Newspace parameters
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(14.8441897358\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-expansion
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.70607 | 1.91348 | 0.956740 | − | 0.290943i | \(-0.0939690\pi\) | ||||
0.956740 | + | 0.290943i | \(0.0939690\pi\) | |||||||
\(3\) | 0.960218 | 0.554382 | 0.277191 | − | 0.960815i | \(-0.410597\pi\) | ||||
0.277191 | + | 0.960815i | \(0.410597\pi\) | |||||||
\(4\) | 5.32282 | 2.66141 | ||||||||
\(5\) | 3.57279 | 1.59780 | 0.798900 | − | 0.601464i | \(-0.205416\pi\) | ||||
0.798900 | + | 0.601464i | \(0.205416\pi\) | |||||||
\(6\) | 2.59842 | 1.06080 | ||||||||
\(7\) | −3.95601 | −1.49523 | −0.747616 | − | 0.664131i | \(-0.768802\pi\) | ||||
−0.747616 | + | 0.664131i | \(0.768802\pi\) | |||||||
\(8\) | 8.99178 | 3.17907 | ||||||||
\(9\) | −2.07798 | −0.692661 | ||||||||
\(10\) | 9.66821 | 3.05736 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 5.11106 | 1.47544 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −10.7053 | −2.86110 | ||||||||
\(15\) | 3.43065 | 0.885791 | ||||||||
\(16\) | 13.6867 | 3.42169 | ||||||||
\(17\) | 2.79876 | 0.678800 | 0.339400 | − | 0.940642i | \(-0.389776\pi\) | ||||
0.339400 | + | 0.940642i | \(0.389776\pi\) | |||||||
\(18\) | −5.62316 | −1.32539 | ||||||||
\(19\) | 0.00685455 | 0.00157254 | 0.000786271 | − | 1.00000i | \(-0.499750\pi\) | ||||
0.000786271 | 1.00000i | \(0.499750\pi\) | ||||||||
\(20\) | 19.0173 | 4.25240 | ||||||||
\(21\) | −3.79863 | −0.828930 | ||||||||
\(22\) | −2.70607 | −0.576936 | ||||||||
\(23\) | −3.94433 | −0.822449 | −0.411224 | − | 0.911534i | \(-0.634899\pi\) | ||||
−0.411224 | + | 0.911534i | \(0.634899\pi\) | |||||||
\(24\) | 8.63406 | 1.76242 | ||||||||
\(25\) | 7.76481 | 1.55296 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.87597 | −0.938381 | ||||||||
\(28\) | −21.0571 | −3.97942 | ||||||||
\(29\) | 6.09411 | 1.13165 | 0.565824 | − | 0.824526i | \(-0.308558\pi\) | ||||
0.565824 | + | 0.824526i | \(0.308558\pi\) | |||||||
\(30\) | 9.28359 | 1.69494 | ||||||||
\(31\) | −0.242210 | −0.0435022 | −0.0217511 | − | 0.999763i | \(-0.506924\pi\) | ||||
−0.0217511 | + | 0.999763i | \(0.506924\pi\) | |||||||
\(32\) | 19.0537 | 3.36826 | ||||||||
\(33\) | −0.960218 | −0.167152 | ||||||||
\(34\) | 7.57365 | 1.29887 | ||||||||
\(35\) | −14.1340 | −2.38908 | ||||||||
\(36\) | −11.0607 | −1.84345 | ||||||||
\(37\) | −0.801720 | −0.131802 | −0.0659010 | − | 0.997826i | \(-0.520992\pi\) | ||||
−0.0659010 | + | 0.997826i | \(0.520992\pi\) | |||||||
\(38\) | 0.0185489 | 0.00300903 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 32.1257 | 5.07952 | ||||||||
\(41\) | 6.58954 | 1.02911 | 0.514557 | − | 0.857456i | \(-0.327956\pi\) | ||||
0.514557 | + | 0.857456i | \(0.327956\pi\) | |||||||
\(42\) | −10.2794 | −1.58614 | ||||||||
\(43\) | −6.24920 | −0.952994 | −0.476497 | − | 0.879176i | \(-0.658094\pi\) | ||||
−0.476497 | + | 0.879176i | \(0.658094\pi\) | |||||||
\(44\) | −5.32282 | −0.802445 | ||||||||
\(45\) | −7.42419 | −1.10673 | ||||||||
\(46\) | −10.6736 | −1.57374 | ||||||||
\(47\) | −6.29173 | −0.917743 | −0.458872 | − | 0.888503i | \(-0.651746\pi\) | ||||
−0.458872 | + | 0.888503i | \(0.651746\pi\) | |||||||
\(48\) | 13.1423 | 1.89692 | ||||||||
\(49\) | 8.65004 | 1.23572 | ||||||||
\(50\) | 21.0121 | 2.97156 | ||||||||
\(51\) | 2.68742 | 0.376315 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.02538 | 1.23973 | 0.619865 | − | 0.784708i | \(-0.287187\pi\) | ||||
0.619865 | + | 0.784708i | \(0.287187\pi\) | |||||||
\(54\) | −13.1947 | −1.79557 | ||||||||
\(55\) | −3.57279 | −0.481755 | ||||||||
\(56\) | −35.5716 | −4.75345 | ||||||||
\(57\) | 0.00658186 | 0.000871789 0 | ||||||||
\(58\) | 16.4911 | 2.16539 | ||||||||
\(59\) | −4.00551 | −0.521472 | −0.260736 | − | 0.965410i | \(-0.583965\pi\) | ||||
−0.260736 | + | 0.965410i | \(0.583965\pi\) | |||||||
\(60\) | 18.2607 | 2.35745 | ||||||||
\(61\) | −6.32993 | −0.810464 | −0.405232 | − | 0.914214i | \(-0.632809\pi\) | ||||
−0.405232 | + | 0.914214i | \(0.632809\pi\) | |||||||
\(62\) | −0.655437 | −0.0832405 | ||||||||
\(63\) | 8.22052 | 1.03569 | ||||||||
\(64\) | 24.1873 | 3.02341 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.59842 | −0.319843 | ||||||||
\(67\) | −8.97718 | −1.09674 | −0.548368 | − | 0.836237i | \(-0.684751\pi\) | ||||
−0.548368 | + | 0.836237i | \(0.684751\pi\) | |||||||
\(68\) | 14.8973 | 1.80656 | ||||||||
\(69\) | −3.78741 | −0.455951 | ||||||||
\(70\) | −38.2476 | −4.57146 | ||||||||
\(71\) | −8.03382 | −0.953439 | −0.476720 | − | 0.879055i | \(-0.658174\pi\) | ||||
−0.476720 | + | 0.879055i | \(0.658174\pi\) | |||||||
\(72\) | −18.6847 | −2.20202 | ||||||||
\(73\) | −0.166373 | −0.0194725 | −0.00973623 | − | 0.999953i | \(-0.503099\pi\) | ||||
−0.00973623 | + | 0.999953i | \(0.503099\pi\) | |||||||
\(74\) | −2.16951 | −0.252200 | ||||||||
\(75\) | 7.45591 | 0.860934 | ||||||||
\(76\) | 0.0364855 | 0.00418518 | ||||||||
\(77\) | 3.95601 | 0.450830 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.30756 | −1.04718 | −0.523591 | − | 0.851970i | \(-0.675408\pi\) | ||||
−0.523591 | + | 0.851970i | \(0.675408\pi\) | |||||||
\(80\) | 48.8998 | 5.46717 | ||||||||
\(81\) | 1.55195 | 0.172439 | ||||||||
\(82\) | 17.8318 | 1.96919 | ||||||||
\(83\) | −0.547068 | −0.0600485 | −0.0300242 | − | 0.999549i | \(-0.509558\pi\) | ||||
−0.0300242 | + | 0.999549i | \(0.509558\pi\) | |||||||
\(84\) | −20.2194 | −2.20612 | ||||||||
\(85\) | 9.99939 | 1.08459 | ||||||||
\(86\) | −16.9108 | −1.82354 | ||||||||
\(87\) | 5.85167 | 0.627365 | ||||||||
\(88\) | −8.99178 | −0.958527 | ||||||||
\(89\) | −17.0658 | −1.80897 | −0.904487 | − | 0.426502i | \(-0.859746\pi\) | ||||
−0.904487 | + | 0.426502i | \(0.859746\pi\) | |||||||
\(90\) | −20.0904 | −2.11771 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −20.9949 | −2.18887 | ||||||||
\(93\) | −0.232574 | −0.0241168 | ||||||||
\(94\) | −17.0259 | −1.75608 | ||||||||
\(95\) | 0.0244899 | 0.00251261 | ||||||||
\(96\) | 18.2957 | 1.86730 | ||||||||
\(97\) | −8.78558 | −0.892040 | −0.446020 | − | 0.895023i | \(-0.647159\pi\) | ||||
−0.446020 | + | 0.895023i | \(0.647159\pi\) | |||||||
\(98\) | 23.4076 | 2.36453 | ||||||||
\(99\) | 2.07798 | 0.208845 | ||||||||
\(100\) | 41.3307 | 4.13307 | ||||||||
\(101\) | −0.664826 | −0.0661527 | −0.0330763 | − | 0.999453i | \(-0.510530\pi\) | ||||
−0.0330763 | + | 0.999453i | \(0.510530\pi\) | |||||||
\(102\) | 7.27236 | 0.720071 | ||||||||
\(103\) | −14.3916 | −1.41804 | −0.709021 | − | 0.705187i | \(-0.750863\pi\) | ||||
−0.709021 | + | 0.705187i | \(0.750863\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13.5717 | −1.32446 | ||||||||
\(106\) | 24.4233 | 2.37220 | ||||||||
\(107\) | 7.11634 | 0.687962 | 0.343981 | − | 0.938977i | \(-0.388224\pi\) | ||||
0.343981 | + | 0.938977i | \(0.388224\pi\) | |||||||
\(108\) | −25.9539 | −2.49741 | ||||||||
\(109\) | 7.76979 | 0.744211 | 0.372105 | − | 0.928191i | \(-0.378636\pi\) | ||||
0.372105 | + | 0.928191i | \(0.378636\pi\) | |||||||
