Newspace parameters
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(56.9958450655\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.12197.1 |
Defining polynomial: |
\( x^{3} - x^{2} - 15x - 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.51691\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −9.55073 | −0.854243 | −0.427122 | − | 0.904194i | \(-0.640472\pi\) | ||||
−0.427122 | + | 0.904194i | \(0.640472\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −19.1015 | −0.604041 | ||||||||
\(11\) | −35.9402 | −0.985126 | −0.492563 | − | 0.870277i | \(-0.663940\pi\) | ||||
−0.492563 | + | 0.870277i | \(0.663940\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | 6.86023 | 0.146360 | 0.0731802 | − | 0.997319i | \(-0.476685\pi\) | ||||
0.0731802 | + | 0.997319i | \(0.476685\pi\) | |||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | 28.6522 | 0.493197 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −16.4786 | −0.235097 | −0.117548 | − | 0.993067i | \(-0.537504\pi\) | ||||
−0.117548 | + | 0.993067i | \(0.537504\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | −27.6437 | −0.333784 | −0.166892 | − | 0.985975i | \(-0.553373\pi\) | ||||
−0.166892 | + | 0.985975i | \(0.553373\pi\) | |||||||
\(20\) | −38.2029 | −0.427122 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | −71.8804 | −0.696589 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | −33.7836 | −0.270269 | ||||||||
\(26\) | 13.7205 | 0.103492 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 28.0000 | 0.188982 | ||||||||
\(29\) | 307.579 | 1.96952 | 0.984758 | − | 0.173932i | \(-0.0556472\pi\) | ||||
0.984758 | + | 0.173932i | \(0.0556472\pi\) | |||||||
\(30\) | 57.3044 | 0.348743 | ||||||||
\(31\) | 278.757 | 1.61504 | 0.807520 | − | 0.589841i | \(-0.200809\pi\) | ||||
0.807520 | + | 0.589841i | \(0.200809\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 107.821 | 0.568763 | ||||||||
\(34\) | −32.9572 | −0.166239 | ||||||||
\(35\) | −66.8551 | −0.322874 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −225.756 | −1.00308 | −0.501541 | − | 0.865134i | \(-0.667233\pi\) | ||||
−0.501541 | + | 0.865134i | \(0.667233\pi\) | |||||||
\(38\) | −55.2874 | −0.236021 | ||||||||
\(39\) | −20.5807 | −0.0845012 | ||||||||
\(40\) | −76.4058 | −0.302021 | ||||||||
\(41\) | 151.015 | 0.575233 | 0.287617 | − | 0.957746i | \(-0.407137\pi\) | ||||
0.287617 | + | 0.957746i | \(0.407137\pi\) | |||||||
\(42\) | −42.0000 | −0.154303 | ||||||||
\(43\) | −434.639 | −1.54144 | −0.770719 | − | 0.637176i | \(-0.780103\pi\) | ||||
−0.770719 | + | 0.637176i | \(0.780103\pi\) | |||||||
\(44\) | −143.761 | −0.492563 | ||||||||
\(45\) | −85.9566 | −0.284748 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | 281.123 | 0.872468 | 0.436234 | − | 0.899833i | \(-0.356312\pi\) | ||||
0.436234 | + | 0.899833i | \(0.356312\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −67.5672 | −0.191109 | ||||||||
\(51\) | 49.4358 | 0.135733 | ||||||||
\(52\) | 27.4409 | 0.0731802 | ||||||||
\(53\) | −337.199 | −0.873922 | −0.436961 | − | 0.899480i | \(-0.643945\pi\) | ||||
−0.436961 | + | 0.899480i | \(0.643945\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | 343.255 | 0.841537 | ||||||||
\(56\) | 56.0000 | 0.133631 | ||||||||
\(57\) | 82.9311 | 0.192710 | ||||||||
\(58\) | 615.158 | 1.39266 | ||||||||
\(59\) | 744.753 | 1.64337 | 0.821683 | − | 0.569945i | \(-0.193036\pi\) | ||||
0.821683 | + | 0.569945i | \(0.193036\pi\) | |||||||
\(60\) | 114.609 | 0.246599 | ||||||||
\(61\) | −345.004 | −0.724151 | −0.362076 | − | 0.932149i | \(-0.617932\pi\) | ||||
−0.362076 | + | 0.932149i | \(0.617932\pi\) | |||||||
\(62\) | 557.514 | 1.14201 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −65.5202 | −0.125027 | ||||||||
\(66\) | 215.641 | 0.402176 | ||||||||
\(67\) | 465.795 | 0.849341 | 0.424671 | − | 0.905348i | \(-0.360390\pi\) | ||||
0.424671 | + | 0.905348i | \(0.360390\pi\) | |||||||
\(68\) | −65.9144 | −0.117548 | ||||||||
\(69\) | 69.0000 | 0.120386 | ||||||||
\(70\) | −133.710 | −0.228306 | ||||||||
\(71\) | 956.929 | 1.59953 | 0.799765 | − | 0.600313i | \(-0.204957\pi\) | ||||
0.799765 | + | 0.600313i | \(0.204957\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | 536.007 | 0.859383 | 0.429691 | − | 0.902976i | \(-0.358622\pi\) | ||||
0.429691 | + | 0.902976i | \(0.358622\pi\) | |||||||
\(74\) | −451.512 | −0.709286 | ||||||||
\(75\) | 101.351 | 0.156040 | ||||||||
\(76\) | −110.575 | −0.166892 | ||||||||
\(77\) | −251.582 | −0.372343 | ||||||||
\(78\) | −41.1614 | −0.0597514 | ||||||||
\(79\) | −541.100 | −0.770614 | −0.385307 | − | 0.922789i | \(-0.625904\pi\) | ||||
−0.385307 | + | 0.922789i | \(0.625904\pi\) | |||||||
\(80\) | −152.812 | −0.213561 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 302.030 | 0.406751 | ||||||||
\(83\) | 352.599 | 0.466299 | 0.233149 | − | 0.972441i | \(-0.425097\pi\) | ||||
0.233149 | + | 0.972441i | \(0.425097\pi\) | |||||||
\(84\) | −84.0000 | −0.109109 | ||||||||
\(85\) | 157.383 | 0.200830 | ||||||||
\(86\) | −869.278 | −1.08996 | ||||||||
\(87\) | −922.736 | −1.13710 | ||||||||
\(88\) | −287.522 | −0.348295 | ||||||||
\(89\) | 1532.67 | 1.82542 | 0.912709 | − | 0.408609i | \(-0.133986\pi\) | ||||
0.912709 | + | 0.408609i | \(0.133986\pi\) | |||||||
\(90\) | −171.913 | −0.201347 | ||||||||
\(91\) | 48.0216 | 0.0553190 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | −836.271 | −0.932443 | ||||||||
\(94\) | 562.246 | 0.616928 | ||||||||
\(95\) | 264.017 | 0.285133 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | −226.807 | −0.237410 | −0.118705 | − | 0.992930i | \(-0.537874\pi\) | ||||
−0.118705 | + | 0.992930i | \(0.537874\pi\) | |||||||
\(98\) | 98.0000 | 0.101015 | ||||||||
\(99\) | −323.462 | −0.328375 | ||||||||
\(100\) | −135.134 | −0.135134 | ||||||||
\(101\) | 1469.57 | 1.44780 | 0.723898 | − | 0.689907i | \(-0.242348\pi\) | ||||
0.723898 | + | 0.689907i | \(0.242348\pi\) | |||||||
\(102\) | 98.8715 | 0.0959779 | ||||||||
\(103\) | 385.377 | 0.368664 | 0.184332 | − | 0.982864i | \(-0.440988\pi\) | ||||
0.184332 | + | 0.982864i | \(0.440988\pi\) | |||||||
\(104\) | 54.8818 | 0.0517462 | ||||||||
\(105\) | 200.565 | 0.186411 | ||||||||
\(106\) | −674.398 | −0.617956 | ||||||||
\(107\) | −800.857 | −0.723568 | −0.361784 | − | 0.932262i | \(-0.617832\pi\) | ||||
−0.361784 | + | 0.932262i | \(0.617832\pi\) | |||||||
\(108\) | −108.000 | −0.0962250 | ||||||||
\(109\) | 1223.90 | 1.07549 | 0.537746 | − | 0.843107i | \(-0.319276\pi\) | ||||
0.537746 | + | 0.843107i | \(0.319276\pi\) | |||||||
\(110\) | 686.510 | 0.595056 | ||||||||
\(111\) | 677.268 | 0.579130 | ||||||||
\(112\) | 112.000 | 0.0944911 | ||||||||
\(113\) | 1282.72 | 1.06786 | 0.533929 | − | 0.845529i | \(-0.320715\pi\) | ||||
0.533929 | + | 0.845529i | \(0.320715\pi\) | |||||||
\(114\) | 165.862 | 0.136267 | ||||||||
\(115\) | 219.667 | 0.178122 | ||||||||
\(116\) | 1230.32 | 0.984758 | ||||||||
\(117\) | 61.7420 | 0.0487868 | ||||||||
\(118\) | 1489.51 | 1.16204 | ||||||||
\(119\) | −115.350 | −0.0888582 | ||||||||
