Newspace parameters
Level: | \( N \) | \(=\) | \( 8526 = 2 \cdot 3 \cdot 7^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8526.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(68.0804527633\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
|
|
Defining polynomial: |
\( x^{3} - 4x - 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1218) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.86081\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8526.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.72161 | 1.66436 | 0.832178 | − | 0.554509i | \(-0.187094\pi\) | ||||
0.832178 | + | 0.554509i | \(0.187094\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.72161 | −1.17688 | ||||||||
\(11\) | −6.04502 | −1.82264 | −0.911320 | − | 0.411698i | \(-0.864936\pi\) | ||||
−0.911320 | + | 0.411698i | \(0.864936\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 2.32340 | 0.644396 | 0.322198 | − | 0.946672i | \(-0.395578\pi\) | ||||
0.322198 | + | 0.946672i | \(0.395578\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.72161 | −0.960916 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.72161 | −0.902623 | −0.451312 | − | 0.892366i | \(-0.649044\pi\) | ||||
−0.451312 | + | 0.892366i | \(0.649044\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.39821 | −0.320771 | −0.160385 | − | 0.987054i | \(-0.551274\pi\) | ||||
−0.160385 | + | 0.987054i | \(0.551274\pi\) | |||||||
\(20\) | 3.72161 | 0.832178 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.04502 | 1.28880 | ||||||||
\(23\) | 7.24860 | 1.51144 | 0.755719 | − | 0.654896i | \(-0.227288\pi\) | ||||
0.755719 | + | 0.654896i | \(0.227288\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 8.85039 | 1.77008 | ||||||||
\(26\) | −2.32340 | −0.455657 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 3.72161 | 0.679470 | ||||||||
\(31\) | −9.72161 | −1.74605 | −0.873027 | − | 0.487673i | \(-0.837846\pi\) | ||||
−0.873027 | + | 0.487673i | \(0.837846\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 6.04502 | 1.05230 | ||||||||
\(34\) | 3.72161 | 0.638251 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.19462 | 1.01839 | 0.509195 | − | 0.860651i | \(-0.329943\pi\) | ||||
0.509195 | + | 0.860651i | \(0.329943\pi\) | |||||||
\(38\) | 1.39821 | 0.226819 | ||||||||
\(39\) | −2.32340 | −0.372042 | ||||||||
\(40\) | −3.72161 | −0.588438 | ||||||||
\(41\) | 4.92520 | 0.769187 | 0.384593 | − | 0.923086i | \(-0.374342\pi\) | ||||
0.384593 | + | 0.923086i | \(0.374342\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.20359 | 0.183545 | 0.0917725 | − | 0.995780i | \(-0.470747\pi\) | ||||
0.0917725 | + | 0.995780i | \(0.470747\pi\) | |||||||
\(44\) | −6.04502 | −0.911320 | ||||||||
\(45\) | 3.72161 | 0.554785 | ||||||||
\(46\) | −7.24860 | −1.06875 | ||||||||
\(47\) | 6.17380 | 0.900541 | 0.450270 | − | 0.892892i | \(-0.351328\pi\) | ||||
0.450270 | + | 0.892892i | \(0.351328\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −8.85039 | −1.25163 | ||||||||
\(51\) | 3.72161 | 0.521130 | ||||||||
\(52\) | 2.32340 | 0.322198 | ||||||||
\(53\) | 4.60179 | 0.632105 | 0.316052 | − | 0.948742i | \(-0.397642\pi\) | ||||
0.316052 | + | 0.948742i | \(0.397642\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −22.4972 | −3.03352 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.39821 | 0.185197 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | −12.4134 | −1.61609 | −0.808046 | − | 0.589120i | \(-0.799475\pi\) | ||||
−0.808046 | + | 0.589120i | \(0.799475\pi\) | |||||||
\(60\) | −3.72161 | −0.480458 | ||||||||
\(61\) | −14.0900 | −1.80404 | −0.902022 | − | 0.431690i | \(-0.857917\pi\) | ||||
−0.902022 | + | 0.431690i | \(0.857917\pi\) | |||||||
\(62\) | 9.72161 | 1.23465 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 8.64681 | 1.07250 | ||||||||
\(66\) | −6.04502 | −0.744090 | ||||||||
\(67\) | −7.89541 | −0.964578 | −0.482289 | − | 0.876012i | \(-0.660194\pi\) | ||||
−0.482289 | + | 0.876012i | \(0.660194\pi\) | |||||||
\(68\) | −3.72161 | −0.451312 | ||||||||
\(69\) | −7.24860 | −0.872629 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.29362 | 0.628237 | 0.314118 | − | 0.949384i | \(-0.398291\pi\) | ||||
0.314118 | + | 0.949384i | \(0.398291\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 15.6170 | 1.82783 | 0.913917 | − | 0.405901i | \(-0.133042\pi\) | ||||
0.913917 | + | 0.405901i | \(0.133042\pi\) | |||||||
\(74\) | −6.19462 | −0.720110 | ||||||||
\(75\) | −8.85039 | −1.02196 | ||||||||
\(76\) | −1.39821 | −0.160385 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.32340 | 0.263074 | ||||||||
\(79\) | −5.29362 | −0.595578 | −0.297789 | − | 0.954632i | \(-0.596249\pi\) | ||||
−0.297789 | + | 0.954632i | \(0.596249\pi\) | |||||||
\(80\) | 3.72161 | 0.416089 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.92520 | −0.543897 | ||||||||
\(83\) | 17.6170 | 1.93372 | 0.966860 | − | 0.255308i | \(-0.0821770\pi\) | ||||
0.966860 | + | 0.255308i | \(0.0821770\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.8504 | −1.50229 | ||||||||
\(86\) | −1.20359 | −0.129786 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 6.04502 | 0.644401 | ||||||||
\(89\) | −4.36842 | −0.463052 | −0.231526 | − | 0.972829i | \(-0.574372\pi\) | ||||
−0.231526 | + | 0.972829i | \(0.574372\pi\) | |||||||
\(90\) | −3.72161 | −0.392292 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.24860 | 0.755719 | ||||||||
\(93\) | 9.72161 | 1.00808 | ||||||||
\(94\) | −6.17380 | −0.636779 | ||||||||
\(95\) | −5.20359 | −0.533877 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 3.26943 | 0.331960 | 0.165980 | − | 0.986129i | \(-0.446921\pi\) | ||||
0.165980 | + | 0.986129i | \(0.446921\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.04502 | −0.607547 | ||||||||
\(100\) | 8.85039 | 0.885039 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | −3.72161 | −0.368494 | ||||||||
\(103\) | −10.6018 | −1.04463 | −0.522313 | − | 0.852754i | \(-0.674931\pi\) | ||||
−0.522313 | + | 0.852754i | \(0.674931\pi\) | |||||||
\(104\) | −2.32340 | −0.227829 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.60179 | −0.446966 | ||||||||
\(107\) | 7.35319 | 0.710860 | 0.355430 | − | 0.934703i | \(-0.384334\pi\) | ||||
0.355430 | + | 0.934703i | \(0.384334\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −5.05398 | −0.484083 | −0.242042 | − | 0.970266i | \(-0.577817\pi\) | ||||
−0.242042 | + | 0.970266i | \(0.577817\pi\) | |||||||
\(110\) | 22.4972 | 2.14502 | ||||||||
\(111\) | −6.19462 | −0.587968 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.99104 | 0.845806 | 0.422903 | − | 0.906175i | \(-0.361011\pi\) | ||||
0.422903 | + | 0.906175i | \(0.361011\pi\) | |||||||
\(114\) | −1.39821 | −0.130954 | ||||||||
\(115\) | 26.9765 | 2.51557 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | 2.32340 | 0.214799 | ||||||||