\(110\) | −9.66821 | −0.921828 | ||||||||
\(111\) | −0.769826 | −0.0730686 | ||||||||
\(112\) | −54.1450 | −5.11622 | ||||||||
\(113\) | −13.4649 | −1.26667 | −0.633334 | − | 0.773878i | \(-0.718314\pi\) | ||||
−0.633334 | + | 0.773878i | \(0.718314\pi\) | |||||||
\(114\) | 0.0178110 | 0.00166815 | ||||||||
\(115\) | −14.0922 | −1.31411 | ||||||||
\(116\) | 32.4378 | 3.01178 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.8392 | −0.997827 | ||||||||
\(119\) | −11.0720 | −1.01496 | ||||||||
\(120\) | 30.8477 | 2.81599 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −17.1292 | −1.55081 | ||||||||
\(123\) | 6.32740 | 0.570522 | ||||||||
\(124\) | −1.28924 | −0.115777 | ||||||||
\(125\) | 9.87808 | 0.883523 | ||||||||
\(126\) | 22.2453 | 1.98177 | ||||||||
\(127\) | 13.1288 | 1.16499 | 0.582495 | − | 0.812834i | \(-0.302076\pi\) | ||||
0.582495 | + | 0.812834i | \(0.302076\pi\) | |||||||
\(128\) | 27.3450 | 2.41698 | ||||||||
\(129\) | −6.00059 | −0.528323 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.5571 | 1.44660 | 0.723300 | − | 0.690534i | \(-0.242625\pi\) | ||||
0.723300 | + | 0.690534i | \(0.242625\pi\) | |||||||
\(132\) | −5.11106 | −0.444861 | ||||||||
\(133\) | −0.0271167 | −0.00235132 | ||||||||
\(134\) | −24.2929 | −2.09859 | ||||||||
\(135\) | −17.4208 | −1.49934 | ||||||||
\(136\) | 25.1659 | 2.15796 | ||||||||
\(137\) | 17.9393 | 1.53266 | 0.766330 | − | 0.642447i | \(-0.222081\pi\) | ||||
0.766330 | + | 0.642447i | \(0.222081\pi\) | |||||||
\(138\) | −10.2490 | −0.872453 | ||||||||
\(139\) | 8.20712 | 0.696119 | 0.348059 | − | 0.937473i | \(-0.386841\pi\) | ||||
0.348059 | + | 0.937473i | \(0.386841\pi\) | |||||||
\(140\) | −75.2327 | −6.35832 | ||||||||
\(141\) | −6.04143 | −0.508780 | ||||||||
\(142\) | −21.7401 | −1.82439 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −28.4408 | −2.37007 | ||||||||
\(145\) | 21.7730 | 1.80815 | ||||||||
\(146\) | −0.450216 | −0.0372602 | ||||||||
\(147\) | 8.30592 | 0.685061 | ||||||||
\(148\) | −4.26741 | −0.350779 | ||||||||
\(149\) | −6.02019 | −0.493193 | −0.246597 | − | 0.969118i | \(-0.579312\pi\) | ||||
−0.246597 | + | 0.969118i | \(0.579312\pi\) | |||||||
\(150\) | 20.1762 | 1.64738 | ||||||||
\(151\) | 9.53009 | 0.775547 | 0.387774 | − | 0.921755i | \(-0.373244\pi\) | ||||
0.387774 | + | 0.921755i | \(0.373244\pi\) | |||||||
\(152\) | 0.0616346 | 0.00499923 | ||||||||
\(153\) | −5.81578 | −0.470178 | ||||||||
\(154\) | 10.7053 | 0.862654 | ||||||||
\(155\) | −0.865364 | −0.0695077 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.58684 | 0.605496 | 0.302748 | − | 0.953071i | \(-0.402096\pi\) | ||||
0.302748 | + | 0.953071i | \(0.402096\pi\) | |||||||
\(158\) | −25.1869 | −2.00376 | ||||||||
\(159\) | 8.66633 | 0.687284 | ||||||||
\(160\) | 68.0750 | 5.38180 | ||||||||
\(161\) | 15.6038 | 1.22975 | ||||||||
\(162\) | 4.19969 | 0.329959 | ||||||||
\(163\) | −0.420278 | −0.0329187 | −0.0164594 | − | 0.999865i | \(-0.505239\pi\) | ||||
−0.0164594 | + | 0.999865i | \(0.505239\pi\) | |||||||
\(164\) | 35.0749 | 2.73889 | ||||||||
\(165\) | −3.43065 | −0.267076 | ||||||||
\(166\) | −1.48040 | −0.114902 | ||||||||
\(167\) | 15.9576 | 1.23484 | 0.617420 | − | 0.786634i | \(-0.288178\pi\) | ||||
0.617420 | + | 0.786634i | \(0.288178\pi\) | |||||||
\(168\) | −34.1565 | −2.63523 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 27.0591 | 2.07534 | ||||||||
\(171\) | −0.0142436 | −0.00108924 | ||||||||
\(172\) | −33.2633 | −2.53631 | ||||||||
\(173\) | −1.43723 | −0.109270 | −0.0546352 | − | 0.998506i | \(-0.517400\pi\) | ||||
−0.0546352 | + | 0.998506i | \(0.517400\pi\) | |||||||
\(174\) | 15.8350 | 1.20045 | ||||||||
\(175\) | −30.7177 | −2.32204 | ||||||||
\(176\) | −13.6867 | −1.03168 | ||||||||
\(177\) | −3.84616 | −0.289095 | ||||||||
\(178\) | −46.1813 | −3.46144 | ||||||||
\(179\) | 16.8302 | 1.25795 | 0.628973 | − | 0.777427i | \(-0.283476\pi\) | ||||
0.628973 | + | 0.777427i | \(0.283476\pi\) | |||||||
\(180\) | −39.5176 | −2.94547 | ||||||||
\(181\) | 4.85465 | 0.360843 | 0.180422 | − | 0.983589i | \(-0.442254\pi\) | ||||
0.180422 | + | 0.983589i | \(0.442254\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.07811 | −0.449307 | ||||||||
\(184\) | −35.4665 | −2.61462 | ||||||||
\(185\) | −2.86437 | −0.210593 | ||||||||
\(186\) | −0.629362 | −0.0461471 | ||||||||
\(187\) | −2.79876 | −0.204666 | ||||||||
\(188\) | −33.4897 | −2.44249 | ||||||||
\(189\) | 19.2894 | 1.40310 | ||||||||
\(190\) | 0.0662713 | 0.00480782 | ||||||||
\(191\) | 11.5662 | 0.836898 | 0.418449 | − | 0.908240i | \(-0.362574\pi\) | ||||
0.418449 | + | 0.908240i | \(0.362574\pi\) | |||||||
\(192\) | 23.2251 | 1.67612 | ||||||||
\(193\) | −26.9954 | −1.94317 | −0.971584 | − | 0.236693i | \(-0.923936\pi\) | ||||
−0.971584 | + | 0.236693i | \(0.923936\pi\) | |||||||
\(194\) | −23.7744 | −1.70690 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 46.0426 | 3.28876 | ||||||||
\(197\) | −16.7441 | −1.19297 | −0.596483 | − | 0.802626i | \(-0.703436\pi\) | ||||
−0.596483 | + | 0.802626i | \(0.703436\pi\) | |||||||
\(198\) | 5.62316 | 0.399621 | ||||||||
\(199\) | 24.3915 | 1.72907 | 0.864535 | − | 0.502572i | \(-0.167613\pi\) | ||||
0.864535 | + | 0.502572i | \(0.167613\pi\) | |||||||
\(200\) | 69.8194 | 4.93698 | ||||||||
\(201\) | −8.62005 | −0.608011 | ||||||||
\(202\) | −1.79907 | −0.126582 | ||||||||
\(203\) | −24.1084 | −1.69208 | ||||||||
\(204\) | 14.3047 | 1.00153 | ||||||||
\(205\) | 23.5430 | 1.64432 | ||||||||
\(206\) | −38.9446 | −2.71340 | ||||||||
\(207\) | 8.19624 | 0.569678 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.00685455 | −0.000474139 0 | ||||||||
\(210\) | −36.7260 | −2.53434 | ||||||||
\(211\) | 20.9742 | 1.44392 | 0.721961 | − | 0.691934i | \(-0.243241\pi\) | ||||
0.721961 | + | 0.691934i | \(0.243241\pi\) | |||||||
\(212\) | 48.0404 | 3.29943 | ||||||||
\(213\) | −7.71422 | −0.528570 | ||||||||
\(214\) | 19.2573 | 1.31640 | ||||||||
\(215\) | −22.3271 | −1.52269 | ||||||||
\(216\) | −43.8436 | −2.98318 | ||||||||
\(217\) | 0.958185 | 0.0650458 | ||||||||
\(218\) | 21.0256 | 1.42403 | ||||||||
\(219\) | −0.159754 | −0.0107952 | ||||||||
\(220\) | −19.0173 | −1.28215 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2.08320 | −0.139815 | ||||||||
\(223\) | 2.16005 | 0.144647 | 0.0723237 | − | 0.997381i | \(-0.476959\pi\) | ||||
0.0723237 | + | 0.997381i | \(0.476959\pi\) | |||||||
\(224\) | −75.3769 | −5.03633 | ||||||||
\(225\) | −16.1351 | −1.07568 | ||||||||
\(226\) | −36.4369 | −2.42375 | ||||||||
\(227\) | 19.0617 | 1.26517 | 0.632586 | − | 0.774490i | \(-0.281994\pi\) | ||||
0.632586 | + | 0.774490i | \(0.281994\pi\) | |||||||
\(228\) | 0.0350340 | 0.00232019 | ||||||||
\(229\) | −18.7054 | −1.23609 | −0.618043 | − | 0.786144i | \(-0.712074\pi\) | ||||
−0.618043 | + | 0.786144i | \(0.712074\pi\) | |||||||
\(230\) | −38.1346 | −2.51452 | ||||||||
\(231\) | 3.79863 | 0.249932 | ||||||||
\(232\) | 54.7969 | 3.59759 | ||||||||
\(233\) | 29.4725 | 1.93081 | 0.965404 | − | 0.260758i | \(-0.0839725\pi\) | ||||