\(120\) | 229.217 | 0.174372 | ||||||||
\(121\) | −39.3008 | −0.0295273 | ||||||||
\(122\) | −690.008 | −0.512052 | ||||||||
\(123\) | −453.045 | −0.332111 | ||||||||
\(124\) | 1115.03 | 0.807520 | ||||||||
\(125\) | 1516.50 | 1.08512 | ||||||||
\(126\) | 126.000 | 0.0890871 | ||||||||
\(127\) | 2271.45 | 1.58708 | 0.793538 | − | 0.608521i | \(-0.208237\pi\) | ||||
0.793538 | + | 0.608521i | \(0.208237\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 1303.92 | 0.889949 | ||||||||
\(130\) | −131.040 | −0.0884077 | ||||||||
\(131\) | 564.729 | 0.376646 | 0.188323 | − | 0.982107i | \(-0.439695\pi\) | ||||
0.188323 | + | 0.982107i | \(0.439695\pi\) | |||||||
\(132\) | 431.283 | 0.284381 | ||||||||
\(133\) | −193.506 | −0.126159 | ||||||||
\(134\) | 931.589 | 0.600575 | ||||||||
\(135\) | 257.870 | 0.164399 | ||||||||
\(136\) | −131.829 | −0.0831193 | ||||||||
\(137\) | 328.883 | 0.205097 | 0.102549 | − | 0.994728i | \(-0.467300\pi\) | ||||
0.102549 | + | 0.994728i | \(0.467300\pi\) | |||||||
\(138\) | 138.000 | 0.0851257 | ||||||||
\(139\) | −2044.79 | −1.24775 | −0.623874 | − | 0.781525i | \(-0.714442\pi\) | ||||
−0.623874 | + | 0.781525i | \(0.714442\pi\) | |||||||
\(140\) | −267.420 | −0.161437 | ||||||||
\(141\) | −843.369 | −0.503720 | ||||||||
\(142\) | 1913.86 | 1.13104 | ||||||||
\(143\) | −246.558 | −0.144183 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −2937.60 | −1.68244 | ||||||||
\(146\) | 1072.01 | 0.607675 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | −903.024 | −0.501541 | ||||||||
\(149\) | 579.529 | 0.318637 | 0.159318 | − | 0.987227i | \(-0.449070\pi\) | ||||
0.159318 | + | 0.987227i | \(0.449070\pi\) | |||||||
\(150\) | 202.702 | 0.110337 | ||||||||
\(151\) | 3304.67 | 1.78100 | 0.890498 | − | 0.454988i | \(-0.150357\pi\) | ||||
0.890498 | + | 0.454988i | \(0.150357\pi\) | |||||||
\(152\) | −221.150 | −0.118011 | ||||||||
\(153\) | −148.307 | −0.0783656 | ||||||||
\(154\) | −503.163 | −0.263286 | ||||||||
\(155\) | −2662.33 | −1.37964 | ||||||||
\(156\) | −82.3227 | −0.0422506 | ||||||||
\(157\) | −1808.40 | −0.919272 | −0.459636 | − | 0.888107i | \(-0.652020\pi\) | ||||
−0.459636 | + | 0.888107i | \(0.652020\pi\) | |||||||
\(158\) | −1082.20 | −0.544906 | ||||||||
\(159\) | 1011.60 | 0.504559 | ||||||||
\(160\) | −305.623 | −0.151010 | ||||||||
\(161\) | −161.000 | −0.0788110 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | −66.5723 | −0.0319898 | −0.0159949 | − | 0.999872i | \(-0.505092\pi\) | ||||
−0.0159949 | + | 0.999872i | \(0.505092\pi\) | |||||||
\(164\) | 604.060 | 0.287617 | ||||||||
\(165\) | −1029.77 | −0.485862 | ||||||||
\(166\) | 705.198 | 0.329723 | ||||||||
\(167\) | −336.954 | −0.156133 | −0.0780667 | − | 0.996948i | \(-0.524875\pi\) | ||||
−0.0780667 | + | 0.996948i | \(0.524875\pi\) | |||||||
\(168\) | −168.000 | −0.0771517 | ||||||||
\(169\) | −2149.94 | −0.978579 | ||||||||
\(170\) | 314.765 | 0.142008 | ||||||||
\(171\) | −248.793 | −0.111261 | ||||||||
\(172\) | −1738.56 | −0.770719 | ||||||||
\(173\) | −318.130 | −0.139809 | −0.0699045 | − | 0.997554i | \(-0.522269\pi\) | ||||
−0.0699045 | + | 0.997554i | \(0.522269\pi\) | |||||||
\(174\) | −1845.47 | −0.804051 | ||||||||
\(175\) | −236.485 | −0.102152 | ||||||||
\(176\) | −575.043 | −0.246281 | ||||||||
\(177\) | −2234.26 | −0.948798 | ||||||||
\(178\) | 3065.33 | 1.29077 | ||||||||
\(179\) | −1968.94 | −0.822152 | −0.411076 | − | 0.911601i | \(-0.634847\pi\) | ||||
−0.411076 | + | 0.911601i | \(0.634847\pi\) | |||||||
\(180\) | −343.826 | −0.142374 | ||||||||
\(181\) | 3805.14 | 1.56262 | 0.781308 | − | 0.624146i | \(-0.214553\pi\) | ||||
0.781308 | + | 0.624146i | \(0.214553\pi\) | |||||||
\(182\) | 96.0432 | 0.0391164 | ||||||||
\(183\) | 1035.01 | 0.418089 | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | 2156.13 | 0.856876 | ||||||||
\(186\) | −1672.54 | −0.659337 | ||||||||
\(187\) | 592.244 | 0.231600 | ||||||||
\(188\) | 1124.49 | 0.436234 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 528.035 | 0.201619 | ||||||||
\(191\) | 1563.67 | 0.592374 | 0.296187 | − | 0.955130i | \(-0.404285\pi\) | ||||
0.296187 | + | 0.955130i | \(0.404285\pi\) | |||||||
\(192\) | −192.000 | −0.0721688 | ||||||||
\(193\) | −4114.00 | −1.53436 | −0.767182 | − | 0.641430i | \(-0.778342\pi\) | ||||
−0.767182 | + | 0.641430i | \(0.778342\pi\) | |||||||
\(194\) | −453.614 | −0.167874 | ||||||||
\(195\) | 196.560 | 0.0721845 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | 1143.47 | 0.413548 | 0.206774 | − | 0.978389i | \(-0.433703\pi\) | ||||
0.206774 | + | 0.978389i | \(0.433703\pi\) | |||||||
\(198\) | −646.924 | −0.232196 | ||||||||
\(199\) | −4.64969 | −0.00165632 | −0.000828161 | − | 1.00000i | \(-0.500264\pi\) | ||||
−0.000828161 | 1.00000i | \(0.500264\pi\) | ||||||||
\(200\) | −270.269 | −0.0955544 | ||||||||
\(201\) | −1397.38 | −0.490367 | ||||||||
\(202\) | 2939.14 | 1.02375 | ||||||||
\(203\) | 2153.05 | 0.744407 | ||||||||
\(204\) | 197.743 | 0.0678666 | ||||||||
\(205\) | −1442.30 | −0.491389 | ||||||||
\(206\) | 770.754 | 0.260685 | ||||||||
\(207\) | −207.000 | −0.0695048 | ||||||||
\(208\) | 109.764 | 0.0365901 | ||||||||
\(209\) | 993.521 | 0.328819 | ||||||||
\(210\) | 401.131 | 0.131813 | ||||||||
\(211\) | −164.636 | −0.0537157 | −0.0268579 | − | 0.999639i | \(-0.508550\pi\) | ||||
−0.0268579 | + | 0.999639i | \(0.508550\pi\) | |||||||
\(212\) | −1348.80 | −0.436961 | ||||||||
\(213\) | −2870.79 | −0.923489 | ||||||||
\(214\) | −1601.71 | −0.511640 | ||||||||
\(215\) | 4151.12 | 1.31676 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | 1951.30 | 0.610427 | ||||||||
\(218\) | 2447.81 | 0.760488 | ||||||||
\(219\) | −1608.02 | −0.496165 | ||||||||
\(220\) | 1373.02 | 0.420768 | ||||||||
\(221\) | −113.047 | −0.0344088 | ||||||||
\(222\) | 1354.54 | 0.409507 | ||||||||
\(223\) | −4061.56 | −1.21965 | −0.609826 | − | 0.792536i | \(-0.708761\pi\) | ||||
−0.609826 | + | 0.792536i | \(0.708761\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | −304.052 | −0.0900896 | ||||||||
\(226\) | 2565.44 | 0.755090 | ||||||||
\(227\) | −3183.98 | −0.930961 | −0.465481 | − | 0.885058i | \(-0.654118\pi\) | ||||
−0.465481 | + | 0.885058i | \(0.654118\pi\) | |||||||
\(228\) | 331.724 | 0.0963552 | ||||||||
\(229\) | 1190.00 | 0.343395 | 0.171697 | − | 0.985150i | \(-0.445075\pi\) | ||||
0.171697 | + | 0.985150i | \(0.445075\pi\) | |||||||
\(230\) | 439.333 | 0.125951 | ||||||||
\(231\) | 754.745 | 0.214972 | ||||||||
\(232\) | 2460.63 | 0.696329 | ||||||||
\(233\) | −6794.69 | −1.91045 | −0.955225 | − | 0.295880i | \(-0.904387\pi\) | ||||
−0.955225 | + | 0.295880i | \(0.904387\pi\) | |||||||
\(234\) | 123.484 | 0.0344975 | ||||||||
\(235\) | −2684.93 | −0.745300 | ||||||||
\(236\) | 2979.01 | 0.821683 | ||||||||
\(237\) | 1623.30 | 0.444914 | ||||||||
\(238\) | −230.700 | −0.0628323 | ||||||||
\(239\) | −4026.00 | −1.08962 | −0.544812 | − | 0.838558i | \(-0.683399\pi\) | ||||
−0.544812 | + | 0.838558i | \(0.683399\pi\) | |||||||
\(240\) | 458.435 | 0.123299 | ||||||||