\(118\) | 12.4134 | 1.14275 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.72161 | 0.339735 | ||||||||
\(121\) | 25.5422 | 2.32202 | ||||||||
\(122\) | 14.0900 | 1.27565 | ||||||||
\(123\) | −4.92520 | −0.444090 | ||||||||
\(124\) | −9.72161 | −0.873027 | ||||||||
\(125\) | 14.3297 | 1.28168 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.89541 | 0.700604 | 0.350302 | − | 0.936637i | \(-0.386079\pi\) | ||||
0.350302 | + | 0.936637i | \(0.386079\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.20359 | −0.105970 | ||||||||
\(130\) | −8.64681 | −0.758375 | ||||||||
\(131\) | 0.946021 | 0.0826543 | 0.0413271 | − | 0.999146i | \(-0.486841\pi\) | ||||
0.0413271 | + | 0.999146i | \(0.486841\pi\) | |||||||
\(132\) | 6.04502 | 0.526151 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.89541 | 0.682060 | ||||||||
\(135\) | −3.72161 | −0.320305 | ||||||||
\(136\) | 3.72161 | 0.319126 | ||||||||
\(137\) | 15.7458 | 1.34525 | 0.672627 | − | 0.739981i | \(-0.265166\pi\) | ||||
0.672627 | + | 0.739981i | \(0.265166\pi\) | |||||||
\(138\) | 7.24860 | 0.617042 | ||||||||
\(139\) | 19.0152 | 1.61285 | 0.806425 | − | 0.591336i | \(-0.201399\pi\) | ||||
0.806425 | + | 0.591336i | \(0.201399\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.17380 | −0.519928 | ||||||||
\(142\) | −5.29362 | −0.444230 | ||||||||
\(143\) | −14.0450 | −1.17450 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −3.72161 | −0.309063 | ||||||||
\(146\) | −15.6170 | −1.29247 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.19462 | 0.509195 | ||||||||
\(149\) | 10.1946 | 0.835176 | 0.417588 | − | 0.908636i | \(-0.362876\pi\) | ||||
0.417588 | + | 0.908636i | \(0.362876\pi\) | |||||||
\(150\) | 8.85039 | 0.722632 | ||||||||
\(151\) | 18.4972 | 1.50528 | 0.752640 | − | 0.658432i | \(-0.228780\pi\) | ||||
0.752640 | + | 0.658432i | \(0.228780\pi\) | |||||||
\(152\) | 1.39821 | 0.113410 | ||||||||
\(153\) | −3.72161 | −0.300874 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −36.1801 | −2.90605 | ||||||||
\(156\) | −2.32340 | −0.186021 | ||||||||
\(157\) | 1.44322 | 0.115182 | 0.0575909 | − | 0.998340i | \(-0.481658\pi\) | ||||
0.0575909 | + | 0.998340i | \(0.481658\pi\) | |||||||
\(158\) | 5.29362 | 0.421138 | ||||||||
\(159\) | −4.60179 | −0.364946 | ||||||||
\(160\) | −3.72161 | −0.294219 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 13.2036 | 1.03418 | 0.517092 | − | 0.855930i | \(-0.327014\pi\) | ||||
0.517092 | + | 0.855930i | \(0.327014\pi\) | |||||||
\(164\) | 4.92520 | 0.384593 | ||||||||
\(165\) | 22.4972 | 1.75140 | ||||||||
\(166\) | −17.6170 | −1.36735 | ||||||||
\(167\) | −18.5872 | −1.43832 | −0.719162 | − | 0.694843i | \(-0.755474\pi\) | ||||
−0.719162 | + | 0.694843i | \(0.755474\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.60179 | −0.584753 | ||||||||
\(170\) | 13.8504 | 1.06228 | ||||||||
\(171\) | −1.39821 | −0.106924 | ||||||||
\(172\) | 1.20359 | 0.0917725 | ||||||||
\(173\) | −4.27839 | −0.325280 | −0.162640 | − | 0.986685i | \(-0.552001\pi\) | ||||
−0.162640 | + | 0.986685i | \(0.552001\pi\) | |||||||
\(174\) | −1.00000 | −0.0758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.04502 | −0.455660 | ||||||||
\(177\) | 12.4134 | 0.933051 | ||||||||
\(178\) | 4.36842 | 0.327427 | ||||||||
\(179\) | −14.4972 | −1.08357 | −0.541786 | − | 0.840517i | \(-0.682252\pi\) | ||||
−0.541786 | + | 0.840517i | \(0.682252\pi\) | |||||||
\(180\) | 3.72161 | 0.277393 | ||||||||
\(181\) | −2.42799 | −0.180471 | −0.0902357 | − | 0.995920i | \(-0.528762\pi\) | ||||
−0.0902357 | + | 0.995920i | \(0.528762\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.0900 | 1.04157 | ||||||||
\(184\) | −7.24860 | −0.534374 | ||||||||
\(185\) | 23.0540 | 1.69496 | ||||||||
\(186\) | −9.72161 | −0.712823 | ||||||||
\(187\) | 22.4972 | 1.64516 | ||||||||
\(188\) | 6.17380 | 0.450270 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.20359 | 0.377508 | ||||||||
\(191\) | 4.94602 | 0.357882 | 0.178941 | − | 0.983860i | \(-0.442733\pi\) | ||||
0.178941 | + | 0.983860i | \(0.442733\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 18.1801 | 1.30863 | 0.654315 | − | 0.756222i | \(-0.272957\pi\) | ||||
0.654315 | + | 0.756222i | \(0.272957\pi\) | |||||||
\(194\) | −3.26943 | −0.234731 | ||||||||
\(195\) | −8.64681 | −0.619211 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.55678 | −0.182163 | −0.0910814 | − | 0.995843i | \(-0.529032\pi\) | ||||
−0.0910814 | + | 0.995843i | \(0.529032\pi\) | |||||||
\(198\) | 6.04502 | 0.429601 | ||||||||
\(199\) | 5.39821 | 0.382669 | 0.191334 | − | 0.981525i | \(-0.438719\pi\) | ||||
0.191334 | + | 0.981525i | \(0.438719\pi\) | |||||||
\(200\) | −8.85039 | −0.625817 | ||||||||
\(201\) | 7.89541 | 0.556899 | ||||||||
\(202\) | −6.00000 | −0.422159 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.72161 | 0.260565 | ||||||||
\(205\) | 18.3297 | 1.28020 | ||||||||
\(206\) | 10.6018 | 0.738662 | ||||||||
\(207\) | 7.24860 | 0.503813 | ||||||||
\(208\) | 2.32340 | 0.161099 | ||||||||
\(209\) | 8.45219 | 0.584650 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.49720 | 0.171914 | 0.0859572 | − | 0.996299i | \(-0.472605\pi\) | ||||
0.0859572 | + | 0.996299i | \(0.472605\pi\) | |||||||
\(212\) | 4.60179 | 0.316052 | ||||||||
\(213\) | −5.29362 | −0.362713 | ||||||||
\(214\) | −7.35319 | −0.502654 | ||||||||
\(215\) | 4.47928 | 0.305484 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.05398 | 0.342299 | ||||||||
\(219\) | −15.6170 | −1.05530 | ||||||||
\(220\) | −22.4972 | −1.51676 | ||||||||
\(221\) | −8.64681 | −0.581647 | ||||||||
\(222\) | 6.19462 | 0.415756 | ||||||||
\(223\) | −13.7875 | −0.923276 | −0.461638 | − | 0.887068i | \(-0.652738\pi\) | ||||
−0.461638 | + | 0.887068i | \(0.652738\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.85039 | 0.590026 | ||||||||
\(226\) | −8.99104 | −0.598075 | ||||||||
\(227\) | 4.42799 | 0.293896 | 0.146948 | − | 0.989144i | \(-0.453055\pi\) | ||||
0.146948 | + | 0.989144i | \(0.453055\pi\) | |||||||
\(228\) | 1.39821 | 0.0925985 | ||||||||
\(229\) | −17.1440 | −1.13291 | −0.566454 | − | 0.824093i | \(-0.691685\pi\) | ||||
−0.566454 | + | 0.824093i | \(0.691685\pi\) | |||||||
\(230\) | −26.9765 | −1.77878 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | 22.0900 | 1.44717 | 0.723583 | − | 0.690237i | \(-0.242494\pi\) | ||||
0.723583 | + | 0.690237i | \(0.242494\pi\) | |||||||
\(234\) | −2.32340 | −0.151886 | ||||||||
\(235\) | 22.9765 | 1.49882 | ||||||||
\(236\) | −12.4134 | −0.808046 | ||||||||
\(237\) | 5.29362 | 0.343857 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.45219 | 0.546726 | 0.273363 | − | 0.961911i | \(-0.411864\pi\) | ||||
0.273363 | + | 0.961911i | \(0.411864\pi\) | |||||||
\(240\) | −3.72161 | −0.240229 | ||||||||
\(241\) | 22.0000 | 1.41714 | 0.708572 | − | 0.705638i | \(-0.249340\pi\) | ||||