0.965404 | + | 0.260758i | \(0.0839725\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.4790 | −1.46637 | ||||||||
\(236\) | −21.3206 | −1.38785 | ||||||||
\(237\) | −8.93728 | −0.580539 | ||||||||
\(238\) | −29.9615 | −1.94211 | ||||||||
\(239\) | 0.858675 | 0.0555431 | 0.0277715 | − | 0.999614i | \(-0.491159\pi\) | ||||
0.0277715 | + | 0.999614i | \(0.491159\pi\) | |||||||
\(240\) | 46.9545 | 3.03090 | ||||||||
\(241\) | −6.76007 | −0.435454 | −0.217727 | − | 0.976010i | \(-0.569864\pi\) | ||||
−0.217727 | + | 0.976010i | \(0.569864\pi\) | |||||||
\(242\) | 2.70607 | 0.173953 | ||||||||
\(243\) | 16.1181 | 1.03398 | ||||||||
\(244\) | −33.6931 | −2.15698 | ||||||||
\(245\) | 30.9048 | 1.97443 | ||||||||
\(246\) | 17.1224 | 1.09168 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −2.17790 | −0.138297 | ||||||||
\(249\) | −0.525304 | −0.0332898 | ||||||||
\(250\) | 26.7308 | 1.69060 | ||||||||
\(251\) | 24.1131 | 1.52200 | 0.761002 | − | 0.648749i | \(-0.224707\pi\) | ||||
0.761002 | + | 0.648749i | \(0.224707\pi\) | |||||||
\(252\) | 43.7563 | 2.75639 | ||||||||
\(253\) | 3.94433 | 0.247978 | ||||||||
\(254\) | 35.5274 | 2.22919 | ||||||||
\(255\) | 9.60159 | 0.601275 | ||||||||
\(256\) | 25.6229 | 1.60143 | ||||||||
\(257\) | 11.8561 | 0.739563 | 0.369781 | − | 0.929119i | \(-0.379433\pi\) | ||||
0.369781 | + | 0.929119i | \(0.379433\pi\) | |||||||
\(258\) | −16.2380 | −1.01094 | ||||||||
\(259\) | 3.17161 | 0.197075 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.6634 | −0.783848 | ||||||||
\(262\) | 44.8046 | 2.76804 | ||||||||
\(263\) | 11.5619 | 0.712939 | 0.356470 | − | 0.934307i | \(-0.383980\pi\) | ||||
0.356470 | + | 0.934307i | \(0.383980\pi\) | |||||||
\(264\) | −8.63406 | −0.531390 | ||||||||
\(265\) | 32.2458 | 1.98084 | ||||||||
\(266\) | −0.0733797 | −0.00449920 | ||||||||
\(267\) | −16.3869 | −1.00286 | ||||||||
\(268\) | −47.7839 | −2.91887 | ||||||||
\(269\) | 24.0669 | 1.46739 | 0.733693 | − | 0.679481i | \(-0.237795\pi\) | ||||
0.733693 | + | 0.679481i | \(0.237795\pi\) | |||||||
\(270\) | −47.1419 | −2.86897 | ||||||||
\(271\) | −18.6610 | −1.13357 | −0.566787 | − | 0.823864i | \(-0.691814\pi\) | ||||
−0.566787 | + | 0.823864i | \(0.691814\pi\) | |||||||
\(272\) | 38.3060 | 2.32264 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 48.5451 | 2.93272 | ||||||||
\(275\) | −7.76481 | −0.468236 | ||||||||
\(276\) | −20.1597 | −1.21347 | ||||||||
\(277\) | 0.407769 | 0.0245005 | 0.0122502 | − | 0.999925i | \(-0.496101\pi\) | ||||
0.0122502 | + | 0.999925i | \(0.496101\pi\) | |||||||
\(278\) | 22.2090 | 1.33201 | ||||||||
\(279\) | 0.503307 | 0.0301322 | ||||||||
\(280\) | −127.090 | −7.59506 | ||||||||
\(281\) | 30.5675 | 1.82350 | 0.911752 | − | 0.410741i | \(-0.134730\pi\) | ||||
0.911752 | + | 0.410741i | \(0.134730\pi\) | |||||||
\(282\) | −16.3485 | −0.973541 | ||||||||
\(283\) | 14.5967 | 0.867683 | 0.433841 | − | 0.900989i | \(-0.357158\pi\) | ||||
0.433841 | + | 0.900989i | \(0.357158\pi\) | |||||||
\(284\) | −42.7626 | −2.53749 | ||||||||
\(285\) | 0.0235156 | 0.00139294 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −26.0683 | −1.53876 | ||||||||
\(288\) | −39.5933 | −2.33306 | ||||||||
\(289\) | −9.16691 | −0.539230 | ||||||||
\(290\) | 58.9191 | 3.45985 | ||||||||
\(291\) | −8.43607 | −0.494531 | ||||||||
\(292\) | −0.885572 | −0.0518242 | ||||||||
\(293\) | 29.1102 | 1.70064 | 0.850319 | − | 0.526268i | \(-0.176409\pi\) | ||||
0.850319 | + | 0.526268i | \(0.176409\pi\) | |||||||
\(294\) | 22.4764 | 1.31085 | ||||||||
\(295\) | −14.3108 | −0.833208 | ||||||||
\(296\) | −7.20889 | −0.419008 | ||||||||
\(297\) | 4.87597 | 0.282932 | ||||||||
\(298\) | −16.2911 | −0.943715 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 39.6864 | 2.29130 | ||||||||
\(301\) | 24.7219 | 1.42495 | ||||||||
\(302\) | 25.7891 | 1.48399 | ||||||||
\(303\) | −0.638378 | −0.0366738 | ||||||||
\(304\) | 0.0938165 | 0.00538075 | ||||||||
\(305\) | −22.6155 | −1.29496 | ||||||||
\(306\) | −15.7379 | −0.899677 | ||||||||
\(307\) | −24.4200 | −1.39372 | −0.696861 | − | 0.717207i | \(-0.745420\pi\) | ||||
−0.696861 | + | 0.717207i | \(0.745420\pi\) | |||||||
\(308\) | 21.0571 | 1.19984 | ||||||||
\(309\) | −13.8190 | −0.786137 | ||||||||
\(310\) | −2.34174 | −0.133002 | ||||||||
\(311\) | 26.3470 | 1.49400 | 0.747002 | − | 0.664822i | \(-0.231493\pi\) | ||||
0.747002 | + | 0.664822i | \(0.231493\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.2630 | −1.65404 | −0.827021 | − | 0.562171i | \(-0.809966\pi\) | ||||
−0.827021 | + | 0.562171i | \(0.809966\pi\) | |||||||
\(314\) | 20.5305 | 1.15860 | ||||||||
\(315\) | 29.3702 | 1.65482 | ||||||||
\(316\) | −49.5424 | −2.78698 | ||||||||
\(317\) | 16.1999 | 0.909875 | 0.454937 | − | 0.890523i | \(-0.349662\pi\) | ||||
0.454937 | + | 0.890523i | \(0.349662\pi\) | |||||||
\(318\) | 23.4517 | 1.31511 | ||||||||
\(319\) | −6.09411 | −0.341205 | ||||||||
\(320\) | 86.4160 | 4.83080 | ||||||||
\(321\) | 6.83323 | 0.381394 | ||||||||
\(322\) | 42.2250 | 2.35311 | ||||||||
\(323\) | 0.0191843 | 0.00106744 | ||||||||
\(324\) | 8.26076 | 0.458931 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.13730 | −0.0629893 | ||||||||
\(327\) | 7.46069 | 0.412577 | ||||||||
\(328\) | 59.2517 | 3.27163 | ||||||||
\(329\) | 24.8902 | 1.37224 | ||||||||
\(330\) | −9.28359 | −0.511045 | ||||||||
\(331\) | −9.41075 | −0.517262 | −0.258631 | − | 0.965976i | \(-0.583271\pi\) | ||||
−0.258631 | + | 0.965976i | \(0.583271\pi\) | |||||||
\(332\) | −2.91194 | −0.159814 | ||||||||
\(333\) | 1.66596 | 0.0912940 | ||||||||
\(334\) | 43.1825 | 2.36284 | ||||||||
\(335\) | −32.0736 | −1.75237 | ||||||||
\(336\) | −51.9909 | −2.83634 | ||||||||
\(337\) | −34.4623 | −1.87728 | −0.938640 | − | 0.344900i | \(-0.887913\pi\) | ||||
−0.938640 | + | 0.344900i | \(0.887913\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.9292 | −0.702218 | ||||||||
\(340\) | 53.2249 | 2.88653 | ||||||||
\(341\) | 0.242210 | 0.0131164 | ||||||||
\(342\) | −0.0385443 | −0.00208424 | ||||||||
\(343\) | −6.52758 | −0.352456 | ||||||||
\(344\) | −56.1914 | −3.02964 | ||||||||
\(345\) | −13.5316 | −0.728518 | ||||||||
\(346\) | −3.88924 | −0.209087 | ||||||||
\(347\) | −17.3788 | −0.932945 | −0.466473 | − | 0.884536i | \(-0.654475\pi\) | ||||
−0.466473 | + | 0.884536i | \(0.654475\pi\) | |||||||
\(348\) | 31.1474 | 1.66967 | ||||||||
\(349\) | −1.75565 | −0.0939780 | −0.0469890 | − | 0.998895i | \(-0.514963\pi\) | ||||
−0.0469890 | + | 0.998895i | \(0.514963\pi\) | |||||||
\(350\) | −83.1242 | −4.44318 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −19.0537 | −1.01557 | ||||||||
\(353\) | 9.12962 | 0.485921 | 0.242960 | − | 0.970036i | \(-0.421882\pi\) | ||||
0.242960 | + | 0.970036i | \(0.421882\pi\) | |||||||
\(354\) | −10.4080 | −0.553178 | ||||||||
\(355\) | −28.7031 | −1.52340 | ||||||||
\(356\) | −90.8383 | −4.81442 | ||||||||
\(357\) | −10.6315 | −0.562678 | ||||||||
\(358\) | 45.5436 | 2.40706 | ||||||||
\(359\) | 5.56656 | 0.293792 | 0.146896 | − | 0.989152i | \(-0.453072\pi\) | ||||