\(241\) | 4787.52 | 1.27963 | 0.639816 | − | 0.768528i | \(-0.279011\pi\) | ||||
0.639816 | + | 0.768528i | \(0.279011\pi\) | |||||||
\(242\) | −78.6016 | −0.0208789 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −1380.02 | −0.362076 | ||||||||
\(245\) | −467.986 | −0.122035 | ||||||||
\(246\) | −906.089 | −0.234838 | ||||||||
\(247\) | −189.642 | −0.0488528 | ||||||||
\(248\) | 2230.06 | 0.571003 | ||||||||
\(249\) | −1057.80 | −0.269218 | ||||||||
\(250\) | 3033.00 | 0.767295 | ||||||||
\(251\) | −5233.59 | −1.31610 | −0.658050 | − | 0.752974i | \(-0.728618\pi\) | ||||
−0.658050 | + | 0.752974i | \(0.728618\pi\) | |||||||
\(252\) | 252.000 | 0.0629941 | ||||||||
\(253\) | 826.625 | 0.205413 | ||||||||
\(254\) | 4542.90 | 1.12223 | ||||||||
\(255\) | −472.148 | −0.115949 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 3160.14 | 0.767020 | 0.383510 | − | 0.923537i | \(-0.374715\pi\) | ||||
0.383510 | + | 0.923537i | \(0.374715\pi\) | |||||||
\(258\) | 2607.83 | 0.629289 | ||||||||
\(259\) | −1580.29 | −0.379130 | ||||||||
\(260\) | −262.081 | −0.0625137 | ||||||||
\(261\) | 2768.21 | 0.656505 | ||||||||
\(262\) | 1129.46 | 0.266329 | ||||||||
\(263\) | 5199.28 | 1.21902 | 0.609509 | − | 0.792779i | \(-0.291367\pi\) | ||||
0.609509 | + | 0.792779i | \(0.291367\pi\) | |||||||
\(264\) | 862.565 | 0.201088 | ||||||||
\(265\) | 3220.50 | 0.746542 | ||||||||
\(266\) | −387.012 | −0.0892076 | ||||||||
\(267\) | −4598.00 | −1.05391 | ||||||||
\(268\) | 1863.18 | 0.424671 | ||||||||
\(269\) | −4909.49 | −1.11278 | −0.556389 | − | 0.830922i | \(-0.687813\pi\) | ||||
−0.556389 | + | 0.830922i | \(0.687813\pi\) | |||||||
\(270\) | 515.739 | 0.116248 | ||||||||
\(271\) | 4007.30 | 0.898252 | 0.449126 | − | 0.893468i | \(-0.351735\pi\) | ||||
0.449126 | + | 0.893468i | \(0.351735\pi\) | |||||||
\(272\) | −263.657 | −0.0587742 | ||||||||
\(273\) | −144.065 | −0.0319384 | ||||||||
\(274\) | 657.766 | 0.145026 | ||||||||
\(275\) | 1214.19 | 0.266249 | ||||||||
\(276\) | 276.000 | 0.0601929 | ||||||||
\(277\) | 2529.96 | 0.548775 | 0.274388 | − | 0.961619i | \(-0.411525\pi\) | ||||
0.274388 | + | 0.961619i | \(0.411525\pi\) | |||||||
\(278\) | −4089.59 | −0.882292 | ||||||||
\(279\) | 2508.81 | 0.538346 | ||||||||
\(280\) | −534.841 | −0.114153 | ||||||||
\(281\) | −8234.37 | −1.74812 | −0.874059 | − | 0.485820i | \(-0.838521\pi\) | ||||
−0.874059 | + | 0.485820i | \(0.838521\pi\) | |||||||
\(282\) | −1686.74 | −0.356184 | ||||||||
\(283\) | 6374.51 | 1.33896 | 0.669479 | − | 0.742831i | \(-0.266517\pi\) | ||||
0.669479 | + | 0.742831i | \(0.266517\pi\) | |||||||
\(284\) | 3827.72 | 0.799765 | ||||||||
\(285\) | −792.052 | −0.164622 | ||||||||
\(286\) | −493.116 | −0.101953 | ||||||||
\(287\) | 1057.10 | 0.217418 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | −4641.46 | −0.944729 | ||||||||
\(290\) | −5875.20 | −1.18967 | ||||||||
\(291\) | 680.420 | 0.137069 | ||||||||
\(292\) | 2144.03 | 0.429691 | ||||||||
\(293\) | 3946.21 | 0.786825 | 0.393413 | − | 0.919362i | \(-0.371294\pi\) | ||||
0.393413 | + | 0.919362i | \(0.371294\pi\) | |||||||
\(294\) | −294.000 | −0.0583212 | ||||||||
\(295\) | −7112.93 | −1.40383 | ||||||||
\(296\) | −1806.05 | −0.354643 | ||||||||
\(297\) | 970.386 | 0.189588 | ||||||||
\(298\) | 1159.06 | 0.225310 | ||||||||
\(299\) | −157.785 | −0.0305182 | ||||||||
\(300\) | 405.403 | 0.0780199 | ||||||||
\(301\) | −3042.47 | −0.582609 | ||||||||
\(302\) | 6609.34 | 1.25935 | ||||||||
\(303\) | −4408.70 | −0.835886 | ||||||||
\(304\) | −442.299 | −0.0834461 | ||||||||
\(305\) | 3295.04 | 0.618601 | ||||||||
\(306\) | −296.615 | −0.0554128 | ||||||||
\(307\) | −251.364 | −0.0467300 | −0.0233650 | − | 0.999727i | \(-0.507438\pi\) | ||||
−0.0233650 | + | 0.999727i | \(0.507438\pi\) | |||||||
\(308\) | −1006.33 | −0.186171 | ||||||||
\(309\) | −1156.13 | −0.212848 | ||||||||
\(310\) | −5324.66 | −0.975550 | ||||||||
\(311\) | −2787.66 | −0.508276 | −0.254138 | − | 0.967168i | \(-0.581792\pi\) | ||||
−0.254138 | + | 0.967168i | \(0.581792\pi\) | |||||||
\(312\) | −164.645 | −0.0298757 | ||||||||
\(313\) | −585.191 | −0.105677 | −0.0528386 | − | 0.998603i | \(-0.516827\pi\) | ||||
−0.0528386 | + | 0.998603i | \(0.516827\pi\) | |||||||
\(314\) | −3616.79 | −0.650024 | ||||||||
\(315\) | −601.696 | −0.107625 | ||||||||
\(316\) | −2164.40 | −0.385307 | ||||||||
\(317\) | 2421.83 | 0.429096 | 0.214548 | − | 0.976713i | \(-0.431172\pi\) | ||||
0.214548 | + | 0.976713i | \(0.431172\pi\) | |||||||
\(318\) | 2023.19 | 0.356777 | ||||||||
\(319\) | −11054.4 | −1.94022 | ||||||||
\(320\) | −611.247 | −0.106780 | ||||||||
\(321\) | 2402.57 | 0.417752 | ||||||||
\(322\) | −322.000 | −0.0557278 | ||||||||
\(323\) | 455.529 | 0.0784716 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −231.763 | −0.0395566 | ||||||||
\(326\) | −133.145 | −0.0226202 | ||||||||
\(327\) | −3671.71 | −0.620936 | ||||||||
\(328\) | 1208.12 | 0.203376 | ||||||||
\(329\) | 1967.86 | 0.329762 | ||||||||
\(330\) | −2059.53 | −0.343556 | ||||||||
\(331\) | 1910.61 | 0.317270 | 0.158635 | − | 0.987337i | \(-0.449291\pi\) | ||||
0.158635 | + | 0.987337i | \(0.449291\pi\) | |||||||
\(332\) | 1410.40 | 0.233149 | ||||||||
\(333\) | −2031.80 | −0.334361 | ||||||||
\(334\) | −673.908 | −0.110403 | ||||||||
\(335\) | −4448.68 | −0.725544 | ||||||||
\(336\) | −336.000 | −0.0545545 | ||||||||
\(337\) | −1119.18 | −0.180907 | −0.0904533 | − | 0.995901i | \(-0.528832\pi\) | ||||
−0.0904533 | + | 0.995901i | \(0.528832\pi\) | |||||||
\(338\) | −4299.87 | −0.691960 | ||||||||
\(339\) | −3848.15 | −0.616528 | ||||||||
\(340\) | 629.530 | 0.100415 | ||||||||
\(341\) | −10018.6 | −1.59102 | ||||||||
\(342\) | −497.587 | −0.0786737 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | −3477.11 | −0.544980 | ||||||||
\(345\) | −659.000 | −0.102839 | ||||||||
\(346\) | −636.260 | −0.0988599 | ||||||||
\(347\) | 11398.3 | 1.76338 | 0.881688 | − | 0.471833i | \(-0.156407\pi\) | ||||
0.881688 | + | 0.471833i | \(0.156407\pi\) | |||||||
\(348\) | −3690.95 | −0.568550 | ||||||||
\(349\) | 1577.30 | 0.241922 | 0.120961 | − | 0.992657i | \(-0.461402\pi\) | ||||
0.120961 | + | 0.992657i | \(0.461402\pi\) | |||||||
\(350\) | −472.970 | −0.0722324 | ||||||||
\(351\) | −185.226 | −0.0281671 | ||||||||
\(352\) | −1150.09 | −0.174147 | ||||||||
\(353\) | −4929.64 | −0.743282 | −0.371641 | − | 0.928377i | \(-0.621205\pi\) | ||||
−0.371641 | + | 0.928377i | \(0.621205\pi\) | |||||||
\(354\) | −4468.52 | −0.670901 | ||||||||
\(355\) | −9139.37 | −1.36639 | ||||||||
\(356\) | 6130.66 | 0.912709 | ||||||||
\(357\) | 346.050 | 0.0513023 | ||||||||
\(358\) | −3937.87 | −0.581349 | ||||||||
\(359\) | 5323.22 | 0.782588 | 0.391294 | − | 0.920266i | \(-0.372028\pi\) | ||||
0.391294 | + | 0.920266i | \(0.372028\pi\) | |||||||
\(360\) | −687.652 | −0.100674 | ||||||||
\(361\) | −6094.83 | −0.888588 | ||||||||
\(362\) | 7610.27 | 1.10494 | ||||||||
\(363\) | 117.902 | 0.0170476 | ||||||||
\(364\) | 192.086 | 0.0276595 | ||||||||
\(365\) | −5119.26 | −0.734122 | ||||||||
\(366\) | 2070.02 | 0.295633 | ||||||||