0.708572 | + | 0.705638i | \(0.249340\pi\) | |||||||
\(242\) | −25.5422 | −1.64192 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −14.0900 | −0.902022 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.92520 | 0.314019 | ||||||||
\(247\) | −3.24860 | −0.206704 | ||||||||
\(248\) | 9.72161 | 0.617323 | ||||||||
\(249\) | −17.6170 | −1.11643 | ||||||||
\(250\) | −14.3297 | −0.906288 | ||||||||
\(251\) | 3.35319 | 0.211652 | 0.105826 | − | 0.994385i | \(-0.466251\pi\) | ||||
0.105826 | + | 0.994385i | \(0.466251\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −43.8179 | −2.75481 | ||||||||
\(254\) | −7.89541 | −0.495402 | ||||||||
\(255\) | 13.8504 | 0.867345 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.14961 | 0.508358 | 0.254179 | − | 0.967157i | \(-0.418195\pi\) | ||||
0.254179 | + | 0.967157i | \(0.418195\pi\) | |||||||
\(258\) | 1.20359 | 0.0749319 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 8.64681 | 0.536252 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | −0.946021 | −0.0584454 | ||||||||
\(263\) | 11.4432 | 0.705619 | 0.352810 | − | 0.935695i | \(-0.385226\pi\) | ||||
0.352810 | + | 0.935695i | \(0.385226\pi\) | |||||||
\(264\) | −6.04502 | −0.372045 | ||||||||
\(265\) | 17.1261 | 1.05205 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.36842 | 0.267343 | ||||||||
\(268\) | −7.89541 | −0.482289 | ||||||||
\(269\) | 7.95498 | 0.485024 | 0.242512 | − | 0.970148i | \(-0.422029\pi\) | ||||
0.242512 | + | 0.970148i | \(0.422029\pi\) | |||||||
\(270\) | 3.72161 | 0.226490 | ||||||||
\(271\) | 29.4224 | 1.78728 | 0.893642 | − | 0.448781i | \(-0.148142\pi\) | ||||
0.893642 | + | 0.448781i | \(0.148142\pi\) | |||||||
\(272\) | −3.72161 | −0.225656 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.7458 | −0.951239 | ||||||||
\(275\) | −53.5008 | −3.22622 | ||||||||
\(276\) | −7.24860 | −0.436315 | ||||||||
\(277\) | −7.20359 | −0.432821 | −0.216411 | − | 0.976302i | \(-0.569435\pi\) | ||||
−0.216411 | + | 0.976302i | \(0.569435\pi\) | |||||||
\(278\) | −19.0152 | −1.14046 | ||||||||
\(279\) | −9.72161 | −0.582018 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.64681 | −0.157895 | −0.0789477 | − | 0.996879i | \(-0.525156\pi\) | ||||
−0.0789477 | + | 0.996879i | \(0.525156\pi\) | |||||||
\(282\) | 6.17380 | 0.367644 | ||||||||
\(283\) | −30.7160 | −1.82588 | −0.912939 | − | 0.408096i | \(-0.866193\pi\) | ||||
−0.912939 | + | 0.408096i | \(0.866193\pi\) | |||||||
\(284\) | 5.29362 | 0.314118 | ||||||||
\(285\) | 5.20359 | 0.308234 | ||||||||
\(286\) | 14.0450 | 0.830499 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −3.14961 | −0.185271 | ||||||||
\(290\) | 3.72161 | 0.218541 | ||||||||
\(291\) | −3.26943 | −0.191657 | ||||||||
\(292\) | 15.6170 | 0.913917 | ||||||||
\(293\) | −4.60179 | −0.268840 | −0.134420 | − | 0.990924i | \(-0.542917\pi\) | ||||
−0.134420 | + | 0.990924i | \(0.542917\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −46.1980 | −2.68975 | ||||||||
\(296\) | −6.19462 | −0.360055 | ||||||||
\(297\) | 6.04502 | 0.350767 | ||||||||
\(298\) | −10.1946 | −0.590559 | ||||||||
\(299\) | 16.8414 | 0.973965 | ||||||||
\(300\) | −8.85039 | −0.510978 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −18.4972 | −1.06439 | ||||||||
\(303\) | −6.00000 | −0.344691 | ||||||||
\(304\) | −1.39821 | −0.0801927 | ||||||||
\(305\) | −52.4376 | −3.00257 | ||||||||
\(306\) | 3.72161 | 0.212750 | ||||||||
\(307\) | −15.6378 | −0.892499 | −0.446249 | − | 0.894909i | \(-0.647241\pi\) | ||||
−0.446249 | + | 0.894909i | \(0.647241\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.6018 | 0.603115 | ||||||||
\(310\) | 36.1801 | 2.05489 | ||||||||
\(311\) | 13.9792 | 0.792686 | 0.396343 | − | 0.918102i | \(-0.370279\pi\) | ||||
0.396343 | + | 0.918102i | \(0.370279\pi\) | |||||||
\(312\) | 2.32340 | 0.131537 | ||||||||
\(313\) | 11.5928 | 0.655265 | 0.327633 | − | 0.944805i | \(-0.393749\pi\) | ||||
0.327633 | + | 0.944805i | \(0.393749\pi\) | |||||||
\(314\) | −1.44322 | −0.0814458 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.29362 | −0.297789 | ||||||||
\(317\) | 19.2936 | 1.08364 | 0.541819 | − | 0.840495i | \(-0.317736\pi\) | ||||
0.541819 | + | 0.840495i | \(0.317736\pi\) | |||||||
\(318\) | 4.60179 | 0.258056 | ||||||||
\(319\) | 6.04502 | 0.338456 | ||||||||
\(320\) | 3.72161 | 0.208044 | ||||||||
\(321\) | −7.35319 | −0.410415 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.20359 | 0.289535 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 20.5630 | 1.14063 | ||||||||
\(326\) | −13.2036 | −0.731279 | ||||||||
\(327\) | 5.05398 | 0.279486 | ||||||||
\(328\) | −4.92520 | −0.271949 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −22.4972 | −1.23843 | ||||||||
\(331\) | 18.4972 | 1.01670 | 0.508349 | − | 0.861151i | \(-0.330256\pi\) | ||||
0.508349 | + | 0.861151i | \(0.330256\pi\) | |||||||
\(332\) | 17.6170 | 0.966860 | ||||||||
\(333\) | 6.19462 | 0.339463 | ||||||||
\(334\) | 18.5872 | 1.01705 | ||||||||
\(335\) | −29.3836 | −1.60540 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.8325 | −1.40718 | −0.703592 | − | 0.710604i | \(-0.748422\pi\) | ||||
−0.703592 | + | 0.710604i | \(0.748422\pi\) | |||||||
\(338\) | 7.60179 | 0.413483 | ||||||||
\(339\) | −8.99104 | −0.488326 | ||||||||
\(340\) | −13.8504 | −0.751143 | ||||||||
\(341\) | 58.7673 | 3.18243 | ||||||||
\(342\) | 1.39821 | 0.0756064 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.20359 | −0.0648930 | ||||||||
\(345\) | −26.9765 | −1.45236 | ||||||||
\(346\) | 4.27839 | 0.230008 | ||||||||
\(347\) | 17.6829 | 0.949266 | 0.474633 | − | 0.880184i | \(-0.342581\pi\) | ||||
0.474633 | + | 0.880184i | \(0.342581\pi\) | |||||||
\(348\) | 1.00000 | 0.0536056 | ||||||||
\(349\) | 21.3144 | 1.14094 | 0.570468 | − | 0.821320i | \(-0.306762\pi\) | ||||
0.570468 | + | 0.821320i | \(0.306762\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.32340 | −0.124014 | ||||||||
\(352\) | 6.04502 | 0.322200 | ||||||||
\(353\) | −18.1801 | −0.967627 | −0.483814 | − | 0.875171i | \(-0.660749\pi\) | ||||
−0.483814 | + | 0.875171i | \(0.660749\pi\) | |||||||
\(354\) | −12.4134 | −0.659767 | ||||||||
\(355\) | 19.7008 | 1.04561 | ||||||||
\(356\) | −4.36842 | −0.231526 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.4972 | 0.766201 | ||||||||
\(359\) | −13.5928 | −0.717402 | −0.358701 | − | 0.933452i | \(-0.616780\pi\) | ||||
−0.358701 | + | 0.933452i | \(0.616780\pi\) | |||||||
\(360\) | −3.72161 | −0.196146 | ||||||||
\(361\) | −17.0450 | −0.897106 | ||||||||
\(362\) | 2.42799 | 0.127613 | ||||||||
\(363\) | −25.5422 | −1.34062 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 58.1205 | 3.04217 | ||||||||
\(366\) | −14.0900 | −0.736498 | ||||||||
\(367\) | 4.12878 | 0.215521 | 0.107760 | − | 0.994177i | \(-0.465632\pi\) | ||||