0.146896 | + | 0.989152i | \(0.453072\pi\) | |||||||
\(360\) | −66.7566 | −3.51838 | ||||||||
\(361\) | −19.0000 | −0.999998 | ||||||||
\(362\) | 13.1370 | 0.690467 | ||||||||
\(363\) | 0.960218 | 0.0503984 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.594415 | −0.0311131 | ||||||||
\(366\) | −16.4478 | −0.859740 | ||||||||
\(367\) | −10.8050 | −0.564017 | −0.282009 | − | 0.959412i | \(-0.591001\pi\) | ||||
−0.282009 | + | 0.959412i | \(0.591001\pi\) | |||||||
\(368\) | −53.9850 | −2.81416 | ||||||||
\(369\) | −13.6930 | −0.712827 | ||||||||
\(370\) | −7.75120 | −0.402966 | ||||||||
\(371\) | −35.7045 | −1.85369 | ||||||||
\(372\) | −1.23795 | −0.0641847 | ||||||||
\(373\) | 3.71923 | 0.192574 | 0.0962872 | − | 0.995354i | \(-0.469303\pi\) | ||||
0.0962872 | + | 0.995354i | \(0.469303\pi\) | |||||||
\(374\) | −7.57365 | −0.391624 | ||||||||
\(375\) | 9.48511 | 0.489809 | ||||||||
\(376\) | −56.5738 | −2.91757 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 52.1985 | 2.68480 | ||||||||
\(379\) | −6.49327 | −0.333537 | −0.166768 | − | 0.985996i | \(-0.553333\pi\) | ||||
−0.166768 | + | 0.985996i | \(0.553333\pi\) | |||||||
\(380\) | 0.130355 | 0.00668707 | ||||||||
\(381\) | 12.6065 | 0.645850 | ||||||||
\(382\) | 31.2988 | 1.60139 | ||||||||
\(383\) | −4.15841 | −0.212485 | −0.106242 | − | 0.994340i | \(-0.533882\pi\) | ||||
−0.106242 | + | 0.994340i | \(0.533882\pi\) | |||||||
\(384\) | 26.2572 | 1.33993 | ||||||||
\(385\) | 14.1340 | 0.720335 | ||||||||
\(386\) | −73.0514 | −3.71822 | ||||||||
\(387\) | 12.9857 | 0.660101 | ||||||||
\(388\) | −46.7640 | −2.37408 | ||||||||
\(389\) | 12.5597 | 0.636803 | 0.318402 | − | 0.947956i | \(-0.396854\pi\) | ||||
0.318402 | + | 0.947956i | \(0.396854\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.0392 | −0.558278 | ||||||||
\(392\) | 77.7792 | 3.92844 | ||||||||
\(393\) | 15.8984 | 0.801969 | ||||||||
\(394\) | −45.3106 | −2.28272 | ||||||||
\(395\) | −33.2539 | −1.67319 | ||||||||
\(396\) | 11.0607 | 0.555822 | ||||||||
\(397\) | −18.0947 | −0.908147 | −0.454073 | − | 0.890964i | \(-0.650030\pi\) | ||||
−0.454073 | + | 0.890964i | \(0.650030\pi\) | |||||||
\(398\) | 66.0052 | 3.30854 | ||||||||
\(399\) | −0.0260379 | −0.00130353 | ||||||||
\(400\) | 106.275 | 5.31375 | ||||||||
\(401\) | 8.08415 | 0.403703 | 0.201852 | − | 0.979416i | \(-0.435304\pi\) | ||||
0.201852 | + | 0.979416i | \(0.435304\pi\) | |||||||
\(402\) | −23.3265 | −1.16342 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −3.53875 | −0.176059 | ||||||||
\(405\) | 5.54480 | 0.275523 | ||||||||
\(406\) | −65.2389 | −3.23775 | ||||||||
\(407\) | 0.801720 | 0.0397398 | ||||||||
\(408\) | 24.1647 | 1.19633 | ||||||||
\(409\) | 18.9341 | 0.936233 | 0.468116 | − | 0.883667i | \(-0.344933\pi\) | ||||
0.468116 | + | 0.883667i | \(0.344933\pi\) | |||||||
\(410\) | 63.7091 | 3.14637 | ||||||||
\(411\) | 17.2257 | 0.849679 | ||||||||
\(412\) | −76.6036 | −3.77399 | ||||||||
\(413\) | 15.8458 | 0.779722 | ||||||||
\(414\) | 22.1796 | 1.09007 | ||||||||
\(415\) | −1.95456 | −0.0959454 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.88062 | 0.385916 | ||||||||
\(418\) | −0.0185489 | −0.000907256 0 | ||||||||
\(419\) | −22.2827 | −1.08858 | −0.544292 | − | 0.838896i | \(-0.683202\pi\) | ||||
−0.544292 | + | 0.838896i | \(0.683202\pi\) | |||||||
\(420\) | −72.2397 | −3.52494 | ||||||||
\(421\) | −16.8899 | −0.823161 | −0.411581 | − | 0.911373i | \(-0.635023\pi\) | ||||
−0.411581 | + | 0.911373i | \(0.635023\pi\) | |||||||
\(422\) | 56.7576 | 2.76292 | ||||||||
\(423\) | 13.0741 | 0.635685 | ||||||||
\(424\) | 81.1542 | 3.94119 | ||||||||
\(425\) | 21.7319 | 1.05415 | ||||||||
\(426\) | −20.8752 | −1.01141 | ||||||||
\(427\) | 25.0413 | 1.21183 | ||||||||
\(428\) | 37.8790 | 1.83095 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −60.4186 | −2.91364 | ||||||||
\(431\) | 12.8476 | 0.618846 | 0.309423 | − | 0.950924i | \(-0.399864\pi\) | ||||
0.309423 | + | 0.950924i | \(0.399864\pi\) | |||||||
\(432\) | −66.7361 | −3.21084 | ||||||||
\(433\) | 12.3159 | 0.591865 | 0.295933 | − | 0.955209i | \(-0.404370\pi\) | ||||
0.295933 | + | 0.955209i | \(0.404370\pi\) | |||||||
\(434\) | 2.59292 | 0.124464 | ||||||||
\(435\) | 20.9068 | 1.00240 | ||||||||
\(436\) | 41.3572 | 1.98065 | ||||||||
\(437\) | −0.0270366 | −0.00129333 | ||||||||
\(438\) | −0.432306 | −0.0206564 | ||||||||
\(439\) | −5.79480 | −0.276571 | −0.138285 | − | 0.990392i | \(-0.544159\pi\) | ||||
−0.138285 | + | 0.990392i | \(0.544159\pi\) | |||||||
\(440\) | −32.1257 | −1.53153 | ||||||||
\(441\) | −17.9746 | −0.855935 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.9984 | −1.23522 | −0.617612 | − | 0.786483i | \(-0.711900\pi\) | ||||
−0.617612 | + | 0.786483i | \(0.711900\pi\) | |||||||
\(444\) | −4.09764 | −0.194465 | ||||||||
\(445\) | −60.9726 | −2.89038 | ||||||||
\(446\) | 5.84524 | 0.276780 | ||||||||
\(447\) | −5.78069 | −0.273417 | ||||||||
\(448\) | −95.6852 | −4.52070 | ||||||||
\(449\) | −23.8705 | −1.12652 | −0.563258 | − | 0.826281i | \(-0.690452\pi\) | ||||
−0.563258 | + | 0.826281i | \(0.690452\pi\) | |||||||
\(450\) | −43.6628 | −2.05828 | ||||||||
\(451\) | −6.58954 | −0.310290 | ||||||||
\(452\) | −71.6711 | −3.37112 | ||||||||
\(453\) | 9.15096 | 0.429949 | ||||||||
\(454\) | 51.5824 | 2.42088 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.0591826 | 0.00277148 | ||||||||
\(457\) | −6.67322 | −0.312160 | −0.156080 | − | 0.987744i | \(-0.549886\pi\) | ||||
−0.156080 | + | 0.987744i | \(0.549886\pi\) | |||||||
\(458\) | −50.6181 | −2.36523 | ||||||||
\(459\) | −13.6467 | −0.636973 | ||||||||
\(460\) | −75.0104 | −3.49738 | ||||||||
\(461\) | −16.3391 | −0.760989 | −0.380495 | − | 0.924783i | \(-0.624246\pi\) | ||||
−0.380495 | + | 0.924783i | \(0.624246\pi\) | |||||||
\(462\) | 10.2794 | 0.478240 | ||||||||
\(463\) | −31.3751 | −1.45812 | −0.729062 | − | 0.684447i | \(-0.760044\pi\) | ||||
−0.729062 | + | 0.684447i | \(0.760044\pi\) | |||||||
\(464\) | 83.4085 | 3.87214 | ||||||||
\(465\) | −0.830938 | −0.0385338 | ||||||||
\(466\) | 79.7547 | 3.69456 | ||||||||
\(467\) | −5.90578 | −0.273287 | −0.136643 | − | 0.990620i | \(-0.543631\pi\) | ||||
−0.136643 | + | 0.990620i | \(0.543631\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 35.5138 | 1.63988 | ||||||||
\(470\) | −60.8298 | −2.80587 | ||||||||
\(471\) | 7.28502 | 0.335676 | ||||||||
\(472\) | −36.0166 | −1.65780 | ||||||||
\(473\) | 6.24920 | 0.287338 | ||||||||
\(474\) | −24.1849 | −1.11085 | ||||||||
\(475\) | 0.0532243 | 0.00244210 | ||||||||
\(476\) | −58.9340 | −2.70123 | ||||||||
\(477\) | −18.7546 | −0.858713 | ||||||||
\(478\) | 2.32363 | 0.106281 | ||||||||
\(479\) | −5.29228 | −0.241811 | −0.120905 | − | 0.992664i | \(-0.538580\pi\) | ||||
−0.120905 | + | 0.992664i | \(0.538580\pi\) | |||||||
\(480\) | 65.3668 | 2.98357 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −18.2932 | −0.833234 | ||||||||
\(483\) | 14.9830 | 0.681752 | ||||||||
\(484\) | 5.32282 | 0.241946 | ||||||||
\(485\) | −31.3890 | −1.42530 | ||||||||
\(486\) | 43.6168 | 1.97850 | ||||||||