\(367\) | −3760.29 | −0.534839 | −0.267419 | − | 0.963580i | \(-0.586171\pi\) | ||||
−0.267419 | + | 0.963580i | \(0.586171\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | 1359.13 | 0.191744 | ||||||||
\(370\) | 4312.27 | 0.605903 | ||||||||
\(371\) | −2360.39 | −0.330311 | ||||||||
\(372\) | −3345.08 | −0.466222 | ||||||||
\(373\) | −9210.62 | −1.27857 | −0.639287 | − | 0.768969i | \(-0.720770\pi\) | ||||
−0.639287 | + | 0.768969i | \(0.720770\pi\) | |||||||
\(374\) | 1184.49 | 0.163766 | ||||||||
\(375\) | −4549.50 | −0.626493 | ||||||||
\(376\) | 2248.98 | 0.308464 | ||||||||
\(377\) | 2110.06 | 0.288259 | ||||||||
\(378\) | −378.000 | −0.0514344 | ||||||||
\(379\) | 6305.61 | 0.854611 | 0.427305 | − | 0.904107i | \(-0.359463\pi\) | ||||
0.427305 | + | 0.904107i | \(0.359463\pi\) | |||||||
\(380\) | 1056.07 | 0.142566 | ||||||||
\(381\) | −6814.35 | −0.916299 | ||||||||
\(382\) | 3127.35 | 0.418872 | ||||||||
\(383\) | 13571.9 | 1.81069 | 0.905344 | − | 0.424679i | \(-0.139613\pi\) | ||||
0.905344 | + | 0.424679i | \(0.139613\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 2402.79 | 0.318071 | ||||||||
\(386\) | −8228.00 | −1.08496 | ||||||||
\(387\) | −3911.75 | −0.513812 | ||||||||
\(388\) | −907.227 | −0.118705 | ||||||||
\(389\) | −7448.01 | −0.970769 | −0.485384 | − | 0.874301i | \(-0.661320\pi\) | ||||
−0.485384 | + | 0.874301i | \(0.661320\pi\) | |||||||
\(390\) | 393.121 | 0.0510422 | ||||||||
\(391\) | 379.008 | 0.0490211 | ||||||||
\(392\) | 392.000 | 0.0505076 | ||||||||
\(393\) | −1694.19 | −0.217456 | ||||||||
\(394\) | 2286.94 | 0.292423 | ||||||||
\(395\) | 5167.90 | 0.658291 | ||||||||
\(396\) | −1293.85 | −0.164188 | ||||||||
\(397\) | 9795.19 | 1.23830 | 0.619152 | − | 0.785271i | \(-0.287477\pi\) | ||||
0.619152 | + | 0.785271i | \(0.287477\pi\) | |||||||
\(398\) | −9.29939 | −0.00117120 | ||||||||
\(399\) | 580.518 | 0.0728377 | ||||||||
\(400\) | −540.537 | −0.0675672 | ||||||||
\(401\) | −7996.68 | −0.995848 | −0.497924 | − | 0.867221i | \(-0.665904\pi\) | ||||
−0.497924 | + | 0.867221i | \(0.665904\pi\) | |||||||
\(402\) | −2794.77 | −0.346742 | ||||||||
\(403\) | 1912.34 | 0.236378 | ||||||||
\(404\) | 5878.27 | 0.723898 | ||||||||
\(405\) | −773.609 | −0.0949159 | ||||||||
\(406\) | 4306.10 | 0.526375 | ||||||||
\(407\) | 8113.72 | 0.988162 | ||||||||
\(408\) | 395.486 | 0.0479889 | ||||||||
\(409\) | 5516.67 | 0.666948 | 0.333474 | − | 0.942759i | \(-0.391779\pi\) | ||||
0.333474 | + | 0.942759i | \(0.391779\pi\) | |||||||
\(410\) | −2884.60 | −0.347465 | ||||||||
\(411\) | −986.648 | −0.118413 | ||||||||
\(412\) | 1541.51 | 0.184332 | ||||||||
\(413\) | 5213.27 | 0.621134 | ||||||||
\(414\) | −414.000 | −0.0491473 | ||||||||
\(415\) | −3367.58 | −0.398332 | ||||||||
\(416\) | 219.527 | 0.0258731 | ||||||||
\(417\) | 6134.38 | 0.720388 | ||||||||
\(418\) | 1987.04 | 0.232510 | ||||||||
\(419\) | 4037.28 | 0.470726 | 0.235363 | − | 0.971908i | \(-0.424372\pi\) | ||||
0.235363 | + | 0.971908i | \(0.424372\pi\) | |||||||
\(420\) | 802.261 | 0.0932056 | ||||||||
\(421\) | 6466.80 | 0.748629 | 0.374314 | − | 0.927302i | \(-0.377878\pi\) | ||||
0.374314 | + | 0.927302i | \(0.377878\pi\) | |||||||
\(422\) | −329.272 | −0.0379828 | ||||||||
\(423\) | 2530.11 | 0.290823 | ||||||||
\(424\) | −2697.59 | −0.308978 | ||||||||
\(425\) | 556.706 | 0.0635393 | ||||||||
\(426\) | −5741.58 | −0.653005 | ||||||||
\(427\) | −2415.03 | −0.273703 | ||||||||
\(428\) | −3203.43 | −0.361784 | ||||||||
\(429\) | 739.674 | 0.0832443 | ||||||||
\(430\) | 8302.24 | 0.931091 | ||||||||
\(431\) | −7418.83 | −0.829124 | −0.414562 | − | 0.910021i | \(-0.636065\pi\) | ||||
−0.414562 | + | 0.910021i | \(0.636065\pi\) | |||||||
\(432\) | −432.000 | −0.0481125 | ||||||||
\(433\) | −16487.7 | −1.82990 | −0.914952 | − | 0.403563i | \(-0.867772\pi\) | ||||
−0.914952 | + | 0.403563i | \(0.867772\pi\) | |||||||
\(434\) | 3902.60 | 0.431637 | ||||||||
\(435\) | 8812.80 | 0.971360 | ||||||||
\(436\) | 4895.61 | 0.537746 | ||||||||
\(437\) | 635.805 | 0.0695988 | ||||||||
\(438\) | −3216.04 | −0.350841 | ||||||||
\(439\) | −15767.2 | −1.71418 | −0.857091 | − | 0.515165i | \(-0.827731\pi\) | ||||
−0.857091 | + | 0.515165i | \(0.827731\pi\) | |||||||
\(440\) | 2746.04 | 0.297528 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | −226.094 | −0.0243307 | ||||||||
\(443\) | −17663.7 | −1.89442 | −0.947208 | − | 0.320619i | \(-0.896109\pi\) | ||||
−0.947208 | + | 0.320619i | \(0.896109\pi\) | |||||||
\(444\) | 2709.07 | 0.289565 | ||||||||
\(445\) | −14638.1 | −1.55935 | ||||||||
\(446\) | −8123.12 | −0.862424 | ||||||||
\(447\) | −1738.59 | −0.183965 | ||||||||
\(448\) | 448.000 | 0.0472456 | ||||||||
\(449\) | 11973.0 | 1.25844 | 0.629222 | − | 0.777226i | \(-0.283374\pi\) | ||||
0.629222 | + | 0.777226i | \(0.283374\pi\) | |||||||
\(450\) | −608.105 | −0.0637029 | ||||||||
\(451\) | −5427.51 | −0.566677 | ||||||||
\(452\) | 5130.87 | 0.533929 | ||||||||
\(453\) | −9914.01 | −1.02826 | ||||||||
\(454\) | −6367.96 | −0.658289 | ||||||||
\(455\) | −458.641 | −0.0472559 | ||||||||
\(456\) | 663.449 | 0.0681334 | ||||||||
\(457\) | −1742.13 | −0.178323 | −0.0891614 | − | 0.996017i | \(-0.528419\pi\) | ||||
−0.0891614 | + | 0.996017i | \(0.528419\pi\) | |||||||
\(458\) | 2380.00 | 0.242817 | ||||||||
\(459\) | 444.922 | 0.0452444 | ||||||||
\(460\) | 878.667 | 0.0890610 | ||||||||
\(461\) | 12085.2 | 1.22097 | 0.610483 | − | 0.792030i | \(-0.290975\pi\) | ||||
0.610483 | + | 0.792030i | \(0.290975\pi\) | |||||||
\(462\) | 1509.49 | 0.152008 | ||||||||
\(463\) | 13460.5 | 1.35110 | 0.675551 | − | 0.737313i | \(-0.263906\pi\) | ||||
0.675551 | + | 0.737313i | \(0.263906\pi\) | |||||||
\(464\) | 4921.26 | 0.492379 | ||||||||
\(465\) | 7986.99 | 0.796533 | ||||||||
\(466\) | −13589.4 | −1.35089 | ||||||||
\(467\) | −3956.79 | −0.392074 | −0.196037 | − | 0.980597i | \(-0.562807\pi\) | ||||
−0.196037 | + | 0.980597i | \(0.562807\pi\) | |||||||
\(468\) | 246.968 | 0.0243934 | ||||||||
\(469\) | 3260.56 | 0.321021 | ||||||||
\(470\) | −5369.86 | −0.527007 | ||||||||
\(471\) | 5425.19 | 0.530742 | ||||||||
\(472\) | 5958.02 | 0.581018 | ||||||||
\(473\) | 15621.0 | 1.51851 | ||||||||
\(474\) | 3246.60 | 0.314602 | ||||||||
\(475\) | 933.903 | 0.0902114 | ||||||||
\(476\) | −461.401 | −0.0444291 | ||||||||
\(477\) | −3034.79 | −0.291307 | ||||||||
\(478\) | −8052.00 | −0.770481 | ||||||||
\(479\) | 16387.3 | 1.56316 | 0.781579 | − | 0.623806i | \(-0.214414\pi\) | ||||
0.781579 | + | 0.623806i | \(0.214414\pi\) | |||||||
\(480\) | 916.870 | 0.0871858 | ||||||||
\(481\) | −1548.74 | −0.146811 | ||||||||
\(482\) | 9575.04 | 0.904836 | ||||||||
\(483\) | 483.000 | 0.0455016 | ||||||||
\(484\) | −157.203 | −0.0147636 | ||||||||
\(485\) | 2166.17 | 0.202806 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | 8974.92 | 0.835097 | 0.417549 | − | 0.908655i | \(-0.362889\pi\) | ||||
0.417549 | + | 0.908655i | \(0.362889\pi\) | |||||||
\(488\) | −2760.03 | −0.256026 | ||||||||
\(489\) | 199.717 | 0.0184693 | ||||||||
\(490\) | −935.971 | −0.0862916 | ||||||||