0.107760 | + | 0.994177i | \(0.465632\pi\) | |||||||
\(368\) | 7.24860 | 0.377859 | ||||||||
\(369\) | 4.92520 | 0.256396 | ||||||||
\(370\) | −23.0540 | −1.19852 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9.72161 | 0.504042 | ||||||||
\(373\) | −37.8809 | −1.96140 | −0.980698 | − | 0.195528i | \(-0.937358\pi\) | ||||
−0.980698 | + | 0.195528i | \(0.937358\pi\) | |||||||
\(374\) | −22.4972 | −1.16330 | ||||||||
\(375\) | −14.3297 | −0.739981 | ||||||||
\(376\) | −6.17380 | −0.318389 | ||||||||
\(377\) | −2.32340 | −0.119661 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.8864 | 1.38106 | 0.690532 | − | 0.723302i | \(-0.257376\pi\) | ||||
0.690532 | + | 0.723302i | \(0.257376\pi\) | |||||||
\(380\) | −5.20359 | −0.266938 | ||||||||
\(381\) | −7.89541 | −0.404494 | ||||||||
\(382\) | −4.94602 | −0.253060 | ||||||||
\(383\) | −22.8864 | −1.16944 | −0.584721 | − | 0.811234i | \(-0.698796\pi\) | ||||
−0.584721 | + | 0.811234i | \(0.698796\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.1801 | −0.925341 | ||||||||
\(387\) | 1.20359 | 0.0611817 | ||||||||
\(388\) | 3.26943 | 0.165980 | ||||||||
\(389\) | 1.05398 | 0.0534388 | 0.0267194 | − | 0.999643i | \(-0.491494\pi\) | ||||
0.0267194 | + | 0.999643i | \(0.491494\pi\) | |||||||
\(390\) | 8.64681 | 0.437848 | ||||||||
\(391\) | −26.9765 | −1.36426 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.946021 | −0.0477205 | ||||||||
\(394\) | 2.55678 | 0.128809 | ||||||||
\(395\) | −19.7008 | −0.991254 | ||||||||
\(396\) | −6.04502 | −0.303773 | ||||||||
\(397\) | −6.58097 | −0.330289 | −0.165145 | − | 0.986269i | \(-0.552809\pi\) | ||||
−0.165145 | + | 0.986269i | \(0.552809\pi\) | |||||||
\(398\) | −5.39821 | −0.270588 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.85039 | 0.442520 | ||||||||
\(401\) | −8.58723 | −0.428826 | −0.214413 | − | 0.976743i | \(-0.568784\pi\) | ||||
−0.214413 | + | 0.976743i | \(0.568784\pi\) | |||||||
\(402\) | −7.89541 | −0.393787 | ||||||||
\(403\) | −22.5872 | −1.12515 | ||||||||
\(404\) | 6.00000 | 0.298511 | ||||||||
\(405\) | 3.72161 | 0.184928 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −37.4466 | −1.85616 | ||||||||
\(408\) | −3.72161 | −0.184247 | ||||||||
\(409\) | −26.0513 | −1.28815 | −0.644076 | − | 0.764961i | \(-0.722758\pi\) | ||||
−0.644076 | + | 0.764961i | \(0.722758\pi\) | |||||||
\(410\) | −18.3297 | −0.905238 | ||||||||
\(411\) | −15.7458 | −0.776683 | ||||||||
\(412\) | −10.6018 | −0.522313 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −7.24860 | −0.356249 | ||||||||
\(415\) | 65.5637 | 3.21840 | ||||||||
\(416\) | −2.32340 | −0.113914 | ||||||||
\(417\) | −19.0152 | −0.931180 | ||||||||
\(418\) | −8.45219 | −0.413410 | ||||||||
\(419\) | 26.4585 | 1.29258 | 0.646290 | − | 0.763092i | \(-0.276320\pi\) | ||||
0.646290 | + | 0.763092i | \(0.276320\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.6289 | −1.59023 | −0.795117 | − | 0.606456i | \(-0.792591\pi\) | ||||
−0.795117 | + | 0.606456i | \(0.792591\pi\) | |||||||
\(422\) | −2.49720 | −0.121562 | ||||||||
\(423\) | 6.17380 | 0.300180 | ||||||||
\(424\) | −4.60179 | −0.223483 | ||||||||
\(425\) | −32.9377 | −1.59771 | ||||||||
\(426\) | 5.29362 | 0.256477 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7.35319 | 0.355430 | ||||||||
\(429\) | 14.0450 | 0.678100 | ||||||||
\(430\) | −4.47928 | −0.216010 | ||||||||
\(431\) | 36.5422 | 1.76018 | 0.880088 | − | 0.474810i | \(-0.157483\pi\) | ||||
0.880088 | + | 0.474810i | \(0.157483\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 2.68556 | 0.129060 | 0.0645299 | − | 0.997916i | \(-0.479445\pi\) | ||||
0.0645299 | + | 0.997916i | \(0.479445\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.72161 | 0.178438 | ||||||||
\(436\) | −5.05398 | −0.242042 | ||||||||
\(437\) | −10.1350 | −0.484825 | ||||||||
\(438\) | 15.6170 | 0.746210 | ||||||||
\(439\) | −19.2486 | −0.918686 | −0.459343 | − | 0.888259i | \(-0.651915\pi\) | ||||
−0.459343 | + | 0.888259i | \(0.651915\pi\) | |||||||
\(440\) | 22.4972 | 1.07251 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.64681 | 0.411287 | ||||||||
\(443\) | −1.95498 | −0.0928841 | −0.0464420 | − | 0.998921i | \(-0.514788\pi\) | ||||
−0.0464420 | + | 0.998921i | \(0.514788\pi\) | |||||||
\(444\) | −6.19462 | −0.293984 | ||||||||
\(445\) | −16.2576 | −0.770682 | ||||||||
\(446\) | 13.7875 | 0.652855 | ||||||||
\(447\) | −10.1946 | −0.482189 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.1946 | 1.04743 | 0.523714 | − | 0.851894i | \(-0.324546\pi\) | ||||
0.523714 | + | 0.851894i | \(0.324546\pi\) | |||||||
\(450\) | −8.85039 | −0.417212 | ||||||||
\(451\) | −29.7729 | −1.40195 | ||||||||
\(452\) | 8.99104 | 0.422903 | ||||||||
\(453\) | −18.4972 | −0.869074 | ||||||||
\(454\) | −4.42799 | −0.207816 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.39821 | −0.0654771 | ||||||||
\(457\) | −12.6018 | −0.589487 | −0.294743 | − | 0.955576i | \(-0.595234\pi\) | ||||
−0.294743 | + | 0.955576i | \(0.595234\pi\) | |||||||
\(458\) | 17.1440 | 0.801087 | ||||||||
\(459\) | 3.72161 | 0.173710 | ||||||||
\(460\) | 26.9765 | 1.25778 | ||||||||
\(461\) | 16.3442 | 0.761227 | 0.380613 | − | 0.924734i | \(-0.375713\pi\) | ||||
0.380613 | + | 0.924734i | \(0.375713\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.299213 | 0.0139056 | 0.00695279 | − | 0.999976i | \(-0.497787\pi\) | ||||
0.00695279 | + | 0.999976i | \(0.497787\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | 36.1801 | 1.67781 | ||||||||
\(466\) | −22.0900 | −1.02330 | ||||||||
\(467\) | 26.0305 | 1.20455 | 0.602273 | − | 0.798290i | \(-0.294262\pi\) | ||||
0.602273 | + | 0.798290i | \(0.294262\pi\) | |||||||
\(468\) | 2.32340 | 0.107399 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −22.9765 | −1.05983 | ||||||||
\(471\) | −1.44322 | −0.0665002 | ||||||||
\(472\) | 12.4134 | 0.571375 | ||||||||
\(473\) | −7.27569 | −0.334537 | ||||||||
\(474\) | −5.29362 | −0.243144 | ||||||||
\(475\) | −12.3747 | −0.567790 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.60179 | 0.210702 | ||||||||
\(478\) | −8.45219 | −0.386594 | ||||||||
\(479\) | −28.2043 | −1.28869 | −0.644343 | − | 0.764737i | \(-0.722869\pi\) | ||||
−0.644343 | + | 0.764737i | \(0.722869\pi\) | |||||||
\(480\) | 3.72161 | 0.169868 | ||||||||
\(481\) | 14.3926 | 0.656247 | ||||||||
\(482\) | −22.0000 | −1.00207 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 25.5422 | 1.16101 | ||||||||
\(485\) | 12.1675 | 0.552499 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 32.1801 | 1.45822 | 0.729109 | − | 0.684398i | \(-0.239935\pi\) | ||||
0.729109 | + | 0.684398i | \(0.239935\pi\) | |||||||
\(488\) | 14.0900 | 0.637826 | ||||||||
\(489\) | −13.2036 | −0.597087 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.8414 | 0.579526 | 0.289763 | − | 0.957098i | \(-0.406424\pi\) | ||||