\(487\) | 15.4866 | 0.701763 | 0.350881 | − | 0.936420i | \(-0.385882\pi\) | ||||
0.350881 | + | 0.936420i | \(0.385882\pi\) | |||||||
\(488\) | −56.9173 | −2.57653 | ||||||||
\(489\) | −0.403558 | −0.0182495 | ||||||||
\(490\) | 83.6305 | 3.77804 | ||||||||
\(491\) | −31.9189 | −1.44048 | −0.720240 | − | 0.693725i | \(-0.755968\pi\) | ||||
−0.720240 | + | 0.693725i | \(0.755968\pi\) | |||||||
\(492\) | 33.6796 | 1.51839 | ||||||||
\(493\) | 17.0560 | 0.768162 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.42419 | 0.333692 | ||||||||
\(496\) | −3.31506 | −0.148851 | ||||||||
\(497\) | 31.7819 | 1.42561 | ||||||||
\(498\) | −1.42151 | −0.0636994 | ||||||||
\(499\) | 5.83312 | 0.261126 | 0.130563 | − | 0.991440i | \(-0.458321\pi\) | ||||
0.130563 | + | 0.991440i | \(0.458321\pi\) | |||||||
\(500\) | 52.5792 | 2.35141 | ||||||||
\(501\) | 15.3228 | 0.684573 | ||||||||
\(502\) | 65.2517 | 2.91233 | ||||||||
\(503\) | 0.285275 | 0.0127198 | 0.00635990 | − | 0.999980i | \(-0.497976\pi\) | ||||
0.00635990 | + | 0.999980i | \(0.497976\pi\) | |||||||
\(504\) | 73.9171 | 3.29253 | ||||||||
\(505\) | −2.37528 | −0.105699 | ||||||||
\(506\) | 10.6736 | 0.474500 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 69.8821 | 3.10052 | ||||||||
\(509\) | −34.6860 | −1.53743 | −0.768714 | − | 0.639592i | \(-0.779103\pi\) | ||||
−0.768714 | + | 0.639592i | \(0.779103\pi\) | |||||||
\(510\) | 25.9826 | 1.15053 | ||||||||
\(511\) | 0.658173 | 0.0291159 | ||||||||
\(512\) | 14.6475 | 0.647332 | ||||||||
\(513\) | −0.0334226 | −0.00147564 | ||||||||
\(514\) | 32.0834 | 1.41514 | ||||||||
\(515\) | −51.4180 | −2.26575 | ||||||||
\(516\) | −31.9401 | −1.40608 | ||||||||
\(517\) | 6.29173 | 0.276710 | ||||||||
\(518\) | 8.58261 | 0.377098 | ||||||||
\(519\) | −1.38005 | −0.0605775 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.6073 | 1.60379 | 0.801897 | − | 0.597463i | \(-0.203824\pi\) | ||||
0.801897 | + | 0.597463i | \(0.203824\pi\) | |||||||
\(522\) | −34.2682 | −1.49988 | ||||||||
\(523\) | −1.29679 | −0.0567048 | −0.0283524 | − | 0.999598i | \(-0.509026\pi\) | ||||
−0.0283524 | + | 0.999598i | \(0.509026\pi\) | |||||||
\(524\) | 88.1303 | 3.84999 | ||||||||
\(525\) | −29.4957 | −1.28730 | ||||||||
\(526\) | 31.2874 | 1.36420 | ||||||||
\(527\) | −0.677888 | −0.0295293 | ||||||||
\(528\) | −13.1423 | −0.571943 | ||||||||
\(529\) | −7.44230 | −0.323578 | ||||||||
\(530\) | 87.2593 | 3.79030 | ||||||||
\(531\) | 8.32337 | 0.361203 | ||||||||
\(532\) | −0.144337 | −0.00625781 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −44.3441 | −1.91896 | ||||||||
\(535\) | 25.4252 | 1.09923 | ||||||||
\(536\) | −80.7208 | −3.48661 | ||||||||
\(537\) | 16.1606 | 0.697383 | ||||||||
\(538\) | 65.1268 | 2.80781 | ||||||||
\(539\) | −8.65004 | −0.372584 | ||||||||
\(540\) | −92.7277 | −3.99037 | ||||||||
\(541\) | 23.0243 | 0.989893 | 0.494947 | − | 0.868923i | \(-0.335188\pi\) | ||||
0.494947 | + | 0.868923i | \(0.335188\pi\) | |||||||
\(542\) | −50.4980 | −2.16907 | ||||||||
\(543\) | 4.66152 | 0.200045 | ||||||||
\(544\) | 53.3270 | 2.28637 | ||||||||
\(545\) | 27.7598 | 1.18910 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.9199 | 0.723441 | 0.361721 | − | 0.932287i | \(-0.382189\pi\) | ||||
0.361721 | + | 0.932287i | \(0.382189\pi\) | |||||||
\(548\) | 95.4878 | 4.07904 | ||||||||
\(549\) | 13.1535 | 0.561377 | ||||||||
\(550\) | −21.0121 | −0.895960 | ||||||||
\(551\) | 0.0417724 | 0.00177956 | ||||||||
\(552\) | −34.0556 | −1.44950 | ||||||||
\(553\) | 36.8208 | 1.56578 | ||||||||
\(554\) | 1.10345 | 0.0468811 | ||||||||
\(555\) | −2.75042 | −0.116749 | ||||||||
\(556\) | 43.6850 | 1.85266 | ||||||||
\(557\) | 9.45511 | 0.400626 | 0.200313 | − | 0.979732i | \(-0.435804\pi\) | ||||
0.200313 | + | 0.979732i | \(0.435804\pi\) | |||||||
\(558\) | 1.36199 | 0.0576574 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −193.448 | −8.17469 | ||||||||
\(561\) | −2.68742 | −0.113463 | ||||||||
\(562\) | 82.7178 | 3.48924 | ||||||||
\(563\) | −41.4269 | −1.74593 | −0.872967 | − | 0.487779i | \(-0.837807\pi\) | ||||
−0.872967 | + | 0.487779i | \(0.837807\pi\) | |||||||
\(564\) | −32.1574 | −1.35407 | ||||||||
\(565\) | −48.1071 | −2.02388 | ||||||||
\(566\) | 39.4997 | 1.66029 | ||||||||
\(567\) | −6.13955 | −0.257837 | ||||||||
\(568\) | −72.2383 | −3.03105 | ||||||||
\(569\) | −9.18281 | −0.384963 | −0.192482 | − | 0.981301i | \(-0.561654\pi\) | ||||
−0.192482 | + | 0.981301i | \(0.561654\pi\) | |||||||
\(570\) | 0.0636349 | 0.00266537 | ||||||||
\(571\) | −17.2362 | −0.721311 | −0.360655 | − | 0.932699i | \(-0.617447\pi\) | ||||
−0.360655 | + | 0.932699i | \(0.617447\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.1060 | 0.463961 | ||||||||
\(574\) | −70.5427 | −2.94440 | ||||||||
\(575\) | −30.6269 | −1.27723 | ||||||||
\(576\) | −50.2607 | −2.09420 | ||||||||
\(577\) | 23.4108 | 0.974603 | 0.487301 | − | 0.873234i | \(-0.337981\pi\) | ||||
0.487301 | + | 0.873234i | \(0.337981\pi\) | |||||||
\(578\) | −24.8063 | −1.03181 | ||||||||
\(579\) | −25.9214 | −1.07726 | ||||||||
\(580\) | 115.893 | 4.81221 | ||||||||
\(581\) | 2.16421 | 0.0897864 | ||||||||
\(582\) | −22.8286 | −0.946276 | ||||||||
\(583\) | −9.02538 | −0.373793 | ||||||||
\(584\) | −1.49599 | −0.0619044 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 78.7743 | 3.25414 | ||||||||
\(587\) | 23.3954 | 0.965633 | 0.482817 | − | 0.875721i | \(-0.339614\pi\) | ||||
0.482817 | + | 0.875721i | \(0.339614\pi\) | |||||||
\(588\) | 44.2109 | 1.82323 | ||||||||
\(589\) | −0.00166024 | −6.84090e−5 0 | ||||||||
\(590\) | −38.7261 | −1.59433 | ||||||||
\(591\) | −16.0780 | −0.661359 | ||||||||
\(592\) | −10.9729 | −0.450985 | ||||||||
\(593\) | 37.8389 | 1.55386 | 0.776929 | − | 0.629588i | \(-0.216776\pi\) | ||||
0.776929 | + | 0.629588i | \(0.216776\pi\) | |||||||
\(594\) | 13.1947 | 0.541386 | ||||||||
\(595\) | −39.5577 | −1.62171 | ||||||||
\(596\) | −32.0444 | −1.31259 | ||||||||
\(597\) | 23.4212 | 0.958566 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.6076 | 1.00544 | 0.502720 | − | 0.864449i | \(-0.332333\pi\) | ||||
0.502720 | + | 0.864449i | \(0.332333\pi\) | |||||||
\(600\) | 67.0419 | 2.73697 | ||||||||
\(601\) | 31.6065 | 1.28926 | 0.644628 | − | 0.764496i | \(-0.277012\pi\) | ||||
0.644628 | + | 0.764496i | \(0.277012\pi\) | |||||||
\(602\) | 66.8992 | 2.72661 | ||||||||
\(603\) | 18.6544 | 0.759666 | ||||||||
\(604\) | 50.7269 | 2.06405 | ||||||||
\(605\) | 3.57279 | 0.145254 | ||||||||
\(606\) | −1.72750 | −0.0701747 | ||||||||
\(607\) | 4.05847 | 0.164728 | 0.0823640 | − | 0.996602i | \(-0.473753\pi\) | ||||
0.0823640 | + | 0.996602i | \(0.473753\pi\) | |||||||
\(608\) | 0.130605 | 0.00529673 | ||||||||
\(609\) | −23.1493 | −0.938056 | ||||||||
\(610\) | −61.1991 | −2.47788 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −30.9563 | −1.25134 | ||||||||
\(613\) | −30.8970 | −1.24792 | −0.623959 | − | 0.781457i | \(-0.714477\pi\) | ||||
−0.623959 | + | 0.781457i | \(0.714477\pi\) | |||||||
\(614\) | −66.0822 | −2.66686 | ||||||||
