 | 0.0904623 | ||||||||
\(382\) | −476.534 | −0.0638262 | ||||||||
\(383\) | 2.37457 | 0.000316801 0 | 0.000158401 | − | 1.00000i | \(-0.499950\pi\) | ||||
0.000158401 | 1.00000i | \(0.499950\pi\) | ||||||||
\(384\) | −1425.25 | −0.189406 | ||||||||
\(385\) | −1766.52 | −0.233845 | ||||||||
\(386\) | 243.549 | 0.0321148 | ||||||||
\(387\) | 3187.95 | 0.418741 | ||||||||
\(388\) | 11251.5 | 1.47218 | ||||||||
\(389\) | 7716.98 | 1.00583 | 0.502913 | − | 0.864337i | \(-0.332261\pi\) | ||||
0.502913 | + | 0.864337i | \(0.332261\pi\) | |||||||
\(390\) | 286.718 | 0.0372271 | ||||||||
\(391\) | −15638.0 | −2.02263 | ||||||||
\(392\) | −184.433 | −0.0237634 | ||||||||
\(393\) | −1472.69 | −0.189027 | ||||||||
\(394\) | −48.6194 | −0.00621678 | ||||||||
\(395\) | 6431.28 | 0.819223 | ||||||||
\(396\) | 3608.68 | 0.457937 | ||||||||
\(397\) | 6403.95 | 0.809584 | 0.404792 | − | 0.914409i | \(-0.367344\pi\) | ||||
0.404792 | + | 0.914409i | \(0.367344\pi\) | |||||||
\(398\) | −432.329 | −0.0544490 | ||||||||
\(399\) | −86.8931 | −0.0109025 | ||||||||
\(400\) | 1566.64 | 0.195830 | ||||||||
\(401\) | −10969.9 | −1.36611 | −0.683054 | − | 0.730368i | \(-0.739349\pi\) | ||||
−0.683054 | + | 0.730368i | \(0.739349\pi\) | |||||||
\(402\) | 520.328 | 0.0645562 | ||||||||
\(403\) | −16038.6 | −1.98248 | ||||||||
\(404\) | 10956.7 | 1.34930 | ||||||||
\(405\) | −405.000 | −0.0496904 | ||||||||
\(406\) | 150.652 | 0.0184155 | ||||||||
\(407\) | −7856.78 | −0.956870 | ||||||||
\(408\) | −862.546 | −0.104663 | ||||||||
\(409\) | −400.353 | −0.0484015 | −0.0242007 | − | 0.999707i | \(-0.507704\pi\) | ||||
−0.0242007 | + | 0.999707i | \(0.507704\pi\) | |||||||
\(410\) | 185.178 | 0.0223056 | ||||||||
\(411\) | 5493.37 | 0.659289 | ||||||||
\(412\) | 10394.6 | 1.24297 | ||||||||
\(413\) | 2187.49 | 0.260628 | ||||||||
\(414\) | −434.953 | −0.0516348 | ||||||||
\(415\) | −580.851 | −0.0687057 | ||||||||
\(416\) | −3635.97 | −0.428529 | ||||||||
\(417\) | −9152.52 | −1.07482 | ||||||||
\(418\) | −49.3009 | −0.00576887 | ||||||||
\(419\) | −15815.4 | −1.84399 | −0.921995 | − | 0.387201i | \(-0.873442\pi\) | ||||
−0.921995 | + | 0.387201i | \(0.873442\pi\) | |||||||
\(420\) | −834.149 | −0.0969102 | ||||||||
\(421\) | 1936.53 | 0.224182 | 0.112091 | − | 0.993698i | \(-0.464245\pi\) | ||||
0.112091 | + | 0.993698i | \(0.464245\pi\) | |||||||
\(422\) | 243.195 | 0.0280534 | ||||||||
\(423\) | −1580.93 | −0.181720 | ||||||||
\(424\) | −753.923 | −0.0863531 | ||||||||
\(425\) | 1909.67 | 0.217960 | ||||||||
\(426\) | −480.571 | −0.0546567 | ||||||||
\(427\) | 1079.19 | 0.122309 | ||||||||
\(428\) | −10054.7 | −1.13554 | ||||||||
\(429\) | 12260.3 | 1.37979 | ||||||||
\(430\) | −418.096 | −0.0468893 | ||||||||
\(431\) | 2030.91 | 0.226973 | 0.113487 | − | 0.993540i | \(-0.463798\pi\) | ||||
0.113487 | + | 0.993540i | \(0.463798\pi\) | |||||||
\(432\) | 1691.97 | 0.188438 | ||||||||
\(433\) | −10784.1 | −1.19689 | −0.598443 | − | 0.801165i | \(-0.704214\pi\) | ||||
−0.598443 | + | 0.801165i | \(0.704214\pi\) | |||||||
\(434\) | −327.321 | −0.0362025 | ||||||||
\(435\) | 1367.51 | 0.150729 | ||||||||
\(436\) | −16439.2 | −1.80573 | ||||||||
\(437\) | −847.089 | −0.0927272 | ||||||||
\(438\) | −43.0590 | −0.00469735 | ||||||||
\(439\) | −6304.19 | −0.685382 | −0.342691 | − | 0.939448i | \(-0.611338\pi\) | ||||
−0.342691 | + | 0.939448i | \(0.611338\pi\) | |||||||
\(440\) | −949.868 | −0.102916 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | −1460.10 | −0.157127 | ||||||||
\(443\) | 15494.8 | 1.66181 | 0.830905 | − | 0.556414i | \(-0.187823\pi\) | ||||
0.830905 | + | 0.556414i | \(0.187823\pi\) | |||||||
\(444\) | −3709.95 | −0.396546 | ||||||||
\(445\) | 4582.20 | 0.488128 | ||||||||
\(446\) | 1267.37 | 0.134556 | ||||||||
\(447\) | 6739.65 | 0.713142 | ||||||||
\(448\) | 3435.07 | 0.362259 | ||||||||
\(449\) | −242.018 | −0.0254377 | −0.0127189 | − | 0.999919i | \(-0.504049\pi\) | ||||
−0.0127189 | + | 0.999919i | \(0.504049\pi\) | |||||||
\(450\) | 53.1153 | 0.00556418 | ||||||||
\(451\) | 7918.34 | 0.826741 | ||||||||
\(452\) | 15522.2 | 1.61528 | ||||||||
\(453\) | −3934.59 | −0.408086 | ||||||||
\(454\) | −220.044 | −0.0227471 | ||||||||
\(455\) | −2833.97 | −0.291997 | ||||||||
\(456\) | −46.7228 | −0.00479824 | ||||||||
\(457\) | −11670.4 | −1.19457 | −0.597283 | − | 0.802030i | \(-0.703753\pi\) | ||||
−0.597283 | + | 0.802030i | \(0.703753\pi\) | |||||||