0.289763 | + | 0.957098i | \(0.406424\pi\) | |||||||
\(492\) | −4.92520 | −0.222045 | ||||||||
\(493\) | 3.72161 | 0.167613 | ||||||||
\(494\) | 3.24860 | 0.146161 | ||||||||
\(495\) | −22.4972 | −1.01117 | ||||||||
\(496\) | −9.72161 | −0.436513 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 17.6170 | 0.789438 | ||||||||
\(499\) | −6.13505 | −0.274642 | −0.137321 | − | 0.990527i | \(-0.543849\pi\) | ||||
−0.137321 | + | 0.990527i | \(0.543849\pi\) | |||||||
\(500\) | 14.3297 | 0.640842 | ||||||||
\(501\) | 18.5872 | 0.830416 | ||||||||
\(502\) | −3.35319 | −0.149660 | ||||||||
\(503\) | 6.82061 | 0.304116 | 0.152058 | − | 0.988372i | \(-0.451410\pi\) | ||||
0.152058 | + | 0.988372i | \(0.451410\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.3297 | 0.993657 | ||||||||
\(506\) | 43.8179 | 1.94794 | ||||||||
\(507\) | 7.60179 | 0.337607 | ||||||||
\(508\) | 7.89541 | 0.350302 | ||||||||
\(509\) | 3.97918 | 0.176374 | 0.0881869 | − | 0.996104i | \(-0.471893\pi\) | ||||
0.0881869 | + | 0.996104i | \(0.471893\pi\) | |||||||
\(510\) | −13.8504 | −0.613306 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.39821 | 0.0617324 | ||||||||
\(514\) | −8.14961 | −0.359464 | ||||||||
\(515\) | −39.4558 | −1.73863 | ||||||||
\(516\) | −1.20359 | −0.0529849 | ||||||||
\(517\) | −37.3207 | −1.64136 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.27839 | 0.187800 | ||||||||
\(520\) | −8.64681 | −0.379188 | ||||||||
\(521\) | 41.1711 | 1.80374 | 0.901869 | − | 0.432009i | \(-0.142195\pi\) | ||||
0.901869 | + | 0.432009i | \(0.142195\pi\) | |||||||
\(522\) | 1.00000 | 0.0437688 | ||||||||
\(523\) | −28.7756 | −1.25827 | −0.629134 | − | 0.777297i | \(-0.716590\pi\) | ||||
−0.629134 | + | 0.777297i | \(0.716590\pi\) | |||||||
\(524\) | 0.946021 | 0.0413271 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.4432 | −0.498948 | ||||||||
\(527\) | 36.1801 | 1.57603 | ||||||||
\(528\) | 6.04502 | 0.263076 | ||||||||
\(529\) | 29.5422 | 1.28444 | ||||||||
\(530\) | −17.1261 | −0.743910 | ||||||||
\(531\) | −12.4134 | −0.538697 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.4432 | 0.495661 | ||||||||
\(534\) | −4.36842 | −0.189040 | ||||||||
\(535\) | 27.3657 | 1.18312 | ||||||||
\(536\) | 7.89541 | 0.341030 | ||||||||
\(537\) | 14.4972 | 0.625600 | ||||||||
\(538\) | −7.95498 | −0.342964 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.72161 | −0.160153 | ||||||||
\(541\) | −3.86495 | −0.166167 | −0.0830836 | − | 0.996543i | \(-0.526477\pi\) | ||||
−0.0830836 | + | 0.996543i | \(0.526477\pi\) | |||||||
\(542\) | −29.4224 | −1.26380 | ||||||||
\(543\) | 2.42799 | 0.104195 | ||||||||
\(544\) | 3.72161 | 0.159563 | ||||||||
\(545\) | −18.8089 | −0.805687 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.7763 | 1.52968 | 0.764841 | − | 0.644219i | \(-0.222817\pi\) | ||||
0.764841 | + | 0.644219i | \(0.222817\pi\) | |||||||
\(548\) | 15.7458 | 0.672627 | ||||||||
\(549\) | −14.0900 | −0.601348 | ||||||||
\(550\) | 53.5008 | 2.28128 | ||||||||
\(551\) | 1.39821 | 0.0595656 | ||||||||
\(552\) | 7.24860 | 0.308521 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.20359 | 0.306051 | ||||||||
\(555\) | −23.0540 | −0.978587 | ||||||||
\(556\) | 19.0152 | 0.806425 | ||||||||
\(557\) | 21.5062 | 0.911245 | 0.455623 | − | 0.890173i | \(-0.349417\pi\) | ||||
0.455623 | + | 0.890173i | \(0.349417\pi\) | |||||||
\(558\) | 9.72161 | 0.411549 | ||||||||
\(559\) | 2.79641 | 0.118276 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.4972 | −0.949833 | ||||||||
\(562\) | 2.64681 | 0.111649 | ||||||||
\(563\) | 20.0484 | 0.844939 | 0.422469 | − | 0.906377i | \(-0.361163\pi\) | ||||
0.422469 | + | 0.906377i | \(0.361163\pi\) | |||||||
\(564\) | −6.17380 | −0.259964 | ||||||||
\(565\) | 33.4611 | 1.40772 | ||||||||
\(566\) | 30.7160 | 1.29109 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.29362 | −0.222115 | ||||||||
\(569\) | 5.93706 | 0.248894 | 0.124447 | − | 0.992226i | \(-0.460284\pi\) | ||||
0.124447 | + | 0.992226i | \(0.460284\pi\) | |||||||
\(570\) | −5.20359 | −0.217954 | ||||||||
\(571\) | −6.13505 | −0.256744 | −0.128372 | − | 0.991726i | \(-0.540975\pi\) | ||||
−0.128372 | + | 0.991726i | \(0.540975\pi\) | |||||||
\(572\) | −14.0450 | −0.587252 | ||||||||
\(573\) | −4.94602 | −0.206623 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 64.1530 | 2.67536 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 22.1142 | 0.920627 | 0.460314 | − | 0.887756i | \(-0.347737\pi\) | ||||
0.460314 | + | 0.887756i | \(0.347737\pi\) | |||||||
\(578\) | 3.14961 | 0.131006 | ||||||||
\(579\) | −18.1801 | −0.755538 | ||||||||
\(580\) | −3.72161 | −0.154532 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.26943 | 0.135522 | ||||||||
\(583\) | −27.8179 | −1.15210 | ||||||||
\(584\) | −15.6170 | −0.646237 | ||||||||
\(585\) | 8.64681 | 0.357502 | ||||||||
\(586\) | 4.60179 | 0.190098 | ||||||||
\(587\) | −42.4585 | −1.75245 | −0.876224 | − | 0.481904i | \(-0.839945\pi\) | ||||
−0.876224 | + | 0.481904i | \(0.839945\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.5928 | 0.560083 | ||||||||
\(590\) | 46.1980 | 1.90194 | ||||||||
\(591\) | 2.55678 | 0.105172 | ||||||||
\(592\) | 6.19462 | 0.254597 | ||||||||
\(593\) | −12.1350 | −0.498327 | −0.249163 | − | 0.968461i | \(-0.580156\pi\) | ||||
−0.249163 | + | 0.968461i | \(0.580156\pi\) | |||||||
\(594\) | −6.04502 | −0.248030 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.1946 | 0.417588 | ||||||||
\(597\) | −5.39821 | −0.220934 | ||||||||
\(598\) | −16.8414 | −0.688697 | ||||||||
\(599\) | 7.74244 | 0.316347 | 0.158174 | − | 0.987411i | \(-0.449439\pi\) | ||||
0.158174 | + | 0.987411i | \(0.449439\pi\) | |||||||
\(600\) | 8.85039 | 0.361316 | ||||||||
\(601\) | 48.1863 | 1.96556 | 0.982781 | − | 0.184776i | \(-0.0591559\pi\) | ||||
0.982781 | + | 0.184776i | \(0.0591559\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.89541 | −0.321526 | ||||||||
\(604\) | 18.4972 | 0.752640 | ||||||||
\(605\) | 95.0582 | 3.86467 | ||||||||
\(606\) | 6.00000 | 0.243733 | ||||||||
\(607\) | 0.817239 | 0.0331707 | 0.0165854 | − | 0.999862i | \(-0.494720\pi\) | ||||
0.0165854 | + | 0.999862i | \(0.494720\pi\) | |||||||
\(608\) | 1.39821 | 0.0567048 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 52.4376 | 2.12314 | ||||||||
\(611\) | 14.3442 | 0.580305 | ||||||||
\(612\) | −3.72161 | −0.150437 | ||||||||
\(613\) | 14.6468 | 0.591579 | 0.295790 | − | 0.955253i | \(-0.404417\pi\) | ||||
0.295790 | + | 0.955253i | \(0.404417\pi\) | |||||||
\(614\) | 15.6378 | 0.631092 | ||||||||
\(615\) | −18.3297 | −0.739124 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.8809 | 1.04192 | 0.520962 | − | 0.853580i | \(-0.325573\pi\) | ||||
0.520962 | + | 0.853580i | \(0.325573\pi\) | |||||||
\(618\) | −10.6018 | −0.426467 | ||||||||