\(615\) | 22.6064 | 0.911580 | ||||||||
\(616\) | 35.5716 | 1.43322 | ||||||||
\(617\) | 33.9704 | 1.36759 | 0.683797 | − | 0.729672i | \(-0.260327\pi\) | ||||
0.683797 | + | 0.729672i | \(0.260327\pi\) | |||||||
\(618\) | −37.3953 | −1.50426 | ||||||||
\(619\) | 10.1642 | 0.408535 | 0.204267 | − | 0.978915i | \(-0.434519\pi\) | ||||
0.204267 | + | 0.978915i | \(0.434519\pi\) | |||||||
\(620\) | −4.60617 | −0.184988 | ||||||||
\(621\) | 19.2324 | 0.771770 | ||||||||
\(622\) | 71.2970 | 2.85875 | ||||||||
\(623\) | 67.5126 | 2.70484 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.53176 | −0.141271 | ||||||||
\(626\) | −79.1877 | −3.16498 | ||||||||
\(627\) | −0.00658186 | −0.000262854 0 | ||||||||
\(628\) | 40.3834 | 1.61147 | ||||||||
\(629\) | −2.24383 | −0.0894672 | ||||||||
\(630\) | 79.4778 | 3.16647 | ||||||||
\(631\) | −0.696721 | −0.0277360 | −0.0138680 | − | 0.999904i | \(-0.504414\pi\) | ||||
−0.0138680 | + | 0.999904i | \(0.504414\pi\) | |||||||
\(632\) | −83.6915 | −3.32907 | ||||||||
\(633\) | 20.1398 | 0.800485 | ||||||||
\(634\) | 43.8380 | 1.74103 | ||||||||
\(635\) | 46.9063 | 1.86142 | ||||||||
\(636\) | 46.1293 | 1.82914 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −16.4911 | −0.652888 | ||||||||
\(639\) | 16.6941 | 0.660410 | ||||||||
\(640\) | 97.6979 | 3.86185 | ||||||||
\(641\) | −40.2357 | −1.58922 | −0.794608 | − | 0.607123i | \(-0.792323\pi\) | ||||
−0.794608 | + | 0.607123i | \(0.792323\pi\) | |||||||
\(642\) | 18.4912 | 0.729790 | ||||||||
\(643\) | 17.1540 | 0.676486 | 0.338243 | − | 0.941059i | \(-0.390167\pi\) | ||||
0.338243 | + | 0.941059i | \(0.390167\pi\) | |||||||
\(644\) | 83.0562 | 3.27287 | ||||||||
\(645\) | −21.4388 | −0.844154 | ||||||||
\(646\) | 0.0519140 | 0.00204253 | ||||||||
\(647\) | −27.6409 | −1.08668 | −0.543338 | − | 0.839514i | \(-0.682840\pi\) | ||||
−0.543338 | + | 0.839514i | \(0.682840\pi\) | |||||||
\(648\) | 13.9548 | 0.548197 | ||||||||
\(649\) | 4.00551 | 0.157230 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.920066 | 0.0360602 | ||||||||
\(652\) | −2.23706 | −0.0876101 | ||||||||
\(653\) | −31.7645 | −1.24304 | −0.621520 | − | 0.783398i | \(-0.713485\pi\) | ||||
−0.621520 | + | 0.783398i | \(0.713485\pi\) | |||||||
\(654\) | 20.1891 | 0.789458 | ||||||||
\(655\) | 59.1549 | 2.31138 | ||||||||
\(656\) | 90.1894 | 3.52131 | ||||||||
\(657\) | 0.345720 | 0.0134878 | ||||||||
\(658\) | 67.3546 | 2.62575 | ||||||||
\(659\) | 23.2018 | 0.903813 | 0.451907 | − | 0.892065i | \(-0.350744\pi\) | ||||
0.451907 | + | 0.892065i | \(0.350744\pi\) | |||||||
\(660\) | −18.2607 | −0.710799 | ||||||||
\(661\) | −31.7645 | −1.23550 | −0.617749 | − | 0.786376i | \(-0.711955\pi\) | ||||
−0.617749 | + | 0.786376i | \(0.711955\pi\) | |||||||
\(662\) | −25.4661 | −0.989770 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.91911 | −0.190898 | ||||||||
\(665\) | −0.0968822 | −0.00375693 | ||||||||
\(666\) | 4.50820 | 0.174689 | ||||||||
\(667\) | −24.0371 | −0.930722 | ||||||||
\(668\) | 84.9396 | 3.28641 | ||||||||
\(669\) | 2.07412 | 0.0801899 | ||||||||
\(670\) | −86.7933 | −3.35312 | ||||||||
\(671\) | 6.32993 | 0.244364 | ||||||||
\(672\) | −72.3782 | −2.79205 | ||||||||
\(673\) | −17.8907 | −0.689635 | −0.344817 | − | 0.938670i | \(-0.612059\pi\) | ||||
−0.344817 | + | 0.938670i | \(0.612059\pi\) | |||||||
\(674\) | −93.2573 | −3.59214 | ||||||||
\(675\) | −37.8610 | −1.45727 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.49534 | 0.249636 | 0.124818 | − | 0.992180i | \(-0.460165\pi\) | ||||
0.124818 | + | 0.992180i | \(0.460165\pi\) | |||||||
\(678\) | −34.9874 | −1.34368 | ||||||||
\(679\) | 34.7559 | 1.33381 | ||||||||
\(680\) | 89.9123 | 3.44798 | ||||||||
\(681\) | 18.3034 | 0.701388 | ||||||||
\(682\) | 0.655437 | 0.0250980 | ||||||||
\(683\) | −18.8733 | −0.722169 | −0.361084 | − | 0.932533i | \(-0.617593\pi\) | ||||
−0.361084 | + | 0.932533i | \(0.617593\pi\) | |||||||
\(684\) | −0.0758162 | −0.00289891 | ||||||||
\(685\) | 64.0934 | 2.44888 | ||||||||
\(686\) | −17.6641 | −0.674418 | ||||||||
\(687\) | −17.9612 | −0.685264 | ||||||||
\(688\) | −85.5312 | −3.26085 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −36.6175 | −1.39400 | ||||||||
\(691\) | −15.6086 | −0.593781 | −0.296890 | − | 0.954912i | \(-0.595950\pi\) | ||||
−0.296890 | + | 0.954912i | \(0.595950\pi\) | |||||||
\(692\) | −7.65010 | −0.290813 | ||||||||
\(693\) | −8.22052 | −0.312272 | ||||||||
\(694\) | −47.0284 | −1.78517 | ||||||||
\(695\) | 29.3223 | 1.11226 | ||||||||
\(696\) | 52.6169 | 1.99444 | ||||||||
\(697\) | 18.4426 | 0.698563 | ||||||||
\(698\) | −4.75092 | −0.179825 | ||||||||
\(699\) | 28.3000 | 1.07041 | ||||||||
\(700\) | −163.505 | −6.17990 | ||||||||
\(701\) | −28.0280 | −1.05860 | −0.529301 | − | 0.848434i | \(-0.677546\pi\) | ||||
−0.529301 | + | 0.848434i | \(0.677546\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.00549543 | −0.000207264 0 | ||||||||
\(704\) | −24.1873 | −0.911593 | ||||||||
\(705\) | −21.5848 | −0.812929 | ||||||||
\(706\) | 24.7054 | 0.929800 | ||||||||
\(707\) | 2.63006 | 0.0989136 | ||||||||
\(708\) | −20.4724 | −0.769400 | ||||||||
\(709\) | −23.0101 | −0.864161 | −0.432081 | − | 0.901835i | \(-0.642220\pi\) | ||||
−0.432081 | + | 0.901835i | \(0.642220\pi\) | |||||||
\(710\) | −77.6727 | −2.91501 | ||||||||
\(711\) | 19.3409 | 0.725342 | ||||||||
\(712\) | −153.452 | −5.75086 | ||||||||
\(713\) | 0.955354 | 0.0357783 | ||||||||
\(714\) | −28.7695 | −1.07667 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 89.5839 | 3.34791 | ||||||||
\(717\) | 0.824515 | 0.0307921 | ||||||||
\(718\) | 15.0635 | 0.562165 | ||||||||
\(719\) | −10.3567 | −0.386239 | −0.193120 | − | 0.981175i | \(-0.561861\pi\) | ||||
−0.193120 | + | 0.981175i | \(0.561861\pi\) | |||||||
\(720\) | −101.613 | −3.78689 | ||||||||
\(721\) | 56.9332 | 2.12030 | ||||||||
\(722\) | −51.4152 | −1.91348 | ||||||||
\(723\) | −6.49114 | −0.241408 | ||||||||
\(724\) | 25.8404 | 0.960351 | ||||||||
\(725\) | 47.3196 | 1.75741 | ||||||||
\(726\) | 2.59842 | 0.0964363 | ||||||||
\(727\) | 4.61443 | 0.171140 | 0.0855699 | − | 0.996332i | \(-0.472729\pi\) | ||||
0.0855699 | + | 0.996332i | \(0.472729\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.8210 | 0.400779 | ||||||||
\(730\) | −1.60853 | −0.0595343 | ||||||||
\(731\) | −17.4900 | −0.646892 | ||||||||
\(732\) | −32.3527 | −1.19579 | ||||||||
\(733\) | 18.5479 | 0.685081 | 0.342541 | − | 0.939503i | \(-0.388713\pi\) | ||||
0.342541 | + | 0.939503i | \(0.388713\pi\) | |||||||
\(734\) | −29.2391 | −1.07924 | ||||||||
\(735\) | 29.6753 | 1.09459 | ||||||||
\(736\) | −75.1542 | −2.77022 | ||||||||
\(737\) | 8.97718 | 0.330679 | ||||||||
\(738\) | −37.0541 | −1.36398 | ||||||||
\(739\) | −11.4875 | −0.422573 | −0.211286 | − | 0.977424i | \(-0.567765\pi\) | ||||
−0.211286 | + | 0.977424i | \(0.567765\pi\) | |||||||
\(740\) | −15.2465 | −0.560474 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −96.6189 | −3.54699 | ||||||||
\(743\) | −6.95186 | −0.255039 | −0.127519 | − | 0.991836i | \(-0.540702\pi\) | ||||