\(458\) | 746.695 | 0.0761807 | ||||||||
\(459\) | 2062.45 | 0.209732 | ||||||||
\(460\) | −8131.81 | −0.824234 | ||||||||
\(461\) | 12128.1 | 1.22530 | 0.612649 | − | 0.790355i | \(-0.290104\pi\) | ||||
0.612649 | + | 0.790355i | \(0.290104\pi\) | |||||||
\(462\) | 250.212 | 0.0251968 | ||||||||
\(463\) | 5161.64 | 0.518103 | 0.259051 | − | 0.965864i | \(-0.416590\pi\) | ||||
0.259051 | + | 0.965864i | \(0.416590\pi\) | |||||||
\(464\) | −5713.05 | −0.571598 | ||||||||
\(465\) | −2971.18 | −0.296313 | ||||||||
\(466\) | 103.058 | 0.0102448 | ||||||||
\(467\) | 11680.2 | 1.15738 | 0.578691 | − | 0.815547i | \(-0.303564\pi\) | ||||
0.578691 | + | 0.815547i | \(0.303564\pi\) | |||||||
\(468\) | 5789.27 | 0.571814 | ||||||||
\(469\) | −5143.01 | −0.506358 | ||||||||
\(470\) | 207.338 | 0.0203485 | ||||||||
\(471\) | 5372.82 | 0.525619 | ||||||||
\(472\) | 1176.22 | 0.114703 | ||||||||
\(473\) | −17878.1 | −1.73792 | ||||||||
\(474\) | −910.932 | −0.0882711 | ||||||||
\(475\) | 103.444 | 0.00999230 | ||||||||
\(476\) | 4247.87 | 0.409036 | ||||||||
\(477\) | 1802.72 | 0.173041 | ||||||||
\(478\) | −467.608 | −0.0447445 | ||||||||
\(479\) | −18458.7 | −1.76075 | −0.880373 | − | 0.474282i | \(-0.842708\pi\) | ||||
−0.880373 | + | 0.474282i | \(0.842708\pi\) | |||||||
\(480\) | −673.572 | −0.0640505 | ||||||||
\(481\) | −12604.3 | −1.19482 | ||||||||
\(482\) | 1252.00 | 0.118313 | ||||||||
\(483\) | 4299.15 | 0.405006 | ||||||||
\(484\) | −9663.70 | −0.907560 | ||||||||
\(485\) | 7081.51 | 0.663000 | ||||||||
\(486\) | 57.3645 | 0.00535413 | ||||||||
\(487\) | 8630.11 | 0.803014 | 0.401507 | − | 0.915856i | \(-0.368487\pi\) | ||||
0.401507 | + | 0.915856i | \(0.368487\pi\) | |||||||
\(488\) | 580.286 | 0.0538286 | ||||||||
\(489\) | −1473.33 | −0.136250 | ||||||||
\(490\) | −57.8367 | −0.00533223 | ||||||||
\(491\) | 17801.6 | 1.63621 | 0.818103 | − | 0.575072i | \(-0.195026\pi\) | ||||
0.818103 | + | 0.575072i | \(0.195026\pi\) | |||||||
\(492\) | 3739.02 | 0.342618 | ||||||||
\(493\) | −6963.99 | −0.636191 | ||||||||
\(494\) | −79.0916 | −0.00720344 | ||||||||
\(495\) | 2271.25 | 0.206232 | ||||||||
\(496\) | 12412.7 | 1.12369 | ||||||||
\(497\) | 4750.04 | 0.428709 | ||||||||
\(498\) | 82.2723 | 0.00740303 | ||||||||
\(499\) | 200.167 | 0.0179574 | 0.00897868 | − | 0.999960i | \(-0.497142\pi\) | ||||
0.00897868 | + | 0.999960i | \(0.497142\pi\) | |||||||
\(500\) | 993.034 | 0.0888197 | ||||||||
\(501\) | −2478.18 | −0.220992 | ||||||||
\(502\) | −707.269 | −0.0628824 | ||||||||
\(503\) | 16400.4 | 1.45379 | 0.726896 | − | 0.686747i | \(-0.240962\pi\) | ||||
0.726896 | + | 0.686747i | \(0.240962\pi\) | |||||||
\(504\) | 237.128 | 0.0209574 | ||||||||
\(505\) | 6895.97 | 0.607657 | ||||||||
\(506\) | 2439.23 | 0.214302 | ||||||||
\(507\) | 13077.7 | 1.14556 | ||||||||
\(508\) | −1781.51 | −0.155594 | ||||||||
\(509\) | −15006.6 | −1.30679 | −0.653394 | − | 0.757018i | \(-0.726656\pi\) | ||||
−0.653394 | + | 0.757018i | \(0.726656\pi\) | |||||||
\(510\) | −270.488 | −0.0234851 | ||||||||
\(511\) | 425.602 | 0.0368445 | ||||||||
\(512\) | 4700.94 | 0.405770 | ||||||||
\(513\) | 111.720 | 0.00961510 | ||||||||
\(514\) | 228.717 | 0.0196270 | ||||||||
\(515\) | 6542.17 | 0.559772 | ||||||||
\(516\) | −8441.98 | −0.720228 | ||||||||
\(517\) | 8865.91 | 0.754201 | ||||||||
\(518\) | −257.234 | −0.0218189 | ||||||||
\(519\) | 8754.01 | 0.740382 | ||||||||
\(520\) | −1523.84 | −0.128509 | ||||||||
\(521\) | 7113.18 | 0.598146 | 0.299073 | − | 0.954230i | \(-0.403323\pi\) | ||||
0.299073 | + | 0.954230i | \(0.403323\pi\) | |||||||
\(522\) | −193.695 | −0.0162410 | ||||||||
\(523\) | −8888.46 | −0.743146 | −0.371573 | − | 0.928404i | \(-0.621181\pi\) | ||||
−0.371573 | + | 0.928404i | \(0.621181\pi\) | |||||||
\(524\) | 3899.83 | 0.325123 | ||||||||
\(525\) | −525.000 | −0.0436436 | ||||||||
\(526\) | −1140.25 | −0.0945196 | ||||||||
\(527\) | 15130.7 | 1.25067 | ||||||||
\(528\) | −9488.60 | −0.782081 | ||||||||
\(529\) | 29743.8 | 2.44463 | ||||||||
\(530\) | −236.424 | −0.0193766 | ||||||||
\(531\) | −2812.49 | −0.229852 | ||||||||
\(532\) | 230.101 | 0.0187521 | ||||||||
\(533\) | 12703.1 | 1.03233 | ||||||||
\(534\) | −649.026 | −0.0525957 | ||||||||
\(535\) | −6328.27 | −0.511392 | ||||||||
\(536\) | −2765.42 | −0.222850 | ||||||||
\(537\) | 2867.23 | 0.230410 | ||||||||
\(538\) | −1127.22 | −0.0903305 | ||||||||
\(539\) | −2473.13 | −0.197635 | ||||||||