\(491\) | 14046.8 | 1.29109 | 0.645544 | − | 0.763723i | \(-0.276631\pi\) | ||||
0.645544 | + | 0.763723i | \(0.276631\pi\) | |||||||
\(492\) | −1812.18 | −0.166056 | ||||||||
\(493\) | −5068.47 | −0.463027 | ||||||||
\(494\) | −379.284 | −0.0345441 | ||||||||
\(495\) | 3089.30 | 0.280512 | ||||||||
\(496\) | 4460.11 | 0.403760 | ||||||||
\(497\) | 6698.51 | 0.604565 | ||||||||
\(498\) | −2115.60 | −0.190366 | ||||||||
\(499\) | −15952.7 | −1.43114 | −0.715570 | − | 0.698541i | \(-0.753833\pi\) | ||||
−0.715570 | + | 0.698541i | \(0.753833\pi\) | |||||||
\(500\) | 6066.00 | 0.542559 | ||||||||
\(501\) | 1010.86 | 0.0901436 | ||||||||
\(502\) | −10467.2 | −0.930623 | ||||||||
\(503\) | 16375.1 | 1.45155 | 0.725776 | − | 0.687931i | \(-0.241481\pi\) | ||||
0.725776 | + | 0.687931i | \(0.241481\pi\) | |||||||
\(504\) | 504.000 | 0.0445435 | ||||||||
\(505\) | −14035.4 | −1.23677 | ||||||||
\(506\) | 1653.25 | 0.145249 | ||||||||
\(507\) | 6449.81 | 0.564983 | ||||||||
\(508\) | 9085.80 | 0.793538 | ||||||||
\(509\) | −22768.3 | −1.98269 | −0.991345 | − | 0.131283i | \(-0.958090\pi\) | ||||
−0.991345 | + | 0.131283i | \(0.958090\pi\) | |||||||
\(510\) | −944.295 | −0.0819884 | ||||||||
\(511\) | 3752.05 | 0.324816 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 746.380 | 0.0642368 | ||||||||
\(514\) | 6320.28 | 0.542365 | ||||||||
\(515\) | −3680.63 | −0.314928 | ||||||||
\(516\) | 5215.67 | 0.444975 | ||||||||
\(517\) | −10103.6 | −0.859491 | ||||||||
\(518\) | −3160.58 | −0.268085 | ||||||||
\(519\) | 954.389 | 0.0807188 | ||||||||
\(520\) | −524.161 | −0.0442038 | ||||||||
\(521\) | 528.725 | 0.0444604 | 0.0222302 | − | 0.999753i | \(-0.492923\pi\) | ||||
0.0222302 | + | 0.999753i | \(0.492923\pi\) | |||||||
\(522\) | 5536.42 | 0.464219 | ||||||||
\(523\) | −13524.7 | −1.13078 | −0.565388 | − | 0.824825i | \(-0.691273\pi\) | ||||
−0.565388 | + | 0.824825i | \(0.691273\pi\) | |||||||
\(524\) | 2258.91 | 0.188323 | ||||||||
\(525\) | 709.455 | 0.0589775 | ||||||||
\(526\) | 10398.6 | 0.861975 | ||||||||
\(527\) | −4593.52 | −0.379691 | ||||||||
\(528\) | 1725.13 | 0.142191 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 6440.99 | 0.527885 | ||||||||
\(531\) | 6702.78 | 0.547789 | ||||||||
\(532\) | −774.024 | −0.0630793 | ||||||||
\(533\) | 1036.00 | 0.0841913 | ||||||||
\(534\) | −9196.00 | −0.745224 | ||||||||
\(535\) | 7648.77 | 0.618103 | ||||||||
\(536\) | 3726.36 | 0.300287 | ||||||||
\(537\) | 5906.81 | 0.474670 | ||||||||
\(538\) | −9818.99 | −0.786852 | ||||||||
\(539\) | −1761.07 | −0.140732 | ||||||||
\(540\) | 1031.48 | 0.0821996 | ||||||||
\(541\) | −10436.3 | −0.829371 | −0.414686 | − | 0.909965i | \(-0.636108\pi\) | ||||
−0.414686 | + | 0.909965i | \(0.636108\pi\) | |||||||
\(542\) | 8014.60 | 0.635160 | ||||||||
\(543\) | −11415.4 | −0.902177 | ||||||||
\(544\) | −527.315 | −0.0415596 | ||||||||
\(545\) | −11689.2 | −0.918732 | ||||||||
\(546\) | −288.129 | −0.0225839 | ||||||||
\(547\) | −17369.1 | −1.35768 | −0.678838 | − | 0.734288i | \(-0.737516\pi\) | ||||
−0.678838 | + | 0.734288i | \(0.737516\pi\) | |||||||
\(548\) | 1315.53 | 0.102549 | ||||||||
\(549\) | −3105.04 | −0.241384 | ||||||||
\(550\) | 2428.38 | 0.188266 | ||||||||
\(551\) | −8502.62 | −0.657393 | ||||||||
\(552\) | 552.000 | 0.0425628 | ||||||||
\(553\) | −3787.70 | −0.291265 | ||||||||
\(554\) | 5059.92 | 0.388043 | ||||||||
\(555\) | −6468.40 | −0.494718 | ||||||||
\(556\) | −8179.17 | −0.623874 | ||||||||
\(557\) | −13555.3 | −1.03116 | −0.515579 | − | 0.856842i | \(-0.672423\pi\) | ||||
−0.515579 | + | 0.856842i | \(0.672423\pi\) | |||||||
\(558\) | 5017.62 | 0.380668 | ||||||||
\(559\) | −2981.72 | −0.225605 | ||||||||
\(560\) | −1069.68 | −0.0807184 | ||||||||
\(561\) | −1776.73 | −0.133714 | ||||||||
\(562\) | −16468.7 | −1.23611 | ||||||||
\(563\) | −5311.89 | −0.397636 | −0.198818 | − | 0.980036i | \(-0.563710\pi\) | ||||
−0.198818 | + | 0.980036i | \(0.563710\pi\) | |||||||
\(564\) | −3373.48 | −0.251860 | ||||||||
\(565\) | −12250.9 | −0.912210 | ||||||||
\(566\) | 12749.0 | 0.946786 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 7655.43 | 0.565519 | ||||||||
\(569\) | 17501.8 | 1.28948 | 0.644738 | − | 0.764403i | \(-0.276966\pi\) | ||||
0.644738 | + | 0.764403i | \(0.276966\pi\) | |||||||
\(570\) | −1584.10 | −0.116405 | ||||||||
\(571\) | 16321.0 | 1.19617 | 0.598083 | − | 0.801434i | \(-0.295929\pi\) | ||||
0.598083 | + | 0.801434i | \(0.295929\pi\) | |||||||
\(572\) | −986.232 | −0.0720917 | ||||||||
\(573\) | −4691.02 | −0.342007 | ||||||||
\(574\) | 2114.21 | 0.153738 | ||||||||
\(575\) | 777.023 | 0.0563549 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 5414.53 | 0.390659 | 0.195329 | − | 0.980738i | \(-0.437422\pi\) | ||||
0.195329 | + | 0.980738i | \(0.437422\pi\) | |||||||
\(578\) | −9282.91 | −0.668025 | ||||||||
\(579\) | 12342.0 | 0.885865 | ||||||||
\(580\) | −11750.4 | −0.841222 | ||||||||
\(581\) | 2468.19 | 0.176244 | ||||||||
\(582\) | 1360.84 | 0.0969221 | ||||||||
\(583\) | 12119.0 | 0.860923 | ||||||||
\(584\) | 4288.06 | 0.303838 | ||||||||
\(585\) | −589.681 | −0.0416758 | ||||||||
\(586\) | 7892.41 | 0.556369 | ||||||||
\(587\) | 20409.5 | 1.43507 | 0.717537 | − | 0.696520i | \(-0.245269\pi\) | ||||
0.717537 | + | 0.696520i | \(0.245269\pi\) | |||||||
\(588\) | −588.000 | −0.0412393 | ||||||||
\(589\) | −7705.87 | −0.539075 | ||||||||
\(590\) | −14225.9 | −0.992660 | ||||||||
\(591\) | −3430.42 | −0.238762 | ||||||||
\(592\) | −3612.10 | −0.250771 | ||||||||
\(593\) | 3585.23 | 0.248276 | 0.124138 | − | 0.992265i | \(-0.460383\pi\) | ||||
0.124138 | + | 0.992265i | \(0.460383\pi\) | |||||||
\(594\) | 1940.77 | 0.134059 | ||||||||
\(595\) | 1101.68 | 0.0759065 | ||||||||
\(596\) | 2318.12 | 0.159318 | ||||||||
\(597\) | 13.9491 | 0.000956278 0 | ||||||||
\(598\) | −315.570 | −0.0215797 | ||||||||
\(599\) | 19228.3 | 1.31159 | 0.655797 | − | 0.754937i | \(-0.272333\pi\) | ||||
0.655797 | + | 0.754937i | \(0.272333\pi\) | |||||||
\(600\) | 810.806 | 0.0551684 | ||||||||
\(601\) | −27989.7 | −1.89971 | −0.949853 | − | 0.312698i | \(-0.898767\pi\) | ||||
−0.949853 | + | 0.312698i | \(0.898767\pi\) | |||||||
\(602\) | −6084.94 | −0.411966 | ||||||||
\(603\) | 4192.15 | 0.283114 | ||||||||
\(604\) | 13218.7 | 0.890498 | ||||||||
\(605\) | 375.351 | 0.0252235 | ||||||||
\(606\) | −8817.41 | −0.591061 | ||||||||
\(607\) | −13757.2 | −0.919915 | −0.459958 | − | 0.887941i | \(-0.652135\pi\) | ||||
−0.459958 | + | 0.887941i | \(0.652135\pi\) | |||||||
\(608\) | −884.598 | −0.0590053 | ||||||||
\(609\) | −6459.15 | −0.429784 | ||||||||
\(610\) | 6590.08 | 0.437417 | ||||||||
\(611\) | 1928.57 | 0.127695 | ||||||||
\(612\) | −593.229 | −0.0391828 | ||||||||
\(613\) | 10360.3 | 0.682626 | 0.341313 | − | 0.939950i | \(-0.389128\pi\) | ||||
0.341313 | + | 0.939950i | \(0.389128\pi\) | |||||||
\(614\) | −502.729 | −0.0330431 | ||||||||
\(615\) | 4326.91 | 0.283704 | ||||||||
\(616\) | −2012.65 | −0.131643 | ||||||||
\(617\) | −2143.45 | −0.139858 | −0.0699288 | − | 0.997552i | \(-0.522277\pi\) | ||||