\(619\) | −34.8719 | −1.40162 | −0.700810 | − | 0.713348i | \(-0.747178\pi\) | ||||
−0.700810 | + | 0.713348i | \(0.747178\pi\) | |||||||
\(620\) | −36.1801 | −1.45303 | ||||||||
\(621\) | −7.24860 | −0.290876 | ||||||||
\(622\) | −13.9792 | −0.560514 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.32340 | −0.0930106 | ||||||||
\(625\) | 9.07750 | 0.363100 | ||||||||
\(626\) | −11.5928 | −0.463343 | ||||||||
\(627\) | −8.45219 | −0.337548 | ||||||||
\(628\) | 1.44322 | 0.0575909 | ||||||||
\(629\) | −23.0540 | −0.919222 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.4737 | −1.65104 | −0.825521 | − | 0.564372i | \(-0.809118\pi\) | ||||
−0.825521 | + | 0.564372i | \(0.809118\pi\) | |||||||
\(632\) | 5.29362 | 0.210569 | ||||||||
\(633\) | −2.49720 | −0.0992549 | ||||||||
\(634\) | −19.2936 | −0.766247 | ||||||||
\(635\) | 29.3836 | 1.16605 | ||||||||
\(636\) | −4.60179 | −0.182473 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.04502 | −0.239324 | ||||||||
\(639\) | 5.29362 | 0.209412 | ||||||||
\(640\) | −3.72161 | −0.147110 | ||||||||
\(641\) | −4.40717 | −0.174073 | −0.0870364 | − | 0.996205i | \(-0.527740\pi\) | ||||
−0.0870364 | + | 0.996205i | \(0.527740\pi\) | |||||||
\(642\) | 7.35319 | 0.290207 | ||||||||
\(643\) | −27.2728 | −1.07553 | −0.537767 | − | 0.843094i | \(-0.680732\pi\) | ||||
−0.537767 | + | 0.843094i | \(0.680732\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.47928 | −0.176371 | ||||||||
\(646\) | −5.20359 | −0.204732 | ||||||||
\(647\) | 12.3476 | 0.485434 | 0.242717 | − | 0.970097i | \(-0.421961\pi\) | ||||
0.242717 | + | 0.970097i | \(0.421961\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 75.0394 | 2.94555 | ||||||||
\(650\) | −20.5630 | −0.806549 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.2036 | 0.517092 | ||||||||
\(653\) | 14.0900 | 0.551386 | 0.275693 | − | 0.961246i | \(-0.411093\pi\) | ||||
0.275693 | + | 0.961246i | \(0.411093\pi\) | |||||||
\(654\) | −5.05398 | −0.197626 | ||||||||
\(655\) | 3.52072 | 0.137566 | ||||||||
\(656\) | 4.92520 | 0.192297 | ||||||||
\(657\) | 15.6170 | 0.609278 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.4737 | −1.61559 | −0.807793 | − | 0.589467i | \(-0.799338\pi\) | ||||
−0.807793 | + | 0.589467i | \(0.799338\pi\) | |||||||
\(660\) | 22.4972 | 0.875702 | ||||||||
\(661\) | 3.82620 | 0.148822 | 0.0744110 | − | 0.997228i | \(-0.476292\pi\) | ||||
0.0744110 | + | 0.997228i | \(0.476292\pi\) | |||||||
\(662\) | −18.4972 | −0.718914 | ||||||||
\(663\) | 8.64681 | 0.335814 | ||||||||
\(664\) | −17.6170 | −0.683673 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.19462 | −0.240037 | ||||||||
\(667\) | −7.24860 | −0.280667 | ||||||||
\(668\) | −18.5872 | −0.719162 | ||||||||
\(669\) | 13.7875 | 0.533054 | ||||||||
\(670\) | 29.3836 | 1.13519 | ||||||||
\(671\) | 85.1745 | 3.28812 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.4938 | 0.404508 | 0.202254 | − | 0.979333i | \(-0.435173\pi\) | ||||
0.202254 | + | 0.979333i | \(0.435173\pi\) | |||||||
\(674\) | 25.8325 | 0.995029 | ||||||||
\(675\) | −8.85039 | −0.340652 | ||||||||
\(676\) | −7.60179 | −0.292377 | ||||||||
\(677\) | −31.1890 | −1.19869 | −0.599346 | − | 0.800490i | \(-0.704573\pi\) | ||||
−0.599346 | + | 0.800490i | \(0.704573\pi\) | |||||||
\(678\) | 8.99104 | 0.345299 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 13.8504 | 0.531138 | ||||||||
\(681\) | −4.42799 | −0.169681 | ||||||||
\(682\) | −58.7673 | −2.25032 | ||||||||
\(683\) | 40.5693 | 1.55234 | 0.776171 | − | 0.630523i | \(-0.217159\pi\) | ||||
0.776171 | + | 0.630523i | \(0.217159\pi\) | |||||||
\(684\) | −1.39821 | −0.0534618 | ||||||||
\(685\) | 58.5998 | 2.23898 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.1440 | 0.654085 | ||||||||
\(688\) | 1.20359 | 0.0458863 | ||||||||
\(689\) | 10.6918 | 0.407326 | ||||||||
\(690\) | 26.9765 | 1.02698 | ||||||||
\(691\) | −24.8656 | −0.945933 | −0.472966 | − | 0.881080i | \(-0.656817\pi\) | ||||
−0.472966 | + | 0.881080i | \(0.656817\pi\) | |||||||
\(692\) | −4.27839 | −0.162640 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.6829 | −0.671232 | ||||||||
\(695\) | 70.7673 | 2.68436 | ||||||||
\(696\) | −1.00000 | −0.0379049 | ||||||||
\(697\) | −18.3297 | −0.694286 | ||||||||
\(698\) | −21.3144 | −0.806764 | ||||||||
\(699\) | −22.0900 | −0.835522 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.0721 | 1.06027 | 0.530134 | − | 0.847914i | \(-0.322141\pi\) | ||||
0.530134 | + | 0.847914i | \(0.322141\pi\) | |||||||
\(702\) | 2.32340 | 0.0876912 | ||||||||
\(703\) | −8.66137 | −0.326670 | ||||||||
\(704\) | −6.04502 | −0.227830 | ||||||||
\(705\) | −22.9765 | −0.865344 | ||||||||
\(706\) | 18.1801 | 0.684216 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 12.4134 | 0.466526 | ||||||||
\(709\) | −6.73684 | −0.253007 | −0.126504 | − | 0.991966i | \(-0.540376\pi\) | ||||
−0.126504 | + | 0.991966i | \(0.540376\pi\) | |||||||
\(710\) | −19.7008 | −0.739357 | ||||||||
\(711\) | −5.29362 | −0.198526 | ||||||||
\(712\) | 4.36842 | 0.163713 | ||||||||
\(713\) | −70.4681 | −2.63905 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −52.2701 | −1.95479 | ||||||||
\(716\) | −14.4972 | −0.541786 | ||||||||
\(717\) | −8.45219 | −0.315653 | ||||||||
\(718\) | 13.5928 | 0.507280 | ||||||||
\(719\) | −50.8448 | −1.89619 | −0.948096 | − | 0.317986i | \(-0.896994\pi\) | ||||
−0.948096 | + | 0.317986i | \(0.896994\pi\) | |||||||
\(720\) | 3.72161 | 0.138696 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 17.0450 | 0.634350 | ||||||||
\(723\) | −22.0000 | −0.818189 | ||||||||
\(724\) | −2.42799 | −0.0902357 | ||||||||
\(725\) | −8.85039 | −0.328695 | ||||||||
\(726\) | 25.5422 | 0.947961 | ||||||||
\(727\) | 34.2909 | 1.27178 | 0.635890 | − | 0.771780i | \(-0.280633\pi\) | ||||
0.635890 | + | 0.771780i | \(0.280633\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −58.1205 | −2.15114 | ||||||||
\(731\) | −4.47928 | −0.165672 | ||||||||
\(732\) | 14.0900 | 0.520783 | ||||||||
\(733\) | 45.2757 | 1.67230 | 0.836148 | − | 0.548504i | \(-0.184802\pi\) | ||||
0.836148 | + | 0.548504i | \(0.184802\pi\) | |||||||
\(734\) | −4.12878 | −0.152396 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.24860 | −0.267187 | ||||||||
\(737\) | 47.7279 | 1.75808 | ||||||||
\(738\) | −4.92520 | −0.181299 | ||||||||
\(739\) | 39.8809 | 1.46704 | 0.733520 | − | 0.679667i | \(-0.237876\pi\) | ||||
0.733520 | + | 0.679667i | \(0.237876\pi\) | |||||||
\(740\) | 23.0540 | 0.847481 | ||||||||
\(741\) | 3.24860 | 0.119340 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.6289 | 1.41716 | 0.708578 | − | 0.705632i | \(-0.249337\pi\) | ||||
0.708578 | + | 0.705632i | \(0.249337\pi\) | |||||||
\(744\) | −9.72161 | −0.356412 | ||||||||
\(745\) | 37.9404 | 1.39003 | ||||||||
\(746\) | 37.8809 | 1.38692 | ||||||||
\(747\) | 17.6170 | 0.644573 | ||||||||