−0.127519 | + | 0.991836i | \(0.540702\pi\) | |||||||
\(744\) | −2.09125 | −0.0766691 | ||||||||
\(745\) | −21.5089 | −0.788023 | ||||||||
\(746\) | 10.0645 | 0.368487 | ||||||||
\(747\) | 1.13680 | 0.0415932 | ||||||||
\(748\) | −14.8973 | −0.544700 | ||||||||
\(749\) | −28.1523 | −1.02866 | ||||||||
\(750\) | 25.6674 | 0.937240 | ||||||||
\(751\) | 9.67208 | 0.352939 | 0.176470 | − | 0.984306i | \(-0.443532\pi\) | ||||
0.176470 | + | 0.984306i | \(0.443532\pi\) | |||||||
\(752\) | −86.1133 | −3.14023 | ||||||||
\(753\) | 23.1538 | 0.843772 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 34.0490 | 1.23917 | ||||||||
\(756\) | 102.674 | 3.73421 | ||||||||
\(757\) | −6.61489 | −0.240422 | −0.120211 | − | 0.992748i | \(-0.538357\pi\) | ||||
−0.120211 | + | 0.992748i | \(0.538357\pi\) | |||||||
\(758\) | −17.5712 | −0.638217 | ||||||||
\(759\) | 3.78741 | 0.137474 | ||||||||
\(760\) | 0.220207 | 0.00798776 | ||||||||
\(761\) | 22.0974 | 0.801031 | 0.400515 | − | 0.916290i | \(-0.368831\pi\) | ||||
0.400515 | + | 0.916290i | \(0.368831\pi\) | |||||||
\(762\) | 34.1140 | 1.23582 | ||||||||
\(763\) | −30.7374 | −1.11277 | ||||||||
\(764\) | 61.5646 | 2.22733 | ||||||||
\(765\) | −20.7786 | −0.751250 | ||||||||
\(766\) | −11.2529 | −0.406585 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 24.6036 | 0.887806 | ||||||||
\(769\) | −2.23113 | −0.0804564 | −0.0402282 | − | 0.999191i | \(-0.512808\pi\) | ||||
−0.0402282 | + | 0.999191i | \(0.512808\pi\) | |||||||
\(770\) | 38.2476 | 1.37835 | ||||||||
\(771\) | 11.3844 | 0.410000 | ||||||||
\(772\) | −143.691 | −5.17157 | ||||||||
\(773\) | 11.1675 | 0.401667 | 0.200833 | − | 0.979625i | \(-0.435635\pi\) | ||||
0.200833 | + | 0.979625i | \(0.435635\pi\) | |||||||
\(774\) | 35.1403 | 1.26309 | ||||||||
\(775\) | −1.88071 | −0.0675572 | ||||||||
\(776\) | −78.9980 | −2.83586 | ||||||||
\(777\) | 3.04544 | 0.109255 | ||||||||
\(778\) | 33.9875 | 1.21851 | ||||||||
\(779\) | 0.0451684 | 0.00161832 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.03382 | 0.287473 | ||||||||
\(782\) | −29.8730 | −1.06825 | ||||||||
\(783\) | −29.7147 | −1.06192 | ||||||||
\(784\) | 118.391 | 4.22825 | ||||||||
\(785\) | 27.1062 | 0.967461 | ||||||||
\(786\) | 43.0222 | 1.53455 | ||||||||
\(787\) | 14.6600 | 0.522572 | 0.261286 | − | 0.965261i | \(-0.415853\pi\) | ||||
0.261286 | + | 0.965261i | \(0.415853\pi\) | |||||||
\(788\) | −89.1257 | −3.17497 | ||||||||
\(789\) | 11.1020 | 0.395241 | ||||||||
\(790\) | −89.9875 | −3.20161 | ||||||||
\(791\) | 53.2672 | 1.89396 | ||||||||
\(792\) | 18.6847 | 0.663934 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −48.9655 | −1.73772 | ||||||||
\(795\) | 30.9629 | 1.09814 | ||||||||
\(796\) | 129.832 | 4.60176 | ||||||||
\(797\) | 0.631320 | 0.0223625 | 0.0111813 | − | 0.999937i | \(-0.496441\pi\) | ||||
0.0111813 | + | 0.999937i | \(0.496441\pi\) | |||||||
\(798\) | −0.0704605 | −0.00249427 | ||||||||
\(799\) | −17.6091 | −0.622964 | ||||||||
\(800\) | 147.949 | 5.23078 | ||||||||
\(801\) | 35.4625 | 1.25300 | ||||||||
\(802\) | 21.8763 | 0.772479 | ||||||||
\(803\) | 0.166373 | 0.00587117 | ||||||||
\(804\) | −45.8829 | −1.61817 | ||||||||
\(805\) | 55.7491 | 1.96490 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.1095 | 0.813492 | ||||||||
\(808\) | −5.97797 | −0.210304 | ||||||||
\(809\) | 6.32576 | 0.222402 | 0.111201 | − | 0.993798i | \(-0.464530\pi\) | ||||
0.111201 | + | 0.993798i | \(0.464530\pi\) | |||||||
\(810\) | 15.0046 | 0.527208 | ||||||||
\(811\) | 51.1786 | 1.79712 | 0.898562 | − | 0.438846i | \(-0.144613\pi\) | ||||
0.898562 | + | 0.438846i | \(0.144613\pi\) | |||||||
\(812\) | −128.324 | −4.50331 | ||||||||
\(813\) | −17.9186 | −0.628433 | ||||||||
\(814\) | 2.16951 | 0.0760413 | ||||||||
\(815\) | −1.50156 | −0.0525975 | ||||||||
\(816\) | 36.7821 | 1.28763 | ||||||||
\(817\) | −0.0428355 | −0.00149862 | ||||||||
\(818\) | 51.2371 | 1.79146 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 125.315 | 4.37620 | ||||||||
\(821\) | −16.8298 | −0.587364 | −0.293682 | − | 0.955903i | \(-0.594881\pi\) | ||||
−0.293682 | + | 0.955903i | \(0.594881\pi\) | |||||||
\(822\) | 46.6139 | 1.62585 | ||||||||
\(823\) | 52.7955 | 1.84034 | 0.920168 | − | 0.391524i | \(-0.128052\pi\) | ||||
0.920168 | + | 0.391524i | \(0.128052\pi\) | |||||||
\(824\) | −129.406 | −4.50806 | ||||||||
\(825\) | −7.45591 | −0.259581 | ||||||||
\(826\) | 42.8799 | 1.49198 | ||||||||
\(827\) | −8.61118 | −0.299440 | −0.149720 | − | 0.988728i | \(-0.547837\pi\) | ||||
−0.149720 | + | 0.988728i | \(0.547837\pi\) | |||||||
\(828\) | 43.6271 | 1.51615 | ||||||||
\(829\) | 11.2584 | 0.391021 | 0.195510 | − | 0.980702i | \(-0.437364\pi\) | ||||
0.195510 | + | 0.980702i | \(0.437364\pi\) | |||||||
\(830\) | −5.28917 | −0.183590 | ||||||||
\(831\) | 0.391547 | 0.0135826 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.2094 | 0.838807 | ||||||||
\(834\) | 21.3255 | 0.738442 | ||||||||
\(835\) | 57.0132 | 1.97302 | ||||||||
\(836\) | −0.0364855 | −0.00126188 | ||||||||
\(837\) | 1.18101 | 0.0408216 | ||||||||
\(838\) | −60.2987 | −2.08298 | ||||||||
\(839\) | −8.76246 | −0.302514 | −0.151257 | − | 0.988494i | \(-0.548332\pi\) | ||||
−0.151257 | + | 0.988494i | \(0.548332\pi\) | |||||||
\(840\) | −122.034 | −4.21057 | ||||||||
\(841\) | 8.13815 | 0.280626 | ||||||||
\(842\) | −45.7051 | −1.57510 | ||||||||
\(843\) | 29.3515 | 1.01092 | ||||||||
\(844\) | 111.642 | 3.84287 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 35.3794 | 1.21637 | ||||||||
\(847\) | −3.95601 | −0.135930 | ||||||||
\(848\) | 123.528 | 4.24197 | ||||||||
\(849\) | 14.0160 | 0.481028 | ||||||||
\(850\) | 58.8080 | 2.01710 | ||||||||
\(851\) | 3.16224 | 0.108400 | ||||||||
\(852\) | −41.0614 | −1.40674 | ||||||||
\(853\) | −21.4641 | −0.734917 | −0.367458 | − | 0.930040i | \(-0.619772\pi\) | ||||
−0.367458 | + | 0.930040i | \(0.619772\pi\) | |||||||
\(854\) | 67.7635 | 2.31882 | ||||||||
\(855\) | −0.0508895 | −0.00174038 | ||||||||
\(856\) | 63.9885 | 2.18708 | ||||||||
\(857\) | −28.8303 | −0.984823 | −0.492412 | − | 0.870362i | \(-0.663885\pi\) | ||||
−0.492412 | + | 0.870362i | \(0.663885\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.5007 | −0.460639 | −0.230320 | − | 0.973115i | \(-0.573977\pi\) | ||||
−0.230320 | + | 0.973115i | \(0.573977\pi\) | |||||||
\(860\) | −118.843 | −4.05251 | ||||||||
\(861\) | −25.0313 | −0.853063 | ||||||||
\(862\) | 34.7665 | 1.18415 | ||||||||
\(863\) | 37.4769 | 1.27573 | 0.637864 | − | 0.770149i | \(-0.279818\pi\) | ||||
0.637864 | + | 0.770149i | \(0.279818\pi\) | |||||||
\(864\) | −92.9055 | −3.16071 | ||||||||
\(865\) | −5.13491 | −0.174592 | ||||||||
\(866\) | 33.3277 | 1.13252 | ||||||||
\(867\) | −8.80224 | −0.298940 | ||||||||
\(868\) | 5.10024 | 0.173114 | ||||||||
\(869\) | 9.30756 | 0.315737 | ||||||||
\(870\) | 56.5752 | 1.91808 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 69.8642 | 2.36590 | ||||||||
\(873\) | 18.2563 | 0.617881 | ||||||||
\(874\) | −0.0731629 | −0.00247477 | ||||||||
\(875\) | −39.0778 | −1.32107 | ||||||||
\(876\) | −0.850342 | −0.0287304 | ||||||||
\(877\) | 9.81599 | 0.331462 | 0.165731 | − | 0.986171i | \(-0.447002\pi\) | ||||
0.165731 | + | 0.986171i | \(0.447002\pi\) | |||||||
\(878\) | −15.6811 | −0.529213 | ||||||||
\(879\) | 27.9522 | 0.942803 | ||||||||
\(880\) | −48.8998 | −1.64841 | ||||||||
\(881\) | 37.2709 | 1.25569 | 0.627844 | − | 0.778339i | \(-0.283938\pi\) | ||||
0.627844 | + | 0.778339i | \(0.283938\pi\) | |||||||
\(882\) | −48.6406 | −1.63781 | ||||||||
\(883\) | −36.1317 | −1.21593 | −0.607964 | − | 0.793965i | \(-0.708013\pi\) | ||||
−0.607964 | + | 0.793965i | \(0.708013\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.7415 | −0.461916 | ||||||||
\(886\) | −70.3536 | −2.36358 | ||||||||
\(887\) | −50.2943 | −1.68872 | −0.844358 | − | 0.535779i | \(-0.820018\pi\) | ||||
−0.844358 | + | 0.535779i | \(0.820018\pi\) | |||||||
\(888\) | −6.92210 | −0.232291 | ||||||||
\(889\) | −51.9376 | −1.74193 | ||||||||
\(890\) | −164.996 | −5.53068 | ||||||||
\(891\) | −1.55195 | −0.0519924 | ||||||||
\(892\) | 11.4975 | 0.384966 | ||||||||
\(893\) | −0.0431270 | −0.00144319 | ||||||||
\(894\) | −15.6430 | −0.523179 | ||||||||
\(895\) | 60.1306 | 2.00994 | ||||||||
\(896\) | −108.177 | −3.61395 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −64.5952 | −2.15557 | ||||||||
\(899\) | −1.47605 | −0.0492291 | ||||||||
\(900\) | −85.8844 | −2.86281 | ||||||||
\(901\) | 25.2599 | 0.841529 | ||||||||
\(902\) | −17.8318 | −0.593733 | ||||||||
\(903\) | 23.7384 | 0.789965 | ||||||||
\(904\) | −121.073 | −4.02683 | ||||||||
\(905\) | 17.3446 | 0.576555 | ||||||||
\(906\) | 24.7631 | 0.822700 | ||||||||
\(907\) | −12.9985 | −0.431609 | −0.215805 | − | 0.976437i | \(-0.569237\pi\) | ||||
−0.215805 | + | 0.976437i | \(0.569237\pi\) | |||||||
\(908\) | 101.462 | 3.36714 | ||||||||
\(909\) | 1.38150 | 0.0458213 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.3455 | 1.46923 | 0.734616 | − | 0.678483i | \(-0.237362\pi\) | ||||
0.734616 | + | 0.678483i | \(0.237362\pi\) | |||||||
\(912\) | 0.0900843 | 0.00298299 | ||||||||
\(913\) | 0.547068 | 0.0181053 | ||||||||
\(914\) | −18.0582 | −0.597312 | ||||||||
\(915\) | −21.7158 | −0.717902 | ||||||||
\(916\) | −99.5653 | −3.28973 | ||||||||
\(917\) | −65.5000 | −2.16300 | ||||||||
\(918\) | −36.9289 | −1.21884 | ||||||||
\(919\) | −47.6103 | −1.57052 | −0.785260 | − | 0.619167i | \(-0.787471\pi\) | ||||
−0.785260 | + | 0.619167i | \(0.787471\pi\) | |||||||
\(920\) | −126.714 | −4.17764 | ||||||||
\(921\) | −23.4485 | −0.772654 | ||||||||
\(922\) | −44.2148 | −1.45614 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 20.2194 | 0.665171 | ||||||||
\(925\) | −6.22520 | −0.204683 | ||||||||
\(926\) | −84.9032 | −2.79009 | ||||||||
\(927\) | 29.9054 | 0.982222 | ||||||||
\(928\) | 116.116 | 3.81168 | ||||||||
\(929\) | −33.0705 | −1.08501 | −0.542503 | − | 0.840054i | \(-0.682523\pi\) | ||||
−0.542503 | + | 0.840054i | \(0.682523\pi\) | |||||||
\(930\) | −2.24858 | −0.0737337 | ||||||||
\(931\) | 0.0592921 | 0.00194322 | ||||||||
\(932\) | 156.877 | 5.13867 | ||||||||
\(933\) | 25.2989 | 0.828249 | ||||||||
\(934\) | −15.9815 | −0.522929 | ||||||||
\(935\) | −9.99939 | −0.327015 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.8560 | −1.43271 | −0.716356 | − | 0.697735i | \(-0.754191\pi\) | ||||
−0.716356 | + | 0.697735i | \(0.754191\pi\) | |||||||
\(938\) | 96.1029 | 3.13787 | ||||||||
\(939\) | −28.0989 | −0.916971 | ||||||||
\(940\) | −119.652 | −3.90261 | ||||||||
\(941\) | 27.1576 | 0.885313 | 0.442657 | − | 0.896691i | \(-0.354036\pi\) | ||||
0.442657 | + | 0.896691i | \(0.354036\pi\) | |||||||
\(942\) | 19.7138 | 0.642310 | ||||||||
\(943\) | −25.9913 | −0.846393 | ||||||||
\(944\) | −54.8223 | −1.78432 | ||||||||
\(945\) | 68.9169 | 2.24187 | ||||||||
\(946\) | 16.9108 | 0.549817 | ||||||||
\(947\) | 24.4338 | 0.793991 | 0.396996 | − | 0.917821i | \(-0.370053\pi\) | ||||
0.396996 | + | 0.917821i | \(0.370053\pi\) | |||||||
\(948\) | −47.5715 | −1.54505 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.144029 | 0.00467291 | ||||||||
\(951\) | 15.5554 | 0.504418 | ||||||||
\(952\) | −99.5565 | −3.22665 | ||||||||
\(953\) | −0.830376 | −0.0268985 | −0.0134493 | − | 0.999910i | \(-0.504281\pi\) | ||||
−0.0134493 | + | 0.999910i | \(0.504281\pi\) | |||||||
\(954\) | −50.7512 | −1.64313 | ||||||||
\(955\) | 41.3234 | 1.33720 | ||||||||
\(956\) | 4.57057 | 0.147823 | ||||||||
\(957\) | −5.85167 | −0.189158 | ||||||||
\(958\) | −14.3213 | −0.462700 | ||||||||
\(959\) | −70.9682 | −2.29168 | ||||||||
\(960\) | 82.9782 | 2.67811 | ||||||||
\(961\) | −30.9413 | −0.998108 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.7876 | −0.476524 | ||||||||
\(964\) | −35.9826 | −1.15892 | ||||||||
\(965\) | −96.4487 | −3.10479 | ||||||||
\(966\) | 40.5452 | 1.30452 | ||||||||
\(967\) | −3.68739 | −0.118578 | −0.0592892 | − | 0.998241i | \(-0.518883\pi\) | ||||
−0.0592892 | + | 0.998241i | \(0.518883\pi\) | |||||||
\(968\) | 8.99178 | 0.289007 | ||||||||
\(969\) | 0.0184211 | 0.000591771 0 | ||||||||
\(970\) | −84.9409 | −2.72729 | ||||||||
\(971\) | −10.8602 | −0.348520 | −0.174260 | − | 0.984700i | \(-0.555753\pi\) | ||||
−0.174260 | + | 0.984700i | \(0.555753\pi\) | |||||||
\(972\) | 85.7938 | 2.75184 | ||||||||
\(973\) | −32.4675 | −1.04086 | ||||||||
\(974\) | 41.9077 | 1.34281 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −86.6361 | −2.77316 | ||||||||
\(977\) | −30.9277 | −0.989466 | −0.494733 | − | 0.869045i | \(-0.664734\pi\) | ||||
−0.494733 | + | 0.869045i | \(0.664734\pi\) | |||||||
\(978\) | −1.09206 | −0.0349201 | ||||||||
\(979\) | 17.0658 | 0.545426 | ||||||||
\(980\) | 164.500 | 5.25477 | ||||||||
\(981\) | −16.1455 | −0.515485 | ||||||||
\(982\) | −86.3748 | −2.75633 | ||||||||
\(983\) | −12.9691 | −0.413650 | −0.206825 | − | 0.978378i | \(-0.566313\pi\) | ||||
−0.206825 | + | 0.978378i | \(0.566313\pi\) | |||||||
\(984\) | 56.8946 | 1.81373 | ||||||||
\(985\) | −59.8230 | −1.90612 | ||||||||
\(986\) | 46.1547 | 1.46986 | ||||||||
\(987\) | 23.9000 | 0.760745 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.6489 | 0.783789 | ||||||||
\(990\) | 20.0904 | 0.638514 | ||||||||
\(991\) | 5.95855 | 0.189279 | 0.0946397 | − | 0.995512i | \(-0.469830\pi\) | ||||
0.0946397 | + | 0.995512i | \(0.469830\pi\) | |||||||
\(992\) | −4.61500 | −0.146527 | ||||||||
\(993\) | −9.03637 | −0.286761 | ||||||||
\(994\) | 86.0041 | 2.72788 | ||||||||
\(995\) | 87.1458 | 2.76271 | ||||||||
\(996\) | −2.79610 | −0.0885977 | ||||||||
\(997\) | −6.47004 | −0.204908 | −0.102454 | − | 0.994738i | \(-0.532669\pi\) | ||||
−0.102454 | + | 0.994738i | \(0.532669\pi\) | |||||||
\(998\) | 15.7848 | 0.499660 | ||||||||
\(999\) | 3.90916 | 0.123680 |
(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 | 1859.2.a.s.1.20 | ✓ | 21 | |
13.12 | even | 2 | 1859.2.a.t.1.2 | yes | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1859.2.a.s.1.20 | ✓ | 21 | 1.1 | even | 1 | trivial | |
1859.2.a.t.1.2 | yes | 21 | 13.12 | even | 2 |