−0.0699288 | + | 0.997552i | \(0.522277\pi\) | |||||||
\(618\) | −2312.26 | −0.150506 | ||||||||
\(619\) | 23282.7 | 1.51181 | 0.755906 | − | 0.654680i | \(-0.227197\pi\) | ||||
0.755906 | + | 0.654680i | \(0.227197\pi\) | |||||||
\(620\) | −10649.3 | −0.689818 | ||||||||
\(621\) | 621.000 | 0.0401286 | ||||||||
\(622\) | −5575.33 | −0.359406 | ||||||||
\(623\) | 10728.7 | 0.689944 | ||||||||
\(624\) | −329.291 | −0.0211253 | ||||||||
\(625\) | −10260.7 | −0.656686 | ||||||||
\(626\) | −1170.38 | −0.0747250 | ||||||||
\(627\) | −2980.56 | −0.189844 | ||||||||
\(628\) | −7233.59 | −0.459636 | ||||||||
\(629\) | 3720.14 | 0.235821 | ||||||||
\(630\) | −1203.39 | −0.0761020 | ||||||||
\(631\) | 10965.6 | 0.691813 | 0.345906 | − | 0.938269i | \(-0.387571\pi\) | ||||
0.345906 | + | 0.938269i | \(0.387571\pi\) | |||||||
\(632\) | −4328.80 | −0.272453 | ||||||||
\(633\) | 493.909 | 0.0310128 | ||||||||
\(634\) | 4843.65 | 0.303416 | ||||||||
\(635\) | −21694.0 | −1.35575 | ||||||||
\(636\) | 4046.39 | 0.252280 | ||||||||
\(637\) | 336.151 | 0.0209086 | ||||||||
\(638\) | −22108.9 | −1.37194 | ||||||||
\(639\) | 8612.36 | 0.533177 | ||||||||
\(640\) | −1222.49 | −0.0755051 | ||||||||
\(641\) | 13655.3 | 0.841425 | 0.420712 | − | 0.907194i | \(-0.361780\pi\) | ||||
0.420712 | + | 0.907194i | \(0.361780\pi\) | |||||||
\(642\) | 4805.14 | 0.295395 | ||||||||
\(643\) | 4110.59 | 0.252109 | 0.126054 | − | 0.992023i | \(-0.459769\pi\) | ||||
0.126054 | + | 0.992023i | \(0.459769\pi\) | |||||||
\(644\) | −644.000 | −0.0394055 | ||||||||
\(645\) | −12453.4 | −0.760233 | ||||||||
\(646\) | 911.059 | 0.0554878 | ||||||||
\(647\) | 18237.5 | 1.10818 | 0.554088 | − | 0.832458i | \(-0.313067\pi\) | ||||
0.554088 | + | 0.832458i | \(0.313067\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | −26766.6 | −1.61892 | ||||||||
\(650\) | −463.526 | −0.0279708 | ||||||||
\(651\) | −5853.89 | −0.352430 | ||||||||
\(652\) | −266.289 | −0.0159949 | ||||||||
\(653\) | −28056.9 | −1.68140 | −0.840699 | − | 0.541503i | \(-0.817855\pi\) | ||||
−0.840699 | + | 0.541503i | \(0.817855\pi\) | |||||||
\(654\) | −7343.42 | −0.439068 | ||||||||
\(655\) | −5393.57 | −0.321747 | ||||||||
\(656\) | 2416.24 | 0.143808 | ||||||||
\(657\) | 4824.07 | 0.286461 | ||||||||
\(658\) | 3935.72 | 0.233177 | ||||||||
\(659\) | 10838.1 | 0.640655 | 0.320328 | − | 0.947307i | \(-0.396207\pi\) | ||||
0.320328 | + | 0.947307i | \(0.396207\pi\) | |||||||
\(660\) | −4119.06 | −0.242931 | ||||||||
\(661\) | −21151.8 | −1.24464 | −0.622321 | − | 0.782762i | \(-0.713810\pi\) | ||||
−0.622321 | + | 0.782762i | \(0.713810\pi\) | |||||||
\(662\) | 3821.22 | 0.224344 | ||||||||
\(663\) | 339.141 | 0.0198660 | ||||||||
\(664\) | 2820.79 | 0.164861 | ||||||||
\(665\) | 1848.12 | 0.107770 | ||||||||
\(666\) | −4063.61 | −0.236429 | ||||||||
\(667\) | −7074.31 | −0.410672 | ||||||||
\(668\) | −1347.82 | −0.0780667 | ||||||||
\(669\) | 12184.7 | 0.704166 | ||||||||
\(670\) | −8897.35 | −0.513037 | ||||||||
\(671\) | 12399.5 | 0.713380 | ||||||||
\(672\) | −672.000 | −0.0385758 | ||||||||
\(673\) | 5933.06 | 0.339826 | 0.169913 | − | 0.985459i | \(-0.445651\pi\) | ||||
0.169913 | + | 0.985459i | \(0.445651\pi\) | |||||||
\(674\) | −2238.36 | −0.127920 | ||||||||
\(675\) | 912.157 | 0.0520132 | ||||||||
\(676\) | −8599.75 | −0.489289 | ||||||||
\(677\) | 22207.5 | 1.26071 | 0.630357 | − | 0.776305i | \(-0.282908\pi\) | ||||
0.630357 | + | 0.776305i | \(0.282908\pi\) | |||||||
\(678\) | −7696.31 | −0.435951 | ||||||||
\(679\) | −1587.65 | −0.0897324 | ||||||||
\(680\) | 1259.06 | 0.0710041 | ||||||||
\(681\) | 9551.94 | 0.537491 | ||||||||
\(682\) | −20037.2 | −1.12502 | ||||||||
\(683\) | 7323.69 | 0.410298 | 0.205149 | − | 0.978731i | \(-0.434232\pi\) | ||||
0.205149 | + | 0.978731i | \(0.434232\pi\) | |||||||
\(684\) | −995.173 | −0.0556307 | ||||||||
\(685\) | −3141.07 | −0.175203 | ||||||||
\(686\) | 686.000 | 0.0381802 | ||||||||
\(687\) | −3570.00 | −0.198259 | ||||||||
\(688\) | −6954.22 | −0.385359 | ||||||||
\(689\) | −2313.26 | −0.127907 | ||||||||
\(690\) | −1318.00 | −0.0727180 | ||||||||
\(691\) | −9596.05 | −0.528294 | −0.264147 | − | 0.964482i | \(-0.585090\pi\) | ||||
−0.264147 | + | 0.964482i | \(0.585090\pi\) | |||||||
\(692\) | −1272.52 | −0.0699045 | ||||||||
\(693\) | −2264.23 | −0.124114 | ||||||||
\(694\) | 22796.5 | 1.24690 | ||||||||
\(695\) | 19529.3 | 1.06588 | ||||||||
\(696\) | −7381.89 | −0.402026 | ||||||||
\(697\) | −2488.51 | −0.135236 | ||||||||
\(698\) | 3154.60 | 0.171065 | ||||||||
\(699\) | 20384.1 | 1.10300 | ||||||||
\(700\) | −945.941 | −0.0510760 | ||||||||
\(701\) | −28684.1 | −1.54548 | −0.772740 | − | 0.634722i | \(-0.781115\pi\) | ||||
−0.772740 | + | 0.634722i | \(0.781115\pi\) | |||||||
\(702\) | −370.452 | −0.0199171 | ||||||||
\(703\) | 6240.73 | 0.334813 | ||||||||
\(704\) | −2300.17 | −0.123141 | ||||||||
\(705\) | 8054.79 | 0.430299 | ||||||||
\(706\) | −9859.29 | −0.525580 | ||||||||
\(707\) | 10287.0 | 0.547216 | ||||||||
\(708\) | −8937.04 | −0.474399 | ||||||||
\(709\) | −10857.3 | −0.575111 | −0.287555 | − | 0.957764i | \(-0.592843\pi\) | ||||
−0.287555 | + | 0.957764i | \(0.592843\pi\) | |||||||
\(710\) | −18278.7 | −0.966182 | ||||||||
\(711\) | −4869.90 | −0.256871 | ||||||||
\(712\) | 12261.3 | 0.645383 | ||||||||
\(713\) | −6411.41 | −0.336759 | ||||||||
\(714\) | 692.101 | 0.0362762 | ||||||||
\(715\) | 2354.81 | 0.123168 | ||||||||
\(716\) | −7875.74 | −0.411076 | ||||||||
\(717\) | 12078.0 | 0.629095 | ||||||||
\(718\) | 10646.4 | 0.553373 | ||||||||
\(719\) | −19066.6 | −0.988962 | −0.494481 | − | 0.869188i | \(-0.664642\pi\) | ||||
−0.494481 | + | 0.869188i | \(0.664642\pi\) | |||||||
\(720\) | −1375.30 | −0.0711869 | ||||||||
\(721\) | 2697.64 | 0.139342 | ||||||||
\(722\) | −12189.7 | −0.628327 | ||||||||
\(723\) | −14362.6 | −0.738796 | ||||||||
\(724\) | 15220.5 | 0.781308 | ||||||||
\(725\) | −10391.1 | −0.532298 | ||||||||
\(726\) | 235.805 | 0.0120545 | ||||||||
\(727\) | 23234.8 | 1.18533 | 0.592663 | − | 0.805451i | \(-0.298077\pi\) | ||||
0.592663 | + | 0.805451i | \(0.298077\pi\) | |||||||
\(728\) | 384.173 | 0.0195582 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −10238.5 | −0.519102 | ||||||||
\(731\) | 7162.24 | 0.362387 | ||||||||
\(732\) | 4140.05 | 0.209044 | ||||||||
\(733\) | −10581.8 | −0.533218 | −0.266609 | − | 0.963805i | \(-0.585903\pi\) | ||||
−0.266609 | + | 0.963805i | \(0.585903\pi\) | |||||||
\(734\) | −7520.59 | −0.378188 | ||||||||
\(735\) | 1403.96 | 0.0704568 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | −16740.8 | −0.836708 | ||||||||
\(738\) | 2718.27 | 0.135584 | ||||||||
\(739\) | −33930.6 | −1.68898 | −0.844491 | − | 0.535570i | \(-0.820097\pi\) | ||||
−0.844491 | + | 0.535570i | \(0.820097\pi\) | |||||||
\(740\) | 8624.54 | 0.428438 | ||||||||
\(741\) | 568.926 | 0.0282052 | ||||||||
\(742\) | −4720.79 | −0.233565 | ||||||||
\(743\) | 35816.7 | 1.76849 | 0.884245 | − | 0.467023i | \(-0.154673\pi\) | ||||
0.884245 | + | 0.467023i | \(0.154673\pi\) | |||||||