\(748\) | 22.4972 | 0.822579 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 14.3297 | 0.523246 | ||||||||
\(751\) | 8.75140 | 0.319343 | 0.159672 | − | 0.987170i | \(-0.448956\pi\) | ||||
0.159672 | + | 0.987170i | \(0.448956\pi\) | |||||||
\(752\) | 6.17380 | 0.225135 | ||||||||
\(753\) | −3.35319 | −0.122197 | ||||||||
\(754\) | 2.32340 | 0.0846134 | ||||||||
\(755\) | 68.8394 | 2.50532 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.25756 | −0.0820526 | −0.0410263 | − | 0.999158i | \(-0.513063\pi\) | ||||
−0.0410263 | + | 0.999158i | \(0.513063\pi\) | |||||||
\(758\) | −26.8864 | −0.976560 | ||||||||
\(759\) | 43.8179 | 1.59049 | ||||||||
\(760\) | 5.20359 | 0.188754 | ||||||||
\(761\) | 0.733473 | 0.0265884 | 0.0132942 | − | 0.999912i | \(-0.495768\pi\) | ||||
0.0132942 | + | 0.999912i | \(0.495768\pi\) | |||||||
\(762\) | 7.89541 | 0.286021 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.94602 | 0.178941 | ||||||||
\(765\) | −13.8504 | −0.500762 | ||||||||
\(766\) | 22.8864 | 0.826921 | ||||||||
\(767\) | −28.8414 | −1.04140 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 6.72721 | 0.242589 | 0.121295 | − | 0.992617i | \(-0.461295\pi\) | ||||
0.121295 | + | 0.992617i | \(0.461295\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.14961 | −0.293501 | ||||||||
\(772\) | 18.1801 | 0.654315 | ||||||||
\(773\) | −14.7368 | −0.530047 | −0.265024 | − | 0.964242i | \(-0.585380\pi\) | ||||
−0.265024 | + | 0.964242i | \(0.585380\pi\) | |||||||
\(774\) | −1.20359 | −0.0432620 | ||||||||
\(775\) | −86.0401 | −3.09065 | ||||||||
\(776\) | −3.26943 | −0.117366 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.05398 | −0.0377870 | ||||||||
\(779\) | −6.88645 | −0.246733 | ||||||||
\(780\) | −8.64681 | −0.309605 | ||||||||
\(781\) | −32.0000 | −1.14505 | ||||||||
\(782\) | 26.9765 | 0.964677 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.37112 | 0.191703 | ||||||||
\(786\) | 0.946021 | 0.0337435 | ||||||||
\(787\) | 14.0692 | 0.501513 | 0.250757 | − | 0.968050i | \(-0.419321\pi\) | ||||
0.250757 | + | 0.968050i | \(0.419321\pi\) | |||||||
\(788\) | −2.55678 | −0.0910814 | ||||||||
\(789\) | −11.4432 | −0.407390 | ||||||||
\(790\) | 19.7008 | 0.700923 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.04502 | 0.214800 | ||||||||
\(793\) | −32.7368 | −1.16252 | ||||||||
\(794\) | 6.58097 | 0.233550 | ||||||||
\(795\) | −17.1261 | −0.607400 | ||||||||
\(796\) | 5.39821 | 0.191334 | ||||||||
\(797\) | 34.7368 | 1.23044 | 0.615221 | − | 0.788355i | \(-0.289067\pi\) | ||||
0.615221 | + | 0.788355i | \(0.289067\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.9765 | −0.812849 | ||||||||
\(800\) | −8.85039 | −0.312909 | ||||||||
\(801\) | −4.36842 | −0.154351 | ||||||||
\(802\) | 8.58723 | 0.303226 | ||||||||
\(803\) | −94.4051 | −3.33149 | ||||||||
\(804\) | 7.89541 | 0.278450 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 22.5872 | 0.795601 | ||||||||
\(807\) | −7.95498 | −0.280029 | ||||||||
\(808\) | −6.00000 | −0.211079 | ||||||||
\(809\) | 16.1496 | 0.567790 | 0.283895 | − | 0.958855i | \(-0.408373\pi\) | ||||
0.283895 | + | 0.958855i | \(0.408373\pi\) | |||||||
\(810\) | −3.72161 | −0.130764 | ||||||||
\(811\) | 35.6620 | 1.25226 | 0.626132 | − | 0.779717i | \(-0.284637\pi\) | ||||
0.626132 | + | 0.779717i | \(0.284637\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.4224 | −1.03189 | ||||||||
\(814\) | 37.4466 | 1.31250 | ||||||||
\(815\) | 49.1386 | 1.72125 | ||||||||
\(816\) | 3.72161 | 0.130282 | ||||||||
\(817\) | −1.68286 | −0.0588759 | ||||||||
\(818\) | 26.0513 | 0.910862 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 18.3297 | 0.640100 | ||||||||
\(821\) | −37.5962 | −1.31212 | −0.656058 | − | 0.754710i | \(-0.727777\pi\) | ||||
−0.656058 | + | 0.754710i | \(0.727777\pi\) | |||||||
\(822\) | 15.7458 | 0.549198 | ||||||||
\(823\) | −48.2555 | −1.68208 | −0.841041 | − | 0.540971i | \(-0.818057\pi\) | ||||
−0.841041 | + | 0.540971i | \(0.818057\pi\) | |||||||
\(824\) | 10.6018 | 0.369331 | ||||||||
\(825\) | 53.5008 | 1.86266 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.7458 | −1.17346 | −0.586728 | − | 0.809784i | \(-0.699584\pi\) | ||||
−0.586728 | + | 0.809784i | \(0.699584\pi\) | |||||||
\(828\) | 7.24860 | 0.251906 | ||||||||
\(829\) | −16.1080 | −0.559452 | −0.279726 | − | 0.960080i | \(-0.590244\pi\) | ||||
−0.279726 | + | 0.960080i | \(0.590244\pi\) | |||||||
\(830\) | −65.5637 | −2.27575 | ||||||||
\(831\) | 7.20359 | 0.249890 | ||||||||
\(832\) | 2.32340 | 0.0805496 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 19.0152 | 0.658444 | ||||||||
\(835\) | −69.1745 | −2.39388 | ||||||||
\(836\) | 8.45219 | 0.292325 | ||||||||
\(837\) | 9.72161 | 0.336028 | ||||||||
\(838\) | −26.4585 | −0.913992 | ||||||||
\(839\) | −16.9073 | −0.583704 | −0.291852 | − | 0.956464i | \(-0.594271\pi\) | ||||
−0.291852 | + | 0.956464i | \(0.594271\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 32.6289 | 1.12447 | ||||||||
\(843\) | 2.64681 | 0.0911609 | ||||||||
\(844\) | 2.49720 | 0.0859572 | ||||||||
\(845\) | −28.2909 | −0.973237 | ||||||||
\(846\) | −6.17380 | −0.212260 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.60179 | 0.158026 | ||||||||
\(849\) | 30.7160 | 1.05417 | ||||||||
\(850\) | 32.9377 | 1.12975 | ||||||||
\(851\) | 44.9023 | 1.53923 | ||||||||
\(852\) | −5.29362 | −0.181356 | ||||||||
\(853\) | −27.6829 | −0.947843 | −0.473922 | − | 0.880567i | \(-0.657162\pi\) | ||||
−0.473922 | + | 0.880567i | \(0.657162\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.20359 | −0.177959 | ||||||||
\(856\) | −7.35319 | −0.251327 | ||||||||
\(857\) | −3.74580 | −0.127954 | −0.0639771 | − | 0.997951i | \(-0.520378\pi\) | ||||
−0.0639771 | + | 0.997951i | \(0.520378\pi\) | |||||||
\(858\) | −14.0450 | −0.479489 | ||||||||
\(859\) | 37.5366 | 1.28073 | 0.640367 | − | 0.768069i | \(-0.278782\pi\) | ||||
0.640367 | + | 0.768069i | \(0.278782\pi\) | |||||||
\(860\) | 4.47928 | 0.152742 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −36.5422 | −1.24463 | ||||||||
\(863\) | 23.2486 | 0.791392 | 0.395696 | − | 0.918382i | \(-0.370503\pi\) | ||||
0.395696 | + | 0.918382i | \(0.370503\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −15.9225 | −0.541381 | ||||||||
\(866\) | −2.68556 | −0.0912590 | ||||||||
\(867\) | 3.14961 | 0.106966 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.0000 | 1.08553 | ||||||||
\(870\) | −3.72161 | −0.126174 | ||||||||
\(871\) | −18.3442 | −0.621570 | ||||||||
\(872\) | 5.05398 | 0.171149 | ||||||||
\(873\) | 3.26943 | 0.110653 | ||||||||
\(874\) | 10.1350 | 0.342823 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −15.6170 | −0.527650 | ||||||||
\(877\) | 48.1205 | 1.62491 | 0.812457 | − | 0.583021i | \(-0.198130\pi\) | ||||
0.812457 | + | 0.583021i | \(0.198130\pi\) | |||||||