\(540\) | 1072.48 | 0.0854668 | ||||||||
\(541\) | −653.827 | −0.0519597 | −0.0259799 | − | 0.999662i | \(-0.508271\pi\) | ||||
−0.0259799 | + | 0.999662i | \(0.508271\pi\) | |||||||
\(542\) | 33.5001 | 0.00265489 | ||||||||
\(543\) | 618.241 | 0.0488605 | ||||||||
\(544\) | 3430.14 | 0.270342 | ||||||||
\(545\) | −10346.6 | −0.813210 | ||||||||
\(546\) | 401.406 | 0.0314626 | ||||||||
\(547\) | 1138.52 | 0.0889940 | 0.0444970 | − | 0.999010i | \(-0.485831\pi\) | ||||
0.0444970 | + | 0.999010i | \(0.485831\pi\) | |||||||
\(548\) | −14546.9 | −1.13397 | ||||||||
\(549\) | −1387.53 | −0.107866 | ||||||||
\(550\) | −297.871 | −0.0230932 | ||||||||
\(551\) | −377.229 | −0.0291660 | ||||||||
\(552\) | 2311.67 | 0.178245 | ||||||||
\(553\) | 9003.80 | 0.692370 | ||||||||
\(554\) | −854.832 | −0.0655566 | ||||||||
\(555\) | −2334.98 | −0.178585 | ||||||||
\(556\) | 24236.7 | 1.84868 | ||||||||
\(557\) | −19804.8 | −1.50657 | −0.753283 | − | 0.657696i | \(-0.771531\pi\) | ||||
−0.753283 | + | 0.657696i | \(0.771531\pi\) | |||||||
\(558\) | 420.841 | 0.0319276 | ||||||||
\(559\) | −28681.1 | −2.17009 | ||||||||
\(560\) | 2193.30 | 0.165507 | ||||||||
\(561\) | −11566.2 | −0.870458 | ||||||||
\(562\) | 1367.04 | 0.102607 | ||||||||
\(563\) | 10276.3 | 0.769265 | 0.384632 | − | 0.923070i | \(-0.374328\pi\) | ||||
0.384632 | + | 0.923070i | \(0.374328\pi\) | |||||||
\(564\) | 4186.46 | 0.312556 | ||||||||
\(565\) | 9769.45 | 0.727440 | ||||||||
\(566\) | 124.182 | 0.00922219 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 2554.12 | 0.188677 | ||||||||
\(569\) | 4139.03 | 0.304951 | 0.152475 | − | 0.988307i | \(-0.451276\pi\) | ||||
0.152475 | + | 0.988307i | \(0.451276\pi\) | |||||||
\(570\) | −14.6519 | −0.00107667 | ||||||||
\(571\) | −4486.81 | −0.328839 | −0.164420 | − | 0.986390i | \(-0.552575\pi\) | ||||
−0.164420 | + | 0.986390i | \(0.552575\pi\) | |||||||
\(572\) | −32466.3 | −2.37323 | ||||||||
\(573\) | −6055.89 | −0.441516 | ||||||||
\(574\) | 259.249 | 0.0188517 | ||||||||
\(575\) | −5118.03 | −0.371194 | ||||||||
\(576\) | −4416.52 | −0.319482 | ||||||||
\(577\) | −1104.77 | −0.0797093 | −0.0398547 | − | 0.999205i | \(-0.512689\pi\) | ||||
−0.0398547 | + | 0.999205i | \(0.512689\pi\) | |||||||
\(578\) | 217.648 | 0.0156626 | ||||||||
\(579\) | 3095.07 | 0.222153 | ||||||||
\(580\) | −3621.28 | −0.259251 | ||||||||
\(581\) | −813.192 | −0.0580669 | ||||||||
\(582\) | −1003.03 | −0.0714381 | ||||||||
\(583\) | −10109.7 | −0.718181 | ||||||||
\(584\) | 228.848 | 0.0162154 | ||||||||
\(585\) | 3643.68 | 0.257517 | ||||||||
\(586\) | 452.041 | 0.0318663 | ||||||||
\(587\) | −10413.2 | −0.732199 | −0.366100 | − | 0.930576i | \(-0.619307\pi\) | ||||
−0.366100 | + | 0.930576i | \(0.619307\pi\) | |||||||
\(588\) | −1167.81 | −0.0819041 | ||||||||
\(589\) | 819.605 | 0.0573365 | ||||||||
\(590\) | 368.854 | 0.0257381 | ||||||||
\(591\) | −617.865 | −0.0430044 | ||||||||
\(592\) | 9754.89 | 0.677235 | ||||||||
\(593\) | −3235.16 | −0.224034 | −0.112017 | − | 0.993706i | \(-0.535731\pi\) | ||||
−0.112017 | + | 0.993706i | \(0.535731\pi\) | |||||||
\(594\) | −321.701 | −0.0222215 | ||||||||
\(595\) | 2673.54 | 0.184209 | ||||||||
\(596\) | −17847.2 | −1.22659 | ||||||||
\(597\) | −5494.13 | −0.376649 | ||||||||
\(598\) | 3913.16 | 0.267594 | ||||||||
\(599\) | 569.048 | 0.0388158 | 0.0194079 | − | 0.999812i | \(-0.493822\pi\) | ||||
0.0194079 | + | 0.999812i | \(0.493822\pi\) | |||||||
\(600\) | −282.295 | −0.0192077 | ||||||||
\(601\) | 3760.89 | 0.255258 | 0.127629 | − | 0.991822i | \(-0.459263\pi\) | ||||
0.127629 | + | 0.991822i | \(0.459263\pi\) | |||||||
\(602\) | −585.335 | −0.0396287 | ||||||||
\(603\) | 6612.44 | 0.446566 | ||||||||
\(604\) | 10419.1 | 0.701902 | ||||||||
\(605\) | −6082.18 | −0.408720 | ||||||||
\(606\) | −976.751 | −0.0654749 | ||||||||
\(607\) | −2224.05 | −0.148717 | −0.0743585 | − | 0.997232i | \(-0.523691\pi\) | ||||
−0.0743585 | + | 0.997232i | \(0.523691\pi\) | |||||||
\(608\) | 185.806 | 0.0123938 | ||||||||
\(609\) | 1914.51 | 0.127389 | ||||||||
\(610\) | 181.973 | 0.0120785 | ||||||||
\(611\) | 14223.2 | 0.941753 | ||||||||
\(612\) | −5461.55 | −0.360735 | ||||||||
\(613\) | 5914.50 | 0.389697 | 0.194849 | − | 0.980833i | \(-0.437578\pi\) | ||||
0.194849 | + | 0.980833i | \(0.437578\pi\) | |||||||
\(614\) | −1474.05 | −0.0968856 | ||||||||
\(615\) | 2353.28 | 0.154298 | ||||||||
\(616\) | −1329.82 | −0.0869802 | ||||||||
\(617\) | −18591.2 | −1.21306 | −0.606528 | − | 0.795062i | \(-0.707438\pi\) | ||||
−0.606528 | + | 0.795062i | \(0.707438\pi\) | |||||||
\(618\) | −926.638 | −0.0603153 | ||||||||
\(619\) | 5125.97 | 0.332844 | 0.166422 | − | 0.986055i | \(-0.446779\pi\) | ||||
0.166422 | + | 0.986055i | \(0.446779\pi\) | |||||||
\(620\) | 7867.96 | 0.509653 | ||||||||
\(621\) | −5527.48 | −0.357182 | ||||||||
\(622\) | −2280.13 | −0.146985 | ||||||||
\(623\) | 6415.08 | 0.412544 | ||||||||
\(624\) | −15222.2 | −0.976565 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 518.957 | 0.0331337 | ||||||||
\(627\) | −626.526 | −0.0399060 | ||||||||
\(628\) | −14227.7 | −0.904056 | ||||||||
\(629\) | 11890.8 | 0.753765 | ||||||||
\(630\) | 74.3614 | 0.00470259 | ||||||||
\(631\) | −10649.0 | −0.671839 | −0.335919 | − | 0.941891i | \(-0.609047\pi\) | ||||
−0.335919 | + | 0.941891i | \(0.609047\pi\) | |||||||
\(632\) | 4841.38 | 0.304715 | ||||||||
\(633\) | 3090.57 | 0.194058 | ||||||||
\(634\) | 715.471 | 0.0448186 | ||||||||
\(635\) | −1121.25 | −0.0700718 | ||||||||
\(636\) | −4773.76 | −0.297629 | ||||||||
\(637\) | −3967.56 | −0.246782 | ||||||||
\(638\) | 1086.24 | 0.0674056 | ||||||||
\(639\) | −6107.20 | −0.378086 | ||||||||
\(640\) | 2375.41 | 0.146713 | ||||||||
\(641\) | 24025.7 | 1.48044 | 0.740218 | − | 0.672367i | \(-0.234722\pi\) | ||||
0.740218 | + | 0.672367i | \(0.234722\pi\) | |||||||
\(642\) | 896.341 | 0.0551024 | ||||||||
\(643\) | 14929.3 | 0.915638 | 0.457819 | − | 0.889045i | \(-0.348631\pi\) | ||||
0.457819 | + | 0.889045i | \(0.348631\pi\) | |||||||
\(644\) | −11384.5 | −0.696605 | ||||||||
\(645\) | −5313.25 | −0.324355 | ||||||||
\(646\) | 74.6144 | 0.00454437 | ||||||||
\(647\) | 14479.1 | 0.879801 | 0.439901 | − | 0.898046i | \(-0.355014\pi\) | ||||
0.439901 | + | 0.898046i | \(0.355014\pi\) | |||||||
\(648\) | −304.878 | −0.0184827 | ||||||||
\(649\) | 15772.5 | 0.953965 | ||||||||
\(650\) | −477.864 | −0.0288360 | ||||||||
\(651\) | −4159.66 | −0.250430 | ||||||||
\(652\) | 3901.50 | 0.234347 | ||||||||
\(653\) | 898.168 | 0.0538255 | 0.0269127 | − | 0.999638i | \(-0.491432\pi\) | ||||
0.0269127 | + | 0.999638i | \(0.491432\pi\) | |||||||
\(654\) | 1465.50 | 0.0876232 | ||||||||
\(655\) | 2454.49 | 0.146420 | ||||||||
\(656\) | −9831.33 | −0.585135 | ||||||||
\(657\) | −547.203 | −0.0324938 | ||||||||
\(658\) | 290.273 | 0.0171976 | ||||||||
\(659\) | −30198.0 | −1.78505 | −0.892526 | − | 0.450997i | \(-0.851069\pi\) | ||||
−0.892526 | + | 0.450997i | \(0.851069\pi\) | |||||||
\(660\) | −6014.47 | −0.354716 | ||||||||
\(661\) | −19337.8 | −1.13790 | −0.568952 | − | 0.822371i | \(-0.692651\pi\) | ||||
−0.568952 | + | 0.822371i | \(0.692651\pi\) | |||||||
\(662\) | 1122.20 | 0.0658848 | ||||||||
\(663\) | −18555.3 | −1.08692 | ||||||||
\(664\) | −437.257 | −0.0255555 | ||||||||
\(665\) | 144.822 | 0.00844504 | ||||||||
\(666\) | 330.729 | 0.0192425 | ||||||||
\(667\) | 18663.9 | 1.08346 | ||||||||
\(668\) | 6562.44 | 0.380102 | ||||||||
\(669\) | 16106.0 | 0.930784 | ||||||||
\(670\) | −867.214 | −0.0500051 | ||||||||
\(671\) | 7781.30 | 0.447681 | ||||||||
\(672\) | −943.001 | −0.0541325 | ||||||||
\(673\) | 10132.2 | 0.580336 | 0.290168 | − | 0.956976i | \(-0.406289\pi\) | ||||
0.290168 | + | 0.956976i | \(0.406289\pi\) | |||||||
\(674\) | 2083.16 | 0.119051 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | −34631.0 | −1.97035 | ||||||||
\(677\) | −33177.3 | −1.88347 | −0.941733 | − | 0.336361i | \(-0.890804\pi\) | ||||
−0.941733 | + | 0.336361i | \(0.890804\pi\) | |||||||
\(678\) | −1383.75 | −0.0783816 | ||||||||
\(679\) | 9914.11 | 0.560337 | ||||||||
\(680\) | 1437.58 | 0.0810714 | ||||||||
\(681\) | −2796.36 | −0.157352 | ||||||||
\(682\) | −2360.08 | −0.132511 | ||||||||
\(683\) | −11423.6 | −0.639987 | −0.319994 | − | 0.947420i | \(-0.603681\pi\) | ||||
−0.319994 | + | 0.947420i | \(0.603681\pi\) | |||||||
\(684\) | −295.844 | −0.0165378 | ||||||||
\(685\) | −9155.61 | −0.510683 | ||||||||
\(686\) | −80.9713 | −0.00450656 | ||||||||
\(687\) | 9489.15 | 0.526978 | ||||||||
\(688\) | 22197.2 | 1.23003 | ||||||||
\(689\) | −16218.6 | −0.896775 | ||||||||
\(690\) | 724.922 | 0.0399961 | ||||||||
\(691\) | −19737.4 | −1.08661 | −0.543304 | − | 0.839536i | \(-0.682827\pi\) | ||||
−0.543304 | + | 0.839536i | \(0.682827\pi\) | |||||||
\(692\) | −23181.4 | −1.27345 | ||||||||
\(693\) | 3179.74 | 0.174298 | ||||||||
\(694\) | −805.929 | −0.0440816 | ||||||||
\(695\) | 15254.2 | 0.832554 | ||||||||
\(696\) | 1029.44 | 0.0560645 | ||||||||
\(697\) | −11984.0 | −0.651258 | ||||||||
\(698\) | −1340.00 | −0.0726643 | ||||||||
\(699\) | 1309.69 | 0.0708682 | ||||||||
\(700\) | 1390.25 | 0.0750663 | ||||||||
\(701\) | 11307.8 | 0.609258 | 0.304629 | − | 0.952471i | \(-0.401468\pi\) | ||||
0.304629 | + | 0.952471i | \(0.401468\pi\) | |||||||
\(702\) | −516.093 | −0.0277474 | ||||||||
\(703\) | 644.108 | 0.0345562 | ||||||||
\(704\) | 24767.9 | 1.32596 | ||||||||
\(705\) | 2634.89 | 0.140760 | ||||||||
\(706\) | 1469.71 | 0.0783475 | ||||||||
\(707\) | 9654.36 | 0.513564 | ||||||||
\(708\) | 7447.72 | 0.395342 | ||||||||
\(709\) | 30859.2 | 1.63461 | 0.817307 | − | 0.576202i | \(-0.195466\pi\) | ||||
0.817307 | + | 0.576202i | \(0.195466\pi\) | |||||||
\(710\) | 800.952 | 0.0423369 | ||||||||
\(711\) | −11576.3 | −0.610613 | ||||||||
\(712\) | 3449.42 | 0.181562 | ||||||||
\(713\) | −40551.0 | −2.12994 | ||||||||
\(714\) | −378.683 | −0.0198485 | ||||||||
\(715\) | −20433.8 | −1.06878 | ||||||||
\(716\) | −7592.69 | −0.396302 | ||||||||
\(717\) | −5942.46 | −0.309519 | ||||||||
\(718\) | −1158.56 | −0.0602187 | ||||||||
\(719\) | 33152.4 | 1.71958 | 0.859789 | − | 0.510650i | \(-0.170595\pi\) | ||||
0.859789 | + | 0.510650i | \(0.170595\pi\) | |||||||
\(720\) | −2819.95 | −0.145963 | ||||||||
\(721\) | 9159.03 | 0.473093 | ||||||||
\(722\) | −1615.15 | −0.0832543 | ||||||||
\(723\) | 15910.7 | 0.818428 | ||||||||
\(724\) | −1637.16 | −0.0840394 | ||||||||
\(725\) | −2279.18 | −0.116754 | ||||||||
\(726\) | 861.485 | 0.0440395 | ||||||||
\(727\) | −16743.0 | −0.854146 | −0.427073 | − | 0.904217i | \(-0.640455\pi\) | ||||
−0.427073 | + | 0.904217i | \(0.640455\pi\) | |||||||
\(728\) | −2133.37 | −0.108610 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 71.7650 | 0.00363855 | ||||||||
\(731\) | 27057.5 | 1.36903 | ||||||||
\(732\) | 3674.31 | 0.185528 | ||||||||
\(733\) | −8827.55 | −0.444820 | −0.222410 | − | 0.974953i | \(-0.571392\pi\) | ||||
−0.222410 | + | 0.974953i | \(0.571392\pi\) | |||||||
\(734\) | −922.195 | −0.0463744 | ||||||||
\(735\) | −735.000 | −0.0368856 | ||||||||
\(736\) | −9192.97 | −0.460404 | ||||||||
\(737\) | −37082.6 | −1.85340 | ||||||||
\(738\) | −333.321 | −0.0166256 | ||||||||
\(739\) | 36154.0 | 1.79966 | 0.899829 | − | 0.436243i | \(-0.143691\pi\) | ||||
0.899829 | + | 0.436243i | \(0.143691\pi\) | |||||||
\(740\) | 6183.25 | 0.307163 | ||||||||
\(741\) | −1005.11 | −0.0498296 | ||||||||
\(742\) | −330.994 | −0.0163762 | ||||||||
\(743\) | −1820.69 | −0.0898987 | −0.0449494 | − | 0.998989i | \(-0.514313\pi\) | ||||
−0.0449494 | + | 0.998989i | \(0.514313\pi\) | |||||||
\(744\) | −2236.67 | −0.110215 | ||||||||
\(745\) | −11232.8 | −0.552398 | ||||||||
\(746\) | −496.338 | −0.0243596 | ||||||||
\(747\) | 1045.53 | 0.0512102 | ||||||||
\(748\) | 30628.5 | 1.49718 | ||||||||
\(749\) | −8859.57 | −0.432205 | ||||||||
\(750\) | −88.5255 | −0.00430999 | ||||||||
\(751\) | 27764.4 | 1.34905 | 0.674526 | − | 0.738251i | \(-0.264348\pi\) | ||||
0.674526 | + | 0.738251i | \(0.264348\pi\) | |||||||
\(752\) | −11007.8 | −0.533795 | ||||||||
\(753\) | −8988.12 | −0.434987 | ||||||||
\(754\) | 1742.62 | 0.0841678 | ||||||||
\(755\) | 6557.65 | 0.316102 | ||||||||
\(756\) | 1501.47 | 0.0722326 | ||||||||
\(757\) | −13518.3 | −0.649050 | −0.324525 | − | 0.945877i | \(-0.605205\pi\) | ||||
−0.324525 | + | 0.945877i | \(0.605205\pi\) | |||||||
\(758\) | −1561.06 | −0.0748025 | ||||||||
\(759\) | 30998.2 | 1.48243 | ||||||||
\(760\) | 77.8714 | 0.00371670 | ||||||||
\(761\) | 30695.2 | 1.46216 | 0.731078 | − | 0.682294i | \(-0.239017\pi\) | ||||
0.731078 | + | 0.682294i | \(0.239017\pi\) | |||||||
\(762\) | 158.815 | 0.00755022 | ||||||||
\(763\) | −14485.2 | −0.687288 | ||||||||
\(764\) | 16036.5 | 0.759400 | ||||||||
\(765\) | −3437.41 | −0.162457 | ||||||||
\(766\) | 0.560560 | 2.64410e−5 0 | ||||||||
\(767\) | 25303.2 | 1.19119 | ||||||||
\(768\) | 11440.9 | 0.537551 | ||||||||
\(769\) | 4536.39 | 0.212726 | 0.106363 | − | 0.994327i | \(-0.466079\pi\) | ||||
0.106363 | + | 0.994327i | \(0.466079\pi\) | |||||||
\(770\) | −417.020 | −0.0195173 | ||||||||
\(771\) | 2906.58 | 0.135769 | ||||||||
\(772\) | −8196.03 | −0.382100 | ||||||||
\(773\) | 31238.9 | 1.45354 | 0.726768 | − | 0.686883i | \(-0.241022\pi\) | ||||
0.726768 | + | 0.686883i | \(0.241022\pi\) | |||||||
\(774\) | 752.573 | 0.0349492 | ||||||||
\(775\) | 4951.97 | 0.229523 | ||||||||
\(776\) | 5330.86 | 0.246607 | ||||||||
\(777\) | −3268.98 | −0.150932 | ||||||||
\(778\) | 1821.73 | 0.0839490 | ||||||||
\(779\) | −649.155 | −0.0298567 | ||||||||
\(780\) | −9648.78 | −0.442926 | ||||||||
\(781\) | 34249.2 | 1.56919 | ||||||||
\(782\) | −3691.64 | −0.168814 | ||||||||
\(783\) | −2461.51 | −0.112347 | ||||||||
\(784\) | 3070.62 | 0.139879 | ||||||||
\(785\) | −8954.70 | −0.407143 | ||||||||
\(786\) | −347.656 | −0.0157767 | ||||||||
\(787\) | 39597.2 | 1.79350 | 0.896752 | − | 0.442534i | \(-0.145921\pi\) | ||||
0.896752 | + | 0.442534i | \(0.145921\pi\) | |||||||
\(788\) | 1636.16 | 0.0739669 | ||||||||
\(789\) | −14490.5 | −0.653836 | ||||||||
\(790\) | 1518.22 | 0.0683745 | ||||||||
\(791\) | 13677.2 | 0.614799 | ||||||||
\(792\) | 1709.76 | 0.0767093 | ||||||||
\(793\) | 12483.3 | 0.559008 | ||||||||
\(794\) | 1511.77 | 0.0675700 | ||||||||
\(795\) | −3004.53 | −0.134037 | ||||||||
\(796\) | 14549.0 | 0.647832 | ||||||||
\(797\) | −16567.0 | −0.736302 | −0.368151 | − | 0.929766i | \(-0.620009\pi\) | ||||
−0.368151 | + | 0.929766i | \(0.620009\pi\) | |||||||
\(798\) | −20.5127 | −0.000909951 0 | ||||||||
\(799\) | −13418.1 | −0.594115 | ||||||||
\(800\) | 1122.62 | 0.0496133 | ||||||||
\(801\) | −8247.96 | −0.363829 | ||||||||
\(802\) | −2589.63 | −0.114019 | ||||||||
\(803\) | 3068.72 | 0.134860 | ||||||||
\(804\) | −17510.3 | −0.768087 | ||||||||
\(805\) | −7165.25 | −0.313717 | ||||||||
\(806\) | −3786.19 | −0.165463 | ||||||||
\(807\) | −14324.9 | −0.624859 | ||||||||
\(808\) | 5191.20 | 0.226022 | ||||||||
\(809\) | −12141.6 | −0.527657 | −0.263828 | − | 0.964570i | \(-0.584985\pi\) | ||||
−0.263828 | + | 0.964570i | \(0.584985\pi\) | |||||||
\(810\) | −95.6075 | −0.00414729 | ||||||||
\(811\) | 30295.6 | 1.31174 | 0.655870 | − | 0.754873i | \(-0.272302\pi\) | ||||
0.655870 | + | 0.754873i | \(0.272302\pi\) | |||||||
\(812\) | −5069.80 | −0.219107 | ||||||||
\(813\) | 425.726 | 0.0183651 | ||||||||
\(814\) | −1854.73 | −0.0798629 | ||||||||
\(815\) | 2455.54 | 0.105538 | ||||||||
\(816\) | 14360.5 | 0.616077 | ||||||||
\(817\) | 1465.67 | 0.0627628 | ||||||||
\(818\) | −94.5106 | −0.00403971 | ||||||||
\(819\) | 5101.15 | 0.217642 | ||||||||
\(820\) | −6231.70 | −0.265391 | ||||||||
\(821\) | −14914.8 | −0.634018 | −0.317009 | − | 0.948423i | \(-0.602678\pi\) | ||||
−0.317009 | + | 0.948423i | \(0.602678\pi\) | |||||||
\(822\) | 1296.81 | 0.0550260 | ||||||||
\(823\) | −31077.6 | −1.31628 | −0.658138 | − | 0.752897i | \(-0.728656\pi\) | ||||
−0.658138 | + | 0.752897i | \(0.728656\pi\) | |||||||
\(824\) | 4924.85 | 0.208210 | ||||||||
\(825\) | −3785.41 | −0.159747 | ||||||||
\(826\) | 516.396 | 0.0217527 | ||||||||
\(827\) | 15527.8 | 0.652908 | 0.326454 | − | 0.945213i | \(-0.394146\pi\) | ||||
0.326454 | + | 0.945213i | \(0.394146\pi\) | |||||||
\(828\) | 14637.3 | 0.614348 | ||||||||
\(829\) | −40221.5 | −1.68510 | −0.842551 | − | 0.538617i | \(-0.818947\pi\) | ||||
−0.842551 | + | 0.538617i | \(0.818947\pi\) | |||||||
\(830\) | −137.120 | −0.00573436 | ||||||||
\(831\) | −10863.4 | −0.453486 | ||||||||
\(832\) | 39734.2 | 1.65569 | ||||||||
\(833\) | 3742.96 | 0.155685 | ||||||||
\(834\) | −2160.62 | −0.0897075 | ||||||||
\(835\) | 4130.29 | 0.171179 | ||||||||
\(836\) | 1659.10 | 0.0686377 | ||||||||
\(837\) | 5348.13 | 0.220858 | ||||||||
\(838\) | −3733.51 | −0.153904 | ||||||||
\(839\) | −21153.7 | −0.870448 | −0.435224 | − | 0.900322i | \(-0.643331\pi\) | ||||
−0.435224 | + | 0.900322i | \(0.643331\pi\) | |||||||
\(840\) | −395.213 | −0.0162335 | ||||||||
\(841\) | −16077.5 | −0.659213 | ||||||||
\(842\) | 457.152 | 0.0187108 | ||||||||
\(843\) | 17372.6 | 0.709780 | ||||||||
\(844\) | −8184.10 | −0.333778 | ||||||||
\(845\) | −21796.2 | −0.887351 | ||||||||
\(846\) | −373.208 | −0.0151669 | ||||||||
\(847\) | −8515.06 | −0.345432 | ||||||||
\(848\) | 12552.0 | 0.508301 | ||||||||
\(849\) | 1578.13 | 0.0637942 | ||||||||
\(850\) | 450.813 | 0.0181915 | ||||||||
\(851\) | −31868.1 | −1.28369 | ||||||||
\(852\) | 16172.4 | 0.650302 | ||||||||
\(853\) | 636.075 | 0.0255320 | 0.0127660 | − | 0.999919i | \(-0.495936\pi\) | ||||
0.0127660 | + | 0.999919i | \(0.495936\pi\) | |||||||
\(854\) | 254.763 | 0.0102082 | ||||||||
\(855\) | −186.200 | −0.00744782 | ||||||||
\(856\) | −4763.83 | −0.190215 | ||||||||
\(857\) | −3941.46 | −0.157104 | −0.0785518 | − | 0.996910i | \(-0.525030\pi\) | ||||
−0.0785518 | + | 0.996910i | \(0.525030\pi\) | |||||||
\(858\) | 2894.26 | 0.115161 | ||||||||
\(859\) | −21781.6 | −0.865165 | −0.432583 | − | 0.901594i | \(-0.642398\pi\) | ||||
−0.432583 | + | 0.901594i | \(0.642398\pi\) | |||||||
\(860\) | 14070.0 | 0.557886 | ||||||||
\(861\) | 3294.59 | 0.130406 | ||||||||
\(862\) | 479.432 | 0.0189438 | ||||||||
\(863\) | −44697.9 | −1.76308 | −0.881538 | − | 0.472112i | \(-0.843492\pi\) | ||||
−0.881538 | + | 0.472112i | \(0.843492\pi\) | |||||||
\(864\) | 1212.43 | 0.0477404 | ||||||||
\(865\) | −14590.0 | −0.573498 | ||||||||
\(866\) | −2545.79 | −0.0998953 | ||||||||
\(867\) | 2765.92 | 0.108345 | ||||||||
\(868\) | 11015.2 | 0.430736 | ||||||||
\(869\) | 64920.1 | 2.53425 | ||||||||
\(870\) | 322.825 | 0.0125802 | ||||||||
\(871\) | −59490.3 | −2.31430 | ||||||||
\(872\) | −7788.78 | −0.302478 | ||||||||
\(873\) | −12746.7 | −0.494171 | ||||||||
\(874\) | −199.971 | −0.00773926 | ||||||||
\(875\) | 875.000 | 0.0338062 | ||||||||
\(876\) | 1449.04 | 0.0558888 | ||||||||
\(877\) | −20171.7 | −0.776682 | −0.388341 | − | 0.921516i | \(-0.626952\pi\) | ||||
−0.388341 | + | 0.921516i | \(0.626952\pi\) | |||||||
\(878\) | −1488.22 | −0.0572038 | ||||||||
\(879\) | 5744.63 | 0.220434 | ||||||||
\(880\) | 15814.3 | 0.605797 | ||||||||
\(881\) | 11577.6 | 0.442744 | 0.221372 | − | 0.975189i | \(-0.428946\pi\) | ||||
0.221372 | + | 0.975189i | \(0.428946\pi\) | |||||||
\(882\) | 104.106 | 0.00397441 | ||||||||
\(883\) | −35388.3 | −1.34871 | −0.674355 | − | 0.738407i | \(-0.735578\pi\) | ||||
−0.674355 | + | 0.738407i | \(0.735578\pi\) | |||||||
\(884\) | 49136.1 | 1.86949 | ||||||||
\(885\) | 4687.48 | 0.178043 | ||||||||
\(886\) | 3657.83 | 0.138699 | ||||||||
\(887\) | −41705.0 | −1.57871 | −0.789356 | − | 0.613936i | \(-0.789585\pi\) | ||||
−0.789356 | + | 0.613936i | \(0.789585\pi\) | |||||||
\(888\) | −1757.74 | −0.0664257 | ||||||||
\(889\) | −1569.75 | −0.0592215 | ||||||||
\(890\) | 1081.71 | 0.0407405 | ||||||||
\(891\) | −4088.24 | −0.153716 | ||||||||
\(892\) | −42650.2 | −1.60093 | ||||||||
\(893\) | −726.838 | −0.0272371 | ||||||||
\(894\) | 1591.02 | 0.0595207 | ||||||||
\(895\) | −4778.72 | −0.178475 | ||||||||
\(896\) | 3325.58 | 0.123995 | ||||||||
\(897\) | 49729.2 | 1.85107 | ||||||||
\(898\) | −57.1328 | −0.00212310 | ||||||||
\(899\) | −18058.3 | −0.669942 | ||||||||
\(900\) | −1787.46 | −0.0662023 | ||||||||
\(901\) | 15300.5 | 0.565740 | ||||||||
\(902\) | 1869.27 | 0.0690020 | ||||||||
\(903\) | −7438.55 | −0.274130 | ||||||||
\(904\) | 7354.31 | 0.270576 | ||||||||
\(905\) | −1030.40 | −0.0378472 | ||||||||
\(906\) | −928.830 | −0.0340600 | ||||||||
\(907\) | −28645.1 | −1.04867 | −0.524336 | − | 0.851511i | \(-0.675687\pi\) | ||||
−0.524336 | + | 0.851511i | \(0.675687\pi\) | |||||||
\(908\) | 7405.02 | 0.270643 | ||||||||
\(909\) | −12412.8 | −0.452921 | ||||||||
\(910\) | −669.010 | −0.0243708 | ||||||||
\(911\) | 13337.8 | 0.485074 | 0.242537 | − | 0.970142i | \(-0.422020\pi\) | ||||
0.242537 | + | 0.970142i | \(0.422020\pi\) | |||||||
\(912\) | 777.887 | 0.0282439 | ||||||||
\(913\) | −5863.36 | −0.212540 | ||||||||
\(914\) | −2755.00 | −0.0997016 | ||||||||
\(915\) | 2312.55 | 0.0835527 | ||||||||
\(916\) | −25128.1 | −0.906394 | ||||||||
\(917\) | 3436.29 | 0.123747 | ||||||||
\(918\) | 486.878 | 0.0175048 | ||||||||
\(919\) | −28911.0 | −1.03774 | −0.518871 | − | 0.854853i | \(-0.673647\pi\) | ||||
−0.518871 | + | 0.854853i | \(0.673647\pi\) | |||||||
\(920\) | −3852.79 | −0.138068 | ||||||||
\(921\) | −18732.5 | −0.670203 | ||||||||
\(922\) | 2863.06 | 0.102267 | ||||||||
\(923\) | 54944.8 | 1.95940 | ||||||||
\(924\) | −8420.25 | −0.299790 | ||||||||
\(925\) | 3891.64 | 0.138331 | ||||||||
\(926\) | 1218.50 | 0.0432422 | ||||||||
\(927\) | −11775.9 | −0.417229 | ||||||||
\(928\) | −4093.84 | −0.144814 | ||||||||
\(929\) | 7093.88 | 0.250530 | 0.125265 | − | 0.992123i | \(-0.460022\pi\) | ||||
0.125265 | + | 0.992123i | \(0.460022\pi\) | |||||||
\(930\) | −701.401 | −0.0247310 | ||||||||
\(931\) | 202.751 | 0.00713736 | ||||||||
\(932\) | −3468.17 | −0.121892 | ||||||||
\(933\) | −28976.3 | −1.01677 | ||||||||
\(934\) | 2757.33 | 0.0965981 | ||||||||
\(935\) | 19277.1 | 0.674254 | ||||||||
\(936\) | 2742.91 | 0.0957851 | ||||||||