\(744\) | −6690.17 | −0.329668 | ||||||||
\(745\) | −5534.92 | −0.272193 | ||||||||
\(746\) | −18421.2 | −0.904088 | ||||||||
\(747\) | 3173.39 | 0.155433 | ||||||||
\(748\) | 2368.98 | 0.115800 | ||||||||
\(749\) | −5606.00 | −0.273483 | ||||||||
\(750\) | −9098.99 | −0.442998 | ||||||||
\(751\) | 36266.5 | 1.76216 | 0.881081 | − | 0.472966i | \(-0.156817\pi\) | ||||
0.881081 | + | 0.472966i | \(0.156817\pi\) | |||||||
\(752\) | 4497.97 | 0.218117 | ||||||||
\(753\) | 15700.8 | 0.759851 | ||||||||
\(754\) | 4220.12 | 0.203830 | ||||||||
\(755\) | −31562.0 | −1.52140 | ||||||||
\(756\) | −756.000 | −0.0363696 | ||||||||
\(757\) | 10970.6 | 0.526727 | 0.263363 | − | 0.964697i | \(-0.415168\pi\) | ||||
0.263363 | + | 0.964697i | \(0.415168\pi\) | |||||||
\(758\) | 12611.2 | 0.604301 | ||||||||
\(759\) | −2479.87 | −0.118595 | ||||||||
\(760\) | 2112.14 | 0.100810 | ||||||||
\(761\) | 12254.8 | 0.583752 | 0.291876 | − | 0.956456i | \(-0.405721\pi\) | ||||
0.291876 | + | 0.956456i | \(0.405721\pi\) | |||||||
\(762\) | −13628.7 | −0.647921 | ||||||||
\(763\) | 8567.32 | 0.406498 | ||||||||
\(764\) | 6254.69 | 0.296187 | ||||||||
\(765\) | 1416.44 | 0.0669433 | ||||||||
\(766\) | 27143.9 | 1.28035 | ||||||||
\(767\) | 5109.17 | 0.240524 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | 9003.57 | 0.422207 | 0.211103 | − | 0.977464i | \(-0.432294\pi\) | ||||
0.211103 | + | 0.977464i | \(0.432294\pi\) | |||||||
\(770\) | 4805.57 | 0.224910 | ||||||||
\(771\) | −9480.42 | −0.442839 | ||||||||
\(772\) | −16456.0 | −0.767182 | ||||||||
\(773\) | 8783.80 | 0.408708 | 0.204354 | − | 0.978897i | \(-0.434491\pi\) | ||||
0.204354 | + | 0.978897i | \(0.434491\pi\) | |||||||
\(774\) | −7823.50 | −0.363320 | ||||||||
\(775\) | −9417.41 | −0.436495 | ||||||||
\(776\) | −1814.45 | −0.0839370 | ||||||||
\(777\) | 4740.88 | 0.218891 | ||||||||
\(778\) | −14896.0 | −0.686437 | ||||||||
\(779\) | −4174.61 | −0.192004 | ||||||||
\(780\) | 786.242 | 0.0360923 | ||||||||
\(781\) | −34392.2 | −1.57574 | ||||||||
\(782\) | 758.015 | 0.0346631 | ||||||||
\(783\) | −8304.63 | −0.379033 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | 17271.5 | 0.785282 | ||||||||
\(786\) | −3388.37 | −0.153765 | ||||||||
\(787\) | 28920.9 | 1.30994 | 0.654968 | − | 0.755656i | \(-0.272682\pi\) | ||||
0.654968 | + | 0.755656i | \(0.272682\pi\) | |||||||
\(788\) | 4573.89 | 0.206774 | ||||||||
\(789\) | −15597.9 | −0.703800 | ||||||||
\(790\) | 10335.8 | 0.465482 | ||||||||
\(791\) | 8979.02 | 0.403612 | ||||||||
\(792\) | −2587.70 | −0.116098 | ||||||||
\(793\) | −2366.80 | −0.105987 | ||||||||
\(794\) | 19590.4 | 0.875613 | ||||||||
\(795\) | −9661.49 | −0.431016 | ||||||||
\(796\) | −18.5988 | −0.000828161 0 | ||||||||
\(797\) | −18091.1 | −0.804039 | −0.402019 | − | 0.915631i | \(-0.631692\pi\) | ||||
−0.402019 | + | 0.915631i | \(0.631692\pi\) | |||||||
\(798\) | 1161.04 | 0.0515040 | ||||||||
\(799\) | −4632.51 | −0.205114 | ||||||||
\(800\) | −1081.07 | −0.0477772 | ||||||||
\(801\) | 13794.0 | 0.608473 | ||||||||
\(802\) | −15993.4 | −0.704171 | ||||||||
\(803\) | −19264.2 | −0.846600 | ||||||||
\(804\) | −5589.53 | −0.245184 | ||||||||
\(805\) | 1537.67 | 0.0673238 | ||||||||
\(806\) | 3824.67 | 0.167144 | ||||||||
\(807\) | 14728.5 | 0.642462 | ||||||||
\(808\) | 11756.5 | 0.511873 | ||||||||
\(809\) | −31525.0 | −1.37004 | −0.685018 | − | 0.728526i | \(-0.740206\pi\) | ||||
−0.685018 | + | 0.728526i | \(0.740206\pi\) | |||||||
\(810\) | −1547.22 | −0.0671157 | ||||||||
\(811\) | 1459.50 | 0.0631936 | 0.0315968 | − | 0.999501i | \(-0.489941\pi\) | ||||
0.0315968 | + | 0.999501i | \(0.489941\pi\) | |||||||
\(812\) | 8612.21 | 0.372203 | ||||||||
\(813\) | −12021.9 | −0.518606 | ||||||||
\(814\) | 16227.4 | 0.698736 | ||||||||
\(815\) | 635.814 | 0.0273271 | ||||||||
\(816\) | 790.972 | 0.0339333 | ||||||||
\(817\) | 12015.0 | 0.514507 | ||||||||
\(818\) | 11033.3 | 0.471604 | ||||||||
\(819\) | 432.194 | 0.0184397 | ||||||||
\(820\) | −5769.21 | −0.245695 | ||||||||
\(821\) | 34470.9 | 1.46534 | 0.732669 | − | 0.680585i | \(-0.238274\pi\) | ||||
0.732669 | + | 0.680585i | \(0.238274\pi\) | |||||||
\(822\) | −1973.30 | −0.0837307 | ||||||||
\(823\) | −12245.1 | −0.518635 | −0.259317 | − | 0.965792i | \(-0.583498\pi\) | ||||
−0.259317 | + | 0.965792i | \(0.583498\pi\) | |||||||
\(824\) | 3083.02 | 0.130342 | ||||||||
\(825\) | −3642.57 | −0.153719 | ||||||||
\(826\) | 10426.5 | 0.439208 | ||||||||
\(827\) | 21699.6 | 0.912418 | 0.456209 | − | 0.889873i | \(-0.349207\pi\) | ||||
0.456209 | + | 0.889873i | \(0.349207\pi\) | |||||||
\(828\) | −828.000 | −0.0347524 | ||||||||
\(829\) | 9666.34 | 0.404977 | 0.202489 | − | 0.979285i | \(-0.435097\pi\) | ||||
0.202489 | + | 0.979285i | \(0.435097\pi\) | |||||||
\(830\) | −6735.16 | −0.281664 | ||||||||
\(831\) | −7589.89 | −0.316835 | ||||||||
\(832\) | 439.054 | 0.0182950 | ||||||||
\(833\) | −807.451 | −0.0335853 | ||||||||
\(834\) | 12268.8 | 0.509391 | ||||||||
\(835\) | 3218.15 | 0.133376 | ||||||||
\(836\) | 3974.08 | 0.164410 | ||||||||
\(837\) | −7526.44 | −0.310814 | ||||||||
\(838\) | 8074.56 | 0.332853 | ||||||||
\(839\) | 6492.29 | 0.267150 | 0.133575 | − | 0.991039i | \(-0.457354\pi\) | ||||
0.133575 | + | 0.991039i | \(0.457354\pi\) | |||||||
\(840\) | 1604.52 | 0.0659063 | ||||||||
\(841\) | 70215.7 | 2.87899 | ||||||||
\(842\) | 12933.6 | 0.529360 | ||||||||
\(843\) | 24703.1 | 1.00928 | ||||||||
\(844\) | −658.545 | −0.0268579 | ||||||||
\(845\) | 20533.5 | 0.835944 | ||||||||
\(846\) | 5060.21 | 0.205643 | ||||||||
\(847\) | −275.106 | −0.0111603 | ||||||||
\(848\) | −5395.19 | −0.218480 | ||||||||
\(849\) | −19123.5 | −0.773048 | ||||||||
\(850\) | 1113.41 | 0.0449291 | ||||||||
\(851\) | 5192.39 | 0.209157 | ||||||||
\(852\) | −11483.2 | −0.461744 | ||||||||
\(853\) | −273.587 | −0.0109818 | −0.00549088 | − | 0.999985i | \(-0.501748\pi\) | ||||
−0.00549088 | + | 0.999985i | \(0.501748\pi\) | |||||||
\(854\) | −4830.05 | −0.193538 | ||||||||
\(855\) | 2376.16 | 0.0950443 | ||||||||
\(856\) | −6406.85 | −0.255820 | ||||||||
\(857\) | 20910.7 | 0.833483 | 0.416741 | − | 0.909025i | \(-0.363172\pi\) | ||||
0.416741 | + | 0.909025i | \(0.363172\pi\) | |||||||
\(858\) | 1479.35 | 0.0588626 | ||||||||
\(859\) | 43191.5 | 1.71557 | 0.857785 | − | 0.514009i | \(-0.171840\pi\) | ||||
0.857785 | + | 0.514009i | \(0.171840\pi\) | |||||||
\(860\) | 16604.5 | 0.658381 | ||||||||
\(861\) | −3171.31 | −0.125526 | ||||||||
\(862\) | −14837.7 | −0.586279 | ||||||||
\(863\) | 15061.2 | 0.594077 | 0.297038 | − | 0.954866i | \(-0.404001\pi\) | ||||
0.297038 | + | 0.954866i | \(0.404001\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | 3038.37 | 0.119431 | ||||||||
\(866\) | −32975.4 | −1.29394 | ||||||||
\(867\) | 13924.4 | 0.545440 | ||||||||
\(868\) | 7805.19 | 0.305214 | ||||||||
\(869\) | 19447.2 | 0.759151 | ||||||||
\(870\) | 17625.6 | 0.686855 | ||||||||
\(871\) | 3195.46 | 0.124310 | ||||||||
\(872\) | 9791.22 | 0.380244 | ||||||||
\(873\) | −2041.26 | −0.0791366 | ||||||||