\(878\) | 19.2486 | 0.649609 | ||||||||
\(879\) | 4.60179 | 0.155215 | ||||||||
\(880\) | −22.4972 | −0.758381 | ||||||||
\(881\) | 26.2605 | 0.884737 | 0.442369 | − | 0.896833i | \(-0.354138\pi\) | ||||
0.442369 | + | 0.896833i | \(0.354138\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.1655 | 0.947845 | 0.473922 | − | 0.880567i | \(-0.342838\pi\) | ||||
0.473922 | + | 0.880567i | \(0.342838\pi\) | |||||||
\(884\) | −8.64681 | −0.290824 | ||||||||
\(885\) | 46.1980 | 1.55293 | ||||||||
\(886\) | 1.95498 | 0.0656790 | ||||||||
\(887\) | −0.921830 | −0.0309520 | −0.0154760 | − | 0.999880i | \(-0.504926\pi\) | ||||
−0.0154760 | + | 0.999880i | \(0.504926\pi\) | |||||||
\(888\) | 6.19462 | 0.207878 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16.2576 | 0.544955 | ||||||||
\(891\) | −6.04502 | −0.202516 | ||||||||
\(892\) | −13.7875 | −0.461638 | ||||||||
\(893\) | −8.63225 | −0.288867 | ||||||||
\(894\) | 10.1946 | 0.340959 | ||||||||
\(895\) | −53.9530 | −1.80345 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.8414 | −0.562319 | ||||||||
\(898\) | −22.1946 | −0.740644 | ||||||||
\(899\) | 9.72161 | 0.324234 | ||||||||
\(900\) | 8.85039 | 0.295013 | ||||||||
\(901\) | −17.1261 | −0.570553 | ||||||||
\(902\) | 29.7729 | 0.991329 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.99104 | −0.299037 | ||||||||
\(905\) | −9.03605 | −0.300369 | ||||||||
\(906\) | 18.4972 | 0.614528 | ||||||||
\(907\) | −45.3836 | −1.50694 | −0.753470 | − | 0.657483i | \(-0.771621\pi\) | ||||
−0.753470 | + | 0.657483i | \(0.771621\pi\) | |||||||
\(908\) | 4.42799 | 0.146948 | ||||||||
\(909\) | 6.00000 | 0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.7008 | 0.387664 | 0.193832 | − | 0.981035i | \(-0.437908\pi\) | ||||
0.193832 | + | 0.981035i | \(0.437908\pi\) | |||||||
\(912\) | 1.39821 | 0.0462993 | ||||||||
\(913\) | −106.495 | −3.52448 | ||||||||
\(914\) | 12.6018 | 0.416830 | ||||||||
\(915\) | 52.4376 | 1.73353 | ||||||||
\(916\) | −17.1440 | −0.566454 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.72161 | −0.122831 | ||||||||
\(919\) | −8.09003 | −0.266866 | −0.133433 | − | 0.991058i | \(-0.542600\pi\) | ||||
−0.133433 | + | 0.991058i | \(0.542600\pi\) | |||||||
\(920\) | −26.9765 | −0.889388 | ||||||||
\(921\) | 15.6378 | 0.515285 | ||||||||
\(922\) | −16.3442 | −0.538269 | ||||||||
\(923\) | 12.2992 | 0.404834 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 54.8248 | 1.80263 | ||||||||
\(926\) | −0.299213 | −0.00983274 | ||||||||
\(927\) | −10.6018 | −0.348209 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | −23.7729 | −0.779963 | −0.389982 | − | 0.920823i | \(-0.627519\pi\) | ||||
−0.389982 | + | 0.920823i | \(0.627519\pi\) | |||||||
\(930\) | −36.1801 | −1.18639 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 22.0900 | 0.723583 | ||||||||
\(933\) | −13.9792 | −0.457658 | ||||||||
\(934\) | −26.0305 | −0.851743 | ||||||||
\(935\) | 83.7259 | 2.73813 | ||||||||
\(936\) | −2.32340 | −0.0759428 | ||||||||
\(937\) | 0.407170 | 0.0133017 | 0.00665084 | − | 0.999978i | \(-0.497883\pi\) | ||||
0.00665084 | + | 0.999978i | \(0.497883\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.5928 | −0.378318 | ||||||||
\(940\) | 22.9765 | 0.749410 | ||||||||
\(941\) | 17.3144 | 0.564435 | 0.282217 | − | 0.959350i | \(-0.408930\pi\) | ||||
0.282217 | + | 0.959350i | \(0.408930\pi\) | |||||||
\(942\) | 1.44322 | 0.0470228 | ||||||||
\(943\) | 35.7008 | 1.16258 | ||||||||
\(944\) | −12.4134 | −0.404023 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.27569 | 0.236553 | ||||||||
\(947\) | −60.1801 | −1.95559 | −0.977795 | − | 0.209565i | \(-0.932795\pi\) | ||||
−0.977795 | + | 0.209565i | \(0.932795\pi\) | |||||||
\(948\) | 5.29362 | 0.171929 | ||||||||
\(949\) | 36.2847 | 1.17785 | ||||||||
\(950\) | 12.3747 | 0.401488 | ||||||||
\(951\) | −19.2936 | −0.625638 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.3297 | 1.30641 | 0.653203 | − | 0.757183i | \(-0.273425\pi\) | ||||
0.653203 | + | 0.757183i | \(0.273425\pi\) | |||||||
\(954\) | −4.60179 | −0.148989 | ||||||||
\(955\) | 18.4072 | 0.595642 | ||||||||
\(956\) | 8.45219 | 0.273363 | ||||||||
\(957\) | −6.04502 | −0.195408 | ||||||||
\(958\) | 28.2043 | 0.911238 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.72161 | −0.120115 | ||||||||
\(961\) | 63.5097 | 2.04870 | ||||||||
\(962\) | −14.3926 | −0.464036 | ||||||||
\(963\) | 7.35319 | 0.236953 | ||||||||
\(964\) | 22.0000 | 0.708572 | ||||||||
\(965\) | 67.6591 | 2.17802 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.15297 | 0.262182 | 0.131091 | − | 0.991370i | \(-0.458152\pi\) | ||||
0.131091 | + | 0.991370i | \(0.458152\pi\) | |||||||
\(968\) | −25.5422 | −0.820958 | ||||||||
\(969\) | −5.20359 | −0.167163 | ||||||||
\(970\) | −12.1675 | −0.390676 | ||||||||
\(971\) | −9.85039 | −0.316114 | −0.158057 | − | 0.987430i | \(-0.550523\pi\) | ||||
−0.158057 | + | 0.987430i | \(0.550523\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −32.1801 | −1.03112 | ||||||||
\(975\) | −20.5630 | −0.658544 | ||||||||
\(976\) | −14.0900 | −0.451011 | ||||||||
\(977\) | −35.7312 | −1.14314 | −0.571572 | − | 0.820552i | \(-0.693666\pi\) | ||||
−0.571572 | + | 0.820552i | \(0.693666\pi\) | |||||||
\(978\) | 13.2036 | 0.422204 | ||||||||
\(979\) | 26.4072 | 0.843977 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.05398 | −0.161361 | ||||||||
\(982\) | −12.8414 | −0.409787 | ||||||||
\(983\) | 22.7577 | 0.725857 | 0.362928 | − | 0.931817i | \(-0.381777\pi\) | ||||
0.362928 | + | 0.931817i | \(0.381777\pi\) | |||||||
\(984\) | 4.92520 | 0.157010 | ||||||||
\(985\) | −9.51533 | −0.303184 | ||||||||
\(986\) | −3.72161 | −0.118520 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.24860 | −0.103352 | ||||||||
\(989\) | 8.72431 | 0.277417 | ||||||||
\(990\) | 22.4972 | 0.715008 | ||||||||
\(991\) | 22.4972 | 0.714647 | 0.357324 | − | 0.933981i | \(-0.383689\pi\) | ||||
0.357324 | + | 0.933981i | \(0.383689\pi\) | |||||||
\(992\) | 9.72161 | 0.308661 | ||||||||
\(993\) | −18.4972 | −0.586991 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.0900 | 0.636897 | ||||||||
\(996\) | −17.6170 | −0.558217 | ||||||||
\(997\) | −3.80875 | −0.120624 | −0.0603121 | − | 0.998180i | \(-0.519210\pi\) | ||||
−0.0603121 | + | 0.998180i | \(0.519210\pi\) | |||||||
\(998\) | 6.13505 | 0.194202 | ||||||||
\(999\) | −6.19462 | −0.195989 |
(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 | 8526.2.a.bo.1.3 | 3 | ||
7.6 | odd | 2 | 1218.2.a.p.1.1 | ✓ | 3 | ||
21.20 | even | 2 | 3654.2.a.be.1.3 | 3 | |||
28.27 | even | 2 | 9744.2.a.bh.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1218.2.a.p.1.1 | ✓ | 3 | 7.6 | odd | 2 | ||
3654.2.a.be.1.3 | 3 | 21.20 | even | 2 | |||
8526.2.a.bo.1.3 | 3 | 1.1 | even | 1 | trivial | ||
9744.2.a.bh.1.1 | 3 | 28.27 | even | 2 |