\(937\) | −19271.1 | −0.671888 | −0.335944 | − | 0.941882i | \(-0.609055\pi\) | ||||
−0.335944 | + | 0.941882i | \(0.609055\pi\) | |||||||
\(938\) | −1214.10 | −0.0422620 | ||||||||
\(939\) | 6595.01 | 0.229201 | ||||||||
\(940\) | −6977.43 | −0.242105 | ||||||||
\(941\) | −18115.2 | −0.627563 | −0.313782 | − | 0.949495i | \(-0.601596\pi\) | ||||
−0.313782 | + | 0.949495i | \(0.601596\pi\) | |||||||
\(942\) | 1268.35 | 0.0438695 | ||||||||
\(943\) | 32117.8 | 1.10912 | ||||||||
\(944\) | −19582.9 | −0.675180 | ||||||||
\(945\) | 945.000 | 0.0325300 | ||||||||
\(946\) | −4220.44 | −0.145051 | ||||||||
\(947\) | −2475.55 | −0.0849468 | −0.0424734 | − | 0.999098i | \(-0.513524\pi\) | ||||
−0.0424734 | + | 0.999098i | \(0.513524\pi\) | |||||||
\(948\) | 30655.1 | 1.05024 | ||||||||
\(949\) | 4923.04 | 0.168397 | ||||||||
\(950\) | 24.4199 | 0.000833984 0 | ||||||||
\(951\) | 9092.35 | 0.310031 | ||||||||
\(952\) | 2012.61 | 0.0685179 | ||||||||
\(953\) | 12866.6 | 0.437344 | 0.218672 | − | 0.975798i | \(-0.429827\pi\) | ||||
0.218672 | + | 0.975798i | \(0.429827\pi\) | |||||||
\(954\) | 425.564 | 0.0144425 | ||||||||
\(955\) | 10093.2 | 0.341997 | ||||||||
\(956\) | 15736.2 | 0.532368 | ||||||||
\(957\) | 13804.2 | 0.466277 | ||||||||
\(958\) | −4357.50 | −0.146957 | ||||||||
\(959\) | −12817.9 | −0.431606 | ||||||||
\(960\) | 7360.87 | 0.247470 | ||||||||
\(961\) | 9444.26 | 0.317017 | ||||||||
\(962\) | −2975.48 | −0.0997228 | ||||||||
\(963\) | 11390.9 | 0.381169 | ||||||||
\(964\) | −42132.9 | −1.40768 | ||||||||
\(965\) | −5158.45 | −0.172079 | ||||||||
\(966\) | 1014.89 | 0.0338029 | ||||||||
\(967\) | −2142.86 | −0.0712614 | −0.0356307 | − | 0.999365i | \(-0.511344\pi\) | ||||
−0.0356307 | + | 0.999365i | \(0.511344\pi\) | |||||||
\(968\) | −4578.58 | −0.152026 | ||||||||
\(969\) | 948.215 | 0.0314356 | ||||||||
\(970\) | 1671.72 | 0.0553357 | ||||||||
\(971\) | 2879.06 | 0.0951529 | 0.0475765 | − | 0.998868i | \(-0.484850\pi\) | ||||
0.0475765 | + | 0.998868i | \(0.484850\pi\) | |||||||
\(972\) | −1930.46 | −0.0637032 | ||||||||
\(973\) | 21355.9 | 0.703636 | ||||||||
\(974\) | 2037.29 | 0.0670217 | ||||||||
\(975\) | −6072.79 | −0.199472 | ||||||||
\(976\) | −9661.18 | −0.316851 | ||||||||
\(977\) | 48741.1 | 1.59607 | 0.798037 | − | 0.602608i | \(-0.205872\pi\) | ||||
0.798037 | + | 0.602608i | \(0.205872\pi\) | |||||||
\(978\) | −347.805 | −0.0113718 | ||||||||
\(979\) | 46254.7 | 1.51002 | ||||||||
\(980\) | 1946.35 | 0.0634426 | ||||||||
\(981\) | 18623.9 | 0.606131 | ||||||||
\(982\) | 4202.40 | 0.136562 | ||||||||
\(983\) | −45756.8 | −1.48466 | −0.742328 | − | 0.670037i | \(-0.766278\pi\) | ||||
−0.742328 | + | 0.670037i | \(0.766278\pi\) | |||||||
\(984\) | 1771.52 | 0.0573922 | ||||||||
\(985\) | 1029.78 | 0.0333110 | ||||||||
\(986\) | −1643.97 | −0.0530982 | ||||||||
\(987\) | 3688.85 | 0.118964 | ||||||||
\(988\) | 2661.63 | 0.0857062 | ||||||||
\(989\) | −72515.7 | −2.33151 | ||||||||
\(990\) | 536.168 | 0.0172127 | ||||||||
\(991\) | −51552.1 | −1.65248 | −0.826240 | − | 0.563319i | \(-0.809524\pi\) | ||||
−0.826240 | + | 0.563319i | \(0.809524\pi\) | |||||||
\(992\) | 8894.70 | 0.284684 | ||||||||
\(993\) | 14261.2 | 0.455756 | ||||||||
\(994\) | 1121.33 | 0.0357812 | ||||||||
\(995\) | 9156.88 | 0.291751 | ||||||||
\(996\) | −2768.67 | −0.0880808 | ||||||||
\(997\) | 25565.3 | 0.812097 | 0.406048 | − | 0.913852i | \(-0.366906\pi\) | ||||
0.406048 | + | 0.913852i | \(0.366906\pi\) | |||||||
\(998\) | 47.2531 | 0.00149877 | ||||||||
\(999\) | 4202.97 | 0.133109 |
(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 | 105.4.a.d.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 315.4.a.l.1.1 | 2 | |||
4.3 | odd | 2 | 1680.4.a.bd.1.2 | 2 | |||
5.2 | odd | 4 | 525.4.d.k.274.3 | 4 | |||
5.3 | odd | 4 | 525.4.d.k.274.2 | 4 | |||
5.4 | even | 2 | 525.4.a.o.1.1 | 2 | |||
7.6 | odd | 2 | 735.4.a.m.1.2 | 2 | |||
15.14 | odd | 2 | 1575.4.a.n.1.2 | 2 | |||
21.20 | even | 2 | 2205.4.a.be.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.d.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
315.4.a.l.1.1 | 2 | 3.2 | odd | 2 | |||
525.4.a.o.1.1 | 2 | 5.4 | even | 2 | |||
525.4.d.k.274.2 | 4 | 5.3 | odd | 4 | |||
525.4.d.k.274.3 | 4 | 5.2 | odd | 4 | |||
735.4.a.m.1.2 | 2 | 7.6 | odd | 2 | |||
1575.4.a.n.1.2 | 2 | 15.14 | odd | 2 | |||
1680.4.a.bd.1.2 | 2 | 4.3 | odd | 2 | |||
2205.4.a.be.1.1 | 2 | 21.20 | even | 2 |