\(874\) | 1271.61 | 0.0492138 | ||||||||
\(875\) | 10615.5 | 0.410136 | ||||||||
\(876\) | −6432.09 | −0.248082 | ||||||||
\(877\) | −11979.5 | −0.461252 | −0.230626 | − | 0.973042i | \(-0.574077\pi\) | ||||
−0.230626 | + | 0.973042i | \(0.574077\pi\) | |||||||
\(878\) | −31534.3 | −1.21211 | ||||||||
\(879\) | −11838.6 | −0.454274 | ||||||||
\(880\) | 5492.08 | 0.210384 | ||||||||
\(881\) | 1497.59 | 0.0572703 | 0.0286352 | − | 0.999590i | \(-0.490884\pi\) | ||||
0.0286352 | + | 0.999590i | \(0.490884\pi\) | |||||||
\(882\) | 882.000 | 0.0336718 | ||||||||
\(883\) | −3415.01 | −0.130152 | −0.0650761 | − | 0.997880i | \(-0.520729\pi\) | ||||
−0.0650761 | + | 0.997880i | \(0.520729\pi\) | |||||||
\(884\) | −452.187 | −0.0172044 | ||||||||
\(885\) | 21338.8 | 0.810504 | ||||||||
\(886\) | −35327.3 | −1.33955 | ||||||||
\(887\) | −36693.1 | −1.38899 | −0.694495 | − | 0.719498i | \(-0.744372\pi\) | ||||
−0.694495 | + | 0.719498i | \(0.744372\pi\) | |||||||
\(888\) | 5418.14 | 0.204753 | ||||||||
\(889\) | 15900.2 | 0.599858 | ||||||||
\(890\) | −29276.2 | −1.10263 | ||||||||
\(891\) | −2911.16 | −0.109458 | ||||||||
\(892\) | −16246.2 | −0.609826 | ||||||||
\(893\) | −7771.28 | −0.291216 | ||||||||
\(894\) | −3477.17 | −0.130083 | ||||||||
\(895\) | 18804.8 | 0.702318 | ||||||||
\(896\) | 896.000 | 0.0334077 | ||||||||
\(897\) | 473.356 | 0.0176197 | ||||||||
\(898\) | 23946.0 | 0.889854 | ||||||||
\(899\) | 85739.7 | 3.18084 | ||||||||
\(900\) | −1216.21 | −0.0450448 | ||||||||
\(901\) | 5556.57 | 0.205456 | ||||||||
\(902\) | −10855.0 | −0.400701 | ||||||||
\(903\) | 9127.42 | 0.336369 | ||||||||
\(904\) | 10261.7 | 0.377545 | ||||||||
\(905\) | −36341.8 | −1.33485 | ||||||||
\(906\) | −19828.0 | −0.727088 | ||||||||
\(907\) | −2621.57 | −0.0959733 | −0.0479866 | − | 0.998848i | \(-0.515280\pi\) | ||||
−0.0479866 | + | 0.998848i | \(0.515280\pi\) | |||||||
\(908\) | −12735.9 | −0.465481 | ||||||||
\(909\) | 13226.1 | 0.482599 | ||||||||
\(910\) | −917.282 | −0.0334150 | ||||||||
\(911\) | 18982.7 | 0.690368 | 0.345184 | − | 0.938535i | \(-0.387817\pi\) | ||||
0.345184 | + | 0.938535i | \(0.387817\pi\) | |||||||
\(912\) | 1326.90 | 0.0481776 | ||||||||
\(913\) | −12672.5 | −0.459363 | ||||||||
\(914\) | −3484.26 | −0.126093 | ||||||||
\(915\) | −9885.12 | −0.357150 | ||||||||
\(916\) | 4760.00 | 0.171697 | ||||||||
\(917\) | 3953.10 | 0.142359 | ||||||||
\(918\) | 889.844 | 0.0319926 | ||||||||
\(919\) | −10192.2 | −0.365845 | −0.182922 | − | 0.983127i | \(-0.558556\pi\) | ||||
−0.182922 | + | 0.983127i | \(0.558556\pi\) | |||||||
\(920\) | 1757.33 | 0.0629756 | ||||||||
\(921\) | 754.093 | 0.0269796 | ||||||||
\(922\) | 24170.5 | 0.863353 | ||||||||
\(923\) | 6564.75 | 0.234108 | ||||||||
\(924\) | 3018.98 | 0.107486 | ||||||||
\(925\) | 7626.85 | 0.271102 | ||||||||
\(926\) | 26920.9 | 0.955373 | ||||||||
\(927\) | 3468.40 | 0.122888 | ||||||||
\(928\) | 9842.52 | 0.348164 | ||||||||
\(929\) | 53333.7 | 1.88355 | 0.941777 | − | 0.336238i | \(-0.109155\pi\) | ||||
0.941777 | + | 0.336238i | \(0.109155\pi\) | |||||||
\(930\) | 15974.0 | 0.563234 | ||||||||
\(931\) | −1354.54 | −0.0476835 | ||||||||
\(932\) | −27178.8 | −0.955225 | ||||||||
\(933\) | 8362.99 | 0.293453 | ||||||||
\(934\) | −7913.58 | −0.277238 | ||||||||
\(935\) | −5656.36 | −0.197843 | ||||||||
\(936\) | 493.936 | 0.0172487 | ||||||||
\(937\) | 40735.5 | 1.42025 | 0.710124 | − | 0.704077i | \(-0.248639\pi\) | ||||
0.710124 | + | 0.704077i | \(0.248639\pi\) | |||||||
\(938\) | 6521.12 | 0.226996 | ||||||||
\(939\) | 1755.57 | 0.0610127 | ||||||||
\(940\) | −10739.7 | −0.372650 | ||||||||
\(941\) | −10130.8 | −0.350963 | −0.175481 | − | 0.984483i | \(-0.556148\pi\) | ||||
−0.175481 | + | 0.984483i | \(0.556148\pi\) | |||||||
\(942\) | 10850.4 | 0.375291 | ||||||||
\(943\) | −3473.34 | −0.119944 | ||||||||
\(944\) | 11916.0 | 0.410841 | ||||||||
\(945\) | 1805.09 | 0.0621370 | ||||||||
\(946\) | 31242.0 | 1.07375 | ||||||||
\(947\) | −3536.91 | −0.121367 | −0.0606833 | − | 0.998157i | \(-0.519328\pi\) | ||||
−0.0606833 | + | 0.998157i | \(0.519328\pi\) | |||||||
\(948\) | 6493.20 | 0.222457 | ||||||||
\(949\) | 3677.13 | 0.125780 | ||||||||
\(950\) | 1867.81 | 0.0637891 | ||||||||
\(951\) | −7265.48 | −0.247739 | ||||||||
\(952\) | −922.801 | −0.0314161 | ||||||||
\(953\) | −30525.8 | −1.03759 | −0.518797 | − | 0.854897i | \(-0.673620\pi\) | ||||
−0.518797 | + | 0.854897i | \(0.673620\pi\) | |||||||
\(954\) | −6069.58 | −0.205985 | ||||||||
\(955\) | −14934.2 | −0.506031 | ||||||||
\(956\) | −16104.0 | −0.544812 | ||||||||
\(957\) | 33163.3 | 1.12019 | ||||||||
\(958\) | 32774.5 | 1.10532 | ||||||||
\(959\) | 2302.18 | 0.0775196 | ||||||||
\(960\) | 1833.74 | 0.0616497 | ||||||||
\(961\) | 47914.4 | 1.60835 | ||||||||
\(962\) | −3097.47 | −0.103811 | ||||||||
\(963\) | −7207.71 | −0.241189 | ||||||||
\(964\) | 19150.1 | 0.639816 | ||||||||
\(965\) | 39291.7 | 1.31072 | ||||||||
\(966\) | 966.000 | 0.0321745 | ||||||||
\(967\) | 33897.9 | 1.12728 | 0.563642 | − | 0.826019i | \(-0.309400\pi\) | ||||
0.563642 | + | 0.826019i | \(0.309400\pi\) | |||||||
\(968\) | −314.407 | −0.0104395 | ||||||||
\(969\) | −1366.59 | −0.0453056 | ||||||||
\(970\) | 4332.34 | 0.143405 | ||||||||
\(971\) | −15613.9 | −0.516040 | −0.258020 | − | 0.966140i | \(-0.583070\pi\) | ||||
−0.258020 | + | 0.966140i | \(0.583070\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | −14313.6 | −0.471605 | ||||||||
\(974\) | 17949.8 | 0.590503 | ||||||||
\(975\) | 695.289 | 0.0228380 | ||||||||
\(976\) | −5520.06 | −0.181038 | ||||||||
\(977\) | −30489.2 | −0.998399 | −0.499199 | − | 0.866487i | \(-0.666372\pi\) | ||||
−0.499199 | + | 0.866487i | \(0.666372\pi\) | |||||||
\(978\) | 399.434 | 0.0130598 | ||||||||
\(979\) | −55084.4 | −1.79827 | ||||||||
\(980\) | −1871.94 | −0.0610174 | ||||||||
\(981\) | 11015.1 | 0.358497 | ||||||||
\(982\) | 28093.7 | 0.912938 | ||||||||
\(983\) | 35753.1 | 1.16007 | 0.580034 | − | 0.814593i | \(-0.303039\pi\) | ||||
0.580034 | + | 0.814593i | \(0.303039\pi\) | |||||||
\(984\) | −3624.36 | −0.117419 | ||||||||
\(985\) | −10921.0 | −0.353271 | ||||||||
\(986\) | −10136.9 | −0.327409 | ||||||||
\(987\) | −5903.58 | −0.190388 | ||||||||
\(988\) | −758.568 | −0.0244264 | ||||||||
\(989\) | 9996.69 | 0.321412 | ||||||||
\(990\) | 6178.59 | 0.198352 | ||||||||
\(991\) | 13696.3 | 0.439030 | 0.219515 | − | 0.975609i | \(-0.429553\pi\) | ||||
0.219515 | + | 0.975609i | \(0.429553\pi\) | |||||||
\(992\) | 8920.22 | 0.285501 | ||||||||
\(993\) | −5731.82 | −0.183176 | ||||||||
\(994\) | 13397.0 | 0.427492 | ||||||||
\(995\) | 44.4080 | 0.00141490 | ||||||||
\(996\) | −4231.19 | −0.134609 | ||||||||
\(997\) | 40838.4 | 1.29726 | 0.648628 | − | 0.761106i | \(-0.275343\pi\) | ||||
0.648628 | + | 0.761106i | \(0.275343\pi\) | |||||||
\(998\) | −31905.3 | −1.01197 | ||||||||
\(999\) | 6095.41 | 0.193043 |
(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 | 966.4.a.f.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.4.a.f.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial |